Subgroups — C₄⋊(C₃⋊#168) #91088

Order 480.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄²×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃⋊#168	C₂	1	2	yes	maximal
3	C₄⋊#168	—	3	1	no	maximal, Hall
4	C₂×C₃×C₄×C₅	C₄	1	1	yes	characteristic
5	C₂×C₃×C₄×C₅	C₄	1	1	yes	characteristic
6	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
7	C₃⋊#168	—	2	2	no	—
8	C₄⋊(C₃⋊C₈)	—	5	1	no	maximal, Hall
9	C₄²×C₅	D₃	1	1	yes	characteristic
10	C₂×#168	—	3	2	no	—
11	C₂²×C₃×C₅	C₂×C₄	1	1	yes	characteristic
12	C₃×C₄×C₅	—	2	1	no	—
13	C₃×C₄×C₅	C₈	1	2	yes	complemented
14	C₃×C₄×C₅	D₄	1	1	yes	characteristic
15	C₃×C₄×C₅	Q₈	1	1	yes	characteristic
16	C₃×C₄²	D₅	1	1	yes	characteristic
17	C₂×C₃⋊C₈	—	5	2	no	—
18	C₂×C₄×C₅	Dic₃	1	1	yes	characteristic
19	C₂×C₄×C₅	Dic₃	1	1	yes	characteristic
20	C₂×C₄×C₅	C₂×D₃	1	1	yes	characteristic
21	#168	—	6	2	no	—
22	C₄⋊C₈	—	15	1	no	Sylow
23	C₂×C₃×C₅	C₄⋊C₄	1	1	yes	characteristic
24	C₂×C₃×C₅	C₂×C₈	1	1	yes	characteristic
25	C₂×C₃×C₅	M₁₆	1	1	yes	characteristic
26	C₂×C₃×C₄	Dic₅	1	1	yes	characteristic
27	C₂×C₃×C₄	Dic₅	1	1	yes	characteristic
28	C₂×C₃×C₄	C₂×D₅	1	1	yes	characteristic
29	C₃⋊C₈	—	10	2	no	—
30	C₂²×C₅	C₂×Dic₃	1	1	yes	characteristic
31	C₄×C₅	—	2	1	no	—
32	C₄×C₅	C₃⋊C₈	1	2	yes	complemented
33	C₄×C₅	Dic₆	1	1	yes	characteristic
34	C₄×C₅	D₁₂	1	1	yes	characteristic
35	C₂×C₈	—	15	2	no	—
36	C₄²	D₁₅	1	1	yes	characteristic
37	C₃×C₅	C₄⋊C₈	1	1	yes	characteristic, complemented, Hall
38	C₂²×C₃	C₂×Dic₅	1	1	yes	characteristic
39	C₃×C₄	—	2	1	no	—
40	C₃×C₄	#168	1	2	yes	complemented
41	C₃×C₄	Dic₁₀	1	1	yes	characteristic
42	C₃×C₄	D₂₀	1	1	yes	characteristic
43	C₂×C₅	C₂×C₃⋊C₈	1	1	yes	characteristic
44	C₂×C₅	#208	1	1	yes	characteristic
45	C₂×C₅	C₄⋊Dic₃	1	1	yes	characteristic
46	C₂×C₄	Dic₁₅	1	1	yes	characteristic
47	C₂×C₄	Dic₁₅	1	1	yes	characteristic
48	C₂×C₄	C₂×D₁₅	1	1	yes	characteristic
49	C₈	—	30	2	no	—
50	C₂×C₃	C₂×#168	1	1	yes	characteristic
51	C₂×C₃	#681	1	1	yes	characteristic
52	C₂×C₃	C₄⋊Dic₅	1	1	yes	characteristic
53	C₅	C₄⋊(C₃⋊C₈)	1	1	yes	characteristic, complemented, Sylow
54	C₂²	C₂×Dic₁₅	1	1	yes	characteristic
55	C₄	—	2	1	no	—
56	C₄	C₃⋊#168	1	2	yes	complemented
57	C₄	Dic₃₀	1	1	yes	characteristic
58	C₄	D₆₀	1	1	yes	characteristic
59	C₃	C₄⋊#168	1	1	yes	characteristic, complemented, Sylow
60	C₂	C₂×C₃⋊#168	1	1	yes	characteristic
61	C₂	#6710	1	1	yes	characteristic
62	C₂	C₄⋊Dic₁₅	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
13. C₃×C₄×C₅	C₈	semidirect
32. C₄×C₅	C₃⋊C₈	semidirect
37. C₃×C₅	C₄⋊C₈	semidirect
40. C₃×C₄	#168	semidirect
53. C₅	C₄⋊(C₃⋊C₈)	semidirect
56. C₄	C₃⋊#168	semidirect
59. C₃	C₄⋊#168	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄²×C₅	2
C₂×C₃⋊#168	2
C₄⋊#168	3
C₄⋊(C₃⋊C₈)	5

Subgroups — C4⋊(C3⋊#168) #91088

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊(C₃⋊#168) #91088