Subgroups — C₂×C₇×C₈×C₉×C₁₉ #72196849

Order 19152.

132 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×C₄×C₇×C₉×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₇×C₈×C₉×C₁₉	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₇×C₈×C₁₉	C₃	1	1	yes	maximal, characteristic
4	C₂×C₃×C₄×C₇×C₁₉	C₂×C₃	1	1	yes	characteristic
5	C₃×C₇×C₈×C₁₉	C₂×C₃	1	2	yes	—
6	C₂×C₈×C₉×C₁₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₇×C₈×C₁₉	C₉	1	1	yes	characteristic, direct product factor, Hall
8	C₂²×C₇×C₉×C₁₉	C₄	1	1	yes	characteristic
9	C₄×C₇×C₉×C₁₉	C₄	1	1	yes	characteristic
10	C₄×C₇×C₉×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₇×C₉×C₁₉	C₈	1	2	yes	direct product factor
12	C₂×C₇×C₉×C₁₉	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₃×C₇×C₁₉	C₃×C₄	1	1	yes	characteristic
14	C₃×C₄×C₇×C₁₉	C₃×C₄	1	1	yes	characteristic
15	C₃×C₄×C₇×C₁₉	C₂²×C₃	1	1	yes	characteristic
16	C₂×C₄×C₉×C₁₉	C₂×C₇	1	1	yes	characteristic
17	C₈×C₉×C₁₉	C₂×C₇	1	2	yes	direct product factor
18	C₇×C₉×C₁₉	C₂×C₈	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₄×C₇×C₁₉	C₂×C₉	1	1	yes	characteristic
20	C₇×C₈×C₁₉	C₂×C₉	1	2	yes	direct product factor
21	C₂×C₇×C₈×C₉	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂×C₃×C₈×C₁₉	C₃×C₇	1	1	yes	characteristic
23	C₂×C₃×C₇×C₁₉	C₃×C₈	1	2	yes	—
24	C₂×C₃×C₇×C₁₉	C₂×C₃×C₄	1	1	yes	characteristic
25	C₂²×C₉×C₁₉	C₄×C₇	1	1	yes	characteristic
26	C₄×C₉×C₁₉	C₄×C₇	1	1	yes	characteristic
27	C₄×C₉×C₁₉	C₂²×C₇	1	1	yes	characteristic
28	C₂²×C₇×C₁₉	C₄×C₉	1	1	yes	characteristic
29	C₄×C₇×C₁₉	C₄×C₉	1	1	yes	characteristic
30	C₄×C₇×C₁₉	C₂²×C₉	1	1	yes	characteristic
31	C₂×C₄×C₇×C₉	C₂×C₁₉	1	1	yes	characteristic
32	C₇×C₈×C₉	C₂×C₁₉	1	2	yes	direct product factor
33	C₂×C₃×C₄×C₁₉	C₂×C₃×C₇	1	1	yes	characteristic
34	C₃×C₈×C₁₉	C₂×C₃×C₇	1	2	yes	—
35	C₃×C₇×C₁₉	C₂×C₃×C₈	1	1	yes	characteristic
36	C₂×C₉×C₁₉	C₇×C₈	1	2	yes	direct product factor
37	C₂×C₉×C₁₉	C₂×C₄×C₇	1	1	yes	characteristic
38	C₂×C₃×C₇×C₈	C₃×C₁₉	1	1	yes	characteristic
39	C₂×C₈×C₁₉	C₇×C₉	1	1	yes	characteristic, direct product factor, Hall
40	C₂×C₇×C₁₉	C₈×C₉	1	2	yes	direct product factor
41	C₂×C₇×C₁₉	C₂×C₄×C₉	1	1	yes	characteristic
42	C₂²×C₇×C₉	C₄×C₁₉	1	1	yes	characteristic
43	C₄×C₇×C₉	C₄×C₁₉	1	1	yes	characteristic
44	C₄×C₇×C₉	C₂²×C₁₉	1	1	yes	characteristic
45	C₂²×C₃×C₁₉	C₃×C₄×C₇	1	1	yes	characteristic
46	C₃×C₄×C₁₉	C₃×C₄×C₇	1	1	yes	characteristic
47	C₃×C₄×C₁₉	C₂²×C₃×C₇	1	1	yes	characteristic
48	C₉×C₁₉	C₂×C₇×C₈	1	1	yes	characteristic, direct product factor, Hall
49	C₂×C₃×C₄×C₇	C₂×C₃×C₁₉	1	1	yes	characteristic
50	C₃×C₇×C₈	C₂×C₃×C₁₉	1	2	yes	—
51	C₂×C₄×C₁₉	C₂×C₇×C₉	1	1	yes	characteristic
52	C₈×C₁₉	C₂×C₇×C₉	1	2	yes	direct product factor
53	C₂×C₈×C₉	C₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
54	C₇×C₁₉	C₂×C₈×C₉	1	1	yes	characteristic, direct product factor, Hall
55	C₂×C₇×C₉	C₈×C₁₉	1	2	yes	direct product factor
56	C₂×C₇×C₉	C₂×C₄×C₁₉	1	1	yes	characteristic
57	C₂×C₃×C₁₉	C₃×C₇×C₈	1	2	yes	—
58	C₂×C₃×C₁₉	C₂×C₃×C₄×C₇	1	1	yes	characteristic
59	C₂×C₇×C₈	C₉×C₁₉	1	1	yes	characteristic, direct product factor, Hall
60	C₂²×C₃×C₇	C₃×C₄×C₁₉	1	1	yes	characteristic
61	C₃×C₄×C₇	C₃×C₄×C₁₉	1	1	yes	characteristic
62	C₃×C₄×C₇	C₂²×C₃×C₁₉	1	1	yes	characteristic
63	C₂²×C₁₉	C₄×C₇×C₉	1	1	yes	characteristic
64	C₄×C₁₉	C₄×C₇×C₉	1	1	yes	characteristic
65	C₄×C₁₉	C₂²×C₇×C₉	1	1	yes	characteristic
66	C₂×C₄×C₉	C₂×C₇×C₁₉	1	1	yes	characteristic
67	C₈×C₉	C₂×C₇×C₁₉	1	2	yes	direct product factor
68	C₇×C₉	C₂×C₈×C₁₉	1	1	yes	characteristic, direct product factor, Hall
69	C₃×C₁₉	C₂×C₃×C₇×C₈	1	1	yes	characteristic
70	C₂×C₄×C₇	C₂×C₉×C₁₉	1	1	yes	characteristic
71	C₇×C₈	C₂×C₉×C₁₉	1	2	yes	direct product factor
72	C₂×C₃×C₈	C₃×C₇×C₁₉	1	1	yes	characteristic
73	C₂×C₃×C₇	C₃×C₈×C₁₉	1	2	yes	—
74	C₂×C₃×C₇	C₂×C₃×C₄×C₁₉	1	1	yes	characteristic
75	C₂×C₁₉	C₇×C₈×C₉	1	2	yes	direct product factor
76	C₂×C₁₉	C₂×C₄×C₇×C₉	1	1	yes	characteristic
77	C₂²×C₉	C₄×C₇×C₁₉	1	1	yes	characteristic
78	C₄×C₉	C₄×C₇×C₁₉	1	1	yes	characteristic
79	C₄×C₉	C₂²×C₇×C₁₉	1	1	yes	characteristic
80	C₂²×C₇	C₄×C₉×C₁₉	1	1	yes	characteristic
81	C₄×C₇	C₄×C₉×C₁₉	1	1	yes	characteristic
82	C₄×C₇	C₂²×C₉×C₁₉	1	1	yes	characteristic
83	C₂×C₃×C₄	C₂×C₃×C₇×C₁₉	1	1	yes	characteristic
84	C₃×C₈	C₂×C₃×C₇×C₁₉	1	2	yes	—
85	C₃×C₇	C₂×C₃×C₈×C₁₉	1	1	yes	characteristic
86	C₁₉	C₂×C₇×C₈×C₉	1	1	yes	characteristic, direct product factor, Sylow
87	C₂×C₉	C₇×C₈×C₁₉	1	2	yes	direct product factor
88	C₂×C₉	C₂×C₄×C₇×C₁₉	1	1	yes	characteristic
89	C₂×C₈	C₇×C₉×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
90	C₂×C₇	C₈×C₉×C₁₉	1	2	yes	direct product factor
91	C₂×C₇	C₂×C₄×C₉×C₁₉	1	1	yes	characteristic
92	C₂²×C₃	C₃×C₄×C₇×C₁₉	1	1	yes	characteristic
93	C₃×C₄	C₃×C₄×C₇×C₁₉	1	1	yes	characteristic
94	C₃×C₄	C₂²×C₃×C₇×C₁₉	1	1	yes	characteristic
95	C₉	C₂×C₇×C₈×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
96	C₂×C₄	C₂×C₇×C₉×C₁₉	1	1	yes	characteristic
97	C₈	C₂×C₇×C₉×C₁₉	1	2	yes	direct product factor
98	C₇	C₂×C₈×C₉×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
99	C₂×C₃	C₃×C₇×C₈×C₁₉	1	2	yes	—
100	C₂×C₃	C₂×C₃×C₄×C₇×C₁₉	1	1	yes	characteristic
101	C₂²	C₄×C₇×C₉×C₁₉	1	1	yes	characteristic
102	C₄	C₄×C₇×C₉×C₁₉	1	1	yes	characteristic
103	C₄	C₂²×C₇×C₉×C₁₉	1	1	yes	characteristic
104	C₃	C₂×C₃×C₇×C₈×C₁₉	1	1	yes	characteristic
105	C₂	C₇×C₈×C₉×C₁₉	1	2	yes	direct product factor
106	C₂	C₂×C₄×C₇×C₉×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄	C₂²×C₃×C₇×C₁₉
socle, prime radical	C₂²×C₃×C₇×C₁₉	C₃×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×C₈×C₉×C₁₉	C₂	direct (N × H)
6. C₂×C₈×C₉×C₁₉	C₇	direct (N × H)
7. C₂×C₇×C₈×C₁₉	C₉	direct (N × H)
11. C₂×C₇×C₉×C₁₉	C₈	direct (N × H)
17. C₈×C₉×C₁₉	C₂×C₇	direct (N × H)
18. C₇×C₉×C₁₉	C₂×C₈	direct (N × H)
20. C₇×C₈×C₁₉	C₂×C₉	direct (N × H)
21. C₂×C₇×C₈×C₉	C₁₉	direct (N × H)
32. C₇×C₈×C₉	C₂×C₁₉	direct (N × H)
36. C₂×C₉×C₁₉	C₇×C₈	direct (N × H)
39. C₂×C₈×C₁₉	C₇×C₉	direct (N × H)
40. C₂×C₇×C₁₉	C₈×C₉	direct (N × H)
48. C₉×C₁₉	C₂×C₇×C₈	direct (N × H)
52. C₈×C₁₉	C₂×C₇×C₉	direct (N × H)
53. C₂×C₈×C₉	C₇×C₁₉	direct (N × H)
54. C₇×C₁₉	C₂×C₈×C₉	direct (N × H)
55. C₂×C₇×C₉	C₈×C₁₉	direct (N × H)
59. C₂×C₇×C₈	C₉×C₁₉	direct (N × H)
67. C₈×C₉	C₂×C₇×C₁₉	direct (N × H)
68. C₇×C₉	C₂×C₈×C₁₉	direct (N × H)
71. C₇×C₈	C₂×C₉×C₁₉	direct (N × H)
75. C₂×C₁₉	C₇×C₈×C₉	direct (N × H)
86. C₁₉	C₂×C₇×C₈×C₉	direct (N × H)
87. C₂×C₉	C₇×C₈×C₁₉	direct (N × H)
89. C₂×C₈	C₇×C₉×C₁₉	direct (N × H)
90. C₂×C₇	C₈×C₉×C₁₉	direct (N × H)
95. C₉	C₂×C₇×C₈×C₁₉	direct (N × H)
97. C₈	C₂×C₇×C₉×C₁₉	direct (N × H)
98. C₇	C₂×C₈×C₉×C₁₉	direct (N × H)
105. C₂	C₇×C₈×C₉×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
C₂×C₄×C₇×C₉×C₁₉	2
C₇×C₈×C₉×C₁₉	2
C₂×C₃×C₇×C₈×C₁₉	3
C₂×C₈×C₉×C₁₉	7
C₂×C₇×C₈×C₉	19

Subgroups — C2×C7×C8×C9×C19 #72196849

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×C₈×C₉×C₁₉ #72196849