Subgroups — C₁₉×#19022 #18024981

Order 4864.

892 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×#3559	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3218	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#501	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3141	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×#1530	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1528	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×#554	—	2	1	no	—
13	C₁₉×#553	—	2	1	no	—
14	C₁₉×#553	—	2	1	no	—
15	C₁₉×#547	—	2	2	no	—
16	C₁₉×#547	—	2	1	no	—
17	C₁₉×#544	—	2	1	no	—
18	C₁₉×#540	—	2	1	no	—
19	C₁₉×#539	—	2	2	no	—
20	C₁₉×#539	—	2	1	no	—
21	C₁₉×#537	—	2	1	no	—
22	C₁₉×#532	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×#125	C₂²	1	1	yes	characteristic
26	C₁₉×#501	—	2	2	no	—
27	C₁₉×#501	C₂²	1	4	yes	—
28	C₁₉×#497	C₂²	1	2	yes	—
29	C₁₉×#491	C₂²	1	2	yes	—
30	C₁₉×#489	C₂²	1	4	yes	—
31	C₁₉×#487	—	2	1	no	—
32	C₁₉×#486	—	2	1	no	—
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	C₂×C₁₉×#107	—	2	1	no	—
39	C₂×C₁₉×#106	—	2	1	no	—
40	C₁₉×#417	—	2	2	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	—
44	C₁₉×#330	C₂²	1	2	yes	—
45	C₁₉×#329	C₂²	1	2	yes	—
46	C₁₉×#329	C₂²	1	4	yes	—
47	C₂×#41×C₁₉	—	2	2	no	—
48	C₂×#41×C₁₉	D₄	1	2	yes	—
49	C₂²×Q₈×C₁₉	—	2	1	no	—
50	C₂×Q₁₆×C₁₉	—	2	2	no	—
51	C₂×SD₁₆×C₁₉	—	2	2	no	—
52	C₂×M₁₆×C₁₉	—	2	1	no	—
53	C₂²×C₈×C₁₉	—	2	1	no	—
54	C₁₉×C₄⋊Q₈	—	2	1	no	—
55	C₁₉×C₄⋊Q₈	—	2	2	no	—
56	C₁₉×C₄⋊Q₈	—	2	1	no	—
57	C₁₉×C₄⋊Q₈	—	2	1	no	—
58	C₁₉×C₄⋊Q₈	—	2	1	no	—
59	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
60	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
61	C₁₉×#127	D₄	1	1	yes	characteristic
62	C₁₉×#126	—	2	2	no	—
63	C₁₉×#126	—	2	2	no	—
64	C₁₉×#126	—	2	1	no	—
65	C₁₉×#125	—	2	2	no	—
66	C₁₉×#125	—	2	1	no	—
67	C₁₉×#125	—	2	1	no	—
68	C₁₉×#125	—	2	1	no	—
69	C₁₉×#125	D₄	1	2	yes	—
70	C₁₉×#125	C₂³	1	1	yes	characteristic
71	C₁₉×#125	C₂³	1	2	yes	—
72	C₁₉×#124	C₂³	1	2	yes	—
73	C₁₉×#124	C₂³	1	1	yes	characteristic
74	C₁₉×#123	—	2	2	no	—
75	C₁₉×#123	—	2	2	no	—
76	C₁₉×#123	—	2	2	no	—
77	C₁₉×#123	—	2	2	no	—
78	C₁₉×#123	—	2	1	no	—
79	C₁₉×#123	—	2	2	no	—
80	C₁₉×#123	—	2	2	no	—
81	C₁₉×C₂²⋊Q₈	—	2	2	no	—
82	C₁₉×C₂²⋊Q₈	—	2	2	no	—
83	C₁₉×C₂²⋊Q₈	—	2	2	no	—
84	C₁₉×C₂²⋊Q₈	—	2	2	no	—
85	C₁₉×C₂²⋊Q₈	—	2	2	no	—
86	C₁₉×C₂²⋊Q₈	—	2	2	no	—
87	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
88	C₁₉×#121	—	2	2	no	—
89	C₁₉×#121	—	2	2	no	—
90	C₁₉×#121	—	2	1	no	—
91	C₁₉×#121	—	2	1	no	—
92	C₁₉×#121	—	2	2	no	—
93	C₁₉×#121	—	2	2	no	—
94	C₁₉×#121	—	2	1	no	—
95	C₁₉×#121	—	2	1	no	—
96	C₁₉×#121	D₄	1	1	yes	characteristic
97	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
98	C₄×D₄×C₁₉	—	2	2	no	—
99	C₄×D₄×C₁₉	—	2	2	no	—
100	C₄×D₄×C₁₉	—	2	1	no	—
101	C₄×D₄×C₁₉	—	2	1	no	—
102	C₄×D₄×C₁₉	—	2	1	no	—
103	C₄×D₄×C₁₉	—	2	1	no	—
104	C₄×D₄×C₁₉	—	2	1	no	—
105	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
106	C₁₉×#117	—	2	1	no	—
107	C₁₉×#117	—	2	1	no	—
108	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
109	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
111	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
112	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
113	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
114	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
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	#41×C₁₉	—	4	4	no	—
131	#41×C₁₉	—	8	4	no	—
132	C₂×Q₈×C₁₉	—	2	2	no	—
133	C₂×Q₈×C₁₉	—	2	2	no	—
134	C₂×Q₈×C₁₉	—	4	1	no	—
135	C₂×Q₈×C₁₉	—	8	2	no	—
136	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
138	C₂×D₄×C₁₉	—	2	2	no	—
139	C₂×D₄×C₁₉	—	2	1	no	—
140	C₂×D₄×C₁₉	—	2	2	no	—
141	C₂×D₄×C₁₉	—	2	2	no	—
142	C₂×D₄×C₁₉	—	2	1	no	—
143	C₂×D₄×C₁₉	—	2	1	no	—
144	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₁₉	—	2	1	no	—
147	C₂²×C₄×C₁₉	—	2	2	no	—
148	C₂²×C₄×C₁₉	—	2	2	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	—	4	1	no	—
154	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
157	Q₁₆×C₁₉	—	8	2	no	—
158	SD₁₆×C₁₉	—	8	2	no	—
159	M₁₆×C₁₉	—	4	2	no	—
160	C₂×C₈×C₁₉	—	2	4	no	—
161	C₂×C₈×C₁₉	—	2	2	no	—
162	C₂×C₈×C₁₉	—	2	2	no	—
163	C₂×C₈×C₁₉	—	2	2	no	—
164	C₄⋊C₄×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	1	no	—
172	C₄⋊C₄×C₁₉	—	2	2	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	1	no	—
179	C₄⋊C₄×C₁₉	—	2	1	no	—
180	C₄⋊C₄×C₁₉	—	2	2	no	—
181	C₄⋊C₄×C₁₉	—	2	2	no	—
182	C₄⋊C₄×C₁₉	—	4	1	no	—
183	C₄⋊C₄×C₁₉	—	4	1	no	—
184	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
185	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
186	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
187	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	1	no	—
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	2	no	—
198	C₂²⋊C₄×C₁₉	—	2	2	no	—
199	C₂²⋊C₄×C₁₉	—	2	1	no	—
200	C₄²×C₁₉	—	2	2	no	—
201	C₄²×C₁₉	—	2	1	no	—
202	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
204	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
205	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
206	#19022	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂³×C₁₉	—	2	2	no	—
208	C₂³×C₁₉	—	2	1	no	—
209	C₂³×C₁₉	#120	1	1	yes	characteristic
210	Q₈×C₁₉	—	4	1	no	—
211	Q₈×C₁₉	—	4	2	no	—
212	Q₈×C₁₉	—	4	2	no	—
213	Q₈×C₁₉	—	4	2	no	—
214	Q₈×C₁₉	—	8	2	no	—
215	Q₈×C₁₉	—	8	2	no	—
216	D₄×C₁₉	—	4	1	no	—
217	D₄×C₁₉	—	4	2	no	—
218	D₄×C₁₉	—	4	4	no	—
219	D₄×C₁₉	—	4	2	no	—
220	D₄×C₁₉	—	4	2	no	—
221	D₄×C₁₉	—	8	1	no	—
222	D₄×C₁₉	—	8	2	no	—
223	D₄×C₁₉	—	8	2	no	—
224	C₂×C₄×C₁₉	—	2	2	no	—
225	C₂×C₄×C₁₉	—	2	2	no	—
226	C₂×C₄×C₁₉	—	2	1	no	—
227	C₂×C₄×C₁₉	—	2	1	no	—
228	C₂×C₄×C₁₉	—	2	2	no	—
229	C₂×C₄×C₁₉	—	2	2	no	—
230	C₂×C₄×C₁₉	—	2	1	no	—
231	C₂×C₄×C₁₉	—	2	2	no	—
232	C₂×C₄×C₁₉	—	4	1	no	—
233	C₂×C₄×C₁₉	—	4	2	no	—
234	C₂×C₄×C₁₉	—	4	2	no	—
235	C₂×C₄×C₁₉	—	4	2	no	—
236	C₂×C₄×C₁₉	—	8	2	no	—
237	C₂×C₄×C₁₉	—	8	1	no	—
238	C₂×C₄×C₁₉	—	8	2	no	—
239	C₂×C₄×C₁₉	—	8	2	no	—
240	C₂×C₄×C₁₉	—	8	2	no	—
241	C₂×C₄×C₁₉	—	8	2	no	—
242	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
243	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
244	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
245	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
248	C₈×C₁₉	—	2	4	no	—
249	C₈×C₁₉	—	4	2	no	—
250	C₈×C₁₉	—	4	2	no	—
251	#3559	C₂×C₁₉	1	1	yes	characteristic
252	#3218	C₂×C₁₉	1	1	yes	characteristic, complemented
253	C₂×#501	C₂×C₁₉	1	1	yes	characteristic, complemented
254	#3141	C₂×C₁₉	1	1	yes	characteristic, complemented
255	#1664	C₂×C₁₉	1	4	yes	complemented
256	#1661	C₂×C₁₉	1	4	yes	complemented
257	#1530	C₂×C₁₉	1	1	yes	characteristic, complemented
258	#1528	C₂×C₁₉	1	1	yes	characteristic, complemented
259	#1524	C₂×C₁₉	1	1	yes	characteristic, complemented
260	C₂²×C₁₉	—	2	1	no	—
261	C₂²×C₁₉	—	2	1	no	—
262	C₂²×C₁₉	—	4	2	no	—
263	C₂²×C₁₉	—	4	1	no	—
264	C₂²×C₁₉	—	4	1	no	—
265	C₂²×C₁₉	—	4	2	no	—
266	C₂²×C₁₉	—	4	2	no	—
267	C₂²×C₁₉	—	4	1	no	—
268	C₂²×C₁₉	#455	1	2	yes	—
269	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
270	C₄×C₁₉	—	2	1	no	—
271	C₄×C₁₉	—	2	1	no	—
272	C₄×C₁₉	—	2	1	no	—
273	C₄×C₁₉	—	2	1	no	—
274	C₄×C₁₉	—	2	1	no	—
275	C₄×C₁₉	—	4	2	no	—
276	C₄×C₁₉	—	4	2	no	—
277	C₄×C₁₉	—	4	1	no	—
278	C₄×C₁₉	—	4	1	no	—
279	C₄×C₁₉	—	4	2	no	—
280	C₄×C₁₉	—	4	1	no	—
281	C₄×C₁₉	—	8	2	no	—
282	C₄×C₁₉	#456	1	2	yes	—
283	#563	C₂²×C₁₉	1	2	yes	—
284	#562	C₂²×C₁₉	1	2	yes	—
285	#554	—	2	1	no	—
286	#553	—	2	1	no	—
287	#553	—	2	1	no	—
288	#547	—	2	2	no	—
289	#547	—	2	1	no	—
290	#544	—	2	1	no	—
291	#540	—	2	1	no	—
292	#539	—	2	2	no	—
293	#539	—	2	1	no	—
294	#537	—	2	1	no	—
295	#532	C₂²×C₁₉	1	1	yes	characteristic
296	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
297	#529	C₂²×C₁₉	1	1	yes	characteristic
298	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
299	#501	—	2	2	no	—
300	#501	C₂²×C₁₉	1	4	yes	—
301	#497	C₂²×C₁₉	1	2	yes	—
302	#491	C₂²×C₁₉	1	2	yes	—
303	#489	C₂²×C₁₉	1	4	yes	—
304	#487	—	2	1	no	—
305	#486	—	2	1	no	—
306	#462	—	2	1	no	—
307	#461	—	2	1	no	—
308	#451	—	2	1	no	—
309	#448	—	2	1	no	—
310	#432	C₂²×C₁₉	1	1	yes	characteristic
311	C₂×#107	—	2	1	no	—
312	C₂×#106	—	2	1	no	—
313	#417	—	2	2	no	—
314	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
315	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
316	#330	C₂²×C₁₉	1	4	yes	—
317	#330	C₂²×C₁₉	1	2	yes	—
318	#329	C₂²×C₁₉	1	2	yes	—
319	#329	C₂²×C₁₉	1	4	yes	—
320	C₂×C₁₉	—	2	2	no	—
321	C₂×C₁₉	—	8	2	no	—
322	C₂×C₁₉	—	8	1	no	—
323	C₂×C₁₉	C₂×#455	1	1	yes	characteristic
324	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
325	C₂×C₁₉	#3021	1	1	yes	characteristic
326	C₂×#41	—	2	2	no	—
327	C₂×#41	D₄×C₁₉	1	2	yes	—
328	C₂²×Q₈	—	2	1	no	—
329	C₂×Q₁₆	—	2	2	no	—
330	C₂×SD₁₆	—	2	2	no	—
331	C₂×M₁₆	—	2	1	no	—
332	C₂²×C₈	—	2	1	no	—
333	C₄⋊Q₈	—	2	1	no	—
334	C₄⋊Q₈	—	2	2	no	—
335	C₄⋊Q₈	—	2	1	no	—
336	C₄⋊Q₈	—	2	1	no	—
337	C₄⋊Q₈	—	2	1	no	—
338	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
339	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
340	#127	D₄×C₁₉	1	1	yes	characteristic
341	#126	—	2	2	no	—
342	#126	—	2	2	no	—
343	#126	—	2	1	no	—
344	#125	—	2	2	no	—
345	#125	—	2	1	no	—
346	#125	—	2	1	no	—
347	#125	—	2	1	no	—
348	#125	D₄×C₁₉	1	2	yes	—
349	#125	C₂³×C₁₉	1	2	yes	—
350	#125	C₂³×C₁₉	1	1	yes	characteristic
351	#124	C₂³×C₁₉	1	1	yes	characteristic
352	#124	C₂³×C₁₉	1	2	yes	—
353	#123	—	2	2	no	—
354	#123	—	2	2	no	—
355	#123	—	2	2	no	—
356	#123	—	2	2	no	—
357	#123	—	2	1	no	—
358	#123	—	2	2	no	—
359	#123	—	2	2	no	—
360	C₂²⋊Q₈	—	2	2	no	—
361	C₂²⋊Q₈	—	2	2	no	—
362	C₂²⋊Q₈	—	2	2	no	—
363	C₂²⋊Q₈	—	2	2	no	—
364	C₂²⋊Q₈	—	2	2	no	—
365	C₂²⋊Q₈	—	2	2	no	—
366	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
367	#121	—	2	2	no	—
368	#121	—	2	2	no	—
369	#121	—	2	1	no	—
370	#121	—	2	1	no	—
371	#121	—	2	2	no	—
372	#121	—	2	2	no	—
373	#121	—	2	1	no	—
374	#121	—	2	1	no	—
375	#121	D₄×C₁₉	1	1	yes	characteristic
376	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
377	C₄×D₄	—	2	2	no	—
378	C₄×D₄	—	2	2	no	—
379	C₄×D₄	—	2	1	no	—
380	C₄×D₄	—	2	1	no	—
381	C₄×D₄	—	2	1	no	—
382	C₄×D₄	—	2	1	no	—
383	C₄×D₄	—	2	1	no	—
384	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
385	#117	—	2	1	no	—
386	#117	—	2	1	no	—
387	C₂×C₄⋊C₄	—	2	2	no	—
388	C₂×C₄⋊C₄	—	2	1	no	—
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
394	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
395	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
396	#107	—	2	4	no	—
397	#106	—	2	4	no	—
398	C₄⋊C₈	—	2	1	no	—
399	#103	—	2	4	no	—
400	#103	—	2	2	no	—
401	#103	—	2	2	no	—
402	#102	—	2	4	no	—
403	C₂²⋊C₈	—	2	1	no	—
404	#97	—	2	1	no	—
405	#97	C₂³×C₁₉	1	2	yes	—
406	#97	C₂³×C₁₉	1	2	yes	—
407	#97	C₂³×C₁₉	1	2	yes	—
408	C₄×C₈	—	2	1	no	—
409	C₁₉	#19022	1	1	yes	characteristic, direct product factor, Sylow
410	#41	—	4	4	no	—
411	#41	—	8	4	no	—
412	C₂×Q₈	—	2	2	no	—
413	C₂×Q₈	—	2	2	no	—
414	C₂×Q₈	—	4	1	no	—
415	C₂×Q₈	—	8	2	no	—
416	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
417	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	1	no	—
420	C₂×D₄	—	2	2	no	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	2	1	no	—
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
425	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	4	1	no	—
434	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
435	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
436	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
437	Q₁₆	—	8	2	no	—
438	SD₁₆	—	8	2	no	—
439	M₁₆	—	4	2	no	—
440	C₂×C₈	—	2	4	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	2	2	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	4	1	no	—
463	C₄⋊C₄	—	4	1	no	—
464	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
465	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
466	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
467	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
468	C₂²⋊C₄	—	2	2	no	—
469	C₂²⋊C₄	—	2	2	no	—
470	C₂²⋊C₄	—	2	2	no	—
471	C₂²⋊C₄	—	2	2	no	—
472	C₂²⋊C₄	—	2	2	no	—
473	C₂²⋊C₄	—	2	1	no	—
474	C₂²⋊C₄	—	2	1	no	—
475	C₂²⋊C₄	—	2	1	no	—
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	2	2	no	—
478	C₂²⋊C₄	—	2	2	no	—
479	C₂²⋊C₄	—	2	1	no	—
480	C₄²	—	2	2	no	—
481	C₄²	—	2	1	no	—
482	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
483	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
484	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
485	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
486	C₂³	—	2	2	no	—
487	C₂³	—	2	1	no	—
488	C₂³	C₁₉×#120	1	1	yes	characteristic
489	Q₈	—	4	1	no	—
490	Q₈	—	4	2	no	—
491	Q₈	—	4	2	no	—
492	Q₈	—	4	2	no	—
493	Q₈	—	8	2	no	—
494	Q₈	—	8	2	no	—
495	D₄	—	4	1	no	—
496	D₄	—	4	2	no	—
497	D₄	—	4	4	no	—
498	D₄	—	4	2	no	—
499	D₄	—	4	2	no	—
500	D₄	—	8	1	no	—
501	D₄	—	8	2	no	—
502	D₄	—	8	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	8	2	no	—
516	C₂×C₄	—	8	1	no	—
517	C₂×C₄	—	8	2	no	—
518	C₂×C₄	—	8	2	no	—
519	C₂×C₄	—	8	2	no	—
520	C₂×C₄	—	8	2	no	—
521	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
522	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
523	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
524	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
525	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
526	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
527	C₈	—	2	4	no	—
528	C₈	—	4	2	no	—
529	C₈	—	4	2	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	4	1	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	1	no	—
538	C₂²	C₁₉×#455	1	2	yes	—
539	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
540	C₄	—	2	1	no	—
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	1	no	—
544	C₄	—	2	1	no	—
545	C₄	—	4	2	no	—
546	C₄	—	4	2	no	—
547	C₄	—	4	1	no	—
548	C₄	—	4	1	no	—
549	C₄	—	4	2	no	—
550	C₄	—	4	1	no	—
551	C₄	—	8	2	no	—
552	C₄	C₁₉×#456	1	2	yes	—
553	C₂	—	2	2	no	—
554	C₂	—	8	2	no	—
555	C₂	—	8	1	no	—
556	C₂	C₂×C₁₉×#455	1	1	yes	characteristic
557	C₂	C₂×C₁₉×#456	1	1	yes	characteristic
558	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×#3559	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. C₂×C₁₉×#501	C₂	semidirect
4. C₁₉×#3141	C₂	semidirect
5. C₁₉×#1664	C₂	semidirect
6. C₁₉×#1661	C₂	semidirect
7. C₁₉×#1530	C₂	semidirect
8. C₁₉×#1528	C₂	semidirect
9. C₁₉×#1524	C₂	semidirect
206. #19022	C₁₉	direct (N × H)
252. #3218	C₂×C₁₉	semidirect
253. C₂×#501	C₂×C₁₉	semidirect
254. #3141	C₂×C₁₉	semidirect
255. #1664	C₂×C₁₉	semidirect
256. #1661	C₂×C₁₉	semidirect
257. #1530	C₂×C₁₉	semidirect
258. #1528	C₂×C₁₉	semidirect
259. #1524	C₂×C₁₉	semidirect
409. C₁₉	#19022	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×#3559	2
C₁₉×#3218	2
C₂×C₁₉×#501	2
C₁₉×#3141	2
C₁₉×#1664	2
C₁₉×#1661	2
C₁₉×#1530	2
C₁₉×#1528	2
C₁₉×#1524	2
#19022	19

Subgroups — C19×#19022 #18024981

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19022 #18024981