Finite Group Databasebeta

← #10600331

Subgroups — #10600331

Order 640.

386 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 83 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×#4075C211yesmaximal, characteristic
2#65820C211yesmaximal, characteristic
3C5×#381C211yesmaximal, characteristic, complemented
4#65500C211yesmaximal, characteristic, complemented
5C2×#3938C211yesmaximal, characteristic
6#64747C211yesmaximal, characteristic, complemented
7#64746C211yesmaximal, characteristic, complemented
8C23×C4×C5C2211yescharacteristic
9C22×C22⋊D5C2211yescharacteristic
10C2×C5×C22⋊C4C2211yescharacteristic
11C2×C5×C22⋊C4C2211yescharacteristic
12C2×C22⋊Dic5C2211yescharacteristic
13C2×C22⋊Dic5C2211yescharacteristic
14C2×C22⋊Dic5C2211yescharacteristic
15#4075—22no—
16#4075C414yescomplemented
17C4×C22⋊D5—22no—
18C2×#685—21no—
19C2×#683—21no—
20#4027—22no—
21D5×C22⋊C4—21no—
22#4023—21no—
23C5×#95—22no—
24#3963—22no—
25#3938—22no—
26#1890—51nomaximal, Sylow
27C24×C5C2311yescharacteristic
28C23×D5D411yescharacteristic
29C22×C4×C5—21no—
30C22×C4×C5—21no—
31C22×C4×C5—21no—
32C22×C4×C5—21no—
33C22×C4×C5—21no—
34C22×C4×C5—21no—
35C22×C4×C5—21no—
36C22×C4×C5C2×C412yescomplemented
37C22×C4×C5D412yes—
38C2×C22⋊D5—21no—
39C2×C22⋊D5—21no—
40C2×C22⋊D5—21no—
41C2×C22⋊D5—21no—
42C2×C22⋊D5C2×C412yes—
43C2×C22⋊D5D412yes—
44C22×Dic5—21no—
45C22×Dic5—21no—
46C22×Dic5D411yescharacteristic
47C22×Dic5D412yes—
48C2×C4×D5—22no—
49C5×C22⋊C4—21no—
50C5×C22⋊C4—21no—
51C5×C22⋊C4—21no—
52C5×C22⋊C4—21no—
53C22⋊Dic5—21no—
54C22⋊Dic5—21no—
55C22⋊Dic5—21no—
56C22⋊Dic5—21no—
57C22⋊Dic5—21no—
58C22⋊Dic5C2×C412yescomplemented
59#685—22no—
60#685—24no—
61#683—22no—
62#683—24no—
63C4×Dic5—22no—
64C2×#123—51no—
65#518—51no—
66C2×#99—51no—
67#381—51no—
68#381D511yescharacteristic, complemented
69#342—51no—
70#342—51no—
71C23×C5—42no—
72C23×C5C22×C411yescharacteristic
73C23×C5C2×D411yescharacteristic
74C23×C5C2×D411yescharacteristic
75C23×C5C2×D411yescharacteristic
76C23×C5C2×D411yescharacteristic
77C23×C5#4111yescharacteristic
78C23×C5#4111yescharacteristic
79C22×D5—21no—
80C22×D5—21no—
81C22×D5—42no—
82C22×D5C22⋊C412yes—
83C2×C4×C5—22no—
84C2×C4×C5—22no—
85C2×C4×C5—22no—
86C2×C4×C5—22no—
87C2×C4×C5—41no—
88C2×C4×C5—41no—
89C2×C4×C5—41no—
90C2×C4×C5—41no—
91C2×C4×C5—42no—
92C2×C4×C5—42no—
93C2×C4×C5—41no—
94C22⋊D5—22no—
95C22⋊D5—22no—
96C22⋊D5—22no—
97C22⋊D5—22no—
98C2×Dic5—21no—
99C2×Dic5—21no—
100C2×Dic5—22no—
101C2×Dic5—22no—
102C2×Dic5—42no—
103C2×Dic5—42no—
104C2×Dic5—42no—
105C2×Dic5—41no—
106C2×Dic5C22⋊C412yes—
107C4×D5—82no—
108C22×D4—51no—
109C23×C4C2×D511yescharacteristic
110#123—54no—
111#123—102no—
112C4×D4—102no—
113C4×D4—102no—
114#117—101no—
115C2×C4⋊C4—101no—
116C2×C22⋊C4—51no—
117C2×C22⋊C4—51no—
118C2×C22⋊C4—51no—
119C2×C22⋊C4—101no—
120C2×C22⋊C4—101no—
121C2×C22⋊C4C2×D511yescharacteristic
122C2×C22⋊C4C2×D511yescharacteristic
123#99—102no—
124#95—22no—
125#95—102no—
126C22×C5—22no—
127C22×C5—22no—
128C22×C5—22no—
129C22×C5—41no—
130C22×C5—41no—
131C22×C5—41no—
132C22×C5—41no—
133C22×C5C2×C22⋊C411yescharacteristic
134C22×C5C4×D411yescharacteristic
135C22×C5C4×D411yescharacteristic
136C22×C5#12011yescharacteristic
137C22×C5#12111yescharacteristic
138C22×C5#12111yescharacteristic
139C22×C5#12311yescharacteristic
140C2×D5—22no—
141C2×D5—42no—
142C2×D5—42no—
143C2×D5—81no—
144C4×C5—42no—
145C4×C5—42no—
146C4×C5—81no—
147Dic5—22no—
148Dic5—42no—
149Dic5—42no—
150Dic5—81no—
151C24—51no—
152C24C22×D511yescharacteristic
153C2×D4—52no—
154C2×D4—52no—
155C2×D4—101no—
156C2×D4—101no—
157C2×D4—101no—
158C2×D4—101no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—51no—
167C22×C4—52no—
168C22×C4—102no—
169C22×C4—101no—
170C22×C4—101no—
171C22×C4C4×D512yescomplemented
172C22×C4C22⋊D512yes—
173C4⋊C4—104no—
174C4⋊C4—102no—
175C22⋊C4—21no—
176C22⋊C4—21no—
177C22⋊C4—21no—
178C22⋊C4—21no—
179C22⋊C4—52no—
180C22⋊C4—104no—
181C22⋊C4—102no—
182C22⋊C4—101no—
183C22⋊C4—101no—
184C22⋊C4—101no—
185C22⋊C4—101no—
186C22⋊C4—101no—
187C42—102no—
188C2×C5—21no—
189C2×C5—21no—
190C2×C5—21no—
191C2×C5—21no—
192C2×C5—21no—
193C2×C5—21no—
194C2×C5#38611yescharacteristic
195C2×C5#45812yes—
196D5—42no—
197C23—42no—
198C23—52no—
199C23—101no—
200C23—101no—
201C23—202no—
202C23C2×C4×D511yescharacteristic
203C23#70911yescharacteristic
204C23D4×D511yescharacteristic
205C23D4×D511yescharacteristic
206C23D4×D511yescharacteristic
207C23#71111yescharacteristic
208C23C2×C22⋊D511yescharacteristic
209D4—102no—
210D4—102no—
211D4—102no—
212D4—102no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—41no—
224C2×C4—52no—
225C2×C4—101no—
226C2×C4—101no—
227C2×C4—102no—
228C2×C4—102no—
229C2×C4—202no—
230C2×C4—202no—
231C2×C4—202no—
232C2×C4—201no—
233C2×C4—402no—
234C5#189011yescharacteristic, complemented, Sylow
235C22—22no—
236C22—22no—
237C22—22no—
238C22—41no—
239C22—41no—
240C22—41no—
241C22—41no—
242C22—102no—
243C22—202no—
244C22—202no—
245C22—401no—
246C22D5×C22⋊C411yescharacteristic
247C22#402711yescharacteristic
248C22#402911yescharacteristic
249C22#403011yescharacteristic
250C22C4×C22⋊D511yescharacteristic
251C22#408311yescharacteristic
252C22#408411yescharacteristic
253C4—42no—
254C4—42no—
255C4—81no—
256C4—102no—
257C4—202no—
258C4—202no—
259C4—401no—
260C2—21no—
261C2—21no—
262C2—21no—
263C2—21no—
264C2—21no—
265C2—21no—
266C2—202no—
267C2#6524511yescharacteristic
268C2#6534212yes—
subgroupG/H
centerC22#4083
commutatorC23×C5C22×C4
FrattiniC24C22×D5
FittingC5×#381C2
socleC22×C5#120
prime radicalC22×C22⋊D5C22
cosocleC24×C5C23
hypercenter#381D5
hypocenterC5#1890
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C24 ◁ #381

Complements

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

NH ≅ G/Ntype
3. C5×#381C2semidirect
4. #65500C2semidirect
6. #64747C2semidirect
7. #64746C2semidirect
16. #4075C4semidirect
36. C22×C4×C5C2×C4semidirect
58. C22⋊Dic5C2×C4semidirect
68. #381D5semidirect
171. C22×C4C4×D5semidirect
234. C5#1890semidirect

Maximal subgroups

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

subgroupindex
C2×#40752
#658202
C5×#3812
#655002
C2×#39382
#647472
#647462
#18905