Finite Group Databasebeta

← #10613690

Subgroups — #10613690

Order 640.

364 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 119 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
1#66062C211yesmaximal, characteristic, complemented
2#66025C211yesmaximal, characteristic
3C5×#501C211yesmaximal, characteristic, complemented
4#65378C211yesmaximal, characteristic, complemented
5#65358C211yesmaximal, characteristic, complemented
6#65175C212yesmaximal
7#65162C212yesmaximal, complemented
8#65157C212yesmaximal, complemented
9#65141C212yesmaximal, complemented
10#65004C211yesmaximal, characteristic, complemented
11#64996C211yesmaximal, characteristic, complemented
12C5×C4⋊Q8C2211yescharacteristic
13C5×#125C2211yescharacteristic
14#4092—21no—
15Q8×Dic5—21no—
16C2×Dic20C2212yes—
17C2×#677C2212yes—
18C2×#676C2212yes—
19#4044—21no—
20#4043C2212yes—
21#4043C2211yescharacteristic
22#4041C2211yescharacteristic
23#4040—21no—
24#4039—21no—
25#4039C2211yescharacteristic
26#4038—21no—
27#4038—21no—
28#4036—21no—
29#4033C2212yes—
30#4033C2211yescharacteristic
31#4021C2211yescharacteristic
32C42×D5C2211yescharacteristic
33#4015C2211yescharacteristic
34C5×#107C2212yes—
35C5×#106C2212yes—
36C5×#97C2211yescharacteristic
37C8×Dic5C2212yes—
38#3942C2212yes—
39#3942C2212yes—
40#3942C2212yes—
41#3941C2212yes—
42#3935C2211yescharacteristic
43#3172—51nomaximal, Sylow
44C2×C5×Q8—21no—
45C2×D20—21no—
46C2×D20C2311yescharacteristic
47C2×C4×D5—21no—
48C2×C4×D5D411yescharacteristic
49C2×C4×D5D411yescharacteristic
50C2×C4×D5C2311yescharacteristic
51C2×Dic10C2312yes—
52C2×Dic10C2311yescharacteristic
53C2×C5×C8C2312yes—
54C5×C4⋊C4—21no—
55C5×C4⋊C4—21no—
56C5×C4⋊C4—21no—
57C5×C4⋊C4C2311yescharacteristic
58C5×C4⋊C4C2311yescharacteristic
59C5×C4⋊C4C2312yes—
60C42×C5C2311yescharacteristic
61#685—22no—
62#685—21no—
63#685—21no—
64#685—21no—
65#685—21no—
66#685—21no—
67C4⋊Dic5—21no—
68C4⋊Dic5—21no—
69C4⋊Dic5—22no—
70C4⋊Dic5—21no—
71#683—22no—
72#683—21no—
73C4×Dic5—21no—
74C4×Dic5—22no—
75C4×Dic5D411yescharacteristic
76C4×Dic5D411yescharacteristic
77C4×Dic5C2311yescharacteristic
78C2×#168C2312yes—
79Dic20—24no—
80#677—24no—
81#676—24no—
82#533—51no—
83#529—51no—
84#501D511yescharacteristic, complemented
85#497—51no—
86#491—51no—
87#489—51no—
88#470—52no—
89#468—52no—
90C4×Q16—52no—
91C4×SD16—52no—
92C4×M16—51no—
93C22×D5—21no—
94C22×D5C2×D411yescharacteristic
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—22no—
103C2×Dic5—21no—
104C2×Dic5C2×D411yescharacteristic
105C2×Dic5C2×D411yescharacteristic
106C2×Dic5C2×D411yescharacteristic
107D20—22no—
108D20—42no—
109C4×D5—22no—
110C4×D5—22no—
111C4×D5—41no—
112C4×D5—42no—
113Dic10—22no—
114Dic10—22no—
115Dic10—22no—
116C5×C8#4114yes—
117#168—22no—
118C2×Q16—52no—
119C2×SD16—52no—
120C2×M16—52no—
121C4⋊Q8—51no—
122C4⋊Q8C2×D511yescharacteristic
123#126—101no—
124#125—101no—
125#125C2×D511yescharacteristic
126#124—51no—
127#123—101no—
128C22⋊Q8—51no—
129C22⋊Q8—52no—
130C22⋊Q8—101no—
131#121—51no—
132C4×Q8—51no—
133C4×Q8—52no—
134C4×Q8—101no—
135C4×D4—51no—
136C4×D4—101no—
137#117—101no—
138#117—101no—
139C2×C42—51no—
140#107C2×D512yes—
141#106C2×D512yes—
142#103—52no—
143#103—52no—
144#103—52no—
145#102—52no—
146#97—51no—
147#97C2×D511yescharacteristic
148C4×C8—52no—
149C22×C5C22×D411yescharacteristic
150C2×D5—21no—
151C2×D5—21no—
152C2×D5—21no—
153C2×D5—41no—
154C2×D5—41no—
155C2×D5—41no—
156C4×C5—21no—
157C4×C5—21no—
158C4×C5—41no—
159C4×C5—41no—
160C4×C5—42no—
161C4×C5C2×#4112yes—
162Dic5—21no—
163Dic5—21no—
164Dic5—42no—
165Dic5—41no—
166Dic5#13712yes—
167C2×Q8—21no—
168C2×Q8—51no—
169C2×Q8—52no—
170C2×D4—51no—
171C2×D4—101no—
172C22×C4—51no—
173C22×C4—51no—
174C22×C4—51no—
175C22×C4—101no—
176Q16—104no—
177SD16—104no—
178M16—104no—
179C2×C8—52no—
180C2×C8C22×D512yes—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—101no—
185C4⋊C4—102no—
186C4⋊C4—101no—
187C4⋊C4—102no—
188C4⋊C4—101no—
189C4⋊C4—101no—
190C4⋊C4C22×D512yes—
191C4⋊C4C22×D511yescharacteristic
192C4⋊C4C22×D511yescharacteristic
193C22⋊C4—101no—
194C22⋊C4—101no—
195C22⋊C4—102no—
196C22⋊C4—101no—
197C22⋊C4—101no—
198C22⋊C4—101no—
199C42—51no—
200C42—51no—
201C42—51no—
202C42—101no—
203C42—102no—
204C42C22×D511yescharacteristic
205C2×C5#53211yescharacteristic
206C2×C5C2×#13711yescharacteristic
207C2×C5#57511yescharacteristic
208D5—41no—
209D5—81no—
210C23—51no—
211C23—101no—
212Q8—42no—
213Q8—102no—
214Q8—102no—
215Q8—102no—
216D4—102no—
217D4—202no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—51no—
222C2×C4—51no—
223C2×C4—51no—
224C2×C4—102no—
225C2×C4—102no—
226C2×C4—101no—
227C2×C4—102no—
228C2×C4—201no—
229C2×C4—202no—
230C2×C4D4×D511yescharacteristic
231C2×C4D4×D511yescharacteristic
232C2×C4C23×D511yescharacteristic
233C8—102no—
234C8#71314yes—
235C5#317211yescharacteristic, complemented, Sylow
236C22—101no—
237C22—101no—
238C22—101no—
239C22—201no—
240C22—201no—
241C22—201no—
242C22C2×D4×D511yescharacteristic
243C4—21no—
244C4—21no—
245C4—41no—
246C4—42no—
247C4—41no—
248C4—52no—
249C4—101no—
250C4—101no—
251C4—201no—
252C4—202no—
253C4C2×#71312yes—
254C2—201no—
255C2—401no—
256C2#6605911yescharacteristic
257C2#6610711yescharacteristic
258C2D5×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#501C2
socleC22×C5C22×D4
prime radical#4041C22
hypercenter#501D5
hypocenterC5#3172
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. #66062C2semidirect
3. C5×#501C2semidirect
4. #65378C2semidirect
5. #65358C2semidirect
7. #65162C2semidirect
8. #65157C2semidirect
9. #65141C2semidirect
10. #65004C2semidirect
11. #64996C2semidirect
84. #501D5semidirect
235. C5#3172semidirect

Maximal subgroups

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

subgroupindex
#660622
#660252
C5×#5012
#653782
#653582
#651752
#651622
#651572
#651412
#650042
#649962
#31725