Finite Group Databasebeta

← #10609515

Subgroups — #10609515

Order 640.

604 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 147 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
1C2×#4042C212yesmaximal, complemented
2C2×#4039C211yesmaximal, characteristic
3C2×#4033C211yesmaximal, characteristic, complemented
4C5×#398C211yesmaximal, characteristic, complemented
5#65280C211yesmaximal, characteristic
6#65279C212yesmaximal, complemented
7#65269C211yesmaximal, characteristic, complemented
8#64961C211yesmaximal, characteristic
9#64958C212yesmaximal, complemented
10#64956C212yesmaximal, complemented
11#64939C211yesmaximal, characteristic, complemented
12C22×D20C2211yescharacteristic
13C22×C4×D5C2212yes—
14C22×Dic10C2211yescharacteristic
15C2×C5×C4⋊C4C2211yescharacteristic
16C2×C5×C4⋊C4C2211yescharacteristic
17C2×C5×C4⋊C4C2212yes—
18C2×#685C2212yes—
19C2×#685C2212yes—
20C2×#685C2212yes—
21C2×#685C2212yes—
22C2×#685C2212yes—
23C2×#683C2211yescharacteristic
24C2×#683C2211yescharacteristic
25C2×#683C2212yes—
26C2×#683C2212yes—
27C2×C4×Dic5C2211yescharacteristic
28C2×C4×Dic5C2211yescharacteristic
29C2×C4×Dic5C2211yescharacteristic
30#4042—28no—
31#4039—24no—
32#4033—24no—
33C5×#95C2211yescharacteristic
34C5×#95C2212yes—
35#3963C2211yescharacteristic
36#3963C2212yes—
37#3963C2212yes—
38#2536—51nomaximal, Sylow
39C23×D5C2312yes—
40C22×C4×C5C2312yes—
41C22×C4×C5C2312yes—
42C22×C4×C5C2311yescharacteristic
43C22×C4×C5C2311yescharacteristic
44C22×C4×C5C2311yescharacteristic
45C22×Dic5C2312yes—
46C22×Dic5C2311yescharacteristic
47C22×Dic5C2311yescharacteristic
48C22×Dic5C2311yescharacteristic
49C22×Dic5C2311yescharacteristic
50C2×D20—24no—
51C2×D20—22no—
52C2×C4×D5—24no—
53C2×C4×D5—24no—
54C2×C4×D5—24no—
55C2×Dic10—22no—
56C2×Dic10—22no—
57C2×Dic10D414yescomplemented
58C5×C4⋊C4—22no—
59C5×C4⋊C4—22no—
60C5×C4⋊C4—24no—
61#685—24no—
62#685—24no—
63#685—24no—
64#685—24no—
65#685—24no—
66#683—22no—
67#683—22no—
68#683—24no—
69#683—24no—
70C4×Dic5—22no—
71C4×Dic5—22no—
72C4×Dic5D414yes—
73C2×C22⋊Q8—52no—
74C2×C4×Q8—51no—
75C2×C4×D4—51no—
76#398—51no—
77#398D511yescharacteristic, complemented
78#394—51no—
79#394—51no—
80#388—52no—
81#388—52no—
82#382—51no—
83#380—52no—
84C23×C5C2411yescharacteristic
85C22×D5—22no—
86C22×D5—22no—
87C22×D5—22no—
88C22×D5—22no—
89C22×D5—22no—
90C22×D5—22no—
91C22×D5#4114yes—
92C2×C4×C5—21no—
93C2×C4×C5—21no—
94C2×C4×C5—22no—
95C2×C4×C5—21no—
96C2×C4×C5—22no—
97C2×C4×C5—22no—
98C2×C4×C5—22no—
99C2×C4×C5—22no—
100C2×C4×C5—22no—
101C2×C4×C5—22no—
102C2×C4×C5—22no—
103C2×C4×C5C2×D412yes—
104C2×C4×C5C2×D412yes—
105C2×Dic5—21no—
106C2×Dic5—21no—
107C2×Dic5—22no—
108C2×Dic5—21no—
109C2×Dic5—22no—
110C2×Dic5—22no—
111C2×Dic5—22no—
112C2×Dic5—22no—
113C2×Dic5C2×D412yes—
114C2×Dic5C2×D412yes—
115C2×Dic5C2×D412yes—
116C2×Dic5C2×D412yes—
117C2×Dic5#4112yes—
118D20—28no—
119C4×D5—48no—
120Dic10—28no—
121C22×Q8—51no—
122C22×D4—51no—
123C23×C4—52no—
124C22⋊Q8—108no—
125C4×Q8—104no—
126C4×D4—104no—
127C2×C4⋊C4—51no—
128C2×C4⋊C4—51no—
129C2×C4⋊C4—52no—
130C2×C4⋊C4—52no—
131C2×C4⋊C4C2×D511yescharacteristic
132C2×C4⋊C4C2×D511yescharacteristic
133C2×C4⋊C4C2×D512yes—
134C2×C22⋊C4—52no—
135C2×C22⋊C4—52no—
136C2×C22⋊C4—52no—
137C2×C22⋊C4—52no—
138C2×C22⋊C4—52no—
139C2×C42—51no—
140C2×C42—51no—
141C2×C42—51no—
142#95—52no—
143#95—52no—
144#95—51no—
145#95C2×D512yes—
146#95C2×D511yescharacteristic
147C22×C5C22×D411yescharacteristic
148C22×C5C22×D411yescharacteristic
149C22×C5C2×#4111yescharacteristic
150C22×C5C2×#4112yes—
151C22×C52−1+412yes—
152C2×D5—24no—
153C2×D5—24no—
154C2×D5—24no—
155C2×D5—42no—
156C2×D5—42no—
157C2×D5—42no—
158C2×D5—42no—
159C4×C5—22no—
160C4×C5—22no—
161C4×C5—42no—
162C4×C5—41no—
163C4×C5—42no—
164Dic5—22no—
165Dic5—22no—
166Dic5—41no—
167Dic5—42no—
168Dic5#12114yes—
169C24—52no—
170C2×Q8—54no—
171C2×Q8—102no—
172C2×Q8—102no—
173C2×D4—104no—
174C2×D4—102no—
175C22×C4—51no—
176C22×C4—51no—
177C22×C4—51no—
178C22×C4—52no—
179C22×C4—51no—
180C22×C4—104no—
181C22×C4—104no—
182C22×C4—104no—
183C22×C4C22×D512yes—
184C22×C4C22×D512yes—
185C22×C4C22×D511yescharacteristic
186C22×C4C22×D511yescharacteristic
187C22×C4C22×D511yescharacteristic
188C4⋊C4—22no—
189C4⋊C4—22no—
190C4⋊C4—24no—
191C4⋊C4—102no—
192C4⋊C4—104no—
193C4⋊C4—104no—
194C4⋊C4—102no—
195C22⋊C4—104no—
196C22⋊C4—104no—
197C22⋊C4—104no—
198C22⋊C4—104no—
199C22⋊C4—104no—
200C42—54no—
201C42—102no—
202C42—102no—
203C2×C5C2×#12111yescharacteristic
204C2×C5#52511yescharacteristic
205C2×C5#53611yescharacteristic
206C2×C5#54812yes—
207C2×C5#55212yes—
208D5—44no—
209C23—54no—
210C23—102no—
211C23—102no—
212C23—102no—
213C23—102no—
214C23—102no—
215C23—102no—
216C23C23×D511yescharacteristic
217Q8—108no—
218D4—108no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—52no—
231C2×C4—52no—
232C2×C4—52no—
233C2×C4—52no—
234C2×C4—52no—
235C2×C4—101no—
236C2×C4—102no—
237C2×C4—101no—
238C2×C4—101no—
239C2×C4—102no—
240C2×C4—102no—
241C2×C4—102no—
242C2×C4—102no—
243C2×C4—208no—
244C2×C4D4×D512yes—
245C2×C4D4×D512yes—
246C5#253611yescharacteristic, complemented, Sylow
247C22—104no—
248C22—104no—
249C22—104no—
250C22—202no—
251C22—202no—
252C22—202no—
253C22—202no—
254C22C2×D4×D511yescharacteristic
255C22C2×D4×D511yescharacteristic
256C22#414712yes—
257C22D5×#4111yescharacteristic
258C22D5×#4112yes—
259C4—22no—
260C4—22no—
261C4—42no—
262C4—42no—
263C4—41no—
264C4—54no—
265C4—102no—
266C4—102no—
267C4—202no—
268C4—201no—
269C2—204no—
270C2D5×#12111yescharacteristic
271C2#6596712yes—
272C2#6599011yescharacteristic
273C2#6602712yes—
274C2#6605811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#398C2
prime radicalC22×D20C22
hypercenter#398D5
hypocenterC5#2536
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#4042C2semidirect
3. C2×#4033C2semidirect
4. C5×#398C2semidirect
6. #65279C2semidirect
7. #65269C2semidirect
9. #64958C2semidirect
10. #64956C2semidirect
11. #64939C2semidirect
57. C2×Dic10D4semidirect
77. #398D5semidirect
246. C5#2536semidirect

Maximal subgroups

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

subgroupindex
C2×#40422
C2×#40392
C2×#40332
C5×#3982
#652802
#652792
#652692
#649612
#649582
#649562
#649392
#25365