Subgroups — C₂×C₅²×C₃⋊D₈₇ #39908235

Order 26100.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₃⋊D₈₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅²×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅²×D₈₇	—	3	4	no	maximal
4	C₃²×C₅²×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅×C₃⋊D₈₇	C₅	1	6	yes	maximal, direct product factor
6	C₅²×D₈₇	—	3	8	no	—
7	C₂×C₃×C₅²×C₂₉	D₃	1	4	yes	complemented
8	C₂×C₅²×D₂₉	—	9	1	no	Hall
9	C₅×C₃⋊D₈₇	C₂×C₅	1	12	yes	direct product factor
10	C₂×C₃²×C₅×C₂₉	C₂×C₅	1	6	yes	complemented
11	C₃×C₅²×C₂₉	C₂×D₃	1	4	yes	complemented
12	C₂×C₅×D₈₇	—	3	24	no	—
13	C₂×C₅²×C₂₉	C₃⋊D₃	1	1	yes	characteristic, complemented
14	C₅²×D₂₉	—	9	2	no	—
15	C₃²×C₅×C₂₉	C₂²×C₅	1	6	yes	complemented
16	C₂×C₃⋊D₈₇	C₅²	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₅²×C₃⋊D₃	—	29	1	no	maximal, Hall
18	C₂×C₃×C₅×C₂₉	C₅×D₃	1	24	yes	complemented
19	C₅×D₈₇	—	3	48	no	—
20	C₅²×C₂₉	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₅×D₂₉	—	9	6	no	—
22	C₂×C₃²×C₂₉	C₂×C₅²	1	1	yes	characteristic, complemented
23	C₃⋊D₈₇	C₂×C₅²	1	2	yes	direct product factor
24	C₂×C₃²×C₅²	D₂₉	1	1	yes	characteristic, complemented
25	C₅²×C₃⋊D₃	—	29	2	no	—
26	C₃×C₅×C₂₉	C₂×C₅×D₃	1	24	yes	complemented
27	C₂×D₈₇	—	3	4	no	—
28	C₂×C₅²×D₃	—	87	4	no	—
29	C₂×C₅×C₂₉	C₅×C₃⋊D₃	1	6	yes	complemented
30	C₅×D₂₉	—	9	12	no	—
31	C₃²×C₂₉	C₂²×C₅²	1	1	yes	characteristic, complemented, Hall
32	C₃²×C₅²	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
33	C₂×C₅×C₃⋊D₃	—	29	6	no	—
34	C₂×C₃×C₂₉	C₅²×D₃	1	4	yes	complemented
35	D₈₇	—	3	8	no	—
36	C₂×C₃×C₅²	D₈₇	1	4	yes	complemented
37	C₅²×D₃	—	87	8	no	—
38	C₅×C₂₉	C₂×C₅×C₃⋊D₃	1	6	yes	complemented
39	C₂×D₂₉	—	9	1	no	Hall
40	C₂²×C₅²	—	261	1	no	Hall
41	C₂×C₃²×C₅	C₅×D₂₉	1	6	yes	complemented
42	C₅×C₃⋊D₃	—	29	12	no	—
43	C₃×C₂₉	C₂×C₅²×D₃	1	4	yes	complemented
44	C₃×C₅²	C₂×D₈₇	1	4	yes	complemented
45	C₂×C₅×D₃	—	87	24	no	—
46	C₂×C₂₉	C₅²×C₃⋊D₃	1	1	yes	characteristic, complemented
47	D₂₉	—	9	2	no	—
48	C₂×C₅²	—	261	2	no	—
49	C₂×C₅²	C₃⋊D₈₇	1	1	yes	characteristic, direct product factor
50	C₃²×C₅	C₂×C₅×D₂₉	1	6	yes	complemented
51	C₂×C₃⋊D₃	—	29	1	no	Hall
52	C₂×C₃×C₅	C₅×D₈₇	1	24	yes	complemented
53	C₅×D₃	—	87	48	no	—
54	C₂₉	C₂×C₅²×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
55	C₅²	C₂×C₃⋊D₈₇	1	1	yes	characteristic, direct product factor, Sylow
56	C₂²×C₅	—	261	6	no	—
57	C₂×C₃²	C₅²×D₂₉	1	1	yes	characteristic, complemented
58	C₃⋊D₃	—	29	2	no	—
59	C₃×C₅	C₂×C₅×D₈₇	1	24	yes	complemented
60	C₂×D₃	—	87	4	no	—
61	C₂×C₅	—	261	12	no	—
62	C₂×C₅	C₅×C₃⋊D₈₇	1	6	yes	direct product factor
63	C₃²	C₂×C₅²×D₂₉	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₃	C₅²×D₈₇	1	4	yes	complemented
65	D₃	—	87	8	no	—
66	C₅	C₂×C₅×C₃⋊D₈₇	1	6	yes	direct product factor
67	C₂²	—	261	1	no	Sylow
68	C₃	C₂×C₅²×D₈₇	1	4	yes	complemented
69	C₂	—	261	2	no	—
70	C₂	C₅²×C₃⋊D₈₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅²	C₃⋊D₈₇
commutator, cosocle, hypocenter	C₃²×C₂₉	C₂²×C₅²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅²×C₂₉	C₂
LCS	G ▷ C₃²×C₂₉
UCS	C₁ ◁ C₂×C₅²

Complements

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

N	H ≅ G/N	type
1. C₅²×C₃⋊D₈₇	C₂	direct (N × H)
2. C₂×C₃²×C₅²×C₂₉	C₂	semidirect
4. C₃²×C₅²×C₂₉	C₂²	semidirect
5. C₂×C₅×C₃⋊D₈₇	C₅	direct (N × H)
7. C₂×C₃×C₅²×C₂₉	D₃	semidirect
9. C₅×C₃⋊D₈₇	C₂×C₅	direct (N × H)
10. C₂×C₃²×C₅×C₂₉	C₂×C₅	semidirect
11. C₃×C₅²×C₂₉	C₂×D₃	semidirect
13. C₂×C₅²×C₂₉	C₃⋊D₃	semidirect
15. C₃²×C₅×C₂₉	C₂²×C₅	semidirect
16. C₂×C₃⋊D₈₇	C₅²	direct (N × H)
18. C₂×C₃×C₅×C₂₉	C₅×D₃	semidirect
20. C₅²×C₂₉	C₂×C₃⋊D₃	semidirect
22. C₂×C₃²×C₂₉	C₂×C₅²	semidirect
23. C₃⋊D₈₇	C₂×C₅²	direct (N × H)
24. C₂×C₃²×C₅²	D₂₉	semidirect
26. C₃×C₅×C₂₉	C₂×C₅×D₃	semidirect
29. C₂×C₅×C₂₉	C₅×C₃⋊D₃	semidirect
31. C₃²×C₂₉	C₂²×C₅²	semidirect
32. C₃²×C₅²	C₂×D₂₉	semidirect
34. C₂×C₃×C₂₉	C₅²×D₃	semidirect
36. C₂×C₃×C₅²	D₈₇	semidirect
38. C₅×C₂₉	C₂×C₅×C₃⋊D₃	semidirect
41. C₂×C₃²×C₅	C₅×D₂₉	semidirect
43. C₃×C₂₉	C₂×C₅²×D₃	semidirect
44. C₃×C₅²	C₂×D₈₇	semidirect
46. C₂×C₂₉	C₅²×C₃⋊D₃	semidirect
49. C₂×C₅²	C₃⋊D₈₇	direct (N × H)
50. C₃²×C₅	C₂×C₅×D₂₉	semidirect
52. C₂×C₃×C₅	C₅×D₈₇	semidirect
54. C₂₉	C₂×C₅²×C₃⋊D₃	semidirect
55. C₅²	C₂×C₃⋊D₈₇	direct (N × H)
57. C₂×C₃²	C₅²×D₂₉	semidirect
59. C₃×C₅	C₂×C₅×D₈₇	semidirect
62. C₂×C₅	C₅×C₃⋊D₈₇	direct (N × H)
63. C₃²	C₂×C₅²×D₂₉	semidirect
64. C₂×C₃	C₅²×D₈₇	semidirect
66. C₅	C₂×C₅×C₃⋊D₈₇	direct (N × H)
68. C₃	C₂×C₅²×D₈₇	semidirect
70. C₂	C₅²×C₃⋊D₈₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅²×C₃⋊D₈₇	2
C₂×C₃²×C₅²×C₂₉	2
C₂×C₅²×D₈₇	3
C₂×C₅×C₃⋊D₈₇	5
C₂×C₅²×C₃⋊D₃	29

Subgroups — C2×C52×C3⋊D87 #39908235

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅²×C₃⋊D₈₇ #39908235