Subgroups — C₁₉×#8413 #18014372

Order 4864.

702 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3518	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1759	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1529	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1506	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1500	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1488	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1485	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈²×C₁₉	C₄	1	1	yes	characteristic, complemented
9	C₁₉×#556	—	2	1	no	—
10	C₁₉×#556	—	2	2	no	—
11	C₁₉×#556	—	2	1	no	—
12	C₁₉×#556	C₄	1	1	yes	characteristic, complemented
13	C₁₉×#555	—	2	1	no	—
14	C₁₉×#555	C₄	1	1	yes	characteristic, complemented
15	D₄×Q₈×C₁₉	C₄	1	1	yes	characteristic, complemented
16	C₁₉×#548	—	2	1	no	—
17	C₁₉×#542	—	2	2	no	—
18	C₁₉×#542	—	2	1	no	—
19	C₁₉×#533	—	2	1	no	—
20	C₁₉×#533	C₂²	1	1	yes	characteristic
21	C₁₉×#529	—	2	1	no	—
22	C₁₉×#529	C₂²	1	1	yes	characteristic
23	C₁₉×#519	—	2	1	no	—
24	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#432	C₂²	1	1	yes	characteristic
26	C₁₉×#431	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#104	—	2	1	no	—
28	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
29	C₁₉×#376	C₂²	1	1	yes	characteristic
30	C₁₉×#339	—	2	1	no	—
31	C₁₉×#330	—	2	1	no	—
32	C₁₉×#329	—	2	1	no	—
33	C₁₉×#328	—	2	1	no	—
34	C₁₉×#328	—	2	2	no	—
35	C₁₉×#327	—	2	1	no	—
36	C₁₉×Q₈⋊C₈	—	2	2	no	—
37	C₁₉×Q₈⋊C₈	—	2	1	no	—
38	C₁₉×D₄⋊C₈	—	2	1	no	—
39	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
40	C₂²×Q₈×C₁₉	—	2	1	no	—
41	C₂×M₁₆×C₁₉	—	2	1	no	—
42	C₁₉×C₄⋊Q₈	—	2	2	no	—
43	C₁₉×C₄⋊Q₈	—	2	1	no	—
44	C₁₉×C₄⋊Q₈	—	2	1	no	—
45	C₁₉×C₄⋊Q₈	—	2	1	no	—
46	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
47	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
48	C₁₉×#126	—	2	2	no	—
49	C₁₉×#126	—	2	2	no	—
50	C₁₉×#126	—	2	2	no	—
51	C₁₉×#126	—	2	2	no	—
52	C₁₉×#126	—	2	1	no	—
53	C₁₉×#125	—	2	1	no	—
54	C₁₉×#125	D₄	1	1	yes	characteristic
55	C₁₉×#124	—	2	2	no	—
56	C₁₉×#124	—	2	2	no	—
57	C₁₉×#124	—	2	2	no	—
58	C₁₉×#124	—	2	2	no	—
59	C₁₉×#124	—	2	1	no	—
60	C₁₉×#124	D₄	1	1	yes	characteristic
61	C₁₉×#123	—	2	2	no	—
62	C₁₉×#123	—	2	1	no	—
63	C₁₉×C₂²⋊Q₈	—	2	2	no	—
64	C₁₉×C₂²⋊Q₈	—	2	2	no	—
65	C₁₉×C₂²⋊Q₈	—	2	1	no	—
66	C₁₉×C₂²⋊Q₈	—	2	1	no	—
67	C₁₉×C₂²⋊Q₈	—	2	1	no	—
68	C₁₉×C₂²⋊Q₈	—	2	2	no	—
69	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
70	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
71	C₁₉×#121	—	2	2	no	—
72	C₁₉×#121	—	2	1	no	—
73	C₁₉×#121	—	2	1	no	—
74	C₁₉×#121	D₄	1	1	yes	characteristic
75	C₄×Q₈×C₁₉	—	2	2	no	—
76	C₄×Q₈×C₁₉	—	2	2	no	—
77	C₄×Q₈×C₁₉	—	2	2	no	—
78	C₄×Q₈×C₁₉	—	2	1	no	—
79	C₄×Q₈×C₁₉	—	2	1	no	—
80	C₄×Q₈×C₁₉	—	2	1	no	—
81	C₄×Q₈×C₁₉	—	2	1	no	—
82	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
83	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
84	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
85	C₄×Q₈×C₁₉	D₄	1	2	yes	—
86	C₄×D₄×C₁₉	—	2	2	no	—
87	C₄×D₄×C₁₉	—	2	1	no	—
88	C₄×D₄×C₁₉	—	2	1	no	—
89	C₄×D₄×C₁₉	—	2	1	no	—
90	C₄×D₄×C₁₉	—	2	1	no	—
91	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
92	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
93	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
94	C₁₉×#117	—	2	2	no	—
95	C₁₉×#117	—	2	2	no	—
96	C₁₉×#117	—	2	1	no	—
97	C₁₉×#117	—	2	1	no	—
98	C₁₉×#117	—	2	1	no	—
99	C₁₉×#117	—	2	1	no	—
100	C₁₉×#117	—	2	1	no	—
101	C₁₉×#117	—	2	1	no	—
102	C₁₉×#117	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₁₉	—	2	1	no	—
104	C₂×C₄²×C₁₉	—	2	1	no	—
105	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
106	C₁₉×C₄⋊C₈	—	2	1	no	—
107	C₁₉×C₄⋊C₈	—	2	1	no	—
108	C₁₉×#104	—	2	4	no	—
109	C₁₉×C₂²⋊C₈	—	2	1	no	—
110	C₁₉×C₂²⋊C₈	—	2	1	no	—
111	C₁₉×#97	—	2	1	no	—
112	C₁₉×#97	—	2	1	no	—
113	C₄×C₈×C₁₉	—	2	1	no	—
114	C₄×C₈×C₁₉	—	2	1	no	—
115	C₁₉×#95	—	2	1	no	—
116	C₁₉×#95	—	2	1	no	—
117	#41×C₁₉	—	2	2	no	—
118	#41×C₁₉	—	4	1	no	—
119	C₂×Q₈×C₁₉	—	2	2	no	—
120	C₂×Q₈×C₁₉	—	2	2	no	—
121	C₂×Q₈×C₁₉	—	2	1	no	—
122	C₂×Q₈×C₁₉	—	4	2	no	—
123	C₂×Q₈×C₁₉	—	4	2	no	—
124	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
125	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
126	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
127	C₂×D₄×C₁₉	—	2	1	no	—
128	C₂×D₄×C₁₉	—	2	2	no	—
129	C₂×D₄×C₁₉	—	2	1	no	—
130	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
131	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	—	2	1	no	—
134	C₂²×C₄×C₁₉	—	2	1	no	—
135	C₂²×C₄×C₁₉	—	2	1	no	—
136	C₂²×C₄×C₁₉	—	2	1	no	—
137	C₂²×C₄×C₁₉	—	4	1	no	—
138	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
141	M₁₆×C₁₉	—	2	2	no	—
142	M₁₆×C₁₉	—	4	1	no	—
143	C₂×C₈×C₁₉	—	4	1	no	—
144	C₂×C₈×C₁₉	—	4	1	no	—
145	C₂×C₈×C₁₉	—	4	1	no	—
146	C₄⋊C₄×C₁₉	—	2	2	no	—
147	C₄⋊C₄×C₁₉	—	2	2	no	—
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	—	2	2	no	—
150	C₄⋊C₄×C₁₉	—	2	1	no	—
151	C₄⋊C₄×C₁₉	—	2	1	no	—
152	C₄⋊C₄×C₁₉	—	2	1	no	—
153	C₄⋊C₄×C₁₉	—	2	1	no	—
154	C₄⋊C₄×C₁₉	—	2	1	no	—
155	C₄⋊C₄×C₁₉	—	2	1	no	—
156	C₄⋊C₄×C₁₉	—	2	1	no	—
157	C₄⋊C₄×C₁₉	—	2	2	no	—
158	C₄⋊C₄×C₁₉	—	2	1	no	—
159	C₄⋊C₄×C₁₉	—	2	1	no	—
160	C₄⋊C₄×C₁₉	—	2	2	no	—
161	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
162	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
163	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
164	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
165	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
166	C₂²⋊C₄×C₁₉	—	2	2	no	—
167	C₂²⋊C₄×C₁₉	—	2	2	no	—
168	C₂²⋊C₄×C₁₉	—	2	2	no	—
169	C₂²⋊C₄×C₁₉	—	2	2	no	—
170	C₂²⋊C₄×C₁₉	—	2	2	no	—
171	C₂²⋊C₄×C₁₉	—	2	2	no	—
172	C₂²⋊C₄×C₁₉	—	2	1	no	—
173	C₂²⋊C₄×C₁₉	—	2	1	no	—
174	C₂²⋊C₄×C₁₉	—	2	1	no	—
175	C₂²⋊C₄×C₁₉	—	2	1	no	—
176	C₂²⋊C₄×C₁₉	—	2	1	no	—
177	C₂²⋊C₄×C₁₉	—	2	1	no	—
178	C₂²⋊C₄×C₁₉	—	2	1	no	—
179	C₂²⋊C₄×C₁₉	—	2	1	no	—
180	C₄²×C₁₉	—	2	2	no	—
181	C₄²×C₁₉	—	2	2	no	—
182	C₄²×C₁₉	—	2	2	no	—
183	C₄²×C₁₉	—	2	1	no	—
184	C₄²×C₁₉	—	2	1	no	—
185	C₄²×C₁₉	—	2	1	no	—
186	C₄²×C₁₉	—	2	1	no	—
187	C₄²×C₁₉	—	2	2	no	—
188	C₄²×C₁₉	—	2	2	no	—
189	C₄²×C₁₉	—	4	1	no	—
190	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
191	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
192	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
193	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
194	#8413	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂³×C₁₉	—	2	1	no	—
196	C₂³×C₁₉	—	2	1	no	—
197	C₂³×C₁₉	#120	1	1	yes	characteristic
198	Q₈×C₁₉	—	2	1	no	—
199	Q₈×C₁₉	—	4	2	no	—
200	Q₈×C₁₉	—	4	1	no	—
201	Q₈×C₁₉	—	4	4	no	—
202	Q₈×C₁₉	—	4	1	no	—
203	Q₈×C₁₉	—	4	1	no	—
204	Q₈×C₁₉	—	8	2	no	—
205	Q₈×C₁₉	#104	1	2	yes	—
206	D₄×C₁₉	—	2	1	no	—
207	D₄×C₁₉	—	2	1	no	—
208	D₄×C₁₉	—	4	2	no	—
209	D₄×C₁₉	—	4	1	no	—
210	D₄×C₁₉	—	8	1	no	—
211	D₄×C₁₉	—	8	2	no	—
212	C₂×C₄×C₁₉	—	2	1	no	—
213	C₂×C₄×C₁₉	—	2	1	no	—
214	C₂×C₄×C₁₉	—	2	1	no	—
215	C₂×C₄×C₁₉	—	2	1	no	—
216	C₂×C₄×C₁₉	—	2	1	no	—
217	C₂×C₄×C₁₉	—	2	2	no	—
218	C₂×C₄×C₁₉	—	2	1	no	—
219	C₂×C₄×C₁₉	—	2	1	no	—
220	C₂×C₄×C₁₉	—	2	1	no	—
221	C₂×C₄×C₁₉	—	2	2	no	—
222	C₂×C₄×C₁₉	—	4	1	no	—
223	C₂×C₄×C₁₉	—	4	1	no	—
224	C₂×C₄×C₁₉	—	4	2	no	—
225	C₂×C₄×C₁₉	—	4	2	no	—
226	C₂×C₄×C₁₉	—	4	4	no	—
227	C₂×C₄×C₁₉	—	4	1	no	—
228	C₂×C₄×C₁₉	—	4	1	no	—
229	C₂×C₄×C₁₉	—	4	2	no	—
230	C₂×C₄×C₁₉	—	8	1	no	—
231	C₂×C₄×C₁₉	—	8	1	no	—
232	C₂×C₄×C₁₉	—	8	1	no	—
233	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
234	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
237	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
238	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
239	C₈×C₁₉	—	4	2	no	—
240	C₈×C₁₉	—	8	1	no	—
241	C₈×C₁₉	—	8	1	no	—
242	#3518	C₂×C₁₉	1	1	yes	characteristic
243	#1759	C₂×C₁₉	1	1	yes	characteristic, complemented
244	#1529	C₂×C₁₉	1	1	yes	characteristic, complemented
245	#1506	C₂×C₁₉	1	1	yes	characteristic, complemented
246	#1500	C₂×C₁₉	1	1	yes	characteristic, complemented
247	#1488	C₂×C₁₉	1	1	yes	characteristic, complemented
248	#1485	C₂×C₁₉	1	1	yes	characteristic, complemented
249	C₂²×C₁₉	—	2	1	no	—
250	C₂²×C₁₉	—	2	1	no	—
251	C₂²×C₁₉	—	2	1	no	—
252	C₂²×C₁₉	—	4	1	no	—
253	C₂²×C₁₉	—	4	1	no	—
254	C₂²×C₁₉	—	4	1	no	—
255	C₂²×C₁₉	—	4	1	no	—
256	C₂²×C₁₉	—	4	1	no	—
257	C₂²×C₁₉	—	4	1	no	—
258	C₂²×C₁₉	#379	1	1	yes	characteristic
259	C₄×C₁₉	—	2	1	no	—
260	C₄×C₁₉	—	2	1	no	—
261	C₄×C₁₉	—	2	1	no	—
262	C₄×C₁₉	—	2	1	no	—
263	C₄×C₁₉	—	2	1	no	—
264	C₄×C₁₉	—	2	2	no	—
265	C₄×C₁₉	—	4	1	no	—
266	C₄×C₁₉	—	4	2	no	—
267	C₄×C₁₉	—	4	1	no	—
268	C₄×C₁₉	—	4	1	no	—
269	C₄×C₁₉	—	4	1	no	—
270	C₄×C₁₉	—	4	2	no	—
271	C₄×C₁₉	—	4	1	no	—
272	C₄×C₁₉	—	8	2	no	—
273	C₄×C₁₉	C₂×#104	1	1	yes	characteristic
274	C₄×C₁₉	#421	1	1	yes	characteristic
275	Q₈²	C₄×C₁₉	1	1	yes	characteristic, complemented
276	#556	—	2	1	no	—
277	#556	—	2	2	no	—
278	#556	—	2	1	no	—
279	#556	C₄×C₁₉	1	1	yes	characteristic, complemented
280	#555	—	2	1	no	—
281	#555	C₄×C₁₉	1	1	yes	characteristic, complemented
282	D₄×Q₈	C₄×C₁₉	1	1	yes	characteristic, complemented
283	#548	—	2	1	no	—
284	#542	—	2	2	no	—
285	#542	—	2	1	no	—
286	#533	—	2	1	no	—
287	#533	C₂²×C₁₉	1	1	yes	characteristic
288	#529	—	2	1	no	—
289	#529	C₂²×C₁₉	1	1	yes	characteristic
290	#519	—	2	1	no	—
291	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
292	#432	C₂²×C₁₉	1	1	yes	characteristic
293	#431	C₂²×C₁₉	1	1	yes	characteristic
294	C₂×#104	—	2	1	no	—
295	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
296	#376	C₂²×C₁₉	1	1	yes	characteristic
297	#339	—	2	1	no	—
298	#330	—	2	1	no	—
299	#329	—	2	1	no	—
300	#328	—	2	1	no	—
301	#328	—	2	2	no	—
302	#327	—	2	1	no	—
303	Q₈⋊C₈	—	2	2	no	—
304	Q₈⋊C₈	—	2	1	no	—
305	D₄⋊C₈	—	2	1	no	—
306	C₂×C₁₉	—	4	1	no	—
307	C₂×C₁₉	—	8	1	no	—
308	C₂×C₁₉	—	8	1	no	—
309	C₂×C₁₉	#1789	1	1	yes	characteristic
310	C₂×C₁₉	#1794	1	1	yes	characteristic
311	C₂×C₁₉	#1796	1	1	yes	characteristic
312	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
313	C₂²×Q₈	—	2	1	no	—
314	C₂×M₁₆	—	2	1	no	—
315	C₄⋊Q₈	—	2	2	no	—
316	C₄⋊Q₈	—	2	1	no	—
317	C₄⋊Q₈	—	2	1	no	—
318	C₄⋊Q₈	—	2	1	no	—
319	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
320	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
321	#126	—	2	2	no	—
322	#126	—	2	2	no	—
323	#126	—	2	2	no	—
324	#126	—	2	2	no	—
325	#126	—	2	1	no	—
326	#125	—	2	1	no	—
327	#125	D₄×C₁₉	1	1	yes	characteristic
328	#124	—	2	2	no	—
329	#124	—	2	2	no	—
330	#124	—	2	2	no	—
331	#124	—	2	2	no	—
332	#124	—	2	1	no	—
333	#124	D₄×C₁₉	1	1	yes	characteristic
334	#123	—	2	2	no	—
335	#123	—	2	1	no	—
336	C₂²⋊Q₈	—	2	2	no	—
337	C₂²⋊Q₈	—	2	2	no	—
338	C₂²⋊Q₈	—	2	1	no	—
339	C₂²⋊Q₈	—	2	1	no	—
340	C₂²⋊Q₈	—	2	1	no	—
341	C₂²⋊Q₈	—	2	2	no	—
342	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
343	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
344	#121	—	2	2	no	—
345	#121	—	2	1	no	—
346	#121	—	2	1	no	—
347	#121	D₄×C₁₉	1	1	yes	characteristic
348	C₄×Q₈	—	2	2	no	—
349	C₄×Q₈	—	2	2	no	—
350	C₄×Q₈	—	2	2	no	—
351	C₄×Q₈	—	2	1	no	—
352	C₄×Q₈	—	2	1	no	—
353	C₄×Q₈	—	2	1	no	—
354	C₄×Q₈	—	2	1	no	—
355	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
356	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
357	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
358	C₄×Q₈	D₄×C₁₉	1	2	yes	—
359	C₄×D₄	—	2	2	no	—
360	C₄×D₄	—	2	1	no	—
361	C₄×D₄	—	2	1	no	—
362	C₄×D₄	—	2	1	no	—
363	C₄×D₄	—	2	1	no	—
364	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
365	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
366	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
367	#117	—	2	2	no	—
368	#117	—	2	2	no	—
369	#117	—	2	1	no	—
370	#117	—	2	1	no	—
371	#117	—	2	1	no	—
372	#117	—	2	1	no	—
373	#117	—	2	1	no	—
374	#117	—	2	1	no	—
375	#117	D₄×C₁₉	1	1	yes	characteristic
376	C₂×C₄²	—	2	1	no	—
377	C₂×C₄²	—	2	1	no	—
378	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
379	C₄⋊C₈	—	2	1	no	—
380	C₄⋊C₈	—	2	1	no	—
381	#104	—	2	4	no	—
382	C₂²⋊C₈	—	2	1	no	—
383	C₂²⋊C₈	—	2	1	no	—
384	#97	—	2	1	no	—
385	#97	—	2	1	no	—
386	C₄×C₈	—	2	1	no	—
387	C₄×C₈	—	2	1	no	—
388	#95	—	2	1	no	—
389	#95	—	2	1	no	—
390	C₁₉	#8413	1	1	yes	characteristic, direct product factor, Sylow
391	#41	—	2	2	no	—
392	#41	—	4	1	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	2	2	no	—
395	C₂×Q₈	—	2	1	no	—
396	C₂×Q₈	—	4	2	no	—
397	C₂×Q₈	—	4	2	no	—
398	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
399	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
400	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
401	C₂×D₄	—	2	1	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	1	no	—
404	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
405	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	4	1	no	—
412	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
413	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
414	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
415	M₁₆	—	2	2	no	—
416	M₁₆	—	4	1	no	—
417	C₂×C₈	—	4	1	no	—
418	C₂×C₈	—	4	1	no	—
419	C₂×C₈	—	4	1	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
436	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
437	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
438	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
439	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	2	2	no	—
443	C₂²⋊C₄	—	2	2	no	—
444	C₂²⋊C₄	—	2	2	no	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₂²⋊C₄	—	2	1	no	—
447	C₂²⋊C₄	—	2	1	no	—
448	C₂²⋊C₄	—	2	1	no	—
449	C₂²⋊C₄	—	2	1	no	—
450	C₂²⋊C₄	—	2	1	no	—
451	C₂²⋊C₄	—	2	1	no	—
452	C₂²⋊C₄	—	2	1	no	—
453	C₂²⋊C₄	—	2	1	no	—
454	C₄²	—	2	2	no	—
455	C₄²	—	2	2	no	—
456	C₄²	—	2	2	no	—
457	C₄²	—	2	1	no	—
458	C₄²	—	2	1	no	—
459	C₄²	—	2	1	no	—
460	C₄²	—	2	1	no	—
461	C₄²	—	2	2	no	—
462	C₄²	—	2	2	no	—
463	C₄²	—	4	1	no	—
464	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
465	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
466	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
467	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
468	C₂³	—	2	1	no	—
469	C₂³	—	2	1	no	—
470	C₂³	C₁₉×#120	1	1	yes	characteristic
471	Q₈	—	2	1	no	—
472	Q₈	—	4	2	no	—
473	Q₈	—	4	1	no	—
474	Q₈	—	4	4	no	—
475	Q₈	—	4	1	no	—
476	Q₈	—	4	1	no	—
477	Q₈	—	8	2	no	—
478	Q₈	C₁₉×#104	1	2	yes	—
479	D₄	—	2	1	no	—
480	D₄	—	2	1	no	—
481	D₄	—	4	2	no	—
482	D₄	—	4	1	no	—
483	D₄	—	8	1	no	—
484	D₄	—	8	2	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	4	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	8	1	no	—
504	C₂×C₄	—	8	1	no	—
505	C₂×C₄	—	8	1	no	—
506	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
507	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
508	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
509	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
510	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
511	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
512	C₈	—	4	2	no	—
513	C₈	—	8	1	no	—
514	C₈	—	8	1	no	—
515	C₂²	—	2	1	no	—
516	C₂²	—	2	1	no	—
517	C₂²	—	2	1	no	—
518	C₂²	—	4	1	no	—
519	C₂²	—	4	1	no	—
520	C₂²	—	4	1	no	—
521	C₂²	—	4	1	no	—
522	C₂²	—	4	1	no	—
523	C₂²	—	4	1	no	—
524	C₂²	C₁₉×#379	1	1	yes	characteristic
525	C₄	—	2	1	no	—
526	C₄	—	2	2	no	—
527	C₄	—	2	1	no	—
528	C₄	—	2	1	no	—
529	C₄	—	2	1	no	—
530	C₄	—	2	1	no	—
531	C₄	—	4	2	no	—
532	C₄	—	4	1	no	—
533	C₄	—	4	1	no	—
534	C₄	—	4	2	no	—
535	C₄	—	4	1	no	—
536	C₄	—	4	1	no	—
537	C₄	—	4	1	no	—
538	C₄	—	8	2	no	—
539	C₄	C₂×C₁₉×#104	1	1	yes	characteristic
540	C₄	C₁₉×#421	1	1	yes	characteristic
541	C₂	—	4	1	no	—
542	C₂	—	8	1	no	—
543	C₂	—	8	1	no	—
544	C₂	C₁₉×#1789	1	1	yes	characteristic
545	C₂	C₁₉×#1794	1	1	yes	characteristic
546	C₂	C₁₉×#1796	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#379
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#3518	C₂
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
2. C₁₉×#1759	C₂	semidirect
3. C₁₉×#1529	C₂	semidirect
4. C₁₉×#1506	C₂	semidirect
5. C₁₉×#1500	C₂	semidirect
6. C₁₉×#1488	C₂	semidirect
7. C₁₉×#1485	C₂	semidirect
8. Q₈²×C₁₉	C₄	semidirect
12. C₁₉×#556	C₄	semidirect
14. C₁₉×#555	C₄	semidirect
15. D₄×Q₈×C₁₉	C₄	semidirect
194. #8413	C₁₉	direct (N × H)
243. #1759	C₂×C₁₉	semidirect
244. #1529	C₂×C₁₉	semidirect
245. #1506	C₂×C₁₉	semidirect
246. #1500	C₂×C₁₉	semidirect
247. #1488	C₂×C₁₉	semidirect
248. #1485	C₂×C₁₉	semidirect
275. Q₈²	C₄×C₁₉	semidirect
279. #556	C₄×C₁₉	semidirect
281. #555	C₄×C₁₉	semidirect
282. D₄×Q₈	C₄×C₁₉	semidirect
390. C₁₉	#8413	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×#3518	2
C₁₉×#1759	2
C₁₉×#1529	2
C₁₉×#1506	2
C₁₉×#1500	2
C₁₉×#1488	2
C₁₉×#1485	2
#8413	19

Subgroups — C19×#8413 #18014372

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8413 #18014372