Subgroups — C₇×C₂₂₃⋊AGL(1,𝔽₅) #44530237

Order 31220.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₅×C₂₂₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇×C₂₂₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇×Dic₂₂₃	—	5	1	no	maximal, Hall
4	C₂₂₃⋊AGL(1,𝔽₅)	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₇×C₂₂₃	—	5	1	no	—
6	D₅×C₂₂₃	C₂×C₇	1	1	yes	characteristic
7	C₇×C₂₂₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
8	C₅×C₂₂₃	C₄×C₇	1	1	yes	characteristic, complemented, Hall
9	Dic₂₂₃	—	5	1	no	Hall
10	C₂×C₂₂₃	—	5	1	no	—
11	C₂₂₃	C₇×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
12	C₇×AGL(1,𝔽₅)	—	223	1	no	maximal, Hall
13	C₇×D₅	D₂₂₃	1	1	yes	characteristic
14	C₅×C₇	Dic₂₂₃	1	1	yes	characteristic, complemented, Hall
15	C₄×C₇	—	1115	1	no	Hall
16	AGL(1,𝔽₅)	—	223	1	no	Hall
17	C₂×C₇	—	5	1	no	—
18	D₅	C₇×D₂₂₃	1	1	yes	characteristic
19	C₇	C₂₂₃⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
20	C₅	C₇×Dic₂₂₃	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	1115	1	no	Sylow
22	C₂	—	5	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.