Subgroups — #13086342

Order 1440.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₈×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	#10623724	C₂	1	2	yes	maximal, complemented
3	C₄×C₅×C₃⋊D₃	C₄	1	1	yes	characteristic
4	C₃²×C₅×C₈	C₄	1	1	yes	characteristic
5	C₅×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
6	#63765	—	5	1	no	maximal, Hall
7	C₅×D₃×C₈	—	6	2	no	—
8	C₂×C₅×C₃⋊D₃	C₈	1	1	yes	characteristic
9	C₃²×C₄×C₅	C₂×C₄	1	1	yes	characteristic
10	C₅×C₃⋊Dic₃	C₈	1	1	yes	characteristic
11	#3944	—	9	1	no	maximal, Hall
12	C₈×C₃⋊D₃	D₅	1	1	yes	characteristic
13	#3708	—	5	2	no	—
14	C₄×C₅×D₃	—	6	2	no	—
15	C₃×C₅×C₈	—	2	2	no	—
16	C₅×C₃⋊C₈	—	6	2	no	—
17	C₂×C₃²×C₅	C₂×C₈	1	1	yes	characteristic
18	C₅×C₃⋊D₃	—	2	1	no	—
19	C₂×C₅×C₈	—	9	1	no	—
20	#672	—	9	2	no	—
21	C₄×C₃⋊D₃	Dic₅	1	1	yes	characteristic
22	C₃²×C₈	Dic₅	1	1	yes	characteristic
23	C₃⋊(C₃⋊C₈)	C₂×D₅	1	1	yes	characteristic
24	C₂×C₅×D₃	—	6	2	no	—
25	C₃×C₄×C₅	—	2	2	no	—
26	C₅×Dic₃	—	6	2	no	—
27	D₃×C₈	—	6	2	no	—
28	C₃²×C₅	M₃₂	1	1	yes	characteristic, complemented, Hall
29	C₂×C₄×C₅	—	9	1	no	—
30	C₅×C₈	—	9	1	no	—
31	C₅×C₈	#157	1	1	yes	characteristic
32	C₂×C₃⋊D₃	#168	1	1	yes	characteristic
33	C₃²×C₄	C₂×Dic₅	1	1	yes	characteristic
34	C₃⋊Dic₃	#168	1	1	yes	characteristic
35	M₃₂	—	45	1	no	Sylow
36	C₂×C₃×C₅	—	2	2	no	—
37	C₅×D₃	—	6	4	no	—
38	C₄×D₃	—	6	2	no	—
39	C₃×C₈	—	2	2	no	—
40	C₃⋊C₈	—	6	2	no	—
41	C₂²×C₅	—	9	1	no	—
42	C₄×C₅	—	9	1	no	—
43	C₄×C₅	C₂×#157	1	1	yes	characteristic
44	C₂×C₃²	C₂×#168	1	1	yes	characteristic
45	C₃⋊D₃	—	2	1	no	—
46	C₂×C₈	—	9	1	no	—
47	C₁₆	—	45	2	no	—
48	C₃×C₅	—	2	2	no	—
49	C₂×D₃	—	6	2	no	—
50	C₃×C₄	—	2	2	no	—
51	Dic₃	—	6	2	no	—
52	C₂×C₅	—	18	1	no	—
53	C₂×C₅	#3787	1	1	yes	characteristic
54	C₃²	#3944	1	1	yes	characteristic, complemented, Sylow
55	C₂×C₄	—	9	1	no	—
56	C₈	—	9	1	no	—
57	C₈	#4379	1	1	yes	characteristic
58	C₂×C₃	—	2	2	no	—
59	D₃	—	6	4	no	—
60	C₅	#63765	1	1	yes	characteristic, complemented, Sylow
61	C₂²	—	9	1	no	—
62	C₄	—	9	1	no	—
63	C₄	C₂×#4379	1	1	yes	characteristic
64	C₃	—	2	2	no	—
65	C₂	—	18	1	no	—
66	C₂	#10624106	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂×#4379
commutator, socle	C₂×C₃²×C₅	C₂×C₈
Fitting	C₃²×C₅×C₈	C₄
prime radical	C₂×C₅×C₃⋊D₃	C₈
cosocle	C₅×C₃⋊(C₃⋊C₈)	C₂²
hypercenter	C₈	#4379
hypocenter	C₃²×C₅	M₃₂
LCS	G ▷ C₂×C₃²×C₅ ▷ C₃²×C₅
UCS	C₁ ◁ C₄ ◁ C₈

Complements

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

N	H ≅ G/N	type
2. #10623724	C₂	semidirect
28. C₃²×C₅	M₃₂	semidirect
54. C₃²	#3944	semidirect
60. C₅	#63765	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₈×C₃⋊D₃	2
#10623724	2
#63765	5
#3944	9