Finite Group Databasebeta

← #10605857

Subgroups — #10605857

Order 640.

814 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 814 conjugacy classes of subgroups — too many to draw. Only its 157 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×#4075C211yesmaximal, characteristic, complemented
2C22×#685C211yesmaximal, characteristic, complemented
3C2×#4028C211yesmaximal, characteristic
4C2×D5×C22⋊C4C211yesmaximal, characteristic, complemented
5C5×#381C211yesmaximal, characteristic, complemented
6#65247C211yesmaximal, characteristic, complemented
7#65235C211yesmaximal, characteristic, complemented
8#64964C212yesmaximal, complemented
9#64961C212yesmaximal, complemented
10#64956C212yesmaximal, complemented
11#64954C212yesmaximal, complemented
12C24×D5C2211yescharacteristic
13C23×C4×C5C2211yescharacteristic
14C22×C22⋊D5C2211yescharacteristic
15C23×Dic5C2211yescharacteristic
16C22×D20C2211yescharacteristic
17C22×D20C2211yescharacteristic
18C22×C4×D5C2212yes—
19C2×C5×C22⋊C4C2211yescharacteristic
20C2×C5×C22⋊C4C2211yescharacteristic
21C2×C22⋊Dic5C2211yescharacteristic
22#4075—24no—
23C2×#685—24no—
24C2×#685C2212yes—
25C2×#685C2211yescharacteristic
26C2×#685C2211yescharacteristic
27C2×#685C2212yes—
28C2×#685C2212yes—
29C2×#685C2212yescomplemented
30C2×#685C2212yescomplemented
31C2×#683C2212yescomplemented
32C2×#683C2212yescomplemented
33#4028—24no—
34D5×C22⋊C4—24no—
35C5×#95C2212yescomplemented
36C5×#95C2212yescomplemented
37#3963C2212yescomplemented
38#3963C2212yescomplemented
39#2412—51nomaximal, Sylow
40C24×C5C2311yescharacteristic
41C23×D5—22no—
42C23×D5—22no—
43C23×D5—24no—
44C23×D5—42no—
45C23×D5D414yes—
46C23×D5C2311yescharacteristic
47C23×D5C2311yescharacteristic
48C23×D5C2311yescharacteristic
49C22×C4×C5—22no—
50C22×C4×C5—22no—
51C22×C4×C5—22no—
52C22×C4×C5C2312yes—
53C22×C4×C5C2311yescharacteristic
54C22×C4×C5C2311yescharacteristic
55C22×C4×C5C2312yes—
56C2×C22⋊D5—22no—
57C2×C22⋊D5—22no—
58C2×C22⋊D5—22no—
59C22×Dic5—22no—
60C22×Dic5—42no—
61C22×Dic5C2312yes—
62C22×Dic5C2311yescharacteristic
63C22×Dic5C2312yes—
64C2×D20—22no—
65C2×D20—22no—
66C2×D20—24no—
67C2×D20—42no—
68C2×C4×D5—24no—
69C2×C4×D5—24no—
70C2×C4×D5—42no—
71C5×C22⋊C4—22no—
72C5×C22⋊C4—22no—
73C22⋊Dic5D414yescomplemented
74#685—22no—
75#685—22no—
76#685—24no—
77#685—24no—
78#685—24no—
79#685—24no—
80#685—42no—
81#683—24no—
82#683—42no—
83C2×#123—51no—
84C2×#120—51no—
85C22×C22⋊C4—51no—
86C22×C22⋊C4—51no—
87#397—52no—
88#394—52no—
89#386—51no—
90#386—52no—
91#385—51no—
92#381D511yescharacteristic, complemented
93#380—52no—
94C23×C5—22no—
95C23×C5—22no—
96C23×C5C2×D412yes—
97C23×C5C2×D412yes—
98C23×C5#4112yes—
99C23×C5C2411yescharacteristic
100C22×D5—21no—
101C22×D5—21no—
102C22×D5—22no—
103C22×D5—28no—
104C22×D5—21no—
105C22×D5—21no—
106C22×D5—22no—
107C22×D5—22no—
108C22×D5—28no—
109C22×D5—21no—
110C22×D5—21no—
111C22×D5—22no—
112C22×D5—21no—
113C22×D5—22no—
114C22×D5—44no—
115C22×D5—48no—
116C22×D5—48no—
117C22×D5C2×D412yes—
118C22×D5C2×D412yes—
119C22×D5#4114yes—
120C2×C4×C5—22no—
121C2×C4×C5—22no—
122C2×C4×C5—22no—
123C2×C4×C5—21no—
124C2×C4×C5—21no—
125C2×C4×C5—22no—
126C2×C4×C5—22no—
127C2×C4×C5—22no—
128C2×C4×C5—22no—
129C2×C4×C5—22no—
130C2×C4×C5—44no—
131C22⋊D5—44no—
132C2×Dic5—22no—
133C2×Dic5—22no—
134C2×Dic5—21no—
135C2×Dic5—22no—
136C2×Dic5—21no—
137C2×Dic5—21no—
138C2×Dic5—22no—
139C2×Dic5—22no—
140C2×Dic5—44no—
141C2×Dic5C2×D414yes—
142D20—44no—
143D20—44no—
144C4×D5—48no—
145C25—51no—
146C22×D4—51no—
147C22×D4—51no—
148C22×D4—51no—
149C23×C4—51no—
150C23×C4—52no—
151C23×C4C2×D511yescharacteristic
152#123—104no—
153#120—104no—
154C2×C4⋊C4—52no—
155C2×C4⋊C4—52no—
156C2×C22⋊C4—51no—
157C2×C22⋊C4—52no—
158C2×C22⋊C4—52no—
159C2×C22⋊C4—52no—
160C2×C22⋊C4—51no—
161C2×C22⋊C4—51no—
162C2×C22⋊C4—52no—
163C2×C22⋊C4—52no—
164C2×C22⋊C4—104no—
165C2×C22⋊C4—104no—
166C2×C22⋊C4C2×D511yescharacteristic
167C2×C22⋊C4C2×D511yescharacteristic
168#95—52no—
169#95—52no—
170#95C2×D512yescomplemented
171#95C2×D512yescomplemented
172C22×C5—22no—
173C22×C5—22no—
174C22×C5—24no—
175C22×C5—24no—
176C22×C5#12114yes—
177C22×C5C22×D411yescharacteristic
178C22×C5C22×D411yescharacteristic
179C22×C5C2×#4111yescharacteristic
180C22×C5C2×#4112yes—
181C22×C5H(5,𝔽2)12yes—
182C2×D5—22no—
183C2×D5—22no—
184C2×D5—24no—
185C2×D5—24no—
186C2×D5—22no—
187C2×D5—22no—
188C2×D5—22no—
189C2×D5—416no—
190C2×D5—42no—
191C2×D5—42no—
192C2×D5—41no—
193C2×D5—41no—
194C2×D5—41no—
195C2×D5—42no—
196C2×D5—42no—
197C2×D5#12314yescomplemented
198C4×C5—42no—
199C4×C5—41no—
200C4×C5—41no—
201C4×C5—42no—
202Dic5—24no—
203Dic5—41no—
204Dic5—42no—
205C24—51no—
206C24—51no—
207C24—54no—
208C24—51no—
209C24—104no—
210C24—102no—
211C24—102no—
212C24—202no—
213C24C22×D511yescharacteristic
214C2×D4—102no—
215C2×D4—102no—
216C2×D4—104no—
217C2×D4—102no—
218C2×D4—102no—
219C2×D4—102no—
220C2×D4—202no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—52no—
225C22×C4—52no—
226C22×C4—51no—
227C22×C4—104no—
228C22×C4—104no—
229C22×C4—102no—
230C22×C4—202no—
231C22×C4—202no—
232C22×C4C22×D511yescharacteristic
233C22×C4C22×D512yes—
234C22×C4C22×D512yes—
235C22×C4C22×D511yescharacteristic
236C4⋊C4—104no—
237C4⋊C4—202no—
238C22⋊C4—22no—
239C22⋊C4—22no—
240C22⋊C4—54no—
241C22⋊C4—104no—
242C22⋊C4—104no—
243C22⋊C4—104no—
244C22⋊C4—104no—
245C22⋊C4—102no—
246C22⋊C4—102no—
247C22⋊C4—202no—
248C2×C5—24no—
249C2×C5C2×#12111yescharacteristic
250C2×C5C2×#12311yescharacteristic
251C2×C5#53411yescharacteristic
252C2×C5#54612yes—
253C2×C5#55112yes—
254D5—24no—
255D5—42no—
256D5—81no—
257C23—22no—
258C23—22no—
259C23—52no—
260C23—54no—
261C23—52no—
262C23—108no—
263C23—101no—
264C23—101no—
265C23—102no—
266C23—101no—
267C23—101no—
268C23—102no—
269C23—102no—
270C23—108no—
271C23—101no—
272C23—101no—
273C23—101no—
274C23—102no—
275C23—102no—
276C23—204no—
277C23—208no—
278C23—208no—
279C23#70912yes—
280C23D4×D512yes—
281C23D4×D512yes—
282C23C23×D511yescharacteristic
283D4—204no—
284D4—204no—
285D4—204no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—44no—
297C2×C4—54no—
298C2×C4—102no—
299C2×C4—102no—
300C2×C4—101no—
301C2×C4—102no—
302C2×C4—101no—
303C2×C4—101no—
304C2×C4—102no—
305C2×C4—102no—
306C2×C4—208no—
307C2×C4—204no—
308C5#241211yescharacteristic, complemented, Sylow
309C22—24no—
310C22—22no—
311C22—22no—
312C22—24no—
313C22—54no—
314C22—102no—
315C22—104no—
316C22—102no—
317C22—104no—
318C22—102no—
319C22—102no—
320C22—102no—
321C22—2016no—
322C22—202no—
323C22—202no—
324C22—201no—
325C22—202no—
326C22—201no—
327C22—201no—
328C22—202no—
329C22#403014yes—
330C22C2×#70911yescharacteristic
331C22C2×D4×D511yescharacteristic
332C22C2×D4×D511yescharacteristic
333C22D5×#4112yes—
334C22#414912yes—
335C4—42no—
336C4—41no—
337C4—41no—
338C4—42no—
339C4—104no—
340C4—201no—
341C4—202no—
342C2—24no—
343C2—104no—
344C2—202no—
345C2—401no—
346C2C2×#403011yescharacteristic
347C2#6586112yes—
348C2D5×#12311yescharacteristic
349C2#6598711yescharacteristic
350C2#6598812yes—
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#381C2
prime radicalC2×#4028C2
hypercenter#381D5
hypocenterC5#2412
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
1. C2×#4075C2semidirect
2. C22×#685C2semidirect
4. C2×D5×C22⋊C4C2semidirect
5. C5×#381C2semidirect
6. #65247C2semidirect
7. #65235C2semidirect
8. #64964C2semidirect
9. #64961C2semidirect
10. #64956C2semidirect
11. #64954C2semidirect
29. C2×#685C22semidirect
30. C2×#685C22semidirect
31. C2×#683C22semidirect
32. C2×#683C22semidirect
35. C5×#95C22semidirect
36. C5×#95C22semidirect
37. #3963C22semidirect
38. #3963C22semidirect
73. C22⋊Dic5D4semidirect
92. #381D5semidirect
170. #95C2×D5semidirect
171. #95C2×D5semidirect
197. C2×D5#123semidirect
308. C5#2412semidirect

Maximal subgroups

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

subgroupindex
C2×#40752
C22×#6852
C2×#40282
C2×D5×C22⋊C42
C5×#3812
#652472
#652352
#649642
#649612
#649562
#649542
#24125