Subgroups — C₂×C₅³×C₇² #72190607

Order 12250.

1280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅³×C₇²	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅²×C₇²	C₅	1	31	yes	maximal, direct product factor
3	C₂×C₅³×C₇	C₇	1	8	yes	maximal, direct product factor
4	C₅²×C₇²	C₂×C₅	1	31	yes	direct product factor
5	C₅³×C₇	C₂×C₇	1	8	yes	direct product factor
6	C₂×C₅×C₇²	C₅²	1	31	yes	direct product factor
7	C₂×C₅²×C₇	C₅×C₇	1	248	yes	direct product factor
8	C₂×C₅³	C₇²	1	1	yes	characteristic, direct product factor, Hall
9	C₅×C₇²	C₂×C₅²	1	31	yes	direct product factor
10	C₅²×C₇	C₂×C₅×C₇	1	248	yes	direct product factor
11	C₅³	C₂×C₇²	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₇²	C₅³	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₅×C₇	C₅²×C₇	1	248	yes	direct product factor
14	C₂×C₅²	C₅×C₇²	1	31	yes	direct product factor
15	C₇²	C₂×C₅³	1	1	yes	characteristic, direct product factor, Sylow
16	C₅×C₇	C₂×C₅²×C₇	1	248	yes	direct product factor
17	C₅²	C₂×C₅×C₇²	1	31	yes	direct product factor
18	C₂×C₇	C₅³×C₇	1	8	yes	direct product factor
19	C₂×C₅	C₅²×C₇²	1	31	yes	direct product factor
20	C₇	C₂×C₅³×C₇	1	8	yes	direct product factor
21	C₅	C₂×C₅²×C₇²	1	31	yes	direct product factor
22	C₂	C₅³×C₇²	1	1	yes	characteristic, direct product factor, 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.