Subgroups — #87822

Order 400.

22 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6033	C₂	1	1	yes	maximal, characteristic
2	#1039	C₄	1	1	yes	characteristic
3	C₂×C₅²	C₈	1	1	yes	characteristic
4	#170	—	10	3	no	—
5	C₅²	C₁₆	1	1	yes	characteristic, complemented, Sylow
6	Dic₅	—	10	3	no	—
7	C₁₆	—	25	1	no	maximal, Sylow
8	C₂×C₅	—	2	3	no	—
9	C₈	—	25	1	no	—
10	C₅	—	2	3	no	—
11	C₄	—	25	1	no	—
12	C₂	#6053	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#6053
commutator, hypocenter	C₅²	C₁₆
Fitting, socle, prime radical	C₂×C₅²	C₈
cosocle	#6033	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂

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

N	H ≅ G/N	type
5. C₅²	C₁₆	semidirect

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

subgroup	index
#6033	2
C₁₆	25