Subgroups — C₁₉×#10411 #18016370

Order 4864.

572 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2548	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1957	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1947	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1803	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#331	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₉×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×#124	—	2	1	no	—
10	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#107	—	2	1	no	—
12	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#103	—	2	1	no	—
15	C₂×C₁₉×#102	—	2	2	no	—
16	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#394	—	2	2	no	—
18	C₁₉×#390	—	2	1	no	—
19	C₁₉×#390	—	2	1	no	—
20	C₁₉×#390	—	2	1	no	—
21	C₁₉×#384	C₂²	1	1	yes	characteristic
22	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#340	—	2	1	no	—
24	C₁₉×#340	—	2	1	no	—
25	C₁₉×#331	—	2	2	no	—
26	C₁₉×Q₈⋊C₈	—	2	2	no	—
27	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
28	C₂²×D₄×C₁₉	—	2	1	no	—
29	C₂²×D₄×C₁₉	—	2	1	no	—
30	C₂²×D₄×C₁₉	D₄	1	2	yes	—
31	C₂²×C₈×C₁₉	—	2	1	no	—
32	C₂²×C₈×C₁₉	—	2	1	no	—
33	C₂²×C₈×C₁₉	—	2	1	no	—
34	C₁₉×#127	—	2	1	no	—
35	C₁₉×#127	—	2	1	no	—
36	C₁₉×#127	—	2	1	no	—
37	C₁₉×#127	—	2	1	no	—
38	C₁₉×#124	—	4	2	no	—
39	C₁₉×#124	—	4	2	no	—
40	C₄×Q₈×C₁₉	—	2	1	no	—
41	C₄×Q₈×C₁₉	—	2	1	no	—
42	C₄×Q₈×C₁₉	—	2	1	no	—
43	C₄×Q₈×C₁₉	—	2	1	no	—
44	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
45	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
46	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
48	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
50	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
51	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
52	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
53	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
54	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
55	C₂×C₄²×C₁₉	—	2	1	no	—
56	C₂×C₄²×C₁₉	—	2	1	no	—
57	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
58	C₁₉×#107	—	4	2	no	—
59	C₁₉×C₄⋊C₈	—	2	1	no	—
60	C₁₉×C₄⋊C₈	—	2	1	no	—
61	C₁₉×C₄⋊C₈	—	2	1	no	—
62	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
63	C₁₉×#103	—	4	2	no	—
64	C₁₉×#102	—	4	4	no	—
65	C₄×C₈×C₁₉	—	2	1	no	—
66	C₄×C₈×C₁₉	—	2	1	no	—
67	C₁₉×#95	—	2	1	no	—
68	C₂⁴×C₁₉	—	2	2	no	—
69	C₂×Q₈×C₁₉	—	2	1	no	—
70	C₂×Q₈×C₁₉	—	2	1	no	—
71	C₂×Q₈×C₁₉	—	2	1	no	—
72	C₂×Q₈×C₁₉	—	2	1	no	—
73	C₂×Q₈×C₁₉	—	2	1	no	—
74	C₂×Q₈×C₁₉	D₈	1	2	yes	—
75	C₂×D₄×C₁₉	—	2	2	no	—
76	C₂×D₄×C₁₉	—	2	2	no	—
77	C₂×D₄×C₁₉	—	4	2	no	—
78	C₂×D₄×C₁₉	—	4	2	no	—
79	C₂×D₄×C₁₉	—	4	1	no	—
80	C₂×D₄×C₁₉	—	4	1	no	—
81	C₂×D₄×C₁₉	—	4	1	no	—
82	C₂×D₄×C₁₉	—	4	1	no	—
83	C₂×D₄×C₁₉	—	4	1	no	—
84	C₂×D₄×C₁₉	—	4	1	no	—
85	C₂×D₄×C₁₉	—	4	1	no	—
86	C₂×D₄×C₁₉	—	4	1	no	—
87	C₂×D₄×C₁₉	—	4	1	no	—
88	C₂×D₄×C₁₉	—	4	1	no	—
89	C₂×D₄×C₁₉	—	4	1	no	—
90	C₂×D₄×C₁₉	—	4	1	no	—
91	C₂²×C₄×C₁₉	—	2	1	no	—
92	C₂²×C₄×C₁₉	—	2	1	no	—
93	C₂²×C₄×C₁₉	—	2	1	no	—
94	C₂²×C₄×C₁₉	—	2	1	no	—
95	C₂²×C₄×C₁₉	—	4	1	no	—
96	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂×C₈×C₁₉	—	2	2	no	—
100	C₂×C₈×C₁₉	—	2	2	no	—
101	C₂×C₈×C₁₉	—	4	1	no	—
102	C₂×C₈×C₁₉	—	4	1	no	—
103	C₂×C₈×C₁₉	—	4	1	no	—
104	C₂×C₈×C₁₉	—	4	1	no	—
105	C₂×C₈×C₁₉	—	4	1	no	—
106	C₂×C₈×C₁₉	—	4	1	no	—
107	C₂×C₈×C₁₉	—	4	1	no	—
108	C₄⋊C₄×C₁₉	—	2	1	no	—
109	C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₄⋊C₄×C₁₉	—	2	1	no	—
111	C₄⋊C₄×C₁₉	—	2	1	no	—
112	C₄⋊C₄×C₁₉	—	2	1	no	—
113	C₄⋊C₄×C₁₉	—	2	1	no	—
114	C₄⋊C₄×C₁₉	—	4	2	no	—
115	C₄⋊C₄×C₁₉	—	4	1	no	—
116	C₄⋊C₄×C₁₉	—	4	1	no	—
117	C₄⋊C₄×C₁₉	—	4	1	no	—
118	C₄⋊C₄×C₁₉	—	4	1	no	—
119	C₄⋊C₄×C₁₉	—	4	1	no	—
120	C₄⋊C₄×C₁₉	—	4	1	no	—
121	C₂²⋊C₄×C₁₉	—	4	4	no	—
122	C₂²⋊C₄×C₁₉	—	4	4	no	—
123	C₂²⋊C₄×C₁₉	—	8	2	no	—
124	C₂²⋊C₄×C₁₉	—	8	2	no	—
125	C₄²×C₁₉	—	4	1	no	—
126	C₄²×C₁₉	—	4	1	no	—
127	C₄²×C₁₉	—	4	1	no	—
128	C₄²×C₁₉	—	4	1	no	—
129	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₁₉	#41	1	1	yes	characteristic
131	C₄²×C₁₉	#41	1	1	yes	characteristic
132	C₄²×C₁₉	#41	1	1	yes	characteristic
133	#10411	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂³×C₁₉	—	4	2	no	—
135	C₂³×C₁₉	—	4	2	no	—
136	C₂³×C₁₉	—	4	2	no	—
137	C₂³×C₁₉	—	4	2	no	—
138	C₂³×C₁₉	—	4	2	no	—
139	C₂³×C₁₉	—	4	2	no	—
140	C₂³×C₁₉	—	4	2	no	—
141	C₂³×C₁₉	#120	1	1	yes	characteristic
142	Q₈×C₁₉	—	2	2	no	—
143	Q₈×C₁₉	—	2	2	no	—
144	Q₈×C₁₉	—	4	1	no	—
145	Q₈×C₁₉	—	4	1	no	—
146	D₄×C₁₉	—	4	4	no	—
147	D₄×C₁₉	—	8	2	no	—
148	D₄×C₁₉	—	8	1	no	—
149	D₄×C₁₉	—	8	1	no	—
150	D₄×C₁₉	—	8	1	no	—
151	D₄×C₁₉	—	8	1	no	—
152	D₄×C₁₉	—	8	1	no	—
153	D₄×C₁₉	—	8	1	no	—
154	D₄×C₁₉	—	8	1	no	—
155	D₄×C₁₉	—	8	1	no	—
156	C₂×C₄×C₁₉	—	2	1	no	—
157	C₂×C₄×C₁₉	—	2	1	no	—
158	C₂×C₄×C₁₉	—	2	2	no	—
159	C₂×C₄×C₁₉	—	4	1	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	—	8	1	no	—
171	C₂×C₄×C₁₉	—	8	1	no	—
172	C₂×C₄×C₁₉	—	8	1	no	—
173	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
175	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
182	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
183	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
184	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
185	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
186	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
187	C₈×C₁₉	—	4	2	no	—
188	C₈×C₁₉	—	4	2	no	—
189	C₈×C₁₉	—	8	1	no	—
190	#2548	C₂×C₁₉	1	1	yes	characteristic
191	#1957	C₂×C₁₉	1	1	yes	characteristic
192	#1947	C₂×C₁₉	1	1	yes	characteristic, complemented
193	#1803	C₂×C₁₉	1	1	yes	characteristic, complemented
194	C₂×#331	C₂×C₁₉	1	1	yes	characteristic
195	C₂×Q₈⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
196	#1279	C₂×C₁₉	1	1	yes	characteristic, complemented
197	C₂²×C₁₉	—	8	2	no	—
198	C₂²×C₁₉	—	8	2	no	—
199	C₂²×C₁₉	—	8	2	no	—
200	C₂²×C₁₉	—	8	2	no	—
201	C₂²×C₁₉	—	8	2	no	—
202	C₂²×C₁₉	—	8	2	no	—
203	C₂²×C₁₉	—	8	2	no	—
204	C₂²×C₁₉	#394	1	1	yes	characteristic
205	C₂²×C₁₉	#447	1	1	yes	characteristic
206	C₂²×C₁₉	#449	1	1	yes	characteristic
207	C₂²×C₁₉	#452	1	1	yes	characteristic
208	C₂²×C₁₉	#452	1	1	yes	characteristic
209	C₂²×C₁₉	#453	1	1	yes	characteristic
210	C₂²×C₁₉	#455	1	1	yes	characteristic
211	C₄×C₁₉	—	2	1	no	—
212	C₄×C₁₉	—	2	1	no	—
213	C₄×C₁₉	—	4	2	no	—
214	C₄×C₁₉	—	8	1	no	—
215	C₄×C₁₉	—	8	1	no	—
216	C₄×C₁₉	—	8	1	no	—
217	C₄×C₁₉	—	16	1	no	—
218	C₄×C₁₉	#463	1	1	yes	characteristic
219	C₄×C₁₉	#464	1	1	yes	characteristic
220	C₄×C₁₉	#466	1	1	yes	characteristic
221	C₄×C₁₉	#468	1	1	yes	characteristic
222	C₄×C₁₉	#480	1	1	yes	characteristic
223	C₄×C₁₉	#482	1	1	yes	characteristic
224	C₄×C₁₉	#488	1	1	yes	characteristic
225	C₄×C₁₉	#489	1	1	yes	characteristic
226	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
227	C₂×#124	—	2	1	no	—
228	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
229	C₂×#107	—	2	1	no	—
230	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
231	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
232	C₂×#103	—	2	1	no	—
233	C₂×#102	—	2	2	no	—
234	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
235	#394	—	2	2	no	—
236	#390	—	2	1	no	—
237	#390	—	2	1	no	—
238	#390	—	2	1	no	—
239	#384	C₂²×C₁₉	1	1	yes	characteristic
240	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
241	#340	—	2	1	no	—
242	#340	—	2	1	no	—
243	#331	—	2	2	no	—
244	Q₈⋊C₈	—	2	2	no	—
245	C₂×C₁₉	—	16	2	no	—
246	C₂×C₁₉	#1621	1	1	yes	characteristic
247	C₂×C₁₉	#1630	1	1	yes	characteristic
248	C₂×C₁₉	#1640	1	1	yes	characteristic
249	C₂×C₁₉	#1641	1	1	yes	characteristic
250	C₂×C₁₉	#2033	1	1	yes	characteristic
251	C₂×C₁₉	#2037	1	1	yes	characteristic
252	C₂×C₁₉	#2042	1	1	yes	characteristic
253	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
254	C₂²×D₄	—	2	1	no	—
255	C₂²×D₄	—	2	1	no	—
256	C₂²×D₄	D₄×C₁₉	1	2	yes	—
257	C₂²×C₈	—	2	1	no	—
258	C₂²×C₈	—	2	1	no	—
259	C₂²×C₈	—	2	1	no	—
260	#127	—	2	1	no	—
261	#127	—	2	1	no	—
262	#127	—	2	1	no	—
263	#127	—	2	1	no	—
264	#124	—	4	2	no	—
265	#124	—	4	2	no	—
266	C₄×Q₈	—	2	1	no	—
267	C₄×Q₈	—	2	1	no	—
268	C₄×Q₈	—	2	1	no	—
269	C₄×Q₈	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
275	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
276	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₂²⋊C₄	—	2	2	no	—
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₄²	—	2	1	no	—
282	C₂×C₄²	—	2	1	no	—
283	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
284	#107	—	4	2	no	—
285	C₄⋊C₈	—	2	1	no	—
286	C₄⋊C₈	—	2	1	no	—
287	C₄⋊C₈	—	2	1	no	—
288	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
289	#103	—	4	2	no	—
290	#102	—	4	4	no	—
291	C₄×C₈	—	2	1	no	—
292	C₄×C₈	—	2	1	no	—
293	#95	—	2	1	no	—
294	C₁₉	#10411	1	1	yes	characteristic, direct product factor, Sylow
295	C₂⁴	—	2	2	no	—
296	C₂×Q₈	—	2	1	no	—
297	C₂×Q₈	—	2	1	no	—
298	C₂×Q₈	—	2	1	no	—
299	C₂×Q₈	—	2	1	no	—
300	C₂×Q₈	—	2	1	no	—
301	C₂×Q₈	D₈×C₁₉	1	2	yes	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	4	2	no	—
305	C₂×D₄	—	4	2	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	—	4	1	no	—
309	C₂×D₄	—	4	1	no	—
310	C₂×D₄	—	4	1	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂×D₄	—	4	1	no	—
313	C₂×D₄	—	4	1	no	—
314	C₂×D₄	—	4	1	no	—
315	C₂×D₄	—	4	1	no	—
316	C₂×D₄	—	4	1	no	—
317	C₂×D₄	—	4	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	4	1	no	—
323	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
324	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	4	1	no	—
329	C₂×C₈	—	4	1	no	—
330	C₂×C₈	—	4	1	no	—
331	C₂×C₈	—	4	1	no	—
332	C₂×C₈	—	4	1	no	—
333	C₂×C₈	—	4	1	no	—
334	C₂×C₈	—	4	1	no	—
335	C₄⋊C₄	—	2	1	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	4	2	no	—
342	C₄⋊C₄	—	4	1	no	—
343	C₄⋊C₄	—	4	1	no	—
344	C₄⋊C₄	—	4	1	no	—
345	C₄⋊C₄	—	4	1	no	—
346	C₄⋊C₄	—	4	1	no	—
347	C₄⋊C₄	—	4	1	no	—
348	C₂²⋊C₄	—	4	4	no	—
349	C₂²⋊C₄	—	4	4	no	—
350	C₂²⋊C₄	—	8	2	no	—
351	C₂²⋊C₄	—	8	2	no	—
352	C₄²	—	4	1	no	—
353	C₄²	—	4	1	no	—
354	C₄²	—	4	1	no	—
355	C₄²	—	4	1	no	—
356	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
357	C₄²	#41×C₁₉	1	1	yes	characteristic
358	C₄²	#41×C₁₉	1	1	yes	characteristic
359	C₄²	#41×C₁₉	1	1	yes	characteristic
360	C₂³	—	4	2	no	—
361	C₂³	—	4	2	no	—
362	C₂³	—	4	2	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	4	2	no	—
367	C₂³	C₁₉×#120	1	1	yes	characteristic
368	Q₈	—	2	2	no	—
369	Q₈	—	2	2	no	—
370	Q₈	—	4	1	no	—
371	Q₈	—	4	1	no	—
372	D₄	—	4	4	no	—
373	D₄	—	8	2	no	—
374	D₄	—	8	1	no	—
375	D₄	—	8	1	no	—
376	D₄	—	8	1	no	—
377	D₄	—	8	1	no	—
378	D₄	—	8	1	no	—
379	D₄	—	8	1	no	—
380	D₄	—	8	1	no	—
381	D₄	—	8	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	8	1	no	—
397	C₂×C₄	—	8	1	no	—
398	C₂×C₄	—	8	1	no	—
399	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
400	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
401	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
402	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
403	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
404	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
405	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
406	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
407	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
408	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
409	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
410	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
411	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
412	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
413	C₈	—	4	2	no	—
414	C₈	—	4	2	no	—
415	C₈	—	8	1	no	—
416	C₂²	—	8	2	no	—
417	C₂²	—	8	2	no	—
418	C₂²	—	8	2	no	—
419	C₂²	—	8	2	no	—
420	C₂²	—	8	2	no	—
421	C₂²	—	8	2	no	—
422	C₂²	—	8	2	no	—
423	C₂²	C₁₉×#394	1	1	yes	characteristic
424	C₂²	C₁₉×#447	1	1	yes	characteristic
425	C₂²	C₁₉×#449	1	1	yes	characteristic
426	C₂²	C₁₉×#452	1	1	yes	characteristic
427	C₂²	C₁₉×#452	1	1	yes	characteristic
428	C₂²	C₁₉×#453	1	1	yes	characteristic
429	C₂²	C₁₉×#455	1	1	yes	characteristic
430	C₄	—	2	1	no	—
431	C₄	—	2	1	no	—
432	C₄	—	4	2	no	—
433	C₄	—	8	1	no	—
434	C₄	—	8	1	no	—
435	C₄	—	8	1	no	—
436	C₄	—	16	1	no	—
437	C₄	C₁₉×#463	1	1	yes	characteristic
438	C₄	C₁₉×#464	1	1	yes	characteristic
439	C₄	C₁₉×#466	1	1	yes	characteristic
440	C₄	C₁₉×#468	1	1	yes	characteristic
441	C₄	C₁₉×#480	1	1	yes	characteristic
442	C₄	C₁₉×#482	1	1	yes	characteristic
443	C₄	C₁₉×#488	1	1	yes	characteristic
444	C₄	C₁₉×#489	1	1	yes	characteristic
445	C₂	—	16	2	no	—
446	C₂	C₁₉×#1621	1	1	yes	characteristic
447	C₂	C₁₉×#1630	1	1	yes	characteristic
448	C₂	C₁₉×#1640	1	1	yes	characteristic
449	C₂	C₁₉×#1641	1	1	yes	characteristic
450	C₂	C₁₉×#2033	1	1	yes	characteristic
451	C₂	C₁₉×#2037	1	1	yes	characteristic
452	C₂	C₁₉×#2042	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂×C₁₉×#127	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×#1947	C₂	semidirect
4. C₁₉×#1803	C₂	semidirect
6. C₂×C₁₉×Q₈⋊C₈	C₂	semidirect
7. C₁₉×#1279	C₂	semidirect
133. #10411	C₁₉	direct (N × H)
192. #1947	C₂×C₁₉	semidirect
193. #1803	C₂×C₁₉	semidirect
195. C₂×Q₈⋊C₈	C₂×C₁₉	semidirect
196. #1279	C₂×C₁₉	semidirect
294. C₁₉	#10411	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×#2548	2
C₁₉×#1957	2
C₁₉×#1947	2
C₁₉×#1803	2
C₂×C₁₉×#331	2
C₂×C₁₉×Q₈⋊C₈	2
C₁₉×#1279	2
#10411	19

Subgroups — C19×#10411 #18016370

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10411 #18016370