Subgroups — C₇×AGL(1,𝔽₁₃) #11763978

Order 1092.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₇×#261	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇×D₁₃	C₂×C₃	1	1	yes	characteristic
5	AGL(1,𝔽₁₃)	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₁₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₃×C₄×C₇	—	13	1	no	maximal, Hall
8	D₁₃⋊C₃	C₂×C₇	1	1	yes	characteristic
9	#261	C₃×C₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₇	—	13	1	no	—
11	C₁₃⋊C₃	C₄×C₇	1	1	yes	characteristic, complemented, Hall
12	C₄×C₇	—	13	1	no	Hall
13	D₁₃	C₂×C₃×C₇	1	1	yes	characteristic
14	C₃×C₇	—	13	1	no	Hall
15	C₂×C₇	—	13	1	no	—
16	C₁₃	C₃×C₄×C₇	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₄	—	13	1	no	Hall
18	C₇	AGL(1,𝔽₁₃)	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₃	—	13	1	no	—
20	C₄	—	13	1	no	Sylow
21	C₃	—	13	1	no	Sylow
22	C₂	—	13	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.