Subgroups — C₁₉×#19000 #18024959

Order 4864.

896 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3529	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3238	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3218	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3141	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1664	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1662	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1661	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1659	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1536	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1529	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1529	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#563	—	2	1	no	—
13	C₁₉×#563	C₂²	1	1	yes	characteristic
14	C₁₉×#562	—	2	1	no	—
15	C₁₉×#562	—	2	1	no	—
16	C₁₉×#562	C₂²	1	1	yes	characteristic
17	C₁₉×#562	C₂²	1	1	yes	characteristic
18	C₁₉×H(3,𝔽₄)	C₂²	1	1	yes	characteristic
19	C₁₉×#560	—	2	1	no	—
20	C₁₉×#560	—	2	1	no	—
21	C₁₉×#560	—	2	1	no	—
22	C₁₉×#532	—	2	1	no	—
23	C₁₉×#532	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₁₉×#529	—	2	1	no	—
26	C₁₉×#529	—	2	1	no	—
27	C₁₉×#529	C₂²	1	1	yes	characteristic
28	C₁₉×#529	C₂²	1	1	yes	characteristic
29	C₁₉×#525	—	2	1	no	—
30	C₁₉×#525	—	2	1	no	—
31	C₁₉×#525	—	2	1	no	—
32	C₁₉×#501	C₂²	1	2	yes	complemented
33	C₁₉×#497	C₂²	1	2	yes	—
34	C₁₉×#491	C₂²	1	2	yes	complemented
35	C₁₉×#489	C₂²	1	2	yes	—
36	C₁₉×#489	C₂²	1	2	yes	—
37	C₁₉×#489	C₂²	1	2	yes	complemented
38	C₁₉×#487	—	2	1	no	—
39	C₁₉×#486	—	2	1	no	—
40	C₁₉×#483	—	2	1	no	—
41	C₁₉×#480	—	2	1	no	—
42	C₁₉×#477	—	2	1	no	—
43	C₁₉×#476	—	2	1	no	—
44	C₁₉×#462	—	2	1	no	—
45	C₁₉×#461	—	2	1	no	—
46	C₁₉×#451	—	2	1	no	—
47	C₁₉×#448	—	2	1	no	—
48	C₁₉×#432	C₂²	1	1	yes	characteristic, complemented
49	C₁₉×#432	C₂²	1	1	yes	characteristic, complemented
50	C₁₉×#417	—	2	1	no	—
51	C₁₉×#417	—	2	1	no	—
52	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
53	C₁₉×#330	C₂²	1	2	yes	complemented
54	C₁₉×#330	C₂²	1	2	yes	complemented
55	C₁₉×#329	C₂²	1	2	yes	—
56	C₁₉×#329	C₂²	1	2	yes	—
57	C₁₉×#329	C₂²	1	2	yes	—
58	C₁₉×#329	C₂²	1	2	yes	complemented
59	C₂×#41×C₁₉	—	2	1	no	—
60	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
61	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
62	C₂²×Q₈×C₁₉	—	2	1	no	—
63	C₂³×C₄×C₁₉	—	2	1	no	—
64	C₂×Q₁₆×C₁₉	—	2	2	no	—
65	C₂×SD₁₆×C₁₉	—	2	2	no	—
66	C₂×M₁₆×C₁₉	—	2	1	no	—
67	C₁₉×C₄⋊Q₈	—	2	1	no	—
68	C₁₉×C₄⋊Q₈	—	2	1	no	—
69	C₁₉×C₄⋊Q₈	—	2	1	no	—
70	C₁₉×C₄⋊Q₈	—	2	1	no	—
71	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
72	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
73	C₁₉×#127	—	2	1	no	—
74	C₁₉×#127	D₄	1	1	yes	characteristic
75	C₁₉×#126	—	2	1	no	—
76	C₁₉×#126	—	2	1	no	—
77	C₁₉×#126	—	2	1	no	—
78	C₁₉×#126	—	2	1	no	—
79	C₁₉×#126	—	2	1	no	—
80	C₁₉×#126	—	2	1	no	—
81	C₁₉×#125	—	2	1	no	—
82	C₁₉×#125	—	2	1	no	—
83	C₁₉×#125	C₂³	1	1	yes	characteristic
84	C₁₉×#125	C₂³	1	1	yes	characteristic
85	C₁₉×#124	—	2	1	no	—
86	C₁₉×#124	—	2	1	no	—
87	C₁₉×#124	—	2	1	no	—
88	C₁₉×#124	—	2	1	no	—
89	C₁₉×#124	C₂³	1	1	yes	characteristic
90	C₁₉×#124	C₂³	1	1	yes	characteristic
91	C₁₉×#124	C₂³	1	1	yes	characteristic
92	C₁₉×#124	C₂³	1	1	yes	characteristic
93	C₁₉×#123	—	2	1	no	—
94	C₁₉×#123	—	2	1	no	—
95	C₁₉×#123	—	2	1	no	—
96	C₁₉×#123	—	2	1	no	—
97	C₁₉×#123	—	2	1	no	—
98	C₁₉×#123	—	2	1	no	—
99	C₁₉×#123	—	2	1	no	—
100	C₁₉×#123	—	2	1	no	—
101	C₁₉×#123	—	2	1	no	—
102	C₁₉×#123	—	2	1	no	—
103	C₁₉×#123	—	2	1	no	—
104	C₁₉×#123	—	2	1	no	—
105	C₁₉×C₂²⋊Q₈	—	2	1	no	—
106	C₁₉×C₂²⋊Q₈	—	2	1	no	—
107	C₁₉×C₂²⋊Q₈	—	2	1	no	—
108	C₁₉×C₂²⋊Q₈	—	2	1	no	—
109	C₁₉×C₂²⋊Q₈	—	2	1	no	—
110	C₁₉×C₂²⋊Q₈	—	2	1	no	—
111	C₁₉×C₂²⋊Q₈	—	2	1	no	—
112	C₁₉×C₂²⋊Q₈	—	2	1	no	—
113	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
114	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
115	C₁₉×#121	—	2	1	no	—
116	C₁₉×#121	—	2	1	no	—
117	C₁₉×#121	—	2	1	no	—
118	C₁₉×#121	—	2	1	no	—
119	C₁₉×#121	—	2	1	no	—
120	C₁₉×#121	—	2	1	no	—
121	C₁₉×#121	—	2	1	no	—
122	C₁₉×#121	—	2	1	no	—
123	C₁₉×#121	—	2	1	no	—
124	C₁₉×#121	—	2	1	no	—
125	C₁₉×#121	—	2	1	no	—
126	C₁₉×#121	—	2	1	no	—
127	C₁₉×#121	—	2	1	no	—
128	C₁₉×#121	—	2	1	no	—
129	C₁₉×#121	D₄	1	1	yes	characteristic
130	C₁₉×#121	D₄	1	1	yes	characteristic
131	C₁₉×#120	—	2	1	no	—
132	C₁₉×#120	—	2	1	no	—
133	C₁₉×#120	—	2	1	no	—
134	C₁₉×#120	—	2	1	no	—
135	C₁₉×#120	—	2	1	no	—
136	C₁₉×#120	—	2	1	no	—
137	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
138	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
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	—	2	1	no	—
143	C₄×D₄×C₁₉	—	2	1	no	—
144	C₄×D₄×C₁₉	—	2	1	no	—
145	C₄×D₄×C₁₉	—	2	1	no	—
146	C₄×D₄×C₁₉	—	2	1	no	—
147	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
148	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
149	C₁₉×#117	—	2	1	no	—
150	C₁₉×#117	—	2	1	no	—
151	C₁₉×#117	—	2	1	no	—
152	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
153	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
154	C₂×C₄²×C₁₉	—	2	1	no	—
155	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
156	C₁₉×#107	—	2	2	no	—
157	C₁₉×#106	—	2	2	no	—
158	C₁₉×C₄⋊C₈	—	2	1	no	—
159	C₁₉×C₄⋊C₈	—	2	1	no	—
160	C₁₉×#103	—	2	2	no	—
161	C₁₉×#103	—	2	2	no	—
162	C₁₉×#103	—	2	2	no	—
163	C₁₉×#103	—	2	2	no	—
164	C₁₉×#103	—	2	2	no	—
165	C₁₉×#102	—	2	2	no	—
166	C₁₉×#102	—	2	2	no	—
167	C₁₉×#102	—	2	2	no	—
168	C₁₉×C₂²⋊C₈	—	2	1	no	—
169	C₁₉×C₂²⋊C₈	—	2	1	no	—
170	C₁₉×#97	C₂³	1	2	yes	—
171	C₁₉×#97	C₂³	1	2	yes	—
172	C₁₉×#97	C₂³	1	2	yes	—
173	C₄×C₈×C₁₉	—	2	1	no	—
174	C₂⁴×C₁₉	—	2	1	no	—
175	#41×C₁₉	—	4	2	no	—
176	#41×C₁₉	—	4	2	no	—
177	#41×C₁₉	—	8	2	no	—
178	C₂×Q₈×C₁₉	—	2	1	no	—
179	C₂×Q₈×C₁₉	—	2	2	no	—
180	C₂×Q₈×C₁₉	—	4	1	no	—
181	C₂×Q₈×C₁₉	—	8	2	no	—
182	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
183	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
184	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
185	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
186	C₂×D₄×C₁₉	—	2	1	no	—
187	C₂×D₄×C₁₉	—	2	1	no	—
188	C₂×D₄×C₁₉	—	2	1	no	—
189	C₂×D₄×C₁₉	—	2	1	no	—
190	C₂×D₄×C₁₉	—	2	1	no	—
191	C₂×D₄×C₁₉	—	2	1	no	—
192	C₂×D₄×C₁₉	—	2	1	no	—
193	C₂×D₄×C₁₉	—	2	1	no	—
194	C₂×D₄×C₁₉	—	2	1	no	—
195	C₂×D₄×C₁₉	—	2	1	no	—
196	C₂×D₄×C₁₉	—	2	1	no	—
197	C₂×D₄×C₁₉	—	2	1	no	—
198	C₂×D₄×C₁₉	—	2	1	no	—
199	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
200	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
201	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
202	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
207	C₂²×C₄×C₁₉	—	2	1	no	—
208	C₂²×C₄×C₁₉	—	2	1	no	—
209	C₂²×C₄×C₁₉	—	2	1	no	—
210	C₂²×C₄×C₁₉	—	2	1	no	—
211	C₂²×C₄×C₁₉	—	2	1	no	—
212	C₂²×C₄×C₁₉	—	4	1	no	—
213	C₂²×C₄×C₁₉	—	8	2	no	—
214	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
217	Q₁₆×C₁₉	—	8	2	no	—
218	SD₁₆×C₁₉	—	8	2	no	—
219	M₁₆×C₁₉	—	4	2	no	—
220	C₂×C₈×C₁₉	—	2	2	no	—
221	C₂×C₈×C₁₉	—	2	2	no	—
222	C₂×C₈×C₁₉	—	2	2	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	—	2	1	no	—
238	C₄⋊C₄×C₁₉	—	2	1	no	—
239	C₄⋊C₄×C₁₉	—	2	2	no	—
240	C₄⋊C₄×C₁₉	—	2	2	no	—
241	C₄⋊C₄×C₁₉	—	4	1	no	—
242	C₄⋊C₄×C₁₉	—	4	1	no	—
243	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
244	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
245	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
246	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
247	C₂²⋊C₄×C₁₉	—	2	1	no	—
248	C₂²⋊C₄×C₁₉	—	2	1	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	1	no	—
256	C₂²⋊C₄×C₁₉	—	2	1	no	—
257	C₂²⋊C₄×C₁₉	—	2	1	no	—
258	C₂²⋊C₄×C₁₉	—	2	1	no	—
259	C₂²⋊C₄×C₁₉	—	2	1	no	—
260	C₂²⋊C₄×C₁₉	—	2	1	no	—
261	C₂²⋊C₄×C₁₉	—	2	1	no	—
262	C₂²⋊C₄×C₁₉	—	2	1	no	—
263	C₂²⋊C₄×C₁₉	—	2	1	no	—
264	C₂²⋊C₄×C₁₉	—	2	1	no	—
265	C₂²⋊C₄×C₁₉	—	2	1	no	—
266	C₂²⋊C₄×C₁₉	—	2	1	no	—
267	C₂²⋊C₄×C₁₉	—	2	1	no	—
268	C₂²⋊C₄×C₁₉	—	2	1	no	—
269	C₂²⋊C₄×C₁₉	—	2	1	no	—
270	C₂²⋊C₄×C₁₉	—	2	1	no	—
271	C₄²×C₁₉	—	2	1	no	—
272	C₄²×C₁₉	—	2	1	no	—
273	C₄²×C₁₉	—	2	1	no	—
274	C₄²×C₁₉	—	2	1	no	—
275	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
276	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
277	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
278	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
279	#19000	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
280	C₂³×C₁₉	—	2	1	no	—
281	C₂³×C₁₉	—	2	1	no	—
282	C₂³×C₁₉	—	2	1	no	—
283	C₂³×C₁₉	—	2	1	no	—
284	C₂³×C₁₉	—	8	1	no	—
285	C₂³×C₁₉	—	8	1	no	—
286	C₂³×C₁₉	—	8	1	no	—
287	C₂³×C₁₉	#120	1	1	yes	characteristic
288	Q₈×C₁₉	—	4	1	no	—
289	Q₈×C₁₉	—	4	1	no	—
290	Q₈×C₁₉	—	4	1	no	—
291	Q₈×C₁₉	—	4	1	no	—
292	Q₈×C₁₉	—	4	2	no	—
293	Q₈×C₁₉	—	4	2	no	—
294	Q₈×C₁₉	—	8	2	no	—
295	Q₈×C₁₉	—	8	1	no	—
296	D₄×C₁₉	—	4	1	no	—
297	D₄×C₁₉	—	4	1	no	—
298	D₄×C₁₉	—	4	1	no	—
299	D₄×C₁₉	—	4	1	no	—
300	D₄×C₁₉	—	8	1	no	—
301	D₄×C₁₉	—	8	1	no	—
302	D₄×C₁₉	—	8	1	no	—
303	D₄×C₁₉	—	8	1	no	—
304	D₄×C₁₉	—	8	1	no	—
305	D₄×C₁₉	—	8	1	no	—
306	D₄×C₁₉	—	8	1	no	—
307	D₄×C₁₉	—	8	1	no	—
308	D₄×C₁₉	—	8	1	no	—
309	D₄×C₁₉	—	8	1	no	—
310	D₄×C₁₉	—	8	1	no	—
311	D₄×C₁₉	—	8	1	no	—
312	D₄×C₁₉	—	8	1	no	—
313	C₂×C₄×C₁₉	—	2	2	no	—
314	C₂×C₄×C₁₉	—	2	1	no	—
315	C₂×C₄×C₁₉	—	2	1	no	—
316	C₂×C₄×C₁₉	—	2	1	no	—
317	C₂×C₄×C₁₉	—	2	1	no	—
318	C₂×C₄×C₁₉	—	2	1	no	—
319	C₂×C₄×C₁₉	—	2	1	no	—
320	C₂×C₄×C₁₉	—	2	1	no	—
321	C₂×C₄×C₁₉	—	2	1	no	—
322	C₂×C₄×C₁₉	—	4	1	no	—
323	C₂×C₄×C₁₉	—	4	1	no	—
324	C₂×C₄×C₁₉	—	4	2	no	—
325	C₂×C₄×C₁₉	—	4	2	no	—
326	C₂×C₄×C₁₉	—	4	2	no	—
327	C₂×C₄×C₁₉	—	4	2	no	—
328	C₂×C₄×C₁₉	—	4	2	no	—
329	C₂×C₄×C₁₉	—	8	1	no	—
330	C₂×C₄×C₁₉	—	8	1	no	—
331	C₂×C₄×C₁₉	—	8	1	no	—
332	C₂×C₄×C₁₉	—	8	1	no	—
333	C₂×C₄×C₁₉	—	8	1	no	—
334	C₂×C₄×C₁₉	—	8	2	no	—
335	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
336	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
337	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
338	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
341	C₈×C₁₉	—	4	2	no	—
342	C₈×C₁₉	—	4	2	no	—
343	C₈×C₁₉	—	4	2	no	—
344	#3529	C₂×C₁₉	1	1	yes	characteristic
345	#3238	C₂×C₁₉	1	1	yes	characteristic, complemented
346	#3218	C₂×C₁₉	1	1	yes	characteristic, complemented
347	#3141	C₂×C₁₉	1	1	yes	characteristic, complemented
348	#1664	C₂×C₁₉	1	2	yes	complemented
349	#1662	C₂×C₁₉	1	2	yes	complemented
350	#1661	C₂×C₁₉	1	2	yes	complemented
351	#1659	C₂×C₁₉	1	2	yes	complemented
352	#1536	C₂×C₁₉	1	1	yes	characteristic, complemented
353	#1529	C₂×C₁₉	1	1	yes	characteristic, complemented
354	#1529	C₂×C₁₉	1	1	yes	characteristic, complemented
355	C₂²×C₁₉	—	2	1	no	—
356	C₂²×C₁₉	—	2	1	no	—
357	C₂²×C₁₉	—	2	1	no	—
358	C₂²×C₁₉	—	4	1	no	—
359	C₂²×C₁₉	—	4	1	no	—
360	C₂²×C₁₉	—	4	1	no	—
361	C₂²×C₁₉	—	4	1	no	—
362	C₂²×C₁₉	—	4	1	no	—
363	C₂²×C₁₉	—	4	1	no	—
364	C₂²×C₁₉	—	4	1	no	—
365	C₂²×C₁₉	—	4	1	no	—
366	C₂²×C₁₉	—	4	1	no	—
367	C₂²×C₁₉	—	4	1	no	—
368	C₂²×C₁₉	—	4	1	no	—
369	C₂²×C₁₉	—	4	1	no	—
370	C₂²×C₁₉	—	8	4	no	—
371	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
372	C₄×C₁₉	—	2	1	no	—
373	C₄×C₁₉	—	2	1	no	—
374	C₄×C₁₉	—	2	1	no	—
375	C₄×C₁₉	—	2	1	no	—
376	C₄×C₁₉	—	2	1	no	—
377	C₄×C₁₉	—	4	1	no	—
378	C₄×C₁₉	—	4	1	no	—
379	C₄×C₁₉	—	4	1	no	—
380	C₄×C₁₉	—	4	1	no	—
381	C₄×C₁₉	—	4	1	no	—
382	C₄×C₁₉	—	4	1	no	—
383	C₄×C₁₉	—	4	1	no	—
384	C₄×C₁₉	—	4	1	no	—
385	C₄×C₁₉	—	8	2	no	—
386	C₄×C₁₉	#455	1	2	yes	—
387	#563	—	2	1	no	—
388	#563	C₂²×C₁₉	1	1	yes	characteristic
389	#562	—	2	1	no	—
390	#562	—	2	1	no	—
391	#562	C₂²×C₁₉	1	1	yes	characteristic
392	#562	C₂²×C₁₉	1	1	yes	characteristic
393	H(3,𝔽₄)	C₂²×C₁₉	1	1	yes	characteristic
394	#560	—	2	1	no	—
395	#560	—	2	1	no	—
396	#560	—	2	1	no	—
397	#532	—	2	1	no	—
398	#532	C₂²×C₁₉	1	1	yes	characteristic
399	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
400	#529	—	2	1	no	—
401	#529	—	2	1	no	—
402	#529	C₂²×C₁₉	1	1	yes	characteristic
403	#529	C₂²×C₁₉	1	1	yes	characteristic
404	#525	—	2	1	no	—
405	#525	—	2	1	no	—
406	#525	—	2	1	no	—
407	#501	C₂²×C₁₉	1	2	yes	complemented
408	#497	C₂²×C₁₉	1	2	yes	—
409	#491	C₂²×C₁₉	1	2	yes	complemented
410	#489	C₂²×C₁₉	1	2	yes	—
411	#489	C₂²×C₁₉	1	2	yes	—
412	#489	C₂²×C₁₉	1	2	yes	complemented
413	#487	—	2	1	no	—
414	#486	—	2	1	no	—
415	#483	—	2	1	no	—
416	#480	—	2	1	no	—
417	#477	—	2	1	no	—
418	#476	—	2	1	no	—
419	#462	—	2	1	no	—
420	#461	—	2	1	no	—
421	#451	—	2	1	no	—
422	#448	—	2	1	no	—
423	#432	C₂²×C₁₉	1	1	yes	characteristic, complemented
424	#432	C₂²×C₁₉	1	1	yes	characteristic, complemented
425	#417	—	2	1	no	—
426	#417	—	2	1	no	—
427	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
428	#330	C₂²×C₁₉	1	2	yes	complemented
429	#330	C₂²×C₁₉	1	2	yes	complemented
430	#329	C₂²×C₁₉	1	2	yes	—
431	#329	C₂²×C₁₉	1	2	yes	—
432	#329	C₂²×C₁₉	1	2	yes	—
433	#329	C₂²×C₁₉	1	2	yes	complemented
434	C₂×C₁₉	—	4	1	no	—
435	C₂×C₁₉	—	8	1	no	—
436	C₂×C₁₉	—	8	1	no	—
437	C₂×C₁₉	—	8	1	no	—
438	C₂×C₁₉	—	8	1	no	—
439	C₂×C₁₉	C₂×#455	1	1	yes	characteristic
440	C₂×C₁₉	#3021	1	1	yes	characteristic
441	C₂×C₁₉	#3022	1	1	yes	characteristic
442	C₂×#41	—	2	1	no	—
443	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
444	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
445	C₂²×Q₈	—	2	1	no	—
446	C₂³×C₄	—	2	1	no	—
447	C₂×Q₁₆	—	2	2	no	—
448	C₂×SD₁₆	—	2	2	no	—
449	C₂×M₁₆	—	2	1	no	—
450	C₄⋊Q₈	—	2	1	no	—
451	C₄⋊Q₈	—	2	1	no	—
452	C₄⋊Q₈	—	2	1	no	—
453	C₄⋊Q₈	—	2	1	no	—
454	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
455	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
456	#127	—	2	1	no	—
457	#127	D₄×C₁₉	1	1	yes	characteristic
458	#126	—	2	1	no	—
459	#126	—	2	1	no	—
460	#126	—	2	1	no	—
461	#126	—	2	1	no	—
462	#126	—	2	1	no	—
463	#126	—	2	1	no	—
464	#125	—	2	1	no	—
465	#125	—	2	1	no	—
466	#125	C₂³×C₁₉	1	1	yes	characteristic
467	#125	C₂³×C₁₉	1	1	yes	characteristic
468	#124	—	2	1	no	—
469	#124	—	2	1	no	—
470	#124	—	2	1	no	—
471	#124	—	2	1	no	—
472	#124	C₂³×C₁₉	1	1	yes	characteristic
473	#124	C₂³×C₁₉	1	1	yes	characteristic
474	#124	C₂³×C₁₉	1	1	yes	characteristic
475	#124	C₂³×C₁₉	1	1	yes	characteristic
476	#123	—	2	1	no	—
477	#123	—	2	1	no	—
478	#123	—	2	1	no	—
479	#123	—	2	1	no	—
480	#123	—	2	1	no	—
481	#123	—	2	1	no	—
482	#123	—	2	1	no	—
483	#123	—	2	1	no	—
484	#123	—	2	1	no	—
485	#123	—	2	1	no	—
486	#123	—	2	1	no	—
487	#123	—	2	1	no	—
488	C₂²⋊Q₈	—	2	1	no	—
489	C₂²⋊Q₈	—	2	1	no	—
490	C₂²⋊Q₈	—	2	1	no	—
491	C₂²⋊Q₈	—	2	1	no	—
492	C₂²⋊Q₈	—	2	1	no	—
493	C₂²⋊Q₈	—	2	1	no	—
494	C₂²⋊Q₈	—	2	1	no	—
495	C₂²⋊Q₈	—	2	1	no	—
496	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
497	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
498	#121	—	2	1	no	—
499	#121	—	2	1	no	—
500	#121	—	2	1	no	—
501	#121	—	2	1	no	—
502	#121	—	2	1	no	—
503	#121	—	2	1	no	—
504	#121	—	2	1	no	—
505	#121	—	2	1	no	—
506	#121	—	2	1	no	—
507	#121	—	2	1	no	—
508	#121	—	2	1	no	—
509	#121	—	2	1	no	—
510	#121	—	2	1	no	—
511	#121	—	2	1	no	—
512	#121	D₄×C₁₉	1	1	yes	characteristic
513	#121	D₄×C₁₉	1	1	yes	characteristic
514	#120	—	2	1	no	—
515	#120	—	2	1	no	—
516	#120	—	2	1	no	—
517	#120	—	2	1	no	—
518	#120	—	2	1	no	—
519	#120	—	2	1	no	—
520	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
521	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
522	C₄×D₄	—	2	1	no	—
523	C₄×D₄	—	2	1	no	—
524	C₄×D₄	—	2	1	no	—
525	C₄×D₄	—	2	1	no	—
526	C₄×D₄	—	2	1	no	—
527	C₄×D₄	—	2	1	no	—
528	C₄×D₄	—	2	1	no	—
529	C₄×D₄	—	2	1	no	—
530	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
531	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
532	#117	—	2	1	no	—
533	#117	—	2	1	no	—
534	#117	—	2	1	no	—
535	C₂×C₄⋊C₄	—	2	1	no	—
536	C₂×C₄⋊C₄	—	2	1	no	—
537	C₂×C₄²	—	2	1	no	—
538	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
539	#107	—	2	2	no	—
540	#106	—	2	2	no	—
541	C₄⋊C₈	—	2	1	no	—
542	C₄⋊C₈	—	2	1	no	—
543	#103	—	2	2	no	—
544	#103	—	2	2	no	—
545	#103	—	2	2	no	—
546	#103	—	2	2	no	—
547	#103	—	2	2	no	—
548	#102	—	2	2	no	—
549	#102	—	2	2	no	—
550	#102	—	2	2	no	—
551	C₂²⋊C₈	—	2	1	no	—
552	C₂²⋊C₈	—	2	1	no	—
553	#97	C₂³×C₁₉	1	2	yes	—
554	#97	C₂³×C₁₉	1	2	yes	—
555	#97	C₂³×C₁₉	1	2	yes	—
556	C₄×C₈	—	2	1	no	—
557	C₁₉	#19000	1	1	yes	characteristic, direct product factor, Sylow
558	C₂⁴	—	2	1	no	—
559	#41	—	4	2	no	—
560	#41	—	4	2	no	—
561	#41	—	8	2	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	—	2	2	no	—
564	C₂×Q₈	—	4	1	no	—
565	C₂×Q₈	—	8	2	no	—
566	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
567	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
568	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
569	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
570	C₂×D₄	—	2	1	no	—
571	C₂×D₄	—	2	1	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	2	1	no	—
574	C₂×D₄	—	2	1	no	—
575	C₂×D₄	—	2	1	no	—
576	C₂×D₄	—	2	1	no	—
577	C₂×D₄	—	2	1	no	—
578	C₂×D₄	—	2	1	no	—
579	C₂×D₄	—	2	1	no	—
580	C₂×D₄	—	2	1	no	—
581	C₂×D₄	—	2	1	no	—
582	C₂×D₄	—	2	1	no	—
583	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
584	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
585	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
586	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	4	1	no	—
597	C₂²×C₄	—	8	2	no	—
598	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
599	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
600	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
601	Q₁₆	—	8	2	no	—
602	SD₁₆	—	8	2	no	—
603	M₁₆	—	4	2	no	—
604	C₂×C₈	—	2	2	no	—
605	C₂×C₈	—	2	2	no	—
606	C₂×C₈	—	2	2	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	—	2	1	no	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	—	2	1	no	—
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	—	2	1	no	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	—	2	2	no	—
624	C₄⋊C₄	—	2	2	no	—
625	C₄⋊C₄	—	4	1	no	—
626	C₄⋊C₄	—	4	1	no	—
627	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
628	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
629	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
630	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
631	C₂²⋊C₄	—	2	1	no	—
632	C₂²⋊C₄	—	2	1	no	—
633	C₂²⋊C₄	—	2	1	no	—
634	C₂²⋊C₄	—	2	1	no	—
635	C₂²⋊C₄	—	2	1	no	—
636	C₂²⋊C₄	—	2	1	no	—
637	C₂²⋊C₄	—	2	1	no	—
638	C₂²⋊C₄	—	2	1	no	—
639	C₂²⋊C₄	—	2	1	no	—
640	C₂²⋊C₄	—	2	1	no	—
641	C₂²⋊C₄	—	2	1	no	—
642	C₂²⋊C₄	—	2	1	no	—
643	C₂²⋊C₄	—	2	1	no	—
644	C₂²⋊C₄	—	2	1	no	—
645	C₂²⋊C₄	—	2	1	no	—
646	C₂²⋊C₄	—	2	1	no	—
647	C₂²⋊C₄	—	2	1	no	—
648	C₂²⋊C₄	—	2	1	no	—
649	C₂²⋊C₄	—	2	1	no	—
650	C₂²⋊C₄	—	2	1	no	—
651	C₂²⋊C₄	—	2	1	no	—
652	C₂²⋊C₄	—	2	1	no	—
653	C₂²⋊C₄	—	2	1	no	—
654	C₂²⋊C₄	—	2	1	no	—
655	C₄²	—	2	1	no	—
656	C₄²	—	2	1	no	—
657	C₄²	—	2	1	no	—
658	C₄²	—	2	1	no	—
659	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
660	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
661	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
662	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
663	C₂³	—	2	1	no	—
664	C₂³	—	2	1	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	2	1	no	—
667	C₂³	—	8	1	no	—
668	C₂³	—	8	1	no	—
669	C₂³	—	8	1	no	—
670	C₂³	C₁₉×#120	1	1	yes	characteristic
671	Q₈	—	4	1	no	—
672	Q₈	—	4	1	no	—
673	Q₈	—	4	1	no	—
674	Q₈	—	4	1	no	—
675	Q₈	—	4	2	no	—
676	Q₈	—	4	2	no	—
677	Q₈	—	8	2	no	—
678	Q₈	—	8	1	no	—
679	D₄	—	4	1	no	—
680	D₄	—	4	1	no	—
681	D₄	—	4	1	no	—
682	D₄	—	4	1	no	—
683	D₄	—	8	1	no	—
684	D₄	—	8	1	no	—
685	D₄	—	8	1	no	—
686	D₄	—	8	1	no	—
687	D₄	—	8	1	no	—
688	D₄	—	8	1	no	—
689	D₄	—	8	1	no	—
690	D₄	—	8	1	no	—
691	D₄	—	8	1	no	—
692	D₄	—	8	1	no	—
693	D₄	—	8	1	no	—
694	D₄	—	8	1	no	—
695	D₄	—	8	1	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	4	1	no	—
706	C₂×C₄	—	4	1	no	—
707	C₂×C₄	—	4	2	no	—
708	C₂×C₄	—	4	2	no	—
709	C₂×C₄	—	4	2	no	—
710	C₂×C₄	—	4	2	no	—
711	C₂×C₄	—	4	2	no	—
712	C₂×C₄	—	8	1	no	—
713	C₂×C₄	—	8	1	no	—
714	C₂×C₄	—	8	1	no	—
715	C₂×C₄	—	8	1	no	—
716	C₂×C₄	—	8	1	no	—
717	C₂×C₄	—	8	2	no	—
718	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
719	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
720	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
721	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
722	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
723	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
724	C₈	—	4	2	no	—
725	C₈	—	4	2	no	—
726	C₈	—	4	2	no	—
727	C₂²	—	2	1	no	—
728	C₂²	—	2	1	no	—
729	C₂²	—	2	1	no	—
730	C₂²	—	4	1	no	—
731	C₂²	—	4	1	no	—
732	C₂²	—	4	1	no	—
733	C₂²	—	4	1	no	—
734	C₂²	—	4	1	no	—
735	C₂²	—	4	1	no	—
736	C₂²	—	4	1	no	—
737	C₂²	—	4	1	no	—
738	C₂²	—	4	1	no	—
739	C₂²	—	4	1	no	—
740	C₂²	—	4	1	no	—
741	C₂²	—	4	1	no	—
742	C₂²	—	8	4	no	—
743	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
744	C₄	—	2	1	no	—
745	C₄	—	2	1	no	—
746	C₄	—	2	1	no	—
747	C₄	—	2	1	no	—
748	C₄	—	2	1	no	—
749	C₄	—	4	1	no	—
750	C₄	—	4	1	no	—
751	C₄	—	4	1	no	—
752	C₄	—	4	1	no	—
753	C₄	—	4	1	no	—
754	C₄	—	4	1	no	—
755	C₄	—	4	1	no	—
756	C₄	—	4	1	no	—
757	C₄	—	8	2	no	—
758	C₄	C₁₉×#455	1	2	yes	—
759	C₂	—	4	1	no	—
760	C₂	—	8	1	no	—
761	C₂	—	8	1	no	—
762	C₂	—	8	1	no	—
763	C₂	—	8	1	no	—
764	C₂	C₂×C₁₉×#455	1	1	yes	characteristic
765	C₂	C₁₉×#3021	1	1	yes	characteristic
766	C₂	C₁₉×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3529	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×#3238	C₂	semidirect
3. C₁₉×#3218	C₂	semidirect
4. C₁₉×#3141	C₂	semidirect
5. C₁₉×#1664	C₂	semidirect
6. C₁₉×#1662	C₂	semidirect
7. C₁₉×#1661	C₂	semidirect
8. C₁₉×#1659	C₂	semidirect
9. C₁₉×#1536	C₂	semidirect
10. C₁₉×#1529	C₂	semidirect
11. C₁₉×#1529	C₂	semidirect
24. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
32. C₁₉×#501	C₂²	semidirect
34. C₁₉×#491	C₂²	semidirect
37. C₁₉×#489	C₂²	semidirect
48. C₁₉×#432	C₂²	semidirect
49. C₁₉×#432	C₂²	semidirect
52. C₄×M₁₆×C₁₉	C₂²	semidirect
53. C₁₉×#330	C₂²	semidirect
54. C₁₉×#330	C₂²	semidirect
58. C₁₉×#329	C₂²	semidirect
279. #19000	C₁₉	direct (N × H)
345. #3238	C₂×C₁₉	semidirect
346. #3218	C₂×C₁₉	semidirect
347. #3141	C₂×C₁₉	semidirect
348. #1664	C₂×C₁₉	semidirect
349. #1662	C₂×C₁₉	semidirect
350. #1661	C₂×C₁₉	semidirect
351. #1659	C₂×C₁₉	semidirect
352. #1536	C₂×C₁₉	semidirect
353. #1529	C₂×C₁₉	semidirect
354. #1529	C₂×C₁₉	semidirect
399. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
407. #501	C₂²×C₁₉	semidirect
409. #491	C₂²×C₁₉	semidirect
412. #489	C₂²×C₁₉	semidirect
423. #432	C₂²×C₁₉	semidirect
424. #432	C₂²×C₁₉	semidirect
427. C₄×M₁₆	C₂²×C₁₉	semidirect
428. #330	C₂²×C₁₉	semidirect
429. #330	C₂²×C₁₉	semidirect
433. #329	C₂²×C₁₉	semidirect
557. C₁₉	#19000	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×#3529	2
C₁₉×#3238	2
C₁₉×#3218	2
C₁₉×#3141	2
C₁₉×#1664	2
C₁₉×#1662	2
C₁₉×#1661	2
C₁₉×#1659	2
C₁₉×#1536	2
C₁₉×#1529	2
#19000	19

Subgroups — C19×#19000 #18024959

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19000 #18024959