Subgroups — C₁₉×#18398 #18024357

Order 4864.

930 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3507	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3229	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3226	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2546	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1609	C₂	1	8	yes	maximal, complemented
6	C₁₉×#1503	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1502	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1461	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#559	—	2	1	no	—
10	C₁₉×#557	—	2	1	no	—
11	C₁₉×#556	—	2	1	no	—
12	C₁₉×#556	—	2	2	no	—
13	C₁₉×#554	—	2	1	no	—
14	C₁₉×#552	—	2	2	no	—
15	C₁₉×#539	C₂²	1	4	yes	—
16	C₁₉×#536	—	2	1	no	—
17	C₁₉×#533	C₂²	1	1	yes	characteristic
18	C₁₉×#532	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
20	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₁₉×#529	—	2	2	no	—
22	C₁₉×#520	—	2	1	no	—
23	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#500	—	2	1	no	—
25	C₁₉×#498	—	2	1	no	—
26	C₁₉×#487	—	2	1	no	—
27	C₁₉×#486	—	2	1	no	—
28	C₁₉×#483	C₂²	1	4	yes	—
29	C₁₉×#480	C₂²	1	4	yes	—
30	C₁₉×#475	—	2	2	no	—
31	C₁₉×#474	—	2	2	no	—
32	C₁₉×#431	C₂²	1	1	yes	characteristic
33	C₁₉×#431	C₂²	1	1	yes	characteristic
34	C₁₉×#398	C₂²	1	4	yes	—
35	C₁₉×#391	—	2	1	no	—
36	C₁₉×#389	—	2	2	no	—
37	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
38	C₁₉×#328	C₂²	1	4	yes	—
39	C₁₉×#327	C₂²	1	4	yes	—
40	C₁₉×#324	C₂²	1	4	yes	—
41	C₂×#41×C₁₉	—	2	1	no	—
42	C₂²×Q₈×C₁₉	—	2	1	no	—
43	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
44	C₁₉×C₄⋊Q₈	—	2	2	no	—
45	C₁₉×C₄⋊Q₈	—	2	1	no	—
46	C₁₉×C₄⋊Q₈	—	2	1	no	—
47	C₁₉×C₄⋊Q₈	—	2	1	no	—
48	C₁₉×C₄⋊Q₈	—	2	1	no	—
49	C₁₉×C₄⋊Q₈	—	4	4	no	—
50	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
51	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
52	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
53	C₁₉×#127	D₄	1	1	yes	characteristic
54	C₁₉×#126	—	2	4	no	—
55	C₁₉×#126	—	2	4	no	—
56	C₁₉×#125	—	2	2	no	—
57	C₁₉×#125	—	2	4	no	—
58	C₁₉×#125	—	2	1	no	—
59	C₁₉×#124	—	2	2	no	—
60	C₁₉×#124	—	2	2	no	—
61	C₁₉×#124	—	2	1	no	—
62	C₁₉×#123	—	2	4	no	—
63	C₁₉×#123	—	2	4	no	—
64	C₁₉×C₂²⋊Q₈	—	2	2	no	—
65	C₁₉×C₂²⋊Q₈	—	2	2	no	—
66	C₁₉×C₂²⋊Q₈	—	2	4	no	—
67	C₁₉×C₂²⋊Q₈	—	2	1	no	—
68	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
69	C₁₉×#121	—	2	1	no	—
70	C₁₉×#121	C₂³	1	2	yes	—
71	C₄×Q₈×C₁₉	—	2	2	no	—
72	C₄×Q₈×C₁₉	—	2	2	no	—
73	C₄×Q₈×C₁₉	—	2	1	no	—
74	C₄×Q₈×C₁₉	—	2	1	no	—
75	C₄×Q₈×C₁₉	—	2	1	no	—
76	C₄×Q₈×C₁₉	—	2	1	no	—
77	C₄×Q₈×C₁₉	—	2	1	no	—
78	C₄×Q₈×C₁₉	D₄	1	2	yes	—
79	C₄×D₄×C₁₉	—	2	2	no	—
80	C₄×D₄×C₁₉	—	2	2	no	—
81	C₄×D₄×C₁₉	—	2	4	no	—
82	C₄×D₄×C₁₉	—	2	1	no	—
83	C₄×D₄×C₁₉	D₄	1	2	yes	—
84	C₁₉×#117	—	2	2	no	—
85	C₁₉×#117	—	2	4	no	—
86	C₁₉×#117	—	2	1	no	—
87	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
88	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
89	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
90	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
91	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
94	C₂×C₄²×C₁₉	—	2	1	no	—
95	C₂×C₄²×C₁₉	D₄	1	2	yes	—
96	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
97	C₁₉×#107	—	2	4	no	—
98	C₁₉×#106	—	2	4	no	—
99	C₁₉×C₄⋊C₈	—	2	1	no	—
100	C₁₉×C₄⋊C₈	—	2	1	no	—
101	C₁₉×#103	—	2	4	no	—
102	C₁₉×#102	—	2	4	no	—
103	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
104	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
105	C₄×C₈×C₁₉	—	2	1	no	—
106	C₄×C₈×C₁₉	—	2	1	no	—
107	C₁₉×#95	—	2	4	no	—
108	C₁₉×#95	C₂³	1	2	yes	—
109	#41×C₁₉	—	4	2	no	—
110	#41×C₁₉	—	4	2	no	—
111	C₂×Q₈×C₁₉	—	2	1	no	—
112	C₂×Q₈×C₁₉	—	2	1	no	—
113	C₂×Q₈×C₁₉	—	2	1	no	—
114	C₂×Q₈×C₁₉	—	2	1	no	—
115	C₂×Q₈×C₁₉	—	2	2	no	—
116	C₂×Q₈×C₁₉	—	2	2	no	—
117	C₂×Q₈×C₁₉	—	4	1	no	—
118	C₂×Q₈×C₁₉	—	4	1	no	—
119	C₂×Q₈×C₁₉	—	4	2	no	—
120	C₂×Q₈×C₁₉	—	4	2	no	—
121	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
122	C₂×D₄×C₁₉	—	2	2	no	—
123	C₂×D₄×C₁₉	—	2	1	no	—
124	C₂×D₄×C₁₉	—	2	1	no	—
125	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₉	—	2	2	no	—
127	C₂²×C₄×C₁₉	—	2	4	no	—
128	C₂²×C₄×C₁₉	—	2	2	no	—
129	C₂²×C₄×C₁₉	—	2	2	no	—
130	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
135	C₂×C₈×C₁₉	—	2	2	no	—
136	C₂×C₈×C₁₉	—	2	2	no	—
137	C₄⋊C₄×C₁₉	—	2	4	no	—
138	C₄⋊C₄×C₁₉	—	2	4	no	—
139	C₄⋊C₄×C₁₉	—	2	4	no	—
140	C₄⋊C₄×C₁₉	—	2	4	no	—
141	C₄⋊C₄×C₁₉	—	2	1	no	—
142	C₄⋊C₄×C₁₉	—	2	1	no	—
143	C₄⋊C₄×C₁₉	—	2	1	no	—
144	C₄⋊C₄×C₁₉	—	2	1	no	—
145	C₄⋊C₄×C₁₉	—	2	2	no	—
146	C₄⋊C₄×C₁₉	—	2	1	no	—
147	C₄⋊C₄×C₁₉	—	2	1	no	—
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	—	2	2	no	—
150	C₄⋊C₄×C₁₉	—	2	2	no	—
151	C₄⋊C₄×C₁₉	—	2	2	no	—
152	C₄⋊C₄×C₁₉	—	2	2	no	—
153	C₄⋊C₄×C₁₉	—	4	8	no	—
154	C₄⋊C₄×C₁₉	—	4	1	no	—
155	C₄⋊C₄×C₁₉	—	4	1	no	—
156	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
157	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
158	C₂²⋊C₄×C₁₉	—	2	4	no	—
159	C₂²⋊C₄×C₁₉	—	2	4	no	—
160	C₂²⋊C₄×C₁₉	—	2	4	no	—
161	C₂²⋊C₄×C₁₉	—	2	2	no	—
162	C₂²⋊C₄×C₁₉	—	2	2	no	—
163	C₂²⋊C₄×C₁₉	—	2	2	no	—
164	C₄²×C₁₉	—	2	4	no	—
165	C₄²×C₁₉	—	2	2	no	—
166	C₄²×C₁₉	—	2	2	no	—
167	C₄²×C₁₉	—	2	2	no	—
168	C₄²×C₁₉	—	4	2	no	—
169	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
173	#18398	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂³×C₁₉	—	2	2	no	—
175	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
176	Q₈×C₁₉	—	4	2	no	—
177	Q₈×C₁₉	—	4	2	no	—
178	Q₈×C₁₉	—	4	2	no	—
179	Q₈×C₁₉	—	4	2	no	—
180	Q₈×C₁₉	—	4	2	no	—
181	Q₈×C₁₉	—	8	2	no	—
182	Q₈×C₁₉	—	8	2	no	—
183	D₄×C₁₉	—	4	2	no	—
184	D₄×C₁₉	—	4	2	no	—
185	D₄×C₁₉	—	4	2	no	—
186	D₄×C₁₉	—	4	2	no	—
187	D₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	2	2	no	—
189	C₂×C₄×C₁₉	—	2	4	no	—
190	C₂×C₄×C₁₉	—	2	2	no	—
191	C₂×C₄×C₁₉	—	2	2	no	—
192	C₂×C₄×C₁₉	—	2	2	no	—
193	C₂×C₄×C₁₉	—	2	2	no	—
194	C₂×C₄×C₁₉	—	2	2	no	—
195	C₂×C₄×C₁₉	—	2	2	no	—
196	C₂×C₄×C₁₉	—	2	2	no	—
197	C₂×C₄×C₁₉	—	4	1	no	—
198	C₂×C₄×C₁₉	—	4	2	no	—
199	C₂×C₄×C₁₉	—	4	2	no	—
200	C₂×C₄×C₁₉	—	4	4	no	—
201	C₂×C₄×C₁₉	—	4	2	no	—
202	C₂×C₄×C₁₉	—	4	2	no	—
203	C₂×C₄×C₁₉	—	4	2	no	—
204	C₂×C₄×C₁₉	—	4	2	no	—
205	C₂×C₄×C₁₉	—	8	4	no	—
206	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
207	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
208	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
209	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
210	C₂×C₄×C₁₉	#135	1	2	yes	—
211	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
212	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
214	C₈×C₁₉	—	4	2	no	—
215	C₈×C₁₉	—	4	2	no	—
216	#3507	C₂×C₁₉	1	1	yes	characteristic
217	#3229	C₂×C₁₉	1	1	yes	characteristic, complemented
218	#3226	C₂×C₁₉	1	1	yes	characteristic
219	#2546	C₂×C₁₉	1	1	yes	characteristic, complemented
220	#1609	C₂×C₁₉	1	8	yes	complemented
221	#1503	C₂×C₁₉	1	1	yes	characteristic, complemented
222	#1502	C₂×C₁₉	1	1	yes	characteristic
223	#1461	C₂×C₁₉	1	1	yes	characteristic, complemented
224	C₂²×C₁₉	—	2	1	no	—
225	C₂²×C₁₉	—	2	1	no	—
226	C₂²×C₁₉	—	4	2	no	—
227	C₂²×C₁₉	—	4	2	no	—
228	C₂²×C₁₉	—	4	2	no	—
229	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
230	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
231	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
232	C₄×C₁₉	—	2	1	no	—
233	C₄×C₁₉	—	2	1	no	—
234	C₄×C₁₉	—	2	1	no	—
235	C₄×C₁₉	—	4	4	no	—
236	C₄×C₁₉	—	4	2	no	—
237	C₄×C₁₉	—	4	2	no	—
238	C₄×C₁₉	—	4	2	no	—
239	C₄×C₁₉	—	4	2	no	—
240	C₄×C₁₉	—	4	2	no	—
241	C₄×C₁₉	—	8	2	no	—
242	C₄×C₁₉	#449	1	2	yes	—
243	C₄×C₁₉	#449	1	2	yes	—
244	C₄×C₁₉	#456	1	2	yes	—
245	#559	—	2	1	no	—
246	#557	—	2	1	no	—
247	#556	—	2	1	no	—
248	#556	—	2	2	no	—
249	#554	—	2	1	no	—
250	#552	—	2	2	no	—
251	#539	C₂²×C₁₉	1	4	yes	—
252	#536	—	2	1	no	—
253	#533	C₂²×C₁₉	1	1	yes	characteristic
254	#532	C₂²×C₁₉	1	1	yes	characteristic
255	C₂×C₄⋊Q₈	—	2	1	no	—
256	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
257	#529	—	2	2	no	—
258	#520	—	2	1	no	—
259	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
260	#500	—	2	1	no	—
261	#498	—	2	1	no	—
262	#487	—	2	1	no	—
263	#486	—	2	1	no	—
264	#483	C₂²×C₁₉	1	4	yes	—
265	#480	C₂²×C₁₉	1	4	yes	—
266	#475	—	2	2	no	—
267	#474	—	2	2	no	—
268	#431	C₂²×C₁₉	1	1	yes	characteristic
269	#431	C₂²×C₁₉	1	1	yes	characteristic
270	#398	C₂²×C₁₉	1	4	yes	—
271	#391	—	2	1	no	—
272	#389	—	2	2	no	—
273	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
274	#328	C₂²×C₁₉	1	4	yes	—
275	#327	C₂²×C₁₉	1	4	yes	—
276	#324	C₂²×C₁₉	1	4	yes	—
277	C₂×C₁₉	—	2	1	no	—
278	C₂×C₁₉	—	2	1	no	—
279	C₂×C₁₉	—	8	2	no	—
280	C₂×C₁₉	C₂×#449	1	1	yes	characteristic
281	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
282	C₂×C₁₉	#3028	1	1	yes	characteristic
283	C₂×#41	—	2	1	no	—
284	C₂²×Q₈	—	2	1	no	—
285	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
286	C₄⋊Q₈	—	2	2	no	—
287	C₄⋊Q₈	—	2	1	no	—
288	C₄⋊Q₈	—	2	1	no	—
289	C₄⋊Q₈	—	2	1	no	—
290	C₄⋊Q₈	—	2	1	no	—
291	C₄⋊Q₈	—	4	4	no	—
292	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
293	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
294	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
295	#127	D₄×C₁₉	1	1	yes	characteristic
296	#126	—	2	4	no	—
297	#126	—	2	4	no	—
298	#125	—	2	2	no	—
299	#125	—	2	4	no	—
300	#125	—	2	1	no	—
301	#124	—	2	2	no	—
302	#124	—	2	2	no	—
303	#124	—	2	1	no	—
304	#123	—	2	4	no	—
305	#123	—	2	4	no	—
306	C₂²⋊Q₈	—	2	2	no	—
307	C₂²⋊Q₈	—	2	2	no	—
308	C₂²⋊Q₈	—	2	4	no	—
309	C₂²⋊Q₈	—	2	1	no	—
310	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
311	#121	—	2	1	no	—
312	#121	C₂³×C₁₉	1	2	yes	—
313	C₄×Q₈	—	2	2	no	—
314	C₄×Q₈	—	2	2	no	—
315	C₄×Q₈	—	2	1	no	—
316	C₄×Q₈	—	2	1	no	—
317	C₄×Q₈	—	2	1	no	—
318	C₄×Q₈	—	2	1	no	—
319	C₄×Q₈	—	2	1	no	—
320	C₄×Q₈	D₄×C₁₉	1	2	yes	—
321	C₄×D₄	—	2	2	no	—
322	C₄×D₄	—	2	2	no	—
323	C₄×D₄	—	2	4	no	—
324	C₄×D₄	—	2	1	no	—
325	C₄×D₄	D₄×C₁₉	1	2	yes	—
326	#117	—	2	2	no	—
327	#117	—	2	4	no	—
328	#117	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	2	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	—	2	4	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
334	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
335	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
336	C₂×C₄²	—	2	1	no	—
337	C₂×C₄²	D₄×C₁₉	1	2	yes	—
338	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
339	#107	—	2	4	no	—
340	#106	—	2	4	no	—
341	C₄⋊C₈	—	2	1	no	—
342	C₄⋊C₈	—	2	1	no	—
343	#103	—	2	4	no	—
344	#102	—	2	4	no	—
345	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
346	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
347	C₄×C₈	—	2	1	no	—
348	C₄×C₈	—	2	1	no	—
349	#95	—	2	4	no	—
350	#95	C₂³×C₁₉	1	2	yes	—
351	C₁₉	#18398	1	1	yes	characteristic, direct product factor, Sylow
352	#41	—	4	2	no	—
353	#41	—	4	2	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	4	1	no	—
361	C₂×Q₈	—	4	1	no	—
362	C₂×Q₈	—	4	2	no	—
363	C₂×Q₈	—	4	2	no	—
364	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
374	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
376	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
377	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	4	no	—
382	C₄⋊C₄	—	2	4	no	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	4	8	no	—
397	C₄⋊C₄	—	4	1	no	—
398	C₄⋊C₄	—	4	1	no	—
399	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
400	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
401	C₂²⋊C₄	—	2	4	no	—
402	C₂²⋊C₄	—	2	4	no	—
403	C₂²⋊C₄	—	2	4	no	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₄²	—	2	4	no	—
408	C₄²	—	2	2	no	—
409	C₄²	—	2	2	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	4	2	no	—
412	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
413	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
414	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
415	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
416	C₂³	—	2	2	no	—
417	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
418	Q₈	—	4	2	no	—
419	Q₈	—	4	2	no	—
420	Q₈	—	4	2	no	—
421	Q₈	—	4	2	no	—
422	Q₈	—	4	2	no	—
423	Q₈	—	8	2	no	—
424	Q₈	—	8	2	no	—
425	D₄	—	4	2	no	—
426	D₄	—	4	2	no	—
427	D₄	—	4	2	no	—
428	D₄	—	4	2	no	—
429	D₄	—	4	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	8	4	no	—
448	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
449	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
450	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
451	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
452	C₂×C₄	C₁₉×#135	1	2	yes	—
453	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
454	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
455	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
456	C₈	—	4	2	no	—
457	C₈	—	4	2	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	4	2	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	4	2	no	—
463	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
464	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
465	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
466	C₄	—	2	1	no	—
467	C₄	—	2	1	no	—
468	C₄	—	2	1	no	—
469	C₄	—	4	4	no	—
470	C₄	—	4	2	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	2	no	—
473	C₄	—	4	2	no	—
474	C₄	—	4	2	no	—
475	C₄	—	8	2	no	—
476	C₄	C₁₉×#449	1	2	yes	—
477	C₄	C₁₉×#449	1	2	yes	—
478	C₄	C₁₉×#456	1	2	yes	—
479	C₂	—	2	1	no	—
480	C₂	—	2	1	no	—
481	C₂	—	8	2	no	—
482	C₂	C₂×C₁₉×#449	1	1	yes	characteristic
483	C₂	C₂×C₁₉×#456	1	1	yes	characteristic
484	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×#532	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×#3229	C₂	semidirect
4. C₁₉×#2546	C₂	semidirect
5. C₁₉×#1609	C₂	semidirect
6. C₁₉×#1503	C₂	semidirect
8. C₁₉×#1461	C₂	semidirect
173. #18398	C₁₉	direct (N × H)
217. #3229	C₂×C₁₉	semidirect
219. #2546	C₂×C₁₉	semidirect
220. #1609	C₂×C₁₉	semidirect
221. #1503	C₂×C₁₉	semidirect
223. #1461	C₂×C₁₉	semidirect
351. C₁₉	#18398	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×#3507	2
C₁₉×#3229	2
C₁₉×#3226	2
C₁₉×#2546	2
C₁₉×#1609	2
C₁₉×#1503	2
C₁₉×#1502	2
C₁₉×#1461	2
#18398	19

Subgroups — C19×#18398 #18024357

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18398 #18024357