Subgroups — C₁₉×#19087 #18025046

Order 4864.

930 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3558	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3240	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3216	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3215	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1661	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1661	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1659	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×#1535	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1533	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#562	C₂²	1	2	yes	—
13	C₁₉×H(3,𝔽₄)	C₂²	1	2	yes	—
14	C₁₉×#559	—	2	1	no	—
15	C₁₉×#548	—	2	1	no	—
16	C₁₉×#546	—	2	2	no	—
17	C₁₉×#546	—	2	1	no	—
18	D₄²×C₁₉	—	2	1	no	—
19	C₁₉×#542	—	2	1	no	—
20	C₁₉×#538	—	2	2	no	—
21	C₁₉×#538	—	2	1	no	—
22	C₁₉×#535	—	2	1	no	—
23	C₁₉×#534	—	2	1	no	—
24	C₁₉×#533	C₂²	1	1	yes	characteristic, complemented
25	C₁₉×#532	C₂²	1	1	yes	characteristic
26	C₁₉×#529	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
28	C₁₉×#501	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#501	C₂²	1	1	yes	characteristic, complemented
30	C₁₉×#497	C₂²	1	2	yes	complemented
31	C₁₉×#497	C₂²	1	2	yes	complemented
32	C₁₉×#489	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×#489	C₂²	1	1	yes	characteristic, complemented
34	C₁₉×#489	C₂²	1	2	yes	complemented
35	C₁₉×#489	C₂²	1	2	yes	complemented
36	C₁₉×#485	—	2	1	no	—
37	C₁₉×#482	—	2	1	no	—
38	C₁₉×#479	—	2	1	no	—
39	C₁₉×#478	—	2	1	no	—
40	C₁₉×#464	—	2	2	no	—
41	C₁₉×#462	—	2	1	no	—
42	C₁₉×#460	—	2	1	no	—
43	C₁₉×#452	—	2	2	no	—
44	C₁₉×#451	—	2	1	no	—
45	C₁₉×#450	—	2	1	no	—
46	C₁₉×#432	C₂²	1	1	yes	characteristic, complemented
47	C₁₉×#432	C₂²	1	1	yes	characteristic, complemented
48	C₁₉×#432	C₂²	1	1	yes	characteristic, complemented
49	C₁₉×#330	C₂²	1	2	yes	complemented
50	C₁₉×#329	C₂²	1	2	yes	complemented
51	C₁₉×#329	C₂²	1	2	yes	complemented
52	C₁₉×#329	C₂²	1	2	yes	complemented
53	C₁₉×#329	C₂²	1	2	yes	complemented
54	C₁₉×#329	C₂²	1	2	yes	complemented
55	C₂×#41×C₁₉	—	2	1	no	—
56	C₂×#41×C₁₉	D₄	1	2	yes	—
57	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
58	C₂²×D₄×C₁₉	—	2	2	no	—
59	C₂²×D₄×C₁₉	—	2	1	no	—
60	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
61	C₂×Q₁₆×C₁₉	—	2	2	no	—
62	C₂×Q₁₆×C₁₉	—	2	2	no	—
63	C₂×SD₁₆×C₁₉	—	2	2	no	—
64	C₂×SD₁₆×C₁₉	—	2	2	no	—
65	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
66	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
67	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
68	C₁₉×#127	—	2	1	no	—
69	C₁₉×#127	D₄	1	1	yes	characteristic
70	C₁₉×#126	—	2	2	no	—
71	C₁₉×#126	—	2	1	no	—
72	C₁₉×#125	—	2	1	no	—
73	C₁₉×#125	C₂³	1	1	yes	characteristic
74	C₁₉×#124	—	2	1	no	—
75	C₁₉×#124	—	2	2	no	—
76	C₁₉×#124	—	2	2	no	—
77	C₁₉×#124	—	2	2	no	—
78	C₁₉×#124	—	2	1	no	—
79	C₁₉×#124	—	2	1	no	—
80	C₁₉×#124	D₄	1	2	yes	—
81	C₁₉×#124	C₂³	1	1	yes	characteristic
82	C₁₉×#124	C₂³	1	2	yes	—
83	C₁₉×#124	C₂³	1	2	yes	—
84	C₁₉×#123	—	2	2	no	—
85	C₁₉×#123	—	2	2	no	—
86	C₁₉×#123	—	2	1	no	—
87	C₁₉×#123	—	2	2	no	—
88	C₁₉×#123	—	2	2	no	—
89	C₁₉×C₂²⋊Q₈	—	2	1	no	—
90	C₁₉×C₂²⋊Q₈	—	2	2	no	—
91	C₁₉×C₂²⋊Q₈	—	2	2	no	—
92	C₁₉×C₂²⋊Q₈	—	2	1	no	—
93	C₁₉×C₂²⋊Q₈	—	2	1	no	—
94	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
95	C₁₉×#121	—	2	2	no	—
96	C₁₉×#121	—	2	2	no	—
97	C₁₉×#121	—	2	2	no	—
98	C₁₉×#121	—	2	1	no	—
99	C₁₉×#121	—	2	2	no	—
100	C₁₉×#121	—	2	2	no	—
101	C₁₉×#121	—	2	1	no	—
102	C₁₉×#121	—	2	1	no	—
103	C₁₉×#121	D₄	1	1	yes	characteristic
104	C₁₉×#120	—	2	2	no	—
105	C₁₉×#120	—	2	2	no	—
106	C₁₉×#120	—	2	2	no	—
107	C₁₉×#120	—	2	2	no	—
108	C₁₉×#120	—	2	2	no	—
109	C₄×Q₈×C₁₉	—	2	1	no	—
110	C₄×Q₈×C₁₉	—	2	1	no	—
111	C₄×Q₈×C₁₉	—	2	1	no	—
112	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
113	C₄×D₄×C₁₉	—	2	2	no	—
114	C₄×D₄×C₁₉	—	2	2	no	—
115	C₄×D₄×C₁₉	—	2	1	no	—
116	C₄×D₄×C₁₉	—	2	1	no	—
117	C₄×D₄×C₁₉	—	2	1	no	—
118	C₄×D₄×C₁₉	—	2	1	no	—
119	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
120	C₁₉×#117	—	2	1	no	—
121	C₁₉×#117	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
123	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
125	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
126	C₁₉×#107	—	2	1	no	—
127	C₁₉×#107	—	2	1	no	—
128	C₁₉×#106	—	2	1	no	—
129	C₁₉×#106	—	2	1	no	—
130	C₁₉×C₄⋊C₈	—	2	1	no	—
131	C₁₉×C₄⋊C₈	—	2	1	no	—
132	C₁₉×C₄⋊C₈	—	2	1	no	—
133	C₁₉×#103	—	2	2	no	—
134	C₁₉×#103	—	2	2	no	—
135	C₁₉×#103	—	2	1	no	—
136	C₁₉×#103	—	2	1	no	—
137	C₁₉×#102	—	2	2	no	—
138	C₁₉×#102	—	2	2	no	—
139	C₁₉×#102	—	2	1	no	—
140	C₁₉×#102	—	2	1	no	—
141	C₁₉×C₂²⋊C₈	—	2	1	no	—
142	C₁₉×C₂²⋊C₈	—	2	1	no	—
143	C₁₉×C₂²⋊C₈	—	2	1	no	—
144	C₁₉×#97	C₂³	1	2	yes	—
145	C₁₉×#97	C₂³	1	2	yes	—
146	C₁₉×#97	C₂³	1	1	yes	characteristic
147	C₁₉×#97	C₂³	1	1	yes	characteristic
148	C₂⁴×C₁₉	—	2	2	no	—
149	C₂⁴×C₁₉	—	2	1	no	—
150	#41×C₁₉	—	8	2	no	—
151	#41×C₁₉	—	8	2	no	—
152	C₂×Q₈×C₁₉	—	2	1	no	—
153	C₂×Q₈×C₁₉	—	2	1	no	—
154	C₂×Q₈×C₁₉	—	2	1	no	—
155	C₂×Q₈×C₁₉	—	8	1	no	—
156	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
158	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
159	C₂×D₄×C₁₉	—	2	2	no	—
160	C₂×D₄×C₁₉	—	2	1	no	—
161	C₂×D₄×C₁₉	—	2	2	no	—
162	C₂×D₄×C₁₉	—	2	2	no	—
163	C₂×D₄×C₁₉	—	2	2	no	—
164	C₂×D₄×C₁₉	—	2	2	no	—
165	C₂×D₄×C₁₉	—	2	2	no	—
166	C₂×D₄×C₁₉	—	2	1	no	—
167	C₂×D₄×C₁₉	—	2	1	no	—
168	C₂×D₄×C₁₉	—	2	1	no	—
169	C₂×D₄×C₁₉	—	8	1	no	—
170	C₂×D₄×C₁₉	—	8	2	no	—
171	C₂×D₄×C₁₉	—	8	4	no	—
172	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
174	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₁₉	—	2	2	no	—
176	C₂²×C₄×C₁₉	—	2	2	no	—
177	C₂²×C₄×C₁₉	—	2	1	no	—
178	C₂²×C₄×C₁₉	—	2	1	no	—
179	C₂²×C₄×C₁₉	—	2	2	no	—
180	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
183	Q₁₆×C₁₉	—	8	2	no	—
184	Q₁₆×C₁₉	—	8	2	no	—
185	SD₁₆×C₁₉	—	8	2	no	—
186	SD₁₆×C₁₉	—	8	2	no	—
187	C₂×C₈×C₁₉	—	2	2	no	—
188	C₂×C₈×C₁₉	—	2	2	no	—
189	C₂×C₈×C₁₉	—	2	1	no	—
190	C₂×C₈×C₁₉	—	2	1	no	—
191	C₄⋊C₄×C₁₉	—	2	2	no	—
192	C₄⋊C₄×C₁₉	—	2	2	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	—	2	1	no	—
200	C₄⋊C₄×C₁₉	—	2	1	no	—
201	C₄⋊C₄×C₁₉	—	2	1	no	—
202	C₄⋊C₄×C₁₉	—	2	1	no	—
203	C₄⋊C₄×C₁₉	—	4	1	no	—
204	C₄⋊C₄×C₁₉	—	4	1	no	—
205	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
206	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
207	C₂²⋊C₄×C₁₉	—	2	2	no	—
208	C₂²⋊C₄×C₁₉	—	2	2	no	—
209	C₂²⋊C₄×C₁₉	—	2	2	no	—
210	C₂²⋊C₄×C₁₉	—	2	2	no	—
211	C₂²⋊C₄×C₁₉	—	2	2	no	—
212	C₂²⋊C₄×C₁₉	—	2	1	no	—
213	C₂²⋊C₄×C₁₉	—	2	2	no	—
214	C₂²⋊C₄×C₁₉	—	2	1	no	—
215	C₂²⋊C₄×C₁₉	—	2	2	no	—
216	C₂²⋊C₄×C₁₉	—	2	1	no	—
217	C₂²⋊C₄×C₁₉	—	2	2	no	—
218	C₂²⋊C₄×C₁₉	—	2	2	no	—
219	C₂²⋊C₄×C₁₉	—	2	1	no	—
220	C₂²⋊C₄×C₁₉	—	2	1	no	—
221	C₂²⋊C₄×C₁₉	—	2	2	no	—
222	C₂²⋊C₄×C₁₉	—	2	2	no	—
223	C₂²⋊C₄×C₁₉	—	4	1	no	—
224	C₄²×C₁₉	—	2	2	no	—
225	C₄²×C₁₉	—	2	1	no	—
226	C₄²×C₁₉	—	4	1	no	—
227	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
228	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
229	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
230	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
231	#19087	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂³×C₁₉	—	2	1	no	—
233	C₂³×C₁₉	—	2	2	no	—
234	C₂³×C₁₉	—	2	2	no	—
235	C₂³×C₁₉	—	4	2	no	—
236	C₂³×C₁₉	—	8	1	no	—
237	C₂³×C₁₉	—	8	1	no	—
238	C₂³×C₁₉	—	8	2	no	—
239	C₂³×C₁₉	—	8	2	no	—
240	C₂³×C₁₉	—	8	2	no	—
241	C₂³×C₁₉	#120	1	1	yes	characteristic
242	Q₈×C₁₉	—	4	2	no	—
243	Q₈×C₁₉	—	4	2	no	—
244	Q₈×C₁₉	—	4	1	no	—
245	Q₈×C₁₉	—	4	2	no	—
246	Q₈×C₁₉	—	4	1	no	—
247	Q₈×C₁₉	—	4	2	no	—
248	Q₈×C₁₉	—	4	1	no	—
249	D₄×C₁₉	—	4	2	no	—
250	D₄×C₁₉	—	4	2	no	—
251	D₄×C₁₉	—	4	1	no	—
252	D₄×C₁₉	—	4	2	no	—
253	D₄×C₁₉	—	4	2	no	—
254	D₄×C₁₉	—	4	2	no	—
255	D₄×C₁₉	—	4	4	no	—
256	D₄×C₁₉	—	8	1	no	—
257	D₄×C₁₉	—	8	2	no	—
258	D₄×C₁₉	—	8	2	no	—
259	D₄×C₁₉	—	8	2	no	—
260	D₄×C₁₉	—	8	2	no	—
261	D₄×C₁₉	—	8	2	no	—
262	C₂×C₄×C₁₉	—	2	1	no	—
263	C₂×C₄×C₁₉	—	2	2	no	—
264	C₂×C₄×C₁₉	—	2	2	no	—
265	C₂×C₄×C₁₉	—	2	1	no	—
266	C₂×C₄×C₁₉	—	2	1	no	—
267	C₂×C₄×C₁₉	—	4	1	no	—
268	C₂×C₄×C₁₉	—	4	1	no	—
269	C₂×C₄×C₁₉	—	4	1	no	—
270	C₂×C₄×C₁₉	—	4	2	no	—
271	C₂×C₄×C₁₉	—	4	1	no	—
272	C₂×C₄×C₁₉	—	4	1	no	—
273	C₂×C₄×C₁₉	—	8	2	no	—
274	C₂×C₄×C₁₉	—	8	1	no	—
275	C₂×C₄×C₁₉	—	8	2	no	—
276	C₂×C₄×C₁₉	—	8	2	no	—
277	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
278	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
279	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
280	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
281	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
282	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
283	C₈×C₁₉	—	4	1	no	—
284	C₈×C₁₉	—	4	1	no	—
285	C₈×C₁₉	—	4	2	no	—
286	C₈×C₁₉	—	4	2	no	—
287	#3558	C₂×C₁₉	1	1	yes	characteristic
288	#3240	C₂×C₁₉	1	1	yes	characteristic, complemented
289	#3216	C₂×C₁₉	1	1	yes	characteristic, complemented
290	#3215	C₂×C₁₉	1	1	yes	characteristic, complemented
291	#1661	C₂×C₁₉	1	2	yes	complemented
292	#1661	C₂×C₁₉	1	2	yes	complemented
293	#1659	C₂×C₁₉	1	2	yes	complemented
294	#1659	C₂×C₁₉	1	2	yes	complemented
295	#1536	C₂×C₁₉	1	1	yes	characteristic, complemented
296	#1535	C₂×C₁₉	1	1	yes	characteristic, complemented
297	#1533	C₂×C₁₉	1	1	yes	characteristic, complemented
298	C₂²×C₁₉	—	2	1	no	—
299	C₂²×C₁₉	—	2	1	no	—
300	C₂²×C₁₉	—	2	1	no	—
301	C₂²×C₁₉	—	4	1	no	—
302	C₂²×C₁₉	—	4	2	no	—
303	C₂²×C₁₉	—	4	2	no	—
304	C₂²×C₁₉	—	4	2	no	—
305	C₂²×C₁₉	—	4	2	no	—
306	C₂²×C₁₉	—	4	1	no	—
307	C₂²×C₁₉	—	4	1	no	—
308	C₂²×C₁₉	—	4	2	no	—
309	C₂²×C₁₉	—	4	2	no	—
310	C₂²×C₁₉	—	16	2	no	—
311	C₂²×C₁₉	—	16	4	no	—
312	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
313	C₄×C₁₉	—	2	1	no	—
314	C₄×C₁₉	—	2	1	no	—
315	C₄×C₁₉	—	2	1	no	—
316	C₄×C₁₉	—	2	1	no	—
317	C₄×C₁₉	—	2	1	no	—
318	C₄×C₁₉	—	2	1	no	—
319	C₄×C₁₉	—	4	1	no	—
320	C₄×C₁₉	—	4	1	no	—
321	C₄×C₁₉	—	4	2	no	—
322	C₄×C₁₉	—	4	2	no	—
323	C₄×C₁₉	—	4	1	no	—
324	C₄×C₁₉	—	8	1	no	—
325	C₄×C₁₉	—	8	1	no	—
326	#562	C₂²×C₁₉	1	2	yes	—
327	H(3,𝔽₄)	C₂²×C₁₉	1	2	yes	—
328	#559	—	2	1	no	—
329	#548	—	2	1	no	—
330	#546	—	2	2	no	—
331	#546	—	2	1	no	—
332	D₄²	—	2	1	no	—
333	#542	—	2	1	no	—
334	#538	—	2	2	no	—
335	#538	—	2	1	no	—
336	#535	—	2	1	no	—
337	#534	—	2	1	no	—
338	#533	C₂²×C₁₉	1	1	yes	characteristic, complemented
339	#532	C₂²×C₁₉	1	1	yes	characteristic
340	#529	C₂²×C₁₉	1	1	yes	characteristic
341	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
342	#501	C₂²×C₁₉	1	1	yes	characteristic, complemented
343	#501	C₂²×C₁₉	1	1	yes	characteristic, complemented
344	#497	C₂²×C₁₉	1	2	yes	complemented
345	#497	C₂²×C₁₉	1	2	yes	complemented
346	#489	C₂²×C₁₉	1	1	yes	characteristic, complemented
347	#489	C₂²×C₁₉	1	1	yes	characteristic, complemented
348	#489	C₂²×C₁₉	1	2	yes	complemented
349	#489	C₂²×C₁₉	1	2	yes	complemented
350	#485	—	2	1	no	—
351	#482	—	2	1	no	—
352	#479	—	2	1	no	—
353	#478	—	2	1	no	—
354	#464	—	2	2	no	—
355	#462	—	2	1	no	—
356	#460	—	2	1	no	—
357	#452	—	2	2	no	—
358	#451	—	2	1	no	—
359	#450	—	2	1	no	—
360	#432	C₂²×C₁₉	1	1	yes	characteristic, complemented
361	#432	C₂²×C₁₉	1	1	yes	characteristic, complemented
362	#432	C₂²×C₁₉	1	1	yes	characteristic, complemented
363	#330	C₂²×C₁₉	1	2	yes	complemented
364	#329	C₂²×C₁₉	1	2	yes	complemented
365	#329	C₂²×C₁₉	1	2	yes	complemented
366	#329	C₂²×C₁₉	1	2	yes	complemented
367	#329	C₂²×C₁₉	1	2	yes	complemented
368	#329	C₂²×C₁₉	1	2	yes	complemented
369	C₂×C₁₉	—	4	1	no	—
370	C₂×C₁₉	—	8	2	no	—
371	C₂×C₁₉	—	8	1	no	—
372	C₂×C₁₉	—	8	2	no	—
373	C₂×C₁₉	#3019	1	1	yes	characteristic
374	C₂×C₁₉	#3019	1	1	yes	characteristic
375	C₂×C₁₉	#3022	1	1	yes	characteristic
376	C₂×#41	—	2	1	no	—
377	C₂×#41	D₄×C₁₉	1	2	yes	—
378	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
379	C₂²×D₄	—	2	2	no	—
380	C₂²×D₄	—	2	1	no	—
381	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
382	C₂×Q₁₆	—	2	2	no	—
383	C₂×Q₁₆	—	2	2	no	—
384	C₂×SD₁₆	—	2	2	no	—
385	C₂×SD₁₆	—	2	2	no	—
386	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
387	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
388	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
389	#127	—	2	1	no	—
390	#127	D₄×C₁₉	1	1	yes	characteristic
391	#126	—	2	2	no	—
392	#126	—	2	1	no	—
393	#125	—	2	1	no	—
394	#125	C₂³×C₁₉	1	1	yes	characteristic
395	#124	—	2	1	no	—
396	#124	—	2	2	no	—
397	#124	—	2	2	no	—
398	#124	—	2	2	no	—
399	#124	—	2	1	no	—
400	#124	—	2	1	no	—
401	#124	D₄×C₁₉	1	2	yes	—
402	#124	C₂³×C₁₉	1	2	yes	—
403	#124	C₂³×C₁₉	1	1	yes	characteristic
404	#124	C₂³×C₁₉	1	2	yes	—
405	#123	—	2	2	no	—
406	#123	—	2	2	no	—
407	#123	—	2	1	no	—
408	#123	—	2	2	no	—
409	#123	—	2	2	no	—
410	C₂²⋊Q₈	—	2	1	no	—
411	C₂²⋊Q₈	—	2	2	no	—
412	C₂²⋊Q₈	—	2	2	no	—
413	C₂²⋊Q₈	—	2	1	no	—
414	C₂²⋊Q₈	—	2	1	no	—
415	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
416	#121	—	2	2	no	—
417	#121	—	2	2	no	—
418	#121	—	2	2	no	—
419	#121	—	2	1	no	—
420	#121	—	2	2	no	—
421	#121	—	2	2	no	—
422	#121	—	2	1	no	—
423	#121	—	2	1	no	—
424	#121	D₄×C₁₉	1	1	yes	characteristic
425	#120	—	2	2	no	—
426	#120	—	2	2	no	—
427	#120	—	2	2	no	—
428	#120	—	2	2	no	—
429	#120	—	2	2	no	—
430	C₄×Q₈	—	2	1	no	—
431	C₄×Q₈	—	2	1	no	—
432	C₄×Q₈	—	2	1	no	—
433	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
434	C₄×D₄	—	2	2	no	—
435	C₄×D₄	—	2	2	no	—
436	C₄×D₄	—	2	1	no	—
437	C₄×D₄	—	2	1	no	—
438	C₄×D₄	—	2	1	no	—
439	C₄×D₄	—	2	1	no	—
440	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
441	#117	—	2	1	no	—
442	#117	—	2	1	no	—
443	C₂×C₂²⋊C₄	—	2	2	no	—
444	C₂×C₂²⋊C₄	—	2	1	no	—
445	C₂×C₂²⋊C₄	—	2	1	no	—
446	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
447	#107	—	2	1	no	—
448	#107	—	2	1	no	—
449	#106	—	2	1	no	—
450	#106	—	2	1	no	—
451	C₄⋊C₈	—	2	1	no	—
452	C₄⋊C₈	—	2	1	no	—
453	C₄⋊C₈	—	2	1	no	—
454	#103	—	2	2	no	—
455	#103	—	2	2	no	—
456	#103	—	2	1	no	—
457	#103	—	2	1	no	—
458	#102	—	2	2	no	—
459	#102	—	2	2	no	—
460	#102	—	2	1	no	—
461	#102	—	2	1	no	—
462	C₂²⋊C₈	—	2	1	no	—
463	C₂²⋊C₈	—	2	1	no	—
464	C₂²⋊C₈	—	2	1	no	—
465	#97	C₂³×C₁₉	1	1	yes	characteristic
466	#97	C₂³×C₁₉	1	1	yes	characteristic
467	#97	C₂³×C₁₉	1	2	yes	—
468	#97	C₂³×C₁₉	1	2	yes	—
469	C₁₉	#19087	1	1	yes	characteristic, direct product factor, Sylow
470	C₂⁴	—	2	2	no	—
471	C₂⁴	—	2	1	no	—
472	#41	—	8	2	no	—
473	#41	—	8	2	no	—
474	C₂×Q₈	—	2	1	no	—
475	C₂×Q₈	—	2	1	no	—
476	C₂×Q₈	—	2	1	no	—
477	C₂×Q₈	—	8	1	no	—
478	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
479	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
480	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
481	C₂×D₄	—	2	2	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	2	2	no	—
484	C₂×D₄	—	2	2	no	—
485	C₂×D₄	—	2	2	no	—
486	C₂×D₄	—	2	2	no	—
487	C₂×D₄	—	2	2	no	—
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	—	2	1	no	—
490	C₂×D₄	—	2	1	no	—
491	C₂×D₄	—	8	1	no	—
492	C₂×D₄	—	8	2	no	—
493	C₂×D₄	—	8	4	no	—
494	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
495	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
496	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
497	C₂²×C₄	—	2	2	no	—
498	C₂²×C₄	—	2	2	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	2	no	—
502	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
503	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
504	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
505	Q₁₆	—	8	2	no	—
506	Q₁₆	—	8	2	no	—
507	SD₁₆	—	8	2	no	—
508	SD₁₆	—	8	2	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	2	no	—
512	C₂×C₈	—	2	2	no	—
513	C₄⋊C₄	—	2	2	no	—
514	C₄⋊C₄	—	2	2	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	4	1	no	—
526	C₄⋊C₄	—	4	1	no	—
527	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
528	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
529	C₂²⋊C₄	—	2	2	no	—
530	C₂²⋊C₄	—	2	2	no	—
531	C₂²⋊C₄	—	2	2	no	—
532	C₂²⋊C₄	—	2	2	no	—
533	C₂²⋊C₄	—	2	2	no	—
534	C₂²⋊C₄	—	2	1	no	—
535	C₂²⋊C₄	—	2	2	no	—
536	C₂²⋊C₄	—	2	1	no	—
537	C₂²⋊C₄	—	2	2	no	—
538	C₂²⋊C₄	—	2	1	no	—
539	C₂²⋊C₄	—	2	2	no	—
540	C₂²⋊C₄	—	2	2	no	—
541	C₂²⋊C₄	—	2	1	no	—
542	C₂²⋊C₄	—	2	1	no	—
543	C₂²⋊C₄	—	2	2	no	—
544	C₂²⋊C₄	—	2	2	no	—
545	C₂²⋊C₄	—	4	1	no	—
546	C₄²	—	2	2	no	—
547	C₄²	—	2	1	no	—
548	C₄²	—	4	1	no	—
549	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
550	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
551	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
552	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
553	C₂³	—	2	1	no	—
554	C₂³	—	2	2	no	—
555	C₂³	—	2	2	no	—
556	C₂³	—	4	2	no	—
557	C₂³	—	8	1	no	—
558	C₂³	—	8	1	no	—
559	C₂³	—	8	2	no	—
560	C₂³	—	8	2	no	—
561	C₂³	—	8	2	no	—
562	C₂³	C₁₉×#120	1	1	yes	characteristic
563	Q₈	—	4	2	no	—
564	Q₈	—	4	2	no	—
565	Q₈	—	4	1	no	—
566	Q₈	—	4	2	no	—
567	Q₈	—	4	1	no	—
568	Q₈	—	4	2	no	—
569	Q₈	—	4	1	no	—
570	D₄	—	4	2	no	—
571	D₄	—	4	2	no	—
572	D₄	—	4	1	no	—
573	D₄	—	4	2	no	—
574	D₄	—	4	2	no	—
575	D₄	—	4	2	no	—
576	D₄	—	4	4	no	—
577	D₄	—	8	1	no	—
578	D₄	—	8	2	no	—
579	D₄	—	8	2	no	—
580	D₄	—	8	2	no	—
581	D₄	—	8	2	no	—
582	D₄	—	8	2	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	2	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	8	2	no	—
595	C₂×C₄	—	8	1	no	—
596	C₂×C₄	—	8	2	no	—
597	C₂×C₄	—	8	2	no	—
598	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
599	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
600	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
601	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
602	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
603	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
604	C₈	—	4	2	no	—
605	C₈	—	4	2	no	—
606	C₈	—	4	1	no	—
607	C₈	—	4	1	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	2	1	no	—
610	C₂²	—	2	1	no	—
611	C₂²	—	4	1	no	—
612	C₂²	—	4	2	no	—
613	C₂²	—	4	2	no	—
614	C₂²	—	4	2	no	—
615	C₂²	—	4	2	no	—
616	C₂²	—	4	1	no	—
617	C₂²	—	4	1	no	—
618	C₂²	—	4	2	no	—
619	C₂²	—	4	2	no	—
620	C₂²	—	16	2	no	—
621	C₂²	—	16	4	no	—
622	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
623	C₄	—	2	1	no	—
624	C₄	—	2	1	no	—
625	C₄	—	2	1	no	—
626	C₄	—	2	1	no	—
627	C₄	—	2	1	no	—
628	C₄	—	2	1	no	—
629	C₄	—	4	1	no	—
630	C₄	—	4	1	no	—
631	C₄	—	4	2	no	—
632	C₄	—	4	2	no	—
633	C₄	—	4	1	no	—
634	C₄	—	8	1	no	—
635	C₄	—	8	1	no	—
636	C₂	—	4	1	no	—
637	C₂	—	8	1	no	—
638	C₂	—	8	2	no	—
639	C₂	—	8	2	no	—
640	C₂	C₁₉×#3019	1	1	yes	characteristic
641	C₂	C₁₉×#3019	1	1	yes	characteristic
642	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×#3558	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×#3240	C₂	semidirect
3. C₁₉×#3216	C₂	semidirect
4. C₁₉×#3215	C₂	semidirect
5. C₁₉×#1661	C₂	semidirect
6. C₁₉×#1661	C₂	semidirect
7. C₁₉×#1659	C₂	semidirect
8. C₁₉×#1659	C₂	semidirect
9. C₁₉×#1536	C₂	semidirect
10. C₁₉×#1535	C₂	semidirect
11. C₁₉×#1533	C₂	semidirect
24. C₁₉×#533	C₂²	semidirect
28. C₁₉×#501	C₂²	semidirect
29. C₁₉×#501	C₂²	semidirect
30. C₁₉×#497	C₂²	semidirect
31. C₁₉×#497	C₂²	semidirect
32. C₁₉×#489	C₂²	semidirect
33. C₁₉×#489	C₂²	semidirect
34. C₁₉×#489	C₂²	semidirect
35. C₁₉×#489	C₂²	semidirect
46. C₁₉×#432	C₂²	semidirect
47. C₁₉×#432	C₂²	semidirect
48. C₁₉×#432	C₂²	semidirect
49. C₁₉×#330	C₂²	semidirect
50. C₁₉×#329	C₂²	semidirect
51. C₁₉×#329	C₂²	semidirect
52. C₁₉×#329	C₂²	semidirect
53. C₁₉×#329	C₂²	semidirect
54. C₁₉×#329	C₂²	semidirect
231. #19087	C₁₉	direct (N × H)
288. #3240	C₂×C₁₉	semidirect
289. #3216	C₂×C₁₉	semidirect
290. #3215	C₂×C₁₉	semidirect
291. #1661	C₂×C₁₉	semidirect
292. #1661	C₂×C₁₉	semidirect
293. #1659	C₂×C₁₉	semidirect
294. #1659	C₂×C₁₉	semidirect
295. #1536	C₂×C₁₉	semidirect
296. #1535	C₂×C₁₉	semidirect
297. #1533	C₂×C₁₉	semidirect
338. #533	C₂²×C₁₉	semidirect
342. #501	C₂²×C₁₉	semidirect
343. #501	C₂²×C₁₉	semidirect
344. #497	C₂²×C₁₉	semidirect
345. #497	C₂²×C₁₉	semidirect
346. #489	C₂²×C₁₉	semidirect
347. #489	C₂²×C₁₉	semidirect
348. #489	C₂²×C₁₉	semidirect
349. #489	C₂²×C₁₉	semidirect
360. #432	C₂²×C₁₉	semidirect
361. #432	C₂²×C₁₉	semidirect
362. #432	C₂²×C₁₉	semidirect
363. #330	C₂²×C₁₉	semidirect
364. #329	C₂²×C₁₉	semidirect
365. #329	C₂²×C₁₉	semidirect
366. #329	C₂²×C₁₉	semidirect
367. #329	C₂²×C₁₉	semidirect
368. #329	C₂²×C₁₉	semidirect
469. C₁₉	#19087	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×#3558	2
C₁₉×#3240	2
C₁₉×#3216	2
C₁₉×#3215	2
C₁₉×#1661	2
C₁₉×#1659	2
C₁₉×#1536	2
C₁₉×#1535	2
C₁₉×#1533	2
#19087	19

Subgroups — C19×#19087 #18025046

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19087 #18025046