Subgroups — C₁₉×#18306 #18024265

Order 4864.

1040 conjugacy classes of subgroups.

The subgroup lattice has 686 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, complemented
2	C₁₉×#3211	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2631	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1606	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1602	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1601	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1600	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1596	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1595	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1521	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1460	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#543	C₂²	1	1	yes	characteristic
13	C₁₉×#539	—	2	2	no	—
14	C₁₉×#539	—	2	1	no	—
15	C₁₉×#538	—	2	2	no	—
16	C₁₉×#538	C₂²	1	2	yes	—
17	C₁₉×#534	—	2	1	no	—
18	C₁₉×#534	C₂²	1	1	yes	characteristic
19	C₁₉×#529	—	2	2	no	—
20	C₁₉×#529	C₂²	1	2	yes	—
21	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic, complemented
22	C₁₉×#525	—	2	1	no	—
23	C₁₉×#525	—	2	2	no	—
24	C₂×C₄×D₄×C₁₉	—	2	1	no	—
25	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#495	—	2	2	no	—
27	C₁₉×#488	—	2	2	no	—
28	C₁₉×#464	—	2	2	no	—
29	C₁₉×#463	—	2	2	no	—
30	C₁₉×#451	C₂²	1	2	yes	complemented
31	C₁₉×#450	C₂²	1	2	yes	complemented
32	C₁₉×#448	C₂²	1	2	yes	—
33	C₁₉×#447	C₂²	1	2	yes	—
34	C₁₉×#431	C₂²	1	2	yes	complemented
35	C₁₉×#397	—	2	1	no	—
36	C₁₉×#393	C₂²	1	1	yes	characteristic
37	C₁₉×#393	C₂²	1	1	yes	characteristic, complemented
38	C₁₉×#392	—	2	1	no	—
39	C₁₉×#392	C₂²	1	1	yes	characteristic
40	C₁₉×#392	C₂²	1	1	yes	characteristic, complemented
41	C₁₉×#386	—	2	1	no	—
42	C₁₉×#386	—	2	1	no	—
43	C₁₉×#383	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×#323	C₂²	1	1	yes	characteristic
49	C₁₉×#323	C₂²	1	1	yes	characteristic
50	C₁₉×#323	C₂²	1	2	yes	complemented
51	C₂×#41×C₁₉	—	2	1	no	—
52	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
53	C₂²×D₄×C₁₉	—	2	1	no	—
54	C₂²×D₄×C₁₉	—	2	1	no	—
55	C₂²×D₄×C₁₉	—	2	1	no	—
56	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
57	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₁₉	—	2	1	no	—
59	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
60	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
61	C₂×Q₁₆×C₁₉	—	2	2	no	—
62	C₂×SD₁₆×C₁₉	—	2	2	no	—
63	C₂×SD₁₆×C₁₉	—	2	2	no	—
64	C₂×D₈×C₁₉	—	2	2	no	—
65	C₁₉×#126	—	2	2	no	—
66	C₁₉×#126	—	2	2	no	—
67	C₁₉×#126	—	2	2	no	—
68	C₁₉×#125	—	2	2	no	—
69	C₁₉×#125	D₄	1	2	yes	complemented
70	C₁₉×#124	—	2	2	no	—
71	C₁₉×#124	—	2	2	no	—
72	C₁₉×#124	—	2	2	no	—
73	C₁₉×#124	D₄	1	2	yes	complemented
74	C₁₉×#123	—	2	2	no	—
75	C₁₉×#123	—	2	2	no	—
76	C₁₉×#123	—	2	2	no	—
77	C₁₉×#123	—	2	2	no	—
78	C₁₉×#123	—	2	2	no	—
79	C₁₉×#123	—	2	2	no	—
80	C₁₉×C₂²⋊Q₈	—	2	1	no	—
81	C₁₉×C₂²⋊Q₈	—	2	2	no	—
82	C₁₉×C₂²⋊Q₈	—	2	2	no	—
83	C₁₉×C₂²⋊Q₈	—	2	1	no	—
84	C₁₉×C₂²⋊Q₈	—	2	2	no	—
85	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
86	C₁₉×#121	—	2	2	no	—
87	C₁₉×#121	—	2	1	no	—
88	C₁₉×#121	—	2	2	no	—
89	C₁₉×#121	—	2	2	no	—
90	C₁₉×#121	—	2	1	no	—
91	C₁₉×#121	C₂³	1	2	yes	—
92	C₁₉×#120	—	2	2	no	—
93	C₁₉×#120	—	2	2	no	—
94	C₁₉×#120	—	2	2	no	—
95	C₄×Q₈×C₁₉	D₄	1	2	yes	complemented
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	C₄×D₄×C₁₉	—	2	2	no	—
102	C₄×D₄×C₁₉	—	2	2	no	—
103	C₄×D₄×C₁₉	D₄	1	2	yes	complemented
104	C₁₉×#117	—	2	1	no	—
105	C₁₉×#117	—	2	2	no	—
106	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
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	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
117	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₁₉	—	2	1	no	—
119	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
120	C₁₉×C₄⋊C₈	—	2	2	no	—
121	C₁₉×#103	—	2	2	no	—
122	C₁₉×#103	—	2	2	no	—
123	C₁₉×#102	—	2	2	no	—
124	C₁₉×#102	—	2	2	no	—
125	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
126	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
127	C₄×C₈×C₁₉	—	2	2	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	—	2	1	no	—
136	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
138	#41×C₁₉	—	8	2	no	—
139	C₂×Q₈×C₁₉	—	2	1	no	—
140	C₂×Q₈×C₁₉	—	2	2	no	—
141	C₂×Q₈×C₁₉	—	8	1	no	—
142	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
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	2	no	—
147	C₂×D₄×C₁₉	—	2	1	no	—
148	C₂×D₄×C₁₉	—	2	2	no	—
149	C₂×D₄×C₁₉	—	2	2	no	—
150	C₂×D₄×C₁₉	—	2	2	no	—
151	C₂×D₄×C₁₉	—	4	1	no	—
152	C₂×D₄×C₁₉	—	4	2	no	—
153	C₂×D₄×C₁₉	—	4	2	no	—
154	C₂×D₄×C₁₉	—	4	2	no	—
155	C₂×D₄×C₁₉	—	4	2	no	—
156	C₂×D₄×C₁₉	—	8	1	no	—
157	C₂×D₄×C₁₉	—	8	1	no	—
158	C₂×D₄×C₁₉	—	8	1	no	—
159	C₂×D₄×C₁₉	—	8	1	no	—
160	C₂×D₄×C₁₉	—	8	1	no	—
161	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₁₉	—	2	1	no	—
163	C₂²×C₄×C₁₉	—	2	1	no	—
164	C₂²×C₄×C₁₉	—	2	1	no	—
165	C₂²×C₄×C₁₉	—	2	2	no	—
166	C₂²×C₄×C₁₉	—	2	1	no	—
167	C₂²×C₄×C₁₉	—	2	1	no	—
168	C₂²×C₄×C₁₉	—	2	2	no	—
169	C₂²×C₄×C₁₉	—	2	1	no	—
170	C₂²×C₄×C₁₉	—	2	1	no	—
171	C₂²×C₄×C₁₉	—	2	1	no	—
172	C₂²×C₄×C₁₉	—	2	1	no	—
173	C₂²×C₄×C₁₉	—	2	1	no	—
174	C₂²×C₄×C₁₉	—	8	1	no	—
175	C₂²×C₄×C₁₉	—	8	1	no	—
176	C₂²×C₄×C₁₉	—	8	2	no	—
177	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
182	Q₁₆×C₁₉	—	8	2	no	—
183	SD₁₆×C₁₉	—	8	2	no	—
184	SD₁₆×C₁₉	—	8	2	no	—
185	D₈×C₁₉	—	8	2	no	—
186	C₂×C₈×C₁₉	—	2	2	no	—
187	C₂×C₈×C₁₉	—	2	2	no	—
188	C₄⋊C₄×C₁₉	—	2	2	no	—
189	C₄⋊C₄×C₁₉	—	2	1	no	—
190	C₄⋊C₄×C₁₉	—	2	1	no	—
191	C₄⋊C₄×C₁₉	—	2	2	no	—
192	C₄⋊C₄×C₁₉	—	2	2	no	—
193	C₄⋊C₄×C₁₉	—	2	2	no	—
194	C₄⋊C₄×C₁₉	—	2	2	no	—
195	C₄⋊C₄×C₁₉	—	2	2	no	—
196	C₄⋊C₄×C₁₉	—	2	2	no	—
197	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
198	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
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	—	2	2	no	—
211	C₂²⋊C₄×C₁₉	—	4	1	no	—
212	C₂²⋊C₄×C₁₉	—	4	2	no	—
213	C₂²⋊C₄×C₁₉	—	4	1	no	—
214	C₂²⋊C₄×C₁₉	—	8	1	no	—
215	C₂²⋊C₄×C₁₉	—	8	1	no	—
216	C₂²⋊C₄×C₁₉	—	8	1	no	—
217	C₂²⋊C₄×C₁₉	—	8	1	no	—
218	C₄²×C₁₉	—	2	2	no	—
219	C₄²×C₁₉	—	2	2	no	—
220	C₄²×C₁₉	C₂×D₄	1	2	yes	—
221	C₄²×C₁₉	C₂×D₄	1	2	yes	—
222	#18306	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
223	C₂³×C₁₉	—	2	1	no	—
224	C₂³×C₁₉	—	2	1	no	—
225	C₂³×C₁₉	—	2	1	no	—
226	C₂³×C₁₉	—	2	2	no	—
227	C₂³×C₁₉	—	2	1	no	—
228	C₂³×C₁₉	—	2	1	no	—
229	C₂³×C₁₉	—	4	1	no	—
230	C₂³×C₁₉	—	4	1	no	—
231	C₂³×C₁₉	—	4	1	no	—
232	C₂³×C₁₉	—	4	1	no	—
233	C₂³×C₁₉	—	4	2	no	—
234	C₂³×C₁₉	—	4	1	no	—
235	C₂³×C₁₉	—	4	1	no	—
236	C₂³×C₁₉	—	4	1	no	—
237	C₂³×C₁₉	—	4	1	no	—
238	C₂³×C₁₉	—	4	1	no	—
239	C₂³×C₁₉	—	4	1	no	—
240	C₂³×C₁₉	—	4	1	no	—
241	C₂³×C₁₉	—	8	1	no	—
242	C₂³×C₁₉	—	8	1	no	—
243	C₂³×C₁₉	#135	1	2	yes	—
244	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
245	Q₈×C₁₉	—	4	2	no	—
246	Q₈×C₁₉	—	4	2	no	—
247	Q₈×C₁₉	—	4	2	no	—
248	Q₈×C₁₉	—	8	1	no	—
249	D₄×C₁₉	—	4	4	no	—
250	D₄×C₁₉	—	4	2	no	—
251	D₄×C₁₉	—	4	2	no	—
252	D₄×C₁₉	—	4	2	no	—
253	D₄×C₁₉	—	4	4	no	—
254	D₄×C₁₉	—	4	2	no	—
255	D₄×C₁₉	—	4	2	no	—
256	D₄×C₁₉	—	8	2	no	—
257	D₄×C₁₉	—	8	1	no	—
258	D₄×C₁₉	—	8	2	no	—
259	D₄×C₁₉	—	8	4	no	—
260	D₄×C₁₉	—	8	4	no	—
261	C₂×C₄×C₁₉	—	2	1	no	—
262	C₂×C₄×C₁₉	—	2	1	no	—
263	C₂×C₄×C₁₉	—	2	2	no	—
264	C₂×C₄×C₁₉	—	2	2	no	—
265	C₂×C₄×C₁₉	—	2	1	no	—
266	C₂×C₄×C₁₉	—	2	1	no	—
267	C₂×C₄×C₁₉	—	2	2	no	—
268	C₂×C₄×C₁₉	—	4	1	no	—
269	C₂×C₄×C₁₉	—	4	1	no	—
270	C₂×C₄×C₁₉	—	4	2	no	—
271	C₂×C₄×C₁₉	—	4	2	no	—
272	C₂×C₄×C₁₉	—	4	4	no	—
273	C₂×C₄×C₁₉	—	4	2	no	—
274	C₂×C₄×C₁₉	—	4	1	no	—
275	C₂×C₄×C₁₉	—	4	1	no	—
276	C₂×C₄×C₁₉	—	4	1	no	—
277	C₂×C₄×C₁₉	—	4	1	no	—
278	C₂×C₄×C₁₉	—	4	1	no	—
279	C₂×C₄×C₁₉	—	4	1	no	—
280	C₂×C₄×C₁₉	—	4	1	no	—
281	C₂×C₄×C₁₉	—	4	1	no	—
282	C₂×C₄×C₁₉	—	4	1	no	—
283	C₂×C₄×C₁₉	—	4	1	no	—
284	C₂×C₄×C₁₉	—	4	1	no	—
285	C₂×C₄×C₁₉	—	8	1	no	—
286	C₂×C₄×C₁₉	—	8	1	no	—
287	C₂×C₄×C₁₉	—	8	1	no	—
288	C₂×C₄×C₁₉	—	8	2	no	—
289	C₂×C₄×C₁₉	—	8	1	no	—
290	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
291	C₂×C₄×C₁₉	#120	1	2	yes	—
292	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
293	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
294	C₈×C₁₉	—	4	2	no	—
295	C₈×C₁₉	—	4	2	no	—
296	#3459	C₂×C₁₉	1	1	yes	characteristic, complemented
297	#3211	C₂×C₁₉	1	2	yes	complemented
298	#2631	C₂×C₁₉	1	1	yes	characteristic, complemented
299	#1606	C₂×C₁₉	1	2	yes	complemented
300	#1602	C₂×C₁₉	1	1	yes	characteristic, complemented
301	#1601	C₂×C₁₉	1	1	yes	characteristic, complemented
302	#1600	C₂×C₁₉	1	2	yes	complemented
303	#1596	C₂×C₁₉	1	1	yes	characteristic, complemented
304	#1595	C₂×C₁₉	1	1	yes	characteristic, complemented
305	#1521	C₂×C₁₉	1	2	yes	complemented
306	#1460	C₂×C₁₉	1	1	yes	characteristic, complemented
307	C₂²×C₁₉	—	2	1	no	—
308	C₂²×C₁₉	—	2	1	no	—
309	C₂²×C₁₉	—	2	2	no	—
310	C₂²×C₁₉	—	4	2	no	—
311	C₂²×C₁₉	—	4	2	no	—
312	C₂²×C₁₉	—	4	1	no	—
313	C₂²×C₁₉	—	4	1	no	—
314	C₂²×C₁₉	—	4	1	no	—
315	C₂²×C₁₉	—	4	2	no	—
316	C₂²×C₁₉	—	4	1	no	—
317	C₂²×C₁₉	—	4	2	no	—
318	C₂²×C₁₉	—	4	2	no	—
319	C₂²×C₁₉	—	4	1	no	—
320	C₂²×C₁₉	—	8	1	no	—
321	C₂²×C₁₉	—	8	1	no	—
322	C₂²×C₁₉	—	8	1	no	—
323	C₂²×C₁₉	—	8	1	no	—
324	C₂²×C₁₉	—	8	1	no	—
325	C₂²×C₁₉	—	8	1	no	—
326	C₂²×C₁₉	—	8	4	no	—
327	C₂²×C₁₉	—	8	1	no	—
328	C₂²×C₁₉	—	8	1	no	—
329	C₂²×C₁₉	—	8	1	no	—
330	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
331	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
332	C₂²×C₁₉	#575	1	1	yes	characteristic
333	C₄×C₁₉	—	2	2	no	—
334	C₄×C₁₉	—	2	1	no	—
335	C₄×C₁₉	—	2	1	no	—
336	C₄×C₁₉	—	2	2	no	—
337	C₄×C₁₉	—	4	2	no	—
338	C₄×C₁₉	—	4	1	no	—
339	C₄×C₁₉	—	4	1	no	—
340	C₄×C₁₉	—	4	2	no	—
341	C₄×C₁₉	—	4	2	no	—
342	C₄×C₁₉	—	8	1	no	—
343	C₄×C₁₉	—	8	1	no	—
344	C₄×C₁₉	—	8	1	no	—
345	#543	C₂²×C₁₉	1	1	yes	characteristic
346	#539	—	2	2	no	—
347	#539	—	2	1	no	—
348	#538	—	2	2	no	—
349	#538	C₂²×C₁₉	1	2	yes	—
350	#534	—	2	1	no	—
351	#534	C₂²×C₁₉	1	1	yes	characteristic
352	#529	—	2	2	no	—
353	#529	C₂²×C₁₉	1	2	yes	—
354	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic, complemented
355	#525	—	2	1	no	—
356	#525	—	2	2	no	—
357	C₂×C₄×D₄	—	2	1	no	—
358	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
359	#495	—	2	2	no	—
360	#488	—	2	2	no	—
361	#464	—	2	2	no	—
362	#463	—	2	2	no	—
363	#451	C₂²×C₁₉	1	2	yes	complemented
364	#450	C₂²×C₁₉	1	2	yes	complemented
365	#448	C₂²×C₁₉	1	2	yes	—
366	#447	C₂²×C₁₉	1	2	yes	—
367	#431	C₂²×C₁₉	1	2	yes	complemented
368	#397	—	2	1	no	—
369	#393	C₂²×C₁₉	1	1	yes	characteristic
370	#393	C₂²×C₁₉	1	1	yes	characteristic, complemented
371	#392	—	2	1	no	—
372	#392	C₂²×C₁₉	1	1	yes	characteristic
373	#392	C₂²×C₁₉	1	1	yes	characteristic, complemented
374	#386	—	2	1	no	—
375	#386	—	2	1	no	—
376	#383	C₂²×C₁₉	1	1	yes	characteristic, complemented
377	#328	C₂²×C₁₉	1	2	yes	complemented
378	#328	C₂²×C₁₉	1	2	yes	complemented
379	#327	C₂²×C₁₉	1	2	yes	—
380	#327	C₂²×C₁₉	1	2	yes	—
381	#323	C₂²×C₁₉	1	1	yes	characteristic
382	#323	C₂²×C₁₉	1	1	yes	characteristic
383	#323	C₂²×C₁₉	1	2	yes	complemented
384	C₂×C₁₉	—	2	1	no	—
385	C₂×C₁₉	—	2	1	no	—
386	C₂×C₁₉	—	4	2	no	—
387	C₂×C₁₉	—	8	1	no	—
388	C₂×C₁₉	—	8	2	no	—
389	C₂×C₁₉	—	16	1	no	—
390	C₂×C₁₉	#3002	1	1	yes	characteristic
391	C₂×C₁₉	#3019	1	1	yes	characteristic
392	C₂×C₁₉	#3027	1	1	yes	characteristic
393	C₂×#41	—	2	1	no	—
394	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
395	C₂²×D₄	—	2	1	no	—
396	C₂²×D₄	—	2	1	no	—
397	C₂²×D₄	—	2	1	no	—
398	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
399	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
400	C₂³×C₄	—	2	1	no	—
401	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
402	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
403	C₂×Q₁₆	—	2	2	no	—
404	C₂×SD₁₆	—	2	2	no	—
405	C₂×SD₁₆	—	2	2	no	—
406	C₂×D₈	—	2	2	no	—
407	#126	—	2	2	no	—
408	#126	—	2	2	no	—
409	#126	—	2	2	no	—
410	#125	—	2	2	no	—
411	#125	D₄×C₁₉	1	2	yes	complemented
412	#124	—	2	2	no	—
413	#124	—	2	2	no	—
414	#124	—	2	2	no	—
415	#124	D₄×C₁₉	1	2	yes	complemented
416	#123	—	2	2	no	—
417	#123	—	2	2	no	—
418	#123	—	2	2	no	—
419	#123	—	2	2	no	—
420	#123	—	2	2	no	—
421	#123	—	2	2	no	—
422	C₂²⋊Q₈	—	2	1	no	—
423	C₂²⋊Q₈	—	2	2	no	—
424	C₂²⋊Q₈	—	2	2	no	—
425	C₂²⋊Q₈	—	2	1	no	—
426	C₂²⋊Q₈	—	2	2	no	—
427	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
428	#121	—	2	2	no	—
429	#121	—	2	1	no	—
430	#121	—	2	2	no	—
431	#121	—	2	2	no	—
432	#121	—	2	1	no	—
433	#121	C₂³×C₁₉	1	2	yes	—
434	#120	—	2	2	no	—
435	#120	—	2	2	no	—
436	#120	—	2	2	no	—
437	C₄×Q₈	D₄×C₁₉	1	2	yes	complemented
438	C₄×D₄	—	2	2	no	—
439	C₄×D₄	—	2	2	no	—
440	C₄×D₄	—	2	2	no	—
441	C₄×D₄	—	2	2	no	—
442	C₄×D₄	—	2	2	no	—
443	C₄×D₄	—	2	2	no	—
444	C₄×D₄	—	2	2	no	—
445	C₄×D₄	D₄×C₁₉	1	2	yes	complemented
446	#117	—	2	1	no	—
447	#117	—	2	2	no	—
448	C₂×C₄⋊C₄	—	2	1	no	—
449	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
450	C₂×C₂²⋊C₄	—	2	1	no	—
451	C₂×C₂²⋊C₄	—	2	1	no	—
452	C₂×C₂²⋊C₄	—	2	1	no	—
453	C₂×C₂²⋊C₄	—	2	1	no	—
454	C₂×C₂²⋊C₄	—	2	1	no	—
455	C₂×C₂²⋊C₄	—	2	1	no	—
456	C₂×C₂²⋊C₄	—	2	1	no	—
457	C₂×C₂²⋊C₄	—	2	1	no	—
458	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
459	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
460	C₂×C₄²	—	2	1	no	—
461	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
462	C₄⋊C₈	—	2	2	no	—
463	#103	—	2	2	no	—
464	#103	—	2	2	no	—
465	#102	—	2	2	no	—
466	#102	—	2	2	no	—
467	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
468	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
469	C₄×C₈	—	2	2	no	—
470	#95	—	2	1	no	—
471	#95	—	2	1	no	—
472	#95	—	2	1	no	—
473	#95	—	2	1	no	—
474	#95	C₂³×C₁₉	1	1	yes	characteristic
475	#95	C₂³×C₁₉	1	1	yes	characteristic
476	C₁₉	#18306	1	1	yes	characteristic, direct product factor, Sylow
477	C₂⁴	—	2	1	no	—
478	C₂⁴	—	2	1	no	—
479	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
480	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
481	#41	—	8	2	no	—
482	C₂×Q₈	—	2	1	no	—
483	C₂×Q₈	—	2	2	no	—
484	C₂×Q₈	—	8	1	no	—
485	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
486	C₂×D₄	—	2	2	no	—
487	C₂×D₄	—	2	2	no	—
488	C₂×D₄	—	2	2	no	—
489	C₂×D₄	—	2	2	no	—
490	C₂×D₄	—	2	1	no	—
491	C₂×D₄	—	2	2	no	—
492	C₂×D₄	—	2	2	no	—
493	C₂×D₄	—	2	2	no	—
494	C₂×D₄	—	4	1	no	—
495	C₂×D₄	—	4	2	no	—
496	C₂×D₄	—	4	2	no	—
497	C₂×D₄	—	4	2	no	—
498	C₂×D₄	—	4	2	no	—
499	C₂×D₄	—	8	1	no	—
500	C₂×D₄	—	8	1	no	—
501	C₂×D₄	—	8	1	no	—
502	C₂×D₄	—	8	1	no	—
503	C₂×D₄	—	8	1	no	—
504	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	2	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	2	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	8	1	no	—
518	C₂²×C₄	—	8	1	no	—
519	C₂²×C₄	—	8	2	no	—
520	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
521	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
522	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
523	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
524	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
525	Q₁₆	—	8	2	no	—
526	SD₁₆	—	8	2	no	—
527	SD₁₆	—	8	2	no	—
528	D₈	—	8	2	no	—
529	C₂×C₈	—	2	2	no	—
530	C₂×C₈	—	2	2	no	—
531	C₄⋊C₄	—	2	2	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	2	2	no	—
535	C₄⋊C₄	—	2	2	no	—
536	C₄⋊C₄	—	2	2	no	—
537	C₄⋊C₄	—	2	2	no	—
538	C₄⋊C₄	—	2	2	no	—
539	C₄⋊C₄	—	2	2	no	—
540	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
541	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
542	C₂²⋊C₄	—	2	2	no	—
543	C₂²⋊C₄	—	2	2	no	—
544	C₂²⋊C₄	—	2	2	no	—
545	C₂²⋊C₄	—	2	2	no	—
546	C₂²⋊C₄	—	2	2	no	—
547	C₂²⋊C₄	—	2	2	no	—
548	C₂²⋊C₄	—	2	2	no	—
549	C₂²⋊C₄	—	2	2	no	—
550	C₂²⋊C₄	—	2	2	no	—
551	C₂²⋊C₄	—	2	2	no	—
552	C₂²⋊C₄	—	2	2	no	—
553	C₂²⋊C₄	—	2	2	no	—
554	C₂²⋊C₄	—	4	1	no	—
555	C₂²⋊C₄	—	4	2	no	—
556	C₂²⋊C₄	—	4	1	no	—
557	C₂²⋊C₄	—	8	1	no	—
558	C₂²⋊C₄	—	8	1	no	—
559	C₂²⋊C₄	—	8	1	no	—
560	C₂²⋊C₄	—	8	1	no	—
561	C₄²	—	2	2	no	—
562	C₄²	—	2	2	no	—
563	C₄²	C₂×D₄×C₁₉	1	2	yes	—
564	C₄²	C₂×D₄×C₁₉	1	2	yes	—
565	C₂³	—	2	1	no	—
566	C₂³	—	2	1	no	—
567	C₂³	—	2	1	no	—
568	C₂³	—	2	2	no	—
569	C₂³	—	2	1	no	—
570	C₂³	—	2	1	no	—
571	C₂³	—	4	1	no	—
572	C₂³	—	4	1	no	—
573	C₂³	—	4	1	no	—
574	C₂³	—	4	1	no	—
575	C₂³	—	4	2	no	—
576	C₂³	—	4	1	no	—
577	C₂³	—	4	1	no	—
578	C₂³	—	4	1	no	—
579	C₂³	—	4	1	no	—
580	C₂³	—	4	1	no	—
581	C₂³	—	4	1	no	—
582	C₂³	—	4	1	no	—
583	C₂³	—	8	1	no	—
584	C₂³	—	8	1	no	—
585	C₂³	C₁₉×#135	1	2	yes	—
586	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
587	Q₈	—	4	2	no	—
588	Q₈	—	4	2	no	—
589	Q₈	—	4	2	no	—
590	Q₈	—	8	1	no	—
591	D₄	—	4	4	no	—
592	D₄	—	4	2	no	—
593	D₄	—	4	2	no	—
594	D₄	—	4	2	no	—
595	D₄	—	4	4	no	—
596	D₄	—	4	2	no	—
597	D₄	—	4	2	no	—
598	D₄	—	8	1	no	—
599	D₄	—	8	2	no	—
600	D₄	—	8	2	no	—
601	D₄	—	8	4	no	—
602	D₄	—	8	4	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	2	no	—
613	C₂×C₄	—	4	2	no	—
614	C₂×C₄	—	4	4	no	—
615	C₂×C₄	—	4	2	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	8	1	no	—
628	C₂×C₄	—	8	1	no	—
629	C₂×C₄	—	8	2	no	—
630	C₂×C₄	—	8	1	no	—
631	C₂×C₄	—	8	1	no	—
632	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
633	C₂×C₄	C₁₉×#120	1	2	yes	—
634	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
635	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
636	C₈	—	4	2	no	—
637	C₈	—	4	2	no	—
638	C₂²	—	2	1	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	4	2	no	—
642	C₂²	—	4	2	no	—
643	C₂²	—	4	1	no	—
644	C₂²	—	4	1	no	—
645	C₂²	—	4	1	no	—
646	C₂²	—	4	2	no	—
647	C₂²	—	4	1	no	—
648	C₂²	—	4	2	no	—
649	C₂²	—	4	2	no	—
650	C₂²	—	4	1	no	—
651	C₂²	—	8	1	no	—
652	C₂²	—	8	1	no	—
653	C₂²	—	8	1	no	—
654	C₂²	—	8	1	no	—
655	C₂²	—	8	1	no	—
656	C₂²	—	8	1	no	—
657	C₂²	—	8	4	no	—
658	C₂²	—	8	1	no	—
659	C₂²	—	8	1	no	—
660	C₂²	—	8	1	no	—
661	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
662	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
663	C₂²	C₁₉×#575	1	1	yes	characteristic
664	C₄	—	2	2	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	2	no	—
668	C₄	—	4	2	no	—
669	C₄	—	4	1	no	—
670	C₄	—	4	1	no	—
671	C₄	—	4	2	no	—
672	C₄	—	4	2	no	—
673	C₄	—	8	1	no	—
674	C₄	—	8	1	no	—
675	C₄	—	8	1	no	—
676	C₂	—	2	1	no	—
677	C₂	—	2	1	no	—
678	C₂	—	4	2	no	—
679	C₂	—	8	1	no	—
680	C₂	—	8	2	no	—
681	C₂	—	16	1	no	—
682	C₂	C₁₉×#3002	1	1	yes	characteristic
683	C₂	C₁₉×#3019	1	1	yes	characteristic
684	C₂	C₁₉×#3027	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
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×#3459	C₂	semidirect
2. C₁₉×#3211	C₂	semidirect
3. C₁₉×#2631	C₂	semidirect
4. C₁₉×#1606	C₂	semidirect
5. C₁₉×#1602	C₂	semidirect
6. C₁₉×#1601	C₂	semidirect
7. C₁₉×#1600	C₂	semidirect
8. C₁₉×#1596	C₂	semidirect
9. C₁₉×#1595	C₂	semidirect
10. C₁₉×#1521	C₂	semidirect
11. C₁₉×#1460	C₂	semidirect
21. C₂×C₁₉×#124	C₂²	semidirect
30. C₁₉×#451	C₂²	semidirect
31. C₁₉×#450	C₂²	semidirect
34. C₁₉×#431	C₂²	semidirect
37. C₁₉×#393	C₂²	semidirect
40. C₁₉×#392	C₂²	semidirect
43. C₁₉×#383	C₂²	semidirect
44. C₁₉×#328	C₂²	semidirect
45. C₁₉×#328	C₂²	semidirect
50. C₁₉×#323	C₂²	semidirect
69. C₁₉×#125	D₄	semidirect
73. C₁₉×#124	D₄	semidirect
95. C₄×Q₈×C₁₉	D₄	semidirect
103. C₄×D₄×C₁₉	D₄	semidirect
222. #18306	C₁₉	direct (N × H)
296. #3459	C₂×C₁₉	semidirect
297. #3211	C₂×C₁₉	semidirect
298. #2631	C₂×C₁₉	semidirect
299. #1606	C₂×C₁₉	semidirect
300. #1602	C₂×C₁₉	semidirect
301. #1601	C₂×C₁₉	semidirect
302. #1600	C₂×C₁₉	semidirect
303. #1596	C₂×C₁₉	semidirect
304. #1595	C₂×C₁₉	semidirect
305. #1521	C₂×C₁₉	semidirect
306. #1460	C₂×C₁₉	semidirect
354. C₂×#124	C₂²×C₁₉	semidirect
363. #451	C₂²×C₁₉	semidirect
364. #450	C₂²×C₁₉	semidirect
367. #431	C₂²×C₁₉	semidirect
370. #393	C₂²×C₁₉	semidirect
373. #392	C₂²×C₁₉	semidirect
376. #383	C₂²×C₁₉	semidirect
377. #328	C₂²×C₁₉	semidirect
378. #328	C₂²×C₁₉	semidirect
383. #323	C₂²×C₁₉	semidirect
411. #125	D₄×C₁₉	semidirect
415. #124	D₄×C₁₉	semidirect
437. C₄×Q₈	D₄×C₁₉	semidirect
445. C₄×D₄	D₄×C₁₉	semidirect
476. C₁₉	#18306	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×#3211	2
C₁₉×#2631	2
C₁₉×#1606	2
C₁₉×#1602	2
C₁₉×#1601	2
C₁₉×#1600	2
C₁₉×#1596	2
C₁₉×#1595	2
C₁₉×#1521	2
C₁₉×#1460	2
#18306	19

Subgroups — C19×#18306 #18024265

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18306 #18024265