Subgroups — C₅×C₇×C₃⋊D₁₅ #15691314

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×C₇×D₁₅	—	3	4	no	maximal
3	C₇×C₃⋊D₁₅	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₅×C₇×C₃⋊D₃	—	5	1	no	maximal
5	C₃×C₅²×C₇	D₃	1	4	yes	complemented
6	C₅×C₃⋊D₁₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×C₇×D₅	—	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	C₂×C₇	1	1	yes	characteristic, complemented, Hall
12	C₇×D₁₅	—	3	4	no	—
13	C₅×D₃×C₇	—	15	4	no	—
14	C₅²×C₇	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
15	C₅×D₁₅	—	3	4	no	—
16	C₇×C₃⋊D₃	—	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	C₅×C₇	1	1	yes	characteristic, direct product factor
21	C₅×C₃⋊D₃	—	5	1	no	—
22	C₃×C₅²	D₃×C₇	1	4	yes	complemented
23	C₂×C₅×C₇	—	45	1	no	—
24	C₇×D₅	—	9	1	no	—
25	C₃²×C₇	C₅×D₅	1	1	yes	characteristic, complemented, Hall
26	C₅×D₅	—	9	1	no	Hall
27	C₃²×C₅	—	2	2	no	—
28	C₃²×C₅	C₇×D₅	1	1	yes	characteristic, complemented
29	C₃²×C₅	C₂×C₅×C₇	1	1	yes	characteristic, complemented
30	D₃×C₇	—	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, direct product factor
34	D₁₅	—	3	4	no	—
35	C₅×D₃	—	15	4	no	—
36	C₅²	C₇×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
37	C₃×C₇	C₅×D₁₅	1	4	yes	complemented
38	C₃⋊D₃	—	5	1	no	Hall
39	C₃×C₅	—	2	8	no	—
40	C₃×C₅	C₅×D₃×C₇	1	4	yes	complemented
41	C₃×C₅	C₇×D₁₅	1	4	yes	complemented
42	C₂×C₇	—	45	1	no	Hall
43	C₂×C₅	—	45	1	no	—
44	D₅	—	9	1	no	—
45	C₃²	C₅×C₇×D₅	1	1	yes	characteristic, complemented, Sylow
46	C₇	C₅×C₃⋊D₁₅	1	1	yes	characteristic, direct product factor, Sylow
47	D₃	—	15	4	no	—
48	C₅	—	2	2	no	—
49	C₅	C₅×C₇×C₃⋊D₃	1	1	yes	characteristic, complemented
50	C₅	C₇×C₃⋊D₁₅	1	1	yes	characteristic, direct product factor
51	C₃	C₅×C₇×D₁₅	1	4	yes	complemented
52	C₂	—	45	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₇	C₃⋊D₁₅
commutator, cosocle, hypocenter	C₃²×C₅	C₂×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₇	C₂
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₅×C₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅²×C₇	C₂	semidirect
3. C₇×C₃⋊D₁₅	C₅	direct (N × H)
5. C₃×C₅²×C₇	D₃	semidirect
6. C₅×C₃⋊D₁₅	C₇	direct (N × H)
9. C₃²×C₅×C₇	D₅	semidirect
10. C₃²×C₅×C₇	C₂×C₅	semidirect
11. C₃²×C₅²	C₂×C₇	semidirect
14. C₅²×C₇	C₃⋊D₃	semidirect
18. C₃×C₅×C₇	C₅×D₃	semidirect
19. C₃×C₅×C₇	D₁₅	semidirect
20. C₃⋊D₁₅	C₅×C₇	direct (N × H)
22. C₃×C₅²	D₃×C₇	semidirect
25. C₃²×C₇	C₅×D₅	semidirect
28. C₃²×C₅	C₇×D₅	semidirect
29. C₃²×C₅	C₂×C₅×C₇	semidirect
32. C₅×C₇	C₅×C₃⋊D₃	semidirect
33. C₅×C₇	C₃⋊D₁₅	direct (N × H)
36. C₅²	C₇×C₃⋊D₃	semidirect
37. C₃×C₇	C₅×D₁₅	semidirect
40. C₃×C₅	C₅×D₃×C₇	semidirect
41. C₃×C₅	C₇×D₁₅	semidirect
45. C₃²	C₅×C₇×D₅	semidirect
46. C₇	C₅×C₃⋊D₁₅	direct (N × H)
49. C₅	C₅×C₇×C₃⋊D₃	semidirect
50. C₅	C₇×C₃⋊D₁₅	direct (N × H)
51. C₃	C₅×C₇×D₁₅	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×C₇×D₁₅	3
C₇×C₃⋊D₁₅	5
C₅×C₇×C₃⋊D₃	5
C₅×C₃⋊D₁₅	7

Subgroups — C5×C7×C3⋊D15 #15691314

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₇×C₃⋊D₁₅ #15691314