Subgroups — A₅×C₃₉₇ #37558441

Order 23820.

18 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	A₄×C₃₉₇	—	5	1	no	maximal, Hall
2	D₅×C₃₉₇	—	6	1	no	maximal
3	D₃×C₃₉₇	—	10	1	no	maximal
4	C₅×C₃₉₇	—	6	1	no	Hall
5	C₂²×C₃₉₇	—	5	1	no	Hall
6	C₃×C₃₉₇	—	10	1	no	Hall
7	C₂×C₃₉₇	—	15	1	no	—
8	C₃₉₇	A₅	1	1	yes	maximal normal, characteristic, direct product factor, Sylow
9	A₅	C₃₉₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	A₄	—	5	1	no	Hall
11	D₅	—	6	1	no	—
12	D₃	—	10	1	no	—
13	C₅	—	6	1	no	Sylow
14	C₂²	—	5	1	no	Sylow
15	C₃	—	10	1	no	Sylow
16	C₂	—	15	1	no	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
8. C₃₉₇	A₅	direct (N × H)
9. A₅	C₃₉₇	direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.