Subgroups — C₅²×D₇⋊C₉ #15691237

Order 3150.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₇⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅²×D₇	C₃	1	1	yes	maximal, characteristic
3	C₅×D₇⋊C₉	C₅	1	6	yes	maximal, direct product factor
4	C₃×C₅²×C₇	C₂×C₃	1	1	yes	characteristic
5	C₂×C₅²×C₉	—	7	1	no	maximal, Hall
6	C₅²×D₇	C₉	1	1	yes	characteristic, complemented, Hall
7	C₅×C₇⋊C₉	C₂×C₅	1	6	yes	complemented
8	C₅²×C₉	—	7	1	no	Hall
9	C₃×C₅×D₇	C₃×C₅	1	6	yes	—
10	C₅²×C₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₅²	—	7	1	no	—
12	D₇⋊C₉	C₅²	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₅×C₇	C₂×C₃×C₅	1	6	yes	—
14	C₂×C₅×C₉	—	7	6	no	—
15	C₃×C₅²	AGL(1,𝔽₇)	1	1	yes	characteristic
16	C₅×D₇	C₅×C₉	1	6	yes	complemented
17	C₇⋊C₉	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅²	—	7	1	no	Hall
19	C₅×C₉	—	7	6	no	—
20	C₃×D₇	C₃×C₅²	1	1	yes	characteristic
21	C₅×C₇	C₂×C₅×C₉	1	6	yes	complemented
22	C₂×C₃×C₅	—	7	6	no	—
23	C₅²	D₇⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
24	C₃×C₇	C₂×C₃×C₅²	1	1	yes	characteristic
25	C₂×C₉	—	7	1	no	Hall
26	C₃×C₅	C₅×AGL(1,𝔽₇)	1	6	yes	—
27	D₇	C₅²×C₉	1	1	yes	characteristic, complemented, Hall
28	C₂×C₅	—	7	6	no	—
29	C₉	—	7	1	no	Sylow
30	C₇	C₂×C₅²×C₉	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	7	1	no	—
32	C₅	C₅×D₇⋊C₉	1	6	yes	direct product factor
33	C₃	C₅²×AGL(1,𝔽₇)	1	1	yes	characteristic
34	C₂	—	7	1	no	Sylow

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.