Subgroups — C₁₉×#18422 #18024381

Order 4864.

960 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3538	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
4	C₁₉×#2639	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1617	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1615	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1599	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×#328	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1472	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#563	—	2	2	no	—
13	C₁₉×#552	—	2	1	no	—
14	C₁₉×#552	—	2	1	no	—
15	C₁₉×#551	—	2	2	no	—
16	D₄×Q₈×C₁₉	—	2	1	no	—
17	D₄×Q₈×C₁₉	—	2	1	no	—
18	C₁₉×#544	—	2	1	no	—
19	C₁₉×#544	C₂²	1	2	yes	—
20	C₁₉×#541	—	2	1	no	—
21	C₁₉×#539	—	2	1	no	—
22	C₁₉×#539	C₂²	1	2	yes	—
23	C₁₉×#536	—	2	1	no	—
24	C₁₉×#525	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
28	C₁₉×#484	C₂²	1	1	yes	characteristic
29	C₁₉×#484	C₂²	1	2	yes	—
30	C₁₉×#482	—	2	1	no	—
31	C₁₉×#481	C₂²	1	1	yes	characteristic
32	C₁₉×#480	—	2	1	no	—
33	C₁₉×#468	—	2	2	no	—
34	C₁₉×#466	—	2	1	no	—
35	C₁₉×#465	—	2	1	no	—
36	C₁₉×#450	C₂²	1	1	yes	characteristic
37	C₁₉×#450	C₂²	1	2	yes	—
38	C₁₉×#449	—	2	1	no	—
39	C₁₉×#448	—	2	1	no	—
40	C₁₉×#447	C₂²	1	1	yes	characteristic
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	—
44	C₁₉×#397	—	2	1	no	—
45	C₁₉×#394	C₂²	1	2	yes	—
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	—
50	C₁₉×#328	C₂²	1	2	yes	—
51	C₁₉×#328	C₂²	1	2	yes	—
52	C₁₉×#327	C₂²	1	2	yes	—
53	C₁₉×#324	C₂²	1	2	yes	—
54	C₁₉×#324	C₂²	1	2	yes	—
55	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
56	C₂²×Q₈×C₁₉	—	2	1	no	—
57	C₂²×Q₈×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	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₉	—	2	1	no	—
62	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂×SD₁₆×C₁₉	—	2	2	no	—
64	C₂×SD₁₆×C₁₉	—	2	1	no	—
65	C₂×D₈×C₁₉	—	2	1	no	—
66	C₂×M₁₆×C₁₉	—	2	1	no	—
67	C₂²×C₈×C₁₉	—	2	1	no	—
68	C₁₉×C₄⋊Q₈	—	2	1	no	—
69	C₁₉×C₄⋊Q₈	—	2	2	no	—
70	C₁₉×C₄⋊Q₈	—	2	2	no	—
71	C₁₉×C₄⋊Q₈	—	2	2	no	—
72	C₁₉×#126	—	2	2	no	—
73	C₁₉×#126	—	2	2	no	—
74	C₁₉×#126	—	2	2	no	—
75	C₁₉×#126	—	2	2	no	—
76	C₁₉×#125	—	2	1	no	—
77	C₁₉×#125	—	2	2	no	—
78	C₁₉×#125	—	2	2	no	—
79	C₁₉×#125	—	2	2	no	—
80	C₁₉×#125	—	2	2	no	—
81	C₁₉×#124	—	2	2	no	—
82	C₁₉×#123	—	2	2	no	—
83	C₁₉×#123	—	2	2	no	—
84	C₁₉×#123	—	2	2	no	—
85	C₁₉×#123	—	2	1	no	—
86	C₁₉×#123	—	2	2	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	—	2	2	no	—
92	C₁₉×C₂²⋊Q₈	—	2	1	no	—
93	C₁₉×C₂²⋊Q₈	—	2	1	no	—
94	C₁₉×C₂²⋊Q₈	—	2	1	no	—
95	C₁₉×C₂²⋊Q₈	—	2	1	no	—
96	C₁₉×C₂²⋊Q₈	—	2	1	no	—
97	C₁₉×C₂²⋊Q₈	—	2	1	no	—
98	C₁₉×C₂²⋊Q₈	—	2	2	no	—
99	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
100	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
101	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
102	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
108	C₁₉×#121	C₂³	1	1	yes	characteristic
109	C₁₉×#120	—	2	1	no	—
110	C₄×Q₈×C₁₉	—	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	2	no	—
116	C₁₉×#117	—	2	1	no	—
117	C₁₉×#117	—	2	2	no	—
118	C₁₉×#117	—	2	2	no	—
119	C₁₉×#117	D₄	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
121	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
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×#107	—	2	2	no	—
132	C₁₉×#106	—	2	1	no	—
133	C₁₉×#103	—	2	2	no	—
134	C₁₉×#103	—	2	1	no	—
135	C₁₉×#102	—	2	1	no	—
136	C₁₉×#102	—	2	1	no	—
137	C₁₉×#102	—	2	1	no	—
138	C₁₉×#102	—	2	2	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	C₂×D₄	1	1	yes	characteristic
150	#41×C₁₉	—	8	1	no	—
151	C₂×Q₈×C₁₉	—	2	2	no	—
152	C₂×Q₈×C₁₉	—	2	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	—	8	2	no	—
157	C₂×Q₈×C₁₉	—	8	1	no	—
158	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
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	1	no	—
163	C₂×D₄×C₁₉	—	2	1	no	—
164	C₂×D₄×C₁₉	—	2	1	no	—
165	C₂×D₄×C₁₉	—	4	4	no	—
166	C₂×D₄×C₁₉	—	4	1	no	—
167	C₂×D₄×C₁₉	—	4	1	no	—
168	C₂×D₄×C₁₉	—	8	1	no	—
169	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₉	—	2	1	no	—
171	C₂²×C₄×C₁₉	—	2	2	no	—
172	C₂²×C₄×C₁₉	—	2	1	no	—
173	C₂²×C₄×C₁₉	—	2	1	no	—
174	C₂²×C₄×C₁₉	—	2	2	no	—
175	C₂²×C₄×C₁₉	—	2	1	no	—
176	C₂²×C₄×C₁₉	—	4	2	no	—
177	C₂²×C₄×C₁₉	—	8	1	no	—
178	C₂²×C₄×C₁₉	—	8	1	no	—
179	C₂²×C₄×C₁₉	—	8	1	no	—
180	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
181	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
182	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
188	SD₁₆×C₁₉	—	8	1	no	—
189	SD₁₆×C₁₉	—	8	2	no	—
190	D₈×C₁₉	—	8	1	no	—
191	M₁₆×C₁₉	—	8	1	no	—
192	C₂×C₈×C₁₉	—	2	1	no	—
193	C₂×C₈×C₁₉	—	2	1	no	—
194	C₂×C₈×C₁₉	—	2	2	no	—
195	C₂×C₈×C₁₉	—	8	1	no	—
196	C₄⋊C₄×C₁₉	—	2	2	no	—
197	C₄⋊C₄×C₁₉	—	2	2	no	—
198	C₄⋊C₄×C₁₉	—	2	2	no	—
199	C₄⋊C₄×C₁₉	—	2	2	no	—
200	C₄⋊C₄×C₁₉	—	2	2	no	—
201	C₄⋊C₄×C₁₉	—	2	2	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	1	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	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	1	no	—
215	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
216	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
217	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
218	C₂²⋊C₄×C₁₉	—	2	2	no	—
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	1	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	1	no	—
230	C₂²⋊C₄×C₁₉	—	4	1	no	—
231	C₂²⋊C₄×C₁₉	—	4	1	no	—
232	C₂²⋊C₄×C₁₉	—	8	2	no	—
233	C₂²⋊C₄×C₁₉	—	8	2	no	—
234	C₄²×C₁₉	—	2	2	no	—
235	C₄²×C₁₉	—	2	2	no	—
236	C₄²×C₁₉	—	2	2	no	—
237	C₄²×C₁₉	—	2	1	no	—
238	#18422	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₂³×C₁₉	—	2	1	no	—
240	C₂³×C₁₉	—	2	1	no	—
241	C₂³×C₁₉	—	2	2	no	—
242	C₂³×C₁₉	—	2	1	no	—
243	C₂³×C₁₉	—	4	1	no	—
244	C₂³×C₁₉	—	4	2	no	—
245	C₂³×C₁₉	—	4	2	no	—
246	C₂³×C₁₉	—	4	1	no	—
247	C₂³×C₁₉	—	4	1	no	—
248	C₂³×C₁₉	—	4	1	no	—
249	C₂³×C₁₉	#120	1	1	yes	characteristic
250	C₂³×C₁₉	#120	1	1	yes	characteristic
251	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
252	Q₈×C₁₉	—	4	2	no	—
253	Q₈×C₁₉	—	4	1	no	—
254	Q₈×C₁₉	—	4	2	no	—
255	Q₈×C₁₉	—	4	2	no	—
256	Q₈×C₁₉	—	8	1	no	—
257	Q₈×C₁₉	—	8	2	no	—
258	D₄×C₁₉	—	4	1	no	—
259	D₄×C₁₉	—	4	1	no	—
260	D₄×C₁₉	—	4	1	no	—
261	D₄×C₁₉	—	4	2	no	—
262	D₄×C₁₉	—	4	1	no	—
263	D₄×C₁₉	—	4	1	no	—
264	D₄×C₁₉	—	4	2	no	—
265	D₄×C₁₉	—	8	1	no	—
266	D₄×C₁₉	—	8	2	no	—
267	D₄×C₁₉	—	8	2	no	—
268	C₂×C₄×C₁₉	—	2	1	no	—
269	C₂×C₄×C₁₉	—	2	1	no	—
270	C₂×C₄×C₁₉	—	2	2	no	—
271	C₂×C₄×C₁₉	—	2	2	no	—
272	C₂×C₄×C₁₉	—	2	1	no	—
273	C₂×C₄×C₁₉	—	2	2	no	—
274	C₂×C₄×C₁₉	—	2	2	no	—
275	C₂×C₄×C₁₉	—	2	2	no	—
276	C₂×C₄×C₁₉	—	2	2	no	—
277	C₂×C₄×C₁₉	—	4	1	no	—
278	C₂×C₄×C₁₉	—	4	1	no	—
279	C₂×C₄×C₁₉	—	4	1	no	—
280	C₂×C₄×C₁₉	—	4	1	no	—
281	C₂×C₄×C₁₉	—	4	1	no	—
282	C₂×C₄×C₁₉	—	4	1	no	—
283	C₂×C₄×C₁₉	—	4	2	no	—
284	C₂×C₄×C₁₉	—	4	2	no	—
285	C₂×C₄×C₁₉	—	4	2	no	—
286	C₂×C₄×C₁₉	—	4	2	no	—
287	C₂×C₄×C₁₉	—	4	2	no	—
288	C₂×C₄×C₁₉	—	4	2	no	—
289	C₂×C₄×C₁₉	—	4	1	no	—
290	C₂×C₄×C₁₉	—	4	2	no	—
291	C₂×C₄×C₁₉	—	8	1	no	—
292	C₂×C₄×C₁₉	—	8	2	no	—
293	C₂×C₄×C₁₉	—	8	4	no	—
294	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
295	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
296	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
297	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
298	C₈×C₁₉	—	4	1	no	—
299	C₈×C₁₉	—	4	1	no	—
300	C₈×C₁₉	—	4	2	no	—
301	#3538	C₂×C₁₉	1	1	yes	characteristic, complemented
302	#3193	C₂×C₁₉	1	1	yes	characteristic, complemented
303	#3188	C₂×C₁₉	1	1	yes	characteristic
304	#2639	C₂×C₁₉	1	1	yes	characteristic, complemented
305	#1617	C₂×C₁₉	1	2	yes	complemented
306	#1615	C₂×C₁₉	1	2	yes	complemented
307	#1599	C₂×C₁₉	1	2	yes	complemented
308	#1597	C₂×C₁₉	1	2	yes	complemented
309	#1504	C₂×C₁₉	1	1	yes	characteristic, complemented
310	C₂×#328	C₂×C₁₉	1	1	yes	characteristic, complemented
311	#1472	C₂×C₁₉	1	1	yes	characteristic, complemented
312	C₂²×C₁₉	—	2	1	no	—
313	C₂²×C₁₉	—	2	1	no	—
314	C₂²×C₁₉	—	2	1	no	—
315	C₂²×C₁₉	—	2	1	no	—
316	C₂²×C₁₉	—	2	1	no	—
317	C₂²×C₁₉	—	2	1	no	—
318	C₂²×C₁₉	—	2	1	no	—
319	C₂²×C₁₉	—	4	2	no	—
320	C₂²×C₁₉	—	4	2	no	—
321	C₂²×C₁₉	—	4	1	no	—
322	C₂²×C₁₉	—	4	1	no	—
323	C₂²×C₁₉	—	4	1	no	—
324	C₂²×C₁₉	—	8	2	no	—
325	C₂²×C₁₉	—	8	2	no	—
326	C₂²×C₁₉	—	8	1	no	—
327	C₂²×C₁₉	—	8	1	no	—
328	C₂²×C₁₉	—	8	1	no	—
329	C₂²×C₁₉	#454	1	2	yes	—
330	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
331	C₂²×C₁₉	#577	1	1	yes	characteristic
332	C₂²×C₁₉	#578	1	1	yes	characteristic
333	C₄×C₁₉	—	2	1	no	—
334	C₄×C₁₉	—	2	1	no	—
335	C₄×C₁₉	—	2	1	no	—
336	C₄×C₁₉	—	2	1	no	—
337	C₄×C₁₉	—	4	2	no	—
338	C₄×C₁₉	—	4	1	no	—
339	C₄×C₁₉	—	4	2	no	—
340	C₄×C₁₉	—	4	1	no	—
341	C₄×C₁₉	—	4	1	no	—
342	C₄×C₁₉	—	4	2	no	—
343	C₄×C₁₉	—	4	2	no	—
344	C₄×C₁₉	—	8	2	no	—
345	C₄×C₁₉	—	8	1	no	—
346	#563	—	2	2	no	—
347	#552	—	2	1	no	—
348	#552	—	2	1	no	—
349	#551	—	2	2	no	—
350	D₄×Q₈	—	2	1	no	—
351	D₄×Q₈	—	2	1	no	—
352	#544	—	2	1	no	—
353	#544	C₂²×C₁₉	1	2	yes	—
354	#541	—	2	1	no	—
355	#539	—	2	1	no	—
356	#539	C₂²×C₁₉	1	2	yes	—
357	#536	—	2	1	no	—
358	#525	C₂²×C₁₉	1	1	yes	characteristic
359	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
360	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
361	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
362	#484	C₂²×C₁₉	1	2	yes	—
363	#484	C₂²×C₁₉	1	1	yes	characteristic
364	#482	—	2	1	no	—
365	#481	C₂²×C₁₉	1	1	yes	characteristic
366	#480	—	2	1	no	—
367	#468	—	2	2	no	—
368	#466	—	2	1	no	—
369	#465	—	2	1	no	—
370	#450	C₂²×C₁₉	1	2	yes	—
371	#450	C₂²×C₁₉	1	1	yes	characteristic
372	#449	—	2	1	no	—
373	#448	—	2	1	no	—
374	#447	C₂²×C₁₉	1	1	yes	characteristic
375	#407	C₂²×C₁₉	1	1	yes	characteristic
376	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
377	#400	C₂²×C₁₉	1	2	yes	—
378	#397	—	2	1	no	—
379	#394	C₂²×C₁₉	1	2	yes	—
380	#393	—	2	1	no	—
381	#386	—	2	2	no	—
382	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
383	#328	C₂²×C₁₉	1	2	yes	—
384	#328	C₂²×C₁₉	1	2	yes	—
385	#328	C₂²×C₁₉	1	2	yes	—
386	#327	C₂²×C₁₉	1	2	yes	—
387	#324	C₂²×C₁₉	1	2	yes	—
388	#324	C₂²×C₁₉	1	2	yes	—
389	C₂×C₁₉	—	2	1	no	—
390	C₂×C₁₉	—	2	1	no	—
391	C₂×C₁₉	—	2	2	no	—
392	C₂×C₁₉	—	4	1	no	—
393	C₂×C₁₉	—	8	1	no	—
394	C₂×C₁₉	—	16	1	no	—
395	C₂×C₁₉	#3013	1	1	yes	characteristic
396	C₂×C₁₉	C₂×#454	1	1	yes	characteristic
397	C₂×C₁₉	#3026	1	1	yes	characteristic
398	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
399	C₂²×Q₈	—	2	1	no	—
400	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
401	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
402	C₂²×D₄	—	2	1	no	—
403	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
404	C₂³×C₄	—	2	1	no	—
405	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
406	C₂×SD₁₆	—	2	2	no	—
407	C₂×SD₁₆	—	2	1	no	—
408	C₂×D₈	—	2	1	no	—
409	C₂×M₁₆	—	2	1	no	—
410	C₂²×C₈	—	2	1	no	—
411	C₄⋊Q₈	—	2	1	no	—
412	C₄⋊Q₈	—	2	2	no	—
413	C₄⋊Q₈	—	2	2	no	—
414	C₄⋊Q₈	—	2	2	no	—
415	#126	—	2	2	no	—
416	#126	—	2	2	no	—
417	#126	—	2	2	no	—
418	#126	—	2	2	no	—
419	#125	—	2	1	no	—
420	#125	—	2	2	no	—
421	#125	—	2	2	no	—
422	#125	—	2	2	no	—
423	#125	—	2	2	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	1	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	1	no	—
440	C₂²⋊Q₈	—	2	1	no	—
441	C₂²⋊Q₈	—	2	2	no	—
442	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
443	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
444	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
445	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
446	#121	—	2	1	no	—
447	#121	—	2	1	no	—
448	#121	—	2	1	no	—
449	#121	—	2	1	no	—
450	#121	D₄×C₁₉	1	1	yes	characteristic
451	#121	C₂³×C₁₉	1	1	yes	characteristic
452	#120	—	2	1	no	—
453	C₄×Q₈	—	2	1	no	—
454	C₄×Q₈	—	2	1	no	—
455	C₄×D₄	—	2	2	no	—
456	C₄×D₄	—	2	1	no	—
457	C₄×D₄	—	2	1	no	—
458	C₄×D₄	—	2	2	no	—
459	#117	—	2	1	no	—
460	#117	—	2	2	no	—
461	#117	—	2	2	no	—
462	#117	D₄×C₁₉	1	1	yes	characteristic
463	C₂×C₄⋊C₄	—	2	1	no	—
464	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
465	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
466	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
467	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
468	C₂×C₂²⋊C₄	—	2	1	no	—
469	C₂×C₂²⋊C₄	—	2	1	no	—
470	C₂×C₂²⋊C₄	—	2	2	no	—
471	C₂×C₂²⋊C₄	—	2	2	no	—
472	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
473	#107	—	2	1	no	—
474	#107	—	2	2	no	—
475	#106	—	2	1	no	—
476	#103	—	2	2	no	—
477	#103	—	2	1	no	—
478	#102	—	2	1	no	—
479	#102	—	2	1	no	—
480	#102	—	2	1	no	—
481	#102	—	2	2	no	—
482	C₂²⋊C₈	—	2	1	no	—
483	C₂²⋊C₈	—	2	1	no	—
484	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
485	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
486	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
487	#95	—	2	1	no	—
488	#95	—	2	2	no	—
489	#95	—	2	2	no	—
490	#95	C₂³×C₁₉	1	2	yes	—
491	C₁₉	#18422	1	1	yes	characteristic, direct product factor, Sylow
492	C₂⁴	—	2	1	no	—
493	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
494	#41	—	8	1	no	—
495	C₂×Q₈	—	2	2	no	—
496	C₂×Q₈	—	2	1	no	—
497	C₂×Q₈	—	2	1	no	—
498	C₂×Q₈	—	2	1	no	—
499	C₂×Q₈	—	8	1	no	—
500	C₂×Q₈	—	8	2	no	—
501	C₂×Q₈	—	8	1	no	—
502	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
503	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
504	C₂×D₄	—	2	1	no	—
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	4	4	no	—
510	C₂×D₄	—	4	1	no	—
511	C₂×D₄	—	4	1	no	—
512	C₂×D₄	—	8	1	no	—
513	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	2	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	2	no	—
520	C₂²×C₄	—	4	2	no	—
521	C₂²×C₄	—	8	1	no	—
522	C₂²×C₄	—	8	1	no	—
523	C₂²×C₄	—	8	1	no	—
524	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
525	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
526	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
527	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
528	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
529	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
530	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
531	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
532	SD₁₆	—	8	1	no	—
533	SD₁₆	—	8	2	no	—
534	D₈	—	8	1	no	—
535	M₁₆	—	8	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	2	no	—
539	C₂×C₈	—	8	1	no	—
540	C₄⋊C₄	—	2	2	no	—
541	C₄⋊C₄	—	2	2	no	—
542	C₄⋊C₄	—	2	2	no	—
543	C₄⋊C₄	—	2	2	no	—
544	C₄⋊C₄	—	2	2	no	—
545	C₄⋊C₄	—	2	2	no	—
546	C₄⋊C₄	—	2	2	no	—
547	C₄⋊C₄	—	2	2	no	—
548	C₄⋊C₄	—	2	2	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	2	1	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	2	no	—
554	C₄⋊C₄	—	2	2	no	—
555	C₄⋊C₄	—	2	2	no	—
556	C₄⋊C₄	—	2	1	no	—
557	C₄⋊C₄	—	2	1	no	—
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
560	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
561	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
562	C₂²⋊C₄	—	2	2	no	—
563	C₂²⋊C₄	—	2	2	no	—
564	C₂²⋊C₄	—	2	2	no	—
565	C₂²⋊C₄	—	2	2	no	—
566	C₂²⋊C₄	—	2	2	no	—
567	C₂²⋊C₄	—	2	2	no	—
568	C₂²⋊C₄	—	2	1	no	—
569	C₂²⋊C₄	—	2	1	no	—
570	C₂²⋊C₄	—	2	2	no	—
571	C₂²⋊C₄	—	2	1	no	—
572	C₂²⋊C₄	—	2	1	no	—
573	C₂²⋊C₄	—	2	1	no	—
574	C₂²⋊C₄	—	4	1	no	—
575	C₂²⋊C₄	—	4	1	no	—
576	C₂²⋊C₄	—	8	2	no	—
577	C₂²⋊C₄	—	8	2	no	—
578	C₄²	—	2	2	no	—
579	C₄²	—	2	2	no	—
580	C₄²	—	2	2	no	—
581	C₄²	—	2	1	no	—
582	C₂³	—	2	2	no	—
583	C₂³	—	2	1	no	—
584	C₂³	—	2	1	no	—
585	C₂³	—	2	1	no	—
586	C₂³	—	4	1	no	—
587	C₂³	—	4	2	no	—
588	C₂³	—	4	2	no	—
589	C₂³	—	4	1	no	—
590	C₂³	—	4	1	no	—
591	C₂³	—	4	1	no	—
592	C₂³	C₁₉×#120	1	1	yes	characteristic
593	C₂³	C₁₉×#120	1	1	yes	characteristic
594	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
595	Q₈	—	4	2	no	—
596	Q₈	—	4	1	no	—
597	Q₈	—	4	2	no	—
598	Q₈	—	4	2	no	—
599	Q₈	—	8	1	no	—
600	Q₈	—	8	2	no	—
601	D₄	—	4	1	no	—
602	D₄	—	4	1	no	—
603	D₄	—	4	1	no	—
604	D₄	—	4	2	no	—
605	D₄	—	4	2	no	—
606	D₄	—	4	1	no	—
607	D₄	—	4	1	no	—
608	D₄	—	8	1	no	—
609	D₄	—	8	2	no	—
610	D₄	—	8	2	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	2	no	—
627	C₂×C₄	—	4	2	no	—
628	C₂×C₄	—	4	2	no	—
629	C₂×C₄	—	4	2	no	—
630	C₂×C₄	—	4	2	no	—
631	C₂×C₄	—	4	2	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	2	no	—
634	C₂×C₄	—	8	1	no	—
635	C₂×C₄	—	8	2	no	—
636	C₂×C₄	—	8	4	no	—
637	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
638	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
639	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
640	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
641	C₈	—	4	1	no	—
642	C₈	—	4	1	no	—
643	C₈	—	4	2	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	1	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	2	1	no	—
650	C₂²	—	2	1	no	—
651	C₂²	—	4	2	no	—
652	C₂²	—	4	2	no	—
653	C₂²	—	4	1	no	—
654	C₂²	—	4	1	no	—
655	C₂²	—	4	1	no	—
656	C₂²	—	8	2	no	—
657	C₂²	—	8	2	no	—
658	C₂²	—	8	1	no	—
659	C₂²	—	8	1	no	—
660	C₂²	—	8	1	no	—
661	C₂²	C₁₉×#454	1	2	yes	—
662	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
663	C₂²	C₁₉×#577	1	1	yes	characteristic
664	C₂²	C₁₉×#578	1	1	yes	characteristic
665	C₄	—	2	1	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	1	no	—
668	C₄	—	2	1	no	—
669	C₄	—	4	2	no	—
670	C₄	—	4	1	no	—
671	C₄	—	4	2	no	—
672	C₄	—	4	1	no	—
673	C₄	—	4	1	no	—
674	C₄	—	4	2	no	—
675	C₄	—	4	2	no	—
676	C₄	—	8	2	no	—
677	C₄	—	8	1	no	—
678	C₂	—	2	1	no	—
679	C₂	—	2	1	no	—
680	C₂	—	2	2	no	—
681	C₂	—	4	1	no	—
682	C₂	—	8	1	no	—
683	C₂	—	16	1	no	—
684	C₂	C₁₉×#3013	1	1	yes	characteristic
685	C₂	C₂×C₁₉×#454	1	1	yes	characteristic
686	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×#3188	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
1. C₁₉×#3538	C₂	semidirect
2. C₁₉×#3193	C₂	semidirect
4. C₁₉×#2639	C₂	semidirect
5. C₁₉×#1617	C₂	semidirect
6. C₁₉×#1615	C₂	semidirect
7. C₁₉×#1599	C₂	semidirect
8. C₁₉×#1597	C₂	semidirect
9. C₁₉×#1504	C₂	semidirect
10. C₂×C₁₉×#328	C₂	semidirect
11. C₁₉×#1472	C₂	semidirect
238. #18422	C₁₉	direct (N × H)
301. #3538	C₂×C₁₉	semidirect
302. #3193	C₂×C₁₉	semidirect
304. #2639	C₂×C₁₉	semidirect
305. #1617	C₂×C₁₉	semidirect
306. #1615	C₂×C₁₉	semidirect
307. #1599	C₂×C₁₉	semidirect
308. #1597	C₂×C₁₉	semidirect
309. #1504	C₂×C₁₉	semidirect
310. C₂×#328	C₂×C₁₉	semidirect
311. #1472	C₂×C₁₉	semidirect
491. C₁₉	#18422	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×#3538	2
C₁₉×#3193	2
C₁₉×#3188	2
C₁₉×#2639	2
C₁₉×#1617	2
C₁₉×#1615	2
C₁₉×#1599	2
C₁₉×#1597	2
C₁₉×#1504	2
C₂×C₁₉×#328	2
C₁₉×#1472	2
#18422	19

Subgroups — C19×#18422 #18024381

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18422 #18024381