Subgroups — C₁₉×#62341 #18068300

Order 4864.

1784 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	C₁₉×#3547	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3357	C₂	1	2	yes	maximal, complemented
3	C₁₉×#3352	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3303	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3300	C₂	1	4	yes	maximal, complemented
6	C₁₉×#3299	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3277	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3276	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3252	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3203	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3202	C₂	1	2	yes	maximal, complemented
12	C₁₉×#3170	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3168	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3063	C₂	1	4	yes	maximal, complemented
15	C₁₉×#2931	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×#137	C₂²	1	4	yes	—
17	C₂×C₁₉×#131	C₂²	1	2	yes	—
18	C₁₉×#562	—	2	4	no	—
19	C₁₉×#555	—	2	2	no	—
20	C₁₉×#555	C₂²	1	2	yes	—
21	C₁₉×#554	C₂²	1	2	yes	—
22	C₁₉×#553	—	2	2	no	—
23	C₁₉×#552	C₂²	1	4	yes	—
24	D₄×Q₈×C₁₉	C₂²	1	2	yes	—
25	C₁₉×#548	C₂²	1	4	yes	—
26	C₁₉×#547	C₂²	1	2	yes	—
27	C₁₉×#544	—	2	2	no	—
28	C₁₉×#542	—	2	4	no	—
29	C₁₉×#540	—	2	2	no	—
30	C₁₉×#537	C₂²	1	4	yes	—
31	C₁₉×#536	C₂²	1	4	yes	—
32	C₁₉×#533	C₂²	1	2	yes	—
33	C₁₉×#532	C₂²	1	1	yes	characteristic
34	C₁₉×#529	C₂²	1	2	yes	—
35	C₁₉×#500	C₂²	1	1	yes	characteristic
36	C₁₉×#499	C₂²	1	1	yes	characteristic
37	C₁₉×#495	C₂²	1	1	yes	characteristic
38	C₁₉×#494	C₂²	1	1	yes	characteristic
39	C₁₉×#488	C₂²	1	2	yes	—
40	C₁₉×#487	C₂²	1	2	yes	—
41	C₁₉×#485	C₂²	1	4	yes	—
42	C₁₉×#485	C₂²	1	4	yes	—
43	C₁₉×#484	C₂²	1	4	yes	—
44	C₁₉×#480	C₂²	1	4	yes	—
45	C₁₉×#479	C₂²	1	4	yes	—
46	C₁₉×#477	C₂²	1	2	yes	—
47	C₁₉×#476	C₂²	1	2	yes	—
48	C₁₉×#470	C₂²	1	4	yes	—
49	C₁₉×#470	C₂²	1	4	yes	—
50	C₁₉×#468	C₂²	1	4	yes	—
51	C₁₉×#468	C₂²	1	4	yes	—
52	C₁₉×#467	C₂²	1	1	yes	characteristic
53	C₁₉×#467	C₂²	1	2	yes	—
54	C₁₉×#467	C₂²	1	2	yes	—
55	C₁₉×#467	C₂²	1	4	yes	—
56	C₁₉×#466	C₂²	1	1	yes	characteristic
57	C₁₉×#465	C₂²	1	2	yes	—
58	C₁₉×#465	C₂²	1	4	yes	—
59	C₁₉×#464	C₂²	1	4	yes	—
60	C₁₉×#462	C₂²	1	2	yes	—
61	C₁₉×#461	C₂²	1	2	yes	—
62	C₁₉×#452	C₂²	1	4	yes	—
63	C₁₉×#451	C₂²	1	4	yes	—
64	C₁₉×#451	C₂²	1	4	yes	—
65	C₁₉×#449	C₂²	1	4	yes	—
66	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
67	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
68	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
69	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	—
70	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
71	C₁₉×#436	C₂²	1	2	yes	—
72	C₁₉×#436	C₂²	1	2	yes	—
73	C₈×D₄×C₁₉	C₂²	1	2	yes	—
74	C₈×D₄×C₁₉	C₂²	1	2	yes	—
75	C₁₉×#428	C₂²	1	4	yes	—
76	C₁₉×#423	C₂²	1	1	yes	characteristic
77	C₁₉×#416	C₂²	1	4	yes	—
78	C₂×C₁₉×#103	C₂²	1	4	yes	—
79	C₁₉×#408	C₂²	1	2	yes	—
80	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
81	C₂×#41×C₁₉	C₂³	1	4	yes	—
82	C₂×#41×C₁₉	C₂³	1	2	yes	—
83	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
84	C₁₉×#137	—	4	8	no	—
85	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
86	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
87	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
88	C₂×Q₁₆×C₁₉	C₂³	1	4	yes	—
89	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
90	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
91	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
92	C₁₉×#131	—	4	4	no	—
93	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
94	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
95	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
98	C₁₉×C₄⋊Q₈	—	2	4	no	—
99	C₁₉×C₄⋊Q₈	—	2	2	no	—
100	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
101	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
102	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
103	C₁₉×#127	D₄	1	1	yes	characteristic
104	C₁₉×#126	—	2	4	no	—
105	C₁₉×#126	—	2	2	no	—
106	C₁₉×#125	—	2	4	no	—
107	C₁₉×#125	—	2	2	no	—
108	C₁₉×#125	—	2	2	no	—
109	C₁₉×#125	C₂³	1	2	yes	—
110	C₁₉×#124	—	2	4	no	—
111	C₁₉×#124	—	2	4	no	—
112	C₁₉×#124	—	2	4	no	—
113	C₁₉×#124	D₄	1	2	yes	—
114	C₁₉×#124	C₂³	1	2	yes	—
115	C₁₉×#123	—	2	4	no	—
116	C₁₉×#123	—	2	4	no	—
117	C₁₉×#123	—	2	4	no	—
118	C₁₉×#123	—	2	2	no	—
119	C₁₉×#123	—	2	4	no	—
120	C₁₉×C₂²⋊Q₈	—	2	4	no	—
121	C₁₉×C₂²⋊Q₈	—	2	2	no	—
122	C₁₉×C₂²⋊Q₈	—	2	4	no	—
123	C₁₉×C₂²⋊Q₈	—	2	4	no	—
124	C₁₉×C₂²⋊Q₈	—	2	4	no	—
125	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
126	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
127	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
128	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
129	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
130	C₁₉×#121	—	2	4	no	—
131	C₁₉×#121	—	2	4	no	—
132	C₁₉×#121	—	2	4	no	—
133	C₁₉×#121	—	2	2	no	—
134	C₁₉×#121	—	2	4	no	—
135	C₁₉×#121	—	2	2	no	—
136	C₁₉×#121	D₄	1	2	yes	—
137	C₁₉×#121	D₄	1	2	yes	—
138	C₁₉×#121	C₂³	1	4	yes	—
139	C₁₉×#121	C₂³	1	2	yes	—
140	C₄×Q₈×C₁₉	—	2	2	no	—
141	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
142	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
143	C₄×D₄×C₁₉	—	2	2	no	—
144	C₄×D₄×C₁₉	—	2	2	no	—
145	C₄×D₄×C₁₉	—	2	2	no	—
146	C₄×D₄×C₁₉	—	2	4	no	—
147	C₄×D₄×C₁₉	C₂³	1	2	yes	—
148	C₄×D₄×C₁₉	C₂³	1	2	yes	—
149	C₄×D₄×C₁₉	C₂³	1	2	yes	—
150	C₁₉×#117	—	2	2	no	—
151	C₁₉×#117	—	2	2	no	—
152	C₁₉×#117	—	2	4	no	—
153	C₁₉×#117	—	2	2	no	—
154	C₁₉×#117	C₂³	1	4	yes	—
155	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
156	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
157	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
158	C₁₉×#107	C₂³	1	2	yes	—
159	C₁₉×#107	C₂³	1	4	yes	—
160	C₁₉×#107	C₂³	1	1	yes	characteristic
161	C₁₉×#107	C₂³	1	1	yes	characteristic
162	C₁₉×#107	C₂³	1	2	yes	—
163	C₁₉×#106	C₂³	1	2	yes	—
164	C₁₉×#106	C₂³	1	4	yes	—
165	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
166	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
167	C₁₉×#103	C₂³	1	2	yes	—
168	C₁₉×#103	C₂³	1	4	yes	—
169	C₁₉×#103	C₂³	1	4	yes	—
170	C₁₉×#103	C₂³	1	4	yes	—
171	C₁₉×#103	C₂³	1	4	yes	—
172	C₁₉×#103	C₂³	1	2	yes	—
173	C₁₉×#103	C₂³	1	4	yes	—
174	C₁₉×#102	C₂³	1	2	yes	—
175	C₁₉×#102	C₂³	1	4	yes	—
176	C₁₉×#102	C₂³	1	2	yes	—
177	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
178	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
179	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
180	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
181	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
182	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
183	#41×C₁₉	—	4	2	no	—
184	#41×C₁₉	—	4	2	no	—
185	#41×C₁₉	—	4	4	no	—
186	#41×C₁₉	—	4	4	no	—
187	C₂×Q₈×C₁₉	—	2	2	no	—
188	C₂×Q₈×C₁₉	—	2	4	no	—
189	C₂×Q₈×C₁₉	—	4	4	no	—
190	C₂×Q₈×C₁₉	—	4	4	no	—
191	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
192	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
193	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
194	C₂×D₄×C₁₉	—	2	2	no	—
195	C₂×D₄×C₁₉	—	2	4	no	—
196	C₂×D₄×C₁₉	—	2	4	no	—
197	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
198	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
199	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
200	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
201	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₁₉	—	2	4	no	—
203	C₂²×C₄×C₁₉	—	2	4	no	—
204	C₂²×C₄×C₁₉	—	2	2	no	—
205	C₂²×C₄×C₁₉	—	2	4	no	—
206	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
210	Q₁₆×C₁₉	—	2	4	no	—
211	Q₁₆×C₁₉	—	4	1	no	—
212	Q₁₆×C₁₉	—	4	2	no	—
213	Q₁₆×C₁₉	—	4	4	no	—
214	SD₁₆×C₁₉	—	2	4	no	—
215	SD₁₆×C₁₉	—	4	4	no	—
216	D₈×C₁₉	—	4	1	no	—
217	M₁₆×C₁₉	—	2	8	no	—
218	M₁₆×C₁₉	—	4	2	no	—
219	C₂×C₈×C₁₉	—	2	2	no	—
220	C₂×C₈×C₁₉	—	4	1	no	—
221	C₂×C₈×C₁₉	—	4	4	no	—
222	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
223	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
224	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
225	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
226	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
227	C₄⋊C₄×C₁₉	—	2	2	no	—
228	C₄⋊C₄×C₁₉	—	2	4	no	—
229	C₄⋊C₄×C₁₉	—	2	4	no	—
230	C₄⋊C₄×C₁₉	—	2	2	no	—
231	C₄⋊C₄×C₁₉	—	2	2	no	—
232	C₄⋊C₄×C₁₉	—	2	4	no	—
233	C₄⋊C₄×C₁₉	—	2	2	no	—
234	C₄⋊C₄×C₁₉	—	2	2	no	—
235	C₄⋊C₄×C₁₉	—	2	4	no	—
236	C₄⋊C₄×C₁₉	—	2	4	no	—
237	C₄⋊C₄×C₁₉	—	2	2	no	—
238	C₄⋊C₄×C₁₉	—	2	4	no	—
239	C₄⋊C₄×C₁₉	—	2	2	no	—
240	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
241	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
242	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
243	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
244	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
245	C₂²⋊C₄×C₁₉	—	2	4	no	—
246	C₂²⋊C₄×C₁₉	—	2	4	no	—
247	C₂²⋊C₄×C₁₉	—	2	4	no	—
248	C₂²⋊C₄×C₁₉	—	2	4	no	—
249	C₂²⋊C₄×C₁₉	—	2	4	no	—
250	C₂²⋊C₄×C₁₉	—	2	2	no	—
251	C₂²⋊C₄×C₁₉	—	2	2	no	—
252	C₂²⋊C₄×C₁₉	—	2	2	no	—
253	C₂²⋊C₄×C₁₉	—	2	4	no	—
254	C₂²⋊C₄×C₁₉	—	2	2	no	—
255	C₂²⋊C₄×C₁₉	—	2	2	no	—
256	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
257	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
258	C₄²×C₁₉	—	2	4	no	—
259	C₄²×C₁₉	—	2	4	no	—
260	C₄²×C₁₉	—	2	2	no	—
261	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
262	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
263	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
264	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
265	#62341	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
266	C₂³×C₁₉	—	2	2	no	—
267	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
268	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
269	Q₈×C₁₉	—	2	2	no	—
270	Q₈×C₁₉	—	2	4	no	—
271	Q₈×C₁₉	—	2	2	no	—
272	Q₈×C₁₉	—	2	4	no	—
273	Q₈×C₁₉	—	4	2	no	—
274	Q₈×C₁₉	—	8	2	no	—
275	Q₈×C₁₉	—	8	4	no	—
276	D₄×C₁₉	—	2	4	no	—
277	D₄×C₁₉	—	2	2	no	—
278	D₄×C₁₉	—	2	2	no	—
279	D₄×C₁₉	—	4	2	no	—
280	D₄×C₁₉	—	4	4	no	—
281	D₄×C₁₉	—	4	2	no	—
282	D₄×C₁₉	—	8	2	no	—
283	D₄×C₁₉	—	8	4	no	—
284	D₄×C₁₉	—	8	4	no	—
285	C₂×C₄×C₁₉	—	2	2	no	—
286	C₂×C₄×C₁₉	—	2	1	no	—
287	C₂×C₄×C₁₉	—	2	4	no	—
288	C₂×C₄×C₁₉	—	2	1	no	—
289	C₂×C₄×C₁₉	—	2	4	no	—
290	C₂×C₄×C₁₉	—	2	2	no	—
291	C₂×C₄×C₁₉	—	2	4	no	—
292	C₂×C₄×C₁₉	—	2	2	no	—
293	C₂×C₄×C₁₉	—	2	2	no	—
294	C₂×C₄×C₁₉	—	2	4	no	—
295	C₂×C₄×C₁₉	—	4	1	no	—
296	C₂×C₄×C₁₉	—	4	4	no	—
297	C₂×C₄×C₁₉	—	8	4	no	—
298	C₂×C₄×C₁₉	—	8	4	no	—
299	C₂×C₄×C₁₉	—	8	4	no	—
300	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
301	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
302	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
303	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
304	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
305	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
307	C₈×C₁₉	—	2	1	no	—
308	C₈×C₁₉	—	2	4	no	—
309	C₈×C₁₉	—	2	1	no	—
310	C₈×C₁₉	—	2	1	no	—
311	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
312	#3547	C₂×C₁₉	1	2	yes	complemented
313	#3357	C₂×C₁₉	1	2	yes	complemented
314	#3352	C₂×C₁₉	1	2	yes	complemented
315	#3303	C₂×C₁₉	1	2	yes	complemented
316	#3300	C₂×C₁₉	1	4	yes	complemented
317	#3299	C₂×C₁₉	1	2	yes	complemented
318	#3277	C₂×C₁₉	1	2	yes	complemented
319	#3276	C₂×C₁₉	1	2	yes	complemented
320	#3252	C₂×C₁₉	1	2	yes	complemented
321	#3203	C₂×C₁₉	1	2	yes	complemented
322	#3202	C₂×C₁₉	1	2	yes	complemented
323	#3170	C₂×C₁₉	1	1	yes	characteristic, complemented
324	#3168	C₂×C₁₉	1	1	yes	characteristic, complemented
325	#3063	C₂×C₁₉	1	4	yes	complemented
326	#2931	C₂×C₁₉	1	1	yes	characteristic, complemented
327	C₂²×C₁₉	—	2	1	no	—
328	C₂²×C₁₉	—	2	4	no	—
329	C₂²×C₁₉	—	2	4	no	—
330	C₂²×C₁₉	—	2	1	no	—
331	C₂²×C₁₉	—	2	1	no	—
332	C₂²×C₁₉	—	2	4	no	—
333	C₂²×C₁₉	—	4	2	no	—
334	C₂²×C₁₉	—	4	2	no	—
335	C₂²×C₁₉	—	4	2	no	—
336	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
337	C₄×C₁₉	—	2	1	no	—
338	C₄×C₁₉	—	2	1	no	—
339	C₄×C₁₉	—	2	4	no	—
340	C₄×C₁₉	—	2	1	no	—
341	C₄×C₁₉	—	2	1	no	—
342	C₄×C₁₉	—	4	2	no	—
343	C₄×C₁₉	—	4	4	no	—
344	C₄×C₁₉	—	4	4	no	—
345	C₄×C₁₉	—	4	2	no	—
346	C₄×C₁₉	—	4	2	no	—
347	C₄×C₁₉	#578	1	2	yes	—
348	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
349	C₄×C₁₉	#585	1	1	yes	characteristic
350	C₂×#137	C₂²×C₁₉	1	4	yes	—
351	C₂×#131	C₂²×C₁₉	1	2	yes	—
352	#562	—	2	4	no	—
353	#555	—	2	2	no	—
354	#555	C₂²×C₁₉	1	2	yes	—
355	#554	C₂²×C₁₉	1	2	yes	—
356	#553	—	2	2	no	—
357	#552	C₂²×C₁₉	1	4	yes	—
358	D₄×Q₈	C₂²×C₁₉	1	2	yes	—
359	#548	C₂²×C₁₉	1	4	yes	—
360	#547	C₂²×C₁₉	1	2	yes	—
361	#544	—	2	2	no	—
362	#542	—	2	4	no	—
363	#540	—	2	2	no	—
364	#537	C₂²×C₁₉	1	4	yes	—
365	#536	C₂²×C₁₉	1	4	yes	—
366	#533	C₂²×C₁₉	1	2	yes	—
367	#532	C₂²×C₁₉	1	1	yes	characteristic
368	#529	C₂²×C₁₉	1	2	yes	—
369	#500	C₂²×C₁₉	1	1	yes	characteristic
370	#499	C₂²×C₁₉	1	1	yes	characteristic
371	#495	C₂²×C₁₉	1	1	yes	characteristic
372	#494	C₂²×C₁₉	1	1	yes	characteristic
373	#488	C₂²×C₁₉	1	2	yes	—
374	#487	C₂²×C₁₉	1	2	yes	—
375	#485	C₂²×C₁₉	1	4	yes	—
376	#485	C₂²×C₁₉	1	4	yes	—
377	#484	C₂²×C₁₉	1	4	yes	—
378	#480	C₂²×C₁₉	1	4	yes	—
379	#479	C₂²×C₁₉	1	4	yes	—
380	#477	C₂²×C₁₉	1	2	yes	—
381	#476	C₂²×C₁₉	1	2	yes	—
382	#470	C₂²×C₁₉	1	4	yes	—
383	#470	C₂²×C₁₉	1	4	yes	—
384	#468	C₂²×C₁₉	1	4	yes	—
385	#468	C₂²×C₁₉	1	4	yes	—
386	#467	C₂²×C₁₉	1	1	yes	characteristic
387	#467	C₂²×C₁₉	1	2	yes	—
388	#467	C₂²×C₁₉	1	2	yes	—
389	#467	C₂²×C₁₉	1	4	yes	—
390	#466	C₂²×C₁₉	1	1	yes	characteristic
391	#465	C₂²×C₁₉	1	2	yes	—
392	#465	C₂²×C₁₉	1	4	yes	—
393	#464	C₂²×C₁₉	1	4	yes	—
394	#462	C₂²×C₁₉	1	2	yes	—
395	#461	C₂²×C₁₉	1	2	yes	—
396	#452	C₂²×C₁₉	1	4	yes	—
397	#451	C₂²×C₁₉	1	4	yes	—
398	#451	C₂²×C₁₉	1	4	yes	—
399	#449	C₂²×C₁₉	1	4	yes	—
400	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
401	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
402	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
403	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
404	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
405	#436	C₂²×C₁₉	1	2	yes	—
406	#436	C₂²×C₁₉	1	2	yes	—
407	C₈×D₄	C₂²×C₁₉	1	2	yes	—
408	C₈×D₄	C₂²×C₁₉	1	2	yes	—
409	#428	C₂²×C₁₉	1	4	yes	—
410	#423	C₂²×C₁₉	1	1	yes	characteristic
411	#416	C₂²×C₁₉	1	4	yes	—
412	C₂×#103	C₂²×C₁₉	1	4	yes	—
413	#408	C₂²×C₁₉	1	2	yes	—
414	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
415	C₂×C₁₉	—	4	1	no	—
416	C₂×C₁₉	—	4	4	no	—
417	C₂×C₁₉	—	8	2	no	—
418	C₂×C₁₉	#3496	1	1	yes	characteristic
419	C₂×C₁₉	C₂×#578	1	1	yes	characteristic
420	C₂×C₁₉	#3584	1	1	yes	characteristic
421	C₂×#41	C₂³×C₁₉	1	4	yes	—
422	C₂×#41	C₂³×C₁₉	1	2	yes	—
423	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
424	#137	—	4	8	no	—
425	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
426	C₂×Q₁₆	C₂³×C₁₉	1	4	yes	—
427	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
428	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
429	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
430	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
431	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
432	#131	—	4	4	no	—
433	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
434	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
435	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
436	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
437	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
438	C₄⋊Q₈	—	2	4	no	—
439	C₄⋊Q₈	—	2	2	no	—
440	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
441	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
442	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
443	#127	D₄×C₁₉	1	1	yes	characteristic
444	#126	—	2	4	no	—
445	#126	—	2	2	no	—
446	#125	—	2	4	no	—
447	#125	—	2	2	no	—
448	#125	—	2	2	no	—
449	#125	C₂³×C₁₉	1	2	yes	—
450	#124	—	2	4	no	—
451	#124	—	2	4	no	—
452	#124	—	2	4	no	—
453	#124	D₄×C₁₉	1	2	yes	—
454	#124	C₂³×C₁₉	1	2	yes	—
455	#123	—	2	4	no	—
456	#123	—	2	4	no	—
457	#123	—	2	4	no	—
458	#123	—	2	2	no	—
459	#123	—	2	4	no	—
460	C₂²⋊Q₈	—	2	4	no	—
461	C₂²⋊Q₈	—	2	2	no	—
462	C₂²⋊Q₈	—	2	4	no	—
463	C₂²⋊Q₈	—	2	4	no	—
464	C₂²⋊Q₈	—	2	4	no	—
465	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
466	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
467	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
468	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
469	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
470	#121	—	2	4	no	—
471	#121	—	2	4	no	—
472	#121	—	2	4	no	—
473	#121	—	2	2	no	—
474	#121	—	2	4	no	—
475	#121	—	2	2	no	—
476	#121	D₄×C₁₉	1	2	yes	—
477	#121	D₄×C₁₉	1	2	yes	—
478	#121	C₂³×C₁₉	1	2	yes	—
479	#121	C₂³×C₁₉	1	4	yes	—
480	C₄×Q₈	—	2	2	no	—
481	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
482	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
483	C₄×D₄	—	2	2	no	—
484	C₄×D₄	—	2	2	no	—
485	C₄×D₄	—	2	2	no	—
486	C₄×D₄	—	2	4	no	—
487	C₄×D₄	C₂³×C₁₉	1	2	yes	—
488	C₄×D₄	C₂³×C₁₉	1	2	yes	—
489	C₄×D₄	C₂³×C₁₉	1	2	yes	—
490	#117	—	2	2	no	—
491	#117	—	2	2	no	—
492	#117	—	2	4	no	—
493	#117	—	2	2	no	—
494	#117	C₂³×C₁₉	1	4	yes	—
495	C₂×C₄⋊C₄	—	2	2	no	—
496	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
497	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
498	#107	C₂³×C₁₉	1	2	yes	—
499	#107	C₂³×C₁₉	1	4	yes	—
500	#107	C₂³×C₁₉	1	1	yes	characteristic
501	#107	C₂³×C₁₉	1	1	yes	characteristic
502	#107	C₂³×C₁₉	1	2	yes	—
503	#106	C₂³×C₁₉	1	2	yes	—
504	#106	C₂³×C₁₉	1	4	yes	—
505	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
506	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
507	#103	C₂³×C₁₉	1	2	yes	—
508	#103	C₂³×C₁₉	1	4	yes	—
509	#103	C₂³×C₁₉	1	4	yes	—
510	#103	C₂³×C₁₉	1	4	yes	—
511	#103	C₂³×C₁₉	1	4	yes	—
512	#103	C₂³×C₁₉	1	2	yes	—
513	#103	C₂³×C₁₉	1	4	yes	—
514	#102	C₂³×C₁₉	1	2	yes	—
515	#102	C₂³×C₁₉	1	4	yes	—
516	#102	C₂³×C₁₉	1	2	yes	—
517	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
518	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
519	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
520	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
521	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
522	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
523	C₁₉	#62341	1	1	yes	characteristic, direct product factor, Sylow
524	#41	—	4	2	no	—
525	#41	—	4	2	no	—
526	#41	—	4	4	no	—
527	#41	—	4	4	no	—
528	C₂×Q₈	—	2	2	no	—
529	C₂×Q₈	—	2	4	no	—
530	C₂×Q₈	—	4	4	no	—
531	C₂×Q₈	—	4	4	no	—
532	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
533	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
534	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
535	C₂×D₄	—	2	2	no	—
536	C₂×D₄	—	2	4	no	—
537	C₂×D₄	—	2	4	no	—
538	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
539	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
540	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
541	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
542	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
543	C₂²×C₄	—	2	4	no	—
544	C₂²×C₄	—	2	4	no	—
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	—	2	4	no	—
547	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
548	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
549	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
550	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
551	Q₁₆	—	2	4	no	—
552	Q₁₆	—	4	1	no	—
553	Q₁₆	—	4	2	no	—
554	Q₁₆	—	4	4	no	—
555	SD₁₆	—	2	4	no	—
556	SD₁₆	—	4	4	no	—
557	D₈	—	4	1	no	—
558	M₁₆	—	2	8	no	—
559	M₁₆	—	4	2	no	—
560	C₂×C₈	—	2	2	no	—
561	C₂×C₈	—	4	1	no	—
562	C₂×C₈	—	4	4	no	—
563	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
564	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
565	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
566	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
567	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
568	C₄⋊C₄	—	2	2	no	—
569	C₄⋊C₄	—	2	4	no	—
570	C₄⋊C₄	—	2	4	no	—
571	C₄⋊C₄	—	2	2	no	—
572	C₄⋊C₄	—	2	2	no	—
573	C₄⋊C₄	—	2	4	no	—
574	C₄⋊C₄	—	2	2	no	—
575	C₄⋊C₄	—	2	2	no	—
576	C₄⋊C₄	—	2	4	no	—
577	C₄⋊C₄	—	2	4	no	—
578	C₄⋊C₄	—	2	2	no	—
579	C₄⋊C₄	—	2	4	no	—
580	C₄⋊C₄	—	2	2	no	—
581	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
582	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
583	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
584	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
585	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
586	C₂²⋊C₄	—	2	4	no	—
587	C₂²⋊C₄	—	2	4	no	—
588	C₂²⋊C₄	—	2	4	no	—
589	C₂²⋊C₄	—	2	4	no	—
590	C₂²⋊C₄	—	2	4	no	—
591	C₂²⋊C₄	—	2	2	no	—
592	C₂²⋊C₄	—	2	2	no	—
593	C₂²⋊C₄	—	2	2	no	—
594	C₂²⋊C₄	—	2	4	no	—
595	C₂²⋊C₄	—	2	2	no	—
596	C₂²⋊C₄	—	2	2	no	—
597	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
598	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
599	C₄²	—	2	4	no	—
600	C₄²	—	2	4	no	—
601	C₄²	—	2	2	no	—
602	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
603	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
604	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
605	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
606	C₂³	—	2	2	no	—
607	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
608	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
609	Q₈	—	2	2	no	—
610	Q₈	—	2	4	no	—
611	Q₈	—	2	2	no	—
612	Q₈	—	2	4	no	—
613	Q₈	—	4	2	no	—
614	Q₈	—	8	4	no	—
615	Q₈	—	8	2	no	—
616	D₄	—	2	4	no	—
617	D₄	—	2	2	no	—
618	D₄	—	2	2	no	—
619	D₄	—	4	4	no	—
620	D₄	—	4	2	no	—
621	D₄	—	4	2	no	—
622	D₄	—	8	4	no	—
623	D₄	—	8	2	no	—
624	D₄	—	8	4	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	4	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	4	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	4	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	4	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	4	no	—
637	C₂×C₄	—	8	4	no	—
638	C₂×C₄	—	8	4	no	—
639	C₂×C₄	—	8	4	no	—
640	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
641	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
642	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
643	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
644	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
645	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
646	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
647	C₈	—	2	1	no	—
648	C₈	—	2	4	no	—
649	C₈	—	2	1	no	—
650	C₈	—	2	1	no	—
651	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
652	C₂²	—	2	4	no	—
653	C₂²	—	2	1	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	4	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	2	4	no	—
658	C₂²	—	4	2	no	—
659	C₂²	—	4	2	no	—
660	C₂²	—	4	2	no	—
661	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
662	C₄	—	2	4	no	—
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	1	no	—
667	C₄	—	4	4	no	—
668	C₄	—	4	2	no	—
669	C₄	—	4	2	no	—
670	C₄	—	4	2	no	—
671	C₄	—	4	4	no	—
672	C₄	C₁₉×#578	1	2	yes	—
673	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
674	C₄	C₁₉×#585	1	1	yes	characteristic
675	C₂	—	4	4	no	—
676	C₂	—	4	1	no	—
677	C₂	—	8	2	no	—
678	C₂	C₁₉×#3496	1	1	yes	characteristic
679	C₂	C₂×C₁₉×#578	1	1	yes	characteristic
680	C₂	C₁₉×#3584	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 ◁ C₁₉×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3547	C₂	semidirect
2. C₁₉×#3357	C₂	semidirect
3. C₁₉×#3352	C₂	semidirect
4. C₁₉×#3303	C₂	semidirect
5. C₁₉×#3300	C₂	semidirect
6. C₁₉×#3299	C₂	semidirect
7. C₁₉×#3277	C₂	semidirect
8. C₁₉×#3276	C₂	semidirect
9. C₁₉×#3252	C₂	semidirect
10. C₁₉×#3203	C₂	semidirect
11. C₁₉×#3202	C₂	semidirect
12. C₁₉×#3170	C₂	semidirect
13. C₁₉×#3168	C₂	semidirect
14. C₁₉×#3063	C₂	semidirect
15. C₁₉×#2931	C₂	semidirect
265. #62341	C₁₉	direct (N × H)
312. #3547	C₂×C₁₉	semidirect
313. #3357	C₂×C₁₉	semidirect
314. #3352	C₂×C₁₉	semidirect
315. #3303	C₂×C₁₉	semidirect
316. #3300	C₂×C₁₉	semidirect
317. #3299	C₂×C₁₉	semidirect
318. #3277	C₂×C₁₉	semidirect
319. #3276	C₂×C₁₉	semidirect
320. #3252	C₂×C₁₉	semidirect
321. #3203	C₂×C₁₉	semidirect
322. #3202	C₂×C₁₉	semidirect
323. #3170	C₂×C₁₉	semidirect
324. #3168	C₂×C₁₉	semidirect
325. #3063	C₂×C₁₉	semidirect
326. #2931	C₂×C₁₉	semidirect
523. C₁₉	#62341	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×#3547	2
C₁₉×#3357	2
C₁₉×#3352	2
C₁₉×#3303	2
C₁₉×#3300	2
C₁₉×#3299	2
C₁₉×#3277	2
C₁₉×#3276	2
C₁₉×#3252	2
C₁₉×#3203	2
C₁₉×#3202	2
C₁₉×#3170	2
C₁₉×#3168	2
C₁₉×#3063	2
C₁₉×#2931	2
#62341	19

Subgroups — C19×#62341 #18068300

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62341 #18068300