Subgroups — C₅×#1010 #92086

Order 480.

292 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₃×Q₈	C₂	1	2	yes	maximal, complemented
3	C₅×#237	C₂	1	6	yes	maximal, complemented
4	C₅×#235	C₂	1	3	yes	maximal, complemented
5	C₂×C₅×Dic₆	C₂	1	3	yes	maximal, complemented
6	C₅×2₋¹⁺⁴	—	3	1	no	maximal, Hall
7	C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
8	C₃×C₅×D₄	C₂²	1	3	yes	—
9	C₂×C₃×C₄×C₅	C₂²	1	3	yes	—
10	C₅×#67	C₂²	1	6	yes	—
11	C₂×C₅×Dic₃	C₂²	1	6	yes	—
12	C₅×D₁₂	C₂²	1	1	yes	characteristic
13	C₄×C₅×D₃	C₂²	1	6	yes	—
14	C₅×Dic₆	C₂²	1	3	yes	—
15	C₅×Dic₆	C₂²	1	6	yes	—
16	#1010	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₅×#41	—	3	6	no	—
18	C₅×#41	—	3	3	no	—
19	C₅×#41	D₃	1	1	yes	characteristic, complemented
20	C₂×C₅×Q₈	—	3	2	no	—
21	C₂×C₅×Q₈	—	3	3	no	—
22	C₂²×C₃×C₅	C₂³	1	3	yes	—
23	C₂×C₅×D₃	C₂³	1	2	yes	—
24	C₃×C₄×C₅	C₂³	1	1	yes	characteristic
25	C₃×C₄×C₅	C₂³	1	3	yes	—
26	C₅×Dic₃	C₂³	1	6	yes	—
27	C₃×#41	C₂×C₅	1	1	yes	characteristic, complemented
28	D₃×Q₈	C₂×C₅	1	2	yes	complemented
29	#237	C₂×C₅	1	6	yes	complemented
30	#235	C₂×C₅	1	3	yes	complemented
31	C₂×Dic₆	C₂×C₅	1	3	yes	complemented
32	C₅×Q₈	—	3	6	no	—
33	C₅×Q₈	—	3	3	no	—
34	C₅×Q₈	C₂×D₃	1	1	yes	characteristic
35	C₅×D₄	—	3	6	no	—
36	C₅×D₄	—	3	1	no	—
37	C₅×D₄	C₂×D₃	1	3	yes	—
38	C₂×C₄×C₅	—	3	6	no	—
39	C₂×C₄×C₅	—	3	6	no	—
40	C₂×C₄×C₅	C₂×D₃	1	3	yes	—
41	2₋¹⁺⁴	—	3	1	no	Sylow
42	C₂×C₃×C₅	—	2	3	no	—
43	C₂×C₃×C₅	C₂⁴	1	1	yes	characteristic
44	C₅×D₃	—	2	2	no	—
45	C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
46	C₃×D₄	C₂²×C₅	1	3	yes	—
47	C₂×C₃×C₄	C₂²×C₅	1	3	yes	—
48	#67	C₂²×C₅	1	6	yes	—
49	C₂×Dic₃	C₂²×C₅	1	6	yes	—
50	D₁₂	C₂²×C₅	1	1	yes	characteristic
51	C₄×D₃	C₂²×C₅	1	6	yes	—
52	Dic₆	C₂²×C₅	1	3	yes	—
53	Dic₆	C₂²×C₅	1	6	yes	—
54	C₂²×C₅	—	3	2	no	—
55	C₂²×C₅	C₂²×D₃	1	3	yes	—
56	C₄×C₅	—	3	6	no	—
57	C₄×C₅	C₂²×D₃	1	3	yes	—
58	C₄×C₅	C₂²×D₃	1	1	yes	characteristic
59	#41	—	3	6	no	—
60	#41	—	3	3	no	—
61	#41	C₅×D₃	1	1	yes	characteristic, complemented
62	C₂×Q₈	—	3	2	no	—
63	C₂×Q₈	—	3	3	no	—
64	C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic, complemented, Hall
65	C₂²×C₃	C₂³×C₅	1	3	yes	—
66	C₂×D₃	C₂³×C₅	1	2	yes	—
67	C₃×C₄	C₂³×C₅	1	1	yes	characteristic
68	C₃×C₄	C₂³×C₅	1	3	yes	—
69	Dic₃	C₂³×C₅	1	6	yes	—
70	C₂×C₅	—	2	3	no	—
71	C₂×C₅	—	6	2	no	—
72	C₂×C₅	C₂³×D₃	1	1	yes	characteristic
73	Q₈	—	3	6	no	—
74	Q₈	—	3	3	no	—
75	Q₈	C₂×C₅×D₃	1	1	yes	characteristic
76	D₄	—	3	6	no	—
77	D₄	—	3	1	no	—
78	D₄	C₂×C₅×D₃	1	3	yes	—
79	C₂×C₄	—	3	6	no	—
80	C₂×C₄	—	3	6	no	—
81	C₂×C₄	C₂×C₅×D₃	1	3	yes	—
82	C₂×C₃	—	2	3	no	—
83	C₂×C₃	C₂⁴×C₅	1	1	yes	characteristic
84	D₃	—	2	2	no	—
85	C₅	#1010	1	1	yes	characteristic, direct product factor, Sylow
86	C₂²	—	3	2	no	—
87	C₂²	C₂²×C₅×D₃	1	3	yes	—
88	C₄	—	3	6	no	—
89	C₄	C₂²×C₅×D₃	1	3	yes	—
90	C₄	C₂²×C₅×D₃	1	1	yes	characteristic
91	C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
92	C₂	—	2	3	no	—
93	C₂	—	6	2	no	—
94	C₂	C₂³×C₅×D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	C₂³×D₃
commutator, cosocle	C₂×C₃	C₂⁴×C₅
Frattini	C₂	C₂³×C₅×D₃
Fitting	C₃×C₅×#41	C₂
socle	C₂×C₃×C₅	C₂⁴
hypercenter	C₅×#41	D₃
hypocenter	C₃	C₅×2₋¹⁺⁴
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₅×#41

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#41	C₂	semidirect
2. C₅×D₃×Q₈	C₂	semidirect
3. C₅×#237	C₂	semidirect
4. C₅×#235	C₂	semidirect
5. C₂×C₅×Dic₆	C₂	semidirect
16. #1010	C₅	direct (N × H)
19. C₅×#41	D₃	semidirect
27. C₃×#41	C₂×C₅	semidirect
28. D₃×Q₈	C₂×C₅	semidirect
29. #237	C₂×C₅	semidirect
30. #235	C₂×C₅	semidirect
31. C₂×Dic₆	C₂×C₅	semidirect
61. #41	C₅×D₃	semidirect
64. C₃×C₅	2₋¹⁺⁴	semidirect
85. C₅	#1010	direct (N × H)
91. C₃	C₅×2₋¹⁺⁴	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#41	2
C₅×D₃×Q₈	2
C₅×#237	2
C₅×#235	2
C₂×C₅×Dic₆	2
C₅×2₋¹⁺⁴	3
#1010	5

Subgroups — C5×#1010 #92086

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#1010 #92086