Subgroups — C₃×#3946 #91016

Order 480.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×Dic₅	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#168	C₂	1	1	yes	maximal, characteristic
4	#3946	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	1	yes	characteristic
7	C₂×C₃×Dic₅	C₄	1	1	yes	characteristic
8	C₃×C₅×C₈	—	2	1	no	—
9	C₃×#168	—	2	1	no	—
10	C₃×C₄⋊C₈	—	5	1	no	maximal, Hall
11	C₂×C₅×C₈	C₂×C₃	1	1	yes	characteristic
12	C₄×Dic₅	C₂×C₃	1	1	yes	characteristic
13	C₂×#168	C₂×C₃	1	1	yes	characteristic
14	C₂²×C₃×C₅	C₂×C₄	1	1	yes	characteristic
15	C₃×C₄×C₅	D₄	1	1	yes	characteristic
16	C₃×C₄×C₅	Q₈	1	1	yes	characteristic
17	C₃×Dic₅	—	2	1	no	—
18	C₃×Dic₅	C₈	1	2	yes	complemented
19	C₂×C₃×C₈	—	5	1	no	—
20	C₂×C₃×C₈	D₅	1	1	yes	characteristic
21	C₃×C₄²	—	5	1	no	—
22	C₂×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
23	C₂×Dic₅	C₃×C₄	1	1	yes	characteristic
24	C₂×Dic₅	C₃×C₄	1	1	yes	characteristic
25	C₅×C₈	—	2	1	no	—
26	#168	—	2	1	no	—
27	C₄⋊C₈	—	5	1	no	Sylow
28	C₂×C₃×C₅	C₄⋊C₄	1	1	yes	characteristic
29	C₂×C₃×C₅	C₂×C₈	1	1	yes	characteristic
30	C₂×C₃×C₅	M₁₆	1	1	yes	characteristic
31	C₂×C₃×C₄	—	5	1	no	—
32	C₂×C₃×C₄	—	5	1	no	—
33	C₂×C₃×C₄	C₂×D₅	1	1	yes	characteristic
34	C₃×C₈	—	2	1	no	—
35	C₃×C₈	—	10	1	no	—
36	C₂²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
37	C₄×C₅	C₃×D₄	1	1	yes	characteristic
38	C₄×C₅	C₃×Q₈	1	1	yes	characteristic
39	Dic₅	—	2	1	no	—
40	Dic₅	C₃×C₈	1	2	yes	complemented
41	C₂×C₈	—	5	1	no	—
42	C₂×C₈	C₃×D₅	1	1	yes	characteristic
43	C₄²	—	5	1	no	—
44	C₃×C₅	C₄⋊C₈	1	1	yes	characteristic, complemented, Hall
45	C₂²×C₃	C₄×D₅	1	1	yes	characteristic
46	C₃×C₄	—	5	2	no	—
47	C₃×C₄	—	10	1	no	—
48	C₃×C₄	Dic₁₀	1	1	yes	characteristic
49	C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
50	C₂×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
51	C₂×C₅	C₂×C₃×C₈	1	1	yes	characteristic
52	C₂×C₅	C₃×M₁₆	1	1	yes	characteristic
53	C₂×C₄	—	5	1	no	—
54	C₂×C₄	—	5	1	no	—
55	C₂×C₄	C₂×C₃×D₅	1	1	yes	characteristic
56	C₈	—	2	1	no	—
57	C₈	—	10	1	no	—
58	C₂×C₃	C₈×D₅	1	1	yes	characteristic
59	C₂×C₃	#676	1	1	yes	characteristic
60	C₂×C₃	#683	1	1	yes	characteristic
61	C₅	C₃×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
62	C₂²	C₃×C₄×D₅	1	1	yes	characteristic
63	C₄	—	5	2	no	—
64	C₄	—	10	1	no	—
65	C₄	C₃×Dic₁₀	1	1	yes	characteristic
66	C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
67	C₃	#3946	1	1	yes	characteristic, direct product factor, Sylow
68	C₂	C₃×C₈×D₅	1	1	yes	characteristic
69	C₂	C₃×#676	1	1	yes	characteristic
70	C₂	C₃×#683	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂×D₅
commutator	C₂×C₅	C₂×C₃×C₈
Frattini	C₂×C₄	C₂×C₃×D₅
Fitting	C₂×C₃×C₅×C₈	C₂
socle, prime radical	C₂²×C₃×C₅	C₂×C₄
cosocle	C₂×C₄×C₅	C₂²×C₃
hypercenter	C₂×C₃×C₈	D₅
hypocenter	C₅	C₃×C₄⋊C₈
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈

Complements

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

N	H ≅ G/N	type
4. #3946	C₃	direct (N × H)
18. C₃×Dic₅	C₈	semidirect
40. Dic₅	C₃×C₈	semidirect
44. C₃×C₅	C₄⋊C₈	semidirect
61. C₅	C₃×C₄⋊C₈	semidirect
67. C₃	#3946	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×C₅×C₈	2
C₃×C₄×Dic₅	2
C₂×C₃×#168	2
#3946	3
C₃×C₄⋊C₈	5

Subgroups — C3×#3946 #91016

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3946 #91016