Subgroups — C₃×#4050 #91621

Order 480.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#709	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×Dic₂₀	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₄₀	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#677	C₂	1	2	yes	maximal, complemented
6	#4050	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₃×C₂²⋊D₅	—	2	2	no	—
9	C₃×D₂₀	C₂²	1	2	yes	—
10	C₃×C₄×D₅	—	2	2	no	—
11	C₃×Dic₁₀	C₂²	1	2	yes	—
12	C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₃×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₃×#135	—	5	1	no	maximal, Hall
15	#709	C₂×C₃	1	2	yes	complemented
16	C₂×C₅×C₈	C₂×C₃	1	1	yes	characteristic, complemented
17	Dic₂₀	C₂×C₃	1	1	yes	characteristic, complemented
18	D₄₀	C₂×C₃	1	1	yes	characteristic, complemented
19	#677	C₂×C₃	1	2	yes	complemented
20	C₂²×C₃×C₅	D₄	1	1	yes	characteristic
21	C₂×C₃×D₅	—	2	2	no	—
22	C₃×C₄×C₅	D₄	1	1	yes	characteristic
23	C₃×C₄×C₅	C₂³	1	1	yes	characteristic
24	C₃×Dic₅	—	2	2	no	—
25	C₃×#41	—	5	2	no	—
26	C₃×Q₁₆	—	5	1	no	—
27	C₃×SD₁₆	—	5	2	no	—
28	C₃×D₈	—	5	1	no	—
29	C₂×C₃×C₈	D₅	1	1	yes	characteristic, complemented
30	C₂×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
31	C₂²⋊D₅	—	2	2	no	—
32	D₂₀	C₂²×C₃	1	2	yes	—
33	C₄×D₅	—	2	2	no	—
34	Dic₁₀	C₂²×C₃	1	2	yes	—
35	C₅×C₈	C₂²×C₃	1	1	yes	characteristic
36	C₅×C₈	C₂²×C₃	1	1	yes	characteristic
37	#135	—	5	1	no	Sylow
38	C₂×C₃×C₅	—	2	1	no	—
39	C₂×C₃×C₅	C₂×D₄	1	1	yes	characteristic
40	C₃×D₅	—	4	2	no	—
41	C₃×Q₈	—	5	2	no	—
42	C₃×D₄	—	5	2	no	—
43	C₃×D₄	—	10	2	no	—
44	C₂×C₃×C₄	—	10	2	no	—
45	C₂×C₃×C₄	C₂×D₅	1	1	yes	characteristic
46	C₃×C₈	C₂×D₅	1	1	yes	characteristic
47	C₃×C₈	C₂×D₅	1	1	yes	characteristic
48	C₂²×C₅	C₃×D₄	1	1	yes	characteristic
49	C₂×D₅	—	2	2	no	—
50	C₄×C₅	C₃×D₄	1	1	yes	characteristic
51	C₄×C₅	C₂³×C₃	1	1	yes	characteristic
52	Dic₅	—	2	2	no	—
53	#41	—	5	2	no	—
54	Q₁₆	—	5	1	no	—
55	SD₁₆	—	5	2	no	—
56	D₈	—	5	1	no	—
57	C₂×C₈	C₃×D₅	1	1	yes	characteristic, complemented
58	C₃×C₅	#135	1	1	yes	characteristic, complemented, Hall
59	C₂²×C₃	—	10	2	no	—
60	C₂²×C₃	D₂₀	1	1	yes	characteristic
61	C₃×C₄	—	10	2	no	—
62	C₃×C₄	D₂₀	1	1	yes	characteristic
63	C₃×C₄	C₂²×D₅	1	1	yes	characteristic
64	C₂×C₅	—	2	1	no	—
65	C₂×C₅	C₂×C₃×D₄	1	1	yes	characteristic
66	D₅	—	4	2	no	—
67	Q₈	—	5	2	no	—
68	D₄	—	5	2	no	—
69	D₄	—	10	2	no	—
70	C₂×C₄	—	10	2	no	—
71	C₂×C₄	C₂×C₃×D₅	1	1	yes	characteristic
72	C₈	C₂×C₃×D₅	1	1	yes	characteristic
73	C₈	C₂×C₃×D₅	1	1	yes	characteristic
74	C₂×C₃	—	2	1	no	—
75	C₂×C₃	—	20	2	no	—
76	C₂×C₃	C₂×D₂₀	1	1	yes	characteristic
77	C₅	C₃×#135	1	1	yes	characteristic, complemented, Sylow
78	C₂²	—	10	2	no	—
79	C₂²	C₃×D₂₀	1	1	yes	characteristic
80	C₄	—	10	2	no	—
81	C₄	C₃×D₂₀	1	1	yes	characteristic
82	C₄	C₂²×C₃×D₅	1	1	yes	characteristic
83	C₃	#4050	1	1	yes	characteristic, direct product factor, Sylow
84	C₂	—	2	1	no	—
85	C₂	—	20	2	no	—
86	C₂	C₂×C₃×D₂₀	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	D₂₀
commutator, cosocle	C₄×C₅	C₂³×C₃
Frattini	C₄	C₂²×C₃×D₅
Fitting	C₂×C₃×C₅×C₈	C₂
socle	C₂×C₃×C₅	C₂×D₄
hypercenter	C₂×C₃×C₈	D₅
hypocenter	C₅	C₃×#135
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈

Complements

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

N	H ≅ G/N	type
1. C₃×#709	C₂	semidirect
2. C₂×C₃×C₅×C₈	C₂	semidirect
3. C₃×Dic₂₀	C₂	semidirect
4. C₃×D₄₀	C₂	semidirect
5. C₃×#677	C₂	semidirect
6. #4050	C₃	direct (N × H)
15. #709	C₂×C₃	semidirect
16. C₂×C₅×C₈	C₂×C₃	semidirect
17. Dic₂₀	C₂×C₃	semidirect
18. D₄₀	C₂×C₃	semidirect
19. #677	C₂×C₃	semidirect
29. C₂×C₃×C₈	D₅	semidirect
57. C₂×C₈	C₃×D₅	semidirect
58. C₃×C₅	#135	semidirect
77. C₅	C₃×#135	semidirect
83. C₃	#4050	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×#709	2
C₂×C₃×C₅×C₈	2
C₃×Dic₂₀	2
C₃×D₄₀	2
C₃×#677	2
#4050	3
C₃×#135	5

Subgroups — C3×#4050 #91621

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#4050 #91621