Finite Group Databasebeta

← #10613713

Subgroups — #10613713

Order 640.

362 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 113 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#66025C211yesmaximal, characteristic
3C5×#501C211yesmaximal, characteristic, complemented
4#65378C211yesmaximal, characteristic, complemented
5#65354C211yesmaximal, characteristic, complemented
6#65171C212yesmaximal
7#65164C212yesmaximal, complemented
8#65159C212yesmaximal, complemented
9#65151C212yesmaximal, complemented
10#65003C211yesmaximal, characteristic, complemented
11#64994C211yesmaximal, characteristic, complemented
12C2×Q8×D5—21no—
13C5×C4⋊Q8C2211yescharacteristic
14C5×#125C2211yescharacteristic
15#4090—21no—
16#4044—21no—
17#4043C2211yescharacteristic
18#4041C2211yescharacteristic
19#4040—21no—
20#4039—21no—
21#4039C2211yescharacteristic
22#4038—21no—
23D5×C4⋊C4—21no—
24D5×C4⋊C4C2212yes—
25#4034—21no—
26#4034C2212yes—
27#4033C2211yescharacteristic
28#4021C2211yescharacteristic
29C42×D5C2211yescharacteristic
30#4015C2211yescharacteristic
31C5×#107C2212yes—
32C5×#106C2212yes—
33C5×#97C2211yescharacteristic
34#3953C2212yes—
35#3952C2212yes—
36#3948C2212yes—
37#3946C2212yes—
38#3942C2212yes—
39#3941C2212yes—
40#3940C2212yes—
41#3939C2212yes—
42#3935C2211yescharacteristic
43#3238—51nomaximal, Sylow
44C2×C5×Q8—21no—
45Q8×D5—44no—
46C2×D20—21no—
47C2×D20C2311yescharacteristic
48C2×C4×D5—22no—
49C2×C4×D5—21no—
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⋊C4—21no—
59C5×C4⋊C4—21no—
60C5×C4⋊C4C2311yescharacteristic
61C5×C4⋊C4C2311yescharacteristic
62C5×C4⋊C4C2312yes—
63C42×C5C2311yescharacteristic
64#685—21no—
65#685—21no—
66#685—21no—
67#685—21no—
68#685—21no—
69C4⋊Dic5—21no—
70C4⋊Dic5—21no—
71C4⋊Dic5C2312yes—
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—51no—
83#501D511yescharacteristic, complemented
84#489—51no—
85#489—51no—
86#483—52no—
87#480—52no—
88#477—52no—
89#476—52no—
90#432—51no—
91C22×D5—21no—
92C22×D5C2×D411yescharacteristic
93C5×Q8—42no—
94C2×C4×C5—21no—
95C2×C4×C5—22no—
96C2×C4×C5—21no—
97C2×C4×C5C2×D411yescharacteristic
98C2×C4×C5C2×D411yescharacteristic
99C2×C4×C5C2411yescharacteristic
100C2×Dic5—21no—
101C2×Dic5—22no—
102C2×Dic5C2×D411yescharacteristic
103C2×Dic5C2×D411yescharacteristic
104C2×Dic5C2×D411yescharacteristic
105D20—22no—
106D20—42no—
107C4×D5—22no—
108C4×D5—22no—
109C4×D5—22no—
110C4×D5—44no—
111C4×D5—42no—
112Dic10—22no—
113Dic10—44no—
114Dic10—42no—
115C5×C8—22no—
116#168—22no—
117C22×Q8—101no—
118C4⋊Q8—52no—
119C4⋊Q8—51no—
120C4⋊Q8—101no—
121C4⋊Q8—101no—
122C4⋊Q8C2×D511yescharacteristic
123#126—101no—
124#125C2×D511yescharacteristic
125#124—51no—
126#123—101no—
127C22⋊Q8—51no—
128#121—51no—
129C4×Q8—51no—
130C4×D4—51no—
131C4×D4—101no—
132#117—101no—
133C2×C4⋊C4—52no—
134C2×C4⋊C4—101no—
135C2×C42—51no—
136#107—52no—
137#107C2×D512yes—
138#106—52no—
139#106C2×D512yes—
140C4⋊C8—52no—
141#103—52no—
142#103—52no—
143#102—52no—
144#102—52no—
145C22⋊C8—52no—
146#97—51no—
147#97C2×D511yescharacteristic
148C22×C5C22×D411yescharacteristic
149C2×D5—21no—
150C2×D5—21no—
151C2×D5—41no—
152C2×D5—41no—
153C2×D5—41no—
154C2×D5AGL(1,ℤ/8)12yes—
155C4×C5—21no—
156C4×C5—21no—
157C4×C5—42no—
158C4×C5—41no—
159C4×C5—41no—
160C4×C52−1+412yes—
161Dic5—21no—
162Dic5—21no—
163Dic5—41no—
164Dic5—42no—
165Dic5#13712yes—
166C2×Q8—21no—
167C2×Q8—51no—
168C2×Q8—102no—
169C2×Q8—101no—
170C2×Q8—204no—
171C2×D4—51no—
172C2×D4—101no—
173C22×C4—51no—
174C22×C4—51no—
175C22×C4—51no—
176C22×C4—101no—
177C22×C4—102no—
178C2×C8—52no—
179C2×C8C22×D512yes—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—52no—
184C4⋊C4—102no—
185C4⋊C4—102no—
186C4⋊C4—101no—
187C4⋊C4—101no—
188C4⋊C4—101no—
189C4⋊C4C22×D512yes—
190C4⋊C4C22×D511yescharacteristic
191C4⋊C4C22×D511yescharacteristic
192C22⋊C4—101no—
193C22⋊C4—101no—
194C22⋊C4—101no—
195C22⋊C4—101no—
196C22⋊C4—101no—
197C42—51no—
198C42—51no—
199C42—51no—
200C42—101no—
201C42C22×D511yescharacteristic
202C2×C5#53611yescharacteristic
203C2×C5C2×AGL(1,ℤ/8)11yescharacteristic
204C2×C5C2×#13711yescharacteristic
205D5—22no—
206D5—81no—
207C23—51no—
208C23—101no—
209Q8—42no—
210Q8—102no—
211Q8—202no—
212Q8—204no—
213D4—102no—
214D4—202no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—51no—
219C2×C4—51no—
220C2×C4—51no—
221C2×C4—102no—
222C2×C4—102no—
223C2×C4—102no—
224C2×C4—101no—
225C2×C4—102no—
226C2×C4—202no—
227C2×C4—204no—
228C2×C4D4×D511yescharacteristic
229C2×C4D4×D511yescharacteristic
230C2×C4C23×D511yescharacteristic
231C8—22no—
232C8—102no—
233C5#323811yescharacteristic, complemented, Sylow
234C22—52no—
235C22—101no—
236C22—101no—
237C22—201no—
238C22—201no—
239C22—201no—
240C22C2×D4×D511yescharacteristic
241C4—21no—
242C4—21no—
243C4—42no—
244C4—41no—
245C4—41no—
246C4—52no—
247C4—101no—
248C4—101no—
249C4—201no—
250C4—202no—
251C4#414712yes—
252C2—102no—
253C2—401no—
254C2#6605811yescharacteristic
255C2D5×AGL(1,ℤ/8)11yescharacteristic
256C2D5×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#501C2
socleC22×C5C22×D4
prime radical#4041C22
hypercenter#501D5
hypocenterC5#3238
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. D5×C4⋊Q8C2semidirect
3. C5×#501C2semidirect
4. #65378C2semidirect
5. #65354C2semidirect
7. #65164C2semidirect
8. #65159C2semidirect
9. #65151C2semidirect
10. #65003C2semidirect
11. #64994C2semidirect
83. #501D5semidirect
233. 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
#660252
C5×#5012
#653782
#653542
#651712
#651642
#651592
#651512
#650032
#649942
#32385