Subgroups — C₅⋊(#16813210⋊C₂) #49088261

Order 35730.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#16813210	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅⋊(D₃₉₇⋊C₃)	C₃	1	1	yes	maximal, characteristic
3	#16813210⋊C₂	—	5	1	no	maximal, Hall
4	C₅×C₃₉₇⋊C₃	C₂×C₃	1	1	yes	characteristic
5	D₁₉₈₅	C₉	1	1	yes	characteristic, complemented, Hall
6	#16813210	D₅	1	1	yes	characteristic, complemented, Hall
7	D₃₉₇⋊C₃	—	5	1	no	—
8	C₅×C₃₉₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	C₃₉₇⋊C₃	C₃×D₅	1	1	yes	characteristic
10	D₃₉₇	—	5	1	no	Hall
11	C₃₉₇	C₉×D₅	1	1	yes	characteristic, complemented, Sylow
12	C₉×D₅	—	397	1	no	maximal, Hall
13	C₅×C₉	—	397	1	no	Hall
14	C₃×D₅	—	397	1	no	—
15	C₂×C₉	—	1985	1	no	Hall
16	C₃×C₅	—	397	1	no	—
17	D₅	—	397	1	no	Hall
18	C₉	—	397	1	no	Sylow
19	C₂×C₃	—	1985	1	no	—
20	C₅	#16813210⋊C₂	1	1	yes	characteristic, complemented, Sylow
21	C₃	—	397	1	no	—
22	C₂	—	1985	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₃₉₇	C₂×C₉
prime radical	C₅⋊(D₃₉₇⋊C₃)	C₃
cosocle	C₅×C₃₉₇⋊C₃	C₂×C₃
LCS	G ▷ C₅×C₃₉₇
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.