Subgroups — C₃×C₁₃×C₅⋊D₉₅ #49150324

Order 37050.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×C₅⋊D₉₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₃×D₉₅	—	5	6	no	maximal
4	C₅²×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅×C₁₃×C₁₉	D₅	1	6	yes	complemented
6	C₃×C₅⋊D₉₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₃×D₉₅	—	5	6	no	—
8	C₃×C₁₃×C₅⋊D₅	—	19	1	no	maximal, Hall
9	C₃×C₁₃×D₁₉	—	25	1	no	Hall
10	C₃×C₅²×C₁₉	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
11	C₅×C₁₃×C₁₉	C₃×D₅	1	6	yes	complemented
12	C₃×C₅²×C₁₃	D₁₉	1	1	yes	characteristic, complemented, Hall
13	C₅⋊D₉₅	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₁₃×C₁₉	C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
15	C₁₃×C₅⋊D₅	—	19	1	no	Hall
16	C₃×D₉₅	—	5	6	no	—
17	C₁₃×D₁₉	—	25	1	no	Hall
18	C₅²×C₁₉	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
19	C₃×D₅×C₁₃	—	95	6	no	—
20	C₅²×C₁₃	C₃×D₁₉	1	1	yes	characteristic, complemented, Hall
21	C₃×C₅×C₁₉	D₅×C₁₃	1	6	yes	complemented
22	C₁₃×C₁₉	C₃×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅×C₁₃	D₉₅	1	6	yes	complemented
24	D₉₅	—	5	6	no	—
25	C₃×C₅⋊D₅	—	19	1	no	Hall
26	D₅×C₁₃	—	95	6	no	—
27	C₃×D₁₉	—	25	1	no	Hall
28	C₅×C₁₉	C₃×D₅×C₁₃	1	6	yes	complemented
29	C₂×C₃×C₁₃	—	475	1	no	Hall
30	C₃×C₅²	C₁₃×D₁₉	1	1	yes	characteristic, complemented, Hall
31	C₅×C₁₃	C₃×D₉₅	1	6	yes	complemented
32	C₃×C₁₉	C₁₃×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
33	C₅⋊D₅	—	19	1	no	Hall
34	C₃×C₁₃	C₅⋊D₉₅	1	1	yes	characteristic, direct product factor, Hall
35	D₁₉	—	25	1	no	Hall
36	C₃×D₅	—	95	6	no	—
37	C₂×C₁₃	—	475	1	no	Hall
38	C₅²	C₃×C₁₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
39	C₁₉	C₃×C₁₃×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₅	C₁₃×D₉₅	1	6	yes	complemented
41	C₁₃	C₃×C₅⋊D₉₅	1	1	yes	characteristic, direct product factor, Sylow
42	D₅	—	95	6	no	—
43	C₂×C₃	—	475	1	no	Hall
44	C₅	C₃×C₁₃×D₉₅	1	6	yes	complemented
45	C₃	C₁₃×C₅⋊D₉₅	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	—	475	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₃	C₅⋊D₉₅
commutator, cosocle, hypocenter	C₅²×C₁₉	C₂×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₃×C₁₉	C₂
LCS	G ▷ C₅²×C₁₉
UCS	C₁ ◁ C₃×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×C₁₃×C₁₉	C₂	semidirect
2. C₁₃×C₅⋊D₉₅	C₃	direct (N × H)
4. C₅²×C₁₃×C₁₉	C₂×C₃	semidirect
5. C₃×C₅×C₁₃×C₁₉	D₅	semidirect
6. C₃×C₅⋊D₉₅	C₁₃	direct (N × H)
10. C₃×C₅²×C₁₉	C₂×C₁₃	semidirect
11. C₅×C₁₃×C₁₉	C₃×D₅	semidirect
12. C₃×C₅²×C₁₃	D₁₉	semidirect
13. C₅⋊D₉₅	C₃×C₁₃	direct (N × H)
14. C₃×C₁₃×C₁₉	C₅⋊D₅	semidirect
18. C₅²×C₁₉	C₂×C₃×C₁₃	semidirect
20. C₅²×C₁₃	C₃×D₁₉	semidirect
21. C₃×C₅×C₁₉	D₅×C₁₃	semidirect
22. C₁₃×C₁₉	C₃×C₅⋊D₅	semidirect
23. C₃×C₅×C₁₃	D₉₅	semidirect
28. C₅×C₁₉	C₃×D₅×C₁₃	semidirect
30. C₃×C₅²	C₁₃×D₁₉	semidirect
31. C₅×C₁₃	C₃×D₉₅	semidirect
32. C₃×C₁₉	C₁₃×C₅⋊D₅	semidirect
34. C₃×C₁₃	C₅⋊D₉₅	direct (N × H)
38. C₅²	C₃×C₁₃×D₁₉	semidirect
39. C₁₉	C₃×C₁₃×C₅⋊D₅	semidirect
40. C₃×C₅	C₁₃×D₉₅	semidirect
41. C₁₃	C₃×C₅⋊D₉₅	direct (N × H)
44. C₅	C₃×C₁₃×D₉₅	semidirect
45. C₃	C₁₃×C₅⋊D₉₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅²×C₁₃×C₁₉	2
C₁₃×C₅⋊D₉₅	3
C₃×C₁₃×D₉₅	5
C₃×C₅⋊D₉₅	13
C₃×C₁₃×C₅⋊D₅	19

Subgroups — C3×C13×C5⋊D95 #49150324

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₃×C₅⋊D₉₅ #49150324