Subgroups — C₁₉×#23633 #18029592

Order 4864.

962 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	C₂×C₁₉×#419	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#103	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2317	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2310	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2074	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2072	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1736	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1735	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1729	C₂	1	1	yes	maximal, characteristic
10	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#419	—	2	4	no	—
18	C₂×C₁₉×#103	—	2	4	no	—
19	C₂×C₁₉×#103	C₂²	1	2	yes	—
20	C₂×C₁₉×#103	C₂²	1	4	yes	—
21	C₂×C₁₉×#103	C₂²	1	2	yes	—
22	C₁₉×#391	—	2	2	no	—
23	C₁₉×#391	C₂²	1	4	yes	—
24	C₁₉×#389	—	2	2	no	—
25	C₁₉×#385	—	2	2	no	—
26	C₁₉×#384	C₂²	1	2	yes	—
27	C₁₉×#382	C₂²	1	2	yes	—
28	C₁₉×#381	—	2	2	no	—
29	C₁₉×#340	C₂²	1	2	yes	—
30	C₁₉×#340	C₂²	1	2	yes	—
31	C₁₉×#340	C₂²	1	4	yes	—
32	C₁₉×#336	C₂²	1	4	yes	—
33	C₂²×Q₈×C₁₉	—	2	1	no	—
34	C₂²×Q₈×C₁₉	—	2	2	no	—
35	C₂²×Q₈×C₁₉	—	2	2	no	—
36	C₂²×Q₈×C₁₉	—	2	2	no	—
37	C₂²×Q₈×C₁₉	—	2	2	no	—
38	C₂²×Q₈×C₁₉	—	2	2	no	—
39	C₂²×Q₈×C₁₉	D₄	1	4	yes	—
40	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
41	C₂³×C₄×C₁₉	—	2	1	no	—
42	C₂³×C₄×C₁₉	—	2	1	no	—
43	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₂×M₁₆×C₁₉	—	2	2	no	—
45	C₂×M₁₆×C₁₉	—	2	2	no	—
46	C₂×M₁₆×C₁₉	—	2	2	no	—
47	C₂²×C₈×C₁₉	—	2	2	no	—
48	C₂²×C₈×C₁₉	—	2	2	no	—
49	C₂²×C₈×C₁₉	—	2	2	no	—
50	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
52	C₁₉×#117	—	2	2	no	—
53	C₁₉×#117	—	2	2	no	—
54	C₁₉×#117	—	2	2	no	—
55	C₁₉×#117	—	2	2	no	—
56	C₁₉×#117	—	2	2	no	—
57	C₁₉×#117	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
62	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
63	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
70	C₂×C₄²×C₁₉	—	2	1	no	—
71	C₂×C₄²×C₁₉	—	2	1	no	—
72	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
73	C₁₉×#103	—	2	8	no	—
74	C₁₉×#103	—	2	4	no	—
75	C₁₉×#103	—	2	4	no	—
76	C₁₉×#95	—	2	8	no	—
77	C₁₉×#95	—	2	4	no	—
78	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₂×Q₈×C₁₉	—	2	4	no	—
80	C₂×Q₈×C₁₉	—	2	2	no	—
81	C₂×Q₈×C₁₉	—	2	8	no	—
82	C₂×Q₈×C₁₉	—	2	8	no	—
83	C₂×Q₈×C₁₉	—	2	2	no	—
84	C₂×Q₈×C₁₉	—	2	2	no	—
85	C₂×Q₈×C₁₉	—	2	2	no	—
86	C₂×Q₈×C₁₉	—	2	2	no	—
87	C₂×Q₈×C₁₉	—	4	2	no	—
88	C₂×Q₈×C₁₉	—	4	2	no	—
89	C₂×Q₈×C₁₉	—	4	4	no	—
90	C₂×Q₈×C₁₉	—	4	4	no	—
91	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
92	C₂²×C₄×C₁₉	—	2	4	no	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	2	1	no	—
95	C₂²×C₄×C₁₉	—	2	1	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	—	4	2	no	—
99	C₂²×C₄×C₁₉	—	4	2	no	—
100	C₂²×C₄×C₁₉	—	4	2	no	—
101	C₂²×C₄×C₁₉	—	8	2	no	—
102	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
103	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₉	#41	1	2	yes	—
106	C₂²×C₄×C₁₉	#41	1	2	yes	—
107	C₂²×C₄×C₁₉	#41	1	2	yes	—
108	C₂²×C₄×C₁₉	#41	1	2	yes	—
109	C₂²×C₄×C₁₉	#41	1	2	yes	—
110	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
111	M₁₆×C₁₉	—	4	4	no	—
112	C₂×C₈×C₁₉	—	2	2	no	—
113	C₂×C₈×C₁₉	—	2	2	no	—
114	C₂×C₈×C₁₉	—	2	2	no	—
115	C₂×C₈×C₁₉	—	2	2	no	—
116	C₂×C₈×C₁₉	—	2	2	no	—
117	C₂×C₈×C₁₉	—	2	2	no	—
118	C₂×C₈×C₁₉	—	4	4	no	—
119	C₄⋊C₄×C₁₉	—	2	4	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	—	2	2	no	—
124	C₄⋊C₄×C₁₉	—	2	1	no	—
125	C₄⋊C₄×C₁₉	—	2	1	no	—
126	C₄⋊C₄×C₁₉	—	2	2	no	—
127	C₄⋊C₄×C₁₉	—	2	2	no	—
128	C₄⋊C₄×C₁₉	—	4	2	no	—
129	C₄⋊C₄×C₁₉	—	8	4	no	—
130	C₂²⋊C₄×C₁₉	—	2	4	no	—
131	C₂²⋊C₄×C₁₉	—	4	2	no	—
132	C₂²⋊C₄×C₁₉	—	4	2	no	—
133	C₄²×C₁₉	—	2	2	no	—
134	C₄²×C₁₉	—	2	2	no	—
135	C₄²×C₁₉	—	4	2	no	—
136	C₄²×C₁₉	—	4	2	no	—
137	#23633	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
138	C₂³×C₁₉	—	2	2	no	—
139	C₂³×C₁₉	—	2	2	no	—
140	C₂³×C₁₉	#121	1	2	yes	—
141	C₂³×C₁₉	#123	1	2	yes	—
142	C₂³×C₁₉	#124	1	2	yes	—
143	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
144	Q₈×C₁₉	—	2	4	no	—
145	Q₈×C₁₉	—	2	4	no	—
146	Q₈×C₁₉	—	4	2	no	—
147	Q₈×C₁₉	—	4	2	no	—
148	Q₈×C₁₉	—	4	8	no	—
149	C₂×C₄×C₁₉	—	2	4	no	—
150	C₂×C₄×C₁₉	—	2	4	no	—
151	C₂×C₄×C₁₉	—	2	4	no	—
152	C₂×C₄×C₁₉	—	2	4	no	—
153	C₂×C₄×C₁₉	—	4	2	no	—
154	C₂×C₄×C₁₉	—	4	2	no	—
155	C₂×C₄×C₁₉	—	4	8	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	4	2	no	—
159	C₂×C₄×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	4	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	—	8	4	no	—
166	C₂×C₄×C₁₉	#121	1	2	yes	—
167	C₂×C₄×C₁₉	#123	1	4	yes	—
168	C₂×C₄×C₁₉	#123	1	4	yes	—
169	C₂×C₄×C₁₉	#123	1	2	yes	—
170	C₂×C₄×C₁₉	#124	1	2	yes	—
171	C₂×C₄×C₁₉	#126	1	4	yes	—
172	C₂×C₄×C₁₉	#126	1	4	yes	—
173	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
179	C₈×C₁₉	—	4	2	no	—
180	C₈×C₁₉	—	4	2	no	—
181	C₂×#419	C₂×C₁₉	1	1	yes	characteristic
182	C₂²×#103	C₂×C₁₉	1	1	yes	characteristic
183	#2317	C₂×C₁₉	1	1	yes	characteristic
184	#2310	C₂×C₁₉	1	1	yes	characteristic
185	#2074	C₂×C₁₉	1	4	yes	complemented
186	#2072	C₂×C₁₉	1	4	yes	complemented
187	#1736	C₂×C₁₉	1	1	yes	characteristic
188	#1735	C₂×C₁₉	1	1	yes	characteristic
189	#1729	C₂×C₁₉	1	1	yes	characteristic
190	C₂²×C₁₉	—	2	4	no	—
191	C₂²×C₁₉	—	2	4	no	—
192	C₂²×C₁₉	—	2	2	no	—
193	C₂²×C₁₉	—	2	2	no	—
194	C₂²×C₁₉	#397	1	4	yes	—
195	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
196	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
197	C₂²×C₁₉	C₂×#124	1	1	yes	characteristic
198	C₂²×C₁₉	#577	1	2	yes	—
199	C₂²×C₁₉	#578	1	2	yes	—
200	C₄×C₁₉	—	4	4	no	—
201	C₄×C₁₉	—	4	4	no	—
202	C₄×C₁₉	—	8	2	no	—
203	C₄×C₁₉	—	8	1	no	—
204	C₄×C₁₉	—	8	2	no	—
205	C₄×C₁₉	—	8	1	no	—
206	C₄×C₁₉	#397	1	4	yes	—
207	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
208	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
209	C₄×C₁₉	C₂×#126	1	1	yes	characteristic
210	C₄×C₁₉	C₂×#126	1	1	yes	characteristic
211	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
212	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
213	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
214	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
215	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
216	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
217	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
218	#419	—	2	4	no	—
219	C₂×#103	—	2	4	no	—
220	C₂×#103	C₂²×C₁₉	1	2	yes	—
221	C₂×#103	C₂²×C₁₉	1	4	yes	—
222	C₂×#103	C₂²×C₁₉	1	2	yes	—
223	#391	—	2	2	no	—
224	#391	C₂²×C₁₉	1	4	yes	—
225	#389	—	2	2	no	—
226	#385	—	2	2	no	—
227	#384	C₂²×C₁₉	1	2	yes	—
228	#382	C₂²×C₁₉	1	2	yes	—
229	#381	—	2	2	no	—
230	#340	C₂²×C₁₉	1	2	yes	—
231	#340	C₂²×C₁₉	1	4	yes	—
232	#340	C₂²×C₁₉	1	2	yes	—
233	#336	C₂²×C₁₉	1	4	yes	—
234	C₂×C₁₉	—	2	4	no	—
235	C₂×C₁₉	C₂×#397	1	1	yes	characteristic
236	C₂×C₁₉	#3043	1	1	yes	characteristic
237	C₂×C₁₉	#3044	1	1	yes	characteristic
238	C₂×C₁₉	#3097	1	2	yes	—
239	C₂×C₁₉	#3137	1	2	yes	—
240	C₂²×Q₈	—	2	1	no	—
241	C₂²×Q₈	—	2	2	no	—
242	C₂²×Q₈	—	2	2	no	—
243	C₂²×Q₈	—	2	2	no	—
244	C₂²×Q₈	—	2	2	no	—
245	C₂²×Q₈	—	2	2	no	—
246	C₂²×Q₈	D₄×C₁₉	1	4	yes	—
247	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
248	C₂³×C₄	—	2	1	no	—
249	C₂³×C₄	—	2	1	no	—
250	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
251	C₂×M₁₆	—	2	2	no	—
252	C₂×M₁₆	—	2	2	no	—
253	C₂×M₁₆	—	2	2	no	—
254	C₂²×C₈	—	2	2	no	—
255	C₂²×C₈	—	2	2	no	—
256	C₂²×C₈	—	2	2	no	—
257	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
258	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
259	#117	—	2	2	no	—
260	#117	—	2	2	no	—
261	#117	—	2	2	no	—
262	#117	—	2	2	no	—
263	#117	—	2	2	no	—
264	#117	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	4	no	—
269	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
270	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
272	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
274	C₂×C₂²⋊C₄	—	2	1	no	—
275	C₂×C₂²⋊C₄	—	2	1	no	—
276	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
277	C₂×C₄²	—	2	1	no	—
278	C₂×C₄²	—	2	1	no	—
279	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
280	#103	—	2	8	no	—
281	#103	—	2	4	no	—
282	#103	—	2	4	no	—
283	#95	—	2	8	no	—
284	#95	—	2	4	no	—
285	C₁₉	#23633	1	1	yes	characteristic, direct product factor, Sylow
286	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
287	C₂×Q₈	—	2	4	no	—
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	—	2	8	no	—
290	C₂×Q₈	—	2	8	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	4	2	no	—
296	C₂×Q₈	—	4	2	no	—
297	C₂×Q₈	—	4	4	no	—
298	C₂×Q₈	—	4	4	no	—
299	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	4	2	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	—	4	2	no	—
309	C₂²×C₄	—	8	2	no	—
310	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
311	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
313	C₂²×C₄	#41×C₁₉	1	2	yes	—
314	C₂²×C₄	#41×C₁₉	1	2	yes	—
315	C₂²×C₄	#41×C₁₉	1	2	yes	—
316	C₂²×C₄	#41×C₁₉	1	2	yes	—
317	C₂²×C₄	#41×C₁₉	1	2	yes	—
318	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
319	M₁₆	—	4	4	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	4	4	no	—
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	4	2	no	—
337	C₄⋊C₄	—	8	4	no	—
338	C₂²⋊C₄	—	2	4	no	—
339	C₂²⋊C₄	—	4	2	no	—
340	C₂²⋊C₄	—	4	2	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	4	2	no	—
344	C₄²	—	4	2	no	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	2	no	—
347	C₂³	C₁₉×#121	1	2	yes	—
348	C₂³	C₁₉×#123	1	2	yes	—
349	C₂³	C₁₉×#124	1	2	yes	—
350	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
351	Q₈	—	2	4	no	—
352	Q₈	—	2	4	no	—
353	Q₈	—	4	8	no	—
354	Q₈	—	4	2	no	—
355	Q₈	—	4	2	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	4	8	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	8	4	no	—
373	C₂×C₄	C₁₉×#121	1	2	yes	—
374	C₂×C₄	C₁₉×#123	1	2	yes	—
375	C₂×C₄	C₁₉×#123	1	4	yes	—
376	C₂×C₄	C₁₉×#123	1	4	yes	—
377	C₂×C₄	C₁₉×#124	1	2	yes	—
378	C₂×C₄	C₁₉×#126	1	4	yes	—
379	C₂×C₄	C₁₉×#126	1	4	yes	—
380	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
381	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
382	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
383	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
384	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
385	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
386	C₈	—	4	2	no	—
387	C₈	—	4	2	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	4	no	—
391	C₂²	—	2	4	no	—
392	C₂²	C₁₉×#397	1	4	yes	—
393	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
394	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
395	C₂²	C₂×C₁₉×#124	1	1	yes	characteristic
396	C₂²	C₁₉×#577	1	2	yes	—
397	C₂²	C₁₉×#578	1	2	yes	—
398	C₄	—	4	4	no	—
399	C₄	—	4	4	no	—
400	C₄	—	8	2	no	—
401	C₄	—	8	1	no	—
402	C₄	—	8	1	no	—
403	C₄	—	8	2	no	—
404	C₄	C₁₉×#397	1	4	yes	—
405	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
406	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
407	C₄	C₂×C₁₉×#126	1	1	yes	characteristic
408	C₄	C₂×C₁₉×#126	1	1	yes	characteristic
409	C₂	—	2	4	no	—
410	C₂	C₂×C₁₉×#397	1	1	yes	characteristic
411	C₂	C₁₉×#3043	1	1	yes	characteristic
412	C₂	C₁₉×#3044	1	1	yes	characteristic
413	C₂	C₁₉×#3097	1	2	yes	—
414	C₂	C₁₉×#3137	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
5. C₁₉×#2074	C₂	semidirect
6. C₁₉×#2072	C₂	semidirect
137. #23633	C₁₉	direct (N × H)
185. #2074	C₂×C₁₉	semidirect
186. #2072	C₂×C₁₉	semidirect
285. C₁₉	#23633	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×#419	2
C₂²×C₁₉×#103	2
C₁₉×#2317	2
C₁₉×#2310	2
C₁₉×#2074	2
C₁₉×#2072	2
C₁₉×#1736	2
C₁₉×#1735	2
C₁₉×#1729	2
#23633	19

Subgroups — C19×#23633 #18029592

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23633 #18029592