Finite Group Databasebeta

← #10613693

Subgroups — #10613693

Order 640.

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

normal subgroups only

This group has 410 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#66059C211yesmaximal, characteristic, complemented
2#66025C211yesmaximal, characteristic, complemented
3C5×#501C211yesmaximal, characteristic, complemented
4#65378C211yesmaximal, characteristic, complemented
5#65356C211yesmaximal, characteristic, complemented
6#65178C212yesmaximal, complemented
7#65172C212yesmaximal, complemented
8#65158C212yesmaximal, complemented
9#65153C212yesmaximal, complemented
10#65001C211yesmaximal, characteristic, complemented
11D5×#97C211yesmaximal, characteristic, complemented
12C2×#713—21no—
13C5×C4⋊Q8C2211yescharacteristic
14C5×#125C2211yescharacteristic
15#4093—21no—
16C2×D40C2212yes—
17C2×#677C2212yes—
18C2×C8×D5C2212yes—
19#4044—21no—
20#4043C2211yescharacteristic
21#4041—21no—
22#4041C2212yes—
23#4041C2211yescharacteristic
24#4040—21no—
25#4039—21no—
26#4039—21no—
27#4039C2212yes—
28#4039C2211yescharacteristic
29#4038—21no—
30#4033C2211yescharacteristic
31#4021C2211yescharacteristic
32#4020C2211yescharacteristic
33C42×D5C2211yescharacteristic
34C5×#107C2212yes—
35C5×#106C2212yes—
36C5×#97C2211yescharacteristic
37#3947C2212yes—
38#3942C2212yes—
39#3941C2212yes—
40#3941C2212yes—
41#3941C2212yes—
42#3935C2211yescharacteristic
43#3180—51nomaximal, Sylow
44C2×C5×Q8—21no—
45#713—44no—
46C2×D20—22no—
47C2×D20—21no—
48C2×D20—21no—
49C2×D20—21no—
50C2×D20C2312yes—
51C2×D20C2311yescharacteristic
52C2×C4×D5—22no—
53C2×C4×D5—21no—
54C2×C4×D5D411yescharacteristic
55C2×C4×D5D411yescharacteristic
56C2×C4×D5C2311yescharacteristic
57C2×Dic10C2311yescharacteristic
58C2×C5×C8C2312yes—
59C5×C4⋊C4—21no—
60C5×C4⋊C4—21no—
61C5×C4⋊C4—21no—
62C5×C4⋊C4C2311yescharacteristic
63C5×C4⋊C4C2311yescharacteristic
64C5×C4⋊C4C2312yes—
65C42×C5C2311yescharacteristic
66#685—21no—
67#685—21no—
68#685—21no—
69#685—21no—
70#685—22no—
71#685—21no—
72#685—22no—
73C4⋊Dic5—21no—
74#683—21no—
75C4×Dic5—21no—
76C4×Dic5D411yescharacteristic
77C4×Dic5D411yescharacteristic
78C4×Dic5C2311yescharacteristic
79C2×#168C2312yes—
80D40—24no—
81#677—24no—
82C8×D5—24no—
83#532—51no—
84#529—51no—
85#501D511yescharacteristic, complemented
86#496—51no—
87#490—51no—
88#489—51no—
89#466—52no—
90#465—52no—
91#442—52no—
92#440—52no—
93C2×#97—51no—
94C22×D5—21no—
95C22×D5—22no—
96C22×D5C2×D411yescharacteristic
97C5×Q8—42no—
98C2×C4×C5—21no—
99C2×C4×C5—21no—
100C2×C4×C5—22no—
101C2×C4×C5C2×D411yescharacteristic
102C2×C4×C5C2×D411yescharacteristic
103C2×C4×C5C2411yescharacteristic
104C2×Dic5—21no—
105C2×Dic5C2×D411yescharacteristic
106C2×Dic5C2×D411yescharacteristic
107C2×Dic5C2×D411yescharacteristic
108D20—22no—
109D20—22no—
110D20—22no—
111D20—42no—
112D20—42no—
113D20—42no—
114D20—44no—
115C4×D5—22no—
116C4×D5—22no—
117C4×D5—41no—
118C4×D5—42no—
119C4×D5—44no—
120Dic10—22no—
121C5×C8#4114yescomplemented
122#168—22no—
123C2×#41—101no—
124C2×SD16—52no—
125C2×D8—52no—
126C22×C8—52no—
127C4⋊Q8C2×D511yescharacteristic
128#127—51no—
129#126—101no—
130#125C2×D511yescharacteristic
131#124—51no—
132#124—101no—
133#123—101no—
134C22⋊Q8—51no—
135#121—51no—
136#121—52no—
137#121—101no—
138C4×Q8—51no—
139C4×D4—51no—
140C4×D4—52no—
141C4×D4—101no—
142C4×D4—101no—
143#117—101no—
144C2×C42—51no—
145#107C2×D512yes—
146#106C2×D512yes—
147#103—52no—
148#102—52no—
149#102—52no—
150#102—52no—
151#97—52no—
152#97—51no—
153#97C2×D511yescharacteristic
154C22×C5C22×D411yescharacteristic
155C2×D5—21no—
156C2×D5—21no—
157C2×D5—42no—
158C2×D5—41no—
159C2×D5—42no—
160C2×D5—41no—
161C2×D5—41no—
162C2×D5—42no—
163C2×D5AGL(1,ℤ/8)12yes—
164C4×C5—21no—
165C4×C5—21no—
166C4×C5—42no—
167C4×C5—41no—
168C4×C5—41no—
169C4×C5C2×#4112yes—
170Dic5—21no—
171Dic5—21no—
172Dic5—21no—
173Dic5—41no—
174#41—204no—
175C2×Q8—21no—
176C2×Q8—51no—
177C2×D4—51no—
178C2×D4—52no—
179C2×D4—101no—
180C2×D4—102no—
181C2×D4—101no—
182C2×D4—101no—
183C22×C4—51no—
184C22×C4—51no—
185C22×C4—51no—
186C22×C4—101no—
187C22×C4—102no—
188SD16—104no—
189D8—104no—
190C2×C8—52no—
191C2×C8—104no—
192C2×C8C22×D512yes—
193C4⋊C4—21no—
194C4⋊C4—21no—
195C4⋊C4—21no—
196C4⋊C4—101no—
197C4⋊C4—101no—
198C4⋊C4C22×D511yescharacteristic
199C4⋊C4C22×D511yescharacteristic
200C4⋊C4C22×D512yes—
201C22⋊C4—101no—
202C22⋊C4—102no—
203C22⋊C4—101no—
204C22⋊C4—102no—
205C22⋊C4—101no—
206C22⋊C4—101no—
207C22⋊C4—101no—
208C42—51no—
209C42—51no—
210C42—51no—
211C42—101no—
212C42C22×D511yescharacteristic
213C2×C5#53211yescharacteristic
214C2×C5C2×AGL(1,ℤ/8)11yescharacteristic
215C2×C5#57511yescharacteristic
216D5—22no—
217D5—82no—
218D5—81no—
219C23—51no—
220C23—101no—
221C23—102no—
222Q8—42no—
223Q8—102no—
224D4—102no—
225D4—102no—
226D4—102no—
227D4—202no—
228D4—202no—
229D4—204no—
230D4—202no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—51no—
235C2×C4—51no—
236C2×C4—51no—
237C2×C4—102no—
238C2×C4—102no—
239C2×C4—101no—
240C2×C4—201no—
241C2×C4—204no—
242C2×C4—202no—
243C2×C4D4×D511yescharacteristic
244C2×C4D4×D511yescharacteristic
245C2×C4C23×D511yescharacteristic
246C8—102no—
247C8#71314yescomplemented
248C5#318011yescharacteristic, complemented, Sylow
249C22—52no—
250C22—101no—
251C22—101no—
252C22—201no—
253C22—202no—
254C22—202no—
255C22—201no—
256C22—201no—
257C22—202no—
258C22C2×D4×D511yescharacteristic
259C4—21no—
260C4—21no—
261C4—42no—
262C4—41no—
263C4—41no—
264C4—101no—
265C4—101no—
266C4—101no—
267C4—201no—
268C4C2×#71312yes—
269C2—102no—
270C2—402no—
271C2—401no—
272C2#6605911yescharacteristic
273C2D5×AGL(1,ℤ/8)11yescharacteristic
274C2#6611111yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#501C2
socleC22×C5C22×D4
hypercenter#501D5
hypocenterC5#3180
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. #66059C2semidirect
2. #66025C2semidirect
3. C5×#501C2semidirect
4. #65378C2semidirect
5. #65356C2semidirect
6. #65178C2semidirect
7. #65172C2semidirect
8. #65158C2semidirect
9. #65153C2semidirect
10. #65001C2semidirect
11. D5×#97C2semidirect
85. #501D5semidirect
121. C5×C8#41semidirect
247. C8#713semidirect
248. C5#3180semidirect

Maximal subgroups

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

subgroupindex
#660592
#660252
C5×#5012
#653782
#653562
#651782
#651722
#651582
#651532
#650012
D5×#972
#31805