Finite Group Databasebeta

← #10605547

Subgroups — #10605547

Order 640.

534 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 141 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×#4022C211yesmaximal, characteristic, complemented
2C2×#4021C211yesmaximal, characteristic, complemented
3C4×C5×C4⋊C4C211yesmaximal, characteristic, complemented
4#65283C212yesmaximal, complemented
5#65280C212yesmaximal, complemented
6#65229C212yesmaximal, complemented
7#65228C212yesmaximal, complemented
8#64962C211yesmaximal, characteristic, complemented
9#64961C211yesmaximal, characteristic, complemented
10#64960C211yesmaximal, characteristic
11#64945C211yesmaximal, characteristic, complemented
12C22×D20C2212yes—
13C22×D20C2211yescharacteristic
14C22×Dic10C2211yescharacteristic
15C2×C5×C4⋊C4C2212yes—
16C2×C42×C5C2212yes—
17C2×C42×C5C2211yescharacteristic
18C2×#685C2211yescharacteristic
19C2×#685C2212yes—
20C2×#685C2212yes—
21C2×#685C2212yes—
22C2×#685C2211yescharacteristic
23C2×#685C2211yescharacteristic
24C2×#685C2212yes—
25C2×#685C2212yes—
26C2×#685C2212yes—
27C2×C4⋊Dic5C2212yes—
28C2×#683C2211yescharacteristic
29C2×#683C2211yescharacteristic
30C2×#683C2211yescharacteristic
31#4022—24no—
32#4021—24no—
33C5×#95C2211yescharacteristic
34C5×#95C2211yescharacteristic
35#3963C2212yes—
36#3963C2212yes—
37#2662—51nomaximal, Sylow
38C23×D5C2311yescharacteristic
39C23×D5C2312yes—
40C22×C4×C5C2312yes—
41C22×C4×C5C2311yescharacteristic
42C22×C4×C5C2311yescharacteristic
43C22×C4×C5C2311yescharacteristic
44C22×C4×C5C2312yes—
45C22×Dic5C2312yes—
46C22×Dic5C2311yescharacteristic
47C22×Dic5C2311yescharacteristic
48C22×Dic5C2311yescharacteristic
49C2×D20—22no—
50C2×D20—24no—
51C2×D20—42no—
52C2×D20—42no—
53C2×D20—42no—
54C2×Dic10—22no—
55C2×Dic10—42no—
56C5×C4⋊C4—24no—
57C42×C5—42no—
58C42×C5D414yescomplemented
59#685—24no—
60#685—24no—
61#685—22no—
62#685—22no—
63#685—22no—
64#685—24no—
65#685—42no—
66#685—42no—
67#685—42no—
68C4⋊Dic5—42no—
69#683—22no—
70#683—22no—
71#683—22no—
72C2×#126—51no—
73C2×#124—51no—
74#396—52no—
75#395—51no—
76#394—52no—
77#394—51no—
78#393—51no—
79#392—51no—
80#390—52no—
81#388—52no—
82C4×C4⋊C4D511yescharacteristic, complemented
83C23×C5C2411yescharacteristic
84C22×D5—21no—
85C22×D5—22no—
86C22×D5—22no—
87C22×D5—22no—
88C22×D5—22no—
89C22×D5—22no—
90C22×D5—22no—
91C22×D5—22no—
92C22×D5—21no—
93C22×D5—22no—
94C22×D5—21no—
95C22×D5—22no—
96C2×C4×C5—22no—
97C2×C4×C5—22no—
98C2×C4×C5—21no—
99C2×C4×C5—22no—
100C2×C4×C5—22no—
101C2×C4×C5—21no—
102C2×C4×C5—22no—
103C2×C4×C5—22no—
104C2×C4×C5—22no—
105C2×C4×C5C2×D412yes—
106C2×C4×C5C2×D412yes—
107C2×C4×C5C2×D412yes—
108C2×C4×C5#4114yes—
109C2×Dic5—21no—
110C2×Dic5—21no—
111C2×Dic5—21no—
112C2×Dic5—22no—
113C2×Dic5—22no—
114C2×Dic5—22no—
115C2×Dic5—22no—
116C2×Dic5—21no—
117C2×Dic5—22no—
118C2×Dic5—21no—
119D20—44no—
120D20—48no—
121Dic10—44no—
122C22×Q8—51no—
123C22×D4—51no—
124C22×D4—52no—
125#126—104no—
126#124—104no—
127C2×C4⋊C4—51no—
128C2×C4⋊C4—51no—
129C2×C4⋊C4—51no—
130C2×C4⋊C4—52no—
131C2×C4⋊C4C2×D512yes—
132C2×C22⋊C4—52no—
133C2×C22⋊C4—52no—
134C2×C22⋊C4—51no—
135C2×C22⋊C4—51no—
136C2×C22⋊C4—51no—
137C2×C22⋊C4—52no—
138C2×C22⋊C4—52no—
139C2×C22⋊C4—52no—
140C2×C22⋊C4—52no—
141C2×C42C2×D512yes—
142C2×C42C2×D511yescharacteristic
143#95—52no—
144#95—52no—
145#95C2×D511yescharacteristic
146#95C2×D511yescharacteristic
147C22×C5C22×D411yescharacteristic
148C22×C5C2×#4112yes—
149C22×C5H(5,𝔽2)11yescharacteristic
150C22×C5H(5,𝔽2)12yes—
151C22×C52−1+411yescharacteristic
152C2×D5—41no—
153C2×D5—42no—
154C2×D5—42no—
155C2×D5—41no—
156C2×D5—41no—
157C2×D5—42no—
158C2×D5—42no—
159C2×D5—42no—
160C2×D5—42no—
161C2×D5—42no—
162C2×D5—42no—
163C2×D5—42no—
164C4×C5—22no—
165C4×C5—22no—
166C4×C5—22no—
167C4×C5—24no—
168C4×C5—42no—
169Dic5—41no—
170Dic5—42no—
171Dic5—41no—
172Dic5—41no—
173C24—51no—
174C24—52no—
175C2×Q8—102no—
176C2×Q8—202no—
177C2×D4—102no—
178C2×D4—104no—
179C2×D4—202no—
180C2×D4—202no—
181C2×D4—202no—
182C22×C4—51no—
183C22×C4—51no—
184C22×C4—52no—
185C22×C4—51no—
186C22×C4C22×D512yes—
187C22×C4C22×D511yescharacteristic
188C22×C4C22×D511yescharacteristic
189C22×C4C22×D511yescharacteristic
190C22×C4C22×D512yes—
191C4⋊C4—24no—
192C4⋊C4—102no—
193C4⋊C4—102no—
194C4⋊C4—102no—
195C4⋊C4—202no—
196C22⋊C4—104no—
197C22⋊C4—104no—
198C22⋊C4—102no—
199C22⋊C4—102no—
200C22⋊C4—102no—
201C22⋊C4—104no—
202C22⋊C4—202no—
203C22⋊C4—202no—
204C22⋊C4—202no—
205C42—42no—
206C42D2014yescomplemented
207C2×C5#53211yescharacteristic
208C2×C5#53511yescharacteristic
209C2×C5#53711yescharacteristic
210C2×C5#53812yes—
211C2×C5#54212yes—
212D5—82no—
213D5—81no—
214C23—101no—
215C23—102no—
216C23—102no—
217C23—102no—
218C23—102no—
219C23—102no—
220C23—101no—
221C23—101no—
222C23—102no—
223C23—102no—
224C23—102no—
225C23—102no—
226C23C23×D511yescharacteristic
227Q8—204no—
228D4—204no—
229D4—208no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—102no—
240C2×C4—101no—
241C2×C4—101no—
242C2×C4—101no—
243C2×C4—102no—
244C2×C4—101no—
245C2×C4—101no—
246C2×C4—102no—
247C2×C4—102no—
248C2×C4—102no—
249C2×C4C2×D2012yes—
250C2×C4C2×D2012yes—
251C2×C4C2×D2012yes—
252C2×C4#70914yes—
253C5#266211yescharacteristic, complemented, Sylow
254C22—201no—
255C22—202no—
256C22—201no—
257C22—202no—
258C22—202no—
259C22—201no—
260C22—202no—
261C22—202no—
262C22—202no—
263C22—202no—
264C22—202no—
265C22—202no—
266C22C22×D2011yescharacteristic
267C22C2×#70912yes—
268C22#414411yescharacteristic
269C22#414711yescharacteristic
270C22#414912yes—
271C4—22no—
272C4—22no—
273C4—22no—
274C4—24no—
275C4—42no—
276C4—201no—
277C4—201no—
278C4—202no—
279C4—201no—
280C2—402no—
281C2—401no—
282C2#6581111yescharacteristic
283C2#6584411yescharacteristic
284C2#6585911yescharacteristic
285C2#6589412yes—
286C2#6591612yes—
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC4×C5×C4⋊C4C2
prime radical#64960C2
hypercenterC4×C4⋊C4D5
hypocenterC5#2662
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#4022C2semidirect
2. C2×#4021C2semidirect
3. C4×C5×C4⋊C4C2semidirect
4. #65283C2semidirect
5. #65280C2semidirect
6. #65229C2semidirect
7. #65228C2semidirect
8. #64962C2semidirect
9. #64961C2semidirect
11. #64945C2semidirect
58. C42×C5D4semidirect
82. C4×C4⋊C4D5semidirect
206. C42D20semidirect
253. C5#2662semidirect

Maximal subgroups

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

subgroupindex
C2×#40222
C2×#40212
C4×C5×C4⋊C42
#652832
#652802
#652292
#652282
#649622
#649612
#649602
#649452
#26625