Finite Group Databasebeta

← #42124795

Subgroups — #42124795

Order 27900.

160 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊(C31⋊#3874)C211yesmaximal, characteristic, complemented
2C31×C3⋊#3874C211yesmaximal, characteristic, complemented
3C3×#17987871C211yesmaximal, characteristic, complemented
4D15⋊D155—31nomaximal
5#3874⋊D31—33nomaximal
6C3×C31×C52⋊C3C2211yescharacteristic, complemented, Hall
7C5×D465—31no—
8C5×D15×C31—31no—
9C3×C5⋊D155D311yescharacteristic, complemented
10#17987871D313yescomplemented
11C31⋊#3874—33no—
12C31×#3874—33no—
13D5×D155—91noHall
14C31×C52⋊C3C2×D313yescomplemented
15C3×C52×C31C2×D311yescharacteristic, complemented
16D15⋊D31—151no—
17D3×D155—151no—
18C5⋊D155C3⋊D311yescharacteristic, complemented
19C5×D155—91no—
20C5×D5×C31—91no—
21C3⋊D3×D31—251nomaximal, Hall
22D465—31no—
23D15×C31—31no—
24C5×D93—151no—
25C5×D3×C31—151no—
26C3×D155—151no—
27C3×D155—151no—
28((C5⋊D5)⋊C3)⋊D3—311nomaximal, Hall
29C52×C31C2×C3⋊D311yescharacteristic, complemented, Hall
30C2×D155—451no—
31D5×D31—451no—
32C3⋊D93—251no—
33C3⋊D3×C31—251no—
34C32×D31—251no—
35C3×C5×C31—31no—
36C3×C5×C31—31no—
37C3×(C5⋊D5)⋊C3—311no—
38C3⋊#3874—311no—
39C3⋊#3874D3111yescharacteristic, complemented
40D3×D31—751no—
41D3×D31—753no—
42C2×C5×C31—451no—
43D155—91no—
44D155—151no—
45D155—151no—
46C5×D31—451no—
47D5×C31—91no—
48D15⋊D5—931no—
49#3874⋊C2—933no—
50C32×C31—251noHall
51C3×C52⋊C3C2×D3111yescharacteristic, complemented, Hall
52D93—151no—
53D93—753no—
54C3×D31—253no—
55C3×D31—251no—
56D3×C31—151no—
57D3×C31—753no—
58C5×C31—31no—
59C5×C31—31no—
60C5×D15—31no—
61C5×D15—931no—
62C3×C5⋊D5—311no—
63(C5⋊D5)⋊C3—313no—
64#3874—33no—
65#3874—933no—
66C2×D31—2251noHall
67D52—2791noHall
68C3×C31—253no—
69C3×C31#3874⋊C211yescharacteristic, complemented
70C3×C52D3×D3111yescharacteristic, complemented
71C52⋊C3D3×D3113yescomplemented
72C2×C31—451no—
73D31—251no—
74D31—451no—
75D3×D5—4651no—
76D3×D5—4651no—
77C5⋊D5—311no—
78C5×D5—91no—
79C5×D5—2791no—
80C2×C3⋊D3—7751noHall
81C31((C5⋊D5)⋊C3)⋊D311yescharacteristic, complemented, Sylow
82D15—31no—
83D15—931no—
84C3×D5—4651no—
85C3×D5—4651no—
86C5×D3—151no—
87C5×D3—4651no—
88C52C3⋊D3×D3111yescharacteristic, complemented, Sylow
89C2×D5—13951no—
90C2×D5—13951no—
91C2×C32—7751no—
92C3⋊D3—7751no—
93C3⋊D3—251no—
94C3×C5—31no—
95C3×C5—31no—
96C2×D3—23251no—
97C2×D3—23253no—
98C2×C5—451no—
99C2×C5—13951no—
100D5—91no—
101D5—2791no—
102D5—4651no—
103D5—4651no—
104C32—251noSylow
105C2×C3—7753no—
106C2×C3—7751no—
107D3—151no—
108D3—23253no—
109D3—753no—
110D3—4651no—
111C5—31no—
112C5—31no—
113C22—69751noSylow
114C3—253no—
115C3#3874⋊D3111yescharacteristic, complemented
116C2—7751no—
117C2—451no—
118C2—13951no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, cosocle, hypocenterC3×C31×C52⋊C3C22
Fitting, socleC3×C52×C31C2×D3
LCSG ▷ C3×C31×C52⋊C3
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3⋊(C31⋊#3874)C2semidirect
2. C31×C3⋊#3874C2semidirect
3. C3×#17987871C2semidirect
6. C3×C31×C52⋊C3C22semidirect
9. C3×C5⋊D155D3semidirect
10. #17987871D3semidirect
14. C31×C52⋊C3C2×D3semidirect
15. C3×C52×C31C2×D3semidirect
18. C5⋊D155C3⋊D3semidirect
29. C52×C31C2×C3⋊D3semidirect
39. C3⋊#3874D31semidirect
51. C3×C52⋊C3C2×D31semidirect
69. C3×C31#3874⋊C2semidirect
70. C3×C52D3×D31semidirect
71. C52⋊C3D3×D31semidirect
81. C31((C5⋊D5)⋊C3)⋊D3semidirect
88. C52C3⋊D3×D31semidirect
115. C3#3874⋊D31semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C31⋊#3874)2
C31×C3⋊#38742
C3×#179878712
D15⋊D1553
#3874⋊D313
C3⋊D3×D3125
((C5⋊D5)⋊C3)⋊D331