Subgroups — C₁₉×#60454 #18066413

Order 4864.

2870 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#568	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3449	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#535	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3062	C₂	1	8	yes	maximal, complemented
6	C₁₉×#3058	C₂	1	4	yes	maximal, complemented
7	C₁₉×#3057	C₂	1	4	yes	maximal, complemented
8	C₁₉×#3055	C₂	1	8	yes	maximal, complemented
9	C₁₉×#2911	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2896	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₉×#418	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
16	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	4	yes	—
17	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
18	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
19	C₂²×D₈×C₁₉	C₂²	1	2	yes	complemented
20	C₁₉×#568	—	2	8	no	—
21	C₂×C₁₉×#131	C₂²	1	4	yes	complemented
22	C₂×C₁₉×#131	C₂²	1	4	yes	complemented
23	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
25	C₂²×M₁₆×C₁₉	C₂²	1	4	yes	complemented
26	C₁₉×#537	C₂²	1	4	yes	complemented
27	C₁₉×#536	—	2	1	no	—
28	C₁₉×#536	C₂²	1	2	yes	complemented
29	C₁₉×#535	—	2	2	no	—
30	C₁₉×#535	—	2	2	no	—
31	C₁₉×#535	—	2	1	no	—
32	C₁₉×#535	C₂²	1	4	yes	—
33	C₁₉×#535	C₂²	1	4	yes	complemented
34	C₁₉×#535	C₂²	1	2	yes	complemented
35	C₁₉×#534	—	2	2	no	—
36	C₁₉×#532	—	2	2	no	—
37	C₂×C₁₉×#127	—	2	1	no	—
38	C₂×C₁₉×#124	—	2	1	no	—
39	C₁₉×#525	—	2	2	no	—
40	C₁₉×#525	C₂²	1	4	yes	complemented
41	C₂×C₁₉×#121	C₂²	1	4	yes	complemented
42	C₂×C₁₉×#120	—	2	2	no	—
43	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
44	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
45	C₁₉×#469	C₂²	1	16	yes	complemented
46	C₁₉×#468	C₂²	1	16	yes	complemented
47	C₁₉×#466	C₂²	1	16	yes	complemented
48	C₁₉×#465	C₂²	1	16	yes	complemented
49	C₁₉×#428	C₂²	1	4	yes	complemented
50	C₁₉×#428	C₂²	1	4	yes	complemented
51	C₁₉×#427	C₂²	1	4	yes	complemented
52	C₁₉×#419	C₂²	1	2	yes	complemented
53	C₁₉×#418	C₂²	1	4	yes	complemented
54	C₁₉×#418	C₂²	1	4	yes	complemented
55	C₁₉×#418	C₂²	1	2	yes	complemented
56	C₁₉×#417	C₂²	1	4	yes	complemented
57	C₁₉×#416	C₂²	1	4	yes	complemented
58	C₂×C₁₉×#102	C₂²	1	4	yes	complemented
59	C₂⁵×C₁₉	—	2	1	no	—
60	C₂×#41×C₁₉	—	2	4	no	—
61	C₂×#41×C₁₉	—	2	1	no	—
62	C₂×#41×C₁₉	—	2	1	no	—
63	C₂×#41×C₁₉	—	2	4	no	—
64	C₂×#41×C₁₉	—	2	4	no	—
65	C₂×#41×C₁₉	—	2	4	no	—
66	C₂×#41×C₁₉	D₄	1	2	yes	—
67	C₂×#41×C₁₉	D₄	1	2	yes	—
68	C₂×#41×C₁₉	C₂³	1	2	yes	—
69	C₂×#41×C₁₉	C₂³	1	2	yes	—
70	C₂×#41×C₁₉	C₂³	1	2	yes	—
71	C₂×#41×C₁₉	C₂³	1	2	yes	—
72	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
73	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₁₉	—	2	1	no	—
75	C₂²×D₄×C₁₉	—	2	4	no	—
76	C₂²×D₄×C₁₉	—	2	4	no	—
77	C₂²×D₄×C₁₉	—	2	1	no	—
78	C₂²×D₄×C₁₉	—	2	1	no	—
79	C₂²×D₄×C₁₉	—	2	1	no	—
80	C₂²×D₄×C₁₉	—	2	4	no	—
81	C₂²×D₄×C₁₉	D₄	1	2	yes	—
82	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
83	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
84	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
85	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
86	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₉	—	2	1	no	—
88	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
89	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₁₉×AGL(1,ℤ/8)	—	2	16	no	—
91	C₁₉×AGL(1,ℤ/8)	—	2	16	no	—
92	C₂×SD₁₆×C₁₉	—	2	8	no	—
93	C₂×SD₁₆×C₁₉	C₂³	1	8	yes	—
94	C₂×D₈×C₁₉	—	2	8	no	—
95	C₂×D₈×C₁₉	C₂³	1	8	yes	—
96	C₁₉×#131	—	2	16	no	—
97	C₁₉×#131	—	2	16	no	—
98	C₂×M₁₆×C₁₉	—	2	4	no	—
99	C₂×M₁₆×C₁₉	—	2	16	no	—
100	C₂×M₁₆×C₁₉	D₄	1	8	yes	complemented
101	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
102	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
103	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
104	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
105	C₂×M₁₆×C₁₉	C₂³	1	8	yes	complemented
106	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
107	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
108	C₂²×C₈×C₁₉	C₂³	1	8	yes	complemented
109	C₁₉×C₄⋊Q₈	—	2	2	no	—
110	C₁₉×#127	—	2	4	no	—
111	C₁₉×#127	—	2	4	no	—
112	C₁₉×#127	—	2	2	no	—
113	C₁₉×#124	—	2	4	no	—
114	C₁₉×#124	—	2	4	no	—
115	C₁₉×#124	—	2	2	no	—
116	C₁₉×#124	—	2	2	no	—
117	C₁₉×#123	—	2	4	no	—
118	C₁₉×#123	—	2	4	no	—
119	C₁₉×C₂²⋊Q₈	—	2	4	no	—
120	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	complemented
121	C₁₉×#121	—	2	4	no	—
122	C₁₉×#121	—	2	8	no	—
123	C₁₉×#121	—	2	8	no	—
124	C₁₉×#121	C₂³	1	16	yes	—
125	C₁₉×#121	C₂³	1	8	yes	complemented
126	C₁₉×#120	—	2	4	no	—
127	C₁₉×#120	—	2	8	no	—
128	C₁₉×#120	—	2	8	no	—
129	C₁₉×#120	—	2	4	no	—
130	C₄×D₄×C₁₉	—	2	8	no	—
131	C₁₉×#117	—	2	1	no	—
132	C₁₉×#117	—	2	1	no	—
133	C₁₉×#117	—	2	1	no	—
134	C₁₉×#117	—	2	1	no	—
135	C₁₉×#117	C₂³	1	2	yes	—
136	C₁₉×#117	C₂³	1	2	yes	—
137	C₁₉×#117	C₂³	1	2	yes	—
138	C₁₉×#117	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
142	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
143	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
144	C₂×C₄²×C₁₉	—	2	1	no	—
145	C₂×C₄²×C₁₉	—	2	1	no	—
146	C₁₉×#107	C₂³	1	8	yes	complemented
147	C₁₉×#106	C₂³	1	8	yes	complemented
148	C₁₉×#103	C₂³	1	8	yes	complemented
149	C₁₉×#102	C₂³	1	16	yes	—
150	C₁₉×#102	C₂³	1	8	yes	complemented
151	C₂⁴×C₁₉	—	2	2	no	—
152	C₂⁴×C₁₉	—	2	1	no	—
153	C₂⁴×C₁₉	—	2	2	no	—
154	C₂⁴×C₁₉	—	2	2	no	—
155	C₂⁴×C₁₉	—	4	4	no	—
156	C₂⁴×C₁₉	—	8	4	no	—
157	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
158	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
159	#41×C₁₉	—	2	8	no	—
160	#41×C₁₉	—	2	8	no	—
161	#41×C₁₉	—	2	4	no	—
162	#41×C₁₉	—	2	4	no	—
163	#41×C₁₉	—	2	4	no	—
164	#41×C₁₉	—	2	4	no	—
165	#41×C₁₉	—	2	4	no	—
166	#41×C₁₉	—	2	4	no	—
167	#41×C₁₉	—	2	4	no	—
168	#41×C₁₉	—	2	4	no	—
169	#41×C₁₉	—	4	4	no	—
170	#41×C₁₉	—	4	4	no	—
171	C₂×Q₈×C₁₉	—	2	4	no	—
172	C₂×Q₈×C₁₉	—	2	1	no	—
173	C₂×Q₈×C₁₉	—	2	2	no	—
174	C₂×Q₈×C₁₉	—	2	2	no	—
175	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
176	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
177	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
178	C₂×D₄×C₁₉	—	2	8	no	—
179	C₂×D₄×C₁₉	—	2	2	no	—
180	C₂×D₄×C₁₉	—	2	2	no	—
181	C₂×D₄×C₁₉	—	2	8	no	—
182	C₂×D₄×C₁₉	—	2	16	no	—
183	C₂×D₄×C₁₉	—	2	4	no	—
184	C₂×D₄×C₁₉	—	2	2	no	—
185	C₂×D₄×C₁₉	—	2	4	no	—
186	C₂×D₄×C₁₉	—	2	4	no	—
187	C₂×D₄×C₁₉	—	2	4	no	—
188	C₂×D₄×C₁₉	—	2	2	no	—
189	C₂×D₄×C₁₉	—	2	2	no	—
190	C₂×D₄×C₁₉	—	2	2	no	—
191	C₂×D₄×C₁₉	—	2	1	no	—
192	C₂×D₄×C₁₉	—	2	4	no	—
193	C₂×D₄×C₁₉	—	2	4	no	—
194	C₂×D₄×C₁₉	—	2	4	no	—
195	C₂×D₄×C₁₉	—	2	2	no	—
196	C₂×D₄×C₁₉	—	4	4	no	—
197	C₂×D₄×C₁₉	—	4	4	no	—
198	C₂×D₄×C₁₉	—	4	4	no	—
199	C₂×D₄×C₁₉	—	4	4	no	—
200	C₂×D₄×C₁₉	—	8	8	no	—
201	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
202	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
203	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
204	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
205	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
206	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₁₉	—	2	4	no	—
208	C₂²×C₄×C₁₉	—	2	4	no	—
209	C₂²×C₄×C₁₉	—	2	2	no	—
210	C₂²×C₄×C₁₉	—	2	1	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	—	4	4	no	—
215	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
216	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
217	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
221	C₂²×C₄×C₁₉	#41	1	4	yes	—
222	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
223	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
226	SD₁₆×C₁₉	—	2	16	no	—
227	D₈×C₁₉	—	2	16	no	—
228	M₁₆×C₁₉	—	2	4	no	—
229	M₁₆×C₁₉	—	2	4	no	—
230	M₁₆×C₁₉	—	2	16	no	—
231	M₁₆×C₁₉	C₂×D₄	1	8	yes	—
232	M₁₆×C₁₉	C₂×D₄	1	8	yes	complemented
233	C₂×C₈×C₁₉	—	2	4	no	—
234	C₂×C₈×C₁₉	—	2	16	no	—
235	C₂×C₈×C₁₉	C₂×D₄	1	8	yes	complemented
236	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
237	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
238	C₄⋊C₄×C₁₉	—	2	2	no	—
239	C₄⋊C₄×C₁₉	—	2	2	no	—
240	C₄⋊C₄×C₁₉	—	2	8	no	—
241	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
242	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
243	C₂²⋊C₄×C₁₉	—	2	2	no	—
244	C₂²⋊C₄×C₁₉	—	2	2	no	—
245	C₂²⋊C₄×C₁₉	—	2	2	no	—
246	C₂²⋊C₄×C₁₉	—	2	2	no	—
247	C₂²⋊C₄×C₁₉	—	2	8	no	—
248	C₂²⋊C₄×C₁₉	—	2	16	no	—
249	C₂²⋊C₄×C₁₉	—	2	8	no	—
250	C₄²×C₁₉	—	2	2	no	—
251	C₄²×C₁₉	—	2	2	no	—
252	C₄²×C₁₉	—	2	2	no	—
253	C₄²×C₁₉	—	2	2	no	—
254	#60454	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
255	C₂³×C₁₉	—	2	4	no	—
256	C₂³×C₁₉	—	2	2	no	—
257	C₂³×C₁₉	—	2	4	no	—
258	C₂³×C₁₉	—	4	2	no	—
259	C₂³×C₁₉	—	4	4	no	—
260	C₂³×C₁₉	—	4	8	no	—
261	C₂³×C₁₉	—	4	2	no	—
262	C₂³×C₁₉	—	4	4	no	—
263	C₂³×C₁₉	—	4	4	no	—
264	C₂³×C₁₉	—	4	4	no	—
265	C₂³×C₁₉	—	8	2	no	—
266	C₂³×C₁₉	—	8	4	no	—
267	C₂³×C₁₉	—	8	4	no	—
268	C₂³×C₁₉	—	8	16	no	—
269	C₂³×C₁₉	#121	1	4	yes	—
270	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
271	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
272	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
273	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
274	Q₈×C₁₉	—	2	4	no	—
275	Q₈×C₁₉	—	2	4	no	—
276	Q₈×C₁₉	—	2	2	no	—
277	Q₈×C₁₉	—	2	2	no	—
278	Q₈×C₁₉	—	4	2	no	—
279	D₄×C₁₉	—	2	8	no	—
280	D₄×C₁₉	—	2	8	no	—
281	D₄×C₁₉	—	2	4	no	—
282	D₄×C₁₉	—	2	4	no	—
283	D₄×C₁₉	—	2	2	no	—
284	D₄×C₁₉	—	2	4	no	—
285	D₄×C₁₉	—	2	4	no	—
286	D₄×C₁₉	—	2	2	no	—
287	D₄×C₁₉	—	4	4	no	—
288	D₄×C₁₉	—	4	4	no	—
289	D₄×C₁₉	—	4	4	no	—
290	D₄×C₁₉	—	4	4	no	—
291	D₄×C₁₉	—	4	4	no	—
292	D₄×C₁₉	—	4	2	no	—
293	D₄×C₁₉	—	8	8	no	—
294	D₄×C₁₉	—	8	16	no	—
295	C₂×C₄×C₁₉	—	2	4	no	—
296	C₂×C₄×C₁₉	—	2	8	no	—
297	C₂×C₄×C₁₉	—	2	4	no	—
298	C₂×C₄×C₁₉	—	2	4	no	—
299	C₂×C₄×C₁₉	—	2	4	no	—
300	C₂×C₄×C₁₉	—	2	4	no	—
301	C₂×C₄×C₁₉	—	2	2	no	—
302	C₂×C₄×C₁₉	—	4	4	no	—
303	C₂×C₄×C₁₉	—	4	2	no	—
304	C₂×C₄×C₁₉	—	4	4	no	—
305	C₂×C₄×C₁₉	—	4	4	no	—
306	C₂×C₄×C₁₉	—	8	2	no	—
307	C₂×C₄×C₁₉	#121	1	4	yes	—
308	C₂×C₄×C₁₉	#121	1	4	yes	—
309	C₂×C₄×C₁₉	#121	1	4	yes	—
310	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
311	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
312	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
313	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
314	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
315	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
316	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
317	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
318	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
319	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
320	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
321	C₈×C₁₉	—	2	4	no	—
322	C₈×C₁₉	C₂²×D₄	1	8	yes	—
323	C₂²×AGL(1,ℤ/8)	C₂×C₁₉	1	1	yes	characteristic, complemented
324	C₂×#568	C₂×C₁₉	1	1	yes	characteristic, complemented
325	#3449	C₂×C₁₉	1	1	yes	characteristic, complemented
326	C₂×#535	C₂×C₁₉	1	1	yes	characteristic, complemented
327	#3062	C₂×C₁₉	1	8	yes	complemented
328	#3058	C₂×C₁₉	1	4	yes	complemented
329	#3057	C₂×C₁₉	1	4	yes	complemented
330	#3055	C₂×C₁₉	1	8	yes	complemented
331	#2911	C₂×C₁₉	1	1	yes	characteristic, complemented
332	#2896	C₂×C₁₉	1	1	yes	characteristic, complemented
333	C₂×#418	C₂×C₁₉	1	1	yes	characteristic, complemented
334	C₂²×C₁₉	—	2	2	no	—
335	C₂²×C₁₉	—	2	2	no	—
336	C₂²×C₁₉	—	2	2	no	—
337	C₂²×C₁₉	—	2	8	no	—
338	C₂²×C₁₉	—	2	4	no	—
339	C₂²×C₁₉	—	4	4	no	—
340	C₂²×C₁₉	—	4	8	no	—
341	C₂²×C₁₉	—	4	4	no	—
342	C₂²×C₁₉	—	4	2	no	—
343	C₂²×C₁₉	—	4	4	no	—
344	C₂²×C₁₉	—	8	4	no	—
345	C₂²×C₁₉	—	8	8	no	—
346	C₂²×C₁₉	—	8	4	no	—
347	C₂²×C₁₉	—	8	8	no	—
348	C₂²×C₁₉	—	8	8	no	—
349	C₂²×C₁₉	C₂×#121	1	2	yes	—
350	C₂²×C₁₉	C₂×#121	1	2	yes	—
351	C₂²×C₁₉	C₂×#121	1	2	yes	—
352	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
353	C₄×C₁₉	—	2	4	no	—
354	C₄×C₁₉	—	4	4	no	—
355	C₄×C₁₉	—	4	4	no	—
356	C₄×C₁₉	—	4	2	no	—
357	C₄×C₁₉	C₂×#121	1	2	yes	—
358	C₄×C₁₉	C₂×#121	1	2	yes	—
359	C₄×C₁₉	C₂×#121	1	2	yes	—
360	C₄×C₁₉	C₂³×D₄	1	1	yes	characteristic
361	C₄×C₁₉	C₂²×#41	1	1	yes	characteristic
362	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
363	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
364	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
365	C₂×AGL(1,ℤ/8)	—	2	8	no	—
366	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	4	yes	—
367	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	4	yes	complemented
368	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
369	C₂²×D₈	C₂²×C₁₉	1	2	yes	complemented
370	#568	—	2	8	no	—
371	C₂×#131	C₂²×C₁₉	1	4	yes	complemented
372	C₂×#131	C₂²×C₁₉	1	4	yes	complemented
373	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
374	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
375	C₂²×M₁₆	C₂²×C₁₉	1	4	yes	complemented
376	#537	C₂²×C₁₉	1	4	yes	complemented
377	#536	—	2	1	no	—
378	#536	C₂²×C₁₉	1	2	yes	complemented
379	#535	—	2	2	no	—
380	#535	—	2	2	no	—
381	#535	—	2	1	no	—
382	#535	C₂²×C₁₉	1	4	yes	—
383	#535	C₂²×C₁₉	1	4	yes	complemented
384	#535	C₂²×C₁₉	1	2	yes	complemented
385	#534	—	2	2	no	—
386	#532	—	2	2	no	—
387	C₂×#127	—	2	1	no	—
388	C₂×#124	—	2	1	no	—
389	#525	—	2	2	no	—
390	#525	C₂²×C₁₉	1	4	yes	complemented
391	C₂×#121	C₂²×C₁₉	1	4	yes	complemented
392	C₂×#120	—	2	2	no	—
393	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
394	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
395	#469	C₂²×C₁₉	1	16	yes	complemented
396	#468	C₂²×C₁₉	1	16	yes	complemented
397	#466	C₂²×C₁₉	1	16	yes	complemented
398	#465	C₂²×C₁₉	1	16	yes	complemented
399	#428	C₂²×C₁₉	1	4	yes	complemented
400	#428	C₂²×C₁₉	1	4	yes	complemented
401	#427	C₂²×C₁₉	1	4	yes	complemented
402	#419	C₂²×C₁₉	1	2	yes	complemented
403	#418	C₂²×C₁₉	1	4	yes	complemented
404	#418	C₂²×C₁₉	1	4	yes	complemented
405	#418	C₂²×C₁₉	1	2	yes	complemented
406	#417	C₂²×C₁₉	1	4	yes	complemented
407	#416	C₂²×C₁₉	1	4	yes	complemented
408	C₂×#102	C₂²×C₁₉	1	4	yes	complemented
409	C₂×C₁₉	—	2	2	no	—
410	C₂×C₁₉	—	2	2	no	—
411	C₂×C₁₉	—	2	2	no	—
412	C₂×C₁₉	—	4	4	no	—
413	C₂×C₁₉	—	8	2	no	—
414	C₂×C₁₉	—	8	4	no	—
415	C₂×C₁₉	C₂²×#121	1	1	yes	characteristic
416	C₂×C₁₉	#3585	1	2	yes	—
417	C₂⁵	—	2	1	no	—
418	C₂×#41	—	2	4	no	—
419	C₂×#41	—	2	1	no	—
420	C₂×#41	—	2	1	no	—
421	C₂×#41	—	2	4	no	—
422	C₂×#41	—	2	4	no	—
423	C₂×#41	—	2	4	no	—
424	C₂×#41	D₄×C₁₉	1	2	yes	—
425	C₂×#41	D₄×C₁₉	1	2	yes	—
426	C₂×#41	C₂³×C₁₉	1	2	yes	—
427	C₂×#41	C₂³×C₁₉	1	2	yes	—
428	C₂×#41	C₂³×C₁₉	1	2	yes	—
429	C₂×#41	C₂³×C₁₉	1	2	yes	—
430	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
431	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
432	C₂²×D₄	—	2	1	no	—
433	C₂²×D₄	—	2	4	no	—
434	C₂²×D₄	—	2	4	no	—
435	C₂²×D₄	—	2	1	no	—
436	C₂²×D₄	—	2	1	no	—
437	C₂²×D₄	—	2	1	no	—
438	C₂²×D₄	—	2	4	no	—
439	C₂²×D₄	D₄×C₁₉	1	2	yes	—
440	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
441	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
442	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
443	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
444	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
445	C₂³×C₄	—	2	1	no	—
446	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
447	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
448	AGL(1,ℤ/8)	—	2	16	no	—
449	AGL(1,ℤ/8)	—	2	16	no	—
450	C₂×SD₁₆	—	2	8	no	—
451	C₂×SD₁₆	C₂³×C₁₉	1	8	yes	—
452	C₂×D₈	—	2	8	no	—
453	C₂×D₈	C₂³×C₁₉	1	8	yes	—
454	#131	—	2	16	no	—
455	#131	—	2	16	no	—
456	C₂×M₁₆	—	2	4	no	—
457	C₂×M₁₆	—	2	16	no	—
458	C₂×M₁₆	D₄×C₁₉	1	8	yes	complemented
459	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
460	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
461	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
462	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
463	C₂×M₁₆	C₂³×C₁₉	1	8	yes	complemented
464	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
465	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
466	C₂²×C₈	C₂³×C₁₉	1	8	yes	complemented
467	C₄⋊Q₈	—	2	2	no	—
468	#127	—	2	4	no	—
469	#127	—	2	4	no	—
470	#127	—	2	2	no	—
471	#124	—	2	4	no	—
472	#124	—	2	4	no	—
473	#124	—	2	2	no	—
474	#124	—	2	2	no	—
475	#123	—	2	4	no	—
476	#123	—	2	4	no	—
477	C₂²⋊Q₈	—	2	4	no	—
478	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	complemented
479	#121	—	2	4	no	—
480	#121	—	2	8	no	—
481	#121	—	2	8	no	—
482	#121	C₂³×C₁₉	1	16	yes	—
483	#121	C₂³×C₁₉	1	8	yes	complemented
484	#120	—	2	4	no	—
485	#120	—	2	8	no	—
486	#120	—	2	8	no	—
487	#120	—	2	4	no	—
488	C₄×D₄	—	2	8	no	—
489	#117	—	2	1	no	—
490	#117	—	2	1	no	—
491	#117	—	2	1	no	—
492	#117	—	2	1	no	—
493	#117	C₂³×C₁₉	1	2	yes	—
494	#117	C₂³×C₁₉	1	2	yes	—
495	#117	C₂³×C₁₉	1	2	yes	—
496	#117	C₂³×C₁₉	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
498	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
499	C₂×C₂²⋊C₄	—	2	1	no	—
500	C₂×C₂²⋊C₄	—	2	1	no	—
501	C₂×C₂²⋊C₄	—	2	4	no	—
502	C₂×C₄²	—	2	1	no	—
503	C₂×C₄²	—	2	1	no	—
504	#107	C₂³×C₁₉	1	8	yes	complemented
505	#106	C₂³×C₁₉	1	8	yes	complemented
506	#103	C₂³×C₁₉	1	8	yes	complemented
507	#102	C₂³×C₁₉	1	16	yes	—
508	#102	C₂³×C₁₉	1	8	yes	complemented
509	C₁₉	#60454	1	1	yes	characteristic, direct product factor, Sylow
510	C₂⁴	—	2	2	no	—
511	C₂⁴	—	2	1	no	—
512	C₂⁴	—	2	2	no	—
513	C₂⁴	—	2	2	no	—
514	C₂⁴	—	4	4	no	—
515	C₂⁴	—	8	4	no	—
516	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
517	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
518	#41	—	2	8	no	—
519	#41	—	2	8	no	—
520	#41	—	2	4	no	—
521	#41	—	2	4	no	—
522	#41	—	2	4	no	—
523	#41	—	2	4	no	—
524	#41	—	2	4	no	—
525	#41	—	2	4	no	—
526	#41	—	2	4	no	—
527	#41	—	2	4	no	—
528	#41	—	4	4	no	—
529	#41	—	4	4	no	—
530	C₂×Q₈	—	2	4	no	—
531	C₂×Q₈	—	2	1	no	—
532	C₂×Q₈	—	2	2	no	—
533	C₂×Q₈	—	2	2	no	—
534	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
535	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
536	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
537	C₂×D₄	—	2	8	no	—
538	C₂×D₄	—	2	2	no	—
539	C₂×D₄	—	2	2	no	—
540	C₂×D₄	—	2	8	no	—
541	C₂×D₄	—	2	16	no	—
542	C₂×D₄	—	2	4	no	—
543	C₂×D₄	—	2	2	no	—
544	C₂×D₄	—	2	4	no	—
545	C₂×D₄	—	2	4	no	—
546	C₂×D₄	—	2	4	no	—
547	C₂×D₄	—	2	2	no	—
548	C₂×D₄	—	2	2	no	—
549	C₂×D₄	—	2	2	no	—
550	C₂×D₄	—	2	1	no	—
551	C₂×D₄	—	2	4	no	—
552	C₂×D₄	—	2	4	no	—
553	C₂×D₄	—	2	4	no	—
554	C₂×D₄	—	2	2	no	—
555	C₂×D₄	—	4	4	no	—
556	C₂×D₄	—	4	4	no	—
557	C₂×D₄	—	4	4	no	—
558	C₂×D₄	—	4	4	no	—
559	C₂×D₄	—	8	8	no	—
560	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
561	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
562	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
563	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
564	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
565	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
566	C₂²×C₄	—	2	4	no	—
567	C₂²×C₄	—	2	4	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	4	4	no	—
574	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
575	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
576	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
577	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
578	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
579	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
580	C₂²×C₄	#41×C₁₉	1	4	yes	—
581	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
582	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
583	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
584	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
585	SD₁₆	—	2	16	no	—
586	D₈	—	2	16	no	—
587	M₁₆	—	2	4	no	—
588	M₁₆	—	2	4	no	—
589	M₁₆	—	2	16	no	—
590	M₁₆	C₂×D₄×C₁₉	1	8	yes	—
591	M₁₆	C₂×D₄×C₁₉	1	8	yes	complemented
592	C₂×C₈	—	2	4	no	—
593	C₂×C₈	—	2	16	no	—
594	C₂×C₈	C₂×D₄×C₁₉	1	8	yes	complemented
595	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
596	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	—	2	8	no	—
600	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
601	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
602	C₂²⋊C₄	—	2	2	no	—
603	C₂²⋊C₄	—	2	2	no	—
604	C₂²⋊C₄	—	2	2	no	—
605	C₂²⋊C₄	—	2	2	no	—
606	C₂²⋊C₄	—	2	8	no	—
607	C₂²⋊C₄	—	2	16	no	—
608	C₂²⋊C₄	—	2	8	no	—
609	C₄²	—	2	2	no	—
610	C₄²	—	2	2	no	—
611	C₄²	—	2	2	no	—
612	C₄²	—	2	2	no	—
613	C₂³	—	2	4	no	—
614	C₂³	—	2	2	no	—
615	C₂³	—	2	4	no	—
616	C₂³	—	4	2	no	—
617	C₂³	—	4	4	no	—
618	C₂³	—	4	8	no	—
619	C₂³	—	4	2	no	—
620	C₂³	—	4	4	no	—
621	C₂³	—	4	4	no	—
622	C₂³	—	4	4	no	—
623	C₂³	—	8	4	no	—
624	C₂³	—	8	4	no	—
625	C₂³	—	8	2	no	—
626	C₂³	—	8	16	no	—
627	C₂³	C₁₉×#121	1	4	yes	—
628	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
629	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
630	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
631	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
632	Q₈	—	2	4	no	—
633	Q₈	—	2	4	no	—
634	Q₈	—	2	2	no	—
635	Q₈	—	2	2	no	—
636	Q₈	—	4	2	no	—
637	D₄	—	2	8	no	—
638	D₄	—	2	8	no	—
639	D₄	—	2	4	no	—
640	D₄	—	2	4	no	—
641	D₄	—	2	2	no	—
642	D₄	—	2	4	no	—
643	D₄	—	2	4	no	—
644	D₄	—	2	2	no	—
645	D₄	—	4	4	no	—
646	D₄	—	4	4	no	—
647	D₄	—	4	4	no	—
648	D₄	—	4	4	no	—
649	D₄	—	4	4	no	—
650	D₄	—	4	2	no	—
651	D₄	—	8	16	no	—
652	D₄	—	8	8	no	—
653	C₂×C₄	—	2	4	no	—
654	C₂×C₄	—	2	8	no	—
655	C₂×C₄	—	2	4	no	—
656	C₂×C₄	—	2	4	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	2	4	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	4	4	no	—
661	C₂×C₄	—	4	2	no	—
662	C₂×C₄	—	4	4	no	—
663	C₂×C₄	—	4	4	no	—
664	C₂×C₄	—	8	2	no	—
665	C₂×C₄	C₁₉×#121	1	4	yes	—
666	C₂×C₄	C₁₉×#121	1	4	yes	—
667	C₂×C₄	C₁₉×#121	1	4	yes	—
668	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
669	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
670	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
671	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
672	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
673	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
674	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
675	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
676	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
677	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
678	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
679	C₈	—	2	4	no	—
680	C₈	C₂²×D₄×C₁₉	1	8	yes	—
681	C₂²	—	2	2	no	—
682	C₂²	—	2	2	no	—
683	C₂²	—	2	2	no	—
684	C₂²	—	2	4	no	—
685	C₂²	—	2	8	no	—
686	C₂²	—	4	4	no	—
687	C₂²	—	4	2	no	—
688	C₂²	—	4	4	no	—
689	C₂²	—	4	8	no	—
690	C₂²	—	4	4	no	—
691	C₂²	—	8	4	no	—
692	C₂²	—	8	8	no	—
693	C₂²	—	8	8	no	—
694	C₂²	—	8	8	no	—
695	C₂²	—	8	4	no	—
696	C₂²	C₂×C₁₉×#121	1	2	yes	—
697	C₂²	C₂×C₁₉×#121	1	2	yes	—
698	C₂²	C₂×C₁₉×#121	1	2	yes	—
699	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
700	C₄	—	2	4	no	—
701	C₄	—	4	2	no	—
702	C₄	—	4	4	no	—
703	C₄	—	4	4	no	—
704	C₄	C₂×C₁₉×#121	1	2	yes	—
705	C₄	C₂×C₁₉×#121	1	2	yes	—
706	C₄	C₂×C₁₉×#121	1	2	yes	—
707	C₄	C₂³×D₄×C₁₉	1	1	yes	characteristic
708	C₄	C₂²×#41×C₁₉	1	1	yes	characteristic
709	C₂	—	2	2	no	—
710	C₂	—	2	2	no	—
711	C₂	—	2	2	no	—
712	C₂	—	4	4	no	—
713	C₂	—	8	4	no	—
714	C₂	—	8	2	no	—
715	C₂	C₂²×C₁₉×#121	1	1	yes	characteristic
716	C₂	C₁₉×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₉×AGL(1,ℤ/8)	C₂	semidirect
2. C₂×C₁₉×#568	C₂	semidirect
3. C₁₉×#3449	C₂	semidirect
4. C₂×C₁₉×#535	C₂	semidirect
5. C₁₉×#3062	C₂	semidirect
6. C₁₉×#3058	C₂	semidirect
7. C₁₉×#3057	C₂	semidirect
8. C₁₉×#3055	C₂	semidirect
9. C₁₉×#2911	C₂	semidirect
10. C₁₉×#2896	C₂	semidirect
11. C₂×C₁₉×#418	C₂	semidirect
17. C₂×C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
18. C₂²×SD₁₆×C₁₉	C₂²	semidirect
19. C₂²×D₈×C₁₉	C₂²	semidirect
21. C₂×C₁₉×#131	C₂²	semidirect
22. C₂×C₁₉×#131	C₂²	semidirect
25. C₂²×M₁₆×C₁₉	C₂²	semidirect
26. C₁₉×#537	C₂²	semidirect
28. C₁₉×#536	C₂²	semidirect
33. C₁₉×#535	C₂²	semidirect
34. C₁₉×#535	C₂²	semidirect
40. C₁₉×#525	C₂²	semidirect
41. C₂×C₁₉×#121	C₂²	semidirect
45. C₁₉×#469	C₂²	semidirect
46. C₁₉×#468	C₂²	semidirect
47. C₁₉×#466	C₂²	semidirect
48. C₁₉×#465	C₂²	semidirect
49. C₁₉×#428	C₂²	semidirect
50. C₁₉×#428	C₂²	semidirect
51. C₁₉×#427	C₂²	semidirect
52. C₁₉×#419	C₂²	semidirect
53. C₁₉×#418	C₂²	semidirect
54. C₁₉×#418	C₂²	semidirect
55. C₁₉×#418	C₂²	semidirect
56. C₁₉×#417	C₂²	semidirect
57. C₁₉×#416	C₂²	semidirect
58. C₂×C₁₉×#102	C₂²	semidirect
100. C₂×M₁₆×C₁₉	D₄	semidirect
105. C₂×M₁₆×C₁₉	C₂³	semidirect
108. C₂²×C₈×C₁₉	C₂³	semidirect
120. C₁₉×C₂²⋊Q₈	C₂³	semidirect
125. C₁₉×#121	C₂³	semidirect
146. C₁₉×#107	C₂³	semidirect
147. C₁₉×#106	C₂³	semidirect
148. C₁₉×#103	C₂³	semidirect
150. C₁₉×#102	C₂³	semidirect
232. M₁₆×C₁₉	C₂×D₄	semidirect
235. C₂×C₈×C₁₉	C₂×D₄	semidirect
254. #60454	C₁₉	direct (N × H)
323. C₂²×AGL(1,ℤ/8)	C₂×C₁₉	semidirect
324. C₂×#568	C₂×C₁₉	semidirect
325. #3449	C₂×C₁₉	semidirect
326. C₂×#535	C₂×C₁₉	semidirect
327. #3062	C₂×C₁₉	semidirect
328. #3058	C₂×C₁₉	semidirect
329. #3057	C₂×C₁₉	semidirect
330. #3055	C₂×C₁₉	semidirect
331. #2911	C₂×C₁₉	semidirect
332. #2896	C₂×C₁₉	semidirect
333. C₂×#418	C₂×C₁₉	semidirect
367. C₂×AGL(1,ℤ/8)	C₂²×C₁₉	semidirect
368. C₂²×SD₁₆	C₂²×C₁₉	semidirect
369. C₂²×D₈	C₂²×C₁₉	semidirect
371. C₂×#131	C₂²×C₁₉	semidirect
372. C₂×#131	C₂²×C₁₉	semidirect
375. C₂²×M₁₆	C₂²×C₁₉	semidirect
376. #537	C₂²×C₁₉	semidirect
378. #536	C₂²×C₁₉	semidirect
383. #535	C₂²×C₁₉	semidirect
384. #535	C₂²×C₁₉	semidirect
390. #525	C₂²×C₁₉	semidirect
391. C₂×#121	C₂²×C₁₉	semidirect
395. #469	C₂²×C₁₉	semidirect
396. #468	C₂²×C₁₉	semidirect
397. #466	C₂²×C₁₉	semidirect
398. #465	C₂²×C₁₉	semidirect
399. #428	C₂²×C₁₉	semidirect
400. #428	C₂²×C₁₉	semidirect
401. #427	C₂²×C₁₉	semidirect
402. #419	C₂²×C₁₉	semidirect
403. #418	C₂²×C₁₉	semidirect
404. #418	C₂²×C₁₉	semidirect
405. #418	C₂²×C₁₉	semidirect
406. #417	C₂²×C₁₉	semidirect
407. #416	C₂²×C₁₉	semidirect
408. C₂×#102	C₂²×C₁₉	semidirect
458. C₂×M₁₆	D₄×C₁₉	semidirect
463. C₂×M₁₆	C₂³×C₁₉	semidirect
466. C₂²×C₈	C₂³×C₁₉	semidirect
478. C₂²⋊Q₈	C₂³×C₁₉	semidirect
483. #121	C₂³×C₁₉	semidirect
504. #107	C₂³×C₁₉	semidirect
505. #106	C₂³×C₁₉	semidirect
506. #103	C₂³×C₁₉	semidirect
508. #102	C₂³×C₁₉	semidirect
509. C₁₉	#60454	direct (N × H)
591. M₁₆	C₂×D₄×C₁₉	semidirect
594. C₂×C₈	C₂×D₄×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×AGL(1,ℤ/8)	2
C₂×C₁₉×#568	2
C₁₉×#3449	2
C₂×C₁₉×#535	2
C₁₉×#3062	2
C₁₉×#3058	2
C₁₉×#3057	2
C₁₉×#3055	2
C₁₉×#2911	2
C₁₉×#2896	2
C₂×C₁₉×#418	2
#60454	19

Subgroups — C19×#60454 #18066413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#60454 #18066413