Subgroups — C₂×C₃²×C₅×C₈×C₄₃ #72207693

Order 30960.

264 conjugacy classes of subgroups.

The subgroup lattice has 108 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₄×C₅×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅×C₈×C₄₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₅×C₈×C₄₃	C₃	1	4	yes	maximal, direct product factor
4	C₂×C₃²×C₈×C₄₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₄×C₅×C₄₃	C₂×C₃	1	4	yes	—
6	C₃×C₅×C₈×C₄₃	C₂×C₃	1	8	yes	direct product factor
7	C₂×C₅×C₈×C₄₃	C₃²	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₃²×C₄×C₄₃	C₂×C₅	1	1	yes	characteristic
9	C₃²×C₈×C₄₃	C₂×C₅	1	2	yes	direct product factor
10	C₂×C₃×C₈×C₄₃	C₃×C₅	1	4	yes	direct product factor
11	C₂²×C₃²×C₅×C₄₃	C₄	1	1	yes	characteristic
12	C₃²×C₄×C₅×C₄₃	C₄	1	1	yes	characteristic
13	C₃²×C₄×C₅×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₃²×C₅×C₄₃	C₈	1	2	yes	direct product factor
15	C₂×C₃²×C₅×C₄₃	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₃×C₅×C₄₃	C₃×C₄	1	4	yes	—
17	C₃×C₄×C₅×C₄₃	C₃×C₄	1	4	yes	—
18	C₃×C₄×C₅×C₄₃	C₂²×C₃	1	4	yes	—
19	C₃²×C₅×C₄₃	C₂×C₈	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₄×C₅×C₄₃	C₂×C₃²	1	1	yes	characteristic
21	C₅×C₈×C₄₃	C₂×C₃²	1	2	yes	direct product factor
22	C₂²×C₃²×C₄₃	C₄×C₅	1	1	yes	characteristic
23	C₃²×C₄×C₄₃	C₄×C₅	1	1	yes	characteristic
24	C₃²×C₄×C₄₃	C₂²×C₅	1	1	yes	characteristic
25	C₂×C₃×C₅×C₄₃	C₃×C₈	1	8	yes	direct product factor
26	C₂×C₃×C₅×C₄₃	C₂×C₃×C₄	1	4	yes	—
27	C₂×C₃×C₄×C₄₃	C₂×C₃×C₅	1	4	yes	—
28	C₃×C₈×C₄₃	C₂×C₃×C₅	1	8	yes	direct product factor
29	C₂²×C₅×C₄₃	C₃²×C₄	1	1	yes	characteristic
30	C₄×C₅×C₄₃	C₃²×C₄	1	1	yes	characteristic
31	C₄×C₅×C₄₃	C₂²×C₃²	1	1	yes	characteristic
32	C₂×C₃²×C₄₃	C₅×C₈	1	2	yes	direct product factor
33	C₂×C₃²×C₄₃	C₂×C₄×C₅	1	1	yes	characteristic
34	C₂×C₃²×C₅×C₈	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
35	C₂×C₈×C₄₃	C₃²×C₅	1	1	yes	characteristic, direct product factor, Hall
36	C₃×C₅×C₄₃	C₂×C₃×C₈	1	4	yes	direct product factor
37	C₂²×C₃×C₄₃	C₃×C₄×C₅	1	4	yes	—
38	C₃×C₄×C₄₃	C₃×C₄×C₅	1	4	yes	—
39	C₃×C₄×C₄₃	C₂²×C₃×C₅	1	4	yes	—
40	C₂×C₅×C₄₃	C₃²×C₈	1	2	yes	direct product factor
41	C₂×C₅×C₄₃	C₂×C₃²×C₄	1	1	yes	characteristic
42	C₃²×C₄₃	C₂×C₅×C₈	1	1	yes	characteristic, direct product factor, Hall
43	C₂×C₃²×C₄×C₅	C₂×C₄₃	1	1	yes	characteristic
44	C₃²×C₅×C₈	C₂×C₄₃	1	2	yes	direct product factor
45	C₂×C₄×C₄₃	C₂×C₃²×C₅	1	1	yes	characteristic
46	C₈×C₄₃	C₂×C₃²×C₅	1	2	yes	direct product factor
47	C₂×C₃×C₄₃	C₃×C₅×C₈	1	8	yes	direct product factor
48	C₂×C₃×C₄₃	C₂×C₃×C₄×C₅	1	4	yes	—
49	C₂×C₃×C₅×C₈	C₃×C₄₃	1	4	yes	direct product factor
50	C₅×C₄₃	C₂×C₃²×C₈	1	1	yes	characteristic, direct product factor, Hall
51	C₂²×C₃²×C₅	C₄×C₄₃	1	1	yes	characteristic
52	C₃²×C₄×C₅	C₄×C₄₃	1	1	yes	characteristic
53	C₃²×C₄×C₅	C₂²×C₄₃	1	1	yes	characteristic
54	C₂²×C₄₃	C₃²×C₄×C₅	1	1	yes	characteristic
55	C₄×C₄₃	C₃²×C₄×C₅	1	1	yes	characteristic
56	C₄×C₄₃	C₂²×C₃²×C₅	1	1	yes	characteristic
57	C₂×C₃²×C₈	C₅×C₄₃	1	1	yes	characteristic, direct product factor, Hall
58	C₃×C₄₃	C₂×C₃×C₅×C₈	1	4	yes	direct product factor
59	C₂×C₃×C₄×C₅	C₂×C₃×C₄₃	1	4	yes	—
60	C₃×C₅×C₈	C₂×C₃×C₄₃	1	8	yes	direct product factor
61	C₂×C₃²×C₅	C₈×C₄₃	1	2	yes	direct product factor
62	C₂×C₃²×C₅	C₂×C₄×C₄₃	1	1	yes	characteristic
63	C₂×C₄₃	C₃²×C₅×C₈	1	2	yes	direct product factor
64	C₂×C₄₃	C₂×C₃²×C₄×C₅	1	1	yes	characteristic
65	C₂×C₅×C₈	C₃²×C₄₃	1	1	yes	characteristic, direct product factor, Hall
66	C₂×C₃²×C₄	C₂×C₅×C₄₃	1	1	yes	characteristic
67	C₃²×C₈	C₂×C₅×C₄₃	1	2	yes	direct product factor
68	C₂²×C₃×C₅	C₃×C₄×C₄₃	1	4	yes	—
69	C₃×C₄×C₅	C₃×C₄×C₄₃	1	4	yes	—
70	C₃×C₄×C₅	C₂²×C₃×C₄₃	1	4	yes	—
71	C₂×C₃×C₈	C₃×C₅×C₄₃	1	4	yes	direct product factor
72	C₃²×C₅	C₂×C₈×C₄₃	1	1	yes	characteristic, direct product factor, Hall
73	C₄₃	C₂×C₃²×C₅×C₈	1	1	yes	characteristic, direct product factor, Sylow
74	C₂×C₄×C₅	C₂×C₃²×C₄₃	1	1	yes	characteristic
75	C₅×C₈	C₂×C₃²×C₄₃	1	2	yes	direct product factor
76	C₂²×C₃²	C₄×C₅×C₄₃	1	1	yes	characteristic
77	C₃²×C₄	C₄×C₅×C₄₃	1	1	yes	characteristic
78	C₃²×C₄	C₂²×C₅×C₄₃	1	1	yes	characteristic
79	C₂×C₃×C₅	C₃×C₈×C₄₃	1	8	yes	direct product factor
80	C₂×C₃×C₅	C₂×C₃×C₄×C₄₃	1	4	yes	—
81	C₂×C₃×C₄	C₂×C₃×C₅×C₄₃	1	4	yes	—
82	C₃×C₈	C₂×C₃×C₅×C₄₃	1	8	yes	direct product factor
83	C₂²×C₅	C₃²×C₄×C₄₃	1	1	yes	characteristic
84	C₄×C₅	C₃²×C₄×C₄₃	1	1	yes	characteristic
85	C₄×C₅	C₂²×C₃²×C₄₃	1	1	yes	characteristic
86	C₂×C₃²	C₅×C₈×C₄₃	1	2	yes	direct product factor
87	C₂×C₃²	C₂×C₄×C₅×C₄₃	1	1	yes	characteristic
88	C₂×C₈	C₃²×C₅×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
89	C₃×C₅	C₂×C₃×C₈×C₄₃	1	4	yes	direct product factor
90	C₂²×C₃	C₃×C₄×C₅×C₄₃	1	4	yes	—
91	C₃×C₄	C₃×C₄×C₅×C₄₃	1	4	yes	—
92	C₃×C₄	C₂²×C₃×C₅×C₄₃	1	4	yes	—
93	C₂×C₅	C₃²×C₈×C₄₃	1	2	yes	direct product factor
94	C₂×C₅	C₂×C₃²×C₄×C₄₃	1	1	yes	characteristic
95	C₃²	C₂×C₅×C₈×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
96	C₂×C₄	C₂×C₃²×C₅×C₄₃	1	1	yes	characteristic
97	C₈	C₂×C₃²×C₅×C₄₃	1	2	yes	direct product factor
98	C₂×C₃	C₃×C₅×C₈×C₄₃	1	8	yes	direct product factor
99	C₂×C₃	C₂×C₃×C₄×C₅×C₄₃	1	4	yes	—
100	C₅	C₂×C₃²×C₈×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
101	C₂²	C₃²×C₄×C₅×C₄₃	1	1	yes	characteristic
102	C₄	C₃²×C₄×C₅×C₄₃	1	1	yes	characteristic
103	C₄	C₂²×C₃²×C₅×C₄₃	1	1	yes	characteristic
104	C₃	C₂×C₃×C₅×C₈×C₄₃	1	4	yes	direct product factor
105	C₂	C₃²×C₅×C₈×C₄₃	1	2	yes	direct product factor
106	C₂	C₂×C₃²×C₄×C₅×C₄₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂²×C₃²×C₅×C₄₃
socle, prime radical	C₂²×C₃²×C₅×C₄₃	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃²×C₅×C₈×C₄₃	C₂	direct (N × H)
3. C₂×C₃×C₅×C₈×C₄₃	C₃	direct (N × H)
4. C₂×C₃²×C₈×C₄₃	C₅	direct (N × H)
6. C₃×C₅×C₈×C₄₃	C₂×C₃	direct (N × H)
7. C₂×C₅×C₈×C₄₃	C₃²	direct (N × H)
9. C₃²×C₈×C₄₃	C₂×C₅	direct (N × H)
10. C₂×C₃×C₈×C₄₃	C₃×C₅	direct (N × H)
14. C₂×C₃²×C₅×C₄₃	C₈	direct (N × H)
19. C₃²×C₅×C₄₃	C₂×C₈	direct (N × H)
21. C₅×C₈×C₄₃	C₂×C₃²	direct (N × H)
25. C₂×C₃×C₅×C₄₃	C₃×C₈	direct (N × H)
28. C₃×C₈×C₄₃	C₂×C₃×C₅	direct (N × H)
32. C₂×C₃²×C₄₃	C₅×C₈	direct (N × H)
34. C₂×C₃²×C₅×C₈	C₄₃	direct (N × H)
35. C₂×C₈×C₄₃	C₃²×C₅	direct (N × H)
36. C₃×C₅×C₄₃	C₂×C₃×C₈	direct (N × H)
40. C₂×C₅×C₄₃	C₃²×C₈	direct (N × H)
42. C₃²×C₄₃	C₂×C₅×C₈	direct (N × H)
44. C₃²×C₅×C₈	C₂×C₄₃	direct (N × H)
46. C₈×C₄₃	C₂×C₃²×C₅	direct (N × H)
47. C₂×C₃×C₄₃	C₃×C₅×C₈	direct (N × H)
49. C₂×C₃×C₅×C₈	C₃×C₄₃	direct (N × H)
50. C₅×C₄₃	C₂×C₃²×C₈	direct (N × H)
57. C₂×C₃²×C₈	C₅×C₄₃	direct (N × H)
58. C₃×C₄₃	C₂×C₃×C₅×C₈	direct (N × H)
60. C₃×C₅×C₈	C₂×C₃×C₄₃	direct (N × H)
61. C₂×C₃²×C₅	C₈×C₄₃	direct (N × H)
63. C₂×C₄₃	C₃²×C₅×C₈	direct (N × H)
65. C₂×C₅×C₈	C₃²×C₄₃	direct (N × H)
67. C₃²×C₈	C₂×C₅×C₄₃	direct (N × H)
71. C₂×C₃×C₈	C₃×C₅×C₄₃	direct (N × H)
72. C₃²×C₅	C₂×C₈×C₄₃	direct (N × H)
73. C₄₃	C₂×C₃²×C₅×C₈	direct (N × H)
75. C₅×C₈	C₂×C₃²×C₄₃	direct (N × H)
79. C₂×C₃×C₅	C₃×C₈×C₄₃	direct (N × H)
82. C₃×C₈	C₂×C₃×C₅×C₄₃	direct (N × H)
86. C₂×C₃²	C₅×C₈×C₄₃	direct (N × H)
88. C₂×C₈	C₃²×C₅×C₄₃	direct (N × H)
89. C₃×C₅	C₂×C₃×C₈×C₄₃	direct (N × H)
93. C₂×C₅	C₃²×C₈×C₄₃	direct (N × H)
95. C₃²	C₂×C₅×C₈×C₄₃	direct (N × H)
97. C₈	C₂×C₃²×C₅×C₄₃	direct (N × H)
98. C₂×C₃	C₃×C₅×C₈×C₄₃	direct (N × H)
100. C₅	C₂×C₃²×C₈×C₄₃	direct (N × H)
104. C₃	C₂×C₃×C₅×C₈×C₄₃	direct (N × H)
105. C₂	C₃²×C₅×C₈×C₄₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₄×C₅×C₄₃	2
C₃²×C₅×C₈×C₄₃	2
C₂×C₃×C₅×C₈×C₄₃	3
C₂×C₃²×C₈×C₄₃	5
C₂×C₃²×C₅×C₈	43

Subgroups — C2×C32×C5×C8×C43 #72207693

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₅×C₈×C₄₃ #72207693