Subgroups — C₃₁×#3573 #16843506

Order 3968.

1424 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#585	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#568	C₂	1	15	yes	maximal, complemented
3	C₂×C₃₁×#131	C₂	1	15	yes	maximal, complemented
4	C₃₁×2₋¹⁺⁴	C₄	1	6	yes	—
5	C₃₁×H(5,𝔽₂)	C₄	1	10	yes	—
6	C₂×#41×C₃₁	C₂²	1	15	yes	—
7	C₃₁×#131	C₂²	1	20	yes	complemented
8	C₃₁×#131	C₂²	1	60	yes	complemented
9	C₂×M₁₆×C₃₁	C₂²	1	45	yes	complemented
10	C₂²×C₈×C₃₁	C₂²	1	15	yes	complemented
11	#41×C₃₁	C₂×C₄	1	60	yes	—
12	#41×C₃₁	C₂³	1	20	yes	—
13	C₂×Q₈×C₃₁	C₂×C₄	1	15	yes	—
14	C₂×D₄×C₃₁	C₂×C₄	1	45	yes	—
15	C₂²×C₄×C₃₁	C₂³	1	15	yes	—
16	M₁₆×C₃₁	C₂³	1	60	yes	—
17	C₂×C₈×C₃₁	C₂³	1	45	yes	—
18	C₂×C₈×C₃₁	C₂³	1	15	yes	—
19	C₂³×C₃₁	C₂²×C₄	1	15	yes	—
20	Q₈×C₃₁	C₂²×C₄	1	20	yes	—
21	D₄×C₃₁	C₂²×C₄	1	60	yes	—
22	C₂×C₄×C₃₁	C₂²×C₄	1	45	yes	—
23	C₂×C₄×C₃₁	C₂⁴	1	15	yes	—
24	C₈×C₃₁	C₂⁴	1	15	yes	—
25	C₈×C₃₁	C₂⁴	1	1	yes	characteristic
26	#3573	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
27	C₂²×C₃₁	—	4	15	no	—
28	C₂²×C₃₁	C₂³×C₄	1	15	yes	—
29	C₄×C₃₁	C₂³×C₄	1	15	yes	—
30	C₄×C₃₁	C₂⁵	1	1	yes	characteristic
31	#585	C₂×C₃₁	1	1	yes	characteristic
32	#568	C₂×C₃₁	1	15	yes	complemented
33	C₂×#131	C₂×C₃₁	1	15	yes	complemented
34	C₂×C₃₁	—	2	15	no	—
35	C₂×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
36	2₋¹⁺⁴	C₄×C₃₁	1	6	yes	—
37	H(5,𝔽₂)	C₄×C₃₁	1	10	yes	—
38	C₂×#41	C₂²×C₃₁	1	15	yes	—
39	#131	C₂²×C₃₁	1	20	yes	complemented
40	#131	C₂²×C₃₁	1	60	yes	complemented
41	C₂×M₁₆	C₂²×C₃₁	1	45	yes	complemented
42	C₂²×C₈	C₂²×C₃₁	1	15	yes	complemented
43	C₃₁	#3573	1	1	yes	characteristic, direct product factor, Sylow
44	#41	C₂×C₄×C₃₁	1	60	yes	—
45	#41	C₂³×C₃₁	1	20	yes	—
46	C₂×Q₈	C₂×C₄×C₃₁	1	15	yes	—
47	C₂×D₄	C₂×C₄×C₃₁	1	45	yes	—
48	C₂²×C₄	C₂³×C₃₁	1	15	yes	—
49	M₁₆	C₂³×C₃₁	1	60	yes	—
50	C₂×C₈	C₂³×C₃₁	1	15	yes	—
51	C₂×C₈	C₂³×C₃₁	1	45	yes	—
52	C₂³	C₂²×C₄×C₃₁	1	15	yes	—
53	Q₈	C₂²×C₄×C₃₁	1	20	yes	—
54	D₄	C₂²×C₄×C₃₁	1	60	yes	—
55	C₂×C₄	C₂²×C₄×C₃₁	1	45	yes	—
56	C₂×C₄	C₂⁴×C₃₁	1	15	yes	—
57	C₈	C₂⁴×C₃₁	1	15	yes	—
58	C₈	C₂⁴×C₃₁	1	1	yes	characteristic
59	C₂²	—	4	15	no	—
60	C₂²	C₂³×C₄×C₃₁	1	15	yes	—
61	C₄	C₂³×C₄×C₃₁	1	15	yes	—
62	C₄	C₂⁵×C₃₁	1	1	yes	characteristic
63	C₂	—	2	15	no	—
64	C₂	C₂⁴×C₄×C₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₈×C₃₁	C₂⁴
commutator	C₂	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₄	C₂⁵×C₃₁
socle	C₂×C₃₁	C₂⁴×C₄
prime radical	C₃₁×#585	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#568	C₂	semidirect
3. C₂×C₃₁×#131	C₂	semidirect
7. C₃₁×#131	C₂²	semidirect
8. C₃₁×#131	C₂²	semidirect
9. C₂×M₁₆×C₃₁	C₂²	semidirect
10. C₂²×C₈×C₃₁	C₂²	semidirect
26. #3573	C₃₁	direct (N × H)
32. #568	C₂×C₃₁	semidirect
33. C₂×#131	C₂×C₃₁	semidirect
39. #131	C₂²×C₃₁	semidirect
40. #131	C₂²×C₃₁	semidirect
41. C₂×M₁₆	C₂²×C₃₁	semidirect
42. C₂²×C₈	C₂²×C₃₁	semidirect
43. C₃₁	#3573	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#585	2
C₃₁×#568	2
C₂×C₃₁×#131	2
#3573	31

Subgroups — C31×#3573 #16843506

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#3573 #16843506