Subgroups — C₂₃×C₃₁⋊#261 #49150508

Order 37076.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×D₁₃×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₁₃×C₂₃×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
3	C₂₃×Dic₃₁	—	13	1	no	maximal, Hall
4	C₃₁⋊#261	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₂₃×C₃₁	—	13	1	no	—
6	C₂₃×#261	—	31	1	no	maximal, Hall
7	D₁₃×C₃₁	C₂×C₂₃	1	1	yes	characteristic
8	C₂₃×C₃₁	#261	1	1	yes	characteristic, complemented, Hall
9	C₂₃×D₁₃	D₃₁	1	1	yes	characteristic
10	C₁₃×C₃₁	C₄×C₂₃	1	1	yes	characteristic, complemented, Hall
11	C₁₃×C₂₃	Dic₃₁	1	1	yes	characteristic, complemented, Hall
12	Dic₃₁	—	13	1	no	Hall
13	C₄×C₂₃	—	403	1	no	Hall
14	C₂×C₃₁	—	13	1	no	—
15	#261	—	31	1	no	Hall
16	C₂×C₂₃	—	13	1	no	—
17	C₃₁	C₂₃×#261	1	1	yes	characteristic, complemented, Sylow
18	D₁₃	C₂₃×D₃₁	1	1	yes	characteristic
19	C₂₃	C₃₁⋊#261	1	1	yes	characteristic, direct product factor, Sylow
20	C₁₃	C₂₃×Dic₃₁	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	403	1	no	Sylow
22	C₂	—	13	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.