Subgroups — C₂⁵×D₃₁ #14521887

Order 1984.

5650 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×D₃₁	C₂	1	62	yes	maximal, direct product factor
3	C₂⁴×C₃₁	C₂²	1	31	yes	complemented
4	C₂³×D₃₁	C₂²	1	620	yes	direct product factor
5	C₂³×C₃₁	C₂³	1	155	yes	complemented
6	C₂²×D₃₁	C₂³	1	1240	yes	direct product factor
7	C₂²×C₃₁	C₂⁴	1	155	yes	complemented
8	C₂×D₃₁	C₂⁴	1	496	yes	direct product factor
9	C₂⁶	—	31	1	no	maximal, Sylow
10	C₂×C₃₁	C₂⁵	1	31	yes	complemented
11	D₃₁	C₂⁵	1	32	yes	direct product factor
12	C₂⁵	—	31	62	no	—
13	C₂⁵	D₃₁	1	1	yes	characteristic, direct product factor
14	C₃₁	C₂⁶	1	1	yes	characteristic, complemented, Sylow
15	C₂⁴	—	31	620	no	—
16	C₂⁴	C₂×D₃₁	1	31	yes	direct product factor
17	C₂³	—	31	1240	no	—
18	C₂³	C₂²×D₃₁	1	155	yes	direct product factor
19	C₂²	—	31	496	no	—
20	C₂²	C₂³×D₃₁	1	155	yes	direct product factor
21	C₂	—	31	32	no	—
22	C₂	C₂⁴×D₃₁	1	31	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁵	D₃₁
commutator, cosocle, hypocenter	C₃₁	C₂⁶
Frattini	C₁	G
Fitting, socle	C₂⁵×C₃₁	C₂
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂⁵

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.