Subgroups — C₁₉×#9258 #18015217

Order 4864.

708 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#451	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1996	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1787	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1520	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1289	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1282	C₂	1	1	yes	maximal, characteristic
8	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×Q₁₆×C₁₉	C₄	1	2	yes	complemented
10	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
12	C₁₉×#451	—	2	1	no	—
13	C₁₉×#451	—	2	2	no	—
14	C₁₉×#451	—	2	1	no	—
15	C₂×C₁₉×#103	—	2	2	no	—
16	C₂×C₁₉×#103	C₄	1	2	yes	complemented
17	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
19	C₁₉×#391	—	2	2	no	—
20	C₁₉×#391	—	2	1	no	—
21	C₁₉×#380	—	2	1	no	—
22	C₁₉×#380	C₂²	1	1	yes	characteristic
23	C₁₉×#380	C₂²	1	1	yes	characteristic
24	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
25	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#342	—	2	1	no	—
27	C₁₉×#342	—	2	1	no	—
28	C₁₉×#328	—	2	2	no	—
29	C₂²×Q₈×C₁₉	—	2	1	no	—
30	C₂²×Q₈×C₁₉	—	2	1	no	—
31	C₂²×Q₈×C₁₉	—	2	1	no	—
32	C₂²×Q₈×C₁₉	—	4	4	no	—
33	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
34	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
36	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
37	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₉	—	2	1	no	—
39	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
40	C₂×Q₁₆×C₁₉	—	2	2	no	—
41	C₂×Q₁₆×C₁₉	—	2	2	no	—
42	C₂×Q₁₆×C₁₉	—	4	4	no	—
43	C₂²×C₈×C₁₉	—	2	1	no	—
44	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
45	C₁₉×C₂²⋊Q₈	—	2	1	no	—
46	C₁₉×C₂²⋊Q₈	—	2	1	no	—
47	C₁₉×C₂²⋊Q₈	—	2	1	no	—
48	C₁₉×C₂²⋊Q₈	—	2	1	no	—
49	C₄×Q₈×C₁₉	—	4	4	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
55	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
59	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₉	—	2	2	no	—
61	C₂×C₄²×C₁₉	—	2	1	no	—
62	C₁₉×#103	—	2	2	no	—
63	C₁₉×#103	—	2	2	no	—
64	C₁₉×#103	—	4	4	no	—
65	C₁₉×C₂²⋊C₈	—	2	1	no	—
66	C₁₉×C₂²⋊C₈	—	2	1	no	—
67	C₁₉×C₂²⋊C₈	—	2	1	no	—
68	C₁₉×C₂²⋊C₈	—	2	1	no	—
69	C₁₉×#95	—	2	2	no	—
70	C₁₉×#95	—	2	2	no	—
71	C₁₉×#95	—	2	1	no	—
72	C₁₉×#95	—	2	1	no	—
73	C₁₉×#95	D₄	1	2	yes	—
74	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₂×Q₈×C₁₉	—	2	4	no	—
76	C₂×Q₈×C₁₉	—	2	2	no	—
77	C₂×Q₈×C₁₉	—	2	2	no	—
78	C₂×Q₈×C₁₉	—	2	1	no	—
79	C₂×Q₈×C₁₉	—	2	1	no	—
80	C₂×Q₈×C₁₉	—	2	4	no	—
81	C₂×Q₈×C₁₉	—	2	4	no	—
82	C₂×Q₈×C₁₉	—	2	1	no	—
83	C₂×Q₈×C₁₉	—	2	1	no	—
84	C₂×Q₈×C₁₉	—	4	2	no	—
85	C₂×Q₈×C₁₉	—	4	2	no	—
86	C₂×Q₈×C₁₉	—	4	2	no	—
87	C₂×Q₈×C₁₉	—	4	4	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	C₂²⋊C₄	1	2	yes	—
92	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
93	C₂²×C₄×C₁₉	—	2	1	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	1	no	—
96	C₂²×C₄×C₁₉	—	2	1	no	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	2	1	no	—
100	C₂²×C₄×C₁₉	—	2	1	no	—
101	C₂²×C₄×C₁₉	—	2	1	no	—
102	C₂²×C₄×C₁₉	—	4	2	no	—
103	C₂²×C₄×C₁₉	—	4	4	no	—
104	C₂²×C₄×C₁₉	—	4	1	no	—
105	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
111	Q₁₆×C₁₉	—	4	4	no	—
112	Q₁₆×C₁₉	—	4	4	no	—
113	C₂×C₈×C₁₉	—	2	2	no	—
114	C₂×C₈×C₁₉	—	4	2	no	—
115	C₂×C₈×C₁₉	—	4	2	no	—
116	C₂×C₈×C₁₉	—	4	1	no	—
117	C₄⋊C₄×C₁₉	—	2	1	no	—
118	C₄⋊C₄×C₁₉	—	2	1	no	—
119	C₄⋊C₄×C₁₉	—	4	4	no	—
120	C₄⋊C₄×C₁₉	—	4	2	no	—
121	C₄⋊C₄×C₁₉	—	4	2	no	—
122	C₄⋊C₄×C₁₉	—	4	1	no	—
123	C₄⋊C₄×C₁₉	—	4	1	no	—
124	C₂²⋊C₄×C₁₉	—	2	1	no	—
125	C₂²⋊C₄×C₁₉	—	2	1	no	—
126	C₂²⋊C₄×C₁₉	—	2	1	no	—
127	C₂²⋊C₄×C₁₉	—	4	1	no	—
128	C₂²⋊C₄×C₁₉	—	4	1	no	—
129	C₂²⋊C₄×C₁₉	—	4	1	no	—
130	C₂²⋊C₄×C₁₉	—	4	1	no	—
131	C₂²⋊C₄×C₁₉	—	4	1	no	—
132	C₂²⋊C₄×C₁₉	—	4	1	no	—
133	C₂²⋊C₄×C₁₉	Q₁₆	1	2	yes	complemented
134	C₄²×C₁₉	—	4	4	no	—
135	C₄²×C₁₉	—	4	2	no	—
136	#9258	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂³×C₁₉	—	4	1	no	—
138	C₂³×C₁₉	—	4	1	no	—
139	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
140	C₂³×C₁₉	#120	1	1	yes	characteristic
141	C₂³×C₁₉	#121	1	1	yes	characteristic
142	C₂³×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
143	C₂³×C₁₉	#135	1	1	yes	characteristic
144	C₂³×C₁₉	#137	1	1	yes	characteristic
145	C₂³×C₁₉	#137	1	1	yes	characteristic
146	Q₈×C₁₉	—	2	4	no	—
147	Q₈×C₁₉	—	2	2	no	—
148	Q₈×C₁₉	—	2	2	no	—
149	Q₈×C₁₉	—	2	2	no	—
150	Q₈×C₁₉	—	4	4	no	—
151	Q₈×C₁₉	—	4	4	no	—
152	Q₈×C₁₉	—	4	2	no	—
153	Q₈×C₁₉	—	4	2	no	—
154	Q₈×C₁₉	—	8	1	no	—
155	Q₈×C₁₉	#99	1	4	yes	—
156	C₂×C₄×C₁₉	—	2	4	no	—
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	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	4	no	—
167	C₂×C₄×C₁₉	—	4	4	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	—	4	2	no	—
171	C₂×C₄×C₁₉	—	4	2	no	—
172	C₂×C₄×C₁₉	—	4	1	no	—
173	C₂×C₄×C₁₉	—	4	2	no	—
174	C₂×C₄×C₁₉	—	4	1	no	—
175	C₂×C₄×C₁₉	—	4	1	no	—
176	C₂×C₄×C₁₉	—	4	1	no	—
177	C₂×C₄×C₁₉	—	4	1	no	—
178	C₂×C₄×C₁₉	—	4	2	no	—
179	C₂×C₄×C₁₉	—	8	1	no	—
180	C₂×C₄×C₁₉	—	8	1	no	—
181	C₂×C₄×C₁₉	—	8	1	no	—
182	C₂×C₄×C₁₉	—	8	1	no	—
183	C₂×C₄×C₁₉	—	8	1	no	—
184	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
187	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
188	C₈×C₁₉	—	4	2	no	—
189	C₈×C₁₉	—	8	1	no	—
190	C₂×#451	C₂×C₁₉	1	1	yes	characteristic
191	Q₈×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic
192	#1996	C₂×C₁₉	1	1	yes	characteristic
193	#1787	C₂×C₁₉	1	1	yes	characteristic
194	#1520	C₂×C₁₉	1	1	yes	characteristic
195	#1289	C₂×C₁₉	1	1	yes	characteristic
196	#1282	C₂×C₁₉	1	1	yes	characteristic
197	C₂²×C₁₉	—	2	1	no	—
198	C₂²×C₁₉	—	2	1	no	—
199	C₂²×C₁₉	—	2	1	no	—
200	C₂²×C₁₉	—	2	1	no	—
201	C₂²×C₁₉	—	2	1	no	—
202	C₂²×C₁₉	—	2	1	no	—
203	C₂²×C₁₉	—	4	1	no	—
204	C₂²×C₁₉	—	4	1	no	—
205	C₂²×C₁₉	—	4	1	no	—
206	C₂²×C₁₉	—	4	1	no	—
207	C₂²×C₁₉	#386	1	1	yes	characteristic
208	C₂²×C₁₉	C₄×Q₁₆	1	1	yes	characteristic
209	C₂²×C₁₉	#441	1	1	yes	characteristic
210	C₂²×C₁₉	#451	1	1	yes	characteristic
211	C₂²×C₁₉	#452	1	1	yes	characteristic
212	C₂²×C₁₉	#462	1	1	yes	characteristic
213	C₂²×C₁₉	#464	1	1	yes	characteristic
214	C₄×C₁₉	—	2	1	no	—
215	C₄×C₁₉	—	2	4	no	—
216	C₄×C₁₉	—	2	1	no	—
217	C₄×C₁₉	—	2	1	no	—
218	C₄×C₁₉	—	4	2	no	—
219	C₄×C₁₉	—	4	2	no	—
220	C₄×C₁₉	—	8	1	no	—
221	C₄×C₁₉	—	8	2	no	—
222	C₄×C₁₉	—	8	1	no	—
223	C₄×C₁₉	—	8	1	no	—
224	C₄×C₁₉	—	16	1	no	—
225	C₄×C₁₉	C₂×#99	1	2	yes	—
226	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
227	C₂²×Q₁₆	C₄×C₁₉	1	2	yes	complemented
228	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
229	C₂×C₄×Q₈	—	2	1	no	—
230	#451	—	2	1	no	—
231	#451	—	2	2	no	—
232	#451	—	2	1	no	—
233	C₂×#103	—	2	2	no	—
234	C₂×#103	C₄×C₁₉	1	2	yes	complemented
235	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
236	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
237	#391	—	2	1	no	—
238	#391	—	2	2	no	—
239	#380	—	2	1	no	—
240	#380	C₂²×C₁₉	1	1	yes	characteristic
241	#380	C₂²×C₁₉	1	1	yes	characteristic
242	C₄×C₂²⋊C₄	—	2	1	no	—
243	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
244	#342	—	2	1	no	—
245	#342	—	2	1	no	—
246	#328	—	2	2	no	—
247	C₂×C₁₉	—	2	1	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	—	2	1	no	—
253	C₂×C₁₉	#1878	1	1	yes	characteristic
254	C₂×C₁₉	#1898	1	1	yes	characteristic
255	C₂×C₁₉	#1905	1	1	yes	characteristic
256	C₂²×Q₈	—	2	1	no	—
257	C₂²×Q₈	—	2	1	no	—
258	C₂²×Q₈	—	2	1	no	—
259	C₂²×Q₈	—	4	4	no	—
260	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
261	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
262	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
263	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
264	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
265	C₂³×C₄	—	2	1	no	—
266	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
267	C₂×Q₁₆	—	2	2	no	—
268	C₂×Q₁₆	—	2	2	no	—
269	C₂×Q₁₆	—	4	4	no	—
270	C₂²×C₈	—	2	1	no	—
271	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
272	C₂²⋊Q₈	—	2	1	no	—
273	C₂²⋊Q₈	—	2	1	no	—
274	C₂²⋊Q₈	—	2	1	no	—
275	C₂²⋊Q₈	—	2	1	no	—
276	C₄×Q₈	—	4	4	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
282	C₂×C₂²⋊C₄	—	2	1	no	—
283	C₂×C₂²⋊C₄	—	2	1	no	—
284	C₂×C₂²⋊C₄	—	2	1	no	—
285	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
286	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
287	C₂×C₄²	—	2	2	no	—
288	C₂×C₄²	—	2	1	no	—
289	#103	—	2	2	no	—
290	#103	—	2	2	no	—
291	#103	—	4	4	no	—
292	C₂²⋊C₈	—	2	1	no	—
293	C₂²⋊C₈	—	2	1	no	—
294	C₂²⋊C₈	—	2	1	no	—
295	C₂²⋊C₈	—	2	1	no	—
296	#95	—	2	2	no	—
297	#95	—	2	2	no	—
298	#95	—	2	1	no	—
299	#95	—	2	1	no	—
300	#95	D₄×C₁₉	1	2	yes	—
301	C₁₉	#9258	1	1	yes	characteristic, direct product factor, Sylow
302	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
303	C₂×Q₈	—	2	4	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	—	2	4	no	—
309	C₂×Q₈	—	2	4	no	—
310	C₂×Q₈	—	2	1	no	—
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	—	4	2	no	—
313	C₂×Q₈	—	4	2	no	—
314	C₂×Q₈	—	4	2	no	—
315	C₂×Q₈	—	4	4	no	—
316	C₂×Q₈	—	4	2	no	—
317	C₂×Q₈	—	4	4	no	—
318	C₂×Q₈	—	4	4	no	—
319	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
320	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	4	2	no	—
331	C₂²×C₄	—	4	4	no	—
332	C₂²×C₄	—	4	1	no	—
333	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
337	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
338	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
339	Q₁₆	—	4	4	no	—
340	Q₁₆	—	4	4	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	4	2	no	—
343	C₂×C₈	—	4	2	no	—
344	C₂×C₈	—	4	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	4	4	no	—
348	C₄⋊C₄	—	4	2	no	—
349	C₄⋊C₄	—	4	2	no	—
350	C₄⋊C₄	—	4	1	no	—
351	C₄⋊C₄	—	4	1	no	—
352	C₂²⋊C₄	—	2	1	no	—
353	C₂²⋊C₄	—	2	1	no	—
354	C₂²⋊C₄	—	2	1	no	—
355	C₂²⋊C₄	—	4	1	no	—
356	C₂²⋊C₄	—	4	1	no	—
357	C₂²⋊C₄	—	4	1	no	—
358	C₂²⋊C₄	—	4	1	no	—
359	C₂²⋊C₄	—	4	1	no	—
360	C₂²⋊C₄	—	4	1	no	—
361	C₂²⋊C₄	Q₁₆×C₁₉	1	2	yes	complemented
362	C₄²	—	4	4	no	—
363	C₄²	—	4	2	no	—
364	C₂³	—	4	1	no	—
365	C₂³	—	4	1	no	—
366	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
367	C₂³	C₁₉×#120	1	1	yes	characteristic
368	C₂³	C₁₉×#121	1	1	yes	characteristic
369	C₂³	C₂×Q₁₆×C₁₉	1	1	yes	characteristic
370	C₂³	C₁₉×#135	1	1	yes	characteristic
371	C₂³	C₁₉×#137	1	1	yes	characteristic
372	C₂³	C₁₉×#137	1	1	yes	characteristic
373	Q₈	—	2	4	no	—
374	Q₈	—	2	2	no	—
375	Q₈	—	2	2	no	—
376	Q₈	—	2	2	no	—
377	Q₈	—	4	4	no	—
378	Q₈	—	4	4	no	—
379	Q₈	—	4	2	no	—
380	Q₈	—	4	2	no	—
381	Q₈	—	8	1	no	—
382	Q₈	C₁₉×#99	1	4	yes	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	4	no	—
394	C₂×C₄	—	4	4	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	8	1	no	—
407	C₂×C₄	—	8	1	no	—
408	C₂×C₄	—	8	1	no	—
409	C₂×C₄	—	8	1	no	—
410	C₂×C₄	—	8	1	no	—
411	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
412	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
413	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
414	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
415	C₈	—	4	2	no	—
416	C₈	—	8	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	4	1	no	—
425	C₂²	—	4	1	no	—
426	C₂²	—	4	1	no	—
427	C₂²	C₁₉×#386	1	1	yes	characteristic
428	C₂²	C₄×Q₁₆×C₁₉	1	1	yes	characteristic
429	C₂²	C₁₉×#441	1	1	yes	characteristic
430	C₂²	C₁₉×#451	1	1	yes	characteristic
431	C₂²	C₁₉×#452	1	1	yes	characteristic
432	C₂²	C₁₉×#462	1	1	yes	characteristic
433	C₂²	C₁₉×#464	1	1	yes	characteristic
434	C₄	—	2	1	no	—
435	C₄	—	2	4	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	2	no	—
440	C₄	—	8	1	no	—
441	C₄	—	8	2	no	—
442	C₄	—	8	1	no	—
443	C₄	—	8	1	no	—
444	C₄	—	16	1	no	—
445	C₄	C₂×C₁₉×#99	1	2	yes	—
446	C₂	—	2	1	no	—
447	C₂	—	2	1	no	—
448	C₂	—	2	1	no	—
449	C₂	—	2	1	no	—
450	C₂	—	2	1	no	—
451	C₂	—	2	1	no	—
452	C₂	C₁₉×#1878	1	1	yes	characteristic
453	C₂	C₁₉×#1898	1	1	yes	characteristic
454	C₂	C₁₉×#1905	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
9. C₂²×Q₁₆×C₁₉	C₄	semidirect
16. C₂×C₁₉×#103	C₄	semidirect
133. C₂²⋊C₄×C₁₉	Q₁₆	semidirect
136. #9258	C₁₉	direct (N × H)
227. C₂²×Q₁₆	C₄×C₁₉	semidirect
234. C₂×#103	C₄×C₁₉	semidirect
301. C₁₉	#9258	direct (N × H)
361. C₂²⋊C₄	Q₁₆×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#451	2
Q₈×C₂²⋊C₄×C₁₉	2
C₁₉×#1996	2
C₁₉×#1787	2
C₁₉×#1520	2
C₁₉×#1289	2
C₁₉×#1282	2
#9258	19

Subgroups — C19×#9258 #18015217

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9258 #18015217