Subgroups — C₁₉×#19627 #18025586

Order 4864.

784 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3209	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3205	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3167	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3141	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3138	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×#486	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1720	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1717	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1711	C₂	1	2	yes	maximal, complemented
10	C₁₉×#1709	C₂	1	2	yes	maximal, complemented
11	C₈×M₁₆×C₁₉	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	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
16	C₁₉×#498	C₂²	1	1	yes	characteristic, complemented
17	C₁₉×#494	C₂²	1	2	yes	complemented
18	C₁₉×#493	C₂²	1	2	yes	—
19	C₁₉×#492	C₂²	1	1	yes	characteristic, complemented
20	C₁₉×#490	—	2	2	no	—
21	C₁₉×#489	—	2	2	no	—
22	C₁₉×#487	C₂²	1	1	yes	characteristic, complemented
23	C₁₉×#487	C₂²	1	2	yes	complemented
24	C₁₉×#487	C₂²	1	2	yes	complemented
25	C₁₉×#486	—	2	2	no	—
26	C₁₉×#486	C₂²	1	2	yes	—
27	C₁₉×#486	C₂²	1	2	yes	—
28	C₁₉×#486	C₂²	1	2	yes	—
29	C₁₉×#486	C₂²	1	2	yes	—
30	C₁₉×#486	C₂²	1	2	yes	—
31	C₁₉×#486	C₂²	1	1	yes	characteristic, complemented
32	C₁₉×#486	C₂²	1	2	yes	complemented
33	C₁₉×#465	—	2	2	no	—
34	C₁₉×#462	—	2	2	no	—
35	C₁₉×#459	—	2	2	no	—
36	C₁₉×#451	—	2	2	no	—
37	C₁₉×#447	—	2	2	no	—
38	C₄×SD₁₆×C₁₉	—	2	2	no	—
39	C₁₉×#431	C₂²	1	1	yes	characteristic
40	C₁₉×#418	—	2	2	no	—
41	C₁₉×#417	—	2	2	no	—
42	C₂×C₁₉×#102	—	2	2	no	—
43	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
45	C₁₉×#322	C₂²	1	2	yes	complemented
46	C₈²×C₁₉	C₂²	1	2	yes	complemented
47	C₂×#41×C₁₉	—	2	1	no	—
48	C₂²×Q₈×C₁₉	—	2	1	no	—
49	C₂²×D₄×C₁₉	—	2	1	no	—
50	C₂²×D₄×C₁₉	—	2	1	no	—
51	C₂²×D₄×C₁₉	—	2	1	no	—
52	C₂×Q₁₆×C₁₉	—	2	4	no	—
53	C₂×SD₁₆×C₁₉	—	2	2	no	—
54	C₂×D₈×C₁₉	—	2	4	no	—
55	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
56	C₂²×C₈×C₁₉	D₄	1	2	yes	—
57	C₁₉×C₄⋊Q₈	—	2	1	no	—
58	C₁₉×C₄⋊Q₈	—	2	1	no	—
59	C₁₉×C₄⋊Q₈	—	2	1	no	—
60	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
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	—	2	1	no	—
65	C₁₉×#127	—	2	1	no	—
66	C₁₉×#127	—	2	1	no	—
67	C₁₉×#127	C₂³	1	2	yes	—
68	C₁₉×#127	C₂³	1	1	yes	characteristic
69	C₁₉×#125	—	2	1	no	—
70	C₁₉×#124	—	2	1	no	—
71	C₁₉×C₂²⋊Q₈	—	2	1	no	—
72	C₁₉×C₂²⋊Q₈	—	2	1	no	—
73	C₁₉×#121	—	2	1	no	—
74	C₁₉×#121	—	2	1	no	—
75	C₄×Q₈×C₁₉	—	2	1	no	—
76	C₄×Q₈×C₁₉	—	2	1	no	—
77	C₄×D₄×C₁₉	—	2	1	no	—
78	C₄×D₄×C₁₉	—	2	1	no	—
79	C₁₉×#117	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
83	C₁₉×#106	—	2	2	no	—
84	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
85	C₁₉×#103	—	2	4	no	—
86	C₁₉×#103	—	2	2	no	—
87	C₁₉×#103	—	2	4	no	—
88	C₁₉×#102	—	2	4	no	—
89	C₁₉×#102	—	2	4	no	—
90	C₁₉×#102	—	2	4	no	—
91	C₁₉×#102	—	2	4	no	—
92	C₁₉×#102	—	2	4	no	—
93	C₁₉×#102	—	2	2	no	—
94	C₁₉×#102	—	2	4	no	—
95	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
96	C₁₉×#97	D₄	1	2	yes	—
97	C₄×C₈×C₁₉	D₄	1	2	yes	—
98	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₁₉	C₂³	1	2	yes	—
101	C₄×C₈×C₁₉	C₂³	1	2	yes	—
102	C₂⁴×C₁₉	—	4	1	no	—
103	#41×C₁₉	—	4	4	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	2	no	—
110	C₂×D₄×C₁₉	—	2	1	no	—
111	C₂×D₄×C₁₉	—	2	1	no	—
112	C₂×D₄×C₁₉	—	2	1	no	—
113	C₂×D₄×C₁₉	—	2	2	no	—
114	C₂×D₄×C₁₉	—	2	2	no	—
115	C₂×D₄×C₁₉	—	2	2	no	—
116	C₂×D₄×C₁₉	—	4	4	no	—
117	C₂×D₄×C₁₉	—	4	1	no	—
118	C₂×D₄×C₁₉	—	4	1	no	—
119	C₂×D₄×C₁₉	—	4	1	no	—
120	C₂×D₄×C₁₉	—	4	1	no	—
121	C₂×D₄×C₁₉	—	4	4	no	—
122	C₂×D₄×C₁₉	—	8	2	no	—
123	C₂²×C₄×C₁₉	—	4	1	no	—
124	C₂²×C₄×C₁₉	—	4	1	no	—
125	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
128	Q₁₆×C₁₉	—	8	4	no	—
129	SD₁₆×C₁₉	—	4	4	no	—
130	D₈×C₁₉	—	8	4	no	—
131	M₁₆×C₁₉	—	2	4	no	—
132	C₂×C₈×C₁₉	—	4	2	no	—
133	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
136	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
137	C₄⋊C₄×C₁₉	—	2	2	no	—
138	C₄⋊C₄×C₁₉	—	2	2	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	—	2	1	no	—
143	C₄⋊C₄×C₁₉	—	2	1	no	—
144	C₄⋊C₄×C₁₉	—	2	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	C₂²⋊C₄×C₁₉	—	4	1	no	—
150	C₂²⋊C₄×C₁₉	—	4	1	no	—
151	C₂²⋊C₄×C₁₉	—	4	1	no	—
152	C₄²×C₁₉	—	4	1	no	—
153	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
157	#19627	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
158	C₂³×C₁₉	—	4	1	no	—
159	C₂³×C₁₉	—	4	2	no	—
160	C₂³×C₁₉	—	8	2	no	—
161	C₂³×C₁₉	—	8	2	no	—
162	C₂³×C₁₉	—	8	2	no	—
163	C₂³×C₁₉	#127	1	1	yes	characteristic
164	Q₈×C₁₉	—	4	2	no	—
165	Q₈×C₁₉	—	4	2	no	—
166	Q₈×C₁₉	—	4	2	no	—
167	Q₈×C₁₉	—	4	4	no	—
168	Q₈×C₁₉	—	8	2	no	—
169	D₄×C₁₉	—	4	4	no	—
170	D₄×C₁₉	—	4	2	no	—
171	D₄×C₁₉	—	4	2	no	—
172	D₄×C₁₉	—	4	4	no	—
173	D₄×C₁₉	—	4	2	no	—
174	D₄×C₁₉	—	4	4	no	—
175	D₄×C₁₉	—	8	2	no	—
176	D₄×C₁₉	—	8	2	no	—
177	D₄×C₁₉	—	8	2	no	—
178	D₄×C₁₉	—	8	2	no	—
179	C₂×C₄×C₁₉	—	2	2	no	—
180	C₂×C₄×C₁₉	—	2	2	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	2	no	—
185	C₂×C₄×C₁₉	—	8	2	no	—
186	C₂×C₄×C₁₉	—	8	2	no	—
187	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
188	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
189	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
190	C₂×C₄×C₁₉	#135	1	4	yes	—
191	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
194	C₈×C₁₉	—	2	4	no	—
195	C₈×C₁₉	—	2	2	no	—
196	C₈×C₁₉	—	2	2	no	—
197	C₈×C₁₉	—	2	4	no	—
198	#3209	C₂×C₁₉	1	1	yes	characteristic, complemented
199	#3205	C₂×C₁₉	1	1	yes	characteristic
200	#3167	C₂×C₁₉	1	1	yes	characteristic, complemented
201	#3141	C₂×C₁₉	1	1	yes	characteristic, complemented
202	#3138	C₂×C₁₉	1	1	yes	characteristic, complemented
203	C₂×#486	C₂×C₁₉	1	1	yes	characteristic, complemented
204	#1720	C₂×C₁₉	1	2	yes	complemented
205	#1717	C₂×C₁₉	1	2	yes	complemented
206	#1711	C₂×C₁₉	1	2	yes	complemented
207	#1709	C₂×C₁₉	1	2	yes	complemented
208	C₈×M₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
209	C₂²×C₁₉	—	2	1	no	—
210	C₂²×C₁₉	—	2	1	no	—
211	C₂²×C₁₉	—	8	1	no	—
212	C₂²×C₁₉	—	8	2	no	—
213	C₂²×C₁₉	—	8	2	no	—
214	C₂²×C₁₉	—	8	1	no	—
215	C₂²×C₁₉	—	8	2	no	—
216	C₂²×C₁₉	—	8	1	no	—
217	C₂²×C₁₉	—	16	4	no	—
218	C₂²×C₁₉	#495	1	2	yes	—
219	C₂²×C₁₉	C₂×#127	1	1	yes	characteristic
220	C₄×C₁₉	—	2	1	no	—
221	C₄×C₁₉	—	2	1	no	—
222	C₄×C₁₉	—	8	1	no	—
223	C₄×C₁₉	—	8	1	no	—
224	C₄×C₁₉	—	8	2	no	—
225	C₄×C₁₉	—	8	1	no	—
226	C₄×C₁₉	#495	1	2	yes	—
227	C₄×C₁₉	C₂×#135	1	2	yes	—
228	C₄×C₁₉	#575	1	2	yes	—
229	C₄×C₁₉	#576	1	2	yes	—
230	#533	C₂²×C₁₉	1	1	yes	characteristic
231	#532	C₂²×C₁₉	1	1	yes	characteristic
232	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
233	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
234	#498	C₂²×C₁₉	1	1	yes	characteristic, complemented
235	#494	C₂²×C₁₉	1	2	yes	complemented
236	#493	C₂²×C₁₉	1	2	yes	—
237	#492	C₂²×C₁₉	1	1	yes	characteristic, complemented
238	#490	—	2	2	no	—
239	#489	—	2	2	no	—
240	#487	C₂²×C₁₉	1	2	yes	complemented
241	#487	C₂²×C₁₉	1	1	yes	characteristic, complemented
242	#487	C₂²×C₁₉	1	2	yes	complemented
243	#486	—	2	2	no	—
244	#486	C₂²×C₁₉	1	2	yes	—
245	#486	C₂²×C₁₉	1	2	yes	—
246	#486	C₂²×C₁₉	1	2	yes	—
247	#486	C₂²×C₁₉	1	2	yes	—
248	#486	C₂²×C₁₉	1	2	yes	—
249	#486	C₂²×C₁₉	1	2	yes	complemented
250	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
251	#465	—	2	2	no	—
252	#462	—	2	2	no	—
253	#459	—	2	2	no	—
254	#451	—	2	2	no	—
255	#447	—	2	2	no	—
256	C₄×SD₁₆	—	2	2	no	—
257	#431	C₂²×C₁₉	1	1	yes	characteristic
258	#418	—	2	2	no	—
259	#417	—	2	2	no	—
260	C₂×#102	—	2	2	no	—
261	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
262	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
263	#322	C₂²×C₁₉	1	2	yes	complemented
264	C₈²	C₂²×C₁₉	1	2	yes	complemented
265	C₂×C₁₉	—	2	2	no	—
266	C₂×C₁₉	—	16	1	no	—
267	C₂×C₁₉	—	16	2	no	—
268	C₂×C₁₉	C₂×#495	1	1	yes	characteristic
269	C₂×C₁₉	#3153	1	1	yes	characteristic
270	C₂×C₁₉	#3155	1	1	yes	characteristic
271	C₂×#41	—	2	1	no	—
272	C₂²×Q₈	—	2	1	no	—
273	C₂²×D₄	—	2	1	no	—
274	C₂²×D₄	—	2	1	no	—
275	C₂²×D₄	—	2	1	no	—
276	C₂×Q₁₆	—	2	4	no	—
277	C₂×SD₁₆	—	2	2	no	—
278	C₂×D₈	—	2	4	no	—
279	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
280	C₂²×C₈	D₄×C₁₉	1	2	yes	—
281	C₄⋊Q₈	—	2	1	no	—
282	C₄⋊Q₈	—	2	1	no	—
283	C₄⋊Q₈	—	2	1	no	—
284	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
285	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
286	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
287	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
288	#127	—	2	1	no	—
289	#127	—	2	1	no	—
290	#127	—	2	1	no	—
291	#127	C₂³×C₁₉	1	2	yes	—
292	#127	C₂³×C₁₉	1	1	yes	characteristic
293	#125	—	2	1	no	—
294	#124	—	2	1	no	—
295	C₂²⋊Q₈	—	2	1	no	—
296	C₂²⋊Q₈	—	2	1	no	—
297	#121	—	2	1	no	—
298	#121	—	2	1	no	—
299	C₄×Q₈	—	2	1	no	—
300	C₄×Q₈	—	2	1	no	—
301	C₄×D₄	—	2	1	no	—
302	C₄×D₄	—	2	1	no	—
303	#117	—	2	1	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
307	#106	—	2	2	no	—
308	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
309	#103	—	2	4	no	—
310	#103	—	2	2	no	—
311	#103	—	2	4	no	—
312	#102	—	2	4	no	—
313	#102	—	2	4	no	—
314	#102	—	2	4	no	—
315	#102	—	2	4	no	—
316	#102	—	2	4	no	—
317	#102	—	2	2	no	—
318	#102	—	2	4	no	—
319	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
320	#97	D₄×C₁₉	1	2	yes	—
321	C₄×C₈	D₄×C₁₉	1	2	yes	—
322	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
323	C₄×C₈	C₂³×C₁₉	1	2	yes	—
324	C₄×C₈	C₂³×C₁₉	1	2	yes	—
325	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
326	C₁₉	#19627	1	1	yes	characteristic, direct product factor, Sylow
327	C₂⁴	—	4	1	no	—
328	#41	—	4	4	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	—	4	1	no	—
334	C₂×Q₈	—	8	2	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	4	4	no	—
342	C₂×D₄	—	4	1	no	—
343	C₂×D₄	—	4	1	no	—
344	C₂×D₄	—	4	1	no	—
345	C₂×D₄	—	4	1	no	—
346	C₂×D₄	—	4	4	no	—
347	C₂×D₄	—	8	2	no	—
348	C₂²×C₄	—	4	1	no	—
349	C₂²×C₄	—	4	1	no	—
350	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
353	Q₁₆	—	8	4	no	—
354	SD₁₆	—	4	4	no	—
355	D₈	—	8	4	no	—
356	M₁₆	—	2	4	no	—
357	C₂×C₈	—	4	2	no	—
358	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
359	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
360	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
361	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	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	C₂²⋊C₄	—	4	1	no	—
375	C₂²⋊C₄	—	4	1	no	—
376	C₂²⋊C₄	—	4	1	no	—
377	C₄²	—	4	1	no	—
378	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
379	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
380	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
381	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
382	C₂³	—	4	1	no	—
383	C₂³	—	4	2	no	—
384	C₂³	—	8	2	no	—
385	C₂³	—	8	2	no	—
386	C₂³	—	8	2	no	—
387	C₂³	C₁₉×#127	1	1	yes	characteristic
388	Q₈	—	4	2	no	—
389	Q₈	—	4	2	no	—
390	Q₈	—	4	2	no	—
391	Q₈	—	4	4	no	—
392	Q₈	—	8	2	no	—
393	D₄	—	4	4	no	—
394	D₄	—	4	2	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	4	no	—
397	D₄	—	4	2	no	—
398	D₄	—	4	4	no	—
399	D₄	—	8	2	no	—
400	D₄	—	8	2	no	—
401	D₄	—	8	2	no	—
402	D₄	—	8	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	8	2	no	—
410	C₂×C₄	—	8	2	no	—
411	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
412	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
413	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
414	C₂×C₄	C₁₉×#135	1	4	yes	—
415	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
417	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
418	C₈	—	2	4	no	—
419	C₈	—	2	2	no	—
420	C₈	—	2	2	no	—
421	C₈	—	2	4	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	8	1	no	—
425	C₂²	—	8	2	no	—
426	C₂²	—	8	2	no	—
427	C₂²	—	8	1	no	—
428	C₂²	—	8	2	no	—
429	C₂²	—	8	1	no	—
430	C₂²	—	16	4	no	—
431	C₂²	C₁₉×#495	1	2	yes	—
432	C₂²	C₂×C₁₉×#127	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	8	1	no	—
436	C₄	—	8	1	no	—
437	C₄	—	8	2	no	—
438	C₄	—	8	1	no	—
439	C₄	C₁₉×#495	1	2	yes	—
440	C₄	C₂×C₁₉×#135	1	2	yes	—
441	C₄	C₁₉×#575	1	2	yes	—
442	C₄	C₁₉×#576	1	2	yes	—
443	C₂	—	2	2	no	—
444	C₂	—	16	2	no	—
445	C₂	—	16	1	no	—
446	C₂	C₂×C₁₉×#495	1	1	yes	characteristic
447	C₂	C₁₉×#3153	1	1	yes	characteristic
448	C₂	C₁₉×#3155	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3205	C₂
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×#3209	C₂	semidirect
3. C₁₉×#3167	C₂	semidirect
4. C₁₉×#3141	C₂	semidirect
5. C₁₉×#3138	C₂	semidirect
6. C₂×C₁₉×#486	C₂	semidirect
7. C₁₉×#1720	C₂	semidirect
8. C₁₉×#1717	C₂	semidirect
9. C₁₉×#1711	C₂	semidirect
10. C₁₉×#1709	C₂	semidirect
11. C₈×M₁₆×C₁₉	C₂	semidirect
16. C₁₉×#498	C₂²	semidirect
17. C₁₉×#494	C₂²	semidirect
19. C₁₉×#492	C₂²	semidirect
22. C₁₉×#487	C₂²	semidirect
23. C₁₉×#487	C₂²	semidirect
24. C₁₉×#487	C₂²	semidirect
31. C₁₉×#486	C₂²	semidirect
32. C₁₉×#486	C₂²	semidirect
45. C₁₉×#322	C₂²	semidirect
46. C₈²×C₁₉	C₂²	semidirect
157. #19627	C₁₉	direct (N × H)
198. #3209	C₂×C₁₉	semidirect
200. #3167	C₂×C₁₉	semidirect
201. #3141	C₂×C₁₉	semidirect
202. #3138	C₂×C₁₉	semidirect
203. C₂×#486	C₂×C₁₉	semidirect
204. #1720	C₂×C₁₉	semidirect
205. #1717	C₂×C₁₉	semidirect
206. #1711	C₂×C₁₉	semidirect
207. #1709	C₂×C₁₉	semidirect
208. C₈×M₁₆	C₂×C₁₉	semidirect
234. #498	C₂²×C₁₉	semidirect
235. #494	C₂²×C₁₉	semidirect
237. #492	C₂²×C₁₉	semidirect
240. #487	C₂²×C₁₉	semidirect
241. #487	C₂²×C₁₉	semidirect
242. #487	C₂²×C₁₉	semidirect
249. #486	C₂²×C₁₉	semidirect
250. #486	C₂²×C₁₉	semidirect
263. #322	C₂²×C₁₉	semidirect
264. C₈²	C₂²×C₁₉	semidirect
326. C₁₉	#19627	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×#3209	2
C₁₉×#3205	2
C₁₉×#3167	2
C₁₉×#3141	2
C₁₉×#3138	2
C₂×C₁₉×#486	2
C₁₉×#1720	2
C₁₉×#1717	2
C₁₉×#1711	2
C₁₉×#1709	2
C₈×M₁₆×C₁₉	2
#19627	19

Subgroups — C19×#19627 #18025586

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19627 #18025586