Subgroups — C₁₉×#19032 #18024991

Order 4864.

896 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3561	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3218	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3165	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#489	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1664	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1661	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1531	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1527	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1524	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#563	C₂²	1	2	yes	—
11	C₁₉×#562	C₂²	1	2	yes	—
12	C₁₉×#556	—	2	1	no	—
13	C₁₉×#551	—	2	2	no	—
14	D₄×Q₈×C₁₉	—	2	1	no	—
15	C₁₉×#548	—	2	1	no	—
16	C₁₉×#546	—	2	1	no	—
17	C₁₉×#543	—	2	1	no	—
18	C₁₉×#542	—	2	1	no	—
19	C₁₉×#542	—	2	2	no	—
20	C₁₉×#538	—	2	1	no	—
21	C₁₉×#536	—	2	1	no	—
22	C₁₉×#533	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₁₉×#529	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
26	C₁₉×#501	C₂²	1	4	yes	complemented
27	C₁₉×#500	—	2	1	no	—
28	C₁₉×#498	—	2	1	no	—
29	C₁₉×#497	C₂²	1	2	yes	complemented
30	C₁₉×#491	C₂²	1	2	yes	complemented
31	C₁₉×#489	—	2	2	no	—
32	C₁₉×#489	C₂²	1	4	yes	—
33	C₁₉×#462	—	2	1	no	—
34	C₁₉×#461	—	2	1	no	—
35	C₁₉×#451	—	2	1	no	—
36	C₁₉×#448	—	2	1	no	—
37	C₁₉×#432	C₂²	1	1	yes	characteristic
38	C₁₉×#428	—	2	2	no	—
39	C₂×C₁₉×#103	—	2	1	no	—
40	C₂×C₁₉×#102	—	2	1	no	—
41	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
42	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
43	C₁₉×#330	C₂²	1	4	yes	complemented
44	C₁₉×#330	C₂²	1	2	yes	complemented
45	C₁₉×#329	C₂²	1	4	yes	—
46	C₁₉×#329	C₂²	1	2	yes	complemented
47	C₂×#41×C₁₉	—	2	1	no	—
48	C₂²×Q₈×C₁₉	—	2	1	no	—
49	C₂²×Q₈×C₁₉	—	2	1	no	—
50	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
51	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
52	C₂×Q₁₆×C₁₉	—	2	2	no	—
53	C₂×SD₁₆×C₁₉	—	2	2	no	—
54	C₂×M₁₆×C₁₉	—	2	1	no	—
55	C₂²×C₈×C₁₉	—	2	1	no	—
56	C₁₉×C₄⋊Q₈	—	2	1	no	—
57	C₁₉×C₄⋊Q₈	—	2	2	no	—
58	C₁₉×C₄⋊Q₈	—	2	1	no	—
59	C₁₉×C₄⋊Q₈	—	2	1	no	—
60	C₁₉×C₄⋊Q₈	—	2	1	no	—
61	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
62	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
63	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
64	C₁₉×#126	—	2	2	no	—
65	C₁₉×#126	—	2	2	no	—
66	C₁₉×#126	—	2	2	no	—
67	C₁₉×#126	—	2	1	no	—
68	C₁₉×#125	C₂³	1	1	yes	characteristic
69	C₁₉×#125	C₂³	1	2	yes	—
70	C₁₉×#124	—	2	1	no	—
71	C₁₉×#124	—	2	2	no	—
72	C₁₉×#124	—	2	2	no	—
73	C₁₉×#124	—	2	1	no	—
74	C₁₉×#124	—	2	1	no	—
75	C₁₉×#124	D₄	1	2	yes	—
76	C₁₉×#124	C₂³	1	2	yes	—
77	C₁₉×#124	C₂³	1	1	yes	characteristic
78	C₁₉×#123	—	2	2	no	—
79	C₁₉×#123	—	2	2	no	—
80	C₁₉×#123	—	2	1	no	—
81	C₁₉×#123	—	2	2	no	—
82	C₁₉×#123	—	2	2	no	—
83	C₁₉×C₂²⋊Q₈	—	2	2	no	—
84	C₁₉×C₂²⋊Q₈	—	2	2	no	—
85	C₁₉×C₂²⋊Q₈	—	2	1	no	—
86	C₁₉×C₂²⋊Q₈	—	2	2	no	—
87	C₁₉×C₂²⋊Q₈	—	2	2	no	—
88	C₁₉×C₂²⋊Q₈	—	2	2	no	—
89	C₁₉×C₂²⋊Q₈	—	2	1	no	—
90	C₁₉×C₂²⋊Q₈	—	2	1	no	—
91	C₁₉×C₂²⋊Q₈	—	2	2	no	—
92	C₁₉×C₂²⋊Q₈	—	2	2	no	—
93	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
94	C₁₉×#121	—	2	1	no	—
95	C₁₉×#121	—	2	2	no	—
96	C₁₉×#121	—	2	2	no	—
97	C₁₉×#121	D₄	1	1	yes	characteristic
98	C₁₉×#120	—	2	2	no	—
99	C₄×Q₈×C₁₉	—	2	1	no	—
100	C₄×Q₈×C₁₉	—	2	1	no	—
101	C₄×Q₈×C₁₉	—	2	1	no	—
102	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
103	C₄×D₄×C₁₉	—	2	2	no	—
104	C₄×D₄×C₁₉	—	2	1	no	—
105	C₄×D₄×C₁₉	—	2	2	no	—
106	C₄×D₄×C₁₉	—	2	1	no	—
107	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
108	C₁₉×#117	—	2	2	no	—
109	C₁₉×#117	—	2	1	no	—
110	C₁₉×#117	D₄	1	2	yes	—
111	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
112	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
114	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
116	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
117	C₁₉×#107	—	2	4	no	—
118	C₁₉×#106	—	2	4	no	—
119	C₁₉×C₄⋊C₈	—	2	1	no	—
120	C₁₉×#103	—	2	4	no	—
121	C₁₉×#103	—	2	2	no	—
122	C₁₉×#103	—	2	2	no	—
123	C₁₉×#102	—	2	4	no	—
124	C₁₉×C₂²⋊C₈	—	2	1	no	—
125	C₁₉×#97	—	2	1	no	—
126	C₁₉×#97	C₂³	1	2	yes	—
127	C₁₉×#97	C₂³	1	2	yes	—
128	C₁₉×#97	C₂³	1	2	yes	—
129	C₄×C₈×C₁₉	—	2	1	no	—
130	C₂⁴×C₁₉	—	2	1	no	—
131	#41×C₁₉	—	8	2	no	—
132	C₂×Q₈×C₁₉	—	2	2	no	—
133	C₂×Q₈×C₁₉	—	2	1	no	—
134	C₂×Q₈×C₁₉	—	2	1	no	—
135	C₂×Q₈×C₁₉	—	2	1	no	—
136	C₂×Q₈×C₁₉	—	2	2	no	—
137	C₂×Q₈×C₁₉	—	4	2	no	—
138	C₂×Q₈×C₁₉	—	4	1	no	—
139	C₂×Q₈×C₁₉	—	8	2	no	—
140	C₂×Q₈×C₁₉	—	8	2	no	—
141	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
143	C₂×D₄×C₁₉	—	2	1	no	—
144	C₂×D₄×C₁₉	—	2	2	no	—
145	C₂×D₄×C₁₉	—	2	2	no	—
146	C₂×D₄×C₁₉	—	2	1	no	—
147	C₂×D₄×C₁₉	—	4	2	no	—
148	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₁₉	—	2	2	no	—
151	C₂²×C₄×C₁₉	—	2	2	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	—	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	C₂×D₄	1	1	yes	characteristic
159	Q₁₆×C₁₉	—	8	2	no	—
160	SD₁₆×C₁₉	—	8	2	no	—
161	M₁₆×C₁₉	—	2	4	no	—
162	C₂×C₈×C₁₉	—	2	2	no	—
163	C₂×C₈×C₁₉	—	2	2	no	—
164	C₂×C₈×C₁₉	—	2	2	no	—
165	C₂×C₈×C₁₉	—	4	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	2	no	—
170	C₄⋊C₄×C₁₉	—	2	1	no	—
171	C₄⋊C₄×C₁₉	—	2	1	no	—
172	C₄⋊C₄×C₁₉	—	2	1	no	—
173	C₄⋊C₄×C₁₉	—	2	1	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	2	no	—
179	C₄⋊C₄×C₁₉	—	2	2	no	—
180	C₄⋊C₄×C₁₉	—	4	1	no	—
181	C₄⋊C₄×C₁₉	—	4	1	no	—
182	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
183	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
184	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
185	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	1	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	1	no	—
196	C₂²⋊C₄×C₁₉	—	2	1	no	—
197	C₂²⋊C₄×C₁₉	—	2	2	no	—
198	C₂²⋊C₄×C₁₉	—	2	2	no	—
199	C₂²⋊C₄×C₁₉	—	2	1	no	—
200	C₂²⋊C₄×C₁₉	—	2	1	no	—
201	C₄²×C₁₉	—	2	2	no	—
202	C₄²×C₁₉	—	2	2	no	—
203	C₄²×C₁₉	—	2	1	no	—
204	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
205	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
206	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
208	#19032	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
209	C₂³×C₁₉	—	2	2	no	—
210	C₂³×C₁₉	—	2	1	no	—
211	C₂³×C₁₉	—	4	2	no	—
212	C₂³×C₁₉	—	8	1	no	—
213	C₂³×C₁₉	—	8	1	no	—
214	C₂³×C₁₉	#120	1	1	yes	characteristic
215	Q₈×C₁₉	—	4	1	no	—
216	Q₈×C₁₉	—	4	2	no	—
217	Q₈×C₁₉	—	4	2	no	—
218	Q₈×C₁₉	—	4	2	no	—
219	Q₈×C₁₉	—	4	2	no	—
220	Q₈×C₁₉	—	4	2	no	—
221	Q₈×C₁₉	—	8	1	no	—
222	Q₈×C₁₉	—	8	2	no	—
223	Q₈×C₁₉	—	8	2	no	—
224	D₄×C₁₉	—	4	1	no	—
225	D₄×C₁₉	—	4	2	no	—
226	D₄×C₁₉	—	4	2	no	—
227	D₄×C₁₉	—	4	2	no	—
228	D₄×C₁₉	—	8	2	no	—
229	D₄×C₁₉	—	8	2	no	—
230	C₂×C₄×C₁₉	—	2	2	no	—
231	C₂×C₄×C₁₉	—	2	2	no	—
232	C₂×C₄×C₁₉	—	2	1	no	—
233	C₂×C₄×C₁₉	—	2	2	no	—
234	C₂×C₄×C₁₉	—	2	1	no	—
235	C₂×C₄×C₁₉	—	2	2	no	—
236	C₂×C₄×C₁₉	—	2	2	no	—
237	C₂×C₄×C₁₉	—	2	1	no	—
238	C₂×C₄×C₁₉	—	4	1	no	—
239	C₂×C₄×C₁₉	—	4	2	no	—
240	C₂×C₄×C₁₉	—	4	2	no	—
241	C₂×C₄×C₁₉	—	8	1	no	—
242	C₂×C₄×C₁₉	—	8	2	no	—
243	C₂×C₄×C₁₉	—	8	2	no	—
244	C₂×C₄×C₁₉	—	8	2	no	—
245	C₂×C₄×C₁₉	—	8	2	no	—
246	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
247	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
248	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
249	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
252	C₈×C₁₉	—	2	4	no	—
253	C₈×C₁₉	—	4	2	no	—
254	C₈×C₁₉	—	4	2	no	—
255	#3561	C₂×C₁₉	1	1	yes	characteristic
256	#3218	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#3165	C₂×C₁₉	1	1	yes	characteristic, complemented
258	C₂×#489	C₂×C₁₉	1	1	yes	characteristic, complemented
259	#1664	C₂×C₁₉	1	4	yes	complemented
260	#1661	C₂×C₁₉	1	4	yes	complemented
261	#1531	C₂×C₁₉	1	1	yes	characteristic, complemented
262	#1527	C₂×C₁₉	1	1	yes	characteristic, complemented
263	#1524	C₂×C₁₉	1	1	yes	characteristic, complemented
264	C₂²×C₁₉	—	2	1	no	—
265	C₂²×C₁₉	—	2	1	no	—
266	C₂²×C₁₉	—	4	1	no	—
267	C₂²×C₁₉	—	4	2	no	—
268	C₂²×C₁₉	—	4	1	no	—
269	C₂²×C₁₉	—	4	2	no	—
270	C₂²×C₁₉	—	4	2	no	—
271	C₂²×C₁₉	—	4	1	no	—
272	C₂²×C₁₉	—	16	2	no	—
273	C₂²×C₁₉	#456	1	2	yes	—
274	C₂²×C₁₉	C₂×#120	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	—	2	1	no	—
280	C₄×C₁₉	—	4	1	no	—
281	C₄×C₁₉	—	4	2	no	—
282	C₄×C₁₉	—	4	2	no	—
283	C₄×C₁₉	—	4	1	no	—
284	C₄×C₁₉	—	4	1	no	—
285	C₄×C₁₉	—	4	2	no	—
286	C₄×C₁₉	—	8	2	no	—
287	C₄×C₁₉	#455	1	2	yes	—
288	#563	C₂²×C₁₉	1	2	yes	—
289	#562	C₂²×C₁₉	1	2	yes	—
290	#556	—	2	1	no	—
291	#551	—	2	2	no	—
292	D₄×Q₈	—	2	1	no	—
293	#548	—	2	1	no	—
294	#546	—	2	1	no	—
295	#543	—	2	1	no	—
296	#542	—	2	1	no	—
297	#542	—	2	2	no	—
298	#538	—	2	1	no	—
299	#536	—	2	1	no	—
300	#533	C₂²×C₁₉	1	1	yes	characteristic
301	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
302	#529	C₂²×C₁₉	1	1	yes	characteristic
303	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
304	#501	C₂²×C₁₉	1	4	yes	complemented
305	#500	—	2	1	no	—
306	#498	—	2	1	no	—
307	#497	C₂²×C₁₉	1	2	yes	complemented
308	#491	C₂²×C₁₉	1	2	yes	complemented
309	#489	—	2	2	no	—
310	#489	C₂²×C₁₉	1	4	yes	—
311	#462	—	2	1	no	—
312	#461	—	2	1	no	—
313	#451	—	2	1	no	—
314	#448	—	2	1	no	—
315	#432	C₂²×C₁₉	1	1	yes	characteristic
316	#428	—	2	2	no	—
317	C₂×#103	—	2	1	no	—
318	C₂×#102	—	2	1	no	—
319	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
320	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
321	#330	C₂²×C₁₉	1	4	yes	complemented
322	#330	C₂²×C₁₉	1	2	yes	complemented
323	#329	C₂²×C₁₉	1	4	yes	—
324	#329	C₂²×C₁₉	1	2	yes	complemented
325	C₂×C₁₉	—	2	2	no	—
326	C₂×C₁₉	—	8	1	no	—
327	C₂×C₁₉	—	8	2	no	—
328	C₂×C₁₉	C₂×#455	1	1	yes	characteristic
329	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
330	C₂×C₁₉	#3021	1	1	yes	characteristic
331	C₂×#41	—	2	1	no	—
332	C₂²×Q₈	—	2	1	no	—
333	C₂²×Q₈	—	2	1	no	—
334	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
335	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
336	C₂×Q₁₆	—	2	2	no	—
337	C₂×SD₁₆	—	2	2	no	—
338	C₂×M₁₆	—	2	1	no	—
339	C₂²×C₈	—	2	1	no	—
340	C₄⋊Q₈	—	2	1	no	—
341	C₄⋊Q₈	—	2	2	no	—
342	C₄⋊Q₈	—	2	1	no	—
343	C₄⋊Q₈	—	2	1	no	—
344	C₄⋊Q₈	—	2	1	no	—
345	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
346	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
347	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
348	#126	—	2	2	no	—
349	#126	—	2	2	no	—
350	#126	—	2	2	no	—
351	#126	—	2	1	no	—
352	#125	C₂³×C₁₉	1	1	yes	characteristic
353	#125	C₂³×C₁₉	1	2	yes	—
354	#124	—	2	1	no	—
355	#124	—	2	2	no	—
356	#124	—	2	2	no	—
357	#124	—	2	1	no	—
358	#124	—	2	1	no	—
359	#124	D₄×C₁₉	1	2	yes	—
360	#124	C₂³×C₁₉	1	2	yes	—
361	#124	C₂³×C₁₉	1	1	yes	characteristic
362	#123	—	2	2	no	—
363	#123	—	2	2	no	—
364	#123	—	2	1	no	—
365	#123	—	2	2	no	—
366	#123	—	2	2	no	—
367	C₂²⋊Q₈	—	2	2	no	—
368	C₂²⋊Q₈	—	2	2	no	—
369	C₂²⋊Q₈	—	2	1	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	1	no	—
375	C₂²⋊Q₈	—	2	2	no	—
376	C₂²⋊Q₈	—	2	2	no	—
377	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
378	#121	—	2	1	no	—
379	#121	—	2	2	no	—
380	#121	—	2	2	no	—
381	#121	D₄×C₁₉	1	1	yes	characteristic
382	#120	—	2	2	no	—
383	C₄×Q₈	—	2	1	no	—
384	C₄×Q₈	—	2	1	no	—
385	C₄×Q₈	—	2	1	no	—
386	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
387	C₄×D₄	—	2	2	no	—
388	C₄×D₄	—	2	1	no	—
389	C₄×D₄	—	2	2	no	—
390	C₄×D₄	—	2	1	no	—
391	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
392	#117	—	2	2	no	—
393	#117	—	2	1	no	—
394	#117	D₄×C₁₉	1	2	yes	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₂²⋊C₄	—	2	2	no	—
398	C₂×C₂²⋊C₄	—	2	1	no	—
399	C₂×C₂²⋊C₄	—	2	1	no	—
400	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
401	#107	—	2	4	no	—
402	#106	—	2	4	no	—
403	C₄⋊C₈	—	2	1	no	—
404	#103	—	2	4	no	—
405	#103	—	2	2	no	—
406	#103	—	2	2	no	—
407	#102	—	2	4	no	—
408	C₂²⋊C₈	—	2	1	no	—
409	#97	—	2	1	no	—
410	#97	C₂³×C₁₉	1	2	yes	—
411	#97	C₂³×C₁₉	1	2	yes	—
412	#97	C₂³×C₁₉	1	2	yes	—
413	C₄×C₈	—	2	1	no	—
414	C₁₉	#19032	1	1	yes	characteristic, direct product factor, Sylow
415	C₂⁴	—	2	1	no	—
416	#41	—	8	2	no	—
417	C₂×Q₈	—	2	2	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	—	2	1	no	—
421	C₂×Q₈	—	2	2	no	—
422	C₂×Q₈	—	4	2	no	—
423	C₂×Q₈	—	4	1	no	—
424	C₂×Q₈	—	8	2	no	—
425	C₂×Q₈	—	8	2	no	—
426	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
427	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	—	4	2	no	—
433	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
434	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	4	1	no	—
441	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
442	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
443	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
444	Q₁₆	—	8	2	no	—
445	SD₁₆	—	8	2	no	—
446	M₁₆	—	2	4	no	—
447	C₂×C₈	—	2	2	no	—
448	C₂×C₈	—	2	2	no	—
449	C₂×C₈	—	2	2	no	—
450	C₂×C₈	—	4	2	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	1	no	—
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	2	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	4	1	no	—
466	C₄⋊C₄	—	4	1	no	—
467	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
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	2	yes	—
471	C₂²⋊C₄	—	2	2	no	—
472	C₂²⋊C₄	—	2	2	no	—
473	C₂²⋊C₄	—	2	2	no	—
474	C₂²⋊C₄	—	2	2	no	—
475	C₂²⋊C₄	—	2	2	no	—
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	2	2	no	—
478	C₂²⋊C₄	—	2	2	no	—
479	C₂²⋊C₄	—	2	2	no	—
480	C₂²⋊C₄	—	2	1	no	—
481	C₂²⋊C₄	—	2	1	no	—
482	C₂²⋊C₄	—	2	2	no	—
483	C₂²⋊C₄	—	2	2	no	—
484	C₂²⋊C₄	—	2	1	no	—
485	C₂²⋊C₄	—	2	1	no	—
486	C₄²	—	2	2	no	—
487	C₄²	—	2	2	no	—
488	C₄²	—	2	1	no	—
489	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
490	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
491	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
492	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
493	C₂³	—	2	2	no	—
494	C₂³	—	2	1	no	—
495	C₂³	—	4	2	no	—
496	C₂³	—	8	1	no	—
497	C₂³	—	8	1	no	—
498	C₂³	C₁₉×#120	1	1	yes	characteristic
499	Q₈	—	4	1	no	—
500	Q₈	—	4	2	no	—
501	Q₈	—	4	2	no	—
502	Q₈	—	4	2	no	—
503	Q₈	—	4	2	no	—
504	Q₈	—	4	2	no	—
505	Q₈	—	8	1	no	—
506	Q₈	—	8	2	no	—
507	Q₈	—	8	2	no	—
508	D₄	—	4	1	no	—
509	D₄	—	4	2	no	—
510	D₄	—	4	2	no	—
511	D₄	—	4	2	no	—
512	D₄	—	8	2	no	—
513	D₄	—	8	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	8	1	no	—
526	C₂×C₄	—	8	2	no	—
527	C₂×C₄	—	8	2	no	—
528	C₂×C₄	—	8	2	no	—
529	C₂×C₄	—	8	2	no	—
530	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
531	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
532	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
533	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
534	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
535	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
536	C₈	—	2	4	no	—
537	C₈	—	4	2	no	—
538	C₈	—	4	2	no	—
539	C₂²	—	2	1	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	4	1	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	4	1	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	4	2	no	—
546	C₂²	—	4	1	no	—
547	C₂²	—	16	2	no	—
548	C₂²	C₁₉×#456	1	2	yes	—
549	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	2	1	no	—
553	C₄	—	2	1	no	—
554	C₄	—	2	1	no	—
555	C₄	—	4	1	no	—
556	C₄	—	4	2	no	—
557	C₄	—	4	2	no	—
558	C₄	—	4	1	no	—
559	C₄	—	4	1	no	—
560	C₄	—	4	2	no	—
561	C₄	—	8	2	no	—
562	C₄	C₁₉×#455	1	2	yes	—
563	C₂	—	2	2	no	—
564	C₂	—	8	2	no	—
565	C₂	—	8	1	no	—
566	C₂	C₂×C₁₉×#455	1	1	yes	characteristic
567	C₂	C₂×C₁₉×#456	1	1	yes	characteristic
568	C₂	C₁₉×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3561	C₂
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×#3218	C₂	semidirect
3. C₁₉×#3165	C₂	semidirect
4. C₂×C₁₉×#489	C₂	semidirect
5. C₁₉×#1664	C₂	semidirect
6. C₁₉×#1661	C₂	semidirect
7. C₁₉×#1531	C₂	semidirect
8. C₁₉×#1527	C₂	semidirect
9. C₁₉×#1524	C₂	semidirect
26. C₁₉×#501	C₂²	semidirect
29. C₁₉×#497	C₂²	semidirect
30. C₁₉×#491	C₂²	semidirect
43. C₁₉×#330	C₂²	semidirect
44. C₁₉×#330	C₂²	semidirect
46. C₁₉×#329	C₂²	semidirect
208. #19032	C₁₉	direct (N × H)
256. #3218	C₂×C₁₉	semidirect
257. #3165	C₂×C₁₉	semidirect
258. C₂×#489	C₂×C₁₉	semidirect
259. #1664	C₂×C₁₉	semidirect
260. #1661	C₂×C₁₉	semidirect
261. #1531	C₂×C₁₉	semidirect
262. #1527	C₂×C₁₉	semidirect
263. #1524	C₂×C₁₉	semidirect
304. #501	C₂²×C₁₉	semidirect
307. #497	C₂²×C₁₉	semidirect
308. #491	C₂²×C₁₉	semidirect
321. #330	C₂²×C₁₉	semidirect
322. #330	C₂²×C₁₉	semidirect
324. #329	C₂²×C₁₉	semidirect
414. C₁₉	#19032	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×#3561	2
C₁₉×#3218	2
C₁₉×#3165	2
C₂×C₁₉×#489	2
C₁₉×#1664	2
C₁₉×#1661	2
C₁₉×#1531	2
C₁₉×#1527	2
C₁₉×#1524	2
#19032	19

Subgroups — C19×#19032 #18024991

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19032 #18024991