Subgroups — C₃×AGL(1,𝔽₅)×C₃₉₇ #37558413

Order 23820.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×C₃₉₇	C₂	1	1	yes	maximal, characteristic
2	AGL(1,𝔽₅)×C₃₉₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₃₉₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₄×C₃₉₇	—	5	1	no	maximal, Hall
5	D₅×C₃₉₇	C₂×C₃	1	1	yes	characteristic
6	C₂×C₃×C₃₉₇	—	5	1	no	—
7	C₅×C₃₉₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₄×C₃₉₇	—	5	1	no	Hall
9	C₃×C₃₉₇	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃₉₇	—	5	1	no	—
11	C₃₉₇	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
12	C₃×AGL(1,𝔽₅)	C₃₉₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×D₅	C₂×C₃₉₇	1	1	yes	characteristic
14	AGL(1,𝔽₅)	C₃×C₃₉₇	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₅	C₄×C₃₉₇	1	1	yes	characteristic, complemented, Hall
16	C₃×C₄	—	5	1	no	Hall
17	D₅	C₂×C₃×C₃₉₇	1	1	yes	characteristic
18	C₂×C₃	—	5	1	no	—
19	C₅	C₃×C₄×C₃₉₇	1	1	yes	characteristic, complemented, Sylow
20	C₄	—	5	1	no	Sylow
21	C₃	AGL(1,𝔽₅)×C₃₉₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	5	1	no	—

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.