Subgroups — #34089248

Order 19700.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊D₅×C₁₉₇	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₁₉₇	C₄	1	1	yes	characteristic, complemented, Hall
3	#16841101	—	5	2	no	maximal
4	D₅×C₁₉₇	—	5	2	no	—
5	D₅×C₁₉₇	—	10	2	no	—
6	C₅×C₁₉₇	—	2	2	no	—
7	C₅×C₁₉₇	AGL(1,𝔽₅)	1	2	yes	complemented
8	Dic₁₉₇	—	25	1	no	Hall
9	C₂×C₁₉₇	—	25	1	no	—
10	C₁₉₇	#1044	1	1	yes	characteristic, complemented, Sylow
11	#1044	—	197	1	no	maximal, Hall
12	C₅⋊D₅	D₁₉₇	1	1	yes	characteristic
13	C₅²	Dic₁₉₇	1	1	yes	characteristic, complemented, Sylow
14	AGL(1,𝔽₅)	—	985	2	no	—
15	D₅	—	5	2	no	—
16	D₅	—	10	2	no	—
17	C₅	—	2	2	no	—
18	C₅	#16841101	1	2	yes	complemented
19	C₄	—	4925	1	no	Sylow
20	C₂	—	25	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²×C₁₉₇	C₄
prime radical, cosocle	C₅⋊D₅×C₁₉₇	C₂
LCS	G ▷ C₅²×C₁₉₇
UCS	C₁

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.