Subgroups — #87718

Order 400.

39 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₂₅	C₂	1	1	yes	maximal, characteristic
3	C₂×Dic₂₅	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₂₅	C₂²	1	1	yes	characteristic
5	C₄×C₂₅	—	2	1	no	—
6	Dic₂₅	—	2	1	no	—
7	Dic₂₅	C₄	1	2	yes	complemented
8	#683	—	5	1	no	maximal
9	C₂×C₂₅	C₂×C₄	1	1	yes	characteristic
10	C₂×C₂₅	D₄	1	1	yes	characteristic
11	C₂×C₂₅	Q₈	1	1	yes	characteristic
12	C₂×C₄×C₅	D₅	1	1	yes	characteristic
13	C₂×Dic₅	—	5	1	no	—
14	C₂×Dic₅	—	5	1	no	—
15	C₂₅	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
16	C₂²×C₅	C₂×D₅	1	1	yes	characteristic
17	C₄×C₅	—	2	1	no	—
18	Dic₅	—	5	2	no	—
19	Dic₅	—	10	1	no	—
20	C₄⋊C₄	—	25	1	no	Sylow
21	C₂×C₅	Dic₁₀	1	1	yes	characteristic
22	C₂×C₅	C₄×D₅	1	1	yes	characteristic
23	C₂×C₅	C₂²⋊D₅	1	1	yes	characteristic
24	C₂×C₄	—	25	1	no	—
25	C₂×C₄	—	25	1	no	—
26	C₂×C₄	D₂₅	1	1	yes	characteristic
27	C₅	#683	1	1	yes	characteristic
28	C₂²	C₂×D₂₅	1	1	yes	characteristic
29	C₄	—	2	1	no	—
30	C₄	—	25	2	no	—
31	C₄	—	50	1	no	—
32	C₂	Dic₅₀	1	1	yes	characteristic
33	C₂	C₄×D₂₅	1	1	yes	characteristic
34	C₂	C₂²⋊D₂₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₂₅
commutator	C₂×C₂₅	C₂×C₄
Frattini, socle, prime radical	C₂²×C₅	C₂×D₅
Fitting	C₂×C₄×C₂₅	C₂
cosocle	C₂²×C₂₅	C₂²
hypercenter	C₂×C₄	D₂₅
hypocenter	C₂₅	C₄⋊C₄
LCS	G ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄

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

N	H ≅ G/N	type
7. Dic₂₅	C₄	semidirect
15. C₂₅	C₄⋊C₄	semidirect

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