Subgroups — C₁₉×#62385 #18068344

Order 4864.

1608 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3555	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3402	C₂	1	2	yes	maximal, complemented
3	C₁₉×#3398	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3390	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3385	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3364	C₂	1	4	yes	maximal, complemented
7	C₁₉×#3363	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3360	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3262	C₂	1	2	yes	maximal
10	C₁₉×#3261	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3252	C₂	1	2	yes	maximal, complemented
12	C₁₉×#3178	C₂	1	4	yes	maximal, complemented
13	C₁₉×#3170	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3168	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#2960	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#563	—	2	4	no	—
17	Q₈²×C₁₉	C₂²	1	2	yes	—
18	C₁₉×#557	C₂²	1	2	yes	—
19	C₁₉×#557	C₂²	1	4	yes	—
20	C₁₉×#556	—	2	2	no	—
21	C₁₉×#556	C₂²	1	2	yes	—
22	C₁₉×#556	C₂²	1	4	yes	—
23	C₁₉×#554	C₂²	1	2	yes	—
24	C₁₉×#552	—	2	2	no	—
25	C₁₉×#544	—	2	2	no	—
26	C₁₉×#542	C₂²	1	4	yes	—
27	C₁₉×#541	—	2	2	no	—
28	C₁₉×#541	—	2	4	no	—
29	C₁₉×#541	C₂²	1	4	yes	—
30	C₁₉×#533	C₂²	1	2	yes	—
31	C₁₉×#533	C₂²	1	1	yes	characteristic
32	C₁₉×#529	C₂²	1	2	yes	—
33	C₁₉×#501	C₂²	1	4	yes	—
34	C₁₉×#500	C₂²	1	1	yes	characteristic
35	C₁₉×#499	C₂²	1	1	yes	characteristic
36	C₁₉×#497	C₂²	1	4	yes	—
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×#488	C₂²	1	4	yes	—
41	C₁₉×#487	C₂²	1	2	yes	—
42	C₁₉×#487	C₂²	1	4	yes	—
43	C₁₉×#479	C₂²	1	4	yes	—
44	C₁₉×#479	C₂²	1	4	yes	—
45	C₁₉×#479	C₂²	1	4	yes	—
46	C₁₉×#477	C₂²	1	2	yes	—
47	C₁₉×#477	C₂²	1	4	yes	—
48	C₁₉×#476	C₂²	1	2	yes	—
49	C₁₉×#474	C₂²	1	4	yes	—
50	C₁₉×#470	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×#466	C₂²	1	1	yes	characteristic
56	C₁₉×#465	C₂²	1	2	yes	—
57	C₁₉×#464	C₂²	1	4	yes	—
58	C₁₉×#464	C₂²	1	4	yes	—
59	C₁₉×#463	C₂²	1	4	yes	—
60	C₁₉×#462	C₂²	1	2	yes	—
61	C₁₉×#462	C₂²	1	4	yes	—
62	C₁₉×#462	C₂²	1	4	yes	—
63	C₁₉×#461	C₂²	1	2	yes	—
64	C₁₉×#446	C₂²	1	2	yes	—
65	C₁₉×#446	C₂²	1	2	yes	—
66	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
67	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
68	C₁₉×#441	C₂²	1	4	yes	—
69	C₁₉×#440	C₂²	1	4	yes	—
70	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
71	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
72	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
73	C₄×Q₁₆×C₁₉	C₂²	1	4	yes	—
74	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	—
75	C₄×SD₁₆×C₁₉	C₂²	1	4	yes	—
76	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
77	C₁₉×#424	C₂²	1	2	yes	—
78	C₁₉×#423	C₂²	1	1	yes	characteristic
79	C₁₉×#405	C₂²	1	2	yes	—
80	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
81	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
82	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
83	C₂×Q₁₆×C₁₉	C₂³	1	4	yes	—
84	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
85	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
86	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
87	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
89	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
91	C₁₉×C₄⋊Q₈	—	2	4	no	—
92	C₁₉×C₄⋊Q₈	—	2	4	no	—
93	C₁₉×C₄⋊Q₈	—	2	2	no	—
94	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
95	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
96	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
97	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
98	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
99	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
100	C₁₉×#126	—	2	4	no	—
101	C₁₉×#126	—	2	4	no	—
102	C₁₉×#126	—	2	4	no	—
103	C₁₉×#126	—	2	4	no	—
104	C₁₉×#126	—	2	4	no	—
105	C₁₉×#126	—	2	4	no	—
106	C₁₉×#126	—	2	2	no	—
107	C₁₉×#125	—	2	4	no	—
108	C₁₉×#125	—	2	4	no	—
109	C₁₉×#125	—	2	4	no	—
110	C₁₉×#125	—	2	4	no	—
111	C₁₉×#125	—	2	4	no	—
112	C₁₉×#125	—	2	2	no	—
113	C₁₉×#125	—	2	2	no	—
114	C₁₉×#125	D₄	1	2	yes	—
115	C₁₉×#125	C₂³	1	2	yes	—
116	C₁₉×#125	C₂³	1	4	yes	—
117	C₁₉×#124	—	2	4	no	—
118	C₁₉×#124	C₂³	1	4	yes	—
119	C₁₉×#124	C₂³	1	2	yes	—
120	C₁₉×#123	—	2	2	no	—
121	C₁₉×#123	—	2	4	no	—
122	C₁₉×C₂²⋊Q₈	—	2	2	no	—
123	C₁₉×C₂²⋊Q₈	—	2	2	no	—
124	C₁₉×C₂²⋊Q₈	—	2	4	no	—
125	C₁₉×C₂²⋊Q₈	—	2	2	no	—
126	C₁₉×C₂²⋊Q₈	—	2	4	no	—
127	C₁₉×C₂²⋊Q₈	—	2	4	no	—
128	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
129	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
130	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
131	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
132	C₁₉×#121	C₂³	1	2	yes	—
133	C₄×Q₈×C₁₉	—	2	2	no	—
134	C₄×Q₈×C₁₉	—	2	2	no	—
135	C₄×Q₈×C₁₉	—	2	4	no	—
136	C₄×Q₈×C₁₉	—	2	2	no	—
137	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
138	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
139	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
140	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
141	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
142	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
143	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
144	C₄×D₄×C₁₉	—	2	2	no	—
145	C₄×D₄×C₁₉	C₂³	1	2	yes	—
146	C₄×D₄×C₁₉	C₂³	1	4	yes	—
147	C₁₉×#117	—	2	2	no	—
148	C₁₉×#117	—	2	4	no	—
149	C₁₉×#117	—	2	2	no	—
150	C₁₉×#117	—	2	2	no	—
151	C₁₉×#117	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
153	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
154	C₁₉×#107	C₂³	1	1	yes	characteristic
155	C₁₉×#107	C₂³	1	2	yes	—
156	C₁₉×#107	C₂³	1	1	yes	characteristic
157	C₁₉×#107	C₂³	1	2	yes	—
158	C₁₉×#107	C₂³	1	4	yes	—
159	C₁₉×#106	C₂³	1	2	yes	—
160	C₁₉×#106	C₂³	1	4	yes	—
161	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
162	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
163	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
164	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
165	C₁₉×#103	C₂³	1	4	yes	—
166	C₁₉×#103	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×#102	C₂³	1	2	yes	—
173	C₁₉×#102	C₂³	1	2	yes	—
174	C₁₉×#102	C₂³	1	4	yes	—
175	C₁₉×#97	C₂³	1	4	yes	—
176	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
177	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
178	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
179	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
180	C₄×C₈×C₁₉	C₂³	1	4	yes	—
181	C₂×Q₈×C₁₉	—	2	2	no	—
182	C₂×Q₈×C₁₉	—	2	4	no	—
183	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
184	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
185	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
186	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
187	C₂×D₄×C₁₉	—	2	2	no	—
188	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₁₉	—	2	2	no	—
190	C₂²×C₄×C₁₉	—	2	4	no	—
191	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
194	Q₁₆×C₁₉	—	2	4	no	—
195	Q₁₆×C₁₉	—	4	1	no	—
196	Q₁₆×C₁₉	—	4	2	no	—
197	Q₁₆×C₁₉	—	4	4	no	—
198	SD₁₆×C₁₉	—	2	4	no	—
199	SD₁₆×C₁₉	—	4	4	no	—
200	D₈×C₁₉	—	4	1	no	—
201	M₁₆×C₁₉	—	4	2	no	—
202	C₂×C₈×C₁₉	—	2	2	no	—
203	C₂×C₈×C₁₉	—	4	1	no	—
204	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
205	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
206	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
207	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
208	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
209	C₄⋊C₄×C₁₉	—	2	2	no	—
210	C₄⋊C₄×C₁₉	—	2	4	no	—
211	C₄⋊C₄×C₁₉	—	2	2	no	—
212	C₄⋊C₄×C₁₉	—	2	4	no	—
213	C₄⋊C₄×C₁₉	—	2	2	no	—
214	C₄⋊C₄×C₁₉	—	2	2	no	—
215	C₄⋊C₄×C₁₉	—	2	2	no	—
216	C₄⋊C₄×C₁₉	—	2	4	no	—
217	C₄⋊C₄×C₁₉	—	2	4	no	—
218	C₄⋊C₄×C₁₉	—	2	2	no	—
219	C₄⋊C₄×C₁₉	—	2	4	no	—
220	C₄⋊C₄×C₁₉	—	2	4	no	—
221	C₄⋊C₄×C₁₉	—	2	4	no	—
222	C₄⋊C₄×C₁₉	—	2	4	no	—
223	C₄⋊C₄×C₁₉	—	2	4	no	—
224	C₄⋊C₄×C₁₉	—	2	4	no	—
225	C₄⋊C₄×C₁₉	—	2	2	no	—
226	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
227	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
228	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
229	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
230	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
231	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
232	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
233	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
234	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
235	C₂²⋊C₄×C₁₉	—	2	4	no	—
236	C₂²⋊C₄×C₁₉	—	2	2	no	—
237	C₂²⋊C₄×C₁₉	—	2	2	no	—
238	C₂²⋊C₄×C₁₉	—	2	2	no	—
239	C₂²⋊C₄×C₁₉	—	2	2	no	—
240	C₂²⋊C₄×C₁₉	—	2	4	no	—
241	C₂²⋊C₄×C₁₉	—	2	4	no	—
242	C₂²⋊C₄×C₁₉	—	2	2	no	—
243	C₂²⋊C₄×C₁₉	—	2	4	no	—
244	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
245	C₄²×C₁₉	—	2	4	no	—
246	C₄²×C₁₉	—	2	2	no	—
247	C₄²×C₁₉	—	2	4	no	—
248	C₄²×C₁₉	—	2	4	no	—
249	C₄²×C₁₉	—	2	4	no	—
250	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
251	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
252	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
253	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
254	C₄²×C₁₉	C₂⁴	1	4	yes	—
255	#62385	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
256	C₂³×C₁₉	—	2	2	no	—
257	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
258	Q₈×C₁₉	—	2	4	no	—
259	Q₈×C₁₉	—	2	2	no	—
260	Q₈×C₁₉	—	2	4	no	—
261	Q₈×C₁₉	—	2	4	no	—
262	Q₈×C₁₉	—	2	2	no	—
263	Q₈×C₁₉	—	4	2	no	—
264	Q₈×C₁₉	—	8	2	no	—
265	Q₈×C₁₉	—	8	4	no	—
266	D₄×C₁₉	—	2	2	no	—
267	D₄×C₁₉	—	2	2	no	—
268	D₄×C₁₉	—	8	2	no	—
269	C₂×C₄×C₁₉	—	2	2	no	—
270	C₂×C₄×C₁₉	—	2	1	no	—
271	C₂×C₄×C₁₉	—	2	1	no	—
272	C₂×C₄×C₁₉	—	2	4	no	—
273	C₂×C₄×C₁₉	—	2	2	no	—
274	C₂×C₄×C₁₉	—	2	2	no	—
275	C₂×C₄×C₁₉	—	2	2	no	—
276	C₂×C₄×C₁₉	—	2	4	no	—
277	C₂×C₄×C₁₉	—	4	1	no	—
278	C₂×C₄×C₁₉	—	4	4	no	—
279	C₂×C₄×C₁₉	—	8	4	no	—
280	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
281	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
282	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
283	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
284	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
285	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
286	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
287	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
288	C₈×C₁₉	—	2	1	no	—
289	C₈×C₁₉	—	2	1	no	—
290	C₈×C₁₉	—	2	1	no	—
291	C₈×C₁₉	—	2	4	no	—
292	C₈×C₁₉	2₋¹⁺⁴	1	2	yes	—
293	#3555	C₂×C₁₉	1	2	yes	complemented
294	#3402	C₂×C₁₉	1	2	yes	complemented
295	#3398	C₂×C₁₉	1	2	yes	complemented
296	#3390	C₂×C₁₉	1	2	yes	complemented
297	#3385	C₂×C₁₉	1	2	yes	complemented
298	#3364	C₂×C₁₉	1	4	yes	complemented
299	#3363	C₂×C₁₉	1	2	yes	complemented
300	#3360	C₂×C₁₉	1	2	yes	complemented
301	#3262	C₂×C₁₉	1	2	yes	—
302	#3261	C₂×C₁₉	1	2	yes	complemented
303	#3252	C₂×C₁₉	1	2	yes	complemented
304	#3178	C₂×C₁₉	1	4	yes	complemented
305	#3170	C₂×C₁₉	1	1	yes	characteristic, complemented
306	#3168	C₂×C₁₉	1	1	yes	characteristic
307	#2960	C₂×C₁₉	1	1	yes	characteristic, complemented
308	C₂²×C₁₉	—	2	1	no	—
309	C₂²×C₁₉	—	2	1	no	—
310	C₂²×C₁₉	—	2	1	no	—
311	C₂²×C₁₉	—	4	2	no	—
312	C₂²×C₁₉	—	4	2	no	—
313	C₂²×C₁₉	—	4	2	no	—
314	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
315	C₄×C₁₉	—	2	1	no	—
316	C₄×C₁₉	—	2	1	no	—
317	C₄×C₁₉	—	2	4	no	—
318	C₄×C₁₉	—	2	1	no	—
319	C₄×C₁₉	—	2	1	no	—
320	C₄×C₁₉	—	2	4	no	—
321	C₄×C₁₉	—	4	4	no	—
322	C₄×C₁₉	—	4	2	no	—
323	C₄×C₁₉	—	4	2	no	—
324	C₄×C₁₉	—	4	4	no	—
325	C₄×C₁₉	—	4	2	no	—
326	C₄×C₁₉	#578	1	2	yes	—
327	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
328	C₄×C₁₉	#585	1	1	yes	characteristic
329	#563	—	2	4	no	—
330	Q₈²	C₂²×C₁₉	1	2	yes	—
331	#557	C₂²×C₁₉	1	2	yes	—
332	#557	C₂²×C₁₉	1	4	yes	—
333	#556	—	2	2	no	—
334	#556	C₂²×C₁₉	1	2	yes	—
335	#556	C₂²×C₁₉	1	4	yes	—
336	#554	C₂²×C₁₉	1	2	yes	—
337	#552	—	2	2	no	—
338	#544	—	2	2	no	—
339	#542	C₂²×C₁₉	1	4	yes	—
340	#541	—	2	2	no	—
341	#541	—	2	4	no	—
342	#541	C₂²×C₁₉	1	4	yes	—
343	#533	C₂²×C₁₉	1	2	yes	—
344	#533	C₂²×C₁₉	1	1	yes	characteristic
345	#529	C₂²×C₁₉	1	2	yes	—
346	#501	C₂²×C₁₉	1	4	yes	—
347	#500	C₂²×C₁₉	1	1	yes	characteristic
348	#499	C₂²×C₁₉	1	1	yes	characteristic
349	#497	C₂²×C₁₉	1	4	yes	—
350	#495	C₂²×C₁₉	1	1	yes	characteristic
351	#494	C₂²×C₁₉	1	1	yes	characteristic
352	#488	C₂²×C₁₉	1	4	yes	—
353	#488	C₂²×C₁₉	1	2	yes	—
354	#487	C₂²×C₁₉	1	2	yes	—
355	#487	C₂²×C₁₉	1	4	yes	—
356	#479	C₂²×C₁₉	1	4	yes	—
357	#479	C₂²×C₁₉	1	4	yes	—
358	#479	C₂²×C₁₉	1	4	yes	—
359	#477	C₂²×C₁₉	1	2	yes	—
360	#477	C₂²×C₁₉	1	4	yes	—
361	#476	C₂²×C₁₉	1	2	yes	—
362	#474	C₂²×C₁₉	1	4	yes	—
363	#470	C₂²×C₁₉	1	4	yes	—
364	#468	C₂²×C₁₉	1	4	yes	—
365	#467	C₂²×C₁₉	1	1	yes	characteristic
366	#467	C₂²×C₁₉	1	2	yes	—
367	#467	C₂²×C₁₉	1	2	yes	—
368	#466	C₂²×C₁₉	1	1	yes	characteristic
369	#465	C₂²×C₁₉	1	2	yes	—
370	#464	C₂²×C₁₉	1	4	yes	—
371	#464	C₂²×C₁₉	1	4	yes	—
372	#463	C₂²×C₁₉	1	4	yes	—
373	#462	C₂²×C₁₉	1	2	yes	—
374	#462	C₂²×C₁₉	1	4	yes	—
375	#462	C₂²×C₁₉	1	4	yes	—
376	#461	C₂²×C₁₉	1	2	yes	—
377	#446	C₂²×C₁₉	1	2	yes	—
378	#446	C₂²×C₁₉	1	2	yes	—
379	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
380	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
381	#441	C₂²×C₁₉	1	4	yes	—
382	#440	C₂²×C₁₉	1	4	yes	—
383	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
384	C₄×Q₁₆	C₂²×C₁₉	1	4	yes	—
385	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
386	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
387	C₄×SD₁₆	C₂²×C₁₉	1	4	yes	—
388	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
389	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
390	#424	C₂²×C₁₉	1	2	yes	—
391	#423	C₂²×C₁₉	1	1	yes	characteristic
392	#405	C₂²×C₁₉	1	2	yes	—
393	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
394	C₂×C₁₉	—	4	1	no	—
395	C₂×C₁₉	—	8	2	no	—
396	C₂×C₁₉	#3497	1	1	yes	characteristic
397	C₂×C₁₉	C₂×#578	1	1	yes	characteristic
398	C₂×C₁₉	#3584	1	1	yes	characteristic
399	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
400	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
401	C₂×Q₁₆	C₂³×C₁₉	1	4	yes	—
402	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
403	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
404	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
405	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
406	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
407	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
408	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
409	C₄⋊Q₈	—	2	4	no	—
410	C₄⋊Q₈	—	2	4	no	—
411	C₄⋊Q₈	—	2	2	no	—
412	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
413	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
414	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
415	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
416	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
417	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
418	#126	—	2	4	no	—
419	#126	—	2	4	no	—
420	#126	—	2	4	no	—
421	#126	—	2	4	no	—
422	#126	—	2	4	no	—
423	#126	—	2	4	no	—
424	#126	—	2	2	no	—
425	#125	—	2	4	no	—
426	#125	—	2	4	no	—
427	#125	—	2	4	no	—
428	#125	—	2	4	no	—
429	#125	—	2	4	no	—
430	#125	—	2	2	no	—
431	#125	—	2	2	no	—
432	#125	D₄×C₁₉	1	2	yes	—
433	#125	C₂³×C₁₉	1	2	yes	—
434	#125	C₂³×C₁₉	1	4	yes	—
435	#124	—	2	4	no	—
436	#124	C₂³×C₁₉	1	2	yes	—
437	#124	C₂³×C₁₉	1	4	yes	—
438	#123	—	2	2	no	—
439	#123	—	2	4	no	—
440	C₂²⋊Q₈	—	2	2	no	—
441	C₂²⋊Q₈	—	2	2	no	—
442	C₂²⋊Q₈	—	2	4	no	—
443	C₂²⋊Q₈	—	2	2	no	—
444	C₂²⋊Q₈	—	2	4	no	—
445	C₂²⋊Q₈	—	2	4	no	—
446	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
447	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
448	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
449	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
450	#121	C₂³×C₁₉	1	2	yes	—
451	C₄×Q₈	—	2	2	no	—
452	C₄×Q₈	—	2	2	no	—
453	C₄×Q₈	—	2	4	no	—
454	C₄×Q₈	—	2	2	no	—
455	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
456	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
457	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
458	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
459	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
460	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
461	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
462	C₄×D₄	—	2	2	no	—
463	C₄×D₄	C₂³×C₁₉	1	2	yes	—
464	C₄×D₄	C₂³×C₁₉	1	4	yes	—
465	#117	—	2	2	no	—
466	#117	—	2	4	no	—
467	#117	—	2	2	no	—
468	#117	—	2	2	no	—
469	#117	C₂³×C₁₉	1	2	yes	—
470	C₂×C₄⋊C₄	—	2	2	no	—
471	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
472	#107	C₂³×C₁₉	1	1	yes	characteristic
473	#107	C₂³×C₁₉	1	2	yes	—
474	#107	C₂³×C₁₉	1	1	yes	characteristic
475	#107	C₂³×C₁₉	1	2	yes	—
476	#107	C₂³×C₁₉	1	4	yes	—
477	#106	C₂³×C₁₉	1	2	yes	—
478	#106	C₂³×C₁₉	1	4	yes	—
479	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
480	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
481	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
482	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
483	#103	C₂³×C₁₉	1	4	yes	—
484	#103	C₂³×C₁₉	1	2	yes	—
485	#103	C₂³×C₁₉	1	2	yes	—
486	#103	C₂³×C₁₉	1	4	yes	—
487	#103	C₂³×C₁₉	1	4	yes	—
488	#103	C₂³×C₁₉	1	4	yes	—
489	#103	C₂³×C₁₉	1	4	yes	—
490	#102	C₂³×C₁₉	1	2	yes	—
491	#102	C₂³×C₁₉	1	2	yes	—
492	#102	C₂³×C₁₉	1	4	yes	—
493	#97	C₂³×C₁₉	1	4	yes	—
494	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
495	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
496	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
497	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
498	C₄×C₈	C₂³×C₁₉	1	4	yes	—
499	C₁₉	#62385	1	1	yes	characteristic, direct product factor, Sylow
500	C₂×Q₈	—	2	2	no	—
501	C₂×Q₈	—	2	4	no	—
502	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
503	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
504	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
505	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
506	C₂×D₄	—	2	2	no	—
507	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
508	C₂²×C₄	—	2	2	no	—
509	C₂²×C₄	—	2	4	no	—
510	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
511	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
512	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
513	Q₁₆	—	2	4	no	—
514	Q₁₆	—	4	1	no	—
515	Q₁₆	—	4	2	no	—
516	Q₁₆	—	4	4	no	—
517	SD₁₆	—	2	4	no	—
518	SD₁₆	—	4	4	no	—
519	D₈	—	4	1	no	—
520	M₁₆	—	4	2	no	—
521	C₂×C₈	—	2	2	no	—
522	C₂×C₈	—	4	1	no	—
523	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
524	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
525	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
526	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
527	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
528	C₄⋊C₄	—	2	2	no	—
529	C₄⋊C₄	—	2	4	no	—
530	C₄⋊C₄	—	2	2	no	—
531	C₄⋊C₄	—	2	4	no	—
532	C₄⋊C₄	—	2	2	no	—
533	C₄⋊C₄	—	2	2	no	—
534	C₄⋊C₄	—	2	2	no	—
535	C₄⋊C₄	—	2	4	no	—
536	C₄⋊C₄	—	2	4	no	—
537	C₄⋊C₄	—	2	2	no	—
538	C₄⋊C₄	—	2	4	no	—
539	C₄⋊C₄	—	2	4	no	—
540	C₄⋊C₄	—	2	4	no	—
541	C₄⋊C₄	—	2	4	no	—
542	C₄⋊C₄	—	2	4	no	—
543	C₄⋊C₄	—	2	4	no	—
544	C₄⋊C₄	—	2	2	no	—
545	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
546	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
547	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
548	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
549	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
550	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
551	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
552	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
553	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
554	C₂²⋊C₄	—	2	4	no	—
555	C₂²⋊C₄	—	2	2	no	—
556	C₂²⋊C₄	—	2	2	no	—
557	C₂²⋊C₄	—	2	2	no	—
558	C₂²⋊C₄	—	2	2	no	—
559	C₂²⋊C₄	—	2	4	no	—
560	C₂²⋊C₄	—	2	4	no	—
561	C₂²⋊C₄	—	2	2	no	—
562	C₂²⋊C₄	—	2	4	no	—
563	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
564	C₄²	—	2	4	no	—
565	C₄²	—	2	2	no	—
566	C₄²	—	2	4	no	—
567	C₄²	—	2	4	no	—
568	C₄²	—	2	4	no	—
569	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
570	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
571	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
572	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
573	C₄²	C₂⁴×C₁₉	1	4	yes	—
574	C₂³	—	2	2	no	—
575	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
576	Q₈	—	2	4	no	—
577	Q₈	—	2	2	no	—
578	Q₈	—	2	4	no	—
579	Q₈	—	2	4	no	—
580	Q₈	—	2	2	no	—
581	Q₈	—	4	2	no	—
582	Q₈	—	8	2	no	—
583	Q₈	—	8	4	no	—
584	D₄	—	2	2	no	—
585	D₄	—	2	2	no	—
586	D₄	—	8	2	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	4	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	4	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	4	no	—
597	C₂×C₄	—	8	4	no	—
598	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
599	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
600	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
601	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
602	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
603	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
604	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
605	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
606	C₈	—	2	1	no	—
607	C₈	—	2	1	no	—
608	C₈	—	2	1	no	—
609	C₈	—	2	4	no	—
610	C₈	C₁₉×2₋¹⁺⁴	1	2	yes	—
611	C₂²	—	2	1	no	—
612	C₂²	—	2	1	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	4	2	no	—
615	C₂²	—	4	2	no	—
616	C₂²	—	4	2	no	—
617	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	4	no	—
621	C₄	—	2	1	no	—
622	C₄	—	2	1	no	—
623	C₄	—	2	4	no	—
624	C₄	—	4	2	no	—
625	C₄	—	4	4	no	—
626	C₄	—	4	2	no	—
627	C₄	—	4	4	no	—
628	C₄	—	4	2	no	—
629	C₄	C₁₉×#578	1	2	yes	—
630	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
631	C₄	C₁₉×#585	1	1	yes	characteristic
632	C₂	—	4	1	no	—
633	C₂	—	8	2	no	—
634	C₂	C₁₉×#3497	1	1	yes	characteristic
635	C₂	C₂×C₁₉×#578	1	1	yes	characteristic
636	C₂	C₁₉×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₁₉×#466	C₂²
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×#3555	C₂	semidirect
2. C₁₉×#3402	C₂	semidirect
3. C₁₉×#3398	C₂	semidirect
4. C₁₉×#3390	C₂	semidirect
5. C₁₉×#3385	C₂	semidirect
6. C₁₉×#3364	C₂	semidirect
7. C₁₉×#3363	C₂	semidirect
8. C₁₉×#3360	C₂	semidirect
10. C₁₉×#3261	C₂	semidirect
11. C₁₉×#3252	C₂	semidirect
12. C₁₉×#3178	C₂	semidirect
13. C₁₉×#3170	C₂	semidirect
15. C₁₉×#2960	C₂	semidirect
255. #62385	C₁₉	direct (N × H)
293. #3555	C₂×C₁₉	semidirect
294. #3402	C₂×C₁₉	semidirect
295. #3398	C₂×C₁₉	semidirect
296. #3390	C₂×C₁₉	semidirect
297. #3385	C₂×C₁₉	semidirect
298. #3364	C₂×C₁₉	semidirect
299. #3363	C₂×C₁₉	semidirect
300. #3360	C₂×C₁₉	semidirect
302. #3261	C₂×C₁₉	semidirect
303. #3252	C₂×C₁₉	semidirect
304. #3178	C₂×C₁₉	semidirect
305. #3170	C₂×C₁₉	semidirect
307. #2960	C₂×C₁₉	semidirect
499. C₁₉	#62385	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×#3555	2
C₁₉×#3402	2
C₁₉×#3398	2
C₁₉×#3390	2
C₁₉×#3385	2
C₁₉×#3364	2
C₁₉×#3363	2
C₁₉×#3360	2
C₁₉×#3262	2
C₁₉×#3261	2
C₁₉×#3252	2
C₁₉×#3178	2
C₁₉×#3170	2
C₁₉×#3168	2
C₁₉×#2960	2
#62385	19

Subgroups — C19×#62385 #18068344

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62385 #18068344