Subgroups — C₂⁴×C₅×C₈×C₄₇ #72206903

Order 30080.

3952 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₄×C₅×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₅×C₈×C₄₇	C₂	1	30	yes	maximal, direct product factor
3	C₂³×C₄×C₅×C₄₇	C₄	1	15	yes	—
4	C₂³×C₄×C₅×C₄₇	C₂²	1	15	yes	—
5	C₂⁵×C₅×C₄₇	C₄	1	1	yes	characteristic
6	C₂²×C₅×C₈×C₄₇	C₂²	1	140	yes	direct product factor
7	C₂²×C₄×C₅×C₄₇	C₂×C₄	1	105	yes	—
8	C₂²×C₄×C₅×C₄₇	C₂³	1	35	yes	—
9	C₂⁴×C₅×C₄₇	C₈	1	16	yes	direct product factor
10	C₂⁴×C₅×C₄₇	C₂×C₄	1	15	yes	—
11	C₂×C₅×C₈×C₄₇	C₂³	1	120	yes	direct product factor
12	C₂⁴×C₈×C₄₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂⁴×C₄×C₄₇	C₂×C₅	1	1	yes	characteristic
14	C₂³×C₈×C₄₇	C₂×C₅	1	30	yes	direct product factor
15	C₂³×C₅×C₄₇	C₂×C₈	1	120	yes	direct product factor
16	C₂³×C₅×C₄₇	C₂²×C₄	1	35	yes	—
17	C₂×C₄×C₅×C₄₇	C₂²×C₄	1	105	yes	—
18	C₂×C₄×C₅×C₄₇	C₂⁴	1	15	yes	—
19	C₅×C₈×C₄₇	C₂⁴	1	16	yes	direct product factor
20	C₂⁵×C₄₇	C₄×C₅	1	1	yes	characteristic
21	C₂³×C₄×C₄₇	C₄×C₅	1	15	yes	—
22	C₂³×C₄×C₄₇	C₂²×C₅	1	15	yes	—
23	C₂²×C₈×C₄₇	C₂²×C₅	1	140	yes	direct product factor
24	C₂²×C₅×C₄₇	C₂²×C₈	1	140	yes	direct product factor
25	C₂²×C₅×C₄₇	C₂³×C₄	1	15	yes	—
26	C₄×C₅×C₄₇	C₂³×C₄	1	15	yes	—
27	C₄×C₅×C₄₇	C₂⁵	1	1	yes	characteristic
28	C₂⁴×C₄₇	C₅×C₈	1	16	yes	direct product factor
29	C₂⁴×C₄₇	C₂×C₄×C₅	1	15	yes	—
30	C₂²×C₄×C₄₇	C₂×C₄×C₅	1	105	yes	—
31	C₂²×C₄×C₄₇	C₂³×C₅	1	35	yes	—
32	C₂×C₈×C₄₇	C₂³×C₅	1	120	yes	direct product factor
33	C₂⁴×C₅×C₈	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
34	C₂×C₅×C₄₇	C₂³×C₈	1	30	yes	direct product factor
35	C₂×C₅×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
36	C₂³×C₄₇	C₂×C₅×C₈	1	120	yes	direct product factor
37	C₂³×C₄₇	C₂²×C₄×C₅	1	35	yes	—
38	C₂×C₄×C₄₇	C₂²×C₄×C₅	1	105	yes	—
39	C₂×C₄×C₄₇	C₂⁴×C₅	1	15	yes	—
40	C₈×C₄₇	C₂⁴×C₅	1	16	yes	direct product factor
41	C₂⁴×C₄×C₅	C₂×C₄₇	1	1	yes	characteristic
42	C₂³×C₅×C₈	C₂×C₄₇	1	30	yes	direct product factor
43	C₅×C₄₇	C₂⁴×C₈	1	1	yes	characteristic, direct product factor, Hall
44	C₂²×C₄₇	C₂²×C₅×C₈	1	140	yes	direct product factor
45	C₂²×C₄₇	C₂³×C₄×C₅	1	15	yes	—
46	C₄×C₄₇	C₂³×C₄×C₅	1	15	yes	—
47	C₄×C₄₇	C₂⁵×C₅	1	1	yes	characteristic
48	C₂⁵×C₅	C₄×C₄₇	1	1	yes	characteristic
49	C₂³×C₄×C₅	C₄×C₄₇	1	15	yes	—
50	C₂³×C₄×C₅	C₂²×C₄₇	1	15	yes	—
51	C₂²×C₅×C₈	C₂²×C₄₇	1	140	yes	direct product factor
52	C₂⁴×C₈	C₅×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
53	C₂×C₄₇	C₂³×C₅×C₈	1	30	yes	direct product factor
54	C₂×C₄₇	C₂⁴×C₄×C₅	1	1	yes	characteristic
55	C₂⁴×C₅	C₈×C₄₇	1	16	yes	direct product factor
56	C₂⁴×C₅	C₂×C₄×C₄₇	1	15	yes	—
57	C₂²×C₄×C₅	C₂×C₄×C₄₇	1	105	yes	—
58	C₂²×C₄×C₅	C₂³×C₄₇	1	35	yes	—
59	C₂×C₅×C₈	C₂³×C₄₇	1	120	yes	direct product factor
60	C₂⁴×C₄	C₂×C₅×C₄₇	1	1	yes	characteristic
61	C₂³×C₈	C₂×C₅×C₄₇	1	30	yes	direct product factor
62	C₄₇	C₂⁴×C₅×C₈	1	1	yes	characteristic, direct product factor, Sylow
63	C₂³×C₅	C₂×C₈×C₄₇	1	120	yes	direct product factor
64	C₂³×C₅	C₂²×C₄×C₄₇	1	35	yes	—
65	C₂×C₄×C₅	C₂²×C₄×C₄₇	1	105	yes	—
66	C₂×C₄×C₅	C₂⁴×C₄₇	1	15	yes	—
67	C₅×C₈	C₂⁴×C₄₇	1	16	yes	direct product factor
68	C₂⁵	C₄×C₅×C₄₇	1	1	yes	characteristic
69	C₂³×C₄	C₄×C₅×C₄₇	1	15	yes	—
70	C₂³×C₄	C₂²×C₅×C₄₇	1	15	yes	—
71	C₂²×C₈	C₂²×C₅×C₄₇	1	140	yes	direct product factor
72	C₂²×C₅	C₂²×C₈×C₄₇	1	140	yes	direct product factor
73	C₂²×C₅	C₂³×C₄×C₄₇	1	15	yes	—
74	C₄×C₅	C₂³×C₄×C₄₇	1	15	yes	—
75	C₄×C₅	C₂⁵×C₄₇	1	1	yes	characteristic
76	C₂⁴	C₅×C₈×C₄₇	1	16	yes	direct product factor
77	C₂⁴	C₂×C₄×C₅×C₄₇	1	15	yes	—
78	C₂²×C₄	C₂×C₄×C₅×C₄₇	1	105	yes	—
79	C₂²×C₄	C₂³×C₅×C₄₇	1	35	yes	—
80	C₂×C₈	C₂³×C₅×C₄₇	1	120	yes	direct product factor
81	C₂×C₅	C₂³×C₈×C₄₇	1	30	yes	direct product factor
82	C₂×C₅	C₂⁴×C₄×C₄₇	1	1	yes	characteristic
83	C₂³	C₂×C₅×C₈×C₄₇	1	120	yes	direct product factor
84	C₂³	C₂²×C₄×C₅×C₄₇	1	35	yes	—
85	C₂×C₄	C₂⁴×C₅×C₄₇	1	15	yes	—
86	C₂×C₄	C₂²×C₄×C₅×C₄₇	1	105	yes	—
87	C₈	C₂⁴×C₅×C₄₇	1	16	yes	direct product factor
88	C₅	C₂⁴×C₈×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
89	C₂²	C₂²×C₅×C₈×C₄₇	1	140	yes	direct product factor
90	C₂²	C₂³×C₄×C₅×C₄₇	1	15	yes	—
91	C₄	C₂⁵×C₅×C₄₇	1	1	yes	characteristic
92	C₄	C₂³×C₄×C₅×C₄₇	1	15	yes	—
93	C₂	C₂³×C₅×C₈×C₄₇	1	30	yes	direct product factor
94	C₂	C₂⁴×C₄×C₅×C₄₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂⁵×C₅×C₄₇
socle, prime radical	C₂⁵×C₅×C₄₇	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂³×C₅×C₈×C₄₇	C₂	direct (N × H)
6. C₂²×C₅×C₈×C₄₇	C₂²	direct (N × H)
9. C₂⁴×C₅×C₄₇	C₈	direct (N × H)
11. C₂×C₅×C₈×C₄₇	C₂³	direct (N × H)
12. C₂⁴×C₈×C₄₇	C₅	direct (N × H)
14. C₂³×C₈×C₄₇	C₂×C₅	direct (N × H)
15. C₂³×C₅×C₄₇	C₂×C₈	direct (N × H)
19. C₅×C₈×C₄₇	C₂⁴	direct (N × H)
23. C₂²×C₈×C₄₇	C₂²×C₅	direct (N × H)
24. C₂²×C₅×C₄₇	C₂²×C₈	direct (N × H)
28. C₂⁴×C₄₇	C₅×C₈	direct (N × H)
32. C₂×C₈×C₄₇	C₂³×C₅	direct (N × H)
33. C₂⁴×C₅×C₈	C₄₇	direct (N × H)
34. C₂×C₅×C₄₇	C₂³×C₈	direct (N × H)
36. C₂³×C₄₇	C₂×C₅×C₈	direct (N × H)
40. C₈×C₄₇	C₂⁴×C₅	direct (N × H)
42. C₂³×C₅×C₈	C₂×C₄₇	direct (N × H)
43. C₅×C₄₇	C₂⁴×C₈	direct (N × H)
44. C₂²×C₄₇	C₂²×C₅×C₈	direct (N × H)
51. C₂²×C₅×C₈	C₂²×C₄₇	direct (N × H)
52. C₂⁴×C₈	C₅×C₄₇	direct (N × H)
53. C₂×C₄₇	C₂³×C₅×C₈	direct (N × H)
55. C₂⁴×C₅	C₈×C₄₇	direct (N × H)
59. C₂×C₅×C₈	C₂³×C₄₇	direct (N × H)
61. C₂³×C₈	C₂×C₅×C₄₇	direct (N × H)
62. C₄₇	C₂⁴×C₅×C₈	direct (N × H)
63. C₂³×C₅	C₂×C₈×C₄₇	direct (N × H)
67. C₅×C₈	C₂⁴×C₄₇	direct (N × H)
71. C₂²×C₈	C₂²×C₅×C₄₇	direct (N × H)
72. C₂²×C₅	C₂²×C₈×C₄₇	direct (N × H)
76. C₂⁴	C₅×C₈×C₄₇	direct (N × H)
80. C₂×C₈	C₂³×C₅×C₄₇	direct (N × H)
81. C₂×C₅	C₂³×C₈×C₄₇	direct (N × H)
83. C₂³	C₂×C₅×C₈×C₄₇	direct (N × H)
87. C₈	C₂⁴×C₅×C₄₇	direct (N × H)
88. C₅	C₂⁴×C₈×C₄₇	direct (N × H)
89. C₂²	C₂²×C₅×C₈×C₄₇	direct (N × H)
93. C₂	C₂³×C₅×C₈×C₄₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₄×C₅×C₄₇	2
C₂³×C₅×C₈×C₄₇	2
C₂⁴×C₈×C₄₇	5
C₂⁴×C₅×C₈	47

Subgroups — C24×C5×C8×C47 #72206903

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×C₅×C₈×C₄₇ #72206903