Subgroups — C₁₉×#18419 #18024378

Order 4864.

1062 conjugacy classes of subgroups.

The subgroup lattice has 734 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
2	C₁₉×#3193	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3190	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2639	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×#1606	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1601	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1504	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₉×#327	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×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
28	C₁₉×#485	—	2	1	no	—
29	C₁₉×#484	—	2	1	no	—
30	C₁₉×#483	C₂²	1	1	yes	characteristic, complemented
31	C₁₉×#480	C₂²	1	1	yes	characteristic, complemented
32	C₁₉×#480	C₂²	1	2	yes	complemented
33	C₁₉×#468	—	2	2	no	—
34	C₁₉×#467	—	2	1	no	—
35	C₁₉×#465	—	2	1	no	—
36	C₁₉×#452	—	2	1	no	—
37	C₁₉×#451	C₂²	1	1	yes	characteristic, complemented
38	C₁₉×#450	—	2	1	no	—
39	C₁₉×#448	C₂²	1	1	yes	characteristic, complemented
40	C₁₉×#448	C₂²	1	2	yes	complemented
41	C₁₉×#407	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
43	C₁₉×#400	—	2	1	no	—
44	C₁₉×#397	C₂²	1	2	yes	complemented
45	C₁₉×#394	—	2	1	no	—
46	C₁₉×#393	C₂²	1	2	yes	complemented
47	C₁₉×#386	—	2	2	no	—
48	C₂×C₁₉×#95	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
56	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
57	C₂²×D₄×C₁₉	—	2	2	no	—
58	C₂²×D₄×C₁₉	—	2	1	no	—
59	C₂²×D₄×C₁₉	—	2	1	no	—
60	C₂²×D₄×C₁₉	—	2	2	no	—
61	C₂²×D₄×C₁₉	D₄	1	2	yes	—
62	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
63	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₁₉	—	2	1	no	—
65	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂×Q₁₆×C₁₉	—	2	1	no	—
67	C₂×SD₁₆×C₁₉	—	2	2	no	—
68	C₂×SD₁₆×C₁₉	—	2	1	no	—
69	C₂×M₁₆×C₁₉	—	2	1	no	—
70	C₂²×C₈×C₁₉	—	2	1	no	—
71	C₁₉×#127	—	2	2	no	—
72	C₁₉×#127	—	2	1	no	—
73	C₁₉×#126	—	2	2	no	—
74	C₁₉×#126	—	2	2	no	—
75	C₁₉×#125	—	2	1	no	—
76	C₁₉×#124	—	2	2	no	—
77	C₁₉×#123	—	2	2	no	—
78	C₁₉×#123	—	2	1	no	—
79	C₁₉×#123	—	2	2	no	—
80	C₁₉×#123	—	2	2	no	—
81	C₁₉×#123	—	2	2	no	—
82	C₁₉×C₂²⋊Q₈	—	2	1	no	—
83	C₁₉×C₂²⋊Q₈	—	2	1	no	—
84	C₁₉×C₂²⋊Q₈	—	2	1	no	—
85	C₁₉×C₂²⋊Q₈	—	2	1	no	—
86	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
87	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
88	C₁₉×#121	—	2	2	no	—
89	C₁₉×#121	—	2	1	no	—
90	C₁₉×#121	—	2	1	no	—
91	C₁₉×#121	—	2	2	no	—
92	C₁₉×#121	—	2	2	no	—
93	C₁₉×#121	—	2	2	no	—
94	C₁₉×#121	—	2	2	no	—
95	C₁₉×#121	—	2	1	no	—
96	C₁₉×#121	—	2	1	no	—
97	C₁₉×#121	—	2	1	no	—
98	C₁₉×#121	—	2	1	no	—
99	C₁₉×#121	—	2	1	no	—
100	C₁₉×#121	—	2	1	no	—
101	C₁₉×#121	—	2	2	no	—
102	C₁₉×#121	D₄	1	1	yes	characteristic
103	C₁₉×#121	D₄	1	2	yes	—
104	C₁₉×#121	C₂³	1	2	yes	—
105	C₁₉×#121	C₂³	1	1	yes	characteristic
106	C₁₉×#120	—	2	2	no	—
107	C₁₉×#120	—	2	2	no	—
108	C₁₉×#120	—	2	2	no	—
109	C₁₉×#120	—	2	1	no	—
110	C₁₉×#120	—	2	2	no	—
111	C₁₉×#120	—	2	2	no	—
112	C₁₉×#120	—	2	2	no	—
113	C₄×D₄×C₁₉	—	2	2	no	—
114	C₄×D₄×C₁₉	—	2	1	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	2	no	—
119	C₁₉×#117	—	2	1	no	—
120	C₁₉×#117	D₄	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
122	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
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	2	no	—
128	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
129	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
130	C₁₉×#107	—	2	1	no	—
131	C₁₉×#107	—	2	2	no	—
132	C₁₉×#106	—	2	1	no	—
133	C₁₉×#103	—	2	1	no	—
134	C₁₉×#103	—	2	1	no	—
135	C₁₉×#103	—	2	2	no	—
136	C₁₉×#103	—	2	1	no	—
137	C₁₉×#102	—	2	2	no	—
138	C₁₉×#102	—	2	1	no	—
139	C₁₉×C₂²⋊C₈	—	2	1	no	—
140	C₁₉×C₂²⋊C₈	—	2	1	no	—
141	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
142	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
143	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
144	C₁₉×#95	—	2	1	no	—
145	C₁₉×#95	—	2	2	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	C₂×D₄	1	1	yes	characteristic
151	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
152	#41×C₁₉	—	8	1	no	—
153	C₂×Q₈×C₁₉	—	2	1	no	—
154	C₂×Q₈×C₁₉	—	2	1	no	—
155	C₂×Q₈×C₁₉	—	8	1	no	—
156	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂×D₄×C₁₉	—	2	2	no	—
158	C₂×D₄×C₁₉	—	2	1	no	—
159	C₂×D₄×C₁₉	—	2	1	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	2	no	—
165	C₂×D₄×C₁₉	—	2	2	no	—
166	C₂×D₄×C₁₉	—	2	1	no	—
167	C₂×D₄×C₁₉	—	2	2	no	—
168	C₂×D₄×C₁₉	—	2	2	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	4	no	—
173	C₂×D₄×C₁₉	—	8	1	no	—
174	C₂×D₄×C₁₉	—	8	2	no	—
175	C₂×D₄×C₁₉	—	8	1	no	—
176	C₂×D₄×C₁₉	—	8	1	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	4	no	—
181	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
182	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
183	C₂²×C₄×C₁₉	—	2	2	no	—
184	C₂²×C₄×C₁₉	—	2	2	no	—
185	C₂²×C₄×C₁₉	—	2	1	no	—
186	C₂²×C₄×C₁₉	—	2	1	no	—
187	C₂²×C₄×C₁₉	—	2	1	no	—
188	C₂²×C₄×C₁₉	—	2	1	no	—
189	C₂²×C₄×C₁₉	—	2	2	no	—
190	C₂²×C₄×C₁₉	—	4	2	no	—
191	C₂²×C₄×C₁₉	—	8	1	no	—
192	C₂²×C₄×C₁₉	—	8	1	no	—
193	C₂²×C₄×C₁₉	—	8	1	no	—
194	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
195	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
201	Q₁₆×C₁₉	—	8	1	no	—
202	SD₁₆×C₁₉	—	8	1	no	—
203	SD₁₆×C₁₉	—	8	2	no	—
204	M₁₆×C₁₉	—	8	1	no	—
205	C₂×C₈×C₁₉	—	2	1	no	—
206	C₂×C₈×C₁₉	—	2	1	no	—
207	C₂×C₈×C₁₉	—	2	2	no	—
208	C₂×C₈×C₁₉	—	8	1	no	—
209	C₄⋊C₄×C₁₉	—	2	2	no	—
210	C₄⋊C₄×C₁₉	—	2	2	no	—
211	C₄⋊C₄×C₁₉	—	2	1	no	—
212	C₄⋊C₄×C₁₉	—	2	1	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	—	4	1	no	—
219	C₄⋊C₄×C₁₉	—	4	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	C₄²×C₁₉	—	2	2	no	—
242	C₄²×C₁₉	—	2	1	no	—
243	#18419	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
244	C₂³×C₁₉	—	2	1	no	—
245	C₂³×C₁₉	—	2	1	no	—
246	C₂³×C₁₉	—	2	2	no	—
247	C₂³×C₁₉	—	2	2	no	—
248	C₂³×C₁₉	—	2	2	no	—
249	C₂³×C₁₉	—	2	1	no	—
250	C₂³×C₁₉	—	2	2	no	—
251	C₂³×C₁₉	—	2	2	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	—	8	1	no	—
257	C₂³×C₁₉	—	8	1	no	—
258	C₂³×C₁₉	—	8	2	no	—
259	C₂³×C₁₉	—	8	2	no	—
260	C₂³×C₁₉	—	8	2	no	—
261	C₂³×C₁₉	#120	1	1	yes	characteristic
262	C₂³×C₁₉	#120	1	1	yes	characteristic
263	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
264	Q₈×C₁₉	—	4	1	no	—
265	Q₈×C₁₉	—	4	2	no	—
266	Q₈×C₁₉	—	4	1	no	—
267	Q₈×C₁₉	—	4	1	no	—
268	D₄×C₁₉	—	4	2	no	—
269	D₄×C₁₉	—	4	1	no	—
270	D₄×C₁₉	—	4	2	no	—
271	D₄×C₁₉	—	4	2	no	—
272	D₄×C₁₉	—	4	2	no	—
273	D₄×C₁₉	—	4	1	no	—
274	D₄×C₁₉	—	4	2	no	—
275	D₄×C₁₉	—	4	1	no	—
276	D₄×C₁₉	—	4	4	no	—
277	D₄×C₁₉	—	4	2	no	—
278	D₄×C₁₉	—	8	1	no	—
279	D₄×C₁₉	—	8	2	no	—
280	D₄×C₁₉	—	8	2	no	—
281	D₄×C₁₉	—	8	1	no	—
282	D₄×C₁₉	—	8	2	no	—
283	D₄×C₁₉	—	8	2	no	—
284	D₄×C₁₉	—	8	2	no	—
285	D₄×C₁₉	—	8	2	no	—
286	D₄×C₁₉	—	8	2	no	—
287	C₂×C₄×C₁₉	—	2	1	no	—
288	C₂×C₄×C₁₉	—	2	2	no	—
289	C₂×C₄×C₁₉	—	2	2	no	—
290	C₂×C₄×C₁₉	—	2	1	no	—
291	C₂×C₄×C₁₉	—	2	1	no	—
292	C₂×C₄×C₁₉	—	4	1	no	—
293	C₂×C₄×C₁₉	—	4	1	no	—
294	C₂×C₄×C₁₉	—	4	1	no	—
295	C₂×C₄×C₁₉	—	4	1	no	—
296	C₂×C₄×C₁₉	—	4	1	no	—
297	C₂×C₄×C₁₉	—	4	1	no	—
298	C₂×C₄×C₁₉	—	4	2	no	—
299	C₂×C₄×C₁₉	—	4	2	no	—
300	C₂×C₄×C₁₉	—	4	2	no	—
301	C₂×C₄×C₁₉	—	4	2	no	—
302	C₂×C₄×C₁₉	—	4	2	no	—
303	C₂×C₄×C₁₉	—	4	1	no	—
304	C₂×C₄×C₁₉	—	4	1	no	—
305	C₂×C₄×C₁₉	—	4	1	no	—
306	C₂×C₄×C₁₉	—	4	2	no	—
307	C₂×C₄×C₁₉	—	4	1	no	—
308	C₂×C₄×C₁₉	—	8	1	no	—
309	C₂×C₄×C₁₉	—	8	2	no	—
310	C₂×C₄×C₁₉	—	8	2	no	—
311	C₂×C₄×C₁₉	—	8	4	no	—
312	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
313	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
314	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
315	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
316	C₈×C₁₉	—	4	1	no	—
317	C₈×C₁₉	—	4	1	no	—
318	C₈×C₁₉	—	4	2	no	—
319	#3537	C₂×C₁₉	1	1	yes	characteristic
320	#3193	C₂×C₁₉	1	1	yes	characteristic, complemented
321	#3190	C₂×C₁₉	1	1	yes	characteristic, complemented
322	#2639	C₂×C₁₉	1	1	yes	characteristic, complemented
323	#1612	C₂×C₁₉	1	2	yes	complemented
324	#1607	C₂×C₁₉	1	2	yes	complemented
325	#1606	C₂×C₁₉	1	2	yes	complemented
326	#1601	C₂×C₁₉	1	2	yes	complemented
327	#1504	C₂×C₁₉	1	1	yes	characteristic, complemented
328	C₂×#327	C₂×C₁₉	1	1	yes	characteristic, complemented
329	#1471	C₂×C₁₉	1	1	yes	characteristic, complemented
330	C₂²×C₁₉	—	2	1	no	—
331	C₂²×C₁₉	—	2	1	no	—
332	C₂²×C₁₉	—	2	1	no	—
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	—	4	2	no	—
338	C₂²×C₁₉	—	4	2	no	—
339	C₂²×C₁₉	—	4	2	no	—
340	C₂²×C₁₉	—	4	2	no	—
341	C₂²×C₁₉	—	4	1	no	—
342	C₂²×C₁₉	—	4	2	no	—
343	C₂²×C₁₉	—	4	2	no	—
344	C₂²×C₁₉	—	4	1	no	—
345	C₂²×C₁₉	—	4	1	no	—
346	C₂²×C₁₉	—	4	2	no	—
347	C₂²×C₁₉	—	4	2	no	—
348	C₂²×C₁₉	—	8	2	no	—
349	C₂²×C₁₉	—	8	2	no	—
350	C₂²×C₁₉	—	16	2	no	—
351	C₂²×C₁₉	—	16	4	no	—
352	C₂²×C₁₉	#455	1	2	yes	—
353	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
354	C₂²×C₁₉	#576	1	1	yes	characteristic
355	C₂²×C₁₉	#577	1	1	yes	characteristic
356	C₄×C₁₉	—	2	1	no	—
357	C₄×C₁₉	—	2	1	no	—
358	C₄×C₁₉	—	2	1	no	—
359	C₄×C₁₉	—	2	1	no	—
360	C₄×C₁₉	—	4	2	no	—
361	C₄×C₁₉	—	4	1	no	—
362	C₄×C₁₉	—	4	2	no	—
363	C₄×C₁₉	—	4	1	no	—
364	C₄×C₁₉	—	4	1	no	—
365	C₄×C₁₉	—	8	2	no	—
366	C₄×C₁₉	—	8	1	no	—
367	C₄×C₁₉	—	8	1	no	—
368	#560	—	2	2	no	—
369	#553	—	2	1	no	—
370	#553	—	2	1	no	—
371	D₄²	—	2	2	no	—
372	D₄²	—	2	1	no	—
373	D₄²	—	2	1	no	—
374	#540	—	2	1	no	—
375	#538	—	2	1	no	—
376	#538	C₂²×C₁₉	1	2	yes	—
377	#535	—	2	1	no	—
378	#534	—	2	1	no	—
379	#534	C₂²×C₁₉	1	2	yes	—
380	#525	C₂²×C₁₉	1	1	yes	characteristic
381	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
382	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
383	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
384	#485	—	2	1	no	—
385	#484	—	2	1	no	—
386	#483	C₂²×C₁₉	1	1	yes	characteristic, complemented
387	#480	C₂²×C₁₉	1	1	yes	characteristic, complemented
388	#480	C₂²×C₁₉	1	2	yes	complemented
389	#468	—	2	2	no	—
390	#467	—	2	1	no	—
391	#465	—	2	1	no	—
392	#452	—	2	1	no	—
393	#451	C₂²×C₁₉	1	1	yes	characteristic, complemented
394	#450	—	2	1	no	—
395	#448	C₂²×C₁₉	1	1	yes	characteristic, complemented
396	#448	C₂²×C₁₉	1	2	yes	complemented
397	#407	C₂²×C₁₉	1	1	yes	characteristic, complemented
398	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
399	#400	—	2	1	no	—
400	#397	C₂²×C₁₉	1	2	yes	complemented
401	#394	—	2	1	no	—
402	#393	C₂²×C₁₉	1	2	yes	complemented
403	#386	—	2	2	no	—
404	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic, complemented
405	#328	C₂²×C₁₉	1	2	yes	complemented
406	#327	C₂²×C₁₉	1	2	yes	complemented
407	#327	C₂²×C₁₉	1	2	yes	complemented
408	#327	C₂²×C₁₉	1	2	yes	complemented
409	#323	C₂²×C₁₉	1	2	yes	complemented
410	#323	C₂²×C₁₉	1	2	yes	complemented
411	C₂×C₁₉	—	2	1	no	—
412	C₂×C₁₉	—	2	1	no	—
413	C₂×C₁₉	—	2	2	no	—
414	C₂×C₁₉	—	4	1	no	—
415	C₂×C₁₉	—	8	2	no	—
416	C₂×C₁₉	—	8	2	no	—
417	C₂×C₁₉	—	8	1	no	—
418	C₂×C₁₉	#3012	1	1	yes	characteristic
419	C₂×C₁₉	C₂×#455	1	1	yes	characteristic
420	C₂×C₁₉	#3026	1	1	yes	characteristic
421	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
422	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
423	C₂²×D₄	—	2	2	no	—
424	C₂²×D₄	—	2	1	no	—
425	C₂²×D₄	—	2	1	no	—
426	C₂²×D₄	—	2	2	no	—
427	C₂²×D₄	D₄×C₁₉	1	2	yes	—
428	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
429	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
430	C₂³×C₄	—	2	1	no	—
431	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
432	C₂×Q₁₆	—	2	1	no	—
433	C₂×SD₁₆	—	2	2	no	—
434	C₂×SD₁₆	—	2	1	no	—
435	C₂×M₁₆	—	2	1	no	—
436	C₂²×C₈	—	2	1	no	—
437	#127	—	2	2	no	—
438	#127	—	2	1	no	—
439	#126	—	2	2	no	—
440	#126	—	2	2	no	—
441	#125	—	2	1	no	—
442	#124	—	2	2	no	—
443	#123	—	2	2	no	—
444	#123	—	2	1	no	—
445	#123	—	2	2	no	—
446	#123	—	2	2	no	—
447	#123	—	2	2	no	—
448	C₂²⋊Q₈	—	2	1	no	—
449	C₂²⋊Q₈	—	2	1	no	—
450	C₂²⋊Q₈	—	2	1	no	—
451	C₂²⋊Q₈	—	2	1	no	—
452	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
453	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
454	#121	—	2	2	no	—
455	#121	—	2	1	no	—
456	#121	—	2	1	no	—
457	#121	—	2	2	no	—
458	#121	—	2	2	no	—
459	#121	—	2	2	no	—
460	#121	—	2	2	no	—
461	#121	—	2	1	no	—
462	#121	—	2	1	no	—
463	#121	—	2	1	no	—
464	#121	—	2	1	no	—
465	#121	—	2	1	no	—
466	#121	—	2	1	no	—
467	#121	—	2	2	no	—
468	#121	D₄×C₁₉	1	2	yes	—
469	#121	D₄×C₁₉	1	1	yes	characteristic
470	#121	C₂³×C₁₉	1	2	yes	—
471	#121	C₂³×C₁₉	1	1	yes	characteristic
472	#120	—	2	2	no	—
473	#120	—	2	2	no	—
474	#120	—	2	2	no	—
475	#120	—	2	1	no	—
476	#120	—	2	2	no	—
477	#120	—	2	2	no	—
478	#120	—	2	2	no	—
479	C₄×D₄	—	2	2	no	—
480	C₄×D₄	—	2	1	no	—
481	C₄×D₄	—	2	1	no	—
482	C₄×D₄	—	2	1	no	—
483	C₄×D₄	—	2	1	no	—
484	C₄×D₄	—	2	2	no	—
485	#117	—	2	1	no	—
486	#117	D₄×C₁₉	1	1	yes	characteristic
487	C₂×C₄⋊C₄	—	2	1	no	—
488	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
489	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
490	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
491	C₂×C₂²⋊C₄	—	2	1	no	—
492	C₂×C₂²⋊C₄	—	2	1	no	—
493	C₂×C₂²⋊C₄	—	2	2	no	—
494	C₂×C₂²⋊C₄	—	2	2	no	—
495	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
496	#107	—	2	1	no	—
497	#107	—	2	2	no	—
498	#106	—	2	1	no	—
499	#103	—	2	1	no	—
500	#103	—	2	1	no	—
501	#103	—	2	2	no	—
502	#103	—	2	1	no	—
503	#102	—	2	2	no	—
504	#102	—	2	1	no	—
505	C₂²⋊C₈	—	2	1	no	—
506	C₂²⋊C₈	—	2	1	no	—
507	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
508	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
509	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
510	#95	—	2	1	no	—
511	#95	—	2	2	no	—
512	#95	—	2	2	no	—
513	#95	C₂³×C₁₉	1	2	yes	—
514	C₁₉	#18419	1	1	yes	characteristic, direct product factor, Sylow
515	C₂⁴	—	2	2	no	—
516	C₂⁴	—	2	1	no	—
517	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
518	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
519	#41	—	8	1	no	—
520	C₂×Q₈	—	2	1	no	—
521	C₂×Q₈	—	2	1	no	—
522	C₂×Q₈	—	8	1	no	—
523	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
524	C₂×D₄	—	2	2	no	—
525	C₂×D₄	—	2	1	no	—
526	C₂×D₄	—	2	1	no	—
527	C₂×D₄	—	2	2	no	—
528	C₂×D₄	—	2	2	no	—
529	C₂×D₄	—	2	2	no	—
530	C₂×D₄	—	2	2	no	—
531	C₂×D₄	—	2	2	no	—
532	C₂×D₄	—	2	2	no	—
533	C₂×D₄	—	2	1	no	—
534	C₂×D₄	—	2	2	no	—
535	C₂×D₄	—	2	2	no	—
536	C₂×D₄	—	2	1	no	—
537	C₂×D₄	—	2	1	no	—
538	C₂×D₄	—	2	1	no	—
539	C₂×D₄	—	4	4	no	—
540	C₂×D₄	—	8	1	no	—
541	C₂×D₄	—	8	2	no	—
542	C₂×D₄	—	8	1	no	—
543	C₂×D₄	—	8	1	no	—
544	C₂×D₄	—	8	1	no	—
545	C₂×D₄	—	8	2	no	—
546	C₂×D₄	—	8	2	no	—
547	C₂×D₄	—	8	4	no	—
548	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
549	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	2	2	no	—
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	4	2	no	—
558	C₂²×C₄	—	8	1	no	—
559	C₂²×C₄	—	8	1	no	—
560	C₂²×C₄	—	8	1	no	—
561	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
562	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
563	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
564	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
565	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
566	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
567	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
568	Q₁₆	—	8	1	no	—
569	SD₁₆	—	8	1	no	—
570	SD₁₆	—	8	2	no	—
571	M₁₆	—	8	1	no	—
572	C₂×C₈	—	2	1	no	—
573	C₂×C₈	—	2	2	no	—
574	C₂×C₈	—	2	1	no	—
575	C₂×C₈	—	8	1	no	—
576	C₄⋊C₄	—	2	2	no	—
577	C₄⋊C₄	—	2	2	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	2	1	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	4	1	no	—
586	C₄⋊C₄	—	4	1	no	—
587	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
588	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
589	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
590	C₂²⋊C₄	—	2	2	no	—
591	C₂²⋊C₄	—	2	2	no	—
592	C₂²⋊C₄	—	2	2	no	—
593	C₂²⋊C₄	—	2	2	no	—
594	C₂²⋊C₄	—	2	2	no	—
595	C₂²⋊C₄	—	2	1	no	—
596	C₂²⋊C₄	—	2	1	no	—
597	C₂²⋊C₄	—	2	1	no	—
598	C₂²⋊C₄	—	2	2	no	—
599	C₂²⋊C₄	—	2	1	no	—
600	C₂²⋊C₄	—	2	2	no	—
601	C₂²⋊C₄	—	2	2	no	—
602	C₂²⋊C₄	—	2	2	no	—
603	C₂²⋊C₄	—	2	1	no	—
604	C₂²⋊C₄	—	4	1	no	—
605	C₂²⋊C₄	—	4	1	no	—
606	C₂²⋊C₄	—	8	2	no	—
607	C₂²⋊C₄	—	8	2	no	—
608	C₄²	—	2	2	no	—
609	C₄²	—	2	1	no	—
610	C₂³	—	2	2	no	—
611	C₂³	—	2	1	no	—
612	C₂³	—	2	1	no	—
613	C₂³	—	2	2	no	—
614	C₂³	—	2	2	no	—
615	C₂³	—	2	1	no	—
616	C₂³	—	2	2	no	—
617	C₂³	—	2	2	no	—
618	C₂³	—	4	1	no	—
619	C₂³	—	4	2	no	—
620	C₂³	—	4	2	no	—
621	C₂³	—	4	2	no	—
622	C₂³	—	8	1	no	—
623	C₂³	—	8	1	no	—
624	C₂³	—	8	2	no	—
625	C₂³	—	8	2	no	—
626	C₂³	—	8	2	no	—
627	C₂³	C₁₉×#120	1	1	yes	characteristic
628	C₂³	C₁₉×#120	1	1	yes	characteristic
629	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
630	Q₈	—	4	1	no	—
631	Q₈	—	4	2	no	—
632	Q₈	—	4	1	no	—
633	Q₈	—	4	1	no	—
634	D₄	—	4	2	no	—
635	D₄	—	4	1	no	—
636	D₄	—	4	2	no	—
637	D₄	—	4	2	no	—
638	D₄	—	4	4	no	—
639	D₄	—	4	2	no	—
640	D₄	—	4	2	no	—
641	D₄	—	4	1	no	—
642	D₄	—	4	2	no	—
643	D₄	—	4	1	no	—
644	D₄	—	8	1	no	—
645	D₄	—	8	2	no	—
646	D₄	—	8	2	no	—
647	D₄	—	8	1	no	—
648	D₄	—	8	2	no	—
649	D₄	—	8	2	no	—
650	D₄	—	8	2	no	—
651	D₄	—	8	2	no	—
652	D₄	—	8	2	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	4	2	no	—
665	C₂×C₄	—	4	2	no	—
666	C₂×C₄	—	4	2	no	—
667	C₂×C₄	—	4	2	no	—
668	C₂×C₄	—	4	2	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	2	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	8	1	no	—
675	C₂×C₄	—	8	2	no	—
676	C₂×C₄	—	8	2	no	—
677	C₂×C₄	—	8	4	no	—
678	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
679	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
680	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
681	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
682	C₈	—	4	1	no	—
683	C₈	—	4	1	no	—
684	C₈	—	4	2	no	—
685	C₂²	—	2	1	no	—
686	C₂²	—	2	1	no	—
687	C₂²	—	2	1	no	—
688	C₂²	—	2	1	no	—
689	C₂²	—	2	1	no	—
690	C₂²	—	2	1	no	—
691	C₂²	—	2	1	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	4	2	no	—
694	C₂²	—	4	2	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	4	1	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	1	no	—
700	C₂²	—	4	1	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	8	2	no	—
704	C₂²	—	8	2	no	—
705	C₂²	—	16	2	no	—
706	C₂²	—	16	4	no	—
707	C₂²	C₁₉×#455	1	2	yes	—
708	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
709	C₂²	C₁₉×#576	1	1	yes	characteristic
710	C₂²	C₁₉×#577	1	1	yes	characteristic
711	C₄	—	2	1	no	—
712	C₄	—	2	1	no	—
713	C₄	—	2	1	no	—
714	C₄	—	2	1	no	—
715	C₄	—	4	2	no	—
716	C₄	—	4	1	no	—
717	C₄	—	4	2	no	—
718	C₄	—	4	1	no	—
719	C₄	—	4	1	no	—
720	C₄	—	8	2	no	—
721	C₄	—	8	1	no	—
722	C₄	—	8	1	no	—
723	C₂	—	2	1	no	—
724	C₂	—	2	1	no	—
725	C₂	—	2	2	no	—
726	C₂	—	4	1	no	—
727	C₂	—	8	2	no	—
728	C₂	—	8	2	no	—
729	C₂	—	8	1	no	—
730	C₂	C₁₉×#3012	1	1	yes	characteristic
731	C₂	C₂×C₁₉×#455	1	1	yes	characteristic
732	C₂	C₁₉×#3026	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#3537	C₂
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
2. C₁₉×#3193	C₂	semidirect
3. C₁₉×#3190	C₂	semidirect
4. C₁₉×#2639	C₂	semidirect
5. C₁₉×#1612	C₂	semidirect
6. C₁₉×#1607	C₂	semidirect
7. C₁₉×#1606	C₂	semidirect
8. C₁₉×#1601	C₂	semidirect
9. C₁₉×#1504	C₂	semidirect
10. C₂×C₁₉×#327	C₂	semidirect
11. C₁₉×#1471	C₂	semidirect
25. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
30. C₁₉×#483	C₂²	semidirect
31. C₁₉×#480	C₂²	semidirect
32. C₁₉×#480	C₂²	semidirect
37. C₁₉×#451	C₂²	semidirect
39. C₁₉×#448	C₂²	semidirect
40. C₁₉×#448	C₂²	semidirect
41. C₁₉×#407	C₂²	semidirect
42. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
44. C₁₉×#397	C₂²	semidirect
46. C₁₉×#393	C₂²	semidirect
48. C₂×C₁₉×#95	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
243. #18419	C₁₉	direct (N × H)
320. #3193	C₂×C₁₉	semidirect
321. #3190	C₂×C₁₉	semidirect
322. #2639	C₂×C₁₉	semidirect
323. #1612	C₂×C₁₉	semidirect
324. #1607	C₂×C₁₉	semidirect
325. #1606	C₂×C₁₉	semidirect
326. #1601	C₂×C₁₉	semidirect
327. #1504	C₂×C₁₉	semidirect
328. C₂×#327	C₂×C₁₉	semidirect
329. #1471	C₂×C₁₉	semidirect
381. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
386. #483	C₂²×C₁₉	semidirect
387. #480	C₂²×C₁₉	semidirect
388. #480	C₂²×C₁₉	semidirect
393. #451	C₂²×C₁₉	semidirect
395. #448	C₂²×C₁₉	semidirect
396. #448	C₂²×C₁₉	semidirect
397. #407	C₂²×C₁₉	semidirect
398. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
400. #397	C₂²×C₁₉	semidirect
402. #393	C₂²×C₁₉	semidirect
404. C₂×#95	C₂²×C₁₉	semidirect
405. #328	C₂²×C₁₉	semidirect
406. #327	C₂²×C₁₉	semidirect
407. #327	C₂²×C₁₉	semidirect
408. #327	C₂²×C₁₉	semidirect
409. #323	C₂²×C₁₉	semidirect
410. #323	C₂²×C₁₉	semidirect
514. C₁₉	#18419	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×#3193	2
C₁₉×#3190	2
C₁₉×#2639	2
C₁₉×#1612	2
C₁₉×#1607	2
C₁₉×#1606	2
C₁₉×#1601	2
C₁₉×#1504	2
C₂×C₁₉×#327	2
C₁₉×#1471	2
#18419	19

Subgroups — C19×#18419 #18024378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18419 #18024378