There could be common code called from all three commands

Try openssl enc -ciphers:

$ openssl help enc
Usage: enc [options]
Valid options are:
 -help               Display this summary
 -ciphers            List ciphers
 -in infile          Input file
 -out outfile        Output file
 -pass val           Passphrase source
 -e                  Encrypt
 -d                  Decrypt
 -p                  Print the iv/key
 -P                  Print the iv/key and exit
 -v                  Verbose output
 -nopad              Disable standard block padding
 -salt               Use salt in the KDF (default)
 -nosalt             Do not use salt in the KDF
 -debug              Print debug info
 -a                  Base64 encode/decode, depending on encryption flag
 -base64             Same as option -a
 -A                  Used with -[base64|a] to specify base64 buffer as a single line
 -bufsize val        Buffer size
 -k val              Passphrase
 -kfile infile       Read passphrase from file
 -K val              Raw key, in hex
 -S val              Salt, in hex
 -iv val             IV in hex
 -md val             Use specified digest to create a key from the passphrase
 -iter +int          Specify the iteration count and force use of PBKDF2
 -pbkdf2             Use password-based key derivation function 2
 -none               Don't encrypt
 -*                  Any supported cipher
 -rand val           Load the file(s) into the random number generator
 -writerand outfile  Write random data to the specified file
 -engine val         Use engine, possibly a hardware device

msp@msppc:~$ openssl enc -ciphers
Supported ciphers:
-aes-128-cbc               -aes-128-cfb               -aes-128-cfb1             
-aes-128-cfb8              -aes-128-ctr               -aes-128-ecb              
-aes-128-ofb               -aes-192-cbc               -aes-192-cfb              
-aes-192-cfb1              -aes-192-cfb8              -aes-192-ctr              
-aes-192-ecb               -aes-192-ofb               -aes-256-cbc              
-aes-256-cfb               -aes-256-cfb1              -aes-256-cfb8             
-aes-256-ctr               -aes-256-ecb               -aes-256-ofb              
-aes128                    -aes128-wrap               -aes192                   
-aes192-wrap               -aes256                    -aes256-wrap              
-aria-128-cbc              -aria-128-cfb              -aria-128-cfb1            
-aria-128-cfb8             -aria-128-ctr              -aria-128-ecb             
-aria-128-ofb              -aria-192-cbc              -aria-192-cfb             
-aria-192-cfb1             -aria-192-cfb8             -aria-192-ctr             
-aria-192-ecb              -aria-192-ofb              -aria-256-cbc             
-aria-256-cfb              -aria-256-cfb1             -aria-256-cfb8            
-aria-256-ctr              -aria-256-ecb              -aria-256-ofb             
-aria128                   -aria192                   -aria256                  
-bf                        -bf-cbc                    -bf-cfb                   
-bf-ecb                    -bf-ofb                    -blowfish                 
-camellia-128-cbc          -camellia-128-cfb          -camellia-128-cfb1        
-camellia-128-cfb8         -camellia-128-ctr          -camellia-128-ecb         
-camellia-128-ofb          -camellia-192-cbc          -camellia-192-cfb         
-camellia-192-cfb1         -camellia-192-cfb8         -camellia-192-ctr         
-camellia-192-ecb          -camellia-192-ofb          -camellia-256-cbc         
-camellia-256-cfb          -camellia-256-cfb1         -camellia-256-cfb8        
-camellia-256-ctr          -camellia-256-ecb          -camellia-256-ofb         
-camellia128               -camellia192               -camellia256              
-cast                      -cast-cbc                  -cast5-cbc                
-cast5-cfb                 -cast5-ecb                 -cast5-ofb                
-chacha20                  -des                       -des-cbc                  
-des-cfb                   -des-cfb1                  -des-cfb8                 
-des-ecb                   -des-ede                   -des-ede-cbc              
-des-ede-cfb               -des-ede-ecb               -des-ede-ofb              
-des-ede3                  -des-ede3-cbc              -des-ede3-cfb             
-des-ede3-cfb1             -des-ede3-cfb8             -des-ede3-ecb             
-des-ede3-ofb              -des-ofb                   -des3                     
-des3-wrap                 -desx                      -desx-cbc                 
-id-aes128-wrap            -id-aes128-wrap-pad        -id-aes192-wrap           
-id-aes192-wrap-pad        -id-aes256-wrap            -id-aes256-wrap-pad       
-id-smime-alg-CMS3DESwrap  -idea                      -idea-cbc                 
-idea-cfb                  -idea-ecb                  -idea-ofb                 
-rc2                       -rc2-128                   -rc2-40                   
-rc2-40-cbc                -rc2-64                    -rc2-64-cbc               
-rc2-cbc                   -rc2-cfb                   -rc2-ecb                  
-rc2-ofb                   -rc4                       -rc4-40                   
-seed                      -seed-cbc                  -seed-cfb                 
-seed-ecb                  -seed-ofb                  -sm4                      
-sm4-cbc                   -sm4-cfb                   -sm4-ctr                  
-sm4-ecb                   -sm4-ofb