Subgroups — C₂×C₄×C₁₁⋊C₅ #89159

Order 440.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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