Subgroups — C₁₉×#19378 #18025337

Order 4864.

584 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×#3252	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3218	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3165	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2969	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1694	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1693	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×#1674	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1673	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×#1569	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1554	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1546	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×#501	—	2	1	no	—
20	C₁₉×#501	—	2	1	no	—
21	C₁₉×#500	C₂²	1	1	yes	characteristic
22	C₁₉×#500	C₂²	1	1	yes	characteristic
23	C₁₉×#498	C₂²	1	1	yes	characteristic
24	C₁₉×#498	C₂²	1	1	yes	characteristic
25	C₁₉×#497	—	2	1	no	—
26	C₁₉×#491	—	2	1	no	—
27	C₁₉×#479	—	2	1	no	—
28	C₁₉×#477	C₂²	1	1	yes	characteristic
29	C₁₉×#476	C₂²	1	1	yes	characteristic
30	C₁₉×#470	—	2	1	no	—
31	C₁₉×#468	—	2	1	no	—
32	C₁₉×#464	—	2	1	no	—
33	C₁₉×#462	C₂²	1	1	yes	characteristic
34	C₁₉×#462	C₂²	1	1	yes	characteristic
35	C₁₉×#462	C₂²	1	1	yes	characteristic
36	C₁₉×#461	C₂²	1	1	yes	characteristic
37	C₁₉×#461	C₂²	1	1	yes	characteristic
38	C₁₉×#461	C₂²	1	1	yes	characteristic
39	C₁₉×#451	—	2	1	no	—
40	C₁₉×#448	—	2	1	no	—
41	C₁₉×#446	C₂²	1	1	yes	characteristic
42	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
43	C₁₉×#436	—	2	1	no	—
44	C₁₉×#436	C₂²	1	1	yes	characteristic
45	C₁₉×#435	—	2	1	no	—
46	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
47	C₁₉×#433	—	2	1	no	—
48	C₁₉×#432	C₂²	1	1	yes	characteristic
49	C₁₉×#431	C₂²	1	1	yes	characteristic
50	C₁₉×#428	—	2	1	no	—
51	C₁₉×#428	—	2	1	no	—
52	C₁₉×#423	C₂²	1	1	yes	characteristic
53	C₁₉×#405	—	2	1	no	—
54	C₄×M₁₆×C₁₉	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×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	C₂×M₁₆×C₁₉	—	2	1	no	—
76	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
77	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
78	C₂²×C₈×C₁₉	—	2	1	no	—
79	C₁₉×C₄⋊Q₈	—	2	1	no	—
80	C₁₉×C₄⋊Q₈	—	2	1	no	—
81	C₁₉×C₄⋊Q₈	—	2	1	no	—
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×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₁₉×#126	—	2	1	no	—
87	C₁₉×#125	—	2	1	no	—
88	C₁₉×#125	D₄	1	1	yes	characteristic
89	C₁₉×#124	D₄	1	1	yes	characteristic
90	C₁₉×#123	—	2	1	no	—
91	C₁₉×C₂²⋊Q₈	—	2	1	no	—
92	C₁₉×C₂²⋊Q₈	—	2	1	no	—
93	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
94	C₁₉×#121	D₄	1	1	yes	characteristic
95	C₄×Q₈×C₁₉	—	2	1	no	—
96	C₄×Q₈×C₁₉	—	2	1	no	—
97	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
98	C₄×D₄×C₁₉	—	2	1	no	—
99	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
100	C₁₉×#117	—	2	1	no	—
101	C₁₉×#117	—	2	1	no	—
102	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
103	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
104	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
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×#107	—	2	1	no	—
110	C₁₉×#106	—	2	1	no	—
111	C₁₉×#106	—	2	1	no	—
112	C₁₉×#106	—	2	1	no	—
113	C₁₉×#106	—	2	1	no	—
114	C₁₉×#106	—	2	1	no	—
115	C₁₉×C₄⋊C₈	—	2	1	no	—
116	C₁₉×C₄⋊C₈	—	2	1	no	—
117	C₁₉×C₄⋊C₈	—	2	1	no	—
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×C₄⋊C₈	C₂³	1	1	yes	characteristic
123	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
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×#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×#97	—	2	1	no	—
137	C₁₉×#97	—	2	1	no	—
138	C₁₉×#97	D₄	1	1	yes	characteristic
139	C₁₉×#97	D₄	1	1	yes	characteristic
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	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	—	2	2	no	—
166	M₁₆×C₁₉	—	2	2	no	—
167	M₁₆×C₁₉	—	4	2	no	—
168	M₁₆×C₁₉	—	8	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	—	2	1	no	—
173	C₂×C₈×C₁₉	—	2	1	no	—
174	C₂×C₈×C₁₉	—	2	1	no	—
175	C₂×C₈×C₁₉	—	4	2	no	—
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	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	2	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	—	4	1	no	—
196	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
197	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
203	C₂²⋊C₄×C₁₉	—	4	1	no	—
204	C₄²×C₁₉	—	2	1	no	—
205	C₄²×C₁₉	—	4	1	no	—
206	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₁₉	#41	1	1	yes	characteristic
209	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
210	#19378	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂³×C₁₉	—	2	1	no	—
212	C₂³×C₁₉	#121	1	1	yes	characteristic
213	Q₈×C₁₉	—	2	1	no	—
214	Q₈×C₁₉	—	2	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	—	8	1	no	—
222	Q₈×C₁₉	—	8	2	no	—
223	D₄×C₁₉	—	2	1	no	—
224	D₄×C₁₉	—	2	1	no	—
225	D₄×C₁₉	—	8	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	—	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	—	4	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	—	4	1	no	—
250	C₈×C₁₉	—	4	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	#137	1	2	yes	—
256	C₈×C₁₉	#137	1	2	yes	—
257	#3252	C₂×C₁₉	1	1	yes	characteristic
258	#3218	C₂×C₁₉	1	1	yes	characteristic
259	#3165	C₂×C₁₉	1	1	yes	characteristic, complemented
260	#2969	C₂×C₁₉	1	1	yes	characteristic
261	#1694	C₂×C₁₉	1	1	yes	characteristic, complemented
262	#1693	C₂×C₁₉	1	1	yes	characteristic, complemented
263	#1692	C₂×C₁₉	1	1	yes	characteristic, complemented
264	#1691	C₂×C₁₉	1	1	yes	characteristic, complemented
265	#1674	C₂×C₁₉	1	1	yes	characteristic, complemented
266	#1673	C₂×C₁₉	1	1	yes	characteristic, complemented
267	#1672	C₂×C₁₉	1	1	yes	characteristic, complemented
268	#1671	C₂×C₁₉	1	1	yes	characteristic, complemented
269	#1569	C₂×C₁₉	1	1	yes	characteristic, complemented
270	#1554	C₂×C₁₉	1	1	yes	characteristic, complemented
271	#1546	C₂×C₁₉	1	1	yes	characteristic, complemented
272	C₂²×C₁₉	—	2	1	no	—
273	C₂²×C₁₉	—	2	1	no	—
274	C₂²×C₁₉	—	2	1	no	—
275	C₂²×C₁₉	—	4	1	no	—
276	C₂²×C₁₉	—	4	1	no	—
277	C₂²×C₁₉	—	4	1	no	—
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	C₂×#137	1	1	yes	characteristic
291	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
292	C₄×C₁₉	#576	1	1	yes	characteristic
293	C₄×C₁₉	#577	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	#501	—	2	1	no	—
298	#501	—	2	1	no	—
299	#500	C₂²×C₁₉	1	1	yes	characteristic
300	#500	C₂²×C₁₉	1	1	yes	characteristic
301	#498	C₂²×C₁₉	1	1	yes	characteristic
302	#498	C₂²×C₁₉	1	1	yes	characteristic
303	#497	—	2	1	no	—
304	#491	—	2	1	no	—
305	#479	—	2	1	no	—
306	#477	C₂²×C₁₉	1	1	yes	characteristic
307	#476	C₂²×C₁₉	1	1	yes	characteristic
308	#470	—	2	1	no	—
309	#468	—	2	1	no	—
310	#464	—	2	1	no	—
311	#462	C₂²×C₁₉	1	1	yes	characteristic
312	#462	C₂²×C₁₉	1	1	yes	characteristic
313	#462	C₂²×C₁₉	1	1	yes	characteristic
314	#461	C₂²×C₁₉	1	1	yes	characteristic
315	#461	C₂²×C₁₉	1	1	yes	characteristic
316	#461	C₂²×C₁₉	1	1	yes	characteristic
317	#451	—	2	1	no	—
318	#448	—	2	1	no	—
319	#446	C₂²×C₁₉	1	1	yes	characteristic
320	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
321	#436	—	2	1	no	—
322	#436	C₂²×C₁₉	1	1	yes	characteristic
323	#435	—	2	1	no	—
324	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
325	#433	—	2	1	no	—
326	#432	C₂²×C₁₉	1	1	yes	characteristic
327	#431	C₂²×C₁₉	1	1	yes	characteristic
328	#428	—	2	1	no	—
329	#428	—	2	1	no	—
330	#423	C₂²×C₁₉	1	1	yes	characteristic
331	#405	—	2	1	no	—
332	C₄×M₁₆	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	#333	C₂²×C₁₉	1	1	yes	characteristic
338	#333	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	—	4	1	no	—
346	C₂×C₁₉	—	8	1	no	—
347	C₂×C₁₉	#3039	1	1	yes	characteristic
348	C₂×C₁₉	#3062	1	1	yes	characteristic
349	C₂×C₁₉	#3069	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	C₂×M₁₆	—	2	1	no	—
359	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
360	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
361	C₂²×C₈	—	2	1	no	—
362	C₄⋊Q₈	—	2	1	no	—
363	C₄⋊Q₈	—	2	1	no	—
364	C₄⋊Q₈	—	2	1	no	—
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	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
369	#126	—	2	1	no	—
370	#125	—	2	1	no	—
371	#125	D₄×C₁₉	1	1	yes	characteristic
372	#124	D₄×C₁₉	1	1	yes	characteristic
373	#123	—	2	1	no	—
374	C₂²⋊Q₈	—	2	1	no	—
375	C₂²⋊Q₈	—	2	1	no	—
376	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
377	#121	D₄×C₁₉	1	1	yes	characteristic
378	C₄×Q₈	—	2	1	no	—
379	C₄×Q₈	—	2	1	no	—
380	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
381	C₄×D₄	—	2	1	no	—
382	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
383	#117	—	2	1	no	—
384	#117	—	2	1	no	—
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₄⋊C₄	—	2	1	no	—
387	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
388	#107	—	2	1	no	—
389	#107	—	2	1	no	—
390	#107	—	2	1	no	—
391	#107	—	2	1	no	—
392	#107	—	2	1	no	—
393	#106	—	2	1	no	—
394	#106	—	2	1	no	—
395	#106	—	2	1	no	—
396	#106	—	2	1	no	—
397	#106	—	2	1	no	—
398	C₄⋊C₈	—	2	1	no	—
399	C₄⋊C₈	—	2	1	no	—
400	C₄⋊C₈	—	2	1	no	—
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	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
406	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
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	#102	—	2	1	no	—
415	C₂²⋊C₈	—	2	1	no	—
416	C₂²⋊C₈	—	2	1	no	—
417	C₂²⋊C₈	—	2	1	no	—
418	C₂²⋊C₈	—	2	1	no	—
419	#97	—	2	1	no	—
420	#97	—	2	1	no	—
421	#97	D₄×C₁₉	1	1	yes	characteristic
422	#97	D₄×C₁₉	1	1	yes	characteristic
423	C₄×C₈	—	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	#19378	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	—	2	2	no	—
450	M₁₆	—	2	2	no	—
451	M₁₆	—	4	2	no	—
452	M₁₆	—	8	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	4	2	no	—
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	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
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	—	2	1	no	—
476	C₄⋊C₄	—	4	1	no	—
477	C₄⋊C₄	—	4	1	no	—
478	C₄⋊C₄	—	4	1	no	—
479	C₄⋊C₄	—	4	1	no	—
480	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
481	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
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	—	2	1	no	—
487	C₂²⋊C₄	—	4	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	4	1	no	—
490	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
491	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
492	C₄²	#41×C₁₉	1	1	yes	characteristic
493	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
494	C₂³	—	2	1	no	—
495	C₂³	C₁₉×#121	1	1	yes	characteristic
496	Q₈	—	2	1	no	—
497	Q₈	—	2	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	—	8	1	no	—
505	Q₈	—	8	2	no	—
506	D₄	—	2	1	no	—
507	D₄	—	2	1	no	—
508	D₄	—	8	1	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	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	4	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	—	4	1	no	—
533	C₈	—	4	1	no	—
534	C₈	—	4	1	no	—
535	C₈	—	4	1	no	—
536	C₈	—	4	1	no	—
537	C₈	—	4	1	no	—
538	C₈	C₁₉×#137	1	2	yes	—
539	C₈	C₁₉×#137	1	2	yes	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	4	1	no	—
544	C₂²	—	4	1	no	—
545	C₂²	—	4	1	no	—
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	C₂×C₁₉×#137	1	1	yes	characteristic
559	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
560	C₄	C₁₉×#576	1	1	yes	characteristic
561	C₄	C₁₉×#577	1	1	yes	characteristic
562	C₂	—	4	1	no	—
563	C₂	—	8	1	no	—
564	C₂	C₁₉×#3039	1	1	yes	characteristic
565	C₂	C₁₉×#3062	1	1	yes	characteristic
566	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
3. C₁₉×#3165	C₂	semidirect
5. C₁₉×#1694	C₂	semidirect
6. C₁₉×#1693	C₂	semidirect
7. C₁₉×#1692	C₂	semidirect
8. C₁₉×#1691	C₂	semidirect
9. C₁₉×#1674	C₂	semidirect
10. C₁₉×#1673	C₂	semidirect
11. C₁₉×#1672	C₂	semidirect
12. C₁₉×#1671	C₂	semidirect
13. C₁₉×#1569	C₂	semidirect
14. C₁₉×#1554	C₂	semidirect
15. C₁₉×#1546	C₂	semidirect
210. #19378	C₁₉	direct (N × H)
259. #3165	C₂×C₁₉	semidirect
261. #1694	C₂×C₁₉	semidirect
262. #1693	C₂×C₁₉	semidirect
263. #1692	C₂×C₁₉	semidirect
264. #1691	C₂×C₁₉	semidirect
265. #1674	C₂×C₁₉	semidirect
266. #1673	C₂×C₁₉	semidirect
267. #1672	C₂×C₁₉	semidirect
268. #1671	C₂×C₁₉	semidirect
269. #1569	C₂×C₁₉	semidirect
270. #1554	C₂×C₁₉	semidirect
271. #1546	C₂×C₁₉	semidirect
427. C₁₉	#19378	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×#3252	2
C₁₉×#3218	2
C₁₉×#3165	2
C₁₉×#2969	2
C₁₉×#1694	2
C₁₉×#1693	2
C₁₉×#1692	2
C₁₉×#1691	2
C₁₉×#1674	2
C₁₉×#1673	2
C₁₉×#1672	2
C₁₉×#1671	2
C₁₉×#1569	2
C₁₉×#1554	2
C₁₉×#1546	2
#19378	19

Subgroups — C19×#19378 #18025337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19378 #18025337