Subgroups — C₁₉×#24524 #18030483

Order 4864.

884 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3094	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#449	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, complemented
5	C₁₉×#2064	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2063	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2046	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2045	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1978	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×#1900	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, complemented
16	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
22	C₁₉×#482	—	2	1	no	—
23	C₁₉×#482	—	2	1	no	—
24	C₁₉×#481	—	2	1	no	—
25	C₁₉×#480	—	2	1	no	—
26	C₁₉×#449	—	2	1	no	—
27	C₁₉×#449	—	2	1	no	—
28	C₁₉×#449	—	2	1	no	—
29	C₁₉×#449	—	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×#418	C₂²	1	1	yes	characteristic
43	C₁₉×#418	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×#100	C₂²	1	1	yes	characteristic
55	C₂×C₁₉×#100	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×D₄×C₁₉	—	2	1	no	—
77	C₂²×D₄×C₁₉	—	2	1	no	—
78	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
79	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₁₉	—	2	1	no	—
81	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
82	C₂×SD₁₆×C₁₉	—	2	2	no	—
83	C₂×SD₁₆×C₁₉	—	2	1	no	—
84	C₂×SD₁₆×C₁₉	—	2	1	no	—
85	C₂×SD₁₆×C₁₉	—	4	1	no	—
86	C₂×D₈×C₁₉	—	2	2	no	—
87	C₂×D₈×C₁₉	—	2	1	no	—
88	C₂×D₈×C₁₉	—	2	1	no	—
89	C₂×D₈×C₁₉	—	4	1	no	—
90	C₂×M₁₆×C₁₉	—	2	1	no	—
91	C₂×M₁₆×C₁₉	—	4	1	no	—
92	C₂×M₁₆×C₁₉	—	4	1	no	—
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	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₁₉	—	2	1	no	—
100	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
102	C₁₉×#121	—	2	1	no	—
103	C₁₉×#121	—	2	1	no	—
104	C₁₉×#121	—	2	1	no	—
105	C₁₉×#121	—	2	1	no	—
106	C₁₉×#117	—	2	1	no	—
107	C₁₉×#117	—	2	1	no	—
108	C₁₉×#117	D₄	1	1	yes	characteristic
109	C₁₉×#117	D₄	1	1	yes	characteristic
110	C₁₉×#117	C₂³	1	1	yes	characteristic
111	C₁₉×#117	C₂³	1	1	yes	characteristic
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×#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	—	2	1	no	—
143	C₁₉×#102	—	2	1	no	—
144	C₁₉×#101	—	2	2	no	—
145	C₁₉×#101	—	4	1	no	—
146	C₁₉×#100	—	2	2	no	—
147	C₁₉×#100	—	4	1	no	—
148	C₁₉×#100	—	4	1	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	—	2	1	no	—
164	C₂⁴×C₁₉	#41	1	1	yes	characteristic
165	#41×C₁₉	—	2	4	no	—
166	#41×C₁₉	—	2	4	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	#41×C₁₉	—	4	2	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	#41	1	2	yes	—
179	C₂×D₄×C₁₉	—	2	1	no	—
180	C₂×D₄×C₁₉	—	2	1	no	—
181	C₂×D₄×C₁₉	—	2	1	no	—
182	C₂×D₄×C₁₉	—	2	1	no	—
183	C₂×D₄×C₁₉	—	2	1	no	—
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	—	2	1	no	—
190	C₂×D₄×C₁₉	—	4	2	no	—
191	C₂×D₄×C₁₉	—	4	2	no	—
192	C₂×D₄×C₁₉	—	4	1	no	—
193	C₂×D₄×C₁₉	—	4	1	no	—
194	C₂×D₄×C₁₉	—	4	1	no	—
195	C₂×D₄×C₁₉	—	4	1	no	—
196	C₂×D₄×C₁₉	—	8	2	no	—
197	C₂×D₄×C₁₉	#41	1	2	yes	—
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	—	2	1	no	—
204	C₂²×C₄×C₁₉	—	2	1	no	—
205	C₂²×C₄×C₁₉	—	2	1	no	—
206	C₂²×C₄×C₁₉	—	4	2	no	—
207	C₂²×C₄×C₁₉	—	4	2	no	—
208	C₂²×C₄×C₁₉	—	4	1	no	—
209	C₂²×C₄×C₁₉	—	4	1	no	—
210	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
215	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
216	SD₁₆×C₁₉	—	4	2	no	—
217	SD₁₆×C₁₉	—	4	2	no	—
218	D₈×C₁₉	—	4	2	no	—
219	D₈×C₁₉	—	4	2	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	—	2	1	no	—
230	M₁₆×C₁₉	—	2	1	no	—
231	M₁₆×C₁₉	—	2	1	no	—
232	M₁₆×C₁₉	—	4	2	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	—	2	1	no	—
241	C₂×C₈×C₁₉	—	2	1	no	—
242	C₂×C₈×C₁₉	—	2	1	no	—
243	C₂×C₈×C₁₉	—	4	2	no	—
244	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
245	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
246	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
247	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
248	C₄⋊C₄×C₁₉	—	2	1	no	—
249	C₄⋊C₄×C₁₉	—	2	1	no	—
250	C₄⋊C₄×C₁₉	—	2	1	no	—
251	C₄⋊C₄×C₁₉	—	2	1	no	—
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	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
260	C₂²⋊C₄×C₁₉	—	4	1	no	—
261	C₂²⋊C₄×C₁₉	—	4	1	no	—
262	C₄²×C₁₉	—	2	1	no	—
263	C₄²×C₁₉	—	2	1	no	—
264	C₄²×C₁₉	—	2	1	no	—
265	C₄²×C₁₉	—	2	1	no	—
266	#24524	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
267	C₂³×C₁₉	—	2	1	no	—
268	C₂³×C₁₉	—	2	1	no	—
269	C₂³×C₁₉	—	2	2	no	—
270	C₂³×C₁₉	—	4	1	no	—
271	C₂³×C₁₉	—	4	1	no	—
272	C₂³×C₁₉	—	4	1	no	—
273	C₂³×C₁₉	—	4	1	no	—
274	C₂³×C₁₉	—	4	1	no	—
275	C₂³×C₁₉	—	4	1	no	—
276	C₂³×C₁₉	—	4	1	no	—
277	C₂³×C₁₉	—	8	1	no	—
278	C₂³×C₁₉	—	8	1	no	—
279	C₂³×C₁₉	—	8	1	no	—
280	C₂³×C₁₉	—	8	1	no	—
281	C₂³×C₁₉	#121	1	1	yes	characteristic
282	C₂³×C₁₉	#121	1	1	yes	characteristic
283	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
284	Q₈×C₁₉	—	2	2	no	—
285	Q₈×C₁₉	—	2	2	no	—
286	Q₈×C₁₉	—	4	1	no	—
287	Q₈×C₁₉	—	4	1	no	—
288	D₄×C₁₉	—	2	2	no	—
289	D₄×C₁₉	—	2	2	no	—
290	D₄×C₁₉	—	4	4	no	—
291	D₄×C₁₉	—	4	4	no	—
292	D₄×C₁₉	—	4	1	no	—
293	D₄×C₁₉	—	4	1	no	—
294	D₄×C₁₉	—	4	1	no	—
295	D₄×C₁₉	—	4	1	no	—
296	D₄×C₁₉	—	4	1	no	—
297	D₄×C₁₉	—	4	1	no	—
298	D₄×C₁₉	—	8	2	no	—
299	D₄×C₁₉	—	8	2	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	1	no	—
307	C₂×C₄×C₁₉	—	2	1	no	—
308	C₂×C₄×C₁₉	—	2	1	no	—
309	C₂×C₄×C₁₉	—	2	1	no	—
310	C₂×C₄×C₁₉	—	2	1	no	—
311	C₂×C₄×C₁₉	—	2	1	no	—
312	C₂×C₄×C₁₉	—	2	1	no	—
313	C₂×C₄×C₁₉	—	2	1	no	—
314	C₂×C₄×C₁₉	—	2	2	no	—
315	C₂×C₄×C₁₉	—	4	4	no	—
316	C₂×C₄×C₁₉	—	4	4	no	—
317	C₂×C₄×C₁₉	—	4	2	no	—
318	C₂×C₄×C₁₉	—	4	1	no	—
319	C₂×C₄×C₁₉	—	4	1	no	—
320	C₂×C₄×C₁₉	—	4	1	no	—
321	C₂×C₄×C₁₉	—	8	1	no	—
322	C₂×C₄×C₁₉	—	8	1	no	—
323	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
324	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
325	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
328	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
329	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
330	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
331	C₈×C₁₉	—	2	1	no	—
332	C₈×C₁₉	—	2	1	no	—
333	C₈×C₁₉	—	2	1	no	—
334	C₈×C₁₉	—	2	1	no	—
335	C₈×C₁₉	—	4	1	no	—
336	C₈×C₁₉	—	4	1	no	—
337	C₈×C₁₉	—	4	1	no	—
338	C₈×C₁₉	—	4	1	no	—
339	C₈×C₁₉	—	4	1	no	—
340	C₈×C₁₉	—	4	1	no	—
341	#3094	C₂×C₁₉	1	1	yes	characteristic, complemented
342	C₂×#449	C₂×C₁₉	1	1	yes	characteristic
343	#2924	C₂×C₁₉	1	1	yes	characteristic, complemented
344	#2896	C₂×C₁₉	1	1	yes	characteristic, complemented
345	#2064	C₂×C₁₉	1	1	yes	characteristic, complemented
346	#2063	C₂×C₁₉	1	1	yes	characteristic, complemented
347	#2046	C₂×C₁₉	1	1	yes	characteristic, complemented
348	#2045	C₂×C₁₉	1	1	yes	characteristic, complemented
349	#1978	C₂×C₁₉	1	1	yes	characteristic, complemented
350	#1977	C₂×C₁₉	1	1	yes	characteristic, complemented
351	#1931	C₂×C₁₉	1	1	yes	characteristic, complemented
352	#1930	C₂×C₁₉	1	1	yes	characteristic, complemented
353	#1900	C₂×C₁₉	1	1	yes	characteristic, complemented
354	#1855	C₂×C₁₉	1	1	yes	characteristic, complemented
355	#1785	C₂×C₁₉	1	1	yes	characteristic, complemented
356	C₂²×C₁₉	—	2	1	no	—
357	C₂²×C₁₉	—	2	1	no	—
358	C₂²×C₁₉	—	2	1	no	—
359	C₂²×C₁₉	—	2	1	no	—
360	C₂²×C₁₉	—	2	1	no	—
361	C₂²×C₁₉	—	2	1	no	—
362	C₂²×C₁₉	—	2	1	no	—
363	C₂²×C₁₉	—	2	1	no	—
364	C₂²×C₁₉	—	4	2	no	—
365	C₂²×C₁₉	—	8	1	no	—
366	C₂²×C₁₉	—	8	1	no	—
367	C₂²×C₁₉	—	8	2	no	—
368	C₂²×C₁₉	—	8	2	no	—
369	C₂²×C₁₉	—	8	1	no	—
370	C₂²×C₁₉	—	8	1	no	—
371	C₂²×C₁₉	—	8	1	no	—
372	C₂²×C₁₉	—	8	1	no	—
373	C₂²×C₁₉	—	8	1	no	—
374	C₂²×C₁₉	—	16	1	no	—
375	C₂²×C₁₉	—	16	1	no	—
376	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
377	C₂²×C₁₉	#551	1	1	yes	characteristic
378	C₂²×C₁₉	#551	1	1	yes	characteristic
379	C₄×C₁₉	—	2	1	no	—
380	C₄×C₁₉	—	2	1	no	—
381	C₄×C₁₉	—	4	2	no	—
382	C₄×C₁₉	—	4	1	no	—
383	C₄×C₁₉	—	4	1	no	—
384	C₄×C₁₉	—	4	1	no	—
385	C₄×C₁₉	—	4	1	no	—
386	C₄×C₁₉	—	8	1	no	—
387	C₄×C₁₉	#525	1	1	yes	characteristic
388	C₄×C₁₉	#535	1	1	yes	characteristic
389	C₄×C₁₉	#546	1	1	yes	characteristic
390	C₄×C₁₉	#546	1	1	yes	characteristic
391	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
392	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
393	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
394	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
395	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
396	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
397	#482	—	2	1	no	—
398	#482	—	2	1	no	—
399	#481	—	2	1	no	—
400	#480	—	2	1	no	—
401	#449	—	2	1	no	—
402	#449	—	2	1	no	—
403	#449	—	2	1	no	—
404	#449	—	2	1	no	—
405	#433	—	2	1	no	—
406	#433	—	2	1	no	—
407	#432	—	2	1	no	—
408	#431	—	2	1	no	—
409	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
410	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
411	#428	C₂²×C₁₉	1	1	yes	characteristic
412	#428	C₂²×C₁₉	1	1	yes	characteristic
413	#424	C₂²×C₁₉	1	1	yes	characteristic
414	#424	C₂²×C₁₉	1	1	yes	characteristic
415	#419	C₂²×C₁₉	1	1	yes	characteristic
416	#419	C₂²×C₁₉	1	1	yes	characteristic
417	#418	C₂²×C₁₉	1	1	yes	characteristic
418	#418	C₂²×C₁₉	1	1	yes	characteristic
419	#418	C₂²×C₁₉	1	1	yes	characteristic
420	#418	C₂²×C₁₉	1	1	yes	characteristic
421	#417	—	2	1	no	—
422	#417	—	2	1	no	—
423	#416	—	2	1	no	—
424	#416	—	2	1	no	—
425	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
426	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
427	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
428	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
429	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
430	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
431	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
432	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
433	#407	C₂²×C₁₉	1	1	yes	characteristic
434	#407	C₂²×C₁₉	1	1	yes	characteristic
435	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
436	#405	C₂²×C₁₉	1	1	yes	characteristic
437	#405	C₂²×C₁₉	1	1	yes	characteristic
438	#343	C₂²×C₁₉	1	1	yes	characteristic
439	#343	C₂²×C₁₉	1	1	yes	characteristic
440	#341	C₂²×C₁₉	1	1	yes	characteristic
441	#341	C₂²×C₁₉	1	1	yes	characteristic
442	C₂×C₁₉	—	2	1	no	—
443	C₂×C₁₉	—	2	1	no	—
444	C₂×C₁₉	—	4	1	no	—
445	C₂×C₁₉	—	4	1	no	—
446	C₂×C₁₉	—	8	2	no	—
447	C₂×C₁₉	—	16	1	no	—
448	C₂×C₁₉	#2411	1	1	yes	characteristic
449	C₂×C₁₉	#3067	1	1	yes	characteristic
450	C₂×C₁₉	#3068	1	1	yes	characteristic
451	C₂×#41	—	2	2	no	—
452	C₂×#41	—	2	2	no	—
453	C₂×#41	—	2	1	no	—
454	C₂×#41	—	2	1	no	—
455	C₂×#41	—	2	1	no	—
456	C₂×#41	—	2	1	no	—
457	C₂×#41	—	4	1	no	—
458	C₂×#41	—	4	1	no	—
459	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
460	C₂²×D₄	—	2	1	no	—
461	C₂²×D₄	—	2	1	no	—
462	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
463	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
464	C₂³×C₄	—	2	1	no	—
465	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
466	C₂×SD₁₆	—	2	2	no	—
467	C₂×SD₁₆	—	2	1	no	—
468	C₂×SD₁₆	—	2	1	no	—
469	C₂×SD₁₆	—	4	1	no	—
470	C₂×D₈	—	2	2	no	—
471	C₂×D₈	—	2	1	no	—
472	C₂×D₈	—	2	1	no	—
473	C₂×D₈	—	4	1	no	—
474	C₂×M₁₆	—	2	1	no	—
475	C₂×M₁₆	—	4	1	no	—
476	C₂×M₁₆	—	4	1	no	—
477	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
478	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
479	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
480	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
481	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
482	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
483	C₂²×C₈	—	2	1	no	—
484	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
485	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
486	#121	—	2	1	no	—
487	#121	—	2	1	no	—
488	#121	—	2	1	no	—
489	#121	—	2	1	no	—
490	#117	—	2	1	no	—
491	#117	—	2	1	no	—
492	#117	D₄×C₁₉	1	1	yes	characteristic
493	#117	D₄×C₁₉	1	1	yes	characteristic
494	#117	C₂³×C₁₉	1	1	yes	characteristic
495	#117	C₂³×C₁₉	1	1	yes	characteristic
496	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
497	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
499	C₂×C₂²⋊C₄	—	2	1	no	—
500	C₂×C₂²⋊C₄	—	2	1	no	—
501	C₂×C₄²	—	2	1	no	—
502	#108	—	4	1	no	—
503	#108	—	4	1	no	—
504	#107	—	2	1	no	—
505	#107	—	2	1	no	—
506	#106	—	2	1	no	—
507	#106	—	2	1	no	—
508	C₄⋊C₈	—	2	1	no	—
509	C₄⋊C₈	—	2	1	no	—
510	C₄⋊C₈	—	2	1	no	—
511	C₄⋊C₈	—	2	1	no	—
512	#103	—	2	1	no	—
513	#103	—	2	1	no	—
514	#103	—	2	1	no	—
515	#103	—	2	1	no	—
516	#103	—	2	1	no	—
517	#103	—	2	1	no	—
518	#102	—	2	1	no	—
519	#102	—	2	1	no	—
520	#102	—	2	1	no	—
521	#102	—	2	1	no	—
522	#102	—	2	1	no	—
523	#102	—	2	1	no	—
524	#102	—	2	1	no	—
525	#102	—	2	1	no	—
526	#102	—	2	1	no	—
527	#102	—	2	1	no	—
528	#101	—	2	2	no	—
529	#101	—	4	1	no	—
530	#100	—	2	2	no	—
531	#100	—	4	1	no	—
532	#100	—	4	1	no	—
533	#100	—	4	1	no	—
534	C₂²⋊C₈	—	2	1	no	—
535	C₂²⋊C₈	—	2	1	no	—
536	C₂²⋊C₈	—	2	1	no	—
537	C₂²⋊C₈	—	2	1	no	—
538	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
539	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
540	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
541	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
542	#97	—	2	1	no	—
543	#97	—	2	1	no	—
544	C₄×C₈	—	2	1	no	—
545	C₄×C₈	—	2	1	no	—
546	C₁₉	#24524	1	1	yes	characteristic, direct product factor, Sylow
547	C₂⁴	—	2	1	no	—
548	C₂⁴	—	2	1	no	—
549	C₂⁴	#41×C₁₉	1	1	yes	characteristic
550	#41	—	2	4	no	—
551	#41	—	2	4	no	—
552	#41	—	4	2	no	—
553	#41	—	4	2	no	—
554	#41	—	4	2	no	—
555	#41	—	4	2	no	—
556	#41	—	4	2	no	—
557	#41	—	4	2	no	—
558	C₂×Q₈	—	2	1	no	—
559	C₂×Q₈	—	2	1	no	—
560	C₂×Q₈	—	2	1	no	—
561	C₂×Q₈	—	2	1	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	#41×C₁₉	1	2	yes	—
564	C₂×D₄	—	2	1	no	—
565	C₂×D₄	—	2	1	no	—
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	2	1	no	—
568	C₂×D₄	—	2	1	no	—
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	2	1	no	—
571	C₂×D₄	—	2	1	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	2	1	no	—
574	C₂×D₄	—	2	1	no	—
575	C₂×D₄	—	4	2	no	—
576	C₂×D₄	—	4	2	no	—
577	C₂×D₄	—	4	1	no	—
578	C₂×D₄	—	4	1	no	—
579	C₂×D₄	—	4	1	no	—
580	C₂×D₄	—	4	1	no	—
581	C₂×D₄	—	8	2	no	—
582	C₂×D₄	#41×C₁₉	1	2	yes	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	4	2	no	—
592	C₂²×C₄	—	4	2	no	—
593	C₂²×C₄	—	4	1	no	—
594	C₂²×C₄	—	4	1	no	—
595	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
596	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
597	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
598	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
599	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
600	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
601	SD₁₆	—	4	2	no	—
602	SD₁₆	—	4	2	no	—
603	D₈	—	4	2	no	—
604	D₈	—	4	2	no	—
605	M₁₆	—	2	1	no	—
606	M₁₆	—	2	1	no	—
607	M₁₆	—	2	1	no	—
608	M₁₆	—	2	1	no	—
609	M₁₆	—	2	1	no	—
610	M₁₆	—	2	1	no	—
611	M₁₆	—	2	1	no	—
612	M₁₆	—	2	1	no	—
613	M₁₆	—	2	1	no	—
614	M₁₆	—	2	1	no	—
615	M₁₆	—	2	1	no	—
616	M₁₆	—	2	1	no	—
617	M₁₆	—	4	2	no	—
618	C₂×C₈	—	2	1	no	—
619	C₂×C₈	—	2	1	no	—
620	C₂×C₈	—	2	1	no	—
621	C₂×C₈	—	2	1	no	—
622	C₂×C₈	—	2	1	no	—
623	C₂×C₈	—	2	1	no	—
624	C₂×C₈	—	2	1	no	—
625	C₂×C₈	—	2	1	no	—
626	C₂×C₈	—	2	1	no	—
627	C₂×C₈	—	2	1	no	—
628	C₂×C₈	—	4	2	no	—
629	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
630	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
631	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
632	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	—	2	1	no	—
635	C₄⋊C₄	—	2	1	no	—
636	C₄⋊C₄	—	2	1	no	—
637	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
638	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
639	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
640	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
641	C₂²⋊C₄	—	2	1	no	—
642	C₂²⋊C₄	—	2	1	no	—
643	C₂²⋊C₄	—	2	1	no	—
644	C₂²⋊C₄	—	2	1	no	—
645	C₂²⋊C₄	—	4	1	no	—
646	C₂²⋊C₄	—	4	1	no	—
647	C₄²	—	2	1	no	—
648	C₄²	—	2	1	no	—
649	C₄²	—	2	1	no	—
650	C₄²	—	2	1	no	—
651	C₂³	—	2	1	no	—
652	C₂³	—	2	1	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	4	1	no	—
655	C₂³	—	4	1	no	—
656	C₂³	—	4	1	no	—
657	C₂³	—	4	1	no	—
658	C₂³	—	4	1	no	—
659	C₂³	—	4	1	no	—
660	C₂³	—	4	1	no	—
661	C₂³	—	8	1	no	—
662	C₂³	—	8	1	no	—
663	C₂³	—	8	1	no	—
664	C₂³	—	8	1	no	—
665	C₂³	C₁₉×#121	1	1	yes	characteristic
666	C₂³	C₁₉×#121	1	1	yes	characteristic
667	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
668	Q₈	—	2	2	no	—
669	Q₈	—	2	2	no	—
670	Q₈	—	4	1	no	—
671	Q₈	—	4	1	no	—
672	D₄	—	2	2	no	—
673	D₄	—	2	2	no	—
674	D₄	—	4	4	no	—
675	D₄	—	4	4	no	—
676	D₄	—	4	1	no	—
677	D₄	—	4	1	no	—
678	D₄	—	4	1	no	—
679	D₄	—	4	1	no	—
680	D₄	—	4	1	no	—
681	D₄	—	4	1	no	—
682	D₄	—	8	2	no	—
683	D₄	—	8	2	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	4	4	no	—
700	C₂×C₄	—	4	4	no	—
701	C₂×C₄	—	4	2	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	4	1	no	—
705	C₂×C₄	—	8	1	no	—
706	C₂×C₄	—	8	1	no	—
707	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
708	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
709	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
710	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
711	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
712	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
713	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
714	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
715	C₈	—	2	1	no	—
716	C₈	—	2	1	no	—
717	C₈	—	2	1	no	—
718	C₈	—	2	1	no	—
719	C₈	—	4	1	no	—
720	C₈	—	4	1	no	—
721	C₈	—	4	1	no	—
722	C₈	—	4	1	no	—
723	C₈	—	4	1	no	—
724	C₈	—	4	1	no	—
725	C₂²	—	2	1	no	—
726	C₂²	—	2	1	no	—
727	C₂²	—	2	1	no	—
728	C₂²	—	2	1	no	—
729	C₂²	—	2	1	no	—
730	C₂²	—	2	1	no	—
731	C₂²	—	2	1	no	—
732	C₂²	—	2	1	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	8	1	no	—
735	C₂²	—	8	1	no	—
736	C₂²	—	8	2	no	—
737	C₂²	—	8	2	no	—
738	C₂²	—	8	1	no	—
739	C₂²	—	8	1	no	—
740	C₂²	—	8	1	no	—
741	C₂²	—	8	1	no	—
742	C₂²	—	8	1	no	—
743	C₂²	—	16	1	no	—
744	C₂²	—	16	1	no	—
745	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
746	C₂²	C₁₉×#551	1	1	yes	characteristic
747	C₂²	C₁₉×#551	1	1	yes	characteristic
748	C₄	—	2	1	no	—
749	C₄	—	2	1	no	—
750	C₄	—	4	2	no	—
751	C₄	—	4	1	no	—
752	C₄	—	4	1	no	—
753	C₄	—	4	1	no	—
754	C₄	—	4	1	no	—
755	C₄	—	8	1	no	—
756	C₄	C₁₉×#525	1	1	yes	characteristic
757	C₄	C₁₉×#535	1	1	yes	characteristic
758	C₄	C₁₉×#546	1	1	yes	characteristic
759	C₄	C₁₉×#546	1	1	yes	characteristic
760	C₂	—	2	1	no	—
761	C₂	—	2	1	no	—
762	C₂	—	4	1	no	—
763	C₂	—	4	1	no	—
764	C₂	—	8	2	no	—
765	C₂	—	16	1	no	—
766	C₂	C₁₉×#2411	1	1	yes	characteristic
767	C₂	C₁₉×#3067	1	1	yes	characteristic
768	C₂	C₁₉×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#449	C₂
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×#3094	C₂	semidirect
3. C₁₉×#2924	C₂	semidirect
4. C₁₉×#2896	C₂	semidirect
5. C₁₉×#2064	C₂	semidirect
6. C₁₉×#2063	C₂	semidirect
7. C₁₉×#2046	C₂	semidirect
8. C₁₉×#2045	C₂	semidirect
9. C₁₉×#1978	C₂	semidirect
10. C₁₉×#1977	C₂	semidirect
11. C₁₉×#1931	C₂	semidirect
12. C₁₉×#1930	C₂	semidirect
13. C₁₉×#1900	C₂	semidirect
14. C₁₉×#1855	C₂	semidirect
15. C₁₉×#1785	C₂	semidirect
266. #24524	C₁₉	direct (N × H)
341. #3094	C₂×C₁₉	semidirect
343. #2924	C₂×C₁₉	semidirect
344. #2896	C₂×C₁₉	semidirect
345. #2064	C₂×C₁₉	semidirect
346. #2063	C₂×C₁₉	semidirect
347. #2046	C₂×C₁₉	semidirect
348. #2045	C₂×C₁₉	semidirect
349. #1978	C₂×C₁₉	semidirect
350. #1977	C₂×C₁₉	semidirect
351. #1931	C₂×C₁₉	semidirect
352. #1930	C₂×C₁₉	semidirect
353. #1900	C₂×C₁₉	semidirect
354. #1855	C₂×C₁₉	semidirect
355. #1785	C₂×C₁₉	semidirect
546. C₁₉	#24524	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×#3094	2
C₂×C₁₉×#449	2
C₁₉×#2924	2
C₁₉×#2896	2
C₁₉×#2064	2
C₁₉×#2063	2
C₁₉×#2046	2
C₁₉×#2045	2
C₁₉×#1978	2
C₁₉×#1977	2
C₁₉×#1931	2
C₁₉×#1930	2
C₁₉×#1900	2
C₁₉×#1855	2
C₁₉×#1785	2
#24524	19

Subgroups — C19×#24524 #18030483

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24524 #18030483