Subgroups — C₂×C₃×C₅×C₁₆×C₄₁ #72197329

Order 19680.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₈×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×C₁₆×C₄₁	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅×C₁₆×C₄₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₄×C₅×C₄₁	C₄	1	1	yes	characteristic
5	C₃×C₅×C₈×C₄₁	C₄	1	1	yes	characteristic
6	C₃×C₅×C₈×C₄₁	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₁₆×C₄₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₅×C₈×C₄₁	C₂×C₃	1	1	yes	characteristic
9	C₅×C₁₆×C₄₁	C₂×C₃	1	2	yes	direct product factor
10	C₂²×C₃×C₅×C₄₁	C₈	1	1	yes	characteristic
11	C₃×C₄×C₅×C₄₁	C₈	1	1	yes	characteristic
12	C₃×C₄×C₅×C₄₁	C₂×C₄	1	1	yes	characteristic
13	C₂×C₃×C₈×C₄₁	C₂×C₅	1	1	yes	characteristic
14	C₃×C₁₆×C₄₁	C₂×C₅	1	2	yes	direct product factor
15	C₂×C₄×C₅×C₄₁	C₃×C₄	1	1	yes	characteristic
16	C₅×C₈×C₄₁	C₃×C₄	1	1	yes	characteristic
17	C₅×C₈×C₄₁	C₂²×C₃	1	1	yes	characteristic
18	C₂×C₁₆×C₄₁	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃×C₅×C₄₁	C₁₆	1	2	yes	direct product factor
20	C₂×C₃×C₅×C₄₁	C₂×C₈	1	1	yes	characteristic
21	C₂×C₃×C₄×C₄₁	C₄×C₅	1	1	yes	characteristic
22	C₃×C₈×C₄₁	C₄×C₅	1	1	yes	characteristic
23	C₃×C₈×C₄₁	C₂²×C₅	1	1	yes	characteristic
24	C₂²×C₅×C₄₁	C₃×C₈	1	1	yes	characteristic
25	C₄×C₅×C₄₁	C₃×C₈	1	1	yes	characteristic
26	C₄×C₅×C₄₁	C₂×C₃×C₄	1	1	yes	characteristic
27	C₂×C₈×C₄₁	C₂×C₃×C₅	1	1	yes	characteristic
28	C₁₆×C₄₁	C₂×C₃×C₅	1	2	yes	direct product factor
29	C₃×C₅×C₄₁	C₂×C₁₆	1	1	yes	characteristic, direct product factor, Hall
30	C₂²×C₃×C₄₁	C₅×C₈	1	1	yes	characteristic
31	C₃×C₄×C₄₁	C₅×C₈	1	1	yes	characteristic
32	C₃×C₄×C₄₁	C₂×C₄×C₅	1	1	yes	characteristic
33	C₂×C₃×C₅×C₁₆	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
34	C₂×C₅×C₄₁	C₃×C₁₆	1	2	yes	direct product factor
35	C₂×C₅×C₄₁	C₂×C₃×C₈	1	1	yes	characteristic
36	C₂×C₄×C₄₁	C₃×C₄×C₅	1	1	yes	characteristic
37	C₈×C₄₁	C₃×C₄×C₅	1	1	yes	characteristic
38	C₈×C₄₁	C₂²×C₃×C₅	1	1	yes	characteristic
39	C₂×C₃×C₄₁	C₅×C₁₆	1	2	yes	direct product factor
40	C₂×C₃×C₄₁	C₂×C₅×C₈	1	1	yes	characteristic
41	C₂×C₃×C₅×C₈	C₂×C₄₁	1	1	yes	characteristic
42	C₃×C₅×C₁₆	C₂×C₄₁	1	2	yes	direct product factor
43	C₅×C₄₁	C₂×C₃×C₁₆	1	1	yes	characteristic, direct product factor, Hall
44	C₂²×C₄₁	C₃×C₅×C₈	1	1	yes	characteristic
45	C₄×C₄₁	C₃×C₅×C₈	1	1	yes	characteristic
46	C₄×C₄₁	C₂×C₃×C₄×C₅	1	1	yes	characteristic
47	C₂×C₅×C₁₆	C₃×C₄₁	1	1	yes	characteristic, direct product factor, Hall
48	C₃×C₄₁	C₂×C₅×C₁₆	1	1	yes	characteristic, direct product factor, Hall
49	C₂×C₃×C₄×C₅	C₄×C₄₁	1	1	yes	characteristic
50	C₃×C₅×C₈	C₄×C₄₁	1	1	yes	characteristic
51	C₃×C₅×C₈	C₂²×C₄₁	1	1	yes	characteristic
52	C₂×C₃×C₁₆	C₅×C₄₁	1	1	yes	characteristic, direct product factor, Hall
53	C₂×C₄₁	C₃×C₅×C₁₆	1	2	yes	direct product factor
54	C₂×C₄₁	C₂×C₃×C₅×C₈	1	1	yes	characteristic
55	C₂×C₅×C₈	C₂×C₃×C₄₁	1	1	yes	characteristic
56	C₅×C₁₆	C₂×C₃×C₄₁	1	2	yes	direct product factor
57	C₂²×C₃×C₅	C₈×C₄₁	1	1	yes	characteristic
58	C₃×C₄×C₅	C₈×C₄₁	1	1	yes	characteristic
59	C₃×C₄×C₅	C₂×C₄×C₄₁	1	1	yes	characteristic
60	C₂×C₃×C₈	C₂×C₅×C₄₁	1	1	yes	characteristic
61	C₃×C₁₆	C₂×C₅×C₄₁	1	2	yes	direct product factor
62	C₄₁	C₂×C₃×C₅×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
63	C₂×C₄×C₅	C₃×C₄×C₄₁	1	1	yes	characteristic
64	C₅×C₈	C₃×C₄×C₄₁	1	1	yes	characteristic
65	C₅×C₈	C₂²×C₃×C₄₁	1	1	yes	characteristic
66	C₂×C₁₆	C₃×C₅×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
67	C₂×C₃×C₅	C₁₆×C₄₁	1	2	yes	direct product factor
68	C₂×C₃×C₅	C₂×C₈×C₄₁	1	1	yes	characteristic
69	C₂×C₃×C₄	C₄×C₅×C₄₁	1	1	yes	characteristic
70	C₃×C₈	C₄×C₅×C₄₁	1	1	yes	characteristic
71	C₃×C₈	C₂²×C₅×C₄₁	1	1	yes	characteristic
72	C₂²×C₅	C₃×C₈×C₄₁	1	1	yes	characteristic
73	C₄×C₅	C₃×C₈×C₄₁	1	1	yes	characteristic
74	C₄×C₅	C₂×C₃×C₄×C₄₁	1	1	yes	characteristic
75	C₂×C₈	C₂×C₃×C₅×C₄₁	1	1	yes	characteristic
76	C₁₆	C₂×C₃×C₅×C₄₁	1	2	yes	direct product factor
77	C₃×C₅	C₂×C₁₆×C₄₁	1	1	yes	characteristic, direct product factor, Hall
78	C₂²×C₃	C₅×C₈×C₄₁	1	1	yes	characteristic
79	C₃×C₄	C₅×C₈×C₄₁	1	1	yes	characteristic
80	C₃×C₄	C₂×C₄×C₅×C₄₁	1	1	yes	characteristic
81	C₂×C₅	C₃×C₁₆×C₄₁	1	2	yes	direct product factor
82	C₂×C₅	C₂×C₃×C₈×C₄₁	1	1	yes	characteristic
83	C₂×C₄	C₃×C₄×C₅×C₄₁	1	1	yes	characteristic
84	C₈	C₃×C₄×C₅×C₄₁	1	1	yes	characteristic
85	C₈	C₂²×C₃×C₅×C₄₁	1	1	yes	characteristic
86	C₂×C₃	C₅×C₁₆×C₄₁	1	2	yes	direct product factor
87	C₂×C₃	C₂×C₅×C₈×C₄₁	1	1	yes	characteristic
88	C₅	C₂×C₃×C₁₆×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
89	C₂²	C₃×C₅×C₈×C₄₁	1	1	yes	characteristic
90	C₄	C₃×C₅×C₈×C₄₁	1	1	yes	characteristic
91	C₄	C₂×C₃×C₄×C₅×C₄₁	1	1	yes	characteristic
92	C₃	C₂×C₅×C₁₆×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
93	C₂	C₃×C₅×C₁₆×C₄₁	1	2	yes	direct product factor
94	C₂	C₂×C₃×C₅×C₈×C₄₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂²×C₃×C₅×C₄₁
socle, prime radical	C₂²×C₃×C₅×C₄₁	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×C₁₆×C₄₁	C₂	direct (N × H)
3. C₂×C₅×C₁₆×C₄₁	C₃	direct (N × H)
7. C₂×C₃×C₁₆×C₄₁	C₅	direct (N × H)
9. C₅×C₁₆×C₄₁	C₂×C₃	direct (N × H)
14. C₃×C₁₆×C₄₁	C₂×C₅	direct (N × H)
18. C₂×C₁₆×C₄₁	C₃×C₅	direct (N × H)
19. C₂×C₃×C₅×C₄₁	C₁₆	direct (N × H)
28. C₁₆×C₄₁	C₂×C₃×C₅	direct (N × H)
29. C₃×C₅×C₄₁	C₂×C₁₆	direct (N × H)
33. C₂×C₃×C₅×C₁₆	C₄₁	direct (N × H)
34. C₂×C₅×C₄₁	C₃×C₁₆	direct (N × H)
39. C₂×C₃×C₄₁	C₅×C₁₆	direct (N × H)
42. C₃×C₅×C₁₆	C₂×C₄₁	direct (N × H)
43. C₅×C₄₁	C₂×C₃×C₁₆	direct (N × H)
47. C₂×C₅×C₁₆	C₃×C₄₁	direct (N × H)
48. C₃×C₄₁	C₂×C₅×C₁₆	direct (N × H)
52. C₂×C₃×C₁₆	C₅×C₄₁	direct (N × H)
53. C₂×C₄₁	C₃×C₅×C₁₆	direct (N × H)
56. C₅×C₁₆	C₂×C₃×C₄₁	direct (N × H)
61. C₃×C₁₆	C₂×C₅×C₄₁	direct (N × H)
62. C₄₁	C₂×C₃×C₅×C₁₆	direct (N × H)
66. C₂×C₁₆	C₃×C₅×C₄₁	direct (N × H)
67. C₂×C₃×C₅	C₁₆×C₄₁	direct (N × H)
76. C₁₆	C₂×C₃×C₅×C₄₁	direct (N × H)
77. C₃×C₅	C₂×C₁₆×C₄₁	direct (N × H)
81. C₂×C₅	C₃×C₁₆×C₄₁	direct (N × H)
86. C₂×C₃	C₅×C₁₆×C₄₁	direct (N × H)
88. C₅	C₂×C₃×C₁₆×C₄₁	direct (N × H)
92. C₃	C₂×C₅×C₁₆×C₄₁	direct (N × H)
93. C₂	C₃×C₅×C₁₆×C₄₁	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×C₃×C₅×C₈×C₄₁	2
C₃×C₅×C₁₆×C₄₁	2
C₂×C₅×C₁₆×C₄₁	3
C₂×C₃×C₁₆×C₄₁	5
C₂×C₃×C₅×C₁₆	41

Subgroups — C2×C3×C5×C16×C41 #72197329

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×C₁₆×C₄₁ #72197329