Subgroups — C₁₉×#24525 #18030484

Order 4864.

858 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3095	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#452	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2924	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2896	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2064	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2063	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2047	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2046	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1979	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1977	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1931	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1930	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1901	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1855	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1785	C₂	1	1	yes	maximal, characteristic
16	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
22	C₁₉×#485	—	2	1	no	—
23	C₁₉×#485	—	2	1	no	—
24	C₁₉×#484	—	2	1	no	—
25	C₁₉×#483	—	2	1	no	—
26	C₁₉×#452	—	2	1	no	—
27	C₁₉×#452	—	2	1	no	—
28	C₁₉×#452	—	2	1	no	—
29	C₁₉×#452	—	2	1	no	—
30	C₁₉×#433	—	2	1	no	—
31	C₁₉×#433	—	2	1	no	—
32	C₁₉×#432	—	2	1	no	—
33	C₁₉×#431	—	2	1	no	—
34	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
36	C₁₉×#428	C₂²	1	1	yes	characteristic
37	C₁₉×#428	C₂²	1	1	yes	characteristic
38	C₁₉×#424	C₂²	1	1	yes	characteristic
39	C₁₉×#424	C₂²	1	1	yes	characteristic
40	C₁₉×#419	C₂²	1	1	yes	characteristic
41	C₁₉×#419	C₂²	1	1	yes	characteristic
42	C₁₉×#419	C₂²	1	1	yes	characteristic
43	C₁₉×#419	C₂²	1	1	yes	characteristic
44	C₁₉×#418	C₂²	1	1	yes	characteristic
45	C₁₉×#418	C₂²	1	1	yes	characteristic
46	C₁₉×#417	—	2	1	no	—
47	C₁₉×#417	—	2	1	no	—
48	C₁₉×#416	—	2	1	no	—
49	C₁₉×#416	—	2	1	no	—
50	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
51	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
52	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
53	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
54	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
55	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
56	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
57	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
58	C₁₉×#407	C₂²	1	1	yes	characteristic
59	C₁₉×#407	C₂²	1	1	yes	characteristic
60	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
61	C₁₉×#405	C₂²	1	1	yes	characteristic
62	C₁₉×#405	C₂²	1	1	yes	characteristic
63	C₁₉×#343	C₂²	1	1	yes	characteristic
64	C₁₉×#343	C₂²	1	1	yes	characteristic
65	C₁₉×#341	C₂²	1	1	yes	characteristic
66	C₁₉×#341	C₂²	1	1	yes	characteristic
67	C₂×#41×C₁₉	—	2	2	no	—
68	C₂×#41×C₁₉	—	2	2	no	—
69	C₂×#41×C₁₉	—	2	1	no	—
70	C₂×#41×C₁₉	—	2	1	no	—
71	C₂×#41×C₁₉	—	2	1	no	—
72	C₂×#41×C₁₉	—	2	1	no	—
73	C₂×#41×C₁₉	—	4	1	no	—
74	C₂×#41×C₁₉	—	4	1	no	—
75	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
76	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₁₉	—	2	1	no	—
78	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₁₉	—	2	1	no	—
80	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
81	C₂×Q₁₆×C₁₉	—	2	2	no	—
82	C₂×Q₁₆×C₁₉	—	2	1	no	—
83	C₂×Q₁₆×C₁₉	—	2	1	no	—
84	C₂×Q₁₆×C₁₉	—	4	1	no	—
85	C₂×SD₁₆×C₁₉	—	2	2	no	—
86	C₂×SD₁₆×C₁₉	—	2	1	no	—
87	C₂×SD₁₆×C₁₉	—	2	1	no	—
88	C₂×SD₁₆×C₁₉	—	4	1	no	—
89	C₂×M₁₆×C₁₉	—	2	1	no	—
90	C₂×M₁₆×C₁₉	—	4	1	no	—
91	C₂×M₁₆×C₁₉	—	4	1	no	—
92	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
93	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
94	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
95	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
96	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
97	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₁₉	—	2	1	no	—
99	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
101	C₁₉×C₂²⋊Q₈	—	2	1	no	—
102	C₁₉×C₂²⋊Q₈	—	2	1	no	—
103	C₁₉×C₂²⋊Q₈	—	2	1	no	—
104	C₁₉×C₂²⋊Q₈	—	2	1	no	—
105	C₁₉×#117	—	2	1	no	—
106	C₁₉×#117	—	2	1	no	—
107	C₁₉×#117	D₄	1	1	yes	characteristic
108	C₁₉×#117	D₄	1	1	yes	characteristic
109	C₁₉×#117	C₂³	1	1	yes	characteristic
110	C₁₉×#117	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
112	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
115	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
117	C₂×C₄²×C₁₉	—	2	1	no	—
118	C₁₉×#108	—	4	1	no	—
119	C₁₉×#108	—	4	1	no	—
120	C₁₉×#107	—	2	1	no	—
121	C₁₉×#107	—	2	1	no	—
122	C₁₉×#106	—	2	1	no	—
123	C₁₉×#106	—	2	1	no	—
124	C₁₉×C₄⋊C₈	—	2	1	no	—
125	C₁₉×C₄⋊C₈	—	2	1	no	—
126	C₁₉×C₄⋊C₈	—	2	1	no	—
127	C₁₉×C₄⋊C₈	—	2	1	no	—
128	C₁₉×#103	—	2	1	no	—
129	C₁₉×#103	—	2	1	no	—
130	C₁₉×#103	—	2	1	no	—
131	C₁₉×#103	—	2	1	no	—
132	C₁₉×#103	—	2	1	no	—
133	C₁₉×#103	—	2	1	no	—
134	C₁₉×#103	—	2	1	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×#101	—	2	2	no	—
145	C₁₉×#101	—	4	1	no	—
146	C₁₉×#101	—	4	1	no	—
147	C₁₉×#101	—	4	1	no	—
148	C₁₉×#100	—	2	2	no	—
149	C₁₉×#100	—	4	1	no	—
150	C₁₉×C₂²⋊C₈	—	2	1	no	—
151	C₁₉×C₂²⋊C₈	—	2	1	no	—
152	C₁₉×C₂²⋊C₈	—	2	1	no	—
153	C₁₉×C₂²⋊C₈	—	2	1	no	—
154	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
155	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
156	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
157	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
158	C₁₉×#97	—	2	1	no	—
159	C₁₉×#97	—	2	1	no	—
160	C₄×C₈×C₁₉	—	2	1	no	—
161	C₄×C₈×C₁₉	—	2	1	no	—
162	C₂⁴×C₁₉	—	2	1	no	—
163	C₂⁴×C₁₉	#41	1	1	yes	characteristic
164	#41×C₁₉	—	2	4	no	—
165	#41×C₁₉	—	2	4	no	—
166	#41×C₁₉	—	4	2	no	—
167	#41×C₁₉	—	4	2	no	—
168	#41×C₁₉	—	4	2	no	—
169	#41×C₁₉	—	4	2	no	—
170	#41×C₁₉	—	4	2	no	—
171	#41×C₁₉	—	4	2	no	—
172	C₂×Q₈×C₁₉	—	2	1	no	—
173	C₂×Q₈×C₁₉	—	2	1	no	—
174	C₂×Q₈×C₁₉	—	2	1	no	—
175	C₂×Q₈×C₁₉	—	2	1	no	—
176	C₂×Q₈×C₁₉	—	2	1	no	—
177	C₂×Q₈×C₁₉	—	2	1	no	—
178	C₂×Q₈×C₁₉	—	2	1	no	—
179	C₂×Q₈×C₁₉	—	2	1	no	—
180	C₂×Q₈×C₁₉	—	2	1	no	—
181	C₂×Q₈×C₁₉	—	2	1	no	—
182	C₂×Q₈×C₁₉	—	2	1	no	—
183	C₂×Q₈×C₁₉	#41	1	2	yes	—
184	C₂×D₄×C₁₉	—	2	1	no	—
185	C₂×D₄×C₁₉	—	2	1	no	—
186	C₂×D₄×C₁₉	—	2	1	no	—
187	C₂×D₄×C₁₉	—	2	1	no	—
188	C₂×D₄×C₁₉	—	2	1	no	—
189	C₂×D₄×C₁₉	—	4	2	no	—
190	C₂×D₄×C₁₉	—	4	2	no	—
191	C₂×D₄×C₁₉	—	4	1	no	—
192	C₂×D₄×C₁₉	—	4	1	no	—
193	C₂×D₄×C₁₉	#41	1	2	yes	—
194	C₂²×C₄×C₁₉	—	2	1	no	—
195	C₂²×C₄×C₁₉	—	2	1	no	—
196	C₂²×C₄×C₁₉	—	2	1	no	—
197	C₂²×C₄×C₁₉	—	2	1	no	—
198	C₂²×C₄×C₁₉	—	2	1	no	—
199	C₂²×C₄×C₁₉	—	2	1	no	—
200	C₂²×C₄×C₁₉	—	2	1	no	—
201	C₂²×C₄×C₁₉	—	2	1	no	—
202	C₂²×C₄×C₁₉	—	2	1	no	—
203	C₂²×C₄×C₁₉	—	4	2	no	—
204	C₂²×C₄×C₁₉	—	4	2	no	—
205	C₂²×C₄×C₁₉	—	4	1	no	—
206	C₂²×C₄×C₁₉	—	4	1	no	—
207	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
212	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
213	Q₁₆×C₁₉	—	4	2	no	—
214	Q₁₆×C₁₉	—	4	2	no	—
215	SD₁₆×C₁₉	—	4	2	no	—
216	SD₁₆×C₁₉	—	4	2	no	—
217	M₁₆×C₁₉	—	2	1	no	—
218	M₁₆×C₁₉	—	2	1	no	—
219	M₁₆×C₁₉	—	2	1	no	—
220	M₁₆×C₁₉	—	2	1	no	—
221	M₁₆×C₁₉	—	2	1	no	—
222	M₁₆×C₁₉	—	2	1	no	—
223	M₁₆×C₁₉	—	2	1	no	—
224	M₁₆×C₁₉	—	2	1	no	—
225	M₁₆×C₁₉	—	2	1	no	—
226	M₁₆×C₁₉	—	2	1	no	—
227	M₁₆×C₁₉	—	2	1	no	—
228	M₁₆×C₁₉	—	2	1	no	—
229	M₁₆×C₁₉	—	4	2	no	—
230	C₂×C₈×C₁₉	—	2	1	no	—
231	C₂×C₈×C₁₉	—	2	1	no	—
232	C₂×C₈×C₁₉	—	2	1	no	—
233	C₂×C₈×C₁₉	—	2	1	no	—
234	C₂×C₈×C₁₉	—	2	1	no	—
235	C₂×C₈×C₁₉	—	2	1	no	—
236	C₂×C₈×C₁₉	—	2	1	no	—
237	C₂×C₈×C₁₉	—	2	1	no	—
238	C₂×C₈×C₁₉	—	2	1	no	—
239	C₂×C₈×C₁₉	—	2	1	no	—
240	C₂×C₈×C₁₉	—	4	2	no	—
241	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
242	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
243	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
244	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
245	C₄⋊C₄×C₁₉	—	2	1	no	—
246	C₄⋊C₄×C₁₉	—	2	1	no	—
247	C₄⋊C₄×C₁₉	—	2	1	no	—
248	C₄⋊C₄×C₁₉	—	2	1	no	—
249	C₄⋊C₄×C₁₉	—	4	1	no	—
250	C₄⋊C₄×C₁₉	—	4	1	no	—
251	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
252	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
253	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
254	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
255	C₂²⋊C₄×C₁₉	—	2	1	no	—
256	C₂²⋊C₄×C₁₉	—	2	1	no	—
257	C₂²⋊C₄×C₁₉	—	2	1	no	—
258	C₂²⋊C₄×C₁₉	—	2	1	no	—
259	C₂²⋊C₄×C₁₉	—	4	1	no	—
260	C₂²⋊C₄×C₁₉	—	4	1	no	—
261	C₄²×C₁₉	—	2	1	no	—
262	C₄²×C₁₉	—	2	1	no	—
263	C₄²×C₁₉	—	2	1	no	—
264	C₄²×C₁₉	—	2	1	no	—
265	#24525	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
266	C₂³×C₁₉	—	2	1	no	—
267	C₂³×C₁₉	—	2	1	no	—
268	C₂³×C₁₉	—	2	2	no	—
269	C₂³×C₁₉	—	4	1	no	—
270	C₂³×C₁₉	—	4	1	no	—
271	C₂³×C₁₉	—	4	1	no	—
272	C₂³×C₁₉	—	4	1	no	—
273	C₂³×C₁₉	—	8	1	no	—
274	C₂³×C₁₉	—	8	1	no	—
275	C₂³×C₁₉	#121	1	1	yes	characteristic
276	C₂³×C₁₉	#121	1	1	yes	characteristic
277	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
278	Q₈×C₁₉	—	2	2	no	—
279	Q₈×C₁₉	—	2	2	no	—
280	Q₈×C₁₉	—	4	1	no	—
281	Q₈×C₁₉	—	4	1	no	—
282	Q₈×C₁₉	—	4	1	no	—
283	Q₈×C₁₉	—	4	1	no	—
284	Q₈×C₁₉	—	4	1	no	—
285	Q₈×C₁₉	—	4	1	no	—
286	D₄×C₁₉	—	2	2	no	—
287	D₄×C₁₉	—	2	2	no	—
288	D₄×C₁₉	—	4	4	no	—
289	D₄×C₁₉	—	4	4	no	—
290	D₄×C₁₉	—	4	1	no	—
291	D₄×C₁₉	—	4	1	no	—
292	C₂×C₄×C₁₉	—	2	1	no	—
293	C₂×C₄×C₁₉	—	2	1	no	—
294	C₂×C₄×C₁₉	—	2	1	no	—
295	C₂×C₄×C₁₉	—	2	1	no	—
296	C₂×C₄×C₁₉	—	2	1	no	—
297	C₂×C₄×C₁₉	—	2	1	no	—
298	C₂×C₄×C₁₉	—	2	1	no	—
299	C₂×C₄×C₁₉	—	2	1	no	—
300	C₂×C₄×C₁₉	—	2	1	no	—
301	C₂×C₄×C₁₉	—	2	1	no	—
302	C₂×C₄×C₁₉	—	2	1	no	—
303	C₂×C₄×C₁₉	—	2	1	no	—
304	C₂×C₄×C₁₉	—	2	1	no	—
305	C₂×C₄×C₁₉	—	2	1	no	—
306	C₂×C₄×C₁₉	—	2	2	no	—
307	C₂×C₄×C₁₉	—	4	4	no	—
308	C₂×C₄×C₁₉	—	4	4	no	—
309	C₂×C₄×C₁₉	—	4	2	no	—
310	C₂×C₄×C₁₉	—	4	1	no	—
311	C₂×C₄×C₁₉	—	4	1	no	—
312	C₂×C₄×C₁₉	—	4	1	no	—
313	C₂×C₄×C₁₉	—	4	1	no	—
314	C₂×C₄×C₁₉	—	4	1	no	—
315	C₂×C₄×C₁₉	—	4	1	no	—
316	C₂×C₄×C₁₉	—	8	1	no	—
317	C₂×C₄×C₁₉	—	8	1	no	—
318	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
319	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
320	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
322	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
323	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
324	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
325	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
326	C₈×C₁₉	—	2	1	no	—
327	C₈×C₁₉	—	2	1	no	—
328	C₈×C₁₉	—	2	1	no	—
329	C₈×C₁₉	—	2	1	no	—
330	C₈×C₁₉	—	4	1	no	—
331	C₈×C₁₉	—	4	1	no	—
332	C₈×C₁₉	—	4	1	no	—
333	C₈×C₁₉	—	4	1	no	—
334	C₈×C₁₉	—	4	1	no	—
335	C₈×C₁₉	—	4	1	no	—
336	#3095	C₂×C₁₉	1	1	yes	characteristic, complemented
337	C₂×#452	C₂×C₁₉	1	1	yes	characteristic
338	#2924	C₂×C₁₉	1	1	yes	characteristic, complemented
339	#2896	C₂×C₁₉	1	1	yes	characteristic
340	#2064	C₂×C₁₉	1	1	yes	characteristic, complemented
341	#2063	C₂×C₁₉	1	1	yes	characteristic, complemented
342	#2047	C₂×C₁₉	1	1	yes	characteristic, complemented
343	#2046	C₂×C₁₉	1	1	yes	characteristic, complemented
344	#1979	C₂×C₁₉	1	1	yes	characteristic, complemented
345	#1977	C₂×C₁₉	1	1	yes	characteristic, complemented
346	#1931	C₂×C₁₉	1	1	yes	characteristic, complemented
347	#1930	C₂×C₁₉	1	1	yes	characteristic, complemented
348	#1901	C₂×C₁₉	1	1	yes	characteristic, complemented
349	#1855	C₂×C₁₉	1	1	yes	characteristic, complemented
350	#1785	C₂×C₁₉	1	1	yes	characteristic
351	C₂²×C₁₉	—	2	1	no	—
352	C₂²×C₁₉	—	2	1	no	—
353	C₂²×C₁₉	—	2	1	no	—
354	C₂²×C₁₉	—	2	1	no	—
355	C₂²×C₁₉	—	2	1	no	—
356	C₂²×C₁₉	—	2	1	no	—
357	C₂²×C₁₉	—	2	1	no	—
358	C₂²×C₁₉	—	2	1	no	—
359	C₂²×C₁₉	—	4	2	no	—
360	C₂²×C₁₉	—	8	1	no	—
361	C₂²×C₁₉	—	8	1	no	—
362	C₂²×C₁₉	—	8	2	no	—
363	C₂²×C₁₉	—	8	2	no	—
364	C₂²×C₁₉	—	8	1	no	—
365	C₂²×C₁₉	—	8	1	no	—
366	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
367	C₂²×C₁₉	#551	1	1	yes	characteristic
368	C₂²×C₁₉	#551	1	1	yes	characteristic
369	C₄×C₁₉	—	2	1	no	—
370	C₄×C₁₉	—	2	1	no	—
371	C₄×C₁₉	—	4	2	no	—
372	C₄×C₁₉	—	4	1	no	—
373	C₄×C₁₉	—	4	1	no	—
374	C₄×C₁₉	—	4	1	no	—
375	C₄×C₁₉	—	4	1	no	—
376	C₄×C₁₉	—	8	1	no	—
377	C₄×C₁₉	—	8	1	no	—
378	C₄×C₁₉	#525	1	1	yes	characteristic
379	C₄×C₁₉	#535	1	1	yes	characteristic
380	C₄×C₁₉	#546	1	1	yes	characteristic
381	C₄×C₁₉	#546	1	1	yes	characteristic
382	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
383	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
384	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
385	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
386	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
387	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
388	#485	—	2	1	no	—
389	#485	—	2	1	no	—
390	#484	—	2	1	no	—
391	#483	—	2	1	no	—
392	#452	—	2	1	no	—
393	#452	—	2	1	no	—
394	#452	—	2	1	no	—
395	#452	—	2	1	no	—
396	#433	—	2	1	no	—
397	#433	—	2	1	no	—
398	#432	—	2	1	no	—
399	#431	—	2	1	no	—
400	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
401	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
402	#428	C₂²×C₁₉	1	1	yes	characteristic
403	#428	C₂²×C₁₉	1	1	yes	characteristic
404	#424	C₂²×C₁₉	1	1	yes	characteristic
405	#424	C₂²×C₁₉	1	1	yes	characteristic
406	#419	C₂²×C₁₉	1	1	yes	characteristic
407	#419	C₂²×C₁₉	1	1	yes	characteristic
408	#419	C₂²×C₁₉	1	1	yes	characteristic
409	#419	C₂²×C₁₉	1	1	yes	characteristic
410	#418	C₂²×C₁₉	1	1	yes	characteristic
411	#418	C₂²×C₁₉	1	1	yes	characteristic
412	#417	—	2	1	no	—
413	#417	—	2	1	no	—
414	#416	—	2	1	no	—
415	#416	—	2	1	no	—
416	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
417	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
418	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
419	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
420	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
421	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
422	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
423	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
424	#407	C₂²×C₁₉	1	1	yes	characteristic
425	#407	C₂²×C₁₉	1	1	yes	characteristic
426	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
427	#405	C₂²×C₁₉	1	1	yes	characteristic
428	#405	C₂²×C₁₉	1	1	yes	characteristic
429	#343	C₂²×C₁₉	1	1	yes	characteristic
430	#343	C₂²×C₁₉	1	1	yes	characteristic
431	#341	C₂²×C₁₉	1	1	yes	characteristic
432	#341	C₂²×C₁₉	1	1	yes	characteristic
433	C₂×C₁₉	—	2	1	no	—
434	C₂×C₁₉	—	2	1	no	—
435	C₂×C₁₉	—	4	1	no	—
436	C₂×C₁₉	—	4	1	no	—
437	C₂×C₁₉	—	8	2	no	—
438	C₂×C₁₉	#2411	1	1	yes	characteristic
439	C₂×C₁₉	#3067	1	1	yes	characteristic
440	C₂×C₁₉	#3069	1	1	yes	characteristic
441	C₂×#41	—	2	2	no	—
442	C₂×#41	—	2	2	no	—
443	C₂×#41	—	2	1	no	—
444	C₂×#41	—	2	1	no	—
445	C₂×#41	—	2	1	no	—
446	C₂×#41	—	2	1	no	—
447	C₂×#41	—	4	1	no	—
448	C₂×#41	—	4	1	no	—
449	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
450	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
451	C₂²×D₄	—	2	1	no	—
452	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
453	C₂³×C₄	—	2	1	no	—
454	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
455	C₂×Q₁₆	—	2	2	no	—
456	C₂×Q₁₆	—	2	1	no	—
457	C₂×Q₁₆	—	2	1	no	—
458	C₂×Q₁₆	—	4	1	no	—
459	C₂×SD₁₆	—	2	2	no	—
460	C₂×SD₁₆	—	2	1	no	—
461	C₂×SD₁₆	—	2	1	no	—
462	C₂×SD₁₆	—	4	1	no	—
463	C₂×M₁₆	—	2	1	no	—
464	C₂×M₁₆	—	4	1	no	—
465	C₂×M₁₆	—	4	1	no	—
466	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
467	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
468	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
469	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
470	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
471	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
472	C₂²×C₈	—	2	1	no	—
473	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
474	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
475	C₂²⋊Q₈	—	2	1	no	—
476	C₂²⋊Q₈	—	2	1	no	—
477	C₂²⋊Q₈	—	2	1	no	—
478	C₂²⋊Q₈	—	2	1	no	—
479	#117	—	2	1	no	—
480	#117	—	2	1	no	—
481	#117	D₄×C₁₉	1	1	yes	characteristic
482	#117	D₄×C₁₉	1	1	yes	characteristic
483	#117	C₂³×C₁₉	1	1	yes	characteristic
484	#117	C₂³×C₁₉	1	1	yes	characteristic
485	C₂×C₄⋊C₄	—	2	1	no	—
486	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
487	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
489	C₂×C₂²⋊C₄	—	2	1	no	—
490	C₂×C₂²⋊C₄	—	2	1	no	—
491	C₂×C₄²	—	2	1	no	—
492	#108	—	4	1	no	—
493	#108	—	4	1	no	—
494	#107	—	2	1	no	—
495	#107	—	2	1	no	—
496	#106	—	2	1	no	—
497	#106	—	2	1	no	—
498	C₄⋊C₈	—	2	1	no	—
499	C₄⋊C₈	—	2	1	no	—
500	C₄⋊C₈	—	2	1	no	—
501	C₄⋊C₈	—	2	1	no	—
502	#103	—	2	1	no	—
503	#103	—	2	1	no	—
504	#103	—	2	1	no	—
505	#103	—	2	1	no	—
506	#103	—	2	1	no	—
507	#103	—	2	1	no	—
508	#103	—	2	1	no	—
509	#103	—	2	1	no	—
510	#103	—	2	1	no	—
511	#103	—	2	1	no	—
512	#102	—	2	1	no	—
513	#102	—	2	1	no	—
514	#102	—	2	1	no	—
515	#102	—	2	1	no	—
516	#102	—	2	1	no	—
517	#102	—	2	1	no	—
518	#101	—	2	2	no	—
519	#101	—	4	1	no	—
520	#101	—	4	1	no	—
521	#101	—	4	1	no	—
522	#100	—	2	2	no	—
523	#100	—	4	1	no	—
524	C₂²⋊C₈	—	2	1	no	—
525	C₂²⋊C₈	—	2	1	no	—
526	C₂²⋊C₈	—	2	1	no	—
527	C₂²⋊C₈	—	2	1	no	—
528	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
529	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
530	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
531	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
532	#97	—	2	1	no	—
533	#97	—	2	1	no	—
534	C₄×C₈	—	2	1	no	—
535	C₄×C₈	—	2	1	no	—
536	C₁₉	#24525	1	1	yes	characteristic, direct product factor, Sylow
537	C₂⁴	—	2	1	no	—
538	C₂⁴	#41×C₁₉	1	1	yes	characteristic
539	#41	—	2	4	no	—
540	#41	—	2	4	no	—
541	#41	—	4	2	no	—
542	#41	—	4	2	no	—
543	#41	—	4	2	no	—
544	#41	—	4	2	no	—
545	#41	—	4	2	no	—
546	#41	—	4	2	no	—
547	C₂×Q₈	—	2	1	no	—
548	C₂×Q₈	—	2	1	no	—
549	C₂×Q₈	—	2	1	no	—
550	C₂×Q₈	—	2	1	no	—
551	C₂×Q₈	—	2	1	no	—
552	C₂×Q₈	—	2	1	no	—
553	C₂×Q₈	—	2	1	no	—
554	C₂×Q₈	—	2	1	no	—
555	C₂×Q₈	—	2	1	no	—
556	C₂×Q₈	—	2	1	no	—
557	C₂×Q₈	—	2	1	no	—
558	C₂×Q₈	#41×C₁₉	1	2	yes	—
559	C₂×D₄	—	2	1	no	—
560	C₂×D₄	—	2	1	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	—	2	1	no	—
564	C₂×D₄	—	4	2	no	—
565	C₂×D₄	—	4	2	no	—
566	C₂×D₄	—	4	1	no	—
567	C₂×D₄	—	4	1	no	—
568	C₂×D₄	#41×C₁₉	1	2	yes	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	4	2	no	—
579	C₂²×C₄	—	4	2	no	—
580	C₂²×C₄	—	4	1	no	—
581	C₂²×C₄	—	4	1	no	—
582	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
583	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
584	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
585	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
586	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
587	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
588	Q₁₆	—	4	2	no	—
589	Q₁₆	—	4	2	no	—
590	SD₁₆	—	4	2	no	—
591	SD₁₆	—	4	2	no	—
592	M₁₆	—	2	1	no	—
593	M₁₆	—	2	1	no	—
594	M₁₆	—	2	1	no	—
595	M₁₆	—	2	1	no	—
596	M₁₆	—	2	1	no	—
597	M₁₆	—	2	1	no	—
598	M₁₆	—	2	1	no	—
599	M₁₆	—	2	1	no	—
600	M₁₆	—	2	1	no	—
601	M₁₆	—	2	1	no	—
602	M₁₆	—	2	1	no	—
603	M₁₆	—	2	1	no	—
604	M₁₆	—	4	2	no	—
605	C₂×C₈	—	2	1	no	—
606	C₂×C₈	—	2	1	no	—
607	C₂×C₈	—	2	1	no	—
608	C₂×C₈	—	2	1	no	—
609	C₂×C₈	—	2	1	no	—
610	C₂×C₈	—	2	1	no	—
611	C₂×C₈	—	2	1	no	—
612	C₂×C₈	—	2	1	no	—
613	C₂×C₈	—	2	1	no	—
614	C₂×C₈	—	2	1	no	—
615	C₂×C₈	—	4	2	no	—
616	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
617	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
618	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
619	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	4	1	no	—
625	C₄⋊C₄	—	4	1	no	—
626	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
627	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
628	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
629	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
630	C₂²⋊C₄	—	2	1	no	—
631	C₂²⋊C₄	—	2	1	no	—
632	C₂²⋊C₄	—	2	1	no	—
633	C₂²⋊C₄	—	2	1	no	—
634	C₂²⋊C₄	—	4	1	no	—
635	C₂²⋊C₄	—	4	1	no	—
636	C₄²	—	2	1	no	—
637	C₄²	—	2	1	no	—
638	C₄²	—	2	1	no	—
639	C₄²	—	2	1	no	—
640	C₂³	—	2	1	no	—
641	C₂³	—	2	1	no	—
642	C₂³	—	2	2	no	—
643	C₂³	—	4	1	no	—
644	C₂³	—	4	1	no	—
645	C₂³	—	4	1	no	—
646	C₂³	—	4	1	no	—
647	C₂³	—	8	1	no	—
648	C₂³	—	8	1	no	—
649	C₂³	C₁₉×#121	1	1	yes	characteristic
650	C₂³	C₁₉×#121	1	1	yes	characteristic
651	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
652	Q₈	—	2	2	no	—
653	Q₈	—	2	2	no	—
654	Q₈	—	4	1	no	—
655	Q₈	—	4	1	no	—
656	Q₈	—	4	1	no	—
657	Q₈	—	4	1	no	—
658	Q₈	—	4	1	no	—
659	Q₈	—	4	1	no	—
660	D₄	—	2	2	no	—
661	D₄	—	2	2	no	—
662	D₄	—	4	4	no	—
663	D₄	—	4	4	no	—
664	D₄	—	4	1	no	—
665	D₄	—	4	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	4	4	no	—
682	C₂×C₄	—	4	4	no	—
683	C₂×C₄	—	4	2	no	—
684	C₂×C₄	—	4	1	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	8	1	no	—
691	C₂×C₄	—	8	1	no	—
692	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
693	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
694	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
695	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
696	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
697	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
698	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
699	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
700	C₈	—	2	1	no	—
701	C₈	—	2	1	no	—
702	C₈	—	2	1	no	—
703	C₈	—	2	1	no	—
704	C₈	—	4	1	no	—
705	C₈	—	4	1	no	—
706	C₈	—	4	1	no	—
707	C₈	—	4	1	no	—
708	C₈	—	4	1	no	—
709	C₈	—	4	1	no	—
710	C₂²	—	2	1	no	—
711	C₂²	—	2	1	no	—
712	C₂²	—	2	1	no	—
713	C₂²	—	2	1	no	—
714	C₂²	—	2	1	no	—
715	C₂²	—	2	1	no	—
716	C₂²	—	2	1	no	—
717	C₂²	—	2	1	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	8	1	no	—
720	C₂²	—	8	1	no	—
721	C₂²	—	8	2	no	—
722	C₂²	—	8	2	no	—
723	C₂²	—	8	1	no	—
724	C₂²	—	8	1	no	—
725	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
726	C₂²	C₁₉×#551	1	1	yes	characteristic
727	C₂²	C₁₉×#551	1	1	yes	characteristic
728	C₄	—	2	1	no	—
729	C₄	—	2	1	no	—
730	C₄	—	4	2	no	—
731	C₄	—	4	1	no	—
732	C₄	—	4	1	no	—
733	C₄	—	4	1	no	—
734	C₄	—	4	1	no	—
735	C₄	—	8	1	no	—
736	C₄	—	8	1	no	—
737	C₄	C₁₉×#525	1	1	yes	characteristic
738	C₄	C₁₉×#535	1	1	yes	characteristic
739	C₄	C₁₉×#546	1	1	yes	characteristic
740	C₄	C₁₉×#546	1	1	yes	characteristic
741	C₂	—	2	1	no	—
742	C₂	—	2	1	no	—
743	C₂	—	4	1	no	—
744	C₂	—	4	1	no	—
745	C₂	—	8	2	no	—
746	C₂	C₁₉×#2411	1	1	yes	characteristic
747	C₂	C₁₉×#3067	1	1	yes	characteristic
748	C₂	C₁₉×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3095	C₂	semidirect
3. C₁₉×#2924	C₂	semidirect
5. C₁₉×#2064	C₂	semidirect
6. C₁₉×#2063	C₂	semidirect
7. C₁₉×#2047	C₂	semidirect
8. C₁₉×#2046	C₂	semidirect
9. C₁₉×#1979	C₂	semidirect
10. C₁₉×#1977	C₂	semidirect
11. C₁₉×#1931	C₂	semidirect
12. C₁₉×#1930	C₂	semidirect
13. C₁₉×#1901	C₂	semidirect
14. C₁₉×#1855	C₂	semidirect
265. #24525	C₁₉	direct (N × H)
336. #3095	C₂×C₁₉	semidirect
338. #2924	C₂×C₁₉	semidirect
340. #2064	C₂×C₁₉	semidirect
341. #2063	C₂×C₁₉	semidirect
342. #2047	C₂×C₁₉	semidirect
343. #2046	C₂×C₁₉	semidirect
344. #1979	C₂×C₁₉	semidirect
345. #1977	C₂×C₁₉	semidirect
346. #1931	C₂×C₁₉	semidirect
347. #1930	C₂×C₁₉	semidirect
348. #1901	C₂×C₁₉	semidirect
349. #1855	C₂×C₁₉	semidirect
536. C₁₉	#24525	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×#3095	2
C₂×C₁₉×#452	2
C₁₉×#2924	2
C₁₉×#2896	2
C₁₉×#2064	2
C₁₉×#2063	2
C₁₉×#2047	2
C₁₉×#2046	2
C₁₉×#1979	2
C₁₉×#1977	2
C₁₉×#1931	2
C₁₉×#1930	2
C₁₉×#1901	2
C₁₉×#1855	2
C₁₉×#1785	2
#24525	19

Subgroups — C19×#24525 #18030484

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24525 #18030484