Subgroups — C₁₉×#19575 #18025534

Order 4864.

568 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3249	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3228	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3216	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2986	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1702	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1698	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1694	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1692	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1682	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1678	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1674	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1672	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
16	C₁₉×#533	C₂²	1	1	yes	characteristic
17	C₁₉×#533	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×#497	—	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×#477	—	2	1	no	—
30	C₁₉×#477	C₂²	1	1	yes	characteristic
31	C₁₉×#477	C₂²	1	1	yes	characteristic
32	C₁₉×#467	—	2	1	no	—
33	C₁₉×#467	—	2	1	no	—
34	C₁₉×#462	—	2	1	no	—
35	C₁₉×#462	C₂²	1	1	yes	characteristic
36	C₁₉×#462	C₂²	1	1	yes	characteristic
37	C₁₉×#462	C₂²	1	1	yes	characteristic
38	C₁₉×#462	C₂²	1	1	yes	characteristic
39	C₁₉×#460	C₂²	1	1	yes	characteristic
40	C₁₉×#460	C₂²	1	1	yes	characteristic
41	C₁₉×#452	—	2	1	no	—
42	C₁₉×#452	—	2	1	no	—
43	C₁₉×#446	—	2	1	no	—
44	C₁₉×#446	C₂²	1	1	yes	characteristic
45	C₁₉×#446	C₂²	1	1	yes	characteristic
46	C₈×Q₈×C₁₉	—	2	1	no	—
47	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
48	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
49	C₁₉×#433	—	2	1	no	—
50	C₁₉×#433	—	2	1	no	—
51	C₁₉×#432	C₂²	1	1	yes	characteristic
52	C₁₉×#431	C₂²	1	1	yes	characteristic
53	C₁₉×#431	C₂²	1	1	yes	characteristic
54	C₂×C₁₉×C₄⋊C₈	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×#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×Q₁₆×C₁₉	—	2	1	no	—
69	C₂×Q₁₆×C₁₉	—	2	1	no	—
70	C₂×Q₁₆×C₁₉	—	2	1	no	—
71	C₂×Q₁₆×C₁₉	—	2	1	no	—
72	C₂×SD₁₆×C₁₉	—	2	1	no	—
73	C₂×SD₁₆×C₁₉	—	2	1	no	—
74	C₂²×C₈×C₁₉	—	2	1	no	—
75	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
76	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
77	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
78	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
79	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
80	C₁₉×#127	C₂³	1	1	yes	characteristic
81	C₁₉×#125	—	2	1	no	—
82	C₁₉×#125	—	2	1	no	—
83	C₁₉×#124	—	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	D₄	1	1	yes	characteristic
88	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
89	C₁₉×#121	—	2	1	no	—
90	C₁₉×#121	—	2	1	no	—
91	C₄×Q₈×C₁₉	—	2	1	no	—
92	C₄×Q₈×C₁₉	—	2	1	no	—
93	C₄×Q₈×C₁₉	—	2	1	no	—
94	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
95	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
96	C₄×D₄×C₁₉	—	2	1	no	—
97	C₄×D₄×C₁₉	—	2	1	no	—
98	C₁₉×#117	—	2	1	no	—
99	C₁₉×#117	—	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×#107	—	2	1	no	—
104	C₁₉×#107	—	2	1	no	—
105	C₁₉×#106	—	2	1	no	—
106	C₁₉×#106	—	2	1	no	—
107	C₁₉×C₄⋊C₈	—	2	1	no	—
108	C₁₉×C₄⋊C₈	—	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×#103	—	2	1	no	—
125	C₁₉×#103	—	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	D₄	1	1	yes	characteristic
135	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
136	C₁₉×#97	—	2	1	no	—
137	C₁₉×#97	—	2	1	no	—
138	C₁₉×#97	—	2	1	no	—
139	C₄×C₈×C₁₉	—	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	—	2	1	no	—
150	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	4	1	no	—
156	C₂²×C₄×C₁₉	—	4	1	no	—
157	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
160	Q₁₆×C₁₉	—	8	1	no	—
161	Q₁₆×C₁₉	—	8	1	no	—
162	Q₁₆×C₁₉	—	8	1	no	—
163	Q₁₆×C₁₉	—	8	1	no	—
164	SD₁₆×C₁₉	—	8	1	no	—
165	SD₁₆×C₁₉	—	8	1	no	—
166	C₂×C₈×C₁₉	—	2	1	no	—
167	C₂×C₈×C₁₉	—	2	1	no	—
168	C₂×C₈×C₁₉	—	2	1	no	—
169	C₂×C₈×C₁₉	—	2	1	no	—
170	C₂×C₈×C₁₉	—	2	1	no	—
171	C₂×C₈×C₁₉	—	2	1	no	—
172	C₂×C₈×C₁₉	—	8	1	no	—
173	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
174	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
175	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
176	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
177	C₄⋊C₄×C₁₉	—	2	1	no	—
178	C₄⋊C₄×C₁₉	—	2	1	no	—
179	C₄⋊C₄×C₁₉	—	2	1	no	—
180	C₄⋊C₄×C₁₉	—	2	1	no	—
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	—	4	1	no	—
191	C₄⋊C₄×C₁₉	—	4	1	no	—
192	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
193	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
194	C₂²⋊C₄×C₁₉	—	2	1	no	—
195	C₂²⋊C₄×C₁₉	—	2	1	no	—
196	C₂²⋊C₄×C₁₉	—	4	1	no	—
197	C₂²⋊C₄×C₁₉	—	4	1	no	—
198	C₂²⋊C₄×C₁₉	—	4	1	no	—
199	C₄²×C₁₉	—	2	1	no	—
200	C₄²×C₁₉	—	2	1	no	—
201	C₄²×C₁₉	—	4	1	no	—
202	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
204	C₄²×C₁₉	#41	1	1	yes	characteristic
205	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
206	#19575	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂³×C₁₉	—	4	1	no	—
208	C₂³×C₁₉	#121	1	1	yes	characteristic
209	Q₈×C₁₉	—	2	1	no	—
210	Q₈×C₁₉	—	2	1	no	—
211	Q₈×C₁₉	—	2	1	no	—
212	Q₈×C₁₉	—	2	1	no	—
213	Q₈×C₁₉	—	4	2	no	—
214	Q₈×C₁₉	—	4	1	no	—
215	Q₈×C₁₉	—	4	1	no	—
216	Q₈×C₁₉	—	4	1	no	—
217	Q₈×C₁₉	—	4	1	no	—
218	Q₈×C₁₉	—	8	1	no	—
219	D₄×C₁₉	—	4	1	no	—
220	D₄×C₁₉	—	4	1	no	—
221	D₄×C₁₉	—	4	1	no	—
222	D₄×C₁₉	—	4	1	no	—
223	D₄×C₁₉	—	8	1	no	—
224	D₄×C₁₉	—	8	2	no	—
225	C₂×C₄×C₁₉	—	2	1	no	—
226	C₂×C₄×C₁₉	—	2	1	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	—	4	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	—	8	2	no	—
238	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
239	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
240	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
241	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
244	C₈×C₁₉	—	2	1	no	—
245	C₈×C₁₉	—	2	1	no	—
246	C₈×C₁₉	—	2	1	no	—
247	C₈×C₁₉	—	2	1	no	—
248	C₈×C₁₉	—	4	1	no	—
249	C₈×C₁₉	—	4	1	no	—
250	C₈×C₁₉	—	4	1	no	—
251	C₈×C₁₉	—	4	1	no	—
252	C₈×C₁₉	—	4	1	no	—
253	C₈×C₁₉	—	4	1	no	—
254	#3249	C₂×C₁₉	1	1	yes	characteristic, complemented
255	#3228	C₂×C₁₉	1	1	yes	characteristic
256	#3216	C₂×C₁₉	1	1	yes	characteristic
257	#2986	C₂×C₁₉	1	1	yes	characteristic, complemented
258	#1702	C₂×C₁₉	1	1	yes	characteristic, complemented
259	#1698	C₂×C₁₉	1	1	yes	characteristic, complemented
260	#1694	C₂×C₁₉	1	1	yes	characteristic, complemented
261	#1692	C₂×C₁₉	1	1	yes	characteristic, complemented
262	#1682	C₂×C₁₉	1	1	yes	characteristic, complemented
263	#1678	C₂×C₁₉	1	1	yes	characteristic, complemented
264	#1674	C₂×C₁₉	1	1	yes	characteristic, complemented
265	#1672	C₂×C₁₉	1	1	yes	characteristic, complemented
266	#1573	C₂×C₁₉	1	1	yes	characteristic, complemented
267	#1554	C₂×C₁₉	1	1	yes	characteristic, complemented
268	#1540	C₂×C₁₉	1	1	yes	characteristic
269	C₂²×C₁₉	—	2	1	no	—
270	C₂²×C₁₉	—	2	1	no	—
271	C₂²×C₁₉	—	2	1	no	—
272	C₂²×C₁₉	—	8	1	no	—
273	C₂²×C₁₉	—	8	1	no	—
274	C₂²×C₁₉	—	8	1	no	—
275	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
276	C₄×C₁₉	—	2	1	no	—
277	C₄×C₁₉	—	2	1	no	—
278	C₄×C₁₉	—	2	1	no	—
279	C₄×C₁₉	—	2	1	no	—
280	C₄×C₁₉	—	4	1	no	—
281	C₄×C₁₉	—	4	1	no	—
282	C₄×C₁₉	—	4	1	no	—
283	C₄×C₁₉	—	4	1	no	—
284	C₄×C₁₉	—	8	1	no	—
285	C₄×C₁₉	—	8	1	no	—
286	C₄×C₁₉	—	8	1	no	—
287	C₄×C₁₉	#576	1	1	yes	characteristic
288	C₄×C₁₉	#577	1	1	yes	characteristic
289	C₄×C₁₉	#578	1	1	yes	characteristic
290	C₄×C₁₉	#578	1	1	yes	characteristic
291	#533	C₂²×C₁₉	1	1	yes	characteristic
292	#533	C₂²×C₁₉	1	1	yes	characteristic
293	#532	C₂²×C₁₉	1	1	yes	characteristic
294	#500	C₂²×C₁₉	1	1	yes	characteristic
295	#498	C₂²×C₁₉	1	1	yes	characteristic
296	#497	—	2	1	no	—
297	#489	—	2	1	no	—
298	#486	C₂²×C₁₉	1	1	yes	characteristic
299	#486	C₂²×C₁₉	1	1	yes	characteristic
300	#482	—	2	1	no	—
301	#482	—	2	1	no	—
302	#478	—	2	1	no	—
303	#478	—	2	1	no	—
304	#477	—	2	1	no	—
305	#477	C₂²×C₁₉	1	1	yes	characteristic
306	#477	C₂²×C₁₉	1	1	yes	characteristic
307	#467	—	2	1	no	—
308	#467	—	2	1	no	—
309	#462	—	2	1	no	—
310	#462	C₂²×C₁₉	1	1	yes	characteristic
311	#462	C₂²×C₁₉	1	1	yes	characteristic
312	#462	C₂²×C₁₉	1	1	yes	characteristic
313	#462	C₂²×C₁₉	1	1	yes	characteristic
314	#460	C₂²×C₁₉	1	1	yes	characteristic
315	#460	C₂²×C₁₉	1	1	yes	characteristic
316	#452	—	2	1	no	—
317	#452	—	2	1	no	—
318	#446	—	2	1	no	—
319	#446	C₂²×C₁₉	1	1	yes	characteristic
320	#446	C₂²×C₁₉	1	1	yes	characteristic
321	C₈×Q₈	—	2	1	no	—
322	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
323	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
324	#433	—	2	1	no	—
325	#433	—	2	1	no	—
326	#432	C₂²×C₁₉	1	1	yes	characteristic
327	#431	C₂²×C₁₉	1	1	yes	characteristic
328	#431	C₂²×C₁₉	1	1	yes	characteristic
329	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
330	#335	C₂²×C₁₉	1	1	yes	characteristic
331	#335	C₂²×C₁₉	1	1	yes	characteristic
332	#334	C₂²×C₁₉	1	1	yes	characteristic
333	#334	C₂²×C₁₉	1	1	yes	characteristic
334	#333	C₂²×C₁₉	1	1	yes	characteristic
335	#333	C₂²×C₁₉	1	1	yes	characteristic
336	#332	C₂²×C₁₉	1	1	yes	characteristic
337	#332	C₂²×C₁₉	1	1	yes	characteristic
338	#332	C₂²×C₁₉	1	1	yes	characteristic
339	#332	C₂²×C₁₉	1	1	yes	characteristic
340	#331	C₂²×C₁₉	1	1	yes	characteristic
341	#331	C₂²×C₁₉	1	1	yes	characteristic
342	C₂×C₁₉	—	4	1	no	—
343	C₂×C₁₉	—	16	1	no	—
344	C₂×C₁₉	#3044	1	1	yes	characteristic
345	C₂×C₁₉	#3062	1	1	yes	characteristic
346	C₂×C₁₉	#3067	1	1	yes	characteristic
347	C₂×#41	—	2	1	no	—
348	C₂×Q₁₆	—	2	1	no	—
349	C₂×Q₁₆	—	2	1	no	—
350	C₂×Q₁₆	—	2	1	no	—
351	C₂×Q₁₆	—	2	1	no	—
352	C₂×SD₁₆	—	2	1	no	—
353	C₂×SD₁₆	—	2	1	no	—
354	C₂²×C₈	—	2	1	no	—
355	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
356	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
357	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
358	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
359	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
360	#127	C₂³×C₁₉	1	1	yes	characteristic
361	#125	—	2	1	no	—
362	#125	—	2	1	no	—
363	#124	—	2	1	no	—
364	C₂²⋊Q₈	—	2	1	no	—
365	C₂²⋊Q₈	—	2	1	no	—
366	C₂²⋊Q₈	—	2	1	no	—
367	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
368	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
369	#121	—	2	1	no	—
370	#121	—	2	1	no	—
371	C₄×Q₈	—	2	1	no	—
372	C₄×Q₈	—	2	1	no	—
373	C₄×Q₈	—	2	1	no	—
374	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
375	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
376	C₄×D₄	—	2	1	no	—
377	C₄×D₄	—	2	1	no	—
378	#117	—	2	1	no	—
379	#117	—	2	1	no	—
380	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
381	#107	—	2	1	no	—
382	#107	—	2	1	no	—
383	#107	—	2	1	no	—
384	#107	—	2	1	no	—
385	#106	—	2	1	no	—
386	#106	—	2	1	no	—
387	C₄⋊C₈	—	2	1	no	—
388	C₄⋊C₈	—	2	1	no	—
389	C₄⋊C₈	—	2	1	no	—
390	C₄⋊C₈	—	2	1	no	—
391	C₄⋊C₈	—	2	1	no	—
392	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
393	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
394	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
395	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
396	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
397	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
398	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
399	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
400	#103	—	2	1	no	—
401	#103	—	2	1	no	—
402	#103	—	2	1	no	—
403	#103	—	2	1	no	—
404	#103	—	2	1	no	—
405	#103	—	2	1	no	—
406	#102	—	2	1	no	—
407	#102	—	2	1	no	—
408	#102	—	2	1	no	—
409	#102	—	2	1	no	—
410	#102	—	2	1	no	—
411	#102	—	2	1	no	—
412	C₂²⋊C₈	—	2	1	no	—
413	C₂²⋊C₈	—	2	1	no	—
414	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
415	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
416	#97	—	2	1	no	—
417	#97	—	2	1	no	—
418	#97	—	2	1	no	—
419	C₄×C₈	—	2	1	no	—
420	C₄×C₈	—	2	1	no	—
421	C₄×C₈	—	2	1	no	—
422	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
423	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
424	C₁₉	#19575	1	1	yes	characteristic, direct product factor, Sylow
425	#41	—	8	1	no	—
426	#41	—	8	1	no	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
432	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
433	C₂×D₄	—	2	1	no	—
434	C₂×D₄	—	2	1	no	—
435	C₂×D₄	—	2	1	no	—
436	C₂×D₄	—	4	1	no	—
437	C₂²×C₄	—	4	1	no	—
438	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
439	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
440	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
441	Q₁₆	—	8	1	no	—
442	Q₁₆	—	8	1	no	—
443	Q₁₆	—	8	1	no	—
444	Q₁₆	—	8	1	no	—
445	SD₁₆	—	8	1	no	—
446	SD₁₆	—	8	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	8	1	no	—
454	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
455	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
456	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
457	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	4	1	no	—
472	C₄⋊C₄	—	4	1	no	—
473	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
474	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
475	C₂²⋊C₄	—	2	1	no	—
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	4	1	no	—
478	C₂²⋊C₄	—	4	1	no	—
479	C₂²⋊C₄	—	4	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	4	1	no	—
483	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
484	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
485	C₄²	#41×C₁₉	1	1	yes	characteristic
486	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
487	C₂³	—	4	1	no	—
488	C₂³	C₁₉×#121	1	1	yes	characteristic
489	Q₈	—	2	1	no	—
490	Q₈	—	2	1	no	—
491	Q₈	—	2	1	no	—
492	Q₈	—	2	1	no	—
493	Q₈	—	4	2	no	—
494	Q₈	—	4	1	no	—
495	Q₈	—	4	1	no	—
496	Q₈	—	4	1	no	—
497	Q₈	—	4	1	no	—
498	Q₈	—	8	1	no	—
499	D₄	—	4	1	no	—
500	D₄	—	4	1	no	—
501	D₄	—	4	1	no	—
502	D₄	—	4	1	no	—
503	D₄	—	8	1	no	—
504	D₄	—	8	2	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	8	2	no	—
518	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
519	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
520	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
521	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
522	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
523	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	2	1	no	—
527	C₈	—	2	1	no	—
528	C₈	—	4	1	no	—
529	C₈	—	4	1	no	—
530	C₈	—	4	1	no	—
531	C₈	—	4	1	no	—
532	C₈	—	4	1	no	—
533	C₈	—	4	1	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	8	1	no	—
538	C₂²	—	8	1	no	—
539	C₂²	—	8	1	no	—
540	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	1	no	—
544	C₄	—	2	1	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	1	no	—
548	C₄	—	4	1	no	—
549	C₄	—	8	1	no	—
550	C₄	—	8	1	no	—
551	C₄	—	8	1	no	—
552	C₄	C₁₉×#576	1	1	yes	characteristic
553	C₄	C₁₉×#577	1	1	yes	characteristic
554	C₄	C₁₉×#578	1	1	yes	characteristic
555	C₄	C₁₉×#578	1	1	yes	characteristic
556	C₂	—	4	1	no	—
557	C₂	—	16	1	no	—
558	C₂	C₁₉×#3044	1	1	yes	characteristic
559	C₂	C₁₉×#3062	1	1	yes	characteristic
560	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×#532	C₂²
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×#3249	C₂	semidirect
4. C₁₉×#2986	C₂	semidirect
5. C₁₉×#1702	C₂	semidirect
6. C₁₉×#1698	C₂	semidirect
7. C₁₉×#1694	C₂	semidirect
8. C₁₉×#1692	C₂	semidirect
9. C₁₉×#1682	C₂	semidirect
10. C₁₉×#1678	C₂	semidirect
11. C₁₉×#1674	C₂	semidirect
12. C₁₉×#1672	C₂	semidirect
13. C₁₉×#1573	C₂	semidirect
14. C₁₉×#1554	C₂	semidirect
206. #19575	C₁₉	direct (N × H)
254. #3249	C₂×C₁₉	semidirect
257. #2986	C₂×C₁₉	semidirect
258. #1702	C₂×C₁₉	semidirect
259. #1698	C₂×C₁₉	semidirect
260. #1694	C₂×C₁₉	semidirect
261. #1692	C₂×C₁₉	semidirect
262. #1682	C₂×C₁₉	semidirect
263. #1678	C₂×C₁₉	semidirect
264. #1674	C₂×C₁₉	semidirect
265. #1672	C₂×C₁₉	semidirect
266. #1573	C₂×C₁₉	semidirect
267. #1554	C₂×C₁₉	semidirect
424. C₁₉	#19575	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×#3249	2
C₁₉×#3228	2
C₁₉×#3216	2
C₁₉×#2986	2
C₁₉×#1702	2
C₁₉×#1698	2
C₁₉×#1694	2
C₁₉×#1692	2
C₁₉×#1682	2
C₁₉×#1678	2
C₁₉×#1674	2
C₁₉×#1672	2
C₁₉×#1573	2
C₁₉×#1554	2
C₁₉×#1540	2
#19575	19

Subgroups — C19×#19575 #18025534

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19575 #18025534