Subgroups — C₇×#14582304 #34062801

Order 19180.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₆₈₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇×C₁₃₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇×#10587739	—	5	1	no	maximal, Hall
4	#14582304	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×D₁₃₇	—	5	1	no	—
6	D₆₈₅	C₂×C₇	1	1	yes	characteristic
7	C₇×C₁₃₇	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
8	C₅×C₁₃₇	C₄×C₇	1	1	yes	characteristic, complemented, Hall
9	#10587739	—	5	1	no	Hall
10	D₁₃₇	—	5	1	no	—
11	C₇×AGL(1,𝔽₅)	—	137	1	no	maximal, Hall
12	C₁₃₇	C₇×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
13	C₇×D₅	—	137	1	no	—
14	C₅×C₇	#10587739	1	1	yes	characteristic, complemented, Hall
15	C₄×C₇	—	685	1	no	Hall
16	AGL(1,𝔽₅)	—	137	1	no	Hall
17	C₂×C₇	—	685	1	no	—
18	D₅	—	137	1	no	—
19	C₇	#14582304	1	1	yes	characteristic, direct product factor, Sylow
20	C₅	C₇×#10587739	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	685	1	no	Sylow
22	C₂	—	685	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.