Subgroups — C₁₉×#33807 #18039766

Order 4864.

466 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3176	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3164	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2255	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2253	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2244	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2240	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2234	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2234	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2233	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2232	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#2228	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#2228	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#2226	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#2224	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#2164	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#544	—	2	1	no	—
17	C₁₉×#540	—	2	1	no	—
18	C₁₉×#501	—	2	1	no	—
19	C₁₉×#501	—	2	1	no	—
20	C₁₉×#500	C₂²	1	1	yes	characteristic
21	C₁₉×#500	C₂²	1	1	yes	characteristic
22	C₁₉×#499	C₂²	1	1	yes	characteristic
23	C₁₉×#499	C₂²	1	1	yes	characteristic
24	C₁₉×#499	C₂²	1	1	yes	characteristic
25	C₁₉×#493	C₂²	1	1	yes	characteristic
26	C₁₉×#490	—	2	1	no	—
27	C₁₉×#469	—	2	1	no	—
28	C₁₉×#466	C₂²	1	1	yes	characteristic
29	C₁₉×#466	C₂²	1	1	yes	characteristic
30	C₁₉×#442	—	2	1	no	—
31	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
32	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
33	C₁₉×#428	—	2	1	no	—
34	C₁₉×#427	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
36	C₁₉×#405	C₂²	1	1	yes	characteristic
37	C₁₉×#367	C₂²	1	1	yes	characteristic
38	C₁₉×#367	C₂²	1	1	yes	characteristic
39	C₁₉×#367	C₂²	1	1	yes	characteristic
40	C₁₉×#367	C₂²	1	1	yes	characteristic
41	C₁₉×#366	C₂²	1	1	yes	characteristic
42	C₁₉×#366	C₂²	1	1	yes	characteristic
43	C₁₉×#366	C₂²	1	1	yes	characteristic
44	C₁₉×#366	C₂²	1	1	yes	characteristic
45	C₁₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
46	C₁₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
47	C₁₉×#357	C₂²	1	1	yes	characteristic
48	C₁₉×#357	C₂²	1	1	yes	characteristic
49	C₁₉×#357	C₂²	1	1	yes	characteristic
50	C₁₉×#357	C₂²	1	1	yes	characteristic
51	C₁₉×#357	C₂²	1	1	yes	characteristic
52	C₁₉×#357	C₂²	1	1	yes	characteristic
53	C₁₉×#357	C₂²	1	1	yes	characteristic
54	C₁₉×#357	C₂²	1	1	yes	characteristic
55	C₁₉×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
56	C₁₉×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
57	C₁₉×#346	C₂²	1	1	yes	characteristic
58	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
59	C₂×D₈×C₁₉	—	2	1	no	—
60	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
61	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
63	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
64	C₁₉×C₄⋊Q₈	—	2	1	no	—
65	C₁₉×C₄⋊Q₈	—	2	1	no	—
66	C₁₉×C₄⋊Q₈	—	4	1	no	—
67	C₁₉×#127	—	2	1	no	—
68	C₁₉×#125	—	2	1	no	—
69	C₁₉×#125	—	2	1	no	—
70	C₁₉×#125	—	2	1	no	—
71	C₁₉×#125	—	4	1	no	—
72	C₁₉×#123	—	4	1	no	—
73	C₁₉×#123	—	4	1	no	—
74	C₁₉×C₂²⋊Q₈	—	4	1	no	—
75	C₁₉×C₂²⋊Q₈	—	4	1	no	—
76	C₁₉×#121	—	2	1	no	—
77	C₁₉×#121	—	2	1	no	—
78	C₁₉×#121	—	4	1	no	—
79	C₁₉×#121	—	4	1	no	—
80	C₄×D₄×C₁₉	—	2	1	no	—
81	C₄×D₄×C₁₉	—	2	1	no	—
82	C₁₉×#117	—	2	1	no	—
83	C₁₉×#117	D₄	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
85	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
87	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
89	C₁₉×#107	—	2	1	no	—
90	C₁₉×#107	—	2	1	no	—
91	C₁₉×#107	—	2	1	no	—
92	C₁₉×#107	C₂³	1	1	yes	characteristic
93	C₁₉×#107	C₂³	1	1	yes	characteristic
94	C₁₉×#107	C₂³	1	1	yes	characteristic
95	C₁₉×#107	C₂³	1	1	yes	characteristic
96	C₁₉×#107	C₂³	1	1	yes	characteristic
97	C₁₉×#107	C₂³	1	1	yes	characteristic
98	C₁₉×#106	—	2	1	no	—
99	C₁₉×#106	—	2	1	no	—
100	C₁₉×#106	—	2	1	no	—
101	C₁₉×#106	—	2	1	no	—
102	C₁₉×#102	—	2	1	no	—
103	C₁₉×#102	—	2	1	no	—
104	C₁₉×#102	—	2	1	no	—
105	C₁₉×#102	—	2	1	no	—
106	C₁₉×#97	D₄	1	1	yes	characteristic
107	C₁₉×#97	D₄	1	1	yes	characteristic
108	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
109	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
110	C₂×Q₈×C₁₉	—	4	1	no	—
111	C₂×Q₈×C₁₉	—	4	1	no	—
112	C₂×D₄×C₁₉	—	2	1	no	—
113	C₂×D₄×C₁₉	—	2	1	no	—
114	C₂×D₄×C₁₉	—	4	1	no	—
115	C₂×D₄×C₁₉	—	4	1	no	—
116	C₂×D₄×C₁₉	—	4	1	no	—
117	C₂×D₄×C₁₉	—	4	1	no	—
118	C₂²×C₄×C₁₉	—	4	1	no	—
119	C₂²×C₄×C₁₉	—	4	1	no	—
120	C₂²×C₄×C₁₉	—	4	1	no	—
121	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
122	D₈×C₁₉	—	2	1	no	—
123	D₈×C₁₉	—	2	1	no	—
124	D₈×C₁₉	—	2	1	no	—
125	D₈×C₁₉	—	2	1	no	—
126	D₈×C₁₉	—	4	2	no	—
127	M₁₆×C₁₉	—	2	2	no	—
128	C₂×C₈×C₁₉	—	2	1	no	—
129	C₂×C₈×C₁₉	—	2	1	no	—
130	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
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	1	no	—
139	C₄⋊C₄×C₁₉	—	2	1	no	—
140	C₄⋊C₄×C₁₉	—	4	1	no	—
141	C₄⋊C₄×C₁₉	—	4	1	no	—
142	C₄⋊C₄×C₁₉	—	4	1	no	—
143	C₄⋊C₄×C₁₉	—	4	1	no	—
144	C₄⋊C₄×C₁₉	—	4	1	no	—
145	C₄⋊C₄×C₁₉	—	4	1	no	—
146	C₄⋊C₄×C₁₉	—	4	1	no	—
147	C₄⋊C₄×C₁₉	—	4	1	no	—
148	C₄⋊C₄×C₁₉	—	4	1	no	—
149	C₄⋊C₄×C₁₉	D₈	1	1	yes	characteristic
150	C₄⋊C₄×C₁₉	D₈	1	1	yes	characteristic
151	C₂²⋊C₄×C₁₉	—	4	1	no	—
152	C₂²⋊C₄×C₁₉	—	4	1	no	—
153	C₂²⋊C₄×C₁₉	—	4	1	no	—
154	C₂²⋊C₄×C₁₉	—	4	1	no	—
155	C₂²⋊C₄×C₁₉	—	4	1	no	—
156	C₂²⋊C₄×C₁₉	D₈	1	1	yes	characteristic
157	C₂²⋊C₄×C₁₉	D₈	1	1	yes	characteristic
158	C₄²×C₁₉	—	4	1	no	—
159	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₁₆×C₁₉	—	2	1	no	—
162	C₁₆×C₁₉	—	2	1	no	—
163	C₁₆×C₁₉	—	2	1	no	—
164	C₁₆×C₁₉	—	2	1	no	—
165	#33807	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂³×C₁₉	—	4	1	no	—
167	C₂³×C₁₉	—	4	1	no	—
168	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
169	Q₈×C₁₉	—	16	1	no	—
170	Q₈×C₁₉	—	16	1	no	—
171	D₄×C₁₉	—	4	1	no	—
172	D₄×C₁₉	—	4	1	no	—
173	D₄×C₁₉	—	4	1	no	—
174	D₄×C₁₉	—	4	1	no	—
175	D₄×C₁₉	—	16	1	no	—
176	D₄×C₁₉	—	16	1	no	—
177	D₄×C₁₉	—	16	1	no	—
178	D₄×C₁₉	—	16	1	no	—
179	C₂×C₄×C₁₉	—	2	1	no	—
180	C₂×C₄×C₁₉	—	2	1	no	—
181	C₂×C₄×C₁₉	—	4	1	no	—
182	C₂×C₄×C₁₉	—	4	1	no	—
183	C₂×C₄×C₁₉	—	4	1	no	—
184	C₂×C₄×C₁₉	—	4	1	no	—
185	C₂×C₄×C₁₉	—	4	1	no	—
186	C₂×C₄×C₁₉	—	4	1	no	—
187	C₂×C₄×C₁₉	—	16	1	no	—
188	C₂×C₄×C₁₉	—	16	1	no	—
189	C₂×C₄×C₁₉	—	16	1	no	—
190	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
191	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
193	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
194	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
196	C₈×C₁₉	—	2	1	no	—
197	C₈×C₁₉	—	2	1	no	—
198	C₈×C₁₉	#137	1	2	yes	—
199	C₈×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
200	C₈×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
201	#3176	C₂×C₁₉	1	1	yes	characteristic
202	#3164	C₂×C₁₉	1	1	yes	characteristic, complemented
203	#2255	C₂×C₁₉	1	1	yes	characteristic, complemented
204	#2253	C₂×C₁₉	1	1	yes	characteristic, complemented
205	#2244	C₂×C₁₉	1	1	yes	characteristic, complemented
206	#2240	C₂×C₁₉	1	1	yes	characteristic, complemented
207	#2234	C₂×C₁₉	1	1	yes	characteristic, complemented
208	#2234	C₂×C₁₉	1	1	yes	characteristic, complemented
209	#2233	C₂×C₁₉	1	1	yes	characteristic, complemented
210	#2232	C₂×C₁₉	1	1	yes	characteristic, complemented
211	#2228	C₂×C₁₉	1	1	yes	characteristic, complemented
212	#2228	C₂×C₁₉	1	1	yes	characteristic, complemented
213	#2226	C₂×C₁₉	1	1	yes	characteristic, complemented
214	#2224	C₂×C₁₉	1	1	yes	characteristic, complemented
215	#2164	C₂×C₁₉	1	1	yes	characteristic, complemented
216	C₂²×C₁₉	—	2	1	no	—
217	C₂²×C₁₉	—	2	1	no	—
218	C₂²×C₁₉	—	2	1	no	—
219	C₂²×C₁₉	—	8	1	no	—
220	C₂²×C₁₉	—	8	1	no	—
221	C₂²×C₁₉	—	8	1	no	—
222	C₂²×C₁₉	—	8	1	no	—
223	C₂²×C₁₉	—	8	1	no	—
224	C₂²×C₁₉	—	8	1	no	—
225	C₂²×C₁₉	C₂²×D₈	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	—	2	1	no	—
230	C₄×C₁₉	—	2	1	no	—
231	C₄×C₁₉	—	8	1	no	—
232	C₄×C₁₉	—	8	1	no	—
233	C₄×C₁₉	—	8	1	no	—
234	C₄×C₁₉	—	8	1	no	—
235	C₄×C₁₉	—	8	1	no	—
236	C₄×C₁₉	—	8	1	no	—
237	C₄×C₁₉	#536	1	1	yes	characteristic
238	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
239	#544	—	2	1	no	—
240	#540	—	2	1	no	—
241	#501	—	2	1	no	—
242	#501	—	2	1	no	—
243	#500	C₂²×C₁₉	1	1	yes	characteristic
244	#500	C₂²×C₁₉	1	1	yes	characteristic
245	#499	C₂²×C₁₉	1	1	yes	characteristic
246	#499	C₂²×C₁₉	1	1	yes	characteristic
247	#499	C₂²×C₁₉	1	1	yes	characteristic
248	#493	C₂²×C₁₉	1	1	yes	characteristic
249	#490	—	2	1	no	—
250	#469	—	2	1	no	—
251	#466	C₂²×C₁₉	1	1	yes	characteristic
252	#466	C₂²×C₁₉	1	1	yes	characteristic
253	#442	—	2	1	no	—
254	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
255	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
256	#428	—	2	1	no	—
257	#427	C₂²×C₁₉	1	1	yes	characteristic
258	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
259	#405	C₂²×C₁₉	1	1	yes	characteristic
260	#367	C₂²×C₁₉	1	1	yes	characteristic
261	#367	C₂²×C₁₉	1	1	yes	characteristic
262	#367	C₂²×C₁₉	1	1	yes	characteristic
263	#367	C₂²×C₁₉	1	1	yes	characteristic
264	#366	C₂²×C₁₉	1	1	yes	characteristic
265	#366	C₂²×C₁₉	1	1	yes	characteristic
266	#366	C₂²×C₁₉	1	1	yes	characteristic
267	#366	C₂²×C₁₉	1	1	yes	characteristic
268	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
269	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
270	#357	C₂²×C₁₉	1	1	yes	characteristic
271	#357	C₂²×C₁₉	1	1	yes	characteristic
272	#357	C₂²×C₁₉	1	1	yes	characteristic
273	#357	C₂²×C₁₉	1	1	yes	characteristic
274	#357	C₂²×C₁₉	1	1	yes	characteristic
275	#357	C₂²×C₁₉	1	1	yes	characteristic
276	#357	C₂²×C₁₉	1	1	yes	characteristic
277	#357	C₂²×C₁₉	1	1	yes	characteristic
278	C₂²⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
279	C₂²⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
280	#346	C₂²×C₁₉	1	1	yes	characteristic
281	C₄×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
282	C₂×C₁₉	—	4	1	no	—
283	C₂×C₁₉	—	16	1	no	—
284	C₂×C₁₉	—	16	1	no	—
285	C₂×C₁₉	#3226	1	1	yes	characteristic
286	C₂×C₁₉	#3415	1	1	yes	characteristic
287	C₂×C₁₉	#3416	1	1	yes	characteristic
288	C₂×D₈	—	2	1	no	—
289	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
290	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
291	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
292	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
293	C₄⋊Q₈	—	2	1	no	—
294	C₄⋊Q₈	—	2	1	no	—
295	C₄⋊Q₈	—	4	1	no	—
296	#127	—	2	1	no	—
297	#125	—	2	1	no	—
298	#125	—	2	1	no	—
299	#125	—	2	1	no	—
300	#125	—	4	1	no	—
301	#123	—	4	1	no	—
302	#123	—	4	1	no	—
303	C₂²⋊Q₈	—	4	1	no	—
304	C₂²⋊Q₈	—	4	1	no	—
305	#121	—	2	1	no	—
306	#121	—	2	1	no	—
307	#121	—	4	1	no	—
308	#121	—	4	1	no	—
309	C₄×D₄	—	2	1	no	—
310	C₄×D₄	—	2	1	no	—
311	#117	—	2	1	no	—
312	#117	D₄×C₁₉	1	1	yes	characteristic
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
315	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
316	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
317	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
318	#107	—	2	1	no	—
319	#107	—	2	1	no	—
320	#107	—	2	1	no	—
321	#107	C₂³×C₁₉	1	1	yes	characteristic
322	#107	C₂³×C₁₉	1	1	yes	characteristic
323	#107	C₂³×C₁₉	1	1	yes	characteristic
324	#107	C₂³×C₁₉	1	1	yes	characteristic
325	#107	C₂³×C₁₉	1	1	yes	characteristic
326	#107	C₂³×C₁₉	1	1	yes	characteristic
327	#106	—	2	1	no	—
328	#106	—	2	1	no	—
329	#106	—	2	1	no	—
330	#106	—	2	1	no	—
331	#102	—	2	1	no	—
332	#102	—	2	1	no	—
333	#102	—	2	1	no	—
334	#102	—	2	1	no	—
335	#97	D₄×C₁₉	1	1	yes	characteristic
336	#97	D₄×C₁₉	1	1	yes	characteristic
337	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
338	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
339	C₁₉	#33807	1	1	yes	characteristic, direct product factor, Sylow
340	C₂×Q₈	—	4	1	no	—
341	C₂×Q₈	—	4	1	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	4	1	no	—
345	C₂×D₄	—	4	1	no	—
346	C₂×D₄	—	4	1	no	—
347	C₂×D₄	—	4	1	no	—
348	C₂²×C₄	—	4	1	no	—
349	C₂²×C₄	—	4	1	no	—
350	C₂²×C₄	—	4	1	no	—
351	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
352	D₈	—	2	1	no	—
353	D₈	—	2	1	no	—
354	D₈	—	2	1	no	—
355	D₈	—	2	1	no	—
356	D₈	—	4	2	no	—
357	M₁₆	—	2	2	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
361	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
362	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
363	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	4	1	no	—
371	C₄⋊C₄	—	4	1	no	—
372	C₄⋊C₄	—	4	1	no	—
373	C₄⋊C₄	—	4	1	no	—
374	C₄⋊C₄	—	4	1	no	—
375	C₄⋊C₄	—	4	1	no	—
376	C₄⋊C₄	—	4	1	no	—
377	C₄⋊C₄	—	4	1	no	—
378	C₄⋊C₄	—	4	1	no	—
379	C₄⋊C₄	D₈×C₁₉	1	1	yes	characteristic
380	C₄⋊C₄	D₈×C₁₉	1	1	yes	characteristic
381	C₂²⋊C₄	—	4	1	no	—
382	C₂²⋊C₄	—	4	1	no	—
383	C₂²⋊C₄	—	4	1	no	—
384	C₂²⋊C₄	—	4	1	no	—
385	C₂²⋊C₄	—	4	1	no	—
386	C₂²⋊C₄	D₈×C₁₉	1	1	yes	characteristic
387	C₂²⋊C₄	D₈×C₁₉	1	1	yes	characteristic
388	C₄²	—	4	1	no	—
389	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
390	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
391	C₁₆	—	2	1	no	—
392	C₁₆	—	2	1	no	—
393	C₁₆	—	2	1	no	—
394	C₁₆	—	2	1	no	—
395	C₂³	—	4	1	no	—
396	C₂³	—	4	1	no	—
397	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
398	Q₈	—	16	1	no	—
399	Q₈	—	16	1	no	—
400	D₄	—	4	1	no	—
401	D₄	—	4	1	no	—
402	D₄	—	4	1	no	—
403	D₄	—	4	1	no	—
404	D₄	—	16	1	no	—
405	D₄	—	16	1	no	—
406	D₄	—	16	1	no	—
407	D₄	—	16	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	16	1	no	—
417	C₂×C₄	—	16	1	no	—
418	C₂×C₄	—	16	1	no	—
419	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
420	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
421	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
422	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
423	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
424	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
425	C₈	—	2	1	no	—
426	C₈	—	2	1	no	—
427	C₈	C₁₉×#137	1	2	yes	—
428	C₈	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
429	C₈	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
430	C₂²	—	2	1	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	8	1	no	—
434	C₂²	—	8	1	no	—
435	C₂²	—	8	1	no	—
436	C₂²	—	8	1	no	—
437	C₂²	—	8	1	no	—
438	C₂²	—	8	1	no	—
439	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	2	1	no	—
445	C₄	—	8	1	no	—
446	C₄	—	8	1	no	—
447	C₄	—	8	1	no	—
448	C₄	—	8	1	no	—
449	C₄	—	8	1	no	—
450	C₄	—	8	1	no	—
451	C₄	C₁₉×#536	1	1	yes	characteristic
452	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
453	C₂	—	4	1	no	—
454	C₂	—	16	1	no	—
455	C₂	—	16	1	no	—
456	C₂	C₁₉×#3226	1	1	yes	characteristic
457	C₂	C₁₉×#3415	1	1	yes	characteristic
458	C₂	C₁₉×#3416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₉
prime radical	C₁₉×#3176	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#117 ◁ C₁₉×#405 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3164	C₂	semidirect
3. C₁₉×#2255	C₂	semidirect
4. C₁₉×#2253	C₂	semidirect
5. C₁₉×#2244	C₂	semidirect
6. C₁₉×#2240	C₂	semidirect
7. C₁₉×#2234	C₂	semidirect
8. C₁₉×#2234	C₂	semidirect
9. C₁₉×#2233	C₂	semidirect
10. C₁₉×#2232	C₂	semidirect
11. C₁₉×#2228	C₂	semidirect
12. C₁₉×#2228	C₂	semidirect
13. C₁₉×#2226	C₂	semidirect
14. C₁₉×#2224	C₂	semidirect
15. C₁₉×#2164	C₂	semidirect
165. #33807	C₁₉	direct (N × H)
202. #3164	C₂×C₁₉	semidirect
203. #2255	C₂×C₁₉	semidirect
204. #2253	C₂×C₁₉	semidirect
205. #2244	C₂×C₁₉	semidirect
206. #2240	C₂×C₁₉	semidirect
207. #2234	C₂×C₁₉	semidirect
208. #2234	C₂×C₁₉	semidirect
209. #2233	C₂×C₁₉	semidirect
210. #2232	C₂×C₁₉	semidirect
211. #2228	C₂×C₁₉	semidirect
212. #2228	C₂×C₁₉	semidirect
213. #2226	C₂×C₁₉	semidirect
214. #2224	C₂×C₁₉	semidirect
215. #2164	C₂×C₁₉	semidirect
339. C₁₉	#33807	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×#3176	2
C₁₉×#3164	2
C₁₉×#2255	2
C₁₉×#2253	2
C₁₉×#2244	2
C₁₉×#2240	2
C₁₉×#2234	2
C₁₉×#2233	2
C₁₉×#2232	2
C₁₉×#2228	2
C₁₉×#2226	2
C₁₉×#2224	2
C₁₉×#2164	2
#33807	19

Subgroups — C19×#33807 #18039766

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33807 #18039766