Subgroups — C₂₉×D₄₅⋊D₅ #39907974

Order 26100.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂₉×D₄₅	C₂	1	2	yes	maximal, complemented
2	C₉×C₂₉×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×D₁₅⋊D₅	—	3	1	no	maximal
4	C₅²×C₉×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₅×D₉×C₂₉	—	5	2	no	maximal
6	C₅×C₂₉×D₁₅	—	3	2	no	—
7	C₃×C₂₉×C₅⋊D₅	D₃	1	1	yes	characteristic
8	D₅²×C₂₉	—	9	1	no	Hall
9	C₂₉×D₄₅	D₅	1	2	yes	complemented
10	C₅×D₉×C₂₉	—	5	2	no	—
11	C₉×D₅×C₂₉	—	5	2	no	—
12	C₉×D₅×C₂₉	—	10	2	no	—
13	C₃×C₅²×C₂₉	C₂×D₃	1	1	yes	characteristic
14	D₃×D₅×C₂₉	—	15	2	no	—
15	C₂₉×C₅⋊D₅	D₉	1	1	yes	characteristic, complemented
16	C₅×D₅×C₂₉	—	9	2	no	—
17	C₅×C₉×C₂₉	—	2	2	no	—
18	C₅×C₉×C₂₉	C₂×D₅	1	2	yes	complemented
19	C₂×D₉×C₂₉	—	25	1	no	Hall
20	D₄₅⋊D₅	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂₉×D₁₅	—	3	2	no	—
22	C₅×D₃×C₂₉	—	15	2	no	—
23	C₃×D₅×C₂₉	—	5	2	no	—
24	C₃×D₅×C₂₉	—	10	2	no	—
25	C₅²×C₂₉	C₂×D₉	1	1	yes	characteristic, complemented, Hall
26	C₂×D₅×C₂₉	—	45	2	no	—
27	C₂×C₉×C₂₉	—	25	1	no	—
28	D₉×C₂₉	—	5	2	no	—
29	C₅×D₄₅	C₂×C₂₉	1	2	yes	complemented
30	C₉×C₅⋊D₅	C₂×C₂₉	1	1	yes	characteristic, complemented
31	C₃×C₅×C₂₉	—	2	2	no	—
32	C₃×C₅×C₂₉	D₃×D₅	1	2	yes	—
33	C₂×D₃×C₂₉	—	75	1	no	—
34	D₁₅⋊D₅	—	3	1	no	—
35	C₂×C₅×C₂₉	—	45	2	no	—
36	D₅×C₂₉	—	5	2	no	—
37	D₅×C₂₉	—	9	2	no	—
38	D₅×C₂₉	—	10	2	no	—
39	C₉×C₂₉	D₅²	1	1	yes	characteristic, complemented, Hall
40	C₅²×C₉	C₂²×C₂₉	1	1	yes	characteristic, complemented, Hall
41	D₅×D₉	—	5	2	no	—
42	C₂×C₃×C₂₉	—	25	1	no	—
43	D₃×C₂₉	—	15	2	no	—
44	C₅×D₁₅	—	3	2	no	—
45	C₃×C₅⋊D₅	D₃×C₂₉	1	1	yes	characteristic
46	C₅×C₂₉	—	2	2	no	—
47	C₅×C₂₉	D₅×D₉	1	2	yes	complemented
48	C₂²×C₂₉	—	225	1	no	Hall
49	D₅²	—	9	1	no	Hall
50	D₄₅	D₅×C₂₉	1	2	yes	complemented
51	C₉×D₅	—	5	2	no	—
52	C₉×D₅	—	10	2	no	—
53	C₅×D₉	—	5	2	no	—
54	C₃×C₂₉	D₁₅⋊D₅	1	1	yes	characteristic
55	C₃×C₅²	C₂×D₃×C₂₉	1	1	yes	characteristic
56	D₃×D₅	—	15	2	no	—
57	C₂×C₂₉	—	25	1	no	—
58	C₂×C₂₉	—	45	2	no	—
59	C₅⋊D₅	D₉×C₂₉	1	1	yes	characteristic, complemented
60	C₅×D₅	—	9	2	no	—
61	C₅×C₉	—	2	2	no	—
62	C₅×C₉	C₂×D₅×C₂₉	1	2	yes	complemented
63	C₂×D₉	—	25	1	no	Hall
64	D₁₅	—	3	2	no	—
65	C₃×D₅	—	5	2	no	—
66	C₃×D₅	—	10	2	no	—
67	C₅×D₃	—	15	2	no	—
68	C₂₉	D₄₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
69	C₅²	C₂×D₉×C₂₉	1	1	yes	characteristic, complemented, Sylow
70	C₂×D₅	—	45	2	no	—
71	C₂×C₉	—	25	1	no	—
72	D₉	—	5	2	no	—
73	C₃×C₅	—	2	2	no	—
74	C₃×C₅	D₃×D₅×C₂₉	1	2	yes	—
75	C₂×D₃	—	75	1	no	—
76	C₂×C₅	—	45	2	no	—
77	D₅	—	5	2	no	—
78	D₅	—	9	2	no	—
79	D₅	—	10	2	no	—
80	C₉	D₅²×C₂₉	1	1	yes	characteristic, complemented, Sylow
81	C₂×C₃	—	25	1	no	—
82	D₃	—	15	2	no	—
83	C₅	—	2	2	no	—
84	C₅	D₅×D₉×C₂₉	1	2	yes	complemented
85	C₂²	—	225	1	no	Sylow
86	C₃	C₂₉×D₁₅⋊D₅	1	1	yes	characteristic
87	C₂	—	25	1	no	—
88	C₂	—	45	2	no	—

	subgroup	G/H
center, hypercenter	C₂₉	D₄₅⋊D₅
commutator, cosocle, hypocenter	C₅²×C₉	C₂²×C₂₉
Frattini	C₃	C₂₉×D₁₅⋊D₅
Fitting	C₅²×C₉×C₂₉	C₂²
socle	C₃×C₅²×C₂₉	C₂×D₃
LCS	G ▷ C₅²×C₉
UCS	C₁ ◁ C₂₉

Complements

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

N	H ≅ G/N	type
1. C₅×C₂₉×D₄₅	C₂	semidirect
2. C₉×C₂₉×C₅⋊D₅	C₂	semidirect
4. C₅²×C₉×C₂₉	C₂²	semidirect
9. C₂₉×D₄₅	D₅	semidirect
15. C₂₉×C₅⋊D₅	D₉	semidirect
18. C₅×C₉×C₂₉	C₂×D₅	semidirect
20. D₄₅⋊D₅	C₂₉	direct (N × H)
25. C₅²×C₂₉	C₂×D₉	semidirect
29. C₅×D₄₅	C₂×C₂₉	semidirect
30. C₉×C₅⋊D₅	C₂×C₂₉	semidirect
39. C₉×C₂₉	D₅²	semidirect
40. C₅²×C₉	C₂²×C₂₉	semidirect
47. C₅×C₂₉	D₅×D₉	semidirect
50. D₄₅	D₅×C₂₉	semidirect
59. C₅⋊D₅	D₉×C₂₉	semidirect
62. C₅×C₉	C₂×D₅×C₂₉	semidirect
68. C₂₉	D₄₅⋊D₅	direct (N × H)
69. C₅²	C₂×D₉×C₂₉	semidirect
80. C₉	D₅²×C₂₉	semidirect
84. C₅	D₅×D₉×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₂₉×D₄₅	2
C₉×C₂₉×C₅⋊D₅	2
C₂₉×D₁₅⋊D₅	3
D₅×D₉×C₂₉	5
D₄₅⋊D₅	29

Subgroups — C29×D45⋊D5 #39907974

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×D₄₅⋊D₅ #39907974