Finite Group Databasebeta

← #11753251

Subgroups — #11753251

Order 960.

668 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#6790C211yesmaximal, characteristic, complemented
2C2×#6773C211yesmaximal, characteristic, complemented
3#91771C211yesmaximal, characteristic, complemented
4C5×#885C211yesmaximal, characteristic, complemented
5C3×#4030C211yesmaximal, characteristic, complemented
6#91572C211yesmaximal, characteristic, complemented
7#91567C211yesmaximal, characteristic, complemented
8#91533C211yesmaximal, characteristic, complemented
9#91476C211yesmaximal, characteristic, complemented
10#91474C211yesmaximal, characteristic, complemented
11#91458C211yesmaximal, characteristic, complemented
12#91455C211yesmaximal, characteristic, complemented
13#91448C211yesmaximal, characteristic, complemented
14#91420C211yesmaximal, characteristic, complemented
15#91403C211yesmaximal, characteristic, complemented
16#66008—31nomaximal, Hall
17C23×D15C2211yescharacteristic
18C22×D3×D5C2211yescharacteristic
19C2×#1220C2211yescharacteristic, complemented
20C2×D60C2211yescharacteristic
21C2×D60C2211yescharacteristic, complemented
22C2×C5×#67C2211yescharacteristic
23C2×C5×Dic6C2211yescharacteristic, complemented
24C2×C3×C22⋊D5C2211yescharacteristic
25C2×C3×C22⋊D5C2211yescharacteristic, complemented
26C2×C3×D20C2211yescharacteristic, complemented
27C2×C3×C4×D5C2211yescharacteristic, complemented
28#6790—24no—
29C2×#1203C2211yescharacteristic
30C2×#1203C2211yescharacteristic, complemented
31C2×#1202C2211yescharacteristic
32C2×#1202C2211yescharacteristic
33C2×#1202C2211yescharacteristic, complemented
34C2×#1202C2211yescharacteristic, complemented
35C2×#1202C2211yescharacteristic, complemented
36C2×#1201C2211yescharacteristic, complemented
37C2×#1200C2211yescharacteristic
38C2×#1200C2211yescharacteristic, complemented
39#6773—24no—
40C3×C5×C22⋊C4C2211yescharacteristic, complemented
41#6714C2211yescharacteristic
42#6714C2211yescharacteristic, complemented
43C5×#217C2211yescharacteristic, complemented
44C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C4×C5×Dic3C2211yescharacteristic, complemented
47C3×#685C2211yescharacteristic, complemented
48C3×#683C2211yescharacteristic, complemented
49#6668C2211yescharacteristic, complemented
50#6667C2211yescharacteristic
51#6667C2211yescharacteristic, complemented
52#6665C2211yescharacteristic, complemented
53Dic3×Dic5C2211yescharacteristic, complemented
54#5607—51nomaximal, Hall
55C2×#713—31no—
56C2×D4×D5—31no—
57C5×#124—31no—
58#4093—31no—
59#4086—31no—
60#4030—31no—
61#4030—31no—
62#4030—31no—
63#4030D311yescharacteristic, complemented
64#4028—31no—
65#4028—31no—
66#4028—31no—
67#4028—31no—
68#4020—31no—
69#4018—31no—
70C23×C3×C5C2311yescharacteristic
71C22×D15—22no—
72C22×D15—41no—
73C22×D15—41no—
74C22×D15C2311yescharacteristic
75C22×D15C2311yescharacteristic
76C22×D15C2311yescharacteristic
77C22×C5×D3C2311yescharacteristic
78C22×C3×D5C2311yescharacteristic
79C22×C3×D5C2311yescharacteristic
80C2×D3×D5—22no—
81C2×D3×D5—41no—
82C2×D3×D5—41no—
83C2×C3×C4×C5C2311yescharacteristic
84C2×C3×C4×C5C2311yescharacteristic
85#1220—41no—
86C2×Dic15C2311yescharacteristic
87D60—22no—
88D60—41no—
89C5×#67—22no—
90C2×C5×Dic3C2311yescharacteristic
91C2×C5×Dic3C2311yescharacteristic
92C2×C5×Dic3C2311yescharacteristic
93C5×Dic6—22no—
94C3×C22⋊D5—22no—
95C3×C22⋊D5—41no—
96C2×C3×Dic5C2311yescharacteristic
97C2×C3×Dic5C2311yescharacteristic
98C3×D20—41no—
99C3×C4×D5—22no—
100#1203—22no—
101#1203—41no—
102#1202—22no—
103#1202—22no—
104#1202—22no—
105#1202—41no—
106#1202—41no—
107#1201—41no—
108#1200—22no—
109#1200D414yescomplemented
110C2×D3×D4—51no—
111C2×#235—51no—
112C3×#121—51no—
113#940—51no—
114#940—51no—
115#938—51no—
116#937—51no—
117#937—51no—
118#930—51no—
119#895—51no—
120#892—51no—
121#885—51no—
122#885D511yescharacteristic, complemented
123#882—51no—
124#882—51no—
125C23×D5—31no—
126C23×D5—31no—
127C2×C5×Q8—31no—
128C2×C5×D4—31no—
129C2×C22⋊D5—31no—
130C2×C22⋊D5—31no—
131C2×C22⋊D5—31no—
132C2×C22⋊D5—31no—
133C2×C22⋊D5C2×D311yescharacteristic
134C2×C22⋊D5C2×D311yescharacteristic, complemented
135#713—64no—
136D4×D5—64no—
137C2×D20—31no—
138C2×D20—31no—
139C2×D20—31no—
140C2×D20—31no—
141C2×D20—31no—
142C2×D20—31no—
143C2×D20—31no—
144C2×D20C2×D311yescharacteristic, complemented
145C2×C4×D5—31no—
146C2×C4×D5—31no—
147C2×C4×D5C2×D311yescharacteristic, complemented
148C5×C22⋊C4—31no—
149C5×C22⋊C4—31no—
150C5×C22⋊C4—31no—
151C5×C22⋊C4C2×D311yescharacteristic, complemented
152C42×C5—31no—
153#685—31no—
154#685—31no—
155#685—31no—
156#685—31no—
157#685—31no—
158#685C2×D311yescharacteristic, complemented
159#683—31no—
160#683C2×D311yescharacteristic, complemented
161C4×Dic5—31no—
162#535—151noSylow
163C22×C3×C5—21no—
164C22×C3×C5—21no—
165C22×C3×C5—21no—
166C22×C3×C5C2411yescharacteristic
167C2×D15—21no—
168C2×D15—21no—
169C2×D15—21no—
170C2×D15—21no—
171C2×D15—21no—
172C2×D15—21no—
173C2×D15—21no—
174C2×D15—21no—
175C2×D15—44no—
176C2×D15C2×D412yes—
177C2×C5×D3—21no—
178C2×C5×D3—21no—
179C2×C5×D3—21no—
180C2×C3×D5—21no—
181C2×C3×D5—21no—
182C2×C3×D5—21no—
183C2×C3×D5—21no—
184C2×C3×D5—21no—
185C2×C3×D5—21no—
186D3×D5—44no—
187C3×C4×C5—21no—
188C3×C4×C5—21no—
189Dic15—21no—
190C3×Dic5—21no—
191C3×Dic5C2×D412yes—
192C5×Dic3—21no—
193C5×Dic3—21no—
194C5×Dic3C2×D412yes—
195C23×D3—51no—
196C23×D3—51no—
197C2×C3×D4—51no—
198C2×C3×D4—51no—
199C2×C3×D4—51no—
200C22×C3×C4—51no—
201C2×#67—51no—
202C2×#67—51no—
203C2×#67—51no—
204C2×#67—51no—
205C2×#67—51no—
206C2×#67—51no—
207C2×#67—51no—
208C2×#67C2×D511yescharacteristic
209D3×D4—104no—
210#235—104no—
211C2×D12—51no—
212C2×D12—51no—
213C2×D12—51no—
214C2×D12—51no—
215C2×C4×D3—51no—
216C2×C4×D3—51no—
217C2×Dic6C2×D511yescharacteristic, complemented
218C3×C4⋊C4—51no—
219C3×C22⋊C4—51no—
220C3×C22⋊C4C2×D511yescharacteristic, complemented
221#217—51no—
222#217C2×D511yescharacteristic, complemented
223(C2×D3)⋊C4—51no—
224(C2×D3)⋊C4—51no—
225(C2×D3)⋊C4—51no—
226(C2×D3)⋊C4—51no—
227(C2×D3)⋊C4C2×D511yescharacteristic, complemented
228(C2×D3)⋊C4C2×D511yescharacteristic, complemented
229C4⋊Dic3—51no—
230C4×Dic3—51no—
231C4×Dic3C2×D511yescharacteristic, complemented
232C23×C5—31no—
233C23×C5C22×D311yescharacteristic
234C22×D5—31no—
235C22×D5—31no—
236C22×D5—31no—
237C22×D5—62no—
238C22×D5—62no—
239C22×D5—121no—
240C22×D5—121no—
241C22×D5—121no—
242C22×D5—121no—
243C22×D5C22×D311yescharacteristic
244C22×D5C22×D311yescharacteristic
245C5×Q8—62no—
246C5×D4—62no—
247C2×C4×C5—31no—
248C2×C4×C5—31no—
249C2×C4×C5—31no—
250C2×C4×C5C22×D311yescharacteristic
251C2×C4×C5C22×D311yescharacteristic
252C22⋊D5—22no—
253C22⋊D5—41no—
254C22⋊D5—62no—
255C22⋊D5—121no—
256C22⋊D5—121no—
257C22⋊D5—121no—
258C2×Dic5—31no—
259C2×Dic5C22×D311yescharacteristic
260C2×Dic5C22×D311yescharacteristic
261D20—41no—
262D20—62no—
263D20—62no—
264D20—62no—
265D20—62no—
266D20—121no—
267D20—121no—
268D20—121no—
269C4×D5—22no—
270C4×D5—34no—
271C4×D5—62no—
272C2×#41—151no—
273C22×D4—151no—
274#127—151no—
275#127—151no—
276#124—31no—
277#124—151no—
278#121—51no—
279#121—151no—
280#121—151no—
281#121—151no—
282#120—151no—
283#120—151no—
284#120—151no—
285#120—151no—
286#117—151no—
287C2×C3×C5—41no—
288C2×C3×C5C22×D411yescharacteristic
289C2×C3×C5H(5,𝔽2)11yescharacteristic
290C2×C3×C5H(5,𝔽2)11yescharacteristic
291D15—22no—
292D15—41no—
293D15—41no—
294C3×D5—41no—
295C3×D5—41no—
296C5×D3—41no—
297C23×C3—51no—
298C23×C3—51no—
299C23×C3C22×D511yescharacteristic
300C22×D3—51no—
301C22×D3—51no—
302C22×D3—51no—
303C22×D3—102no—
304C22×D3—102no—
305C22×D3—201no—
306C22×D3—201no—
307C22×D3—201no—
308C22×D3—201no—
309C22×D3C22×D511yescharacteristic
310C3×D4—102no—
311C3×D4—201no—
312C3×D4—201no—
313C2×C3×C4—51no—
314C2×C3×C4—51no—
315C2×C3×C4—102no—
316C2×C3×C4C22×D511yescharacteristic
317C2×C3×C4C22×D511yescharacteristic
318#67—22no—
319#67—102no—
320#67—102no—
321#67—102no—
322#67—201no—
323#67—201no—
324#67—201no—
325#67—201no—
326C2×Dic3—51no—
327C2×Dic3C22×D511yescharacteristic
328C2×Dic3C22×D511yescharacteristic
329C2×Dic3C22×D511yescharacteristic
330D12—102no—
331D12—102no—
332D12—201no—
333D12—201no—
334C4×D3—54no—
335C4×D3—102no—
336Dic6—22no—
337C22×C5—21no—
338C22×C5—21no—
339C22×C5—21no—
340C22×C5—61no—
341C22×C5—61no—
342C22×C5—61no—
343C22×C5C23×D311yescharacteristic
344C2×D5—21no—
345C2×D5—21no—
346C2×D5—21no—
347C2×D5—21no—
348C2×D5—21no—
349C2×D5—21no—
350C2×D5—32no—
351C2×D5—61no—
352C2×D5—61no—
353C2×D5—61no—
354C2×D5—61no—
355C2×D5—61no—
356C2×D5—61no—
357C2×D5—61no—
358C2×D5—61no—
359C2×D5—124no—
360C2×D5—124no—
361C4×C5—21no—
362C4×C5—21no—
363C4×C5—32no—
364C4×C5—61no—
365C4×C5—61no—
366Dic5—21no—
367Dic5—61no—
368Dic5D3×D412yes—
369C24—151no—
370C24—151no—
371#41—304no—
372C2×Q8—31no—
373C2×D4—31no—
374C2×D4—51no—
375C2×D4—51no—
376C2×D4—51no—
377C2×D4—151no—
378C2×D4—151no—
379C2×D4—151no—
380C2×D4—151no—
381C2×D4—151no—
382C2×D4—151no—
383C2×D4—151no—
384C2×D4—151no—
385C2×D4—151no—
386C2×D4—151no—
387C2×D4—151no—
388C2×D4—304no—
389C22×C4—51no—
390C22×C4—151no—
391C22×C4—151no—
392C4⋊C4—51no—
393C4⋊C4—151no—
394C22⋊C4—31no—
395C22⋊C4—31no—
396C22⋊C4—31no—
397C22⋊C4—51no—
398C22⋊C4—151no—
399C22⋊C4—151no—
400C22⋊C4—151no—
401C22⋊C4—151no—
402C22⋊C4—151no—
403C22⋊C4D3×D511yescharacteristic, complemented
404C42—31no—
405C42—151no—
406C3×C5#53511yescharacteristic, complemented, Hall
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—101no—
411C22×C3—101no—
412C22×C3—101no—
413C22×C3—101no—
414C22×C3—101no—
415C22×C3—101no—
416C22×C3C23×D511yescharacteristic
417C2×D3—21no—
418C2×D3—21no—
419C2×D3—21no—
420C2×D3—52no—
421C2×D3—101no—
422C2×D3—101no—
423C2×D3—101no—
424C2×D3—101no—
425C2×D3—101no—
426C2×D3—101no—
427C2×D3—101no—
428C2×D3—101no—
429C2×D3—204no—
430C2×D3—204no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—52no—
434C3×C4—101no—
435Dic3—21no—
436Dic3—21no—
437Dic3—101no—
438Dic3D4×D512yes—
439C2×C5—41no—
440C2×C5—121no—
441C2×C5C2×D3×D411yescharacteristic
442C2×C5#100411yescharacteristic
443C2×C5#100911yescharacteristic
444D5—41no—
445D5—41no—
446D5—62no—
447D5—121no—
448D5—121no—
449C23—31no—
450C23—51no—
451C23—51no—
452C23—151no—
453C23—151no—
454C23—151no—
455C23—302no—
456C23—302no—
457C23—601no—
458C23—601no—
459C23—601no—
460C23—601no—
461C23C2×D3×D511yescharacteristic
462Q8—62no—
463D4—62no—
464D4—102no—
465D4—201no—
466D4—201no—
467D4—302no—
468D4—302no—
469D4—302no—
470D4—302no—
471D4—302no—
472D4—601no—
473D4—601no—
474D4—601no—
475D4—601no—
476D4—601no—
477D4—601no—
478C2×C4—31no—
479C2×C4—31no—
480C2×C4—31no—
481C2×C4—51no—
482C2×C4—51no—
483C2×C4—102no—
484C2×C4—154no—
485C2×C4—151no—
486C2×C4—302no—
487C2×C4C2×D3×D511yescharacteristic
488C2×C4C2×D3×D511yescharacteristic
489C2×C3—41no—
490C2×C3—201no—
491C2×C3—201no—
492C2×C3C2×D4×D511yescharacteristic
493C2×C3#414911yescharacteristic
494C2×C3#414911yescharacteristic
495D3—41no—
496D3—102no—
497D3—201no—
498D3—201no—
499C5#560711yescharacteristic, complemented, Sylow
500C22—21no—
501C22—21no—
502C22—21no—
503C22—61no—
504C22—61no—
505C22—61no—
506C22—101no—
507C22—101no—
508C22—101no—
509C22—101no—
510C22—101no—
511C22—101no—
512C22—152no—
513C22—301no—
514C22—301no—
515C22—301no—
516C22—301no—
517C22—301no—
518C22—301no—
519C22—301no—
520C22—301no—
521C22—604no—
522C22—604no—
523C22C22×D3×D511yescharacteristic
524C4—21no—
525C4—21no—
526C4—32no—
527C4—52no—
528C4—61no—
529C4—61no—
530C4—101no—
531C4—301no—
532C3#6600811yescharacteristic, complemented, Sylow
533C2—41no—
534C2—121no—
535C2—201no—
536C2—201no—
537C2—302no—
538C2—601no—
539C2—601no—
540C2#9201911yescharacteristic
541C2D3×D4×D511yescharacteristic
542C2#9202611yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C22⋊C4C22
hypercenterC22⋊C4D3×D5
hypocenterC3×C5#535
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×#6790C2semidirect
2. C2×#6773C2semidirect
3. #91771C2semidirect
4. C5×#885C2semidirect
5. C3×#4030C2semidirect
6. #91572C2semidirect
7. #91567C2semidirect
8. #91533C2semidirect
9. #91476C2semidirect
10. #91474C2semidirect
11. #91458C2semidirect
12. #91455C2semidirect
13. #91448C2semidirect
14. #91420C2semidirect
15. #91403C2semidirect
19. C2×#1220C22semidirect
21. C2×D60C22semidirect
23. C2×C5×Dic6C22semidirect
25. C2×C3×C22⋊D5C22semidirect
26. C2×C3×D20C22semidirect
27. C2×C3×C4×D5C22semidirect
30. C2×#1203C22semidirect
33. C2×#1202C22semidirect
34. C2×#1202C22semidirect
35. C2×#1202C22semidirect
36. C2×#1201C22semidirect
38. C2×#1200C22semidirect
40. C3×C5×C22⋊C4C22semidirect
42. #6714C22semidirect
43. C5×#217C22semidirect
44. C5×(C2×D3)⋊C4C22semidirect
45. C5×(C2×D3)⋊C4C22semidirect
46. C4×C5×Dic3C22semidirect
47. C3×#685C22semidirect
48. C3×#683C22semidirect
49. #6668C22semidirect
51. #6667C22semidirect
52. #6665C22semidirect
53. Dic3×Dic5C22semidirect
63. #4030D3semidirect
109. #1200D4semidirect
122. #885D5semidirect
134. C2×C22⋊D5C2×D3semidirect
144. C2×D20C2×D3semidirect
147. C2×C4×D5C2×D3semidirect
151. C5×C22⋊C4C2×D3semidirect
158. #685C2×D3semidirect
160. #683C2×D3semidirect
217. C2×Dic6C2×D5semidirect
220. C3×C22⋊C4C2×D5semidirect
222. #217C2×D5semidirect
227. (C2×D3)⋊C4C2×D5semidirect
228. (C2×D3)⋊C4C2×D5semidirect
231. C4×Dic3C2×D5semidirect
403. C22⋊C4D3×D5semidirect
406. C3×C5#535semidirect
499. C5#5607semidirect
532. C3#66008semidirect

Maximal subgroups

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

subgroupindex
C2×#67902
C2×#67732
#917712
C5×#8852
C3×#40302
#915722
#915672
#915332
#914762
#914742
#914582
#914552
#914482
#914202
#914032
#660083
#56075