Subgroups — C₁₉×#18433 #18024392

Order 4864.

872 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3563	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3218	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3209	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2660	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1605	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1603	C₂	1	4	yes	maximal
7	C₁₉×#1506	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1500	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1470	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#564	—	2	1	no	—
11	C₁₉×#563	—	2	1	no	—
12	C₁₉×#557	—	2	1	no	—
13	C₁₉×#554	—	2	1	no	—
14	C₁₉×#552	—	2	1	no	—
15	C₁₉×#552	—	2	1	no	—
16	C₁₉×#552	—	2	2	no	—
17	C₁₉×#544	—	2	1	no	—
18	C₁₉×#544	C₂²	1	2	yes	—
19	C₁₉×#541	—	2	1	no	—
20	C₁₉×#541	—	2	2	no	—
21	C₁₉×#539	C₂²	1	2	yes	—
22	C₁₉×#533	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₁₉×#529	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
26	C₁₉×#497	—	2	1	no	—
27	C₁₉×#494	—	2	1	no	—
28	C₁₉×#491	—	2	1	no	—
29	C₁₉×#487	—	2	1	no	—
30	C₁₉×#462	—	2	2	no	—
31	C₁₉×#462	—	2	1	no	—
32	C₁₉×#461	—	2	1	no	—
33	C₁₉×#451	C₂²	1	4	yes	—
34	C₁₉×#451	C₂²	1	2	yes	—
35	C₁₉×#448	C₂²	1	2	yes	—
36	C₁₉×#432	C₂²	1	1	yes	characteristic
37	C₁₉×#431	C₂²	1	1	yes	characteristic
38	C₁₉×#398	—	2	2	no	—
39	C₁₉×#395	C₂²	1	4	yes	—
40	C₁₉×#384	—	2	1	no	—
41	C₁₉×#382	—	2	1	no	—
42	C₁₉×#376	C₂²	1	1	yes	characteristic
43	C₁₉×#328	C₂²	1	2	yes	—
44	C₁₉×#328	C₂²	1	4	yes	—
45	C₁₉×#327	C₂²	1	2	yes	—
46	C₁₉×#324	C₂²	1	4	yes	—
47	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
48	C₂×Q₁₆×C₁₉	—	2	4	no	—
49	C₂×Q₁₆×C₁₉	—	2	2	no	—
50	C₂×SD₁₆×C₁₉	—	2	2	no	—
51	C₁₉×C₄⋊Q₈	—	2	1	no	—
52	C₁₉×C₄⋊Q₈	—	2	2	no	—
53	C₁₉×C₄⋊Q₈	—	2	2	no	—
54	C₁₉×C₄⋊Q₈	—	2	1	no	—
55	C₁₉×C₄⋊Q₈	—	2	1	no	—
56	C₁₉×C₄⋊Q₈	—	2	1	no	—
57	C₁₉×C₄⋊Q₈	—	2	1	no	—
58	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
59	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
60	C₁₉×#126	—	2	2	no	—
61	C₁₉×#126	—	2	2	no	—
62	C₁₉×#126	—	2	2	no	—
63	C₁₉×#126	—	2	2	no	—
64	C₁₉×#126	—	2	1	no	—
65	C₁₉×#125	—	2	2	no	—
66	C₁₉×#125	—	2	2	no	—
67	C₁₉×#125	—	2	2	no	—
68	C₁₉×#125	—	2	2	no	—
69	C₁₉×#125	—	2	1	no	—
70	C₁₉×#125	—	2	2	no	—
71	C₁₉×#125	—	2	2	no	—
72	C₁₉×#125	—	2	2	no	—
73	C₁₉×#125	—	2	2	no	—
74	C₁₉×#125	—	2	1	no	—
75	C₁₉×#125	—	2	1	no	—
76	C₁₉×#125	—	2	1	no	—
77	C₁₉×#125	—	2	1	no	—
78	C₁₉×#125	—	2	1	no	—
79	C₁₉×#125	D₄	1	1	yes	characteristic
80	C₁₉×#124	D₄	1	1	yes	characteristic
81	C₁₉×#123	—	2	2	no	—
82	C₁₉×#123	—	2	1	no	—
83	C₁₉×#123	—	2	2	no	—
84	C₁₉×C₂²⋊Q₈	—	2	1	no	—
85	C₁₉×C₂²⋊Q₈	—	2	1	no	—
86	C₁₉×C₂²⋊Q₈	—	2	2	no	—
87	C₁₉×C₂²⋊Q₈	—	2	2	no	—
88	C₁₉×C₂²⋊Q₈	—	2	2	no	—
89	C₁₉×C₂²⋊Q₈	—	2	1	no	—
90	C₁₉×C₂²⋊Q₈	—	2	2	no	—
91	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
92	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
93	C₁₉×#121	C₂³	1	1	yes	characteristic
94	C₄×Q₈×C₁₉	—	2	1	no	—
95	C₄×Q₈×C₁₉	—	2	2	no	—
96	C₄×Q₈×C₁₉	—	2	1	no	—
97	C₄×Q₈×C₁₉	—	2	1	no	—
98	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
99	C₄×Q₈×C₁₉	D₄	1	2	yes	—
100	C₄×D₄×C₁₉	—	2	1	no	—
101	C₄×D₄×C₁₉	—	2	2	no	—
102	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
103	C₁₉×#117	—	2	2	no	—
104	C₁₉×#117	—	2	1	no	—
105	C₁₉×#117	—	2	1	no	—
106	C₁₉×#117	—	2	2	no	—
107	C₁₉×#117	—	2	1	no	—
108	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
109	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
111	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
112	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
115	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
116	C₂×C₄²×C₁₉	—	2	1	no	—
117	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
118	C₁₉×C₄⋊C₈	—	2	1	no	—
119	C₁₉×C₄⋊C₈	—	2	1	no	—
120	C₁₉×#103	—	2	2	no	—
121	C₁₉×#103	—	2	2	no	—
122	C₁₉×#103	—	2	4	no	—
123	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
124	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
125	C₁₉×#97	—	2	1	no	—
126	C₄×C₈×C₁₉	—	2	1	no	—
127	C₁₉×#95	—	2	1	no	—
128	C₁₉×#95	—	2	4	no	—
129	C₁₉×#95	C₂³	1	2	yes	—
130	C₂×Q₈×C₁₉	—	2	2	no	—
131	C₂×Q₈×C₁₉	—	2	1	no	—
132	C₂×Q₈×C₁₉	—	2	2	no	—
133	C₂×Q₈×C₁₉	—	2	2	no	—
134	C₂×Q₈×C₁₉	—	8	2	no	—
135	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
136	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂×D₄×C₁₉	—	2	1	no	—
138	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	—	2	2	no	—
140	C₂²×C₄×C₁₉	—	2	2	no	—
141	C₂²×C₄×C₁₉	—	2	1	no	—
142	C₂²×C₄×C₁₉	—	2	2	no	—
143	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
148	Q₁₆×C₁₉	—	8	2	no	—
149	Q₁₆×C₁₉	—	8	4	no	—
150	SD₁₆×C₁₉	—	8	2	no	—
151	C₂×C₈×C₁₉	—	2	2	no	—
152	C₂×C₈×C₁₉	—	2	2	no	—
153	C₄⋊C₄×C₁₉	—	2	2	no	—
154	C₄⋊C₄×C₁₉	—	2	2	no	—
155	C₄⋊C₄×C₁₉	—	2	2	no	—
156	C₄⋊C₄×C₁₉	—	2	2	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	2	no	—
165	C₄⋊C₄×C₁₉	—	2	1	no	—
166	C₄⋊C₄×C₁₉	—	2	2	no	—
167	C₄⋊C₄×C₁₉	—	2	1	no	—
168	C₄⋊C₄×C₁₉	—	2	1	no	—
169	C₄⋊C₄×C₁₉	—	2	1	no	—
170	C₄⋊C₄×C₁₉	—	2	1	no	—
171	C₄⋊C₄×C₁₉	—	2	1	no	—
172	C₄⋊C₄×C₁₉	—	2	1	no	—
173	C₄⋊C₄×C₁₉	—	2	2	no	—
174	C₄⋊C₄×C₁₉	—	2	2	no	—
175	C₄⋊C₄×C₁₉	—	2	2	no	—
176	C₄⋊C₄×C₁₉	—	2	1	no	—
177	C₄⋊C₄×C₁₉	—	2	2	no	—
178	C₄⋊C₄×C₁₉	—	4	1	no	—
179	C₄⋊C₄×C₁₉	—	4	1	no	—
180	C₄⋊C₄×C₁₉	—	4	1	no	—
181	C₄⋊C₄×C₁₉	—	4	1	no	—
182	C₄⋊C₄×C₁₉	—	8	4	no	—
183	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
184	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
185	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
186	C₂²⋊C₄×C₁₉	—	2	2	no	—
187	C₂²⋊C₄×C₁₉	—	2	2	no	—
188	C₂²⋊C₄×C₁₉	—	2	2	no	—
189	C₂²⋊C₄×C₁₉	—	2	2	no	—
190	C₂²⋊C₄×C₁₉	—	2	1	no	—
191	C₂²⋊C₄×C₁₉	—	2	1	no	—
192	C₂²⋊C₄×C₁₉	—	2	1	no	—
193	C₂²⋊C₄×C₁₉	—	2	1	no	—
194	C₂²⋊C₄×C₁₉	—	2	1	no	—
195	C₄²×C₁₉	—	2	4	no	—
196	C₄²×C₁₉	—	2	2	no	—
197	C₄²×C₁₉	—	2	2	no	—
198	C₄²×C₁₉	—	2	2	no	—
199	C₄²×C₁₉	—	2	2	no	—
200	C₄²×C₁₉	—	2	1	no	—
201	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
202	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
204	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
205	#18433	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₂³×C₁₉	—	2	1	no	—
207	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
208	Q₈×C₁₉	—	4	1	no	—
209	Q₈×C₁₉	—	4	2	no	—
210	Q₈×C₁₉	—	4	2	no	—
211	Q₈×C₁₉	—	4	2	no	—
212	Q₈×C₁₉	—	4	4	no	—
213	Q₈×C₁₉	—	4	2	no	—
214	Q₈×C₁₉	—	8	2	no	—
215	D₄×C₁₉	—	4	1	no	—
216	D₄×C₁₉	—	4	2	no	—
217	C₂×C₄×C₁₉	—	2	2	no	—
218	C₂×C₄×C₁₉	—	2	2	no	—
219	C₂×C₄×C₁₉	—	2	4	no	—
220	C₂×C₄×C₁₉	—	2	2	no	—
221	C₂×C₄×C₁₉	—	2	1	no	—
222	C₂×C₄×C₁₉	—	2	1	no	—
223	C₂×C₄×C₁₉	—	2	2	no	—
224	C₂×C₄×C₁₉	—	2	1	no	—
225	C₂×C₄×C₁₉	—	2	2	no	—
226	C₂×C₄×C₁₉	—	2	2	no	—
227	C₂×C₄×C₁₉	—	2	4	no	—
228	C₂×C₄×C₁₉	—	4	1	no	—
229	C₂×C₄×C₁₉	—	4	2	no	—
230	C₂×C₄×C₁₉	—	4	2	no	—
231	C₂×C₄×C₁₉	—	4	2	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	—	8	2	no	—
236	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
237	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
238	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
239	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
240	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
242	C₈×C₁₉	—	4	2	no	—
243	C₈×C₁₉	—	4	2	no	—
244	#3563	C₂×C₁₉	1	1	yes	characteristic
245	#3218	C₂×C₁₉	1	1	yes	characteristic
246	#3209	C₂×C₁₉	1	1	yes	characteristic, complemented
247	#2660	C₂×C₁₉	1	1	yes	characteristic, complemented
248	#1605	C₂×C₁₉	1	4	yes	complemented
249	#1603	C₂×C₁₉	1	4	yes	—
250	#1506	C₂×C₁₉	1	1	yes	characteristic, complemented
251	#1500	C₂×C₁₉	1	1	yes	characteristic
252	#1470	C₂×C₁₉	1	1	yes	characteristic, complemented
253	C₂²×C₁₉	—	2	1	no	—
254	C₂²×C₁₉	—	2	1	no	—
255	C₂²×C₁₉	—	4	1	no	—
256	C₂²×C₁₉	—	4	1	no	—
257	C₂²×C₁₉	—	4	1	no	—
258	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
259	C₂²×C₁₉	#578	1	2	yes	—
260	C₄×C₁₉	—	2	1	no	—
261	C₄×C₁₉	—	2	1	no	—
262	C₄×C₁₉	—	2	1	no	—
263	C₄×C₁₉	—	2	1	no	—
264	C₄×C₁₉	—	2	1	no	—
265	C₄×C₁₉	—	4	4	no	—
266	C₄×C₁₉	—	4	2	no	—
267	C₄×C₁₉	—	4	1	no	—
268	C₄×C₁₉	—	4	1	no	—
269	C₄×C₁₉	—	4	2	no	—
270	C₄×C₁₉	—	4	2	no	—
271	C₄×C₁₉	—	4	2	no	—
272	C₄×C₁₉	—	4	1	no	—
273	C₄×C₁₉	—	8	2	no	—
274	C₄×C₁₉	#456	1	2	yes	—
275	#564	—	2	1	no	—
276	#563	—	2	1	no	—
277	#557	—	2	1	no	—
278	#554	—	2	1	no	—
279	#552	—	2	1	no	—
280	#552	—	2	1	no	—
281	#552	—	2	2	no	—
282	#544	—	2	1	no	—
283	#544	C₂²×C₁₉	1	2	yes	—
284	#541	—	2	1	no	—
285	#541	—	2	2	no	—
286	#539	C₂²×C₁₉	1	2	yes	—
287	#533	C₂²×C₁₉	1	1	yes	characteristic
288	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
289	#529	C₂²×C₁₉	1	1	yes	characteristic
290	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
291	#497	—	2	1	no	—
292	#494	—	2	1	no	—
293	#491	—	2	1	no	—
294	#487	—	2	1	no	—
295	#462	—	2	2	no	—
296	#462	—	2	1	no	—
297	#461	—	2	1	no	—
298	#451	C₂²×C₁₉	1	4	yes	—
299	#451	C₂²×C₁₉	1	2	yes	—
300	#448	C₂²×C₁₉	1	2	yes	—
301	#432	C₂²×C₁₉	1	1	yes	characteristic
302	#431	C₂²×C₁₉	1	1	yes	characteristic
303	#398	—	2	2	no	—
304	#395	C₂²×C₁₉	1	4	yes	—
305	#384	—	2	1	no	—
306	#382	—	2	1	no	—
307	#376	C₂²×C₁₉	1	1	yes	characteristic
308	#328	C₂²×C₁₉	1	4	yes	—
309	#328	C₂²×C₁₉	1	2	yes	—
310	#327	C₂²×C₁₉	1	2	yes	—
311	#324	C₂²×C₁₉	1	4	yes	—
312	C₂×C₁₉	—	2	2	no	—
313	C₂×C₁₉	—	8	1	no	—
314	C₂×C₁₉	#3011	1	1	yes	characteristic
315	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
316	C₂×C₁₉	#3027	1	1	yes	characteristic
317	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
318	C₂×Q₁₆	—	2	4	no	—
319	C₂×Q₁₆	—	2	2	no	—
320	C₂×SD₁₆	—	2	2	no	—
321	C₄⋊Q₈	—	2	1	no	—
322	C₄⋊Q₈	—	2	2	no	—
323	C₄⋊Q₈	—	2	2	no	—
324	C₄⋊Q₈	—	2	1	no	—
325	C₄⋊Q₈	—	2	1	no	—
326	C₄⋊Q₈	—	2	1	no	—
327	C₄⋊Q₈	—	2	1	no	—
328	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
329	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
330	#126	—	2	2	no	—
331	#126	—	2	2	no	—
332	#126	—	2	2	no	—
333	#126	—	2	2	no	—
334	#126	—	2	1	no	—
335	#125	—	2	2	no	—
336	#125	—	2	2	no	—
337	#125	—	2	2	no	—
338	#125	—	2	2	no	—
339	#125	—	2	1	no	—
340	#125	—	2	2	no	—
341	#125	—	2	2	no	—
342	#125	—	2	2	no	—
343	#125	—	2	2	no	—
344	#125	—	2	1	no	—
345	#125	—	2	1	no	—
346	#125	—	2	1	no	—
347	#125	—	2	1	no	—
348	#125	—	2	1	no	—
349	#125	D₄×C₁₉	1	1	yes	characteristic
350	#124	D₄×C₁₉	1	1	yes	characteristic
351	#123	—	2	2	no	—
352	#123	—	2	1	no	—
353	#123	—	2	2	no	—
354	C₂²⋊Q₈	—	2	1	no	—
355	C₂²⋊Q₈	—	2	1	no	—
356	C₂²⋊Q₈	—	2	2	no	—
357	C₂²⋊Q₈	—	2	2	no	—
358	C₂²⋊Q₈	—	2	2	no	—
359	C₂²⋊Q₈	—	2	1	no	—
360	C₂²⋊Q₈	—	2	2	no	—
361	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
362	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
363	#121	C₂³×C₁₉	1	1	yes	characteristic
364	C₄×Q₈	—	2	1	no	—
365	C₄×Q₈	—	2	2	no	—
366	C₄×Q₈	—	2	1	no	—
367	C₄×Q₈	—	2	1	no	—
368	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
369	C₄×Q₈	D₄×C₁₉	1	2	yes	—
370	C₄×D₄	—	2	1	no	—
371	C₄×D₄	—	2	2	no	—
372	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
373	#117	—	2	2	no	—
374	#117	—	2	1	no	—
375	#117	—	2	1	no	—
376	#117	—	2	2	no	—
377	#117	—	2	1	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	—	2	4	no	—
382	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
383	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
384	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
386	C₂×C₄²	—	2	1	no	—
387	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
388	C₄⋊C₈	—	2	1	no	—
389	C₄⋊C₈	—	2	1	no	—
390	#103	—	2	2	no	—
391	#103	—	2	2	no	—
392	#103	—	2	4	no	—
393	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
394	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
395	#97	—	2	1	no	—
396	C₄×C₈	—	2	1	no	—
397	#95	—	2	1	no	—
398	#95	—	2	4	no	—
399	#95	C₂³×C₁₉	1	2	yes	—
400	C₁₉	#18433	1	1	yes	characteristic, direct product factor, Sylow
401	C₂×Q₈	—	2	2	no	—
402	C₂×Q₈	—	2	1	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	8	2	no	—
406	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
407	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
408	C₂×D₄	—	2	1	no	—
409	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
415	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
416	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
417	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
418	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
419	Q₁₆	—	8	2	no	—
420	Q₁₆	—	8	4	no	—
421	SD₁₆	—	8	2	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	4	1	no	—
450	C₄⋊C₄	—	4	1	no	—
451	C₄⋊C₄	—	4	1	no	—
452	C₄⋊C₄	—	4	1	no	—
453	C₄⋊C₄	—	8	4	no	—
454	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
455	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
456	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
457	C₂²⋊C₄	—	2	2	no	—
458	C₂²⋊C₄	—	2	2	no	—
459	C₂²⋊C₄	—	2	2	no	—
460	C₂²⋊C₄	—	2	2	no	—
461	C₂²⋊C₄	—	2	1	no	—
462	C₂²⋊C₄	—	2	1	no	—
463	C₂²⋊C₄	—	2	1	no	—
464	C₂²⋊C₄	—	2	1	no	—
465	C₂²⋊C₄	—	2	1	no	—
466	C₄²	—	2	4	no	—
467	C₄²	—	2	2	no	—
468	C₄²	—	2	2	no	—
469	C₄²	—	2	2	no	—
470	C₄²	—	2	2	no	—
471	C₄²	—	2	1	no	—
472	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
473	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
474	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
475	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
476	C₂³	—	2	1	no	—
477	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
478	Q₈	—	4	1	no	—
479	Q₈	—	4	2	no	—
480	Q₈	—	4	2	no	—
481	Q₈	—	4	2	no	—
482	Q₈	—	4	4	no	—
483	Q₈	—	4	2	no	—
484	Q₈	—	8	2	no	—
485	D₄	—	4	1	no	—
486	D₄	—	4	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	4	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	8	2	no	—
506	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
507	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
508	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
509	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
510	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
511	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
512	C₈	—	4	2	no	—
513	C₈	—	4	2	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	2	1	no	—
516	C₂²	—	4	1	no	—
517	C₂²	—	4	1	no	—
518	C₂²	—	4	1	no	—
519	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
520	C₂²	C₁₉×#578	1	2	yes	—
521	C₄	—	2	1	no	—
522	C₄	—	2	1	no	—
523	C₄	—	2	1	no	—
524	C₄	—	2	1	no	—
525	C₄	—	2	1	no	—
526	C₄	—	4	4	no	—
527	C₄	—	4	2	no	—
528	C₄	—	4	1	no	—
529	C₄	—	4	1	no	—
530	C₄	—	4	2	no	—
531	C₄	—	4	2	no	—
532	C₄	—	4	2	no	—
533	C₄	—	4	1	no	—
534	C₄	—	8	2	no	—
535	C₄	C₁₉×#456	1	2	yes	—
536	C₂	—	2	2	no	—
537	C₂	—	8	1	no	—
538	C₂	C₁₉×#3011	1	1	yes	characteristic
539	C₂	C₂×C₁₉×#456	1	1	yes	characteristic
540	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×#121	C₂³
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
3. C₁₉×#3209	C₂	semidirect
4. C₁₉×#2660	C₂	semidirect
5. C₁₉×#1605	C₂	semidirect
7. C₁₉×#1506	C₂	semidirect
9. C₁₉×#1470	C₂	semidirect
205. #18433	C₁₉	direct (N × H)
246. #3209	C₂×C₁₉	semidirect
247. #2660	C₂×C₁₉	semidirect
248. #1605	C₂×C₁₉	semidirect
250. #1506	C₂×C₁₉	semidirect
252. #1470	C₂×C₁₉	semidirect
400. C₁₉	#18433	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×#3563	2
C₁₉×#3218	2
C₁₉×#3209	2
C₁₉×#2660	2
C₁₉×#1605	2
C₁₉×#1603	2
C₁₉×#1506	2
C₁₉×#1500	2
C₁₉×#1470	2
#18433	19

Subgroups — C19×#18433 #18024392

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18433 #18024392