Subgroups — C₁₉×#10323 #18016282

Order 4864.

664 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3187	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2855	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2854	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1817	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1520	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1519	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1289	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×#123	—	2	1	no	—
9	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
11	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#483	—	2	1	no	—
13	C₁₉×#481	—	2	1	no	—
14	C₁₉×#465	—	2	2	no	—
15	C₁₉×#450	—	2	1	no	—
16	C₁₉×#448	—	2	1	no	—
17	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
19	C₁₉×#391	—	2	1	no	—
20	C₁₉×#390	—	2	1	no	—
21	C₁₉×#389	—	2	1	no	—
22	C₁₉×#389	—	2	1	no	—
23	C₁₉×#388	—	2	2	no	—
24	C₁₉×#387	—	2	2	no	—
25	C₁₉×#386	—	2	1	no	—
26	C₁₉×#385	—	2	1	no	—
27	C₁₉×#381	—	2	1	no	—
28	C₁₉×#380	C₂²	1	1	yes	characteristic
29	C₁₉×#380	C₂²	1	1	yes	characteristic
30	C₁₉×#336	—	2	2	no	—
31	C₁₉×#328	—	2	2	no	—
32	C₁₉×#327	—	2	2	no	—
33	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
34	C₂²×D₄×C₁₉	—	2	1	no	—
35	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
39	C₂×SD₁₆×C₁₉	—	2	2	no	—
40	C₂²×C₈×C₁₉	—	2	1	no	—
41	C₂²×C₈×C₁₉	D₄	1	2	yes	—
42	C₁₉×#123	—	4	2	no	—
43	C₁₉×#123	—	4	2	no	—
44	C₁₉×C₂²⋊Q₈	—	2	1	no	—
45	C₁₉×C₂²⋊Q₈	—	2	1	no	—
46	C₁₉×C₂²⋊Q₈	—	2	1	no	—
47	C₁₉×C₂²⋊Q₈	—	2	1	no	—
48	C₁₉×#121	—	2	1	no	—
49	C₁₉×#121	—	2	1	no	—
50	C₁₉×#121	—	2	1	no	—
51	C₁₉×#121	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
59	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₄²×C₁₉	—	2	1	no	—
66	C₂×C₄²×C₁₉	—	2	1	no	—
67	C₂×C₄²×C₁₉	—	2	1	no	—
68	C₂×C₄²×C₁₉	—	2	1	no	—
69	C₂×C₄²×C₁₉	—	2	1	no	—
70	C₂×C₄²×C₁₉	—	2	1	no	—
71	C₁₉×#106	—	2	2	no	—
72	C₁₉×#103	—	2	2	no	—
73	C₁₉×#102	—	2	2	no	—
74	C₁₉×C₂²⋊C₈	—	2	1	no	—
75	C₁₉×C₂²⋊C₈	—	2	1	no	—
76	C₁₉×C₂²⋊C₈	—	2	1	no	—
77	C₁₉×C₂²⋊C₈	—	2	1	no	—
78	C₁₉×#95	—	2	2	no	—
79	C₁₉×#95	—	2	2	no	—
80	C₁₉×#95	—	2	2	no	—
81	C₁₉×#95	—	2	2	no	—
82	C₁₉×#95	D₄	1	2	yes	—
83	C₁₉×#95	D₄	1	2	yes	—
84	C₂⁴×C₁₉	—	2	1	no	—
85	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
86	C₂×Q₈×C₁₉	—	2	1	no	—
87	C₂×Q₈×C₁₉	—	2	1	no	—
88	C₂×Q₈×C₁₉	—	4	2	no	—
89	C₂×D₄×C₁₉	—	2	1	no	—
90	C₂×D₄×C₁₉	—	2	1	no	—
91	C₂×D₄×C₁₉	—	4	2	no	—
92	C₂×D₄×C₁₉	—	4	1	no	—
93	C₂×D₄×C₁₉	—	4	1	no	—
94	C₂×D₄×C₁₉	—	4	1	no	—
95	C₂×D₄×C₁₉	—	4	1	no	—
96	C₂×D₄×C₁₉	—	4	1	no	—
97	C₂×D₄×C₁₉	—	4	1	no	—
98	C₂²×C₄×C₁₉	—	2	1	no	—
99	C₂²×C₄×C₁₉	—	2	1	no	—
100	C₂²×C₄×C₁₉	—	2	1	no	—
101	C₂²×C₄×C₁₉	—	2	1	no	—
102	C₂²×C₄×C₁₉	—	2	1	no	—
103	C₂²×C₄×C₁₉	—	2	1	no	—
104	C₂²×C₄×C₁₉	—	2	1	no	—
105	C₂²×C₄×C₁₉	—	2	1	no	—
106	C₂²×C₄×C₁₉	—	2	1	no	—
107	C₂²×C₄×C₁₉	—	2	2	no	—
108	C₂²×C₄×C₁₉	—	2	1	no	—
109	C₂²×C₄×C₁₉	—	2	1	no	—
110	C₂²×C₄×C₁₉	—	2	2	no	—
111	C₂²×C₄×C₁₉	—	2	1	no	—
112	C₂²×C₄×C₁₉	—	4	2	no	—
113	C₂²×C₄×C₁₉	—	4	2	no	—
114	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	complemented
115	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
121	SD₁₆×C₁₉	—	8	2	no	—
122	C₂×C₈×C₁₉	—	2	2	no	—
123	C₂×C₈×C₁₉	—	4	2	no	—
124	C₂×C₈×C₁₉	—	4	2	no	—
125	C₂×C₈×C₁₉	—	4	1	no	—
126	C₄⋊C₄×C₁₉	—	2	1	no	—
127	C₄⋊C₄×C₁₉	—	2	1	no	—
128	C₄⋊C₄×C₁₉	—	2	1	no	—
129	C₄⋊C₄×C₁₉	—	2	1	no	—
130	C₄⋊C₄×C₁₉	—	4	2	no	—
131	C₄⋊C₄×C₁₉	—	4	2	no	—
132	C₄⋊C₄×C₁₉	—	4	4	no	—
133	C₄⋊C₄×C₁₉	—	4	4	no	—
134	C₄⋊C₄×C₁₉	—	4	1	no	—
135	C₄⋊C₄×C₁₉	—	4	1	no	—
136	C₂²⋊C₄×C₁₉	—	4	4	no	—
137	C₂²⋊C₄×C₁₉	—	4	4	no	—
138	C₂²⋊C₄×C₁₉	—	4	1	no	—
139	C₂²⋊C₄×C₁₉	—	4	1	no	—
140	C₂²⋊C₄×C₁₉	—	4	1	no	—
141	C₂²⋊C₄×C₁₉	—	4	1	no	—
142	C₂²⋊C₄×C₁₉	—	4	1	no	—
143	C₂²⋊C₄×C₁₉	—	4	1	no	—
144	C₂²⋊C₄×C₁₉	—	4	1	no	—
145	C₂²⋊C₄×C₁₉	—	4	1	no	—
146	C₄²×C₁₉	—	4	1	no	—
147	C₄²×C₁₉	—	4	1	no	—
148	C₄²×C₁₉	—	4	1	no	—
149	C₄²×C₁₉	—	4	1	no	—
150	#10323	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂³×C₁₉	—	4	1	no	—
152	C₂³×C₁₉	—	4	1	no	—
153	C₂³×C₁₉	—	4	2	no	—
154	C₂³×C₁₉	—	4	2	no	—
155	C₂³×C₁₉	—	4	1	no	—
156	C₂³×C₁₉	—	4	1	no	—
157	C₂³×C₁₉	—	4	1	no	—
158	C₂³×C₁₉	#120	1	1	yes	characteristic
159	C₂³×C₁₉	#120	1	1	yes	characteristic
160	C₂³×C₁₉	#121	1	1	yes	characteristic
161	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
162	C₂³×C₁₉	#135	1	1	yes	characteristic
163	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
164	C₂³×C₁₉	#137	1	1	yes	characteristic
165	Q₈×C₁₉	—	4	2	no	—
166	Q₈×C₁₉	—	8	1	no	—
167	D₄×C₁₉	—	4	2	no	—
168	D₄×C₁₉	—	8	1	no	—
169	D₄×C₁₉	—	8	1	no	—
170	D₄×C₁₉	—	8	1	no	—
171	D₄×C₁₉	—	8	1	no	—
172	D₄×C₁₉	—	8	1	no	—
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	2	2	no	—
175	C₂×C₄×C₁₉	—	2	2	no	—
176	C₂×C₄×C₁₉	—	2	2	no	—
177	C₂×C₄×C₁₉	—	2	2	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	2	2	no	—
180	C₂×C₄×C₁₉	—	2	2	no	—
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	4	1	no	—
183	C₂×C₄×C₁₉	—	4	1	no	—
184	C₂×C₄×C₁₉	—	4	1	no	—
185	C₂×C₄×C₁₉	—	4	1	no	—
186	C₂×C₄×C₁₉	—	4	1	no	—
187	C₂×C₄×C₁₉	—	4	1	no	—
188	C₂×C₄×C₁₉	—	4	1	no	—
189	C₂×C₄×C₁₉	—	4	1	no	—
190	C₂×C₄×C₁₉	—	4	1	no	—
191	C₂×C₄×C₁₉	—	4	1	no	—
192	C₂×C₄×C₁₉	—	4	1	no	—
193	C₂×C₄×C₁₉	—	4	2	no	—
194	C₂×C₄×C₁₉	—	4	2	no	—
195	C₂×C₄×C₁₉	—	4	2	no	—
196	C₂×C₄×C₁₉	—	4	2	no	—
197	C₂×C₄×C₁₉	—	4	2	no	—
198	C₂×C₄×C₁₉	—	4	2	no	—
199	C₂×C₄×C₁₉	—	4	1	no	—
200	C₂×C₄×C₁₉	—	4	1	no	—
201	C₂×C₄×C₁₉	—	4	1	no	—
202	C₂×C₄×C₁₉	—	4	2	no	—
203	C₂×C₄×C₁₉	—	4	2	no	—
204	C₂×C₄×C₁₉	—	4	1	no	—
205	C₂×C₄×C₁₉	—	4	1	no	—
206	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
207	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
208	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
209	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
210	C₈×C₁₉	—	4	2	no	—
211	C₈×C₁₉	—	8	1	no	—
212	#3187	C₂×C₁₉	1	1	yes	characteristic
213	#2855	C₂×C₁₉	1	1	yes	characteristic, complemented
214	#2854	C₂×C₁₉	1	1	yes	characteristic
215	#1817	C₂×C₁₉	1	1	yes	characteristic, complemented
216	#1520	C₂×C₁₉	1	1	yes	characteristic, complemented
217	#1519	C₂×C₁₉	1	1	yes	characteristic
218	#1289	C₂×C₁₉	1	1	yes	characteristic, complemented
219	C₂²×C₁₉	—	2	1	no	—
220	C₂²×C₁₉	—	2	1	no	—
221	C₂²×C₁₉	—	2	1	no	—
222	C₂²×C₁₉	—	2	1	no	—
223	C₂²×C₁₉	—	2	1	no	—
224	C₂²×C₁₉	—	2	1	no	—
225	C₂²×C₁₉	—	4	1	no	—
226	C₂²×C₁₉	—	4	1	no	—
227	C₂²×C₁₉	—	4	1	no	—
228	C₂²×C₁₉	—	4	1	no	—
229	C₂²×C₁₉	—	8	2	no	—
230	C₂²×C₁₉	—	8	2	no	—
231	C₂²×C₁₉	—	8	1	no	—
232	C₂²×C₁₉	—	8	1	no	—
233	C₂²×C₁₉	—	8	1	no	—
234	C₂²×C₁₉	#392	1	1	yes	characteristic
235	C₂²×C₁₉	#448	1	1	yes	characteristic
236	C₂²×C₁₉	#449	1	1	yes	characteristic
237	C₂²×C₁₉	#450	1	1	yes	characteristic
238	C₂²×C₁₉	#452	1	1	yes	characteristic
239	C₂²×C₁₉	#465	1	1	yes	characteristic
240	C₂²×C₁₉	#468	1	1	yes	characteristic
241	C₄×C₁₉	—	2	1	no	—
242	C₄×C₁₉	—	2	1	no	—
243	C₄×C₁₉	—	2	1	no	—
244	C₄×C₁₉	—	4	2	no	—
245	C₄×C₁₉	—	4	2	no	—
246	C₄×C₁₉	—	8	2	no	—
247	C₄×C₁₉	—	8	2	no	—
248	C₄×C₁₉	—	8	1	no	—
249	C₄×C₁₉	—	8	1	no	—
250	C₄×C₁₉	—	8	1	no	—
251	C₄×C₁₉	#458	1	2	yes	—
252	C₂×#123	—	2	1	no	—
253	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
254	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
255	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
256	#483	—	2	1	no	—
257	#481	—	2	1	no	—
258	#465	—	2	2	no	—
259	#450	—	2	1	no	—
260	#448	—	2	1	no	—
261	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
262	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
263	#391	—	2	1	no	—
264	#390	—	2	1	no	—
265	#389	—	2	1	no	—
266	#389	—	2	1	no	—
267	#388	—	2	2	no	—
268	#387	—	2	2	no	—
269	#386	—	2	1	no	—
270	#385	—	2	1	no	—
271	#381	—	2	1	no	—
272	#380	C₂²×C₁₉	1	1	yes	characteristic
273	#380	C₂²×C₁₉	1	1	yes	characteristic
274	#336	—	2	2	no	—
275	#328	—	2	2	no	—
276	#327	—	2	2	no	—
277	C₂×C₁₉	—	2	1	no	—
278	C₂×C₁₉	—	2	1	no	—
279	C₂×C₁₉	—	2	1	no	—
280	C₂×C₁₉	—	2	1	no	—
281	C₂×C₁₉	—	2	1	no	—
282	C₂×C₁₉	—	2	1	no	—
283	C₂×C₁₉	—	16	1	no	—
284	C₂×C₁₉	#2000	1	1	yes	characteristic
285	C₂×C₁₉	#2010	1	1	yes	characteristic
286	C₂×C₁₉	#2022	1	1	yes	characteristic
287	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
288	C₂²×D₄	—	2	1	no	—
289	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
290	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
291	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
292	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
293	C₂×SD₁₆	—	2	2	no	—
294	C₂²×C₈	—	2	1	no	—
295	C₂²×C₈	D₄×C₁₉	1	2	yes	—
296	#123	—	4	2	no	—
297	#123	—	4	2	no	—
298	C₂²⋊Q₈	—	2	1	no	—
299	C₂²⋊Q₈	—	2	1	no	—
300	C₂²⋊Q₈	—	2	1	no	—
301	C₂²⋊Q₈	—	2	1	no	—
302	#121	—	2	1	no	—
303	#121	—	2	1	no	—
304	#121	—	2	1	no	—
305	#121	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
312	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	—	2	1	no	—
316	C₂×C₂²⋊C₄	—	2	1	no	—
317	C₂×C₂²⋊C₄	—	2	1	no	—
318	C₂×C₂²⋊C₄	—	2	1	no	—
319	C₂×C₄²	—	2	1	no	—
320	C₂×C₄²	—	2	1	no	—
321	C₂×C₄²	—	2	1	no	—
322	C₂×C₄²	—	2	1	no	—
323	C₂×C₄²	—	2	1	no	—
324	C₂×C₄²	—	2	1	no	—
325	#106	—	2	2	no	—
326	#103	—	2	2	no	—
327	#102	—	2	2	no	—
328	C₂²⋊C₈	—	2	1	no	—
329	C₂²⋊C₈	—	2	1	no	—
330	C₂²⋊C₈	—	2	1	no	—
331	C₂²⋊C₈	—	2	1	no	—
332	#95	—	2	2	no	—
333	#95	—	2	2	no	—
334	#95	—	2	2	no	—
335	#95	—	2	2	no	—
336	#95	D₄×C₁₉	1	2	yes	—
337	#95	D₄×C₁₉	1	2	yes	—
338	C₁₉	#10323	1	1	yes	characteristic, direct product factor, Sylow
339	C₂⁴	—	2	1	no	—
340	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
341	C₂×Q₈	—	2	1	no	—
342	C₂×Q₈	—	2	1	no	—
343	C₂×Q₈	—	4	2	no	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	—	4	2	no	—
347	C₂×D₄	—	4	1	no	—
348	C₂×D₄	—	4	1	no	—
349	C₂×D₄	—	4	1	no	—
350	C₂×D₄	—	4	1	no	—
351	C₂×D₄	—	4	1	no	—
352	C₂×D₄	—	4	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	4	2	no	—
368	C₂²×C₄	—	4	2	no	—
369	C₂²×C₄	SD₁₆×C₁₉	1	2	yes	complemented
370	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
373	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
374	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
375	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
376	SD₁₆	—	8	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	4	2	no	—
379	C₂×C₈	—	4	2	no	—
380	C₂×C₈	—	4	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	4	2	no	—
386	C₄⋊C₄	—	4	2	no	—
387	C₄⋊C₄	—	4	4	no	—
388	C₄⋊C₄	—	4	4	no	—
389	C₄⋊C₄	—	4	1	no	—
390	C₄⋊C₄	—	4	1	no	—
391	C₂²⋊C₄	—	4	4	no	—
392	C₂²⋊C₄	—	4	4	no	—
393	C₂²⋊C₄	—	4	1	no	—
394	C₂²⋊C₄	—	4	1	no	—
395	C₂²⋊C₄	—	4	1	no	—
396	C₂²⋊C₄	—	4	1	no	—
397	C₂²⋊C₄	—	4	1	no	—
398	C₂²⋊C₄	—	4	1	no	—
399	C₂²⋊C₄	—	4	1	no	—
400	C₂²⋊C₄	—	4	1	no	—
401	C₄²	—	4	1	no	—
402	C₄²	—	4	1	no	—
403	C₄²	—	4	1	no	—
404	C₄²	—	4	1	no	—
405	C₂³	—	4	1	no	—
406	C₂³	—	4	1	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	—	4	1	no	—
410	C₂³	—	4	1	no	—
411	C₂³	—	4	1	no	—
412	C₂³	C₁₉×#120	1	1	yes	characteristic
413	C₂³	C₁₉×#120	1	1	yes	characteristic
414	C₂³	C₁₉×#121	1	1	yes	characteristic
415	C₂³	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
416	C₂³	C₁₉×#135	1	1	yes	characteristic
417	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
418	C₂³	C₁₉×#137	1	1	yes	characteristic
419	Q₈	—	4	2	no	—
420	Q₈	—	8	1	no	—
421	D₄	—	4	2	no	—
422	D₄	—	8	1	no	—
423	D₄	—	8	1	no	—
424	D₄	—	8	1	no	—
425	D₄	—	8	1	no	—
426	D₄	—	8	1	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
461	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
462	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
463	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
464	C₈	—	4	2	no	—
465	C₈	—	8	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	4	1	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	4	1	no	—
475	C₂²	—	4	1	no	—
476	C₂²	—	8	2	no	—
477	C₂²	—	8	2	no	—
478	C₂²	—	8	1	no	—
479	C₂²	—	8	1	no	—
480	C₂²	—	8	1	no	—
481	C₂²	C₁₉×#392	1	1	yes	characteristic
482	C₂²	C₁₉×#448	1	1	yes	characteristic
483	C₂²	C₁₉×#449	1	1	yes	characteristic
484	C₂²	C₁₉×#450	1	1	yes	characteristic
485	C₂²	C₁₉×#452	1	1	yes	characteristic
486	C₂²	C₁₉×#465	1	1	yes	characteristic
487	C₂²	C₁₉×#468	1	1	yes	characteristic
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	4	2	no	—
492	C₄	—	4	2	no	—
493	C₄	—	8	2	no	—
494	C₄	—	8	2	no	—
495	C₄	—	8	1	no	—
496	C₄	—	8	1	no	—
497	C₄	—	8	1	no	—
498	C₄	C₁₉×#458	1	2	yes	—
499	C₂	—	2	1	no	—
500	C₂	—	2	1	no	—
501	C₂	—	2	1	no	—
502	C₂	—	2	1	no	—
503	C₂	—	2	1	no	—
504	C₂	—	2	1	no	—
505	C₂	—	16	1	no	—
506	C₂	C₁₉×#2000	1	1	yes	characteristic
507	C₂	C₁₉×#2010	1	1	yes	characteristic
508	C₂	C₁₉×#2022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂×C₁₉×#121	C₂²
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2855	C₂	semidirect
4. C₁₉×#1817	C₂	semidirect
5. C₁₉×#1520	C₂	semidirect
7. C₁₉×#1289	C₂	semidirect
114. C₂²×C₄×C₁₉	SD₁₆	semidirect
150. #10323	C₁₉	direct (N × H)
213. #2855	C₂×C₁₉	semidirect
215. #1817	C₂×C₁₉	semidirect
216. #1520	C₂×C₁₉	semidirect
218. #1289	C₂×C₁₉	semidirect
338. C₁₉	#10323	direct (N × H)
369. C₂²×C₄	SD₁₆×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3187	2
C₁₉×#2855	2
C₁₉×#2854	2
C₁₉×#1817	2
C₁₉×#1520	2
C₁₉×#1519	2
C₁₉×#1289	2
#10323	19

Subgroups — C19×#10323 #18016282

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10323 #18016282