Subgroups — C₁₉×#18160 #18024119

Order 4864.

976 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3461	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3114	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2536	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1611	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1610	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1609	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1599	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1598	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1597	C₂	1	2	yes	maximal, complemented
10	C₁₉×#1512	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1467	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#544	C₂²	1	1	yes	characteristic
13	C₁₉×#542	—	2	2	no	—
14	C₁₉×#541	—	2	2	no	—
15	C₁₉×#539	—	2	1	no	—
16	C₁₉×#539	C₂²	1	2	yes	—
17	C₁₉×#537	C₂²	1	1	yes	characteristic
18	C₁₉×#536	—	2	1	no	—
19	C₁₉×#533	—	2	2	no	—
20	C₁₉×#529	—	2	2	no	—
21	C₁₉×#529	—	2	1	no	—
22	C₁₉×#529	C₂²	1	2	yes	—
23	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
24	C₄×#41×C₁₉	—	2	1	no	—
25	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#483	C₂²	1	2	yes	—
28	C₁₉×#480	C₂²	1	2	yes	—
29	C₁₉×#478	—	2	2	no	—
30	C₁₉×#463	—	2	2	no	—
31	C₁₉×#450	C₂²	1	2	yes	—
32	C₁₉×#447	C₂²	1	2	yes	—
33	C₁₉×#442	—	2	2	no	—
34	C₁₉×#440	—	2	2	no	—
35	C₁₉×#432	C₂²	1	2	yes	—
36	C₁₉×#398	C₂²	1	1	yes	characteristic
37	C₁₉×#398	C₂²	1	1	yes	characteristic
38	C₁₉×#394	C₂²	1	1	yes	characteristic
39	C₁₉×#394	C₂²	1	1	yes	characteristic
40	C₁₉×#388	—	2	1	no	—
41	C₁₉×#388	—	2	1	no	—
42	C₁₉×#382	C₂²	1	1	yes	characteristic
43	C₁₉×#380	—	2	1	no	—
44	C₁₉×#328	C₂²	1	2	yes	—
45	C₁₉×#328	C₂²	1	2	yes	—
46	C₁₉×#327	C₂²	1	2	yes	—
47	C₁₉×#327	C₂²	1	2	yes	—
48	C₁₉×#324	C₂²	1	2	yes	—
49	C₁₉×#324	C₂²	1	1	yes	characteristic
50	C₁₉×#324	C₂²	1	1	yes	characteristic
51	C₂×#41×C₁₉	—	2	1	no	—
52	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
53	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₁₉	—	2	1	no	—
55	C₂×SD₁₆×C₁₉	—	2	2	no	—
56	C₂×D₈×C₁₉	—	2	2	no	—
57	C₁₉×C₄⋊Q₈	—	2	2	no	—
58	C₁₉×C₄⋊Q₈	—	2	2	no	—
59	C₁₉×#126	—	2	2	no	—
60	C₁₉×#126	—	2	2	no	—
61	C₁₉×#126	—	2	2	no	—
62	C₁₉×#126	—	2	2	no	—
63	C₁₉×#125	—	2	1	no	—
64	C₁₉×#125	—	2	2	no	—
65	C₁₉×#125	—	2	2	no	—
66	C₁₉×#125	—	2	2	no	—
67	C₁₉×#125	D₄	1	2	yes	—
68	C₁₉×#124	—	2	2	no	—
69	C₁₉×#124	—	2	1	no	—
70	C₁₉×#124	D₄	1	2	yes	—
71	C₁₉×#123	—	2	2	no	—
72	C₁₉×#123	—	2	2	no	—
73	C₁₉×#123	—	2	2	no	—
74	C₁₉×#123	—	2	2	no	—
75	C₁₉×C₂²⋊Q₈	—	2	2	no	—
76	C₁₉×C₂²⋊Q₈	—	2	2	no	—
77	C₁₉×C₂²⋊Q₈	—	2	2	no	—
78	C₁₉×C₂²⋊Q₈	—	2	2	no	—
79	C₁₉×C₂²⋊Q₈	—	2	1	no	—
80	C₁₉×C₂²⋊Q₈	—	2	2	no	—
81	C₁₉×C₂²⋊Q₈	—	4	4	no	—
82	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
83	C₁₉×#121	—	2	2	no	—
84	C₁₉×#121	—	2	1	no	—
85	C₁₉×#121	C₂³	1	2	yes	—
86	C₄×Q₈×C₁₉	—	2	1	no	—
87	C₄×Q₈×C₁₉	—	2	1	no	—
88	C₄×Q₈×C₁₉	—	2	1	no	—
89	C₄×Q₈×C₁₉	—	2	2	no	—
90	C₄×Q₈×C₁₉	—	2	2	no	—
91	C₄×Q₈×C₁₉	D₄	1	2	yes	—
92	C₄×D₄×C₁₉	—	2	1	no	—
93	C₄×D₄×C₁₉	—	2	1	no	—
94	C₄×D₄×C₁₉	—	2	1	no	—
95	C₄×D₄×C₁₉	—	2	2	no	—
96	C₄×D₄×C₁₉	—	2	2	no	—
97	C₄×D₄×C₁₉	—	2	2	no	—
98	C₄×D₄×C₁₉	—	2	2	no	—
99	C₄×D₄×C₁₉	D₄	1	2	yes	—
100	C₁₉×#117	—	2	2	no	—
101	C₁₉×#117	—	2	2	no	—
102	C₁₉×#117	—	2	1	no	—
103	C₁₉×#117	—	2	2	no	—
104	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
105	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
106	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
111	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
112	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
116	C₂×C₄²×C₁₉	—	2	2	no	—
117	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
118	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
119	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
120	C₁₉×#107	—	2	2	no	—
121	C₁₉×#106	—	2	2	no	—
122	C₁₉×C₄⋊C₈	—	2	2	no	—
123	C₁₉×#103	—	2	2	no	—
124	C₁₉×#102	—	2	2	no	—
125	C₁₉×#102	—	2	2	no	—
126	C₁₉×#102	—	2	2	no	—
127	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
128	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
129	C₁₉×#97	—	2	2	no	—
130	C₁₉×#95	—	2	1	no	—
131	C₁₉×#95	—	2	1	no	—
132	C₁₉×#95	—	2	1	no	—
133	C₁₉×#95	C₂³	1	1	yes	characteristic
134	C₁₉×#95	C₂³	1	1	yes	characteristic
135	C₂⁴×C₁₉	—	2	1	no	—
136	#41×C₁₉	—	4	2	no	—
137	#41×C₁₉	—	4	2	no	—
138	C₂×Q₈×C₁₉	—	2	1	no	—
139	C₂×Q₈×C₁₉	—	2	1	no	—
140	C₂×Q₈×C₁₉	—	2	2	no	—
141	C₂×Q₈×C₁₉	—	2	2	no	—
142	C₂×Q₈×C₁₉	—	4	1	no	—
143	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
144	C₂×D₄×C₁₉	—	2	1	no	—
145	C₂×D₄×C₁₉	—	2	2	no	—
146	C₂×D₄×C₁₉	—	2	1	no	—
147	C₂×D₄×C₁₉	—	2	2	no	—
148	C₂×D₄×C₁₉	—	4	2	no	—
149	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₁₉	—	2	2	no	—
151	C₂²×C₄×C₁₉	—	2	2	no	—
152	C₂²×C₄×C₁₉	—	2	2	no	—
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	C₂²×C₄×C₁₉	—	2	1	no	—
155	C₂²×C₄×C₁₉	—	2	1	no	—
156	C₂²×C₄×C₁₉	—	4	2	no	—
157	C₂²×C₄×C₁₉	—	4	2	no	—
158	C₂²×C₄×C₁₉	—	4	2	no	—
159	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
166	SD₁₆×C₁₉	—	4	4	no	—
167	D₈×C₁₉	—	4	4	no	—
168	C₂×C₈×C₁₉	—	2	2	no	—
169	C₂×C₈×C₁₉	—	2	2	no	—
170	C₄⋊C₄×C₁₉	—	2	1	no	—
171	C₄⋊C₄×C₁₉	—	2	2	no	—
172	C₄⋊C₄×C₁₉	—	2	1	no	—
173	C₄⋊C₄×C₁₉	—	2	2	no	—
174	C₄⋊C₄×C₁₉	—	2	2	no	—
175	C₄⋊C₄×C₁₉	—	2	1	no	—
176	C₄⋊C₄×C₁₉	—	2	1	no	—
177	C₄⋊C₄×C₁₉	—	2	2	no	—
178	C₄⋊C₄×C₁₉	—	2	2	no	—
179	C₄⋊C₄×C₁₉	—	2	2	no	—
180	C₄⋊C₄×C₁₉	—	2	2	no	—
181	C₄⋊C₄×C₁₉	—	2	2	no	—
182	C₄⋊C₄×C₁₉	—	2	2	no	—
183	C₄⋊C₄×C₁₉	—	2	2	no	—
184	C₄⋊C₄×C₁₉	—	2	2	no	—
185	C₄⋊C₄×C₁₉	—	2	2	no	—
186	C₄⋊C₄×C₁₉	—	4	2	no	—
187	C₄⋊C₄×C₁₉	—	4	2	no	—
188	C₄⋊C₄×C₁₉	—	4	2	no	—
189	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
190	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
191	C₂²⋊C₄×C₁₉	—	2	2	no	—
192	C₂²⋊C₄×C₁₉	—	2	2	no	—
193	C₂²⋊C₄×C₁₉	—	2	2	no	—
194	C₂²⋊C₄×C₁₉	—	2	2	no	—
195	C₂²⋊C₄×C₁₉	—	2	2	no	—
196	C₂²⋊C₄×C₁₉	—	2	2	no	—
197	C₂²⋊C₄×C₁₉	—	2	2	no	—
198	C₂²⋊C₄×C₁₉	—	2	2	no	—
199	C₂²⋊C₄×C₁₉	—	2	2	no	—
200	C₂²⋊C₄×C₁₉	—	4	2	no	—
201	C₂²⋊C₄×C₁₉	—	4	2	no	—
202	C₂²⋊C₄×C₁₉	—	4	2	no	—
203	C₂²⋊C₄×C₁₉	—	4	1	no	—
204	C₂²⋊C₄×C₁₉	—	4	1	no	—
205	C₂²⋊C₄×C₁₉	—	4	2	no	—
206	C₄²×C₁₉	—	2	2	no	—
207	C₄²×C₁₉	—	2	2	no	—
208	C₄²×C₁₉	—	2	1	no	—
209	C₄²×C₁₉	—	2	2	no	—
210	C₄²×C₁₉	—	2	1	no	—
211	C₄²×C₁₉	—	2	1	no	—
212	C₄²×C₁₉	—	2	1	no	—
213	C₄²×C₁₉	C₂×D₄	1	2	yes	—
214	C₄²×C₁₉	C₂×D₄	1	2	yes	—
215	#18160	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂³×C₁₉	—	2	2	no	—
217	C₂³×C₁₉	—	2	2	no	—
218	C₂³×C₁₉	—	4	1	no	—
219	C₂³×C₁₉	—	4	1	no	—
220	C₂³×C₁₉	—	4	1	no	—
221	C₂³×C₁₉	—	4	1	no	—
222	C₂³×C₁₉	—	4	1	no	—
223	C₂³×C₁₉	—	4	1	no	—
224	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
225	Q₈×C₁₉	—	4	4	no	—
226	Q₈×C₁₉	—	4	2	no	—
227	Q₈×C₁₉	—	4	2	no	—
228	Q₈×C₁₉	—	8	1	no	—
229	D₄×C₁₉	—	2	4	no	—
230	D₄×C₁₉	—	4	2	no	—
231	D₄×C₁₉	—	4	2	no	—
232	D₄×C₁₉	—	4	2	no	—
233	D₄×C₁₉	—	4	2	no	—
234	D₄×C₁₉	—	4	2	no	—
235	D₄×C₁₉	—	8	1	no	—
236	C₂×C₄×C₁₉	—	2	1	no	—
237	C₂×C₄×C₁₉	—	2	1	no	—
238	C₂×C₄×C₁₉	—	2	1	no	—
239	C₂×C₄×C₁₉	—	2	1	no	—
240	C₂×C₄×C₁₉	—	2	1	no	—
241	C₂×C₄×C₁₉	—	2	2	no	—
242	C₂×C₄×C₁₉	—	2	2	no	—
243	C₂×C₄×C₁₉	—	2	1	no	—
244	C₂×C₄×C₁₉	—	2	1	no	—
245	C₂×C₄×C₁₉	—	2	2	no	—
246	C₂×C₄×C₁₉	—	2	1	no	—
247	C₂×C₄×C₁₉	—	2	1	no	—
248	C₂×C₄×C₁₉	—	4	1	no	—
249	C₂×C₄×C₁₉	—	4	1	no	—
250	C₂×C₄×C₁₉	—	4	4	no	—
251	C₂×C₄×C₁₉	—	4	4	no	—
252	C₂×C₄×C₁₉	—	4	1	no	—
253	C₂×C₄×C₁₉	—	4	1	no	—
254	C₂×C₄×C₁₉	—	4	1	no	—
255	C₂×C₄×C₁₉	—	4	1	no	—
256	C₂×C₄×C₁₉	—	4	1	no	—
257	C₂×C₄×C₁₉	—	4	1	no	—
258	C₂×C₄×C₁₉	—	4	1	no	—
259	C₂×C₄×C₁₉	—	4	1	no	—
260	C₂×C₄×C₁₉	—	4	1	no	—
261	C₂×C₄×C₁₉	—	4	1	no	—
262	C₂×C₄×C₁₉	—	4	1	no	—
263	C₂×C₄×C₁₉	—	8	4	no	—
264	C₂×C₄×C₁₉	—	8	2	no	—
265	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
266	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
267	C₂×C₄×C₁₉	#120	1	2	yes	—
268	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
269	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
270	C₈×C₁₉	—	4	2	no	—
271	C₈×C₁₉	—	4	2	no	—
272	#3461	C₂×C₁₉	1	1	yes	characteristic, complemented
273	#3114	C₂×C₁₉	1	2	yes	complemented
274	#2536	C₂×C₁₉	1	1	yes	characteristic, complemented
275	#1611	C₂×C₁₉	1	1	yes	characteristic, complemented
276	#1610	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#1609	C₂×C₁₉	1	2	yes	complemented
278	#1599	C₂×C₁₉	1	1	yes	characteristic, complemented
279	#1598	C₂×C₁₉	1	1	yes	characteristic
280	#1597	C₂×C₁₉	1	2	yes	complemented
281	#1512	C₂×C₁₉	1	2	yes	complemented
282	#1467	C₂×C₁₉	1	1	yes	characteristic, complemented
283	C₂²×C₁₉	—	2	1	no	—
284	C₂²×C₁₉	—	2	1	no	—
285	C₂²×C₁₉	—	4	2	no	—
286	C₂²×C₁₉	—	4	2	no	—
287	C₂²×C₁₉	—	4	2	no	—
288	C₂²×C₁₉	—	4	2	no	—
289	C₂²×C₁₉	—	4	2	no	—
290	C₂²×C₁₉	—	4	2	no	—
291	C₂²×C₁₉	—	8	1	no	—
292	C₂²×C₁₉	—	8	1	no	—
293	C₂²×C₁₉	—	8	1	no	—
294	C₂²×C₁₉	—	8	1	no	—
295	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
296	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
297	C₂²×C₁₉	#575	1	1	yes	characteristic
298	C₄×C₁₉	—	2	2	no	—
299	C₄×C₁₉	—	2	2	no	—
300	C₄×C₁₉	—	2	1	no	—
301	C₄×C₁₉	—	2	1	no	—
302	C₄×C₁₉	—	2	2	no	—
303	C₄×C₁₉	—	4	1	no	—
304	C₄×C₁₉	—	4	2	no	—
305	C₄×C₁₉	—	4	2	no	—
306	C₄×C₁₉	—	4	1	no	—
307	C₄×C₁₉	—	4	1	no	—
308	C₄×C₁₉	—	4	2	no	—
309	C₄×C₁₉	—	8	1	no	—
310	C₄×C₁₉	—	8	1	no	—
311	C₄×C₁₉	—	8	1	no	—
312	#544	C₂²×C₁₉	1	1	yes	characteristic
313	#542	—	2	2	no	—
314	#541	—	2	2	no	—
315	#539	—	2	1	no	—
316	#539	C₂²×C₁₉	1	2	yes	—
317	#537	C₂²×C₁₉	1	1	yes	characteristic
318	#536	—	2	1	no	—
319	#533	—	2	2	no	—
320	#529	—	2	2	no	—
321	#529	—	2	1	no	—
322	#529	C₂²×C₁₉	1	2	yes	—
323	C₂×C₂²⋊Q₈	—	2	1	no	—
324	C₄×#41	—	2	1	no	—
325	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
326	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
327	#483	C₂²×C₁₉	1	2	yes	—
328	#480	C₂²×C₁₉	1	2	yes	—
329	#478	—	2	2	no	—
330	#463	—	2	2	no	—
331	#450	C₂²×C₁₉	1	2	yes	—
332	#447	C₂²×C₁₉	1	2	yes	—
333	#442	—	2	2	no	—
334	#440	—	2	2	no	—
335	#432	C₂²×C₁₉	1	2	yes	—
336	#398	C₂²×C₁₉	1	1	yes	characteristic
337	#398	C₂²×C₁₉	1	1	yes	characteristic
338	#394	C₂²×C₁₉	1	1	yes	characteristic
339	#394	C₂²×C₁₉	1	1	yes	characteristic
340	#388	—	2	1	no	—
341	#388	—	2	1	no	—
342	#382	C₂²×C₁₉	1	1	yes	characteristic
343	#380	—	2	1	no	—
344	#328	C₂²×C₁₉	1	2	yes	—
345	#328	C₂²×C₁₉	1	2	yes	—
346	#327	C₂²×C₁₉	1	2	yes	—
347	#327	C₂²×C₁₉	1	2	yes	—
348	#324	C₂²×C₁₉	1	2	yes	—
349	#324	C₂²×C₁₉	1	1	yes	characteristic
350	#324	C₂²×C₁₉	1	1	yes	characteristic
351	C₂×C₁₉	—	2	1	no	—
352	C₂×C₁₉	—	2	1	no	—
353	C₂×C₁₉	—	8	2	no	—
354	C₂×C₁₉	—	8	2	no	—
355	C₂×C₁₉	#3006	1	1	yes	characteristic
356	C₂×C₁₉	#3020	1	1	yes	characteristic
357	C₂×C₁₉	#3025	1	1	yes	characteristic
358	C₂×#41	—	2	1	no	—
359	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
360	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
361	C₂³×C₄	—	2	1	no	—
362	C₂×SD₁₆	—	2	2	no	—
363	C₂×D₈	—	2	2	no	—
364	C₄⋊Q₈	—	2	2	no	—
365	C₄⋊Q₈	—	2	2	no	—
366	#126	—	2	2	no	—
367	#126	—	2	2	no	—
368	#126	—	2	2	no	—
369	#126	—	2	2	no	—
370	#125	—	2	1	no	—
371	#125	—	2	2	no	—
372	#125	—	2	2	no	—
373	#125	—	2	2	no	—
374	#125	D₄×C₁₉	1	2	yes	—
375	#124	—	2	2	no	—
376	#124	—	2	1	no	—
377	#124	D₄×C₁₉	1	2	yes	—
378	#123	—	2	2	no	—
379	#123	—	2	2	no	—
380	#123	—	2	2	no	—
381	#123	—	2	2	no	—
382	C₂²⋊Q₈	—	2	2	no	—
383	C₂²⋊Q₈	—	2	2	no	—
384	C₂²⋊Q₈	—	2	2	no	—
385	C₂²⋊Q₈	—	2	2	no	—
386	C₂²⋊Q₈	—	2	1	no	—
387	C₂²⋊Q₈	—	2	2	no	—
388	C₂²⋊Q₈	—	4	4	no	—
389	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
390	#121	—	2	2	no	—
391	#121	—	2	1	no	—
392	#121	C₂³×C₁₉	1	2	yes	—
393	C₄×Q₈	—	2	1	no	—
394	C₄×Q₈	—	2	1	no	—
395	C₄×Q₈	—	2	1	no	—
396	C₄×Q₈	—	2	2	no	—
397	C₄×Q₈	—	2	2	no	—
398	C₄×Q₈	D₄×C₁₉	1	2	yes	—
399	C₄×D₄	—	2	1	no	—
400	C₄×D₄	—	2	1	no	—
401	C₄×D₄	—	2	1	no	—
402	C₄×D₄	—	2	2	no	—
403	C₄×D₄	—	2	2	no	—
404	C₄×D₄	—	2	2	no	—
405	C₄×D₄	—	2	2	no	—
406	C₄×D₄	D₄×C₁₉	1	2	yes	—
407	#117	—	2	2	no	—
408	#117	—	2	2	no	—
409	#117	—	2	1	no	—
410	#117	—	2	2	no	—
411	C₂×C₄⋊C₄	—	2	1	no	—
412	C₂×C₄⋊C₄	—	2	1	no	—
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₂²⋊C₄	—	2	1	no	—
420	C₂×C₂²⋊C₄	—	2	1	no	—
421	C₂×C₂²⋊C₄	—	2	1	no	—
422	C₂×C₂²⋊C₄	—	2	1	no	—
423	C₂×C₄²	—	2	2	no	—
424	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
425	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
426	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
427	#107	—	2	2	no	—
428	#106	—	2	2	no	—
429	C₄⋊C₈	—	2	2	no	—
430	#103	—	2	2	no	—
431	#102	—	2	2	no	—
432	#102	—	2	2	no	—
433	#102	—	2	2	no	—
434	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
435	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
436	#97	—	2	2	no	—
437	#95	—	2	1	no	—
438	#95	—	2	1	no	—
439	#95	—	2	1	no	—
440	#95	C₂³×C₁₉	1	1	yes	characteristic
441	#95	C₂³×C₁₉	1	1	yes	characteristic
442	C₁₉	#18160	1	1	yes	characteristic, direct product factor, Sylow
443	C₂⁴	—	2	1	no	—
444	#41	—	4	2	no	—
445	#41	—	4	2	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	2	2	no	—
449	C₂×Q₈	—	2	2	no	—
450	C₂×Q₈	—	4	1	no	—
451	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	2	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	—	4	2	no	—
457	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	4	2	no	—
465	C₂²×C₄	—	4	2	no	—
466	C₂²×C₄	—	4	2	no	—
467	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
468	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
469	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
470	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
471	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
472	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
473	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
474	SD₁₆	—	4	4	no	—
475	D₈	—	4	4	no	—
476	C₂×C₈	—	2	2	no	—
477	C₂×C₈	—	2	2	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	4	2	no	—
495	C₄⋊C₄	—	4	2	no	—
496	C₄⋊C₄	—	4	2	no	—
497	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
498	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	—	2	2	no	—
501	C₂²⋊C₄	—	2	2	no	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	2	2	no	—
506	C₂²⋊C₄	—	2	2	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	4	2	no	—
509	C₂²⋊C₄	—	4	2	no	—
510	C₂²⋊C₄	—	4	2	no	—
511	C₂²⋊C₄	—	4	1	no	—
512	C₂²⋊C₄	—	4	1	no	—
513	C₂²⋊C₄	—	4	2	no	—
514	C₄²	—	2	2	no	—
515	C₄²	—	2	2	no	—
516	C₄²	—	2	1	no	—
517	C₄²	—	2	2	no	—
518	C₄²	—	2	1	no	—
519	C₄²	—	2	1	no	—
520	C₄²	—	2	1	no	—
521	C₄²	C₂×D₄×C₁₉	1	2	yes	—
522	C₄²	C₂×D₄×C₁₉	1	2	yes	—
523	C₂³	—	2	2	no	—
524	C₂³	—	2	2	no	—
525	C₂³	—	4	1	no	—
526	C₂³	—	4	1	no	—
527	C₂³	—	4	1	no	—
528	C₂³	—	4	1	no	—
529	C₂³	—	4	1	no	—
530	C₂³	—	4	1	no	—
531	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
532	Q₈	—	4	4	no	—
533	Q₈	—	4	2	no	—
534	Q₈	—	4	2	no	—
535	Q₈	—	8	1	no	—
536	D₄	—	2	4	no	—
537	D₄	—	4	2	no	—
538	D₄	—	4	2	no	—
539	D₄	—	4	2	no	—
540	D₄	—	4	2	no	—
541	D₄	—	4	2	no	—
542	D₄	—	8	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	4	no	—
558	C₂×C₄	—	4	4	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	8	4	no	—
571	C₂×C₄	—	8	2	no	—
572	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
573	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
574	C₂×C₄	C₁₉×#120	1	2	yes	—
575	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
576	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
577	C₈	—	4	2	no	—
578	C₈	—	4	2	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	2	no	—
587	C₂²	—	8	1	no	—
588	C₂²	—	8	1	no	—
589	C₂²	—	8	1	no	—
590	C₂²	—	8	1	no	—
591	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
592	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
593	C₂²	C₁₉×#575	1	1	yes	characteristic
594	C₄	—	2	2	no	—
595	C₄	—	2	2	no	—
596	C₄	—	2	1	no	—
597	C₄	—	2	1	no	—
598	C₄	—	2	2	no	—
599	C₄	—	4	1	no	—
600	C₄	—	4	2	no	—
601	C₄	—	4	2	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	1	no	—
604	C₄	—	4	2	no	—
605	C₄	—	8	1	no	—
606	C₄	—	8	1	no	—
607	C₄	—	8	1	no	—
608	C₂	—	2	1	no	—
609	C₂	—	2	1	no	—
610	C₂	—	8	2	no	—
611	C₂	—	8	2	no	—
612	C₂	C₁₉×#3006	1	1	yes	characteristic
613	C₂	C₁₉×#3020	1	1	yes	characteristic
614	C₂	C₁₉×#3025	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#1598	C₂
LCS	G ▷ C₂²×C₄ ▷ 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×#3461	C₂	semidirect
2. C₁₉×#3114	C₂	semidirect
3. C₁₉×#2536	C₂	semidirect
4. C₁₉×#1611	C₂	semidirect
5. C₁₉×#1610	C₂	semidirect
6. C₁₉×#1609	C₂	semidirect
7. C₁₉×#1599	C₂	semidirect
9. C₁₉×#1597	C₂	semidirect
10. C₁₉×#1512	C₂	semidirect
11. C₁₉×#1467	C₂	semidirect
215. #18160	C₁₉	direct (N × H)
272. #3461	C₂×C₁₉	semidirect
273. #3114	C₂×C₁₉	semidirect
274. #2536	C₂×C₁₉	semidirect
275. #1611	C₂×C₁₉	semidirect
276. #1610	C₂×C₁₉	semidirect
277. #1609	C₂×C₁₉	semidirect
278. #1599	C₂×C₁₉	semidirect
280. #1597	C₂×C₁₉	semidirect
281. #1512	C₂×C₁₉	semidirect
282. #1467	C₂×C₁₉	semidirect
442. C₁₉	#18160	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×#3461	2
C₁₉×#3114	2
C₁₉×#2536	2
C₁₉×#1611	2
C₁₉×#1610	2
C₁₉×#1609	2
C₁₉×#1599	2
C₁₉×#1598	2
C₁₉×#1597	2
C₁₉×#1512	2
C₁₉×#1467	2
#18160	19

Subgroups — C19×#18160 #18024119

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18160 #18024119