Subgroups — C₁₉×#19576 #18025535

Order 4864.

618 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3251	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3212	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3207	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2994	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1702	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1699	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1687	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1686	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1681	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1680	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1668	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1665	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1574	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1547	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1540	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#532	C₂²	1	1	yes	characteristic
17	C₁₉×#532	C₂²	1	1	yes	characteristic
18	C₁₉×#529	C₂²	1	1	yes	characteristic
19	C₁₉×#495	—	2	1	no	—
20	C₁₉×#493	C₂²	1	1	yes	characteristic
21	C₁₉×#492	C₂²	1	1	yes	characteristic
22	C₁₉×#488	—	2	1	no	—
23	C₁₉×#487	C₂²	1	1	yes	characteristic
24	C₁₉×#486	C₂²	1	1	yes	characteristic
25	C₁₉×#478	—	2	1	no	—
26	C₁₉×#475	C₂²	1	1	yes	characteristic
27	C₁₉×#474	C₂²	1	1	yes	characteristic
28	C₁₉×#469	—	2	1	no	—
29	C₁₉×#468	—	2	1	no	—
30	C₁₉×#463	—	2	1	no	—
31	C₁₉×#463	—	2	1	no	—
32	C₁₉×#463	—	2	1	no	—
33	C₁₉×#462	C₂²	1	1	yes	characteristic
34	C₁₉×#461	C₂²	1	1	yes	characteristic
35	C₁₉×#460	C₂²	1	1	yes	characteristic
36	C₁₉×#460	C₂²	1	1	yes	characteristic
37	C₁₉×#459	C₂²	1	1	yes	characteristic
38	C₁₉×#459	C₂²	1	1	yes	characteristic
39	C₁₉×#452	—	2	1	no	—
40	C₁₉×#449	—	2	1	no	—
41	C₁₉×#449	—	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	C₂²	1	1	yes	characteristic
46	C₁₉×#435	—	2	1	no	—
47	C₈×D₄×C₁₉	—	2	1	no	—
48	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
49	C₁₉×#433	—	2	1	no	—
50	C₁₉×#431	C₂²	1	1	yes	characteristic
51	C₁₉×#431	C₂²	1	1	yes	characteristic
52	C₁₉×#424	—	2	1	no	—
53	C₁₉×#423	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×#332	C₂²	1	1	yes	characteristic
60	C₁₉×#332	C₂²	1	1	yes	characteristic
61	C₁₉×#332	C₂²	1	1	yes	characteristic
62	C₁₉×#332	C₂²	1	1	yes	characteristic
63	C₁₉×#331	C₂²	1	1	yes	characteristic
64	C₁₉×#331	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×Q₁₆×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×SD₁₆×C₁₉	—	2	1	no	—
74	C₂×SD₁₆×C₁₉	—	2	1	no	—
75	C₂×D₈×C₁₉	—	2	1	no	—
76	C₂×D₈×C₁₉	—	2	1	no	—
77	C₂×D₈×C₁₉	—	2	1	no	—
78	C₂×D₈×C₁₉	—	2	1	no	—
79	C₂×M₁₆×C₁₉	—	2	1	no	—
80	C₂×M₁₆×C₁₉	—	2	1	no	—
81	C₂²×C₈×C₁₉	—	2	1	no	—
82	C₂²×C₈×C₁₉	—	2	1	no	—
83	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₁₉×#127	C₂³	1	1	yes	characteristic
86	C₁₉×#127	C₂³	1	1	yes	characteristic
87	C₁₉×#126	—	2	1	no	—
88	C₁₉×#125	D₄	1	1	yes	characteristic
89	C₁₉×#124	—	2	1	no	—
90	C₁₉×#124	—	2	1	no	—
91	C₁₉×#124	D₄	1	1	yes	characteristic
92	C₁₉×#123	—	2	1	no	—
93	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
94	C₁₉×#121	—	2	1	no	—
95	C₁₉×#121	—	2	1	no	—
96	C₁₉×#121	—	2	1	no	—
97	C₁₉×#121	—	2	1	no	—
98	C₁₉×#121	D₄	1	1	yes	characteristic
99	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
100	C₄×D₄×C₁₉	—	2	1	no	—
101	C₄×D₄×C₁₉	—	2	1	no	—
102	C₄×D₄×C₁₉	—	2	1	no	—
103	C₄×D₄×C₁₉	—	2	1	no	—
104	C₄×D₄×C₁₉	—	2	1	no	—
105	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
106	C₁₉×#117	—	2	1	no	—
107	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
108	C₁₉×#107	—	2	1	no	—
109	C₁₉×#106	—	2	1	no	—
110	C₁₉×C₄⋊C₈	—	2	1	no	—
111	C₁₉×C₄⋊C₈	—	2	1	no	—
112	C₁₉×C₄⋊C₈	—	2	1	no	—
113	C₁₉×C₄⋊C₈	—	2	1	no	—
114	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
115	C₁₉×C₄⋊C₈	D₄	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×C₄⋊C₈	C₂³	1	1	yes	characteristic
121	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
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×#103	—	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×#102	—	2	1	no	—
133	C₁₉×#102	—	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	D₄	1	1	yes	characteristic
138	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
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	#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	C₂×D₄	1	1	yes	characteristic
151	C₂×D₄×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	—	4	1	no	—
159	C₂×D₄×C₁₉	—	4	1	no	—
160	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₉	—	2	1	no	—
162	C₂²×C₄×C₁₉	—	4	1	no	—
163	C₂²×C₄×C₁₉	—	4	1	no	—
164	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
167	Q₁₆×C₁₉	—	8	1	no	—
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	SD₁₆×C₁₉	—	8	1	no	—
173	D₈×C₁₉	—	8	1	no	—
174	D₈×C₁₉	—	8	1	no	—
175	D₈×C₁₉	—	8	1	no	—
176	D₈×C₁₉	—	8	1	no	—
177	M₁₆×C₁₉	—	8	1	no	—
178	M₁₆×C₁₉	—	8	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	—	2	1	no	—
183	C₂×C₈×C₁₉	—	2	1	no	—
184	C₂×C₈×C₁₉	—	2	1	no	—
185	C₂×C₈×C₁₉	—	8	1	no	—
186	C₂×C₈×C₁₉	—	8	1	no	—
187	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
188	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
190	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
197	C₄⋊C₄×C₁₉	—	2	1	no	—
198	C₄⋊C₄×C₁₉	—	2	1	no	—
199	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
200	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	4	1	no	—
207	C₂²⋊C₄×C₁₉	—	4	1	no	—
208	C₂²⋊C₄×C₁₉	—	4	1	no	—
209	C₂²⋊C₄×C₁₉	—	4	1	no	—
210	C₄²×C₁₉	—	2	1	no	—
211	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
212	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
213	C₄²×C₁₉	#41	1	1	yes	characteristic
214	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
215	#19576	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂³×C₁₉	—	2	1	no	—
217	C₂³×C₁₉	—	4	1	no	—
218	C₂³×C₁₉	—	4	1	no	—
219	C₂³×C₁₉	#121	1	1	yes	characteristic
220	Q₈×C₁₉	—	2	1	no	—
221	Q₈×C₁₉	—	2	1	no	—
222	Q₈×C₁₉	—	4	1	no	—
223	Q₈×C₁₉	—	4	1	no	—
224	Q₈×C₁₉	—	4	1	no	—
225	Q₈×C₁₉	—	4	1	no	—
226	D₄×C₁₉	—	2	1	no	—
227	D₄×C₁₉	—	2	1	no	—
228	D₄×C₁₉	—	4	2	no	—
229	D₄×C₁₉	—	4	1	no	—
230	D₄×C₁₉	—	4	1	no	—
231	D₄×C₁₉	—	4	1	no	—
232	D₄×C₁₉	—	4	1	no	—
233	D₄×C₁₉	—	4	1	no	—
234	D₄×C₁₉	—	4	1	no	—
235	D₄×C₁₉	—	4	1	no	—
236	D₄×C₁₉	—	4	1	no	—
237	D₄×C₁₉	—	8	1	no	—
238	D₄×C₁₉	—	8	1	no	—
239	D₄×C₁₉	—	8	2	no	—
240	D₄×C₁₉	—	8	2	no	—
241	C₂×C₄×C₁₉	—	2	1	no	—
242	C₂×C₄×C₁₉	—	2	1	no	—
243	C₂×C₄×C₁₉	—	2	1	no	—
244	C₂×C₄×C₁₉	—	2	1	no	—
245	C₂×C₄×C₁₉	—	2	1	no	—
246	C₂×C₄×C₁₉	—	2	1	no	—
247	C₂×C₄×C₁₉	—	2	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	—	4	1	no	—
252	C₂×C₄×C₁₉	—	4	1	no	—
253	C₂×C₄×C₁₉	—	8	2	no	—
254	C₂×C₄×C₁₉	—	8	2	no	—
255	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
256	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
257	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
258	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
261	C₈×C₁₉	—	2	1	no	—
262	C₈×C₁₉	—	2	1	no	—
263	C₈×C₁₉	—	2	1	no	—
264	C₈×C₁₉	—	2	1	no	—
265	C₈×C₁₉	—	4	1	no	—
266	C₈×C₁₉	—	4	1	no	—
267	C₈×C₁₉	—	4	1	no	—
268	C₈×C₁₉	—	4	1	no	—
269	C₈×C₁₉	—	4	1	no	—
270	C₈×C₁₉	—	4	1	no	—
271	#3251	C₂×C₁₉	1	1	yes	characteristic, complemented
272	#3212	C₂×C₁₉	1	1	yes	characteristic, complemented
273	#3207	C₂×C₁₉	1	1	yes	characteristic, complemented
274	#2994	C₂×C₁₉	1	1	yes	characteristic, complemented
275	#1702	C₂×C₁₉	1	1	yes	characteristic, complemented
276	#1699	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#1687	C₂×C₁₉	1	1	yes	characteristic, complemented
278	#1686	C₂×C₁₉	1	1	yes	characteristic, complemented
279	#1681	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#1680	C₂×C₁₉	1	1	yes	characteristic, complemented
281	#1668	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#1665	C₂×C₁₉	1	1	yes	characteristic, complemented
283	#1574	C₂×C₁₉	1	1	yes	characteristic, complemented
284	#1547	C₂×C₁₉	1	1	yes	characteristic, complemented
285	#1540	C₂×C₁₉	1	1	yes	characteristic, complemented
286	C₂²×C₁₉	—	2	1	no	—
287	C₂²×C₁₉	—	2	1	no	—
288	C₂²×C₁₉	—	2	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	—	8	1	no	—
296	C₂²×C₁₉	—	8	1	no	—
297	C₂²×C₁₉	—	8	1	no	—
298	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
299	C₄×C₁₉	—	2	1	no	—
300	C₄×C₁₉	—	2	1	no	—
301	C₄×C₁₉	—	2	1	no	—
302	C₄×C₁₉	—	2	1	no	—
303	C₄×C₁₉	—	4	1	no	—
304	C₄×C₁₉	—	4	1	no	—
305	C₄×C₁₉	—	4	1	no	—
306	C₄×C₁₉	—	8	1	no	—
307	C₄×C₁₉	—	8	1	no	—
308	C₄×C₁₉	#576	1	1	yes	characteristic
309	C₄×C₁₉	#576	1	1	yes	characteristic
310	C₄×C₁₉	#577	1	1	yes	characteristic
311	C₄×C₁₉	#577	1	1	yes	characteristic
312	#532	C₂²×C₁₉	1	1	yes	characteristic
313	#532	C₂²×C₁₉	1	1	yes	characteristic
314	#529	C₂²×C₁₉	1	1	yes	characteristic
315	#495	—	2	1	no	—
316	#493	C₂²×C₁₉	1	1	yes	characteristic
317	#492	C₂²×C₁₉	1	1	yes	characteristic
318	#488	—	2	1	no	—
319	#487	C₂²×C₁₉	1	1	yes	characteristic
320	#486	C₂²×C₁₉	1	1	yes	characteristic
321	#478	—	2	1	no	—
322	#475	C₂²×C₁₉	1	1	yes	characteristic
323	#474	C₂²×C₁₉	1	1	yes	characteristic
324	#469	—	2	1	no	—
325	#468	—	2	1	no	—
326	#463	—	2	1	no	—
327	#463	—	2	1	no	—
328	#463	—	2	1	no	—
329	#462	C₂²×C₁₉	1	1	yes	characteristic
330	#461	C₂²×C₁₉	1	1	yes	characteristic
331	#460	C₂²×C₁₉	1	1	yes	characteristic
332	#460	C₂²×C₁₉	1	1	yes	characteristic
333	#459	C₂²×C₁₉	1	1	yes	characteristic
334	#459	C₂²×C₁₉	1	1	yes	characteristic
335	#452	—	2	1	no	—
336	#449	—	2	1	no	—
337	#449	—	2	1	no	—
338	#449	—	2	1	no	—
339	#446	C₂²×C₁₉	1	1	yes	characteristic
340	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
341	#436	C₂²×C₁₉	1	1	yes	characteristic
342	#435	—	2	1	no	—
343	C₈×D₄	—	2	1	no	—
344	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
345	#433	—	2	1	no	—
346	#431	C₂²×C₁₉	1	1	yes	characteristic
347	#431	C₂²×C₁₉	1	1	yes	characteristic
348	#424	—	2	1	no	—
349	#423	C₂²×C₁₉	1	1	yes	characteristic
350	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
351	#335	C₂²×C₁₉	1	1	yes	characteristic
352	#335	C₂²×C₁₉	1	1	yes	characteristic
353	#334	C₂²×C₁₉	1	1	yes	characteristic
354	#334	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	#332	C₂²×C₁₉	1	1	yes	characteristic
359	#331	C₂²×C₁₉	1	1	yes	characteristic
360	#331	C₂²×C₁₉	1	1	yes	characteristic
361	#331	C₂²×C₁₉	1	1	yes	characteristic
362	#331	C₂²×C₁₉	1	1	yes	characteristic
363	C₂×C₁₉	—	4	1	no	—
364	C₂×C₁₉	—	8	1	no	—
365	C₂×C₁₉	—	16	1	no	—
366	C₂×C₁₉	—	16	1	no	—
367	C₂×C₁₉	#3045	1	1	yes	characteristic
368	C₂×C₁₉	#3062	1	1	yes	characteristic
369	C₂×C₁₉	#3067	1	1	yes	characteristic
370	C₂×#41	—	2	1	no	—
371	C₂×#41	—	2	1	no	—
372	C₂×Q₁₆	—	2	1	no	—
373	C₂×SD₁₆	—	2	1	no	—
374	C₂×SD₁₆	—	2	1	no	—
375	C₂×SD₁₆	—	2	1	no	—
376	C₂×SD₁₆	—	2	1	no	—
377	C₂×SD₁₆	—	2	1	no	—
378	C₂×D₈	—	2	1	no	—
379	C₂×D₈	—	2	1	no	—
380	C₂×D₈	—	2	1	no	—
381	C₂×D₈	—	2	1	no	—
382	C₂×M₁₆	—	2	1	no	—
383	C₂×M₁₆	—	2	1	no	—
384	C₂²×C₈	—	2	1	no	—
385	C₂²×C₈	—	2	1	no	—
386	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
387	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
388	#127	C₂³×C₁₉	1	1	yes	characteristic
389	#127	C₂³×C₁₉	1	1	yes	characteristic
390	#126	—	2	1	no	—
391	#125	D₄×C₁₉	1	1	yes	characteristic
392	#124	—	2	1	no	—
393	#124	—	2	1	no	—
394	#124	D₄×C₁₉	1	1	yes	characteristic
395	#123	—	2	1	no	—
396	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
397	#121	—	2	1	no	—
398	#121	—	2	1	no	—
399	#121	—	2	1	no	—
400	#121	—	2	1	no	—
401	#121	D₄×C₁₉	1	1	yes	characteristic
402	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
403	C₄×D₄	—	2	1	no	—
404	C₄×D₄	—	2	1	no	—
405	C₄×D₄	—	2	1	no	—
406	C₄×D₄	—	2	1	no	—
407	C₄×D₄	—	2	1	no	—
408	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
409	#117	—	2	1	no	—
410	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
411	#107	—	2	1	no	—
412	#106	—	2	1	no	—
413	C₄⋊C₈	—	2	1	no	—
414	C₄⋊C₈	—	2	1	no	—
415	C₄⋊C₈	—	2	1	no	—
416	C₄⋊C₈	—	2	1	no	—
417	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
418	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
419	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
420	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
421	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
422	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
423	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
424	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
425	#103	—	2	1	no	—
426	#103	—	2	1	no	—
427	#103	—	2	1	no	—
428	#103	—	2	1	no	—
429	#103	—	2	1	no	—
430	#102	—	2	1	no	—
431	#102	—	2	1	no	—
432	#102	—	2	1	no	—
433	#102	—	2	1	no	—
434	#102	—	2	1	no	—
435	#102	—	2	1	no	—
436	#102	—	2	1	no	—
437	C₂²⋊C₈	—	2	1	no	—
438	C₂²⋊C₈	—	2	1	no	—
439	C₂²⋊C₈	—	2	1	no	—
440	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
441	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
442	#97	—	2	1	no	—
443	C₄×C₈	—	2	1	no	—
444	C₄×C₈	—	2	1	no	—
445	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
446	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
447	C₁₉	#19576	1	1	yes	characteristic, direct product factor, Sylow
448	#41	—	8	1	no	—
449	#41	—	8	1	no	—
450	#41	—	8	1	no	—
451	#41	—	8	1	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
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	—	2	1	no	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	4	1	no	—
463	C₂×D₄	—	4	1	no	—
464	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	4	1	no	—
467	C₂²×C₄	—	4	1	no	—
468	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
469	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
470	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
471	Q₁₆	—	8	1	no	—
472	SD₁₆	—	8	1	no	—
473	SD₁₆	—	8	1	no	—
474	SD₁₆	—	8	1	no	—
475	SD₁₆	—	8	1	no	—
476	SD₁₆	—	8	1	no	—
477	D₈	—	8	1	no	—
478	D₈	—	8	1	no	—
479	D₈	—	8	1	no	—
480	D₈	—	8	1	no	—
481	M₁₆	—	8	1	no	—
482	M₁₆	—	8	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	8	1	no	—
490	C₂×C₈	—	8	1	no	—
491	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
492	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
493	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
494	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
504	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
505	C₂²⋊C₄	—	2	1	no	—
506	C₂²⋊C₄	—	2	1	no	—
507	C₂²⋊C₄	—	2	1	no	—
508	C₂²⋊C₄	—	2	1	no	—
509	C₂²⋊C₄	—	2	1	no	—
510	C₂²⋊C₄	—	4	1	no	—
511	C₂²⋊C₄	—	4	1	no	—
512	C₂²⋊C₄	—	4	1	no	—
513	C₂²⋊C₄	—	4	1	no	—
514	C₄²	—	2	1	no	—
515	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
516	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
517	C₄²	#41×C₁₉	1	1	yes	characteristic
518	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
519	C₂³	—	2	1	no	—
520	C₂³	—	4	1	no	—
521	C₂³	—	4	1	no	—
522	C₂³	C₁₉×#121	1	1	yes	characteristic
523	Q₈	—	2	1	no	—
524	Q₈	—	2	1	no	—
525	Q₈	—	4	1	no	—
526	Q₈	—	4	1	no	—
527	Q₈	—	4	1	no	—
528	Q₈	—	4	1	no	—
529	D₄	—	2	1	no	—
530	D₄	—	2	1	no	—
531	D₄	—	4	2	no	—
532	D₄	—	4	1	no	—
533	D₄	—	4	1	no	—
534	D₄	—	4	1	no	—
535	D₄	—	4	1	no	—
536	D₄	—	4	1	no	—
537	D₄	—	4	1	no	—
538	D₄	—	4	1	no	—
539	D₄	—	4	1	no	—
540	D₄	—	8	1	no	—
541	D₄	—	8	1	no	—
542	D₄	—	8	2	no	—
543	D₄	—	8	2	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	8	2	no	—
557	C₂×C₄	—	8	2	no	—
558	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
559	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
560	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
561	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
562	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
563	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
564	C₈	—	2	1	no	—
565	C₈	—	2	1	no	—
566	C₈	—	2	1	no	—
567	C₈	—	2	1	no	—
568	C₈	—	4	1	no	—
569	C₈	—	4	1	no	—
570	C₈	—	4	1	no	—
571	C₈	—	4	1	no	—
572	C₈	—	4	1	no	—
573	C₈	—	4	1	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	8	1	no	—
581	C₂²	—	8	1	no	—
582	C₂²	—	8	1	no	—
583	C₂²	—	8	1	no	—
584	C₂²	—	8	1	no	—
585	C₂²	—	8	1	no	—
586	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	4	1	no	—
592	C₄	—	4	1	no	—
593	C₄	—	4	1	no	—
594	C₄	—	8	1	no	—
595	C₄	—	8	1	no	—
596	C₄	C₁₉×#576	1	1	yes	characteristic
597	C₄	C₁₉×#576	1	1	yes	characteristic
598	C₄	C₁₉×#577	1	1	yes	characteristic
599	C₄	C₁₉×#577	1	1	yes	characteristic
600	C₂	—	4	1	no	—
601	C₂	—	8	1	no	—
602	C₂	—	16	1	no	—
603	C₂	—	16	1	no	—
604	C₂	C₁₉×#3045	1	1	yes	characteristic
605	C₂	C₁₉×#3062	1	1	yes	characteristic
606	C₂	C₁₉×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
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×#3251	C₂	semidirect
2. C₁₉×#3212	C₂	semidirect
3. C₁₉×#3207	C₂	semidirect
4. C₁₉×#2994	C₂	semidirect
5. C₁₉×#1702	C₂	semidirect
6. C₁₉×#1699	C₂	semidirect
7. C₁₉×#1687	C₂	semidirect
8. C₁₉×#1686	C₂	semidirect
9. C₁₉×#1681	C₂	semidirect
10. C₁₉×#1680	C₂	semidirect
11. C₁₉×#1668	C₂	semidirect
12. C₁₉×#1665	C₂	semidirect
13. C₁₉×#1574	C₂	semidirect
14. C₁₉×#1547	C₂	semidirect
15. C₁₉×#1540	C₂	semidirect
215. #19576	C₁₉	direct (N × H)
271. #3251	C₂×C₁₉	semidirect
272. #3212	C₂×C₁₉	semidirect
273. #3207	C₂×C₁₉	semidirect
274. #2994	C₂×C₁₉	semidirect
275. #1702	C₂×C₁₉	semidirect
276. #1699	C₂×C₁₉	semidirect
277. #1687	C₂×C₁₉	semidirect
278. #1686	C₂×C₁₉	semidirect
279. #1681	C₂×C₁₉	semidirect
280. #1680	C₂×C₁₉	semidirect
281. #1668	C₂×C₁₉	semidirect
282. #1665	C₂×C₁₉	semidirect
283. #1574	C₂×C₁₉	semidirect
284. #1547	C₂×C₁₉	semidirect
285. #1540	C₂×C₁₉	semidirect
447. C₁₉	#19576	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×#3251	2
C₁₉×#3212	2
C₁₉×#3207	2
C₁₉×#2994	2
C₁₉×#1702	2
C₁₉×#1699	2
C₁₉×#1687	2
C₁₉×#1686	2
C₁₉×#1681	2
C₁₉×#1680	2
C₁₉×#1668	2
C₁₉×#1665	2
C₁₉×#1574	2
C₁₉×#1547	2
C₁₉×#1540	2
#19576	19

Subgroups — C19×#19576 #18025535

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19576 #18025535