Subgroups — C₁₉×#18323 #18024282

Order 4864.

1008 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3459	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3196	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2564	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1615	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1614	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1613	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1603	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1602	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1601	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1504	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1465	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#543	C₂²	1	1	yes	characteristic
13	C₁₉×#539	—	2	2	no	—
14	C₁₉×#539	C₂²	1	2	yes	—
15	C₁₉×#538	—	2	2	no	—
16	C₁₉×#538	—	2	1	no	—
17	C₁₉×#534	—	2	1	no	—
18	C₁₉×#534	C₂²	1	1	yes	characteristic
19	C₁₉×#529	—	2	2	no	—
20	C₁₉×#529	—	2	1	no	—
21	C₁₉×#525	—	2	2	no	—
22	C₁₉×#525	C₂²	1	2	yes	—
23	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₄×D₄×C₁₉	—	2	1	no	—
25	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#485	—	2	2	no	—
27	C₁₉×#484	C₂²	1	2	yes	complemented
28	C₁₉×#481	C₂²	1	2	yes	—
29	C₁₉×#470	—	2	2	no	—
30	C₁₉×#468	—	2	2	no	—
31	C₁₉×#452	—	2	2	no	—
32	C₁₉×#451	C₂²	1	2	yes	complemented
33	C₁₉×#448	C₂²	1	2	yes	—
34	C₁₉×#407	C₂²	1	2	yes	complemented
35	C₁₉×#400	C₂²	1	1	yes	characteristic, complemented
36	C₁₉×#399	C₂²	1	1	yes	characteristic
37	C₁₉×#395	C₂²	1	1	yes	characteristic, complemented
38	C₁₉×#393	C₂²	1	1	yes	characteristic
39	C₁₉×#387	—	2	1	no	—
40	C₁₉×#386	—	2	1	no	—
41	C₁₉×#385	—	2	1	no	—
42	C₁₉×#380	—	2	1	no	—
43	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic, complemented
44	C₁₉×#328	C₂²	1	2	yes	complemented
45	C₁₉×#328	C₂²	1	2	yes	complemented
46	C₁₉×#327	C₂²	1	2	yes	—
47	C₁₉×#327	C₂²	1	2	yes	—
48	C₁₉×#324	C₂²	1	2	yes	complemented
49	C₁₉×#323	C₂²	1	1	yes	characteristic
50	C₁₉×#323	C₂²	1	1	yes	characteristic
51	C₂×#41×C₁₉	D₄	1	2	yes	—
52	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
53	C₂²×D₄×C₁₉	—	2	1	no	—
54	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₁₉	—	2	1	no	—
56	C₂³×C₄×C₁₉	—	2	1	no	—
57	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
58	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
59	C₂×Q₁₆×C₁₉	—	2	2	no	—
60	C₂×SD₁₆×C₁₉	—	2	2	no	—
61	C₂×M₁₆×C₁₉	—	2	2	no	—
62	C₁₉×#126	—	2	2	no	—
63	C₁₉×#126	—	2	2	no	—
64	C₁₉×#126	—	2	2	no	—
65	C₁₉×#125	—	2	1	no	—
66	C₁₉×#125	—	2	2	no	—
67	C₁₉×#124	—	2	2	no	—
68	C₁₉×#124	—	2	1	no	—
69	C₁₉×#123	—	2	2	no	—
70	C₁₉×#123	—	2	2	no	—
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	1	no	—
78	C₁₉×C₂²⋊Q₈	—	2	2	no	—
79	C₁₉×C₂²⋊Q₈	—	2	2	no	—
80	C₁₉×C₂²⋊Q₈	—	2	2	no	—
81	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
82	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
83	C₁₉×#121	—	2	2	no	—
84	C₁₉×#121	—	2	2	no	—
85	C₁₉×#121	—	2	2	no	—
86	C₁₉×#121	—	2	1	no	—
87	C₁₉×#121	D₄	1	2	yes	—
88	C₁₉×#121	C₂³	1	2	yes	—
89	C₁₉×#120	—	2	2	no	—
90	C₁₉×#120	—	2	2	no	—
91	C₁₉×#120	—	2	2	no	—
92	C₄×Q₈×C₁₉	—	2	1	no	—
93	C₄×D₄×C₁₉	—	2	2	no	—
94	C₄×D₄×C₁₉	—	2	2	no	—
95	C₄×D₄×C₁₉	—	2	1	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	—	2	2	no	—
100	C₄×D₄×C₁₉	—	2	2	no	—
101	C₁₉×#117	—	2	2	no	—
102	C₁₉×#117	D₄	1	2	yes	—
103	C₂×C₄⋊C₄×C₁₉	—	2	1	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	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
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	D₄	1	1	yes	characteristic
115	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₁₉	—	2	1	no	—
117	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
118	C₁₉×#107	—	2	2	no	—
119	C₁₉×#106	—	2	2	no	—
120	C₁₉×#103	—	2	2	no	—
121	C₁₉×#103	—	2	2	no	—
122	C₁₉×#103	—	2	2	no	—
123	C₁₉×#102	—	2	2	no	—
124	C₁₉×C₂²⋊C₈	—	2	2	no	—
125	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
126	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
127	C₁₉×#95	—	2	1	no	—
128	C₁₉×#95	—	2	1	no	—
129	C₁₉×#95	—	2	1	no	—
130	C₁₉×#95	—	2	1	no	—
131	C₁₉×#95	—	2	1	no	—
132	C₁₉×#95	C₂³	1	1	yes	characteristic
133	C₁₉×#95	C₂³	1	1	yes	characteristic
134	C₂⁴×C₁₉	—	2	1	no	—
135	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
137	#41×C₁₉	—	8	2	no	—
138	C₂×Q₈×C₁₉	—	2	1	no	—
139	C₂×Q₈×C₁₉	—	2	2	no	—
140	C₂×Q₈×C₁₉	—	8	1	no	—
141	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
142	C₂×D₄×C₁₉	—	2	2	no	—
143	C₂×D₄×C₁₉	—	2	2	no	—
144	C₂×D₄×C₁₉	—	2	2	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	—	2	2	no	—
149	C₂×D₄×C₁₉	—	4	1	no	—
150	C₂×D₄×C₁₉	—	4	2	no	—
151	C₂×D₄×C₁₉	—	4	2	no	—
152	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
157	C₂²×C₄×C₁₉	—	2	2	no	—
158	C₂²×C₄×C₁₉	—	2	1	no	—
159	C₂²×C₄×C₁₉	—	2	2	no	—
160	C₂²×C₄×C₁₉	—	2	1	no	—
161	C₂²×C₄×C₁₉	—	2	1	no	—
162	C₂²×C₄×C₁₉	—	2	1	no	—
163	C₂²×C₄×C₁₉	—	2	1	no	—
164	C₂²×C₄×C₁₉	—	4	2	no	—
165	C₂²×C₄×C₁₉	—	4	2	no	—
166	C₂²×C₄×C₁₉	—	8	1	no	—
167	C₂²×C₄×C₁₉	—	8	1	no	—
168	C₂²×C₄×C₁₉	—	8	2	no	—
169	C₂²×C₄×C₁₉	—	8	1	no	—
170	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
176	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
177	Q₁₆×C₁₉	—	8	2	no	—
178	SD₁₆×C₁₉	—	8	2	no	—
179	M₁₆×C₁₉	—	8	2	no	—
180	C₂×C₈×C₁₉	—	2	2	no	—
181	C₂×C₈×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	1	no	—
186	C₄⋊C₄×C₁₉	—	2	1	no	—
187	C₄⋊C₄×C₁₉	—	2	2	no	—
188	C₄⋊C₄×C₁₉	—	2	2	no	—
189	C₄⋊C₄×C₁₉	—	2	2	no	—
190	C₄⋊C₄×C₁₉	—	2	2	no	—
191	C₄⋊C₄×C₁₉	—	2	2	no	—
192	C₄⋊C₄×C₁₉	—	4	2	no	—
193	C₄⋊C₄×C₁₉	—	4	1	no	—
194	C₄⋊C₄×C₁₉	—	4	1	no	—
195	C₄⋊C₄×C₁₉	—	8	1	no	—
196	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
197	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
198	C₂²⋊C₄×C₁₉	—	2	2	no	—
199	C₂²⋊C₄×C₁₉	—	2	2	no	—
200	C₂²⋊C₄×C₁₉	—	2	2	no	—
201	C₂²⋊C₄×C₁₉	—	2	2	no	—
202	C₂²⋊C₄×C₁₉	—	2	2	no	—
203	C₂²⋊C₄×C₁₉	—	2	2	no	—
204	C₂²⋊C₄×C₁₉	—	2	2	no	—
205	C₂²⋊C₄×C₁₉	—	2	2	no	—
206	C₂²⋊C₄×C₁₉	—	2	2	no	—
207	C₂²⋊C₄×C₁₉	—	2	2	no	—
208	C₂²⋊C₄×C₁₉	—	2	2	no	—
209	C₂²⋊C₄×C₁₉	—	2	2	no	—
210	C₂²⋊C₄×C₁₉	—	4	2	no	—
211	C₂²⋊C₄×C₁₉	—	4	2	no	—
212	C₂²⋊C₄×C₁₉	—	8	1	no	—
213	C₄²×C₁₉	—	2	2	no	—
214	C₄²×C₁₉	—	2	2	no	—
215	C₄²×C₁₉	—	2	1	no	—
216	C₄²×C₁₉	—	2	1	no	—
217	#18323	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂³×C₁₉	—	2	1	no	—
219	C₂³×C₁₉	—	2	1	no	—
220	C₂³×C₁₉	—	2	1	no	—
221	C₂³×C₁₉	—	2	1	no	—
222	C₂³×C₁₉	—	2	2	no	—
223	C₂³×C₁₉	—	4	1	no	—
224	C₂³×C₁₉	—	4	1	no	—
225	C₂³×C₁₉	—	4	1	no	—
226	C₂³×C₁₉	—	4	1	no	—
227	C₂³×C₁₉	—	4	2	no	—
228	C₂³×C₁₉	—	8	1	no	—
229	C₂³×C₁₉	—	8	1	no	—
230	C₂³×C₁₉	#120	1	2	yes	—
231	C₂³×C₁₉	#137	1	2	yes	—
232	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
233	Q₈×C₁₉	—	4	2	no	—
234	Q₈×C₁₉	—	4	2	no	—
235	Q₈×C₁₉	—	4	2	no	—
236	Q₈×C₁₉	—	8	1	no	—
237	D₄×C₁₉	—	4	2	no	—
238	D₄×C₁₉	—	4	4	no	—
239	D₄×C₁₉	—	4	4	no	—
240	D₄×C₁₉	—	4	2	no	—
241	D₄×C₁₉	—	4	2	no	—
242	D₄×C₁₉	—	8	2	no	—
243	D₄×C₁₉	—	8	2	no	—
244	D₄×C₁₉	—	8	1	no	—
245	C₂×C₄×C₁₉	—	2	2	no	—
246	C₂×C₄×C₁₉	—	2	1	no	—
247	C₂×C₄×C₁₉	—	2	2	no	—
248	C₂×C₄×C₁₉	—	2	1	no	—
249	C₂×C₄×C₁₉	—	2	2	no	—
250	C₂×C₄×C₁₉	—	2	1	no	—
251	C₂×C₄×C₁₉	—	2	2	no	—
252	C₂×C₄×C₁₉	—	2	1	no	—
253	C₂×C₄×C₁₉	—	2	1	no	—
254	C₂×C₄×C₁₉	—	4	2	no	—
255	C₂×C₄×C₁₉	—	4	1	no	—
256	C₂×C₄×C₁₉	—	4	2	no	—
257	C₂×C₄×C₁₉	—	4	1	no	—
258	C₂×C₄×C₁₉	—	4	2	no	—
259	C₂×C₄×C₁₉	—	4	4	no	—
260	C₂×C₄×C₁₉	—	4	1	no	—
261	C₂×C₄×C₁₉	—	4	2	no	—
262	C₂×C₄×C₁₉	—	4	1	no	—
263	C₂×C₄×C₁₉	—	4	1	no	—
264	C₂×C₄×C₁₉	—	4	1	no	—
265	C₂×C₄×C₁₉	—	4	1	no	—
266	C₂×C₄×C₁₉	—	4	1	no	—
267	C₂×C₄×C₁₉	—	4	1	no	—
268	C₂×C₄×C₁₉	—	4	1	no	—
269	C₂×C₄×C₁₉	—	4	1	no	—
270	C₂×C₄×C₁₉	—	4	1	no	—
271	C₂×C₄×C₁₉	—	4	1	no	—
272	C₂×C₄×C₁₉	—	4	1	no	—
273	C₂×C₄×C₁₉	—	4	1	no	—
274	C₂×C₄×C₁₉	—	8	1	no	—
275	C₂×C₄×C₁₉	—	8	1	no	—
276	C₂×C₄×C₁₉	—	8	2	no	—
277	C₂×C₄×C₁₉	—	8	1	no	—
278	C₂×C₄×C₁₉	—	8	4	no	—
279	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
280	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
281	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
282	C₈×C₁₉	—	4	2	no	—
283	C₈×C₁₉	—	4	2	no	—
284	#3459	C₂×C₁₉	1	1	yes	characteristic
285	#3196	C₂×C₁₉	1	2	yes	complemented
286	#2564	C₂×C₁₉	1	1	yes	characteristic, complemented
287	#1615	C₂×C₁₉	1	2	yes	complemented
288	#1614	C₂×C₁₉	1	1	yes	characteristic, complemented
289	#1613	C₂×C₁₉	1	1	yes	characteristic, complemented
290	#1603	C₂×C₁₉	1	2	yes	complemented
291	#1602	C₂×C₁₉	1	1	yes	characteristic, complemented
292	#1601	C₂×C₁₉	1	1	yes	characteristic, complemented
293	#1504	C₂×C₁₉	1	2	yes	complemented
294	#1465	C₂×C₁₉	1	1	yes	characteristic, complemented
295	C₂²×C₁₉	—	2	1	no	—
296	C₂²×C₁₉	—	2	1	no	—
297	C₂²×C₁₉	—	2	2	no	—
298	C₂²×C₁₉	—	2	2	no	—
299	C₂²×C₁₉	—	2	2	no	—
300	C₂²×C₁₉	—	2	2	no	—
301	C₂²×C₁₉	—	4	2	no	—
302	C₂²×C₁₉	—	4	2	no	—
303	C₂²×C₁₉	—	4	2	no	—
304	C₂²×C₁₉	—	4	1	no	—
305	C₂²×C₁₉	—	4	1	no	—
306	C₂²×C₁₉	—	4	2	no	—
307	C₂²×C₁₉	—	4	2	no	—
308	C₂²×C₁₉	—	4	2	no	—
309	C₂²×C₁₉	—	8	1	no	—
310	C₂²×C₁₉	—	8	4	no	—
311	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
312	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
313	C₂²×C₁₉	#575	1	1	yes	characteristic
314	C₄×C₁₉	—	2	2	no	—
315	C₄×C₁₉	—	2	1	no	—
316	C₄×C₁₉	—	2	1	no	—
317	C₄×C₁₉	—	4	2	no	—
318	C₄×C₁₉	—	4	1	no	—
319	C₄×C₁₉	—	4	2	no	—
320	C₄×C₁₉	—	4	1	no	—
321	C₄×C₁₉	—	4	2	no	—
322	C₄×C₁₉	—	4	1	no	—
323	C₄×C₁₉	—	4	2	no	—
324	C₄×C₁₉	—	8	1	no	—
325	C₄×C₁₉	—	8	1	no	—
326	C₄×C₁₉	—	8	1	no	—
327	#543	C₂²×C₁₉	1	1	yes	characteristic
328	#539	—	2	2	no	—
329	#539	C₂²×C₁₉	1	2	yes	—
330	#538	—	2	2	no	—
331	#538	—	2	1	no	—
332	#534	—	2	1	no	—
333	#534	C₂²×C₁₉	1	1	yes	characteristic
334	#529	—	2	2	no	—
335	#529	—	2	1	no	—
336	#525	—	2	2	no	—
337	#525	C₂²×C₁₉	1	2	yes	—
338	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
339	C₂×C₄×D₄	—	2	1	no	—
340	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
341	#485	—	2	2	no	—
342	#484	C₂²×C₁₉	1	2	yes	complemented
343	#481	C₂²×C₁₉	1	2	yes	—
344	#470	—	2	2	no	—
345	#468	—	2	2	no	—
346	#452	—	2	2	no	—
347	#451	C₂²×C₁₉	1	2	yes	complemented
348	#448	C₂²×C₁₉	1	2	yes	—
349	#407	C₂²×C₁₉	1	2	yes	complemented
350	#400	C₂²×C₁₉	1	1	yes	characteristic, complemented
351	#399	C₂²×C₁₉	1	1	yes	characteristic
352	#395	C₂²×C₁₉	1	1	yes	characteristic, complemented
353	#393	C₂²×C₁₉	1	1	yes	characteristic
354	#387	—	2	1	no	—
355	#386	—	2	1	no	—
356	#385	—	2	1	no	—
357	#380	—	2	1	no	—
358	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic, complemented
359	#328	C₂²×C₁₉	1	2	yes	complemented
360	#328	C₂²×C₁₉	1	2	yes	complemented
361	#327	C₂²×C₁₉	1	2	yes	—
362	#327	C₂²×C₁₉	1	2	yes	—
363	#324	C₂²×C₁₉	1	2	yes	complemented
364	#323	C₂²×C₁₉	1	1	yes	characteristic
365	#323	C₂²×C₁₉	1	1	yes	characteristic
366	C₂×C₁₉	—	2	1	no	—
367	C₂×C₁₉	—	2	1	no	—
368	C₂×C₁₉	—	4	2	no	—
369	C₂×C₁₉	—	4	2	no	—
370	C₂×C₁₉	—	8	2	no	—
371	C₂×C₁₉	#3007	1	1	yes	characteristic
372	C₂×C₁₉	#3018	1	1	yes	characteristic
373	C₂×C₁₉	#3026	1	1	yes	characteristic
374	C₂×#41	D₄×C₁₉	1	2	yes	—
375	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
376	C₂²×D₄	—	2	1	no	—
377	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
378	C₂³×C₄	—	2	1	no	—
379	C₂³×C₄	—	2	1	no	—
380	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
381	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
382	C₂×Q₁₆	—	2	2	no	—
383	C₂×SD₁₆	—	2	2	no	—
384	C₂×M₁₆	—	2	2	no	—
385	#126	—	2	2	no	—
386	#126	—	2	2	no	—
387	#126	—	2	2	no	—
388	#125	—	2	1	no	—
389	#125	—	2	2	no	—
390	#124	—	2	2	no	—
391	#124	—	2	1	no	—
392	#123	—	2	2	no	—
393	#123	—	2	2	no	—
394	#123	—	2	2	no	—
395	#123	—	2	2	no	—
396	#123	—	2	2	no	—
397	#123	—	2	2	no	—
398	C₂²⋊Q₈	—	2	2	no	—
399	C₂²⋊Q₈	—	2	2	no	—
400	C₂²⋊Q₈	—	2	1	no	—
401	C₂²⋊Q₈	—	2	2	no	—
402	C₂²⋊Q₈	—	2	2	no	—
403	C₂²⋊Q₈	—	2	2	no	—
404	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
405	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
406	#121	—	2	2	no	—
407	#121	—	2	2	no	—
408	#121	—	2	2	no	—
409	#121	—	2	1	no	—
410	#121	D₄×C₁₉	1	2	yes	—
411	#121	C₂³×C₁₉	1	2	yes	—
412	#120	—	2	2	no	—
413	#120	—	2	2	no	—
414	#120	—	2	2	no	—
415	C₄×Q₈	—	2	1	no	—
416	C₄×D₄	—	2	2	no	—
417	C₄×D₄	—	2	2	no	—
418	C₄×D₄	—	2	1	no	—
419	C₄×D₄	—	2	2	no	—
420	C₄×D₄	—	2	2	no	—
421	C₄×D₄	—	2	2	no	—
422	C₄×D₄	—	2	2	no	—
423	C₄×D₄	—	2	2	no	—
424	#117	—	2	2	no	—
425	#117	D₄×C₁₉	1	2	yes	—
426	C₂×C₄⋊C₄	—	2	1	no	—
427	C₂×C₄⋊C₄	—	2	1	no	—
428	C₂×C₄⋊C₄	—	2	1	no	—
429	C₂×C₄⋊C₄	—	2	1	no	—
430	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
431	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
432	C₂×C₂²⋊C₄	—	2	1	no	—
433	C₂×C₂²⋊C₄	—	2	1	no	—
434	C₂×C₂²⋊C₄	—	2	1	no	—
435	C₂×C₂²⋊C₄	—	2	1	no	—
436	C₂×C₂²⋊C₄	—	2	1	no	—
437	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
438	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
439	C₂×C₄²	—	2	1	no	—
440	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
441	#107	—	2	2	no	—
442	#106	—	2	2	no	—
443	#103	—	2	2	no	—
444	#103	—	2	2	no	—
445	#103	—	2	2	no	—
446	#102	—	2	2	no	—
447	C₂²⋊C₈	—	2	2	no	—
448	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
449	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
450	#95	—	2	1	no	—
451	#95	—	2	1	no	—
452	#95	—	2	1	no	—
453	#95	—	2	1	no	—
454	#95	—	2	1	no	—
455	#95	C₂³×C₁₉	1	1	yes	characteristic
456	#95	C₂³×C₁₉	1	1	yes	characteristic
457	C₁₉	#18323	1	1	yes	characteristic, direct product factor, Sylow
458	C₂⁴	—	2	1	no	—
459	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
460	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
461	#41	—	8	2	no	—
462	C₂×Q₈	—	2	1	no	—
463	C₂×Q₈	—	2	2	no	—
464	C₂×Q₈	—	8	1	no	—
465	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
466	C₂×D₄	—	2	2	no	—
467	C₂×D₄	—	2	2	no	—
468	C₂×D₄	—	2	2	no	—
469	C₂×D₄	—	2	2	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	—	2	2	no	—
472	C₂×D₄	—	2	2	no	—
473	C₂×D₄	—	4	1	no	—
474	C₂×D₄	—	4	2	no	—
475	C₂×D₄	—	4	2	no	—
476	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	2	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	4	2	no	—
489	C₂²×C₄	—	4	2	no	—
490	C₂²×C₄	—	8	1	no	—
491	C₂²×C₄	—	8	1	no	—
492	C₂²×C₄	—	8	2	no	—
493	C₂²×C₄	—	8	1	no	—
494	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
495	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
496	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
497	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
498	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
499	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
500	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
501	Q₁₆	—	8	2	no	—
502	SD₁₆	—	8	2	no	—
503	M₁₆	—	8	2	no	—
504	C₂×C₈	—	2	2	no	—
505	C₂×C₈	—	2	2	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	2	2	no	—
514	C₄⋊C₄	—	2	2	no	—
515	C₄⋊C₄	—	2	2	no	—
516	C₄⋊C₄	—	4	2	no	—
517	C₄⋊C₄	—	4	1	no	—
518	C₄⋊C₄	—	4	1	no	—
519	C₄⋊C₄	—	8	1	no	—
520	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
521	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
522	C₂²⋊C₄	—	2	2	no	—
523	C₂²⋊C₄	—	2	2	no	—
524	C₂²⋊C₄	—	2	2	no	—
525	C₂²⋊C₄	—	2	2	no	—
526	C₂²⋊C₄	—	2	2	no	—
527	C₂²⋊C₄	—	2	2	no	—
528	C₂²⋊C₄	—	2	2	no	—
529	C₂²⋊C₄	—	2	2	no	—
530	C₂²⋊C₄	—	2	2	no	—
531	C₂²⋊C₄	—	2	2	no	—
532	C₂²⋊C₄	—	2	2	no	—
533	C₂²⋊C₄	—	2	2	no	—
534	C₂²⋊C₄	—	4	2	no	—
535	C₂²⋊C₄	—	4	2	no	—
536	C₂²⋊C₄	—	8	1	no	—
537	C₄²	—	2	2	no	—
538	C₄²	—	2	2	no	—
539	C₄²	—	2	1	no	—
540	C₄²	—	2	1	no	—
541	C₂³	—	2	1	no	—
542	C₂³	—	2	1	no	—
543	C₂³	—	2	1	no	—
544	C₂³	—	2	1	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	4	1	no	—
547	C₂³	—	4	1	no	—
548	C₂³	—	4	1	no	—
549	C₂³	—	4	1	no	—
550	C₂³	—	4	2	no	—
551	C₂³	—	8	1	no	—
552	C₂³	—	8	1	no	—
553	C₂³	C₁₉×#120	1	2	yes	—
554	C₂³	C₁₉×#137	1	2	yes	—
555	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
556	Q₈	—	4	2	no	—
557	Q₈	—	4	2	no	—
558	Q₈	—	4	2	no	—
559	Q₈	—	8	1	no	—
560	D₄	—	4	2	no	—
561	D₄	—	4	4	no	—
562	D₄	—	4	4	no	—
563	D₄	—	4	2	no	—
564	D₄	—	4	2	no	—
565	D₄	—	8	2	no	—
566	D₄	—	8	2	no	—
567	D₄	—	8	1	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	4	2	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	2	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	4	4	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	8	1	no	—
598	C₂×C₄	—	8	2	no	—
599	C₂×C₄	—	8	1	no	—
600	C₂×C₄	—	8	1	no	—
601	C₂×C₄	—	8	4	no	—
602	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
603	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
604	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
605	C₈	—	4	2	no	—
606	C₈	—	4	2	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	4	2	no	—
614	C₂²	—	4	2	no	—
615	C₂²	—	4	2	no	—
616	C₂²	—	4	1	no	—
617	C₂²	—	4	1	no	—
618	C₂²	—	4	2	no	—
619	C₂²	—	4	2	no	—
620	C₂²	—	4	2	no	—
621	C₂²	—	8	1	no	—
622	C₂²	—	8	4	no	—
623	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
624	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
625	C₂²	C₁₉×#575	1	1	yes	characteristic
626	C₄	—	2	2	no	—
627	C₄	—	2	1	no	—
628	C₄	—	2	1	no	—
629	C₄	—	4	2	no	—
630	C₄	—	4	1	no	—
631	C₄	—	4	2	no	—
632	C₄	—	4	1	no	—
633	C₄	—	4	2	no	—
634	C₄	—	4	1	no	—
635	C₄	—	4	2	no	—
636	C₄	—	8	1	no	—
637	C₄	—	8	1	no	—
638	C₄	—	8	1	no	—
639	C₂	—	2	1	no	—
640	C₂	—	2	1	no	—
641	C₂	—	4	2	no	—
642	C₂	—	4	2	no	—
643	C₂	—	8	2	no	—
644	C₂	C₁₉×#3007	1	1	yes	characteristic
645	C₂	C₁₉×#3018	1	1	yes	characteristic
646	C₂	C₁₉×#3026	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#3459	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₁₉×#3196	C₂	semidirect
3. C₁₉×#2564	C₂	semidirect
4. C₁₉×#1615	C₂	semidirect
5. C₁₉×#1614	C₂	semidirect
6. C₁₉×#1613	C₂	semidirect
7. C₁₉×#1603	C₂	semidirect
8. C₁₉×#1602	C₂	semidirect
9. C₁₉×#1601	C₂	semidirect
10. C₁₉×#1504	C₂	semidirect
11. C₁₉×#1465	C₂	semidirect
23. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
27. C₁₉×#484	C₂²	semidirect
32. C₁₉×#451	C₂²	semidirect
34. C₁₉×#407	C₂²	semidirect
35. C₁₉×#400	C₂²	semidirect
37. C₁₉×#395	C₂²	semidirect
43. C₂×C₁₉×#95	C₂²	semidirect
44. C₁₉×#328	C₂²	semidirect
45. C₁₉×#328	C₂²	semidirect
48. C₁₉×#324	C₂²	semidirect
217. #18323	C₁₉	direct (N × H)
285. #3196	C₂×C₁₉	semidirect
286. #2564	C₂×C₁₉	semidirect
287. #1615	C₂×C₁₉	semidirect
288. #1614	C₂×C₁₉	semidirect
289. #1613	C₂×C₁₉	semidirect
290. #1603	C₂×C₁₉	semidirect
291. #1602	C₂×C₁₉	semidirect
292. #1601	C₂×C₁₉	semidirect
293. #1504	C₂×C₁₉	semidirect
294. #1465	C₂×C₁₉	semidirect
338. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
342. #484	C₂²×C₁₉	semidirect
347. #451	C₂²×C₁₉	semidirect
349. #407	C₂²×C₁₉	semidirect
350. #400	C₂²×C₁₉	semidirect
352. #395	C₂²×C₁₉	semidirect
358. C₂×#95	C₂²×C₁₉	semidirect
359. #328	C₂²×C₁₉	semidirect
360. #328	C₂²×C₁₉	semidirect
363. #324	C₂²×C₁₉	semidirect
457. C₁₉	#18323	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×#3459	2
C₁₉×#3196	2
C₁₉×#2564	2
C₁₉×#1615	2
C₁₉×#1614	2
C₁₉×#1613	2
C₁₉×#1603	2
C₁₉×#1602	2
C₁₉×#1601	2
C₁₉×#1504	2
C₁₉×#1465	2
#18323	19

Subgroups — C19×#18323 #18024282

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18323 #18024282