Subgroups — C₁₉×#19673 #18025632

Order 4864.

862 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3206	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3205	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3169	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3151	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3141	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×#486	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1721	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1719	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1717	C₂	1	2	yes	maximal, complemented
10	C₁₉×#1717	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
13	C₁₉×#532	C₂²	1	1	yes	characteristic
14	C₁₉×#532	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
17	C₁₉×#500	C₂²	1	1	yes	characteristic, complemented
18	C₁₉×#496	—	2	2	no	—
19	C₁₉×#493	C₂²	1	2	yes	—
20	C₁₉×#493	C₂²	1	2	yes	—
21	C₁₉×#493	C₂²	1	1	yes	characteristic, complemented
22	C₁₉×#492	C₂²	1	2	yes	—
23	C₁₉×#492	C₂²	1	2	yes	complemented
24	C₁₉×#489	—	2	2	no	—
25	C₁₉×#487	C₂²	1	2	yes	complemented
26	C₁₉×#487	C₂²	1	2	yes	complemented
27	C₁₉×#486	—	2	2	no	—
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	1	yes	characteristic, complemented
33	C₁₉×#486	C₂²	1	2	yes	complemented
34	C₁₉×#466	—	2	2	no	—
35	C₁₉×#461	—	2	2	no	—
36	C₁₉×#459	—	2	2	no	—
37	C₁₉×#448	—	2	2	no	—
38	C₁₉×#447	—	2	2	no	—
39	C₄×D₈×C₁₉	—	2	2	no	—
40	C₁₉×#431	C₂²	1	1	yes	characteristic
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	C₁₉×#322	C₂²	1	2	yes	complemented
47	C₂×#41×C₁₉	—	2	1	no	—
48	C₂×#41×C₁₉	—	2	1	no	—
49	C₂²×Q₈×C₁₉	—	2	1	no	—
50	C₂²×D₄×C₁₉	—	2	1	no	—
51	C₂²×D₄×C₁₉	—	2	1	no	—
52	C₂²×D₄×C₁₉	—	2	1	no	—
53	C₁₉×AGL(1,ℤ/8)	—	4	8	no	—
54	C₂×SD₁₆×C₁₉	—	2	4	no	—
55	C₂×SD₁₆×C₁₉	—	2	4	no	—
56	C₂×D₈×C₁₉	—	2	2	no	—
57	C₂×D₈×C₁₉	—	2	4	no	—
58	C₂×D₈×C₁₉	—	2	4	no	—
59	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
60	C₂²×C₈×C₁₉	D₄	1	2	yes	—
61	C₁₉×C₄⋊Q₈	—	2	1	no	—
62	C₁₉×C₄⋊Q₈	—	2	1	no	—
63	C₁₉×C₄⋊Q₈	—	2	1	no	—
64	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
65	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
66	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
67	C₁₉×#127	—	2	1	no	—
68	C₁₉×#127	—	2	1	no	—
69	C₁₉×#127	—	2	1	no	—
70	C₁₉×#127	C₂³	1	2	yes	—
71	C₁₉×#127	C₂³	1	1	yes	characteristic
72	C₁₉×#127	C₂³	1	1	yes	characteristic
73	C₁₉×#124	—	2	1	no	—
74	C₁₉×#124	—	2	1	no	—
75	C₁₉×#121	—	2	1	no	—
76	C₁₉×#121	—	2	1	no	—
77	C₁₉×#121	—	2	1	no	—
78	C₁₉×#121	—	2	1	no	—
79	C₄×D₄×C₁₉	—	2	1	no	—
80	C₄×D₄×C₁₉	—	2	1	no	—
81	C₄×D₄×C₁₉	—	2	1	no	—
82	C₄×D₄×C₁₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
85	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
86	C₁₉×#107	—	2	2	no	—
87	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
88	C₁₉×#103	—	2	4	no	—
89	C₁₉×#103	—	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	2	no	—
95	C₁₉×#102	—	2	4	no	—
96	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
97	C₁₉×#97	D₄	1	2	yes	—
98	C₄×C₈×C₁₉	D₄	1	2	yes	—
99	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₁₉	C₂³	1	2	yes	—
102	C₄×C₈×C₁₉	C₂³	1	2	yes	—
103	C₂⁴×C₁₉	—	4	1	no	—
104	#41×C₁₉	—	4	4	no	—
105	#41×C₁₉	—	4	4	no	—
106	C₂×Q₈×C₁₉	—	2	1	no	—
107	C₂×Q₈×C₁₉	—	2	1	no	—
108	C₂×Q₈×C₁₉	—	2	2	no	—
109	C₂×Q₈×C₁₉	—	4	1	no	—
110	C₂×Q₈×C₁₉	—	8	2	no	—
111	C₂×D₄×C₁₉	—	2	1	no	—
112	C₂×D₄×C₁₉	—	2	1	no	—
113	C₂×D₄×C₁₉	—	2	1	no	—
114	C₂×D₄×C₁₉	—	2	1	no	—
115	C₂×D₄×C₁₉	—	2	1	no	—
116	C₂×D₄×C₁₉	—	2	1	no	—
117	C₂×D₄×C₁₉	—	2	2	no	—
118	C₂×D₄×C₁₉	—	2	2	no	—
119	C₂×D₄×C₁₉	—	2	2	no	—
120	C₂×D₄×C₁₉	—	4	4	no	—
121	C₂×D₄×C₁₉	—	4	1	no	—
122	C₂×D₄×C₁₉	—	4	1	no	—
123	C₂×D₄×C₁₉	—	4	1	no	—
124	C₂×D₄×C₁₉	—	4	1	no	—
125	C₂×D₄×C₁₉	—	4	1	no	—
126	C₂×D₄×C₁₉	—	4	4	no	—
127	C₂×D₄×C₁₉	—	8	2	no	—
128	C₂²×C₄×C₁₉	—	4	1	no	—
129	C₂²×C₄×C₁₉	—	4	1	no	—
130	C₂²×C₄×C₁₉	—	4	1	no	—
131	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
134	SD₁₆×C₁₉	—	4	8	no	—
135	SD₁₆×C₁₉	—	8	4	no	—
136	D₈×C₁₉	—	4	4	no	—
137	D₈×C₁₉	—	4	8	no	—
138	D₈×C₁₉	—	8	4	no	—
139	M₁₆×C₁₉	—	2	4	no	—
140	C₂×C₈×C₁₉	—	4	2	no	—
141	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
142	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
143	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
144	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
145	C₄⋊C₄×C₁₉	—	2	2	no	—
146	C₄⋊C₄×C₁₉	—	2	2	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	—	2	1	no	—
151	C₄⋊C₄×C₁₉	—	4	1	no	—
152	C₄⋊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	—	4	1	no	—
157	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
161	#19673	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
162	C₂³×C₁₉	—	4	1	no	—
163	C₂³×C₁₉	—	4	1	no	—
164	C₂³×C₁₉	—	4	2	no	—
165	C₂³×C₁₉	—	8	2	no	—
166	C₂³×C₁₉	—	8	2	no	—
167	C₂³×C₁₉	—	8	2	no	—
168	C₂³×C₁₉	#127	1	1	yes	characteristic
169	Q₈×C₁₉	—	4	2	no	—
170	Q₈×C₁₉	—	4	2	no	—
171	Q₈×C₁₉	—	4	4	no	—
172	Q₈×C₁₉	—	8	2	no	—
173	D₄×C₁₉	—	4	2	no	—
174	D₄×C₁₉	—	4	4	no	—
175	D₄×C₁₉	—	4	2	no	—
176	D₄×C₁₉	—	4	2	no	—
177	D₄×C₁₉	—	4	2	no	—
178	D₄×C₁₉	—	4	4	no	—
179	D₄×C₁₉	—	4	2	no	—
180	D₄×C₁₉	—	4	4	no	—
181	D₄×C₁₉	—	4	2	no	—
182	D₄×C₁₉	—	8	2	no	—
183	D₄×C₁₉	—	8	2	no	—
184	D₄×C₁₉	—	8	2	no	—
185	D₄×C₁₉	—	8	2	no	—
186	D₄×C₁₉	—	8	2	no	—
187	C₂×C₄×C₁₉	—	2	2	no	—
188	C₂×C₄×C₁₉	—	2	2	no	—
189	C₂×C₄×C₁₉	—	4	1	no	—
190	C₂×C₄×C₁₉	—	4	1	no	—
191	C₂×C₄×C₁₉	—	4	2	no	—
192	C₂×C₄×C₁₉	—	8	2	no	—
193	C₂×C₄×C₁₉	—	8	2	no	—
194	C₂×C₄×C₁₉	—	8	2	no	—
195	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
196	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
197	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
198	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
199	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
202	C₈×C₁₉	—	2	4	no	—
203	C₈×C₁₉	—	2	2	no	—
204	C₈×C₁₉	—	2	2	no	—
205	C₈×C₁₉	—	2	4	no	—
206	#3206	C₂×C₁₉	1	1	yes	characteristic, complemented
207	#3205	C₂×C₁₉	1	1	yes	characteristic, complemented
208	#3169	C₂×C₁₉	1	1	yes	characteristic, complemented
209	#3151	C₂×C₁₉	1	1	yes	characteristic, complemented
210	#3141	C₂×C₁₉	1	1	yes	characteristic, complemented
211	C₂×#486	C₂×C₁₉	1	1	yes	characteristic, complemented
212	#1721	C₂×C₁₉	1	2	yes	complemented
213	#1719	C₂×C₁₉	1	2	yes	complemented
214	#1717	C₂×C₁₉	1	2	yes	complemented
215	#1717	C₂×C₁₉	1	2	yes	complemented
216	#1451	C₂×C₁₉	1	1	yes	characteristic, complemented
217	C₂²×C₁₉	—	2	1	no	—
218	C₂²×C₁₉	—	2	1	no	—
219	C₂²×C₁₉	—	8	1	no	—
220	C₂²×C₁₉	—	8	1	no	—
221	C₂²×C₁₉	—	8	2	no	—
222	C₂²×C₁₉	—	8	2	no	—
223	C₂²×C₁₉	—	8	1	no	—
224	C₂²×C₁₉	—	8	1	no	—
225	C₂²×C₁₉	—	8	2	no	—
226	C₂²×C₁₉	—	8	1	no	—
227	C₂²×C₁₉	—	8	1	no	—
228	C₂²×C₁₉	—	16	4	no	—
229	C₂²×C₁₉	#496	1	2	yes	—
230	C₂²×C₁₉	C₂×#127	1	1	yes	characteristic
231	C₄×C₁₉	—	2	1	no	—
232	C₄×C₁₉	—	2	1	no	—
233	C₄×C₁₉	—	8	1	no	—
234	C₄×C₁₉	—	8	1	no	—
235	C₄×C₁₉	—	8	2	no	—
236	C₄×C₁₉	#496	1	2	yes	—
237	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
238	C₄×C₁₉	#575	1	2	yes	—
239	C₄×C₁₉	#576	1	2	yes	—
240	C₂×AGL(1,ℤ/8)	—	2	2	no	—
241	#532	C₂²×C₁₉	1	1	yes	characteristic
242	#532	C₂²×C₁₉	1	1	yes	characteristic
243	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
244	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
245	#500	C₂²×C₁₉	1	1	yes	characteristic, complemented
246	#496	—	2	2	no	—
247	#493	C₂²×C₁₉	1	2	yes	—
248	#493	C₂²×C₁₉	1	2	yes	—
249	#493	C₂²×C₁₉	1	1	yes	characteristic, complemented
250	#492	C₂²×C₁₉	1	2	yes	—
251	#492	C₂²×C₁₉	1	2	yes	complemented
252	#489	—	2	2	no	—
253	#487	C₂²×C₁₉	1	2	yes	complemented
254	#487	C₂²×C₁₉	1	2	yes	complemented
255	#486	—	2	2	no	—
256	#486	C₂²×C₁₉	1	2	yes	—
257	#486	C₂²×C₁₉	1	2	yes	—
258	#486	C₂²×C₁₉	1	2	yes	—
259	#486	C₂²×C₁₉	1	2	yes	complemented
260	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
261	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
262	#466	—	2	2	no	—
263	#461	—	2	2	no	—
264	#459	—	2	2	no	—
265	#448	—	2	2	no	—
266	#447	—	2	2	no	—
267	C₄×D₈	—	2	2	no	—
268	#431	C₂²×C₁₉	1	1	yes	characteristic
269	#417	—	2	2	no	—
270	C₂×#102	—	2	2	no	—
271	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
272	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
273	#322	C₂²×C₁₉	1	2	yes	complemented
274	#322	C₂²×C₁₉	1	2	yes	complemented
275	C₂×C₁₉	—	2	2	no	—
276	C₂×C₁₉	—	16	1	no	—
277	C₂×C₁₉	—	16	1	no	—
278	C₂×C₁₉	—	16	2	no	—
279	C₂×C₁₉	C₂×#496	1	1	yes	characteristic
280	C₂×C₁₉	#3153	1	1	yes	characteristic
281	C₂×C₁₉	#3155	1	1	yes	characteristic
282	C₂×#41	—	2	1	no	—
283	C₂×#41	—	2	1	no	—
284	C₂²×Q₈	—	2	1	no	—
285	C₂²×D₄	—	2	1	no	—
286	C₂²×D₄	—	2	1	no	—
287	C₂²×D₄	—	2	1	no	—
288	AGL(1,ℤ/8)	—	4	8	no	—
289	C₂×SD₁₆	—	2	4	no	—
290	C₂×SD₁₆	—	2	4	no	—
291	C₂×D₈	—	2	4	no	—
292	C₂×D₈	—	2	2	no	—
293	C₂×D₈	—	2	4	no	—
294	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
295	C₂²×C₈	D₄×C₁₉	1	2	yes	—
296	C₄⋊Q₈	—	2	1	no	—
297	C₄⋊Q₈	—	2	1	no	—
298	C₄⋊Q₈	—	2	1	no	—
299	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
300	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
301	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
302	#127	—	2	1	no	—
303	#127	—	2	1	no	—
304	#127	—	2	1	no	—
305	#127	C₂³×C₁₉	1	2	yes	—
306	#127	C₂³×C₁₉	1	1	yes	characteristic
307	#127	C₂³×C₁₉	1	1	yes	characteristic
308	#124	—	2	1	no	—
309	#124	—	2	1	no	—
310	#121	—	2	1	no	—
311	#121	—	2	1	no	—
312	#121	—	2	1	no	—
313	#121	—	2	1	no	—
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	—	2	1	no	—
317	C₄×D₄	—	2	1	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
321	#107	—	2	2	no	—
322	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
323	#103	—	2	4	no	—
324	#103	—	2	4	no	—
325	#102	—	2	4	no	—
326	#102	—	2	4	no	—
327	#102	—	2	4	no	—
328	#102	—	2	2	no	—
329	#102	—	2	2	no	—
330	#102	—	2	4	no	—
331	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
332	#97	D₄×C₁₉	1	2	yes	—
333	C₄×C₈	D₄×C₁₉	1	2	yes	—
334	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
335	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
336	C₄×C₈	C₂³×C₁₉	1	2	yes	—
337	C₄×C₈	C₂³×C₁₉	1	2	yes	—
338	C₁₉	#19673	1	1	yes	characteristic, direct product factor, Sylow
339	C₂⁴	—	4	1	no	—
340	#41	—	4	4	no	—
341	#41	—	4	4	no	—
342	C₂×Q₈	—	2	1	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	1	no	—
345	C₂×Q₈	—	4	1	no	—
346	C₂×Q₈	—	8	2	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	4	4	no	—
357	C₂×D₄	—	4	1	no	—
358	C₂×D₄	—	4	1	no	—
359	C₂×D₄	—	4	1	no	—
360	C₂×D₄	—	4	1	no	—
361	C₂×D₄	—	4	1	no	—
362	C₂×D₄	—	4	4	no	—
363	C₂×D₄	—	8	2	no	—
364	C₂²×C₄	—	4	1	no	—
365	C₂²×C₄	—	4	1	no	—
366	C₂²×C₄	—	4	1	no	—
367	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
370	SD₁₆	—	4	8	no	—
371	SD₁₆	—	8	4	no	—
372	D₈	—	4	4	no	—
373	D₈	—	4	8	no	—
374	D₈	—	8	4	no	—
375	M₁₆	—	2	4	no	—
376	C₂×C₈	—	4	2	no	—
377	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
378	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
379	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
380	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	4	1	no	—
388	C₄⋊C₄	—	4	1	no	—
389	C₂²⋊C₄	—	4	1	no	—
390	C₂²⋊C₄	—	4	1	no	—
391	C₂²⋊C₄	—	4	1	no	—
392	C₂²⋊C₄	—	4	1	no	—
393	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
394	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
395	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
396	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
397	C₂³	—	4	1	no	—
398	C₂³	—	4	1	no	—
399	C₂³	—	4	2	no	—
400	C₂³	—	8	2	no	—
401	C₂³	—	8	2	no	—
402	C₂³	—	8	2	no	—
403	C₂³	C₁₉×#127	1	1	yes	characteristic
404	Q₈	—	4	2	no	—
405	Q₈	—	4	2	no	—
406	Q₈	—	4	4	no	—
407	Q₈	—	8	2	no	—
408	D₄	—	4	2	no	—
409	D₄	—	4	4	no	—
410	D₄	—	4	2	no	—
411	D₄	—	4	2	no	—
412	D₄	—	4	2	no	—
413	D₄	—	4	4	no	—
414	D₄	—	4	2	no	—
415	D₄	—	4	4	no	—
416	D₄	—	4	2	no	—
417	D₄	—	8	2	no	—
418	D₄	—	8	2	no	—
419	D₄	—	8	2	no	—
420	D₄	—	8	2	no	—
421	D₄	—	8	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	8	2	no	—
428	C₂×C₄	—	8	2	no	—
429	C₂×C₄	—	8	2	no	—
430	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
431	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
432	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
433	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	4	yes	—
434	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
435	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
436	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
437	C₈	—	2	4	no	—
438	C₈	—	2	2	no	—
439	C₈	—	2	2	no	—
440	C₈	—	2	4	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	8	1	no	—
444	C₂²	—	8	1	no	—
445	C₂²	—	8	2	no	—
446	C₂²	—	8	2	no	—
447	C₂²	—	8	1	no	—
448	C₂²	—	8	1	no	—
449	C₂²	—	8	2	no	—
450	C₂²	—	8	1	no	—
451	C₂²	—	8	1	no	—
452	C₂²	—	16	4	no	—
453	C₂²	C₁₉×#496	1	2	yes	—
454	C₂²	C₂×C₁₉×#127	1	1	yes	characteristic
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	8	1	no	—
458	C₄	—	8	1	no	—
459	C₄	—	8	2	no	—
460	C₄	C₁₉×#496	1	2	yes	—
461	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
462	C₄	C₁₉×#575	1	2	yes	—
463	C₄	C₁₉×#576	1	2	yes	—
464	C₂	—	2	2	no	—
465	C₂	—	16	2	no	—
466	C₂	—	16	1	no	—
467	C₂	—	16	1	no	—
468	C₂	C₂×C₁₉×#496	1	1	yes	characteristic
469	C₂	C₁₉×#3153	1	1	yes	characteristic
470	C₂	C₁₉×#3155	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
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×#3206	C₂	semidirect
2. C₁₉×#3205	C₂	semidirect
3. C₁₉×#3169	C₂	semidirect
4. C₁₉×#3151	C₂	semidirect
5. C₁₉×#3141	C₂	semidirect
6. C₂×C₁₉×#486	C₂	semidirect
7. C₁₉×#1721	C₂	semidirect
8. C₁₉×#1719	C₂	semidirect
9. C₁₉×#1717	C₂	semidirect
10. C₁₉×#1717	C₂	semidirect
11. C₁₉×#1451	C₂	semidirect
17. C₁₉×#500	C₂²	semidirect
21. C₁₉×#493	C₂²	semidirect
23. C₁₉×#492	C₂²	semidirect
25. C₁₉×#487	C₂²	semidirect
26. C₁₉×#487	C₂²	semidirect
31. C₁₉×#486	C₂²	semidirect
32. C₁₉×#486	C₂²	semidirect
33. C₁₉×#486	C₂²	semidirect
45. C₁₉×#322	C₂²	semidirect
46. C₁₉×#322	C₂²	semidirect
161. #19673	C₁₉	direct (N × H)
206. #3206	C₂×C₁₉	semidirect
207. #3205	C₂×C₁₉	semidirect
208. #3169	C₂×C₁₉	semidirect
209. #3151	C₂×C₁₉	semidirect
210. #3141	C₂×C₁₉	semidirect
211. C₂×#486	C₂×C₁₉	semidirect
212. #1721	C₂×C₁₉	semidirect
213. #1719	C₂×C₁₉	semidirect
214. #1717	C₂×C₁₉	semidirect
215. #1717	C₂×C₁₉	semidirect
216. #1451	C₂×C₁₉	semidirect
245. #500	C₂²×C₁₉	semidirect
249. #493	C₂²×C₁₉	semidirect
251. #492	C₂²×C₁₉	semidirect
253. #487	C₂²×C₁₉	semidirect
254. #487	C₂²×C₁₉	semidirect
259. #486	C₂²×C₁₉	semidirect
260. #486	C₂²×C₁₉	semidirect
261. #486	C₂²×C₁₉	semidirect
273. #322	C₂²×C₁₉	semidirect
274. #322	C₂²×C₁₉	semidirect
338. C₁₉	#19673	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×#3206	2
C₁₉×#3205	2
C₁₉×#3169	2
C₁₉×#3151	2
C₁₉×#3141	2
C₂×C₁₉×#486	2
C₁₉×#1721	2
C₁₉×#1719	2
C₁₉×#1717	2
C₁₉×#1451	2
#19673	19

Subgroups — C19×#19673 #18025632

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19673 #18025632