Subgroups — C₁₉×#18157 #18024116

Order 4864.

926 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3455	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3113	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3112	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2599	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1612	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1609	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1606	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1603	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1515	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1514	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1464	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#542	—	2	1	no	—
13	C₁₉×#542	—	2	1	no	—
14	C₁₉×#541	—	2	1	no	—
15	C₁₉×#540	—	2	1	no	—
16	C₁₉×#539	—	2	1	no	—
17	C₁₉×#539	C₂²	1	2	yes	—
18	C₁₉×#538	—	2	1	no	—
19	C₁₉×#538	C₂²	1	2	yes	—
20	C₁₉×#533	C₂²	1	1	yes	characteristic
21	C₁₉×#532	C₂²	1	1	yes	characteristic
22	C₁₉×#529	—	2	2	no	—
23	C₁₉×#529	—	2	2	no	—
24	C₁₉×#525	—	2	1	no	—
25	C₄×#41×C₁₉	—	2	1	no	—
26	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
28	C₁₉×#483	C₂²	1	2	yes	—
29	C₁₉×#480	C₂²	1	2	yes	—
30	C₁₉×#477	—	2	1	no	—
31	C₁₉×#475	—	2	1	no	—
32	C₁₉×#462	—	2	1	no	—
33	C₁₉×#460	—	2	1	no	—
34	C₁₉×#451	C₂²	1	2	yes	—
35	C₁₉×#448	C₂²	1	2	yes	—
36	C₁₉×#441	—	2	2	no	—
37	C₁₉×#440	—	2	2	no	—
38	C₁₉×#432	C₂²	1	1	yes	characteristic
39	C₁₉×#432	C₂²	1	1	yes	characteristic
40	C₁₉×#398	C₂²	1	1	yes	characteristic
41	C₁₉×#397	C₂²	1	1	yes	characteristic
42	C₁₉×#395	C₂²	1	1	yes	characteristic
43	C₁₉×#393	C₂²	1	1	yes	characteristic
44	C₁₉×#388	—	2	1	no	—
45	C₁₉×#387	—	2	1	no	—
46	C₁₉×#387	—	2	1	no	—
47	C₁₉×#385	—	2	1	no	—
48	C₁₉×#383	C₂²	1	1	yes	characteristic
49	C₁₉×#328	C₂²	1	2	yes	—
50	C₁₉×#328	C₂²	1	2	yes	—
51	C₁₉×#327	C₂²	1	2	yes	—
52	C₁₉×#327	C₂²	1	2	yes	—
53	C₁₉×#324	C₂²	1	2	yes	—
54	C₁₉×#323	C₂²	1	2	yes	—
55	C₂×#41×C₁₉	—	2	1	no	—
56	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
58	C₂×Q₁₆×C₁₉	—	2	2	no	—
59	C₂×SD₁₆×C₁₉	—	2	2	no	—
60	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
61	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
62	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
63	C₁₉×#127	D₄	1	1	yes	characteristic
64	C₁₉×#126	—	2	2	no	—
65	C₁₉×#126	—	2	2	no	—
66	C₁₉×#126	—	2	2	no	—
67	C₁₉×#126	—	2	2	no	—
68	C₁₉×#125	—	2	2	no	—
69	C₁₉×#125	—	2	2	no	—
70	C₁₉×#125	—	2	1	no	—
71	C₁₉×#124	—	2	2	no	—
72	C₁₉×#124	—	2	2	no	—
73	C₁₉×#124	—	2	1	no	—
74	C₁₉×#123	—	2	2	no	—
75	C₁₉×#123	—	2	2	no	—
76	C₁₉×#123	—	2	2	no	—
77	C₁₉×#123	—	2	2	no	—
78	C₁₉×#123	—	2	2	no	—
79	C₁₉×C₂²⋊Q₈	—	2	1	no	—
80	C₁₉×C₂²⋊Q₈	—	2	1	no	—
81	C₁₉×C₂²⋊Q₈	—	2	2	no	—
82	C₁₉×C₂²⋊Q₈	—	2	2	no	—
83	C₁₉×C₂²⋊Q₈	—	2	1	no	—
84	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
85	C₁₉×#121	—	2	1	no	—
86	C₁₉×#121	—	2	1	no	—
87	C₁₉×#121	—	2	2	no	—
88	C₁₉×#121	—	2	2	no	—
89	C₁₉×#121	—	2	1	no	—
90	C₁₉×#121	C₂³	1	2	yes	—
91	C₁₉×#120	—	2	2	no	—
92	C₄×Q₈×C₁₉	—	2	1	no	—
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×Q₈×C₁₉	D₄	1	2	yes	—
100	C₄×D₄×C₁₉	—	2	1	no	—
101	C₄×D₄×C₁₉	—	2	1	no	—
102	C₄×D₄×C₁₉	—	2	2	no	—
103	C₄×D₄×C₁₉	—	2	2	no	—
104	C₄×D₄×C₁₉	—	2	2	no	—
105	C₄×D₄×C₁₉	—	2	2	no	—
106	C₄×D₄×C₁₉	—	2	1	no	—
107	C₄×D₄×C₁₉	D₄	1	2	yes	—
108	C₁₉×#117	—	2	2	no	—
109	C₁₉×#117	—	2	1	no	—
110	C₁₉×#117	—	2	1	no	—
111	C₁₉×#117	—	2	1	no	—
112	C₁₉×#117	—	2	1	no	—
113	C₁₉×#117	—	2	1	no	—
114	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
115	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
116	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
117	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
120	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
123	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
124	C₂×C₄²×C₁₉	—	2	2	no	—
125	C₂×C₄²×C₁₉	—	2	1	no	—
126	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
127	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
128	C₁₉×#107	—	2	2	no	—
129	C₁₉×#106	—	2	2	no	—
130	C₁₉×C₄⋊C₈	—	2	1	no	—
131	C₁₉×C₄⋊C₈	—	2	1	no	—
132	C₁₉×#103	—	2	2	no	—
133	C₁₉×#103	—	2	2	no	—
134	C₁₉×#103	—	2	2	no	—
135	C₁₉×#102	—	2	2	no	—
136	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
137	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
138	C₁₉×#97	—	2	1	no	—
139	C₁₉×#97	—	2	1	no	—
140	C₁₉×#95	—	2	1	no	—
141	C₁₉×#95	—	2	1	no	—
142	C₁₉×#95	—	2	1	no	—
143	C₁₉×#95	—	2	1	no	—
144	C₁₉×#95	—	2	1	no	—
145	C₁₉×#95	—	2	1	no	—
146	C₁₉×#95	C₂³	1	1	yes	characteristic
147	C₁₉×#95	C₂³	1	1	yes	characteristic
148	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
149	#41×C₁₉	—	4	2	no	—
150	#41×C₁₉	—	4	2	no	—
151	C₂×Q₈×C₁₉	—	2	1	no	—
152	C₂×Q₈×C₁₉	—	2	1	no	—
153	C₂×Q₈×C₁₉	—	2	1	no	—
154	C₂×Q₈×C₁₉	—	2	1	no	—
155	C₂×Q₈×C₁₉	—	4	2	no	—
156	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
157	C₂×D₄×C₁₉	—	2	2	no	—
158	C₂×D₄×C₁₉	—	2	2	no	—
159	C₂×D₄×C₁₉	—	2	2	no	—
160	C₂×D₄×C₁₉	—	2	1	no	—
161	C₂×D₄×C₁₉	—	2	1	no	—
162	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
163	C₂²×C₄×C₁₉	—	2	1	no	—
164	C₂²×C₄×C₁₉	—	2	2	no	—
165	C₂²×C₄×C₁₉	—	2	2	no	—
166	C₂²×C₄×C₁₉	—	2	2	no	—
167	C₂²×C₄×C₁₉	—	2	1	no	—
168	C₂²×C₄×C₁₉	—	2	1	no	—
169	C₂²×C₄×C₁₉	—	2	1	no	—
170	C₂²×C₄×C₁₉	—	2	1	no	—
171	C₂²×C₄×C₁₉	—	2	1	no	—
172	C₂²×C₄×C₁₉	—	4	1	no	—
173	C₂²×C₄×C₁₉	—	4	1	no	—
174	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
180	Q₁₆×C₁₉	—	4	4	no	—
181	SD₁₆×C₁₉	—	4	4	no	—
182	C₂×C₈×C₁₉	—	2	2	no	—
183	C₂×C₈×C₁₉	—	2	2	no	—
184	C₄⋊C₄×C₁₉	—	2	2	no	—
185	C₄⋊C₄×C₁₉	—	2	2	no	—
186	C₄⋊C₄×C₁₉	—	2	2	no	—
187	C₄⋊C₄×C₁₉	—	2	2	no	—
188	C₄⋊C₄×C₁₉	—	2	1	no	—
189	C₄⋊C₄×C₁₉	—	2	1	no	—
190	C₄⋊C₄×C₁₉	—	2	1	no	—
191	C₄⋊C₄×C₁₉	—	2	1	no	—
192	C₄⋊C₄×C₁₉	—	2	1	no	—
193	C₄⋊C₄×C₁₉	—	2	1	no	—
194	C₄⋊C₄×C₁₉	—	2	2	no	—
195	C₄⋊C₄×C₁₉	—	2	1	no	—
196	C₄⋊C₄×C₁₉	—	2	1	no	—
197	C₄⋊C₄×C₁₉	—	2	2	no	—
198	C₄⋊C₄×C₁₉	—	2	1	no	—
199	C₄⋊C₄×C₁₉	—	2	1	no	—
200	C₄⋊C₄×C₁₉	—	4	2	no	—
201	C₄⋊C₄×C₁₉	—	4	2	no	—
202	C₄⋊C₄×C₁₉	—	4	1	no	—
203	C₄⋊C₄×C₁₉	—	4	1	no	—
204	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
205	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
206	C₂²⋊C₄×C₁₉	—	2	2	no	—
207	C₂²⋊C₄×C₁₉	—	2	2	no	—
208	C₂²⋊C₄×C₁₉	—	2	2	no	—
209	C₂²⋊C₄×C₁₉	—	2	2	no	—
210	C₂²⋊C₄×C₁₉	—	2	2	no	—
211	C₂²⋊C₄×C₁₉	—	2	2	no	—
212	C₂²⋊C₄×C₁₉	—	2	2	no	—
213	C₂²⋊C₄×C₁₉	—	2	1	no	—
214	C₂²⋊C₄×C₁₉	—	2	1	no	—
215	C₂²⋊C₄×C₁₉	—	2	2	no	—
216	C₂²⋊C₄×C₁₉	—	2	1	no	—
217	C₂²⋊C₄×C₁₉	—	2	1	no	—
218	C₂²⋊C₄×C₁₉	—	2	2	no	—
219	C₂²⋊C₄×C₁₉	—	4	2	no	—
220	C₂²⋊C₄×C₁₉	—	4	2	no	—
221	C₄²×C₁₉	—	2	2	no	—
222	C₄²×C₁₉	—	2	2	no	—
223	C₄²×C₁₉	—	2	1	no	—
224	C₄²×C₁₉	—	2	2	no	—
225	C₄²×C₁₉	—	2	1	no	—
226	C₄²×C₁₉	—	4	1	no	—
227	C₄²×C₁₉	—	4	1	no	—
228	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
229	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
230	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
231	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
232	#18157	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
233	C₂³×C₁₉	—	2	1	no	—
234	C₂³×C₁₉	—	2	2	no	—
235	C₂³×C₁₉	—	2	1	no	—
236	C₂³×C₁₉	—	2	1	no	—
237	C₂³×C₁₉	—	4	1	no	—
238	C₂³×C₁₉	—	4	1	no	—
239	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
240	Q₈×C₁₉	—	2	2	no	—
241	Q₈×C₁₉	—	2	2	no	—
242	Q₈×C₁₉	—	4	2	no	—
243	Q₈×C₁₉	—	4	1	no	—
244	Q₈×C₁₉	—	4	1	no	—
245	Q₈×C₁₉	—	4	2	no	—
246	Q₈×C₁₉	—	8	1	no	—
247	D₄×C₁₉	—	4	2	no	—
248	D₄×C₁₉	—	4	2	no	—
249	D₄×C₁₉	—	4	2	no	—
250	D₄×C₁₉	—	4	2	no	—
251	D₄×C₁₉	—	8	1	no	—
252	D₄×C₁₉	—	8	2	no	—
253	D₄×C₁₉	—	8	2	no	—
254	C₂×C₄×C₁₉	—	2	1	no	—
255	C₂×C₄×C₁₉	—	2	1	no	—
256	C₂×C₄×C₁₉	—	2	2	no	—
257	C₂×C₄×C₁₉	—	2	1	no	—
258	C₂×C₄×C₁₉	—	2	1	no	—
259	C₂×C₄×C₁₉	—	2	2	no	—
260	C₂×C₄×C₁₉	—	2	2	no	—
261	C₂×C₄×C₁₉	—	2	2	no	—
262	C₂×C₄×C₁₉	—	2	1	no	—
263	C₂×C₄×C₁₉	—	2	1	no	—
264	C₂×C₄×C₁₉	—	2	1	no	—
265	C₂×C₄×C₁₉	—	4	1	no	—
266	C₂×C₄×C₁₉	—	4	1	no	—
267	C₂×C₄×C₁₉	—	4	2	no	—
268	C₂×C₄×C₁₉	—	4	2	no	—
269	C₂×C₄×C₁₉	—	4	4	no	—
270	C₂×C₄×C₁₉	—	4	1	no	—
271	C₂×C₄×C₁₉	—	4	1	no	—
272	C₂×C₄×C₁₉	—	4	1	no	—
273	C₂×C₄×C₁₉	—	4	1	no	—
274	C₂×C₄×C₁₉	—	4	1	no	—
275	C₂×C₄×C₁₉	—	4	1	no	—
276	C₂×C₄×C₁₉	—	4	1	no	—
277	C₂×C₄×C₁₉	—	4	1	no	—
278	C₂×C₄×C₁₉	—	4	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	—	8	2	no	—
284	C₂×C₄×C₁₉	—	8	2	no	—
285	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
286	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
287	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
288	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
289	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
290	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
291	C₈×C₁₉	—	4	2	no	—
292	C₈×C₁₉	—	4	2	no	—
293	#3455	C₂×C₁₉	1	1	yes	characteristic
294	#3113	C₂×C₁₉	1	1	yes	characteristic, complemented
295	#3112	C₂×C₁₉	1	1	yes	characteristic, complemented
296	#2599	C₂×C₁₉	1	1	yes	characteristic, complemented
297	#1612	C₂×C₁₉	1	2	yes	complemented
298	#1609	C₂×C₁₉	1	2	yes	complemented
299	#1606	C₂×C₁₉	1	2	yes	complemented
300	#1603	C₂×C₁₉	1	2	yes	complemented
301	#1515	C₂×C₁₉	1	1	yes	characteristic, complemented
302	#1514	C₂×C₁₉	1	1	yes	characteristic, complemented
303	#1464	C₂×C₁₉	1	1	yes	characteristic, complemented
304	C₂²×C₁₉	—	2	1	no	—
305	C₂²×C₁₉	—	2	1	no	—
306	C₂²×C₁₉	—	4	2	no	—
307	C₂²×C₁₉	—	4	1	no	—
308	C₂²×C₁₉	—	4	2	no	—
309	C₂²×C₁₉	—	4	2	no	—
310	C₂²×C₁₉	—	4	1	no	—
311	C₂²×C₁₉	—	4	2	no	—
312	C₂²×C₁₉	—	4	1	no	—
313	C₂²×C₁₉	—	8	1	no	—
314	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
315	C₂²×C₁₉	#575	1	1	yes	characteristic
316	C₂²×C₁₉	#575	1	1	yes	characteristic
317	C₄×C₁₉	—	2	1	no	—
318	C₄×C₁₉	—	2	1	no	—
319	C₄×C₁₉	—	2	1	no	—
320	C₄×C₁₉	—	2	1	no	—
321	C₄×C₁₉	—	2	1	no	—
322	C₄×C₁₉	—	2	1	no	—
323	C₄×C₁₉	—	4	1	no	—
324	C₄×C₁₉	—	4	2	no	—
325	C₄×C₁₉	—	4	1	no	—
326	C₄×C₁₉	—	4	2	no	—
327	C₄×C₁₉	—	4	2	no	—
328	C₄×C₁₉	—	4	1	no	—
329	C₄×C₁₉	—	4	2	no	—
330	C₄×C₁₉	—	8	1	no	—
331	C₄×C₁₉	—	8	1	no	—
332	C₄×C₁₉	—	8	1	no	—
333	#542	—	2	1	no	—
334	#542	—	2	1	no	—
335	#541	—	2	1	no	—
336	#540	—	2	1	no	—
337	#539	—	2	1	no	—
338	#539	C₂²×C₁₉	1	2	yes	—
339	#538	—	2	1	no	—
340	#538	C₂²×C₁₉	1	2	yes	—
341	#533	C₂²×C₁₉	1	1	yes	characteristic
342	#532	C₂²×C₁₉	1	1	yes	characteristic
343	#529	—	2	2	no	—
344	#529	—	2	2	no	—
345	#525	—	2	1	no	—
346	C₄×#41	—	2	1	no	—
347	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
348	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
349	#483	C₂²×C₁₉	1	2	yes	—
350	#480	C₂²×C₁₉	1	2	yes	—
351	#477	—	2	1	no	—
352	#475	—	2	1	no	—
353	#462	—	2	1	no	—
354	#460	—	2	1	no	—
355	#451	C₂²×C₁₉	1	2	yes	—
356	#448	C₂²×C₁₉	1	2	yes	—
357	#441	—	2	2	no	—
358	#440	—	2	2	no	—
359	#432	C₂²×C₁₉	1	1	yes	characteristic
360	#432	C₂²×C₁₉	1	1	yes	characteristic
361	#398	C₂²×C₁₉	1	1	yes	characteristic
362	#397	C₂²×C₁₉	1	1	yes	characteristic
363	#395	C₂²×C₁₉	1	1	yes	characteristic
364	#393	C₂²×C₁₉	1	1	yes	characteristic
365	#388	—	2	1	no	—
366	#387	—	2	1	no	—
367	#387	—	2	1	no	—
368	#385	—	2	1	no	—
369	#383	C₂²×C₁₉	1	1	yes	characteristic
370	#328	C₂²×C₁₉	1	2	yes	—
371	#328	C₂²×C₁₉	1	2	yes	—
372	#327	C₂²×C₁₉	1	2	yes	—
373	#327	C₂²×C₁₉	1	2	yes	—
374	#324	C₂²×C₁₉	1	2	yes	—
375	#323	C₂²×C₁₉	1	2	yes	—
376	C₂×C₁₉	—	2	1	no	—
377	C₂×C₁₉	—	2	1	no	—
378	C₂×C₁₉	—	8	2	no	—
379	C₂×C₁₉	—	8	1	no	—
380	C₂×C₁₉	#3005	1	1	yes	characteristic
381	C₂×C₁₉	#3022	1	1	yes	characteristic
382	C₂×C₁₉	#3025	1	1	yes	characteristic
383	C₂×#41	—	2	1	no	—
384	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
385	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
386	C₂×Q₁₆	—	2	2	no	—
387	C₂×SD₁₆	—	2	2	no	—
388	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
389	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
390	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
391	#127	D₄×C₁₉	1	1	yes	characteristic
392	#126	—	2	2	no	—
393	#126	—	2	2	no	—
394	#126	—	2	2	no	—
395	#126	—	2	2	no	—
396	#125	—	2	2	no	—
397	#125	—	2	2	no	—
398	#125	—	2	1	no	—
399	#124	—	2	2	no	—
400	#124	—	2	2	no	—
401	#124	—	2	1	no	—
402	#123	—	2	2	no	—
403	#123	—	2	2	no	—
404	#123	—	2	2	no	—
405	#123	—	2	2	no	—
406	#123	—	2	2	no	—
407	C₂²⋊Q₈	—	2	1	no	—
408	C₂²⋊Q₈	—	2	1	no	—
409	C₂²⋊Q₈	—	2	2	no	—
410	C₂²⋊Q₈	—	2	2	no	—
411	C₂²⋊Q₈	—	2	1	no	—
412	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
413	#121	—	2	1	no	—
414	#121	—	2	1	no	—
415	#121	—	2	2	no	—
416	#121	—	2	2	no	—
417	#121	—	2	1	no	—
418	#121	C₂³×C₁₉	1	2	yes	—
419	#120	—	2	2	no	—
420	C₄×Q₈	—	2	1	no	—
421	C₄×Q₈	—	2	1	no	—
422	C₄×Q₈	—	2	1	no	—
423	C₄×Q₈	—	2	1	no	—
424	C₄×Q₈	—	2	1	no	—
425	C₄×Q₈	—	2	1	no	—
426	C₄×Q₈	—	2	1	no	—
427	C₄×Q₈	D₄×C₁₉	1	2	yes	—
428	C₄×D₄	—	2	1	no	—
429	C₄×D₄	—	2	1	no	—
430	C₄×D₄	—	2	2	no	—
431	C₄×D₄	—	2	2	no	—
432	C₄×D₄	—	2	2	no	—
433	C₄×D₄	—	2	2	no	—
434	C₄×D₄	—	2	1	no	—
435	C₄×D₄	D₄×C₁₉	1	2	yes	—
436	#117	—	2	2	no	—
437	#117	—	2	1	no	—
438	#117	—	2	1	no	—
439	#117	—	2	1	no	—
440	#117	—	2	1	no	—
441	#117	—	2	1	no	—
442	C₂×C₄⋊C₄	—	2	1	no	—
443	C₂×C₄⋊C₄	—	2	1	no	—
444	C₂×C₄⋊C₄	—	2	1	no	—
445	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
446	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
448	C₂×C₂²⋊C₄	—	2	1	no	—
449	C₂×C₂²⋊C₄	—	2	1	no	—
450	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
451	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
452	C₂×C₄²	—	2	2	no	—
453	C₂×C₄²	—	2	1	no	—
454	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
455	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
456	#107	—	2	2	no	—
457	#106	—	2	2	no	—
458	C₄⋊C₈	—	2	1	no	—
459	C₄⋊C₈	—	2	1	no	—
460	#103	—	2	2	no	—
461	#103	—	2	2	no	—
462	#103	—	2	2	no	—
463	#102	—	2	2	no	—
464	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
465	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
466	#97	—	2	1	no	—
467	#97	—	2	1	no	—
468	#95	—	2	1	no	—
469	#95	—	2	1	no	—
470	#95	—	2	1	no	—
471	#95	—	2	1	no	—
472	#95	—	2	1	no	—
473	#95	—	2	1	no	—
474	#95	C₂³×C₁₉	1	1	yes	characteristic
475	#95	C₂³×C₁₉	1	1	yes	characteristic
476	C₁₉	#18157	1	1	yes	characteristic, direct product factor, Sylow
477	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
478	#41	—	4	2	no	—
479	#41	—	4	2	no	—
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×Q₈	—	2	1	no	—
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	4	2	no	—
485	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
486	C₂×D₄	—	2	2	no	—
487	C₂×D₄	—	2	2	no	—
488	C₂×D₄	—	2	2	no	—
489	C₂×D₄	—	2	1	no	—
490	C₂×D₄	—	2	1	no	—
491	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	2	no	—
494	C₂²×C₄	—	2	2	no	—
495	C₂²×C₄	—	2	2	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	4	1	no	—
502	C₂²×C₄	—	4	1	no	—
503	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
504	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
505	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
506	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
507	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
508	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
509	Q₁₆	—	4	4	no	—
510	SD₁₆	—	4	4	no	—
511	C₂×C₈	—	2	2	no	—
512	C₂×C₈	—	2	2	no	—
513	C₄⋊C₄	—	2	2	no	—
514	C₄⋊C₄	—	2	2	no	—
515	C₄⋊C₄	—	2	2	no	—
516	C₄⋊C₄	—	2	2	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	2	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	2	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	4	2	no	—
530	C₄⋊C₄	—	4	2	no	—
531	C₄⋊C₄	—	4	1	no	—
532	C₄⋊C₄	—	4	1	no	—
533	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
534	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
535	C₂²⋊C₄	—	2	2	no	—
536	C₂²⋊C₄	—	2	2	no	—
537	C₂²⋊C₄	—	2	2	no	—
538	C₂²⋊C₄	—	2	2	no	—
539	C₂²⋊C₄	—	2	2	no	—
540	C₂²⋊C₄	—	2	2	no	—
541	C₂²⋊C₄	—	2	2	no	—
542	C₂²⋊C₄	—	2	1	no	—
543	C₂²⋊C₄	—	2	1	no	—
544	C₂²⋊C₄	—	2	2	no	—
545	C₂²⋊C₄	—	2	1	no	—
546	C₂²⋊C₄	—	2	1	no	—
547	C₂²⋊C₄	—	2	2	no	—
548	C₂²⋊C₄	—	4	2	no	—
549	C₂²⋊C₄	—	4	2	no	—
550	C₄²	—	2	2	no	—
551	C₄²	—	2	2	no	—
552	C₄²	—	2	1	no	—
553	C₄²	—	2	2	no	—
554	C₄²	—	2	1	no	—
555	C₄²	—	4	1	no	—
556	C₄²	—	4	1	no	—
557	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
558	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
559	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
560	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
561	C₂³	—	2	1	no	—
562	C₂³	—	2	2	no	—
563	C₂³	—	2	1	no	—
564	C₂³	—	2	1	no	—
565	C₂³	—	4	1	no	—
566	C₂³	—	4	1	no	—
567	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
568	Q₈	—	2	2	no	—
569	Q₈	—	2	2	no	—
570	Q₈	—	4	2	no	—
571	Q₈	—	4	1	no	—
572	Q₈	—	4	1	no	—
573	Q₈	—	4	2	no	—
574	Q₈	—	8	1	no	—
575	D₄	—	4	2	no	—
576	D₄	—	4	2	no	—
577	D₄	—	4	2	no	—
578	D₄	—	4	2	no	—
579	D₄	—	8	1	no	—
580	D₄	—	8	2	no	—
581	D₄	—	8	2	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	4	4	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	8	2	no	—
612	C₂×C₄	—	8	2	no	—
613	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
614	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
615	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
616	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
617	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
618	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
619	C₈	—	4	2	no	—
620	C₈	—	4	2	no	—
621	C₂²	—	2	1	no	—
622	C₂²	—	2	1	no	—
623	C₂²	—	4	2	no	—
624	C₂²	—	4	1	no	—
625	C₂²	—	4	2	no	—
626	C₂²	—	4	2	no	—
627	C₂²	—	4	1	no	—
628	C₂²	—	4	2	no	—
629	C₂²	—	4	1	no	—
630	C₂²	—	8	1	no	—
631	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
632	C₂²	C₁₉×#575	1	1	yes	characteristic
633	C₂²	C₁₉×#575	1	1	yes	characteristic
634	C₄	—	2	1	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	1	no	—
637	C₄	—	2	1	no	—
638	C₄	—	2	1	no	—
639	C₄	—	2	1	no	—
640	C₄	—	4	1	no	—
641	C₄	—	4	2	no	—
642	C₄	—	4	1	no	—
643	C₄	—	4	2	no	—
644	C₄	—	4	2	no	—
645	C₄	—	4	1	no	—
646	C₄	—	4	2	no	—
647	C₄	—	8	1	no	—
648	C₄	—	8	1	no	—
649	C₄	—	8	1	no	—
650	C₂	—	2	1	no	—
651	C₂	—	2	1	no	—
652	C₂	—	8	1	no	—
653	C₂	—	8	2	no	—
654	C₂	C₁₉×#3005	1	1	yes	characteristic
655	C₂	C₁₉×#3022	1	1	yes	characteristic
656	C₂	C₁₉×#3025	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#3455	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3113	C₂	semidirect
3. C₁₉×#3112	C₂	semidirect
4. C₁₉×#2599	C₂	semidirect
5. C₁₉×#1612	C₂	semidirect
6. C₁₉×#1609	C₂	semidirect
7. C₁₉×#1606	C₂	semidirect
8. C₁₉×#1603	C₂	semidirect
9. C₁₉×#1515	C₂	semidirect
10. C₁₉×#1514	C₂	semidirect
11. C₁₉×#1464	C₂	semidirect
232. #18157	C₁₉	direct (N × H)
294. #3113	C₂×C₁₉	semidirect
295. #3112	C₂×C₁₉	semidirect
296. #2599	C₂×C₁₉	semidirect
297. #1612	C₂×C₁₉	semidirect
298. #1609	C₂×C₁₉	semidirect
299. #1606	C₂×C₁₉	semidirect
300. #1603	C₂×C₁₉	semidirect
301. #1515	C₂×C₁₉	semidirect
302. #1514	C₂×C₁₉	semidirect
303. #1464	C₂×C₁₉	semidirect
476. C₁₉	#18157	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×#3455	2
C₁₉×#3113	2
C₁₉×#3112	2
C₁₉×#2599	2
C₁₉×#1612	2
C₁₉×#1609	2
C₁₉×#1606	2
C₁₉×#1603	2
C₁₉×#1515	2
C₁₉×#1514	2
C₁₉×#1464	2
#18157	19

Subgroups — C19×#18157 #18024116

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18157 #18024116