Subgroups — C₂×D₃×C₂₉×C₅²⋊C₃ #39908071

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

	subgroup	G/H
center, hypercenter	C₂×C₂₉	D₃×C₅²⋊C₃
commutator, cosocle, hypocenter	C₃×C₅²	C₂²×C₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₂₉	C₂×C₃
LCS	G ▷ C₃×C₅²
UCS	C₁ ◁ C₂×C₂₉

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. D₃×C₂₉×C₅²⋊C₃	C₂	direct (N × H)
3. C₂×C₅²×D₃×C₂₉	C₃	semidirect
5. C₃×C₂₉×C₅²⋊C₃	C₂²	semidirect
6. C₅²×D₃×C₂₉	C₂×C₃	semidirect
9. C₂×C₂₉×C₅²⋊C₃	D₃	direct (N × H)
10. C₂×C₃×C₅²×C₂₉	C₂×C₃	semidirect
13. C₂₉×C₅²⋊C₃	C₂×D₃	direct (N × H)
14. C₃×C₅²×C₂₉	C₂²×C₃	semidirect
17. C₂×C₅²×C₂₉	C₃×D₃	semidirect
19. C₂×D₃×C₅²⋊C₃	C₂₉	direct (N × H)
22. C₅²×C₂₉	C₂×C₃×D₃	semidirect
26. C₂×C₃×C₅²⋊C₃	C₂×C₂₉	semidirect
27. D₃×C₅²⋊C₃	C₂×C₂₉	direct (N × H)
30. C₂×D₃×C₂₉	C₅²⋊C₃	direct (N × H)
31. C₂×C₅²×D₃	C₃×C₂₉	semidirect
36. C₃×C₅²⋊C₃	C₂²×C₂₉	semidirect
40. C₂×C₃×C₂₉	C₂×C₅²⋊C₃	semidirect
41. D₃×C₂₉	C₂×C₅²⋊C₃	direct (N × H)
42. C₂×C₃×C₅²	C₂×C₃×C₂₉	semidirect
43. C₅²×D₃	C₂×C₃×C₂₉	semidirect
46. C₂×C₅²⋊C₃	D₃×C₂₉	direct (N × H)
52. C₃×C₂₉	C₂²×C₅²⋊C₃	semidirect
53. C₃×C₅²	C₂²×C₃×C₂₉	semidirect
55. C₅²⋊C₃	C₂×D₃×C₂₉	direct (N × H)
58. C₂×C₂₉	D₃×C₅²⋊C₃	direct (N × H)
60. C₂×C₅²	C₃×D₃×C₂₉	semidirect
64. C₂₉	C₂×D₃×C₅²⋊C₃	direct (N × H)
65. C₅²	C₂×C₃×D₃×C₂₉	semidirect
71. C₂×D₃	C₂₉×C₅²⋊C₃	direct (N × H)
78. C₂×C₃	C₂×C₂₉×C₅²⋊C₃	semidirect
79. D₃	C₂×C₂₉×C₅²⋊C₃	direct (N × H)
84. C₃	C₂²×C₂₉×C₅²⋊C₃	semidirect
86. C₂	D₃×C₂₉×C₅²⋊C₃	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
D₃×C₂₉×C₅²⋊C₃	2
C₂×C₅²×D₃×C₂₉	3
C₂²×C₂₉×C₅²⋊C₃	3
C₂×C₃×D₃×C₂₉	25
C₂×D₃×C₅²⋊C₃	29

Subgroups — C2×D3×C29×C52⋊C3 #39908071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×C₂₉×C₅²⋊C₃ #39908071