Subgroups — #38759737

Order 25220.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₃₀₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₃×C₉₇	C₄	1	1	yes	characteristic, complemented, Hall
3	#19097930	—	5	1	no	maximal, Hall
4	D₁₂₆₁	—	5	1	no	—
5	#14515595	—	13	1	no	maximal, Hall
6	C₁₃×C₉₇	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
7	D₄₈₅	—	13	1	no	—
8	C₅×C₉₇	#261	1	1	yes	characteristic, complemented, Hall
9	#87604	—	65	1	no	Hall
10	#63121	—	97	1	no	maximal, Hall
11	D₉₇	—	65	1	no	—
12	D₆₅	—	97	1	no	—
13	C₉₇	#63121	1	1	yes	characteristic, complemented, Sylow
14	C₅×C₁₃	#87604	1	1	yes	characteristic, complemented, Hall
15	#261	—	485	1	no	Hall
16	D₁₃	—	485	1	no	—
17	AGL(1,𝔽₅)	—	1261	1	no	Hall
18	C₁₃	#14515595	1	1	yes	characteristic, complemented, Sylow
19	D₅	—	1261	1	no	—
20	C₅	#19097930	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	6305	1	no	Sylow
22	C₂	—	6305	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₃×C₉₇	C₄
prime radical, cosocle	D₆₃₀₅	C₂
LCS	G ▷ C₅×C₁₃×C₉₇
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.