Finite Group Databasebeta

← C3×C5×#11763984 #30655312

Subgroups — C3×C5×#11763984 #30655312

Order 16380.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#10587717C211yesmaximal, characteristic
2C3×C5×C7⋊#261C311yesmaximal, characteristic, complemented
3C5×#11763984C313yesmaximal, direct product factor
4C3×C5×#63271C411yescharacteristic, complemented, Hall
5C3×#11763984C511yesmaximal, characteristic, direct product factor, Hall
6C5×#10587717C2×C313yes—
7C3×C5×C7×D13C2×C311yescharacteristic
8C3×C5×AGL(1,𝔽13)—71nomaximal, Hall
9C5×C7⋊#261C3211yescharacteristic, complemented, Hall
10C3×#10587717C2×C511yescharacteristic
11C3×C5×C7×C13C3×C411yescharacteristic, complemented
12C5×#63271C3×C413yescomplemented
13C3×C5×ΓL(1,𝔽8)⋊C4—131nomaximal, Hall
14C3×C5×D13⋊C3—71no—
15C3×C7⋊#261C3×C511yescharacteristic, complemented
16#11763984C3×C513yesdirect product factor
17C5×C7×D13C2×C3211yescharacteristic
18C3×#63271C4×C511yescharacteristic, complemented, Hall
19C3×C5×#261—211no—
20C5×AGL(1,𝔽13)—73no—
21C2×C3×C5×ΓL(1,𝔽8)—131no—
22C3×C5×C13⋊C3—71noHall
23C3×C7×D13C2×C3×C511yescharacteristic
24#10587717C2×C3×C513yes—
25C3×AGL(1,𝔽13)—71noHall
26C5×C7×C13C32×C411yescharacteristic, complemented, Hall
27C3×C5×Dic7—391no—
28C5×ΓL(1,𝔽8)⋊C4—133no—
29C3×C5×D13AGL(1,𝔽7)11yescharacteristic
30C5×D13⋊C3—73no—
31C7⋊#261C32×C511yescharacteristic, complemented, Hall
32C3×C5×ΓL(1,𝔽8)—131noHall
33C3×C7×C13C3×C4×C511yescharacteristic, complemented
34#63271C3×C4×C513yescomplemented
35C5×#261—211noHall
36C3×ΓL(1,𝔽8)⋊C4—131noHall
37C3×D13⋊C3—71no—
38C2×C3×C5×C7—131no—
39C2×C5×ΓL(1,𝔽8)—133no—
40C3×C5×C13ΓL(1,𝔽8)⋊C411yescharacteristic, complemented
41C5×C13⋊C3—73no—
42C7×D13C2×C32×C511yescharacteristic
43C32×C4×C5—911noHall
44C3×#261—211no—
45AGL(1,𝔽13)—73no—
46C5×Dic7—391noHall
47C5×D13C3×AGL(1,𝔽7)11yescharacteristic
48C2×C3×ΓL(1,𝔽8)—131no—
49C3×C13⋊C3—71noHall
50C3×C5×C7AGL(1,𝔽13)11yescharacteristic, complemented
51C5×ΓL(1,𝔽8)—133no—
52C7×C13C32×C4×C511yescharacteristic, complemented, Hall
53C2×C32×C5—911no—
54C3×Dic7—391no—
55ΓL(1,𝔽8)⋊C4—133no—
56C3×D13C5×AGL(1,𝔽7)11yescharacteristic
57D13⋊C3—73no—
58C2×C5×C7—131no—
59C5×C13C3×ΓL(1,𝔽8)⋊C411yescharacteristic, complemented, Hall
60C3×ΓL(1,𝔽8)—131noHall
61C3×C4×C5—2731no—
62C3×C4×C5—913no—
63#261—211noHall
64C32×C5—911noHall
65C2×C3×C7—391no—
66C2×ΓL(1,𝔽8)—133no—
67C3×C13C5×ΓL(1,𝔽8)⋊C411yescharacteristic, complemented
68C13⋊C3—73no—
69C32×C4—911noHall
70C5×C7C3×AGL(1,𝔽13)11yescharacteristic, complemented, Hall
71C2×C3×C5—391no—
72C2×C3×C5—913no—
73Dic7—391noHall
74D13C3×C5×AGL(1,𝔽7)11yescharacteristic
75C3×C7C5×AGL(1,𝔽13)11yescharacteristic, complemented
76ΓL(1,𝔽8)—133no—
77C4×C5—2731noHall
78C2×C32—911no—
79C3×C5—913no—
80C3×C5#1176398411yescharacteristic, direct product factor
81C2×C7—391no—
82C13C3×C5×ΓL(1,𝔽8)⋊C411yescharacteristic, complemented, Sylow
83C3×C4—2731no—
84C3×C4—913no—
85C2×C5—391no—
86C32—911noSylow
87C7C3×C5×AGL(1,𝔽13)11yescharacteristic, complemented, Sylow
88C2×C3—391no—
89C2×C3—913no—
90C5C3×#1176398411yescharacteristic, direct product factor, Sylow
91C4—2731noSylow
92C3—913no—
93C3C5×#1176398411yescharacteristic, direct product factor
94C2—391no—
subgroupG/H
center, hypercenterC3×C5#11763984
commutator, hypocenterC7×C13C32×C4×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C13C3×C4
prime radicalC3×C5×#10587717C2
cosocleC7×D13C2×C32×C5
LCSG ▷ C7×C13
UCSC1 ◁ C3×C5

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C3×C5×C7⋊#261C3semidirect
3. C5×#11763984C3direct (N × H)
4. C3×C5×#63271C4semidirect
5. C3×#11763984C5direct (N × H)
9. C5×C7⋊#261C32semidirect
11. C3×C5×C7×C13C3×C4semidirect
12. C5×#63271C3×C4semidirect
15. C3×C7⋊#261C3×C5semidirect
16. #11763984C3×C5direct (N × H)
18. C3×#63271C4×C5semidirect
26. C5×C7×C13C32×C4semidirect
31. C7⋊#261C32×C5semidirect
33. C3×C7×C13C3×C4×C5semidirect
34. #63271C3×C4×C5semidirect
40. C3×C5×C13ΓL(1,𝔽8)⋊C4semidirect
50. C3×C5×C7AGL(1,𝔽13)semidirect
52. C7×C13C32×C4×C5semidirect
59. C5×C13C3×ΓL(1,𝔽8)⋊C4semidirect
67. C3×C13C5×ΓL(1,𝔽8)⋊C4semidirect
70. C5×C7C3×AGL(1,𝔽13)semidirect
75. C3×C7C5×AGL(1,𝔽13)semidirect
80. C3×C5#11763984direct (N × H)
82. C13C3×C5×ΓL(1,𝔽8)⋊C4semidirect
87. C7C3×C5×AGL(1,𝔽13)semidirect
90. C5C3×#11763984direct (N × H)
93. C3C5×#11763984direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×C5×#105877172
C3×C5×C7⋊#2613
C5×#117639843
C3×#117639845
C3×C5×AGL(1,𝔽13)7
C3×C5×ΓL(1,𝔽8)⋊C413