Subgroups — C₁₉×#9251 #18015210

Order 4864.

528 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#474	C₂	1	1	yes	maximal, characteristic
2	D₄×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1966	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1546	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×#474	—	2	1	no	—
12	C₁₉×#474	—	2	1	no	—
13	C₁₉×#474	—	2	1	no	—
14	C₁₉×#474	—	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×#107	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	C₂×C₁₉×#101	—	2	1	no	—
25	C₂×C₁₉×#101	—	2	1	no	—
26	C₁₉×#407	—	2	1	no	—
27	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
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×#107	—	2	2	no	—
59	C₁₉×#107	—	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×#101	—	4	2	no	—
70	C₁₉×#101	—	4	2	no	—
71	C₁₉×C₂²⋊C₈	—	2	2	no	—
72	C₁₉×C₂²⋊C₈	—	2	2	no	—
73	C₁₉×C₂²⋊C₈	—	2	1	no	—
74	C₁₉×#97	—	2	1	no	—
75	C₄×C₈×C₁₉	—	2	1	no	—
76	C₄×C₈×C₁₉	—	2	1	no	—
77	C₂⁴×C₁₉	—	2	1	no	—
78	C₂×Q₈×C₁₉	—	4	1	no	—
79	C₂×Q₈×C₁₉	—	4	1	no	—
80	C₂×Q₈×C₁₉	—	4	1	no	—
81	C₂×Q₈×C₁₉	—	4	1	no	—
82	C₂×Q₈×C₁₉	—	4	1	no	—
83	C₂×Q₈×C₁₉	—	4	1	no	—
84	C₂×D₄×C₁₉	—	2	2	no	—
85	C₂×D₄×C₁₉	—	2	1	no	—
86	C₂×D₄×C₁₉	—	4	1	no	—
87	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
88	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	—	2	1	no	—
90	C₂²×C₄×C₁₉	—	2	1	no	—
91	C₂²×C₄×C₁₉	—	2	1	no	—
92	C₂²×C₄×C₁₉	—	2	1	no	—
93	C₂²×C₄×C₁₉	—	2	1	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	4	1	no	—
96	C₂²×C₄×C₁₉	—	4	1	no	—
97	C₂²×C₄×C₁₉	—	4	1	no	—
98	C₂²×C₄×C₁₉	—	4	1	no	—
99	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
102	M₁₆×C₁₉	—	2	1	no	—
103	M₁₆×C₁₉	—	2	1	no	—
104	M₁₆×C₁₉	—	2	1	no	—
105	M₁₆×C₁₉	—	4	4	no	—
106	M₁₆×C₁₉	—	4	1	no	—
107	M₁₆×C₁₉	—	4	1	no	—
108	M₁₆×C₁₉	—	4	1	no	—
109	M₁₆×C₁₉	—	4	1	no	—
110	M₁₆×C₁₉	D₈	1	2	yes	—
111	C₂×C₈×C₁₉	—	2	1	no	—
112	C₂×C₈×C₁₉	—	2	2	no	—
113	C₂×C₈×C₁₉	—	2	2	no	—
114	C₂×C₈×C₁₉	—	2	1	no	—
115	C₂×C₈×C₁₉	—	4	4	no	—
116	C₂×C₈×C₁₉	—	4	2	no	—
117	C₂×C₈×C₁₉	—	4	1	no	—
118	C₂×C₈×C₁₉	—	4	1	no	—
119	C₄⋊C₄×C₁₉	—	2	1	no	—
120	C₄⋊C₄×C₁₉	—	2	2	no	—
121	C₄⋊C₄×C₁₉	—	2	2	no	—
122	C₄⋊C₄×C₁₉	—	4	1	no	—
123	C₄⋊C₄×C₁₉	—	4	1	no	—
124	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
125	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
126	C₂²⋊C₄×C₁₉	—	2	1	no	—
127	C₂²⋊C₄×C₁₉	—	2	1	no	—
128	C₂²⋊C₄×C₁₉	—	2	1	no	—
129	C₂²⋊C₄×C₁₉	—	2	1	no	—
130	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₁₉	#41	1	1	yes	characteristic
134	#9251	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
135	C₂³×C₁₉	—	2	1	no	—
136	C₂³×C₁₉	—	2	1	no	—
137	C₂³×C₁₉	—	4	2	no	—
138	C₂³×C₁₉	—	4	1	no	—
139	C₂³×C₁₉	—	4	1	no	—
140	C₂³×C₁₉	—	8	1	no	—
141	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
142	Q₈×C₁₉	—	8	1	no	—
143	Q₈×C₁₉	—	8	1	no	—
144	Q₈×C₁₉	—	8	1	no	—
145	Q₈×C₁₉	—	8	1	no	—
146	D₄×C₁₉	—	2	1	no	—
147	D₄×C₁₉	—	2	1	no	—
148	D₄×C₁₉	—	2	1	no	—
149	D₄×C₁₉	—	4	2	no	—
150	D₄×C₁₉	#101	1	2	yes	complemented
151	C₂×C₄×C₁₉	—	2	1	no	—
152	C₂×C₄×C₁₉	—	2	1	no	—
153	C₂×C₄×C₁₉	—	2	1	no	—
154	C₂×C₄×C₁₉	—	2	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	1	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	4	2	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
177	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
178	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
179	C₈×C₁₉	—	2	2	no	—
180	C₈×C₁₉	—	4	2	no	—
181	C₈×C₁₉	—	4	2	no	—
182	C₈×C₁₉	—	4	1	no	—
183	C₈×C₁₉	—	8	1	no	—
184	C₈×C₁₉	—	8	1	no	—
185	C₂×#474	C₂×C₁₉	1	1	yes	characteristic
186	D₄×M₁₆	C₂×C₁₉	1	1	yes	characteristic
187	#1966	C₂×C₁₉	1	1	yes	characteristic, complemented
188	#1546	C₂×C₁₉	1	1	yes	characteristic, complemented
189	#1486	C₂×C₁₉	1	1	yes	characteristic
190	#1292	C₂×C₁₉	1	1	yes	characteristic, complemented
191	#1283	C₂×C₁₉	1	1	yes	characteristic, complemented
192	C₂²×C₁₉	—	2	1	no	—
193	C₂²×C₁₉	—	2	1	no	—
194	C₂²×C₁₉	—	2	2	no	—
195	C₂²×C₁₉	—	4	1	no	—
196	C₂²×C₁₉	—	4	1	no	—
197	C₂²×C₁₉	—	4	1	no	—
198	C₂²×C₁₉	—	4	1	no	—
199	C₂²×C₁₉	—	4	1	no	—
200	C₂²×C₁₉	—	8	2	no	—
201	C₂²×C₁₉	—	8	2	no	—
202	C₂²×C₁₉	#386	1	1	yes	characteristic
203	C₂²×C₁₉	C₄×D₈	1	1	yes	characteristic
204	C₂²×C₁₉	#442	1	1	yes	characteristic
205	C₄×C₁₉	—	2	1	no	—
206	C₄×C₁₉	—	2	1	no	—
207	C₄×C₁₉	—	2	1	no	—
208	C₄×C₁₉	—	4	1	no	—
209	C₄×C₁₉	—	4	1	no	—
210	C₄×C₁₉	—	8	2	no	—
211	C₄×C₁₉	C₂×#101	1	1	yes	characteristic
212	C₄×C₁₉	#413	1	1	yes	characteristic
213	C₄×C₁₉	#447	1	1	yes	characteristic
214	C₄×C₁₉	#449	1	1	yes	characteristic
215	C₄×C₁₉	#459	1	1	yes	characteristic
216	C₄×C₁₉	#463	1	1	yes	characteristic
217	C₂²×M₁₆	—	2	1	no	—
218	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
219	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
220	#474	—	2	1	no	—
221	#474	—	2	1	no	—
222	#474	—	2	1	no	—
223	#474	—	2	1	no	—
224	#436	—	2	1	no	—
225	#435	—	2	2	no	—
226	C₈×D₄	—	2	1	no	—
227	#431	C₂²×C₁₉	1	1	yes	characteristic
228	C₂×#107	C₄×C₁₉	1	2	yes	—
229	#423	C₂²×C₁₉	1	1	yes	characteristic
230	#423	C₂²×C₁₉	1	1	yes	characteristic
231	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
232	C₂×#102	C₄×C₁₉	1	2	yes	—
233	C₂×#101	—	2	1	no	—
234	C₂×#101	—	2	1	no	—
235	#407	—	2	1	no	—
236	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
237	#332	—	2	2	no	—
238	D₄⋊C₈	—	2	1	no	—
239	D₄⋊C₈	—	2	1	no	—
240	C₂×C₁₉	—	2	1	no	—
241	C₂×C₁₉	—	2	1	no	—
242	C₂×C₁₉	—	4	2	no	—
243	C₂×C₁₉	—	8	1	no	—
244	C₂×C₁₉	#1879	1	1	yes	characteristic
245	C₂×C₁₉	#1901	1	1	yes	characteristic
246	C₂×C₁₉	#1902	1	1	yes	characteristic
247	C₂²×Q₈	—	2	1	no	—
248	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
249	C₂³×C₄	—	2	1	no	—
250	C₂×M₁₆	—	2	2	no	—
251	C₂×M₁₆	—	2	1	no	—
252	C₂×M₁₆	—	2	1	no	—
253	C₂×M₁₆	—	4	2	no	—
254	C₂×M₁₆	—	4	2	no	—
255	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
256	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
257	C₂²×C₈	—	2	2	no	—
258	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
259	C₄⋊Q₈	—	2	1	no	—
260	C₄⋊Q₈	—	2	1	no	—
261	C₄⋊Q₈	—	2	1	no	—
262	C₄⋊Q₈	—	2	1	no	—
263	C₄×D₄	—	2	1	no	—
264	C₄×D₄	—	2	1	no	—
265	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
266	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
267	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
268	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
271	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
272	C₂×C₂²⋊C₄	—	2	1	no	—
273	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
274	#107	—	2	2	no	—
275	#107	—	2	2	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	—	2	1	no	—
278	C₄⋊C₈	—	2	1	no	—
279	C₄⋊C₈	—	2	1	no	—
280	C₄⋊C₈	—	2	1	no	—
281	C₄⋊C₈	—	2	1	no	—
282	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
283	#102	—	2	2	no	—
284	#102	—	2	2	no	—
285	#101	—	4	2	no	—
286	#101	—	4	2	no	—
287	C₂²⋊C₈	—	2	2	no	—
288	C₂²⋊C₈	—	2	2	no	—
289	C₂²⋊C₈	—	2	1	no	—
290	#97	—	2	1	no	—
291	C₄×C₈	—	2	1	no	—
292	C₄×C₈	—	2	1	no	—
293	C₁₉	#9251	1	1	yes	characteristic, direct product factor, Sylow
294	C₂⁴	—	2	1	no	—
295	C₂×Q₈	—	4	1	no	—
296	C₂×Q₈	—	4	1	no	—
297	C₂×Q₈	—	4	1	no	—
298	C₂×Q₈	—	4	1	no	—
299	C₂×Q₈	—	4	1	no	—
300	C₂×Q₈	—	4	1	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	4	1	no	—
304	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
305	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	4	1	no	—
313	C₂²×C₄	—	4	1	no	—
314	C₂²×C₄	—	4	1	no	—
315	C₂²×C₄	—	4	1	no	—
316	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
318	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
319	M₁₆	—	2	1	no	—
320	M₁₆	—	2	1	no	—
321	M₁₆	—	2	1	no	—
322	M₁₆	—	4	4	no	—
323	M₁₆	—	4	1	no	—
324	M₁₆	—	4	1	no	—
325	M₁₆	—	4	1	no	—
326	M₁₆	—	4	1	no	—
327	M₁₆	D₈×C₁₉	1	2	yes	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	4	4	no	—
333	C₂×C₈	—	4	2	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	4	1	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	4	1	no	—
340	C₄⋊C₄	—	4	1	no	—
341	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
342	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
343	C₂²⋊C₄	—	2	1	no	—
344	C₂²⋊C₄	—	2	1	no	—
345	C₂²⋊C₄	—	2	1	no	—
346	C₂²⋊C₄	—	2	1	no	—
347	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
348	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
349	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
350	C₄²	#41×C₁₉	1	1	yes	characteristic
351	C₂³	—	2	1	no	—
352	C₂³	—	2	1	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	4	1	no	—
355	C₂³	—	4	1	no	—
356	C₂³	—	8	1	no	—
357	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
358	Q₈	—	8	1	no	—
359	Q₈	—	8	1	no	—
360	Q₈	—	8	1	no	—
361	Q₈	—	8	1	no	—
362	D₄	—	2	1	no	—
363	D₄	—	2	1	no	—
364	D₄	—	2	1	no	—
365	D₄	—	4	2	no	—
366	D₄	C₁₉×#101	1	2	yes	complemented
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
386	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
387	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
388	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
389	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
390	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
391	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
392	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
393	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
394	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
395	C₈	—	2	2	no	—
396	C₈	—	4	2	no	—
397	C₈	—	4	2	no	—
398	C₈	—	4	1	no	—
399	C₈	—	8	1	no	—
400	C₈	—	8	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	—	4	1	no	—
407	C₂²	—	4	1	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	8	2	no	—
410	C₂²	—	8	2	no	—
411	C₂²	C₁₉×#386	1	1	yes	characteristic
412	C₂²	C₄×D₈×C₁₉	1	1	yes	characteristic
413	C₂²	C₁₉×#442	1	1	yes	characteristic
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	4	1	no	—
418	C₄	—	4	1	no	—
419	C₄	—	8	2	no	—
420	C₄	C₂×C₁₉×#101	1	1	yes	characteristic
421	C₄	C₁₉×#413	1	1	yes	characteristic
422	C₄	C₁₉×#447	1	1	yes	characteristic
423	C₄	C₁₉×#449	1	1	yes	characteristic
424	C₄	C₁₉×#459	1	1	yes	characteristic
425	C₄	C₁₉×#463	1	1	yes	characteristic
426	C₂	—	2	1	no	—
427	C₂	—	2	1	no	—
428	C₂	—	4	2	no	—
429	C₂	—	8	1	no	—
430	C₂	C₁₉×#1879	1	1	yes	characteristic
431	C₂	C₁₉×#1901	1	1	yes	characteristic
432	C₂	C₁₉×#1902	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×#1966	C₂	semidirect
4. C₁₉×#1546	C₂	semidirect
6. C₁₉×#1292	C₂	semidirect
7. C₁₉×#1283	C₂	semidirect
134. #9251	C₁₉	direct (N × H)
150. D₄×C₁₉	#101	semidirect
187. #1966	C₂×C₁₉	semidirect
188. #1546	C₂×C₁₉	semidirect
190. #1292	C₂×C₁₉	semidirect
191. #1283	C₂×C₁₉	semidirect
293. C₁₉	#9251	direct (N × H)
366. D₄	C₁₉×#101	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#474	2
D₄×M₁₆×C₁₉	2
C₁₉×#1966	2
C₁₉×#1546	2
C₁₉×#1486	2
C₁₉×#1292	2
C₁₉×#1283	2
#9251	19

Subgroups — C19×#9251 #18015210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9251 #18015210