Subgroups — C₃×#4086 #91657

Order 480.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₂²⋊D₅	C₂	1	4	yes	maximal, complemented
3	C₂×C₃×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
5	#4086	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂³×C₃×C₅	C₂²	1	2	yes	—
7	C₂²×C₃×D₅	C₂²	1	2	yes	—
8	C₃×C₅×D₄	—	2	2	no	—
9	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₃×C₂²⋊D₅	—	2	8	no	—
11	C₂×C₃×Dic₅	C₂²	1	2	yes	—
12	C₃×D₂₀	—	2	2	no	—
13	C₃×#127	—	5	1	no	maximal, Hall
14	C₂×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
15	C₂×C₂²⋊D₅	C₂×C₃	1	4	yes	complemented
16	C₂×D₂₀	C₂×C₃	1	1	yes	characteristic, complemented
17	C₄×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
18	C₂²×C₃×C₅	—	2	4	no	—
19	C₂²×C₃×C₅	—	2	2	no	—
20	C₂²×C₃×C₅	C₂³	1	1	yes	characteristic
21	C₂×C₃×D₅	—	2	2	no	—
22	C₂×C₃×D₅	—	2	4	no	—
23	C₃×C₄×C₅	D₄	1	2	yes	complemented
24	C₃×Dic₅	D₄	1	4	yes	complemented
25	C₂×C₃×D₄	—	5	4	no	—
26	C₂×C₃×D₄	—	5	1	no	—
27	C₂×C₃×D₄	D₅	1	1	yes	characteristic, complemented
28	C₃×C₄²	—	5	1	no	—
29	C₂³×C₅	C₂²×C₃	1	2	yes	—
30	C₂²×D₅	C₂²×C₃	1	2	yes	—
31	C₅×D₄	—	2	2	no	—
32	C₂×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
33	C₂²⋊D₅	—	2	8	no	—
34	C₂×Dic₅	C₂²×C₃	1	2	yes	—
35	D₂₀	—	2	2	no	—
36	#127	—	5	1	no	Sylow
37	C₂×C₃×C₅	—	4	2	no	—
38	C₂×C₃×C₅	C₂×D₄	1	2	yes	—
39	C₂×C₃×C₅	C₂×D₄	1	1	yes	characteristic
40	C₃×D₅	—	4	2	no	—
41	C₂³×C₃	—	5	2	no	—
42	C₂³×C₃	C₂×D₅	1	2	yes	—
43	C₃×D₄	—	2	2	no	—
44	C₃×D₄	—	10	8	no	—
45	C₃×D₄	—	10	2	no	—
46	C₂×C₃×C₄	—	5	2	no	—
47	C₂×C₃×C₄	C₂×D₅	1	1	yes	characteristic
48	C₂²×C₅	—	2	4	no	—
49	C₂²×C₅	—	2	2	no	—
50	C₂²×C₅	C₂³×C₃	1	1	yes	characteristic
51	C₂×D₅	—	2	2	no	—
52	C₂×D₅	—	2	4	no	—
53	C₄×C₅	C₃×D₄	1	2	yes	complemented
54	Dic₅	C₃×D₄	1	4	yes	complemented
55	C₂×D₄	—	5	4	no	—
56	C₂×D₄	—	5	1	no	—
57	C₂×D₄	C₃×D₅	1	1	yes	characteristic, complemented
58	C₄²	—	5	1	no	—
59	C₃×C₅	#127	1	1	yes	characteristic, complemented, Hall
60	C₂²×C₃	—	2	4	no	—
61	C₂²×C₃	—	2	2	no	—
62	C₂²×C₃	—	10	4	no	—
63	C₂²×C₃	—	10	2	no	—
64	C₂²×C₃	C₂²×D₅	1	1	yes	characteristic
65	C₃×C₄	—	5	4	no	—
66	C₃×C₄	C₂²⋊D₅	1	2	yes	complemented
67	C₂×C₅	—	4	2	no	—
68	C₂×C₅	C₂×C₃×D₄	1	2	yes	—
69	C₂×C₅	C₂×C₃×D₄	1	1	yes	characteristic
70	D₅	—	4	2	no	—
71	C₂³	—	5	2	no	—
72	C₂³	C₂×C₃×D₅	1	2	yes	—
73	D₄	—	2	2	no	—
74	D₄	—	10	8	no	—
75	D₄	—	10	2	no	—
76	C₂×C₄	—	5	2	no	—
77	C₂×C₄	C₂×C₃×D₅	1	1	yes	characteristic
78	C₂×C₃	—	4	2	no	—
79	C₂×C₃	—	20	2	no	—
80	C₂×C₃	D₄×D₅	1	2	yes	—
81	C₂×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
82	C₅	C₃×#127	1	1	yes	characteristic, complemented, Sylow
83	C₂²	—	2	4	no	—
84	C₂²	—	2	2	no	—
85	C₂²	—	10	4	no	—
86	C₂²	—	10	2	no	—
87	C₂²	C₂²×C₃×D₅	1	1	yes	characteristic
88	C₄	—	5	4	no	—
89	C₄	C₃×C₂²⋊D₅	1	2	yes	complemented
90	C₃	#4086	1	1	yes	characteristic, direct product factor, Sylow
91	C₂	—	4	2	no	—
92	C₂	—	20	2	no	—
93	C₂	C₃×D₄×D₅	1	2	yes	—
94	C₂	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×D₅
commutator, cosocle	C₂²×C₅	C₂³×C₃
Frattini	C₂²	C₂²×C₃×D₅
Fitting	C₂×C₃×C₅×D₄	C₂
socle	C₂²×C₃×C₅	C₂³
hypercenter	C₂×C₃×D₄	D₅
hypocenter	C₅	C₃×#127
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×D₄	C₂	semidirect
2. C₂×C₃×C₂²⋊D₅	C₂	semidirect
3. C₂×C₃×D₂₀	C₂	semidirect
4. C₃×C₄×Dic₅	C₂	semidirect
5. #4086	C₃	direct (N × H)
14. C₂×C₅×D₄	C₂×C₃	semidirect
15. C₂×C₂²⋊D₅	C₂×C₃	semidirect
16. C₂×D₂₀	C₂×C₃	semidirect
17. C₄×Dic₅	C₂×C₃	semidirect
23. C₃×C₄×C₅	D₄	semidirect
24. C₃×Dic₅	D₄	semidirect
27. C₂×C₃×D₄	D₅	semidirect
53. C₄×C₅	C₃×D₄	semidirect
54. Dic₅	C₃×D₄	semidirect
57. C₂×D₄	C₃×D₅	semidirect
59. C₃×C₅	#127	semidirect
66. C₃×C₄	C₂²⋊D₅	semidirect
82. C₅	C₃×#127	semidirect
89. C₄	C₃×C₂²⋊D₅	semidirect
90. C₃	#4086	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×D₄	2
C₂×C₃×C₂²⋊D₅	2
C₂×C₃×D₂₀	2
C₃×C₄×Dic₅	2
#4086	3
C₃×#127	5

Subgroups — C3×#4086 #91657

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#4086 #91657