Subgroups — C₃×C₅×C₂₉×A₅ #39908240

Order 26100.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂₉×A₅	C₃	1	1	yes	maximal, characteristic, direct product factor
2	C₃×C₂₉×A₅	C₅	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₅×A₄×C₂₉	—	5	1	no	maximal
4	C₃×C₅×D₅×C₂₉	—	6	1	no	maximal
5	C₃×C₅×D₃×C₂₉	—	10	1	no	maximal
6	C₃×C₅²×C₂₉	—	6	1	no	—
7	C₂²×C₃×C₅×C₂₉	—	5	1	no	—
8	C₅×A₄×C₂₉	—	5	1	no	—
9	C₅×A₄×C₂₉	—	5	2	no	—
10	C₂₉×A₅	C₃×C₅	1	1	yes	characteristic, direct product factor
11	C₅×D₅×C₂₉	—	6	1	no	—
12	C₃²×C₅×C₂₉	—	10	1	no	—
13	C₃×A₄×C₂₉	—	5	1	no	Hall
14	C₃×C₅×A₅	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×C₃×C₅×C₂₉	—	15	1	no	—
16	C₅×D₃×C₂₉	—	10	1	no	—
17	C₃×D₅×C₂₉	—	6	1	no	—
18	C₅²×C₂₉	—	6	1	no	Hall
19	C₂²×C₅×C₂₉	—	5	1	no	—
20	C₃×D₃×C₂₉	—	10	1	no	—
21	C₃×C₅×C₂₉	—	6	1	no	—
22	C₃×C₅×C₂₉	—	10	1	no	—
23	C₃×C₅×C₂₉	—	12	2	no	—
24	C₃×C₅×C₂₉	—	20	1	no	—
25	C₃×C₅×C₂₉	A₅	1	1	yes	maximal normal, characteristic, direct product factor
26	C₂²×C₃×C₂₉	—	5	1	no	—
27	A₄×C₂₉	—	5	1	no	—
28	A₄×C₂₉	—	5	2	no	—
29	C₅×A₅	C₃×C₂₉	1	1	yes	characteristic, direct product factor
30	C₂×C₅×C₂₉	—	15	1	no	—
31	D₅×C₂₉	—	6	1	no	—
32	C₃²×C₂₉	—	10	1	no	Hall
33	C₃×C₅×A₄	—	5	1	no	—
34	C₃×A₅	C₅×C₂₉	1	1	yes	characteristic, direct product factor
35	C₂×C₃×C₂₉	—	15	1	no	—
36	D₃×C₂₉	—	10	1	no	—
37	C₃×C₅×D₅	—	6	1	no	—
38	C₅×C₂₉	—	6	1	no	—
39	C₅×C₂₉	—	12	2	no	—
40	C₅×C₂₉	C₃×A₅	1	1	yes	characteristic, direct product factor
41	C₂²×C₂₉	—	5	1	no	Hall
42	C₃×C₅×D₃	—	10	1	no	—
43	C₃×C₂₉	—	10	1	no	—
44	C₃×C₂₉	—	20	1	no	—
45	C₃×C₂₉	C₅×A₅	1	1	yes	characteristic, direct product factor
46	C₃×C₅²	—	6	1	no	—
47	C₂²×C₃×C₅	—	5	1	no	—
48	C₅×A₄	—	5	1	no	—
49	C₅×A₄	—	5	2	no	—
50	A₅	C₃×C₅×C₂₉	1	1	yes	characteristic, direct product factor
51	C₂×C₂₉	—	15	1	no	—
52	C₅×D₅	—	6	1	no	—
53	C₃²×C₅	—	10	1	no	—
54	C₃×A₄	—	5	1	no	Hall
55	C₂×C₃×C₅	—	15	1	no	—
56	C₃×D₅	—	6	1	no	—
57	C₅×D₃	—	10	1	no	—
58	C₂₉	C₃×C₅×A₅	1	1	yes	characteristic, direct product factor, Sylow
59	C₅²	—	6	1	no	Sylow
60	C₂²×C₅	—	5	1	no	—
61	C₃×D₃	—	10	1	no	—
62	C₃×C₅	—	6	1	no	—
63	C₃×C₅	—	10	1	no	—
64	C₃×C₅	—	12	2	no	—
65	C₃×C₅	—	20	1	no	—
66	C₃×C₅	C₂₉×A₅	1	1	yes	characteristic, direct product factor
67	C₂²×C₃	—	5	1	no	—
68	A₄	—	5	1	no	—
69	A₄	—	5	2	no	—
70	C₂×C₅	—	15	1	no	—
71	D₅	—	6	1	no	—
72	C₃²	—	10	1	no	Sylow
73	C₂×C₃	—	15	1	no	—
74	D₃	—	10	1	no	—
75	C₅	—	6	1	no	—
76	C₅	—	12	2	no	—
77	C₅	C₃×C₂₉×A₅	1	1	yes	characteristic, direct product factor
78	C₂²	—	5	1	no	Sylow
79	C₃	—	10	1	no	—
80	C₃	—	20	1	no	—
81	C₃	C₅×C₂₉×A₅	1	1	yes	characteristic, direct product factor
82	C₂	—	15	1	no	—

	subgroup	G/H
center, Fitting, hypercenter	C₃×C₅×C₂₉	A₅
commutator, hypocenter	A₅	C₃×C₅×C₂₉
Frattini	C₁	G
LCS	G ▷ A₅
UCS	C₁ ◁ C₃×C₅×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₅×C₂₉×A₅	C₃	direct (N × H)
2. C₃×C₂₉×A₅	C₅	direct (N × H)
10. C₂₉×A₅	C₃×C₅	direct (N × H)
14. C₃×C₅×A₅	C₂₉	direct (N × H)
25. C₃×C₅×C₂₉	A₅	direct (N × H)
29. C₅×A₅	C₃×C₂₉	direct (N × H)
34. C₃×A₅	C₅×C₂₉	direct (N × H)
40. C₅×C₂₉	C₃×A₅	direct (N × H)
45. C₃×C₂₉	C₅×A₅	direct (N × H)
50. A₅	C₃×C₅×C₂₉	direct (N × H)
58. C₂₉	C₃×C₅×A₅	direct (N × H)
66. C₃×C₅	C₂₉×A₅	direct (N × H)
77. C₅	C₃×C₂₉×A₅	direct (N × H)
81. C₃	C₅×C₂₉×A₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₂₉×A₅	3
C₃×C₂₉×A₅	5
C₃×C₅×A₄×C₂₉	5
C₃×C₅×D₅×C₂₉	6
C₃×C₅×D₃×C₂₉	10
C₃×C₅×A₅	29

Subgroups — C3×C5×C29×A5 #39908240

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₂₉×A₅ #39908240