Subgroups — C₃⋊#22547261 #37558425

Order 23820.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₃₉₇	C₂	1	1	yes	maximal, characteristic
2	#22547261	—	3	1	no	maximal, Hall
3	C₃×C₅×C₃₉₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊#13097544	—	5	1	no	maximal, Hall
5	C₅×D₃₉₇	D₃	1	1	yes	characteristic
6	C₃×D₃₉₇	D₅	1	1	yes	characteristic
7	C₅×C₃₉₇	Dic₃	1	1	yes	characteristic, complemented, Hall
8	#13097544	—	15	1	no	Hall
9	C₃×C₃₉₇	Dic₅	1	1	yes	characteristic, complemented, Hall
10	D₃₉₇	D₁₅	1	1	yes	characteristic
11	C₃₉₇	Dic₁₅	1	1	yes	characteristic, complemented, Sylow
12	Dic₁₅	—	397	1	no	maximal, Hall
13	C₂×C₃×C₅	—	397	1	no	—
14	Dic₅	—	1191	1	no	Hall
15	C₃×C₅	#13097544	1	1	yes	characteristic, complemented, Hall
16	Dic₃	—	1985	1	no	Hall
17	C₂×C₅	—	397	1	no	—
18	C₂×C₃	—	397	1	no	—
19	C₅	C₃⋊#13097544	1	1	yes	characteristic, complemented, Sylow
20	C₄	—	5955	1	no	Sylow
21	C₃	#22547261	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	397	1	no	—

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