Subgroups — C₁₉×#33938 #18039897

Order 4864.

480 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3396	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3383	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2244	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2243	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2242	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2229	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2228	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2226	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2211	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2211	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#2207	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#2183	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#2176	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#2175	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₉×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#559	—	2	1	no	—
17	C₁₉×#557	—	2	1	no	—
18	C₂×C₁₉×Q₃₂	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×SD₃₂	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×SD₃₂	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×#495	C₂²	1	1	yes	characteristic
25	C₁₉×#495	C₂²	1	1	yes	characteristic
26	C₁₉×#493	C₂²	1	1	yes	characteristic
27	C₁₉×#479	—	2	1	no	—
28	C₁₉×#479	—	2	1	no	—
29	C₁₉×#475	—	2	1	no	—
30	C₁₉×#463	—	2	1	no	—
31	C₁₉×#463	—	2	1	no	—
32	C₁₉×#460	—	2	1	no	—
33	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
34	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
35	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
36	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
37	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
38	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
39	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
40	C₁₉×#367	C₂²	1	1	yes	characteristic
41	C₁₉×#367	C₂²	1	1	yes	characteristic
42	C₁₉×#366	C₂²	1	1	yes	characteristic
43	C₁₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
44	C₁₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
45	C₁₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
46	C₁₉×#358	C₂²	1	1	yes	characteristic
47	C₁₉×#358	C₂²	1	1	yes	characteristic
48	C₁₉×#358	C₂²	1	1	yes	characteristic
49	C₁₉×#358	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×#357	C₂²	1	1	yes	characteristic
56	C₁₉×#346	C₂²	1	1	yes	characteristic
57	C₁₉×#346	C₂²	1	1	yes	characteristic
58	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
59	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
60	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
61	C₂×SD₁₆×C₁₉	—	2	1	no	—
62	C₂×SD₁₆×C₁₉	—	2	1	no	—
63	C₂×D₈×C₁₉	—	2	1	no	—
64	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
66	C₁₉×C₄⋊Q₈	—	2	1	no	—
67	C₁₉×C₄⋊Q₈	—	4	1	no	—
68	C₁₉×#127	—	2	1	no	—
69	C₁₉×#125	—	2	1	no	—
70	C₁₉×#125	—	2	1	no	—
71	C₁₉×#125	—	4	1	no	—
72	C₁₉×#125	—	4	1	no	—
73	C₁₉×#124	—	2	1	no	—
74	C₁₉×#124	—	2	1	no	—
75	C₁₉×#124	—	4	1	no	—
76	C₁₉×#123	—	4	1	no	—
77	C₁₉×#123	—	4	1	no	—
78	C₄×Q₈×C₁₉	—	2	1	no	—
79	C₄×Q₈×C₁₉	—	2	1	no	—
80	C₄×Q₈×C₁₉	—	2	1	no	—
81	C₄×Q₈×C₁₉	—	2	1	no	—
82	C₄×Q₈×C₁₉	—	4	1	no	—
83	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
84	C₄×D₄×C₁₉	—	2	1	no	—
85	C₄×D₄×C₁₉	—	2	1	no	—
86	C₄×D₄×C₁₉	—	4	1	no	—
87	C₁₉×Q₃₂	—	2	2	no	—
88	C₁₉×SD₃₂	—	2	2	no	—
89	C₁₉×SD₃₂	—	2	2	no	—
90	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
91	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
92	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
93	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
94	C₁₉×#107	—	2	1	no	—
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×#107	C₂³	1	1	yes	characteristic
99	C₁₉×#106	—	2	1	no	—
100	C₁₉×#106	—	2	1	no	—
101	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
102	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
103	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
104	C₁₉×#103	—	2	1	no	—
105	C₁₉×#103	—	2	1	no	—
106	C₁₉×#103	—	2	1	no	—
107	C₁₉×#103	—	2	1	no	—
108	C₁₉×#102	—	2	1	no	—
109	C₁₉×#102	—	2	1	no	—
110	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
111	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
112	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
113	C₂×Q₈×C₁₉	—	2	1	no	—
114	C₂×Q₈×C₁₉	—	2	1	no	—
115	C₂×Q₈×C₁₉	—	4	1	no	—
116	C₂×Q₈×C₁₉	D₈	1	1	yes	characteristic
117	C₂×D₄×C₁₉	—	2	1	no	—
118	C₂×D₄×C₁₉	—	2	1	no	—
119	C₂×D₄×C₁₉	—	4	1	no	—
120	C₂×D₄×C₁₉	—	4	1	no	—
121	C₂²×C₄×C₁₉	—	4	1	no	—
122	C₂²×C₄×C₁₉	—	4	1	no	—
123	Q₁₆×C₁₉	—	2	1	no	—
124	Q₁₆×C₁₉	—	2	1	no	—
125	Q₁₆×C₁₉	—	2	1	no	—
126	Q₁₆×C₁₉	#41	1	2	yes	—
127	SD₁₆×C₁₉	—	8	1	no	—
128	SD₁₆×C₁₉	—	8	1	no	—
129	D₈×C₁₉	—	2	1	no	—
130	D₈×C₁₉	—	2	1	no	—
131	D₈×C₁₉	—	2	1	no	—
132	D₈×C₁₉	—	2	1	no	—
133	D₈×C₁₉	—	8	1	no	—
134	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
138	C₄⋊C₄×C₁₉	—	2	1	no	—
139	C₄⋊C₄×C₁₉	—	2	1	no	—
140	C₄⋊C₄×C₁₉	—	2	1	no	—
141	C₄⋊C₄×C₁₉	—	2	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	—	4	1	no	—
150	C₄⋊C₄×C₁₉	—	4	1	no	—
151	C₄⋊C₄×C₁₉	D₈	1	1	yes	characteristic
152	C₄⋊C₄×C₁₉	D₈	1	1	yes	characteristic
153	C₄⋊C₄×C₁₉	D₈	1	1	yes	characteristic
154	C₂²⋊C₄×C₁₉	—	4	1	no	—
155	C₂²⋊C₄×C₁₉	—	4	1	no	—
156	C₂²⋊C₄×C₁₉	—	4	1	no	—
157	C₂²⋊C₄×C₁₉	—	4	1	no	—
158	C₂²⋊C₄×C₁₉	—	4	1	no	—
159	C₂²⋊C₄×C₁₉	—	4	1	no	—
160	C₄²×C₁₉	—	4	1	no	—
161	C₄²×C₁₉	—	4	1	no	—
162	C₄²×C₁₉	—	4	1	no	—
163	C₄²×C₁₉	—	4	1	no	—
164	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₁₆×C₁₉	—	2	1	no	—
168	C₁₆×C₁₉	—	2	1	no	—
169	C₁₆×C₁₉	—	2	1	no	—
170	C₁₆×C₁₉	—	2	1	no	—
171	#33938	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂³×C₁₉	—	4	1	no	—
173	C₂³×C₁₉	—	4	1	no	—
174	Q₈×C₁₉	—	2	2	no	—
175	Q₈×C₁₉	—	4	1	no	—
176	Q₈×C₁₉	—	4	1	no	—
177	Q₈×C₁₉	—	4	1	no	—
178	Q₈×C₁₉	—	4	1	no	—
179	Q₈×C₁₉	—	8	2	no	—
180	D₄×C₁₉	—	4	1	no	—
181	D₄×C₁₉	—	4	1	no	—
182	D₄×C₁₉	—	4	1	no	—
183	D₄×C₁₉	—	4	1	no	—
184	D₄×C₁₉	—	8	2	no	—
185	D₄×C₁₉	—	16	1	no	—
186	C₂×C₄×C₁₉	—	4	1	no	—
187	C₂×C₄×C₁₉	—	4	1	no	—
188	C₂×C₄×C₁₉	—	4	1	no	—
189	C₂×C₄×C₁₉	—	4	1	no	—
190	C₂×C₄×C₁₉	—	4	1	no	—
191	C₂×C₄×C₁₉	—	4	1	no	—
192	C₂×C₄×C₁₉	—	16	1	no	—
193	C₂×C₄×C₁₉	—	16	1	no	—
194	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
197	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
198	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
199	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
201	C₈×C₁₉	—	2	1	no	—
202	C₈×C₁₉	—	2	1	no	—
203	C₈×C₁₉	—	2	1	no	—
204	C₈×C₁₉	C₂×#41	1	1	yes	characteristic
205	C₈×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
206	#3396	C₂×C₁₉	1	1	yes	characteristic
207	#3383	C₂×C₁₉	1	1	yes	characteristic, complemented
208	#2244	C₂×C₁₉	1	1	yes	characteristic
209	#2243	C₂×C₁₉	1	1	yes	characteristic, complemented
210	#2242	C₂×C₁₉	1	1	yes	characteristic, complemented
211	#2229	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	#2211	C₂×C₁₉	1	1	yes	characteristic, complemented
215	#2211	C₂×C₁₉	1	1	yes	characteristic, complemented
216	#2207	C₂×C₁₉	1	1	yes	characteristic
217	#2183	C₂×C₁₉	1	1	yes	characteristic, complemented
218	#2176	C₂×C₁₉	1	1	yes	characteristic, complemented
219	#2175	C₂×C₁₉	1	1	yes	characteristic, complemented
220	C₄×SD₃₂	C₂×C₁₉	1	1	yes	characteristic, complemented
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	—	8	1	no	—
226	C₂²×C₁₉	—	8	1	no	—
227	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
228	C₄×C₁₉	—	2	1	no	—
229	C₄×C₁₉	—	2	1	no	—
230	C₄×C₁₉	—	2	1	no	—
231	C₄×C₁₉	—	2	1	no	—
232	C₄×C₁₉	—	2	1	no	—
233	C₄×C₁₉	—	2	1	no	—
234	C₄×C₁₉	—	4	2	no	—
235	C₄×C₁₉	—	8	1	no	—
236	C₄×C₁₉	—	8	1	no	—
237	C₄×C₁₉	—	8	1	no	—
238	C₄×C₁₉	—	8	1	no	—
239	C₄×C₁₉	—	8	1	no	—
240	C₄×C₁₉	#548	1	1	yes	characteristic
241	C₄×C₁₉	#577	1	1	yes	characteristic
242	#559	—	2	1	no	—
243	#557	—	2	1	no	—
244	C₂×Q₃₂	C₂²×C₁₉	1	1	yes	characteristic
245	C₂×SD₃₂	C₂²×C₁₉	1	1	yes	characteristic
246	C₂×SD₃₂	C₂²×C₁₉	1	1	yes	characteristic
247	#500	C₂²×C₁₉	1	1	yes	characteristic
248	#499	C₂²×C₁₉	1	1	yes	characteristic
249	#499	C₂²×C₁₉	1	1	yes	characteristic
250	#495	C₂²×C₁₉	1	1	yes	characteristic
251	#495	C₂²×C₁₉	1	1	yes	characteristic
252	#493	C₂²×C₁₉	1	1	yes	characteristic
253	#479	—	2	1	no	—
254	#479	—	2	1	no	—
255	#475	—	2	1	no	—
256	#463	—	2	1	no	—
257	#463	—	2	1	no	—
258	#460	—	2	1	no	—
259	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
260	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
261	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
262	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
263	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
264	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
265	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
266	#367	C₂²×C₁₉	1	1	yes	characteristic
267	#367	C₂²×C₁₉	1	1	yes	characteristic
268	#366	C₂²×C₁₉	1	1	yes	characteristic
269	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
270	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
271	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
272	#358	C₂²×C₁₉	1	1	yes	characteristic
273	#358	C₂²×C₁₉	1	1	yes	characteristic
274	#358	C₂²×C₁₉	1	1	yes	characteristic
275	#358	C₂²×C₁₉	1	1	yes	characteristic
276	#357	C₂²×C₁₉	1	1	yes	characteristic
277	#357	C₂²×C₁₉	1	1	yes	characteristic
278	#357	C₂²×C₁₉	1	1	yes	characteristic
279	#357	C₂²×C₁₉	1	1	yes	characteristic
280	#357	C₂²×C₁₉	1	1	yes	characteristic
281	#357	C₂²×C₁₉	1	1	yes	characteristic
282	#346	C₂²×C₁₉	1	1	yes	characteristic
283	#346	C₂²×C₁₉	1	1	yes	characteristic
284	C₄×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
285	C₂×C₁₉	—	16	1	no	—
286	C₂×C₁₉	—	16	1	no	—
287	C₂×C₁₉	#3358	1	1	yes	characteristic
288	C₂×C₁₉	#3414	1	1	yes	characteristic
289	C₂×C₁₉	#3416	1	1	yes	characteristic
290	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
291	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
292	C₂×SD₁₆	—	2	1	no	—
293	C₂×SD₁₆	—	2	1	no	—
294	C₂×D₈	—	2	1	no	—
295	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
296	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
297	C₄⋊Q₈	—	2	1	no	—
298	C₄⋊Q₈	—	4	1	no	—
299	#127	—	2	1	no	—
300	#125	—	2	1	no	—
301	#125	—	2	1	no	—
302	#125	—	4	1	no	—
303	#125	—	4	1	no	—
304	#124	—	2	1	no	—
305	#124	—	2	1	no	—
306	#124	—	4	1	no	—
307	#123	—	4	1	no	—
308	#123	—	4	1	no	—
309	C₄×Q₈	—	2	1	no	—
310	C₄×Q₈	—	2	1	no	—
311	C₄×Q₈	—	2	1	no	—
312	C₄×Q₈	—	2	1	no	—
313	C₄×Q₈	—	4	1	no	—
314	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	—	2	1	no	—
317	C₄×D₄	—	4	1	no	—
318	Q₃₂	—	2	2	no	—
319	SD₃₂	—	2	2	no	—
320	SD₃₂	—	2	2	no	—
321	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
322	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
323	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
324	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
325	#107	—	2	1	no	—
326	#107	C₂³×C₁₉	1	1	yes	characteristic
327	#107	C₂³×C₁₉	1	1	yes	characteristic
328	#107	C₂³×C₁₉	1	1	yes	characteristic
329	#107	C₂³×C₁₉	1	1	yes	characteristic
330	#106	—	2	1	no	—
331	#106	—	2	1	no	—
332	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
333	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
334	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
335	#103	—	2	1	no	—
336	#103	—	2	1	no	—
337	#103	—	2	1	no	—
338	#103	—	2	1	no	—
339	#102	—	2	1	no	—
340	#102	—	2	1	no	—
341	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
342	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
343	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
344	C₁₉	#33938	1	1	yes	characteristic, direct product factor, Sylow
345	C₂×Q₈	—	2	1	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	4	1	no	—
348	C₂×Q₈	D₈×C₁₉	1	1	yes	characteristic
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	4	1	no	—
352	C₂×D₄	—	4	1	no	—
353	C₂²×C₄	—	4	1	no	—
354	C₂²×C₄	—	4	1	no	—
355	Q₁₆	—	2	1	no	—
356	Q₁₆	—	2	1	no	—
357	Q₁₆	—	2	1	no	—
358	Q₁₆	#41×C₁₉	1	2	yes	—
359	SD₁₆	—	8	1	no	—
360	SD₁₆	—	8	1	no	—
361	D₈	—	2	1	no	—
362	D₈	—	2	1	no	—
363	D₈	—	2	1	no	—
364	D₈	—	2	1	no	—
365	D₈	—	8	1	no	—
366	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
367	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
368	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
369	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	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	—	4	1	no	—
380	C₄⋊C₄	—	4	1	no	—
381	C₄⋊C₄	—	4	1	no	—
382	C₄⋊C₄	—	4	1	no	—
383	C₄⋊C₄	D₈×C₁₉	1	1	yes	characteristic
384	C₄⋊C₄	D₈×C₁₉	1	1	yes	characteristic
385	C₄⋊C₄	D₈×C₁₉	1	1	yes	characteristic
386	C₂²⋊C₄	—	4	1	no	—
387	C₂²⋊C₄	—	4	1	no	—
388	C₂²⋊C₄	—	4	1	no	—
389	C₂²⋊C₄	—	4	1	no	—
390	C₂²⋊C₄	—	4	1	no	—
391	C₂²⋊C₄	—	4	1	no	—
392	C₄²	—	4	1	no	—
393	C₄²	—	4	1	no	—
394	C₄²	—	4	1	no	—
395	C₄²	—	4	1	no	—
396	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
397	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
398	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
399	C₁₆	—	2	1	no	—
400	C₁₆	—	2	1	no	—
401	C₁₆	—	2	1	no	—
402	C₁₆	—	2	1	no	—
403	C₂³	—	4	1	no	—
404	C₂³	—	4	1	no	—
405	Q₈	—	2	2	no	—
406	Q₈	—	4	1	no	—
407	Q₈	—	4	1	no	—
408	Q₈	—	4	1	no	—
409	Q₈	—	4	1	no	—
410	Q₈	—	8	2	no	—
411	D₄	—	4	1	no	—
412	D₄	—	4	1	no	—
413	D₄	—	4	1	no	—
414	D₄	—	4	1	no	—
415	D₄	—	8	2	no	—
416	D₄	—	16	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	16	1	no	—
424	C₂×C₄	—	16	1	no	—
425	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
426	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
427	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
428	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
429	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
430	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
431	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
432	C₈	—	2	1	no	—
433	C₈	—	2	1	no	—
434	C₈	—	2	1	no	—
435	C₈	C₂×#41×C₁₉	1	1	yes	characteristic
436	C₈	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
437	C₂²	—	8	1	no	—
438	C₂²	—	8	1	no	—
439	C₂²	—	8	1	no	—
440	C₂²	—	8	1	no	—
441	C₂²	—	8	1	no	—
442	C₂²	—	8	1	no	—
443	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
444	C₄	—	2	1	no	—
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	2	1	no	—
450	C₄	—	4	2	no	—
451	C₄	—	8	1	no	—
452	C₄	—	8	1	no	—
453	C₄	—	8	1	no	—
454	C₄	—	8	1	no	—
455	C₄	—	8	1	no	—
456	C₄	C₁₉×#548	1	1	yes	characteristic
457	C₄	C₁₉×#577	1	1	yes	characteristic
458	C₂	—	16	1	no	—
459	C₂	—	16	1	no	—
460	C₂	C₁₉×#3358	1	1	yes	characteristic
461	C₂	C₁₉×#3414	1	1	yes	characteristic
462	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×#493	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄×Q₈×C₁₉ ◁ C₈×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3383	C₂	semidirect
4. C₁₉×#2243	C₂	semidirect
5. C₁₉×#2242	C₂	semidirect
6. C₁₉×#2229	C₂	semidirect
7. C₁₉×#2228	C₂	semidirect
8. C₁₉×#2226	C₂	semidirect
9. C₁₉×#2211	C₂	semidirect
10. C₁₉×#2211	C₂	semidirect
12. C₁₉×#2183	C₂	semidirect
13. C₁₉×#2176	C₂	semidirect
14. C₁₉×#2175	C₂	semidirect
15. C₄×C₁₉×SD₃₂	C₂	semidirect
171. #33938	C₁₉	direct (N × H)
207. #3383	C₂×C₁₉	semidirect
209. #2243	C₂×C₁₉	semidirect
210. #2242	C₂×C₁₉	semidirect
211. #2229	C₂×C₁₉	semidirect
212. #2228	C₂×C₁₉	semidirect
213. #2226	C₂×C₁₉	semidirect
214. #2211	C₂×C₁₉	semidirect
215. #2211	C₂×C₁₉	semidirect
217. #2183	C₂×C₁₉	semidirect
218. #2176	C₂×C₁₉	semidirect
219. #2175	C₂×C₁₉	semidirect
220. C₄×SD₃₂	C₂×C₁₉	semidirect
344. C₁₉	#33938	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×#3396	2
C₁₉×#3383	2
C₁₉×#2244	2
C₁₉×#2243	2
C₁₉×#2242	2
C₁₉×#2229	2
C₁₉×#2228	2
C₁₉×#2226	2
C₁₉×#2211	2
C₁₉×#2207	2
C₁₉×#2183	2
C₁₉×#2176	2
C₁₉×#2175	2
C₄×C₁₉×SD₃₂	2
#33938	19

Subgroups — C19×#33938 #18039897

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33938 #18039897