Subgroups — C₁₉×#18393 #18024352

Order 4864.

910 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3491	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3232	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2611	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1615	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1614	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1613	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1609	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1608	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1607	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1500	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1458	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#552	—	2	2	no	—
13	C₁₉×#552	—	2	2	no	—
14	C₁₉×#551	—	2	2	no	—
15	C₁₉×#551	—	2	2	no	—
16	C₁₉×#543	C₂²	1	1	yes	characteristic
17	C₁₉×#539	—	2	1	no	—
18	C₁₉×#539	C₂²	1	2	yes	—
19	C₁₉×#534	C₂²	1	1	yes	characteristic
20	C₁₉×#529	—	2	1	no	—
21	C₁₉×#529	C₂²	1	2	yes	—
22	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₁₉×#123	—	2	1	no	—
24	C₁₉×#518	—	2	1	no	—
25	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
26	C₁₉×#499	—	2	2	no	—
27	C₁₉×#488	—	2	2	no	—
28	C₁₉×#484	C₂²	1	2	yes	complemented
29	C₁₉×#483	C₂²	1	2	yes	complemented
30	C₁₉×#481	C₂²	1	2	yes	—
31	C₁₉×#480	C₂²	1	2	yes	—
32	C₁₉×#479	—	2	2	no	—
33	C₁₉×#478	—	2	2	no	—
34	C₁₉×#431	C₂²	1	2	yes	complemented
35	C₁₉×#400	C₂²	1	1	yes	characteristic, complemented
36	C₁₉×#399	C₂²	1	1	yes	characteristic
37	C₁₉×#398	C₂²	1	1	yes	characteristic, complemented
38	C₁₉×#397	C₂²	1	1	yes	characteristic
39	C₁₉×#389	—	2	1	no	—
40	C₁₉×#388	—	2	1	no	—
41	C₁₉×#387	—	2	1	no	—
42	C₁₉×#385	—	2	1	no	—
43	C₁₉×#376	C₂²	1	1	yes	characteristic, complemented
44	C₁₉×#328	C₂²	1	2	yes	complemented
45	C₁₉×#328	C₂²	1	2	yes	complemented
46	C₁₉×#327	C₂²	1	2	yes	—
47	C₁₉×#327	C₂²	1	2	yes	—
48	C₁₉×#324	C₂²	1	2	yes	complemented
49	C₁₉×#323	C₂²	1	1	yes	characteristic
50	C₁₉×#323	C₂²	1	1	yes	characteristic
51	C₂²×D₄×C₁₉	—	2	1	no	—
52	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
53	C₁₉×#126	—	2	2	no	—
54	C₁₉×#126	—	2	2	no	—
55	C₁₉×#126	—	2	2	no	—
56	C₁₉×#126	—	2	2	no	—
57	C₁₉×#125	—	2	1	no	—
58	C₁₉×#125	—	2	2	no	—
59	C₁₉×#125	—	2	2	no	—
60	C₁₉×#125	—	2	2	no	—
61	C₁₉×#125	—	2	2	no	—
62	C₁₉×#125	D₄	1	2	yes	—
63	C₁₉×#124	—	2	1	no	—
64	C₁₉×#124	D₄	1	2	yes	—
65	C₁₉×#123	—	2	2	no	—
66	C₁₉×#123	—	2	2	no	—
67	C₁₉×#123	—	2	2	no	—
68	C₁₉×#123	—	2	2	no	—
69	C₁₉×#123	—	2	2	no	—
70	C₁₉×#123	—	2	2	no	—
71	C₁₉×#123	—	2	2	no	—
72	C₁₉×C₂²⋊Q₈	—	2	2	no	—
73	C₁₉×C₂²⋊Q₈	—	2	2	no	—
74	C₁₉×C₂²⋊Q₈	—	2	2	no	—
75	C₁₉×C₂²⋊Q₈	—	2	1	no	—
76	C₁₉×C₂²⋊Q₈	—	2	2	no	—
77	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
78	C₁₉×#121	—	2	1	no	—
79	C₁₉×#121	C₂³	1	2	yes	—
80	C₁₉×#120	—	2	2	no	—
81	C₄×Q₈×C₁₉	—	2	1	no	—
82	C₄×Q₈×C₁₉	D₄	1	2	yes	—
83	C₄×D₄×C₁₉	—	2	2	no	—
84	C₄×D₄×C₁₉	—	2	2	no	—
85	C₄×D₄×C₁₉	—	2	1	no	—
86	C₄×D₄×C₁₉	—	2	2	no	—
87	C₄×D₄×C₁₉	—	2	2	no	—
88	C₄×D₄×C₁₉	D₄	1	2	yes	—
89	C₁₉×#117	—	2	2	no	—
90	C₁₉×#117	—	2	2	no	—
91	C₁₉×#117	—	2	2	no	—
92	C₁₉×#117	—	2	2	no	—
93	C₁₉×#117	—	2	2	no	—
94	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
95	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
96	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
97	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
98	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
99	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
105	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
111	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₁₉	—	2	1	no	—
113	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
114	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
115	C₁₉×#107	—	2	2	no	—
116	C₁₉×#107	—	2	2	no	—
117	C₁₉×#106	—	2	2	no	—
118	C₁₉×#106	—	2	2	no	—
119	C₁₉×C₄⋊C₈	—	2	2	no	—
120	C₁₉×#103	—	2	2	no	—
121	C₁₉×#103	—	2	2	no	—
122	C₁₉×#102	—	2	2	no	—
123	C₁₉×#102	—	2	2	no	—
124	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
125	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
126	C₄×C₈×C₁₉	—	2	2	no	—
127	C₁₉×#95	—	2	1	no	—
128	C₁₉×#95	—	2	1	no	—
129	C₁₉×#95	—	2	1	no	—
130	C₁₉×#95	—	2	1	no	—
131	C₁₉×#95	—	2	1	no	—
132	C₁₉×#95	C₂³	1	1	yes	characteristic
133	C₁₉×#95	C₂³	1	1	yes	characteristic
134	C₂⁴×C₁₉	—	2	1	no	—
135	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₂×Q₈×C₁₉	—	2	1	no	—
137	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
138	C₂×D₄×C₁₉	—	2	2	no	—
139	C₂×D₄×C₁₉	—	2	2	no	—
140	C₂×D₄×C₁₉	—	2	1	no	—
141	C₂×D₄×C₁₉	—	4	2	no	—
142	C₂×D₄×C₁₉	—	4	2	no	—
143	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₁₉	—	2	1	no	—
145	C₂²×C₄×C₁₉	—	2	2	no	—
146	C₂²×C₄×C₁₉	—	2	1	no	—
147	C₂²×C₄×C₁₉	—	2	1	no	—
148	C₂²×C₄×C₁₉	—	2	1	no	—
149	C₂²×C₄×C₁₉	—	2	2	no	—
150	C₂²×C₄×C₁₉	—	2	1	no	—
151	C₂²×C₄×C₁₉	—	2	1	no	—
152	C₂²×C₄×C₁₉	—	2	2	no	—
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	C₂²×C₄×C₁₉	—	2	1	no	—
155	C₂²×C₄×C₁₉	—	2	1	no	—
156	C₂²×C₄×C₁₉	—	4	1	no	—
157	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
163	C₂×C₈×C₁₉	—	2	2	no	—
164	C₂×C₈×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	2	2	no	—
166	C₄⋊C₄×C₁₉	—	2	2	no	—
167	C₄⋊C₄×C₁₉	—	2	2	no	—
168	C₄⋊C₄×C₁₉	—	2	2	no	—
169	C₄⋊C₄×C₁₉	—	2	1	no	—
170	C₄⋊C₄×C₁₉	—	2	1	no	—
171	C₄⋊C₄×C₁₉	—	2	2	no	—
172	C₄⋊C₄×C₁₉	—	2	2	no	—
173	C₄⋊C₄×C₁₉	—	2	2	no	—
174	C₄⋊C₄×C₁₉	—	2	2	no	—
175	C₄⋊C₄×C₁₉	—	2	2	no	—
176	C₄⋊C₄×C₁₉	—	2	2	no	—
177	C₄⋊C₄×C₁₉	—	2	2	no	—
178	C₄⋊C₄×C₁₉	—	2	2	no	—
179	C₄⋊C₄×C₁₉	—	4	2	no	—
180	C₄⋊C₄×C₁₉	—	4	2	no	—
181	C₄⋊C₄×C₁₉	—	4	1	no	—
182	C₄⋊C₄×C₁₉	—	4	1	no	—
183	C₄⋊C₄×C₁₉	—	4	2	no	—
184	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
185	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
186	C₂²⋊C₄×C₁₉	—	2	2	no	—
187	C₂²⋊C₄×C₁₉	—	2	2	no	—
188	C₂²⋊C₄×C₁₉	—	2	2	no	—
189	C₂²⋊C₄×C₁₉	—	2	2	no	—
190	C₂²⋊C₄×C₁₉	—	2	2	no	—
191	C₂²⋊C₄×C₁₉	—	2	2	no	—
192	C₂²⋊C₄×C₁₉	—	2	2	no	—
193	C₂²⋊C₄×C₁₉	—	2	2	no	—
194	C₂²⋊C₄×C₁₉	—	2	2	no	—
195	C₂²⋊C₄×C₁₉	—	2	2	no	—
196	C₂²⋊C₄×C₁₉	—	2	2	no	—
197	C₂²⋊C₄×C₁₉	—	2	2	no	—
198	C₂²⋊C₄×C₁₉	—	4	2	no	—
199	C₂²⋊C₄×C₁₉	—	4	2	no	—
200	C₄²×C₁₉	—	2	2	no	—
201	C₄²×C₁₉	—	2	1	no	—
202	C₄²×C₁₉	—	2	1	no	—
203	C₄²×C₁₉	—	2	2	no	—
204	C₄²×C₁₉	—	4	2	no	—
205	C₄²×C₁₉	C₂×D₄	1	2	yes	—
206	C₄²×C₁₉	C₂×D₄	1	2	yes	—
207	#18393	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂³×C₁₉	—	2	1	no	—
209	C₂³×C₁₉	—	2	1	no	—
210	C₂³×C₁₉	—	2	2	no	—
211	C₂³×C₁₉	—	4	1	no	—
212	C₂³×C₁₉	—	4	1	no	—
213	C₂³×C₁₉	—	4	2	no	—
214	C₂³×C₁₉	—	8	1	no	—
215	C₂³×C₁₉	—	8	1	no	—
216	C₂³×C₁₉	#135	1	2	yes	—
217	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
218	Q₈×C₁₉	—	4	2	no	—
219	Q₈×C₁₉	—	8	1	no	—
220	D₄×C₁₉	—	4	2	no	—
221	D₄×C₁₉	—	4	4	no	—
222	D₄×C₁₉	—	4	2	no	—
223	D₄×C₁₉	—	4	2	no	—
224	D₄×C₁₉	—	8	1	no	—
225	C₂×C₄×C₁₉	—	2	1	no	—
226	C₂×C₄×C₁₉	—	2	1	no	—
227	C₂×C₄×C₁₉	—	2	2	no	—
228	C₂×C₄×C₁₉	—	2	1	no	—
229	C₂×C₄×C₁₉	—	2	1	no	—
230	C₂×C₄×C₁₉	—	2	2	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	1	no	—
236	C₂×C₄×C₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	—	4	1	no	—
238	C₂×C₄×C₁₉	—	4	2	no	—
239	C₂×C₄×C₁₉	—	4	2	no	—
240	C₂×C₄×C₁₉	—	4	1	no	—
241	C₂×C₄×C₁₉	—	4	2	no	—
242	C₂×C₄×C₁₉	—	4	1	no	—
243	C₂×C₄×C₁₉	—	4	1	no	—
244	C₂×C₄×C₁₉	—	4	1	no	—
245	C₂×C₄×C₁₉	—	4	1	no	—
246	C₂×C₄×C₁₉	—	4	1	no	—
247	C₂×C₄×C₁₉	—	4	1	no	—
248	C₂×C₄×C₁₉	—	4	1	no	—
249	C₂×C₄×C₁₉	—	4	1	no	—
250	C₂×C₄×C₁₉	—	4	1	no	—
251	C₂×C₄×C₁₉	—	4	1	no	—
252	C₂×C₄×C₁₉	—	4	1	no	—
253	C₂×C₄×C₁₉	—	4	1	no	—
254	C₂×C₄×C₁₉	—	8	2	no	—
255	C₂×C₄×C₁₉	—	8	1	no	—
256	C₂×C₄×C₁₉	—	8	2	no	—
257	C₂×C₄×C₁₉	—	8	1	no	—
258	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
259	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
260	C₂×C₄×C₁₉	#120	1	2	yes	—
261	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
262	C₈×C₁₉	—	4	2	no	—
263	C₈×C₁₉	—	4	2	no	—
264	#3491	C₂×C₁₉	1	1	yes	characteristic
265	#3232	C₂×C₁₉	1	2	yes	complemented
266	#2611	C₂×C₁₉	1	1	yes	characteristic, complemented
267	#1615	C₂×C₁₉	1	2	yes	complemented
268	#1614	C₂×C₁₉	1	1	yes	characteristic, complemented
269	#1613	C₂×C₁₉	1	1	yes	characteristic
270	#1609	C₂×C₁₉	1	2	yes	complemented
271	#1608	C₂×C₁₉	1	1	yes	characteristic, complemented
272	#1607	C₂×C₁₉	1	1	yes	characteristic
273	#1500	C₂×C₁₉	1	2	yes	complemented
274	#1458	C₂×C₁₉	1	1	yes	characteristic, complemented
275	C₂²×C₁₉	—	2	1	no	—
276	C₂²×C₁₉	—	2	1	no	—
277	C₂²×C₁₉	—	2	2	no	—
278	C₂²×C₁₉	—	4	2	no	—
279	C₂²×C₁₉	—	4	1	no	—
280	C₂²×C₁₉	—	4	1	no	—
281	C₂²×C₁₉	—	4	2	no	—
282	C₂²×C₁₉	—	4	2	no	—
283	C₂²×C₁₉	—	4	2	no	—
284	C₂²×C₁₉	—	8	1	no	—
285	C₂²×C₁₉	—	16	2	no	—
286	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
287	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
288	C₂²×C₁₉	#575	1	1	yes	characteristic
289	C₄×C₁₉	—	2	1	no	—
290	C₄×C₁₉	—	2	1	no	—
291	C₄×C₁₉	—	2	2	no	—
292	C₄×C₁₉	—	2	2	no	—
293	C₄×C₁₉	—	4	2	no	—
294	C₄×C₁₉	—	4	1	no	—
295	C₄×C₁₉	—	4	2	no	—
296	C₄×C₁₉	—	4	1	no	—
297	C₄×C₁₉	—	4	2	no	—
298	C₄×C₁₉	—	4	1	no	—
299	C₄×C₁₉	—	4	2	no	—
300	C₄×C₁₉	—	8	1	no	—
301	C₄×C₁₉	—	8	1	no	—
302	C₄×C₁₉	—	8	1	no	—
303	#552	—	2	2	no	—
304	#552	—	2	2	no	—
305	#551	—	2	2	no	—
306	#551	—	2	2	no	—
307	#543	C₂²×C₁₉	1	1	yes	characteristic
308	#539	—	2	1	no	—
309	#539	C₂²×C₁₉	1	2	yes	—
310	#534	C₂²×C₁₉	1	1	yes	characteristic
311	#529	—	2	1	no	—
312	#529	C₂²×C₁₉	1	2	yes	—
313	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic, complemented
314	C₂×#123	—	2	1	no	—
315	#518	—	2	1	no	—
316	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
317	#499	—	2	2	no	—
318	#488	—	2	2	no	—
319	#484	C₂²×C₁₉	1	2	yes	complemented
320	#483	C₂²×C₁₉	1	2	yes	complemented
321	#481	C₂²×C₁₉	1	2	yes	—
322	#480	C₂²×C₁₉	1	2	yes	—
323	#479	—	2	2	no	—
324	#478	—	2	2	no	—
325	#431	C₂²×C₁₉	1	2	yes	complemented
326	#400	C₂²×C₁₉	1	1	yes	characteristic, complemented
327	#399	C₂²×C₁₉	1	1	yes	characteristic
328	#398	C₂²×C₁₉	1	1	yes	characteristic, complemented
329	#397	C₂²×C₁₉	1	1	yes	characteristic
330	#389	—	2	1	no	—
331	#388	—	2	1	no	—
332	#387	—	2	1	no	—
333	#385	—	2	1	no	—
334	#376	C₂²×C₁₉	1	1	yes	characteristic, complemented
335	#328	C₂²×C₁₉	1	2	yes	complemented
336	#328	C₂²×C₁₉	1	2	yes	complemented
337	#327	C₂²×C₁₉	1	2	yes	—
338	#327	C₂²×C₁₉	1	2	yes	—
339	#324	C₂²×C₁₉	1	2	yes	complemented
340	#323	C₂²×C₁₉	1	1	yes	characteristic
341	#323	C₂²×C₁₉	1	1	yes	characteristic
342	C₂×C₁₉	—	2	1	no	—
343	C₂×C₁₉	—	2	1	no	—
344	C₂×C₁₉	—	4	2	no	—
345	C₂×C₁₉	—	8	2	no	—
346	C₂×C₁₉	#3002	1	1	yes	characteristic
347	C₂×C₁₉	#3018	1	1	yes	characteristic
348	C₂×C₁₉	#3028	1	1	yes	characteristic
349	C₂²×D₄	—	2	1	no	—
350	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
351	#126	—	2	2	no	—
352	#126	—	2	2	no	—
353	#126	—	2	2	no	—
354	#126	—	2	2	no	—
355	#125	—	2	1	no	—
356	#125	—	2	2	no	—
357	#125	—	2	2	no	—
358	#125	—	2	2	no	—
359	#125	—	2	2	no	—
360	#125	D₄×C₁₉	1	2	yes	—
361	#124	—	2	1	no	—
362	#124	D₄×C₁₉	1	2	yes	—
363	#123	—	2	2	no	—
364	#123	—	2	2	no	—
365	#123	—	2	2	no	—
366	#123	—	2	2	no	—
367	#123	—	2	2	no	—
368	#123	—	2	2	no	—
369	#123	—	2	2	no	—
370	C₂²⋊Q₈	—	2	2	no	—
371	C₂²⋊Q₈	—	2	2	no	—
372	C₂²⋊Q₈	—	2	2	no	—
373	C₂²⋊Q₈	—	2	1	no	—
374	C₂²⋊Q₈	—	2	2	no	—
375	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
376	#121	—	2	1	no	—
377	#121	C₂³×C₁₉	1	2	yes	—
378	#120	—	2	2	no	—
379	C₄×Q₈	—	2	1	no	—
380	C₄×Q₈	D₄×C₁₉	1	2	yes	—
381	C₄×D₄	—	2	2	no	—
382	C₄×D₄	—	2	2	no	—
383	C₄×D₄	—	2	1	no	—
384	C₄×D₄	—	2	2	no	—
385	C₄×D₄	—	2	2	no	—
386	C₄×D₄	D₄×C₁₉	1	2	yes	—
387	#117	—	2	2	no	—
388	#117	—	2	2	no	—
389	#117	—	2	2	no	—
390	#117	—	2	2	no	—
391	#117	—	2	2	no	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄⋊C₄	—	2	1	no	—
394	C₂×C₄⋊C₄	—	2	1	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	—	2	1	no	—
398	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
402	C₂×C₂²⋊C₄	—	2	2	no	—
403	C₂×C₂²⋊C₄	—	2	1	no	—
404	C₂×C₂²⋊C₄	—	2	1	no	—
405	C₂×C₂²⋊C₄	—	2	1	no	—
406	C₂×C₂²⋊C₄	—	2	1	no	—
407	C₂×C₂²⋊C₄	—	2	1	no	—
408	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
409	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
410	C₂×C₄²	—	2	1	no	—
411	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
412	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
413	#107	—	2	2	no	—
414	#107	—	2	2	no	—
415	#106	—	2	2	no	—
416	#106	—	2	2	no	—
417	C₄⋊C₈	—	2	2	no	—
418	#103	—	2	2	no	—
419	#103	—	2	2	no	—
420	#102	—	2	2	no	—
421	#102	—	2	2	no	—
422	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
423	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
424	C₄×C₈	—	2	2	no	—
425	#95	—	2	1	no	—
426	#95	—	2	1	no	—
427	#95	—	2	1	no	—
428	#95	—	2	1	no	—
429	#95	—	2	1	no	—
430	#95	C₂³×C₁₉	1	1	yes	characteristic
431	#95	C₂³×C₁₉	1	1	yes	characteristic
432	C₁₉	#18393	1	1	yes	characteristic, direct product factor, Sylow
433	C₂⁴	—	2	1	no	—
434	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	4	2	no	—
441	C₂×D₄	—	4	2	no	—
442	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	4	1	no	—
456	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
458	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
459	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
460	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
461	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
462	C₂×C₈	—	2	2	no	—
463	C₂×C₈	—	2	2	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	2	no	—
474	C₄⋊C₄	—	2	2	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	—	2	2	no	—
477	C₄⋊C₄	—	2	2	no	—
478	C₄⋊C₄	—	4	2	no	—
479	C₄⋊C₄	—	4	2	no	—
480	C₄⋊C₄	—	4	1	no	—
481	C₄⋊C₄	—	4	1	no	—
482	C₄⋊C₄	—	4	2	no	—
483	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
484	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
485	C₂²⋊C₄	—	2	2	no	—
486	C₂²⋊C₄	—	2	2	no	—
487	C₂²⋊C₄	—	2	2	no	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	2	no	—
490	C₂²⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	—	2	2	no	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	2	2	no	—
494	C₂²⋊C₄	—	2	2	no	—
495	C₂²⋊C₄	—	2	2	no	—
496	C₂²⋊C₄	—	2	2	no	—
497	C₂²⋊C₄	—	4	2	no	—
498	C₂²⋊C₄	—	4	2	no	—
499	C₄²	—	2	2	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	2	2	no	—
503	C₄²	—	4	2	no	—
504	C₄²	C₂×D₄×C₁₉	1	2	yes	—
505	C₄²	C₂×D₄×C₁₉	1	2	yes	—
506	C₂³	—	2	1	no	—
507	C₂³	—	2	1	no	—
508	C₂³	—	2	2	no	—
509	C₂³	—	4	1	no	—
510	C₂³	—	4	1	no	—
511	C₂³	—	4	2	no	—
512	C₂³	—	8	1	no	—
513	C₂³	—	8	1	no	—
514	C₂³	C₁₉×#135	1	2	yes	—
515	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
516	Q₈	—	4	2	no	—
517	Q₈	—	8	1	no	—
518	D₄	—	4	2	no	—
519	D₄	—	4	4	no	—
520	D₄	—	4	2	no	—
521	D₄	—	4	2	no	—
522	D₄	—	8	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	8	2	no	—
553	C₂×C₄	—	8	1	no	—
554	C₂×C₄	—	8	2	no	—
555	C₂×C₄	—	8	1	no	—
556	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
557	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
558	C₂×C₄	C₁₉×#120	1	2	yes	—
559	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
560	C₈	—	4	2	no	—
561	C₈	—	4	2	no	—
562	C₂²	—	2	1	no	—
563	C₂²	—	2	1	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	4	2	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	4	2	no	—
569	C₂²	—	4	2	no	—
570	C₂²	—	4	2	no	—
571	C₂²	—	8	1	no	—
572	C₂²	—	16	2	no	—
573	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
574	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
575	C₂²	C₁₉×#575	1	1	yes	characteristic
576	C₄	—	2	1	no	—
577	C₄	—	2	1	no	—
578	C₄	—	2	2	no	—
579	C₄	—	2	2	no	—
580	C₄	—	4	2	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	2	no	—
583	C₄	—	4	1	no	—
584	C₄	—	4	2	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	2	no	—
587	C₄	—	8	1	no	—
588	C₄	—	8	1	no	—
589	C₄	—	8	1	no	—
590	C₂	—	2	1	no	—
591	C₂	—	2	1	no	—
592	C₂	—	4	2	no	—
593	C₂	—	8	2	no	—
594	C₂	C₁₉×#3002	1	1	yes	characteristic
595	C₂	C₁₉×#3018	1	1	yes	characteristic
596	C₂	C₁₉×#3028	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#534	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
2. C₁₉×#3232	C₂	semidirect
3. C₁₉×#2611	C₂	semidirect
4. C₁₉×#1615	C₂	semidirect
5. C₁₉×#1614	C₂	semidirect
7. C₁₉×#1609	C₂	semidirect
8. C₁₉×#1608	C₂	semidirect
10. C₁₉×#1500	C₂	semidirect
11. C₁₉×#1458	C₂	semidirect
22. C₂×C₁₉×#125	C₂²	semidirect
28. C₁₉×#484	C₂²	semidirect
29. C₁₉×#483	C₂²	semidirect
34. C₁₉×#431	C₂²	semidirect
35. C₁₉×#400	C₂²	semidirect
37. C₁₉×#398	C₂²	semidirect
43. C₁₉×#376	C₂²	semidirect
44. C₁₉×#328	C₂²	semidirect
45. C₁₉×#328	C₂²	semidirect
48. C₁₉×#324	C₂²	semidirect
207. #18393	C₁₉	direct (N × H)
265. #3232	C₂×C₁₉	semidirect
266. #2611	C₂×C₁₉	semidirect
267. #1615	C₂×C₁₉	semidirect
268. #1614	C₂×C₁₉	semidirect
270. #1609	C₂×C₁₉	semidirect
271. #1608	C₂×C₁₉	semidirect
273. #1500	C₂×C₁₉	semidirect
274. #1458	C₂×C₁₉	semidirect
313. C₂×#125	C₂²×C₁₉	semidirect
319. #484	C₂²×C₁₉	semidirect
320. #483	C₂²×C₁₉	semidirect
325. #431	C₂²×C₁₉	semidirect
326. #400	C₂²×C₁₉	semidirect
328. #398	C₂²×C₁₉	semidirect
334. #376	C₂²×C₁₉	semidirect
335. #328	C₂²×C₁₉	semidirect
336. #328	C₂²×C₁₉	semidirect
339. #324	C₂²×C₁₉	semidirect
432. C₁₉	#18393	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×#3491	2
C₁₉×#3232	2
C₁₉×#2611	2
C₁₉×#1615	2
C₁₉×#1614	2
C₁₉×#1613	2
C₁₉×#1609	2
C₁₉×#1608	2
C₁₉×#1607	2
C₁₉×#1500	2
C₁₉×#1458	2
#18393	19

Subgroups — C19×#18393 #18024352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18393 #18024352