Subgroups — A₅×#92789 #44478359

Order 30420.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃²×A₅	C₃	1	1	yes	maximal, characteristic, complemented
2	A₄×#92789	—	5	1	no	maximal, Hall
3	D₅×#92789	—	6	1	no	maximal
4	D₃×#92789	—	10	1	no	maximal
5	C₅×#92789	—	6	1	no	—
6	C₁₃⋊C₃×A₅	—	13	2	no	maximal
7	C₂²⋊#92789	—	5	2	no	—
8	A₄×C₁₃²	—	5	1	no	—
9	C₂²×#92789	—	5	1	no	—
10	D₅×C₁₃²	—	6	1	no	—
11	C₃×#92789	—	10	1	no	Hall
12	D₃×C₁₃²	—	10	1	no	—
13	C₂×#92789	—	15	1	no	—
14	C₅×C₁₃²	—	6	1	no	Hall
15	C₁₃×A₅	—	3	4	no	—
16	C₁₃×A₅	C₁₃⋊C₃	1	2	yes	complemented
17	C₂²×C₁₃²	—	5	1	no	Hall
18	C₃×C₁₃²	—	10	1	no	—
19	#92789	—	20	1	no	—
20	#92789	A₅	1	1	yes	maximal normal, characteristic, direct product factor
21	A₄×C₁₃⋊C₃	—	65	2	no	—
22	D₅×C₁₃⋊C₃	—	78	2	no	—
23	C₂×C₁₃²	—	15	1	no	—
24	D₃×C₁₃⋊C₃	—	130	2	no	—
25	C₅×C₁₃⋊C₃	—	78	2	no	—
26	C₃×A₅	—	169	1	no	Hall
27	C₁₃²	C₃×A₅	1	1	yes	characteristic, complemented, Sylow
28	C₂²⋊(C₁₃⋊C₃)	—	65	4	no	—
29	A₄×C₁₃	—	5	2	no	—
30	A₄×C₁₃	—	15	4	no	—
31	C₂²×C₁₃⋊C₃	—	65	2	no	—
32	D₅×C₁₃	—	6	2	no	—
33	D₅×C₁₃	—	18	4	no	—
34	C₃×C₁₃⋊C₃	—	130	2	no	—
35	D₃×C₁₃	—	10	2	no	—
36	D₃×C₁₃	—	30	4	no	—
37	C₂×C₁₃⋊C₃	—	195	2	no	—
38	C₅×C₁₃	—	6	2	no	—
39	C₅×C₁₃	—	18	4	no	—
40	A₅	#92789	1	1	yes	characteristic, direct product factor
41	C₂²×C₁₃	—	5	2	no	—
42	C₂²×C₁₃	—	15	4	no	—
43	C₃×C₁₃	—	10	2	no	—
44	C₃×C₁₃	—	30	4	no	—
45	C₁₃⋊C₃	—	260	2	no	—
46	C₁₃⋊C₃	—	13	2	no	—
47	C₃×A₄	—	845	1	no	Hall
48	C₃×D₅	—	1014	1	no	—
49	C₂×C₁₃	—	15	2	no	—
50	C₂×C₁₃	—	45	4	no	—
51	C₃×D₃	—	1690	1	no	—
52	C₃×C₅	—	1014	1	no	—
53	C₁₃	—	3	4	no	—
54	C₁₃	C₁₃⋊C₃×A₅	1	2	yes	complemented
55	C₂²×C₃	—	845	1	no	—
56	A₄	—	5	1	no	—
57	A₄	—	845	2	no	—
58	D₅	—	6	1	no	—
59	C₃²	—	1690	1	no	Sylow
60	C₂×C₃	—	2535	1	no	—
61	D₃	—	10	1	no	—
62	C₅	—	6	1	no	Sylow
63	C₂²	—	5	1	no	Sylow
64	C₃	—	10	1	no	—
65	C₃	—	3380	1	no	—
66	C₃	—	169	1	no	—
67	C₂	—	15	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, socle, hypocenter	C₁₃²×A₅	C₃
Fitting, cosocle	C₁₃²	C₃×A₅
LCS	G ▷ C₁₃²×A₅
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₃²×A₅	C₃	semidirect
16. C₁₃×A₅	C₁₃⋊C₃	semidirect
20. #92789	A₅	direct (N × H)
27. C₁₃²	C₃×A₅	semidirect
40. A₅	#92789	direct (N × H)
54. C₁₃	C₁₃⋊C₃×A₅	semidirect

Maximal subgroups

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

subgroup	index
C₁₃²×A₅	3
A₄×#92789	5
D₅×#92789	6
D₃×#92789	10
C₁₃⋊C₃×A₅	13

Subgroups — A5×#92789 #44478359

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — A₅×#92789 #44478359