Subgroups — C₂₉×((C₅⋊D₅)⋊C₃)⋊D₃ #39908062

Order 26100.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×C₃⋊#3874	C₂	1	2	yes	maximal, complemented
2	C₃×C₂₉×(C₅⋊D₅)⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×D₁₅⋊D₅	—	3	1	no	maximal
4	C₂₉×#3874⋊C₂	—	3	3	no	maximal
5	C₃×C₂₉×C₅²⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₅×C₂₉×D₁₅	—	3	2	no	—
7	C₃×C₂₉×C₅⋊D₅	D₃	1	1	yes	characteristic, complemented
8	C₂₉×(C₅⋊D₅)⋊C₃	D₃	1	3	yes	complemented
9	C₂₉×#3874	—	3	6	no	—
10	D₅²×C₂₉	—	9	1	no	Hall
11	C₂₉×C₅²⋊C₃	C₂×D₃	1	3	yes	complemented
12	C₃×C₅²×C₂₉	C₂×D₃	1	1	yes	characteristic, complemented
13	D₃×D₅×C₂₉	—	15	2	no	—
14	C₂₉×C₅⋊D₅	C₃⋊D₃	1	1	yes	characteristic, complemented
15	C₅×D₅×C₂₉	—	9	2	no	—
16	C₂×C₃⋊D₃×C₂₉	—	25	1	no	maximal, Hall
17	((C₅⋊D₅)⋊C₃)⋊D₃	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₂₉×D₁₅	—	3	2	no	—
19	C₅×D₃×C₂₉	—	15	2	no	—
20	C₃×D₅×C₂₉	—	15	2	no	—
21	C₅²×C₂₉	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
22	C₂×D₅×C₂₉	—	45	2	no	—
23	C₂×C₃²×C₂₉	—	25	1	no	—
24	C₃⋊D₃×C₂₉	—	25	2	no	—
25	C₃×(C₅⋊D₅)⋊C₃	C₂×C₂₉	1	1	yes	characteristic, complemented
26	C₃⋊#3874	C₂×C₂₉	1	2	yes	complemented
27	C₃×C₅×C₂₉	—	3	2	no	—
28	C₂×D₃×C₂₉	—	75	1	no	—
29	C₂×D₃×C₂₉	—	75	3	no	—
30	D₁₅⋊D₅	—	3	1	no	—
31	#3874⋊C₂	—	3	3	no	—
32	C₂×C₅×C₂₉	—	45	2	no	—
33	D₅×C₂₉	—	9	2	no	—
34	D₅×C₂₉	—	15	2	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	3	no	—
38	C₂×C₃×C₂₉	—	25	1	no	—
39	D₃×C₂₉	—	15	2	no	—
40	D₃×C₂₉	—	75	6	no	—
41	C₅×D₁₅	—	3	2	no	—
42	C₃×C₅⋊D₅	D₃×C₂₉	1	1	yes	characteristic, complemented
43	(C₅⋊D₅)⋊C₃	D₃×C₂₉	1	3	yes	complemented
44	#3874	—	3	6	no	—
45	C₅×C₂₉	—	3	2	no	—
46	C₂²×C₂₉	—	225	1	no	Hall
47	D₅²	—	9	1	no	Hall
48	C₃×C₂₉	—	25	3	no	—
49	C₃×C₂₉	#3874⋊C₂	1	1	yes	characteristic, complemented
50	C₃×C₅²	C₂×D₃×C₂₉	1	1	yes	characteristic, complemented
51	C₅²⋊C₃	C₂×D₃×C₂₉	1	3	yes	complemented
52	D₃×D₅	—	15	2	no	—
53	C₂×C₂₉	—	25	1	no	—
54	C₂×C₂₉	—	45	2	no	—
55	C₅⋊D₅	C₃⋊D₃×C₂₉	1	1	yes	characteristic, complemented
56	C₅×D₅	—	9	2	no	—
57	C₂×C₃⋊D₃	—	25	1	no	Hall
58	D₁₅	—	3	2	no	—
59	C₃×D₅	—	15	2	no	—
60	C₅×D₃	—	15	2	no	—
61	C₂₉	((C₅⋊D₅)⋊C₃)⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
62	C₅²	C₂×C₃⋊D₃×C₂₉	1	1	yes	characteristic, complemented, Sylow
63	C₂×D₅	—	45	2	no	—
64	C₂×C₃²	—	25	1	no	—
65	C₃⋊D₃	—	25	2	no	—
66	C₃×C₅	—	3	2	no	—
67	C₂×D₃	—	75	1	no	—
68	C₂×D₃	—	75	3	no	—
69	C₂×C₅	—	45	2	no	—
70	D₅	—	9	2	no	—
71	D₅	—	15	2	no	—
72	C₃²	—	25	1	no	Sylow
73	C₂×C₃	—	25	3	no	—
74	C₂×C₃	—	25	1	no	—
75	D₃	—	15	2	no	—
76	D₃	—	75	6	no	—
77	C₅	—	3	2	no	—
78	C₂²	—	225	1	no	Sylow
79	C₃	—	25	3	no	—
80	C₃	C₂₉×#3874⋊C₂	1	1	yes	characteristic, complemented
81	C₂	—	25	1	no	—
82	C₂	—	45	2	no	—

	subgroup	G/H
center, hypercenter	C₂₉	((C₅⋊D₅)⋊C₃)⋊D₃
commutator, cosocle, hypocenter	C₃×C₅²⋊C₃	C₂²×C₂₉
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₂₉	C₂×D₃
LCS	G ▷ C₃×C₅²⋊C₃
UCS	C₁ ◁ C₂₉

Complements

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

N	H ≅ G/N	type
1. C₂₉×C₃⋊#3874	C₂	semidirect
2. C₃×C₂₉×(C₅⋊D₅)⋊C₃	C₂	semidirect
5. C₃×C₂₉×C₅²⋊C₃	C₂²	semidirect
7. C₃×C₂₉×C₅⋊D₅	D₃	semidirect
8. C₂₉×(C₅⋊D₅)⋊C₃	D₃	semidirect
11. C₂₉×C₅²⋊C₃	C₂×D₃	semidirect
12. C₃×C₅²×C₂₉	C₂×D₃	semidirect
14. C₂₉×C₅⋊D₅	C₃⋊D₃	semidirect
17. ((C₅⋊D₅)⋊C₃)⋊D₃	C₂₉	direct (N × H)
21. C₅²×C₂₉	C₂×C₃⋊D₃	semidirect
25. C₃×(C₅⋊D₅)⋊C₃	C₂×C₂₉	semidirect
26. C₃⋊#3874	C₂×C₂₉	semidirect
36. C₃×C₅²⋊C₃	C₂²×C₂₉	semidirect
42. C₃×C₅⋊D₅	D₃×C₂₉	semidirect
43. (C₅⋊D₅)⋊C₃	D₃×C₂₉	semidirect
49. C₃×C₂₉	#3874⋊C₂	semidirect
50. C₃×C₅²	C₂×D₃×C₂₉	semidirect
51. C₅²⋊C₃	C₂×D₃×C₂₉	semidirect
55. C₅⋊D₅	C₃⋊D₃×C₂₉	semidirect
61. C₂₉	((C₅⋊D₅)⋊C₃)⋊D₃	direct (N × H)
62. C₅²	C₂×C₃⋊D₃×C₂₉	semidirect
80. C₃	C₂₉×#3874⋊C₂	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×C₃⋊#3874	2
C₃×C₂₉×(C₅⋊D₅)⋊C₃	2
C₂₉×D₁₅⋊D₅	3
C₂₉×#3874⋊C₂	3
C₂×C₃⋊D₃×C₂₉	25
((C₅⋊D₅)⋊C₃)⋊D₃	29

Subgroups — C29×((C5⋊D5)⋊C3)⋊D3 #39908062

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×((C₅⋊D₅)⋊C₃)⋊D₃ #39908062