Subgroups — C₁₉×#11079 #18017038

Order 4864.

990 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#104	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#417	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2311	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#382	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#343	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1736	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#339	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	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#104	—	2	2	no	—
16	C₂×C₁₉×#104	—	2	2	no	—
17	C₂×C₁₉×#104	C₄	1	4	yes	complemented
18	C₁₉×#417	—	2	2	no	—
19	C₁₉×#417	—	2	2	no	—
20	C₂×C₁₉×#103	—	2	1	no	—
21	C₂×C₁₉×#102	—	2	1	no	—
22	C₁₉×#391	—	2	1	no	—
23	C₁₉×#390	—	2	1	no	—
24	C₁₉×#386	—	2	2	no	—
25	C₁₉×#382	—	2	2	no	—
26	C₁₉×#382	—	2	2	no	—
27	C₁₉×#380	—	2	2	no	—
28	C₂×C₁₉×#95	—	2	2	no	—
29	C₁₉×#343	—	2	2	no	—
30	C₁₉×#340	—	2	2	no	—
31	C₁₉×#339	—	2	2	no	—
32	C₂×#41×C₁₉	—	2	1	no	—
33	C₂×#41×C₁₉	—	2	1	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	C₂×C₄	1	2	yes	—
43	C₂×#41×C₁₉	Q₈	1	2	yes	—
44	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
45	C₂²×D₄×C₁₉	—	2	1	no	—
46	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₉	—	2	1	no	—
48	C₂³×C₄×C₁₉	—	2	1	no	—
49	C₂³×C₄×C₁₉	—	2	1	no	—
50	C₂³×C₄×C₁₉	D₄	1	2	yes	—
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	C₂×C₄	1	2	yes	—
63	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
64	C₂²×C₈×C₁₉	—	2	1	no	—
65	C₂²×C₈×C₁₉	—	2	1	no	—
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	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	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	D₄	1	2	yes	—
82	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
83	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
85	C₂×C₄²×C₁₉	—	2	1	no	—
86	C₂×C₄²×C₁₉	—	2	1	no	—
87	C₂×C₄²×C₁₉	—	2	1	no	—
88	C₂×C₄²×C₁₉	—	2	1	no	—
89	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
90	C₂×C₄²×C₁₉	D₄	1	2	yes	—
91	C₂×C₄²×C₁₉	D₄	1	2	yes	—
92	C₁₉×#104	—	2	8	no	—
93	C₁₉×#103	—	2	4	no	—
94	C₁₉×#102	—	2	4	no	—
95	C₁₉×#95	—	2	8	no	—
96	C₁₉×#95	—	2	4	no	—
97	C₂⁴×C₁₉	—	2	1	no	—
98	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
99	#41×C₁₉	—	2	2	no	—
100	#41×C₁₉	—	2	2	no	—
101	#41×C₁₉	—	2	2	no	—
102	#41×C₁₉	—	2	2	no	—
103	#41×C₁₉	—	2	2	no	—
104	#41×C₁₉	—	2	2	no	—
105	#41×C₁₉	—	2	2	no	—
106	#41×C₁₉	—	2	2	no	—
107	#41×C₁₉	—	4	1	no	—
108	#41×C₁₉	—	4	1	no	—
109	#41×C₁₉	—	4	1	no	—
110	#41×C₁₉	—	4	1	no	—
111	#41×C₁₉	—	4	1	no	—
112	#41×C₁₉	—	4	1	no	—
113	#41×C₁₉	—	4	1	no	—
114	#41×C₁₉	—	4	1	no	—
115	C₂×Q₈×C₁₉	—	2	1	no	—
116	C₂×Q₈×C₁₉	—	2	1	no	—
117	C₂×Q₈×C₁₉	—	2	1	no	—
118	C₂×Q₈×C₁₉	—	2	1	no	—
119	C₂×Q₈×C₁₉	—	2	1	no	—
120	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
121	C₂×D₄×C₁₉	—	2	2	no	—
122	C₂×D₄×C₁₉	—	2	2	no	—
123	C₂×D₄×C₁₉	—	2	1	no	—
124	C₂×D₄×C₁₉	—	2	1	no	—
125	C₂×D₄×C₁₉	—	2	1	no	—
126	C₂×D₄×C₁₉	—	2	1	no	—
127	C₂×D₄×C₁₉	—	2	1	no	—
128	C₂×D₄×C₁₉	—	4	1	no	—
129	C₂×D₄×C₁₉	—	4	1	no	—
130	C₂×D₄×C₁₉	—	4	1	no	—
131	C₂×D₄×C₁₉	—	4	1	no	—
132	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	2	2	no	—
135	C₂²×C₄×C₁₉	—	2	1	no	—
136	C₂²×C₄×C₁₉	—	2	2	no	—
137	C₂²×C₄×C₁₉	—	2	2	no	—
138	C₂²×C₄×C₁₉	—	2	2	no	—
139	C₂²×C₄×C₁₉	—	2	2	no	—
140	C₂²×C₄×C₁₉	—	2	2	no	—
141	C₂²×C₄×C₁₉	—	2	2	no	—
142	C₂²×C₄×C₁₉	—	2	2	no	—
143	C₂²×C₄×C₁₉	—	2	2	no	—
144	C₂²×C₄×C₁₉	—	4	2	no	—
145	C₂²×C₄×C₁₉	—	4	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	4	no	—
151	C₂²×C₄×C₁₉	—	4	4	no	—
152	C₂²×C₄×C₁₉	—	4	1	no	—
153	C₂²×C₄×C₁₉	—	4	1	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	—	2	2	no	—
171	M₁₆×C₁₉	—	2	2	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	—	4	1	no	—
179	C₂×C₈×C₁₉	—	4	1	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	—	4	1	no	—
187	C₄⋊C₄×C₁₉	—	4	1	no	—
188	C₄⋊C₄×C₁₉	—	4	1	no	—
189	C₄⋊C₄×C₁₉	—	4	1	no	—
190	C₄⋊C₄×C₁₉	—	4	1	no	—
191	C₄⋊C₄×C₁₉	—	4	1	no	—
192	C₂²⋊C₄×C₁₉	—	4	1	no	—
193	C₂²⋊C₄×C₁₉	—	4	1	no	—
194	C₂²⋊C₄×C₁₉	—	8	4	no	—
195	C₄²×C₁₉	—	2	2	no	—
196	C₄²×C₁₉	—	2	2	no	—
197	C₄²×C₁₉	—	2	2	no	—
198	C₄²×C₁₉	—	4	1	no	—
199	C₄²×C₁₉	—	4	1	no	—
200	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	complemented
201	#11079	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂³×C₁₉	—	2	2	no	—
203	C₂³×C₁₉	—	2	2	no	—
204	C₂³×C₁₉	—	2	2	no	—
205	C₂³×C₁₉	—	4	1	no	—
206	C₂³×C₁₉	—	4	1	no	—
207	C₂³×C₁₉	—	4	2	no	—
208	C₂³×C₁₉	—	4	2	no	—
209	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
210	C₂³×C₁₉	#120	1	1	yes	characteristic
211	C₂³×C₁₉	#120	1	1	yes	characteristic
212	C₂³×C₁₉	#121	1	1	yes	characteristic
213	C₂³×C₁₉	#121	1	1	yes	characteristic
214	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
215	C₂³×C₁₉	#124	1	1	yes	characteristic
216	Q₈×C₁₉	—	2	2	no	—
217	Q₈×C₁₉	—	2	2	no	—
218	Q₈×C₁₉	—	4	1	no	—
219	Q₈×C₁₉	—	4	1	no	—
220	D₄×C₁₉	—	2	2	no	—
221	D₄×C₁₉	—	2	2	no	—
222	D₄×C₁₉	—	4	2	no	—
223	D₄×C₁₉	—	4	2	no	—
224	D₄×C₁₉	—	4	2	no	—
225	D₄×C₁₉	—	4	2	no	—
226	D₄×C₁₉	—	4	1	no	—
227	D₄×C₁₉	—	4	1	no	—
228	C₂×C₄×C₁₉	—	2	2	no	—
229	C₂×C₄×C₁₉	—	2	4	no	—
230	C₂×C₄×C₁₉	—	4	4	no	—
231	C₂×C₄×C₁₉	—	4	2	no	—
232	C₂×C₄×C₁₉	—	4	2	no	—
233	C₂×C₄×C₁₉	—	4	4	no	—
234	C₂×C₄×C₁₉	—	4	1	no	—
235	C₂×C₄×C₁₉	—	4	1	no	—
236	C₂×C₄×C₁₉	—	4	2	no	—
237	C₂×C₄×C₁₉	—	4	2	no	—
238	C₂×C₄×C₁₉	—	4	2	no	—
239	C₂×C₄×C₁₉	—	4	2	no	—
240	C₂×C₄×C₁₉	—	4	4	no	—
241	C₂×C₄×C₁₉	—	4	4	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	2	no	—
246	C₂×C₄×C₁₉	—	4	2	no	—
247	C₂×C₄×C₁₉	—	4	4	no	—
248	C₂×C₄×C₁₉	—	8	2	no	—
249	C₂×C₄×C₁₉	—	8	2	no	—
250	C₂×C₄×C₁₉	—	8	2	no	—
251	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
252	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
253	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
254	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
255	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
257	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
258	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
259	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
260	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
261	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
262	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
263	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
264	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
265	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
266	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
267	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
268	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
269	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
270	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
271	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
272	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
273	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
274	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
275	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
276	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
277	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
278	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
279	C₈×C₁₉	—	4	2	no	—
280	C₈×C₁₉	—	4	2	no	—
281	C₂²×#104	C₂×C₁₉	1	1	yes	characteristic
282	C₂×#417	C₂×C₁₉	1	1	yes	characteristic
283	#2311	C₂×C₁₉	1	1	yes	characteristic
284	C₂×#382	C₂×C₁₉	1	1	yes	characteristic, complemented
285	C₂×#343	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#1736	C₂×C₁₉	1	1	yes	characteristic, complemented
287	C₂×#339	C₂×C₁₉	1	1	yes	characteristic, complemented
288	C₂²×C₁₉	—	2	2	no	—
289	C₂²×C₁₉	—	2	2	no	—
290	C₂²×C₁₉	—	2	1	no	—
291	C₂²×C₁₉	—	2	1	no	—
292	C₂²×C₁₉	—	2	1	no	—
293	C₂²×C₁₉	—	2	1	no	—
294	C₂²×C₁₉	—	2	2	no	—
295	C₂²×C₁₉	—	2	2	no	—
296	C₂²×C₁₉	—	4	4	no	—
297	C₂²×C₁₉	—	4	2	no	—
298	C₂²×C₁₉	—	8	1	no	—
299	C₂²×C₁₉	—	8	1	no	—
300	C₂²×C₁₉	—	8	2	no	—
301	C₂²×C₁₉	#385	1	1	yes	characteristic
302	C₂²×C₁₉	#386	1	1	yes	characteristic
303	C₂²×C₁₉	#388	1	1	yes	characteristic
304	C₂²×C₁₉	#392	1	1	yes	characteristic
305	C₂²×C₁₉	#393	1	1	yes	characteristic
306	C₂²×C₁₉	#394	1	1	yes	characteristic
307	C₂²×C₁₉	#396	1	1	yes	characteristic
308	C₂²×C₁₉	#454	1	2	yes	—
309	C₂²×C₁₉	#455	1	2	yes	—
310	C₄×C₁₉	—	4	4	no	—
311	C₄×C₁₉	—	4	2	no	—
312	C₄×C₁₉	—	8	2	no	—
313	C₄×C₁₉	—	8	2	no	—
314	C₄×C₁₉	—	8	2	no	—
315	C₄×C₁₉	#380	1	1	yes	characteristic
316	C₄×C₁₉	#385	1	1	yes	characteristic
317	C₄×C₁₉	#388	1	1	yes	characteristic
318	C₄×C₁₉	#390	1	1	yes	characteristic
319	C₄×C₁₉	#394	1	1	yes	characteristic
320	C₄×C₁₉	#396	1	1	yes	characteristic
321	C₄×C₁₉	#397	1	1	yes	characteristic
322	C₄×C₁₉	#399	1	1	yes	characteristic
323	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
324	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
325	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
326	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
327	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
328	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
329	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
330	C₂×#104	—	2	2	no	—
331	C₂×#104	—	2	2	no	—
332	C₂×#104	C₄×C₁₉	1	4	yes	complemented
333	#417	—	2	2	no	—
334	#417	—	2	2	no	—
335	C₂×#103	—	2	1	no	—
336	C₂×#102	—	2	1	no	—
337	#391	—	2	1	no	—
338	#390	—	2	1	no	—
339	#386	—	2	2	no	—
340	#382	—	2	2	no	—
341	#382	—	2	2	no	—
342	#380	—	2	2	no	—
343	C₂×#95	—	2	2	no	—
344	#343	—	2	2	no	—
345	#340	—	2	2	no	—
346	#339	—	2	2	no	—
347	C₂×C₁₉	—	2	1	no	—
348	C₂×C₁₉	—	2	1	no	—
349	C₂×C₁₉	—	2	1	no	—
350	C₂×C₁₉	—	2	1	no	—
351	C₂×C₁₉	—	8	2	no	—
352	C₂×C₁₉	#1439	1	1	yes	characteristic
353	C₂×C₁₉	#1860	1	2	yes	—
354	C₂×C₁₉	#2003	1	1	yes	characteristic
355	C₂×C₁₉	#2004	1	1	yes	characteristic
356	C₂×C₁₉	#2040	1	2	yes	—
357	C₂×#41	—	2	1	no	—
358	C₂×#41	—	2	1	no	—
359	C₂×#41	—	2	1	no	—
360	C₂×#41	—	2	1	no	—
361	C₂×#41	—	2	1	no	—
362	C₂×#41	—	2	1	no	—
363	C₂×#41	—	2	1	no	—
364	C₂×#41	—	2	1	no	—
365	C₂×#41	—	2	1	no	—
366	C₂×#41	—	2	1	no	—
367	C₂×#41	C₂×C₄×C₁₉	1	2	yes	—
368	C₂×#41	Q₈×C₁₉	1	2	yes	—
369	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
370	C₂²×D₄	—	2	1	no	—
371	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
372	C₂³×C₄	—	2	1	no	—
373	C₂³×C₄	—	2	1	no	—
374	C₂³×C₄	—	2	1	no	—
375	C₂³×C₄	D₄×C₁₉	1	2	yes	—
376	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
377	C₂×M₁₆	—	2	1	no	—
378	C₂×M₁₆	—	2	1	no	—
379	C₂×M₁₆	—	2	1	no	—
380	C₂×M₁₆	—	2	1	no	—
381	C₂×M₁₆	—	2	1	no	—
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	C₂×C₄×C₁₉	1	2	yes	—
388	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
389	C₂²×C₈	—	2	1	no	—
390	C₂²×C₈	—	2	1	no	—
391	#117	—	2	1	no	—
392	#117	—	2	1	no	—
393	#117	—	2	1	no	—
394	#117	—	2	1	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	—	2	1	no	—
398	C₂×C₄⋊C₄	—	2	1	no	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	—	2	1	no	—
406	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
407	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
408	C₂×C₂²⋊C₄	—	2	1	no	—
409	C₂×C₂²⋊C₄	—	2	4	no	—
410	C₂×C₄²	—	2	1	no	—
411	C₂×C₄²	—	2	1	no	—
412	C₂×C₄²	—	2	1	no	—
413	C₂×C₄²	—	2	1	no	—
414	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
415	C₂×C₄²	D₄×C₁₉	1	2	yes	—
416	C₂×C₄²	D₄×C₁₉	1	2	yes	—
417	#104	—	2	8	no	—
418	#103	—	2	4	no	—
419	#102	—	2	4	no	—
420	#95	—	2	8	no	—
421	#95	—	2	4	no	—
422	C₁₉	#11079	1	1	yes	characteristic, direct product factor, Sylow
423	C₂⁴	—	2	1	no	—
424	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
425	#41	—	2	2	no	—
426	#41	—	2	2	no	—
427	#41	—	2	2	no	—
428	#41	—	2	2	no	—
429	#41	—	2	2	no	—
430	#41	—	2	2	no	—
431	#41	—	2	2	no	—
432	#41	—	2	2	no	—
433	#41	—	4	1	no	—
434	#41	—	4	1	no	—
435	#41	—	4	1	no	—
436	#41	—	4	1	no	—
437	#41	—	4	1	no	—
438	#41	—	4	1	no	—
439	#41	—	4	1	no	—
440	#41	—	4	1	no	—
441	C₂×Q₈	—	2	1	no	—
442	C₂×Q₈	—	2	1	no	—
443	C₂×Q₈	—	2	1	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	C₄⋊C₄×C₁₉	1	2	yes	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	4	1	no	—
455	C₂×D₄	—	4	1	no	—
456	C₂×D₄	—	4	1	no	—
457	C₂×D₄	—	4	1	no	—
458	C₂×D₄	C₄⋊C₄×C₁₉	1	2	yes	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	4	2	no	—
471	C₂²×C₄	—	4	2	no	—
472	C₂²×C₄	—	4	1	no	—
473	C₂²×C₄	—	4	1	no	—
474	C₂²×C₄	—	4	1	no	—
475	C₂²×C₄	—	4	1	no	—
476	C₂²×C₄	—	4	4	no	—
477	C₂²×C₄	—	4	4	no	—
478	C₂²×C₄	—	4	1	no	—
479	C₂²×C₄	—	4	1	no	—
480	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
481	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
482	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
483	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
484	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
485	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
486	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
487	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
488	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
489	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
490	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
491	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
492	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
493	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
494	M₁₆	—	2	2	no	—
495	M₁₆	—	2	2	no	—
496	M₁₆	—	2	2	no	—
497	M₁₆	—	2	2	no	—
498	M₁₆	—	4	1	no	—
499	M₁₆	—	4	1	no	—
500	M₁₆	—	4	1	no	—
501	M₁₆	—	4	1	no	—
502	C₂×C₈	—	2	2	no	—
503	C₂×C₈	—	2	2	no	—
504	C₂×C₈	—	4	1	no	—
505	C₂×C₈	—	4	1	no	—
506	C₂×C₈	—	4	1	no	—
507	C₂×C₈	—	4	1	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	4	1	no	—
513	C₄⋊C₄	—	4	1	no	—
514	C₄⋊C₄	—	4	1	no	—
515	C₄⋊C₄	—	4	1	no	—
516	C₄⋊C₄	—	4	1	no	—
517	C₄⋊C₄	—	4	1	no	—
518	C₂²⋊C₄	—	4	1	no	—
519	C₂²⋊C₄	—	4	1	no	—
520	C₂²⋊C₄	—	8	4	no	—
521	C₄²	—	2	2	no	—
522	C₄²	—	2	2	no	—
523	C₄²	—	2	2	no	—
524	C₄²	—	4	1	no	—
525	C₄²	—	4	1	no	—
526	C₄²	C₂²⋊C₄×C₁₉	1	4	yes	complemented
527	C₂³	—	2	2	no	—
528	C₂³	—	2	2	no	—
529	C₂³	—	2	2	no	—
530	C₂³	—	4	1	no	—
531	C₂³	—	4	1	no	—
532	C₂³	—	4	2	no	—
533	C₂³	—	4	2	no	—
534	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
535	C₂³	C₁₉×#120	1	1	yes	characteristic
536	C₂³	C₁₉×#120	1	1	yes	characteristic
537	C₂³	C₁₉×#121	1	1	yes	characteristic
538	C₂³	C₁₉×#121	1	1	yes	characteristic
539	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
540	C₂³	C₁₉×#124	1	1	yes	characteristic
541	Q₈	—	2	2	no	—
542	Q₈	—	2	2	no	—
543	Q₈	—	4	1	no	—
544	Q₈	—	4	1	no	—
545	D₄	—	2	2	no	—
546	D₄	—	2	2	no	—
547	D₄	—	4	2	no	—
548	D₄	—	4	2	no	—
549	D₄	—	4	2	no	—
550	D₄	—	4	2	no	—
551	D₄	—	4	1	no	—
552	D₄	—	4	1	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	4	no	—
558	C₂×C₄	—	4	4	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	4	2	no	—
564	C₂×C₄	—	4	2	no	—
565	C₂×C₄	—	4	4	no	—
566	C₂×C₄	—	4	4	no	—
567	C₂×C₄	—	4	2	no	—
568	C₂×C₄	—	4	2	no	—
569	C₂×C₄	—	4	2	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	4	4	no	—
573	C₂×C₄	—	8	2	no	—
574	C₂×C₄	—	8	2	no	—
575	C₂×C₄	—	8	2	no	—
576	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
577	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
578	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
579	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
580	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
581	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
582	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
583	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
584	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
585	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
586	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
587	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
588	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
589	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
590	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
591	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
592	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
593	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
594	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
595	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
596	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
597	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
598	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
599	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
600	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
601	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
602	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
603	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
604	C₈	—	4	2	no	—
605	C₈	—	4	2	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	2	1	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	2	2	no	—
614	C₂²	—	4	2	no	—
615	C₂²	—	4	4	no	—
616	C₂²	—	8	1	no	—
617	C₂²	—	8	1	no	—
618	C₂²	—	8	2	no	—
619	C₂²	C₁₉×#385	1	1	yes	characteristic
620	C₂²	C₁₉×#386	1	1	yes	characteristic
621	C₂²	C₁₉×#388	1	1	yes	characteristic
622	C₂²	C₁₉×#392	1	1	yes	characteristic
623	C₂²	C₁₉×#393	1	1	yes	characteristic
624	C₂²	C₁₉×#394	1	1	yes	characteristic
625	C₂²	C₁₉×#396	1	1	yes	characteristic
626	C₂²	C₁₉×#454	1	2	yes	—
627	C₂²	C₁₉×#455	1	2	yes	—
628	C₄	—	4	4	no	—
629	C₄	—	4	2	no	—
630	C₄	—	8	2	no	—
631	C₄	—	8	2	no	—
632	C₄	—	8	2	no	—
633	C₄	C₁₉×#380	1	1	yes	characteristic
634	C₄	C₁₉×#385	1	1	yes	characteristic
635	C₄	C₁₉×#388	1	1	yes	characteristic
636	C₄	C₁₉×#390	1	1	yes	characteristic
637	C₄	C₁₉×#394	1	1	yes	characteristic
638	C₄	C₁₉×#396	1	1	yes	characteristic
639	C₄	C₁₉×#397	1	1	yes	characteristic
640	C₄	C₁₉×#399	1	1	yes	characteristic
641	C₂	—	2	1	no	—
642	C₂	—	2	1	no	—
643	C₂	—	2	1	no	—
644	C₂	—	2	1	no	—
645	C₂	—	8	2	no	—
646	C₂	C₁₉×#1439	1	1	yes	characteristic
647	C₂	C₁₉×#1860	1	2	yes	—
648	C₂	C₁₉×#2003	1	1	yes	characteristic
649	C₂	C₁₉×#2004	1	1	yes	characteristic
650	C₂	C₁₉×#2040	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
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 ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×C₁₉×#382	C₂	semidirect
5. C₂×C₁₉×#343	C₂	semidirect
6. C₁₉×#1736	C₂	semidirect
7. C₂×C₁₉×#339	C₂	semidirect
17. C₂×C₁₉×#104	C₄	semidirect
200. C₄²×C₁₉	C₂²⋊C₄	semidirect
201. #11079	C₁₉	direct (N × H)
284. C₂×#382	C₂×C₁₉	semidirect
285. C₂×#343	C₂×C₁₉	semidirect
286. #1736	C₂×C₁₉	semidirect
287. C₂×#339	C₂×C₁₉	semidirect
332. C₂×#104	C₄×C₁₉	semidirect
422. C₁₉	#11079	direct (N × H)
526. C₄²	C₂²⋊C₄×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#104	2
C₂×C₁₉×#417	2
C₁₉×#2311	2
C₂×C₁₉×#382	2
C₂×C₁₉×#343	2
C₁₉×#1736	2
C₂×C₁₉×#339	2
#11079	19

Subgroups — C19×#11079 #18017038

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11079 #18017038