Subgroups — C₅×#1202 #10597108

Order 600.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₂₀	—	3	1	no	maximal, Hall
5	C₂×C₃×C₅²	C₂²	1	1	yes	characteristic
6	C₅×D₁₅	—	2	1	no	—
7	C₃×C₅×D₅	—	2	1	no	—
8	C₅×#67	—	5	1	no	maximal
9	#1202	C₅	1	1	yes	maximal, characteristic, direct product factor
10	C₂×C₅×D₅	—	3	1	no	—
11	C₂×C₅×D₅	D₃	1	1	yes	characteristic, complemented
12	C₄×C₅²	—	3	1	no	—
13	C₃×C₅²	D₄	1	1	yes	characteristic, complemented, Hall
14	C₂²×C₃×C₅	—	5	1	no	—
15	C₂×D₁₅	C₂×C₅	1	1	yes	characteristic, complemented
16	C₂×C₅×D₃	—	5	1	no	—
17	C₂×C₃×D₅	C₂×C₅	1	1	yes	characteristic, complemented
18	C₅×Dic₃	—	2	2	no	—
19	C₅×Dic₃	D₅	1	1	yes	characteristic, complemented
20	C₅×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
21	C₂×C₅²	C₂×D₃	1	1	yes	characteristic
22	C₅×D₅	—	2	1	no	—
23	C₅×D₅	—	6	1	no	—
24	C₅×D₄	—	15	1	no	—
25	D₂₀	—	3	1	no	—
26	C₂×C₃×C₅	—	2	2	no	—
27	C₂×C₃×C₅	—	10	1	no	—
28	C₂×C₃×C₅	C₂×D₅	1	1	yes	characteristic
29	C₂×C₃×C₅	C₂²×C₅	1	1	yes	characteristic
30	D₁₅	—	2	1	no	—
31	C₃×D₅	—	2	1	no	—
32	C₅×D₃	—	10	1	no	—
33	C₅²	#67	1	1	yes	characteristic, complemented, Sylow
34	#67	—	5	1	no	Hall
35	C₂²×C₅	—	5	1	no	—
36	C₂²×C₅	—	15	1	no	—
37	C₂×D₅	—	3	1	no	—
38	C₂×D₅	C₅×D₃	1	1	yes	characteristic, complemented
39	C₄×C₅	—	3	1	no	—
40	C₄×C₅	—	3	1	no	—
41	C₄×C₅	—	6	2	no	—
42	C₃×C₅	—	2	2	no	—
43	C₃×C₅	D₂₀	1	1	yes	characteristic, complemented
44	C₃×C₅	C₅×D₄	1	1	yes	characteristic, complemented
45	C₂²×C₃	—	5	1	no	—
46	C₂×D₃	—	5	1	no	—
47	Dic₃	C₅×D₅	1	1	yes	characteristic, complemented
48	C₂×C₅	—	2	2	no	—
49	C₂×C₅	—	10	1	no	—
50	C₂×C₅	—	30	1	no	—
51	C₂×C₅	D₃×D₅	1	1	yes	characteristic
52	C₂×C₅	C₂×C₅×D₃	1	1	yes	characteristic
53	D₅	—	2	1	no	—
54	D₅	—	6	1	no	—
55	D₄	—	15	1	no	Sylow
56	C₂×C₃	—	10	1	no	—
57	C₂×C₃	C₂×C₅×D₅	1	1	yes	characteristic
58	D₃	—	10	1	no	—
59	C₅	—	2	2	no	—
60	C₅	#1202	1	1	yes	characteristic, direct product factor
61	C₅	C₅×#67	1	1	yes	characteristic, complemented
62	C₂²	—	5	1	no	—
63	C₂²	—	15	1	no	—
64	C₄	—	3	1	no	—
65	C₃	C₅×D₂₀	1	1	yes	characteristic, complemented, Sylow
66	C₂	—	10	1	no	—
67	C₂	—	30	1	no	—
68	C₂	C₅×D₃×D₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅	D₃×D₅
commutator, cosocle	C₂×C₃×C₅	C₂²×C₅
Frattini	C₂	C₅×D₃×D₅
Fitting, socle	C₂×C₃×C₅²	C₂²
hypocenter	C₃×C₅	C₅×D₄
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×D₁₅	C₂	semidirect
2. C₂×C₃×C₅×D₅	C₂	semidirect
3. C₅²×Dic₃	C₂	semidirect
9. #1202	C₅	direct (N × H)
11. C₂×C₅×D₅	D₃	semidirect
13. C₃×C₅²	D₄	semidirect
15. C₂×D₁₅	C₂×C₅	semidirect
17. C₂×C₃×D₅	C₂×C₅	semidirect
19. C₅×Dic₃	D₅	semidirect
20. C₅×Dic₃	C₂×C₅	semidirect
33. C₅²	#67	semidirect
38. C₂×D₅	C₅×D₃	semidirect
43. C₃×C₅	D₂₀	semidirect
44. C₃×C₅	C₅×D₄	semidirect
47. Dic₃	C₅×D₅	semidirect
60. C₅	#1202	direct (N × H)
61. C₅	C₅×#67	semidirect
65. C₃	C₅×D₂₀	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₁₅	2
C₂×C₃×C₅×D₅	2
C₅²×Dic₃	2
C₅×D₂₀	3
C₅×#67	5
#1202	5

Subgroups — C5×#1202 #10597108

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#1202 #10597108