Finite Group Databasebeta

← #13099039

Subgroups — #13099039

Order 1600.

501 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 501 conjugacy classes of subgroups — too many to draw. Only its 125 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×#87746C211yesmaximal, characteristic, complemented
2C2×D4×D25C211yesmaximal, characteristic, complemented
3C25×#127C211yesmaximal, characteristic, complemented
4#11716502C211yesmaximal, characteristic, complemented
5#11716501C214yesmaximal, complemented
6#11716499C214yesmaximal, complemented
7#11716498C211yesmaximal, characteristic, complemented
8#11716437C211yesmaximal, characteristic, complemented
9#11716434C211yesmaximal, characteristic, complemented
10C23×D25C2212yes—
11C2×D4×C25C2211yescharacteristic
12C2×D4×C25C2211yescharacteristic, complemented
13C2×D4×C25C2214yescomplemented
14C2×C22⋊D25C2212yes—
15C2×C22⋊D25C2212yes—
16C2×C22⋊D25C2214yescomplemented
17C22×Dic25C2212yescomplemented
18#87746—24no—
19D4×D25—24no—
20C2×D100C2211yescharacteristic
21C2×C4×D25C2211yescharacteristic
22C2×Dic50C2211yescharacteristic, complemented
23C42×C25C2211yescharacteristic, complemented
24C22⋊Dic25C2214yescomplemented
25#87720C2212yes—
26#87720C2214yescomplemented
27#87718C2212yescomplemented
28C4×Dic25C2211yescharacteristic, complemented
29#66049—51nomaximal
30C23×C25C2312yes—
31C23×C25C2312yes—
32C22×D25—24no—
33C22×D25—44no—
34C22×D25C2312yes—
35C22×D25C2311yescharacteristic
36D4×C25—22no—
37D4×C25—22no—
38D4×C25—44no—
39C2×C4×C25C2312yes—
40C2×C4×C25C2311yescharacteristic
41C22⋊D25—24no—
42C22⋊D25—24no—
43C22⋊D25—44no—
44C2×Dic25—24no—
45C2×Dic25C2312yes—
46C2×Dic25C2312yes—
47C2×Dic25C2311yescharacteristic
48D100—22no—
49C4×D25D414yescomplemented
50Dic50—22no—
51C2×#711—51no—
52C2×D4×D5—51no—
53C5×#127D511yescharacteristic
54#4086—51no—
55#4085—54no—
56#4083—54no—
57#4082—51no—
58#4021—51no—
59#4018—51no—
60C22×C25—22no—
61C22×C25—22no—
62C22×C25—24no—
63C22×C25—24no—
64C22×C25C2411yescharacteristic
65C2×D25—22no—
66C2×D25—22no—
67C2×D25—24no—
68C2×D25—48no—
69C2×D25C2×D412yes—
70C4×C25—22no—
71C4×C25C2×D412yes—
72Dic25—22no—
73Dic25—22no—
74Dic25C2×D412yes—
75C23×D5—52no—
76C2×C5×D4C2×D511yescharacteristic
77C2×C5×D4C2×D511yescharacteristic
78C2×C5×D4C2×D514yes—
79C2×C22⋊D5—52no—
80C2×C22⋊D5—52no—
81C2×C22⋊D5—54no—
82C22×Dic5—52no—
83#711—104no—
84D4×D5—104no—
85C2×D20—51no—
86C2×C4×D5—51no—
87C2×Dic10—51no—
88C42×C5C2×D511yescharacteristic
89C22⋊Dic5—54no—
90#685—52no—
91#685—54no—
92#683—52no—
93C4×Dic5—51no—
94#535—251noSylow
95C2×C25—42no—
96C2×C25—42no—
97C2×C25C22×D411yescharacteristic
98C2×C25H(5,𝔽2)12yes—
99D25—22no—
100D25—42no—
101C23×C5C22×D512yes—
102C23×C5C22×D512yes—
103C22×D5—51no—
104C22×D5—52no—
105C22×D5—104no—
106C22×D5—204no—
107C5×D4—22no—
108C5×D4—22no—
109C5×D4—44no—
110C2×C4×C5C22×D512yes—
111C2×C4×C5C22×D511yescharacteristic
112C22⋊D5—104no—
113C22⋊D5—104no—
114C22⋊D5—204no—
115C2×Dic5—51no—
116C2×Dic5—52no—
117C2×Dic5—52no—
118C2×Dic5—104no—
119D20—102no—
120C4×D5—54no—
121Dic10—102no—
122C2×#41—251no—
123C22×D4—251no—
124#127—251no—
125#127D2511yescharacteristic, complemented
126#124—251no—
127#124—251no—
128#121—254no—
129#120—254no—
130#117—251no—
131C25#53511yescharacteristic, complemented, Sylow
132C22×C5—22no—
133C22×C5—22no—
134C22×C5—24no—
135C22×C5—24no—
136C22×C5C23×D511yescharacteristic
137C2×D5—52no—
138C2×D5—102no—
139C2×D5—102no—
140C2×D5—104no—
141C2×D5—208no—
142C4×C5—22no—
143C4×C5D4×D512yes—
144Dic5—52no—
145Dic5—102no—
146Dic5—102no—
147C24—252no—
148#41—504no—
149C2×Q8—251no—
150C2×D4—252no—
151C2×D4—252no—
152C2×D4—254no—
153C2×D4—251no—
154C2×D4—504no—
155C2×D4C2×D2511yescharacteristic
156C2×D4C2×D2511yescharacteristic, complemented
157C2×D4C2×D2514yescomplemented
158C22×C4—251no—
159C22×C4—252no—
160C4⋊C4—252no—
161C22⋊C4—254no—
162C22⋊C4—252no—
163C22⋊C4—254no—
164C42—251no—
165C42C2×D2511yescharacteristic, complemented
166C2×C5—42no—
167C2×C5—42no—
168C2×C5C2×D4×D511yescharacteristic
169C2×C5#414412yes—
170D5—102no—
171D5—202no—
172C23—251no—
173C23—252no—
174C23—504no—
175C23—1004no—
176C23C22×D2512yes—
177C23C22×D2512yes—
178Q8—502no—
179D4—22no—
180D4—22no—
181D4—44no—
182D4—504no—
183D4—504no—
184D4—502no—
185D4—1004no—
186C2×C4—251no—
187C2×C4—254no—
188C2×C4—252no—
189C2×C4—252no—
190C2×C4—504no—
191C2×C4C22×D2512yes—
192C2×C4C22×D2511yescharacteristic
193C5#6604911yescharacteristic
194C22—22no—
195C22—22no—
196C22—24no—
197C22—24no—
198C22—252no—
199C22—502no—
200C22—502no—
201C22—504no—
202C22—1008no—
203C22C23×D2511yescharacteristic
204C4—22no—
205C4—252no—
206C4—502no—
207C4—502no—
208C4D4×D2512yes—
209C2—42no—
210C2—42no—
211C2—502no—
212C2—1002no—
213C2C2×D4×D2511yescharacteristic
214C2#1171656312yes—
subgroupG/H
centerC22C23×D25
commutator, cosocleC22×C25C24
Frattini, socleC22×C5C23×D5
FittingC25×#127C2
hypercenter#127D25
hypocenterC25#535
LCSG ▷ C22×C25 ▷ C25
UCSC1 ◁ C22 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C2×#87746C2semidirect
2. C2×D4×D25C2semidirect
3. C25×#127C2semidirect
4. #11716502C2semidirect
5. #11716501C2semidirect
6. #11716499C2semidirect
7. #11716498C2semidirect
8. #11716437C2semidirect
9. #11716434C2semidirect
12. C2×D4×C25C22semidirect
13. C2×D4×C25C22semidirect
16. C2×C22⋊D25C22semidirect
17. C22×Dic25C22semidirect
22. C2×Dic50C22semidirect
23. C42×C25C22semidirect
24. C22⋊Dic25C22semidirect
26. #87720C22semidirect
27. #87718C22semidirect
28. C4×Dic25C22semidirect
49. C4×D25D4semidirect
125. #127D25semidirect
131. C25#535semidirect
156. C2×D4C2×D25semidirect
157. C2×D4C2×D25semidirect
165. C42C2×D25semidirect

Maximal subgroups

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

subgroupindex
C2×#877462
C2×D4×D252
C25×#1272
#117165022
#117165012
#117164992
#117164982
#117164372
#117164342
#660495