Subgroups — C₁₉×#19307 #18025266

Order 4864.

656 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3185	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3110	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3077	C₂	1	1	yes	maximal, characteristic
4	D₄×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1703	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1699	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1691	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1689	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1683	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1679	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1671	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1669	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1569	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1561	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1559	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×M₁₆×C₁₉	—	2	1	no	—
17	C₁₉×#533	C₂²	1	1	yes	characteristic
18	C₁₉×#533	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#498	C₂²	1	1	yes	characteristic, complemented
21	C₁₉×#494	C₂²	1	1	yes	characteristic, complemented
22	C₁₉×#487	C₂²	1	1	yes	characteristic, complemented
23	C₁₉×#487	C₂²	1	1	yes	characteristic, complemented
24	C₁₉×#484	—	2	1	no	—
25	C₁₉×#478	—	2	1	no	—
26	C₁₉×#478	—	2	1	no	—
27	C₁₉×#476	C₂²	1	1	yes	characteristic
28	C₁₉×#476	C₂²	1	1	yes	characteristic
29	C₁₉×#474	C₂²	1	1	yes	characteristic
30	C₁₉×#474	C₂²	1	1	yes	characteristic
31	C₁₉×#474	C₂²	1	1	yes	characteristic
32	C₁₉×#474	C₂²	1	1	yes	characteristic
33	C₁₉×#470	—	2	1	no	—
34	C₁₉×#470	—	2	1	no	—
35	C₁₉×#461	C₂²	1	1	yes	characteristic
36	C₁₉×#461	C₂²	1	1	yes	characteristic
37	C₁₉×#450	—	2	1	no	—
38	C₁₉×#441	—	2	1	no	—
39	C₁₉×#441	—	2	1	no	—
40	C₁₉×#440	—	2	1	no	—
41	C₁₉×#440	—	2	1	no	—
42	C₁₉×#436	C₂²	1	1	yes	characteristic
43	C₁₉×#436	C₂²	1	1	yes	characteristic
44	C₁₉×#435	—	2	1	no	—
45	C₁₉×#435	—	2	1	no	—
46	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
47	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
48	C₁₉×#432	C₂²	1	1	yes	characteristic
49	C₁₉×#428	—	2	1	no	—
50	C₁₉×#423	C₂²	1	1	yes	characteristic
51	C₁₉×#423	C₂²	1	1	yes	characteristic
52	C₁₉×#418	—	2	1	no	—
53	C₁₉×#407	—	2	1	no	—
54	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
55	C₁₉×#335	C₂²	1	1	yes	characteristic, complemented
56	C₁₉×#335	C₂²	1	1	yes	characteristic, complemented
57	C₁₉×#334	C₂²	1	1	yes	characteristic, complemented
58	C₁₉×#334	C₂²	1	1	yes	characteristic, complemented
59	C₁₉×#333	C₂²	1	1	yes	characteristic, complemented
60	C₁₉×#333	C₂²	1	1	yes	characteristic, complemented
61	C₁₉×#332	C₂²	1	1	yes	characteristic, complemented
62	C₁₉×#332	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×#332	C₂²	1	1	yes	characteristic, complemented
64	C₁₉×#332	C₂²	1	1	yes	characteristic, complemented
65	C₁₉×#332	C₂²	1	1	yes	characteristic, complemented
66	C₁₉×#332	C₂²	1	1	yes	characteristic, complemented
67	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
68	C₂³×C₄×C₁₉	—	2	1	no	—
69	C₂×Q₁₆×C₁₉	—	2	1	no	—
70	C₂×Q₁₆×C₁₉	—	2	1	no	—
71	C₂×SD₁₆×C₁₉	—	2	1	no	—
72	C₂×SD₁₆×C₁₉	—	2	1	no	—
73	C₂×M₁₆×C₁₉	—	2	1	no	—
74	C₂×M₁₆×C₁₉	—	2	1	no	—
75	C₂×M₁₆×C₁₉	—	2	1	no	—
76	C₂×M₁₆×C₁₉	—	2	1	no	—
77	C₂×M₁₆×C₁₉	—	4	4	no	—
78	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
79	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
80	C₂²×C₈×C₁₉	—	2	1	no	—
81	C₂²×C₈×C₁₉	—	2	1	no	—
82	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₁₉×#125	—	2	1	no	—
87	C₁₉×#125	—	2	1	no	—
88	C₁₉×C₂²⋊Q₈	—	2	1	no	—
89	C₁₉×C₂²⋊Q₈	—	2	1	no	—
90	C₁₉×C₂²⋊Q₈	—	2	1	no	—
91	C₁₉×C₂²⋊Q₈	—	2	1	no	—
92	C₄×Q₈×C₁₉	—	2	1	no	—
93	C₄×Q₈×C₁₉	—	2	1	no	—
94	C₄×Q₈×C₁₉	—	2	1	no	—
95	C₄×Q₈×C₁₉	—	2	1	no	—
96	C₄×D₄×C₁₉	—	2	1	no	—
97	C₄×D₄×C₁₉	—	2	1	no	—
98	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
99	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
100	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
101	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
102	C₁₉×#117	—	2	1	no	—
103	C₁₉×#117	—	2	1	no	—
104	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
106	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
107	C₁₉×#107	—	2	1	no	—
108	C₁₉×#107	—	2	1	no	—
109	C₁₉×#107	—	2	1	no	—
110	C₁₉×#107	—	2	1	no	—
111	C₁₉×#106	—	2	1	no	—
112	C₁₉×#106	—	2	1	no	—
113	C₁₉×#106	—	2	1	no	—
114	C₁₉×#106	—	2	1	no	—
115	C₁₉×C₄⋊C₈	—	2	1	no	—
116	C₁₉×C₄⋊C₈	—	2	1	no	—
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×C₄⋊C₈	C₂³	1	1	yes	characteristic
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×#103	—	2	1	no	—
128	C₁₉×#103	—	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×#102	—	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	—	2	1	no	—
139	C₁₉×C₂²⋊C₈	—	2	1	no	—
140	C₁₉×#97	—	2	1	no	—
141	C₁₉×#97	D₄	1	1	yes	characteristic
142	C₁₉×#97	D₄	1	1	yes	characteristic
143	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
145	C₂⁴×C₁₉	—	2	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×D₄×C₁₉	—	2	2	no	—
151	C₂×D₄×C₁₉	—	2	1	no	—
152	C₂×D₄×C₁₉	—	4	1	no	—
153	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₉	—	2	1	no	—
156	C₂²×C₄×C₁₉	—	2	1	no	—
157	C₂²×C₄×C₁₉	—	2	1	no	—
158	C₂²×C₄×C₁₉	—	2	1	no	—
159	C₂²×C₄×C₁₉	—	2	1	no	—
160	C₂²×C₄×C₁₉	—	4	2	no	—
161	C₂²×C₄×C₁₉	—	4	2	no	—
162	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
165	Q₁₆×C₁₉	—	4	2	no	—
166	Q₁₆×C₁₉	—	4	2	no	—
167	SD₁₆×C₁₉	—	4	2	no	—
168	SD₁₆×C₁₉	—	4	2	no	—
169	M₁₆×C₁₉	—	2	2	no	—
170	M₁₆×C₁₉	—	4	1	no	—
171	M₁₆×C₁₉	—	4	2	no	—
172	M₁₆×C₁₉	—	4	2	no	—
173	M₁₆×C₁₉	—	4	2	no	—
174	M₁₆×C₁₉	—	4	2	no	—
175	C₂×C₈×C₁₉	—	2	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	—	4	2	no	—
182	C₂×C₈×C₁₉	—	4	2	no	—
183	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
184	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
185	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
186	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	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	—	4	1	no	—
199	C₄⋊C₄×C₁₉	—	4	1	no	—
200	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
201	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	C₄²×C₁₉	—	4	1	no	—
209	C₄²×C₁₉	—	4	1	no	—
210	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
211	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
212	C₄²×C₁₉	#41	1	1	yes	characteristic
213	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
214	#19307	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₂³×C₁₉	—	2	1	no	—
216	C₂³×C₁₉	—	2	1	no	—
217	C₂³×C₁₉	—	4	2	no	—
218	C₂³×C₁₉	—	4	2	no	—
219	C₂³×C₁₉	—	8	1	no	—
220	C₂³×C₁₉	#121	1	1	yes	characteristic
221	Q₈×C₁₉	—	4	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	Q₈×C₁₉	—	4	1	no	—
227	Q₈×C₁₉	—	8	1	no	—
228	D₄×C₁₉	—	2	1	no	—
229	D₄×C₁₉	—	2	1	no	—
230	D₄×C₁₉	—	2	1	no	—
231	D₄×C₁₉	—	4	2	no	—
232	D₄×C₁₉	#137	1	2	yes	—
233	C₂×C₄×C₁₉	—	2	1	no	—
234	C₂×C₄×C₁₉	—	2	1	no	—
235	C₂×C₄×C₁₉	—	2	1	no	—
236	C₂×C₄×C₁₉	—	2	1	no	—
237	C₂×C₄×C₁₉	—	2	1	no	—
238	C₂×C₄×C₁₉	—	2	1	no	—
239	C₂×C₄×C₁₉	—	4	1	no	—
240	C₂×C₄×C₁₉	—	4	2	no	—
241	C₂×C₄×C₁₉	—	4	2	no	—
242	C₂×C₄×C₁₉	—	4	2	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	#121	1	1	yes	characteristic
252	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
253	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
254	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
257	C₈×C₁₉	—	2	1	no	—
258	C₈×C₁₉	—	2	1	no	—
259	C₈×C₁₉	—	2	1	no	—
260	C₈×C₁₉	—	4	1	no	—
261	C₈×C₁₉	—	4	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	AGL(1,ℤ/8)	1	2	yes	—
267	#3185	C₂×C₁₉	1	1	yes	characteristic, complemented
268	#3110	C₂×C₁₉	1	1	yes	characteristic
269	#3077	C₂×C₁₉	1	1	yes	characteristic
270	D₄×M₁₆	C₂×C₁₉	1	1	yes	characteristic
271	#1703	C₂×C₁₉	1	1	yes	characteristic, complemented
272	#1699	C₂×C₁₉	1	1	yes	characteristic, complemented
273	#1691	C₂×C₁₉	1	1	yes	characteristic, complemented
274	#1689	C₂×C₁₉	1	1	yes	characteristic, complemented
275	#1683	C₂×C₁₉	1	1	yes	characteristic, complemented
276	#1679	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#1671	C₂×C₁₉	1	1	yes	characteristic, complemented
278	#1669	C₂×C₁₉	1	1	yes	characteristic, complemented
279	#1569	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#1561	C₂×C₁₉	1	1	yes	characteristic, complemented
281	#1559	C₂×C₁₉	1	1	yes	characteristic, complemented
282	C₂²×C₁₉	—	2	1	no	—
283	C₂²×C₁₉	—	2	1	no	—
284	C₂²×C₁₉	—	2	2	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	—	8	4	no	—
292	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
293	C₄×C₁₉	—	2	1	no	—
294	C₄×C₁₉	—	2	1	no	—
295	C₄×C₁₉	—	2	1	no	—
296	C₄×C₁₉	—	2	1	no	—
297	C₄×C₁₉	—	4	1	no	—
298	C₄×C₁₉	—	4	1	no	—
299	C₄×C₁₉	—	8	1	no	—
300	C₄×C₁₉	—	8	1	no	—
301	C₄×C₁₉	—	8	1	no	—
302	C₄×C₁₉	—	8	1	no	—
303	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
304	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
305	C₄×C₁₉	#575	1	1	yes	characteristic
306	C₄×C₁₉	#575	1	1	yes	characteristic
307	C₂²×M₁₆	—	2	1	no	—
308	#533	C₂²×C₁₉	1	1	yes	characteristic
309	#533	C₂²×C₁₉	1	1	yes	characteristic
310	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
311	#498	C₂²×C₁₉	1	1	yes	characteristic, complemented
312	#494	C₂²×C₁₉	1	1	yes	characteristic, complemented
313	#487	C₂²×C₁₉	1	1	yes	characteristic, complemented
314	#487	C₂²×C₁₉	1	1	yes	characteristic, complemented
315	#484	—	2	1	no	—
316	#478	—	2	1	no	—
317	#478	—	2	1	no	—
318	#476	C₂²×C₁₉	1	1	yes	characteristic
319	#476	C₂²×C₁₉	1	1	yes	characteristic
320	#474	C₂²×C₁₉	1	1	yes	characteristic
321	#474	C₂²×C₁₉	1	1	yes	characteristic
322	#474	C₂²×C₁₉	1	1	yes	characteristic
323	#474	C₂²×C₁₉	1	1	yes	characteristic
324	#470	—	2	1	no	—
325	#470	—	2	1	no	—
326	#461	C₂²×C₁₉	1	1	yes	characteristic
327	#461	C₂²×C₁₉	1	1	yes	characteristic
328	#450	—	2	1	no	—
329	#441	—	2	1	no	—
330	#441	—	2	1	no	—
331	#440	—	2	1	no	—
332	#440	—	2	1	no	—
333	#436	C₂²×C₁₉	1	1	yes	characteristic
334	#436	C₂²×C₁₉	1	1	yes	characteristic
335	#435	—	2	1	no	—
336	#435	—	2	1	no	—
337	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
338	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
339	#432	C₂²×C₁₉	1	1	yes	characteristic
340	#428	—	2	1	no	—
341	#423	C₂²×C₁₉	1	1	yes	characteristic
342	#423	C₂²×C₁₉	1	1	yes	characteristic
343	#418	—	2	1	no	—
344	#407	—	2	1	no	—
345	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
346	#335	C₂²×C₁₉	1	1	yes	characteristic, complemented
347	#335	C₂²×C₁₉	1	1	yes	characteristic, complemented
348	#334	C₂²×C₁₉	1	1	yes	characteristic, complemented
349	#334	C₂²×C₁₉	1	1	yes	characteristic, complemented
350	#333	C₂²×C₁₉	1	1	yes	characteristic, complemented
351	#333	C₂²×C₁₉	1	1	yes	characteristic, complemented
352	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
353	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
354	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
355	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
356	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
357	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
358	C₂×C₁₉	—	4	1	no	—
359	C₂×C₁₉	—	4	2	no	—
360	C₂×C₁₉	—	8	1	no	—
361	C₂×C₁₉	#3036	1	1	yes	characteristic
362	C₂×C₁₉	#3056	1	1	yes	characteristic
363	C₂×C₁₉	#3069	1	1	yes	characteristic
364	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
365	C₂³×C₄	—	2	1	no	—
366	C₂×Q₁₆	—	2	1	no	—
367	C₂×Q₁₆	—	2	1	no	—
368	C₂×SD₁₆	—	2	1	no	—
369	C₂×SD₁₆	—	2	1	no	—
370	C₂×M₁₆	—	2	1	no	—
371	C₂×M₁₆	—	2	1	no	—
372	C₂×M₁₆	—	2	1	no	—
373	C₂×M₁₆	—	2	1	no	—
374	C₂×M₁₆	—	4	4	no	—
375	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
376	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
377	C₂²×C₈	—	2	1	no	—
378	C₂²×C₈	—	2	1	no	—
379	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
380	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
381	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
382	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
383	#125	—	2	1	no	—
384	#125	—	2	1	no	—
385	C₂²⋊Q₈	—	2	1	no	—
386	C₂²⋊Q₈	—	2	1	no	—
387	C₂²⋊Q₈	—	2	1	no	—
388	C₂²⋊Q₈	—	2	1	no	—
389	C₄×Q₈	—	2	1	no	—
390	C₄×Q₈	—	2	1	no	—
391	C₄×Q₈	—	2	1	no	—
392	C₄×Q₈	—	2	1	no	—
393	C₄×D₄	—	2	1	no	—
394	C₄×D₄	—	2	1	no	—
395	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
396	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
397	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
398	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
399	#117	—	2	1	no	—
400	#117	—	2	1	no	—
401	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
402	C₂×C₂²⋊C₄	—	2	1	no	—
403	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
404	#107	—	2	1	no	—
405	#107	—	2	1	no	—
406	#107	—	2	1	no	—
407	#107	—	2	1	no	—
408	#106	—	2	1	no	—
409	#106	—	2	1	no	—
410	#106	—	2	1	no	—
411	#106	—	2	1	no	—
412	C₄⋊C₈	—	2	1	no	—
413	C₄⋊C₈	—	2	1	no	—
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	#103	—	2	1	no	—
425	#103	—	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	#97	—	2	1	no	—
438	#97	D₄×C₁₉	1	1	yes	characteristic
439	#97	D₄×C₁₉	1	1	yes	characteristic
440	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
441	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
442	C₁₉	#19307	1	1	yes	characteristic, direct product factor, Sylow
443	C₂⁴	—	2	1	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	4	1	no	—
451	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
452	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	4	2	no	—
459	C₂²×C₄	—	4	2	no	—
460	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
461	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
462	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
463	Q₁₆	—	4	2	no	—
464	Q₁₆	—	4	2	no	—
465	SD₁₆	—	4	2	no	—
466	SD₁₆	—	4	2	no	—
467	M₁₆	—	2	2	no	—
468	M₁₆	—	4	1	no	—
469	M₁₆	—	4	2	no	—
470	M₁₆	—	4	2	no	—
471	M₁₆	—	4	2	no	—
472	M₁₆	—	4	2	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	4	2	no	—
480	C₂×C₈	—	4	2	no	—
481	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
482	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
483	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
484	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	1	no	—
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	—	4	1	no	—
495	C₄⋊C₄	—	4	1	no	—
496	C₄⋊C₄	—	4	1	no	—
497	C₄⋊C₄	—	4	1	no	—
498	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
499	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
500	C₂²⋊C₄	—	2	1	no	—
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	2	1	no	—
503	C₂²⋊C₄	—	2	1	no	—
504	C₂²⋊C₄	—	4	1	no	—
505	C₂²⋊C₄	—	4	1	no	—
506	C₄²	—	4	1	no	—
507	C₄²	—	4	1	no	—
508	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
509	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
510	C₄²	#41×C₁₉	1	1	yes	characteristic
511	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
512	C₂³	—	2	1	no	—
513	C₂³	—	2	1	no	—
514	C₂³	—	4	2	no	—
515	C₂³	—	4	2	no	—
516	C₂³	—	8	1	no	—
517	C₂³	C₁₉×#121	1	1	yes	characteristic
518	Q₈	—	4	1	no	—
519	Q₈	—	4	1	no	—
520	Q₈	—	4	1	no	—
521	Q₈	—	4	1	no	—
522	Q₈	—	4	1	no	—
523	Q₈	—	4	1	no	—
524	Q₈	—	8	1	no	—
525	D₄	—	2	1	no	—
526	D₄	—	2	1	no	—
527	D₄	—	2	1	no	—
528	D₄	—	4	2	no	—
529	D₄	C₁₉×#137	1	2	yes	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	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	C₁₉×#121	1	1	yes	characteristic
549	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
550	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
551	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
552	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
553	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
554	C₈	—	2	1	no	—
555	C₈	—	2	1	no	—
556	C₈	—	2	1	no	—
557	C₈	—	4	1	no	—
558	C₈	—	4	1	no	—
559	C₈	—	4	1	no	—
560	C₈	—	4	1	no	—
561	C₈	—	4	1	no	—
562	C₈	—	4	1	no	—
563	C₈	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
564	C₂²	—	2	1	no	—
565	C₂²	—	2	1	no	—
566	C₂²	—	2	2	no	—
567	C₂²	—	2	1	no	—
568	C₂²	—	4	1	no	—
569	C₂²	—	4	1	no	—
570	C₂²	—	4	1	no	—
571	C₂²	—	4	1	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	8	4	no	—
574	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
575	C₄	—	2	1	no	—
576	C₄	—	2	1	no	—
577	C₄	—	2	1	no	—
578	C₄	—	2	1	no	—
579	C₄	—	4	1	no	—
580	C₄	—	4	1	no	—
581	C₄	—	8	1	no	—
582	C₄	—	8	1	no	—
583	C₄	—	8	1	no	—
584	C₄	—	8	1	no	—
585	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
586	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
587	C₄	C₁₉×#575	1	1	yes	characteristic
588	C₄	C₁₉×#575	1	1	yes	characteristic
589	C₂	—	4	1	no	—
590	C₂	—	4	2	no	—
591	C₂	—	8	1	no	—
592	C₂	C₁₉×#3036	1	1	yes	characteristic
593	C₂	C₁₉×#3056	1	1	yes	characteristic
594	C₂	C₁₉×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂²×D₄×C₁₉	D₄
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×#3185	C₂	semidirect
5. C₁₉×#1703	C₂	semidirect
6. C₁₉×#1699	C₂	semidirect
7. C₁₉×#1691	C₂	semidirect
8. C₁₉×#1689	C₂	semidirect
9. C₁₉×#1683	C₂	semidirect
10. C₁₉×#1679	C₂	semidirect
11. C₁₉×#1671	C₂	semidirect
12. C₁₉×#1669	C₂	semidirect
13. C₁₉×#1569	C₂	semidirect
14. C₁₉×#1561	C₂	semidirect
15. C₁₉×#1559	C₂	semidirect
20. C₁₉×#498	C₂²	semidirect
21. C₁₉×#494	C₂²	semidirect
22. C₁₉×#487	C₂²	semidirect
23. C₁₉×#487	C₂²	semidirect
55. C₁₉×#335	C₂²	semidirect
56. C₁₉×#335	C₂²	semidirect
57. C₁₉×#334	C₂²	semidirect
58. C₁₉×#334	C₂²	semidirect
59. C₁₉×#333	C₂²	semidirect
60. C₁₉×#333	C₂²	semidirect
61. C₁₉×#332	C₂²	semidirect
62. C₁₉×#332	C₂²	semidirect
63. C₁₉×#332	C₂²	semidirect
64. C₁₉×#332	C₂²	semidirect
65. C₁₉×#332	C₂²	semidirect
66. C₁₉×#332	C₂²	semidirect
214. #19307	C₁₉	direct (N × H)
267. #3185	C₂×C₁₉	semidirect
271. #1703	C₂×C₁₉	semidirect
272. #1699	C₂×C₁₉	semidirect
273. #1691	C₂×C₁₉	semidirect
274. #1689	C₂×C₁₉	semidirect
275. #1683	C₂×C₁₉	semidirect
276. #1679	C₂×C₁₉	semidirect
277. #1671	C₂×C₁₉	semidirect
278. #1669	C₂×C₁₉	semidirect
279. #1569	C₂×C₁₉	semidirect
280. #1561	C₂×C₁₉	semidirect
281. #1559	C₂×C₁₉	semidirect
311. #498	C₂²×C₁₉	semidirect
312. #494	C₂²×C₁₉	semidirect
313. #487	C₂²×C₁₉	semidirect
314. #487	C₂²×C₁₉	semidirect
346. #335	C₂²×C₁₉	semidirect
347. #335	C₂²×C₁₉	semidirect
348. #334	C₂²×C₁₉	semidirect
349. #334	C₂²×C₁₉	semidirect
350. #333	C₂²×C₁₉	semidirect
351. #333	C₂²×C₁₉	semidirect
352. #332	C₂²×C₁₉	semidirect
353. #332	C₂²×C₁₉	semidirect
354. #332	C₂²×C₁₉	semidirect
355. #332	C₂²×C₁₉	semidirect
356. #332	C₂²×C₁₉	semidirect
357. #332	C₂²×C₁₉	semidirect
442. C₁₉	#19307	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×#3185	2
C₁₉×#3110	2
C₁₉×#3077	2
D₄×M₁₆×C₁₉	2
C₁₉×#1703	2
C₁₉×#1699	2
C₁₉×#1691	2
C₁₉×#1689	2
C₁₉×#1683	2
C₁₉×#1679	2
C₁₉×#1671	2
C₁₉×#1669	2
C₁₉×#1569	2
C₁₉×#1561	2
C₁₉×#1559	2
#19307	19

Subgroups — C19×#19307 #18025266

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19307 #18025266