Subgroups — C₇×(C₁₃⋊C₃)⋊D₄₁ #36375608

Order 22386.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₃⋊C₃×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₅₃₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₃×C₄₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	(C₁₃⋊C₃)⋊D₄₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₇×D₄₁	—	13	1	no	maximal, Hall
6	C₁₃⋊C₃×C₄₁	C₂×C₇	1	1	yes	characteristic, complemented, Hall
7	D₅₃₃	C₃×C₇	1	1	yes	characteristic, complemented, Hall
8	C₃×C₇×C₄₁	—	13	1	no	Hall
9	C₇×D₄₁	—	13	1	no	Hall
10	C₇×D₁₃⋊C₃	—	41	1	no	maximal, Hall
11	C₁₃×C₄₁	C₂×C₃×C₇	1	1	yes	characteristic, complemented, Hall
12	C₇×C₄₁	D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
13	C₇×C₁₃⋊C₃	D₄₁	1	1	yes	characteristic, complemented, Hall
14	C₃×D₄₁	—	13	1	no	Hall
15	C₇×D₁₃	—	41	1	no	Hall
16	C₃×C₄₁	—	13	1	no	Hall
17	C₇×C₁₃	C₃×D₄₁	1	1	yes	characteristic, complemented, Hall
18	D₄₁	—	13	1	no	Hall
19	D₁₃⋊C₃	—	41	1	no	Hall
20	C₂×C₃×C₇	—	533	1	no	Hall
21	C₄₁	C₇×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
22	C₁₃⋊C₃	C₇×D₄₁	1	1	yes	characteristic, complemented, Hall
23	D₁₃	—	41	1	no	Hall
24	C₃×C₇	—	13	1	no	Hall
25	C₂×C₇	—	533	1	no	Hall
26	C₁₃	C₃×C₇×D₄₁	1	1	yes	characteristic, complemented, Sylow
27	C₇	(C₁₃⋊C₃)⋊D₄₁	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₃	—	533	1	no	Hall
29	C₃	—	13	1	no	Sylow
30	C₂	—	533	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	(C₁₃⋊C₃)⋊D₄₁
commutator, cosocle, hypocenter	C₁₃×C₄₁	C₂×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₄₁	C₂×C₃
LCS	G ▷ C₁₃×C₄₁
UCS	C₁ ◁ C₇

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.