Subgroups — C₁₉×#62377 #18068336

Order 4864.

1628 conjugacy classes of subgroups.

The subgroup lattice has 592 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×#3396	C₂	1	2	yes	maximal, complemented
3	C₁₉×#3393	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3383	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3380	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3376	C₂	1	4	yes	maximal, complemented
7	C₁₉×#3371	C₂	1	4	yes	maximal, complemented
8	C₁₉×#3263	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3260	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3256	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3177	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#3176	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#3175	C₂	1	2	yes	maximal, complemented
14	C₁₉×#3168	C₂	1	2	yes	maximal, complemented
15	C₁₉×#2960	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#563	—	2	4	no	—
17	C₁₉×#559	C₂²	1	4	yes	—
18	C₁₉×#557	C₂²	1	4	yes	—
19	C₁₉×#556	C₂²	1	4	yes	—
20	C₁₉×#554	C₂²	1	4	yes	—
21	C₁₉×#552	—	2	4	no	—
22	C₁₉×#542	—	2	4	no	—
23	C₁₉×#542	C₂²	1	4	yes	—
24	C₁₉×#541	C₂²	1	2	yes	—
25	C₁₉×#540	C₂²	1	2	yes	—
26	C₁₉×#539	—	2	4	no	—
27	C₁₉×#533	C₂²	1	1	yes	characteristic
28	C₁₉×#529	C₂²	1	4	yes	—
29	C₁₉×#500	C₂²	1	2	yes	—
30	C₁₉×#499	C₂²	1	2	yes	—
31	C₁₉×#499	C₂²	1	1	yes	characteristic
32	C₁₉×#499	C₂²	1	1	yes	characteristic
33	C₁₉×#495	C₂²	1	2	yes	—
34	C₁₉×#495	C₂²	1	2	yes	—
35	C₁₉×#494	C₂²	1	1	yes	characteristic
36	C₁₉×#493	C₂²	1	1	yes	characteristic
37	C₁₉×#491	C₂²	1	2	yes	—
38	C₁₉×#490	C₂²	1	2	yes	—
39	C₁₉×#489	C₂²	1	4	yes	—
40	C₁₉×#488	C₂²	1	4	yes	—
41	C₁₉×#479	C₂²	1	4	yes	—
42	C₁₉×#479	C₂²	1	4	yes	—
43	C₁₉×#478	C₂²	1	4	yes	—
44	C₁₉×#478	C₂²	1	4	yes	—
45	C₁₉×#476	C₂²	1	4	yes	—
46	C₁₉×#475	C₂²	1	4	yes	—
47	C₁₉×#470	C₂²	1	2	yes	—
48	C₁₉×#469	C₂²	1	2	yes	—
49	C₁₉×#468	C₂²	1	4	yes	—
50	C₁₉×#467	C₂²	1	2	yes	—
51	C₁₉×#466	C₂²	1	2	yes	—
52	C₁₉×#465	C₂²	1	4	yes	—
53	C₁₉×#464	C₂²	1	4	yes	—
54	C₁₉×#464	C₂²	1	4	yes	—
55	C₁₉×#463	C₂²	1	4	yes	—
56	C₁₉×#463	C₂²	1	4	yes	—
57	C₁₉×#461	C₂²	1	4	yes	—
58	C₁₉×#460	C₂²	1	4	yes	—
59	C₁₉×#446	C₂²	1	2	yes	—
60	C₁₉×#446	C₂²	1	2	yes	—
61	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
62	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
63	C₁₉×#442	C₂²	1	2	yes	—
64	C₁₉×#441	C₂²	1	2	yes	—
65	C₁₉×#440	C₂²	1	4	yes	—
66	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
67	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
68	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
69	C₄×SD₁₆×C₁₉	C₂²	1	4	yes	—
70	C₄×D₈×C₁₉	C₂²	1	2	yes	—
71	C₄×D₈×C₁₉	C₂²	1	2	yes	—
72	C₄×D₈×C₁₉	C₂²	1	2	yes	—
73	C₁₉×#424	C₂²	1	1	yes	characteristic
74	C₁₉×#424	C₂²	1	1	yes	characteristic
75	C₁₉×#423	C₂²	1	1	yes	characteristic
76	C₁₉×#405	C₂²	1	1	yes	characteristic
77	C₁₉×#405	C₂²	1	1	yes	characteristic
78	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
79	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
80	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
81	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
82	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
83	C₂×D₈×C₁₉	C₂³	1	2	yes	—
84	C₂×D₈×C₁₉	C₂³	1	2	yes	—
85	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
89	C₁₉×C₄⋊Q₈	—	2	4	no	—
90	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
91	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
92	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
93	C₁₉×#127	C₂³	1	2	yes	—
94	C₁₉×#126	—	2	4	no	—
95	C₁₉×#126	—	2	4	no	—
96	C₁₉×#126	—	2	4	no	—
97	C₁₉×#126	—	2	4	no	—
98	C₁₉×#126	—	2	4	no	—
99	C₁₉×#125	—	2	4	no	—
100	C₁₉×#125	—	2	4	no	—
101	C₁₉×#125	—	2	4	no	—
102	C₁₉×#125	D₄	1	2	yes	—
103	C₁₉×#125	C₂³	1	2	yes	—
104	C₁₉×#125	C₂³	1	4	yes	—
105	C₁₉×#125	C₂³	1	2	yes	—
106	C₁₉×#124	—	2	4	no	—
107	C₁₉×#124	—	2	4	no	—
108	C₁₉×#124	C₂³	1	4	yes	—
109	C₁₉×#124	C₂³	1	4	yes	—
110	C₁₉×#123	—	2	4	no	—
111	C₁₉×#123	—	2	4	no	—
112	C₁₉×#123	—	2	4	no	—
113	C₁₉×#123	—	2	4	no	—
114	C₁₉×#123	—	2	4	no	—
115	C₁₉×C₂²⋊Q₈	—	2	4	no	—
116	C₁₉×C₂²⋊Q₈	—	2	4	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	D₄	1	2	yes	—
121	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
122	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
123	C₁₉×#121	—	2	4	no	—
124	C₁₉×#121	C₂³	1	4	yes	—
125	C₄×Q₈×C₁₉	—	2	4	no	—
126	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
127	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
128	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
129	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
130	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
131	C₄×D₄×C₁₉	—	2	4	no	—
132	C₄×D₄×C₁₉	—	2	4	no	—
133	C₄×D₄×C₁₉	C₂³	1	4	yes	—
134	C₄×D₄×C₁₉	C₂³	1	4	yes	—
135	C₄×D₄×C₁₉	C₂³	1	4	yes	—
136	C₁₉×#117	—	2	4	no	—
137	C₁₉×#117	—	2	4	no	—
138	C₁₉×#117	C₂³	1	1	yes	characteristic
139	C₁₉×#117	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
141	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
142	C₁₉×#107	C₂³	1	2	yes	—
143	C₁₉×#107	C₂³	1	2	yes	—
144	C₁₉×#107	C₂³	1	4	yes	—
145	C₁₉×#106	C₂³	1	4	yes	—
146	C₁₉×#106	C₂³	1	2	yes	—
147	C₁₉×#106	C₂³	1	2	yes	—
148	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
149	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
150	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
151	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
152	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
153	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
154	C₁₉×#103	C₂³	1	4	yes	—
155	C₁₉×#103	C₂³	1	4	yes	—
156	C₁₉×#103	C₂³	1	4	yes	—
157	C₁₉×#103	C₂³	1	4	yes	—
158	C₁₉×#102	C₂³	1	4	yes	—
159	C₁₉×#102	C₂³	1	4	yes	—
160	C₁₉×#102	C₂³	1	4	yes	—
161	C₁₉×#102	C₂³	1	4	yes	—
162	C₁₉×#97	C₂³	1	2	yes	—
163	C₁₉×#97	C₂³	1	1	yes	characteristic
164	C₁₉×#97	C₂³	1	1	yes	characteristic
165	C₄×C₈×C₁₉	C₂³	1	2	yes	—
166	C₄×C₈×C₁₉	C₂³	1	2	yes	—
167	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
168	C₄×C₈×C₁₉	C₂³	1	2	yes	—
169	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
170	C₂×Q₈×C₁₉	—	2	4	no	—
171	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
172	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
173	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
174	C₂×D₄×C₁₉	—	2	4	no	—
175	C₂×D₄×C₁₉	—	2	4	no	—
176	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
177	C₂²×C₄×C₁₉	—	2	4	no	—
178	C₂²×C₄×C₁₉	—	2	4	no	—
179	C₂²×C₄×C₁₉	—	2	4	no	—
180	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
181	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
182	Q₁₆×C₁₉	—	2	4	no	—
183	Q₁₆×C₁₉	—	4	2	no	—
184	SD₁₆×C₁₉	—	4	4	no	—
185	SD₁₆×C₁₉	—	4	4	no	—
186	D₈×C₁₉	—	2	4	no	—
187	D₈×C₁₉	—	4	2	no	—
188	M₁₆×C₁₉	—	4	1	no	—
189	M₁₆×C₁₉	—	4	1	no	—
190	C₂×C₈×C₁₉	—	2	2	no	—
191	C₂×C₈×C₁₉	—	4	1	no	—
192	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
193	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
194	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
195	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
196	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
197	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
198	C₄⋊C₄×C₁₉	—	2	4	no	—
199	C₄⋊C₄×C₁₉	—	2	4	no	—
200	C₄⋊C₄×C₁₉	—	2	4	no	—
201	C₄⋊C₄×C₁₉	—	2	4	no	—
202	C₄⋊C₄×C₁₉	—	2	4	no	—
203	C₄⋊C₄×C₁₉	—	2	4	no	—
204	C₄⋊C₄×C₁₉	—	2	4	no	—
205	C₄⋊C₄×C₁₉	—	2	4	no	—
206	C₄⋊C₄×C₁₉	—	2	4	no	—
207	C₄⋊C₄×C₁₉	—	2	4	no	—
208	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
209	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
210	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
211	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
212	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
213	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
214	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
215	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
216	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
217	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
218	C₂²⋊C₄×C₁₉	—	2	4	no	—
219	C₂²⋊C₄×C₁₉	—	2	4	no	—
220	C₂²⋊C₄×C₁₉	—	2	4	no	—
221	C₂²⋊C₄×C₁₉	—	2	4	no	—
222	C₂²⋊C₄×C₁₉	—	2	4	no	—
223	C₂²⋊C₄×C₁₉	—	2	4	no	—
224	C₂²⋊C₄×C₁₉	—	2	4	no	—
225	C₂²⋊C₄×C₁₉	—	2	4	no	—
226	C₂²⋊C₄×C₁₉	—	2	4	no	—
227	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
228	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
229	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
230	C₄²×C₁₉	—	2	4	no	—
231	C₄²×C₁₉	—	2	4	no	—
232	C₄²×C₁₉	—	2	4	no	—
233	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
234	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
235	C₄²×C₁₉	C₂⁴	1	2	yes	—
236	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
237	C₄²×C₁₉	C₂⁴	1	2	yes	—
238	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
239	#62377	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
240	C₂³×C₁₉	—	2	4	no	—
241	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
242	Q₈×C₁₉	—	2	4	no	—
243	Q₈×C₁₉	—	2	4	no	—
244	Q₈×C₁₉	—	4	2	no	—
245	Q₈×C₁₉	—	4	2	no	—
246	Q₈×C₁₉	—	8	4	no	—
247	D₄×C₁₉	—	2	4	no	—
248	D₄×C₁₉	—	2	4	no	—
249	D₄×C₁₉	—	8	4	no	—
250	D₄×C₁₉	—	8	4	no	—
251	C₂×C₄×C₁₉	—	2	1	no	—
252	C₂×C₄×C₁₉	—	2	1	no	—
253	C₂×C₄×C₁₉	—	2	4	no	—
254	C₂×C₄×C₁₉	—	2	4	no	—
255	C₂×C₄×C₁₉	—	2	4	no	—
256	C₂×C₄×C₁₉	—	4	2	no	—
257	C₂×C₄×C₁₉	—	8	4	no	—
258	C₂×C₄×C₁₉	—	8	4	no	—
259	C₂×C₄×C₁₉	—	8	4	no	—
260	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
261	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
262	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
263	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
265	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
266	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
267	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
268	C₈×C₁₉	—	2	1	no	—
269	C₈×C₁₉	—	2	2	no	—
270	C₈×C₁₉	—	2	1	no	—
271	C₈×C₁₉	—	2	2	no	—
272	C₈×C₁₉	—	2	1	no	—
273	C₈×C₁₉	2₋¹⁺⁴	1	2	yes	—
274	#3557	C₂×C₁₉	1	2	yes	complemented
275	#3396	C₂×C₁₉	1	2	yes	complemented
276	#3393	C₂×C₁₉	1	2	yes	complemented
277	#3383	C₂×C₁₉	1	2	yes	complemented
278	#3380	C₂×C₁₉	1	2	yes	complemented
279	#3376	C₂×C₁₉	1	4	yes	complemented
280	#3371	C₂×C₁₉	1	4	yes	complemented
281	#3263	C₂×C₁₉	1	2	yes	complemented
282	#3260	C₂×C₁₉	1	2	yes	complemented
283	#3256	C₂×C₁₉	1	2	yes	complemented
284	#3177	C₂×C₁₉	1	1	yes	characteristic, complemented
285	#3176	C₂×C₁₉	1	1	yes	characteristic
286	#3175	C₂×C₁₉	1	2	yes	complemented
287	#3168	C₂×C₁₉	1	2	yes	complemented
288	#2960	C₂×C₁₉	1	1	yes	characteristic, complemented
289	C₂²×C₁₉	—	2	2	no	—
290	C₂²×C₁₉	—	2	1	no	—
291	C₂²×C₁₉	—	4	4	no	—
292	C₂²×C₁₉	—	4	4	no	—
293	C₂²×C₁₉	—	4	4	no	—
294	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
295	C₄×C₁₉	—	2	2	no	—
296	C₄×C₁₉	—	2	2	no	—
297	C₄×C₁₉	—	2	2	no	—
298	C₄×C₁₉	—	2	2	no	—
299	C₄×C₁₉	—	2	2	no	—
300	C₄×C₁₉	—	2	2	no	—
301	C₄×C₁₉	—	2	1	no	—
302	C₄×C₁₉	—	4	4	no	—
303	C₄×C₁₉	—	4	4	no	—
304	C₄×C₁₉	—	4	4	no	—
305	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
306	C₄×C₁₉	#585	1	1	yes	characteristic
307	#563	—	2	4	no	—
308	#559	C₂²×C₁₉	1	4	yes	—
309	#557	C₂²×C₁₉	1	4	yes	—
310	#556	C₂²×C₁₉	1	4	yes	—
311	#554	C₂²×C₁₉	1	4	yes	—
312	#552	—	2	4	no	—
313	#542	—	2	4	no	—
314	#542	C₂²×C₁₉	1	4	yes	—
315	#541	C₂²×C₁₉	1	2	yes	—
316	#540	C₂²×C₁₉	1	2	yes	—
317	#539	—	2	4	no	—
318	#533	C₂²×C₁₉	1	1	yes	characteristic
319	#529	C₂²×C₁₉	1	4	yes	—
320	#500	C₂²×C₁₉	1	2	yes	—
321	#499	C₂²×C₁₉	1	1	yes	characteristic
322	#499	C₂²×C₁₉	1	2	yes	—
323	#499	C₂²×C₁₉	1	1	yes	characteristic
324	#495	C₂²×C₁₉	1	2	yes	—
325	#495	C₂²×C₁₉	1	2	yes	—
326	#494	C₂²×C₁₉	1	1	yes	characteristic
327	#493	C₂²×C₁₉	1	1	yes	characteristic
328	#491	C₂²×C₁₉	1	2	yes	—
329	#490	C₂²×C₁₉	1	2	yes	—
330	#489	C₂²×C₁₉	1	4	yes	—
331	#488	C₂²×C₁₉	1	4	yes	—
332	#479	C₂²×C₁₉	1	4	yes	—
333	#479	C₂²×C₁₉	1	4	yes	—
334	#478	C₂²×C₁₉	1	4	yes	—
335	#478	C₂²×C₁₉	1	4	yes	—
336	#476	C₂²×C₁₉	1	4	yes	—
337	#475	C₂²×C₁₉	1	4	yes	—
338	#470	C₂²×C₁₉	1	2	yes	—
339	#469	C₂²×C₁₉	1	2	yes	—
340	#468	C₂²×C₁₉	1	4	yes	—
341	#467	C₂²×C₁₉	1	2	yes	—
342	#466	C₂²×C₁₉	1	2	yes	—
343	#465	C₂²×C₁₉	1	4	yes	—
344	#464	C₂²×C₁₉	1	4	yes	—
345	#464	C₂²×C₁₉	1	4	yes	—
346	#463	C₂²×C₁₉	1	4	yes	—
347	#463	C₂²×C₁₉	1	4	yes	—
348	#461	C₂²×C₁₉	1	4	yes	—
349	#460	C₂²×C₁₉	1	4	yes	—
350	#446	C₂²×C₁₉	1	2	yes	—
351	#446	C₂²×C₁₉	1	2	yes	—
352	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
353	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
354	#442	C₂²×C₁₉	1	2	yes	—
355	#441	C₂²×C₁₉	1	2	yes	—
356	#440	C₂²×C₁₉	1	4	yes	—
357	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
358	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
359	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
360	C₄×SD₁₆	C₂²×C₁₉	1	4	yes	—
361	C₄×D₈	C₂²×C₁₉	1	2	yes	—
362	C₄×D₈	C₂²×C₁₉	1	2	yes	—
363	C₄×D₈	C₂²×C₁₉	1	2	yes	—
364	#424	C₂²×C₁₉	1	1	yes	characteristic
365	#424	C₂²×C₁₉	1	1	yes	characteristic
366	#423	C₂²×C₁₉	1	1	yes	characteristic
367	#405	C₂²×C₁₉	1	1	yes	characteristic
368	#405	C₂²×C₁₉	1	1	yes	characteristic
369	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
370	C₂×C₁₉	—	4	1	no	—
371	C₂×C₁₉	—	8	4	no	—
372	C₂×C₁₉	#3497	1	1	yes	characteristic
373	C₂×C₁₉	#3584	1	2	yes	—
374	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
375	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
376	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
377	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
378	C₂×D₈	C₂³×C₁₉	1	2	yes	—
379	C₂×D₈	C₂³×C₁₉	1	2	yes	—
380	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
381	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
382	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
383	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
384	C₄⋊Q₈	—	2	4	no	—
385	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
386	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
387	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
388	#127	C₂³×C₁₉	1	2	yes	—
389	#126	—	2	4	no	—
390	#126	—	2	4	no	—
391	#126	—	2	4	no	—
392	#126	—	2	4	no	—
393	#126	—	2	4	no	—
394	#125	—	2	4	no	—
395	#125	—	2	4	no	—
396	#125	—	2	4	no	—
397	#125	D₄×C₁₉	1	2	yes	—
398	#125	C₂³×C₁₉	1	4	yes	—
399	#125	C₂³×C₁₉	1	2	yes	—
400	#125	C₂³×C₁₉	1	2	yes	—
401	#124	—	2	4	no	—
402	#124	—	2	4	no	—
403	#124	C₂³×C₁₉	1	4	yes	—
404	#124	C₂³×C₁₉	1	4	yes	—
405	#123	—	2	4	no	—
406	#123	—	2	4	no	—
407	#123	—	2	4	no	—
408	#123	—	2	4	no	—
409	#123	—	2	4	no	—
410	C₂²⋊Q₈	—	2	4	no	—
411	C₂²⋊Q₈	—	2	4	no	—
412	C₂²⋊Q₈	—	2	4	no	—
413	C₂²⋊Q₈	—	2	4	no	—
414	C₂²⋊Q₈	—	2	4	no	—
415	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
416	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
417	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
418	#121	—	2	4	no	—
419	#121	C₂³×C₁₉	1	4	yes	—
420	C₄×Q₈	—	2	4	no	—
421	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
422	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
423	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
424	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
425	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
426	C₄×D₄	—	2	4	no	—
427	C₄×D₄	—	2	4	no	—
428	C₄×D₄	C₂³×C₁₉	1	4	yes	—
429	C₄×D₄	C₂³×C₁₉	1	4	yes	—
430	C₄×D₄	C₂³×C₁₉	1	4	yes	—
431	#117	—	2	4	no	—
432	#117	—	2	4	no	—
433	#117	C₂³×C₁₉	1	1	yes	characteristic
434	#117	C₂³×C₁₉	1	1	yes	characteristic
435	C₂×C₄⋊C₄	—	2	4	no	—
436	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
437	#107	C₂³×C₁₉	1	2	yes	—
438	#107	C₂³×C₁₉	1	2	yes	—
439	#107	C₂³×C₁₉	1	4	yes	—
440	#106	C₂³×C₁₉	1	4	yes	—
441	#106	C₂³×C₁₉	1	2	yes	—
442	#106	C₂³×C₁₉	1	2	yes	—
443	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
444	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
445	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
446	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
447	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
448	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
449	#103	C₂³×C₁₉	1	4	yes	—
450	#103	C₂³×C₁₉	1	4	yes	—
451	#103	C₂³×C₁₉	1	4	yes	—
452	#103	C₂³×C₁₉	1	4	yes	—
453	#102	C₂³×C₁₉	1	4	yes	—
454	#102	C₂³×C₁₉	1	4	yes	—
455	#102	C₂³×C₁₉	1	4	yes	—
456	#102	C₂³×C₁₉	1	4	yes	—
457	#97	C₂³×C₁₉	1	2	yes	—
458	#97	C₂³×C₁₉	1	1	yes	characteristic
459	#97	C₂³×C₁₉	1	1	yes	characteristic
460	C₄×C₈	C₂³×C₁₉	1	2	yes	—
461	C₄×C₈	C₂³×C₁₉	1	2	yes	—
462	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
463	C₄×C₈	C₂³×C₁₉	1	2	yes	—
464	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
465	C₁₉	#62377	1	1	yes	characteristic, direct product factor, Sylow
466	C₂×Q₈	—	2	4	no	—
467	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
468	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
469	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
470	C₂×D₄	—	2	4	no	—
471	C₂×D₄	—	2	4	no	—
472	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	4	no	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
477	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
478	Q₁₆	—	2	4	no	—
479	Q₁₆	—	4	2	no	—
480	SD₁₆	—	4	4	no	—
481	SD₁₆	—	4	4	no	—
482	D₈	—	2	4	no	—
483	D₈	—	4	2	no	—
484	M₁₆	—	4	1	no	—
485	M₁₆	—	4	1	no	—
486	C₂×C₈	—	2	2	no	—
487	C₂×C₈	—	4	1	no	—
488	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
489	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
490	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
491	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
492	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
493	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
494	C₄⋊C₄	—	2	4	no	—
495	C₄⋊C₄	—	2	4	no	—
496	C₄⋊C₄	—	2	4	no	—
497	C₄⋊C₄	—	2	4	no	—
498	C₄⋊C₄	—	2	4	no	—
499	C₄⋊C₄	—	2	4	no	—
500	C₄⋊C₄	—	2	4	no	—
501	C₄⋊C₄	—	2	4	no	—
502	C₄⋊C₄	—	2	4	no	—
503	C₄⋊C₄	—	2	4	no	—
504	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
505	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
506	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
507	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
508	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
509	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
510	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
511	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
512	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
513	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
514	C₂²⋊C₄	—	2	4	no	—
515	C₂²⋊C₄	—	2	4	no	—
516	C₂²⋊C₄	—	2	4	no	—
517	C₂²⋊C₄	—	2	4	no	—
518	C₂²⋊C₄	—	2	4	no	—
519	C₂²⋊C₄	—	2	4	no	—
520	C₂²⋊C₄	—	2	4	no	—
521	C₂²⋊C₄	—	2	4	no	—
522	C₂²⋊C₄	—	2	4	no	—
523	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
524	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
525	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
526	C₄²	—	2	4	no	—
527	C₄²	—	2	4	no	—
528	C₄²	—	2	4	no	—
529	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
530	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
531	C₄²	C₂⁴×C₁₉	1	2	yes	—
532	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
533	C₄²	C₂⁴×C₁₉	1	2	yes	—
534	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
535	C₂³	—	2	4	no	—
536	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
537	Q₈	—	2	4	no	—
538	Q₈	—	2	4	no	—
539	Q₈	—	4	2	no	—
540	Q₈	—	4	2	no	—
541	Q₈	—	8	4	no	—
542	D₄	—	2	4	no	—
543	D₄	—	2	4	no	—
544	D₄	—	8	4	no	—
545	D₄	—	8	4	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	4	no	—
550	C₂×C₄	—	2	4	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	8	4	no	—
553	C₂×C₄	—	8	4	no	—
554	C₂×C₄	—	8	4	no	—
555	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
556	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
557	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
558	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
559	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
560	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
561	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
562	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
563	C₈	—	2	1	no	—
564	C₈	—	2	2	no	—
565	C₈	—	2	1	no	—
566	C₈	—	2	2	no	—
567	C₈	—	2	1	no	—
568	C₈	C₁₉×2₋¹⁺⁴	1	2	yes	—
569	C₂²	—	2	1	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	4	4	no	—
572	C₂²	—	4	4	no	—
573	C₂²	—	4	4	no	—
574	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
575	C₄	—	2	1	no	—
576	C₄	—	2	2	no	—
577	C₄	—	2	2	no	—
578	C₄	—	2	2	no	—
579	C₄	—	2	2	no	—
580	C₄	—	2	2	no	—
581	C₄	—	2	2	no	—
582	C₄	—	4	4	no	—
583	C₄	—	4	4	no	—
584	C₄	—	4	4	no	—
585	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
586	C₄	C₁₉×#585	1	1	yes	characteristic
587	C₂	—	4	1	no	—
588	C₂	—	8	4	no	—
589	C₂	C₁₉×#3497	1	1	yes	characteristic
590	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×#3176	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×#3396	C₂	semidirect
3. C₁₉×#3393	C₂	semidirect
4. C₁₉×#3383	C₂	semidirect
5. C₁₉×#3380	C₂	semidirect
6. C₁₉×#3376	C₂	semidirect
7. C₁₉×#3371	C₂	semidirect
8. C₁₉×#3263	C₂	semidirect
9. C₁₉×#3260	C₂	semidirect
10. C₁₉×#3256	C₂	semidirect
11. C₁₉×#3177	C₂	semidirect
13. C₁₉×#3175	C₂	semidirect
14. C₁₉×#3168	C₂	semidirect
15. C₁₉×#2960	C₂	semidirect
239. #62377	C₁₉	direct (N × H)
274. #3557	C₂×C₁₉	semidirect
275. #3396	C₂×C₁₉	semidirect
276. #3393	C₂×C₁₉	semidirect
277. #3383	C₂×C₁₉	semidirect
278. #3380	C₂×C₁₉	semidirect
279. #3376	C₂×C₁₉	semidirect
280. #3371	C₂×C₁₉	semidirect
281. #3263	C₂×C₁₉	semidirect
282. #3260	C₂×C₁₉	semidirect
283. #3256	C₂×C₁₉	semidirect
284. #3177	C₂×C₁₉	semidirect
286. #3175	C₂×C₁₉	semidirect
287. #3168	C₂×C₁₉	semidirect
288. #2960	C₂×C₁₉	semidirect
465. C₁₉	#62377	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×#3396	2
C₁₉×#3393	2
C₁₉×#3383	2
C₁₉×#3380	2
C₁₉×#3376	2
C₁₉×#3371	2
C₁₉×#3263	2
C₁₉×#3260	2
C₁₉×#3256	2
C₁₉×#3177	2
C₁₉×#3176	2
C₁₉×#3175	2
C₁₉×#3168	2
C₁₉×#2960	2
#62377	19

Subgroups — C19×#62377 #18068336

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62377 #18068336