Subgroups — C₁₉×#19759 #18025718

Order 4864.

762 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3391	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3294	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3284	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3274	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1721	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1685	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1682	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1667	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1667	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1641	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1625	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1621	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1619	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1581	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
17	C₂×C₁₉×#135	—	2	1	no	—
18	C₁₉×#550	C₂²	1	1	yes	characteristic
19	C₁₉×#550	C₂²	1	1	yes	characteristic, complemented
20	C₁₉×#547	C₂²	1	1	yes	characteristic
21	D₄²×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#493	—	2	1	no	—
23	C₁₉×#493	C₂²	1	1	yes	characteristic
24	C₁₉×#493	C₂²	1	1	yes	characteristic
25	C₁₉×#493	C₂²	1	1	yes	characteristic, complemented
26	C₁₉×#492	C₂²	1	1	yes	characteristic, complemented
27	C₁₉×#486	C₂²	1	1	yes	characteristic
28	C₁₉×#486	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#480	—	2	1	no	—
30	C₁₉×#474	C₂²	1	1	yes	characteristic
31	C₁₉×#469	—	2	1	no	—
32	C₁₉×#466	—	2	1	no	—
33	C₁₉×#465	—	2	1	no	—
34	C₁₉×#462	C₂²	1	1	yes	characteristic, complemented
35	C₁₉×#460	C₂²	1	1	yes	characteristic
36	C₁₉×#459	—	2	1	no	—
37	C₁₉×#459	—	2	1	no	—
38	C₁₉×#459	C₂²	1	1	yes	characteristic
39	C₁₉×#459	C₂²	1	1	yes	characteristic
40	C₁₉×#459	C₂²	1	1	yes	characteristic
41	C₁₉×#459	C₂²	1	1	yes	characteristic
42	C₁₉×#459	C₂²	1	1	yes	characteristic, complemented
43	C₁₉×#452	—	2	1	no	—
44	C₁₉×#449	—	2	1	no	—
45	C₁₉×#449	—	2	1	no	—
46	C₁₉×#447	—	2	1	no	—
47	C₁₉×#447	—	2	1	no	—
48	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
49	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
50	C₄×D₈×C₁₉	—	2	1	no	—
51	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
52	C₁₉×#436	C₂²	1	1	yes	characteristic
53	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
54	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₁₉×#102	—	2	1	no	—
56	C₁₉×#335	C₂²	1	1	yes	characteristic, complemented
57	C₁₉×#335	C₂²	1	1	yes	characteristic, complemented
58	C₁₉×#332	C₂²	1	1	yes	characteristic, complemented
59	C₁₉×#331	C₂²	1	1	yes	characteristic
60	C₁₉×#331	C₂²	1	1	yes	characteristic, complemented
61	C₁₉×#331	C₂²	1	1	yes	characteristic, complemented
62	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
66	C₁₉×#322	C₂²	1	1	yes	characteristic, complemented
67	C₂×#41×C₁₉	—	2	1	no	—
68	C₂×#41×C₁₉	—	2	1	no	—
69	C₂×#41×C₁₉	—	2	1	no	—
70	C₂²×D₄×C₁₉	—	2	1	no	—
71	C₂²×D₄×C₁₉	—	2	1	no	—
72	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
73	C₁₉×#135	—	4	4	no	—
74	C₂×Q₁₆×C₁₉	—	2	1	no	—
75	C₂×SD₁₆×C₁₉	—	2	1	no	—
76	C₂×SD₁₆×C₁₉	—	2	1	no	—
77	C₂×SD₁₆×C₁₉	—	2	1	no	—
78	C₂×SD₁₆×C₁₉	D₄	1	1	yes	characteristic
79	C₂×D₈×C₁₉	—	2	1	no	—
80	C₂×D₈×C₁₉	—	2	1	no	—
81	C₂×D₈×C₁₉	—	2	1	no	—
82	C₂×D₈×C₁₉	—	2	1	no	—
83	C₂×D₈×C₁₉	—	2	1	no	—
84	C₂×D₈×C₁₉	—	2	1	no	—
85	C₂×D₈×C₁₉	—	2	1	no	—
86	C₂×D₈×C₁₉	—	2	1	no	—
87	C₂×D₈×C₁₉	—	2	1	no	—
88	C₂×D₈×C₁₉	—	4	1	no	—
89	C₂×D₈×C₁₉	D₄	1	1	yes	characteristic
90	C₂×M₁₆×C₁₉	—	2	1	no	—
91	C₂²×C₈×C₁₉	—	2	1	no	—
92	C₂²×C₈×C₁₉	—	2	1	no	—
93	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
94	C₁₉×#127	—	2	1	no	—
95	C₁₉×#127	—	2	1	no	—
96	C₁₉×#127	C₂³	1	1	yes	characteristic
97	C₁₉×#127	C₂³	1	1	yes	characteristic
98	C₁₉×#127	C₂³	1	1	yes	characteristic
99	C₁₉×#123	—	4	1	no	—
100	C₁₉×C₂²⋊Q₈	—	2	1	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	—	4	1	no	—
107	C₁₉×#121	—	4	1	no	—
108	C₁₉×#120	—	4	1	no	—
109	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
110	C₄×D₄×C₁₉	—	2	1	no	—
111	C₄×D₄×C₁₉	—	2	1	no	—
112	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
113	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
114	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
116	C₁₉×#107	—	2	1	no	—
117	C₁₉×#107	D₄	1	1	yes	characteristic
118	C₁₉×#106	D₄	1	1	yes	characteristic
119	C₁₉×C₄⋊C₈	—	2	1	no	—
120	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
121	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
122	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
123	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
124	C₁₉×#103	—	2	1	no	—
125	C₁₉×#103	D₄	1	1	yes	characteristic
126	C₁₉×#102	—	2	1	no	—
127	C₁₉×#102	—	2	1	no	—
128	C₁₉×#102	—	2	1	no	—
129	C₁₉×#102	—	2	1	no	—
130	C₁₉×#102	—	2	1	no	—
131	C₁₉×#102	—	2	1	no	—
132	C₁₉×#102	—	2	1	no	—
133	C₁₉×#102	—	2	1	no	—
134	C₁₉×#102	—	2	1	no	—
135	C₁₉×#102	—	4	1	no	—
136	C₁₉×#102	D₄	1	1	yes	characteristic
137	C₁₉×#102	D₄	1	1	yes	characteristic
138	C₁₉×#102	D₄	1	1	yes	characteristic
139	C₁₉×C₂²⋊C₈	—	2	1	no	—
140	C₁₉×C₂²⋊C₈	—	2	1	no	—
141	C₁₉×C₂²⋊C₈	—	2	1	no	—
142	C₄×C₈×C₁₉	—	2	1	no	—
143	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
145	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
146	C₂⁴×C₁₉	—	4	1	no	—
147	#41×C₁₉	—	4	2	no	—
148	#41×C₁₉	—	4	2	no	—
149	#41×C₁₉	—	4	2	no	—
150	#41×C₁₉	—	8	1	no	—
151	#41×C₁₉	—	8	1	no	—
152	#41×C₁₉	—	8	1	no	—
153	C₂×Q₈×C₁₉	—	2	1	no	—
154	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂×D₄×C₁₉	—	2	1	no	—
156	C₂×D₄×C₁₉	—	2	1	no	—
157	C₂×D₄×C₁₉	—	2	1	no	—
158	C₂×D₄×C₁₉	—	2	1	no	—
159	C₂×D₄×C₁₉	—	2	1	no	—
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	—	4	1	no	—
165	C₂×D₄×C₁₉	—	4	1	no	—
166	C₂×D₄×C₁₉	—	4	1	no	—
167	C₂×D₄×C₁₉	—	4	1	no	—
168	C₂×D₄×C₁₉	—	4	1	no	—
169	C₂×D₄×C₁₉	—	4	1	no	—
170	C₂×D₄×C₁₉	—	4	2	no	—
171	C₂×D₄×C₁₉	—	4	2	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	C₂×D₄	1	1	yes	characteristic
176	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
177	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₉	—	2	1	no	—
179	C₂²×C₄×C₁₉	—	2	1	no	—
180	C₂²×C₄×C₁₉	—	2	1	no	—
181	C₂²×C₄×C₁₉	—	4	1	no	—
182	C₂²×C₄×C₁₉	—	4	1	no	—
183	C₂²×C₄×C₁₉	—	4	1	no	—
184	Q₁₆×C₁₉	—	4	2	no	—
185	SD₁₆×C₁₉	—	4	2	no	—
186	SD₁₆×C₁₉	—	4	2	no	—
187	SD₁₆×C₁₉	—	8	1	no	—
188	SD₁₆×C₁₉	D₈	1	4	yes	complemented
189	D₈×C₁₉	—	4	1	no	—
190	D₈×C₁₉	—	4	2	no	—
191	D₈×C₁₉	—	4	2	no	—
192	D₈×C₁₉	—	4	2	no	—
193	D₈×C₁₉	—	4	2	no	—
194	D₈×C₁₉	—	8	1	no	—
195	D₈×C₁₉	—	8	1	no	—
196	D₈×C₁₉	—	8	1	no	—
197	D₈×C₁₉	—	8	1	no	—
198	D₈×C₁₉	—	8	1	no	—
199	D₈×C₁₉	—	8	2	no	—
200	M₁₆×C₁₉	—	4	2	no	—
201	C₂×C₈×C₁₉	—	2	1	no	—
202	C₂×C₈×C₁₉	—	2	1	no	—
203	C₂×C₈×C₁₉	—	2	1	no	—
204	C₂×C₈×C₁₉	—	2	1	no	—
205	C₂×C₈×C₁₉	—	2	1	no	—
206	C₂×C₈×C₁₉	—	4	2	no	—
207	C₂×C₈×C₁₉	—	8	1	no	—
208	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
209	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
210	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
211	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	4	1	no	—
216	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
217	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
218	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
219	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
220	C₂²⋊C₄×C₁₉	—	2	1	no	—
221	C₂²⋊C₄×C₁₉	—	2	1	no	—
222	C₂²⋊C₄×C₁₉	—	2	1	no	—
223	C₂²⋊C₄×C₁₉	—	4	1	no	—
224	C₂²⋊C₄×C₁₉	—	4	1	no	—
225	C₂²⋊C₄×C₁₉	—	4	1	no	—
226	C₂²⋊C₄×C₁₉	—	4	1	no	—
227	C₄²×C₁₉	—	2	1	no	—
228	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
229	#19759	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₂³×C₁₉	—	2	1	no	—
231	C₂³×C₁₉	—	2	1	no	—
232	C₂³×C₁₉	—	2	1	no	—
233	C₂³×C₁₉	—	4	1	no	—
234	C₂³×C₁₉	—	4	1	no	—
235	C₂³×C₁₉	—	4	1	no	—
236	C₂³×C₁₉	—	8	2	no	—
237	C₂³×C₁₉	—	8	2	no	—
238	C₂³×C₁₉	—	16	1	no	—
239	Q₈×C₁₉	—	2	1	no	—
240	Q₈×C₁₉	—	4	1	no	—
241	Q₈×C₁₉	—	4	1	no	—
242	Q₈×C₁₉	C₂×D₈	1	2	yes	—
243	D₄×C₁₉	—	2	1	no	—
244	D₄×C₁₉	—	2	1	no	—
245	D₄×C₁₉	—	2	1	no	—
246	D₄×C₁₉	—	2	1	no	—
247	D₄×C₁₉	—	2	1	no	—
248	D₄×C₁₉	—	4	1	no	—
249	D₄×C₁₉	—	4	1	no	—
250	D₄×C₁₉	—	4	1	no	—
251	D₄×C₁₉	—	4	1	no	—
252	D₄×C₁₉	—	4	1	no	—
253	D₄×C₁₉	—	4	1	no	—
254	D₄×C₁₉	—	4	1	no	—
255	D₄×C₁₉	—	4	1	no	—
256	D₄×C₁₉	—	4	1	no	—
257	D₄×C₁₉	—	4	1	no	—
258	D₄×C₁₉	—	4	1	no	—
259	D₄×C₁₉	—	4	1	no	—
260	D₄×C₁₉	—	8	2	no	—
261	D₄×C₁₉	—	8	2	no	—
262	D₄×C₁₉	—	8	1	no	—
263	D₄×C₁₉	—	8	1	no	—
264	D₄×C₁₉	—	8	1	no	—
265	D₄×C₁₉	—	8	2	no	—
266	D₄×C₁₉	—	8	2	no	—
267	D₄×C₁₉	—	8	2	no	—
268	D₄×C₁₉	—	16	1	no	—
269	D₄×C₁₉	—	16	1	no	—
270	D₄×C₁₉	C₂×D₈	1	2	yes	—
271	C₂×C₄×C₁₉	—	2	1	no	—
272	C₂×C₄×C₁₉	—	2	1	no	—
273	C₂×C₄×C₁₉	—	2	1	no	—
274	C₂×C₄×C₁₉	—	2	1	no	—
275	C₂×C₄×C₁₉	—	2	1	no	—
276	C₂×C₄×C₁₉	—	4	1	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	—	8	2	no	—
284	C₂×C₄×C₁₉	—	8	2	no	—
285	C₂×C₄×C₁₉	—	8	2	no	—
286	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
287	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
288	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
289	C₈×C₁₉	—	2	1	no	—
290	C₈×C₁₉	—	2	1	no	—
291	C₈×C₁₉	—	2	1	no	—
292	C₈×C₁₉	—	4	1	no	—
293	C₈×C₁₉	—	4	1	no	—
294	C₈×C₁₉	—	4	1	no	—
295	C₈×C₁₉	—	4	1	no	—
296	C₈×C₁₉	—	4	1	no	—
297	C₈×C₁₉	C₂×D₈	1	2	yes	—
298	#3391	C₂×C₁₉	1	1	yes	characteristic, complemented
299	#3294	C₂×C₁₉	1	1	yes	characteristic, complemented
300	#3284	C₂×C₁₉	1	1	yes	characteristic, complemented
301	#3274	C₂×C₁₉	1	1	yes	characteristic, complemented
302	#1721	C₂×C₁₉	1	1	yes	characteristic, complemented
303	#1685	C₂×C₁₉	1	1	yes	characteristic, complemented
304	#1682	C₂×C₁₉	1	1	yes	characteristic, complemented
305	#1667	C₂×C₁₉	1	1	yes	characteristic, complemented
306	#1667	C₂×C₁₉	1	1	yes	characteristic, complemented
307	#1641	C₂×C₁₉	1	1	yes	characteristic, complemented
308	#1625	C₂×C₁₉	1	1	yes	characteristic, complemented
309	#1621	C₂×C₁₉	1	1	yes	characteristic, complemented
310	#1619	C₂×C₁₉	1	1	yes	characteristic, complemented
311	#1581	C₂×C₁₉	1	1	yes	characteristic, complemented
312	SD₁₆⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
313	C₂²×C₁₉	—	2	2	no	—
314	C₂²×C₁₉	—	4	1	no	—
315	C₂²×C₁₉	—	4	1	no	—
316	C₂²×C₁₉	—	4	1	no	—
317	C₂²×C₁₉	—	4	1	no	—
318	C₂²×C₁₉	—	4	1	no	—
319	C₂²×C₁₉	—	4	1	no	—
320	C₂²×C₁₉	—	4	1	no	—
321	C₂²×C₁₉	—	4	1	no	—
322	C₂²×C₁₉	—	8	1	no	—
323	C₂²×C₁₉	—	8	1	no	—
324	C₂²×C₁₉	—	8	1	no	—
325	C₂²×C₁₉	—	8	1	no	—
326	C₂²×C₁₉	—	8	1	no	—
327	C₂²×C₁₉	—	8	1	no	—
328	C₂²×C₁₉	—	8	1	no	—
329	C₂²×C₁₉	—	8	1	no	—
330	C₂²×C₁₉	—	8	1	no	—
331	C₂²×C₁₉	—	16	4	no	—
332	C₂²×C₁₉	D₄²	1	1	yes	characteristic
333	C₄×C₁₉	—	2	2	no	—
334	C₄×C₁₉	—	2	1	no	—
335	C₄×C₁₉	—	4	1	no	—
336	C₄×C₁₉	—	4	1	no	—
337	C₄×C₁₉	—	4	1	no	—
338	C₄×C₁₉	—	4	1	no	—
339	C₄×C₁₉	—	8	1	no	—
340	C₄×C₁₉	C₂²×D₈	1	1	yes	characteristic
341	C₄×C₁₉	#575	1	1	yes	characteristic
342	C₄×C₁₉	#576	1	1	yes	characteristic
343	C₄×C₁₉	#576	1	1	yes	characteristic
344	C₂×AGL(1,ℤ/8)	—	2	1	no	—
345	C₂×#135	—	2	1	no	—
346	#550	C₂²×C₁₉	1	1	yes	characteristic
347	#550	C₂²×C₁₉	1	1	yes	characteristic, complemented
348	#547	C₂²×C₁₉	1	1	yes	characteristic
349	D₄²	C₂²×C₁₉	1	1	yes	characteristic
350	#493	—	2	1	no	—
351	#493	C₂²×C₁₉	1	1	yes	characteristic
352	#493	C₂²×C₁₉	1	1	yes	characteristic
353	#493	C₂²×C₁₉	1	1	yes	characteristic, complemented
354	#492	C₂²×C₁₉	1	1	yes	characteristic, complemented
355	#486	C₂²×C₁₉	1	1	yes	characteristic
356	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
357	#480	—	2	1	no	—
358	#474	C₂²×C₁₉	1	1	yes	characteristic
359	#469	—	2	1	no	—
360	#466	—	2	1	no	—
361	#465	—	2	1	no	—
362	#462	C₂²×C₁₉	1	1	yes	characteristic, complemented
363	#460	C₂²×C₁₉	1	1	yes	characteristic
364	#459	—	2	1	no	—
365	#459	—	2	1	no	—
366	#459	C₂²×C₁₉	1	1	yes	characteristic
367	#459	C₂²×C₁₉	1	1	yes	characteristic
368	#459	C₂²×C₁₉	1	1	yes	characteristic
369	#459	C₂²×C₁₉	1	1	yes	characteristic
370	#459	C₂²×C₁₉	1	1	yes	characteristic, complemented
371	#452	—	2	1	no	—
372	#449	—	2	1	no	—
373	#449	—	2	1	no	—
374	#447	—	2	1	no	—
375	#447	—	2	1	no	—
376	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
377	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
378	C₄×D₈	—	2	1	no	—
379	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
380	#436	C₂²×C₁₉	1	1	yes	characteristic
381	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
382	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
383	C₂×#102	—	2	1	no	—
384	#335	C₂²×C₁₉	1	1	yes	characteristic, complemented
385	#335	C₂²×C₁₉	1	1	yes	characteristic, complemented
386	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
387	#331	C₂²×C₁₉	1	1	yes	characteristic
388	#331	C₂²×C₁₉	1	1	yes	characteristic, complemented
389	#331	C₂²×C₁₉	1	1	yes	characteristic, complemented
390	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
391	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
392	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
393	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
394	#322	C₂²×C₁₉	1	1	yes	characteristic, complemented
395	C₂×C₁₉	—	4	2	no	—
396	C₂×C₁₉	—	8	1	no	—
397	C₂×C₁₉	—	8	1	no	—
398	C₂×C₁₉	—	16	1	no	—
399	C₂×C₁₉	—	16	1	no	—
400	C₂×C₁₉	—	16	1	no	—
401	C₂×C₁₉	#3268	1	1	yes	characteristic
402	C₂×C₁₉	D₄×D₈	1	1	yes	characteristic
403	C₂×C₁₉	#3288	1	1	yes	characteristic
404	C₂×#41	—	2	1	no	—
405	C₂×#41	—	2	1	no	—
406	C₂×#41	—	2	1	no	—
407	C₂²×D₄	—	2	1	no	—
408	C₂²×D₄	—	2	1	no	—
409	AGL(1,ℤ/8)	—	4	4	no	—
410	#135	—	4	4	no	—
411	C₂×Q₁₆	—	2	1	no	—
412	C₂×SD₁₆	—	2	1	no	—
413	C₂×SD₁₆	—	2	1	no	—
414	C₂×SD₁₆	—	2	1	no	—
415	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
416	C₂×D₈	—	2	1	no	—
417	C₂×D₈	—	2	1	no	—
418	C₂×D₈	—	2	1	no	—
419	C₂×D₈	—	2	1	no	—
420	C₂×D₈	—	2	1	no	—
421	C₂×D₈	—	2	1	no	—
422	C₂×D₈	—	2	1	no	—
423	C₂×D₈	—	2	1	no	—
424	C₂×D₈	—	2	1	no	—
425	C₂×D₈	—	4	1	no	—
426	C₂×D₈	D₄×C₁₉	1	1	yes	characteristic
427	C₂×M₁₆	—	2	1	no	—
428	C₂²×C₈	—	2	1	no	—
429	C₂²×C₈	—	2	1	no	—
430	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
431	#127	—	2	1	no	—
432	#127	—	2	1	no	—
433	#127	C₂³×C₁₉	1	1	yes	characteristic
434	#127	C₂³×C₁₉	1	1	yes	characteristic
435	#127	C₂³×C₁₉	1	1	yes	characteristic
436	#123	—	4	1	no	—
437	C₂²⋊Q₈	—	2	1	no	—
438	#121	—	2	1	no	—
439	#121	—	2	1	no	—
440	#121	—	2	1	no	—
441	#121	—	2	1	no	—
442	#121	—	2	1	no	—
443	#121	—	4	1	no	—
444	#121	—	4	1	no	—
445	#120	—	4	1	no	—
446	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
447	C₄×D₄	—	2	1	no	—
448	C₄×D₄	—	2	1	no	—
449	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
450	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
451	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
452	C₂×C₄⋊C₄	—	2	1	no	—
453	#107	—	2	1	no	—
454	#107	D₄×C₁₉	1	1	yes	characteristic
455	#106	D₄×C₁₉	1	1	yes	characteristic
456	C₄⋊C₈	—	2	1	no	—
457	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
458	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
459	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
460	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
461	#103	—	2	1	no	—
462	#103	D₄×C₁₉	1	1	yes	characteristic
463	#102	—	2	1	no	—
464	#102	—	2	1	no	—
465	#102	—	2	1	no	—
466	#102	—	2	1	no	—
467	#102	—	2	1	no	—
468	#102	—	2	1	no	—
469	#102	—	2	1	no	—
470	#102	—	2	1	no	—
471	#102	—	2	1	no	—
472	#102	—	4	1	no	—
473	#102	D₄×C₁₉	1	1	yes	characteristic
474	#102	D₄×C₁₉	1	1	yes	characteristic
475	#102	D₄×C₁₉	1	1	yes	characteristic
476	C₂²⋊C₈	—	2	1	no	—
477	C₂²⋊C₈	—	2	1	no	—
478	C₂²⋊C₈	—	2	1	no	—
479	C₄×C₈	—	2	1	no	—
480	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
481	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
482	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
483	C₁₉	#19759	1	1	yes	characteristic, direct product factor, Sylow
484	C₂⁴	—	4	1	no	—
485	#41	—	4	2	no	—
486	#41	—	4	2	no	—
487	#41	—	4	2	no	—
488	#41	—	8	1	no	—
489	#41	—	8	1	no	—
490	#41	—	8	1	no	—
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
493	C₂×D₄	—	2	1	no	—
494	C₂×D₄	—	2	1	no	—
495	C₂×D₄	—	2	1	no	—
496	C₂×D₄	—	2	1	no	—
497	C₂×D₄	—	2	1	no	—
498	C₂×D₄	—	2	1	no	—
499	C₂×D₄	—	2	1	no	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	—	2	1	no	—
502	C₂×D₄	—	4	1	no	—
503	C₂×D₄	—	4	1	no	—
504	C₂×D₄	—	4	1	no	—
505	C₂×D₄	—	4	1	no	—
506	C₂×D₄	—	4	1	no	—
507	C₂×D₄	—	4	1	no	—
508	C₂×D₄	—	4	2	no	—
509	C₂×D₄	—	4	2	no	—
510	C₂×D₄	—	4	1	no	—
511	C₂×D₄	—	8	1	no	—
512	C₂×D₄	—	8	1	no	—
513	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
514	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
515	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	4	1	no	—
520	C₂²×C₄	—	4	1	no	—
521	C₂²×C₄	—	4	1	no	—
522	Q₁₆	—	4	2	no	—
523	SD₁₆	—	4	2	no	—
524	SD₁₆	—	4	2	no	—
525	SD₁₆	—	8	1	no	—
526	SD₁₆	D₈×C₁₉	1	4	yes	complemented
527	D₈	—	4	1	no	—
528	D₈	—	4	2	no	—
529	D₈	—	4	2	no	—
530	D₈	—	4	2	no	—
531	D₈	—	4	2	no	—
532	D₈	—	8	1	no	—
533	D₈	—	8	1	no	—
534	D₈	—	8	1	no	—
535	D₈	—	8	1	no	—
536	D₈	—	8	1	no	—
537	D₈	—	8	2	no	—
538	M₁₆	—	4	2	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	4	2	no	—
545	C₂×C₈	—	8	1	no	—
546	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
547	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
548	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
549	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	2	1	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	4	1	no	—
554	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
555	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
556	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
557	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
558	C₂²⋊C₄	—	2	1	no	—
559	C₂²⋊C₄	—	2	1	no	—
560	C₂²⋊C₄	—	2	1	no	—
561	C₂²⋊C₄	—	4	1	no	—
562	C₂²⋊C₄	—	4	1	no	—
563	C₂²⋊C₄	—	4	1	no	—
564	C₂²⋊C₄	—	4	1	no	—
565	C₄²	—	2	1	no	—
566	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
567	C₂³	—	2	1	no	—
568	C₂³	—	2	1	no	—
569	C₂³	—	2	1	no	—
570	C₂³	—	4	1	no	—
571	C₂³	—	4	1	no	—
572	C₂³	—	4	1	no	—
573	C₂³	—	8	2	no	—
574	C₂³	—	8	2	no	—
575	C₂³	—	16	1	no	—
576	Q₈	—	2	1	no	—
577	Q₈	—	4	1	no	—
578	Q₈	—	4	1	no	—
579	Q₈	C₂×D₈×C₁₉	1	2	yes	—
580	D₄	—	2	1	no	—
581	D₄	—	2	1	no	—
582	D₄	—	2	1	no	—
583	D₄	—	2	1	no	—
584	D₄	—	2	1	no	—
585	D₄	—	4	1	no	—
586	D₄	—	4	1	no	—
587	D₄	—	4	1	no	—
588	D₄	—	4	1	no	—
589	D₄	—	4	1	no	—
590	D₄	—	4	1	no	—
591	D₄	—	4	1	no	—
592	D₄	—	4	1	no	—
593	D₄	—	4	1	no	—
594	D₄	—	4	1	no	—
595	D₄	—	4	1	no	—
596	D₄	—	4	1	no	—
597	D₄	—	8	2	no	—
598	D₄	—	8	2	no	—
599	D₄	—	8	1	no	—
600	D₄	—	8	1	no	—
601	D₄	—	8	1	no	—
602	D₄	—	8	2	no	—
603	D₄	—	8	2	no	—
604	D₄	—	8	2	no	—
605	D₄	—	16	1	no	—
606	D₄	—	16	1	no	—
607	D₄	C₂×D₈×C₁₉	1	2	yes	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	8	2	no	—
621	C₂×C₄	—	8	2	no	—
622	C₂×C₄	—	8	2	no	—
623	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
624	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
625	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
626	C₈	—	2	1	no	—
627	C₈	—	2	1	no	—
628	C₈	—	2	1	no	—
629	C₈	—	4	1	no	—
630	C₈	—	4	1	no	—
631	C₈	—	4	1	no	—
632	C₈	—	4	1	no	—
633	C₈	—	4	1	no	—
634	C₈	C₂×D₈×C₁₉	1	2	yes	—
635	C₂²	—	2	2	no	—
636	C₂²	—	4	1	no	—
637	C₂²	—	4	1	no	—
638	C₂²	—	4	1	no	—
639	C₂²	—	4	1	no	—
640	C₂²	—	4	1	no	—
641	C₂²	—	4	1	no	—
642	C₂²	—	4	1	no	—
643	C₂²	—	4	1	no	—
644	C₂²	—	8	1	no	—
645	C₂²	—	8	1	no	—
646	C₂²	—	8	1	no	—
647	C₂²	—	8	1	no	—
648	C₂²	—	8	1	no	—
649	C₂²	—	8	1	no	—
650	C₂²	—	8	1	no	—
651	C₂²	—	8	1	no	—
652	C₂²	—	8	1	no	—
653	C₂²	—	16	4	no	—
654	C₂²	D₄²×C₁₉	1	1	yes	characteristic
655	C₄	—	2	2	no	—
656	C₄	—	2	1	no	—
657	C₄	—	4	1	no	—
658	C₄	—	4	1	no	—
659	C₄	—	4	1	no	—
660	C₄	—	4	1	no	—
661	C₄	—	8	1	no	—
662	C₄	C₂²×D₈×C₁₉	1	1	yes	characteristic
663	C₄	C₁₉×#575	1	1	yes	characteristic
664	C₄	C₁₉×#576	1	1	yes	characteristic
665	C₄	C₁₉×#576	1	1	yes	characteristic
666	C₂	—	4	2	no	—
667	C₂	—	8	1	no	—
668	C₂	—	8	1	no	—
669	C₂	—	16	1	no	—
670	C₂	—	16	1	no	—
671	C₂	—	16	1	no	—
672	C₂	C₁₉×#3268	1	1	yes	characteristic
673	C₂	D₄×D₈×C₁₉	1	1	yes	characteristic
674	C₂	C₁₉×#3288	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3391	C₂	semidirect
2. C₁₉×#3294	C₂	semidirect
3. C₁₉×#3284	C₂	semidirect
4. C₁₉×#3274	C₂	semidirect
5. C₁₉×#1721	C₂	semidirect
6. C₁₉×#1685	C₂	semidirect
7. C₁₉×#1682	C₂	semidirect
8. C₁₉×#1667	C₂	semidirect
9. C₁₉×#1667	C₂	semidirect
10. C₁₉×#1641	C₂	semidirect
11. C₁₉×#1625	C₂	semidirect
12. C₁₉×#1621	C₂	semidirect
13. C₁₉×#1619	C₂	semidirect
14. C₁₉×#1581	C₂	semidirect
15. C₁₉×SD₁₆⋊C₈	C₂	semidirect
19. C₁₉×#550	C₂²	semidirect
25. C₁₉×#493	C₂²	semidirect
26. C₁₉×#492	C₂²	semidirect
28. C₁₉×#486	C₂²	semidirect
34. C₁₉×#462	C₂²	semidirect
42. C₁₉×#459	C₂²	semidirect
48. C₈×Q₈×C₁₉	C₂²	semidirect
54. C₈×D₄×C₁₉	C₂²	semidirect
56. C₁₉×#335	C₂²	semidirect
57. C₁₉×#335	C₂²	semidirect
58. C₁₉×#332	C₂²	semidirect
60. C₁₉×#331	C₂²	semidirect
61. C₁₉×#331	C₂²	semidirect
62. C₁₉×Q₈⋊C₈	C₂²	semidirect
65. C₁₉×D₄⋊C₈	C₂²	semidirect
66. C₁₉×#322	C₂²	semidirect
188. SD₁₆×C₁₉	D₈	semidirect
229. #19759	C₁₉	direct (N × H)
298. #3391	C₂×C₁₉	semidirect
299. #3294	C₂×C₁₉	semidirect
300. #3284	C₂×C₁₉	semidirect
301. #3274	C₂×C₁₉	semidirect
302. #1721	C₂×C₁₉	semidirect
303. #1685	C₂×C₁₉	semidirect
304. #1682	C₂×C₁₉	semidirect
305. #1667	C₂×C₁₉	semidirect
306. #1667	C₂×C₁₉	semidirect
307. #1641	C₂×C₁₉	semidirect
308. #1625	C₂×C₁₉	semidirect
309. #1621	C₂×C₁₉	semidirect
310. #1619	C₂×C₁₉	semidirect
311. #1581	C₂×C₁₉	semidirect
312. SD₁₆⋊C₈	C₂×C₁₉	semidirect
347. #550	C₂²×C₁₉	semidirect
353. #493	C₂²×C₁₉	semidirect
354. #492	C₂²×C₁₉	semidirect
356. #486	C₂²×C₁₉	semidirect
362. #462	C₂²×C₁₉	semidirect
370. #459	C₂²×C₁₉	semidirect
376. C₈×Q₈	C₂²×C₁₉	semidirect
382. C₈×D₄	C₂²×C₁₉	semidirect
384. #335	C₂²×C₁₉	semidirect
385. #335	C₂²×C₁₉	semidirect
386. #332	C₂²×C₁₉	semidirect
388. #331	C₂²×C₁₉	semidirect
389. #331	C₂²×C₁₉	semidirect
390. Q₈⋊C₈	C₂²×C₁₉	semidirect
393. D₄⋊C₈	C₂²×C₁₉	semidirect
394. #322	C₂²×C₁₉	semidirect
483. C₁₉	#19759	direct (N × H)
526. SD₁₆	D₈×C₁₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₉×#3391	2
C₁₉×#3294	2
C₁₉×#3284	2
C₁₉×#3274	2
C₁₉×#1721	2
C₁₉×#1685	2
C₁₉×#1682	2
C₁₉×#1667	2
C₁₉×#1641	2
C₁₉×#1625	2
C₁₉×#1621	2
C₁₉×#1619	2
C₁₉×#1581	2
C₁₉×SD₁₆⋊C₈	2
#19759	19

Subgroups — C19×#19759 #18025718

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19759 #18025718