Finite Group Databasebeta

← D5×D13×#3861 #50304093

Subgroups — D5×D13×#3861 #50304093

Order 38220.

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

normal subgroups only

This group has 400 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
1D65×#3861C211yesmaximal, characteristic, complemented
2D5×C13×#3861C211yesmaximal, characteristic, complemented
3C5×D13×#3861C211yesmaximal, characteristic, complemented
4C72×D5×D13C311yesmaximal, characteristic, complemented, Hall
5C5×C13×#3861C2211yescharacteristic, complemented, Hall
6C2×D13×#3861—51nomaximal, Hall
7C72×D65C2×C311yescharacteristic, complemented
8C72×D5×C13C2×C311yescharacteristic, complemented
9C5×C72×D13C2×C311yescharacteristic, complemented
10D5×ΓL(1,𝔽8)×D13—78nomaximal
11C2×C13×#3861—51no—
12D13×#3861—51no—
13D13×#3861D511yescharacteristic, direct product factor
14C5×C72×C13C22×C311yescharacteristic, complemented, Hall
15C2×D5×#3861—131nomaximal, Hall
16ΓL(1,𝔽8)×D65—78no—
17D5×C13×ΓL(1,𝔽8)—78no—
18C5×ΓL(1,𝔽8)×D13—78no—
19C2×C72×D13—51noHall
20C13×#3861C2×D511yescharacteristic, complemented, Hall
21C7×D5×D13ΓL(1,𝔽8)18yescomplemented
22C2×C5×#3861—131no—
23D5×#3861—131no—
24D5×#3861D1311yescharacteristic, direct product factor
25C5×C13×ΓL(1,𝔽8)—78no—
26C2×C72×C13—51no—
27C72×D13—51no—
28C72×D13C3×D511yescharacteristic, complemented
29C2×ΓL(1,𝔽8)×D13—358no—
30C2×C72×D5—131noHall
31C7×D65C2×ΓL(1,𝔽8)18yescomplemented
32C7×D5×C13C2×ΓL(1,𝔽8)18yescomplemented
33C5×C7×D13C2×ΓL(1,𝔽8)18yescomplemented
34C3×D5×D13—491noHall
35C5×#3861C2×D1311yescharacteristic, complemented, Hall
36C72×C13C2×C3×D511yescharacteristic, complemented, Hall
37C22×#3861—651noHall
38C2×C13×ΓL(1,𝔽8)—358no—
39ΓL(1,𝔽8)×D13—78no—
40ΓL(1,𝔽8)×D13—358no—
41C2×C5×C72—131no—
42C72×D5—131no—
43C72×D5C3×D1311yescharacteristic, complemented
44C5×C7×C13C22×ΓL(1,𝔽8)18yescomplemented
45C2×D5×ΓL(1,𝔽8)—918no—
46C3×D65—491no—
47C3×D5×C13—491no—
48C3×C5×D13—491no—
49C2×C7×D13—58no—
50C2×#3861—51no—
51C2×#3861—131no—
52C2×#3861—651no—
53C13×ΓL(1,𝔽8)—78no—
54D5×D13#386111yescharacteristic, direct product factor, Hall
55C5×C72C2×C3×D1311yescharacteristic, complemented, Hall
56C2×C5×ΓL(1,𝔽8)—918no—
57D5×ΓL(1,𝔽8)—78no—
58D5×ΓL(1,𝔽8)—918no—
59C22×C72—651noHall
60C3×C5×C13—491noHall
61C2×C7×C13—58no—
62C7×D13—58no—
63C7×D13D5×ΓL(1,𝔽8)18yescomplemented
64C2×C3×D13—2451noHall
65#3861D5×D1311yescharacteristic, direct product factor, Hall
66C2×C7×D5—138no—
67D65C2×#386111yescharacteristic, complemented
68C5×D13C2×#386111yescharacteristic, complemented
69D5×C13C2×#386111yescharacteristic, complemented
70C5×ΓL(1,𝔽8)—78no—
71C2×C72—51no—
72C2×C72—131no—
73C2×C72—651no—
74C7×C13C2×D5×ΓL(1,𝔽8)18yescomplemented
75C22×ΓL(1,𝔽8)—4558no—
76C2×C3×C13—2451no—
77C3×D13—491no—
78C3×D13—2451no—
79C2×C5×C7—138no—
80C7×D5—138no—
81C7×D5ΓL(1,𝔽8)×D1318yescomplemented
82C5×C13C22×#386111yescharacteristic, complemented, Hall
83C2×C3×D5—6371noHall
84C2×D13—51noHall
85C72C3×D5×D1311yescharacteristic, complemented, Sylow
86C2×ΓL(1,𝔽8)—358no—
87C2×ΓL(1,𝔽8)—918no—
88C2×ΓL(1,𝔽8)—4558no—
89C3×C13—491noHall
90C5×C7C2×ΓL(1,𝔽8)×D1318yescomplemented
91C2×C3×C5—6371no—
92C3×D5—491no—
93C3×D5—6371no—
94C22×C7—658no—
95C2×C13—51no—
96D13—51no—
97D13D5×#386111yescharacteristic, direct product factor
98ΓL(1,𝔽8)—78no—
99C2×D5—131noHall
100C3×C5—491noHall
101C2×C7—58no—
102C2×C7—138no—
103C2×C7—658no—
104C13C2×D5×#386111yescharacteristic, complemented, Sylow
105C22×C3—31851noHall
106C2×C5—131no—
107D5—131no—
108D5D13×#386111yescharacteristic, direct product factor
109C7D5×ΓL(1,𝔽8)×D1318yescomplemented
110C2×C3—31851no—
111C2×C3—6371no—
112C2×C3—2451no—
113C5C2×D13×#386111yescharacteristic, complemented, Sylow
114C22—651noSylow
115C3—491noSylow
116C2—51no—
117C2—131no—
118C2—651no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C72×C13C22×C3
LCSG ▷ C5×C72×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. D65×#3861C2semidirect
2. D5×C13×#3861C2semidirect
3. C5×D13×#3861C2semidirect
4. C72×D5×D13C3semidirect
5. C5×C13×#3861C22semidirect
7. C72×D65C2×C3semidirect
8. C72×D5×C13C2×C3semidirect
9. C5×C72×D13C2×C3semidirect
13. D13×#3861D5direct (N × H)
14. C5×C72×C13C22×C3semidirect
20. C13×#3861C2×D5semidirect
21. C7×D5×D13ΓL(1,𝔽8)semidirect
24. D5×#3861D13direct (N × H)
28. C72×D13C3×D5semidirect
31. C7×D65C2×ΓL(1,𝔽8)semidirect
32. C7×D5×C13C2×ΓL(1,𝔽8)semidirect
33. C5×C7×D13C2×ΓL(1,𝔽8)semidirect
35. C5×#3861C2×D13semidirect
36. C72×C13C2×C3×D5semidirect
43. C72×D5C3×D13semidirect
44. C5×C7×C13C22×ΓL(1,𝔽8)semidirect
54. D5×D13#3861direct (N × H)
55. C5×C72C2×C3×D13semidirect
63. C7×D13D5×ΓL(1,𝔽8)semidirect
65. #3861D5×D13direct (N × H)
67. D65C2×#3861semidirect
68. C5×D13C2×#3861semidirect
69. D5×C13C2×#3861semidirect
74. C7×C13C2×D5×ΓL(1,𝔽8)semidirect
81. C7×D5ΓL(1,𝔽8)×D13semidirect
82. C5×C13C22×#3861semidirect
85. C72C3×D5×D13semidirect
90. C5×C7C2×ΓL(1,𝔽8)×D13semidirect
97. D13D5×#3861direct (N × H)
104. C13C2×D5×#3861semidirect
108. D5D13×#3861direct (N × H)
109. C7D5×ΓL(1,𝔽8)×D13semidirect
113. C5C2×D13×#3861semidirect

Maximal subgroups

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

subgroupindex
D65×#38612
D5×C13×#38612
C5×D13×#38612
C72×D5×D133
C2×D13×#38615
D5×ΓL(1,𝔽8)×D137
C2×D5×#386113