Subgroups — C₁₉×#8496 #18014455

Order 4864.

676 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×#3550	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1995	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1559	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1557	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1537	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1506	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1505	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#563	—	2	2	no	—
9	C₁₉×#559	—	2	1	no	—
10	Q₈²×C₁₉	—	2	1	no	—
11	C₁₉×#556	—	2	1	no	—
12	C₁₉×#556	C₄	1	2	yes	complemented
13	D₄×Q₈×C₁₉	—	2	1	no	—
14	D₄×Q₈×C₁₉	C₄	1	2	yes	complemented
15	C₁₉×#542	—	2	2	no	—
16	C₁₉×#542	—	2	2	no	—
17	C₁₉×#536	—	2	2	no	—
18	C₁₉×#533	C₂²	1	1	yes	characteristic
19	C₁₉×#533	C₂²	1	1	yes	characteristic
20	C₁₉×#532	C₂²	1	1	yes	characteristic
21	C₁₉×#432	C₂²	1	1	yes	characteristic
22	C₁₉×#432	C₂²	1	1	yes	characteristic
23	C₁₉×#423	C₂²	1	1	yes	characteristic
24	C₁₉×#376	C₂²	1	1	yes	characteristic
25	C₁₉×#339	—	2	2	no	—
26	C₁₉×#333	—	2	1	no	—
27	C₁₉×#332	—	2	1	no	—
28	C₁₉×#332	—	2	1	no	—
29	C₁₉×#331	—	2	1	no	—
30	C₁₉×#330	—	2	2	no	—
31	C₁₉×#328	—	2	2	no	—
32	C₁₉×#327	—	2	2	no	—
33	C₂×#41×C₁₉	—	2	1	no	—
34	C₂²×Q₈×C₁₉	—	2	2	no	—
35	C₂×M₁₆×C₁₉	—	2	1	no	—
36	C₁₉×C₄⋊Q₈	—	2	4	no	—
37	C₁₉×C₄⋊Q₈	—	2	2	no	—
38	C₁₉×C₄⋊Q₈	—	2	2	no	—
39	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
40	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
41	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
42	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
43	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
44	C₁₉×#127	D₄	1	1	yes	characteristic
45	C₁₉×#126	—	2	4	no	—
46	C₁₉×#126	—	2	4	no	—
47	C₁₉×#125	—	2	1	no	—
48	C₁₉×#125	D₄	1	2	yes	—
49	C₁₉×#124	—	2	4	no	—
50	C₁₉×#124	—	2	2	no	—
51	C₁₉×#124	—	2	2	no	—
52	C₁₉×#124	—	2	1	no	—
53	C₁₉×#123	—	2	4	no	—
54	C₁₉×#123	—	2	4	no	—
55	C₁₉×C₂²⋊Q₈	—	2	4	no	—
56	C₁₉×C₂²⋊Q₈	—	2	2	no	—
57	C₁₉×C₂²⋊Q₈	—	2	1	no	—
58	C₁₉×C₂²⋊Q₈	—	2	1	no	—
59	C₁₉×C₂²⋊Q₈	—	2	1	no	—
60	C₁₉×C₂²⋊Q₈	—	2	2	no	—
61	C₁₉×C₂²⋊Q₈	—	2	4	no	—
62	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
63	C₁₉×#121	—	2	1	no	—
64	C₁₉×#121	D₄	1	2	yes	—
65	C₄×Q₈×C₁₉	—	2	2	no	—
66	C₄×Q₈×C₁₉	—	2	2	no	—
67	C₄×Q₈×C₁₉	—	2	1	no	—
68	C₄×Q₈×C₁₉	—	2	1	no	—
69	C₄×Q₈×C₁₉	—	2	1	no	—
70	C₄×Q₈×C₁₉	C₂×C₄	1	2	yes	—
71	C₄×D₄×C₁₉	—	2	2	no	—
72	C₄×D₄×C₁₉	—	2	2	no	—
73	C₄×D₄×C₁₉	—	2	1	no	—
74	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
75	C₁₉×#117	—	2	1	no	—
76	C₁₉×#117	—	2	2	no	—
77	C₁₉×#117	D₄	1	2	yes	—
78	C₂×C₄²×C₁₉	—	2	1	no	—
79	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
80	C₁₉×C₄⋊C₈	—	2	1	no	—
81	C₁₉×C₄⋊C₈	—	2	1	no	—
82	C₁₉×C₄⋊C₈	—	2	1	no	—
83	C₁₉×C₄⋊C₈	—	2	1	no	—
84	C₁₉×C₂²⋊C₈	—	2	1	no	—
85	C₁₉×C₂²⋊C₈	—	2	1	no	—
86	C₁₉×#97	—	2	1	no	—
87	C₁₉×#97	—	2	1	no	—
88	C₁₉×#95	—	2	1	no	—
89	C₁₉×#95	—	2	1	no	—
90	#41×C₁₉	—	8	2	no	—
91	C₂×Q₈×C₁₉	—	2	4	no	—
92	C₂×Q₈×C₁₉	—	2	1	no	—
93	C₂×Q₈×C₁₉	—	2	1	no	—
94	C₂×Q₈×C₁₉	—	2	1	no	—
95	C₂×Q₈×C₁₉	—	2	1	no	—
96	C₂×Q₈×C₁₉	—	8	4	no	—
97	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
98	C₂×D₄×C₁₉	—	2	2	no	—
99	C₂×D₄×C₁₉	—	2	1	no	—
100	C₂×D₄×C₁₉	—	2	1	no	—
101	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
102	C₂²×C₄×C₁₉	—	2	4	no	—
103	C₂²×C₄×C₁₉	—	2	2	no	—
104	C₂²×C₄×C₁₉	—	4	1	no	—
105	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
108	M₁₆×C₁₉	—	4	2	no	—
109	C₂×C₈×C₁₉	—	4	1	no	—
110	C₂×C₈×C₁₉	—	4	1	no	—
111	C₂×C₈×C₁₉	—	4	1	no	—
112	C₄⋊C₄×C₁₉	—	2	4	no	—
113	C₄⋊C₄×C₁₉	—	2	4	no	—
114	C₄⋊C₄×C₁₉	—	2	1	no	—
115	C₄⋊C₄×C₁₉	—	2	1	no	—
116	C₄⋊C₄×C₁₉	—	2	2	no	—
117	C₄⋊C₄×C₁₉	—	2	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	2	no	—
122	C₄⋊C₄×C₁₉	—	2	2	no	—
123	C₄⋊C₄×C₁₉	—	2	2	no	—
124	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
125	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
126	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
127	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
128	C₂²⋊C₄×C₁₉	—	2	4	no	—
129	C₂²⋊C₄×C₁₉	—	2	4	no	—
130	C₂²⋊C₄×C₁₉	—	2	4	no	—
131	C₂²⋊C₄×C₁₉	—	2	2	no	—
132	C₂²⋊C₄×C₁₉	—	2	2	no	—
133	C₂²⋊C₄×C₁₉	—	2	2	no	—
134	C₂²⋊C₄×C₁₉	—	2	2	no	—
135	C₄²×C₁₉	—	2	4	no	—
136	C₄²×C₁₉	—	2	2	no	—
137	C₄²×C₁₉	—	2	2	no	—
138	C₄²×C₁₉	—	2	2	no	—
139	C₄²×C₁₉	—	4	1	no	—
140	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
141	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
144	#8496	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂³×C₁₉	—	2	2	no	—
146	C₂³×C₁₉	#120	1	1	yes	characteristic
147	Q₈×C₁₉	—	4	2	no	—
148	Q₈×C₁₉	—	4	2	no	—
149	Q₈×C₁₉	—	4	2	no	—
150	Q₈×C₁₉	—	4	1	no	—
151	Q₈×C₁₉	—	4	1	no	—
152	Q₈×C₁₉	—	8	1	no	—
153	Q₈×C₁₉	—	8	4	no	—
154	D₄×C₁₉	—	4	2	no	—
155	D₄×C₁₉	—	4	1	no	—
156	D₄×C₁₉	—	4	1	no	—
157	D₄×C₁₉	—	8	1	no	—
158	D₄×C₁₉	—	8	2	no	—
159	C₂×C₄×C₁₉	—	2	1	no	—
160	C₂×C₄×C₁₉	—	2	1	no	—
161	C₂×C₄×C₁₉	—	2	2	no	—
162	C₂×C₄×C₁₉	—	2	2	no	—
163	C₂×C₄×C₁₉	—	2	2	no	—
164	C₂×C₄×C₁₉	—	2	2	no	—
165	C₂×C₄×C₁₉	—	2	2	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	4	no	—
169	C₂×C₄×C₁₉	—	4	2	no	—
170	C₂×C₄×C₁₉	—	8	4	no	—
171	C₂×C₄×C₁₉	—	8	1	no	—
172	C₂×C₄×C₁₉	—	8	1	no	—
173	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
179	C₈×C₁₉	—	8	1	no	—
180	C₈×C₁₉	—	8	1	no	—
181	C₈×C₁₉	—	8	1	no	—
182	#3550	C₂×C₁₉	1	1	yes	characteristic
183	#1995	C₂×C₁₉	1	1	yes	characteristic, complemented
184	#1559	C₂×C₁₉	1	1	yes	characteristic, complemented
185	#1557	C₂×C₁₉	1	1	yes	characteristic
186	#1537	C₂×C₁₉	1	1	yes	characteristic, complemented
187	#1506	C₂×C₁₉	1	1	yes	characteristic, complemented
188	#1505	C₂×C₁₉	1	1	yes	characteristic
189	C₂²×C₁₉	—	2	1	no	—
190	C₂²×C₁₉	—	2	1	no	—
191	C₂²×C₁₉	—	2	1	no	—
192	C₂²×C₁₉	—	4	2	no	—
193	C₂²×C₁₉	—	4	2	no	—
194	C₂²×C₁₉	—	4	2	no	—
195	C₂²×C₁₉	#379	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	2	no	—
202	C₄×C₁₉	—	4	2	no	—
203	C₄×C₁₉	—	4	2	no	—
204	C₄×C₁₉	—	4	2	no	—
205	C₄×C₁₉	—	4	2	no	—
206	C₄×C₁₉	—	8	2	no	—
207	C₄×C₁₉	#454	1	1	yes	characteristic
208	C₄×C₁₉	#456	1	1	yes	characteristic
209	#563	—	2	2	no	—
210	#559	—	2	1	no	—
211	Q₈²	—	2	1	no	—
212	#556	—	2	1	no	—
213	#556	C₄×C₁₉	1	2	yes	complemented
214	D₄×Q₈	—	2	1	no	—
215	D₄×Q₈	C₄×C₁₉	1	2	yes	complemented
216	#542	—	2	2	no	—
217	#542	—	2	2	no	—
218	#536	—	2	2	no	—
219	#533	C₂²×C₁₉	1	1	yes	characteristic
220	#533	C₂²×C₁₉	1	1	yes	characteristic
221	#532	C₂²×C₁₉	1	1	yes	characteristic
222	#432	C₂²×C₁₉	1	1	yes	characteristic
223	#432	C₂²×C₁₉	1	1	yes	characteristic
224	#423	C₂²×C₁₉	1	1	yes	characteristic
225	#376	C₂²×C₁₉	1	1	yes	characteristic
226	#339	—	2	2	no	—
227	#333	—	2	1	no	—
228	#332	—	2	1	no	—
229	#332	—	2	1	no	—
230	#331	—	2	1	no	—
231	#330	—	2	2	no	—
232	#328	—	2	2	no	—
233	#327	—	2	2	no	—
234	C₂×C₁₉	—	4	1	no	—
235	C₂×C₁₉	—	8	2	no	—
236	C₂×C₁₉	#1793	1	1	yes	characteristic
237	C₂×C₁₉	#1795	1	1	yes	characteristic
238	C₂×C₁₉	#1796	1	1	yes	characteristic
239	C₂×#41	—	2	1	no	—
240	C₂²×Q₈	—	2	2	no	—
241	C₂×M₁₆	—	2	1	no	—
242	C₄⋊Q₈	—	2	4	no	—
243	C₄⋊Q₈	—	2	2	no	—
244	C₄⋊Q₈	—	2	2	no	—
245	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
246	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
247	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
248	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
249	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
250	#127	D₄×C₁₉	1	1	yes	characteristic
251	#126	—	2	4	no	—
252	#126	—	2	4	no	—
253	#125	—	2	1	no	—
254	#125	D₄×C₁₉	1	2	yes	—
255	#124	—	2	4	no	—
256	#124	—	2	2	no	—
257	#124	—	2	2	no	—
258	#124	—	2	1	no	—
259	#123	—	2	4	no	—
260	#123	—	2	4	no	—
261	C₂²⋊Q₈	—	2	4	no	—
262	C₂²⋊Q₈	—	2	2	no	—
263	C₂²⋊Q₈	—	2	1	no	—
264	C₂²⋊Q₈	—	2	1	no	—
265	C₂²⋊Q₈	—	2	1	no	—
266	C₂²⋊Q₈	—	2	2	no	—
267	C₂²⋊Q₈	—	2	4	no	—
268	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
269	#121	—	2	1	no	—
270	#121	D₄×C₁₉	1	2	yes	—
271	C₄×Q₈	—	2	2	no	—
272	C₄×Q₈	—	2	2	no	—
273	C₄×Q₈	—	2	1	no	—
274	C₄×Q₈	—	2	1	no	—
275	C₄×Q₈	—	2	1	no	—
276	C₄×Q₈	C₂×C₄×C₁₉	1	2	yes	—
277	C₄×D₄	—	2	2	no	—
278	C₄×D₄	—	2	2	no	—
279	C₄×D₄	—	2	1	no	—
280	C₄×D₄	C₂×C₄×C₁₉	1	2	yes	—
281	#117	—	2	1	no	—
282	#117	—	2	2	no	—
283	#117	D₄×C₁₉	1	2	yes	—
284	C₂×C₄²	—	2	1	no	—
285	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
286	C₄⋊C₈	—	2	1	no	—
287	C₄⋊C₈	—	2	1	no	—
288	C₄⋊C₈	—	2	1	no	—
289	C₄⋊C₈	—	2	1	no	—
290	C₂²⋊C₈	—	2	1	no	—
291	C₂²⋊C₈	—	2	1	no	—
292	#97	—	2	1	no	—
293	#97	—	2	1	no	—
294	#95	—	2	1	no	—
295	#95	—	2	1	no	—
296	C₁₉	#8496	1	1	yes	characteristic, direct product factor, Sylow
297	#41	—	8	2	no	—
298	C₂×Q₈	—	2	4	no	—
299	C₂×Q₈	—	2	1	no	—
300	C₂×Q₈	—	2	1	no	—
301	C₂×Q₈	—	2	1	no	—
302	C₂×Q₈	—	2	1	no	—
303	C₂×Q₈	—	8	4	no	—
304	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	1	no	—
307	C₂×D₄	—	2	1	no	—
308	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	4	1	no	—
312	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
314	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
315	M₁₆	—	4	2	no	—
316	C₂×C₈	—	4	1	no	—
317	C₂×C₈	—	4	1	no	—
318	C₂×C₈	—	4	1	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	2	4	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
332	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
333	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
334	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
335	C₂²⋊C₄	—	2	4	no	—
336	C₂²⋊C₄	—	2	4	no	—
337	C₂²⋊C₄	—	2	4	no	—
338	C₂²⋊C₄	—	2	2	no	—
339	C₂²⋊C₄	—	2	2	no	—
340	C₂²⋊C₄	—	2	2	no	—
341	C₂²⋊C₄	—	2	2	no	—
342	C₄²	—	2	4	no	—
343	C₄²	—	2	2	no	—
344	C₄²	—	2	2	no	—
345	C₄²	—	2	2	no	—
346	C₄²	—	4	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	2	no	—
352	C₂³	C₁₉×#120	1	1	yes	characteristic
353	Q₈	—	4	2	no	—
354	Q₈	—	4	2	no	—
355	Q₈	—	4	2	no	—
356	Q₈	—	4	1	no	—
357	Q₈	—	4	1	no	—
358	Q₈	—	8	1	no	—
359	Q₈	—	8	4	no	—
360	D₄	—	4	2	no	—
361	D₄	—	4	1	no	—
362	D₄	—	4	1	no	—
363	D₄	—	8	1	no	—
364	D₄	—	8	2	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	4	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	8	4	no	—
377	C₂×C₄	—	8	1	no	—
378	C₂×C₄	—	8	1	no	—
379	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
380	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
381	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
382	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
383	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
384	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
385	C₈	—	8	1	no	—
386	C₈	—	8	1	no	—
387	C₈	—	8	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	4	2	no	—
394	C₂²	C₁₉×#379	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	2	no	—
402	C₄	—	4	2	no	—
403	C₄	—	4	2	no	—
404	C₄	—	4	2	no	—
405	C₄	—	8	2	no	—
406	C₄	C₁₉×#454	1	1	yes	characteristic
407	C₄	C₁₉×#456	1	1	yes	characteristic
408	C₂	—	4	1	no	—
409	C₂	—	8	2	no	—
410	C₂	C₁₉×#1793	1	1	yes	characteristic
411	C₂	C₁₉×#1795	1	1	yes	characteristic
412	C₂	C₁₉×#1796	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#379
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#532	C₂²
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
2. C₁₉×#1995	C₂	semidirect
3. C₁₉×#1559	C₂	semidirect
5. C₁₉×#1537	C₂	semidirect
6. C₁₉×#1506	C₂	semidirect
12. C₁₉×#556	C₄	semidirect
14. D₄×Q₈×C₁₉	C₄	semidirect
144. #8496	C₁₉	direct (N × H)
183. #1995	C₂×C₁₉	semidirect
184. #1559	C₂×C₁₉	semidirect
186. #1537	C₂×C₁₉	semidirect
187. #1506	C₂×C₁₉	semidirect
213. #556	C₄×C₁₉	semidirect
215. D₄×Q₈	C₄×C₁₉	semidirect
296. C₁₉	#8496	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×#3550	2
C₁₉×#1995	2
C₁₉×#1559	2
C₁₉×#1557	2
C₁₉×#1537	2
C₁₉×#1506	2
C₁₉×#1505	2
#8496	19

Subgroups — C19×#8496 #18014455

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8496 #18014455