Subgroups — C₂×C₄×C₅₃×C₅₉ #72202249

Order 25016.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅₃×C₅₉	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅₃×C₅₉	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅₃×C₅₉	C₄	1	2	yes	direct product factor
4	C₂×C₅₃×C₅₉	C₂²	1	1	yes	characteristic
5	C₅₃×C₅₉	C₂×C₄	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₄×C₅₉	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₄×C₅₃	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₅₉	C₂×C₅₃	1	1	yes	characteristic
9	C₄×C₅₉	C₂×C₅₃	1	2	yes	direct product factor
10	C₂²×C₅₃	C₂×C₅₉	1	1	yes	characteristic
11	C₄×C₅₃	C₂×C₅₉	1	2	yes	direct product factor
12	C₂×C₅₉	C₄×C₅₃	1	2	yes	direct product factor
13	C₂×C₅₉	C₂²×C₅₃	1	1	yes	characteristic
14	C₂×C₅₃	C₄×C₅₉	1	2	yes	direct product factor
15	C₂×C₅₃	C₂²×C₅₉	1	1	yes	characteristic
16	C₅₉	C₂×C₄×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
17	C₅₃	C₂×C₄×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₄	C₅₃×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
19	C₂²	C₂×C₅₃×C₅₉	1	1	yes	characteristic
20	C₄	C₂×C₅₃×C₅₉	1	2	yes	direct product factor
21	C₂	C₄×C₅₃×C₅₉	1	2	yes	direct product factor
22	C₂	C₂²×C₅₃×C₅₉	1	1	yes	characteristic

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.