Subgroups — C₅×C₃⋊D₁₀₅ #15691315

Order 3150.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅²×C₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₁₀₅	—	3	4	no	maximal
3	C₃⋊D₁₀₅	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₅×C₃⋊D₂₁	—	5	1	no	maximal
5	C₃×C₅²×C₇	D₃	1	4	yes	complemented
6	C₅×C₃⋊D₁₅	—	7	1	no	maximal, Hall
7	C₅×D₃₅	—	9	1	no	Hall
8	C₃²×C₅×C₇	—	2	2	no	—
9	C₃²×C₅×C₇	D₅	1	1	yes	characteristic, complemented
10	C₃²×C₅×C₇	C₂×C₅	1	1	yes	characteristic, complemented
11	C₃²×C₅²	D₇	1	1	yes	characteristic, complemented, Hall
12	D₁₀₅	—	3	4	no	—
13	C₅×D₂₁	—	15	4	no	—
14	C₅²×C₇	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
15	C₅×D₁₅	—	21	4	no	—
16	C₃⋊D₂₁	—	5	1	no	Hall
17	C₃×C₅×C₇	—	2	8	no	—
18	C₃×C₅×C₇	C₅×D₃	1	4	yes	complemented
19	C₃×C₅×C₇	D₁₅	1	4	yes	complemented
20	C₃⋊D₁₅	—	7	1	no	—
21	C₅×C₃⋊D₃	—	35	1	no	—
22	C₃×C₅²	D₂₁	1	4	yes	complemented
23	D₃₅	—	9	1	no	—
24	C₅×D₇	—	45	1	no	—
25	C₃²×C₇	C₅×D₅	1	1	yes	characteristic, complemented, Hall
26	C₅×D₅	—	63	1	no	Hall
27	C₃²×C₅	—	2	2	no	—
28	C₃²×C₅	C₅×D₇	1	1	yes	characteristic, complemented
29	C₃²×C₅	D₃₅	1	1	yes	characteristic, complemented
30	D₂₁	—	15	4	no	—
31	C₅×C₇	—	2	2	no	—
32	C₅×C₇	C₅×C₃⋊D₃	1	1	yes	characteristic, complemented
33	C₅×C₇	C₃⋊D₁₅	1	1	yes	characteristic, complemented
34	D₁₅	—	21	4	no	—
35	C₅×D₃	—	105	4	no	—
36	C₅²	C₃⋊D₂₁	1	1	yes	characteristic, complemented, Sylow
37	C₃×C₇	C₅×D₁₅	1	4	yes	complemented
38	C₃⋊D₃	—	35	1	no	Hall
39	C₃×C₅	—	2	8	no	—
40	C₃×C₅	C₅×D₂₁	1	4	yes	complemented
41	C₃×C₅	D₁₀₅	1	4	yes	complemented
42	D₇	—	45	1	no	Hall
43	C₂×C₅	—	315	1	no	—
44	D₅	—	63	1	no	—
45	C₃²	C₅×D₃₅	1	1	yes	characteristic, complemented, Sylow
46	C₇	C₅×C₃⋊D₁₅	1	1	yes	characteristic, complemented, Sylow
47	D₃	—	105	4	no	—
48	C₅	—	2	2	no	—
49	C₅	C₅×C₃⋊D₂₁	1	1	yes	characteristic, complemented
50	C₅	C₃⋊D₁₀₅	1	1	yes	characteristic, direct product factor
51	C₃	C₅×D₁₀₅	1	4	yes	complemented
52	C₂	—	315	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	C₃⋊D₁₀₅
commutator, cosocle, hypocenter	C₃²×C₅×C₇	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₇	C₂
LCS	G ▷ C₃²×C₅×C₇
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅²×C₇	C₂	semidirect
3. C₃⋊D₁₀₅	C₅	direct (N × H)
5. C₃×C₅²×C₇	D₃	semidirect
9. C₃²×C₅×C₇	D₅	semidirect
10. C₃²×C₅×C₇	C₂×C₅	semidirect
11. C₃²×C₅²	D₇	semidirect
14. C₅²×C₇	C₃⋊D₃	semidirect
18. C₃×C₅×C₇	C₅×D₃	semidirect
19. C₃×C₅×C₇	D₁₅	semidirect
22. C₃×C₅²	D₂₁	semidirect
25. C₃²×C₇	C₅×D₅	semidirect
28. C₃²×C₅	C₅×D₇	semidirect
29. C₃²×C₅	D₃₅	semidirect
32. C₅×C₇	C₅×C₃⋊D₃	semidirect
33. C₅×C₇	C₃⋊D₁₅	semidirect
36. C₅²	C₃⋊D₂₁	semidirect
37. C₃×C₇	C₅×D₁₅	semidirect
40. C₃×C₅	C₅×D₂₁	semidirect
41. C₃×C₅	D₁₀₅	semidirect
45. C₃²	C₅×D₃₅	semidirect
46. C₇	C₅×C₃⋊D₁₅	semidirect
49. C₅	C₅×C₃⋊D₂₁	semidirect
50. C₅	C₃⋊D₁₀₅	direct (N × H)
51. C₃	C₅×D₁₀₅	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅²×C₇	2
C₅×D₁₀₅	3
C₃⋊D₁₀₅	5
C₅×C₃⋊D₂₁	5
C₅×C₃⋊D₁₅	7

Subgroups — C5×C3⋊D105 #15691315

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₃⋊D₁₀₅ #15691315