Subgroups — C₁₉×#19240 #18025199

Order 4864.

584 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3249	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3209	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3165	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2962	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1694	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1692	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1674	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1672	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1565	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1542	C₂	1	1	yes	maximal, characteristic
11	C₂×C₁₉×#332	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#533	C₂²	1	1	yes	characteristic
13	C₁₉×#533	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₁₉×#501	—	2	2	no	—
16	C₁₉×#500	C₂²	1	2	yes	—
17	C₁₉×#498	C₂²	1	2	yes	—
18	C₁₉×#494	—	2	1	no	—
19	C₁₉×#487	—	2	1	no	—
20	C₁₉×#477	—	2	1	no	—
21	C₁₉×#477	C₂²	1	2	yes	—
22	C₁₉×#467	—	2	2	no	—
23	C₁₉×#462	—	2	1	no	—
24	C₁₉×#462	C₂²	1	2	yes	—
25	C₁₉×#462	C₂²	1	2	yes	—
26	C₁₉×#462	C₂²	1	2	yes	—
27	C₁₉×#451	—	2	2	no	—
28	C₁₉×#446	—	2	2	no	—
29	C₁₉×#446	C₂²	1	2	yes	—
30	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
31	C₁₉×#431	C₂²	1	1	yes	characteristic
32	C₁₉×#428	—	2	1	no	—
33	C₁₉×#428	—	2	1	no	—
34	C₁₉×#424	—	2	1	no	—
35	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₁₉×#405	—	2	1	no	—
38	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
39	C₁₉×#335	C₂²	1	2	yes	—
40	C₁₉×#334	C₂²	1	2	yes	—
41	C₁₉×#333	C₂²	1	1	yes	characteristic
42	C₁₉×#333	C₂²	1	1	yes	characteristic
43	C₁₉×#332	C₂²	1	2	yes	—
44	C₁₉×#332	C₂²	1	1	yes	characteristic
45	C₁₉×#332	C₂²	1	2	yes	—
46	C₁₉×#332	C₂²	1	1	yes	characteristic
47	C₂²×Q₈×C₁₉	—	2	1	no	—
48	C₂×Q₁₆×C₁₉	—	2	2	no	—
49	C₂×Q₁₆×C₁₉	—	2	2	no	—
50	C₂×Q₁₆×C₁₉	—	2	2	no	—
51	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
52	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
53	C₂²×C₈×C₁₉	—	2	1	no	—
54	C₂²×C₈×C₁₉	—	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×C₄⋊Q₈	C₂³	1	2	yes	—
61	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
62	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
63	C₁₉×#125	—	2	1	no	—
64	C₁₉×#125	—	2	1	no	—
65	C₁₉×C₂²⋊Q₈	—	2	1	no	—
66	C₁₉×C₂²⋊Q₈	—	2	1	no	—
67	C₁₉×C₂²⋊Q₈	—	2	1	no	—
68	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
69	C₄×Q₈×C₁₉	—	2	1	no	—
70	C₄×Q₈×C₁₉	—	2	1	no	—
71	C₄×Q₈×C₁₉	—	2	1	no	—
72	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
73	C₁₉×#117	—	2	1	no	—
74	C₁₉×#117	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
78	C₁₉×#107	—	2	2	no	—
79	C₁₉×#107	—	2	2	no	—
80	C₁₉×#107	—	2	2	no	—
81	C₁₉×#106	—	2	2	no	—
82	C₁₉×#106	—	2	2	no	—
83	C₁₉×C₄⋊C₈	—	2	2	no	—
84	C₁₉×C₄⋊C₈	—	2	2	no	—
85	C₁₉×C₄⋊C₈	—	2	1	no	—
86	C₁₉×C₄⋊C₈	—	2	1	no	—
87	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
88	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
89	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
90	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
91	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
92	C₁₉×#103	—	2	2	no	—
93	C₁₉×#103	—	2	2	no	—
94	C₁₉×#103	—	2	2	no	—
95	C₁₉×#103	—	2	2	no	—
96	C₁₉×C₂²⋊C₈	—	2	1	no	—
97	C₁₉×#97	—	2	2	no	—
98	C₁₉×#97	D₄	1	2	yes	—
99	C₄×C₈×C₁₉	—	2	2	no	—
100	C₄×C₈×C₁₉	—	2	1	no	—
101	C₄×C₈×C₁₉	C₂³	1	2	yes	—
102	C₂×Q₈×C₁₉	—	2	1	no	—
103	C₂×Q₈×C₁₉	—	2	1	no	—
104	C₂×Q₈×C₁₉	—	2	2	no	—
105	C₂×Q₈×C₁₉	—	2	1	no	—
106	C₂×Q₈×C₁₉	—	4	1	no	—
107	C₂×Q₈×C₁₉	—	8	1	no	—
108	C₂×Q₈×C₁₉	—	8	1	no	—
109	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₉	—	4	1	no	—
111	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
114	Q₁₆×C₁₉	—	8	2	no	—
115	Q₁₆×C₁₉	—	8	2	no	—
116	Q₁₆×C₁₉	—	8	2	no	—
117	M₁₆×C₁₉	—	2	2	no	—
118	M₁₆×C₁₉	Q₁₆	1	4	yes	complemented
119	C₂×C₈×C₁₉	—	2	2	no	—
120	C₂×C₈×C₁₉	—	2	1	no	—
121	C₂×C₈×C₁₉	—	2	1	no	—
122	C₂×C₈×C₁₉	—	2	1	no	—
123	C₂×C₈×C₁₉	—	2	1	no	—
124	C₂×C₈×C₁₉	—	4	2	no	—
125	C₂×C₈×C₁₉	—	8	1	no	—
126	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
128	C₄⋊C₄×C₁₉	—	2	1	no	—
129	C₄⋊C₄×C₁₉	—	2	1	no	—
130	C₄⋊C₄×C₁₉	—	2	1	no	—
131	C₄⋊C₄×C₁₉	—	2	2	no	—
132	C₄⋊C₄×C₁₉	—	2	2	no	—
133	C₄⋊C₄×C₁₉	—	2	2	no	—
134	C₄⋊C₄×C₁₉	—	2	1	no	—
135	C₄⋊C₄×C₁₉	—	2	1	no	—
136	C₄⋊C₄×C₁₉	—	2	1	no	—
137	C₄⋊C₄×C₁₉	—	2	2	no	—
138	C₄⋊C₄×C₁₉	—	2	1	no	—
139	C₄⋊C₄×C₁₉	—	4	1	no	—
140	C₄⋊C₄×C₁₉	—	4	1	no	—
141	C₄⋊C₄×C₁₉	—	4	1	no	—
142	C₄⋊C₄×C₁₉	—	4	1	no	—
143	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
144	C₂²⋊C₄×C₁₉	—	2	2	no	—
145	C₂²⋊C₄×C₁₉	—	4	1	no	—
146	C₄²×C₁₉	—	2	2	no	—
147	C₄²×C₁₉	—	4	1	no	—
148	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₁₉	#41	1	1	yes	characteristic
151	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
152	#19240	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
153	C₂³×C₁₉	#121	1	1	yes	characteristic
154	Q₈×C₁₉	—	2	2	no	—
155	Q₈×C₁₉	—	2	2	no	—
156	Q₈×C₁₉	—	4	1	no	—
157	Q₈×C₁₉	—	4	2	no	—
158	Q₈×C₁₉	—	4	2	no	—
159	Q₈×C₁₉	—	4	1	no	—
160	Q₈×C₁₉	—	8	1	no	—
161	Q₈×C₁₉	—	8	1	no	—
162	Q₈×C₁₉	—	8	2	no	—
163	C₂×C₄×C₁₉	—	2	1	no	—
164	C₂×C₄×C₁₉	—	2	1	no	—
165	C₂×C₄×C₁₉	—	2	2	no	—
166	C₂×C₄×C₁₉	—	2	2	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	—	4	2	no	—
171	C₂×C₄×C₁₉	—	8	2	no	—
172	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
176	C₂×C₄×C₁₉	#137	1	2	yes	—
177	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
180	C₈×C₁₉	—	2	2	no	—
181	C₈×C₁₉	—	4	1	no	—
182	C₈×C₁₉	—	4	1	no	—
183	C₈×C₁₉	—	4	2	no	—
184	C₈×C₁₉	—	4	1	no	—
185	C₈×C₁₉	—	4	1	no	—
186	C₈×C₁₉	C₂×Q₁₆	1	4	yes	—
187	#3249	C₂×C₁₉	1	1	yes	characteristic
188	#3209	C₂×C₁₉	1	1	yes	characteristic
189	#3165	C₂×C₁₉	1	1	yes	characteristic
190	#2962	C₂×C₁₉	1	1	yes	characteristic
191	#1694	C₂×C₁₉	1	2	yes	complemented
192	#1692	C₂×C₁₉	1	2	yes	complemented
193	#1674	C₂×C₁₉	1	2	yes	complemented
194	#1672	C₂×C₁₉	1	2	yes	complemented
195	#1565	C₂×C₁₉	1	1	yes	characteristic
196	#1542	C₂×C₁₉	1	1	yes	characteristic
197	C₂×#332	C₂×C₁₉	1	1	yes	characteristic
198	C₂²×C₁₉	—	2	1	no	—
199	C₂²×C₁₉	—	2	1	no	—
200	C₂²×C₁₉	#462	1	2	yes	—
201	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
202	C₄×C₁₉	—	2	1	no	—
203	C₄×C₁₉	—	2	1	no	—
204	C₄×C₁₉	—	2	1	no	—
205	C₄×C₁₉	—	4	2	no	—
206	C₄×C₁₉	—	4	2	no	—
207	C₄×C₁₉	—	8	2	no	—
208	C₄×C₁₉	—	8	1	no	—
209	C₄×C₁₉	—	8	1	no	—
210	C₄×C₁₉	#462	1	2	yes	—
211	C₄×C₁₉	C₂²×Q₁₆	1	1	yes	characteristic
212	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
213	C₄×C₁₉	#576	1	1	yes	characteristic
214	C₄×C₁₉	#577	1	1	yes	characteristic
215	#533	C₂²×C₁₉	1	1	yes	characteristic
216	#533	C₂²×C₁₉	1	1	yes	characteristic
217	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
218	#501	—	2	2	no	—
219	#500	C₂²×C₁₉	1	2	yes	—
220	#498	C₂²×C₁₉	1	2	yes	—
221	#494	—	2	1	no	—
222	#487	—	2	1	no	—
223	#477	—	2	1	no	—
224	#477	C₂²×C₁₉	1	2	yes	—
225	#467	—	2	2	no	—
226	#462	—	2	1	no	—
227	#462	C₂²×C₁₉	1	2	yes	—
228	#462	C₂²×C₁₉	1	2	yes	—
229	#462	C₂²×C₁₉	1	2	yes	—
230	#451	—	2	2	no	—
231	#446	—	2	2	no	—
232	#446	C₂²×C₁₉	1	2	yes	—
233	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
234	#431	C₂²×C₁₉	1	1	yes	characteristic
235	#428	—	2	1	no	—
236	#428	—	2	1	no	—
237	#424	—	2	1	no	—
238	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
239	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
240	#405	—	2	1	no	—
241	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
242	#335	C₂²×C₁₉	1	2	yes	—
243	#334	C₂²×C₁₉	1	2	yes	—
244	#333	C₂²×C₁₉	1	1	yes	characteristic
245	#333	C₂²×C₁₉	1	1	yes	characteristic
246	#332	C₂²×C₁₉	1	2	yes	—
247	#332	C₂²×C₁₉	1	2	yes	—
248	#332	C₂²×C₁₉	1	1	yes	characteristic
249	#332	C₂²×C₁₉	1	1	yes	characteristic
250	C₂×C₁₉	—	2	2	no	—
251	C₂×C₁₉	C₂×#462	1	1	yes	characteristic
252	C₂×C₁₉	#3062	1	1	yes	characteristic
253	C₂×C₁₉	#3069	1	1	yes	characteristic
254	C₂²×Q₈	—	2	1	no	—
255	C₂×Q₁₆	—	2	2	no	—
256	C₂×Q₁₆	—	2	2	no	—
257	C₂×Q₁₆	—	2	2	no	—
258	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
259	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
260	C₂²×C₈	—	2	1	no	—
261	C₂²×C₈	—	2	1	no	—
262	C₄⋊Q₈	—	2	1	no	—
263	C₄⋊Q₈	—	2	1	no	—
264	C₄⋊Q₈	—	2	1	no	—
265	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
266	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
267	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
268	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
269	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
270	#125	—	2	1	no	—
271	#125	—	2	1	no	—
272	C₂²⋊Q₈	—	2	1	no	—
273	C₂²⋊Q₈	—	2	1	no	—
274	C₂²⋊Q₈	—	2	1	no	—
275	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
276	C₄×Q₈	—	2	1	no	—
277	C₄×Q₈	—	2	1	no	—
278	C₄×Q₈	—	2	1	no	—
279	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
280	#117	—	2	1	no	—
281	#117	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
285	#107	—	2	2	no	—
286	#107	—	2	2	no	—
287	#107	—	2	2	no	—
288	#106	—	2	2	no	—
289	#106	—	2	2	no	—
290	C₄⋊C₈	—	2	2	no	—
291	C₄⋊C₈	—	2	2	no	—
292	C₄⋊C₈	—	2	1	no	—
293	C₄⋊C₈	—	2	1	no	—
294	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
295	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
296	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
297	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
298	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
299	#103	—	2	2	no	—
300	#103	—	2	2	no	—
301	#103	—	2	2	no	—
302	#103	—	2	2	no	—
303	C₂²⋊C₈	—	2	1	no	—
304	#97	—	2	2	no	—
305	#97	D₄×C₁₉	1	2	yes	—
306	C₄×C₈	—	2	2	no	—
307	C₄×C₈	—	2	1	no	—
308	C₄×C₈	C₂³×C₁₉	1	2	yes	—
309	C₁₉	#19240	1	1	yes	characteristic, direct product factor, Sylow
310	C₂×Q₈	—	2	1	no	—
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	4	1	no	—
315	C₂×Q₈	—	8	1	no	—
316	C₂×Q₈	—	8	1	no	—
317	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
318	C₂²×C₄	—	4	1	no	—
319	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
321	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
322	Q₁₆	—	8	2	no	—
323	Q₁₆	—	8	2	no	—
324	Q₁₆	—	8	2	no	—
325	M₁₆	—	2	2	no	—
326	M₁₆	Q₁₆×C₁₉	1	4	yes	complemented
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	4	2	no	—
333	C₂×C₈	—	8	1	no	—
334	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
335	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	4	1	no	—
348	C₄⋊C₄	—	4	1	no	—
349	C₄⋊C₄	—	4	1	no	—
350	C₄⋊C₄	—	4	1	no	—
351	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
352	C₂²⋊C₄	—	2	2	no	—
353	C₂²⋊C₄	—	4	1	no	—
354	C₄²	—	2	2	no	—
355	C₄²	—	4	1	no	—
356	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
357	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
358	C₄²	#41×C₁₉	1	1	yes	characteristic
359	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
360	C₂³	C₁₉×#121	1	1	yes	characteristic
361	Q₈	—	2	2	no	—
362	Q₈	—	2	2	no	—
363	Q₈	—	4	1	no	—
364	Q₈	—	4	2	no	—
365	Q₈	—	4	2	no	—
366	Q₈	—	4	1	no	—
367	Q₈	—	8	1	no	—
368	Q₈	—	8	1	no	—
369	Q₈	—	8	2	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	8	2	no	—
379	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
380	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
381	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
382	C₂×C₄	C₂×Q₁₆×C₁₉	1	2	yes	—
383	C₂×C₄	C₁₉×#137	1	2	yes	—
384	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
385	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
386	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
387	C₈	—	2	2	no	—
388	C₈	—	4	1	no	—
389	C₈	—	4	1	no	—
390	C₈	—	4	2	no	—
391	C₈	—	4	1	no	—
392	C₈	—	4	1	no	—
393	C₈	C₂×Q₁₆×C₁₉	1	4	yes	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	C₁₉×#462	1	2	yes	—
397	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	4	2	no	—
402	C₄	—	4	2	no	—
403	C₄	—	8	2	no	—
404	C₄	—	8	1	no	—
405	C₄	—	8	1	no	—
406	C₄	C₁₉×#462	1	2	yes	—
407	C₄	C₂²×Q₁₆×C₁₉	1	1	yes	characteristic
408	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
409	C₄	C₁₉×#576	1	1	yes	characteristic
410	C₄	C₁₉×#577	1	1	yes	characteristic
411	C₂	—	2	2	no	—
412	C₂	C₂×C₁₉×#462	1	1	yes	characteristic
413	C₂	C₁₉×#3062	1	1	yes	characteristic
414	C₂	C₁₉×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂³×C₁₉	#121
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
5. C₁₉×#1694	C₂	semidirect
6. C₁₉×#1692	C₂	semidirect
7. C₁₉×#1674	C₂	semidirect
8. C₁₉×#1672	C₂	semidirect
118. M₁₆×C₁₉	Q₁₆	semidirect
152. #19240	C₁₉	direct (N × H)
191. #1694	C₂×C₁₉	semidirect
192. #1692	C₂×C₁₉	semidirect
193. #1674	C₂×C₁₉	semidirect
194. #1672	C₂×C₁₉	semidirect
309. C₁₉	#19240	direct (N × H)
326. M₁₆	Q₁₆×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3249	2
C₁₉×#3209	2
C₁₉×#3165	2
C₁₉×#2962	2
C₁₉×#1694	2
C₁₉×#1692	2
C₁₉×#1674	2
C₁₉×#1672	2
C₁₉×#1565	2
C₁₉×#1542	2
C₂×C₁₉×#332	2
#19240	19

Subgroups — C19×#19240 #18025199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19240 #18025199