Subgroups — C₁₉×#8414 #18014373

Order 4864.

758 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3517	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1759	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1529	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1505	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1500	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1488	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1484	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#557	C₄	1	1	yes	characteristic, complemented
9	C₁₉×#553	—	2	2	no	—
10	C₁₉×#553	—	2	1	no	—
11	C₁₉×#550	—	2	1	no	—
12	C₁₉×#550	—	2	1	no	—
13	C₁₉×#550	C₄	1	1	yes	characteristic, complemented
14	C₁₉×#550	C₄	1	1	yes	characteristic, complemented
15	C₁₉×#547	—	2	1	no	—
16	C₁₉×#547	C₄	1	1	yes	characteristic, complemented
17	C₁₉×#540	—	2	2	no	—
18	C₁₉×#540	—	2	1	no	—
19	C₁₉×#532	—	2	1	no	—
20	C₁₉×#532	C₂²	1	1	yes	characteristic
21	C₁₉×#529	—	2	1	no	—
22	C₁₉×#529	C₂²	1	1	yes	characteristic
23	C₁₉×#520	—	2	1	no	—
24	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#432	C₂²	1	1	yes	characteristic
26	C₁₉×#431	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#104	—	2	1	no	—
28	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
29	C₁₉×#376	C₂²	1	1	yes	characteristic
30	C₁₉×#339	—	2	1	no	—
31	C₁₉×#330	—	2	1	no	—
32	C₁₉×#329	—	2	1	no	—
33	C₁₉×#328	—	2	1	no	—
34	C₁₉×#327	—	2	1	no	—
35	C₁₉×#327	—	2	2	no	—
36	C₁₉×Q₈⋊C₈	—	2	1	no	—
37	C₁₉×D₄⋊C₈	—	2	2	no	—
38	C₁₉×D₄⋊C₈	—	2	1	no	—
39	C₂×#41×C₁₉	—	2	1	no	—
40	C₂×#41×C₁₉	—	2	1	no	—
41	C₂×#41×C₁₉	—	2	1	no	—
42	C₂×#41×C₁₉	—	2	1	no	—
43	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
44	C₂×M₁₆×C₁₉	—	2	1	no	—
45	C₁₉×C₄⋊Q₈	—	2	1	no	—
46	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
47	C₁₉×#127	—	2	2	no	—
48	C₁₉×#127	—	2	1	no	—
49	C₁₉×#127	—	2	1	no	—
50	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
51	C₁₉×#126	—	2	2	no	—
52	C₁₉×#126	—	2	1	no	—
53	C₁₉×#125	—	2	2	no	—
54	C₁₉×#125	—	2	1	no	—
55	C₁₉×#125	D₄	1	1	yes	characteristic
56	C₁₉×#124	—	2	1	no	—
57	C₁₉×#124	D₄	1	1	yes	characteristic
58	C₁₉×#123	—	2	2	no	—
59	C₁₉×#123	—	2	2	no	—
60	C₁₉×#123	—	2	2	no	—
61	C₁₉×#123	—	2	1	no	—
62	C₁₉×#123	—	2	2	no	—
63	C₁₉×C₂²⋊Q₈	—	2	1	no	—
64	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
65	C₁₉×#121	—	2	2	no	—
66	C₁₉×#121	—	2	2	no	—
67	C₁₉×#121	—	2	2	no	—
68	C₁₉×#121	—	2	2	no	—
69	C₁₉×#121	—	2	2	no	—
70	C₁₉×#121	—	2	1	no	—
71	C₁₉×#121	—	2	2	no	—
72	C₁₉×#121	—	2	2	no	—
73	C₁₉×#121	—	2	1	no	—
74	C₁₉×#121	—	2	1	no	—
75	C₁₉×#121	—	2	1	no	—
76	C₁₉×#121	D₄	1	1	yes	characteristic
77	C₁₉×#121	D₄	1	2	yes	—
78	C₄×Q₈×C₁₉	—	2	1	no	—
79	C₄×Q₈×C₁₉	—	2	1	no	—
80	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
81	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
82	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
83	C₄×D₄×C₁₉	—	2	2	no	—
84	C₄×D₄×C₁₉	—	2	2	no	—
85	C₄×D₄×C₁₉	—	2	2	no	—
86	C₄×D₄×C₁₉	—	2	2	no	—
87	C₄×D₄×C₁₉	—	2	1	no	—
88	C₄×D₄×C₁₉	—	2	1	no	—
89	C₄×D₄×C₁₉	—	2	1	no	—
90	C₄×D₄×C₁₉	—	2	1	no	—
91	C₄×D₄×C₁₉	—	2	1	no	—
92	C₄×D₄×C₁₉	—	2	1	no	—
93	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
94	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
95	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
96	C₄×D₄×C₁₉	D₄	1	2	yes	—
97	C₁₉×#117	—	2	2	no	—
98	C₁₉×#117	—	2	1	no	—
99	C₁₉×#117	—	2	1	no	—
100	C₁₉×#117	D₄	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
102	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
103	C₂×C₄²×C₁₉	—	2	1	no	—
104	C₂×C₄²×C₁₉	—	2	1	no	—
105	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
106	C₁₉×C₄⋊C₈	—	2	1	no	—
107	C₁₉×C₄⋊C₈	—	2	1	no	—
108	C₁₉×#104	—	2	4	no	—
109	C₁₉×C₂²⋊C₈	—	2	1	no	—
110	C₁₉×C₂²⋊C₈	—	2	1	no	—
111	C₁₉×#97	—	2	1	no	—
112	C₁₉×#97	—	2	1	no	—
113	C₄×C₈×C₁₉	—	2	1	no	—
114	C₄×C₈×C₁₉	—	2	1	no	—
115	C₁₉×#95	—	2	1	no	—
116	C₁₉×#95	—	2	1	no	—
117	#41×C₁₉	—	2	2	no	—
118	#41×C₁₉	—	4	1	no	—
119	#41×C₁₉	—	4	2	no	—
120	#41×C₁₉	—	4	2	no	—
121	#41×C₁₉	—	8	2	no	—
122	#41×C₁₉	—	8	2	no	—
123	#41×C₁₉	—	8	2	no	—
124	C₂×Q₈×C₁₉	—	2	1	no	—
125	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
126	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
127	C₂×D₄×C₁₉	—	2	2	no	—
128	C₂×D₄×C₁₉	—	2	1	no	—
129	C₂×D₄×C₁₉	—	2	2	no	—
130	C₂×D₄×C₁₉	—	2	2	no	—
131	C₂×D₄×C₁₉	—	2	2	no	—
132	C₂×D₄×C₁₉	—	2	2	no	—
133	C₂×D₄×C₁₉	—	2	1	no	—
134	C₂×D₄×C₁₉	—	2	2	no	—
135	C₂×D₄×C₁₉	—	2	1	no	—
136	C₂×D₄×C₁₉	—	2	1	no	—
137	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
138	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
139	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
140	C₂²×C₄×C₁₉	—	2	2	no	—
141	C₂²×C₄×C₁₉	—	2	2	no	—
142	C₂²×C₄×C₁₉	—	2	2	no	—
143	C₂²×C₄×C₁₉	—	2	1	no	—
144	C₂²×C₄×C₁₉	—	2	1	no	—
145	C₂²×C₄×C₁₉	—	2	1	no	—
146	C₂²×C₄×C₁₉	—	2	1	no	—
147	C₂²×C₄×C₁₉	—	2	2	no	—
148	C₂²×C₄×C₁₉	—	4	1	no	—
149	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	M₁₆×C₁₉	—	2	2	no	—
153	M₁₆×C₁₉	—	4	1	no	—
154	C₂×C₈×C₁₉	—	4	1	no	—
155	C₂×C₈×C₁₉	—	4	1	no	—
156	C₂×C₈×C₁₉	—	4	1	no	—
157	C₄⋊C₄×C₁₉	—	2	2	no	—
158	C₄⋊C₄×C₁₉	—	2	2	no	—
159	C₄⋊C₄×C₁₉	—	2	2	no	—
160	C₄⋊C₄×C₁₉	—	2	2	no	—
161	C₄⋊C₄×C₁₉	—	2	1	no	—
162	C₄⋊C₄×C₁₉	—	2	1	no	—
163	C₄⋊C₄×C₁₉	—	2	1	no	—
164	C₄⋊C₄×C₁₉	—	2	1	no	—
165	C₄⋊C₄×C₁₉	—	2	1	no	—
166	C₄⋊C₄×C₁₉	—	2	1	no	—
167	C₄⋊C₄×C₁₉	—	2	1	no	—
168	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
169	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
170	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
171	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
172	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
173	C₂²⋊C₄×C₁₉	—	2	2	no	—
174	C₂²⋊C₄×C₁₉	—	2	2	no	—
175	C₂²⋊C₄×C₁₉	—	2	2	no	—
176	C₂²⋊C₄×C₁₉	—	2	1	no	—
177	C₂²⋊C₄×C₁₉	—	2	1	no	—
178	C₂²⋊C₄×C₁₉	—	2	1	no	—
179	C₂²⋊C₄×C₁₉	—	2	1	no	—
180	C₂²⋊C₄×C₁₉	—	2	1	no	—
181	C₂²⋊C₄×C₁₉	—	2	1	no	—
182	C₂²⋊C₄×C₁₉	—	2	2	no	—
183	C₂²⋊C₄×C₁₉	—	2	1	no	—
184	C₂²⋊C₄×C₁₉	—	2	1	no	—
185	C₂²⋊C₄×C₁₉	—	2	2	no	—
186	C₄²×C₁₉	—	2	2	no	—
187	C₄²×C₁₉	—	2	1	no	—
188	C₄²×C₁₉	—	2	1	no	—
189	C₄²×C₁₉	—	2	1	no	—
190	C₄²×C₁₉	—	2	1	no	—
191	C₄²×C₁₉	—	2	2	no	—
192	C₄²×C₁₉	—	4	1	no	—
193	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
194	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
195	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
196	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
197	#8414	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₂³×C₁₉	—	2	1	no	—
199	C₂³×C₁₉	—	2	2	no	—
200	C₂³×C₁₉	—	2	1	no	—
201	C₂³×C₁₉	#120	1	1	yes	characteristic
202	Q₈×C₁₉	—	2	1	no	—
203	Q₈×C₁₉	—	4	1	no	—
204	Q₈×C₁₉	—	4	2	no	—
205	Q₈×C₁₉	#104	1	2	yes	—
206	D₄×C₁₉	—	2	1	no	—
207	D₄×C₁₉	—	2	1	no	—
208	D₄×C₁₉	—	4	2	no	—
209	D₄×C₁₉	—	4	2	no	—
210	D₄×C₁₉	—	4	1	no	—
211	D₄×C₁₉	—	4	4	no	—
212	D₄×C₁₉	—	4	2	no	—
213	D₄×C₁₉	—	4	1	no	—
214	D₄×C₁₉	—	4	1	no	—
215	D₄×C₁₉	—	8	1	no	—
216	D₄×C₁₉	—	8	2	no	—
217	D₄×C₁₉	—	8	2	no	—
218	D₄×C₁₉	—	8	2	no	—
219	D₄×C₁₉	—	8	2	no	—
220	D₄×C₁₉	—	8	2	no	—
221	C₂×C₄×C₁₉	—	2	1	no	—
222	C₂×C₄×C₁₉	—	2	1	no	—
223	C₂×C₄×C₁₉	—	2	1	no	—
224	C₂×C₄×C₁₉	—	2	1	no	—
225	C₂×C₄×C₁₉	—	2	1	no	—
226	C₂×C₄×C₁₉	—	2	1	no	—
227	C₂×C₄×C₁₉	—	2	1	no	—
228	C₂×C₄×C₁₉	—	2	2	no	—
229	C₂×C₄×C₁₉	—	2	1	no	—
230	C₂×C₄×C₁₉	—	4	1	no	—
231	C₂×C₄×C₁₉	—	4	1	no	—
232	C₂×C₄×C₁₉	—	4	2	no	—
233	C₂×C₄×C₁₉	—	4	4	no	—
234	C₂×C₄×C₁₉	—	4	2	no	—
235	C₂×C₄×C₁₉	—	4	1	no	—
236	C₂×C₄×C₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	—	4	2	no	—
238	C₂×C₄×C₁₉	—	8	1	no	—
239	C₂×C₄×C₁₉	—	8	2	no	—
240	C₂×C₄×C₁₉	—	8	2	no	—
241	C₂×C₄×C₁₉	—	8	2	no	—
242	C₂×C₄×C₁₉	—	8	1	no	—
243	C₂×C₄×C₁₉	—	8	1	no	—
244	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
245	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
247	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
248	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
249	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
250	C₈×C₁₉	—	4	2	no	—
251	C₈×C₁₉	—	8	1	no	—
252	C₈×C₁₉	—	8	1	no	—
253	#3517	C₂×C₁₉	1	1	yes	characteristic
254	#1759	C₂×C₁₉	1	1	yes	characteristic, complemented
255	#1529	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#1505	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#1500	C₂×C₁₉	1	1	yes	characteristic, complemented
258	#1488	C₂×C₁₉	1	1	yes	characteristic, complemented
259	#1484	C₂×C₁₉	1	1	yes	characteristic, complemented
260	C₂²×C₁₉	—	2	1	no	—
261	C₂²×C₁₉	—	2	1	no	—
262	C₂²×C₁₉	—	2	1	no	—
263	C₂²×C₁₉	—	4	1	no	—
264	C₂²×C₁₉	—	4	2	no	—
265	C₂²×C₁₉	—	4	1	no	—
266	C₂²×C₁₉	—	4	1	no	—
267	C₂²×C₁₉	—	4	2	no	—
268	C₂²×C₁₉	—	4	1	no	—
269	C₂²×C₁₉	—	4	1	no	—
270	C₂²×C₁₉	—	4	2	no	—
271	C₂²×C₁₉	—	4	1	no	—
272	C₂²×C₁₉	#379	1	1	yes	characteristic
273	C₄×C₁₉	—	2	1	no	—
274	C₄×C₁₉	—	2	1	no	—
275	C₄×C₁₉	—	2	1	no	—
276	C₄×C₁₉	—	2	1	no	—
277	C₄×C₁₉	—	2	1	no	—
278	C₄×C₁₉	—	2	2	no	—
279	C₄×C₁₉	—	4	1	no	—
280	C₄×C₁₉	—	4	1	no	—
281	C₄×C₁₉	—	4	1	no	—
282	C₄×C₁₉	—	4	1	no	—
283	C₄×C₁₉	—	4	2	no	—
284	C₄×C₁₉	—	4	1	no	—
285	C₄×C₁₉	—	8	2	no	—
286	C₄×C₁₉	C₂×#104	1	1	yes	characteristic
287	C₄×C₁₉	#421	1	1	yes	characteristic
288	#557	C₄×C₁₉	1	1	yes	characteristic, complemented
289	#553	—	2	2	no	—
290	#553	—	2	1	no	—
291	#550	—	2	1	no	—
292	#550	—	2	1	no	—
293	#550	C₄×C₁₉	1	1	yes	characteristic, complemented
294	#550	C₄×C₁₉	1	1	yes	characteristic, complemented
295	#547	—	2	1	no	—
296	#547	C₄×C₁₉	1	1	yes	characteristic, complemented
297	#540	—	2	2	no	—
298	#540	—	2	1	no	—
299	#532	—	2	1	no	—
300	#532	C₂²×C₁₉	1	1	yes	characteristic
301	#529	—	2	1	no	—
302	#529	C₂²×C₁₉	1	1	yes	characteristic
303	#520	—	2	1	no	—
304	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
305	#432	C₂²×C₁₉	1	1	yes	characteristic
306	#431	C₂²×C₁₉	1	1	yes	characteristic
307	C₂×#104	—	2	1	no	—
308	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
309	#376	C₂²×C₁₉	1	1	yes	characteristic
310	#339	—	2	1	no	—
311	#330	—	2	1	no	—
312	#329	—	2	1	no	—
313	#328	—	2	1	no	—
314	#327	—	2	1	no	—
315	#327	—	2	2	no	—
316	Q₈⋊C₈	—	2	1	no	—
317	D₄⋊C₈	—	2	2	no	—
318	D₄⋊C₈	—	2	1	no	—
319	C₂×C₁₉	—	4	1	no	—
320	C₂×C₁₉	—	8	1	no	—
321	C₂×C₁₉	—	8	2	no	—
322	C₂×C₁₉	—	8	1	no	—
323	C₂×C₁₉	#1789	1	1	yes	characteristic
324	C₂×C₁₉	#1794	1	1	yes	characteristic
325	C₂×C₁₉	#1795	1	1	yes	characteristic
326	C₂×#41	—	2	1	no	—
327	C₂×#41	—	2	1	no	—
328	C₂×#41	—	2	1	no	—
329	C₂×#41	—	2	1	no	—
330	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
331	C₂×M₁₆	—	2	1	no	—
332	C₄⋊Q₈	—	2	1	no	—
333	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
334	#127	—	2	2	no	—
335	#127	—	2	1	no	—
336	#127	—	2	1	no	—
337	#127	C₂×C₄×C₁₉	1	1	yes	characteristic
338	#126	—	2	2	no	—
339	#126	—	2	1	no	—
340	#125	—	2	2	no	—
341	#125	—	2	1	no	—
342	#125	D₄×C₁₉	1	1	yes	characteristic
343	#124	—	2	1	no	—
344	#124	D₄×C₁₉	1	1	yes	characteristic
345	#123	—	2	2	no	—
346	#123	—	2	2	no	—
347	#123	—	2	2	no	—
348	#123	—	2	1	no	—
349	#123	—	2	2	no	—
350	C₂²⋊Q₈	—	2	1	no	—
351	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
352	#121	—	2	2	no	—
353	#121	—	2	2	no	—
354	#121	—	2	2	no	—
355	#121	—	2	2	no	—
356	#121	—	2	2	no	—
357	#121	—	2	1	no	—
358	#121	—	2	2	no	—
359	#121	—	2	2	no	—
360	#121	—	2	1	no	—
361	#121	—	2	1	no	—
362	#121	—	2	1	no	—
363	#121	D₄×C₁₉	1	1	yes	characteristic
364	#121	D₄×C₁₉	1	2	yes	—
365	C₄×Q₈	—	2	1	no	—
366	C₄×Q₈	—	2	1	no	—
367	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
368	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
369	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
370	C₄×D₄	—	2	2	no	—
371	C₄×D₄	—	2	2	no	—
372	C₄×D₄	—	2	2	no	—
373	C₄×D₄	—	2	2	no	—
374	C₄×D₄	—	2	1	no	—
375	C₄×D₄	—	2	1	no	—
376	C₄×D₄	—	2	1	no	—
377	C₄×D₄	—	2	1	no	—
378	C₄×D₄	—	2	1	no	—
379	C₄×D₄	—	2	1	no	—
380	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
381	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
382	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
383	C₄×D₄	D₄×C₁₉	1	2	yes	—
384	#117	—	2	2	no	—
385	#117	—	2	1	no	—
386	#117	—	2	1	no	—
387	#117	D₄×C₁₉	1	1	yes	characteristic
388	C₂×C₄⋊C₄	—	2	2	no	—
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄²	—	2	1	no	—
391	C₂×C₄²	—	2	1	no	—
392	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
393	C₄⋊C₈	—	2	1	no	—
394	C₄⋊C₈	—	2	1	no	—
395	#104	—	2	4	no	—
396	C₂²⋊C₈	—	2	1	no	—
397	C₂²⋊C₈	—	2	1	no	—
398	#97	—	2	1	no	—
399	#97	—	2	1	no	—
400	C₄×C₈	—	2	1	no	—
401	C₄×C₈	—	2	1	no	—
402	#95	—	2	1	no	—
403	#95	—	2	1	no	—
404	C₁₉	#8414	1	1	yes	characteristic, direct product factor, Sylow
405	#41	—	2	2	no	—
406	#41	—	4	1	no	—
407	#41	—	4	2	no	—
408	#41	—	4	2	no	—
409	#41	—	8	2	no	—
410	#41	—	8	2	no	—
411	#41	—	8	2	no	—
412	C₂×Q₈	—	2	1	no	—
413	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
414	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	2	no	—
421	C₂×D₄	—	2	1	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
426	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
427	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	4	1	no	—
437	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
439	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
440	M₁₆	—	2	2	no	—
441	M₁₆	—	4	1	no	—
442	C₂×C₈	—	4	1	no	—
443	C₂×C₈	—	4	1	no	—
444	C₂×C₈	—	4	1	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
457	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
458	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
459	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
460	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
461	C₂²⋊C₄	—	2	2	no	—
462	C₂²⋊C₄	—	2	2	no	—
463	C₂²⋊C₄	—	2	2	no	—
464	C₂²⋊C₄	—	2	1	no	—
465	C₂²⋊C₄	—	2	1	no	—
466	C₂²⋊C₄	—	2	1	no	—
467	C₂²⋊C₄	—	2	1	no	—
468	C₂²⋊C₄	—	2	1	no	—
469	C₂²⋊C₄	—	2	1	no	—
470	C₂²⋊C₄	—	2	2	no	—
471	C₂²⋊C₄	—	2	1	no	—
472	C₂²⋊C₄	—	2	1	no	—
473	C₂²⋊C₄	—	2	2	no	—
474	C₄²	—	2	2	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	2	2	no	—
480	C₄²	—	4	1	no	—
481	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
482	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
483	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
484	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
485	C₂³	—	2	1	no	—
486	C₂³	—	2	2	no	—
487	C₂³	—	2	1	no	—
488	C₂³	C₁₉×#120	1	1	yes	characteristic
489	Q₈	—	2	1	no	—
490	Q₈	—	4	1	no	—
491	Q₈	—	4	2	no	—
492	Q₈	C₁₉×#104	1	2	yes	—
493	D₄	—	2	1	no	—
494	D₄	—	2	1	no	—
495	D₄	—	4	2	no	—
496	D₄	—	4	1	no	—
497	D₄	—	4	2	no	—
498	D₄	—	4	4	no	—
499	D₄	—	4	2	no	—
500	D₄	—	4	1	no	—
501	D₄	—	4	1	no	—
502	D₄	—	8	2	no	—
503	D₄	—	8	1	no	—
504	D₄	—	8	2	no	—
505	D₄	—	8	2	no	—
506	D₄	—	8	2	no	—
507	D₄	—	8	2	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	4	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	8	2	no	—
526	C₂×C₄	—	8	1	no	—
527	C₂×C₄	—	8	2	no	—
528	C₂×C₄	—	8	2	no	—
529	C₂×C₄	—	8	1	no	—
530	C₂×C₄	—	8	1	no	—
531	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
532	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
533	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
534	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
535	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
536	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
537	C₈	—	4	2	no	—
538	C₈	—	8	1	no	—
539	C₈	—	8	1	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	4	1	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	4	1	no	—
546	C₂²	—	4	1	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	2	no	—
551	C₂²	—	4	1	no	—
552	C₂²	C₁₉×#379	1	1	yes	characteristic
553	C₄	—	2	1	no	—
554	C₄	—	2	2	no	—
555	C₄	—	2	1	no	—
556	C₄	—	2	1	no	—
557	C₄	—	2	1	no	—
558	C₄	—	2	1	no	—
559	C₄	—	4	1	no	—
560	C₄	—	4	1	no	—
561	C₄	—	4	1	no	—
562	C₄	—	4	1	no	—
563	C₄	—	4	2	no	—
564	C₄	—	4	1	no	—
565	C₄	—	8	2	no	—
566	C₄	C₂×C₁₉×#104	1	1	yes	characteristic
567	C₄	C₁₉×#421	1	1	yes	characteristic
568	C₂	—	4	1	no	—
569	C₂	—	8	1	no	—
570	C₂	—	8	2	no	—
571	C₂	—	8	1	no	—
572	C₂	C₁₉×#1789	1	1	yes	characteristic
573	C₂	C₁₉×#1794	1	1	yes	characteristic
574	C₂	C₁₉×#1795	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#379
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#3517	C₂
LCS	G ▷ C₄² ▷ 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
2. C₁₉×#1759	C₂	semidirect
3. C₁₉×#1529	C₂	semidirect
4. C₁₉×#1505	C₂	semidirect
5. C₁₉×#1500	C₂	semidirect
6. C₁₉×#1488	C₂	semidirect
7. C₁₉×#1484	C₂	semidirect
8. C₁₉×#557	C₄	semidirect
13. C₁₉×#550	C₄	semidirect
14. C₁₉×#550	C₄	semidirect
16. C₁₉×#547	C₄	semidirect
197. #8414	C₁₉	direct (N × H)
254. #1759	C₂×C₁₉	semidirect
255. #1529	C₂×C₁₉	semidirect
256. #1505	C₂×C₁₉	semidirect
257. #1500	C₂×C₁₉	semidirect
258. #1488	C₂×C₁₉	semidirect
259. #1484	C₂×C₁₉	semidirect
288. #557	C₄×C₁₉	semidirect
293. #550	C₄×C₁₉	semidirect
294. #550	C₄×C₁₉	semidirect
296. #547	C₄×C₁₉	semidirect
404. C₁₉	#8414	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×#3517	2
C₁₉×#1759	2
C₁₉×#1529	2
C₁₉×#1505	2
C₁₉×#1500	2
C₁₉×#1488	2
C₁₉×#1484	2
#8414	19

Subgroups — C19×#8414 #18014373

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8414 #18014373