Subgroups — C₁₉×#18424 #18024383

Order 4864.

1020 conjugacy classes of subgroups.

The subgroup lattice has 722 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×#3192	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3188	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2639	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1616	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1615	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×#1504	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₉×#327	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×#484	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#482	—	2	1	no	—
30	C₁₉×#481	—	2	1	no	—
31	C₁₉×#481	C₂²	1	2	yes	—
32	C₁₉×#481	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×#469	—	2	2	no	—
34	C₁₉×#466	—	2	1	no	—
35	C₁₉×#465	—	2	1	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×#400	C₂²	1	2	yes	complemented
44	C₁₉×#397	—	2	1	no	—
45	C₁₉×#394	C₂²	1	2	yes	complemented
46	C₁₉×#393	—	2	1	no	—
47	C₁₉×#386	—	2	2	no	—
48	C₂×C₁₉×#95	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	—	2	1	no	—
64	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×SD₁₆×C₁₉	—	2	1	no	—
66	C₂×D₈×C₁₉	—	2	2	no	—
67	C₂×D₈×C₁₉	—	2	1	no	—
68	C₂×M₁₆×C₁₉	—	2	1	no	—
69	C₂²×C₈×C₁₉	—	2	1	no	—
70	C₁₉×C₄⋊Q₈	—	2	1	no	—
71	C₁₉×#126	—	2	2	no	—
72	C₁₉×#125	—	2	2	no	—
73	C₁₉×#124	—	2	2	no	—
74	C₁₉×#124	—	2	1	no	—
75	C₁₉×#124	—	2	2	no	—
76	C₁₉×#123	—	2	2	no	—
77	C₁₉×#123	—	2	2	no	—
78	C₁₉×#123	—	2	2	no	—
79	C₁₉×#123	—	2	1	no	—
80	C₁₉×#123	—	2	2	no	—
81	C₁₉×C₂²⋊Q₈	—	2	1	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	2	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	1	no	—
90	C₁₉×C₂²⋊Q₈	—	2	2	no	—
91	C₁₉×C₂²⋊Q₈	—	2	2	no	—
92	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
93	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
94	C₁₉×#121	—	2	1	no	—
95	C₁₉×#121	—	2	2	no	—
96	C₁₉×#121	—	2	2	no	—
97	C₁₉×#121	—	2	2	no	—
98	C₁₉×#121	—	2	2	no	—
99	C₁₉×#121	—	2	1	no	—
100	C₁₉×#121	—	2	1	no	—
101	C₁₉×#121	—	2	2	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	D₄	1	1	yes	characteristic
107	C₁₉×#121	D₄	1	2	yes	—
108	C₁₉×#121	C₂³	1	2	yes	—
109	C₁₉×#121	C₂³	1	1	yes	characteristic
110	C₁₉×#120	—	2	2	no	—
111	C₁₉×#120	—	2	1	no	—
112	C₄×Q₈×C₁₉	—	2	1	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	2	no	—
118	C₁₉×#117	D₄	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₁₉	—	2	1	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	2	no	—
128	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
129	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
130	C₁₉×#107	—	2	1	no	—
131	C₁₉×#106	—	2	1	no	—
132	C₁₉×#106	—	2	2	no	—
133	C₁₉×#103	—	2	1	no	—
134	C₁₉×#102	—	2	2	no	—
135	C₁₉×#102	—	2	1	no	—
136	C₁₉×#102	—	2	2	no	—
137	C₁₉×#102	—	2	1	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	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	4	no	—
171	C₂×D₄×C₁₉	—	4	1	no	—
172	C₂×D₄×C₁₉	—	4	1	no	—
173	C₂×D₄×C₁₉	—	8	1	no	—
174	C₂×D₄×C₁₉	—	8	1	no	—
175	C₂×D₄×C₁₉	—	8	1	no	—
176	C₂×D₄×C₁₉	—	8	1	no	—
177	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
178	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
179	C₂²×C₄×C₁₉	—	2	2	no	—
180	C₂²×C₄×C₁₉	—	2	2	no	—
181	C₂²×C₄×C₁₉	—	2	2	no	—
182	C₂²×C₄×C₁₉	—	2	1	no	—
183	C₂²×C₄×C₁₉	—	2	1	no	—
184	C₂²×C₄×C₁₉	—	2	2	no	—
185	C₂²×C₄×C₁₉	—	2	1	no	—
186	C₂²×C₄×C₁₉	—	4	2	no	—
187	C₂²×C₄×C₁₉	—	8	1	no	—
188	C₂²×C₄×C₁₉	—	8	1	no	—
189	C₂²×C₄×C₁₉	—	8	1	no	—
190	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
191	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
192	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
198	SD₁₆×C₁₉	—	8	1	no	—
199	D₈×C₁₉	—	8	1	no	—
200	D₈×C₁₉	—	8	2	no	—
201	M₁₆×C₁₉	—	8	1	no	—
202	C₂×C₈×C₁₉	—	2	1	no	—
203	C₂×C₈×C₁₉	—	2	1	no	—
204	C₂×C₈×C₁₉	—	2	2	no	—
205	C₂×C₈×C₁₉	—	8	1	no	—
206	C₄⋊C₄×C₁₉	—	2	2	no	—
207	C₄⋊C₄×C₁₉	—	2	2	no	—
208	C₄⋊C₄×C₁₉	—	2	2	no	—
209	C₄⋊C₄×C₁₉	—	2	2	no	—
210	C₄⋊C₄×C₁₉	—	2	1	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	2	no	—
215	C₄⋊C₄×C₁₉	—	2	2	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	C₂×D₄	1	2	yes	—
220	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
221	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
222	C₂²⋊C₄×C₁₉	—	2	2	no	—
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	1	no	—
228	C₂²⋊C₄×C₁₉	—	2	2	no	—
229	C₂²⋊C₄×C₁₉	—	2	2	no	—
230	C₂²⋊C₄×C₁₉	—	2	1	no	—
231	C₂²⋊C₄×C₁₉	—	2	1	no	—
232	C₂²⋊C₄×C₁₉	—	2	2	no	—
233	C₂²⋊C₄×C₁₉	—	2	1	no	—
234	C₂²⋊C₄×C₁₉	—	2	2	no	—
235	C₂²⋊C₄×C₁₉	—	2	1	no	—
236	C₂²⋊C₄×C₁₉	—	4	1	no	—
237	C₂²⋊C₄×C₁₉	—	4	1	no	—
238	C₂²⋊C₄×C₁₉	—	8	2	no	—
239	C₂²⋊C₄×C₁₉	—	8	2	no	—
240	C₄²×C₁₉	—	2	2	no	—
241	C₄²×C₁₉	—	2	1	no	—
242	#18424	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
243	C₂³×C₁₉	—	2	1	no	—
244	C₂³×C₁₉	—	2	1	no	—
245	C₂³×C₁₉	—	2	2	no	—
246	C₂³×C₁₉	—	2	2	no	—
247	C₂³×C₁₉	—	2	1	no	—
248	C₂³×C₁₉	—	4	1	no	—
249	C₂³×C₁₉	—	4	2	no	—
250	C₂³×C₁₉	—	4	2	no	—
251	C₂³×C₁₉	—	4	2	no	—
252	C₂³×C₁₉	—	4	1	no	—
253	C₂³×C₁₉	—	4	1	no	—
254	C₂³×C₁₉	—	4	1	no	—
255	C₂³×C₁₉	—	8	1	no	—
256	C₂³×C₁₉	—	8	1	no	—
257	C₂³×C₁₉	#120	1	1	yes	characteristic
258	C₂³×C₁₉	#120	1	1	yes	characteristic
259	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
260	Q₈×C₁₉	—	4	1	no	—
261	Q₈×C₁₉	—	4	2	no	—
262	Q₈×C₁₉	—	8	1	no	—
263	Q₈×C₁₉	—	8	2	no	—
264	D₄×C₁₉	—	4	2	no	—
265	D₄×C₁₉	—	4	1	no	—
266	D₄×C₁₉	—	4	2	no	—
267	D₄×C₁₉	—	4	2	no	—
268	D₄×C₁₉	—	4	1	no	—
269	D₄×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	1	no	—
274	D₄×C₁₉	—	4	2	no	—
275	D₄×C₁₉	—	8	2	no	—
276	D₄×C₁₉	—	8	1	no	—
277	D₄×C₁₉	—	8	2	no	—
278	D₄×C₁₉	—	8	2	no	—
279	D₄×C₁₉	—	8	2	no	—
280	D₄×C₁₉	—	8	2	no	—
281	C₂×C₄×C₁₉	—	2	1	no	—
282	C₂×C₄×C₁₉	—	2	2	no	—
283	C₂×C₄×C₁₉	—	2	1	no	—
284	C₂×C₄×C₁₉	—	2	2	no	—
285	C₂×C₄×C₁₉	—	2	1	no	—
286	C₂×C₄×C₁₉	—	2	2	no	—
287	C₂×C₄×C₁₉	—	2	2	no	—
288	C₂×C₄×C₁₉	—	2	2	no	—
289	C₂×C₄×C₁₉	—	4	1	no	—
290	C₂×C₄×C₁₉	—	4	1	no	—
291	C₂×C₄×C₁₉	—	4	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	2	no	—
296	C₂×C₄×C₁₉	—	4	2	no	—
297	C₂×C₄×C₁₉	—	4	2	no	—
298	C₂×C₄×C₁₉	—	4	2	no	—
299	C₂×C₄×C₁₉	—	4	2	no	—
300	C₂×C₄×C₁₉	—	4	1	no	—
301	C₂×C₄×C₁₉	—	4	2	no	—
302	C₂×C₄×C₁₉	—	8	1	no	—
303	C₂×C₄×C₁₉	—	8	2	no	—
304	C₂×C₄×C₁₉	—	8	2	no	—
305	C₂×C₄×C₁₉	—	8	2	no	—
306	C₂×C₄×C₁₉	—	8	4	no	—
307	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
308	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
309	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
310	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
311	C₈×C₁₉	—	4	1	no	—
312	C₈×C₁₉	—	4	1	no	—
313	C₈×C₁₉	—	4	2	no	—
314	#3536	C₂×C₁₉	1	1	yes	characteristic, complemented
315	#3192	C₂×C₁₉	1	1	yes	characteristic, complemented
316	#3188	C₂×C₁₉	1	1	yes	characteristic, complemented
317	#2639	C₂×C₁₉	1	1	yes	characteristic, complemented
318	#1616	C₂×C₁₉	1	2	yes	complemented
319	#1615	C₂×C₁₉	1	2	yes	complemented
320	#1598	C₂×C₁₉	1	2	yes	complemented
321	#1597	C₂×C₁₉	1	2	yes	complemented
322	#1504	C₂×C₁₉	1	1	yes	characteristic, complemented
323	C₂×#327	C₂×C₁₉	1	1	yes	characteristic, complemented
324	#1472	C₂×C₁₉	1	1	yes	characteristic, complemented
325	C₂²×C₁₉	—	2	1	no	—
326	C₂²×C₁₉	—	2	1	no	—
327	C₂²×C₁₉	—	2	1	no	—
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	—	4	2	no	—
333	C₂²×C₁₉	—	4	2	no	—
334	C₂²×C₁₉	—	4	1	no	—
335	C₂²×C₁₉	—	4	2	no	—
336	C₂²×C₁₉	—	4	1	no	—
337	C₂²×C₁₉	—	4	2	no	—
338	C₂²×C₁₉	—	4	1	no	—
339	C₂²×C₁₉	—	4	2	no	—
340	C₂²×C₁₉	—	8	2	no	—
341	C₂²×C₁₉	—	8	2	no	—
342	C₂²×C₁₉	—	8	1	no	—
343	C₂²×C₁₉	—	8	1	no	—
344	C₂²×C₁₉	—	8	1	no	—
345	C₂²×C₁₉	—	16	2	no	—
346	C₂²×C₁₉	#454	1	2	yes	—
347	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
348	C₂²×C₁₉	#576	1	1	yes	characteristic
349	C₂²×C₁₉	#577	1	1	yes	characteristic
350	C₄×C₁₉	—	2	1	no	—
351	C₄×C₁₉	—	2	1	no	—
352	C₄×C₁₉	—	2	1	no	—
353	C₄×C₁₉	—	2	1	no	—
354	C₄×C₁₉	—	4	2	no	—
355	C₄×C₁₉	—	4	2	no	—
356	C₄×C₁₉	—	4	1	no	—
357	C₄×C₁₉	—	4	1	no	—
358	C₄×C₁₉	—	4	1	no	—
359	C₄×C₁₉	—	4	2	no	—
360	C₄×C₁₉	—	8	2	no	—
361	C₄×C₁₉	—	8	1	no	—
362	#562	—	2	2	no	—
363	#554	—	2	1	no	—
364	#548	—	2	1	no	—
365	#547	—	2	1	no	—
366	#546	—	2	1	no	—
367	#546	—	2	2	no	—
368	#543	—	2	1	no	—
369	#542	—	2	1	no	—
370	#539	C₂²×C₁₉	1	2	yes	—
371	#538	—	2	1	no	—
372	#537	—	2	1	no	—
373	#537	C₂²×C₁₉	1	2	yes	—
374	#525	C₂²×C₁₉	1	1	yes	characteristic
375	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
376	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
377	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
378	#484	C₂²×C₁₉	1	1	yes	characteristic, complemented
379	#482	—	2	1	no	—
380	#481	—	2	1	no	—
381	#481	C₂²×C₁₉	1	2	yes	—
382	#481	C₂²×C₁₉	1	1	yes	characteristic, complemented
383	#469	—	2	2	no	—
384	#466	—	2	1	no	—
385	#465	—	2	1	no	—
386	#450	C₂²×C₁₉	1	1	yes	characteristic, complemented
387	#449	—	2	1	no	—
388	#447	—	2	1	no	—
389	#447	C₂²×C₁₉	1	2	yes	—
390	#447	C₂²×C₁₉	1	1	yes	characteristic, complemented
391	#407	C₂²×C₁₉	1	1	yes	characteristic
392	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
393	#400	C₂²×C₁₉	1	2	yes	complemented
394	#397	—	2	1	no	—
395	#394	C₂²×C₁₉	1	2	yes	complemented
396	#393	—	2	1	no	—
397	#386	—	2	2	no	—
398	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
399	#328	C₂²×C₁₉	1	2	yes	complemented
400	#327	C₂²×C₁₉	1	2	yes	—
401	#327	C₂²×C₁₉	1	2	yes	—
402	#327	C₂²×C₁₉	1	2	yes	complemented
403	#324	C₂²×C₁₉	1	2	yes	complemented
404	#324	C₂²×C₁₉	1	2	yes	complemented
405	C₂×C₁₉	—	2	1	no	—
406	C₂×C₁₉	—	2	1	no	—
407	C₂×C₁₉	—	2	2	no	—
408	C₂×C₁₉	—	4	1	no	—
409	C₂×C₁₉	—	8	1	no	—
410	C₂×C₁₉	—	8	2	no	—
411	C₂×C₁₉	—	16	1	no	—
412	C₂×C₁₉	#3012	1	1	yes	characteristic
413	C₂×C₁₉	C₂×#454	1	1	yes	characteristic
414	C₂×C₁₉	#3026	1	1	yes	characteristic
415	C₂×#41	—	2	1	no	—
416	C₂×#41	—	2	2	no	—
417	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
418	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
419	C₂²×D₄	—	2	1	no	—
420	C₂²×D₄	—	2	1	no	—
421	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
422	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
423	C₂³×C₄	—	2	1	no	—
424	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
425	C₂×SD₁₆	—	2	1	no	—
426	C₂×D₈	—	2	2	no	—
427	C₂×D₈	—	2	1	no	—
428	C₂×M₁₆	—	2	1	no	—
429	C₂²×C₈	—	2	1	no	—
430	C₄⋊Q₈	—	2	1	no	—
431	#126	—	2	2	no	—
432	#125	—	2	2	no	—
433	#124	—	2	2	no	—
434	#124	—	2	1	no	—
435	#124	—	2	2	no	—
436	#123	—	2	2	no	—
437	#123	—	2	2	no	—
438	#123	—	2	2	no	—
439	#123	—	2	1	no	—
440	#123	—	2	2	no	—
441	C₂²⋊Q₈	—	2	1	no	—
442	C₂²⋊Q₈	—	2	2	no	—
443	C₂²⋊Q₈	—	2	2	no	—
444	C₂²⋊Q₈	—	2	2	no	—
445	C₂²⋊Q₈	—	2	2	no	—
446	C₂²⋊Q₈	—	2	1	no	—
447	C₂²⋊Q₈	—	2	1	no	—
448	C₂²⋊Q₈	—	2	1	no	—
449	C₂²⋊Q₈	—	2	1	no	—
450	C₂²⋊Q₈	—	2	2	no	—
451	C₂²⋊Q₈	—	2	2	no	—
452	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
453	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
454	#121	—	2	1	no	—
455	#121	—	2	2	no	—
456	#121	—	2	2	no	—
457	#121	—	2	2	no	—
458	#121	—	2	2	no	—
459	#121	—	2	1	no	—
460	#121	—	2	1	no	—
461	#121	—	2	2	no	—
462	#121	—	2	1	no	—
463	#121	—	2	1	no	—
464	#121	—	2	1	no	—
465	#121	—	2	1	no	—
466	#121	D₄×C₁₉	1	2	yes	—
467	#121	D₄×C₁₉	1	1	yes	characteristic
468	#121	C₂³×C₁₉	1	2	yes	—
469	#121	C₂³×C₁₉	1	1	yes	characteristic
470	#120	—	2	2	no	—
471	#120	—	2	1	no	—
472	C₄×Q₈	—	2	1	no	—
473	C₄×D₄	—	2	2	no	—
474	C₄×D₄	—	2	1	no	—
475	C₄×D₄	—	2	1	no	—
476	C₄×D₄	—	2	1	no	—
477	C₄×D₄	—	2	2	no	—
478	#117	D₄×C₁₉	1	1	yes	characteristic
479	C₂×C₄⋊C₄	—	2	1	no	—
480	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
481	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
482	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
483	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
484	C₂×C₂²⋊C₄	—	2	2	no	—
485	C₂×C₂²⋊C₄	—	2	1	no	—
486	C₂×C₂²⋊C₄	—	2	1	no	—
487	C₂×C₂²⋊C₄	—	2	2	no	—
488	C₂×C₂²⋊C₄	—	2	2	no	—
489	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
490	#107	—	2	1	no	—
491	#106	—	2	1	no	—
492	#106	—	2	2	no	—
493	#103	—	2	1	no	—
494	#102	—	2	2	no	—
495	#102	—	2	1	no	—
496	#102	—	2	2	no	—
497	#102	—	2	1	no	—
498	#102	—	2	1	no	—
499	C₂²⋊C₈	—	2	1	no	—
500	C₂²⋊C₈	—	2	1	no	—
501	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
502	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
503	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
504	#95	—	2	1	no	—
505	#95	—	2	2	no	—
506	#95	—	2	2	no	—
507	#95	C₂³×C₁₉	1	2	yes	—
508	C₁₉	#18424	1	1	yes	characteristic, direct product factor, Sylow
509	C₂⁴	—	2	1	no	—
510	C₂⁴	—	2	1	no	—
511	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
512	#41	—	8	2	no	—
513	#41	—	8	2	no	—
514	#41	—	8	1	no	—
515	#41	—	8	2	no	—
516	C₂×Q₈	—	2	2	no	—
517	C₂×Q₈	—	2	1	no	—
518	C₂×Q₈	—	2	1	no	—
519	C₂×Q₈	—	8	1	no	—
520	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
521	C₂×D₄	—	2	1	no	—
522	C₂×D₄	—	2	1	no	—
523	C₂×D₄	—	2	2	no	—
524	C₂×D₄	—	2	2	no	—
525	C₂×D₄	—	2	2	no	—
526	C₂×D₄	—	2	1	no	—
527	C₂×D₄	—	2	2	no	—
528	C₂×D₄	—	2	1	no	—
529	C₂×D₄	—	2	1	no	—
530	C₂×D₄	—	2	1	no	—
531	C₂×D₄	—	4	4	no	—
532	C₂×D₄	—	4	1	no	—
533	C₂×D₄	—	4	1	no	—
534	C₂×D₄	—	8	1	no	—
535	C₂×D₄	—	8	1	no	—
536	C₂×D₄	—	8	1	no	—
537	C₂×D₄	—	8	1	no	—
538	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
539	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
540	C₂²×C₄	—	2	2	no	—
541	C₂²×C₄	—	2	2	no	—
542	C₂²×C₄	—	2	2	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	4	2	no	—
548	C₂²×C₄	—	8	1	no	—
549	C₂²×C₄	—	8	1	no	—
550	C₂²×C₄	—	8	1	no	—
551	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
552	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
553	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
554	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
555	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
556	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
557	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
558	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
559	SD₁₆	—	8	1	no	—
560	D₈	—	8	1	no	—
561	D₈	—	8	2	no	—
562	M₁₆	—	8	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	2	2	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	—	8	1	no	—
567	C₄⋊C₄	—	2	2	no	—
568	C₄⋊C₄	—	2	2	no	—
569	C₄⋊C₄	—	2	2	no	—
570	C₄⋊C₄	—	2	2	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	1	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	1	no	—
580	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
581	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
582	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
583	C₂²⋊C₄	—	2	2	no	—
584	C₂²⋊C₄	—	2	2	no	—
585	C₂²⋊C₄	—	2	2	no	—
586	C₂²⋊C₄	—	2	2	no	—
587	C₂²⋊C₄	—	2	2	no	—
588	C₂²⋊C₄	—	2	1	no	—
589	C₂²⋊C₄	—	2	2	no	—
590	C₂²⋊C₄	—	2	2	no	—
591	C₂²⋊C₄	—	2	1	no	—
592	C₂²⋊C₄	—	2	1	no	—
593	C₂²⋊C₄	—	2	2	no	—
594	C₂²⋊C₄	—	2	1	no	—
595	C₂²⋊C₄	—	2	2	no	—
596	C₂²⋊C₄	—	2	1	no	—
597	C₂²⋊C₄	—	4	1	no	—
598	C₂²⋊C₄	—	4	1	no	—
599	C₂²⋊C₄	—	8	2	no	—
600	C₂²⋊C₄	—	8	2	no	—
601	C₄²	—	2	2	no	—
602	C₄²	—	2	1	no	—
603	C₂³	—	2	2	no	—
604	C₂³	—	2	1	no	—
605	C₂³	—	2	1	no	—
606	C₂³	—	2	2	no	—
607	C₂³	—	2	1	no	—
608	C₂³	—	4	1	no	—
609	C₂³	—	4	2	no	—
610	C₂³	—	4	2	no	—
611	C₂³	—	4	2	no	—
612	C₂³	—	4	1	no	—
613	C₂³	—	4	1	no	—
614	C₂³	—	4	1	no	—
615	C₂³	—	8	1	no	—
616	C₂³	—	8	1	no	—
617	C₂³	C₁₉×#120	1	1	yes	characteristic
618	C₂³	C₁₉×#120	1	1	yes	characteristic
619	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
620	Q₈	—	4	1	no	—
621	Q₈	—	4	2	no	—
622	Q₈	—	8	1	no	—
623	Q₈	—	8	2	no	—
624	D₄	—	4	2	no	—
625	D₄	—	4	1	no	—
626	D₄	—	4	2	no	—
627	D₄	—	4	2	no	—
628	D₄	—	4	1	no	—
629	D₄	—	4	1	no	—
630	D₄	—	4	2	no	—
631	D₄	—	4	2	no	—
632	D₄	—	4	1	no	—
633	D₄	—	4	2	no	—
634	D₄	—	4	1	no	—
635	D₄	—	8	2	no	—
636	D₄	—	8	1	no	—
637	D₄	—	8	2	no	—
638	D₄	—	8	2	no	—
639	D₄	—	8	2	no	—
640	D₄	—	8	2	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	2	no	—
656	C₂×C₄	—	4	2	no	—
657	C₂×C₄	—	4	2	no	—
658	C₂×C₄	—	4	2	no	—
659	C₂×C₄	—	4	2	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	2	no	—
662	C₂×C₄	—	8	1	no	—
663	C₂×C₄	—	8	2	no	—
664	C₂×C₄	—	8	2	no	—
665	C₂×C₄	—	8	2	no	—
666	C₂×C₄	—	8	4	no	—
667	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
668	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
669	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
670	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
671	C₈	—	4	1	no	—
672	C₈	—	4	1	no	—
673	C₈	—	4	2	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	2	1	no	—
677	C₂²	—	2	1	no	—
678	C₂²	—	2	1	no	—
679	C₂²	—	2	1	no	—
680	C₂²	—	2	1	no	—
681	C₂²	—	4	2	no	—
682	C₂²	—	4	2	no	—
683	C₂²	—	4	1	no	—
684	C₂²	—	4	2	no	—
685	C₂²	—	4	1	no	—
686	C₂²	—	4	2	no	—
687	C₂²	—	4	1	no	—
688	C₂²	—	4	2	no	—
689	C₂²	—	8	2	no	—
690	C₂²	—	8	2	no	—
691	C₂²	—	8	1	no	—
692	C₂²	—	8	1	no	—
693	C₂²	—	8	1	no	—
694	C₂²	—	16	2	no	—
695	C₂²	C₁₉×#454	1	2	yes	—
696	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
697	C₂²	C₁₉×#576	1	1	yes	characteristic
698	C₂²	C₁₉×#577	1	1	yes	characteristic
699	C₄	—	2	1	no	—
700	C₄	—	2	1	no	—
701	C₄	—	2	1	no	—
702	C₄	—	2	1	no	—
703	C₄	—	4	2	no	—
704	C₄	—	4	2	no	—
705	C₄	—	4	1	no	—
706	C₄	—	4	1	no	—
707	C₄	—	4	1	no	—
708	C₄	—	4	2	no	—
709	C₄	—	8	2	no	—
710	C₄	—	8	1	no	—
711	C₂	—	2	1	no	—
712	C₂	—	2	1	no	—
713	C₂	—	2	2	no	—
714	C₂	—	4	1	no	—
715	C₂	—	8	2	no	—
716	C₂	—	8	1	no	—
717	C₂	—	16	1	no	—
718	C₂	C₁₉×#3012	1	1	yes	characteristic
719	C₂	C₂×C₁₉×#454	1	1	yes	characteristic
720	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×#3192	C₂	semidirect
3. C₁₉×#3188	C₂	semidirect
4. C₁₉×#2639	C₂	semidirect
5. C₁₉×#1616	C₂	semidirect
6. C₁₉×#1615	C₂	semidirect
7. C₁₉×#1598	C₂	semidirect
8. C₁₉×#1597	C₂	semidirect
9. C₁₉×#1504	C₂	semidirect
10. C₂×C₁₉×#327	C₂	semidirect
11. C₁₉×#1472	C₂	semidirect
28. C₁₉×#484	C₂²	semidirect
32. C₁₉×#481	C₂²	semidirect
36. C₁₉×#450	C₂²	semidirect
40. C₁₉×#447	C₂²	semidirect
43. C₁₉×#400	C₂²	semidirect
45. C₁₉×#394	C₂²	semidirect
49. C₁₉×#328	C₂²	semidirect
52. C₁₉×#327	C₂²	semidirect
53. C₁₉×#324	C₂²	semidirect
54. C₁₉×#324	C₂²	semidirect
242. #18424	C₁₉	direct (N × H)
314. #3536	C₂×C₁₉	semidirect
315. #3192	C₂×C₁₉	semidirect
316. #3188	C₂×C₁₉	semidirect
317. #2639	C₂×C₁₉	semidirect
318. #1616	C₂×C₁₉	semidirect
319. #1615	C₂×C₁₉	semidirect
320. #1598	C₂×C₁₉	semidirect
321. #1597	C₂×C₁₉	semidirect
322. #1504	C₂×C₁₉	semidirect
323. C₂×#327	C₂×C₁₉	semidirect
324. #1472	C₂×C₁₉	semidirect
378. #484	C₂²×C₁₉	semidirect
382. #481	C₂²×C₁₉	semidirect
386. #450	C₂²×C₁₉	semidirect
390. #447	C₂²×C₁₉	semidirect
393. #400	C₂²×C₁₉	semidirect
395. #394	C₂²×C₁₉	semidirect
399. #328	C₂²×C₁₉	semidirect
402. #327	C₂²×C₁₉	semidirect
403. #324	C₂²×C₁₉	semidirect
404. #324	C₂²×C₁₉	semidirect
508. C₁₉	#18424	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×#3192	2
C₁₉×#3188	2
C₁₉×#2639	2
C₁₉×#1616	2
C₁₉×#1615	2
C₁₉×#1598	2
C₁₉×#1597	2
C₁₉×#1504	2
C₂×C₁₉×#327	2
C₁₉×#1472	2
#18424	19

Subgroups — C19×#18424 #18024383

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18424 #18024383