Finite Group Databasebeta

← C2×C31⋊#90646 #42124528

Subgroups — C2×C31⋊#90646 #42124528

Order 27900.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×C52⋊C9C211yesmaximal, characteristic, complemented
2C31⋊#90646C212yesmaximal, direct product factor
3C2×C5×D465—31nomaximal
4C31×C52⋊C9C2211yescharacteristic, complemented, Hall
5C5×D465—32no—
6C2×C3×C52×C31D311yescharacteristic
7C2×C5×D155—91noHall
8C3×C52×C31C2×D311yescharacteristic
9C2×D465—31no—
10C2×C5×D93—151no—
11C2×C52×C31D911yescharacteristic, complemented
12C5×D155—92no—
13C2×D279—251nomaximal, Hall
14C2×C3×C5×C31—31no—
15C2×C3×C5×C31—31no—
16D465—32no—
17C5×D93—152no—
18C2×#90646—311nomaximal, Hall
19C52×C31C2×D911yescharacteristic, complemented, Hall
20C2×D155—91no—
21C2×C5×D31—451no—
22C2×C9×C31—251no—
23D279—252no—
24C3×C5×C31—31no—
25C3×C5×C31—31no—
26C2×C52⋊C9D3111yescharacteristic, complemented
27#90646—312no—
28C2×D93—151no—
29C2×C5×C31—31no—
30C2×C5×C31—31no—
31D155—92no—
32C5×D31—452no—
33C2×C5×D15—931no—
34C9×C31—251noHall
35C52⋊C9C2×D3111yescharacteristic, complemented, Hall
36C2×C3×C31#387411yescharacteristic
37D93—152no—
38C5×C31—31no—
39C5×C31—31no—
40C2×C3×C52D9311yescharacteristic
41C5×D15—932no—
42C2×D31—451noHall
43C2×C5×D5—2791noHall
44C3×C31C2×#387411yescharacteristic
45C3×C52C2×D9311yescharacteristic
46C2×C31#9064611yescharacteristic, complemented
47D31—452no—
48C2×D15—931no—
49C2×C5×D3—4651no—
50C2×C52D27911yescharacteristic, complemented
51C5×D5—2792no—
52C2×D9—7751noHall
53C31C2×#9064611yescharacteristic, complemented, Sylow
54C2×C3×C5—31no—
55C2×C3×C5—31no—
56D15—932no—
57C5×D3—4652no—
58C52C2×D27911yescharacteristic, complemented, Sylow
59C22×C5—13951no—
60C2×D5—2791no—
61C2×C9—251no—
62D9—7752no—
63C3×C5—31no—
64C3×C5—31no—
65C2×D3—4651no—
66C2×C5—31no—
67C2×C5—31no—
68C2×C5—13952no—
69D5—2792no—
70C9—251noSylow
71C2×C3C31⋊#387411yescharacteristic
72D3—4652no—
73C5—31no—
74C5—31no—
75C22—13951noSylow
76C3C2×C31⋊#387411yescharacteristic
77C2—13952no—
78C2C31⋊#9064611yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2C31⋊#90646
commutator, cosocle, hypocenterC31×C52⋊C9C22
FrattiniC3C2×C31⋊#3874
Fitting, socleC2×C3×C52×C31D3
LCSG ▷ C31×C52⋊C9
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C31×C52⋊C9C2semidirect
2. C31⋊#90646C2direct (N × H)
4. C31×C52⋊C9C22semidirect
11. C2×C52×C31D9semidirect
19. C52×C31C2×D9semidirect
26. C2×C52⋊C9D31semidirect
35. C52⋊C9C2×D31semidirect
46. C2×C31#90646semidirect
50. C2×C52D279semidirect
53. C31C2×#90646semidirect
58. C52C2×D279semidirect
78. C2C31⋊#90646direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×C52⋊C92
C31⋊#906462
C2×C5×D4653
C2×D27925
C2×#9064631