Subgroups — C₁₉×#19544 #18025503

Order 4864.

586 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3238	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3227	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3212	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2993	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1698	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1697	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1692	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1691	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1678	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1677	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1672	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1671	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1572	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1557	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1548	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#532	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₁₉×#529	C₂²	1	1	yes	characteristic
19	C₁₉×#501	—	2	1	no	—
20	C₁₉×#498	C₂²	1	1	yes	characteristic
21	C₁₉×#498	C₂²	1	1	yes	characteristic
22	C₁₉×#495	—	2	1	no	—
23	C₁₉×#489	—	2	1	no	—
24	C₁₉×#488	—	2	1	no	—
25	C₁₉×#486	C₂²	1	1	yes	characteristic
26	C₁₉×#486	C₂²	1	1	yes	characteristic
27	C₁₉×#483	—	2	1	no	—
28	C₁₉×#481	—	2	1	no	—
29	C₁₉×#481	—	2	1	no	—
30	C₁₉×#480	—	2	1	no	—
31	C₁₉×#477	C₂²	1	1	yes	characteristic
32	C₁₉×#477	C₂²	1	1	yes	characteristic
33	C₁₉×#476	—	2	1	no	—
34	C₁₉×#476	—	2	1	no	—
35	C₁₉×#476	C₂²	1	1	yes	characteristic
36	C₁₉×#476	C₂²	1	1	yes	characteristic
37	C₁₉×#462	C₂²	1	1	yes	characteristic
38	C₁₉×#461	C₂²	1	1	yes	characteristic
39	C₁₉×#460	C₂²	1	1	yes	characteristic
40	C₁₉×#459	C₂²	1	1	yes	characteristic
41	C₁₉×#452	—	2	1	no	—
42	C₁₉×#449	—	2	1	no	—
43	C₁₉×#446	C₂²	1	1	yes	characteristic
44	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
45	C₁₉×#436	—	2	1	no	—
46	C₁₉×#436	C₂²	1	1	yes	characteristic
47	C₁₉×#435	—	2	1	no	—
48	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
49	C₁₉×#433	—	2	1	no	—
50	C₁₉×#432	C₂²	1	1	yes	characteristic
51	C₁₉×#431	C₂²	1	1	yes	characteristic
52	C₁₉×#431	C₂²	1	1	yes	characteristic
53	C₁₉×#424	—	2	1	no	—
54	C₁₉×#423	C₂²	1	1	yes	characteristic
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×#333	C₂²	1	1	yes	characteristic
62	C₁₉×#333	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	C₂²×Q₈×C₁₉	—	2	1	no	—
69	C₂×Q₁₆×C₁₉	—	2	1	no	—
70	C₂×SD₁₆×C₁₉	—	2	1	no	—
71	C₂×SD₁₆×C₁₉	—	2	1	no	—
72	C₂×D₈×C₁₉	—	2	1	no	—
73	C₂×M₁₆×C₁₉	—	2	1	no	—
74	C₂×M₁₆×C₁₉	—	2	1	no	—
75	C₂²×C₈×C₁₉	—	2	1	no	—
76	C₁₉×C₄⋊Q₈	—	2	1	no	—
77	C₁₉×C₄⋊Q₈	—	2	1	no	—
78	C₁₉×C₄⋊Q₈	—	2	1	no	—
79	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
80	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
81	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₁₉×#127	C₂³	1	1	yes	characteristic
83	C₁₉×#126	—	2	1	no	—
84	C₁₉×#125	D₄	1	1	yes	characteristic
85	C₁₉×#124	—	2	1	no	—
86	C₁₉×#124	D₄	1	1	yes	characteristic
87	C₁₉×#123	—	2	1	no	—
88	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
89	C₁₉×#121	—	2	1	no	—
90	C₁₉×#121	—	2	1	no	—
91	C₁₉×#121	D₄	1	1	yes	characteristic
92	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
93	C₄×D₄×C₁₉	—	2	1	no	—
94	C₄×D₄×C₁₉	—	2	1	no	—
95	C₄×D₄×C₁₉	—	2	1	no	—
96	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
97	C₁₉×#117	—	2	1	no	—
98	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
99	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
101	C₁₉×#107	—	2	1	no	—
102	C₁₉×#107	—	2	1	no	—
103	C₁₉×#106	—	2	1	no	—
104	C₁₉×#106	—	2	1	no	—
105	C₁₉×#106	—	2	1	no	—
106	C₁₉×#106	—	2	1	no	—
107	C₁₉×#106	—	2	1	no	—
108	C₁₉×#106	—	2	1	no	—
109	C₁₉×C₄⋊C₈	—	2	1	no	—
110	C₁₉×C₄⋊C₈	—	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	D₄	1	1	yes	characteristic
137	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
138	C₁₉×#97	—	2	1	no	—
139	C₁₉×#97	—	2	1	no	—
140	C₄×C₈×C₁₉	—	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	C₂×Q₈×C₁₉	—	2	1	no	—
147	C₂×Q₈×C₁₉	—	2	1	no	—
148	C₂×Q₈×C₁₉	—	2	1	no	—
149	C₂×Q₈×C₁₉	—	4	1	no	—
150	C₂×Q₈×C₁₉	—	8	2	no	—
151	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	4	1	no	—
157	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₉	—	2	1	no	—
159	C₂²×C₄×C₁₉	—	4	1	no	—
160	C₂²×C₄×C₁₉	—	4	1	no	—
161	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
164	Q₁₆×C₁₉	—	8	1	no	—
165	SD₁₆×C₁₉	—	8	1	no	—
166	SD₁₆×C₁₉	—	8	1	no	—
167	D₈×C₁₉	—	8	1	no	—
168	M₁₆×C₁₉	—	8	1	no	—
169	M₁₆×C₁₉	—	8	1	no	—
170	C₂×C₈×C₁₉	—	2	1	no	—
171	C₂×C₈×C₁₉	—	2	1	no	—
172	C₂×C₈×C₁₉	—	2	1	no	—
173	C₂×C₈×C₁₉	—	2	1	no	—
174	C₂×C₈×C₁₉	—	2	1	no	—
175	C₂×C₈×C₁₉	—	2	1	no	—
176	C₂×C₈×C₁₉	—	8	1	no	—
177	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
178	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
179	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
180	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
181	C₄⋊C₄×C₁₉	—	2	1	no	—
182	C₄⋊C₄×C₁₉	—	2	1	no	—
183	C₄⋊C₄×C₁₉	—	2	1	no	—
184	C₄⋊C₄×C₁₉	—	2	1	no	—
185	C₄⋊C₄×C₁₉	—	2	1	no	—
186	C₄⋊C₄×C₁₉	—	2	1	no	—
187	C₄⋊C₄×C₁₉	—	2	1	no	—
188	C₄⋊C₄×C₁₉	—	2	1	no	—
189	C₄⋊C₄×C₁₉	—	2	1	no	—
190	C₄⋊C₄×C₁₉	—	2	1	no	—
191	C₄⋊C₄×C₁₉	—	4	1	no	—
192	C₄⋊C₄×C₁₉	—	4	1	no	—
193	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
194	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
199	C₂²⋊C₄×C₁₉	—	2	1	no	—
200	C₂²⋊C₄×C₁₉	—	4	1	no	—
201	C₂²⋊C₄×C₁₉	—	4	1	no	—
202	C₄²×C₁₉	—	2	1	no	—
203	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
204	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
205	C₄²×C₁₉	#41	1	1	yes	characteristic
206	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
207	#19544	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂³×C₁₉	—	2	1	no	—
209	C₂³×C₁₉	—	4	1	no	—
210	C₂³×C₁₉	#121	1	1	yes	characteristic
211	Q₈×C₁₉	—	2	1	no	—
212	Q₈×C₁₉	—	2	1	no	—
213	Q₈×C₁₉	—	4	1	no	—
214	Q₈×C₁₉	—	4	1	no	—
215	Q₈×C₁₉	—	8	1	no	—
216	Q₈×C₁₉	—	8	1	no	—
217	Q₈×C₁₉	—	8	2	no	—
218	D₄×C₁₉	—	2	1	no	—
219	D₄×C₁₉	—	2	1	no	—
220	D₄×C₁₉	—	4	1	no	—
221	D₄×C₁₉	—	4	1	no	—
222	D₄×C₁₉	—	4	1	no	—
223	D₄×C₁₉	—	4	1	no	—
224	D₄×C₁₉	—	8	1	no	—
225	D₄×C₁₉	—	8	1	no	—
226	D₄×C₁₉	—	8	2	no	—
227	C₂×C₄×C₁₉	—	2	1	no	—
228	C₂×C₄×C₁₉	—	2	1	no	—
229	C₂×C₄×C₁₉	—	2	1	no	—
230	C₂×C₄×C₁₉	—	2	1	no	—
231	C₂×C₄×C₁₉	—	2	1	no	—
232	C₂×C₄×C₁₉	—	2	1	no	—
233	C₂×C₄×C₁₉	—	2	1	no	—
234	C₂×C₄×C₁₉	—	4	1	no	—
235	C₂×C₄×C₁₉	—	4	1	no	—
236	C₂×C₄×C₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	—	4	1	no	—
238	C₂×C₄×C₁₉	—	4	1	no	—
239	C₂×C₄×C₁₉	—	4	1	no	—
240	C₂×C₄×C₁₉	—	8	2	no	—
241	C₂×C₄×C₁₉	—	8	2	no	—
242	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
243	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
244	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
245	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
248	C₈×C₁₉	—	2	1	no	—
249	C₈×C₁₉	—	2	1	no	—
250	C₈×C₁₉	—	2	1	no	—
251	C₈×C₁₉	—	2	1	no	—
252	C₈×C₁₉	—	4	1	no	—
253	C₈×C₁₉	—	4	1	no	—
254	C₈×C₁₉	—	4	1	no	—
255	C₈×C₁₉	—	4	1	no	—
256	C₈×C₁₉	—	4	1	no	—
257	C₈×C₁₉	—	4	1	no	—
258	#3238	C₂×C₁₉	1	1	yes	characteristic, complemented
259	#3227	C₂×C₁₉	1	1	yes	characteristic, complemented
260	#3212	C₂×C₁₉	1	1	yes	characteristic
261	#2993	C₂×C₁₉	1	1	yes	characteristic, complemented
262	#1698	C₂×C₁₉	1	1	yes	characteristic, complemented
263	#1697	C₂×C₁₉	1	1	yes	characteristic, complemented
264	#1692	C₂×C₁₉	1	1	yes	characteristic, complemented
265	#1691	C₂×C₁₉	1	1	yes	characteristic, complemented
266	#1678	C₂×C₁₉	1	1	yes	characteristic, complemented
267	#1677	C₂×C₁₉	1	1	yes	characteristic, complemented
268	#1672	C₂×C₁₉	1	1	yes	characteristic, complemented
269	#1671	C₂×C₁₉	1	1	yes	characteristic, complemented
270	#1572	C₂×C₁₉	1	1	yes	characteristic, complemented
271	#1557	C₂×C₁₉	1	1	yes	characteristic, complemented
272	#1548	C₂×C₁₉	1	1	yes	characteristic, complemented
273	C₂²×C₁₉	—	2	1	no	—
274	C₂²×C₁₉	—	2	1	no	—
275	C₂²×C₁₉	—	2	1	no	—
276	C₂²×C₁₉	—	4	1	no	—
277	C₂²×C₁₉	—	4	1	no	—
278	C₂²×C₁₉	—	4	1	no	—
279	C₂²×C₁₉	—	8	1	no	—
280	C₂²×C₁₉	—	8	1	no	—
281	C₂²×C₁₉	—	8	1	no	—
282	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
283	C₄×C₁₉	—	2	1	no	—
284	C₄×C₁₉	—	2	1	no	—
285	C₄×C₁₉	—	2	1	no	—
286	C₄×C₁₉	—	2	1	no	—
287	C₄×C₁₉	—	4	1	no	—
288	C₄×C₁₉	—	4	1	no	—
289	C₄×C₁₉	—	4	1	no	—
290	C₄×C₁₉	—	8	1	no	—
291	C₄×C₁₉	—	8	1	no	—
292	C₄×C₁₉	—	8	1	no	—
293	C₄×C₁₉	#577	1	1	yes	characteristic
294	C₄×C₁₉	#577	1	1	yes	characteristic
295	C₄×C₁₉	#577	1	1	yes	characteristic
296	C₄×C₁₉	#578	1	1	yes	characteristic
297	#532	C₂²×C₁₉	1	1	yes	characteristic
298	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
299	#529	C₂²×C₁₉	1	1	yes	characteristic
300	#501	—	2	1	no	—
301	#498	C₂²×C₁₉	1	1	yes	characteristic
302	#498	C₂²×C₁₉	1	1	yes	characteristic
303	#495	—	2	1	no	—
304	#489	—	2	1	no	—
305	#488	—	2	1	no	—
306	#486	C₂²×C₁₉	1	1	yes	characteristic
307	#486	C₂²×C₁₉	1	1	yes	characteristic
308	#483	—	2	1	no	—
309	#481	—	2	1	no	—
310	#481	—	2	1	no	—
311	#480	—	2	1	no	—
312	#477	C₂²×C₁₉	1	1	yes	characteristic
313	#477	C₂²×C₁₉	1	1	yes	characteristic
314	#476	—	2	1	no	—
315	#476	—	2	1	no	—
316	#476	C₂²×C₁₉	1	1	yes	characteristic
317	#476	C₂²×C₁₉	1	1	yes	characteristic
318	#462	C₂²×C₁₉	1	1	yes	characteristic
319	#461	C₂²×C₁₉	1	1	yes	characteristic
320	#460	C₂²×C₁₉	1	1	yes	characteristic
321	#459	C₂²×C₁₉	1	1	yes	characteristic
322	#452	—	2	1	no	—
323	#449	—	2	1	no	—
324	#446	C₂²×C₁₉	1	1	yes	characteristic
325	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
326	#436	—	2	1	no	—
327	#436	C₂²×C₁₉	1	1	yes	characteristic
328	#435	—	2	1	no	—
329	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
330	#433	—	2	1	no	—
331	#432	C₂²×C₁₉	1	1	yes	characteristic
332	#431	C₂²×C₁₉	1	1	yes	characteristic
333	#431	C₂²×C₁₉	1	1	yes	characteristic
334	#424	—	2	1	no	—
335	#423	C₂²×C₁₉	1	1	yes	characteristic
336	#335	C₂²×C₁₉	1	1	yes	characteristic
337	#335	C₂²×C₁₉	1	1	yes	characteristic
338	#334	C₂²×C₁₉	1	1	yes	characteristic
339	#334	C₂²×C₁₉	1	1	yes	characteristic
340	#333	C₂²×C₁₉	1	1	yes	characteristic
341	#333	C₂²×C₁₉	1	1	yes	characteristic
342	#333	C₂²×C₁₉	1	1	yes	characteristic
343	#333	C₂²×C₁₉	1	1	yes	characteristic
344	#332	C₂²×C₁₉	1	1	yes	characteristic
345	#332	C₂²×C₁₉	1	1	yes	characteristic
346	#331	C₂²×C₁₉	1	1	yes	characteristic
347	#331	C₂²×C₁₉	1	1	yes	characteristic
348	C₂×C₁₉	—	4	1	no	—
349	C₂×C₁₉	—	8	1	no	—
350	C₂×C₁₉	—	16	1	no	—
351	C₂×C₁₉	#3046	1	1	yes	characteristic
352	C₂×C₁₉	#3057	1	1	yes	characteristic
353	C₂×C₁₉	#3068	1	1	yes	characteristic
354	C₂×#41	—	2	1	no	—
355	C₂²×Q₈	—	2	1	no	—
356	C₂×Q₁₆	—	2	1	no	—
357	C₂×SD₁₆	—	2	1	no	—
358	C₂×SD₁₆	—	2	1	no	—
359	C₂×D₈	—	2	1	no	—
360	C₂×M₁₆	—	2	1	no	—
361	C₂×M₁₆	—	2	1	no	—
362	C₂²×C₈	—	2	1	no	—
363	C₄⋊Q₈	—	2	1	no	—
364	C₄⋊Q₈	—	2	1	no	—
365	C₄⋊Q₈	—	2	1	no	—
366	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
367	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
368	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
369	#127	C₂³×C₁₉	1	1	yes	characteristic
370	#126	—	2	1	no	—
371	#125	D₄×C₁₉	1	1	yes	characteristic
372	#124	—	2	1	no	—
373	#124	D₄×C₁₉	1	1	yes	characteristic
374	#123	—	2	1	no	—
375	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
376	#121	—	2	1	no	—
377	#121	—	2	1	no	—
378	#121	D₄×C₁₉	1	1	yes	characteristic
379	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
380	C₄×D₄	—	2	1	no	—
381	C₄×D₄	—	2	1	no	—
382	C₄×D₄	—	2	1	no	—
383	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
384	#117	—	2	1	no	—
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₄⋊C₄	—	2	1	no	—
387	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
388	#107	—	2	1	no	—
389	#107	—	2	1	no	—
390	#106	—	2	1	no	—
391	#106	—	2	1	no	—
392	#106	—	2	1	no	—
393	#106	—	2	1	no	—
394	#106	—	2	1	no	—
395	#106	—	2	1	no	—
396	C₄⋊C₈	—	2	1	no	—
397	C₄⋊C₈	—	2	1	no	—
398	C₄⋊C₈	—	2	1	no	—
399	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
400	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
401	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
402	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
403	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
404	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
405	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
406	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
407	#103	—	2	1	no	—
408	#103	—	2	1	no	—
409	#103	—	2	1	no	—
410	#103	—	2	1	no	—
411	#102	—	2	1	no	—
412	#102	—	2	1	no	—
413	#102	—	2	1	no	—
414	#102	—	2	1	no	—
415	#102	—	2	1	no	—
416	#102	—	2	1	no	—
417	#102	—	2	1	no	—
418	#102	—	2	1	no	—
419	C₂²⋊C₈	—	2	1	no	—
420	C₂²⋊C₈	—	2	1	no	—
421	C₂²⋊C₈	—	2	1	no	—
422	C₂²⋊C₈	—	2	1	no	—
423	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
424	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
425	#97	—	2	1	no	—
426	#97	—	2	1	no	—
427	C₄×C₈	—	2	1	no	—
428	C₄×C₈	—	2	1	no	—
429	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
430	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
431	C₁₉	#19544	1	1	yes	characteristic, direct product factor, Sylow
432	#41	—	8	1	no	—
433	#41	—	8	1	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	4	1	no	—
438	C₂×Q₈	—	8	2	no	—
439	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	4	1	no	—
445	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	4	1	no	—
448	C₂²×C₄	—	4	1	no	—
449	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
450	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
451	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
452	Q₁₆	—	8	1	no	—
453	SD₁₆	—	8	1	no	—
454	SD₁₆	—	8	1	no	—
455	D₈	—	8	1	no	—
456	M₁₆	—	8	1	no	—
457	M₁₆	—	8	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	8	1	no	—
465	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
466	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
467	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
468	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	4	1	no	—
480	C₄⋊C₄	—	4	1	no	—
481	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
482	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
483	C₂²⋊C₄	—	2	1	no	—
484	C₂²⋊C₄	—	2	1	no	—
485	C₂²⋊C₄	—	2	1	no	—
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	—	2	1	no	—
488	C₂²⋊C₄	—	4	1	no	—
489	C₂²⋊C₄	—	4	1	no	—
490	C₄²	—	2	1	no	—
491	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
492	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
493	C₄²	#41×C₁₉	1	1	yes	characteristic
494	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
495	C₂³	—	2	1	no	—
496	C₂³	—	4	1	no	—
497	C₂³	C₁₉×#121	1	1	yes	characteristic
498	Q₈	—	2	1	no	—
499	Q₈	—	2	1	no	—
500	Q₈	—	4	1	no	—
501	Q₈	—	4	1	no	—
502	Q₈	—	8	1	no	—
503	Q₈	—	8	1	no	—
504	Q₈	—	8	2	no	—
505	D₄	—	2	1	no	—
506	D₄	—	2	1	no	—
507	D₄	—	4	1	no	—
508	D₄	—	4	1	no	—
509	D₄	—	4	1	no	—
510	D₄	—	4	1	no	—
511	D₄	—	8	1	no	—
512	D₄	—	8	1	no	—
513	D₄	—	8	2	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	8	2	no	—
528	C₂×C₄	—	8	2	no	—
529	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
530	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
531	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
532	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
533	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
534	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
535	C₈	—	2	1	no	—
536	C₈	—	2	1	no	—
537	C₈	—	2	1	no	—
538	C₈	—	2	1	no	—
539	C₈	—	4	1	no	—
540	C₈	—	4	1	no	—
541	C₈	—	4	1	no	—
542	C₈	—	4	1	no	—
543	C₈	—	4	1	no	—
544	C₈	—	4	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	8	1	no	—
552	C₂²	—	8	1	no	—
553	C₂²	—	8	1	no	—
554	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
555	C₄	—	2	1	no	—
556	C₄	—	2	1	no	—
557	C₄	—	2	1	no	—
558	C₄	—	2	1	no	—
559	C₄	—	4	1	no	—
560	C₄	—	4	1	no	—
561	C₄	—	4	1	no	—
562	C₄	—	8	1	no	—
563	C₄	—	8	1	no	—
564	C₄	—	8	1	no	—
565	C₄	C₁₉×#577	1	1	yes	characteristic
566	C₄	C₁₉×#577	1	1	yes	characteristic
567	C₄	C₁₉×#577	1	1	yes	characteristic
568	C₄	C₁₉×#578	1	1	yes	characteristic
569	C₂	—	4	1	no	—
570	C₂	—	8	1	no	—
571	C₂	—	16	1	no	—
572	C₂	C₁₉×#3046	1	1	yes	characteristic
573	C₂	C₁₉×#3057	1	1	yes	characteristic
574	C₂	C₁₉×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3212	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×#3238	C₂	semidirect
2. C₁₉×#3227	C₂	semidirect
4. C₁₉×#2993	C₂	semidirect
5. C₁₉×#1698	C₂	semidirect
6. C₁₉×#1697	C₂	semidirect
7. C₁₉×#1692	C₂	semidirect
8. C₁₉×#1691	C₂	semidirect
9. C₁₉×#1678	C₂	semidirect
10. C₁₉×#1677	C₂	semidirect
11. C₁₉×#1672	C₂	semidirect
12. C₁₉×#1671	C₂	semidirect
13. C₁₉×#1572	C₂	semidirect
14. C₁₉×#1557	C₂	semidirect
15. C₁₉×#1548	C₂	semidirect
207. #19544	C₁₉	direct (N × H)
258. #3238	C₂×C₁₉	semidirect
259. #3227	C₂×C₁₉	semidirect
261. #2993	C₂×C₁₉	semidirect
262. #1698	C₂×C₁₉	semidirect
263. #1697	C₂×C₁₉	semidirect
264. #1692	C₂×C₁₉	semidirect
265. #1691	C₂×C₁₉	semidirect
266. #1678	C₂×C₁₉	semidirect
267. #1677	C₂×C₁₉	semidirect
268. #1672	C₂×C₁₉	semidirect
269. #1671	C₂×C₁₉	semidirect
270. #1572	C₂×C₁₉	semidirect
271. #1557	C₂×C₁₉	semidirect
272. #1548	C₂×C₁₉	semidirect
431. C₁₉	#19544	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×#3238	2
C₁₉×#3227	2
C₁₉×#3212	2
C₁₉×#2993	2
C₁₉×#1698	2
C₁₉×#1697	2
C₁₉×#1692	2
C₁₉×#1691	2
C₁₉×#1678	2
C₁₉×#1677	2
C₁₉×#1672	2
C₁₉×#1671	2
C₁₉×#1572	2
C₁₉×#1557	2
C₁₉×#1548	2
#19544	19

Subgroups — C19×#19544 #18025503

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19544 #18025503