Subgroups — C₂×C₂₉×#90646 #39907913

Order 26100.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×C₅²⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#90646	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅×C₂₉×D₁₅	—	3	1	no	maximal
4	C₂₉×C₅²⋊C₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₅×C₂₉×D₁₅	—	3	2	no	—
6	C₂×C₃×C₅²×C₂₉	D₃	1	1	yes	characteristic
7	C₂×C₅×D₅×C₂₉	—	9	1	no	Hall
8	C₃×C₅²×C₂₉	C₂×D₃	1	1	yes	characteristic
9	C₂×C₂₉×D₁₅	—	3	1	no	—
10	C₂×C₅×D₃×C₂₉	—	15	1	no	—
11	C₂×C₅²×C₂₉	D₉	1	1	yes	characteristic, complemented
12	C₅×D₅×C₂₉	—	9	2	no	—
13	C₂×D₉×C₂₉	—	25	1	no	maximal, Hall
14	C₂×#90646	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×C₃×C₅×C₂₉	—	3	1	no	—
16	C₂×C₃×C₅×C₂₉	—	3	1	no	—
17	C₂₉×D₁₅	—	3	2	no	—
18	C₅×D₃×C₂₉	—	15	2	no	—
19	C₅²×C₂₉	C₂×D₉	1	1	yes	characteristic, complemented, Hall
20	C₂²×C₅×C₂₉	—	45	1	no	—
21	C₂×D₅×C₂₉	—	9	1	no	—
22	C₂×C₉×C₂₉	—	25	1	no	—
23	D₉×C₂₉	—	25	2	no	—
24	C₂×C₅²⋊C₉	C₂×C₂₉	1	1	yes	characteristic, complemented
25	#90646	C₂×C₂₉	1	2	yes	direct product factor
26	C₃×C₅×C₂₉	—	3	1	no	—
27	C₃×C₅×C₂₉	—	3	1	no	—
28	C₂×D₃×C₂₉	—	15	1	no	—
29	C₂×C₅×D₁₅	—	3	1	no	—
30	C₂×C₅×C₂₉	—	3	1	no	—
31	C₂×C₅×C₂₉	—	3	1	no	—
32	C₂×C₅×C₂₉	—	45	2	no	—
33	D₅×C₂₉	—	9	2	no	—
34	C₉×C₂₉	—	25	1	no	Hall
35	C₅²⋊C₉	C₂²×C₂₉	1	1	yes	characteristic, complemented, Hall
36	C₂×C₃×C₂₉	#3874	1	1	yes	characteristic
37	D₃×C₂₉	—	15	2	no	—
38	C₂×C₃×C₅²	D₃×C₂₉	1	1	yes	characteristic
39	C₅×D₁₅	—	3	2	no	—
40	C₅×C₂₉	—	3	1	no	—
41	C₅×C₂₉	—	3	1	no	—
42	C₂²×C₂₉	—	45	1	no	Hall
43	C₂×C₅×D₅	—	9	1	no	Hall
44	C₃×C₂₉	C₂×#3874	1	1	yes	characteristic
45	C₃×C₅²	C₂×D₃×C₂₉	1	1	yes	characteristic
46	C₂×D₁₅	—	3	1	no	—
47	C₂×C₅×D₃	—	15	1	no	—
48	C₂×C₂₉	—	45	2	no	—
49	C₂×C₂₉	#90646	1	1	yes	characteristic, direct product factor
50	C₂×C₅²	D₉×C₂₉	1	1	yes	characteristic, complemented
51	C₅×D₅	—	9	2	no	—
52	C₂×D₉	—	25	1	no	Hall
53	C₂×C₃×C₅	—	3	1	no	—
54	C₂×C₃×C₅	—	3	1	no	—
55	D₁₅	—	3	2	no	—
56	C₅×D₃	—	15	2	no	—
57	C₂₉	C₂×#90646	1	1	yes	characteristic, direct product factor, Sylow
58	C₅²	C₂×D₉×C₂₉	1	1	yes	characteristic, complemented, Sylow
59	C₂²×C₅	—	45	1	no	—
60	C₂×D₅	—	9	1	no	—
61	C₂×C₉	—	25	1	no	—
62	D₉	—	25	2	no	—
63	C₃×C₅	—	3	1	no	—
64	C₃×C₅	—	3	1	no	—
65	C₂×D₃	—	15	1	no	—
66	C₂×C₅	—	3	1	no	—
67	C₂×C₅	—	3	1	no	—
68	C₂×C₅	—	45	2	no	—
69	D₅	—	9	2	no	—
70	C₉	—	25	1	no	Sylow
71	C₂×C₃	C₂₉×#3874	1	1	yes	characteristic
72	D₃	—	15	2	no	—
73	C₅	—	3	1	no	—
74	C₅	—	3	1	no	—
75	C₂²	—	45	1	no	Sylow
76	C₃	C₂×C₂₉×#3874	1	1	yes	characteristic
77	C₂	—	45	2	no	—
78	C₂	C₂₉×#90646	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₂₉	#90646
commutator, cosocle, hypocenter	C₅²⋊C₉	C₂²×C₂₉
Frattini	C₃	C₂×C₂₉×#3874
Fitting, socle	C₂×C₃×C₅²×C₂₉	D₃
LCS	G ▷ C₅²⋊C₉
UCS	C₁ ◁ C₂×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₉×C₅²⋊C₉	C₂	semidirect
2. C₂₉×#90646	C₂	direct (N × H)
4. C₂₉×C₅²⋊C₉	C₂²	semidirect
11. C₂×C₅²×C₂₉	D₉	semidirect
14. C₂×#90646	C₂₉	direct (N × H)
19. C₅²×C₂₉	C₂×D₉	semidirect
24. C₂×C₅²⋊C₉	C₂×C₂₉	semidirect
25. #90646	C₂×C₂₉	direct (N × H)
35. C₅²⋊C₉	C₂²×C₂₉	semidirect
49. C₂×C₂₉	#90646	direct (N × H)
50. C₂×C₅²	D₉×C₂₉	semidirect
57. C₂₉	C₂×#90646	direct (N × H)
58. C₅²	C₂×D₉×C₂₉	semidirect
78. C₂	C₂₉×#90646	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×C₂₉×C₅²⋊C₉	2
C₂₉×#90646	2
C₂×C₅×C₂₉×D₁₅	3
C₂×D₉×C₂₉	25
C₂×#90646	29

Subgroups — C2×C29×#90646 #39907913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₉×#90646 #39907913