Subgroups — C₁₉×#26850 #18032809

Order 4864.

776 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3136	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3096	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3081	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2946	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2063	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2060	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2051	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2002	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1957	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1937	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1931	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1931	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1887	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1859	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1772	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
17	C₁₉×#544	C₂²	1	1	yes	characteristic
18	C₁₉×#535	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
20	C₁₉×#520	C₂²	1	1	yes	characteristic
21	C₁₉×#518	C₂²	1	1	yes	characteristic
22	C₁₉×#490	—	2	1	no	—
23	C₁₉×#489	—	2	1	no	—
24	C₁₉×#488	—	2	1	no	—
25	C₁₉×#486	—	2	1	no	—
26	C₁₉×#482	—	2	1	no	—
27	C₁₉×#482	—	2	1	no	—
28	C₁₉×#481	—	2	1	no	—
29	C₁₉×#480	—	2	1	no	—
30	C₁₉×#478	—	2	1	no	—
31	C₁₉×#478	—	2	1	no	—
32	C₁₉×#476	—	2	1	no	—
33	C₁₉×#474	—	2	1	no	—
34	C₁₉×#442	—	2	1	no	—
35	C₁₉×#440	—	2	1	no	—
36	C₄×SD₁₆×C₁₉	—	2	1	no	—
37	C₄×D₈×C₁₉	—	2	1	no	—
38	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
39	C₁₉×#428	C₂²	1	1	yes	characteristic
40	C₁₉×#428	C₂²	1	1	yes	characteristic
41	C₁₉×#428	C₂²	1	1	yes	characteristic
42	C₁₉×#427	C₂²	1	1	yes	characteristic
43	C₁₉×#424	C₂²	1	1	yes	characteristic
44	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
45	C₁₉×#418	C₂²	1	1	yes	characteristic
46	C₁₉×#418	C₂²	1	1	yes	characteristic
47	C₁₉×#418	C₂²	1	1	yes	characteristic
48	C₁₉×#417	C₂²	1	1	yes	characteristic
49	C₁₉×#416	C₂²	1	1	yes	characteristic
50	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
51	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
52	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
53	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
54	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
55	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
56	C₁₉×#408	C₂²	1	1	yes	characteristic
57	C₁₉×#405	C₂²	1	1	yes	characteristic
58	C₁₉×#405	C₂²	1	1	yes	characteristic
59	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
60	C₁₉×#384	C₂²	1	1	yes	characteristic
61	C₁₉×#343	C₂²	1	1	yes	characteristic
62	C₁₉×#343	C₂²	1	1	yes	characteristic
63	C₁₉×#341	C₂²	1	1	yes	characteristic
64	C₁₉×#339	C₂²	1	1	yes	characteristic
65	C₁₉×#339	C₂²	1	1	yes	characteristic
66	C₁₉×#339	C₂²	1	1	yes	characteristic
67	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₁₉	—	4	1	no	—
69	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
71	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
72	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
73	C₂×SD₁₆×C₁₉	—	2	1	no	—
74	C₂×D₈×C₁₉	—	2	1	no	—
75	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
76	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
77	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
78	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
81	C₁₉×C₄⋊Q₈	—	2	1	no	—
82	C₁₉×C₄⋊Q₈	—	2	1	no	—
83	C₁₉×#127	—	2	1	no	—
84	C₁₉×#127	—	2	2	no	—
85	C₁₉×#127	—	2	2	no	—
86	C₁₉×#125	—	2	1	no	—
87	C₁₉×#125	—	2	1	no	—
88	C₁₉×#124	—	2	1	no	—
89	C₁₉×C₂²⋊Q₈	—	4	1	no	—
90	C₁₉×#121	—	2	1	no	—
91	C₁₉×#121	—	2	1	no	—
92	C₁₉×#120	—	4	1	no	—
93	C₄×Q₈×C₁₉	—	2	1	no	—
94	C₄×D₄×C₁₉	—	2	1	no	—
95	C₄×D₄×C₁₉	—	2	1	no	—
96	C₄×D₄×C₁₉	—	2	1	no	—
97	C₄×D₄×C₁₉	—	2	1	no	—
98	C₄×D₄×C₁₉	—	2	1	no	—
99	C₄×D₄×C₁₉	—	4	1	no	—
100	C₁₉×#117	—	2	1	no	—
101	C₁₉×#117	C₂³	1	1	yes	characteristic
102	C₁₉×#117	C₂³	1	1	yes	characteristic
103	C₁₉×#117	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
105	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
106	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
109	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
110	C₁₉×#108	—	2	2	no	—
111	C₁₉×#107	—	2	1	no	—
112	C₁₉×#107	—	2	1	no	—
113	C₁₉×#107	—	2	1	no	—
114	C₁₉×#107	D₄	1	1	yes	characteristic, complemented
115	C₁₉×#107	D₄	1	1	yes	characteristic, complemented
116	C₁₉×#106	—	2	1	no	—
117	C₁₉×#106	—	2	1	no	—
118	C₁₉×#106	—	2	1	no	—
119	C₁₉×#106	D₄	1	1	yes	characteristic, complemented
120	C₁₉×#106	D₄	1	1	yes	characteristic, complemented
121	C₁₉×C₄⋊C₈	—	2	1	no	—
122	C₁₉×C₄⋊C₈	—	2	1	no	—
123	C₁₉×#104	—	2	2	no	—
124	C₁₉×#103	—	2	1	no	—
125	C₁₉×#103	D₄	1	1	yes	characteristic, complemented
126	C₁₉×#103	D₄	1	1	yes	characteristic, complemented
127	C₁₉×#102	—	2	1	no	—
128	C₁₉×#102	—	2	1	no	—
129	C₁₉×#102	—	2	1	no	—
130	C₁₉×#102	—	2	1	no	—
131	C₁₉×#102	—	2	1	no	—
132	C₁₉×#102	—	2	1	no	—
133	C₁₉×#102	—	2	1	no	—
134	C₁₉×#102	—	2	1	no	—
135	C₁₉×#102	—	2	1	no	—
136	C₁₉×#102	—	2	1	no	—
137	C₁₉×#102	—	2	1	no	—
138	C₁₉×#102	—	2	1	no	—
139	C₁₉×#102	—	2	1	no	—
140	C₁₉×#102	—	2	1	no	—
141	C₁₉×#102	—	2	1	no	—
142	C₁₉×#102	D₄	1	1	yes	characteristic, complemented
143	C₁₉×#102	D₄	1	1	yes	characteristic, complemented
144	C₁₉×#100	—	2	2	no	—
145	C₁₉×#100	—	2	2	no	—
146	C₁₉×C₂²⋊C₈	—	2	1	no	—
147	C₁₉×C₂²⋊C₈	—	2	1	no	—
148	C₁₉×#97	—	2	1	no	—
149	C₁₉×#97	—	2	1	no	—
150	C₄×C₈×C₁₉	—	2	1	no	—
151	C₄×C₈×C₁₉	—	2	1	no	—
152	C₄×C₈×C₁₉	—	2	2	no	—
153	C₂⁴×C₁₉	—	2	1	no	—
154	C₂⁴×C₁₉	—	2	1	no	—
155	#41×C₁₉	—	2	1	no	—
156	#41×C₁₉	—	2	1	no	—
157	#41×C₁₉	—	2	1	no	—
158	#41×C₁₉	—	2	1	no	—
159	C₂×Q₈×C₁₉	—	4	1	no	—
160	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₂×D₄×C₁₉	—	2	1	no	—
162	C₂×D₄×C₁₉	—	2	1	no	—
163	C₂×D₄×C₁₉	—	2	1	no	—
164	C₂×D₄×C₁₉	—	2	1	no	—
165	C₂×D₄×C₁₉	—	2	1	no	—
166	C₂×D₄×C₁₉	—	2	1	no	—
167	C₂×D₄×C₁₉	—	2	1	no	—
168	C₂×D₄×C₁₉	—	2	1	no	—
169	C₂×D₄×C₁₉	—	2	1	no	—
170	C₂×D₄×C₁₉	—	2	1	no	—
171	C₂×D₄×C₁₉	—	2	1	no	—
172	C₂×D₄×C₁₉	—	2	1	no	—
173	C₂×D₄×C₁₉	—	4	4	no	—
174	C₂×D₄×C₁₉	—	4	1	no	—
175	C₂×D₄×C₁₉	—	4	1	no	—
176	C₂×D₄×C₁₉	—	8	2	no	—
177	C₂×D₄×C₁₉	—	8	2	no	—
178	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
179	C₂×D₄×C₁₉	#41	1	2	yes	—
180	C₂²×C₄×C₁₉	—	2	1	no	—
181	C₂²×C₄×C₁₉	—	2	1	no	—
182	C₂²×C₄×C₁₉	—	2	1	no	—
183	C₂²×C₄×C₁₉	—	2	1	no	—
184	C₂²×C₄×C₁₉	—	4	1	no	—
185	C₂²×C₄×C₁₉	—	4	1	no	—
186	C₂²×C₄×C₁₉	—	4	1	no	—
187	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
188	SD₁₆×C₁₉	—	2	4	no	—
189	D₈×C₁₉	—	2	4	no	—
190	M₁₆×C₁₉	—	2	1	no	—
191	M₁₆×C₁₉	—	2	1	no	—
192	M₁₆×C₁₉	—	2	1	no	—
193	M₁₆×C₁₉	—	2	1	no	—
194	M₁₆×C₁₉	—	2	1	no	—
195	M₁₆×C₁₉	—	2	1	no	—
196	M₁₆×C₁₉	—	2	1	no	—
197	M₁₆×C₁₉	#41	1	2	yes	—
198	C₂×C₈×C₁₉	—	2	1	no	—
199	C₂×C₈×C₁₉	—	2	1	no	—
200	C₂×C₈×C₁₉	—	2	1	no	—
201	C₂×C₈×C₁₉	—	2	1	no	—
202	C₂×C₈×C₁₉	—	2	1	no	—
203	C₂×C₈×C₁₉	—	2	1	no	—
204	C₂×C₈×C₁₉	—	2	1	no	—
205	C₂×C₈×C₁₉	—	2	1	no	—
206	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
207	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
209	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
210	C₄⋊C₄×C₁₉	—	2	1	no	—
211	C₄⋊C₄×C₁₉	—	2	1	no	—
212	C₄⋊C₄×C₁₉	—	2	1	no	—
213	C₄⋊C₄×C₁₉	—	2	1	no	—
214	C₄⋊C₄×C₁₉	—	4	1	no	—
215	C₄⋊C₄×C₁₉	—	4	1	no	—
216	C₄⋊C₄×C₁₉	—	4	1	no	—
217	C₄⋊C₄×C₁₉	—	4	1	no	—
218	C₄⋊C₄×C₁₉	—	8	2	no	—
219	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
220	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
221	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
222	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
223	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
224	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
225	C₂²⋊C₄×C₁₉	—	2	1	no	—
226	C₂²⋊C₄×C₁₉	—	2	1	no	—
227	C₂²⋊C₄×C₁₉	—	2	1	no	—
228	C₂²⋊C₄×C₁₉	—	4	1	no	—
229	C₂²⋊C₄×C₁₉	—	4	1	no	—
230	C₂²⋊C₄×C₁₉	—	4	1	no	—
231	C₂²⋊C₄×C₁₉	—	4	1	no	—
232	C₂²⋊C₄×C₁₉	—	4	1	no	—
233	C₄²×C₁₉	—	2	1	no	—
234	C₄²×C₁₉	—	2	1	no	—
235	C₄²×C₁₉	—	2	1	no	—
236	C₄²×C₁₉	—	2	1	no	—
237	C₄²×C₁₉	—	4	1	no	—
238	C₄²×C₁₉	#41	1	2	yes	—
239	#26850	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
240	C₂³×C₁₉	—	2	1	no	—
241	C₂³×C₁₉	—	2	2	no	—
242	C₂³×C₁₉	—	4	1	no	—
243	C₂³×C₁₉	—	4	1	no	—
244	C₂³×C₁₉	—	4	1	no	—
245	C₂³×C₁₉	—	4	1	no	—
246	C₂³×C₁₉	—	4	1	no	—
247	C₂³×C₁₉	—	8	1	no	—
248	C₂³×C₁₉	—	8	1	no	—
249	C₂³×C₁₉	—	8	1	no	—
250	C₂³×C₁₉	—	8	1	no	—
251	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
252	Q₈×C₁₉	—	2	1	no	—
253	Q₈×C₁₉	—	2	1	no	—
254	Q₈×C₁₉	—	16	1	no	—
255	D₄×C₁₉	—	2	1	no	—
256	D₄×C₁₉	—	2	2	no	—
257	D₄×C₁₉	—	2	1	no	—
258	D₄×C₁₉	—	2	2	no	—
259	D₄×C₁₉	—	4	1	no	—
260	D₄×C₁₉	—	4	1	no	—
261	D₄×C₁₉	—	4	1	no	—
262	D₄×C₁₉	—	4	1	no	—
263	D₄×C₁₉	—	4	1	no	—
264	D₄×C₁₉	—	4	1	no	—
265	D₄×C₁₉	—	4	1	no	—
266	D₄×C₁₉	—	4	1	no	—
267	D₄×C₁₉	—	8	8	no	—
268	D₄×C₁₉	—	16	1	no	—
269	D₄×C₁₉	—	16	1	no	—
270	C₂×C₄×C₁₉	—	2	2	no	—
271	C₂×C₄×C₁₉	—	2	2	no	—
272	C₂×C₄×C₁₉	—	2	2	no	—
273	C₂×C₄×C₁₉	—	2	1	no	—
274	C₂×C₄×C₁₉	—	2	1	no	—
275	C₂×C₄×C₁₉	—	2	1	no	—
276	C₂×C₄×C₁₉	—	2	1	no	—
277	C₂×C₄×C₁₉	—	2	1	no	—
278	C₂×C₄×C₁₉	—	2	1	no	—
279	C₂×C₄×C₁₉	—	2	1	no	—
280	C₂×C₄×C₁₉	—	4	1	no	—
281	C₂×C₄×C₁₉	—	4	1	no	—
282	C₂×C₄×C₁₉	—	4	1	no	—
283	C₂×C₄×C₁₉	—	4	1	no	—
284	C₂×C₄×C₁₉	—	8	1	no	—
285	C₂×C₄×C₁₉	—	8	1	no	—
286	C₂×C₄×C₁₉	—	16	1	no	—
287	C₂×C₄×C₁₉	—	16	1	no	—
288	C₂×C₄×C₁₉	—	16	1	no	—
289	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
290	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
291	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
292	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
293	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
294	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
295	C₈×C₁₉	—	2	2	no	—
296	C₈×C₁₉	—	2	1	no	—
297	C₈×C₁₉	—	2	1	no	—
298	C₈×C₁₉	—	2	1	no	—
299	C₈×C₁₉	—	2	1	no	—
300	C₈×C₁₉	—	4	1	no	—
301	C₈×C₁₉	—	4	1	no	—
302	C₈×C₁₉	—	4	1	no	—
303	#3136	C₂×C₁₉	1	1	yes	characteristic, complemented
304	#3096	C₂×C₁₉	1	1	yes	characteristic, complemented
305	#3081	C₂×C₁₉	1	1	yes	characteristic, complemented
306	#2946	C₂×C₁₉	1	1	yes	characteristic, complemented
307	#2063	C₂×C₁₉	1	1	yes	characteristic, complemented
308	#2060	C₂×C₁₉	1	1	yes	characteristic, complemented
309	#2051	C₂×C₁₉	1	1	yes	characteristic, complemented
310	#2002	C₂×C₁₉	1	1	yes	characteristic
311	#1957	C₂×C₁₉	1	1	yes	characteristic, complemented
312	#1937	C₂×C₁₉	1	1	yes	characteristic, complemented
313	#1931	C₂×C₁₉	1	1	yes	characteristic, complemented
314	#1931	C₂×C₁₉	1	1	yes	characteristic, complemented
315	#1887	C₂×C₁₉	1	1	yes	characteristic, complemented
316	#1859	C₂×C₁₉	1	1	yes	characteristic, complemented
317	#1772	C₂×C₁₉	1	1	yes	characteristic, complemented
318	C₂²×C₁₉	—	2	1	no	—
319	C₂²×C₁₉	—	2	1	no	—
320	C₂²×C₁₉	—	4	1	no	—
321	C₂²×C₁₉	—	4	2	no	—
322	C₂²×C₁₉	—	4	1	no	—
323	C₂²×C₁₉	—	4	1	no	—
324	C₂²×C₁₉	—	8	2	no	—
325	C₂²×C₁₉	—	8	2	no	—
326	C₂²×C₁₉	—	8	1	no	—
327	C₂²×C₁₉	—	8	1	no	—
328	C₂²×C₁₉	—	8	1	no	—
329	C₂²×C₁₉	—	8	1	no	—
330	C₂²×C₁₉	—	8	1	no	—
331	C₂²×C₁₉	—	16	1	no	—
332	C₂²×C₁₉	—	16	1	no	—
333	C₂²×C₁₉	#542	1	1	yes	characteristic
334	C₂²×C₁₉	D₄²	1	1	yes	characteristic
335	C₂²×C₁₉	#551	1	1	yes	characteristic
336	C₄×C₁₉	—	2	4	no	—
337	C₄×C₁₉	—	4	1	no	—
338	C₄×C₁₉	—	4	1	no	—
339	C₄×C₁₉	—	4	1	no	—
340	C₄×C₁₉	—	4	1	no	—
341	C₄×C₁₉	—	4	1	no	—
342	C₄×C₁₉	—	4	1	no	—
343	C₄×C₁₉	—	4	1	no	—
344	C₄×C₁₉	—	8	1	no	—
345	C₄×C₁₉	—	8	1	no	—
346	C₄×C₁₉	#525	1	1	yes	characteristic
347	C₄×C₁₉	#532	1	1	yes	characteristic
348	C₄×C₁₉	#547	1	1	yes	characteristic
349	C₄×C₁₉	#548	1	1	yes	characteristic
350	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	1	yes	characteristic
351	#544	C₂²×C₁₉	1	1	yes	characteristic
352	#535	C₂²×C₁₉	1	1	yes	characteristic
353	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
354	#520	C₂²×C₁₉	1	1	yes	characteristic
355	#518	C₂²×C₁₉	1	1	yes	characteristic
356	#490	—	2	1	no	—
357	#489	—	2	1	no	—
358	#488	—	2	1	no	—
359	#486	—	2	1	no	—
360	#482	—	2	1	no	—
361	#482	—	2	1	no	—
362	#481	—	2	1	no	—
363	#480	—	2	1	no	—
364	#478	—	2	1	no	—
365	#478	—	2	1	no	—
366	#476	—	2	1	no	—
367	#474	—	2	1	no	—
368	#442	—	2	1	no	—
369	#440	—	2	1	no	—
370	C₄×SD₁₆	—	2	1	no	—
371	C₄×D₈	—	2	1	no	—
372	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
373	#428	C₂²×C₁₉	1	1	yes	characteristic
374	#428	C₂²×C₁₉	1	1	yes	characteristic
375	#428	C₂²×C₁₉	1	1	yes	characteristic
376	#427	C₂²×C₁₉	1	1	yes	characteristic
377	#424	C₂²×C₁₉	1	1	yes	characteristic
378	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
379	#418	C₂²×C₁₉	1	1	yes	characteristic
380	#418	C₂²×C₁₉	1	1	yes	characteristic
381	#418	C₂²×C₁₉	1	1	yes	characteristic
382	#417	C₂²×C₁₉	1	1	yes	characteristic
383	#416	C₂²×C₁₉	1	1	yes	characteristic
384	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
385	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
386	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
387	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
388	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
389	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
390	#408	C₂²×C₁₉	1	1	yes	characteristic
391	#405	C₂²×C₁₉	1	1	yes	characteristic
392	#405	C₂²×C₁₉	1	1	yes	characteristic
393	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
394	#384	C₂²×C₁₉	1	1	yes	characteristic
395	#343	C₂²×C₁₉	1	1	yes	characteristic
396	#343	C₂²×C₁₉	1	1	yes	characteristic
397	#341	C₂²×C₁₉	1	1	yes	characteristic
398	#339	C₂²×C₁₉	1	1	yes	characteristic
399	#339	C₂²×C₁₉	1	1	yes	characteristic
400	#339	C₂²×C₁₉	1	1	yes	characteristic
401	C₂×C₁₉	—	2	1	no	—
402	C₂×C₁₉	—	2	1	no	—
403	C₂×C₁₉	—	8	1	no	—
404	C₂×C₁₉	—	8	2	no	—
405	C₂×C₁₉	—	16	1	no	—
406	C₂×C₁₉	#2461	1	1	yes	characteristic
407	C₂×C₁₉	#3291	1	1	yes	characteristic
408	C₂×C₁₉	#3292	1	1	yes	characteristic
409	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
410	C₂²×D₄	—	4	1	no	—
411	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
412	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
413	AGL(1,ℤ/8)	—	2	2	no	—
414	AGL(1,ℤ/8)	—	2	2	no	—
415	C₂×SD₁₆	—	2	1	no	—
416	C₂×D₈	—	2	1	no	—
417	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
418	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
419	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
420	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
421	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
422	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
423	C₄⋊Q₈	—	2	1	no	—
424	C₄⋊Q₈	—	2	1	no	—
425	#127	—	2	1	no	—
426	#127	—	2	2	no	—
427	#127	—	2	2	no	—
428	#125	—	2	1	no	—
429	#125	—	2	1	no	—
430	#124	—	2	1	no	—
431	C₂²⋊Q₈	—	4	1	no	—
432	#121	—	2	1	no	—
433	#121	—	2	1	no	—
434	#120	—	4	1	no	—
435	C₄×Q₈	—	2	1	no	—
436	C₄×D₄	—	2	1	no	—
437	C₄×D₄	—	2	1	no	—
438	C₄×D₄	—	2	1	no	—
439	C₄×D₄	—	2	1	no	—
440	C₄×D₄	—	2	1	no	—
441	C₄×D₄	—	4	1	no	—
442	#117	—	2	1	no	—
443	#117	C₂³×C₁₉	1	1	yes	characteristic
444	#117	C₂³×C₁₉	1	1	yes	characteristic
445	#117	C₂³×C₁₉	1	1	yes	characteristic
446	C₂×C₄⋊C₄	—	2	1	no	—
447	C₂×C₄⋊C₄	—	4	1	no	—
448	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
449	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
450	C₂×C₂²⋊C₄	—	4	1	no	—
451	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
452	#108	—	2	2	no	—
453	#107	—	2	1	no	—
454	#107	—	2	1	no	—
455	#107	—	2	1	no	—
456	#107	D₄×C₁₉	1	1	yes	characteristic, complemented
457	#107	D₄×C₁₉	1	1	yes	characteristic, complemented
458	#106	—	2	1	no	—
459	#106	—	2	1	no	—
460	#106	—	2	1	no	—
461	#106	D₄×C₁₉	1	1	yes	characteristic, complemented
462	#106	D₄×C₁₉	1	1	yes	characteristic, complemented
463	C₄⋊C₈	—	2	1	no	—
464	C₄⋊C₈	—	2	1	no	—
465	#104	—	2	2	no	—
466	#103	—	2	1	no	—
467	#103	D₄×C₁₉	1	1	yes	characteristic, complemented
468	#103	D₄×C₁₉	1	1	yes	characteristic, complemented
469	#102	—	2	1	no	—
470	#102	—	2	1	no	—
471	#102	—	2	1	no	—
472	#102	—	2	1	no	—
473	#102	—	2	1	no	—
474	#102	—	2	1	no	—
475	#102	—	2	1	no	—
476	#102	—	2	1	no	—
477	#102	—	2	1	no	—
478	#102	—	2	1	no	—
479	#102	—	2	1	no	—
480	#102	—	2	1	no	—
481	#102	—	2	1	no	—
482	#102	—	2	1	no	—
483	#102	—	2	1	no	—
484	#102	D₄×C₁₉	1	1	yes	characteristic, complemented
485	#102	D₄×C₁₉	1	1	yes	characteristic, complemented
486	#100	—	2	2	no	—
487	#100	—	2	2	no	—
488	C₂²⋊C₈	—	2	1	no	—
489	C₂²⋊C₈	—	2	1	no	—
490	#97	—	2	1	no	—
491	#97	—	2	1	no	—
492	C₄×C₈	—	2	1	no	—
493	C₄×C₈	—	2	1	no	—
494	C₄×C₈	—	2	2	no	—
495	C₁₉	#26850	1	1	yes	characteristic, direct product factor, Sylow
496	C₂⁴	—	2	1	no	—
497	C₂⁴	—	2	1	no	—
498	#41	—	2	1	no	—
499	#41	—	2	1	no	—
500	#41	—	2	1	no	—
501	#41	—	2	1	no	—
502	C₂×Q₈	—	4	1	no	—
503	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
504	C₂×D₄	—	2	1	no	—
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	2	1	no	—
516	C₂×D₄	—	4	4	no	—
517	C₂×D₄	—	4	1	no	—
518	C₂×D₄	—	4	1	no	—
519	C₂×D₄	—	8	2	no	—
520	C₂×D₄	—	8	2	no	—
521	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
522	C₂×D₄	#41×C₁₉	1	2	yes	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	4	1	no	—
528	C₂²×C₄	—	4	1	no	—
529	C₂²×C₄	—	4	1	no	—
530	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
531	SD₁₆	—	2	4	no	—
532	D₈	—	2	4	no	—
533	M₁₆	—	2	1	no	—
534	M₁₆	—	2	1	no	—
535	M₁₆	—	2	1	no	—
536	M₁₆	—	2	1	no	—
537	M₁₆	—	2	1	no	—
538	M₁₆	—	2	1	no	—
539	M₁₆	—	2	1	no	—
540	M₁₆	#41×C₁₉	1	2	yes	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	2	1	no	—
546	C₂×C₈	—	2	1	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	—	2	1	no	—
549	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
550	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
551	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
552	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	—	2	1	no	—
555	C₄⋊C₄	—	2	1	no	—
556	C₄⋊C₄	—	2	1	no	—
557	C₄⋊C₄	—	4	1	no	—
558	C₄⋊C₄	—	4	1	no	—
559	C₄⋊C₄	—	4	1	no	—
560	C₄⋊C₄	—	4	1	no	—
561	C₄⋊C₄	—	8	2	no	—
562	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
563	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
564	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
565	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
566	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
567	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
568	C₂²⋊C₄	—	2	1	no	—
569	C₂²⋊C₄	—	2	1	no	—
570	C₂²⋊C₄	—	2	1	no	—
571	C₂²⋊C₄	—	4	1	no	—
572	C₂²⋊C₄	—	4	1	no	—
573	C₂²⋊C₄	—	4	1	no	—
574	C₂²⋊C₄	—	4	1	no	—
575	C₂²⋊C₄	—	4	1	no	—
576	C₄²	—	2	1	no	—
577	C₄²	—	2	1	no	—
578	C₄²	—	2	1	no	—
579	C₄²	—	2	1	no	—
580	C₄²	—	4	1	no	—
581	C₄²	#41×C₁₉	1	2	yes	—
582	C₂³	—	2	1	no	—
583	C₂³	—	2	2	no	—
584	C₂³	—	4	1	no	—
585	C₂³	—	4	1	no	—
586	C₂³	—	4	1	no	—
587	C₂³	—	4	1	no	—
588	C₂³	—	4	1	no	—
589	C₂³	—	8	1	no	—
590	C₂³	—	8	1	no	—
591	C₂³	—	8	1	no	—
592	C₂³	—	8	1	no	—
593	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
594	Q₈	—	2	1	no	—
595	Q₈	—	2	1	no	—
596	Q₈	—	16	1	no	—
597	D₄	—	2	1	no	—
598	D₄	—	2	2	no	—
599	D₄	—	2	1	no	—
600	D₄	—	2	2	no	—
601	D₄	—	4	1	no	—
602	D₄	—	4	1	no	—
603	D₄	—	4	1	no	—
604	D₄	—	4	1	no	—
605	D₄	—	4	1	no	—
606	D₄	—	4	1	no	—
607	D₄	—	4	1	no	—
608	D₄	—	4	1	no	—
609	D₄	—	8	8	no	—
610	D₄	—	16	1	no	—
611	D₄	—	16	1	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	8	1	no	—
627	C₂×C₄	—	8	1	no	—
628	C₂×C₄	—	16	1	no	—
629	C₂×C₄	—	16	1	no	—
630	C₂×C₄	—	16	1	no	—
631	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
632	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
633	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
634	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
635	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
636	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
637	C₈	—	2	2	no	—
638	C₈	—	2	1	no	—
639	C₈	—	2	1	no	—
640	C₈	—	2	1	no	—
641	C₈	—	2	1	no	—
642	C₈	—	4	1	no	—
643	C₈	—	4	1	no	—
644	C₈	—	4	1	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	4	1	no	—
648	C₂²	—	4	2	no	—
649	C₂²	—	4	1	no	—
650	C₂²	—	4	1	no	—
651	C₂²	—	8	2	no	—
652	C₂²	—	8	2	no	—
653	C₂²	—	8	1	no	—
654	C₂²	—	8	1	no	—
655	C₂²	—	8	1	no	—
656	C₂²	—	8	1	no	—
657	C₂²	—	8	1	no	—
658	C₂²	—	16	1	no	—
659	C₂²	—	16	1	no	—
660	C₂²	C₁₉×#542	1	1	yes	characteristic
661	C₂²	D₄²×C₁₉	1	1	yes	characteristic
662	C₂²	C₁₉×#551	1	1	yes	characteristic
663	C₄	—	2	4	no	—
664	C₄	—	4	1	no	—
665	C₄	—	4	1	no	—
666	C₄	—	4	1	no	—
667	C₄	—	4	1	no	—
668	C₄	—	4	1	no	—
669	C₄	—	4	1	no	—
670	C₄	—	4	1	no	—
671	C₄	—	8	1	no	—
672	C₄	—	8	1	no	—
673	C₄	C₁₉×#525	1	1	yes	characteristic
674	C₄	C₁₉×#532	1	1	yes	characteristic
675	C₄	C₁₉×#547	1	1	yes	characteristic
676	C₄	C₁₉×#548	1	1	yes	characteristic
677	C₂	—	2	1	no	—
678	C₂	—	2	1	no	—
679	C₂	—	8	1	no	—
680	C₂	—	8	2	no	—
681	C₂	—	16	1	no	—
682	C₂	C₁₉×#2461	1	1	yes	characteristic
683	C₂	C₁₉×#3291	1	1	yes	characteristic
684	C₂	C₁₉×#3292	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#2002	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3136	C₂	semidirect
2. C₁₉×#3096	C₂	semidirect
3. C₁₉×#3081	C₂	semidirect
4. C₁₉×#2946	C₂	semidirect
5. C₁₉×#2063	C₂	semidirect
6. C₁₉×#2060	C₂	semidirect
7. C₁₉×#2051	C₂	semidirect
9. C₁₉×#1957	C₂	semidirect
10. C₁₉×#1937	C₂	semidirect
11. C₁₉×#1931	C₂	semidirect
12. C₁₉×#1931	C₂	semidirect
13. C₁₉×#1887	C₂	semidirect
14. C₁₉×#1859	C₂	semidirect
15. C₁₉×#1772	C₂	semidirect
114. C₁₉×#107	D₄	semidirect
115. C₁₉×#107	D₄	semidirect
119. C₁₉×#106	D₄	semidirect
120. C₁₉×#106	D₄	semidirect
125. C₁₉×#103	D₄	semidirect
126. C₁₉×#103	D₄	semidirect
142. C₁₉×#102	D₄	semidirect
143. C₁₉×#102	D₄	semidirect
239. #26850	C₁₉	direct (N × H)
303. #3136	C₂×C₁₉	semidirect
304. #3096	C₂×C₁₉	semidirect
305. #3081	C₂×C₁₉	semidirect
306. #2946	C₂×C₁₉	semidirect
307. #2063	C₂×C₁₉	semidirect
308. #2060	C₂×C₁₉	semidirect
309. #2051	C₂×C₁₉	semidirect
311. #1957	C₂×C₁₉	semidirect
312. #1937	C₂×C₁₉	semidirect
313. #1931	C₂×C₁₉	semidirect
314. #1931	C₂×C₁₉	semidirect
315. #1887	C₂×C₁₉	semidirect
316. #1859	C₂×C₁₉	semidirect
317. #1772	C₂×C₁₉	semidirect
456. #107	D₄×C₁₉	semidirect
457. #107	D₄×C₁₉	semidirect
461. #106	D₄×C₁₉	semidirect
462. #106	D₄×C₁₉	semidirect
467. #103	D₄×C₁₉	semidirect
468. #103	D₄×C₁₉	semidirect
484. #102	D₄×C₁₉	semidirect
485. #102	D₄×C₁₉	semidirect
495. C₁₉	#26850	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3136	2
C₁₉×#3096	2
C₁₉×#3081	2
C₁₉×#2946	2
C₁₉×#2063	2
C₁₉×#2060	2
C₁₉×#2051	2
C₁₉×#2002	2
C₁₉×#1957	2
C₁₉×#1937	2
C₁₉×#1931	2
C₁₉×#1887	2
C₁₉×#1859	2
C₁₉×#1772	2
#26850	19

Subgroups — C19×#26850 #18032809

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#26850 #18032809