Subgroups — C₁₉×#9349 #18015308

Order 4864.

474 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×#3040	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2970	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1527	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1488	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1469	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1307	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1299	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×#137	C₄	1	1	yes	characteristic
9	C₂×C₁₉×AGL(1,ℤ/8)	C₄	1	1	yes	characteristic
10	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
11	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#464	—	2	1	no	—
13	C₁₉×#464	—	2	1	no	—
14	C₁₉×#463	—	2	1	no	—
15	C₁₉×#463	—	2	1	no	—
16	C₁₉×#446	—	2	1	no	—
17	C₁₉×#435	—	2	2	no	—
18	C₈×D₄×C₁₉	—	2	1	no	—
19	C₁₉×#432	—	2	1	no	—
20	C₁₉×#432	C₂²	1	1	yes	characteristic
21	C₁₉×#432	C₂²	1	1	yes	characteristic
22	C₁₉×#431	C₂²	1	1	yes	characteristic
23	C₁₉×#423	C₂²	1	1	yes	characteristic
24	C₁₉×#419	C₄	1	1	yes	characteristic
25	C₁₉×#418	C₄	1	1	yes	characteristic
26	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#97	—	2	1	no	—
28	C₁₉×#329	—	2	1	no	—
29	C₁₉×#329	—	2	1	no	—
30	C₁₉×Q₈⋊C₈	—	2	1	no	—
31	C₁₉×D₄⋊C₈	—	2	1	no	—
32	C₁₉×#323	—	2	2	no	—
33	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₁₉×#137	—	4	2	no	—
37	C₁₉×AGL(1,ℤ/8)	—	4	2	no	—
38	C₂×Q₁₆×C₁₉	—	2	1	no	—
39	C₂×SD₁₆×C₁₉	—	2	1	no	—
40	C₂×SD₁₆×C₁₉	—	2	1	no	—
41	C₂×D₈×C₁₉	—	2	1	no	—
42	C₂×M₁₆×C₁₉	—	2	1	no	—
43	C₂×M₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₂×M₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₈×C₁₉	—	2	2	no	—
46	C₁₉×#124	—	2	1	no	—
47	C₁₉×#124	—	2	1	no	—
48	C₁₉×#124	—	2	1	no	—
49	C₁₉×#124	—	2	1	no	—
50	C₄×Q₈×C₁₉	D₄	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	D₄	1	1	yes	characteristic
55	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
56	C₁₉×#117	—	2	1	no	—
57	C₁₉×#117	C₂×C₄	1	1	yes	characteristic
58	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
60	C₂×C₄²×C₁₉	—	2	1	no	—
61	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
62	C₁₉×C₄⋊C₈	—	2	2	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	—	2	1	no	—
67	C₁₉×C₄⋊C₈	—	2	1	no	—
68	C₁₉×#103	—	2	1	no	—
69	C₁₉×#103	—	2	1	no	—
70	C₁₉×#102	—	2	1	no	—
71	C₁₉×#102	—	2	1	no	—
72	C₁₉×C₂²⋊C₈	—	2	2	no	—
73	C₁₉×C₂²⋊C₈	—	2	1	no	—
74	C₁₉×C₂²⋊C₈	—	2	1	no	—
75	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
76	C₁₉×#97	—	2	2	no	—
77	C₁₉×#97	—	2	1	no	—
78	C₁₉×#97	—	2	1	no	—
79	C₁₉×#97	D₄	1	1	yes	characteristic
80	C₁₉×#97	D₄	1	1	yes	characteristic
81	C₄×C₈×C₁₉	—	2	1	no	—
82	C₄×C₈×C₁₉	—	2	1	no	—
83	C₂⁴×C₁₉	—	2	1	no	—
84	#41×C₁₉	—	2	2	no	—
85	#41×C₁₉	—	4	1	no	—
86	C₂×Q₈×C₁₉	—	2	1	no	—
87	C₂×Q₈×C₁₉	—	2	1	no	—
88	C₂×Q₈×C₁₉	—	4	1	no	—
89	C₂×Q₈×C₁₉	—	4	1	no	—
90	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
91	C₂×D₄×C₁₉	—	2	1	no	—
92	C₂×D₄×C₁₉	—	2	1	no	—
93	C₂×D₄×C₁₉	—	2	1	no	—
94	C₂×D₄×C₁₉	—	4	1	no	—
95	C₂×D₄×C₁₉	—	4	1	no	—
96	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	—	2	1	no	—
98	C₂²×C₄×C₁₉	—	2	1	no	—
99	C₂²×C₄×C₁₉	—	2	1	no	—
100	C₂²×C₄×C₁₉	—	2	1	no	—
101	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
104	Q₁₆×C₁₉	—	4	2	no	—
105	SD₁₆×C₁₉	—	4	2	no	—
106	SD₁₆×C₁₉	—	4	2	no	—
107	D₈×C₁₉	—	4	2	no	—
108	M₁₆×C₁₉	—	4	2	no	—
109	M₁₆×C₁₉	—	4	1	no	—
110	M₁₆×C₁₉	—	4	1	no	—
111	C₂×C₈×C₁₉	—	2	1	no	—
112	C₂×C₈×C₁₉	—	2	1	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	—	4	4	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	1	no	—
121	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
122	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
123	C₂²⋊C₄×C₁₉	—	2	1	no	—
124	C₂²⋊C₄×C₁₉	—	2	1	no	—
125	C₂²⋊C₄×C₁₉	—	2	1	no	—
126	C₂²⋊C₄×C₁₉	—	4	1	no	—
127	C₂²⋊C₄×C₁₉	—	4	1	no	—
128	C₂²⋊C₄×C₁₉	—	4	1	no	—
129	C₂²⋊C₄×C₁₉	—	4	1	no	—
130	C₄²×C₁₉	—	2	1	no	—
131	C₄²×C₁₉	—	2	1	no	—
132	C₄²×C₁₉	—	2	1	no	—
133	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₁₉	#41	1	1	yes	characteristic
137	#9349	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
138	C₂³×C₁₉	—	2	1	no	—
139	C₂³×C₁₉	—	4	2	no	—
140	C₂³×C₁₉	—	4	1	no	—
141	C₂³×C₁₉	—	8	1	no	—
142	C₂³×C₁₉	—	8	1	no	—
143	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
144	Q₈×C₁₉	—	2	1	no	—
145	Q₈×C₁₉	—	2	1	no	—
146	Q₈×C₁₉	—	4	1	no	—
147	Q₈×C₁₉	—	4	1	no	—
148	Q₈×C₁₉	—	8	1	no	—
149	D₄×C₁₉	—	2	1	no	—
150	D₄×C₁₉	—	4	2	no	—
151	D₄×C₁₉	—	4	1	no	—
152	D₄×C₁₉	—	4	1	no	—
153	D₄×C₁₉	—	8	1	no	—
154	D₄×C₁₉	#100	1	2	yes	—
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	—	4	1	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	8	1	no	—
166	C₂×C₄×C₁₉	—	8	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	—	2	2	no	—
174	C₈×C₁₉	—	4	2	no	—
175	C₈×C₁₉	—	4	1	no	—
176	C₈×C₁₉	—	4	1	no	—
177	C₈×C₁₉	—	4	1	no	—
178	C₈×C₁₉	—	8	1	no	—
179	C₈×C₁₉	—	8	1	no	—
180	#3040	C₂×C₁₉	1	1	yes	characteristic
181	#2970	C₂×C₁₉	1	1	yes	characteristic, complemented
182	#1527	C₂×C₁₉	1	1	yes	characteristic, complemented
183	#1488	C₂×C₁₉	1	1	yes	characteristic, complemented
184	#1469	C₂×C₁₉	1	1	yes	characteristic, complemented
185	#1307	C₂×C₁₉	1	1	yes	characteristic, complemented
186	#1299	C₂×C₁₉	1	1	yes	characteristic, complemented
187	C₂²×C₁₉	—	2	1	no	—
188	C₂²×C₁₉	—	2	1	no	—
189	C₂²×C₁₉	—	2	2	no	—
190	C₂²×C₁₉	—	2	1	no	—
191	C₂²×C₁₉	—	4	1	no	—
192	C₂²×C₁₉	—	4	1	no	—
193	C₂²×C₁₉	—	8	1	no	—
194	C₂²×C₁₉	—	8	1	no	—
195	C₂²×C₁₉	—	8	1	no	—
196	C₂²×C₁₉	—	16	2	no	—
197	C₂²×C₁₉	#386	1	1	yes	characteristic
198	C₄×C₁₉	—	2	1	no	—
199	C₄×C₁₉	—	2	1	no	—
200	C₄×C₁₉	—	2	1	no	—
201	C₄×C₁₉	—	2	1	no	—
202	C₄×C₁₉	—	2	1	no	—
203	C₄×C₁₉	—	4	1	no	—
204	C₄×C₁₉	—	4	1	no	—
205	C₄×C₁₉	—	4	1	no	—
206	C₄×C₁₉	—	8	1	no	—
207	C₄×C₁₉	C₂×#100	1	1	yes	characteristic
208	C₄×C₁₉	#413	1	1	yes	characteristic
209	C₂×#137	C₄×C₁₉	1	1	yes	characteristic
210	C₂×AGL(1,ℤ/8)	C₄×C₁₉	1	1	yes	characteristic
211	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
212	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
213	#464	—	2	1	no	—
214	#464	—	2	1	no	—
215	#463	—	2	1	no	—
216	#463	—	2	1	no	—
217	#446	—	2	1	no	—
218	#435	—	2	2	no	—
219	C₈×D₄	—	2	1	no	—
220	#432	—	2	1	no	—
221	#432	C₂²×C₁₉	1	1	yes	characteristic
222	#432	C₂²×C₁₉	1	1	yes	characteristic
223	#431	C₂²×C₁₉	1	1	yes	characteristic
224	#423	C₂²×C₁₉	1	1	yes	characteristic
225	#419	C₄×C₁₉	1	1	yes	characteristic
226	#418	C₄×C₁₉	1	1	yes	characteristic
227	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
228	C₂×#97	—	2	1	no	—
229	#329	—	2	1	no	—
230	#329	—	2	1	no	—
231	Q₈⋊C₈	—	2	1	no	—
232	D₄⋊C₈	—	2	1	no	—
233	#323	—	2	2	no	—
234	C₂×C₁₉	—	4	1	no	—
235	C₂×C₁₉	—	4	2	no	—
236	C₂×C₁₉	—	16	1	no	—
237	C₂×C₁₉	#1881	1	1	yes	characteristic
238	C₂×C₁₉	#1900	1	1	yes	characteristic
239	C₂×C₁₉	#1906	1	1	yes	characteristic
240	C₂×#41	C₂×C₄×C₁₉	1	1	yes	characteristic
241	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
242	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
243	#137	—	4	2	no	—
244	AGL(1,ℤ/8)	—	4	2	no	—
245	C₂×Q₁₆	—	2	1	no	—
246	C₂×SD₁₆	—	2	1	no	—
247	C₂×SD₁₆	—	2	1	no	—
248	C₂×D₈	—	2	1	no	—
249	C₂×M₁₆	—	2	1	no	—
250	C₂×M₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
251	C₂×M₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
252	C₂²×C₈	—	2	2	no	—
253	#124	—	2	1	no	—
254	#124	—	2	1	no	—
255	#124	—	2	1	no	—
256	#124	—	2	1	no	—
257	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
258	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
259	C₄×D₄	—	2	1	no	—
260	C₄×D₄	—	2	1	no	—
261	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
262	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
263	#117	—	2	1	no	—
264	#117	C₂×C₄×C₁₉	1	1	yes	characteristic
265	C₂×C₂²⋊C₄	—	2	1	no	—
266	C₂×C₂²⋊C₄	—	2	1	no	—
267	C₂×C₄²	—	2	1	no	—
268	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
269	C₄⋊C₈	—	2	2	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	#103	—	2	1	no	—
276	#103	—	2	1	no	—
277	#102	—	2	1	no	—
278	#102	—	2	1	no	—
279	C₂²⋊C₈	—	2	2	no	—
280	C₂²⋊C₈	—	2	1	no	—
281	C₂²⋊C₈	—	2	1	no	—
282	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
283	#97	—	2	2	no	—
284	#97	—	2	1	no	—
285	#97	—	2	1	no	—
286	#97	D₄×C₁₉	1	1	yes	characteristic
287	#97	D₄×C₁₉	1	1	yes	characteristic
288	C₄×C₈	—	2	1	no	—
289	C₄×C₈	—	2	1	no	—
290	C₁₉	#9349	1	1	yes	characteristic, direct product factor, Sylow
291	C₂⁴	—	2	1	no	—
292	#41	—	2	2	no	—
293	#41	—	4	1	no	—
294	C₂×Q₈	—	2	1	no	—
295	C₂×Q₈	—	2	1	no	—
296	C₂×Q₈	—	4	1	no	—
297	C₂×Q₈	—	4	1	no	—
298	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	—	4	1	no	—
303	C₂×D₄	—	4	1	no	—
304	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
310	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
311	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
312	Q₁₆	—	4	2	no	—
313	SD₁₆	—	4	2	no	—
314	SD₁₆	—	4	2	no	—
315	D₈	—	4	2	no	—
316	M₁₆	—	4	2	no	—
317	M₁₆	—	4	1	no	—
318	M₁₆	—	4	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	4	4	no	—
325	C₂×C₈	—	4	1	no	—
326	C₂×C₈	—	4	1	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
330	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
331	C₂²⋊C₄	—	2	1	no	—
332	C₂²⋊C₄	—	2	1	no	—
333	C₂²⋊C₄	—	2	1	no	—
334	C₂²⋊C₄	—	4	1	no	—
335	C₂²⋊C₄	—	4	1	no	—
336	C₂²⋊C₄	—	4	1	no	—
337	C₂²⋊C₄	—	4	1	no	—
338	C₄²	—	2	1	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	2	1	no	—
341	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
342	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
343	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
344	C₄²	#41×C₁₉	1	1	yes	characteristic
345	C₂³	—	2	1	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	1	no	—
348	C₂³	—	8	1	no	—
349	C₂³	—	8	1	no	—
350	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
351	Q₈	—	2	1	no	—
352	Q₈	—	2	1	no	—
353	Q₈	—	4	1	no	—
354	Q₈	—	4	1	no	—
355	Q₈	—	8	1	no	—
356	D₄	—	2	1	no	—
357	D₄	—	4	2	no	—
358	D₄	—	4	1	no	—
359	D₄	—	4	1	no	—
360	D₄	—	8	1	no	—
361	D₄	C₁₉×#100	1	2	yes	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	8	1	no	—
373	C₂×C₄	—	8	1	no	—
374	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
375	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
376	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
377	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
378	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
379	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
380	C₈	—	2	2	no	—
381	C₈	—	4	2	no	—
382	C₈	—	4	1	no	—
383	C₈	—	4	1	no	—
384	C₈	—	4	1	no	—
385	C₈	—	8	1	no	—
386	C₈	—	8	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	4	1	no	—
392	C₂²	—	4	1	no	—
393	C₂²	—	8	1	no	—
394	C₂²	—	8	1	no	—
395	C₂²	—	8	1	no	—
396	C₂²	—	16	2	no	—
397	C₂²	C₁₉×#386	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	4	1	no	—
404	C₄	—	4	1	no	—
405	C₄	—	4	1	no	—
406	C₄	—	8	1	no	—
407	C₄	C₂×C₁₉×#100	1	1	yes	characteristic
408	C₄	C₁₉×#413	1	1	yes	characteristic
409	C₂	—	4	1	no	—
410	C₂	—	4	2	no	—
411	C₂	—	16	1	no	—
412	C₂	C₁₉×#1881	1	1	yes	characteristic
413	C₂	C₁₉×#1900	1	1	yes	characteristic
414	C₂	C₁₉×#1906	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	C₂×C₁₉×AGL(1,ℤ/8)	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
2. C₁₉×#2970	C₂	semidirect
3. C₁₉×#1527	C₂	semidirect
4. C₁₉×#1488	C₂	semidirect
5. C₁₉×#1469	C₂	semidirect
6. C₁₉×#1307	C₂	semidirect
7. C₁₉×#1299	C₂	semidirect
137. #9349	C₁₉	direct (N × H)
181. #2970	C₂×C₁₉	semidirect
182. #1527	C₂×C₁₉	semidirect
183. #1488	C₂×C₁₉	semidirect
184. #1469	C₂×C₁₉	semidirect
185. #1307	C₂×C₁₉	semidirect
186. #1299	C₂×C₁₉	semidirect
290. C₁₉	#9349	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×#3040	2
C₁₉×#2970	2
C₁₉×#1527	2
C₁₉×#1488	2
C₁₉×#1469	2
C₁₉×#1307	2
C₁₉×#1299	2
#9349	19

Subgroups — C19×#9349 #18015308

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9349 #18015308