Subgroups — #44537627

Order 31434.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30628398	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₂₃₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₃₁×C₁₆₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	#14559031	—	13	1	no	maximal
5	#11925881	—	13	1	no	—
6	D₁₆₉⋊C₃	—	31	1	no	maximal, Hall
7	D₄₀₃	—	13	1	no	—
8	C₁₆₉⋊C₃	—	31	1	no	Hall
9	C₁₃×C₃₁	D₁₃⋊C₃	1	1	yes	characteristic
10	D₁₆₉	—	31	1	no	Hall
11	D₃₁⋊C₃	—	169	1	no	Hall
12	C₁₆₉	D₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
13	C₃₁⋊C₃	—	169	1	no	Hall
14	D₁₃⋊C₃	—	403	1	no	—
15	D₃₁	—	169	1	no	Hall
16	C₁₃⋊C₃	—	403	1	no	—
17	C₃₁	D₁₆₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
18	D₁₃	—	403	1	no	—
19	C₁₃	#14559031	1	1	yes	characteristic
20	C₂×C₃	—	5239	1	no	Hall
21	C₃	—	5239	1	no	Sylow
22	C₂	—	5239	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃₁×C₁₆₉	C₂×C₃
Frattini	C₁₃	#14559031
socle	C₁₃×C₃₁	D₁₃⋊C₃
LCS	G ▷ C₃₁×C₁₆₉
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.