Subgroups — C₃⋊((C₁₃⋊C₃)⋊D₁₃₇) #44545396

Order 32058.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃⋊C₃×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	(C₁₃⋊C₃)⋊D₁₃₇	—	3	1	no	maximal
3	D₅₃₄₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₃×C₁₃₇	C₂×C₃	1	1	yes	characteristic, complemented
5	C₁₃⋊C₃×C₁₃₇	—	2	1	no	—
6	C₁₃⋊C₃×C₁₃₇	D₃	1	1	yes	characteristic, complemented
7	D₁₇₈₁	—	3	1	no	Hall
8	C₃×D₄₁₁	—	13	1	no	maximal, Hall
9	C₁₃×C₁₃₇	C₃×D₃	1	1	yes	characteristic, complemented, Hall
10	C₃²×C₁₃₇	—	13	1	no	Hall
11	D₄₁₁	—	13	1	no	—
12	C₃×D₁₃₇	—	39	1	no	—
13	C₃×C₁₃₇	—	13	1	no	—
14	C₃×C₁₃₇	—	26	1	no	—
15	C₃×C₁₃₇	D₁₃⋊C₃	1	1	yes	characteristic, complemented
16	D₁₃₇	—	39	1	no	Hall
17	C₃⋊(D₁₃⋊C₃)	—	137	1	no	maximal, Hall
18	C₁₃₇	C₃⋊(D₁₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
19	C₃×C₁₃⋊C₃	D₁₃₇	1	1	yes	characteristic, complemented, Hall
20	D₃₉	—	137	1	no	—
21	D₁₃⋊C₃	—	411	1	no	—
22	C₃×C₁₃	C₃×D₁₃₇	1	1	yes	characteristic, complemented
23	C₁₃⋊C₃	—	2	1	no	—
24	C₁₃⋊C₃	D₄₁₁	1	1	yes	characteristic, complemented
25	D₁₃	—	411	1	no	Hall
26	C₃×D₃	—	1781	1	no	Hall
27	C₁₃	C₃×D₄₁₁	1	1	yes	characteristic, complemented, Sylow
28	C₃²	—	13	1	no	Sylow
29	C₂×C₃	—	5343	1	no	—
30	D₃	—	1781	1	no	—
31	C₃	—	13	1	no	—
32	C₃	—	26	1	no	—
33	C₃	(C₁₃⋊C₃)⋊D₁₃₇	1	1	yes	characteristic, complemented
34	C₂	—	5343	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₃×C₁₃₇	C₂×C₃
LCS	G ▷ C₃×C₁₃×C₁₃₇
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.