Subgroups — C₂⁴×C₁₆×C₃₁ #21519379

Order 7936.

2590 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₈×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₁₆×C₃₁	C₂	1	30	yes	maximal, direct product factor
3	C₂⁴×C₄×C₃₁	C₄	1	1	yes	characteristic
4	C₂³×C₈×C₃₁	C₄	1	15	yes	—
5	C₂³×C₈×C₃₁	C₂²	1	15	yes	—
6	C₂²×C₁₆×C₃₁	C₂²	1	140	yes	direct product factor
7	C₂⁵×C₃₁	C₈	1	1	yes	characteristic
8	C₂³×C₄×C₃₁	C₈	1	15	yes	—
9	C₂³×C₄×C₃₁	C₂×C₄	1	15	yes	—
10	C₂²×C₈×C₃₁	C₂×C₄	1	105	yes	—
11	C₂²×C₈×C₃₁	C₂³	1	35	yes	—
12	C₂×C₁₆×C₃₁	C₂³	1	120	yes	direct product factor
13	C₂⁴×C₃₁	C₁₆	1	16	yes	direct product factor
14	C₂⁴×C₃₁	C₂×C₈	1	15	yes	—
15	C₂²×C₄×C₃₁	C₂×C₈	1	105	yes	—
16	C₂²×C₄×C₃₁	C₂²×C₄	1	35	yes	—
17	C₂×C₈×C₃₁	C₂²×C₄	1	105	yes	—
18	C₂×C₈×C₃₁	C₂⁴	1	15	yes	—
19	C₁₆×C₃₁	C₂⁴	1	16	yes	direct product factor
20	C₂⁴×C₁₆	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂³×C₃₁	C₂×C₁₆	1	120	yes	direct product factor
22	C₂³×C₃₁	C₂²×C₈	1	35	yes	—
23	C₂×C₄×C₃₁	C₂²×C₈	1	105	yes	—
24	C₂×C₄×C₃₁	C₂³×C₄	1	15	yes	—
25	C₈×C₃₁	C₂³×C₄	1	15	yes	—
26	C₈×C₃₁	C₂⁵	1	1	yes	characteristic
27	C₂⁴×C₈	C₂×C₃₁	1	1	yes	characteristic
28	C₂³×C₁₆	C₂×C₃₁	1	30	yes	direct product factor
29	C₂²×C₃₁	C₂²×C₁₆	1	140	yes	direct product factor
30	C₂²×C₃₁	C₂³×C₈	1	15	yes	—
31	C₄×C₃₁	C₂³×C₈	1	15	yes	—
32	C₄×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
33	C₂⁴×C₄	C₄×C₃₁	1	1	yes	characteristic
34	C₂³×C₈	C₄×C₃₁	1	15	yes	—
35	C₂³×C₈	C₂²×C₃₁	1	15	yes	—
36	C₂²×C₁₆	C₂²×C₃₁	1	140	yes	direct product factor
37	C₂×C₃₁	C₂³×C₁₆	1	30	yes	direct product factor
38	C₂×C₃₁	C₂⁴×C₈	1	1	yes	characteristic
39	C₂⁵	C₈×C₃₁	1	1	yes	characteristic
40	C₂³×C₄	C₈×C₃₁	1	15	yes	—
41	C₂³×C₄	C₂×C₄×C₃₁	1	15	yes	—
42	C₂²×C₈	C₂×C₄×C₃₁	1	105	yes	—
43	C₂²×C₈	C₂³×C₃₁	1	35	yes	—
44	C₂×C₁₆	C₂³×C₃₁	1	120	yes	direct product factor
45	C₃₁	C₂⁴×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
46	C₂⁴	C₁₆×C₃₁	1	16	yes	direct product factor
47	C₂⁴	C₂×C₈×C₃₁	1	15	yes	—
48	C₂²×C₄	C₂×C₈×C₃₁	1	105	yes	—
49	C₂²×C₄	C₂²×C₄×C₃₁	1	35	yes	—
50	C₂×C₈	C₂²×C₄×C₃₁	1	105	yes	—
51	C₂×C₈	C₂⁴×C₃₁	1	15	yes	—
52	C₁₆	C₂⁴×C₃₁	1	16	yes	direct product factor
53	C₂³	C₂×C₁₆×C₃₁	1	120	yes	direct product factor
54	C₂³	C₂²×C₈×C₃₁	1	35	yes	—
55	C₂×C₄	C₂²×C₈×C₃₁	1	105	yes	—
56	C₂×C₄	C₂³×C₄×C₃₁	1	15	yes	—
57	C₈	C₂³×C₄×C₃₁	1	15	yes	—
58	C₈	C₂⁵×C₃₁	1	1	yes	characteristic
59	C₂²	C₂²×C₁₆×C₃₁	1	140	yes	direct product factor
60	C₂²	C₂³×C₈×C₃₁	1	15	yes	—
61	C₄	C₂³×C₈×C₃₁	1	15	yes	—
62	C₄	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
63	C₂	C₂³×C₁₆×C₃₁	1	30	yes	direct product factor
64	C₂	C₂⁴×C₈×C₃₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₈	C₂⁵×C₃₁
socle	C₂⁵×C₃₁	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂³×C₁₆×C₃₁	C₂	direct (N × H)
6. C₂²×C₁₆×C₃₁	C₂²	direct (N × H)
12. C₂×C₁₆×C₃₁	C₂³	direct (N × H)
13. C₂⁴×C₃₁	C₁₆	direct (N × H)
19. C₁₆×C₃₁	C₂⁴	direct (N × H)
20. C₂⁴×C₁₆	C₃₁	direct (N × H)
21. C₂³×C₃₁	C₂×C₁₆	direct (N × H)
28. C₂³×C₁₆	C₂×C₃₁	direct (N × H)
29. C₂²×C₃₁	C₂²×C₁₆	direct (N × H)
36. C₂²×C₁₆	C₂²×C₃₁	direct (N × H)
37. C₂×C₃₁	C₂³×C₁₆	direct (N × H)
44. C₂×C₁₆	C₂³×C₃₁	direct (N × H)
45. C₃₁	C₂⁴×C₁₆	direct (N × H)
46. C₂⁴	C₁₆×C₃₁	direct (N × H)
52. C₁₆	C₂⁴×C₃₁	direct (N × H)
53. C₂³	C₂×C₁₆×C₃₁	direct (N × H)
59. C₂²	C₂²×C₁₆×C₃₁	direct (N × H)
63. C₂	C₂³×C₁₆×C₃₁	direct (N × H)

Subgroups — C24×C16×C31 #21519379

Conjugacy classes of subgroups

Complements

Subgroups — C₂⁴×C₁₆×C₃₁ #21519379