Subgroups — #22547261⋊C₃ #37558407

Order 23820.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₃₉₇⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#22547261	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×C₃₉₇⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	#13097544⋊C₃	—	5	1	no	maximal, Hall
5	C₅×D₃₉₇	C₂×C₃	1	1	yes	characteristic
6	D₃₉₇⋊C₃	D₅	1	1	yes	characteristic
7	C₅×C₃₉₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	#13097544	—	5	1	no	Hall
9	C₃₉₇⋊C₃	Dic₅	1	1	yes	characteristic, complemented, Hall
10	D₃₉₇	C₃×D₅	1	1	yes	characteristic
11	C₃₉₇	C₃×Dic₅	1	1	yes	characteristic, complemented, Sylow
12	C₃×Dic₅	—	397	1	no	maximal, Hall
13	C₂×C₃×C₅	—	397	1	no	—
14	Dic₅	—	397	1	no	Hall
15	C₃×C₅	—	1588	1	no	Hall
16	C₃×C₄	—	1985	1	no	Hall
17	C₂×C₅	—	397	1	no	—
18	C₂×C₃	—	397	1	no	—
19	C₅	#13097544⋊C₃	1	1	yes	characteristic, complemented, Sylow
20	C₄	—	1985	1	no	Sylow
21	C₃	—	1588	1	no	Sylow
22	C₂	—	397	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₃₉₇	C₃×C₄
prime radical	C₅×D₃₉₇⋊C₃	C₂
cosocle	C₅×D₃₉₇	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.