Subgroups — C₃×#4150 #92071

Order 480.

292 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×Q₈×D₅	C₂	1	2	yes	maximal, complemented
3	C₃×#711	C₂	1	6	yes	maximal, complemented
4	C₃×#709	C₂	1	3	yes	maximal, complemented
5	C₂×C₃×Dic₁₀	C₂	1	3	yes	maximal, complemented
6	#4150	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
8	C₃×C₅×D₄	C₂²	1	3	yes	—
9	C₂×C₃×C₄×C₅	C₂²	1	3	yes	—
10	C₃×C₂²⋊D₅	C₂²	1	6	yes	—
11	C₂×C₃×Dic₅	C₂²	1	6	yes	—
12	C₃×D₂₀	C₂²	1	1	yes	characteristic
13	C₃×C₄×D₅	C₂²	1	6	yes	—
14	C₃×Dic₁₀	C₂²	1	3	yes	—
15	C₃×Dic₁₀	C₂²	1	6	yes	—
16	C₃×2₋¹⁺⁴	—	5	1	no	maximal, Hall
17	C₅×#41	C₂×C₃	1	1	yes	characteristic, complemented
18	Q₈×D₅	C₂×C₃	1	2	yes	complemented
19	#711	C₂×C₃	1	6	yes	complemented
20	#709	C₂×C₃	1	3	yes	complemented
21	C₂×Dic₁₀	C₂×C₃	1	3	yes	complemented
22	C₂²×C₃×C₅	C₂³	1	3	yes	—
23	C₂×C₃×D₅	C₂³	1	2	yes	—
24	C₃×C₄×C₅	C₂³	1	1	yes	characteristic
25	C₃×C₄×C₅	C₂³	1	3	yes	—
26	C₃×Dic₅	C₂³	1	6	yes	—
27	C₃×#41	—	5	6	no	—
28	C₃×#41	—	5	3	no	—
29	C₃×#41	D₅	1	1	yes	characteristic, complemented
30	C₂×C₃×Q₈	—	5	2	no	—
31	C₂×C₃×Q₈	—	5	3	no	—
32	C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
33	C₅×D₄	C₂²×C₃	1	3	yes	—
34	C₂×C₄×C₅	C₂²×C₃	1	3	yes	—
35	C₂²⋊D₅	C₂²×C₃	1	6	yes	—
36	C₂×Dic₅	C₂²×C₃	1	6	yes	—
37	D₂₀	C₂²×C₃	1	1	yes	characteristic
38	C₄×D₅	C₂²×C₃	1	6	yes	—
39	Dic₁₀	C₂²×C₃	1	3	yes	—
40	Dic₁₀	C₂²×C₃	1	6	yes	—
41	2₋¹⁺⁴	—	5	1	no	Sylow
42	C₂×C₃×C₅	—	2	3	no	—
43	C₂×C₃×C₅	C₂⁴	1	1	yes	characteristic
44	C₃×D₅	—	2	2	no	—
45	C₃×Q₈	—	5	6	no	—
46	C₃×Q₈	—	5	3	no	—
47	C₃×Q₈	C₂×D₅	1	1	yes	characteristic
48	C₃×D₄	—	5	6	no	—
49	C₃×D₄	—	5	1	no	—
50	C₃×D₄	C₂×D₅	1	3	yes	—
51	C₂×C₃×C₄	—	5	6	no	—
52	C₂×C₃×C₄	—	5	6	no	—
53	C₂×C₃×C₄	C₂×D₅	1	3	yes	—
54	C₂²×C₅	C₂³×C₃	1	3	yes	—
55	C₂×D₅	C₂³×C₃	1	2	yes	—
56	C₄×C₅	C₂³×C₃	1	1	yes	characteristic
57	C₄×C₅	C₂³×C₃	1	3	yes	—
58	Dic₅	C₂³×C₃	1	6	yes	—
59	#41	—	5	6	no	—
60	#41	—	5	3	no	—
61	#41	C₃×D₅	1	1	yes	characteristic, complemented
62	C₂×Q₈	—	5	2	no	—
63	C₂×Q₈	—	5	3	no	—
64	C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic, complemented, Hall
65	C₂²×C₃	—	5	2	no	—
66	C₂²×C₃	C₂²×D₅	1	3	yes	—
67	C₃×C₄	—	5	6	no	—
68	C₃×C₄	C₂²×D₅	1	3	yes	—
69	C₃×C₄	C₂²×D₅	1	1	yes	characteristic
70	C₂×C₅	—	2	3	no	—
71	C₂×C₅	C₂⁴×C₃	1	1	yes	characteristic
72	D₅	—	2	2	no	—
73	Q₈	—	5	6	no	—
74	Q₈	—	5	3	no	—
75	Q₈	C₂×C₃×D₅	1	1	yes	characteristic
76	D₄	—	5	6	no	—
77	D₄	—	5	1	no	—
78	D₄	C₂×C₃×D₅	1	3	yes	—
79	C₂×C₄	—	5	6	no	—
80	C₂×C₄	—	5	6	no	—
81	C₂×C₄	C₂×C₃×D₅	1	3	yes	—
82	C₂×C₃	—	2	3	no	—
83	C₂×C₃	—	10	2	no	—
84	C₂×C₃	C₂³×D₅	1	1	yes	characteristic
85	C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
86	C₂²	—	5	2	no	—
87	C₂²	C₂²×C₃×D₅	1	3	yes	—
88	C₄	—	5	6	no	—
89	C₄	C₂²×C₃×D₅	1	3	yes	—
90	C₄	C₂²×C₃×D₅	1	1	yes	characteristic
91	C₃	#4150	1	1	yes	characteristic, direct product factor, Sylow
92	C₂	—	2	3	no	—
93	C₂	—	10	2	no	—
94	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	C₃×C₅×#41	C₂
socle	C₂×C₃×C₅	C₂⁴
hypercenter	C₃×#41	D₅
hypocenter	C₅	C₃×2₋¹⁺⁴
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₃×#41

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#41	C₂	semidirect
2. C₃×Q₈×D₅	C₂	semidirect
3. C₃×#711	C₂	semidirect
4. C₃×#709	C₂	semidirect
5. C₂×C₃×Dic₁₀	C₂	semidirect
6. #4150	C₃	direct (N × H)
17. C₅×#41	C₂×C₃	semidirect
18. Q₈×D₅	C₂×C₃	semidirect
19. #711	C₂×C₃	semidirect
20. #709	C₂×C₃	semidirect
21. C₂×Dic₁₀	C₂×C₃	semidirect
29. C₃×#41	D₅	semidirect
61. #41	C₃×D₅	semidirect
64. C₃×C₅	2₋¹⁺⁴	semidirect
85. C₅	C₃×2₋¹⁺⁴	semidirect
91. C₃	#4150	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×#41	2
C₃×Q₈×D₅	2
C₃×#711	2
C₃×#709	2
C₂×C₃×Dic₁₀	2
#4150	3
C₃×2₋¹⁺⁴	5

Subgroups — C3×#4150 #92071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#4150 #92071