Subgroups — #44537663

Order 31434.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#92788	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃⋊D₄₀₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃²×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	(C₁₃⋊C₃)⋊D₃₁	—	13	14	no	maximal
5	C₃₁×C₁₃⋊C₃	—	13	14	no	—
6	#11759815	—	31	1	no	maximal, Hall
7	D₄₀₃	—	13	14	no	—
8	#92788	D₃₁	1	1	yes	characteristic, complemented, Hall
9	C₁₃×C₃₁	D₁₃⋊C₃	1	14	yes	complemented
10	C₁₃⋊D₁₃	—	31	1	no	Hall
11	C₃×D₃₁	—	169	1	no	Hall
12	C₁₃²	C₃×D₃₁	1	1	yes	characteristic, complemented, Sylow
13	C₃×C₃₁	—	169	1	no	Hall
14	D₁₃⋊C₃	—	403	14	no	—
15	D₃₁	—	169	1	no	Hall
16	C₁₃⋊C₃	—	13	14	no	—
17	C₃₁	#11759815	1	1	yes	characteristic, complemented, Sylow
18	D₁₃	—	403	14	no	—
19	C₁₃	(C₁₃⋊C₃)⋊D₃₁	1	14	yes	complemented
20	C₂×C₃	—	5239	1	no	Hall
21	C₃	—	169	1	no	Sylow
22	C₂	—	5239	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃²×C₃₁	C₂×C₃
LCS	G ▷ C₁₃²×C₃₁
UCS	C₁

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.