Subgroups — C₁₉×#18450 #18024409

Order 4864.

1096 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3537	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3194	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3186	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2815	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1612	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1607	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1600	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1595	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1516	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1510	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1471	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#560	—	2	2	no	—
13	C₁₉×#553	—	2	1	no	—
14	C₁₉×#553	—	2	1	no	—
15	D₄²×C₁₉	—	2	2	no	—
16	D₄²×C₁₉	—	2	1	no	—
17	D₄²×C₁₉	—	2	1	no	—
18	C₁₉×#540	—	2	1	no	—
19	C₁₉×#538	—	2	1	no	—
20	C₁₉×#538	C₂²	1	2	yes	—
21	C₁₉×#535	—	2	1	no	—
22	C₁₉×#534	—	2	1	no	—
23	C₁₉×#534	C₂²	1	2	yes	—
24	C₁₉×#525	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic, complemented
28	C₁₉×#483	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#482	—	2	1	no	—
30	C₁₉×#480	—	2	1	no	—
31	C₁₉×#480	C₂²	1	2	yes	complemented
32	C₁₉×#480	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×#469	—	2	1	no	—
34	C₁₉×#468	—	2	1	no	—
35	C₁₉×#466	—	2	2	no	—
36	C₁₉×#450	C₂²	1	1	yes	characteristic, complemented
37	C₁₉×#449	—	2	1	no	—
38	C₁₉×#447	—	2	1	no	—
39	C₁₉×#447	C₂²	1	2	yes	complemented
40	C₁₉×#447	C₂²	1	1	yes	characteristic, complemented
41	C₁₉×#407	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
43	C₁₉×#397	—	2	1	no	—
44	C₁₉×#397	C₂²	1	2	yes	complemented
45	C₁₉×#392	—	2	1	no	—
46	C₁₉×#392	—	2	2	no	—
47	C₁₉×#392	C₂²	1	2	yes	complemented
48	C₁₉×#381	C₂²	1	1	yes	characteristic, complemented
49	C₁₉×#328	C₂²	1	2	yes	complemented
50	C₁₉×#327	C₂²	1	2	yes	complemented
51	C₁₉×#327	C₂²	1	2	yes	complemented
52	C₁₉×#327	C₂²	1	2	yes	complemented
53	C₁₉×#323	C₂²	1	2	yes	complemented
54	C₁₉×#323	C₂²	1	2	yes	complemented
55	C₂×#41×C₁₉	D₄	1	1	yes	characteristic, complemented
56	C₂²×D₄×C₁₉	—	2	2	no	—
57	C₂²×D₄×C₁₉	—	2	1	no	—
58	C₂²×D₄×C₁₉	—	2	1	no	—
59	C₂²×D₄×C₁₉	—	2	2	no	—
60	C₂²×D₄×C₁₉	—	2	1	no	—
61	C₂²×D₄×C₁₉	—	2	2	no	—
62	C₂²×D₄×C₁₉	D₄	1	2	yes	—
63	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
64	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic, complemented
65	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₂×SD₁₆×C₁₉	—	2	1	no	—
68	C₂×D₈×C₁₉	—	2	2	no	—
69	C₂×D₈×C₁₉	—	2	1	no	—
70	C₂×M₁₆×C₁₉	—	2	1	no	—
71	C₂²×C₈×C₁₉	—	2	1	no	—
72	C₁₉×#127	—	2	2	no	—
73	C₁₉×#127	—	2	1	no	—
74	C₁₉×#126	—	2	2	no	—
75	C₁₉×#126	—	2	2	no	—
76	C₁₉×#125	—	2	1	no	—
77	C₁₉×#124	—	2	2	no	—
78	C₁₉×#123	—	2	2	no	—
79	C₁₉×#123	—	2	1	no	—
80	C₁₉×#123	—	2	2	no	—
81	C₁₉×#123	—	2	2	no	—
82	C₁₉×#123	—	2	2	no	—
83	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic, complemented
84	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
85	C₁₉×#121	—	2	2	no	—
86	C₁₉×#121	—	2	1	no	—
87	C₁₉×#121	—	2	1	no	—
88	C₁₉×#121	—	2	2	no	—
89	C₁₉×#121	—	2	2	no	—
90	C₁₉×#121	—	2	2	no	—
91	C₁₉×#121	—	2	2	no	—
92	C₁₉×#121	—	2	1	no	—
93	C₁₉×#121	—	2	1	no	—
94	C₁₉×#121	—	2	1	no	—
95	C₁₉×#121	—	2	1	no	—
96	C₁₉×#121	—	2	1	no	—
97	C₁₉×#121	—	2	1	no	—
98	C₁₉×#121	—	2	2	no	—
99	C₁₉×#121	—	2	1	no	—
100	C₁₉×#121	—	2	1	no	—
101	C₁₉×#121	—	2	1	no	—
102	C₁₉×#121	—	2	1	no	—
103	C₁₉×#121	D₄	1	2	yes	complemented
104	C₁₉×#121	D₄	1	1	yes	characteristic, complemented
105	C₁₉×#121	C₂³	1	2	yes	—
106	C₁₉×#121	C₂³	1	1	yes	characteristic
107	C₁₉×#120	—	2	2	no	—
108	C₁₉×#120	—	2	2	no	—
109	C₁₉×#120	—	2	2	no	—
110	C₁₉×#120	—	2	1	no	—
111	C₁₉×#120	—	2	2	no	—
112	C₁₉×#120	—	2	2	no	—
113	C₁₉×#120	—	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	—	2	2	no	—
120	C₁₉×#117	—	2	1	no	—
121	C₁₉×#117	D₄	1	1	yes	characteristic, complemented
122	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic, complemented
124	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
125	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
129	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
130	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
131	C₁₉×#107	—	2	2	no	—
132	C₁₉×#107	—	2	1	no	—
133	C₁₉×#106	—	2	1	no	—
134	C₁₉×#103	—	2	1	no	—
135	C₁₉×#102	—	2	2	no	—
136	C₁₉×#102	—	2	1	no	—
137	C₁₉×#102	—	2	2	no	—
138	C₁₉×#102	—	2	1	no	—
139	C₁₉×#102	—	2	1	no	—
140	C₁₉×C₂²⋊C₈	—	2	1	no	—
141	C₁₉×C₂²⋊C₈	—	2	1	no	—
142	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
143	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
144	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
145	C₁₉×#95	—	2	1	no	—
146	C₁₉×#95	—	2	2	no	—
147	C₁₉×#95	C₂³	1	2	yes	—
148	C₂⁴×C₁₉	—	2	2	no	—
149	C₂⁴×C₁₉	—	2	1	no	—
150	C₂⁴×C₁₉	—	2	1	no	—
151	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
152	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
153	#41×C₁₉	—	8	1	no	—
154	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂×D₄×C₁₉	—	2	2	no	—
156	C₂×D₄×C₁₉	—	2	1	no	—
157	C₂×D₄×C₁₉	—	2	1	no	—
158	C₂×D₄×C₁₉	—	2	2	no	—
159	C₂×D₄×C₁₉	—	2	2	no	—
160	C₂×D₄×C₁₉	—	2	2	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	1	no	—
165	C₂×D₄×C₁₉	—	2	2	no	—
166	C₂×D₄×C₁₉	—	2	2	no	—
167	C₂×D₄×C₁₉	—	2	1	no	—
168	C₂×D₄×C₁₉	—	2	1	no	—
169	C₂×D₄×C₁₉	—	2	1	no	—
170	C₂×D₄×C₁₉	—	2	1	no	—
171	C₂×D₄×C₁₉	—	2	1	no	—
172	C₂×D₄×C₁₉	—	4	1	no	—
173	C₂×D₄×C₁₉	—	4	1	no	—
174	C₂×D₄×C₁₉	—	8	1	no	—
175	C₂×D₄×C₁₉	—	8	1	no	—
176	C₂×D₄×C₁₉	—	8	2	no	—
177	C₂×D₄×C₁₉	—	8	1	no	—
178	C₂×D₄×C₁₉	—	8	2	no	—
179	C₂×D₄×C₁₉	—	8	2	no	—
180	C₂×D₄×C₁₉	—	8	2	no	—
181	C₂×D₄×C₁₉	—	8	2	no	—
182	C₂×D₄×C₁₉	—	8	2	no	—
183	C₂×D₄×C₁₉	—	8	2	no	—
184	C₂×D₄×C₁₉	—	8	2	no	—
185	C₂×D₄×C₁₉	—	8	2	no	—
186	C₂×D₄×C₁₉	—	8	4	no	—
187	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
188	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
189	C₂²×C₄×C₁₉	—	2	2	no	—
190	C₂²×C₄×C₁₉	—	2	2	no	—
191	C₂²×C₄×C₁₉	—	2	1	no	—
192	C₂²×C₄×C₁₉	—	2	1	no	—
193	C₂²×C₄×C₁₉	—	2	1	no	—
194	C₂²×C₄×C₁₉	—	2	2	no	—
195	C₂²×C₄×C₁₉	—	8	1	no	—
196	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
197	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
203	SD₁₆×C₁₉	—	8	1	no	—
204	D₈×C₁₉	—	8	2	no	—
205	D₈×C₁₉	—	8	1	no	—
206	M₁₆×C₁₉	—	8	1	no	—
207	C₂×C₈×C₁₉	—	2	2	no	—
208	C₂×C₈×C₁₉	—	2	1	no	—
209	C₂×C₈×C₁₉	—	2	1	no	—
210	C₂×C₈×C₁₉	—	8	1	no	—
211	C₄⋊C₄×C₁₉	—	2	2	no	—
212	C₄⋊C₄×C₁₉	—	2	2	no	—
213	C₄⋊C₄×C₁₉	—	2	1	no	—
214	C₄⋊C₄×C₁₉	—	2	1	no	—
215	C₄⋊C₄×C₁₉	—	2	1	no	—
216	C₄⋊C₄×C₁₉	—	2	1	no	—
217	C₄⋊C₄×C₁₉	—	2	1	no	—
218	C₄⋊C₄×C₁₉	—	2	1	no	—
219	C₄⋊C₄×C₁₉	—	2	1	no	—
220	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
221	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
222	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
223	C₂²⋊C₄×C₁₉	—	2	2	no	—
224	C₂²⋊C₄×C₁₉	—	2	2	no	—
225	C₂²⋊C₄×C₁₉	—	2	2	no	—
226	C₂²⋊C₄×C₁₉	—	2	2	no	—
227	C₂²⋊C₄×C₁₉	—	2	2	no	—
228	C₂²⋊C₄×C₁₉	—	2	1	no	—
229	C₂²⋊C₄×C₁₉	—	2	1	no	—
230	C₂²⋊C₄×C₁₉	—	2	1	no	—
231	C₂²⋊C₄×C₁₉	—	2	2	no	—
232	C₂²⋊C₄×C₁₉	—	2	1	no	—
233	C₂²⋊C₄×C₁₉	—	2	2	no	—
234	C₂²⋊C₄×C₁₉	—	2	2	no	—
235	C₂²⋊C₄×C₁₉	—	2	2	no	—
236	C₂²⋊C₄×C₁₉	—	2	1	no	—
237	C₂²⋊C₄×C₁₉	—	4	1	no	—
238	C₂²⋊C₄×C₁₉	—	4	1	no	—
239	C₂²⋊C₄×C₁₉	—	8	2	no	—
240	C₂²⋊C₄×C₁₉	—	8	2	no	—
241	C₂²⋊C₄×C₁₉	—	8	1	no	—
242	C₄²×C₁₉	—	2	2	no	—
243	C₄²×C₁₉	—	2	1	no	—
244	#18450	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
245	C₂³×C₁₉	—	2	2	no	—
246	C₂³×C₁₉	—	2	2	no	—
247	C₂³×C₁₉	—	2	2	no	—
248	C₂³×C₁₉	—	2	1	no	—
249	C₂³×C₁₉	—	2	2	no	—
250	C₂³×C₁₉	—	2	2	no	—
251	C₂³×C₁₉	—	4	1	no	—
252	C₂³×C₁₉	—	4	1	no	—
253	C₂³×C₁₉	—	4	2	no	—
254	C₂³×C₁₉	—	4	2	no	—
255	C₂³×C₁₉	—	4	2	no	—
256	C₂³×C₁₉	—	4	1	no	—
257	C₂³×C₁₉	—	4	1	no	—
258	C₂³×C₁₉	—	4	2	no	—
259	C₂³×C₁₉	—	4	1	no	—
260	C₂³×C₁₉	—	4	2	no	—
261	C₂³×C₁₉	—	8	1	no	—
262	C₂³×C₁₉	—	8	1	no	—
263	C₂³×C₁₉	—	8	2	no	—
264	C₂³×C₁₉	—	8	2	no	—
265	C₂³×C₁₉	—	8	2	no	—
266	C₂³×C₁₉	#120	1	1	yes	characteristic
267	C₂³×C₁₉	#120	1	1	yes	characteristic
268	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
269	Q₈×C₁₉	—	4	1	no	—
270	D₄×C₁₉	—	4	2	no	—
271	D₄×C₁₉	—	4	1	no	—
272	D₄×C₁₉	—	4	2	no	—
273	D₄×C₁₉	—	4	2	no	—
274	D₄×C₁₉	—	4	2	no	—
275	D₄×C₁₉	—	4	1	no	—
276	D₄×C₁₉	—	4	1	no	—
277	D₄×C₁₉	—	4	4	no	—
278	D₄×C₁₉	—	4	2	no	—
279	D₄×C₁₉	—	4	2	no	—
280	D₄×C₁₉	—	4	2	no	—
281	D₄×C₁₉	—	4	2	no	—
282	D₄×C₁₉	—	8	1	no	—
283	D₄×C₁₉	—	8	2	no	—
284	D₄×C₁₉	—	8	2	no	—
285	D₄×C₁₉	—	8	1	no	—
286	D₄×C₁₉	—	8	2	no	—
287	D₄×C₁₉	—	8	2	no	—
288	D₄×C₁₉	—	8	2	no	—
289	D₄×C₁₉	—	8	2	no	—
290	D₄×C₁₉	—	8	2	no	—
291	D₄×C₁₉	—	8	2	no	—
292	D₄×C₁₉	—	8	2	no	—
293	D₄×C₁₉	—	8	8	no	—
294	C₂×C₄×C₁₉	—	2	1	no	—
295	C₂×C₄×C₁₉	—	2	2	no	—
296	C₂×C₄×C₁₉	—	2	2	no	—
297	C₂×C₄×C₁₉	—	2	1	no	—
298	C₂×C₄×C₁₉	—	2	1	no	—
299	C₂×C₄×C₁₉	—	4	1	no	—
300	C₂×C₄×C₁₉	—	4	1	no	—
301	C₂×C₄×C₁₉	—	4	1	no	—
302	C₂×C₄×C₁₉	—	4	1	no	—
303	C₂×C₄×C₁₉	—	4	1	no	—
304	C₂×C₄×C₁₉	—	4	1	no	—
305	C₂×C₄×C₁₉	—	4	2	no	—
306	C₂×C₄×C₁₉	—	4	2	no	—
307	C₂×C₄×C₁₉	—	4	2	no	—
308	C₂×C₄×C₁₉	—	4	2	no	—
309	C₂×C₄×C₁₉	—	4	1	no	—
310	C₂×C₄×C₁₉	—	4	2	no	—
311	C₂×C₄×C₁₉	—	4	2	no	—
312	C₂×C₄×C₁₉	—	8	1	no	—
313	C₂×C₄×C₁₉	—	8	2	no	—
314	C₂×C₄×C₁₉	—	8	2	no	—
315	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
316	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
317	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
318	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
319	C₈×C₁₉	—	4	2	no	—
320	C₈×C₁₉	—	4	1	no	—
321	C₈×C₁₉	—	4	1	no	—
322	#3537	C₂×C₁₉	1	1	yes	characteristic, complemented
323	#3194	C₂×C₁₉	1	1	yes	characteristic, complemented
324	#3186	C₂×C₁₉	1	1	yes	characteristic, complemented
325	#2815	C₂×C₁₉	1	1	yes	characteristic, complemented
326	#1612	C₂×C₁₉	1	2	yes	complemented
327	#1607	C₂×C₁₉	1	2	yes	complemented
328	#1600	C₂×C₁₉	1	2	yes	complemented
329	#1595	C₂×C₁₉	1	2	yes	complemented
330	#1516	C₂×C₁₉	1	1	yes	characteristic, complemented
331	#1510	C₂×C₁₉	1	1	yes	characteristic, complemented
332	#1471	C₂×C₁₉	1	1	yes	characteristic, complemented
333	C₂²×C₁₉	—	2	1	no	—
334	C₂²×C₁₉	—	2	1	no	—
335	C₂²×C₁₉	—	2	1	no	—
336	C₂²×C₁₉	—	2	1	no	—
337	C₂²×C₁₉	—	2	1	no	—
338	C₂²×C₁₉	—	2	1	no	—
339	C₂²×C₁₉	—	2	1	no	—
340	C₂²×C₁₉	—	2	1	no	—
341	C₂²×C₁₉	—	4	2	no	—
342	C₂²×C₁₉	—	4	2	no	—
343	C₂²×C₁₉	—	4	1	no	—
344	C₂²×C₁₉	—	4	2	no	—
345	C₂²×C₁₉	—	4	2	no	—
346	C₂²×C₁₉	—	4	1	no	—
347	C₂²×C₁₉	—	4	1	no	—
348	C₂²×C₁₉	—	4	2	no	—
349	C₂²×C₁₉	—	4	2	no	—
350	C₂²×C₁₉	—	8	2	no	—
351	C₂²×C₁₉	—	8	2	no	—
352	C₂²×C₁₉	—	8	2	no	—
353	C₂²×C₁₉	—	8	2	no	—
354	C₂²×C₁₉	—	8	2	no	—
355	C₂²×C₁₉	—	8	1	no	—
356	C₂²×C₁₉	—	8	1	no	—
357	C₂²×C₁₉	—	8	1	no	—
358	C₂²×C₁₉	—	16	2	no	—
359	C₂²×C₁₉	—	16	4	no	—
360	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
361	C₂²×C₁₉	#576	1	2	yes	—
362	C₄×C₁₉	—	2	1	no	—
363	C₄×C₁₉	—	2	1	no	—
364	C₄×C₁₉	—	2	1	no	—
365	C₄×C₁₉	—	2	1	no	—
366	C₄×C₁₉	—	4	2	no	—
367	C₄×C₁₉	—	4	1	no	—
368	C₄×C₁₉	—	4	2	no	—
369	C₄×C₁₉	—	4	1	no	—
370	C₄×C₁₉	—	4	1	no	—
371	C₄×C₁₉	—	8	2	no	—
372	C₄×C₁₉	—	8	1	no	—
373	#560	—	2	2	no	—
374	#553	—	2	1	no	—
375	#553	—	2	1	no	—
376	D₄²	—	2	2	no	—
377	D₄²	—	2	1	no	—
378	D₄²	—	2	1	no	—
379	#540	—	2	1	no	—
380	#538	—	2	1	no	—
381	#538	C₂²×C₁₉	1	2	yes	—
382	#535	—	2	1	no	—
383	#534	—	2	1	no	—
384	#534	C₂²×C₁₉	1	2	yes	—
385	#525	C₂²×C₁₉	1	1	yes	characteristic
386	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
387	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
388	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic, complemented
389	#483	C₂²×C₁₉	1	1	yes	characteristic, complemented
390	#482	—	2	1	no	—
391	#480	—	2	1	no	—
392	#480	C₂²×C₁₉	1	1	yes	characteristic, complemented
393	#480	C₂²×C₁₉	1	2	yes	complemented
394	#469	—	2	1	no	—
395	#468	—	2	1	no	—
396	#466	—	2	2	no	—
397	#450	C₂²×C₁₉	1	1	yes	characteristic, complemented
398	#449	—	2	1	no	—
399	#447	—	2	1	no	—
400	#447	C₂²×C₁₉	1	1	yes	characteristic, complemented
401	#447	C₂²×C₁₉	1	2	yes	complemented
402	#407	C₂²×C₁₉	1	1	yes	characteristic, complemented
403	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
404	#397	—	2	1	no	—
405	#397	C₂²×C₁₉	1	2	yes	complemented
406	#392	—	2	1	no	—
407	#392	—	2	2	no	—
408	#392	C₂²×C₁₉	1	2	yes	complemented
409	#381	C₂²×C₁₉	1	1	yes	characteristic, complemented
410	#328	C₂²×C₁₉	1	2	yes	complemented
411	#327	C₂²×C₁₉	1	2	yes	complemented
412	#327	C₂²×C₁₉	1	2	yes	complemented
413	#327	C₂²×C₁₉	1	2	yes	complemented
414	#323	C₂²×C₁₉	1	2	yes	complemented
415	#323	C₂²×C₁₉	1	2	yes	complemented
416	C₂×C₁₉	—	2	2	no	—
417	C₂×C₁₉	—	4	1	no	—
418	C₂×C₁₉	—	4	1	no	—
419	C₂×C₁₉	—	8	2	no	—
420	C₂×C₁₉	—	8	2	no	—
421	C₂×C₁₉	—	8	1	no	—
422	C₂×C₁₉	—	16	1	no	—
423	C₂×C₁₉	#3008	1	1	yes	characteristic
424	C₂×C₁₉	#3019	1	1	yes	characteristic
425	C₂×C₁₉	#3026	1	1	yes	characteristic
426	C₂×#41	D₄×C₁₉	1	1	yes	characteristic, complemented
427	C₂²×D₄	—	2	2	no	—
428	C₂²×D₄	—	2	1	no	—
429	C₂²×D₄	—	2	1	no	—
430	C₂²×D₄	—	2	2	no	—
431	C₂²×D₄	—	2	1	no	—
432	C₂²×D₄	—	2	2	no	—
433	C₂²×D₄	D₄×C₁₉	1	2	yes	—
434	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
435	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic, complemented
436	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
437	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
438	C₂×SD₁₆	—	2	1	no	—
439	C₂×D₈	—	2	2	no	—
440	C₂×D₈	—	2	1	no	—
441	C₂×M₁₆	—	2	1	no	—
442	C₂²×C₈	—	2	1	no	—
443	#127	—	2	2	no	—
444	#127	—	2	1	no	—
445	#126	—	2	2	no	—
446	#126	—	2	2	no	—
447	#125	—	2	1	no	—
448	#124	—	2	2	no	—
449	#123	—	2	2	no	—
450	#123	—	2	1	no	—
451	#123	—	2	2	no	—
452	#123	—	2	2	no	—
453	#123	—	2	2	no	—
454	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
455	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
456	#121	—	2	2	no	—
457	#121	—	2	1	no	—
458	#121	—	2	1	no	—
459	#121	—	2	2	no	—
460	#121	—	2	2	no	—
461	#121	—	2	2	no	—
462	#121	—	2	2	no	—
463	#121	—	2	1	no	—
464	#121	—	2	1	no	—
465	#121	—	2	1	no	—
466	#121	—	2	1	no	—
467	#121	—	2	1	no	—
468	#121	—	2	1	no	—
469	#121	—	2	2	no	—
470	#121	—	2	1	no	—
471	#121	—	2	1	no	—
472	#121	—	2	1	no	—
473	#121	—	2	1	no	—
474	#121	D₄×C₁₉	1	2	yes	complemented
475	#121	D₄×C₁₉	1	1	yes	characteristic, complemented
476	#121	C₂³×C₁₉	1	2	yes	—
477	#121	C₂³×C₁₉	1	1	yes	characteristic
478	#120	—	2	2	no	—
479	#120	—	2	2	no	—
480	#120	—	2	2	no	—
481	#120	—	2	1	no	—
482	#120	—	2	2	no	—
483	#120	—	2	2	no	—
484	#120	—	2	2	no	—
485	C₄×D₄	—	2	2	no	—
486	C₄×D₄	—	2	1	no	—
487	C₄×D₄	—	2	1	no	—
488	C₄×D₄	—	2	1	no	—
489	C₄×D₄	—	2	1	no	—
490	C₄×D₄	—	2	2	no	—
491	#117	—	2	1	no	—
492	#117	D₄×C₁₉	1	1	yes	characteristic, complemented
493	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
494	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic, complemented
495	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
496	C₂×C₂²⋊C₄	—	2	1	no	—
497	C₂×C₂²⋊C₄	—	2	1	no	—
498	C₂×C₂²⋊C₄	—	2	1	no	—
499	C₂×C₂²⋊C₄	—	2	2	no	—
500	C₂×C₂²⋊C₄	—	2	2	no	—
501	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
502	#107	—	2	2	no	—
503	#107	—	2	1	no	—
504	#106	—	2	1	no	—
505	#103	—	2	1	no	—
506	#102	—	2	2	no	—
507	#102	—	2	1	no	—
508	#102	—	2	2	no	—
509	#102	—	2	1	no	—
510	#102	—	2	1	no	—
511	C₂²⋊C₈	—	2	1	no	—
512	C₂²⋊C₈	—	2	1	no	—
513	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
514	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
515	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
516	#95	—	2	1	no	—
517	#95	—	2	2	no	—
518	#95	C₂³×C₁₉	1	2	yes	—
519	C₁₉	#18450	1	1	yes	characteristic, direct product factor, Sylow
520	C₂⁴	—	2	2	no	—
521	C₂⁴	—	2	1	no	—
522	C₂⁴	—	2	1	no	—
523	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
524	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
525	#41	—	8	1	no	—
526	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
527	C₂×D₄	—	2	2	no	—
528	C₂×D₄	—	2	1	no	—
529	C₂×D₄	—	2	1	no	—
530	C₂×D₄	—	2	2	no	—
531	C₂×D₄	—	2	2	no	—
532	C₂×D₄	—	2	2	no	—
533	C₂×D₄	—	2	2	no	—
534	C₂×D₄	—	2	2	no	—
535	C₂×D₄	—	2	2	no	—
536	C₂×D₄	—	2	1	no	—
537	C₂×D₄	—	2	2	no	—
538	C₂×D₄	—	2	2	no	—
539	C₂×D₄	—	2	1	no	—
540	C₂×D₄	—	2	1	no	—
541	C₂×D₄	—	2	1	no	—
542	C₂×D₄	—	2	1	no	—
543	C₂×D₄	—	2	1	no	—
544	C₂×D₄	—	4	1	no	—
545	C₂×D₄	—	4	1	no	—
546	C₂×D₄	—	8	1	no	—
547	C₂×D₄	—	8	1	no	—
548	C₂×D₄	—	8	2	no	—
549	C₂×D₄	—	8	1	no	—
550	C₂×D₄	—	8	2	no	—
551	C₂×D₄	—	8	2	no	—
552	C₂×D₄	—	8	2	no	—
553	C₂×D₄	—	8	2	no	—
554	C₂×D₄	—	8	2	no	—
555	C₂×D₄	—	8	2	no	—
556	C₂×D₄	—	8	2	no	—
557	C₂×D₄	—	8	2	no	—
558	C₂×D₄	—	8	4	no	—
559	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
560	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	8	1	no	—
568	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
569	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
570	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
571	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
572	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
573	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
574	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
575	SD₁₆	—	8	1	no	—
576	D₈	—	8	2	no	—
577	D₈	—	8	1	no	—
578	M₁₆	—	8	1	no	—
579	C₂×C₈	—	2	2	no	—
580	C₂×C₈	—	2	1	no	—
581	C₂×C₈	—	2	1	no	—
582	C₂×C₈	—	8	1	no	—
583	C₄⋊C₄	—	2	2	no	—
584	C₄⋊C₄	—	2	2	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
593	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
594	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
595	C₂²⋊C₄	—	2	2	no	—
596	C₂²⋊C₄	—	2	2	no	—
597	C₂²⋊C₄	—	2	2	no	—
598	C₂²⋊C₄	—	2	2	no	—
599	C₂²⋊C₄	—	2	2	no	—
600	C₂²⋊C₄	—	2	1	no	—
601	C₂²⋊C₄	—	2	1	no	—
602	C₂²⋊C₄	—	2	1	no	—
603	C₂²⋊C₄	—	2	2	no	—
604	C₂²⋊C₄	—	2	1	no	—
605	C₂²⋊C₄	—	2	2	no	—
606	C₂²⋊C₄	—	2	2	no	—
607	C₂²⋊C₄	—	2	2	no	—
608	C₂²⋊C₄	—	2	1	no	—
609	C₂²⋊C₄	—	4	1	no	—
610	C₂²⋊C₄	—	4	1	no	—
611	C₂²⋊C₄	—	8	2	no	—
612	C₂²⋊C₄	—	8	2	no	—
613	C₂²⋊C₄	—	8	1	no	—
614	C₄²	—	2	2	no	—
615	C₄²	—	2	1	no	—
616	C₂³	—	2	2	no	—
617	C₂³	—	2	2	no	—
618	C₂³	—	2	2	no	—
619	C₂³	—	2	1	no	—
620	C₂³	—	2	2	no	—
621	C₂³	—	2	2	no	—
622	C₂³	—	4	1	no	—
623	C₂³	—	4	1	no	—
624	C₂³	—	4	2	no	—
625	C₂³	—	4	2	no	—
626	C₂³	—	4	2	no	—
627	C₂³	—	4	1	no	—
628	C₂³	—	4	1	no	—
629	C₂³	—	4	2	no	—
630	C₂³	—	4	1	no	—
631	C₂³	—	4	2	no	—
632	C₂³	—	8	1	no	—
633	C₂³	—	8	1	no	—
634	C₂³	—	8	2	no	—
635	C₂³	—	8	2	no	—
636	C₂³	—	8	2	no	—
637	C₂³	C₁₉×#120	1	1	yes	characteristic
638	C₂³	C₁₉×#120	1	1	yes	characteristic
639	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
640	Q₈	—	4	1	no	—
641	D₄	—	4	2	no	—
642	D₄	—	4	1	no	—
643	D₄	—	4	2	no	—
644	D₄	—	4	2	no	—
645	D₄	—	4	2	no	—
646	D₄	—	4	1	no	—
647	D₄	—	4	1	no	—
648	D₄	—	4	4	no	—
649	D₄	—	4	2	no	—
650	D₄	—	4	2	no	—
651	D₄	—	4	2	no	—
652	D₄	—	4	2	no	—
653	D₄	—	8	1	no	—
654	D₄	—	8	2	no	—
655	D₄	—	8	2	no	—
656	D₄	—	8	1	no	—
657	D₄	—	8	2	no	—
658	D₄	—	8	2	no	—
659	D₄	—	8	2	no	—
660	D₄	—	8	2	no	—
661	D₄	—	8	2	no	—
662	D₄	—	8	2	no	—
663	D₄	—	8	2	no	—
664	D₄	—	8	8	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	—	4	2	no	—
677	C₂×C₄	—	4	2	no	—
678	C₂×C₄	—	4	2	no	—
679	C₂×C₄	—	4	2	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	2	no	—
682	C₂×C₄	—	4	2	no	—
683	C₂×C₄	—	8	1	no	—
684	C₂×C₄	—	8	2	no	—
685	C₂×C₄	—	8	2	no	—
686	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
687	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
688	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
689	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
690	C₈	—	4	2	no	—
691	C₈	—	4	1	no	—
692	C₈	—	4	1	no	—
693	C₂²	—	2	1	no	—
694	C₂²	—	2	1	no	—
695	C₂²	—	2	1	no	—
696	C₂²	—	2	1	no	—
697	C₂²	—	2	1	no	—
698	C₂²	—	2	1	no	—
699	C₂²	—	2	1	no	—
700	C₂²	—	2	1	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	4	1	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	4	2	no	—
706	C₂²	—	4	1	no	—
707	C₂²	—	4	1	no	—
708	C₂²	—	4	2	no	—
709	C₂²	—	4	2	no	—
710	C₂²	—	8	2	no	—
711	C₂²	—	8	2	no	—
712	C₂²	—	8	2	no	—
713	C₂²	—	8	2	no	—
714	C₂²	—	8	2	no	—
715	C₂²	—	8	1	no	—
716	C₂²	—	8	1	no	—
717	C₂²	—	8	1	no	—
718	C₂²	—	16	2	no	—
719	C₂²	—	16	4	no	—
720	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
721	C₂²	C₁₉×#576	1	2	yes	—
722	C₄	—	2	1	no	—
723	C₄	—	2	1	no	—
724	C₄	—	2	1	no	—
725	C₄	—	2	1	no	—
726	C₄	—	4	2	no	—
727	C₄	—	4	1	no	—
728	C₄	—	4	2	no	—
729	C₄	—	4	1	no	—
730	C₄	—	4	1	no	—
731	C₄	—	8	2	no	—
732	C₄	—	8	1	no	—
733	C₂	—	2	2	no	—
734	C₂	—	4	1	no	—
735	C₂	—	4	1	no	—
736	C₂	—	8	2	no	—
737	C₂	—	8	2	no	—
738	C₂	—	8	1	no	—
739	C₂	—	16	1	no	—
740	C₂	C₁₉×#3008	1	1	yes	characteristic
741	C₂	C₁₉×#3019	1	1	yes	characteristic
742	C₂	C₁₉×#3026	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ 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
1. C₁₉×#3537	C₂	semidirect
2. C₁₉×#3194	C₂	semidirect
3. C₁₉×#3186	C₂	semidirect
4. C₁₉×#2815	C₂	semidirect
5. C₁₉×#1612	C₂	semidirect
6. C₁₉×#1607	C₂	semidirect
7. C₁₉×#1600	C₂	semidirect
8. C₁₉×#1595	C₂	semidirect
9. C₁₉×#1516	C₂	semidirect
10. C₁₉×#1510	C₂	semidirect
11. C₁₉×#1471	C₂	semidirect
27. C₂×C₁₉×#121	C₂²	semidirect
28. C₁₉×#483	C₂²	semidirect
31. C₁₉×#480	C₂²	semidirect
32. C₁₉×#480	C₂²	semidirect
36. C₁₉×#450	C₂²	semidirect
39. C₁₉×#447	C₂²	semidirect
40. C₁₉×#447	C₂²	semidirect
41. C₁₉×#407	C₂²	semidirect
42. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
44. C₁₉×#397	C₂²	semidirect
47. C₁₉×#392	C₂²	semidirect
48. C₁₉×#381	C₂²	semidirect
49. C₁₉×#328	C₂²	semidirect
50. C₁₉×#327	C₂²	semidirect
51. C₁₉×#327	C₂²	semidirect
52. C₁₉×#327	C₂²	semidirect
53. C₁₉×#323	C₂²	semidirect
54. C₁₉×#323	C₂²	semidirect
55. C₂×#41×C₁₉	D₄	semidirect
64. C₂²×D₄×C₁₉	D₄	semidirect
83. C₁₉×C₂²⋊Q₈	D₄	semidirect
103. C₁₉×#121	D₄	semidirect
104. C₁₉×#121	D₄	semidirect
121. C₁₉×#117	D₄	semidirect
123. C₂×C₄⋊C₄×C₁₉	D₄	semidirect
244. #18450	C₁₉	direct (N × H)
322. #3537	C₂×C₁₉	semidirect
323. #3194	C₂×C₁₉	semidirect
324. #3186	C₂×C₁₉	semidirect
325. #2815	C₂×C₁₉	semidirect
326. #1612	C₂×C₁₉	semidirect
327. #1607	C₂×C₁₉	semidirect
328. #1600	C₂×C₁₉	semidirect
329. #1595	C₂×C₁₉	semidirect
330. #1516	C₂×C₁₉	semidirect
331. #1510	C₂×C₁₉	semidirect
332. #1471	C₂×C₁₉	semidirect
388. C₂×#121	C₂²×C₁₉	semidirect
389. #483	C₂²×C₁₉	semidirect
392. #480	C₂²×C₁₉	semidirect
393. #480	C₂²×C₁₉	semidirect
397. #450	C₂²×C₁₉	semidirect
400. #447	C₂²×C₁₉	semidirect
401. #447	C₂²×C₁₉	semidirect
402. #407	C₂²×C₁₉	semidirect
403. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
405. #397	C₂²×C₁₉	semidirect
408. #392	C₂²×C₁₉	semidirect
409. #381	C₂²×C₁₉	semidirect
410. #328	C₂²×C₁₉	semidirect
411. #327	C₂²×C₁₉	semidirect
412. #327	C₂²×C₁₉	semidirect
413. #327	C₂²×C₁₉	semidirect
414. #323	C₂²×C₁₉	semidirect
415. #323	C₂²×C₁₉	semidirect
426. C₂×#41	D₄×C₁₉	semidirect
435. C₂²×D₄	D₄×C₁₉	semidirect
454. C₂²⋊Q₈	D₄×C₁₉	semidirect
474. #121	D₄×C₁₉	semidirect
475. #121	D₄×C₁₉	semidirect
492. #117	D₄×C₁₉	semidirect
494. C₂×C₄⋊C₄	D₄×C₁₉	semidirect
519. C₁₉	#18450	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×#3537	2
C₁₉×#3194	2
C₁₉×#3186	2
C₁₉×#2815	2
C₁₉×#1612	2
C₁₉×#1607	2
C₁₉×#1600	2
C₁₉×#1595	2
C₁₉×#1516	2
C₁₉×#1510	2
C₁₉×#1471	2
#18450	19

Subgroups — C19×#18450 #18024409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18450 #18024409