Subgroups — A₅×C₁₆₉⋊C₃ #44478355

Order 30420.

63 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	A₅×C₁₆₉	C₃	1	1	yes	maximal, characteristic, complemented
2	A₄×C₁₆₉⋊C₃	—	5	1	no	maximal, Hall
3	D₅×C₁₆₉⋊C₃	—	6	1	no	maximal
4	D₃×C₁₆₉⋊C₃	—	10	1	no	maximal
5	C₅×C₁₆₉⋊C₃	—	6	1	no	—
6	C₁₃⋊C₃×A₅	—	13	1	no	maximal
7	C₂²⋊(C₁₆₉⋊C₃)	—	5	2	no	—
8	A₄×C₁₆₉	—	5	1	no	—
9	C₂²×C₁₆₉⋊C₃	—	5	1	no	—
10	D₅×C₁₆₉	—	6	1	no	—
11	C₃×C₁₆₉⋊C₃	—	10	1	no	Hall
12	D₃×C₁₆₉	—	10	1	no	—
13	C₂×C₁₆₉⋊C₃	—	15	1	no	—
14	C₅×C₁₆₉	—	6	1	no	Hall
15	C₁₃×A₅	C₁₃⋊C₃	1	1	yes	characteristic
16	C₂²×C₁₆₉	—	5	1	no	Hall
17	C₃×C₁₆₉	—	10	1	no	—
18	C₁₆₉⋊C₃	—	20	1	no	—
19	C₁₆₉⋊C₃	A₅	1	1	yes	maximal normal, characteristic, direct product factor
20	A₄×C₁₃⋊C₃	—	65	1	no	—
21	D₅×C₁₃⋊C₃	—	78	1	no	—
22	C₂×C₁₆₉	—	15	1	no	—
23	D₃×C₁₃⋊C₃	—	130	1	no	—
24	C₅×C₁₃⋊C₃	—	78	1	no	—
25	C₃×A₅	—	169	1	no	Hall
26	C₁₆₉	C₃×A₅	1	1	yes	characteristic, complemented, Sylow
27	C₂²⋊(C₁₃⋊C₃)	—	65	2	no	—
28	A₄×C₁₃	—	5	1	no	—
29	C₂²×C₁₃⋊C₃	—	65	1	no	—
30	D₅×C₁₃	—	6	1	no	—
31	C₃×C₁₃⋊C₃	—	130	1	no	—
32	D₃×C₁₃	—	10	1	no	—
33	C₂×C₁₃⋊C₃	—	195	1	no	—
34	C₅×C₁₃	—	6	1	no	—
35	A₅	C₁₆₉⋊C₃	1	1	yes	characteristic, direct product factor
36	C₂²×C₁₃	—	5	1	no	—
37	C₃×C₁₃	—	10	1	no	—
38	C₁₃⋊C₃	—	260	1	no	—
39	C₁₃⋊C₃	—	13	1	no	—
40	C₃×A₄	—	845	1	no	Hall
41	C₃×D₅	—	1014	1	no	—
42	C₂×C₁₃	—	15	1	no	—
43	C₃×D₃	—	1690	1	no	—
44	C₃×C₅	—	1014	1	no	—
45	C₁₃	C₁₃⋊C₃×A₅	1	1	yes	characteristic
46	C₂²×C₃	—	845	1	no	—
47	A₄	—	5	1	no	—
48	A₄	—	845	2	no	—
49	D₅	—	6	1	no	—
50	C₃²	—	1690	1	no	Sylow
51	C₂×C₃	—	2535	1	no	—
52	D₃	—	10	1	no	—
53	C₅	—	6	1	no	Sylow
54	C₂²	—	5	1	no	Sylow
55	C₃	—	10	1	no	—
56	C₃	—	3380	1	no	—
57	C₃	—	169	1	no	—
58	C₂	—	15	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, hypocenter	A₅×C₁₆₉	C₃
Frattini	C₁₃	C₁₃⋊C₃×A₅
Fitting, cosocle	C₁₆₉	C₃×A₅
socle	C₁₃×A₅	C₁₃⋊C₃
LCS	G ▷ A₅×C₁₆₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. A₅×C₁₆₉	C₃	semidirect
19. C₁₆₉⋊C₃	A₅	direct (N × H)
26. C₁₆₉	C₃×A₅	semidirect
35. A₅	C₁₆₉⋊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
A₅×C₁₆₉	3
A₄×C₁₆₉⋊C₃	5
D₅×C₁₆₉⋊C₃	6
D₃×C₁₆₉⋊C₃	10
C₁₃⋊C₃×A₅	13

Subgroups — A5×C169⋊C3 #44478355

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — A₅×C₁₆₉⋊C₃ #44478355