Subgroups — C₁₉×#19545 #18025504

Order 4864.

564 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3233	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3229	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3218	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2993	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×#1692	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1691	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×#1672	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1671	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1572	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1559	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1549	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×#499	—	2	1	no	—
20	C₁₉×#498	C₂²	1	1	yes	characteristic
21	C₁₉×#498	C₂²	1	1	yes	characteristic
22	C₁₉×#497	—	2	1	no	—
23	C₁₉×#491	—	2	1	no	—
24	C₁₉×#488	—	2	1	no	—
25	C₁₉×#487	C₂²	1	1	yes	characteristic
26	C₁₉×#487	C₂²	1	1	yes	characteristic
27	C₁₉×#485	—	2	1	no	—
28	C₁₉×#483	—	2	1	no	—
29	C₁₉×#483	—	2	1	no	—
30	C₁₉×#482	—	2	1	no	—
31	C₁₉×#477	C₂²	1	1	yes	characteristic
32	C₁₉×#476	C₂²	1	1	yes	characteristic
33	C₁₉×#475	—	2	1	no	—
34	C₁₉×#475	—	2	1	no	—
35	C₁₉×#475	C₂²	1	1	yes	characteristic
36	C₁₉×#474	C₂²	1	1	yes	characteristic
37	C₁₉×#462	C₂²	1	1	yes	characteristic
38	C₁₉×#462	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	—	2	1	no	—
46	C₁₉×#436	C₂²	1	1	yes	characteristic
47	C₁₉×#435	—	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×#431	C₂²	1	1	yes	characteristic
53	C₁₉×#424	—	2	1	no	—
54	C₁₉×#423	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×#333	C₂²	1	1	yes	characteristic
60	C₁₉×#333	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×SD₁₆×C₁₉	—	2	1	no	—
71	C₂×SD₁₆×C₁₉	—	2	1	no	—
72	C₂×M₁₆×C₁₉	—	2	1	no	—
73	C₂×M₁₆×C₁₉	—	2	1	no	—
74	C₂²×C₈×C₁₉	—	2	1	no	—
75	C₁₉×C₄⋊Q₈	—	2	1	no	—
76	C₁₉×C₄⋊Q₈	—	2	1	no	—
77	C₁₉×C₄⋊Q₈	—	2	1	no	—
78	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
79	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
80	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
81	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₁₉×#126	—	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	1	no	—
87	C₁₉×C₂²⋊Q₈	—	2	1	no	—
88	C₁₉×C₂²⋊Q₈	—	2	1	no	—
89	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
90	C₁₉×#121	D₄	1	1	yes	characteristic
91	C₄×Q₈×C₁₉	—	2	1	no	—
92	C₄×Q₈×C₁₉	—	2	1	no	—
93	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
94	C₄×D₄×C₁₉	—	2	1	no	—
95	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
96	C₁₉×#117	—	2	1	no	—
97	C₁₉×#117	—	2	1	no	—
98	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
99	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
101	C₁₉×#107	—	2	1	no	—
102	C₁₉×#107	—	2	1	no	—
103	C₁₉×#106	—	2	1	no	—
104	C₁₉×#106	—	2	1	no	—
105	C₁₉×#106	—	2	1	no	—
106	C₁₉×#106	—	2	1	no	—
107	C₁₉×#106	—	2	1	no	—
108	C₁₉×#106	—	2	1	no	—
109	C₁₉×C₄⋊C₈	—	2	1	no	—
110	C₁₉×C₄⋊C₈	—	2	1	no	—
111	C₁₉×C₄⋊C₈	—	2	1	no	—
112	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
113	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
114	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
115	C₁₉×C₄⋊C₈	C₂³	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×#103	—	2	1	no	—
121	C₁₉×#103	—	2	1	no	—
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×#102	—	2	1	no	—
131	C₁₉×#102	—	2	1	no	—
132	C₁₉×C₂²⋊C₈	—	2	1	no	—
133	C₁₉×C₂²⋊C₈	—	2	1	no	—
134	C₁₉×C₂²⋊C₈	—	2	1	no	—
135	C₁₉×C₂²⋊C₈	—	2	1	no	—
136	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
137	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
138	C₁₉×#97	—	2	1	no	—
139	C₁₉×#97	—	2	1	no	—
140	C₄×C₈×C₁₉	—	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	SD₁₆×C₁₉	—	8	1	no	—
162	SD₁₆×C₁₉	—	8	1	no	—
163	M₁₆×C₁₉	—	8	1	no	—
164	M₁₆×C₁₉	—	8	1	no	—
165	C₂×C₈×C₁₉	—	2	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	—	8	1	no	—
172	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
174	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
175	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
176	C₄⋊C₄×C₁₉	—	2	1	no	—
177	C₄⋊C₄×C₁₉	—	2	1	no	—
178	C₄⋊C₄×C₁₉	—	2	1	no	—
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	—	4	1	no	—
189	C₄⋊C₄×C₁₉	—	4	1	no	—
190	C₄⋊C₄×C₁₉	—	4	1	no	—
191	C₄⋊C₄×C₁₉	—	4	1	no	—
192	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
193	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
194	C₂²⋊C₄×C₁₉	—	2	1	no	—
195	C₂²⋊C₄×C₁₉	—	2	1	no	—
196	C₂²⋊C₄×C₁₉	—	2	1	no	—
197	C₂²⋊C₄×C₁₉	—	2	1	no	—
198	C₂²⋊C₄×C₁₉	—	2	1	no	—
199	C₂²⋊C₄×C₁₉	—	4	1	no	—
200	C₄²×C₁₉	—	2	1	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	#41	1	1	yes	characteristic
205	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
206	#19545	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂³×C₁₉	—	2	1	no	—
208	C₂³×C₁₉	#121	1	1	yes	characteristic
209	Q₈×C₁₉	—	2	1	no	—
210	Q₈×C₁₉	—	2	1	no	—
211	Q₈×C₁₉	—	4	1	no	—
212	Q₈×C₁₉	—	4	1	no	—
213	Q₈×C₁₉	—	4	1	no	—
214	Q₈×C₁₉	—	4	1	no	—
215	Q₈×C₁₉	—	4	1	no	—
216	Q₈×C₁₉	—	4	1	no	—
217	Q₈×C₁₉	—	8	1	no	—
218	Q₈×C₁₉	—	8	2	no	—
219	D₄×C₁₉	—	2	1	no	—
220	D₄×C₁₉	—	2	1	no	—
221	D₄×C₁₉	—	8	1	no	—
222	C₂×C₄×C₁₉	—	2	1	no	—
223	C₂×C₄×C₁₉	—	2	1	no	—
224	C₂×C₄×C₁₉	—	2	1	no	—
225	C₂×C₄×C₁₉	—	2	1	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	—	4	1	no	—
230	C₂×C₄×C₁₉	—	4	1	no	—
231	C₂×C₄×C₁₉	—	4	1	no	—
232	C₂×C₄×C₁₉	—	4	1	no	—
233	C₂×C₄×C₁₉	—	4	1	no	—
234	C₂×C₄×C₁₉	—	4	1	no	—
235	C₂×C₄×C₁₉	—	4	1	no	—
236	C₂×C₄×C₁₉	—	8	2	no	—
237	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
238	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
239	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
240	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
243	C₈×C₁₉	—	2	1	no	—
244	C₈×C₁₉	—	2	1	no	—
245	C₈×C₁₉	—	2	1	no	—
246	C₈×C₁₉	—	2	1	no	—
247	C₈×C₁₉	—	4	1	no	—
248	C₈×C₁₉	—	4	1	no	—
249	C₈×C₁₉	—	4	1	no	—
250	C₈×C₁₉	—	4	1	no	—
251	C₈×C₁₉	—	4	1	no	—
252	C₈×C₁₉	—	4	1	no	—
253	#3233	C₂×C₁₉	1	1	yes	characteristic
254	#3229	C₂×C₁₉	1	1	yes	characteristic, complemented
255	#3218	C₂×C₁₉	1	1	yes	characteristic
256	#2993	C₂×C₁₉	1	1	yes	characteristic
257	#1700	C₂×C₁₉	1	1	yes	characteristic, complemented
258	#1699	C₂×C₁₉	1	1	yes	characteristic, complemented
259	#1692	C₂×C₁₉	1	1	yes	characteristic, complemented
260	#1691	C₂×C₁₉	1	1	yes	characteristic, complemented
261	#1680	C₂×C₁₉	1	1	yes	characteristic, complemented
262	#1679	C₂×C₁₉	1	1	yes	characteristic, complemented
263	#1672	C₂×C₁₉	1	1	yes	characteristic, complemented
264	#1671	C₂×C₁₉	1	1	yes	characteristic, complemented
265	#1572	C₂×C₁₉	1	1	yes	characteristic, complemented
266	#1559	C₂×C₁₉	1	1	yes	characteristic, complemented
267	#1549	C₂×C₁₉	1	1	yes	characteristic, complemented
268	C₂²×C₁₉	—	2	1	no	—
269	C₂²×C₁₉	—	2	1	no	—
270	C₂²×C₁₉	—	2	1	no	—
271	C₂²×C₁₉	—	4	1	no	—
272	C₂²×C₁₉	—	4	1	no	—
273	C₂²×C₁₉	—	4	1	no	—
274	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
275	C₄×C₁₉	—	2	1	no	—
276	C₄×C₁₉	—	2	1	no	—
277	C₄×C₁₉	—	2	1	no	—
278	C₄×C₁₉	—	2	1	no	—
279	C₄×C₁₉	—	4	1	no	—
280	C₄×C₁₉	—	4	1	no	—
281	C₄×C₁₉	—	4	1	no	—
282	C₄×C₁₉	—	8	1	no	—
283	C₄×C₁₉	—	8	1	no	—
284	C₄×C₁₉	—	8	1	no	—
285	C₄×C₁₉	—	8	1	no	—
286	C₄×C₁₉	#577	1	1	yes	characteristic
287	C₄×C₁₉	#577	1	1	yes	characteristic
288	C₄×C₁₉	#577	1	1	yes	characteristic
289	C₄×C₁₉	#578	1	1	yes	characteristic
290	#533	C₂²×C₁₉	1	1	yes	characteristic
291	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
292	#529	C₂²×C₁₉	1	1	yes	characteristic
293	#499	—	2	1	no	—
294	#498	C₂²×C₁₉	1	1	yes	characteristic
295	#498	C₂²×C₁₉	1	1	yes	characteristic
296	#497	—	2	1	no	—
297	#491	—	2	1	no	—
298	#488	—	2	1	no	—
299	#487	C₂²×C₁₉	1	1	yes	characteristic
300	#487	C₂²×C₁₉	1	1	yes	characteristic
301	#485	—	2	1	no	—
302	#483	—	2	1	no	—
303	#483	—	2	1	no	—
304	#482	—	2	1	no	—
305	#477	C₂²×C₁₉	1	1	yes	characteristic
306	#476	C₂²×C₁₉	1	1	yes	characteristic
307	#475	—	2	1	no	—
308	#475	—	2	1	no	—
309	#475	C₂²×C₁₉	1	1	yes	characteristic
310	#474	C₂²×C₁₉	1	1	yes	characteristic
311	#462	C₂²×C₁₉	1	1	yes	characteristic
312	#462	C₂²×C₁₉	1	1	yes	characteristic
313	#461	C₂²×C₁₉	1	1	yes	characteristic
314	#461	C₂²×C₁₉	1	1	yes	characteristic
315	#451	—	2	1	no	—
316	#448	—	2	1	no	—
317	#446	C₂²×C₁₉	1	1	yes	characteristic
318	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
319	#436	—	2	1	no	—
320	#436	C₂²×C₁₉	1	1	yes	characteristic
321	#435	—	2	1	no	—
322	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
323	#433	—	2	1	no	—
324	#432	C₂²×C₁₉	1	1	yes	characteristic
325	#431	C₂²×C₁₉	1	1	yes	characteristic
326	#431	C₂²×C₁₉	1	1	yes	characteristic
327	#424	—	2	1	no	—
328	#423	C₂²×C₁₉	1	1	yes	characteristic
329	#335	C₂²×C₁₉	1	1	yes	characteristic
330	#335	C₂²×C₁₉	1	1	yes	characteristic
331	#334	C₂²×C₁₉	1	1	yes	characteristic
332	#334	C₂²×C₁₉	1	1	yes	characteristic
333	#333	C₂²×C₁₉	1	1	yes	characteristic
334	#333	C₂²×C₁₉	1	1	yes	characteristic
335	#332	C₂²×C₁₉	1	1	yes	characteristic
336	#332	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	C₂×C₁₉	—	4	1	no	—
342	C₂×C₁₉	—	8	1	no	—
343	C₂×C₁₉	#3046	1	1	yes	characteristic
344	C₂×C₁₉	#3057	1	1	yes	characteristic
345	C₂×C₁₉	#3069	1	1	yes	characteristic
346	C₂²×Q₈	—	2	1	no	—
347	C₂×Q₁₆	—	2	1	no	—
348	C₂×Q₁₆	—	2	1	no	—
349	C₂×SD₁₆	—	2	1	no	—
350	C₂×SD₁₆	—	2	1	no	—
351	C₂×M₁₆	—	2	1	no	—
352	C₂×M₁₆	—	2	1	no	—
353	C₂²×C₈	—	2	1	no	—
354	C₄⋊Q₈	—	2	1	no	—
355	C₄⋊Q₈	—	2	1	no	—
356	C₄⋊Q₈	—	2	1	no	—
357	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
358	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
359	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
360	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
361	#126	—	2	1	no	—
362	#125	—	2	1	no	—
363	#125	D₄×C₁₉	1	1	yes	characteristic
364	#124	D₄×C₁₉	1	1	yes	characteristic
365	#123	—	2	1	no	—
366	C₂²⋊Q₈	—	2	1	no	—
367	C₂²⋊Q₈	—	2	1	no	—
368	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
369	#121	D₄×C₁₉	1	1	yes	characteristic
370	C₄×Q₈	—	2	1	no	—
371	C₄×Q₈	—	2	1	no	—
372	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
373	C₄×D₄	—	2	1	no	—
374	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
375	#117	—	2	1	no	—
376	#117	—	2	1	no	—
377	C₂×C₄⋊C₄	—	2	1	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
380	#107	—	2	1	no	—
381	#107	—	2	1	no	—
382	#106	—	2	1	no	—
383	#106	—	2	1	no	—
384	#106	—	2	1	no	—
385	#106	—	2	1	no	—
386	#106	—	2	1	no	—
387	#106	—	2	1	no	—
388	C₄⋊C₈	—	2	1	no	—
389	C₄⋊C₈	—	2	1	no	—
390	C₄⋊C₈	—	2	1	no	—
391	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
392	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
393	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
394	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
395	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
396	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
397	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
398	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
399	#103	—	2	1	no	—
400	#103	—	2	1	no	—
401	#103	—	2	1	no	—
402	#103	—	2	1	no	—
403	#103	—	2	1	no	—
404	#103	—	2	1	no	—
405	#103	—	2	1	no	—
406	#103	—	2	1	no	—
407	#103	—	2	1	no	—
408	#103	—	2	1	no	—
409	#102	—	2	1	no	—
410	#102	—	2	1	no	—
411	C₂²⋊C₈	—	2	1	no	—
412	C₂²⋊C₈	—	2	1	no	—
413	C₂²⋊C₈	—	2	1	no	—
414	C₂²⋊C₈	—	2	1	no	—
415	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
416	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
417	#97	—	2	1	no	—
418	#97	—	2	1	no	—
419	C₄×C₈	—	2	1	no	—
420	C₄×C₈	—	2	1	no	—
421	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
422	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
423	C₁₉	#19545	1	1	yes	characteristic, direct product factor, Sylow
424	C₂×Q₈	—	2	1	no	—
425	C₂×Q₈	—	2	1	no	—
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	4	1	no	—
429	C₂×Q₈	—	8	1	no	—
430	C₂×Q₈	—	8	1	no	—
431	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	4	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	#41×C₁₉	1	1	yes	characteristic
439	Q₁₆	—	8	1	no	—
440	Q₁₆	—	8	1	no	—
441	SD₁₆	—	8	1	no	—
442	SD₁₆	—	8	1	no	—
443	M₁₆	—	8	1	no	—
444	M₁₆	—	8	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	8	1	no	—
452	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
453	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
454	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
455	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	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	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	4	1	no	—
469	C₄⋊C₄	—	4	1	no	—
470	C₄⋊C₄	—	4	1	no	—
471	C₄⋊C₄	—	4	1	no	—
472	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
473	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
474	C₂²⋊C₄	—	2	1	no	—
475	C₂²⋊C₄	—	2	1	no	—
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	2	1	no	—
478	C₂²⋊C₄	—	2	1	no	—
479	C₂²⋊C₄	—	4	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	4	1	no	—
482	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
483	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
484	C₄²	#41×C₁₉	1	1	yes	characteristic
485	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
486	C₂³	—	2	1	no	—
487	C₂³	C₁₉×#121	1	1	yes	characteristic
488	Q₈	—	2	1	no	—
489	Q₈	—	2	1	no	—
490	Q₈	—	4	1	no	—
491	Q₈	—	4	1	no	—
492	Q₈	—	4	1	no	—
493	Q₈	—	4	1	no	—
494	Q₈	—	4	1	no	—
495	Q₈	—	4	1	no	—
496	Q₈	—	8	1	no	—
497	Q₈	—	8	2	no	—
498	D₄	—	2	1	no	—
499	D₄	—	2	1	no	—
500	D₄	—	8	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	8	2	no	—
516	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
517	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
518	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
519	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
520	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
521	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
522	C₈	—	2	1	no	—
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	4	1	no	—
527	C₈	—	4	1	no	—
528	C₈	—	4	1	no	—
529	C₈	—	4	1	no	—
530	C₈	—	4	1	no	—
531	C₈	—	4	1	no	—
532	C₂²	—	2	1	no	—
533	C₂²	—	2	1	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	4	1	no	—
536	C₂²	—	4	1	no	—
537	C₂²	—	4	1	no	—
538	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
539	C₄	—	2	1	no	—
540	C₄	—	2	1	no	—
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	4	1	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	1	no	—
546	C₄	—	8	1	no	—
547	C₄	—	8	1	no	—
548	C₄	—	8	1	no	—
549	C₄	—	8	1	no	—
550	C₄	C₁₉×#577	1	1	yes	characteristic
551	C₄	C₁₉×#577	1	1	yes	characteristic
552	C₄	C₁₉×#577	1	1	yes	characteristic
553	C₄	C₁₉×#578	1	1	yes	characteristic
554	C₂	—	4	1	no	—
555	C₂	—	8	1	no	—
556	C₂	C₁₉×#3046	1	1	yes	characteristic
557	C₂	C₁₉×#3057	1	1	yes	characteristic
558	C₂	C₁₉×#3069	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×#3229	C₂	semidirect
5. C₁₉×#1700	C₂	semidirect
6. C₁₉×#1699	C₂	semidirect
7. C₁₉×#1692	C₂	semidirect
8. C₁₉×#1691	C₂	semidirect
9. C₁₉×#1680	C₂	semidirect
10. C₁₉×#1679	C₂	semidirect
11. C₁₉×#1672	C₂	semidirect
12. C₁₉×#1671	C₂	semidirect
13. C₁₉×#1572	C₂	semidirect
14. C₁₉×#1559	C₂	semidirect
15. C₁₉×#1549	C₂	semidirect
206. #19545	C₁₉	direct (N × H)
254. #3229	C₂×C₁₉	semidirect
257. #1700	C₂×C₁₉	semidirect
258. #1699	C₂×C₁₉	semidirect
259. #1692	C₂×C₁₉	semidirect
260. #1691	C₂×C₁₉	semidirect
261. #1680	C₂×C₁₉	semidirect
262. #1679	C₂×C₁₉	semidirect
263. #1672	C₂×C₁₉	semidirect
264. #1671	C₂×C₁₉	semidirect
265. #1572	C₂×C₁₉	semidirect
266. #1559	C₂×C₁₉	semidirect
267. #1549	C₂×C₁₉	semidirect
423. C₁₉	#19545	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×#3233	2
C₁₉×#3229	2
C₁₉×#3218	2
C₁₉×#2993	2
C₁₉×#1700	2
C₁₉×#1699	2
C₁₉×#1692	2
C₁₉×#1691	2
C₁₉×#1680	2
C₁₉×#1679	2
C₁₉×#1672	2
C₁₉×#1671	2
C₁₉×#1572	2
C₁₉×#1559	2
C₁₉×#1549	2
#19545	19

Subgroups — C19×#19545 #18025504

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19545 #18025504