Subgroups — C₂×AGL(1,𝔽₁₃) #64629

Order 312.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	AGL(1,𝔽₁₃)	C₂	1	2	yes	maximal, direct product factor
3	C₂×#261	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₁₃⋊C₃	C₄	1	1	yes	characteristic, complemented
5	D₁₃⋊C₃	C₄	1	1	yes	characteristic, complemented
6	D₁₃⋊C₃	C₂²	1	1	yes	characteristic
7	C₂×D₁₃	C₂×C₃	1	1	yes	characteristic
8	#261	C₂×C₃	1	2	yes	complemented
9	C₁₃⋊C₃	C₂×C₄	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₃	C₃×C₄	1	1	yes	characteristic, complemented
11	D₁₃	C₃×C₄	1	1	yes	characteristic, complemented
12	D₁₃	C₂²×C₃	1	1	yes	characteristic
13	C₂×C₃×C₄	—	13	1	no	maximal, Hall
14	C₁₃	C₂×C₃×C₄	1	1	yes	characteristic, complemented, Sylow
15	C₂²×C₃	—	13	1	no	—
16	C₃×C₄	—	13	2	no	—
17	C₂×C₄	—	13	1	no	Sylow
18	C₂×C₃	—	13	1	no	—
19	C₂×C₃	—	13	1	no	—
20	C₂×C₃	—	13	1	no	—
21	C₂²	—	13	1	no	—
22	C₄	—	13	2	no	—
23	C₃	—	13	1	no	Sylow
24	C₂	—	13	1	no	—
25	C₂	—	13	1	no	—
26	C₂	AGL(1,𝔽₁₃)	1	1	yes	characteristic, direct product factor

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.