Subgroups — C₄×AGL(1,𝔽₁₁) #89155

Order 440.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×AGL(1,𝔽₁₁)	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₁⋊C₅	C₂²	1	1	yes	characteristic
5	AGL(1,𝔽₁₁)	C₄	1	2	yes	direct product factor
6	C₄×D₁₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
7	C₁₁⋊C₅	C₂×C₄	1	1	yes	characteristic, complemented, Hall
8	C₂×D₁₁	C₂×C₅	1	1	yes	characteristic
9	C₄×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented
10	Dic₁₁	C₂×C₅	1	1	yes	characteristic, complemented
11	C₂×C₄×C₅	—	11	1	no	maximal, Hall
12	C₂×C₁₁	C₂²×C₅	1	1	yes	characteristic
13	D₁₁	C₄×C₅	1	2	yes	complemented
14	C₂²×C₅	—	11	1	no	—
15	C₄×C₅	—	11	1	no	—
16	C₄×C₅	—	22	1	no	—
17	C₁₁	C₂×C₄×C₅	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₅	—	11	2	no	—
19	C₂×C₅	—	22	1	no	—
20	C₂×C₄	—	11	1	no	Sylow
21	C₅	—	22	1	no	Sylow
22	C₂²	—	11	1	no	—
23	C₄	—	11	1	no	—
24	C₄	AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor
25	C₂	—	11	2	no	—
26	C₂	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic

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

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