Subgroups — C₉×C₁₃×D₁₃₇ #44545381

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	C₃×C₁₃×D₁₃₇	C₃	1	1	yes	maximal, characteristic
3	C₃×C₁₃×C₁₃₇	C₂×C₃	1	1	yes	characteristic
4	C₁₃×D₁₃₇	C₉	1	1	yes	characteristic, direct product factor, Hall
5	C₉×D₁₃₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₃×C₁₃₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
7	C₉×C₁₃₇	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
8	C₃×D₁₃₇	C₃×C₁₃	1	1	yes	characteristic
9	C₃×C₁₃₇	C₂×C₃×C₁₃	1	1	yes	characteristic
10	D₁₃₇	C₉×C₁₃	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₉×C₁₃	—	137	1	no	maximal, Hall
12	C₁₃₇	C₂×C₉×C₁₃	1	1	yes	characteristic, complemented, Sylow
13	C₉×C₁₃	D₁₃₇	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃×C₁₃	—	137	1	no	—
15	C₃×C₁₃	C₃×D₁₃₇	1	1	yes	characteristic
16	C₂×C₁₃	—	137	1	no	Hall
17	C₂×C₉	—	137	1	no	Hall
18	C₁₃	C₉×D₁₃₇	1	1	yes	characteristic, direct product factor, Sylow
19	C₉	C₁₃×D₁₃₇	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	—	137	1	no	—
21	C₃	C₃×C₁₃×D₁₃₇	1	1	yes	characteristic
22	C₂	—	137	1	no	Sylow

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.