Subgroups — C₁₉×#33916 #18039875

Order 4864.

464 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3342	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3336	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2255	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2237	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2237	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2237	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2236	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2229	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2227	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2219	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#2216	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#2176	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#2168	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#2159	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#2158	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#556	—	2	1	no	—
17	C₁₉×#552	—	2	1	no	—
18	C₂×C₁₉×Q₃₂	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
20	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#500	C₂²	1	1	yes	characteristic
22	C₁₉×#499	C₂²	1	1	yes	characteristic
23	C₁₉×#485	—	2	1	no	—
24	C₁₉×#485	—	2	1	no	—
25	C₁₉×#485	—	2	1	no	—
26	C₁₉×#483	—	2	1	no	—
27	C₁₉×#479	—	2	1	no	—
28	C₁₉×#475	—	2	1	no	—
29	C₁₉×#467	C₂²	1	1	yes	characteristic
30	C₁₉×#467	C₂²	1	1	yes	characteristic
31	C₁₉×#467	C₂²	1	1	yes	characteristic
32	C₁₉×#467	C₂²	1	1	yes	characteristic
33	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
34	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
35	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
36	C₁₉×#427	C₂²	1	1	yes	characteristic
37	C₁₉×#427	C₂²	1	1	yes	characteristic
38	C₁₉×#427	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
40	C₁₉×#367	C₂²	1	1	yes	characteristic
41	C₁₉×#367	C₂²	1	1	yes	characteristic
42	C₁₉×#367	C₂²	1	1	yes	characteristic
43	C₁₉×#367	C₂²	1	1	yes	characteristic
44	C₁₉×#366	C₂²	1	1	yes	characteristic
45	C₁₉×#366	C₂²	1	1	yes	characteristic
46	C₁₉×#366	C₂²	1	1	yes	characteristic
47	C₁₉×#366	C₂²	1	1	yes	characteristic
48	C₁₉×#366	C₂²	1	1	yes	characteristic
49	C₁₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
50	C₁₉×#358	C₂²	1	1	yes	characteristic
51	C₁₉×#358	C₂²	1	1	yes	characteristic
52	C₁₉×#358	C₂²	1	1	yes	characteristic
53	C₁₉×#358	C₂²	1	1	yes	characteristic
54	C₁₉×#358	C₂²	1	1	yes	characteristic
55	C₁₉×#358	C₂²	1	1	yes	characteristic
56	C₁₉×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
57	C₁₉×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
58	C₁₉×#346	C₂²	1	1	yes	characteristic
59	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
60	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₁₉×C₄⋊Q₈	—	2	1	no	—
64	C₁₉×#126	—	4	1	no	—
65	C₁₉×#126	—	4	1	no	—
66	C₁₉×#126	—	4	1	no	—
67	C₁₉×#125	—	2	1	no	—
68	C₁₉×#125	—	4	1	no	—
69	C₁₉×#124	—	4	1	no	—
70	C₁₉×#123	—	4	1	no	—
71	C₁₉×C₂²⋊Q₈	—	2	1	no	—
72	C₁₉×C₂²⋊Q₈	—	2	1	no	—
73	C₁₉×C₂²⋊Q₈	—	2	1	no	—
74	C₁₉×C₂²⋊Q₈	—	2	1	no	—
75	C₄×Q₈×C₁₉	—	2	1	no	—
76	C₄×Q₈×C₁₉	—	2	1	no	—
77	C₄×Q₈×C₁₉	—	4	1	no	—
78	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
79	C₁₉×#117	—	2	1	no	—
80	C₁₉×#117	—	2	1	no	—
81	C₁₉×#117	—	2	1	no	—
82	C₁₉×#117	—	4	1	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
84	C₁₉×Q₃₂	—	2	2	no	—
85	C₁₉×M₃₂	—	2	2	no	—
86	C₂×C₁₆×C₁₉	—	2	2	no	—
87	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
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×#106	—	2	1	no	—
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×#103	—	2	1	no	—
109	C₁₉×#103	—	2	1	no	—
110	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
111	C₁₉×C₂²⋊C₈	D₄	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×D₄×C₁₉	D₈	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	—	4	1	no	—
118	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
120	Q₁₆×C₁₉	—	2	1	no	—
121	Q₁₆×C₁₉	—	2	1	no	—
122	Q₁₆×C₁₉	—	2	1	no	—
123	Q₁₆×C₁₉	—	2	1	no	—
124	C₂×C₈×C₁₉	—	2	1	no	—
125	C₂×C₈×C₁₉	—	2	1	no	—
126	C₂×C₈×C₁₉	—	2	1	no	—
127	C₂×C₈×C₁₉	—	2	1	no	—
128	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
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	—	2	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	—	4	1	no	—
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	—	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	—	4	1	no	—
160	C₄²×C₁₉	—	4	1	no	—
161	C₄²×C₁₉	—	4	1	no	—
162	C₄²×C₁₉	—	4	1	no	—
163	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₁₆×C₁₉	—	2	1	no	—
165	C₁₆×C₁₉	—	2	1	no	—
166	C₁₆×C₁₉	—	2	1	no	—
167	C₁₆×C₁₉	#41	1	2	yes	—
168	#33916	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
169	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
170	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
171	Q₈×C₁₉	—	4	1	no	—
172	Q₈×C₁₉	—	4	1	no	—
173	Q₈×C₁₉	—	4	1	no	—
174	Q₈×C₁₉	—	4	1	no	—
175	Q₈×C₁₉	—	8	2	no	—
176	D₄×C₁₉	—	4	1	no	—
177	C₂×C₄×C₁₉	—	2	1	no	—
178	C₂×C₄×C₁₉	—	2	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	—	4	1	no	—
188	C₂×C₄×C₁₉	—	4	1	no	—
189	C₂×C₄×C₁₉	—	8	2	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	C₂²×D₄	1	1	yes	characteristic
195	C₈×C₁₉	—	2	1	no	—
196	C₈×C₁₉	—	2	1	no	—
197	C₈×C₁₉	—	2	1	no	—
198	C₈×C₁₉	C₂×#41	1	1	yes	characteristic
199	C₈×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
200	#3342	C₂×C₁₉	1	1	yes	characteristic
201	#3336	C₂×C₁₉	1	1	yes	characteristic
202	#2255	C₂×C₁₉	1	1	yes	characteristic, complemented
203	#2237	C₂×C₁₉	1	1	yes	characteristic, complemented
204	#2237	C₂×C₁₉	1	1	yes	characteristic, complemented
205	#2237	C₂×C₁₉	1	1	yes	characteristic, complemented
206	#2236	C₂×C₁₉	1	1	yes	characteristic, complemented
207	#2229	C₂×C₁₉	1	1	yes	characteristic, complemented
208	#2227	C₂×C₁₉	1	1	yes	characteristic, complemented
209	#2219	C₂×C₁₉	1	1	yes	characteristic, complemented
210	#2216	C₂×C₁₉	1	1	yes	characteristic, complemented
211	#2176	C₂×C₁₉	1	1	yes	characteristic, complemented
212	#2168	C₂×C₁₉	1	1	yes	characteristic
213	#2159	C₂×C₁₉	1	1	yes	characteristic, complemented
214	#2158	C₂×C₁₉	1	1	yes	characteristic, complemented
215	C₂²×C₁₉	—	2	1	no	—
216	C₂²×C₁₉	—	2	1	no	—
217	C₂²×C₁₉	—	2	1	no	—
218	C₂²×C₁₉	—	2	1	no	—
219	C₂²×C₁₉	—	2	1	no	—
220	C₂²×C₁₉	—	2	1	no	—
221	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
222	C₄×C₁₉	—	2	1	no	—
223	C₄×C₁₉	—	2	1	no	—
224	C₄×C₁₉	—	2	1	no	—
225	C₄×C₁₉	—	2	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	—	8	1	no	—
233	C₄×C₁₉	—	8	1	no	—
234	C₄×C₁₉	#547	1	1	yes	characteristic
235	C₄×C₁₉	#578	1	1	yes	characteristic
236	#556	—	2	1	no	—
237	#552	—	2	1	no	—
238	C₂×Q₃₂	C₂²×C₁₉	1	1	yes	characteristic
239	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic
240	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
241	#500	C₂²×C₁₉	1	1	yes	characteristic
242	#499	C₂²×C₁₉	1	1	yes	characteristic
243	#485	—	2	1	no	—
244	#485	—	2	1	no	—
245	#485	—	2	1	no	—
246	#483	—	2	1	no	—
247	#479	—	2	1	no	—
248	#475	—	2	1	no	—
249	#467	C₂²×C₁₉	1	1	yes	characteristic
250	#467	C₂²×C₁₉	1	1	yes	characteristic
251	#467	C₂²×C₁₉	1	1	yes	characteristic
252	#467	C₂²×C₁₉	1	1	yes	characteristic
253	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
254	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
255	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
256	#427	C₂²×C₁₉	1	1	yes	characteristic
257	#427	C₂²×C₁₉	1	1	yes	characteristic
258	#427	C₂²×C₁₉	1	1	yes	characteristic
259	C₂×#107	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	#366	C₂²×C₁₉	1	1	yes	characteristic
269	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
270	#358	C₂²×C₁₉	1	1	yes	characteristic
271	#358	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	C₂²⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
277	C₂²⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
278	#346	C₂²×C₁₉	1	1	yes	characteristic
279	C₂×C₁₉	—	4	1	no	—
280	C₂×C₁₉	—	4	1	no	—
281	C₂×C₁₉	#3334	1	1	yes	characteristic
282	C₂×C₁₉	#3414	1	1	yes	characteristic
283	C₂×C₁₉	#3417	1	1	yes	characteristic
284	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
285	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
286	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
287	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
288	C₄⋊Q₈	—	2	1	no	—
289	#126	—	4	1	no	—
290	#126	—	4	1	no	—
291	#126	—	4	1	no	—
292	#125	—	2	1	no	—
293	#125	—	4	1	no	—
294	#124	—	4	1	no	—
295	#123	—	4	1	no	—
296	C₂²⋊Q₈	—	2	1	no	—
297	C₂²⋊Q₈	—	2	1	no	—
298	C₂²⋊Q₈	—	2	1	no	—
299	C₂²⋊Q₈	—	2	1	no	—
300	C₄×Q₈	—	2	1	no	—
301	C₄×Q₈	—	2	1	no	—
302	C₄×Q₈	—	4	1	no	—
303	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
304	#117	—	2	1	no	—
305	#117	—	2	1	no	—
306	#117	—	2	1	no	—
307	#117	—	4	1	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	Q₃₂	—	2	2	no	—
310	M₃₂	—	2	2	no	—
311	C₂×C₁₆	—	2	2	no	—
312	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
313	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
314	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
315	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
316	#107	—	2	1	no	—
317	#107	—	2	1	no	—
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	#107	C₂³×C₁₉	1	1	yes	characteristic
323	#107	C₂³×C₁₉	1	1	yes	characteristic
324	#106	—	2	1	no	—
325	#106	—	2	1	no	—
326	#106	—	2	1	no	—
327	#106	—	2	1	no	—
328	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
329	#103	—	2	1	no	—
330	#103	—	2	1	no	—
331	#103	—	2	1	no	—
332	#103	—	2	1	no	—
333	#103	—	2	1	no	—
334	#103	—	2	1	no	—
335	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
336	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
337	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
338	C₁₉	#33916	1	1	yes	characteristic, direct product factor, Sylow
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	4	1	no	—
342	C₂×D₄	D₈×C₁₉	1	1	yes	characteristic
343	C₂²×C₄	—	4	1	no	—
344	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
345	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
346	Q₁₆	—	2	1	no	—
347	Q₁₆	—	2	1	no	—
348	Q₁₆	—	2	1	no	—
349	Q₁₆	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
355	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
356	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
357	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	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	—	4	1	no	—
372	C₄⋊C₄	—	4	1	no	—
373	C₄⋊C₄	—	4	1	no	—
374	C₄⋊C₄	D₈×C₁₉	1	1	yes	characteristic
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	—	4	1	no	—
380	C₂²⋊C₄	—	4	1	no	—
381	C₂²⋊C₄	—	4	1	no	—
382	C₂²⋊C₄	D₈×C₁₉	1	1	yes	characteristic
383	C₂²⋊C₄	D₈×C₁₉	1	1	yes	characteristic
384	C₄²	—	4	1	no	—
385	C₄²	—	4	1	no	—
386	C₄²	—	4	1	no	—
387	C₄²	—	4	1	no	—
388	C₄²	—	4	1	no	—
389	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
390	C₁₆	—	2	1	no	—
391	C₁₆	—	2	1	no	—
392	C₁₆	—	2	1	no	—
393	C₁₆	#41×C₁₉	1	2	yes	—
394	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
395	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
396	Q₈	—	4	1	no	—
397	Q₈	—	4	1	no	—
398	Q₈	—	4	1	no	—
399	Q₈	—	4	1	no	—
400	Q₈	—	8	2	no	—
401	D₄	—	4	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	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	—	8	2	no	—
415	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
416	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
417	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
418	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
419	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
420	C₈	—	2	1	no	—
421	C₈	—	2	1	no	—
422	C₈	—	2	1	no	—
423	C₈	C₂×#41×C₁₉	1	1	yes	characteristic
424	C₈	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	8	1	no	—
437	C₄	—	8	1	no	—
438	C₄	—	8	1	no	—
439	C₄	—	8	1	no	—
440	C₄	—	8	1	no	—
441	C₄	—	8	1	no	—
442	C₄	—	8	1	no	—
443	C₄	—	8	1	no	—
444	C₄	C₁₉×#547	1	1	yes	characteristic
445	C₄	C₁₉×#578	1	1	yes	characteristic
446	C₂	—	4	1	no	—
447	C₂	—	4	1	no	—
448	C₂	C₁₉×#3334	1	1	yes	characteristic
449	C₂	C₁₉×#3414	1	1	yes	characteristic
450	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	C₂×D₄×C₁₉	D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄×D₄×C₁₉ ◁ C₈×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×#2255	C₂	semidirect
4. C₁₉×#2237	C₂	semidirect
5. C₁₉×#2237	C₂	semidirect
6. C₁₉×#2237	C₂	semidirect
7. C₁₉×#2236	C₂	semidirect
8. C₁₉×#2229	C₂	semidirect
9. C₁₉×#2227	C₂	semidirect
10. C₁₉×#2219	C₂	semidirect
11. C₁₉×#2216	C₂	semidirect
12. C₁₉×#2176	C₂	semidirect
14. C₁₉×#2159	C₂	semidirect
15. C₁₉×#2158	C₂	semidirect
168. #33916	C₁₉	direct (N × H)
202. #2255	C₂×C₁₉	semidirect
203. #2237	C₂×C₁₉	semidirect
204. #2237	C₂×C₁₉	semidirect
205. #2237	C₂×C₁₉	semidirect
206. #2236	C₂×C₁₉	semidirect
207. #2229	C₂×C₁₉	semidirect
208. #2227	C₂×C₁₉	semidirect
209. #2219	C₂×C₁₉	semidirect
210. #2216	C₂×C₁₉	semidirect
211. #2176	C₂×C₁₉	semidirect
213. #2159	C₂×C₁₉	semidirect
214. #2158	C₂×C₁₉	semidirect
338. C₁₉	#33916	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×#3342	2
C₁₉×#3336	2
C₁₉×#2255	2
C₁₉×#2237	2
C₁₉×#2236	2
C₁₉×#2229	2
C₁₉×#2227	2
C₁₉×#2219	2
C₁₉×#2216	2
C₁₉×#2176	2
C₁₉×#2168	2
C₁₉×#2159	2
C₁₉×#2158	2
#33916	19

Subgroups — C19×#33916 #18039875

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33916 #18039875