Subgroups — C₁₉×#18246 #18024205

Order 4864.

900 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3563	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3114	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3101	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2633	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1611	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1609	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1599	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1597	C₂	1	2	yes	maximal
9	C₁₉×#1521	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1515	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1470	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#564	—	2	1	no	—
13	C₁₉×#563	—	2	1	no	—
14	C₁₉×#557	—	2	1	no	—
15	C₁₉×#554	—	2	1	no	—
16	C₁₉×#552	—	2	1	no	—
17	C₁₉×#552	—	2	2	no	—
18	C₁₉×#552	—	2	1	no	—
19	C₁₉×#544	—	2	1	no	—
20	C₁₉×#544	C₂²	1	2	yes	—
21	C₁₉×#541	—	2	1	no	—
22	C₁₉×#541	—	2	2	no	—
23	C₁₉×#539	C₂²	1	2	yes	—
24	C₁₉×#533	C₂²	1	1	yes	characteristic
25	C₁₉×#529	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
28	C₁₉×#483	C₂²	1	2	yes	—
29	C₁₉×#483	C₂²	1	1	yes	characteristic
30	C₁₉×#480	C₂²	1	1	yes	characteristic
31	C₁₉×#478	—	2	1	no	—
32	C₁₉×#476	—	2	1	no	—
33	C₁₉×#463	—	2	1	no	—
34	C₁₉×#461	—	2	1	no	—
35	C₁₉×#450	C₂²	1	2	yes	—
36	C₁₉×#450	C₂²	1	1	yes	characteristic
37	C₁₉×#447	C₂²	1	1	yes	characteristic
38	C₁₉×#442	—	2	1	no	—
39	C₁₉×#440	—	2	1	no	—
40	C₄×SD₁₆×C₁₉	—	2	2	no	—
41	C₁₉×#432	C₂²	1	1	yes	characteristic
42	C₁₉×#431	C₂²	1	1	yes	characteristic
43	C₁₉×#399	—	2	1	no	—
44	C₁₉×#398	C₂²	1	2	yes	—
45	C₁₉×#397	—	2	1	no	—
46	C₁₉×#394	C₂²	1	2	yes	—
47	C₁₉×#385	—	2	2	no	—
48	C₁₉×#383	C₂²	1	1	yes	characteristic
49	C₁₉×#328	C₂²	1	2	yes	—
50	C₁₉×#328	C₂²	1	2	yes	—
51	C₁₉×#328	C₂²	1	2	yes	—
52	C₁₉×#327	C₂²	1	2	yes	—
53	C₁₉×#324	C₂²	1	2	yes	—
54	C₁₉×#324	C₂²	1	2	yes	—
55	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₉	—	2	1	no	—
57	C₂×SD₁₆×C₁₉	—	2	2	no	—
58	C₂×SD₁₆×C₁₉	—	2	1	no	—
59	C₂×D₈×C₁₉	—	2	1	no	—
60	C₁₉×C₄⋊Q₈	—	2	1	no	—
61	C₁₉×C₄⋊Q₈	—	2	2	no	—
62	C₁₉×C₄⋊Q₈	—	2	2	no	—
63	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
64	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
65	C₁₉×#126	—	2	2	no	—
66	C₁₉×#126	—	2	2	no	—
67	C₁₉×#126	—	2	2	no	—
68	C₁₉×#126	—	2	2	no	—
69	C₁₉×#126	—	2	1	no	—
70	C₁₉×#125	—	2	2	no	—
71	C₁₉×#125	—	2	2	no	—
72	C₁₉×#125	—	2	2	no	—
73	C₁₉×#125	—	2	2	no	—
74	C₁₉×#125	—	2	1	no	—
75	C₁₉×#125	—	2	2	no	—
76	C₁₉×#125	—	2	2	no	—
77	C₁₉×#125	—	2	2	no	—
78	C₁₉×#125	—	2	2	no	—
79	C₁₉×#125	—	2	1	no	—
80	C₁₉×#125	—	2	1	no	—
81	C₁₉×#125	—	2	1	no	—
82	C₁₉×#125	—	2	1	no	—
83	C₁₉×#125	—	2	1	no	—
84	C₁₉×#125	D₄	1	1	yes	characteristic
85	C₁₉×#124	D₄	1	1	yes	characteristic
86	C₁₉×#123	—	2	2	no	—
87	C₁₉×#123	—	2	1	no	—
88	C₁₉×#123	—	2	2	no	—
89	C₁₉×C₂²⋊Q₈	—	2	1	no	—
90	C₁₉×C₂²⋊Q₈	—	2	1	no	—
91	C₁₉×C₂²⋊Q₈	—	2	2	no	—
92	C₁₉×C₂²⋊Q₈	—	2	2	no	—
93	C₁₉×C₂²⋊Q₈	—	2	2	no	—
94	C₁₉×C₂²⋊Q₈	—	2	1	no	—
95	C₁₉×C₂²⋊Q₈	—	2	2	no	—
96	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
97	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
98	C₁₉×#121	C₂³	1	1	yes	characteristic
99	C₄×Q₈×C₁₉	—	2	1	no	—
100	C₄×Q₈×C₁₉	—	2	2	no	—
101	C₄×Q₈×C₁₉	—	2	1	no	—
102	C₄×Q₈×C₁₉	—	2	1	no	—
103	C₄×Q₈×C₁₉	D₄	1	2	yes	—
104	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
105	C₄×D₄×C₁₉	—	2	1	no	—
106	C₄×D₄×C₁₉	—	2	2	no	—
107	C₄×D₄×C₁₉	—	2	1	no	—
108	C₄×D₄×C₁₉	—	2	1	no	—
109	C₄×D₄×C₁₉	—	2	1	no	—
110	C₄×D₄×C₁₉	—	2	1	no	—
111	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
112	C₁₉×#117	—	2	2	no	—
113	C₁₉×#117	—	2	1	no	—
114	C₁₉×#117	—	2	1	no	—
115	C₁₉×#117	—	2	2	no	—
116	C₁₉×#117	—	2	1	no	—
117	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
118	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
119	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
120	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
125	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
127	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
128	C₁₉×#107	—	2	1	no	—
129	C₁₉×#106	—	2	2	no	—
130	C₁₉×#106	—	2	1	no	—
131	C₁₉×C₄⋊C₈	—	2	1	no	—
132	C₁₉×C₄⋊C₈	—	2	1	no	—
133	C₁₉×#103	—	2	2	no	—
134	C₁₉×#103	—	2	1	no	—
135	C₁₉×#102	—	2	1	no	—
136	C₁₉×#102	—	2	2	no	—
137	C₁₉×#102	—	2	1	no	—
138	C₁₉×#102	—	2	1	no	—
139	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
140	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
141	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
142	C₁₉×#97	—	2	1	no	—
143	C₄×C₈×C₁₉	—	2	1	no	—
144	C₁₉×#95	—	2	1	no	—
145	C₁₉×#95	—	2	1	no	—
146	C₁₉×#95	—	2	2	no	—
147	C₁₉×#95	C₂³	1	2	yes	—
148	C₂⁴×C₁₉	—	2	1	no	—
149	C₂×Q₈×C₁₉	—	2	2	no	—
150	C₂×Q₈×C₁₉	—	2	1	no	—
151	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
152	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂×D₄×C₁₉	—	2	1	no	—
154	C₂×D₄×C₁₉	—	2	1	no	—
155	C₂×D₄×C₁₉	—	2	1	no	—
156	C₂×D₄×C₁₉	—	4	2	no	—
157	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₉	—	2	2	no	—
159	C₂²×C₄×C₁₉	—	2	1	no	—
160	C₂²×C₄×C₁₉	—	2	2	no	—
161	C₂²×C₄×C₁₉	—	2	1	no	—
162	C₂²×C₄×C₁₉	—	4	1	no	—
163	C₂²×C₄×C₁₉	—	4	1	no	—
164	C₂²×C₄×C₁₉	—	8	2	no	—
165	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
170	SD₁₆×C₁₉	—	4	2	no	—
171	SD₁₆×C₁₉	—	4	4	no	—
172	D₈×C₁₉	—	4	2	no	—
173	C₂×C₈×C₁₉	—	2	1	no	—
174	C₂×C₈×C₁₉	—	2	2	no	—
175	C₂×C₈×C₁₉	—	2	1	no	—
176	C₄⋊C₄×C₁₉	—	2	2	no	—
177	C₄⋊C₄×C₁₉	—	2	2	no	—
178	C₄⋊C₄×C₁₉	—	2	2	no	—
179	C₄⋊C₄×C₁₉	—	2	2	no	—
180	C₄⋊C₄×C₁₉	—	2	2	no	—
181	C₄⋊C₄×C₁₉	—	2	2	no	—
182	C₄⋊C₄×C₁₉	—	2	2	no	—
183	C₄⋊C₄×C₁₉	—	2	2	no	—
184	C₄⋊C₄×C₁₉	—	2	1	no	—
185	C₄⋊C₄×C₁₉	—	2	1	no	—
186	C₄⋊C₄×C₁₉	—	2	1	no	—
187	C₄⋊C₄×C₁₉	—	2	2	no	—
188	C₄⋊C₄×C₁₉	—	2	1	no	—
189	C₄⋊C₄×C₁₉	—	2	2	no	—
190	C₄⋊C₄×C₁₉	—	2	1	no	—
191	C₄⋊C₄×C₁₉	—	2	1	no	—
192	C₄⋊C₄×C₁₉	—	2	1	no	—
193	C₄⋊C₄×C₁₉	—	2	1	no	—
194	C₄⋊C₄×C₁₉	—	2	1	no	—
195	C₄⋊C₄×C₁₉	—	2	1	no	—
196	C₄⋊C₄×C₁₉	—	2	2	no	—
197	C₄⋊C₄×C₁₉	—	2	2	no	—
198	C₄⋊C₄×C₁₉	—	2	2	no	—
199	C₄⋊C₄×C₁₉	—	2	1	no	—
200	C₄⋊C₄×C₁₉	—	2	2	no	—
201	C₄⋊C₄×C₁₉	—	2	1	no	—
202	C₄⋊C₄×C₁₉	—	2	1	no	—
203	C₄⋊C₄×C₁₉	—	8	2	no	—
204	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
205	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
206	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
207	C₂²⋊C₄×C₁₉	—	2	2	no	—
208	C₂²⋊C₄×C₁₉	—	2	2	no	—
209	C₂²⋊C₄×C₁₉	—	2	2	no	—
210	C₂²⋊C₄×C₁₉	—	2	2	no	—
211	C₂²⋊C₄×C₁₉	—	2	1	no	—
212	C₂²⋊C₄×C₁₉	—	2	1	no	—
213	C₂²⋊C₄×C₁₉	—	2	1	no	—
214	C₂²⋊C₄×C₁₉	—	2	1	no	—
215	C₂²⋊C₄×C₁₉	—	2	1	no	—
216	C₂²⋊C₄×C₁₉	—	4	4	no	—
217	C₂²⋊C₄×C₁₉	—	4	1	no	—
218	C₂²⋊C₄×C₁₉	—	4	1	no	—
219	C₂²⋊C₄×C₁₉	—	8	2	no	—
220	C₄²×C₁₉	—	2	2	no	—
221	C₄²×C₁₉	—	2	2	no	—
222	C₄²×C₁₉	—	2	2	no	—
223	C₄²×C₁₉	—	2	2	no	—
224	C₄²×C₁₉	—	2	1	no	—
225	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
226	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
227	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
228	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
229	#18246	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₂³×C₁₉	—	2	2	no	—
231	C₂³×C₁₉	—	2	1	no	—
232	C₂³×C₁₉	—	4	1	no	—
233	C₂³×C₁₉	—	4	2	no	—
234	C₂³×C₁₉	—	4	1	no	—
235	C₂³×C₁₉	—	4	2	no	—
236	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
237	Q₈×C₁₉	—	4	1	no	—
238	Q₈×C₁₉	—	4	2	no	—
239	Q₈×C₁₉	—	4	2	no	—
240	Q₈×C₁₉	—	8	2	no	—
241	D₄×C₁₉	—	2	2	no	—
242	D₄×C₁₉	—	2	2	no	—
243	D₄×C₁₉	—	4	1	no	—
244	D₄×C₁₉	—	4	1	no	—
245	D₄×C₁₉	—	4	1	no	—
246	D₄×C₁₉	—	4	2	no	—
247	C₂×C₄×C₁₉	—	2	2	no	—
248	C₂×C₄×C₁₉	—	2	2	no	—
249	C₂×C₄×C₁₉	—	2	1	no	—
250	C₂×C₄×C₁₉	—	2	1	no	—
251	C₂×C₄×C₁₉	—	2	2	no	—
252	C₂×C₄×C₁₉	—	2	1	no	—
253	C₂×C₄×C₁₉	—	2	2	no	—
254	C₂×C₄×C₁₉	—	2	2	no	—
255	C₂×C₄×C₁₉	—	2	2	no	—
256	C₂×C₄×C₁₉	—	2	2	no	—
257	C₂×C₄×C₁₉	—	4	1	no	—
258	C₂×C₄×C₁₉	—	4	1	no	—
259	C₂×C₄×C₁₉	—	4	2	no	—
260	C₂×C₄×C₁₉	—	4	2	no	—
261	C₂×C₄×C₁₉	—	4	2	no	—
262	C₂×C₄×C₁₉	—	4	2	no	—
263	C₂×C₄×C₁₉	—	4	1	no	—
264	C₂×C₄×C₁₉	—	4	2	no	—
265	C₂×C₄×C₁₉	—	4	2	no	—
266	C₂×C₄×C₁₉	—	8	2	no	—
267	C₂×C₄×C₁₉	—	8	2	no	—
268	C₂×C₄×C₁₉	—	8	2	no	—
269	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
270	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
271	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
272	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
273	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
275	C₈×C₁₉	—	4	1	no	—
276	C₈×C₁₉	—	4	1	no	—
277	C₈×C₁₉	—	4	2	no	—
278	#3563	C₂×C₁₉	1	1	yes	characteristic, complemented
279	#3114	C₂×C₁₉	1	1	yes	characteristic
280	#3101	C₂×C₁₉	1	1	yes	characteristic, complemented
281	#2633	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#1611	C₂×C₁₉	1	2	yes	complemented
283	#1609	C₂×C₁₉	1	2	yes	complemented
284	#1599	C₂×C₁₉	1	2	yes	complemented
285	#1597	C₂×C₁₉	1	2	yes	—
286	#1521	C₂×C₁₉	1	1	yes	characteristic, complemented
287	#1515	C₂×C₁₉	1	1	yes	characteristic, complemented
288	#1470	C₂×C₁₉	1	1	yes	characteristic, complemented
289	C₂²×C₁₉	—	2	1	no	—
290	C₂²×C₁₉	—	2	1	no	—
291	C₂²×C₁₉	—	4	4	no	—
292	C₂²×C₁₉	—	4	1	no	—
293	C₂²×C₁₉	—	4	1	no	—
294	C₂²×C₁₉	—	4	1	no	—
295	C₂²×C₁₉	—	4	2	no	—
296	C₂²×C₁₉	—	8	2	no	—
297	C₂²×C₁₉	—	8	1	no	—
298	C₂²×C₁₉	—	8	1	no	—
299	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
300	C₂²×C₁₉	#577	1	2	yes	—
301	C₄×C₁₉	—	2	1	no	—
302	C₄×C₁₉	—	2	1	no	—
303	C₄×C₁₉	—	2	1	no	—
304	C₄×C₁₉	—	2	1	no	—
305	C₄×C₁₉	—	2	1	no	—
306	C₄×C₁₉	—	2	1	no	—
307	C₄×C₁₉	—	4	2	no	—
308	C₄×C₁₉	—	4	1	no	—
309	C₄×C₁₉	—	4	1	no	—
310	C₄×C₁₉	—	4	2	no	—
311	C₄×C₁₉	—	4	2	no	—
312	C₄×C₁₉	—	4	2	no	—
313	C₄×C₁₉	—	4	1	no	—
314	C₄×C₁₉	—	8	2	no	—
315	C₄×C₁₉	—	8	1	no	—
316	#564	—	2	1	no	—
317	#563	—	2	1	no	—
318	#557	—	2	1	no	—
319	#554	—	2	1	no	—
320	#552	—	2	1	no	—
321	#552	—	2	2	no	—
322	#552	—	2	1	no	—
323	#544	—	2	1	no	—
324	#544	C₂²×C₁₉	1	2	yes	—
325	#541	—	2	1	no	—
326	#541	—	2	2	no	—
327	#539	C₂²×C₁₉	1	2	yes	—
328	#533	C₂²×C₁₉	1	1	yes	characteristic
329	#529	C₂²×C₁₉	1	1	yes	characteristic
330	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
331	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
332	#483	C₂²×C₁₉	1	2	yes	—
333	#483	C₂²×C₁₉	1	1	yes	characteristic
334	#480	C₂²×C₁₉	1	1	yes	characteristic
335	#478	—	2	1	no	—
336	#476	—	2	1	no	—
337	#463	—	2	1	no	—
338	#461	—	2	1	no	—
339	#450	C₂²×C₁₉	1	2	yes	—
340	#450	C₂²×C₁₉	1	1	yes	characteristic
341	#447	C₂²×C₁₉	1	1	yes	characteristic
342	#442	—	2	1	no	—
343	#440	—	2	1	no	—
344	C₄×SD₁₆	—	2	2	no	—
345	#432	C₂²×C₁₉	1	1	yes	characteristic
346	#431	C₂²×C₁₉	1	1	yes	characteristic
347	#399	—	2	1	no	—
348	#398	C₂²×C₁₉	1	2	yes	—
349	#397	—	2	1	no	—
350	#394	C₂²×C₁₉	1	2	yes	—
351	#385	—	2	2	no	—
352	#383	C₂²×C₁₉	1	1	yes	characteristic
353	#328	C₂²×C₁₉	1	2	yes	—
354	#328	C₂²×C₁₉	1	2	yes	—
355	#328	C₂²×C₁₉	1	2	yes	—
356	#327	C₂²×C₁₉	1	2	yes	—
357	#324	C₂²×C₁₉	1	2	yes	—
358	#324	C₂²×C₁₉	1	2	yes	—
359	C₂×C₁₉	—	2	2	no	—
360	C₂×C₁₉	—	8	1	no	—
361	C₂×C₁₉	—	8	2	no	—
362	C₂×C₁₉	#3010	1	1	yes	characteristic
363	C₂×C₁₉	#3020	1	1	yes	characteristic
364	C₂×C₁₉	#3025	1	1	yes	characteristic
365	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
366	C₂³×C₄	—	2	1	no	—
367	C₂×SD₁₆	—	2	2	no	—
368	C₂×SD₁₆	—	2	1	no	—
369	C₂×D₈	—	2	1	no	—
370	C₄⋊Q₈	—	2	1	no	—
371	C₄⋊Q₈	—	2	2	no	—
372	C₄⋊Q₈	—	2	2	no	—
373	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
374	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
375	#126	—	2	2	no	—
376	#126	—	2	2	no	—
377	#126	—	2	2	no	—
378	#126	—	2	2	no	—
379	#126	—	2	1	no	—
380	#125	—	2	2	no	—
381	#125	—	2	2	no	—
382	#125	—	2	2	no	—
383	#125	—	2	2	no	—
384	#125	—	2	1	no	—
385	#125	—	2	2	no	—
386	#125	—	2	2	no	—
387	#125	—	2	2	no	—
388	#125	—	2	2	no	—
389	#125	—	2	1	no	—
390	#125	—	2	1	no	—
391	#125	—	2	1	no	—
392	#125	—	2	1	no	—
393	#125	—	2	1	no	—
394	#125	D₄×C₁₉	1	1	yes	characteristic
395	#124	D₄×C₁₉	1	1	yes	characteristic
396	#123	—	2	2	no	—
397	#123	—	2	1	no	—
398	#123	—	2	2	no	—
399	C₂²⋊Q₈	—	2	1	no	—
400	C₂²⋊Q₈	—	2	1	no	—
401	C₂²⋊Q₈	—	2	2	no	—
402	C₂²⋊Q₈	—	2	2	no	—
403	C₂²⋊Q₈	—	2	2	no	—
404	C₂²⋊Q₈	—	2	1	no	—
405	C₂²⋊Q₈	—	2	2	no	—
406	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
407	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
408	#121	C₂³×C₁₉	1	1	yes	characteristic
409	C₄×Q₈	—	2	1	no	—
410	C₄×Q₈	—	2	2	no	—
411	C₄×Q₈	—	2	1	no	—
412	C₄×Q₈	—	2	1	no	—
413	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
414	C₄×Q₈	D₄×C₁₉	1	2	yes	—
415	C₄×D₄	—	2	1	no	—
416	C₄×D₄	—	2	2	no	—
417	C₄×D₄	—	2	1	no	—
418	C₄×D₄	—	2	1	no	—
419	C₄×D₄	—	2	1	no	—
420	C₄×D₄	—	2	1	no	—
421	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
422	#117	—	2	2	no	—
423	#117	—	2	1	no	—
424	#117	—	2	1	no	—
425	#117	—	2	2	no	—
426	#117	—	2	1	no	—
427	C₂×C₄⋊C₄	—	2	1	no	—
428	C₂×C₄⋊C₄	—	2	2	no	—
429	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
430	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
431	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
432	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
433	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
434	C₂×C₂²⋊C₄	—	2	1	no	—
435	C₂×C₂²⋊C₄	—	2	2	no	—
436	C₂×C₂²⋊C₄	—	2	2	no	—
437	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
438	#107	—	2	1	no	—
439	#106	—	2	2	no	—
440	#106	—	2	1	no	—
441	C₄⋊C₈	—	2	1	no	—
442	C₄⋊C₈	—	2	1	no	—
443	#103	—	2	2	no	—
444	#103	—	2	1	no	—
445	#102	—	2	1	no	—
446	#102	—	2	2	no	—
447	#102	—	2	1	no	—
448	#102	—	2	1	no	—
449	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
450	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
451	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
452	#97	—	2	1	no	—
453	C₄×C₈	—	2	1	no	—
454	#95	—	2	1	no	—
455	#95	—	2	1	no	—
456	#95	—	2	2	no	—
457	#95	C₂³×C₁₉	1	2	yes	—
458	C₁₉	#18246	1	1	yes	characteristic, direct product factor, Sylow
459	C₂⁴	—	2	1	no	—
460	C₂×Q₈	—	2	2	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
463	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	4	2	no	—
468	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	4	1	no	—
474	C₂²×C₄	—	4	1	no	—
475	C₂²×C₄	—	8	2	no	—
476	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
477	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
479	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
480	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
481	SD₁₆	—	4	2	no	—
482	SD₁₆	—	4	4	no	—
483	D₈	—	4	2	no	—
484	C₂×C₈	—	2	2	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	8	2	no	—
515	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
516	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
517	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
518	C₂²⋊C₄	—	2	2	no	—
519	C₂²⋊C₄	—	2	2	no	—
520	C₂²⋊C₄	—	2	2	no	—
521	C₂²⋊C₄	—	2	2	no	—
522	C₂²⋊C₄	—	2	1	no	—
523	C₂²⋊C₄	—	2	1	no	—
524	C₂²⋊C₄	—	2	1	no	—
525	C₂²⋊C₄	—	2	1	no	—
526	C₂²⋊C₄	—	2	1	no	—
527	C₂²⋊C₄	—	4	4	no	—
528	C₂²⋊C₄	—	4	1	no	—
529	C₂²⋊C₄	—	4	1	no	—
530	C₂²⋊C₄	—	8	2	no	—
531	C₄²	—	2	2	no	—
532	C₄²	—	2	2	no	—
533	C₄²	—	2	2	no	—
534	C₄²	—	2	2	no	—
535	C₄²	—	2	1	no	—
536	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
537	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
538	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
539	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
540	C₂³	—	2	2	no	—
541	C₂³	—	2	1	no	—
542	C₂³	—	4	1	no	—
543	C₂³	—	4	2	no	—
544	C₂³	—	4	1	no	—
545	C₂³	—	4	2	no	—
546	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
547	Q₈	—	4	1	no	—
548	Q₈	—	4	2	no	—
549	Q₈	—	4	2	no	—
550	Q₈	—	8	2	no	—
551	D₄	—	2	2	no	—
552	D₄	—	2	2	no	—
553	D₄	—	4	1	no	—
554	D₄	—	4	1	no	—
555	D₄	—	4	1	no	—
556	D₄	—	4	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	2	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	2	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	8	2	no	—
577	C₂×C₄	—	8	2	no	—
578	C₂×C₄	—	8	2	no	—
579	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
580	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
581	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
582	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
583	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
584	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
585	C₈	—	4	1	no	—
586	C₈	—	4	1	no	—
587	C₈	—	4	2	no	—
588	C₂²	—	2	1	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	4	4	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	2	no	—
595	C₂²	—	8	2	no	—
596	C₂²	—	8	1	no	—
597	C₂²	—	8	1	no	—
598	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
599	C₂²	C₁₉×#577	1	2	yes	—
600	C₄	—	2	1	no	—
601	C₄	—	2	1	no	—
602	C₄	—	2	1	no	—
603	C₄	—	2	1	no	—
604	C₄	—	2	1	no	—
605	C₄	—	2	1	no	—
606	C₄	—	4	2	no	—
607	C₄	—	4	1	no	—
608	C₄	—	4	1	no	—
609	C₄	—	4	2	no	—
610	C₄	—	4	2	no	—
611	C₄	—	4	2	no	—
612	C₄	—	4	1	no	—
613	C₄	—	8	2	no	—
614	C₄	—	8	1	no	—
615	C₂	—	2	2	no	—
616	C₂	—	8	2	no	—
617	C₂	—	8	1	no	—
618	C₂	C₁₉×#3010	1	1	yes	characteristic
619	C₂	C₁₉×#3020	1	1	yes	characteristic
620	C₂	C₁₉×#3025	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#447	C₂²
LCS	G ▷ C₂²×C₄ ▷ 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
1. C₁₉×#3563	C₂	semidirect
3. C₁₉×#3101	C₂	semidirect
4. C₁₉×#2633	C₂	semidirect
5. C₁₉×#1611	C₂	semidirect
6. C₁₉×#1609	C₂	semidirect
7. C₁₉×#1599	C₂	semidirect
9. C₁₉×#1521	C₂	semidirect
10. C₁₉×#1515	C₂	semidirect
11. C₁₉×#1470	C₂	semidirect
229. #18246	C₁₉	direct (N × H)
278. #3563	C₂×C₁₉	semidirect
280. #3101	C₂×C₁₉	semidirect
281. #2633	C₂×C₁₉	semidirect
282. #1611	C₂×C₁₉	semidirect
283. #1609	C₂×C₁₉	semidirect
284. #1599	C₂×C₁₉	semidirect
286. #1521	C₂×C₁₉	semidirect
287. #1515	C₂×C₁₉	semidirect
288. #1470	C₂×C₁₉	semidirect
458. C₁₉	#18246	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×#3563	2
C₁₉×#3114	2
C₁₉×#3101	2
C₁₉×#2633	2
C₁₉×#1611	2
C₁₉×#1609	2
C₁₉×#1599	2
C₁₉×#1597	2
C₁₉×#1521	2
C₁₉×#1515	2
C₁₉×#1470	2
#18246	19

Subgroups — C19×#18246 #18024205

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18246 #18024205