Subgroups — C₁₉×#26195 #18032154

Order 4864.

758 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×#3096	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3045	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2952	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2913	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2092	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2090	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2078	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2037	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1931	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1922	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1907	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1883	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1876	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1860	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1860	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
19	C₁₉×#535	C₂²	1	1	yes	characteristic
20	C₁₉×#520	C₂²	1	1	yes	characteristic
21	C₁₉×#520	C₂²	1	1	yes	characteristic
22	C₁₉×#520	C₂²	1	1	yes	characteristic
23	C₁₉×#482	—	2	1	no	—
24	C₁₉×#482	—	2	1	no	—
25	C₁₉×#481	—	2	1	no	—
26	C₁₉×#480	—	2	1	no	—
27	C₁₉×#464	—	2	1	no	—
28	C₁₉×#463	—	2	1	no	—
29	C₁₉×#460	—	2	1	no	—
30	C₁₉×#459	—	2	1	no	—
31	C₁₉×#442	—	2	1	no	—
32	C₁₉×#441	—	2	1	no	—
33	C₄×SD₁₆×C₁₉	—	2	1	no	—
34	C₄×SD₁₆×C₁₉	—	2	1	no	—
35	C₁₉×#428	—	2	1	no	—
36	C₁₉×#428	—	2	1	no	—
37	C₁₉×#428	C₂²	1	1	yes	characteristic
38	C₁₉×#428	C₂²	1	1	yes	characteristic
39	C₁₉×#428	C₂²	1	1	yes	characteristic
40	C₁₉×#427	—	2	1	no	—
41	C₁₉×#427	C₂²	1	1	yes	characteristic
42	C₂×C₁₉×#107	—	2	1	no	—
43	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
44	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
45	C₁₉×#424	C₂²	1	1	yes	characteristic
46	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
47	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
48	C₁₉×#418	C₂²	1	1	yes	characteristic
49	C₁₉×#417	C₂²	1	1	yes	characteristic
50	C₁₉×#417	C₂²	1	1	yes	characteristic
51	C₁₉×#417	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	C₁₉×#408	C₂²	1	1	yes	characteristic
56	C₁₉×#405	C₂²	1	1	yes	characteristic
57	C₁₉×#390	C₂²	1	1	yes	characteristic
58	C₁₉×#382	C₂²	1	1	yes	characteristic
59	C₁₉×#343	C₂²	1	1	yes	characteristic
60	C₁₉×#343	C₂²	1	1	yes	characteristic
61	C₁₉×#343	C₂²	1	1	yes	characteristic
62	C₁₉×#341	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×#336	C₂²	1	1	yes	characteristic
67	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
70	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
71	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
72	C₁₉×#135	—	2	2	no	—
73	C₁₉×#135	—	2	2	no	—
74	C₂×Q₁₆×C₁₉	D₄	1	1	yes	characteristic
75	C₂×SD₁₆×C₁₉	—	2	1	no	—
76	C₂×SD₁₆×C₁₉	D₄	1	1	yes	characteristic
77	C₂×SD₁₆×C₁₉	D₄	1	1	yes	characteristic
78	C₂×D₈×C₁₉	—	2	1	no	—
79	C₂×D₈×C₁₉	D₄	1	1	yes	characteristic
80	C₁₉×#131	—	2	2	no	—
81	C₁₉×#131	—	2	2	no	—
82	C₂×M₁₆×C₁₉	—	2	1	no	—
83	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
84	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₁₉	—	2	1	no	—
88	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
90	C₁₉×#127	—	2	1	no	—
91	C₁₉×#124	—	2	1	no	—
92	C₁₉×#121	—	2	1	no	—
93	C₁₉×#121	—	2	1	no	—
94	C₁₉×#120	—	4	1	no	—
95	C₄×Q₈×C₁₉	—	2	1	no	—
96	C₄×Q₈×C₁₉	—	2	1	no	—
97	C₄×Q₈×C₁₉	—	2	1	no	—
98	C₄×D₄×C₁₉	—	2	1	no	—
99	C₄×D₄×C₁₉	—	2	1	no	—
100	C₄×D₄×C₁₉	—	2	1	no	—
101	C₄×D₄×C₁₉	—	4	1	no	—
102	C₄×D₄×C₁₉	—	4	1	no	—
103	C₄×D₄×C₁₉	—	4	1	no	—
104	C₁₉×#117	—	2	1	no	—
105	C₁₉×#117	—	2	1	no	—
106	C₁₉×#117	—	2	1	no	—
107	C₁₉×#117	C₂³	1	1	yes	characteristic
108	C₁₉×#117	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
111	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
112	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
115	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
116	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
117	C₁₉×#107	—	2	1	no	—
118	C₁₉×#107	—	2	1	no	—
119	C₁₉×#107	—	2	1	no	—
120	C₁₉×#107	—	2	1	no	—
121	C₁₉×#107	—	2	1	no	—
122	C₁₉×#107	D₄	1	1	yes	characteristic
123	C₁₉×#107	D₄	1	1	yes	characteristic
124	C₁₉×#106	—	2	1	no	—
125	C₁₉×#106	—	2	1	no	—
126	C₁₉×#106	—	2	1	no	—
127	C₁₉×#106	—	2	1	no	—
128	C₁₉×#106	—	2	1	no	—
129	C₁₉×#106	D₄	1	1	yes	characteristic
130	C₁₉×#106	D₄	1	1	yes	characteristic
131	C₁₉×C₄⋊C₈	—	2	1	no	—
132	C₁₉×C₄⋊C₈	—	2	1	no	—
133	C₁₉×#104	—	2	2	no	—
134	C₁₉×#104	—	2	2	no	—
135	C₁₉×#103	—	2	1	no	—
136	C₁₉×#103	—	2	1	no	—
137	C₁₉×#103	—	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	—	2	1	no	—
143	C₁₉×#102	—	2	1	no	—
144	C₁₉×#102	—	2	1	no	—
145	C₁₉×#102	—	2	1	no	—
146	C₁₉×#102	—	2	1	no	—
147	C₁₉×#100	—	2	2	no	—
148	C₁₉×C₂²⋊C₈	—	2	1	no	—
149	C₁₉×C₂²⋊C₈	—	2	1	no	—
150	C₁₉×#97	—	2	1	no	—
151	C₄×C₈×C₁₉	—	2	1	no	—
152	C₁₉×#95	—	4	1	no	—
153	C₂⁴×C₁₉	—	2	1	no	—
154	#41×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	#41×C₁₉	—	2	1	no	—
160	#41×C₁₉	#41	1	2	yes	—
161	#41×C₁₉	#41	1	2	yes	—
162	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	4	1	no	—
173	C₂×D₄×C₁₉	—	4	1	no	—
174	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
175	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₉	—	2	1	no	—
177	C₂²×C₄×C₁₉	—	2	1	no	—
178	C₂²×C₄×C₁₉	—	2	1	no	—
179	C₂²×C₄×C₁₉	—	2	1	no	—
180	C₂²×C₄×C₁₉	—	2	1	no	—
181	C₂²×C₄×C₁₉	—	2	1	no	—
182	C₂²×C₄×C₁₉	—	4	1	no	—
183	C₂²×C₄×C₁₉	—	4	1	no	—
184	C₂²×C₄×C₁₉	—	4	1	no	—
185	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
186	Q₁₆×C₁₉	—	2	2	no	—
187	SD₁₆×C₁₉	—	2	2	no	—
188	SD₁₆×C₁₉	—	2	2	no	—
189	SD₁₆×C₁₉	—	4	2	no	—
190	D₈×C₁₉	—	2	2	no	—
191	D₈×C₁₉	—	4	2	no	—
192	M₁₆×C₁₉	—	2	4	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	—	2	1	no	—
198	M₁₆×C₁₉	—	2	1	no	—
199	M₁₆×C₁₉	—	2	1	no	—
200	M₁₆×C₁₉	#41	1	2	yes	—
201	C₂×C₈×C₁₉	—	2	4	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	—	2	1	no	—
207	C₂×C₈×C₁₉	—	2	1	no	—
208	C₂×C₈×C₁₉	—	2	1	no	—
209	C₂×C₈×C₁₉	—	2	1	no	—
210	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
211	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
212	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
213	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
214	C₄⋊C₄×C₁₉	—	2	1	no	—
215	C₄⋊C₄×C₁₉	—	2	1	no	—
216	C₄⋊C₄×C₁₉	—	2	1	no	—
217	C₄⋊C₄×C₁₉	—	2	1	no	—
218	C₄⋊C₄×C₁₉	—	2	1	no	—
219	C₄⋊C₄×C₁₉	—	2	1	no	—
220	C₄⋊C₄×C₁₉	—	4	1	no	—
221	C₄⋊C₄×C₁₉	—	4	1	no	—
222	C₄⋊C₄×C₁₉	—	4	1	no	—
223	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
224	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
225	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
226	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
227	C₂²⋊C₄×C₁₉	—	2	1	no	—
228	C₂²⋊C₄×C₁₉	—	2	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	C₂²⋊C₄×C₁₉	—	4	1	no	—
234	C₂²⋊C₄×C₁₉	—	8	2	no	—
235	C₄²×C₁₉	—	2	1	no	—
236	C₄²×C₁₉	—	2	1	no	—
237	C₄²×C₁₉	—	2	1	no	—
238	C₄²×C₁₉	—	2	1	no	—
239	C₄²×C₁₉	—	4	1	no	—
240	C₄²×C₁₉	—	4	1	no	—
241	C₄²×C₁₉	—	4	1	no	—
242	#26195	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
243	C₂³×C₁₉	—	2	1	no	—
244	C₂³×C₁₉	—	2	1	no	—
245	C₂³×C₁₉	—	4	1	no	—
246	C₂³×C₁₉	—	4	1	no	—
247	C₂³×C₁₉	—	4	1	no	—
248	C₂³×C₁₉	—	8	1	no	—
249	C₂³×C₁₉	—	8	1	no	—
250	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
251	Q₈×C₁₉	—	2	1	no	—
252	Q₈×C₁₉	—	2	1	no	—
253	Q₈×C₁₉	—	2	1	no	—
254	Q₈×C₁₉	#123	1	2	yes	—
255	D₄×C₁₉	—	2	2	no	—
256	D₄×C₁₉	—	2	2	no	—
257	D₄×C₁₉	—	2	1	no	—
258	D₄×C₁₉	—	2	1	no	—
259	D₄×C₁₉	—	2	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	—	16	1	no	—
267	D₄×C₁₉	—	16	1	no	—
268	D₄×C₁₉	#123	1	2	yes	—
269	C₂×C₄×C₁₉	—	2	1	no	—
270	C₂×C₄×C₁₉	—	2	2	no	—
271	C₂×C₄×C₁₉	—	2	2	no	—
272	C₂×C₄×C₁₉	—	2	1	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	—	4	1	no	—
278	C₂×C₄×C₁₉	—	4	1	no	—
279	C₂×C₄×C₁₉	—	4	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	—	4	1	no	—
285	C₂×C₄×C₁₉	—	8	1	no	—
286	C₂×C₄×C₁₉	—	8	1	no	—
287	C₂×C₄×C₁₉	—	8	1	no	—
288	C₂×C₄×C₁₉	—	16	1	no	—
289	C₂×C₄×C₁₉	—	16	1	no	—
290	C₂×C₄×C₁₉	—	16	1	no	—
291	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
292	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
293	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
294	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
295	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
296	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
297	C₈×C₁₉	—	2	1	no	—
298	C₈×C₁₉	—	2	1	no	—
299	C₈×C₁₉	—	2	1	no	—
300	C₈×C₁₉	—	2	2	no	—
301	C₈×C₁₉	—	2	1	no	—
302	C₈×C₁₉	—	4	1	no	—
303	C₈×C₁₉	—	4	1	no	—
304	C₈×C₁₉	—	4	1	no	—
305	#3096	C₂×C₁₉	1	1	yes	characteristic, complemented
306	#3045	C₂×C₁₉	1	1	yes	characteristic
307	#2952	C₂×C₁₉	1	1	yes	characteristic, complemented
308	#2913	C₂×C₁₉	1	1	yes	characteristic, complemented
309	#2092	C₂×C₁₉	1	1	yes	characteristic, complemented
310	#2090	C₂×C₁₉	1	1	yes	characteristic, complemented
311	#2078	C₂×C₁₉	1	1	yes	characteristic, complemented
312	#2037	C₂×C₁₉	1	1	yes	characteristic, complemented
313	#1931	C₂×C₁₉	1	1	yes	characteristic, complemented
314	#1922	C₂×C₁₉	1	1	yes	characteristic, complemented
315	#1907	C₂×C₁₉	1	1	yes	characteristic, complemented
316	#1883	C₂×C₁₉	1	1	yes	characteristic, complemented
317	#1876	C₂×C₁₉	1	1	yes	characteristic, complemented
318	#1860	C₂×C₁₉	1	1	yes	characteristic, complemented
319	#1860	C₂×C₁₉	1	1	yes	characteristic, complemented
320	C₂²×C₁₉	—	2	1	no	—
321	C₂²×C₁₉	—	2	1	no	—
322	C₂²×C₁₉	—	2	2	no	—
323	C₂²×C₁₉	—	4	1	no	—
324	C₂²×C₁₉	—	4	1	no	—
325	C₂²×C₁₉	—	4	1	no	—
326	C₂²×C₁₉	—	4	1	no	—
327	C₂²×C₁₉	—	4	1	no	—
328	C₂²×C₁₉	—	8	2	no	—
329	C₂²×C₁₉	—	8	1	no	—
330	C₂²×C₁₉	—	8	1	no	—
331	C₂²×C₁₉	—	8	1	no	—
332	C₂²×C₁₉	—	16	1	no	—
333	C₂²×C₁₉	#539	1	1	yes	characteristic
334	C₂²×C₁₉	D₄²	1	1	yes	characteristic
335	C₂²×C₁₉	#553	1	1	yes	characteristic
336	C₄×C₁₉	—	2	2	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	—	8	1	no	—
343	C₄×C₁₉	—	8	1	no	—
344	C₄×C₁₉	—	8	1	no	—
345	C₄×C₁₉	—	8	1	no	—
346	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
347	C₄×C₁₉	#525	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	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic
352	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
353	#535	C₂²×C₁₉	1	1	yes	characteristic
354	#520	C₂²×C₁₉	1	1	yes	characteristic
355	#520	C₂²×C₁₉	1	1	yes	characteristic
356	#520	C₂²×C₁₉	1	1	yes	characteristic
357	#482	—	2	1	no	—
358	#482	—	2	1	no	—
359	#481	—	2	1	no	—
360	#480	—	2	1	no	—
361	#464	—	2	1	no	—
362	#463	—	2	1	no	—
363	#460	—	2	1	no	—
364	#459	—	2	1	no	—
365	#442	—	2	1	no	—
366	#441	—	2	1	no	—
367	C₄×SD₁₆	—	2	1	no	—
368	C₄×SD₁₆	—	2	1	no	—
369	#428	—	2	1	no	—
370	#428	—	2	1	no	—
371	#428	C₂²×C₁₉	1	1	yes	characteristic
372	#428	C₂²×C₁₉	1	1	yes	characteristic
373	#428	C₂²×C₁₉	1	1	yes	characteristic
374	#427	—	2	1	no	—
375	#427	C₂²×C₁₉	1	1	yes	characteristic
376	C₂×#107	—	2	1	no	—
377	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
378	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
379	#424	C₂²×C₁₉	1	1	yes	characteristic
380	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
381	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
382	#418	C₂²×C₁₉	1	1	yes	characteristic
383	#417	C₂²×C₁₉	1	1	yes	characteristic
384	#417	C₂²×C₁₉	1	1	yes	characteristic
385	#417	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	#408	C₂²×C₁₉	1	1	yes	characteristic
390	#405	C₂²×C₁₉	1	1	yes	characteristic
391	#390	C₂²×C₁₉	1	1	yes	characteristic
392	#382	C₂²×C₁₉	1	1	yes	characteristic
393	#343	C₂²×C₁₉	1	1	yes	characteristic
394	#343	C₂²×C₁₉	1	1	yes	characteristic
395	#343	C₂²×C₁₉	1	1	yes	characteristic
396	#341	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	#336	C₂²×C₁₉	1	1	yes	characteristic
401	C₂×C₁₉	—	2	1	no	—
402	C₂×C₁₉	—	2	1	no	—
403	C₂×C₁₉	—	4	2	no	—
404	C₂×C₁₉	—	8	1	no	—
405	C₂×C₁₉	—	16	1	no	—
406	C₂×C₁₉	#2443	1	1	yes	characteristic
407	C₂×C₁₉	#3288	1	1	yes	characteristic
408	C₂×C₁₉	#3290	1	1	yes	characteristic
409	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
410	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
411	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
412	AGL(1,ℤ/8)	—	2	2	no	—
413	AGL(1,ℤ/8)	—	2	2	no	—
414	#135	—	2	2	no	—
415	#135	—	2	2	no	—
416	C₂×Q₁₆	D₄×C₁₉	1	1	yes	characteristic
417	C₂×SD₁₆	—	2	1	no	—
418	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
419	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
420	C₂×D₈	—	2	1	no	—
421	C₂×D₈	D₄×C₁₉	1	1	yes	characteristic
422	#131	—	2	2	no	—
423	#131	—	2	2	no	—
424	C₂×M₁₆	—	2	1	no	—
425	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
426	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
427	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
428	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
429	C₂²×C₈	—	2	1	no	—
430	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
431	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
432	#127	—	2	1	no	—
433	#124	—	2	1	no	—
434	#121	—	2	1	no	—
435	#121	—	2	1	no	—
436	#120	—	4	1	no	—
437	C₄×Q₈	—	2	1	no	—
438	C₄×Q₈	—	2	1	no	—
439	C₄×Q₈	—	2	1	no	—
440	C₄×D₄	—	2	1	no	—
441	C₄×D₄	—	2	1	no	—
442	C₄×D₄	—	2	1	no	—
443	C₄×D₄	—	4	1	no	—
444	C₄×D₄	—	4	1	no	—
445	C₄×D₄	—	4	1	no	—
446	#117	—	2	1	no	—
447	#117	—	2	1	no	—
448	#117	—	2	1	no	—
449	#117	C₂³×C₁₉	1	1	yes	characteristic
450	#117	C₂³×C₁₉	1	1	yes	characteristic
451	C₂×C₄⋊C₄	—	2	1	no	—
452	C₂×C₄⋊C₄	—	2	1	no	—
453	C₂×C₄⋊C₄	—	2	1	no	—
454	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
455	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
456	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
457	C₂×C₂²⋊C₄	—	4	1	no	—
458	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
459	#107	—	2	1	no	—
460	#107	—	2	1	no	—
461	#107	—	2	1	no	—
462	#107	—	2	1	no	—
463	#107	—	2	1	no	—
464	#107	D₄×C₁₉	1	1	yes	characteristic
465	#107	D₄×C₁₉	1	1	yes	characteristic
466	#106	—	2	1	no	—
467	#106	—	2	1	no	—
468	#106	—	2	1	no	—
469	#106	—	2	1	no	—
470	#106	—	2	1	no	—
471	#106	D₄×C₁₉	1	1	yes	characteristic
472	#106	D₄×C₁₉	1	1	yes	characteristic
473	C₄⋊C₈	—	2	1	no	—
474	C₄⋊C₈	—	2	1	no	—
475	#104	—	2	2	no	—
476	#104	—	2	2	no	—
477	#103	—	2	1	no	—
478	#103	—	2	1	no	—
479	#103	—	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	—	2	1	no	—
485	#102	—	2	1	no	—
486	#102	—	2	1	no	—
487	#102	—	2	1	no	—
488	#102	—	2	1	no	—
489	#100	—	2	2	no	—
490	C₂²⋊C₈	—	2	1	no	—
491	C₂²⋊C₈	—	2	1	no	—
492	#97	—	2	1	no	—
493	C₄×C₈	—	2	1	no	—
494	#95	—	4	1	no	—
495	C₁₉	#26195	1	1	yes	characteristic, direct product factor, Sylow
496	C₂⁴	—	2	1	no	—
497	#41	—	2	1	no	—
498	#41	—	2	1	no	—
499	#41	—	2	1	no	—
500	#41	—	2	1	no	—
501	#41	—	2	1	no	—
502	#41	—	2	1	no	—
503	#41	#41×C₁₉	1	2	yes	—
504	#41	#41×C₁₉	1	2	yes	—
505	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
506	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
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	—	4	1	no	—
516	C₂×D₄	—	4	1	no	—
517	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
518	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	4	1	no	—
526	C₂²×C₄	—	4	1	no	—
527	C₂²×C₄	—	4	1	no	—
528	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
529	Q₁₆	—	2	2	no	—
530	SD₁₆	—	2	2	no	—
531	SD₁₆	—	2	2	no	—
532	SD₁₆	—	4	2	no	—
533	D₈	—	2	2	no	—
534	D₈	—	4	2	no	—
535	M₁₆	—	2	4	no	—
536	M₁₆	—	2	1	no	—
537	M₁₆	—	2	1	no	—
538	M₁₆	—	2	1	no	—
539	M₁₆	—	2	1	no	—
540	M₁₆	—	2	1	no	—
541	M₁₆	—	2	1	no	—
542	M₁₆	—	2	1	no	—
543	M₁₆	#41×C₁₉	1	2	yes	—
544	C₂×C₈	—	2	4	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	—	2	1	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
554	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
555	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
556	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
557	C₄⋊C₄	—	2	1	no	—
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	4	1	no	—
564	C₄⋊C₄	—	4	1	no	—
565	C₄⋊C₄	—	4	1	no	—
566	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
567	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
568	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
569	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
570	C₂²⋊C₄	—	2	1	no	—
571	C₂²⋊C₄	—	2	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	C₂²⋊C₄	—	4	1	no	—
577	C₂²⋊C₄	—	8	2	no	—
578	C₄²	—	2	1	no	—
579	C₄²	—	2	1	no	—
580	C₄²	—	2	1	no	—
581	C₄²	—	2	1	no	—
582	C₄²	—	4	1	no	—
583	C₄²	—	4	1	no	—
584	C₄²	—	4	1	no	—
585	C₂³	—	2	1	no	—
586	C₂³	—	2	1	no	—
587	C₂³	—	4	1	no	—
588	C₂³	—	4	1	no	—
589	C₂³	—	4	1	no	—
590	C₂³	—	8	1	no	—
591	C₂³	—	8	1	no	—
592	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
593	Q₈	—	2	1	no	—
594	Q₈	—	2	1	no	—
595	Q₈	—	2	1	no	—
596	Q₈	C₁₉×#123	1	2	yes	—
597	D₄	—	2	2	no	—
598	D₄	—	2	2	no	—
599	D₄	—	2	1	no	—
600	D₄	—	2	1	no	—
601	D₄	—	2	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	—	16	1	no	—
609	D₄	—	16	1	no	—
610	D₄	C₁₉×#123	1	2	yes	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	1	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	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	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	—	4	1	no	—
627	C₂×C₄	—	8	1	no	—
628	C₂×C₄	—	8	1	no	—
629	C₂×C₄	—	8	1	no	—
630	C₂×C₄	—	16	1	no	—
631	C₂×C₄	—	16	1	no	—
632	C₂×C₄	—	16	1	no	—
633	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
634	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
635	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
636	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
637	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
638	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
639	C₈	—	2	1	no	—
640	C₈	—	2	1	no	—
641	C₈	—	2	1	no	—
642	C₈	—	2	2	no	—
643	C₈	—	2	1	no	—
644	C₈	—	4	1	no	—
645	C₈	—	4	1	no	—
646	C₈	—	4	1	no	—
647	C₂²	—	2	1	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	2	2	no	—
650	C₂²	—	4	1	no	—
651	C₂²	—	4	1	no	—
652	C₂²	—	4	1	no	—
653	C₂²	—	4	1	no	—
654	C₂²	—	4	1	no	—
655	C₂²	—	8	2	no	—
656	C₂²	—	8	1	no	—
657	C₂²	—	8	1	no	—
658	C₂²	—	8	1	no	—
659	C₂²	—	16	1	no	—
660	C₂²	C₁₉×#539	1	1	yes	characteristic
661	C₂²	D₄²×C₁₉	1	1	yes	characteristic
662	C₂²	C₁₉×#553	1	1	yes	characteristic
663	C₄	—	2	2	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	—	8	1	no	—
670	C₄	—	8	1	no	—
671	C₄	—	8	1	no	—
672	C₄	—	8	1	no	—
673	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
674	C₄	C₁₉×#525	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	—	4	2	no	—
680	C₂	—	8	1	no	—
681	C₂	—	16	1	no	—
682	C₂	C₁₉×#2443	1	1	yes	characteristic
683	C₂	C₁₉×#3288	1	1	yes	characteristic
684	C₂	C₁₉×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#3045	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×#3096	C₂	semidirect
3. C₁₉×#2952	C₂	semidirect
4. C₁₉×#2913	C₂	semidirect
5. C₁₉×#2092	C₂	semidirect
6. C₁₉×#2090	C₂	semidirect
7. C₁₉×#2078	C₂	semidirect
8. C₁₉×#2037	C₂	semidirect
9. C₁₉×#1931	C₂	semidirect
10. C₁₉×#1922	C₂	semidirect
11. C₁₉×#1907	C₂	semidirect
12. C₁₉×#1883	C₂	semidirect
13. C₁₉×#1876	C₂	semidirect
14. C₁₉×#1860	C₂	semidirect
15. C₁₉×#1860	C₂	semidirect
242. #26195	C₁₉	direct (N × H)
305. #3096	C₂×C₁₉	semidirect
307. #2952	C₂×C₁₉	semidirect
308. #2913	C₂×C₁₉	semidirect
309. #2092	C₂×C₁₉	semidirect
310. #2090	C₂×C₁₉	semidirect
311. #2078	C₂×C₁₉	semidirect
312. #2037	C₂×C₁₉	semidirect
313. #1931	C₂×C₁₉	semidirect
314. #1922	C₂×C₁₉	semidirect
315. #1907	C₂×C₁₉	semidirect
316. #1883	C₂×C₁₉	semidirect
317. #1876	C₂×C₁₉	semidirect
318. #1860	C₂×C₁₉	semidirect
319. #1860	C₂×C₁₉	semidirect
495. C₁₉	#26195	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×#3096	2
C₁₉×#3045	2
C₁₉×#2952	2
C₁₉×#2913	2
C₁₉×#2092	2
C₁₉×#2090	2
C₁₉×#2078	2
C₁₉×#2037	2
C₁₉×#1931	2
C₁₉×#1922	2
C₁₉×#1907	2
C₁₉×#1883	2
C₁₉×#1876	2
C₁₉×#1860	2
#26195	19

Subgroups — C19×#26195 #18032154

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#26195 #18032154