Subgroups — C₁₉×#29509 #18035468

Order 4864.

676 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2645	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2327	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2085	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2074	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2043	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#2016	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1971	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1969	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1935	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1933	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1878	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#1878	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1865	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#1863	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#1746	C₂	1	1	yes	maximal, characteristic
16	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
33	C₁₉×#401	—	2	1	no	—
34	C₁₉×#400	—	2	1	no	—
35	C₁₉×#400	—	2	1	no	—
36	C₁₉×#400	—	2	1	no	—
37	C₁₉×#391	C₂²	1	1	yes	characteristic
38	C₁₉×#391	C₂²	1	1	yes	characteristic
39	C₁₉×#391	C₂²	1	1	yes	characteristic
40	C₁₉×#391	C₂²	1	1	yes	characteristic
41	C₁₉×#391	C₂²	1	1	yes	characteristic
42	C₁₉×#389	C₂²	1	1	yes	characteristic
43	C₁₉×#389	C₂²	1	1	yes	characteristic
44	C₁₉×#389	C₂²	1	1	yes	characteristic
45	C₁₉×#387	—	2	1	no	—
46	C₁₉×#387	—	2	1	no	—
47	C₁₉×#387	—	2	1	no	—
48	C₁₉×#387	—	2	1	no	—
49	C₁₉×#382	C₂²	1	1	yes	characteristic
50	C₁₉×#376	C₂²	1	1	yes	characteristic
51	C₁₉×#340	C₂²	1	1	yes	characteristic
52	C₁₉×#340	C₂²	1	1	yes	characteristic
53	C₁₉×#340	C₂²	1	1	yes	characteristic
54	C₁₉×#340	C₂²	1	1	yes	characteristic
55	C₁₉×#336	C₂²	1	1	yes	characteristic
56	C₁₉×#336	C₂²	1	1	yes	characteristic
57	C₁₉×#336	C₂²	1	1	yes	characteristic
58	C₁₉×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
60	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
61	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₂×Q₁₆×C₁₉	—	2	2	no	—
63	C₂×Q₁₆×C₁₉	—	2	2	no	—
64	C₂×Q₁₆×C₁₉	—	2	2	no	—
65	C₂×Q₁₆×C₁₉	—	2	2	no	—
66	C₂×Q₁₆×C₁₉	—	4	1	no	—
67	C₂×Q₁₆×C₁₉	—	4	1	no	—
68	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
72	C₁₉×C₄⋊Q₈	—	2	2	no	—
73	C₁₉×C₄⋊Q₈	—	2	2	no	—
74	C₄×Q₈×C₁₉	—	4	1	no	—
75	C₄×Q₈×C₁₉	—	4	1	no	—
76	C₄×Q₈×C₁₉	—	4	1	no	—
77	C₄×Q₈×C₁₉	—	4	1	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₁₉	—	2	1	no	—
91	C₂×C₄²×C₁₉	—	2	1	no	—
92	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
95	C₁₉×#107	—	4	1	no	—
96	C₁₉×#106	—	4	1	no	—
97	C₁₉×#103	—	2	2	no	—
98	C₁₉×#103	—	2	2	no	—
99	C₁₉×#103	—	2	2	no	—
100	C₁₉×#103	—	2	2	no	—
101	C₁₉×#103	—	4	1	no	—
102	C₁₉×#103	—	4	1	no	—
103	C₁₉×#103	—	4	1	no	—
104	C₁₉×#103	—	4	1	no	—
105	C₁₉×#97	—	2	2	no	—
106	C₄×C₈×C₁₉	—	2	2	no	—
107	C₁₉×#95	—	2	1	no	—
108	C₁₉×#95	—	2	1	no	—
109	C₁₉×#95	—	2	1	no	—
110	C₁₉×#95	—	2	1	no	—
111	C₁₉×#95	—	2	1	no	—
112	C₁₉×#95	—	2	1	no	—
113	C₁₉×#95	—	2	1	no	—
114	C₁₉×#95	—	2	1	no	—
115	C₁₉×#95	—	2	1	no	—
116	C₁₉×#95	—	2	1	no	—
117	C₁₉×#95	—	2	1	no	—
118	C₁₉×#95	—	2	1	no	—
119	C₁₉×#95	—	2	1	no	—
120	C₁₉×#95	—	2	1	no	—
121	C₁₉×#95	—	2	1	no	—
122	C₁₉×#95	D₄	1	1	yes	characteristic
123	C₁₉×#95	D₄	1	1	yes	characteristic
124	C₁₉×#95	D₄	1	1	yes	characteristic
125	C₁₉×#95	D₄	1	1	yes	characteristic
126	C₂×Q₈×C₁₉	—	2	1	no	—
127	C₂×Q₈×C₁₉	—	2	1	no	—
128	C₂×Q₈×C₁₉	—	2	1	no	—
129	C₂×Q₈×C₁₉	—	2	1	no	—
130	C₂×Q₈×C₁₉	—	2	1	no	—
131	C₂×Q₈×C₁₉	—	2	1	no	—
132	C₂×Q₈×C₁₉	—	2	1	no	—
133	C₂×Q₈×C₁₉	—	2	1	no	—
134	C₂×Q₈×C₁₉	—	2	1	no	—
135	C₂×Q₈×C₁₉	—	2	1	no	—
136	C₂×Q₈×C₁₉	—	2	1	no	—
137	C₂×Q₈×C₁₉	—	2	1	no	—
138	C₂×Q₈×C₁₉	—	2	1	no	—
139	C₂×Q₈×C₁₉	—	2	1	no	—
140	C₂×Q₈×C₁₉	—	2	1	no	—
141	C₂×Q₈×C₁₉	—	2	1	no	—
142	C₂×Q₈×C₁₉	#41	1	2	yes	—
143	C₂×Q₈×C₁₉	#41	1	2	yes	—
144	C₂²×C₄×C₁₉	—	2	1	no	—
145	C₂²×C₄×C₁₉	—	2	1	no	—
146	C₂²×C₄×C₁₉	—	2	1	no	—
147	C₂²×C₄×C₁₉	—	2	1	no	—
148	C₂²×C₄×C₁₉	—	2	1	no	—
149	C₂²×C₄×C₁₉	—	2	1	no	—
150	C₂²×C₄×C₁₉	—	2	1	no	—
151	C₂²×C₄×C₁₉	—	2	1	no	—
152	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
159	Q₁₆×C₁₉	—	4	4	no	—
160	Q₁₆×C₁₉	—	4	4	no	—
161	C₂×C₈×C₁₉	—	2	1	no	—
162	C₂×C₈×C₁₉	—	2	1	no	—
163	C₂×C₈×C₁₉	—	2	1	no	—
164	C₂×C₈×C₁₉	—	2	1	no	—
165	C₂×C₈×C₁₉	—	2	1	no	—
166	C₂×C₈×C₁₉	—	2	1	no	—
167	C₂×C₈×C₁₉	—	2	1	no	—
168	C₂×C₈×C₁₉	—	2	1	no	—
169	C₂×C₈×C₁₉	—	2	1	no	—
170	C₂×C₈×C₁₉	—	2	1	no	—
171	C₂×C₈×C₁₉	#41	1	2	yes	—
172	C₂×C₈×C₁₉	#41	1	2	yes	—
173	C₄⋊C₄×C₁₉	—	2	4	no	—
174	C₄⋊C₄×C₁₉	—	2	4	no	—
175	C₄⋊C₄×C₁₉	—	2	1	no	—
176	C₄⋊C₄×C₁₉	—	2	1	no	—
177	C₄⋊C₄×C₁₉	—	2	1	no	—
178	C₄⋊C₄×C₁₉	—	2	1	no	—
179	C₄⋊C₄×C₁₉	—	2	1	no	—
180	C₄⋊C₄×C₁₉	—	2	1	no	—
181	C₄⋊C₄×C₁₉	—	2	1	no	—
182	C₄⋊C₄×C₁₉	—	2	1	no	—
183	C₄⋊C₄×C₁₉	—	2	1	no	—
184	C₄⋊C₄×C₁₉	—	2	1	no	—
185	C₄⋊C₄×C₁₉	—	4	2	no	—
186	C₄⋊C₄×C₁₉	—	4	2	no	—
187	C₄⋊C₄×C₁₉	—	8	1	no	—
188	C₄⋊C₄×C₁₉	—	8	1	no	—
189	C₄⋊C₄×C₁₉	—	8	1	no	—
190	C₄²×C₁₉	—	2	1	no	—
191	C₄²×C₁₉	—	2	1	no	—
192	C₄²×C₁₉	—	2	1	no	—
193	C₄²×C₁₉	—	2	1	no	—
194	C₄²×C₁₉	—	2	1	no	—
195	C₄²×C₁₉	—	2	1	no	—
196	C₄²×C₁₉	—	4	2	no	—
197	C₄²×C₁₉	—	4	2	no	—
198	#29509	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
200	Q₈×C₁₉	—	2	2	no	—
201	Q₈×C₁₉	—	2	2	no	—
202	Q₈×C₁₉	—	2	2	no	—
203	Q₈×C₁₉	—	2	2	no	—
204	Q₈×C₁₉	—	4	1	no	—
205	Q₈×C₁₉	—	4	1	no	—
206	Q₈×C₁₉	—	4	1	no	—
207	Q₈×C₁₉	—	4	1	no	—
208	Q₈×C₁₉	—	4	1	no	—
209	Q₈×C₁₉	—	4	1	no	—
210	Q₈×C₁₉	—	4	1	no	—
211	Q₈×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	—	2	1	no	—
213	C₂×C₄×C₁₉	—	2	1	no	—
214	C₂×C₄×C₁₉	—	2	2	no	—
215	C₂×C₄×C₁₉	—	2	2	no	—
216	C₂×C₄×C₁₉	—	2	1	no	—
217	C₂×C₄×C₁₉	—	2	1	no	—
218	C₂×C₄×C₁₉	—	2	1	no	—
219	C₂×C₄×C₁₉	—	2	1	no	—
220	C₂×C₄×C₁₉	—	2	1	no	—
221	C₂×C₄×C₁₉	—	2	1	no	—
222	C₂×C₄×C₁₉	—	2	1	no	—
223	C₂×C₄×C₁₉	—	2	1	no	—
224	C₂×C₄×C₁₉	—	2	1	no	—
225	C₂×C₄×C₁₉	—	2	1	no	—
226	C₂×C₄×C₁₉	—	2	1	no	—
227	C₂×C₄×C₁₉	—	2	1	no	—
228	C₂×C₄×C₁₉	—	2	1	no	—
229	C₂×C₄×C₁₉	—	2	1	no	—
230	C₂×C₄×C₁₉	—	2	1	no	—
231	C₂×C₄×C₁₉	—	2	1	no	—
232	C₂×C₄×C₁₉	—	4	1	no	—
233	C₂×C₄×C₁₉	—	4	1	no	—
234	C₂×C₄×C₁₉	—	4	1	no	—
235	C₂×C₄×C₁₉	—	4	1	no	—
236	C₂×C₄×C₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	—	4	1	no	—
238	C₂×C₄×C₁₉	—	4	1	no	—
239	C₂×C₄×C₁₉	—	4	1	no	—
240	C₂×C₄×C₁₉	—	4	1	no	—
241	C₂×C₄×C₁₉	—	4	1	no	—
242	C₂×C₄×C₁₉	—	4	1	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	—	4	1	no	—
252	C₂×C₄×C₁₉	—	4	1	no	—
253	C₂×C₄×C₁₉	—	4	1	no	—
254	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
255	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
256	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
257	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
258	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
259	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
260	C₈×C₁₉	—	2	2	no	—
261	C₈×C₁₉	—	2	2	no	—
262	C₈×C₁₉	—	4	1	no	—
263	C₈×C₁₉	—	4	1	no	—
264	#2645	C₂×C₁₉	1	1	yes	characteristic
265	#2327	C₂×C₁₉	1	1	yes	characteristic
266	#2085	C₂×C₁₉	1	1	yes	characteristic
267	#2074	C₂×C₁₉	1	1	yes	characteristic
268	#2043	C₂×C₁₉	1	1	yes	characteristic
269	#2016	C₂×C₁₉	1	1	yes	characteristic
270	#1971	C₂×C₁₉	1	1	yes	characteristic
271	#1969	C₂×C₁₉	1	1	yes	characteristic
272	#1935	C₂×C₁₉	1	1	yes	characteristic
273	#1933	C₂×C₁₉	1	1	yes	characteristic
274	#1878	C₂×C₁₉	1	1	yes	characteristic
275	#1878	C₂×C₁₉	1	1	yes	characteristic
276	#1865	C₂×C₁₉	1	1	yes	characteristic
277	#1863	C₂×C₁₉	1	1	yes	characteristic
278	#1746	C₂×C₁₉	1	1	yes	characteristic
279	C₂²×C₁₉	#525	1	1	yes	characteristic
280	C₂²×C₁₉	#532	1	1	yes	characteristic
281	C₂²×C₁₉	#535	1	1	yes	characteristic
282	C₂²×C₁₉	#577	1	1	yes	characteristic
283	C₂²×C₁₉	#578	1	1	yes	characteristic
284	C₂²×C₁₉	#578	1	1	yes	characteristic
285	C₂²×C₁₉	#578	1	1	yes	characteristic
286	C₄×C₁₉	—	4	2	no	—
287	C₄×C₁₉	—	4	2	no	—
288	C₄×C₁₉	—	4	1	no	—
289	C₄×C₁₉	—	4	1	no	—
290	C₄×C₁₉	—	4	1	no	—
291	C₄×C₁₉	—	4	1	no	—
292	C₄×C₁₉	—	4	1	no	—
293	C₄×C₁₉	—	4	1	no	—
294	C₄×C₁₉	—	8	1	no	—
295	C₄×C₁₉	—	8	1	no	—
296	C₄×C₁₉	—	8	1	no	—
297	C₄×C₁₉	—	8	1	no	—
298	C₄×C₁₉	—	8	1	no	—
299	C₄×C₁₉	—	8	1	no	—
300	C₄×C₁₉	#551	1	1	yes	characteristic
301	C₄×C₁₉	#551	1	1	yes	characteristic
302	C₄×C₁₉	#553	1	1	yes	characteristic
303	C₄×C₁₉	#553	1	1	yes	characteristic
304	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
305	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
306	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
307	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
308	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
309	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
310	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
311	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
312	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
313	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
314	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
315	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
316	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
317	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
318	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
319	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
320	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
321	#401	—	2	1	no	—
322	#400	—	2	1	no	—
323	#400	—	2	1	no	—
324	#400	—	2	1	no	—
325	#391	C₂²×C₁₉	1	1	yes	characteristic
326	#391	C₂²×C₁₉	1	1	yes	characteristic
327	#391	C₂²×C₁₉	1	1	yes	characteristic
328	#391	C₂²×C₁₉	1	1	yes	characteristic
329	#391	C₂²×C₁₉	1	1	yes	characteristic
330	#389	C₂²×C₁₉	1	1	yes	characteristic
331	#389	C₂²×C₁₉	1	1	yes	characteristic
332	#389	C₂²×C₁₉	1	1	yes	characteristic
333	#387	—	2	1	no	—
334	#387	—	2	1	no	—
335	#387	—	2	1	no	—
336	#387	—	2	1	no	—
337	#382	C₂²×C₁₉	1	1	yes	characteristic
338	#376	C₂²×C₁₉	1	1	yes	characteristic
339	#340	C₂²×C₁₉	1	1	yes	characteristic
340	#340	C₂²×C₁₉	1	1	yes	characteristic
341	#340	C₂²×C₁₉	1	1	yes	characteristic
342	#340	C₂²×C₁₉	1	1	yes	characteristic
343	#336	C₂²×C₁₉	1	1	yes	characteristic
344	#336	C₂²×C₁₉	1	1	yes	characteristic
345	#336	C₂²×C₁₉	1	1	yes	characteristic
346	#336	C₂²×C₁₉	1	1	yes	characteristic
347	C₂×C₁₉	#2603	1	1	yes	characteristic
348	C₂×C₁₉	#3121	1	1	yes	characteristic
349	C₂×C₁₉	#3127	1	1	yes	characteristic
350	C₂×C₁₉	#3177	1	1	yes	characteristic
351	C₂×C₁₉	#3178	1	1	yes	characteristic
352	C₂×C₁₉	#3223	1	1	yes	characteristic
353	C₂×C₁₉	#3225	1	1	yes	characteristic
354	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
355	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
356	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
357	C₂×Q₁₆	—	2	2	no	—
358	C₂×Q₁₆	—	2	2	no	—
359	C₂×Q₁₆	—	2	2	no	—
360	C₂×Q₁₆	—	2	2	no	—
361	C₂×Q₁₆	—	4	1	no	—
362	C₂×Q₁₆	—	4	1	no	—
363	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
364	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
365	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
366	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
367	C₄⋊Q₈	—	2	2	no	—
368	C₄⋊Q₈	—	2	2	no	—
369	C₄×Q₈	—	4	1	no	—
370	C₄×Q₈	—	4	1	no	—
371	C₄×Q₈	—	4	1	no	—
372	C₄×Q₈	—	4	1	no	—
373	C₂×C₄⋊C₄	—	2	1	no	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	—	2	1	no	—
377	C₂×C₄⋊C₄	—	2	1	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
381	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
384	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
385	C₂×C₄²	—	2	1	no	—
386	C₂×C₄²	—	2	1	no	—
387	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
388	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
389	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
390	#107	—	4	1	no	—
391	#106	—	4	1	no	—
392	#103	—	2	2	no	—
393	#103	—	2	2	no	—
394	#103	—	2	2	no	—
395	#103	—	2	2	no	—
396	#103	—	4	1	no	—
397	#103	—	4	1	no	—
398	#103	—	4	1	no	—
399	#103	—	4	1	no	—
400	#97	—	2	2	no	—
401	C₄×C₈	—	2	2	no	—
402	#95	—	2	1	no	—
403	#95	—	2	1	no	—
404	#95	—	2	1	no	—
405	#95	—	2	1	no	—
406	#95	—	2	1	no	—
407	#95	—	2	1	no	—
408	#95	—	2	1	no	—
409	#95	—	2	1	no	—
410	#95	—	2	1	no	—
411	#95	—	2	1	no	—
412	#95	—	2	1	no	—
413	#95	—	2	1	no	—
414	#95	—	2	1	no	—
415	#95	—	2	1	no	—
416	#95	—	2	1	no	—
417	#95	D₄×C₁₉	1	1	yes	characteristic
418	#95	D₄×C₁₉	1	1	yes	characteristic
419	#95	D₄×C₁₉	1	1	yes	characteristic
420	#95	D₄×C₁₉	1	1	yes	characteristic
421	C₁₉	#29509	1	1	yes	characteristic, direct product factor, Sylow
422	C₂×Q₈	—	2	1	no	—
423	C₂×Q₈	—	2	1	no	—
424	C₂×Q₈	—	2	1	no	—
425	C₂×Q₈	—	2	1	no	—
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	#41×C₁₉	1	2	yes	—
439	C₂×Q₈	#41×C₁₉	1	2	yes	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
449	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
450	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
451	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
453	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
454	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
455	Q₁₆	—	4	4	no	—
456	Q₁₆	—	4	4	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	#41×C₁₉	1	2	yes	—
468	C₂×C₈	#41×C₁₉	1	2	yes	—
469	C₄⋊C₄	—	2	4	no	—
470	C₄⋊C₄	—	2	4	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	4	2	no	—
482	C₄⋊C₄	—	4	2	no	—
483	C₄⋊C₄	—	8	1	no	—
484	C₄⋊C₄	—	8	1	no	—
485	C₄⋊C₄	—	8	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	2	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	4	2	no	—
493	C₄²	—	4	2	no	—
494	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
495	Q₈	—	2	2	no	—
496	Q₈	—	2	2	no	—
497	Q₈	—	2	2	no	—
498	Q₈	—	2	2	no	—
499	Q₈	—	4	1	no	—
500	Q₈	—	4	1	no	—
501	Q₈	—	4	1	no	—
502	Q₈	—	4	1	no	—
503	Q₈	—	4	1	no	—
504	Q₈	—	4	1	no	—
505	Q₈	—	4	1	no	—
506	Q₈	—	4	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	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	—	4	1	no	—
549	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
550	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
551	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
552	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
553	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
554	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
555	C₈	—	2	2	no	—
556	C₈	—	2	2	no	—
557	C₈	—	4	1	no	—
558	C₈	—	4	1	no	—
559	C₂²	C₁₉×#525	1	1	yes	characteristic
560	C₂²	C₁₉×#532	1	1	yes	characteristic
561	C₂²	C₁₉×#535	1	1	yes	characteristic
562	C₂²	C₁₉×#577	1	1	yes	characteristic
563	C₂²	C₁₉×#578	1	1	yes	characteristic
564	C₂²	C₁₉×#578	1	1	yes	characteristic
565	C₂²	C₁₉×#578	1	1	yes	characteristic
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	2	no	—
571	C₄	—	4	2	no	—
572	C₄	—	4	1	no	—
573	C₄	—	4	1	no	—
574	C₄	—	8	1	no	—
575	C₄	—	8	1	no	—
576	C₄	—	8	1	no	—
577	C₄	—	8	1	no	—
578	C₄	—	8	1	no	—
579	C₄	—	8	1	no	—
580	C₄	C₁₉×#551	1	1	yes	characteristic
581	C₄	C₁₉×#551	1	1	yes	characteristic
582	C₄	C₁₉×#553	1	1	yes	characteristic
583	C₄	C₁₉×#553	1	1	yes	characteristic
584	C₂	C₁₉×#2603	1	1	yes	characteristic
585	C₂	C₁₉×#3121	1	1	yes	characteristic
586	C₂	C₁₉×#3127	1	1	yes	characteristic
587	C₂	C₁₉×#3177	1	1	yes	characteristic
588	C₂	C₁₉×#3178	1	1	yes	characteristic
589	C₂	C₁₉×#3223	1	1	yes	characteristic
590	C₂	C₁₉×#3225	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₁₉×#376 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
198. #29509	C₁₉	direct (N × H)
421. C₁₉	#29509	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×#2645	2
C₁₉×#2327	2
C₁₉×#2085	2
C₁₉×#2074	2
C₁₉×#2043	2
C₁₉×#2016	2
C₁₉×#1971	2
C₁₉×#1969	2
C₁₉×#1935	2
C₁₉×#1933	2
C₁₉×#1878	2
C₁₉×#1865	2
C₁₉×#1863	2
C₁₉×#1746	2
#29509	19

Subgroups — C19×#29509 #18035468

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#29509 #18035468