Subgroups — C₁₉×#18597 #18024556

Order 4864.

876 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3515	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3252	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3185	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3076	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1654	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1653	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1644	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1643	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1636	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1635	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1632	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1632	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1550	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1489	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1483	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#557	C₂²	1	1	yes	characteristic
17	C₁₉×#554	C₂²	1	1	yes	characteristic
18	C₁₉×#554	C₂²	1	1	yes	characteristic
19	C₁₉×#553	—	2	1	no	—
20	C₁₉×#552	—	2	1	no	—
21	C₁₉×#552	—	2	2	no	—
22	C₁₉×#552	—	2	1	no	—
23	C₁₉×#547	—	2	1	no	—
24	C₁₉×#547	C₂²	1	1	yes	characteristic
25	C₁₉×#541	—	2	1	no	—
26	C₁₉×#539	—	2	2	no	—
27	C₁₉×#533	C₂²	1	1	yes	characteristic
28	C₁₉×#533	C₂²	1	1	yes	characteristic
29	C₁₉×#529	—	2	1	no	—
30	C₁₉×#529	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#125	—	2	1	no	—
32	C₁₉×#520	—	2	1	no	—
33	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
34	C₁₉×#498	C₂²	1	1	yes	characteristic
35	C₁₉×#494	C₂²	1	1	yes	characteristic
36	C₁₉×#487	C₂²	1	1	yes	characteristic
37	C₁₉×#487	C₂²	1	1	yes	characteristic
38	C₁₉×#479	—	2	1	no	—
39	C₁₉×#479	—	2	1	no	—
40	C₁₉×#478	—	2	1	no	—
41	C₁₉×#477	C₂²	1	1	yes	characteristic
42	C₁₉×#477	C₂²	1	1	yes	characteristic
43	C₁₉×#476	C₂²	1	1	yes	characteristic
44	C₁₉×#476	C₂²	1	1	yes	characteristic
45	C₁₉×#475	C₂²	1	1	yes	characteristic
46	C₁₉×#474	C₂²	1	1	yes	characteristic
47	C₁₉×#470	—	2	2	no	—
48	C₁₉×#470	—	2	1	no	—
49	C₁₉×#468	—	2	1	no	—
50	C₁₉×#464	—	2	1	no	—
51	C₁₉×#462	C₂²	1	1	yes	characteristic
52	C₁₉×#461	C₂²	1	1	yes	characteristic
53	C₁₉×#441	—	2	2	no	—
54	C₁₉×#427	—	2	1	no	—
55	C₁₉×#423	C₂²	1	1	yes	characteristic
56	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
57	C₁₉×#416	—	2	1	no	—
58	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
59	C₁₉×#333	C₂²	1	1	yes	characteristic
60	C₁₉×#333	C₂²	1	1	yes	characteristic
61	C₁₉×#332	C₂²	1	1	yes	characteristic
62	C₁₉×#332	C₂²	1	1	yes	characteristic
63	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
66	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
67	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
68	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
69	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
70	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
71	C₂×#41×C₁₉	—	2	1	no	—
72	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
73	C₂×Q₁₆×C₁₉	—	2	2	no	—
74	C₂×Q₁₆×C₁₉	—	2	1	no	—
75	C₂×SD₁₆×C₁₉	—	2	1	no	—
76	C₂×M₁₆×C₁₉	—	2	1	no	—
77	C₂×M₁₆×C₁₉	—	2	1	no	—
78	C₂²×C₈×C₁₉	—	2	1	no	—
79	C₁₉×C₄⋊Q₈	—	2	1	no	—
80	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
81	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₁₉×#126	—	2	2	no	—
85	C₁₉×#126	—	2	2	no	—
86	C₁₉×#126	—	2	2	no	—
87	C₁₉×#126	—	2	1	no	—
88	C₁₉×#125	—	2	2	no	—
89	C₁₉×#125	—	2	2	no	—
90	C₁₉×#125	—	2	2	no	—
91	C₁₉×#125	—	2	1	no	—
92	C₁₉×#125	—	2	1	no	—
93	C₁₉×#125	—	2	2	no	—
94	C₁₉×#125	—	2	1	no	—
95	C₁₉×#125	—	2	1	no	—
96	C₁₉×#125	—	2	1	no	—
97	C₁₉×#125	D₄	1	1	yes	characteristic
98	C₁₉×#124	D₄	1	1	yes	characteristic
99	C₁₉×#123	—	2	2	no	—
100	C₁₉×#123	—	2	2	no	—
101	C₁₉×#123	—	2	2	no	—
102	C₁₉×#123	—	2	1	no	—
103	C₁₉×#123	—	2	2	no	—
104	C₁₉×C₂²⋊Q₈	—	2	1	no	—
105	C₁₉×C₂²⋊Q₈	—	2	2	no	—
106	C₁₉×C₂²⋊Q₈	—	2	2	no	—
107	C₁₉×C₂²⋊Q₈	—	2	1	no	—
108	C₁₉×C₂²⋊Q₈	—	2	1	no	—
109	C₁₉×C₂²⋊Q₈	—	2	1	no	—
110	C₁₉×C₂²⋊Q₈	—	2	1	no	—
111	C₁₉×C₂²⋊Q₈	—	2	1	no	—
112	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
113	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
114	C₁₉×#121	—	2	2	no	—
115	C₁₉×#121	—	2	1	no	—
116	C₁₉×#121	D₄	1	1	yes	characteristic
117	C₄×Q₈×C₁₉	—	2	1	no	—
118	C₄×Q₈×C₁₉	—	2	1	no	—
119	C₄×Q₈×C₁₉	—	2	1	no	—
120	C₄×Q₈×C₁₉	—	2	1	no	—
121	C₄×Q₈×C₁₉	—	2	1	no	—
122	C₄×Q₈×C₁₉	D₄	1	2	yes	—
123	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
124	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
125	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
126	C₄×D₄×C₁₉	—	2	2	no	—
127	C₄×D₄×C₁₉	—	2	2	no	—
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	D₄	1	1	yes	characteristic
134	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
135	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
136	C₁₉×#117	—	2	2	no	—
137	C₁₉×#117	—	2	2	no	—
138	C₁₉×#117	—	2	1	no	—
139	C₁₉×#117	—	2	1	no	—
140	C₁₉×#117	—	2	1	no	—
141	C₁₉×#117	—	2	1	no	—
142	C₁₉×#117	D₄	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
144	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
145	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
146	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
147	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
148	C₂×C₄²×C₁₉	—	2	1	no	—
149	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
150	C₁₉×#107	—	2	1	no	—
151	C₁₉×#107	—	2	1	no	—
152	C₁₉×#107	—	2	1	no	—
153	C₁₉×#106	—	2	1	no	—
154	C₁₉×#106	—	2	1	no	—
155	C₁₉×#106	—	2	2	no	—
156	C₁₉×#106	—	2	1	no	—
157	C₁₉×C₄⋊C₈	—	2	1	no	—
158	C₁₉×C₄⋊C₈	—	2	1	no	—
159	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
160	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
161	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
162	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
163	C₁₉×#103	—	2	1	no	—
164	C₁₉×#103	—	2	1	no	—
165	C₁₉×#103	—	2	2	no	—
166	C₁₉×#103	—	2	1	no	—
167	C₁₉×#103	—	2	2	no	—
168	C₁₉×#103	—	2	1	no	—
169	C₁₉×#103	—	2	1	no	—
170	C₁₉×#102	—	2	1	no	—
171	C₁₉×#102	—	2	1	no	—
172	C₁₉×#102	—	2	1	no	—
173	C₁₉×#97	—	2	1	no	—
174	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
175	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
176	#41×C₁₉	—	2	2	no	—
177	#41×C₁₉	—	4	1	no	—
178	#41×C₁₉	—	4	2	no	—
179	#41×C₁₉	—	4	2	no	—
180	C₂×Q₈×C₁₉	—	2	1	no	—
181	C₂×Q₈×C₁₉	—	2	1	no	—
182	C₂×Q₈×C₁₉	—	2	1	no	—
183	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
184	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
185	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
186	C₂×D₄×C₁₉	—	2	2	no	—
187	C₂×D₄×C₁₉	—	2	1	no	—
188	C₂×D₄×C₁₉	—	2	1	no	—
189	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
190	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	1	no	—
195	C₂²×C₄×C₁₉	—	2	1	no	—
196	C₂²×C₄×C₁₉	—	2	1	no	—
197	C₂²×C₄×C₁₉	—	2	1	no	—
198	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
201	Q₁₆×C₁₉	—	4	4	no	—
202	Q₁₆×C₁₉	—	8	1	no	—
203	SD₁₆×C₁₉	—	8	1	no	—
204	M₁₆×C₁₉	—	4	2	no	—
205	M₁₆×C₁₉	—	8	1	no	—
206	C₂×C₈×C₁₉	—	2	1	no	—
207	C₂×C₈×C₁₉	—	2	1	no	—
208	C₂×C₈×C₁₉	—	2	1	no	—
209	C₂×C₈×C₁₉	—	2	1	no	—
210	C₂×C₈×C₁₉	—	2	1	no	—
211	C₂×C₈×C₁₉	—	2	1	no	—
212	C₂×C₈×C₁₉	—	4	2	no	—
213	C₄⋊C₄×C₁₉	—	2	2	no	—
214	C₄⋊C₄×C₁₉	—	2	2	no	—
215	C₄⋊C₄×C₁₉	—	2	2	no	—
216	C₄⋊C₄×C₁₉	—	2	2	no	—
217	C₄⋊C₄×C₁₉	—	2	2	no	—
218	C₄⋊C₄×C₁₉	—	2	2	no	—
219	C₄⋊C₄×C₁₉	—	2	2	no	—
220	C₄⋊C₄×C₁₉	—	2	2	no	—
221	C₄⋊C₄×C₁₉	—	2	1	no	—
222	C₄⋊C₄×C₁₉	—	2	1	no	—
223	C₄⋊C₄×C₁₉	—	2	2	no	—
224	C₄⋊C₄×C₁₉	—	2	2	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	1	no	—
236	C₄⋊C₄×C₁₉	—	4	1	no	—
237	C₄⋊C₄×C₁₉	—	4	1	no	—
238	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
239	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
243	C₂²⋊C₄×C₁₉	—	2	2	no	—
244	C₂²⋊C₄×C₁₉	—	2	2	no	—
245	C₂²⋊C₄×C₁₉	—	2	2	no	—
246	C₂²⋊C₄×C₁₉	—	2	2	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	—	4	1	no	—
256	C₄²×C₁₉	—	2	2	no	—
257	C₄²×C₁₉	—	2	1	no	—
258	C₄²×C₁₉	—	2	1	no	—
259	C₄²×C₁₉	—	2	2	no	—
260	C₄²×C₁₉	—	2	1	no	—
261	C₄²×C₁₉	—	2	1	no	—
262	C₄²×C₁₉	—	4	1	no	—
263	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
264	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
265	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
266	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
267	#18597	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
268	C₂³×C₁₉	—	2	1	no	—
269	C₂³×C₁₉	—	2	1	no	—
270	C₂³×C₁₉	#120	1	1	yes	characteristic
271	Q₈×C₁₉	—	2	1	no	—
272	Q₈×C₁₉	—	2	1	no	—
273	Q₈×C₁₉	—	2	1	no	—
274	Q₈×C₁₉	—	2	1	no	—
275	Q₈×C₁₉	—	4	2	no	—
276	Q₈×C₁₉	—	4	2	no	—
277	Q₈×C₁₉	—	4	1	no	—
278	Q₈×C₁₉	—	4	1	no	—
279	Q₈×C₁₉	—	4	1	no	—
280	Q₈×C₁₉	—	4	1	no	—
281	D₄×C₁₉	—	2	1	no	—
282	D₄×C₁₉	—	2	1	no	—
283	D₄×C₁₉	—	2	1	no	—
284	D₄×C₁₉	—	4	2	no	—
285	D₄×C₁₉	—	4	4	no	—
286	D₄×C₁₉	—	8	1	no	—
287	D₄×C₁₉	#137	1	2	yes	—
288	C₂×C₄×C₁₉	—	2	1	no	—
289	C₂×C₄×C₁₉	—	2	1	no	—
290	C₂×C₄×C₁₉	—	2	1	no	—
291	C₂×C₄×C₁₉	—	2	1	no	—
292	C₂×C₄×C₁₉	—	2	1	no	—
293	C₂×C₄×C₁₉	—	2	1	no	—
294	C₂×C₄×C₁₉	—	2	1	no	—
295	C₂×C₄×C₁₉	—	2	1	no	—
296	C₂×C₄×C₁₉	—	2	2	no	—
297	C₂×C₄×C₁₉	—	2	2	no	—
298	C₂×C₄×C₁₉	—	2	1	no	—
299	C₂×C₄×C₁₉	—	2	1	no	—
300	C₂×C₄×C₁₉	—	4	1	no	—
301	C₂×C₄×C₁₉	—	4	2	no	—
302	C₂×C₄×C₁₉	—	4	4	no	—
303	C₂×C₄×C₁₉	—	4	1	no	—
304	C₂×C₄×C₁₉	—	4	1	no	—
305	C₂×C₄×C₁₉	—	4	1	no	—
306	C₂×C₄×C₁₉	—	4	1	no	—
307	C₂×C₄×C₁₉	—	4	1	no	—
308	C₂×C₄×C₁₉	—	4	1	no	—
309	C₂×C₄×C₁₉	—	8	1	no	—
310	C₂×C₄×C₁₉	—	8	2	no	—
311	C₂×C₄×C₁₉	—	8	2	no	—
312	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
313	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
314	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
315	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
316	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
317	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
318	C₈×C₁₉	—	2	2	no	—
319	C₈×C₁₉	—	4	1	no	—
320	C₈×C₁₉	—	4	1	no	—
321	C₈×C₁₉	—	4	1	no	—
322	C₈×C₁₉	—	4	1	no	—
323	C₈×C₁₉	—	4	1	no	—
324	#3515	C₂×C₁₉	1	1	yes	characteristic
325	#3252	C₂×C₁₉	1	1	yes	characteristic, complemented
326	#3185	C₂×C₁₉	1	1	yes	characteristic, complemented
327	#3076	C₂×C₁₉	1	1	yes	characteristic, complemented
328	#1654	C₂×C₁₉	1	1	yes	characteristic, complemented
329	#1653	C₂×C₁₉	1	1	yes	characteristic, complemented
330	#1644	C₂×C₁₉	1	1	yes	characteristic, complemented
331	#1643	C₂×C₁₉	1	1	yes	characteristic, complemented
332	#1636	C₂×C₁₉	1	1	yes	characteristic, complemented
333	#1635	C₂×C₁₉	1	1	yes	characteristic, complemented
334	#1632	C₂×C₁₉	1	1	yes	characteristic, complemented
335	#1632	C₂×C₁₉	1	1	yes	characteristic, complemented
336	#1550	C₂×C₁₉	1	1	yes	characteristic, complemented
337	#1489	C₂×C₁₉	1	1	yes	characteristic, complemented
338	#1483	C₂×C₁₉	1	1	yes	characteristic, complemented
339	C₂²×C₁₉	—	2	1	no	—
340	C₂²×C₁₉	—	2	2	no	—
341	C₂²×C₁₉	—	2	1	no	—
342	C₂²×C₁₉	—	2	1	no	—
343	C₂²×C₁₉	—	4	1	no	—
344	C₂²×C₁₉	—	4	1	no	—
345	C₂²×C₁₉	—	4	1	no	—
346	C₂²×C₁₉	—	4	1	no	—
347	C₂²×C₁₉	—	4	1	no	—
348	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
349	C₄×C₁₉	—	2	1	no	—
350	C₄×C₁₉	—	2	1	no	—
351	C₄×C₁₉	—	2	1	no	—
352	C₄×C₁₉	—	2	1	no	—
353	C₄×C₁₉	—	4	1	no	—
354	C₄×C₁₉	—	4	1	no	—
355	C₄×C₁₉	—	4	2	no	—
356	C₄×C₁₉	—	4	1	no	—
357	C₄×C₁₉	—	4	1	no	—
358	C₄×C₁₉	—	4	1	no	—
359	C₄×C₁₉	—	4	1	no	—
360	C₄×C₁₉	—	4	2	no	—
361	C₄×C₁₉	—	8	1	no	—
362	C₄×C₁₉	—	8	1	no	—
363	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
364	C₄×C₁₉	#575	1	1	yes	characteristic
365	C₄×C₁₉	#577	1	1	yes	characteristic
366	C₄×C₁₉	#578	1	1	yes	characteristic
367	#557	C₂²×C₁₉	1	1	yes	characteristic
368	#554	C₂²×C₁₉	1	1	yes	characteristic
369	#554	C₂²×C₁₉	1	1	yes	characteristic
370	#553	—	2	1	no	—
371	#552	—	2	1	no	—
372	#552	—	2	2	no	—
373	#552	—	2	1	no	—
374	#547	—	2	1	no	—
375	#547	C₂²×C₁₉	1	1	yes	characteristic
376	#541	—	2	1	no	—
377	#539	—	2	2	no	—
378	#533	C₂²×C₁₉	1	1	yes	characteristic
379	#533	C₂²×C₁₉	1	1	yes	characteristic
380	#529	—	2	1	no	—
381	#529	C₂²×C₁₉	1	1	yes	characteristic
382	C₂×#125	—	2	1	no	—
383	#520	—	2	1	no	—
384	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
385	#498	C₂²×C₁₉	1	1	yes	characteristic
386	#494	C₂²×C₁₉	1	1	yes	characteristic
387	#487	C₂²×C₁₉	1	1	yes	characteristic
388	#487	C₂²×C₁₉	1	1	yes	characteristic
389	#479	—	2	1	no	—
390	#479	—	2	1	no	—
391	#478	—	2	1	no	—
392	#477	C₂²×C₁₉	1	1	yes	characteristic
393	#477	C₂²×C₁₉	1	1	yes	characteristic
394	#476	C₂²×C₁₉	1	1	yes	characteristic
395	#476	C₂²×C₁₉	1	1	yes	characteristic
396	#475	C₂²×C₁₉	1	1	yes	characteristic
397	#474	C₂²×C₁₉	1	1	yes	characteristic
398	#470	—	2	2	no	—
399	#470	—	2	1	no	—
400	#468	—	2	1	no	—
401	#464	—	2	1	no	—
402	#462	C₂²×C₁₉	1	1	yes	characteristic
403	#461	C₂²×C₁₉	1	1	yes	characteristic
404	#441	—	2	2	no	—
405	#427	—	2	1	no	—
406	#423	C₂²×C₁₉	1	1	yes	characteristic
407	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
408	#416	—	2	1	no	—
409	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
410	#333	C₂²×C₁₉	1	1	yes	characteristic
411	#333	C₂²×C₁₉	1	1	yes	characteristic
412	#332	C₂²×C₁₉	1	1	yes	characteristic
413	#332	C₂²×C₁₉	1	1	yes	characteristic
414	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
415	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
416	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
417	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
418	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
419	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
420	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
421	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
422	C₂×C₁₉	—	4	1	no	—
423	C₂×C₁₉	—	4	2	no	—
424	C₂×C₁₉	—	8	1	no	—
425	C₂×C₁₉	#3007	1	1	yes	characteristic
426	C₂×C₁₉	#3013	1	1	yes	characteristic
427	C₂×C₁₉	#3018	1	1	yes	characteristic
428	C₂×#41	—	2	1	no	—
429	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
430	C₂×Q₁₆	—	2	2	no	—
431	C₂×Q₁₆	—	2	1	no	—
432	C₂×SD₁₆	—	2	1	no	—
433	C₂×M₁₆	—	2	1	no	—
434	C₂×M₁₆	—	2	1	no	—
435	C₂²×C₈	—	2	1	no	—
436	C₄⋊Q₈	—	2	1	no	—
437	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
438	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
439	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
440	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
441	#126	—	2	2	no	—
442	#126	—	2	2	no	—
443	#126	—	2	2	no	—
444	#126	—	2	1	no	—
445	#125	—	2	2	no	—
446	#125	—	2	2	no	—
447	#125	—	2	2	no	—
448	#125	—	2	1	no	—
449	#125	—	2	1	no	—
450	#125	—	2	2	no	—
451	#125	—	2	1	no	—
452	#125	—	2	1	no	—
453	#125	—	2	1	no	—
454	#125	D₄×C₁₉	1	1	yes	characteristic
455	#124	D₄×C₁₉	1	1	yes	characteristic
456	#123	—	2	2	no	—
457	#123	—	2	2	no	—
458	#123	—	2	2	no	—
459	#123	—	2	1	no	—
460	#123	—	2	2	no	—
461	C₂²⋊Q₈	—	2	1	no	—
462	C₂²⋊Q₈	—	2	2	no	—
463	C₂²⋊Q₈	—	2	2	no	—
464	C₂²⋊Q₈	—	2	1	no	—
465	C₂²⋊Q₈	—	2	1	no	—
466	C₂²⋊Q₈	—	2	1	no	—
467	C₂²⋊Q₈	—	2	1	no	—
468	C₂²⋊Q₈	—	2	1	no	—
469	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
470	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
471	#121	—	2	2	no	—
472	#121	—	2	1	no	—
473	#121	D₄×C₁₉	1	1	yes	characteristic
474	C₄×Q₈	—	2	1	no	—
475	C₄×Q₈	—	2	1	no	—
476	C₄×Q₈	—	2	1	no	—
477	C₄×Q₈	—	2	1	no	—
478	C₄×Q₈	—	2	1	no	—
479	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
480	C₄×Q₈	D₄×C₁₉	1	2	yes	—
481	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
482	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
483	C₄×D₄	—	2	2	no	—
484	C₄×D₄	—	2	2	no	—
485	C₄×D₄	—	2	1	no	—
486	C₄×D₄	—	2	1	no	—
487	C₄×D₄	—	2	1	no	—
488	C₄×D₄	—	2	1	no	—
489	C₄×D₄	—	2	1	no	—
490	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
491	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
492	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
493	#117	—	2	2	no	—
494	#117	—	2	2	no	—
495	#117	—	2	1	no	—
496	#117	—	2	1	no	—
497	#117	—	2	1	no	—
498	#117	—	2	1	no	—
499	#117	D₄×C₁₉	1	1	yes	characteristic
500	C₂×C₄⋊C₄	—	2	2	no	—
501	C₂×C₄⋊C₄	—	2	2	no	—
502	C₂×C₄⋊C₄	—	2	1	no	—
503	C₂×C₄⋊C₄	—	2	1	no	—
504	C₂×C₄⋊C₄	—	2	1	no	—
505	C₂×C₄²	—	2	1	no	—
506	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
507	#107	—	2	1	no	—
508	#107	—	2	1	no	—
509	#107	—	2	1	no	—
510	#106	—	2	1	no	—
511	#106	—	2	1	no	—
512	#106	—	2	2	no	—
513	#106	—	2	1	no	—
514	C₄⋊C₈	—	2	1	no	—
515	C₄⋊C₈	—	2	1	no	—
516	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
517	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
518	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
519	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
520	#103	—	2	1	no	—
521	#103	—	2	1	no	—
522	#103	—	2	2	no	—
523	#103	—	2	1	no	—
524	#103	—	2	2	no	—
525	#103	—	2	1	no	—
526	#103	—	2	1	no	—
527	#102	—	2	1	no	—
528	#102	—	2	1	no	—
529	#102	—	2	1	no	—
530	#97	—	2	1	no	—
531	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
532	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
533	C₁₉	#18597	1	1	yes	characteristic, direct product factor, Sylow
534	#41	—	2	2	no	—
535	#41	—	4	1	no	—
536	#41	—	4	2	no	—
537	#41	—	4	2	no	—
538	C₂×Q₈	—	2	1	no	—
539	C₂×Q₈	—	2	1	no	—
540	C₂×Q₈	—	2	1	no	—
541	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
542	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
543	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
544	C₂×D₄	—	2	2	no	—
545	C₂×D₄	—	2	1	no	—
546	C₂×D₄	—	2	1	no	—
547	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
548	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
557	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
558	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
559	Q₁₆	—	4	4	no	—
560	Q₁₆	—	8	1	no	—
561	SD₁₆	—	8	1	no	—
562	M₁₆	—	4	2	no	—
563	M₁₆	—	8	1	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	—	2	1	no	—
567	C₂×C₈	—	2	1	no	—
568	C₂×C₈	—	2	1	no	—
569	C₂×C₈	—	2	1	no	—
570	C₂×C₈	—	4	2	no	—
571	C₄⋊C₄	—	2	2	no	—
572	C₄⋊C₄	—	2	2	no	—
573	C₄⋊C₄	—	2	2	no	—
574	C₄⋊C₄	—	2	2	no	—
575	C₄⋊C₄	—	2	2	no	—
576	C₄⋊C₄	—	2	2	no	—
577	C₄⋊C₄	—	2	2	no	—
578	C₄⋊C₄	—	2	2	no	—
579	C₄⋊C₄	—	2	1	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	2	2	no	—
582	C₄⋊C₄	—	2	2	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	2	1	no	—
593	C₄⋊C₄	—	2	1	no	—
594	C₄⋊C₄	—	4	1	no	—
595	C₄⋊C₄	—	4	1	no	—
596	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
597	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
598	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
599	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
600	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
601	C₂²⋊C₄	—	2	2	no	—
602	C₂²⋊C₄	—	2	2	no	—
603	C₂²⋊C₄	—	2	2	no	—
604	C₂²⋊C₄	—	2	2	no	—
605	C₂²⋊C₄	—	2	1	no	—
606	C₂²⋊C₄	—	2	1	no	—
607	C₂²⋊C₄	—	2	1	no	—
608	C₂²⋊C₄	—	2	1	no	—
609	C₂²⋊C₄	—	2	1	no	—
610	C₂²⋊C₄	—	2	1	no	—
611	C₂²⋊C₄	—	2	1	no	—
612	C₂²⋊C₄	—	2	1	no	—
613	C₂²⋊C₄	—	4	1	no	—
614	C₄²	—	2	2	no	—
615	C₄²	—	2	1	no	—
616	C₄²	—	2	1	no	—
617	C₄²	—	2	2	no	—
618	C₄²	—	2	1	no	—
619	C₄²	—	2	1	no	—
620	C₄²	—	4	1	no	—
621	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
622	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
623	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
624	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
625	C₂³	—	2	1	no	—
626	C₂³	—	2	1	no	—
627	C₂³	C₁₉×#120	1	1	yes	characteristic
628	Q₈	—	2	1	no	—
629	Q₈	—	2	1	no	—
630	Q₈	—	2	1	no	—
631	Q₈	—	2	1	no	—
632	Q₈	—	4	2	no	—
633	Q₈	—	4	2	no	—
634	Q₈	—	4	1	no	—
635	Q₈	—	4	1	no	—
636	Q₈	—	4	1	no	—
637	Q₈	—	4	1	no	—
638	D₄	—	2	1	no	—
639	D₄	—	2	1	no	—
640	D₄	—	2	1	no	—
641	D₄	—	4	2	no	—
642	D₄	—	4	4	no	—
643	D₄	—	8	1	no	—
644	D₄	C₁₉×#137	1	2	yes	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	2	no	—
659	C₂×C₄	—	4	4	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	4	1	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	8	1	no	—
667	C₂×C₄	—	8	2	no	—
668	C₂×C₄	—	8	2	no	—
669	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
670	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
671	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
672	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
673	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
674	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
675	C₈	—	2	2	no	—
676	C₈	—	4	1	no	—
677	C₈	—	4	1	no	—
678	C₈	—	4	1	no	—
679	C₈	—	4	1	no	—
680	C₈	—	4	1	no	—
681	C₂²	—	2	1	no	—
682	C₂²	—	2	2	no	—
683	C₂²	—	2	1	no	—
684	C₂²	—	2	1	no	—
685	C₂²	—	4	1	no	—
686	C₂²	—	4	1	no	—
687	C₂²	—	4	1	no	—
688	C₂²	—	4	1	no	—
689	C₂²	—	4	1	no	—
690	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
691	C₄	—	2	1	no	—
692	C₄	—	2	1	no	—
693	C₄	—	2	1	no	—
694	C₄	—	2	1	no	—
695	C₄	—	4	1	no	—
696	C₄	—	4	1	no	—
697	C₄	—	4	2	no	—
698	C₄	—	4	1	no	—
699	C₄	—	4	1	no	—
700	C₄	—	4	1	no	—
701	C₄	—	4	1	no	—
702	C₄	—	4	2	no	—
703	C₄	—	8	1	no	—
704	C₄	—	8	1	no	—
705	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
706	C₄	C₁₉×#575	1	1	yes	characteristic
707	C₄	C₁₉×#577	1	1	yes	characteristic
708	C₄	C₁₉×#578	1	1	yes	characteristic
709	C₂	—	4	1	no	—
710	C₂	—	4	2	no	—
711	C₂	—	8	1	no	—
712	C₂	C₁₉×#3007	1	1	yes	characteristic
713	C₂	C₁₉×#3013	1	1	yes	characteristic
714	C₂	C₁₉×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3515	C₂
LCS	G ▷ C₄² ▷ 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×#3252	C₂	semidirect
3. C₁₉×#3185	C₂	semidirect
4. C₁₉×#3076	C₂	semidirect
5. C₁₉×#1654	C₂	semidirect
6. C₁₉×#1653	C₂	semidirect
7. C₁₉×#1644	C₂	semidirect
8. C₁₉×#1643	C₂	semidirect
9. C₁₉×#1636	C₂	semidirect
10. C₁₉×#1635	C₂	semidirect
11. C₁₉×#1632	C₂	semidirect
12. C₁₉×#1632	C₂	semidirect
13. C₁₉×#1550	C₂	semidirect
14. C₁₉×#1489	C₂	semidirect
15. C₁₉×#1483	C₂	semidirect
267. #18597	C₁₉	direct (N × H)
325. #3252	C₂×C₁₉	semidirect
326. #3185	C₂×C₁₉	semidirect
327. #3076	C₂×C₁₉	semidirect
328. #1654	C₂×C₁₉	semidirect
329. #1653	C₂×C₁₉	semidirect
330. #1644	C₂×C₁₉	semidirect
331. #1643	C₂×C₁₉	semidirect
332. #1636	C₂×C₁₉	semidirect
333. #1635	C₂×C₁₉	semidirect
334. #1632	C₂×C₁₉	semidirect
335. #1632	C₂×C₁₉	semidirect
336. #1550	C₂×C₁₉	semidirect
337. #1489	C₂×C₁₉	semidirect
338. #1483	C₂×C₁₉	semidirect
533. C₁₉	#18597	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×#3515	2
C₁₉×#3252	2
C₁₉×#3185	2
C₁₉×#3076	2
C₁₉×#1654	2
C₁₉×#1653	2
C₁₉×#1644	2
C₁₉×#1643	2
C₁₉×#1636	2
C₁₉×#1635	2
C₁₉×#1632	2
C₁₉×#1550	2
C₁₉×#1489	2
C₁₉×#1483	2
#18597	19

Subgroups — C19×#18597 #18024556

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18597 #18024556