Subgroups — C₁₉×#9053 #18015012

Order 4864.

538 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3169	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2935	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1980	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1502	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1480	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1279	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	C₁₉×#532	C₂²	1	1	yes	characteristic
11	C₁₉×#500	C₄	1	1	yes	characteristic, complemented
12	C₁₉×#493	C₄	1	1	yes	characteristic, complemented
13	C₁₉×#486	C₄	1	1	yes	characteristic, complemented
14	C₁₉×#486	C₄	1	1	yes	characteristic, complemented
15	C₁₉×#466	—	2	2	no	—
16	C₄×D₈×C₁₉	—	2	2	no	—
17	C₁₉×#436	—	2	1	no	—
18	C₁₉×#435	—	2	2	no	—
19	C₈×D₄×C₁₉	—	2	1	no	—
20	C₁₉×#431	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#104	—	2	1	no	—
23	C₂×C₁₉×#104	—	2	1	no	—
24	C₁₉×#408	—	2	1	no	—
25	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
27	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
28	C₁₉×#327	—	2	2	no	—
29	C₁₉×D₄⋊C₈	—	2	1	no	—
30	C₁₉×D₄⋊C₈	—	2	1	no	—
31	C₂×#41×C₁₉	—	2	1	no	—
32	C₂×#41×C₁₉	—	2	1	no	—
33	C₂×D₈×C₁₉	—	2	2	no	—
34	C₁₉×#131	—	4	2	no	—
35	C₁₉×#131	—	4	2	no	—
36	C₂×M₁₆×C₁₉	—	2	2	no	—
37	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
38	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
39	C₂²×C₈×C₁₉	—	2	2	no	—
40	C₂²×C₈×C₁₉	—	2	1	no	—
41	C₂²×C₈×C₁₉	—	2	1	no	—
42	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
43	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
44	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
45	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
46	C₁₉×#124	—	2	1	no	—
47	C₁₉×#124	—	2	1	no	—
48	C₁₉×#121	—	2	1	no	—
49	C₁₉×#121	—	2	1	no	—
50	C₁₉×#121	—	2	1	no	—
51	C₁₉×#121	D₄	1	2	yes	—
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	D₄	1	2	yes	—
56	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₄²×C₁₉	—	2	1	no	—
58	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
59	C₁₉×#107	—	2	2	no	—
60	C₁₉×C₄⋊C₈	—	2	1	no	—
61	C₁₉×C₄⋊C₈	—	2	1	no	—
62	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
63	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
64	C₁₉×#104	—	4	2	no	—
65	C₁₉×#104	—	4	2	no	—
66	C₁₉×#102	—	2	2	no	—
67	C₁₉×#102	—	2	2	no	—
68	C₁₉×C₂²⋊C₈	—	2	2	no	—
69	C₁₉×C₂²⋊C₈	—	2	2	no	—
70	C₁₉×C₂²⋊C₈	—	2	1	no	—
71	C₁₉×#97	—	2	1	no	—
72	C₄×C₈×C₁₉	—	2	1	no	—
73	C₄×C₈×C₁₉	—	2	1	no	—
74	C₄×C₈×C₁₉	—	2	1	no	—
75	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
76	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
77	C₁₉×#95	—	2	1	no	—
78	#41×C₁₉	—	4	1	no	—
79	#41×C₁₉	—	4	1	no	—
80	#41×C₁₉	—	4	1	no	—
81	#41×C₁₉	—	4	1	no	—
82	#41×C₁₉	—	4	1	no	—
83	#41×C₁₉	—	4	1	no	—
84	#41×C₁₉	—	4	1	no	—
85	#41×C₁₉	—	4	1	no	—
86	C₂×Q₈×C₁₉	—	2	1	no	—
87	C₂×Q₈×C₁₉	—	2	1	no	—
88	C₂×D₄×C₁₉	—	2	2	no	—
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	—	2	1	no	—
94	C₂×D₄×C₁₉	—	4	1	no	—
95	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	4	1	no	—
98	C₂²×C₄×C₁₉	—	4	1	no	—
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
102	D₈×C₁₉	—	4	4	no	—
103	M₁₆×C₁₉	—	2	1	no	—
104	M₁₆×C₁₉	—	2	1	no	—
105	M₁₆×C₁₉	—	2	1	no	—
106	M₁₆×C₁₉	—	4	4	no	—
107	M₁₆×C₁₉	D₈	1	2	yes	complemented
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	—	2	1	no	—
113	C₂×C₈×C₁₉	—	2	1	no	—
114	C₂×C₈×C₁₉	—	4	2	no	—
115	C₂×C₈×C₁₉	—	4	4	no	—
116	C₂×C₈×C₁₉	—	4	1	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	2	no	—
121	C₄⋊C₄×C₁₉	—	2	1	no	—
122	C₄⋊C₄×C₁₉	—	2	1	no	—
123	C₄⋊C₄×C₁₉	—	4	1	no	—
124	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
125	C₂²⋊C₄×C₁₉	—	2	2	no	—
126	C₂²⋊C₄×C₁₉	—	2	2	no	—
127	C₂²⋊C₄×C₁₉	—	4	1	no	—
128	C₂²⋊C₄×C₁₉	—	4	1	no	—
129	C₄²×C₁₉	—	4	1	no	—
130	C₄²×C₁₉	—	4	1	no	—
131	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₁₉	#41	1	1	yes	characteristic
135	#9053	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂³×C₁₉	—	2	2	no	—
137	C₂³×C₁₉	—	4	1	no	—
138	C₂³×C₁₉	#121	1	1	yes	characteristic
139	Q₈×C₁₉	—	4	1	no	—
140	Q₈×C₁₉	—	4	1	no	—
141	Q₈×C₁₉	—	4	1	no	—
142	Q₈×C₁₉	—	4	1	no	—
143	D₄×C₁₉	—	4	2	no	—
144	D₄×C₁₉	—	4	2	no	—
145	D₄×C₁₉	—	4	2	no	—
146	D₄×C₁₉	—	4	2	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	—	4	1	no	—
152	D₄×C₁₉	—	4	1	no	—
153	D₄×C₁₉	—	4	1	no	—
154	D₄×C₁₉	—	4	1	no	—
155	D₄×C₁₉	—	8	1	no	—
156	D₄×C₁₉	—	8	1	no	—
157	C₂×C₄×C₁₉	—	2	1	no	—
158	C₂×C₄×C₁₉	—	2	1	no	—
159	C₂×C₄×C₁₉	—	2	2	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	—	4	2	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	—	8	1	no	—
168	C₂×C₄×C₁₉	—	8	1	no	—
169	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
177	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
178	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
179	C₈×C₁₉	—	2	2	no	—
180	C₈×C₁₉	—	2	2	no	—
181	C₈×C₁₉	—	4	1	no	—
182	C₈×C₁₉	—	4	1	no	—
183	C₈×C₁₉	—	4	1	no	—
184	C₈×C₁₉	—	4	1	no	—
185	C₈×C₁₉	—	8	1	no	—
186	#3169	C₂×C₁₉	1	1	yes	characteristic
187	#2935	C₂×C₁₉	1	1	yes	characteristic, complemented
188	#1980	C₂×C₁₉	1	1	yes	characteristic, complemented
189	#1502	C₂×C₁₉	1	1	yes	characteristic, complemented
190	#1480	C₂×C₁₉	1	1	yes	characteristic, complemented
191	#1279	C₂×C₁₉	1	1	yes	characteristic, complemented
192	#1278	C₂×C₁₉	1	1	yes	characteristic, complemented
193	C₂²×C₁₉	—	2	1	no	—
194	C₂²×C₁₉	—	2	1	no	—
195	C₂²×C₁₉	—	4	2	no	—
196	C₂²×C₁₉	—	4	2	no	—
197	C₂²×C₁₉	—	4	2	no	—
198	C₂²×C₁₉	—	8	1	no	—
199	C₂²×C₁₉	—	8	1	no	—
200	C₂²×C₁₉	—	8	1	no	—
201	C₂²×C₁₉	#386	1	1	yes	characteristic
202	C₂²×C₁₉	#459	1	1	yes	characteristic
203	C₂²×C₁₉	#463	1	1	yes	characteristic
204	C₄×C₁₉	—	2	1	no	—
205	C₄×C₁₉	—	2	1	no	—
206	C₄×C₁₉	—	2	1	no	—
207	C₄×C₁₉	—	4	2	no	—
208	C₄×C₁₉	—	8	2	no	—
209	C₄×C₁₉	—	8	1	no	—
210	C₄×C₁₉	C₄×D₈	1	1	yes	characteristic
211	C₄×C₁₉	#442	1	1	yes	characteristic
212	C₄×C₁₉	#443	1	1	yes	characteristic
213	C₄×C₁₉	#444	1	1	yes	characteristic
214	C₄×C₁₉	#447	1	1	yes	characteristic
215	C₄×C₁₉	#449	1	1	yes	characteristic
216	C₂×#131	—	2	1	no	—
217	#532	C₂²×C₁₉	1	1	yes	characteristic
218	#532	C₂²×C₁₉	1	1	yes	characteristic
219	#500	C₄×C₁₉	1	1	yes	characteristic, complemented
220	#493	C₄×C₁₉	1	1	yes	characteristic, complemented
221	#486	C₄×C₁₉	1	1	yes	characteristic, complemented
222	#486	C₄×C₁₉	1	1	yes	characteristic, complemented
223	#466	—	2	2	no	—
224	C₄×D₈	—	2	2	no	—
225	#436	—	2	1	no	—
226	#435	—	2	2	no	—
227	C₈×D₄	—	2	1	no	—
228	#431	C₂²×C₁₉	1	1	yes	characteristic
229	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
230	C₂×#104	—	2	1	no	—
231	C₂×#104	—	2	1	no	—
232	#408	—	2	1	no	—
233	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
234	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
235	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
236	#327	—	2	2	no	—
237	D₄⋊C₈	—	2	1	no	—
238	D₄⋊C₈	—	2	1	no	—
239	C₂×C₁₉	—	2	1	no	—
240	C₂×C₁₉	—	2	1	no	—
241	C₂×C₁₉	—	8	2	no	—
242	C₂×C₁₉	—	16	1	no	—
243	C₂×C₁₉	#1876	1	1	yes	characteristic
244	C₂×C₁₉	#1879	1	1	yes	characteristic
245	C₂×C₁₉	#1884	1	1	yes	characteristic
246	C₂×#41	—	2	1	no	—
247	C₂×#41	—	2	1	no	—
248	C₂×D₈	—	2	2	no	—
249	#131	—	4	2	no	—
250	#131	—	4	2	no	—
251	C₂×M₁₆	—	2	2	no	—
252	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
253	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
254	C₂²×C₈	—	2	2	no	—
255	C₂²×C₈	—	2	1	no	—
256	C₂²×C₈	—	2	1	no	—
257	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
258	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
259	#127	C₂×C₄×C₁₉	1	1	yes	characteristic
260	#127	C₂×C₄×C₁₉	1	1	yes	characteristic
261	#124	—	2	1	no	—
262	#124	—	2	1	no	—
263	#121	—	2	1	no	—
264	#121	—	2	1	no	—
265	#121	—	2	1	no	—
266	#121	D₄×C₁₉	1	2	yes	—
267	C₄×D₄	—	2	1	no	—
268	C₄×D₄	—	2	1	no	—
269	C₄×D₄	—	2	1	no	—
270	C₄×D₄	D₄×C₁₉	1	2	yes	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄²	—	2	1	no	—
273	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
274	#107	—	2	2	no	—
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
278	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
279	#104	—	4	2	no	—
280	#104	—	4	2	no	—
281	#102	—	2	2	no	—
282	#102	—	2	2	no	—
283	C₂²⋊C₈	—	2	2	no	—
284	C₂²⋊C₈	—	2	2	no	—
285	C₂²⋊C₈	—	2	1	no	—
286	#97	—	2	1	no	—
287	C₄×C₈	—	2	1	no	—
288	C₄×C₈	—	2	1	no	—
289	C₄×C₈	—	2	1	no	—
290	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
291	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
292	#95	—	2	1	no	—
293	C₁₉	#9053	1	1	yes	characteristic, direct product factor, Sylow
294	#41	—	4	1	no	—
295	#41	—	4	1	no	—
296	#41	—	4	1	no	—
297	#41	—	4	1	no	—
298	#41	—	4	1	no	—
299	#41	—	4	1	no	—
300	#41	—	4	1	no	—
301	#41	—	4	1	no	—
302	C₂×Q₈	—	2	1	no	—
303	C₂×Q₈	—	2	1	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	2	1	no	—
307	C₂×D₄	—	2	1	no	—
308	C₂×D₄	—	2	1	no	—
309	C₂×D₄	—	2	1	no	—
310	C₂×D₄	—	4	1	no	—
311	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	4	1	no	—
314	C₂²×C₄	—	4	1	no	—
315	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
317	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
318	D₈	—	4	4	no	—
319	M₁₆	—	2	1	no	—
320	M₁₆	—	2	1	no	—
321	M₁₆	—	2	1	no	—
322	M₁₆	—	4	4	no	—
323	M₁₆	D₈×C₁₉	1	2	yes	complemented
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	4	2	no	—
331	C₂×C₈	—	4	4	no	—
332	C₂×C₈	—	4	1	no	—
333	C₂×C₈	—	4	1	no	—
334	C₂×C₈	—	4	1	no	—
335	C₄⋊C₄	—	2	1	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	4	1	no	—
340	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
341	C₂²⋊C₄	—	2	2	no	—
342	C₂²⋊C₄	—	2	2	no	—
343	C₂²⋊C₄	—	4	1	no	—
344	C₂²⋊C₄	—	4	1	no	—
345	C₄²	—	4	1	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	#41×C₁₉	1	1	yes	characteristic
351	C₂³	—	2	2	no	—
352	C₂³	—	4	1	no	—
353	C₂³	C₁₉×#121	1	1	yes	characteristic
354	Q₈	—	4	1	no	—
355	Q₈	—	4	1	no	—
356	Q₈	—	4	1	no	—
357	Q₈	—	4	1	no	—
358	D₄	—	4	2	no	—
359	D₄	—	4	2	no	—
360	D₄	—	4	2	no	—
361	D₄	—	4	2	no	—
362	D₄	—	4	1	no	—
363	D₄	—	4	1	no	—
364	D₄	—	4	1	no	—
365	D₄	—	4	1	no	—
366	D₄	—	4	1	no	—
367	D₄	—	4	1	no	—
368	D₄	—	4	1	no	—
369	D₄	—	4	1	no	—
370	D₄	—	8	1	no	—
371	D₄	—	8	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	8	1	no	—
381	C₂×C₄	—	8	1	no	—
382	C₂×C₄	—	8	1	no	—
383	C₂×C₄	—	8	1	no	—
384	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
385	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
386	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
387	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
388	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
389	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
390	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
391	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
392	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
393	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
394	C₈	—	2	2	no	—
395	C₈	—	2	2	no	—
396	C₈	—	4	1	no	—
397	C₈	—	4	1	no	—
398	C₈	—	4	1	no	—
399	C₈	—	4	1	no	—
400	C₈	—	8	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	4	2	no	—
404	C₂²	—	4	2	no	—
405	C₂²	—	4	2	no	—
406	C₂²	—	8	1	no	—
407	C₂²	—	8	1	no	—
408	C₂²	—	8	1	no	—
409	C₂²	C₁₉×#386	1	1	yes	characteristic
410	C₂²	C₁₉×#459	1	1	yes	characteristic
411	C₂²	C₁₉×#463	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	4	2	no	—
416	C₄	—	8	2	no	—
417	C₄	—	8	1	no	—
418	C₄	C₄×D₈×C₁₉	1	1	yes	characteristic
419	C₄	C₁₉×#442	1	1	yes	characteristic
420	C₄	C₁₉×#443	1	1	yes	characteristic
421	C₄	C₁₉×#444	1	1	yes	characteristic
422	C₄	C₁₉×#447	1	1	yes	characteristic
423	C₄	C₁₉×#449	1	1	yes	characteristic
424	C₂	—	2	1	no	—
425	C₂	—	2	1	no	—
426	C₂	—	8	2	no	—
427	C₂	—	16	1	no	—
428	C₂	C₁₉×#1876	1	1	yes	characteristic
429	C₂	C₁₉×#1879	1	1	yes	characteristic
430	C₂	C₁₉×#1884	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	#120
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
socle	C₂²×C₁₉	#386
prime radical	C₁₉×#3169	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. C₁₉×#2935	C₂	semidirect
3. C₁₉×#1980	C₂	semidirect
4. C₁₉×#1502	C₂	semidirect
5. C₁₉×#1480	C₂	semidirect
6. C₁₉×#1279	C₂	semidirect
7. C₁₉×#1278	C₂	semidirect
11. C₁₉×#500	C₄	semidirect
12. C₁₉×#493	C₄	semidirect
13. C₁₉×#486	C₄	semidirect
14. C₁₉×#486	C₄	semidirect
107. M₁₆×C₁₉	D₈	semidirect
135. #9053	C₁₉	direct (N × H)
187. #2935	C₂×C₁₉	semidirect
188. #1980	C₂×C₁₉	semidirect
189. #1502	C₂×C₁₉	semidirect
190. #1480	C₂×C₁₉	semidirect
191. #1279	C₂×C₁₉	semidirect
192. #1278	C₂×C₁₉	semidirect
219. #500	C₄×C₁₉	semidirect
220. #493	C₄×C₁₉	semidirect
221. #486	C₄×C₁₉	semidirect
222. #486	C₄×C₁₉	semidirect
293. C₁₉	#9053	direct (N × H)
323. M₁₆	D₈×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3169	2
C₁₉×#2935	2
C₁₉×#1980	2
C₁₉×#1502	2
C₁₉×#1480	2
C₁₉×#1279	2
C₁₉×#1278	2
#9053	19

Subgroups — C19×#9053 #18015012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9053 #18015012