Subgroups — C₁₉×#8312 #18014271

Order 4864.

1120 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1797	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×Q₈⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×D₄⋊C₈	C₂	1	2	yes	maximal, complemented
6	C₂²×#41×C₁₉	C₄	1	1	yes	characteristic
7	C₄×#41×C₁₉	—	2	4	no	—
8	C₄×#41×C₁₉	—	2	4	no	—
9	C₂×C₄×Q₈×C₁₉	C₄	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₄×C₁₉	—	2	1	no	—
12	C₂×C₄×D₄×C₁₉	—	2	1	no	—
13	C₂×C₄×D₄×C₁₉	C₄	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#117	—	2	1	no	—
16	C₂×C₁₉×#117	C₄	1	1	yes	characteristic
17	C₂²×C₄²×C₁₉	—	2	1	no	—
18	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
21	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
22	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
23	C₁₉×#336	—	2	1	no	—
24	C₁₉×#336	—	2	1	no	—
25	C₁₉×Q₈⋊C₈	—	2	4	no	—
26	C₁₉×D₄⋊C₈	—	2	4	no	—
27	C₂×#41×C₁₉	—	2	2	no	—
28	C₂×#41×C₁₉	—	2	2	no	—
29	C₂×#41×C₁₉	—	2	2	no	—
30	C₂×#41×C₁₉	—	2	2	no	—
31	C₂×#41×C₁₉	—	2	2	no	—
32	C₂×#41×C₁₉	C₈	1	4	yes	complemented
33	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂²×D₄×C₁₉	—	2	1	no	—
35	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₉	—	2	1	no	—
37	C₂³×C₄×C₁₉	—	2	1	no	—
38	C₂³×C₄×C₁₉	—	2	1	no	—
39	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₁₉	—	2	2	no	—
43	C₂²×C₈×C₁₉	—	2	2	no	—
44	C₄×Q₈×C₁₉	—	2	2	no	—
45	C₄×Q₈×C₁₉	—	2	2	no	—
46	C₄×Q₈×C₁₉	—	2	2	no	—
47	C₄×Q₈×C₁₉	D₄	1	4	yes	—
48	C₄×D₄×C₁₉	—	2	8	no	—
49	C₄×D₄×C₁₉	—	2	8	no	—
50	C₄×D₄×C₁₉	—	2	2	no	—
51	C₄×D₄×C₁₉	—	2	2	no	—
52	C₄×D₄×C₁₉	—	2	2	no	—
53	C₄×D₄×C₁₉	D₄	1	4	yes	—
54	C₁₉×#117	—	2	8	no	—
55	C₁₉×#117	—	2	2	no	—
56	C₁₉×#117	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
61	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₄²×C₁₉	—	2	8	no	—
65	C₂×C₄²×C₁₉	—	2	1	no	—
66	C₂×C₄²×C₁₉	—	2	1	no	—
67	C₂×C₄²×C₁₉	—	2	1	no	—
68	C₂×C₄²×C₁₉	—	2	2	no	—
69	C₂×C₄²×C₁₉	—	2	2	no	—
70	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
74	C₁₉×C₄⋊C₈	—	2	2	no	—
75	C₁₉×C₄⋊C₈	—	2	2	no	—
76	C₁₉×C₂²⋊C₈	—	2	4	no	—
77	C₁₉×C₂²⋊C₈	—	4	2	no	—
78	C₄×C₈×C₁₉	—	2	2	no	—
79	C₄×C₈×C₁₉	—	2	2	no	—
80	C₂⁴×C₁₉	—	2	1	no	—
81	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
82	#41×C₁₉	—	2	8	no	—
83	#41×C₁₉	—	2	8	no	—
84	#41×C₁₉	—	2	8	no	—
85	#41×C₁₉	—	2	8	no	—
86	C₂×Q₈×C₁₉	—	2	1	no	—
87	C₂×Q₈×C₁₉	—	2	1	no	—
88	C₂×Q₈×C₁₉	—	2	1	no	—
89	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
90	C₂×Q₈×C₁₉	C₂×C₈	1	2	yes	—
91	C₂×Q₈×C₁₉	M₁₆	1	2	yes	—
92	C₂×D₄×C₁₉	—	2	4	no	—
93	C₂×D₄×C₁₉	—	2	4	no	—
94	C₂×D₄×C₁₉	—	2	4	no	—
95	C₂×D₄×C₁₉	—	2	1	no	—
96	C₂×D₄×C₁₉	—	2	1	no	—
97	C₂×D₄×C₁₉	—	2	1	no	—
98	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
99	C₂×D₄×C₁₉	C₂×C₈	1	2	yes	—
100	C₂×D₄×C₁₉	M₁₆	1	2	yes	—
101	C₂²×C₄×C₁₉	—	2	4	no	—
102	C₂²×C₄×C₁₉	—	2	4	no	—
103	C₂²×C₄×C₁₉	—	2	1	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	1	no	—
108	C₂²×C₄×C₁₉	—	2	1	no	—
109	C₂²×C₄×C₁₉	—	2	4	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	—	2	2	no	—
114	C₂²×C₄×C₁₉	—	2	2	no	—
115	C₂²×C₄×C₁₉	—	2	4	no	—
116	C₂²×C₄×C₁₉	—	2	2	no	—
117	C₂²×C₄×C₁₉	—	2	1	no	—
118	C₂²×C₄×C₁₉	—	2	1	no	—
119	C₂²×C₄×C₁₉	—	4	1	no	—
120	C₂²×C₄×C₁₉	—	4	2	no	—
121	C₂²×C₄×C₁₉	—	4	2	no	—
122	C₂²×C₄×C₁₉	—	4	2	no	—
123	C₂²×C₄×C₁₉	—	4	1	no	—
124	C₂²×C₄×C₁₉	—	4	1	no	—
125	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
129	C₂²×C₄×C₁₉	M₁₆	1	2	yes	—
130	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₁₉	—	2	4	no	—
134	C₂×C₈×C₁₉	—	4	2	no	—
135	C₂×C₈×C₁₉	—	4	2	no	—
136	C₂×C₈×C₁₉	—	4	2	no	—
137	C₂×C₈×C₁₉	—	4	2	no	—
138	C₂×C₈×C₁₉	—	4	2	no	—
139	C₄⋊C₄×C₁₉	—	2	4	no	—
140	C₄⋊C₄×C₁₉	—	2	1	no	—
141	C₄⋊C₄×C₁₉	—	2	1	no	—
142	C₄⋊C₄×C₁₉	—	2	4	no	—
143	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
144	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
145	C₂²⋊C₄×C₁₉	—	2	4	no	—
146	C₂²⋊C₄×C₁₉	—	2	4	no	—
147	C₂²⋊C₄×C₁₉	—	2	4	no	—
148	C₄²×C₁₉	—	2	4	no	—
149	C₄²×C₁₉	—	2	4	no	—
150	C₄²×C₁₉	—	2	1	no	—
151	C₄²×C₁₉	—	2	1	no	—
152	C₄²×C₁₉	—	2	2	no	—
153	C₄²×C₁₉	—	2	4	no	—
154	C₄²×C₁₉	—	2	2	no	—
155	C₄²×C₁₉	C₂×D₄	1	2	yes	—
156	C₄²×C₁₉	C₂×D₄	1	2	yes	—
157	#8312	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
158	C₂³×C₁₉	—	2	1	no	—
159	C₂³×C₁₉	—	2	2	no	—
160	C₂³×C₁₉	—	2	2	no	—
161	C₂³×C₁₉	—	2	1	no	—
162	C₂³×C₁₉	—	2	2	no	—
163	C₂³×C₁₉	—	2	1	no	—
164	C₂³×C₁₉	—	2	1	no	—
165	C₂³×C₁₉	—	2	1	no	—
166	C₂³×C₁₉	—	2	1	no	—
167	C₂³×C₁₉	—	4	1	no	—
168	C₂³×C₁₉	—	4	1	no	—
169	C₂³×C₁₉	—	4	1	no	—
170	C₂³×C₁₉	—	4	1	no	—
171	C₂³×C₁₉	C₂²⋊C₈	1	2	yes	—
172	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
173	Q₈×C₁₉	—	2	2	no	—
174	Q₈×C₁₉	—	2	2	no	—
175	Q₈×C₁₉	—	2	2	no	—
176	Q₈×C₁₉	C₂²⋊C₈	1	4	yes	complemented
177	D₄×C₁₉	—	2	16	no	—
178	D₄×C₁₉	—	2	2	no	—
179	D₄×C₁₉	—	2	2	no	—
180	D₄×C₁₉	—	2	2	no	—
181	D₄×C₁₉	C₂²⋊C₈	1	4	yes	complemented
182	C₂×C₄×C₁₉	—	2	16	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	1	no	—
188	C₂×C₄×C₁₉	—	2	2	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	—	2	2	no	—
193	C₂×C₄×C₁₉	—	2	2	no	—
194	C₂×C₄×C₁₉	—	2	2	no	—
195	C₂×C₄×C₁₉	—	2	2	no	—
196	C₂×C₄×C₁₉	—	2	1	no	—
197	C₂×C₄×C₁₉	—	2	2	no	—
198	C₂×C₄×C₁₉	—	2	2	no	—
199	C₂×C₄×C₁₉	—	2	1	no	—
200	C₂×C₄×C₁₉	—	2	1	no	—
201	C₂×C₄×C₁₉	—	4	4	no	—
202	C₂×C₄×C₁₉	—	4	8	no	—
203	C₂×C₄×C₁₉	—	4	1	no	—
204	C₂×C₄×C₁₉	—	4	1	no	—
205	C₂×C₄×C₁₉	—	4	1	no	—
206	C₂×C₄×C₁₉	—	4	1	no	—
207	C₂×C₄×C₁₉	—	4	2	no	—
208	C₂×C₄×C₁₉	—	4	4	no	—
209	C₂×C₄×C₁₉	—	4	2	no	—
210	C₂×C₄×C₁₉	—	4	4	no	—
211	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
212	C₂×C₄×C₁₉	#104	1	2	yes	—
213	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂×C₄×C₁₉	#120	1	2	yes	—
216	C₂×C₄×C₁₉	#120	1	2	yes	—
217	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
218	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
219	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
220	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
221	C₂×C₄×C₁₉	#135	1	2	yes	—
222	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
223	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
224	C₈×C₁₉	—	4	4	no	—
225	C₈×C₁₉	—	8	2	no	—
226	C₂×C₄×#41	C₂×C₁₉	1	1	yes	characteristic
227	#1797	C₂×C₁₉	1	1	yes	characteristic, complemented
228	C₄×C₂²⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
229	C₂×Q₈⋊C₈	C₂×C₁₉	1	2	yes	complemented
230	C₂×D₄⋊C₈	C₂×C₁₉	1	2	yes	complemented
231	C₂²×C₁₉	—	2	2	no	—
232	C₂²×C₁₉	—	2	2	no	—
233	C₂²×C₁₉	—	2	2	no	—
234	C₂²×C₁₉	—	2	4	no	—
235	C₂²×C₁₉	—	4	2	no	—
236	C₂²×C₁₉	—	4	2	no	—
237	C₂²×C₁₉	—	4	1	no	—
238	C₂²×C₁₉	—	4	2	no	—
239	C₂²×C₁₉	—	4	1	no	—
240	C₂²×C₁₉	—	4	2	no	—
241	C₂²×C₁₉	—	4	1	no	—
242	C₂²×C₁₉	—	4	2	no	—
243	C₂²×C₁₉	—	4	1	no	—
244	C₂²×C₁₉	—	4	2	no	—
245	C₂²×C₁₉	#379	1	1	yes	characteristic
246	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
247	C₂²×C₁₉	#407	1	1	yes	characteristic
248	C₂²×C₁₉	#416	1	1	yes	characteristic
249	C₂²×C₁₉	#417	1	1	yes	characteristic
250	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
251	C₂²×C₁₉	#421	1	1	yes	characteristic
252	C₄×C₁₉	—	2	2	no	—
253	C₄×C₁₉	—	2	4	no	—
254	C₄×C₁₉	—	2	2	no	—
255	C₄×C₁₉	—	2	2	no	—
256	C₄×C₁₉	—	4	1	no	—
257	C₄×C₁₉	—	4	2	no	—
258	C₄×C₁₉	—	4	2	no	—
259	C₄×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
260	C₄×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
261	C₄×C₁₉	#407	1	1	yes	characteristic
262	C₄×C₁₉	#407	1	1	yes	characteristic
263	C₄×C₁₉	#449	1	2	yes	—
264	C₄×C₁₉	#452	1	2	yes	—
265	C₂²×#41	C₄×C₁₉	1	1	yes	characteristic
266	C₄×#41	—	2	4	no	—
267	C₄×#41	—	2	4	no	—
268	C₂×C₄×Q₈	C₄×C₁₉	1	1	yes	characteristic
269	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
270	C₂×C₄×D₄	—	2	1	no	—
271	C₂×C₄×D₄	—	2	1	no	—
272	C₂×C₄×D₄	C₄×C₁₉	1	1	yes	characteristic
273	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
274	C₂×#117	—	2	1	no	—
275	C₂×#117	C₄×C₁₉	1	1	yes	characteristic
276	C₂²×C₄²	—	2	1	no	—
277	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
278	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
279	C₂×C₂²⋊C₈	—	2	1	no	—
280	C₂×C₂²⋊C₈	—	2	1	no	—
281	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
282	#336	—	2	1	no	—
283	#336	—	2	1	no	—
284	Q₈⋊C₈	—	2	4	no	—
285	D₄⋊C₈	—	2	4	no	—
286	C₂×C₁₉	—	4	2	no	—
287	C₂×C₁₉	—	4	4	no	—
288	C₂×C₁₉	#1476	1	1	yes	characteristic
289	C₂×C₁₉	#1477	1	1	yes	characteristic
290	C₂×C₁₉	#1488	1	1	yes	characteristic
291	C₂×C₁₉	#1489	1	1	yes	characteristic
292	C₂×C₁₉	#1779	1	1	yes	characteristic
293	C₂×C₁₉	#1788	1	1	yes	characteristic
294	C₂×C₁₉	#1789	1	1	yes	characteristic
295	C₂×#41	—	2	2	no	—
296	C₂×#41	—	2	2	no	—
297	C₂×#41	—	2	2	no	—
298	C₂×#41	—	2	2	no	—
299	C₂×#41	—	2	2	no	—
300	C₂×#41	C₈×C₁₉	1	4	yes	complemented
301	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
302	C₂²×D₄	—	2	1	no	—
303	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
304	C₂³×C₄	—	2	1	no	—
305	C₂³×C₄	—	2	1	no	—
306	C₂³×C₄	—	2	1	no	—
307	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
308	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
309	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
310	C₂²×C₈	—	2	2	no	—
311	C₂²×C₈	—	2	2	no	—
312	C₄×Q₈	—	2	2	no	—
313	C₄×Q₈	—	2	2	no	—
314	C₄×Q₈	—	2	2	no	—
315	C₄×Q₈	D₄×C₁₉	1	4	yes	—
316	C₄×D₄	—	2	8	no	—
317	C₄×D₄	—	2	8	no	—
318	C₄×D₄	—	2	2	no	—
319	C₄×D₄	—	2	2	no	—
320	C₄×D₄	—	2	2	no	—
321	C₄×D₄	D₄×C₁₉	1	4	yes	—
322	#117	—	2	8	no	—
323	#117	—	2	2	no	—
324	#117	—	2	2	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
329	C₂×C₂²⋊C₄	—	2	1	no	—
330	C₂×C₂²⋊C₄	—	2	1	no	—
331	C₂×C₂²⋊C₄	—	2	1	no	—
332	C₂×C₄²	—	2	8	no	—
333	C₂×C₄²	—	2	1	no	—
334	C₂×C₄²	—	2	1	no	—
335	C₂×C₄²	—	2	1	no	—
336	C₂×C₄²	—	2	2	no	—
337	C₂×C₄²	—	2	2	no	—
338	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
339	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
340	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
341	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
342	C₄⋊C₈	—	2	2	no	—
343	C₄⋊C₈	—	2	2	no	—
344	C₂²⋊C₈	—	2	4	no	—
345	C₂²⋊C₈	—	4	2	no	—
346	C₄×C₈	—	2	2	no	—
347	C₄×C₈	—	2	2	no	—
348	C₁₉	#8312	1	1	yes	characteristic, direct product factor, Sylow
349	C₂⁴	—	2	1	no	—
350	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
351	#41	—	2	8	no	—
352	#41	—	2	8	no	—
353	#41	—	2	8	no	—
354	#41	—	2	8	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
359	C₂×Q₈	C₂×C₈×C₁₉	1	2	yes	—
360	C₂×Q₈	M₁₆×C₁₉	1	2	yes	—
361	C₂×D₄	—	2	4	no	—
362	C₂×D₄	—	2	4	no	—
363	C₂×D₄	—	2	4	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
368	C₂×D₄	C₂×C₈×C₁₉	1	2	yes	—
369	C₂×D₄	M₁₆×C₁₉	1	2	yes	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	4	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	4	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	4	1	no	—
389	C₂²×C₄	—	4	2	no	—
390	C₂²×C₄	—	4	2	no	—
391	C₂²×C₄	—	4	1	no	—
392	C₂²×C₄	—	4	1	no	—
393	C₂²×C₄	—	4	2	no	—
394	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
395	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
396	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
397	C₂²×C₄	C₂×C₈×C₁₉	1	2	yes	—
398	C₂²×C₄	M₁₆×C₁₉	1	2	yes	—
399	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
401	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
402	C₂×C₈	—	2	4	no	—
403	C₂×C₈	—	4	2	no	—
404	C₂×C₈	—	4	2	no	—
405	C₂×C₈	—	4	2	no	—
406	C₂×C₈	—	4	2	no	—
407	C₂×C₈	—	4	2	no	—
408	C₄⋊C₄	—	2	4	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	4	no	—
412	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
413	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
414	C₂²⋊C₄	—	2	4	no	—
415	C₂²⋊C₄	—	2	4	no	—
416	C₂²⋊C₄	—	2	4	no	—
417	C₄²	—	2	4	no	—
418	C₄²	—	2	4	no	—
419	C₄²	—	2	1	no	—
420	C₄²	—	2	1	no	—
421	C₄²	—	2	2	no	—
422	C₄²	—	2	4	no	—
423	C₄²	—	2	2	no	—
424	C₄²	C₂×D₄×C₁₉	1	2	yes	—
425	C₄²	C₂×D₄×C₁₉	1	2	yes	—
426	C₂³	—	2	1	no	—
427	C₂³	—	2	2	no	—
428	C₂³	—	2	2	no	—
429	C₂³	—	2	1	no	—
430	C₂³	—	2	2	no	—
431	C₂³	—	2	1	no	—
432	C₂³	—	2	1	no	—
433	C₂³	—	2	1	no	—
434	C₂³	—	2	1	no	—
435	C₂³	—	4	1	no	—
436	C₂³	—	4	1	no	—
437	C₂³	—	4	1	no	—
438	C₂³	—	4	1	no	—
439	C₂³	C₁₉×C₂²⋊C₈	1	2	yes	—
440	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
441	Q₈	—	2	2	no	—
442	Q₈	—	2	2	no	—
443	Q₈	—	2	2	no	—
444	Q₈	C₁₉×C₂²⋊C₈	1	4	yes	complemented
445	D₄	—	2	16	no	—
446	D₄	—	2	2	no	—
447	D₄	—	2	2	no	—
448	D₄	—	2	2	no	—
449	D₄	C₁₉×C₂²⋊C₈	1	4	yes	complemented
450	C₂×C₄	—	2	16	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	4	4	no	—
470	C₂×C₄	—	4	8	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	4	no	—
479	C₂×C₄	C₁₉×C₂²⋊C₈	1	2	yes	—
480	C₂×C₄	C₁₉×#104	1	2	yes	—
481	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
482	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
483	C₂×C₄	C₁₉×#120	1	2	yes	—
484	C₂×C₄	C₁₉×#120	1	2	yes	—
485	C₂×C₄	C₂²×C₈×C₁₉	1	1	yes	characteristic
486	C₂×C₄	C₂×M₁₆×C₁₉	1	1	yes	characteristic
487	C₂×C₄	C₂×M₁₆×C₁₉	1	1	yes	characteristic
488	C₂×C₄	C₂×M₁₆×C₁₉	1	1	yes	characteristic
489	C₂×C₄	C₁₉×#135	1	2	yes	—
490	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
491	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
492	C₈	—	4	4	no	—
493	C₈	—	8	2	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	2	2	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	2	4	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	1	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	4	1	no	—
503	C₂²	—	4	2	no	—
504	C₂²	—	4	1	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	1	no	—
507	C₂²	—	4	2	no	—
508	C₂²	C₁₉×#379	1	1	yes	characteristic
509	C₂²	C₂×C₁₉×C₂²⋊C₈	1	1	yes	characteristic
510	C₂²	C₁₉×#407	1	1	yes	characteristic
511	C₂²	C₁₉×#416	1	1	yes	characteristic
512	C₂²	C₁₉×#417	1	1	yes	characteristic
513	C₂²	C₂×C₁₉×#104	1	1	yes	characteristic
514	C₂²	C₁₉×#421	1	1	yes	characteristic
515	C₄	—	2	2	no	—
516	C₄	—	2	4	no	—
517	C₄	—	2	2	no	—
518	C₄	—	2	2	no	—
519	C₄	—	4	1	no	—
520	C₄	—	4	2	no	—
521	C₄	—	4	2	no	—
522	C₄	C₂×C₁₉×C₂²⋊C₈	1	1	yes	characteristic
523	C₄	C₂×C₁₉×C₂²⋊C₈	1	1	yes	characteristic
524	C₄	C₁₉×#407	1	1	yes	characteristic
525	C₄	C₁₉×#407	1	1	yes	characteristic
526	C₄	C₁₉×#449	1	2	yes	—
527	C₄	C₁₉×#452	1	2	yes	—
528	C₂	—	4	2	no	—
529	C₂	—	4	4	no	—
530	C₂	C₁₉×#1476	1	1	yes	characteristic
531	C₂	C₁₉×#1477	1	1	yes	characteristic
532	C₂	C₁₉×#1488	1	1	yes	characteristic
533	C₂	C₁₉×#1489	1	1	yes	characteristic
534	C₂	C₁₉×#1779	1	1	yes	characteristic
535	C₂	C₁₉×#1788	1	1	yes	characteristic
536	C₂	C₁₉×#1789	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂×D₄
commutator	C₂×C₄	C₂²×C₈×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂²×#41×C₁₉	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#1797	C₂	semidirect
3. C₄×C₁₉×C₂²⋊C₈	C₂	semidirect
4. C₂×C₁₉×Q₈⋊C₈	C₂	semidirect
5. C₂×C₁₉×D₄⋊C₈	C₂	semidirect
32. C₂×#41×C₁₉	C₈	semidirect
157. #8312	C₁₉	direct (N × H)
176. Q₈×C₁₉	C₂²⋊C₈	semidirect
181. D₄×C₁₉	C₂²⋊C₈	semidirect
227. #1797	C₂×C₁₉	semidirect
228. C₄×C₂²⋊C₈	C₂×C₁₉	semidirect
229. C₂×Q₈⋊C₈	C₂×C₁₉	semidirect
230. C₂×D₄⋊C₈	C₂×C₁₉	semidirect
300. C₂×#41	C₈×C₁₉	semidirect
348. C₁₉	#8312	direct (N × H)
444. Q₈	C₁₉×C₂²⋊C₈	semidirect
449. D₄	C₁₉×C₂²⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#41×C₁₉	2
C₁₉×#1797	2
C₄×C₁₉×C₂²⋊C₈	2
C₂×C₁₉×Q₈⋊C₈	2
C₂×C₁₉×D₄⋊C₈	2
#8312	19

Subgroups — C19×#8312 #18014271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8312 #18014271