Subgroups — C₁₉×#19018 #18024977

Order 4864.

1034 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3558	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3214	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3171	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3153	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1661	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1659	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1656	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1655	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1529	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1527	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1525	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×#137	—	2	1	no	—
13	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
14	C₁₉×#562	C₂²	1	2	yes	—
15	C₁₉×H(3,𝔽₄)	C₂²	1	2	yes	—
16	C₁₉×#559	—	2	1	no	—
17	C₁₉×#548	—	2	1	no	—
18	C₁₉×#546	—	2	2	no	—
19	C₁₉×#546	—	2	1	no	—
20	D₄²×C₁₉	—	2	1	no	—
21	C₁₉×#542	—	2	1	no	—
22	C₁₉×#538	—	2	2	no	—
23	C₁₉×#538	—	2	1	no	—
24	C₁₉×#535	—	2	1	no	—
25	C₁₉×#534	—	2	1	no	—
26	C₁₉×#532	C₂²	1	1	yes	characteristic
27	C₁₉×#532	C₂²	1	1	yes	characteristic, complemented
28	C₁₉×#529	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
30	C₁₉×#501	C₂²	1	1	yes	characteristic, complemented
31	C₁₉×#497	C₂²	1	2	yes	complemented
32	C₁₉×#496	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×#496	C₂²	1	2	yes	complemented
34	C₁₉×#496	C₂²	1	2	yes	complemented
35	C₁₉×#495	—	2	2	no	—
36	C₁₉×#490	C₂²	1	1	yes	characteristic, complemented
37	C₁₉×#489	C₂²	1	1	yes	characteristic, complemented
38	C₁₉×#489	C₂²	1	2	yes	complemented
39	C₁₉×#469	—	2	1	no	—
40	C₁₉×#468	—	2	1	no	—
41	C₁₉×#461	—	2	1	no	—
42	C₁₉×#459	—	2	1	no	—
43	C₁₉×#449	—	2	2	no	—
44	C₄×SD₁₆×C₁₉	—	2	1	no	—
45	C₄×D₈×C₁₉	—	2	1	no	—
46	C₁₉×#432	C₂²	1	1	yes	characteristic, complemented
47	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
48	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
49	C₁₉×#330	C₂²	1	2	yes	complemented
50	C₁₉×#329	C₂²	1	2	yes	complemented
51	C₁₉×#329	C₂²	1	2	yes	complemented
52	C₁₉×#329	C₂²	1	2	yes	complemented
53	C₁₉×#329	C₂²	1	2	yes	complemented
54	C₁₉×#329	C₂²	1	2	yes	complemented
55	C₂×#41×C₁₉	—	2	1	no	—
56	C₂×#41×C₁₉	—	2	1	no	—
57	C₂×#41×C₁₉	D₄	1	2	yes	—
58	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
59	C₂²×D₄×C₁₉	—	2	2	no	—
60	C₂²×D₄×C₁₉	—	2	1	no	—
61	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
62	C₁₉×#137	—	4	4	no	—
63	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
64	C₂×Q₁₆×C₁₉	—	2	2	no	—
65	C₂×SD₁₆×C₁₉	—	2	1	no	—
66	C₂×SD₁₆×C₁₉	—	2	2	no	—
67	C₂×SD₁₆×C₁₉	—	2	2	no	—
68	C₂×SD₁₆×C₁₉	—	2	2	no	—
69	C₂×D₈×C₁₉	—	2	1	no	—
70	C₂×D₈×C₁₉	—	2	2	no	—
71	C₂×D₈×C₁₉	—	2	2	no	—
72	C₂×M₁₆×C₁₉	—	2	1	no	—
73	C₂×M₁₆×C₁₉	—	2	1	no	—
74	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
75	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
76	C₁₉×#127	—	2	1	no	—
77	C₁₉×#127	D₄	1	1	yes	characteristic
78	C₁₉×#127	C₂³	1	1	yes	characteristic
79	C₁₉×#126	—	2	2	no	—
80	C₁₉×#126	—	2	1	no	—
81	C₁₉×#125	C₂³	1	1	yes	characteristic
82	C₁₉×#124	—	2	1	no	—
83	C₁₉×#124	—	2	2	no	—
84	C₁₉×#124	—	2	2	no	—
85	C₁₉×#124	—	2	2	no	—
86	C₁₉×#124	—	2	1	no	—
87	C₁₉×#124	—	2	1	no	—
88	C₁₉×#124	—	2	1	no	—
89	C₁₉×#124	D₄	1	2	yes	—
90	C₁₉×#124	C₂³	1	1	yes	characteristic
91	C₁₉×#124	C₂³	1	2	yes	—
92	C₁₉×#124	C₂³	1	2	yes	—
93	C₁₉×#123	—	2	2	no	—
94	C₁₉×#123	—	2	2	no	—
95	C₁₉×#123	—	2	1	no	—
96	C₁₉×#123	—	2	2	no	—
97	C₁₉×#123	—	2	2	no	—
98	C₁₉×C₂²⋊Q₈	—	2	1	no	—
99	C₁₉×C₂²⋊Q₈	—	2	2	no	—
100	C₁₉×C₂²⋊Q₈	—	2	2	no	—
101	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
102	C₁₉×#121	—	2	2	no	—
103	C₁₉×#121	—	2	2	no	—
104	C₁₉×#121	—	2	2	no	—
105	C₁₉×#121	—	2	1	no	—
106	C₁₉×#121	—	2	2	no	—
107	C₁₉×#121	—	2	2	no	—
108	C₁₉×#121	—	2	1	no	—
109	C₁₉×#121	—	2	1	no	—
110	C₁₉×#121	—	2	1	no	—
111	C₁₉×#121	—	2	1	no	—
112	C₁₉×#121	D₄	1	1	yes	characteristic
113	C₁₉×#120	—	2	2	no	—
114	C₁₉×#120	—	2	2	no	—
115	C₁₉×#120	—	2	2	no	—
116	C₁₉×#120	—	2	2	no	—
117	C₁₉×#120	—	2	2	no	—
118	C₄×Q₈×C₁₉	—	2	1	no	—
119	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
120	C₄×D₄×C₁₉	—	2	2	no	—
121	C₄×D₄×C₁₉	—	2	2	no	—
122	C₄×D₄×C₁₉	—	2	1	no	—
123	C₄×D₄×C₁₉	—	2	1	no	—
124	C₄×D₄×C₁₉	—	2	1	no	—
125	C₄×D₄×C₁₉	—	2	1	no	—
126	C₄×D₄×C₁₉	—	2	1	no	—
127	C₄×D₄×C₁₉	—	2	1	no	—
128	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
129	C₁₉×#117	—	2	1	no	—
130	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
131	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
132	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
133	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
134	C₁₉×#107	—	2	1	no	—
135	C₁₉×#106	—	2	1	no	—
136	C₁₉×C₄⋊C₈	—	2	1	no	—
137	C₁₉×#103	—	2	1	no	—
138	C₁₉×#103	—	2	2	no	—
139	C₁₉×#102	—	2	1	no	—
140	C₁₉×#102	—	2	2	no	—
141	C₁₉×#102	—	2	1	no	—
142	C₁₉×#102	—	2	1	no	—
143	C₁₉×C₂²⋊C₈	—	2	1	no	—
144	C₁₉×#97	C₂³	1	1	yes	characteristic
145	C₁₉×#97	C₂³	1	2	yes	—
146	C₁₉×#97	C₂³	1	1	yes	characteristic
147	C₁₉×#97	C₂³	1	2	yes	—
148	C₄×C₈×C₁₉	—	2	1	no	—
149	C₄×C₈×C₁₉	—	2	1	no	—
150	C₂⁴×C₁₉	—	2	2	no	—
151	C₂⁴×C₁₉	—	2	1	no	—
152	#41×C₁₉	—	4	2	no	—
153	#41×C₁₉	—	4	2	no	—
154	#41×C₁₉	—	8	2	no	—
155	#41×C₁₉	—	8	2	no	—
156	C₂×Q₈×C₁₉	—	2	1	no	—
157	C₂×Q₈×C₁₉	—	2	1	no	—
158	C₂×Q₈×C₁₉	—	4	2	no	—
159	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
160	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
161	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
162	C₂×D₄×C₁₉	—	2	2	no	—
163	C₂×D₄×C₁₉	—	2	1	no	—
164	C₂×D₄×C₁₉	—	2	2	no	—
165	C₂×D₄×C₁₉	—	2	2	no	—
166	C₂×D₄×C₁₉	—	2	2	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	—	2	1	no	—
173	C₂×D₄×C₁₉	—	2	1	no	—
174	C₂×D₄×C₁₉	—	2	1	no	—
175	C₂×D₄×C₁₉	—	4	2	no	—
176	C₂×D₄×C₁₉	—	4	1	no	—
177	C₂×D₄×C₁₉	—	8	2	no	—
178	C₂×D₄×C₁₉	—	8	4	no	—
179	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
180	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
181	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
182	C₂²×C₄×C₁₉	—	2	2	no	—
183	C₂²×C₄×C₁₉	—	2	2	no	—
184	C₂²×C₄×C₁₉	—	2	1	no	—
185	C₂²×C₄×C₁₉	—	2	1	no	—
186	C₂²×C₄×C₁₉	—	2	2	no	—
187	C₂²×C₄×C₁₉	—	4	1	no	—
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	Q₁₆×C₁₉	—	4	4	no	—
192	SD₁₆×C₁₉	—	4	2	no	—
193	SD₁₆×C₁₉	—	4	4	no	—
194	SD₁₆×C₁₉	—	4	4	no	—
195	SD₁₆×C₁₉	—	8	2	no	—
196	D₈×C₁₉	—	4	2	no	—
197	D₈×C₁₉	—	4	4	no	—
198	D₈×C₁₉	—	8	2	no	—
199	M₁₆×C₁₉	—	2	4	no	—
200	M₁₆×C₁₉	—	4	2	no	—
201	C₂×C₈×C₁₉	—	2	2	no	—
202	C₂×C₈×C₁₉	—	2	1	no	—
203	C₂×C₈×C₁₉	—	2	1	no	—
204	C₂×C₈×C₁₉	—	2	2	no	—
205	C₄⋊C₄×C₁₉	—	2	2	no	—
206	C₄⋊C₄×C₁₉	—	2	2	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	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	1	no	—
215	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
216	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
217	C₂²⋊C₄×C₁₉	—	2	2	no	—
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	1	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	1	no	—
227	C₂²⋊C₄×C₁₉	—	2	2	no	—
228	C₂²⋊C₄×C₁₉	—	2	2	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	2	no	—
233	C₂²⋊C₄×C₁₉	—	4	1	no	—
234	C₂²⋊C₄×C₁₉	—	4	1	no	—
235	C₄²×C₁₉	—	2	2	no	—
236	C₄²×C₁₉	—	2	1	no	—
237	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
238	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
239	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
240	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
241	#19018	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
242	C₂³×C₁₉	—	2	1	no	—
243	C₂³×C₁₉	—	2	2	no	—
244	C₂³×C₁₉	—	2	2	no	—
245	C₂³×C₁₉	—	4	2	no	—
246	C₂³×C₁₉	—	4	1	no	—
247	C₂³×C₁₉	—	8	1	no	—
248	C₂³×C₁₉	—	8	1	no	—
249	C₂³×C₁₉	—	8	2	no	—
250	C₂³×C₁₉	—	8	2	no	—
251	C₂³×C₁₉	—	8	2	no	—
252	C₂³×C₁₉	#120	1	1	yes	characteristic
253	Q₈×C₁₉	—	4	2	no	—
254	Q₈×C₁₉	—	4	1	no	—
255	Q₈×C₁₉	—	4	2	no	—
256	Q₈×C₁₉	—	4	1	no	—
257	Q₈×C₁₉	—	4	1	no	—
258	Q₈×C₁₉	—	4	2	no	—
259	D₄×C₁₉	—	4	2	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	1	no	—
265	D₄×C₁₉	—	4	1	no	—
266	D₄×C₁₉	—	4	1	no	—
267	D₄×C₁₉	—	4	1	no	—
268	D₄×C₁₉	—	4	2	no	—
269	D₄×C₁₉	—	4	4	no	—
270	D₄×C₁₉	—	4	2	no	—
271	D₄×C₁₉	—	4	2	no	—
272	D₄×C₁₉	—	8	1	no	—
273	D₄×C₁₉	—	8	2	no	—
274	D₄×C₁₉	—	8	2	no	—
275	D₄×C₁₉	—	8	2	no	—
276	D₄×C₁₉	—	8	2	no	—
277	D₄×C₁₉	—	8	2	no	—
278	D₄×C₁₉	—	8	2	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	1	no	—
284	C₂×C₄×C₁₉	—	2	1	no	—
285	C₂×C₄×C₁₉	—	4	1	no	—
286	C₂×C₄×C₁₉	—	4	1	no	—
287	C₂×C₄×C₁₉	—	4	2	no	—
288	C₂×C₄×C₁₉	—	4	1	no	—
289	C₂×C₄×C₁₉	—	8	2	no	—
290	C₂×C₄×C₁₉	—	8	1	no	—
291	C₂×C₄×C₁₉	—	8	2	no	—
292	C₂×C₄×C₁₉	—	8	2	no	—
293	C₂×C₄×C₁₉	—	8	2	no	—
294	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
295	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
296	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
297	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
298	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
299	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
300	C₈×C₁₉	—	2	4	no	—
301	C₈×C₁₉	—	2	2	no	—
302	C₈×C₁₉	—	4	1	no	—
303	C₈×C₁₉	—	4	2	no	—
304	#3558	C₂×C₁₉	1	1	yes	characteristic, complemented
305	#3214	C₂×C₁₉	1	1	yes	characteristic, complemented
306	#3171	C₂×C₁₉	1	1	yes	characteristic, complemented
307	#3153	C₂×C₁₉	1	1	yes	characteristic, complemented
308	#1661	C₂×C₁₉	1	2	yes	complemented
309	#1659	C₂×C₁₉	1	2	yes	complemented
310	#1656	C₂×C₁₉	1	2	yes	complemented
311	#1655	C₂×C₁₉	1	2	yes	complemented
312	#1529	C₂×C₁₉	1	1	yes	characteristic, complemented
313	#1527	C₂×C₁₉	1	1	yes	characteristic, complemented
314	#1525	C₂×C₁₉	1	1	yes	characteristic, complemented
315	C₂²×C₁₉	—	2	1	no	—
316	C₂²×C₁₉	—	2	1	no	—
317	C₂²×C₁₉	—	2	1	no	—
318	C₂²×C₁₉	—	4	1	no	—
319	C₂²×C₁₉	—	4	2	no	—
320	C₂²×C₁₉	—	4	2	no	—
321	C₂²×C₁₉	—	4	1	no	—
322	C₂²×C₁₉	—	4	2	no	—
323	C₂²×C₁₉	—	4	2	no	—
324	C₂²×C₁₉	—	4	2	no	—
325	C₂²×C₁₉	—	4	2	no	—
326	C₂²×C₁₉	—	4	1	no	—
327	C₂²×C₁₉	—	8	1	no	—
328	C₂²×C₁₉	—	8	1	no	—
329	C₂²×C₁₉	—	8	1	no	—
330	C₂²×C₁₉	—	16	2	no	—
331	C₂²×C₁₉	—	16	4	no	—
332	C₂²×C₁₉	C₂×#120	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	—	2	1	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	—	8	1	no	—
344	C₄×C₁₉	#453	1	2	yes	—
345	C₂×#137	—	2	1	no	—
346	C₂×AGL(1,ℤ/8)	—	2	1	no	—
347	#562	C₂²×C₁₉	1	2	yes	—
348	H(3,𝔽₄)	C₂²×C₁₉	1	2	yes	—
349	#559	—	2	1	no	—
350	#548	—	2	1	no	—
351	#546	—	2	2	no	—
352	#546	—	2	1	no	—
353	D₄²	—	2	1	no	—
354	#542	—	2	1	no	—
355	#538	—	2	2	no	—
356	#538	—	2	1	no	—
357	#535	—	2	1	no	—
358	#534	—	2	1	no	—
359	#532	C₂²×C₁₉	1	1	yes	characteristic
360	#532	C₂²×C₁₉	1	1	yes	characteristic, complemented
361	#529	C₂²×C₁₉	1	1	yes	characteristic
362	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
363	#501	C₂²×C₁₉	1	1	yes	characteristic, complemented
364	#497	C₂²×C₁₉	1	2	yes	complemented
365	#496	C₂²×C₁₉	1	2	yes	complemented
366	#496	C₂²×C₁₉	1	1	yes	characteristic, complemented
367	#496	C₂²×C₁₉	1	2	yes	complemented
368	#495	—	2	2	no	—
369	#490	C₂²×C₁₉	1	1	yes	characteristic, complemented
370	#489	C₂²×C₁₉	1	1	yes	characteristic, complemented
371	#489	C₂²×C₁₉	1	2	yes	complemented
372	#469	—	2	1	no	—
373	#468	—	2	1	no	—
374	#461	—	2	1	no	—
375	#459	—	2	1	no	—
376	#449	—	2	2	no	—
377	C₄×SD₁₆	—	2	1	no	—
378	C₄×D₈	—	2	1	no	—
379	#432	C₂²×C₁₉	1	1	yes	characteristic, complemented
380	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
381	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
382	#330	C₂²×C₁₉	1	2	yes	complemented
383	#329	C₂²×C₁₉	1	2	yes	complemented
384	#329	C₂²×C₁₉	1	2	yes	complemented
385	#329	C₂²×C₁₉	1	2	yes	complemented
386	#329	C₂²×C₁₉	1	2	yes	complemented
387	#329	C₂²×C₁₉	1	2	yes	complemented
388	C₂×C₁₉	—	4	1	no	—
389	C₂×C₁₉	—	8	2	no	—
390	C₂×C₁₉	—	8	1	no	—
391	C₂×C₁₉	—	8	2	no	—
392	C₂×C₁₉	—	16	1	no	—
393	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
394	C₂×C₁₉	#3018	1	1	yes	characteristic
395	C₂×C₁₉	#3019	1	1	yes	characteristic
396	C₂×#41	—	2	1	no	—
397	C₂×#41	—	2	1	no	—
398	C₂×#41	D₄×C₁₉	1	2	yes	—
399	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
400	C₂²×D₄	—	2	2	no	—
401	C₂²×D₄	—	2	1	no	—
402	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
403	#137	—	4	4	no	—
404	AGL(1,ℤ/8)	—	4	4	no	—
405	C₂×Q₁₆	—	2	2	no	—
406	C₂×SD₁₆	—	2	2	no	—
407	C₂×SD₁₆	—	2	1	no	—
408	C₂×SD₁₆	—	2	2	no	—
409	C₂×SD₁₆	—	2	2	no	—
410	C₂×D₈	—	2	2	no	—
411	C₂×D₈	—	2	1	no	—
412	C₂×D₈	—	2	2	no	—
413	C₂×M₁₆	—	2	1	no	—
414	C₂×M₁₆	—	2	1	no	—
415	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
416	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
417	#127	—	2	1	no	—
418	#127	D₄×C₁₉	1	1	yes	characteristic
419	#127	C₂³×C₁₉	1	1	yes	characteristic
420	#126	—	2	2	no	—
421	#126	—	2	1	no	—
422	#125	C₂³×C₁₉	1	1	yes	characteristic
423	#124	—	2	1	no	—
424	#124	—	2	2	no	—
425	#124	—	2	2	no	—
426	#124	—	2	2	no	—
427	#124	—	2	1	no	—
428	#124	—	2	1	no	—
429	#124	—	2	1	no	—
430	#124	D₄×C₁₉	1	2	yes	—
431	#124	C₂³×C₁₉	1	2	yes	—
432	#124	C₂³×C₁₉	1	1	yes	characteristic
433	#124	C₂³×C₁₉	1	2	yes	—
434	#123	—	2	2	no	—
435	#123	—	2	2	no	—
436	#123	—	2	1	no	—
437	#123	—	2	2	no	—
438	#123	—	2	2	no	—
439	C₂²⋊Q₈	—	2	1	no	—
440	C₂²⋊Q₈	—	2	2	no	—
441	C₂²⋊Q₈	—	2	2	no	—
442	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
443	#121	—	2	2	no	—
444	#121	—	2	2	no	—
445	#121	—	2	2	no	—
446	#121	—	2	1	no	—
447	#121	—	2	2	no	—
448	#121	—	2	2	no	—
449	#121	—	2	1	no	—
450	#121	—	2	1	no	—
451	#121	—	2	1	no	—
452	#121	—	2	1	no	—
453	#121	D₄×C₁₉	1	1	yes	characteristic
454	#120	—	2	2	no	—
455	#120	—	2	2	no	—
456	#120	—	2	2	no	—
457	#120	—	2	2	no	—
458	#120	—	2	2	no	—
459	C₄×Q₈	—	2	1	no	—
460	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
461	C₄×D₄	—	2	2	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	1	no	—
467	C₄×D₄	—	2	1	no	—
468	C₄×D₄	—	2	1	no	—
469	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
470	#117	—	2	1	no	—
471	C₂×C₂²⋊C₄	—	2	2	no	—
472	C₂×C₂²⋊C₄	—	2	1	no	—
473	C₂×C₂²⋊C₄	—	2	1	no	—
474	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
475	#107	—	2	1	no	—
476	#106	—	2	1	no	—
477	C₄⋊C₈	—	2	1	no	—
478	#103	—	2	1	no	—
479	#103	—	2	2	no	—
480	#102	—	2	1	no	—
481	#102	—	2	2	no	—
482	#102	—	2	1	no	—
483	#102	—	2	1	no	—
484	C₂²⋊C₈	—	2	1	no	—
485	#97	C₂³×C₁₉	1	1	yes	characteristic
486	#97	C₂³×C₁₉	1	1	yes	characteristic
487	#97	C₂³×C₁₉	1	2	yes	—
488	#97	C₂³×C₁₉	1	2	yes	—
489	C₄×C₈	—	2	1	no	—
490	C₄×C₈	—	2	1	no	—
491	C₁₉	#19018	1	1	yes	characteristic, direct product factor, Sylow
492	C₂⁴	—	2	2	no	—
493	C₂⁴	—	2	1	no	—
494	#41	—	4	2	no	—
495	#41	—	4	2	no	—
496	#41	—	8	2	no	—
497	#41	—	8	2	no	—
498	C₂×Q₈	—	2	1	no	—
499	C₂×Q₈	—	2	1	no	—
500	C₂×Q₈	—	4	2	no	—
501	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
502	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
503	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
504	C₂×D₄	—	2	2	no	—
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	—	2	2	no	—
507	C₂×D₄	—	2	2	no	—
508	C₂×D₄	—	2	2	no	—
509	C₂×D₄	—	2	2	no	—
510	C₂×D₄	—	2	2	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	2	1	no	—
516	C₂×D₄	—	2	1	no	—
517	C₂×D₄	—	4	2	no	—
518	C₂×D₄	—	4	1	no	—
519	C₂×D₄	—	8	2	no	—
520	C₂×D₄	—	8	4	no	—
521	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
522	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
523	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
524	C₂²×C₄	—	2	2	no	—
525	C₂²×C₄	—	2	2	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	2	no	—
529	C₂²×C₄	—	4	1	no	—
530	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
531	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
532	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
533	Q₁₆	—	4	4	no	—
534	SD₁₆	—	4	2	no	—
535	SD₁₆	—	4	4	no	—
536	SD₁₆	—	4	4	no	—
537	SD₁₆	—	8	2	no	—
538	D₈	—	4	2	no	—
539	D₈	—	4	4	no	—
540	D₈	—	8	2	no	—
541	M₁₆	—	2	4	no	—
542	M₁₆	—	4	2	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	2	no	—
545	C₂×C₈	—	2	1	no	—
546	C₂×C₈	—	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	1	no	—
554	C₄⋊C₄	—	2	1	no	—
555	C₄⋊C₄	—	2	1	no	—
556	C₄⋊C₄	—	2	1	no	—
557	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
558	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
559	C₂²⋊C₄	—	2	2	no	—
560	C₂²⋊C₄	—	2	2	no	—
561	C₂²⋊C₄	—	2	2	no	—
562	C₂²⋊C₄	—	2	2	no	—
563	C₂²⋊C₄	—	2	2	no	—
564	C₂²⋊C₄	—	2	1	no	—
565	C₂²⋊C₄	—	2	2	no	—
566	C₂²⋊C₄	—	2	1	no	—
567	C₂²⋊C₄	—	2	2	no	—
568	C₂²⋊C₄	—	2	1	no	—
569	C₂²⋊C₄	—	2	2	no	—
570	C₂²⋊C₄	—	2	2	no	—
571	C₂²⋊C₄	—	2	1	no	—
572	C₂²⋊C₄	—	2	1	no	—
573	C₂²⋊C₄	—	2	2	no	—
574	C₂²⋊C₄	—	2	2	no	—
575	C₂²⋊C₄	—	4	1	no	—
576	C₂²⋊C₄	—	4	1	no	—
577	C₄²	—	2	2	no	—
578	C₄²	—	2	1	no	—
579	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
580	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
581	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
582	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
583	C₂³	—	2	1	no	—
584	C₂³	—	2	2	no	—
585	C₂³	—	2	2	no	—
586	C₂³	—	4	2	no	—
587	C₂³	—	4	1	no	—
588	C₂³	—	8	1	no	—
589	C₂³	—	8	1	no	—
590	C₂³	—	8	2	no	—
591	C₂³	—	8	2	no	—
592	C₂³	—	8	2	no	—
593	C₂³	C₁₉×#120	1	1	yes	characteristic
594	Q₈	—	4	2	no	—
595	Q₈	—	4	1	no	—
596	Q₈	—	4	2	no	—
597	Q₈	—	4	1	no	—
598	Q₈	—	4	1	no	—
599	Q₈	—	4	2	no	—
600	D₄	—	4	2	no	—
601	D₄	—	4	1	no	—
602	D₄	—	4	2	no	—
603	D₄	—	4	1	no	—
604	D₄	—	4	1	no	—
605	D₄	—	4	1	no	—
606	D₄	—	4	1	no	—
607	D₄	—	4	1	no	—
608	D₄	—	4	1	no	—
609	D₄	—	4	2	no	—
610	D₄	—	4	4	no	—
611	D₄	—	4	2	no	—
612	D₄	—	4	2	no	—
613	D₄	—	8	1	no	—
614	D₄	—	8	2	no	—
615	D₄	—	8	2	no	—
616	D₄	—	8	2	no	—
617	D₄	—	8	2	no	—
618	D₄	—	8	2	no	—
619	D₄	—	8	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	2	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	8	2	no	—
631	C₂×C₄	—	8	1	no	—
632	C₂×C₄	—	8	2	no	—
633	C₂×C₄	—	8	2	no	—
634	C₂×C₄	—	8	2	no	—
635	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
636	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
637	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
638	C₂×C₄	C₂²×D₄×C₁₉	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	—	2	4	no	—
642	C₈	—	2	2	no	—
643	C₈	—	4	1	no	—
644	C₈	—	4	2	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	1	no	—
648	C₂²	—	4	1	no	—
649	C₂²	—	4	2	no	—
650	C₂²	—	4	2	no	—
651	C₂²	—	4	1	no	—
652	C₂²	—	4	2	no	—
653	C₂²	—	4	2	no	—
654	C₂²	—	4	2	no	—
655	C₂²	—	4	2	no	—
656	C₂²	—	4	1	no	—
657	C₂²	—	8	1	no	—
658	C₂²	—	8	1	no	—
659	C₂²	—	8	1	no	—
660	C₂²	—	16	2	no	—
661	C₂²	—	16	4	no	—
662	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	1	no	—
668	C₄	—	4	1	no	—
669	C₄	—	4	2	no	—
670	C₄	—	4	1	no	—
671	C₄	—	4	1	no	—
672	C₄	—	4	2	no	—
673	C₄	—	8	1	no	—
674	C₄	C₁₉×#453	1	2	yes	—
675	C₂	—	4	1	no	—
676	C₂	—	8	1	no	—
677	C₂	—	8	2	no	—
678	C₂	—	8	2	no	—
679	C₂	—	16	1	no	—
680	C₂	C₂×C₁₉×#453	1	1	yes	characteristic
681	C₂	C₁₉×#3018	1	1	yes	characteristic
682	C₂	C₁₉×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₉×#3558	C₂	semidirect
2. C₁₉×#3214	C₂	semidirect
3. C₁₉×#3171	C₂	semidirect
4. C₁₉×#3153	C₂	semidirect
5. C₁₉×#1661	C₂	semidirect
6. C₁₉×#1659	C₂	semidirect
7. C₁₉×#1656	C₂	semidirect
8. C₁₉×#1655	C₂	semidirect
9. C₁₉×#1529	C₂	semidirect
10. C₁₉×#1527	C₂	semidirect
11. C₁₉×#1525	C₂	semidirect
27. C₁₉×#532	C₂²	semidirect
30. C₁₉×#501	C₂²	semidirect
31. C₁₉×#497	C₂²	semidirect
32. C₁₉×#496	C₂²	semidirect
33. C₁₉×#496	C₂²	semidirect
34. C₁₉×#496	C₂²	semidirect
36. C₁₉×#490	C₂²	semidirect
37. C₁₉×#489	C₂²	semidirect
38. C₁₉×#489	C₂²	semidirect
46. C₁₉×#432	C₂²	semidirect
47. C₄×M₁₆×C₁₉	C₂²	semidirect
48. C₄×M₁₆×C₁₉	C₂²	semidirect
49. C₁₉×#330	C₂²	semidirect
50. C₁₉×#329	C₂²	semidirect
51. C₁₉×#329	C₂²	semidirect
52. C₁₉×#329	C₂²	semidirect
53. C₁₉×#329	C₂²	semidirect
54. C₁₉×#329	C₂²	semidirect
241. #19018	C₁₉	direct (N × H)
304. #3558	C₂×C₁₉	semidirect
305. #3214	C₂×C₁₉	semidirect
306. #3171	C₂×C₁₉	semidirect
307. #3153	C₂×C₁₉	semidirect
308. #1661	C₂×C₁₉	semidirect
309. #1659	C₂×C₁₉	semidirect
310. #1656	C₂×C₁₉	semidirect
311. #1655	C₂×C₁₉	semidirect
312. #1529	C₂×C₁₉	semidirect
313. #1527	C₂×C₁₉	semidirect
314. #1525	C₂×C₁₉	semidirect
360. #532	C₂²×C₁₉	semidirect
363. #501	C₂²×C₁₉	semidirect
364. #497	C₂²×C₁₉	semidirect
365. #496	C₂²×C₁₉	semidirect
366. #496	C₂²×C₁₉	semidirect
367. #496	C₂²×C₁₉	semidirect
369. #490	C₂²×C₁₉	semidirect
370. #489	C₂²×C₁₉	semidirect
371. #489	C₂²×C₁₉	semidirect
379. #432	C₂²×C₁₉	semidirect
380. C₄×M₁₆	C₂²×C₁₉	semidirect
381. C₄×M₁₆	C₂²×C₁₉	semidirect
382. #330	C₂²×C₁₉	semidirect
383. #329	C₂²×C₁₉	semidirect
384. #329	C₂²×C₁₉	semidirect
385. #329	C₂²×C₁₉	semidirect
386. #329	C₂²×C₁₉	semidirect
387. #329	C₂²×C₁₉	semidirect
491. C₁₉	#19018	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×#3558	2
C₁₉×#3214	2
C₁₉×#3171	2
C₁₉×#3153	2
C₁₉×#1661	2
C₁₉×#1659	2
C₁₉×#1656	2
C₁₉×#1655	2
C₁₉×#1529	2
C₁₉×#1527	2
C₁₉×#1525	2
#19018	19

Subgroups — C19×#19018 #18024977

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19018 #18024977