Subgroups — C₁₉×#18386 #18024345

Order 4864.

984 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3491	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3211	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2610	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1603	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×#1597	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
10	C₁₉×#1500	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1458	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#552	—	2	2	no	—
13	C₁₉×#552	—	2	2	no	—
14	C₁₉×#551	—	2	2	no	—
15	C₁₉×#551	—	2	2	no	—
16	C₁₉×#543	C₂²	1	1	yes	characteristic
17	C₁₉×#539	—	2	1	no	—
18	C₁₉×#539	C₂²	1	2	yes	—
19	C₁₉×#534	C₂²	1	1	yes	characteristic
20	C₁₉×#529	—	2	1	no	—
21	C₁₉×#529	C₂²	1	2	yes	—
22	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₁₉×#123	—	2	1	no	—
24	C₁₉×#518	—	2	1	no	—
25	C₂×C₁₉×#117	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×#395	C₂²	1	1	yes	characteristic, complemented
36	C₁₉×#394	C₂²	1	1	yes	characteristic, complemented
37	C₁₉×#393	C₂²	1	1	yes	characteristic
38	C₁₉×#392	C₂²	1	1	yes	characteristic
39	C₁₉×#390	—	2	1	no	—
40	C₁₉×#388	—	2	1	no	—
41	C₁₉×#388	—	2	1	no	—
42	C₁₉×#386	—	2	1	no	—
43	C₁₉×#376	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	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₁₉	—	2	1	no	—
53	C₂²×D₄×C₁₉	—	2	1	no	—
54	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
56	C₂×Q₁₆×C₁₉	—	2	2	no	—
57	C₂×SD₁₆×C₁₉	—	2	2	no	—
58	C₂×SD₁₆×C₁₉	—	2	2	no	—
59	C₂×D₈×C₁₉	—	2	2	no	—
60	C₁₉×#126	—	2	2	no	—
61	C₁₉×#126	—	2	2	no	—
62	C₁₉×#126	—	2	2	no	—
63	C₁₉×#126	—	2	2	no	—
64	C₁₉×#125	—	2	1	no	—
65	C₁₉×#125	—	2	2	no	—
66	C₁₉×#125	—	2	2	no	—
67	C₁₉×#125	D₄	1	2	yes	complemented
68	C₁₉×#124	—	2	1	no	—
69	C₁₉×#124	—	2	2	no	—
70	C₁₉×#124	—	2	2	no	—
71	C₁₉×#124	D₄	1	2	yes	complemented
72	C₁₉×#123	—	2	2	no	—
73	C₁₉×#123	—	2	2	no	—
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×C₂²⋊Q₈	—	2	2	no	—
80	C₁₉×C₂²⋊Q₈	—	2	2	no	—
81	C₁₉×C₂²⋊Q₈	—	2	2	no	—
82	C₁₉×C₂²⋊Q₈	—	2	1	no	—
83	C₁₉×C₂²⋊Q₈	—	2	2	no	—
84	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
85	C₁₉×#121	—	2	1	no	—
86	C₁₉×#121	C₂³	1	2	yes	—
87	C₁₉×#120	—	2	2	no	—
88	C₄×Q₈×C₁₉	—	2	1	no	—
89	C₄×Q₈×C₁₉	D₄	1	2	yes	complemented
90	C₄×D₄×C₁₉	—	2	2	no	—
91	C₄×D₄×C₁₉	—	2	2	no	—
92	C₄×D₄×C₁₉	—	2	1	no	—
93	C₄×D₄×C₁₉	—	2	2	no	—
94	C₄×D₄×C₁₉	—	2	2	no	—
95	C₄×D₄×C₁₉	D₄	1	2	yes	complemented
96	C₁₉×#117	—	2	2	no	—
97	C₁₉×#117	—	2	2	no	—
98	C₁₉×#117	—	2	2	no	—
99	C₁₉×#117	—	2	2	no	—
100	C₁₉×#117	—	2	2	no	—
101	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
102	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
103	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
104	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
106	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
107	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
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	D₄	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	D₄	1	1	yes	characteristic
120	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
121	C₁₉×C₄⋊C₈	—	2	2	no	—
122	C₁₉×#103	—	2	2	no	—
123	C₁₉×#103	—	2	2	no	—
124	C₁₉×#102	—	2	2	no	—
125	C₁₉×#102	—	2	2	no	—
126	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
127	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
128	C₄×C₈×C₁₉	—	2	2	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	C₂×Q₈×C₁₉	—	2	1	no	—
138	C₂×Q₈×C₁₉	—	2	2	no	—
139	C₂×Q₈×C₁₉	—	8	1	no	—
140	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
141	C₂×D₄×C₁₉	—	2	2	no	—
142	C₂×D₄×C₁₉	—	2	2	no	—
143	C₂×D₄×C₁₉	—	2	1	no	—
144	C₂×D₄×C₁₉	—	2	2	no	—
145	C₂×D₄×C₁₉	—	4	2	no	—
146	C₂×D₄×C₁₉	—	4	2	no	—
147	C₂×D₄×C₁₉	—	4	2	no	—
148	C₂×D₄×C₁₉	—	4	2	no	—
149	C₂×D₄×C₁₉	—	8	1	no	—
150	C₂×D₄×C₁₉	—	8	1	no	—
151	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₁₉	—	2	1	no	—
153	C₂²×C₄×C₁₉	—	2	2	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	1	no	—
160	C₂²×C₄×C₁₉	—	2	2	no	—
161	C₂²×C₄×C₁₉	—	2	1	no	—
162	C₂²×C₄×C₁₉	—	2	1	no	—
163	C₂²×C₄×C₁₉	—	4	1	no	—
164	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
170	Q₁₆×C₁₉	—	8	2	no	—
171	SD₁₆×C₁₉	—	8	2	no	—
172	SD₁₆×C₁₉	—	8	2	no	—
173	D₈×C₁₉	—	8	2	no	—
174	C₂×C₈×C₁₉	—	2	2	no	—
175	C₂×C₈×C₁₉	—	2	2	no	—
176	C₄⋊C₄×C₁₉	—	2	2	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	1	no	—
181	C₄⋊C₄×C₁₉	—	2	1	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	—	2	2	no	—
187	C₄⋊C₄×C₁₉	—	2	2	no	—
188	C₄⋊C₄×C₁₉	—	8	1	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	—	2	2	no	—
201	C₂²⋊C₄×C₁₉	—	2	2	no	—
202	C₂²⋊C₄×C₁₉	—	2	2	no	—
203	C₂²⋊C₄×C₁₉	—	4	2	no	—
204	C₂²⋊C₄×C₁₉	—	4	2	no	—
205	C₂²⋊C₄×C₁₉	—	4	1	no	—
206	C₂²⋊C₄×C₁₉	—	4	1	no	—
207	C₂²⋊C₄×C₁₉	—	4	2	no	—
208	C₂²⋊C₄×C₁₉	—	8	1	no	—
209	C₂²⋊C₄×C₁₉	—	8	1	no	—
210	C₄²×C₁₉	—	2	2	no	—
211	C₄²×C₁₉	—	2	1	no	—
212	C₄²×C₁₉	—	2	1	no	—
213	C₄²×C₁₉	—	2	2	no	—
214	C₄²×C₁₉	—	4	2	no	—
215	C₄²×C₁₉	C₂×D₄	1	2	yes	—
216	C₄²×C₁₉	C₂×D₄	1	2	yes	—
217	#18386	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	2	no	—
221	C₂³×C₁₉	—	4	1	no	—
222	C₂³×C₁₉	—	4	1	no	—
223	C₂³×C₁₉	—	4	2	no	—
224	C₂³×C₁₉	—	4	1	no	—
225	C₂³×C₁₉	—	4	1	no	—
226	C₂³×C₁₉	—	4	1	no	—
227	C₂³×C₁₉	—	4	1	no	—
228	C₂³×C₁₉	—	4	1	no	—
229	C₂³×C₁₉	—	4	1	no	—
230	C₂³×C₁₉	—	4	1	no	—
231	C₂³×C₁₉	—	8	1	no	—
232	C₂³×C₁₉	—	8	1	no	—
233	C₂³×C₁₉	#135	1	2	yes	—
234	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
235	Q₈×C₁₉	—	4	2	no	—
236	Q₈×C₁₉	—	4	2	no	—
237	Q₈×C₁₉	—	4	2	no	—
238	Q₈×C₁₉	—	8	1	no	—
239	D₄×C₁₉	—	4	2	no	—
240	D₄×C₁₉	—	4	2	no	—
241	D₄×C₁₉	—	4	2	no	—
242	D₄×C₁₉	—	4	4	no	—
243	D₄×C₁₉	—	4	2	no	—
244	D₄×C₁₉	—	4	2	no	—
245	D₄×C₁₉	—	8	1	no	—
246	D₄×C₁₉	—	8	4	no	—
247	C₂×C₄×C₁₉	—	2	1	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	1	no	—
252	C₂×C₄×C₁₉	—	2	2	no	—
253	C₂×C₄×C₁₉	—	2	2	no	—
254	C₂×C₄×C₁₉	—	2	2	no	—
255	C₂×C₄×C₁₉	—	2	1	no	—
256	C₂×C₄×C₁₉	—	2	1	no	—
257	C₂×C₄×C₁₉	—	2	1	no	—
258	C₂×C₄×C₁₉	—	4	1	no	—
259	C₂×C₄×C₁₉	—	4	1	no	—
260	C₂×C₄×C₁₉	—	4	2	no	—
261	C₂×C₄×C₁₉	—	4	2	no	—
262	C₂×C₄×C₁₉	—	4	1	no	—
263	C₂×C₄×C₁₉	—	4	2	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	—	8	2	no	—
274	C₂×C₄×C₁₉	—	8	1	no	—
275	C₂×C₄×C₁₉	—	8	2	no	—
276	C₂×C₄×C₁₉	—	8	1	no	—
277	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
278	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
279	C₂×C₄×C₁₉	#120	1	2	yes	—
280	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
281	C₈×C₁₉	—	4	2	no	—
282	C₈×C₁₉	—	4	2	no	—
283	#3491	C₂×C₁₉	1	1	yes	characteristic, complemented
284	#3211	C₂×C₁₉	1	2	yes	complemented
285	#2610	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#1603	C₂×C₁₉	1	2	yes	complemented
287	#1602	C₂×C₁₉	1	1	yes	characteristic, complemented
288	#1601	C₂×C₁₉	1	1	yes	characteristic, complemented
289	#1597	C₂×C₁₉	1	2	yes	complemented
290	#1596	C₂×C₁₉	1	1	yes	characteristic, complemented
291	#1595	C₂×C₁₉	1	1	yes	characteristic
292	#1500	C₂×C₁₉	1	2	yes	complemented
293	#1458	C₂×C₁₉	1	1	yes	characteristic, complemented
294	C₂²×C₁₉	—	2	1	no	—
295	C₂²×C₁₉	—	2	1	no	—
296	C₂²×C₁₉	—	2	2	no	—
297	C₂²×C₁₉	—	4	2	no	—
298	C₂²×C₁₉	—	4	1	no	—
299	C₂²×C₁₉	—	4	1	no	—
300	C₂²×C₁₉	—	4	2	no	—
301	C₂²×C₁₉	—	4	2	no	—
302	C₂²×C₁₉	—	4	2	no	—
303	C₂²×C₁₉	—	8	1	no	—
304	C₂²×C₁₉	—	8	1	no	—
305	C₂²×C₁₉	—	8	1	no	—
306	C₂²×C₁₉	—	8	1	no	—
307	C₂²×C₁₉	—	8	1	no	—
308	C₂²×C₁₉	—	8	1	no	—
309	C₂²×C₁₉	—	8	1	no	—
310	C₂²×C₁₉	—	8	1	no	—
311	C₂²×C₁₉	—	16	2	no	—
312	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
313	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
314	C₂²×C₁₉	#575	1	1	yes	characteristic
315	C₄×C₁₉	—	2	1	no	—
316	C₄×C₁₉	—	2	1	no	—
317	C₄×C₁₉	—	2	2	no	—
318	C₄×C₁₉	—	2	2	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	—	4	1	no	—
325	C₄×C₁₉	—	4	2	no	—
326	C₄×C₁₉	—	8	1	no	—
327	C₄×C₁₉	—	8	1	no	—
328	#552	—	2	2	no	—
329	#552	—	2	2	no	—
330	#551	—	2	2	no	—
331	#551	—	2	2	no	—
332	#543	C₂²×C₁₉	1	1	yes	characteristic
333	#539	—	2	1	no	—
334	#539	C₂²×C₁₉	1	2	yes	—
335	#534	C₂²×C₁₉	1	1	yes	characteristic
336	#529	—	2	1	no	—
337	#529	C₂²×C₁₉	1	2	yes	—
338	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic, complemented
339	C₂×#123	—	2	1	no	—
340	#518	—	2	1	no	—
341	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
342	#495	—	2	2	no	—
343	#488	—	2	2	no	—
344	#464	—	2	2	no	—
345	#463	—	2	2	no	—
346	#451	C₂²×C₁₉	1	2	yes	complemented
347	#450	C₂²×C₁₉	1	2	yes	complemented
348	#448	C₂²×C₁₉	1	2	yes	—
349	#447	C₂²×C₁₉	1	2	yes	—
350	#431	C₂²×C₁₉	1	2	yes	complemented
351	#395	C₂²×C₁₉	1	1	yes	characteristic, complemented
352	#394	C₂²×C₁₉	1	1	yes	characteristic, complemented
353	#393	C₂²×C₁₉	1	1	yes	characteristic
354	#392	C₂²×C₁₉	1	1	yes	characteristic
355	#390	—	2	1	no	—
356	#388	—	2	1	no	—
357	#388	—	2	1	no	—
358	#386	—	2	1	no	—
359	#376	C₂²×C₁₉	1	1	yes	characteristic, complemented
360	#328	C₂²×C₁₉	1	2	yes	complemented
361	#328	C₂²×C₁₉	1	2	yes	complemented
362	#327	C₂²×C₁₉	1	2	yes	—
363	#327	C₂²×C₁₉	1	2	yes	—
364	#324	C₂²×C₁₉	1	2	yes	complemented
365	#323	C₂²×C₁₉	1	1	yes	characteristic
366	#323	C₂²×C₁₉	1	1	yes	characteristic
367	C₂×C₁₉	—	2	1	no	—
368	C₂×C₁₉	—	2	1	no	—
369	C₂×C₁₉	—	4	2	no	—
370	C₂×C₁₉	—	8	2	no	—
371	C₂×C₁₉	—	16	1	no	—
372	C₂×C₁₉	#3002	1	1	yes	characteristic
373	C₂×C₁₉	#3018	1	1	yes	characteristic
374	C₂×C₁₉	#3027	1	1	yes	characteristic
375	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
376	C₂²×D₄	—	2	1	no	—
377	C₂²×D₄	—	2	1	no	—
378	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
379	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
380	C₂×Q₁₆	—	2	2	no	—
381	C₂×SD₁₆	—	2	2	no	—
382	C₂×SD₁₆	—	2	2	no	—
383	C₂×D₈	—	2	2	no	—
384	#126	—	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	#125	—	2	2	no	—
391	#125	D₄×C₁₉	1	2	yes	complemented
392	#124	—	2	1	no	—
393	#124	—	2	2	no	—
394	#124	—	2	2	no	—
395	#124	D₄×C₁₉	1	2	yes	complemented
396	#123	—	2	2	no	—
397	#123	—	2	2	no	—
398	#123	—	2	2	no	—
399	#123	—	2	2	no	—
400	#123	—	2	2	no	—
401	#123	—	2	2	no	—
402	#123	—	2	2	no	—
403	C₂²⋊Q₈	—	2	2	no	—
404	C₂²⋊Q₈	—	2	2	no	—
405	C₂²⋊Q₈	—	2	2	no	—
406	C₂²⋊Q₈	—	2	1	no	—
407	C₂²⋊Q₈	—	2	2	no	—
408	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
409	#121	—	2	1	no	—
410	#121	C₂³×C₁₉	1	2	yes	—
411	#120	—	2	2	no	—
412	C₄×Q₈	—	2	1	no	—
413	C₄×Q₈	D₄×C₁₉	1	2	yes	complemented
414	C₄×D₄	—	2	2	no	—
415	C₄×D₄	—	2	2	no	—
416	C₄×D₄	—	2	1	no	—
417	C₄×D₄	—	2	2	no	—
418	C₄×D₄	—	2	2	no	—
419	C₄×D₄	D₄×C₁₉	1	2	yes	complemented
420	#117	—	2	2	no	—
421	#117	—	2	2	no	—
422	#117	—	2	2	no	—
423	#117	—	2	2	no	—
424	#117	—	2	2	no	—
425	C₂×C₄⋊C₄	—	2	1	no	—
426	C₂×C₄⋊C₄	—	2	1	no	—
427	C₂×C₄⋊C₄	—	2	1	no	—
428	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
429	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
430	C₂×C₂²⋊C₄	—	2	2	no	—
431	C₂×C₂²⋊C₄	—	2	1	no	—
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	—	2	1	no	—
438	C₂×C₂²⋊C₄	—	2	1	no	—
439	C₂×C₂²⋊C₄	—	2	1	no	—
440	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
441	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
442	C₂×C₄²	—	2	1	no	—
443	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
444	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
445	C₄⋊C₈	—	2	2	no	—
446	#103	—	2	2	no	—
447	#103	—	2	2	no	—
448	#102	—	2	2	no	—
449	#102	—	2	2	no	—
450	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
451	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
452	C₄×C₈	—	2	2	no	—
453	#95	—	2	1	no	—
454	#95	—	2	1	no	—
455	#95	—	2	1	no	—
456	#95	C₂³×C₁₉	1	1	yes	characteristic
457	#95	C₂³×C₁₉	1	1	yes	characteristic
458	C₁₉	#18386	1	1	yes	characteristic, direct product factor, Sylow
459	C₂⁴	—	2	1	no	—
460	C₂⁴	—	2	1	no	—
461	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
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	1	no	—
469	C₂×D₄	—	2	2	no	—
470	C₂×D₄	—	4	2	no	—
471	C₂×D₄	—	4	2	no	—
472	C₂×D₄	—	4	2	no	—
473	C₂×D₄	—	4	2	no	—
474	C₂×D₄	—	8	1	no	—
475	C₂×D₄	—	8	1	no	—
476	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	2	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	4	1	no	—
489	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
490	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
491	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
492	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
493	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
494	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
495	Q₁₆	—	8	2	no	—
496	SD₁₆	—	8	2	no	—
497	SD₁₆	—	8	2	no	—
498	D₈	—	8	2	no	—
499	C₂×C₈	—	2	2	no	—
500	C₂×C₈	—	2	2	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	—	2	2	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	8	1	no	—
514	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
515	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
516	C₂²⋊C₄	—	2	2	no	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	—	2	2	no	—
519	C₂²⋊C₄	—	2	2	no	—
520	C₂²⋊C₄	—	2	2	no	—
521	C₂²⋊C₄	—	2	2	no	—
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	—	4	2	no	—
529	C₂²⋊C₄	—	4	2	no	—
530	C₂²⋊C₄	—	4	1	no	—
531	C₂²⋊C₄	—	4	1	no	—
532	C₂²⋊C₄	—	4	2	no	—
533	C₂²⋊C₄	—	8	1	no	—
534	C₂²⋊C₄	—	8	1	no	—
535	C₄²	—	2	2	no	—
536	C₄²	—	2	1	no	—
537	C₄²	—	2	1	no	—
538	C₄²	—	2	2	no	—
539	C₄²	—	4	2	no	—
540	C₄²	C₂×D₄×C₁₉	1	2	yes	—
541	C₄²	C₂×D₄×C₁₉	1	2	yes	—
542	C₂³	—	2	1	no	—
543	C₂³	—	2	1	no	—
544	C₂³	—	2	2	no	—
545	C₂³	—	4	1	no	—
546	C₂³	—	4	1	no	—
547	C₂³	—	4	2	no	—
548	C₂³	—	4	1	no	—
549	C₂³	—	4	1	no	—
550	C₂³	—	4	1	no	—
551	C₂³	—	4	1	no	—
552	C₂³	—	4	1	no	—
553	C₂³	—	4	1	no	—
554	C₂³	—	4	1	no	—
555	C₂³	—	8	1	no	—
556	C₂³	—	8	1	no	—
557	C₂³	C₁₉×#135	1	2	yes	—
558	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
559	Q₈	—	4	2	no	—
560	Q₈	—	4	2	no	—
561	Q₈	—	4	2	no	—
562	Q₈	—	8	1	no	—
563	D₄	—	4	2	no	—
564	D₄	—	4	2	no	—
565	D₄	—	4	2	no	—
566	D₄	—	4	4	no	—
567	D₄	—	4	2	no	—
568	D₄	—	4	2	no	—
569	D₄	—	8	1	no	—
570	D₄	—	8	4	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	2	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	2	no	—
598	C₂×C₄	—	8	1	no	—
599	C₂×C₄	—	8	2	no	—
600	C₂×C₄	—	8	1	no	—
601	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
602	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
603	C₂×C₄	C₁₉×#120	1	2	yes	—
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	—	4	2	no	—
611	C₂²	—	4	1	no	—
612	C₂²	—	4	1	no	—
613	C₂²	—	4	2	no	—
614	C₂²	—	4	2	no	—
615	C₂²	—	4	2	no	—
616	C₂²	—	8	1	no	—
617	C₂²	—	8	1	no	—
618	C₂²	—	8	1	no	—
619	C₂²	—	8	1	no	—
620	C₂²	—	8	1	no	—
621	C₂²	—	8	1	no	—
622	C₂²	—	8	1	no	—
623	C₂²	—	8	1	no	—
624	C₂²	—	16	2	no	—
625	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
626	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
627	C₂²	C₁₉×#575	1	1	yes	characteristic
628	C₄	—	2	1	no	—
629	C₄	—	2	1	no	—
630	C₄	—	2	2	no	—
631	C₄	—	2	2	no	—
632	C₄	—	4	2	no	—
633	C₄	—	4	1	no	—
634	C₄	—	4	2	no	—
635	C₄	—	4	1	no	—
636	C₄	—	4	2	no	—
637	C₄	—	4	1	no	—
638	C₄	—	4	2	no	—
639	C₄	—	8	1	no	—
640	C₄	—	8	1	no	—
641	C₂	—	2	1	no	—
642	C₂	—	2	1	no	—
643	C₂	—	4	2	no	—
644	C₂	—	8	2	no	—
645	C₂	—	16	1	no	—
646	C₂	C₁₉×#3002	1	1	yes	characteristic
647	C₂	C₁₉×#3018	1	1	yes	characteristic
648	C₂	C₁₉×#3027	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#1595	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×#3491	C₂	semidirect
2. C₁₉×#3211	C₂	semidirect
3. C₁₉×#2610	C₂	semidirect
4. C₁₉×#1603	C₂	semidirect
5. C₁₉×#1602	C₂	semidirect
6. C₁₉×#1601	C₂	semidirect
7. C₁₉×#1597	C₂	semidirect
8. C₁₉×#1596	C₂	semidirect
10. C₁₉×#1500	C₂	semidirect
11. C₁₉×#1458	C₂	semidirect
22. C₂×C₁₉×#124	C₂²	semidirect
30. C₁₉×#451	C₂²	semidirect
31. C₁₉×#450	C₂²	semidirect
34. C₁₉×#431	C₂²	semidirect
35. C₁₉×#395	C₂²	semidirect
36. C₁₉×#394	C₂²	semidirect
43. C₁₉×#376	C₂²	semidirect
44. C₁₉×#328	C₂²	semidirect
45. C₁₉×#328	C₂²	semidirect
48. C₁₉×#324	C₂²	semidirect
67. C₁₉×#125	D₄	semidirect
71. C₁₉×#124	D₄	semidirect
89. C₄×Q₈×C₁₉	D₄	semidirect
95. C₄×D₄×C₁₉	D₄	semidirect
217. #18386	C₁₉	direct (N × H)
283. #3491	C₂×C₁₉	semidirect
284. #3211	C₂×C₁₉	semidirect
285. #2610	C₂×C₁₉	semidirect
286. #1603	C₂×C₁₉	semidirect
287. #1602	C₂×C₁₉	semidirect
288. #1601	C₂×C₁₉	semidirect
289. #1597	C₂×C₁₉	semidirect
290. #1596	C₂×C₁₉	semidirect
292. #1500	C₂×C₁₉	semidirect
293. #1458	C₂×C₁₉	semidirect
338. C₂×#124	C₂²×C₁₉	semidirect
346. #451	C₂²×C₁₉	semidirect
347. #450	C₂²×C₁₉	semidirect
350. #431	C₂²×C₁₉	semidirect
351. #395	C₂²×C₁₉	semidirect
352. #394	C₂²×C₁₉	semidirect
359. #376	C₂²×C₁₉	semidirect
360. #328	C₂²×C₁₉	semidirect
361. #328	C₂²×C₁₉	semidirect
364. #324	C₂²×C₁₉	semidirect
391. #125	D₄×C₁₉	semidirect
395. #124	D₄×C₁₉	semidirect
413. C₄×Q₈	D₄×C₁₉	semidirect
419. C₄×D₄	D₄×C₁₉	semidirect
458. C₁₉	#18386	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×#3491	2
C₁₉×#3211	2
C₁₉×#2610	2
C₁₉×#1603	2
C₁₉×#1602	2
C₁₉×#1601	2
C₁₉×#1597	2
C₁₉×#1596	2
C₁₉×#1595	2
C₁₉×#1500	2
C₁₉×#1458	2
#18386	19

Subgroups — C19×#18386 #18024345

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18386 #18024345