Subgroups — C₁₉×#19590 #18025549

Order 4864.

580 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3248	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3230	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3218	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2994	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1700	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1699	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1694	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1693	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1680	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1679	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1674	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1673	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1573	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1552	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₉×#332	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#533	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₁₉×#529	C₂²	1	1	yes	characteristic
19	C₁₉×#500	C₂²	1	1	yes	characteristic
20	C₁₉×#500	C₂²	1	1	yes	characteristic
21	C₁₉×#497	—	2	1	no	—
22	C₁₉×#491	—	2	1	no	—
23	C₁₉×#487	C₂²	1	1	yes	characteristic
24	C₁₉×#487	C₂²	1	1	yes	characteristic
25	C₁₉×#484	—	2	1	no	—
26	C₁₉×#484	—	2	1	no	—
27	C₁₉×#479	—	2	1	no	—
28	C₁₉×#477	—	2	1	no	—
29	C₁₉×#477	—	2	1	no	—
30	C₁₉×#475	C₂²	1	1	yes	characteristic
31	C₁₉×#474	C₂²	1	1	yes	characteristic
32	C₁₉×#467	—	2	1	no	—
33	C₁₉×#465	—	2	1	no	—
34	C₁₉×#464	—	2	1	no	—
35	C₁₉×#462	C₂²	1	1	yes	characteristic
36	C₁₉×#462	C₂²	1	1	yes	characteristic
37	C₁₉×#462	C₂²	1	1	yes	characteristic
38	C₁₉×#461	C₂²	1	1	yes	characteristic
39	C₁₉×#461	C₂²	1	1	yes	characteristic
40	C₁₉×#461	C₂²	1	1	yes	characteristic
41	C₁₉×#451	—	2	1	no	—
42	C₁₉×#448	—	2	1	no	—
43	C₁₉×#446	C₂²	1	1	yes	characteristic
44	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
45	C₁₉×#436	C₂²	1	1	yes	characteristic
46	C₁₉×#435	—	2	1	no	—
47	C₈×D₄×C₁₉	—	2	1	no	—
48	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
49	C₁₉×#433	—	2	1	no	—
50	C₁₉×#432	C₂²	1	1	yes	characteristic
51	C₁₉×#431	C₂²	1	1	yes	characteristic
52	C₁₉×#424	—	2	1	no	—
53	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
54	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
55	C₁₉×#335	C₂²	1	1	yes	characteristic
56	C₁₉×#335	C₂²	1	1	yes	characteristic
57	C₁₉×#334	C₂²	1	1	yes	characteristic
58	C₁₉×#334	C₂²	1	1	yes	characteristic
59	C₁₉×#332	C₂²	1	1	yes	characteristic
60	C₁₉×#332	C₂²	1	1	yes	characteristic
61	C₁₉×#332	C₂²	1	1	yes	characteristic
62	C₁₉×#332	C₂²	1	1	yes	characteristic
63	C₁₉×#332	C₂²	1	1	yes	characteristic
64	C₁₉×#332	C₂²	1	1	yes	characteristic
65	C₁₉×#332	C₂²	1	1	yes	characteristic
66	C₁₉×#332	C₂²	1	1	yes	characteristic
67	C₂²×Q₈×C₁₉	—	2	1	no	—
68	C₂×Q₁₆×C₁₉	—	2	1	no	—
69	C₂×Q₁₆×C₁₉	—	2	1	no	—
70	C₂×Q₁₆×C₁₉	—	2	1	no	—
71	C₂×SD₁₆×C₁₉	—	2	1	no	—
72	C₂×SD₁₆×C₁₉	—	2	1	no	—
73	C₂×SD₁₆×C₁₉	—	2	1	no	—
74	C₂×M₁₆×C₁₉	—	2	1	no	—
75	C₂²×C₈×C₁₉	—	2	1	no	—
76	C₂²×C₈×C₁₉	—	2	1	no	—
77	C₂²×C₈×C₁₉	—	2	1	no	—
78	C₁₉×C₄⋊Q₈	—	2	1	no	—
79	C₁₉×C₄⋊Q₈	—	2	1	no	—
80	C₁₉×C₄⋊Q₈	—	2	1	no	—
81	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₁₉×#126	—	2	1	no	—
86	C₁₉×#125	—	2	1	no	—
87	C₁₉×#125	D₄	1	1	yes	characteristic
88	C₁₉×#124	D₄	1	1	yes	characteristic
89	C₁₉×#123	—	2	1	no	—
90	C₁₉×C₂²⋊Q₈	—	2	1	no	—
91	C₁₉×C₂²⋊Q₈	—	2	1	no	—
92	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
93	C₁₉×#121	D₄	1	1	yes	characteristic
94	C₄×Q₈×C₁₉	—	2	1	no	—
95	C₄×Q₈×C₁₉	—	2	1	no	—
96	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
97	C₄×D₄×C₁₉	—	2	1	no	—
98	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
99	C₁₉×#117	—	2	1	no	—
100	C₁₉×#117	—	2	1	no	—
101	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
102	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
103	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
104	C₁₉×#107	—	2	1	no	—
105	C₁₉×#107	—	2	1	no	—
106	C₁₉×#107	—	2	1	no	—
107	C₁₉×#107	—	2	1	no	—
108	C₁₉×#107	—	2	1	no	—
109	C₁₉×#106	—	2	1	no	—
110	C₁₉×C₄⋊C₈	—	2	1	no	—
111	C₁₉×C₄⋊C₈	—	2	1	no	—
112	C₁₉×C₄⋊C₈	—	2	1	no	—
113	C₁₉×C₄⋊C₈	—	2	1	no	—
114	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
115	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
116	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
119	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
121	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
122	C₁₉×#103	—	2	1	no	—
123	C₁₉×#103	—	2	1	no	—
124	C₁₉×#103	—	2	1	no	—
125	C₁₉×#103	—	2	1	no	—
126	C₁₉×#103	—	2	1	no	—
127	C₁₉×#103	—	2	1	no	—
128	C₁₉×#103	—	2	1	no	—
129	C₁₉×#103	—	2	1	no	—
130	C₁₉×#103	—	2	1	no	—
131	C₁₉×#103	—	2	1	no	—
132	C₁₉×#103	—	2	1	no	—
133	C₁₉×#102	—	2	1	no	—
134	C₁₉×C₂²⋊C₈	—	2	1	no	—
135	C₁₉×C₂²⋊C₈	—	2	1	no	—
136	C₁₉×C₂²⋊C₈	—	2	1	no	—
137	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
138	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
139	C₁₉×#97	—	2	1	no	—
140	C₁₉×#97	—	2	1	no	—
141	C₄×C₈×C₁₉	—	2	1	no	—
142	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
144	C₂×Q₈×C₁₉	—	2	1	no	—
145	C₂×Q₈×C₁₉	—	2	1	no	—
146	C₂×Q₈×C₁₉	—	2	1	no	—
147	C₂×Q₈×C₁₉	—	2	1	no	—
148	C₂×Q₈×C₁₉	—	4	1	no	—
149	C₂×Q₈×C₁₉	—	8	1	no	—
150	C₂×Q₈×C₁₉	—	8	1	no	—
151	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂×D₄×C₁₉	—	2	1	no	—
153	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₉	—	2	1	no	—
155	C₂²×C₄×C₁₉	—	4	1	no	—
156	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
159	Q₁₆×C₁₉	—	8	1	no	—
160	Q₁₆×C₁₉	—	8	1	no	—
161	Q₁₆×C₁₉	—	8	1	no	—
162	SD₁₆×C₁₉	—	8	1	no	—
163	SD₁₆×C₁₉	—	8	1	no	—
164	SD₁₆×C₁₉	—	8	1	no	—
165	M₁₆×C₁₉	—	8	1	no	—
166	C₂×C₈×C₁₉	—	2	1	no	—
167	C₂×C₈×C₁₉	—	2	1	no	—
168	C₂×C₈×C₁₉	—	2	1	no	—
169	C₂×C₈×C₁₉	—	2	1	no	—
170	C₂×C₈×C₁₉	—	2	1	no	—
171	C₂×C₈×C₁₉	—	2	1	no	—
172	C₂×C₈×C₁₉	—	8	1	no	—
173	C₂×C₈×C₁₉	—	8	1	no	—
174	C₂×C₈×C₁₉	—	8	1	no	—
175	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
176	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
177	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
178	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
179	C₄⋊C₄×C₁₉	—	2	1	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	—	2	1	no	—
185	C₄⋊C₄×C₁₉	—	2	1	no	—
186	C₄⋊C₄×C₁₉	—	2	1	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	1	no	—
191	C₄⋊C₄×C₁₉	—	4	1	no	—
192	C₄⋊C₄×C₁₉	—	4	1	no	—
193	C₄⋊C₄×C₁₉	—	4	1	no	—
194	C₄⋊C₄×C₁₉	—	4	1	no	—
195	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
196	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
197	C₂²⋊C₄×C₁₉	—	2	1	no	—
198	C₂²⋊C₄×C₁₉	—	2	1	no	—
199	C₂²⋊C₄×C₁₉	—	2	1	no	—
200	C₂²⋊C₄×C₁₉	—	2	1	no	—
201	C₂²⋊C₄×C₁₉	—	2	1	no	—
202	C₂²⋊C₄×C₁₉	—	4	1	no	—
203	C₄²×C₁₉	—	2	1	no	—
204	C₄²×C₁₉	—	4	1	no	—
205	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
206	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₁₉	#41	1	1	yes	characteristic
208	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
209	#19590	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₂³×C₁₉	—	2	1	no	—
211	C₂³×C₁₉	#121	1	1	yes	characteristic
212	Q₈×C₁₉	—	2	1	no	—
213	Q₈×C₁₉	—	2	1	no	—
214	Q₈×C₁₉	—	4	1	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	—	4	1	no	—
220	Q₈×C₁₉	—	4	1	no	—
221	Q₈×C₁₉	—	4	1	no	—
222	Q₈×C₁₉	—	8	2	no	—
223	D₄×C₁₉	—	2	1	no	—
224	D₄×C₁₉	—	2	1	no	—
225	D₄×C₁₉	—	4	2	no	—
226	C₂×C₄×C₁₉	—	2	2	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	1	no	—
232	C₂×C₄×C₁₉	—	2	1	no	—
233	C₂×C₄×C₁₉	—	2	1	no	—
234	C₂×C₄×C₁₉	—	4	1	no	—
235	C₂×C₄×C₁₉	—	4	1	no	—
236	C₂×C₄×C₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	—	4	1	no	—
238	C₂×C₄×C₁₉	—	4	1	no	—
239	C₂×C₄×C₁₉	—	4	1	no	—
240	C₂×C₄×C₁₉	—	8	2	no	—
241	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
242	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
243	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
244	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
247	C₈×C₁₉	—	2	1	no	—
248	C₈×C₁₉	—	2	1	no	—
249	C₈×C₁₉	—	2	1	no	—
250	C₈×C₁₉	—	2	1	no	—
251	C₈×C₁₉	—	4	1	no	—
252	C₈×C₁₉	—	4	1	no	—
253	C₈×C₁₉	—	4	1	no	—
254	C₈×C₁₉	—	4	1	no	—
255	C₈×C₁₉	—	4	1	no	—
256	C₈×C₁₉	—	4	1	no	—
257	#3248	C₂×C₁₉	1	1	yes	characteristic
258	#3230	C₂×C₁₉	1	1	yes	characteristic, complemented
259	#3218	C₂×C₁₉	1	1	yes	characteristic
260	#2994	C₂×C₁₉	1	1	yes	characteristic
261	#1700	C₂×C₁₉	1	1	yes	characteristic, complemented
262	#1699	C₂×C₁₉	1	1	yes	characteristic, complemented
263	#1694	C₂×C₁₉	1	1	yes	characteristic, complemented
264	#1693	C₂×C₁₉	1	1	yes	characteristic, complemented
265	#1680	C₂×C₁₉	1	1	yes	characteristic, complemented
266	#1679	C₂×C₁₉	1	1	yes	characteristic, complemented
267	#1674	C₂×C₁₉	1	1	yes	characteristic, complemented
268	#1673	C₂×C₁₉	1	1	yes	characteristic, complemented
269	#1573	C₂×C₁₉	1	1	yes	characteristic, complemented
270	#1552	C₂×C₁₉	1	1	yes	characteristic, complemented
271	C₂×#332	C₂×C₁₉	1	1	yes	characteristic, complemented
272	C₂²×C₁₉	—	2	1	no	—
273	C₂²×C₁₉	—	2	1	no	—
274	C₂²×C₁₉	—	4	1	no	—
275	C₂²×C₁₉	—	4	1	no	—
276	C₂²×C₁₉	—	4	1	no	—
277	C₂²×C₁₉	#473	1	2	yes	—
278	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
279	C₄×C₁₉	—	2	1	no	—
280	C₄×C₁₉	—	2	1	no	—
281	C₄×C₁₉	—	2	1	no	—
282	C₄×C₁₉	—	2	1	no	—
283	C₄×C₁₉	—	4	1	no	—
284	C₄×C₁₉	—	4	1	no	—
285	C₄×C₁₉	—	4	1	no	—
286	C₄×C₁₉	—	8	1	no	—
287	C₄×C₁₉	—	8	1	no	—
288	C₄×C₁₉	—	8	1	no	—
289	C₄×C₁₉	—	8	1	no	—
290	C₄×C₁₉	#576	1	1	yes	characteristic
291	C₄×C₁₉	#577	1	1	yes	characteristic
292	C₄×C₁₉	#577	1	1	yes	characteristic
293	C₄×C₁₉	#578	1	1	yes	characteristic
294	#533	C₂²×C₁₉	1	1	yes	characteristic
295	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
296	#529	C₂²×C₁₉	1	1	yes	characteristic
297	#500	C₂²×C₁₉	1	1	yes	characteristic
298	#500	C₂²×C₁₉	1	1	yes	characteristic
299	#497	—	2	1	no	—
300	#491	—	2	1	no	—
301	#487	C₂²×C₁₉	1	1	yes	characteristic
302	#487	C₂²×C₁₉	1	1	yes	characteristic
303	#484	—	2	1	no	—
304	#484	—	2	1	no	—
305	#479	—	2	1	no	—
306	#477	—	2	1	no	—
307	#477	—	2	1	no	—
308	#475	C₂²×C₁₉	1	1	yes	characteristic
309	#474	C₂²×C₁₉	1	1	yes	characteristic
310	#467	—	2	1	no	—
311	#465	—	2	1	no	—
312	#464	—	2	1	no	—
313	#462	C₂²×C₁₉	1	1	yes	characteristic
314	#462	C₂²×C₁₉	1	1	yes	characteristic
315	#462	C₂²×C₁₉	1	1	yes	characteristic
316	#461	C₂²×C₁₉	1	1	yes	characteristic
317	#461	C₂²×C₁₉	1	1	yes	characteristic
318	#461	C₂²×C₁₉	1	1	yes	characteristic
319	#451	—	2	1	no	—
320	#448	—	2	1	no	—
321	#446	C₂²×C₁₉	1	1	yes	characteristic
322	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
323	#436	C₂²×C₁₉	1	1	yes	characteristic
324	#435	—	2	1	no	—
325	C₈×D₄	—	2	1	no	—
326	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
327	#433	—	2	1	no	—
328	#432	C₂²×C₁₉	1	1	yes	characteristic
329	#431	C₂²×C₁₉	1	1	yes	characteristic
330	#424	—	2	1	no	—
331	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
332	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
333	#335	C₂²×C₁₉	1	1	yes	characteristic
334	#335	C₂²×C₁₉	1	1	yes	characteristic
335	#334	C₂²×C₁₉	1	1	yes	characteristic
336	#334	C₂²×C₁₉	1	1	yes	characteristic
337	#332	C₂²×C₁₉	1	1	yes	characteristic
338	#332	C₂²×C₁₉	1	1	yes	characteristic
339	#332	C₂²×C₁₉	1	1	yes	characteristic
340	#332	C₂²×C₁₉	1	1	yes	characteristic
341	#332	C₂²×C₁₉	1	1	yes	characteristic
342	#332	C₂²×C₁₉	1	1	yes	characteristic
343	#332	C₂²×C₁₉	1	1	yes	characteristic
344	#332	C₂²×C₁₉	1	1	yes	characteristic
345	C₂×C₁₉	—	2	2	no	—
346	C₂×C₁₉	—	8	1	no	—
347	C₂×C₁₉	#3046	1	1	yes	characteristic
348	C₂×C₁₉	#3062	1	1	yes	characteristic
349	C₂×C₁₉	C₂×#473	1	1	yes	characteristic
350	C₂²×Q₈	—	2	1	no	—
351	C₂×Q₁₆	—	2	1	no	—
352	C₂×Q₁₆	—	2	1	no	—
353	C₂×Q₁₆	—	2	1	no	—
354	C₂×SD₁₆	—	2	1	no	—
355	C₂×SD₁₆	—	2	1	no	—
356	C₂×SD₁₆	—	2	1	no	—
357	C₂×M₁₆	—	2	1	no	—
358	C₂²×C₈	—	2	1	no	—
359	C₂²×C₈	—	2	1	no	—
360	C₂²×C₈	—	2	1	no	—
361	C₄⋊Q₈	—	2	1	no	—
362	C₄⋊Q₈	—	2	1	no	—
363	C₄⋊Q₈	—	2	1	no	—
364	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
365	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
366	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
367	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
368	#126	—	2	1	no	—
369	#125	—	2	1	no	—
370	#125	D₄×C₁₉	1	1	yes	characteristic
371	#124	D₄×C₁₉	1	1	yes	characteristic
372	#123	—	2	1	no	—
373	C₂²⋊Q₈	—	2	1	no	—
374	C₂²⋊Q₈	—	2	1	no	—
375	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
376	#121	D₄×C₁₉	1	1	yes	characteristic
377	C₄×Q₈	—	2	1	no	—
378	C₄×Q₈	—	2	1	no	—
379	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
380	C₄×D₄	—	2	1	no	—
381	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
382	#117	—	2	1	no	—
383	#117	—	2	1	no	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
387	#107	—	2	1	no	—
388	#107	—	2	1	no	—
389	#107	—	2	1	no	—
390	#107	—	2	1	no	—
391	#107	—	2	1	no	—
392	#106	—	2	1	no	—
393	C₄⋊C₈	—	2	1	no	—
394	C₄⋊C₈	—	2	1	no	—
395	C₄⋊C₈	—	2	1	no	—
396	C₄⋊C₈	—	2	1	no	—
397	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
398	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
399	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
400	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
401	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
402	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
403	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
404	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
405	#103	—	2	1	no	—
406	#103	—	2	1	no	—
407	#103	—	2	1	no	—
408	#103	—	2	1	no	—
409	#103	—	2	1	no	—
410	#103	—	2	1	no	—
411	#103	—	2	1	no	—
412	#103	—	2	1	no	—
413	#103	—	2	1	no	—
414	#103	—	2	1	no	—
415	#103	—	2	1	no	—
416	#102	—	2	1	no	—
417	C₂²⋊C₈	—	2	1	no	—
418	C₂²⋊C₈	—	2	1	no	—
419	C₂²⋊C₈	—	2	1	no	—
420	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
421	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
422	#97	—	2	1	no	—
423	#97	—	2	1	no	—
424	C₄×C₈	—	2	1	no	—
425	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
426	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
427	C₁₉	#19590	1	1	yes	characteristic, direct product factor, Sylow
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	4	1	no	—
433	C₂×Q₈	—	8	1	no	—
434	C₂×Q₈	—	8	1	no	—
435	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	4	1	no	—
440	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
441	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
442	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
443	Q₁₆	—	8	1	no	—
444	Q₁₆	—	8	1	no	—
445	Q₁₆	—	8	1	no	—
446	SD₁₆	—	8	1	no	—
447	SD₁₆	—	8	1	no	—
448	SD₁₆	—	8	1	no	—
449	M₁₆	—	8	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	8	1	no	—
457	C₂×C₈	—	8	1	no	—
458	C₂×C₈	—	8	1	no	—
459	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
460	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
461	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
462	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	4	1	no	—
476	C₄⋊C₄	—	4	1	no	—
477	C₄⋊C₄	—	4	1	no	—
478	C₄⋊C₄	—	4	1	no	—
479	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
480	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
481	C₂²⋊C₄	—	2	1	no	—
482	C₂²⋊C₄	—	2	1	no	—
483	C₂²⋊C₄	—	2	1	no	—
484	C₂²⋊C₄	—	2	1	no	—
485	C₂²⋊C₄	—	2	1	no	—
486	C₂²⋊C₄	—	4	1	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	4	1	no	—
489	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
490	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
491	C₄²	#41×C₁₉	1	1	yes	characteristic
492	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
493	C₂³	—	2	1	no	—
494	C₂³	C₁₉×#121	1	1	yes	characteristic
495	Q₈	—	2	1	no	—
496	Q₈	—	2	1	no	—
497	Q₈	—	4	1	no	—
498	Q₈	—	4	1	no	—
499	Q₈	—	4	1	no	—
500	Q₈	—	4	1	no	—
501	Q₈	—	4	1	no	—
502	Q₈	—	4	1	no	—
503	Q₈	—	4	1	no	—
504	Q₈	—	4	1	no	—
505	Q₈	—	8	2	no	—
506	D₄	—	2	1	no	—
507	D₄	—	2	1	no	—
508	D₄	—	4	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	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	C₁₉×#121	1	1	yes	characteristic
525	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
526	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
527	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
528	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
529	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
530	C₈	—	2	1	no	—
531	C₈	—	2	1	no	—
532	C₈	—	2	1	no	—
533	C₈	—	2	1	no	—
534	C₈	—	4	1	no	—
535	C₈	—	4	1	no	—
536	C₈	—	4	1	no	—
537	C₈	—	4	1	no	—
538	C₈	—	4	1	no	—
539	C₈	—	4	1	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	4	1	no	—
544	C₂²	—	4	1	no	—
545	C₂²	C₁₉×#473	1	2	yes	—
546	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	1	no	—
554	C₄	—	8	1	no	—
555	C₄	—	8	1	no	—
556	C₄	—	8	1	no	—
557	C₄	—	8	1	no	—
558	C₄	C₁₉×#576	1	1	yes	characteristic
559	C₄	C₁₉×#577	1	1	yes	characteristic
560	C₄	C₁₉×#577	1	1	yes	characteristic
561	C₄	C₁₉×#578	1	1	yes	characteristic
562	C₂	—	2	2	no	—
563	C₂	—	8	1	no	—
564	C₂	C₁₉×#3046	1	1	yes	characteristic
565	C₂	C₁₉×#3062	1	1	yes	characteristic
566	C₂	C₂×C₁₉×#473	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#121	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×#3230	C₂	semidirect
5. C₁₉×#1700	C₂	semidirect
6. C₁₉×#1699	C₂	semidirect
7. C₁₉×#1694	C₂	semidirect
8. C₁₉×#1693	C₂	semidirect
9. C₁₉×#1680	C₂	semidirect
10. C₁₉×#1679	C₂	semidirect
11. C₁₉×#1674	C₂	semidirect
12. C₁₉×#1673	C₂	semidirect
13. C₁₉×#1573	C₂	semidirect
14. C₁₉×#1552	C₂	semidirect
15. C₂×C₁₉×#332	C₂	semidirect
209. #19590	C₁₉	direct (N × H)
258. #3230	C₂×C₁₉	semidirect
261. #1700	C₂×C₁₉	semidirect
262. #1699	C₂×C₁₉	semidirect
263. #1694	C₂×C₁₉	semidirect
264. #1693	C₂×C₁₉	semidirect
265. #1680	C₂×C₁₉	semidirect
266. #1679	C₂×C₁₉	semidirect
267. #1674	C₂×C₁₉	semidirect
268. #1673	C₂×C₁₉	semidirect
269. #1573	C₂×C₁₉	semidirect
270. #1552	C₂×C₁₉	semidirect
271. C₂×#332	C₂×C₁₉	semidirect
427. C₁₉	#19590	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×#3248	2
C₁₉×#3230	2
C₁₉×#3218	2
C₁₉×#2994	2
C₁₉×#1700	2
C₁₉×#1699	2
C₁₉×#1694	2
C₁₉×#1693	2
C₁₉×#1680	2
C₁₉×#1679	2
C₁₉×#1674	2
C₁₉×#1673	2
C₁₉×#1573	2
C₁₉×#1552	2
C₂×C₁₉×#332	2
#19590	19

Subgroups — C19×#19590 #18025549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19590 #18025549