Subgroups — C₅×C₈²×C₃₁ #72188596

Order 9920.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×C₈×C₃₁	C₂	1	3	yes	maximal
2	C₄²×C₅×C₃₁	C₂²	1	1	yes	characteristic
3	C₂×C₅×C₈×C₃₁	C₄	1	6	yes	—
4	C₈²×C₃₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₄×C₅×C₃₁	C₂×C₄	1	3	yes	—
6	C₅×C₈×C₃₁	C₈	1	12	yes	direct product factor
7	C₄×C₈×C₃₁	C₂×C₅	1	3	yes	—
8	C₂²×C₅×C₃₁	C₄²	1	1	yes	characteristic
9	C₄×C₅×C₃₁	C₂×C₈	1	6	yes	—
10	C₂×C₈×C₃₁	C₄×C₅	1	6	yes	—
11	C₄²×C₃₁	C₂²×C₅	1	1	yes	characteristic
12	C₅×C₈²	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₅×C₃₁	C₄×C₈	1	3	yes	—
14	C₂×C₄×C₃₁	C₂×C₄×C₅	1	3	yes	—
15	C₈×C₃₁	C₅×C₈	1	12	yes	direct product factor
16	C₄×C₅×C₈	C₂×C₃₁	1	3	yes	—
17	C₅×C₃₁	C₈²	1	1	yes	characteristic, direct product factor, Hall
18	C₂²×C₃₁	C₄²×C₅	1	1	yes	characteristic
19	C₄×C₃₁	C₂×C₅×C₈	1	6	yes	—
20	C₂×C₅×C₈	C₄×C₃₁	1	6	yes	—
21	C₄²×C₅	C₂²×C₃₁	1	1	yes	characteristic
22	C₈²	C₅×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
23	C₂×C₃₁	C₄×C₅×C₈	1	3	yes	—
24	C₂×C₄×C₅	C₂×C₄×C₃₁	1	3	yes	—
25	C₅×C₈	C₈×C₃₁	1	12	yes	direct product factor
26	C₄×C₈	C₂×C₅×C₃₁	1	3	yes	—
27	C₃₁	C₅×C₈²	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²×C₅	C₄²×C₃₁	1	1	yes	characteristic
29	C₄×C₅	C₂×C₈×C₃₁	1	6	yes	—
30	C₂×C₈	C₄×C₅×C₃₁	1	6	yes	—
31	C₄²	C₂²×C₅×C₃₁	1	1	yes	characteristic
32	C₂×C₅	C₄×C₈×C₃₁	1	3	yes	—
33	C₂×C₄	C₂×C₄×C₅×C₃₁	1	3	yes	—
34	C₈	C₅×C₈×C₃₁	1	12	yes	direct product factor
35	C₅	C₈²×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
36	C₂²	C₄²×C₅×C₃₁	1	1	yes	characteristic
37	C₄	C₂×C₅×C₈×C₃₁	1	6	yes	—
38	C₂	C₄×C₅×C₈×C₃₁	1	3	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄²	C₂²×C₅×C₃₁
socle, prime radical	C₂²×C₅×C₃₁	C₄²
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. C₈²×C₃₁	C₅	direct (N × H)
6. C₅×C₈×C₃₁	C₈	direct (N × H)
12. C₅×C₈²	C₃₁	direct (N × H)
15. C₈×C₃₁	C₅×C₈	direct (N × H)
17. C₅×C₃₁	C₈²	direct (N × H)
22. C₈²	C₅×C₃₁	direct (N × H)
25. C₅×C₈	C₈×C₃₁	direct (N × H)
27. C₃₁	C₅×C₈²	direct (N × H)
34. C₈	C₅×C₈×C₃₁	direct (N × H)
35. C₅	C₈²×C₃₁	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×C₅×C₈×C₃₁	2
C₈²×C₃₁	5
C₅×C₈²	31

Subgroups — C5×C82×C31 #72188596

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₈²×C₃₁ #72188596