Subgroups — C₁₉×#19563 #18025522

Order 4864.

608 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3246	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3228	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3214	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2979	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1701	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1697	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1693	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1691	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1681	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1677	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1673	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1671	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1573	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1554	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1540	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#533	C₂²	1	1	yes	characteristic
17	C₁₉×#532	C₂²	1	1	yes	characteristic
18	C₁₉×#532	C₂²	1	1	yes	characteristic
19	C₁₉×#500	C₂²	1	1	yes	characteristic
20	C₁₉×#498	C₂²	1	1	yes	characteristic
21	C₁₉×#496	—	2	1	no	—
22	C₁₉×#489	—	2	1	no	—
23	C₁₉×#486	C₂²	1	1	yes	characteristic
24	C₁₉×#486	C₂²	1	1	yes	characteristic
25	C₁₉×#482	—	2	1	no	—
26	C₁₉×#482	—	2	1	no	—
27	C₁₉×#478	—	2	1	no	—
28	C₁₉×#478	—	2	1	no	—
29	C₁₉×#476	C₂²	1	1	yes	characteristic
30	C₁₉×#476	C₂²	1	1	yes	characteristic
31	C₁₉×#475	—	2	1	no	—
32	C₁₉×#465	—	2	1	no	—
33	C₁₉×#465	—	2	1	no	—
34	C₁₉×#461	C₂²	1	1	yes	characteristic
35	C₁₉×#461	C₂²	1	1	yes	characteristic
36	C₁₉×#461	C₂²	1	1	yes	characteristic
37	C₁₉×#461	C₂²	1	1	yes	characteristic
38	C₁₉×#460	—	2	1	no	—
39	C₁₉×#459	C₂²	1	1	yes	characteristic
40	C₁₉×#459	C₂²	1	1	yes	characteristic
41	C₁₉×#449	—	2	1	no	—
42	C₁₉×#449	—	2	1	no	—
43	C₁₉×#436	—	2	1	no	—
44	C₁₉×#436	C₂²	1	1	yes	characteristic
45	C₁₉×#436	C₂²	1	1	yes	characteristic
46	C₈×D₄×C₁₉	—	2	1	no	—
47	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
48	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
49	C₁₉×#432	C₂²	1	1	yes	characteristic
50	C₁₉×#431	C₂²	1	1	yes	characteristic
51	C₁₉×#431	C₂²	1	1	yes	characteristic
52	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
53	C₁₉×#408	—	2	1	no	—
54	C₁₉×#408	—	2	1	no	—
55	C₁₉×#335	C₂²	1	1	yes	characteristic
56	C₁₉×#335	C₂²	1	1	yes	characteristic
57	C₁₉×#334	C₂²	1	1	yes	characteristic
58	C₁₉×#334	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×#332	C₂²	1	1	yes	characteristic
64	C₁₉×#332	C₂²	1	1	yes	characteristic
65	C₁₉×#331	C₂²	1	1	yes	characteristic
66	C₁₉×#331	C₂²	1	1	yes	characteristic
67	C₂×#41×C₁₉	—	2	1	no	—
68	C₂×#41×C₁₉	—	2	1	no	—
69	C₂×SD₁₆×C₁₉	—	2	1	no	—
70	C₂×SD₁₆×C₁₉	—	2	1	no	—
71	C₂×SD₁₆×C₁₉	—	2	1	no	—
72	C₂×SD₁₆×C₁₉	—	2	1	no	—
73	C₂×D₈×C₁₉	—	2	1	no	—
74	C₂×D₈×C₁₉	—	2	1	no	—
75	C₂×M₁₆×C₁₉	—	2	1	no	—
76	C₂×M₁₆×C₁₉	—	2	1	no	—
77	C₂²×C₈×C₁₉	—	2	1	no	—
78	C₂²×C₈×C₁₉	—	2	1	no	—
79	C₂²×C₈×C₁₉	—	2	1	no	—
80	C₁₉×C₄⋊Q₈	D₄	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×#127	D₄	1	1	yes	characteristic
85	C₁₉×#127	C₂³	1	1	yes	characteristic
86	C₁₉×#125	—	2	1	no	—
87	C₁₉×#124	—	2	1	no	—
88	C₁₉×#124	—	2	1	no	—
89	C₁₉×C₂²⋊Q₈	—	2	1	no	—
90	C₁₉×C₂²⋊Q₈	—	2	1	no	—
91	C₁₉×#121	—	2	1	no	—
92	C₁₉×#121	—	2	1	no	—
93	C₁₉×#121	—	2	1	no	—
94	C₁₉×#121	D₄	1	1	yes	characteristic
95	C₁₉×#121	D₄	1	1	yes	characteristic
96	C₄×Q₈×C₁₉	—	2	1	no	—
97	C₄×Q₈×C₁₉	—	2	1	no	—
98	C₄×D₄×C₁₉	—	2	1	no	—
99	C₄×D₄×C₁₉	—	2	1	no	—
100	C₄×D₄×C₁₉	—	2	1	no	—
101	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
102	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
103	C₁₉×#117	—	2	1	no	—
104	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
105	C₁₉×#107	—	2	1	no	—
106	C₁₉×#107	—	2	1	no	—
107	C₁₉×#106	—	2	1	no	—
108	C₁₉×#106	—	2	1	no	—
109	C₁₉×#106	—	2	1	no	—
110	C₁₉×#106	—	2	1	no	—
111	C₁₉×C₄⋊C₈	—	2	1	no	—
112	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
113	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
114	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
115	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
116	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
119	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₁₉×#103	—	2	1	no	—
121	C₁₉×#103	—	2	1	no	—
122	C₁₉×#103	—	2	1	no	—
123	C₁₉×#103	—	2	1	no	—
124	C₁₉×#102	—	2	1	no	—
125	C₁₉×#102	—	2	1	no	—
126	C₁₉×#102	—	2	1	no	—
127	C₁₉×#102	—	2	1	no	—
128	C₁₉×#102	—	2	1	no	—
129	C₁₉×#102	—	2	1	no	—
130	C₁₉×#102	—	2	1	no	—
131	C₁₉×#102	—	2	1	no	—
132	C₁₉×C₂²⋊C₈	—	2	1	no	—
133	C₁₉×C₂²⋊C₈	—	2	1	no	—
134	C₁₉×C₂²⋊C₈	—	2	1	no	—
135	C₁₉×C₂²⋊C₈	—	2	1	no	—
136	C₁₉×C₂²⋊C₈	—	2	1	no	—
137	C₁₉×C₂²⋊C₈	—	2	1	no	—
138	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
139	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
140	C₁₉×#97	—	2	1	no	—
141	C₄×C₈×C₁₉	—	2	1	no	—
142	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
144	#41×C₁₉	—	8	1	no	—
145	#41×C₁₉	—	8	1	no	—
146	#41×C₁₉	—	8	1	no	—
147	#41×C₁₉	—	8	1	no	—
148	C₂×Q₈×C₁₉	—	2	1	no	—
149	C₂×Q₈×C₁₉	—	2	1	no	—
150	C₂×Q₈×C₁₉	—	2	1	no	—
151	C₂×Q₈×C₁₉	—	2	1	no	—
152	C₂×D₄×C₁₉	—	2	1	no	—
153	C₂×D₄×C₁₉	—	2	1	no	—
154	C₂×D₄×C₁₉	—	2	1	no	—
155	C₂×D₄×C₁₉	—	2	1	no	—
156	C₂×D₄×C₁₉	—	2	1	no	—
157	C₂×D₄×C₁₉	—	2	1	no	—
158	C₂×D₄×C₁₉	—	2	1	no	—
159	C₂×D₄×C₁₉	—	4	1	no	—
160	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₉	—	2	1	no	—
163	C₂²×C₄×C₁₉	—	2	1	no	—
164	C₂²×C₄×C₁₉	—	4	1	no	—
165	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
168	SD₁₆×C₁₉	—	8	1	no	—
169	SD₁₆×C₁₉	—	8	1	no	—
170	SD₁₆×C₁₉	—	8	1	no	—
171	SD₁₆×C₁₉	—	8	1	no	—
172	D₈×C₁₉	—	8	1	no	—
173	D₈×C₁₉	—	8	1	no	—
174	M₁₆×C₁₉	—	8	1	no	—
175	M₁₆×C₁₉	—	8	1	no	—
176	C₂×C₈×C₁₉	—	2	1	no	—
177	C₂×C₈×C₁₉	—	2	1	no	—
178	C₂×C₈×C₁₉	—	2	1	no	—
179	C₂×C₈×C₁₉	—	2	1	no	—
180	C₂×C₈×C₁₉	—	2	1	no	—
181	C₂×C₈×C₁₉	—	2	1	no	—
182	C₂×C₈×C₁₉	—	8	1	no	—
183	C₂×C₈×C₁₉	—	8	1	no	—
184	C₂×C₈×C₁₉	—	8	1	no	—
185	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
186	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
187	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
188	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₄⋊C₄×C₁₉	—	2	1	no	—
190	C₄⋊C₄×C₁₉	—	2	1	no	—
191	C₄⋊C₄×C₁₉	—	2	1	no	—
192	C₄⋊C₄×C₁₉	—	2	1	no	—
193	C₄⋊C₄×C₁₉	—	2	1	no	—
194	C₄⋊C₄×C₁₉	—	2	1	no	—
195	C₄⋊C₄×C₁₉	—	2	1	no	—
196	C₄⋊C₄×C₁₉	—	4	1	no	—
197	C₄⋊C₄×C₁₉	—	4	1	no	—
198	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
199	C₄⋊C₄×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	—	4	1	no	—
205	C₂²⋊C₄×C₁₉	—	4	1	no	—
206	C₂²⋊C₄×C₁₉	—	4	1	no	—
207	C₄²×C₁₉	—	4	1	no	—
208	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
210	C₄²×C₁₉	#41	1	1	yes	characteristic
211	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
212	#19563	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
213	C₂³×C₁₉	—	2	1	no	—
214	C₂³×C₁₉	—	2	1	no	—
215	C₂³×C₁₉	—	4	1	no	—
216	C₂³×C₁₉	#121	1	1	yes	characteristic
217	Q₈×C₁₉	—	4	1	no	—
218	Q₈×C₁₉	—	4	1	no	—
219	Q₈×C₁₉	—	4	1	no	—
220	Q₈×C₁₉	—	4	1	no	—
221	Q₈×C₁₉	—	8	1	no	—
222	Q₈×C₁₉	—	8	1	no	—
223	D₄×C₁₉	—	2	1	no	—
224	D₄×C₁₉	—	2	1	no	—
225	D₄×C₁₉	—	2	1	no	—
226	D₄×C₁₉	—	2	1	no	—
227	D₄×C₁₉	—	4	2	no	—
228	D₄×C₁₉	—	4	1	no	—
229	D₄×C₁₉	—	4	1	no	—
230	D₄×C₁₉	—	4	1	no	—
231	D₄×C₁₉	—	4	1	no	—
232	D₄×C₁₉	—	8	1	no	—
233	D₄×C₁₉	—	8	1	no	—
234	D₄×C₁₉	—	8	1	no	—
235	D₄×C₁₉	—	8	1	no	—
236	D₄×C₁₉	—	8	2	no	—
237	C₂×C₄×C₁₉	—	2	1	no	—
238	C₂×C₄×C₁₉	—	2	1	no	—
239	C₂×C₄×C₁₉	—	2	1	no	—
240	C₂×C₄×C₁₉	—	2	1	no	—
241	C₂×C₄×C₁₉	—	2	1	no	—
242	C₂×C₄×C₁₉	—	2	1	no	—
243	C₂×C₄×C₁₉	—	4	1	no	—
244	C₂×C₄×C₁₉	—	4	1	no	—
245	C₂×C₄×C₁₉	—	4	1	no	—
246	C₂×C₄×C₁₉	—	4	1	no	—
247	C₂×C₄×C₁₉	—	4	1	no	—
248	C₂×C₄×C₁₉	—	4	1	no	—
249	C₂×C₄×C₁₉	—	4	1	no	—
250	C₂×C₄×C₁₉	—	4	1	no	—
251	C₂×C₄×C₁₉	—	8	2	no	—
252	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
253	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
254	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
255	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
258	C₈×C₁₉	—	2	1	no	—
259	C₈×C₁₉	—	2	1	no	—
260	C₈×C₁₉	—	2	1	no	—
261	C₈×C₁₉	—	2	1	no	—
262	C₈×C₁₉	—	4	1	no	—
263	C₈×C₁₉	—	4	1	no	—
264	C₈×C₁₉	—	4	1	no	—
265	C₈×C₁₉	—	4	1	no	—
266	C₈×C₁₉	—	4	1	no	—
267	C₈×C₁₉	—	4	1	no	—
268	#3246	C₂×C₁₉	1	1	yes	characteristic, complemented
269	#3228	C₂×C₁₉	1	1	yes	characteristic, complemented
270	#3214	C₂×C₁₉	1	1	yes	characteristic
271	#2979	C₂×C₁₉	1	1	yes	characteristic, complemented
272	#1701	C₂×C₁₉	1	1	yes	characteristic, complemented
273	#1697	C₂×C₁₉	1	1	yes	characteristic, complemented
274	#1693	C₂×C₁₉	1	1	yes	characteristic, complemented
275	#1691	C₂×C₁₉	1	1	yes	characteristic, complemented
276	#1681	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#1677	C₂×C₁₉	1	1	yes	characteristic, complemented
278	#1673	C₂×C₁₉	1	1	yes	characteristic, complemented
279	#1671	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#1573	C₂×C₁₉	1	1	yes	characteristic, complemented
281	#1554	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#1540	C₂×C₁₉	1	1	yes	characteristic, complemented
283	C₂²×C₁₉	—	2	1	no	—
284	C₂²×C₁₉	—	2	1	no	—
285	C₂²×C₁₉	—	2	1	no	—
286	C₂²×C₁₉	—	4	1	no	—
287	C₂²×C₁₉	—	4	1	no	—
288	C₂²×C₁₉	—	4	1	no	—
289	C₂²×C₁₉	—	4	1	no	—
290	C₂²×C₁₉	—	4	1	no	—
291	C₂²×C₁₉	—	4	1	no	—
292	C₂²×C₁₉	—	8	1	no	—
293	C₂²×C₁₉	—	8	1	no	—
294	C₂²×C₁₉	—	8	1	no	—
295	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
296	C₄×C₁₉	—	2	1	no	—
297	C₄×C₁₉	—	2	1	no	—
298	C₄×C₁₉	—	2	1	no	—
299	C₄×C₁₉	—	2	1	no	—
300	C₄×C₁₉	—	4	1	no	—
301	C₄×C₁₉	—	4	1	no	—
302	C₄×C₁₉	—	8	1	no	—
303	C₄×C₁₉	—	8	1	no	—
304	C₄×C₁₉	—	8	1	no	—
305	C₄×C₁₉	#576	1	1	yes	characteristic
306	C₄×C₁₉	#577	1	1	yes	characteristic
307	C₄×C₁₉	#577	1	1	yes	characteristic
308	C₄×C₁₉	#577	1	1	yes	characteristic
309	#533	C₂²×C₁₉	1	1	yes	characteristic
310	#532	C₂²×C₁₉	1	1	yes	characteristic
311	#532	C₂²×C₁₉	1	1	yes	characteristic
312	#500	C₂²×C₁₉	1	1	yes	characteristic
313	#498	C₂²×C₁₉	1	1	yes	characteristic
314	#496	—	2	1	no	—
315	#489	—	2	1	no	—
316	#486	C₂²×C₁₉	1	1	yes	characteristic
317	#486	C₂²×C₁₉	1	1	yes	characteristic
318	#482	—	2	1	no	—
319	#482	—	2	1	no	—
320	#478	—	2	1	no	—
321	#478	—	2	1	no	—
322	#476	C₂²×C₁₉	1	1	yes	characteristic
323	#476	C₂²×C₁₉	1	1	yes	characteristic
324	#475	—	2	1	no	—
325	#465	—	2	1	no	—
326	#465	—	2	1	no	—
327	#461	C₂²×C₁₉	1	1	yes	characteristic
328	#461	C₂²×C₁₉	1	1	yes	characteristic
329	#461	C₂²×C₁₉	1	1	yes	characteristic
330	#461	C₂²×C₁₉	1	1	yes	characteristic
331	#460	—	2	1	no	—
332	#459	C₂²×C₁₉	1	1	yes	characteristic
333	#459	C₂²×C₁₉	1	1	yes	characteristic
334	#449	—	2	1	no	—
335	#449	—	2	1	no	—
336	#436	—	2	1	no	—
337	#436	C₂²×C₁₉	1	1	yes	characteristic
338	#436	C₂²×C₁₉	1	1	yes	characteristic
339	C₈×D₄	—	2	1	no	—
340	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
341	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
342	#432	C₂²×C₁₉	1	1	yes	characteristic
343	#431	C₂²×C₁₉	1	1	yes	characteristic
344	#431	C₂²×C₁₉	1	1	yes	characteristic
345	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
346	#408	—	2	1	no	—
347	#408	—	2	1	no	—
348	#335	C₂²×C₁₉	1	1	yes	characteristic
349	#335	C₂²×C₁₉	1	1	yes	characteristic
350	#334	C₂²×C₁₉	1	1	yes	characteristic
351	#334	C₂²×C₁₉	1	1	yes	characteristic
352	#333	C₂²×C₁₉	1	1	yes	characteristic
353	#333	C₂²×C₁₉	1	1	yes	characteristic
354	#332	C₂²×C₁₉	1	1	yes	characteristic
355	#332	C₂²×C₁₉	1	1	yes	characteristic
356	#332	C₂²×C₁₉	1	1	yes	characteristic
357	#332	C₂²×C₁₉	1	1	yes	characteristic
358	#331	C₂²×C₁₉	1	1	yes	characteristic
359	#331	C₂²×C₁₉	1	1	yes	characteristic
360	C₂×C₁₉	—	4	1	no	—
361	C₂×C₁₉	—	8	1	no	—
362	C₂×C₁₉	—	8	1	no	—
363	C₂×C₁₉	—	16	1	no	—
364	C₂×C₁₉	#3042	1	1	yes	characteristic
365	C₂×C₁₉	#3062	1	1	yes	characteristic
366	C₂×C₁₉	#3067	1	1	yes	characteristic
367	C₂×#41	—	2	1	no	—
368	C₂×#41	—	2	1	no	—
369	C₂×SD₁₆	—	2	1	no	—
370	C₂×SD₁₆	—	2	1	no	—
371	C₂×SD₁₆	—	2	1	no	—
372	C₂×SD₁₆	—	2	1	no	—
373	C₂×D₈	—	2	1	no	—
374	C₂×D₈	—	2	1	no	—
375	C₂×M₁₆	—	2	1	no	—
376	C₂×M₁₆	—	2	1	no	—
377	C₂²×C₈	—	2	1	no	—
378	C₂²×C₈	—	2	1	no	—
379	C₂²×C₈	—	2	1	no	—
380	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
381	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
382	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
383	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
384	#127	D₄×C₁₉	1	1	yes	characteristic
385	#127	C₂³×C₁₉	1	1	yes	characteristic
386	#125	—	2	1	no	—
387	#124	—	2	1	no	—
388	#124	—	2	1	no	—
389	C₂²⋊Q₈	—	2	1	no	—
390	C₂²⋊Q₈	—	2	1	no	—
391	#121	—	2	1	no	—
392	#121	—	2	1	no	—
393	#121	—	2	1	no	—
394	#121	D₄×C₁₉	1	1	yes	characteristic
395	#121	D₄×C₁₉	1	1	yes	characteristic
396	C₄×Q₈	—	2	1	no	—
397	C₄×Q₈	—	2	1	no	—
398	C₄×D₄	—	2	1	no	—
399	C₄×D₄	—	2	1	no	—
400	C₄×D₄	—	2	1	no	—
401	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
402	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
403	#117	—	2	1	no	—
404	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
405	#107	—	2	1	no	—
406	#107	—	2	1	no	—
407	#106	—	2	1	no	—
408	#106	—	2	1	no	—
409	#106	—	2	1	no	—
410	#106	—	2	1	no	—
411	C₄⋊C₈	—	2	1	no	—
412	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
413	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
414	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
415	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
416	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
417	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
418	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
419	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
420	#103	—	2	1	no	—
421	#103	—	2	1	no	—
422	#103	—	2	1	no	—
423	#103	—	2	1	no	—
424	#102	—	2	1	no	—
425	#102	—	2	1	no	—
426	#102	—	2	1	no	—
427	#102	—	2	1	no	—
428	#102	—	2	1	no	—
429	#102	—	2	1	no	—
430	#102	—	2	1	no	—
431	#102	—	2	1	no	—
432	C₂²⋊C₈	—	2	1	no	—
433	C₂²⋊C₈	—	2	1	no	—
434	C₂²⋊C₈	—	2	1	no	—
435	C₂²⋊C₈	—	2	1	no	—
436	C₂²⋊C₈	—	2	1	no	—
437	C₂²⋊C₈	—	2	1	no	—
438	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
439	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
440	#97	—	2	1	no	—
441	C₄×C₈	—	2	1	no	—
442	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
443	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
444	C₁₉	#19563	1	1	yes	characteristic, direct product factor, Sylow
445	#41	—	8	1	no	—
446	#41	—	8	1	no	—
447	#41	—	8	1	no	—
448	#41	—	8	1	no	—
449	C₂×Q₈	—	2	1	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	4	1	no	—
461	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
462	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	4	1	no	—
466	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
467	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
468	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
469	SD₁₆	—	8	1	no	—
470	SD₁₆	—	8	1	no	—
471	SD₁₆	—	8	1	no	—
472	SD₁₆	—	8	1	no	—
473	D₈	—	8	1	no	—
474	D₈	—	8	1	no	—
475	M₁₆	—	8	1	no	—
476	M₁₆	—	8	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	8	1	no	—
484	C₂×C₈	—	8	1	no	—
485	C₂×C₈	—	8	1	no	—
486	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
487	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
488	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
489	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	4	1	no	—
498	C₄⋊C₄	—	4	1	no	—
499	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
500	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	2	1	no	—
503	C₂²⋊C₄	—	2	1	no	—
504	C₂²⋊C₄	—	2	1	no	—
505	C₂²⋊C₄	—	4	1	no	—
506	C₂²⋊C₄	—	4	1	no	—
507	C₂²⋊C₄	—	4	1	no	—
508	C₄²	—	4	1	no	—
509	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
510	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
511	C₄²	#41×C₁₉	1	1	yes	characteristic
512	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
513	C₂³	—	2	1	no	—
514	C₂³	—	2	1	no	—
515	C₂³	—	4	1	no	—
516	C₂³	C₁₉×#121	1	1	yes	characteristic
517	Q₈	—	4	1	no	—
518	Q₈	—	4	1	no	—
519	Q₈	—	4	1	no	—
520	Q₈	—	4	1	no	—
521	Q₈	—	8	1	no	—
522	Q₈	—	8	1	no	—
523	D₄	—	2	1	no	—
524	D₄	—	2	1	no	—
525	D₄	—	2	1	no	—
526	D₄	—	2	1	no	—
527	D₄	—	4	2	no	—
528	D₄	—	4	1	no	—
529	D₄	—	4	1	no	—
530	D₄	—	4	1	no	—
531	D₄	—	4	1	no	—
532	D₄	—	8	1	no	—
533	D₄	—	8	1	no	—
534	D₄	—	8	1	no	—
535	D₄	—	8	1	no	—
536	D₄	—	8	2	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	8	2	no	—
552	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
553	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
554	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
555	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
556	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
557	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
558	C₈	—	2	1	no	—
559	C₈	—	2	1	no	—
560	C₈	—	2	1	no	—
561	C₈	—	2	1	no	—
562	C₈	—	4	1	no	—
563	C₈	—	4	1	no	—
564	C₈	—	4	1	no	—
565	C₈	—	4	1	no	—
566	C₈	—	4	1	no	—
567	C₈	—	4	1	no	—
568	C₂²	—	2	1	no	—
569	C₂²	—	2	1	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	4	1	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	8	1	no	—
578	C₂²	—	8	1	no	—
579	C₂²	—	8	1	no	—
580	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
581	C₄	—	2	1	no	—
582	C₄	—	2	1	no	—
583	C₄	—	2	1	no	—
584	C₄	—	2	1	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	1	no	—
587	C₄	—	8	1	no	—
588	C₄	—	8	1	no	—
589	C₄	—	8	1	no	—
590	C₄	C₁₉×#576	1	1	yes	characteristic
591	C₄	C₁₉×#577	1	1	yes	characteristic
592	C₄	C₁₉×#577	1	1	yes	characteristic
593	C₄	C₁₉×#577	1	1	yes	characteristic
594	C₂	—	4	1	no	—
595	C₂	—	8	1	no	—
596	C₂	—	8	1	no	—
597	C₂	—	16	1	no	—
598	C₂	C₁₉×#3042	1	1	yes	characteristic
599	C₂	C₁₉×#3062	1	1	yes	characteristic
600	C₂	C₁₉×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3214	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
1. C₁₉×#3246	C₂	semidirect
2. C₁₉×#3228	C₂	semidirect
4. C₁₉×#2979	C₂	semidirect
5. C₁₉×#1701	C₂	semidirect
6. C₁₉×#1697	C₂	semidirect
7. C₁₉×#1693	C₂	semidirect
8. C₁₉×#1691	C₂	semidirect
9. C₁₉×#1681	C₂	semidirect
10. C₁₉×#1677	C₂	semidirect
11. C₁₉×#1673	C₂	semidirect
12. C₁₉×#1671	C₂	semidirect
13. C₁₉×#1573	C₂	semidirect
14. C₁₉×#1554	C₂	semidirect
15. C₁₉×#1540	C₂	semidirect
212. #19563	C₁₉	direct (N × H)
268. #3246	C₂×C₁₉	semidirect
269. #3228	C₂×C₁₉	semidirect
271. #2979	C₂×C₁₉	semidirect
272. #1701	C₂×C₁₉	semidirect
273. #1697	C₂×C₁₉	semidirect
274. #1693	C₂×C₁₉	semidirect
275. #1691	C₂×C₁₉	semidirect
276. #1681	C₂×C₁₉	semidirect
277. #1677	C₂×C₁₉	semidirect
278. #1673	C₂×C₁₉	semidirect
279. #1671	C₂×C₁₉	semidirect
280. #1573	C₂×C₁₉	semidirect
281. #1554	C₂×C₁₉	semidirect
282. #1540	C₂×C₁₉	semidirect
444. C₁₉	#19563	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×#3246	2
C₁₉×#3228	2
C₁₉×#3214	2
C₁₉×#2979	2
C₁₉×#1701	2
C₁₉×#1697	2
C₁₉×#1693	2
C₁₉×#1691	2
C₁₉×#1681	2
C₁₉×#1677	2
C₁₉×#1673	2
C₁₉×#1671	2
C₁₉×#1573	2
C₁₉×#1554	2
C₁₉×#1540	2
#19563	19

Subgroups — C19×#19563 #18025522

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19563 #18025522