Subgroups — C₃×C₇×C₂₉×A₅ #49141696

Order 36540.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₂₉×A₅	C₃	1	1	yes	maximal, characteristic, direct product factor
2	C₃×C₇×A₄×C₂₉	—	5	1	no	maximal, Hall
3	C₃×C₇×D₅×C₂₉	—	6	1	no	maximal
4	C₃×C₂₉×A₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×D₃×C₇×C₂₉	—	10	1	no	maximal
6	C₃×C₅×C₇×C₂₉	—	6	1	no	—
7	C₇×A₄×C₂₉	—	5	1	no	—
8	C₇×A₄×C₂₉	—	5	2	no	—
9	C₂²×C₃×C₇×C₂₉	—	5	1	no	—
10	C₇×D₅×C₂₉	—	6	1	no	—
11	C₃²×C₇×C₂₉	—	10	1	no	Hall
12	C₂₉×A₅	C₃×C₇	1	1	yes	characteristic, direct product factor
13	C₃×C₇×A₅	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₃×C₇×C₂₉	—	15	1	no	—
15	D₃×C₇×C₂₉	—	10	1	no	—
16	C₃×A₄×C₂₉	—	5	1	no	Hall
17	C₅×C₇×C₂₉	—	6	1	no	Hall
18	C₃×D₅×C₂₉	—	6	1	no	—
19	C₂²×C₇×C₂₉	—	5	1	no	Hall
20	C₃×C₇×C₂₉	—	10	1	no	—
21	C₃×C₇×C₂₉	—	20	1	no	—
22	C₃×C₇×C₂₉	A₅	1	1	yes	maximal normal, characteristic, direct product factor
23	C₃×D₃×C₂₉	—	10	1	no	—
24	C₃×C₅×C₂₉	—	6	1	no	—
25	C₇×A₅	C₃×C₂₉	1	1	yes	characteristic, direct product factor
26	C₂×C₇×C₂₉	—	15	1	no	—
27	C₂²×C₃×C₂₉	—	5	1	no	—
28	A₄×C₂₉	—	5	1	no	—
29	A₄×C₂₉	—	5	2	no	—
30	D₅×C₂₉	—	6	1	no	—
31	C₃²×C₂₉	—	10	1	no	Hall
32	C₃×C₇×A₄	—	5	1	no	Hall
33	C₃×C₇×D₅	—	6	1	no	—
34	C₇×C₂₉	C₃×A₅	1	1	yes	characteristic, direct product factor, Hall
35	C₃×A₅	C₇×C₂₉	1	1	yes	characteristic, direct product factor, Hall
36	C₂×C₃×C₂₉	—	15	1	no	—
37	D₃×C₂₉	—	10	1	no	—
38	C₅×C₂₉	—	6	1	no	Hall
39	C₃×D₃×C₇	—	10	1	no	—
40	C₂²×C₂₉	—	5	1	no	Hall
41	C₃×C₅×C₇	—	6	1	no	—
42	C₃×C₂₉	—	10	1	no	—
43	C₃×C₂₉	—	20	1	no	—
44	C₃×C₂₉	C₇×A₅	1	1	yes	characteristic, direct product factor
45	C₂²×C₃×C₇	—	5	1	no	—
46	C₇×A₄	—	5	1	no	—
47	C₇×A₄	—	5	2	no	—
48	C₇×D₅	—	6	1	no	—
49	C₃²×C₇	—	10	1	no	Hall
50	A₅	C₃×C₇×C₂₉	1	1	yes	characteristic, direct product factor
51	C₂×C₂₉	—	15	1	no	—
52	C₂×C₃×C₇	—	15	1	no	—
53	D₃×C₇	—	10	1	no	—
54	C₃×A₄	—	5	1	no	Hall
55	C₅×C₇	—	6	1	no	Hall
56	C₃×D₅	—	6	1	no	—
57	C₂₉	C₃×C₇×A₅	1	1	yes	characteristic, direct product factor, Sylow
58	C₂²×C₇	—	5	1	no	Hall
59	C₃×C₇	—	10	1	no	—
60	C₃×C₇	—	20	1	no	—
61	C₃×C₇	C₂₉×A₅	1	1	yes	characteristic, direct product factor
62	C₃×D₃	—	10	1	no	—
63	C₃×C₅	—	6	1	no	—
64	C₂×C₇	—	15	1	no	—
65	C₂²×C₃	—	5	1	no	—
66	A₄	—	5	1	no	—
67	A₄	—	5	2	no	—
68	D₅	—	6	1	no	—
69	C₃²	—	10	1	no	Sylow
70	C₇	C₃×C₂₉×A₅	1	1	yes	characteristic, direct product factor, Sylow
71	C₂×C₃	—	15	1	no	—
72	D₃	—	10	1	no	—
73	C₅	—	6	1	no	Sylow
74	C₂²	—	5	1	no	Sylow
75	C₃	—	10	1	no	—
76	C₃	—	20	1	no	—
77	C₃	C₇×C₂₉×A₅	1	1	yes	characteristic, direct product factor
78	C₂	—	15	1	no	—

	subgroup	G/H
center, Fitting, hypercenter	C₃×C₇×C₂₉	A₅
commutator, hypocenter	A₅	C₃×C₇×C₂₉
Frattini	C₁	G
LCS	G ▷ A₅
UCS	C₁ ◁ C₃×C₇×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₇×C₂₉×A₅	C₃	direct (N × H)
4. C₃×C₂₉×A₅	C₇	direct (N × H)
12. C₂₉×A₅	C₃×C₇	direct (N × H)
13. C₃×C₇×A₅	C₂₉	direct (N × H)
22. C₃×C₇×C₂₉	A₅	direct (N × H)
25. C₇×A₅	C₃×C₂₉	direct (N × H)
34. C₇×C₂₉	C₃×A₅	direct (N × H)
35. C₃×A₅	C₇×C₂₉	direct (N × H)
44. C₃×C₂₉	C₇×A₅	direct (N × H)
50. A₅	C₃×C₇×C₂₉	direct (N × H)
57. C₂₉	C₃×C₇×A₅	direct (N × H)
61. C₃×C₇	C₂₉×A₅	direct (N × H)
70. C₇	C₃×C₂₉×A₅	direct (N × H)
77. C₃	C₇×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
C₇×C₂₉×A₅	3
C₃×C₇×A₄×C₂₉	5
C₃×C₇×D₅×C₂₉	6
C₃×C₂₉×A₅	7
C₃×D₃×C₇×C₂₉	10
C₃×C₇×A₅	29

Subgroups — C3×C7×C29×A5 #49141696

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×C₂₉×A₅ #49141696