Subgroups — #38759749

Order 25220.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₁₃×C₉₇	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₃×C₉₇	C₄	1	1	yes	characteristic, complemented, Hall
3	#19097931	—	5	1	no	maximal, Hall
4	D₁₃×C₉₇	D₅	1	1	yes	characteristic
5	Dic₄₈₅	—	13	1	no	maximal, Hall
6	C₁₃×C₉₇	Dic₅	1	1	yes	characteristic, complemented, Hall
7	C₂×C₅×C₉₇	—	13	1	no	—
8	C₅×C₉₇	#261	1	1	yes	characteristic, complemented, Hall
9	Dic₉₇	—	65	1	no	Hall
10	#63118	—	97	1	no	maximal, Hall
11	C₂×C₉₇	—	13	1	no	—
12	C₅×D₁₃	D₉₇	1	1	yes	characteristic
13	C₉₇	#63118	1	1	yes	characteristic, complemented, Sylow
14	C₅×C₁₃	Dic₉₇	1	1	yes	characteristic, complemented, Hall
15	#261	—	485	1	no	Hall
16	D₁₃	D₄₈₅	1	1	yes	characteristic
17	Dic₅	—	1261	1	no	Hall
18	C₁₃	Dic₄₈₅	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅	—	13	1	no	—
20	C₅	#19097931	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	6305	1	no	Sylow
22	C₂	—	13	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₃×C₉₇	C₄
prime radical, cosocle	C₅×D₁₃×C₉₇	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.