Subgroups — C₇×C₂₃×Dic₅₃ #46802413

Order 34132.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₂₃×C₅₃	C₂	1	1	yes	maximal, characteristic
2	C₇×C₂₃×C₅₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₂₃×Dic₅₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₂₃×C₅₃	C₂×C₇	1	1	yes	characteristic
5	C₇×Dic₅₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂₃×C₅₃	C₄×C₇	1	1	yes	characteristic, complemented, Hall
7	C₂×C₇×C₅₃	C₂×C₂₃	1	1	yes	characteristic
8	C₄×C₇×C₂₃	—	53	1	no	maximal, Hall
9	C₇×C₅₃	C₄×C₂₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₇×C₂₃	D₅₃	1	1	yes	characteristic
11	Dic₅₃	C₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
12	C₇×C₂₃	Dic₅₃	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₅₃	C₂×C₇×C₂₃	1	1	yes	characteristic
14	C₄×C₂₃	—	53	1	no	Hall
15	C₅₃	C₄×C₇×C₂₃	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₂₃	C₇×D₅₃	1	1	yes	characteristic
17	C₄×C₇	—	53	1	no	Hall
18	C₂₃	C₇×Dic₅₃	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₇	C₂₃×D₅₃	1	1	yes	characteristic
20	C₇	C₂₃×Dic₅₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	53	1	no	Sylow
22	C₂	C₇×C₂₃×D₅₃	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.