Subgroups — C₃×C₆₇×Dic₂₉ #37552162

Order 23316.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₂₉×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×Dic₂₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₂₉×C₆₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₂₉×C₆₇	C₂×C₃	1	1	yes	characteristic
5	C₂₉×C₆₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×C₄×C₆₇	—	29	1	no	maximal, Hall
7	C₂×C₃×C₆₇	D₂₉	1	1	yes	characteristic
8	C₃×Dic₂₉	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₄×C₆₇	—	29	1	no	Hall
10	C₃×C₆₇	Dic₂₉	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₃×C₂₉	C₂×C₆₇	1	1	yes	characteristic
12	C₂×C₆₇	C₃×D₂₉	1	1	yes	characteristic
13	Dic₂₉	C₃×C₆₇	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₂₉	C₄×C₆₇	1	1	yes	characteristic, complemented, Hall
15	C₆₇	C₃×Dic₂₉	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₂₉	C₂×C₃×C₆₇	1	1	yes	characteristic
17	C₂₉	C₃×C₄×C₆₇	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	29	1	no	Hall
19	C₂×C₃	D₂₉×C₆₇	1	1	yes	characteristic
20	C₄	—	29	1	no	Sylow
21	C₃	C₆₇×Dic₂₉	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₃×D₂₉×C₆₇	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.