Finite Group Databasebeta

← #10607271

Subgroups — #10607271

Order 640.

664 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×C22⋊C4C211yesmaximal, characteristic
2C2×#4025C211yesmaximal, characteristic, complemented
3C5×#388C211yesmaximal, characteristic, complemented
4#65283C211yesmaximal, characteristic, complemented
5#65276C211yesmaximal, characteristic, complemented
6#65244C211yesmaximal, characteristic
7#65244C211yesmaximal, characteristic
8#65242C211yesmaximal, characteristic, complemented
9#65242C211yesmaximal, characteristic, complemented
10#65229C211yesmaximal, characteristic, complemented
11C4×#685C211yesmaximal, characteristic, complemented
12#64963C211yesmaximal, characteristic, complemented
13#64959C211yesmaximal, characteristic, complemented
14#64957C211yesmaximal, characteristic, complemented
15#64957C211yesmaximal, characteristic, complemented
16C24×D5C2211yescharacteristic
17C22×C4×D5C2211yescharacteristic
18C22×C4×D5C2211yescharacteristic
19C2×C5×C4⋊C4C2211yescharacteristic, complemented
20C2×C5×C22⋊C4C2211yescharacteristic
21C2×C5×C22⋊C4C2211yescharacteristic
22C2×C5×C22⋊C4C2211yescharacteristic
23C2×C42×C5C2211yescharacteristic, complemented
24C2×C22⋊Dic5C2211yescharacteristic
25C2×C22⋊Dic5C2211yescharacteristic
26C2×C22⋊Dic5C2211yescharacteristic
27C2×#685C2211yescharacteristic
28C2×#685C2211yescharacteristic
29C2×#685C2211yescharacteristic
30C2×#685C2211yescharacteristic
31C2×#685C2211yescharacteristic
32C2×#685C2211yescharacteristic
33C2×#685C2211yescharacteristic
34C2×#685C2211yescharacteristic
35C2×#685C2211yescharacteristic
36C2×#685C2211yescharacteristic
37C2×C4⋊Dic5C2211yescharacteristic, complemented
38C2×C4⋊Dic5C2211yescharacteristic, complemented
39C2×C4⋊Dic5C2211yescharacteristic, complemented
40C2×#683C2211yescharacteristic, complemented
41C2×#683C2211yescharacteristic, complemented
42C2×C4×Dic5C2211yescharacteristic, complemented
43D5×C22⋊C4—24no—
44#4025—24no—
45C5×#95C2211yescharacteristic, complemented
46C5×#95C2211yescharacteristic, complemented
47#3963C2211yescharacteristic, complemented
48#3963C2211yescharacteristic, complemented
49#3963C2211yescharacteristic, complemented
50#3963C2211yescharacteristic, complemented
51#3963C2211yescharacteristic, complemented
52#3963C2211yescharacteristic, complemented
53#2480—51nomaximal, Sylow
54C24×C5C2311yescharacteristic
55C23×D5—22no—
56C23×D5—22no—
57C23×D5—22no—
58C23×D5—22no—
59C23×D5—22no—
60C23×D5—41no—
61C23×D5—41no—
62C23×D5C2311yescharacteristic
63C23×D5C2311yescharacteristic
64C22×C4×C5C2311yescharacteristic
65C22×C4×C5C2311yescharacteristic
66C22×C4×C5C2311yescharacteristic
67C22×C4×C5C2311yescharacteristic
68C22×C4×C5C2311yescharacteristic
69C22×C4×C5C2311yescharacteristic
70C22×Dic5C2311yescharacteristic
71C22×Dic5C2311yescharacteristic
72C22×Dic5C2311yescharacteristic
73C22×Dic5C2311yescharacteristic
74C22×Dic5C2311yescharacteristic
75C22×Dic5C2311yescharacteristic
76C2×C4×D5—22no—
77C2×C4×D5—22no—
78C2×C4×D5—22no—
79C2×C4×D5—22no—
80C2×C4×D5—41no—
81C2×C4×D5—41no—
82C5×C4⋊C4—41no—
83C5×C22⋊C4—41no—
84C5×C22⋊C4—41no—
85C5×C22⋊C4D414yes—
86C42×C5—41no—
87C22⋊Dic5—22no—
88C22⋊Dic5—22no—
89C22⋊Dic5—22no—
90#685—22no—
91#685—22no—
92#685—22no—
93#685—22no—
94#685—22no—
95#685—22no—
96#685—22no—
97#685—22no—
98#685—41no—
99#685—41no—
100C4⋊Dic5—22no—
101C4⋊Dic5—41no—
102C4⋊Dic5—41no—
103#683—22no—
104#683—22no—
105C4×Dic5—22no—
106C2×#126—51no—
107C22×C22⋊C4—51no—
108#397—51no—
109#397—51no—
110#397—51no—
111#396—51no—
112#388—51no—
113#388—51no—
114#388D511yescharacteristic, complemented
115#385—51no—
116#385—51no—
117#380—51no—
118#379—51no—
119#379—51no—
120C4×C22⋊C4—51no—
121C23×C5—21no—
122C23×C5—21no—
123C23×C5—21no—
124C23×C5—21no—
125C23×C5—21no—
126C23×C5—21no—
127C23×C5C2×D412yes—
128C23×C5C2411yescharacteristic
129C22×D5—21no—
130C22×D5—21no—
131C22×D5—21no—
132C22×D5—21no—
133C22×D5—28no—
134C22×D5—21no—
135C22×D5—21no—
136C22×D5—21no—
137C22×D5—21no—
138C22×D5—21no—
139C22×D5—21no—
140C22×D5—44no—
141C22×D5—44no—
142C22×D5—44no—
143C22×D5—44no—
144C22×D5—44no—
145C22×D5—44no—
146C22×D5#4112yes—
147C22×D5#4112yes—
148C22×D5#4112yes—
149C22×D5#4112yes—
150C2×C4×C5—21no—
151C2×C4×C5—21no—
152C2×C4×C5—21no—
153C2×C4×C5—21no—
154C2×C4×C5—21no—
155C2×C4×C5—21no—
156C2×C4×C5—21no—
157C2×C4×C5—21no—
158C2×C4×C5—21no—
159C2×C4×C5—21no—
160C2×C4×C5—21no—
161C2×C4×C5—21no—
162C2×C4×C5—21no—
163C2×C4×C5—21no—
164C2×C4×C5—21no—
165C2×C4×C5—21no—
166C2×C4×C5C2×D412yes—
167C2×C4×C5C2×D412yes—
168C2×Dic5—21no—
169C2×Dic5—21no—
170C2×Dic5—21no—
171C2×Dic5—21no—
172C2×Dic5—21no—
173C2×Dic5—21no—
174C2×Dic5—21no—
175C2×Dic5—21no—
176C2×Dic5—21no—
177C2×Dic5—21no—
178C2×Dic5—21no—
179C2×Dic5—21no—
180C2×Dic5—21no—
181C2×Dic5—21no—
182C2×Dic5—21no—
183C2×Dic5—21no—
184C2×Dic5—21no—
185C2×Dic5—21no—
186C4×D5—44no—
187C4×D5—44no—
188C25—51no—
189C23×C4—51no—
190C23×C4—51no—
191#126—104no—
192C2×C4⋊C4—51no—
193C2×C4⋊C4—51no—
194C2×C4⋊C4—51no—
195C2×C4⋊C4—51no—
196C2×C4⋊C4—51no—
197C2×C4⋊C4C2×D511yescharacteristic, complemented
198C2×C22⋊C4—51no—
199C2×C22⋊C4—51no—
200C2×C22⋊C4—51no—
201C2×C22⋊C4—51no—
202C2×C22⋊C4—51no—
203C2×C22⋊C4—51no—
204C2×C22⋊C4—51no—
205C2×C22⋊C4—51no—
206C2×C22⋊C4—51no—
207C2×C22⋊C4—51no—
208C2×C22⋊C4—51no—
209C2×C22⋊C4—51no—
210C2×C22⋊C4—51no—
211C2×C22⋊C4—104no—
212C2×C22⋊C4C2×D511yescharacteristic
213C2×C22⋊C4C2×D511yescharacteristic
214C2×C22⋊C4C2×D511yescharacteristic
215C2×C42—51no—
216C2×C42C2×D511yescharacteristic, complemented
217#95—51no—
218#95—51no—
219#95—51no—
220#95—51no—
221#95—51no—
222#95—51no—
223#95C2×D511yescharacteristic, complemented
224#95C2×D511yescharacteristic, complemented
225C22×C5—22no—
226C22×C5—22no—
227C22×C5—22no—
228C22×C5—41no—
229C22×C5—41no—
230C22×C5—41no—
231C22×C5—41no—
232C22×C5C22×D411yescharacteristic
233C22×C5C2×#4111yescharacteristic
234C22×C5C2×#4111yescharacteristic
235C22×C5C2×#4111yescharacteristic
236C22×C5C2×#4111yescharacteristic
237C22×C5H(5,𝔽2)11yescharacteristic
238C22×C5H(5,𝔽2)11yescharacteristic
239C2×D5—22no—
240C2×D5—22no—
241C2×D5—22no—
242C2×D5—22no—
243C2×D5—22no—
244C2×D5—22no—
245C2×D5—22no—
246C2×D5—22no—
247C2×D5—22no—
248C2×D5—416no—
249C2×D5—41no—
250C2×D5—41no—
251C2×D5—41no—
252C2×D5—41no—
253C2×D5#12614yescomplemented
254C4×C5—22no—
255C4×C5—22no—
256C4×C5—41no—
257C4×C5—41no—
258C4×C5—41no—
259C4×C5—41no—
260Dic5—41no—
261Dic5—41no—
262Dic5—41no—
263Dic5—41no—
264Dic5—41no—
265Dic5—41no—
266C24—51no—
267C24—51no—
268C24—102no—
269C24—102no—
270C24—102no—
271C24—102no—
272C24—102no—
273C24—201no—
274C24—201no—
275C24C22×D511yescharacteristic
276C22×C4—51no—
277C22×C4—51no—
278C22×C4—51no—
279C22×C4—51no—
280C22×C4—51no—
281C22×C4—51no—
282C22×C4—102no—
283C22×C4—102no—
284C22×C4—102no—
285C22×C4—102no—
286C22×C4—201no—
287C22×C4—201no—
288C22×C4C22×D511yescharacteristic
289C22×C4C22×D511yescharacteristic
290C22×C4C22×D511yescharacteristic
291C22×C4C22×D511yescharacteristic
292C22×C4C22×D511yescharacteristic
293C22×C4C22×D511yescharacteristic
294C4⋊C4—41no—
295C4⋊C4—102no—
296C4⋊C4—102no—
297C4⋊C4—102no—
298C4⋊C4—201no—
299C4⋊C4—201no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—102no—
303C22⋊C4—102no—
304C22⋊C4—102no—
305C22⋊C4—102no—
306C22⋊C4—102no—
307C22⋊C4—102no—
308C22⋊C4—102no—
309C22⋊C4—102no—
310C22⋊C4—102no—
311C22⋊C4—102no—
312C22⋊C4—102no—
313C22⋊C4—201no—
314C22⋊C4—201no—
315C22⋊C4D2014yes—
316C42—41no—
317C42—102no—
318C2×C5—42no—
319C2×C5#52511yescharacteristic
320C2×C5C2×#12611yescharacteristic
321C2×C5#53811yescharacteristic
322C2×C5#54611yescharacteristic
323C2×C5#54611yescharacteristic
324C2×C5#55111yescharacteristic
325C2×C5#55111yescharacteristic
326D5—24no—
327D5—42no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—52no—
335C23—52no—
336C23—52no—
337C23—52no—
338C23—108no—
339C23—101no—
340C23—101no—
341C23—101no—
342C23—101no—
343C23—101no—
344C23—101no—
345C23—101no—
346C23—101no—
347C23—101no—
348C23—101no—
349C23—204no—
350C23—204no—
351C23—204no—
352C23—204no—
353C23—204no—
354C23—204no—
355C23C2×D2012yes—
356C23C23×D511yescharacteristic
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—101no—
374C2×C4—101no—
375C2×C4—101no—
376C2×C4—101no—
377C2×C4—101no—
378C2×C4—101no—
379C2×C4—101no—
380C2×C4—101no—
381C2×C4—101no—
382C2×C4—101no—
383C2×C4—101no—
384C2×C4—101no—
385C2×C4—101no—
386C2×C4—101no—
387C2×C4—101no—
388C2×C4—101no—
389C2×C4—101no—
390C2×C4—101no—
391C2×C4—204no—
392C2×C4—204no—
393C2×C4C2×D2012yes—
394C2×C4C2×D2012yes—
395C5#248011yescharacteristic, complemented, Sylow
396C22—22no—
397C22—22no—
398C22—22no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—54no—
404C22—102no—
405C22—102no—
406C22—102no—
407C22—102no—
408C22—102no—
409C22—102no—
410C22—102no—
411C22—102no—
412C22—102no—
413C22—2016no—
414C22—201no—
415C22—201no—
416C22—201no—
417C22—201no—
418C22C22×D2011yescharacteristic
419C22#414411yescharacteristic
420C22#414411yescharacteristic
421C22D5×#4111yescharacteristic
422C22D5×#4111yescharacteristic
423C22D5×#4111yescharacteristic
424C22D5×#4111yescharacteristic
425C4—22no—
426C4—22no—
427C4—41no—
428C4—41no—
429C4—41no—
430C4—41no—
431C4—201no—
432C4—201no—
433C4—201no—
434C4—201no—
435C4—201no—
436C4—201no—
437C2—42no—
438C2—104no—
439C2—202no—
440C2#6585811yescharacteristic
441C2#6588811yescharacteristic
442C2#6588811yescharacteristic
443C2#6594711yescharacteristic
444C2#6599311yescharacteristic
445C2#6601311yescharacteristic
446C2D5×#12611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#388C2
prime radicalC24×D5C22
hypercenter#388D5
hypocenterC5#2480
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×#4025C2semidirect
3. C5×#388C2semidirect
4. #65283C2semidirect
5. #65276C2semidirect
8. #65242C2semidirect
9. #65242C2semidirect
10. #65229C2semidirect
11. C4×#685C2semidirect
12. #64963C2semidirect
13. #64959C2semidirect
14. #64957C2semidirect
15. #64957C2semidirect
19. C2×C5×C4⋊C4C22semidirect
23. C2×C42×C5C22semidirect
37. C2×C4⋊Dic5C22semidirect
38. C2×C4⋊Dic5C22semidirect
39. C2×C4⋊Dic5C22semidirect
40. C2×#683C22semidirect
41. C2×#683C22semidirect
42. C2×C4×Dic5C22semidirect
45. C5×#95C22semidirect
46. C5×#95C22semidirect
47. #3963C22semidirect
48. #3963C22semidirect
49. #3963C22semidirect
50. #3963C22semidirect
51. #3963C22semidirect
52. #3963C22semidirect
114. #388D5semidirect
197. C2×C4⋊C4C2×D5semidirect
216. C2×C42C2×D5semidirect
223. #95C2×D5semidirect
224. #95C2×D5semidirect
253. C2×D5#126semidirect
395. C5#2480semidirect

Maximal subgroups

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

subgroupindex
C2×D5×C22⋊C42
C2×#40252
C5×#3882
#652832
#652762
#652442
#652422
#652292
C4×#6852
#649632
#649592
#649572
#24805