Subgroups — C₁₉×#9051 #18015010

Order 4864.

436 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3108	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2992	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1985	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1524	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1491	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1302	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1283	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#529	C₂²	1	1	yes	characteristic
9	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×#483	C₄	1	1	yes	characteristic
11	C₁₉×#480	C₄	1	1	yes	characteristic
12	C₁₉×#479	—	2	1	no	—
13	C₁₉×#464	—	2	1	no	—
14	C₁₉×#451	C₄	1	1	yes	characteristic
15	C₁₉×#448	C₄	1	1	yes	characteristic
16	C₁₉×#446	—	2	1	no	—
17	C₄×Q₁₆×C₁₉	—	2	1	no	—
18	C₄×SD₁₆×C₁₉	—	2	1	no	—
19	C₁₉×#435	—	2	1	no	—
20	C₁₉×#435	—	2	1	no	—
21	C₈×D₄×C₁₉	—	2	1	no	—
22	C₁₉×#433	—	2	1	no	—
23	C₁₉×#432	C₂²	1	1	yes	characteristic
24	C₁₉×#431	C₂²	1	1	yes	characteristic
25	C₁₉×#424	—	2	1	no	—
26	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
29	C₁₉×#336	—	2	1	no	—
30	C₁₉×#336	—	2	1	no	—
31	C₁₉×#330	—	2	1	no	—
32	C₁₉×#329	—	2	1	no	—
33	C₁₉×Q₈⋊C₈	—	2	1	no	—
34	C₁₉×Q₈⋊C₈	—	2	1	no	—
35	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂×Q₁₆×C₁₉	—	2	1	no	—
37	C₂×SD₁₆×C₁₉	—	2	1	no	—
38	C₂×M₁₆×C₁₉	—	2	1	no	—
39	C₂×M₁₆×C₁₉	—	2	1	no	—
40	C₂²×C₈×C₁₉	—	2	1	no	—
41	C₂²×C₈×C₁₉	—	2	1	no	—
42	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
43	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
44	C₁₉×#126	—	2	1	no	—
45	C₁₉×#125	D₄	1	1	yes	characteristic
46	C₁₉×#124	D₄	1	1	yes	characteristic
47	C₁₉×#123	—	2	1	no	—
48	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
49	C₁₉×#121	C₂×C₄	1	1	yes	characteristic
50	C₄×Q₈×C₁₉	—	2	1	no	—
51	C₄×Q₈×C₁₉	—	2	1	no	—
52	C₄×Q₈×C₁₉	—	2	1	no	—
53	C₄×Q₈×C₁₉	—	2	1	no	—
54	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
55	C₄×D₄×C₁₉	—	2	1	no	—
56	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
57	C₁₉×#117	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₉	C₂×C₄	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	—	2	1	no	—
67	C₁₉×C₄⋊C₈	—	2	1	no	—
68	C₁₉×C₄⋊C₈	—	2	1	no	—
69	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
70	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
71	C₁₉×#103	—	2	1	no	—
72	C₁₉×#103	—	2	1	no	—
73	C₁₉×#103	—	2	1	no	—
74	C₁₉×#102	—	2	1	no	—
75	C₁₉×C₂²⋊C₈	—	2	1	no	—
76	C₁₉×C₂²⋊C₈	—	2	1	no	—
77	C₁₉×C₂²⋊C₈	—	2	1	no	—
78	C₁₉×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
79	C₁₉×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
80	C₁₉×#97	—	2	1	no	—
81	C₁₉×#97	—	2	1	no	—
82	C₁₉×#97	—	2	1	no	—
83	C₁₉×#97	—	2	1	no	—
84	C₁₉×#97	—	2	1	no	—
85	C₄×C₈×C₁₉	—	2	1	no	—
86	C₄×C₈×C₁₉	—	2	1	no	—
87	C₄×C₈×C₁₉	—	2	1	no	—
88	C₂×Q₈×C₁₉	—	2	1	no	—
89	C₂×Q₈×C₁₉	—	2	1	no	—
90	C₂×Q₈×C₁₉	—	4	2	no	—
91	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
92	C₂×D₄×C₁₉	—	2	1	no	—
93	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	—	2	1	no	—
95	C₂²×C₄×C₁₉	—	2	1	no	—
96	C₂²×C₄×C₁₉	—	2	1	no	—
97	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
100	Q₁₆×C₁₉	—	4	2	no	—
101	SD₁₆×C₁₉	—	4	2	no	—
102	M₁₆×C₁₉	—	2	2	no	—
103	M₁₆×C₁₉	—	4	1	no	—
104	M₁₆×C₁₉	—	8	1	no	—
105	C₂×C₈×C₁₉	—	2	2	no	—
106	C₂×C₈×C₁₉	—	2	1	no	—
107	C₂×C₈×C₁₉	—	2	1	no	—
108	C₂×C₈×C₁₉	—	2	1	no	—
109	C₂×C₈×C₁₉	—	2	1	no	—
110	C₂×C₈×C₁₉	—	2	1	no	—
111	C₂×C₈×C₁₉	—	2	1	no	—
112	C₂×C₈×C₁₉	—	4	1	no	—
113	C₂×C₈×C₁₉	—	4	1	no	—
114	C₂×C₈×C₁₉	—	4	1	no	—
115	C₂×C₈×C₁₉	—	4	1	no	—
116	C₂×C₈×C₁₉	—	4	1	no	—
117	C₂×C₈×C₁₉	—	8	1	no	—
118	C₄⋊C₄×C₁₉	—	2	1	no	—
119	C₄⋊C₄×C₁₉	—	2	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	—	4	1	no	—
125	C₄⋊C₄×C₁₉	—	4	1	no	—
126	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
127	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
128	C₂²⋊C₄×C₁₉	—	2	1	no	—
129	C₂²⋊C₄×C₁₉	—	2	1	no	—
130	C₂²⋊C₄×C₁₉	—	2	1	no	—
131	C₂²⋊C₄×C₁₉	—	2	1	no	—
132	C₂²⋊C₄×C₁₉	—	2	1	no	—
133	C₄²×C₁₉	—	2	1	no	—
134	C₄²×C₁₉	—	4	1	no	—
135	C₄²×C₁₉	—	4	1	no	—
136	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₁₉	#41	1	1	yes	characteristic
140	#9051	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂³×C₁₉	—	2	1	no	—
142	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
143	Q₈×C₁₉	—	2	2	no	—
144	Q₈×C₁₉	—	2	2	no	—
145	Q₈×C₁₉	—	4	1	no	—
146	Q₈×C₁₉	—	4	1	no	—
147	Q₈×C₁₉	—	4	1	no	—
148	D₄×C₁₉	—	4	1	no	—
149	D₄×C₁₉	—	4	1	no	—
150	D₄×C₁₉	—	4	1	no	—
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	—	2	2	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	—	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	1	no	—
167	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
171	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
173	C₈×C₁₉	—	4	2	no	—
174	C₈×C₁₉	—	4	1	no	—
175	C₈×C₁₉	—	4	1	no	—
176	C₈×C₁₉	—	4	2	no	—
177	C₈×C₁₉	—	4	1	no	—
178	C₈×C₁₉	—	4	1	no	—
179	C₈×C₁₉	—	4	1	no	—
180	C₈×C₁₉	—	4	1	no	—
181	#3108	C₂×C₁₉	1	1	yes	characteristic
182	#2992	C₂×C₁₉	1	1	yes	characteristic
183	#1985	C₂×C₁₉	1	1	yes	characteristic, complemented
184	#1524	C₂×C₁₉	1	1	yes	characteristic
185	#1491	C₂×C₁₉	1	1	yes	characteristic, complemented
186	#1302	C₂×C₁₉	1	1	yes	characteristic, complemented
187	#1283	C₂×C₁₉	1	1	yes	characteristic, complemented
188	C₂²×C₁₉	—	2	1	no	—
189	C₂²×C₁₉	—	2	1	no	—
190	C₂²×C₁₉	—	4	1	no	—
191	C₂²×C₁₉	—	4	1	no	—
192	C₂²×C₁₉	—	4	1	no	—
193	C₂²×C₁₉	#386	1	1	yes	characteristic
194	C₂²×C₁₉	#443	1	1	yes	characteristic
195	C₂²×C₁₉	#444	1	1	yes	characteristic
196	C₄×C₁₉	—	2	1	no	—
197	C₄×C₁₉	—	2	1	no	—
198	C₄×C₁₉	—	2	1	no	—
199	C₄×C₁₉	—	2	1	no	—
200	C₄×C₁₉	—	2	1	no	—
201	C₄×C₁₉	—	4	1	no	—
202	C₄×C₁₉	—	4	1	no	—
203	C₄×C₁₉	—	4	2	no	—
204	C₄×C₁₉	—	4	1	no	—
205	C₄×C₁₉	—	8	1	no	—
206	C₄×C₁₉	#455	1	1	yes	characteristic
207	C₄×C₁₉	#456	1	1	yes	characteristic
208	#529	C₂²×C₁₉	1	1	yes	characteristic
209	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
210	#483	C₄×C₁₉	1	1	yes	characteristic
211	#480	C₄×C₁₉	1	1	yes	characteristic
212	#479	—	2	1	no	—
213	#464	—	2	1	no	—
214	#451	C₄×C₁₉	1	1	yes	characteristic
215	#448	C₄×C₁₉	1	1	yes	characteristic
216	#446	—	2	1	no	—
217	C₄×Q₁₆	—	2	1	no	—
218	C₄×SD₁₆	—	2	1	no	—
219	#435	—	2	1	no	—
220	#435	—	2	1	no	—
221	C₈×D₄	—	2	1	no	—
222	#433	—	2	1	no	—
223	#432	C₂²×C₁₉	1	1	yes	characteristic
224	#431	C₂²×C₁₉	1	1	yes	characteristic
225	#424	—	2	1	no	—
226	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
227	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
228	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
229	#336	—	2	1	no	—
230	#336	—	2	1	no	—
231	#330	—	2	1	no	—
232	#329	—	2	1	no	—
233	Q₈⋊C₈	—	2	1	no	—
234	Q₈⋊C₈	—	2	1	no	—
235	C₂×C₁₉	—	2	1	no	—
236	C₂×C₁₉	—	2	1	no	—
237	C₂×C₁₉	—	8	1	no	—
238	C₂×C₁₉	#1876	1	1	yes	characteristic
239	C₂×C₁₉	#1882	1	1	yes	characteristic
240	C₂×C₁₉	#1891	1	1	yes	characteristic
241	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
242	C₂×Q₁₆	—	2	1	no	—
243	C₂×SD₁₆	—	2	1	no	—
244	C₂×M₁₆	—	2	1	no	—
245	C₂×M₁₆	—	2	1	no	—
246	C₂²×C₈	—	2	1	no	—
247	C₂²×C₈	—	2	1	no	—
248	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
249	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
250	#126	—	2	1	no	—
251	#125	D₄×C₁₉	1	1	yes	characteristic
252	#124	D₄×C₁₉	1	1	yes	characteristic
253	#123	—	2	1	no	—
254	C₂²⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
255	#121	C₂×C₄×C₁₉	1	1	yes	characteristic
256	C₄×Q₈	—	2	1	no	—
257	C₄×Q₈	—	2	1	no	—
258	C₄×Q₈	—	2	1	no	—
259	C₄×Q₈	—	2	1	no	—
260	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
261	C₄×D₄	—	2	1	no	—
262	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
263	#117	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
266	C₂×C₄²	—	2	1	no	—
267	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
268	#107	—	2	1	no	—
269	#106	—	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	—	2	1	no	—
275	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
276	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
277	#103	—	2	1	no	—
278	#103	—	2	1	no	—
279	#103	—	2	1	no	—
280	#102	—	2	1	no	—
281	C₂²⋊C₈	—	2	1	no	—
282	C₂²⋊C₈	—	2	1	no	—
283	C₂²⋊C₈	—	2	1	no	—
284	C₂²⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
285	C₂²⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
286	#97	—	2	1	no	—
287	#97	—	2	1	no	—
288	#97	—	2	1	no	—
289	#97	—	2	1	no	—
290	#97	—	2	1	no	—
291	C₄×C₈	—	2	1	no	—
292	C₄×C₈	—	2	1	no	—
293	C₄×C₈	—	2	1	no	—
294	C₁₉	#9051	1	1	yes	characteristic, direct product factor, Sylow
295	C₂×Q₈	—	2	1	no	—
296	C₂×Q₈	—	2	1	no	—
297	C₂×Q₈	—	4	2	no	—
298	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
306	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
307	Q₁₆	—	4	2	no	—
308	SD₁₆	—	4	2	no	—
309	M₁₆	—	2	2	no	—
310	M₁₆	—	4	1	no	—
311	M₁₆	—	8	1	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	4	1	no	—
320	C₂×C₈	—	4	1	no	—
321	C₂×C₈	—	4	1	no	—
322	C₂×C₈	—	4	1	no	—
323	C₂×C₈	—	4	1	no	—
324	C₂×C₈	—	8	1	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	4	1	no	—
332	C₄⋊C₄	—	4	1	no	—
333	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
334	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
335	C₂²⋊C₄	—	2	1	no	—
336	C₂²⋊C₄	—	2	1	no	—
337	C₂²⋊C₄	—	2	1	no	—
338	C₂²⋊C₄	—	2	1	no	—
339	C₂²⋊C₄	—	2	1	no	—
340	C₄²	—	2	1	no	—
341	C₄²	—	4	1	no	—
342	C₄²	—	4	1	no	—
343	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
344	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
345	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
346	C₄²	#41×C₁₉	1	1	yes	characteristic
347	C₂³	—	2	1	no	—
348	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
349	Q₈	—	2	2	no	—
350	Q₈	—	2	2	no	—
351	Q₈	—	4	1	no	—
352	Q₈	—	4	1	no	—
353	Q₈	—	4	1	no	—
354	D₄	—	4	1	no	—
355	D₄	—	4	1	no	—
356	D₄	—	4	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
374	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
375	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
376	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
377	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
378	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
379	C₈	—	4	2	no	—
380	C₈	—	4	1	no	—
381	C₈	—	4	1	no	—
382	C₈	—	4	2	no	—
383	C₈	—	4	1	no	—
384	C₈	—	4	1	no	—
385	C₈	—	4	1	no	—
386	C₈	—	4	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	4	1	no	—
391	C₂²	—	4	1	no	—
392	C₂²	C₁₉×#386	1	1	yes	characteristic
393	C₂²	C₁₉×#443	1	1	yes	characteristic
394	C₂²	C₁₉×#444	1	1	yes	characteristic
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	4	2	no	—
401	C₄	—	4	1	no	—
402	C₄	—	4	1	no	—
403	C₄	—	4	1	no	—
404	C₄	—	8	1	no	—
405	C₄	C₁₉×#455	1	1	yes	characteristic
406	C₄	C₁₉×#456	1	1	yes	characteristic
407	C₂	—	2	1	no	—
408	C₂	—	2	1	no	—
409	C₂	—	8	1	no	—
410	C₂	C₁₉×#1876	1	1	yes	characteristic
411	C₂	C₁₉×#1882	1	1	yes	characteristic
412	C₂	C₁₉×#1891	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	#120
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
socle	C₂²×C₁₉	#386
prime radical	C₁₉×#121	C₂×C₄
LCS	G ▷ C₂²×C₄ ▷ 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
3. C₁₉×#1985	C₂	semidirect
5. C₁₉×#1491	C₂	semidirect
6. C₁₉×#1302	C₂	semidirect
7. C₁₉×#1283	C₂	semidirect
140. #9051	C₁₉	direct (N × H)
183. #1985	C₂×C₁₉	semidirect
185. #1491	C₂×C₁₉	semidirect
186. #1302	C₂×C₁₉	semidirect
187. #1283	C₂×C₁₉	semidirect
294. C₁₉	#9051	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×#3108	2
C₁₉×#2992	2
C₁₉×#1985	2
C₁₉×#1524	2
C₁₉×#1491	2
C₁₉×#1302	2
C₁₉×#1283	2
#9051	19

Subgroups — C19×#9051 #18015010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9051 #18015010