Subgroups — C₁₉×#18360 #18024319

Order 4864.

928 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3215	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3213	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2632	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1603	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1597	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1515	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1514	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1467	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#559	—	2	1	no	—
11	C₁₉×#557	—	2	1	no	—
12	C₁₉×#556	—	2	1	no	—
13	C₁₉×#556	—	2	2	no	—
14	C₁₉×#554	—	2	1	no	—
15	C₁₉×#552	—	2	2	no	—
16	C₁₉×#539	C₂²	1	4	yes	—
17	C₁₉×#536	—	2	1	no	—
18	C₁₉×#533	C₂²	1	1	yes	characteristic
19	C₁₉×#532	C₂²	1	1	yes	characteristic
20	C₁₉×#529	—	2	2	no	—
21	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
22	C₁₉×#520	—	2	1	no	—
23	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#497	—	2	1	no	—
25	C₁₉×#496	—	2	1	no	—
26	C₁₉×#489	—	2	1	no	—
27	C₁₉×#489	—	2	1	no	—
28	C₁₉×#464	—	2	2	no	—
29	C₁₉×#463	—	2	2	no	—
30	C₁₉×#451	C₂²	1	2	yes	—
31	C₁₉×#450	C₂²	1	2	yes	—
32	C₁₉×#448	C₂²	1	2	yes	—
33	C₁₉×#447	C₂²	1	2	yes	—
34	C₁₉×#432	C₂²	1	1	yes	characteristic
35	C₁₉×#432	C₂²	1	1	yes	characteristic
36	C₁₉×#399	—	2	1	no	—
37	C₁₉×#395	C₂²	1	2	yes	—
38	C₁₉×#394	C₂²	1	2	yes	—
39	C₁₉×#393	—	2	1	no	—
40	C₁₉×#388	—	2	2	no	—
41	C₁₉×#383	C₂²	1	1	yes	characteristic
42	C₁₉×#328	C₂²	1	4	yes	—
43	C₁₉×#327	C₂²	1	4	yes	—
44	C₁₉×#324	C₂²	1	4	yes	—
45	C₂×#41×C₁₉	—	2	1	no	—
46	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
47	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
49	C₂×Q₁₆×C₁₉	—	2	2	no	—
50	C₂×SD₁₆×C₁₉	—	2	2	no	—
51	C₂×SD₁₆×C₁₉	—	2	2	no	—
52	C₂×D₈×C₁₉	—	2	2	no	—
53	C₁₉×C₄⋊Q₈	—	2	2	no	—
54	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
55	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
56	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
57	C₁₉×#127	D₄	1	1	yes	characteristic
58	C₁₉×#126	—	2	4	no	—
59	C₁₉×#126	—	2	4	no	—
60	C₁₉×#125	—	2	2	no	—
61	C₁₉×#125	—	2	4	no	—
62	C₁₉×#125	—	2	1	no	—
63	C₁₉×#124	—	2	2	no	—
64	C₁₉×#124	—	2	2	no	—
65	C₁₉×#124	—	2	1	no	—
66	C₁₉×#124	—	2	1	no	—
67	C₁₉×#124	—	2	1	no	—
68	C₁₉×#124	—	2	1	no	—
69	C₁₉×#124	—	2	1	no	—
70	C₁₉×#123	—	2	4	no	—
71	C₁₉×#123	—	2	4	no	—
72	C₁₉×C₂²⋊Q₈	—	2	2	no	—
73	C₁₉×C₂²⋊Q₈	—	2	2	no	—
74	C₁₉×C₂²⋊Q₈	—	2	4	no	—
75	C₁₉×C₂²⋊Q₈	—	2	1	no	—
76	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
77	C₁₉×#121	—	2	1	no	—
78	C₁₉×#121	C₂³	1	2	yes	—
79	C₄×Q₈×C₁₉	—	2	2	no	—
80	C₄×Q₈×C₁₉	—	2	2	no	—
81	C₄×Q₈×C₁₉	—	2	1	no	—
82	C₄×Q₈×C₁₉	—	2	1	no	—
83	C₄×Q₈×C₁₉	—	2	1	no	—
84	C₄×Q₈×C₁₉	—	2	1	no	—
85	C₄×Q₈×C₁₉	—	2	1	no	—
86	C₄×Q₈×C₁₉	D₄	1	2	yes	—
87	C₄×D₄×C₁₉	—	2	2	no	—
88	C₄×D₄×C₁₉	—	2	2	no	—
89	C₄×D₄×C₁₉	—	2	4	no	—
90	C₄×D₄×C₁₉	—	2	1	no	—
91	C₄×D₄×C₁₉	D₄	1	2	yes	—
92	C₁₉×#117	—	2	2	no	—
93	C₁₉×#117	—	2	4	no	—
94	C₁₉×#117	—	2	1	no	—
95	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
96	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
97	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
99	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
101	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
103	C₂×C₄²×C₁₉	D₄	1	2	yes	—
104	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
105	C₁₉×C₄⋊C₈	—	2	1	no	—
106	C₁₉×C₄⋊C₈	—	2	1	no	—
107	C₁₉×#103	—	2	2	no	—
108	C₁₉×#103	—	2	2	no	—
109	C₁₉×#102	—	2	2	no	—
110	C₁₉×#102	—	2	2	no	—
111	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
112	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
113	C₁₉×#97	—	2	1	no	—
114	C₁₉×#97	—	2	1	no	—
115	C₁₉×#95	—	2	1	no	—
116	C₁₉×#95	—	2	1	no	—
117	C₁₉×#95	—	2	2	no	—
118	C₁₉×#95	C₂³	1	2	yes	—
119	C₂⁴×C₁₉	—	2	1	no	—
120	#41×C₁₉	—	4	4	no	—
121	C₂×Q₈×C₁₉	—	2	1	no	—
122	C₂×Q₈×C₁₉	—	2	1	no	—
123	C₂×Q₈×C₁₉	—	2	1	no	—
124	C₂×Q₈×C₁₉	—	2	1	no	—
125	C₂×Q₈×C₁₉	—	2	1	no	—
126	C₂×Q₈×C₁₉	—	2	1	no	—
127	C₂×Q₈×C₁₉	—	4	2	no	—
128	C₂×Q₈×C₁₉	—	8	1	no	—
129	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
130	C₂×D₄×C₁₉	—	2	2	no	—
131	C₂×D₄×C₁₉	—	2	1	no	—
132	C₂×D₄×C₁₉	—	2	1	no	—
133	C₂×D₄×C₁₉	—	2	1	no	—
134	C₂×D₄×C₁₉	—	2	1	no	—
135	C₂×D₄×C₁₉	—	8	1	no	—
136	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₁₉	—	2	4	no	—
138	C₂²×C₄×C₁₉	—	2	2	no	—
139	C₂²×C₄×C₁₉	—	2	1	no	—
140	C₂²×C₄×C₁₉	—	2	2	no	—
141	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
146	Q₁₆×C₁₉	—	8	2	no	—
147	SD₁₆×C₁₉	—	8	2	no	—
148	SD₁₆×C₁₉	—	8	2	no	—
149	D₈×C₁₉	—	8	2	no	—
150	C₂×C₈×C₁₉	—	2	2	no	—
151	C₂×C₈×C₁₉	—	2	2	no	—
152	C₄⋊C₄×C₁₉	—	2	4	no	—
153	C₄⋊C₄×C₁₉	—	2	4	no	—
154	C₄⋊C₄×C₁₉	—	2	4	no	—
155	C₄⋊C₄×C₁₉	—	2	1	no	—
156	C₄⋊C₄×C₁₉	—	2	1	no	—
157	C₄⋊C₄×C₁₉	—	2	1	no	—
158	C₄⋊C₄×C₁₉	—	2	1	no	—
159	C₄⋊C₄×C₁₉	—	2	2	no	—
160	C₄⋊C₄×C₁₉	—	2	1	no	—
161	C₄⋊C₄×C₁₉	—	2	1	no	—
162	C₄⋊C₄×C₁₉	—	2	2	no	—
163	C₄⋊C₄×C₁₉	—	2	2	no	—
164	C₄⋊C₄×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	8	2	no	—
166	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
167	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
168	C₂²⋊C₄×C₁₉	—	2	4	no	—
169	C₂²⋊C₄×C₁₉	—	2	4	no	—
170	C₂²⋊C₄×C₁₉	—	2	4	no	—
171	C₂²⋊C₄×C₁₉	—	2	2	no	—
172	C₂²⋊C₄×C₁₉	—	2	2	no	—
173	C₂²⋊C₄×C₁₉	—	2	2	no	—
174	C₂²⋊C₄×C₁₉	—	4	4	no	—
175	C₂²⋊C₄×C₁₉	—	4	1	no	—
176	C₂²⋊C₄×C₁₉	—	4	1	no	—
177	C₂²⋊C₄×C₁₉	—	4	1	no	—
178	C₂²⋊C₄×C₁₉	—	4	1	no	—
179	C₂²⋊C₄×C₁₉	—	8	2	no	—
180	C₄²×C₁₉	—	2	4	no	—
181	C₄²×C₁₉	—	2	2	no	—
182	C₄²×C₁₉	—	2	2	no	—
183	C₄²×C₁₉	—	2	2	no	—
184	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
185	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
186	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
187	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
188	#18360	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₂³×C₁₉	—	2	2	no	—
190	C₂³×C₁₉	—	4	2	no	—
191	C₂³×C₁₉	—	4	2	no	—
192	C₂³×C₁₉	—	4	1	no	—
193	C₂³×C₁₉	—	4	2	no	—
194	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
195	Q₈×C₁₉	—	4	2	no	—
196	Q₈×C₁₉	—	4	2	no	—
197	Q₈×C₁₉	—	4	2	no	—
198	Q₈×C₁₉	—	4	2	no	—
199	Q₈×C₁₉	—	4	2	no	—
200	Q₈×C₁₉	—	4	2	no	—
201	Q₈×C₁₉	—	4	2	no	—
202	D₄×C₁₉	—	4	2	no	—
203	D₄×C₁₉	—	4	2	no	—
204	D₄×C₁₉	—	4	2	no	—
205	D₄×C₁₉	—	4	2	no	—
206	D₄×C₁₉	—	4	2	no	—
207	D₄×C₁₉	—	4	4	no	—
208	C₂×C₄×C₁₉	—	2	2	no	—
209	C₂×C₄×C₁₉	—	2	2	no	—
210	C₂×C₄×C₁₉	—	2	2	no	—
211	C₂×C₄×C₁₉	—	2	2	no	—
212	C₂×C₄×C₁₉	—	2	2	no	—
213	C₂×C₄×C₁₉	—	2	2	no	—
214	C₂×C₄×C₁₉	—	2	2	no	—
215	C₂×C₄×C₁₉	—	2	2	no	—
216	C₂×C₄×C₁₉	—	4	1	no	—
217	C₂×C₄×C₁₉	—	4	1	no	—
218	C₂×C₄×C₁₉	—	4	4	no	—
219	C₂×C₄×C₁₉	—	4	2	no	—
220	C₂×C₄×C₁₉	—	4	2	no	—
221	C₂×C₄×C₁₉	—	4	2	no	—
222	C₂×C₄×C₁₉	—	4	2	no	—
223	C₂×C₄×C₁₉	—	4	1	no	—
224	C₂×C₄×C₁₉	—	4	2	no	—
225	C₂×C₄×C₁₉	—	8	4	no	—
226	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
227	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
228	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
229	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
230	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
232	C₈×C₁₉	—	4	2	no	—
233	C₈×C₁₉	—	4	2	no	—
234	#3507	C₂×C₁₉	1	1	yes	characteristic, complemented
235	#3215	C₂×C₁₉	1	1	yes	characteristic, complemented
236	#3213	C₂×C₁₉	1	1	yes	characteristic
237	#2632	C₂×C₁₉	1	1	yes	characteristic, complemented
238	#1603	C₂×C₁₉	1	4	yes	complemented
239	#1597	C₂×C₁₉	1	4	yes	complemented
240	#1515	C₂×C₁₉	1	1	yes	characteristic, complemented
241	#1514	C₂×C₁₉	1	1	yes	characteristic, complemented
242	#1467	C₂×C₁₉	1	1	yes	characteristic, complemented
243	C₂²×C₁₉	—	2	1	no	—
244	C₂²×C₁₉	—	2	1	no	—
245	C₂²×C₁₉	—	4	2	no	—
246	C₂²×C₁₉	—	4	2	no	—
247	C₂²×C₁₉	—	4	2	no	—
248	C₂²×C₁₉	—	8	4	no	—
249	C₂²×C₁₉	—	8	1	no	—
250	C₂²×C₁₉	—	8	1	no	—
251	C₂²×C₁₉	—	8	1	no	—
252	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
253	C₂²×C₁₉	#575	1	2	yes	—
254	C₄×C₁₉	—	2	1	no	—
255	C₄×C₁₉	—	2	1	no	—
256	C₄×C₁₉	—	2	1	no	—
257	C₄×C₁₉	—	2	1	no	—
258	C₄×C₁₉	—	2	1	no	—
259	C₄×C₁₉	—	2	1	no	—
260	C₄×C₁₉	—	4	2	no	—
261	C₄×C₁₉	—	4	2	no	—
262	C₄×C₁₉	—	4	2	no	—
263	C₄×C₁₉	—	4	2	no	—
264	C₄×C₁₉	—	4	2	no	—
265	C₄×C₁₉	—	8	2	no	—
266	C₄×C₁₉	—	8	1	no	—
267	#559	—	2	1	no	—
268	#557	—	2	1	no	—
269	#556	—	2	1	no	—
270	#556	—	2	2	no	—
271	#554	—	2	1	no	—
272	#552	—	2	2	no	—
273	#539	C₂²×C₁₉	1	4	yes	—
274	#536	—	2	1	no	—
275	#533	C₂²×C₁₉	1	1	yes	characteristic
276	#532	C₂²×C₁₉	1	1	yes	characteristic
277	#529	—	2	2	no	—
278	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
279	#520	—	2	1	no	—
280	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
281	#497	—	2	1	no	—
282	#496	—	2	1	no	—
283	#489	—	2	1	no	—
284	#489	—	2	1	no	—
285	#464	—	2	2	no	—
286	#463	—	2	2	no	—
287	#451	C₂²×C₁₉	1	2	yes	—
288	#450	C₂²×C₁₉	1	2	yes	—
289	#448	C₂²×C₁₉	1	2	yes	—
290	#447	C₂²×C₁₉	1	2	yes	—
291	#432	C₂²×C₁₉	1	1	yes	characteristic
292	#432	C₂²×C₁₉	1	1	yes	characteristic
293	#399	—	2	1	no	—
294	#395	C₂²×C₁₉	1	2	yes	—
295	#394	C₂²×C₁₉	1	2	yes	—
296	#393	—	2	1	no	—
297	#388	—	2	2	no	—
298	#383	C₂²×C₁₉	1	1	yes	characteristic
299	#328	C₂²×C₁₉	1	4	yes	—
300	#327	C₂²×C₁₉	1	4	yes	—
301	#324	C₂²×C₁₉	1	4	yes	—
302	C₂×C₁₉	—	2	2	no	—
303	C₂×C₁₉	—	8	2	no	—
304	C₂×C₁₉	—	16	1	no	—
305	C₂×C₁₉	#3005	1	1	yes	characteristic
306	C₂×C₁₉	#3020	1	1	yes	characteristic
307	C₂×C₁₉	#3027	1	1	yes	characteristic
308	C₂×#41	—	2	1	no	—
309	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
310	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
311	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
312	C₂×Q₁₆	—	2	2	no	—
313	C₂×SD₁₆	—	2	2	no	—
314	C₂×SD₁₆	—	2	2	no	—
315	C₂×D₈	—	2	2	no	—
316	C₄⋊Q₈	—	2	2	no	—
317	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
318	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
319	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
320	#127	D₄×C₁₉	1	1	yes	characteristic
321	#126	—	2	4	no	—
322	#126	—	2	4	no	—
323	#125	—	2	2	no	—
324	#125	—	2	4	no	—
325	#125	—	2	1	no	—
326	#124	—	2	2	no	—
327	#124	—	2	2	no	—
328	#124	—	2	1	no	—
329	#124	—	2	1	no	—
330	#124	—	2	1	no	—
331	#124	—	2	1	no	—
332	#124	—	2	1	no	—
333	#123	—	2	4	no	—
334	#123	—	2	4	no	—
335	C₂²⋊Q₈	—	2	2	no	—
336	C₂²⋊Q₈	—	2	2	no	—
337	C₂²⋊Q₈	—	2	4	no	—
338	C₂²⋊Q₈	—	2	1	no	—
339	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
340	#121	—	2	1	no	—
341	#121	C₂³×C₁₉	1	2	yes	—
342	C₄×Q₈	—	2	2	no	—
343	C₄×Q₈	—	2	2	no	—
344	C₄×Q₈	—	2	1	no	—
345	C₄×Q₈	—	2	1	no	—
346	C₄×Q₈	—	2	1	no	—
347	C₄×Q₈	—	2	1	no	—
348	C₄×Q₈	—	2	1	no	—
349	C₄×Q₈	D₄×C₁₉	1	2	yes	—
350	C₄×D₄	—	2	2	no	—
351	C₄×D₄	—	2	2	no	—
352	C₄×D₄	—	2	4	no	—
353	C₄×D₄	—	2	1	no	—
354	C₄×D₄	D₄×C₁₉	1	2	yes	—
355	#117	—	2	2	no	—
356	#117	—	2	4	no	—
357	#117	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	2	no	—
359	C₂×C₄⋊C₄	—	2	2	no	—
360	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
362	C₂×C₂²⋊C₄	—	2	1	no	—
363	C₂×C₂²⋊C₄	—	2	1	no	—
364	C₂×C₂²⋊C₄	—	2	2	no	—
365	C₂×C₂²⋊C₄	—	2	2	no	—
366	C₂×C₄²	D₄×C₁₉	1	2	yes	—
367	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
368	C₄⋊C₈	—	2	1	no	—
369	C₄⋊C₈	—	2	1	no	—
370	#103	—	2	2	no	—
371	#103	—	2	2	no	—
372	#102	—	2	2	no	—
373	#102	—	2	2	no	—
374	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
375	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
376	#97	—	2	1	no	—
377	#97	—	2	1	no	—
378	#95	—	2	1	no	—
379	#95	—	2	1	no	—
380	#95	—	2	2	no	—
381	#95	C₂³×C₁₉	1	2	yes	—
382	C₁₉	#18360	1	1	yes	characteristic, direct product factor, Sylow
383	C₂⁴	—	2	1	no	—
384	#41	—	4	4	no	—
385	C₂×Q₈	—	2	1	no	—
386	C₂×Q₈	—	2	1	no	—
387	C₂×Q₈	—	2	1	no	—
388	C₂×Q₈	—	2	1	no	—
389	C₂×Q₈	—	2	1	no	—
390	C₂×Q₈	—	2	1	no	—
391	C₂×Q₈	—	4	2	no	—
392	C₂×Q₈	—	8	1	no	—
393	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	2	1	no	—
399	C₂×D₄	—	8	1	no	—
400	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
401	C₂²×C₄	—	2	4	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
406	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
407	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
408	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
409	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
410	Q₁₆	—	8	2	no	—
411	SD₁₆	—	8	2	no	—
412	SD₁₆	—	8	2	no	—
413	D₈	—	8	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₄⋊C₄	—	2	4	no	—
417	C₄⋊C₄	—	2	4	no	—
418	C₄⋊C₄	—	2	4	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	8	2	no	—
430	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
431	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
432	C₂²⋊C₄	—	2	4	no	—
433	C₂²⋊C₄	—	2	4	no	—
434	C₂²⋊C₄	—	2	4	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	2	2	no	—
437	C₂²⋊C₄	—	2	2	no	—
438	C₂²⋊C₄	—	4	4	no	—
439	C₂²⋊C₄	—	4	1	no	—
440	C₂²⋊C₄	—	4	1	no	—
441	C₂²⋊C₄	—	4	1	no	—
442	C₂²⋊C₄	—	4	1	no	—
443	C₂²⋊C₄	—	8	2	no	—
444	C₄²	—	2	4	no	—
445	C₄²	—	2	2	no	—
446	C₄²	—	2	2	no	—
447	C₄²	—	2	2	no	—
448	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
449	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
450	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
451	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
452	C₂³	—	2	2	no	—
453	C₂³	—	4	2	no	—
454	C₂³	—	4	2	no	—
455	C₂³	—	4	1	no	—
456	C₂³	—	4	2	no	—
457	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
458	Q₈	—	4	2	no	—
459	Q₈	—	4	2	no	—
460	Q₈	—	4	2	no	—
461	Q₈	—	4	2	no	—
462	Q₈	—	4	2	no	—
463	Q₈	—	4	2	no	—
464	Q₈	—	4	2	no	—
465	D₄	—	4	2	no	—
466	D₄	—	4	2	no	—
467	D₄	—	4	2	no	—
468	D₄	—	4	2	no	—
469	D₄	—	4	2	no	—
470	D₄	—	4	4	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	4	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	8	4	no	—
489	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
490	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
491	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
492	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
493	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
494	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
495	C₈	—	4	2	no	—
496	C₈	—	4	2	no	—
497	C₂²	—	2	1	no	—
498	C₂²	—	2	1	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	2	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	8	4	no	—
503	C₂²	—	8	1	no	—
504	C₂²	—	8	1	no	—
505	C₂²	—	8	1	no	—
506	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
507	C₂²	C₁₉×#575	1	2	yes	—
508	C₄	—	2	1	no	—
509	C₄	—	2	1	no	—
510	C₄	—	2	1	no	—
511	C₄	—	2	1	no	—
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	4	2	no	—
515	C₄	—	4	2	no	—
516	C₄	—	4	2	no	—
517	C₄	—	4	2	no	—
518	C₄	—	4	2	no	—
519	C₄	—	8	2	no	—
520	C₄	—	8	1	no	—
521	C₂	—	2	2	no	—
522	C₂	—	8	2	no	—
523	C₂	—	16	1	no	—
524	C₂	C₁₉×#3005	1	1	yes	characteristic
525	C₂	C₁₉×#3020	1	1	yes	characteristic
526	C₂	C₁₉×#3027	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#3213	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3507	C₂	semidirect
2. C₁₉×#3215	C₂	semidirect
4. C₁₉×#2632	C₂	semidirect
5. C₁₉×#1603	C₂	semidirect
6. C₁₉×#1597	C₂	semidirect
7. C₁₉×#1515	C₂	semidirect
8. C₁₉×#1514	C₂	semidirect
9. C₁₉×#1467	C₂	semidirect
188. #18360	C₁₉	direct (N × H)
234. #3507	C₂×C₁₉	semidirect
235. #3215	C₂×C₁₉	semidirect
237. #2632	C₂×C₁₉	semidirect
238. #1603	C₂×C₁₉	semidirect
239. #1597	C₂×C₁₉	semidirect
240. #1515	C₂×C₁₉	semidirect
241. #1514	C₂×C₁₉	semidirect
242. #1467	C₂×C₁₉	semidirect
382. C₁₉	#18360	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3507	2
C₁₉×#3215	2
C₁₉×#3213	2
C₁₉×#2632	2
C₁₉×#1603	2
C₁₉×#1597	2
C₁₉×#1515	2
C₁₉×#1514	2
C₁₉×#1467	2
#18360	19

Subgroups — C19×#18360 #18024319

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18360 #18024319