Subgroups — C₁₃×Dic₆₉₇ #49136136

Order 36244.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×C₁₇×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₁₃×C₁₇×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₆₉₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₃×Dic₄₁	—	17	1	no	maximal, Hall
5	C₂×C₁₇×C₄₁	C₂×C₁₃	1	1	yes	characteristic
6	C₂×C₁₃×C₄₁	D₁₇	1	1	yes	characteristic
7	C₁₃×Dic₁₇	—	41	1	no	maximal, Hall
8	C₁₇×C₄₁	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
9	C₁₃×C₄₁	Dic₁₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₃×C₁₇	D₄₁	1	1	yes	characteristic
11	C₁₃×C₁₇	Dic₄₁	1	1	yes	characteristic, complemented, Hall
12	Dic₄₁	—	17	1	no	Hall
13	C₂×C₄₁	C₁₃×D₁₇	1	1	yes	characteristic
14	Dic₁₇	—	41	1	no	Hall
15	C₄×C₁₃	—	697	1	no	Hall
16	C₄₁	C₁₃×Dic₁₇	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₁₇	C₁₃×D₄₁	1	1	yes	characteristic
18	C₂×C₁₃	D₆₉₇	1	1	yes	characteristic
19	C₁₇	C₁₃×Dic₄₁	1	1	yes	characteristic, complemented, Sylow
20	C₁₃	Dic₆₉₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	697	1	no	Sylow
22	C₂	C₁₃×D₆₉₇	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.