Subgroups — C₁₉×#18470 #18024429

Order 4864.

906 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3560	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3238	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3226	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2821	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1612	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1610	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1609	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1607	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1521	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1514	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1473	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#563	—	2	1	no	—
13	C₁₉×#560	—	2	1	no	—
14	C₁₉×#553	—	2	1	no	—
15	C₁₉×#553	—	2	1	no	—
16	C₁₉×#551	—	2	1	no	—
17	C₁₉×#547	—	2	1	no	—
18	C₁₉×#546	—	2	1	no	—
19	C₁₉×#546	—	2	1	no	—
20	C₁₉×#542	—	2	1	no	—
21	C₁₉×#539	—	2	1	no	—
22	C₁₉×#539	C₂²	1	1	yes	characteristic
23	C₁₉×#538	—	2	1	no	—
24	C₁₉×#538	—	2	1	no	—
25	C₁₉×#538	C₂²	1	1	yes	characteristic
26	C₁₉×#537	C₂²	1	1	yes	characteristic
27	C₁₉×#534	C₂²	1	1	yes	characteristic
28	C₁₉×#532	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₁₉×#529	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#126	C₂²	1	1	yes	characteristic
32	C₁₉×#501	—	2	1	no	—
33	C₁₉×#500	—	2	1	no	—
34	C₁₉×#489	—	2	1	no	—
35	C₁₉×#486	—	2	1	no	—
36	C₁₉×#483	C₂²	1	2	yes	complemented
37	C₁₉×#480	C₂²	1	2	yes	—
38	C₁₉×#480	C₂²	1	2	yes	—
39	C₁₉×#480	C₂²	1	2	yes	complemented
40	C₁₉×#477	—	2	1	no	—
41	C₁₉×#476	—	2	1	no	—
42	C₁₉×#474	—	2	1	no	—
43	C₁₉×#474	—	2	1	no	—
44	C₁₉×#432	C₂²	1	1	yes	characteristic, complemented
45	C₁₉×#431	C₂²	1	1	yes	characteristic, complemented
46	C₁₉×#400	—	2	1	no	—
47	C₁₉×#399	—	2	1	no	—
48	C₁₉×#398	C₂²	1	2	yes	complemented
49	C₁₉×#397	C₂²	1	2	yes	—
50	C₁₉×#395	—	2	1	no	—
51	C₁₉×#393	—	2	1	no	—
52	C₁₉×#383	C₂²	1	1	yes	characteristic, complemented
53	C₁₉×#328	C₂²	1	2	yes	complemented
54	C₁₉×#327	C₂²	1	2	yes	—
55	C₁₉×#327	C₂²	1	2	yes	—
56	C₁₉×#327	C₂²	1	2	yes	complemented
57	C₁₉×#324	C₂²	1	2	yes	complemented
58	C₁₉×#323	C₂²	1	2	yes	—
59	C₂×#41×C₁₉	—	2	1	no	—
60	C₂×#41×C₁₉	—	2	1	no	—
61	C₂²×Q₈×C₁₉	—	2	1	no	—
62	C₂²×D₄×C₁₉	—	2	1	no	—
63	C₁₉×C₄⋊Q₈	—	2	1	no	—
64	C₁₉×C₄⋊Q₈	—	2	1	no	—
65	C₁₉×C₄⋊Q₈	—	2	1	no	—
66	C₁₉×C₄⋊Q₈	—	2	1	no	—
67	C₁₉×C₄⋊Q₈	—	2	1	no	—
68	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
69	C₁₉×#127	D₄	1	1	yes	characteristic
70	C₁₉×#126	—	2	1	no	—
71	C₁₉×#126	—	2	1	no	—
72	C₁₉×#126	—	2	1	no	—
73	C₁₉×#126	—	2	1	no	—
74	C₁₉×#126	—	2	1	no	—
75	C₁₉×#126	—	2	1	no	—
76	C₁₉×#126	—	2	1	no	—
77	C₁₉×#126	—	2	1	no	—
78	C₁₉×#126	—	2	1	no	—
79	C₁₉×#125	—	2	1	no	—
80	C₁₉×#125	—	2	1	no	—
81	C₁₉×#125	D₄	1	1	yes	characteristic
82	C₁₉×#124	—	2	1	no	—
83	C₁₉×#124	—	2	1	no	—
84	C₁₉×#124	—	2	1	no	—
85	C₁₉×#124	—	2	1	no	—
86	C₁₉×#124	D₄	1	1	yes	characteristic
87	C₁₉×#123	—	2	1	no	—
88	C₁₉×#123	—	2	1	no	—
89	C₁₉×#123	—	2	1	no	—
90	C₁₉×#123	—	2	1	no	—
91	C₁₉×#123	—	2	1	no	—
92	C₁₉×#123	—	2	1	no	—
93	C₁₉×#123	—	2	1	no	—
94	C₁₉×#123	—	2	1	no	—
95	C₁₉×#123	—	2	1	no	—
96	C₁₉×#123	—	2	1	no	—
97	C₁₉×#123	—	2	1	no	—
98	C₁₉×#123	—	2	1	no	—
99	C₁₉×C₂²⋊Q₈	—	2	1	no	—
100	C₁₉×C₂²⋊Q₈	—	2	1	no	—
101	C₁₉×C₂²⋊Q₈	—	2	1	no	—
102	C₁₉×C₂²⋊Q₈	—	2	1	no	—
103	C₁₉×C₂²⋊Q₈	—	2	1	no	—
104	C₁₉×C₂²⋊Q₈	—	2	1	no	—
105	C₁₉×C₂²⋊Q₈	—	2	1	no	—
106	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
107	C₁₉×#121	—	2	1	no	—
108	C₁₉×#121	—	2	1	no	—
109	C₁₉×#121	—	2	1	no	—
110	C₁₉×#121	—	2	1	no	—
111	C₁₉×#121	—	2	1	no	—
112	C₁₉×#121	—	2	1	no	—
113	C₁₉×#121	—	2	1	no	—
114	C₁₉×#121	—	2	1	no	—
115	C₁₉×#121	—	2	1	no	—
116	C₁₉×#121	—	2	1	no	—
117	C₁₉×#121	—	2	1	no	—
118	C₁₉×#121	—	2	1	no	—
119	C₁₉×#121	C₂³	1	1	yes	characteristic
120	C₁₉×#121	C₂³	1	1	yes	characteristic
121	C₁₉×#121	C₂³	1	1	yes	characteristic
122	C₁₉×#120	—	2	1	no	—
123	C₁₉×#120	—	2	1	no	—
124	C₁₉×#120	—	2	1	no	—
125	C₁₉×#120	—	2	1	no	—
126	C₁₉×#120	—	2	1	no	—
127	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
128	C₄×D₄×C₁₉	—	2	1	no	—
129	C₄×D₄×C₁₉	—	2	1	no	—
130	C₄×D₄×C₁₉	—	2	1	no	—
131	C₄×D₄×C₁₉	—	2	1	no	—
132	C₄×D₄×C₁₉	—	2	1	no	—
133	C₄×D₄×C₁₉	—	2	1	no	—
134	C₄×D₄×C₁₉	—	2	1	no	—
135	C₄×D₄×C₁₉	—	2	1	no	—
136	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
137	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
138	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
139	C₁₉×#117	—	2	1	no	—
140	C₁₉×#117	—	2	1	no	—
141	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
142	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
143	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
144	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
149	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
150	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
151	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
152	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
153	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
155	C₁₉×#107	—	2	2	no	—
156	C₁₉×#107	—	2	2	no	—
157	C₁₉×#107	—	2	2	no	—
158	C₁₉×#106	—	2	2	no	—
159	C₁₉×C₄⋊C₈	—	2	1	no	—
160	C₁₉×C₄⋊C₈	—	2	1	no	—
161	C₁₉×#103	—	2	2	no	—
162	C₁₉×#102	—	2	2	no	—
163	C₁₉×#102	—	2	2	no	—
164	C₁₉×#102	—	2	2	no	—
165	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
166	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
167	C₁₉×#97	—	2	1	no	—
168	C₄×C₈×C₁₉	—	2	1	no	—
169	C₁₉×#95	—	2	1	no	—
170	C₁₉×#95	—	2	1	no	—
171	C₁₉×#95	—	2	2	no	—
172	C₁₉×#95	—	2	2	no	—
173	C₁₉×#95	C₂³	1	2	yes	—
174	C₂⁴×C₁₉	—	2	1	no	—
175	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
176	#41×C₁₉	—	8	2	no	—
177	#41×C₁₉	—	8	2	no	—
178	C₂×Q₈×C₁₉	—	2	1	no	—
179	C₂×Q₈×C₁₉	—	2	1	no	—
180	C₂×Q₈×C₁₉	—	4	1	no	—
181	C₂×Q₈×C₁₉	—	4	1	no	—
182	C₂×Q₈×C₁₉	—	8	2	no	—
183	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
184	C₂×D₄×C₁₉	—	2	1	no	—
185	C₂×D₄×C₁₉	—	2	1	no	—
186	C₂×D₄×C₁₉	—	2	1	no	—
187	C₂×D₄×C₁₉	—	2	1	no	—
188	C₂×D₄×C₁₉	—	2	1	no	—
189	C₂×D₄×C₁₉	—	2	1	no	—
190	C₂×D₄×C₁₉	—	2	1	no	—
191	C₂×D₄×C₁₉	—	2	1	no	—
192	C₂×D₄×C₁₉	—	2	1	no	—
193	C₂×D₄×C₁₉	—	2	1	no	—
194	C₂×D₄×C₁₉	—	2	1	no	—
195	C₂×D₄×C₁₉	—	2	1	no	—
196	C₂×D₄×C₁₉	—	8	2	no	—
197	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
198	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
199	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₁₉	—	2	1	no	—
201	C₂²×C₄×C₁₉	—	2	1	no	—
202	C₂²×C₄×C₁₉	—	2	1	no	—
203	C₂²×C₄×C₁₉	—	2	1	no	—
204	C₂²×C₄×C₁₉	—	2	1	no	—
205	C₂²×C₄×C₁₉	—	2	1	no	—
206	C₂²×C₄×C₁₉	—	2	1	no	—
207	C₂²×C₄×C₁₉	—	2	1	no	—
208	C₂²×C₄×C₁₉	—	2	2	no	—
209	C₂²×C₄×C₁₉	—	2	2	no	—
210	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
216	C₂×C₈×C₁₉	—	2	2	no	—
217	C₂×C₈×C₁₉	—	2	2	no	—
218	C₄⋊C₄×C₁₉	—	2	1	no	—
219	C₄⋊C₄×C₁₉	—	2	1	no	—
220	C₄⋊C₄×C₁₉	—	2	1	no	—
221	C₄⋊C₄×C₁₉	—	2	1	no	—
222	C₄⋊C₄×C₁₉	—	2	1	no	—
223	C₄⋊C₄×C₁₉	—	2	1	no	—
224	C₄⋊C₄×C₁₉	—	2	1	no	—
225	C₄⋊C₄×C₁₉	—	2	1	no	—
226	C₄⋊C₄×C₁₉	—	2	1	no	—
227	C₄⋊C₄×C₁₉	—	2	1	no	—
228	C₄⋊C₄×C₁₉	—	2	1	no	—
229	C₄⋊C₄×C₁₉	—	2	1	no	—
230	C₄⋊C₄×C₁₉	—	2	1	no	—
231	C₄⋊C₄×C₁₉	—	2	1	no	—
232	C₄⋊C₄×C₁₉	—	2	1	no	—
233	C₄⋊C₄×C₁₉	—	2	1	no	—
234	C₄⋊C₄×C₁₉	—	2	1	no	—
235	C₄⋊C₄×C₁₉	—	2	2	no	—
236	C₄⋊C₄×C₁₉	—	2	2	no	—
237	C₄⋊C₄×C₁₉	—	4	1	no	—
238	C₄⋊C₄×C₁₉	—	4	1	no	—
239	C₄⋊C₄×C₁₉	—	8	2	no	—
240	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
241	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
242	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
243	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
244	C₂²⋊C₄×C₁₉	—	2	1	no	—
245	C₂²⋊C₄×C₁₉	—	2	1	no	—
246	C₂²⋊C₄×C₁₉	—	2	1	no	—
247	C₂²⋊C₄×C₁₉	—	2	1	no	—
248	C₂²⋊C₄×C₁₉	—	2	1	no	—
249	C₂²⋊C₄×C₁₉	—	2	1	no	—
250	C₂²⋊C₄×C₁₉	—	2	1	no	—
251	C₂²⋊C₄×C₁₉	—	2	1	no	—
252	C₂²⋊C₄×C₁₉	—	2	1	no	—
253	C₂²⋊C₄×C₁₉	—	2	1	no	—
254	C₂²⋊C₄×C₁₉	—	2	1	no	—
255	C₂²⋊C₄×C₁₉	—	2	1	no	—
256	C₂²⋊C₄×C₁₉	—	2	1	no	—
257	C₂²⋊C₄×C₁₉	—	2	1	no	—
258	C₂²⋊C₄×C₁₉	—	2	1	no	—
259	C₂²⋊C₄×C₁₉	—	2	1	no	—
260	C₂²⋊C₄×C₁₉	—	2	1	no	—
261	C₂²⋊C₄×C₁₉	—	2	1	no	—
262	C₂²⋊C₄×C₁₉	—	2	1	no	—
263	C₂²⋊C₄×C₁₉	—	2	1	no	—
264	C₂²⋊C₄×C₁₉	—	2	1	no	—
265	C₂²⋊C₄×C₁₉	—	2	1	no	—
266	C₂²⋊C₄×C₁₉	—	2	1	no	—
267	C₂²⋊C₄×C₁₉	—	2	1	no	—
268	C₂²⋊C₄×C₁₉	—	2	1	no	—
269	C₂²⋊C₄×C₁₉	—	8	2	no	—
270	C₄²×C₁₉	—	2	1	no	—
271	C₄²×C₁₉	—	2	1	no	—
272	C₄²×C₁₉	—	2	1	no	—
273	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
274	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
275	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
276	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
277	#18470	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
278	C₂³×C₁₉	—	2	1	no	—
279	C₂³×C₁₉	—	2	1	no	—
280	C₂³×C₁₉	—	2	1	no	—
281	C₂³×C₁₉	—	2	1	no	—
282	C₂³×C₁₉	—	2	2	no	—
283	C₂³×C₁₉	—	4	1	no	—
284	C₂³×C₁₉	—	4	1	no	—
285	C₂³×C₁₉	—	8	1	no	—
286	C₂³×C₁₉	—	8	1	no	—
287	C₂³×C₁₉	—	8	1	no	—
288	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
289	Q₈×C₁₉	—	4	1	no	—
290	Q₈×C₁₉	—	8	1	no	—
291	Q₈×C₁₉	—	8	2	no	—
292	Q₈×C₁₉	—	8	2	no	—
293	Q₈×C₁₉	—	8	1	no	—
294	D₄×C₁₉	—	4	1	no	—
295	D₄×C₁₉	—	4	1	no	—
296	D₄×C₁₉	—	4	1	no	—
297	D₄×C₁₉	—	4	2	no	—
298	D₄×C₁₉	—	4	2	no	—
299	D₄×C₁₉	—	4	2	no	—
300	D₄×C₁₉	—	8	1	no	—
301	D₄×C₁₉	—	8	1	no	—
302	D₄×C₁₉	—	8	1	no	—
303	D₄×C₁₉	—	8	1	no	—
304	D₄×C₁₉	—	8	1	no	—
305	D₄×C₁₉	—	8	1	no	—
306	D₄×C₁₉	—	8	1	no	—
307	D₄×C₁₉	—	8	1	no	—
308	D₄×C₁₉	—	8	1	no	—
309	C₂×C₄×C₁₉	—	2	2	no	—
310	C₂×C₄×C₁₉	—	2	1	no	—
311	C₂×C₄×C₁₉	—	2	1	no	—
312	C₂×C₄×C₁₉	—	2	1	no	—
313	C₂×C₄×C₁₉	—	2	1	no	—
314	C₂×C₄×C₁₉	—	2	1	no	—
315	C₂×C₄×C₁₉	—	2	1	no	—
316	C₂×C₄×C₁₉	—	2	1	no	—
317	C₂×C₄×C₁₉	—	2	1	no	—
318	C₂×C₄×C₁₉	—	2	2	no	—
319	C₂×C₄×C₁₉	—	4	1	no	—
320	C₂×C₄×C₁₉	—	4	1	no	—
321	C₂×C₄×C₁₉	—	4	1	no	—
322	C₂×C₄×C₁₉	—	4	1	no	—
323	C₂×C₄×C₁₉	—	4	2	no	—
324	C₂×C₄×C₁₉	—	4	2	no	—
325	C₂×C₄×C₁₉	—	4	2	no	—
326	C₂×C₄×C₁₉	—	4	2	no	—
327	C₂×C₄×C₁₉	—	4	2	no	—
328	C₂×C₄×C₁₉	—	4	2	no	—
329	C₂×C₄×C₁₉	—	8	1	no	—
330	C₂×C₄×C₁₉	—	8	1	no	—
331	C₂×C₄×C₁₉	—	8	1	no	—
332	C₂×C₄×C₁₉	—	8	1	no	—
333	C₂×C₄×C₁₉	—	8	1	no	—
334	C₂×C₄×C₁₉	—	8	1	no	—
335	C₂×C₄×C₁₉	—	8	1	no	—
336	C₂×C₄×C₁₉	—	8	1	no	—
337	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
338	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
339	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
340	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
341	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
343	C₈×C₁₉	—	4	2	no	—
344	C₈×C₁₉	—	4	2	no	—
345	#3560	C₂×C₁₉	1	1	yes	characteristic
346	#3238	C₂×C₁₉	1	1	yes	characteristic, complemented
347	#3226	C₂×C₁₉	1	1	yes	characteristic, complemented
348	#2821	C₂×C₁₉	1	1	yes	characteristic, complemented
349	#1612	C₂×C₁₉	1	2	yes	complemented
350	#1610	C₂×C₁₉	1	2	yes	complemented
351	#1609	C₂×C₁₉	1	2	yes	complemented
352	#1607	C₂×C₁₉	1	2	yes	complemented
353	#1521	C₂×C₁₉	1	1	yes	characteristic, complemented
354	#1514	C₂×C₁₉	1	1	yes	characteristic, complemented
355	#1473	C₂×C₁₉	1	1	yes	characteristic, complemented
356	C₂²×C₁₉	—	2	1	no	—
357	C₂²×C₁₉	—	2	1	no	—
358	C₂²×C₁₉	—	4	1	no	—
359	C₂²×C₁₉	—	4	1	no	—
360	C₂²×C₁₉	—	4	1	no	—
361	C₂²×C₁₉	—	4	1	no	—
362	C₂²×C₁₉	—	4	1	no	—
363	C₂²×C₁₉	—	4	1	no	—
364	C₂²×C₁₉	—	4	1	no	—
365	C₂²×C₁₉	—	4	1	no	—
366	C₂²×C₁₉	—	4	1	no	—
367	C₂²×C₁₉	—	4	1	no	—
368	C₂²×C₁₉	—	4	1	no	—
369	C₂²×C₁₉	—	4	1	no	—
370	C₂²×C₁₉	—	8	2	no	—
371	C₂²×C₁₉	—	16	2	no	—
372	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
373	C₂²×C₁₉	#576	1	2	yes	—
374	C₄×C₁₉	—	2	1	no	—
375	C₄×C₁₉	—	2	1	no	—
376	C₄×C₁₉	—	2	1	no	—
377	C₄×C₁₉	—	2	1	no	—
378	C₄×C₁₉	—	2	1	no	—
379	C₄×C₁₉	—	2	1	no	—
380	C₄×C₁₉	—	4	1	no	—
381	C₄×C₁₉	—	4	1	no	—
382	C₄×C₁₉	—	4	1	no	—
383	C₄×C₁₉	—	4	1	no	—
384	C₄×C₁₉	—	4	1	no	—
385	C₄×C₁₉	—	4	1	no	—
386	C₄×C₁₉	—	4	1	no	—
387	C₄×C₁₉	—	4	1	no	—
388	C₄×C₁₉	—	8	2	no	—
389	C₄×C₁₉	—	8	2	no	—
390	#563	—	2	1	no	—
391	#560	—	2	1	no	—
392	#553	—	2	1	no	—
393	#553	—	2	1	no	—
394	#551	—	2	1	no	—
395	#547	—	2	1	no	—
396	#546	—	2	1	no	—
397	#546	—	2	1	no	—
398	#542	—	2	1	no	—
399	#539	—	2	1	no	—
400	#539	C₂²×C₁₉	1	1	yes	characteristic
401	#538	—	2	1	no	—
402	#538	—	2	1	no	—
403	#538	C₂²×C₁₉	1	1	yes	characteristic
404	#537	C₂²×C₁₉	1	1	yes	characteristic
405	#534	C₂²×C₁₉	1	1	yes	characteristic
406	#532	C₂²×C₁₉	1	1	yes	characteristic
407	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
408	#529	C₂²×C₁₉	1	1	yes	characteristic
409	C₂×#126	C₂²×C₁₉	1	1	yes	characteristic
410	#501	—	2	1	no	—
411	#500	—	2	1	no	—
412	#489	—	2	1	no	—
413	#486	—	2	1	no	—
414	#483	C₂²×C₁₉	1	2	yes	complemented
415	#480	C₂²×C₁₉	1	2	yes	—
416	#480	C₂²×C₁₉	1	2	yes	—
417	#480	C₂²×C₁₉	1	2	yes	complemented
418	#477	—	2	1	no	—
419	#476	—	2	1	no	—
420	#474	—	2	1	no	—
421	#474	—	2	1	no	—
422	#432	C₂²×C₁₉	1	1	yes	characteristic, complemented
423	#431	C₂²×C₁₉	1	1	yes	characteristic, complemented
424	#400	—	2	1	no	—
425	#399	—	2	1	no	—
426	#398	C₂²×C₁₉	1	2	yes	complemented
427	#397	C₂²×C₁₉	1	2	yes	—
428	#395	—	2	1	no	—
429	#393	—	2	1	no	—
430	#383	C₂²×C₁₉	1	1	yes	characteristic, complemented
431	#328	C₂²×C₁₉	1	2	yes	complemented
432	#327	C₂²×C₁₉	1	2	yes	—
433	#327	C₂²×C₁₉	1	2	yes	—
434	#327	C₂²×C₁₉	1	2	yes	complemented
435	#324	C₂²×C₁₉	1	2	yes	complemented
436	#323	C₂²×C₁₉	1	2	yes	—
437	C₂×C₁₉	—	2	2	no	—
438	C₂×C₁₉	—	8	1	no	—
439	C₂×C₁₉	—	8	1	no	—
440	C₂×C₁₉	—	8	1	no	—
441	C₂×C₁₉	—	8	1	no	—
442	C₂×C₁₉	#3008	1	1	yes	characteristic
443	C₂×C₁₉	#3022	1	1	yes	characteristic
444	C₂×C₁₉	#3028	1	1	yes	characteristic
445	C₂×#41	—	2	1	no	—
446	C₂×#41	—	2	1	no	—
447	C₂²×Q₈	—	2	1	no	—
448	C₂²×D₄	—	2	1	no	—
449	C₄⋊Q₈	—	2	1	no	—
450	C₄⋊Q₈	—	2	1	no	—
451	C₄⋊Q₈	—	2	1	no	—
452	C₄⋊Q₈	—	2	1	no	—
453	C₄⋊Q₈	—	2	1	no	—
454	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
455	#127	D₄×C₁₉	1	1	yes	characteristic
456	#126	—	2	1	no	—
457	#126	—	2	1	no	—
458	#126	—	2	1	no	—
459	#126	—	2	1	no	—
460	#126	—	2	1	no	—
461	#126	—	2	1	no	—
462	#126	—	2	1	no	—
463	#126	—	2	1	no	—
464	#126	—	2	1	no	—
465	#125	—	2	1	no	—
466	#125	—	2	1	no	—
467	#125	D₄×C₁₉	1	1	yes	characteristic
468	#124	—	2	1	no	—
469	#124	—	2	1	no	—
470	#124	—	2	1	no	—
471	#124	—	2	1	no	—
472	#124	D₄×C₁₉	1	1	yes	characteristic
473	#123	—	2	1	no	—
474	#123	—	2	1	no	—
475	#123	—	2	1	no	—
476	#123	—	2	1	no	—
477	#123	—	2	1	no	—
478	#123	—	2	1	no	—
479	#123	—	2	1	no	—
480	#123	—	2	1	no	—
481	#123	—	2	1	no	—
482	#123	—	2	1	no	—
483	#123	—	2	1	no	—
484	#123	—	2	1	no	—
485	C₂²⋊Q₈	—	2	1	no	—
486	C₂²⋊Q₈	—	2	1	no	—
487	C₂²⋊Q₈	—	2	1	no	—
488	C₂²⋊Q₈	—	2	1	no	—
489	C₂²⋊Q₈	—	2	1	no	—
490	C₂²⋊Q₈	—	2	1	no	—
491	C₂²⋊Q₈	—	2	1	no	—
492	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
493	#121	—	2	1	no	—
494	#121	—	2	1	no	—
495	#121	—	2	1	no	—
496	#121	—	2	1	no	—
497	#121	—	2	1	no	—
498	#121	—	2	1	no	—
499	#121	—	2	1	no	—
500	#121	—	2	1	no	—
501	#121	—	2	1	no	—
502	#121	—	2	1	no	—
503	#121	—	2	1	no	—
504	#121	—	2	1	no	—
505	#121	C₂³×C₁₉	1	1	yes	characteristic
506	#121	C₂³×C₁₉	1	1	yes	characteristic
507	#121	C₂³×C₁₉	1	1	yes	characteristic
508	#120	—	2	1	no	—
509	#120	—	2	1	no	—
510	#120	—	2	1	no	—
511	#120	—	2	1	no	—
512	#120	—	2	1	no	—
513	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
514	C₄×D₄	—	2	1	no	—
515	C₄×D₄	—	2	1	no	—
516	C₄×D₄	—	2	1	no	—
517	C₄×D₄	—	2	1	no	—
518	C₄×D₄	—	2	1	no	—
519	C₄×D₄	—	2	1	no	—
520	C₄×D₄	—	2	1	no	—
521	C₄×D₄	—	2	1	no	—
522	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
523	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
524	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
525	#117	—	2	1	no	—
526	#117	—	2	1	no	—
527	C₂×C₄⋊C₄	—	2	1	no	—
528	C₂×C₄⋊C₄	—	2	1	no	—
529	C₂×C₄⋊C₄	—	2	2	no	—
530	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
531	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
532	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
534	C₂×C₂²⋊C₄	—	2	1	no	—
535	C₂×C₂²⋊C₄	—	2	1	no	—
536	C₂×C₂²⋊C₄	—	2	2	no	—
537	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
538	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
539	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
540	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
541	#107	—	2	2	no	—
542	#107	—	2	2	no	—
543	#107	—	2	2	no	—
544	#106	—	2	2	no	—
545	C₄⋊C₈	—	2	1	no	—
546	C₄⋊C₈	—	2	1	no	—
547	#103	—	2	2	no	—
548	#102	—	2	2	no	—
549	#102	—	2	2	no	—
550	#102	—	2	2	no	—
551	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
552	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
553	#97	—	2	1	no	—
554	C₄×C₈	—	2	1	no	—
555	#95	—	2	1	no	—
556	#95	—	2	1	no	—
557	#95	—	2	2	no	—
558	#95	—	2	2	no	—
559	#95	C₂³×C₁₉	1	2	yes	—
560	C₁₉	#18470	1	1	yes	characteristic, direct product factor, Sylow
561	C₂⁴	—	2	1	no	—
562	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
563	#41	—	8	2	no	—
564	#41	—	8	2	no	—
565	C₂×Q₈	—	2	1	no	—
566	C₂×Q₈	—	2	1	no	—
567	C₂×Q₈	—	4	1	no	—
568	C₂×Q₈	—	4	1	no	—
569	C₂×Q₈	—	8	2	no	—
570	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
571	C₂×D₄	—	2	1	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	2	1	no	—
574	C₂×D₄	—	2	1	no	—
575	C₂×D₄	—	2	1	no	—
576	C₂×D₄	—	2	1	no	—
577	C₂×D₄	—	2	1	no	—
578	C₂×D₄	—	2	1	no	—
579	C₂×D₄	—	2	1	no	—
580	C₂×D₄	—	2	1	no	—
581	C₂×D₄	—	2	1	no	—
582	C₂×D₄	—	2	1	no	—
583	C₂×D₄	—	8	2	no	—
584	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
585	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
586	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	—	2	2	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
598	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
599	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
600	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
601	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
602	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
603	C₂×C₈	—	2	2	no	—
604	C₂×C₈	—	2	2	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	—	2	1	no	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	—	2	1	no	—
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	—	2	1	no	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	2	no	—
624	C₄⋊C₄	—	4	1	no	—
625	C₄⋊C₄	—	4	1	no	—
626	C₄⋊C₄	—	8	2	no	—
627	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
628	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
629	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
630	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
631	C₂²⋊C₄	—	2	1	no	—
632	C₂²⋊C₄	—	2	1	no	—
633	C₂²⋊C₄	—	2	1	no	—
634	C₂²⋊C₄	—	2	1	no	—
635	C₂²⋊C₄	—	2	1	no	—
636	C₂²⋊C₄	—	2	1	no	—
637	C₂²⋊C₄	—	2	1	no	—
638	C₂²⋊C₄	—	2	1	no	—
639	C₂²⋊C₄	—	2	1	no	—
640	C₂²⋊C₄	—	2	1	no	—
641	C₂²⋊C₄	—	2	1	no	—
642	C₂²⋊C₄	—	2	1	no	—
643	C₂²⋊C₄	—	2	1	no	—
644	C₂²⋊C₄	—	2	1	no	—
645	C₂²⋊C₄	—	2	1	no	—
646	C₂²⋊C₄	—	2	1	no	—
647	C₂²⋊C₄	—	2	1	no	—
648	C₂²⋊C₄	—	2	1	no	—
649	C₂²⋊C₄	—	2	1	no	—
650	C₂²⋊C₄	—	2	1	no	—
651	C₂²⋊C₄	—	2	1	no	—
652	C₂²⋊C₄	—	2	1	no	—
653	C₂²⋊C₄	—	2	1	no	—
654	C₂²⋊C₄	—	2	1	no	—
655	C₂²⋊C₄	—	2	1	no	—
656	C₂²⋊C₄	—	8	2	no	—
657	C₄²	—	2	1	no	—
658	C₄²	—	2	1	no	—
659	C₄²	—	2	1	no	—
660	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
661	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
662	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
663	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
664	C₂³	—	2	1	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	2	1	no	—
667	C₂³	—	2	1	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	4	1	no	—
670	C₂³	—	4	1	no	—
671	C₂³	—	8	1	no	—
672	C₂³	—	8	1	no	—
673	C₂³	—	8	1	no	—
674	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
675	Q₈	—	4	1	no	—
676	Q₈	—	8	1	no	—
677	Q₈	—	8	2	no	—
678	Q₈	—	8	2	no	—
679	Q₈	—	8	1	no	—
680	D₄	—	4	1	no	—
681	D₄	—	4	1	no	—
682	D₄	—	4	1	no	—
683	D₄	—	4	2	no	—
684	D₄	—	4	2	no	—
685	D₄	—	4	2	no	—
686	D₄	—	8	1	no	—
687	D₄	—	8	1	no	—
688	D₄	—	8	1	no	—
689	D₄	—	8	1	no	—
690	D₄	—	8	1	no	—
691	D₄	—	8	1	no	—
692	D₄	—	8	1	no	—
693	D₄	—	8	1	no	—
694	D₄	—	8	1	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	4	1	no	—
706	C₂×C₄	—	4	1	no	—
707	C₂×C₄	—	4	1	no	—
708	C₂×C₄	—	4	1	no	—
709	C₂×C₄	—	4	2	no	—
710	C₂×C₄	—	4	2	no	—
711	C₂×C₄	—	4	2	no	—
712	C₂×C₄	—	4	2	no	—
713	C₂×C₄	—	4	2	no	—
714	C₂×C₄	—	4	2	no	—
715	C₂×C₄	—	8	1	no	—
716	C₂×C₄	—	8	1	no	—
717	C₂×C₄	—	8	1	no	—
718	C₂×C₄	—	8	1	no	—
719	C₂×C₄	—	8	1	no	—
720	C₂×C₄	—	8	1	no	—
721	C₂×C₄	—	8	1	no	—
722	C₂×C₄	—	8	1	no	—
723	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
724	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
725	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
726	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
727	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
728	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
729	C₈	—	4	2	no	—
730	C₈	—	4	2	no	—
731	C₂²	—	2	1	no	—
732	C₂²	—	2	1	no	—
733	C₂²	—	4	1	no	—
734	C₂²	—	4	1	no	—
735	C₂²	—	4	1	no	—
736	C₂²	—	4	1	no	—
737	C₂²	—	4	1	no	—
738	C₂²	—	4	1	no	—
739	C₂²	—	4	1	no	—
740	C₂²	—	4	1	no	—
741	C₂²	—	4	1	no	—
742	C₂²	—	4	1	no	—
743	C₂²	—	4	1	no	—
744	C₂²	—	4	1	no	—
745	C₂²	—	8	2	no	—
746	C₂²	—	16	2	no	—
747	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
748	C₂²	C₁₉×#576	1	2	yes	—
749	C₄	—	2	1	no	—
750	C₄	—	2	1	no	—
751	C₄	—	2	1	no	—
752	C₄	—	2	1	no	—
753	C₄	—	2	1	no	—
754	C₄	—	2	1	no	—
755	C₄	—	4	1	no	—
756	C₄	—	4	1	no	—
757	C₄	—	4	1	no	—
758	C₄	—	4	1	no	—
759	C₄	—	4	1	no	—
760	C₄	—	4	1	no	—
761	C₄	—	4	1	no	—
762	C₄	—	4	1	no	—
763	C₄	—	8	2	no	—
764	C₄	—	8	2	no	—
765	C₂	—	2	2	no	—
766	C₂	—	8	1	no	—
767	C₂	—	8	1	no	—
768	C₂	—	8	1	no	—
769	C₂	—	8	1	no	—
770	C₂	C₁₉×#3008	1	1	yes	characteristic
771	C₂	C₁₉×#3022	1	1	yes	characteristic
772	C₂	C₁₉×#3028	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#3560	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
2. C₁₉×#3238	C₂	semidirect
3. C₁₉×#3226	C₂	semidirect
4. C₁₉×#2821	C₂	semidirect
5. C₁₉×#1612	C₂	semidirect
6. C₁₉×#1610	C₂	semidirect
7. C₁₉×#1609	C₂	semidirect
8. C₁₉×#1607	C₂	semidirect
9. C₁₉×#1521	C₂	semidirect
10. C₁₉×#1514	C₂	semidirect
11. C₁₉×#1473	C₂	semidirect
29. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
36. C₁₉×#483	C₂²	semidirect
39. C₁₉×#480	C₂²	semidirect
44. C₁₉×#432	C₂²	semidirect
45. C₁₉×#431	C₂²	semidirect
48. C₁₉×#398	C₂²	semidirect
52. C₁₉×#383	C₂²	semidirect
53. C₁₉×#328	C₂²	semidirect
56. C₁₉×#327	C₂²	semidirect
57. C₁₉×#324	C₂²	semidirect
277. #18470	C₁₉	direct (N × H)
346. #3238	C₂×C₁₉	semidirect
347. #3226	C₂×C₁₉	semidirect
348. #2821	C₂×C₁₉	semidirect
349. #1612	C₂×C₁₉	semidirect
350. #1610	C₂×C₁₉	semidirect
351. #1609	C₂×C₁₉	semidirect
352. #1607	C₂×C₁₉	semidirect
353. #1521	C₂×C₁₉	semidirect
354. #1514	C₂×C₁₉	semidirect
355. #1473	C₂×C₁₉	semidirect
407. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
414. #483	C₂²×C₁₉	semidirect
417. #480	C₂²×C₁₉	semidirect
422. #432	C₂²×C₁₉	semidirect
423. #431	C₂²×C₁₉	semidirect
426. #398	C₂²×C₁₉	semidirect
430. #383	C₂²×C₁₉	semidirect
431. #328	C₂²×C₁₉	semidirect
434. #327	C₂²×C₁₉	semidirect
435. #324	C₂²×C₁₉	semidirect
560. C₁₉	#18470	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×#3560	2
C₁₉×#3238	2
C₁₉×#3226	2
C₁₉×#2821	2
C₁₉×#1612	2
C₁₉×#1610	2
C₁₉×#1609	2
C₁₉×#1607	2
C₁₉×#1521	2
C₁₉×#1514	2
C₁₉×#1473	2
#18470	19

Subgroups — C19×#18470 #18024429

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18470 #18024429