Subgroups — C₃₇×Dic₂₀₉ #44525815

Order 30932.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×C₁₉×C₃₇	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₁₉×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₃₇×Dic₁₉	—	11	1	no	maximal, Hall
4	C₃₇×Dic₁₁	—	19	1	no	maximal, Hall
5	C₂×C₁₉×C₃₇	D₁₁	1	1	yes	characteristic
6	Dic₂₀₉	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₁×C₃₇	D₁₉	1	1	yes	characteristic
8	C₁₉×C₃₇	Dic₁₁	1	1	yes	characteristic, complemented, Hall
9	C₂×C₁₁×C₁₉	C₂×C₃₇	1	1	yes	characteristic
10	C₁₁×C₃₇	Dic₁₉	1	1	yes	characteristic, complemented, Hall
11	C₁₁×C₁₉	C₄×C₃₇	1	1	yes	characteristic, complemented, Hall
12	C₄×C₃₇	—	209	1	no	Hall
13	Dic₁₉	—	11	1	no	Hall
14	C₂×C₃₇	D₂₀₉	1	1	yes	characteristic
15	Dic₁₁	—	19	1	no	Hall
16	C₂×C₁₉	D₁₁×C₃₇	1	1	yes	characteristic
17	C₃₇	Dic₂₀₉	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₁₁	C₃₇×D₁₉	1	1	yes	characteristic
19	C₁₉	C₃₇×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
20	C₁₁	C₃₇×Dic₁₉	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	209	1	no	Sylow
22	C₂	C₃₇×D₂₀₉	1	1	yes	characteristic

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.