Subgroups — C₁₉×#18420 #18024379

Order 4864.

1108 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3536	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3193	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3188	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2656	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1618	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1614	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1600	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1596	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1504	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₉×#328	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1471	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#562	—	2	2	no	—
13	C₁₉×#554	—	2	1	no	—
14	C₁₉×#548	—	2	1	no	—
15	C₁₉×#547	—	2	1	no	—
16	C₁₉×#546	—	2	2	no	—
17	C₁₉×#546	—	2	1	no	—
18	C₁₉×#543	C₂²	1	2	yes	—
19	C₁₉×#542	—	2	1	no	—
20	C₁₉×#539	—	2	1	no	—
21	C₁₉×#538	C₂²	1	2	yes	—
22	C₁₉×#537	—	2	1	no	—
23	C₁₉×#537	—	2	1	no	—
24	C₁₉×#525	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#121	—	2	2	no	—
27	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
29	C₁₉×#484	C₂²	1	1	yes	characteristic
30	C₁₉×#484	C₂²	1	2	yes	—
31	C₁₉×#482	—	2	1	no	—
32	C₁₉×#481	C₂²	1	1	yes	characteristic
33	C₁₉×#480	—	2	1	no	—
34	C₁₉×#468	—	2	2	no	—
35	C₁₉×#466	—	2	1	no	—
36	C₁₉×#465	—	2	1	no	—
37	C₁₉×#450	C₂²	1	1	yes	characteristic
38	C₁₉×#450	C₂²	1	2	yes	—
39	C₁₉×#449	—	2	1	no	—
40	C₁₉×#448	—	2	1	no	—
41	C₁₉×#447	C₂²	1	1	yes	characteristic
42	C₁₉×#407	C₂²	1	1	yes	characteristic
43	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
44	C₁₉×#399	—	2	1	no	—
45	C₁₉×#399	C₂²	1	2	yes	—
46	C₁₉×#392	—	2	1	no	—
47	C₁₉×#392	C₂²	1	2	yes	—
48	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
49	C₁₉×#328	C₂²	1	2	yes	—
50	C₁₉×#328	C₂²	1	2	yes	—
51	C₁₉×#328	C₂²	1	2	yes	—
52	C₁₉×#327	C₂²	1	2	yes	—
53	C₁₉×#323	C₂²	1	2	yes	—
54	C₁₉×#323	C₂²	1	2	yes	—
55	C₂×#41×C₁₉	—	2	2	no	—
56	C₂×#41×C₁₉	—	2	1	no	—
57	C₂×#41×C₁₉	D₄	1	1	yes	characteristic, complemented
58	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic, complemented
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	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₉	—	2	1	no	—
65	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂×SD₁₆×C₁₉	—	2	2	no	—
67	C₂×SD₁₆×C₁₉	—	2	1	no	—
68	C₂×D₈×C₁₉	—	2	1	no	—
69	C₂×M₁₆×C₁₉	—	2	1	no	—
70	C₂²×C₈×C₁₉	—	2	1	no	—
71	C₁₉×C₄⋊Q₈	—	2	1	no	—
72	C₁₉×#126	—	2	2	no	—
73	C₁₉×#125	—	2	2	no	—
74	C₁₉×#124	—	2	1	no	—
75	C₁₉×#124	—	2	2	no	—
76	C₁₉×#124	—	2	2	no	—
77	C₁₉×#123	—	2	2	no	—
78	C₁₉×#123	—	2	2	no	—
79	C₁₉×#123	—	2	2	no	—
80	C₁₉×#123	—	2	1	no	—
81	C₁₉×#123	—	2	2	no	—
82	C₁₉×C₂²⋊Q₈	—	2	1	no	—
83	C₁₉×C₂²⋊Q₈	—	2	2	no	—
84	C₁₉×C₂²⋊Q₈	—	2	2	no	—
85	C₁₉×C₂²⋊Q₈	—	2	2	no	—
86	C₁₉×C₂²⋊Q₈	—	2	1	no	—
87	C₁₉×C₂²⋊Q₈	—	2	1	no	—
88	C₁₉×C₂²⋊Q₈	—	2	2	no	—
89	C₁₉×C₂²⋊Q₈	—	2	2	no	—
90	C₁₉×C₂²⋊Q₈	—	2	2	no	—
91	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic, complemented
92	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	complemented
93	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
94	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
95	C₁₉×#121	—	2	1	no	—
96	C₁₉×#121	—	2	2	no	—
97	C₁₉×#121	—	2	2	no	—
98	C₁₉×#121	—	2	2	no	—
99	C₁₉×#121	—	2	2	no	—
100	C₁₉×#121	—	2	2	no	—
101	C₁₉×#121	—	2	1	no	—
102	C₁₉×#121	—	2	1	no	—
103	C₁₉×#121	—	2	1	no	—
104	C₁₉×#121	—	2	1	no	—
105	C₁₉×#121	—	2	1	no	—
106	C₁₉×#121	—	2	1	no	—
107	C₁₉×#121	—	2	1	no	—
108	C₁₉×#121	—	2	1	no	—
109	C₁₉×#121	—	4	8	no	—
110	C₁₉×#121	D₄	1	1	yes	characteristic, complemented
111	C₁₉×#121	C₂³	1	1	yes	characteristic
112	C₁₉×#120	—	2	1	no	—
113	C₁₉×#120	—	2	2	no	—
114	C₄×Q₈×C₁₉	—	2	1	no	—
115	C₄×D₄×C₁₉	—	2	2	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	D₄	1	1	yes	characteristic, complemented
121	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
122	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
123	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
124	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic, complemented
126	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
131	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
132	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
133	C₁₉×#107	—	2	1	no	—
134	C₁₉×#107	—	2	2	no	—
135	C₁₉×#106	—	2	1	no	—
136	C₁₉×#103	—	2	2	no	—
137	C₁₉×#103	—	2	1	no	—
138	C₁₉×#102	—	2	1	no	—
139	C₁₉×#102	—	2	1	no	—
140	C₁₉×#102	—	2	1	no	—
141	C₁₉×#102	—	2	2	no	—
142	C₁₉×C₂²⋊C₈	—	2	1	no	—
143	C₁₉×C₂²⋊C₈	—	2	1	no	—
144	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
145	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
146	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
147	C₁₉×#95	—	2	1	no	—
148	C₁₉×#95	C₂³	1	2	yes	—
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	#41×C₁₉	—	8	4	no	—
154	#41×C₁₉	—	8	2	no	—
155	C₂×Q₈×C₁₉	—	2	2	no	—
156	C₂×Q₈×C₁₉	—	2	1	no	—
157	C₂×Q₈×C₁₉	—	8	1	no	—
158	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
159	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
160	C₂×D₄×C₁₉	—	2	1	no	—
161	C₂×D₄×C₁₉	—	2	2	no	—
162	C₂×D₄×C₁₉	—	2	1	no	—
163	C₂×D₄×C₁₉	—	2	2	no	—
164	C₂×D₄×C₁₉	—	2	2	no	—
165	C₂×D₄×C₁₉	—	2	1	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	—	4	4	no	—
172	C₂×D₄×C₁₉	—	4	4	no	—
173	C₂×D₄×C₁₉	—	4	4	no	—
174	C₂×D₄×C₁₉	—	4	1	no	—
175	C₂×D₄×C₁₉	—	4	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	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₁₉	—	2	1	no	—
182	C₂²×C₄×C₁₉	—	2	2	no	—
183	C₂²×C₄×C₁₉	—	2	2	no	—
184	C₂²×C₄×C₁₉	—	2	2	no	—
185	C₂²×C₄×C₁₉	—	2	2	no	—
186	C₂²×C₄×C₁₉	—	2	4	no	—
187	C₂²×C₄×C₁₉	—	2	1	no	—
188	C₂²×C₄×C₁₉	—	2	1	no	—
189	C₂²×C₄×C₁₉	—	2	1	no	—
190	C₂²×C₄×C₁₉	—	8	1	no	—
191	C₂²×C₄×C₁₉	—	8	1	no	—
192	C₂²×C₄×C₁₉	—	8	1	no	—
193	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
194	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
200	SD₁₆×C₁₉	—	8	1	no	—
201	SD₁₆×C₁₉	—	8	2	no	—
202	D₈×C₁₉	—	8	1	no	—
203	M₁₆×C₁₉	—	8	1	no	—
204	C₂×C₈×C₁₉	—	2	1	no	—
205	C₂×C₈×C₁₉	—	2	1	no	—
206	C₂×C₈×C₁₉	—	2	2	no	—
207	C₂×C₈×C₁₉	—	8	1	no	—
208	C₄⋊C₄×C₁₉	—	2	2	no	—
209	C₄⋊C₄×C₁₉	—	2	2	no	—
210	C₄⋊C₄×C₁₉	—	2	2	no	—
211	C₄⋊C₄×C₁₉	—	2	2	no	—
212	C₄⋊C₄×C₁₉	—	2	1	no	—
213	C₄⋊C₄×C₁₉	—	2	1	no	—
214	C₄⋊C₄×C₁₉	—	2	2	no	—
215	C₄⋊C₄×C₁₉	—	2	1	no	—
216	C₄⋊C₄×C₁₉	—	2	1	no	—
217	C₄⋊C₄×C₁₉	—	2	2	no	—
218	C₄⋊C₄×C₁₉	—	2	1	no	—
219	C₄⋊C₄×C₁₉	—	2	1	no	—
220	C₄⋊C₄×C₁₉	—	2	1	no	—
221	C₄⋊C₄×C₁₉	—	4	4	no	—
222	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
223	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
224	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	2	no	—
229	C₂²⋊C₄×C₁₉	—	2	2	no	—
230	C₂²⋊C₄×C₁₉	—	2	2	no	—
231	C₂²⋊C₄×C₁₉	—	2	1	no	—
232	C₂²⋊C₄×C₁₉	—	2	1	no	—
233	C₂²⋊C₄×C₁₉	—	2	2	no	—
234	C₂²⋊C₄×C₁₉	—	2	1	no	—
235	C₂²⋊C₄×C₁₉	—	2	1	no	—
236	C₂²⋊C₄×C₁₉	—	2	2	no	—
237	C₂²⋊C₄×C₁₉	—	2	2	no	—
238	C₂²⋊C₄×C₁₉	—	2	1	no	—
239	C₂²⋊C₄×C₁₉	—	4	4	no	—
240	C₂²⋊C₄×C₁₉	—	4	4	no	—
241	C₂²⋊C₄×C₁₉	—	4	1	no	—
242	C₂²⋊C₄×C₁₉	—	4	1	no	—
243	C₄²×C₁₉	—	2	2	no	—
244	C₄²×C₁₉	—	2	1	no	—
245	#18420	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
246	C₂³×C₁₉	—	2	1	no	—
247	C₂³×C₁₉	—	2	1	no	—
248	C₂³×C₁₉	—	2	2	no	—
249	C₂³×C₁₉	—	2	2	no	—
250	C₂³×C₁₉	—	2	1	no	—
251	C₂³×C₁₉	—	2	2	no	—
252	C₂³×C₁₉	—	2	2	no	—
253	C₂³×C₁₉	—	4	1	no	—
254	C₂³×C₁₉	—	4	2	no	—
255	C₂³×C₁₉	—	4	2	no	—
256	C₂³×C₁₉	—	4	2	no	—
257	C₂³×C₁₉	—	4	2	no	—
258	C₂³×C₁₉	—	4	1	no	—
259	C₂³×C₁₉	—	4	1	no	—
260	C₂³×C₁₉	—	4	1	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	2	no	—
265	Q₈×C₁₉	—	4	1	no	—
266	Q₈×C₁₉	—	4	2	no	—
267	Q₈×C₁₉	—	8	2	no	—
268	D₄×C₁₉	—	4	1	no	—
269	D₄×C₁₉	—	4	2	no	—
270	D₄×C₁₉	—	4	1	no	—
271	D₄×C₁₉	—	4	1	no	—
272	D₄×C₁₉	—	4	2	no	—
273	D₄×C₁₉	—	4	1	no	—
274	D₄×C₁₉	—	4	1	no	—
275	D₄×C₁₉	—	4	4	no	—
276	D₄×C₁₉	—	4	2	no	—
277	D₄×C₁₉	—	8	1	no	—
278	D₄×C₁₉	—	8	2	no	—
279	D₄×C₁₉	—	8	1	no	—
280	D₄×C₁₉	—	8	2	no	—
281	D₄×C₁₉	—	8	2	no	—
282	D₄×C₁₉	—	8	8	no	—
283	D₄×C₁₉	—	8	2	no	—
284	D₄×C₁₉	—	8	2	no	—
285	C₂×C₄×C₁₉	—	2	4	no	—
286	C₂×C₄×C₁₉	—	2	1	no	—
287	C₂×C₄×C₁₉	—	2	2	no	—
288	C₂×C₄×C₁₉	—	2	1	no	—
289	C₂×C₄×C₁₉	—	2	2	no	—
290	C₂×C₄×C₁₉	—	2	1	no	—
291	C₂×C₄×C₁₉	—	2	2	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	2	no	—
304	C₂×C₄×C₁₉	—	4	1	no	—
305	C₂×C₄×C₁₉	—	8	1	no	—
306	C₂×C₄×C₁₉	—	8	4	no	—
307	C₂×C₄×C₁₉	—	8	2	no	—
308	C₂×C₄×C₁₉	—	8	2	no	—
309	C₂×C₄×C₁₉	—	8	2	no	—
310	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
311	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
312	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
313	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
314	C₈×C₁₉	—	4	1	no	—
315	C₈×C₁₉	—	4	1	no	—
316	C₈×C₁₉	—	4	2	no	—
317	#3536	C₂×C₁₉	1	1	yes	characteristic, complemented
318	#3193	C₂×C₁₉	1	1	yes	characteristic, complemented
319	#3188	C₂×C₁₉	1	1	yes	characteristic, complemented
320	#2656	C₂×C₁₉	1	1	yes	characteristic, complemented
321	#1618	C₂×C₁₉	1	2	yes	complemented
322	#1614	C₂×C₁₉	1	2	yes	complemented
323	#1600	C₂×C₁₉	1	2	yes	complemented
324	#1596	C₂×C₁₉	1	2	yes	complemented
325	#1504	C₂×C₁₉	1	1	yes	characteristic, complemented
326	C₂×#328	C₂×C₁₉	1	1	yes	characteristic, complemented
327	#1471	C₂×C₁₉	1	1	yes	characteristic, complemented
328	C₂²×C₁₉	—	2	1	no	—
329	C₂²×C₁₉	—	2	1	no	—
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	—	4	2	no	—
336	C₂²×C₁₉	—	4	2	no	—
337	C₂²×C₁₉	—	4	1	no	—
338	C₂²×C₁₉	—	4	2	no	—
339	C₂²×C₁₉	—	4	1	no	—
340	C₂²×C₁₉	—	4	2	no	—
341	C₂²×C₁₉	—	4	1	no	—
342	C₂²×C₁₉	—	4	2	no	—
343	C₂²×C₁₉	—	8	2	no	—
344	C₂²×C₁₉	—	8	2	no	—
345	C₂²×C₁₉	—	8	2	no	—
346	C₂²×C₁₉	—	8	2	no	—
347	C₂²×C₁₉	—	8	1	no	—
348	C₂²×C₁₉	—	8	1	no	—
349	C₂²×C₁₉	—	8	1	no	—
350	C₂²×C₁₉	#453	1	2	yes	—
351	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
352	C₂²×C₁₉	#577	1	1	yes	characteristic
353	C₂²×C₁₉	#578	1	1	yes	characteristic
354	C₄×C₁₉	—	2	1	no	—
355	C₄×C₁₉	—	2	1	no	—
356	C₄×C₁₉	—	2	1	no	—
357	C₄×C₁₉	—	2	1	no	—
358	C₄×C₁₉	—	4	4	no	—
359	C₄×C₁₉	—	4	1	no	—
360	C₄×C₁₉	—	4	2	no	—
361	C₄×C₁₉	—	4	2	no	—
362	C₄×C₁₉	—	4	1	no	—
363	C₄×C₁₉	—	4	1	no	—
364	C₄×C₁₉	—	4	2	no	—
365	C₄×C₁₉	—	8	1	no	—
366	#562	—	2	2	no	—
367	#554	—	2	1	no	—
368	#548	—	2	1	no	—
369	#547	—	2	1	no	—
370	#546	—	2	2	no	—
371	#546	—	2	1	no	—
372	#543	C₂²×C₁₉	1	2	yes	—
373	#542	—	2	1	no	—
374	#539	—	2	1	no	—
375	#538	C₂²×C₁₉	1	2	yes	—
376	#537	—	2	1	no	—
377	#537	—	2	1	no	—
378	#525	C₂²×C₁₉	1	1	yes	characteristic
379	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
380	C₂×#121	—	2	2	no	—
381	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
382	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
383	#484	C₂²×C₁₉	1	1	yes	characteristic
384	#484	C₂²×C₁₉	1	2	yes	—
385	#482	—	2	1	no	—
386	#481	C₂²×C₁₉	1	1	yes	characteristic
387	#480	—	2	1	no	—
388	#468	—	2	2	no	—
389	#466	—	2	1	no	—
390	#465	—	2	1	no	—
391	#450	C₂²×C₁₉	1	1	yes	characteristic
392	#450	C₂²×C₁₉	1	2	yes	—
393	#449	—	2	1	no	—
394	#448	—	2	1	no	—
395	#447	C₂²×C₁₉	1	1	yes	characteristic
396	#407	C₂²×C₁₉	1	1	yes	characteristic
397	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
398	#399	—	2	1	no	—
399	#399	C₂²×C₁₉	1	2	yes	—
400	#392	—	2	1	no	—
401	#392	C₂²×C₁₉	1	2	yes	—
402	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
403	#328	C₂²×C₁₉	1	2	yes	—
404	#328	C₂²×C₁₉	1	2	yes	—
405	#328	C₂²×C₁₉	1	2	yes	—
406	#327	C₂²×C₁₉	1	2	yes	—
407	#323	C₂²×C₁₉	1	2	yes	—
408	#323	C₂²×C₁₉	1	2	yes	—
409	C₂×C₁₉	—	2	1	no	—
410	C₂×C₁₉	—	2	1	no	—
411	C₂×C₁₉	—	2	2	no	—
412	C₂×C₁₉	—	4	1	no	—
413	C₂×C₁₉	—	8	1	no	—
414	C₂×C₁₉	—	8	2	no	—
415	C₂×C₁₉	—	16	1	no	—
416	C₂×C₁₉	#3013	1	1	yes	characteristic
417	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
418	C₂×C₁₉	#3026	1	1	yes	characteristic
419	C₂×#41	—	2	2	no	—
420	C₂×#41	—	2	1	no	—
421	C₂×#41	D₄×C₁₉	1	1	yes	characteristic, complemented
422	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
423	C₂²×D₄	—	2	1	no	—
424	C₂²×D₄	—	2	2	no	—
425	C₂²×D₄	D₄×C₁₉	1	2	yes	—
426	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
427	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
428	C₂³×C₄	—	2	1	no	—
429	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
430	C₂×SD₁₆	—	2	2	no	—
431	C₂×SD₁₆	—	2	1	no	—
432	C₂×D₈	—	2	1	no	—
433	C₂×M₁₆	—	2	1	no	—
434	C₂²×C₈	—	2	1	no	—
435	C₄⋊Q₈	—	2	1	no	—
436	#126	—	2	2	no	—
437	#125	—	2	2	no	—
438	#124	—	2	1	no	—
439	#124	—	2	2	no	—
440	#124	—	2	2	no	—
441	#123	—	2	2	no	—
442	#123	—	2	2	no	—
443	#123	—	2	2	no	—
444	#123	—	2	1	no	—
445	#123	—	2	2	no	—
446	C₂²⋊Q₈	—	2	1	no	—
447	C₂²⋊Q₈	—	2	2	no	—
448	C₂²⋊Q₈	—	2	2	no	—
449	C₂²⋊Q₈	—	2	2	no	—
450	C₂²⋊Q₈	—	2	1	no	—
451	C₂²⋊Q₈	—	2	1	no	—
452	C₂²⋊Q₈	—	2	2	no	—
453	C₂²⋊Q₈	—	2	2	no	—
454	C₂²⋊Q₈	—	2	2	no	—
455	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	complemented
456	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
457	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
458	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
459	#121	—	2	1	no	—
460	#121	—	2	2	no	—
461	#121	—	2	2	no	—
462	#121	—	2	2	no	—
463	#121	—	2	2	no	—
464	#121	—	2	2	no	—
465	#121	—	2	1	no	—
466	#121	—	2	1	no	—
467	#121	—	2	1	no	—
468	#121	—	2	1	no	—
469	#121	—	2	1	no	—
470	#121	—	2	1	no	—
471	#121	—	2	1	no	—
472	#121	—	2	1	no	—
473	#121	—	4	8	no	—
474	#121	D₄×C₁₉	1	1	yes	characteristic, complemented
475	#121	C₂³×C₁₉	1	1	yes	characteristic
476	#120	—	2	1	no	—
477	#120	—	2	2	no	—
478	C₄×Q₈	—	2	1	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	2	no	—
484	#117	D₄×C₁₉	1	1	yes	characteristic, complemented
485	C₂×C₄⋊C₄	—	2	1	no	—
486	C₂×C₄⋊C₄	—	2	1	no	—
487	C₂×C₄⋊C₄	—	2	2	no	—
488	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
489	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic, complemented
490	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
491	C₂×C₂²⋊C₄	—	2	1	no	—
492	C₂×C₂²⋊C₄	—	2	2	no	—
493	C₂×C₂²⋊C₄	—	2	2	no	—
494	C₂×C₂²⋊C₄	—	2	2	no	—
495	C₂×C₂²⋊C₄	—	2	1	no	—
496	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
497	#107	—	2	1	no	—
498	#107	—	2	2	no	—
499	#106	—	2	1	no	—
500	#103	—	2	2	no	—
501	#103	—	2	1	no	—
502	#102	—	2	1	no	—
503	#102	—	2	1	no	—
504	#102	—	2	1	no	—
505	#102	—	2	2	no	—
506	C₂²⋊C₈	—	2	1	no	—
507	C₂²⋊C₈	—	2	1	no	—
508	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
509	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
510	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
511	#95	—	2	1	no	—
512	#95	C₂³×C₁₉	1	2	yes	—
513	C₁₉	#18420	1	1	yes	characteristic, direct product factor, Sylow
514	C₂⁴	—	2	1	no	—
515	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
516	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
517	#41	—	8	1	no	—
518	#41	—	8	4	no	—
519	#41	—	8	2	no	—
520	C₂×Q₈	—	2	2	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×Q₈	C₂×D₄×C₁₉	1	2	yes	—
525	C₂×D₄	—	2	1	no	—
526	C₂×D₄	—	2	2	no	—
527	C₂×D₄	—	2	1	no	—
528	C₂×D₄	—	2	2	no	—
529	C₂×D₄	—	2	2	no	—
530	C₂×D₄	—	2	1	no	—
531	C₂×D₄	—	2	2	no	—
532	C₂×D₄	—	2	1	no	—
533	C₂×D₄	—	2	1	no	—
534	C₂×D₄	—	2	1	no	—
535	C₂×D₄	—	2	1	no	—
536	C₂×D₄	—	4	4	no	—
537	C₂×D₄	—	4	4	no	—
538	C₂×D₄	—	4	4	no	—
539	C₂×D₄	—	4	1	no	—
540	C₂×D₄	—	4	1	no	—
541	C₂×D₄	—	8	1	no	—
542	C₂×D₄	—	8	1	no	—
543	C₂×D₄	—	8	2	no	—
544	C₂×D₄	—	8	2	no	—
545	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	4	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	8	1	no	—
556	C₂²×C₄	—	8	1	no	—
557	C₂²×C₄	—	8	1	no	—
558	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
559	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
560	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
561	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
562	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
563	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
564	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
565	SD₁₆	—	8	1	no	—
566	SD₁₆	—	8	2	no	—
567	D₈	—	8	1	no	—
568	M₁₆	—	8	1	no	—
569	C₂×C₈	—	2	1	no	—
570	C₂×C₈	—	2	1	no	—
571	C₂×C₈	—	2	2	no	—
572	C₂×C₈	—	8	1	no	—
573	C₄⋊C₄	—	2	2	no	—
574	C₄⋊C₄	—	2	2	no	—
575	C₄⋊C₄	—	2	2	no	—
576	C₄⋊C₄	—	2	2	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	2	2	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	2	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	4	4	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	2	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	1	no	—
601	C₂²⋊C₄	—	2	2	no	—
602	C₂²⋊C₄	—	2	2	no	—
603	C₂²⋊C₄	—	2	1	no	—
604	C₂²⋊C₄	—	4	4	no	—
605	C₂²⋊C₄	—	4	4	no	—
606	C₂²⋊C₄	—	4	1	no	—
607	C₂²⋊C₄	—	4	1	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	1	no	—
615	C₂³	—	2	2	no	—
616	C₂³	—	2	2	no	—
617	C₂³	—	4	1	no	—
618	C₂³	—	4	2	no	—
619	C₂³	—	4	2	no	—
620	C₂³	—	4	2	no	—
621	C₂³	—	4	2	no	—
622	C₂³	—	4	1	no	—
623	C₂³	—	4	1	no	—
624	C₂³	—	4	1	no	—
625	C₂³	C₁₉×#120	1	1	yes	characteristic
626	C₂³	C₁₉×#120	1	1	yes	characteristic
627	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
628	Q₈	—	4	2	no	—
629	Q₈	—	4	1	no	—
630	Q₈	—	4	2	no	—
631	Q₈	—	8	2	no	—
632	D₄	—	4	1	no	—
633	D₄	—	4	2	no	—
634	D₄	—	4	1	no	—
635	D₄	—	4	1	no	—
636	D₄	—	4	2	no	—
637	D₄	—	4	4	no	—
638	D₄	—	4	2	no	—
639	D₄	—	4	1	no	—
640	D₄	—	4	1	no	—
641	D₄	—	8	1	no	—
642	D₄	—	8	2	no	—
643	D₄	—	8	1	no	—
644	D₄	—	8	2	no	—
645	D₄	—	8	2	no	—
646	D₄	—	8	8	no	—
647	D₄	—	8	2	no	—
648	D₄	—	8	2	no	—
649	C₂×C₄	—	2	4	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	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	2	no	—
663	C₂×C₄	—	4	2	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	1	no	—
669	C₂×C₄	—	8	1	no	—
670	C₂×C₄	—	8	4	no	—
671	C₂×C₄	—	8	2	no	—
672	C₂×C₄	—	8	2	no	—
673	C₂×C₄	—	8	2	no	—
674	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
675	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
676	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
677	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
678	C₈	—	4	1	no	—
679	C₈	—	4	1	no	—
680	C₈	—	4	2	no	—
681	C₂²	—	2	1	no	—
682	C₂²	—	2	1	no	—
683	C₂²	—	2	1	no	—
684	C₂²	—	2	1	no	—
685	C₂²	—	2	1	no	—
686	C₂²	—	2	1	no	—
687	C₂²	—	2	1	no	—
688	C₂²	—	4	2	no	—
689	C₂²	—	4	2	no	—
690	C₂²	—	4	1	no	—
691	C₂²	—	4	2	no	—
692	C₂²	—	4	1	no	—
693	C₂²	—	4	2	no	—
694	C₂²	—	4	1	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	8	2	no	—
697	C₂²	—	8	2	no	—
698	C₂²	—	8	2	no	—
699	C₂²	—	8	2	no	—
700	C₂²	—	8	1	no	—
701	C₂²	—	8	1	no	—
702	C₂²	—	8	1	no	—
703	C₂²	C₁₉×#453	1	2	yes	—
704	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
705	C₂²	C₁₉×#577	1	1	yes	characteristic
706	C₂²	C₁₉×#578	1	1	yes	characteristic
707	C₄	—	2	1	no	—
708	C₄	—	2	1	no	—
709	C₄	—	2	1	no	—
710	C₄	—	2	1	no	—
711	C₄	—	4	4	no	—
712	C₄	—	4	1	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	2	no	—
715	C₄	—	4	1	no	—
716	C₄	—	4	1	no	—
717	C₄	—	4	2	no	—
718	C₄	—	8	1	no	—
719	C₂	—	2	1	no	—
720	C₂	—	2	1	no	—
721	C₂	—	2	2	no	—
722	C₂	—	4	1	no	—
723	C₂	—	8	2	no	—
724	C₂	—	8	1	no	—
725	C₂	—	16	1	no	—
726	C₂	C₁₉×#3013	1	1	yes	characteristic
727	C₂	C₂×C₁₉×#453	1	1	yes	characteristic
728	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×#3536	C₂	semidirect
2. C₁₉×#3193	C₂	semidirect
3. C₁₉×#3188	C₂	semidirect
4. C₁₉×#2656	C₂	semidirect
5. C₁₉×#1618	C₂	semidirect
6. C₁₉×#1614	C₂	semidirect
7. C₁₉×#1600	C₂	semidirect
8. C₁₉×#1596	C₂	semidirect
9. C₁₉×#1504	C₂	semidirect
10. C₂×C₁₉×#328	C₂	semidirect
11. C₁₉×#1471	C₂	semidirect
57. C₂×#41×C₁₉	D₄	semidirect
58. C₂²×Q₈×C₁₉	D₄	semidirect
91. C₁₉×C₂²⋊Q₈	D₄	semidirect
92. C₁₉×C₂²⋊Q₈	D₄	semidirect
110. C₁₉×#121	D₄	semidirect
120. C₁₉×#117	D₄	semidirect
125. C₂×C₄⋊C₄×C₁₉	D₄	semidirect
245. #18420	C₁₉	direct (N × H)
317. #3536	C₂×C₁₉	semidirect
318. #3193	C₂×C₁₉	semidirect
319. #3188	C₂×C₁₉	semidirect
320. #2656	C₂×C₁₉	semidirect
321. #1618	C₂×C₁₉	semidirect
322. #1614	C₂×C₁₉	semidirect
323. #1600	C₂×C₁₉	semidirect
324. #1596	C₂×C₁₉	semidirect
325. #1504	C₂×C₁₉	semidirect
326. C₂×#328	C₂×C₁₉	semidirect
327. #1471	C₂×C₁₉	semidirect
421. C₂×#41	D₄×C₁₉	semidirect
422. C₂²×Q₈	D₄×C₁₉	semidirect
455. C₂²⋊Q₈	D₄×C₁₉	semidirect
456. C₂²⋊Q₈	D₄×C₁₉	semidirect
474. #121	D₄×C₁₉	semidirect
484. #117	D₄×C₁₉	semidirect
489. C₂×C₄⋊C₄	D₄×C₁₉	semidirect
513. C₁₉	#18420	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×#3536	2
C₁₉×#3193	2
C₁₉×#3188	2
C₁₉×#2656	2
C₁₉×#1618	2
C₁₉×#1614	2
C₁₉×#1600	2
C₁₉×#1596	2
C₁₉×#1504	2
C₂×C₁₉×#328	2
C₁₉×#1471	2
#18420	19

Subgroups — C19×#18420 #18024379

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18420 #18024379