Subgroups — C₅×#14555936 #26015136

Order 11300.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×D₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₁₁₃	C₄	1	1	yes	characteristic, complemented, Hall
3	#14555936	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₅×#90673	—	5	1	no	maximal
5	C₅×D₁₁₃	—	2	2	no	—
6	C₅×D₁₁₃	D₅	1	1	yes	characteristic
7	C₅×D₁₁₃	C₂×C₅	1	1	yes	characteristic
8	C₅×C₁₁₃	—	2	2	no	—
9	C₅×C₁₁₃	Dic₅	1	1	yes	characteristic, complemented
10	C₅×C₁₁₃	C₄×C₅	1	1	yes	characteristic, complemented
11	#90673	—	5	1	no	Hall
12	D₁₁₃	C₅×D₅	1	1	yes	characteristic
13	C₁₁₃	C₅×Dic₅	1	1	yes	characteristic, complemented, Sylow
14	C₅×Dic₅	—	113	1	no	maximal, Hall
15	C₂×C₅²	—	113	1	no	—
16	C₅²	#90673	1	1	yes	characteristic, complemented, Sylow
17	C₄×C₅	—	565	1	no	—
18	Dic₅	—	113	1	no	—
19	C₂×C₅	—	113	1	no	—
20	C₂×C₅	—	113	1	no	—
21	C₂×C₅	—	226	2	no	—
22	C₅	—	2	2	no	—
23	C₅	C₅×#90673	1	1	yes	characteristic, complemented
24	C₅	#14555936	1	1	yes	characteristic, direct product factor
25	C₄	—	565	1	no	Sylow
26	C₂	—	113	1	no	—

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.