Subgroups — C₃₁×C₃₁⋊AGL(1,𝔽₅) #34063607

Order 19220.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₃₁²	C₂	1	1	yes	maximal, characteristic
2	C₅×C₃₁²	C₄	1	1	yes	characteristic, complemented, Hall
3	C₃₁×Dic₃₁	—	5	1	no	maximal, Hall
4	C₂×C₃₁²	—	5	1	no	—
5	C₃₁²	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
6	C₃₁⋊AGL(1,𝔽₅)	C₃₁	1	1	yes	maximal, characteristic, direct product factor
7	AGL(1,𝔽₅)×C₃₁	—	31	1	no	maximal
8	D₅×C₃₁	—	2	15	no	—
9	D₅×C₃₁	D₃₁	1	1	yes	characteristic
10	D₅×C₃₁	C₂×C₃₁	1	1	yes	characteristic
11	C₅×C₃₁	—	2	15	no	—
12	C₅×C₃₁	Dic₃₁	1	1	yes	characteristic, complemented
13	C₅×C₃₁	C₄×C₃₁	1	1	yes	characteristic, complemented
14	C₄×C₃₁	—	155	1	no	—
15	Dic₃₁	—	5	1	no	—
16	C₂×C₃₁	—	5	1	no	—
17	C₂×C₃₁	—	5	1	no	—
18	C₂×C₃₁	—	10	15	no	—
19	C₃₁	—	2	15	no	—
20	C₃₁	AGL(1,𝔽₅)×C₃₁	1	1	yes	characteristic, complemented
21	C₃₁	C₃₁⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
22	AGL(1,𝔽₅)	—	31	1	no	Hall
23	D₅	C₃₁×D₃₁	1	1	yes	characteristic
24	C₅	C₃₁×Dic₃₁	1	1	yes	characteristic, complemented, Sylow
25	C₄	—	155	1	no	Sylow
26	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.