Subgroups — C₁₉×#23591 #18029550

Order 4864.

1182 conjugacy classes of subgroups.

The subgroup lattice has 582 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	C₁₉×#2328	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2061	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2040	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	C₁₉×#1759	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	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#442	—	2	2	no	—
27	C₁₉×#440	—	2	2	no	—
28	C₄×SD₁₆×C₁₉	—	2	2	no	—
29	C₄×D₈×C₁₉	—	2	2	no	—
30	C₁₉×#428	C₂²	1	2	yes	—
31	C₂×C₁₉×#104	C₂²	1	2	yes	—
32	C₂×C₁₉×#104	C₂²	1	2	yes	—
33	C₁₉×#418	C₂²	1	2	yes	—
34	C₁₉×#417	C₂²	1	2	yes	—
35	C₂×C₁₉×#100	C₂²	1	2	yes	—
36	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
37	C₁₉×#390	C₂²	1	1	yes	characteristic
38	C₁₉×#390	C₂²	1	1	yes	characteristic
39	C₁₉×#386	—	2	2	no	—
40	C₁₉×#386	—	2	2	no	—
41	C₁₉×#382	C₂²	1	1	yes	characteristic
42	C₁₉×#376	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	D₄	1	2	yes	complemented
90	C₄×D₄×C₁₉	D₄	1	2	yes	complemented
91	C₁₉×#117	—	2	2	no	—
92	C₁₉×#117	—	2	2	no	—
93	C₁₉×#117	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
98	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
99	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
100	C₂×C₄²×C₁₉	—	2	2	no	—
101	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
104	C₁₉×#107	—	2	2	no	—
105	C₁₉×#106	—	2	2	no	—
106	C₁₉×#104	—	2	4	no	—
107	C₁₉×#104	—	2	4	no	—
108	C₁₉×#103	—	2	2	no	—
109	C₁₉×#102	—	2	2	no	—
110	C₁₉×#102	—	2	2	no	—
111	C₁₉×#102	—	2	2	no	—
112	C₁₉×#100	—	2	4	no	—
113	C₁₉×#97	—	2	2	no	—
114	C₄×C₈×C₁₉	—	2	2	no	—
115	C₁₉×#95	—	2	1	no	—
116	C₁₉×#95	—	2	1	no	—
117	C₁₉×#95	—	2	2	no	—
118	C₂⁴×C₁₉	—	2	1	no	—
119	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
120	#41×C₁₉	—	2	2	no	—
121	#41×C₁₉	—	2	2	no	—
122	#41×C₁₉	—	2	2	no	—
123	#41×C₁₉	—	2	2	no	—
124	#41×C₁₉	—	8	4	no	—
125	C₂×Q₈×C₁₉	—	2	2	no	—
126	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
127	C₂×D₄×C₁₉	—	2	2	no	—
128	C₂×D₄×C₁₉	—	2	4	no	—
129	C₂×D₄×C₁₉	—	2	4	no	—
130	C₂×D₄×C₁₉	—	2	2	no	—
131	C₂×D₄×C₁₉	—	2	8	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	1	no	—
136	C₂×D₄×C₁₉	—	2	1	no	—
137	C₂×D₄×C₁₉	—	2	1	no	—
138	C₂×D₄×C₁₉	—	2	2	no	—
139	C₂×D₄×C₁₉	—	8	2	no	—
140	C₂×D₄×C₁₉	—	8	2	no	—
141	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
142	C₂×D₄×C₁₉	#41	1	2	yes	complemented
143	C₂²×C₄×C₁₉	—	2	1	no	—
144	C₂²×C₄×C₁₉	—	2	2	no	—
145	C₂²×C₄×C₁₉	—	2	2	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	1	no	—
150	C₂²×C₄×C₁₉	—	2	1	no	—
151	C₂²×C₄×C₁₉	—	4	2	no	—
152	C₂²×C₄×C₁₉	—	8	2	no	—
153	C₂²×C₄×C₁₉	—	8	2	no	—
154	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
158	SD₁₆×C₁₉	—	2	8	no	—
159	D₈×C₁₉	—	2	8	no	—
160	M₁₆×C₁₉	—	2	2	no	—
161	M₁₆×C₁₉	—	2	2	no	—
162	M₁₆×C₁₉	—	2	2	no	—
163	M₁₆×C₁₉	#41	1	4	yes	complemented
164	C₂×C₈×C₁₉	—	2	2	no	—
165	C₂×C₈×C₁₉	—	2	2	no	—
166	C₄⋊C₄×C₁₉	—	2	2	no	—
167	C₄⋊C₄×C₁₉	—	2	2	no	—
168	C₄⋊C₄×C₁₉	—	2	4	no	—
169	C₄⋊C₄×C₁₉	—	2	2	no	—
170	C₄⋊C₄×C₁₉	—	2	2	no	—
171	C₄⋊C₄×C₁₉	—	2	2	no	—
172	C₄⋊C₄×C₁₉	—	2	2	no	—
173	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
174	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
175	C₂²⋊C₄×C₁₉	—	2	4	no	—
176	C₂²⋊C₄×C₁₉	—	2	4	no	—
177	C₂²⋊C₄×C₁₉	—	2	4	no	—
178	C₂²⋊C₄×C₁₉	—	2	2	no	—
179	C₂²⋊C₄×C₁₉	—	2	4	no	—
180	C₂²⋊C₄×C₁₉	—	2	2	no	—
181	C₂²⋊C₄×C₁₉	—	2	2	no	—
182	C₂²⋊C₄×C₁₉	—	4	1	no	—
183	C₂²⋊C₄×C₁₉	—	4	1	no	—
184	C₂²⋊C₄×C₁₉	—	8	2	no	—
185	C₂²⋊C₄×C₁₉	—	8	2	no	—
186	C₄²×C₁₉	—	2	2	no	—
187	C₄²×C₁₉	—	2	2	no	—
188	C₄²×C₁₉	—	2	2	no	—
189	C₄²×C₁₉	—	2	1	no	—
190	C₄²×C₁₉	—	2	2	no	—
191	C₄²×C₁₉	C₂×D₄	1	2	yes	—
192	C₄²×C₁₉	C₂×D₄	1	2	yes	—
193	C₄²×C₁₉	#41	1	2	yes	complemented
194	#23591	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂³×C₁₉	—	2	2	no	—
196	C₂³×C₁₉	—	2	2	no	—
197	C₂³×C₁₉	—	2	2	no	—
198	C₂³×C₁₉	—	2	2	no	—
199	C₂³×C₁₉	—	2	2	no	—
200	C₂³×C₁₉	—	4	2	no	—
201	C₂³×C₁₉	—	4	2	no	—
202	C₂³×C₁₉	—	4	2	no	—
203	C₂³×C₁₉	—	4	2	no	—
204	C₂³×C₁₉	—	4	1	no	—
205	C₂³×C₁₉	—	4	1	no	—
206	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
207	Q₈×C₁₉	—	2	2	no	—
208	Q₈×C₁₉	—	2	2	no	—
209	Q₈×C₁₉	—	8	2	no	—
210	D₄×C₁₉	—	2	2	no	—
211	D₄×C₁₉	—	2	4	no	—
212	D₄×C₁₉	—	2	2	no	—
213	D₄×C₁₉	—	4	2	no	—
214	D₄×C₁₉	—	4	2	no	—
215	D₄×C₁₉	—	4	2	no	—
216	D₄×C₁₉	—	4	2	no	—
217	D₄×C₁₉	—	4	2	no	—
218	D₄×C₁₉	—	8	4	no	—
219	D₄×C₁₉	—	8	8	no	—
220	D₄×C₁₉	—	8	2	no	—
221	D₄×C₁₉	—	8	4	no	—
222	C₂×C₄×C₁₉	—	2	2	no	—
223	C₂×C₄×C₁₉	—	2	2	no	—
224	C₂×C₄×C₁₉	—	2	2	no	—
225	C₂×C₄×C₁₉	—	2	2	no	—
226	C₂×C₄×C₁₉	—	2	2	no	—
227	C₂×C₄×C₁₉	—	4	1	no	—
228	C₂×C₄×C₁₉	—	4	1	no	—
229	C₂×C₄×C₁₉	—	4	4	no	—
230	C₂×C₄×C₁₉	—	4	4	no	—
231	C₂×C₄×C₁₉	—	4	1	no	—
232	C₂×C₄×C₁₉	—	4	1	no	—
233	C₂×C₄×C₁₉	—	4	2	no	—
234	C₂×C₄×C₁₉	—	4	2	no	—
235	C₂×C₄×C₁₉	—	4	2	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	1	no	—
240	C₂×C₄×C₁₉	—	4	1	no	—
241	C₂×C₄×C₁₉	—	8	2	no	—
242	C₂×C₄×C₁₉	—	8	2	no	—
243	C₂×C₄×C₁₉	—	8	4	no	—
244	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
245	C₂×C₄×C₁₉	#120	1	2	yes	—
246	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
247	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
248	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
249	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
250	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
251	C₈×C₁₉	—	2	4	no	—
252	C₈×C₁₉	—	4	2	no	—
253	#3460	C₂×C₁₉	1	1	yes	characteristic, complemented
254	C₄×AGL(1,ℤ/8)	C₂×C₁₉	1	2	yes	complemented
255	#2328	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#2061	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#2040	C₂×C₁₉	1	1	yes	characteristic, complemented
258	#2037	C₂×C₁₉	1	2	yes	complemented
259	#2027	C₂×C₁₉	1	1	yes	characteristic, complemented
260	#2006	C₂×C₁₉	1	1	yes	characteristic, complemented
261	#2002	C₂×C₁₉	1	2	yes	complemented
262	#1759	C₂×C₁₉	1	2	yes	complemented
263	C₄×#100	C₂×C₁₉	1	1	yes	characteristic, complemented
264	C₂²×C₁₉	—	2	1	no	—
265	C₂²×C₁₉	—	2	1	no	—
266	C₂²×C₁₉	—	4	4	no	—
267	C₂²×C₁₉	—	4	4	no	—
268	C₂²×C₁₉	—	4	2	no	—
269	C₂²×C₁₉	—	4	2	no	—
270	C₂²×C₁₉	—	4	2	no	—
271	C₂²×C₁₉	—	4	2	no	—
272	C₂²×C₁₉	—	4	2	no	—
273	C₂²×C₁₉	—	4	2	no	—
274	C₂²×C₁₉	—	4	2	no	—
275	C₂²×C₁₉	—	8	2	no	—
276	C₂²×C₁₉	—	8	2	no	—
277	C₂²×C₁₉	—	8	1	no	—
278	C₂²×C₁₉	—	8	1	no	—
279	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
280	C₂²×C₁₉	#525	1	1	yes	characteristic
281	C₂²×C₁₉	#532	1	1	yes	characteristic
282	C₄×C₁₉	—	2	1	no	—
283	C₄×C₁₉	—	2	1	no	—
284	C₄×C₁₉	—	2	2	no	—
285	C₄×C₁₉	—	4	2	no	—
286	C₄×C₁₉	—	4	2	no	—
287	C₄×C₁₉	—	4	2	no	—
288	C₄×C₁₉	—	4	2	no	—
289	C₄×C₁₉	—	4	2	no	—
290	C₄×C₁₉	—	8	1	no	—
291	C₄×C₁₉	—	8	1	no	—
292	C₄×C₁₉	#525	1	2	yes	—
293	C₄×C₁₉	#532	1	2	yes	—
294	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	2	yes	—
295	#544	C₂²×C₁₉	1	1	yes	characteristic
296	#542	—	2	2	no	—
297	#540	—	2	2	no	—
298	#538	—	2	2	no	—
299	#537	C₂²×C₁₉	1	1	yes	characteristic
300	#535	C₂²×C₁₉	1	2	yes	—
301	#532	—	2	2	no	—
302	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
303	#529	—	2	2	no	—
304	#525	—	2	2	no	—
305	C₄×#41	C₂²×C₁₉	1	2	yes	—
306	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
307	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
308	#442	—	2	2	no	—
309	#440	—	2	2	no	—
310	C₄×SD₁₆	—	2	2	no	—
311	C₄×D₈	—	2	2	no	—
312	#428	C₂²×C₁₉	1	2	yes	—
313	C₂×#104	C₂²×C₁₉	1	2	yes	—
314	C₂×#104	C₂²×C₁₉	1	2	yes	—
315	#418	C₂²×C₁₉	1	2	yes	—
316	#417	C₂²×C₁₉	1	2	yes	—
317	C₂×#100	C₂²×C₁₉	1	2	yes	—
318	C₄×M₁₆	C₂²×C₁₉	1	2	yes	—
319	#390	C₂²×C₁₉	1	1	yes	characteristic
320	#390	C₂²×C₁₉	1	1	yes	characteristic
321	#386	—	2	2	no	—
322	#386	—	2	2	no	—
323	#382	C₂²×C₁₉	1	1	yes	characteristic
324	#376	C₂²×C₁₉	1	1	yes	characteristic
325	#343	C₂²×C₁₉	1	1	yes	characteristic
326	#343	C₂²×C₁₉	1	1	yes	characteristic
327	#339	C₂²×C₁₉	1	2	yes	—
328	#339	C₂²×C₁₉	1	2	yes	—
329	C₂×C₁₉	—	2	1	no	—
330	C₂×C₁₉	—	2	1	no	—
331	C₂×C₁₉	—	8	2	no	—
332	C₂×C₁₉	—	8	2	no	—
333	C₂×C₁₉	—	8	2	no	—
334	C₂×C₁₉	#2388	1	1	yes	characteristic
335	C₂×C₁₉	#3019	1	1	yes	characteristic
336	C₂×C₁₉	#3021	1	1	yes	characteristic
337	C₂×#41	—	2	2	no	—
338	C₂×#41	C₂³×C₁₉	1	2	yes	—
339	C₂²×D₄	—	2	2	no	—
340	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
341	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
342	C₂³×C₄	—	2	1	no	—
343	C₂³×C₄	D₄×C₁₉	1	2	yes	—
344	AGL(1,ℤ/8)	—	2	4	no	—
345	AGL(1,ℤ/8)	—	2	4	no	—
346	C₂×SD₁₆	—	2	2	no	—
347	C₂×D₈	—	2	2	no	—
348	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
349	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
350	C₄⋊Q₈	—	2	2	no	—
351	#127	—	2	2	no	—
352	#127	—	2	2	no	—
353	#127	—	2	2	no	—
354	#126	—	2	4	no	—
355	#125	—	2	2	no	—
356	#124	—	2	4	no	—
357	#124	—	2	2	no	—
358	#123	—	2	4	no	—
359	#123	—	2	4	no	—
360	C₂²⋊Q₈	—	2	2	no	—
361	C₂²⋊Q₈	—	2	2	no	—
362	C₂²⋊Q₈	—	2	2	no	—
363	#121	—	2	2	no	—
364	#121	—	2	4	no	—
365	#121	—	2	2	no	—
366	#121	—	2	2	no	—
367	#121	—	2	2	no	—
368	#121	—	2	2	no	—
369	#120	—	2	4	no	—
370	C₄×Q₈	D₄×C₁₉	1	2	yes	complemented
371	C₄×Q₈	D₄×C₁₉	1	2	yes	complemented
372	C₄×D₄	—	2	4	no	—
373	C₄×D₄	—	2	2	no	—
374	C₄×D₄	—	2	2	no	—
375	C₄×D₄	—	2	2	no	—
376	C₄×D₄	—	2	2	no	—
377	C₄×D₄	—	2	2	no	—
378	C₄×D₄	—	2	2	no	—
379	C₄×D₄	D₄×C₁₉	1	2	yes	complemented
380	C₄×D₄	D₄×C₁₉	1	2	yes	complemented
381	#117	—	2	2	no	—
382	#117	—	2	2	no	—
383	#117	C₂³×C₁₉	1	2	yes	—
384	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
386	C₂×C₂²⋊C₄	—	2	1	no	—
387	C₂×C₂²⋊C₄	—	2	2	no	—
388	C₂×C₂²⋊C₄	—	2	2	no	—
389	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
390	C₂×C₄²	—	2	2	no	—
391	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
392	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
393	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
394	#107	—	2	2	no	—
395	#106	—	2	2	no	—
396	#104	—	2	4	no	—
397	#104	—	2	4	no	—
398	#103	—	2	2	no	—
399	#102	—	2	2	no	—
400	#102	—	2	2	no	—
401	#102	—	2	2	no	—
402	#100	—	2	4	no	—
403	#97	—	2	2	no	—
404	C₄×C₈	—	2	2	no	—
405	#95	—	2	1	no	—
406	#95	—	2	1	no	—
407	#95	—	2	2	no	—
408	C₁₉	#23591	1	1	yes	characteristic, direct product factor, Sylow
409	C₂⁴	—	2	1	no	—
410	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
411	#41	—	2	2	no	—
412	#41	—	2	2	no	—
413	#41	—	2	2	no	—
414	#41	—	2	2	no	—
415	#41	—	8	4	no	—
416	C₂×Q₈	—	2	2	no	—
417	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	4	no	—
420	C₂×D₄	—	2	4	no	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	2	8	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	1	no	—
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	8	2	no	—
431	C₂×D₄	—	8	2	no	—
432	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
433	C₂×D₄	#41×C₁₉	1	2	yes	complemented
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	4	2	no	—
443	C₂²×C₄	—	8	2	no	—
444	C₂²×C₄	—	8	2	no	—
445	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
446	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
447	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
448	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
449	SD₁₆	—	2	8	no	—
450	D₈	—	2	8	no	—
451	M₁₆	—	2	2	no	—
452	M₁₆	—	2	2	no	—
453	M₁₆	—	2	2	no	—
454	M₁₆	#41×C₁₉	1	4	yes	complemented
455	C₂×C₈	—	2	2	no	—
456	C₂×C₈	—	2	2	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	2	4	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
465	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
466	C₂²⋊C₄	—	2	4	no	—
467	C₂²⋊C₄	—	2	4	no	—
468	C₂²⋊C₄	—	2	4	no	—
469	C₂²⋊C₄	—	2	2	no	—
470	C₂²⋊C₄	—	2	4	no	—
471	C₂²⋊C₄	—	2	2	no	—
472	C₂²⋊C₄	—	2	2	no	—
473	C₂²⋊C₄	—	4	1	no	—
474	C₂²⋊C₄	—	4	1	no	—
475	C₂²⋊C₄	—	8	2	no	—
476	C₂²⋊C₄	—	8	2	no	—
477	C₄²	—	2	2	no	—
478	C₄²	—	2	2	no	—
479	C₄²	—	2	2	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	2	no	—
482	C₄²	C₂×D₄×C₁₉	1	2	yes	—
483	C₄²	C₂×D₄×C₁₉	1	2	yes	—
484	C₄²	#41×C₁₉	1	2	yes	complemented
485	C₂³	—	2	2	no	—
486	C₂³	—	2	2	no	—
487	C₂³	—	2	2	no	—
488	C₂³	—	2	2	no	—
489	C₂³	—	2	2	no	—
490	C₂³	—	4	2	no	—
491	C₂³	—	4	2	no	—
492	C₂³	—	4	2	no	—
493	C₂³	—	4	2	no	—
494	C₂³	—	4	1	no	—
495	C₂³	—	4	1	no	—
496	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
497	Q₈	—	2	2	no	—
498	Q₈	—	2	2	no	—
499	Q₈	—	8	2	no	—
500	D₄	—	2	2	no	—
501	D₄	—	2	4	no	—
502	D₄	—	2	2	no	—
503	D₄	—	4	2	no	—
504	D₄	—	4	2	no	—
505	D₄	—	4	2	no	—
506	D₄	—	4	2	no	—
507	D₄	—	4	2	no	—
508	D₄	—	8	8	no	—
509	D₄	—	8	2	no	—
510	D₄	—	8	4	no	—
511	D₄	—	8	4	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	4	no	—
520	C₂×C₄	—	4	4	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	8	2	no	—
532	C₂×C₄	—	8	2	no	—
533	C₂×C₄	—	8	4	no	—
534	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
535	C₂×C₄	C₁₉×#120	1	2	yes	—
536	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
537	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
538	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
539	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
540	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
541	C₈	—	2	4	no	—
542	C₈	—	4	2	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	1	no	—
545	C₂²	—	4	4	no	—
546	C₂²	—	4	4	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	4	2	no	—
550	C₂²	—	4	2	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	8	2	no	—
555	C₂²	—	8	2	no	—
556	C₂²	—	8	1	no	—
557	C₂²	—	8	1	no	—
558	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
559	C₂²	C₁₉×#525	1	1	yes	characteristic
560	C₂²	C₁₉×#532	1	1	yes	characteristic
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	2	2	no	—
564	C₄	—	4	2	no	—
565	C₄	—	4	2	no	—
566	C₄	—	4	2	no	—
567	C₄	—	4	2	no	—
568	C₄	—	4	2	no	—
569	C₄	—	8	1	no	—
570	C₄	—	8	1	no	—
571	C₄	C₁₉×#525	1	2	yes	—
572	C₄	C₁₉×#532	1	2	yes	—
573	C₂	—	2	1	no	—
574	C₂	—	2	1	no	—
575	C₂	—	8	2	no	—
576	C₂	—	8	2	no	—
577	C₂	—	8	2	no	—
578	C₂	C₁₉×#2388	1	1	yes	characteristic
579	C₂	C₁₉×#3019	1	1	yes	characteristic
580	C₂	C₁₉×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×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. C₁₉×#2328	C₂	semidirect
4. C₁₉×#2061	C₂	semidirect
5. C₁₉×#2040	C₂	semidirect
6. C₁₉×#2037	C₂	semidirect
7. C₁₉×#2027	C₂	semidirect
8. C₁₉×#2006	C₂	semidirect
9. C₁₉×#2002	C₂	semidirect
10. C₁₉×#1759	C₂	semidirect
11. C₄×C₁₉×#100	C₂	semidirect
80. C₄×Q₈×C₁₉	D₄	semidirect
81. C₄×Q₈×C₁₉	D₄	semidirect
89. C₄×D₄×C₁₉	D₄	semidirect
90. C₄×D₄×C₁₉	D₄	semidirect
142. C₂×D₄×C₁₉	#41	semidirect
163. M₁₆×C₁₉	#41	semidirect
193. C₄²×C₁₉	#41	semidirect
194. #23591	C₁₉	direct (N × H)
253. #3460	C₂×C₁₉	semidirect
254. C₄×AGL(1,ℤ/8)	C₂×C₁₉	semidirect
255. #2328	C₂×C₁₉	semidirect
256. #2061	C₂×C₁₉	semidirect
257. #2040	C₂×C₁₉	semidirect
258. #2037	C₂×C₁₉	semidirect
259. #2027	C₂×C₁₉	semidirect
260. #2006	C₂×C₁₉	semidirect
261. #2002	C₂×C₁₉	semidirect
262. #1759	C₂×C₁₉	semidirect
263. C₄×#100	C₂×C₁₉	semidirect
370. C₄×Q₈	D₄×C₁₉	semidirect
371. C₄×Q₈	D₄×C₁₉	semidirect
379. C₄×D₄	D₄×C₁₉	semidirect
380. C₄×D₄	D₄×C₁₉	semidirect
408. C₁₉	#23591	direct (N × H)
433. C₂×D₄	#41×C₁₉	semidirect
454. M₁₆	#41×C₁₉	semidirect
484. 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
C₁₉×#2328	2
C₁₉×#2061	2
C₁₉×#2040	2
C₁₉×#2037	2
C₁₉×#2027	2
C₁₉×#2006	2
C₁₉×#2002	2
C₁₉×#1759	2
C₄×C₁₉×#100	2
#23591	19

Subgroups — C19×#23591 #18029550

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23591 #18029550