Subgroups — C₃×#3952 #91022

Order 480.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×D₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#168	C₂	1	1	yes	maximal, characteristic, complemented
4	#3952	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₃×D₅	C₄	1	1	yes	characteristic
6	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
7	C₂×C₃×Dic₅	C₄	1	1	yes	characteristic
8	C₃×C₄×D₅	—	2	1	no	—
9	C₃×C₄×D₅	—	2	1	no	—
10	C₃×C₅×C₈	—	2	1	no	—
11	C₃×#168	—	2	1	no	—
12	C₃×C₂²⋊C₈	—	5	1	no	maximal, Hall
13	C₂×C₄×D₅	C₂×C₃	1	1	yes	characteristic
14	C₂×C₅×C₈	C₂×C₃	1	1	yes	characteristic, complemented
15	C₂×#168	C₂×C₃	1	1	yes	characteristic, complemented
16	C₂²×C₃×C₅	C₂×C₄	1	1	yes	characteristic
17	C₂×C₃×D₅	—	2	1	no	—
18	C₂×C₃×D₅	—	2	1	no	—
19	C₂×C₃×D₅	C₈	1	2	yes	complemented
20	C₃×C₄×C₅	D₄	1	1	yes	characteristic
21	C₃×C₄×C₅	D₄	1	1	yes	characteristic
22	C₃×Dic₅	—	2	1	no	—
23	C₂²×C₃×C₄	—	5	1	no	—
24	C₂×C₃×C₈	—	5	1	no	—
25	C₂×C₃×C₈	D₅	1	1	yes	characteristic, complemented
26	C₂²×D₅	C₃×C₄	1	1	yes	characteristic
27	C₂×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
28	C₂×Dic₅	C₃×C₄	1	1	yes	characteristic
29	C₄×D₅	—	2	1	no	—
30	C₄×D₅	—	2	1	no	—
31	C₅×C₈	—	2	1	no	—
32	#168	—	2	1	no	—
33	C₂²⋊C₈	—	5	1	no	Sylow
34	C₂×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₃×C₅	C₂×C₈	1	1	yes	characteristic
36	C₂×C₃×C₅	M₁₆	1	1	yes	characteristic
37	C₃×D₅	—	2	2	no	—
38	C₂³×C₃	—	5	1	no	—
39	C₂×C₃×C₄	—	5	1	no	—
40	C₂×C₃×C₄	—	10	1	no	—
41	C₂×C₃×C₄	—	10	1	no	—
42	C₂×C₃×C₄	C₂×D₅	1	1	yes	characteristic
43	C₃×C₈	—	2	1	no	—
44	C₃×C₈	—	10	1	no	—
45	C₂²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
46	C₂×D₅	—	2	1	no	—
47	C₂×D₅	—	2	1	no	—
48	C₂×D₅	C₃×C₈	1	2	yes	complemented
49	C₄×C₅	C₃×D₄	1	1	yes	characteristic
50	C₄×C₅	C₃×D₄	1	1	yes	characteristic
51	Dic₅	—	2	1	no	—
52	C₂²×C₄	—	5	1	no	—
53	C₂×C₈	—	5	1	no	—
54	C₂×C₈	C₃×D₅	1	1	yes	characteristic, complemented
55	C₃×C₅	C₂²⋊C₈	1	1	yes	characteristic, complemented, Hall
56	C₂²×C₃	—	5	2	no	—
57	C₂²×C₃	—	10	1	no	—
58	C₂²×C₃	—	10	1	no	—
59	C₂²×C₃	C₄×D₅	1	1	yes	characteristic
60	C₃×C₄	—	10	1	no	—
61	C₃×C₄	D₂₀	1	1	yes	characteristic
62	C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
63	C₂×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
64	C₂×C₅	C₂×C₃×C₈	1	1	yes	characteristic
65	C₂×C₅	C₃×M₁₆	1	1	yes	characteristic
66	D₅	—	2	2	no	—
67	C₂³	—	5	1	no	—
68	C₂×C₄	—	5	1	no	—
69	C₂×C₄	—	10	1	no	—
70	C₂×C₄	—	10	1	no	—
71	C₂×C₄	C₂×C₃×D₅	1	1	yes	characteristic
72	C₈	—	2	1	no	—
73	C₈	—	10	1	no	—
74	C₂×C₃	—	10	2	no	—
75	C₂×C₃	C₈×D₅	1	1	yes	characteristic
76	C₂×C₃	#676	1	1	yes	characteristic
77	C₂×C₃	#685	1	1	yes	characteristic
78	C₅	C₃×C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
79	C₂²	—	5	2	no	—
80	C₂²	—	10	1	no	—
81	C₂²	—	10	1	no	—
82	C₂²	C₃×C₄×D₅	1	1	yes	characteristic
83	C₄	—	10	1	no	—
84	C₄	C₃×D₂₀	1	1	yes	characteristic
85	C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
86	C₃	#3952	1	1	yes	characteristic, direct product factor, Sylow
87	C₂	—	10	2	no	—
88	C₂	C₃×C₈×D₅	1	1	yes	characteristic
89	C₂	C₃×#676	1	1	yes	characteristic
90	C₂	C₃×#685	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	C₂²×C₃×C₅	C₂×C₄
prime radical	C₂²×C₃×D₅	C₄
cosocle	C₂×C₄×C₅	C₂²×C₃
hypercenter	C₂×C₃×C₈	D₅
hypocenter	C₅	C₃×C₂²⋊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
2. C₂×C₃×C₅×C₈	C₂	semidirect
3. C₂×C₃×#168	C₂	semidirect
4. #3952	C₃	direct (N × H)
14. C₂×C₅×C₈	C₂×C₃	semidirect
15. C₂×#168	C₂×C₃	semidirect
19. C₂×C₃×D₅	C₈	semidirect
25. C₂×C₃×C₈	D₅	semidirect
48. C₂×D₅	C₃×C₈	semidirect
54. C₂×C₈	C₃×D₅	semidirect
55. C₃×C₅	C₂²⋊C₈	semidirect
78. C₅	C₃×C₂²⋊C₈	semidirect
86. C₃	#3952	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×C₄×D₅	2
C₂×C₃×C₅×C₈	2
C₂×C₃×#168	2
#3952	3
C₃×C₂²⋊C₈	5

Subgroups — C3×#3952 #91022

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3952 #91022