Subgroups — C₂×(C₂₄₁⋊C₃)⋊D₁₃ #49178131

Order 37596.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₂₄₁⋊C₃)⋊D₁₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₃×C₂₄₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃₁₃₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₃×C₂₄₁⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₃×C₂₄₁	C₂×C₃	1	1	yes	characteristic, complemented
6	D₃₁₃₃	C₂×C₃	1	2	yes	complemented
7	C₁₃×C₂₄₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₂₄₁⋊C₃	—	13	1	no	maximal, Hall
9	C₂×C₂₄₁⋊C₃	D₁₃	1	1	yes	characteristic, complemented
10	D₂₄₁⋊C₃	—	13	2	no	—
11	C₂×D₂₄₁	—	13	1	no	Hall
12	C₂₄₁⋊C₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₂₄₁	C₃×D₁₃	1	1	yes	characteristic, complemented
14	D₂₄₁	—	13	2	no	—
15	C₂₄₁	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₃×D₁₃	—	241	1	no	maximal, Hall
17	C₂×C₃×C₁₃	—	241	1	no	—
18	C₃×D₁₃	—	241	2	no	—
19	C₂×D₁₃	—	241	1	no	Hall
20	C₃×C₁₃	—	241	1	no	Hall
21	C₂×C₁₃	D₂₄₁⋊C₃	1	1	yes	characteristic, complemented
22	D₁₃	—	241	2	no	—
23	C₁₃	C₂×D₂₄₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₃	—	3133	1	no	Hall
25	C₂×C₃	—	3133	2	no	—
26	C₂×C₃	—	241	1	no	—
27	C₂²	—	3133	1	no	Sylow
28	C₃	—	241	1	no	Sylow
29	C₂	—	3133	2	no	—
30	C₂	(C₂₄₁⋊C₃)⋊D₁₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	(C₂₄₁⋊C₃)⋊D₁₃
commutator, cosocle, hypocenter	C₁₃×C₂₄₁	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₃×C₂₄₁	C₂×C₃
LCS	G ▷ C₁₃×C₂₄₁
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.