Finite Group Databasebeta

← #50304021

Subgroups — #50304021

Order 38220.

200 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 35 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⋊#16838470C211yesmaximal, characteristic, complemented
2C7×C5⋊#10587716C211yesmaximal, characteristic, complemented
3C5×#16838468C211yesmaximal, characteristic, complemented
4D65⋊(C7⋊D7)C311yesmaximal, characteristic, complemented, Hall
5C5×C7×#63270C2211yescharacteristic, complemented, Hall
6#10587716⋊D7—51nomaximal, Hall
7C13×C5⋊(C7⋊D7)C2×C311yescharacteristic, complemented
8C72×D65C2×C311yescharacteristic, complemented
9C5×C7⋊D91C2×C311yescharacteristic, complemented
10(C5⋊(D13⋊C3))⋊D7—71nomaximal
11#10587722⋊D5—71nomaximal
12#16838470—51no—
13#16838468D511yescharacteristic, complemented
14C7×#10587716—51no—
15C5×C72×C13C22×C311yescharacteristic, complemented, Hall
16D5×ΓL(1,𝔽8)⋊D7—131nomaximal, Hall
17C5⋊#10587720—71no—
18C13⋊C3×D35—71no—
19C5⋊#10587716D711yescharacteristic, complemented
20C7×C5⋊(D13⋊C3)—71no—
21C5×#10587722—71no—
22C5×(C13⋊C3)⋊D7—71no—
23D13×C7⋊D7—51noHall
24C7×#63270C2×D511yescharacteristic, complemented, Hall
25D35⋊D13—71no—
26D35⋊D13—71no—
27D35⋊D13—212no—
28C5⋊(ΓL(1,𝔽8)⋊D7)—131no—
29C7×D5×ΓL(1,𝔽8)—131no—
30C5×ΓL(1,𝔽8)⋊D7—131no—
31C5×#63270C2×D711yescharacteristic, complemented
32C5×C7×C13⋊C3—71no—
33C7⋊D91C3×D511yescharacteristic, complemented
34C13×C7⋊D7—51no—
35C72×D13—51no—
36#10587716⋊C2—351no—
37D7×D13⋊C3—351no—
38D5×C7⋊D7—131noHall
39C13×D35—71no—
40C13×D35—71no—
41C13×D35—212no—
42C7×D65—32no—
43C7×D65AGL(1,𝔽7)11yescharacteristic, complemented
44C7×D65C3×D711yescharacteristic, complemented
45C5×D91—71no—
46C5×D91—71no—
47C5×D91—212no—
48D5×D13⋊C3—491noHall
49C5×C7×ΓL(1,𝔽8)—131noHall
50C72×C13C2×C3×D511yescharacteristic, complemented, Hall
51C2×ΓL(1,𝔽8)⋊D7—651noHall
52#10587722—71no—
53#10587720—351no—
54#10587716—51no—
55(C13⋊C3)⋊D7—71no—
56D7×C13⋊C3—351no—
57C7×D13⋊C3—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×C3×D711yescharacteristic, complemented
64C3×D5×D7—911no—
65D5×AGL(1,𝔽7)—911no—
66C5⋊(D13⋊C3)—71no—
67D5×C13⋊C3—491no—
68C5×D13⋊C3—491no—
69D7×D13—351no—
70D7×D13—351no—
71D7×D13—1052no—
72C2×C7×ΓL(1,𝔽8)—651no—
73ΓL(1,𝔽8)⋊D7—131no—
74ΓL(1,𝔽8)⋊D7—651no—
75#63270D5×D711yescharacteristic, complemented
76C7×C13⋊C3—71no—
77D5×D13—491noHall
78C5×C72C2×D13⋊C311yescharacteristic, complemented, Hall
79C3×D35—911no—
80C3×C7×D5—911no—
81C3×C5×D7—911no—
82C5⋊AGL(1,𝔽7)—911no—
83D5×ΓL(1,𝔽8)—131no—
84C5×AGL(1,𝔽7)—911no—
85C2×C7⋊D7—651noHall
86C5×C13⋊C3—71noHall
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
97C7×ΓL(1,𝔽8)—131noHall
98D5×D7—2732no—
99D5×D7—911no—
100D5×D7—911no—
101D65ΓL(1,𝔽8)⋊D711yescharacteristic, complemented
102C5×D13—491no—
103D5×C13—491no—
104C3×C5×C7—911no—
105C5×ΓL(1,𝔽8)—131no—
106C2×C72—651no—
107C7⋊D7—51no—
108C7⋊D7—131no—
109C7×C13—32no—
110C7×C13D5×AGL(1,𝔽7)11yescharacteristic, complemented
111C7×C13C3×D5×D711yescharacteristic, complemented
112C2×C3×D7—4551no—
113C2×AGL(1,𝔽7)—4551no—
114C2×C13⋊C3—2451no—
115D13⋊C3—351no—
116D13⋊C3—491no—
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×ΓL(1,𝔽8)⋊D711yescharacteristic, complemented, Hall
127C2×C3×D5—6371noHall
128C2×D13—2451noHall
129C72D5×D13⋊C311yescharacteristic, complemented, Sylow
130C2×C3×C7—4551no—
131C3×D7—911no—
132C3×D7—4551no—
133C2×ΓL(1,𝔽8)—651no—
134AGL(1,𝔽7)—911no—
135AGL(1,𝔽7)—4551no—
136C13⋊C3—71noHall
137C5×C7—32no—
138C5×C7D7×D13⋊C311yescharacteristic, complemented
139C5×C7#10587716⋊C211yescharacteristic, complemented
140C2×C3×C5—6371no—
141C3×D5—911no—
142C3×D5—6371no—
143C2×D7—13652no—
144C2×D7—4551no—
145C2×D7—4551no—
146C2×C13—2451no—
147D13—51no—
148D13—491no—
149C3×C7—911no—
150ΓL(1,𝔽8)—131no—
151C2×D5—6371noHall
152C3×C5—911noHall
153C2×C7—651no—
154C2×C7—651no—
155C2×C7—1952no—
156D7—2732no—
157D7—351no—
158D7—351no—
159D7—911no—
160D7—911no—
161D7—1052no—
162C13D5×ΓL(1,𝔽8)⋊D711yescharacteristic, complemented, Sylow
163C22×C3—31851noHall
164C2×C5—6371no—
165D5—131no—
166D5—491no—
167C7—32no—
168C7#10587722⋊D511yescharacteristic, complemented
169C7(C5⋊(D13⋊C3))⋊D711yescharacteristic, complemented
170C2×C3—31851no—
171C2×C3—6371no—
172C2×C3—4551no—
173C5#10587716⋊D711yescharacteristic, complemented, Sylow
174C22—31851noSylow
175C3—911noSylow
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⋊#16838470C2semidirect
2. C7×C5⋊#10587716C2semidirect
3. C5×#16838468C2semidirect
4. D65⋊(C7⋊D7)C3semidirect
5. C5×C7×#63270C22semidirect
7. C13×C5⋊(C7⋊D7)C2×C3semidirect
8. C72×D65C2×C3semidirect
9. C5×C7⋊D91C2×C3semidirect
13. #16838468D5semidirect
15. C5×C72×C13C22×C3semidirect
19. C5⋊#10587716D7semidirect
24. C7×#63270C2×D5semidirect
31. C5×#63270C2×D7semidirect
33. C7⋊D91C3×D5semidirect
43. C7×D65AGL(1,𝔽7)semidirect
44. C7×D65C3×D7semidirect
50. C72×C13C2×C3×D5semidirect
58. C5⋊(C7⋊D7)D13⋊C3semidirect
62. C5×C7×C13C2×AGL(1,𝔽7)semidirect
63. C5×C7×C13C2×C3×D7semidirect
75. #63270D5×D7semidirect
78. C5×C72C2×D13⋊C3semidirect
101. D65ΓL(1,𝔽8)⋊D7semidirect
110. C7×C13D5×AGL(1,𝔽7)semidirect
111. C7×C13C3×D5×D7semidirect
126. C5×C13C2×ΓL(1,𝔽8)⋊D7semidirect
129. C72D5×D13⋊C3semidirect
138. C5×C7D7×D13⋊C3semidirect
139. C5×C7#10587716⋊C2semidirect
162. C13D5×ΓL(1,𝔽8)⋊D7semidirect
168. C7#10587722⋊D5semidirect
169. C7(C5⋊(D13⋊C3))⋊D7semidirect
173. C5#10587716⋊D7semidirect

Maximal subgroups

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

subgroupindex
C5⋊#168384702
C7×C5⋊#105877162
C5×#168384682
D65⋊(C7⋊D7)3
#10587716⋊D75
(C5⋊(D13⋊C3))⋊D77
#10587722⋊D57
D5×ΓL(1,𝔽8)⋊D713