Finite Group Databasebeta

← #13105450

Subgroups — #13105450

Order 1600.

544 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 142 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
1C4⋊C4×C5⋊D5C211yesmaximal, characteristic
2C5×#4035C212yesmaximal, complemented
3#11717018C211yesmaximal, characteristic
4#11717001C211yesmaximal, characteristic
5#11717001C211yesmaximal, characteristic
6#11717001C211yesmaximal, characteristic
7#11717001C211yesmaximal, characteristic
8C4×#6036C211yesmaximal, characteristic
9#11716986C212yesmaximal, complemented
10#11716964C212yesmaximal, complemented
11#11716963C212yesmaximal, complemented
12C2×C4×C5⋊D5C2211yescharacteristic
13C2×C4×C5⋊D5C2211yescharacteristic
14C2×C4×C5⋊D5C2211yescharacteristic
15C2×#6036C2211yescharacteristic
16C2×#6036C2211yescharacteristic
17C2×#6036C2211yescharacteristic
18C2×#6036C2211yescharacteristic
19C52×C4⋊C4C2211yescharacteristic
20C4⋊#1039C2211yescharacteristic
21#87806C2211yescharacteristic
22#87806C2211yescharacteristic
23C5×C4⋊Dic5C2212yes—
24C5×#683C2212yes—
25C5×#683C2212yes—
26C5×#683C2212yes—
27C5×#683C2212yes—
28C4×C5×Dic5C2212yes—
29#87781C2212yes—
30#87780C2212yes—
31#87780C2212yes—
32#87780C2212yes—
33#87780C2212yes—
34Dic52C2212yes—
35D5×#125—52nomaximal
36C22×C5⋊D5C2311yescharacteristic
37C2×C4×C52C2311yescharacteristic
38C2×C4×C52C2311yescharacteristic
39C2×C4×C52C2311yescharacteristic
40C2×#1039C2311yescharacteristic
41C2×#1039C2311yescharacteristic
42C2×#1039C2311yescharacteristic
43C4×C5⋊D5—22no—
44C4×C5⋊D5—22no—
45C4×C5⋊D5—22no—
46C2×C5×Dic5C2312yes—
47C2×C5×Dic5C2312yes—
48C2×C5×Dic5C2312yes—
49C2×C5×Dic5C2312yes—
50#6036—22no—
51#6036—22no—
52#6036—22no—
53#6036Q814yes—
54C5×#125—52no—
55D5×C4⋊C4—52no—
56D5×C4⋊C4—52no—
57D5×C4⋊C4—52no—
58D5×C4⋊C4—52no—
59D5×C4⋊C4—52no—
60D5×C4⋊C4—52no—
61D5×C4⋊C4—102no—
62#4036—52no—
63#4036—52no—
64#4035—52no—
65#4035—52no—
66#4035—52no—
67#4035D512yescomplemented
68C42×D5—52no—
69#4016—52no—
70C22×C52C2411yescharacteristic
71C2×C5⋊D5C2×Q812yes—
72C2×C5⋊D5#4112yes—
73C2×C5⋊D5#4112yes—
74C4×C52—21no—
75C4×C52—21no—
76C4×C52—21no—
77#1039—21no—
78#1039—21no—
79#1039—21no—
80C5×Dic5—22no—
81C5×Dic5—22no—
82C5×Dic5—22no—
83C5×Dic5C2×Q814yes—
84C2×C4×D5—52no—
85C2×C4×D5—52no—
86C2×C4×D5—52no—
87C2×C4×D5—52no—
88C2×C4×D5—52no—
89C2×C4×D5—52no—
90C2×C4×D5—52no—
91C2×C4×D5—102no—
92C2×C4×D5—102no—
93C2×C4×D5—102no—
94C5×C4⋊C4—22no—
95C5×C4⋊C4—52no—
96C5×C4⋊C4—52no—
97C5×C4⋊C4—52no—
98C5×C4⋊C4—52no—
99C5×C4⋊C4—52no—
100C5×C4⋊C4C2×D512yes—
101C42×C5—52no—
102C4⋊Dic5—52no—
103C4⋊Dic5—52no—
104C4⋊Dic5—52no—
105C4⋊Dic5—52no—
106C4⋊Dic5—52no—
107C4⋊Dic5—102no—
108C4⋊Dic5C2×D512yes—
109#683—52no—
110#683—52no—
111#683—52no—
112#683—52no—
113#683—52no—
114#683—52no—
115#683—52no—
116#683—52no—
117#683—102no—
118#683—102no—
119#683C2×D512yes—
120#683C2×D512yes—
121#683C2×D512yes—
122#683C2×D512yes—
123C4×Dic5—52no—
124C4×Dic5—52no—
125C4×Dic5C2×D512yes—
126C2×#125—251noSylow
127C2×C52C22×Q811yescharacteristic
128C2×C52C2×#4111yescharacteristic
129C2×C52C2×#4111yescharacteristic
130C5⋊D5#12514yescomplemented
131C22×D5—52no—
132C22×D5—102no—
133C2×C4×C5—22no—
134C2×C4×C5—22no—
135C2×C4×C5—22no—
136C2×C4×C5—52no—
137C2×C4×C5—52no—
138C2×C4×C5—52no—
139C2×C4×C5—52no—
140C2×C4×C5C22×D512yes—
141C2×C4×C5C22×D512yes—
142C2×C4×C5C22×D512yes—
143C2×Dic5—52no—
144C2×Dic5—52no—
145C2×Dic5—52no—
146C2×Dic5—102no—
147C2×Dic5—102no—
148C2×Dic5—102no—
149C2×Dic5C22×D512yes—
150C2×Dic5C22×D512yes—
151C2×Dic5C22×D512yes—
152C2×Dic5C22×D512yes—
153C4×D5—58no—
154C4×D5—104no—
155C4×D5—104no—
156C4×D5—104no—
157C4×D5—104no—
158C4×D5—104no—
159C4×D5—104no—
160C4×D5—108no—
161C4×D5—204no—
162C4×D5—204no—
163#125—52no—
164#125—252no—
165#125—252no—
166#125—252no—
167C2×C4⋊C4—251no—
168C2×C4⋊C4—251no—
169C2×C4⋊C4—251no—
170C2×C4⋊C4—251no—
171C2×C4⋊C4—251no—
172C2×C4⋊C4—251no—
173C2×C42—251no—
174C52C2×#12511yescharacteristic, complemented, Sylow
175C22×C5—22no—
176C22×C5C23×D512yes—
177C2×D5—54no—
178C2×D5—54no—
179C2×D5—54no—
180C2×D5—104no—
181C2×D5—104no—
182C2×D5—104no—
183C4×C5—24no—
184C4×C5—22no—
185C4×C5—22no—
186C4×C5—22no—
187C4×C5—42no—
188C4×C5—42no—
189C4×C5—54no—
190C4×C5—102no—
191C4×C5—102no—
192C4×C5—102no—
193Dic5—22no—
194Dic5—22no—
195Dic5—22no—
196Dic5—104no—
197Dic5—102no—
198Dic5—102no—
199Dic5—102no—
200Dic5—202no—
201Dic5—202no—
202Dic5Q8×D514yes—
203C22×C4—251no—
204C22×C4—251no—
205C22×C4—251no—
206C22×C4—251no—
207C22×C4—251no—
208C22×C4—251no—
209C22×C4—251no—
210C4⋊C4—52no—
211C4⋊C4—52no—
212C4⋊C4—52no—
213C4⋊C4—52no—
214C4⋊C4—52no—
215C4⋊C4—252no—
216C4⋊C4—252no—
217C4⋊C4—252no—
218C4⋊C4—252no—
219C4⋊C4—252no—
220C4⋊C4—251no—
221C4⋊C4—251no—
222C4⋊C4—251no—
223C4⋊C4D5211yescharacteristic
224C42—52no—
225C42—252no—
226C2×C5—22no—
227C2×C5—22no—
228C2×C5—22no—
229C2×C5C2×Q8×D512yes—
230C2×C5D5×#4112yes—
231C2×C5D5×#4112yes—
232D5—58no—
233D5—108no—
234C23—251no—
235C2×C4—52no—
236C2×C4—52no—
237C2×C4—52no—
238C2×C4—52no—
239C2×C4—254no—
240C2×C4—251no—
241C2×C4—251no—
242C2×C4—251no—
243C2×C4—502no—
244C2×C4—502no—
245C2×C4—502no—
246C2×C4—502no—
247C2×C4—502no—
248C2×C4—502no—
249C2×C4C2×D5211yescharacteristic
250C2×C4C2×D5211yescharacteristic
251C2×C4C2×D5211yescharacteristic
252C5—22no—
253C5D5×#12512yescomplemented
254C22—252no—
255C22—252no—
256C22—252no—
257C22C22×D5211yescharacteristic
258C4—21no—
259C4—21no—
260C4—21no—
261C4—54no—
262C4—102no—
263C4—102no—
264C4—102no—
265C4—501no—
266C4—501no—
267C4—501no—
268C2—254no—
269C2#1171747111yescharacteristic
270C2#1171747711yescharacteristic
271C2Q8×D5211yescharacteristic
subgroupG/H
center, FrattiniC22C22×D52
commutator, socle, cosocleC22×C52C24
FittingC52×C4⋊C4C22
prime radicalC22×C5⋊D5C23
hypercenterC4⋊C4D52
hypocenterC52C2×#125
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C5×#4035C2semidirect
9. #11716986C2semidirect
10. #11716964C2semidirect
11. #11716963C2semidirect
67. #4035D5semidirect
130. C5⋊D5#125semidirect
174. C52C2×#125semidirect
253. C5D5×#125semidirect

Maximal subgroups

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

subgroupindex
C4⋊C4×C5⋊D52
C5×#40352
#117170182
#117170012
C4×#60362
#117169862
#117169642
#117169632
D5×#1255