Subgroups — C₂×(C₁₃⋊C₃)⋊D₂₂₇ #47978331

Order 35412.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₁₃⋊C₃)⋊D₂₂₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₃⋊C₃×C₂₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₉₅₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₃⋊C₃×C₂₂₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₃×C₂₂₇	C₂×C₃	1	1	yes	characteristic, complemented
6	D₂₉₅₁	C₂×C₃	1	2	yes	complemented
7	C₁₃×C₂₂₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×D₂₂₇	—	13	1	no	maximal, Hall
9	C₂×C₃×C₂₂₇	—	13	1	no	—
10	C₃×D₂₂₇	—	13	2	no	—
11	C₂×D₂₂₇	—	13	1	no	Hall
12	C₃×C₂₂₇	—	13	1	no	Hall
13	C₂×C₂₂₇	D₁₃⋊C₃	1	1	yes	characteristic, complemented
14	D₂₂₇	—	13	2	no	—
15	C₂₂₇	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
16	C₂×D₁₃⋊C₃	—	227	1	no	maximal, Hall
17	C₂×C₁₃⋊C₃	D₂₂₇	1	1	yes	characteristic, complemented
18	D₁₃⋊C₃	—	227	2	no	—
19	C₂×D₁₃	—	227	1	no	Hall
20	C₁₃⋊C₃	C₂×D₂₂₇	1	1	yes	characteristic, complemented, Hall
21	C₂×C₁₃	C₃×D₂₂₇	1	1	yes	characteristic, complemented
22	D₁₃	—	227	2	no	—
23	C₁₃	C₂×C₃×D₂₂₇	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₃	—	2951	1	no	Hall
25	C₂×C₃	—	13	1	no	—
26	C₂×C₃	—	2951	2	no	—
27	C₂²	—	2951	1	no	Sylow
28	C₃	—	13	1	no	Sylow
29	C₂	—	2951	2	no	—
30	C₂	(C₁₃⋊C₃)⋊D₂₂₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	(C₁₃⋊C₃)⋊D₂₂₇
commutator, cosocle, hypocenter	C₁₃×C₂₂₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₃×C₂₂₇	C₂×C₃
LCS	G ▷ C₁₃×C₂₂₇
UCS	C₁ ◁ C₂

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.