Subgroups — C₂⁴×C₄³×C₁₉ #72197149

Order 19456.

756906 conjugacy classes of subgroups.

The subgroup lattice has 100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₄²×C₁₉	C₂	1	7	yes	maximal
2	C₂³×C₄³×C₁₉	C₂	1	120	yes	maximal, direct product factor
3	C₂⁴×C₄³	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂⁶×C₄×C₁₉	C₂²	1	7	yes	—
5	C₂⁴×C₄²×C₁₉	C₄	1	448	yes	direct product factor
6	C₂⁴×C₄²×C₁₉	C₂²	1	420	yes	—
7	C₂²×C₄³×C₁₉	C₂²	1	2240	yes	direct product factor
8	C₂⁷×C₁₉	C₂³	1	1	yes	characteristic
9	C₂⁵×C₄×C₁₉	C₂×C₄	1	672	yes	—
10	C₂⁵×C₄×C₁₉	C₂³	1	210	yes	—
11	C₂³×C₄²×C₁₉	C₂×C₄	1	13440	yes	direct product factor
12	C₂³×C₄²×C₁₉	C₂³	1	3920	yes	—
13	C₂×C₄³×C₁₉	C₂³	1	7680	yes	direct product factor
14	C₂⁶×C₁₉	C₂²×C₄	1	112	yes	—
15	C₂⁶×C₁₉	C₂⁴	1	15	yes	—
16	C₂⁴×C₄×C₁₉	C₄²	1	7168	yes	direct product factor
17	C₂⁴×C₄×C₁₉	C₂²×C₄	1	10080	yes	—
18	C₂⁴×C₄×C₁₉	C₂⁴	1	980	yes	—
19	C₂²×C₄²×C₁₉	C₂²×C₄	1	62720	yes	direct product factor
20	C₂²×C₄²×C₁₉	C₂⁴	1	6720	yes	—
21	C₄³×C₁₉	C₂⁴	1	4096	yes	direct product factor
22	C₂⁵×C₁₉	C₂×C₄²	1	1792	yes	—
23	C₂⁵×C₁₉	C₂³×C₄	1	840	yes	—
24	C₂⁵×C₁₉	C₂⁵	1	35	yes	—
25	C₂³×C₄×C₁₉	C₂×C₄²	1	53760	yes	direct product factor
26	C₂³×C₄×C₁₉	C₂³×C₄	1	23520	yes	—
27	C₂³×C₄×C₁₉	C₂⁵	1	840	yes	—
28	C₂×C₄²×C₁₉	C₂³×C₄	1	53760	yes	direct product factor
29	C₂×C₄²×C₁₉	C₂⁵	1	1792	yes	—
30	C₂⁵×C₄²	C₂×C₁₉	1	7	yes	—
31	C₂³×C₄³	C₂×C₁₉	1	120	yes	direct product factor
32	C₂⁴×C₁₉	C₄³	1	4096	yes	direct product factor
33	C₂⁴×C₁₉	C₂²×C₄²	1	6720	yes	—
34	C₂⁴×C₁₉	C₂⁴×C₄	1	980	yes	—
35	C₂⁴×C₁₉	C₂⁶	1	15	yes	—
36	C₂²×C₄×C₁₉	C₂²×C₄²	1	62720	yes	direct product factor
37	C₂²×C₄×C₁₉	C₂⁴×C₄	1	10080	yes	—
38	C₂²×C₄×C₁₉	C₂⁶	1	112	yes	—
39	C₄²×C₁₉	C₂⁴×C₄	1	7168	yes	direct product factor
40	C₂⁶×C₄	C₂²×C₁₉	1	7	yes	—
41	C₂⁴×C₄²	C₄×C₁₉	1	448	yes	direct product factor
42	C₂⁴×C₄²	C₂²×C₁₉	1	420	yes	—
43	C₂²×C₄³	C₂²×C₁₉	1	2240	yes	direct product factor
44	C₂³×C₁₉	C₂×C₄³	1	7680	yes	direct product factor
45	C₂³×C₁₉	C₂³×C₄²	1	3920	yes	—
46	C₂³×C₁₉	C₂⁵×C₄	1	210	yes	—
47	C₂³×C₁₉	C₂⁷	1	1	yes	characteristic
48	C₂×C₄×C₁₉	C₂³×C₄²	1	13440	yes	direct product factor
49	C₂×C₄×C₁₉	C₂⁵×C₄	1	672	yes	—
50	C₂⁷	C₂³×C₁₉	1	1	yes	characteristic
51	C₂⁵×C₄	C₂×C₄×C₁₉	1	672	yes	—
52	C₂⁵×C₄	C₂³×C₁₉	1	210	yes	—
53	C₂³×C₄²	C₂×C₄×C₁₉	1	13440	yes	direct product factor
54	C₂³×C₄²	C₂³×C₁₉	1	3920	yes	—
55	C₂×C₄³	C₂³×C₁₉	1	7680	yes	direct product factor
56	C₂²×C₁₉	C₂²×C₄³	1	2240	yes	direct product factor
57	C₂²×C₁₉	C₂⁴×C₄²	1	420	yes	—
58	C₂²×C₁₉	C₂⁶×C₄	1	7	yes	—
59	C₄×C₁₉	C₂⁴×C₄²	1	448	yes	direct product factor
60	C₂⁶	C₂²×C₄×C₁₉	1	112	yes	—
61	C₂⁶	C₂⁴×C₁₉	1	15	yes	—
62	C₂⁴×C₄	C₄²×C₁₉	1	7168	yes	direct product factor
63	C₂⁴×C₄	C₂²×C₄×C₁₉	1	10080	yes	—
64	C₂⁴×C₄	C₂⁴×C₁₉	1	980	yes	—
65	C₂²×C₄²	C₂²×C₄×C₁₉	1	62720	yes	direct product factor
66	C₂²×C₄²	C₂⁴×C₁₉	1	6720	yes	—
67	C₄³	C₂⁴×C₁₉	1	4096	yes	direct product factor
68	C₂×C₁₉	C₂³×C₄³	1	120	yes	direct product factor
69	C₂×C₁₉	C₂⁵×C₄²	1	7	yes	—
70	C₂⁵	C₂×C₄²×C₁₉	1	1792	yes	—
71	C₂⁵	C₂³×C₄×C₁₉	1	840	yes	—
72	C₂⁵	C₂⁵×C₁₉	1	35	yes	—
73	C₂³×C₄	C₂×C₄²×C₁₉	1	53760	yes	direct product factor
74	C₂³×C₄	C₂³×C₄×C₁₉	1	23520	yes	—
75	C₂³×C₄	C₂⁵×C₁₉	1	840	yes	—
76	C₂×C₄²	C₂³×C₄×C₁₉	1	53760	yes	direct product factor
77	C₂×C₄²	C₂⁵×C₁₉	1	1792	yes	—
78	C₁₉	C₂⁴×C₄³	1	1	yes	characteristic, direct product factor, Sylow
79	C₂⁴	C₄³×C₁₉	1	4096	yes	direct product factor
80	C₂⁴	C₂²×C₄²×C₁₉	1	6720	yes	—
81	C₂⁴	C₂⁴×C₄×C₁₉	1	980	yes	—
82	C₂⁴	C₂⁶×C₁₉	1	15	yes	—
83	C₂²×C₄	C₂²×C₄²×C₁₉	1	62720	yes	direct product factor
84	C₂²×C₄	C₂⁴×C₄×C₁₉	1	10080	yes	—
85	C₂²×C₄	C₂⁶×C₁₉	1	112	yes	—
86	C₄²	C₂⁴×C₄×C₁₉	1	7168	yes	direct product factor
87	C₂³	C₂×C₄³×C₁₉	1	7680	yes	direct product factor
88	C₂³	C₂³×C₄²×C₁₉	1	3920	yes	—
89	C₂³	C₂⁵×C₄×C₁₉	1	210	yes	—
90	C₂³	C₂⁷×C₁₉	1	1	yes	characteristic
91	C₂×C₄	C₂³×C₄²×C₁₉	1	13440	yes	direct product factor
92	C₂×C₄	C₂⁵×C₄×C₁₉	1	672	yes	—
93	C₂²	C₂²×C₄³×C₁₉	1	2240	yes	direct product factor
94	C₂²	C₂⁴×C₄²×C₁₉	1	420	yes	—
95	C₂²	C₂⁶×C₄×C₁₉	1	7	yes	—
96	C₄	C₂⁴×C₄²×C₁₉	1	448	yes	direct product factor
97	C₂	C₂³×C₄³×C₁₉	1	120	yes	direct product factor
98	C₂	C₂⁵×C₄²×C₁₉	1	7	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂³	C₂⁷×C₁₉
socle, prime radical	C₂⁷×C₁₉	C₂³
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂³×C₄³×C₁₉	C₂	direct (N × H)
3. C₂⁴×C₄³	C₁₉	direct (N × H)
5. C₂⁴×C₄²×C₁₉	C₄	direct (N × H)
7. C₂²×C₄³×C₁₉	C₂²	direct (N × H)
11. C₂³×C₄²×C₁₉	C₂×C₄	direct (N × H)
13. C₂×C₄³×C₁₉	C₂³	direct (N × H)
16. C₂⁴×C₄×C₁₉	C₄²	direct (N × H)
19. C₂²×C₄²×C₁₉	C₂²×C₄	direct (N × H)
21. C₄³×C₁₉	C₂⁴	direct (N × H)
25. C₂³×C₄×C₁₉	C₂×C₄²	direct (N × H)
28. C₂×C₄²×C₁₉	C₂³×C₄	direct (N × H)
31. C₂³×C₄³	C₂×C₁₉	direct (N × H)
32. C₂⁴×C₁₉	C₄³	direct (N × H)
36. C₂²×C₄×C₁₉	C₂²×C₄²	direct (N × H)
39. C₄²×C₁₉	C₂⁴×C₄	direct (N × H)
41. C₂⁴×C₄²	C₄×C₁₉	direct (N × H)
43. C₂²×C₄³	C₂²×C₁₉	direct (N × H)
44. C₂³×C₁₉	C₂×C₄³	direct (N × H)
48. C₂×C₄×C₁₉	C₂³×C₄²	direct (N × H)
53. C₂³×C₄²	C₂×C₄×C₁₉	direct (N × H)
55. C₂×C₄³	C₂³×C₁₉	direct (N × H)
56. C₂²×C₁₉	C₂²×C₄³	direct (N × H)
59. C₄×C₁₉	C₂⁴×C₄²	direct (N × H)
62. C₂⁴×C₄	C₄²×C₁₉	direct (N × H)
65. C₂²×C₄²	C₂²×C₄×C₁₉	direct (N × H)
67. C₄³	C₂⁴×C₁₉	direct (N × H)
68. C₂×C₁₉	C₂³×C₄³	direct (N × H)
73. C₂³×C₄	C₂×C₄²×C₁₉	direct (N × H)
76. C₂×C₄²	C₂³×C₄×C₁₉	direct (N × H)
78. C₁₉	C₂⁴×C₄³	direct (N × H)
79. C₂⁴	C₄³×C₁₉	direct (N × H)
83. C₂²×C₄	C₂²×C₄²×C₁₉	direct (N × H)
86. C₄²	C₂⁴×C₄×C₁₉	direct (N × H)
87. C₂³	C₂×C₄³×C₁₉	direct (N × H)
91. C₂×C₄	C₂³×C₄²×C₁₉	direct (N × H)
93. C₂²	C₂²×C₄³×C₁₉	direct (N × H)
96. C₄	C₂⁴×C₄²×C₁₉	direct (N × H)
97. C₂	C₂³×C₄³×C₁₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×C₄²×C₁₉	2
C₂³×C₄³×C₁₉	2
C₂⁴×C₄³	19

Subgroups — C24×C43×C19 #72197149

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×C₄³×C₁₉ #72197149