Subgroups — C₁₉×#17622 #18023581

Order 4864.

1074 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3505	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2973	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2349	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1520	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1519	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1513	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1512	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1509	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1504	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₉×#328	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₉×#327	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#553	—	2	2	no	—
13	C₁₉×#553	C₄	1	2	yes	complemented
14	C₁₉×#552	C₄	1	2	yes	complemented
15	C₁₉×#551	—	2	2	no	—
16	C₁₉×#548	C₄	1	2	yes	complemented
17	C₁₉×#546	C₄	1	2	yes	complemented
18	C₁₉×#539	—	2	1	no	—
19	C₁₉×#538	—	2	1	no	—
20	C₁₉×#534	—	2	1	no	—
21	C₁₉×#529	C₂²	1	2	yes	—
22	C₁₉×#525	C₂²	1	2	yes	—
23	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
25	C₁₉×#518	—	2	1	no	—
26	C₂×C₄×D₄×C₁₉	—	2	1	no	—
27	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
28	C₁₉×#435	—	2	2	no	—
29	C₁₉×#435	—	2	2	no	—
30	C₁₉×#432	C₂²	1	2	yes	complemented
31	C₁₉×#407	C₂²	1	2	yes	complemented
32	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
34	C₁₉×#389	—	2	1	no	—
35	C₁₉×#385	—	2	1	no	—
36	C₁₉×#385	—	2	1	no	—
37	C₁₉×#382	C₂²	1	1	yes	characteristic, complemented
38	C₁₉×#380	C₂²	1	1	yes	characteristic
39	C₁₉×#380	C₂²	1	1	yes	characteristic, complemented
40	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
42	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic, complemented
43	C₁₉×#328	C₂²	1	2	yes	complemented
44	C₁₉×#328	C₂²	1	2	yes	complemented
45	C₁₉×#328	C₂²	1	2	yes	complemented
46	C₁₉×#328	C₂²	1	2	yes	complemented
47	C₁₉×#327	C₂²	1	2	yes	—
48	C₁₉×#327	C₂²	1	2	yes	—
49	C₁₉×#327	C₂²	1	2	yes	—
50	C₁₉×#327	C₂²	1	2	yes	—
51	C₂×#41×C₁₉	C₂×C₄	1	2	yes	complemented
52	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
53	C₂²×D₄×C₁₉	—	2	1	no	—
54	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
55	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₁₉	—	2	1	no	—
57	C₂³×C₄×C₁₉	—	2	1	no	—
58	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂×M₁₆×C₁₉	—	2	2	no	—
61	C₂²×C₈×C₁₉	—	2	1	no	—
62	C₂²×C₈×C₁₉	—	2	1	no	—
63	C₁₉×#126	—	2	2	no	—
64	C₁₉×#126	—	2	2	no	—
65	C₁₉×#126	—	2	2	no	—
66	C₁₉×#125	—	2	2	no	—
67	C₁₉×#125	C₂×C₄	1	2	yes	complemented
68	C₁₉×#124	—	2	2	no	—
69	C₁₉×#124	C₂×C₄	1	2	yes	complemented
70	C₁₉×#123	—	2	2	no	—
71	C₁₉×#123	—	2	2	no	—
72	C₁₉×#123	—	2	2	no	—
73	C₁₉×#123	—	2	2	no	—
74	C₁₉×#123	—	2	2	no	—
75	C₁₉×C₂²⋊Q₈	—	2	1	no	—
76	C₁₉×C₂²⋊Q₈	—	2	1	no	—
77	C₁₉×C₂²⋊Q₈	—	2	2	no	—
78	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	complemented
79	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	complemented
80	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
81	C₁₉×#121	—	2	2	no	—
82	C₁₉×#121	—	2	2	no	—
83	C₁₉×#121	—	2	1	no	—
84	C₁₉×#121	—	2	1	no	—
85	C₁₉×#121	—	2	2	no	—
86	C₁₉×#121	C₂×C₄	1	2	yes	complemented
87	C₁₉×#121	C₂×C₄	1	2	yes	complemented
88	C₁₉×#121	C₂³	1	2	yes	—
89	C₁₉×#120	—	2	2	no	—
90	C₁₉×#120	—	2	2	no	—
91	C₄×Q₈×C₁₉	C₂×C₄	1	2	yes	complemented
92	C₄×D₄×C₁₉	—	2	2	no	—
93	C₄×D₄×C₁₉	—	2	2	no	—
94	C₄×D₄×C₁₉	—	2	2	no	—
95	C₄×D₄×C₁₉	—	2	2	no	—
96	C₄×D₄×C₁₉	—	2	2	no	—
97	C₄×D₄×C₁₉	—	4	4	no	—
98	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
99	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
100	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	complemented
101	C₄×D₄×C₁₉	D₄	1	2	yes	—
102	C₄×D₄×C₁₉	D₄	1	2	yes	—
103	C₁₉×#117	—	2	2	no	—
104	C₁₉×#117	—	2	2	no	—
105	C₁₉×#117	C₂×C₄	1	2	yes	complemented
106	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
108	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
109	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
111	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
112	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
113	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
117	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
118	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
119	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
120	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
121	C₂×C₄²×C₁₉	—	2	1	no	—
122	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
123	C₁₉×C₄⋊C₈	—	2	2	no	—
124	C₁₉×C₂²⋊C₈	—	2	1	no	—
125	C₁₉×C₂²⋊C₈	—	2	1	no	—
126	C₁₉×C₂²⋊C₈	—	2	2	no	—
127	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
128	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
129	C₁₉×#97	—	2	2	no	—
130	C₁₉×#95	—	2	1	no	—
131	C₁₉×#95	—	2	1	no	—
132	C₁₉×#95	—	2	1	no	—
133	C₁₉×#95	C₂³	1	1	yes	characteristic
134	C₁₉×#95	C₂³	1	1	yes	characteristic
135	C₁₉×#95	C₂³	1	1	yes	characteristic
136	C₁₉×#95	C₂³	1	1	yes	characteristic
137	C₂⁴×C₁₉	—	2	1	no	—
138	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
140	#41×C₁₉	—	8	2	no	—
141	C₂×Q₈×C₁₉	—	2	1	no	—
142	C₂×Q₈×C₁₉	—	8	1	no	—
143	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
144	C₂×D₄×C₁₉	—	2	2	no	—
145	C₂×D₄×C₁₉	—	2	2	no	—
146	C₂×D₄×C₁₉	—	2	2	no	—
147	C₂×D₄×C₁₉	—	2	2	no	—
148	C₂×D₄×C₁₉	—	2	2	no	—
149	C₂×D₄×C₁₉	—	2	2	no	—
150	C₂×D₄×C₁₉	—	2	1	no	—
151	C₂×D₄×C₁₉	—	4	2	no	—
152	C₂×D₄×C₁₉	—	4	2	no	—
153	C₂×D₄×C₁₉	—	8	1	no	—
154	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
155	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
156	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
157	C₂²×C₄×C₁₉	—	2	1	no	—
158	C₂²×C₄×C₁₉	—	2	1	no	—
159	C₂²×C₄×C₁₉	—	2	1	no	—
160	C₂²×C₄×C₁₉	—	2	1	no	—
161	C₂²×C₄×C₁₉	—	2	2	no	—
162	C₂²×C₄×C₁₉	—	2	2	no	—
163	C₂²×C₄×C₁₉	—	2	1	no	—
164	C₂²×C₄×C₁₉	—	2	1	no	—
165	C₂²×C₄×C₁₉	—	2	1	no	—
166	C₂²×C₄×C₁₉	—	4	2	no	—
167	C₂²×C₄×C₁₉	—	4	2	no	—
168	C₂²×C₄×C₁₉	—	4	2	no	—
169	C₂²×C₄×C₁₉	—	4	2	no	—
170	C₂²×C₄×C₁₉	—	8	1	no	—
171	C₂²×C₄×C₁₉	—	8	1	no	—
172	C₂²×C₄×C₁₉	—	8	1	no	—
173	C₂²×C₄×C₁₉	—	8	1	no	—
174	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
177	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
184	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
185	M₁₆×C₁₉	—	8	2	no	—
186	C₂×C₈×C₁₉	—	2	2	no	—
187	C₂×C₈×C₁₉	—	2	2	no	—
188	C₂×C₈×C₁₉	—	8	1	no	—
189	C₂×C₈×C₁₉	—	8	1	no	—
190	C₄⋊C₄×C₁₉	—	2	2	no	—
191	C₄⋊C₄×C₁₉	—	2	1	no	—
192	C₄⋊C₄×C₁₉	—	2	1	no	—
193	C₄⋊C₄×C₁₉	—	2	2	no	—
194	C₄⋊C₄×C₁₉	—	2	2	no	—
195	C₄⋊C₄×C₁₉	—	2	2	no	—
196	C₄⋊C₄×C₁₉	—	2	2	no	—
197	C₄⋊C₄×C₁₉	—	2	2	no	—
198	C₄⋊C₄×C₁₉	—	4	2	no	—
199	C₄⋊C₄×C₁₉	—	4	2	no	—
200	C₄⋊C₄×C₁₉	—	8	1	no	—
201	C₄⋊C₄×C₁₉	—	8	1	no	—
202	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
203	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
204	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
205	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
206	C₂²⋊C₄×C₁₉	—	2	2	no	—
207	C₂²⋊C₄×C₁₉	—	2	2	no	—
208	C₂²⋊C₄×C₁₉	—	2	2	no	—
209	C₂²⋊C₄×C₁₉	—	2	2	no	—
210	C₂²⋊C₄×C₁₉	—	2	2	no	—
211	C₂²⋊C₄×C₁₉	—	2	2	no	—
212	C₂²⋊C₄×C₁₉	—	2	2	no	—
213	C₂²⋊C₄×C₁₉	—	2	2	no	—
214	C₂²⋊C₄×C₁₉	—	2	2	no	—
215	C₂²⋊C₄×C₁₉	—	2	2	no	—
216	C₂²⋊C₄×C₁₉	—	4	2	no	—
217	C₂²⋊C₄×C₁₉	—	4	2	no	—
218	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
219	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
220	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
221	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
222	C₄²×C₁₉	—	2	2	no	—
223	C₄²×C₁₉	—	2	2	no	—
224	C₄²×C₁₉	—	4	2	no	—
225	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
226	C₄²×C₁₉	C₂×D₄	1	2	yes	—
227	#17622	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₂³×C₁₉	—	2	1	no	—
229	C₂³×C₁₉	—	2	1	no	—
230	C₂³×C₁₉	—	2	2	no	—
231	C₂³×C₁₉	—	4	1	no	—
232	C₂³×C₁₉	—	4	1	no	—
233	C₂³×C₁₉	—	4	1	no	—
234	C₂³×C₁₉	—	4	1	no	—
235	C₂³×C₁₉	—	4	2	no	—
236	C₂³×C₁₉	—	8	1	no	—
237	C₂³×C₁₉	—	8	1	no	—
238	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
239	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
242	C₂³×C₁₉	#137	1	2	yes	—
243	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
244	Q₈×C₁₉	—	4	2	no	—
245	Q₈×C₁₉	—	8	1	no	—
246	D₄×C₁₉	—	2	4	no	—
247	D₄×C₁₉	—	2	4	no	—
248	D₄×C₁₉	—	4	2	no	—
249	D₄×C₁₉	—	4	2	no	—
250	D₄×C₁₉	—	4	2	no	—
251	D₄×C₁₉	—	4	4	no	—
252	D₄×C₁₉	—	8	1	no	—
253	D₄×C₁₉	—	8	2	no	—
254	D₄×C₁₉	—	8	2	no	—
255	C₂×C₄×C₁₉	—	2	1	no	—
256	C₂×C₄×C₁₉	—	2	1	no	—
257	C₂×C₄×C₁₉	—	2	2	no	—
258	C₂×C₄×C₁₉	—	2	2	no	—
259	C₂×C₄×C₁₉	—	2	2	no	—
260	C₂×C₄×C₁₉	—	2	2	no	—
261	C₂×C₄×C₁₉	—	4	1	no	—
262	C₂×C₄×C₁₉	—	4	1	no	—
263	C₂×C₄×C₁₉	—	4	1	no	—
264	C₂×C₄×C₁₉	—	4	1	no	—
265	C₂×C₄×C₁₉	—	4	1	no	—
266	C₂×C₄×C₁₉	—	4	2	no	—
267	C₂×C₄×C₁₉	—	4	1	no	—
268	C₂×C₄×C₁₉	—	4	1	no	—
269	C₂×C₄×C₁₉	—	4	1	no	—
270	C₂×C₄×C₁₉	—	4	2	no	—
271	C₂×C₄×C₁₉	—	4	1	no	—
272	C₂×C₄×C₁₉	—	4	1	no	—
273	C₂×C₄×C₁₉	—	4	2	no	—
274	C₂×C₄×C₁₉	—	4	1	no	—
275	C₂×C₄×C₁₉	—	4	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	1	no	—
286	C₂×C₄×C₁₉	—	8	1	no	—
287	C₂×C₄×C₁₉	—	8	4	no	—
288	C₂×C₄×C₁₉	—	8	4	no	—
289	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
290	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
291	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
292	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
293	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
294	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
295	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
296	C₈×C₁₉	—	4	2	no	—
297	C₈×C₁₉	—	4	2	no	—
298	#3505	C₂×C₁₉	1	1	yes	characteristic
299	#2973	C₂×C₁₉	1	1	yes	characteristic, complemented
300	#2349	C₂×C₁₉	1	1	yes	characteristic, complemented
301	#1520	C₂×C₁₉	1	1	yes	characteristic, complemented
302	#1519	C₂×C₁₉	1	1	yes	characteristic, complemented
303	#1513	C₂×C₁₉	1	2	yes	complemented
304	#1512	C₂×C₁₉	1	2	yes	complemented
305	#1509	C₂×C₁₉	1	2	yes	complemented
306	#1504	C₂×C₁₉	1	2	yes	complemented
307	C₂×#328	C₂×C₁₉	1	1	yes	characteristic, complemented
308	C₂×#327	C₂×C₁₉	1	1	yes	characteristic, complemented
309	C₂²×C₁₉	—	2	1	no	—
310	C₂²×C₁₉	—	2	1	no	—
311	C₂²×C₁₉	—	2	1	no	—
312	C₂²×C₁₉	—	2	1	no	—
313	C₂²×C₁₉	—	2	1	no	—
314	C₂²×C₁₉	—	2	1	no	—
315	C₂²×C₁₉	—	2	2	no	—
316	C₂²×C₁₉	—	2	2	no	—
317	C₂²×C₁₉	—	2	2	no	—
318	C₂²×C₁₉	—	4	2	no	—
319	C₂²×C₁₉	—	4	2	no	—
320	C₂²×C₁₉	—	4	2	no	—
321	C₂²×C₁₉	—	4	2	no	—
322	C₂²×C₁₉	—	4	2	no	—
323	C₂²×C₁₉	—	4	2	no	—
324	C₂²×C₁₉	—	4	2	no	—
325	C₂²×C₁₉	—	16	2	no	—
326	C₂²×C₁₉	#417	1	2	yes	—
327	C₂²×C₁₉	#417	1	2	yes	—
328	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
329	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
330	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
331	C₄×C₁₉	—	2	1	no	—
332	C₄×C₁₉	—	2	1	no	—
333	C₄×C₁₉	—	2	2	no	—
334	C₄×C₁₉	—	2	1	no	—
335	C₄×C₁₉	—	2	1	no	—
336	C₄×C₁₉	—	2	2	no	—
337	C₄×C₁₉	—	2	2	no	—
338	C₄×C₁₉	—	4	2	no	—
339	C₄×C₁₉	—	4	2	no	—
340	C₄×C₁₉	—	4	2	no	—
341	C₄×C₁₉	—	4	2	no	—
342	C₄×C₁₉	—	8	1	no	—
343	C₄×C₁₉	—	8	1	no	—
344	C₄×C₁₉	—	8	1	no	—
345	#553	—	2	2	no	—
346	#553	C₄×C₁₉	1	2	yes	complemented
347	#552	C₄×C₁₉	1	2	yes	complemented
348	#551	—	2	2	no	—
349	#548	C₄×C₁₉	1	2	yes	complemented
350	#546	C₄×C₁₉	1	2	yes	complemented
351	#539	—	2	1	no	—
352	#538	—	2	1	no	—
353	#534	—	2	1	no	—
354	#529	C₂²×C₁₉	1	2	yes	—
355	#525	C₂²×C₁₉	1	2	yes	—
356	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
357	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
358	#518	—	2	1	no	—
359	C₂×C₄×D₄	—	2	1	no	—
360	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
361	#435	—	2	2	no	—
362	#435	—	2	2	no	—
363	#432	C₂²×C₁₉	1	2	yes	complemented
364	#407	C₂²×C₁₉	1	2	yes	complemented
365	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
366	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
367	#389	—	2	1	no	—
368	#385	—	2	1	no	—
369	#385	—	2	1	no	—
370	#382	C₂²×C₁₉	1	1	yes	characteristic, complemented
371	#380	C₂²×C₁₉	1	1	yes	characteristic
372	#380	C₂²×C₁₉	1	1	yes	characteristic, complemented
373	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
374	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
375	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic, complemented
376	#328	C₂²×C₁₉	1	2	yes	complemented
377	#328	C₂²×C₁₉	1	2	yes	complemented
378	#328	C₂²×C₁₉	1	2	yes	complemented
379	#328	C₂²×C₁₉	1	2	yes	complemented
380	#327	C₂²×C₁₉	1	2	yes	—
381	#327	C₂²×C₁₉	1	2	yes	—
382	#327	C₂²×C₁₉	1	2	yes	—
383	#327	C₂²×C₁₉	1	2	yes	—
384	C₂×C₁₉	—	2	1	no	—
385	C₂×C₁₉	—	2	1	no	—
386	C₂×C₁₉	—	2	2	no	—
387	C₂×C₁₉	—	2	2	no	—
388	C₂×C₁₉	—	4	2	no	—
389	C₂×C₁₉	—	8	2	no	—
390	C₂×C₁₉	#2883	1	1	yes	characteristic
391	C₂×C₁₉	C₂×#417	1	1	yes	characteristic
392	C₂×C₁₉	#2901	1	1	yes	characteristic
393	C₂×#41	C₂×C₄×C₁₉	1	2	yes	complemented
394	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
395	C₂²×D₄	—	2	1	no	—
396	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
397	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
398	C₂³×C₄	—	2	1	no	—
399	C₂³×C₄	—	2	1	no	—
400	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
401	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
402	C₂×M₁₆	—	2	2	no	—
403	C₂²×C₈	—	2	1	no	—
404	C₂²×C₈	—	2	1	no	—
405	#126	—	2	2	no	—
406	#126	—	2	2	no	—
407	#126	—	2	2	no	—
408	#125	—	2	2	no	—
409	#125	C₂×C₄×C₁₉	1	2	yes	complemented
410	#124	—	2	2	no	—
411	#124	C₂×C₄×C₁₉	1	2	yes	complemented
412	#123	—	2	2	no	—
413	#123	—	2	2	no	—
414	#123	—	2	2	no	—
415	#123	—	2	2	no	—
416	#123	—	2	2	no	—
417	C₂²⋊Q₈	—	2	1	no	—
418	C₂²⋊Q₈	—	2	1	no	—
419	C₂²⋊Q₈	—	2	2	no	—
420	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	complemented
421	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	complemented
422	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
423	#121	—	2	2	no	—
424	#121	—	2	2	no	—
425	#121	—	2	1	no	—
426	#121	—	2	1	no	—
427	#121	—	2	2	no	—
428	#121	C₂×C₄×C₁₉	1	2	yes	complemented
429	#121	C₂×C₄×C₁₉	1	2	yes	complemented
430	#121	C₂³×C₁₉	1	2	yes	—
431	#120	—	2	2	no	—
432	#120	—	2	2	no	—
433	C₄×Q₈	C₂×C₄×C₁₉	1	2	yes	complemented
434	C₄×D₄	—	2	2	no	—
435	C₄×D₄	—	2	2	no	—
436	C₄×D₄	—	2	2	no	—
437	C₄×D₄	—	2	2	no	—
438	C₄×D₄	—	2	2	no	—
439	C₄×D₄	—	4	4	no	—
440	C₄×D₄	C₂×C₄×C₁₉	1	2	yes	—
441	C₄×D₄	C₂×C₄×C₁₉	1	2	yes	—
442	C₄×D₄	C₂×C₄×C₁₉	1	2	yes	complemented
443	C₄×D₄	D₄×C₁₉	1	2	yes	—
444	C₄×D₄	D₄×C₁₉	1	2	yes	—
445	#117	—	2	2	no	—
446	#117	—	2	2	no	—
447	#117	C₂×C₄×C₁₉	1	2	yes	complemented
448	C₂×C₄⋊C₄	—	2	1	no	—
449	C₂×C₄⋊C₄	—	2	1	no	—
450	C₂×C₄⋊C₄	—	2	1	no	—
451	C₂×C₄⋊C₄	—	2	1	no	—
452	C₂×C₄⋊C₄	—	2	1	no	—
453	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
454	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
455	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
456	C₂×C₂²⋊C₄	—	2	1	no	—
457	C₂×C₂²⋊C₄	—	2	1	no	—
458	C₂×C₂²⋊C₄	—	2	2	no	—
459	C₂×C₂²⋊C₄	—	2	1	no	—
460	C₂×C₂²⋊C₄	—	2	1	no	—
461	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
462	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
463	C₂×C₄²	—	2	1	no	—
464	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
465	C₄⋊C₈	—	2	2	no	—
466	C₂²⋊C₈	—	2	1	no	—
467	C₂²⋊C₈	—	2	1	no	—
468	C₂²⋊C₈	—	2	2	no	—
469	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
470	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
471	#97	—	2	2	no	—
472	#95	—	2	1	no	—
473	#95	—	2	1	no	—
474	#95	—	2	1	no	—
475	#95	C₂³×C₁₉	1	1	yes	characteristic
476	#95	C₂³×C₁₉	1	1	yes	characteristic
477	#95	C₂³×C₁₉	1	1	yes	characteristic
478	#95	C₂³×C₁₉	1	1	yes	characteristic
479	C₁₉	#17622	1	1	yes	characteristic, direct product factor, Sylow
480	C₂⁴	—	2	1	no	—
481	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
482	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
483	#41	—	8	2	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	8	1	no	—
486	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
487	C₂×D₄	—	2	2	no	—
488	C₂×D₄	—	2	2	no	—
489	C₂×D₄	—	2	2	no	—
490	C₂×D₄	—	2	2	no	—
491	C₂×D₄	—	2	2	no	—
492	C₂×D₄	—	2	2	no	—
493	C₂×D₄	—	2	1	no	—
494	C₂×D₄	—	4	2	no	—
495	C₂×D₄	—	4	2	no	—
496	C₂×D₄	—	8	1	no	—
497	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
498	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
499	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	2	no	—
505	C₂²×C₄	—	2	2	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	4	2	no	—
510	C₂²×C₄	—	4	2	no	—
511	C₂²×C₄	—	4	2	no	—
512	C₂²×C₄	—	4	2	no	—
513	C₂²×C₄	—	8	1	no	—
514	C₂²×C₄	—	8	1	no	—
515	C₂²×C₄	—	8	1	no	—
516	C₂²×C₄	—	8	1	no	—
517	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
518	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
519	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
520	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
521	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
522	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
523	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
524	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
525	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
526	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
527	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
528	M₁₆	—	8	2	no	—
529	C₂×C₈	—	2	2	no	—
530	C₂×C₈	—	2	2	no	—
531	C₂×C₈	—	8	1	no	—
532	C₂×C₈	—	8	1	no	—
533	C₄⋊C₄	—	2	2	no	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	2	2	no	—
537	C₄⋊C₄	—	2	2	no	—
538	C₄⋊C₄	—	2	2	no	—
539	C₄⋊C₄	—	2	2	no	—
540	C₄⋊C₄	—	2	2	no	—
541	C₄⋊C₄	—	4	2	no	—
542	C₄⋊C₄	—	4	2	no	—
543	C₄⋊C₄	—	8	1	no	—
544	C₄⋊C₄	—	8	1	no	—
545	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
546	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
547	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
548	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
549	C₂²⋊C₄	—	2	2	no	—
550	C₂²⋊C₄	—	2	2	no	—
551	C₂²⋊C₄	—	2	2	no	—
552	C₂²⋊C₄	—	2	2	no	—
553	C₂²⋊C₄	—	2	2	no	—
554	C₂²⋊C₄	—	2	2	no	—
555	C₂²⋊C₄	—	2	2	no	—
556	C₂²⋊C₄	—	2	2	no	—
557	C₂²⋊C₄	—	2	2	no	—
558	C₂²⋊C₄	—	2	2	no	—
559	C₂²⋊C₄	—	4	2	no	—
560	C₂²⋊C₄	—	4	2	no	—
561	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
562	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
563	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
564	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
565	C₄²	—	2	2	no	—
566	C₄²	—	2	2	no	—
567	C₄²	—	4	2	no	—
568	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
569	C₄²	C₂×D₄×C₁₉	1	2	yes	—
570	C₂³	—	2	1	no	—
571	C₂³	—	2	1	no	—
572	C₂³	—	2	2	no	—
573	C₂³	—	4	1	no	—
574	C₂³	—	4	1	no	—
575	C₂³	—	4	1	no	—
576	C₂³	—	4	1	no	—
577	C₂³	—	4	2	no	—
578	C₂³	—	8	1	no	—
579	C₂³	—	8	1	no	—
580	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
581	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
582	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
583	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
584	C₂³	C₁₉×#137	1	2	yes	—
585	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
586	Q₈	—	4	2	no	—
587	Q₈	—	8	1	no	—
588	D₄	—	2	4	no	—
589	D₄	—	2	4	no	—
590	D₄	—	4	2	no	—
591	D₄	—	4	4	no	—
592	D₄	—	4	2	no	—
593	D₄	—	4	2	no	—
594	D₄	—	8	1	no	—
595	D₄	—	8	2	no	—
596	D₄	—	8	2	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	2	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	2	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	2	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	—	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	—	8	2	no	—
626	C₂×C₄	—	8	2	no	—
627	C₂×C₄	—	8	1	no	—
628	C₂×C₄	—	8	1	no	—
629	C₂×C₄	—	8	4	no	—
630	C₂×C₄	—	8	4	no	—
631	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
632	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
633	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
634	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
635	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
636	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
637	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
638	C₈	—	4	2	no	—
639	C₈	—	4	2	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	4	2	no	—
650	C₂²	—	4	2	no	—
651	C₂²	—	4	2	no	—
652	C₂²	—	4	2	no	—
653	C₂²	—	4	2	no	—
654	C₂²	—	4	2	no	—
655	C₂²	—	4	2	no	—
656	C₂²	—	16	2	no	—
657	C₂²	C₁₉×#417	1	2	yes	—
658	C₂²	C₁₉×#417	1	2	yes	—
659	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
660	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
661	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
662	C₄	—	2	1	no	—
663	C₄	—	2	1	no	—
664	C₄	—	2	2	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	2	no	—
669	C₄	—	4	2	no	—
670	C₄	—	4	2	no	—
671	C₄	—	4	2	no	—
672	C₄	—	4	2	no	—
673	C₄	—	8	1	no	—
674	C₄	—	8	1	no	—
675	C₄	—	8	1	no	—
676	C₂	—	2	1	no	—
677	C₂	—	2	1	no	—
678	C₂	—	2	2	no	—
679	C₂	—	2	2	no	—
680	C₂	—	4	2	no	—
681	C₂	—	8	2	no	—
682	C₂	C₁₉×#2883	1	1	yes	characteristic
683	C₂	C₂×C₁₉×#417	1	1	yes	characteristic
684	C₂	C₁₉×#2901	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#3505	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2973	C₂	semidirect
3. C₁₉×#2349	C₂	semidirect
4. C₁₉×#1520	C₂	semidirect
5. C₁₉×#1519	C₂	semidirect
6. C₁₉×#1513	C₂	semidirect
7. C₁₉×#1512	C₂	semidirect
8. C₁₉×#1509	C₂	semidirect
9. C₁₉×#1504	C₂	semidirect
10. C₂×C₁₉×#328	C₂	semidirect
11. C₂×C₁₉×#327	C₂	semidirect
13. C₁₉×#553	C₄	semidirect
14. C₁₉×#552	C₄	semidirect
16. C₁₉×#548	C₄	semidirect
17. C₁₉×#546	C₄	semidirect
30. C₁₉×#432	C₂²	semidirect
31. C₁₉×#407	C₂²	semidirect
37. C₁₉×#382	C₂²	semidirect
39. C₁₉×#380	C₂²	semidirect
40. C₄×C₄⋊C₄×C₁₉	C₂²	semidirect
42. C₂×C₁₉×#95	C₂²	semidirect
43. C₁₉×#328	C₂²	semidirect
44. C₁₉×#328	C₂²	semidirect
45. C₁₉×#328	C₂²	semidirect
46. C₁₉×#328	C₂²	semidirect
51. C₂×#41×C₁₉	C₂×C₄	semidirect
52. C₂²×Q₈×C₁₉	C₂×C₄	semidirect
54. C₂²×D₄×C₁₉	C₂×C₄	semidirect
67. C₁₉×#125	C₂×C₄	semidirect
69. C₁₉×#124	C₂×C₄	semidirect
78. C₁₉×C₂²⋊Q₈	C₂×C₄	semidirect
79. C₁₉×C₂²⋊Q₈	C₂×C₄	semidirect
86. C₁₉×#121	C₂×C₄	semidirect
87. C₁₉×#121	C₂×C₄	semidirect
91. C₄×Q₈×C₁₉	C₂×C₄	semidirect
100. C₄×D₄×C₁₉	C₂×C₄	semidirect
105. C₁₉×#117	C₂×C₄	semidirect
111. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
112. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
227. #17622	C₁₉	direct (N × H)
299. #2973	C₂×C₁₉	semidirect
300. #2349	C₂×C₁₉	semidirect
301. #1520	C₂×C₁₉	semidirect
302. #1519	C₂×C₁₉	semidirect
303. #1513	C₂×C₁₉	semidirect
304. #1512	C₂×C₁₉	semidirect
305. #1509	C₂×C₁₉	semidirect
306. #1504	C₂×C₁₉	semidirect
307. C₂×#328	C₂×C₁₉	semidirect
308. C₂×#327	C₂×C₁₉	semidirect
346. #553	C₄×C₁₉	semidirect
347. #552	C₄×C₁₉	semidirect
349. #548	C₄×C₁₉	semidirect
350. #546	C₄×C₁₉	semidirect
363. #432	C₂²×C₁₉	semidirect
364. #407	C₂²×C₁₉	semidirect
370. #382	C₂²×C₁₉	semidirect
372. #380	C₂²×C₁₉	semidirect
373. C₄×C₄⋊C₄	C₂²×C₁₉	semidirect
375. C₂×#95	C₂²×C₁₉	semidirect
376. #328	C₂²×C₁₉	semidirect
377. #328	C₂²×C₁₉	semidirect
378. #328	C₂²×C₁₉	semidirect
379. #328	C₂²×C₁₉	semidirect
393. C₂×#41	C₂×C₄×C₁₉	semidirect
394. C₂²×Q₈	C₂×C₄×C₁₉	semidirect
396. C₂²×D₄	C₂×C₄×C₁₉	semidirect
409. #125	C₂×C₄×C₁₉	semidirect
411. #124	C₂×C₄×C₁₉	semidirect
420. C₂²⋊Q₈	C₂×C₄×C₁₉	semidirect
421. C₂²⋊Q₈	C₂×C₄×C₁₉	semidirect
428. #121	C₂×C₄×C₁₉	semidirect
429. #121	C₂×C₄×C₁₉	semidirect
433. C₄×Q₈	C₂×C₄×C₁₉	semidirect
442. C₄×D₄	C₂×C₄×C₁₉	semidirect
447. #117	C₂×C₄×C₁₉	semidirect
453. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
454. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
479. C₁₉	#17622	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×#3505	2
C₁₉×#2973	2
C₁₉×#2349	2
C₁₉×#1520	2
C₁₉×#1519	2
C₁₉×#1513	2
C₁₉×#1512	2
C₁₉×#1509	2
C₁₉×#1504	2
C₂×C₁₉×#328	2
C₂×C₁₉×#327	2
#17622	19

Subgroups — C19×#17622 #18023581

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#17622 #18023581