Subgroups — C₁₃×Dic₂₉⋊C₇ #24902206

Order 10556.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×C₂₉⋊C₇	C₂	1	1	yes	maximal, characteristic
2	C₁₃×C₂₉⋊C₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₃×Dic₂₉	C₇	1	1	yes	maximal, characteristic, complemented, Hall
4	Dic₂₉⋊C₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₃×C₂₉	C₂×C₇	1	1	yes	characteristic
6	C₂×C₂₉⋊C₇	C₂×C₁₃	1	1	yes	characteristic
7	C₁₃×C₂₉	C₄×C₇	1	1	yes	characteristic, complemented, Hall
8	C₄×C₇×C₁₃	—	29	1	no	maximal, Hall
9	C₂₉⋊C₇	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₇×C₁₃	—	29	1	no	—
11	Dic₂₉	C₇×C₁₃	1	1	yes	characteristic, complemented, Hall
12	C₇×C₁₃	—	29	1	no	Hall
13	C₂×C₂₉	C₂×C₇×C₁₃	1	1	yes	characteristic
14	C₄×C₁₃	—	29	1	no	Hall
15	C₂₉	C₄×C₇×C₁₃	1	1	yes	characteristic, complemented, Sylow
16	C₄×C₇	—	29	1	no	Hall
17	C₂×C₁₃	D₂₉⋊C₇	1	1	yes	characteristic
18	C₂×C₇	—	29	1	no	—
19	C₁₃	Dic₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
20	C₇	—	29	1	no	Sylow
21	C₄	—	29	1	no	Sylow
22	C₂	C₁₃×D₂₉⋊C₇	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.