Subgroups — C₁₃×#11927412 #30629439

Order 15860.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×D₃₀₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₃×C₆₁	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₃×#6923	—	5	1	no	maximal, Hall
4	C₁₃×D₆₁	—	5	1	no	—
5	#11927412	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₃×C₆₁	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
7	D₃₀₅	C₂×C₁₃	1	1	yes	characteristic
8	C₅×C₆₁	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
9	C₁₃×AGL(1,𝔽₅)	—	61	1	no	maximal, Hall
10	#6923	—	5	1	no	Hall
11	D₅×C₁₃	—	61	1	no	—
12	D₆₁	—	5	1	no	—
13	C₅×C₁₃	#6923	1	1	yes	characteristic, complemented, Hall
14	C₆₁	C₁₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
15	C₄×C₁₃	—	305	1	no	Hall
16	C₂×C₁₃	—	305	1	no	—
17	AGL(1,𝔽₅)	—	61	1	no	Hall
18	C₁₃	#11927412	1	1	yes	characteristic, direct product factor, Sylow
19	D₅	—	61	1	no	—
20	C₅	C₁₃×#6923	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	305	1	no	Sylow
22	C₂	—	305	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.