Subgroups — C₅×Dic₇₉⋊C₁₃ #35206708

Order 20540.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₇₉⋊C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇₉⋊C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₇₉⋊C₁₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₇₉⋊C₁₃	C₂×C₅	1	1	yes	characteristic
5	C₅×Dic₇₉	C₁₃	1	1	yes	maximal, characteristic, complemented, Hall
6	C₇₉⋊C₁₃	C₄×C₅	1	1	yes	characteristic, complemented, Hall
7	C₂×C₅×C₇₉	C₂×C₁₃	1	1	yes	characteristic
8	C₅×C₇₉	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
9	Dic₇₉	C₅×C₁₃	1	1	yes	characteristic, complemented, Hall
10	C₄×C₅×C₁₃	—	79	1	no	maximal, Hall
11	C₂×C₇₉	C₂×C₅×C₁₃	1	1	yes	characteristic
12	C₂×C₅×C₁₃	—	79	1	no	—
13	C₇₉	C₄×C₅×C₁₃	1	1	yes	characteristic, complemented, Sylow
14	C₅×C₁₃	—	79	1	no	Hall
15	C₄×C₁₃	—	79	1	no	Hall
16	C₂×C₁₃	—	79	1	no	—
17	C₄×C₅	—	1027	1	no	Hall
18	C₁₃	—	79	1	no	Sylow
19	C₂×C₅	D₇₉⋊C₁₃	1	1	yes	characteristic
20	C₅	Dic₇₉⋊C₁₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	1027	1	no	Sylow
22	C₂	C₅×D₇₉⋊C₁₃	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.