Subgroups — #11746314

Order 960.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#108	C₂	1	1	yes	maximal, characteristic
2	#91103	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃⋊#672	C₂	1	1	yes	maximal, characteristic
4	#64713	—	3	1	no	maximal, Hall
5	C₃×C₅×M₁₆	—	2	1	no	—
6	C₂×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
7	#6710	—	2	1	no	—
8	C₃⋊#672	C₄	1	2	yes	—
9	#4493	—	5	1	no	maximal, Hall
10	C₅×#108	D₃	1	1	yes	characteristic
11	#3951	—	3	1	no	—
12	C₂×#672	—	3	1	no	—
13	C₂×C₃×C₄×C₅	D₄	1	1	yes	characteristic
14	C₃×C₅×C₈	—	4	1	no	—
15	C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
16	C₃×C₅×C₈	Q₈	1	1	yes	characteristic
17	C₃⋊#168	—	4	1	no	—
18	C₃×#108	D₅	1	1	yes	characteristic
19	#819	—	5	1	no	—
20	C₂×C₃⋊C₁₆	—	5	1	no	—
21	C₅×M₁₆	—	2	1	no	—
22	C₂×C₅×C₈	C₂×D₃	1	1	yes	characteristic
23	#681	—	6	1	no	—
24	#672	—	3	2	no	—
25	#368	—	15	1	no	Sylow
26	C₂²×C₃×C₅	Q₁₆	1	1	yes	characteristic
27	C₃×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
28	C₃×C₄×C₅	D₈	1	1	yes	characteristic
29	C₃×M₁₆	—	2	1	no	—
30	C₂×C₃×C₈	C₂×D₅	1	1	yes	characteristic
31	#208	—	10	1	no	—
32	C₃⋊C₁₆	—	5	2	no	—
33	C₂×C₄×C₅	#67	1	1	yes	characteristic
34	C₅×C₈	—	4	1	no	—
35	C₅×C₈	Dic₆	1	1	yes	characteristic
36	C₅×C₈	C₄×D₃	1	1	yes	characteristic
37	#168	—	12	1	no	—
38	C₂×C₁₆	—	15	1	no	—
39	#108	—	15	1	no	—
40	#108	D₁₅	1	1	yes	characteristic
41	C₂×C₃×C₅	—	2	1	no	—
42	C₂×C₃×C₅	#107	1	1	yes	characteristic
43	C₂×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
44	C₃×C₈	—	4	1	no	—
45	C₃×C₈	Dic₁₀	1	1	yes	characteristic
46	C₃×C₈	C₄×D₅	1	1	yes	characteristic
47	C₃⋊C₈	—	20	1	no	—
48	C₂²×C₅	#216	1	1	yes	characteristic
49	C₄×C₅	Dic₃⋊C₄	1	1	yes	characteristic
50	C₄×C₅	#213	1	1	yes	characteristic
51	M₁₆	—	2	1	no	—
52	M₁₆	—	30	1	no	—
53	C₂×C₈	C₂×D₁₅	1	1	yes	characteristic
54	C₁₆	—	15	2	no	—
55	C₃×C₅	#368	1	1	yes	characteristic, complemented, Hall
56	C₂²×C₃	#689	1	1	yes	characteristic
57	C₃×C₄	#683	1	1	yes	characteristic
58	C₃×C₄	#686	1	1	yes	characteristic
59	C₂×C₅	—	2	1	no	—
60	C₂×C₅	#807	1	1	yes	characteristic
61	C₂×C₄	#1220	1	1	yes	characteristic
62	C₈	—	4	1	no	—
63	C₈	—	60	1	no	—
64	C₈	Dic₃₀	1	1	yes	characteristic
65	C₈	C₄×D₁₅	1	1	yes	characteristic
66	C₂×C₃	—	2	1	no	—
67	C₂×C₃	#3939	1	1	yes	characteristic
68	C₅	#4493	1	1	yes	characteristic, complemented, Sylow
69	C₂²	#6718	1	1	yes	characteristic
70	C₄	#6712	1	1	yes	characteristic
71	C₄	#6715	1	1	yes	characteristic
72	C₃	#64713	1	1	yes	characteristic, complemented, Sylow
73	C₂	—	2	1	no	—
74	C₂	#91091	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#6715
commutator	C₃×C₅×C₈	C₂×C₄
Frattini	C₂×C₈	C₂×D₁₅
Fitting	C₃×C₅×#108	C₂
socle	C₂×C₃×C₅	#107
prime radical	C₂²×C₃×C₅	Q₁₆
cosocle	C₂×C₃×C₅×C₈	C₂²
hypercenter	#108	D₁₅
hypocenter	C₃×C₅	#368
LCS	G ▷ C₃×C₅×C₈ ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #108

Complements

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

N	H ≅ G/N	type
55. C₃×C₅	#368	semidirect
68. C₅	#4493	semidirect
72. C₃	#64713	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#108	2
#91103	2
C₂×C₃⋊#672	2
#64713	3
#4493	5