Subgroups — C₁₉×#18761 #18024720

Order 4864.

878 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#557	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3229	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3104	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#3078	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1653	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1636	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1546	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1487	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1479	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#557	—	2	2	no	—
11	C₁₉×#557	—	2	2	no	—
12	C₁₉×#557	—	2	2	no	—
13	C₁₉×#557	C₂²	1	4	yes	—
14	C₁₉×#533	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
16	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#125	—	2	2	no	—
18	C₂×C₁₉×#125	—	2	1	no	—
19	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
20	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
21	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#498	C₂²	1	2	yes	—
24	C₁₉×#487	C₂²	1	2	yes	—
25	C₁₉×#484	—	2	1	no	—
26	C₁₉×#483	—	2	2	no	—
27	C₁₉×#479	—	2	2	no	—
28	C₁₉×#477	C₂²	1	2	yes	—
29	C₁₉×#477	C₂²	1	2	yes	—
30	C₁₉×#475	—	2	2	no	—
31	C₁₉×#475	C₂²	1	2	yes	—
32	C₁₉×#462	C₂²	1	2	yes	—
33	C₁₉×#451	—	2	1	no	—
34	C₄×Q₁₆×C₁₉	—	2	2	no	—
35	C₁₉×#431	C₂²	1	1	yes	characteristic
36	C₁₉×#431	C₂²	1	1	yes	characteristic
37	C₁₉×#428	—	2	1	no	—
38	C₁₉×#423	C₂²	1	1	yes	characteristic
39	C₁₉×#419	—	2	1	no	—
40	C₁₉×#332	C₂²	1	4	yes	—
41	C₁₉×Q₈⋊C₈	C₂²	1	4	yes	—
42	C₁₉×Q₈⋊C₈	C₂²	1	4	yes	—
43	C₂²×Q₈×C₁₉	—	2	1	no	—
44	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
45	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
46	C₂×Q₁₆×C₁₉	—	2	2	no	—
47	C₂×M₁₆×C₁₉	—	2	1	no	—
48	C₁₉×C₄⋊Q₈	—	2	4	no	—
49	C₁₉×C₄⋊Q₈	—	2	4	no	—
50	C₁₉×C₄⋊Q₈	—	2	1	no	—
51	C₁₉×C₄⋊Q₈	—	2	1	no	—
52	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
53	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
54	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
55	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
56	C₁₉×#125	—	2	8	no	—
57	C₁₉×#125	—	2	4	no	—
58	C₁₉×#125	—	2	8	no	—
59	C₁₉×#125	—	2	4	no	—
60	C₁₉×#125	—	2	1	no	—
61	C₁₉×C₂²⋊Q₈	—	2	1	no	—
62	C₁₉×C₂²⋊Q₈	—	2	1	no	—
63	C₄×Q₈×C₁₉	—	2	4	no	—
64	C₄×Q₈×C₁₉	—	2	4	no	—
65	C₄×Q₈×C₁₉	—	2	4	no	—
66	C₄×Q₈×C₁₉	—	2	4	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	—	2	1	no	—
71	C₄×Q₈×C₁₉	—	2	1	no	—
72	C₄×Q₈×C₁₉	—	2	1	no	—
73	C₄×Q₈×C₁₉	D₄	1	2	yes	—
74	C₄×Q₈×C₁₉	D₄	1	2	yes	—
75	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
76	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
77	C₁₉×#117	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
86	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₁₉	—	2	2	no	—
88	C₂×C₄²×C₁₉	—	2	1	no	—
89	C₂×C₄²×C₁₉	—	2	1	no	—
90	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
91	C₁₉×#107	—	2	2	no	—
92	C₁₉×#107	—	2	2	no	—
93	C₁₉×#106	—	2	2	no	—
94	C₁₉×#106	—	2	4	no	—
95	C₁₉×C₄⋊C₈	—	2	1	no	—
96	C₁₉×C₄⋊C₈	—	2	1	no	—
97	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
98	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
99	C₁₉×#103	—	2	2	no	—
100	C₁₉×#103	—	2	2	no	—
101	C₁₉×#103	—	2	2	no	—
102	C₁₉×#103	—	2	2	no	—
103	C₁₉×#103	—	2	4	no	—
104	C₁₉×C₂²⋊C₈	—	2	1	no	—
105	C₁₉×C₂²⋊C₈	—	2	1	no	—
106	C₄×C₈×C₁₉	—	2	1	no	—
107	C₄×C₈×C₁₉	C₂³	1	2	yes	—
108	C₂×Q₈×C₁₉	—	2	4	no	—
109	C₂×Q₈×C₁₉	—	2	1	no	—
110	C₂×Q₈×C₁₉	—	2	1	no	—
111	C₂×Q₈×C₁₉	—	2	2	no	—
112	C₂×Q₈×C₁₉	—	2	2	no	—
113	C₂×Q₈×C₁₉	—	2	2	no	—
114	C₂×Q₈×C₁₉	—	2	2	no	—
115	C₂×Q₈×C₁₉	—	2	1	no	—
116	C₂×Q₈×C₁₉	—	2	1	no	—
117	C₂×Q₈×C₁₉	—	4	2	no	—
118	C₂×Q₈×C₁₉	—	4	2	no	—
119	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
120	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₁₉	—	2	1	no	—
122	C₂²×C₄×C₁₉	—	2	1	no	—
123	C₂²×C₄×C₁₉	—	2	1	no	—
124	C₂²×C₄×C₁₉	—	2	1	no	—
125	C₂²×C₄×C₁₉	—	2	2	no	—
126	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
129	Q₁₆×C₁₉	—	4	4	no	—
130	M₁₆×C₁₉	—	4	2	no	—
131	C₂×C₈×C₁₉	—	2	2	no	—
132	C₂×C₈×C₁₉	—	2	2	no	—
133	C₂×C₈×C₁₉	—	2	2	no	—
134	C₄⋊C₄×C₁₉	—	2	8	no	—
135	C₄⋊C₄×C₁₉	—	2	8	no	—
136	C₄⋊C₄×C₁₉	—	2	8	no	—
137	C₄⋊C₄×C₁₉	—	2	2	no	—
138	C₄⋊C₄×C₁₉	—	2	2	no	—
139	C₄⋊C₄×C₁₉	—	2	2	no	—
140	C₄⋊C₄×C₁₉	—	2	1	no	—
141	C₄⋊C₄×C₁₉	—	2	1	no	—
142	C₄⋊C₄×C₁₉	—	2	2	no	—
143	C₄⋊C₄×C₁₉	—	2	2	no	—
144	C₄⋊C₄×C₁₉	—	2	2	no	—
145	C₄⋊C₄×C₁₉	—	2	2	no	—
146	C₄⋊C₄×C₁₉	—	2	1	no	—
147	C₄⋊C₄×C₁₉	—	2	1	no	—
148	C₄⋊C₄×C₁₉	—	2	1	no	—
149	C₄⋊C₄×C₁₉	—	2	1	no	—
150	C₄⋊C₄×C₁₉	—	4	1	no	—
151	C₄⋊C₄×C₁₉	—	4	1	no	—
152	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
153	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
154	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
155	C₂²⋊C₄×C₁₉	—	4	1	no	—
156	C₄²×C₁₉	—	2	8	no	—
157	C₄²×C₁₉	—	2	2	no	—
158	C₄²×C₁₉	—	2	2	no	—
159	C₄²×C₁₉	—	2	2	no	—
160	C₄²×C₁₉	—	2	2	no	—
161	C₄²×C₁₉	—	4	1	no	—
162	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
166	#18761	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂³×C₁₉	#120	1	1	yes	characteristic
168	Q₈×C₁₉	—	2	4	no	—
169	Q₈×C₁₉	—	2	2	no	—
170	Q₈×C₁₉	—	2	2	no	—
171	Q₈×C₁₉	—	2	2	no	—
172	Q₈×C₁₉	—	4	2	no	—
173	Q₈×C₁₉	—	4	2	no	—
174	Q₈×C₁₉	—	4	2	no	—
175	Q₈×C₁₉	—	4	2	no	—
176	Q₈×C₁₉	—	4	4	no	—
177	Q₈×C₁₉	—	4	2	no	—
178	Q₈×C₁₉	#137	1	4	yes	—
179	C₂×C₄×C₁₉	—	2	4	no	—
180	C₂×C₄×C₁₉	—	2	2	no	—
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	2	2	no	—
183	C₂×C₄×C₁₉	—	2	2	no	—
184	C₂×C₄×C₁₉	—	2	2	no	—
185	C₂×C₄×C₁₉	—	2	4	no	—
186	C₂×C₄×C₁₉	—	4	1	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	4	4	no	—
191	C₂×C₄×C₁₉	—	4	1	no	—
192	C₂×C₄×C₁₉	—	4	1	no	—
193	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
194	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
195	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
196	C₂×C₄×C₁₉	#135	1	2	yes	—
197	C₂×C₄×C₁₉	#137	1	2	yes	—
198	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
201	C₈×C₁₉	—	4	2	no	—
202	C₈×C₁₉	—	4	2	no	—
203	C₈×C₁₉	—	4	2	no	—
204	C₂×#557	C₂×C₁₉	1	1	yes	characteristic
205	#3229	C₂×C₁₉	1	1	yes	characteristic
206	#3104	C₂×C₁₉	1	1	yes	characteristic
207	#3078	C₂×C₁₉	1	1	yes	characteristic
208	#1653	C₂×C₁₉	1	4	yes	complemented
209	#1636	C₂×C₁₉	1	4	yes	complemented
210	#1546	C₂×C₁₉	1	1	yes	characteristic
211	#1487	C₂×C₁₉	1	1	yes	characteristic
212	#1479	C₂×C₁₉	1	1	yes	characteristic
213	C₂²×C₁₉	—	2	1	no	—
214	C₂²×C₁₉	—	2	1	no	—
215	C₂²×C₁₉	#452	1	2	yes	—
216	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
217	C₄×C₁₉	—	2	4	no	—
218	C₄×C₁₉	—	2	1	no	—
219	C₄×C₁₉	—	2	1	no	—
220	C₄×C₁₉	—	2	1	no	—
221	C₄×C₁₉	—	4	2	no	—
222	C₄×C₁₉	—	4	4	no	—
223	C₄×C₁₉	—	4	2	no	—
224	C₄×C₁₉	—	4	2	no	—
225	C₄×C₁₉	—	8	1	no	—
226	C₄×C₁₉	—	8	1	no	—
227	C₄×C₁₉	#452	1	2	yes	—
228	C₄×C₁₉	C₂×#135	1	1	yes	characteristic
229	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
230	C₄×C₁₉	C₂×#137	1	2	yes	—
231	#557	—	2	2	no	—
232	#557	—	2	2	no	—
233	#557	—	2	2	no	—
234	#557	C₂²×C₁₉	1	4	yes	—
235	#533	C₂²×C₁₉	1	1	yes	characteristic
236	C₂×C₄⋊Q₈	—	2	1	no	—
237	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
238	C₂×#125	—	2	2	no	—
239	C₂×#125	—	2	1	no	—
240	C₂×C₄×Q₈	—	2	1	no	—
241	C₂×C₄×Q₈	—	2	1	no	—
242	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
243	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
244	#498	C₂²×C₁₉	1	2	yes	—
245	#487	C₂²×C₁₉	1	2	yes	—
246	#484	—	2	1	no	—
247	#483	—	2	2	no	—
248	#479	—	2	2	no	—
249	#477	C₂²×C₁₉	1	2	yes	—
250	#477	C₂²×C₁₉	1	2	yes	—
251	#475	—	2	2	no	—
252	#475	C₂²×C₁₉	1	2	yes	—
253	#462	C₂²×C₁₉	1	2	yes	—
254	#451	—	2	1	no	—
255	C₄×Q₁₆	—	2	2	no	—
256	#431	C₂²×C₁₉	1	1	yes	characteristic
257	#431	C₂²×C₁₉	1	1	yes	characteristic
258	#428	—	2	1	no	—
259	#423	C₂²×C₁₉	1	1	yes	characteristic
260	#419	—	2	1	no	—
261	#332	C₂²×C₁₉	1	4	yes	—
262	Q₈⋊C₈	C₂²×C₁₉	1	4	yes	—
263	Q₈⋊C₈	C₂²×C₁₉	1	4	yes	—
264	C₂×C₁₉	—	2	2	no	—
265	C₂×C₁₉	C₂×#452	1	1	yes	characteristic
266	C₂×C₁₉	#3004	1	1	yes	characteristic
267	C₂×C₁₉	#3020	1	1	yes	characteristic
268	C₂²×Q₈	—	2	1	no	—
269	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
270	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
271	C₂×Q₁₆	—	2	2	no	—
272	C₂×M₁₆	—	2	1	no	—
273	C₄⋊Q₈	—	2	4	no	—
274	C₄⋊Q₈	—	2	4	no	—
275	C₄⋊Q₈	—	2	1	no	—
276	C₄⋊Q₈	—	2	1	no	—
277	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
278	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
279	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
280	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
281	#125	—	2	8	no	—
282	#125	—	2	4	no	—
283	#125	—	2	8	no	—
284	#125	—	2	4	no	—
285	#125	—	2	1	no	—
286	C₂²⋊Q₈	—	2	1	no	—
287	C₂²⋊Q₈	—	2	1	no	—
288	C₄×Q₈	—	2	4	no	—
289	C₄×Q₈	—	2	4	no	—
290	C₄×Q₈	—	2	4	no	—
291	C₄×Q₈	—	2	4	no	—
292	C₄×Q₈	—	2	1	no	—
293	C₄×Q₈	—	2	1	no	—
294	C₄×Q₈	—	2	1	no	—
295	C₄×Q₈	—	2	1	no	—
296	C₄×Q₈	—	2	1	no	—
297	C₄×Q₈	—	2	1	no	—
298	C₄×Q₈	D₄×C₁₉	1	2	yes	—
299	C₄×Q₈	D₄×C₁₉	1	2	yes	—
300	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
301	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
302	#117	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	2	no	—
304	C₂×C₄⋊C₄	—	2	2	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
310	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
311	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
312	C₂×C₄²	—	2	2	no	—
313	C₂×C₄²	—	2	1	no	—
314	C₂×C₄²	—	2	1	no	—
315	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
316	#107	—	2	2	no	—
317	#107	—	2	2	no	—
318	#106	—	2	2	no	—
319	#106	—	2	4	no	—
320	C₄⋊C₈	—	2	1	no	—
321	C₄⋊C₈	—	2	1	no	—
322	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
323	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
324	#103	—	2	2	no	—
325	#103	—	2	2	no	—
326	#103	—	2	2	no	—
327	#103	—	2	2	no	—
328	#103	—	2	4	no	—
329	C₂²⋊C₈	—	2	1	no	—
330	C₂²⋊C₈	—	2	1	no	—
331	C₄×C₈	—	2	1	no	—
332	C₄×C₈	C₂³×C₁₉	1	2	yes	—
333	C₁₉	#18761	1	1	yes	characteristic, direct product factor, Sylow
334	C₂×Q₈	—	2	4	no	—
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	1	no	—
342	C₂×Q₈	—	2	1	no	—
343	C₂×Q₈	—	4	2	no	—
344	C₂×Q₈	—	4	2	no	—
345	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
346	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
355	Q₁₆	—	4	4	no	—
356	M₁₆	—	4	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₄⋊C₄	—	2	8	no	—
361	C₄⋊C₄	—	2	8	no	—
362	C₄⋊C₄	—	2	8	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	4	1	no	—
377	C₄⋊C₄	—	4	1	no	—
378	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
379	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
380	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
381	C₂²⋊C₄	—	4	1	no	—
382	C₄²	—	2	8	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	4	1	no	—
388	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
389	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
390	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
391	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
392	C₂³	C₁₉×#120	1	1	yes	characteristic
393	Q₈	—	2	4	no	—
394	Q₈	—	2	2	no	—
395	Q₈	—	2	2	no	—
396	Q₈	—	2	2	no	—
397	Q₈	—	4	2	no	—
398	Q₈	—	4	2	no	—
399	Q₈	—	4	4	no	—
400	Q₈	—	4	2	no	—
401	Q₈	—	4	2	no	—
402	Q₈	—	4	2	no	—
403	Q₈	C₁₉×#137	1	4	yes	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	4	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
419	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
420	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
421	C₂×C₄	C₁₉×#135	1	2	yes	—
422	C₂×C₄	C₁₉×#137	1	2	yes	—
423	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
424	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
425	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
426	C₈	—	4	2	no	—
427	C₈	—	4	2	no	—
428	C₈	—	4	2	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	C₁₉×#452	1	2	yes	—
432	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
433	C₄	—	2	4	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	4	2	no	—
438	C₄	—	4	4	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	2	no	—
441	C₄	—	8	1	no	—
442	C₄	—	8	1	no	—
443	C₄	C₁₉×#452	1	2	yes	—
444	C₄	C₂×C₁₉×#135	1	1	yes	characteristic
445	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
446	C₄	C₂×C₁₉×#137	1	2	yes	—
447	C₂	—	2	2	no	—
448	C₂	C₂×C₁₉×#452	1	1	yes	characteristic
449	C₂	C₁₉×#3004	1	1	yes	characteristic
450	C₂	C₁₉×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂³×C₁₉	#120
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
5. C₁₉×#1653	C₂	semidirect
6. C₁₉×#1636	C₂	semidirect
166. #18761	C₁₉	direct (N × H)
208. #1653	C₂×C₁₉	semidirect
209. #1636	C₂×C₁₉	semidirect
333. C₁₉	#18761	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×#557	2
C₁₉×#3229	2
C₁₉×#3104	2
C₁₉×#3078	2
C₁₉×#1653	2
C₁₉×#1636	2
C₁₉×#1546	2
C₁₉×#1487	2
C₁₉×#1479	2
#18761	19

Subgroups — C19×#18761 #18024720

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18761 #18024720