Subgroups — C₃×#3941 #91011

Order 480.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₂₀	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#168	C₂	1	1	yes	maximal, characteristic, complemented
4	#3941	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₃×D₅	—	2	1	no	—
6	C₂×C₃×C₄×C₅	—	2	1	no	—
7	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₃×D₂₀	—	2	1	no	—
9	C₃×D₂₀	C₄	1	2	yes	complemented
10	C₃×#168	—	2	1	no	—
11	C₃×#102	—	5	1	no	maximal, Hall
12	C₂×D₂₀	C₂×C₃	1	1	yes	characteristic
13	C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
14	C₂×#168	C₂×C₃	1	1	yes	characteristic, complemented
15	C₂²×C₃×C₅	D₄	1	1	yes	characteristic
16	C₂×C₃×D₅	—	2	2	no	—
17	C₂×C₃×D₅	—	4	1	no	—
18	C₂×C₃×D₅	—	4	1	no	—
19	C₃×C₄×C₅	—	4	1	no	—
20	C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
21	C₃×C₄×C₅	D₄	1	1	yes	characteristic
22	C₂×C₃×D₄	—	5	1	no	—
23	C₂×C₃×C₈	—	5	1	no	—
24	C₃×C₄⋊C₄	D₅	1	1	yes	characteristic, complemented
25	C₂²×D₅	—	2	1	no	—
26	C₂×C₄×C₅	—	2	1	no	—
27	C₂×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
28	D₂₀	—	2	1	no	—
29	D₂₀	C₃×C₄	1	2	yes	complemented
30	#168	—	2	1	no	—
31	#102	—	5	1	no	Sylow
32	C₂×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₃×C₅	D₈	1	1	yes	characteristic
34	C₂×C₃×C₅	SD₁₆	1	1	yes	characteristic
35	C₃×D₅	—	4	2	no	—
36	C₂³×C₃	—	10	1	no	—
37	C₃×D₄	—	5	2	no	—
38	C₃×D₄	—	10	1	no	—
39	C₂×C₃×C₄	—	2	1	no	—
40	C₂×C₃×C₄	C₂×D₅	1	1	yes	characteristic
41	C₃×C₈	—	10	1	no	—
42	C₂²×C₅	C₃×D₄	1	1	yes	characteristic
43	C₂×D₅	—	2	2	no	—
44	C₂×D₅	—	4	1	no	—
45	C₂×D₅	—	4	1	no	—
46	C₄×C₅	—	4	1	no	—
47	C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
48	C₄×C₅	C₃×D₄	1	1	yes	characteristic
49	C₂×D₄	—	5	1	no	—
50	C₂×C₈	—	5	1	no	—
51	C₄⋊C₄	C₃×D₅	1	1	yes	characteristic, complemented
52	C₃×C₅	#102	1	1	yes	characteristic, complemented, Hall
53	C₂²×C₃	—	10	2	no	—
54	C₂²×C₃	—	20	1	no	—
55	C₂²×C₃	—	20	1	no	—
56	C₂²×C₃	C₂²⋊D₅	1	1	yes	characteristic
57	C₃×C₄	—	4	1	no	—
58	C₃×C₄	C₄×D₅	1	1	yes	characteristic
59	C₃×C₄	D₂₀	1	1	yes	characteristic
60	C₂×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
61	C₂×C₅	C₃×D₈	1	1	yes	characteristic
62	C₂×C₅	C₃×SD₁₆	1	1	yes	characteristic
63	D₅	—	4	2	no	—
64	C₂³	—	10	1	no	—
65	D₄	—	5	2	no	—
66	D₄	—	10	1	no	—
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	C₂×C₃×D₅	1	1	yes	characteristic
69	C₈	—	10	1	no	—
70	C₂×C₃	—	20	2	no	—
71	C₂×C₃	#685	1	1	yes	characteristic
72	C₂×C₃	#686	1	1	yes	characteristic
73	C₂×C₃	#688	1	1	yes	characteristic
74	C₅	C₃×#102	1	1	yes	characteristic, complemented, Sylow
75	C₂²	—	10	2	no	—
76	C₂²	—	20	1	no	—
77	C₂²	—	20	1	no	—
78	C₂²	C₃×C₂²⋊D₅	1	1	yes	characteristic
79	C₄	—	4	1	no	—
80	C₄	C₃×C₄×D₅	1	1	yes	characteristic
81	C₄	C₃×D₂₀	1	1	yes	characteristic
82	C₃	#3941	1	1	yes	characteristic, direct product factor, Sylow
83	C₂	—	20	2	no	—
84	C₂	C₃×#685	1	1	yes	characteristic
85	C₂	C₃×#686	1	1	yes	characteristic
86	C₂	C₃×#688	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²⋊D₅
commutator	C₄×C₅	C₂×C₃×C₄
Frattini	C₂×C₄	C₂×C₃×D₅
Fitting	C₃×C₅×C₄⋊C₄	C₂
socle	C₂²×C₃×C₅	D₄
prime radical	C₂×C₃×D₂₀	C₂
cosocle	C₂×C₄×C₅	C₂²×C₃
hypercenter	C₃×C₄⋊C₄	D₅
hypocenter	C₅	C₃×#102
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₃×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×C₄⋊C₄	C₂	semidirect
3. C₂×C₃×#168	C₂	semidirect
4. #3941	C₃	direct (N × H)
9. C₃×D₂₀	C₄	semidirect
13. C₅×C₄⋊C₄	C₂×C₃	semidirect
14. C₂×#168	C₂×C₃	semidirect
24. C₃×C₄⋊C₄	D₅	semidirect
29. D₂₀	C₃×C₄	semidirect
51. C₄⋊C₄	C₃×D₅	semidirect
52. C₃×C₅	#102	semidirect
74. C₅	C₃×#102	semidirect
82. C₃	#3941	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×D₂₀	2
C₃×C₅×C₄⋊C₄	2
C₂×C₃×#168	2
#3941	3
C₃×#102	5

Subgroups — C3×#3941 #91011

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3941 #91011