Subgroups — C₂×C₃⋊(C₅⋊D₉₅) #19152907

Order 5700.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₅⋊D₉₅)	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅⋊D₉₅	—	3	1	no	maximal, Hall
4	C₃×C₅²×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₂₈₅	—	5	6	no	maximal
6	C₂×C₅²×C₁₉	D₃	1	1	yes	characteristic, complemented
7	C₅⋊D₉₅	—	3	2	no	—
8	C₂×C₃×C₅×C₁₉	D₅	1	6	yes	complemented
9	D₂₈₅	—	5	12	no	—
10	C₅²×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	C₂×D₉₅	—	15	6	no	—
12	C₂×C₃⋊(C₅⋊D₅)	—	19	1	no	maximal, Hall
13	C₃×C₅×C₁₉	C₂×D₅	1	6	yes	complemented
14	C₂×D₅₇	—	25	1	no	Hall
15	C₂×C₅×C₁₉	D₁₅	1	6	yes	complemented
16	D₉₅	—	15	12	no	—
17	C₂×C₃×C₅²	D₁₉	1	1	yes	characteristic, complemented
18	C₃⋊(C₅⋊D₅)	—	19	2	no	—
19	C₂×C₃×C₁₉	C₅⋊D₅	1	1	yes	characteristic, complemented
20	D₅₇	—	25	2	no	—
21	C₂×C₅⋊D₅	—	57	1	no	Hall
22	C₅×C₁₉	C₂×D₁₅	1	6	yes	complemented
23	C₂×D₁₉	—	75	1	no	Hall
24	C₃×C₅²	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
25	C₂×D₁₅	—	95	6	no	—
26	C₃×C₁₉	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
27	C₂×C₅²	D₅₇	1	1	yes	characteristic, complemented
28	C₅⋊D₅	—	57	2	no	—
29	C₂×C₁₉	C₃⋊(C₅⋊D₅)	1	1	yes	characteristic, complemented
30	D₁₉	—	75	2	no	—
31	C₂×C₃×C₅	D₉₅	1	6	yes	complemented
32	D₁₅	—	95	12	no	—
33	C₅²	C₂×D₅₇	1	1	yes	characteristic, complemented, Sylow
34	C₂×D₅	—	285	6	no	—
35	C₁₉	C₂×C₃⋊(C₅⋊D₅)	1	1	yes	characteristic, complemented, Sylow
36	C₃×C₅	C₂×D₉₅	1	6	yes	complemented
37	C₂×D₃	—	475	1	no	Hall
38	C₂×C₅	D₂₈₅	1	6	yes	complemented
39	D₅	—	285	12	no	—
40	C₂×C₃	C₅⋊D₉₅	1	1	yes	characteristic, complemented
41	D₃	—	475	2	no	—
42	C₅	C₂×D₂₈₅	1	6	yes	complemented
43	C₂²	—	1425	1	no	Sylow
44	C₃	C₂×C₅⋊D₉₅	1	1	yes	characteristic, complemented, Sylow
45	C₂	—	1425	2	no	—
46	C₂	C₃⋊(C₅⋊D₉₅)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊(C₅⋊D₉₅)
commutator, hypocenter	C₃×C₅²×C₁₉	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₁₉	C₂
LCS	G ▷ C₃×C₅²×C₁₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₃⋊(C₅⋊D₉₅)	C₂	direct (N × H)
2. C₂×C₃×C₅²×C₁₉	C₂	semidirect
4. C₃×C₅²×C₁₉	C₂²	semidirect
6. C₂×C₅²×C₁₉	D₃	semidirect
8. C₂×C₃×C₅×C₁₉	D₅	semidirect
10. C₅²×C₁₉	C₂×D₃	semidirect
13. C₃×C₅×C₁₉	C₂×D₅	semidirect
15. C₂×C₅×C₁₉	D₁₅	semidirect
17. C₂×C₃×C₅²	D₁₉	semidirect
19. C₂×C₃×C₁₉	C₅⋊D₅	semidirect
22. C₅×C₁₉	C₂×D₁₅	semidirect
24. C₃×C₅²	C₂×D₁₉	semidirect
26. C₃×C₁₉	C₂×C₅⋊D₅	semidirect
27. C₂×C₅²	D₅₇	semidirect
29. C₂×C₁₉	C₃⋊(C₅⋊D₅)	semidirect
31. C₂×C₃×C₅	D₉₅	semidirect
33. C₅²	C₂×D₅₇	semidirect
35. C₁₉	C₂×C₃⋊(C₅⋊D₅)	semidirect
36. C₃×C₅	C₂×D₉₅	semidirect
38. C₂×C₅	D₂₈₅	semidirect
40. C₂×C₃	C₅⋊D₉₅	semidirect
42. C₅	C₂×D₂₈₅	semidirect
44. C₃	C₂×C₅⋊D₉₅	semidirect
46. C₂	C₃⋊(C₅⋊D₉₅)	direct (N × H)

Subgroups — C2×C3⋊(C5⋊D95) #19152907

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃⋊(C₅⋊D₉₅) #19152907