Subgroups — #11751038

Order 960.

276 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄²×C₅	C₂	1	1	yes	maximal, characteristic
2	#91115	C₂	1	6	yes	maximal
3	#65226	—	3	1	no	maximal, Hall
4	C₂²×C₃×C₄×C₅	C₂²	1	3	yes	—
5	C₂²×Dic₁₅	C₂²	1	4	yes	—
6	C₃×C₄²×C₅	C₄	1	4	yes	complemented
7	#4937	—	5	1	no	maximal, Hall
8	C₂×C₄²×C₅	D₃	1	1	yes	characteristic
9	#3963	—	3	6	no	—
10	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
11	C₂×C₃×C₄×C₅	—	2	6	no	—
12	C₂×C₃×C₄×C₅	C₂×C₄	1	6	yes	—
13	C₂×Dic₁₅	—	2	12	no	—
14	C₂×C₃×C₄²	D₅	1	1	yes	characteristic
15	C₃⋊#95	—	5	6	no	—
16	C₂²×C₄×C₅	C₂×D₃	1	3	yes	—
17	C₂²×Dic₅	—	3	4	no	—
18	C₄²×C₅	Dic₃	1	4	yes	complemented
19	#383	—	15	1	no	Sylow
20	C₂²×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
21	C₂²×C₃×C₅	#41	1	6	yes	—
22	C₃×C₄×C₅	—	2	6	no	—
23	Dic₁₅	—	4	4	no	—
24	C₂²×C₃×C₄	C₂×D₅	1	3	yes	—
25	C₂²×Dic₃	—	5	4	no	—
26	C₃×C₄²	Dic₅	1	4	yes	complemented
27	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
28	C₂×C₄×C₅	—	2	6	no	—
29	C₂×C₄×C₅	C₂×Dic₃	1	6	yes	—
30	C₂×Dic₅	—	6	12	no	—
31	C₂×C₄²	D₁₅	1	1	yes	characteristic
32	#95	—	15	6	no	—
33	C₂×C₃×C₅	#117	1	3	yes	—
34	C₂×C₃×C₅	#126	1	4	yes	—
35	C₂³×C₃	C₂²×D₅	1	1	yes	characteristic
36	C₂×C₃×C₄	—	2	6	no	—
37	C₂×C₃×C₄	C₂×Dic₅	1	6	yes	—
38	C₂×Dic₃	—	10	12	no	—
39	C₂²×C₅	#235	1	6	yes	—
40	C₂²×C₅	C₂²×Dic₃	1	1	yes	characteristic
41	C₄×C₅	—	2	6	no	—
42	Dic₅	—	12	4	no	—
43	C₂²×C₄	—	15	4	no	—
44	C₂²×C₄	C₂×D₁₅	1	3	yes	—
45	C₄²	Dic₁₅	1	4	yes	complemented
46	C₃×C₅	#383	1	1	yes	characteristic, complemented, Hall
47	C₂²×C₃	#709	1	6	yes	—
48	C₂²×C₃	C₂²×Dic₅	1	1	yes	characteristic
49	C₃×C₄	—	2	6	no	—
50	Dic₃	—	20	4	no	—
51	C₂×C₅	#876	1	4	yes	—
52	C₂×C₅	#926	1	3	yes	—
53	C₂³	C₂²×D₁₅	1	1	yes	characteristic
54	C₂×C₄	—	2	6	no	—
55	C₂×C₄	—	30	12	no	—
56	C₂×C₄	C₂×Dic₁₅	1	6	yes	—
57	C₂×C₃	#4022	1	4	yes	—
58	C₂×C₃	#4072	1	3	yes	—
59	C₅	#4937	1	1	yes	characteristic, complemented, Sylow
60	C₂²	#6817	1	6	yes	—
61	C₂²	C₂²×Dic₁₅	1	1	yes	characteristic
62	C₄	—	2	6	no	—
63	C₄	—	60	4	no	—
64	C₃	#65226	1	1	yes	characteristic, complemented, Sylow
65	C₂	#91765	1	4	yes	—
66	C₂	#91815	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₁₅
commutator	C₂²×C₃×C₅	C₂²×C₄
Fitting	C₂×C₃×C₄²×C₅	C₂
socle, prime radical, cosocle	C₂³×C₃×C₅	C₂³
hypercenter	C₂×C₄²	D₁₅
hypocenter	C₃×C₅	#383
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
6. C₃×C₄²×C₅	C₄	semidirect
18. C₄²×C₅	Dic₃	semidirect
26. C₃×C₄²	Dic₅	semidirect
45. C₄²	Dic₁₅	semidirect
46. C₃×C₅	#383	semidirect
59. C₅	#4937	semidirect
64. C₃	#65226	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄²×C₅	2
#91115	2
#65226	3
#4937	5