Finite Group Databasebeta

← #50304153

Subgroups — #50304153

Order 38220.

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

normal subgroups only

This group has 208 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⋊#16838459C211yesmaximal, characteristic, complemented
2C5⋊#16838457C211yesmaximal, characteristic, complemented
3C5×#16838447C211yesmaximal, characteristic, complemented
4D35⋊D91C311yesmaximal, characteristic, complemented, Hall
5C5×#14274262C2211yescharacteristic, complemented, Hall
6#21439609—51nomaximal, Hall
7C7×D455C2×C311yescharacteristic, complemented
8C7×C13×D35C2×C311yescharacteristic, complemented
9C5×C7⋊D91C2×C311yescharacteristic, complemented
10#10587723⋊D5—71nomaximal
11D5×#10587723—71nomaximal
12#16838459—51no—
13#16838457—51no—
14#16838447D511yescharacteristic, complemented
15C5×C72×C13C22×C311yescharacteristic, complemented, Hall
16#64424⋊D5—131nomaximal, Hall
17C5⋊#10587723—71no—
18C5⋊#10587721—71no—
19C5⋊#10587717—71no—
20D5×#63271—71no—
21C5×#10587723—71no—
22C5×#10587723—71no—
23C5×#10587723—143no—
24D7×D91—51noHall
25#14274262C2×D511yescharacteristic, complemented, Hall
26D35⋊D13—71no—
27D5×D91—71no—
28C5⋊#64423—131no—
29C5⋊#64423—131no—
30C5×#64424—131no—
31C5×#63271—71no—
32C5×#63271—71no—
33C5×#63271—143no—
34C7⋊D91C3×D511yescharacteristic, complemented
35C7×D91—51no—
36C7×C13×D7—51no—
37C2×#10587723—351no—
38#10587717⋊C2—351no—
39D35⋊D7—131noHall
40D455AGL(1,𝔽7)11yescharacteristic, complemented
41C13×D35AGL(1,𝔽7)11yescharacteristic, complemented
42C7×D65—71no—
43C7×D5×C13—71no—
44C5×D91—71no—
45C5×D91—71no—
46C5×D91—143no—
47D5×D13⋊C3—491noHall
48C5×#3861—131noHall
49C72×C13C2×C3×D511yescharacteristic, complemented, Hall
50#64423⋊C2—651noHall
51C2×#63271—351no—
52#10587723—71no—
53#10587723—71no—
54#10587723—143no—
55#10587723—351no—
56#10587721—351no—
57#10587717—351no—
58C7×D35—131no—
59C7×D35D13⋊C311yescharacteristic, complemented
60C5×C7⋊D7—131no—
61C5×C7×C13—23no—
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—
69C2×D91—351no—
70D7×D13—351no—
71#64424—131no—
72#64423—651no—
73#64423—651no—
74#63271—71no—
75#63271—71no—
76#63271—143no—
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—
85C5×AGL(1,𝔽7)—1823no—
86D72—651noHall
87C5×C13⋊C3—491noHall
88C2×C7×C13—351no—
89D91—51no—
90D91—71no—
91D91—71no—
92D91—143no—
93C7×D13—351no—
94C13×D7—51no—
95C2×D13⋊C3—2451noHall
96#3861—131noHall
97D5×D7—911no—
98D5×D7—911no—
99D65—71no—
100C5×D13—491no—
101D5×C13—71no—
102C5×ΓL(1,𝔽8)—911no—
103C5×ΓL(1,𝔽8)—911no—
104C5×ΓL(1,𝔽8)—1823no—
105C7⋊D7—131no—
106C7×D7—51no—
107C7×D7—651no—
108C7×C13—23no—
109C7×C13D5×AGL(1,𝔽7)11yescharacteristic, complemented
110C7×C13D5×AGL(1,𝔽7)11yescharacteristic, complemented
111C2×AGL(1,𝔽7)—4551no—
112C2×AGL(1,𝔽7)—4551no—
113C2×C13⋊C3—2451no—
114D13⋊C3—491no—
115D13⋊C3—2451no—
116D35—131no—
117D35#1058772311yescharacteristic, complemented
118C5×D7—911no—
119C5×D7—911no—
120C5×D7—1823no—
121C7×D5—71no—
122C7×D5—911no—
123C5×C13#64423⋊C211yescharacteristic, complemented, Hall
124C2×C3×D5—6371noHall
125C2×D13—2451noHall
126C72D5×D13⋊C311yescharacteristic, complemented, Sylow
127C2×ΓL(1,𝔽8)—4551no—
128C2×ΓL(1,𝔽8)—4551no—
129AGL(1,𝔽7)—911no—
130AGL(1,𝔽7)—911no—
131AGL(1,𝔽7)—1823no—
132AGL(1,𝔽7)—4551no—
133AGL(1,𝔽7)—4551no—
134C13⋊C3—491noHall
135C5×C7—23no—
136C5×C7#10587717⋊C211yescharacteristic, complemented
137C5×C7C2×#1058772311yescharacteristic, complemented
138C2×C3×C5—6371no—
139C3×D5—6371no—
140C3×D5—6371no—
141C2×D7—4551no—
142C2×D7—4551no—
143C2×C13—351no—
144D13—351no—
145D13—491no—
146ΓL(1,𝔽8)—911no—
147ΓL(1,𝔽8)—911no—
148ΓL(1,𝔽8)—1823no—
149C2×D5—6371noHall
150C3×C5—6371noHall
151C2×C7—351no—
152C2×C7—4551no—
153D7—51no—
154D7—651no—
155D7—911no—
156D7—911no—
157D7—1823no—
158C13#64424⋊D511yescharacteristic, complemented, Sylow
159C22×C3—31851noHall
160C2×C5—6371no—
161D5—71no—
162D5—911no—
163C7—23no—
164C7D5×#1058772311yescharacteristic, complemented
165C7#10587723⋊D511yescharacteristic, complemented
166C2×C3—31851no—
167C2×C3—31851no—
168C2×C3—6371no—
169C5#2143960911yescharacteristic, complemented, Sylow
170C22—31851noSylow
171C3—6371noSylow
172C2—351no—
173C2—6371no—
174C2—4551no—
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⋊#16838459C2semidirect
2. C5⋊#16838457C2semidirect
3. C5×#16838447C2semidirect
4. D35⋊D91C3semidirect
5. C5×#14274262C22semidirect
7. C7×D455C2×C3semidirect
8. C7×C13×D35C2×C3semidirect
9. C5×C7⋊D91C2×C3semidirect
14. #16838447D5semidirect
15. C5×C72×C13C22×C3semidirect
25. #14274262C2×D5semidirect
34. C7⋊D91C3×D5semidirect
40. D455AGL(1,𝔽7)semidirect
41. C13×D35AGL(1,𝔽7)semidirect
49. C72×C13C2×C3×D5semidirect
59. C7×D35D13⋊C3semidirect
62. C5×C7×C13C2×AGL(1,𝔽7)semidirect
63. C5×C7×C13C2×AGL(1,𝔽7)semidirect
78. C5×C72C2×D13⋊C3semidirect
109. C7×C13D5×AGL(1,𝔽7)semidirect
110. C7×C13D5×AGL(1,𝔽7)semidirect
117. D35#10587723semidirect
123. C5×C13#64423⋊C2semidirect
126. C72D5×D13⋊C3semidirect
136. C5×C7#10587717⋊C2semidirect
137. C5×C7C2×#10587723semidirect
158. C13#64424⋊D5semidirect
164. C7D5×#10587723semidirect
165. C7#10587723⋊D5semidirect
169. C5#21439609semidirect

Maximal subgroups

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

subgroupindex
C5⋊#168384592
C5⋊#168384572
C5×#168384472
D35⋊D913
#214396095
#10587723⋊D57
D5×#105877237
#64424⋊D513