Finite Group Databasebeta

← C5×D15×#3861 #36348036

Subgroups — C5×D15×#3861 #36348036

Order 22050.

480 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 110 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×C52×#3861C211yesmaximal, characteristic, complemented, Hall
2C5×C72×D15C311yesmaximal, characteristic, complemented
3C5×D5×#3861—31nomaximal
4D15×#3861C511yesmaximal, characteristic, direct product factor
5C5×D3×#3861—51nomaximal
6C52×#3861—21no—
7C52×#3861D311yescharacteristic, complemented
8C3×C52×C72C2×C311yescharacteristic, complemented
9C5×ΓL(1,𝔽8)×D15—78nomaximal
10C5×C72×D5—31noHall
11C3×C5×#3861—22no—
12C3×C5×#3861D511yescharacteristic, complemented
13C3×C5×#3861C2×C511yescharacteristic, complemented
14C3×C52×ΓL(1,𝔽8)—78no—
15C72×D15C3×C511yescharacteristic, complemented
16C5×D3×C72—51no—
17C2×C5×#3861—151no—
18D5×#3861—31no—
19C52×C72C3×D311yescharacteristic, complemented, Hall
20C5×C7×D15ΓL(1,𝔽8)18yescomplemented
21C5×D5×ΓL(1,𝔽8)—218no—
22D3×#3861—51noHall
23C3×C5×C72—22no—
24C3×C5×C72C3×D511yescharacteristic, complemented
25C3×C5×C72C2×C3×C511yescharacteristic, complemented
26C5×#3861—24no—
27C5×#3861—22no—
28C5×#3861—21no—
29C5×#3861—21no—
30C5×#3861C5×D311yescharacteristic, complemented
31C5×#3861D1511yescharacteristic, direct product factor
32ΓL(1,𝔽8)×D15—78no—
33C5×D3×ΓL(1,𝔽8)—358no—
34C3×C52×C7C2×ΓL(1,𝔽8)18yescomplemented
35C52×ΓL(1,𝔽8)—78no—
36C52×ΓL(1,𝔽8)—148no—
37C2×C5×C72—151no—
38C72×D5—31no—
39C3×C5×D15—491noHall
40C3×#3861C5×D511yescharacteristic, complemented, Hall
41C5×C7×D5—38no—
42C3×C5×ΓL(1,𝔽8)—78no—
43C3×C5×ΓL(1,𝔽8)—78no—
44C3×C5×ΓL(1,𝔽8)—1416no—
45D3×C72—51no—
46C2×#3861—151no—
47C5×C72—22no—
48C5×C72C3×C5×D311yescharacteristic, complemented
49C5×C72C3×D1511yescharacteristic, complemented
50C32×C52—491noHall
51C7×D15C5×ΓL(1,𝔽8)18yescomplemented
52C5×D3×C7—58no—
53C2×C5×ΓL(1,𝔽8)—1058no—
54D5×ΓL(1,𝔽8)—218no—
55C52×C7D3×ΓL(1,𝔽8)18yescomplemented
56C5×D15#386111yescharacteristic, direct product factor
57C3×C5×D5—1471no—
58C3×C72C3×C5×D511yescharacteristic, complemented
59#3861—21no—
60#3861C5×D1511yescharacteristic, direct product factor
61D3×ΓL(1,𝔽8)—358no—
62C3×C5×C7—216no—
63C3×C5×C7D5×ΓL(1,𝔽8)18yescomplemented
64C3×C5×C7C2×C5×ΓL(1,𝔽8)18yescomplemented
65C5×ΓL(1,𝔽8)—78no—
66C5×ΓL(1,𝔽8)—78no—
67C5×ΓL(1,𝔽8)—1416no—
68C5×ΓL(1,𝔽8)—1432no—
69C5×ΓL(1,𝔽8)—148no—
70C5×ΓL(1,𝔽8)—148no—
71C2×C72—151noHall
72C3×D15—491no—
73C3×C5×D3—2451no—
74C3×C52—491no—
75C3×C52—981no—
76C3×C52C2×#386111yescharacteristic, complemented
77C2×C5×C7—158no—
78C7×D5—38no—
79C3×ΓL(1,𝔽8)—78no—
80C5×D5—31noHall
81C72C3×C5×D1511yescharacteristic, complemented, Sylow
82C32×C5—491no—
83C32×C5—491no—
84C32×C5—982no—
85D3×C7—58no—
86C2×ΓL(1,𝔽8)—1058no—
87C5×C7—216no—
88C5×C7C5×D3×ΓL(1,𝔽8)18yescomplemented
89C5×C7ΓL(1,𝔽8)×D1518yescomplemented
90C2×C3×C5—7351no—
91D15C5×#386111yescharacteristic, direct product factor
92C3×D5—1471no—
93C5×D3—51no—
94C52D3×#386111yescharacteristic, complemented, Sylow
95C3×C7C5×D5×ΓL(1,𝔽8)18yescomplemented
96ΓL(1,𝔽8)—78no—
97ΓL(1,𝔽8)—148no—
98C3×D3—2451noHall
99C3×C5—22no—
100C3×C5—491no—
101C3×C5—491no—
102C3×C5—982no—
103C3×C5—984no—
104C3×C5—981no—
105C3×C5—981no—
106C3×C5D5×#386111yescharacteristic, complemented
107C3×C5C2×C5×#386111yescharacteristic, complemented
108C2×C7—158no—
109C2×C5—151no—
110D5—31no—
111C32—491noSylow
112C7C5×ΓL(1,𝔽8)×D1518yescomplemented
113C2×C3—7351no—
114D3—51no—
115C5—22no—
116C5C5×D3×#386111yescharacteristic, complemented
117C5D15×#386111yescharacteristic, direct product factor
118C3—491no—
119C3—981no—
120C3C5×D5×#386111yescharacteristic, complemented
121C2—151noSylow
subgroupG/H
center, hypercenterC5D15×#3861
commutator, cosocle, hypocenterC3×C5×C72C2×C3×C5
FrattiniC1G
Fitting, socleC3×C52×C72C2×C3
LCSG ▷ C3×C5×C72
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C3×C52×#3861C2semidirect
2. C5×C72×D15C3semidirect
4. D15×#3861C5direct (N × H)
7. C52×#3861D3semidirect
8. C3×C52×C72C2×C3semidirect
12. C3×C5×#3861D5semidirect
13. C3×C5×#3861C2×C5semidirect
15. C72×D15C3×C5semidirect
19. C52×C72C3×D3semidirect
20. C5×C7×D15ΓL(1,𝔽8)semidirect
24. C3×C5×C72C3×D5semidirect
25. C3×C5×C72C2×C3×C5semidirect
30. C5×#3861C5×D3semidirect
31. C5×#3861D15direct (N × H)
34. C3×C52×C7C2×ΓL(1,𝔽8)semidirect
40. C3×#3861C5×D5semidirect
48. C5×C72C3×C5×D3semidirect
49. C5×C72C3×D15semidirect
51. C7×D15C5×ΓL(1,𝔽8)semidirect
55. C52×C7D3×ΓL(1,𝔽8)semidirect
56. C5×D15#3861direct (N × H)
58. C3×C72C3×C5×D5semidirect
60. #3861C5×D15direct (N × H)
63. C3×C5×C7D5×ΓL(1,𝔽8)semidirect
64. C3×C5×C7C2×C5×ΓL(1,𝔽8)semidirect
76. C3×C52C2×#3861semidirect
81. C72C3×C5×D15semidirect
88. C5×C7C5×D3×ΓL(1,𝔽8)semidirect
89. C5×C7ΓL(1,𝔽8)×D15semidirect
91. D15C5×#3861direct (N × H)
94. C52D3×#3861semidirect
95. C3×C7C5×D5×ΓL(1,𝔽8)semidirect
106. C3×C5D5×#3861semidirect
107. C3×C5C2×C5×#3861semidirect
112. C7C5×ΓL(1,𝔽8)×D15semidirect
116. C5C5×D3×#3861semidirect
117. C5D15×#3861direct (N × H)
120. C3C5×D5×#3861semidirect

Maximal subgroups

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

subgroupindex
C3×C52×#38612
C5×C72×D153
C5×D5×#38613
D15×#38615
C5×D3×#38615
C5×ΓL(1,𝔽8)×D157