Finite Group Databasebeta

← #10612798

Subgroups — #10612798

Order 640.

362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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
1D5×C4⋊Q8C211yesmaximal, characteristic, complemented
2#65891C211yesmaximal, characteristic
3C5×#476C211yesmaximal, characteristic, complemented
4#65380C211yesmaximal, characteristic, complemented
5#65297C211yesmaximal, characteristic, complemented
6#65151C212yesmaximal, complemented
7#65145C212yesmaximal, complemented
8#65139C211yesmaximal, characteristic, complemented
9#65124C211yesmaximal, characteristic, complemented
10#65063C212yesmaximal
11#65054C212yesmaximal, complemented
12C2×Q8×D5—21no—
13C5×C4⋊Q8C2211yescharacteristic
14C4×C5×D4C2211yescharacteristic
15#4090—21no—
16#4084C2211yescharacteristic
17#4082C2211yescharacteristic
18C4×C22⋊D5—21no—
19#4072—21no—
20#4043C2211yescharacteristic
21D5×C4⋊C4—21no—
22D5×C4⋊C4C2212yes—
23#4036C2211yescharacteristic
24#4034—21no—
25#4034C2212yes—
26#4029—21no—
27#4025—21no—
28C42×D5C2211yescharacteristic
29#4015C2211yescharacteristic
30C4×Dic10C2211yescharacteristic
31C5×#106C2212yes—
32C5×C4⋊C8C2211yescharacteristic
33C5×#102C2212yes—
34#3964C2212yes—
35#3952C2212yes—
36#3950C2212yes—
37#3948C2212yes—
38#3947C2212yes—
39#3942C2212yes—
40#3940C2212yes—
41#3939C2212yes—
42C4⋊#168C2211yescharacteristic
43#3238—51nomaximal, Sylow
44C2×C5×Q8—21no—
45C2×C5×D4C2311yescharacteristic
46C22×C4×C5—21no—
47C2×C22⋊D5—21no—
48Q8×D5—44no—
49C2×C4×D5—22no—
50C2×C4×D5D411yescharacteristic
51C2×C4×D5D411yescharacteristic
52C2×C4×D5C2311yescharacteristic
53C2×Dic10—21no—
54C2×Dic10—22no—
55C2×Dic10C2311yescharacteristic
56C2×C5×C8C2312yes—
57C5×C4⋊C4—21no—
58C5×C4⋊C4C2311yescharacteristic
59C5×C4⋊C4C2312yes—
60C5×C22⋊C4—21no—
61C42×C5C2311yescharacteristic
62C22⋊Dic5—21no—
63C22⋊Dic5—21no—
64C22⋊Dic5—21no—
65#685—21no—
66C4⋊Dic5—21no—
67C4⋊Dic5—21no—
68C4⋊Dic5—21no—
69C4⋊Dic5C2311yescharacteristic
70C4⋊Dic5C2312yes—
71#683—21no—
72#683—21no—
73#683—22no—
74#683—22no—
75C4×Dic5—21no—
76C4×Dic5D411yescharacteristic
77C4×Dic5D411yescharacteristic
78C4×Dic5C2311yescharacteristic
79C2×#168C2312yes—
80C2×C4⋊Q8—51no—
81#529—51no—
82#501—52no—
83#489—52no—
84#483—52no—
85#480—52no—
86#477—51no—
87#477—51no—
88#476—51no—
89#476D511yescharacteristic, complemented
90#432—51no—
91C23×C5—21no—
92C22×D5C2×D411yescharacteristic
93C5×Q8—42no—
94C5×D4—21no—
95C5×D4—21no—
96C2×C4×C5—22no—
97C2×C4×C5—21no—
98C2×C4×C5—42no—
99C2×C4×C5C2×D411yescharacteristic
100C2×C4×C5C2×D411yescharacteristic
101C2×C4×C5C2411yescharacteristic
102C22⋊D5—42no—
103C2×Dic5—21no—
104C2×Dic5—21no—
105C2×Dic5—22no—
106C2×Dic5C2×D411yescharacteristic
107C2×Dic5C2×D411yescharacteristic
108C2×Dic5C2×D411yescharacteristic
109C4×D5—22no—
110C4×D5—22no—
111C4×D5—21no—
112C4×D5—21no—
113C4×D5—44no—
114Dic10—21no—
115Dic10—21no—
116Dic10—44no—
117Dic10—42no—
118C5×C8—22no—
119#168—22no—
120C22×Q8—101no—
121C4⋊Q8—52no—
122C4⋊Q8—51no—
123C4⋊Q8—101no—
124C4⋊Q8—101no—
125C4⋊Q8C2×D511yescharacteristic
126#126—101no—
127#125—51no—
128#124—51no—
129#123—101no—
130C22⋊Q8—51no—
131#121—51no—
132C4×Q8—51no—
133C4×D4—101no—
134C4×D4C2×D511yescharacteristic
135#117—101no—
136C2×C4⋊C4—52no—
137C2×C4⋊C4—101no—
138C2×C42—51no—
139#107—52no—
140#107—52no—
141#106—52no—
142#106C2×D512yes—
143C4⋊C8—51no—
144C4⋊C8C2×D511yescharacteristic
145#103—52no—
146#103—52no—
147#102—52no—
148#102C2×D512yes—
149C22⋊C8—52no—
150#97—52no—
151C22×C5—41no—
152C22×C5—41no—
153C22×C5—41no—
154C22×C5C22×D411yescharacteristic
155C2×D5—21no—
156C2×D5—21no—
157C2×D5AGL(1,ℤ/8)12yes—
158C4×C5—21no—
159C4×C5—42no—
160C4×C5—41no—
161C4×C5#13712yes—
162C4×C52−1+411yescharacteristic
163C4×C52−1+411yescharacteristic
164Dic5—21no—
165Dic5—21no—
166Dic5—21no—
167Dic5—41no—
168Dic5—42no—
169Dic5—41no—
170C2×Q8—21no—
171C2×Q8—51no—
172C2×Q8—102no—
173C2×Q8—101no—
174C2×Q8—204no—
175C2×D4—101no—
176C2×D4C22×D511yescharacteristic
177C22×C4—21no—
178C22×C4—51no—
179C22×C4—51no—
180C22×C4—51no—
181C22×C4—102no—
182C2×C8—52no—
183C2×C8C22×D512yes—
184C4⋊C4—21no—
185C4⋊C4—52no—
186C4⋊C4—51no—
187C4⋊C4—102no—
188C4⋊C4—102no—
189C4⋊C4—101no—
190C4⋊C4—101no—
191C4⋊C4—101no—
192C4⋊C4—101no—
193C4⋊C4—101no—
194C4⋊C4C22×D512yes—
195C4⋊C4C22×D511yescharacteristic
196C22⋊C4—21no—
197C22⋊C4—101no—
198C22⋊C4—101no—
199C22⋊C4—101no—
200C22⋊C4—101no—
201C42—51no—
202C42—51no—
203C42—51no—
204C42—101no—
205C42C22×D511yescharacteristic
206C2×C5—81no—
207C2×C5#53611yescharacteristic
208C2×C5C2×AGL(1,ℤ/8)11yescharacteristic
209C2×C5C2×#13711yescharacteristic
210D5—22no—
211C23—21no—
212C23—51no—
213Q8—42no—
214Q8—101no—
215Q8—101no—
216Q8—202no—
217Q8—204no—
218D4—21no—
219D4—21no—
220D4—202no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—42no—
224C2×C4—51no—
225C2×C4—51no—
226C2×C4—51no—
227C2×C4—102no—
228C2×C4—101no—
229C2×C4—101no—
230C2×C4—102no—
231C2×C4—101no—
232C2×C4—101no—
233C2×C4—102no—
234C2×C4—204no—
235C2×C4D4×D511yescharacteristic
236C2×C4D4×D511yescharacteristic
237C2×C4C23×D511yescharacteristic
238C8—22no—
239C8—102no—
240C5#323811yescharacteristic, complemented, Sylow
241C22—41no—
242C22—41no—
243C22—41no—
244C22—52no—
245C22—101no—
246C22—101no—
247C22C2×D4×D511yescharacteristic
248C4—21no—
249C4—41no—
250C4—42no—
251C4—101no—
252C4—101no—
253C4—101no—
254C4—202no—
255C4—201no—
256C4—201no—
257C4#406112yes—
258C4#414711yescharacteristic
259C4#415011yescharacteristic
260C2—81no—
261C2—102no—
262C2#6596211yescharacteristic
263C2C2×#406111yescharacteristic
264C2D5×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#476C2
socleC22×C5C22×D4
prime radical#4084C22
hypercenter#476D5
hypocenterC5#3238
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. D5×C4⋊Q8C2semidirect
3. C5×#476C2semidirect
4. #65380C2semidirect
5. #65297C2semidirect
6. #65151C2semidirect
7. #65145C2semidirect
8. #65139C2semidirect
9. #65124C2semidirect
11. #65054C2semidirect
89. #476D5semidirect
240. C5#3238semidirect

Maximal subgroups

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

subgroupindex
D5×C4⋊Q82
#658912
C5×#4762
#653802
#652972
#651512
#651452
#651392
#651242
#650632
#650542
#32385