Subgroups — C₁₉×#9249 #18015208

Order 4864.

512 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#476	C₂	1	1	yes	maximal, characteristic
2	D₄×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1997	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1549	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1486	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1292	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1283	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×M₁₆×C₁₉	—	2	1	no	—
9	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#476	—	2	1	no	—
12	C₁₉×#476	—	2	1	no	—
13	C₁₉×#476	—	2	1	no	—
14	C₁₉×#476	—	2	1	no	—
15	C₁₉×#436	—	2	1	no	—
16	C₁₉×#435	—	2	2	no	—
17	C₈×D₄×C₁₉	—	2	1	no	—
18	C₁₉×#431	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#106	C₄	1	2	yes	—
20	C₁₉×#423	C₂²	1	1	yes	characteristic
21	C₁₉×#423	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#102	C₄	1	2	yes	—
24	C₁₉×#407	—	2	1	no	—
25	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#343	—	2	1	no	—
27	C₁₉×#343	—	2	1	no	—
28	C₁₉×#332	—	2	2	no	—
29	C₁₉×D₄⋊C₈	—	2	1	no	—
30	C₁₉×D₄⋊C₈	—	2	1	no	—
31	C₂²×Q₈×C₁₉	—	2	1	no	—
32	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₉	—	2	1	no	—
34	C₂×M₁₆×C₁₉	—	2	2	no	—
35	C₂×M₁₆×C₁₉	—	2	1	no	—
36	C₂×M₁₆×C₁₉	—	2	1	no	—
37	C₂×M₁₆×C₁₉	—	4	2	no	—
38	C₂×M₁₆×C₁₉	—	4	2	no	—
39	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
40	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₁₉	—	2	2	no	—
42	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
43	C₁₉×C₄⋊Q₈	—	2	1	no	—
44	C₁₉×C₄⋊Q₈	—	2	1	no	—
45	C₁₉×C₄⋊Q₈	—	2	1	no	—
46	C₁₉×C₄⋊Q₈	—	2	1	no	—
47	C₄×D₄×C₁₉	—	2	1	no	—
48	C₄×D₄×C₁₉	—	2	1	no	—
49	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
50	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
51	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
52	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
56	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
58	C₁₉×#106	—	2	2	no	—
59	C₁₉×#106	—	2	2	no	—
60	C₁₉×C₄⋊C₈	—	2	1	no	—
61	C₁₉×C₄⋊C₈	—	2	1	no	—
62	C₁₉×C₄⋊C₈	—	2	1	no	—
63	C₁₉×C₄⋊C₈	—	2	1	no	—
64	C₁₉×C₄⋊C₈	—	2	1	no	—
65	C₁₉×C₄⋊C₈	—	2	1	no	—
66	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
67	C₁₉×#102	—	2	2	no	—
68	C₁₉×#102	—	2	2	no	—
69	C₁₉×C₂²⋊C₈	—	2	2	no	—
70	C₁₉×C₂²⋊C₈	—	2	2	no	—
71	C₁₉×C₂²⋊C₈	—	2	1	no	—
72	C₁₉×#97	—	2	1	no	—
73	C₄×C₈×C₁₉	—	2	1	no	—
74	C₄×C₈×C₁₉	—	2	1	no	—
75	C₂⁴×C₁₉	—	2	1	no	—
76	C₂×Q₈×C₁₉	—	4	1	no	—
77	C₂×Q₈×C₁₉	—	4	1	no	—
78	C₂×Q₈×C₁₉	—	8	2	no	—
79	C₂×D₄×C₁₉	—	2	2	no	—
80	C₂×D₄×C₁₉	—	2	1	no	—
81	C₂×D₄×C₁₉	—	4	1	no	—
82	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
83	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	—	2	1	no	—
85	C₂²×C₄×C₁₉	—	2	1	no	—
86	C₂²×C₄×C₁₉	—	2	1	no	—
87	C₂²×C₄×C₁₉	—	2	1	no	—
88	C₂²×C₄×C₁₉	—	2	1	no	—
89	C₂²×C₄×C₁₉	—	2	2	no	—
90	C₂²×C₄×C₁₉	—	4	1	no	—
91	C₂²×C₄×C₁₉	—	4	1	no	—
92	C₂²×C₄×C₁₉	—	4	1	no	—
93	C₂²×C₄×C₁₉	—	4	1	no	—
94	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
97	M₁₆×C₁₉	—	2	1	no	—
98	M₁₆×C₁₉	—	2	1	no	—
99	M₁₆×C₁₉	—	2	1	no	—
100	M₁₆×C₁₉	—	4	4	no	—
101	M₁₆×C₁₉	—	4	1	no	—
102	M₁₆×C₁₉	—	4	1	no	—
103	M₁₆×C₁₉	—	4	1	no	—
104	M₁₆×C₁₉	—	4	1	no	—
105	M₁₆×C₁₉	SD₁₆	1	2	yes	—
106	C₂×C₈×C₁₉	—	2	1	no	—
107	C₂×C₈×C₁₉	—	2	2	no	—
108	C₂×C₈×C₁₉	—	2	2	no	—
109	C₂×C₈×C₁₉	—	2	1	no	—
110	C₂×C₈×C₁₉	—	4	4	no	—
111	C₂×C₈×C₁₉	—	4	2	no	—
112	C₂×C₈×C₁₉	—	4	1	no	—
113	C₂×C₈×C₁₉	—	4	1	no	—
114	C₄⋊C₄×C₁₉	—	2	1	no	—
115	C₄⋊C₄×C₁₉	—	2	2	no	—
116	C₄⋊C₄×C₁₉	—	2	2	no	—
117	C₄⋊C₄×C₁₉	—	4	1	no	—
118	C₄⋊C₄×C₁₉	—	4	1	no	—
119	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
120	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
121	C₂²⋊C₄×C₁₉	—	2	1	no	—
122	C₂²⋊C₄×C₁₉	—	2	1	no	—
123	C₂²⋊C₄×C₁₉	—	2	1	no	—
124	C₂²⋊C₄×C₁₉	—	2	1	no	—
125	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₁₉	#41	1	1	yes	characteristic
129	#9249	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂³×C₁₉	—	2	1	no	—
131	C₂³×C₁₉	—	2	1	no	—
132	C₂³×C₁₉	—	4	2	no	—
133	C₂³×C₁₉	—	4	1	no	—
134	C₂³×C₁₉	—	4	1	no	—
135	C₂³×C₁₉	—	8	1	no	—
136	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
137	Q₈×C₁₉	—	8	2	no	—
138	Q₈×C₁₉	—	8	2	no	—
139	D₄×C₁₉	—	2	1	no	—
140	D₄×C₁₉	—	2	1	no	—
141	D₄×C₁₉	—	2	1	no	—
142	D₄×C₁₉	—	4	2	no	—
143	D₄×C₁₉	#101	1	2	yes	—
144	C₂×C₄×C₁₉	—	2	1	no	—
145	C₂×C₄×C₁₉	—	2	1	no	—
146	C₂×C₄×C₁₉	—	2	1	no	—
147	C₂×C₄×C₁₉	—	2	1	no	—
148	C₂×C₄×C₁₉	—	4	1	no	—
149	C₂×C₄×C₁₉	—	4	1	no	—
150	C₂×C₄×C₁₉	—	4	1	no	—
151	C₂×C₄×C₁₉	—	4	1	no	—
152	C₂×C₄×C₁₉	—	4	1	no	—
153	C₂×C₄×C₁₉	—	4	1	no	—
154	C₂×C₄×C₁₉	—	4	1	no	—
155	C₂×C₄×C₁₉	—	4	1	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	4	1	no	—
159	C₂×C₄×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	—	8	2	no	—
161	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
164	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
165	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
166	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
167	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
168	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
169	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
171	C₈×C₁₉	—	2	2	no	—
172	C₈×C₁₉	—	4	2	no	—
173	C₈×C₁₉	—	4	2	no	—
174	C₈×C₁₉	—	4	1	no	—
175	C₈×C₁₉	—	8	1	no	—
176	C₈×C₁₉	—	8	1	no	—
177	C₂×#476	C₂×C₁₉	1	1	yes	characteristic
178	D₄×M₁₆	C₂×C₁₉	1	1	yes	characteristic
179	#1997	C₂×C₁₉	1	1	yes	characteristic, complemented
180	#1549	C₂×C₁₉	1	1	yes	characteristic, complemented
181	#1486	C₂×C₁₉	1	1	yes	characteristic
182	#1292	C₂×C₁₉	1	1	yes	characteristic, complemented
183	#1283	C₂×C₁₉	1	1	yes	characteristic, complemented
184	C₂²×C₁₉	—	2	1	no	—
185	C₂²×C₁₉	—	2	1	no	—
186	C₂²×C₁₉	—	2	2	no	—
187	C₂²×C₁₉	—	4	1	no	—
188	C₂²×C₁₉	—	4	1	no	—
189	C₂²×C₁₉	—	4	1	no	—
190	C₂²×C₁₉	—	4	1	no	—
191	C₂²×C₁₉	—	4	1	no	—
192	C₂²×C₁₉	—	8	2	no	—
193	C₂²×C₁₉	—	8	2	no	—
194	C₂²×C₁₉	#386	1	1	yes	characteristic
195	C₂²×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
196	C₂²×C₁₉	#440	1	1	yes	characteristic
197	C₄×C₁₉	—	2	1	no	—
198	C₄×C₁₉	—	2	1	no	—
199	C₄×C₁₉	—	2	1	no	—
200	C₄×C₁₉	—	4	1	no	—
201	C₄×C₁₉	—	4	1	no	—
202	C₄×C₁₉	—	8	2	no	—
203	C₄×C₁₉	C₂×#101	1	1	yes	characteristic
204	C₄×C₁₉	#413	1	1	yes	characteristic
205	C₄×C₁₉	#450	1	1	yes	characteristic
206	C₄×C₁₉	#452	1	1	yes	characteristic
207	C₄×C₁₉	#461	1	1	yes	characteristic
208	C₄×C₁₉	#463	1	1	yes	characteristic
209	C₂²×M₁₆	—	2	1	no	—
210	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
211	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
212	#476	—	2	1	no	—
213	#476	—	2	1	no	—
214	#476	—	2	1	no	—
215	#476	—	2	1	no	—
216	#436	—	2	1	no	—
217	#435	—	2	2	no	—
218	C₈×D₄	—	2	1	no	—
219	#431	C₂²×C₁₉	1	1	yes	characteristic
220	C₂×#106	C₄×C₁₉	1	2	yes	—
221	#423	C₂²×C₁₉	1	1	yes	characteristic
222	#423	C₂²×C₁₉	1	1	yes	characteristic
223	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
224	C₂×#102	C₄×C₁₉	1	2	yes	—
225	#407	—	2	1	no	—
226	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
227	#343	—	2	1	no	—
228	#343	—	2	1	no	—
229	#332	—	2	2	no	—
230	D₄⋊C₈	—	2	1	no	—
231	D₄⋊C₈	—	2	1	no	—
232	C₂×C₁₉	—	2	1	no	—
233	C₂×C₁₉	—	2	1	no	—
234	C₂×C₁₉	—	4	2	no	—
235	C₂×C₁₉	—	8	1	no	—
236	C₂×C₁₉	#1877	1	1	yes	characteristic
237	C₂×C₁₉	#1901	1	1	yes	characteristic
238	C₂×C₁₉	#1903	1	1	yes	characteristic
239	C₂²×Q₈	—	2	1	no	—
240	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
241	C₂³×C₄	—	2	1	no	—
242	C₂×M₁₆	—	2	2	no	—
243	C₂×M₁₆	—	2	1	no	—
244	C₂×M₁₆	—	2	1	no	—
245	C₂×M₁₆	—	4	2	no	—
246	C₂×M₁₆	—	4	2	no	—
247	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
248	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
249	C₂²×C₈	—	2	2	no	—
250	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
251	C₄⋊Q₈	—	2	1	no	—
252	C₄⋊Q₈	—	2	1	no	—
253	C₄⋊Q₈	—	2	1	no	—
254	C₄⋊Q₈	—	2	1	no	—
255	C₄×D₄	—	2	1	no	—
256	C₄×D₄	—	2	1	no	—
257	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
258	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
259	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
260	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
263	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
264	C₂×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
266	#106	—	2	2	no	—
267	#106	—	2	2	no	—
268	C₄⋊C₈	—	2	1	no	—
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	—	2	1	no	—
271	C₄⋊C₈	—	2	1	no	—
272	C₄⋊C₈	—	2	1	no	—
273	C₄⋊C₈	—	2	1	no	—
274	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
275	#102	—	2	2	no	—
276	#102	—	2	2	no	—
277	C₂²⋊C₈	—	2	2	no	—
278	C₂²⋊C₈	—	2	2	no	—
279	C₂²⋊C₈	—	2	1	no	—
280	#97	—	2	1	no	—
281	C₄×C₈	—	2	1	no	—
282	C₄×C₈	—	2	1	no	—
283	C₁₉	#9249	1	1	yes	characteristic, direct product factor, Sylow
284	C₂⁴	—	2	1	no	—
285	C₂×Q₈	—	4	1	no	—
286	C₂×Q₈	—	4	1	no	—
287	C₂×Q₈	—	8	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	4	1	no	—
291	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
292	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	4	1	no	—
300	C₂²×C₄	—	4	1	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	—	4	1	no	—
303	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
305	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
306	M₁₆	—	2	1	no	—
307	M₁₆	—	2	1	no	—
308	M₁₆	—	2	1	no	—
309	M₁₆	—	4	4	no	—
310	M₁₆	—	4	1	no	—
311	M₁₆	—	4	1	no	—
312	M₁₆	—	4	1	no	—
313	M₁₆	—	4	1	no	—
314	M₁₆	SD₁₆×C₁₉	1	2	yes	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	4	4	no	—
320	C₂×C₈	—	4	2	no	—
321	C₂×C₈	—	4	1	no	—
322	C₂×C₈	—	4	1	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
329	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
330	C₂²⋊C₄	—	2	1	no	—
331	C₂²⋊C₄	—	2	1	no	—
332	C₂²⋊C₄	—	2	1	no	—
333	C₂²⋊C₄	—	2	1	no	—
334	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
335	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
336	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
337	C₄²	#41×C₁₉	1	1	yes	characteristic
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	1	no	—
342	C₂³	—	4	1	no	—
343	C₂³	—	8	1	no	—
344	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
345	Q₈	—	8	2	no	—
346	Q₈	—	8	2	no	—
347	D₄	—	2	1	no	—
348	D₄	—	2	1	no	—
349	D₄	—	2	1	no	—
350	D₄	—	4	2	no	—
351	D₄	C₁₉×#101	1	2	yes	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	8	2	no	—
369	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
370	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
371	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
372	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
373	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
374	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
375	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
376	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
377	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
378	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
379	C₈	—	2	2	no	—
380	C₈	—	4	2	no	—
381	C₈	—	4	2	no	—
382	C₈	—	4	1	no	—
383	C₈	—	8	1	no	—
384	C₈	—	8	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	2	no	—
388	C₂²	—	4	1	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	4	1	no	—
391	C₂²	—	4	1	no	—
392	C₂²	—	4	1	no	—
393	C₂²	—	8	2	no	—
394	C₂²	—	8	2	no	—
395	C₂²	C₁₉×#386	1	1	yes	characteristic
396	C₂²	C₄×SD₁₆×C₁₉	1	1	yes	characteristic
397	C₂²	C₁₉×#440	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	4	1	no	—
402	C₄	—	4	1	no	—
403	C₄	—	8	2	no	—
404	C₄	C₂×C₁₉×#101	1	1	yes	characteristic
405	C₄	C₁₉×#413	1	1	yes	characteristic
406	C₄	C₁₉×#450	1	1	yes	characteristic
407	C₄	C₁₉×#452	1	1	yes	characteristic
408	C₄	C₁₉×#461	1	1	yes	characteristic
409	C₄	C₁₉×#463	1	1	yes	characteristic
410	C₂	—	2	1	no	—
411	C₂	—	2	1	no	—
412	C₂	—	4	2	no	—
413	C₂	—	8	1	no	—
414	C₂	C₁₉×#1877	1	1	yes	characteristic
415	C₂	C₁₉×#1901	1	1	yes	characteristic
416	C₂	C₁₉×#1903	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂²×D₄×C₁₉	C₂×C₄
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×#1997	C₂	semidirect
4. C₁₉×#1549	C₂	semidirect
6. C₁₉×#1292	C₂	semidirect
7. C₁₉×#1283	C₂	semidirect
129. #9249	C₁₉	direct (N × H)
179. #1997	C₂×C₁₉	semidirect
180. #1549	C₂×C₁₉	semidirect
182. #1292	C₂×C₁₉	semidirect
183. #1283	C₂×C₁₉	semidirect
283. C₁₉	#9249	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#476	2
D₄×M₁₆×C₁₉	2
C₁₉×#1997	2
C₁₉×#1549	2
C₁₉×#1486	2
C₁₉×#1292	2
C₁₉×#1283	2
#9249	19

Subgroups — C19×#9249 #18015208

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9249 #18015208