Subgroups — (C₁₃⋊C₃)⋊D₄₀₃ #44537646

Order 31434.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₃₁×C₁₃⋊C₃	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	1	no	maximal
5	C₃×D₄₀₃	—	13	1	no	maximal
6	C₃×C₁₃×C₃₁	—	13	1	no	—
7	C₃₁×C₁₃⋊C₃	D₁₃	1	1	yes	characteristic, complemented
8	(C₁₃⋊C₃)⋊D₁₃	—	31	1	no	maximal, Hall
9	D₄₀₃	—	13	1	no	—
10	D₄₀₃	—	13	1	no	—
11	D₄₀₃	—	39	4	no	—
12	C₁₃×C₁₃⋊C₃	D₃₁	1	1	yes	characteristic, complemented, Hall
13	C₁₃×C₃₁	—	3	4	no	—
14	C₁₃×C₃₁	D₁₃⋊C₃	1	1	yes	characteristic, complemented
15	C₁₃×C₃₁	C₃×D₁₃	1	1	yes	characteristic, complemented
16	C₁₃⋊D₁₃	—	31	1	no	Hall
17	C₃×D₃₁	—	169	1	no	Hall
18	C₁₃²	C₃×D₃₁	1	1	yes	characteristic, complemented, Sylow
19	C₃×C₃₁	—	13	1	no	Hall
20	C₃×D₁₃	—	403	1	no	—
21	D₁₃⋊C₃	—	403	1	no	—
22	D₃₁	—	169	1	no	Hall
23	C₃×C₁₃	—	13	1	no	—
24	C₁₃⋊C₃	D₄₀₃	1	1	yes	characteristic, complemented
25	C₃₁	(C₁₃⋊C₃)⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
26	D₁₃	—	403	1	no	—
27	D₁₃	—	403	1	no	—
28	D₁₃	—	1209	4	no	—
29	C₁₃	—	3	4	no	—
30	C₁₃	C₃×D₄₀₃	1	1	yes	characteristic, complemented
31	C₁₃	(C₁₃⋊C₃)⋊D₃₁	1	1	yes	characteristic, complemented
32	C₂×C₃	—	5239	1	no	Hall
33	C₃	—	13	1	no	Sylow
34	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.