Subgroups — C₁₉×#18456 #18024415

Order 4864.

996 conjugacy classes of subgroups.

The subgroup lattice has 702 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×#3194	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3186	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2816	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1610	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1609	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1598	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1597	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×#1472	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	1	no	—
17	C₁₉×#546	—	2	2	no	—
18	C₁₉×#543	—	2	1	no	—
19	C₁₉×#542	—	2	1	no	—
20	C₁₉×#539	C₂²	1	2	yes	—
21	C₁₉×#538	—	2	1	no	—
22	C₁₉×#537	—	2	1	no	—
23	C₁₉×#537	C₂²	1	2	yes	—
24	C₁₉×#525	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
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	—
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	—
40	C₁₉×#447	C₂²	1	1	yes	characteristic, complemented
41	C₁₉×#407	C₂²	1	1	yes	characteristic
42	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
43	C₁₉×#399	—	2	1	no	—
44	C₁₉×#398	C₂²	1	2	yes	complemented
45	C₁₉×#394	—	2	2	no	—
46	C₁₉×#394	C₂²	1	2	yes	complemented
47	C₁₉×#393	—	2	1	no	—
48	C₁₉×#381	C₂²	1	1	yes	characteristic
49	C₁₉×#328	C₂²	1	2	yes	complemented
50	C₁₉×#327	C₂²	1	2	yes	—
51	C₁₉×#327	C₂²	1	2	yes	—
52	C₁₉×#327	C₂²	1	2	yes	complemented
53	C₁₉×#324	C₂²	1	2	yes	complemented
54	C₁₉×#324	C₂²	1	2	yes	complemented
55	C₂×#41×C₁₉	—	2	1	no	—
56	C₂×#41×C₁₉	—	2	2	no	—
57	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
58	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
59	C₂²×D₄×C₁₉	—	2	1	no	—
60	C₂²×D₄×C₁₉	—	2	1	no	—
61	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
62	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂×SD₁₆×C₁₉	—	2	1	no	—
65	C₂×D₈×C₁₉	—	2	2	no	—
66	C₂×D₈×C₁₉	—	2	1	no	—
67	C₂×M₁₆×C₁₉	—	2	1	no	—
68	C₂²×C₈×C₁₉	—	2	1	no	—
69	C₁₉×C₄⋊Q₈	—	2	1	no	—
70	C₁₉×#126	—	2	2	no	—
71	C₁₉×#125	—	2	2	no	—
72	C₁₉×#124	—	2	2	no	—
73	C₁₉×#124	—	2	1	no	—
74	C₁₉×#124	—	2	2	no	—
75	C₁₉×#123	—	2	2	no	—
76	C₁₉×#123	—	2	2	no	—
77	C₁₉×#123	—	2	2	no	—
78	C₁₉×#123	—	2	1	no	—
79	C₁₉×#123	—	2	2	no	—
80	C₁₉×C₂²⋊Q₈	—	2	1	no	—
81	C₁₉×C₂²⋊Q₈	—	2	2	no	—
82	C₁₉×C₂²⋊Q₈	—	2	2	no	—
83	C₁₉×C₂²⋊Q₈	—	2	2	no	—
84	C₁₉×C₂²⋊Q₈	—	2	2	no	—
85	C₁₉×C₂²⋊Q₈	—	2	1	no	—
86	C₁₉×C₂²⋊Q₈	—	2	1	no	—
87	C₁₉×C₂²⋊Q₈	—	2	1	no	—
88	C₁₉×C₂²⋊Q₈	—	2	1	no	—
89	C₁₉×C₂²⋊Q₈	—	2	2	no	—
90	C₁₉×C₂²⋊Q₈	—	2	2	no	—
91	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
92	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
93	C₁₉×#121	—	2	1	no	—
94	C₁₉×#121	—	2	2	no	—
95	C₁₉×#121	—	2	2	no	—
96	C₁₉×#121	—	2	2	no	—
97	C₁₉×#121	—	2	2	no	—
98	C₁₉×#121	—	2	1	no	—
99	C₁₉×#121	—	2	1	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	D₄	1	2	yes	—
106	C₁₉×#121	D₄	1	1	yes	characteristic
107	C₁₉×#121	C₂³	1	2	yes	—
108	C₁₉×#121	C₂³	1	1	yes	characteristic
109	C₁₉×#120	—	2	2	no	—
110	C₁₉×#120	—	2	1	no	—
111	C₄×Q₈×C₁₉	—	2	1	no	—
112	C₄×D₄×C₁₉	—	2	2	no	—
113	C₄×D₄×C₁₉	—	2	1	no	—
114	C₄×D₄×C₁₉	—	2	1	no	—
115	C₄×D₄×C₁₉	—	2	1	no	—
116	C₄×D₄×C₁₉	—	2	2	no	—
117	C₁₉×#117	D₄	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
119	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
120	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
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	D₄	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	1	no	—
149	C₂⁴×C₁₉	—	2	1	no	—
150	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
151	#41×C₁₉	—	8	2	no	—
152	#41×C₁₉	—	8	2	no	—
153	#41×C₁₉	—	8	1	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	—	2	1	no	—
158	C₂×Q₈×C₁₉	—	8	1	no	—
159	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
160	C₂×D₄×C₁₉	—	2	1	no	—
161	C₂×D₄×C₁₉	—	2	1	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	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	—	4	1	no	—
171	C₂×D₄×C₁₉	—	4	1	no	—
172	C₂×D₄×C₁₉	—	8	1	no	—
173	C₂×D₄×C₁₉	—	8	1	no	—
174	C₂×D₄×C₁₉	—	8	2	no	—
175	C₂×D₄×C₁₉	—	8	2	no	—
176	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
177	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
178	C₂²×C₄×C₁₉	—	2	2	no	—
179	C₂²×C₄×C₁₉	—	2	2	no	—
180	C₂²×C₄×C₁₉	—	2	2	no	—
181	C₂²×C₄×C₁₉	—	2	1	no	—
182	C₂²×C₄×C₁₉	—	2	1	no	—
183	C₂²×C₄×C₁₉	—	2	2	no	—
184	C₂²×C₄×C₁₉	—	2	1	no	—
185	C₂²×C₄×C₁₉	—	8	1	no	—
186	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
187	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
188	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
194	SD₁₆×C₁₉	—	8	1	no	—
195	D₈×C₁₉	—	8	2	no	—
196	D₈×C₁₉	—	8	1	no	—
197	M₁₆×C₁₉	—	8	1	no	—
198	C₂×C₈×C₁₉	—	2	2	no	—
199	C₂×C₈×C₁₉	—	2	1	no	—
200	C₂×C₈×C₁₉	—	2	1	no	—
201	C₂×C₈×C₁₉	—	8	1	no	—
202	C₄⋊C₄×C₁₉	—	2	2	no	—
203	C₄⋊C₄×C₁₉	—	2	2	no	—
204	C₄⋊C₄×C₁₉	—	2	2	no	—
205	C₄⋊C₄×C₁₉	—	2	2	no	—
206	C₄⋊C₄×C₁₉	—	2	1	no	—
207	C₄⋊C₄×C₁₉	—	2	1	no	—
208	C₄⋊C₄×C₁₉	—	2	1	no	—
209	C₄⋊C₄×C₁₉	—	2	1	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	1	no	—
215	C₄⋊C₄×C₁₉	—	8	2	no	—
216	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
217	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
218	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
219	C₂²⋊C₄×C₁₉	—	2	2	no	—
220	C₂²⋊C₄×C₁₉	—	2	2	no	—
221	C₂²⋊C₄×C₁₉	—	2	2	no	—
222	C₂²⋊C₄×C₁₉	—	2	2	no	—
223	C₂²⋊C₄×C₁₉	—	2	2	no	—
224	C₂²⋊C₄×C₁₉	—	2	1	no	—
225	C₂²⋊C₄×C₁₉	—	2	2	no	—
226	C₂²⋊C₄×C₁₉	—	2	2	no	—
227	C₂²⋊C₄×C₁₉	—	2	1	no	—
228	C₂²⋊C₄×C₁₉	—	2	1	no	—
229	C₂²⋊C₄×C₁₉	—	2	2	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	—	4	1	no	—
234	C₂²⋊C₄×C₁₉	—	4	1	no	—
235	C₂²⋊C₄×C₁₉	—	8	2	no	—
236	C₂²⋊C₄×C₁₉	—	8	2	no	—
237	C₂²⋊C₄×C₁₉	—	8	1	no	—
238	C₄²×C₁₉	—	2	2	no	—
239	C₄²×C₁₉	—	2	1	no	—
240	#18456	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
241	C₂³×C₁₉	—	2	2	no	—
242	C₂³×C₁₉	—	2	2	no	—
243	C₂³×C₁₉	—	2	1	no	—
244	C₂³×C₁₉	—	4	1	no	—
245	C₂³×C₁₉	—	4	1	no	—
246	C₂³×C₁₉	—	4	2	no	—
247	C₂³×C₁₉	—	4	2	no	—
248	C₂³×C₁₉	—	4	2	no	—
249	C₂³×C₁₉	—	4	1	no	—
250	C₂³×C₁₉	—	4	2	no	—
251	C₂³×C₁₉	—	8	1	no	—
252	C₂³×C₁₉	—	8	1	no	—
253	C₂³×C₁₉	#120	1	1	yes	characteristic
254	C₂³×C₁₉	#120	1	1	yes	characteristic
255	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
256	Q₈×C₁₉	—	4	1	no	—
257	Q₈×C₁₉	—	4	2	no	—
258	Q₈×C₁₉	—	8	1	no	—
259	Q₈×C₁₉	—	8	2	no	—
260	D₄×C₁₉	—	4	2	no	—
261	D₄×C₁₉	—	4	1	no	—
262	D₄×C₁₉	—	4	2	no	—
263	D₄×C₁₉	—	4	2	no	—
264	D₄×C₁₉	—	4	1	no	—
265	D₄×C₁₉	—	4	1	no	—
266	D₄×C₁₉	—	4	2	no	—
267	D₄×C₁₉	—	4	2	no	—
268	D₄×C₁₉	—	4	2	no	—
269	D₄×C₁₉	—	4	2	no	—
270	D₄×C₁₉	—	8	2	no	—
271	D₄×C₁₉	—	8	1	no	—
272	D₄×C₁₉	—	8	2	no	—
273	D₄×C₁₉	—	8	2	no	—
274	D₄×C₁₉	—	8	2	no	—
275	D₄×C₁₉	—	8	2	no	—
276	C₂×C₄×C₁₉	—	2	1	no	—
277	C₂×C₄×C₁₉	—	2	2	no	—
278	C₂×C₄×C₁₉	—	2	1	no	—
279	C₂×C₄×C₁₉	—	2	2	no	—
280	C₂×C₄×C₁₉	—	2	1	no	—
281	C₂×C₄×C₁₉	—	2	2	no	—
282	C₂×C₄×C₁₉	—	2	2	no	—
283	C₂×C₄×C₁₉	—	2	2	no	—
284	C₂×C₄×C₁₉	—	4	1	no	—
285	C₂×C₄×C₁₉	—	4	1	no	—
286	C₂×C₄×C₁₉	—	4	1	no	—
287	C₂×C₄×C₁₉	—	4	1	no	—
288	C₂×C₄×C₁₉	—	4	1	no	—
289	C₂×C₄×C₁₉	—	4	1	no	—
290	C₂×C₄×C₁₉	—	4	2	no	—
291	C₂×C₄×C₁₉	—	4	2	no	—
292	C₂×C₄×C₁₉	—	4	2	no	—
293	C₂×C₄×C₁₉	—	4	2	no	—
294	C₂×C₄×C₁₉	—	4	1	no	—
295	C₂×C₄×C₁₉	—	4	2	no	—
296	C₂×C₄×C₁₉	—	4	2	no	—
297	C₂×C₄×C₁₉	—	8	1	no	—
298	C₂×C₄×C₁₉	—	8	2	no	—
299	C₂×C₄×C₁₉	—	8	2	no	—
300	C₂×C₄×C₁₉	—	8	2	no	—
301	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
302	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
303	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
304	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
305	C₈×C₁₉	—	4	2	no	—
306	C₈×C₁₉	—	4	1	no	—
307	C₈×C₁₉	—	4	1	no	—
308	#3536	C₂×C₁₉	1	1	yes	characteristic, complemented
309	#3194	C₂×C₁₉	1	1	yes	characteristic, complemented
310	#3186	C₂×C₁₉	1	1	yes	characteristic, complemented
311	#2816	C₂×C₁₉	1	1	yes	characteristic, complemented
312	#1610	C₂×C₁₉	1	2	yes	complemented
313	#1609	C₂×C₁₉	1	2	yes	complemented
314	#1598	C₂×C₁₉	1	2	yes	complemented
315	#1597	C₂×C₁₉	1	2	yes	complemented
316	#1516	C₂×C₁₉	1	1	yes	characteristic, complemented
317	#1510	C₂×C₁₉	1	1	yes	characteristic, complemented
318	#1472	C₂×C₁₉	1	1	yes	characteristic, complemented
319	C₂²×C₁₉	—	2	1	no	—
320	C₂²×C₁₉	—	2	1	no	—
321	C₂²×C₁₉	—	2	1	no	—
322	C₂²×C₁₉	—	2	1	no	—
323	C₂²×C₁₉	—	2	1	no	—
324	C₂²×C₁₉	—	2	1	no	—
325	C₂²×C₁₉	—	2	1	no	—
326	C₂²×C₁₉	—	2	1	no	—
327	C₂²×C₁₉	—	4	1	no	—
328	C₂²×C₁₉	—	4	2	no	—
329	C₂²×C₁₉	—	4	1	no	—
330	C₂²×C₁₉	—	4	2	no	—
331	C₂²×C₁₉	—	4	1	no	—
332	C₂²×C₁₉	—	4	2	no	—
333	C₂²×C₁₉	—	8	2	no	—
334	C₂²×C₁₉	—	8	4	no	—
335	C₂²×C₁₉	—	8	1	no	—
336	C₂²×C₁₉	—	8	1	no	—
337	C₂²×C₁₉	—	8	1	no	—
338	C₂²×C₁₉	—	16	2	no	—
339	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
340	C₂²×C₁₉	#576	1	2	yes	—
341	C₄×C₁₉	—	2	1	no	—
342	C₄×C₁₉	—	2	1	no	—
343	C₄×C₁₉	—	2	1	no	—
344	C₄×C₁₉	—	2	1	no	—
345	C₄×C₁₉	—	4	2	no	—
346	C₄×C₁₉	—	4	2	no	—
347	C₄×C₁₉	—	4	1	no	—
348	C₄×C₁₉	—	4	1	no	—
349	C₄×C₁₉	—	4	1	no	—
350	C₄×C₁₉	—	4	2	no	—
351	C₄×C₁₉	—	8	2	no	—
352	C₄×C₁₉	—	8	1	no	—
353	#562	—	2	2	no	—
354	#554	—	2	1	no	—
355	#548	—	2	1	no	—
356	#547	—	2	1	no	—
357	#546	—	2	1	no	—
358	#546	—	2	2	no	—
359	#543	—	2	1	no	—
360	#542	—	2	1	no	—
361	#539	C₂²×C₁₉	1	2	yes	—
362	#538	—	2	1	no	—
363	#537	—	2	1	no	—
364	#537	C₂²×C₁₉	1	2	yes	—
365	#525	C₂²×C₁₉	1	1	yes	characteristic
366	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
367	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
368	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
369	#483	C₂²×C₁₉	1	1	yes	characteristic, complemented
370	#482	—	2	1	no	—
371	#480	—	2	1	no	—
372	#480	C₂²×C₁₉	1	2	yes	—
373	#480	C₂²×C₁₉	1	1	yes	characteristic, complemented
374	#469	—	2	1	no	—
375	#468	—	2	1	no	—
376	#466	—	2	2	no	—
377	#450	C₂²×C₁₉	1	1	yes	characteristic, complemented
378	#449	—	2	1	no	—
379	#447	—	2	1	no	—
380	#447	C₂²×C₁₉	1	2	yes	—
381	#447	C₂²×C₁₉	1	1	yes	characteristic, complemented
382	#407	C₂²×C₁₉	1	1	yes	characteristic
383	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
384	#399	—	2	1	no	—
385	#398	C₂²×C₁₉	1	2	yes	complemented
386	#394	—	2	2	no	—
387	#394	C₂²×C₁₉	1	2	yes	complemented
388	#393	—	2	1	no	—
389	#381	C₂²×C₁₉	1	1	yes	characteristic
390	#328	C₂²×C₁₉	1	2	yes	complemented
391	#327	C₂²×C₁₉	1	2	yes	—
392	#327	C₂²×C₁₉	1	2	yes	—
393	#327	C₂²×C₁₉	1	2	yes	complemented
394	#324	C₂²×C₁₉	1	2	yes	complemented
395	#324	C₂²×C₁₉	1	2	yes	complemented
396	C₂×C₁₉	—	2	2	no	—
397	C₂×C₁₉	—	4	1	no	—
398	C₂×C₁₉	—	4	1	no	—
399	C₂×C₁₉	—	8	1	no	—
400	C₂×C₁₉	—	8	2	no	—
401	C₂×C₁₉	—	16	1	no	—
402	C₂×C₁₉	#3008	1	1	yes	characteristic
403	C₂×C₁₉	#3020	1	1	yes	characteristic
404	C₂×C₁₉	#3026	1	1	yes	characteristic
405	C₂×#41	—	2	1	no	—
406	C₂×#41	—	2	2	no	—
407	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
408	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
409	C₂²×D₄	—	2	1	no	—
410	C₂²×D₄	—	2	1	no	—
411	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
412	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
413	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
414	C₂×SD₁₆	—	2	1	no	—
415	C₂×D₈	—	2	2	no	—
416	C₂×D₈	—	2	1	no	—
417	C₂×M₁₆	—	2	1	no	—
418	C₂²×C₈	—	2	1	no	—
419	C₄⋊Q₈	—	2	1	no	—
420	#126	—	2	2	no	—
421	#125	—	2	2	no	—
422	#124	—	2	2	no	—
423	#124	—	2	1	no	—
424	#124	—	2	2	no	—
425	#123	—	2	2	no	—
426	#123	—	2	2	no	—
427	#123	—	2	2	no	—
428	#123	—	2	1	no	—
429	#123	—	2	2	no	—
430	C₂²⋊Q₈	—	2	1	no	—
431	C₂²⋊Q₈	—	2	2	no	—
432	C₂²⋊Q₈	—	2	2	no	—
433	C₂²⋊Q₈	—	2	2	no	—
434	C₂²⋊Q₈	—	2	2	no	—
435	C₂²⋊Q₈	—	2	1	no	—
436	C₂²⋊Q₈	—	2	1	no	—
437	C₂²⋊Q₈	—	2	1	no	—
438	C₂²⋊Q₈	—	2	1	no	—
439	C₂²⋊Q₈	—	2	2	no	—
440	C₂²⋊Q₈	—	2	2	no	—
441	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
442	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
443	#121	—	2	1	no	—
444	#121	—	2	2	no	—
445	#121	—	2	2	no	—
446	#121	—	2	2	no	—
447	#121	—	2	2	no	—
448	#121	—	2	1	no	—
449	#121	—	2	1	no	—
450	#121	—	2	2	no	—
451	#121	—	2	1	no	—
452	#121	—	2	1	no	—
453	#121	—	2	1	no	—
454	#121	—	2	1	no	—
455	#121	D₄×C₁₉	1	2	yes	—
456	#121	D₄×C₁₉	1	1	yes	characteristic
457	#121	C₂³×C₁₉	1	2	yes	—
458	#121	C₂³×C₁₉	1	1	yes	characteristic
459	#120	—	2	2	no	—
460	#120	—	2	1	no	—
461	C₄×Q₈	—	2	1	no	—
462	C₄×D₄	—	2	2	no	—
463	C₄×D₄	—	2	1	no	—
464	C₄×D₄	—	2	1	no	—
465	C₄×D₄	—	2	1	no	—
466	C₄×D₄	—	2	2	no	—
467	#117	D₄×C₁₉	1	1	yes	characteristic
468	C₂×C₄⋊C₄	—	2	1	no	—
469	C₂×C₄⋊C₄	—	2	2	no	—
470	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
471	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
472	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
473	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
474	C₂×C₂²⋊C₄	—	2	2	no	—
475	C₂×C₂²⋊C₄	—	2	1	no	—
476	C₂×C₂²⋊C₄	—	2	1	no	—
477	C₂×C₂²⋊C₄	—	2	1	no	—
478	C₂×C₂²⋊C₄	—	2	2	no	—
479	C₂×C₂²⋊C₄	—	2	2	no	—
480	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
481	#107	—	2	2	no	—
482	#107	—	2	1	no	—
483	#106	—	2	1	no	—
484	#103	—	2	1	no	—
485	#102	—	2	2	no	—
486	#102	—	2	1	no	—
487	#102	—	2	2	no	—
488	#102	—	2	1	no	—
489	#102	—	2	1	no	—
490	C₂²⋊C₈	—	2	1	no	—
491	C₂²⋊C₈	—	2	1	no	—
492	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
493	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
494	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
495	#95	—	2	1	no	—
496	#95	—	2	2	no	—
497	#95	C₂³×C₁₉	1	2	yes	—
498	C₁₉	#18456	1	1	yes	characteristic, direct product factor, Sylow
499	C₂⁴	—	2	1	no	—
500	C₂⁴	—	2	1	no	—
501	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
502	#41	—	8	2	no	—
503	#41	—	8	2	no	—
504	#41	—	8	1	no	—
505	#41	—	8	2	no	—
506	C₂×Q₈	—	2	2	no	—
507	C₂×Q₈	—	2	1	no	—
508	C₂×Q₈	—	2	1	no	—
509	C₂×Q₈	—	8	1	no	—
510	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	2	no	—
514	C₂×D₄	—	2	2	no	—
515	C₂×D₄	—	2	2	no	—
516	C₂×D₄	—	2	1	no	—
517	C₂×D₄	—	2	2	no	—
518	C₂×D₄	—	2	1	no	—
519	C₂×D₄	—	2	1	no	—
520	C₂×D₄	—	2	1	no	—
521	C₂×D₄	—	4	1	no	—
522	C₂×D₄	—	4	1	no	—
523	C₂×D₄	—	8	1	no	—
524	C₂×D₄	—	8	1	no	—
525	C₂×D₄	—	8	2	no	—
526	C₂×D₄	—	8	2	no	—
527	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
528	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
529	C₂²×C₄	—	2	2	no	—
530	C₂²×C₄	—	2	2	no	—
531	C₂²×C₄	—	2	2	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	2	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	8	1	no	—
537	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
538	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
539	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
540	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
541	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
542	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
543	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
544	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
545	SD₁₆	—	8	1	no	—
546	D₈	—	8	2	no	—
547	D₈	—	8	1	no	—
548	M₁₆	—	8	1	no	—
549	C₂×C₈	—	2	2	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	—	8	1	no	—
553	C₄⋊C₄	—	2	2	no	—
554	C₄⋊C₄	—	2	2	no	—
555	C₄⋊C₄	—	2	2	no	—
556	C₄⋊C₄	—	2	2	no	—
557	C₄⋊C₄	—	2	1	no	—
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	—	2	2	no	—
562	C₄⋊C₄	—	2	2	no	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	8	2	no	—
567	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
568	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
569	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
570	C₂²⋊C₄	—	2	2	no	—
571	C₂²⋊C₄	—	2	2	no	—
572	C₂²⋊C₄	—	2	2	no	—
573	C₂²⋊C₄	—	2	2	no	—
574	C₂²⋊C₄	—	2	2	no	—
575	C₂²⋊C₄	—	2	1	no	—
576	C₂²⋊C₄	—	2	2	no	—
577	C₂²⋊C₄	—	2	2	no	—
578	C₂²⋊C₄	—	2	1	no	—
579	C₂²⋊C₄	—	2	1	no	—
580	C₂²⋊C₄	—	2	2	no	—
581	C₂²⋊C₄	—	2	1	no	—
582	C₂²⋊C₄	—	2	2	no	—
583	C₂²⋊C₄	—	2	1	no	—
584	C₂²⋊C₄	—	4	1	no	—
585	C₂²⋊C₄	—	4	1	no	—
586	C₂²⋊C₄	—	8	2	no	—
587	C₂²⋊C₄	—	8	2	no	—
588	C₂²⋊C₄	—	8	1	no	—
589	C₄²	—	2	2	no	—
590	C₄²	—	2	1	no	—
591	C₂³	—	2	2	no	—
592	C₂³	—	2	2	no	—
593	C₂³	—	2	1	no	—
594	C₂³	—	4	1	no	—
595	C₂³	—	4	1	no	—
596	C₂³	—	4	2	no	—
597	C₂³	—	4	2	no	—
598	C₂³	—	4	2	no	—
599	C₂³	—	4	1	no	—
600	C₂³	—	4	2	no	—
601	C₂³	—	8	1	no	—
602	C₂³	—	8	1	no	—
603	C₂³	C₁₉×#120	1	1	yes	characteristic
604	C₂³	C₁₉×#120	1	1	yes	characteristic
605	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
606	Q₈	—	4	1	no	—
607	Q₈	—	4	2	no	—
608	Q₈	—	8	1	no	—
609	Q₈	—	8	2	no	—
610	D₄	—	4	2	no	—
611	D₄	—	4	1	no	—
612	D₄	—	4	2	no	—
613	D₄	—	4	2	no	—
614	D₄	—	4	1	no	—
615	D₄	—	4	1	no	—
616	D₄	—	4	2	no	—
617	D₄	—	4	2	no	—
618	D₄	—	4	2	no	—
619	D₄	—	4	2	no	—
620	D₄	—	8	2	no	—
621	D₄	—	8	1	no	—
622	D₄	—	8	2	no	—
623	D₄	—	8	2	no	—
624	D₄	—	8	2	no	—
625	D₄	—	8	2	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	2	no	—
641	C₂×C₄	—	4	2	no	—
642	C₂×C₄	—	4	2	no	—
643	C₂×C₄	—	4	2	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	2	no	—
646	C₂×C₄	—	4	2	no	—
647	C₂×C₄	—	8	1	no	—
648	C₂×C₄	—	8	2	no	—
649	C₂×C₄	—	8	2	no	—
650	C₂×C₄	—	8	2	no	—
651	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
652	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
653	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
654	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
655	C₈	—	4	2	no	—
656	C₈	—	4	1	no	—
657	C₈	—	4	1	no	—
658	C₂²	—	2	1	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	1	no	—
662	C₂²	—	2	1	no	—
663	C₂²	—	2	1	no	—
664	C₂²	—	2	1	no	—
665	C₂²	—	2	1	no	—
666	C₂²	—	4	1	no	—
667	C₂²	—	4	2	no	—
668	C₂²	—	4	1	no	—
669	C₂²	—	4	2	no	—
670	C₂²	—	4	1	no	—
671	C₂²	—	4	2	no	—
672	C₂²	—	8	2	no	—
673	C₂²	—	8	4	no	—
674	C₂²	—	8	1	no	—
675	C₂²	—	8	1	no	—
676	C₂²	—	8	1	no	—
677	C₂²	—	16	2	no	—
678	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
679	C₂²	C₁₉×#576	1	2	yes	—
680	C₄	—	2	1	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	1	no	—
684	C₄	—	4	2	no	—
685	C₄	—	4	2	no	—
686	C₄	—	4	1	no	—
687	C₄	—	4	1	no	—
688	C₄	—	4	1	no	—
689	C₄	—	4	2	no	—
690	C₄	—	8	2	no	—
691	C₄	—	8	1	no	—
692	C₂	—	2	2	no	—
693	C₂	—	4	1	no	—
694	C₂	—	4	1	no	—
695	C₂	—	8	2	no	—
696	C₂	—	8	1	no	—
697	C₂	—	16	1	no	—
698	C₂	C₁₉×#3008	1	1	yes	characteristic
699	C₂	C₁₉×#3020	1	1	yes	characteristic
700	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×#3194	C₂	semidirect
3. C₁₉×#3186	C₂	semidirect
4. C₁₉×#2816	C₂	semidirect
5. C₁₉×#1610	C₂	semidirect
6. C₁₉×#1609	C₂	semidirect
7. C₁₉×#1598	C₂	semidirect
8. C₁₉×#1597	C₂	semidirect
9. C₁₉×#1516	C₂	semidirect
10. C₁₉×#1510	C₂	semidirect
11. C₁₉×#1472	C₂	semidirect
28. C₁₉×#483	C₂²	semidirect
32. C₁₉×#480	C₂²	semidirect
36. C₁₉×#450	C₂²	semidirect
40. C₁₉×#447	C₂²	semidirect
44. C₁₉×#398	C₂²	semidirect
46. C₁₉×#394	C₂²	semidirect
49. C₁₉×#328	C₂²	semidirect
52. C₁₉×#327	C₂²	semidirect
53. C₁₉×#324	C₂²	semidirect
54. C₁₉×#324	C₂²	semidirect
240. #18456	C₁₉	direct (N × H)
308. #3536	C₂×C₁₉	semidirect
309. #3194	C₂×C₁₉	semidirect
310. #3186	C₂×C₁₉	semidirect
311. #2816	C₂×C₁₉	semidirect
312. #1610	C₂×C₁₉	semidirect
313. #1609	C₂×C₁₉	semidirect
314. #1598	C₂×C₁₉	semidirect
315. #1597	C₂×C₁₉	semidirect
316. #1516	C₂×C₁₉	semidirect
317. #1510	C₂×C₁₉	semidirect
318. #1472	C₂×C₁₉	semidirect
369. #483	C₂²×C₁₉	semidirect
373. #480	C₂²×C₁₉	semidirect
377. #450	C₂²×C₁₉	semidirect
381. #447	C₂²×C₁₉	semidirect
385. #398	C₂²×C₁₉	semidirect
387. #394	C₂²×C₁₉	semidirect
390. #328	C₂²×C₁₉	semidirect
393. #327	C₂²×C₁₉	semidirect
394. #324	C₂²×C₁₉	semidirect
395. #324	C₂²×C₁₉	semidirect
498. C₁₉	#18456	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×#3194	2
C₁₉×#3186	2
C₁₉×#2816	2
C₁₉×#1610	2
C₁₉×#1609	2
C₁₉×#1598	2
C₁₉×#1597	2
C₁₉×#1516	2
C₁₉×#1510	2
C₁₉×#1472	2
#18456	19

Subgroups — C19×#18456 #18024415

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18456 #18024415