Subgroups — C₂×C₅²×C₃₄₃ #72195039

Order 17150.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₃₄₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅×C₃₄₃	C₅	1	6	yes	maximal, direct product factor
3	C₂×C₅²×C₄₉	C₇	1	1	yes	maximal, characteristic
4	C₅×C₃₄₃	C₂×C₅	1	6	yes	direct product factor
5	C₅²×C₄₉	C₂×C₇	1	1	yes	characteristic
6	C₂×C₃₄₃	C₅²	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₅×C₄₉	C₅×C₇	1	6	yes	—
8	C₂×C₅²×C₇	C₄₉	1	1	yes	characteristic
9	C₃₄₃	C₂×C₅²	1	1	yes	characteristic, direct product factor, Sylow
10	C₅×C₄₉	C₂×C₅×C₇	1	6	yes	—
11	C₅²×C₇	C₂×C₄₉	1	1	yes	characteristic
12	C₂×C₄₉	C₅²×C₇	1	1	yes	characteristic
13	C₂×C₅×C₇	C₅×C₄₉	1	6	yes	—
14	C₂×C₅²	C₃₄₃	1	1	yes	characteristic, direct product factor, Hall
15	C₄₉	C₂×C₅²×C₇	1	1	yes	characteristic
16	C₅×C₇	C₂×C₅×C₄₉	1	6	yes	—
17	C₅²	C₂×C₃₄₃	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₇	C₅²×C₄₉	1	1	yes	characteristic
19	C₂×C₅	C₅×C₃₄₃	1	6	yes	direct product factor
20	C₇	C₂×C₅²×C₄₉	1	1	yes	characteristic
21	C₅	C₂×C₅×C₃₄₃	1	6	yes	direct product factor
22	C₂	C₅²×C₃₄₃	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.