Subgroups — C₁₉×#10434 #18016393

Order 4864.

546 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2538	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1845	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1803	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1802	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
9	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#107	—	2	2	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	1	no	—
16	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#396	—	2	2	no	—
18	C₁₉×#390	—	2	1	no	—
19	C₁₉×#389	—	2	1	no	—
20	C₁₉×#384	C₂²	1	1	yes	characteristic
21	C₁₉×#384	C₂²	1	1	yes	characteristic
22	C₁₉×#380	—	2	1	no	—
23	C₁₉×#340	—	2	1	no	—
24	C₁₉×#340	—	2	1	no	—
25	C₁₉×Q₈⋊C₈	—	2	2	no	—
26	C₁₉×D₄⋊C₈	—	2	2	no	—
27	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
28	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	—	2	1	no	—
30	C₂²×C₈×C₁₉	—	2	1	no	—
31	C₂²×C₈×C₁₉	—	2	1	no	—
32	C₂²×C₈×C₁₉	—	2	1	no	—
33	C₁₉×C₂²⋊Q₈	—	4	2	no	—
34	C₁₉×C₂²⋊Q₈	—	4	2	no	—
35	C₄×Q₈×C₁₉	—	2	1	no	—
36	C₄×Q₈×C₁₉	—	2	1	no	—
37	C₄×Q₈×C₁₉	—	2	1	no	—
38	C₄×Q₈×C₁₉	—	2	1	no	—
39	C₄×D₄×C₁₉	—	2	1	no	—
40	C₄×D₄×C₁₉	—	2	1	no	—
41	C₄×D₄×C₁₉	—	2	1	no	—
42	C₄×D₄×C₁₉	—	2	1	no	—
43	C₂×C₄⋊C₄×C₁₉	—	2	2	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	—	2	1	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
51	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
52	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
53	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
54	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
55	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
56	C₂×C₄²×C₁₉	—	2	1	no	—
57	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
58	C₁₉×#107	—	4	4	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	—	2	1	no	—
63	C₁₉×#103	—	4	2	no	—
64	C₁₉×#102	—	4	2	no	—
65	C₄×C₈×C₁₉	—	2	1	no	—
66	C₄×C₈×C₁₉	D₄	1	2	yes	—
67	C₁₉×#95	—	2	2	no	—
68	C₂⁴×C₁₉	—	2	1	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	1	no	—
76	C₂×D₄×C₁₉	—	2	1	no	—
77	C₂×D₄×C₁₉	—	2	1	no	—
78	C₂×D₄×C₁₉	—	2	1	no	—
79	C₂×D₄×C₁₉	—	2	1	no	—
80	C₂×D₄×C₁₉	Q₁₆	1	2	yes	—
81	C₂²×C₄×C₁₉	—	2	1	no	—
82	C₂²×C₄×C₁₉	—	2	1	no	—
83	C₂²×C₄×C₁₉	—	2	2	no	—
84	C₂²×C₄×C₁₉	—	2	1	no	—
85	C₂²×C₄×C₁₉	—	4	1	no	—
86	C₂²×C₄×C₁₉	—	4	1	no	—
87	C₂²×C₄×C₁₉	—	4	1	no	—
88	C₂²×C₄×C₁₉	—	4	1	no	—
89	C₂²×C₄×C₁₉	—	4	1	no	—
90	C₂²×C₄×C₁₉	—	4	1	no	—
91	C₂²×C₄×C₁₉	—	4	1	no	—
92	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂×C₈×C₁₉	—	2	2	no	—
96	C₂×C₈×C₁₉	—	2	2	no	—
97	C₂×C₈×C₁₉	—	2	2	no	—
98	C₂×C₈×C₁₉	—	4	1	no	—
99	C₂×C₈×C₁₉	—	4	1	no	—
100	C₂×C₈×C₁₉	—	4	1	no	—
101	C₂×C₈×C₁₉	—	4	1	no	—
102	C₂×C₈×C₁₉	—	4	1	no	—
103	C₂×C₈×C₁₉	—	4	1	no	—
104	C₄⋊C₄×C₁₉	—	2	1	no	—
105	C₄⋊C₄×C₁₉	—	2	1	no	—
106	C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₄⋊C₄×C₁₉	—	2	1	no	—
108	C₄⋊C₄×C₁₉	—	4	2	no	—
109	C₄⋊C₄×C₁₉	—	4	4	no	—
110	C₄⋊C₄×C₁₉	—	4	2	no	—
111	C₄⋊C₄×C₁₉	—	4	1	no	—
112	C₄⋊C₄×C₁₉	—	4	1	no	—
113	C₄⋊C₄×C₁₉	—	4	1	no	—
114	C₄⋊C₄×C₁₉	—	4	1	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	1	no	—
123	C₂²⋊C₄×C₁₉	—	4	1	no	—
124	C₂²⋊C₄×C₁₉	—	8	2	no	—
125	C₄²×C₁₉	—	4	1	no	—
126	C₄²×C₁₉	—	4	1	no	—
127	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₁₉	#41	1	1	yes	characteristic
129	C₄²×C₁₉	#41	1	1	yes	characteristic
130	C₄²×C₁₉	#41	1	1	yes	characteristic
131	#10434	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₂³×C₁₉	—	2	2	no	—
133	C₂³×C₁₉	—	4	1	no	—
134	C₂³×C₁₉	—	4	1	no	—
135	C₂³×C₁₉	—	4	1	no	—
136	C₂³×C₁₉	—	4	1	no	—
137	C₂³×C₁₉	—	4	1	no	—
138	C₂³×C₁₉	—	4	1	no	—
139	C₂³×C₁₉	#120	1	1	yes	characteristic
140	Q₈×C₁₉	—	2	2	no	—
141	Q₈×C₁₉	—	2	2	no	—
142	Q₈×C₁₉	—	4	1	no	—
143	Q₈×C₁₉	—	4	1	no	—
144	D₄×C₁₉	—	2	2	no	—
145	D₄×C₁₉	—	2	2	no	—
146	D₄×C₁₉	—	4	1	no	—
147	D₄×C₁₉	—	4	1	no	—
148	C₂×C₄×C₁₉	—	2	1	no	—
149	C₂×C₄×C₁₉	—	2	1	no	—
150	C₂×C₄×C₁₉	—	2	2	no	—
151	C₂×C₄×C₁₉	—	4	1	no	—
152	C₂×C₄×C₁₉	—	4	1	no	—
153	C₂×C₄×C₁₉	—	4	1	no	—
154	C₂×C₄×C₁₉	—	4	1	no	—
155	C₂×C₄×C₁₉	—	4	2	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	—	4	2	no	—
158	C₂×C₄×C₁₉	—	4	1	no	—
159	C₂×C₄×C₁₉	—	4	1	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	8	1	no	—
163	C₂×C₄×C₁₉	—	8	1	no	—
164	C₂×C₄×C₁₉	—	8	1	no	—
165	C₂×C₄×C₁₉	—	8	1	no	—
166	C₂×C₄×C₁₉	—	8	1	no	—
167	C₂×C₄×C₁₉	—	8	1	no	—
168	C₂×C₄×C₁₉	—	8	1	no	—
169	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
171	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
179	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
180	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
182	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
183	C₈×C₁₉	—	2	4	no	—
184	C₈×C₁₉	—	8	1	no	—
185	C₈×C₁₉	—	8	1	no	—
186	#2538	C₂×C₁₉	1	1	yes	characteristic
187	#1845	C₂×C₁₉	1	1	yes	characteristic, complemented
188	#1803	C₂×C₁₉	1	1	yes	characteristic, complemented
189	#1802	C₂×C₁₉	1	1	yes	characteristic
190	C₂×Q₈⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
191	C₂×D₄⋊C₈	C₂×C₁₉	1	1	yes	characteristic
192	#1296	C₂×C₁₉	1	1	yes	characteristic, complemented
193	C₂²×C₁₉	—	4	2	no	—
194	C₂²×C₁₉	—	4	2	no	—
195	C₂²×C₁₉	—	4	2	no	—
196	C₂²×C₁₉	—	8	1	no	—
197	C₂²×C₁₉	—	8	1	no	—
198	C₂²×C₁₉	—	8	1	no	—
199	C₂²×C₁₉	—	8	1	no	—
200	C₂²×C₁₉	#394	1	1	yes	characteristic
201	C₂²×C₁₉	#447	1	1	yes	characteristic
202	C₂²×C₁₉	#449	1	1	yes	characteristic
203	C₂²×C₁₉	#451	1	1	yes	characteristic
204	C₂²×C₁₉	#452	1	1	yes	characteristic
205	C₂²×C₁₉	#453	1	1	yes	characteristic
206	C₂²×C₁₉	#456	1	1	yes	characteristic
207	C₄×C₁₉	—	2	1	no	—
208	C₄×C₁₉	—	2	1	no	—
209	C₄×C₁₉	—	4	2	no	—
210	C₄×C₁₉	—	8	2	no	—
211	C₄×C₁₉	—	8	1	no	—
212	C₄×C₁₉	—	8	1	no	—
213	C₄×C₁₉	—	16	1	no	—
214	C₄×C₁₉	#466	1	1	yes	characteristic
215	C₄×C₁₉	#467	1	1	yes	characteristic
216	C₄×C₁₉	#468	1	1	yes	characteristic
217	C₄×C₁₉	#468	1	1	yes	characteristic
218	C₄×C₁₉	#480	1	1	yes	characteristic
219	C₄×C₁₉	#482	1	1	yes	characteristic
220	C₄×C₁₉	#484	1	1	yes	characteristic
221	C₄×C₁₉	#485	1	1	yes	characteristic
222	C₂×C₂²⋊Q₈	—	2	1	no	—
223	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
224	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
225	C₂×#107	—	2	2	no	—
226	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
227	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
228	C₂×#103	—	2	1	no	—
229	C₂×#102	—	2	1	no	—
230	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
231	#396	—	2	2	no	—
232	#390	—	2	1	no	—
233	#389	—	2	1	no	—
234	#384	C₂²×C₁₉	1	1	yes	characteristic
235	#384	C₂²×C₁₉	1	1	yes	characteristic
236	#380	—	2	1	no	—
237	#340	—	2	1	no	—
238	#340	—	2	1	no	—
239	Q₈⋊C₈	—	2	2	no	—
240	D₄⋊C₈	—	2	2	no	—
241	C₂×C₁₉	—	8	2	no	—
242	C₂×C₁₉	#1621	1	1	yes	characteristic
243	C₂×C₁₉	#1632	1	1	yes	characteristic
244	C₂×C₁₉	#1649	1	1	yes	characteristic
245	C₂×C₁₉	#1650	1	1	yes	characteristic
246	C₂×C₁₉	#2033	1	1	yes	characteristic
247	C₂×C₁₉	#2036	1	1	yes	characteristic
248	C₂×C₁₉	#2039	1	1	yes	characteristic
249	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
250	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
251	C₂³×C₄	—	2	1	no	—
252	C₂²×C₈	—	2	1	no	—
253	C₂²×C₈	—	2	1	no	—
254	C₂²×C₈	—	2	1	no	—
255	C₂²⋊Q₈	—	4	2	no	—
256	C₂²⋊Q₈	—	4	2	no	—
257	C₄×Q₈	—	2	1	no	—
258	C₄×Q₈	—	2	1	no	—
259	C₄×Q₈	—	2	1	no	—
260	C₄×Q₈	—	2	1	no	—
261	C₄×D₄	—	2	1	no	—
262	C₄×D₄	—	2	1	no	—
263	C₄×D₄	—	2	1	no	—
264	C₄×D₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
273	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
274	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	—	2	1	no	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₄²	—	2	1	no	—
279	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
280	#107	—	4	4	no	—
281	C₄⋊C₈	—	2	1	no	—
282	C₄⋊C₈	—	2	1	no	—
283	C₄⋊C₈	—	2	1	no	—
284	C₄⋊C₈	—	2	1	no	—
285	#103	—	4	2	no	—
286	#102	—	4	2	no	—
287	C₄×C₈	—	2	1	no	—
288	C₄×C₈	D₄×C₁₉	1	2	yes	—
289	#95	—	2	2	no	—
290	C₁₉	#10434	1	1	yes	characteristic, direct product factor, Sylow
291	C₂⁴	—	2	1	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×Q₈	—	2	1	no	—
295	C₂×Q₈	—	2	1	no	—
296	C₂×Q₈	—	2	1	no	—
297	C₂×Q₈	D₈×C₁₉	1	2	yes	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	Q₁₆×C₁₉	1	2	yes	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	4	1	no	—
309	C₂²×C₄	—	4	1	no	—
310	C₂²×C₄	—	4	1	no	—
311	C₂²×C₄	—	4	1	no	—
312	C₂²×C₄	—	4	1	no	—
313	C₂²×C₄	—	4	1	no	—
314	C₂²×C₄	—	4	1	no	—
315	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	4	1	no	—
322	C₂×C₈	—	4	1	no	—
323	C₂×C₈	—	4	1	no	—
324	C₂×C₈	—	4	1	no	—
325	C₂×C₈	—	4	1	no	—
326	C₂×C₈	—	4	1	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₄⋊C₄	—	4	4	no	—
333	C₄⋊C₄	—	4	2	no	—
334	C₄⋊C₄	—	4	1	no	—
335	C₄⋊C₄	—	4	1	no	—
336	C₄⋊C₄	—	4	1	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	4	1	no	—
339	C₄⋊C₄	—	4	1	no	—
340	C₄⋊C₄	—	4	1	no	—
341	C₄⋊C₄	—	4	1	no	—
342	C₄⋊C₄	—	4	1	no	—
343	C₄⋊C₄	—	4	1	no	—
344	C₂²⋊C₄	—	4	4	no	—
345	C₂²⋊C₄	—	4	1	no	—
346	C₂²⋊C₄	—	4	1	no	—
347	C₂²⋊C₄	—	8	2	no	—
348	C₄²	—	4	1	no	—
349	C₄²	—	4	1	no	—
350	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
351	C₄²	#41×C₁₉	1	1	yes	characteristic
352	C₄²	#41×C₁₉	1	1	yes	characteristic
353	C₄²	#41×C₁₉	1	1	yes	characteristic
354	C₂³	—	2	2	no	—
355	C₂³	—	4	1	no	—
356	C₂³	—	4	1	no	—
357	C₂³	—	4	1	no	—
358	C₂³	—	4	1	no	—
359	C₂³	—	4	1	no	—
360	C₂³	—	4	1	no	—
361	C₂³	C₁₉×#120	1	1	yes	characteristic
362	Q₈	—	2	2	no	—
363	Q₈	—	2	2	no	—
364	Q₈	—	4	1	no	—
365	Q₈	—	4	1	no	—
366	D₄	—	2	2	no	—
367	D₄	—	2	2	no	—
368	D₄	—	4	1	no	—
369	D₄	—	4	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	8	1	no	—
385	C₂×C₄	—	8	1	no	—
386	C₂×C₄	—	8	1	no	—
387	C₂×C₄	—	8	1	no	—
388	C₂×C₄	—	8	1	no	—
389	C₂×C₄	—	8	1	no	—
390	C₂×C₄	—	8	1	no	—
391	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
392	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
393	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
394	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
395	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
396	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
397	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
398	C₂×C₄	C₂×Q₁₆×C₁₉	1	1	yes	characteristic
399	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
400	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
401	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
402	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
403	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
404	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
405	C₈	—	2	4	no	—
406	C₈	—	8	1	no	—
407	C₈	—	8	1	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	8	1	no	—
412	C₂²	—	8	1	no	—
413	C₂²	—	8	1	no	—
414	C₂²	—	8	1	no	—
415	C₂²	C₁₉×#394	1	1	yes	characteristic
416	C₂²	C₁₉×#447	1	1	yes	characteristic
417	C₂²	C₁₉×#449	1	1	yes	characteristic
418	C₂²	C₁₉×#451	1	1	yes	characteristic
419	C₂²	C₁₉×#452	1	1	yes	characteristic
420	C₂²	C₁₉×#453	1	1	yes	characteristic
421	C₂²	C₁₉×#456	1	1	yes	characteristic
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	4	2	no	—
425	C₄	—	8	1	no	—
426	C₄	—	8	1	no	—
427	C₄	—	8	2	no	—
428	C₄	—	16	1	no	—
429	C₄	C₁₉×#466	1	1	yes	characteristic
430	C₄	C₁₉×#467	1	1	yes	characteristic
431	C₄	C₁₉×#468	1	1	yes	characteristic
432	C₄	C₁₉×#468	1	1	yes	characteristic
433	C₄	C₁₉×#480	1	1	yes	characteristic
434	C₄	C₁₉×#482	1	1	yes	characteristic
435	C₄	C₁₉×#484	1	1	yes	characteristic
436	C₄	C₁₉×#485	1	1	yes	characteristic
437	C₂	—	8	2	no	—
438	C₂	C₁₉×#1621	1	1	yes	characteristic
439	C₂	C₁₉×#1632	1	1	yes	characteristic
440	C₂	C₁₉×#1649	1	1	yes	characteristic
441	C₂	C₁₉×#1650	1	1	yes	characteristic
442	C₂	C₁₉×#2033	1	1	yes	characteristic
443	C₂	C₁₉×#2036	1	1	yes	characteristic
444	C₂	C₁₉×#2039	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂²×D₄×C₁₉	D₄
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
2. C₁₉×#1845	C₂	semidirect
3. C₁₉×#1803	C₂	semidirect
5. C₂×C₁₉×Q₈⋊C₈	C₂	semidirect
7. C₁₉×#1296	C₂	semidirect
131. #10434	C₁₉	direct (N × H)
187. #1845	C₂×C₁₉	semidirect
188. #1803	C₂×C₁₉	semidirect
190. C₂×Q₈⋊C₈	C₂×C₁₉	semidirect
192. #1296	C₂×C₁₉	semidirect
290. C₁₉	#10434	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×#2538	2
C₁₉×#1845	2
C₁₉×#1803	2
C₁₉×#1802	2
C₂×C₁₉×Q₈⋊C₈	2
C₂×C₁₉×D₄⋊C₈	2
C₁₉×#1296	2
#10434	19

Subgroups — C19×#10434 #18016393

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10434 #18016393