Subgroups — C₂×C₂₉×C₃⋊((C₅⋊D₅)⋊C₃) #39908075

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	C₂₉×C₃⋊((C₅⋊D₅)⋊C₃)	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₂₉×C₃⋊(C₅⋊D₅)	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₉×(C₅⋊D₅)⋊C₃	—	3	1	no	maximal
5	C₃×C₂₉×C₅²⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂₉×C₃⋊(C₅⋊D₅)	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	C₂₉×(C₅⋊D₅)⋊C₃	—	3	2	no	—
10	C₂×C₃×C₅²×C₂₉	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×C₂₉×C₅⋊D₅	—	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×C₂₉×D₁₅	—	15	2	no	—
16	C₂×C₅²×C₂₉	C₃×D₃	1	1	yes	characteristic, complemented
17	C₂₉×C₅⋊D₅	—	3	2	no	—
18	C₂×C₃×D₃×C₂₉	—	25	1	no	maximal, Hall
19	C₂×C₃⋊((C₅⋊D₅)⋊C₃)	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂×C₃×C₅×C₂₉	—	3	2	no	—
21	C₂₉×D₁₅	—	15	4	no	—
22	C₅²×C₂₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
23	C₂×D₅×C₂₉	—	45	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	C₃⋊((C₅⋊D₅)⋊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	—	25	1	no	—
31	C₂×C₃⋊(C₅⋊D₅)	C₃×C₂₉	1	1	yes	characteristic, complemented
32	C₂×(C₅⋊D₅)⋊C₃	—	3	1	no	—
33	C₂×C₅×C₂₉	—	3	2	no	—
34	D₅×C₂₉	—	45	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	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented
41	D₃×C₂₉	—	25	2	no	—
42	C₂×C₃×C₅²	C₂×C₃×C₂₉	1	1	yes	characteristic, complemented
43	C₃⋊(C₅⋊D₅)	C₂×C₃×C₂₉	1	2	yes	complemented
44	C₂×C₅²⋊C₃	—	2	1	no	—
45	C₂×C₅²⋊C₃	D₃×C₂₉	1	1	yes	characteristic, complemented
46	(C₅⋊D₅)⋊C₃	—	3	2	no	—
47	C₅×C₂₉	—	3	2	no	—
48	C₂²×C₂₉	—	75	1	no	Hall
49	C₂×C₅⋊D₅	—	3	1	no	Hall
50	C₃×C₂₉	—	25	1	no	—
51	C₃×C₂₉	—	50	1	no	—
52	C₃×C₂₉	C₂×(C₅⋊D₅)⋊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, complemented
56	C₂×D₁₅	—	15	2	no	—
57	C₂×C₂₉	—	75	2	no	—
58	C₂×C₂₉	C₃⋊((C₅⋊D₅)⋊C₃)	1	1	yes	characteristic, direct product factor
59	C₂×C₅²	C₃×D₃×C₂₉	1	1	yes	characteristic, complemented
60	C₅⋊D₅	—	3	2	no	—
61	C₂×C₃×D₃	—	25	1	no	Hall
62	C₂×C₃×C₅	—	3	2	no	—
63	D₁₅	—	15	4	no	—
64	C₂₉	C₂×C₃⋊((C₅⋊D₅)⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
65	C₅²	C₂×C₃×D₃×C₂₉	1	1	yes	characteristic, complemented, Sylow
66	C₂×D₅	—	45	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	—	25	1	no	—
72	C₂×C₅	—	3	2	no	—
73	D₅	—	45	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	C₂₉×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented
79	D₃	—	25	2	no	—
80	C₅	—	3	2	no	—
81	C₂²	—	75	1	no	Sylow
82	C₃	—	25	1	no	—
83	C₃	—	50	1	no	—
84	C₃	C₂×C₂₉×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented
85	C₂	—	75	2	no	—
86	C₂	C₂₉×C₃⋊((C₅⋊D₅)⋊C₃)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₂₉	C₃⋊((C₅⋊D₅)⋊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. C₂₉×C₃⋊((C₅⋊D₅)⋊C₃)	C₂	direct (N × H)
3. C₂×C₂₉×C₃⋊(C₅⋊D₅)	C₃	semidirect
5. C₃×C₂₉×C₅²⋊C₃	C₂²	semidirect
6. C₂₉×C₃⋊(C₅⋊D₅)	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
19. C₂×C₃⋊((C₅⋊D₅)⋊C₃)	C₂₉	direct (N × H)
22. C₅²×C₂₉	C₂×C₃×D₃	semidirect
26. C₂×C₃×C₅²⋊C₃	C₂×C₂₉	semidirect
27. C₃⋊((C₅⋊D₅)⋊C₃)	C₂×C₂₉	direct (N × H)
31. C₂×C₃⋊(C₅⋊D₅)	C₃×C₂₉	semidirect
36. C₃×C₅²⋊C₃	C₂²×C₂₉	semidirect
40. C₂×C₃×C₂₉	(C₅⋊D₅)⋊C₃	semidirect
42. C₂×C₃×C₅²	C₂×C₃×C₂₉	semidirect
43. C₃⋊(C₅⋊D₅)	C₂×C₃×C₂₉	semidirect
45. C₂×C₅²⋊C₃	D₃×C₂₉	semidirect
52. C₃×C₂₉	C₂×(C₅⋊D₅)⋊C₃	semidirect
53. C₃×C₅²	C₂²×C₃×C₂₉	semidirect
55. C₅²⋊C₃	C₂×D₃×C₂₉	semidirect
58. C₂×C₂₉	C₃⋊((C₅⋊D₅)⋊C₃)	direct (N × H)
59. C₂×C₅²	C₃×D₃×C₂₉	semidirect
64. C₂₉	C₂×C₃⋊((C₅⋊D₅)⋊C₃)	direct (N × H)
65. C₅²	C₂×C₃×D₃×C₂₉	semidirect
78. C₂×C₃	C₂₉×(C₅⋊D₅)⋊C₃	semidirect
84. C₃	C₂×C₂₉×(C₅⋊D₅)⋊C₃	semidirect
86. C₂	C₂₉×C₃⋊((C₅⋊D₅)⋊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
C₂₉×C₃⋊((C₅⋊D₅)⋊C₃)	2
C₂×C₂₉×C₃⋊(C₅⋊D₅)	3
C₂×C₂₉×(C₅⋊D₅)⋊C₃	3
C₂×C₃×D₃×C₂₉	25
C₂×C₃⋊((C₅⋊D₅)⋊C₃)	29

Subgroups — C2×C29×C3⋊((C5⋊D5)⋊C3) #39908075

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₉×C₃⋊((C₅⋊D₅)⋊C₃) #39908075