Finite Group Databasebeta

← #50304206

Subgroups — #50304206

Order 38220.

200 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 32 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
1C5⋊(D13⋊#3862)C211yesmaximal, characteristic, complemented
2C5⋊#16838453C211yesmaximal, characteristic, complemented
3C5×#16838452C211yesmaximal, characteristic, complemented
4D65⋊(C7⋊D7)C311yesmaximal, characteristic, complemented, Hall
5C5×C13⋊#3862C2211yescharacteristic, complemented, Hall
6D13⋊#64425—51nomaximal, Hall
7C13×C5⋊(C7⋊D7)C2×C311yescharacteristic, complemented
8C72×D65C2×C311yescharacteristic, complemented
9C5×C7⋊D91C2×C311yescharacteristic, complemented
10#10587723⋊D5—71nomaximal
11#10587722⋊D5—71nomaximal
12D13⋊#3862—51no—
13#16838453—51no—
14#16838452D511yescharacteristic, complemented
15C5×C72×C13C22×C311yescharacteristic, complemented, Hall
16D5×#64425—131nomaximal, Hall
17C5⋊#10587721—71no—
18C5⋊#10587720—71no—
19C5⋊#10587717—71no—
20C5⋊#10587716—71no—
21C5×#10587723—71no—
22C5×#10587722—71no—
23D13×C7⋊D7—51noHall
24C13⋊#3862C2×D511yescharacteristic, complemented, Hall
25D35⋊D13—71no—
26D35⋊D13—71no—
27D35⋊D13—212no—
28D5×#3862—131no—
29C5⋊#64425—131no—
30C5×#64425—131no—
31C5×#63270—71no—
32C5×#63271—71no—
33C7⋊D91C3×D511yescharacteristic, complemented
34C13×C7⋊D7—51no—
35C72×D13—51no—
36#10587716⋊C2—351no—
37#10587717⋊C2—351no—
38D5×C7⋊D7—131noHall
39C13×D35—71no—
40C13×D35—71no—
41C13×D35—212no—
42C7×D65—32no—
43C7×D65AGL(1,𝔽7)11yescharacteristic, complemented
44C7×D65AGL(1,𝔽7)11yescharacteristic, complemented
45C5×D91—71no—
46C5×D91—71no—
47C5×D91—212no—
48D5×D13⋊C3—491noHall
49C5×#3862—131noHall
50C72×C13C2×C3×D511yescharacteristic, complemented, Hall
51C2×#64425—651noHall
52#10587723—71no—
53#10587722—71no—
54#10587721—351no—
55#10587720—351no—
56#10587717—351no—
57#10587716—351no—
58C5⋊(C7⋊D7)D13⋊C311yescharacteristic, complemented
59C72×D5—131no—
60C5×C7⋊D7—131no—
61C5×C7×C13—32no—
62C5×C7×C13C2×AGL(1,𝔽7)11yescharacteristic, complemented
63C5×C7×C13C2×AGL(1,𝔽7)11yescharacteristic, complemented
64D5×AGL(1,𝔽7)—911no—
65D5×AGL(1,𝔽7)—911no—
66C5⋊(D13⋊C3)—491no—
67D5×C13⋊C3—491no—
68C5×D13⋊C3—491no—
69D7×D13—351no—
70D7×D13—351no—
71D7×D13—1052no—
72C2×#3862—651no—
73#64425—131no—
74#64425—651no—
75#63271—71no—
76#63270—71no—
77D5×D13—491noHall
78C5×C72C2×D13⋊C311yescharacteristic, complemented, Hall
79C5⋊AGL(1,𝔽7)—911no—
80C5⋊AGL(1,𝔽7)—911no—
81D5×ΓL(1,𝔽8)—911no—
82D5×ΓL(1,𝔽8)—911no—
83C5×AGL(1,𝔽7)—911no—
84C5×AGL(1,𝔽7)—911no—
85C2×C7⋊D7—651noHall
86C5×C13⋊C3—491noHall
87D91—71no—
88D91—71no—
89D91—212no—
90C7×D13—51no—
91C7×D13—51no—
92C7×D13—152no—
93C13×D7—351no—
94C13×D7—351no—
95C13×D7—1052no—
96C2×D13⋊C3—2451noHall
97#3862—131noHall
98D5×D7—2732no—
99D5×D7—911no—
100D5×D7—911no—
101D65#6442511yescharacteristic, complemented
102C5×D13—491no—
103D5×C13—491no—
104C5×ΓL(1,𝔽8)—911no—
105C5×ΓL(1,𝔽8)—911no—
106C2×C72—651no—
107C7⋊D7—51no—
108C7⋊D7—131no—
109C7×C13—32no—
110C7×C13D5×AGL(1,𝔽7)11yescharacteristic, complemented
111C7×C13D5×AGL(1,𝔽7)11yescharacteristic, complemented
112C2×AGL(1,𝔽7)—4551no—
113C2×AGL(1,𝔽7)—4551no—
114C2×C13⋊C3—2451no—
115D13⋊C3—491no—
116D13⋊C3—2451no—
117D35—71no—
118D35—71no—
119D35—212no—
120C5×D7—2732no—
121C5×D7—911no—
122C5×D7—911no—
123C7×D5—131no—
124C7×D5—131no—
125C7×D5—392no—
126C5×C13C2×#6442511yescharacteristic, complemented, Hall
127C2×C3×D5—6371noHall
128C2×D13—2451noHall
129C72D5×D13⋊C311yescharacteristic, complemented, Sylow
130C2×ΓL(1,𝔽8)—4551no—
131C2×ΓL(1,𝔽8)—4551no—
132AGL(1,𝔽7)—911no—
133AGL(1,𝔽7)—911no—
134AGL(1,𝔽7)—4551no—
135AGL(1,𝔽7)—4551no—
136C13⋊C3—491noHall
137C5×C7—32no—
138C5×C7#10587717⋊C211yescharacteristic, complemented
139C5×C7#10587716⋊C211yescharacteristic, complemented
140C2×C3×C5—6371no—
141C3×D5—6371no—
142C3×D5—6371no—
143C2×D7—13652no—
144C2×D7—4551no—
145C2×D7—4551no—
146C2×C13—2451no—
147D13—51no—
148D13—491no—
149ΓL(1,𝔽8)—911no—
150ΓL(1,𝔽8)—911no—
151C2×D5—6371noHall
152C3×C5—6371noHall
153C2×C7—651no—
154C2×C7—651no—
155C2×C7—1952no—
156D7—2732no—
157D7—351no—
158D7—351no—
159D7—911no—
160D7—911no—
161D7—1052no—
162C13D5×#6442511yescharacteristic, complemented, Sylow
163C22×C3—31851noHall
164C2×C5—6371no—
165D5—131no—
166D5—491no—
167C7—32no—
168C7#10587722⋊D511yescharacteristic, complemented
169C7#10587723⋊D511yescharacteristic, complemented
170C2×C3—31851no—
171C2×C3—31851no—
172C2×C3—6371no—
173C5D13⋊#6442511yescharacteristic, complemented, Sylow
174C22—31851noSylow
175C3—6371noSylow
176C2—651no—
177C2—6371no—
178C2—2451no—
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. C5⋊(D13⋊#3862)C2semidirect
2. C5⋊#16838453C2semidirect
3. C5×#16838452C2semidirect
4. D65⋊(C7⋊D7)C3semidirect
5. C5×C13⋊#3862C22semidirect
7. C13×C5⋊(C7⋊D7)C2×C3semidirect
8. C72×D65C2×C3semidirect
9. C5×C7⋊D91C2×C3semidirect
14. #16838452D5semidirect
15. C5×C72×C13C22×C3semidirect
24. C13⋊#3862C2×D5semidirect
33. C7⋊D91C3×D5semidirect
43. C7×D65AGL(1,𝔽7)semidirect
44. C7×D65AGL(1,𝔽7)semidirect
50. C72×C13C2×C3×D5semidirect
58. C5⋊(C7⋊D7)D13⋊C3semidirect
62. C5×C7×C13C2×AGL(1,𝔽7)semidirect
63. C5×C7×C13C2×AGL(1,𝔽7)semidirect
78. C5×C72C2×D13⋊C3semidirect
101. D65#64425semidirect
110. C7×C13D5×AGL(1,𝔽7)semidirect
111. C7×C13D5×AGL(1,𝔽7)semidirect
126. C5×C13C2×#64425semidirect
129. C72D5×D13⋊C3semidirect
138. C5×C7#10587717⋊C2semidirect
139. C5×C7#10587716⋊C2semidirect
162. C13D5×#64425semidirect
168. C7#10587722⋊D5semidirect
169. C7#10587723⋊D5semidirect
173. C5D13⋊#64425semidirect

Maximal subgroups

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

subgroupindex
C5⋊(D13⋊#3862)2
C5⋊#168384532
C5×#168384522
D65⋊(C7⋊D7)3
D13⋊#644255
#10587723⋊D57
#10587722⋊D57
D5×#6442513