Subgroups — C₅×#1007 #92083

Order 480.

292 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#239	C₂	1	4	yes	maximal, complemented
3	C₅×D₃×Q₈	C₂	1	4	yes	maximal, complemented
4	C₅×#235	C₂	1	6	yes	maximal, complemented
5	C₅×2₋¹⁺⁴	—	3	1	no	maximal, Hall
6	C₃×C₅×Q₈	C₂²	1	4	yes	—
7	C₂×C₃×C₄×C₅	C₂²	1	3	yes	—
8	C₅×#67	C₂²	1	4	yes	—
9	C₅×D₁₂	C₂²	1	6	yes	—
10	C₄×C₅×D₃	C₂²	1	12	yes	—
11	C₅×Dic₆	C₂²	1	6	yes	—
12	#1007	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₅×#41	—	3	4	no	—
14	C₅×#41	—	3	6	no	—
15	C₂×C₅×Q₈	—	3	4	no	—
16	C₂×C₅×Q₈	D₃	1	1	yes	characteristic, complemented
17	C₂²×C₃×C₅	C₂³	1	1	yes	characteristic
18	C₂×C₅×D₃	C₂³	1	4	yes	—
19	C₃×C₄×C₅	C₂³	1	6	yes	—
20	C₅×Dic₃	C₂³	1	4	yes	—
21	C₂×C₃×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
22	#239	C₂×C₅	1	4	yes	complemented
23	D₃×Q₈	C₂×C₅	1	4	yes	complemented
24	#235	C₂×C₅	1	6	yes	complemented
25	C₅×Q₈	—	3	6	no	—
26	C₅×Q₈	C₂×D₃	1	4	yes	—
27	C₅×D₄	—	3	4	no	—
28	C₅×D₄	—	3	6	no	—
29	C₂×C₄×C₅	—	3	12	no	—
30	C₂×C₄×C₅	C₂×D₃	1	3	yes	—
31	2₋¹⁺⁴	—	3	1	no	Sylow
32	C₂×C₃×C₅	—	2	1	no	—
33	C₂×C₃×C₅	C₂⁴	1	1	yes	characteristic
34	C₅×D₃	—	2	4	no	—
35	C₃×Q₈	C₂²×C₅	1	4	yes	—
36	C₂×C₃×C₄	C₂²×C₅	1	3	yes	—
37	#67	C₂²×C₅	1	4	yes	—
38	D₁₂	C₂²×C₅	1	6	yes	—
39	C₄×D₃	C₂²×C₅	1	12	yes	—
40	Dic₆	C₂²×C₅	1	6	yes	—
41	C₂²×C₅	—	3	4	no	—
42	C₂²×C₅	C₂²×D₃	1	1	yes	characteristic
43	C₄×C₅	—	3	4	no	—
44	C₄×C₅	C₂²×D₃	1	6	yes	—
45	#41	—	3	4	no	—
46	#41	—	3	6	no	—
47	C₂×Q₈	—	3	4	no	—
48	C₂×Q₈	C₅×D₃	1	1	yes	characteristic, complemented
49	C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic, complemented, Hall
50	C₂²×C₃	C₂³×C₅	1	1	yes	characteristic
51	C₂×D₃	C₂³×C₅	1	4	yes	—
52	C₃×C₄	C₂³×C₅	1	6	yes	—
53	Dic₃	C₂³×C₅	1	4	yes	—
54	C₂×C₅	—	2	1	no	—
55	C₂×C₅	—	6	4	no	—
56	C₂×C₅	C₂³×D₃	1	1	yes	characteristic
57	Q₈	—	3	6	no	—
58	Q₈	C₂×C₅×D₃	1	4	yes	—
59	D₄	—	3	4	no	—
60	D₄	—	3	6	no	—
61	C₂×C₄	—	3	12	no	—
62	C₂×C₄	C₂×C₅×D₃	1	3	yes	—
63	C₂×C₃	—	2	1	no	—
64	C₂×C₃	C₂⁴×C₅	1	1	yes	characteristic
65	D₃	—	2	4	no	—
66	C₅	#1007	1	1	yes	characteristic, direct product factor, Sylow
67	C₂²	—	3	4	no	—
68	C₂²	C₂²×C₅×D₃	1	1	yes	characteristic
69	C₄	—	3	4	no	—
70	C₄	C₂²×C₅×D₃	1	6	yes	—
71	C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
72	C₂	—	2	1	no	—
73	C₂	—	6	4	no	—
74	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	C₂×C₃×C₅×Q₈	C₂
socle	C₂×C₃×C₅	C₂⁴
hypercenter	C₂×C₅×Q₈	D₃
hypocenter	C₃	C₅×2₋¹⁺⁴
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₅×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×Q₈	C₂	semidirect
2. C₅×#239	C₂	semidirect
3. C₅×D₃×Q₈	C₂	semidirect
4. C₅×#235	C₂	semidirect
12. #1007	C₅	direct (N × H)
16. C₂×C₅×Q₈	D₃	semidirect
21. C₂×C₃×Q₈	C₂×C₅	semidirect
22. #239	C₂×C₅	semidirect
23. D₃×Q₈	C₂×C₅	semidirect
24. #235	C₂×C₅	semidirect
48. C₂×Q₈	C₅×D₃	semidirect
49. C₃×C₅	2₋¹⁺⁴	semidirect
66. C₅	#1007	direct (N × H)
71. 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
C₂×C₃×C₅×Q₈	2
C₅×#239	2
C₅×D₃×Q₈	2
C₅×#235	2
C₅×2₋¹⁺⁴	3
#1007	5

Subgroups — C5×#1007 #92083

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#1007 #92083