Finite Group Databasebeta

← #11753239

Subgroups — #11753239

Order 960.

668 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×#67C211yesmaximal, characteristic, complemented
2C2×#6766C211yesmaximal, characteristic, complemented
3#91772C211yesmaximal, characteristic, complemented
4C5×#885C211yesmaximal, characteristic, complemented
5C3×#4028C211yesmaximal, characteristic, complemented
6#91549C211yesmaximal, characteristic, complemented
7D5×#217C211yesmaximal, characteristic, complemented
8#91533C211yesmaximal, characteristic, complemented
9#91474C211yesmaximal, characteristic, complemented
10#91473C211yesmaximal, characteristic, complemented
11Dic3×D20C211yesmaximal, characteristic, complemented
12#91421C211yesmaximal, characteristic, complemented
13#91414C211yesmaximal, characteristic, complemented
14#91408C211yesmaximal, characteristic, complemented
15#91395C211yesmaximal, characteristic, complemented
16#66010—31nomaximal, Hall
17C23×C3×D5C2211yescharacteristic
18C22×D3×D5C2211yescharacteristic
19C2×#1220C2211yescharacteristic
20C2×C4×D15C2211yescharacteristic, complemented
21C2×C5×#67C2211yescharacteristic
22C2×C5×Dic6C2211yescharacteristic, complemented
23C2×C3×C22⋊D5C2211yescharacteristic, complemented
24C2×C3×D20C2211yescharacteristic
25C2×C3×D20C2211yescharacteristic, complemented
26D5×#67—24no—
27C2×#1202C2211yescharacteristic
28C2×#1202C2211yescharacteristic, complemented
29C2×#1201C2211yescharacteristic
30C2×#1201C2211yescharacteristic, complemented
31C2×#1200C2211yescharacteristic, complemented
32C2×D5×Dic3C2211yescharacteristic
33C2×D5×Dic3C2211yescharacteristic, complemented
34C2×D5×Dic3C2211yescharacteristic, complemented
35C2×D5×Dic3C2211yescharacteristic, complemented
36#6766—24no—
37C3×C5×C22⋊C4C2211yescharacteristic, complemented
38#6719C2211yescharacteristic, complemented
39#6714C2211yescharacteristic, complemented
40C4⋊Dic15C2211yescharacteristic, complemented
41#6712C2211yescharacteristic, complemented
42C5×#217C2211yescharacteristic, complemented
43C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C4×C5×Dic3C2211yescharacteristic, complemented
46C3×#685C2211yescharacteristic
47C3×#685C2211yescharacteristic, complemented
48Dic3⋊Dic5C2211yescharacteristic, complemented
49#6668C2211yescharacteristic, complemented
50(C2×D3)⋊Dic5C2211yescharacteristic, complemented
51#6665C2211yescharacteristic
52#6665C2211yescharacteristic
53#6665C2211yescharacteristic, complemented
54#5591—51nomaximal, Hall
55C2×#713—31no—
56C2×D4×D5—31no—
57C5×#124—31no—
58#4092—31no—
59#4084—31no—
60#4030—31no—
61#4030—31no—
62#4029—31no—
63#4029—31no—
64#4028—31no—
65#4028D311yescharacteristic, complemented
66D5×C22⋊C4—31no—
67D5×C22⋊C4—31no—
68C4×D20—31no—
69C4×D20—31no—
70C23×C3×C5C2311yescharacteristic
71C22×D15C2311yescharacteristic
72C22×C5×D3C2311yescharacteristic
73C22×C3×D5—22no—
74C22×C3×D5—22no—
75C22×C3×D5—41no—
76C22×C3×D5C2311yescharacteristic
77C22×C3×D5C2311yescharacteristic
78C22×C3×D5C2311yescharacteristic
79C2×D3×D5—22no—
80C2×D3×D5—22no—
81C2×D3×D5—41no—
82C2×C3×C4×C5C2311yescharacteristic
83C2×C3×C4×C5C2311yescharacteristic
84#1220—22no—
85C2×Dic15C2311yescharacteristic
86C2×Dic15C2311yescharacteristic
87C2×Dic15C2311yescharacteristic
88C4×D15—22no—
89C5×#67—22no—
90C2×C5×Dic3C2311yescharacteristic
91C2×C5×Dic3C2311yescharacteristic
92C2×C5×Dic3C2311yescharacteristic
93C5×Dic6—22no—
94C3×C22⋊D5—41no—
95C2×C3×Dic5C2311yescharacteristic
96C3×D20—22no—
97C3×D20—22no—
98#1202—22no—
99#1202D414yescomplemented
100#1201—22no—
101#1201—41no—
102#1200—41no—
103D5×Dic3—22no—
104D5×Dic3—22no—
105D5×Dic3—22no—
106D5×Dic3—41no—
107C22×#67—51no—
108C2×#237—51no—
109C3×#120—51no—
110C2×#217—51no—
111#939—51no—
112#939—51no—
113#938—51no—
114#937—51no—
115D4×Dic3—51no—
116#886—51no—
117#885D511yescharacteristic, complemented
118#883—51no—
119#67⋊C4—51no—
120D3×C22⋊C4—51no—
121#878—51no—
122C23×D5—31no—
123C23×D5C2×D311yescharacteristic
124C2×C5×Q8—31no—
125C2×C5×D4—31no—
126C2×C22⋊D5—31no—
127C2×C22⋊D5—31no—
128C2×C22⋊D5—31no—
129C2×C22⋊D5C2×D311yescharacteristic, complemented
130#713—64no—
131D4×D5—64no—
132C2×D20—31no—
133C2×D20—31no—
134C2×D20C2×D311yescharacteristic
135C2×D20C2×D311yescharacteristic, complemented
136C2×C4×D5—31no—
137C2×C4×D5—31no—
138C2×C4×D5—31no—
139C2×C4×D5—31no—
140C2×C4×D5—31no—
141C2×C4×D5—31no—
142C5×C22⋊C4—31no—
143C5×C22⋊C4—31no—
144C5×C22⋊C4—31no—
145C5×C22⋊C4C2×D311yescharacteristic, complemented
146C42×C5—31no—
147C22⋊Dic5—31no—
148C22⋊Dic5—31no—
149#685—31no—
150#685—31no—
151#685—31no—
152#685—31no—
153#685C2×D311yescharacteristic
154#685C2×D311yescharacteristic, complemented
155C4⋊Dic5—31no—
156C4⋊Dic5—31no—
157#683—31no—
158#683—31no—
159#546—151noSylow
160C22×C3×C5—21no—
161C22×C3×C5—21no—
162C22×C3×C5—21no—
163C22×C3×C5C2411yescharacteristic
164C2×D15—21no—
165C2×D15—21no—
166C2×D15C2×D412yes—
167C2×C5×D3—21no—
168C2×C5×D3—21no—
169C2×C5×D3—21no—
170C2×C3×D5—21no—
171C2×C3×D5—21no—
172C2×C3×D5—21no—
173C2×C3×D5—21no—
174C2×C3×D5—21no—
175C2×C3×D5—21no—
176C2×C3×D5—21no—
177C2×C3×D5—44no—
178C2×C3×D5C2×D412yes—
179C2×C3×D5#4112yescomplemented
180D3×D5—44no—
181C3×C4×C5—21no—
182C3×C4×C5—21no—
183Dic15—21no—
184Dic15—21no—
185Dic15—21no—
186C3×Dic5—21no—
187C5×Dic3—21no—
188C5×Dic3—21no—
189C5×Dic3C2×D412yes—
190C24×C3—51no—
191C23×D3—51no—
192C2×C3×D4—51no—
193C2×C3×D4—51no—
194C2×C3×D4—51no—
195C2×#67—51no—
196C2×#67—51no—
197C2×#67—51no—
198C2×#67—51no—
199C2×#67—51no—
200C2×#67—104no—
201C2×#67C2×D511yescharacteristic
202C22×Dic3—51no—
203C22×Dic3—51no—
204C22×Dic3—51no—
205C22×Dic3—51no—
206#237—104no—
207C2×C4×D3—51no—
208C2×C4×D3—51no—
209C2×Dic6C2×D511yescharacteristic, complemented
210C3×C22⋊C4—51no—
211C3×C22⋊C4—51no—
212C3×C22⋊C4C2×D511yescharacteristic, complemented
213#217—51no—
214#217—51no—
215#217—51no—
216#217—51no—
217#217C2×D511yescharacteristic, complemented
218(C2×D3)⋊C4—51no—
219(C2×D3)⋊C4—51no—
220(C2×D3)⋊C4C2×D511yescharacteristic, complemented
221(C2×D3)⋊C4C2×D511yescharacteristic, complemented
222C4⋊Dic3—51no—
223C4⋊Dic3—51no—
224Dic3⋊C4—51no—
225Dic3⋊C4—51no—
226C4×Dic3C2×D511yescharacteristic, complemented
227C23×C5—31no—
228C23×C5C22×D311yescharacteristic
229C22×D5—22no—
230C22×D5—22no—
231C22×D5—31no—
232C22×D5—41no—
233C22×D5—62no—
234C22×D5—62no—
235C22×D5—121no—
236C22×D5C22×D311yescharacteristic
237C22×D5C22×D311yescharacteristic
238C22×D5C22×D311yescharacteristic
239C5×Q8—62no—
240C5×D4—62no—
241C2×C4×C5—31no—
242C2×C4×C5—31no—
243C2×C4×C5—31no—
244C2×C4×C5C22×D311yescharacteristic
245C2×C4×C5C22×D311yescharacteristic
246C22⋊D5—41no—
247C22⋊D5—62no—
248C22⋊D5—62no—
249C22⋊D5—121no—
250C2×Dic5—31no—
251C2×Dic5—31no—
252C2×Dic5—31no—
253C2×Dic5C22×D311yescharacteristic
254D20—22no—
255D20—22no—
256D20—34no—
257D20—62no—
258C4×D5—62no—
259C4×D5—62no—
260C4×D5—62no—
261C4×D5—62no—
262C4×D5—121no—
263C4×D5—121no—
264C2×#41—151no—
265C22×D4—151no—
266#124—31no—
267#123—151no—
268#123—151no—
269C22⋊Q8—151no—
270#121—151no—
271#121—151no—
272#121—151no—
273#120—51no—
274#120—151no—
275C4×D4—151no—
276C4×D4—151no—
277C2×C22⋊C4—151no—
278C2×C22⋊C4—151no—
279C2×C3×C5—41no—
280C2×C3×C5C22×D411yescharacteristic
281C2×C3×C5C2×#4111yescharacteristic
282C2×C3×C5H(5,𝔽2)11yescharacteristic
283D15—22no—
284C3×D5—22no—
285C3×D5—22no—
286C3×D5—41no—
287C5×D3—41no—
288C23×C3—51no—
289C23×C3—51no—
290C23×C3—51no—
291C23×C3—102no—
292C23×C3—102no—
293C23×C3—201no—
294C23×C3C22×D511yescharacteristic
295C22×D3—51no—
296C22×D3—102no—
297C22×D3—102no—
298C22×D3—201no—
299C22×D3C22×D511yescharacteristic
300C3×D4—102no—
301C3×D4—102no—
302C3×D4—201no—
303C2×C3×C4—51no—
304C2×C3×C4C22×D511yescharacteristic
305C2×C3×C4C22×D511yescharacteristic
306#67—22no—
307#67—54no—
308#67—102no—
309#67—102no—
310#67—102no—
311#67—201no—
312C2×Dic3—51no—
313C2×Dic3—51no—
314C2×Dic3—51no—
315C2×Dic3—102no—
316C2×Dic3—102no—
317C2×Dic3—102no—
318C2×Dic3—201no—
319C2×Dic3C22×D511yescharacteristic
320C2×Dic3C22×D511yescharacteristic
321C2×Dic3C22×D511yescharacteristic
322C4×D3—102no—
323C4×D3—201no—
324Dic6—22no—
325C22×C5—21no—
326C22×C5—21no—
327C22×C5—21no—
328C22×C5—61no—
329C22×C5—61no—
330C22×C5—61no—
331C22×C5C23×D311yescharacteristic
332C2×D5—21no—
333C2×D5—21no—
334C2×D5—21no—
335C2×D5—21no—
336C2×D5—21no—
337C2×D5—21no—
338C2×D5—21no—
339C2×D5—32no—
340C2×D5—44no—
341C2×D5—61no—
342C2×D5—61no—
343C2×D5—124no—
344C2×D5D3×D412yes—
345C2×D5#23712yescomplemented
346C4×C5—21no—
347C4×C5—21no—
348C4×C5—32no—
349C4×C5—61no—
350C4×C5—61no—
351Dic5—21no—
352Dic5—61no—
353Dic5—61no—
354Dic5—61no—
355C24—51no—
356C24—151no—
357#41—304no—
358C2×Q8—31no—
359C2×D4—31no—
360C2×D4—51no—
361C2×D4—51no—
362C2×D4—51no—
363C2×D4—151no—
364C2×D4—151no—
365C2×D4—151no—
366C2×D4—151no—
367C2×D4—151no—
368C2×D4—304no—
369C22×C4—151no—
370C22×C4—151no—
371C22×C4—151no—
372C22×C4—151no—
373C22×C4—151no—
374C22×C4—151no—
375C4⋊C4—151no—
376C4⋊C4—151no—
377C4⋊C4—151no—
378C4⋊C4—151no—
379C22⋊C4—31no—
380C22⋊C4—31no—
381C22⋊C4—31no—
382C22⋊C4—51no—
383C22⋊C4—51no—
384C22⋊C4—151no—
385C22⋊C4—151no—
386C22⋊C4—151no—
387C22⋊C4—151no—
388C22⋊C4—151no—
389C22⋊C4—151no—
390C22⋊C4D3×D511yescharacteristic, complemented
391C42—31no—
392C3×C5#54611yescharacteristic, complemented, Hall
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—52no—
397C22×C3—52no—
398C22×C3—101no—
399C22×C3—101no—
400C22×C3—101no—
401C22×C3—101no—
402C22×C3—101no—
403C22×C3—101no—
404C22×C3—101no—
405C22×C3—204no—
406C22×C3C23×D511yescharacteristic
407C2×D3—21no—
408C2×D3—21no—
409C2×D3—21no—
410C2×D3—52no—
411C2×D3—101no—
412C2×D3—101no—
413C2×D3—204no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—101no—
417Dic3—21no—
418Dic3—21no—
419Dic3—101no—
420Dic3—101no—
421Dic3—101no—
422Dic3D4×D512yes—
423C2×C5—41no—
424C2×C5—121no—
425C2×C5C2×D3×D411yescharacteristic
426C2×C5C2×#23711yescharacteristic
427C2×C5#100411yescharacteristic
428D5—22no—
429D5—22no—
430D5—41no—
431D5—62no—
432C23—31no—
433C23—51no—
434C23—51no—
435C23—51no—
436C23—102no—
437C23—102no—
438C23—151no—
439C23—201no—
440C23—302no—
441C23—302no—
442C23—601no—
443C23C2×D3×D511yescharacteristic
444Q8—62no—
445D4—62no—
446D4—102no—
447D4—102no—
448D4—154no—
449D4—201no—
450D4—302no—
451D4—302no—
452D4—302no—
453D4—601no—
454C2×C4—31no—
455C2×C4—31no—
456C2×C4—31no—
457C2×C4—51no—
458C2×C4—151no—
459C2×C4—151no—
460C2×C4—151no—
461C2×C4—302no—
462C2×C4—302no—
463C2×C4—302no—
464C2×C4—302no—
465C2×C4—601no—
466C2×C4—601no—
467C2×C4C2×D3×D511yescharacteristic
468C2×C4C2×D3×D511yescharacteristic
469C2×C3—41no—
470C2×C3—102no—
471C2×C3—102no—
472C2×C3—201no—
473C2×C3C2×D4×D511yescharacteristic
474C2×C3D5×#4111yescharacteristic
475C2×C3#414911yescharacteristic
476D3—41no—
477D3—102no—
478C5#559111yescharacteristic, complemented, Sylow
479C22—21no—
480C22—21no—
481C22—21no—
482C22—52no—
483C22—52no—
484C22—61no—
485C22—61no—
486C22—61no—
487C22—101no—
488C22—101no—
489C22—101no—
490C22—101no—
491C22—101no—
492C22—101no—
493C22—101no—
494C22—152no—
495C22—204no—
496C22—301no—
497C22—301no—
498C22—604no—
499C22C22×D3×D511yescharacteristic
500C4—21no—
501C4—21no—
502C4—32no—
503C4—61no—
504C4—61no—
505C4—101no—
506C4—301no—
507C4—301no—
508C4—301no—
509C3#6601011yescharacteristic, complemented, Sylow
510C2—41no—
511C2—102no—
512C2—102no—
513C2—121no—
514C2—201no—
515C2—302no—
516C2#9201711yescharacteristic
517C2D3×D4×D511yescharacteristic
518C2D5×#23711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C22⋊C4C22
hypercenterC22⋊C4D3×D5
hypocenterC3×C5#546
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×D5×#67C2semidirect
2. C2×#6766C2semidirect
3. #91772C2semidirect
4. C5×#885C2semidirect
5. C3×#4028C2semidirect
6. #91549C2semidirect
7. D5×#217C2semidirect
8. #91533C2semidirect
9. #91474C2semidirect
10. #91473C2semidirect
11. Dic3×D20C2semidirect
12. #91421C2semidirect
13. #91414C2semidirect
14. #91408C2semidirect
15. #91395C2semidirect
20. C2×C4×D15C22semidirect
22. C2×C5×Dic6C22semidirect
23. C2×C3×C22⋊D5C22semidirect
25. C2×C3×D20C22semidirect
28. C2×#1202C22semidirect
30. C2×#1201C22semidirect
31. C2×#1200C22semidirect
33. C2×D5×Dic3C22semidirect
34. C2×D5×Dic3C22semidirect
35. C2×D5×Dic3C22semidirect
37. C3×C5×C22⋊C4C22semidirect
38. #6719C22semidirect
39. #6714C22semidirect
40. C4⋊Dic15C22semidirect
41. #6712C22semidirect
42. C5×#217C22semidirect
43. C5×(C2×D3)⋊C4C22semidirect
44. C5×(C2×D3)⋊C4C22semidirect
45. C4×C5×Dic3C22semidirect
47. C3×#685C22semidirect
48. Dic3⋊Dic5C22semidirect
49. #6668C22semidirect
50. (C2×D3)⋊Dic5C22semidirect
53. #6665C22semidirect
65. #4028D3semidirect
99. #1202D4semidirect
117. #885D5semidirect
129. C2×C22⋊D5C2×D3semidirect
135. C2×D20C2×D3semidirect
145. C5×C22⋊C4C2×D3semidirect
154. #685C2×D3semidirect
179. C2×C3×D5#41semidirect
209. C2×Dic6C2×D5semidirect
212. C3×C22⋊C4C2×D5semidirect
217. #217C2×D5semidirect
220. (C2×D3)⋊C4C2×D5semidirect
221. (C2×D3)⋊C4C2×D5semidirect
226. C4×Dic3C2×D5semidirect
345. C2×D5#237semidirect
390. C22⋊C4D3×D5semidirect
392. C3×C5#546semidirect
478. C5#5591semidirect
509. C3#66010semidirect

Maximal subgroups

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

subgroupindex
C2×D5×#672
C2×#67662
#917722
C5×#8852
C3×#40282
#915492
D5×#2172
#915332
#914742
#914732
Dic3×D202
#914212
#914142
#914082
#913952
#660103
#55915