Subgroups — C₁₉×#62379 #18068338

Order 4864.

1720 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3554	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3396	C₂	1	2	yes	maximal, complemented
3	C₁₉×#3396	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3391	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3383	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#3380	C₂	1	2	yes	maximal, complemented
7	Q₈×D₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#3373	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3370	C₂	1	4	yes	maximal, complemented
10	C₁₉×#3368	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3257	C₂	1	4	yes	maximal, complemented
12	C₁₉×#3251	C₂	1	2	yes	maximal, complemented
13	C₁₉×#3176	C₂	1	2	yes	maximal, complemented
14	C₁₉×#3175	C₂	1	2	yes	maximal, complemented
15	C₁₉×#3169	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#3168	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₉×#2960	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₉×#562	—	2	4	no	—
19	C₁₉×#559	C₂²	1	4	yes	—
20	C₁₉×#559	C₂²	1	2	yes	—
21	C₁₉×#557	C₂²	1	2	yes	—
22	C₁₉×#554	C₂²	1	4	yes	—
23	C₁₉×#550	C₂²	1	2	yes	—
24	D₄×Q₈×C₁₉	C₂²	1	2	yes	—
25	C₁₉×#548	—	2	2	no	—
26	C₁₉×#547	—	2	2	no	—
27	C₁₉×#542	—	2	2	no	—
28	C₁₉×#542	C₂²	1	4	yes	—
29	C₁₉×#540	C₂²	1	4	yes	—
30	C₁₉×#539	—	2	4	no	—
31	C₁₉×#536	—	2	2	no	—
32	C₁₉×#533	C₂²	1	1	yes	characteristic
33	C₁₉×#532	C₂²	1	2	yes	—
34	C₁₉×#529	C₂²	1	2	yes	—
35	C₁₉×#500	C₂²	1	1	yes	characteristic
36	C₁₉×#500	C₂²	1	2	yes	—
37	C₁₉×#499	C₂²	1	1	yes	characteristic
38	C₁₉×#499	C₂²	1	2	yes	—
39	C₁₉×#495	C₂²	1	1	yes	characteristic
40	C₁₉×#495	C₂²	1	2	yes	—
41	C₁₉×#493	C₂²	1	1	yes	characteristic
42	C₁₉×#493	C₂²	1	2	yes	—
43	C₁₉×#490	C₂²	1	4	yes	—
44	C₁₉×#489	C₂²	1	4	yes	—
45	C₁₉×#488	C₂²	1	2	yes	—
46	C₁₉×#486	C₂²	1	2	yes	—
47	C₁₉×#479	C₂²	1	4	yes	—
48	C₁₉×#478	C₂²	1	4	yes	—
49	C₁₉×#478	C₂²	1	4	yes	—
50	C₁₉×#476	C₂²	1	4	yes	—
51	C₁₉×#475	C₂²	1	2	yes	—
52	C₁₉×#474	C₂²	1	2	yes	—
53	C₁₉×#474	C₂²	1	4	yes	—
54	C₁₉×#469	C₂²	1	4	yes	—
55	C₁₉×#468	C₂²	1	4	yes	—
56	C₁₉×#467	C₂²	1	1	yes	characteristic
57	C₁₉×#466	C₂²	1	1	yes	characteristic
58	C₁₉×#466	C₂²	1	2	yes	—
59	C₁₉×#466	C₂²	1	2	yes	—
60	C₁₉×#465	C₂²	1	2	yes	—
61	C₁₉×#463	C₂²	1	4	yes	—
62	C₁₉×#463	C₂²	1	4	yes	—
63	C₁₉×#463	C₂²	1	4	yes	—
64	C₁₉×#460	C₂²	1	2	yes	—
65	C₁₉×#460	C₂²	1	4	yes	—
66	C₁₉×#459	C₂²	1	2	yes	—
67	C₁₉×#459	C₂²	1	4	yes	—
68	C₁₉×#446	C₂²	1	1	yes	characteristic
69	C₁₉×#446	C₂²	1	2	yes	—
70	C₁₉×#446	C₂²	1	1	yes	characteristic
71	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
72	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
73	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
74	C₁₉×#442	C₂²	1	4	yes	—
75	C₁₉×#440	C₂²	1	4	yes	—
76	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
77	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
78	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	—
79	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
80	C₄×D₈×C₁₉	C₂²	1	2	yes	—
81	C₄×D₈×C₁₉	C₂²	1	2	yes	—
82	C₄×D₈×C₁₉	C₂²	1	2	yes	—
83	C₄×D₈×C₁₉	C₂²	1	2	yes	—
84	C₄×D₈×C₁₉	C₂²	1	2	yes	—
85	C₁₉×#424	C₂²	1	2	yes	—
86	C₁₉×#423	C₂²	1	1	yes	characteristic
87	C₁₉×#405	C₂²	1	2	yes	—
88	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
89	C₂×#41×C₁₉	—	2	2	no	—
90	C₂×#41×C₁₉	—	2	2	no	—
91	C₂²×Q₈×C₁₉	—	2	2	no	—
92	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
93	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
94	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
95	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
96	C₂×D₈×C₁₉	C₂³	1	2	yes	—
97	C₂×D₈×C₁₉	C₂³	1	2	yes	—
98	C₂×D₈×C₁₉	C₂³	1	4	yes	—
99	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
100	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
102	C₁₉×C₄⋊Q₈	—	2	2	no	—
103	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
104	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
105	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
106	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
107	C₁₉×#127	C₂³	1	2	yes	—
108	C₁₉×#127	C₂³	1	4	yes	—
109	C₁₉×#126	—	2	4	no	—
110	C₁₉×#126	—	2	2	no	—
111	C₁₉×#125	—	2	4	no	—
112	C₁₉×#125	D₄	1	2	yes	—
113	C₁₉×#125	C₂³	1	2	yes	—
114	C₁₉×#125	C₂³	1	4	yes	—
115	C₁₉×#124	—	2	2	no	—
116	C₁₉×#124	—	2	4	no	—
117	C₁₉×#124	—	2	4	no	—
118	C₁₉×#124	—	2	2	no	—
119	C₁₉×#124	C₂³	1	2	yes	—
120	C₁₉×#124	C₂³	1	4	yes	—
121	C₁₉×#123	—	2	2	no	—
122	C₁₉×#123	—	2	4	no	—
123	C₁₉×#123	—	2	4	no	—
124	C₁₉×#123	—	2	4	no	—
125	C₁₉×#123	—	2	4	no	—
126	C₁₉×#123	—	2	4	no	—
127	C₁₉×#123	—	2	4	no	—
128	C₁₉×C₂²⋊Q₈	—	2	4	no	—
129	C₁₉×C₂²⋊Q₈	—	2	4	no	—
130	C₁₉×C₂²⋊Q₈	—	2	4	no	—
131	C₁₉×C₂²⋊Q₈	—	2	4	no	—
132	C₁₉×C₂²⋊Q₈	—	2	4	no	—
133	C₁₉×C₂²⋊Q₈	—	2	2	no	—
134	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
135	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
136	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
137	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
138	C₁₉×#121	—	2	2	no	—
139	C₁₉×#121	—	2	4	no	—
140	C₁₉×#121	—	2	2	no	—
141	C₁₉×#121	—	2	4	no	—
142	C₁₉×#121	—	2	4	no	—
143	C₁₉×#121	C₂³	1	2	yes	—
144	C₁₉×#121	C₂³	1	4	yes	—
145	C₄×Q₈×C₁₉	—	2	2	no	—
146	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
147	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
148	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
149	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
150	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
151	C₄×D₄×C₁₉	—	2	2	no	—
152	C₄×D₄×C₁₉	—	2	4	no	—
153	C₄×D₄×C₁₉	—	2	2	no	—
154	C₄×D₄×C₁₉	—	2	2	no	—
155	C₄×D₄×C₁₉	C₂³	1	4	yes	—
156	C₄×D₄×C₁₉	C₂³	1	2	yes	—
157	C₄×D₄×C₁₉	C₂³	1	4	yes	—
158	C₄×D₄×C₁₉	C₂³	1	4	yes	—
159	C₄×D₄×C₁₉	C₂³	1	4	yes	—
160	C₁₉×#117	—	2	2	no	—
161	C₁₉×#117	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
163	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
164	C₁₉×#107	C₂³	1	1	yes	characteristic
165	C₁₉×#107	C₂³	1	1	yes	characteristic
166	C₁₉×#107	C₂³	1	2	yes	—
167	C₁₉×#107	C₂³	1	2	yes	—
168	C₁₉×#107	C₂³	1	4	yes	—
169	C₁₉×#106	C₂³	1	2	yes	—
170	C₁₉×#106	C₂³	1	4	yes	—
171	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
172	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
173	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
174	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
175	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
176	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
177	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
178	C₁₉×#103	C₂³	1	2	yes	—
179	C₁₉×#103	C₂³	1	2	yes	—
180	C₁₉×#103	C₂³	1	4	yes	—
181	C₁₉×#102	C₂³	1	4	yes	—
182	C₁₉×#102	C₂³	1	2	yes	—
183	C₁₉×#102	C₂³	1	4	yes	—
184	C₁₉×#102	C₂³	1	4	yes	—
185	C₁₉×#102	C₂³	1	4	yes	—
186	C₁₉×#102	C₂³	1	4	yes	—
187	C₁₉×#102	C₂³	1	2	yes	—
188	C₁₉×#97	C₂³	1	2	yes	—
189	C₁₉×#97	C₂³	1	2	yes	—
190	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
191	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
192	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
193	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
194	C₄×C₈×C₁₉	C₂³	1	2	yes	—
195	C₄×C₈×C₁₉	C₂³	1	2	yes	—
196	#41×C₁₉	—	8	4	no	—
197	#41×C₁₉	—	8	4	no	—
198	C₂×Q₈×C₁₉	—	2	2	no	—
199	C₂×Q₈×C₁₉	—	2	4	no	—
200	C₂×Q₈×C₁₉	—	8	4	no	—
201	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
202	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
204	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
205	C₂×D₄×C₁₉	—	2	2	no	—
206	C₂×D₄×C₁₉	—	2	4	no	—
207	C₂×D₄×C₁₉	—	2	2	no	—
208	C₂×D₄×C₁₉	—	2	2	no	—
209	C₂×D₄×C₁₉	—	2	4	no	—
210	C₂×D₄×C₁₉	—	2	4	no	—
211	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
212	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₁₉	—	2	2	no	—
214	C₂²×C₄×C₁₉	—	2	4	no	—
215	C₂²×C₄×C₁₉	—	2	4	no	—
216	C₂²×C₄×C₁₉	—	2	4	no	—
217	C₂²×C₄×C₁₉	—	2	4	no	—
218	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
221	Q₁₆×C₁₉	—	2	2	no	—
222	SD₁₆×C₁₉	—	4	2	no	—
223	SD₁₆×C₁₉	—	4	4	no	—
224	D₈×C₁₉	—	2	2	no	—
225	D₈×C₁₉	—	2	4	no	—
226	D₈×C₁₉	—	4	2	no	—
227	D₈×C₁₉	—	4	4	no	—
228	M₁₆×C₁₉	—	4	2	no	—
229	C₂×C₈×C₁₉	—	2	2	no	—
230	C₂×C₈×C₁₉	—	4	1	no	—
231	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
232	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
233	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
234	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
235	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
236	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
237	C₄⋊C₄×C₁₉	—	2	2	no	—
238	C₄⋊C₄×C₁₉	—	2	4	no	—
239	C₄⋊C₄×C₁₉	—	2	4	no	—
240	C₄⋊C₄×C₁₉	—	2	2	no	—
241	C₄⋊C₄×C₁₉	—	2	2	no	—
242	C₄⋊C₄×C₁₉	—	2	2	no	—
243	C₄⋊C₄×C₁₉	—	2	4	no	—
244	C₄⋊C₄×C₁₉	—	2	4	no	—
245	C₄⋊C₄×C₁₉	—	2	2	no	—
246	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
247	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
248	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
249	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
250	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
251	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
252	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
253	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
254	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
255	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
256	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
257	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
258	C₂²⋊C₄×C₁₉	—	2	2	no	—
259	C₂²⋊C₄×C₁₉	—	2	2	no	—
260	C₂²⋊C₄×C₁₉	—	2	2	no	—
261	C₂²⋊C₄×C₁₉	—	2	2	no	—
262	C₂²⋊C₄×C₁₉	—	2	4	no	—
263	C₂²⋊C₄×C₁₉	—	2	4	no	—
264	C₂²⋊C₄×C₁₉	—	2	4	no	—
265	C₂²⋊C₄×C₁₉	—	2	2	no	—
266	C₂²⋊C₄×C₁₉	—	2	4	no	—
267	C₂²⋊C₄×C₁₉	—	2	4	no	—
268	C₂²⋊C₄×C₁₉	—	2	4	no	—
269	C₂²⋊C₄×C₁₉	—	2	4	no	—
270	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
271	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
272	C₄²×C₁₉	—	2	2	no	—
273	C₄²×C₁₉	—	2	4	no	—
274	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
275	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
276	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
277	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
278	C₄²×C₁₉	C₂⁴	1	2	yes	—
279	C₄²×C₁₉	C₂⁴	1	2	yes	—
280	#62379	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
281	C₂³×C₁₉	—	2	4	no	—
282	C₂³×C₁₉	—	2	2	no	—
283	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
284	Q₈×C₁₉	—	2	2	no	—
285	Q₈×C₁₉	—	2	2	no	—
286	Q₈×C₁₉	—	2	2	no	—
287	Q₈×C₁₉	—	2	2	no	—
288	Q₈×C₁₉	—	4	2	no	—
289	Q₈×C₁₉	—	4	4	no	—
290	Q₈×C₁₉	—	8	4	no	—
291	D₄×C₁₉	—	2	4	no	—
292	D₄×C₁₉	—	2	2	no	—
293	D₄×C₁₉	—	2	4	no	—
294	D₄×C₁₉	—	2	2	no	—
295	D₄×C₁₉	—	4	4	no	—
296	D₄×C₁₉	—	8	2	no	—
297	D₄×C₁₉	—	8	4	no	—
298	D₄×C₁₉	—	8	4	no	—
299	D₄×C₁₉	—	8	2	no	—
300	D₄×C₁₉	—	8	4	no	—
301	C₂×C₄×C₁₉	—	2	2	no	—
302	C₂×C₄×C₁₉	—	2	1	no	—
303	C₂×C₄×C₁₉	—	2	1	no	—
304	C₂×C₄×C₁₉	—	2	2	no	—
305	C₂×C₄×C₁₉	—	2	2	no	—
306	C₂×C₄×C₁₉	—	2	4	no	—
307	C₂×C₄×C₁₉	—	2	2	no	—
308	C₂×C₄×C₁₉	—	4	1	no	—
309	C₂×C₄×C₁₉	—	4	4	no	—
310	C₂×C₄×C₁₉	—	8	4	no	—
311	C₂×C₄×C₁₉	—	8	4	no	—
312	C₂×C₄×C₁₉	—	8	4	no	—
313	C₂×C₄×C₁₉	—	8	4	no	—
314	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
315	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
316	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
317	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
318	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
320	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
321	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
322	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
324	C₈×C₁₉	—	2	1	no	—
325	C₈×C₁₉	—	2	1	no	—
326	C₈×C₁₉	—	2	1	no	—
327	C₈×C₁₉	—	2	2	no	—
328	C₈×C₁₉	—	2	2	no	—
329	C₈×C₁₉	2₋¹⁺⁴	1	2	yes	—
330	#3554	C₂×C₁₉	1	2	yes	complemented
331	#3396	C₂×C₁₉	1	2	yes	complemented
332	#3396	C₂×C₁₉	1	1	yes	characteristic, complemented
333	#3391	C₂×C₁₉	1	1	yes	characteristic, complemented
334	#3383	C₂×C₁₉	1	1	yes	characteristic, complemented
335	#3380	C₂×C₁₉	1	2	yes	complemented
336	Q₈×D₈	C₂×C₁₉	1	1	yes	characteristic, complemented
337	#3373	C₂×C₁₉	1	2	yes	complemented
338	#3370	C₂×C₁₉	1	4	yes	complemented
339	#3368	C₂×C₁₉	1	2	yes	complemented
340	#3257	C₂×C₁₉	1	4	yes	complemented
341	#3251	C₂×C₁₉	1	2	yes	complemented
342	#3176	C₂×C₁₉	1	2	yes	complemented
343	#3175	C₂×C₁₉	1	2	yes	complemented
344	#3169	C₂×C₁₉	1	1	yes	characteristic, complemented
345	#3168	C₂×C₁₉	1	1	yes	characteristic, complemented
346	#2960	C₂×C₁₉	1	1	yes	characteristic, complemented
347	C₂²×C₁₉	—	2	1	no	—
348	C₂²×C₁₉	—	2	1	no	—
349	C₂²×C₁₉	—	2	1	no	—
350	C₂²×C₁₉	—	4	4	no	—
351	C₂²×C₁₉	—	4	2	no	—
352	C₂²×C₁₉	—	4	4	no	—
353	C₂²×C₁₉	—	4	2	no	—
354	C₂²×C₁₉	—	4	2	no	—
355	C₂²×C₁₉	—	4	4	no	—
356	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
357	C₄×C₁₉	—	2	1	no	—
358	C₄×C₁₉	—	2	1	no	—
359	C₄×C₁₉	—	2	2	no	—
360	C₄×C₁₉	—	2	2	no	—
361	C₄×C₁₉	—	2	1	no	—
362	C₄×C₁₉	—	2	1	no	—
363	C₄×C₁₉	—	2	2	no	—
364	C₄×C₁₉	—	2	2	no	—
365	C₄×C₁₉	—	4	2	no	—
366	C₄×C₁₉	—	4	2	no	—
367	C₄×C₁₉	—	4	2	no	—
368	C₄×C₁₉	—	4	4	no	—
369	C₄×C₁₉	#576	1	2	yes	—
370	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
371	C₄×C₁₉	#585	1	1	yes	characteristic
372	#562	—	2	4	no	—
373	#559	C₂²×C₁₉	1	4	yes	—
374	#559	C₂²×C₁₉	1	2	yes	—
375	#557	C₂²×C₁₉	1	2	yes	—
376	#554	C₂²×C₁₉	1	4	yes	—
377	#550	C₂²×C₁₉	1	2	yes	—
378	D₄×Q₈	C₂²×C₁₉	1	2	yes	—
379	#548	—	2	2	no	—
380	#547	—	2	2	no	—
381	#542	—	2	2	no	—
382	#542	C₂²×C₁₉	1	4	yes	—
383	#540	C₂²×C₁₉	1	4	yes	—
384	#539	—	2	4	no	—
385	#536	—	2	2	no	—
386	#533	C₂²×C₁₉	1	1	yes	characteristic
387	#532	C₂²×C₁₉	1	2	yes	—
388	#529	C₂²×C₁₉	1	2	yes	—
389	#500	C₂²×C₁₉	1	2	yes	—
390	#500	C₂²×C₁₉	1	1	yes	characteristic
391	#499	C₂²×C₁₉	1	1	yes	characteristic
392	#499	C₂²×C₁₉	1	2	yes	—
393	#495	C₂²×C₁₉	1	1	yes	characteristic
394	#495	C₂²×C₁₉	1	2	yes	—
395	#493	C₂²×C₁₉	1	1	yes	characteristic
396	#493	C₂²×C₁₉	1	2	yes	—
397	#490	C₂²×C₁₉	1	4	yes	—
398	#489	C₂²×C₁₉	1	4	yes	—
399	#488	C₂²×C₁₉	1	2	yes	—
400	#486	C₂²×C₁₉	1	2	yes	—
401	#479	C₂²×C₁₉	1	4	yes	—
402	#478	C₂²×C₁₉	1	4	yes	—
403	#478	C₂²×C₁₉	1	4	yes	—
404	#476	C₂²×C₁₉	1	4	yes	—
405	#475	C₂²×C₁₉	1	2	yes	—
406	#474	C₂²×C₁₉	1	2	yes	—
407	#474	C₂²×C₁₉	1	4	yes	—
408	#469	C₂²×C₁₉	1	4	yes	—
409	#468	C₂²×C₁₉	1	4	yes	—
410	#467	C₂²×C₁₉	1	1	yes	characteristic
411	#466	C₂²×C₁₉	1	1	yes	characteristic
412	#466	C₂²×C₁₉	1	2	yes	—
413	#466	C₂²×C₁₉	1	2	yes	—
414	#465	C₂²×C₁₉	1	2	yes	—
415	#463	C₂²×C₁₉	1	4	yes	—
416	#463	C₂²×C₁₉	1	4	yes	—
417	#463	C₂²×C₁₉	1	4	yes	—
418	#460	C₂²×C₁₉	1	2	yes	—
419	#460	C₂²×C₁₉	1	4	yes	—
420	#459	C₂²×C₁₉	1	4	yes	—
421	#459	C₂²×C₁₉	1	2	yes	—
422	#446	C₂²×C₁₉	1	1	yes	characteristic
423	#446	C₂²×C₁₉	1	2	yes	—
424	#446	C₂²×C₁₉	1	1	yes	characteristic
425	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
426	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
427	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
428	#442	C₂²×C₁₉	1	4	yes	—
429	#440	C₂²×C₁₉	1	4	yes	—
430	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
431	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
432	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
433	C₄×D₈	C₂²×C₁₉	1	2	yes	—
434	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
435	C₄×D₈	C₂²×C₁₉	1	2	yes	—
436	C₄×D₈	C₂²×C₁₉	1	2	yes	—
437	C₄×D₈	C₂²×C₁₉	1	2	yes	—
438	C₄×D₈	C₂²×C₁₉	1	2	yes	—
439	#424	C₂²×C₁₉	1	2	yes	—
440	#423	C₂²×C₁₉	1	1	yes	characteristic
441	#405	C₂²×C₁₉	1	2	yes	—
442	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
443	C₂×C₁₉	—	4	1	no	—
444	C₂×C₁₉	—	8	4	no	—
445	C₂×C₁₉	—	8	2	no	—
446	C₂×C₁₉	#3497	1	1	yes	characteristic
447	C₂×C₁₉	C₂×#576	1	1	yes	characteristic
448	C₂×C₁₉	#3584	1	1	yes	characteristic
449	C₂×#41	—	2	2	no	—
450	C₂×#41	—	2	2	no	—
451	C₂²×Q₈	—	2	2	no	—
452	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
453	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
454	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
455	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
456	C₂×D₈	C₂³×C₁₉	1	2	yes	—
457	C₂×D₈	C₂³×C₁₉	1	2	yes	—
458	C₂×D₈	C₂³×C₁₉	1	4	yes	—
459	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
460	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
461	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
462	C₄⋊Q₈	—	2	2	no	—
463	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
464	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
465	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
466	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
467	#127	C₂³×C₁₉	1	2	yes	—
468	#127	C₂³×C₁₉	1	4	yes	—
469	#126	—	2	4	no	—
470	#126	—	2	2	no	—
471	#125	—	2	4	no	—
472	#125	D₄×C₁₉	1	2	yes	—
473	#125	C₂³×C₁₉	1	2	yes	—
474	#125	C₂³×C₁₉	1	4	yes	—
475	#124	—	2	2	no	—
476	#124	—	2	4	no	—
477	#124	—	2	4	no	—
478	#124	—	2	2	no	—
479	#124	C₂³×C₁₉	1	2	yes	—
480	#124	C₂³×C₁₉	1	4	yes	—
481	#123	—	2	2	no	—
482	#123	—	2	4	no	—
483	#123	—	2	4	no	—
484	#123	—	2	4	no	—
485	#123	—	2	4	no	—
486	#123	—	2	4	no	—
487	#123	—	2	4	no	—
488	C₂²⋊Q₈	—	2	4	no	—
489	C₂²⋊Q₈	—	2	4	no	—
490	C₂²⋊Q₈	—	2	4	no	—
491	C₂²⋊Q₈	—	2	4	no	—
492	C₂²⋊Q₈	—	2	4	no	—
493	C₂²⋊Q₈	—	2	2	no	—
494	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
495	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
496	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
497	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
498	#121	—	2	2	no	—
499	#121	—	2	4	no	—
500	#121	—	2	2	no	—
501	#121	—	2	4	no	—
502	#121	—	2	4	no	—
503	#121	C₂³×C₁₉	1	2	yes	—
504	#121	C₂³×C₁₉	1	4	yes	—
505	C₄×Q₈	—	2	2	no	—
506	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
507	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
508	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
509	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
510	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
511	C₄×D₄	—	2	2	no	—
512	C₄×D₄	—	2	4	no	—
513	C₄×D₄	—	2	2	no	—
514	C₄×D₄	—	2	2	no	—
515	C₄×D₄	C₂³×C₁₉	1	2	yes	—
516	C₄×D₄	C₂³×C₁₉	1	4	yes	—
517	C₄×D₄	C₂³×C₁₉	1	4	yes	—
518	C₄×D₄	C₂³×C₁₉	1	4	yes	—
519	C₄×D₄	C₂³×C₁₉	1	4	yes	—
520	#117	—	2	2	no	—
521	#117	C₂³×C₁₉	1	2	yes	—
522	C₂×C₄⋊C₄	—	2	4	no	—
523	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
524	#107	C₂³×C₁₉	1	1	yes	characteristic
525	#107	C₂³×C₁₉	1	1	yes	characteristic
526	#107	C₂³×C₁₉	1	2	yes	—
527	#107	C₂³×C₁₉	1	2	yes	—
528	#107	C₂³×C₁₉	1	4	yes	—
529	#106	C₂³×C₁₉	1	2	yes	—
530	#106	C₂³×C₁₉	1	4	yes	—
531	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
532	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
533	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
534	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
535	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
536	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
537	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
538	#103	C₂³×C₁₉	1	2	yes	—
539	#103	C₂³×C₁₉	1	2	yes	—
540	#103	C₂³×C₁₉	1	4	yes	—
541	#102	C₂³×C₁₉	1	4	yes	—
542	#102	C₂³×C₁₉	1	2	yes	—
543	#102	C₂³×C₁₉	1	4	yes	—
544	#102	C₂³×C₁₉	1	4	yes	—
545	#102	C₂³×C₁₉	1	4	yes	—
546	#102	C₂³×C₁₉	1	4	yes	—
547	#102	C₂³×C₁₉	1	2	yes	—
548	#97	C₂³×C₁₉	1	2	yes	—
549	#97	C₂³×C₁₉	1	2	yes	—
550	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
551	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
552	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
553	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
554	C₄×C₈	C₂³×C₁₉	1	2	yes	—
555	C₄×C₈	C₂³×C₁₉	1	2	yes	—
556	C₁₉	#62379	1	1	yes	characteristic, direct product factor, Sylow
557	#41	—	8	4	no	—
558	#41	—	8	4	no	—
559	C₂×Q₈	—	2	2	no	—
560	C₂×Q₈	—	2	4	no	—
561	C₂×Q₈	—	8	4	no	—
562	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
563	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
564	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
565	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
566	C₂×D₄	—	2	2	no	—
567	C₂×D₄	—	2	4	no	—
568	C₂×D₄	—	2	2	no	—
569	C₂×D₄	—	2	2	no	—
570	C₂×D₄	—	2	4	no	—
571	C₂×D₄	—	2	4	no	—
572	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
573	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	4	no	—
576	C₂²×C₄	—	2	4	no	—
577	C₂²×C₄	—	2	4	no	—
578	C₂²×C₄	—	2	4	no	—
579	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
580	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
581	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
582	Q₁₆	—	2	2	no	—
583	SD₁₆	—	4	2	no	—
584	SD₁₆	—	4	4	no	—
585	D₈	—	2	2	no	—
586	D₈	—	2	4	no	—
587	D₈	—	4	2	no	—
588	D₈	—	4	4	no	—
589	M₁₆	—	4	2	no	—
590	C₂×C₈	—	2	2	no	—
591	C₂×C₈	—	4	1	no	—
592	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
593	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
594	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
595	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
596	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
597	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	2	no	—
602	C₄⋊C₄	—	2	2	no	—
603	C₄⋊C₄	—	2	2	no	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	2	no	—
607	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
608	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
609	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
610	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
611	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
612	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
613	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
614	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
615	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
616	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
617	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
618	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
619	C₂²⋊C₄	—	2	2	no	—
620	C₂²⋊C₄	—	2	2	no	—
621	C₂²⋊C₄	—	2	2	no	—
622	C₂²⋊C₄	—	2	2	no	—
623	C₂²⋊C₄	—	2	4	no	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	2	2	no	—
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
632	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
633	C₄²	—	2	2	no	—
634	C₄²	—	2	4	no	—
635	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
636	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
637	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
638	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
639	C₄²	C₂⁴×C₁₉	1	2	yes	—
640	C₄²	C₂⁴×C₁₉	1	2	yes	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	4	no	—
643	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
644	Q₈	—	2	2	no	—
645	Q₈	—	2	2	no	—
646	Q₈	—	2	2	no	—
647	Q₈	—	2	2	no	—
648	Q₈	—	4	2	no	—
649	Q₈	—	4	4	no	—
650	Q₈	—	8	4	no	—
651	D₄	—	2	4	no	—
652	D₄	—	2	2	no	—
653	D₄	—	2	4	no	—
654	D₄	—	2	2	no	—
655	D₄	—	4	4	no	—
656	D₄	—	8	4	no	—
657	D₄	—	8	2	no	—
658	D₄	—	8	4	no	—
659	D₄	—	8	4	no	—
660	D₄	—	8	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	4	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	4	no	—
670	C₂×C₄	—	8	4	no	—
671	C₂×C₄	—	8	4	no	—
672	C₂×C₄	—	8	4	no	—
673	C₂×C₄	—	8	4	no	—
674	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
675	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
676	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
677	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
678	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
679	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
680	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
681	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
682	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
683	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
684	C₈	—	2	1	no	—
685	C₈	—	2	1	no	—
686	C₈	—	2	1	no	—
687	C₈	—	2	2	no	—
688	C₈	—	2	2	no	—
689	C₈	C₁₉×2₋¹⁺⁴	1	2	yes	—
690	C₂²	—	2	1	no	—
691	C₂²	—	2	1	no	—
692	C₂²	—	2	1	no	—
693	C₂²	—	4	2	no	—
694	C₂²	—	4	4	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	4	4	no	—
697	C₂²	—	4	4	no	—
698	C₂²	—	4	2	no	—
699	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
700	C₄	—	2	1	no	—
701	C₄	—	2	1	no	—
702	C₄	—	2	2	no	—
703	C₄	—	2	2	no	—
704	C₄	—	2	1	no	—
705	C₄	—	2	1	no	—
706	C₄	—	2	2	no	—
707	C₄	—	2	2	no	—
708	C₄	—	4	2	no	—
709	C₄	—	4	2	no	—
710	C₄	—	4	4	no	—
711	C₄	—	4	2	no	—
712	C₄	C₁₉×#576	1	2	yes	—
713	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
714	C₄	C₁₉×#585	1	1	yes	characteristic
715	C₂	—	4	1	no	—
716	C₂	—	8	2	no	—
717	C₂	—	8	4	no	—
718	C₂	C₁₉×#3497	1	1	yes	characteristic
719	C₂	C₂×C₁₉×#576	1	1	yes	characteristic
720	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×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3554	C₂	semidirect
2. C₁₉×#3396	C₂	semidirect
3. C₁₉×#3396	C₂	semidirect
4. C₁₉×#3391	C₂	semidirect
5. C₁₉×#3383	C₂	semidirect
6. C₁₉×#3380	C₂	semidirect
7. Q₈×D₈×C₁₉	C₂	semidirect
8. C₁₉×#3373	C₂	semidirect
9. C₁₉×#3370	C₂	semidirect
10. C₁₉×#3368	C₂	semidirect
11. C₁₉×#3257	C₂	semidirect
12. C₁₉×#3251	C₂	semidirect
13. C₁₉×#3176	C₂	semidirect
14. C₁₉×#3175	C₂	semidirect
15. C₁₉×#3169	C₂	semidirect
16. C₁₉×#3168	C₂	semidirect
17. C₁₉×#2960	C₂	semidirect
280. #62379	C₁₉	direct (N × H)
330. #3554	C₂×C₁₉	semidirect
331. #3396	C₂×C₁₉	semidirect
332. #3396	C₂×C₁₉	semidirect
333. #3391	C₂×C₁₉	semidirect
334. #3383	C₂×C₁₉	semidirect
335. #3380	C₂×C₁₉	semidirect
336. Q₈×D₈	C₂×C₁₉	semidirect
337. #3373	C₂×C₁₉	semidirect
338. #3370	C₂×C₁₉	semidirect
339. #3368	C₂×C₁₉	semidirect
340. #3257	C₂×C₁₉	semidirect
341. #3251	C₂×C₁₉	semidirect
342. #3176	C₂×C₁₉	semidirect
343. #3175	C₂×C₁₉	semidirect
344. #3169	C₂×C₁₉	semidirect
345. #3168	C₂×C₁₉	semidirect
346. #2960	C₂×C₁₉	semidirect
556. C₁₉	#62379	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×#3554	2
C₁₉×#3396	2
C₁₉×#3391	2
C₁₉×#3383	2
C₁₉×#3380	2
Q₈×D₈×C₁₉	2
C₁₉×#3373	2
C₁₉×#3370	2
C₁₉×#3368	2
C₁₉×#3257	2
C₁₉×#3251	2
C₁₉×#3176	2
C₁₉×#3175	2
C₁₉×#3169	2
C₁₉×#3168	2
C₁₉×#2960	2
#62379	19

Subgroups — C19×#62379 #18068338

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62379 #18068338