Subgroups — #11745877

Order 960.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#91096	C₂	1	1	yes	maximal, characteristic
2	C₅×#815	C₂	1	1	yes	maximal, characteristic
3	C₃×#3944	C₂	1	1	yes	maximal, characteristic
4	#64686	—	3	1	no	maximal, Hall
5	C₂×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
6	C₄×C₅×Dic₃	C₄	1	1	yes	characteristic
7	C₂×C₅×C₃⋊C₈	C₄	1	1	yes	characteristic
8	C₃⋊#672	C₄	1	2	yes	complemented
9	C₃×#672	C₄	1	2	yes	complemented
10	#4512	—	5	1	no	maximal, Hall
11	C₅×#97	—	3	1	no	—
12	#3944	—	3	1	no	—
13	#3944	D₃	1	1	yes	characteristic
14	C₂×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
15	C₂×C₅×Dic₃	—	2	1	no	—
16	C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
17	C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
18	C₅×C₃⋊C₈	—	2	1	no	—
19	C₃×M₃₂	—	5	1	no	—
20	#815	D₅	1	1	yes	characteristic
21	#812	—	5	1	no	—
22	C₂×C₅×C₈	—	3	1	no	—
23	C₂×C₅×C₈	C₂×D₃	1	1	yes	characteristic
24	C₄²×C₅	—	3	1	no	—
25	#672	—	3	2	no	—
26	#672	Dic₃	1	2	yes	complemented
27	#347	—	15	1	no	Sylow
28	C₂²×C₃×C₅	M₁₆	1	1	yes	characteristic
29	C₃×C₄×C₅	C₄²	1	1	yes	characteristic
30	C₃×C₄×C₅	M₁₆	1	1	yes	characteristic
31	C₅×Dic₃	—	4	1	no	—
32	C₂×C₃×C₈	C₂×D₅	1	1	yes	characteristic
33	C₄×Dic₃	Dic₅	1	1	yes	characteristic
34	C₂×C₃⋊C₈	Dic₅	1	1	yes	characteristic
35	C₃×C₁₆	—	5	2	no	—
36	C₃⋊C₁₆	—	5	2	no	—
37	C₂×C₄×C₅	—	6	1	no	—
38	C₂×C₄×C₅	C₄×D₃	1	1	yes	characteristic
39	C₅×C₈	—	6	1	no	—
40	C₅×C₈	C₄×D₃	1	1	yes	characteristic
41	C₅×C₈	C₂×Dic₃	1	1	yes	characteristic
42	M₃₂	—	5	1	no	—
43	M₃₂	—	15	1	no	—
44	#97	—	3	1	no	—
45	C₂×C₃×C₅	—	2	1	no	—
46	C₂×C₃×C₅	#97	1	1	yes	characteristic
47	C₂×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
48	C₂×Dic₃	—	2	1	no	—
49	C₃×C₈	C₄×D₅	1	1	yes	characteristic
50	C₃×C₈	C₄×D₅	1	1	yes	characteristic
51	C₃⋊C₈	—	2	1	no	—
52	C₂²×C₅	ΓL(1,𝔽₂₅)	1	1	yes	characteristic
53	C₄×C₅	—	12	1	no	—
54	C₄×C₅	ΓL(1,𝔽₂₅)	1	1	yes	characteristic
55	C₄×C₅	C₄×Dic₃	1	1	yes	characteristic
56	C₂×C₈	—	3	1	no	—
57	C₂×C₈	D₃×D₅	1	1	yes	characteristic
58	C₄²	—	3	1	no	—
59	C₁₆	—	5	2	no	—
60	C₁₆	—	15	2	no	—
61	C₃×C₅	#347	1	1	yes	characteristic, complemented, Hall
62	C₂²×C₃	#681	1	1	yes	characteristic
63	C₃×C₄	#681	1	1	yes	characteristic
64	C₃×C₄	C₄×Dic₅	1	1	yes	characteristic
65	Dic₃	—	4	1	no	—
66	C₂×C₅	—	2	1	no	—
67	C₂×C₅	#815	1	1	yes	characteristic
68	C₂×C₄	—	6	1	no	—
69	C₂×C₄	D₃×Dic₅	1	1	yes	characteristic
70	C₈	—	6	1	no	—
71	C₈	D₅×Dic₃	1	1	yes	characteristic
72	C₈	#1200	1	1	yes	characteristic
73	C₂×C₃	—	2	1	no	—
74	C₂×C₃	#3935	1	1	yes	characteristic
75	C₅	#4512	1	1	yes	characteristic, complemented, Sylow
76	C₂²	#6650	1	1	yes	characteristic
77	C₄	—	12	1	no	—
78	C₄	#6650	1	1	yes	characteristic
79	C₄	Dic₃×Dic₅	1	1	yes	characteristic
80	C₃	#64686	1	1	yes	characteristic, complemented, Sylow
81	C₂	—	2	1	no	—
82	C₂	#90953	1	1	yes	characteristic

	subgroup	G/H
center	C₄	Dic₃×Dic₅
commutator	C₃×C₄×C₅	C₄²
Frattini, hypercenter	C₂×C₈	D₃×D₅
Fitting, cosocle	C₂×C₃×C₅×C₈	C₂²
socle	C₂×C₃×C₅	#97
prime radical	C₂²×C₃×C₅	M₁₆
hypocenter	C₃×C₅	#347
LCS	G ▷ C₃×C₄×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
8. C₃⋊#672	C₄	semidirect
9. C₃×#672	C₄	semidirect
26. #672	Dic₃	semidirect
61. C₃×C₅	#347	semidirect
75. C₅	#4512	semidirect
80. C₃	#64686	semidirect

Maximal subgroups

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

subgroup	index
#91096	2
C₅×#815	2
C₃×#3944	2
#64686	3
#4512	5