Subgroups — C₂×C₅×C₁₃×D₉₅ #37590868

Order 24700.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃×D₉₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅²×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×C₁₃×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₅×C₁₃×D₁₉	—	5	1	no	maximal
5	C₂×C₁₃×D₉₅	C₅	1	1	yes	maximal, characteristic, direct product factor
6	C₁₃×D₉₅	C₂×C₅	1	2	yes	direct product factor
7	C₅×C₁₃×D₁₉	—	5	2	no	—
8	C₂×C₅×C₁₃×C₁₉	—	2	2	no	—
9	C₂×C₅×C₁₃×C₁₉	D₅	1	1	yes	characteristic, complemented
10	C₂×C₅×C₁₃×C₁₉	C₂×C₅	1	1	yes	characteristic, complemented
11	C₂×C₅×D₉₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₅×D₅×C₁₃	—	19	1	no	maximal, Hall
13	C₅×C₁₃×C₁₉	—	2	2	no	—
14	C₅×C₁₃×C₁₉	C₂×D₅	1	1	yes	characteristic, complemented
15	C₅×C₁₃×C₁₉	C₂²×C₅	1	1	yes	characteristic, complemented
16	C₂×C₁₃×D₁₉	—	5	1	no	Hall
17	C₂×C₅²×C₁₉	C₂×C₁₃	1	1	yes	characteristic, complemented
18	C₅×D₉₅	C₂×C₁₃	1	2	yes	direct product factor
19	C₂×C₅²×C₁₃	D₁₉	1	1	yes	characteristic, complemented
20	C₅×D₅×C₁₃	—	19	2	no	—
21	C₂×C₁₃×C₁₉	C₅×D₅	1	1	yes	characteristic, complemented
22	C₁₃×D₁₉	—	5	2	no	—
23	C₅²×C₁₉	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
24	C₂×D₉₅	C₅×C₁₃	1	1	yes	characteristic, direct product factor
25	C₂×C₅×D₁₉	—	5	1	no	—
26	C₅²×C₁₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
27	C₂²×C₅×C₁₃	—	95	1	no	—
28	C₂×D₅×C₁₃	—	19	1	no	—
29	C₁₃×C₁₉	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Hall
30	C₂×C₅×C₁₉	—	2	2	no	—
31	C₂×C₅×C₁₉	D₅×C₁₃	1	1	yes	characteristic, complemented
32	C₂×C₅×C₁₉	C₂×C₅×C₁₃	1	1	yes	characteristic, complemented
33	D₉₅	C₂×C₅×C₁₃	1	2	yes	direct product factor
34	C₅×D₁₉	—	5	2	no	—
35	C₂×C₅×C₁₃	—	2	2	no	—
36	C₂×C₅×C₁₃	—	95	2	no	—
37	C₂×C₅×C₁₃	C₅×D₁₉	1	1	yes	characteristic, complemented
38	C₂×C₅×C₁₃	D₉₅	1	1	yes	characteristic, direct product factor
39	D₅×C₁₃	—	19	2	no	—
40	C₂×C₅×D₅	—	19	1	no	Hall
41	C₅×C₁₉	—	2	2	no	—
42	C₅×C₁₉	C₂×D₅×C₁₃	1	1	yes	characteristic, complemented
43	C₅×C₁₉	C₂²×C₅×C₁₃	1	1	yes	characteristic, complemented
44	C₂×D₁₉	—	5	1	no	Hall
45	C₅×C₁₃	—	2	2	no	—
46	C₅×C₁₃	C₂×C₅×D₁₉	1	1	yes	characteristic, complemented
47	C₅×C₁₃	C₂×D₉₅	1	1	yes	characteristic, direct product factor
48	C₂²×C₁₃	—	95	1	no	Hall
49	C₂×C₅²	C₁₃×D₁₉	1	1	yes	characteristic, complemented
50	C₅×D₅	—	19	2	no	—
51	C₂×C₁₉	C₅×D₅×C₁₃	1	1	yes	characteristic, complemented
52	D₁₉	—	5	2	no	—
53	C₂×C₁₃	—	95	2	no	—
54	C₂×C₁₃	C₅×D₉₅	1	1	yes	characteristic, direct product factor
55	C₅²	C₂×C₁₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
56	C₂²×C₅	—	95	1	no	—
57	C₂×D₅	—	19	1	no	—
58	C₁₉	C₂×C₅×D₅×C₁₃	1	1	yes	characteristic, complemented, Sylow
59	C₁₃	C₂×C₅×D₉₅	1	1	yes	characteristic, direct product factor, Sylow
60	C₂×C₅	—	2	2	no	—
61	C₂×C₅	—	95	2	no	—
62	C₂×C₅	C₅×C₁₃×D₁₉	1	1	yes	characteristic, complemented
63	C₂×C₅	C₁₃×D₉₅	1	1	yes	characteristic, direct product factor
64	D₅	—	19	2	no	—
65	C₅	—	2	2	no	—
66	C₅	C₂×C₁₃×D₉₅	1	1	yes	characteristic, direct product factor
67	C₅	C₂×C₅×C₁₃×D₁₉	1	1	yes	characteristic, complemented
68	C₂²	—	95	1	no	Sylow
69	C₂	—	95	2	no	—
70	C₂	C₅×C₁₃×D₉₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₃	D₉₅
commutator, cosocle, hypocenter	C₅×C₁₉	C₂²×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₁₃×C₁₉	C₂
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₂×C₅×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₃×D₉₅	C₂	direct (N × H)
2. C₂×C₅²×C₁₃×C₁₉	C₂	semidirect
3. C₅²×C₁₃×C₁₉	C₂²	semidirect
5. C₂×C₁₃×D₉₅	C₅	direct (N × H)
6. C₁₃×D₉₅	C₂×C₅	direct (N × H)
9. C₂×C₅×C₁₃×C₁₉	D₅	semidirect
10. C₂×C₅×C₁₃×C₁₉	C₂×C₅	semidirect
11. C₂×C₅×D₉₅	C₁₃	direct (N × H)
14. C₅×C₁₃×C₁₉	C₂×D₅	semidirect
15. C₅×C₁₃×C₁₉	C₂²×C₅	semidirect
17. C₂×C₅²×C₁₉	C₂×C₁₃	semidirect
18. C₅×D₉₅	C₂×C₁₃	direct (N × H)
19. C₂×C₅²×C₁₃	D₁₉	semidirect
21. C₂×C₁₃×C₁₉	C₅×D₅	semidirect
23. C₅²×C₁₉	C₂²×C₁₃	semidirect
24. C₂×D₉₅	C₅×C₁₃	direct (N × H)
26. C₅²×C₁₃	C₂×D₁₉	semidirect
29. C₁₃×C₁₉	C₂×C₅×D₅	semidirect
31. C₂×C₅×C₁₉	D₅×C₁₃	semidirect
32. C₂×C₅×C₁₉	C₂×C₅×C₁₃	semidirect
33. D₉₅	C₂×C₅×C₁₃	direct (N × H)
37. C₂×C₅×C₁₃	C₅×D₁₉	semidirect
38. C₂×C₅×C₁₃	D₉₅	direct (N × H)
42. C₅×C₁₉	C₂×D₅×C₁₃	semidirect
43. C₅×C₁₉	C₂²×C₅×C₁₃	semidirect
46. C₅×C₁₃	C₂×C₅×D₁₉	semidirect
47. C₅×C₁₃	C₂×D₉₅	direct (N × H)
49. C₂×C₅²	C₁₃×D₁₉	semidirect
51. C₂×C₁₉	C₅×D₅×C₁₃	semidirect
54. C₂×C₁₃	C₅×D₉₅	direct (N × H)
55. C₅²	C₂×C₁₃×D₁₉	semidirect
58. C₁₉	C₂×C₅×D₅×C₁₃	semidirect
59. C₁₃	C₂×C₅×D₉₅	direct (N × H)
62. C₂×C₅	C₅×C₁₃×D₁₉	semidirect
63. C₂×C₅	C₁₃×D₉₅	direct (N × H)
66. C₅	C₂×C₁₃×D₉₅	direct (N × H)
67. C₅	C₂×C₅×C₁₃×D₁₉	semidirect
70. C₂	C₅×C₁₃×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
C₅×C₁₃×D₉₅	2
C₂×C₅²×C₁₃×C₁₉	2
C₂×C₅×C₁₃×D₁₉	5
C₂×C₁₃×D₉₅	5
C₂×C₅×D₉₅	13
C₂×C₅×D₅×C₁₃	19

Subgroups — C2×C5×C13×D95 #37590868

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₁₃×D₉₅ #37590868