Subgroups — C₁₉×#11033 #18016992

Order 4864.

1264 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#575	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#421	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2896	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#410	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#410	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1742	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×#41×C₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×#575	—	2	2	no	—
11	C₁₉×#575	—	2	2	no	—
12	C₁₉×#575	—	2	2	no	—
13	C₁₉×#575	—	2	2	no	—
14	C₂×C₁₉×#137	—	2	1	no	—
15	C₂×C₁₉×#137	C₄	1	2	yes	complemented
16	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
17	C₂×C₁₉×AGL(1,ℤ/8)	C₄	1	2	yes	complemented
18	C₂×C₁₉×#135	—	2	2	no	—
19	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
24	C₁₉×#421	—	2	2	no	—
25	C₁₉×#421	—	2	2	no	—
26	C₂×C₁₉×#104	—	2	2	no	—
27	C₁₉×#419	—	2	1	no	—
28	C₁₉×#418	—	2	1	no	—
29	C₁₉×#417	—	2	2	no	—
30	C₁₉×#416	—	2	2	no	—
31	C₁₉×#410	—	2	2	no	—
32	C₁₉×#410	—	2	2	no	—
33	C₁₉×#410	—	2	2	no	—
34	C₁₉×#410	—	2	2	no	—
35	C₂×C₁₉×#99	—	2	2	no	—
36	C₂×C₁₉×#99	—	2	2	no	—
37	C₁₉×#343	—	2	2	no	—
38	C₁₉×#339	—	2	2	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	—	2	1	no	—
45	C₂×#41×C₁₉	—	2	1	no	—
46	C₂×#41×C₁₉	—	2	1	no	—
47	C₂×#41×C₁₉	—	2	1	no	—
48	C₂×#41×C₁₉	—	2	1	no	—
49	C₂×#41×C₁₉	—	2	1	no	—
50	C₂×#41×C₁₉	—	2	1	no	—
51	C₂×#41×C₁₉	—	2	1	no	—
52	C₂×#41×C₁₉	—	2	1	no	—
53	C₂×#41×C₁₉	—	2	1	no	—
54	C₂×#41×C₁₉	—	2	1	no	—
55	C₂×#41×C₁₉	—	2	1	no	—
56	C₂×#41×C₁₉	—	2	1	no	—
57	C₂×#41×C₁₉	—	2	1	no	—
58	C₂×#41×C₁₉	—	2	1	no	—
59	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
60	C₂×#41×C₁₉	D₄	1	2	yes	—
61	C₂×#41×C₁₉	D₄	1	2	yes	—
62	C₂×#41×C₁₉	D₄	1	2	yes	—
63	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
64	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
65	C₂²×D₄×C₁₉	—	2	1	no	—
66	C₂²×D₄×C₁₉	—	2	1	no	—
67	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
68	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
69	C₂³×C₄×C₁₉	—	2	1	no	—
70	C₂³×C₄×C₁₉	—	2	1	no	—
71	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₁₉×#137	—	2	4	no	—
73	C₁₉×#137	—	2	4	no	—
74	C₁₉×#137	—	2	4	no	—
75	C₁₉×#137	—	2	4	no	—
76	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
77	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
78	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
79	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
80	C₁₉×#135	—	2	8	no	—
81	C₁₉×#135	—	2	8	no	—
82	C₂×Q₁₆×C₁₉	—	2	2	no	—
83	C₂×SD₁₆×C₁₉	—	2	2	no	—
84	C₂×SD₁₆×C₁₉	—	2	2	no	—
85	C₂×D₈×C₁₉	—	2	2	no	—
86	C₂×M₁₆×C₁₉	—	2	1	no	—
87	C₂×M₁₆×C₁₉	—	2	1	no	—
88	C₂×M₁₆×C₁₉	—	2	1	no	—
89	C₂×M₁₆×C₁₉	—	2	1	no	—
90	C₂×M₁₆×C₁₉	—	2	1	no	—
91	C₂×M₁₆×C₁₉	—	2	1	no	—
92	C₂×M₁₆×C₁₉	—	2	1	no	—
93	C₂×M₁₆×C₁₉	—	2	1	no	—
94	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
95	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
96	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
97	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
98	C₂²×C₈×C₁₉	—	2	1	no	—
99	C₂²×C₈×C₁₉	—	2	1	no	—
100	C₁₉×#117	—	2	1	no	—
101	C₁₉×#117	—	2	1	no	—
102	C₁₉×#117	—	2	1	no	—
103	C₁₉×#117	—	2	1	no	—
104	C₁₉×#117	—	2	1	no	—
105	C₁₉×#117	—	2	1	no	—
106	C₁₉×#117	—	2	1	no	—
107	C₁₉×#117	—	2	1	no	—
108	C₁₉×#117	—	2	1	no	—
109	C₁₉×#117	—	2	1	no	—
110	C₁₉×#117	D₄	1	2	yes	—
111	C₁₉×#117	D₄	1	2	yes	—
112	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
113	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
114	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
117	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
118	C₂×C₄²×C₁₉	—	2	1	no	—
119	C₂×C₄²×C₁₉	—	2	1	no	—
120	C₂×C₄²×C₁₉	—	2	1	no	—
121	C₁₉×#104	—	2	8	no	—
122	C₁₉×#103	—	2	4	no	—
123	C₁₉×#102	—	2	4	no	—
124	C₁₉×#99	—	2	8	no	—
125	C₁₉×#99	—	2	8	no	—
126	C₂⁴×C₁₉	—	2	1	no	—
127	C₂⁴×C₁₉	—	2	1	no	—
128	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
129	#41×C₁₉	—	2	2	no	—
130	#41×C₁₉	—	2	2	no	—
131	#41×C₁₉	—	2	2	no	—
132	#41×C₁₉	—	2	2	no	—
133	#41×C₁₉	—	2	2	no	—
134	#41×C₁₉	—	2	2	no	—
135	#41×C₁₉	—	2	2	no	—
136	#41×C₁₉	—	2	2	no	—
137	#41×C₁₉	—	2	2	no	—
138	#41×C₁₉	—	2	2	no	—
139	#41×C₁₉	—	2	2	no	—
140	#41×C₁₉	—	2	2	no	—
141	#41×C₁₉	—	2	2	no	—
142	#41×C₁₉	—	2	2	no	—
143	#41×C₁₉	—	2	2	no	—
144	#41×C₁₉	—	2	2	no	—
145	#41×C₁₉	—	4	1	no	—
146	#41×C₁₉	—	4	1	no	—
147	#41×C₁₉	—	4	1	no	—
148	#41×C₁₉	—	4	1	no	—
149	#41×C₁₉	—	4	1	no	—
150	#41×C₁₉	—	4	1	no	—
151	#41×C₁₉	—	4	1	no	—
152	#41×C₁₉	—	4	1	no	—
153	#41×C₁₉	—	4	1	no	—
154	#41×C₁₉	—	4	1	no	—
155	#41×C₁₉	—	4	1	no	—
156	#41×C₁₉	—	4	1	no	—
157	#41×C₁₉	—	4	1	no	—
158	#41×C₁₉	—	4	1	no	—
159	#41×C₁₉	—	4	1	no	—
160	#41×C₁₉	—	4	1	no	—
161	C₂×Q₈×C₁₉	—	2	1	no	—
162	C₂×Q₈×C₁₉	—	2	1	no	—
163	C₂×Q₈×C₁₉	—	2	1	no	—
164	C₂×Q₈×C₁₉	—	2	1	no	—
165	C₂×Q₈×C₁₉	—	2	1	no	—
166	C₂×Q₈×C₁₉	—	2	1	no	—
167	C₂×Q₈×C₁₉	—	2	1	no	—
168	C₂×Q₈×C₁₉	—	2	1	no	—
169	C₂×Q₈×C₁₉	—	2	1	no	—
170	C₂×Q₈×C₁₉	—	2	1	no	—
171	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
172	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
173	C₂×D₄×C₁₉	—	2	2	no	—
174	C₂×D₄×C₁₉	—	2	2	no	—
175	C₂×D₄×C₁₉	—	2	2	no	—
176	C₂×D₄×C₁₉	—	2	2	no	—
177	C₂×D₄×C₁₉	—	2	1	no	—
178	C₂×D₄×C₁₉	—	2	1	no	—
179	C₂×D₄×C₁₉	—	2	1	no	—
180	C₂×D₄×C₁₉	—	2	1	no	—
181	C₂×D₄×C₁₉	—	2	1	no	—
182	C₂×D₄×C₁₉	—	2	1	no	—
183	C₂×D₄×C₁₉	—	2	1	no	—
184	C₂×D₄×C₁₉	—	2	1	no	—
185	C₂×D₄×C₁₉	—	2	1	no	—
186	C₂×D₄×C₁₉	—	2	1	no	—
187	C₂×D₄×C₁₉	—	4	1	no	—
188	C₂×D₄×C₁₉	—	4	1	no	—
189	C₂×D₄×C₁₉	—	4	1	no	—
190	C₂×D₄×C₁₉	—	4	1	no	—
191	C₂×D₄×C₁₉	—	4	1	no	—
192	C₂×D₄×C₁₉	—	4	1	no	—
193	C₂×D₄×C₁₉	—	4	1	no	—
194	C₂×D₄×C₁₉	—	4	1	no	—
195	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
196	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
197	C₂²×C₄×C₁₉	—	2	1	no	—
198	C₂²×C₄×C₁₉	—	2	1	no	—
199	C₂²×C₄×C₁₉	—	2	2	no	—
200	C₂²×C₄×C₁₉	—	2	2	no	—
201	C₂²×C₄×C₁₉	—	2	2	no	—
202	C₂²×C₄×C₁₉	—	2	2	no	—
203	C₂²×C₄×C₁₉	—	2	2	no	—
204	C₂²×C₄×C₁₉	—	4	1	no	—
205	C₂²×C₄×C₁₉	—	4	1	no	—
206	C₂²×C₄×C₁₉	—	4	1	no	—
207	C₂²×C₄×C₁₉	—	4	1	no	—
208	C₂²×C₄×C₁₉	—	4	1	no	—
209	C₂²×C₄×C₁₉	—	4	1	no	—
210	C₂²×C₄×C₁₉	—	4	1	no	—
211	C₂²×C₄×C₁₉	—	4	1	no	—
212	C₂²×C₄×C₁₉	—	4	1	no	—
213	C₂²×C₄×C₁₉	—	4	1	no	—
214	C₂²×C₄×C₁₉	C₂²×C₄	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	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
225	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
226	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
227	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
228	Q₁₆×C₁₉	—	2	8	no	—
229	SD₁₆×C₁₉	—	2	8	no	—
230	SD₁₆×C₁₉	—	2	8	no	—
231	D₈×C₁₉	—	2	8	no	—
232	M₁₆×C₁₉	—	2	2	no	—
233	M₁₆×C₁₉	—	2	2	no	—
234	M₁₆×C₁₉	—	2	2	no	—
235	M₁₆×C₁₉	—	2	2	no	—
236	M₁₆×C₁₉	—	2	2	no	—
237	M₁₆×C₁₉	—	4	1	no	—
238	M₁₆×C₁₉	—	4	1	no	—
239	M₁₆×C₁₉	C₂²⋊C₄	1	4	yes	—
240	C₂×C₈×C₁₉	—	2	2	no	—
241	C₂×C₈×C₁₉	—	2	2	no	—
242	C₂×C₈×C₁₉	—	2	2	no	—
243	C₂×C₈×C₁₉	—	2	2	no	—
244	C₂×C₈×C₁₉	—	4	1	no	—
245	C₂×C₈×C₁₉	—	4	1	no	—
246	C₄⋊C₄×C₁₉	—	2	2	no	—
247	C₄⋊C₄×C₁₉	—	2	2	no	—
248	C₄⋊C₄×C₁₉	—	4	1	no	—
249	C₄⋊C₄×C₁₉	—	4	1	no	—
250	C₄⋊C₄×C₁₉	—	4	1	no	—
251	C₄⋊C₄×C₁₉	—	4	1	no	—
252	C₂²⋊C₄×C₁₉	—	2	2	no	—
253	C₂²⋊C₄×C₁₉	—	2	2	no	—
254	C₂²⋊C₄×C₁₉	—	2	2	no	—
255	C₂²⋊C₄×C₁₉	—	2	2	no	—
256	C₂²⋊C₄×C₁₉	—	4	1	no	—
257	C₂²⋊C₄×C₁₉	—	4	1	no	—
258	C₄²×C₁₉	—	2	2	no	—
259	C₄²×C₁₉	—	2	2	no	—
260	C₄²×C₁₉	—	4	1	no	—
261	C₄²×C₁₉	—	4	1	no	—
262	C₄²×C₁₉	—	4	1	no	—
263	C₄²×C₁₉	—	4	1	no	—
264	#11033	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
265	C₂³×C₁₉	—	2	2	no	—
266	C₂³×C₁₉	—	2	2	no	—
267	C₂³×C₁₉	—	4	1	no	—
268	C₂³×C₁₉	—	4	1	no	—
269	C₂³×C₁₉	—	4	1	no	—
270	C₂³×C₁₉	—	4	1	no	—
271	C₂³×C₁₉	—	8	1	no	—
272	C₂³×C₁₉	—	8	2	no	—
273	C₂³×C₁₉	—	8	2	no	—
274	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
275	C₂³×C₁₉	#120	1	1	yes	characteristic
276	C₂³×C₁₉	#120	1	1	yes	characteristic
277	C₂³×C₁₉	#121	1	1	yes	characteristic
278	C₂³×C₁₉	#121	1	1	yes	characteristic
279	C₂³×C₁₉	#121	1	1	yes	characteristic
280	C₂³×C₁₉	#127	1	1	yes	characteristic
281	Q₈×C₁₉	—	2	2	no	—
282	Q₈×C₁₉	—	2	2	no	—
283	Q₈×C₁₉	—	2	2	no	—
284	Q₈×C₁₉	—	2	2	no	—
285	Q₈×C₁₉	—	4	1	no	—
286	Q₈×C₁₉	—	4	1	no	—
287	Q₈×C₁₉	—	4	1	no	—
288	Q₈×C₁₉	—	4	1	no	—
289	D₄×C₁₉	—	2	2	no	—
290	D₄×C₁₉	—	2	2	no	—
291	D₄×C₁₉	—	2	2	no	—
292	D₄×C₁₉	—	2	2	no	—
293	D₄×C₁₉	—	4	2	no	—
294	D₄×C₁₉	—	4	2	no	—
295	D₄×C₁₉	—	4	2	no	—
296	D₄×C₁₉	—	4	2	no	—
297	D₄×C₁₉	—	4	2	no	—
298	D₄×C₁₉	—	4	2	no	—
299	D₄×C₁₉	—	4	2	no	—
300	D₄×C₁₉	—	4	2	no	—
301	D₄×C₁₉	—	4	1	no	—
302	D₄×C₁₉	—	4	1	no	—
303	D₄×C₁₉	—	4	1	no	—
304	D₄×C₁₉	—	4	1	no	—
305	C₂×C₄×C₁₉	—	2	2	no	—
306	C₂×C₄×C₁₉	—	2	2	no	—
307	C₂×C₄×C₁₉	—	4	1	no	—
308	C₂×C₄×C₁₉	—	4	1	no	—
309	C₂×C₄×C₁₉	—	4	1	no	—
310	C₂×C₄×C₁₉	—	4	1	no	—
311	C₂×C₄×C₁₉	—	4	2	no	—
312	C₂×C₄×C₁₉	—	4	2	no	—
313	C₂×C₄×C₁₉	—	4	2	no	—
314	C₂×C₄×C₁₉	—	4	2	no	—
315	C₂×C₄×C₁₉	—	4	2	no	—
316	C₂×C₄×C₁₉	—	4	2	no	—
317	C₂×C₄×C₁₉	—	4	2	no	—
318	C₂×C₄×C₁₉	—	4	2	no	—
319	C₂×C₄×C₁₉	—	4	2	no	—
320	C₂×C₄×C₁₉	—	4	2	no	—
321	C₂×C₄×C₁₉	—	4	2	no	—
322	C₂×C₄×C₁₉	—	8	2	no	—
323	C₂×C₄×C₁₉	—	8	2	no	—
324	C₂×C₄×C₁₉	—	8	2	no	—
325	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
326	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
327	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
328	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
329	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
330	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
331	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
332	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
333	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
334	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
335	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
336	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
337	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
338	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
339	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
340	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
341	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
342	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
343	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
344	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
345	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
346	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
347	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
348	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
349	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
350	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
351	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
352	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
353	C₈×C₁₉	—	2	4	no	—
354	C₈×C₁₉	—	4	2	no	—
355	C₂×#575	C₂×C₁₉	1	1	yes	characteristic
356	C₂×#421	C₂×C₁₉	1	1	yes	characteristic, complemented
357	#2896	C₂×C₁₉	1	1	yes	characteristic, complemented
358	C₂×#410	C₂×C₁₉	1	1	yes	characteristic, complemented
359	C₂×#410	C₂×C₁₉	1	1	yes	characteristic, complemented
360	#1742	C₂×C₁₉	1	1	yes	characteristic, complemented
361	#1733	C₂×C₁₉	1	1	yes	characteristic, complemented
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	2	no	—
370	C₂²×C₁₉	—	4	2	no	—
371	C₂²×C₁₉	—	8	2	no	—
372	C₂²×C₁₉	—	8	2	no	—
373	C₂²×C₁₉	—	8	2	no	—
374	C₂²×C₁₉	—	8	2	no	—
375	C₂²×C₁₉	—	8	2	no	—
376	C₂²×C₁₉	—	8	2	no	—
377	C₂²×C₁₉	#386	1	1	yes	characteristic
378	C₂²×C₁₉	#386	1	1	yes	characteristic
379	C₂²×C₁₉	#390	1	1	yes	characteristic
380	C₂²×C₁₉	#392	1	1	yes	characteristic
381	C₂²×C₁₉	#392	1	1	yes	characteristic
382	C₂²×C₁₉	#392	1	1	yes	characteristic
383	C₂²×C₁₉	#394	1	1	yes	characteristic
384	C₄×C₁₉	—	4	2	no	—
385	C₄×C₁₉	—	4	2	no	—
386	C₄×C₁₉	—	8	2	no	—
387	C₄×C₁₉	—	8	2	no	—
388	C₄×C₁₉	—	8	2	no	—
389	C₄×C₁₉	#379	1	1	yes	characteristic
390	C₄×C₁₉	#386	1	1	yes	characteristic
391	C₄×C₁₉	#386	1	1	yes	characteristic
392	C₄×C₁₉	#390	1	1	yes	characteristic
393	C₄×C₁₉	#392	1	1	yes	characteristic
394	C₄×C₁₉	#394	1	1	yes	characteristic
395	C₄×C₁₉	#394	1	1	yes	characteristic
396	C₄×C₁₉	#394	1	1	yes	characteristic
397	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
398	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
399	#575	—	2	2	no	—
400	#575	—	2	2	no	—
401	#575	—	2	2	no	—
402	#575	—	2	2	no	—
403	C₂×#137	—	2	1	no	—
404	C₂×#137	C₄×C₁₉	1	2	yes	complemented
405	C₂×AGL(1,ℤ/8)	—	2	1	no	—
406	C₂×AGL(1,ℤ/8)	C₄×C₁₉	1	2	yes	complemented
407	C₂×#135	—	2	2	no	—
408	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
409	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
410	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
411	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
412	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
413	#421	—	2	2	no	—
414	#421	—	2	2	no	—
415	C₂×#104	—	2	2	no	—
416	#419	—	2	1	no	—
417	#418	—	2	1	no	—
418	#417	—	2	2	no	—
419	#416	—	2	2	no	—
420	#410	—	2	2	no	—
421	#410	—	2	2	no	—
422	#410	—	2	2	no	—
423	#410	—	2	2	no	—
424	C₂×#99	—	2	2	no	—
425	C₂×#99	—	2	2	no	—
426	#343	—	2	2	no	—
427	#339	—	2	2	no	—
428	C₂×C₁₉	—	2	1	no	—
429	C₂×C₁₉	—	2	1	no	—
430	C₂×C₁₉	—	2	1	no	—
431	C₂×C₁₉	—	2	1	no	—
432	C₂×C₁₉	—	2	1	no	—
433	C₂×C₁₉	—	2	1	no	—
434	C₂×C₁₉	—	2	1	no	—
435	C₂×C₁₉	—	8	2	no	—
436	C₂×C₁₉	—	8	2	no	—
437	C₂×C₁₉	#1438	1	1	yes	characteristic
438	C₂×#41	—	2	1	no	—
439	C₂×#41	—	2	1	no	—
440	C₂×#41	—	2	1	no	—
441	C₂×#41	—	2	1	no	—
442	C₂×#41	—	2	1	no	—
443	C₂×#41	—	2	1	no	—
444	C₂×#41	—	2	1	no	—
445	C₂×#41	—	2	1	no	—
446	C₂×#41	—	2	1	no	—
447	C₂×#41	—	2	1	no	—
448	C₂×#41	—	2	1	no	—
449	C₂×#41	—	2	1	no	—
450	C₂×#41	—	2	1	no	—
451	C₂×#41	—	2	1	no	—
452	C₂×#41	—	2	1	no	—
453	C₂×#41	—	2	1	no	—
454	C₂×#41	—	2	1	no	—
455	C₂×#41	—	2	1	no	—
456	C₂×#41	—	2	1	no	—
457	C₂×#41	—	2	1	no	—
458	C₂×#41	C₂×C₄×C₁₉	1	2	yes	—
459	C₂×#41	D₄×C₁₉	1	2	yes	—
460	C₂×#41	D₄×C₁₉	1	2	yes	—
461	C₂×#41	D₄×C₁₉	1	2	yes	—
462	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
463	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
464	C₂²×D₄	—	2	1	no	—
465	C₂²×D₄	—	2	1	no	—
466	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
467	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
468	C₂³×C₄	—	2	1	no	—
469	C₂³×C₄	—	2	1	no	—
470	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
471	#137	—	2	4	no	—
472	#137	—	2	4	no	—
473	#137	—	2	4	no	—
474	#137	—	2	4	no	—
475	AGL(1,ℤ/8)	—	2	4	no	—
476	AGL(1,ℤ/8)	—	2	4	no	—
477	AGL(1,ℤ/8)	—	2	4	no	—
478	AGL(1,ℤ/8)	—	2	4	no	—
479	#135	—	2	8	no	—
480	#135	—	2	8	no	—
481	C₂×Q₁₆	—	2	2	no	—
482	C₂×SD₁₆	—	2	2	no	—
483	C₂×SD₁₆	—	2	2	no	—
484	C₂×D₈	—	2	2	no	—
485	C₂×M₁₆	—	2	1	no	—
486	C₂×M₁₆	—	2	1	no	—
487	C₂×M₁₆	—	2	1	no	—
488	C₂×M₁₆	—	2	1	no	—
489	C₂×M₁₆	—	2	1	no	—
490	C₂×M₁₆	—	2	1	no	—
491	C₂×M₁₆	—	2	1	no	—
492	C₂×M₁₆	—	2	1	no	—
493	C₂×M₁₆	C₂×C₄×C₁₉	1	2	yes	—
494	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
495	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
496	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
497	C₂²×C₈	—	2	1	no	—
498	C₂²×C₈	—	2	1	no	—
499	#117	—	2	1	no	—
500	#117	—	2	1	no	—
501	#117	—	2	1	no	—
502	#117	—	2	1	no	—
503	#117	—	2	1	no	—
504	#117	—	2	1	no	—
505	#117	—	2	1	no	—
506	#117	—	2	1	no	—
507	#117	—	2	1	no	—
508	#117	—	2	1	no	—
509	#117	D₄×C₁₉	1	2	yes	—
510	#117	D₄×C₁₉	1	2	yes	—
511	C₂×C₄⋊C₄	—	2	1	no	—
512	C₂×C₄⋊C₄	—	2	1	no	—
513	C₂×C₄⋊C₄	—	2	1	no	—
514	C₂×C₂²⋊C₄	—	2	1	no	—
515	C₂×C₂²⋊C₄	—	2	1	no	—
516	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
517	C₂×C₄²	—	2	1	no	—
518	C₂×C₄²	—	2	1	no	—
519	C₂×C₄²	—	2	1	no	—
520	#104	—	2	8	no	—
521	#103	—	2	4	no	—
522	#102	—	2	4	no	—
523	#99	—	2	8	no	—
524	#99	—	2	8	no	—
525	C₁₉	#11033	1	1	yes	characteristic, direct product factor, Sylow
526	C₂⁴	—	2	1	no	—
527	C₂⁴	—	2	1	no	—
528	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
529	#41	—	2	2	no	—
530	#41	—	2	2	no	—
531	#41	—	2	2	no	—
532	#41	—	2	2	no	—
533	#41	—	2	2	no	—
534	#41	—	2	2	no	—
535	#41	—	2	2	no	—
536	#41	—	2	2	no	—
537	#41	—	2	2	no	—
538	#41	—	2	2	no	—
539	#41	—	2	2	no	—
540	#41	—	2	2	no	—
541	#41	—	2	2	no	—
542	#41	—	2	2	no	—
543	#41	—	2	2	no	—
544	#41	—	2	2	no	—
545	#41	—	4	1	no	—
546	#41	—	4	1	no	—
547	#41	—	4	1	no	—
548	#41	—	4	1	no	—
549	#41	—	4	1	no	—
550	#41	—	4	1	no	—
551	#41	—	4	1	no	—
552	#41	—	4	1	no	—
553	#41	—	4	1	no	—
554	#41	—	4	1	no	—
555	#41	—	4	1	no	—
556	#41	—	4	1	no	—
557	#41	—	4	1	no	—
558	#41	—	4	1	no	—
559	#41	—	4	1	no	—
560	#41	—	4	1	no	—
561	C₂×Q₈	—	2	1	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	—	2	1	no	—
564	C₂×Q₈	—	2	1	no	—
565	C₂×Q₈	—	2	1	no	—
566	C₂×Q₈	—	2	1	no	—
567	C₂×Q₈	—	2	1	no	—
568	C₂×Q₈	—	2	1	no	—
569	C₂×Q₈	—	2	1	no	—
570	C₂×Q₈	—	2	1	no	—
571	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
572	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	—	2	2	no	—
576	C₂×D₄	—	2	2	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	—	2	1	no	—
584	C₂×D₄	—	2	1	no	—
585	C₂×D₄	—	2	1	no	—
586	C₂×D₄	—	2	1	no	—
587	C₂×D₄	—	4	1	no	—
588	C₂×D₄	—	4	1	no	—
589	C₂×D₄	—	4	1	no	—
590	C₂×D₄	—	4	1	no	—
591	C₂×D₄	—	4	1	no	—
592	C₂×D₄	—	4	1	no	—
593	C₂×D₄	—	4	1	no	—
594	C₂×D₄	—	4	1	no	—
595	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
596	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	4	1	no	—
605	C₂²×C₄	—	4	1	no	—
606	C₂²×C₄	—	4	1	no	—
607	C₂²×C₄	—	4	1	no	—
608	C₂²×C₄	—	4	1	no	—
609	C₂²×C₄	—	4	1	no	—
610	C₂²×C₄	—	4	1	no	—
611	C₂²×C₄	—	4	1	no	—
612	C₂²×C₄	—	4	1	no	—
613	C₂²×C₄	—	4	1	no	—
614	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
615	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
616	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
617	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
618	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
619	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
620	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
621	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
622	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
623	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
624	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
625	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
626	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
627	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
628	Q₁₆	—	2	8	no	—
629	SD₁₆	—	2	8	no	—
630	SD₁₆	—	2	8	no	—
631	D₈	—	2	8	no	—
632	M₁₆	—	2	2	no	—
633	M₁₆	—	2	2	no	—
634	M₁₆	—	2	2	no	—
635	M₁₆	—	2	2	no	—
636	M₁₆	—	2	2	no	—
637	M₁₆	—	4	1	no	—
638	M₁₆	—	4	1	no	—
639	M₁₆	C₂²⋊C₄×C₁₉	1	4	yes	—
640	C₂×C₈	—	2	2	no	—
641	C₂×C₈	—	2	2	no	—
642	C₂×C₈	—	2	2	no	—
643	C₂×C₈	—	2	2	no	—
644	C₂×C₈	—	4	1	no	—
645	C₂×C₈	—	4	1	no	—
646	C₄⋊C₄	—	2	2	no	—
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	—	4	1	no	—
649	C₄⋊C₄	—	4	1	no	—
650	C₄⋊C₄	—	4	1	no	—
651	C₄⋊C₄	—	4	1	no	—
652	C₂²⋊C₄	—	2	2	no	—
653	C₂²⋊C₄	—	2	2	no	—
654	C₂²⋊C₄	—	2	2	no	—
655	C₂²⋊C₄	—	2	2	no	—
656	C₂²⋊C₄	—	4	1	no	—
657	C₂²⋊C₄	—	4	1	no	—
658	C₄²	—	2	2	no	—
659	C₄²	—	2	2	no	—
660	C₄²	—	4	1	no	—
661	C₄²	—	4	1	no	—
662	C₄²	—	4	1	no	—
663	C₄²	—	4	1	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	4	1	no	—
667	C₂³	—	4	1	no	—
668	C₂³	—	4	1	no	—
669	C₂³	—	4	1	no	—
670	C₂³	—	8	1	no	—
671	C₂³	—	8	2	no	—
672	C₂³	—	8	2	no	—
673	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
674	C₂³	C₁₉×#120	1	1	yes	characteristic
675	C₂³	C₁₉×#120	1	1	yes	characteristic
676	C₂³	C₁₉×#121	1	1	yes	characteristic
677	C₂³	C₁₉×#121	1	1	yes	characteristic
678	C₂³	C₁₉×#121	1	1	yes	characteristic
679	C₂³	C₁₉×#127	1	1	yes	characteristic
680	Q₈	—	2	2	no	—
681	Q₈	—	2	2	no	—
682	Q₈	—	2	2	no	—
683	Q₈	—	2	2	no	—
684	Q₈	—	4	1	no	—
685	Q₈	—	4	1	no	—
686	Q₈	—	4	1	no	—
687	Q₈	—	4	1	no	—
688	D₄	—	2	2	no	—
689	D₄	—	2	2	no	—
690	D₄	—	2	2	no	—
691	D₄	—	2	2	no	—
692	D₄	—	4	2	no	—
693	D₄	—	4	2	no	—
694	D₄	—	4	2	no	—
695	D₄	—	4	2	no	—
696	D₄	—	4	2	no	—
697	D₄	—	4	2	no	—
698	D₄	—	4	2	no	—
699	D₄	—	4	2	no	—
700	D₄	—	4	1	no	—
701	D₄	—	4	1	no	—
702	D₄	—	4	1	no	—
703	D₄	—	4	1	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	4	1	no	—
707	C₂×C₄	—	4	1	no	—
708	C₂×C₄	—	4	1	no	—
709	C₂×C₄	—	4	1	no	—
710	C₂×C₄	—	4	2	no	—
711	C₂×C₄	—	4	2	no	—
712	C₂×C₄	—	4	2	no	—
713	C₂×C₄	—	4	2	no	—
714	C₂×C₄	—	4	2	no	—
715	C₂×C₄	—	4	2	no	—
716	C₂×C₄	—	4	2	no	—
717	C₂×C₄	—	4	2	no	—
718	C₂×C₄	—	4	2	no	—
719	C₂×C₄	—	4	2	no	—
720	C₂×C₄	—	4	2	no	—
721	C₂×C₄	—	8	2	no	—
722	C₂×C₄	—	8	2	no	—
723	C₂×C₄	—	8	2	no	—
724	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
725	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
726	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
727	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
728	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
729	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
730	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
731	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
732	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
733	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
734	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
735	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
736	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
737	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
738	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
739	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
740	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
741	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
742	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
743	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
744	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
745	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
746	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
747	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
748	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
749	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
750	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
751	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
752	C₈	—	2	4	no	—
753	C₈	—	4	2	no	—
754	C₂²	—	4	1	no	—
755	C₂²	—	4	1	no	—
756	C₂²	—	4	1	no	—
757	C₂²	—	4	1	no	—
758	C₂²	—	4	1	no	—
759	C₂²	—	4	1	no	—
760	C₂²	—	4	1	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	8	2	no	—
764	C₂²	—	8	2	no	—
765	C₂²	—	8	2	no	—
766	C₂²	—	8	2	no	—
767	C₂²	—	8	2	no	—
768	C₂²	—	8	2	no	—
769	C₂²	C₁₉×#386	1	1	yes	characteristic
770	C₂²	C₁₉×#386	1	1	yes	characteristic
771	C₂²	C₁₉×#390	1	1	yes	characteristic
772	C₂²	C₁₉×#392	1	1	yes	characteristic
773	C₂²	C₁₉×#392	1	1	yes	characteristic
774	C₂²	C₁₉×#392	1	1	yes	characteristic
775	C₂²	C₁₉×#394	1	1	yes	characteristic
776	C₄	—	4	2	no	—
777	C₄	—	4	2	no	—
778	C₄	—	8	2	no	—
779	C₄	—	8	2	no	—
780	C₄	—	8	2	no	—
781	C₄	C₁₉×#379	1	1	yes	characteristic
782	C₄	C₁₉×#386	1	1	yes	characteristic
783	C₄	C₁₉×#386	1	1	yes	characteristic
784	C₄	C₁₉×#390	1	1	yes	characteristic
785	C₄	C₁₉×#392	1	1	yes	characteristic
786	C₄	C₁₉×#394	1	1	yes	characteristic
787	C₄	C₁₉×#394	1	1	yes	characteristic
788	C₄	C₁₉×#394	1	1	yes	characteristic
789	C₂	—	2	1	no	—
790	C₂	—	2	1	no	—
791	C₂	—	2	1	no	—
792	C₂	—	2	1	no	—
793	C₂	—	2	1	no	—
794	C₂	—	2	1	no	—
795	C₂	—	2	1	no	—
796	C₂	—	8	2	no	—
797	C₂	—	8	2	no	—
798	C₂	C₁₉×#1438	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₉	#394
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
socle	C₂×C₁₉	#1438
prime radical	C₂×C₁₉×#575	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#421	C₂	semidirect
3. C₁₉×#2896	C₂	semidirect
4. C₂×C₁₉×#410	C₂	semidirect
5. C₂×C₁₉×#410	C₂	semidirect
6. C₁₉×#1742	C₂	semidirect
7. C₁₉×#1733	C₂	semidirect
15. C₂×C₁₉×#137	C₄	semidirect
17. C₂×C₁₉×AGL(1,ℤ/8)	C₄	semidirect
264. #11033	C₁₉	direct (N × H)
356. C₂×#421	C₂×C₁₉	semidirect
357. #2896	C₂×C₁₉	semidirect
358. C₂×#410	C₂×C₁₉	semidirect
359. C₂×#410	C₂×C₁₉	semidirect
360. #1742	C₂×C₁₉	semidirect
361. #1733	C₂×C₁₉	semidirect
404. C₂×#137	C₄×C₁₉	semidirect
406. C₂×AGL(1,ℤ/8)	C₄×C₁₉	semidirect
525. C₁₉	#11033	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#575	2
C₂×C₁₉×#421	2
C₁₉×#2896	2
C₂×C₁₉×#410	2
C₁₉×#1742	2
C₁₉×#1733	2
#11033	19

Subgroups — C19×#11033 #18016992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11033 #18016992