Subgroups — C₁₉×#23670 #18029629

Order 4864.

950 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#428	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#423	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2296	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#389	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2088	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2088	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2087	C₂	1	2	yes	maximal, complemented
8	C₁₉×#2086	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1736	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1736	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1736	C₂	1	1	yes	maximal, characteristic
12	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#428	—	2	4	no	—
21	C₂×C₁₉×#107	C₂²	1	2	yes	—
22	C₂×C₁₉×#106	C₂²	1	2	yes	—
23	C₁₉×#423	—	2	4	no	—
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
25	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
26	C₁₉×#389	—	2	1	no	—
27	C₁₉×#389	—	2	1	no	—
28	C₁₉×#389	C₂²	1	2	yes	—
29	C₁₉×#389	C₂²	1	2	yes	—
30	C₁₉×#389	C₂²	1	1	yes	characteristic
31	C₁₉×#389	C₂²	1	1	yes	characteristic
32	C₁₉×#389	C₂²	1	1	yes	characteristic
33	C₁₉×#389	C₂²	1	1	yes	characteristic
34	C₁₉×#385	—	2	1	no	—
35	C₁₉×#385	—	2	1	no	—
36	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₁₉×#95	—	2	1	no	—
39	C₁₉×#340	C₂²	1	2	yes	—
40	C₁₉×#340	C₂²	1	2	yes	—
41	C₁₉×#340	C₂²	1	2	yes	—
42	C₁₉×#340	C₂²	1	2	yes	—
43	C₁₉×#340	C₂²	1	2	yes	—
44	C₁₉×#340	C₂²	1	2	yes	—
45	C₂³×C₄×C₁₉	—	2	1	no	—
46	C₂³×C₄×C₁₉	—	2	1	no	—
47	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
50	C₂×M₁₆×C₁₉	—	2	2	no	—
51	C₂×M₁₆×C₁₉	—	2	2	no	—
52	C₂×M₁₆×C₁₉	—	2	2	no	—
53	C₂×M₁₆×C₁₉	—	2	2	no	—
54	C₂×M₁₆×C₁₉	—	2	2	no	—
55	C₂×M₁₆×C₁₉	D₄	1	4	yes	—
56	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
57	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
58	C₁₉×#117	—	2	2	no	—
59	C₁₉×#117	—	2	2	no	—
60	C₁₉×#117	—	2	2	no	—
61	C₁₉×#117	Q₈	1	4	yes	—
62	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
65	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
66	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
73	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
74	C₂×C₄⋊C₄×C₁₉	Q₈	1	4	yes	—
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
79	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₄²×C₁₉	—	2	1	no	—
84	C₂×C₄²×C₁₉	—	2	2	no	—
85	C₂×C₄²×C₁₉	—	2	2	no	—
86	C₂×C₄²×C₁₉	—	2	1	no	—
87	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
91	C₁₉×#107	—	2	4	no	—
92	C₁₉×#106	—	2	4	no	—
93	C₁₉×C₄⋊C₈	—	2	4	no	—
94	C₁₉×C₄⋊C₈	—	2	4	no	—
95	C₁₉×#95	—	2	2	no	—
96	C₁₉×#95	—	2	2	no	—
97	C₁₉×#95	—	2	1	no	—
98	C₁₉×#95	—	2	1	no	—
99	C₁₉×#95	—	2	1	no	—
100	C₁₉×#95	—	2	1	no	—
101	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	—	2	2	no	—
103	C₂²×C₄×C₁₉	—	2	2	no	—
104	C₂²×C₄×C₁₉	—	2	4	no	—
105	C₂²×C₄×C₁₉	—	2	1	no	—
106	C₂²×C₄×C₁₉	—	2	1	no	—
107	C₂²×C₄×C₁₉	—	2	2	no	—
108	C₂²×C₄×C₁₉	—	2	2	no	—
109	C₂²×C₄×C₁₉	—	2	2	no	—
110	C₂²×C₄×C₁₉	—	2	1	no	—
111	C₂²×C₄×C₁₉	—	2	1	no	—
112	C₂²×C₄×C₁₉	—	2	2	no	—
113	C₂²×C₄×C₁₉	—	4	1	no	—
114	C₂²×C₄×C₁₉	—	4	1	no	—
115	C₂²×C₄×C₁₉	—	4	2	no	—
116	C₂²×C₄×C₁₉	—	4	2	no	—
117	C₂²×C₄×C₁₉	—	4	2	no	—
118	C₂²×C₄×C₁₉	—	4	2	no	—
119	C₂²×C₄×C₁₉	—	4	2	no	—
120	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
127	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
128	C₂²×C₄×C₁₉	#41	1	2	yes	—
129	C₂²×C₄×C₁₉	#41	1	2	yes	—
130	C₂²×C₄×C₁₉	#41	1	2	yes	—
131	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
132	M₁₆×C₁₉	—	2	8	no	—
133	M₁₆×C₁₉	—	4	4	no	—
134	C₂×C₈×C₁₉	—	2	2	no	—
135	C₂×C₈×C₁₉	—	2	2	no	—
136	C₂×C₈×C₁₉	—	2	2	no	—
137	C₂×C₈×C₁₉	—	2	2	no	—
138	C₂×C₈×C₁₉	—	2	2	no	—
139	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
140	C₄⋊C₄×C₁₉	—	2	4	no	—
141	C₄⋊C₄×C₁₉	—	2	2	no	—
142	C₄⋊C₄×C₁₉	—	2	1	no	—
143	C₄⋊C₄×C₁₉	—	2	1	no	—
144	C₄⋊C₄×C₁₉	—	2	2	no	—
145	C₄⋊C₄×C₁₉	—	2	1	no	—
146	C₄⋊C₄×C₁₉	—	2	1	no	—
147	C₄⋊C₄×C₁₉	—	2	2	no	—
148	C₄⋊C₄×C₁₉	—	2	1	no	—
149	C₄⋊C₄×C₁₉	—	2	1	no	—
150	C₄⋊C₄×C₁₉	—	4	2	no	—
151	C₄⋊C₄×C₁₉	—	4	2	no	—
152	C₄⋊C₄×C₁₉	—	4	4	no	—
153	C₄⋊C₄×C₁₉	—	4	2	no	—
154	C₄⋊C₄×C₁₉	—	4	2	no	—
155	C₄⋊C₄×C₁₉	—	4	4	no	—
156	C₄⋊C₄×C₁₉	—	4	2	no	—
157	C₄⋊C₄×C₁₉	C₂×Q₈	1	4	yes	—
158	C₄⋊C₄×C₁₉	C₂×Q₈	1	2	yes	—
159	C₄⋊C₄×C₁₉	C₂×Q₈	1	2	yes	—
160	C₂²⋊C₄×C₁₉	—	2	4	no	—
161	C₂²⋊C₄×C₁₉	—	4	2	no	—
162	C₄²×C₁₉	—	2	2	no	—
163	C₄²×C₁₉	—	2	2	no	—
164	C₄²×C₁₉	—	2	4	no	—
165	C₄²×C₁₉	—	2	1	no	—
166	C₄²×C₁₉	—	2	1	no	—
167	C₄²×C₁₉	—	2	1	no	—
168	C₄²×C₁₉	—	2	1	no	—
169	C₄²×C₁₉	—	4	2	no	—
170	#23670	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
171	C₂³×C₁₉	—	2	1	no	—
172	C₂³×C₁₉	—	2	1	no	—
173	C₂³×C₁₉	—	2	1	no	—
174	C₂³×C₁₉	—	2	1	no	—
175	C₂³×C₁₉	#121	1	2	yes	—
176	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
177	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
178	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₉	—	2	1	no	—
180	C₂×C₄×C₁₉	—	2	1	no	—
181	C₂×C₄×C₁₉	—	2	1	no	—
182	C₂×C₄×C₁₉	—	2	1	no	—
183	C₂×C₄×C₁₉	—	2	1	no	—
184	C₂×C₄×C₁₉	—	2	1	no	—
185	C₂×C₄×C₁₉	—	2	2	no	—
186	C₂×C₄×C₁₉	—	2	2	no	—
187	C₂×C₄×C₁₉	—	2	4	no	—
188	C₂×C₄×C₁₉	—	2	1	no	—
189	C₂×C₄×C₁₉	—	2	1	no	—
190	C₂×C₄×C₁₉	—	2	1	no	—
191	C₂×C₄×C₁₉	—	2	1	no	—
192	C₂×C₄×C₁₉	—	4	4	no	—
193	C₂×C₄×C₁₉	—	4	4	no	—
194	C₂×C₄×C₁₉	—	4	8	no	—
195	C₂×C₄×C₁₉	—	4	2	no	—
196	C₂×C₄×C₁₉	—	4	1	no	—
197	C₂×C₄×C₁₉	—	4	1	no	—
198	C₂×C₄×C₁₉	—	4	1	no	—
199	C₂×C₄×C₁₉	—	4	1	no	—
200	C₂×C₄×C₁₉	—	4	2	no	—
201	C₂×C₄×C₁₉	—	4	1	no	—
202	C₂×C₄×C₁₉	—	4	1	no	—
203	C₂×C₄×C₁₉	—	4	2	no	—
204	C₂×C₄×C₁₉	—	4	2	no	—
205	C₂×C₄×C₁₉	—	4	1	no	—
206	C₂×C₄×C₁₉	—	4	1	no	—
207	C₂×C₄×C₁₉	—	4	1	no	—
208	C₂×C₄×C₁₉	—	4	1	no	—
209	C₂×C₄×C₁₉	—	4	2	no	—
210	C₂×C₄×C₁₉	—	8	4	no	—
211	C₂×C₄×C₁₉	#121	1	2	yes	—
212	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
213	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
214	C₂×C₄×C₁₉	#123	1	4	yes	—
215	C₂×C₄×C₁₉	#125	1	4	yes	—
216	C₂×C₄×C₁₉	#125	1	4	yes	—
217	C₂×C₄×C₁₉	C₄⋊Q₈	1	4	yes	—
218	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
219	C₂×C₄×C₁₉	#137	1	2	yes	—
220	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
222	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
223	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
226	C₈×C₁₉	—	2	4	no	—
227	C₈×C₁₉	—	4	2	no	—
228	C₂×#428	C₂×C₁₉	1	1	yes	characteristic
229	C₂×#423	C₂×C₁₉	1	1	yes	characteristic
230	#2296	C₂×C₁₉	1	1	yes	characteristic
231	C₂×#389	C₂×C₁₉	1	1	yes	characteristic
232	#2088	C₂×C₁₉	1	2	yes	complemented
233	#2088	C₂×C₁₉	1	2	yes	complemented
234	#2087	C₂×C₁₉	1	2	yes	complemented
235	#2086	C₂×C₁₉	1	2	yes	complemented
236	#1736	C₂×C₁₉	1	1	yes	characteristic
237	#1736	C₂×C₁₉	1	1	yes	characteristic
238	#1736	C₂×C₁₉	1	1	yes	characteristic
239	C₂²×C₁₉	—	2	2	no	—
240	C₂²×C₁₉	—	2	2	no	—
241	C₂²×C₁₉	—	2	2	no	—
242	C₂²×C₁₉	—	2	2	no	—
243	C₂²×C₁₉	—	2	2	no	—
244	C₂²×C₁₉	—	2	2	no	—
245	C₂²×C₁₉	#398	1	4	yes	—
246	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
247	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
248	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
249	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
250	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
251	C₂²×C₁₉	#575	1	1	yes	characteristic
252	C₂²×C₁₉	#575	1	1	yes	characteristic
253	C₄×C₁₉	—	2	2	no	—
254	C₄×C₁₉	—	2	2	no	—
255	C₄×C₁₉	—	4	4	no	—
256	C₄×C₁₉	—	4	2	no	—
257	C₄×C₁₉	—	4	2	no	—
258	C₄×C₁₉	—	4	1	no	—
259	C₄×C₁₉	—	4	1	no	—
260	C₄×C₁₉	—	8	1	no	—
261	C₄×C₁₉	—	8	2	no	—
262	C₄×C₁₉	—	8	1	no	—
263	C₄×C₁₉	#398	1	4	yes	—
264	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
265	C₄×C₁₉	C₂×#125	1	1	yes	characteristic
266	C₄×C₁₉	C₂×#125	1	1	yes	characteristic
267	C₄×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
268	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
269	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
270	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
271	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
272	C₂²×C₄⋊C₄	—	2	1	no	—
273	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
274	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
275	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
276	#428	—	2	4	no	—
277	C₂×#107	C₂²×C₁₉	1	2	yes	—
278	C₂×#106	C₂²×C₁₉	1	2	yes	—
279	#423	—	2	4	no	—
280	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
281	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
282	#389	—	2	1	no	—
283	#389	—	2	1	no	—
284	#389	C₂²×C₁₉	1	1	yes	characteristic
285	#389	C₂²×C₁₉	1	2	yes	—
286	#389	C₂²×C₁₉	1	1	yes	characteristic
287	#389	C₂²×C₁₉	1	2	yes	—
288	#389	C₂²×C₁₉	1	1	yes	characteristic
289	#389	C₂²×C₁₉	1	1	yes	characteristic
290	#385	—	2	1	no	—
291	#385	—	2	1	no	—
292	C₄×C₄⋊C₄	—	2	1	no	—
293	C₄×C₄⋊C₄	—	2	1	no	—
294	C₂×#95	—	2	1	no	—
295	#340	C₂²×C₁₉	1	2	yes	—
296	#340	C₂²×C₁₉	1	2	yes	—
297	#340	C₂²×C₁₉	1	2	yes	—
298	#340	C₂²×C₁₉	1	2	yes	—
299	#340	C₂²×C₁₉	1	2	yes	—
300	#340	C₂²×C₁₉	1	2	yes	—
301	C₂×C₁₉	—	2	4	no	—
302	C₂×C₁₉	C₂×#398	1	1	yes	characteristic
303	C₂×C₁₉	#3055	1	1	yes	characteristic
304	C₂×C₁₉	#3056	1	1	yes	characteristic
305	C₂×C₁₉	#3077	1	1	yes	characteristic
306	C₂×C₁₉	#3078	1	1	yes	characteristic
307	C₂×C₁₉	#3079	1	1	yes	characteristic
308	C₂×C₁₉	#3080	1	1	yes	characteristic
309	C₂³×C₄	—	2	1	no	—
310	C₂³×C₄	—	2	1	no	—
311	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
312	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
313	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
314	C₂×M₁₆	—	2	2	no	—
315	C₂×M₁₆	—	2	2	no	—
316	C₂×M₁₆	—	2	2	no	—
317	C₂×M₁₆	—	2	2	no	—
318	C₂×M₁₆	—	2	2	no	—
319	C₂×M₁₆	D₄×C₁₉	1	4	yes	—
320	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
321	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
322	#117	—	2	2	no	—
323	#117	—	2	2	no	—
324	#117	—	2	2	no	—
325	#117	Q₈×C₁₉	1	4	yes	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	2	no	—
329	C₂×C₄⋊C₄	—	2	2	no	—
330	C₂×C₄⋊C₄	—	2	2	no	—
331	C₂×C₄⋊C₄	—	2	2	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	—	4	4	no	—
338	C₂×C₄⋊C₄	Q₈×C₁₉	1	4	yes	—
339	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
340	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
341	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
342	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
343	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
344	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
345	C₂×C₂²⋊C₄	—	2	1	no	—
346	C₂×C₂²⋊C₄	—	2	1	no	—
347	C₂×C₄²	—	2	1	no	—
348	C₂×C₄²	—	2	2	no	—
349	C₂×C₄²	—	2	2	no	—
350	C₂×C₄²	—	2	1	no	—
351	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
352	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
353	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
354	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
355	#107	—	2	4	no	—
356	#106	—	2	4	no	—
357	C₄⋊C₈	—	2	4	no	—
358	C₄⋊C₈	—	2	4	no	—
359	#95	—	2	2	no	—
360	#95	—	2	2	no	—
361	#95	—	2	1	no	—
362	#95	—	2	1	no	—
363	#95	—	2	1	no	—
364	#95	—	2	1	no	—
365	C₁₉	#23670	1	1	yes	characteristic, direct product factor, Sylow
366	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	4	1	no	—
379	C₂²×C₄	—	4	1	no	—
380	C₂²×C₄	—	4	2	no	—
381	C₂²×C₄	—	4	2	no	—
382	C₂²×C₄	—	4	2	no	—
383	C₂²×C₄	—	4	2	no	—
384	C₂²×C₄	—	4	2	no	—
385	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
387	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
388	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
391	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
392	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
393	C₂²×C₄	#41×C₁₉	1	2	yes	—
394	C₂²×C₄	#41×C₁₉	1	2	yes	—
395	C₂²×C₄	#41×C₁₉	1	2	yes	—
396	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
397	M₁₆	—	2	8	no	—
398	M₁₆	—	4	4	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
405	C₄⋊C₄	—	2	4	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	4	2	no	—
416	C₄⋊C₄	—	4	2	no	—
417	C₄⋊C₄	—	4	4	no	—
418	C₄⋊C₄	—	4	2	no	—
419	C₄⋊C₄	—	4	2	no	—
420	C₄⋊C₄	—	4	4	no	—
421	C₄⋊C₄	—	4	2	no	—
422	C₄⋊C₄	C₂×Q₈×C₁₉	1	4	yes	—
423	C₄⋊C₄	C₂×Q₈×C₁₉	1	2	yes	—
424	C₄⋊C₄	C₂×Q₈×C₁₉	1	2	yes	—
425	C₂²⋊C₄	—	2	4	no	—
426	C₂²⋊C₄	—	4	2	no	—
427	C₄²	—	2	2	no	—
428	C₄²	—	2	2	no	—
429	C₄²	—	2	4	no	—
430	C₄²	—	2	1	no	—
431	C₄²	—	2	1	no	—
432	C₄²	—	2	1	no	—
433	C₄²	—	2	1	no	—
434	C₄²	—	4	2	no	—
435	C₂³	—	2	1	no	—
436	C₂³	—	2	1	no	—
437	C₂³	—	2	1	no	—
438	C₂³	—	2	1	no	—
439	C₂³	C₁₉×#121	1	2	yes	—
440	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
441	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
442	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	4	4	no	—
457	C₂×C₄	—	4	4	no	—
458	C₂×C₄	—	4	8	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	8	4	no	—
475	C₂×C₄	C₁₉×#121	1	2	yes	—
476	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
477	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
478	C₂×C₄	C₁₉×#123	1	4	yes	—
479	C₂×C₄	C₁₉×#125	1	4	yes	—
480	C₂×C₄	C₁₉×#125	1	4	yes	—
481	C₂×C₄	C₁₉×C₄⋊Q₈	1	4	yes	—
482	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
483	C₂×C₄	C₁₉×#137	1	2	yes	—
484	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
485	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
486	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
487	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
488	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
489	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
490	C₈	—	2	4	no	—
491	C₈	—	4	2	no	—
492	C₂²	—	2	2	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	2	2	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	2	2	no	—
498	C₂²	C₁₉×#398	1	4	yes	—
499	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
500	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
501	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
502	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
503	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
504	C₂²	C₁₉×#575	1	1	yes	characteristic
505	C₂²	C₁₉×#575	1	1	yes	characteristic
506	C₄	—	2	2	no	—
507	C₄	—	2	2	no	—
508	C₄	—	4	1	no	—
509	C₄	—	4	1	no	—
510	C₄	—	4	4	no	—
511	C₄	—	4	2	no	—
512	C₄	—	4	2	no	—
513	C₄	—	8	2	no	—
514	C₄	—	8	1	no	—
515	C₄	—	8	1	no	—
516	C₄	C₁₉×#398	1	4	yes	—
517	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
518	C₄	C₂×C₁₉×#125	1	1	yes	characteristic
519	C₄	C₂×C₁₉×#125	1	1	yes	characteristic
520	C₄	C₂×C₁₉×C₄⋊Q₈	1	1	yes	characteristic
521	C₂	—	2	4	no	—
522	C₂	C₂×C₁₉×#398	1	1	yes	characteristic
523	C₂	C₁₉×#3055	1	1	yes	characteristic
524	C₂	C₁₉×#3056	1	1	yes	characteristic
525	C₂	C₁₉×#3077	1	1	yes	characteristic
526	C₂	C₁₉×#3078	1	1	yes	characteristic
527	C₂	C₁₉×#3079	1	1	yes	characteristic
528	C₂	C₁₉×#3080	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₁₉×#2088	C₂	semidirect
6. C₁₉×#2088	C₂	semidirect
7. C₁₉×#2087	C₂	semidirect
8. C₁₉×#2086	C₂	semidirect
170. #23670	C₁₉	direct (N × H)
232. #2088	C₂×C₁₉	semidirect
233. #2088	C₂×C₁₉	semidirect
234. #2087	C₂×C₁₉	semidirect
235. #2086	C₂×C₁₉	semidirect
365. C₁₉	#23670	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#428	2
C₂×C₁₉×#423	2
C₁₉×#2296	2
C₂×C₁₉×#389	2
C₁₉×#2088	2
C₁₉×#2087	2
C₁₉×#2086	2
C₁₉×#1736	2
#23670	19

Subgroups — C19×#23670 #18029629

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23670 #18029629