Subgroups — C₁₉×#18709 #18024668

Order 4864.

874 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3554	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3252	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3237	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3167	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1653	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1651	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1642	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1640	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1637	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1636	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1631	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1630	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1557	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1494	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1493	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#562	—	2	2	no	—
17	C₁₉×#559	—	2	1	no	—
18	C₁₉×#559	C₂²	1	1	yes	characteristic
19	C₁₉×#557	C₂²	1	1	yes	characteristic
20	C₁₉×#554	—	2	1	no	—
21	C₁₉×#550	C₂²	1	1	yes	characteristic
22	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#548	—	2	1	no	—
24	C₁₉×#547	—	2	1	no	—
25	C₁₉×#542	—	2	1	no	—
26	C₁₉×#542	—	2	1	no	—
27	C₁₉×#540	—	2	1	no	—
28	C₁₉×#539	—	2	2	no	—
29	C₁₉×#536	—	2	1	no	—
30	C₁₉×#533	C₂²	1	1	yes	characteristic
31	C₁₉×#533	C₂²	1	1	yes	characteristic
32	C₁₉×#532	C₂²	1	1	yes	characteristic
33	C₁₉×#529	C₂²	1	1	yes	characteristic
34	C₁₉×#501	—	2	1	no	—
35	C₁₉×#498	C₂²	1	1	yes	characteristic
36	C₁₉×#492	C₂²	1	1	yes	characteristic
37	C₁₉×#491	—	2	1	no	—
38	C₁₉×#487	C₂²	1	1	yes	characteristic
39	C₁₉×#486	C₂²	1	1	yes	characteristic
40	C₁₉×#485	—	2	1	no	—
41	C₁₉×#485	—	2	1	no	—
42	C₁₉×#479	—	2	1	no	—
43	C₁₉×#477	C₂²	1	1	yes	characteristic
44	C₁₉×#477	C₂²	1	1	yes	characteristic
45	C₁₉×#477	C₂²	1	1	yes	characteristic
46	C₁₉×#476	C₂²	1	1	yes	characteristic
47	C₁₉×#475	C₂²	1	1	yes	characteristic
48	C₁₉×#475	C₂²	1	1	yes	characteristic
49	C₁₉×#470	—	2	1	no	—
50	C₁₉×#468	—	2	1	no	—
51	C₁₉×#465	—	2	2	no	—
52	C₁₉×#464	—	2	1	no	—
53	C₁₉×#462	C₂²	1	1	yes	characteristic
54	C₁₉×#461	C₂²	1	1	yes	characteristic
55	C₄×SD₁₆×C₁₉	—	2	2	no	—
56	C₁₉×#432	C₂²	1	1	yes	characteristic
57	C₁₉×#423	C₂²	1	1	yes	characteristic
58	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
59	C₁₉×#332	C₂²	1	1	yes	characteristic
60	C₁₉×#332	C₂²	1	1	yes	characteristic
61	C₁₉×#331	C₂²	1	1	yes	characteristic
62	C₁₉×#331	C₂²	1	1	yes	characteristic
63	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
66	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
67	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
68	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
69	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
70	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
71	C₂×#41×C₁₉	—	2	1	no	—
72	C₂×#41×C₁₉	—	2	1	no	—
73	C₂²×Q₈×C₁₉	—	2	1	no	—
74	C₂×Q₁₆×C₁₉	—	2	1	no	—
75	C₂×SD₁₆×C₁₉	—	2	2	no	—
76	C₂×SD₁₆×C₁₉	—	2	1	no	—
77	C₂×M₁₆×C₁₉	—	2	1	no	—
78	C₂²×C₈×C₁₉	—	2	1	no	—
79	C₁₉×C₄⋊Q₈	—	2	1	no	—
80	C₁₉×C₄⋊Q₈	—	2	1	no	—
81	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
82	C₁₉×C₄⋊Q₈	D₄	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×#127	—	2	1	no	—
87	C₁₉×#127	C₂³	1	1	yes	characteristic
88	C₁₉×#126	—	2	2	no	—
89	C₁₉×#126	—	2	1	no	—
90	C₁₉×#125	—	2	2	no	—
91	C₁₉×#125	—	2	1	no	—
92	C₁₉×#125	—	2	1	no	—
93	C₁₉×#125	—	2	1	no	—
94	C₁₉×#125	D₄	1	1	yes	characteristic
95	C₁₉×#124	—	2	2	no	—
96	C₁₉×#124	—	2	2	no	—
97	C₁₉×#124	—	2	1	no	—
98	C₁₉×#124	—	2	1	no	—
99	C₁₉×#124	—	2	1	no	—
100	C₁₉×#124	D₄	1	1	yes	characteristic
101	C₁₉×#123	—	2	2	no	—
102	C₁₉×#123	—	2	2	no	—
103	C₁₉×#123	—	2	2	no	—
104	C₁₉×#123	—	2	2	no	—
105	C₁₉×#123	—	2	2	no	—
106	C₁₉×#123	—	2	2	no	—
107	C₁₉×#123	—	2	1	no	—
108	C₁₉×C₂²⋊Q₈	—	2	2	no	—
109	C₁₉×C₂²⋊Q₈	—	2	2	no	—
110	C₁₉×C₂²⋊Q₈	—	2	2	no	—
111	C₁₉×C₂²⋊Q₈	—	2	2	no	—
112	C₁₉×C₂²⋊Q₈	—	2	1	no	—
113	C₁₉×C₂²⋊Q₈	—	2	2	no	—
114	C₁₉×C₂²⋊Q₈	—	2	1	no	—
115	C₁₉×C₂²⋊Q₈	—	2	1	no	—
116	C₁₉×C₂²⋊Q₈	—	2	1	no	—
117	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
118	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
119	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
120	C₁₉×#121	—	2	2	no	—
121	C₁₉×#121	—	2	2	no	—
122	C₁₉×#121	—	2	2	no	—
123	C₁₉×#121	—	2	1	no	—
124	C₁₉×#121	—	2	1	no	—
125	C₁₉×#121	D₄	1	2	yes	—
126	C₁₉×#121	D₄	1	1	yes	characteristic
127	C₄×Q₈×C₁₉	—	2	1	no	—
128	C₄×Q₈×C₁₉	—	2	1	no	—
129	C₄×Q₈×C₁₉	—	2	1	no	—
130	C₄×Q₈×C₁₉	—	2	1	no	—
131	C₄×Q₈×C₁₉	—	2	1	no	—
132	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
133	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
134	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
135	C₄×D₄×C₁₉	—	2	2	no	—
136	C₄×D₄×C₁₉	—	2	1	no	—
137	C₄×D₄×C₁₉	—	2	1	no	—
138	C₄×D₄×C₁₉	—	2	1	no	—
139	C₄×D₄×C₁₉	—	2	1	no	—
140	C₄×D₄×C₁₉	—	2	1	no	—
141	C₄×D₄×C₁₉	—	2	1	no	—
142	C₄×D₄×C₁₉	D₄	1	2	yes	—
143	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
144	C₁₉×#117	—	2	1	no	—
145	C₁₉×#117	—	2	1	no	—
146	C₁₉×#117	—	2	1	no	—
147	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
148	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
149	C₁₉×#107	—	2	1	no	—
150	C₁₉×#107	—	2	1	no	—
151	C₁₉×#107	—	2	1	no	—
152	C₁₉×#106	—	2	2	no	—
153	C₁₉×#106	—	2	1	no	—
154	C₁₉×#106	—	2	1	no	—
155	C₁₉×#106	—	2	1	no	—
156	C₁₉×C₄⋊C₈	—	2	1	no	—
157	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
158	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
159	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
160	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
161	C₁₉×#103	—	2	1	no	—
162	C₁₉×#103	—	2	1	no	—
163	C₁₉×#103	—	2	1	no	—
164	C₁₉×#103	—	2	1	no	—
165	C₁₉×#103	—	2	1	no	—
166	C₁₉×#103	—	2	2	no	—
167	C₁₉×#103	—	2	1	no	—
168	C₁₉×#103	—	2	1	no	—
169	C₁₉×#102	—	2	2	no	—
170	C₁₉×#102	—	2	1	no	—
171	C₁₉×C₂²⋊C₈	—	2	1	no	—
172	C₁₉×#97	—	2	1	no	—
173	C₄×C₈×C₁₉	—	2	1	no	—
174	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
175	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
176	#41×C₁₉	—	8	1	no	—
177	#41×C₁₉	—	8	1	no	—
178	#41×C₁₉	—	8	1	no	—
179	#41×C₁₉	—	8	1	no	—
180	C₂×Q₈×C₁₉	—	2	2	no	—
181	C₂×Q₈×C₁₉	—	2	1	no	—
182	C₂×Q₈×C₁₉	—	2	1	no	—
183	C₂×Q₈×C₁₉	—	2	1	no	—
184	C₂×Q₈×C₁₉	—	2	1	no	—
185	C₂×Q₈×C₁₉	—	8	1	no	—
186	C₂×Q₈×C₁₉	—	8	1	no	—
187	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
188	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
190	C₂×D₄×C₁₉	—	2	2	no	—
191	C₂×D₄×C₁₉	—	2	2	no	—
192	C₂×D₄×C₁₉	—	2	1	no	—
193	C₂×D₄×C₁₉	—	2	2	no	—
194	C₂×D₄×C₁₉	—	2	1	no	—
195	C₂×D₄×C₁₉	—	2	1	no	—
196	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
197	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
198	C₂²×C₄×C₁₉	—	2	2	no	—
199	C₂²×C₄×C₁₉	—	2	2	no	—
200	C₂²×C₄×C₁₉	—	2	2	no	—
201	C₂²×C₄×C₁₉	—	2	1	no	—
202	C₂²×C₄×C₁₉	—	2	2	no	—
203	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
206	Q₁₆×C₁₉	—	8	1	no	—
207	SD₁₆×C₁₉	—	4	4	no	—
208	SD₁₆×C₁₉	—	8	1	no	—
209	M₁₆×C₁₉	—	8	1	no	—
210	C₂×C₈×C₁₉	—	2	1	no	—
211	C₂×C₈×C₁₉	—	2	1	no	—
212	C₂×C₈×C₁₉	—	2	1	no	—
213	C₂×C₈×C₁₉	—	2	1	no	—
214	C₂×C₈×C₁₉	—	2	1	no	—
215	C₂×C₈×C₁₉	—	2	1	no	—
216	C₂×C₈×C₁₉	—	4	2	no	—
217	C₄⋊C₄×C₁₉	—	2	2	no	—
218	C₄⋊C₄×C₁₉	—	2	2	no	—
219	C₄⋊C₄×C₁₉	—	2	2	no	—
220	C₄⋊C₄×C₁₉	—	2	2	no	—
221	C₄⋊C₄×C₁₉	—	2	1	no	—
222	C₄⋊C₄×C₁₉	—	2	1	no	—
223	C₄⋊C₄×C₁₉	—	2	1	no	—
224	C₄⋊C₄×C₁₉	—	2	1	no	—
225	C₄⋊C₄×C₁₉	—	2	1	no	—
226	C₄⋊C₄×C₁₉	—	2	1	no	—
227	C₄⋊C₄×C₁₉	—	2	1	no	—
228	C₄⋊C₄×C₁₉	—	2	1	no	—
229	C₄⋊C₄×C₁₉	—	2	1	no	—
230	C₄⋊C₄×C₁₉	—	2	1	no	—
231	C₄⋊C₄×C₁₉	—	2	1	no	—
232	C₄⋊C₄×C₁₉	—	2	1	no	—
233	C₄⋊C₄×C₁₉	—	2	1	no	—
234	C₄⋊C₄×C₁₉	—	2	1	no	—
235	C₄⋊C₄×C₁₉	—	2	1	no	—
236	C₄⋊C₄×C₁₉	—	2	1	no	—
237	C₄⋊C₄×C₁₉	—	4	1	no	—
238	C₄⋊C₄×C₁₉	—	4	1	no	—
239	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
240	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
241	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
242	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
243	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
244	C₂²⋊C₄×C₁₉	—	2	2	no	—
245	C₂²⋊C₄×C₁₉	—	2	2	no	—
246	C₂²⋊C₄×C₁₉	—	2	2	no	—
247	C₂²⋊C₄×C₁₉	—	2	2	no	—
248	C₂²⋊C₄×C₁₉	—	2	2	no	—
249	C₂²⋊C₄×C₁₉	—	2	1	no	—
250	C₂²⋊C₄×C₁₉	—	2	1	no	—
251	C₂²⋊C₄×C₁₉	—	2	1	no	—
252	C₂²⋊C₄×C₁₉	—	2	1	no	—
253	C₂²⋊C₄×C₁₉	—	2	1	no	—
254	C₂²⋊C₄×C₁₉	—	2	1	no	—
255	C₂²⋊C₄×C₁₉	—	2	2	no	—
256	C₂²⋊C₄×C₁₉	—	2	2	no	—
257	C₂²⋊C₄×C₁₉	—	2	1	no	—
258	C₂²⋊C₄×C₁₉	—	4	1	no	—
259	C₄²×C₁₉	—	2	2	no	—
260	C₄²×C₁₉	—	2	1	no	—
261	C₄²×C₁₉	—	2	1	no	—
262	C₄²×C₁₉	—	2	1	no	—
263	C₄²×C₁₉	—	4	1	no	—
264	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
265	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
266	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
267	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
268	#18709	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
269	C₂³×C₁₉	—	2	1	no	—
270	C₂³×C₁₉	—	2	2	no	—
271	C₂³×C₁₉	#120	1	1	yes	characteristic
272	Q₈×C₁₉	—	2	1	no	—
273	Q₈×C₁₉	—	2	1	no	—
274	Q₈×C₁₉	—	2	1	no	—
275	Q₈×C₁₉	—	2	1	no	—
276	Q₈×C₁₉	—	2	1	no	—
277	Q₈×C₁₉	—	2	1	no	—
278	Q₈×C₁₉	—	4	2	no	—
279	Q₈×C₁₉	—	4	1	no	—
280	Q₈×C₁₉	—	4	1	no	—
281	Q₈×C₁₉	—	4	1	no	—
282	Q₈×C₁₉	—	4	1	no	—
283	Q₈×C₁₉	—	8	1	no	—
284	Q₈×C₁₉	—	8	2	no	—
285	D₄×C₁₉	—	2	1	no	—
286	D₄×C₁₉	—	2	1	no	—
287	D₄×C₁₉	—	4	2	no	—
288	D₄×C₁₉	—	4	1	no	—
289	D₄×C₁₉	—	4	1	no	—
290	D₄×C₁₉	—	4	1	no	—
291	D₄×C₁₉	—	4	1	no	—
292	D₄×C₁₉	—	8	1	no	—
293	D₄×C₁₉	—	8	2	no	—
294	D₄×C₁₉	—	8	2	no	—
295	D₄×C₁₉	—	8	2	no	—
296	C₂×C₄×C₁₉	—	2	1	no	—
297	C₂×C₄×C₁₉	—	2	1	no	—
298	C₂×C₄×C₁₉	—	2	1	no	—
299	C₂×C₄×C₁₉	—	2	1	no	—
300	C₂×C₄×C₁₉	—	2	1	no	—
301	C₂×C₄×C₁₉	—	2	1	no	—
302	C₂×C₄×C₁₉	—	2	1	no	—
303	C₂×C₄×C₁₉	—	2	1	no	—
304	C₂×C₄×C₁₉	—	2	1	no	—
305	C₂×C₄×C₁₉	—	2	2	no	—
306	C₂×C₄×C₁₉	—	2	1	no	—
307	C₂×C₄×C₁₉	—	2	1	no	—
308	C₂×C₄×C₁₉	—	4	1	no	—
309	C₂×C₄×C₁₉	—	4	1	no	—
310	C₂×C₄×C₁₉	—	4	1	no	—
311	C₂×C₄×C₁₉	—	4	1	no	—
312	C₂×C₄×C₁₉	—	4	1	no	—
313	C₂×C₄×C₁₉	—	8	2	no	—
314	C₂×C₄×C₁₉	—	8	2	no	—
315	C₂×C₄×C₁₉	—	8	2	no	—
316	C₂×C₄×C₁₉	—	8	2	no	—
317	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
318	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
319	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
320	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
322	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
323	C₈×C₁₉	—	2	2	no	—
324	C₈×C₁₉	—	4	1	no	—
325	C₈×C₁₉	—	4	1	no	—
326	C₈×C₁₉	—	4	1	no	—
327	C₈×C₁₉	—	4	1	no	—
328	C₈×C₁₉	—	4	1	no	—
329	#3554	C₂×C₁₉	1	1	yes	characteristic
330	#3252	C₂×C₁₉	1	1	yes	characteristic, complemented
331	#3237	C₂×C₁₉	1	1	yes	characteristic, complemented
332	#3167	C₂×C₁₉	1	1	yes	characteristic, complemented
333	#1653	C₂×C₁₉	1	1	yes	characteristic, complemented
334	#1651	C₂×C₁₉	1	1	yes	characteristic, complemented
335	#1642	C₂×C₁₉	1	1	yes	characteristic, complemented
336	#1640	C₂×C₁₉	1	1	yes	characteristic, complemented
337	#1637	C₂×C₁₉	1	1	yes	characteristic, complemented
338	#1636	C₂×C₁₉	1	1	yes	characteristic, complemented
339	#1631	C₂×C₁₉	1	1	yes	characteristic, complemented
340	#1630	C₂×C₁₉	1	1	yes	characteristic, complemented
341	#1557	C₂×C₁₉	1	1	yes	characteristic, complemented
342	#1494	C₂×C₁₉	1	1	yes	characteristic, complemented
343	#1493	C₂×C₁₉	1	1	yes	characteristic, complemented
344	C₂²×C₁₉	—	2	1	no	—
345	C₂²×C₁₉	—	2	1	no	—
346	C₂²×C₁₉	—	2	1	no	—
347	C₂²×C₁₉	—	4	1	no	—
348	C₂²×C₁₉	—	4	2	no	—
349	C₂²×C₁₉	—	4	1	no	—
350	C₂²×C₁₉	—	4	2	no	—
351	C₂²×C₁₉	—	4	2	no	—
352	C₂²×C₁₉	—	4	1	no	—
353	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
354	C₄×C₁₉	—	2	1	no	—
355	C₄×C₁₉	—	2	1	no	—
356	C₄×C₁₉	—	2	1	no	—
357	C₄×C₁₉	—	2	1	no	—
358	C₄×C₁₉	—	4	1	no	—
359	C₄×C₁₉	—	4	1	no	—
360	C₄×C₁₉	—	4	2	no	—
361	C₄×C₁₉	—	4	1	no	—
362	C₄×C₁₉	—	4	1	no	—
363	C₄×C₁₉	—	4	1	no	—
364	C₄×C₁₉	—	4	1	no	—
365	C₄×C₁₉	—	4	1	no	—
366	C₄×C₁₉	—	8	1	no	—
367	C₄×C₁₉	—	8	1	no	—
368	C₄×C₁₉	#577	1	1	yes	characteristic
369	C₄×C₁₉	#577	1	1	yes	characteristic
370	C₄×C₁₉	#577	1	1	yes	characteristic
371	C₄×C₁₉	#578	1	1	yes	characteristic
372	#562	—	2	2	no	—
373	#559	—	2	1	no	—
374	#559	C₂²×C₁₉	1	1	yes	characteristic
375	#557	C₂²×C₁₉	1	1	yes	characteristic
376	#554	—	2	1	no	—
377	#550	C₂²×C₁₉	1	1	yes	characteristic
378	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
379	#548	—	2	1	no	—
380	#547	—	2	1	no	—
381	#542	—	2	1	no	—
382	#542	—	2	1	no	—
383	#540	—	2	1	no	—
384	#539	—	2	2	no	—
385	#536	—	2	1	no	—
386	#533	C₂²×C₁₉	1	1	yes	characteristic
387	#533	C₂²×C₁₉	1	1	yes	characteristic
388	#532	C₂²×C₁₉	1	1	yes	characteristic
389	#529	C₂²×C₁₉	1	1	yes	characteristic
390	#501	—	2	1	no	—
391	#498	C₂²×C₁₉	1	1	yes	characteristic
392	#492	C₂²×C₁₉	1	1	yes	characteristic
393	#491	—	2	1	no	—
394	#487	C₂²×C₁₉	1	1	yes	characteristic
395	#486	C₂²×C₁₉	1	1	yes	characteristic
396	#485	—	2	1	no	—
397	#485	—	2	1	no	—
398	#479	—	2	1	no	—
399	#477	C₂²×C₁₉	1	1	yes	characteristic
400	#477	C₂²×C₁₉	1	1	yes	characteristic
401	#477	C₂²×C₁₉	1	1	yes	characteristic
402	#476	C₂²×C₁₉	1	1	yes	characteristic
403	#475	C₂²×C₁₉	1	1	yes	characteristic
404	#475	C₂²×C₁₉	1	1	yes	characteristic
405	#470	—	2	1	no	—
406	#468	—	2	1	no	—
407	#465	—	2	2	no	—
408	#464	—	2	1	no	—
409	#462	C₂²×C₁₉	1	1	yes	characteristic
410	#461	C₂²×C₁₉	1	1	yes	characteristic
411	C₄×SD₁₆	—	2	2	no	—
412	#432	C₂²×C₁₉	1	1	yes	characteristic
413	#423	C₂²×C₁₉	1	1	yes	characteristic
414	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
415	#332	C₂²×C₁₉	1	1	yes	characteristic
416	#332	C₂²×C₁₉	1	1	yes	characteristic
417	#331	C₂²×C₁₉	1	1	yes	characteristic
418	#331	C₂²×C₁₉	1	1	yes	characteristic
419	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
420	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
421	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
422	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
423	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
424	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
425	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
426	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
427	C₂×C₁₉	—	4	1	no	—
428	C₂×C₁₉	—	8	1	no	—
429	C₂×C₁₉	—	8	2	no	—
430	C₂×C₁₉	#3009	1	1	yes	characteristic
431	C₂×C₁₉	#3013	1	1	yes	characteristic
432	C₂×C₁₉	#3018	1	1	yes	characteristic
433	C₂×#41	—	2	1	no	—
434	C₂×#41	—	2	1	no	—
435	C₂²×Q₈	—	2	1	no	—
436	C₂×Q₁₆	—	2	1	no	—
437	C₂×SD₁₆	—	2	2	no	—
438	C₂×SD₁₆	—	2	1	no	—
439	C₂×M₁₆	—	2	1	no	—
440	C₂²×C₈	—	2	1	no	—
441	C₄⋊Q₈	—	2	1	no	—
442	C₄⋊Q₈	—	2	1	no	—
443	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
444	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
445	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
446	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
447	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
448	#127	—	2	1	no	—
449	#127	C₂³×C₁₉	1	1	yes	characteristic
450	#126	—	2	2	no	—
451	#126	—	2	1	no	—
452	#125	—	2	2	no	—
453	#125	—	2	1	no	—
454	#125	—	2	1	no	—
455	#125	—	2	1	no	—
456	#125	D₄×C₁₉	1	1	yes	characteristic
457	#124	—	2	2	no	—
458	#124	—	2	2	no	—
459	#124	—	2	1	no	—
460	#124	—	2	1	no	—
461	#124	—	2	1	no	—
462	#124	D₄×C₁₉	1	1	yes	characteristic
463	#123	—	2	2	no	—
464	#123	—	2	2	no	—
465	#123	—	2	2	no	—
466	#123	—	2	2	no	—
467	#123	—	2	2	no	—
468	#123	—	2	2	no	—
469	#123	—	2	1	no	—
470	C₂²⋊Q₈	—	2	2	no	—
471	C₂²⋊Q₈	—	2	2	no	—
472	C₂²⋊Q₈	—	2	2	no	—
473	C₂²⋊Q₈	—	2	2	no	—
474	C₂²⋊Q₈	—	2	1	no	—
475	C₂²⋊Q₈	—	2	2	no	—
476	C₂²⋊Q₈	—	2	1	no	—
477	C₂²⋊Q₈	—	2	1	no	—
478	C₂²⋊Q₈	—	2	1	no	—
479	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
480	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
481	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
482	#121	—	2	2	no	—
483	#121	—	2	2	no	—
484	#121	—	2	2	no	—
485	#121	—	2	1	no	—
486	#121	—	2	1	no	—
487	#121	D₄×C₁₉	1	1	yes	characteristic
488	#121	D₄×C₁₉	1	2	yes	—
489	C₄×Q₈	—	2	1	no	—
490	C₄×Q₈	—	2	1	no	—
491	C₄×Q₈	—	2	1	no	—
492	C₄×Q₈	—	2	1	no	—
493	C₄×Q₈	—	2	1	no	—
494	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
495	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
496	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
497	C₄×D₄	—	2	2	no	—
498	C₄×D₄	—	2	1	no	—
499	C₄×D₄	—	2	1	no	—
500	C₄×D₄	—	2	1	no	—
501	C₄×D₄	—	2	1	no	—
502	C₄×D₄	—	2	1	no	—
503	C₄×D₄	—	2	1	no	—
504	C₄×D₄	D₄×C₁₉	1	2	yes	—
505	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
506	#117	—	2	1	no	—
507	#117	—	2	1	no	—
508	#117	—	2	1	no	—
509	C₂×C₄⋊C₄	—	2	2	no	—
510	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
511	#107	—	2	1	no	—
512	#107	—	2	1	no	—
513	#107	—	2	1	no	—
514	#106	—	2	2	no	—
515	#106	—	2	1	no	—
516	#106	—	2	1	no	—
517	#106	—	2	1	no	—
518	C₄⋊C₈	—	2	1	no	—
519	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
520	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
521	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
522	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
523	#103	—	2	1	no	—
524	#103	—	2	1	no	—
525	#103	—	2	1	no	—
526	#103	—	2	1	no	—
527	#103	—	2	1	no	—
528	#103	—	2	2	no	—
529	#103	—	2	1	no	—
530	#103	—	2	1	no	—
531	#102	—	2	2	no	—
532	#102	—	2	1	no	—
533	C₂²⋊C₈	—	2	1	no	—
534	#97	—	2	1	no	—
535	C₄×C₈	—	2	1	no	—
536	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
537	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
538	C₁₉	#18709	1	1	yes	characteristic, direct product factor, Sylow
539	#41	—	8	1	no	—
540	#41	—	8	1	no	—
541	#41	—	8	1	no	—
542	#41	—	8	1	no	—
543	C₂×Q₈	—	2	2	no	—
544	C₂×Q₈	—	2	1	no	—
545	C₂×Q₈	—	2	1	no	—
546	C₂×Q₈	—	2	1	no	—
547	C₂×Q₈	—	2	1	no	—
548	C₂×Q₈	—	8	1	no	—
549	C₂×Q₈	—	8	1	no	—
550	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
551	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
552	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
553	C₂×D₄	—	2	2	no	—
554	C₂×D₄	—	2	2	no	—
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	—	2	2	no	—
557	C₂×D₄	—	2	1	no	—
558	C₂×D₄	—	2	1	no	—
559	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
560	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
567	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
568	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
569	Q₁₆	—	8	1	no	—
570	SD₁₆	—	4	4	no	—
571	SD₁₆	—	8	1	no	—
572	M₁₆	—	8	1	no	—
573	C₂×C₈	—	2	1	no	—
574	C₂×C₈	—	2	1	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	—	2	1	no	—
577	C₂×C₈	—	2	1	no	—
578	C₂×C₈	—	2	1	no	—
579	C₂×C₈	—	4	2	no	—
580	C₄⋊C₄	—	2	2	no	—
581	C₄⋊C₄	—	2	2	no	—
582	C₄⋊C₄	—	2	2	no	—
583	C₄⋊C₄	—	2	2	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	2	1	no	—
593	C₄⋊C₄	—	2	1	no	—
594	C₄⋊C₄	—	2	1	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	2	1	no	—
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	2	1	no	—
600	C₄⋊C₄	—	4	1	no	—
601	C₄⋊C₄	—	4	1	no	—
602	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
603	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
604	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
605	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
606	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
607	C₂²⋊C₄	—	2	2	no	—
608	C₂²⋊C₄	—	2	2	no	—
609	C₂²⋊C₄	—	2	2	no	—
610	C₂²⋊C₄	—	2	2	no	—
611	C₂²⋊C₄	—	2	2	no	—
612	C₂²⋊C₄	—	2	1	no	—
613	C₂²⋊C₄	—	2	1	no	—
614	C₂²⋊C₄	—	2	1	no	—
615	C₂²⋊C₄	—	2	1	no	—
616	C₂²⋊C₄	—	2	1	no	—
617	C₂²⋊C₄	—	2	1	no	—
618	C₂²⋊C₄	—	2	2	no	—
619	C₂²⋊C₄	—	2	2	no	—
620	C₂²⋊C₄	—	2	1	no	—
621	C₂²⋊C₄	—	4	1	no	—
622	C₄²	—	2	2	no	—
623	C₄²	—	2	1	no	—
624	C₄²	—	2	1	no	—
625	C₄²	—	2	1	no	—
626	C₄²	—	4	1	no	—
627	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
628	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
629	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
630	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
631	C₂³	—	2	1	no	—
632	C₂³	—	2	2	no	—
633	C₂³	C₁₉×#120	1	1	yes	characteristic
634	Q₈	—	2	1	no	—
635	Q₈	—	2	1	no	—
636	Q₈	—	2	1	no	—
637	Q₈	—	2	1	no	—
638	Q₈	—	2	1	no	—
639	Q₈	—	2	1	no	—
640	Q₈	—	4	2	no	—
641	Q₈	—	4	1	no	—
642	Q₈	—	4	1	no	—
643	Q₈	—	4	1	no	—
644	Q₈	—	4	1	no	—
645	Q₈	—	8	1	no	—
646	Q₈	—	8	2	no	—
647	D₄	—	2	1	no	—
648	D₄	—	2	1	no	—
649	D₄	—	4	2	no	—
650	D₄	—	4	1	no	—
651	D₄	—	4	1	no	—
652	D₄	—	4	1	no	—
653	D₄	—	4	1	no	—
654	D₄	—	8	2	no	—
655	D₄	—	8	1	no	—
656	D₄	—	8	2	no	—
657	D₄	—	8	2	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	8	2	no	—
676	C₂×C₄	—	8	2	no	—
677	C₂×C₄	—	8	2	no	—
678	C₂×C₄	—	8	2	no	—
679	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
680	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
681	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
682	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
683	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
684	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
685	C₈	—	2	2	no	—
686	C₈	—	4	1	no	—
687	C₈	—	4	1	no	—
688	C₈	—	4	1	no	—
689	C₈	—	4	1	no	—
690	C₈	—	4	1	no	—
691	C₂²	—	2	1	no	—
692	C₂²	—	2	1	no	—
693	C₂²	—	2	1	no	—
694	C₂²	—	4	1	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	4	1	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	1	no	—
700	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
701	C₄	—	2	1	no	—
702	C₄	—	2	1	no	—
703	C₄	—	2	1	no	—
704	C₄	—	2	1	no	—
705	C₄	—	4	1	no	—
706	C₄	—	4	1	no	—
707	C₄	—	4	2	no	—
708	C₄	—	4	1	no	—
709	C₄	—	4	1	no	—
710	C₄	—	4	1	no	—
711	C₄	—	4	1	no	—
712	C₄	—	4	1	no	—
713	C₄	—	8	1	no	—
714	C₄	—	8	1	no	—
715	C₄	C₁₉×#577	1	1	yes	characteristic
716	C₄	C₁₉×#577	1	1	yes	characteristic
717	C₄	C₁₉×#577	1	1	yes	characteristic
718	C₄	C₁₉×#578	1	1	yes	characteristic
719	C₂	—	4	1	no	—
720	C₂	—	8	1	no	—
721	C₂	—	8	2	no	—
722	C₂	C₁₉×#3009	1	1	yes	characteristic
723	C₂	C₁₉×#3013	1	1	yes	characteristic
724	C₂	C₁₉×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3554	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
2. C₁₉×#3252	C₂	semidirect
3. C₁₉×#3237	C₂	semidirect
4. C₁₉×#3167	C₂	semidirect
5. C₁₉×#1653	C₂	semidirect
6. C₁₉×#1651	C₂	semidirect
7. C₁₉×#1642	C₂	semidirect
8. C₁₉×#1640	C₂	semidirect
9. C₁₉×#1637	C₂	semidirect
10. C₁₉×#1636	C₂	semidirect
11. C₁₉×#1631	C₂	semidirect
12. C₁₉×#1630	C₂	semidirect
13. C₁₉×#1557	C₂	semidirect
14. C₁₉×#1494	C₂	semidirect
15. C₁₉×#1493	C₂	semidirect
268. #18709	C₁₉	direct (N × H)
330. #3252	C₂×C₁₉	semidirect
331. #3237	C₂×C₁₉	semidirect
332. #3167	C₂×C₁₉	semidirect
333. #1653	C₂×C₁₉	semidirect
334. #1651	C₂×C₁₉	semidirect
335. #1642	C₂×C₁₉	semidirect
336. #1640	C₂×C₁₉	semidirect
337. #1637	C₂×C₁₉	semidirect
338. #1636	C₂×C₁₉	semidirect
339. #1631	C₂×C₁₉	semidirect
340. #1630	C₂×C₁₉	semidirect
341. #1557	C₂×C₁₉	semidirect
342. #1494	C₂×C₁₉	semidirect
343. #1493	C₂×C₁₉	semidirect
538. C₁₉	#18709	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×#3554	2
C₁₉×#3252	2
C₁₉×#3237	2
C₁₉×#3167	2
C₁₉×#1653	2
C₁₉×#1651	2
C₁₉×#1642	2
C₁₉×#1640	2
C₁₉×#1637	2
C₁₉×#1636	2
C₁₉×#1631	2
C₁₉×#1630	2
C₁₉×#1557	2
C₁₉×#1494	2
C₁₉×#1493	2
#18709	19

Subgroups — C19×#18709 #18024668

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18709 #18024668