Subgroups — C₂×C₅²⋊C₃×D₈₇ #39908072

Order 26100.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₂₉×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅²⋊C₃×D₈₇	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅²×D₈₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₉×C₅²⋊C₃	—	3	1	no	maximal
5	C₃×C₂₉×C₅²⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₅²×D₈₇	C₂×C₃	1	2	yes	complemented
7	C₂×C₂₉×C₅²⋊C₃	—	2	1	no	—
8	C₂×C₂₉×C₅²⋊C₃	D₃	1	1	yes	characteristic, complemented
9	D₂₉×C₅²⋊C₃	—	3	2	no	—
10	C₂×C₃×C₅²×C₂₉	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×C₅²×D₂₉	—	3	1	no	Hall
12	C₂₉×C₅²⋊C₃	—	2	1	no	—
13	C₂₉×C₅²⋊C₃	C₂×D₃	1	1	yes	characteristic, complemented
14	C₃×C₅²×C₂₉	C₂²×C₃	1	1	yes	characteristic, complemented
15	C₂×C₅×D₈₇	—	3	2	no	—
16	C₂×C₅²×C₂₉	C₃×D₃	1	1	yes	characteristic, complemented
17	C₅²×D₂₉	—	3	2	no	—
18	C₂×C₃×D₈₇	—	25	1	no	maximal, Hall
19	C₂×D₃×C₅²⋊C₃	—	29	1	no	maximal, Hall
20	C₂×C₃×C₅×C₂₉	—	3	2	no	—
21	C₅×D₈₇	—	3	4	no	—
22	C₅²×C₂₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
23	C₂×C₅×D₂₉	—	9	2	no	—
24	C₂×C₃²×C₂₉	—	25	1	no	—
25	C₃×D₈₇	—	25	2	no	—
26	C₂×C₃×C₅²⋊C₃	D₂₉	1	1	yes	characteristic, complemented
27	D₃×C₅²⋊C₃	—	29	2	no	—
28	C₃×C₅×C₂₉	—	3	2	no	—
29	C₂×D₈₇	C₅²⋊C₃	1	1	yes	characteristic, direct product factor
30	C₂×C₃×D₂₉	—	75	1	no	—
31	C₂×C₅²×D₃	—	29	1	no	—
32	C₂²×C₅²⋊C₃	—	87	1	no	—
33	C₂×C₅×C₂₉	—	3	2	no	—
34	C₅×D₂₉	—	9	4	no	—
35	C₃²×C₂₉	—	25	1	no	Hall
36	C₃×C₅²⋊C₃	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
37	C₂×C₃×C₂₉	—	25	1	no	—
38	C₂×C₃×C₂₉	—	50	1	no	—
39	C₂×C₃×C₂₉	C₂×C₅²⋊C₃	1	1	yes	characteristic, complemented
40	D₈₇	C₂×C₅²⋊C₃	1	2	yes	direct product factor
41	C₃×D₂₉	—	75	2	no	—
42	C₂×C₃×C₅²	C₃×D₂₉	1	1	yes	characteristic, complemented
43	C₅²×D₃	—	29	2	no	—
44	C₂×C₅²⋊C₃	—	2	1	no	—
45	C₂×C₅²⋊C₃	—	87	2	no	—
46	C₂×C₅²⋊C₃	D₈₇	1	1	yes	characteristic, direct product factor
47	C₅×C₂₉	—	3	2	no	—
48	C₂×D₂₉	—	3	1	no	Hall
49	C₂²×C₅²	—	87	1	no	Hall
50	C₃×C₂₉	—	25	1	no	—
51	C₃×C₂₉	—	50	1	no	—
52	C₃×C₂₉	C₂²×C₅²⋊C₃	1	1	yes	characteristic, complemented
53	C₃×C₅²	C₂×C₃×D₂₉	1	1	yes	characteristic, complemented
54	C₅²⋊C₃	—	2	1	no	—
55	C₅²⋊C₃	C₂×D₈₇	1	1	yes	characteristic, direct product factor
56	C₂×C₅×D₃	—	87	2	no	—
57	C₂×C₂₉	D₃×C₅²⋊C₃	1	1	yes	characteristic, complemented
58	D₂₉	—	3	2	no	—
59	C₂×C₅²	—	87	2	no	—
60	C₂×C₅²	C₃×D₈₇	1	1	yes	characteristic, complemented
61	C₂×C₃×D₃	—	725	1	no	Hall
62	C₂×C₃×C₅	—	3	2	no	—
63	C₅×D₃	—	87	4	no	—
64	C₂₉	C₂×D₃×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
65	C₅²	C₂×C₃×D₈₇	1	1	yes	characteristic, complemented, Sylow
66	C₂²×C₅	—	261	2	no	—
67	C₂×C₃²	—	25	1	no	—
68	C₃×D₃	—	725	2	no	—
69	C₃×C₅	—	3	2	no	—
70	C₂²×C₃	—	2175	1	no	—
71	C₂×D₃	—	29	1	no	—
72	C₂×C₅	—	3	2	no	—
73	C₂×C₅	—	261	4	no	—
74	C₃²	—	25	1	no	Sylow
75	C₂×C₃	—	25	1	no	—
76	C₂×C₃	—	50	1	no	—
77	C₂×C₃	—	2175	2	no	—
78	C₂×C₃	D₂₉×C₅²⋊C₃	1	1	yes	characteristic, complemented
79	D₃	—	29	2	no	—
80	C₅	—	3	2	no	—
81	C₂²	—	87	1	no	Sylow
82	C₃	—	25	1	no	—
83	C₃	—	50	1	no	—
84	C₃	C₂×D₂₉×C₅²⋊C₃	1	1	yes	characteristic, complemented
85	C₂	—	87	2	no	—
86	C₂	C₅²⋊C₃×D₈₇	1	1	yes	characteristic, direct product factor

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₂₉×C₅²⋊C₃	C₂	semidirect
2. C₅²⋊C₃×D₈₇	C₂	direct (N × H)
3. C₂×C₅²×D₈₇	C₃	semidirect
5. C₃×C₂₉×C₅²⋊C₃	C₂²	semidirect
6. C₅²×D₈₇	C₂×C₃	semidirect
8. C₂×C₂₉×C₅²⋊C₃	D₃	semidirect
10. C₂×C₃×C₅²×C₂₉	C₂×C₃	semidirect
13. C₂₉×C₅²⋊C₃	C₂×D₃	semidirect
14. C₃×C₅²×C₂₉	C₂²×C₃	semidirect
16. C₂×C₅²×C₂₉	C₃×D₃	semidirect
22. C₅²×C₂₉	C₂×C₃×D₃	semidirect
26. C₂×C₃×C₅²⋊C₃	D₂₉	semidirect
29. C₂×D₈₇	C₅²⋊C₃	direct (N × H)
36. C₃×C₅²⋊C₃	C₂×D₂₉	semidirect
39. C₂×C₃×C₂₉	C₂×C₅²⋊C₃	semidirect
40. D₈₇	C₂×C₅²⋊C₃	direct (N × H)
42. C₂×C₃×C₅²	C₃×D₂₉	semidirect
46. C₂×C₅²⋊C₃	D₈₇	direct (N × H)
52. C₃×C₂₉	C₂²×C₅²⋊C₃	semidirect
53. C₃×C₅²	C₂×C₃×D₂₉	semidirect
55. C₅²⋊C₃	C₂×D₈₇	direct (N × H)
57. C₂×C₂₉	D₃×C₅²⋊C₃	semidirect
60. C₂×C₅²	C₃×D₈₇	semidirect
64. C₂₉	C₂×D₃×C₅²⋊C₃	semidirect
65. C₅²	C₂×C₃×D₈₇	semidirect
78. C₂×C₃	D₂₉×C₅²⋊C₃	semidirect
84. C₃	C₂×D₂₉×C₅²⋊C₃	semidirect
86. 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
C₂×C₃×C₂₉×C₅²⋊C₃	2
C₅²⋊C₃×D₈₇	2
C₂×C₅²×D₈₇	3
C₂×D₂₉×C₅²⋊C₃	3
C₂×C₃×D₈₇	25
C₂×D₃×C₅²⋊C₃	29

Subgroups — C2×C52⋊C3×D87 #39908072

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅²⋊C₃×D₈₇ #39908072