Subgroups — C₁₉×#62376 #18068335

Order 4864.

1628 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3557	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3394	C₂	1	4	yes	maximal, complemented
3	C₁₉×#3381	C₂	1	4	yes	maximal, complemented
4	C₁₉×#3377	C₂	1	4	yes	maximal, complemented
5	C₁₉×#3370	C₂	1	4	yes	maximal, complemented
6	C₁₉×#3262	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3261	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#3259	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#3256	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3174	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3173	C₂	1	2	yes	maximal, complemented
12	C₁₉×#3168	C₂	1	2	yes	maximal, complemented
13	C₁₉×#2960	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#563	—	2	4	no	—
15	C₁₉×#559	C₂²	1	4	yes	—
16	C₁₉×#557	C₂²	1	4	yes	—
17	C₁₉×#556	C₂²	1	4	yes	—
18	C₁₉×#554	C₂²	1	4	yes	—
19	C₁₉×#552	—	2	4	no	—
20	C₁₉×#542	—	2	4	no	—
21	C₁₉×#542	C₂²	1	4	yes	—
22	C₁₉×#541	C₂²	1	2	yes	—
23	C₁₉×#540	C₂²	1	2	yes	—
24	C₁₉×#539	—	2	4	no	—
25	C₁₉×#533	C₂²	1	1	yes	characteristic
26	C₁₉×#529	C₂²	1	4	yes	—
27	C₁₉×#499	C₂²	1	2	yes	—
28	C₁₉×#499	C₂²	1	2	yes	—
29	C₁₉×#498	C₂²	1	2	yes	—
30	C₁₉×#495	C₂²	1	2	yes	—
31	C₁₉×#495	C₂²	1	2	yes	—
32	C₁₉×#492	C₂²	1	2	yes	—
33	C₁₉×#491	C₂²	1	2	yes	—
34	C₁₉×#490	C₂²	1	2	yes	—
35	C₁₉×#489	C₂²	1	4	yes	—
36	C₁₉×#488	C₂²	1	4	yes	—
37	C₁₉×#479	C₂²	1	4	yes	—
38	C₁₉×#479	C₂²	1	4	yes	—
39	C₁₉×#478	C₂²	1	4	yes	—
40	C₁₉×#478	C₂²	1	4	yes	—
41	C₁₉×#477	C₂²	1	4	yes	—
42	C₁₉×#474	C₂²	1	4	yes	—
43	C₁₉×#470	C₂²	1	2	yes	—
44	C₁₉×#469	C₂²	1	2	yes	—
45	C₁₉×#468	C₂²	1	4	yes	—
46	C₁₉×#467	C₂²	1	2	yes	—
47	C₁₉×#466	C₂²	1	2	yes	—
48	C₁₉×#465	C₂²	1	4	yes	—
49	C₁₉×#464	C₂²	1	4	yes	—
50	C₁₉×#464	C₂²	1	4	yes	—
51	C₁₉×#463	C₂²	1	4	yes	—
52	C₁₉×#463	C₂²	1	4	yes	—
53	C₁₉×#462	C₂²	1	4	yes	—
54	C₁₉×#459	C₂²	1	4	yes	—
55	C₁₉×#446	C₂²	1	4	yes	—
56	C₈×Q₈×C₁₉	C₂²	1	4	yes	—
57	C₁₉×#442	C₂²	1	2	yes	—
58	C₁₉×#441	C₂²	1	2	yes	—
59	C₁₉×#440	C₂²	1	4	yes	—
60	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
61	C₄×SD₁₆×C₁₉	C₂²	1	4	yes	—
62	C₄×SD₁₆×C₁₉	C₂²	1	4	yes	—
63	C₄×SD₁₆×C₁₉	C₂²	1	4	yes	—
64	C₄×D₈×C₁₉	C₂²	1	2	yes	—
65	C₁₉×#424	C₂²	1	1	yes	characteristic
66	C₁₉×#424	C₂²	1	1	yes	characteristic
67	C₁₉×#423	C₂²	1	1	yes	characteristic
68	C₁₉×#405	C₂²	1	1	yes	characteristic
69	C₁₉×#405	C₂²	1	1	yes	characteristic
70	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
71	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
72	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
73	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
74	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
75	C₂×D₈×C₁₉	C₂³	1	2	yes	—
76	C₂×D₈×C₁₉	C₂³	1	2	yes	—
77	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
78	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
81	C₁₉×C₄⋊Q₈	—	2	4	no	—
82	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
83	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
84	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
85	C₁₉×#127	C₂³	1	2	yes	—
86	C₁₉×#126	—	2	4	no	—
87	C₁₉×#126	—	2	4	no	—
88	C₁₉×#126	—	2	4	no	—
89	C₁₉×#126	—	2	4	no	—
90	C₁₉×#126	—	2	4	no	—
91	C₁₉×#125	—	2	4	no	—
92	C₁₉×#125	—	2	4	no	—
93	C₁₉×#125	—	2	4	no	—
94	C₁₉×#125	D₄	1	2	yes	—
95	C₁₉×#125	C₂³	1	2	yes	—
96	C₁₉×#125	C₂³	1	4	yes	—
97	C₁₉×#125	C₂³	1	2	yes	—
98	C₁₉×#124	—	2	4	no	—
99	C₁₉×#124	—	2	4	no	—
100	C₁₉×#124	C₂³	1	4	yes	—
101	C₁₉×#124	C₂³	1	4	yes	—
102	C₁₉×#123	—	2	4	no	—
103	C₁₉×#123	—	2	4	no	—
104	C₁₉×#123	—	2	4	no	—
105	C₁₉×#123	—	2	4	no	—
106	C₁₉×#123	—	2	4	no	—
107	C₁₉×C₂²⋊Q₈	—	2	4	no	—
108	C₁₉×C₂²⋊Q₈	—	2	4	no	—
109	C₁₉×C₂²⋊Q₈	—	2	4	no	—
110	C₁₉×C₂²⋊Q₈	—	2	4	no	—
111	C₁₉×C₂²⋊Q₈	—	2	4	no	—
112	C₁₉×C₂²⋊Q₈	D₄	1	4	yes	—
113	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
114	C₁₉×#121	—	2	4	no	—
115	C₁₉×#121	C₂³	1	4	yes	—
116	C₄×Q₈×C₁₉	—	2	4	no	—
117	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
118	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
119	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
120	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
121	C₄×D₄×C₁₉	—	2	4	no	—
122	C₄×D₄×C₁₉	—	2	4	no	—
123	C₄×D₄×C₁₉	C₂³	1	4	yes	—
124	C₄×D₄×C₁₉	C₂³	1	4	yes	—
125	C₄×D₄×C₁₉	C₂³	1	4	yes	—
126	C₁₉×#117	—	2	4	no	—
127	C₁₉×#117	—	2	4	no	—
128	C₁₉×#117	C₂³	1	1	yes	characteristic
129	C₁₉×#117	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
131	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
132	C₁₉×#107	C₂³	1	2	yes	—
133	C₁₉×#107	C₂³	1	2	yes	—
134	C₁₉×#107	C₂³	1	4	yes	—
135	C₁₉×#106	C₂³	1	4	yes	—
136	C₁₉×#106	C₂³	1	2	yes	—
137	C₁₉×#106	C₂³	1	2	yes	—
138	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
139	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
140	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
141	C₁₉×#103	C₂³	1	4	yes	—
142	C₁₉×#103	C₂³	1	4	yes	—
143	C₁₉×#103	C₂³	1	4	yes	—
144	C₁₉×#103	C₂³	1	4	yes	—
145	C₁₉×#102	C₂³	1	4	yes	—
146	C₁₉×#102	C₂³	1	4	yes	—
147	C₁₉×#102	C₂³	1	4	yes	—
148	C₁₉×#102	C₂³	1	4	yes	—
149	C₁₉×#97	C₂³	1	2	yes	—
150	C₁₉×#97	C₂³	1	2	yes	—
151	C₄×C₈×C₁₉	C₂³	1	2	yes	—
152	C₄×C₈×C₁₉	C₂³	1	2	yes	—
153	C₄×C₈×C₁₉	C₂³	1	2	yes	—
154	C₄×C₈×C₁₉	C₂³	1	2	yes	—
155	C₂×Q₈×C₁₉	—	2	4	no	—
156	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
157	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
158	C₂×D₄×C₁₉	—	2	4	no	—
159	C₂×D₄×C₁₉	—	2	4	no	—
160	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
161	C₂²×C₄×C₁₉	—	2	4	no	—
162	C₂²×C₄×C₁₉	—	2	4	no	—
163	C₂²×C₄×C₁₉	—	2	4	no	—
164	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
165	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
166	Q₁₆×C₁₉	—	4	2	no	—
167	Q₁₆×C₁₉	—	4	2	no	—
168	SD₁₆×C₁₉	—	2	8	no	—
169	SD₁₆×C₁₉	—	4	4	no	—
170	D₈×C₁₉	—	4	2	no	—
171	D₈×C₁₉	—	4	2	no	—
172	M₁₆×C₁₉	—	4	1	no	—
173	M₁₆×C₁₉	—	4	1	no	—
174	C₂×C₈×C₁₉	—	2	2	no	—
175	C₂×C₈×C₁₉	—	4	1	no	—
176	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
177	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
178	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
179	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
180	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
181	C₄⋊C₄×C₁₉	—	2	4	no	—
182	C₄⋊C₄×C₁₉	—	2	4	no	—
183	C₄⋊C₄×C₁₉	—	2	4	no	—
184	C₄⋊C₄×C₁₉	—	2	4	no	—
185	C₄⋊C₄×C₁₉	—	2	4	no	—
186	C₄⋊C₄×C₁₉	—	2	4	no	—
187	C₄⋊C₄×C₁₉	—	2	4	no	—
188	C₄⋊C₄×C₁₉	—	2	4	no	—
189	C₄⋊C₄×C₁₉	—	2	4	no	—
190	C₄⋊C₄×C₁₉	—	2	4	no	—
191	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
192	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
193	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
194	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
195	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
196	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
197	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
198	C₂²⋊C₄×C₁₉	—	2	4	no	—
199	C₂²⋊C₄×C₁₉	—	2	4	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	—	2	4	no	—
204	C₂²⋊C₄×C₁₉	—	2	4	no	—
205	C₂²⋊C₄×C₁₉	—	2	4	no	—
206	C₂²⋊C₄×C₁₉	—	2	4	no	—
207	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
208	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
209	C₄²×C₁₉	—	2	4	no	—
210	C₄²×C₁₉	—	2	4	no	—
211	C₄²×C₁₉	—	2	4	no	—
212	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
213	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
214	C₄²×C₁₉	C₂⁴	1	2	yes	—
215	C₄²×C₁₉	C₂⁴	1	2	yes	—
216	C₄²×C₁₉	C₂⁴	1	2	yes	—
217	#62376	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂³×C₁₉	—	2	4	no	—
219	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
220	Q₈×C₁₉	—	2	4	no	—
221	Q₈×C₁₉	—	2	4	no	—
222	Q₈×C₁₉	—	4	4	no	—
223	Q₈×C₁₉	—	8	4	no	—
224	D₄×C₁₉	—	2	4	no	—
225	D₄×C₁₉	—	2	4	no	—
226	D₄×C₁₉	—	8	4	no	—
227	D₄×C₁₉	—	8	4	no	—
228	C₂×C₄×C₁₉	—	2	1	no	—
229	C₂×C₄×C₁₉	—	2	1	no	—
230	C₂×C₄×C₁₉	—	2	4	no	—
231	C₂×C₄×C₁₉	—	2	4	no	—
232	C₂×C₄×C₁₉	—	2	4	no	—
233	C₂×C₄×C₁₉	—	4	2	no	—
234	C₂×C₄×C₁₉	—	8	4	no	—
235	C₂×C₄×C₁₉	—	8	4	no	—
236	C₂×C₄×C₁₉	—	8	4	no	—
237	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
238	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
239	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
240	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
242	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
243	C₈×C₁₉	—	2	1	no	—
244	C₈×C₁₉	—	2	2	no	—
245	C₈×C₁₉	—	2	2	no	—
246	C₈×C₁₉	—	2	2	no	—
247	C₈×C₁₉	2₋¹⁺⁴	1	2	yes	—
248	#3557	C₂×C₁₉	1	2	yes	complemented
249	#3394	C₂×C₁₉	1	4	yes	complemented
250	#3381	C₂×C₁₉	1	4	yes	complemented
251	#3377	C₂×C₁₉	1	4	yes	complemented
252	#3370	C₂×C₁₉	1	4	yes	complemented
253	#3262	C₂×C₁₉	1	2	yes	complemented
254	#3261	C₂×C₁₉	1	1	yes	characteristic, complemented
255	#3259	C₂×C₁₉	1	1	yes	characteristic
256	#3256	C₂×C₁₉	1	2	yes	complemented
257	#3174	C₂×C₁₉	1	2	yes	complemented
258	#3173	C₂×C₁₉	1	2	yes	complemented
259	#3168	C₂×C₁₉	1	2	yes	complemented
260	#2960	C₂×C₁₉	1	1	yes	characteristic, complemented
261	C₂²×C₁₉	—	2	2	no	—
262	C₂²×C₁₉	—	2	1	no	—
263	C₂²×C₁₉	—	4	4	no	—
264	C₂²×C₁₉	—	4	4	no	—
265	C₂²×C₁₉	—	4	4	no	—
266	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
267	C₄×C₁₉	—	2	2	no	—
268	C₄×C₁₉	—	2	2	no	—
269	C₄×C₁₉	—	2	4	no	—
270	C₄×C₁₉	—	2	4	no	—
271	C₄×C₁₉	—	2	1	no	—
272	C₄×C₁₉	—	4	4	no	—
273	C₄×C₁₉	—	4	4	no	—
274	C₄×C₁₉	—	4	4	no	—
275	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
276	C₄×C₁₉	#585	1	1	yes	characteristic
277	#563	—	2	4	no	—
278	#559	C₂²×C₁₉	1	4	yes	—
279	#557	C₂²×C₁₉	1	4	yes	—
280	#556	C₂²×C₁₉	1	4	yes	—
281	#554	C₂²×C₁₉	1	4	yes	—
282	#552	—	2	4	no	—
283	#542	—	2	4	no	—
284	#542	C₂²×C₁₉	1	4	yes	—
285	#541	C₂²×C₁₉	1	2	yes	—
286	#540	C₂²×C₁₉	1	2	yes	—
287	#539	—	2	4	no	—
288	#533	C₂²×C₁₉	1	1	yes	characteristic
289	#529	C₂²×C₁₉	1	4	yes	—
290	#499	C₂²×C₁₉	1	2	yes	—
291	#499	C₂²×C₁₉	1	2	yes	—
292	#498	C₂²×C₁₉	1	2	yes	—
293	#495	C₂²×C₁₉	1	2	yes	—
294	#495	C₂²×C₁₉	1	2	yes	—
295	#492	C₂²×C₁₉	1	2	yes	—
296	#491	C₂²×C₁₉	1	2	yes	—
297	#490	C₂²×C₁₉	1	2	yes	—
298	#489	C₂²×C₁₉	1	4	yes	—
299	#488	C₂²×C₁₉	1	4	yes	—
300	#479	C₂²×C₁₉	1	4	yes	—
301	#479	C₂²×C₁₉	1	4	yes	—
302	#478	C₂²×C₁₉	1	4	yes	—
303	#478	C₂²×C₁₉	1	4	yes	—
304	#477	C₂²×C₁₉	1	4	yes	—
305	#474	C₂²×C₁₉	1	4	yes	—
306	#470	C₂²×C₁₉	1	2	yes	—
307	#469	C₂²×C₁₉	1	2	yes	—
308	#468	C₂²×C₁₉	1	4	yes	—
309	#467	C₂²×C₁₉	1	2	yes	—
310	#466	C₂²×C₁₉	1	2	yes	—
311	#465	C₂²×C₁₉	1	4	yes	—
312	#464	C₂²×C₁₉	1	4	yes	—
313	#464	C₂²×C₁₉	1	4	yes	—
314	#463	C₂²×C₁₉	1	4	yes	—
315	#463	C₂²×C₁₉	1	4	yes	—
316	#462	C₂²×C₁₉	1	4	yes	—
317	#459	C₂²×C₁₉	1	4	yes	—
318	#446	C₂²×C₁₉	1	4	yes	—
319	C₈×Q₈	C₂²×C₁₉	1	4	yes	—
320	#442	C₂²×C₁₉	1	2	yes	—
321	#441	C₂²×C₁₉	1	2	yes	—
322	#440	C₂²×C₁₉	1	4	yes	—
323	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
324	C₄×SD₁₆	C₂²×C₁₉	1	4	yes	—
325	C₄×SD₁₆	C₂²×C₁₉	1	4	yes	—
326	C₄×SD₁₆	C₂²×C₁₉	1	4	yes	—
327	C₄×D₈	C₂²×C₁₉	1	2	yes	—
328	#424	C₂²×C₁₉	1	1	yes	characteristic
329	#424	C₂²×C₁₉	1	1	yes	characteristic
330	#423	C₂²×C₁₉	1	1	yes	characteristic
331	#405	C₂²×C₁₉	1	1	yes	characteristic
332	#405	C₂²×C₁₉	1	1	yes	characteristic
333	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
334	C₂×C₁₉	—	4	1	no	—
335	C₂×C₁₉	—	8	4	no	—
336	C₂×C₁₉	#3497	1	1	yes	characteristic
337	C₂×C₁₉	#3584	1	2	yes	—
338	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
339	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
340	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
341	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
342	C₂×D₈	C₂³×C₁₉	1	2	yes	—
343	C₂×D₈	C₂³×C₁₉	1	2	yes	—
344	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
345	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
346	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
347	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
348	C₄⋊Q₈	—	2	4	no	—
349	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
350	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
351	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
352	#127	C₂³×C₁₉	1	2	yes	—
353	#126	—	2	4	no	—
354	#126	—	2	4	no	—
355	#126	—	2	4	no	—
356	#126	—	2	4	no	—
357	#126	—	2	4	no	—
358	#125	—	2	4	no	—
359	#125	—	2	4	no	—
360	#125	—	2	4	no	—
361	#125	D₄×C₁₉	1	2	yes	—
362	#125	C₂³×C₁₉	1	4	yes	—
363	#125	C₂³×C₁₉	1	2	yes	—
364	#125	C₂³×C₁₉	1	2	yes	—
365	#124	—	2	4	no	—
366	#124	—	2	4	no	—
367	#124	C₂³×C₁₉	1	4	yes	—
368	#124	C₂³×C₁₉	1	4	yes	—
369	#123	—	2	4	no	—
370	#123	—	2	4	no	—
371	#123	—	2	4	no	—
372	#123	—	2	4	no	—
373	#123	—	2	4	no	—
374	C₂²⋊Q₈	—	2	4	no	—
375	C₂²⋊Q₈	—	2	4	no	—
376	C₂²⋊Q₈	—	2	4	no	—
377	C₂²⋊Q₈	—	2	4	no	—
378	C₂²⋊Q₈	—	2	4	no	—
379	C₂²⋊Q₈	D₄×C₁₉	1	4	yes	—
380	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
381	#121	—	2	4	no	—
382	#121	C₂³×C₁₉	1	4	yes	—
383	C₄×Q₈	—	2	4	no	—
384	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
385	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
386	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
387	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
388	C₄×D₄	—	2	4	no	—
389	C₄×D₄	—	2	4	no	—
390	C₄×D₄	C₂³×C₁₉	1	4	yes	—
391	C₄×D₄	C₂³×C₁₉	1	4	yes	—
392	C₄×D₄	C₂³×C₁₉	1	4	yes	—
393	#117	—	2	4	no	—
394	#117	—	2	4	no	—
395	#117	C₂³×C₁₉	1	1	yes	characteristic
396	#117	C₂³×C₁₉	1	1	yes	characteristic
397	C₂×C₄⋊C₄	—	2	4	no	—
398	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
399	#107	C₂³×C₁₉	1	2	yes	—
400	#107	C₂³×C₁₉	1	2	yes	—
401	#107	C₂³×C₁₉	1	4	yes	—
402	#106	C₂³×C₁₉	1	4	yes	—
403	#106	C₂³×C₁₉	1	2	yes	—
404	#106	C₂³×C₁₉	1	2	yes	—
405	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
406	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
407	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
408	#103	C₂³×C₁₉	1	4	yes	—
409	#103	C₂³×C₁₉	1	4	yes	—
410	#103	C₂³×C₁₉	1	4	yes	—
411	#103	C₂³×C₁₉	1	4	yes	—
412	#102	C₂³×C₁₉	1	4	yes	—
413	#102	C₂³×C₁₉	1	4	yes	—
414	#102	C₂³×C₁₉	1	4	yes	—
415	#102	C₂³×C₁₉	1	4	yes	—
416	#97	C₂³×C₁₉	1	2	yes	—
417	#97	C₂³×C₁₉	1	2	yes	—
418	C₄×C₈	C₂³×C₁₉	1	2	yes	—
419	C₄×C₈	C₂³×C₁₉	1	2	yes	—
420	C₄×C₈	C₂³×C₁₉	1	2	yes	—
421	C₄×C₈	C₂³×C₁₉	1	2	yes	—
422	C₁₉	#62376	1	1	yes	characteristic, direct product factor, Sylow
423	C₂×Q₈	—	2	4	no	—
424	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
425	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
426	C₂×D₄	—	2	4	no	—
427	C₂×D₄	—	2	4	no	—
428	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	2	4	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
433	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
434	Q₁₆	—	4	2	no	—
435	Q₁₆	—	4	2	no	—
436	SD₁₆	—	2	8	no	—
437	SD₁₆	—	4	4	no	—
438	D₈	—	4	2	no	—
439	D₈	—	4	2	no	—
440	M₁₆	—	4	1	no	—
441	M₁₆	—	4	1	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	4	1	no	—
444	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
445	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
446	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
447	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
448	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
449	C₄⋊C₄	—	2	4	no	—
450	C₄⋊C₄	—	2	4	no	—
451	C₄⋊C₄	—	2	4	no	—
452	C₄⋊C₄	—	2	4	no	—
453	C₄⋊C₄	—	2	4	no	—
454	C₄⋊C₄	—	2	4	no	—
455	C₄⋊C₄	—	2	4	no	—
456	C₄⋊C₄	—	2	4	no	—
457	C₄⋊C₄	—	2	4	no	—
458	C₄⋊C₄	—	2	4	no	—
459	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
460	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
461	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
462	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
463	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
464	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
465	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
466	C₂²⋊C₄	—	2	4	no	—
467	C₂²⋊C₄	—	2	4	no	—
468	C₂²⋊C₄	—	2	4	no	—
469	C₂²⋊C₄	—	2	4	no	—
470	C₂²⋊C₄	—	2	4	no	—
471	C₂²⋊C₄	—	2	4	no	—
472	C₂²⋊C₄	—	2	4	no	—
473	C₂²⋊C₄	—	2	4	no	—
474	C₂²⋊C₄	—	2	4	no	—
475	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
476	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
477	C₄²	—	2	4	no	—
478	C₄²	—	2	4	no	—
479	C₄²	—	2	4	no	—
480	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
481	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
482	C₄²	C₂⁴×C₁₉	1	2	yes	—
483	C₄²	C₂⁴×C₁₉	1	2	yes	—
484	C₄²	C₂⁴×C₁₉	1	2	yes	—
485	C₂³	—	2	4	no	—
486	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
487	Q₈	—	2	4	no	—
488	Q₈	—	2	4	no	—
489	Q₈	—	4	4	no	—
490	Q₈	—	8	4	no	—
491	D₄	—	2	4	no	—
492	D₄	—	2	4	no	—
493	D₄	—	8	4	no	—
494	D₄	—	8	4	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	8	4	no	—
502	C₂×C₄	—	8	4	no	—
503	C₂×C₄	—	8	4	no	—
504	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
505	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
506	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
507	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
508	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
509	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
510	C₈	—	2	1	no	—
511	C₈	—	2	2	no	—
512	C₈	—	2	2	no	—
513	C₈	—	2	2	no	—
514	C₈	C₁₉×2₋¹⁺⁴	1	2	yes	—
515	C₂²	—	2	1	no	—
516	C₂²	—	2	2	no	—
517	C₂²	—	4	4	no	—
518	C₂²	—	4	4	no	—
519	C₂²	—	4	4	no	—
520	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
521	C₄	—	2	1	no	—
522	C₄	—	2	2	no	—
523	C₄	—	2	2	no	—
524	C₄	—	2	4	no	—
525	C₄	—	2	4	no	—
526	C₄	—	4	4	no	—
527	C₄	—	4	4	no	—
528	C₄	—	4	4	no	—
529	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
530	C₄	C₁₉×#585	1	1	yes	characteristic
531	C₂	—	4	1	no	—
532	C₂	—	8	4	no	—
533	C₂	C₁₉×#3497	1	1	yes	characteristic
534	C₂	C₁₉×#3584	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₁₉×#3259	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3557	C₂	semidirect
2. C₁₉×#3394	C₂	semidirect
3. C₁₉×#3381	C₂	semidirect
4. C₁₉×#3377	C₂	semidirect
5. C₁₉×#3370	C₂	semidirect
6. C₁₉×#3262	C₂	semidirect
7. C₁₉×#3261	C₂	semidirect
9. C₁₉×#3256	C₂	semidirect
10. C₁₉×#3174	C₂	semidirect
11. C₁₉×#3173	C₂	semidirect
12. C₁₉×#3168	C₂	semidirect
13. C₁₉×#2960	C₂	semidirect
217. #62376	C₁₉	direct (N × H)
248. #3557	C₂×C₁₉	semidirect
249. #3394	C₂×C₁₉	semidirect
250. #3381	C₂×C₁₉	semidirect
251. #3377	C₂×C₁₉	semidirect
252. #3370	C₂×C₁₉	semidirect
253. #3262	C₂×C₁₉	semidirect
254. #3261	C₂×C₁₉	semidirect
256. #3256	C₂×C₁₉	semidirect
257. #3174	C₂×C₁₉	semidirect
258. #3173	C₂×C₁₉	semidirect
259. #3168	C₂×C₁₉	semidirect
260. #2960	C₂×C₁₉	semidirect
422. C₁₉	#62376	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×#3557	2
C₁₉×#3394	2
C₁₉×#3381	2
C₁₉×#3377	2
C₁₉×#3370	2
C₁₉×#3262	2
C₁₉×#3261	2
C₁₉×#3259	2
C₁₉×#3256	2
C₁₉×#3174	2
C₁₉×#3173	2
C₁₉×#3168	2
C₁₉×#2960	2
#62376	19

Subgroups — C19×#62376 #18068335

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62376 #18068335