Subgroups — C₅×C₃⋊#95 #91074

Order 480.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×Dic₃	C₂	1	2	yes	maximal
3	C₅×#95	—	3	1	no	maximal, Hall
4	C₂³×C₃×C₅	C₂²	1	1	yes	characteristic
5	C₂×C₃×C₄×C₅	—	2	2	no	—
6	C₂×C₃×C₄×C₅	C₄	1	2	yes	complemented
7	C₂×C₅×Dic₃	—	2	2	no	—
8	C₂×C₅×Dic₃	—	2	2	no	—
9	C₂×C₅×Dic₃	C₄	1	4	yes	complemented
10	C₃⋊#95	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₄×C₅	—	3	2	no	—
12	C₂²×C₄×C₅	D₃	1	1	yes	characteristic
13	C₂²×C₃×C₅	C₂×C₄	1	2	yes	—
14	C₂²×C₃×C₅	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₃×C₅	D₄	1	1	yes	characteristic
16	C₂²×C₃×C₅	D₄	1	2	yes	—
17	C₂²×C₃×C₅	Q₈	1	1	yes	characteristic
18	C₃×C₄×C₅	—	2	2	no	—
19	C₅×Dic₃	—	2	4	no	—
20	C₂²×C₃×C₄	C₂×C₅	1	1	yes	characteristic
21	C₂²×Dic₃	C₂×C₅	1	2	yes	—
22	C₂³×C₅	C₂×D₃	1	1	yes	characteristic
23	C₂×C₄×C₅	—	2	2	no	—
24	C₂×C₄×C₅	—	3	4	no	—
25	C₂×C₄×C₅	—	6	2	no	—
26	C₂×C₄×C₅	—	6	2	no	—
27	C₂×C₄×C₅	Dic₃	1	2	yes	complemented
28	#95	—	3	1	no	Sylow
29	C₂×C₃×C₅	C₄²	1	1	yes	characteristic
30	C₂×C₃×C₅	C₂²⋊C₄	1	2	yes	—
31	C₂×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₃×C₅	C₄⋊C₄	1	2	yes	—
33	C₂×C₃×C₅	C₄⋊C₄	1	1	yes	characteristic
34	C₂³×C₃	C₂²×C₅	1	1	yes	characteristic
35	C₂×C₃×C₄	—	2	2	no	—
36	C₂×C₃×C₄	C₄×C₅	1	2	yes	complemented
37	C₂×Dic₃	—	2	2	no	—
38	C₂×Dic₃	—	2	2	no	—
39	C₂×Dic₃	C₄×C₅	1	4	yes	complemented
40	C₂²×C₅	Dic₆	1	1	yes	characteristic
41	C₂²×C₅	C₄×D₃	1	2	yes	—
42	C₂²×C₅	D₁₂	1	1	yes	characteristic
43	C₂²×C₅	C₂×Dic₃	1	1	yes	characteristic
44	C₂²×C₅	#67	1	2	yes	—
45	C₄×C₅	—	2	2	no	—
46	C₄×C₅	—	6	4	no	—
47	C₂²×C₄	—	3	2	no	—
48	C₂²×C₄	C₅×D₃	1	1	yes	characteristic
49	C₃×C₅	#95	1	1	yes	characteristic, complemented, Hall
50	C₂²×C₃	C₂×C₄×C₅	1	2	yes	—
51	C₂²×C₃	C₂×C₄×C₅	1	1	yes	characteristic
52	C₂²×C₃	C₅×D₄	1	1	yes	characteristic
53	C₂²×C₃	C₅×D₄	1	2	yes	—
54	C₂²×C₃	C₅×Q₈	1	1	yes	characteristic
55	C₃×C₄	—	2	2	no	—
56	Dic₃	—	2	4	no	—
57	C₂×C₅	C₄×Dic₃	1	1	yes	characteristic
58	C₂×C₅	Dic₃⋊C₄	1	2	yes	—
59	C₂×C₅	C₄⋊Dic₃	1	1	yes	characteristic
60	C₂×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
61	C₂×C₅	#217	1	1	yes	characteristic
62	C₂³	C₂×C₅×D₃	1	1	yes	characteristic
63	C₂×C₄	—	2	2	no	—
64	C₂×C₄	—	3	4	no	—
65	C₂×C₄	—	6	2	no	—
66	C₂×C₄	—	6	2	no	—
67	C₂×C₄	C₅×Dic₃	1	2	yes	complemented
68	C₂×C₃	C₄²×C₅	1	1	yes	characteristic
69	C₂×C₃	C₅×C₂²⋊C₄	1	2	yes	—
70	C₂×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₃	C₅×C₄⋊C₄	1	2	yes	—
72	C₂×C₃	C₅×C₄⋊C₄	1	1	yes	characteristic
73	C₅	C₃⋊#95	1	1	yes	characteristic, direct product factor, Sylow
74	C₂²	C₅×Dic₆	1	1	yes	characteristic
75	C₂²	C₄×C₅×D₃	1	2	yes	—
76	C₂²	C₅×D₁₂	1	1	yes	characteristic
77	C₂²	C₂×C₅×Dic₃	1	1	yes	characteristic
78	C₂²	C₅×#67	1	2	yes	—
79	C₄	—	2	2	no	—
80	C₄	—	6	4	no	—
81	C₃	C₅×#95	1	1	yes	characteristic, complemented, Sylow
82	C₂	C₄×C₅×Dic₃	1	1	yes	characteristic
83	C₂	C₅×Dic₃⋊C₄	1	2	yes	—
84	C₂	C₅×C₄⋊Dic₃	1	1	yes	characteristic
85	C₂	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
86	C₂	C₅×#217	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂×D₃
commutator	C₂×C₃	C₄²×C₅
Frattini	C₂³	C₂×C₅×D₃
Fitting	C₂²×C₃×C₄×C₅	C₂
socle, prime radical	C₂³×C₃×C₅	C₂²
cosocle	C₂³×C₃	C₂²×C₅
hypercenter	C₂²×C₄×C₅	D₃
hypocenter	C₃	C₅×#95
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄×C₅

Complements

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

N	H ≅ G/N	type
6. C₂×C₃×C₄×C₅	C₄	semidirect
9. C₂×C₅×Dic₃	C₄	semidirect
10. C₃⋊#95	C₅	direct (N × H)
27. C₂×C₄×C₅	Dic₃	semidirect
36. C₂×C₃×C₄	C₄×C₅	semidirect
39. C₂×Dic₃	C₄×C₅	semidirect
49. C₃×C₅	#95	semidirect
67. C₂×C₄	C₅×Dic₃	semidirect
73. C₅	C₃⋊#95	direct (N × H)
81. C₃	C₅×#95	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₄×C₅	2
C₂²×C₅×Dic₃	2
C₅×#95	3
C₃⋊#95	5

Subgroups — C5×C3⋊#95 #91074

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₃⋊#95 #91074