Subgroups — C₁₉×#18385 #18024344

Order 4864.

1012 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3505	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3189	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3187	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2564	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1618	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1615	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1606	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1603	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₉×#328	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₉×#327	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1459	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#553	—	2	2	no	—
13	C₁₉×#553	—	2	1	no	—
14	C₁₉×#552	—	2	1	no	—
15	C₁₉×#551	—	2	2	no	—
16	C₁₉×#548	—	2	1	no	—
17	C₁₉×#546	—	2	1	no	—
18	C₁₉×#539	C₂²	1	2	yes	—
19	C₁₉×#538	C₂²	1	2	yes	—
20	C₁₉×#534	—	2	1	no	—
21	C₁₉×#529	—	2	1	no	—
22	C₁₉×#525	—	2	1	no	—
23	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
26	C₁₉×#518	—	2	1	no	—
27	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
28	C₁₉×#484	—	2	1	no	—
29	C₁₉×#484	C₂²	1	2	yes	complemented
30	C₁₉×#483	—	2	1	no	—
31	C₁₉×#481	C₂²	1	2	yes	—
32	C₁₉×#467	—	2	2	no	—
33	C₁₉×#465	—	2	2	no	—
34	C₁₉×#451	—	2	1	no	—
35	C₁₉×#451	C₂²	1	2	yes	complemented
36	C₁₉×#450	—	2	1	no	—
37	C₁₉×#448	C₂²	1	2	yes	—
38	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₁₉×#400	C₂²	1	1	yes	characteristic, complemented
41	C₁₉×#399	C₂²	1	1	yes	characteristic, complemented
42	C₁₉×#395	C₂²	1	1	yes	characteristic, complemented
43	C₁₉×#393	C₂²	1	1	yes	characteristic, complemented
44	C₁₉×#387	—	2	1	no	—
45	C₁₉×#386	—	2	1	no	—
46	C₁₉×#385	—	2	1	no	—
47	C₁₉×#380	—	2	1	no	—
48	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
49	C₁₉×#328	C₂²	1	2	yes	complemented
50	C₁₉×#328	C₂²	1	2	yes	complemented
51	C₁₉×#327	C₂²	1	2	yes	—
52	C₁₉×#327	C₂²	1	2	yes	—
53	C₁₉×#324	C₂²	1	2	yes	complemented
54	C₁₉×#323	C₂²	1	2	yes	complemented
55	C₂×#41×C₁₉	—	2	1	no	—
56	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
57	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
58	C₂²×D₄×C₁₉	—	2	1	no	—
59	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
60	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₁₉	—	2	1	no	—
62	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂×Q₁₆×C₁₉	—	2	2	no	—
65	C₂×SD₁₆×C₁₉	—	2	2	no	—
66	C₂²×C₈×C₁₉	—	2	1	no	—
67	C₂²×C₈×C₁₉	—	2	1	no	—
68	C₁₉×#126	—	2	2	no	—
69	C₁₉×#126	—	2	2	no	—
70	C₁₉×#126	—	2	2	no	—
71	C₁₉×#125	—	2	1	no	—
72	C₁₉×#125	—	2	2	no	—
73	C₁₉×#124	—	2	1	no	—
74	C₁₉×#124	—	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	1	no	—
83	C₁₉×C₂²⋊Q₈	—	2	1	no	—
84	C₁₉×C₂²⋊Q₈	—	2	1	no	—
85	C₁₉×C₂²⋊Q₈	—	2	1	no	—
86	C₁₉×C₂²⋊Q₈	—	2	1	no	—
87	C₁₉×C₂²⋊Q₈	—	2	1	no	—
88	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
89	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
90	C₁₉×#121	—	2	1	no	—
91	C₁₉×#121	—	2	2	no	—
92	C₁₉×#121	—	2	2	no	—
93	C₁₉×#121	—	2	2	no	—
94	C₁₉×#121	—	2	1	no	—
95	C₁₉×#121	—	2	1	no	—
96	C₁₉×#121	D₄	1	2	yes	—
97	C₁₉×#121	C₂³	1	2	yes	—
98	C₁₉×#120	—	2	2	no	—
99	C₁₉×#120	—	2	2	no	—
100	C₄×Q₈×C₁₉	—	2	1	no	—
101	C₄×D₄×C₁₉	—	2	2	no	—
102	C₄×D₄×C₁₉	—	2	2	no	—
103	C₄×D₄×C₁₉	—	2	2	no	—
104	C₄×D₄×C₁₉	—	2	1	no	—
105	C₄×D₄×C₁₉	—	2	1	no	—
106	C₄×D₄×C₁₉	—	2	1	no	—
107	C₄×D₄×C₁₉	—	2	1	no	—
108	C₄×D₄×C₁₉	—	2	1	no	—
109	C₄×D₄×C₁₉	—	2	2	no	—
110	C₄×D₄×C₁₉	—	2	2	no	—
111	C₁₉×#117	—	2	2	no	—
112	C₁₉×#117	—	2	1	no	—
113	C₁₉×#117	—	2	2	no	—
114	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
115	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
116	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
117	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
118	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
122	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
123	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
129	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
131	C₁₉×#107	—	2	2	no	—
132	C₁₉×#106	—	2	2	no	—
133	C₁₉×#103	—	2	2	no	—
134	C₁₉×#103	—	2	2	no	—
135	C₁₉×#103	—	2	2	no	—
136	C₁₉×#102	—	2	2	no	—
137	C₁₉×C₂²⋊C₈	—	2	1	no	—
138	C₁₉×C₂²⋊C₈	—	2	1	no	—
139	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
140	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
141	C₁₉×#95	—	2	1	no	—
142	C₁₉×#95	—	2	1	no	—
143	C₁₉×#95	—	2	1	no	—
144	C₁₉×#95	—	2	1	no	—
145	C₁₉×#95	—	2	1	no	—
146	C₁₉×#95	C₂³	1	1	yes	characteristic
147	C₁₉×#95	C₂³	1	1	yes	characteristic
148	C₂⁴×C₁₉	—	2	1	no	—
149	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
151	#41×C₁₉	—	8	2	no	—
152	C₂×Q₈×C₁₉	—	2	1	no	—
153	C₂×Q₈×C₁₉	—	2	1	no	—
154	C₂×Q₈×C₁₉	—	2	1	no	—
155	C₂×Q₈×C₁₉	—	8	1	no	—
156	C₂×Q₈×C₁₉	—	8	1	no	—
157	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
158	C₂×D₄×C₁₉	—	2	1	no	—
159	C₂×D₄×C₁₉	—	2	1	no	—
160	C₂×D₄×C₁₉	—	2	2	no	—
161	C₂×D₄×C₁₉	—	2	2	no	—
162	C₂×D₄×C₁₉	—	2	2	no	—
163	C₂×D₄×C₁₉	—	2	2	no	—
164	C₂×D₄×C₁₉	—	2	2	no	—
165	C₂×D₄×C₁₉	—	2	2	no	—
166	C₂×D₄×C₁₉	—	2	1	no	—
167	C₂×D₄×C₁₉	—	4	2	no	—
168	C₂×D₄×C₁₉	—	4	2	no	—
169	C₂×D₄×C₁₉	—	8	1	no	—
170	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₁₉	—	2	1	no	—
172	C₂²×C₄×C₁₉	—	2	1	no	—
173	C₂²×C₄×C₁₉	—	2	2	no	—
174	C₂²×C₄×C₁₉	—	2	2	no	—
175	C₂²×C₄×C₁₉	—	2	1	no	—
176	C₂²×C₄×C₁₉	—	2	1	no	—
177	C₂²×C₄×C₁₉	—	2	1	no	—
178	C₂²×C₄×C₁₉	—	2	1	no	—
179	C₂²×C₄×C₁₉	—	2	1	no	—
180	C₂²×C₄×C₁₉	—	2	1	no	—
181	C₂²×C₄×C₁₉	—	2	1	no	—
182	C₂²×C₄×C₁₉	—	4	2	no	—
183	C₂²×C₄×C₁₉	—	4	2	no	—
184	C₂²×C₄×C₁₉	—	8	1	no	—
185	C₂²×C₄×C₁₉	—	8	1	no	—
186	C₂²×C₄×C₁₉	—	8	1	no	—
187	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
196	Q₁₆×C₁₉	—	8	2	no	—
197	SD₁₆×C₁₉	—	8	2	no	—
198	C₂×C₈×C₁₉	—	2	2	no	—
199	C₂×C₈×C₁₉	—	2	2	no	—
200	C₂×C₈×C₁₉	—	8	1	no	—
201	C₂×C₈×C₁₉	—	8	1	no	—
202	C₄⋊C₄×C₁₉	—	2	2	no	—
203	C₄⋊C₄×C₁₉	—	2	2	no	—
204	C₄⋊C₄×C₁₉	—	2	2	no	—
205	C₄⋊C₄×C₁₉	—	2	2	no	—
206	C₄⋊C₄×C₁₉	—	2	2	no	—
207	C₄⋊C₄×C₁₉	—	2	1	no	—
208	C₄⋊C₄×C₁₉	—	2	1	no	—
209	C₄⋊C₄×C₁₉	—	2	2	no	—
210	C₄⋊C₄×C₁₉	—	2	1	no	—
211	C₄⋊C₄×C₁₉	—	2	1	no	—
212	C₄⋊C₄×C₁₉	—	2	1	no	—
213	C₄⋊C₄×C₁₉	—	2	1	no	—
214	C₄⋊C₄×C₁₉	—	4	2	no	—
215	C₄⋊C₄×C₁₉	—	4	1	no	—
216	C₄⋊C₄×C₁₉	—	4	1	no	—
217	C₄⋊C₄×C₁₉	—	8	1	no	—
218	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
219	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
220	C₂²⋊C₄×C₁₉	—	2	2	no	—
221	C₂²⋊C₄×C₁₉	—	2	2	no	—
222	C₂²⋊C₄×C₁₉	—	2	2	no	—
223	C₂²⋊C₄×C₁₉	—	2	2	no	—
224	C₂²⋊C₄×C₁₉	—	2	2	no	—
225	C₂²⋊C₄×C₁₉	—	2	2	no	—
226	C₂²⋊C₄×C₁₉	—	2	1	no	—
227	C₂²⋊C₄×C₁₉	—	2	2	no	—
228	C₂²⋊C₄×C₁₉	—	2	1	no	—
229	C₂²⋊C₄×C₁₉	—	2	2	no	—
230	C₂²⋊C₄×C₁₉	—	2	2	no	—
231	C₂²⋊C₄×C₁₉	—	2	2	no	—
232	C₂²⋊C₄×C₁₉	—	2	1	no	—
233	C₂²⋊C₄×C₁₉	—	2	1	no	—
234	C₂²⋊C₄×C₁₉	—	4	2	no	—
235	C₂²⋊C₄×C₁₉	—	4	1	no	—
236	C₂²⋊C₄×C₁₉	—	4	1	no	—
237	C₂²⋊C₄×C₁₉	—	8	1	no	—
238	C₄²×C₁₉	—	2	2	no	—
239	C₄²×C₁₉	—	2	2	no	—
240	C₄²×C₁₉	—	2	1	no	—
241	C₄²×C₁₉	—	2	1	no	—
242	#18385	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
243	C₂³×C₁₉	—	2	1	no	—
244	C₂³×C₁₉	—	2	2	no	—
245	C₂³×C₁₉	—	2	1	no	—
246	C₂³×C₁₉	—	2	1	no	—
247	C₂³×C₁₉	—	4	1	no	—
248	C₂³×C₁₉	—	4	1	no	—
249	C₂³×C₁₉	—	4	1	no	—
250	C₂³×C₁₉	—	4	1	no	—
251	C₂³×C₁₉	—	4	2	no	—
252	C₂³×C₁₉	—	8	1	no	—
253	C₂³×C₁₉	—	8	1	no	—
254	C₂³×C₁₉	#120	1	1	yes	characteristic
255	C₂³×C₁₉	#120	1	1	yes	characteristic
256	C₂³×C₁₉	#135	1	2	yes	—
257	C₂³×C₁₉	#137	1	2	yes	—
258	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
259	Q₈×C₁₉	—	4	2	no	—
260	Q₈×C₁₉	—	4	2	no	—
261	Q₈×C₁₉	—	4	2	no	—
262	Q₈×C₁₉	—	4	2	no	—
263	D₄×C₁₉	—	4	2	no	—
264	D₄×C₁₉	—	4	2	no	—
265	D₄×C₁₉	—	4	2	no	—
266	D₄×C₁₉	—	4	2	no	—
267	D₄×C₁₉	—	4	2	no	—
268	D₄×C₁₉	—	4	2	no	—
269	D₄×C₁₉	—	4	4	no	—
270	D₄×C₁₉	—	8	2	no	—
271	D₄×C₁₉	—	8	2	no	—
272	C₂×C₄×C₁₉	—	2	2	no	—
273	C₂×C₄×C₁₉	—	2	1	no	—
274	C₂×C₄×C₁₉	—	2	1	no	—
275	C₂×C₄×C₁₉	—	2	2	no	—
276	C₂×C₄×C₁₉	—	2	1	no	—
277	C₂×C₄×C₁₉	—	2	2	no	—
278	C₂×C₄×C₁₉	—	2	2	no	—
279	C₂×C₄×C₁₉	—	2	1	no	—
280	C₂×C₄×C₁₉	—	2	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	—	4	1	no	—
286	C₂×C₄×C₁₉	—	4	1	no	—
287	C₂×C₄×C₁₉	—	4	2	no	—
288	C₂×C₄×C₁₉	—	4	1	no	—
289	C₂×C₄×C₁₉	—	4	1	no	—
290	C₂×C₄×C₁₉	—	4	2	no	—
291	C₂×C₄×C₁₉	—	4	1	no	—
292	C₂×C₄×C₁₉	—	4	1	no	—
293	C₂×C₄×C₁₉	—	4	1	no	—
294	C₂×C₄×C₁₉	—	4	1	no	—
295	C₂×C₄×C₁₉	—	4	1	no	—
296	C₂×C₄×C₁₉	—	4	1	no	—
297	C₂×C₄×C₁₉	—	4	1	no	—
298	C₂×C₄×C₁₉	—	4	1	no	—
299	C₂×C₄×C₁₉	—	4	1	no	—
300	C₂×C₄×C₁₉	—	4	1	no	—
301	C₂×C₄×C₁₉	—	4	1	no	—
302	C₂×C₄×C₁₉	—	8	1	no	—
303	C₂×C₄×C₁₉	—	8	1	no	—
304	C₂×C₄×C₁₉	—	8	1	no	—
305	C₂×C₄×C₁₉	—	8	2	no	—
306	C₂×C₄×C₁₉	—	8	2	no	—
307	C₂×C₄×C₁₉	—	8	4	no	—
308	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
309	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
310	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
311	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
312	C₈×C₁₉	—	4	2	no	—
313	C₈×C₁₉	—	4	2	no	—
314	#3505	C₂×C₁₉	1	1	yes	characteristic
315	#3189	C₂×C₁₉	1	1	yes	characteristic, complemented
316	#3187	C₂×C₁₉	1	1	yes	characteristic, complemented
317	#2564	C₂×C₁₉	1	1	yes	characteristic, complemented
318	#1618	C₂×C₁₉	1	2	yes	complemented
319	#1615	C₂×C₁₉	1	2	yes	complemented
320	#1606	C₂×C₁₉	1	2	yes	complemented
321	#1603	C₂×C₁₉	1	2	yes	complemented
322	C₂×#328	C₂×C₁₉	1	1	yes	characteristic, complemented
323	C₂×#327	C₂×C₁₉	1	1	yes	characteristic, complemented
324	#1459	C₂×C₁₉	1	1	yes	characteristic, complemented
325	C₂²×C₁₉	—	2	1	no	—
326	C₂²×C₁₉	—	2	1	no	—
327	C₂²×C₁₉	—	2	1	no	—
328	C₂²×C₁₉	—	2	1	no	—
329	C₂²×C₁₉	—	2	1	no	—
330	C₂²×C₁₉	—	2	1	no	—
331	C₂²×C₁₉	—	4	2	no	—
332	C₂²×C₁₉	—	4	2	no	—
333	C₂²×C₁₉	—	4	2	no	—
334	C₂²×C₁₉	—	4	1	no	—
335	C₂²×C₁₉	—	4	2	no	—
336	C₂²×C₁₉	—	4	2	no	—
337	C₂²×C₁₉	—	4	1	no	—
338	C₂²×C₁₉	—	4	1	no	—
339	C₂²×C₁₉	—	4	2	no	—
340	C₂²×C₁₉	—	8	1	no	—
341	C₂²×C₁₉	—	16	2	no	—
342	C₂²×C₁₉	#452	1	2	yes	—
343	C₂²×C₁₉	#452	1	2	yes	—
344	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
345	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
346	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
347	C₄×C₁₉	—	2	1	no	—
348	C₄×C₁₉	—	2	1	no	—
349	C₄×C₁₉	—	2	1	no	—
350	C₄×C₁₉	—	2	1	no	—
351	C₄×C₁₉	—	4	2	no	—
352	C₄×C₁₉	—	4	1	no	—
353	C₄×C₁₉	—	4	2	no	—
354	C₄×C₁₉	—	4	1	no	—
355	C₄×C₁₉	—	4	2	no	—
356	C₄×C₁₉	—	4	1	no	—
357	C₄×C₁₉	—	4	2	no	—
358	C₄×C₁₉	—	8	1	no	—
359	C₄×C₁₉	—	8	1	no	—
360	C₄×C₁₉	—	8	1	no	—
361	#553	—	2	2	no	—
362	#553	—	2	1	no	—
363	#552	—	2	1	no	—
364	#551	—	2	2	no	—
365	#548	—	2	1	no	—
366	#546	—	2	1	no	—
367	#539	C₂²×C₁₉	1	2	yes	—
368	#538	C₂²×C₁₉	1	2	yes	—
369	#534	—	2	1	no	—
370	#529	—	2	1	no	—
371	#525	—	2	1	no	—
372	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
373	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
374	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
375	#518	—	2	1	no	—
376	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
377	#484	—	2	1	no	—
378	#484	C₂²×C₁₉	1	2	yes	complemented
379	#483	—	2	1	no	—
380	#481	C₂²×C₁₉	1	2	yes	—
381	#467	—	2	2	no	—
382	#465	—	2	2	no	—
383	#451	—	2	1	no	—
384	#451	C₂²×C₁₉	1	2	yes	complemented
385	#450	—	2	1	no	—
386	#448	C₂²×C₁₉	1	2	yes	—
387	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
388	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
389	#400	C₂²×C₁₉	1	1	yes	characteristic, complemented
390	#399	C₂²×C₁₉	1	1	yes	characteristic, complemented
391	#395	C₂²×C₁₉	1	1	yes	characteristic, complemented
392	#393	C₂²×C₁₉	1	1	yes	characteristic, complemented
393	#387	—	2	1	no	—
394	#386	—	2	1	no	—
395	#385	—	2	1	no	—
396	#380	—	2	1	no	—
397	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
398	#328	C₂²×C₁₉	1	2	yes	complemented
399	#328	C₂²×C₁₉	1	2	yes	complemented
400	#327	C₂²×C₁₉	1	2	yes	—
401	#327	C₂²×C₁₉	1	2	yes	—
402	#324	C₂²×C₁₉	1	2	yes	complemented
403	#323	C₂²×C₁₉	1	2	yes	complemented
404	C₂×C₁₉	—	2	1	no	—
405	C₂×C₁₉	—	2	1	no	—
406	C₂×C₁₉	—	2	2	no	—
407	C₂×C₁₉	—	2	2	no	—
408	C₂×C₁₉	—	8	1	no	—
409	C₂×C₁₉	—	8	2	no	—
410	C₂×C₁₉	C₂×#452	1	1	yes	characteristic
411	C₂×C₁₉	#3018	1	1	yes	characteristic
412	C₂×C₁₉	#3026	1	1	yes	characteristic
413	C₂×#41	—	2	1	no	—
414	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
415	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
416	C₂²×D₄	—	2	1	no	—
417	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
418	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
419	C₂³×C₄	—	2	1	no	—
420	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
421	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
422	C₂×Q₁₆	—	2	2	no	—
423	C₂×SD₁₆	—	2	2	no	—
424	C₂²×C₈	—	2	1	no	—
425	C₂²×C₈	—	2	1	no	—
426	#126	—	2	2	no	—
427	#126	—	2	2	no	—
428	#126	—	2	2	no	—
429	#125	—	2	1	no	—
430	#125	—	2	2	no	—
431	#124	—	2	1	no	—
432	#124	—	2	2	no	—
433	#123	—	2	2	no	—
434	#123	—	2	2	no	—
435	#123	—	2	2	no	—
436	#123	—	2	2	no	—
437	#123	—	2	2	no	—
438	C₂²⋊Q₈	—	2	1	no	—
439	C₂²⋊Q₈	—	2	2	no	—
440	C₂²⋊Q₈	—	2	1	no	—
441	C₂²⋊Q₈	—	2	1	no	—
442	C₂²⋊Q₈	—	2	1	no	—
443	C₂²⋊Q₈	—	2	1	no	—
444	C₂²⋊Q₈	—	2	1	no	—
445	C₂²⋊Q₈	—	2	1	no	—
446	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
447	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
448	#121	—	2	1	no	—
449	#121	—	2	2	no	—
450	#121	—	2	2	no	—
451	#121	—	2	2	no	—
452	#121	—	2	1	no	—
453	#121	—	2	1	no	—
454	#121	D₄×C₁₉	1	2	yes	—
455	#121	C₂³×C₁₉	1	2	yes	—
456	#120	—	2	2	no	—
457	#120	—	2	2	no	—
458	C₄×Q₈	—	2	1	no	—
459	C₄×D₄	—	2	2	no	—
460	C₄×D₄	—	2	2	no	—
461	C₄×D₄	—	2	2	no	—
462	C₄×D₄	—	2	1	no	—
463	C₄×D₄	—	2	1	no	—
464	C₄×D₄	—	2	1	no	—
465	C₄×D₄	—	2	1	no	—
466	C₄×D₄	—	2	1	no	—
467	C₄×D₄	—	2	2	no	—
468	C₄×D₄	—	2	2	no	—
469	#117	—	2	2	no	—
470	#117	—	2	1	no	—
471	#117	—	2	2	no	—
472	C₂×C₄⋊C₄	—	2	1	no	—
473	C₂×C₄⋊C₄	—	2	1	no	—
474	C₂×C₄⋊C₄	—	2	1	no	—
475	C₂×C₄⋊C₄	—	2	1	no	—
476	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
477	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
478	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
479	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
480	C₂×C₂²⋊C₄	—	2	2	no	—
481	C₂×C₂²⋊C₄	—	2	1	no	—
482	C₂×C₂²⋊C₄	—	2	1	no	—
483	C₂×C₂²⋊C₄	—	2	1	no	—
484	C₂×C₂²⋊C₄	—	2	1	no	—
485	C₂×C₂²⋊C₄	—	2	1	no	—
486	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
487	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
488	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
489	#107	—	2	2	no	—
490	#106	—	2	2	no	—
491	#103	—	2	2	no	—
492	#103	—	2	2	no	—
493	#103	—	2	2	no	—
494	#102	—	2	2	no	—
495	C₂²⋊C₈	—	2	1	no	—
496	C₂²⋊C₈	—	2	1	no	—
497	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
498	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
499	#95	—	2	1	no	—
500	#95	—	2	1	no	—
501	#95	—	2	1	no	—
502	#95	—	2	1	no	—
503	#95	—	2	1	no	—
504	#95	C₂³×C₁₉	1	1	yes	characteristic
505	#95	C₂³×C₁₉	1	1	yes	characteristic
506	C₁₉	#18385	1	1	yes	characteristic, direct product factor, Sylow
507	C₂⁴	—	2	1	no	—
508	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
509	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
510	#41	—	8	2	no	—
511	C₂×Q₈	—	2	1	no	—
512	C₂×Q₈	—	2	1	no	—
513	C₂×Q₈	—	2	1	no	—
514	C₂×Q₈	—	8	1	no	—
515	C₂×Q₈	—	8	1	no	—
516	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
517	C₂×D₄	—	2	1	no	—
518	C₂×D₄	—	2	1	no	—
519	C₂×D₄	—	2	2	no	—
520	C₂×D₄	—	2	2	no	—
521	C₂×D₄	—	2	2	no	—
522	C₂×D₄	—	2	2	no	—
523	C₂×D₄	—	2	2	no	—
524	C₂×D₄	—	2	2	no	—
525	C₂×D₄	—	2	1	no	—
526	C₂×D₄	—	4	2	no	—
527	C₂×D₄	—	4	2	no	—
528	C₂×D₄	—	8	1	no	—
529	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	2	no	—
533	C₂²×C₄	—	2	2	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	4	2	no	—
542	C₂²×C₄	—	4	2	no	—
543	C₂²×C₄	—	8	1	no	—
544	C₂²×C₄	—	8	1	no	—
545	C₂²×C₄	—	8	1	no	—
546	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
547	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
548	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
549	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
550	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
551	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
552	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
553	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
554	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
555	Q₁₆	—	8	2	no	—
556	SD₁₆	—	8	2	no	—
557	C₂×C₈	—	2	2	no	—
558	C₂×C₈	—	2	2	no	—
559	C₂×C₈	—	8	1	no	—
560	C₂×C₈	—	8	1	no	—
561	C₄⋊C₄	—	2	2	no	—
562	C₄⋊C₄	—	2	2	no	—
563	C₄⋊C₄	—	2	2	no	—
564	C₄⋊C₄	—	2	2	no	—
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	2	1	no	—
568	C₄⋊C₄	—	2	2	no	—
569	C₄⋊C₄	—	2	1	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	4	2	no	—
574	C₄⋊C₄	—	4	1	no	—
575	C₄⋊C₄	—	4	1	no	—
576	C₄⋊C₄	—	8	1	no	—
577	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
578	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
579	C₂²⋊C₄	—	2	2	no	—
580	C₂²⋊C₄	—	2	2	no	—
581	C₂²⋊C₄	—	2	2	no	—
582	C₂²⋊C₄	—	2	2	no	—
583	C₂²⋊C₄	—	2	2	no	—
584	C₂²⋊C₄	—	2	2	no	—
585	C₂²⋊C₄	—	2	1	no	—
586	C₂²⋊C₄	—	2	2	no	—
587	C₂²⋊C₄	—	2	1	no	—
588	C₂²⋊C₄	—	2	2	no	—
589	C₂²⋊C₄	—	2	2	no	—
590	C₂²⋊C₄	—	2	2	no	—
591	C₂²⋊C₄	—	2	1	no	—
592	C₂²⋊C₄	—	2	1	no	—
593	C₂²⋊C₄	—	4	2	no	—
594	C₂²⋊C₄	—	4	1	no	—
595	C₂²⋊C₄	—	4	1	no	—
596	C₂²⋊C₄	—	8	1	no	—
597	C₄²	—	2	2	no	—
598	C₄²	—	2	2	no	—
599	C₄²	—	2	1	no	—
600	C₄²	—	2	1	no	—
601	C₂³	—	2	1	no	—
602	C₂³	—	2	2	no	—
603	C₂³	—	2	1	no	—
604	C₂³	—	2	1	no	—
605	C₂³	—	4	1	no	—
606	C₂³	—	4	1	no	—
607	C₂³	—	4	1	no	—
608	C₂³	—	4	1	no	—
609	C₂³	—	4	2	no	—
610	C₂³	—	8	1	no	—
611	C₂³	—	8	1	no	—
612	C₂³	C₁₉×#120	1	1	yes	characteristic
613	C₂³	C₁₉×#120	1	1	yes	characteristic
614	C₂³	C₁₉×#135	1	2	yes	—
615	C₂³	C₁₉×#137	1	2	yes	—
616	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
617	Q₈	—	4	2	no	—
618	Q₈	—	4	2	no	—
619	Q₈	—	4	2	no	—
620	Q₈	—	4	2	no	—
621	D₄	—	4	2	no	—
622	D₄	—	4	2	no	—
623	D₄	—	4	2	no	—
624	D₄	—	4	2	no	—
625	D₄	—	4	4	no	—
626	D₄	—	4	2	no	—
627	D₄	—	4	2	no	—
628	D₄	—	8	2	no	—
629	D₄	—	8	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	2	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	2	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	8	1	no	—
661	C₂×C₄	—	8	1	no	—
662	C₂×C₄	—	8	1	no	—
663	C₂×C₄	—	8	2	no	—
664	C₂×C₄	—	8	2	no	—
665	C₂×C₄	—	8	4	no	—
666	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
667	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
668	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
669	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
670	C₈	—	4	2	no	—
671	C₈	—	4	2	no	—
672	C₂²	—	2	1	no	—
673	C₂²	—	2	1	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	2	1	no	—
677	C₂²	—	2	1	no	—
678	C₂²	—	4	2	no	—
679	C₂²	—	4	2	no	—
680	C₂²	—	4	2	no	—
681	C₂²	—	4	1	no	—
682	C₂²	—	4	2	no	—
683	C₂²	—	4	2	no	—
684	C₂²	—	4	1	no	—
685	C₂²	—	4	1	no	—
686	C₂²	—	4	2	no	—
687	C₂²	—	8	1	no	—
688	C₂²	—	16	2	no	—
689	C₂²	C₁₉×#452	1	2	yes	—
690	C₂²	C₁₉×#452	1	2	yes	—
691	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
692	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
693	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
694	C₄	—	2	1	no	—
695	C₄	—	2	1	no	—
696	C₄	—	2	1	no	—
697	C₄	—	2	1	no	—
698	C₄	—	4	2	no	—
699	C₄	—	4	1	no	—
700	C₄	—	4	2	no	—
701	C₄	—	4	1	no	—
702	C₄	—	4	2	no	—
703	C₄	—	4	1	no	—
704	C₄	—	4	2	no	—
705	C₄	—	8	1	no	—
706	C₄	—	8	1	no	—
707	C₄	—	8	1	no	—
708	C₂	—	2	1	no	—
709	C₂	—	2	1	no	—
710	C₂	—	2	2	no	—
711	C₂	—	2	2	no	—
712	C₂	—	8	1	no	—
713	C₂	—	8	2	no	—
714	C₂	C₂×C₁₉×#452	1	1	yes	characteristic
715	C₂	C₁₉×#3018	1	1	yes	characteristic
716	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×#3505	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×#3189	C₂	semidirect
3. C₁₉×#3187	C₂	semidirect
4. C₁₉×#2564	C₂	semidirect
5. C₁₉×#1618	C₂	semidirect
6. C₁₉×#1615	C₂	semidirect
7. C₁₉×#1606	C₂	semidirect
8. C₁₉×#1603	C₂	semidirect
9. C₂×C₁₉×#328	C₂	semidirect
10. C₂×C₁₉×#327	C₂	semidirect
11. C₁₉×#1459	C₂	semidirect
29. C₁₉×#484	C₂²	semidirect
35. C₁₉×#451	C₂²	semidirect
40. C₁₉×#400	C₂²	semidirect
41. C₁₉×#399	C₂²	semidirect
42. C₁₉×#395	C₂²	semidirect
43. C₁₉×#393	C₂²	semidirect
49. C₁₉×#328	C₂²	semidirect
50. C₁₉×#328	C₂²	semidirect
53. C₁₉×#324	C₂²	semidirect
54. C₁₉×#323	C₂²	semidirect
242. #18385	C₁₉	direct (N × H)
315. #3189	C₂×C₁₉	semidirect
316. #3187	C₂×C₁₉	semidirect
317. #2564	C₂×C₁₉	semidirect
318. #1618	C₂×C₁₉	semidirect
319. #1615	C₂×C₁₉	semidirect
320. #1606	C₂×C₁₉	semidirect
321. #1603	C₂×C₁₉	semidirect
322. C₂×#328	C₂×C₁₉	semidirect
323. C₂×#327	C₂×C₁₉	semidirect
324. #1459	C₂×C₁₉	semidirect
378. #484	C₂²×C₁₉	semidirect
384. #451	C₂²×C₁₉	semidirect
389. #400	C₂²×C₁₉	semidirect
390. #399	C₂²×C₁₉	semidirect
391. #395	C₂²×C₁₉	semidirect
392. #393	C₂²×C₁₉	semidirect
398. #328	C₂²×C₁₉	semidirect
399. #328	C₂²×C₁₉	semidirect
402. #324	C₂²×C₁₉	semidirect
403. #323	C₂²×C₁₉	semidirect
506. C₁₉	#18385	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×#3505	2
C₁₉×#3189	2
C₁₉×#3187	2
C₁₉×#2564	2
C₁₉×#1618	2
C₁₉×#1615	2
C₁₉×#1606	2
C₁₉×#1603	2
C₂×C₁₉×#328	2
C₂×C₁₉×#327	2
C₁₉×#1459	2
#18385	19

Subgroups — C19×#18385 #18024344

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18385 #18024344