Subgroups — C₁₉×#62368 #18068327

Order 4864.

1782 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3522	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3403	C₂	1	2	yes	maximal, complemented
3	C₁₉×#3399	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3389	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3385	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3375	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3370	C₂	1	4	yes	maximal, complemented
8	C₁₉×#3366	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3250	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3247	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3245	C₂	1	2	yes	maximal, complemented
12	C₁₉×#3180	C₂	1	4	yes	maximal, complemented
13	C₁₉×#3169	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3168	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₉×#446	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#559	C₂²	1	4	yes	—
17	C₁₉×#559	C₂²	1	2	yes	—
18	Q₈²×C₁₉	C₂²	1	2	yes	—
19	C₁₉×#554	C₂²	1	2	yes	—
20	C₁₉×#554	C₂²	1	4	yes	—
21	C₁₉×#550	C₂²	1	2	yes	—
22	C₁₉×#548	—	2	2	no	—
23	C₁₉×#547	—	2	2	no	—
24	C₁₉×#547	—	2	4	no	—
25	C₁₉×#542	—	2	2	no	—
26	C₁₉×#542	—	2	4	no	—
27	C₁₉×#532	C₂²	1	2	yes	—
28	C₁₉×#532	C₂²	1	4	yes	—
29	C₁₉×#529	C₂²	1	2	yes	—
30	C₁₉×#529	C₂²	1	4	yes	—
31	C₁₉×#520	—	2	2	no	—
32	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
33	C₁₉×#501	C₂²	1	4	yes	—
34	C₁₉×#500	C₂²	1	1	yes	characteristic
35	C₁₉×#499	C₂²	1	1	yes	characteristic
36	C₁₉×#496	C₂²	1	4	yes	—
37	C₁₉×#495	C₂²	1	1	yes	characteristic
38	C₁₉×#493	C₂²	1	1	yes	characteristic
39	C₁₉×#490	C₂²	1	4	yes	—
40	C₁₉×#489	C₂²	1	4	yes	—
41	C₁₉×#488	C₂²	1	2	yes	—
42	C₁₉×#486	C₂²	1	2	yes	—
43	C₁₉×#479	C₂²	1	4	yes	—
44	C₁₉×#478	C₂²	1	4	yes	—
45	C₁₉×#478	C₂²	1	4	yes	—
46	C₁₉×#477	C₂²	1	2	yes	—
47	C₁₉×#476	C₂²	1	2	yes	—
48	C₁₉×#474	C₂²	1	4	yes	—
49	C₁₉×#474	C₂²	1	4	yes	—
50	C₁₉×#467	C₂²	1	1	yes	characteristic
51	C₁₉×#466	C₂²	1	1	yes	characteristic
52	C₁₉×#466	C₂²	1	2	yes	—
53	C₁₉×#466	C₂²	1	2	yes	—
54	C₁₉×#466	C₂²	1	4	yes	—
55	C₁₉×#465	C₂²	1	2	yes	—
56	C₁₉×#465	C₂²	1	4	yes	—
57	C₁₉×#464	C₂²	1	4	yes	—
58	C₁₉×#463	C₂²	1	4	yes	—
59	C₁₉×#463	C₂²	1	4	yes	—
60	C₁₉×#460	C₂²	1	2	yes	—
61	C₁₉×#459	C₂²	1	4	yes	—
62	C₁₉×#459	C₂²	1	4	yes	—
63	C₁₉×#459	C₂²	1	2	yes	—
64	C₁₉×#446	C₂²	1	2	yes	—
65	C₁₉×#446	C₂²	1	2	yes	—
66	C₁₉×#446	C₂²	1	2	yes	—
67	C₁₉×#446	C₂²	1	2	yes	—
68	C₁₉×#442	C₂²	1	4	yes	—
69	C₁₉×#442	C₂²	1	4	yes	—
70	C₁₉×#440	C₂²	1	4	yes	—
71	C₁₉×#440	C₂²	1	4	yes	—
72	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
73	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	—
74	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
75	C₄×D₈×C₁₉	C₂²	1	2	yes	—
76	C₄×D₈×C₁₉	C₂²	1	2	yes	—
77	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
78	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
79	C₂×C₁₉×#97	C₂²	1	2	yes	—
80	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
81	C₂×#41×C₁₉	—	2	2	no	—
82	C₂×#41×C₁₉	—	2	2	no	—
83	C₂×#41×C₁₉	—	2	4	no	—
84	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
85	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
87	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
88	C₂×D₈×C₁₉	C₂³	1	2	yes	—
89	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×D₈×C₁₉	C₂³	1	2	yes	—
91	C₂×D₈×C₁₉	C₂³	1	4	yes	—
92	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
95	C₁₉×C₄⋊Q₈	—	2	2	no	—
96	C₁₉×C₄⋊Q₈	—	2	4	no	—
97	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
98	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
99	C₁₉×#127	C₂³	1	4	yes	—
100	C₁₉×#127	C₂³	1	2	yes	—
101	C₁₉×#126	—	2	4	no	—
102	C₁₉×#126	—	2	2	no	—
103	C₁₉×#125	C₂³	1	2	yes	—
104	C₁₉×#125	C₂³	1	4	yes	—
105	C₁₉×#124	—	2	2	no	—
106	C₁₉×#124	—	2	4	no	—
107	C₁₉×#124	—	2	4	no	—
108	C₁₉×#124	—	2	2	no	—
109	C₁₉×#124	C₂³	1	2	yes	—
110	C₁₉×#124	C₂³	1	4	yes	—
111	C₁₉×#123	—	2	2	no	—
112	C₁₉×#123	—	2	4	no	—
113	C₁₉×#123	—	2	4	no	—
114	C₁₉×#123	—	2	4	no	—
115	C₁₉×#123	—	2	4	no	—
116	C₁₉×C₂²⋊Q₈	—	2	2	no	—
117	C₁₉×C₂²⋊Q₈	—	2	4	no	—
118	C₁₉×C₂²⋊Q₈	—	2	4	no	—
119	C₁₉×C₂²⋊Q₈	—	2	4	no	—
120	C₁₉×C₂²⋊Q₈	—	2	4	no	—
121	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
122	C₁₉×#121	—	2	2	no	—
123	C₁₉×#121	—	2	4	no	—
124	C₁₉×#121	—	2	2	no	—
125	C₁₉×#121	—	2	4	no	—
126	C₁₉×#121	C₂³	1	2	yes	—
127	C₁₉×#121	C₂³	1	4	yes	—
128	C₄×Q₈×C₁₉	—	2	2	no	—
129	C₄×Q₈×C₁₉	D₄	1	2	yes	—
130	C₄×Q₈×C₁₉	D₄	1	2	yes	—
131	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
132	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
133	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
134	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
135	C₄×D₄×C₁₉	—	2	2	no	—
136	C₄×D₄×C₁₉	—	2	4	no	—
137	C₄×D₄×C₁₉	—	2	2	no	—
138	C₄×D₄×C₁₉	—	2	4	no	—
139	C₄×D₄×C₁₉	—	2	2	no	—
140	C₄×D₄×C₁₉	—	2	4	no	—
141	C₄×D₄×C₁₉	C₂³	1	4	yes	—
142	C₄×D₄×C₁₉	C₂³	1	2	yes	—
143	C₄×D₄×C₁₉	C₂³	1	4	yes	—
144	C₄×D₄×C₁₉	C₂³	1	4	yes	—
145	C₄×D₄×C₁₉	C₂³	1	4	yes	—
146	C₁₉×#117	—	2	2	no	—
147	C₁₉×#117	—	2	4	no	—
148	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
150	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
152	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
154	C₁₉×#107	C₂³	1	2	yes	—
155	C₁₉×#107	C₂³	1	2	yes	—
156	C₁₉×#107	C₂³	1	1	yes	characteristic
157	C₁₉×#107	C₂³	1	1	yes	characteristic
158	C₁₉×#107	C₂³	1	4	yes	—
159	C₁₉×#106	C₂³	1	2	yes	—
160	C₁₉×#106	C₂³	1	4	yes	—
161	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
162	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
163	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
164	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
165	C₁₉×#103	C₂³	1	2	yes	—
166	C₁₉×#103	C₂³	1	2	yes	—
167	C₁₉×#103	C₂³	1	4	yes	—
168	C₁₉×#102	C₂³	1	4	yes	—
169	C₁₉×#102	C₂³	1	2	yes	—
170	C₁₉×#102	C₂³	1	4	yes	—
171	C₁₉×#102	C₂³	1	2	yes	—
172	C₁₉×#102	C₂³	1	4	yes	—
173	C₁₉×#102	C₂³	1	4	yes	—
174	C₁₉×#102	C₂³	1	4	yes	—
175	C₁₉×#97	C₂³	1	4	yes	—
176	C₁₉×#97	C₂³	1	4	yes	—
177	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
178	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
179	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
180	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
181	#41×C₁₉	—	4	8	no	—
182	#41×C₁₉	—	8	4	no	—
183	#41×C₁₉	—	8	8	no	—
184	C₂×Q₈×C₁₉	—	2	4	no	—
185	C₂×Q₈×C₁₉	—	2	2	no	—
186	C₂×Q₈×C₁₉	—	4	2	no	—
187	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
188	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
189	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
190	C₂×D₄×C₁₉	—	2	2	no	—
191	C₂×D₄×C₁₉	—	2	4	no	—
192	C₂×D₄×C₁₉	—	2	4	no	—
193	C₂×D₄×C₁₉	—	2	2	no	—
194	C₂×D₄×C₁₉	—	2	4	no	—
195	C₂×D₄×C₁₉	—	2	2	no	—
196	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
197	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₁₉	—	2	4	no	—
199	C₂²×C₄×C₁₉	—	2	2	no	—
200	C₂²×C₄×C₁₉	—	2	4	no	—
201	C₂²×C₄×C₁₉	—	2	4	no	—
202	C₂²×C₄×C₁₉	—	2	4	no	—
203	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
205	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
207	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
208	Q₁₆×C₁₉	—	4	1	no	—
209	SD₁₆×C₁₉	—	2	4	no	—
210	SD₁₆×C₁₉	—	4	4	no	—
211	D₈×C₁₉	—	2	4	no	—
212	D₈×C₁₉	—	4	2	no	—
213	D₈×C₁₉	—	4	4	no	—
214	D₈×C₁₉	—	4	1	no	—
215	C₂×C₈×C₁₉	—	2	2	no	—
216	C₂×C₈×C₁₉	—	4	1	no	—
217	C₂×C₈×C₁₉	—	4	2	no	—
218	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
219	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
220	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
221	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
222	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
223	C₄⋊C₄×C₁₉	—	2	2	no	—
224	C₄⋊C₄×C₁₉	—	2	4	no	—
225	C₄⋊C₄×C₁₉	—	2	4	no	—
226	C₄⋊C₄×C₁₉	—	2	2	no	—
227	C₄⋊C₄×C₁₉	—	2	2	no	—
228	C₄⋊C₄×C₁₉	—	2	4	no	—
229	C₄⋊C₄×C₁₉	—	2	2	no	—
230	C₄⋊C₄×C₁₉	—	2	4	no	—
231	C₄⋊C₄×C₁₉	—	2	2	no	—
232	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
233	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
234	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
235	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
236	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
237	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
238	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
239	C₂²⋊C₄×C₁₉	—	2	2	no	—
240	C₂²⋊C₄×C₁₉	—	2	2	no	—
241	C₂²⋊C₄×C₁₉	—	2	4	no	—
242	C₂²⋊C₄×C₁₉	—	2	2	no	—
243	C₂²⋊C₄×C₁₉	—	2	4	no	—
244	C₂²⋊C₄×C₁₉	—	2	4	no	—
245	C₂²⋊C₄×C₁₉	—	2	2	no	—
246	C₂²⋊C₄×C₁₉	—	2	4	no	—
247	C₂²⋊C₄×C₁₉	—	2	2	no	—
248	C₂²⋊C₄×C₁₉	—	2	4	no	—
249	C₂²⋊C₄×C₁₉	—	2	4	no	—
250	C₂²⋊C₄×C₁₉	—	2	4	no	—
251	C₄²×C₁₉	—	2	4	no	—
252	C₄²×C₁₉	—	2	2	no	—
253	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
254	C₄²×C₁₉	C₂×D₄	1	4	yes	—
255	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
256	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
257	C₄²×C₁₉	C₂⁴	1	4	yes	—
258	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
259	#62368	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
260	C₂³×C₁₉	—	2	4	no	—
261	C₂³×C₁₉	—	2	2	no	—
262	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
263	Q₈×C₁₉	—	2	4	no	—
264	Q₈×C₁₉	—	2	2	no	—
265	Q₈×C₁₉	—	2	2	no	—
266	Q₈×C₁₉	—	4	2	no	—
267	Q₈×C₁₉	—	8	4	no	—
268	Q₈×C₁₉	—	8	2	no	—
269	D₄×C₁₉	—	2	4	no	—
270	D₄×C₁₉	—	2	2	no	—
271	D₄×C₁₉	—	2	2	no	—
272	D₄×C₁₉	—	2	4	no	—
273	D₄×C₁₉	—	4	8	no	—
274	D₄×C₁₉	—	4	8	no	—
275	D₄×C₁₉	—	4	4	no	—
276	D₄×C₁₉	—	4	4	no	—
277	D₄×C₁₉	—	8	4	no	—
278	D₄×C₁₉	—	8	2	no	—
279	C₂×C₄×C₁₉	—	2	2	no	—
280	C₂×C₄×C₁₉	—	2	4	no	—
281	C₂×C₄×C₁₉	—	2	2	no	—
282	C₂×C₄×C₁₉	—	2	1	no	—
283	C₂×C₄×C₁₉	—	2	1	no	—
284	C₂×C₄×C₁₉	—	2	2	no	—
285	C₂×C₄×C₁₉	—	2	4	no	—
286	C₂×C₄×C₁₉	—	2	2	no	—
287	C₂×C₄×C₁₉	—	2	2	no	—
288	C₂×C₄×C₁₉	—	4	2	no	—
289	C₂×C₄×C₁₉	—	4	8	no	—
290	C₂×C₄×C₁₉	—	4	4	no	—
291	C₂×C₄×C₁₉	—	8	4	no	—
292	C₂×C₄×C₁₉	—	8	4	no	—
293	C₂×C₄×C₁₉	—	8	4	no	—
294	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
295	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
296	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
297	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
298	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
299	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
300	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
301	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
302	C₈×C₁₉	—	2	1	no	—
303	C₈×C₁₉	—	2	1	no	—
304	C₈×C₁₉	—	2	4	no	—
305	C₈×C₁₉	—	2	1	no	—
306	C₈×C₁₉	2₋¹⁺⁴	1	2	yes	—
307	#3522	C₂×C₁₉	1	2	yes	complemented
308	#3403	C₂×C₁₉	1	2	yes	complemented
309	#3399	C₂×C₁₉	1	2	yes	complemented
310	#3389	C₂×C₁₉	1	2	yes	complemented
311	#3385	C₂×C₁₉	1	2	yes	complemented
312	#3375	C₂×C₁₉	1	2	yes	complemented
313	#3370	C₂×C₁₉	1	4	yes	complemented
314	#3366	C₂×C₁₉	1	2	yes	complemented
315	#3250	C₂×C₁₉	1	2	yes	complemented
316	#3247	C₂×C₁₉	1	2	yes	complemented
317	#3245	C₂×C₁₉	1	2	yes	complemented
318	#3180	C₂×C₁₉	1	4	yes	complemented
319	#3169	C₂×C₁₉	1	1	yes	characteristic, complemented
320	#3168	C₂×C₁₉	1	1	yes	characteristic, complemented
321	C₂×#446	C₂×C₁₉	1	1	yes	characteristic, complemented
322	C₂²×C₁₉	—	2	1	no	—
323	C₂²×C₁₉	—	2	1	no	—
324	C₂²×C₁₉	—	4	4	no	—
325	C₂²×C₁₉	—	4	2	no	—
326	C₂²×C₁₉	—	4	4	no	—
327	C₂²×C₁₉	—	4	2	no	—
328	C₂²×C₁₉	—	4	4	no	—
329	C₂²×C₁₉	—	4	2	no	—
330	C₂²×C₁₉	#576	1	2	yes	—
331	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
332	C₄×C₁₉	—	2	1	no	—
333	C₄×C₁₉	—	2	1	no	—
334	C₄×C₁₉	—	2	4	no	—
335	C₄×C₁₉	—	2	1	no	—
336	C₄×C₁₉	—	2	4	no	—
337	C₄×C₁₉	—	2	1	no	—
338	C₄×C₁₉	—	4	2	no	—
339	C₄×C₁₉	—	4	2	no	—
340	C₄×C₁₉	—	4	4	no	—
341	C₄×C₁₉	—	4	2	no	—
342	C₄×C₁₉	#575	1	2	yes	—
343	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
344	C₄×C₁₉	#585	1	1	yes	characteristic
345	#559	C₂²×C₁₉	1	4	yes	—
346	#559	C₂²×C₁₉	1	2	yes	—
347	Q₈²	C₂²×C₁₉	1	2	yes	—
348	#554	C₂²×C₁₉	1	2	yes	—
349	#554	C₂²×C₁₉	1	4	yes	—
350	#550	C₂²×C₁₉	1	2	yes	—
351	#548	—	2	2	no	—
352	#547	—	2	2	no	—
353	#547	—	2	4	no	—
354	#542	—	2	2	no	—
355	#542	—	2	4	no	—
356	#532	C₂²×C₁₉	1	2	yes	—
357	#532	C₂²×C₁₉	1	4	yes	—
358	#529	C₂²×C₁₉	1	2	yes	—
359	#529	C₂²×C₁₉	1	4	yes	—
360	#520	—	2	2	no	—
361	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
362	#501	C₂²×C₁₉	1	4	yes	—
363	#500	C₂²×C₁₉	1	1	yes	characteristic
364	#499	C₂²×C₁₉	1	1	yes	characteristic
365	#496	C₂²×C₁₉	1	4	yes	—
366	#495	C₂²×C₁₉	1	1	yes	characteristic
367	#493	C₂²×C₁₉	1	1	yes	characteristic
368	#490	C₂²×C₁₉	1	4	yes	—
369	#489	C₂²×C₁₉	1	4	yes	—
370	#488	C₂²×C₁₉	1	2	yes	—
371	#486	C₂²×C₁₉	1	2	yes	—
372	#479	C₂²×C₁₉	1	4	yes	—
373	#478	C₂²×C₁₉	1	4	yes	—
374	#478	C₂²×C₁₉	1	4	yes	—
375	#477	C₂²×C₁₉	1	2	yes	—
376	#476	C₂²×C₁₉	1	2	yes	—
377	#474	C₂²×C₁₉	1	4	yes	—
378	#474	C₂²×C₁₉	1	4	yes	—
379	#467	C₂²×C₁₉	1	1	yes	characteristic
380	#466	C₂²×C₁₉	1	1	yes	characteristic
381	#466	C₂²×C₁₉	1	2	yes	—
382	#466	C₂²×C₁₉	1	2	yes	—
383	#466	C₂²×C₁₉	1	4	yes	—
384	#465	C₂²×C₁₉	1	2	yes	—
385	#465	C₂²×C₁₉	1	4	yes	—
386	#464	C₂²×C₁₉	1	4	yes	—
387	#463	C₂²×C₁₉	1	4	yes	—
388	#463	C₂²×C₁₉	1	4	yes	—
389	#460	C₂²×C₁₉	1	2	yes	—
390	#459	C₂²×C₁₉	1	2	yes	—
391	#459	C₂²×C₁₉	1	4	yes	—
392	#459	C₂²×C₁₉	1	4	yes	—
393	#446	C₂²×C₁₉	1	2	yes	—
394	#446	C₂²×C₁₉	1	2	yes	—
395	#446	C₂²×C₁₉	1	2	yes	—
396	#446	C₂²×C₁₉	1	2	yes	—
397	#442	C₂²×C₁₉	1	4	yes	—
398	#442	C₂²×C₁₉	1	4	yes	—
399	#440	C₂²×C₁₉	1	4	yes	—
400	#440	C₂²×C₁₉	1	4	yes	—
401	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
402	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
403	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
404	C₄×D₈	C₂²×C₁₉	1	2	yes	—
405	C₄×D₈	C₂²×C₁₉	1	2	yes	—
406	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
407	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
408	C₂×#97	C₂²×C₁₉	1	2	yes	—
409	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
410	C₂×C₁₉	—	2	2	no	—
411	C₂×C₁₉	—	8	4	no	—
412	C₂×C₁₉	—	8	2	no	—
413	C₂×C₁₉	#3497	1	1	yes	characteristic
414	C₂×C₁₉	C₂×#575	1	1	yes	characteristic
415	C₂×C₁₉	C₂×#576	1	1	yes	characteristic
416	C₂×#41	—	2	2	no	—
417	C₂×#41	—	2	2	no	—
418	C₂×#41	—	2	4	no	—
419	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
420	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
421	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
422	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
423	C₂×D₈	C₂³×C₁₉	1	2	yes	—
424	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
425	C₂×D₈	C₂³×C₁₉	1	2	yes	—
426	C₂×D₈	C₂³×C₁₉	1	4	yes	—
427	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
428	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
429	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
430	C₄⋊Q₈	—	2	2	no	—
431	C₄⋊Q₈	—	2	4	no	—
432	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
433	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
434	#127	C₂³×C₁₉	1	4	yes	—
435	#127	C₂³×C₁₉	1	2	yes	—
436	#126	—	2	4	no	—
437	#126	—	2	2	no	—
438	#125	C₂³×C₁₉	1	2	yes	—
439	#125	C₂³×C₁₉	1	4	yes	—
440	#124	—	2	2	no	—
441	#124	—	2	4	no	—
442	#124	—	2	4	no	—
443	#124	—	2	2	no	—
444	#124	C₂³×C₁₉	1	2	yes	—
445	#124	C₂³×C₁₉	1	4	yes	—
446	#123	—	2	2	no	—
447	#123	—	2	4	no	—
448	#123	—	2	4	no	—
449	#123	—	2	4	no	—
450	#123	—	2	4	no	—
451	C₂²⋊Q₈	—	2	2	no	—
452	C₂²⋊Q₈	—	2	4	no	—
453	C₂²⋊Q₈	—	2	4	no	—
454	C₂²⋊Q₈	—	2	4	no	—
455	C₂²⋊Q₈	—	2	4	no	—
456	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
457	#121	—	2	2	no	—
458	#121	—	2	4	no	—
459	#121	—	2	2	no	—
460	#121	—	2	4	no	—
461	#121	C₂³×C₁₉	1	2	yes	—
462	#121	C₂³×C₁₉	1	4	yes	—
463	C₄×Q₈	—	2	2	no	—
464	C₄×Q₈	D₄×C₁₉	1	2	yes	—
465	C₄×Q₈	D₄×C₁₉	1	2	yes	—
466	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
467	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
468	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
469	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
470	C₄×D₄	—	2	2	no	—
471	C₄×D₄	—	2	4	no	—
472	C₄×D₄	—	2	2	no	—
473	C₄×D₄	—	2	4	no	—
474	C₄×D₄	—	2	2	no	—
475	C₄×D₄	—	2	4	no	—
476	C₄×D₄	C₂³×C₁₉	1	2	yes	—
477	C₄×D₄	C₂³×C₁₉	1	4	yes	—
478	C₄×D₄	C₂³×C₁₉	1	4	yes	—
479	C₄×D₄	C₂³×C₁₉	1	4	yes	—
480	C₄×D₄	C₂³×C₁₉	1	4	yes	—
481	#117	—	2	2	no	—
482	#117	—	2	4	no	—
483	C₂×C₄⋊C₄	—	2	2	no	—
484	C₂×C₄⋊C₄	—	2	4	no	—
485	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
486	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
487	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
488	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
489	#107	C₂³×C₁₉	1	2	yes	—
490	#107	C₂³×C₁₉	1	2	yes	—
491	#107	C₂³×C₁₉	1	1	yes	characteristic
492	#107	C₂³×C₁₉	1	1	yes	characteristic
493	#107	C₂³×C₁₉	1	4	yes	—
494	#106	C₂³×C₁₉	1	2	yes	—
495	#106	C₂³×C₁₉	1	4	yes	—
496	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
497	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
498	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
499	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
500	#103	C₂³×C₁₉	1	2	yes	—
501	#103	C₂³×C₁₉	1	2	yes	—
502	#103	C₂³×C₁₉	1	4	yes	—
503	#102	C₂³×C₁₉	1	4	yes	—
504	#102	C₂³×C₁₉	1	2	yes	—
505	#102	C₂³×C₁₉	1	4	yes	—
506	#102	C₂³×C₁₉	1	2	yes	—
507	#102	C₂³×C₁₉	1	4	yes	—
508	#102	C₂³×C₁₉	1	4	yes	—
509	#102	C₂³×C₁₉	1	4	yes	—
510	#97	C₂³×C₁₉	1	4	yes	—
511	#97	C₂³×C₁₉	1	4	yes	—
512	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
513	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
514	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
515	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
516	C₁₉	#62368	1	1	yes	characteristic, direct product factor, Sylow
517	#41	—	4	8	no	—
518	#41	—	8	4	no	—
519	#41	—	8	8	no	—
520	C₂×Q₈	—	2	4	no	—
521	C₂×Q₈	—	2	2	no	—
522	C₂×Q₈	—	4	2	no	—
523	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
524	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
525	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
526	C₂×D₄	—	2	2	no	—
527	C₂×D₄	—	2	4	no	—
528	C₂×D₄	—	2	4	no	—
529	C₂×D₄	—	2	2	no	—
530	C₂×D₄	—	2	4	no	—
531	C₂×D₄	—	2	2	no	—
532	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
533	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
534	C₂²×C₄	—	2	4	no	—
535	C₂²×C₄	—	2	2	no	—
536	C₂²×C₄	—	2	4	no	—
537	C₂²×C₄	—	2	4	no	—
538	C₂²×C₄	—	2	4	no	—
539	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
540	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
541	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
542	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
543	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
544	Q₁₆	—	4	1	no	—
545	SD₁₆	—	2	4	no	—
546	SD₁₆	—	4	4	no	—
547	D₈	—	2	4	no	—
548	D₈	—	4	2	no	—
549	D₈	—	4	4	no	—
550	D₈	—	4	1	no	—
551	C₂×C₈	—	2	2	no	—
552	C₂×C₈	—	4	1	no	—
553	C₂×C₈	—	4	2	no	—
554	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
555	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
556	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
557	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
558	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
559	C₄⋊C₄	—	2	2	no	—
560	C₄⋊C₄	—	2	4	no	—
561	C₄⋊C₄	—	2	4	no	—
562	C₄⋊C₄	—	2	2	no	—
563	C₄⋊C₄	—	2	2	no	—
564	C₄⋊C₄	—	2	4	no	—
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	—	2	4	no	—
567	C₄⋊C₄	—	2	2	no	—
568	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
569	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
570	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
571	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
572	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
573	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
574	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
575	C₂²⋊C₄	—	2	2	no	—
576	C₂²⋊C₄	—	2	2	no	—
577	C₂²⋊C₄	—	2	4	no	—
578	C₂²⋊C₄	—	2	2	no	—
579	C₂²⋊C₄	—	2	4	no	—
580	C₂²⋊C₄	—	2	4	no	—
581	C₂²⋊C₄	—	2	2	no	—
582	C₂²⋊C₄	—	2	4	no	—
583	C₂²⋊C₄	—	2	2	no	—
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	—	2	4	no	—
586	C₂²⋊C₄	—	2	4	no	—
587	C₄²	—	2	4	no	—
588	C₄²	—	2	2	no	—
589	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
590	C₄²	C₂×D₄×C₁₉	1	4	yes	—
591	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
592	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
593	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
594	C₄²	C₂⁴×C₁₉	1	4	yes	—
595	C₂³	—	2	4	no	—
596	C₂³	—	2	2	no	—
597	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
598	Q₈	—	2	4	no	—
599	Q₈	—	2	2	no	—
600	Q₈	—	2	2	no	—
601	Q₈	—	4	2	no	—
602	Q₈	—	8	4	no	—
603	Q₈	—	8	2	no	—
604	D₄	—	2	4	no	—
605	D₄	—	2	2	no	—
606	D₄	—	2	2	no	—
607	D₄	—	2	4	no	—
608	D₄	—	4	8	no	—
609	D₄	—	4	8	no	—
610	D₄	—	4	4	no	—
611	D₄	—	4	4	no	—
612	D₄	—	8	4	no	—
613	D₄	—	8	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	4	2	no	—
624	C₂×C₄	—	4	8	no	—
625	C₂×C₄	—	4	4	no	—
626	C₂×C₄	—	8	4	no	—
627	C₂×C₄	—	8	4	no	—
628	C₂×C₄	—	8	4	no	—
629	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
630	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
631	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
632	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
633	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
634	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
635	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
636	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
637	C₈	—	2	1	no	—
638	C₈	—	2	1	no	—
639	C₈	—	2	4	no	—
640	C₈	—	2	1	no	—
641	C₈	C₁₉×2₋¹⁺⁴	1	2	yes	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	4	4	no	—
645	C₂²	—	4	2	no	—
646	C₂²	—	4	4	no	—
647	C₂²	—	4	2	no	—
648	C₂²	—	4	4	no	—
649	C₂²	—	4	2	no	—
650	C₂²	C₁₉×#576	1	2	yes	—
651	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
652	C₄	—	2	1	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	4	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	4	no	—
657	C₄	—	2	1	no	—
658	C₄	—	4	2	no	—
659	C₄	—	4	2	no	—
660	C₄	—	4	4	no	—
661	C₄	—	4	2	no	—
662	C₄	C₁₉×#575	1	2	yes	—
663	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
664	C₄	C₁₉×#585	1	1	yes	characteristic
665	C₂	—	2	2	no	—
666	C₂	—	8	4	no	—
667	C₂	—	8	2	no	—
668	C₂	C₁₉×#3497	1	1	yes	characteristic
669	C₂	C₂×C₁₉×#575	1	1	yes	characteristic
670	C₂	C₂×C₁₉×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3522	C₂	semidirect
2. C₁₉×#3403	C₂	semidirect
3. C₁₉×#3399	C₂	semidirect
4. C₁₉×#3389	C₂	semidirect
5. C₁₉×#3385	C₂	semidirect
6. C₁₉×#3375	C₂	semidirect
7. C₁₉×#3370	C₂	semidirect
8. C₁₉×#3366	C₂	semidirect
9. C₁₉×#3250	C₂	semidirect
10. C₁₉×#3247	C₂	semidirect
11. C₁₉×#3245	C₂	semidirect
12. C₁₉×#3180	C₂	semidirect
13. C₁₉×#3169	C₂	semidirect
14. C₁₉×#3168	C₂	semidirect
15. C₂×C₁₉×#446	C₂	semidirect
259. #62368	C₁₉	direct (N × H)
307. #3522	C₂×C₁₉	semidirect
308. #3403	C₂×C₁₉	semidirect
309. #3399	C₂×C₁₉	semidirect
310. #3389	C₂×C₁₉	semidirect
311. #3385	C₂×C₁₉	semidirect
312. #3375	C₂×C₁₉	semidirect
313. #3370	C₂×C₁₉	semidirect
314. #3366	C₂×C₁₉	semidirect
315. #3250	C₂×C₁₉	semidirect
316. #3247	C₂×C₁₉	semidirect
317. #3245	C₂×C₁₉	semidirect
318. #3180	C₂×C₁₉	semidirect
319. #3169	C₂×C₁₉	semidirect
320. #3168	C₂×C₁₉	semidirect
321. C₂×#446	C₂×C₁₉	semidirect
516. C₁₉	#62368	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×#3522	2
C₁₉×#3403	2
C₁₉×#3399	2
C₁₉×#3389	2
C₁₉×#3385	2
C₁₉×#3375	2
C₁₉×#3370	2
C₁₉×#3366	2
C₁₉×#3250	2
C₁₉×#3247	2
C₁₉×#3245	2
C₁₉×#3180	2
C₁₉×#3169	2
C₁₉×#3168	2
C₂×C₁₉×#446	2
#62368	19

Subgroups — C19×#62368 #18068327

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62368 #18068327