Subgroups — C₁₉×#9443 #18015402

Order 4864.

712 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2879	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2432	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1782	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1511	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1284	C₂	1	2	yes	maximal, complemented
6	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₁₉	—	2	1	no	—
8	C₂×C₁₉×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
9	C₂×C₁₉×#124	C₄	1	1	yes	characteristic, complemented
10	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#99	—	2	1	no	—
12	C₂×C₁₉×#99	—	2	1	no	—
13	C₁₉×#408	—	2	4	no	—
14	C₁₉×#407	—	2	1	no	—
15	C₁₉×#407	C₂²	1	2	yes	—
16	C₁₉×#394	—	2	1	no	—
17	C₁₉×#394	—	2	1	no	—
18	C₁₉×#391	C₄	1	1	yes	characteristic, complemented
19	C₁₉×#390	C₄	1	1	yes	characteristic, complemented
20	C₁₉×#385	—	2	1	no	—
21	C₁₉×#385	—	2	1	no	—
22	C₁₉×#381	C₂²	1	2	yes	—
23	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#328	—	2	4	no	—
25	C₂×#41×C₁₉	—	2	2	no	—
26	C₂×#41×C₁₉	—	2	2	no	—
27	C₂×#41×C₁₉	—	4	2	no	—
28	C₂×#41×C₁₉	—	4	2	no	—
29	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
33	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
37	C₂×M₁₆×C₁₉	—	2	2	no	—
38	C₂×M₁₆×C₁₉	—	2	2	no	—
39	C₂×M₁₆×C₁₉	—	4	2	no	—
40	C₂×M₁₆×C₁₉	—	4	2	no	—
41	C₂²×C₈×C₁₉	—	2	2	no	—
42	C₁₉×C₄⋊Q₈	—	4	2	no	—
43	C₁₉×#124	—	4	2	no	—
44	C₁₉×C₂²⋊Q₈	—	2	2	no	—
45	C₁₉×C₂²⋊Q₈	—	2	2	no	—
46	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
48	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
49	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
50	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
55	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
57	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
59	C₁₉×#99	—	4	2	no	—
60	C₁₉×#99	—	4	2	no	—
61	C₁₉×C₂²⋊C₈	—	2	4	no	—
62	C₁₉×C₂²⋊C₈	—	2	2	no	—
63	C₁₉×C₂²⋊C₈	D₄	1	4	yes	—
64	C₁₉×#95	—	2	1	no	—
65	C₁₉×#95	—	2	1	no	—
66	C₁₉×#95	—	2	1	no	—
67	C₁₉×#95	—	2	2	no	—
68	C₁₉×#95	—	2	2	no	—
69	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
70	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
71	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
72	#41×C₁₉	—	4	4	no	—
73	#41×C₁₉	—	4	4	no	—
74	#41×C₁₉	—	4	8	no	—
75	C₂×Q₈×C₁₉	—	2	2	no	—
76	C₂×Q₈×C₁₉	—	2	2	no	—
77	C₂×Q₈×C₁₉	—	2	2	no	—
78	C₂×Q₈×C₁₉	—	4	1	no	—
79	C₂×Q₈×C₁₉	—	4	1	no	—
80	C₂×Q₈×C₁₉	—	4	1	no	—
81	C₂×D₄×C₁₉	—	2	2	no	—
82	C₂×D₄×C₁₉	—	2	2	no	—
83	C₂×D₄×C₁₉	—	2	2	no	—
84	C₂×D₄×C₁₉	—	2	2	no	—
85	C₂×D₄×C₁₉	—	2	2	no	—
86	C₂×D₄×C₁₉	—	2	2	no	—
87	C₂×D₄×C₁₉	—	4	1	no	—
88	C₂×D₄×C₁₉	—	4	1	no	—
89	C₂×D₄×C₁₉	—	4	1	no	—
90	C₂²×C₄×C₁₉	—	2	2	no	—
91	C₂²×C₄×C₁₉	—	2	2	no	—
92	C₂²×C₄×C₁₉	—	2	1	no	—
93	C₂²×C₄×C₁₉	—	2	1	no	—
94	C₂²×C₄×C₁₉	—	2	1	no	—
95	C₂²×C₄×C₁₉	—	2	1	no	—
96	C₂²×C₄×C₁₉	—	2	1	no	—
97	C₂²×C₄×C₁₉	—	2	1	no	—
98	C₂²×C₄×C₁₉	—	2	1	no	—
99	C₂²×C₄×C₁₉	—	2	1	no	—
100	C₂²×C₄×C₁₉	—	4	1	no	—
101	C₂²×C₄×C₁₉	—	4	1	no	—
102	C₂²×C₄×C₁₉	—	4	1	no	—
103	C₂²×C₄×C₁₉	—	4	1	no	—
104	C₂²×C₄×C₁₉	—	4	2	no	—
105	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₉	#41	1	2	yes	—
111	M₁₆×C₁₉	—	4	4	no	—
112	M₁₆×C₁₉	—	4	2	no	—
113	M₁₆×C₁₉	—	4	2	no	—
114	C₂×C₈×C₁₉	—	2	4	no	—
115	C₂×C₈×C₁₉	—	4	4	no	—
116	C₄⋊C₄×C₁₉	—	2	2	no	—
117	C₄⋊C₄×C₁₉	—	4	2	no	—
118	C₄⋊C₄×C₁₉	—	4	2	no	—
119	C₄⋊C₄×C₁₉	—	4	1	no	—
120	C₄⋊C₄×C₁₉	—	4	1	no	—
121	C₂²⋊C₄×C₁₉	—	4	2	no	—
122	C₂²⋊C₄×C₁₉	—	4	2	no	—
123	C₂²⋊C₄×C₁₉	—	4	2	no	—
124	C₂²⋊C₄×C₁₉	—	4	2	no	—
125	C₂²⋊C₄×C₁₉	—	4	2	no	—
126	C₂²⋊C₄×C₁₉	—	4	2	no	—
127	C₂²⋊C₄×C₁₉	—	4	2	no	—
128	C₂²⋊C₄×C₁₉	—	4	2	no	—
129	C₄²×C₁₉	—	4	1	no	—
130	C₄²×C₁₉	—	4	1	no	—
131	#9443	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₂³×C₁₉	—	2	1	no	—
133	C₂³×C₁₉	—	2	1	no	—
134	C₂³×C₁₉	—	2	1	no	—
135	C₂³×C₁₉	—	2	1	no	—
136	C₂³×C₁₉	—	2	1	no	—
137	C₂³×C₁₉	—	2	1	no	—
138	C₂³×C₁₉	—	2	1	no	—
139	C₂³×C₁₉	—	4	1	no	—
140	C₂³×C₁₉	—	4	1	no	—
141	C₂³×C₁₉	—	4	1	no	—
142	C₂³×C₁₉	—	4	1	no	—
143	C₂³×C₁₉	—	4	1	no	—
144	C₂³×C₁₉	—	4	1	no	—
145	C₂³×C₁₉	#99	1	2	yes	—
146	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂³×C₁₉	#121	1	2	yes	—
148	Q₈×C₁₉	—	4	4	no	—
149	Q₈×C₁₉	—	8	2	no	—
150	D₄×C₁₉	—	4	4	no	—
151	D₄×C₁₉	—	4	4	no	—
152	D₄×C₁₉	—	4	4	no	—
153	C₂×C₄×C₁₉	—	2	2	no	—
154	C₂×C₄×C₁₉	—	2	2	no	—
155	C₂×C₄×C₁₉	—	2	4	no	—
156	C₂×C₄×C₁₉	—	2	1	no	—
157	C₂×C₄×C₁₉	—	2	1	no	—
158	C₂×C₄×C₁₉	—	2	1	no	—
159	C₂×C₄×C₁₉	—	2	1	no	—
160	C₂×C₄×C₁₉	—	2	1	no	—
161	C₂×C₄×C₁₉	—	2	1	no	—
162	C₂×C₄×C₁₉	—	2	2	no	—
163	C₂×C₄×C₁₉	—	2	1	no	—
164	C₂×C₄×C₁₉	—	2	1	no	—
165	C₂×C₄×C₁₉	—	2	1	no	—
166	C₂×C₄×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	4	2	no	—
168	C₂×C₄×C₁₉	—	4	2	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	1	no	—
173	C₂×C₄×C₁₉	—	4	1	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	1	no	—
179	C₂×C₄×C₁₉	—	4	1	no	—
180	C₂×C₄×C₁₉	—	4	1	no	—
181	C₂×C₄×C₁₉	—	8	2	no	—
182	C₂×C₄×C₁₉	—	8	2	no	—
183	C₂×C₄×C₁₉	—	8	2	no	—
184	C₂×C₄×C₁₉	#99	1	2	yes	—
185	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
186	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
187	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
188	C₈×C₁₉	—	4	4	no	—
189	#2879	C₂×C₁₉	1	1	yes	characteristic
190	#2432	C₂×C₁₉	1	1	yes	characteristic
191	#1782	C₂×C₁₉	1	1	yes	characteristic
192	#1511	C₂×C₁₉	1	2	yes	complemented
193	#1284	C₂×C₁₉	1	2	yes	complemented
194	C₂²×C₁₉	—	2	1	no	—
195	C₂²×C₁₉	—	2	1	no	—
196	C₂²×C₁₉	—	2	2	no	—
197	C₂²×C₁₉	—	2	2	no	—
198	C₂²×C₁₉	—	2	2	no	—
199	C₂²×C₁₉	—	2	2	no	—
200	C₂²×C₁₉	—	4	2	no	—
201	C₂²×C₁₉	—	4	2	no	—
202	C₂²×C₁₉	—	4	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	—	8	1	no	—
208	C₂²×C₁₉	—	8	1	no	—
209	C₂²×C₁₉	—	8	1	no	—
210	C₂²×C₁₉	—	8	1	no	—
211	C₂²×C₁₉	#386	1	1	yes	characteristic
212	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
213	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
214	C₄×C₁₉	—	2	1	no	—
215	C₄×C₁₉	—	2	1	no	—
216	C₄×C₁₉	—	2	2	no	—
217	C₄×C₁₉	—	2	2	no	—
218	C₄×C₁₉	—	4	2	no	—
219	C₄×C₁₉	—	4	1	no	—
220	C₄×C₁₉	—	8	1	no	—
221	C₄×C₁₉	—	8	1	no	—
222	C₄×C₁₉	—	8	1	no	—
223	C₄×C₁₉	—	16	2	no	—
224	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
225	C₂²×M₁₆	—	2	1	no	—
226	C₂×C₄⋊Q₈	C₄×C₁₉	1	1	yes	characteristic, complemented
227	C₂×#124	C₄×C₁₉	1	1	yes	characteristic, complemented
228	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
229	C₂×#99	—	2	1	no	—
230	C₂×#99	—	2	1	no	—
231	#408	—	2	4	no	—
232	#407	—	2	1	no	—
233	#407	C₂²×C₁₉	1	2	yes	—
234	#394	—	2	1	no	—
235	#394	—	2	1	no	—
236	#391	C₄×C₁₉	1	1	yes	characteristic, complemented
237	#390	C₄×C₁₉	1	1	yes	characteristic, complemented
238	#385	—	2	1	no	—
239	#385	—	2	1	no	—
240	#381	C₂²×C₁₉	1	2	yes	—
241	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
242	#328	—	2	4	no	—
243	C₂×C₁₉	—	2	1	no	—
244	C₂×C₁₉	—	2	1	no	—
245	C₂×C₁₉	—	4	2	no	—
246	C₂×C₁₉	—	4	2	no	—
247	C₂×C₁₉	—	8	1	no	—
248	C₂×C₁₉	#1884	1	1	yes	characteristic
249	C₂×C₁₉	#1898	1	1	yes	characteristic
250	C₂×C₁₉	#1909	1	1	yes	characteristic
251	C₂×#41	—	2	2	no	—
252	C₂×#41	—	2	2	no	—
253	C₂×#41	—	4	2	no	—
254	C₂×#41	—	4	2	no	—
255	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
256	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
257	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
258	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
259	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
260	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
261	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
262	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
263	C₂×M₁₆	—	2	2	no	—
264	C₂×M₁₆	—	2	2	no	—
265	C₂×M₁₆	—	4	2	no	—
266	C₂×M₁₆	—	4	2	no	—
267	C₂²×C₈	—	2	2	no	—
268	C₄⋊Q₈	—	4	2	no	—
269	#124	—	4	2	no	—
270	C₂²⋊Q₈	—	2	2	no	—
271	C₂²⋊Q₈	—	2	2	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
276	C₂×C₂²⋊C₄	—	2	1	no	—
277	C₂×C₂²⋊C₄	—	2	1	no	—
278	C₂×C₂²⋊C₄	—	2	1	no	—
279	C₂×C₂²⋊C₄	—	2	1	no	—
280	C₂×C₂²⋊C₄	—	2	1	no	—
281	C₂×C₂²⋊C₄	—	2	1	no	—
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
284	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
285	#99	—	4	2	no	—
286	#99	—	4	2	no	—
287	C₂²⋊C₈	—	2	4	no	—
288	C₂²⋊C₈	—	2	2	no	—
289	C₂²⋊C₈	D₄×C₁₉	1	4	yes	—
290	#95	—	2	1	no	—
291	#95	—	2	1	no	—
292	#95	—	2	1	no	—
293	#95	—	2	2	no	—
294	#95	—	2	2	no	—
295	C₁₉	#9443	1	1	yes	characteristic, direct product factor, Sylow
296	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
297	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
298	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
299	#41	—	4	4	no	—
300	#41	—	4	4	no	—
301	#41	—	4	8	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	4	1	no	—
306	C₂×Q₈	—	4	1	no	—
307	C₂×Q₈	—	4	1	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	4	1	no	—
315	C₂×D₄	—	4	1	no	—
316	C₂×D₄	—	4	1	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	4	1	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	—	4	2	no	—
332	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
333	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
334	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
337	C₂²×C₄	#41×C₁₉	1	2	yes	—
338	M₁₆	—	4	4	no	—
339	M₁₆	—	4	2	no	—
340	M₁₆	—	4	2	no	—
341	C₂×C₈	—	2	4	no	—
342	C₂×C₈	—	4	4	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	4	2	no	—
345	C₄⋊C₄	—	4	1	no	—
346	C₄⋊C₄	—	4	1	no	—
347	C₄⋊C₄	—	4	2	no	—
348	C₂²⋊C₄	—	4	2	no	—
349	C₂²⋊C₄	—	4	2	no	—
350	C₂²⋊C₄	—	4	2	no	—
351	C₂²⋊C₄	—	4	2	no	—
352	C₂²⋊C₄	—	4	2	no	—
353	C₂²⋊C₄	—	4	2	no	—
354	C₂²⋊C₄	—	4	2	no	—
355	C₂²⋊C₄	—	4	2	no	—
356	C₄²	—	4	1	no	—
357	C₄²	—	4	1	no	—
358	C₂³	—	2	1	no	—
359	C₂³	—	2	1	no	—
360	C₂³	—	2	1	no	—
361	C₂³	—	2	1	no	—
362	C₂³	—	2	1	no	—
363	C₂³	—	2	1	no	—
364	C₂³	—	2	1	no	—
365	C₂³	—	4	1	no	—
366	C₂³	—	4	1	no	—
367	C₂³	—	4	1	no	—
368	C₂³	—	4	1	no	—
369	C₂³	—	4	1	no	—
370	C₂³	—	4	1	no	—
371	C₂³	C₁₉×#99	1	2	yes	—
372	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
373	C₂³	C₁₉×#121	1	2	yes	—
374	Q₈	—	4	4	no	—
375	Q₈	—	8	2	no	—
376	D₄	—	4	4	no	—
377	D₄	—	4	4	no	—
378	D₄	—	4	4	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	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	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	8	2	no	—
408	C₂×C₄	—	8	2	no	—
409	C₂×C₄	—	8	2	no	—
410	C₂×C₄	C₁₉×#99	1	2	yes	—
411	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
412	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
413	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
414	C₈	—	4	4	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	4	1	no	—
425	C₂²	—	4	1	no	—
426	C₂²	—	4	1	no	—
427	C₂²	—	4	1	no	—
428	C₂²	—	8	1	no	—
429	C₂²	—	8	1	no	—
430	C₂²	—	8	1	no	—
431	C₂²	—	8	1	no	—
432	C₂²	C₁₉×#386	1	1	yes	characteristic
433	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
434	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	2	no	—
438	C₄	—	2	2	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	1	no	—
441	C₄	—	8	1	no	—
442	C₄	—	8	1	no	—
443	C₄	—	8	1	no	—
444	C₄	—	16	2	no	—
445	C₂	—	2	1	no	—
446	C₂	—	2	1	no	—
447	C₂	—	4	2	no	—
448	C₂	—	4	2	no	—
449	C₂	—	8	1	no	—
450	C₂	C₁₉×#1884	1	1	yes	characteristic
451	C₂	C₁₉×#1898	1	1	yes	characteristic
452	C₂	C₁₉×#1909	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	C₂²×#41×C₁₉	C₂²
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
4. C₁₉×#1511	C₂	semidirect
5. C₁₉×#1284	C₂	semidirect
8. C₂×C₁₉×C₄⋊Q₈	C₄	semidirect
9. C₂×C₁₉×#124	C₄	semidirect
18. C₁₉×#391	C₄	semidirect
19. C₁₉×#390	C₄	semidirect
131. #9443	C₁₉	direct (N × H)
192. #1511	C₂×C₁₉	semidirect
193. #1284	C₂×C₁₉	semidirect
226. C₂×C₄⋊Q₈	C₄×C₁₉	semidirect
227. C₂×#124	C₄×C₁₉	semidirect
236. #391	C₄×C₁₉	semidirect
237. #390	C₄×C₁₉	semidirect
295. C₁₉	#9443	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×#2879	2
C₁₉×#2432	2
C₁₉×#1782	2
C₁₉×#1511	2
C₁₉×#1284	2
#9443	19

Subgroups — C19×#9443 #18015402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9443 #18015402