Subgroups — C₁₉×#18591 #18024550

Order 4864.

894 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3503	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3255	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3165	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3107	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1653	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1651	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1649	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1648	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1546	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1489	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1485	C₂	1	1	yes	maximal, characteristic, complemented
12	Q₈²×C₁₉	—	2	1	no	—
13	C₁₉×#557	C₂²	1	2	yes	—
14	C₁₉×#554	—	2	1	no	—
15	C₁₉×#554	—	2	2	no	—
16	D₄×Q₈×C₁₉	—	2	2	no	—
17	D₄×Q₈×C₁₉	C₂²	1	2	yes	—
18	C₁₉×#544	—	2	2	no	—
19	C₁₉×#544	—	2	1	no	—
20	C₁₉×#533	—	2	1	no	—
21	C₁₉×#533	C₂²	1	1	yes	characteristic
22	C₁₉×#533	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
24	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₁₉×#520	—	2	1	no	—
26	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#501	—	2	2	no	—
28	C₁₉×#500	C₂²	1	2	yes	—
29	C₁₉×#498	C₂²	1	2	yes	—
30	C₁₉×#485	—	2	1	no	—
31	C₁₉×#475	—	2	1	no	—
32	C₁₉×#475	C₂²	1	1	yes	characteristic
33	C₁₉×#475	C₂²	1	2	yes	—
34	C₁₉×#474	C₂²	1	1	yes	characteristic
35	C₁₉×#470	—	2	2	no	—
36	C₁₉×#462	—	2	1	no	—
37	C₁₉×#462	C₂²	1	2	yes	—
38	C₁₉×#462	C₂²	1	1	yes	characteristic
39	C₁₉×#461	C₂²	1	1	yes	characteristic
40	C₁₉×#452	—	2	1	no	—
41	C₄×Q₁₆×C₁₉	—	2	1	no	—
42	C₄×SD₁₆×C₁₉	—	2	1	no	—
43	C₁₉×#431	C₂²	1	1	yes	characteristic
44	C₁₉×#428	—	2	2	no	—
45	C₁₉×#423	C₂²	1	1	yes	characteristic
46	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
47	C₁₉×#332	C₂²	1	2	yes	—
48	C₁₉×#332	C₂²	1	2	yes	—
49	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
50	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
51	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
52	C₁₉×D₄⋊C₈	C₂²	1	2	yes	—
53	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
54	C₂²×Q₈×C₁₉	—	2	2	no	—
55	C₂²×Q₈×C₁₉	—	2	1	no	—
56	C₂×Q₁₆×C₁₉	—	2	1	no	—
57	C₂×Q₁₆×C₁₉	—	2	2	no	—
58	C₂×SD₁₆×C₁₉	—	2	1	no	—
59	C₂×M₁₆×C₁₉	—	2	1	no	—
60	C₂×M₁₆×C₁₉	—	2	1	no	—
61	C₁₉×C₄⋊Q₈	—	2	2	no	—
62	C₁₉×C₄⋊Q₈	—	2	2	no	—
63	C₁₉×C₄⋊Q₈	—	2	4	no	—
64	C₁₉×C₄⋊Q₈	—	2	2	no	—
65	C₁₉×C₄⋊Q₈	—	2	2	no	—
66	C₁₉×C₄⋊Q₈	—	2	1	no	—
67	C₁₉×C₄⋊Q₈	—	2	1	no	—
68	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
69	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
70	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
71	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
72	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
73	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
74	C₁₉×#125	—	2	2	no	—
75	C₁₉×#125	—	2	4	no	—
76	C₁₉×#125	—	2	2	no	—
77	C₁₉×#125	—	2	1	no	—
78	C₁₉×#125	—	2	1	no	—
79	C₁₉×C₂²⋊Q₈	—	2	2	no	—
80	C₁₉×C₂²⋊Q₈	—	2	4	no	—
81	C₁₉×C₂²⋊Q₈	—	2	4	no	—
82	C₁₉×C₂²⋊Q₈	—	2	1	no	—
83	C₁₉×C₂²⋊Q₈	—	2	2	no	—
84	C₁₉×C₂²⋊Q₈	—	2	4	no	—
85	C₁₉×C₂²⋊Q₈	—	2	1	no	—
86	C₁₉×C₂²⋊Q₈	—	2	1	no	—
87	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
88	C₄×Q₈×C₁₉	—	2	2	no	—
89	C₄×Q₈×C₁₉	—	2	2	no	—
90	C₄×Q₈×C₁₉	—	2	2	no	—
91	C₄×Q₈×C₁₉	—	2	1	no	—
92	C₄×Q₈×C₁₉	—	2	1	no	—
93	C₄×Q₈×C₁₉	—	2	1	no	—
94	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
95	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
96	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
97	C₄×D₄×C₁₉	—	2	4	no	—
98	C₄×D₄×C₁₉	—	2	2	no	—
99	C₄×D₄×C₁₉	—	2	1	no	—
100	C₄×D₄×C₁₉	—	2	1	no	—
101	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
102	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
103	C₁₉×#117	—	2	2	no	—
104	C₁₉×#117	—	2	1	no	—
105	C₁₉×#117	—	2	1	no	—
106	C₁₉×#117	—	2	1	no	—
107	C₁₉×#117	D₄	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
109	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
110	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
111	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
112	C₂×C₄²×C₁₉	—	2	1	no	—
113	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
114	C₁₉×#107	—	2	4	no	—
115	C₁₉×#107	—	2	1	no	—
116	C₁₉×#106	—	2	4	no	—
117	C₁₉×#106	—	2	1	no	—
118	C₁₉×#106	—	2	2	no	—
119	C₁₉×C₄⋊C₈	—	2	1	no	—
120	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
121	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
122	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
123	C₁₉×#103	—	2	1	no	—
124	C₁₉×#103	—	2	2	no	—
125	C₁₉×#103	—	2	1	no	—
126	C₁₉×#103	—	2	1	no	—
127	C₁₉×#103	—	2	2	no	—
128	C₁₉×#102	—	2	1	no	—
129	C₁₉×C₂²⋊C₈	—	2	1	no	—
130	C₁₉×#97	—	2	1	no	—
131	C₄×C₈×C₁₉	—	2	1	no	—
132	C₄×C₈×C₁₉	C₂³	1	2	yes	—
133	#41×C₁₉	—	2	2	no	—
134	#41×C₁₉	—	2	2	no	—
135	C₂×Q₈×C₁₉	—	2	4	no	—
136	C₂×Q₈×C₁₉	—	2	1	no	—
137	C₂×Q₈×C₁₉	—	2	2	no	—
138	C₂×Q₈×C₁₉	—	2	2	no	—
139	C₂×Q₈×C₁₉	—	2	1	no	—
140	C₂×Q₈×C₁₉	—	2	1	no	—
141	C₂×Q₈×C₁₉	—	8	1	no	—
142	C₂×Q₈×C₁₉	—	8	1	no	—
143	C₂×Q₈×C₁₉	—	8	2	no	—
144	C₂×Q₈×C₁₉	—	8	2	no	—
145	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
146	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₂×D₄×C₁₉	—	2	1	no	—
148	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₉	—	2	1	no	—
150	C₂²×C₄×C₁₉	—	2	4	no	—
151	C₂²×C₄×C₁₉	—	2	2	no	—
152	C₂²×C₄×C₁₉	—	2	1	no	—
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
157	Q₁₆×C₁₉	—	4	2	no	—
158	Q₁₆×C₁₉	—	8	2	no	—
159	SD₁₆×C₁₉	—	4	2	no	—
160	M₁₆×C₁₉	—	2	4	no	—
161	M₁₆×C₁₉	—	8	1	no	—
162	C₂×C₈×C₁₉	—	2	2	no	—
163	C₂×C₈×C₁₉	—	2	2	no	—
164	C₂×C₈×C₁₉	—	2	1	no	—
165	C₂×C₈×C₁₉	—	2	1	no	—
166	C₄⋊C₄×C₁₉	—	2	4	no	—
167	C₄⋊C₄×C₁₉	—	2	4	no	—
168	C₄⋊C₄×C₁₉	—	2	4	no	—
169	C₄⋊C₄×C₁₉	—	2	4	no	—
170	C₄⋊C₄×C₁₉	—	2	1	no	—
171	C₄⋊C₄×C₁₉	—	2	2	no	—
172	C₄⋊C₄×C₁₉	—	2	1	no	—
173	C₄⋊C₄×C₁₉	—	2	2	no	—
174	C₄⋊C₄×C₁₉	—	2	1	no	—
175	C₄⋊C₄×C₁₉	—	2	1	no	—
176	C₄⋊C₄×C₁₉	—	2	2	no	—
177	C₄⋊C₄×C₁₉	—	2	2	no	—
178	C₄⋊C₄×C₁₉	—	2	1	no	—
179	C₄⋊C₄×C₁₉	—	2	2	no	—
180	C₄⋊C₄×C₁₉	—	2	1	no	—
181	C₄⋊C₄×C₁₉	—	2	1	no	—
182	C₄⋊C₄×C₁₉	—	2	1	no	—
183	C₄⋊C₄×C₁₉	—	2	1	no	—
184	C₄⋊C₄×C₁₉	—	4	1	no	—
185	C₄⋊C₄×C₁₉	—	4	1	no	—
186	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
187	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
188	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
190	C₂²⋊C₄×C₁₉	—	2	4	no	—
191	C₂²⋊C₄×C₁₉	—	2	2	no	—
192	C₂²⋊C₄×C₁₉	—	2	1	no	—
193	C₂²⋊C₄×C₁₉	—	2	1	no	—
194	C₂²⋊C₄×C₁₉	—	2	1	no	—
195	C₂²⋊C₄×C₁₉	—	4	1	no	—
196	C₄²×C₁₉	—	2	4	no	—
197	C₄²×C₁₉	—	2	1	no	—
198	C₄²×C₁₉	—	2	1	no	—
199	C₄²×C₁₉	—	2	1	no	—
200	C₄²×C₁₉	—	2	2	no	—
201	C₄²×C₁₉	—	4	1	no	—
202	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
204	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
205	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
206	#18591	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂³×C₁₉	—	2	1	no	—
208	C₂³×C₁₉	#120	1	1	yes	characteristic
209	Q₈×C₁₉	—	2	1	no	—
210	Q₈×C₁₉	—	2	2	no	—
211	Q₈×C₁₉	—	2	2	no	—
212	Q₈×C₁₉	—	4	2	no	—
213	Q₈×C₁₉	—	4	2	no	—
214	Q₈×C₁₉	—	4	2	no	—
215	Q₈×C₁₉	—	4	1	no	—
216	Q₈×C₁₉	—	4	1	no	—
217	Q₈×C₁₉	—	4	1	no	—
218	Q₈×C₁₉	—	4	1	no	—
219	Q₈×C₁₉	—	8	2	no	—
220	Q₈×C₁₉	—	8	4	no	—
221	Q₈×C₁₉	#137	1	2	yes	—
222	D₄×C₁₉	—	2	4	no	—
223	D₄×C₁₉	—	2	1	no	—
224	D₄×C₁₉	#137	1	2	yes	—
225	C₂×C₄×C₁₉	—	2	4	no	—
226	C₂×C₄×C₁₉	—	2	1	no	—
227	C₂×C₄×C₁₉	—	2	1	no	—
228	C₂×C₄×C₁₉	—	2	1	no	—
229	C₂×C₄×C₁₉	—	2	1	no	—
230	C₂×C₄×C₁₉	—	2	1	no	—
231	C₂×C₄×C₁₉	—	2	2	no	—
232	C₂×C₄×C₁₉	—	2	2	no	—
233	C₂×C₄×C₁₉	—	2	1	no	—
234	C₂×C₄×C₁₉	—	2	1	no	—
235	C₂×C₄×C₁₉	—	2	2	no	—
236	C₂×C₄×C₁₉	—	2	4	no	—
237	C₂×C₄×C₁₉	—	4	1	no	—
238	C₂×C₄×C₁₉	—	4	1	no	—
239	C₂×C₄×C₁₉	—	4	2	no	—
240	C₂×C₄×C₁₉	—	4	1	no	—
241	C₂×C₄×C₁₉	—	4	1	no	—
242	C₂×C₄×C₁₉	—	8	2	no	—
243	C₂×C₄×C₁₉	—	8	4	no	—
244	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
245	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
246	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
247	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
250	C₈×C₁₉	—	2	4	no	—
251	C₈×C₁₉	—	4	1	no	—
252	C₈×C₁₉	—	4	1	no	—
253	C₈×C₁₉	—	4	2	no	—
254	#3503	C₂×C₁₉	1	1	yes	characteristic
255	#3255	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#3165	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#3107	C₂×C₁₉	1	1	yes	characteristic
258	#1653	C₂×C₁₉	1	2	yes	complemented
259	#1651	C₂×C₁₉	1	2	yes	complemented
260	#1649	C₂×C₁₉	1	2	yes	complemented
261	#1648	C₂×C₁₉	1	2	yes	complemented
262	#1546	C₂×C₁₉	1	1	yes	characteristic, complemented
263	#1489	C₂×C₁₉	1	1	yes	characteristic
264	#1485	C₂×C₁₉	1	1	yes	characteristic, complemented
265	C₂²×C₁₉	—	2	1	no	—
266	C₂²×C₁₉	—	2	2	no	—
267	C₂²×C₁₉	—	2	1	no	—
268	C₂²×C₁₉	—	2	1	no	—
269	C₂²×C₁₉	—	4	1	no	—
270	C₂²×C₁₉	—	4	1	no	—
271	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
272	C₄×C₁₉	—	2	1	no	—
273	C₄×C₁₉	—	2	2	no	—
274	C₄×C₁₉	—	2	1	no	—
275	C₄×C₁₉	—	2	1	no	—
276	C₄×C₁₉	—	4	1	no	—
277	C₄×C₁₉	—	4	2	no	—
278	C₄×C₁₉	—	4	4	no	—
279	C₄×C₁₉	—	4	1	no	—
280	C₄×C₁₉	—	4	2	no	—
281	C₄×C₁₉	—	8	1	no	—
282	C₄×C₁₉	—	8	1	no	—
283	C₄×C₁₉	#456	1	2	yes	—
284	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
285	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
286	C₄×C₁₉	#576	1	1	yes	characteristic
287	C₄×C₁₉	#577	1	1	yes	characteristic
288	Q₈²	—	2	1	no	—
289	#557	C₂²×C₁₉	1	2	yes	—
290	#554	—	2	1	no	—
291	#554	—	2	2	no	—
292	D₄×Q₈	—	2	2	no	—
293	D₄×Q₈	C₂²×C₁₉	1	2	yes	—
294	#544	—	2	2	no	—
295	#544	—	2	1	no	—
296	#533	—	2	1	no	—
297	#533	C₂²×C₁₉	1	1	yes	characteristic
298	#533	C₂²×C₁₉	1	1	yes	characteristic
299	C₂×C₄⋊Q₈	—	2	1	no	—
300	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
301	#520	—	2	1	no	—
302	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
303	#501	—	2	2	no	—
304	#500	C₂²×C₁₉	1	2	yes	—
305	#498	C₂²×C₁₉	1	2	yes	—
306	#485	—	2	1	no	—
307	#475	—	2	1	no	—
308	#475	C₂²×C₁₉	1	1	yes	characteristic
309	#475	C₂²×C₁₉	1	2	yes	—
310	#474	C₂²×C₁₉	1	1	yes	characteristic
311	#470	—	2	2	no	—
312	#462	—	2	1	no	—
313	#462	C₂²×C₁₉	1	1	yes	characteristic
314	#462	C₂²×C₁₉	1	2	yes	—
315	#461	C₂²×C₁₉	1	1	yes	characteristic
316	#452	—	2	1	no	—
317	C₄×Q₁₆	—	2	1	no	—
318	C₄×SD₁₆	—	2	1	no	—
319	#431	C₂²×C₁₉	1	1	yes	characteristic
320	#428	—	2	2	no	—
321	#423	C₂²×C₁₉	1	1	yes	characteristic
322	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
323	#332	C₂²×C₁₉	1	2	yes	—
324	#332	C₂²×C₁₉	1	2	yes	—
325	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
326	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
327	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
328	D₄⋊C₈	C₂²×C₁₉	1	2	yes	—
329	C₂×C₁₉	—	4	1	no	—
330	C₂×C₁₉	—	4	2	no	—
331	C₂×C₁₉	#3004	1	1	yes	characteristic
332	C₂×C₁₉	#3012	1	1	yes	characteristic
333	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
334	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
335	C₂²×Q₈	—	2	2	no	—
336	C₂²×Q₈	—	2	1	no	—
337	C₂×Q₁₆	—	2	1	no	—
338	C₂×Q₁₆	—	2	2	no	—
339	C₂×SD₁₆	—	2	1	no	—
340	C₂×M₁₆	—	2	1	no	—
341	C₂×M₁₆	—	2	1	no	—
342	C₄⋊Q₈	—	2	2	no	—
343	C₄⋊Q₈	—	2	2	no	—
344	C₄⋊Q₈	—	2	4	no	—
345	C₄⋊Q₈	—	2	2	no	—
346	C₄⋊Q₈	—	2	2	no	—
347	C₄⋊Q₈	—	2	1	no	—
348	C₄⋊Q₈	—	2	1	no	—
349	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
350	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
351	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
352	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
353	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
354	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
355	#125	—	2	2	no	—
356	#125	—	2	4	no	—
357	#125	—	2	2	no	—
358	#125	—	2	1	no	—
359	#125	—	2	1	no	—
360	C₂²⋊Q₈	—	2	2	no	—
361	C₂²⋊Q₈	—	2	4	no	—
362	C₂²⋊Q₈	—	2	4	no	—
363	C₂²⋊Q₈	—	2	1	no	—
364	C₂²⋊Q₈	—	2	2	no	—
365	C₂²⋊Q₈	—	2	4	no	—
366	C₂²⋊Q₈	—	2	1	no	—
367	C₂²⋊Q₈	—	2	1	no	—
368	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
369	C₄×Q₈	—	2	2	no	—
370	C₄×Q₈	—	2	2	no	—
371	C₄×Q₈	—	2	2	no	—
372	C₄×Q₈	—	2	1	no	—
373	C₄×Q₈	—	2	1	no	—
374	C₄×Q₈	—	2	1	no	—
375	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
376	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
377	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
378	C₄×D₄	—	2	4	no	—
379	C₄×D₄	—	2	2	no	—
380	C₄×D₄	—	2	1	no	—
381	C₄×D₄	—	2	1	no	—
382	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
383	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
384	#117	—	2	2	no	—
385	#117	—	2	1	no	—
386	#117	—	2	1	no	—
387	#117	—	2	1	no	—
388	#117	D₄×C₁₉	1	1	yes	characteristic
389	C₂×C₄⋊C₄	—	2	2	no	—
390	C₂×C₄⋊C₄	—	2	2	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
393	C₂×C₄²	—	2	1	no	—
394	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
395	#107	—	2	4	no	—
396	#107	—	2	1	no	—
397	#106	—	2	4	no	—
398	#106	—	2	1	no	—
399	#106	—	2	2	no	—
400	C₄⋊C₈	—	2	1	no	—
401	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
402	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
403	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
404	#103	—	2	1	no	—
405	#103	—	2	2	no	—
406	#103	—	2	1	no	—
407	#103	—	2	1	no	—
408	#103	—	2	2	no	—
409	#102	—	2	1	no	—
410	C₂²⋊C₈	—	2	1	no	—
411	#97	—	2	1	no	—
412	C₄×C₈	—	2	1	no	—
413	C₄×C₈	C₂³×C₁₉	1	2	yes	—
414	C₁₉	#18591	1	1	yes	characteristic, direct product factor, Sylow
415	#41	—	2	2	no	—
416	#41	—	2	2	no	—
417	C₂×Q₈	—	2	4	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	2	no	—
420	C₂×Q₈	—	2	2	no	—
421	C₂×Q₈	—	2	1	no	—
422	C₂×Q₈	—	2	1	no	—
423	C₂×Q₈	—	8	1	no	—
424	C₂×Q₈	—	8	1	no	—
425	C₂×Q₈	—	8	2	no	—
426	C₂×Q₈	—	8	2	no	—
427	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
428	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	4	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
439	Q₁₆	—	4	2	no	—
440	Q₁₆	—	8	2	no	—
441	SD₁₆	—	4	2	no	—
442	M₁₆	—	2	4	no	—
443	M₁₆	—	8	1	no	—
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	2	no	—
448	C₄⋊C₄	—	2	4	no	—
449	C₄⋊C₄	—	2	4	no	—
450	C₄⋊C₄	—	2	4	no	—
451	C₄⋊C₄	—	2	4	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	4	1	no	—
467	C₄⋊C₄	—	4	1	no	—
468	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
469	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
470	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
471	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
472	C₂²⋊C₄	—	2	4	no	—
473	C₂²⋊C₄	—	2	2	no	—
474	C₂²⋊C₄	—	2	1	no	—
475	C₂²⋊C₄	—	2	1	no	—
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	4	1	no	—
478	C₄²	—	2	4	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	2	2	no	—
483	C₄²	—	4	1	no	—
484	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
485	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
486	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
487	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
488	C₂³	—	2	1	no	—
489	C₂³	C₁₉×#120	1	1	yes	characteristic
490	Q₈	—	2	1	no	—
491	Q₈	—	2	2	no	—
492	Q₈	—	2	2	no	—
493	Q₈	—	4	2	no	—
494	Q₈	—	4	2	no	—
495	Q₈	—	4	2	no	—
496	Q₈	—	4	1	no	—
497	Q₈	—	4	1	no	—
498	Q₈	—	4	1	no	—
499	Q₈	—	4	1	no	—
500	Q₈	—	8	2	no	—
501	Q₈	—	8	4	no	—
502	Q₈	C₁₉×#137	1	2	yes	—
503	D₄	—	2	4	no	—
504	D₄	—	2	1	no	—
505	D₄	C₁₉×#137	1	2	yes	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	8	2	no	—
524	C₂×C₄	—	8	4	no	—
525	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
526	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
527	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
528	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
529	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
530	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
531	C₈	—	2	4	no	—
532	C₈	—	4	1	no	—
533	C₈	—	4	1	no	—
534	C₈	—	4	2	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	2	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	4	1	no	—
540	C₂²	—	4	1	no	—
541	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
542	C₄	—	2	1	no	—
543	C₄	—	2	2	no	—
544	C₄	—	2	1	no	—
545	C₄	—	2	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	2	no	—
548	C₄	—	4	4	no	—
549	C₄	—	4	1	no	—
550	C₄	—	4	2	no	—
551	C₄	—	8	1	no	—
552	C₄	—	8	1	no	—
553	C₄	C₁₉×#456	1	2	yes	—
554	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
555	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
556	C₄	C₁₉×#576	1	1	yes	characteristic
557	C₄	C₁₉×#577	1	1	yes	characteristic
558	C₂	—	4	1	no	—
559	C₂	—	4	2	no	—
560	C₂	C₁₉×#3004	1	1	yes	characteristic
561	C₂	C₁₉×#3012	1	1	yes	characteristic
562	C₂	C₂×C₁₉×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂×#41×C₁₉	D₄
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×#3255	C₂	semidirect
3. C₁₉×#3165	C₂	semidirect
5. C₁₉×#1653	C₂	semidirect
6. C₁₉×#1651	C₂	semidirect
7. C₁₉×#1649	C₂	semidirect
8. C₁₉×#1648	C₂	semidirect
9. C₁₉×#1546	C₂	semidirect
11. C₁₉×#1485	C₂	semidirect
206. #18591	C₁₉	direct (N × H)
255. #3255	C₂×C₁₉	semidirect
256. #3165	C₂×C₁₉	semidirect
258. #1653	C₂×C₁₉	semidirect
259. #1651	C₂×C₁₉	semidirect
260. #1649	C₂×C₁₉	semidirect
261. #1648	C₂×C₁₉	semidirect
262. #1546	C₂×C₁₉	semidirect
264. #1485	C₂×C₁₉	semidirect
414. C₁₉	#18591	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×#3503	2
C₁₉×#3255	2
C₁₉×#3165	2
C₁₉×#3107	2
C₁₉×#1653	2
C₁₉×#1651	2
C₁₉×#1649	2
C₁₉×#1648	2
C₁₉×#1546	2
C₁₉×#1489	2
C₁₉×#1485	2
#18591	19

Subgroups — C19×#18591 #18024550

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18591 #18024550