Subgroups — C₁₉×#9384 #18015343

Order 4864.

640 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2972	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2543	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1799	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1519	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1294	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₉×#121	—	2	1	no	—
7	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
8	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₈×D₄×C₁₉	—	2	4	no	—
10	C₁₉×#431	—	2	1	no	—
11	C₂×C₁₉×#99	—	2	1	no	—
12	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
13	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
14	C₁₉×#398	C₄	1	1	yes	characteristic, complemented
15	C₁₉×#397	C₄	1	1	yes	characteristic, complemented
16	C₁₉×#394	C₄	1	1	yes	characteristic, complemented
17	C₁₉×#392	C₄	1	1	yes	characteristic, complemented
18	C₁₉×#388	—	2	1	no	—
19	C₁₉×#386	—	2	1	no	—
20	C₁₉×#386	—	2	1	no	—
21	C₁₉×#380	C₂²	1	2	yes	—
22	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
23	C₁₉×#342	—	2	1	no	—
24	C₁₉×#327	—	2	4	no	—
25	C₂²×D₄×C₁₉	—	2	1	no	—
26	C₂²×D₄×C₁₉	—	2	1	no	—
27	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	—	2	1	no	—
30	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
32	C₂²×C₈×C₁₉	—	2	2	no	—
33	C₂²×C₈×C₁₉	—	2	2	no	—
34	C₁₉×#121	—	2	2	no	—
35	C₁₉×#121	—	2	2	no	—
36	C₁₉×#121	—	4	2	no	—
37	C₁₉×#121	—	4	2	no	—
38	C₄×D₄×C₁₉	—	2	2	no	—
39	C₄×D₄×C₁₉	—	2	2	no	—
40	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
41	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
42	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
45	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
46	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
48	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
49	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
51	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
53	C₁₉×C₄⋊C₈	—	2	2	no	—
54	C₁₉×#99	—	4	2	no	—
55	C₁₉×C₂²⋊C₈	—	2	2	no	—
56	C₁₉×C₂²⋊C₈	—	2	2	no	—
57	C₁₉×C₂²⋊C₈	D₄	1	4	yes	complemented
58	C₄×C₈×C₁₉	—	2	2	no	—
59	C₁₉×#95	—	2	1	no	—
60	C₁₉×#95	—	2	1	no	—
61	C₁₉×#95	—	2	1	no	—
62	C₁₉×#95	—	2	2	no	—
63	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
64	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
65	C₂⁴×C₁₉	—	2	1	no	—
66	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
67	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
68	C₂×D₄×C₁₉	—	2	2	no	—
69	C₂×D₄×C₁₉	—	2	2	no	—
70	C₂×D₄×C₁₉	—	2	2	no	—
71	C₂×D₄×C₁₉	—	4	2	no	—
72	C₂×D₄×C₁₉	—	4	2	no	—
73	C₂×D₄×C₁₉	—	4	2	no	—
74	C₂×D₄×C₁₉	—	4	1	no	—
75	C₂×D₄×C₁₉	—	4	1	no	—
76	C₂×D₄×C₁₉	—	4	2	no	—
77	C₂×D₄×C₁₉	—	8	1	no	—
78	C₂×D₄×C₁₉	—	8	1	no	—
79	C₂×D₄×C₁₉	D₈	1	2	yes	—
80	C₂×D₄×C₁₉	SD₁₆	1	2	yes	—
81	C₂²×C₄×C₁₉	—	2	1	no	—
82	C₂²×C₄×C₁₉	—	2	1	no	—
83	C₂²×C₄×C₁₉	—	2	1	no	—
84	C₂²×C₄×C₁₉	—	2	1	no	—
85	C₂²×C₄×C₁₉	—	2	1	no	—
86	C₂²×C₄×C₁₉	—	4	2	no	—
87	C₂²×C₄×C₁₉	—	4	1	no	—
88	C₂²×C₄×C₁₉	—	4	1	no	—
89	C₂²×C₄×C₁₉	—	4	2	no	—
90	C₂²×C₄×C₁₉	—	8	1	no	—
91	C₂²×C₄×C₁₉	—	8	1	no	—
92	C₂²×C₄×C₁₉	—	8	1	no	—
93	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	#41	1	2	yes	—
100	C₂×C₈×C₁₉	—	2	4	no	—
101	C₂×C₈×C₁₉	—	8	2	no	—
102	C₂×C₈×C₁₉	—	8	2	no	—
103	C₄⋊C₄×C₁₉	—	2	2	no	—
104	C₄⋊C₄×C₁₉	—	2	2	no	—
105	C₄⋊C₄×C₁₉	—	4	2	no	—
106	C₄⋊C₄×C₁₉	—	8	2	no	—
107	C₂²⋊C₄×C₁₉	—	2	2	no	—
108	C₂²⋊C₄×C₁₉	—	2	2	no	—
109	C₂²⋊C₄×C₁₉	—	4	2	no	—
110	C₂²⋊C₄×C₁₉	—	4	2	no	—
111	C₂²⋊C₄×C₁₉	—	4	2	no	—
112	C₂²⋊C₄×C₁₉	—	4	1	no	—
113	C₂²⋊C₄×C₁₉	—	4	1	no	—
114	C₂²⋊C₄×C₁₉	—	4	2	no	—
115	C₂²⋊C₄×C₁₉	—	4	2	no	—
116	C₂²⋊C₄×C₁₉	—	8	1	no	—
117	C₄²×C₁₉	—	2	1	no	—
118	C₄²×C₁₉	—	2	1	no	—
119	#9384	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂³×C₁₉	—	2	1	no	—
121	C₂³×C₁₉	—	2	1	no	—
122	C₂³×C₁₉	—	4	1	no	—
123	C₂³×C₁₉	—	4	1	no	—
124	C₂³×C₁₉	—	4	1	no	—
125	C₂³×C₁₉	—	4	1	no	—
126	C₂³×C₁₉	—	4	1	no	—
127	C₂³×C₁₉	—	4	1	no	—
128	C₂³×C₁₉	—	4	1	no	—
129	C₂³×C₁₉	—	4	1	no	—
130	C₂³×C₁₉	—	4	1	no	—
131	C₂³×C₁₉	—	4	1	no	—
132	C₂³×C₁₉	—	4	1	no	—
133	C₂³×C₁₉	#102	1	2	yes	—
134	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	C₂³×C₁₉	#121	1	2	yes	—
136	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
137	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
138	C₂³×C₁₉	#135	1	2	yes	—
139	D₄×C₁₉	—	2	4	no	—
140	D₄×C₁₉	—	2	4	no	—
141	D₄×C₁₉	—	8	2	no	—
142	D₄×C₁₉	—	8	4	no	—
143	D₄×C₁₉	—	8	2	no	—
144	D₄×C₁₉	—	8	2	no	—
145	C₂×C₄×C₁₉	—	2	1	no	—
146	C₂×C₄×C₁₉	—	2	1	no	—
147	C₂×C₄×C₁₉	—	2	2	no	—
148	C₂×C₄×C₁₉	—	2	1	no	—
149	C₂×C₄×C₁₉	—	2	1	no	—
150	C₂×C₄×C₁₉	—	4	2	no	—
151	C₂×C₄×C₁₉	—	4	2	no	—
152	C₂×C₄×C₁₉	—	4	1	no	—
153	C₂×C₄×C₁₉	—	4	1	no	—
154	C₂×C₄×C₁₉	—	4	2	no	—
155	C₂×C₄×C₁₉	—	4	1	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	4	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	—	8	1	no	—
166	C₂×C₄×C₁₉	—	8	2	no	—
167	C₂×C₄×C₁₉	—	8	2	no	—
168	C₂×C₄×C₁₉	—	8	2	no	—
169	C₂×C₄×C₁₉	—	8	2	no	—
170	C₂×C₄×C₁₉	—	8	2	no	—
171	C₂×C₄×C₁₉	#102	1	2	yes	—
172	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
173	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
175	C₈×C₁₉	—	4	4	no	—
176	#2972	C₂×C₁₉	1	1	yes	characteristic, complemented
177	#2543	C₂×C₁₉	1	1	yes	characteristic
178	#1799	C₂×C₁₉	1	1	yes	characteristic, complemented
179	#1519	C₂×C₁₉	1	2	yes	complemented
180	#1294	C₂×C₁₉	1	2	yes	complemented
181	C₂²×C₁₉	—	2	1	no	—
182	C₂²×C₁₉	—	2	2	no	—
183	C₂²×C₁₉	—	2	1	no	—
184	C₂²×C₁₉	—	2	2	no	—
185	C₂²×C₁₉	—	2	2	no	—
186	C₂²×C₁₉	—	4	1	no	—
187	C₂²×C₁₉	—	4	1	no	—
188	C₂²×C₁₉	—	4	2	no	—
189	C₂²×C₁₉	—	4	2	no	—
190	C₂²×C₁₉	—	4	1	no	—
191	C₂²×C₁₉	—	4	1	no	—
192	C₂²×C₁₉	—	8	1	no	—
193	C₂²×C₁₉	—	8	1	no	—
194	C₂²×C₁₉	—	8	1	no	—
195	C₂²×C₁₉	—	8	1	no	—
196	C₂²×C₁₉	—	8	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	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
202	C₂²×C₁₉	#416	1	1	yes	characteristic
203	C₂²×C₁₉	#465	1	2	yes	—
204	C₂²×C₁₉	#466	1	2	yes	—
205	C₄×C₁₉	—	2	2	no	—
206	C₄×C₁₉	—	2	1	no	—
207	C₄×C₁₉	—	2	1	no	—
208	C₄×C₁₉	—	2	2	no	—
209	C₄×C₁₉	—	4	2	no	—
210	C₄×C₁₉	—	4	1	no	—
211	C₄×C₁₉	—	4	1	no	—
212	C₄×C₁₉	—	8	1	no	—
213	C₄×C₁₉	—	8	1	no	—
214	C₄×C₁₉	—	16	2	no	—
215	C₂×#121	—	2	1	no	—
216	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
217	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
218	C₈×D₄	—	2	4	no	—
219	#431	—	2	1	no	—
220	C₂×#99	—	2	1	no	—
221	C₂×C₂²⋊C₈	—	2	1	no	—
222	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
223	#398	C₄×C₁₉	1	1	yes	characteristic, complemented
224	#397	C₄×C₁₉	1	1	yes	characteristic, complemented
225	#394	C₄×C₁₉	1	1	yes	characteristic, complemented
226	#392	C₄×C₁₉	1	1	yes	characteristic, complemented
227	#388	—	2	1	no	—
228	#386	—	2	1	no	—
229	#386	—	2	1	no	—
230	#380	C₂²×C₁₉	1	2	yes	—
231	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
232	#342	—	2	1	no	—
233	#327	—	2	4	no	—
234	C₂×C₁₉	—	2	1	no	—
235	C₂×C₁₉	—	2	2	no	—
236	C₂×C₁₉	—	2	1	no	—
237	C₂×C₁₉	—	2	2	no	—
238	C₂×C₁₉	—	4	2	no	—
239	C₂×C₁₉	—	16	1	no	—
240	C₂×C₁₉	#1884	1	1	yes	characteristic
241	C₂×C₁₉	#1893	1	1	yes	characteristic
242	C₂×C₁₉	#1913	1	1	yes	characteristic
243	C₂²×D₄	—	2	1	no	—
244	C₂²×D₄	—	2	1	no	—
245	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
246	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
247	C₂³×C₄	—	2	1	no	—
248	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
249	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
250	C₂²×C₈	—	2	2	no	—
251	C₂²×C₈	—	2	2	no	—
252	#121	—	2	2	no	—
253	#121	—	2	2	no	—
254	#121	—	4	2	no	—
255	#121	—	4	2	no	—
256	C₄×D₄	—	2	2	no	—
257	C₄×D₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
262	C₂×C₂²⋊C₄	—	2	1	no	—
263	C₂×C₂²⋊C₄	—	2	1	no	—
264	C₂×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₂²⋊C₄	—	2	1	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	—	2	1	no	—
268	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
270	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
271	C₄⋊C₈	—	2	2	no	—
272	#99	—	4	2	no	—
273	C₂²⋊C₈	—	2	2	no	—
274	C₂²⋊C₈	—	2	2	no	—
275	C₂²⋊C₈	D₄×C₁₉	1	4	yes	complemented
276	C₄×C₈	—	2	2	no	—
277	#95	—	2	1	no	—
278	#95	—	2	1	no	—
279	#95	—	2	1	no	—
280	#95	—	2	2	no	—
281	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
282	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
283	C₁₉	#9384	1	1	yes	characteristic, direct product factor, Sylow
284	C₂⁴	—	2	1	no	—
285	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
286	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	—	4	2	no	—
292	C₂×D₄	—	4	1	no	—
293	C₂×D₄	—	4	1	no	—
294	C₂×D₄	—	4	2	no	—
295	C₂×D₄	—	4	2	no	—
296	C₂×D₄	—	8	1	no	—
297	C₂×D₄	—	8	1	no	—
298	C₂×D₄	D₈×C₁₉	1	2	yes	—
299	C₂×D₄	SD₁₆×C₁₉	1	2	yes	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	4	2	no	—
306	C₂²×C₄	—	4	1	no	—
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	—	4	2	no	—
309	C₂²×C₄	—	8	1	no	—
310	C₂²×C₄	—	8	1	no	—
311	C₂²×C₄	—	8	1	no	—
312	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
313	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
314	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
315	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
317	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
318	C₂²×C₄	#41×C₁₉	1	2	yes	—
319	C₂×C₈	—	2	4	no	—
320	C₂×C₈	—	8	2	no	—
321	C₂×C₈	—	8	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	4	2	no	—
325	C₄⋊C₄	—	8	2	no	—
326	C₂²⋊C₄	—	2	2	no	—
327	C₂²⋊C₄	—	2	2	no	—
328	C₂²⋊C₄	—	4	2	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₂²⋊C₄	—	4	1	no	—
331	C₂²⋊C₄	—	4	1	no	—
332	C₂²⋊C₄	—	4	2	no	—
333	C₂²⋊C₄	—	4	2	no	—
334	C₂²⋊C₄	—	4	2	no	—
335	C₂²⋊C₄	—	8	1	no	—
336	C₄²	—	2	1	no	—
337	C₄²	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	4	1	no	—
341	C₂³	—	4	1	no	—
342	C₂³	—	4	1	no	—
343	C₂³	—	4	1	no	—
344	C₂³	—	4	1	no	—
345	C₂³	—	4	1	no	—
346	C₂³	—	4	1	no	—
347	C₂³	—	4	1	no	—
348	C₂³	—	4	1	no	—
349	C₂³	—	4	1	no	—
350	C₂³	—	4	1	no	—
351	C₂³	C₁₉×#102	1	2	yes	—
352	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
353	C₂³	C₁₉×#121	1	2	yes	—
354	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
355	C₂³	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
356	C₂³	C₁₉×#135	1	2	yes	—
357	D₄	—	2	4	no	—
358	D₄	—	2	4	no	—
359	D₄	—	8	2	no	—
360	D₄	—	8	4	no	—
361	D₄	—	8	2	no	—
362	D₄	—	8	2	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	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	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	8	1	no	—
384	C₂×C₄	—	8	2	no	—
385	C₂×C₄	—	8	2	no	—
386	C₂×C₄	—	8	2	no	—
387	C₂×C₄	—	8	2	no	—
388	C₂×C₄	—	8	2	no	—
389	C₂×C₄	C₁₉×#102	1	2	yes	—
390	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
391	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
392	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
393	C₈	—	4	4	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	8	1	no	—
406	C₂²	—	8	1	no	—
407	C₂²	—	8	1	no	—
408	C₂²	—	8	1	no	—
409	C₂²	—	8	1	no	—
410	C₂²	—	8	1	no	—
411	C₂²	—	8	1	no	—
412	C₂²	—	8	1	no	—
413	C₂²	C₁₉×#386	1	1	yes	characteristic
414	C₂²	C₂×C₁₉×#102	1	1	yes	characteristic
415	C₂²	C₁₉×#416	1	1	yes	characteristic
416	C₂²	C₁₉×#465	1	2	yes	—
417	C₂²	C₁₉×#466	1	2	yes	—
418	C₄	—	2	2	no	—
419	C₄	—	2	1	no	—
420	C₄	—	2	1	no	—
421	C₄	—	2	2	no	—
422	C₄	—	4	2	no	—
423	C₄	—	4	1	no	—
424	C₄	—	4	1	no	—
425	C₄	—	8	1	no	—
426	C₄	—	8	1	no	—
427	C₄	—	16	2	no	—
428	C₂	—	2	1	no	—
429	C₂	—	2	2	no	—
430	C₂	—	2	1	no	—
431	C₂	—	2	2	no	—
432	C₂	—	4	2	no	—
433	C₂	—	16	1	no	—
434	C₂	C₁₉×#1884	1	1	yes	characteristic
435	C₂	C₁₉×#1893	1	1	yes	characteristic
436	C₂	C₁₉×#1913	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₁₉×#2543	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2972	C₂	semidirect
3. C₁₉×#1799	C₂	semidirect
4. C₁₉×#1519	C₂	semidirect
5. C₁₉×#1294	C₂	semidirect
14. C₁₉×#398	C₄	semidirect
15. C₁₉×#397	C₄	semidirect
16. C₁₉×#394	C₄	semidirect
17. C₁₉×#392	C₄	semidirect
57. C₁₉×C₂²⋊C₈	D₄	semidirect
119. #9384	C₁₉	direct (N × H)
176. #2972	C₂×C₁₉	semidirect
178. #1799	C₂×C₁₉	semidirect
179. #1519	C₂×C₁₉	semidirect
180. #1294	C₂×C₁₉	semidirect
223. #398	C₄×C₁₉	semidirect
224. #397	C₄×C₁₉	semidirect
225. #394	C₄×C₁₉	semidirect
226. #392	C₄×C₁₉	semidirect
275. C₂²⋊C₈	D₄×C₁₉	semidirect
283. C₁₉	#9384	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×#2972	2
C₁₉×#2543	2
C₁₉×#1799	2
C₁₉×#1519	2
C₁₉×#1294	2
#9384	19

Subgroups — C19×#9384 #18015343

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9384 #18015343