Subgroups — C₃×C₁₃×#90673 #31798693

Order 17628.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×D₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#90673	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₃×C₁₁₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₃×D₁₁₃	C₂×C₃	1	1	yes	characteristic
5	C₁₃×C₁₁₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×#90673	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×D₁₁₃	C₂×C₁₃	1	1	yes	characteristic
8	#90673	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₁₁₃	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
10	D₁₁₃	C₂×C₃×C₁₃	1	1	yes	characteristic
11	C₃×C₄×C₁₃	—	113	1	no	maximal, Hall
12	C₁₁₃	C₃×C₄×C₁₃	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₃×C₁₃	—	113	1	no	—
14	C₄×C₁₃	—	113	1	no	Hall
15	C₃×C₁₃	#90673	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₁₃	—	113	1	no	—
17	C₁₃	C₃×#90673	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×C₄	—	113	1	no	Hall
19	C₂×C₃	—	113	1	no	—
20	C₄	—	113	1	no	Sylow
21	C₃	C₁₃×#90673	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	113	1	no	—

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.