Subgroups — D₃₁×#92789 #44537677

Order 31434.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#92789	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃²×D₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃²×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₁₃⋊C₃×D₃₁	—	13	2	no	maximal
5	C₃₁×C₁₃⋊C₃	—	13	2	no	—
6	C₂×#92789	—	31	1	no	maximal, Hall
7	C₁₃×D₃₁	—	3	4	no	—
8	C₁₃×D₃₁	C₁₃⋊C₃	1	2	yes	complemented
9	#92789	D₃₁	1	1	yes	characteristic, direct product factor, Hall
10	C₁₃×C₃₁	—	3	4	no	—
11	C₁₃×C₃₁	C₂×C₁₃⋊C₃	1	2	yes	complemented
12	C₂×C₁₃²	—	31	1	no	Hall
13	C₃×D₃₁	—	169	1	no	Hall
14	C₁₃²	C₃×D₃₁	1	1	yes	characteristic, complemented, Sylow
15	C₃×C₃₁	—	169	1	no	Hall
16	C₂×C₁₃⋊C₃	—	403	2	no	—
17	D₃₁	#92789	1	1	yes	characteristic, direct product factor, Hall
18	C₁₃⋊C₃	—	13	2	no	—
19	C₃₁	C₂×#92789	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₁₃	—	31	2	no	—
21	C₂×C₁₃	—	93	4	no	—
22	C₁₃	—	3	4	no	—
23	C₁₃	C₁₃⋊C₃×D₃₁	1	2	yes	complemented
24	C₂×C₃	—	5239	1	no	Hall
25	C₃	—	169	1	no	Sylow
26	C₂	—	31	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.