Subgroups — C₁₉×#19343 #18025302

Order 4864.

590 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3255	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3254	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3167	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2960	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1704	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1702	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1672	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1666	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1566	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1561	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1560	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#533	C₂²	1	1	yes	characteristic
13	C₁₉×#533	C₂²	1	1	yes	characteristic
14	C₁₉×#532	C₂²	1	1	yes	characteristic
15	C₁₉×#498	C₂²	1	1	yes	characteristic
16	C₁₉×#492	C₂²	1	1	yes	characteristic
17	C₁₉×#487	C₂²	1	1	yes	characteristic
18	C₁₉×#486	C₂²	1	1	yes	characteristic
19	C₁₉×#477	C₂²	1	2	yes	—
20	C₁₉×#475	—	2	1	no	—
21	C₁₉×#475	C₂²	1	2	yes	—
22	C₁₉×#474	—	2	1	no	—
23	C₁₉×#470	—	2	2	no	—
24	C₁₉×#468	—	2	2	no	—
25	C₁₉×#465	—	2	1	no	—
26	C₁₉×#465	—	2	1	no	—
27	C₁₉×#462	—	2	1	no	—
28	C₁₉×#462	C₂²	1	2	yes	—
29	C₁₉×#461	—	2	1	no	—
30	C₁₉×#460	C₂²	1	2	yes	—
31	C₁₉×#446	—	2	1	no	—
32	C₁₉×#446	C₂²	1	2	yes	—
33	C₈×Q₈×C₁₉	—	2	1	no	—
34	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
35	C₄×SD₁₆×C₁₉	—	2	1	no	—
36	C₄×SD₁₆×C₁₉	—	2	1	no	—
37	C₁₉×#424	—	2	1	no	—
38	C₁₉×#423	C₂²	1	1	yes	characteristic
39	C₁₉×#423	C₂²	1	1	yes	characteristic
40	C₁₉×#423	C₂²	1	1	yes	characteristic
41	C₁₉×#405	—	2	1	no	—
42	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
43	C₁₉×#334	C₂²	1	2	yes	—
44	C₁₉×#334	C₂²	1	2	yes	—
45	C₁₉×#333	C₂²	1	2	yes	—
46	C₁₉×#332	C₂²	1	2	yes	—
47	C₁₉×#332	C₂²	1	2	yes	—
48	C₁₉×#331	C₂²	1	2	yes	—
49	C₂×#41×C₁₉	—	2	1	no	—
50	C₂×Q₁₆×C₁₉	—	2	2	no	—
51	C₂×SD₁₆×C₁₉	—	2	2	no	—
52	C₂×SD₁₆×C₁₉	—	2	1	no	—
53	C₂×SD₁₆×C₁₉	—	2	1	no	—
54	C₂×M₁₆×C₁₉	—	2	1	no	—
55	C₂×M₁₆×C₁₉	—	2	1	no	—
56	C₂×M₁₆×C₁₉	—	2	1	no	—
57	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
58	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
59	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
60	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
61	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
62	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
63	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₁₉×#127	C₂³	1	1	yes	characteristic
65	C₁₉×#125	—	2	1	no	—
66	C₁₉×#125	—	2	1	no	—
67	C₁₉×#124	—	2	1	no	—
68	C₁₉×C₂²⋊Q₈	—	2	1	no	—
69	C₁₉×C₂²⋊Q₈	—	2	1	no	—
70	C₁₉×C₂²⋊Q₈	—	2	1	no	—
71	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
72	C₁₉×#121	—	2	1	no	—
73	C₁₉×#121	—	2	1	no	—
74	C₄×Q₈×C₁₉	—	2	1	no	—
75	C₄×Q₈×C₁₉	—	2	1	no	—
76	C₄×Q₈×C₁₉	—	2	1	no	—
77	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
78	C₄×D₄×C₁₉	—	2	1	no	—
79	C₄×D₄×C₁₉	—	2	1	no	—
80	C₁₉×#117	—	2	1	no	—
81	C₁₉×#117	—	2	1	no	—
82	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
83	C₁₉×#107	—	2	2	no	—
84	C₁₉×#106	—	2	1	no	—
85	C₁₉×#106	—	2	1	no	—
86	C₁₉×#106	—	2	2	no	—
87	C₁₉×C₄⋊C₈	—	2	2	no	—
88	C₁₉×C₄⋊C₈	—	2	2	no	—
89	C₁₉×C₄⋊C₈	—	2	1	no	—
90	C₁₉×C₄⋊C₈	—	2	1	no	—
91	C₁₉×C₄⋊C₈	—	2	1	no	—
92	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
93	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
94	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
95	C₁₉×#103	—	2	2	no	—
96	C₁₉×#103	—	2	2	no	—
97	C₁₉×#103	—	2	1	no	—
98	C₁₉×#103	—	2	1	no	—
99	C₁₉×#103	—	2	2	no	—
100	C₁₉×#102	—	2	1	no	—
101	C₁₉×#102	—	2	1	no	—
102	C₁₉×#102	—	2	2	no	—
103	C₁₉×#97	—	2	2	no	—
104	C₄×C₈×C₁₉	—	2	2	no	—
105	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
106	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
107	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
109	#41×C₁₉	—	8	2	no	—
110	C₂×Q₈×C₁₉	—	2	1	no	—
111	C₂×Q₈×C₁₉	—	2	1	no	—
112	C₂×Q₈×C₁₉	—	2	1	no	—
113	C₂×Q₈×C₁₉	—	2	1	no	—
114	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
115	C₂×D₄×C₁₉	—	2	1	no	—
116	C₂×D₄×C₁₉	—	2	1	no	—
117	C₂×D₄×C₁₉	—	2	1	no	—
118	C₂×D₄×C₁₉	—	4	1	no	—
119	C₂²×C₄×C₁₉	—	4	1	no	—
120	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
123	Q₁₆×C₁₉	—	8	2	no	—
124	SD₁₆×C₁₉	—	4	2	no	—
125	SD₁₆×C₁₉	—	4	2	no	—
126	SD₁₆×C₁₉	—	8	2	no	—
127	M₁₆×C₁₉	—	4	2	no	—
128	M₁₆×C₁₉	—	8	1	no	—
129	M₁₆×C₁₉	—	8	1	no	—
130	C₂×C₈×C₁₉	—	2	2	no	—
131	C₂×C₈×C₁₉	—	2	2	no	—
132	C₂×C₈×C₁₉	—	2	2	no	—
133	C₂×C₈×C₁₉	—	2	2	no	—
134	C₂×C₈×C₁₉	—	4	1	no	—
135	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	2	2	no	—
143	C₄⋊C₄×C₁₉	—	2	2	no	—
144	C₄⋊C₄×C₁₉	—	2	1	no	—
145	C₄⋊C₄×C₁₉	—	2	1	no	—
146	C₄⋊C₄×C₁₉	—	2	1	no	—
147	C₄⋊C₄×C₁₉	—	2	1	no	—
148	C₄⋊C₄×C₁₉	—	2	1	no	—
149	C₄⋊C₄×C₁₉	—	2	1	no	—
150	C₄⋊C₄×C₁₉	—	4	1	no	—
151	C₄⋊C₄×C₁₉	—	4	1	no	—
152	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
153	C₂²⋊C₄×C₁₉	—	2	2	no	—
154	C₂²⋊C₄×C₁₉	—	4	1	no	—
155	C₂²⋊C₄×C₁₉	—	4	1	no	—
156	C₂²⋊C₄×C₁₉	—	4	1	no	—
157	C₄²×C₁₉	—	2	2	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	C₄²×C₁₉	#41	1	1	yes	characteristic
162	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
163	#19343	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂³×C₁₉	—	4	1	no	—
165	C₂³×C₁₉	#121	1	1	yes	characteristic
166	Q₈×C₁₉	—	2	2	no	—
167	Q₈×C₁₉	—	2	2	no	—
168	Q₈×C₁₉	—	4	2	no	—
169	Q₈×C₁₉	—	4	1	no	—
170	Q₈×C₁₉	—	4	1	no	—
171	Q₈×C₁₉	—	4	1	no	—
172	Q₈×C₁₉	—	4	1	no	—
173	Q₈×C₁₉	—	8	1	no	—
174	D₄×C₁₉	—	4	1	no	—
175	D₄×C₁₉	—	4	1	no	—
176	D₄×C₁₉	—	4	1	no	—
177	D₄×C₁₉	—	4	1	no	—
178	D₄×C₁₉	—	8	1	no	—
179	D₄×C₁₉	—	8	2	no	—
180	C₂×C₄×C₁₉	—	2	1	no	—
181	C₂×C₄×C₁₉	—	2	1	no	—
182	C₂×C₄×C₁₉	—	2	1	no	—
183	C₂×C₄×C₁₉	—	2	1	no	—
184	C₂×C₄×C₁₉	—	2	2	no	—
185	C₂×C₄×C₁₉	—	2	2	no	—
186	C₂×C₄×C₁₉	—	2	2	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	—	8	2	no	—
191	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
192	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
193	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
194	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
197	C₈×C₁₉	—	2	1	no	—
198	C₈×C₁₉	—	2	1	no	—
199	C₈×C₁₉	—	2	1	no	—
200	C₈×C₁₉	—	4	2	no	—
201	C₈×C₁₉	—	4	2	no	—
202	C₈×C₁₉	—	4	2	no	—
203	C₈×C₁₉	#137	1	2	yes	—
204	#3255	C₂×C₁₉	1	1	yes	characteristic, complemented
205	#3254	C₂×C₁₉	1	1	yes	characteristic
206	#3167	C₂×C₁₉	1	1	yes	characteristic
207	#2960	C₂×C₁₉	1	1	yes	characteristic, complemented
208	#1704	C₂×C₁₉	1	2	yes	complemented
209	#1702	C₂×C₁₉	1	2	yes	complemented
210	#1672	C₂×C₁₉	1	2	yes	complemented
211	#1666	C₂×C₁₉	1	2	yes	complemented
212	#1566	C₂×C₁₉	1	1	yes	characteristic, complemented
213	#1561	C₂×C₁₉	1	1	yes	characteristic, complemented
214	#1560	C₂×C₁₉	1	1	yes	characteristic
215	C₂²×C₁₉	—	2	1	no	—
216	C₂²×C₁₉	—	2	1	no	—
217	C₂²×C₁₉	—	2	1	no	—
218	C₂²×C₁₉	—	8	1	no	—
219	C₂²×C₁₉	—	8	1	no	—
220	C₂²×C₁₉	—	8	1	no	—
221	C₂²×C₁₉	C₂×#121	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	—	4	2	no	—
226	C₄×C₁₉	—	4	2	no	—
227	C₄×C₁₉	—	8	1	no	—
228	C₄×C₁₉	—	8	1	no	—
229	C₄×C₁₉	—	8	1	no	—
230	C₄×C₁₉	#471	1	2	yes	—
231	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
232	C₄×C₁₉	#575	1	1	yes	characteristic
233	C₄×C₁₉	#577	1	1	yes	characteristic
234	C₄×C₁₉	#577	1	1	yes	characteristic
235	#533	C₂²×C₁₉	1	1	yes	characteristic
236	#533	C₂²×C₁₉	1	1	yes	characteristic
237	#532	C₂²×C₁₉	1	1	yes	characteristic
238	#498	C₂²×C₁₉	1	1	yes	characteristic
239	#492	C₂²×C₁₉	1	1	yes	characteristic
240	#487	C₂²×C₁₉	1	1	yes	characteristic
241	#486	C₂²×C₁₉	1	1	yes	characteristic
242	#477	C₂²×C₁₉	1	2	yes	—
243	#475	—	2	1	no	—
244	#475	C₂²×C₁₉	1	2	yes	—
245	#474	—	2	1	no	—
246	#470	—	2	2	no	—
247	#468	—	2	2	no	—
248	#465	—	2	1	no	—
249	#465	—	2	1	no	—
250	#462	—	2	1	no	—
251	#462	C₂²×C₁₉	1	2	yes	—
252	#461	—	2	1	no	—
253	#460	C₂²×C₁₉	1	2	yes	—
254	#446	—	2	1	no	—
255	#446	C₂²×C₁₉	1	2	yes	—
256	C₈×Q₈	—	2	1	no	—
257	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
258	C₄×SD₁₆	—	2	1	no	—
259	C₄×SD₁₆	—	2	1	no	—
260	#424	—	2	1	no	—
261	#423	C₂²×C₁₉	1	1	yes	characteristic
262	#423	C₂²×C₁₉	1	1	yes	characteristic
263	#423	C₂²×C₁₉	1	1	yes	characteristic
264	#405	—	2	1	no	—
265	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
266	#334	C₂²×C₁₉	1	2	yes	—
267	#334	C₂²×C₁₉	1	2	yes	—
268	#333	C₂²×C₁₉	1	2	yes	—
269	#332	C₂²×C₁₉	1	2	yes	—
270	#332	C₂²×C₁₉	1	2	yes	—
271	#331	C₂²×C₁₉	1	2	yes	—
272	C₂×C₁₉	—	4	1	no	—
273	C₂×C₁₉	—	16	1	no	—
274	C₂×C₁₉	#3037	1	1	yes	characteristic
275	C₂×C₁₉	#3060	1	1	yes	characteristic
276	C₂×C₁₉	C₂×#471	1	1	yes	characteristic
277	C₂×#41	—	2	1	no	—
278	C₂×Q₁₆	—	2	2	no	—
279	C₂×SD₁₆	—	2	2	no	—
280	C₂×SD₁₆	—	2	1	no	—
281	C₂×SD₁₆	—	2	1	no	—
282	C₂×M₁₆	—	2	1	no	—
283	C₂×M₁₆	—	2	1	no	—
284	C₂×M₁₆	—	2	1	no	—
285	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
286	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
287	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
288	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
289	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
290	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
291	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
292	#127	C₂³×C₁₉	1	1	yes	characteristic
293	#125	—	2	1	no	—
294	#125	—	2	1	no	—
295	#124	—	2	1	no	—
296	C₂²⋊Q₈	—	2	1	no	—
297	C₂²⋊Q₈	—	2	1	no	—
298	C₂²⋊Q₈	—	2	1	no	—
299	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
300	#121	—	2	1	no	—
301	#121	—	2	1	no	—
302	C₄×Q₈	—	2	1	no	—
303	C₄×Q₈	—	2	1	no	—
304	C₄×Q₈	—	2	1	no	—
305	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
306	C₄×D₄	—	2	1	no	—
307	C₄×D₄	—	2	1	no	—
308	#117	—	2	1	no	—
309	#117	—	2	1	no	—
310	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
311	#107	—	2	2	no	—
312	#106	—	2	1	no	—
313	#106	—	2	1	no	—
314	#106	—	2	2	no	—
315	C₄⋊C₈	—	2	2	no	—
316	C₄⋊C₈	—	2	2	no	—
317	C₄⋊C₈	—	2	1	no	—
318	C₄⋊C₈	—	2	1	no	—
319	C₄⋊C₈	—	2	1	no	—
320	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
321	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
322	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
323	#103	—	2	2	no	—
324	#103	—	2	2	no	—
325	#103	—	2	1	no	—
326	#103	—	2	1	no	—
327	#103	—	2	2	no	—
328	#102	—	2	1	no	—
329	#102	—	2	1	no	—
330	#102	—	2	2	no	—
331	#97	—	2	2	no	—
332	C₄×C₈	—	2	2	no	—
333	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
334	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
335	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
336	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
337	C₁₉	#19343	1	1	yes	characteristic, direct product factor, Sylow
338	#41	—	8	2	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	2	1	no	—
342	C₂×Q₈	—	2	1	no	—
343	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	4	1	no	—
348	C₂²×C₄	—	4	1	no	—
349	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
351	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
352	Q₁₆	—	8	2	no	—
353	SD₁₆	—	4	2	no	—
354	SD₁₆	—	4	2	no	—
355	SD₁₆	—	8	2	no	—
356	M₁₆	—	4	2	no	—
357	M₁₆	—	8	1	no	—
358	M₁₆	—	8	1	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	4	1	no	—
364	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
365	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
366	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
367	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	4	1	no	—
380	C₄⋊C₄	—	4	1	no	—
381	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
382	C₂²⋊C₄	—	2	2	no	—
383	C₂²⋊C₄	—	4	1	no	—
384	C₂²⋊C₄	—	4	1	no	—
385	C₂²⋊C₄	—	4	1	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	4	1	no	—
388	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
389	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
390	C₄²	#41×C₁₉	1	1	yes	characteristic
391	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
392	C₂³	—	4	1	no	—
393	C₂³	C₁₉×#121	1	1	yes	characteristic
394	Q₈	—	2	2	no	—
395	Q₈	—	2	2	no	—
396	Q₈	—	4	2	no	—
397	Q₈	—	4	1	no	—
398	Q₈	—	4	1	no	—
399	Q₈	—	4	1	no	—
400	Q₈	—	4	1	no	—
401	Q₈	—	8	1	no	—
402	D₄	—	4	1	no	—
403	D₄	—	4	1	no	—
404	D₄	—	4	1	no	—
405	D₄	—	4	1	no	—
406	D₄	—	8	1	no	—
407	D₄	—	8	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	8	2	no	—
419	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
420	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
421	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
422	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
423	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
424	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
425	C₈	—	2	1	no	—
426	C₈	—	2	1	no	—
427	C₈	—	2	1	no	—
428	C₈	—	4	2	no	—
429	C₈	—	4	2	no	—
430	C₈	—	4	2	no	—
431	C₈	C₁₉×#137	1	2	yes	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	8	1	no	—
436	C₂²	—	8	1	no	—
437	C₂²	—	8	1	no	—
438	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	4	2	no	—
443	C₄	—	4	2	no	—
444	C₄	—	8	1	no	—
445	C₄	—	8	1	no	—
446	C₄	—	8	1	no	—
447	C₄	C₁₉×#471	1	2	yes	—
448	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
449	C₄	C₁₉×#575	1	1	yes	characteristic
450	C₄	C₁₉×#577	1	1	yes	characteristic
451	C₄	C₁₉×#577	1	1	yes	characteristic
452	C₂	—	4	1	no	—
453	C₂	—	16	1	no	—
454	C₂	C₁₉×#3037	1	1	yes	characteristic
455	C₂	C₁₉×#3060	1	1	yes	characteristic
456	C₂	C₂×C₁₉×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3255	C₂	semidirect
4. C₁₉×#2960	C₂	semidirect
5. C₁₉×#1704	C₂	semidirect
6. C₁₉×#1702	C₂	semidirect
7. C₁₉×#1672	C₂	semidirect
8. C₁₉×#1666	C₂	semidirect
9. C₁₉×#1566	C₂	semidirect
10. C₁₉×#1561	C₂	semidirect
163. #19343	C₁₉	direct (N × H)
204. #3255	C₂×C₁₉	semidirect
207. #2960	C₂×C₁₉	semidirect
208. #1704	C₂×C₁₉	semidirect
209. #1702	C₂×C₁₉	semidirect
210. #1672	C₂×C₁₉	semidirect
211. #1666	C₂×C₁₉	semidirect
212. #1566	C₂×C₁₉	semidirect
213. #1561	C₂×C₁₉	semidirect
337. C₁₉	#19343	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×#3255	2
C₁₉×#3254	2
C₁₉×#3167	2
C₁₉×#2960	2
C₁₉×#1704	2
C₁₉×#1702	2
C₁₉×#1672	2
C₁₉×#1666	2
C₁₉×#1566	2
C₁₉×#1561	2
C₁₉×#1560	2
#19343	19

Subgroups — C19×#19343 #18025302

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19343 #18025302