Subgroups — C₁₉×#18269 #18024228

Order 4864.

924 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3538	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3092	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#484	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2503	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1617	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1615	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1508	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1501	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1472	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#563	—	2	2	no	—
11	C₁₉×#552	—	2	1	no	—
12	C₁₉×#552	—	2	1	no	—
13	C₁₉×#551	—	2	2	no	—
14	D₄×Q₈×C₁₉	—	2	1	no	—
15	D₄×Q₈×C₁₉	—	2	1	no	—
16	C₁₉×#544	—	2	1	no	—
17	C₁₉×#544	C₂²	1	2	yes	—
18	C₁₉×#541	—	2	1	no	—
19	C₁₉×#539	—	2	1	no	—
20	C₁₉×#539	C₂²	1	2	yes	—
21	C₁₉×#536	—	2	1	no	—
22	C₁₉×#525	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#484	—	2	2	no	—
27	C₁₉×#484	C₂²	1	4	yes	—
28	C₁₉×#484	C₂²	1	2	yes	—
29	C₁₉×#483	—	2	1	no	—
30	C₁₉×#481	C₂²	1	2	yes	—
31	C₁₉×#480	—	2	1	no	—
32	C₁₉×#428	—	2	1	no	—
33	C₂×C₁₉×#107	—	2	1	no	—
34	C₁₉×#417	—	2	1	no	—
35	C₂×C₁₉×#103	—	2	1	no	—
36	C₁₉×#407	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₁₉×#400	C₂²	1	4	yes	—
39	C₁₉×#391	—	2	1	no	—
40	C₁₉×#382	—	2	1	no	—
41	C₁₉×#381	—	2	2	no	—
42	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
43	C₁₉×#328	C₂²	1	2	yes	—
44	C₁₉×#328	C₂²	1	4	yes	—
45	C₁₉×#327	C₂²	1	2	yes	—
46	C₁₉×#324	C₂²	1	4	yes	—
47	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
48	C₂²×Q₈×C₁₉	—	2	1	no	—
49	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
50	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₉	—	2	1	no	—
52	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
53	C₂×M₁₆×C₁₉	—	2	1	no	—
54	C₂²×C₈×C₁₉	—	2	1	no	—
55	C₁₉×C₄⋊Q₈	—	2	1	no	—
56	C₁₉×C₄⋊Q₈	—	2	2	no	—
57	C₁₉×C₄⋊Q₈	—	2	2	no	—
58	C₁₉×C₄⋊Q₈	—	2	2	no	—
59	C₁₉×#126	—	2	2	no	—
60	C₁₉×#126	—	2	2	no	—
61	C₁₉×#126	—	2	2	no	—
62	C₁₉×#126	—	2	2	no	—
63	C₁₉×#125	—	2	1	no	—
64	C₁₉×#125	—	2	2	no	—
65	C₁₉×#125	—	2	2	no	—
66	C₁₉×#125	—	2	2	no	—
67	C₁₉×#125	—	2	2	no	—
68	C₁₉×#124	—	2	2	no	—
69	C₁₉×#123	—	2	2	no	—
70	C₁₉×#123	—	2	2	no	—
71	C₁₉×#123	—	2	2	no	—
72	C₁₉×#123	—	2	1	no	—
73	C₁₉×#123	—	2	2	no	—
74	C₁₉×C₂²⋊Q₈	—	2	1	no	—
75	C₁₉×C₂²⋊Q₈	—	2	1	no	—
76	C₁₉×C₂²⋊Q₈	—	2	2	no	—
77	C₁₉×C₂²⋊Q₈	—	2	2	no	—
78	C₁₉×C₂²⋊Q₈	—	2	2	no	—
79	C₁₉×C₂²⋊Q₈	—	2	1	no	—
80	C₁₉×C₂²⋊Q₈	—	2	1	no	—
81	C₁₉×C₂²⋊Q₈	—	2	1	no	—
82	C₁₉×C₂²⋊Q₈	—	2	1	no	—
83	C₁₉×C₂²⋊Q₈	—	2	1	no	—
84	C₁₉×C₂²⋊Q₈	—	2	1	no	—
85	C₁₉×C₂²⋊Q₈	—	2	2	no	—
86	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
87	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
88	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
89	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
90	C₁₉×#121	D₄	1	1	yes	characteristic
91	C₁₉×#121	C₂³	1	1	yes	characteristic
92	C₁₉×#120	—	2	1	no	—
93	C₄×Q₈×C₁₉	—	2	1	no	—
94	C₄×Q₈×C₁₉	—	2	1	no	—
95	C₄×D₄×C₁₉	—	2	2	no	—
96	C₄×D₄×C₁₉	—	2	1	no	—
97	C₄×D₄×C₁₉	—	2	1	no	—
98	C₄×D₄×C₁₉	—	2	2	no	—
99	C₁₉×#117	—	2	1	no	—
100	C₁₉×#117	—	2	2	no	—
101	C₁₉×#117	—	2	2	no	—
102	C₁₉×#117	D₄	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
104	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
105	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
106	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
108	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
109	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
113	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
116	C₂×C₄²×C₁₉	—	2	1	no	—
117	C₁₉×#107	—	2	4	no	—
118	C₁₉×#107	—	2	2	no	—
119	C₁₉×#106	—	2	2	no	—
120	C₁₉×#103	—	2	4	no	—
121	C₁₉×#103	—	2	2	no	—
122	C₁₉×#102	—	2	2	no	—
123	C₁₉×C₂²⋊C₈	—	2	1	no	—
124	C₁₉×C₂²⋊C₈	—	2	1	no	—
125	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
126	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
127	C₁₉×#95	—	2	4	no	—
128	C₁₉×#95	—	2	4	no	—
129	C₁₉×#95	C₂³	1	2	yes	—
130	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
131	#41×C₁₉	—	4	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	—	4	2	no	—
137	C₂×Q₈×C₁₉	—	4	2	no	—
138	C₂×Q₈×C₁₉	—	8	2	no	—
139	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
140	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
141	C₂×D₄×C₁₉	—	2	1	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	C₂²×C₄×C₁₉	—	2	1	no	—
146	C₂²×C₄×C₁₉	—	2	2	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	2	no	—
151	C₂²×C₄×C₁₉	—	4	2	no	—
152	C₂²×C₄×C₁₉	—	4	4	no	—
153	C₂²×C₄×C₁₉	—	4	1	no	—
154	C₂²×C₄×C₁₉	—	4	1	no	—
155	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
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	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
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	M₁₆×C₁₉	—	4	2	no	—
164	C₂×C₈×C₁₉	—	2	2	no	—
165	C₂×C₈×C₁₉	—	2	2	no	—
166	C₂×C₈×C₁₉	—	4	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	2	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	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	2	no	—
181	C₄⋊C₄×C₁₉	—	2	2	no	—
182	C₄⋊C₄×C₁₉	—	2	2	no	—
183	C₄⋊C₄×C₁₉	—	2	1	no	—
184	C₄⋊C₄×C₁₉	—	2	2	no	—
185	C₄⋊C₄×C₁₉	—	2	2	no	—
186	C₄⋊C₄×C₁₉	—	4	1	no	—
187	C₄⋊C₄×C₁₉	—	4	1	no	—
188	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
189	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
190	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	1	no	—
198	C₂²⋊C₄×C₁₉	—	2	1	no	—
199	C₂²⋊C₄×C₁₉	—	2	2	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	2	no	—
204	C₄²×C₁₉	—	2	2	no	—
205	C₄²×C₁₉	—	2	2	no	—
206	C₄²×C₁₉	—	2	2	no	—
207	C₄²×C₁₉	—	2	1	no	—
208	C₄²×C₁₉	—	4	2	no	—
209	#18269	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₂³×C₁₉	—	2	2	no	—
211	C₂³×C₁₉	—	2	2	no	—
212	C₂³×C₁₉	—	2	1	no	—
213	C₂³×C₁₉	—	4	1	no	—
214	C₂³×C₁₉	#120	1	1	yes	characteristic
215	C₂³×C₁₉	#120	1	1	yes	characteristic
216	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
217	Q₈×C₁₉	—	4	2	no	—
218	Q₈×C₁₉	—	4	1	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	D₄×C₁₉	—	4	1	no	—
224	D₄×C₁₉	—	4	2	no	—
225	D₄×C₁₉	—	4	2	no	—
226	D₄×C₁₉	—	8	1	no	—
227	C₂×C₄×C₁₉	—	2	2	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	1	no	—
232	C₂×C₄×C₁₉	—	2	2	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	4	no	—
238	C₂×C₄×C₁₉	—	4	1	no	—
239	C₂×C₄×C₁₉	—	4	1	no	—
240	C₂×C₄×C₁₉	—	4	1	no	—
241	C₂×C₄×C₁₉	—	4	2	no	—
242	C₂×C₄×C₁₉	—	4	2	no	—
243	C₂×C₄×C₁₉	—	4	2	no	—
244	C₂×C₄×C₁₉	—	4	2	no	—
245	C₂×C₄×C₁₉	—	4	2	no	—
246	C₂×C₄×C₁₉	—	4	4	no	—
247	C₂×C₄×C₁₉	—	4	2	no	—
248	C₂×C₄×C₁₉	—	4	2	no	—
249	C₂×C₄×C₁₉	—	8	1	no	—
250	C₂×C₄×C₁₉	—	8	2	no	—
251	C₂×C₄×C₁₉	—	8	2	no	—
252	C₂×C₄×C₁₉	—	8	2	no	—
253	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
254	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
255	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
257	C₈×C₁₉	—	4	2	no	—
258	C₈×C₁₉	—	4	2	no	—
259	#3538	C₂×C₁₉	1	1	yes	characteristic
260	#3092	C₂×C₁₉	1	1	yes	characteristic
261	C₂×#484	C₂×C₁₉	1	1	yes	characteristic, complemented
262	#2503	C₂×C₁₉	1	1	yes	characteristic, complemented
263	#1617	C₂×C₁₉	1	4	yes	complemented
264	#1615	C₂×C₁₉	1	4	yes	complemented
265	#1508	C₂×C₁₉	1	1	yes	characteristic, complemented
266	#1501	C₂×C₁₉	1	1	yes	characteristic
267	#1472	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	—	2	1	no	—
272	C₂²×C₁₉	—	2	1	no	—
273	C₂²×C₁₉	—	2	1	no	—
274	C₂²×C₁₉	—	2	1	no	—
275	C₂²×C₁₉	—	4	4	no	—
276	C₂²×C₁₉	—	4	1	no	—
277	C₂²×C₁₉	—	4	1	no	—
278	C₂²×C₁₉	—	4	1	no	—
279	C₂²×C₁₉	#454	1	2	yes	—
280	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
281	C₂²×C₁₉	#578	1	2	yes	—
282	C₄×C₁₉	—	2	1	no	—
283	C₄×C₁₉	—	2	1	no	—
284	C₄×C₁₉	—	2	1	no	—
285	C₄×C₁₉	—	4	2	no	—
286	C₄×C₁₉	—	4	1	no	—
287	C₄×C₁₉	—	4	2	no	—
288	C₄×C₁₉	—	4	1	no	—
289	C₄×C₁₉	—	4	1	no	—
290	C₄×C₁₉	—	4	2	no	—
291	C₄×C₁₉	—	4	2	no	—
292	C₄×C₁₉	—	8	2	no	—
293	C₄×C₁₉	—	8	2	no	—
294	C₄×C₁₉	#458	1	2	yes	—
295	#563	—	2	2	no	—
296	#552	—	2	1	no	—
297	#552	—	2	1	no	—
298	#551	—	2	2	no	—
299	D₄×Q₈	—	2	1	no	—
300	D₄×Q₈	—	2	1	no	—
301	#544	—	2	1	no	—
302	#544	C₂²×C₁₉	1	2	yes	—
303	#541	—	2	1	no	—
304	#539	—	2	1	no	—
305	#539	C₂²×C₁₉	1	2	yes	—
306	#536	—	2	1	no	—
307	#525	C₂²×C₁₉	1	1	yes	characteristic
308	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
309	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
310	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
311	#484	—	2	2	no	—
312	#484	C₂²×C₁₉	1	4	yes	—
313	#484	C₂²×C₁₉	1	2	yes	—
314	#483	—	2	1	no	—
315	#481	C₂²×C₁₉	1	2	yes	—
316	#480	—	2	1	no	—
317	#428	—	2	1	no	—
318	C₂×#107	—	2	1	no	—
319	#417	—	2	1	no	—
320	C₂×#103	—	2	1	no	—
321	#407	C₂²×C₁₉	1	1	yes	characteristic
322	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
323	#400	C₂²×C₁₉	1	4	yes	—
324	#391	—	2	1	no	—
325	#382	—	2	1	no	—
326	#381	—	2	2	no	—
327	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
328	#328	C₂²×C₁₉	1	4	yes	—
329	#328	C₂²×C₁₉	1	2	yes	—
330	#327	C₂²×C₁₉	1	2	yes	—
331	#324	C₂²×C₁₉	1	4	yes	—
332	C₂×C₁₉	—	2	2	no	—
333	C₂×C₁₉	—	2	2	no	—
334	C₂×C₁₉	—	4	1	no	—
335	C₂×C₁₉	—	8	1	no	—
336	C₂×C₁₉	#3011	1	1	yes	characteristic
337	C₂×C₁₉	C₂×#454	1	1	yes	characteristic
338	C₂×C₁₉	C₂×#458	1	1	yes	characteristic
339	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
340	C₂²×Q₈	—	2	1	no	—
341	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
342	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
343	C₂³×C₄	—	2	1	no	—
344	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
345	C₂×M₁₆	—	2	1	no	—
346	C₂²×C₈	—	2	1	no	—
347	C₄⋊Q₈	—	2	1	no	—
348	C₄⋊Q₈	—	2	2	no	—
349	C₄⋊Q₈	—	2	2	no	—
350	C₄⋊Q₈	—	2	2	no	—
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	#124	—	2	2	no	—
361	#123	—	2	2	no	—
362	#123	—	2	2	no	—
363	#123	—	2	2	no	—
364	#123	—	2	1	no	—
365	#123	—	2	2	no	—
366	C₂²⋊Q₈	—	2	1	no	—
367	C₂²⋊Q₈	—	2	1	no	—
368	C₂²⋊Q₈	—	2	2	no	—
369	C₂²⋊Q₈	—	2	2	no	—
370	C₂²⋊Q₈	—	2	2	no	—
371	C₂²⋊Q₈	—	2	1	no	—
372	C₂²⋊Q₈	—	2	1	no	—
373	C₂²⋊Q₈	—	2	1	no	—
374	C₂²⋊Q₈	—	2	1	no	—
375	C₂²⋊Q₈	—	2	1	no	—
376	C₂²⋊Q₈	—	2	1	no	—
377	C₂²⋊Q₈	—	2	2	no	—
378	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
379	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
380	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
381	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
382	#121	D₄×C₁₉	1	1	yes	characteristic
383	#121	C₂³×C₁₉	1	1	yes	characteristic
384	#120	—	2	1	no	—
385	C₄×Q₈	—	2	1	no	—
386	C₄×Q₈	—	2	1	no	—
387	C₄×D₄	—	2	2	no	—
388	C₄×D₄	—	2	1	no	—
389	C₄×D₄	—	2	1	no	—
390	C₄×D₄	—	2	2	no	—
391	#117	—	2	1	no	—
392	#117	—	2	2	no	—
393	#117	—	2	2	no	—
394	#117	D₄×C₁₉	1	1	yes	characteristic
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	—	2	1	no	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
402	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
404	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
405	C₂×C₂²⋊C₄	—	2	1	no	—
406	C₂×C₂²⋊C₄	—	2	1	no	—
407	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
408	C₂×C₄²	—	2	1	no	—
409	#107	—	2	4	no	—
410	#107	—	2	2	no	—
411	#106	—	2	2	no	—
412	#103	—	2	4	no	—
413	#103	—	2	2	no	—
414	#102	—	2	2	no	—
415	C₂²⋊C₈	—	2	1	no	—
416	C₂²⋊C₈	—	2	1	no	—
417	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
418	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
419	#95	—	2	4	no	—
420	#95	—	2	4	no	—
421	#95	C₂³×C₁₉	1	2	yes	—
422	C₁₉	#18269	1	1	yes	characteristic, direct product factor, Sylow
423	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
424	#41	—	4	2	no	—
425	C₂×Q₈	—	2	2	no	—
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	—	4	2	no	—
430	C₂×Q₈	—	4	2	no	—
431	C₂×Q₈	—	8	2	no	—
432	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
433	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
434	C₂×D₄	—	2	1	no	—
435	C₂×D₄	—	2	1	no	—
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	—	2	2	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	4	2	no	—
445	C₂²×C₄	—	4	4	no	—
446	C₂²×C₄	—	4	1	no	—
447	C₂²×C₄	—	4	1	no	—
448	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
449	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
450	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
451	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
453	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
455	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
456	M₁₆	—	4	2	no	—
457	C₂×C₈	—	2	2	no	—
458	C₂×C₈	—	2	2	no	—
459	C₂×C₈	—	4	2	no	—
460	C₄⋊C₄	—	2	2	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	—	2	2	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	2	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	2	no	—
474	C₄⋊C₄	—	2	2	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	2	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	4	1	no	—
480	C₄⋊C₄	—	4	1	no	—
481	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
482	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
483	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
484	C₂²⋊C₄	—	2	2	no	—
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	1	no	—
491	C₂²⋊C₄	—	2	1	no	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	2	1	no	—
494	C₂²⋊C₄	—	2	1	no	—
495	C₂²⋊C₄	—	2	1	no	—
496	C₂²⋊C₄	—	4	2	no	—
497	C₄²	—	2	2	no	—
498	C₄²	—	2	2	no	—
499	C₄²	—	2	2	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	4	2	no	—
502	C₂³	—	2	2	no	—
503	C₂³	—	2	2	no	—
504	C₂³	—	2	1	no	—
505	C₂³	—	4	1	no	—
506	C₂³	C₁₉×#120	1	1	yes	characteristic
507	C₂³	C₁₉×#120	1	1	yes	characteristic
508	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
509	Q₈	—	4	2	no	—
510	Q₈	—	4	1	no	—
511	Q₈	—	4	2	no	—
512	Q₈	—	4	2	no	—
513	Q₈	—	8	1	no	—
514	Q₈	—	8	2	no	—
515	D₄	—	4	1	no	—
516	D₄	—	4	2	no	—
517	D₄	—	4	2	no	—
518	D₄	—	8	1	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	4	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	8	1	no	—
542	C₂×C₄	—	8	2	no	—
543	C₂×C₄	—	8	2	no	—
544	C₂×C₄	—	8	2	no	—
545	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
546	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
547	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
548	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
549	C₈	—	4	2	no	—
550	C₈	—	4	2	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	2	1	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	2	1	no	—
556	C₂²	—	2	1	no	—
557	C₂²	—	2	1	no	—
558	C₂²	—	4	4	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	1	no	—
562	C₂²	C₁₉×#454	1	2	yes	—
563	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
564	C₂²	C₁₉×#578	1	2	yes	—
565	C₄	—	2	1	no	—
566	C₄	—	2	1	no	—
567	C₄	—	2	1	no	—
568	C₄	—	4	2	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	2	no	—
571	C₄	—	4	1	no	—
572	C₄	—	4	1	no	—
573	C₄	—	4	2	no	—
574	C₄	—	4	2	no	—
575	C₄	—	8	2	no	—
576	C₄	—	8	2	no	—
577	C₄	C₁₉×#458	1	2	yes	—
578	C₂	—	2	2	no	—
579	C₂	—	2	2	no	—
580	C₂	—	4	1	no	—
581	C₂	—	8	1	no	—
582	C₂	C₁₉×#3011	1	1	yes	characteristic
583	C₂	C₂×C₁₉×#454	1	1	yes	characteristic
584	C₂	C₂×C₁₉×#458	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#525	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₂×C₁₉×#484	C₂	semidirect
4. C₁₉×#2503	C₂	semidirect
5. C₁₉×#1617	C₂	semidirect
6. C₁₉×#1615	C₂	semidirect
7. C₁₉×#1508	C₂	semidirect
9. C₁₉×#1472	C₂	semidirect
209. #18269	C₁₉	direct (N × H)
261. C₂×#484	C₂×C₁₉	semidirect
262. #2503	C₂×C₁₉	semidirect
263. #1617	C₂×C₁₉	semidirect
264. #1615	C₂×C₁₉	semidirect
265. #1508	C₂×C₁₉	semidirect
267. #1472	C₂×C₁₉	semidirect
422. C₁₉	#18269	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×#3538	2
C₁₉×#3092	2
C₂×C₁₉×#484	2
C₁₉×#2503	2
C₁₉×#1617	2
C₁₉×#1615	2
C₁₉×#1508	2
C₁₉×#1501	2
C₁₉×#1472	2
#18269	19

Subgroups — C19×#18269 #18024228

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18269 #18024228