Subgroups — C₁₃×D₁₂₃₃ #44545385

Order 32058.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₃×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₄₁₁	—	3	1	no	maximal
3	C₃×C₁₃×C₁₃₇	D₃	1	1	yes	characteristic
4	C₁₃×D₁₃₇	—	9	1	no	Hall
5	D₁₂₃₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₃×C₁₃₇	D₉	1	1	yes	characteristic, complemented, Hall
7	C₉×C₁₃₇	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
8	D₄₁₁	—	3	1	no	—
9	C₃×C₁₃₇	D₃×C₁₃	1	1	yes	characteristic
10	D₁₃₇	—	9	1	no	Hall
11	C₁₃×D₉	—	137	1	no	maximal, Hall
12	C₁₃₇	C₁₃×D₉	1	1	yes	characteristic, complemented, Sylow
13	C₉×C₁₃	D₁₃₇	1	1	yes	characteristic, complemented, Hall
14	D₃×C₁₃	—	411	1	no	—
15	C₃×C₁₃	D₄₁₁	1	1	yes	characteristic
16	C₂×C₁₃	—	1233	1	no	Hall
17	D₉	—	137	1	no	Hall
18	C₁₃	D₁₂₃₃	1	1	yes	characteristic, direct product factor, Sylow
19	C₉	C₁₃×D₁₃₇	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	411	1	no	—
21	C₃	C₁₃×D₄₁₁	1	1	yes	characteristic
22	C₂	—	1233	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃	D₁₂₃₃
commutator, cosocle, hypocenter	C₉×C₁₃₇	C₂×C₁₃
Frattini	C₃	C₁₃×D₄₁₁
Fitting	C₉×C₁₃×C₁₃₇	C₂
socle	C₃×C₁₃×C₁₃₇	D₃
LCS	G ▷ C₉×C₁₃₇
UCS	C₁ ◁ C₁₃

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.