Subgroups — Dic₃×C₁₃×C₁₇₃ #41008749

Order 26988.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₃×C₁₇₃	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₃×C₁₇₃	—	3	1	no	maximal, Hall
3	C₃×C₁₃×C₁₇₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₃×C₁₇₃	D₃	1	1	yes	characteristic
5	C₁₃×C₁₇₃	Dic₃	1	1	yes	characteristic, direct product factor, Hall
6	Dic₃×C₁₇₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₁₇₃	C₂×C₁₃	1	1	yes	characteristic
8	C₄×C₁₇₃	—	3	1	no	Hall
9	C₃×C₁₇₃	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₇₃	D₃×C₁₃	1	1	yes	characteristic
11	C₁₇₃	Dic₃×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
12	Dic₃×C₁₃	C₁₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₁₃	C₂×C₁₇₃	1	1	yes	characteristic
14	C₄×C₁₃	—	3	1	no	Hall
15	C₃×C₁₃	C₄×C₁₇₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₃	D₃×C₁₇₃	1	1	yes	characteristic
17	C₁₃	Dic₃×C₁₇₃	1	1	yes	characteristic, direct product factor, Sylow
18	Dic₃	C₁₃×C₁₇₃	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃	C₂×C₁₃×C₁₇₃	1	1	yes	characteristic
20	C₄	—	3	1	no	Sylow
21	C₃	C₄×C₁₃×C₁₇₃	1	1	yes	characteristic, complemented, Sylow
22	C₂	D₃×C₁₃×C₁₇₃	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.