Subgroups — C₁₉×#18461 #18024420

Order 4864.

880 conjugacy classes of subgroups.

The subgroup lattice has 638 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×#3215	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3211	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2820	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1605	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1603	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×#1518	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1512	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×C₁₉×#124	C₂²	1	1	yes	characteristic
28	C₁₉×#497	—	2	1	no	—
29	C₁₉×#495	—	2	1	no	—
30	C₁₉×#489	—	2	1	no	—
31	C₁₉×#488	—	2	1	no	—
32	C₁₉×#464	—	2	1	no	—
33	C₁₉×#464	—	2	2	no	—
34	C₁₉×#463	—	2	1	no	—
35	C₁₉×#451	C₂²	1	1	yes	characteristic
36	C₁₉×#451	C₂²	1	2	yes	—
37	C₁₉×#450	C₂²	1	1	yes	characteristic
38	C₁₉×#450	C₂²	1	2	yes	—
39	C₁₉×#448	C₂²	1	1	yes	characteristic
40	C₁₉×#447	C₂²	1	1	yes	characteristic
41	C₁₉×#432	C₂²	1	1	yes	characteristic
42	C₁₉×#431	C₂²	1	1	yes	characteristic
43	C₁₉×#399	—	2	1	no	—
44	C₁₉×#397	—	2	1	no	—
45	C₁₉×#396	—	2	2	no	—
46	C₁₉×#395	C₂²	1	2	yes	—
47	C₁₉×#394	C₂²	1	2	yes	—
48	C₁₉×#382	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×Q₈×C₁₉	C₂³	1	1	yes	characteristic
56	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
57	C₂×Q₁₆×C₁₉	—	2	1	no	—
58	C₂×Q₁₆×C₁₉	—	2	2	no	—
59	C₂×SD₁₆×C₁₉	—	2	1	no	—
60	C₂×SD₁₆×C₁₉	—	2	2	no	—
61	C₂×SD₁₆×C₁₉	—	2	1	no	—
62	C₂×D₈×C₁₉	—	2	1	no	—
63	C₁₉×C₄⋊Q₈	—	2	1	no	—
64	C₁₉×C₄⋊Q₈	—	2	2	no	—
65	C₁₉×C₄⋊Q₈	—	2	2	no	—
66	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
67	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
68	C₁₉×#126	—	2	2	no	—
69	C₁₉×#126	—	2	2	no	—
70	C₁₉×#126	—	2	2	no	—
71	C₁₉×#126	—	2	2	no	—
72	C₁₉×#126	—	2	1	no	—
73	C₁₉×#125	—	2	2	no	—
74	C₁₉×#125	—	2	2	no	—
75	C₁₉×#125	—	2	2	no	—
76	C₁₉×#125	—	2	2	no	—
77	C₁₉×#125	—	2	1	no	—
78	C₁₉×#125	—	2	2	no	—
79	C₁₉×#125	—	2	2	no	—
80	C₁₉×#125	—	2	2	no	—
81	C₁₉×#125	—	2	2	no	—
82	C₁₉×#125	—	2	1	no	—
83	C₁₉×#125	—	2	1	no	—
84	C₁₉×#125	—	2	1	no	—
85	C₁₉×#125	—	2	1	no	—
86	C₁₉×#125	—	2	1	no	—
87	C₁₉×#125	D₄	1	1	yes	characteristic
88	C₁₉×#124	—	2	1	no	—
89	C₁₉×#124	—	2	1	no	—
90	C₁₉×#124	—	2	1	no	—
91	C₁₉×#124	—	2	1	no	—
92	C₁₉×#124	D₄	1	1	yes	characteristic
93	C₁₉×#123	—	2	2	no	—
94	C₁₉×#123	—	2	1	no	—
95	C₁₉×#123	—	2	2	no	—
96	C₁₉×C₂²⋊Q₈	—	2	1	no	—
97	C₁₉×C₂²⋊Q₈	—	2	1	no	—
98	C₁₉×C₂²⋊Q₈	—	2	2	no	—
99	C₁₉×C₂²⋊Q₈	—	2	2	no	—
100	C₁₉×C₂²⋊Q₈	—	2	2	no	—
101	C₁₉×C₂²⋊Q₈	—	2	1	no	—
102	C₁₉×C₂²⋊Q₈	—	2	2	no	—
103	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
104	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
105	C₁₉×#121	C₂³	1	1	yes	characteristic
106	C₄×Q₈×C₁₉	—	2	1	no	—
107	C₄×Q₈×C₁₉	—	2	2	no	—
108	C₄×Q₈×C₁₉	—	2	1	no	—
109	C₄×Q₈×C₁₉	—	2	1	no	—
110	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
111	C₄×Q₈×C₁₉	D₄	1	2	yes	—
112	C₄×D₄×C₁₉	—	2	1	no	—
113	C₄×D₄×C₁₉	—	2	2	no	—
114	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
115	C₁₉×#117	—	2	2	no	—
116	C₁₉×#117	—	2	1	no	—
117	C₁₉×#117	—	2	1	no	—
118	C₁₉×#117	—	2	2	no	—
119	C₁₉×#117	—	2	1	no	—
120	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
121	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
122	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
123	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
124	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
127	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
129	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
130	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
131	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
132	C₁₉×C₄⋊C₈	—	2	1	no	—
133	C₁₉×C₄⋊C₈	—	2	1	no	—
134	C₁₉×#103	—	2	1	no	—
135	C₁₉×#103	—	2	1	no	—
136	C₁₉×#103	—	2	2	no	—
137	C₁₉×#102	—	2	1	no	—
138	C₁₉×#102	—	2	1	no	—
139	C₁₉×#102	—	2	2	no	—
140	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
141	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
142	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
143	C₁₉×#97	—	2	1	no	—
144	C₄×C₈×C₁₉	—	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	—	2	1	no	—
152	C₂×Q₈×C₁₉	—	2	1	no	—
153	C₂×Q₈×C₁₉	—	8	1	no	—
154	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
155	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₂×D₄×C₁₉	—	2	1	no	—
157	C₂×D₄×C₁₉	—	2	1	no	—
158	C₂×D₄×C₁₉	—	2	1	no	—
159	C₂×D₄×C₁₉	—	8	1	no	—
160	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₉	—	2	2	no	—
162	C₂²×C₄×C₁₉	—	2	1	no	—
163	C₂²×C₄×C₁₉	—	2	1	no	—
164	C₂²×C₄×C₁₉	—	2	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	Q₁₆×C₁₉	—	8	1	no	—
171	Q₁₆×C₁₉	—	8	2	no	—
172	SD₁₆×C₁₉	—	8	1	no	—
173	SD₁₆×C₁₉	—	8	1	no	—
174	SD₁₆×C₁₉	—	8	2	no	—
175	D₈×C₁₉	—	8	1	no	—
176	C₂×C₈×C₁₉	—	2	1	no	—
177	C₂×C₈×C₁₉	—	2	1	no	—
178	C₂×C₈×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	2	no	—
185	C₄⋊C₄×C₁₉	—	2	2	no	—
186	C₄⋊C₄×C₁₉	—	2	2	no	—
187	C₄⋊C₄×C₁₉	—	2	1	no	—
188	C₄⋊C₄×C₁₉	—	2	1	no	—
189	C₄⋊C₄×C₁₉	—	2	1	no	—
190	C₄⋊C₄×C₁₉	—	2	2	no	—
191	C₄⋊C₄×C₁₉	—	2	1	no	—
192	C₄⋊C₄×C₁₉	—	2	2	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	1	no	—
197	C₄⋊C₄×C₁₉	—	2	1	no	—
198	C₄⋊C₄×C₁₉	—	2	1	no	—
199	C₄⋊C₄×C₁₉	—	2	2	no	—
200	C₄⋊C₄×C₁₉	—	2	2	no	—
201	C₄⋊C₄×C₁₉	—	2	2	no	—
202	C₄⋊C₄×C₁₉	—	2	1	no	—
203	C₄⋊C₄×C₁₉	—	2	2	no	—
204	C₄⋊C₄×C₁₉	—	8	1	no	—
205	C₄⋊C₄×C₁₉	—	8	2	no	—
206	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
207	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
209	C₂²⋊C₄×C₁₉	—	2	2	no	—
210	C₂²⋊C₄×C₁₉	—	2	2	no	—
211	C₂²⋊C₄×C₁₉	—	2	2	no	—
212	C₂²⋊C₄×C₁₉	—	2	2	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	—	2	1	no	—
217	C₂²⋊C₄×C₁₉	—	2	1	no	—
218	C₂²⋊C₄×C₁₉	—	4	1	no	—
219	C₂²⋊C₄×C₁₉	—	4	1	no	—
220	C₂²⋊C₄×C₁₉	—	4	1	no	—
221	C₂²⋊C₄×C₁₉	—	4	1	no	—
222	C₂²⋊C₄×C₁₉	—	8	2	no	—
223	C₂²⋊C₄×C₁₉	—	8	2	no	—
224	C₄²×C₁₉	—	2	2	no	—
225	C₄²×C₁₉	—	2	2	no	—
226	C₄²×C₁₉	—	2	2	no	—
227	C₄²×C₁₉	—	2	2	no	—
228	C₄²×C₁₉	—	2	1	no	—
229	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
230	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
231	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
232	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
233	#18461	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂³×C₁₉	—	2	1	no	—
235	C₂³×C₁₉	—	4	2	no	—
236	C₂³×C₁₉	—	4	2	no	—
237	C₂³×C₁₉	—	4	1	no	—
238	C₂³×C₁₉	—	4	1	no	—
239	C₂³×C₁₉	—	4	1	no	—
240	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
241	Q₈×C₁₉	—	4	1	no	—
242	Q₈×C₁₉	—	4	2	no	—
243	Q₈×C₁₉	—	4	2	no	—
244	Q₈×C₁₉	—	4	1	no	—
245	Q₈×C₁₉	—	4	1	no	—
246	Q₈×C₁₉	—	4	2	no	—
247	Q₈×C₁₉	—	8	2	no	—
248	D₄×C₁₉	—	4	1	no	—
249	D₄×C₁₉	—	4	1	no	—
250	D₄×C₁₉	—	4	1	no	—
251	D₄×C₁₉	—	4	2	no	—
252	D₄×C₁₉	—	4	1	no	—
253	D₄×C₁₉	—	4	1	no	—
254	C₂×C₄×C₁₉	—	2	1	no	—
255	C₂×C₄×C₁₉	—	2	1	no	—
256	C₂×C₄×C₁₉	—	2	2	no	—
257	C₂×C₄×C₁₉	—	2	1	no	—
258	C₂×C₄×C₁₉	—	2	1	no	—
259	C₂×C₄×C₁₉	—	2	2	no	—
260	C₂×C₄×C₁₉	—	2	1	no	—
261	C₂×C₄×C₁₉	—	2	2	no	—
262	C₂×C₄×C₁₉	—	2	2	no	—
263	C₂×C₄×C₁₉	—	2	2	no	—
264	C₂×C₄×C₁₉	—	2	2	no	—
265	C₂×C₄×C₁₉	—	4	1	no	—
266	C₂×C₄×C₁₉	—	4	1	no	—
267	C₂×C₄×C₁₉	—	4	2	no	—
268	C₂×C₄×C₁₉	—	4	2	no	—
269	C₂×C₄×C₁₉	—	4	2	no	—
270	C₂×C₄×C₁₉	—	4	2	no	—
271	C₂×C₄×C₁₉	—	4	2	no	—
272	C₂×C₄×C₁₉	—	4	1	no	—
273	C₂×C₄×C₁₉	—	4	2	no	—
274	C₂×C₄×C₁₉	—	8	2	no	—
275	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
276	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
277	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
278	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
279	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
280	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
281	C₈×C₁₉	—	4	1	no	—
282	C₈×C₁₉	—	4	1	no	—
283	C₈×C₁₉	—	4	2	no	—
284	#3563	C₂×C₁₉	1	1	yes	characteristic, complemented
285	#3215	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#3211	C₂×C₁₉	1	1	yes	characteristic
287	#2820	C₂×C₁₉	1	1	yes	characteristic, complemented
288	#1605	C₂×C₁₉	1	2	yes	complemented
289	#1603	C₂×C₁₉	1	2	yes	complemented
290	#1599	C₂×C₁₉	1	2	yes	complemented
291	#1597	C₂×C₁₉	1	2	yes	—
292	#1518	C₂×C₁₉	1	1	yes	characteristic, complemented
293	#1512	C₂×C₁₉	1	1	yes	characteristic, complemented
294	#1470	C₂×C₁₉	1	1	yes	characteristic, complemented
295	C₂²×C₁₉	—	2	1	no	—
296	C₂²×C₁₉	—	2	1	no	—
297	C₂²×C₁₉	—	4	1	no	—
298	C₂²×C₁₉	—	4	1	no	—
299	C₂²×C₁₉	—	4	1	no	—
300	C₂²×C₁₉	—	8	2	no	—
301	C₂²×C₁₉	—	8	2	no	—
302	C₂²×C₁₉	—	8	1	no	—
303	C₂²×C₁₉	—	8	1	no	—
304	C₂²×C₁₉	—	8	1	no	—
305	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
306	C₂²×C₁₉	#577	1	1	yes	characteristic
307	C₂²×C₁₉	#578	1	1	yes	characteristic
308	C₄×C₁₉	—	2	1	no	—
309	C₄×C₁₉	—	2	1	no	—
310	C₄×C₁₉	—	2	1	no	—
311	C₄×C₁₉	—	2	1	no	—
312	C₄×C₁₉	—	2	1	no	—
313	C₄×C₁₉	—	2	1	no	—
314	C₄×C₁₉	—	4	2	no	—
315	C₄×C₁₉	—	4	1	no	—
316	C₄×C₁₉	—	4	1	no	—
317	C₄×C₁₉	—	4	2	no	—
318	C₄×C₁₉	—	4	2	no	—
319	C₄×C₁₉	—	4	2	no	—
320	C₄×C₁₉	—	4	1	no	—
321	C₄×C₁₉	—	8	2	no	—
322	C₄×C₁₉	—	8	1	no	—
323	#564	—	2	1	no	—
324	#563	—	2	1	no	—
325	#557	—	2	1	no	—
326	#554	—	2	1	no	—
327	#552	—	2	1	no	—
328	#552	—	2	2	no	—
329	#552	—	2	1	no	—
330	#544	—	2	1	no	—
331	#544	C₂²×C₁₉	1	2	yes	—
332	#541	—	2	1	no	—
333	#541	—	2	2	no	—
334	#539	C₂²×C₁₉	1	2	yes	—
335	#533	C₂²×C₁₉	1	1	yes	characteristic
336	#529	C₂²×C₁₉	1	1	yes	characteristic
337	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
338	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
339	#497	—	2	1	no	—
340	#495	—	2	1	no	—
341	#489	—	2	1	no	—
342	#488	—	2	1	no	—
343	#464	—	2	1	no	—
344	#464	—	2	2	no	—
345	#463	—	2	1	no	—
346	#451	C₂²×C₁₉	1	2	yes	—
347	#451	C₂²×C₁₉	1	1	yes	characteristic
348	#450	C₂²×C₁₉	1	2	yes	—
349	#450	C₂²×C₁₉	1	1	yes	characteristic
350	#448	C₂²×C₁₉	1	1	yes	characteristic
351	#447	C₂²×C₁₉	1	1	yes	characteristic
352	#432	C₂²×C₁₉	1	1	yes	characteristic
353	#431	C₂²×C₁₉	1	1	yes	characteristic
354	#399	—	2	1	no	—
355	#397	—	2	1	no	—
356	#396	—	2	2	no	—
357	#395	C₂²×C₁₉	1	2	yes	—
358	#394	C₂²×C₁₉	1	2	yes	—
359	#382	C₂²×C₁₉	1	1	yes	characteristic
360	#328	C₂²×C₁₉	1	2	yes	—
361	#328	C₂²×C₁₉	1	2	yes	—
362	#328	C₂²×C₁₉	1	2	yes	—
363	#327	C₂²×C₁₉	1	2	yes	—
364	#324	C₂²×C₁₉	1	2	yes	—
365	#324	C₂²×C₁₉	1	2	yes	—
366	C₂×C₁₉	—	2	1	no	—
367	C₂×C₁₉	—	2	1	no	—
368	C₂×C₁₉	—	8	1	no	—
369	C₂×C₁₉	—	16	1	no	—
370	C₂×C₁₉	#3013	1	1	yes	characteristic
371	C₂×C₁₉	#3020	1	1	yes	characteristic
372	C₂×C₁₉	#3027	1	1	yes	characteristic
373	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
374	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
375	C₂×Q₁₆	—	2	1	no	—
376	C₂×Q₁₆	—	2	2	no	—
377	C₂×SD₁₆	—	2	1	no	—
378	C₂×SD₁₆	—	2	2	no	—
379	C₂×SD₁₆	—	2	1	no	—
380	C₂×D₈	—	2	1	no	—
381	C₄⋊Q₈	—	2	1	no	—
382	C₄⋊Q₈	—	2	2	no	—
383	C₄⋊Q₈	—	2	2	no	—
384	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
385	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
386	#126	—	2	2	no	—
387	#126	—	2	2	no	—
388	#126	—	2	2	no	—
389	#126	—	2	2	no	—
390	#126	—	2	1	no	—
391	#125	—	2	2	no	—
392	#125	—	2	2	no	—
393	#125	—	2	2	no	—
394	#125	—	2	2	no	—
395	#125	—	2	1	no	—
396	#125	—	2	2	no	—
397	#125	—	2	2	no	—
398	#125	—	2	2	no	—
399	#125	—	2	2	no	—
400	#125	—	2	1	no	—
401	#125	—	2	1	no	—
402	#125	—	2	1	no	—
403	#125	—	2	1	no	—
404	#125	—	2	1	no	—
405	#125	D₄×C₁₉	1	1	yes	characteristic
406	#124	—	2	1	no	—
407	#124	—	2	1	no	—
408	#124	—	2	1	no	—
409	#124	—	2	1	no	—
410	#124	D₄×C₁₉	1	1	yes	characteristic
411	#123	—	2	2	no	—
412	#123	—	2	1	no	—
413	#123	—	2	2	no	—
414	C₂²⋊Q₈	—	2	1	no	—
415	C₂²⋊Q₈	—	2	1	no	—
416	C₂²⋊Q₈	—	2	2	no	—
417	C₂²⋊Q₈	—	2	2	no	—
418	C₂²⋊Q₈	—	2	2	no	—
419	C₂²⋊Q₈	—	2	1	no	—
420	C₂²⋊Q₈	—	2	2	no	—
421	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
422	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
423	#121	C₂³×C₁₉	1	1	yes	characteristic
424	C₄×Q₈	—	2	1	no	—
425	C₄×Q₈	—	2	2	no	—
426	C₄×Q₈	—	2	1	no	—
427	C₄×Q₈	—	2	1	no	—
428	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
429	C₄×Q₈	D₄×C₁₉	1	2	yes	—
430	C₄×D₄	—	2	1	no	—
431	C₄×D₄	—	2	2	no	—
432	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
433	#117	—	2	2	no	—
434	#117	—	2	1	no	—
435	#117	—	2	1	no	—
436	#117	—	2	2	no	—
437	#117	—	2	1	no	—
438	C₂×C₄⋊C₄	—	2	1	no	—
439	C₂×C₄⋊C₄	—	2	1	no	—
440	C₂×C₄⋊C₄	—	2	2	no	—
441	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
442	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
443	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
444	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
445	C₂×C₂²⋊C₄	—	2	1	no	—
446	C₂×C₂²⋊C₄	—	2	1	no	—
447	C₂×C₂²⋊C₄	—	2	2	no	—
448	C₂×C₂²⋊C₄	—	2	2	no	—
449	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
450	C₄⋊C₈	—	2	1	no	—
451	C₄⋊C₈	—	2	1	no	—
452	#103	—	2	1	no	—
453	#103	—	2	1	no	—
454	#103	—	2	2	no	—
455	#102	—	2	1	no	—
456	#102	—	2	1	no	—
457	#102	—	2	2	no	—
458	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
459	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
460	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
461	#97	—	2	1	no	—
462	C₄×C₈	—	2	1	no	—
463	#95	—	2	1	no	—
464	#95	—	2	2	no	—
465	#95	C₂³×C₁₉	1	2	yes	—
466	C₁₉	#18461	1	1	yes	characteristic, direct product factor, Sylow
467	C₂⁴	—	2	1	no	—
468	C₂×Q₈	—	2	2	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	—	2	1	no	—
472	C₂×Q₈	—	8	1	no	—
473	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
474	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	8	1	no	—
479	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
485	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
486	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
487	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
488	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
489	Q₁₆	—	8	1	no	—
490	Q₁₆	—	8	2	no	—
491	SD₁₆	—	8	1	no	—
492	SD₁₆	—	8	1	no	—
493	SD₁₆	—	8	2	no	—
494	D₈	—	8	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	2	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	—	2	2	no	—
505	C₄⋊C₄	—	2	2	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	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	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	2	no	—
519	C₄⋊C₄	—	2	2	no	—
520	C₄⋊C₄	—	2	2	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	2	no	—
523	C₄⋊C₄	—	8	1	no	—
524	C₄⋊C₄	—	8	2	no	—
525	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
526	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
527	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
528	C₂²⋊C₄	—	2	2	no	—
529	C₂²⋊C₄	—	2	2	no	—
530	C₂²⋊C₄	—	2	2	no	—
531	C₂²⋊C₄	—	2	2	no	—
532	C₂²⋊C₄	—	2	1	no	—
533	C₂²⋊C₄	—	2	1	no	—
534	C₂²⋊C₄	—	2	1	no	—
535	C₂²⋊C₄	—	2	1	no	—
536	C₂²⋊C₄	—	2	1	no	—
537	C₂²⋊C₄	—	4	1	no	—
538	C₂²⋊C₄	—	4	1	no	—
539	C₂²⋊C₄	—	4	1	no	—
540	C₂²⋊C₄	—	4	1	no	—
541	C₂²⋊C₄	—	8	2	no	—
542	C₂²⋊C₄	—	8	2	no	—
543	C₄²	—	2	2	no	—
544	C₄²	—	2	2	no	—
545	C₄²	—	2	2	no	—
546	C₄²	—	2	2	no	—
547	C₄²	—	2	1	no	—
548	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
549	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
550	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
551	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
552	C₂³	—	2	1	no	—
553	C₂³	—	4	2	no	—
554	C₂³	—	4	2	no	—
555	C₂³	—	4	1	no	—
556	C₂³	—	4	1	no	—
557	C₂³	—	4	1	no	—
558	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
559	Q₈	—	4	1	no	—
560	Q₈	—	4	2	no	—
561	Q₈	—	4	2	no	—
562	Q₈	—	4	1	no	—
563	Q₈	—	4	1	no	—
564	Q₈	—	4	2	no	—
565	Q₈	—	8	2	no	—
566	D₄	—	4	1	no	—
567	D₄	—	4	1	no	—
568	D₄	—	4	1	no	—
569	D₄	—	4	2	no	—
570	D₄	—	4	1	no	—
571	D₄	—	4	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	4	2	no	—
587	C₂×C₄	—	4	2	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	2	no	—
592	C₂×C₄	—	8	2	no	—
593	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
594	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
595	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
596	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
597	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
598	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
599	C₈	—	4	1	no	—
600	C₈	—	4	1	no	—
601	C₈	—	4	2	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	8	2	no	—
608	C₂²	—	8	2	no	—
609	C₂²	—	8	1	no	—
610	C₂²	—	8	1	no	—
611	C₂²	—	8	1	no	—
612	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
613	C₂²	C₁₉×#577	1	1	yes	characteristic
614	C₂²	C₁₉×#578	1	1	yes	characteristic
615	C₄	—	2	1	no	—
616	C₄	—	2	1	no	—
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	4	2	no	—
622	C₄	—	4	1	no	—
623	C₄	—	4	1	no	—
624	C₄	—	4	2	no	—
625	C₄	—	4	2	no	—
626	C₄	—	4	2	no	—
627	C₄	—	4	1	no	—
628	C₄	—	8	2	no	—
629	C₄	—	8	1	no	—
630	C₂	—	2	1	no	—
631	C₂	—	2	1	no	—
632	C₂	—	8	1	no	—
633	C₂	—	16	1	no	—
634	C₂	C₁₉×#3013	1	1	yes	characteristic
635	C₂	C₁₉×#3020	1	1	yes	characteristic
636	C₂	C₁₉×#3027	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
2. C₁₉×#3215	C₂	semidirect
4. C₁₉×#2820	C₂	semidirect
5. C₁₉×#1605	C₂	semidirect
6. C₁₉×#1603	C₂	semidirect
7. C₁₉×#1599	C₂	semidirect
9. C₁₉×#1518	C₂	semidirect
10. C₁₉×#1512	C₂	semidirect
11. C₁₉×#1470	C₂	semidirect
233. #18461	C₁₉	direct (N × H)
284. #3563	C₂×C₁₉	semidirect
285. #3215	C₂×C₁₉	semidirect
287. #2820	C₂×C₁₉	semidirect
288. #1605	C₂×C₁₉	semidirect
289. #1603	C₂×C₁₉	semidirect
290. #1599	C₂×C₁₉	semidirect
292. #1518	C₂×C₁₉	semidirect
293. #1512	C₂×C₁₉	semidirect
294. #1470	C₂×C₁₉	semidirect
466. C₁₉	#18461	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×#3215	2
C₁₉×#3211	2
C₁₉×#2820	2
C₁₉×#1605	2
C₁₉×#1603	2
C₁₉×#1599	2
C₁₉×#1597	2
C₁₉×#1518	2
C₁₉×#1512	2
C₁₉×#1470	2
#18461	19

Subgroups — C19×#18461 #18024420

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18461 #18024420