Subgroups — #44537665

Order 31434.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30628407	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	#14559031	—	13	1	no	maximal
5	#14559023	—	13	1	no	maximal
6	#11925881	—	13	1	no	—
7	#11925881	—	13	1	no	—
8	#11925881	—	26	6	no	—
9	#11759817	—	31	1	no	maximal, Hall
10	D₄₀₃	C₁₃⋊C₃	1	1	yes	characteristic, complemented
11	C₁₃×D₃₁	—	13	1	no	—
12	#92788	—	31	1	no	Hall
13	C₁₃×C₃₁	—	2	6	no	—
14	C₁₃×C₃₁	D₁₃⋊C₃	1	1	yes	characteristic, complemented
15	C₁₃×C₃₁	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
16	C₁₃×D₁₃	—	31	1	no	Hall
17	D₃₁⋊C₃	—	169	1	no	Hall
18	C₁₃²	D₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
19	C₃₁⋊C₃	—	169	1	no	Hall
20	C₂×C₁₃⋊C₃	—	403	1	no	—
21	D₁₃⋊C₃	—	403	1	no	—
22	D₃₁	—	13	1	no	Hall
23	C₁₃⋊C₃	—	806	6	no	—
24	C₁₃⋊C₃	—	403	1	no	—
25	C₁₃⋊C₃	—	403	1	no	—
26	C₃₁	#11759817	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₁₃	—	403	1	no	—
28	D₁₃	—	31	1	no	—
29	C₁₃	—	2	6	no	—
30	C₁₃	#14559023	1	1	yes	characteristic, complemented
31	C₁₃	#14559031	1	1	yes	characteristic, complemented
32	C₂×C₃	—	5239	1	no	Hall
33	C₃	—	5239	1	no	Sylow
34	C₂	—	403	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.