Subgroups — C₁₃×Dic₁₂₃ #20264166

Order 6396.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₃×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₁₃×Dic₄₁	—	3	1	no	maximal, Hall
3	C₃×C₁₃×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₃×C₄₁	D₃	1	1	yes	characteristic
5	C₁₃×C₄₁	Dic₃	1	1	yes	characteristic, complemented, Hall
6	Dic₁₂₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₄₁	C₂×C₁₃	1	1	yes	characteristic
8	Dic₄₁	—	3	1	no	Hall
9	Dic₃×C₁₃	—	41	1	no	maximal, Hall
10	C₃×C₄₁	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₄₁	D₃×C₁₃	1	1	yes	characteristic
12	C₂×C₃×C₁₃	D₄₁	1	1	yes	characteristic
13	C₄×C₁₃	—	123	1	no	Hall
14	C₄₁	Dic₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
15	C₃×C₁₃	Dic₄₁	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₃	D₁₂₃	1	1	yes	characteristic
17	C₁₃	Dic₁₂₃	1	1	yes	characteristic, direct product factor, Sylow
18	Dic₃	—	41	1	no	Hall
19	C₂×C₃	C₁₃×D₄₁	1	1	yes	characteristic
20	C₄	—	123	1	no	Sylow
21	C₃	C₁₃×Dic₄₁	1	1	yes	characteristic, complemented, Sylow
22	C₂	C₁₃×D₁₂₃	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.