Finite Group Databasebeta

← #10608842

Subgroups — #10608842

Order 640.

800 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4083C211yesmaximal, characteristic
2C2×#4081C211yesmaximal, characteristic, complemented
3C2×#4027C211yesmaximal, characteristic, complemented
4C2×D5×C22⋊C4C211yesmaximal, characteristic, complemented
5C5×#394C211yesmaximal, characteristic, complemented
6#65281C211yesmaximal, characteristic, complemented
7#65278C211yesmaximal, characteristic, complemented
8#65248C211yesmaximal, characteristic, complemented
9#65247C211yesmaximal, characteristic, complemented
10#65245C211yesmaximal, characteristic, complemented
11#65244C211yesmaximal, characteristic, complemented
12#65241C211yesmaximal, characteristic, complemented
13#65234C211yesmaximal, characteristic, complemented
14#64958C211yesmaximal, characteristic, complemented
15#64956C211yesmaximal, characteristic, complemented
16C24×D5C2211yescharacteristic
17C22×C5×D4C2211yescharacteristic
18C22×C22⋊D5C2211yescharacteristic
19C22×C22⋊D5C2211yescharacteristic
20C23×Dic5C2211yescharacteristic, complemented
21C22×C4×D5C2211yescharacteristic
22C22×C4×D5C2211yescharacteristic
23C2×C5×C4⋊C4C2211yescharacteristic, complemented
24C2×C5×C22⋊C4C2211yescharacteristic
25C2×C5×C22⋊C4C2211yescharacteristic
26C2×C5×C22⋊C4C2211yescharacteristic, complemented
27C2×C5×C22⋊C4C2211yescharacteristic, complemented
28C2×C22⋊Dic5C2211yescharacteristic
29C2×C22⋊Dic5C2211yescharacteristic
30C2×C22⋊Dic5C2211yescharacteristic
31C2×C22⋊Dic5C2211yescharacteristic, complemented
32#4083—24no—
33#4081—24no—
34C2×#685C2211yescharacteristic
35C2×#685C2211yescharacteristic
36C2×#685C2211yescharacteristic
37C2×#685C2211yescharacteristic
38C2×#685C2211yescharacteristic
39C2×#685C2211yescharacteristic
40C2×#685C2211yescharacteristic
41C2×#685C2211yescharacteristic
42C2×#683C2211yescharacteristic, complemented
43C2×#683C2211yescharacteristic, complemented
44C2×#683C2211yescharacteristic, complemented
45C2×#683C2211yescharacteristic, complemented
46C2×C4×Dic5C2211yescharacteristic, complemented
47#4027—24no—
48D5×C22⋊C4—24no—
49C5×#95C2211yescharacteristic, complemented
50#3963C2211yescharacteristic, complemented
51#3963C2211yescharacteristic, complemented
52#3963C2211yescharacteristic, complemented
53#3963C2211yescharacteristic, complemented
54#3963C2211yescharacteristic, complemented
55#2418—51nomaximal, Sylow
56C24×C5C2311yescharacteristic
57C24×C5C2311yescharacteristic
58C23×D5—22no—
59C23×D5—22no—
60C23×D5—22no—
61C23×D5—22no—
62C23×D5—22no—
63C23×D5—41no—
64C23×D5—41no—
65C23×D5C2311yescharacteristic
66C23×D5C2311yescharacteristic
67C2×C5×D4—22no—
68C2×C5×D4—22no—
69C2×C5×D4—41no—
70C22×C4×C5C2311yescharacteristic
71C22×C4×C5C2311yescharacteristic
72C22×C4×C5C2311yescharacteristic
73C22×C4×C5C2311yescharacteristic
74C22×C4×C5C2311yescharacteristic
75C2×C22⋊D5—22no—
76C2×C22⋊D5—22no—
77C2×C22⋊D5—22no—
78C2×C22⋊D5—22no—
79C2×C22⋊D5—41no—
80C2×C22⋊D5D414yes—
81C22×Dic5—22no—
82C22×Dic5—22no—
83C22×Dic5—41no—
84C22×Dic5C2311yescharacteristic
85C22×Dic5C2311yescharacteristic
86C22×Dic5C2311yescharacteristic
87C22×Dic5C2311yescharacteristic
88C22×Dic5C2311yescharacteristic
89C22×Dic5C2311yescharacteristic
90C2×C4×D5—22no—
91C2×C4×D5—22no—
92C2×C4×D5—22no—
93C2×C4×D5—22no—
94C2×C4×D5—41no—
95C2×C4×D5—41no—
96C5×C4⋊C4—41no—
97C5×C22⋊C4—22no—
98C5×C22⋊C4—22no—
99C5×C22⋊C4—41no—
100C5×C22⋊C4—41no—
101C22⋊Dic5—22no—
102C22⋊Dic5—22no—
103C22⋊Dic5—22no—
104C22⋊Dic5D414yescomplemented
105#685—22no—
106#685—22no—
107#685—22no—
108#685—22no—
109#685—22no—
110#685—22no—
111#685—22no—
112#685—41no—
113#683—22no—
114#683—22no—
115#683—22no—
116#683—41no—
117C4×Dic5—22no—
118C2×#123—51no—
119C2×#120—51no—
120C2×C4×D4—51no—
121C22×C22⋊C4—51no—
122#399—51no—
123#397—51no—
124#394—51no—
125#394D511yescharacteristic, complemented
126#388—51no—
127#388—51no—
128#386—51no—
129#386—51no—
130#385—51no—
131#380—51no—
132#379—51no—
133C23×C5—21no—
134C23×C5—21no—
135C23×C5—21no—
136C23×C5—21no—
137C23×C5—21no—
138C23×C5—21no—
139C23×C5—21no—
140C23×C5—21no—
141C23×C5—21no—
142C23×C5—21no—
143C23×C5—21no—
144C23×C5—21no—
145C23×C5C2×D412yes—
146C23×C5C2×D412yes—
147C23×C5C2411yescharacteristic
148C22×D5—21no—
149C22×D5—21no—
150C22×D5—21no—
151C22×D5—21no—
152C22×D5—28no—
153C22×D5—21no—
154C22×D5—21no—
155C22×D5—21no—
156C22×D5—21no—
157C22×D5—21no—
158C22×D5—21no—
159C22×D5—44no—
160C22×D5—44no—
161C22×D5—44no—
162C22×D5—44no—
163C22×D5—44no—
164C22×D5—44no—
165C22×D5C2×D412yes—
166C22×D5#4112yes—
167C22×D5#4112yes—
168C22×D5#4112yes—
169C5×D4—44no—
170C2×C4×C5—21no—
171C2×C4×C5—21no—
172C2×C4×C5—21no—
173C2×C4×C5—21no—
174C2×C4×C5—21no—
175C2×C4×C5—21no—
176C2×C4×C5—21no—
177C2×C4×C5—21no—
178C2×C4×C5—21no—
179C2×C4×C5—21no—
180C2×C4×C5—21no—
181C2×C4×C5—21no—
182C2×C4×C5—21no—
183C2×C4×C5—21no—
184C2×C4×C5—21no—
185C22⋊D5—28no—
186C22⋊D5—44no—
187C2×Dic5—21no—
188C2×Dic5—21no—
189C2×Dic5—21no—
190C2×Dic5—21no—
191C2×Dic5—21no—
192C2×Dic5—21no—
193C2×Dic5—21no—
194C2×Dic5—21no—
195C2×Dic5—21no—
196C2×Dic5—21no—
197C2×Dic5—21no—
198C2×Dic5—21no—
199C2×Dic5—21no—
200C2×Dic5—21no—
201C2×Dic5—21no—
202C2×Dic5—44no—
203C2×Dic5C2×D412yes—
204C2×Dic5C2×D412yes—
205C2×Dic5C2×D412yes—
206C4×D5—44no—
207C4×D5—44no—
208C25—51no—
209C22×D4—51no—
210C22×D4—51no—
211C22×D4C2×D511yescharacteristic
212C23×C4—51no—
213C23×C4—51no—
214C23×C4—51no—
215#123—104no—
216#120—104no—
217C4×D4—104no—
218C2×C4⋊C4—51no—
219C2×C4⋊C4—51no—
220C2×C4⋊C4—51no—
221C2×C4⋊C4—51no—
222C2×C4⋊C4C2×D511yescharacteristic, complemented
223C2×C22⋊C4—51no—
224C2×C22⋊C4—51no—
225C2×C22⋊C4—51no—
226C2×C22⋊C4—51no—
227C2×C22⋊C4—51no—
228C2×C22⋊C4—51no—
229C2×C22⋊C4—51no—
230C2×C22⋊C4—51no—
231C2×C22⋊C4—51no—
232C2×C22⋊C4—51no—
233C2×C22⋊C4—51no—
234C2×C22⋊C4—51no—
235C2×C22⋊C4—104no—
236C2×C22⋊C4C2×D511yescharacteristic
237C2×C22⋊C4C2×D511yescharacteristic
238C2×C22⋊C4C2×D511yescharacteristic, complemented
239C2×C22⋊C4C2×D511yescharacteristic, complemented
240C2×C42—51no—
241#95—51no—
242#95—51no—
243#95—51no—
244#95—51no—
245#95—51no—
246#95C2×D511yescharacteristic, complemented
247C22×C5—22no—
248C22×C5—22no—
249C22×C5—22no—
250C22×C5—22no—
251C22×C5—22no—
252C22×C5—22no—
253C22×C5—41no—
254C22×C5—41no—
255C22×C5—41no—
256C22×C5—41no—
257C22×C5—41no—
258C22×C5—41no—
259C22×C5—41no—
260C22×C5—41no—
261C22×C5C22×D411yescharacteristic
262C22×C5C22×D411yescharacteristic
263C22×C5C2×#4111yescharacteristic
264C22×C5C2×#4111yescharacteristic
265C22×C5C2×#4111yescharacteristic
266C22×C5H(5,𝔽2)11yescharacteristic
267C22×C5H(5,𝔽2)11yescharacteristic
268C2×D5—22no—
269C2×D5—22no—
270C2×D5—22no—
271C2×D5—22no—
272C2×D5—22no—
273C2×D5—22no—
274C2×D5—22no—
275C2×D5—22no—
276C2×D5—22no—
277C2×D5—416no—
278C2×D5—41no—
279C2×D5—41no—
280C2×D5—41no—
281C2×D5—41no—
282C2×D5#12314yescomplemented
283C4×C5—41no—
284C4×C5—41no—
285C4×C5—41no—
286C4×C5—41no—
287C4×C5—41no—
288Dic5—22no—
289Dic5—22no—
290Dic5—22no—
291Dic5—41no—
292Dic5—41no—
293Dic5—41no—
294C24—51no—
295C24—51no—
296C24—102no—
297C24—102no—
298C24—102no—
299C24—102no—
300C24—102no—
301C24—201no—
302C24—201no—
303C24C22×D511yescharacteristic
304C24C22×D511yescharacteristic
305C2×D4—22no—
306C2×D4—22no—
307C2×D4—41no—
308C2×D4—54no—
309C2×D4—102no—
310C2×D4—102no—
311C2×D4—102no—
312C2×D4—102no—
313C2×D4—201no—
314C22×C4—51no—
315C22×C4—51no—
316C22×C4—51no—
317C22×C4—51no—
318C22×C4—51no—
319C22×C4—51no—
320C22×C4—102no—
321C22×C4—102no—
322C22×C4—102no—
323C22×C4—102no—
324C22×C4—102no—
325C22×C4—102no—
326C22×C4—201no—
327C22×C4—201no—
328C22×C4—201no—
329C22×C4C22×D511yescharacteristic
330C22×C4C22×D511yescharacteristic
331C22×C4C22×D511yescharacteristic
332C22×C4C22×D511yescharacteristic
333C22×C4C22×D511yescharacteristic
334C4⋊C4—41no—
335C4⋊C4—102no—
336C4⋊C4—102no—
337C4⋊C4—102no—
338C4⋊C4—201no—
339C22⋊C4—22no—
340C22⋊C4—22no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—54no—
344C22⋊C4—102no—
345C22⋊C4—102no—
346C22⋊C4—102no—
347C22⋊C4—102no—
348C22⋊C4—102no—
349C22⋊C4—102no—
350C22⋊C4—102no—
351C22⋊C4—102no—
352C22⋊C4—102no—
353C22⋊C4—102no—
354C22⋊C4—201no—
355C42—102no—
356C2×C5—42no—
357C2×C5—42no—
358C2×C5C2×#12311yescharacteristic
359C2×C5#52511yescharacteristic
360C2×C5#53811yescharacteristic
361C2×C5D4211yescharacteristic
362C2×C5#54611yescharacteristic
363C2×C5#54611yescharacteristic
364C2×C5#55111yescharacteristic
365D5—24no—
366D5—42no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—52no—
380C23—52no—
381C23—52no—
382C23—52no—
383C23—108no—
384C23—101no—
385C23—101no—
386C23—101no—
387C23—101no—
388C23—101no—
389C23—101no—
390C23—101no—
391C23—101no—
392C23—101no—
393C23—101no—
394C23—204no—
395C23—204no—
396C23—204no—
397C23—204no—
398C23—204no—
399C23—204no—
400C23D4×D512yes—
401C23D4×D512yes—
402C23C23×D511yescharacteristic
403D4—44no—
404D4—108no—
405D4—204no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—52no—
422C2×C4—52no—
423C2×C4—52no—
424C2×C4—101no—
425C2×C4—101no—
426C2×C4—101no—
427C2×C4—101no—
428C2×C4—101no—
429C2×C4—101no—
430C2×C4—101no—
431C2×C4—101no—
432C2×C4—101no—
433C2×C4—101no—
434C2×C4—101no—
435C2×C4—101no—
436C2×C4—101no—
437C2×C4—101no—
438C2×C4—101no—
439C2×C4—204no—
440C2×C4—204no—
441C2×C4—204no—
442C5#241811yescharacteristic, complemented, Sylow
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—54no—
458C22—102no—
459C22—102no—
460C22—102no—
461C22—102no—
462C22—102no—
463C22—102no—
464C22—102no—
465C22—102no—
466C22—102no—
467C22—2016no—
468C22—201no—
469C22—201no—
470C22—201no—
471C22—201no—
472C22C2×D4×D511yescharacteristic
473C22C2×D4×D511yescharacteristic
474C22#414411yescharacteristic
475C22#414411yescharacteristic
476C22D5×#4111yescharacteristic
477C22D5×#4111yescharacteristic
478C22D5×#4111yescharacteristic
479C4—41no—
480C4—41no—
481C4—41no—
482C4—41no—
483C4—41no—
484C4—102no—
485C4—102no—
486C4—102no—
487C4—201no—
488C4—201no—
489C4—201no—
490C2—42no—
491C2—42no—
492C2—104no—
493C2—202no—
494C2#6592411yescharacteristic
495C2#6594411yescharacteristic
496C2#6594411yescharacteristic
497C2#6594711yescharacteristic
498C2D5×#12311yescharacteristic
499C2#6599011yescharacteristic
500C2#6601311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#394C2
prime radicalC2×#4083C2
hypercenter#394D5
hypocenterC5#2418
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#4081C2semidirect
3. C2×#4027C2semidirect
4. C2×D5×C22⋊C4C2semidirect
5. C5×#394C2semidirect
6. #65281C2semidirect
7. #65278C2semidirect
8. #65248C2semidirect
9. #65247C2semidirect
10. #65245C2semidirect
11. #65244C2semidirect
12. #65241C2semidirect
13. #65234C2semidirect
14. #64958C2semidirect
15. #64956C2semidirect
20. C23×Dic5C22semidirect
23. C2×C5×C4⋊C4C22semidirect
26. C2×C5×C22⋊C4C22semidirect
27. C2×C5×C22⋊C4C22semidirect
31. C2×C22⋊Dic5C22semidirect
42. C2×#683C22semidirect
43. C2×#683C22semidirect
44. C2×#683C22semidirect
45. C2×#683C22semidirect
46. C2×C4×Dic5C22semidirect
49. C5×#95C22semidirect
50. #3963C22semidirect
51. #3963C22semidirect
52. #3963C22semidirect
53. #3963C22semidirect
54. #3963C22semidirect
104. C22⋊Dic5D4semidirect
125. #394D5semidirect
222. C2×C4⋊C4C2×D5semidirect
238. C2×C22⋊C4C2×D5semidirect
239. C2×C22⋊C4C2×D5semidirect
246. #95C2×D5semidirect
282. C2×D5#123semidirect
442. C5#2418semidirect

Maximal subgroups

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

subgroupindex
C2×#40832
C2×#40812
C2×#40272
C2×D5×C22⋊C42
C5×#3942
#652812
#652782
#652482
#652472
#652452
#652442
#652412
#652342
#649582
#649562
#24185