Finite Group Databasebeta

← #13106475

Subgroups — #13106475

Order 1600.

524 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 136 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
1#11717264C211yesmaximal, characteristic, complemented
2C5×#4092C212yesmaximal, complemented
3#11717020C211yesmaximal, characteristic
4#11717015C212yesmaximal, complemented
5#11717014C212yesmaximal, complemented
6#11716997C212yesmaximal
7D5×#683C212yesmaximal, complemented
8#11716965C212yesmaximal, complemented
9#11716956C211yesmaximal, characteristic, complemented
10C2×C52×Q8C2211yescharacteristic
11C2×#6045C2211yescharacteristic
12C2×C4×C5×D5C2212yes—
13C2×#6039C2211yescharacteristic
14C2×#6037C2211yescharacteristic
15C2×D5×Dic5C2212yes—
16C2×D5×Dic5C2212yes—
17#87806C2212yes—
18#87806C2212yes—
19C4×#1039C2211yescharacteristic
20C5×#685C2212yes—
21C5×#685C2212yes—
22C5×C4⋊Dic5C2212yes—
23C5×#683C2212yes—
24C5×#683C2212yes—
25#87781C2211yescharacteristic
26#87781C2211yescharacteristic
27#87781C2212yes—
28#87780C2212yes—
29#87778C2212yes—
30Dic52C2212yes—
31#65970—52nomaximal
32C22×C5×D5C2312yes—
33C52×Q8—41no—
34C2×C4×C52C2312yes—
35C2×C4×C52C2311yescharacteristic
36C2×#1039C2312yes—
37C2×#1039C2311yescharacteristic
38C2×#1039C2311yescharacteristic
39#6045—41no—
40C2×C5×Dic5C2312yes—
41C2×C5×Dic5C2312yes—
42C2×C5×Dic5C2312yes—
43C4×C5×D5—42no—
44#6039—22no—
45#6037Q814yescomplemented
46D5×Dic5—24no—
47D5×Dic5—42no—
48C5×C22⋊Q8—52no—
49#4092D512yescomplemented
50#4090—52no—
51#4090—102no—
52C4×C22⋊D5—52no—
53C2×#683—52no—
54#4042—52no—
55#4042—52no—
56D5×C4⋊C4—52no—
57#4035—52no—
58#4035—52no—
59#4033—52no—
60#4027—52no—
61#4027—52no—
62#4024—52no—
63#4024—52no—
64C22×C52C2411yescharacteristic
65C2×C5×D5—22no—
66C2×C5×D5—22no—
67C2×C5×D5C2×Q814yes—
68C4×C52—21no—
69C4×C52—22no—
70#1039—22no—
71#1039C2×Q812yes—
72#1039#4112yes—
73C5×Dic5—22no—
74C5×Dic5—22no—
75C5×Dic5—22no—
76C2×C5×Q8—22no—
77C2×C5×Q8C2×D512yes—
78C22×C4×C5—52no—
79C2×C22⋊D5—52no—
80C22×Dic5—52no—
81C22×Dic5—52no—
82C2×C4×D5—52no—
83C2×C4×D5—52no—
84C2×C4×D5C2×D512yes—
85C2×Dic10—52no—
86C2×Dic10—52no—
87C2×Dic10—102no—
88C5×C4⋊C4—52no—
89C5×C4⋊C4—52no—
90C5×C4⋊C4—52no—
91C5×C22⋊C4—52no—
92C5×C22⋊C4—52no—
93C22⋊Dic5—52no—
94#685—52no—
95#685C2×D512yes—
96#685C2×D512yes—
97C4⋊Dic5—52no—
98C4⋊Dic5C2×D512yes—
99#683—52no—
100#683—52no—
101#683—52no—
102#683—52no—
103#683—52no—
104#683—52no—
105#683—52no—
106#683—52no—
107#683—52no—
108#683—104no—
109#683—104no—
110#683C2×D512yes—
111#683C2×D512yes—
112C4×Dic5—52no—
113C4×Dic5—52no—
114C4×Dic5—52no—
115C4×Dic5—102no—
116#554—251noSylow
117C2×C52C22×Q811yescharacteristic
118C2×C52C2×#4111yescharacteristic
119C2×C52H(5,𝔽2)11yescharacteristic
120C5×D5—24no—
121C23×C5—52no—
122C22×D5C22×D512yes—
123C5×Q8—42no—
124C5×Q8—44no—
125C2×C4×C5—22no—
126C2×C4×C5—24no—
127C2×C4×C5—52no—
128C2×C4×C5—52no—
129C2×C4×C5—52no—
130C2×C4×C5—202no—
131C2×C4×C5C22×D512yes—
132C2×C4×C5C22×D512yes—
133C2×C4×C5C22×D512yes—
134C22⋊D5—58no—
135C2×Dic5—52no—
136C2×Dic5—52no—
137C2×Dic5—52no—
138C2×Dic5—52no—
139C2×Dic5—102no—
140C2×Dic5—102no—
141C2×Dic5—104no—
142C2×Dic5—104no—
143C2×Dic5—202no—
144C2×Dic5C22×D512yes—
145C2×Dic5C22×D512yes—
146C2×Dic5C22×D512yes—
147C4×D5—42no—
148C4×D5—104no—
149C4×D5—202no—
150Dic10—104no—
151Dic10—202no—
152Dic10—204no—
153C4⋊Q8—251no—
154#125—252no—
155C22⋊Q8—52no—
156C22⋊Q8—252no—
157C22⋊Q8—252no—
158C4×Q8—251no—
159C4×D4—251no—
160C4×D4—252no—
161C2×C4⋊C4—252no—
162C52#55411yescharacteristic, complemented, Sylow
163C22×C5—22no—
164C22×C5—54no—
165C22×C5—102no—
166C22×C5—102no—
167C22×C5C23×D512yes—
168C2×D5—22no—
169C2×D5—22no—
170C2×D5Q8×D514yes—
171C4×C5—24no—
172C4×C5—22no—
173C4×C5—22no—
174C4×C5—22no—
175C4×C5—44no—
176C4×C5—102no—
177C4×C5—102no—
178C4×C5—102no—
179Dic5—22no—
180Dic5—22no—
181Dic5—22no—
182Dic5—54no—
183Dic5—54no—
184Dic5—104no—
185Dic5—104no—
186Dic5—102no—
187Dic5—102no—
188Dic5—204no—
189C2×Q8—251no—
190C2×Q8—251no—
191C2×Q8D5211yescharacteristic
192C2×D4—251no—
193C22×C4—52no—
194C22×C4—252no—
195C22×C4—252no—
196C4⋊C4—52no—
197C4⋊C4—52no—
198C4⋊C4—52no—
199C4⋊C4—251no—
200C4⋊C4—252no—
201C4⋊C4—251no—
202C4⋊C4—252no—
203C4⋊C4—252no—
204C4⋊C4—252no—
205C22⋊C4—52no—
206C22⋊C4—52no—
207C22⋊C4—252no—
208C42—252no—
209C42—251no—
210C2×C5—22no—
211C2×C5—22no—
212C2×C5—22no—
213C2×C5—104no—
214C2×C5#414412yes—
215C2×C5C2×Q8×D512yes—
216C2×C5D5×#4112yes—
217D5—24no—
218C23—52no—
219Q8—41no—
220Q8—502no—
221Q8—1001no—
222D4—254no—
223C2×C4—52no—
224C2×C4—52no—
225C2×C4—52no—
226C2×C4—202no—
227C2×C4—251no—
228C2×C4—251no—
229C2×C4—252no—
230C2×C4—504no—
231C2×C4—1002no—
232C2×C4C2×D5211yescharacteristic
233C2×C4C2×D5212yes—
234C5—22no—
235C5#6597012yescomplemented
236C22—54no—
237C22—102no—
238C22—102no—
239C22C22×D5211yescharacteristic
240C4—22no—
241C4—21no—
242C4—102no—
243C4—102no—
244C4—102no—
245C4—252no—
246C4—252no—
247C4—502no—
248C2—104no—
249C2Q8×D5211yescharacteristic
250C2#1171748411yescharacteristic
251C2#1171749511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D52
commutator, socle, cosocleC22×C52C24
FittingC2×C52×Q8C22
prime radicalC2×#6037C22
hypercenterC2×Q8D52
hypocenterC52#554
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. #11717264C2semidirect
2. C5×#4092C2semidirect
4. #11717015C2semidirect
5. #11717014C2semidirect
7. D5×#683C2semidirect
8. #11716965C2semidirect
9. #11716956C2semidirect
45. #6037Q8semidirect
49. #4092D5semidirect
162. C52#554semidirect
235. C5#65970semidirect

Maximal subgroups

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

subgroupindex
#117172642
C5×#40922
#117170202
#117170152
#117170142
#117169972
D5×#6832
#117169652
#117169562
#659705