Subgroups — C₂×PSL(2,𝔽₁₁) #13050430

Order 1320.

41 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	PSL(2,𝔽₁₁)	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂×A₅	—	11	2	no	maximal, Hall
3	C₂×C₁₁⋊C₅	—	12	1	no	maximal
4	A₅	—	11	2	no	—
5	C₁₁⋊C₅	—	12	1	no	Hall
6	C₂²×D₃	—	55	1	no	maximal, Hall
7	C₂×A₄	—	55	1	no	Hall
8	C₂×C₁₁	—	12	1	no	—
9	C₂×D₅	—	66	1	no	—
10	C₂²×C₃	—	55	1	no	—
11	C₂×D₃	—	55	1	no	—
12	C₂×D₃	—	55	2	no	—
13	C₂×D₃	—	55	1	no	—
14	C₂×D₃	—	55	2	no	—
15	A₄	—	55	1	no	—
16	C₁₁	—	12	1	no	Sylow
17	C₂×C₅	—	66	1	no	—
18	D₅	—	66	1	no	—
19	D₅	—	66	1	no	—
20	C₂³	—	55	1	no	Sylow
21	C₂×C₃	—	55	1	no	—
22	C₂×C₃	—	55	1	no	—
23	C₂×C₃	—	55	1	no	—
24	D₃	—	55	2	no	—
25	D₃	—	55	2	no	—
26	C₅	—	66	1	no	Sylow
27	C₂²	—	55	1	no	—
28	C₂²	—	55	1	no	—
29	C₂²	—	165	1	no	—
30	C₃	—	55	1	no	Sylow
31	C₂	—	55	1	no	—
32	C₂	—	55	1	no	—
33	C₂	PSL(2,𝔽₁₁)	1	1	yes	maximal normal, characteristic, direct product factor

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

N	H ≅ G/N	type
1. PSL(2,𝔽₁₁)	C₂	direct (N × H)
33. C₂	PSL(2,𝔽₁₁)	direct (N × H)

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