Finite Group Databasebeta

← D5×D13×#3862 #50304198

Subgroups — D5×D13×#3862 #50304198

Order 38220.

200 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 50 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×#3862C211yesmaximal, characteristic, complemented
2D5×C13×#3862C211yesmaximal, characteristic, complemented
3C5×D13×#3862C211yesmaximal, characteristic, complemented
4C72×D5×D13C311yesmaximal, characteristic, complemented, Hall
5C5×C13×#3862C2211yescharacteristic, complemented, Hall
6C2×D13×#3862—51nomaximal, Hall
7C72×D65C2×C311yescharacteristic, complemented
8C72×D5×C13C2×C311yescharacteristic, complemented
9C5×C72×D13C2×C311yescharacteristic, complemented
10D5×ΓL(1,𝔽8)×D13—72nomaximal
11C2×C13×#3862—51no—
12D13×#3862—51no—
13D13×#3862D511yescharacteristic, direct product factor
14C5×C72×C13C22×C311yescharacteristic, complemented, Hall
15C2×D5×#3862—131nomaximal, Hall
16ΓL(1,𝔽8)×D65—72no—
17D5×C13×ΓL(1,𝔽8)—72no—
18C5×ΓL(1,𝔽8)×D13—72no—
19C2×C72×D13—51noHall
20C13×#3862C2×D511yescharacteristic, complemented, Hall
21C7×D5×D13—32no—
22C7×D5×D13ΓL(1,𝔽8)12yescomplemented
23C2×C5×#3862—131no—
24D5×#3862—131no—
25D5×#3862D1311yescharacteristic, direct product factor
26C5×C13×ΓL(1,𝔽8)—72no—
27C2×C72×C13—51no—
28C72×D13—51no—
29C72×D13C3×D511yescharacteristic, complemented
30C2×ΓL(1,𝔽8)×D13—352no—
31C2×C72×D5—131noHall
32C7×D65—32no—
33C7×D65C2×ΓL(1,𝔽8)12yescomplemented
34C7×D5×C13—32no—
35C7×D5×C13C2×ΓL(1,𝔽8)12yescomplemented
36C5×C7×D13—32no—
37C5×C7×D13C2×ΓL(1,𝔽8)12yescomplemented
38C3×D5×D13—491noHall
39C5×#3862C2×D1311yescharacteristic, complemented, Hall
40C72×C13C2×C3×D511yescharacteristic, complemented, Hall
41C22×#3862—651noHall
42C2×C13×ΓL(1,𝔽8)—352no—
43ΓL(1,𝔽8)×D13—72no—
44ΓL(1,𝔽8)×D13—352no—
45C2×C5×C72—131no—
46C72×D5—131no—
47C72×D5C3×D1311yescharacteristic, complemented
48C5×C7×C13—32no—
49C5×C7×C13C22×ΓL(1,𝔽8)12yescomplemented
50C2×D5×ΓL(1,𝔽8)—912no—
51C3×D65—491no—
52C3×D5×C13—491no—
53C3×C5×D13—491no—
54C2×C7×D13—52no—
55C2×C7×D13—152no—
56C2×#3862—51no—
57C2×#3862—131no—
58C2×#3862—651no—
59C13×ΓL(1,𝔽8)—72no—
60D5×D13#386211yescharacteristic, direct product factor, Hall
61C5×C72C2×C3×D1311yescharacteristic, complemented, Hall
62C2×C5×ΓL(1,𝔽8)—912no—
63D5×ΓL(1,𝔽8)—72no—
64D5×ΓL(1,𝔽8)—912no—
65C22×C72—651noHall
66C3×C5×C13—491noHall
67C2×C7×C13—52no—
68C2×C7×C13—152no—
69C7×D13—32no—
70C7×D13—52no—
71C7×D13—152no—
72C7×D13D5×ΓL(1,𝔽8)12yescomplemented
73C2×C3×D13—2451noHall
74#3862D5×D1311yescharacteristic, direct product factor, Hall
75C2×C7×D5—132no—
76C2×C7×D5—392no—
77D65C2×#386211yescharacteristic, complemented
78C5×D13C2×#386211yescharacteristic, complemented
79D5×C13C2×#386211yescharacteristic, complemented
80C5×ΓL(1,𝔽8)—72no—
81C2×C72—51no—
82C2×C72—131no—
83C2×C72—651no—
84C7×C13—32no—
85C7×C13C2×D5×ΓL(1,𝔽8)12yescomplemented
86C22×ΓL(1,𝔽8)—4552no—
87C2×C3×C13—2451no—
88C3×D13—491no—
89C3×D13—2451no—
90C2×C5×C7—132no—
91C2×C5×C7—392no—
92C7×D5—32no—
93C7×D5—132no—
94C7×D5—392no—
95C7×D5ΓL(1,𝔽8)×D1312yescomplemented
96C5×C13C22×#386211yescharacteristic, complemented, Hall
97C2×C3×D5—6371noHall
98C2×D13—51noHall
99C72C3×D5×D1311yescharacteristic, complemented, Sylow
100C2×ΓL(1,𝔽8)—352no—
101C2×ΓL(1,𝔽8)—912no—
102C2×ΓL(1,𝔽8)—4552no—
103C3×C13—491noHall
104C5×C7—32no—
105C5×C7C2×ΓL(1,𝔽8)×D1312yescomplemented
106C2×C3×C5—6371no—
107C3×D5—491no—
108C3×D5—6371no—
109C22×C7—652no—
110C22×C7—1952no—
111C2×C13—51no—
112D13—51no—
113D13D5×#386211yescharacteristic, direct product factor
114ΓL(1,𝔽8)—72no—
115C2×D5—131noHall
116C3×C5—491noHall
117C2×C7—52no—
118C2×C7—132no—
119C2×C7—152no—
120C2×C7—392no—
121C2×C7—652no—
122C2×C7—1952no—
123C13C2×D5×#386211yescharacteristic, complemented, Sylow
124C22×C3—31851noHall
125C2×C5—131no—
126D5—131no—
127D5D13×#386211yescharacteristic, direct product factor
128C7—32no—
129C7D5×ΓL(1,𝔽8)×D1312yescomplemented
130C2×C3—31851no—
131C2×C3—6371no—
132C2×C3—2451no—
133C5C2×D13×#386211yescharacteristic, complemented, Sylow
134C22—651noSylow
135C3—491noSylow
136C2—51no—
137C2—131no—
138C2—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×#3862C2semidirect
2. D5×C13×#3862C2semidirect
3. C5×D13×#3862C2semidirect
4. C72×D5×D13C3semidirect
5. C5×C13×#3862C22semidirect
7. C72×D65C2×C3semidirect
8. C72×D5×C13C2×C3semidirect
9. C5×C72×D13C2×C3semidirect
13. D13×#3862D5direct (N × H)
14. C5×C72×C13C22×C3semidirect
20. C13×#3862C2×D5semidirect
22. C7×D5×D13ΓL(1,𝔽8)semidirect
25. D5×#3862D13direct (N × H)
29. C72×D13C3×D5semidirect
33. C7×D65C2×ΓL(1,𝔽8)semidirect
35. C7×D5×C13C2×ΓL(1,𝔽8)semidirect
37. C5×C7×D13C2×ΓL(1,𝔽8)semidirect
39. C5×#3862C2×D13semidirect
40. C72×C13C2×C3×D5semidirect
47. C72×D5C3×D13semidirect
49. C5×C7×C13C22×ΓL(1,𝔽8)semidirect
60. D5×D13#3862direct (N × H)
61. C5×C72C2×C3×D13semidirect
72. C7×D13D5×ΓL(1,𝔽8)semidirect
74. #3862D5×D13direct (N × H)
77. D65C2×#3862semidirect
78. C5×D13C2×#3862semidirect
79. D5×C13C2×#3862semidirect
85. C7×C13C2×D5×ΓL(1,𝔽8)semidirect
95. C7×D5ΓL(1,𝔽8)×D13semidirect
96. C5×C13C22×#3862semidirect
99. C72C3×D5×D13semidirect
105. C5×C7C2×ΓL(1,𝔽8)×D13semidirect
113. D13D5×#3862direct (N × H)
123. C13C2×D5×#3862semidirect
127. D5D13×#3862direct (N × H)
129. C7D5×ΓL(1,𝔽8)×D13semidirect
133. C5C2×D13×#3862semidirect

Maximal subgroups

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

subgroupindex
D65×#38622
D5×C13×#38622
C5×D13×#38622
C72×D5×D133
C2×D13×#38625
D5×ΓL(1,𝔽8)×D137
C2×D5×#386213