Subgroups — C₅×AGL(1,𝔽₉) #67193

Order 360.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#157	C₂	1	1	yes	maximal, characteristic
2	C₅×C₃⋊D₃	C₄	1	1	yes	characteristic
3	AGL(1,𝔽₉)	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃²×C₅	C₈	1	1	yes	characteristic, complemented, Hall
5	C₅×C₈	—	9	1	no	maximal, Hall
6	#157	C₂×C₅	1	1	yes	characteristic
7	C₅×D₃	—	12	1	no	—
8	C₄×C₅	—	9	1	no	—
9	C₃⋊D₃	C₄×C₅	1	1	yes	characteristic
10	C₃×C₅	—	4	1	no	—
11	C₂×C₅	—	9	1	no	—
12	C₃²	C₅×C₈	1	1	yes	characteristic, complemented, Sylow
13	C₈	—	9	1	no	Sylow
14	D₃	—	12	1	no	—
15	C₅	AGL(1,𝔽₉)	1	1	yes	characteristic, direct product factor, Sylow
16	C₄	—	9	1	no	—
17	C₃	—	4	1	no	—
18	C₂	—	9	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.