Subgroups — C₁₉×#23049 #18029008

Order 4864.

866 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#471	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2949	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2947	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2946	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2913	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1973	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1952	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1931	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1930	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1883	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1882	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1857	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1856	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1773	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1765	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×#137	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
20	C₁₉×#520	C₂²	1	1	yes	characteristic
21	C₁₉×#520	C₂²	1	1	yes	characteristic
22	C₁₉×#519	C₂²	1	1	yes	characteristic
23	C₁₉×#518	C₂²	1	1	yes	characteristic
24	C₁₉×#471	C₄	1	8	yes	complemented
25	C₁₉×#442	—	2	1	no	—
26	C₁₉×#441	—	2	1	no	—
27	C₁₉×#440	—	2	1	no	—
28	C₁₉×#440	—	2	1	no	—
29	C₁₉×#440	—	2	1	no	—
30	C₁₉×#440	—	2	1	no	—
31	C₄×Q₁₆×C₁₉	—	2	1	no	—
32	C₄×SD₁₆×C₁₉	—	2	1	no	—
33	C₄×SD₁₆×C₁₉	—	2	1	no	—
34	C₄×SD₁₆×C₁₉	—	2	1	no	—
35	C₄×SD₁₆×C₁₉	—	2	1	no	—
36	C₄×D₈×C₁₉	—	2	1	no	—
37	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
38	C₁₉×#428	—	2	1	no	—
39	C₁₉×#428	—	2	1	no	—
40	C₁₉×#428	C₂²	1	1	yes	characteristic
41	C₁₉×#428	C₂²	1	1	yes	characteristic
42	C₁₉×#428	C₂²	1	1	yes	characteristic
43	C₁₉×#428	C₂²	1	1	yes	characteristic
44	C₁₉×#427	—	2	1	no	—
45	C₁₉×#427	C₂²	1	1	yes	characteristic
46	C₂×C₁₉×#107	—	2	1	no	—
47	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
48	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
49	C₁₉×#419	C₂²	1	1	yes	characteristic
50	C₁₉×#418	C₂²	1	1	yes	characteristic
51	C₁₉×#416	C₂²	1	1	yes	characteristic
52	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
53	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
54	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
55	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
56	C₁₉×#405	C₂²	1	1	yes	characteristic
57	C₁₉×#405	C₂²	1	1	yes	characteristic
58	C₁₉×#405	C₂²	1	1	yes	characteristic
59	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
60	C₁₉×#391	C₂²	1	1	yes	characteristic
61	C₁₉×#390	C₂²	1	1	yes	characteristic
62	C₁₉×#343	C₂²	1	1	yes	characteristic
63	C₁₉×#343	C₂²	1	1	yes	characteristic
64	C₁₉×#341	C₂²	1	1	yes	characteristic
65	C₁₉×#339	C₂²	1	1	yes	characteristic
66	C₁₉×#339	C₂²	1	1	yes	characteristic
67	C₁₉×#339	C₂²	1	1	yes	characteristic
68	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
69	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
71	C₁₉×#137	—	2	2	no	—
72	C₁₉×#137	C₂×C₄	1	4	yes	complemented
73	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
74	C₁₉×AGL(1,ℤ/8)	C₂×C₄	1	4	yes	—
75	C₂×Q₁₆×C₁₉	—	2	1	no	—
76	C₂×SD₁₆×C₁₉	—	2	1	no	—
77	C₂×SD₁₆×C₁₉	—	2	1	no	—
78	C₂×SD₁₆×C₁₉	—	2	1	no	—
79	C₂×SD₁₆×C₁₉	—	2	1	no	—
80	C₂×SD₁₆×C₁₉	—	2	2	no	—
81	C₂×SD₁₆×C₁₉	C₂×C₄	1	4	yes	complemented
82	C₂×D₈×C₁₉	—	2	1	no	—
83	C₁₉×#131	—	2	2	no	—
84	C₁₉×#131	C₂×C₄	1	4	yes	complemented
85	C₂×M₁₆×C₁₉	—	2	1	no	—
86	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
87	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₁₉	—	2	1	no	—
91	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
93	C₄×Q₈×C₁₉	—	2	1	no	—
94	C₄×Q₈×C₁₉	—	2	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×Q₈×C₁₉	—	2	1	no	—
99	C₄×D₄×C₁₉	—	2	1	no	—
100	C₄×D₄×C₁₉	—	2	1	no	—
101	C₄×D₄×C₁₉	—	2	1	no	—
102	C₄×D₄×C₁₉	—	2	1	no	—
103	C₄×D₄×C₁₉	—	2	1	no	—
104	C₄×D₄×C₁₉	—	2	1	no	—
105	C₄×D₄×C₁₉	—	4	1	no	—
106	C₄×D₄×C₁₉	—	4	1	no	—
107	C₁₉×#117	—	2	1	no	—
108	C₁₉×#117	—	2	1	no	—
109	C₁₉×#117	—	4	1	no	—
110	C₁₉×#117	C₂³	1	1	yes	characteristic
111	C₁₉×#117	C₂³	1	1	yes	characteristic
112	C₁₉×#117	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
114	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
115	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
117	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
118	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
119	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
120	C₁₉×#108	C₂×C₄	1	4	yes	complemented
121	C₁₉×#107	—	2	1	no	—
122	C₁₉×#107	—	2	1	no	—
123	C₁₉×#107	—	2	1	no	—
124	C₁₉×#107	—	2	1	no	—
125	C₁₉×#107	—	2	1	no	—
126	C₁₉×#107	—	2	1	no	—
127	C₁₉×#107	D₄	1	1	yes	characteristic
128	C₁₉×#107	D₄	1	1	yes	characteristic
129	C₁₉×#106	—	2	1	no	—
130	C₁₉×#106	—	2	1	no	—
131	C₁₉×#106	—	2	1	no	—
132	C₁₉×#106	—	2	1	no	—
133	C₁₉×#106	D₄	1	1	yes	characteristic
134	C₁₉×#106	D₄	1	1	yes	characteristic
135	C₁₉×#104	—	2	2	no	—
136	C₁₉×#103	—	2	1	no	—
137	C₁₉×#103	—	2	1	no	—
138	C₁₉×#103	—	2	1	no	—
139	C₁₉×#103	—	2	1	no	—
140	C₁₉×#103	D₄	1	1	yes	characteristic
141	C₁₉×#103	D₄	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
147	C₁₉×#102	D₄	1	1	yes	characteristic
148	C₁₉×#101	C₂×C₄	1	4	yes	complemented
149	C₁₉×#100	C₂×C₄	1	4	yes	complemented
150	C₁₉×#97	—	2	1	no	—
151	C₁₉×#97	—	2	1	no	—
152	C₁₉×#97	—	2	1	no	—
153	C₁₉×#97	—	2	2	no	—
154	C₄×C₈×C₁₉	—	2	1	no	—
155	C₄×C₈×C₁₉	—	2	1	no	—
156	C₄×C₈×C₁₉	—	2	1	no	—
157	C₁₉×#95	—	4	1	no	—
158	C₂⁴×C₁₉	—	2	1	no	—
159	#41×C₁₉	—	2	1	no	—
160	#41×C₁₉	—	2	1	no	—
161	#41×C₁₉	C₂²×C₄	1	2	yes	—
162	#41×C₁₉	#41	1	2	yes	—
163	C₂×Q₈×C₁₉	—	2	1	no	—
164	C₂×Q₈×C₁₉	—	2	1	no	—
165	C₂×Q₈×C₁₉	—	2	1	no	—
166	C₂×Q₈×C₁₉	—	2	1	no	—
167	C₂×Q₈×C₁₉	—	2	1	no	—
168	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
169	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
174	C₂×D₄×C₁₉	—	2	1	no	—
175	C₂×D₄×C₁₉	—	2	1	no	—
176	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
177	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
183	C₂²×C₄×C₁₉	—	4	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	Q₁₆×C₁₉	—	2	4	no	—
189	SD₁₆×C₁₉	—	2	4	no	—
190	SD₁₆×C₁₉	—	2	4	no	—
191	SD₁₆×C₁₉	—	2	4	no	—
192	SD₁₆×C₁₉	—	2	4	no	—
193	D₈×C₁₉	—	2	4	no	—
194	M₁₆×C₁₉	—	2	1	no	—
195	M₁₆×C₁₉	—	2	1	no	—
196	M₁₆×C₁₉	—	2	1	no	—
197	M₁₆×C₁₉	—	2	4	no	—
198	M₁₆×C₁₉	—	2	1	no	—
199	M₁₆×C₁₉	—	2	1	no	—
200	M₁₆×C₁₉	C₂²×C₄	1	2	yes	—
201	M₁₆×C₁₉	C₂²×C₄	1	2	yes	—
202	M₁₆×C₁₉	C₂²×C₄	1	2	yes	—
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	4	no	—
209	C₂×C₈×C₁₉	—	2	1	no	—
210	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
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	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
215	C₂×C₈×C₁₉	#41	1	2	yes	—
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	—	4	1	no	—
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	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
228	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
229	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
230	C₂²⋊C₄×C₁₉	—	2	1	no	—
231	C₂²⋊C₄×C₁₉	—	2	1	no	—
232	C₂²⋊C₄×C₁₉	—	2	1	no	—
233	C₂²⋊C₄×C₁₉	—	4	1	no	—
234	C₂²⋊C₄×C₁₉	—	4	1	no	—
235	C₂²⋊C₄×C₁₉	—	4	1	no	—
236	C₂²⋊C₄×C₁₉	—	4	1	no	—
237	C₂²⋊C₄×C₁₉	—	8	2	no	—
238	C₄²×C₁₉	—	2	1	no	—
239	C₄²×C₁₉	—	2	1	no	—
240	C₄²×C₁₉	—	2	1	no	—
241	C₄²×C₁₉	—	2	1	no	—
242	C₄²×C₁₉	—	2	1	no	—
243	C₄²×C₁₉	—	4	1	no	—
244	C₄²×C₁₉	—	4	1	no	—
245	C₄²×C₁₉	—	4	1	no	—
246	C₄²×C₁₉	—	4	1	no	—
247	#23049	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
248	C₂³×C₁₉	—	2	1	no	—
249	C₂³×C₁₉	—	2	2	no	—
250	C₂³×C₁₉	—	4	1	no	—
251	C₂³×C₁₉	—	4	1	no	—
252	C₂³×C₁₉	—	8	1	no	—
253	C₂³×C₁₉	—	8	1	no	—
254	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
255	Q₈×C₁₉	—	2	1	no	—
256	Q₈×C₁₉	—	2	2	no	—
257	Q₈×C₁₉	—	2	2	no	—
258	Q₈×C₁₉	—	4	1	no	—
259	Q₈×C₁₉	—	4	1	no	—
260	Q₈×C₁₉	C₄×D₄	1	2	yes	—
261	D₄×C₁₉	—	2	2	no	—
262	D₄×C₁₉	—	2	2	no	—
263	D₄×C₁₉	—	2	2	no	—
264	D₄×C₁₉	—	2	2	no	—
265	D₄×C₁₉	—	2	1	no	—
266	D₄×C₁₉	—	4	1	no	—
267	D₄×C₁₉	—	4	1	no	—
268	D₄×C₁₉	C₄×D₄	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	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	—	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	—	4	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	—	16	1	no	—
292	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
293	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
294	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
295	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
296	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
297	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
298	C₈×C₁₉	—	2	2	no	—
299	C₈×C₁₉	—	2	2	no	—
300	C₈×C₁₉	—	2	2	no	—
301	C₈×C₁₉	—	2	1	no	—
302	C₈×C₁₉	—	2	1	no	—
303	C₈×C₁₉	—	4	1	no	—
304	C₈×C₁₉	C₄×D₄	1	2	yes	—
305	C₈×C₁₉	C₄×D₄	1	2	yes	—
306	C₂×#471	C₂×C₁₉	1	1	yes	characteristic
307	#2949	C₂×C₁₉	1	1	yes	characteristic, complemented
308	#2947	C₂×C₁₉	1	1	yes	characteristic, complemented
309	#2946	C₂×C₁₉	1	1	yes	characteristic
310	#2913	C₂×C₁₉	1	1	yes	characteristic, complemented
311	#1973	C₂×C₁₉	1	1	yes	characteristic, complemented
312	#1952	C₂×C₁₉	1	1	yes	characteristic, complemented
313	#1931	C₂×C₁₉	1	1	yes	characteristic, complemented
314	#1930	C₂×C₁₉	1	1	yes	characteristic, complemented
315	#1883	C₂×C₁₉	1	1	yes	characteristic
316	#1882	C₂×C₁₉	1	1	yes	characteristic, complemented
317	#1857	C₂×C₁₉	1	1	yes	characteristic, complemented
318	#1856	C₂×C₁₉	1	1	yes	characteristic, complemented
319	#1773	C₂×C₁₉	1	1	yes	characteristic, complemented
320	#1765	C₂×C₁₉	1	1	yes	characteristic, complemented
321	C₂²×C₁₉	—	2	1	no	—
322	C₂²×C₁₉	—	2	1	no	—
323	C₂²×C₁₉	—	2	2	no	—
324	C₂²×C₁₉	—	4	1	no	—
325	C₂²×C₁₉	—	4	1	no	—
326	C₂²×C₁₉	—	4	2	no	—
327	C₂²×C₁₉	—	8	2	no	—
328	C₂²×C₁₉	—	8	1	no	—
329	C₂²×C₁₉	—	8	1	no	—
330	C₂²×C₁₉	—	16	1	no	—
331	C₂²×C₁₉	#520	1	1	yes	characteristic
332	C₂²×C₁₉	D₄²	1	1	yes	characteristic
333	C₂²×C₁₉	#553	1	1	yes	characteristic
334	C₄×C₁₉	—	2	2	no	—
335	C₄×C₁₉	—	4	2	no	—
336	C₄×C₁₉	—	4	1	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	C₂×C₄×D₄	1	1	yes	characteristic
346	C₄×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
347	C₄×C₁₉	#547	1	1	yes	characteristic
348	C₄×C₁₉	#548	1	1	yes	characteristic
349	C₂×#137	C₂²×C₁₉	1	1	yes	characteristic
350	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	1	yes	characteristic
351	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
352	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
353	#520	C₂²×C₁₉	1	1	yes	characteristic
354	#520	C₂²×C₁₉	1	1	yes	characteristic
355	#519	C₂²×C₁₉	1	1	yes	characteristic
356	#518	C₂²×C₁₉	1	1	yes	characteristic
357	#471	C₄×C₁₉	1	8	yes	complemented
358	#442	—	2	1	no	—
359	#441	—	2	1	no	—
360	#440	—	2	1	no	—
361	#440	—	2	1	no	—
362	#440	—	2	1	no	—
363	#440	—	2	1	no	—
364	C₄×Q₁₆	—	2	1	no	—
365	C₄×SD₁₆	—	2	1	no	—
366	C₄×SD₁₆	—	2	1	no	—
367	C₄×SD₁₆	—	2	1	no	—
368	C₄×SD₁₆	—	2	1	no	—
369	C₄×D₈	—	2	1	no	—
370	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
371	#428	—	2	1	no	—
372	#428	—	2	1	no	—
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	#428	C₂²×C₁₉	1	1	yes	characteristic
377	#427	—	2	1	no	—
378	#427	C₂²×C₁₉	1	1	yes	characteristic
379	C₂×#107	—	2	1	no	—
380	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
381	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
382	#419	C₂²×C₁₉	1	1	yes	characteristic
383	#418	C₂²×C₁₉	1	1	yes	characteristic
384	#416	C₂²×C₁₉	1	1	yes	characteristic
385	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
386	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
387	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
388	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
389	#405	C₂²×C₁₉	1	1	yes	characteristic
390	#405	C₂²×C₁₉	1	1	yes	characteristic
391	#405	C₂²×C₁₉	1	1	yes	characteristic
392	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
393	#391	C₂²×C₁₉	1	1	yes	characteristic
394	#390	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	—	4	2	no	—
404	C₂×C₁₉	—	8	2	no	—
405	C₂×C₁₉	#2361	1	1	yes	characteristic
406	C₂×C₁₉	#3288	1	1	yes	characteristic
407	C₂×C₁₉	#3289	1	1	yes	characteristic
408	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
409	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
410	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
411	#137	—	2	2	no	—
412	#137	C₂×C₄×C₁₉	1	4	yes	complemented
413	AGL(1,ℤ/8)	—	2	2	no	—
414	AGL(1,ℤ/8)	C₂×C₄×C₁₉	1	4	yes	—
415	C₂×Q₁₆	—	2	1	no	—
416	C₂×SD₁₆	—	2	1	no	—
417	C₂×SD₁₆	—	2	1	no	—
418	C₂×SD₁₆	—	2	1	no	—
419	C₂×SD₁₆	—	2	1	no	—
420	C₂×SD₁₆	—	2	2	no	—
421	C₂×SD₁₆	C₂×C₄×C₁₉	1	4	yes	complemented
422	C₂×D₈	—	2	1	no	—
423	#131	—	2	2	no	—
424	#131	C₂×C₄×C₁₉	1	4	yes	complemented
425	C₂×M₁₆	—	2	1	no	—
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	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
430	C₂²×C₈	—	2	1	no	—
431	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
432	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
433	C₄×Q₈	—	2	1	no	—
434	C₄×Q₈	—	2	1	no	—
435	C₄×Q₈	—	2	1	no	—
436	C₄×Q₈	—	2	1	no	—
437	C₄×Q₈	—	2	1	no	—
438	C₄×Q₈	—	2	1	no	—
439	C₄×D₄	—	2	1	no	—
440	C₄×D₄	—	2	1	no	—
441	C₄×D₄	—	2	1	no	—
442	C₄×D₄	—	2	1	no	—
443	C₄×D₄	—	2	1	no	—
444	C₄×D₄	—	2	1	no	—
445	C₄×D₄	—	4	1	no	—
446	C₄×D₄	—	4	1	no	—
447	#117	—	2	1	no	—
448	#117	—	2	1	no	—
449	#117	—	4	1	no	—
450	#117	C₂³×C₁₉	1	1	yes	characteristic
451	#117	C₂³×C₁₉	1	1	yes	characteristic
452	#117	C₂³×C₁₉	1	1	yes	characteristic
453	C₂×C₄⋊C₄	—	2	1	no	—
454	C₂×C₄⋊C₄	—	2	1	no	—
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×C₂²⋊C₄	—	4	1	no	—
459	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
460	#108	C₂×C₄×C₁₉	1	4	yes	complemented
461	#107	—	2	1	no	—
462	#107	—	2	1	no	—
463	#107	—	2	1	no	—
464	#107	—	2	1	no	—
465	#107	—	2	1	no	—
466	#107	—	2	1	no	—
467	#107	D₄×C₁₉	1	1	yes	characteristic
468	#107	D₄×C₁₉	1	1	yes	characteristic
469	#106	—	2	1	no	—
470	#106	—	2	1	no	—
471	#106	—	2	1	no	—
472	#106	—	2	1	no	—
473	#106	D₄×C₁₉	1	1	yes	characteristic
474	#106	D₄×C₁₉	1	1	yes	characteristic
475	#104	—	2	2	no	—
476	#103	—	2	1	no	—
477	#103	—	2	1	no	—
478	#103	—	2	1	no	—
479	#103	—	2	1	no	—
480	#103	D₄×C₁₉	1	1	yes	characteristic
481	#103	D₄×C₁₉	1	1	yes	characteristic
482	#102	—	2	1	no	—
483	#102	—	2	1	no	—
484	#102	—	2	1	no	—
485	#102	—	2	1	no	—
486	#102	D₄×C₁₉	1	1	yes	characteristic
487	#102	D₄×C₁₉	1	1	yes	characteristic
488	#101	C₂×C₄×C₁₉	1	4	yes	complemented
489	#100	C₂×C₄×C₁₉	1	4	yes	complemented
490	#97	—	2	1	no	—
491	#97	—	2	1	no	—
492	#97	—	2	1	no	—
493	#97	—	2	2	no	—
494	C₄×C₈	—	2	1	no	—
495	C₄×C₈	—	2	1	no	—
496	C₄×C₈	—	2	1	no	—
497	#95	—	4	1	no	—
498	C₁₉	#23049	1	1	yes	characteristic, direct product factor, Sylow
499	C₂⁴	—	2	1	no	—
500	#41	—	2	1	no	—
501	#41	—	2	1	no	—
502	#41	C₂²×C₄×C₁₉	1	2	yes	—
503	#41	#41×C₁₉	1	2	yes	—
504	C₂×Q₈	—	2	1	no	—
505	C₂×Q₈	—	2	1	no	—
506	C₂×Q₈	—	2	1	no	—
507	C₂×Q₈	—	2	1	no	—
508	C₂×Q₈	—	2	1	no	—
509	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
510	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
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	—	2	1	no	—
517	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
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	—	4	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	4	no	—
530	SD₁₆	—	2	4	no	—
531	SD₁₆	—	2	4	no	—
532	SD₁₆	—	2	4	no	—
533	SD₁₆	—	2	4	no	—
534	D₈	—	2	4	no	—
535	M₁₆	—	2	1	no	—
536	M₁₆	—	2	1	no	—
537	M₁₆	—	2	1	no	—
538	M₁₆	—	2	4	no	—
539	M₁₆	—	2	1	no	—
540	M₁₆	—	2	1	no	—
541	M₁₆	C₂²×C₄×C₁₉	1	2	yes	—
542	M₁₆	C₂²×C₄×C₁₉	1	2	yes	—
543	M₁₆	C₂²×C₄×C₁₉	1	2	yes	—
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	—	2	4	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
552	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
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	#41×C₁₉	1	2	yes	—
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	—	4	1	no	—
562	C₄⋊C₄	—	4	1	no	—
563	C₄⋊C₄	—	4	1	no	—
564	C₄⋊C₄	—	4	1	no	—
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	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
569	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
570	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
571	C₂²⋊C₄	—	2	1	no	—
572	C₂²⋊C₄	—	2	1	no	—
573	C₂²⋊C₄	—	2	1	no	—
574	C₂²⋊C₄	—	4	1	no	—
575	C₂²⋊C₄	—	4	1	no	—
576	C₂²⋊C₄	—	4	1	no	—
577	C₂²⋊C₄	—	4	1	no	—
578	C₂²⋊C₄	—	8	2	no	—
579	C₄²	—	2	1	no	—
580	C₄²	—	2	1	no	—
581	C₄²	—	2	1	no	—
582	C₄²	—	2	1	no	—
583	C₄²	—	2	1	no	—
584	C₄²	—	4	1	no	—
585	C₄²	—	4	1	no	—
586	C₄²	—	4	1	no	—
587	C₄²	—	4	1	no	—
588	C₂³	—	2	1	no	—
589	C₂³	—	2	2	no	—
590	C₂³	—	4	1	no	—
591	C₂³	—	4	1	no	—
592	C₂³	—	8	1	no	—
593	C₂³	—	8	1	no	—
594	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
595	Q₈	—	2	1	no	—
596	Q₈	—	2	2	no	—
597	Q₈	—	2	2	no	—
598	Q₈	—	4	1	no	—
599	Q₈	—	4	1	no	—
600	Q₈	C₄×D₄×C₁₉	1	2	yes	—
601	D₄	—	2	2	no	—
602	D₄	—	2	2	no	—
603	D₄	—	2	2	no	—
604	D₄	—	2	2	no	—
605	D₄	—	2	1	no	—
606	D₄	—	4	1	no	—
607	D₄	—	4	1	no	—
608	D₄	C₄×D₄×C₁₉	1	2	yes	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	1	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	—	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	—	16	1	no	—
632	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
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	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
638	C₈	—	2	2	no	—
639	C₈	—	2	2	no	—
640	C₈	—	2	2	no	—
641	C₈	—	2	1	no	—
642	C₈	—	2	1	no	—
643	C₈	—	4	1	no	—
644	C₈	C₄×D₄×C₁₉	1	2	yes	—
645	C₈	C₄×D₄×C₁₉	1	2	yes	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	1	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	4	1	no	—
650	C₂²	—	4	1	no	—
651	C₂²	—	4	2	no	—
652	C₂²	—	8	2	no	—
653	C₂²	—	8	1	no	—
654	C₂²	—	8	1	no	—
655	C₂²	—	16	1	no	—
656	C₂²	C₁₉×#520	1	1	yes	characteristic
657	C₂²	D₄²×C₁₉	1	1	yes	characteristic
658	C₂²	C₁₉×#553	1	1	yes	characteristic
659	C₄	—	2	2	no	—
660	C₄	—	4	1	no	—
661	C₄	—	4	1	no	—
662	C₄	—	4	1	no	—
663	C₄	—	4	1	no	—
664	C₄	—	4	1	no	—
665	C₄	—	4	1	no	—
666	C₄	—	4	2	no	—
667	C₄	—	8	1	no	—
668	C₄	—	8	1	no	—
669	C₄	—	8	1	no	—
670	C₄	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
671	C₄	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
672	C₄	C₁₉×#547	1	1	yes	characteristic
673	C₄	C₁₉×#548	1	1	yes	characteristic
674	C₂	—	2	1	no	—
675	C₂	—	2	1	no	—
676	C₂	—	4	2	no	—
677	C₂	—	8	2	no	—
678	C₂	C₁₉×#2361	1	1	yes	characteristic
679	C₂	C₁₉×#3288	1	1	yes	characteristic
680	C₂	C₁₉×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×AGL(1,ℤ/8)	C₂²
LCS	G ▷ C₂×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
2. C₁₉×#2949	C₂	semidirect
3. C₁₉×#2947	C₂	semidirect
5. C₁₉×#2913	C₂	semidirect
6. C₁₉×#1973	C₂	semidirect
7. C₁₉×#1952	C₂	semidirect
8. C₁₉×#1931	C₂	semidirect
9. C₁₉×#1930	C₂	semidirect
11. C₁₉×#1882	C₂	semidirect
12. C₁₉×#1857	C₂	semidirect
13. C₁₉×#1856	C₂	semidirect
14. C₁₉×#1773	C₂	semidirect
15. C₁₉×#1765	C₂	semidirect
24. C₁₉×#471	C₄	semidirect
72. C₁₉×#137	C₂×C₄	semidirect
81. C₂×SD₁₆×C₁₉	C₂×C₄	semidirect
84. C₁₉×#131	C₂×C₄	semidirect
120. C₁₉×#108	C₂×C₄	semidirect
148. C₁₉×#101	C₂×C₄	semidirect
149. C₁₉×#100	C₂×C₄	semidirect
247. #23049	C₁₉	direct (N × H)
307. #2949	C₂×C₁₉	semidirect
308. #2947	C₂×C₁₉	semidirect
310. #2913	C₂×C₁₉	semidirect
311. #1973	C₂×C₁₉	semidirect
312. #1952	C₂×C₁₉	semidirect
313. #1931	C₂×C₁₉	semidirect
314. #1930	C₂×C₁₉	semidirect
316. #1882	C₂×C₁₉	semidirect
317. #1857	C₂×C₁₉	semidirect
318. #1856	C₂×C₁₉	semidirect
319. #1773	C₂×C₁₉	semidirect
320. #1765	C₂×C₁₉	semidirect
357. #471	C₄×C₁₉	semidirect
412. #137	C₂×C₄×C₁₉	semidirect
421. C₂×SD₁₆	C₂×C₄×C₁₉	semidirect
424. #131	C₂×C₄×C₁₉	semidirect
460. #108	C₂×C₄×C₁₉	semidirect
488. #101	C₂×C₄×C₁₉	semidirect
489. #100	C₂×C₄×C₁₉	semidirect
498. C₁₉	#23049	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#471	2
C₁₉×#2949	2
C₁₉×#2947	2
C₁₉×#2946	2
C₁₉×#2913	2
C₁₉×#1973	2
C₁₉×#1952	2
C₁₉×#1931	2
C₁₉×#1930	2
C₁₉×#1883	2
C₁₉×#1882	2
C₁₉×#1857	2
C₁₉×#1856	2
C₁₉×#1773	2
C₁₉×#1765	2
#23049	19

Subgroups — C19×#23049 #18029008

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23049 #18029008