Subgroups — C₁₉×#23748 #18029707

Order 4864.

782 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2317	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2317	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2101	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2101	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2100	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2099	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1736	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1736	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1735	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₉×#340	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1729	C₂	1	1	yes	maximal, characteristic
12	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#389	—	2	1	no	—
20	C₁₉×#389	—	2	1	no	—
21	C₁₉×#389	C₂²	1	2	yes	—
22	C₁₉×#389	C₂²	1	2	yes	—
23	C₁₉×#385	—	2	2	no	—
24	C₁₉×#385	—	2	2	no	—
25	C₁₉×#384	—	2	1	no	—
26	C₁₉×#384	C₂²	1	2	yes	—
27	C₁₉×#382	—	2	1	no	—
28	C₁₉×#382	C₂²	1	2	yes	—
29	C₁₉×#340	C₂²	1	2	yes	—
30	C₁₉×#340	C₂²	1	2	yes	—
31	C₁₉×#340	C₂²	1	1	yes	characteristic
32	C₁₉×#340	C₂²	1	1	yes	characteristic
33	C₁₉×#340	C₂²	1	1	yes	characteristic
34	C₁₉×#340	C₂²	1	1	yes	characteristic
35	C₁₉×#340	C₂²	1	2	yes	—
36	C₁₉×#340	C₂²	1	2	yes	—
37	C₁₉×#340	C₂²	1	2	yes	—
38	C₁₉×#340	C₂²	1	2	yes	—
39	C₁₉×#336	C₂²	1	2	yes	—
40	C₁₉×#336	C₂²	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	1	yes	characteristic
51	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
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	C₁₉×#117	Q₈	1	4	yes	—
59	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
66	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
67	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
69	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
77	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
80	C₂×C₄²×C₁₉	—	2	1	no	—
81	C₂×C₄²×C₁₉	—	2	1	no	—
82	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
83	C₁₉×#95	—	2	2	no	—
84	C₁₉×#95	—	2	2	no	—
85	C₁₉×#95	—	2	2	no	—
86	C₁₉×#95	—	2	2	no	—
87	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	—	2	1	no	—
89	C₂²×C₄×C₁₉	—	2	1	no	—
90	C₂²×C₄×C₁₉	—	2	1	no	—
91	C₂²×C₄×C₁₉	—	2	1	no	—
92	C₂²×C₄×C₁₉	—	2	2	no	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	4	2	no	—
95	C₂²×C₄×C₁₉	—	4	2	no	—
96	C₂²×C₄×C₁₉	—	8	1	no	—
97	C₂²×C₄×C₁₉	—	8	1	no	—
98	C₂²×C₄×C₁₉	—	8	1	no	—
99	C₂²×C₄×C₁₉	—	8	1	no	—
100	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
104	C₂²×C₄×C₁₉	#41	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	C₂⁴	1	1	yes	characteristic
110	M₁₆×C₁₉	—	4	4	no	—
111	C₂×C₈×C₁₉	—	2	1	no	—
112	C₂×C₈×C₁₉	—	2	1	no	—
113	C₂×C₈×C₁₉	—	2	1	no	—
114	C₂×C₈×C₁₉	—	2	1	no	—
115	C₂×C₈×C₁₉	—	2	1	no	—
116	C₂×C₈×C₁₉	—	2	1	no	—
117	C₂×C₈×C₁₉	—	2	2	no	—
118	C₂×C₈×C₁₉	—	2	2	no	—
119	C₂×C₈×C₁₉	—	2	2	no	—
120	C₂×C₈×C₁₉	—	4	4	no	—
121	C₄⋊C₄×C₁₉	—	2	2	no	—
122	C₄⋊C₄×C₁₉	—	2	2	no	—
123	C₄⋊C₄×C₁₉	—	2	1	no	—
124	C₄⋊C₄×C₁₉	—	2	1	no	—
125	C₄⋊C₄×C₁₉	—	2	2	no	—
126	C₄⋊C₄×C₁₉	—	2	2	no	—
127	C₄⋊C₄×C₁₉	—	2	2	no	—
128	C₄⋊C₄×C₁₉	—	2	2	no	—
129	C₄⋊C₄×C₁₉	—	2	1	no	—
130	C₄⋊C₄×C₁₉	—	2	1	no	—
131	C₄⋊C₄×C₁₉	—	2	1	no	—
132	C₄⋊C₄×C₁₉	—	2	1	no	—
133	C₄⋊C₄×C₁₉	—	4	2	no	—
134	C₄⋊C₄×C₁₉	—	4	2	no	—
135	C₄⋊C₄×C₁₉	—	8	2	no	—
136	C₄⋊C₄×C₁₉	—	8	2	no	—
137	C₄⋊C₄×C₁₉	—	8	2	no	—
138	C₄⋊C₄×C₁₉	—	8	2	no	—
139	C₄⋊C₄×C₁₉	C₂×Q₈	1	2	yes	—
140	C₄⋊C₄×C₁₉	C₂×Q₈	1	2	yes	—
141	C₂²⋊C₄×C₁₉	—	2	4	no	—
142	C₂²⋊C₄×C₁₉	—	2	4	no	—
143	C₂²⋊C₄×C₁₉	—	4	2	no	—
144	C₄²×C₁₉	—	2	4	no	—
145	C₄²×C₁₉	—	2	2	no	—
146	C₄²×C₁₉	—	2	2	no	—
147	C₄²×C₁₉	—	4	2	no	—
148	#23748	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
149	C₂³×C₁₉	—	2	1	no	—
150	C₂³×C₁₉	—	2	1	no	—
151	C₂³×C₁₉	—	2	1	no	—
152	C₂³×C₁₉	—	2	1	no	—
153	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
154	C₂³×C₁₉	#123	1	2	yes	—
155	C₂³×C₁₉	#124	1	2	yes	—
156	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₁₉	—	2	2	no	—
158	C₂×C₄×C₁₉	—	2	2	no	—
159	C₂×C₄×C₁₉	—	2	2	no	—
160	C₂×C₄×C₁₉	—	2	2	no	—
161	C₂×C₄×C₁₉	—	2	2	no	—
162	C₂×C₄×C₁₉	—	2	2	no	—
163	C₂×C₄×C₁₉	—	2	2	no	—
164	C₂×C₄×C₁₉	—	2	2	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	4	2	no	—
170	C₂×C₄×C₁₉	—	4	1	no	—
171	C₂×C₄×C₁₉	—	4	1	no	—
172	C₂×C₄×C₁₉	—	4	2	no	—
173	C₂×C₄×C₁₉	—	4	1	no	—
174	C₂×C₄×C₁₉	—	4	2	no	—
175	C₂×C₄×C₁₉	—	4	2	no	—
176	C₂×C₄×C₁₉	—	4	1	no	—
177	C₂×C₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	—	4	2	no	—
179	C₂×C₄×C₁₉	—	4	1	no	—
180	C₂×C₄×C₁₉	—	4	1	no	—
181	C₂×C₄×C₁₉	—	8	4	no	—
182	C₂×C₄×C₁₉	—	8	4	no	—
183	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
184	C₂×C₄×C₁₉	#123	1	2	yes	—
185	C₂×C₄×C₁₉	#124	1	2	yes	—
186	C₂×C₄×C₁₉	#125	1	4	yes	—
187	C₂×C₄×C₁₉	#125	1	4	yes	—
188	C₂×C₄×C₁₉	#126	1	4	yes	—
189	C₂×C₄×C₁₉	#126	1	4	yes	—
190	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
191	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
196	C₈×C₁₉	—	4	1	no	—
197	C₈×C₁₉	—	4	1	no	—
198	C₈×C₁₉	—	4	2	no	—
199	#2317	C₂×C₁₉	1	1	yes	characteristic
200	#2317	C₂×C₁₉	1	1	yes	characteristic
201	#2101	C₂×C₁₉	1	2	yes	complemented
202	#2101	C₂×C₁₉	1	2	yes	complemented
203	#2100	C₂×C₁₉	1	2	yes	complemented
204	#2099	C₂×C₁₉	1	2	yes	complemented
205	#1736	C₂×C₁₉	1	1	yes	characteristic
206	#1736	C₂×C₁₉	1	1	yes	characteristic
207	#1735	C₂×C₁₉	1	1	yes	characteristic
208	C₂×#340	C₂×C₁₉	1	1	yes	characteristic
209	#1729	C₂×C₁₉	1	1	yes	characteristic
210	C₂²×C₁₉	—	2	2	no	—
211	C₂²×C₁₉	—	2	2	no	—
212	C₂²×C₁₉	—	2	2	no	—
213	C₂²×C₁₉	—	2	2	no	—
214	C₂²×C₁₉	—	2	2	no	—
215	C₂²×C₁₉	—	2	2	no	—
216	C₂²×C₁₉	#400	1	4	yes	—
217	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
218	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
219	C₂²×C₁₉	C₂×#124	1	1	yes	characteristic
220	C₂²×C₁₉	#576	1	1	yes	characteristic
221	C₂²×C₁₉	#577	1	1	yes	characteristic
222	C₂²×C₁₉	#577	1	1	yes	characteristic
223	C₂²×C₁₉	#578	1	1	yes	characteristic
224	C₄×C₁₉	—	4	2	no	—
225	C₄×C₁₉	—	4	2	no	—
226	C₄×C₁₉	—	4	2	no	—
227	C₄×C₁₉	—	4	2	no	—
228	C₄×C₁₉	—	8	2	no	—
229	C₄×C₁₉	—	8	1	no	—
230	C₄×C₁₉	—	8	2	no	—
231	C₄×C₁₉	—	8	1	no	—
232	C₄×C₁₉	#400	1	4	yes	—
233	C₄×C₁₉	C₂×#125	1	1	yes	characteristic
234	C₄×C₁₉	C₂×#125	1	1	yes	characteristic
235	C₄×C₁₉	C₂×#126	1	1	yes	characteristic
236	C₄×C₁₉	C₂×#126	1	1	yes	characteristic
237	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
238	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
239	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
240	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
241	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
242	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
243	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
244	#389	—	2	1	no	—
245	#389	—	2	1	no	—
246	#389	C₂²×C₁₉	1	2	yes	—
247	#389	C₂²×C₁₉	1	2	yes	—
248	#385	—	2	2	no	—
249	#385	—	2	2	no	—
250	#384	—	2	1	no	—
251	#384	C₂²×C₁₉	1	2	yes	—
252	#382	—	2	1	no	—
253	#382	C₂²×C₁₉	1	2	yes	—
254	#340	C₂²×C₁₉	1	1	yes	characteristic
255	#340	C₂²×C₁₉	1	2	yes	—
256	#340	C₂²×C₁₉	1	2	yes	—
257	#340	C₂²×C₁₉	1	2	yes	—
258	#340	C₂²×C₁₉	1	1	yes	characteristic
259	#340	C₂²×C₁₉	1	2	yes	—
260	#340	C₂²×C₁₉	1	2	yes	—
261	#340	C₂²×C₁₉	1	1	yes	characteristic
262	#340	C₂²×C₁₉	1	1	yes	characteristic
263	#340	C₂²×C₁₉	1	2	yes	—
264	#336	C₂²×C₁₉	1	2	yes	—
265	#336	C₂²×C₁₉	1	2	yes	—
266	C₂×C₁₉	—	2	4	no	—
267	C₂×C₁₉	C₂×#400	1	1	yes	characteristic
268	C₂×C₁₉	#3083	1	1	yes	characteristic
269	C₂×C₁₉	#3084	1	1	yes	characteristic
270	C₂×C₁₉	#3096	1	1	yes	characteristic
271	C₂×C₁₉	#3097	1	1	yes	characteristic
272	C₂×C₁₉	#3136	1	1	yes	characteristic
273	C₂×C₁₉	#3137	1	1	yes	characteristic
274	C₂³×C₄	—	2	1	no	—
275	C₂³×C₄	—	2	1	no	—
276	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
277	C₂×M₁₆	—	2	2	no	—
278	C₂×M₁₆	—	2	2	no	—
279	C₂×M₁₆	—	2	2	no	—
280	C₂²×C₈	—	2	2	no	—
281	C₂²×C₈	—	2	2	no	—
282	C₂²×C₈	—	2	2	no	—
283	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
284	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
285	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
286	#117	—	2	2	no	—
287	#117	—	2	2	no	—
288	#117	—	2	2	no	—
289	#117	—	2	2	no	—
290	#117	—	2	2	no	—
291	#117	Q₈×C₁₉	1	4	yes	—
292	C₂×C₄⋊C₄	—	2	2	no	—
293	C₂×C₄⋊C₄	—	2	2	no	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	2	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
303	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
305	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
306	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
310	C₂×C₂²⋊C₄	—	2	1	no	—
311	C₂×C₂²⋊C₄	—	2	1	no	—
312	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
313	C₂×C₄²	—	2	1	no	—
314	C₂×C₄²	—	2	1	no	—
315	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
316	#95	—	2	2	no	—
317	#95	—	2	2	no	—
318	#95	—	2	2	no	—
319	#95	—	2	2	no	—
320	C₁₉	#23748	1	1	yes	characteristic, direct product factor, Sylow
321	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	4	2	no	—
329	C₂²×C₄	—	4	2	no	—
330	C₂²×C₄	—	8	1	no	—
331	C₂²×C₄	—	8	1	no	—
332	C₂²×C₄	—	8	1	no	—
333	C₂²×C₄	—	8	1	no	—
334	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
335	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
336	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
337	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
338	C₂²×C₄	#41×C₁₉	1	2	yes	—
339	C₂²×C₄	#41×C₁₉	1	2	yes	—
340	C₂²×C₄	#41×C₁₉	1	2	yes	—
341	C₂²×C₄	#41×C₁₉	1	2	yes	—
342	C₂²×C₄	#41×C₁₉	1	2	yes	—
343	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
344	M₁₆	—	4	4	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	4	4	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	4	2	no	—
368	C₄⋊C₄	—	4	2	no	—
369	C₄⋊C₄	—	8	2	no	—
370	C₄⋊C₄	—	8	2	no	—
371	C₄⋊C₄	—	8	2	no	—
372	C₄⋊C₄	—	8	2	no	—
373	C₄⋊C₄	C₂×Q₈×C₁₉	1	2	yes	—
374	C₄⋊C₄	C₂×Q₈×C₁₉	1	2	yes	—
375	C₂²⋊C₄	—	2	4	no	—
376	C₂²⋊C₄	—	2	4	no	—
377	C₂²⋊C₄	—	4	2	no	—
378	C₄²	—	2	4	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	4	2	no	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	1	no	—
386	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
387	C₂³	C₁₉×#123	1	2	yes	—
388	C₂³	C₁₉×#124	1	2	yes	—
389	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	8	4	no	—
415	C₂×C₄	—	8	4	no	—
416	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
417	C₂×C₄	C₁₉×#123	1	2	yes	—
418	C₂×C₄	C₁₉×#124	1	2	yes	—
419	C₂×C₄	C₁₉×#125	1	4	yes	—
420	C₂×C₄	C₁₉×#125	1	4	yes	—
421	C₂×C₄	C₁₉×#126	1	4	yes	—
422	C₂×C₄	C₁₉×#126	1	4	yes	—
423	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
424	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
425	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
426	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
427	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
428	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
429	C₈	—	4	1	no	—
430	C₈	—	4	1	no	—
431	C₈	—	4	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	2	no	—
438	C₂²	C₁₉×#400	1	4	yes	—
439	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
440	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
441	C₂²	C₂×C₁₉×#124	1	1	yes	characteristic
442	C₂²	C₁₉×#576	1	1	yes	characteristic
443	C₂²	C₁₉×#577	1	1	yes	characteristic
444	C₂²	C₁₉×#577	1	1	yes	characteristic
445	C₂²	C₁₉×#578	1	1	yes	characteristic
446	C₄	—	4	2	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	8	2	no	—
451	C₄	—	8	2	no	—
452	C₄	—	8	1	no	—
453	C₄	—	8	1	no	—
454	C₄	C₁₉×#400	1	4	yes	—
455	C₄	C₂×C₁₉×#125	1	1	yes	characteristic
456	C₄	C₂×C₁₉×#125	1	1	yes	characteristic
457	C₄	C₂×C₁₉×#126	1	1	yes	characteristic
458	C₄	C₂×C₁₉×#126	1	1	yes	characteristic
459	C₂	—	2	4	no	—
460	C₂	C₂×C₁₉×#400	1	1	yes	characteristic
461	C₂	C₁₉×#3083	1	1	yes	characteristic
462	C₂	C₁₉×#3084	1	1	yes	characteristic
463	C₂	C₁₉×#3096	1	1	yes	characteristic
464	C₂	C₁₉×#3097	1	1	yes	characteristic
465	C₂	C₁₉×#3136	1	1	yes	characteristic
466	C₂	C₁₉×#3137	1	1	yes	characteristic

	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
3. C₁₉×#2101	C₂	semidirect
4. C₁₉×#2101	C₂	semidirect
5. C₁₉×#2100	C₂	semidirect
6. C₁₉×#2099	C₂	semidirect
148. #23748	C₁₉	direct (N × H)
201. #2101	C₂×C₁₉	semidirect
202. #2101	C₂×C₁₉	semidirect
203. #2100	C₂×C₁₉	semidirect
204. #2099	C₂×C₁₉	semidirect
320. C₁₉	#23748	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×#2317	2
C₁₉×#2101	2
C₁₉×#2100	2
C₁₉×#2099	2
C₁₉×#1736	2
C₁₉×#1735	2
C₂×C₁₉×#340	2
C₁₉×#1729	2
#23748	19

Subgroups — C19×#23748 #18029707

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23748 #18029707