Subgroups — C₁₉×#19560 #18025519

Order 4864.

602 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3254	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3230	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3206	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2979	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1699	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1693	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1679	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1673	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1574	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1546	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1544	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#533	C₂²	1	1	yes	characteristic
13	C₁₉×#532	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₁₉×#500	C₂²	1	2	yes	—
16	C₁₉×#492	—	2	1	no	—
17	C₁₉×#487	—	2	1	no	—
18	C₁₉×#487	C₂²	1	2	yes	—
19	C₁₉×#484	—	2	2	no	—
20	C₁₉×#477	—	2	1	no	—
21	C₁₉×#477	—	2	1	no	—
22	C₁₉×#477	—	2	1	no	—
23	C₁₉×#474	C₂²	1	2	yes	—
24	C₁₉×#468	—	2	2	no	—
25	C₁₉×#461	C₂²	1	2	yes	—
26	C₁₉×#461	C₂²	1	2	yes	—
27	C₁₉×#461	C₂²	1	2	yes	—
28	C₁₉×#460	—	2	1	no	—
29	C₁₉×#448	—	2	2	no	—
30	C₁₉×#436	—	2	1	no	—
31	C₁₉×#436	C₂²	1	2	yes	—
32	C₈×D₄×C₁₉	—	2	1	no	—
33	C₈×D₄×C₁₉	C₂²	1	2	yes	—
34	C₁₉×#431	C₂²	1	1	yes	characteristic
35	C₁₉×#431	C₂²	1	1	yes	characteristic
36	C₁₉×#431	C₂²	1	1	yes	characteristic
37	C₁₉×#423	C₂²	1	1	yes	characteristic
38	C₁₉×#408	—	2	2	no	—
39	C₁₉×#335	C₂²	1	2	yes	—
40	C₁₉×#334	C₂²	1	2	yes	—
41	C₁₉×#332	C₂²	1	1	yes	characteristic
42	C₁₉×#332	C₂²	1	2	yes	—
43	C₁₉×#332	C₂²	1	1	yes	characteristic
44	C₁₉×#332	C₂²	1	1	yes	characteristic
45	C₁₉×#332	C₂²	1	2	yes	—
46	C₁₉×#332	C₂²	1	1	yes	characteristic
47	C₂×#41×C₁₉	—	2	1	no	—
48	C₂²×Q₈×C₁₉	—	2	1	no	—
49	C₂×SD₁₆×C₁₉	—	2	2	no	—
50	C₂×SD₁₆×C₁₉	—	2	2	no	—
51	C₂×SD₁₆×C₁₉	—	2	2	no	—
52	C₂×M₁₆×C₁₉	—	2	1	no	—
53	C₂×M₁₆×C₁₉	—	2	2	no	—
54	C₂²×C₈×C₁₉	—	2	2	no	—
55	C₁₉×C₄⋊Q₈	—	2	1	no	—
56	C₁₉×C₄⋊Q₈	—	2	1	no	—
57	C₁₉×C₄⋊Q₈	—	2	1	no	—
58	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
59	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
60	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
61	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
62	C₁₉×#127	D₄	1	1	yes	characteristic
63	C₁₉×#125	—	2	1	no	—
64	C₁₉×#124	—	2	1	no	—
65	C₁₉×C₂²⋊Q₈	—	2	1	no	—
66	C₁₉×C₂²⋊Q₈	—	2	1	no	—
67	C₁₉×#121	—	2	1	no	—
68	C₁₉×#121	D₄	1	2	yes	—
69	C₄×Q₈×C₁₉	—	2	1	no	—
70	C₄×Q₈×C₁₉	—	2	1	no	—
71	C₄×D₄×C₁₉	—	2	1	no	—
72	C₄×D₄×C₁₉	C₂³	1	2	yes	—
73	C₁₉×#117	—	2	1	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
77	C₁₉×#107	—	2	2	no	—
78	C₁₉×#107	—	2	2	no	—
79	C₁₉×#107	—	2	2	no	—
80	C₁₉×C₄⋊C₈	—	2	1	no	—
81	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
82	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
83	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
84	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
85	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
86	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
87	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
88	C₁₉×#103	—	2	2	no	—
89	C₁₉×#103	—	2	2	no	—
90	C₁₉×#103	—	2	2	no	—
91	C₁₉×#103	—	2	2	no	—
92	C₁₉×#103	—	2	2	no	—
93	C₁₉×#102	—	2	2	no	—
94	C₁₉×C₂²⋊C₈	—	2	1	no	—
95	C₁₉×C₂²⋊C₈	—	2	1	no	—
96	C₁₉×C₂²⋊C₈	—	2	2	no	—
97	C₁₉×C₂²⋊C₈	—	2	2	no	—
98	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
99	C₄×C₈×C₁₉	—	2	1	no	—
100	C₄×C₈×C₁₉	—	2	1	no	—
101	C₄×C₈×C₁₉	C₂³	1	2	yes	—
102	#41×C₁₉	—	8	1	no	—
103	#41×C₁₉	—	8	1	no	—
104	C₂×Q₈×C₁₉	—	2	1	no	—
105	C₂×Q₈×C₁₉	—	2	1	no	—
106	C₂×Q₈×C₁₉	—	2	1	no	—
107	C₂×Q₈×C₁₉	—	2	2	no	—
108	C₂×Q₈×C₁₉	—	4	1	no	—
109	C₂×Q₈×C₁₉	—	8	1	no	—
110	C₂×Q₈×C₁₉	—	8	1	no	—
111	C₂×D₄×C₁₉	—	2	2	no	—
112	C₂×D₄×C₁₉	—	2	1	no	—
113	C₂×D₄×C₁₉	—	2	1	no	—
114	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₉	—	2	2	no	—
116	C₂²×C₄×C₁₉	—	4	1	no	—
117	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
120	SD₁₆×C₁₉	—	8	2	no	—
121	SD₁₆×C₁₉	—	8	2	no	—
122	SD₁₆×C₁₉	—	8	2	no	—
123	M₁₆×C₁₉	—	8	2	no	—
124	M₁₆×C₁₉	—	8	1	no	—
125	C₂×C₈×C₁₉	—	2	1	no	—
126	C₂×C₈×C₁₉	—	2	1	no	—
127	C₂×C₈×C₁₉	—	2	2	no	—
128	C₂×C₈×C₁₉	—	2	1	no	—
129	C₂×C₈×C₁₉	—	2	1	no	—
130	C₂×C₈×C₁₉	—	8	2	no	—
131	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
132	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
133	C₄⋊C₄×C₁₉	—	2	1	no	—
134	C₄⋊C₄×C₁₉	—	2	2	no	—
135	C₄⋊C₄×C₁₉	—	2	1	no	—
136	C₄⋊C₄×C₁₉	—	2	1	no	—
137	C₄⋊C₄×C₁₉	—	2	2	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	C₂×D₄	1	2	yes	—
145	C₂²⋊C₄×C₁₉	—	2	2	no	—
146	C₂²⋊C₄×C₁₉	—	2	2	no	—
147	C₂²⋊C₄×C₁₉	—	4	1	no	—
148	C₄²×C₁₉	—	4	1	no	—
149	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₁₉	#41	1	1	yes	characteristic
152	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
153	#19560	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
154	C₂³×C₁₉	—	2	2	no	—
155	C₂³×C₁₉	#121	1	1	yes	characteristic
156	Q₈×C₁₉	—	4	1	no	—
157	Q₈×C₁₉	—	4	2	no	—
158	Q₈×C₁₉	—	4	2	no	—
159	Q₈×C₁₉	—	4	1	no	—
160	Q₈×C₁₉	—	4	1	no	—
161	Q₈×C₁₉	—	4	1	no	—
162	Q₈×C₁₉	—	8	1	no	—
163	Q₈×C₁₉	—	8	2	no	—
164	D₄×C₁₉	—	2	2	no	—
165	D₄×C₁₉	—	2	2	no	—
166	D₄×C₁₉	—	4	2	no	—
167	D₄×C₁₉	—	8	1	no	—
168	D₄×C₁₉	—	8	2	no	—
169	C₂×C₄×C₁₉	—	2	1	no	—
170	C₂×C₄×C₁₉	—	2	1	no	—
171	C₂×C₄×C₁₉	—	2	1	no	—
172	C₂×C₄×C₁₉	—	2	1	no	—
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	2	2	no	—
175	C₂×C₄×C₁₉	—	4	2	no	—
176	C₂×C₄×C₁₉	—	4	2	no	—
177	C₂×C₄×C₁₉	—	4	1	no	—
178	C₂×C₄×C₁₉	—	4	1	no	—
179	C₂×C₄×C₁₉	—	4	2	no	—
180	C₂×C₄×C₁₉	—	8	2	no	—
181	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
182	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
183	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
184	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
187	C₈×C₁₉	—	2	2	no	—
188	C₈×C₁₉	—	2	2	no	—
189	C₈×C₁₉	—	4	2	no	—
190	C₈×C₁₉	—	4	1	no	—
191	C₈×C₁₉	—	4	1	no	—
192	C₈×C₁₉	—	4	1	no	—
193	C₈×C₁₉	—	4	1	no	—
194	#3254	C₂×C₁₉	1	1	yes	characteristic
195	#3230	C₂×C₁₉	1	1	yes	characteristic, complemented
196	#3206	C₂×C₁₉	1	1	yes	characteristic
197	#2979	C₂×C₁₉	1	1	yes	characteristic
198	#1699	C₂×C₁₉	1	2	yes	complemented
199	#1693	C₂×C₁₉	1	2	yes	complemented
200	#1679	C₂×C₁₉	1	2	yes	complemented
201	#1673	C₂×C₁₉	1	2	yes	complemented
202	#1574	C₂×C₁₉	1	1	yes	characteristic, complemented
203	#1546	C₂×C₁₉	1	1	yes	characteristic, complemented
204	#1544	C₂×C₁₉	1	1	yes	characteristic, complemented
205	C₂²×C₁₉	—	2	1	no	—
206	C₂²×C₁₉	—	2	1	no	—
207	C₂²×C₁₉	—	2	1	no	—
208	C₂²×C₁₉	—	4	2	no	—
209	C₂²×C₁₉	—	4	2	no	—
210	C₂²×C₁₉	—	4	2	no	—
211	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
212	C₄×C₁₉	—	2	1	no	—
213	C₄×C₁₉	—	2	1	no	—
214	C₄×C₁₉	—	2	1	no	—
215	C₄×C₁₉	—	4	2	no	—
216	C₄×C₁₉	—	8	1	no	—
217	C₄×C₁₉	—	8	2	no	—
218	C₄×C₁₉	—	8	1	no	—
219	C₄×C₁₉	#473	1	2	yes	—
220	C₄×C₁₉	#576	1	1	yes	characteristic
221	C₄×C₁₉	#577	1	1	yes	characteristic
222	C₄×C₁₉	#577	1	1	yes	characteristic
223	C₄×C₁₉	#577	1	1	yes	characteristic
224	#533	C₂²×C₁₉	1	1	yes	characteristic
225	#532	C₂²×C₁₉	1	1	yes	characteristic
226	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
227	#500	C₂²×C₁₉	1	2	yes	—
228	#492	—	2	1	no	—
229	#487	—	2	1	no	—
230	#487	C₂²×C₁₉	1	2	yes	—
231	#484	—	2	2	no	—
232	#477	—	2	1	no	—
233	#477	—	2	1	no	—
234	#477	—	2	1	no	—
235	#474	C₂²×C₁₉	1	2	yes	—
236	#468	—	2	2	no	—
237	#461	C₂²×C₁₉	1	2	yes	—
238	#461	C₂²×C₁₉	1	2	yes	—
239	#461	C₂²×C₁₉	1	2	yes	—
240	#460	—	2	1	no	—
241	#448	—	2	2	no	—
242	#436	—	2	1	no	—
243	#436	C₂²×C₁₉	1	2	yes	—
244	C₈×D₄	—	2	1	no	—
245	C₈×D₄	C₂²×C₁₉	1	2	yes	—
246	#431	C₂²×C₁₉	1	1	yes	characteristic
247	#431	C₂²×C₁₉	1	1	yes	characteristic
248	#431	C₂²×C₁₉	1	1	yes	characteristic
249	#423	C₂²×C₁₉	1	1	yes	characteristic
250	#408	—	2	2	no	—
251	#335	C₂²×C₁₉	1	2	yes	—
252	#334	C₂²×C₁₉	1	2	yes	—
253	#332	C₂²×C₁₉	1	1	yes	characteristic
254	#332	C₂²×C₁₉	1	1	yes	characteristic
255	#332	C₂²×C₁₉	1	1	yes	characteristic
256	#332	C₂²×C₁₉	1	1	yes	characteristic
257	#332	C₂²×C₁₉	1	2	yes	—
258	#332	C₂²×C₁₉	1	2	yes	—
259	C₂×C₁₉	—	4	1	no	—
260	C₂×C₁₉	—	8	2	no	—
261	C₂×C₁₉	#3042	1	1	yes	characteristic
262	C₂×C₁₉	#3062	1	1	yes	characteristic
263	C₂×C₁₉	C₂×#473	1	1	yes	characteristic
264	C₂×#41	—	2	1	no	—
265	C₂²×Q₈	—	2	1	no	—
266	C₂×SD₁₆	—	2	2	no	—
267	C₂×SD₁₆	—	2	2	no	—
268	C₂×SD₁₆	—	2	2	no	—
269	C₂×M₁₆	—	2	1	no	—
270	C₂×M₁₆	—	2	2	no	—
271	C₂²×C₈	—	2	2	no	—
272	C₄⋊Q₈	—	2	1	no	—
273	C₄⋊Q₈	—	2	1	no	—
274	C₄⋊Q₈	—	2	1	no	—
275	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
276	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
277	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
278	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
279	#127	D₄×C₁₉	1	1	yes	characteristic
280	#125	—	2	1	no	—
281	#124	—	2	1	no	—
282	C₂²⋊Q₈	—	2	1	no	—
283	C₂²⋊Q₈	—	2	1	no	—
284	#121	—	2	1	no	—
285	#121	D₄×C₁₉	1	2	yes	—
286	C₄×Q₈	—	2	1	no	—
287	C₄×Q₈	—	2	1	no	—
288	C₄×D₄	—	2	1	no	—
289	C₄×D₄	C₂³×C₁₉	1	2	yes	—
290	#117	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
294	#107	—	2	2	no	—
295	#107	—	2	2	no	—
296	#107	—	2	2	no	—
297	C₄⋊C₈	—	2	1	no	—
298	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
299	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
300	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
301	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
302	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
303	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
304	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
305	#103	—	2	2	no	—
306	#103	—	2	2	no	—
307	#103	—	2	2	no	—
308	#103	—	2	2	no	—
309	#103	—	2	2	no	—
310	#102	—	2	2	no	—
311	C₂²⋊C₈	—	2	1	no	—
312	C₂²⋊C₈	—	2	1	no	—
313	C₂²⋊C₈	—	2	2	no	—
314	C₂²⋊C₈	—	2	2	no	—
315	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
316	C₄×C₈	—	2	1	no	—
317	C₄×C₈	—	2	1	no	—
318	C₄×C₈	C₂³×C₁₉	1	2	yes	—
319	C₁₉	#19560	1	1	yes	characteristic, direct product factor, Sylow
320	#41	—	8	1	no	—
321	#41	—	8	1	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	4	1	no	—
327	C₂×Q₈	—	8	1	no	—
328	C₂×Q₈	—	8	1	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	4	1	no	—
335	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
337	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
338	SD₁₆	—	8	2	no	—
339	SD₁₆	—	8	2	no	—
340	SD₁₆	—	8	2	no	—
341	M₁₆	—	8	2	no	—
342	M₁₆	—	8	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	8	2	no	—
349	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
350	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	4	1	no	—
359	C₄⋊C₄	—	4	1	no	—
360	C₄⋊C₄	—	4	1	no	—
361	C₄⋊C₄	—	4	1	no	—
362	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
363	C₂²⋊C₄	—	2	2	no	—
364	C₂²⋊C₄	—	2	2	no	—
365	C₂²⋊C₄	—	4	1	no	—
366	C₄²	—	4	1	no	—
367	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
368	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
369	C₄²	#41×C₁₉	1	1	yes	characteristic
370	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
371	C₂³	—	2	2	no	—
372	C₂³	C₁₉×#121	1	1	yes	characteristic
373	Q₈	—	4	1	no	—
374	Q₈	—	4	2	no	—
375	Q₈	—	4	2	no	—
376	Q₈	—	4	1	no	—
377	Q₈	—	4	1	no	—
378	Q₈	—	4	1	no	—
379	Q₈	—	8	1	no	—
380	Q₈	—	8	2	no	—
381	D₄	—	2	2	no	—
382	D₄	—	2	2	no	—
383	D₄	—	4	2	no	—
384	D₄	—	8	1	no	—
385	D₄	—	8	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	8	2	no	—
398	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
399	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
400	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
401	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
402	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
403	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
404	C₈	—	2	2	no	—
405	C₈	—	2	2	no	—
406	C₈	—	4	2	no	—
407	C₈	—	4	1	no	—
408	C₈	—	4	1	no	—
409	C₈	—	4	1	no	—
410	C₈	—	4	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	4	2	no	—
417	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	2	1	no	—
421	C₄	—	4	2	no	—
422	C₄	—	8	1	no	—
423	C₄	—	8	2	no	—
424	C₄	—	8	1	no	—
425	C₄	C₁₉×#473	1	2	yes	—
426	C₄	C₁₉×#576	1	1	yes	characteristic
427	C₄	C₁₉×#577	1	1	yes	characteristic
428	C₄	C₁₉×#577	1	1	yes	characteristic
429	C₄	C₁₉×#577	1	1	yes	characteristic
430	C₂	—	4	1	no	—
431	C₂	—	8	2	no	—
432	C₂	C₁₉×#3042	1	1	yes	characteristic
433	C₂	C₁₉×#3062	1	1	yes	characteristic
434	C₂	C₂×C₁₉×#473	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
2. C₁₉×#3230	C₂	semidirect
5. C₁₉×#1699	C₂	semidirect
6. C₁₉×#1693	C₂	semidirect
7. C₁₉×#1679	C₂	semidirect
8. C₁₉×#1673	C₂	semidirect
9. C₁₉×#1574	C₂	semidirect
10. C₁₉×#1546	C₂	semidirect
11. C₁₉×#1544	C₂	semidirect
153. #19560	C₁₉	direct (N × H)
195. #3230	C₂×C₁₉	semidirect
198. #1699	C₂×C₁₉	semidirect
199. #1693	C₂×C₁₉	semidirect
200. #1679	C₂×C₁₉	semidirect
201. #1673	C₂×C₁₉	semidirect
202. #1574	C₂×C₁₉	semidirect
203. #1546	C₂×C₁₉	semidirect
204. #1544	C₂×C₁₉	semidirect
319. C₁₉	#19560	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×#3254	2
C₁₉×#3230	2
C₁₉×#3206	2
C₁₉×#2979	2
C₁₉×#1699	2
C₁₉×#1693	2
C₁₉×#1679	2
C₁₉×#1673	2
C₁₉×#1574	2
C₁₉×#1546	2
C₁₉×#1544	2
#19560	19

Subgroups — C19×#19560 #18025519

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19560 #18025519