Subgroups — C₁₉×#8427 #18014386

Order 4864.

700 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3509	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1988	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1806	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1550	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1546	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
8	C₁₉×#557	—	2	1	no	—
9	C₁₉×#557	C₄	1	2	yes	complemented
10	C₁₉×#556	—	2	1	no	—
11	C₁₉×#556	C₄	1	2	yes	complemented
12	C₁₉×#552	—	2	2	no	—
13	C₁₉×#552	—	2	2	no	—
14	C₁₉×#541	—	2	2	no	—
15	C₁₉×#536	—	2	1	no	—
16	C₁₉×#533	—	2	1	no	—
17	C₁₉×#533	—	2	1	no	—
18	C₁₉×#533	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₁₉×#519	—	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	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#340	—	2	2	no	—
28	C₁₉×#339	—	2	1	no	—
29	C₁₉×#333	—	2	1	no	—
30	C₁₉×#332	—	2	2	no	—
31	C₁₉×#332	—	2	1	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	D₄	1	1	yes	characteristic
36	C₂²×Q₈×C₁₉	—	2	1	no	—
37	C₂×M₁₆×C₁₉	—	2	1	no	—
38	C₂²×C₈×C₁₉	—	2	1	no	—
39	C₁₉×C₄⋊Q₈	—	2	2	no	—
40	C₁₉×C₄⋊Q₈	—	2	1	no	—
41	C₁₉×C₄⋊Q₈	—	2	1	no	—
42	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
43	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
44	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
45	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
46	C₁₉×#126	—	2	4	no	—
47	C₁₉×#126	—	2	4	no	—
48	C₁₉×#125	—	2	2	no	—
49	C₁₉×#125	—	2	4	no	—
50	C₁₉×#125	—	2	2	no	—
51	C₁₉×#125	—	2	4	no	—
52	C₁₉×#125	—	2	1	no	—
53	C₁₉×#124	—	2	2	no	—
54	C₁₉×#123	—	2	4	no	—
55	C₁₉×C₂²⋊Q₈	—	2	2	no	—
56	C₁₉×C₂²⋊Q₈	—	2	2	no	—
57	C₁₉×C₂²⋊Q₈	—	2	2	no	—
58	C₁₉×C₂²⋊Q₈	—	2	2	no	—
59	C₁₉×C₂²⋊Q₈	—	2	1	no	—
60	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
61	C₄×Q₈×C₁₉	—	2	2	no	—
62	C₄×Q₈×C₁₉	—	2	2	no	—
63	C₄×Q₈×C₁₉	—	2	2	no	—
64	C₄×Q₈×C₁₉	—	2	2	no	—
65	C₄×Q₈×C₁₉	—	2	2	no	—
66	C₄×Q₈×C₁₉	—	2	2	no	—
67	C₄×Q₈×C₁₉	—	2	1	no	—
68	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
69	C₄×Q₈×C₁₉	C₂×C₄	1	2	yes	—
70	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
71	C₄×D₄×C₁₉	—	2	1	no	—
72	C₄×D₄×C₁₉	—	2	1	no	—
73	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
74	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
75	C₁₉×#117	—	2	4	no	—
76	C₁₉×#117	—	2	2	no	—
77	C₁₉×#117	—	2	1	no	—
78	C₁₉×#117	—	2	2	no	—
79	C₁₉×#117	—	2	1	no	—
80	C₁₉×#117	D₄	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
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×C₂²⋊C₈	—	2	1	no	—
94	C₄×C₈×C₁₉	—	2	1	no	—
95	C₁₉×#95	—	2	1	no	—
96	#41×C₁₉	—	2	1	no	—
97	#41×C₁₉	—	2	1	no	—
98	#41×C₁₉	—	2	1	no	—
99	#41×C₁₉	—	2	1	no	—
100	C₂×Q₈×C₁₉	—	2	2	no	—
101	C₂×Q₈×C₁₉	—	2	1	no	—
102	C₂×Q₈×C₁₉	—	2	2	no	—
103	C₂×Q₈×C₁₉	—	4	1	no	—
104	C₂×Q₈×C₁₉	—	4	1	no	—
105	C₂×Q₈×C₁₉	—	4	1	no	—
106	C₂×Q₈×C₁₉	—	4	1	no	—
107	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
108	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
109	C₂×D₄×C₁₉	—	2	1	no	—
110	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	2	1	no	—
113	C₂²×C₄×C₁₉	—	2	1	no	—
114	C₂²×C₄×C₁₉	—	2	1	no	—
115	C₂²×C₄×C₁₉	—	4	1	no	—
116	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
119	M₁₆×C₁₉	—	4	1	no	—
120	M₁₆×C₁₉	—	4	1	no	—
121	C₂×C₈×C₁₉	—	4	2	no	—
122	C₂×C₈×C₁₉	—	4	1	no	—
123	C₂×C₈×C₁₉	—	4	1	no	—
124	C₂×C₈×C₁₉	—	4	1	no	—
125	C₄⋊C₄×C₁₉	—	2	4	no	—
126	C₄⋊C₄×C₁₉	—	2	4	no	—
127	C₄⋊C₄×C₁₉	—	2	4	no	—
128	C₄⋊C₄×C₁₉	—	2	4	no	—
129	C₄⋊C₄×C₁₉	—	2	2	no	—
130	C₄⋊C₄×C₁₉	—	2	1	no	—
131	C₄⋊C₄×C₁₉	—	2	2	no	—
132	C₄⋊C₄×C₁₉	—	2	2	no	—
133	C₄⋊C₄×C₁₉	—	2	2	no	—
134	C₄⋊C₄×C₁₉	—	2	1	no	—
135	C₄⋊C₄×C₁₉	—	2	1	no	—
136	C₄⋊C₄×C₁₉	—	2	1	no	—
137	C₄⋊C₄×C₁₉	—	2	1	no	—
138	C₄⋊C₄×C₁₉	—	2	2	no	—
139	C₄⋊C₄×C₁₉	—	2	2	no	—
140	C₄⋊C₄×C₁₉	—	4	1	no	—
141	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
142	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
143	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
144	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
145	C₂²⋊C₄×C₁₉	—	2	4	no	—
146	C₂²⋊C₄×C₁₉	—	2	4	no	—
147	C₂²⋊C₄×C₁₉	—	2	1	no	—
148	C₂²⋊C₄×C₁₉	—	2	2	no	—
149	C₂²⋊C₄×C₁₉	—	2	1	no	—
150	C₂²⋊C₄×C₁₉	—	2	1	no	—
151	C₄²×C₁₉	—	2	4	no	—
152	C₄²×C₁₉	—	2	4	no	—
153	C₄²×C₁₉	—	2	1	no	—
154	C₄²×C₁₉	—	2	2	no	—
155	C₄²×C₁₉	—	2	1	no	—
156	C₄²×C₁₉	—	2	1	no	—
157	C₄²×C₁₉	—	4	1	no	—
158	C₄²×C₁₉	—	4	1	no	—
159	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
160	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
163	#8427	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂³×C₁₉	—	2	1	no	—
165	C₂³×C₁₉	#120	1	1	yes	characteristic
166	Q₈×C₁₉	—	2	1	no	—
167	Q₈×C₁₉	—	2	1	no	—
168	Q₈×C₁₉	—	4	2	no	—
169	Q₈×C₁₉	—	4	2	no	—
170	Q₈×C₁₉	—	4	2	no	—
171	Q₈×C₁₉	—	4	2	no	—
172	Q₈×C₁₉	—	4	2	no	—
173	Q₈×C₁₉	—	4	1	no	—
174	Q₈×C₁₉	—	4	1	no	—
175	D₄×C₁₉	—	2	1	no	—
176	D₄×C₁₉	—	2	1	no	—
177	D₄×C₁₉	—	4	1	no	—
178	D₄×C₁₉	—	4	1	no	—
179	C₂×C₄×C₁₉	—	2	1	no	—
180	C₂×C₄×C₁₉	—	2	1	no	—
181	C₂×C₄×C₁₉	—	2	1	no	—
182	C₂×C₄×C₁₉	—	2	1	no	—
183	C₂×C₄×C₁₉	—	2	2	no	—
184	C₂×C₄×C₁₉	—	2	2	no	—
185	C₂×C₄×C₁₉	—	2	4	no	—
186	C₂×C₄×C₁₉	—	2	1	no	—
187	C₂×C₄×C₁₉	—	4	1	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	4	2	no	—
191	C₂×C₄×C₁₉	—	4	1	no	—
192	C₂×C₄×C₁₉	—	4	1	no	—
193	C₂×C₄×C₁₉	—	4	1	no	—
194	C₂×C₄×C₁₉	—	4	1	no	—
195	C₂×C₄×C₁₉	—	4	2	no	—
196	C₂×C₄×C₁₉	—	8	1	no	—
197	C₂×C₄×C₁₉	—	8	1	no	—
198	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
199	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
201	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
202	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
203	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
204	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
205	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
206	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
207	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
208	C₈×C₁₉	—	8	1	no	—
209	C₈×C₁₉	—	8	1	no	—
210	C₈×C₁₉	—	8	1	no	—
211	#3509	C₂×C₁₉	1	1	yes	characteristic
212	#1988	C₂×C₁₉	1	1	yes	characteristic, complemented
213	#1806	C₂×C₁₉	1	1	yes	characteristic
214	#1550	C₂×C₁₉	1	1	yes	characteristic, complemented
215	#1546	C₂×C₁₉	1	1	yes	characteristic, complemented
216	#1503	C₂×C₁₉	1	1	yes	characteristic, complemented
217	#1477	C₂×C₁₉	1	1	yes	characteristic
218	C₂²×C₁₉	—	2	1	no	—
219	C₂²×C₁₉	—	2	1	no	—
220	C₂²×C₁₉	—	4	1	no	—
221	C₂²×C₁₉	—	4	1	no	—
222	C₂²×C₁₉	—	4	1	no	—
223	C₂²×C₁₉	#379	1	1	yes	characteristic
224	C₂²×C₁₉	#449	1	1	yes	characteristic
225	C₂²×C₁₉	#452	1	1	yes	characteristic
226	C₄×C₁₉	—	2	1	no	—
227	C₄×C₁₉	—	2	1	no	—
228	C₄×C₁₉	—	2	1	no	—
229	C₄×C₁₉	—	4	1	no	—
230	C₄×C₁₉	—	4	2	no	—
231	C₄×C₁₉	—	4	1	no	—
232	C₄×C₁₉	—	4	2	no	—
233	C₄×C₁₉	—	4	1	no	—
234	C₄×C₁₉	—	4	4	no	—
235	C₄×C₁₉	—	8	2	no	—
236	C₄×C₁₉	#416	1	1	yes	characteristic
237	C₄×C₁₉	#417	1	1	yes	characteristic
238	C₄×C₁₉	#449	1	1	yes	characteristic
239	C₄×C₁₉	#452	1	1	yes	characteristic
240	C₄×C₁₉	#454	1	1	yes	characteristic
241	C₄×C₁₉	#456	1	1	yes	characteristic
242	#557	—	2	1	no	—
243	#557	C₄×C₁₉	1	2	yes	complemented
244	#556	—	2	1	no	—
245	#556	C₄×C₁₉	1	2	yes	complemented
246	#552	—	2	2	no	—
247	#552	—	2	2	no	—
248	#541	—	2	2	no	—
249	#536	—	2	1	no	—
250	#533	—	2	1	no	—
251	#533	—	2	1	no	—
252	#533	C₂²×C₁₉	1	1	yes	characteristic
253	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
254	#519	—	2	1	no	—
255	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
256	#431	C₂²×C₁₉	1	1	yes	characteristic
257	#423	C₂²×C₁₉	1	1	yes	characteristic
258	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
259	C₂×#104	—	2	1	no	—
260	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
261	#340	—	2	2	no	—
262	#339	—	2	1	no	—
263	#333	—	2	1	no	—
264	#332	—	2	2	no	—
265	#332	—	2	1	no	—
266	#328	—	2	2	no	—
267	Q₈⋊C₈	—	2	1	no	—
268	D₄⋊C₈	—	2	1	no	—
269	C₂×C₁₉	—	2	1	no	—
270	C₂×C₁₉	—	2	1	no	—
271	C₂×C₁₉	—	8	1	no	—
272	C₂×C₁₉	#1788	1	1	yes	characteristic
273	C₂×C₁₉	#1793	1	1	yes	characteristic
274	C₂×C₁₉	#1796	1	1	yes	characteristic
275	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
276	C₂²×Q₈	—	2	1	no	—
277	C₂×M₁₆	—	2	1	no	—
278	C₂²×C₈	—	2	1	no	—
279	C₄⋊Q₈	—	2	2	no	—
280	C₄⋊Q₈	—	2	1	no	—
281	C₄⋊Q₈	—	2	1	no	—
282	C₄⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
283	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
284	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
285	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
286	#126	—	2	4	no	—
287	#126	—	2	4	no	—
288	#125	—	2	2	no	—
289	#125	—	2	4	no	—
290	#125	—	2	2	no	—
291	#125	—	2	4	no	—
292	#125	—	2	1	no	—
293	#124	—	2	2	no	—
294	#123	—	2	4	no	—
295	C₂²⋊Q₈	—	2	2	no	—
296	C₂²⋊Q₈	—	2	2	no	—
297	C₂²⋊Q₈	—	2	2	no	—
298	C₂²⋊Q₈	—	2	2	no	—
299	C₂²⋊Q₈	—	2	1	no	—
300	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
301	C₄×Q₈	—	2	2	no	—
302	C₄×Q₈	—	2	2	no	—
303	C₄×Q₈	—	2	2	no	—
304	C₄×Q₈	—	2	2	no	—
305	C₄×Q₈	—	2	2	no	—
306	C₄×Q₈	—	2	2	no	—
307	C₄×Q₈	—	2	1	no	—
308	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
309	C₄×Q₈	C₂×C₄×C₁₉	1	2	yes	—
310	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
311	C₄×D₄	—	2	1	no	—
312	C₄×D₄	—	2	1	no	—
313	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
314	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
315	#117	—	2	4	no	—
316	#117	—	2	2	no	—
317	#117	—	2	1	no	—
318	#117	—	2	2	no	—
319	#117	—	2	1	no	—
320	#117	D₄×C₁₉	1	1	yes	characteristic
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
324	C₂×C₄²	—	2	1	no	—
325	C₂×C₄²	—	2	1	no	—
326	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
327	C₄⋊C₈	—	2	1	no	—
328	C₄⋊C₈	—	2	1	no	—
329	C₄⋊C₈	—	2	1	no	—
330	C₄⋊C₈	—	2	1	no	—
331	C₄⋊C₈	—	2	1	no	—
332	#104	—	4	2	no	—
333	C₂²⋊C₈	—	2	1	no	—
334	C₄×C₈	—	2	1	no	—
335	#95	—	2	1	no	—
336	C₁₉	#8427	1	1	yes	characteristic, direct product factor, Sylow
337	#41	—	2	1	no	—
338	#41	—	2	1	no	—
339	#41	—	2	1	no	—
340	#41	—	2	1	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	1	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	4	1	no	—
345	C₂×Q₈	—	4	1	no	—
346	C₂×Q₈	—	4	1	no	—
347	C₂×Q₈	—	4	1	no	—
348	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
349	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	4	1	no	—
357	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
360	M₁₆	—	4	1	no	—
361	M₁₆	—	4	1	no	—
362	C₂×C₈	—	4	2	no	—
363	C₂×C₈	—	4	1	no	—
364	C₂×C₈	—	4	1	no	—
365	C₂×C₈	—	4	1	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	—	2	4	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	4	1	no	—
382	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
383	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
384	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
385	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
386	C₂²⋊C₄	—	2	4	no	—
387	C₂²⋊C₄	—	2	4	no	—
388	C₂²⋊C₄	—	2	1	no	—
389	C₂²⋊C₄	—	2	2	no	—
390	C₂²⋊C₄	—	2	1	no	—
391	C₂²⋊C₄	—	2	1	no	—
392	C₄²	—	2	4	no	—
393	C₄²	—	2	4	no	—
394	C₄²	—	2	1	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	2	1	no	—
397	C₄²	—	2	1	no	—
398	C₄²	—	4	1	no	—
399	C₄²	—	4	1	no	—
400	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
401	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
402	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
403	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
404	C₂³	—	2	1	no	—
405	C₂³	C₁₉×#120	1	1	yes	characteristic
406	Q₈	—	2	1	no	—
407	Q₈	—	2	1	no	—
408	Q₈	—	4	2	no	—
409	Q₈	—	4	2	no	—
410	Q₈	—	4	2	no	—
411	Q₈	—	4	2	no	—
412	Q₈	—	4	2	no	—
413	Q₈	—	4	1	no	—
414	Q₈	—	4	1	no	—
415	D₄	—	2	1	no	—
416	D₄	—	2	1	no	—
417	D₄	—	4	1	no	—
418	D₄	—	4	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	8	1	no	—
437	C₂×C₄	—	8	1	no	—
438	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
439	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
440	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
441	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
442	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
443	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
444	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
445	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
446	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
447	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
448	C₈	—	8	1	no	—
449	C₈	—	8	1	no	—
450	C₈	—	8	1	no	—
451	C₂²	—	2	1	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	4	1	no	—
454	C₂²	—	4	1	no	—
455	C₂²	—	4	1	no	—
456	C₂²	C₁₉×#379	1	1	yes	characteristic
457	C₂²	C₁₉×#449	1	1	yes	characteristic
458	C₂²	C₁₉×#452	1	1	yes	characteristic
459	C₄	—	2	1	no	—
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	4	1	no	—
463	C₄	—	4	4	no	—
464	C₄	—	4	1	no	—
465	C₄	—	4	2	no	—
466	C₄	—	4	1	no	—
467	C₄	—	4	2	no	—
468	C₄	—	8	2	no	—
469	C₄	C₁₉×#416	1	1	yes	characteristic
470	C₄	C₁₉×#417	1	1	yes	characteristic
471	C₄	C₁₉×#449	1	1	yes	characteristic
472	C₄	C₁₉×#452	1	1	yes	characteristic
473	C₄	C₁₉×#454	1	1	yes	characteristic
474	C₄	C₁₉×#456	1	1	yes	characteristic
475	C₂	—	2	1	no	—
476	C₂	—	2	1	no	—
477	C₂	—	8	1	no	—
478	C₂	C₁₉×#1788	1	1	yes	characteristic
479	C₂	C₁₉×#1793	1	1	yes	characteristic
480	C₂	C₁₉×#1796	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	C₂×#41×C₁₉	D₄
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×#1988	C₂	semidirect
4. C₁₉×#1550	C₂	semidirect
5. C₁₉×#1546	C₂	semidirect
6. C₁₉×#1503	C₂	semidirect
9. C₁₉×#557	C₄	semidirect
11. C₁₉×#556	C₄	semidirect
163. #8427	C₁₉	direct (N × H)
212. #1988	C₂×C₁₉	semidirect
214. #1550	C₂×C₁₉	semidirect
215. #1546	C₂×C₁₉	semidirect
216. #1503	C₂×C₁₉	semidirect
243. #557	C₄×C₁₉	semidirect
245. #556	C₄×C₁₉	semidirect
336. C₁₉	#8427	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×#3509	2
C₁₉×#1988	2
C₁₉×#1806	2
C₁₉×#1550	2
C₁₉×#1546	2
C₁₉×#1503	2
C₁₉×#1477	2
#8427	19

Subgroups — C19×#8427 #18014386

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8427 #18014386