Subgroups — C₅×Dic₁₃₄₉ #41008678

Order 26980.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₉×C₇₁	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₉×C₇₁	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₃₄₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₁₉×C₇₁	C₂×C₅	1	1	yes	characteristic
5	C₅×Dic₇₁	—	19	1	no	maximal, Hall
6	C₁₉×C₇₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
7	C₂×C₅×C₇₁	D₁₉	1	1	yes	characteristic
8	C₅×Dic₁₉	—	71	1	no	maximal, Hall
9	C₅×C₇₁	Dic₁₉	1	1	yes	characteristic, complemented, Hall
10	Dic₇₁	—	19	1	no	Hall
11	C₂×C₅×C₁₉	D₇₁	1	1	yes	characteristic
12	C₂×C₇₁	C₅×D₁₉	1	1	yes	characteristic
13	C₅×C₁₉	Dic₇₁	1	1	yes	characteristic, complemented, Hall
14	Dic₁₉	—	71	1	no	Hall
15	C₇₁	C₅×Dic₁₉	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₁₉	C₅×D₇₁	1	1	yes	characteristic
17	C₄×C₅	—	1349	1	no	Hall
18	C₁₉	C₅×Dic₇₁	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅	D₁₃₄₉	1	1	yes	characteristic
20	C₅	Dic₁₃₄₉	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	1349	1	no	Sylow
22	C₂	C₅×D₁₃₄₉	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.