Subgroups — C₂²×C₅×C₃₁₁⋊C₅ #44527367

Order 31100.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₃₁₁⋊C₅	C₂	1	3	yes	maximal, direct product factor
2	C₅×C₃₁₁⋊C₅	C₂²	1	1	yes	characteristic, direct product factor, Hall
3	C₂²×C₃₁₁⋊C₅	C₅	1	5	yes	maximal, direct product factor
4	C₂²×C₅×C₃₁₁	C₅	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×C₃₁₁	C₂×C₅	1	3	yes	complemented
6	C₂×C₃₁₁⋊C₅	C₂×C₅	1	15	yes	direct product factor
7	C₅×C₃₁₁	C₂²×C₅	1	1	yes	characteristic, complemented
8	C₃₁₁⋊C₅	C₂²×C₅	1	5	yes	direct product factor
9	C₂²×C₃₁₁	C₅²	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃₁₁	C₂×C₅²	1	3	yes	complemented
11	C₃₁₁	C₂²×C₅²	1	1	yes	characteristic, complemented, Sylow
12	C₂²×C₅²	—	311	1	no	maximal, Hall
13	C₂×C₅²	—	311	3	no	—
14	C₅²	—	311	1	no	Sylow
15	C₂²×C₅	—	311	5	no	—
16	C₂²×C₅	C₃₁₁⋊C₅	1	1	yes	characteristic, direct product factor
17	C₂×C₅	—	311	15	no	—
18	C₂×C₅	C₂×C₃₁₁⋊C₅	1	3	yes	direct product factor
19	C₅	—	311	5	no	—
20	C₅	C₂²×C₃₁₁⋊C₅	1	1	yes	characteristic, direct product factor
21	C₂²	C₅×C₃₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₅×C₃₁₁⋊C₅	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₅	C₃₁₁⋊C₅
commutator, cosocle, hypocenter	C₃₁₁	C₂²×C₅²
Frattini	C₁	G
Fitting, socle	C₂²×C₅×C₃₁₁	C₅
LCS	G ▷ C₃₁₁
UCS	C₁ ◁ C₂²×C₅

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.