Subgroups — C₁₉×#11093 #18017052

Order 4864.

910 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2896	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#417	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#410	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2317	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#344	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1736	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1733	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#419	—	2	1	no	—
16	C₁₉×#418	—	2	1	no	—
17	C₁₉×#417	—	2	2	no	—
18	C₁₉×#417	—	2	2	no	—
19	C₁₉×#417	—	2	1	no	—
20	C₁₉×#417	—	2	1	no	—
21	C₁₉×#416	—	2	2	no	—
22	C₂×C₁₉×#103	—	2	1	no	—
23	C₂×C₁₉×#102	—	2	1	no	—
24	C₁₉×#410	—	2	2	no	—
25	C₁₉×#410	C₄	1	4	yes	complemented
26	C₂×C₁₉×#99	—	2	2	no	—
27	C₁₉×#389	—	2	2	no	—
28	C₁₉×#385	—	2	2	no	—
29	C₁₉×#384	—	2	1	no	—
30	C₁₉×#382	—	2	1	no	—
31	C₁₉×#344	—	2	2	no	—
32	C₁₉×#340	—	2	2	no	—
33	C₁₉×#339	—	2	2	no	—
34	C₂×#41×C₁₉	—	2	1	no	—
35	C₂×#41×C₁₉	—	2	1	no	—
36	C₂×#41×C₁₉	—	2	1	no	—
37	C₂×#41×C₁₉	—	2	1	no	—
38	C₂×#41×C₁₉	—	2	1	no	—
39	C₂×#41×C₁₉	—	2	1	no	—
40	C₂×#41×C₁₉	—	2	1	no	—
41	C₂×#41×C₁₉	—	2	1	no	—
42	C₂×#41×C₁₉	—	2	1	no	—
43	C₂×#41×C₁₉	—	2	1	no	—
44	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
45	C₂×#41×C₁₉	Q₈	1	2	yes	—
46	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
47	C₂²×D₄×C₁₉	—	2	1	no	—
48	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₉	—	2	1	no	—
50	C₂³×C₄×C₁₉	—	2	1	no	—
51	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
52	C₂×M₁₆×C₁₉	—	2	1	no	—
53	C₂×M₁₆×C₁₉	—	2	1	no	—
54	C₂×M₁₆×C₁₉	—	2	1	no	—
55	C₂×M₁₆×C₁₉	—	2	1	no	—
56	C₂×M₁₆×C₁₉	—	2	1	no	—
57	C₂×M₁₆×C₁₉	—	2	1	no	—
58	C₂×M₁₆×C₁₉	—	2	1	no	—
59	C₂×M₁₆×C₁₉	—	2	1	no	—
60	C₂×M₁₆×C₁₉	—	2	1	no	—
61	C₂×M₁₆×C₁₉	—	2	1	no	—
62	C₂×M₁₆×C₁₉	—	2	1	no	—
63	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
64	C₂²×C₈×C₁₉	—	2	1	no	—
65	C₂²×C₈×C₁₉	D₄	1	2	yes	—
66	C₁₉×#117	—	2	1	no	—
67	C₁₉×#117	—	2	1	no	—
68	C₁₉×#117	—	2	1	no	—
69	C₁₉×#117	—	2	1	no	—
70	C₁₉×#117	—	2	1	no	—
71	C₁₉×#117	—	2	1	no	—
72	C₁₉×#117	—	2	1	no	—
73	C₁₉×#117	—	2	1	no	—
74	C₁₉×#117	—	2	1	no	—
75	C₁₉×#117	C₂×C₄	1	2	yes	—
76	C₁₉×#117	C₂×C₄	1	2	yes	—
77	C₁₉×#117	D₄	1	2	yes	—
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	—	2	4	no	—
86	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
89	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
92	C₂×C₄²×C₁₉	—	2	1	no	—
93	C₂×C₄²×C₁₉	—	2	1	no	—
94	C₂×C₄²×C₁₉	—	2	1	no	—
95	C₁₉×#103	—	2	4	no	—
96	C₁₉×#103	—	2	2	no	—
97	C₁₉×#103	—	2	2	no	—
98	C₁₉×#102	—	2	4	no	—
99	C₁₉×#102	—	2	2	no	—
100	C₁₉×#102	—	2	2	no	—
101	C₁₉×#99	—	2	8	no	—
102	C₁₉×#95	—	2	4	no	—
103	C₂⁴×C₁₉	—	2	1	no	—
104	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
105	#41×C₁₉	—	2	2	no	—
106	#41×C₁₉	—	2	2	no	—
107	#41×C₁₉	—	2	2	no	—
108	#41×C₁₉	—	2	2	no	—
109	#41×C₁₉	—	2	2	no	—
110	#41×C₁₉	—	2	2	no	—
111	#41×C₁₉	—	2	2	no	—
112	#41×C₁₉	—	2	2	no	—
113	#41×C₁₉	—	4	1	no	—
114	#41×C₁₉	—	4	1	no	—
115	#41×C₁₉	—	4	1	no	—
116	#41×C₁₉	—	4	1	no	—
117	#41×C₁₉	—	4	1	no	—
118	#41×C₁₉	—	4	1	no	—
119	#41×C₁₉	—	4	1	no	—
120	#41×C₁₉	—	4	1	no	—
121	C₂×Q₈×C₁₉	—	2	1	no	—
122	C₂×Q₈×C₁₉	—	2	1	no	—
123	C₂×Q₈×C₁₉	—	2	1	no	—
124	C₂×Q₈×C₁₉	—	2	1	no	—
125	C₂×Q₈×C₁₉	—	2	1	no	—
126	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	complemented
127	C₂×D₄×C₁₉	—	2	2	no	—
128	C₂×D₄×C₁₉	—	2	2	no	—
129	C₂×D₄×C₁₉	—	2	1	no	—
130	C₂×D₄×C₁₉	—	2	1	no	—
131	C₂×D₄×C₁₉	—	2	1	no	—
132	C₂×D₄×C₁₉	—	2	1	no	—
133	C₂×D₄×C₁₉	—	2	1	no	—
134	C₂×D₄×C₁₉	—	4	1	no	—
135	C₂×D₄×C₁₉	—	4	1	no	—
136	C₂×D₄×C₁₉	—	4	1	no	—
137	C₂×D₄×C₁₉	—	4	1	no	—
138	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	complemented
139	C₂²×C₄×C₁₉	—	2	2	no	—
140	C₂²×C₄×C₁₉	—	2	1	no	—
141	C₂²×C₄×C₁₉	—	2	2	no	—
142	C₂²×C₄×C₁₉	—	2	2	no	—
143	C₂²×C₄×C₁₉	—	2	1	no	—
144	C₂²×C₄×C₁₉	—	2	1	no	—
145	C₂²×C₄×C₁₉	—	2	2	no	—
146	C₂²×C₄×C₁₉	—	4	1	no	—
147	C₂²×C₄×C₁₉	—	4	1	no	—
148	C₂²×C₄×C₁₉	—	4	1	no	—
149	C₂²×C₄×C₁₉	—	4	1	no	—
150	C₂²×C₄×C₁₉	—	4	1	no	—
151	C₂²×C₄×C₁₉	—	4	1	no	—
152	C₂²×C₄×C₁₉	—	4	1	no	—
153	C₂²×C₄×C₁₉	—	8	2	no	—
154	C₂²×C₄×C₁₉	C₂²×C₄	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	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
162	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
163	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
164	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
165	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
166	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
167	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
168	M₁₆×C₁₉	—	2	2	no	—
169	M₁₆×C₁₉	—	2	2	no	—
170	M₁₆×C₁₉	—	4	1	no	—
171	M₁₆×C₁₉	—	4	1	no	—
172	M₁₆×C₁₉	—	4	1	no	—
173	M₁₆×C₁₉	—	4	1	no	—
174	M₁₆×C₁₉	—	4	1	no	—
175	M₁₆×C₁₉	—	4	1	no	—
176	C₂×C₈×C₁₉	—	2	2	no	—
177	C₂×C₈×C₁₉	—	2	2	no	—
178	C₂×C₈×C₁₉	—	2	2	no	—
179	C₂×C₈×C₁₉	—	2	2	no	—
180	C₂×C₈×C₁₉	—	4	1	no	—
181	C₂×C₈×C₁₉	—	4	1	no	—
182	C₄⋊C₄×C₁₉	—	2	2	no	—
183	C₄⋊C₄×C₁₉	—	2	2	no	—
184	C₄⋊C₄×C₁₉	—	2	2	no	—
185	C₄⋊C₄×C₁₉	—	2	2	no	—
186	C₄⋊C₄×C₁₉	—	2	1	no	—
187	C₄⋊C₄×C₁₉	—	2	1	no	—
188	C₄⋊C₄×C₁₉	—	2	2	no	—
189	C₄⋊C₄×C₁₉	—	2	1	no	—
190	C₄⋊C₄×C₁₉	—	2	1	no	—
191	C₄⋊C₄×C₁₉	—	4	1	no	—
192	C₄⋊C₄×C₁₉	—	4	1	no	—
193	C₄⋊C₄×C₁₉	—	4	1	no	—
194	C₄⋊C₄×C₁₉	—	8	4	no	—
195	C₂²⋊C₄×C₁₉	—	2	2	no	—
196	C₂²⋊C₄×C₁₉	—	2	2	no	—
197	C₂²⋊C₄×C₁₉	—	4	1	no	—
198	C₂²⋊C₄×C₁₉	—	4	1	no	—
199	C₂²⋊C₄×C₁₉	—	4	1	no	—
200	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
201	C₄²×C₁₉	—	2	2	no	—
202	C₄²×C₁₉	—	2	2	no	—
203	C₄²×C₁₉	—	2	2	no	—
204	C₄²×C₁₉	—	4	1	no	—
205	C₄²×C₁₉	—	4	1	no	—
206	C₄²×C₁₉	—	4	1	no	—
207	#11093	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂³×C₁₉	—	2	2	no	—
209	C₂³×C₁₉	—	4	1	no	—
210	C₂³×C₁₉	—	4	1	no	—
211	C₂³×C₁₉	—	4	1	no	—
212	C₂³×C₁₉	—	4	1	no	—
213	C₂³×C₁₉	—	8	1	no	—
214	C₂³×C₁₉	—	8	1	no	—
215	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂³×C₁₉	#120	1	1	yes	characteristic
217	C₂³×C₁₉	#121	1	1	yes	characteristic
218	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
219	C₂³×C₁₉	#123	1	1	yes	characteristic
220	C₂³×C₁₉	#124	1	1	yes	characteristic
221	C₂³×C₁₉	#127	1	1	yes	characteristic
222	Q₈×C₁₉	—	2	2	no	—
223	Q₈×C₁₉	—	2	2	no	—
224	Q₈×C₁₉	—	4	1	no	—
225	Q₈×C₁₉	—	4	1	no	—
226	D₄×C₁₉	—	2	2	no	—
227	D₄×C₁₉	—	2	2	no	—
228	D₄×C₁₉	—	4	2	no	—
229	D₄×C₁₉	—	4	2	no	—
230	D₄×C₁₉	—	4	2	no	—
231	D₄×C₁₉	—	4	2	no	—
232	D₄×C₁₉	—	4	1	no	—
233	D₄×C₁₉	—	4	1	no	—
234	C₂×C₄×C₁₉	—	2	2	no	—
235	C₂×C₄×C₁₉	—	2	4	no	—
236	C₂×C₄×C₁₉	—	4	2	no	—
237	C₂×C₄×C₁₉	—	4	2	no	—
238	C₂×C₄×C₁₉	—	4	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	2	no	—
244	C₂×C₄×C₁₉	—	4	2	no	—
245	C₂×C₄×C₁₉	—	4	4	no	—
246	C₂×C₄×C₁₉	—	4	2	no	—
247	C₂×C₄×C₁₉	—	4	2	no	—
248	C₂×C₄×C₁₉	—	4	1	no	—
249	C₂×C₄×C₁₉	—	4	1	no	—
250	C₂×C₄×C₁₉	—	4	2	no	—
251	C₂×C₄×C₁₉	—	8	1	no	—
252	C₂×C₄×C₁₉	—	8	1	no	—
253	C₂×C₄×C₁₉	—	8	2	no	—
254	C₂×C₄×C₁₉	—	8	2	no	—
255	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
256	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
257	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
258	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
259	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
260	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
261	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
262	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
263	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
264	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
265	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
266	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
267	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
268	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
269	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
270	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
271	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
272	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
273	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
274	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
275	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
276	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
277	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
278	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
279	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
280	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
281	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
282	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
283	C₈×C₁₉	—	4	2	no	—
284	C₈×C₁₉	—	4	2	no	—
285	#2896	C₂×C₁₉	1	1	yes	characteristic
286	C₂×#417	C₂×C₁₉	1	1	yes	characteristic
287	C₂×#410	C₂×C₁₉	1	1	yes	characteristic
288	#2317	C₂×C₁₉	1	1	yes	characteristic, complemented
289	C₂×#344	C₂×C₁₉	1	1	yes	characteristic, complemented
290	#1736	C₂×C₁₉	1	1	yes	characteristic, complemented
291	#1733	C₂×C₁₉	1	1	yes	characteristic, complemented
292	C₂²×C₁₉	—	2	1	no	—
293	C₂²×C₁₉	—	2	1	no	—
294	C₂²×C₁₉	—	2	1	no	—
295	C₂²×C₁₉	—	2	1	no	—
296	C₂²×C₁₉	—	2	1	no	—
297	C₂²×C₁₉	—	2	1	no	—
298	C₂²×C₁₉	—	4	1	no	—
299	C₂²×C₁₉	—	4	1	no	—
300	C₂²×C₁₉	—	4	1	no	—
301	C₂²×C₁₉	—	4	1	no	—
302	C₂²×C₁₉	—	4	2	no	—
303	C₂²×C₁₉	—	8	2	no	—
304	C₂²×C₁₉	—	8	2	no	—
305	C₂²×C₁₉	—	8	1	no	—
306	C₂²×C₁₉	—	8	1	no	—
307	C₂²×C₁₉	#380	1	1	yes	characteristic
308	C₂²×C₁₉	#386	1	1	yes	characteristic
309	C₂²×C₁₉	#390	1	1	yes	characteristic
310	C₂²×C₁₉	#392	1	1	yes	characteristic
311	C₂²×C₁₉	#393	1	1	yes	characteristic
312	C₂²×C₁₉	#397	1	1	yes	characteristic
313	C₂²×C₁₉	#399	1	1	yes	characteristic
314	C₄×C₁₉	—	4	4	no	—
315	C₄×C₁₉	—	4	2	no	—
316	C₄×C₁₉	—	8	2	no	—
317	C₄×C₁₉	—	8	1	no	—
318	C₄×C₁₉	—	8	2	no	—
319	C₄×C₁₉	—	8	1	no	—
320	C₄×C₁₉	#385	1	1	yes	characteristic
321	C₄×C₁₉	#385	1	1	yes	characteristic
322	C₄×C₁₉	#388	1	1	yes	characteristic
323	C₄×C₁₉	#388	1	1	yes	characteristic
324	C₄×C₁₉	#394	1	1	yes	characteristic
325	C₄×C₁₉	#394	1	1	yes	characteristic
326	C₄×C₁₉	#396	1	1	yes	characteristic
327	C₄×C₁₉	#396	1	1	yes	characteristic
328	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
329	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
330	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
331	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
332	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
333	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
334	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
335	#419	—	2	1	no	—
336	#418	—	2	1	no	—
337	#417	—	2	2	no	—
338	#417	—	2	2	no	—
339	#417	—	2	1	no	—
340	#417	—	2	1	no	—
341	#416	—	2	2	no	—
342	C₂×#103	—	2	1	no	—
343	C₂×#102	—	2	1	no	—
344	#410	—	2	2	no	—
345	#410	C₄×C₁₉	1	4	yes	complemented
346	C₂×#99	—	2	2	no	—
347	#389	—	2	2	no	—
348	#385	—	2	2	no	—
349	#384	—	2	1	no	—
350	#382	—	2	1	no	—
351	#344	—	2	2	no	—
352	#340	—	2	2	no	—
353	#339	—	2	2	no	—
354	C₂×C₁₉	—	2	1	no	—
355	C₂×C₁₉	—	2	1	no	—
356	C₂×C₁₉	—	2	1	no	—
357	C₂×C₁₉	—	2	1	no	—
358	C₂×C₁₉	—	2	1	no	—
359	C₂×C₁₉	—	2	1	no	—
360	C₂×C₁₉	—	8	2	no	—
361	C₂×C₁₉	#1439	1	1	yes	characteristic
362	C₂×C₁₉	#2008	1	1	yes	characteristic
363	C₂×C₁₉	#2009	1	1	yes	characteristic
364	C₂×#41	—	2	1	no	—
365	C₂×#41	—	2	1	no	—
366	C₂×#41	—	2	1	no	—
367	C₂×#41	—	2	1	no	—
368	C₂×#41	—	2	1	no	—
369	C₂×#41	—	2	1	no	—
370	C₂×#41	—	2	1	no	—
371	C₂×#41	—	2	1	no	—
372	C₂×#41	—	2	1	no	—
373	C₂×#41	—	2	1	no	—
374	C₂×#41	C₂×C₄×C₁₉	1	2	yes	—
375	C₂×#41	Q₈×C₁₉	1	2	yes	—
376	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
377	C₂²×D₄	—	2	1	no	—
378	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
379	C₂³×C₄	—	2	1	no	—
380	C₂³×C₄	—	2	1	no	—
381	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
382	C₂×M₁₆	—	2	1	no	—
383	C₂×M₁₆	—	2	1	no	—
384	C₂×M₁₆	—	2	1	no	—
385	C₂×M₁₆	—	2	1	no	—
386	C₂×M₁₆	—	2	1	no	—
387	C₂×M₁₆	—	2	1	no	—
388	C₂×M₁₆	—	2	1	no	—
389	C₂×M₁₆	—	2	1	no	—
390	C₂×M₁₆	—	2	1	no	—
391	C₂×M₁₆	—	2	1	no	—
392	C₂×M₁₆	—	2	1	no	—
393	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
394	C₂²×C₈	—	2	1	no	—
395	C₂²×C₈	D₄×C₁₉	1	2	yes	—
396	#117	—	2	1	no	—
397	#117	—	2	1	no	—
398	#117	—	2	1	no	—
399	#117	—	2	1	no	—
400	#117	—	2	1	no	—
401	#117	—	2	1	no	—
402	#117	—	2	1	no	—
403	#117	—	2	1	no	—
404	#117	—	2	1	no	—
405	#117	C₂×C₄×C₁₉	1	2	yes	—
406	#117	C₂×C₄×C₁₉	1	2	yes	—
407	#117	D₄×C₁₉	1	2	yes	—
408	C₂×C₄⋊C₄	—	2	1	no	—
409	C₂×C₄⋊C₄	—	2	1	no	—
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	—	2	1	no	—
412	C₂×C₄⋊C₄	—	2	1	no	—
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₄⋊C₄	—	2	1	no	—
415	C₂×C₄⋊C₄	—	2	4	no	—
416	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
417	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
418	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
419	C₂×C₂²⋊C₄	—	2	1	no	—
420	C₂×C₂²⋊C₄	—	2	1	no	—
421	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
422	C₂×C₄²	—	2	1	no	—
423	C₂×C₄²	—	2	1	no	—
424	C₂×C₄²	—	2	1	no	—
425	#103	—	2	4	no	—
426	#103	—	2	2	no	—
427	#103	—	2	2	no	—
428	#102	—	2	4	no	—
429	#102	—	2	2	no	—
430	#102	—	2	2	no	—
431	#99	—	2	8	no	—
432	#95	—	2	4	no	—
433	C₁₉	#11093	1	1	yes	characteristic, direct product factor, Sylow
434	C₂⁴	—	2	1	no	—
435	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
436	#41	—	2	2	no	—
437	#41	—	2	2	no	—
438	#41	—	2	2	no	—
439	#41	—	2	2	no	—
440	#41	—	2	2	no	—
441	#41	—	2	2	no	—
442	#41	—	2	2	no	—
443	#41	—	2	2	no	—
444	#41	—	4	1	no	—
445	#41	—	4	1	no	—
446	#41	—	4	1	no	—
447	#41	—	4	1	no	—
448	#41	—	4	1	no	—
449	#41	—	4	1	no	—
450	#41	—	4	1	no	—
451	#41	—	4	1	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	C₄⋊C₄×C₁₉	1	2	yes	complemented
458	C₂×D₄	—	2	2	no	—
459	C₂×D₄	—	2	2	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	4	1	no	—
466	C₂×D₄	—	4	1	no	—
467	C₂×D₄	—	4	1	no	—
468	C₂×D₄	—	4	1	no	—
469	C₂×D₄	C₄⋊C₄×C₁₉	1	2	yes	complemented
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	4	1	no	—
478	C₂²×C₄	—	4	1	no	—
479	C₂²×C₄	—	4	1	no	—
480	C₂²×C₄	—	4	1	no	—
481	C₂²×C₄	—	4	1	no	—
482	C₂²×C₄	—	4	1	no	—
483	C₂²×C₄	—	4	1	no	—
484	C₂²×C₄	—	8	2	no	—
485	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
486	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
487	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
488	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
489	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
490	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
491	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
492	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
493	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
494	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
495	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
496	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
497	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
498	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
499	M₁₆	—	2	2	no	—
500	M₁₆	—	2	2	no	—
501	M₁₆	—	4	1	no	—
502	M₁₆	—	4	1	no	—
503	M₁₆	—	4	1	no	—
504	M₁₆	—	4	1	no	—
505	M₁₆	—	4	1	no	—
506	M₁₆	—	4	1	no	—
507	C₂×C₈	—	2	2	no	—
508	C₂×C₈	—	2	2	no	—
509	C₂×C₈	—	2	2	no	—
510	C₂×C₈	—	2	2	no	—
511	C₂×C₈	—	4	1	no	—
512	C₂×C₈	—	4	1	no	—
513	C₄⋊C₄	—	2	2	no	—
514	C₄⋊C₄	—	2	2	no	—
515	C₄⋊C₄	—	2	2	no	—
516	C₄⋊C₄	—	2	2	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	2	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	4	1	no	—
523	C₄⋊C₄	—	4	1	no	—
524	C₄⋊C₄	—	4	1	no	—
525	C₄⋊C₄	—	8	4	no	—
526	C₂²⋊C₄	—	2	2	no	—
527	C₂²⋊C₄	—	2	2	no	—
528	C₂²⋊C₄	—	4	1	no	—
529	C₂²⋊C₄	—	4	1	no	—
530	C₂²⋊C₄	—	4	1	no	—
531	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
532	C₄²	—	2	2	no	—
533	C₄²	—	2	2	no	—
534	C₄²	—	2	2	no	—
535	C₄²	—	4	1	no	—
536	C₄²	—	4	1	no	—
537	C₄²	—	4	1	no	—
538	C₂³	—	2	2	no	—
539	C₂³	—	4	1	no	—
540	C₂³	—	4	1	no	—
541	C₂³	—	4	1	no	—
542	C₂³	—	4	1	no	—
543	C₂³	—	8	1	no	—
544	C₂³	—	8	1	no	—
545	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
546	C₂³	C₁₉×#120	1	1	yes	characteristic
547	C₂³	C₁₉×#121	1	1	yes	characteristic
548	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
549	C₂³	C₁₉×#123	1	1	yes	characteristic
550	C₂³	C₁₉×#124	1	1	yes	characteristic
551	C₂³	C₁₉×#127	1	1	yes	characteristic
552	Q₈	—	2	2	no	—
553	Q₈	—	2	2	no	—
554	Q₈	—	4	1	no	—
555	Q₈	—	4	1	no	—
556	D₄	—	2	2	no	—
557	D₄	—	2	2	no	—
558	D₄	—	4	2	no	—
559	D₄	—	4	2	no	—
560	D₄	—	4	2	no	—
561	D₄	—	4	2	no	—
562	D₄	—	4	1	no	—
563	D₄	—	4	1	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	4	2	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	4	2	no	—
574	C₂×C₄	—	4	2	no	—
575	C₂×C₄	—	4	4	no	—
576	C₂×C₄	—	4	2	no	—
577	C₂×C₄	—	4	2	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	8	2	no	—
582	C₂×C₄	—	8	2	no	—
583	C₂×C₄	—	8	1	no	—
584	C₂×C₄	—	8	1	no	—
585	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
586	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
587	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
588	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
589	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
590	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
591	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
592	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
593	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
594	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
595	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
596	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
597	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
598	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
599	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
600	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
601	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
602	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
603	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
604	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
605	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
606	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
607	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
608	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
609	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
610	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
611	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
612	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
613	C₈	—	4	2	no	—
614	C₈	—	4	2	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	1	no	—
621	C₂²	—	4	1	no	—
622	C₂²	—	4	1	no	—
623	C₂²	—	4	1	no	—
624	C₂²	—	4	1	no	—
625	C₂²	—	4	2	no	—
626	C₂²	—	8	2	no	—
627	C₂²	—	8	2	no	—
628	C₂²	—	8	1	no	—
629	C₂²	—	8	1	no	—
630	C₂²	C₁₉×#380	1	1	yes	characteristic
631	C₂²	C₁₉×#386	1	1	yes	characteristic
632	C₂²	C₁₉×#390	1	1	yes	characteristic
633	C₂²	C₁₉×#392	1	1	yes	characteristic
634	C₂²	C₁₉×#393	1	1	yes	characteristic
635	C₂²	C₁₉×#397	1	1	yes	characteristic
636	C₂²	C₁₉×#399	1	1	yes	characteristic
637	C₄	—	4	4	no	—
638	C₄	—	4	2	no	—
639	C₄	—	8	2	no	—
640	C₄	—	8	2	no	—
641	C₄	—	8	1	no	—
642	C₄	—	8	1	no	—
643	C₄	C₁₉×#385	1	1	yes	characteristic
644	C₄	C₁₉×#385	1	1	yes	characteristic
645	C₄	C₁₉×#388	1	1	yes	characteristic
646	C₄	C₁₉×#388	1	1	yes	characteristic
647	C₄	C₁₉×#394	1	1	yes	characteristic
648	C₄	C₁₉×#394	1	1	yes	characteristic
649	C₄	C₁₉×#396	1	1	yes	characteristic
650	C₄	C₁₉×#396	1	1	yes	characteristic
651	C₂	—	2	1	no	—
652	C₂	—	2	1	no	—
653	C₂	—	2	1	no	—
654	C₂	—	2	1	no	—
655	C₂	—	2	1	no	—
656	C₂	—	2	1	no	—
657	C₂	—	8	2	no	—
658	C₂	C₁₉×#1439	1	1	yes	characteristic
659	C₂	C₁₉×#2008	1	1	yes	characteristic
660	C₂	C₁₉×#2009	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₉×#2317	C₂	semidirect
5. C₂×C₁₉×#344	C₂	semidirect
6. C₁₉×#1736	C₂	semidirect
7. C₁₉×#1733	C₂	semidirect
25. C₁₉×#410	C₄	semidirect
126. C₂×Q₈×C₁₉	C₄⋊C₄	semidirect
138. C₂×D₄×C₁₉	C₄⋊C₄	semidirect
207. #11093	C₁₉	direct (N × H)
288. #2317	C₂×C₁₉	semidirect
289. C₂×#344	C₂×C₁₉	semidirect
290. #1736	C₂×C₁₉	semidirect
291. #1733	C₂×C₁₉	semidirect
345. #410	C₄×C₁₉	semidirect
433. C₁₉	#11093	direct (N × H)
457. C₂×Q₈	C₄⋊C₄×C₁₉	semidirect
469. C₂×D₄	C₄⋊C₄×C₁₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₉×#2896	2
C₂×C₁₉×#417	2
C₂×C₁₉×#410	2
C₁₉×#2317	2
C₂×C₁₉×#344	2
C₁₉×#1736	2
C₁₉×#1733	2
#11093	19

Subgroups — C19×#11093 #18017052

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11093 #18017052