Subgroups — C₃×C₅×Dic₃₄₇ #35209651

Order 20820.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₃₄₇	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₃₄₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₃₄₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×Dic₃₄₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₃₄₇	C₂×C₃	1	1	yes	characteristic
6	C₂×C₃×C₃₄₇	C₂×C₅	1	1	yes	characteristic
7	C₅×C₃₄₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	Dic₃₄₇	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₃₄₇	C₄×C₅	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃₄₇	C₂×C₃×C₅	1	1	yes	characteristic
11	C₃₄₇	C₃×C₄×C₅	1	1	yes	characteristic, complemented, Sylow
12	C₃×C₄×C₅	—	347	1	no	maximal, Hall
13	C₂×C₃×C₅	D₃₄₇	1	1	yes	characteristic
14	C₄×C₅	—	347	1	no	Hall
15	C₃×C₅	Dic₃₄₇	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₄	—	347	1	no	Hall
17	C₂×C₅	C₃×D₃₄₇	1	1	yes	characteristic
18	C₂×C₃	C₅×D₃₄₇	1	1	yes	characteristic
19	C₅	C₃×Dic₃₄₇	1	1	yes	characteristic, direct product factor, Sylow
20	C₄	—	347	1	no	Sylow
21	C₃	C₅×Dic₃₄₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₃×C₅×D₃₄₇	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.