Subgroups — C₁₉×#23587 #18029546

Order 4864.

1274 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3460	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₁₉×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
3	C₄×C₁₉×#127	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2060	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2039	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2037	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2027	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2006	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2002	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₉×#104	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₉×#100	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	2	yes	—
13	C₁₉×#544	C₂²	1	1	yes	characteristic
14	C₁₉×#542	—	2	2	no	—
15	C₁₉×#540	—	2	2	no	—
16	C₁₉×#538	—	2	2	no	—
17	C₁₉×#537	C₂²	1	1	yes	characteristic
18	C₁₉×#535	C₂²	1	2	yes	—
19	C₁₉×#532	—	2	2	no	—
20	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
21	C₁₉×#529	—	2	2	no	—
22	C₁₉×#525	—	2	2	no	—
23	C₄×#41×C₁₉	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₁₉	—	2	2	no	—
25	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#442	—	2	2	no	—
28	C₁₉×#440	—	2	2	no	—
29	C₄×SD₁₆×C₁₉	—	2	2	no	—
30	C₄×D₈×C₁₉	—	2	2	no	—
31	C₁₉×#428	C₂²	1	2	yes	—
32	C₂×C₁₉×#104	C₂²	1	2	yes	—
33	C₂×C₁₉×#104	C₂²	1	2	yes	—
34	C₁₉×#418	C₂²	1	2	yes	—
35	C₁₉×#417	C₂²	1	2	yes	—
36	C₂×C₁₉×#100	C₂²	1	2	yes	—
37	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
38	C₁₉×#390	—	2	2	no	—
39	C₁₉×#390	C₂²	1	1	yes	characteristic
40	C₁₉×#390	C₂²	1	1	yes	characteristic
41	C₁₉×#384	C₂²	1	1	yes	characteristic
42	C₄³×C₁₉	C₂²	1	1	yes	characteristic
43	C₁₉×#343	C₂²	1	1	yes	characteristic
44	C₁₉×#343	C₂²	1	1	yes	characteristic
45	C₁₉×#339	C₂²	1	2	yes	—
46	C₁₉×#339	C₂²	1	2	yes	—
47	C₂×#41×C₁₉	—	2	2	no	—
48	C₂×#41×C₁₉	C₂³	1	2	yes	—
49	C₂²×D₄×C₁₉	—	2	2	no	—
50	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₁₉	—	2	1	no	—
53	C₂³×C₄×C₁₉	D₄	1	2	yes	—
54	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
55	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
56	C₂×SD₁₆×C₁₉	—	2	2	no	—
57	C₂×D₈×C₁₉	—	2	2	no	—
58	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
59	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
60	C₁₉×C₄⋊Q₈	—	2	2	no	—
61	C₁₉×#127	—	2	2	no	—
62	C₁₉×#127	—	2	2	no	—
63	C₁₉×#127	—	2	2	no	—
64	C₁₉×#126	—	2	4	no	—
65	C₁₉×#125	—	2	2	no	—
66	C₁₉×#124	—	2	4	no	—
67	C₁₉×#124	—	2	2	no	—
68	C₁₉×#123	—	2	4	no	—
69	C₁₉×#123	—	2	4	no	—
70	C₁₉×C₂²⋊Q₈	—	2	2	no	—
71	C₁₉×C₂²⋊Q₈	—	2	2	no	—
72	C₁₉×C₂²⋊Q₈	—	2	2	no	—
73	C₁₉×#121	—	2	2	no	—
74	C₁₉×#121	—	2	4	no	—
75	C₁₉×#121	—	2	2	no	—
76	C₁₉×#121	—	2	2	no	—
77	C₁₉×#121	—	2	2	no	—
78	C₁₉×#121	—	2	2	no	—
79	C₁₉×#120	—	2	4	no	—
80	C₄×Q₈×C₁₉	D₄	1	2	yes	complemented
81	C₄×Q₈×C₁₉	D₄	1	2	yes	complemented
82	C₄×D₄×C₁₉	—	2	4	no	—
83	C₄×D₄×C₁₉	—	2	2	no	—
84	C₄×D₄×C₁₉	—	2	2	no	—
85	C₄×D₄×C₁₉	—	2	2	no	—
86	C₄×D₄×C₁₉	—	2	2	no	—
87	C₄×D₄×C₁₉	—	2	2	no	—
88	C₄×D₄×C₁₉	—	2	2	no	—
89	C₄×D₄×C₁₉	—	4	8	no	—
90	C₄×D₄×C₁₉	D₄	1	2	yes	complemented
91	C₄×D₄×C₁₉	D₄	1	2	yes	complemented
92	C₁₉×#117	—	2	2	no	—
93	C₁₉×#117	—	2	2	no	—
94	C₁₉×#117	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
96	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
98	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
99	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
101	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
102	C₂×C₄²×C₁₉	—	2	1	no	—
103	C₂×C₄²×C₁₉	—	2	2	no	—
104	C₂×C₄²×C₁₉	—	2	1	no	—
105	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
108	C₁₉×#107	—	2	2	no	—
109	C₁₉×#106	—	2	2	no	—
110	C₁₉×#104	—	2	4	no	—
111	C₁₉×#104	—	2	4	no	—
112	C₁₉×#103	—	2	2	no	—
113	C₁₉×#102	—	2	2	no	—
114	C₁₉×#102	—	2	2	no	—
115	C₁₉×#102	—	2	2	no	—
116	C₁₉×#100	—	2	4	no	—
117	C₁₉×#97	—	2	2	no	—
118	C₄×C₈×C₁₉	—	2	2	no	—
119	C₂⁴×C₁₉	—	2	1	no	—
120	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
121	#41×C₁₉	—	2	2	no	—
122	#41×C₁₉	—	2	2	no	—
123	#41×C₁₉	—	2	2	no	—
124	#41×C₁₉	—	2	2	no	—
125	#41×C₁₉	—	8	4	no	—
126	C₂×Q₈×C₁₉	—	2	2	no	—
127	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
128	C₂×D₄×C₁₉	—	2	8	no	—
129	C₂×D₄×C₁₉	—	2	2	no	—
130	C₂×D₄×C₁₉	—	2	4	no	—
131	C₂×D₄×C₁₉	—	2	4	no	—
132	C₂×D₄×C₁₉	—	2	2	no	—
133	C₂×D₄×C₁₉	—	2	2	no	—
134	C₂×D₄×C₁₉	—	2	2	no	—
135	C₂×D₄×C₁₉	—	2	2	no	—
136	C₂×D₄×C₁₉	—	2	1	no	—
137	C₂×D₄×C₁₉	—	2	1	no	—
138	C₂×D₄×C₁₉	—	2	1	no	—
139	C₂×D₄×C₁₉	—	2	2	no	—
140	C₂×D₄×C₁₉	—	4	4	no	—
141	C₂×D₄×C₁₉	—	4	4	no	—
142	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
143	C₂×D₄×C₁₉	#41	1	2	yes	complemented
144	C₂²×C₄×C₁₉	—	2	1	no	—
145	C₂²×C₄×C₁₉	—	2	1	no	—
146	C₂²×C₄×C₁₉	—	2	2	no	—
147	C₂²×C₄×C₁₉	—	2	2	no	—
148	C₂²×C₄×C₁₉	—	2	2	no	—
149	C₂²×C₄×C₁₉	—	2	2	no	—
150	C₂²×C₄×C₁₉	—	2	2	no	—
151	C₂²×C₄×C₁₉	—	2	1	no	—
152	C₂²×C₄×C₁₉	—	4	4	no	—
153	C₂²×C₄×C₁₉	—	4	4	no	—
154	C₂²×C₄×C₁₉	—	4	1	no	—
155	C₂²×C₄×C₁₉	—	4	1	no	—
156	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
160	SD₁₆×C₁₉	—	2	8	no	—
161	D₈×C₁₉	—	2	8	no	—
162	M₁₆×C₁₉	—	2	2	no	—
163	M₁₆×C₁₉	—	2	2	no	—
164	M₁₆×C₁₉	—	2	2	no	—
165	M₁₆×C₁₉	#41	1	4	yes	complemented
166	C₂×C₈×C₁₉	—	2	2	no	—
167	C₂×C₈×C₁₉	—	2	2	no	—
168	C₄⋊C₄×C₁₉	—	2	2	no	—
169	C₄⋊C₄×C₁₉	—	2	2	no	—
170	C₄⋊C₄×C₁₉	—	2	4	no	—
171	C₄⋊C₄×C₁₉	—	2	2	no	—
172	C₄⋊C₄×C₁₉	—	2	2	no	—
173	C₄⋊C₄×C₁₉	—	2	2	no	—
174	C₄⋊C₄×C₁₉	—	2	2	no	—
175	C₄⋊C₄×C₁₉	—	4	4	no	—
176	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
177	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
178	C₂²⋊C₄×C₁₉	—	2	4	no	—
179	C₂²⋊C₄×C₁₉	—	2	4	no	—
180	C₂²⋊C₄×C₁₉	—	2	4	no	—
181	C₂²⋊C₄×C₁₉	—	2	2	no	—
182	C₂²⋊C₄×C₁₉	—	2	4	no	—
183	C₂²⋊C₄×C₁₉	—	2	2	no	—
184	C₂²⋊C₄×C₁₉	—	2	2	no	—
185	C₂²⋊C₄×C₁₉	—	4	4	no	—
186	C₂²⋊C₄×C₁₉	—	4	4	no	—
187	C₂²⋊C₄×C₁₉	—	4	2	no	—
188	C₄²×C₁₉	—	2	4	no	—
189	C₄²×C₁₉	—	2	2	no	—
190	C₄²×C₁₉	—	2	2	no	—
191	C₄²×C₁₉	—	2	2	no	—
192	C₄²×C₁₉	—	2	1	no	—
193	C₄²×C₁₉	—	2	2	no	—
194	C₄²×C₁₉	—	4	2	no	—
195	C₄²×C₁₉	C₂×D₄	1	2	yes	—
196	C₄²×C₁₉	C₂×D₄	1	2	yes	—
197	C₄²×C₁₉	#41	1	2	yes	complemented
198	#23587	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂³×C₁₉	—	2	2	no	—
200	C₂³×C₁₉	—	2	2	no	—
201	C₂³×C₁₉	—	2	2	no	—
202	C₂³×C₁₉	—	2	2	no	—
203	C₂³×C₁₉	—	2	2	no	—
204	C₂³×C₁₉	—	4	2	no	—
205	C₂³×C₁₉	—	4	2	no	—
206	C₂³×C₁₉	—	4	2	no	—
207	C₂³×C₁₉	—	4	2	no	—
208	C₂³×C₁₉	—	4	1	no	—
209	C₂³×C₁₉	—	4	1	no	—
210	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
211	Q₈×C₁₉	—	2	2	no	—
212	Q₈×C₁₉	—	2	2	no	—
213	Q₈×C₁₉	—	8	2	no	—
214	D₄×C₁₉	—	2	2	no	—
215	D₄×C₁₉	—	2	4	no	—
216	D₄×C₁₉	—	2	2	no	—
217	D₄×C₁₉	—	4	16	no	—
218	D₄×C₁₉	—	4	2	no	—
219	D₄×C₁₉	—	4	2	no	—
220	D₄×C₁₉	—	4	2	no	—
221	D₄×C₁₉	—	4	2	no	—
222	D₄×C₁₉	—	4	2	no	—
223	D₄×C₁₉	—	8	4	no	—
224	D₄×C₁₉	—	8	2	no	—
225	D₄×C₁₉	—	8	4	no	—
226	C₂×C₄×C₁₉	—	2	2	no	—
227	C₂×C₄×C₁₉	—	2	2	no	—
228	C₂×C₄×C₁₉	—	2	2	no	—
229	C₂×C₄×C₁₉	—	2	2	no	—
230	C₂×C₄×C₁₉	—	2	2	no	—
231	C₂×C₄×C₁₉	—	2	2	no	—
232	C₂×C₄×C₁₉	—	2	2	no	—
233	C₂×C₄×C₁₉	—	2	2	no	—
234	C₂×C₄×C₁₉	—	2	2	no	—
235	C₂×C₄×C₁₉	—	4	1	no	—
236	C₂×C₄×C₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	—	4	1	no	—
238	C₂×C₄×C₁₉	—	4	2	no	—
239	C₂×C₄×C₁₉	—	4	2	no	—
240	C₂×C₄×C₁₉	—	4	4	no	—
241	C₂×C₄×C₁₉	—	4	4	no	—
242	C₂×C₄×C₁₉	—	4	2	no	—
243	C₂×C₄×C₁₉	—	4	2	no	—
244	C₂×C₄×C₁₉	—	4	1	no	—
245	C₂×C₄×C₁₉	—	8	2	no	—
246	C₂×C₄×C₁₉	—	8	2	no	—
247	C₂×C₄×C₁₉	—	8	2	no	—
248	C₂×C₄×C₁₉	—	8	2	no	—
249	C₂×C₄×C₁₉	#120	1	2	yes	—
250	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
251	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
252	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
253	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
254	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
255	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
256	C₈×C₁₉	—	2	4	no	—
257	C₈×C₁₉	—	4	2	no	—
258	#3460	C₂×C₁₉	1	1	yes	characteristic, complemented
259	C₄×AGL(1,ℤ/8)	C₂×C₁₉	1	2	yes	complemented
260	C₄×#127	C₂×C₁₉	1	1	yes	characteristic, complemented
261	#2060	C₂×C₁₉	1	1	yes	characteristic, complemented
262	#2039	C₂×C₁₉	1	1	yes	characteristic, complemented
263	#2037	C₂×C₁₉	1	2	yes	complemented
264	#2027	C₂×C₁₉	1	1	yes	characteristic, complemented
265	#2006	C₂×C₁₉	1	1	yes	characteristic, complemented
266	#2002	C₂×C₁₉	1	2	yes	complemented
267	C₄×#104	C₂×C₁₉	1	2	yes	complemented
268	C₄×#100	C₂×C₁₉	1	1	yes	characteristic, complemented
269	C₂²×C₁₉	—	2	1	no	—
270	C₂²×C₁₉	—	2	1	no	—
271	C₂²×C₁₉	—	4	4	no	—
272	C₂²×C₁₉	—	4	4	no	—
273	C₂²×C₁₉	—	4	2	no	—
274	C₂²×C₁₉	—	4	2	no	—
275	C₂²×C₁₉	—	4	2	no	—
276	C₂²×C₁₉	—	4	2	no	—
277	C₂²×C₁₉	—	4	2	no	—
278	C₂²×C₁₉	—	4	2	no	—
279	C₂²×C₁₉	—	4	2	no	—
280	C₂²×C₁₉	—	8	2	no	—
281	C₂²×C₁₉	—	8	2	no	—
282	C₂²×C₁₉	—	8	1	no	—
283	C₂²×C₁₉	—	8	1	no	—
284	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
285	C₂²×C₁₉	#525	1	1	yes	characteristic
286	C₂²×C₁₉	#532	1	1	yes	characteristic
287	C₄×C₁₉	—	2	4	no	—
288	C₄×C₁₉	—	2	1	no	—
289	C₄×C₁₉	—	2	2	no	—
290	C₄×C₁₉	—	4	2	no	—
291	C₄×C₁₉	—	4	2	no	—
292	C₄×C₁₉	—	4	2	no	—
293	C₄×C₁₉	—	4	2	no	—
294	C₄×C₁₉	—	4	2	no	—
295	C₄×C₁₉	—	8	1	no	—
296	C₄×C₁₉	#453	1	2	yes	—
297	C₄×C₁₉	#525	1	2	yes	—
298	C₄×C₁₉	#532	1	2	yes	—
299	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	2	yes	—
300	#544	C₂²×C₁₉	1	1	yes	characteristic
301	#542	—	2	2	no	—
302	#540	—	2	2	no	—
303	#538	—	2	2	no	—
304	#537	C₂²×C₁₉	1	1	yes	characteristic
305	#535	C₂²×C₁₉	1	2	yes	—
306	#532	—	2	2	no	—
307	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
308	#529	—	2	2	no	—
309	#525	—	2	2	no	—
310	C₄×#41	C₂²×C₁₉	1	2	yes	—
311	C₂×C₄×D₄	—	2	2	no	—
312	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
313	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
314	#442	—	2	2	no	—
315	#440	—	2	2	no	—
316	C₄×SD₁₆	—	2	2	no	—
317	C₄×D₈	—	2	2	no	—
318	#428	C₂²×C₁₉	1	2	yes	—
319	C₂×#104	C₂²×C₁₉	1	2	yes	—
320	C₂×#104	C₂²×C₁₉	1	2	yes	—
321	#418	C₂²×C₁₉	1	2	yes	—
322	#417	C₂²×C₁₉	1	2	yes	—
323	C₂×#100	C₂²×C₁₉	1	2	yes	—
324	C₄×M₁₆	C₂²×C₁₉	1	2	yes	—
325	#390	—	2	2	no	—
326	#390	C₂²×C₁₉	1	1	yes	characteristic
327	#390	C₂²×C₁₉	1	1	yes	characteristic
328	#384	C₂²×C₁₉	1	1	yes	characteristic
329	C₄³	C₂²×C₁₉	1	1	yes	characteristic
330	#343	C₂²×C₁₉	1	1	yes	characteristic
331	#343	C₂²×C₁₉	1	1	yes	characteristic
332	#339	C₂²×C₁₉	1	2	yes	—
333	#339	C₂²×C₁₉	1	2	yes	—
334	C₂×C₁₉	—	2	1	no	—
335	C₂×C₁₉	—	2	1	no	—
336	C₂×C₁₉	—	8	2	no	—
337	C₂×C₁₉	—	8	2	no	—
338	C₂×C₁₉	—	8	2	no	—
339	C₂×C₁₉	#2388	1	1	yes	characteristic
340	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
341	C₂×C₁₉	#3018	1	1	yes	characteristic
342	C₂×#41	—	2	2	no	—
343	C₂×#41	C₂³×C₁₉	1	2	yes	—
344	C₂²×D₄	—	2	2	no	—
345	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
346	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
347	C₂³×C₄	—	2	1	no	—
348	C₂³×C₄	D₄×C₁₉	1	2	yes	—
349	AGL(1,ℤ/8)	—	2	4	no	—
350	AGL(1,ℤ/8)	—	2	4	no	—
351	C₂×SD₁₆	—	2	2	no	—
352	C₂×D₈	—	2	2	no	—
353	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
354	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
355	C₄⋊Q₈	—	2	2	no	—
356	#127	—	2	2	no	—
357	#127	—	2	2	no	—
358	#127	—	2	2	no	—
359	#126	—	2	4	no	—
360	#125	—	2	2	no	—
361	#124	—	2	4	no	—
362	#124	—	2	2	no	—
363	#123	—	2	4	no	—
364	#123	—	2	4	no	—
365	C₂²⋊Q₈	—	2	2	no	—
366	C₂²⋊Q₈	—	2	2	no	—
367	C₂²⋊Q₈	—	2	2	no	—
368	#121	—	2	2	no	—
369	#121	—	2	4	no	—
370	#121	—	2	2	no	—
371	#121	—	2	2	no	—
372	#121	—	2	2	no	—
373	#121	—	2	2	no	—
374	#120	—	2	4	no	—
375	C₄×Q₈	D₄×C₁₉	1	2	yes	complemented
376	C₄×Q₈	D₄×C₁₉	1	2	yes	complemented
377	C₄×D₄	—	2	4	no	—
378	C₄×D₄	—	2	2	no	—
379	C₄×D₄	—	2	2	no	—
380	C₄×D₄	—	2	2	no	—
381	C₄×D₄	—	2	2	no	—
382	C₄×D₄	—	2	2	no	—
383	C₄×D₄	—	2	2	no	—
384	C₄×D₄	—	4	8	no	—
385	C₄×D₄	D₄×C₁₉	1	2	yes	complemented
386	C₄×D₄	D₄×C₁₉	1	2	yes	complemented
387	#117	—	2	2	no	—
388	#117	—	2	2	no	—
389	#117	C₂³×C₁₉	1	2	yes	—
390	C₂×C₄⋊C₄	—	2	2	no	—
391	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
393	C₂×C₂²⋊C₄	—	2	2	no	—
394	C₂×C₂²⋊C₄	—	2	2	no	—
395	C₂×C₂²⋊C₄	—	2	1	no	—
396	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
397	C₂×C₄²	—	2	1	no	—
398	C₂×C₄²	—	2	2	no	—
399	C₂×C₄²	—	2	1	no	—
400	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
401	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
402	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
403	#107	—	2	2	no	—
404	#106	—	2	2	no	—
405	#104	—	2	4	no	—
406	#104	—	2	4	no	—
407	#103	—	2	2	no	—
408	#102	—	2	2	no	—
409	#102	—	2	2	no	—
410	#102	—	2	2	no	—
411	#100	—	2	4	no	—
412	#97	—	2	2	no	—
413	C₄×C₈	—	2	2	no	—
414	C₁₉	#23587	1	1	yes	characteristic, direct product factor, Sylow
415	C₂⁴	—	2	1	no	—
416	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
417	#41	—	2	2	no	—
418	#41	—	2	2	no	—
419	#41	—	2	2	no	—
420	#41	—	2	2	no	—
421	#41	—	8	4	no	—
422	C₂×Q₈	—	2	2	no	—
423	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
424	C₂×D₄	—	2	8	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	4	no	—
427	C₂×D₄	—	2	4	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	1	no	—
434	C₂×D₄	—	2	1	no	—
435	C₂×D₄	—	2	1	no	—
436	C₂×D₄	—	4	4	no	—
437	C₂×D₄	—	4	4	no	—
438	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
439	C₂×D₄	#41×C₁₉	1	2	yes	complemented
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	4	4	no	—
449	C₂²×C₄	—	4	4	no	—
450	C₂²×C₄	—	4	1	no	—
451	C₂²×C₄	—	4	1	no	—
452	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
453	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
454	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
455	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
456	SD₁₆	—	2	8	no	—
457	D₈	—	2	8	no	—
458	M₁₆	—	2	2	no	—
459	M₁₆	—	2	2	no	—
460	M₁₆	—	2	2	no	—
461	M₁₆	#41×C₁₉	1	4	yes	complemented
462	C₂×C₈	—	2	2	no	—
463	C₂×C₈	—	2	2	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	2	4	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	4	4	no	—
472	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
473	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
474	C₂²⋊C₄	—	2	4	no	—
475	C₂²⋊C₄	—	2	4	no	—
476	C₂²⋊C₄	—	2	4	no	—
477	C₂²⋊C₄	—	2	2	no	—
478	C₂²⋊C₄	—	2	4	no	—
479	C₂²⋊C₄	—	2	2	no	—
480	C₂²⋊C₄	—	2	2	no	—
481	C₂²⋊C₄	—	4	4	no	—
482	C₂²⋊C₄	—	4	4	no	—
483	C₂²⋊C₄	—	4	2	no	—
484	C₄²	—	2	4	no	—
485	C₄²	—	2	2	no	—
486	C₄²	—	2	2	no	—
487	C₄²	—	2	2	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	2	no	—
490	C₄²	—	4	2	no	—
491	C₄²	C₂×D₄×C₁₉	1	2	yes	—
492	C₄²	C₂×D₄×C₁₉	1	2	yes	—
493	C₄²	#41×C₁₉	1	2	yes	complemented
494	C₂³	—	2	2	no	—
495	C₂³	—	2	2	no	—
496	C₂³	—	2	2	no	—
497	C₂³	—	2	2	no	—
498	C₂³	—	2	2	no	—
499	C₂³	—	4	2	no	—
500	C₂³	—	4	2	no	—
501	C₂³	—	4	2	no	—
502	C₂³	—	4	2	no	—
503	C₂³	—	4	1	no	—
504	C₂³	—	4	1	no	—
505	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
506	Q₈	—	2	2	no	—
507	Q₈	—	2	2	no	—
508	Q₈	—	8	2	no	—
509	D₄	—	2	2	no	—
510	D₄	—	2	4	no	—
511	D₄	—	2	2	no	—
512	D₄	—	4	16	no	—
513	D₄	—	4	2	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	2	no	—
516	D₄	—	4	2	no	—
517	D₄	—	4	2	no	—
518	D₄	—	8	2	no	—
519	D₄	—	8	4	no	—
520	D₄	—	8	4	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	4	no	—
534	C₂×C₄	—	4	4	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	8	2	no	—
541	C₂×C₄	—	8	2	no	—
542	C₂×C₄	—	8	2	no	—
543	C₂×C₄	—	8	2	no	—
544	C₂×C₄	C₁₉×#120	1	2	yes	—
545	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
546	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
547	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
548	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
549	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
550	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
551	C₈	—	2	4	no	—
552	C₈	—	4	2	no	—
553	C₂²	—	2	1	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	4	4	no	—
556	C₂²	—	4	4	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	2	no	—
561	C₂²	—	4	2	no	—
562	C₂²	—	4	2	no	—
563	C₂²	—	4	2	no	—
564	C₂²	—	8	2	no	—
565	C₂²	—	8	2	no	—
566	C₂²	—	8	1	no	—
567	C₂²	—	8	1	no	—
568	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
569	C₂²	C₁₉×#525	1	1	yes	characteristic
570	C₂²	C₁₉×#532	1	1	yes	characteristic
571	C₄	—	2	4	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	2	no	—
574	C₄	—	4	2	no	—
575	C₄	—	4	2	no	—
576	C₄	—	4	2	no	—
577	C₄	—	4	2	no	—
578	C₄	—	4	2	no	—
579	C₄	—	8	1	no	—
580	C₄	C₁₉×#453	1	2	yes	—
581	C₄	C₁₉×#525	1	2	yes	—
582	C₄	C₁₉×#532	1	2	yes	—
583	C₂	—	2	1	no	—
584	C₂	—	2	1	no	—
585	C₂	—	8	2	no	—
586	C₂	—	8	2	no	—
587	C₂	—	8	2	no	—
588	C₂	C₁₉×#2388	1	1	yes	characteristic
589	C₂	C₂×C₁₉×#453	1	1	yes	characteristic
590	C₂	C₁₉×#3018	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂×#120
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3460	C₂	semidirect
2. C₄×C₁₉×AGL(1,ℤ/8)	C₂	semidirect
3. C₄×C₁₉×#127	C₂	semidirect
4. C₁₉×#2060	C₂	semidirect
5. C₁₉×#2039	C₂	semidirect
6. C₁₉×#2037	C₂	semidirect
7. C₁₉×#2027	C₂	semidirect
8. C₁₉×#2006	C₂	semidirect
9. C₁₉×#2002	C₂	semidirect
10. C₄×C₁₉×#104	C₂	semidirect
11. C₄×C₁₉×#100	C₂	semidirect
80. C₄×Q₈×C₁₉	D₄	semidirect
81. C₄×Q₈×C₁₉	D₄	semidirect
90. C₄×D₄×C₁₉	D₄	semidirect
91. C₄×D₄×C₁₉	D₄	semidirect
143. C₂×D₄×C₁₉	#41	semidirect
165. M₁₆×C₁₉	#41	semidirect
197. C₄²×C₁₉	#41	semidirect
198. #23587	C₁₉	direct (N × H)
258. #3460	C₂×C₁₉	semidirect
259. C₄×AGL(1,ℤ/8)	C₂×C₁₉	semidirect
260. C₄×#127	C₂×C₁₉	semidirect
261. #2060	C₂×C₁₉	semidirect
262. #2039	C₂×C₁₉	semidirect
263. #2037	C₂×C₁₉	semidirect
264. #2027	C₂×C₁₉	semidirect
265. #2006	C₂×C₁₉	semidirect
266. #2002	C₂×C₁₉	semidirect
267. C₄×#104	C₂×C₁₉	semidirect
268. C₄×#100	C₂×C₁₉	semidirect
375. C₄×Q₈	D₄×C₁₉	semidirect
376. C₄×Q₈	D₄×C₁₉	semidirect
385. C₄×D₄	D₄×C₁₉	semidirect
386. C₄×D₄	D₄×C₁₉	semidirect
414. C₁₉	#23587	direct (N × H)
439. C₂×D₄	#41×C₁₉	semidirect
461. M₁₆	#41×C₁₉	semidirect
493. C₄²	#41×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3460	2
C₄×C₁₉×AGL(1,ℤ/8)	2
C₄×C₁₉×#127	2
C₁₉×#2060	2
C₁₉×#2039	2
C₁₉×#2037	2
C₁₉×#2027	2
C₁₉×#2006	2
C₁₉×#2002	2
C₄×C₁₉×#104	2
C₄×C₁₉×#100	2
#23587	19

Subgroups — C19×#23587 #18029546

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23587 #18029546