Subgroups — C₁₃×Dic₃₀₅ #30629413

Order 15860.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₃×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₃×C₆₁	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₃×Dic₆₁	—	5	1	no	maximal, Hall
4	C₂×C₁₃×C₆₁	D₅	1	1	yes	characteristic
5	Dic₃₀₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₃×C₆₁	Dic₅	1	1	yes	characteristic, complemented, Hall
7	C₂×C₅×C₆₁	C₂×C₁₃	1	1	yes	characteristic
8	C₅×C₆₁	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
9	C₁₃×Dic₅	—	61	1	no	maximal, Hall
10	Dic₆₁	—	5	1	no	Hall
11	C₂×C₅×C₁₃	D₆₁	1	1	yes	characteristic
12	C₂×C₆₁	D₅×C₁₃	1	1	yes	characteristic
13	C₅×C₁₃	Dic₆₁	1	1	yes	characteristic, complemented, Hall
14	C₆₁	C₁₃×Dic₅	1	1	yes	characteristic, complemented, Sylow
15	C₄×C₁₃	—	305	1	no	Hall
16	C₂×C₁₃	D₃₀₅	1	1	yes	characteristic
17	Dic₅	—	61	1	no	Hall
18	C₁₃	Dic₃₀₅	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₅	C₁₃×D₆₁	1	1	yes	characteristic
20	C₅	C₁₃×Dic₆₁	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	305	1	no	Sylow
22	C₂	C₁₃×D₃₀₅	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.