Finite Group Databasebeta

← C2×D5×#14274263 #50304305

Subgroups — C2×D5×#14274263 #50304305

Order 38220.

400 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#14274263C211yesmaximal, characteristic, complemented
2D5×#14274263C212yesmaximal, direct product factor
3C2×C72×D5×C13C311yesmaximal, characteristic, complemented, Hall
4C5×#14274263C2211yescharacteristic, complemented, Hall
5C22×#14274263—51nomaximal, Hall
6C72×D5×C13C2×C312yescomplemented
7C2×C5×C72×C13C2×C311yescharacteristic, complemented
8C2×D5×#63270—78nomaximal
9C2×#14274263—52no—
10C2×#14274263D511yescharacteristic, direct product factor
11C5×C72×C13C22×C311yescharacteristic, complemented, Hall
12C2×D5×#3861—131nomaximal, Hall
13D5×#63270—716no—
14C2×C5×#63270—78no—
15C22×C72×C13—51noHall
16#14274263C2×D511yescharacteristic, direct product factor, Hall
17C2×C7×D5×C13ΓL(1,𝔽8)18yescomplemented
18C2×C5×#3861—131no—
19D5×#3861—132no—
20C5×#63270—78no—
21C2×C72×C13—52no—
22C2×C72×C13C3×D511yescharacteristic, complemented
23C22×#63270—358no—
24C2×C72×D5C13⋊C311yescharacteristic, complemented, Hall
25C2×C5×C7×C13C2×ΓL(1,𝔽8)18yescomplemented
26C7×D5×C13C2×ΓL(1,𝔽8)116yescomplemented
27C2×D5×C13⋊C3—491noHall
28C5×#3861—131noHall
29C72×C13C2×C3×D511yescharacteristic, complemented, Hall
30C22×#3861—651noHall
31C2×#63270—78no—
32C2×#63270—3516no—
33C2×C5×C72C2×C13⋊C311yescharacteristic, complemented
34C72×D5C2×C13⋊C312yescomplemented
35C5×C7×C13C22×ΓL(1,𝔽8)18yescomplemented
36C2×D5×ΓL(1,𝔽8)—918no—
37C2×C5×C13⋊C3—491no—
38D5×C13⋊C3—492no—
39C22×C7×C13—58no—
40C2×#3861—131no—
41C2×#3861—652no—
42#63270—78no—
43C2×D5×C13#386111yescharacteristic, complemented, Hall
44C5×C72C22×C13⋊C311yescharacteristic, complemented, Hall
45C2×C5×ΓL(1,𝔽8)—918no—
46D5×ΓL(1,𝔽8)—9116no—
47C22×C72—51noHall
48C5×C13⋊C3—491noHall
49C2×C7×C13—516no—
50C2×C7×C13D5×ΓL(1,𝔽8)18yescomplemented
51C22×C13⋊C3—2451noHall
52#3861—131noHall
53C2×C7×D5#6327018yescomplemented
54C2×C5×C13C2×#386111yescharacteristic, complemented
55D5×C13C2×#386112yescomplemented
56C5×ΓL(1,𝔽8)—918no—
57C2×C72—52no—
58C2×C72D5×C13⋊C311yescharacteristic, complemented
59C7×C13C2×D5×ΓL(1,𝔽8)18yescomplemented
60C22×ΓL(1,𝔽8)—4558no—
61C2×C13⋊C3—491no—
62C2×C13⋊C3—2452no—
63C2×C5×C7C2×#6327018yescomplemented
64C7×D5C2×#63270116yescomplemented
65C5×C13C22×#386111yescharacteristic, complemented, Hall
66C2×C3×D5—6371noHall
67C22×C13—51noHall
68C72C2×D5×C13⋊C311yescharacteristic, complemented, Sylow
69C2×ΓL(1,𝔽8)—918no—
70C2×ΓL(1,𝔽8)—45516no—
71C13⋊C3—491noHall
72C5×C7C22×#6327018yescomplemented
73C2×C3×C5—6371no—
74C3×D5—6372no—
75C22×C7—58no—
76C2×C13—52no—
77C2×C13D5×#386111yescharacteristic, complemented
78ΓL(1,𝔽8)—918no—
79C2×D5#1427426311yescharacteristic, direct product factor, Hall
80C3×C5—6371noHall
81C2×C7—516no—
82C2×C7D5×#6327018yescomplemented
83C13C2×D5×#386111yescharacteristic, complemented, Sylow
84C22×C3—31851noHall
85C2×C5C2×#1427426311yescharacteristic, complemented
86D5C2×#1427426312yesdirect product factor
87C7C2×D5×#6327018yescomplemented
88C2×C3—31852no—
89C2×C3—6371no—
90C5C22×#1427426311yescharacteristic, complemented, Sylow
91C22—51noSylow
92C3—6371noSylow
93C2—52no—
94C2D5×#1427426311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2D5×#14274263
commutator, cosocle, hypocenterC5×C72×C13C22×C3
FrattiniC1G
Fitting, socleC2×C5×C72×C13C2×C3
LCSG ▷ C5×C72×C13
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C5×#14274263C2semidirect
2. D5×#14274263C2direct (N × H)
3. C2×C72×D5×C13C3semidirect
4. C5×#14274263C22semidirect
6. C72×D5×C13C2×C3semidirect
7. C2×C5×C72×C13C2×C3semidirect
10. C2×#14274263D5direct (N × H)
11. C5×C72×C13C22×C3semidirect
16. #14274263C2×D5direct (N × H)
17. C2×C7×D5×C13ΓL(1,𝔽8)semidirect
22. C2×C72×C13C3×D5semidirect
24. C2×C72×D5C13⋊C3semidirect
25. C2×C5×C7×C13C2×ΓL(1,𝔽8)semidirect
26. C7×D5×C13C2×ΓL(1,𝔽8)semidirect
29. C72×C13C2×C3×D5semidirect
33. C2×C5×C72C2×C13⋊C3semidirect
34. C72×D5C2×C13⋊C3semidirect
35. C5×C7×C13C22×ΓL(1,𝔽8)semidirect
43. C2×D5×C13#3861semidirect
44. C5×C72C22×C13⋊C3semidirect
50. C2×C7×C13D5×ΓL(1,𝔽8)semidirect
53. C2×C7×D5#63270semidirect
54. C2×C5×C13C2×#3861semidirect
55. D5×C13C2×#3861semidirect
58. C2×C72D5×C13⋊C3semidirect
59. C7×C13C2×D5×ΓL(1,𝔽8)semidirect
63. C2×C5×C7C2×#63270semidirect
64. C7×D5C2×#63270semidirect
65. C5×C13C22×#3861semidirect
68. C72C2×D5×C13⋊C3semidirect
72. C5×C7C22×#63270semidirect
77. C2×C13D5×#3861semidirect
79. C2×D5#14274263direct (N × H)
82. C2×C7D5×#63270semidirect
83. C13C2×D5×#3861semidirect
85. C2×C5C2×#14274263semidirect
86. D5C2×#14274263direct (N × H)
87. C7C2×D5×#63270semidirect
90. C5C22×#14274263semidirect
94. C2D5×#14274263direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#142742632
D5×#142742632
C2×C72×D5×C133
C22×#142742635
C2×D5×#632707
C2×D5×#386113