Subgroups — C₈×#4380 #13086368

Order 1440.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#4380	C₂	1	1	yes	maximal, characteristic
2	#10624113	C₂	1	1	yes	maximal, characteristic
3	C₈×C₃⋊D₁₅	C₂	1	1	yes	maximal, characteristic
4	C₂×#4380	C₄	1	2	yes	—
5	C₄×C₃⋊D₁₅	C₂²	1	1	yes	characteristic
6	#67127	C₄	1	2	yes	complemented
7	C₃²×C₅×C₈	C₄	1	1	yes	characteristic, complemented
8	C₃⋊(C₃⋊#168)	C₄	1	1	yes	characteristic, complemented
9	C₈×#157	—	5	1	no	maximal, Hall
10	C₈×D₁₅	—	6	2	no	—
11	C₂×C₃⋊D₁₅	C₂×C₄	1	1	yes	characteristic
12	#4380	C₈	1	4	yes	direct product factor
13	C₃²×C₄×C₅	C₂×C₄	1	1	yes	characteristic
14	C₃⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
15	C₈×AGL(1,𝔽₅)	—	9	1	no	maximal, Hall
16	C₄×#157	—	5	1	no	—
17	#3787	—	5	1	no	—
18	C₈×C₃⋊D₃	—	5	1	no	—
19	C₄×D₁₅	—	6	2	no	—
20	C₃×C₅×C₈	—	2	2	no	—
21	C₃⋊#168	—	6	2	no	—
22	C₂×C₃²×C₅	C₄²	1	1	yes	characteristic
23	C₃⋊D₁₅	C₂×C₈	1	2	yes	—
24	C₄×AGL(1,𝔽₅)	—	9	1	no	—
25	D₅⋊C₈	—	9	1	no	—
26	C₈×D₅	—	9	1	no	—
27	C₂×#157	—	5	2	no	—
28	C₄×C₃⋊D₃	—	5	1	no	—
29	#622	—	5	2	no	—
30	C₃²×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
31	C₃⋊(C₃⋊C₈)	—	5	1	no	—
32	C₂×D₁₅	—	6	2	no	—
33	C₃×C₄×C₅	—	2	2	no	—
34	Dic₁₅	—	6	2	no	—
35	D₃×C₈	—	30	2	no	—
36	C₃²×C₅	C₄×C₈	1	1	yes	characteristic, complemented, Hall
37	C₂×AGL(1,𝔽₅)	—	9	2	no	—
38	C₄×D₅	—	9	1	no	—
39	#170	—	9	2	no	—
40	C₅×C₈	#157	1	1	yes	characteristic, complemented
41	#168	—	9	1	no	—
42	C₂×C₃⋊D₃	—	5	1	no	—
43	#157	—	5	4	no	—
44	C₃²×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
45	C₃⋊Dic₃	—	5	1	no	—
46	C₄×C₈	—	45	1	no	Sylow
47	C₂×C₃×C₅	—	2	2	no	—
48	D₁₅	—	6	4	no	—
49	C₄×D₃	—	30	2	no	—
50	C₃×C₈	—	2	2	no	—
51	C₃⋊C₈	—	30	2	no	—
52	C₂×D₅	—	9	1	no	—
53	AGL(1,𝔽₅)	—	9	4	no	—
54	C₄×C₅	C₂×#157	1	1	yes	characteristic
55	Dic₅	—	9	1	no	—
56	C₂×C₃²	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
57	C₃⋊D₃	—	5	2	no	—
58	C₂×C₈	—	45	1	no	—
59	C₂×C₈	—	45	1	no	—
60	C₄²	—	45	1	no	—
61	C₃×C₅	—	2	2	no	—
62	C₂×D₃	—	30	2	no	—
63	C₃×C₄	—	2	2	no	—
64	Dic₃	—	30	2	no	—
65	C₂×C₅	C₄×#157	1	1	yes	characteristic
66	D₅	—	9	2	no	—
67	C₃²	C₈×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
68	C₂×C₄	—	45	2	no	—
69	C₂×C₄	—	45	1	no	—
70	C₈	—	45	2	no	—
71	C₈	—	45	1	no	—
72	C₈	#4380	1	1	yes	characteristic, direct product factor
73	C₂×C₃	—	2	2	no	—
74	D₃	—	30	4	no	—
75	C₅	C₈×#157	1	1	yes	characteristic, complemented, Sylow
76	C₂²	—	45	1	no	—
77	C₄	—	45	4	no	—
78	C₄	—	45	1	no	—
79	C₄	C₂×#4380	1	1	yes	characteristic
80	C₃	—	2	2	no	—
81	C₂	—	45	2	no	—
82	C₂	C₄×#4380	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₈	#4380
commutator, hypocenter	C₃²×C₅	C₄×C₈
Frattini	C₄	C₂×#4380
Fitting	C₃²×C₅×C₈	C₄
socle	C₂×C₃²×C₅	C₄²
prime radical	C₂×C₃⋊D₁₅	C₂×C₄
cosocle	C₄×C₃⋊D₁₅	C₂²
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₈

Complements

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

N	H ≅ G/N	type
6. #67127	C₄	semidirect
7. C₃²×C₅×C₈	C₄	semidirect
8. C₃⋊(C₃⋊#168)	C₄	semidirect
12. #4380	C₈	direct (N × H)
30. C₃²×C₈	AGL(1,𝔽₅)	semidirect
36. C₃²×C₅	C₄×C₈	semidirect
40. C₅×C₈	#157	semidirect
67. C₃²	C₈×AGL(1,𝔽₅)	semidirect
72. C₈	#4380	direct (N × H)
75. C₅	C₈×#157	semidirect

Maximal subgroups

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

subgroup	index
C₄×#4380	2
#10624113	2
C₈×C₃⋊D₁₅	2
C₈×#157	5
C₈×AGL(1,𝔽₅)	9

Subgroups — C8×#4380 #13086368

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#4380 #13086368