Finite Group Databasebeta

← #13105087

Subgroups — #13105087

Order 1600.

752 conjugacy classes of subgroups; only the 192 normal subgroups are shown.

normal subgroups only

This group has 752 conjugacy classes of subgroups — too many to draw. Only its 192 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
1C2×#87877C211yesmaximal, characteristic
2#11717192C211yesmaximal, characteristic, complemented
3C4×C5×D20C212yesmaximal, complemented
4D5×#685C214yesmaximal, complemented
5#11717017C212yesmaximal, complemented
6#11716997C214yesmaximal, complemented
7#11716967C211yesmaximal, characteristic, complemented
8C22×D52C2212yes—
9C2×C4×C5⋊D5C2211yescharacteristic
10C2×C5×D20C2212yes—
11C2×C4×C5×D5C2214yescomplemented
12C2×#6037C2212yes—
13C2×D5×Dic5C2214yescomplemented
14#87877C418yescomplemented
15C42×C52C2211yescharacteristic, complemented
16#87808C2212yes—
17#87806C2212yescomplemented
18C4×#1039C2211yescharacteristic, complemented
19C5×#685C2214yescomplemented
20C5×C4⋊Dic5C2212yescomplemented
21#87779C2212yes—
22#87778C2214yescomplemented
23Dic52C2212yescomplemented
24#65879—52nomaximal
25C22×C5⋊D5C2311yescharacteristic
26C22×C5×D5C2314yes—
27C2×D52—44no—
28C2×D52C2×C418yescomplemented
29C2×C4×C52C2312yes—
30C2×C4×C52C2311yescharacteristic
31C2×#1039C2312yes—
32C2×#1039C2311yescharacteristic
33C4×C5⋊D5C2×C414yescomplemented
34C2×C5×Dic5C2314yes—
35C5×D20C2×C418yescomplemented
36C4×C5×D5—44no—
37#6037C2×C418yescomplemented
38D5×Dic5—44no—
39C2×D4×D5—52no—
40C4×C5×D4—52no—
41D4×Dic5—52no—
42C4×C22⋊D5—54no—
43C2×#685—54no—
44#4039—52no—
45#4038—52no—
46#4027—54no—
47D5×C22⋊C4—54no—
48C4×D20D512yescomplemented
49#4018—52no—
50#4018—102no—
51C22×C52C2411yescharacteristic
52C2×C5⋊D5—22no—
53C2×C5⋊D5C22×C412yes—
54C2×C5×D5—24no—
55C2×C5×D5—24no—
56C2×C5×D5C22×C418yes—
57D52—48no—
58C4×C52—22no—
59C4×C52C22×C412yes—
60#1039—22no—
61#1039C22×C412yes—
62C5×Dic5—24no—
63C23×D5—54no—
64C2×C5×D4—52no—
65C22×C4×C5—54no—
66C2×C22⋊D5—54no—
67C22×Dic5—54no—
68D4×D5—516no—
69C2×D20C2×D512yes—
70C2×C4×D5—52no—
71C2×C4×D5—54no—
72C2×C4×D5—102no—
73C2×C4×D5C2×D514yescomplemented
74C5×C4⋊C4—52no—
75C5×C22⋊C4—54no—
76C42×C5—22no—
77C42×C5C2×D512yescomplemented
78C22⋊Dic5—54no—
79#685—54no—
80#685—52no—
81#685—52no—
82#685—54no—
83#685—104no—
84#685C2×D514yescomplemented
85C4⋊Dic5C2×D512yescomplemented
86#683—52no—
87#683—52no—
88#683—104no—
89C4×Dic5—52no—
90C4×Dic5—54no—
91C4×Dic5—102no—
92#518—251noSylow
93C2×C52C23×C411yescharacteristic
94C2×C52H(5,𝔽2)12yes—
95C5⋊D5—22no—
96C5×D5—28no—
97C23×C5—54no—
98C22×D5—52no—
99C22×D5—516no—
100C22×D5—102no—
101C22×D5—204no—
102C22×D5—204no—
103C22×D5C22×D514yes—
104C5×D4—58no—
105C2×C4×C5—22no—
106C2×C4×C5—24no—
107C2×C4×C5—54no—
108C2×C4×C5—204no—
109C2×C4×C5C22×D512yes—
110C2×C4×C5C22×D512yes—
111C2×C4×C5C22×D512yes—
112C22⋊D5—516no—
113C2×Dic5—52no—
114C2×Dic5—52no—
115C2×Dic5—52no—
116C2×Dic5—102no—
117C2×Dic5—104no—
118C2×Dic5—204no—
119C2×Dic5C22×D514yes—
120D20C4×D518yescomplemented
121C4×D5—44no—
122C4×D5—58no—
123C4×D5—108no—
124C4×D5—204no—
125C22×D4—251no—
126C4×D4—52no—
127C4×D4—254no—
128C4×D4—252no—
129#117—251no—
130#117—251no—
131C2×C22⋊C4—254no—
132C52#51811yescharacteristic, complemented, Sylow
133C22×C5—22no—
134C22×C5—58no—
135C22×C5—104no—
136C22×C5—104no—
137C22×C5C23×D512yes—
138C2×D5—24no—
139C2×D5—24no—
140C2×D5—54no—
141C2×D5—104no—
142C2×D5—102no—
143C2×D5—102no—
144C2×D5—204no—
145C2×D5—2016no—
146C2×D5C2×C4×D518yes—
147C4×C5—22no—
148C4×C5—22no—
149C4×C5—24no—
150C4×C5—44no—
151C4×C5—104no—
152C4×C5C2×C4×D514yes—
153Dic5—24no—
154Dic5—54no—
155Dic5—104no—
156Dic5—102no—
157Dic5—102no—
158Dic5—204no—
159C24—252no—
160C2×D4—52no—
161C2×D4—258no—
162C2×D4—252no—
163C22×C4—54no—
164C22×C4—254no—
165C22×C4—251no—
166C4⋊C4—52no—
167C4⋊C4—252no—
168C22⋊C4—54no—
169C22⋊C4—252no—
170C22⋊C4—254no—
171C22⋊C4—252no—
172C42—252no—
173C42—251no—
174C42D5211yescharacteristic, complemented
175C2×C5—22no—
176C2×C5—24no—
177C2×C5—108no—
178C2×C5C22×C4×D512yes—
179C2×C5#414412yes—
180C2×C5#414912yes—
181D5—28no—
182D5—104no—
183D5—204no—
184C23—54no—
185C23—258no—
186C23—251no—
187C23—1004no—
188D4—58no—
189D4—258no—
190C2×C4—54no—
191C2×C4—204no—
192C2×C4—251no—
193C2×C4—254no—
194C2×C4—252no—
195C2×C4—1004no—
196C2×C4C2×D5212yes—
197C2×C4C2×D5211yescharacteristic
198C5—22no—
199C5#6587912yescomplemented
200C22—58no—
201C22—104no—
202C22—104no—
203C22—252no—
204C22—502no—
205C22—1008no—
206C22C22×D5211yescharacteristic
207C4—22no—
208C4—104no—
209C4—252no—
210C4—502no—
211C4C4×D5212yes—
212C2—108no—
213C2—502no—
214C2C2×C4×D5211yescharacteristic
215C2#1171747212yes—
subgroupG/H
center, FrattiniC22C22×D52
commutatorC2×C52C23×C4
FittingC42×C52C22
socle, cosocleC22×C52C24
prime radicalC2×#87877C2
hypercenterC42D52
hypocenterC52#518
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C42

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #11717192C2semidirect
3. C4×C5×D20C2semidirect
4. D5×#685C2semidirect
5. #11717017C2semidirect
6. #11716997C2semidirect
7. #11716967C2semidirect
11. C2×C4×C5×D5C22semidirect
13. C2×D5×Dic5C22semidirect
14. #87877C4semidirect
15. C42×C52C22semidirect
17. #87806C22semidirect
18. C4×#1039C22semidirect
19. C5×#685C22semidirect
20. C5×C4⋊Dic5C22semidirect
22. #87778C22semidirect
23. Dic52C22semidirect
28. C2×D52C2×C4semidirect
33. C4×C5⋊D5C2×C4semidirect
35. C5×D20C2×C4semidirect
37. #6037C2×C4semidirect
48. C4×D20D5semidirect
73. C2×C4×D5C2×D5semidirect
77. C42×C5C2×D5semidirect
84. #685C2×D5semidirect
85. C4⋊Dic5C2×D5semidirect
120. D20C4×D5semidirect
132. C52#518semidirect
174. C42D52semidirect
199. C5#65879semidirect

Maximal subgroups

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

subgroupindex
C2×#878772
#117171922
C4×C5×D202
D5×#6852
#117170172
#117169972
#117169672
#658795