Finite Group Databasebeta

← #50304053

Subgroups — #50304053

Order 38220.

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

normal subgroups only

This group has 168 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⋊#16838479C211yesmaximal, characteristic, complemented
2C7×C5⋊#10587722C211yesmaximal, characteristic, complemented
3C5×#16838470C211yesmaximal, characteristic, complemented
4(C7⋊D7)⋊D65C311yesmaximal, characteristic, complemented, Hall
5C5×C7×#63270C2211yescharacteristic, complemented, Hall
6#10587722⋊D7—51nomaximal, Hall
7C7×D455C2×C311yescharacteristic, complemented
8C7×D455C2×C311yescharacteristic, complemented
9C5×C13×C7⋊D7C2×C311yescharacteristic, complemented
10D7×C5⋊(D13⋊C3)—71nomaximal
11#10587720⋊D5—71nomaximal
12#16838479—51no—
13#16838470D511yescharacteristic, complemented
14C7×#10587722—51no—
15C5×C72×C13C22×C311yescharacteristic, complemented, Hall
16(C5⋊AGL(1,𝔽7))⋊D7—131nomaximal, Hall
17C5⋊#10587722D711yescharacteristic, complemented
18C5⋊((C13⋊C3)⋊D7)—71no—
19C5⋊#10587716—71no—
20C7×C5⋊(D13⋊C3)—71no—
21C5×#10587720—71no—
22C5×D7×C13⋊C3—71no—
23(C7⋊D7)⋊D13—51noHall
24C7×#63270C2×D511yescharacteristic, complemented, Hall
25D7×D65—71no—
26D7×D65—71no—
27ΓL(1,𝔽8)×D35—131no—
28C7×C5⋊AGL(1,𝔽7)—131no—
29C5×ΓL(1,𝔽8)⋊D7—131no—
30C5×#63270C2×D711yescharacteristic, complemented
31C5×C7×C13⋊C3—71no—
32C13×C7⋊D7C3×D511yescharacteristic, complemented
33C7×D91—51no—
34C7×D91—51no—
35#10587716⋊C2—351no—
36D7×D13⋊C3—351no—
37D35⋊D7—131noHall
38D455AGL(1,𝔽7)11yescharacteristic, complemented
39D455C3×D711yescharacteristic, complemented
40C7×D65—71no—
41C7×D65—71no—
42C5×C13×D7—71no—
43C5×C13×D7—71no—
44C5×C13×D7—421no—
45C2×C5⋊(D13⋊C3)—491noHall
46C5×C7×ΓL(1,𝔽8)—131noHall
47C72×C13C2×C3×D511yescharacteristic, complemented, Hall
48D7×AGL(1,𝔽7)—651noHall
49#10587722—51no—
50#10587720—71no—
51#10587716—351no—
52(C13⋊C3)⋊D7—351no—
53D7×C13⋊C3—71no—
54C7×D13⋊C3—351no—
55C7×D35—131no—
56C7×D35—131no—
57C5×C7⋊D7D13⋊C311yescharacteristic, complemented
58C5×C7×C13—61no—
59C5×C7×C13C2×AGL(1,𝔽7)11yescharacteristic, complemented
60C5×C7×C13C2×C3×D711yescharacteristic, complemented
61C3×D5×D7—911no—
62D5×AGL(1,𝔽7)—911no—
63C2×C5×C13⋊C3—491no—
64C5⋊(D13⋊C3)—71no—
65C5⋊(D13⋊C3)—491no—
66D7×D13—351no—
67D7×D13—351no—
68ΓL(1,𝔽8)⋊D7—131no—
69D7×ΓL(1,𝔽8)—651no—
70C7×AGL(1,𝔽7)—651no—
71#63270D5×D711yescharacteristic, complemented
72C7×C13⋊C3—71no—
73C2×D65—491noHall
74C5×C72C2×D13⋊C311yescharacteristic, complemented, Hall
75C3×D35—911no—
76C3×C7×D5—911no—
77C3×C5×D7—911no—
78C5⋊AGL(1,𝔽7)—131no—
79D5×ΓL(1,𝔽8)—911no—
80C5×AGL(1,𝔽7)—911no—
81D72—651noHall
82C5×C13⋊C3—71noHall
83D91—51no—
84D91—51no—
85C7×D13—351no—
86C7×D13—351no—
87C13×D7—71no—
88C13×D7—71no—
89C13×D7—421no—
90C2×D13⋊C3—2451noHall
91C7×ΓL(1,𝔽8)—131noHall
92D5×D7—911no—
93D5×D7—911no—
94C2×C5×C13—491no—
95D65—71no—
96D65—71no—
97C3×C5×C7—911no—
98C5×ΓL(1,𝔽8)—131no—
99C7⋊D7C5⋊(D13⋊C3)11yescharacteristic, complemented
100C7×D7—651no—
101C7×D7—651no—
102C7×C13—61no—
103C7×C13D5×AGL(1,𝔽7)11yescharacteristic, complemented
104C7×C13C3×D5×D711yescharacteristic, complemented
105C2×C3×D7—4551no—
106C2×AGL(1,𝔽7)—4551no—
107C2×C13⋊C3—491no—
108D13⋊C3—351no—
109D13⋊C3—2451no—
110D35—131no—
111D35—131no—
112C5×D7—71no—
113C5×D7—71no—
114C5×D7—421no—
115C7×D5—911no—
116C7×D5—911no—
117C5×C13D7×AGL(1,𝔽7)11yescharacteristic, complemented, Hall
118C2×C3×D5—6371noHall
119C2×D13—2451noHall
120C72C2×C5⋊(D13⋊C3)11yescharacteristic, complemented, Sylow
121C2×C3×C7—4551no—
122C3×D7—911no—
123C3×D7—4551no—
124C2×ΓL(1,𝔽8)—4551no—
125AGL(1,𝔽7)—651no—
126AGL(1,𝔽7)—911no—
127C13⋊C3—71noHall
128C5×C7—61no—
129C5×C7D7×D13⋊C311yescharacteristic, complemented
130C5×C7#10587716⋊C211yescharacteristic, complemented
131C2×C3×C5—6371no—
132C3×D5—911no—
133C3×D5—6371no—
134C2×D7—4551no—
135C2×D7—4551no—
136C2×C13—491no—
137D13—351no—
138D13—351no—
139C3×C7—911no—
140ΓL(1,𝔽8)—131no—
141C2×D5—6371noHall
142C3×C5—911noHall
143C2×C7—4551no—
144C2×C7—4551no—
145D7—71no—
146D7—71no—
147D7—421no—
148D7—651no—
149D7—651no—
150C13(C5⋊AGL(1,𝔽7))⋊D711yescharacteristic, complemented, Sylow
151C22×C3—31851noHall
152C2×C5—491no—
153D5—911no—
154D5—911no—
155C7—61no—
156C7#10587720⋊D511yescharacteristic, complemented
157C7D7×C5⋊(D13⋊C3)11yescharacteristic, complemented
158C2×C3—31851no—
159C2×C3—6371no—
160C2×C3—4551no—
161C5#10587722⋊D711yescharacteristic, complemented, Sylow
162C22—31851noSylow
163C3—911noSylow
164C2—491no—
165C2—4551no—
166C2—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⋊#16838479C2semidirect
2. C7×C5⋊#10587722C2semidirect
3. C5×#16838470C2semidirect
4. (C7⋊D7)⋊D65C3semidirect
5. C5×C7×#63270C22semidirect
7. C7×D455C2×C3semidirect
8. C7×D455C2×C3semidirect
9. C5×C13×C7⋊D7C2×C3semidirect
13. #16838470D5semidirect
15. C5×C72×C13C22×C3semidirect
17. C5⋊#10587722D7semidirect
24. C7×#63270C2×D5semidirect
30. C5×#63270C2×D7semidirect
32. C13×C7⋊D7C3×D5semidirect
38. D455AGL(1,𝔽7)semidirect
39. D455C3×D7semidirect
47. C72×C13C2×C3×D5semidirect
57. C5×C7⋊D7D13⋊C3semidirect
59. C5×C7×C13C2×AGL(1,𝔽7)semidirect
60. C5×C7×C13C2×C3×D7semidirect
71. #63270D5×D7semidirect
74. C5×C72C2×D13⋊C3semidirect
99. C7⋊D7C5⋊(D13⋊C3)semidirect
103. C7×C13D5×AGL(1,𝔽7)semidirect
104. C7×C13C3×D5×D7semidirect
117. C5×C13D7×AGL(1,𝔽7)semidirect
120. C72C2×C5⋊(D13⋊C3)semidirect
129. C5×C7D7×D13⋊C3semidirect
130. C5×C7#10587716⋊C2semidirect
150. C13(C5⋊AGL(1,𝔽7))⋊D7semidirect
156. C7#10587720⋊D5semidirect
157. C7D7×C5⋊(D13⋊C3)semidirect
161. C5#10587722⋊D7semidirect

Maximal subgroups

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

subgroupindex
C5⋊#168384792
C7×C5⋊#105877222
C5×#168384702
(C7⋊D7)⋊D653
#10587722⋊D75
D7×C5⋊(D13⋊C3)7
#10587720⋊D57
(C5⋊AGL(1,𝔽7))⋊D713