Finite Group Databasebeta

← #10607324

Subgroups — #10607324

Order 640.

576 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4034C211yesmaximal, characteristic, complemented
2C2×#4031C211yesmaximal, characteristic
3C2×#4031C211yesmaximal, characteristic
4C2×C4×Dic10C211yesmaximal, characteristic, complemented
5C5×#388C211yesmaximal, characteristic, complemented
6#65283C211yesmaximal, characteristic, complemented
7#65246C211yesmaximal, characteristic
8#65237C211yesmaximal, characteristic, complemented
9#65237C211yesmaximal, characteristic, complemented
10#65233C211yesmaximal, characteristic, complemented
11#65229C211yesmaximal, characteristic, complemented
12#64965C211yesmaximal, characteristic, complemented
13#64959C211yesmaximal, characteristic, complemented
14#64938C211yesmaximal, characteristic, complemented
15#64935C211yesmaximal, characteristic, complemented
16C22×C22⋊D5C2211yescharacteristic
17C22×Dic10C2211yescharacteristic
18C22×Dic10C2211yescharacteristic
19C2×C5×C4⋊C4C2211yescharacteristic
20C2×C5×C22⋊C4C2211yescharacteristic
21C2×C5×C22⋊C4C2211yescharacteristic
22C2×C5×C22⋊C4C2211yescharacteristic
23C2×C42×C5C2211yescharacteristic
24C2×C22⋊Dic5C2211yescharacteristic
25C2×C22⋊Dic5C2211yescharacteristic
26C2×C22⋊Dic5C2211yescharacteristic
27C2×#685C2211yescharacteristic
28C2×#685C2211yescharacteristic
29C2×#685C2211yescharacteristic
30C2×#685C2211yescharacteristic
31C2×#685C2211yescharacteristic
32C2×#685C2211yescharacteristic
33C2×C4⋊Dic5C2211yescharacteristic
34C2×C4⋊Dic5C2211yescharacteristic
35C2×#683C2211yescharacteristic
36C2×#683C2211yescharacteristic
37C2×#683C2211yescharacteristic
38C2×#683C2211yescharacteristic
39C2×#683C2211yescharacteristic
40C2×#683C2211yescharacteristic
41C2×C4×Dic5C2211yescharacteristic
42C2×C4×Dic5C2211yescharacteristic
43C2×C4×Dic5C2211yescharacteristic
44C2×C4×Dic5C2211yescharacteristic
45#4034—24no—
46#4031—24no—
47#4031—24no—
48C4×Dic10—24no—
49C5×#95C2211yescharacteristic
50C5×#95C2211yescharacteristic
51#3963C2211yescharacteristic
52#3963C2211yescharacteristic
53#3963C2211yescharacteristic
54#3963C2211yescharacteristic
55#2545—51nomaximal, Sylow
56C24×C5C2311yescharacteristic
57C23×D5C2311yescharacteristic
58C22×C4×C5C2311yescharacteristic
59C22×C4×C5C2311yescharacteristic
60C22×C4×C5C2311yescharacteristic
61C22×C4×C5C2311yescharacteristic
62C22×C4×C5C2311yescharacteristic
63C22×C4×C5C2311yescharacteristic
64C2×C22⋊D5—22no—
65C2×C22⋊D5—22no—
66C2×C22⋊D5—22no—
67C22×Dic5C2311yescharacteristic
68C22×Dic5C2311yescharacteristic
69C22×Dic5C2311yescharacteristic
70C22×Dic5C2311yescharacteristic
71C22×Dic5C2311yescharacteristic
72C22×Dic5C2311yescharacteristic
73C22×Dic5C2311yescharacteristic
74C2×Dic10—22no—
75C2×Dic10—22no—
76C2×Dic10—22no—
77C2×Dic10—22no—
78C2×Dic10—22no—
79C2×Dic10D414yes—
80C5×C4⋊C4—22no—
81C5×C22⋊C4—22no—
82C5×C22⋊C4—22no—
83C5×C22⋊C4—22no—
84C42×C5—22no—
85C22⋊Dic5—22no—
86C22⋊Dic5—22no—
87C22⋊Dic5—22no—
88#685—22no—
89#685—22no—
90#685—22no—
91#685—22no—
92#685—22no—
93#685—22no—
94C4⋊Dic5—22no—
95C4⋊Dic5—22no—
96#683—22no—
97#683—22no—
98#683—22no—
99#683—22no—
100#683—22no—
101#683—22no—
102C4×Dic5—22no—
103C4×Dic5—22no—
104C4×Dic5—22no—
105C4×Dic5D414yes—
106C2×C4⋊Q8—51no—
107C2×#124—51no—
108C2×#124—51no—
109C2×C4×Q8—51no—
110#396—51no—
111#396—51no—
112#396—51no—
113#396—51no—
114#391—51no—
115#390—51no—
116#388—51no—
117#388—51no—
118#388—51no—
119#388D511yescharacteristic, complemented
120C4×C4⋊C4—51no—
121C23×C5—21no—
122C23×C5—21no—
123C23×C5—21no—
124C23×C5—21no—
125C23×C5—21no—
126C23×C5—21no—
127C23×C5—21no—
128C23×C5C2411yescharacteristic
129C22×D5—21no—
130C22×D5—21no—
131C22×D5—21no—
132C22×D5—21no—
133C22×D5—21no—
134C22×D5—21no—
135C22×D5—21no—
136C2×C4×C5—21no—
137C2×C4×C5—21no—
138C2×C4×C5—21no—
139C2×C4×C5—21no—
140C2×C4×C5—21no—
141C2×C4×C5—21no—
142C2×C4×C5—21no—
143C2×C4×C5—21no—
144C2×C4×C5—21no—
145C2×C4×C5—21no—
146C2×C4×C5—21no—
147C2×C4×C5—21no—
148C2×C4×C5—21no—
149C2×C4×C5—21no—
150C2×C4×C5—21no—
151C2×C4×C5C2×D412yes—
152C2×C4×C5C2×D412yes—
153C2×C4×C5#4112yes—
154C22⋊D5—44no—
155C2×Dic5—21no—
156C2×Dic5—21no—
157C2×Dic5—21no—
158C2×Dic5—21no—
159C2×Dic5—21no—
160C2×Dic5—21no—
161C2×Dic5—21no—
162C2×Dic5—21no—
163C2×Dic5—21no—
164C2×Dic5—21no—
165C2×Dic5—21no—
166C2×Dic5—21no—
167C2×Dic5—21no—
168C2×Dic5—21no—
169C2×Dic5—21no—
170C2×Dic5C2×D412yes—
171C2×Dic5C2×D412yes—
172C2×Dic5C2×D412yes—
173C2×Dic5C2×D412yes—
174C2×Dic5#4112yes—
175C2×Dic5#4112yes—
176Dic10—28no—
177Dic10—44no—
178C22×Q8—51no—
179C22×Q8—51no—
180C22×D4—51no—
181C4⋊Q8—104no—
182#124—104no—
183#124—104no—
184C4×Q8—104no—
185C2×C4⋊C4—51no—
186C2×C4⋊C4—51no—
187C2×C4⋊C4—51no—
188C2×C4⋊C4—51no—
189C2×C4⋊C4—51no—
190C2×C4⋊C4—51no—
191C2×C4⋊C4—51no—
192C2×C4⋊C4—51no—
193C2×C4⋊C4C2×D511yescharacteristic
194C2×C22⋊C4—51no—
195C2×C22⋊C4—51no—
196C2×C22⋊C4—51no—
197C2×C22⋊C4—51no—
198C2×C22⋊C4—51no—
199C2×C22⋊C4—51no—
200C2×C22⋊C4—51no—
201C2×C22⋊C4—51no—
202C2×C22⋊C4—51no—
203C2×C22⋊C4C2×D511yescharacteristic
204C2×C22⋊C4C2×D511yescharacteristic
205C2×C22⋊C4C2×D511yescharacteristic
206C2×C42—51no—
207C2×C42—51no—
208C2×C42—51no—
209C2×C42—51no—
210C2×C42C2×D511yescharacteristic
211#95—51no—
212#95—51no—
213#95—51no—
214#95—51no—
215#95C2×D511yescharacteristic
216#95C2×D511yescharacteristic
217C22×C5—41no—
218C22×C5—41no—
219C22×C5—41no—
220C22×C5—41no—
221C22×C5—41no—
222C22×C5—41no—
223C22×C5—41no—
224C22×C5C22×D411yescharacteristic
225C22×C5C22×D411yescharacteristic
226C22×C5C2×#4111yescharacteristic
227C22×C5C2×#4111yescharacteristic
228C22×C5C2×#4111yescharacteristic
229C22×C52−1+411yescharacteristic
230C22×C52−1+411yescharacteristic
231C2×D5—41no—
232C2×D5—41no—
233C2×D5—41no—
234C2×D5—41no—
235C2×D5—41no—
236C2×D5—41no—
237C2×D5—41no—
238C4×C5—22no—
239C4×C5—22no—
240C4×C5—22no—
241C4×C5—41no—
242C4×C5—41no—
243C4×C5—41no—
244Dic5—22no—
245Dic5—22no—
246Dic5—22no—
247Dic5—41no—
248Dic5—41no—
249Dic5—41no—
250Dic5#12114yes—
251C24—51no—
252C24C22×D511yescharacteristic
253C2×Q8—54no—
254C2×Q8—102no—
255C2×Q8—102no—
256C2×Q8—102no—
257C2×Q8—102no—
258C2×Q8—102no—
259C2×D4—102no—
260C2×D4—102no—
261C2×D4—102no—
262C22×C4—51no—
263C22×C4—51no—
264C22×C4—51no—
265C22×C4—51no—
266C22×C4—51no—
267C22×C4—51no—
268C22×C4—51no—
269C22×C4C22×D511yescharacteristic
270C22×C4C22×D511yescharacteristic
271C22×C4C22×D511yescharacteristic
272C22×C4C22×D511yescharacteristic
273C22×C4C22×D511yescharacteristic
274C22×C4C22×D511yescharacteristic
275C4⋊C4—22no—
276C4⋊C4—102no—
277C4⋊C4—102no—
278C4⋊C4—102no—
279C4⋊C4—102no—
280C4⋊C4—102no—
281C4⋊C4—102no—
282C4⋊C4—102no—
283C4⋊C4—102no—
284C22⋊C4—22no—
285C22⋊C4—22no—
286C22⋊C4—22no—
287C22⋊C4—102no—
288C22⋊C4—102no—
289C22⋊C4—102no—
290C22⋊C4—102no—
291C22⋊C4—102no—
292C22⋊C4—102no—
293C22⋊C4—102no—
294C22⋊C4—102no—
295C22⋊C4—102no—
296C42—22no—
297C42—54no—
298C42—102no—
299C42—102no—
300C42—102no—
301C2×C5—81no—
302C2×C5C2×#12111yescharacteristic
303C2×C5#53211yescharacteristic
304C2×C5#53611yescharacteristic
305C2×C5#54811yescharacteristic
306C2×C5#54811yescharacteristic
307C2×C5#55611yescharacteristic
308C2×C5#55611yescharacteristic
309D5—81no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—101no—
318C23—101no—
319C23—101no—
320C23—101no—
321C23—101no—
322C23—101no—
323C23—101no—
324C23C23×D511yescharacteristic
325Q8—108no—
326Q8—204no—
327D4—204no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—52no—
344C2×C4—52no—
345C2×C4—52no—
346C2×C4—52no—
347C2×C4—52no—
348C2×C4—52no—
349C2×C4—101no—
350C2×C4—101no—
351C2×C4—101no—
352C2×C4—101no—
353C2×C4—101no—
354C2×C4—101no—
355C2×C4—101no—
356C2×C4—101no—
357C2×C4—101no—
358C2×C4—101no—
359C2×C4—101no—
360C2×C4—101no—
361C2×C4—101no—
362C2×C4—101no—
363C2×C4—101no—
364C2×C4#70912yes—
365C2×C4D4×D512yes—
366C2×C4D4×D512yes—
367C5#254511yescharacteristic, complemented, Sylow
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—201no—
376C22—201no—
377C22—201no—
378C22—201no—
379C22—201no—
380C22—201no—
381C22—201no—
382C22C2×#70911yescharacteristic
383C22C2×D4×D511yescharacteristic
384C22C2×D4×D511yescharacteristic
385C22D5×#4111yescharacteristic
386C22D5×#4111yescharacteristic
387C22#415011yescharacteristic
388C22#415011yescharacteristic
389C4—22no—
390C4—22no—
391C4—22no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—54no—
396C4—102no—
397C4—102no—
398C4—102no—
399C4—201no—
400C4—201no—
401C4—201no—
402C2—81no—
403C2—401no—
404C2#6586711yescharacteristic
405C2#6588211yescharacteristic
406C2#6588611yescharacteristic
407C2D5×#12111yescharacteristic
408C2#6598211yescharacteristic
409C2#6601111yescharacteristic
410C2#6603611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#388C2
prime radicalC22×C22⋊D5C22
hypercenter#388D5
hypocenterC5#2545
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#4034C2semidirect
4. C2×C4×Dic10C2semidirect
5. C5×#388C2semidirect
6. #65283C2semidirect
8. #65237C2semidirect
9. #65237C2semidirect
10. #65233C2semidirect
11. #65229C2semidirect
12. #64965C2semidirect
13. #64959C2semidirect
14. #64938C2semidirect
15. #64935C2semidirect
119. #388D5semidirect
367. C5#2545semidirect

Maximal subgroups

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

subgroupindex
C2×#40342
C2×#40312
C2×C4×Dic102
C5×#3882
#652832
#652462
#652372
#652332
#652292
#649652
#649592
#649382
#649352
#25455