Subgroups — C₂×C₁₉×#405 #14560729

Order 2432.

592 conjugacy classes of subgroups.

The subgroup lattice has 152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#117	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#405	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₉×#97	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×C₈×C₁₉	C₂	1	2	yes	maximal, complemented
7	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×M₁₆×C₁₉	C₄	1	8	yes	complemented
9	C₂×M₁₆×C₁₉	C₂²	1	4	yes	—
10	C₂²×C₈×C₁₉	C₄	1	8	yes	complemented
11	C₂²×C₈×C₁₉	C₂²	1	2	yes	—
12	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₁₉	C₂²	1	4	yes	—
14	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#117	C₄	1	4	yes	—
16	C₁₉×#117	C₂²	1	4	yes	—
17	C₂×C₄⋊C₄×C₁₉	C₄	1	2	yes	—
18	C₂×C₂²⋊C₄×C₁₉	C₄	1	2	yes	—
19	C₂×C₄²×C₁₉	C₂²	1	2	yes	—
20	C₁₉×#97	C₂²	1	8	yes	complemented
21	C₄×C₈×C₁₉	C₂²	1	8	yes	complemented
22	C₂⁴×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₄×C₁₉	C₂×C₄	1	4	yes	—
24	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
26	C₂²×C₄×C₁₉	C₂×C₄	1	4	yes	—
27	C₂²×C₄×C₁₉	C₂×C₄	1	4	yes	—
28	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
29	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
30	M₁₆×C₁₉	C₂×C₄	1	16	yes	complemented
31	C₂×C₈×C₁₉	C₂×C₄	1	4	yes	—
32	C₂×C₈×C₁₉	C₂×C₄	1	4	yes	—
33	C₂×C₈×C₁₉	C₂×C₄	1	8	yes	—
34	C₂×C₈×C₁₉	C₂×C₄	1	16	yes	complemented
35	C₂×C₈×C₁₉	C₂³	1	2	yes	—
36	C₂×C₈×C₁₉	C₂³	1	2	yes	—
37	C₂×C₈×C₁₉	C₂³	1	4	yes	—
38	C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
39	C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
40	C₄²×C₁₉	C₂×C₄	1	4	yes	—
41	C₄²×C₁₉	C₂³	1	4	yes	—
42	C₂³×C₁₉	—	2	4	no	—
43	C₂³×C₁₉	C₄²	1	4	yes	—
44	C₂³×C₁₉	C₂²×C₄	1	2	yes	—
45	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
46	C₂×C₄×C₁₉	—	2	8	no	—
47	C₂×C₄×C₁₉	C₄²	1	8	yes	—
48	C₂×C₄×C₁₉	C₄²	1	4	yes	—
49	C₂×C₄×C₁₉	C₂²×C₄	1	8	yes	—
50	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
52	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
53	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
54	C₂×C₄×C₁₉	C₂²×C₄	1	4	yes	—
55	C₂×C₄×C₁₉	C₂²×C₄	1	4	yes	—
56	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
57	C₈×C₁₉	C₂²×C₄	1	4	yes	—
58	C₈×C₁₉	C₂²×C₄	1	4	yes	—
59	C₈×C₁₉	C₂²×C₄	1	8	yes	—
60	C₂×#405	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	C₂²×C₁₉	—	2	4	no	—
62	C₂²×C₁₉	—	2	8	no	—
63	C₂²×C₁₉	C₂×C₄²	1	4	yes	—
64	C₂²×C₁₉	C₂×C₄²	1	2	yes	—
65	C₂²×C₁₉	#131	1	4	yes	—
66	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
67	C₄×C₁₉	—	2	8	no	—
68	C₄×C₁₉	C₂×C₄²	1	2	yes	—
69	C₄×C₁₉	C₂×C₄²	1	4	yes	—
70	C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
71	C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
72	C₂²×M₁₆	C₂×C₁₉	1	1	yes	characteristic
73	C₂³×C₈	C₂×C₁₉	1	1	yes	characteristic
74	C₂×#117	C₂×C₁₉	1	1	yes	characteristic
75	#405	C₂×C₁₉	1	8	yes	direct product factor
76	C₂×#97	C₂×C₁₉	1	2	yes	complemented
77	C₂×C₄×C₈	C₂×C₁₉	1	2	yes	complemented
78	C₂×C₁₉	—	2	4	no	—
79	C₂×C₁₉	#405	1	4	yes	direct product factor
80	C₂×C₁₉	C₂²×C₄²	1	1	yes	characteristic
81	C₂×C₁₉	C₂×#131	1	2	yes	—
82	C₂³×C₄	C₂²×C₁₉	1	1	yes	characteristic
83	C₂×M₁₆	C₄×C₁₉	1	8	yes	complemented
84	C₂×M₁₆	C₂²×C₁₉	1	4	yes	—
85	C₂²×C₈	C₄×C₁₉	1	8	yes	complemented
86	C₂²×C₈	C₂²×C₁₉	1	1	yes	characteristic
87	C₂²×C₈	C₂²×C₁₉	1	2	yes	—
88	C₂²×C₈	C₂²×C₁₉	1	1	yes	characteristic
89	C₂²×C₈	C₂²×C₁₉	1	4	yes	—
90	#117	C₄×C₁₉	1	4	yes	—
91	#117	C₂²×C₁₉	1	4	yes	—
92	C₂×C₄⋊C₄	C₄×C₁₉	1	2	yes	—
93	C₂×C₂²⋊C₄	C₄×C₁₉	1	2	yes	—
94	C₂×C₄²	C₂²×C₁₉	1	2	yes	—
95	#97	C₂²×C₁₉	1	8	yes	complemented
96	C₄×C₈	C₂²×C₁₉	1	8	yes	complemented
97	C₁₉	C₂×#405	1	1	yes	characteristic, direct product factor, Sylow
98	C₂⁴	C₂×C₄×C₁₉	1	1	yes	characteristic
99	C₂²×C₄	C₂×C₄×C₁₉	1	4	yes	—
100	C₂²×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
101	C₂²×C₄	C₂×C₄×C₁₉	1	2	yes	—
102	C₂²×C₄	C₂×C₄×C₁₉	1	4	yes	—
103	C₂²×C₄	C₂×C₄×C₁₉	1	4	yes	—
104	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
105	C₂²×C₄	C₂³×C₁₉	1	2	yes	—
106	M₁₆	C₂×C₄×C₁₉	1	16	yes	complemented
107	C₂×C₈	C₂×C₄×C₁₉	1	4	yes	—
108	C₂×C₈	C₂×C₄×C₁₉	1	4	yes	—
109	C₂×C₈	C₂×C₄×C₁₉	1	8	yes	—
110	C₂×C₈	C₂×C₄×C₁₉	1	16	yes	complemented
111	C₂×C₈	C₂³×C₁₉	1	2	yes	—
112	C₂×C₈	C₂³×C₁₉	1	4	yes	—
113	C₂×C₈	C₂³×C₁₉	1	2	yes	—
114	C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
115	C₂²⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
116	C₄²	C₂×C₄×C₁₉	1	4	yes	—
117	C₄²	C₂³×C₁₉	1	4	yes	—
118	C₂³	—	2	4	no	—
119	C₂³	C₄²×C₁₉	1	4	yes	—
120	C₂³	C₂²×C₄×C₁₉	1	2	yes	—
121	C₂³	C₂²×C₄×C₁₉	1	1	yes	characteristic
122	C₂×C₄	—	2	8	no	—
123	C₂×C₄	C₄²×C₁₉	1	8	yes	—
124	C₂×C₄	C₄²×C₁₉	1	4	yes	—
125	C₂×C₄	C₂²×C₄×C₁₉	1	8	yes	—
126	C₂×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
127	C₂×C₄	C₂²×C₄×C₁₉	1	2	yes	—
128	C₂×C₄	C₂²×C₄×C₁₉	1	2	yes	—
129	C₂×C₄	C₂²×C₄×C₁₉	1	2	yes	—
130	C₂×C₄	C₂²×C₄×C₁₉	1	4	yes	—
131	C₂×C₄	C₂²×C₄×C₁₉	1	4	yes	—
132	C₂×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
133	C₈	C₂²×C₄×C₁₉	1	4	yes	—
134	C₈	C₂²×C₄×C₁₉	1	4	yes	—
135	C₈	C₂²×C₄×C₁₉	1	8	yes	—
136	C₂²	—	2	8	no	—
137	C₂²	—	2	4	no	—
138	C₂²	C₂×C₄²×C₁₉	1	4	yes	—
139	C₂²	C₂×C₄²×C₁₉	1	2	yes	—
140	C₂²	C₁₉×#131	1	4	yes	—
141	C₂²	C₂³×C₄×C₁₉	1	1	yes	characteristic
142	C₄	—	2	8	no	—
143	C₄	C₂×C₄²×C₁₉	1	2	yes	—
144	C₄	C₂×C₄²×C₁₉	1	4	yes	—
145	C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
146	C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
147	C₂	—	2	4	no	—
148	C₂	C₁₉×#405	1	4	yes	direct product factor
149	C₂	C₂²×C₄²×C₁₉	1	1	yes	characteristic
150	C₂	C₂×C₁₉×#131	1	2	yes	—

	subgroup	G/H
center	C₂²×C₈×C₁₉	C₂²
commutator	C₂	C₂²×C₄²×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
socle	C₂³×C₁₉	C₂²×C₄
prime radical	C₂⁴×C₁₉	C₂×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₉×#405	C₂	direct (N × H)
5. C₂×C₁₉×#97	C₂	semidirect
6. C₂×C₄×C₈×C₁₉	C₂	semidirect
8. C₂×M₁₆×C₁₉	C₄	semidirect
10. C₂²×C₈×C₁₉	C₄	semidirect
20. C₁₉×#97	C₂²	semidirect
21. C₄×C₈×C₁₉	C₂²	semidirect
30. M₁₆×C₁₉	C₂×C₄	semidirect
34. C₂×C₈×C₁₉	C₂×C₄	semidirect
60. C₂×#405	C₁₉	direct (N × H)
75. #405	C₂×C₁₉	direct (N × H)
76. C₂×#97	C₂×C₁₉	semidirect
77. C₂×C₄×C₈	C₂×C₁₉	semidirect
79. C₂×C₁₉	#405	direct (N × H)
83. C₂×M₁₆	C₄×C₁₉	semidirect
85. C₂²×C₈	C₄×C₁₉	semidirect
95. #97	C₂²×C₁₉	semidirect
96. C₄×C₈	C₂²×C₁₉	semidirect
97. C₁₉	C₂×#405	direct (N × H)
106. M₁₆	C₂×C₄×C₁₉	semidirect
110. C₂×C₈	C₂×C₄×C₁₉	semidirect
148. C₂	C₁₉×#405	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×M₁₆×C₁₉	2
C₂³×C₈×C₁₉	2
C₂×C₁₉×#117	2
C₁₉×#405	2
C₂×C₁₉×#97	2
C₂×C₄×C₈×C₁₉	2
C₂×#405	19

Subgroups — C2×C19×#405 #14560729

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#405 #14560729