Finite Group Databasebeta

← C3×C5⋊(C5⋊#64424) #36347985

Subgroups — C3×C5⋊(C5⋊#64424) #36347985

Order 22050.

960 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C52×#3861C211yesmaximal, characteristic, complemented, Hall
2C3×C5⋊(C5⋊(C7⋊D7))C311yesmaximal, characteristic, complemented
3C5⋊(C5⋊#64424)C313yesmaximal, direct product factor
4C3×C5⋊#64424—56nomaximal
5C52×#3861C2×C313yescomplemented
6C3×C52×C72C2×C311yescharacteristic, complemented
7C3×C5⋊(C5⋊AGL(1,𝔽7))—78nomaximal
8C5⋊(C5⋊(C7⋊D7))C3211yescharacteristic, complemented, Hall
9C3×C5×#3861D516yescomplemented
10C3×C52×ΓL(1,𝔽8)—78no—
11C3×C5⋊(C7⋊D7)—56no—
12C5⋊#64424—518no—
13C52×C72C2×C3211yescharacteristic, complemented, Hall
14C3×C5⋊D35—78no—
15C5⋊(C5⋊AGL(1,𝔽7))—724no—
16C3×#64424—251noHall
17C3×C5×C72C3×D516yescomplemented
18C5×#3861C3×D5118yescomplemented
19C3×C5⋊AGL(1,𝔽7)—3548no—
20C3×C52×C7AGL(1,𝔽7)18yescomplemented
21C52×ΓL(1,𝔽8)—724no—
22C5⋊(C7⋊D7)—56no—
23C32×C5⋊D5—491noHall
24C3×#3861C5⋊D511yescharacteristic, complemented, Hall
25C5⋊D35—78no—
26C3×C5×ΓL(1,𝔽8)—748no—
27C3×C7⋊D7—251no—
28#64424—253no—
29C5×C72C32×D516yescomplemented
30C32×C52—491noHall
31C3×D35—3548no—
32C5⋊AGL(1,𝔽7)—35144no—
33C52×C7C3×AGL(1,𝔽7)18yescomplemented
34C3×C5⋊D5—493no—
35C3×C5⋊D5—491no—
36C3×C72C3×C5⋊D511yescharacteristic, complemented
37#3861C3×C5⋊D513yescomplemented
38C3×AGL(1,𝔽7)—1758no—
39C3×C5×C7C5⋊AGL(1,𝔽7)148yescomplemented
40C5×ΓL(1,𝔽8)—7144no—
41C7⋊D7—251noHall
42C32×D5—2456no—
43C3×C52—493no—
44C3×C52#6442411yescharacteristic, complemented
45D35—3548no—
46C3×ΓL(1,𝔽8)—78no—
47C5⋊D5—491noHall
48C72C32×C5⋊D511yescharacteristic, complemented, Sylow
49C32×C5—496no—
50C3×D7—1758no—
51AGL(1,𝔽7)—17524no—
52C5×C7C3×C5⋊AGL(1,𝔽7)148yescomplemented
53C3×D5—24518no—
54C3×D5—2456no—
55C52C3×#6442411yescharacteristic, complemented, Sylow
56C3×C7C5⋊(C5⋊AGL(1,𝔽7))18yescomplemented
57ΓL(1,𝔽8)—724no—
58C2×C32—12251noHall
59C3×C5—4918no—
60C3×C5C5⋊#6442416yescomplemented
61D7—1758no—
62D5—2456no—
63C32—491noSylow
64C7C3×C5⋊(C5⋊AGL(1,𝔽7))18yescomplemented
65C2×C3—12253no—
66C2×C3—12251no—
67C5C3×C5⋊#6442416yescomplemented
68C3—493no—
69C3C5⋊(C5⋊#64424)11yescharacteristic, direct product factor
70C2—12251noSylow
subgroupG/H
center, hypercenterC3C5⋊(C5⋊#64424)
commutator, cosocle, hypocenterC52×C72C2×C32
FrattiniC1G
Fitting, socleC3×C52×C72C2×C3
LCSG ▷ C52×C72
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C52×#3861C2semidirect
2. C3×C5⋊(C5⋊(C7⋊D7))C3semidirect
3. C5⋊(C5⋊#64424)C3direct (N × H)
5. C52×#3861C2×C3semidirect
6. C3×C52×C72C2×C3semidirect
8. C5⋊(C5⋊(C7⋊D7))C32semidirect
9. C3×C5×#3861D5semidirect
13. C52×C72C2×C32semidirect
17. C3×C5×C72C3×D5semidirect
18. C5×#3861C3×D5semidirect
20. C3×C52×C7AGL(1,𝔽7)semidirect
24. C3×#3861C5⋊D5semidirect
29. C5×C72C32×D5semidirect
33. C52×C7C3×AGL(1,𝔽7)semidirect
36. C3×C72C3×C5⋊D5semidirect
37. #3861C3×C5⋊D5semidirect
39. C3×C5×C7C5⋊AGL(1,𝔽7)semidirect
44. C3×C52#64424semidirect
48. C72C32×C5⋊D5semidirect
52. C5×C7C3×C5⋊AGL(1,𝔽7)semidirect
55. C52C3×#64424semidirect
56. C3×C7C5⋊(C5⋊AGL(1,𝔽7))semidirect
60. C3×C5C5⋊#64424semidirect
64. C7C3×C5⋊(C5⋊AGL(1,𝔽7))semidirect
67. C5C3×C5⋊#64424semidirect
69. C3C5⋊(C5⋊#64424)direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C52×#38612
C3×C5⋊(C5⋊(C7⋊D7))3
C5⋊(C5⋊#64424)3
C3×C5⋊#644245
C3×C5⋊(C5⋊AGL(1,𝔽7))7