Subgroups — C₄²×C₅×C₈×C₃₁ #72197484

Order 19840.

816 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄³×C₅×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₅×C₈×C₃₁	C₂	1	6	yes	maximal
3	C₂²×C₅×C₈×C₃₁	C₂²	1	4	yes	—
4	C₂×C₄²×C₅×C₃₁	C₄	1	4	yes	—
5	C₂×C₄²×C₅×C₃₁	C₂²	1	3	yes	—
6	C₄×C₅×C₈×C₃₁	C₄	1	24	yes	direct product factor
7	C₂²×C₄×C₅×C₃₁	C₂×C₄	1	6	yes	—
8	C₂²×C₄×C₅×C₃₁	C₂³	1	1	yes	characteristic
9	C₄²×C₅×C₃₁	C₈	1	16	yes	direct product factor
10	C₄²×C₅×C₃₁	C₂×C₄	1	12	yes	—
11	C₂×C₅×C₈×C₃₁	C₂×C₄	1	24	yes	—
12	C₄²×C₈×C₃₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₄×C₈×C₃₁	C₂×C₅	1	6	yes	—
14	C₄³×C₃₁	C₂×C₅	1	1	yes	characteristic
15	C₂³×C₅×C₃₁	C₂²×C₄	1	1	yes	characteristic
16	C₂×C₄×C₅×C₃₁	C₄²	1	12	yes	—
17	C₂×C₄×C₅×C₃₁	C₂×C₈	1	24	yes	—
18	C₂×C₄×C₅×C₃₁	C₂²×C₄	1	6	yes	—
19	C₅×C₈×C₃₁	C₄²	1	16	yes	direct product factor
20	C₂²×C₈×C₃₁	C₂²×C₅	1	4	yes	—
21	C₂×C₄²×C₃₁	C₄×C₅	1	4	yes	—
22	C₂×C₄²×C₃₁	C₂²×C₅	1	3	yes	—
23	C₄×C₈×C₃₁	C₄×C₅	1	24	yes	direct product factor
24	C₄²×C₅×C₈	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂²×C₅×C₃₁	C₂×C₄²	1	3	yes	—
26	C₂²×C₅×C₃₁	C₂²×C₈	1	4	yes	—
27	C₄×C₅×C₃₁	C₄×C₈	1	24	yes	direct product factor
28	C₄×C₅×C₃₁	C₂×C₄²	1	4	yes	—
29	C₂²×C₄×C₃₁	C₂×C₄×C₅	1	6	yes	—
30	C₂²×C₄×C₃₁	C₂³×C₅	1	1	yes	characteristic
31	C₂×C₈×C₃₁	C₂×C₄×C₅	1	24	yes	—
32	C₄²×C₃₁	C₅×C₈	1	16	yes	direct product factor
33	C₄²×C₃₁	C₂×C₄×C₅	1	12	yes	—
34	C₂×C₄×C₅×C₈	C₂×C₃₁	1	6	yes	—
35	C₄³×C₅	C₂×C₃₁	1	1	yes	characteristic
36	C₂×C₅×C₃₁	C₄³	1	1	yes	characteristic
37	C₂×C₅×C₃₁	C₂×C₄×C₈	1	6	yes	—
38	C₂³×C₃₁	C₂²×C₄×C₅	1	1	yes	characteristic
39	C₂×C₄×C₃₁	C₄²×C₅	1	12	yes	—
40	C₂×C₄×C₃₁	C₂×C₅×C₈	1	24	yes	—
41	C₂×C₄×C₃₁	C₂²×C₄×C₅	1	6	yes	—
42	C₈×C₃₁	C₄²×C₅	1	16	yes	direct product factor
43	C₂²×C₅×C₈	C₂²×C₃₁	1	4	yes	—
44	C₂×C₄²×C₅	C₄×C₃₁	1	4	yes	—
45	C₂×C₄²×C₅	C₂²×C₃₁	1	3	yes	—
46	C₄×C₅×C₈	C₄×C₃₁	1	24	yes	direct product factor
47	C₅×C₃₁	C₄²×C₈	1	1	yes	characteristic, direct product factor, Hall
48	C₄²×C₈	C₅×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
49	C₂²×C₃₁	C₂×C₄²×C₅	1	3	yes	—
50	C₂²×C₃₁	C₂²×C₅×C₈	1	4	yes	—
51	C₄×C₃₁	C₄×C₅×C₈	1	24	yes	direct product factor
52	C₄×C₃₁	C₂×C₄²×C₅	1	4	yes	—
53	C₂²×C₄×C₅	C₂×C₄×C₃₁	1	6	yes	—
54	C₂²×C₄×C₅	C₂³×C₃₁	1	1	yes	characteristic
55	C₂×C₅×C₈	C₂×C₄×C₃₁	1	24	yes	—
56	C₄²×C₅	C₈×C₃₁	1	16	yes	direct product factor
57	C₄²×C₅	C₂×C₄×C₃₁	1	12	yes	—
58	C₂×C₄×C₈	C₂×C₅×C₃₁	1	6	yes	—
59	C₄³	C₂×C₅×C₃₁	1	1	yes	characteristic
60	C₂×C₃₁	C₄³×C₅	1	1	yes	characteristic
61	C₂×C₃₁	C₂×C₄×C₅×C₈	1	6	yes	—
62	C₂³×C₅	C₂²×C₄×C₃₁	1	1	yes	characteristic
63	C₂×C₄×C₅	C₄²×C₃₁	1	12	yes	—
64	C₂×C₄×C₅	C₂×C₈×C₃₁	1	24	yes	—
65	C₂×C₄×C₅	C₂²×C₄×C₃₁	1	6	yes	—
66	C₅×C₈	C₄²×C₃₁	1	16	yes	direct product factor
67	C₂²×C₈	C₂²×C₅×C₃₁	1	4	yes	—
68	C₂×C₄²	C₄×C₅×C₃₁	1	4	yes	—
69	C₂×C₄²	C₂²×C₅×C₃₁	1	3	yes	—
70	C₄×C₈	C₄×C₅×C₃₁	1	24	yes	direct product factor
71	C₃₁	C₄²×C₅×C₈	1	1	yes	characteristic, direct product factor, Sylow
72	C₂²×C₅	C₂×C₄²×C₃₁	1	3	yes	—
73	C₂²×C₅	C₂²×C₈×C₃₁	1	4	yes	—
74	C₄×C₅	C₄×C₈×C₃₁	1	24	yes	direct product factor
75	C₄×C₅	C₂×C₄²×C₃₁	1	4	yes	—
76	C₂²×C₄	C₂×C₄×C₅×C₃₁	1	6	yes	—
77	C₂²×C₄	C₂³×C₅×C₃₁	1	1	yes	characteristic
78	C₂×C₈	C₂×C₄×C₅×C₃₁	1	24	yes	—
79	C₄²	C₅×C₈×C₃₁	1	16	yes	direct product factor
80	C₄²	C₂×C₄×C₅×C₃₁	1	12	yes	—
81	C₂×C₅	C₄³×C₃₁	1	1	yes	characteristic
82	C₂×C₅	C₂×C₄×C₈×C₃₁	1	6	yes	—
83	C₂³	C₂²×C₄×C₅×C₃₁	1	1	yes	characteristic
84	C₂×C₄	C₂×C₅×C₈×C₃₁	1	24	yes	—
85	C₂×C₄	C₄²×C₅×C₃₁	1	12	yes	—
86	C₂×C₄	C₂²×C₄×C₅×C₃₁	1	6	yes	—
87	C₈	C₄²×C₅×C₃₁	1	16	yes	direct product factor
88	C₅	C₄²×C₈×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
89	C₂²	C₂×C₄²×C₅×C₃₁	1	3	yes	—
90	C₂²	C₂²×C₅×C₈×C₃₁	1	4	yes	—
91	C₄	C₄×C₅×C₈×C₃₁	1	24	yes	direct product factor
92	C₄	C₂×C₄²×C₅×C₃₁	1	4	yes	—
93	C₂	C₂×C₄×C₅×C₈×C₃₁	1	6	yes	—
94	C₂	C₄³×C₅×C₃₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₄	C₂³×C₅×C₃₁
socle, prime radical	C₂³×C₅×C₃₁	C₂²×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₄×C₅×C₈×C₃₁	C₄	direct (N × H)
9. C₄²×C₅×C₃₁	C₈	direct (N × H)
12. C₄²×C₈×C₃₁	C₅	direct (N × H)
19. C₅×C₈×C₃₁	C₄²	direct (N × H)
23. C₄×C₈×C₃₁	C₄×C₅	direct (N × H)
24. C₄²×C₅×C₈	C₃₁	direct (N × H)
27. C₄×C₅×C₃₁	C₄×C₈	direct (N × H)
32. C₄²×C₃₁	C₅×C₈	direct (N × H)
42. C₈×C₃₁	C₄²×C₅	direct (N × H)
46. C₄×C₅×C₈	C₄×C₃₁	direct (N × H)
47. C₅×C₃₁	C₄²×C₈	direct (N × H)
48. C₄²×C₈	C₅×C₃₁	direct (N × H)
51. C₄×C₃₁	C₄×C₅×C₈	direct (N × H)
56. C₄²×C₅	C₈×C₃₁	direct (N × H)
66. C₅×C₈	C₄²×C₃₁	direct (N × H)
70. C₄×C₈	C₄×C₅×C₃₁	direct (N × H)
71. C₃₁	C₄²×C₅×C₈	direct (N × H)
74. C₄×C₅	C₄×C₈×C₃₁	direct (N × H)
79. C₄²	C₅×C₈×C₃₁	direct (N × H)
87. C₈	C₄²×C₅×C₃₁	direct (N × H)
88. C₅	C₄²×C₈×C₃₁	direct (N × H)
91. C₄	C₄×C₅×C₈×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
C₄³×C₅×C₃₁	2
C₂×C₄×C₅×C₈×C₃₁	2
C₄²×C₈×C₃₁	5
C₄²×C₅×C₈	31

Subgroups — C42×C5×C8×C31 #72197484

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×C₅×C₈×C₃₁ #72197484