Subgroups — C₃×#3956 #91026

Order 480.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Dic₁₀	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₃×#681	C₂	1	1	yes	maximal, characteristic
4	#3956	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
6	C₂×C₃×Dic₅	C₄	1	2	yes	—
7	C₃×Dic₁₀	—	2	1	no	—
8	C₃×Dic₁₀	—	2	1	no	—
9	C₃×C₅×C₈	—	2	1	no	—
10	C₃×#168	—	2	1	no	—
11	C₃×#101	—	5	1	no	maximal, Hall
12	C₂×Dic₁₀	C₂×C₃	1	1	yes	characteristic
13	C₅×M₁₆	C₂×C₃	1	1	yes	characteristic
14	#681	C₂×C₃	1	1	yes	characteristic
15	C₂²×C₃×C₅	C₂×C₄	1	1	yes	characteristic
16	C₃×C₄×C₅	D₄	1	1	yes	characteristic
17	C₃×C₄×C₅	D₄	1	1	yes	characteristic
18	C₃×Dic₅	—	2	2	no	—
19	C₂×C₃×Q₈	—	5	1	no	—
20	C₃×M₁₆	—	5	1	no	—
21	C₃×M₁₆	D₅	1	1	yes	characteristic
22	C₂×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
23	C₂×Dic₅	C₃×C₄	1	2	yes	—
24	Dic₁₀	—	2	1	no	—
25	Dic₁₀	—	2	1	no	—
26	C₅×C₈	—	2	1	no	—
27	#168	—	2	1	no	—
28	#101	—	5	1	no	Sylow
29	C₂×C₃×C₅	—	2	1	no	—
30	C₂×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
31	C₃×Q₈	—	10	1	no	—
32	C₃×Q₈	—	10	1	no	—
33	C₂×C₃×C₄	—	5	2	no	—
34	C₂×C₃×C₄	C₂×D₅	1	1	yes	characteristic
35	C₃×C₈	—	2	1	no	—
36	C₃×C₈	—	10	1	no	—
37	C₂²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
38	C₄×C₅	C₃×D₄	1	1	yes	characteristic
39	C₄×C₅	C₃×D₄	1	1	yes	characteristic
40	Dic₅	—	2	2	no	—
41	C₂×Q₈	—	5	1	no	—
42	M₁₆	—	5	1	no	—
43	M₁₆	C₃×D₅	1	1	yes	characteristic
44	C₃×C₅	#101	1	1	yes	characteristic, complemented, Hall
45	C₂²×C₃	C₄×D₅	1	1	yes	characteristic
46	C₃×C₄	—	10	2	no	—
47	C₃×C₄	D₂₀	1	1	yes	characteristic
48	C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
49	C₂×C₅	—	2	1	no	—
50	C₂×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
51	Q₈	—	10	1	no	—
52	Q₈	—	10	1	no	—
53	C₂×C₄	—	5	2	no	—
54	C₂×C₄	C₂×C₃×D₅	1	1	yes	characteristic
55	C₈	—	2	1	no	—
56	C₈	—	10	1	no	—
57	C₂×C₃	—	2	1	no	—
58	C₂×C₃	#685	1	1	yes	characteristic
59	C₅	C₃×#101	1	1	yes	characteristic, complemented, Sylow
60	C₂²	C₃×C₄×D₅	1	1	yes	characteristic
61	C₄	—	10	2	no	—
62	C₄	C₃×D₂₀	1	1	yes	characteristic
63	C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
64	C₃	#3956	1	1	yes	characteristic, direct product factor, Sylow
65	C₂	—	2	1	no	—
66	C₂	C₃×#685	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	#685
commutator	C₂²×C₅	C₂×C₃×C₄
Frattini	C₂×C₄	C₂×C₃×D₅
Fitting	C₃×C₅×M₁₆	C₂
socle	C₂×C₃×C₅	C₂²⋊C₄
prime radical	C₂²×C₃×C₅	C₂×C₄
cosocle	C₂×C₄×C₅	C₂²×C₃
hypercenter	C₃×M₁₆	D₅
hypocenter	C₅	C₃×#101
LCS	G ▷ C₂²×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×M₁₆

Complements

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

N	H ≅ G/N	type
4. #3956	C₃	direct (N × H)
44. C₃×C₅	#101	semidirect
59. C₅	C₃×#101	semidirect
64. C₃	#3956	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×Dic₁₀	2
C₃×C₅×M₁₆	2
C₃×#681	2
#3956	3
C₃×#101	5

Subgroups — C3×#3956 #91026

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3956 #91026