Subgroups — C₃×#4147 #92068

Order 480.

292 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#713	C₂	1	4	yes	maximal, complemented
3	C₃×Q₈×D₅	C₂	1	4	yes	maximal, complemented
4	C₃×#709	C₂	1	6	yes	maximal, complemented
5	#4147	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₅×Q₈	C₂²	1	4	yes	—
7	C₂×C₃×C₄×C₅	C₂²	1	3	yes	—
8	C₃×C₂²⋊D₅	C₂²	1	4	yes	—
9	C₃×D₂₀	C₂²	1	6	yes	—
10	C₃×C₄×D₅	C₂²	1	12	yes	—
11	C₃×Dic₁₀	C₂²	1	6	yes	—
12	C₃×2₋¹⁺⁴	—	5	1	no	maximal, Hall
13	C₂×C₅×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
14	#713	C₂×C₃	1	4	yes	complemented
15	Q₈×D₅	C₂×C₃	1	4	yes	complemented
16	#709	C₂×C₃	1	6	yes	complemented
17	C₂²×C₃×C₅	C₂³	1	1	yes	characteristic
18	C₂×C₃×D₅	C₂³	1	4	yes	—
19	C₃×C₄×C₅	C₂³	1	6	yes	—
20	C₃×Dic₅	C₂³	1	4	yes	—
21	C₃×#41	—	5	4	no	—
22	C₃×#41	—	5	6	no	—
23	C₂×C₃×Q₈	—	5	4	no	—
24	C₂×C₃×Q₈	D₅	1	1	yes	characteristic, complemented
25	C₅×Q₈	C₂²×C₃	1	4	yes	—
26	C₂×C₄×C₅	C₂²×C₃	1	3	yes	—
27	C₂²⋊D₅	C₂²×C₃	1	4	yes	—
28	D₂₀	C₂²×C₃	1	6	yes	—
29	C₄×D₅	C₂²×C₃	1	12	yes	—
30	Dic₁₀	C₂²×C₃	1	6	yes	—
31	2₋¹⁺⁴	—	5	1	no	Sylow
32	C₂×C₃×C₅	—	2	1	no	—
33	C₂×C₃×C₅	C₂⁴	1	1	yes	characteristic
34	C₃×D₅	—	2	4	no	—
35	C₃×Q₈	—	5	6	no	—
36	C₃×Q₈	C₂×D₅	1	4	yes	—
37	C₃×D₄	—	5	4	no	—
38	C₃×D₄	—	5	6	no	—
39	C₂×C₃×C₄	—	5	12	no	—
40	C₂×C₃×C₄	C₂×D₅	1	3	yes	—
41	C₂²×C₅	C₂³×C₃	1	1	yes	characteristic
42	C₂×D₅	C₂³×C₃	1	4	yes	—
43	C₄×C₅	C₂³×C₃	1	6	yes	—
44	Dic₅	C₂³×C₃	1	4	yes	—
45	#41	—	5	4	no	—
46	#41	—	5	6	no	—
47	C₂×Q₈	—	5	4	no	—
48	C₂×Q₈	C₃×D₅	1	1	yes	characteristic, complemented
49	C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic, complemented, Hall
50	C₂²×C₃	—	5	4	no	—
51	C₂²×C₃	C₂²×D₅	1	1	yes	characteristic
52	C₃×C₄	—	5	4	no	—
53	C₃×C₄	C₂²×D₅	1	6	yes	—
54	C₂×C₅	—	2	1	no	—
55	C₂×C₅	C₂⁴×C₃	1	1	yes	characteristic
56	D₅	—	2	4	no	—
57	Q₈	—	5	6	no	—
58	Q₈	C₂×C₃×D₅	1	4	yes	—
59	D₄	—	5	4	no	—
60	D₄	—	5	6	no	—
61	C₂×C₄	—	5	12	no	—
62	C₂×C₄	C₂×C₃×D₅	1	3	yes	—
63	C₂×C₃	—	2	1	no	—
64	C₂×C₃	—	10	4	no	—
65	C₂×C₃	C₂³×D₅	1	1	yes	characteristic
66	C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
67	C₂²	—	5	4	no	—
68	C₂²	C₂²×C₃×D₅	1	1	yes	characteristic
69	C₄	—	5	4	no	—
70	C₄	C₂²×C₃×D₅	1	6	yes	—
71	C₃	#4147	1	1	yes	characteristic, direct product factor, Sylow
72	C₂	—	2	1	no	—
73	C₂	—	10	4	no	—
74	C₂	C₂³×C₃×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂³×D₅
commutator, cosocle	C₂×C₅	C₂⁴×C₃
Frattini	C₂	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×Q₈	C₂
socle	C₂×C₃×C₅	C₂⁴
hypercenter	C₂×C₃×Q₈	D₅
hypocenter	C₅	C₃×2₋¹⁺⁴
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×Q₈	C₂	semidirect
2. C₃×#713	C₂	semidirect
3. C₃×Q₈×D₅	C₂	semidirect
4. C₃×#709	C₂	semidirect
5. #4147	C₃	direct (N × H)
13. C₂×C₅×Q₈	C₂×C₃	semidirect
14. #713	C₂×C₃	semidirect
15. Q₈×D₅	C₂×C₃	semidirect
16. #709	C₂×C₃	semidirect
24. C₂×C₃×Q₈	D₅	semidirect
48. C₂×Q₈	C₃×D₅	semidirect
49. C₃×C₅	2₋¹⁺⁴	semidirect
66. C₅	C₃×2₋¹⁺⁴	semidirect
71. C₃	#4147	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×Q₈	2
C₃×#713	2
C₃×Q₈×D₅	2
C₃×#709	2
#4147	3
C₃×2₋¹⁺⁴	5

Subgroups — C3×#4147 #92068

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#4147 #92068