Subgroups — C₅×Dic₅×C₃₁₃ #44531021

Order 31300.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×C₃₁₃	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₃₁₃	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₅×C₃₁₃	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₄×C₅×C₃₁₃	—	5	1	no	maximal
5	C₂×C₅×C₃₁₃	—	2	2	no	—
6	C₂×C₅×C₃₁₃	D₅	1	1	yes	characteristic
7	C₂×C₅×C₃₁₃	C₂×C₅	1	1	yes	characteristic
8	C₅×C₃₁₃	—	2	2	no	—
9	C₅×C₃₁₃	Dic₅	1	1	yes	characteristic, direct product factor
10	C₅×C₃₁₃	C₄×C₅	1	1	yes	characteristic, complemented
11	C₄×C₃₁₃	—	5	1	no	Hall
12	C₂×C₃₁₃	C₅×D₅	1	1	yes	characteristic
13	C₃₁₃	C₅×Dic₅	1	1	yes	characteristic, direct product factor, Sylow
14	C₅×Dic₅	C₃₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×C₅²	C₂×C₃₁₃	1	1	yes	characteristic
16	C₅²	C₄×C₃₁₃	1	1	yes	characteristic, complemented, Sylow
17	C₄×C₅	—	5	1	no	—
18	Dic₅	C₅×C₃₁₃	1	1	yes	characteristic, direct product factor
19	C₂×C₅	—	2	2	no	—
20	C₂×C₅	D₅×C₃₁₃	1	1	yes	characteristic
21	C₂×C₅	C₂×C₅×C₃₁₃	1	1	yes	characteristic
22	C₅	—	2	2	no	—
23	C₅	C₄×C₅×C₃₁₃	1	1	yes	characteristic, complemented
24	C₅	Dic₅×C₃₁₃	1	1	yes	characteristic, direct product factor
25	C₄	—	5	1	no	Sylow
26	C₂	C₅×D₅×C₃₁₃	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.