Subgroups — A₅×#10597244 #49137838

Order 36300.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁²×A₅	C₅	1	1	yes	maximal, characteristic, complemented
2	A₄×#10597244	—	5	1	no	maximal
3	D₅×#10597244	—	6	1	no	maximal
4	D₃×#10597244	—	10	1	no	maximal
5	C₁₁⋊C₅×A₅	—	11	2	no	maximal
6	C₅×#10597244	—	6	1	no	Hall
7	C₂²×#10597244	—	5	1	no	—
8	C₃×#10597244	—	10	1	no	—
9	C₁₁²×A₄	—	5	1	no	Hall
10	D₅×C₁₁²	—	6	1	no	—
11	C₂×#10597244	—	15	1	no	—
12	D₃×C₁₁²	—	10	1	no	—
13	A₄×C₁₁⋊C₅	—	55	2	no	—
14	C₁₁×A₅	—	5	2	no	—
15	C₁₁×A₅	C₁₁⋊C₅	1	2	yes	complemented
16	C₅×C₁₁²	—	6	1	no	—
17	#10597244	—	12	2	no	—
18	#10597244	A₅	1	1	yes	maximal normal, characteristic, direct product factor
19	D₅×C₁₁⋊C₅	—	66	2	no	—
20	C₂²×C₁₁²	—	5	1	no	Hall
21	C₃×C₁₁²	—	10	1	no	Hall
22	D₃×C₁₁⋊C₅	—	110	2	no	—
23	C₅×A₅	—	121	1	no	Hall
24	C₅×C₁₁⋊C₅	—	66	2	no	—
25	C₂×C₁₁²	—	15	1	no	—
26	C₂²×C₁₁⋊C₅	—	55	2	no	—
27	C₃×C₁₁⋊C₅	—	110	2	no	—
28	C₁₁×A₄	—	5	2	no	—
29	C₁₁×A₄	—	25	2	no	—
30	C₁₁²	C₅×A₅	1	1	yes	characteristic, complemented, Sylow
31	D₅×C₁₁	—	6	2	no	—
32	D₅×C₁₁	—	30	2	no	—
33	C₂×C₁₁⋊C₅	—	165	2	no	—
34	D₃×C₁₁	—	10	2	no	—
35	D₃×C₁₁	—	50	2	no	—
36	C₅×A₄	—	605	1	no	—
37	A₅	#10597244	1	1	yes	characteristic, direct product factor
38	C₅×C₁₁	—	6	2	no	—
39	C₅×C₁₁	—	30	2	no	—
40	C₁₁⋊C₅	—	11	2	no	—
41	C₁₁⋊C₅	—	132	4	no	—
42	C₅×D₅	—	726	1	no	—
43	C₂²×C₁₁	—	5	2	no	—
44	C₂²×C₁₁	—	25	2	no	—
45	C₃×C₁₁	—	10	2	no	—
46	C₃×C₁₁	—	50	2	no	—
47	C₅×D₃	—	1210	1	no	—
48	C₅²	—	726	1	no	Sylow
49	C₂×C₁₁	—	15	2	no	—
50	C₂×C₁₁	—	75	2	no	—
51	C₂²×C₅	—	605	1	no	—
52	C₃×C₅	—	1210	1	no	—
53	A₄	—	5	1	no	Hall
54	C₁₁	—	5	2	no	—
55	C₁₁	C₁₁⋊C₅×A₅	1	2	yes	complemented
56	C₂×C₅	—	1815	1	no	—
57	D₅	—	6	1	no	—
58	D₃	—	10	1	no	—
59	C₅	—	6	1	no	—
60	C₅	—	121	1	no	—
61	C₅	—	1452	2	no	—
62	C₂²	—	5	1	no	Sylow
63	C₃	—	10	1	no	Sylow
64	C₂	—	15	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, socle, hypocenter	C₁₁²×A₅	C₅
Fitting, cosocle	C₁₁²	C₅×A₅
LCS	G ▷ C₁₁²×A₅
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₁²×A₅	C₅	semidirect
15. C₁₁×A₅	C₁₁⋊C₅	semidirect
18. #10597244	A₅	direct (N × H)
30. C₁₁²	C₅×A₅	semidirect
37. A₅	#10597244	direct (N × H)
55. C₁₁	C₁₁⋊C₅×A₅	semidirect

Maximal subgroups

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

subgroup	index
C₁₁²×A₅	5
A₄×#10597244	5
D₅×#10597244	6
D₃×#10597244	10
C₁₁⋊C₅×A₅	11

Subgroups — A5×#10597244 #49137838

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — A₅×#10597244 #49137838