Subgroups — C₅×Dic₅₃₇ #24924394

Order 10740.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₁₇₉	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₁₇₉	—	3	1	no	maximal, Hall
3	C₃×C₅×C₁₇₉	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₅₃₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₁₇₉	D₃	1	1	yes	characteristic
6	C₂×C₃×C₁₇₉	C₂×C₅	1	1	yes	characteristic
7	C₅×C₁₇₉	Dic₃	1	1	yes	characteristic, complemented, Hall
8	Dic₁₇₉	—	3	1	no	Hall
9	C₃×C₁₇₉	C₄×C₅	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₇₉	C₅×D₃	1	1	yes	characteristic
11	C₁₇₉	C₅×Dic₃	1	1	yes	characteristic, complemented, Sylow
12	C₅×Dic₃	—	179	1	no	maximal, Hall
13	C₂×C₃×C₅	D₁₇₉	1	1	yes	characteristic
14	C₄×C₅	—	537	1	no	Hall
15	C₃×C₅	Dic₁₇₉	1	1	yes	characteristic, complemented, Hall
16	Dic₃	—	179	1	no	Hall
17	C₂×C₅	D₅₃₇	1	1	yes	characteristic
18	C₂×C₃	C₅×D₁₇₉	1	1	yes	characteristic
19	C₅	Dic₅₃₇	1	1	yes	characteristic, direct product factor, Sylow
20	C₄	—	537	1	no	Sylow
21	C₃	C₅×Dic₁₇₉	1	1	yes	characteristic, complemented, Sylow
22	C₂	C₅×D₅₃₇	1	1	yes	characteristic

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