Subgroups — C₂×C₁₉×#1733 #18026301

Order 4864.

2270 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#117	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₉×#117	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1733	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₉×#339	C₂	1	4	yes	maximal, complemented
6	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₁₉	—	2	4	no	—
8	C₂²×M₁₆×C₁₉	—	2	2	no	—
9	C₂²×M₁₆×C₁₉	—	2	1	no	—
10	C₂²×M₁₆×C₁₉	C₄	1	8	yes	complemented
11	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
12	C₂²×M₁₆×C₁₉	C₂²	1	4	yes	—
13	C₂³×C₈×C₁₉	—	2	1	no	—
14	C₂×C₁₉×#117	—	2	1	no	—
15	C₂×C₁₉×#117	—	2	2	no	—
16	C₂×C₁₉×#117	—	2	2	no	—
17	C₂×C₁₉×#117	—	2	4	no	—
18	C₂×C₁₉×#117	—	2	2	no	—
19	C₂×C₁₉×#117	—	2	1	no	—
20	C₂×C₁₉×#117	C₄	1	2	yes	complemented
21	C₂×C₁₉×#117	C₄	1	4	yes	complemented
22	C₂×C₁₉×#117	C₄	1	8	yes	complemented
23	C₂×C₁₉×#117	C₂²	1	2	yes	—
24	C₂×C₁₉×#117	C₂²	1	4	yes	—
25	C₂×C₁₉×#117	C₂²	1	4	yes	—
26	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
27	C₂²×C₄⋊C₄×C₁₉	C₄	1	2	yes	complemented
28	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
29	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
30	C₂²×C₄²×C₁₉	—	2	1	no	—
31	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
32	C₁₉×#339	C₂²	1	16	yes	complemented
33	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₉	—	2	2	no	—
35	C₂³×C₄×C₁₉	—	2	2	no	—
36	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
37	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
40	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
41	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₉	D₄	1	2	yes	—
43	C₂³×C₄×C₁₉	D₄	1	4	yes	—
44	C₂³×C₄×C₁₉	D₄	1	2	yes	—
45	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₉	Q₈	1	4	yes	—
48	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
50	C₂×M₁₆×C₁₉	—	2	16	no	—
51	C₂×M₁₆×C₁₉	—	2	8	no	—
52	C₂×M₁₆×C₁₉	—	2	4	no	—
53	C₂×M₁₆×C₁₉	—	2	8	no	—
54	C₂×M₁₆×C₁₉	—	2	4	no	—
55	C₂×M₁₆×C₁₉	—	2	2	no	—
56	C₂×M₁₆×C₁₉	C₂×C₄	1	8	yes	complemented
57	C₂×M₁₆×C₁₉	C₂×C₄	1	16	yes	complemented
58	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
59	C₂²×C₈×C₁₉	—	2	8	no	—
60	C₂²×C₈×C₁₉	—	2	4	no	—
61	C₂²×C₈×C₁₉	—	2	2	no	—
62	C₁₉×#117	—	2	4	no	—
63	C₁₉×#117	—	2	4	no	—
64	C₁₉×#117	—	2	4	no	—
65	C₁₉×#117	—	2	16	no	—
66	C₁₉×#117	—	2	2	no	—
67	C₁₉×#117	—	2	4	no	—
68	C₁₉×#117	—	2	2	no	—
69	C₁₉×#117	—	2	4	no	—
70	C₁₉×#117	—	2	8	no	—
71	C₁₉×#117	C₂×C₄	1	4	yes	—
72	C₁₉×#117	C₂×C₄	1	8	yes	complemented
73	C₁₉×#117	C₂×C₄	1	16	yes	complemented
74	C₁₉×#117	C₂³	1	4	yes	—
75	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
79	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
80	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	complemented
81	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
82	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
83	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
84	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
86	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
87	C₂×C₄²×C₁₉	—	2	4	no	—
88	C₂×C₄²×C₁₉	—	2	2	no	—
89	C₂×C₄²×C₁₉	—	2	4	no	—
90	C₂×C₄²×C₁₉	—	2	2	no	—
91	C₂×C₄²×C₁₉	—	2	4	no	—
92	C₂×C₄²×C₁₉	—	2	2	no	—
93	C₂×C₄²×C₁₉	C₂×C₄	1	8	yes	complemented
94	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
95	C₂⁴×C₁₉	—	4	4	no	—
96	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
97	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
98	C₂⁴×C₁₉	C₂²⋊C₄	1	4	yes	—
99	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
100	C₂⁴×C₁₉	C₄⋊C₄	1	4	yes	—
101	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₉	—	2	4	no	—
104	C₂²×C₄×C₁₉	—	2	8	no	—
105	C₂²×C₄×C₁₉	—	2	8	no	—
106	C₂²×C₄×C₁₉	—	2	4	no	—
107	C₂²×C₄×C₁₉	—	4	8	no	—
108	C₂²×C₄×C₁₉	—	4	8	no	—
109	C₂²×C₄×C₁₉	C₄²	1	4	yes	—
110	C₂²×C₄×C₁₉	C₄²	1	4	yes	—
111	C₂²×C₄×C₁₉	C₄²	1	8	yes	—
112	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
114	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
115	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
116	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
118	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
119	C₂²×C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
120	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
121	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
122	C₂²×C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
123	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
124	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
125	C₂²×C₄×C₁₉	C₄⋊C₄	1	8	yes	—
126	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
127	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
128	C₂²×C₄×C₁₉	C₄⋊C₄	1	8	yes	—
129	C₂²×C₄×C₁₉	C₄⋊C₄	1	8	yes	—
130	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
131	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
132	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
133	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
134	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
135	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
137	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
139	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
140	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
146	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
149	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
150	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
151	M₁₆×C₁₉	—	2	8	no	—
152	M₁₆×C₁₉	—	2	16	no	—
153	M₁₆×C₁₉	—	2	4	no	—
154	M₁₆×C₁₉	C₂²×C₄	1	8	yes	complemented
155	C₂×C₈×C₁₉	—	2	16	no	—
156	C₂×C₈×C₁₉	—	2	8	no	—
157	C₂×C₈×C₁₉	—	2	4	no	—
158	C₄⋊C₄×C₁₉	—	2	16	no	—
159	C₄⋊C₄×C₁₉	—	2	4	no	—
160	C₄⋊C₄×C₁₉	—	2	8	no	—
161	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
162	C₂²⋊C₄×C₁₉	—	2	4	no	—
163	C₂²⋊C₄×C₁₉	—	2	8	no	—
164	C₂²⋊C₄×C₁₉	—	2	16	no	—
165	C₂²⋊C₄×C₁₉	—	2	4	no	—
166	C₄²×C₁₉	—	2	4	no	—
167	C₄²×C₁₉	—	2	8	no	—
168	C₄²×C₁₉	—	2	8	no	—
169	C₄²×C₁₉	—	2	4	no	—
170	C₄²×C₁₉	—	2	4	no	—
171	C₄²×C₁₉	C₂²×C₄	1	8	yes	complemented
172	C₂×#1733	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂³×C₁₉	—	2	4	no	—
174	C₂³×C₁₉	—	2	4	no	—
175	C₂³×C₁₉	—	2	4	no	—
176	C₂³×C₁₉	—	4	4	no	—
177	C₂³×C₁₉	—	4	8	no	—
178	C₂³×C₁₉	—	4	8	no	—
179	C₂³×C₁₉	—	4	4	no	—
180	C₂³×C₁₉	#95	1	4	yes	—
181	C₂³×C₁₉	#95	1	4	yes	—
182	C₂³×C₁₉	#95	1	8	yes	—
183	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
185	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
186	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
187	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
188	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
189	C₂³×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
190	C₂³×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
191	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₉	—	2	8	no	—
193	C₂×C₄×C₁₉	—	2	8	no	—
194	C₂×C₄×C₁₉	—	4	8	no	—
195	C₂×C₄×C₁₉	—	4	16	no	—
196	C₂×C₄×C₁₉	—	4	16	no	—
197	C₂×C₄×C₁₉	—	4	8	no	—
198	C₂×C₄×C₁₉	#95	1	8	yes	—
199	C₂×C₄×C₁₉	#95	1	8	yes	—
200	C₂×C₄×C₁₉	#95	1	8	yes	—
201	C₂×C₄×C₁₉	#95	1	8	yes	—
202	C₂×C₄×C₁₉	#95	1	8	yes	—
203	C₂×C₄×C₁₉	#95	1	4	yes	—
204	C₂×C₄×C₁₉	#95	1	4	yes	—
205	C₂×C₄×C₁₉	C₂×C₄²	1	2	yes	—
206	C₂×C₄×C₁₉	C₂×C₄²	1	4	yes	—
207	C₂×C₄×C₁₉	C₂×C₄²	1	4	yes	—
208	C₂×C₄×C₁₉	C₂×C₄²	1	2	yes	—
209	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
210	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
211	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
212	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
213	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
214	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
215	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
217	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
219	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
220	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
221	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
222	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
223	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
224	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
225	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
226	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
227	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
228	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
229	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
230	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
231	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
232	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
235	C₈×C₁₉	—	2	8	no	—
236	C₂³×M₁₆	C₂×C₁₉	1	1	yes	characteristic
237	C₂²×#117	C₂×C₁₉	1	1	yes	characteristic
238	C₂²×#117	C₂×C₁₉	1	1	yes	characteristic
239	#1733	C₂×C₁₉	1	8	yes	direct product factor
240	C₂×#339	C₂×C₁₉	1	4	yes	complemented
241	C₂²×C₁₉	—	2	4	no	—
242	C₂²×C₁₉	—	2	2	no	—
243	C₂²×C₁₉	—	2	2	no	—
244	C₂²×C₁₉	—	2	4	no	—
245	C₂²×C₁₉	—	2	4	no	—
246	C₂²×C₁₉	—	2	8	no	—
247	C₂²×C₁₉	—	2	8	no	—
248	C₂²×C₁₉	—	2	4	no	—
249	C₂²×C₁₉	—	4	8	no	—
250	C₂²×C₁₉	—	4	4	no	—
251	C₂²×C₁₉	—	4	4	no	—
252	C₂²×C₁₉	C₂×#95	1	4	yes	—
253	C₂²×C₁₉	C₂×#95	1	4	yes	—
254	C₂²×C₁₉	C₂×#95	1	2	yes	—
255	C₂²×C₁₉	C₂×#95	1	2	yes	—
256	C₂²×C₁₉	#421	1	4	yes	—
257	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
258	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
259	C₂²×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
260	C₄×C₁₉	—	4	8	no	—
261	C₄×C₁₉	—	4	8	no	—
262	C₄×C₁₉	C₂×#95	1	4	yes	—
263	C₄×C₁₉	C₂×#95	1	2	yes	—
264	C₄×C₁₉	C₂×#95	1	4	yes	—
265	C₄×C₁₉	C₂×#95	1	2	yes	—
266	C₄×C₁₉	C₂²×C₄²	1	1	yes	characteristic
267	C₄×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
268	C₄×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
269	C₄×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
270	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
271	C₂²×M₁₆	—	2	4	no	—
272	C₂²×M₁₆	—	2	2	no	—
273	C₂²×M₁₆	—	2	1	no	—
274	C₂²×M₁₆	C₄×C₁₉	1	8	yes	complemented
275	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
276	C₂²×M₁₆	C₂²×C₁₉	1	4	yes	—
277	C₂³×C₈	—	2	1	no	—
278	C₂×#117	—	2	1	no	—
279	C₂×#117	—	2	2	no	—
280	C₂×#117	—	2	4	no	—
281	C₂×#117	—	2	2	no	—
282	C₂×#117	—	2	1	no	—
283	C₂×#117	—	2	2	no	—
284	C₂×#117	C₄×C₁₉	1	2	yes	complemented
285	C₂×#117	C₄×C₁₉	1	4	yes	complemented
286	C₂×#117	C₄×C₁₉	1	8	yes	complemented
287	C₂×#117	C₂²×C₁₉	1	2	yes	—
288	C₂×#117	C₂²×C₁₉	1	4	yes	—
289	C₂×#117	C₂²×C₁₉	1	4	yes	—
290	C₂²×C₄⋊C₄	—	2	1	no	—
291	C₂²×C₄⋊C₄	C₄×C₁₉	1	2	yes	complemented
292	C₂²×C₂²⋊C₄	—	2	1	no	—
293	C₂²×C₂²⋊C₄	—	2	1	no	—
294	C₂²×C₄²	—	2	1	no	—
295	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
296	#339	C₂²×C₁₉	1	16	yes	complemented
297	C₂×C₁₉	—	2	1	no	—
298	C₂×C₁₉	—	2	1	no	—
299	C₂×C₁₉	—	2	4	no	—
300	C₂×C₁₉	—	2	2	no	—
301	C₂×C₁₉	—	2	4	no	—
302	C₂×C₁₉	#1733	1	4	yes	direct product factor
303	C₂×C₁₉	C₂²×#95	1	1	yes	characteristic
304	C₂×C₁₉	C₂×#421	1	2	yes	—
305	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
306	C₂³×C₄	—	2	2	no	—
307	C₂³×C₄	—	2	2	no	—
308	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
309	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
310	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
311	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
312	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
313	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
314	C₂³×C₄	D₄×C₁₉	1	2	yes	—
315	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
316	C₂³×C₄	D₄×C₁₉	1	4	yes	—
317	C₂³×C₄	D₄×C₁₉	1	2	yes	—
318	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
319	C₂³×C₄	Q₈×C₁₉	1	4	yes	—
320	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
321	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
322	C₂×M₁₆	—	2	8	no	—
323	C₂×M₁₆	—	2	16	no	—
324	C₂×M₁₆	—	2	4	no	—
325	C₂×M₁₆	—	2	8	no	—
326	C₂×M₁₆	—	2	4	no	—
327	C₂×M₁₆	—	2	2	no	—
328	C₂×M₁₆	C₂×C₄×C₁₉	1	8	yes	complemented
329	C₂×M₁₆	C₂×C₄×C₁₉	1	16	yes	complemented
330	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
331	C₂²×C₈	—	2	8	no	—
332	C₂²×C₈	—	2	4	no	—
333	C₂²×C₈	—	2	2	no	—
334	#117	—	2	4	no	—
335	#117	—	2	4	no	—
336	#117	—	2	4	no	—
337	#117	—	2	16	no	—
338	#117	—	2	2	no	—
339	#117	—	2	4	no	—
340	#117	—	2	2	no	—
341	#117	—	2	4	no	—
342	#117	—	2	8	no	—
343	#117	C₂×C₄×C₁₉	1	4	yes	—
344	#117	C₂×C₄×C₁₉	1	8	yes	complemented
345	#117	C₂×C₄×C₁₉	1	16	yes	complemented
346	#117	C₂³×C₁₉	1	4	yes	—
347	C₂×C₄⋊C₄	—	2	8	no	—
348	C₂×C₄⋊C₄	—	2	4	no	—
349	C₂×C₄⋊C₄	—	2	2	no	—
350	C₂×C₄⋊C₄	—	2	4	no	—
351	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
352	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	complemented
353	C₂×C₂²⋊C₄	—	2	4	no	—
354	C₂×C₂²⋊C₄	—	2	2	no	—
355	C₂×C₂²⋊C₄	—	2	8	no	—
356	C₂×C₂²⋊C₄	—	2	2	no	—
357	C₂×C₂²⋊C₄	—	2	4	no	—
358	C₂×C₂²⋊C₄	—	2	4	no	—
359	C₂×C₄²	—	2	4	no	—
360	C₂×C₄²	—	2	2	no	—
361	C₂×C₄²	—	2	2	no	—
362	C₂×C₄²	—	2	4	no	—
363	C₂×C₄²	—	2	2	no	—
364	C₂×C₄²	—	2	4	no	—
365	C₂×C₄²	C₂×C₄×C₁₉	1	8	yes	complemented
366	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
367	C₁₉	C₂×#1733	1	1	yes	characteristic, direct product factor, Sylow
368	C₂⁴	—	4	4	no	—
369	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
370	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
371	C₂⁴	C₂²⋊C₄×C₁₉	1	2	yes	—
372	C₂⁴	C₂²⋊C₄×C₁₉	1	4	yes	—
373	C₂⁴	C₄⋊C₄×C₁₉	1	4	yes	—
374	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
375	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	8	no	—
378	C₂²×C₄	—	2	8	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	4	8	no	—
381	C₂²×C₄	—	4	8	no	—
382	C₂²×C₄	C₄²×C₁₉	1	4	yes	—
383	C₂²×C₄	C₄²×C₁₉	1	4	yes	—
384	C₂²×C₄	C₄²×C₁₉	1	8	yes	—
385	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
386	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
387	C₂²×C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
388	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
389	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
390	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
391	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
392	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
393	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
394	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
395	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
396	C₂²×C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
397	C₂²×C₄	C₄⋊C₄×C₁₉	1	4	yes	—
398	C₂²×C₄	C₄⋊C₄×C₁₉	1	4	yes	—
399	C₂²×C₄	C₄⋊C₄×C₁₉	1	4	yes	—
400	C₂²×C₄	C₄⋊C₄×C₁₉	1	4	yes	—
401	C₂²×C₄	C₄⋊C₄×C₁₉	1	8	yes	—
402	C₂²×C₄	C₄⋊C₄×C₁₉	1	8	yes	—
403	C₂²×C₄	C₄⋊C₄×C₁₉	1	4	yes	—
404	C₂²×C₄	C₄⋊C₄×C₁₉	1	8	yes	—
405	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
406	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
407	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
408	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
409	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
410	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
411	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
412	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
413	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
414	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
415	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
416	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
417	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
418	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
419	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
420	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
421	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
422	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
423	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
424	M₁₆	—	2	8	no	—
425	M₁₆	—	2	16	no	—
426	M₁₆	—	2	4	no	—
427	M₁₆	C₂²×C₄×C₁₉	1	8	yes	complemented
428	C₂×C₈	—	2	16	no	—
429	C₂×C₈	—	2	8	no	—
430	C₂×C₈	—	2	4	no	—
431	C₄⋊C₄	—	2	16	no	—
432	C₄⋊C₄	—	2	4	no	—
433	C₄⋊C₄	—	2	8	no	—
434	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
435	C₂²⋊C₄	—	2	4	no	—
436	C₂²⋊C₄	—	2	8	no	—
437	C₂²⋊C₄	—	2	16	no	—
438	C₂²⋊C₄	—	2	4	no	—
439	C₄²	—	2	4	no	—
440	C₄²	—	2	8	no	—
441	C₄²	—	2	8	no	—
442	C₄²	—	2	4	no	—
443	C₄²	—	2	4	no	—
444	C₄²	C₂²×C₄×C₁₉	1	8	yes	complemented
445	C₂³	—	2	4	no	—
446	C₂³	—	2	4	no	—
447	C₂³	—	2	4	no	—
448	C₂³	—	4	8	no	—
449	C₂³	—	4	4	no	—
450	C₂³	—	4	8	no	—
451	C₂³	—	4	4	no	—
452	C₂³	C₁₉×#95	1	4	yes	—
453	C₂³	C₁₉×#95	1	4	yes	—
454	C₂³	C₁₉×#95	1	8	yes	—
455	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
456	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
457	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
458	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
459	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
460	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
461	C₂³	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
462	C₂³	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
463	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
464	C₂×C₄	—	2	8	no	—
465	C₂×C₄	—	2	8	no	—
466	C₂×C₄	—	4	16	no	—
467	C₂×C₄	—	4	8	no	—
468	C₂×C₄	—	4	16	no	—
469	C₂×C₄	—	4	8	no	—
470	C₂×C₄	C₁₉×#95	1	8	yes	—
471	C₂×C₄	C₁₉×#95	1	8	yes	—
472	C₂×C₄	C₁₉×#95	1	8	yes	—
473	C₂×C₄	C₁₉×#95	1	8	yes	—
474	C₂×C₄	C₁₉×#95	1	8	yes	—
475	C₂×C₄	C₁₉×#95	1	4	yes	—
476	C₂×C₄	C₁₉×#95	1	4	yes	—
477	C₂×C₄	C₂×C₄²×C₁₉	1	2	yes	—
478	C₂×C₄	C₂×C₄²×C₁₉	1	4	yes	—
479	C₂×C₄	C₂×C₄²×C₁₉	1	4	yes	—
480	C₂×C₄	C₂×C₄²×C₁₉	1	2	yes	—
481	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
482	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
483	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
484	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
485	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
486	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
487	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
488	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
489	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
490	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
491	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
492	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
493	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
494	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
495	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
496	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
497	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
498	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
499	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
500	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
501	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
502	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
503	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
504	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
505	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
506	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
507	C₈	—	2	8	no	—
508	C₂²	—	2	4	no	—
509	C₂²	—	2	4	no	—
510	C₂²	—	2	8	no	—
511	C₂²	—	2	8	no	—
512	C₂²	—	2	4	no	—
513	C₂²	—	2	2	no	—
514	C₂²	—	2	2	no	—
515	C₂²	—	2	4	no	—
516	C₂²	—	4	4	no	—
517	C₂²	—	4	4	no	—
518	C₂²	—	4	8	no	—
519	C₂²	C₂×C₁₉×#95	1	4	yes	—
520	C₂²	C₂×C₁₉×#95	1	2	yes	—
521	C₂²	C₂×C₁₉×#95	1	4	yes	—
522	C₂²	C₂×C₁₉×#95	1	2	yes	—
523	C₂²	C₁₉×#421	1	4	yes	—
524	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
525	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
526	C₂²	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
527	C₄	—	4	8	no	—
528	C₄	—	4	8	no	—
529	C₄	C₂×C₁₉×#95	1	2	yes	—
530	C₄	C₂×C₁₉×#95	1	4	yes	—
531	C₄	C₂×C₁₉×#95	1	2	yes	—
532	C₄	C₂×C₁₉×#95	1	4	yes	—
533	C₄	C₂²×C₄²×C₁₉	1	1	yes	characteristic
534	C₄	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
535	C₄	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
536	C₄	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
537	C₂	—	2	1	no	—
538	C₂	—	2	2	no	—
539	C₂	—	2	4	no	—
540	C₂	—	2	4	no	—
541	C₂	—	2	1	no	—
542	C₂	C₁₉×#1733	1	4	yes	direct product factor
543	C₂	C₂²×C₁₉×#95	1	1	yes	characteristic
544	C₂	C₂×C₁₉×#421	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂×D₄
commutator	C₄	C₂²×C₄²×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁵×C₁₉	D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ C₂⁴×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₉×#1733	C₂	direct (N × H)
5. C₂×C₁₉×#339	C₂	semidirect
10. C₂²×M₁₆×C₁₉	C₄	semidirect
20. C₂×C₁₉×#117	C₄	semidirect
21. C₂×C₁₉×#117	C₄	semidirect
22. C₂×C₁₉×#117	C₄	semidirect
27. C₂²×C₄⋊C₄×C₁₉	C₄	semidirect
32. C₁₉×#339	C₂²	semidirect
56. C₂×M₁₆×C₁₉	C₂×C₄	semidirect
57. C₂×M₁₆×C₁₉	C₂×C₄	semidirect
72. C₁₉×#117	C₂×C₄	semidirect
73. C₁₉×#117	C₂×C₄	semidirect
80. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
93. C₂×C₄²×C₁₉	C₂×C₄	semidirect
154. M₁₆×C₁₉	C₂²×C₄	semidirect
171. C₄²×C₁₉	C₂²×C₄	semidirect
172. C₂×#1733	C₁₉	direct (N × H)
239. #1733	C₂×C₁₉	direct (N × H)
240. C₂×#339	C₂×C₁₉	semidirect
274. C₂²×M₁₆	C₄×C₁₉	semidirect
284. C₂×#117	C₄×C₁₉	semidirect
285. C₂×#117	C₄×C₁₉	semidirect
286. C₂×#117	C₄×C₁₉	semidirect
291. C₂²×C₄⋊C₄	C₄×C₁₉	semidirect
296. #339	C₂²×C₁₉	semidirect
302. C₂×C₁₉	#1733	direct (N × H)
328. C₂×M₁₆	C₂×C₄×C₁₉	semidirect
329. C₂×M₁₆	C₂×C₄×C₁₉	semidirect
344. #117	C₂×C₄×C₁₉	semidirect
345. #117	C₂×C₄×C₁₉	semidirect
352. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
365. C₂×C₄²	C₂×C₄×C₁₉	semidirect
367. C₁₉	C₂×#1733	direct (N × H)
427. M₁₆	C₂²×C₄×C₁₉	semidirect
444. C₄²	C₂²×C₄×C₁₉	semidirect
542. C₂	C₁₉×#1733	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×M₁₆×C₁₉	2
C₂²×C₁₉×#117	2
C₁₉×#1733	2
C₂×C₁₉×#339	2
C₂×#1733	19

Subgroups — C2×C19×#1733 #18026301

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#1733 #18026301