Subgroups — C₂×C₅×D₁₂₃₅ #37590870

Order 24700.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₁₂₃₅	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×D₂₄₇	—	5	1	no	maximal
5	C₂×D₁₂₃₅	C₅	1	1	yes	maximal, characteristic, direct product factor
6	D₁₂₃₅	C₂×C₅	1	2	yes	direct product factor
7	C₅×D₂₄₇	—	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	—	13	1	no	maximal, Hall
12	C₂×C₅×D₆₅	—	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×D₂₄₇	—	5	1	no	Hall
17	C₂×C₅²×C₁₉	D₁₃	1	1	yes	characteristic, complemented
18	C₅×D₉₅	—	13	2	no	—
19	C₂×C₅²×C₁₃	D₁₉	1	1	yes	characteristic, complemented
20	C₅×D₆₅	—	19	2	no	—
21	C₂×C₁₃×C₁₉	C₅×D₅	1	1	yes	characteristic, complemented
22	D₂₄₇	—	5	2	no	—
23	C₅²×C₁₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
24	C₂×D₉₅	—	13	1	no	—
25	C₂×C₅×D₁₉	—	65	1	no	—
26	C₅²×C₁₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
27	C₂×D₆₅	—	19	1	no	—
28	C₂×C₅×D₁₃	—	95	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	C₅×D₁₃	1	1	yes	characteristic, complemented
32	C₂×C₅×C₁₉	D₆₅	1	1	yes	characteristic, complemented
33	D₉₅	—	13	2	no	—
34	C₅×D₁₉	—	65	2	no	—
35	C₂×C₅×C₁₃	—	2	2	no	—
36	C₂×C₅×C₁₃	C₅×D₁₉	1	1	yes	characteristic, complemented
37	C₂×C₅×C₁₃	D₉₅	1	1	yes	characteristic, complemented
38	D₆₅	—	19	2	no	—
39	C₅×D₁₃	—	95	2	no	—
40	C₂×C₅×D₅	—	247	1	no	Hall
41	C₅×C₁₉	—	2	2	no	—
42	C₅×C₁₉	C₂×C₅×D₁₃	1	1	yes	characteristic, complemented
43	C₅×C₁₉	C₂×D₆₅	1	1	yes	characteristic, complemented
44	C₂×D₁₉	—	65	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, complemented
48	C₂×D₁₃	—	95	1	no	Hall
49	C₂×C₅²	D₂₄₇	1	1	yes	characteristic, complemented
50	C₅×D₅	—	247	2	no	—
51	C₂×C₁₉	C₅×D₆₅	1	1	yes	characteristic, complemented
52	D₁₉	—	65	2	no	—
53	C₂×C₁₃	C₅×D₉₅	1	1	yes	characteristic, complemented
54	D₁₃	—	95	2	no	—
55	C₅²	C₂×D₂₄₇	1	1	yes	characteristic, complemented, Sylow
56	C₂²×C₅	—	1235	1	no	—
57	C₂×D₅	—	247	1	no	—
58	C₁₉	C₂×C₅×D₆₅	1	1	yes	characteristic, complemented, Sylow
59	C₁₃	C₂×C₅×D₉₅	1	1	yes	characteristic, complemented, Sylow
60	C₂×C₅	—	2	2	no	—
61	C₂×C₅	—	1235	2	no	—
62	C₂×C₅	C₅×D₂₄₇	1	1	yes	characteristic, complemented
63	C₂×C₅	D₁₂₃₅	1	1	yes	characteristic, direct product factor
64	D₅	—	247	2	no	—
65	C₅	—	2	2	no	—
66	C₅	C₂×D₁₂₃₅	1	1	yes	characteristic, direct product factor
67	C₅	C₂×C₅×D₂₄₇	1	1	yes	characteristic, complemented
68	C₂²	—	1235	1	no	Sylow
69	C₂	—	1235	2	no	—
70	C₂	C₅×D₁₂₃₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	D₁₂₃₅
commutator, cosocle, hypocenter	C₅×C₁₃×C₁₉	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₁₃×C₁₉	C₂
LCS	G ▷ C₅×C₁₃×C₁₉
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₁₂₃₅	C₂	direct (N × H)
2. C₂×C₅²×C₁₃×C₁₉	C₂	semidirect
3. C₅²×C₁₃×C₁₉	C₂²	semidirect
5. C₂×D₁₂₃₅	C₅	direct (N × H)
6. D₁₂₃₅	C₂×C₅	direct (N × H)
9. C₂×C₅×C₁₃×C₁₉	D₅	semidirect
10. C₂×C₅×C₁₃×C₁₉	C₂×C₅	semidirect
14. C₅×C₁₃×C₁₉	C₂×D₅	semidirect
15. C₅×C₁₃×C₁₉	C₂²×C₅	semidirect
17. C₂×C₅²×C₁₉	D₁₃	semidirect
19. C₂×C₅²×C₁₃	D₁₉	semidirect
21. C₂×C₁₃×C₁₉	C₅×D₅	semidirect
23. C₅²×C₁₉	C₂×D₁₃	semidirect
26. C₅²×C₁₃	C₂×D₁₉	semidirect
29. C₁₃×C₁₉	C₂×C₅×D₅	semidirect
31. C₂×C₅×C₁₉	C₅×D₁₃	semidirect
32. C₂×C₅×C₁₉	D₆₅	semidirect
36. C₂×C₅×C₁₃	C₅×D₁₉	semidirect
37. C₂×C₅×C₁₃	D₉₅	semidirect
42. C₅×C₁₉	C₂×C₅×D₁₃	semidirect
43. C₅×C₁₉	C₂×D₆₅	semidirect
46. C₅×C₁₃	C₂×C₅×D₁₉	semidirect
47. C₅×C₁₃	C₂×D₉₅	semidirect
49. C₂×C₅²	D₂₄₇	semidirect
51. C₂×C₁₉	C₅×D₆₅	semidirect
53. C₂×C₁₃	C₅×D₉₅	semidirect
55. C₅²	C₂×D₂₄₇	semidirect
58. C₁₉	C₂×C₅×D₆₅	semidirect
59. C₁₃	C₂×C₅×D₉₅	semidirect
62. C₂×C₅	C₅×D₂₄₇	semidirect
63. C₂×C₅	D₁₂₃₅	direct (N × H)
66. C₅	C₂×D₁₂₃₅	direct (N × H)
67. C₅	C₂×C₅×D₂₄₇	semidirect
70. C₂	C₅×D₁₂₃₅	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×D₁₂₃₅	2
C₂×C₅²×C₁₃×C₁₉	2
C₂×C₅×D₂₄₇	5
C₂×D₁₂₃₅	5
C₂×C₅×D₉₅	13
C₂×C₅×D₆₅	19

Subgroups — C2×C5×D1235 #37590870

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₁₂₃₅ #37590870