Subgroups — C₁₉×#11317 #18017276

Order 4864.

610 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#341	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1735	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#339	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#339	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1729	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1729	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#336	C₂	1	1	yes	maximal, characteristic
8	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#341	—	2	2	no	—
16	C₁₉×#340	C₄	1	2	yes	complemented
17	C₁₉×#340	C₄	1	2	yes	complemented
18	C₁₉×#339	—	2	2	no	—
19	C₁₉×#339	—	2	2	no	—
20	C₁₉×#336	—	2	2	no	—
21	C₁₉×#336	—	2	2	no	—
22	C₁₉×#336	—	2	2	no	—
23	C₂³×C₄×C₁₉	—	2	1	no	—
24	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
25	C₂×M₁₆×C₁₉	—	2	1	no	—
26	C₂×M₁₆×C₁₉	—	2	1	no	—
27	C₂×M₁₆×C₁₉	—	2	1	no	—
28	C₂×M₁₆×C₁₉	—	2	1	no	—
29	C₂×M₁₆×C₁₉	—	2	1	no	—
30	C₂×M₁₆×C₁₉	—	2	1	no	—
31	C₂×M₁₆×C₁₉	—	2	1	no	—
32	C₂×M₁₆×C₁₉	—	2	1	no	—
33	C₂×M₁₆×C₁₉	—	2	1	no	—
34	C₂×M₁₆×C₁₉	—	2	1	no	—
35	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
36	C₂×M₁₆×C₁₉	Q₈	1	2	yes	—
37	C₂²×C₈×C₁₉	—	2	1	no	—
38	C₂²×C₈×C₁₉	—	2	1	no	—
39	C₂²×C₈×C₁₉	—	2	1	no	—
40	C₂²×C₈×C₁₉	—	2	1	no	—
41	C₂²×C₈×C₁₉	—	2	1	no	—
42	C₂²×C₈×C₁₉	—	2	1	no	—
43	C₂²×C₈×C₁₉	—	2	1	no	—
44	C₂²×C₈×C₁₉	—	2	1	no	—
45	C₂²×C₈×C₁₉	—	2	1	no	—
46	C₂²×C₈×C₁₉	—	2	1	no	—
47	C₂²×C₈×C₁₉	—	2	1	no	—
48	C₂²×C₈×C₁₉	—	2	1	no	—
49	C₂²×C₈×C₁₉	—	2	1	no	—
50	C₂²×C₈×C₁₉	—	2	1	no	—
51	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
52	C₂²×C₈×C₁₉	D₄	1	2	yes	—
53	C₁₉×#117	—	2	1	no	—
54	C₁₉×#117	—	2	1	no	—
55	C₁₉×#117	—	2	1	no	—
56	C₁₉×#117	—	2	1	no	—
57	C₁₉×#117	—	2	1	no	—
58	C₁₉×#117	—	2	1	no	—
59	C₁₉×#117	—	2	1	no	—
60	C₁₉×#117	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
63	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
64	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₄²×C₁₉	—	2	1	no	—
67	C₂×C₄²×C₁₉	—	2	1	no	—
68	C₂×C₄²×C₁₉	—	2	1	no	—
69	C₂×C₄²×C₁₉	—	2	1	no	—
70	C₂×C₄²×C₁₉	—	2	1	no	—
71	C₂×C₄²×C₁₉	—	2	1	no	—
72	C₂×C₄²×C₁₉	—	2	1	no	—
73	C₂×C₄²×C₁₉	D₄	1	2	yes	—
74	C₂⁴×C₁₉	#41	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	—	2	4	no	—
76	C₂²×C₄×C₁₉	—	2	2	no	—
77	C₂²×C₄×C₁₉	—	2	1	no	—
78	C₂²×C₄×C₁₉	—	2	2	no	—
79	C₂²×C₄×C₁₉	—	2	1	no	—
80	C₂²×C₄×C₁₉	—	4	2	no	—
81	C₂²×C₄×C₁₉	—	4	1	no	—
82	C₂²×C₄×C₁₉	—	4	1	no	—
83	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
97	M₁₆×C₁₉	—	2	2	no	—
98	M₁₆×C₁₉	—	2	2	no	—
99	M₁₆×C₁₉	—	2	2	no	—
100	M₁₆×C₁₉	—	2	2	no	—
101	M₁₆×C₁₉	—	4	1	no	—
102	M₁₆×C₁₉	—	4	1	no	—
103	M₁₆×C₁₉	—	4	1	no	—
104	M₁₆×C₁₉	—	4	1	no	—
105	C₂×C₈×C₁₉	—	2	2	no	—
106	C₂×C₈×C₁₉	—	2	2	no	—
107	C₂×C₈×C₁₉	—	2	2	no	—
108	C₂×C₈×C₁₉	—	2	2	no	—
109	C₂×C₈×C₁₉	—	2	2	no	—
110	C₂×C₈×C₁₉	—	2	2	no	—
111	C₂×C₈×C₁₉	—	2	2	no	—
112	C₂×C₈×C₁₉	—	2	2	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	—	4	1	no	—
118	C₂×C₈×C₁₉	—	4	1	no	—
119	C₂×C₈×C₁₉	—	4	1	no	—
120	C₂×C₈×C₁₉	—	4	1	no	—
121	C₂×C₈×C₁₉	—	4	1	no	—
122	C₂×C₈×C₁₉	—	4	1	no	—
123	C₂×C₈×C₁₉	—	4	1	no	—
124	C₂×C₈×C₁₉	—	4	1	no	—
125	C₄⋊C₄×C₁₉	—	2	2	no	—
126	C₄⋊C₄×C₁₉	—	2	1	no	—
127	C₄⋊C₄×C₁₉	—	2	1	no	—
128	C₄⋊C₄×C₁₉	—	2	2	no	—
129	C₄⋊C₄×C₁₉	—	2	1	no	—
130	C₄⋊C₄×C₁₉	—	2	1	no	—
131	C₂²⋊C₄×C₁₉	—	4	1	no	—
132	C₂²⋊C₄×C₁₉	—	4	1	no	—
133	C₂²⋊C₄×C₁₉	—	4	1	no	—
134	C₂²⋊C₄×C₁₉	—	4	1	no	—
135	C₄²×C₁₉	—	2	2	no	—
136	C₄²×C₁₉	—	2	2	no	—
137	C₄²×C₁₉	—	4	1	no	—
138	C₄²×C₁₉	—	4	1	no	—
139	C₄²×C₁₉	—	4	1	no	—
140	C₄²×C₁₉	—	4	1	no	—
141	C₄²×C₁₉	—	4	1	no	—
142	C₄²×C₁₉	—	4	1	no	—
143	#11317	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
144	C₂³×C₁₉	—	2	2	no	—
145	C₂³×C₁₉	—	2	2	no	—
146	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
147	C₂³×C₁₉	#123	1	1	yes	characteristic
148	C₂³×C₁₉	#124	1	1	yes	characteristic
149	C₂³×C₁₉	#125	1	1	yes	characteristic
150	C₂³×C₁₉	#126	1	1	yes	characteristic
151	C₂³×C₁₉	#126	1	1	yes	characteristic
152	C₂³×C₁₉	#126	1	1	yes	characteristic
153	C₂×C₄×C₁₉	—	2	4	no	—
154	C₂×C₄×C₁₉	—	4	4	no	—
155	C₂×C₄×C₁₉	—	4	4	no	—
156	C₂×C₄×C₁₉	—	4	2	no	—
157	C₂×C₄×C₁₉	—	4	2	no	—
158	C₂×C₄×C₁₉	—	4	2	no	—
159	C₂×C₄×C₁₉	—	4	1	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	2	no	—
165	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
166	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
167	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
171	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
182	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
183	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
184	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
185	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
186	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
187	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
188	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
189	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
190	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
191	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
192	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
193	C₈×C₁₉	—	4	2	no	—
194	C₈×C₁₉	—	4	2	no	—
195	C₈×C₁₉	—	4	2	no	—
196	C₈×C₁₉	—	4	2	no	—
197	C₂×#341	C₂×C₁₉	1	1	yes	characteristic
198	#1735	C₂×C₁₉	1	1	yes	characteristic
199	C₂×#339	C₂×C₁₉	1	1	yes	characteristic
200	C₂×#339	C₂×C₁₉	1	1	yes	characteristic
201	#1729	C₂×C₁₉	1	1	yes	characteristic
202	#1729	C₂×C₁₉	1	1	yes	characteristic
203	C₂×#336	C₂×C₁₉	1	1	yes	characteristic
204	C₂²×C₁₉	—	2	2	no	—
205	C₂²×C₁₉	—	2	2	no	—
206	C₂²×C₁₉	—	2	2	no	—
207	C₂²×C₁₉	—	2	2	no	—
208	C₂²×C₁₉	—	2	1	no	—
209	C₂²×C₁₉	—	2	1	no	—
210	C₂²×C₁₉	—	2	1	no	—
211	C₂²×C₁₉	—	2	1	no	—
212	C₂²×C₁₉	#387	1	1	yes	characteristic
213	C₂²×C₁₉	#388	1	1	yes	characteristic
214	C₂²×C₁₉	#388	1	1	yes	characteristic
215	C₂²×C₁₉	#397	1	1	yes	characteristic
216	C₂²×C₁₉	#400	1	1	yes	characteristic
217	C₂²×C₁₉	#400	1	1	yes	characteristic
218	C₂²×C₁₉	#401	1	1	yes	characteristic
219	C₂²×C₁₉	#443	1	2	yes	—
220	C₂²×C₁₉	#444	1	2	yes	—
221	C₄×C₁₉	—	4	4	no	—
222	C₄×C₁₉	—	8	2	no	—
223	C₄×C₁₉	—	8	1	no	—
224	C₄×C₁₉	—	8	1	no	—
225	C₄×C₁₉	#383	1	1	yes	characteristic
226	C₄×C₁₉	#387	1	1	yes	characteristic
227	C₄×C₁₉	#387	1	1	yes	characteristic
228	C₄×C₁₉	#388	1	1	yes	characteristic
229	C₄×C₁₉	#396	1	1	yes	characteristic
230	C₄×C₁₉	#397	1	1	yes	characteristic
231	C₄×C₁₉	#397	1	1	yes	characteristic
232	C₄×C₁₉	#400	1	1	yes	characteristic
233	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
234	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
235	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
236	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
237	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
238	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
239	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
240	#341	—	2	2	no	—
241	#340	C₄×C₁₉	1	2	yes	complemented
242	#340	C₄×C₁₉	1	2	yes	complemented
243	#339	—	2	2	no	—
244	#339	—	2	2	no	—
245	#336	—	2	2	no	—
246	#336	—	2	2	no	—
247	#336	—	2	2	no	—
248	C₂×C₁₉	—	2	1	no	—
249	C₂×C₁₉	—	2	1	no	—
250	C₂×C₁₉	—	2	1	no	—
251	C₂×C₁₉	—	2	1	no	—
252	C₂×C₁₉	#1443	1	1	yes	characteristic
253	C₂×C₁₉	#1922	1	2	yes	—
254	C₂×C₁₉	#1929	1	2	yes	—
255	C₂×C₁₉	#1937	1	1	yes	characteristic
256	C₂×C₁₉	#1938	1	1	yes	characteristic
257	C₂³×C₄	—	2	1	no	—
258	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
259	C₂×M₁₆	—	2	1	no	—
260	C₂×M₁₆	—	2	1	no	—
261	C₂×M₁₆	—	2	1	no	—
262	C₂×M₁₆	—	2	1	no	—
263	C₂×M₁₆	—	2	1	no	—
264	C₂×M₁₆	—	2	1	no	—
265	C₂×M₁₆	—	2	1	no	—
266	C₂×M₁₆	—	2	1	no	—
267	C₂×M₁₆	—	2	1	no	—
268	C₂×M₁₆	—	2	1	no	—
269	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
270	C₂×M₁₆	Q₈×C₁₉	1	2	yes	—
271	C₂²×C₈	—	2	1	no	—
272	C₂²×C₈	—	2	1	no	—
273	C₂²×C₈	—	2	1	no	—
274	C₂²×C₈	—	2	1	no	—
275	C₂²×C₈	—	2	1	no	—
276	C₂²×C₈	—	2	1	no	—
277	C₂²×C₈	—	2	1	no	—
278	C₂²×C₈	—	2	1	no	—
279	C₂²×C₈	—	2	1	no	—
280	C₂²×C₈	—	2	1	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	2	1	no	—
283	C₂²×C₈	—	2	1	no	—
284	C₂²×C₈	—	2	1	no	—
285	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
286	C₂²×C₈	D₄×C₁₉	1	2	yes	—
287	#117	—	2	1	no	—
288	#117	—	2	1	no	—
289	#117	—	2	1	no	—
290	#117	—	2	1	no	—
291	#117	—	2	1	no	—
292	#117	—	2	1	no	—
293	#117	—	2	1	no	—
294	#117	—	2	1	no	—
295	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
296	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
297	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
298	C₂×C₂²⋊C₄	—	2	1	no	—
299	C₂×C₂²⋊C₄	—	2	1	no	—
300	C₂×C₄²	—	2	1	no	—
301	C₂×C₄²	—	2	1	no	—
302	C₂×C₄²	—	2	1	no	—
303	C₂×C₄²	—	2	1	no	—
304	C₂×C₄²	—	2	1	no	—
305	C₂×C₄²	—	2	1	no	—
306	C₂×C₄²	—	2	1	no	—
307	C₂×C₄²	D₄×C₁₉	1	2	yes	—
308	C₁₉	#11317	1	1	yes	characteristic, direct product factor, Sylow
309	C₂⁴	#41×C₁₉	1	1	yes	characteristic
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	4	2	no	—
316	C₂²×C₄	—	4	1	no	—
317	C₂²×C₄	—	4	1	no	—
318	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
322	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
323	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
324	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
325	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
326	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
327	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
328	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
329	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
330	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
331	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
332	M₁₆	—	2	2	no	—
333	M₁₆	—	2	2	no	—
334	M₁₆	—	2	2	no	—
335	M₁₆	—	2	2	no	—
336	M₁₆	—	4	1	no	—
337	M₁₆	—	4	1	no	—
338	M₁₆	—	4	1	no	—
339	M₁₆	—	4	1	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	4	1	no	—
349	C₂×C₈	—	4	1	no	—
350	C₂×C₈	—	4	1	no	—
351	C₂×C₈	—	4	1	no	—
352	C₂×C₈	—	4	1	no	—
353	C₂×C₈	—	4	1	no	—
354	C₂×C₈	—	4	1	no	—
355	C₂×C₈	—	4	1	no	—
356	C₂×C₈	—	4	1	no	—
357	C₂×C₈	—	4	1	no	—
358	C₂×C₈	—	4	1	no	—
359	C₂×C₈	—	4	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₂²⋊C₄	—	4	1	no	—
367	C₂²⋊C₄	—	4	1	no	—
368	C₂²⋊C₄	—	4	1	no	—
369	C₂²⋊C₄	—	4	1	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	4	1	no	—
373	C₄²	—	4	1	no	—
374	C₄²	—	4	1	no	—
375	C₄²	—	4	1	no	—
376	C₄²	—	4	1	no	—
377	C₄²	—	4	1	no	—
378	C₂³	—	2	2	no	—
379	C₂³	—	2	2	no	—
380	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
381	C₂³	C₁₉×#123	1	1	yes	characteristic
382	C₂³	C₁₉×#124	1	1	yes	characteristic
383	C₂³	C₁₉×#125	1	1	yes	characteristic
384	C₂³	C₁₉×#126	1	1	yes	characteristic
385	C₂³	C₁₉×#126	1	1	yes	characteristic
386	C₂³	C₁₉×#126	1	1	yes	characteristic
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
400	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
401	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
402	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
403	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
404	C₂×C₄	C₄×Q₈×C₁₉	1	1	yes	characteristic
405	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
406	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
407	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
408	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
409	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
410	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
411	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
412	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
413	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
414	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
415	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
416	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
417	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
418	C₂×C₄	C₁₉×#125	1	1	yes	characteristic
419	C₂×C₄	C₁₉×#125	1	1	yes	characteristic
420	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
421	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
422	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
423	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
424	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
425	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
426	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
427	C₈	—	4	2	no	—
428	C₈	—	4	2	no	—
429	C₈	—	4	2	no	—
430	C₈	—	4	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	2	1	no	—
439	C₂²	C₁₉×#387	1	1	yes	characteristic
440	C₂²	C₁₉×#388	1	1	yes	characteristic
441	C₂²	C₁₉×#388	1	1	yes	characteristic
442	C₂²	C₁₉×#397	1	1	yes	characteristic
443	C₂²	C₁₉×#400	1	1	yes	characteristic
444	C₂²	C₁₉×#400	1	1	yes	characteristic
445	C₂²	C₁₉×#401	1	1	yes	characteristic
446	C₂²	C₁₉×#443	1	2	yes	—
447	C₂²	C₁₉×#444	1	2	yes	—
448	C₄	—	4	4	no	—
449	C₄	—	8	2	no	—
450	C₄	—	8	1	no	—
451	C₄	—	8	1	no	—
452	C₄	C₁₉×#383	1	1	yes	characteristic
453	C₄	C₁₉×#387	1	1	yes	characteristic
454	C₄	C₁₉×#387	1	1	yes	characteristic
455	C₄	C₁₉×#388	1	1	yes	characteristic
456	C₄	C₁₉×#396	1	1	yes	characteristic
457	C₄	C₁₉×#397	1	1	yes	characteristic
458	C₄	C₁₉×#397	1	1	yes	characteristic
459	C₄	C₁₉×#400	1	1	yes	characteristic
460	C₂	—	2	1	no	—
461	C₂	—	2	1	no	—
462	C₂	—	2	1	no	—
463	C₂	—	2	1	no	—
464	C₂	C₁₉×#1443	1	1	yes	characteristic
465	C₂	C₁₉×#1922	1	2	yes	—
466	C₂	C₁₉×#1929	1	2	yes	—
467	C₂	C₁₉×#1937	1	1	yes	characteristic
468	C₂	C₁₉×#1938	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
socle	C₂³×C₁₉	C₄×D₄
prime radical	C₂⁴×C₁₉	#41
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ C₂³×C₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
16. C₁₉×#340	C₄	semidirect
17. C₁₉×#340	C₄	semidirect
143. #11317	C₁₉	direct (N × H)
241. #340	C₄×C₁₉	semidirect
242. #340	C₄×C₁₉	semidirect
308. C₁₉	#11317	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#341	2
C₁₉×#1735	2
C₂×C₁₉×#339	2
C₁₉×#1729	2
C₂×C₁₉×#336	2
#11317	19

Subgroups — C19×#11317 #18017276

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11317 #18017276