Subgroups — C₂₃×Dic₇×C₂₉ #32916359

Order 18676.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₂₃×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₇×C₂₃×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₄×C₂₃×C₂₉	—	7	1	no	maximal, Hall
4	C₂×C₂₃×C₂₉	D₇	1	1	yes	characteristic
5	Dic₇×C₂₉	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂₃×C₂₉	Dic₇	1	1	yes	characteristic, direct product factor, Hall
7	C₂₃×Dic₇	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₇×C₂₉	C₂×C₂₃	1	1	yes	characteristic
9	C₂×C₇×C₂₃	C₂×C₂₉	1	1	yes	characteristic
10	C₇×C₂₉	C₄×C₂₃	1	1	yes	characteristic, complemented, Hall
11	C₇×C₂₃	C₄×C₂₉	1	1	yes	characteristic, complemented, Hall
12	C₄×C₂₉	—	7	1	no	Hall
13	C₄×C₂₃	—	7	1	no	Hall
14	C₂×C₂₉	D₇×C₂₃	1	1	yes	characteristic
15	C₂×C₂₃	D₇×C₂₉	1	1	yes	characteristic
16	C₂₉	C₂₃×Dic₇	1	1	yes	characteristic, direct product factor, Sylow
17	Dic₇	C₂₃×C₂₉	1	1	yes	characteristic, direct product factor, Hall
18	C₂₃	Dic₇×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₇	C₂×C₂₃×C₂₉	1	1	yes	characteristic
20	C₇	C₄×C₂₃×C₂₉	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	7	1	no	Sylow
22	C₂	D₇×C₂₃×C₂₉	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.