Subgroups — C₁₉×#18654 #18024613

Order 4864.

904 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3509	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3229	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3039	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1650	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1648	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1546	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1493	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1476	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₉×#137	—	2	1	no	—
11	C₁₉×#557	—	2	1	no	—
12	C₁₉×#557	C₂²	1	2	yes	—
13	C₁₉×#556	—	2	1	no	—
14	C₁₉×#556	C₂²	1	2	yes	—
15	C₁₉×#552	—	2	2	no	—
16	C₁₉×#552	—	2	2	no	—
17	C₁₉×#541	—	2	2	no	—
18	C₁₉×#536	—	2	1	no	—
19	C₁₉×#533	—	2	1	no	—
20	C₁₉×#533	—	2	1	no	—
21	C₁₉×#533	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₁₉×#519	—	2	1	no	—
25	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#500	—	2	2	no	—
27	C₁₉×#500	C₂²	1	4	yes	—
28	C₁₉×#498	—	2	1	no	—
29	C₁₉×#487	—	2	1	no	—
30	C₁₉×#483	—	2	2	no	—
31	C₁₉×#475	C₂²	1	4	yes	—
32	C₁₉×#462	—	2	1	no	—
33	C₁₉×#462	C₂²	1	2	yes	—
34	C₁₉×#461	—	2	1	no	—
35	C₁₉×#461	C₂²	1	2	yes	—
36	C₁₉×#431	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#107	—	2	2	no	—
38	C₁₉×#423	C₂²	1	1	yes	characteristic
39	C₁₉×#419	—	2	1	no	—
40	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
41	C₁₉×#332	C₂²	1	4	yes	—
42	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
43	C₁₉×Q₈⋊C₈	C₂²	1	4	yes	—
44	C₁₉×D₄⋊C₈	C₂²	1	2	yes	—
45	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
46	C₂²×Q₈×C₁₉	—	2	1	no	—
47	C₂²×Q₈×C₁₉	—	2	1	no	—
48	C₁₉×#137	—	4	4	no	—
49	C₂×Q₁₆×C₁₉	—	2	2	no	—
50	C₂×SD₁₆×C₁₉	—	2	2	no	—
51	C₂×M₁₆×C₁₉	—	2	1	no	—
52	C₂²×C₈×C₁₉	—	2	1	no	—
53	C₁₉×C₄⋊Q₈	—	2	2	no	—
54	C₁₉×C₄⋊Q₈	—	2	1	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	—	2	1	no	—
59	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
60	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
61	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
62	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
63	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
64	C₁₉×#126	—	2	4	no	—
65	C₁₉×#126	—	2	4	no	—
66	C₁₉×#125	—	2	2	no	—
67	C₁₉×#125	—	2	4	no	—
68	C₁₉×#125	—	2	2	no	—
69	C₁₉×#125	—	2	4	no	—
70	C₁₉×#125	—	2	1	no	—
71	C₁₉×#124	—	2	2	no	—
72	C₁₉×#123	—	2	4	no	—
73	C₁₉×C₂²⋊Q₈	—	2	2	no	—
74	C₁₉×C₂²⋊Q₈	—	2	2	no	—
75	C₁₉×C₂²⋊Q₈	—	2	2	no	—
76	C₁₉×C₂²⋊Q₈	—	2	2	no	—
77	C₁₉×C₂²⋊Q₈	—	2	1	no	—
78	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
79	C₄×Q₈×C₁₉	—	2	2	no	—
80	C₄×Q₈×C₁₉	—	2	2	no	—
81	C₄×Q₈×C₁₉	—	2	2	no	—
82	C₄×Q₈×C₁₉	—	2	2	no	—
83	C₄×Q₈×C₁₉	—	2	2	no	—
84	C₄×Q₈×C₁₉	—	2	2	no	—
85	C₄×Q₈×C₁₉	—	2	1	no	—
86	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
87	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
88	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
89	C₄×D₄×C₁₉	—	2	1	no	—
90	C₄×D₄×C₁₉	—	2	1	no	—
91	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
92	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
93	C₁₉×#117	—	2	4	no	—
94	C₁₉×#117	—	2	2	no	—
95	C₁₉×#117	—	2	1	no	—
96	C₁₉×#117	—	2	2	no	—
97	C₁₉×#117	—	2	1	no	—
98	C₁₉×#117	D₄	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
101	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
102	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
103	C₂×C₄²×C₁₉	—	2	1	no	—
104	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
105	C₁₉×#107	—	2	8	no	—
106	C₁₉×#106	—	2	4	no	—
107	C₁₉×C₄⋊C₈	—	2	1	no	—
108	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
109	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
110	C₁₉×#103	—	2	4	no	—
111	C₁₉×#103	—	2	2	no	—
112	C₁₉×#103	—	2	2	no	—
113	C₁₉×C₂²⋊C₈	—	2	1	no	—
114	C₄×C₈×C₁₉	—	2	1	no	—
115	C₄×C₈×C₁₉	—	2	1	no	—
116	C₄×C₈×C₁₉	C₂³	1	2	yes	—
117	#41×C₁₉	—	2	2	no	—
118	#41×C₁₉	—	2	2	no	—
119	C₂×Q₈×C₁₉	—	2	1	no	—
120	C₂×Q₈×C₁₉	—	2	2	no	—
121	C₂×Q₈×C₁₉	—	2	2	no	—
122	C₂×Q₈×C₁₉	—	2	2	no	—
123	C₂×Q₈×C₁₉	—	4	1	no	—
124	C₂×Q₈×C₁₉	—	4	2	no	—
125	C₂×Q₈×C₁₉	—	4	2	no	—
126	C₂×Q₈×C₁₉	—	4	2	no	—
127	C₂×Q₈×C₁₉	—	4	2	no	—
128	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
129	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₂×D₄×C₁₉	—	2	1	no	—
131	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	—	2	1	no	—
134	C₂²×C₄×C₁₉	—	2	1	no	—
135	C₂²×C₄×C₁₉	—	2	1	no	—
136	C₂²×C₄×C₁₉	—	4	1	no	—
137	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
140	Q₁₆×C₁₉	—	4	4	no	—
141	SD₁₆×C₁₉	—	4	4	no	—
142	M₁₆×C₁₉	—	4	2	no	—
143	C₂×C₈×C₁₉	—	2	4	no	—
144	C₂×C₈×C₁₉	—	2	2	no	—
145	C₂×C₈×C₁₉	—	2	2	no	—
146	C₂×C₈×C₁₉	—	2	2	no	—
147	C₄⋊C₄×C₁₉	—	2	4	no	—
148	C₄⋊C₄×C₁₉	—	2	4	no	—
149	C₄⋊C₄×C₁₉	—	2	4	no	—
150	C₄⋊C₄×C₁₉	—	2	4	no	—
151	C₄⋊C₄×C₁₉	—	2	2	no	—
152	C₄⋊C₄×C₁₉	—	2	2	no	—
153	C₄⋊C₄×C₁₉	—	2	1	no	—
154	C₄⋊C₄×C₁₉	—	2	1	no	—
155	C₄⋊C₄×C₁₉	—	2	1	no	—
156	C₄⋊C₄×C₁₉	—	2	1	no	—
157	C₄⋊C₄×C₁₉	—	2	2	no	—
158	C₄⋊C₄×C₁₉	—	2	2	no	—
159	C₄⋊C₄×C₁₉	—	2	1	no	—
160	C₄⋊C₄×C₁₉	—	2	2	no	—
161	C₄⋊C₄×C₁₉	—	2	2	no	—
162	C₄⋊C₄×C₁₉	—	2	2	no	—
163	C₄⋊C₄×C₁₉	—	4	1	no	—
164	C₄⋊C₄×C₁₉	—	4	1	no	—
165	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
166	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
167	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂²⋊C₄×C₁₉	—	2	4	no	—
170	C₂²⋊C₄×C₁₉	—	2	4	no	—
171	C₂²⋊C₄×C₁₉	—	2	1	no	—
172	C₂²⋊C₄×C₁₉	—	2	2	no	—
173	C₂²⋊C₄×C₁₉	—	2	1	no	—
174	C₂²⋊C₄×C₁₉	—	2	1	no	—
175	C₄²×C₁₉	—	2	4	no	—
176	C₄²×C₁₉	—	2	4	no	—
177	C₄²×C₁₉	—	2	1	no	—
178	C₄²×C₁₉	—	2	1	no	—
179	C₄²×C₁₉	—	2	1	no	—
180	C₄²×C₁₉	—	2	2	no	—
181	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
184	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
185	#18654	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂³×C₁₉	—	2	1	no	—
187	C₂³×C₁₉	#120	1	1	yes	characteristic
188	Q₈×C₁₉	—	2	1	no	—
189	Q₈×C₁₉	—	2	1	no	—
190	Q₈×C₁₉	—	2	4	no	—
191	Q₈×C₁₉	—	4	2	no	—
192	Q₈×C₁₉	—	4	2	no	—
193	Q₈×C₁₉	—	4	4	no	—
194	Q₈×C₁₉	—	4	2	no	—
195	Q₈×C₁₉	—	4	2	no	—
196	Q₈×C₁₉	—	4	2	no	—
197	Q₈×C₁₉	—	8	2	no	—
198	D₄×C₁₉	—	2	1	no	—
199	D₄×C₁₉	—	2	1	no	—
200	D₄×C₁₉	—	4	2	no	—
201	C₂×C₄×C₁₉	—	2	2	no	—
202	C₂×C₄×C₁₉	—	2	2	no	—
203	C₂×C₄×C₁₉	—	2	1	no	—
204	C₂×C₄×C₁₉	—	2	1	no	—
205	C₂×C₄×C₁₉	—	2	2	no	—
206	C₂×C₄×C₁₉	—	2	2	no	—
207	C₂×C₄×C₁₉	—	2	4	no	—
208	C₂×C₄×C₁₉	—	2	1	no	—
209	C₂×C₄×C₁₉	—	4	4	no	—
210	C₂×C₄×C₁₉	—	4	2	no	—
211	C₂×C₄×C₁₉	—	4	2	no	—
212	C₂×C₄×C₁₉	—	4	2	no	—
213	C₂×C₄×C₁₉	—	4	2	no	—
214	C₂×C₄×C₁₉	—	8	2	no	—
215	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
216	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
217	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
218	C₂×C₄×C₁₉	#135	1	2	yes	—
219	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
220	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
223	C₈×C₁₉	—	2	4	no	—
224	C₈×C₁₉	—	4	2	no	—
225	C₈×C₁₉	—	4	2	no	—
226	#3509	C₂×C₁₉	1	1	yes	characteristic
227	#3229	C₂×C₁₉	1	1	yes	characteristic, complemented
228	C₂×#500	C₂×C₁₉	1	1	yes	characteristic, complemented
229	#3039	C₂×C₁₉	1	1	yes	characteristic
230	#1650	C₂×C₁₉	1	4	yes	complemented
231	#1648	C₂×C₁₉	1	4	yes	complemented
232	#1546	C₂×C₁₉	1	1	yes	characteristic, complemented
233	#1493	C₂×C₁₉	1	1	yes	characteristic, complemented
234	#1476	C₂×C₁₉	1	1	yes	characteristic
235	C₂²×C₁₉	—	2	1	no	—
236	C₂²×C₁₉	—	2	1	no	—
237	C₂²×C₁₉	—	4	1	no	—
238	C₂²×C₁₉	—	4	1	no	—
239	C₂²×C₁₉	—	4	1	no	—
240	C₂²×C₁₉	#449	1	2	yes	—
241	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
242	C₄×C₁₉	—	2	1	no	—
243	C₄×C₁₉	—	2	1	no	—
244	C₄×C₁₉	—	4	1	no	—
245	C₄×C₁₉	—	4	4	no	—
246	C₄×C₁₉	—	4	1	no	—
247	C₄×C₁₉	—	4	2	no	—
248	C₄×C₁₉	—	4	1	no	—
249	C₄×C₁₉	—	4	2	no	—
250	C₄×C₁₉	—	8	2	no	—
251	C₄×C₁₉	#449	1	2	yes	—
252	C₄×C₁₉	#456	1	2	yes	—
253	C₄×C₁₉	C₂×#135	1	1	yes	characteristic
254	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
255	C₄×C₁₉	#578	1	2	yes	—
256	C₂×#137	—	2	1	no	—
257	#557	—	2	1	no	—
258	#557	C₂²×C₁₉	1	2	yes	—
259	#556	—	2	1	no	—
260	#556	C₂²×C₁₉	1	2	yes	—
261	#552	—	2	2	no	—
262	#552	—	2	2	no	—
263	#541	—	2	2	no	—
264	#536	—	2	1	no	—
265	#533	—	2	1	no	—
266	#533	—	2	1	no	—
267	#533	C₂²×C₁₉	1	1	yes	characteristic
268	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
269	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
270	#519	—	2	1	no	—
271	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
272	#500	—	2	2	no	—
273	#500	C₂²×C₁₉	1	4	yes	—
274	#498	—	2	1	no	—
275	#487	—	2	1	no	—
276	#483	—	2	2	no	—
277	#475	C₂²×C₁₉	1	4	yes	—
278	#462	—	2	1	no	—
279	#462	C₂²×C₁₉	1	2	yes	—
280	#461	—	2	1	no	—
281	#461	C₂²×C₁₉	1	2	yes	—
282	#431	C₂²×C₁₉	1	1	yes	characteristic
283	C₂×#107	—	2	2	no	—
284	#423	C₂²×C₁₉	1	1	yes	characteristic
285	#419	—	2	1	no	—
286	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
287	#332	C₂²×C₁₉	1	4	yes	—
288	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
289	Q₈⋊C₈	C₂²×C₁₉	1	4	yes	—
290	D₄⋊C₈	C₂²×C₁₉	1	2	yes	—
291	C₂×C₁₉	—	2	2	no	—
292	C₂×C₁₉	—	8	1	no	—
293	C₂×C₁₉	C₂×#449	1	1	yes	characteristic
294	C₂×C₁₉	#3011	1	1	yes	characteristic
295	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
296	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
297	C₂²×Q₈	—	2	1	no	—
298	C₂²×Q₈	—	2	1	no	—
299	#137	—	4	4	no	—
300	C₂×Q₁₆	—	2	2	no	—
301	C₂×SD₁₆	—	2	2	no	—
302	C₂×M₁₆	—	2	1	no	—
303	C₂²×C₈	—	2	1	no	—
304	C₄⋊Q₈	—	2	2	no	—
305	C₄⋊Q₈	—	2	1	no	—
306	C₄⋊Q₈	—	2	1	no	—
307	C₄⋊Q₈	—	2	1	no	—
308	C₄⋊Q₈	—	2	1	no	—
309	C₄⋊Q₈	—	2	1	no	—
310	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
311	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
312	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
313	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
314	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
315	#126	—	2	4	no	—
316	#126	—	2	4	no	—
317	#125	—	2	2	no	—
318	#125	—	2	4	no	—
319	#125	—	2	2	no	—
320	#125	—	2	4	no	—
321	#125	—	2	1	no	—
322	#124	—	2	2	no	—
323	#123	—	2	4	no	—
324	C₂²⋊Q₈	—	2	2	no	—
325	C₂²⋊Q₈	—	2	2	no	—
326	C₂²⋊Q₈	—	2	2	no	—
327	C₂²⋊Q₈	—	2	2	no	—
328	C₂²⋊Q₈	—	2	1	no	—
329	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
330	C₄×Q₈	—	2	2	no	—
331	C₄×Q₈	—	2	2	no	—
332	C₄×Q₈	—	2	2	no	—
333	C₄×Q₈	—	2	2	no	—
334	C₄×Q₈	—	2	2	no	—
335	C₄×Q₈	—	2	2	no	—
336	C₄×Q₈	—	2	1	no	—
337	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
338	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
339	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
340	C₄×D₄	—	2	1	no	—
341	C₄×D₄	—	2	1	no	—
342	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
343	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
344	#117	—	2	4	no	—
345	#117	—	2	2	no	—
346	#117	—	2	1	no	—
347	#117	—	2	2	no	—
348	#117	—	2	1	no	—
349	#117	D₄×C₁₉	1	1	yes	characteristic
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
354	C₂×C₄²	—	2	1	no	—
355	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
356	#107	—	2	8	no	—
357	#106	—	2	4	no	—
358	C₄⋊C₈	—	2	1	no	—
359	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
360	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
361	#103	—	2	4	no	—
362	#103	—	2	2	no	—
363	#103	—	2	2	no	—
364	C₂²⋊C₈	—	2	1	no	—
365	C₄×C₈	—	2	1	no	—
366	C₄×C₈	—	2	1	no	—
367	C₄×C₈	C₂³×C₁₉	1	2	yes	—
368	C₁₉	#18654	1	1	yes	characteristic, direct product factor, Sylow
369	#41	—	2	2	no	—
370	#41	—	2	2	no	—
371	C₂×Q₈	—	2	1	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	4	1	no	—
376	C₂×Q₈	—	4	2	no	—
377	C₂×Q₈	—	4	2	no	—
378	C₂×Q₈	—	4	2	no	—
379	C₂×Q₈	—	4	2	no	—
380	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
381	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	4	1	no	—
389	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
392	Q₁₆	—	4	4	no	—
393	SD₁₆	—	4	4	no	—
394	M₁₆	—	4	2	no	—
395	C₂×C₈	—	2	4	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₄⋊C₄	—	2	4	no	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	4	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	4	1	no	—
416	C₄⋊C₄	—	4	1	no	—
417	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
418	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
419	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
420	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
421	C₂²⋊C₄	—	2	4	no	—
422	C₂²⋊C₄	—	2	4	no	—
423	C₂²⋊C₄	—	2	1	no	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	—	2	1	no	—
426	C₂²⋊C₄	—	2	1	no	—
427	C₄²	—	2	4	no	—
428	C₄²	—	2	4	no	—
429	C₄²	—	2	1	no	—
430	C₄²	—	2	1	no	—
431	C₄²	—	2	1	no	—
432	C₄²	—	2	2	no	—
433	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
434	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
435	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
436	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
437	C₂³	—	2	1	no	—
438	C₂³	C₁₉×#120	1	1	yes	characteristic
439	Q₈	—	2	1	no	—
440	Q₈	—	2	1	no	—
441	Q₈	—	2	4	no	—
442	Q₈	—	4	4	no	—
443	Q₈	—	4	2	no	—
444	Q₈	—	4	2	no	—
445	Q₈	—	4	2	no	—
446	Q₈	—	4	2	no	—
447	Q₈	—	4	2	no	—
448	Q₈	—	8	2	no	—
449	D₄	—	2	1	no	—
450	D₄	—	2	1	no	—
451	D₄	—	4	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	4	4	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	8	2	no	—
466	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
467	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
468	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
469	C₂×C₄	C₁₉×#135	1	2	yes	—
470	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
471	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
472	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
473	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
474	C₈	—	2	4	no	—
475	C₈	—	4	2	no	—
476	C₈	—	4	2	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	4	1	no	—
480	C₂²	—	4	1	no	—
481	C₂²	—	4	1	no	—
482	C₂²	C₁₉×#449	1	2	yes	—
483	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
484	C₄	—	2	1	no	—
485	C₄	—	2	1	no	—
486	C₄	—	4	1	no	—
487	C₄	—	4	4	no	—
488	C₄	—	4	1	no	—
489	C₄	—	4	2	no	—
490	C₄	—	4	1	no	—
491	C₄	—	4	2	no	—
492	C₄	—	8	2	no	—
493	C₄	C₁₉×#449	1	2	yes	—
494	C₄	C₁₉×#456	1	2	yes	—
495	C₄	C₂×C₁₉×#135	1	1	yes	characteristic
496	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
497	C₄	C₁₉×#578	1	2	yes	—
498	C₂	—	2	2	no	—
499	C₂	—	8	1	no	—
500	C₂	C₂×C₁₉×#449	1	1	yes	characteristic
501	C₂	C₁₉×#3011	1	1	yes	characteristic
502	C₂	C₂×C₁₉×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂×#41×C₁₉	D₄
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×#3229	C₂	semidirect
3. C₂×C₁₉×#500	C₂	semidirect
5. C₁₉×#1650	C₂	semidirect
6. C₁₉×#1648	C₂	semidirect
7. C₁₉×#1546	C₂	semidirect
8. C₁₉×#1493	C₂	semidirect
185. #18654	C₁₉	direct (N × H)
227. #3229	C₂×C₁₉	semidirect
228. C₂×#500	C₂×C₁₉	semidirect
230. #1650	C₂×C₁₉	semidirect
231. #1648	C₂×C₁₉	semidirect
232. #1546	C₂×C₁₉	semidirect
233. #1493	C₂×C₁₉	semidirect
368. C₁₉	#18654	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×#3509	2
C₁₉×#3229	2
C₂×C₁₉×#500	2
C₁₉×#3039	2
C₁₉×#1650	2
C₁₉×#1648	2
C₁₉×#1546	2
C₁₉×#1493	2
C₁₉×#1476	2
#18654	19

Subgroups — C19×#18654 #18024613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18654 #18024613