Subgroups — #11746317

Order 960.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₆₀	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#108	C₂	1	1	yes	maximal, characteristic
3	#91096	C₂	1	1	yes	maximal, characteristic
4	#64716	—	3	1	no	maximal, Hall
5	C₂×Dic₃₀	—	2	1	no	—
6	C₃×C₅×M₁₆	—	2	1	no	—
7	C₂×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
8	Dic₆₀	—	2	1	no	—
9	Dic₆₀	C₄	1	2	yes	—
10	C₃⋊#672	—	2	1	no	—
11	#4496	—	5	1	no	maximal, Hall
12	C₂×Dic₂₀	—	3	1	no	—
13	C₅×#108	D₃	1	1	yes	characteristic
14	#3944	—	3	1	no	—
15	C₂×C₃×C₄×C₅	D₄	1	1	yes	characteristic
16	C₂×Dic₁₅	—	4	1	no	—
17	Dic₃₀	—	2	2	no	—
18	Dic₃₀	—	4	1	no	—
19	C₃×C₅×C₈	—	4	1	no	—
20	C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
21	C₃×C₅×C₈	D₄	1	1	yes	characteristic
22	C₂×Dic₁₂	—	5	1	no	—
23	C₃×#108	D₅	1	1	yes	characteristic
24	#812	—	5	1	no	—
25	C₂×Dic₁₀	—	6	1	no	—
26	C₅×M₁₆	—	2	1	no	—
27	C₂×C₅×C₈	C₂×D₃	1	1	yes	characteristic
28	Dic₂₀	—	3	2	no	—
29	Dic₂₀	—	6	1	no	—
30	#672	—	6	1	no	—
31	#362	—	15	1	no	Sylow
32	C₂²×C₃×C₅	SD₁₆	1	1	yes	characteristic
33	C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
34	C₃×C₄×C₅	D₈	1	1	yes	characteristic
35	Dic₁₅	—	4	2	no	—
36	C₂×Dic₆	—	10	1	no	—
37	C₃×M₁₆	—	2	1	no	—
38	C₂×C₃×C₈	C₂×D₅	1	1	yes	characteristic
39	Dic₁₂	—	5	2	no	—
40	Dic₁₂	—	10	1	no	—
41	C₃⋊C₁₆	—	10	1	no	—
42	C₂×C₄×C₅	#67	1	1	yes	characteristic
43	C₂×Dic₅	—	12	1	no	—
44	Dic₁₀	—	6	2	no	—
45	Dic₁₀	—	12	1	no	—
46	C₅×C₈	—	4	1	no	—
47	C₅×C₈	C₄×D₃	1	1	yes	characteristic
48	C₅×C₈	D₁₂	1	1	yes	characteristic
49	C₂×Q₁₆	—	15	1	no	—
50	M₃₂	—	15	1	no	—
51	#108	D₁₅	1	1	yes	characteristic
52	C₂×C₃×C₅	—	2	1	no	—
53	C₂×C₃×C₅	#102	1	1	yes	characteristic
54	C₂×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
55	C₂×Dic₃	—	20	1	no	—
56	Dic₆	—	10	2	no	—
57	Dic₆	—	20	1	no	—
58	C₃×C₈	—	4	1	no	—
59	C₃×C₈	C₄×D₅	1	1	yes	characteristic
60	C₃×C₈	D₂₀	1	1	yes	characteristic
61	C₂²×C₅	#215	1	1	yes	characteristic
62	C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
63	C₄×C₅	#213	1	1	yes	characteristic
64	Dic₅	—	12	2	no	—
65	C₂×Q₈	—	30	1	no	—
66	Q₁₆	—	15	2	no	—
67	Q₁₆	—	30	1	no	—
68	M₁₆	—	2	1	no	—
69	C₂×C₈	C₂×D₁₅	1	1	yes	characteristic
70	C₁₆	—	30	1	no	—
71	C₃×C₅	#362	1	1	yes	characteristic, complemented, Hall
72	C₂²×C₃	#688	1	1	yes	characteristic
73	C₃×C₄	#685	1	1	yes	characteristic
74	C₃×C₄	#686	1	1	yes	characteristic
75	Dic₃	—	20	2	no	—
76	C₂×C₅	—	2	1	no	—
77	C₂×C₅	#809	1	1	yes	characteristic
78	Q₈	—	30	2	no	—
79	Q₈	—	60	1	no	—
80	C₂×C₄	—	60	1	no	—
81	C₂×C₄	#1220	1	1	yes	characteristic
82	C₈	—	4	1	no	—
83	C₈	C₄×D₁₅	1	1	yes	characteristic
84	C₈	D₆₀	1	1	yes	characteristic
85	C₂×C₃	—	2	1	no	—
86	C₂×C₃	#3941	1	1	yes	characteristic
87	C₅	#4496	1	1	yes	characteristic, complemented, Sylow
88	C₂²	#6717	1	1	yes	characteristic
89	C₄	—	60	2	no	—
90	C₄	#6714	1	1	yes	characteristic
91	C₄	#6715	1	1	yes	characteristic
92	C₃	#64716	1	1	yes	characteristic, complemented, Sylow
93	C₂	—	2	1	no	—
94	C₂	#91093	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#91093
commutator	C₃×C₅×C₈	C₂×C₄
Frattini	C₂×C₈	C₂×D₁₅
Fitting	C₃×C₅×#108	C₂
socle	C₂×C₃×C₅	#102
prime radical	C₂²×C₃×C₅	SD₁₆
cosocle	C₂×C₃×C₅×C₈	C₂²
hypercenter	#108	D₁₅
hypocenter	C₃×C₅	#362
LCS	G ▷ C₃×C₅×C₈ ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #108

Complements

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

N	H ≅ G/N	type
71. C₃×C₅	#362	semidirect
87. C₅	#4496	semidirect
92. C₃	#64716	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₆₀	2
C₃×C₅×#108	2
#91096	2
#64716	3
#4496	5