Subgroups — C₁₉×#33809 #18039768

Order 4864.

454 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3175	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×#2252	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2243	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2242	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2237	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2236	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2234	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#2232	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#2229	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#2228	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#2227	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×#542	—	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×#500	C₂²	1	1	yes	characteristic
23	C₁₉×#499	C₂²	1	1	yes	characteristic
24	C₁₉×#499	C₂²	1	1	yes	characteristic
25	C₁₉×#495	C₂²	1	1	yes	characteristic
26	C₁₉×#489	—	2	1	no	—
27	C₁₉×#468	—	2	1	no	—
28	C₁₉×#467	C₂²	1	1	yes	characteristic
29	C₁₉×#466	C₂²	1	1	yes	characteristic
30	C₁₉×#440	—	2	1	no	—
31	C₄×Q₁₆×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×#366	C₂²	1	1	yes	characteristic
40	C₁₉×#366	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×#358	C₂²	1	1	yes	characteristic
48	C₁₉×#358	C₂²	1	1	yes	characteristic
49	C₁₉×#358	C₂²	1	1	yes	characteristic
50	C₁₉×#358	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×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
60	C₂×SD₁₆×C₁₉	—	2	1	no	—
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	—	2	1	no	—
67	C₁₉×C₄⋊Q₈	—	4	1	no	—
68	C₁₉×#126	—	4	1	no	—
69	C₁₉×#125	—	2	1	no	—
70	C₁₉×#125	—	2	1	no	—
71	C₁₉×#125	—	4	1	no	—
72	C₁₉×#124	—	2	1	no	—
73	C₁₉×#124	—	4	1	no	—
74	C₁₉×#123	—	4	1	no	—
75	C₁₉×C₂²⋊Q₈	—	2	1	no	—
76	C₁₉×C₂²⋊Q₈	—	4	1	no	—
77	C₁₉×C₂²⋊Q₈	—	4	1	no	—
78	C₁₉×C₂²⋊Q₈	—	4	1	no	—
79	C₁₉×#121	—	2	1	no	—
80	C₄×Q₈×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	—	2	1	no	—
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×#107	C₂³	1	1	yes	characteristic
99	C₁₉×#106	—	2	1	no	—
100	C₁₉×#106	—	2	1	no	—
101	C₁₉×#106	—	2	1	no	—
102	C₁₉×#103	—	2	1	no	—
103	C₁₉×#103	—	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	—	2	1	no	—
111	C₂×Q₈×C₁₉	—	4	1	no	—
112	C₂×Q₈×C₁₉	—	4	1	no	—
113	C₂×Q₈×C₁₉	—	4	1	no	—
114	C₂×D₄×C₁₉	—	2	1	no	—
115	C₂×D₄×C₁₉	—	4	1	no	—
116	C₂²×C₄×C₁₉	—	4	1	no	—
117	C₂²×C₄×C₁₉	—	4	1	no	—
118	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
119	Q₁₆×C₁₉	—	2	1	no	—
120	Q₁₆×C₁₉	—	2	1	no	—
121	SD₁₆×C₁₉	—	4	2	no	—
122	D₈×C₁₉	—	2	1	no	—
123	D₈×C₁₉	—	2	1	no	—
124	M₁₆×C₁₉	—	2	2	no	—
125	C₂×C₈×C₁₉	—	2	1	no	—
126	C₂×C₈×C₁₉	—	2	1	no	—
127	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
131	C₄⋊C₄×C₁₉	—	2	1	no	—
132	C₄⋊C₄×C₁₉	—	2	1	no	—
133	C₄⋊C₄×C₁₉	—	2	1	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	—	4	1	no	—
138	C₄⋊C₄×C₁₉	—	4	1	no	—
139	C₄⋊C₄×C₁₉	—	4	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	D₈	1	1	yes	characteristic
148	C₄⋊C₄×C₁₉	D₈	1	1	yes	characteristic
149	C₂²⋊C₄×C₁₉	—	4	1	no	—
150	C₂²⋊C₄×C₁₉	—	4	1	no	—
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	D₈	1	1	yes	characteristic
156	C₂²⋊C₄×C₁₉	D₈	1	1	yes	characteristic
157	C₄²×C₁₉	—	4	1	no	—
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	#33809	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂³×C₁₉	—	4	1	no	—
167	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
168	Q₈×C₁₉	—	4	1	no	—
169	Q₈×C₁₉	—	4	1	no	—
170	Q₈×C₁₉	—	16	1	no	—
171	Q₈×C₁₉	—	16	1	no	—
172	Q₈×C₁₉	—	16	1	no	—
173	D₄×C₁₉	—	4	1	no	—
174	D₄×C₁₉	—	4	1	no	—
175	D₄×C₁₉	—	16	1	no	—
176	C₂×C₄×C₁₉	—	2	1	no	—
177	C₂×C₄×C₁₉	—	2	1	no	—
178	C₂×C₄×C₁₉	—	4	1	no	—
179	C₂×C₄×C₁₉	—	4	1	no	—
180	C₂×C₄×C₁₉	—	4	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	—	16	1	no	—
186	C₂×C₄×C₁₉	—	16	1	no	—
187	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
188	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
189	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
190	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
191	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
193	C₈×C₁₉	—	2	1	no	—
194	C₈×C₁₉	—	2	1	no	—
195	C₈×C₁₉	#137	1	2	yes	—
196	C₈×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
197	C₈×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
198	#3175	C₂×C₁₉	1	1	yes	characteristic
199	#3164	C₂×C₁₉	1	1	yes	characteristic, complemented
200	#2255	C₂×C₁₉	1	1	yes	characteristic, complemented
201	#2252	C₂×C₁₉	1	1	yes	characteristic, complemented
202	#2243	C₂×C₁₉	1	1	yes	characteristic, complemented
203	#2242	C₂×C₁₉	1	1	yes	characteristic, complemented
204	#2237	C₂×C₁₉	1	1	yes	characteristic, complemented
205	#2236	C₂×C₁₉	1	1	yes	characteristic, complemented
206	#2234	C₂×C₁₉	1	1	yes	characteristic
207	#2232	C₂×C₁₉	1	1	yes	characteristic
208	#2229	C₂×C₁₉	1	1	yes	characteristic, complemented
209	#2228	C₂×C₁₉	1	1	yes	characteristic, complemented
210	#2227	C₂×C₁₉	1	1	yes	characteristic, complemented
211	#2224	C₂×C₁₉	1	1	yes	characteristic, complemented
212	#2164	C₂×C₁₉	1	1	yes	characteristic, complemented
213	C₂²×C₁₉	—	2	1	no	—
214	C₂²×C₁₉	—	2	1	no	—
215	C₂²×C₁₉	—	2	1	no	—
216	C₂²×C₁₉	—	8	1	no	—
217	C₂²×C₁₉	—	8	1	no	—
218	C₂²×C₁₉	—	8	1	no	—
219	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
220	C₄×C₁₉	—	2	1	no	—
221	C₄×C₁₉	—	2	1	no	—
222	C₄×C₁₉	—	2	1	no	—
223	C₄×C₁₉	—	2	1	no	—
224	C₄×C₁₉	—	2	1	no	—
225	C₄×C₁₉	—	8	1	no	—
226	C₄×C₁₉	—	8	1	no	—
227	C₄×C₁₉	—	8	1	no	—
228	C₄×C₁₉	—	8	1	no	—
229	C₄×C₁₉	—	8	1	no	—
230	C₄×C₁₉	—	8	1	no	—
231	C₄×C₁₉	—	8	1	no	—
232	C₄×C₁₉	#536	1	1	yes	characteristic
233	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
234	#544	—	2	1	no	—
235	#542	—	2	1	no	—
236	#501	—	2	1	no	—
237	#501	—	2	1	no	—
238	#500	C₂²×C₁₉	1	1	yes	characteristic
239	#500	C₂²×C₁₉	1	1	yes	characteristic
240	#500	C₂²×C₁₉	1	1	yes	characteristic
241	#499	C₂²×C₁₉	1	1	yes	characteristic
242	#499	C₂²×C₁₉	1	1	yes	characteristic
243	#495	C₂²×C₁₉	1	1	yes	characteristic
244	#489	—	2	1	no	—
245	#468	—	2	1	no	—
246	#467	C₂²×C₁₉	1	1	yes	characteristic
247	#466	C₂²×C₁₉	1	1	yes	characteristic
248	#440	—	2	1	no	—
249	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
250	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
251	#428	—	2	1	no	—
252	#427	C₂²×C₁₉	1	1	yes	characteristic
253	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
254	#405	C₂²×C₁₉	1	1	yes	characteristic
255	#367	C₂²×C₁₉	1	1	yes	characteristic
256	#367	C₂²×C₁₉	1	1	yes	characteristic
257	#366	C₂²×C₁₉	1	1	yes	characteristic
258	#366	C₂²×C₁₉	1	1	yes	characteristic
259	#366	C₂²×C₁₉	1	1	yes	characteristic
260	#366	C₂²×C₁₉	1	1	yes	characteristic
261	#366	C₂²×C₁₉	1	1	yes	characteristic
262	#366	C₂²×C₁₉	1	1	yes	characteristic
263	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
264	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
265	#358	C₂²×C₁₉	1	1	yes	characteristic
266	#358	C₂²×C₁₉	1	1	yes	characteristic
267	#358	C₂²×C₁₉	1	1	yes	characteristic
268	#358	C₂²×C₁₉	1	1	yes	characteristic
269	#357	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	C₂²⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
274	C₂²⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
275	#346	C₂²×C₁₉	1	1	yes	characteristic
276	C₄×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
277	C₂×C₁₉	—	4	1	no	—
278	C₂×C₁₉	—	16	1	no	—
279	C₂×C₁₉	#3226	1	1	yes	characteristic
280	C₂×C₁₉	#3415	1	1	yes	characteristic
281	C₂×C₁₉	#3417	1	1	yes	characteristic
282	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
283	C₂×SD₁₆	—	2	1	no	—
284	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
285	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
286	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
287	C₄⋊Q₈	—	2	1	no	—
288	C₄⋊Q₈	—	2	1	no	—
289	C₄⋊Q₈	—	2	1	no	—
290	C₄⋊Q₈	—	4	1	no	—
291	#126	—	4	1	no	—
292	#125	—	2	1	no	—
293	#125	—	2	1	no	—
294	#125	—	4	1	no	—
295	#124	—	2	1	no	—
296	#124	—	4	1	no	—
297	#123	—	4	1	no	—
298	C₂²⋊Q₈	—	2	1	no	—
299	C₂²⋊Q₈	—	4	1	no	—
300	C₂²⋊Q₈	—	4	1	no	—
301	C₂²⋊Q₈	—	4	1	no	—
302	#121	—	2	1	no	—
303	C₄×Q₈	—	2	1	no	—
304	C₄×D₄	—	2	1	no	—
305	#117	—	2	1	no	—
306	#117	D₄×C₁₉	1	1	yes	characteristic
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
309	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
310	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
311	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
312	#107	—	2	1	no	—
313	#107	—	2	1	no	—
314	#107	—	2	1	no	—
315	#107	—	2	1	no	—
316	#107	C₂³×C₁₉	1	1	yes	characteristic
317	#107	C₂³×C₁₉	1	1	yes	characteristic
318	#107	C₂³×C₁₉	1	1	yes	characteristic
319	#107	C₂³×C₁₉	1	1	yes	characteristic
320	#107	C₂³×C₁₉	1	1	yes	characteristic
321	#107	C₂³×C₁₉	1	1	yes	characteristic
322	#106	—	2	1	no	—
323	#106	—	2	1	no	—
324	#106	—	2	1	no	—
325	#103	—	2	1	no	—
326	#103	—	2	1	no	—
327	#102	—	2	1	no	—
328	#102	—	2	1	no	—
329	#97	D₄×C₁₉	1	1	yes	characteristic
330	#97	D₄×C₁₉	1	1	yes	characteristic
331	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
332	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
333	C₁₉	#33809	1	1	yes	characteristic, direct product factor, Sylow
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	4	1	no	—
336	C₂×Q₈	—	4	1	no	—
337	C₂×Q₈	—	4	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	4	1	no	—
340	C₂²×C₄	—	4	1	no	—
341	C₂²×C₄	—	4	1	no	—
342	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
343	Q₁₆	—	2	1	no	—
344	Q₁₆	—	2	1	no	—
345	SD₁₆	—	4	2	no	—
346	D₈	—	2	1	no	—
347	D₈	—	2	1	no	—
348	M₁₆	—	2	2	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
352	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
353	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
354	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	4	1	no	—
362	C₄⋊C₄	—	4	1	no	—
363	C₄⋊C₄	—	4	1	no	—
364	C₄⋊C₄	—	4	1	no	—
365	C₄⋊C₄	—	4	1	no	—
366	C₄⋊C₄	—	4	1	no	—
367	C₄⋊C₄	—	4	1	no	—
368	C₄⋊C₄	—	4	1	no	—
369	C₄⋊C₄	—	4	1	no	—
370	C₄⋊C₄	—	4	1	no	—
371	C₄⋊C₄	D₈×C₁₉	1	1	yes	characteristic
372	C₄⋊C₄	D₈×C₁₉	1	1	yes	characteristic
373	C₂²⋊C₄	—	4	1	no	—
374	C₂²⋊C₄	—	4	1	no	—
375	C₂²⋊C₄	—	4	1	no	—
376	C₂²⋊C₄	—	4	1	no	—
377	C₂²⋊C₄	—	4	1	no	—
378	C₂²⋊C₄	—	4	1	no	—
379	C₂²⋊C₄	D₈×C₁₉	1	1	yes	characteristic
380	C₂²⋊C₄	D₈×C₁₉	1	1	yes	characteristic
381	C₄²	—	4	1	no	—
382	C₄²	—	4	1	no	—
383	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
384	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
385	C₁₆	—	2	1	no	—
386	C₁₆	—	2	1	no	—
387	C₁₆	—	2	1	no	—
388	C₁₆	—	2	1	no	—
389	C₂³	—	4	1	no	—
390	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
391	Q₈	—	4	1	no	—
392	Q₈	—	4	1	no	—
393	Q₈	—	16	1	no	—
394	Q₈	—	16	1	no	—
395	Q₈	—	16	1	no	—
396	D₄	—	4	1	no	—
397	D₄	—	4	1	no	—
398	D₄	—	16	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	16	1	no	—
409	C₂×C₄	—	16	1	no	—
410	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
411	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
412	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
413	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
414	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
415	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
416	C₈	—	2	1	no	—
417	C₈	—	2	1	no	—
418	C₈	C₁₉×#137	1	2	yes	—
419	C₈	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
420	C₈	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	8	1	no	—
425	C₂²	—	8	1	no	—
426	C₂²	—	8	1	no	—
427	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	8	1	no	—
434	C₄	—	8	1	no	—
435	C₄	—	8	1	no	—
436	C₄	—	8	1	no	—
437	C₄	—	8	1	no	—
438	C₄	—	8	1	no	—
439	C₄	—	8	1	no	—
440	C₄	C₁₉×#536	1	1	yes	characteristic
441	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
442	C₂	—	4	1	no	—
443	C₂	—	16	1	no	—
444	C₂	C₁₉×#3226	1	1	yes	characteristic
445	C₂	C₁₉×#3415	1	1	yes	characteristic
446	C₂	C₁₉×#3417	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₉
prime radical	C₁₉×#466	C₂²
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×#2252	C₂	semidirect
5. C₁₉×#2243	C₂	semidirect
6. C₁₉×#2242	C₂	semidirect
7. C₁₉×#2237	C₂	semidirect
8. C₁₉×#2236	C₂	semidirect
11. C₁₉×#2229	C₂	semidirect
12. C₁₉×#2228	C₂	semidirect
13. C₁₉×#2227	C₂	semidirect
14. C₁₉×#2224	C₂	semidirect
15. C₁₉×#2164	C₂	semidirect
165. #33809	C₁₉	direct (N × H)
199. #3164	C₂×C₁₉	semidirect
200. #2255	C₂×C₁₉	semidirect
201. #2252	C₂×C₁₉	semidirect
202. #2243	C₂×C₁₉	semidirect
203. #2242	C₂×C₁₉	semidirect
204. #2237	C₂×C₁₉	semidirect
205. #2236	C₂×C₁₉	semidirect
208. #2229	C₂×C₁₉	semidirect
209. #2228	C₂×C₁₉	semidirect
210. #2227	C₂×C₁₉	semidirect
211. #2224	C₂×C₁₉	semidirect
212. #2164	C₂×C₁₉	semidirect
333. C₁₉	#33809	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×#3175	2
C₁₉×#3164	2
C₁₉×#2255	2
C₁₉×#2252	2
C₁₉×#2243	2
C₁₉×#2242	2
C₁₉×#2237	2
C₁₉×#2236	2
C₁₉×#2234	2
C₁₉×#2232	2
C₁₉×#2229	2
C₁₉×#2228	2
C₁₉×#2227	2
C₁₉×#2224	2
C₁₉×#2164	2
#33809	19

Subgroups — C19×#33809 #18039768

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33809 #18039768