Subgroups — C₁₉×#8426 #18014385

Order 4864.

836 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3508	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1982	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1806	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1550	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1545	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1503	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1477	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#559	—	2	1	no	—
9	C₁₉×#559	C₄	1	2	yes	complemented
10	C₁₉×#550	—	2	1	no	—
11	C₁₉×#550	C₄	1	2	yes	complemented
12	C₁₉×#546	—	2	2	no	—
13	C₁₉×#546	—	2	2	no	—
14	C₁₉×#540	—	2	2	no	—
15	C₁₉×#535	—	2	1	no	—
16	C₁₉×#533	C₂²	1	1	yes	characteristic
17	C₁₉×#532	—	2	1	no	—
18	C₁₉×#532	—	2	1	no	—
19	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
20	C₁₉×#518	—	2	1	no	—
21	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#431	C₂²	1	1	yes	characteristic
23	C₁₉×#423	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#104	—	2	1	no	—
26	C₂×C₁₉×#102	—	2	2	no	—
27	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
28	C₁₉×#339	—	2	1	no	—
29	C₁₉×#333	—	2	1	no	—
30	C₁₉×#332	—	2	1	no	—
31	C₁₉×#331	—	2	2	no	—
32	C₁₉×#328	—	2	2	no	—
33	C₁₉×Q₈⋊C₈	—	2	1	no	—
34	C₁₉×D₄⋊C₈	—	2	1	no	—
35	C₂×#41×C₁₉	—	2	2	no	—
36	C₂×#41×C₁₉	—	2	2	no	—
37	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
38	C₂²×D₄×C₁₉	—	2	1	no	—
39	C₂²×D₄×C₁₉	—	2	1	no	—
40	C₂²×D₄×C₁₉	D₄	1	2	yes	—
41	C₂×M₁₆×C₁₉	—	2	1	no	—
42	C₂²×C₈×C₁₉	—	2	1	no	—
43	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
44	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
45	C₁₉×#127	—	2	2	no	—
46	C₁₉×#127	—	2	1	no	—
47	C₁₉×#127	—	2	1	no	—
48	C₁₉×#127	C₂×C₄	1	2	yes	—
49	C₁₉×#127	D₄	1	2	yes	—
50	C₁₉×#125	—	2	1	no	—
51	C₁₉×#124	—	2	2	no	—
52	C₁₉×#124	—	2	2	no	—
53	C₁₉×#124	—	2	2	no	—
54	C₁₉×#123	—	2	4	no	—
55	C₁₉×#123	—	2	4	no	—
56	C₁₉×C₂²⋊Q₈	—	2	1	no	—
57	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
58	C₁₉×#121	—	2	2	no	—
59	C₁₉×#121	—	2	2	no	—
60	C₁₉×#121	—	2	2	no	—
61	C₁₉×#121	—	2	4	no	—
62	C₁₉×#121	—	2	4	no	—
63	C₁₉×#121	—	2	2	no	—
64	C₁₉×#120	—	2	4	no	—
65	C₄×Q₈×C₁₉	—	2	1	no	—
66	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
67	C₄×Q₈×C₁₉	C₂×C₄	1	2	yes	—
68	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
69	C₄×D₄×C₁₉	—	2	2	no	—
70	C₄×D₄×C₁₉	—	2	2	no	—
71	C₄×D₄×C₁₉	—	2	2	no	—
72	C₄×D₄×C₁₉	—	2	1	no	—
73	C₄×D₄×C₁₉	—	2	1	no	—
74	C₄×D₄×C₁₉	—	2	2	no	—
75	C₄×D₄×C₁₉	—	2	2	no	—
76	C₄×D₄×C₁₉	—	2	2	no	—
77	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
78	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
79	C₁₉×#117	—	2	1	no	—
80	C₁₉×#117	—	2	1	no	—
81	C₁₉×#117	D₄	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
84	C₂×C₄²×C₁₉	—	2	1	no	—
85	C₂×C₄²×C₁₉	—	2	1	no	—
86	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
87	C₁₉×C₄⋊C₈	—	2	1	no	—
88	C₁₉×C₄⋊C₈	—	2	1	no	—
89	C₁₉×C₄⋊C₈	—	2	1	no	—
90	C₁₉×C₄⋊C₈	—	2	1	no	—
91	C₁₉×C₄⋊C₈	—	2	1	no	—
92	C₁₉×#104	—	4	2	no	—
93	C₁₉×#102	—	4	4	no	—
94	C₁₉×C₂²⋊C₈	—	2	1	no	—
95	C₄×C₈×C₁₉	—	2	1	no	—
96	C₁₉×#95	—	2	1	no	—
97	C₂⁴×C₁₉	—	2	2	no	—
98	#41×C₁₉	—	2	1	no	—
99	#41×C₁₉	—	2	1	no	—
100	#41×C₁₉	—	2	1	no	—
101	#41×C₁₉	—	2	1	no	—
102	#41×C₁₉	—	8	4	no	—
103	#41×C₁₉	—	8	2	no	—
104	#41×C₁₉	—	8	2	no	—
105	C₂×Q₈×C₁₉	—	2	1	no	—
106	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
107	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
108	C₂×D₄×C₁₉	—	2	1	no	—
109	C₂×D₄×C₁₉	—	2	4	no	—
110	C₂×D₄×C₁₉	—	2	4	no	—
111	C₂×D₄×C₁₉	—	2	2	no	—
112	C₂×D₄×C₁₉	—	2	2	no	—
113	C₂×D₄×C₁₉	—	2	2	no	—
114	C₂×D₄×C₁₉	—	2	2	no	—
115	C₂×D₄×C₁₉	—	2	2	no	—
116	C₂×D₄×C₁₉	—	4	2	no	—
117	C₂×D₄×C₁₉	—	4	2	no	—
118	C₂×D₄×C₁₉	—	4	1	no	—
119	C₂×D₄×C₁₉	—	4	1	no	—
120	C₂×D₄×C₁₉	—	4	1	no	—
121	C₂×D₄×C₁₉	—	4	1	no	—
122	C₂×D₄×C₁₉	—	8	2	no	—
123	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
124	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
125	C₂²×C₄×C₁₉	—	2	4	no	—
126	C₂²×C₄×C₁₉	—	2	4	no	—
127	C₂²×C₄×C₁₉	—	2	1	no	—
128	C₂²×C₄×C₁₉	—	2	1	no	—
129	C₂²×C₄×C₁₉	—	2	1	no	—
130	C₂²×C₄×C₁₉	—	4	1	no	—
131	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
134	M₁₆×C₁₉	—	4	1	no	—
135	M₁₆×C₁₉	—	4	1	no	—
136	C₂×C₈×C₁₉	—	4	2	no	—
137	C₂×C₈×C₁₉	—	4	1	no	—
138	C₂×C₈×C₁₉	—	4	1	no	—
139	C₂×C₈×C₁₉	—	4	1	no	—
140	C₄⋊C₄×C₁₉	—	2	1	no	—
141	C₄⋊C₄×C₁₉	—	2	2	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	1	no	—
146	C₄⋊C₄×C₁₉	—	2	2	no	—
147	C₄⋊C₄×C₁₉	—	2	2	no	—
148	C₄⋊C₄×C₁₉	—	4	1	no	—
149	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
150	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
151	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
152	C₂²⋊C₄×C₁₉	—	2	4	no	—
153	C₂²⋊C₄×C₁₉	—	2	4	no	—
154	C₂²⋊C₄×C₁₉	—	2	4	no	—
155	C₂²⋊C₄×C₁₉	—	2	4	no	—
156	C₂²⋊C₄×C₁₉	—	2	1	no	—
157	C₂²⋊C₄×C₁₉	—	2	2	no	—
158	C₂²⋊C₄×C₁₉	—	2	1	no	—
159	C₂²⋊C₄×C₁₉	—	2	1	no	—
160	C₄²×C₁₉	—	2	1	no	—
161	C₄²×C₁₉	—	2	2	no	—
162	C₄²×C₁₉	—	2	1	no	—
163	C₄²×C₁₉	—	2	1	no	—
164	C₄²×C₁₉	—	4	1	no	—
165	C₄²×C₁₉	—	4	1	no	—
166	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
167	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
170	#8426	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
171	C₂³×C₁₉	—	2	4	no	—
172	C₂³×C₁₉	—	2	1	no	—
173	C₂³×C₁₉	—	4	2	no	—
174	C₂³×C₁₉	—	4	2	no	—
175	C₂³×C₁₉	—	8	2	no	—
176	C₂³×C₁₉	—	8	2	no	—
177	C₂³×C₁₉	#120	1	1	yes	characteristic
178	Q₈×C₁₉	—	2	1	no	—
179	Q₈×C₁₉	—	2	1	no	—
180	Q₈×C₁₉	—	4	2	no	—
181	Q₈×C₁₉	—	4	1	no	—
182	Q₈×C₁₉	—	4	1	no	—
183	D₄×C₁₉	—	2	1	no	—
184	D₄×C₁₉	—	2	1	no	—
185	D₄×C₁₉	—	4	4	no	—
186	D₄×C₁₉	—	4	4	no	—
187	D₄×C₁₉	—	4	1	no	—
188	D₄×C₁₉	—	4	1	no	—
189	D₄×C₁₉	—	4	2	no	—
190	D₄×C₁₉	—	4	2	no	—
191	D₄×C₁₉	—	4	2	no	—
192	D₄×C₁₉	—	4	2	no	—
193	D₄×C₁₉	—	4	2	no	—
194	D₄×C₁₉	—	4	2	no	—
195	D₄×C₁₉	—	8	2	no	—
196	D₄×C₁₉	—	8	4	no	—
197	D₄×C₁₉	—	8	4	no	—
198	C₂×C₄×C₁₉	—	2	1	no	—
199	C₂×C₄×C₁₉	—	2	1	no	—
200	C₂×C₄×C₁₉	—	2	1	no	—
201	C₂×C₄×C₁₉	—	2	1	no	—
202	C₂×C₄×C₁₉	—	2	1	no	—
203	C₂×C₄×C₁₉	—	2	2	no	—
204	C₂×C₄×C₁₉	—	2	2	no	—
205	C₂×C₄×C₁₉	—	4	1	no	—
206	C₂×C₄×C₁₉	—	4	2	no	—
207	C₂×C₄×C₁₉	—	4	1	no	—
208	C₂×C₄×C₁₉	—	4	1	no	—
209	C₂×C₄×C₁₉	—	4	1	no	—
210	C₂×C₄×C₁₉	—	4	1	no	—
211	C₂×C₄×C₁₉	—	4	2	no	—
212	C₂×C₄×C₁₉	—	8	4	no	—
213	C₂×C₄×C₁₉	—	8	4	no	—
214	C₂×C₄×C₁₉	—	8	1	no	—
215	C₂×C₄×C₁₉	—	8	1	no	—
216	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
220	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
221	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
222	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
223	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
224	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
225	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
226	C₈×C₁₉	—	8	1	no	—
227	C₈×C₁₉	—	8	1	no	—
228	C₈×C₁₉	—	8	1	no	—
229	#3508	C₂×C₁₉	1	1	yes	characteristic
230	#1982	C₂×C₁₉	1	1	yes	characteristic, complemented
231	#1806	C₂×C₁₉	1	1	yes	characteristic, complemented
232	#1550	C₂×C₁₉	1	1	yes	characteristic, complemented
233	#1545	C₂×C₁₉	1	1	yes	characteristic, complemented
234	#1503	C₂×C₁₉	1	1	yes	characteristic, complemented
235	#1477	C₂×C₁₉	1	1	yes	characteristic, complemented
236	C₂²×C₁₉	—	2	1	no	—
237	C₂²×C₁₉	—	2	1	no	—
238	C₂²×C₁₉	—	4	1	no	—
239	C₂²×C₁₉	—	4	4	no	—
240	C₂²×C₁₉	—	4	1	no	—
241	C₂²×C₁₉	—	4	4	no	—
242	C₂²×C₁₉	—	4	1	no	—
243	C₂²×C₁₉	—	4	4	no	—
244	C₂²×C₁₉	—	16	2	no	—
245	C₂²×C₁₉	—	16	2	no	—
246	C₂²×C₁₉	#379	1	1	yes	characteristic
247	C₂²×C₁₉	#449	1	1	yes	characteristic
248	C₂²×C₁₉	#452	1	1	yes	characteristic
249	C₄×C₁₉	—	2	1	no	—
250	C₄×C₁₉	—	2	1	no	—
251	C₄×C₁₉	—	2	1	no	—
252	C₄×C₁₉	—	4	1	no	—
253	C₄×C₁₉	—	4	2	no	—
254	C₄×C₁₉	—	4	1	no	—
255	C₄×C₁₉	—	4	2	no	—
256	C₄×C₁₉	—	4	1	no	—
257	C₄×C₁₉	—	8	2	no	—
258	C₄×C₁₉	#416	1	1	yes	characteristic
259	C₄×C₁₉	#417	1	1	yes	characteristic
260	C₄×C₁₉	#449	1	1	yes	characteristic
261	C₄×C₁₉	#452	1	1	yes	characteristic
262	C₄×C₁₉	#453	1	1	yes	characteristic
263	C₄×C₁₉	#455	1	1	yes	characteristic
264	#559	—	2	1	no	—
265	#559	C₄×C₁₉	1	2	yes	complemented
266	#550	—	2	1	no	—
267	#550	C₄×C₁₉	1	2	yes	complemented
268	#546	—	2	2	no	—
269	#546	—	2	2	no	—
270	#540	—	2	2	no	—
271	#535	—	2	1	no	—
272	#533	C₂²×C₁₉	1	1	yes	characteristic
273	#532	—	2	1	no	—
274	#532	—	2	1	no	—
275	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
276	#518	—	2	1	no	—
277	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
278	#431	C₂²×C₁₉	1	1	yes	characteristic
279	#423	C₂²×C₁₉	1	1	yes	characteristic
280	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
281	C₂×#104	—	2	1	no	—
282	C₂×#102	—	2	2	no	—
283	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
284	#339	—	2	1	no	—
285	#333	—	2	1	no	—
286	#332	—	2	1	no	—
287	#331	—	2	2	no	—
288	#328	—	2	2	no	—
289	Q₈⋊C₈	—	2	1	no	—
290	D₄⋊C₈	—	2	1	no	—
291	C₂×C₁₉	—	2	1	no	—
292	C₂×C₁₉	—	2	1	no	—
293	C₂×C₁₉	—	8	1	no	—
294	C₂×C₁₉	—	8	4	no	—
295	C₂×C₁₉	#1788	1	1	yes	characteristic
296	C₂×C₁₉	#1792	1	1	yes	characteristic
297	C₂×C₁₉	#1795	1	1	yes	characteristic
298	C₂×#41	—	2	2	no	—
299	C₂×#41	—	2	2	no	—
300	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
301	C₂²×D₄	—	2	1	no	—
302	C₂²×D₄	—	2	1	no	—
303	C₂²×D₄	D₄×C₁₉	1	2	yes	—
304	C₂×M₁₆	—	2	1	no	—
305	C₂²×C₈	—	2	1	no	—
306	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
307	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
308	#127	—	2	2	no	—
309	#127	—	2	1	no	—
310	#127	—	2	1	no	—
311	#127	C₂×C₄×C₁₉	1	2	yes	—
312	#127	D₄×C₁₉	1	2	yes	—
313	#125	—	2	1	no	—
314	#124	—	2	2	no	—
315	#124	—	2	2	no	—
316	#124	—	2	2	no	—
317	#123	—	2	4	no	—
318	#123	—	2	4	no	—
319	C₂²⋊Q₈	—	2	1	no	—
320	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
321	#121	—	2	2	no	—
322	#121	—	2	2	no	—
323	#121	—	2	2	no	—
324	#121	—	2	4	no	—
325	#121	—	2	4	no	—
326	#121	—	2	2	no	—
327	#120	—	2	4	no	—
328	C₄×Q₈	—	2	1	no	—
329	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
330	C₄×Q₈	C₂×C₄×C₁₉	1	2	yes	—
331	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
332	C₄×D₄	—	2	2	no	—
333	C₄×D₄	—	2	2	no	—
334	C₄×D₄	—	2	2	no	—
335	C₄×D₄	—	2	1	no	—
336	C₄×D₄	—	2	1	no	—
337	C₄×D₄	—	2	2	no	—
338	C₄×D₄	—	2	2	no	—
339	C₄×D₄	—	2	2	no	—
340	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
341	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
342	#117	—	2	1	no	—
343	#117	—	2	1	no	—
344	#117	D₄×C₁₉	1	1	yes	characteristic
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₂²⋊C₄	—	2	4	no	—
347	C₂×C₄²	—	2	1	no	—
348	C₂×C₄²	—	2	1	no	—
349	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
350	C₄⋊C₈	—	2	1	no	—
351	C₄⋊C₈	—	2	1	no	—
352	C₄⋊C₈	—	2	1	no	—
353	C₄⋊C₈	—	2	1	no	—
354	C₄⋊C₈	—	2	1	no	—
355	#104	—	4	2	no	—
356	#102	—	4	4	no	—
357	C₂²⋊C₈	—	2	1	no	—
358	C₄×C₈	—	2	1	no	—
359	#95	—	2	1	no	—
360	C₁₉	#8426	1	1	yes	characteristic, direct product factor, Sylow
361	C₂⁴	—	2	2	no	—
362	#41	—	2	1	no	—
363	#41	—	2	1	no	—
364	#41	—	2	1	no	—
365	#41	—	2	1	no	—
366	#41	—	8	4	no	—
367	#41	—	8	2	no	—
368	#41	—	8	2	no	—
369	C₂×Q₈	—	2	1	no	—
370	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
371	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
372	C₂×D₄	—	2	1	no	—
373	C₂×D₄	—	2	4	no	—
374	C₂×D₄	—	2	4	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	4	2	no	—
381	C₂×D₄	—	4	2	no	—
382	C₂×D₄	—	4	1	no	—
383	C₂×D₄	—	4	1	no	—
384	C₂×D₄	—	4	1	no	—
385	C₂×D₄	—	4	1	no	—
386	C₂×D₄	—	8	2	no	—
387	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
388	C₂×D₄	C₂²⋊C₄×C₁₉	1	4	yes	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	4	1	no	—
395	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
398	M₁₆	—	4	1	no	—
399	M₁₆	—	4	1	no	—
400	C₂×C₈	—	4	2	no	—
401	C₂×C₈	—	4	1	no	—
402	C₂×C₈	—	4	1	no	—
403	C₂×C₈	—	4	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	4	1	no	—
413	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
414	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
415	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
416	C₂²⋊C₄	—	2	4	no	—
417	C₂²⋊C₄	—	2	4	no	—
418	C₂²⋊C₄	—	2	4	no	—
419	C₂²⋊C₄	—	2	4	no	—
420	C₂²⋊C₄	—	2	1	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	—	2	1	no	—
423	C₂²⋊C₄	—	2	1	no	—
424	C₄²	—	2	1	no	—
425	C₄²	—	2	2	no	—
426	C₄²	—	2	1	no	—
427	C₄²	—	2	1	no	—
428	C₄²	—	4	1	no	—
429	C₄²	—	4	1	no	—
430	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
431	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
432	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
433	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
434	C₂³	—	2	4	no	—
435	C₂³	—	2	1	no	—
436	C₂³	—	4	2	no	—
437	C₂³	—	4	2	no	—
438	C₂³	—	8	2	no	—
439	C₂³	—	8	2	no	—
440	C₂³	C₁₉×#120	1	1	yes	characteristic
441	Q₈	—	2	1	no	—
442	Q₈	—	2	1	no	—
443	Q₈	—	4	2	no	—
444	Q₈	—	4	1	no	—
445	Q₈	—	4	1	no	—
446	D₄	—	2	1	no	—
447	D₄	—	2	1	no	—
448	D₄	—	4	4	no	—
449	D₄	—	4	4	no	—
450	D₄	—	4	1	no	—
451	D₄	—	4	1	no	—
452	D₄	—	4	2	no	—
453	D₄	—	4	2	no	—
454	D₄	—	4	2	no	—
455	D₄	—	4	2	no	—
456	D₄	—	4	2	no	—
457	D₄	—	4	2	no	—
458	D₄	—	8	2	no	—
459	D₄	—	8	4	no	—
460	D₄	—	8	4	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	8	4	no	—
476	C₂×C₄	—	8	4	no	—
477	C₂×C₄	—	8	1	no	—
478	C₂×C₄	—	8	1	no	—
479	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
480	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
481	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
482	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
483	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
484	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
485	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
486	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
487	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
488	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
489	C₈	—	8	1	no	—
490	C₈	—	8	1	no	—
491	C₈	—	8	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	2	1	no	—
494	C₂²	—	4	1	no	—
495	C₂²	—	4	4	no	—
496	C₂²	—	4	1	no	—
497	C₂²	—	4	4	no	—
498	C₂²	—	4	1	no	—
499	C₂²	—	4	4	no	—
500	C₂²	—	16	2	no	—
501	C₂²	—	16	2	no	—
502	C₂²	C₁₉×#379	1	1	yes	characteristic
503	C₂²	C₁₉×#449	1	1	yes	characteristic
504	C₂²	C₁₉×#452	1	1	yes	characteristic
505	C₄	—	2	1	no	—
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	4	1	no	—
509	C₄	—	4	1	no	—
510	C₄	—	4	2	no	—
511	C₄	—	4	1	no	—
512	C₄	—	4	2	no	—
513	C₄	—	8	2	no	—
514	C₄	C₁₉×#416	1	1	yes	characteristic
515	C₄	C₁₉×#417	1	1	yes	characteristic
516	C₄	C₁₉×#449	1	1	yes	characteristic
517	C₄	C₁₉×#452	1	1	yes	characteristic
518	C₄	C₁₉×#453	1	1	yes	characteristic
519	C₄	C₁₉×#455	1	1	yes	characteristic
520	C₂	—	2	1	no	—
521	C₂	—	2	1	no	—
522	C₂	—	8	4	no	—
523	C₂	—	8	1	no	—
524	C₂	C₁₉×#1788	1	1	yes	characteristic
525	C₂	C₁₉×#1792	1	1	yes	characteristic
526	C₂	C₁₉×#1795	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#379
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#3508	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×#1982	C₂	semidirect
3. C₁₉×#1806	C₂	semidirect
4. C₁₉×#1550	C₂	semidirect
5. C₁₉×#1545	C₂	semidirect
6. C₁₉×#1503	C₂	semidirect
7. C₁₉×#1477	C₂	semidirect
9. C₁₉×#559	C₄	semidirect
11. C₁₉×#550	C₄	semidirect
170. #8426	C₁₉	direct (N × H)
230. #1982	C₂×C₁₉	semidirect
231. #1806	C₂×C₁₉	semidirect
232. #1550	C₂×C₁₉	semidirect
233. #1545	C₂×C₁₉	semidirect
234. #1503	C₂×C₁₉	semidirect
235. #1477	C₂×C₁₉	semidirect
265. #559	C₄×C₁₉	semidirect
267. #550	C₄×C₁₉	semidirect
360. C₁₉	#8426	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×#3508	2
C₁₉×#1982	2
C₁₉×#1806	2
C₁₉×#1550	2
C₁₉×#1545	2
C₁₉×#1503	2
C₁₉×#1477	2
#8426	19

Subgroups — C19×#8426 #18014385

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8426 #18014385