Subgroups — C₃×A₅×C₂₉⋊C₇ #49141697

Order 36540.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	A₅×C₂₉⋊C₇	C₃	1	1	yes	maximal, characteristic, direct product factor
2	C₃×A₄×C₂₉⋊C₇	—	5	1	no	maximal, Hall
3	C₃×D₅×C₂₉⋊C₇	—	6	1	no	maximal
4	C₃×C₂₉×A₅	C₇	1	1	yes	maximal, characteristic, complemented, Hall
5	C₃×D₃×C₂₉⋊C₇	—	10	1	no	maximal
6	C₃×C₅×C₂₉⋊C₇	—	6	1	no	—
7	C₂²×C₃×C₂₉⋊C₇	—	5	1	no	—
8	A₄×C₂₉⋊C₇	—	5	1	no	—
9	A₄×C₂₉⋊C₇	—	5	2	no	—
10	D₅×C₂₉⋊C₇	—	6	1	no	—
11	C₃²×C₂₉⋊C₇	—	10	1	no	Hall
12	C₂₉×A₅	C₃×C₇	1	1	yes	characteristic, complemented
13	C₃×C₇×A₅	—	29	1	no	maximal, Hall
14	C₂×C₃×C₂₉⋊C₇	—	15	1	no	—
15	D₃×C₂₉⋊C₇	—	10	1	no	—
16	C₃×A₄×C₂₉	—	5	1	no	Hall
17	C₅×C₂₉⋊C₇	—	6	1	no	Hall
18	C₃×D₅×C₂₉	—	6	1	no	—
19	C₂²×C₂₉⋊C₇	—	5	1	no	Hall
20	C₃×C₂₉⋊C₇	—	10	1	no	—
21	C₃×C₂₉⋊C₇	—	20	1	no	—
22	C₃×C₂₉⋊C₇	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	—	29	1	no	—
26	C₂×C₂₉⋊C₇	—	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	—	145	1	no	Hall
33	C₃×C₇×D₅	—	174	1	no	—
34	C₂₉⋊C₇	C₃×A₅	1	1	yes	characteristic, direct product factor, Hall
35	C₃×A₅	C₂₉⋊C₇	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	—	290	1	no	—
40	C₂²×C₂₉	—	5	1	no	Hall
41	C₃×C₅×C₇	—	174	1	no	—
42	C₃×C₂₉	—	10	1	no	—
43	C₃×C₂₉	—	20	1	no	—
44	C₃×C₂₉	C₇×A₅	1	1	yes	characteristic, complemented
45	C₂²×C₃×C₇	—	145	1	no	—
46	C₇×A₄	—	145	1	no	—
47	C₇×A₄	—	145	2	no	—
48	C₇×D₅	—	174	1	no	—
49	C₃²×C₇	—	290	1	no	Hall
50	A₅	C₃×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor
51	C₂×C₂₉	—	15	1	no	—
52	C₂×C₃×C₇	—	435	1	no	—
53	D₃×C₇	—	290	1	no	—
54	C₃×A₄	—	5	1	no	Hall
55	C₅×C₇	—	174	1	no	Hall
56	C₃×D₅	—	6	1	no	—
57	C₂₉	C₃×C₇×A₅	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₇	—	145	1	no	Hall
59	C₃×C₇	—	29	1	no	—
60	C₃×C₇	—	290	1	no	—
61	C₃×C₇	—	580	1	no	—
62	C₃×D₃	—	10	1	no	—
63	C₃×C₅	—	6	1	no	—
64	C₂×C₇	—	435	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	—	29	1	no	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	A₅×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor
78	C₂	—	15	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. A₅×C₂₉⋊C₇	C₃	direct (N × H)
4. C₃×C₂₉×A₅	C₇	semidirect
12. C₂₉×A₅	C₃×C₇	semidirect
22. C₃×C₂₉⋊C₇	A₅	direct (N × H)
34. C₂₉⋊C₇	C₃×A₅	direct (N × H)
35. C₃×A₅	C₂₉⋊C₇	direct (N × H)
44. C₃×C₂₉	C₇×A₅	semidirect
50. A₅	C₃×C₂₉⋊C₇	direct (N × H)
57. C₂₉	C₃×C₇×A₅	semidirect
77. C₃	A₅×C₂₉⋊C₇	direct (N × H)

Maximal subgroups

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

subgroup	index
A₅×C₂₉⋊C₇	3
C₃×A₄×C₂₉⋊C₇	5
C₃×D₅×C₂₉⋊C₇	6
C₃×C₂₉×A₅	7
C₃×D₃×C₂₉⋊C₇	10
C₃×C₇×A₅	29

Subgroups — C3×A5×C29⋊C7 #49141697

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×A₅×C₂₉⋊C₇ #49141697