Subgroups — C₁₉×#9211 #18015170

Order 4864.

536 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3106	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₉×#131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1525	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1492	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1489	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1299	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1278	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×#131	—	2	1	no	—
9	C₁₉×#532	C₂²	1	1	yes	characteristic
10	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#482	—	2	1	no	—
12	C₁₉×#477	C₄	1	1	yes	characteristic
13	C₁₉×#476	C₄	1	1	yes	characteristic
14	C₁₉×#460	C₄	1	1	yes	characteristic
15	C₁₉×#459	C₄	1	1	yes	characteristic
16	C₁₉×#449	—	2	1	no	—
17	C₄×SD₁₆×C₁₉	—	2	1	no	—
18	C₄×D₈×C₁₉	—	2	1	no	—
19	C₁₉×#431	C₂²	1	1	yes	characteristic
20	C₁₉×#423	C₂²	1	1	yes	characteristic
21	C₁₉×#405	—	2	2	no	—
22	C₁₉×#405	—	2	1	no	—
23	C₄×M₁₆×C₁₉	—	2	1	no	—
24	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
25	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₉	—	2	1	no	—
27	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
28	C₁₉×#329	—	2	2	no	—
29	C₁₉×Q₈⋊C₈	—	2	1	no	—
30	C₁₉×D₄⋊C₈	—	2	1	no	—
31	C₁₉×D₄⋊C₈	—	2	1	no	—
32	C₁₉×D₄⋊C₈	—	2	1	no	—
33	C₂×#41×C₁₉	—	2	1	no	—
34	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
35	C₂×SD₁₆×C₁₉	—	2	1	no	—
36	C₂×D₈×C₁₉	—	2	1	no	—
37	C₁₉×#131	—	2	4	no	—
38	C₁₉×#131	—	2	4	no	—
39	C₂×M₁₆×C₁₉	—	2	2	no	—
40	C₂×M₁₆×C₁₉	—	2	1	no	—
41	C₂×M₁₆×C₁₉	—	2	1	no	—
42	C₂×M₁₆×C₁₉	—	2	1	no	—
43	C₂²×C₈×C₁₉	—	2	2	no	—
44	C₂²×C₈×C₁₉	—	2	1	no	—
45	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
46	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
47	C₁₉×#124	—	2	1	no	—
48	C₁₉×#121	—	2	1	no	—
49	C₁₉×#121	—	2	1	no	—
50	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
51	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
52	C₄×D₄×C₁₉	—	2	1	no	—
53	C₄×D₄×C₁₉	—	2	1	no	—
54	C₄×D₄×C₁₉	—	2	1	no	—
55	C₄×D₄×C₁₉	—	2	1	no	—
56	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
57	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
58	C₁₉×#117	—	2	1	no	—
59	C₁₉×#117	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₉	—	2	1	no	—
61	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
62	C₁₉×#107	—	2	1	no	—
63	C₁₉×#106	—	2	1	no	—
64	C₁₉×C₄⋊C₈	—	2	1	no	—
65	C₁₉×C₄⋊C₈	—	2	1	no	—
66	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
67	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
68	C₁₉×#103	—	2	1	no	—
69	C₁₉×#102	—	2	1	no	—
70	C₁₉×#102	—	2	1	no	—
71	C₁₉×#102	—	2	1	no	—
72	C₁₉×C₂²⋊C₈	—	2	1	no	—
73	C₁₉×#97	—	2	2	no	—
74	C₁₉×#97	—	2	1	no	—
75	C₁₉×#97	D₄	1	2	yes	—
76	C₄×C₈×C₁₉	—	2	2	no	—
77	C₄×C₈×C₁₉	—	2	1	no	—
78	C₄×C₈×C₁₉	—	2	1	no	—
79	C₄×C₈×C₁₉	—	2	1	no	—
80	C₄×C₈×C₁₉	—	2	1	no	—
81	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
82	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
83	#41×C₁₉	—	2	2	no	—
84	#41×C₁₉	—	2	2	no	—
85	#41×C₁₉	—	8	1	no	—
86	#41×C₁₉	—	8	1	no	—
87	C₂×Q₈×C₁₉	—	2	1	no	—
88	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×D₄×C₁₉	—	2	1	no	—
90	C₂×D₄×C₁₉	—	2	1	no	—
91	C₂×D₄×C₁₉	—	2	1	no	—
92	C₂×D₄×C₁₉	—	2	1	no	—
93	C₂×D₄×C₁₉	—	4	1	no	—
94	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	—	2	1	no	—
96	C₂²×C₄×C₁₉	—	2	1	no	—
97	C₂²×C₄×C₁₉	—	2	1	no	—
98	C₂²×C₄×C₁₉	—	4	1	no	—
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
102	SD₁₆×C₁₉	—	4	2	no	—
103	D₈×C₁₉	—	4	2	no	—
104	M₁₆×C₁₉	—	2	8	no	—
105	M₁₆×C₁₉	—	2	2	no	—
106	M₁₆×C₁₉	—	2	2	no	—
107	M₁₆×C₁₉	—	2	2	no	—
108	M₁₆×C₁₉	—	4	1	no	—
109	M₁₆×C₁₉	—	8	1	no	—
110	C₂×C₈×C₁₉	—	2	8	no	—
111	C₂×C₈×C₁₉	—	2	2	no	—
112	C₂×C₈×C₁₉	—	2	2	no	—
113	C₂×C₈×C₁₉	—	2	1	no	—
114	C₂×C₈×C₁₉	—	2	2	no	—
115	C₂×C₈×C₁₉	—	2	1	no	—
116	C₂×C₈×C₁₉	—	2	1	no	—
117	C₂×C₈×C₁₉	—	2	1	no	—
118	C₂×C₈×C₁₉	—	4	1	no	—
119	C₂×C₈×C₁₉	—	4	1	no	—
120	C₄⋊C₄×C₁₉	—	2	1	no	—
121	C₄⋊C₄×C₁₉	—	2	1	no	—
122	C₄⋊C₄×C₁₉	—	2	1	no	—
123	C₄⋊C₄×C₁₉	—	2	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	—	4	1	no	—
130	C₂²⋊C₄×C₁₉	—	4	1	no	—
131	C₄²×C₁₉	—	2	1	no	—
132	C₄²×C₁₉	—	2	1	no	—
133	C₄²×C₁₉	—	2	1	no	—
134	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
135	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
138	#9211	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
139	C₂³×C₁₉	—	2	1	no	—
140	C₂³×C₁₉	—	4	1	no	—
141	C₂³×C₁₉	#123	1	1	yes	characteristic
142	Q₈×C₁₉	—	2	1	no	—
143	Q₈×C₁₉	—	8	1	no	—
144	Q₈×C₁₉	#104	1	2	yes	—
145	D₄×C₁₉	—	2	4	no	—
146	D₄×C₁₉	—	2	1	no	—
147	D₄×C₁₉	—	4	1	no	—
148	D₄×C₁₉	—	4	1	no	—
149	D₄×C₁₉	—	4	1	no	—
150	D₄×C₁₉	—	4	1	no	—
151	D₄×C₁₉	—	8	1	no	—
152	D₄×C₁₉	—	8	2	no	—
153	D₄×C₁₉	#104	1	2	yes	—
154	C₂×C₄×C₁₉	—	2	4	no	—
155	C₂×C₄×C₁₉	—	2	1	no	—
156	C₂×C₄×C₁₉	—	2	1	no	—
157	C₂×C₄×C₁₉	—	2	1	no	—
158	C₂×C₄×C₁₉	—	2	1	no	—
159	C₂×C₄×C₁₉	—	2	1	no	—
160	C₂×C₄×C₁₉	—	2	1	no	—
161	C₂×C₄×C₁₉	—	2	1	no	—
162	C₂×C₄×C₁₉	—	2	1	no	—
163	C₂×C₄×C₁₉	—	2	1	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	8	1	no	—
170	C₂×C₄×C₁₉	—	8	1	no	—
171	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
175	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
177	C₈×C₁₉	—	2	2	no	—
178	C₈×C₁₉	—	2	4	no	—
179	C₈×C₁₉	—	2	2	no	—
180	C₈×C₁₉	—	4	2	no	—
181	C₈×C₁₉	—	4	1	no	—
182	C₈×C₁₉	—	4	1	no	—
183	C₈×C₁₉	—	8	1	no	—
184	#3106	C₂×C₁₉	1	1	yes	characteristic
185	C₄×#131	C₂×C₁₉	1	1	yes	characteristic, complemented
186	#1525	C₂×C₁₉	1	1	yes	characteristic, complemented
187	#1492	C₂×C₁₉	1	1	yes	characteristic, complemented
188	#1489	C₂×C₁₉	1	1	yes	characteristic, complemented
189	#1299	C₂×C₁₉	1	1	yes	characteristic, complemented
190	#1278	C₂×C₁₉	1	1	yes	characteristic, complemented
191	C₂²×C₁₉	—	2	1	no	—
192	C₂²×C₁₉	—	2	1	no	—
193	C₂²×C₁₉	—	2	2	no	—
194	C₂²×C₁₉	—	2	1	no	—
195	C₂²×C₁₉	—	4	1	no	—
196	C₂²×C₁₉	—	4	1	no	—
197	C₂²×C₁₉	—	8	1	no	—
198	C₂²×C₁₉	—	8	1	no	—
199	C₂²×C₁₉	—	8	1	no	—
200	C₂²×C₁₉	#386	1	1	yes	characteristic
201	C₄×C₁₉	—	2	1	no	—
202	C₄×C₁₉	—	2	1	no	—
203	C₄×C₁₉	—	2	2	no	—
204	C₄×C₁₉	—	2	1	no	—
205	C₄×C₁₉	—	4	1	no	—
206	C₄×C₁₉	—	4	1	no	—
207	C₄×C₁₉	—	8	1	no	—
208	C₄×C₁₉	C₂×#104	1	1	yes	characteristic
209	C₄×C₁₉	C₂×#104	1	1	yes	characteristic
210	C₄×C₁₉	#443	1	1	yes	characteristic
211	C₄×C₁₉	#444	1	1	yes	characteristic
212	C₄×C₁₉	#471	1	1	yes	characteristic
213	C₄×C₁₉	#472	1	1	yes	characteristic
214	C₂×#131	—	2	1	no	—
215	#532	C₂²×C₁₉	1	1	yes	characteristic
216	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
217	#482	—	2	1	no	—
218	#477	C₄×C₁₉	1	1	yes	characteristic
219	#476	C₄×C₁₉	1	1	yes	characteristic
220	#460	C₄×C₁₉	1	1	yes	characteristic
221	#459	C₄×C₁₉	1	1	yes	characteristic
222	#449	—	2	1	no	—
223	C₄×SD₁₆	—	2	1	no	—
224	C₄×D₈	—	2	1	no	—
225	#431	C₂²×C₁₉	1	1	yes	characteristic
226	#423	C₂²×C₁₉	1	1	yes	characteristic
227	#405	—	2	1	no	—
228	#405	—	2	2	no	—
229	C₄×M₁₆	—	2	1	no	—
230	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
231	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
232	C₂×C₄×C₈	—	2	1	no	—
233	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
234	#329	—	2	2	no	—
235	Q₈⋊C₈	—	2	1	no	—
236	D₄⋊C₈	—	2	1	no	—
237	D₄⋊C₈	—	2	1	no	—
238	D₄⋊C₈	—	2	1	no	—
239	C₂×C₁₉	—	4	1	no	—
240	C₂×C₁₉	—	4	2	no	—
241	C₂×C₁₉	—	16	1	no	—
242	C₂×C₁₉	#1876	1	1	yes	characteristic
243	C₂×C₁₉	#1896	1	1	yes	characteristic
244	C₂×C₁₉	#1907	1	1	yes	characteristic
245	C₂×#41	—	2	1	no	—
246	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
247	C₂×SD₁₆	—	2	1	no	—
248	C₂×D₈	—	2	1	no	—
249	#131	—	2	4	no	—
250	#131	—	2	4	no	—
251	C₂×M₁₆	—	2	2	no	—
252	C₂×M₁₆	—	2	1	no	—
253	C₂×M₁₆	—	2	1	no	—
254	C₂×M₁₆	—	2	1	no	—
255	C₂²×C₈	—	2	2	no	—
256	C₂²×C₈	—	2	1	no	—
257	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
258	#127	C₂×C₄×C₁₉	1	1	yes	characteristic
259	#124	—	2	1	no	—
260	#121	—	2	1	no	—
261	#121	—	2	1	no	—
262	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
263	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
264	C₄×D₄	—	2	1	no	—
265	C₄×D₄	—	2	1	no	—
266	C₄×D₄	—	2	1	no	—
267	C₄×D₄	—	2	1	no	—
268	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
269	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
270	#117	—	2	1	no	—
271	#117	D₄×C₁₉	1	1	yes	characteristic
272	C₂×C₄²	—	2	1	no	—
273	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
274	#107	—	2	1	no	—
275	#106	—	2	1	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	—	2	1	no	—
278	C₄⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
279	C₄⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
280	#103	—	2	1	no	—
281	#102	—	2	1	no	—
282	#102	—	2	1	no	—
283	#102	—	2	1	no	—
284	C₂²⋊C₈	—	2	1	no	—
285	#97	—	2	2	no	—
286	#97	—	2	1	no	—
287	#97	D₄×C₁₉	1	2	yes	—
288	C₄×C₈	—	2	2	no	—
289	C₄×C₈	—	2	1	no	—
290	C₄×C₈	—	2	1	no	—
291	C₄×C₈	—	2	1	no	—
292	C₄×C₈	—	2	1	no	—
293	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
294	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
295	C₁₉	#9211	1	1	yes	characteristic, direct product factor, Sylow
296	#41	—	2	2	no	—
297	#41	—	2	2	no	—
298	#41	—	8	1	no	—
299	#41	—	8	1	no	—
300	C₂×Q₈	—	2	1	no	—
301	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	4	1	no	—
312	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
313	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
314	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
315	SD₁₆	—	4	2	no	—
316	D₈	—	4	2	no	—
317	M₁₆	—	2	8	no	—
318	M₁₆	—	2	2	no	—
319	M₁₆	—	2	2	no	—
320	M₁₆	—	2	2	no	—
321	M₁₆	—	4	1	no	—
322	M₁₆	—	8	1	no	—
323	C₂×C₈	—	2	8	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	4	1	no	—
332	C₂×C₈	—	4	1	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	2	1	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
338	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
339	C₂²⋊C₄	—	2	1	no	—
340	C₂²⋊C₄	—	2	1	no	—
341	C₂²⋊C₄	—	2	1	no	—
342	C₂²⋊C₄	—	4	1	no	—
343	C₂²⋊C₄	—	4	1	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	2	1	no	—
346	C₄²	—	2	1	no	—
347	C₄²	C₂²×C₄×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	C₂×D₄×C₁₉	1	1	yes	characteristic
351	C₂³	—	2	1	no	—
352	C₂³	—	4	1	no	—
353	C₂³	C₁₉×#123	1	1	yes	characteristic
354	Q₈	—	2	1	no	—
355	Q₈	—	8	1	no	—
356	Q₈	C₁₉×#104	1	2	yes	—
357	D₄	—	2	4	no	—
358	D₄	—	2	1	no	—
359	D₄	—	4	1	no	—
360	D₄	—	4	1	no	—
361	D₄	—	4	1	no	—
362	D₄	—	4	1	no	—
363	D₄	—	8	1	no	—
364	D₄	—	8	2	no	—
365	D₄	C₁₉×#104	1	2	yes	—
366	C₂×C₄	—	2	4	no	—
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	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	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	—	8	1	no	—
382	C₂×C₄	—	8	1	no	—
383	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
384	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
385	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
386	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
387	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
388	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
389	C₈	—	2	2	no	—
390	C₈	—	2	4	no	—
391	C₈	—	2	2	no	—
392	C₈	—	4	2	no	—
393	C₈	—	4	1	no	—
394	C₈	—	4	1	no	—
395	C₈	—	8	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	8	1	no	—
403	C₂²	—	8	1	no	—
404	C₂²	—	8	1	no	—
405	C₂²	C₁₉×#386	1	1	yes	characteristic
406	C₄	—	2	1	no	—
407	C₄	—	2	2	no	—
408	C₄	—	2	1	no	—
409	C₄	—	2	1	no	—
410	C₄	—	4	1	no	—
411	C₄	—	4	1	no	—
412	C₄	—	8	1	no	—
413	C₄	C₂×C₁₉×#104	1	1	yes	characteristic
414	C₄	C₂×C₁₉×#104	1	1	yes	characteristic
415	C₄	C₁₉×#443	1	1	yes	characteristic
416	C₄	C₁₉×#444	1	1	yes	characteristic
417	C₄	C₁₉×#471	1	1	yes	characteristic
418	C₄	C₁₉×#472	1	1	yes	characteristic
419	C₂	—	4	1	no	—
420	C₂	—	4	2	no	—
421	C₂	—	16	1	no	—
422	C₂	C₁₉×#1876	1	1	yes	characteristic
423	C₂	C₁₉×#1896	1	1	yes	characteristic
424	C₂	C₁₉×#1907	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	#121
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
socle	C₂²×C₁₉	#386
prime radical	C₁₉×#3106	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₄×C₁₉×#131	C₂	semidirect
3. C₁₉×#1525	C₂	semidirect
4. C₁₉×#1492	C₂	semidirect
5. C₁₉×#1489	C₂	semidirect
6. C₁₉×#1299	C₂	semidirect
7. C₁₉×#1278	C₂	semidirect
138. #9211	C₁₉	direct (N × H)
185. C₄×#131	C₂×C₁₉	semidirect
186. #1525	C₂×C₁₉	semidirect
187. #1492	C₂×C₁₉	semidirect
188. #1489	C₂×C₁₉	semidirect
189. #1299	C₂×C₁₉	semidirect
190. #1278	C₂×C₁₉	semidirect
295. C₁₉	#9211	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×#3106	2
C₄×C₁₉×#131	2
C₁₉×#1525	2
C₁₉×#1492	2
C₁₉×#1489	2
C₁₉×#1299	2
C₁₉×#1278	2
#9211	19

Subgroups — C19×#9211 #18015170

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9211 #18015170