Subgroups — C₁₉×#23457 #18029416

Order 4864.

1202 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#544	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#419	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₉×#103	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2310	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2026	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2024	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	C₁₉×#544	—	2	4	no	—
14	C₁₉×#544	—	2	4	no	—
15	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
16	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₁₉×#125	—	2	1	no	—
18	C₂×C₁₉×#125	C₂²	1	2	yes	—
19	C₂×C₁₉×C₂²⋊Q₈	—	2	2	no	—
20	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#419	—	2	4	no	—
25	C₂×C₁₉×#103	—	2	4	no	—
26	C₂×C₁₉×#103	C₂²	1	2	yes	—
27	C₂×C₁₉×#103	C₂²	1	4	yes	—
28	C₂×C₁₉×#103	C₂²	1	2	yes	—
29	C₁₉×#391	—	2	1	no	—
30	C₁₉×#391	—	2	1	no	—
31	C₁₉×#391	C₂²	1	4	yes	—
32	C₁₉×#381	—	2	2	no	—
33	C₁₉×#340	C₂²	1	2	yes	—
34	C₁₉×#340	C₂²	1	2	yes	—
35	C₁₉×#340	C₂²	1	4	yes	—
36	C₁₉×#336	C₂²	1	4	yes	—
37	C₂²×Q₈×C₁₉	—	2	1	no	—
38	C₂²×Q₈×C₁₉	—	2	2	no	—
39	C₂²×Q₈×C₁₉	—	2	2	no	—
40	C₂²×Q₈×C₁₉	—	2	2	no	—
41	C₂²×Q₈×C₁₉	—	2	2	no	—
42	C₂²×Q₈×C₁₉	—	2	2	no	—
43	C₂²×Q₈×C₁₉	—	2	2	no	—
44	C₂²×Q₈×C₁₉	Q₈	1	4	yes	complemented
45	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
46	C₂³×C₄×C₁₉	—	2	1	no	—
47	C₂³×C₄×C₁₉	—	2	1	no	—
48	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
49	C₂×M₁₆×C₁₉	—	2	2	no	—
50	C₂×M₁₆×C₁₉	—	2	2	no	—
51	C₂×M₁₆×C₁₉	—	2	2	no	—
52	C₂²×C₈×C₁₉	—	2	2	no	—
53	C₂²×C₈×C₁₉	—	2	2	no	—
54	C₂²×C₈×C₁₉	—	2	2	no	—
55	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
57	C₁₉×C₄⋊Q₈	—	2	8	no	—
58	C₁₉×C₄⋊Q₈	—	2	4	no	—
59	C₁₉×C₄⋊Q₈	—	2	4	no	—
60	C₁₉×#125	—	2	8	no	—
61	C₁₉×#125	—	2	4	no	—
62	C₁₉×#125	—	2	4	no	—
63	C₁₉×C₂²⋊Q₈	—	2	16	no	—
64	C₁₉×#117	—	2	2	no	—
65	C₁₉×#117	—	2	2	no	—
66	C₁₉×#117	—	2	2	no	—
67	C₁₉×#117	—	2	2	no	—
68	C₁₉×#117	—	2	2	no	—
69	C₁₉×#117	D₄	1	4	yes	—
70	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
75	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
78	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
79	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
85	C₂×C₄²×C₁₉	—	2	1	no	—
86	C₂×C₄²×C₁₉	—	2	1	no	—
87	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
88	C₁₉×#103	—	2	8	no	—
89	C₁₉×#103	—	2	4	no	—
90	C₁₉×#103	—	2	4	no	—
91	C₁₉×#95	—	2	4	no	—
92	C₁₉×#95	—	2	4	no	—
93	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
94	C₂×Q₈×C₁₉	—	2	8	no	—
95	C₂×Q₈×C₁₉	—	2	4	no	—
96	C₂×Q₈×C₁₉	—	2	2	no	—
97	C₂×Q₈×C₁₉	—	2	8	no	—
98	C₂×Q₈×C₁₉	—	2	8	no	—
99	C₂×Q₈×C₁₉	—	2	2	no	—
100	C₂×Q₈×C₁₉	—	2	2	no	—
101	C₂×Q₈×C₁₉	—	2	2	no	—
102	C₂×Q₈×C₁₉	—	2	2	no	—
103	C₂×Q₈×C₁₉	—	4	2	no	—
104	C₂×Q₈×C₁₉	—	4	2	no	—
105	C₂×Q₈×C₁₉	—	4	4	no	—
106	C₂×Q₈×C₁₉	—	4	4	no	—
107	C₂×Q₈×C₁₉	—	8	4	no	—
108	C₂×Q₈×C₁₉	C₂×Q₈	1	4	yes	—
109	C₂²×C₄×C₁₉	—	2	4	no	—
110	C₂²×C₄×C₁₉	—	2	1	no	—
111	C₂²×C₄×C₁₉	—	2	1	no	—
112	C₂²×C₄×C₁₉	—	2	2	no	—
113	C₂²×C₄×C₁₉	—	2	2	no	—
114	C₂²×C₄×C₁₉	—	2	4	no	—
115	C₂²×C₄×C₁₉	—	2	2	no	—
116	C₂²×C₄×C₁₉	—	4	2	no	—
117	C₂²×C₄×C₁₉	—	4	2	no	—
118	C₂²×C₄×C₁₉	—	8	2	no	—
119	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
125	C₂²×C₄×C₁₉	#41	1	2	yes	—
126	C₂²×C₄×C₁₉	#41	1	2	yes	—
127	C₂²×C₄×C₁₉	#41	1	2	yes	—
128	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
129	M₁₆×C₁₉	—	4	4	no	—
130	C₂×C₈×C₁₉	—	2	2	no	—
131	C₂×C₈×C₁₉	—	2	2	no	—
132	C₂×C₈×C₁₉	—	2	2	no	—
133	C₂×C₈×C₁₉	—	2	2	no	—
134	C₂×C₈×C₁₉	—	2	2	no	—
135	C₂×C₈×C₁₉	—	2	2	no	—
136	C₂×C₈×C₁₉	—	4	4	no	—
137	C₄⋊C₄×C₁₉	—	2	8	no	—
138	C₄⋊C₄×C₁₉	—	2	8	no	—
139	C₄⋊C₄×C₁₉	—	2	8	no	—
140	C₄⋊C₄×C₁₉	—	2	4	no	—
141	C₄⋊C₄×C₁₉	—	2	2	no	—
142	C₄⋊C₄×C₁₉	—	2	2	no	—
143	C₄⋊C₄×C₁₉	—	2	2	no	—
144	C₄⋊C₄×C₁₉	—	2	1	no	—
145	C₄⋊C₄×C₁₉	—	2	1	no	—
146	C₄⋊C₄×C₁₉	—	2	2	no	—
147	C₄⋊C₄×C₁₉	—	2	2	no	—
148	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
149	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
150	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
151	C₂²⋊C₄×C₁₉	—	2	4	no	—
152	C₂²⋊C₄×C₁₉	—	2	4	no	—
153	C₂²⋊C₄×C₁₉	—	4	2	no	—
154	C₄²×C₁₉	—	2	4	no	—
155	C₄²×C₁₉	—	2	2	no	—
156	C₄²×C₁₉	—	2	2	no	—
157	C₄²×C₁₉	—	4	2	no	—
158	#23457	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
159	C₂³×C₁₉	—	2	2	no	—
160	C₂³×C₁₉	—	2	2	no	—
161	C₂³×C₁₉	#120	1	2	yes	—
162	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
163	C₂³×C₁₉	#124	1	2	yes	—
164	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
165	Q₈×C₁₉	—	2	4	no	—
166	Q₈×C₁₉	—	2	4	no	—
167	Q₈×C₁₉	—	4	2	no	—
168	Q₈×C₁₉	—	4	2	no	—
169	Q₈×C₁₉	—	4	8	no	—
170	Q₈×C₁₉	—	8	8	no	—
171	C₂×C₄×C₁₉	—	2	2	no	—
172	C₂×C₄×C₁₉	—	2	2	no	—
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	2	2	no	—
175	C₂×C₄×C₁₉	—	2	4	no	—
176	C₂×C₄×C₁₉	—	2	4	no	—
177	C₂×C₄×C₁₉	—	2	4	no	—
178	C₂×C₄×C₁₉	—	2	4	no	—
179	C₂×C₄×C₁₉	—	4	2	no	—
180	C₂×C₄×C₁₉	—	4	2	no	—
181	C₂×C₄×C₁₉	—	4	4	no	—
182	C₂×C₄×C₁₉	—	4	2	no	—
183	C₂×C₄×C₁₉	—	4	2	no	—
184	C₂×C₄×C₁₉	—	4	8	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	8	4	no	—
189	C₂×C₄×C₁₉	#120	1	2	yes	—
190	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
191	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
192	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
193	C₂×C₄×C₁₉	#124	1	4	yes	—
194	C₂×C₄×C₁₉	#124	1	4	yes	—
195	C₂×C₄×C₁₉	#124	1	2	yes	—
196	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
199	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
202	C₈×C₁₉	—	4	2	no	—
203	C₈×C₁₉	—	4	2	no	—
204	C₂×#544	C₂×C₁₉	1	1	yes	characteristic
205	C₂×#419	C₂×C₁₉	1	1	yes	characteristic
206	C₂²×#103	C₂×C₁₉	1	1	yes	characteristic
207	#2310	C₂×C₁₉	1	1	yes	characteristic
208	#2026	C₂×C₁₉	1	4	yes	complemented
209	#2024	C₂×C₁₉	1	4	yes	complemented
210	#1736	C₂×C₁₉	1	1	yes	characteristic
211	#1735	C₂×C₁₉	1	1	yes	characteristic
212	#1729	C₂×C₁₉	1	1	yes	characteristic
213	C₂²×C₁₉	—	2	4	no	—
214	C₂²×C₁₉	—	2	4	no	—
215	C₂²×C₁₉	—	2	2	no	—
216	C₂²×C₁₉	—	2	2	no	—
217	C₂²×C₁₉	#393	1	4	yes	—
218	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
219	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
220	C₂²×C₁₉	C₂×#124	1	1	yes	characteristic
221	C₂²×C₁₉	#577	1	2	yes	—
222	C₂²×C₁₉	#578	1	2	yes	—
223	C₄×C₁₉	—	4	4	no	—
224	C₄×C₁₉	—	4	2	no	—
225	C₄×C₁₉	—	4	4	no	—
226	C₄×C₁₉	—	4	2	no	—
227	C₄×C₁₉	—	4	2	no	—
228	C₄×C₁₉	—	4	2	no	—
229	C₄×C₁₉	—	8	2	no	—
230	C₄×C₁₉	#393	1	4	yes	—
231	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
232	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
233	C₄×C₁₉	C₂×#124	1	1	yes	characteristic
234	C₄×C₁₉	C₂×#124	1	1	yes	characteristic
235	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
236	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
237	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
238	#544	—	2	4	no	—
239	#544	—	2	4	no	—
240	C₂×C₄⋊Q₈	—	2	1	no	—
241	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
242	C₂×#125	—	2	1	no	—
243	C₂×#125	C₂²×C₁₉	1	2	yes	—
244	C₂×C₂²⋊Q₈	—	2	2	no	—
245	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
246	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
247	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
248	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
249	#419	—	2	4	no	—
250	C₂×#103	—	2	4	no	—
251	C₂×#103	C₂²×C₁₉	1	4	yes	—
252	C₂×#103	C₂²×C₁₉	1	2	yes	—
253	C₂×#103	C₂²×C₁₉	1	2	yes	—
254	#391	—	2	1	no	—
255	#391	—	2	1	no	—
256	#391	C₂²×C₁₉	1	4	yes	—
257	#381	—	2	2	no	—
258	#340	C₂²×C₁₉	1	2	yes	—
259	#340	C₂²×C₁₉	1	2	yes	—
260	#340	C₂²×C₁₉	1	4	yes	—
261	#336	C₂²×C₁₉	1	4	yes	—
262	C₂×C₁₉	—	2	4	no	—
263	C₂×C₁₉	C₂×#393	1	1	yes	characteristic
264	C₂×C₁₉	#3009	1	1	yes	characteristic
265	C₂×C₁₉	#3011	1	1	yes	characteristic
266	C₂×C₁₉	#3082	1	2	yes	—
267	C₂×C₁₉	#3137	1	2	yes	—
268	C₂²×Q₈	—	2	1	no	—
269	C₂²×Q₈	—	2	2	no	—
270	C₂²×Q₈	—	2	2	no	—
271	C₂²×Q₈	—	2	2	no	—
272	C₂²×Q₈	—	2	2	no	—
273	C₂²×Q₈	—	2	2	no	—
274	C₂²×Q₈	—	2	2	no	—
275	C₂²×Q₈	Q₈×C₁₉	1	4	yes	complemented
276	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
277	C₂³×C₄	—	2	1	no	—
278	C₂³×C₄	—	2	1	no	—
279	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
280	C₂×M₁₆	—	2	2	no	—
281	C₂×M₁₆	—	2	2	no	—
282	C₂×M₁₆	—	2	2	no	—
283	C₂²×C₈	—	2	2	no	—
284	C₂²×C₈	—	2	2	no	—
285	C₂²×C₈	—	2	2	no	—
286	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
287	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
288	C₄⋊Q₈	—	2	8	no	—
289	C₄⋊Q₈	—	2	4	no	—
290	C₄⋊Q₈	—	2	4	no	—
291	#125	—	2	8	no	—
292	#125	—	2	4	no	—
293	#125	—	2	4	no	—
294	C₂²⋊Q₈	—	2	16	no	—
295	#117	—	2	2	no	—
296	#117	—	2	2	no	—
297	#117	—	2	2	no	—
298	#117	—	2	2	no	—
299	#117	—	2	2	no	—
300	#117	D₄×C₁₉	1	4	yes	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	2	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	D₄×C₁₉	1	1	yes	characteristic
307	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
308	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
309	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
310	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
311	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
312	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
313	C₂×C₂²⋊C₄	—	2	1	no	—
314	C₂×C₂²⋊C₄	—	2	1	no	—
315	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
316	C₂×C₄²	—	2	1	no	—
317	C₂×C₄²	—	2	1	no	—
318	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
319	#103	—	2	8	no	—
320	#103	—	2	4	no	—
321	#103	—	2	4	no	—
322	#95	—	2	4	no	—
323	#95	—	2	4	no	—
324	C₁₉	#23457	1	1	yes	characteristic, direct product factor, Sylow
325	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
326	C₂×Q₈	—	2	8	no	—
327	C₂×Q₈	—	2	4	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	8	no	—
330	C₂×Q₈	—	2	8	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	4	2	no	—
336	C₂×Q₈	—	4	4	no	—
337	C₂×Q₈	—	4	4	no	—
338	C₂×Q₈	—	4	2	no	—
339	C₂×Q₈	—	8	4	no	—
340	C₂×Q₈	C₂×Q₈×C₁₉	1	4	yes	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	—	8	2	no	—
351	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
352	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
353	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
355	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
356	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
357	C₂²×C₄	#41×C₁₉	1	2	yes	—
358	C₂²×C₄	#41×C₁₉	1	2	yes	—
359	C₂²×C₄	#41×C₁₉	1	2	yes	—
360	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
361	M₁₆	—	4	4	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	4	4	no	—
369	C₄⋊C₄	—	2	8	no	—
370	C₄⋊C₄	—	2	8	no	—
371	C₄⋊C₄	—	2	8	no	—
372	C₄⋊C₄	—	2	4	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
381	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
382	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
383	C₂²⋊C₄	—	2	4	no	—
384	C₂²⋊C₄	—	2	4	no	—
385	C₂²⋊C₄	—	4	2	no	—
386	C₄²	—	2	4	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	4	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	C₁₉×#120	1	2	yes	—
393	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
394	C₂³	C₁₉×#124	1	2	yes	—
395	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
396	Q₈	—	2	4	no	—
397	Q₈	—	2	4	no	—
398	Q₈	—	4	8	no	—
399	Q₈	—	4	2	no	—
400	Q₈	—	4	2	no	—
401	Q₈	—	8	8	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	4	8	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	8	4	no	—
420	C₂×C₄	C₁₉×#120	1	2	yes	—
421	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
422	C₂×C₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
423	C₂×C₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
424	C₂×C₄	C₁₉×#124	1	2	yes	—
425	C₂×C₄	C₁₉×#124	1	4	yes	—
426	C₂×C₄	C₁₉×#124	1	4	yes	—
427	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
428	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
429	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
430	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
431	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
432	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
433	C₈	—	4	2	no	—
434	C₈	—	4	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	4	no	—
438	C₂²	—	2	4	no	—
439	C₂²	C₁₉×#393	1	4	yes	—
440	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
441	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
442	C₂²	C₂×C₁₉×#124	1	1	yes	characteristic
443	C₂²	C₁₉×#577	1	2	yes	—
444	C₂²	C₁₉×#578	1	2	yes	—
445	C₄	—	4	2	no	—
446	C₄	—	4	4	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	4	4	no	—
451	C₄	—	8	2	no	—
452	C₄	C₁₉×#393	1	4	yes	—
453	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
454	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
455	C₄	C₂×C₁₉×#124	1	1	yes	characteristic
456	C₄	C₂×C₁₉×#124	1	1	yes	characteristic
457	C₂	—	2	4	no	—
458	C₂	C₂×C₁₉×#393	1	1	yes	characteristic
459	C₂	C₁₉×#3009	1	1	yes	characteristic
460	C₂	C₁₉×#3011	1	1	yes	characteristic
461	C₂	C₁₉×#3082	1	2	yes	—
462	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×#2026	C₂	semidirect
6. C₁₉×#2024	C₂	semidirect
44. C₂²×Q₈×C₁₉	Q₈	semidirect
158. #23457	C₁₉	direct (N × H)
208. #2026	C₂×C₁₉	semidirect
209. #2024	C₂×C₁₉	semidirect
275. C₂²×Q₈	Q₈×C₁₉	semidirect
324. C₁₉	#23457	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×#544	2
C₂×C₁₉×#419	2
C₂²×C₁₉×#103	2
C₁₉×#2310	2
C₁₉×#2026	2
C₁₉×#2024	2
C₁₉×#1736	2
C₁₉×#1735	2
C₁₉×#1729	2
#23457	19

Subgroups — C19×#23457 #18029416

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23457 #18029416