Subgroups — C₂×D₃₁₁⋊C₂₅ #44527342

Order 31100.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁₁⋊C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃₁₁⋊C₂₅	C₂	1	2	yes	maximal, direct product factor
3	C₃₁₁⋊C₂₅	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₅×D₃₁₁	C₅	1	1	yes	maximal, characteristic
5	C₂×C₅×C₃₁₁	C₂×C₅	1	1	yes	characteristic
6	C₅×D₃₁₁	C₂×C₅	1	2	yes	—
7	C₅×C₃₁₁	C₂²×C₅	1	1	yes	characteristic
8	C₂×D₃₁₁	C₂₅	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃₁₁	C₂×C₂₅	1	1	yes	characteristic, complemented
10	D₃₁₁	C₂×C₂₅	1	2	yes	complemented
11	C₃₁₁	C₂²×C₂₅	1	1	yes	characteristic, complemented, Sylow
12	C₂²×C₂₅	—	311	1	no	maximal, Hall
13	C₂×C₂₅	—	311	2	no	—
14	C₂×C₂₅	—	311	1	no	—
15	C₂₅	—	311	1	no	Sylow
16	C₂²×C₅	—	311	1	no	—
17	C₂×C₅	—	311	2	no	—
18	C₂×C₅	D₃₁₁⋊C₅	1	1	yes	characteristic
19	C₅	C₂×D₃₁₁⋊C₅	1	1	yes	characteristic
20	C₂²	—	311	1	no	Sylow
21	C₂	—	311	2	no	—
22	C₂	D₃₁₁⋊C₂₅	1	1	yes	characteristic, direct product factor

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.