Finite Group Databasebeta

← #10612749

Subgroups — #10612749

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#65914C211yesmaximal, characteristic
3C5×#475C211yesmaximal, characteristic, complemented
4#65376C211yesmaximal, characteristic, complemented
5#65309C211yesmaximal, characteristic, complemented
6#65152C212yesmaximal
7#65145C212yesmaximal, complemented
8#65135C211yesmaximal, characteristic, complemented
9#65124C211yesmaximal, characteristic, complemented
10#65098C212yesmaximal, complemented
11#65084C212yesmaximal, complemented
12C2×Q8×D5—21no—
13C5×C4⋊Q8C2211yescharacteristic
14C4×C5×Q8C2211yescharacteristic
15#4093C2211yescharacteristic
16#4092C2211yescharacteristic
17#4090—21no—
18#4044—21no—
19#4041C2211yescharacteristic
20#4040—21no—
21D5×C4⋊C4—21no—
22D5×C4⋊C4C2212yes—
23#4036C2211yescharacteristic
24#4034—21no—
25#4034C2212yes—
26C4×D20—21no—
27C4×D20C2211yescharacteristic
28#4018—21no—
29C42×D5C2211yescharacteristic
30#4015C2211yescharacteristic
31C5×#106C2212yes—
32C5×C4⋊C8C2211yescharacteristic
33C5×#103C2212yes—
34#3967C2212yes—
35#3953C2212yes—
36#3952C2212yes—
37#3950C2212yes—
38#3947C2212yes—
39#3941C2212yes—
40#3940C2212yes—
41#3939C2212yes—
42C4⋊#168C2211yescharacteristic
43#3239—51nomaximal, Sylow
44C2×C5×Q8—21no—
45C2×C5×Q8C2311yescharacteristic
46Q8×D5—44no—
47C2×D20—21no—
48C2×D20C2311yescharacteristic
49C2×C4×D5—22no—
50C2×C4×D5—21no—
51C2×C4×D5D411yescharacteristic
52C2×C4×D5D411yescharacteristic
53C2×C4×D5C2311yescharacteristic
54C2×Dic10—21no—
55C2×Dic10—22no—
56C2×C5×C8C2312yes—
57C5×C4⋊C4—21no—
58C5×C4⋊C4—21no—
59C5×C4⋊C4C2311yescharacteristic
60C5×C4⋊C4C2312yes—
61C42×C5—21no—
62C42×C5C2311yescharacteristic
63#685—21no—
64#685—21no—
65#685—21no—
66#685—21no—
67#685—21no—
68C4⋊Dic5—21no—
69C4⋊Dic5—21no—
70C4⋊Dic5C2311yescharacteristic
71C4⋊Dic5C2312yes—
72#683—21no—
73#683—21no—
74#683—22no—
75#683—22no—
76C4×Dic5D411yescharacteristic
77C4×Dic5D411yescharacteristic
78C4×Dic5C2311yescharacteristic
79C2×#168C2312yes—
80C2×C4⋊Q8—51no—
81#529—51no—
82#501—52no—
83#489—52no—
84#484—52no—
85#481—52no—
86#475—51no—
87#475D511yescharacteristic, complemented
88#474—51no—
89#474—51no—
90#432—51no—
91C22×D5—21no—
92C22×D5C2×D411yescharacteristic
93C5×Q8—21no—
94C5×Q8—21no—
95C5×Q8—42no—
96C2×C4×C5—22no—
97C2×C4×C5—21no—
98C2×C4×C5—21no—
99C2×C4×C5C2×D411yescharacteristic
100C2×C4×C5C2×D411yescharacteristic
101C2×C4×C5C2411yescharacteristic
102C2×Dic5—21no—
103C2×Dic5—22no—
104C2×Dic5C2×D411yescharacteristic
105C2×Dic5C2×D411yescharacteristic
106C2×Dic5C2×D411yescharacteristic
107D20—21no—
108D20—21no—
109D20—42no—
110C4×D5—22no—
111C4×D5—22no—
112C4×D5—21no—
113C4×D5—21no—
114C4×D5—44no—
115C4×D5—42no—
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×Q8C2×D511yescharacteristic
133C4×D4—51no—
134C4×D4—101no—
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#103C2×D512yes—
147#102—52no—
148#102—52no—
149C22⋊C8—52no—
150#97—52no—
151C22×C5C22×D411yescharacteristic
152C2×D5—21no—
153C2×D5—21no—
154C2×D5—41no—
155C2×D5—41no—
156C2×D5—41no—
157C2×D5#13712yes—
158C4×C5—21no—
159C4×C5—41no—
160C4×C5—42no—
161C4×C5—41no—
162C4×C5AGL(1,ℤ/8)12yes—
163C4×C52−1+411yescharacteristic
164C4×C52−1+411yescharacteristic
165Dic5—21no—
166Dic5—21no—
167Dic5—21no—
168Dic5—42no—
169Dic5—41no—
170C2×Q8—21no—
171C2×Q8—102no—
172C2×Q8—101no—
173C2×Q8—204no—
174C2×Q8C22×D511yescharacteristic
175C2×D4—51no—
176C2×D4—101no—
177C22×C4—51no—
178C22×C4—51no—
179C22×C4—51no—
180C22×C4—102no—
181C22×C4—101no—
182C2×C8—52no—
183C2×C8C22×D512yes—
184C4⋊C4—21no—
185C4⋊C4—21no—
186C4⋊C4—52no—
187C4⋊C4—51no—
188C4⋊C4—102no—
189C4⋊C4—102no—
190C4⋊C4—101no—
191C4⋊C4—101no—
192C4⋊C4—101no—
193C4⋊C4—101no—
194C4⋊C4C22×D512yes—
195C4⋊C4C22×D511yescharacteristic
196C22⋊C4—101no—
197C22⋊C4—101no—
198C22⋊C4—101no—
199C22⋊C4—101no—
200C22⋊C4—101no—
201C42—21no—
202C42—51no—
203C42—51no—
204C42—51no—
205C42C22×D511yescharacteristic
206C2×C5#53611yescharacteristic
207C2×C5C2×AGL(1,ℤ/8)11yescharacteristic
208C2×C5C2×#13711yescharacteristic
209D5—22no—
210D5—81no—
211C23—51no—
212C23—101no—
213Q8—21no—
214Q8—21no—
215Q8—42no—
216Q8—204no—
217Q8—202no—
218D4—101no—
219D4—101no—
220D4—202no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
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—102no—
233C2×C4—204no—
234C2×C4—202no—
235C2×C4D4×D511yescharacteristic
236C2×C4D4×D511yescharacteristic
237C2×C4C23×D511yescharacteristic
238C8—22no—
239C8—102no—
240C5#323911yescharacteristic, complemented, Sylow
241C22—52no—
242C22—101no—
243C22—101no—
244C22—201no—
245C22—201no—
246C22—201no—
247C22C2×D4×D511yescharacteristic
248C4—21no—
249C4—42no—
250C4—41no—
251C4—41no—
252C4—101no—
253C4—101no—
254C4—101no—
255C4—202no—
256C4—201no—
257C4#406012yes—
258C4#414711yescharacteristic
259C4#415011yescharacteristic
260C2—102no—
261C2—401no—
262C2#6596211yescharacteristic
263C2C2×#406011yescharacteristic
264C2D5×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#475C2
socleC22×C5C22×D4
prime radical#4041C22
hypercenter#475D5
hypocenterC5#3239
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. D5×C4⋊Q8C2semidirect
3. C5×#475C2semidirect
4. #65376C2semidirect
5. #65309C2semidirect
7. #65145C2semidirect
8. #65135C2semidirect
9. #65124C2semidirect
10. #65098C2semidirect
11. #65084C2semidirect
87. #475D5semidirect
240. C5#3239semidirect

Maximal subgroups

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

subgroupindex
D5×C4⋊Q82
#659142
C5×#4752
#653762
#653092
#651522
#651452
#651352
#651242
#650982
#650842
#32395