Subgroups — C₁₉×#19871 #18025830

Order 4864.

632 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3399	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3396	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3394	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3304	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1721	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1686	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1682	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1668	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1667	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1640	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1628	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1621	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1620	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1584	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#559	C₂²	1	1	yes	characteristic
17	C₁₉×#559	C₂²	1	1	yes	characteristic
18	C₁₉×#556	C₂²	1	1	yes	characteristic
19	C₁₉×#550	C₂²	1	1	yes	characteristic
20	C₁₉×#496	—	2	1	no	—
21	C₁₉×#495	—	2	1	no	—
22	C₁₉×#495	—	2	1	no	—
23	C₁₉×#493	C₂²	1	1	yes	characteristic
24	C₁₉×#493	C₂²	1	1	yes	characteristic
25	C₁₉×#493	C₂²	1	1	yes	characteristic
26	C₁₉×#492	C₂²	1	1	yes	characteristic
27	C₁₉×#486	C₂²	1	1	yes	characteristic
28	C₁₉×#486	C₂²	1	1	yes	characteristic
29	C₁₉×#482	—	2	1	no	—
30	C₁₉×#475	C₂²	1	1	yes	characteristic
31	C₁₉×#465	—	2	1	no	—
32	C₁₉×#464	—	2	1	no	—
33	C₁₉×#463	—	2	1	no	—
34	C₁₉×#463	—	2	1	no	—
35	C₁₉×#463	—	2	1	no	—
36	C₁₉×#463	—	2	1	no	—
37	C₁₉×#462	C₂²	1	1	yes	characteristic
38	C₁₉×#460	C₂²	1	1	yes	characteristic
39	C₁₉×#460	C₂²	1	1	yes	characteristic
40	C₁₉×#460	C₂²	1	1	yes	characteristic
41	C₁₉×#460	C₂²	1	1	yes	characteristic
42	C₁₉×#459	—	2	1	no	—
43	C₁₉×#459	C₂²	1	1	yes	characteristic
44	C₁₉×#459	C₂²	1	1	yes	characteristic
45	C₁₉×#452	—	2	1	no	—
46	C₁₉×#446	C₂²	1	1	yes	characteristic
47	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
48	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
49	C₁₉×#442	—	2	1	no	—
50	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
51	C₄×SD₁₆×C₁₉	—	2	1	no	—
52	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
53	C₄×D₈×C₁₉	—	2	1	no	—
54	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
55	C₁₉×#416	—	2	1	no	—
56	C₁₉×#335	C₂²	1	1	yes	characteristic
57	C₁₉×#335	C₂²	1	1	yes	characteristic
58	C₁₉×#332	C₂²	1	1	yes	characteristic
59	C₁₉×#331	C₂²	1	1	yes	characteristic
60	C₁₉×#331	C₂²	1	1	yes	characteristic
61	C₁₉×#331	C₂²	1	1	yes	characteristic
62	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
63	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₁₉×#322	C₂²	1	1	yes	characteristic
67	C₂×#41×C₁₉	—	2	1	no	—
68	C₂×Q₁₆×C₁₉	—	2	1	no	—
69	C₂×Q₁₆×C₁₉	D₄	1	1	yes	characteristic
70	C₂×SD₁₆×C₁₉	—	2	1	no	—
71	C₂×SD₁₆×C₁₉	—	2	1	no	—
72	C₂×SD₁₆×C₁₉	—	2	1	no	—
73	C₂×SD₁₆×C₁₉	—	2	1	no	—
74	C₂×SD₁₆×C₁₉	—	2	1	no	—
75	C₂×SD₁₆×C₁₉	—	2	1	no	—
76	C₂×SD₁₆×C₁₉	D₄	1	1	yes	characteristic
77	C₂×D₈×C₁₉	—	2	1	no	—
78	C₂×D₈×C₁₉	—	2	1	no	—
79	C₂×D₈×C₁₉	—	2	1	no	—
80	C₂×D₈×C₁₉	—	2	1	no	—
81	C₂×D₈×C₁₉	—	2	1	no	—
82	C₂×D₈×C₁₉	—	2	1	no	—
83	C₂×D₈×C₁₉	—	4	1	no	—
84	C₂²×C₈×C₁₉	—	2	1	no	—
85	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₁₉×#127	—	2	1	no	—
87	C₁₉×#127	C₂³	1	1	yes	characteristic
88	C₁₉×#127	C₂³	1	1	yes	characteristic
89	C₁₉×#127	C₂³	1	1	yes	characteristic
90	C₁₉×#126	—	4	1	no	—
91	C₁₉×#124	—	2	1	no	—
92	C₁₉×#124	—	2	1	no	—
93	C₁₉×#124	—	2	1	no	—
94	C₁₉×#124	—	2	1	no	—
95	C₁₉×#124	—	2	1	no	—
96	C₁₉×#123	—	4	1	no	—
97	C₁₉×#123	—	4	1	no	—
98	C₁₉×C₂²⋊Q₈	—	2	1	no	—
99	C₁₉×#121	—	2	1	no	—
100	C₁₉×#121	—	4	1	no	—
101	C₄×Q₈×C₁₉	—	2	1	no	—
102	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
103	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
104	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
105	C₄×D₄×C₁₉	—	2	1	no	—
106	C₄×D₄×C₁₉	—	2	1	no	—
107	C₄×D₄×C₁₉	—	2	1	no	—
108	C₄×D₄×C₁₉	—	2	1	no	—
109	C₄×D₄×C₁₉	—	2	1	no	—
110	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
111	C₁₉×#117	—	2	1	no	—
112	C₁₉×#107	D₄	1	1	yes	characteristic
113	C₁₉×#106	—	2	1	no	—
114	C₁₉×#106	D₄	1	1	yes	characteristic
115	C₁₉×C₄⋊C₈	—	2	1	no	—
116	C₁₉×C₄⋊C₈	—	2	1	no	—
117	C₁₉×C₄⋊C₈	—	2	1	no	—
118	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
119	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
121	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
122	C₁₉×#103	—	2	1	no	—
123	C₁₉×#103	—	2	1	no	—
124	C₁₉×#103	D₄	1	1	yes	characteristic
125	C₁₉×#103	D₄	1	1	yes	characteristic
126	C₁₉×#103	D₄	1	1	yes	characteristic
127	C₁₉×#102	—	2	1	no	—
128	C₁₉×#102	—	2	1	no	—
129	C₁₉×#102	—	2	1	no	—
130	C₁₉×#102	—	2	1	no	—
131	C₁₉×#102	—	2	1	no	—
132	C₁₉×#102	—	2	1	no	—
133	C₁₉×#102	—	2	1	no	—
134	C₁₉×#102	—	2	1	no	—
135	C₁₉×#102	—	4	1	no	—
136	C₁₉×#102	D₄	1	1	yes	characteristic
137	C₁₉×C₂²⋊C₈	—	2	1	no	—
138	C₁₉×#97	—	2	1	no	—
139	C₄×C₈×C₁₉	—	2	1	no	—
140	C₄×C₈×C₁₉	—	2	1	no	—
141	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
144	#41×C₁₉	—	4	2	no	—
145	#41×C₁₉	—	8	1	no	—
146	C₂×Q₈×C₁₉	—	2	1	no	—
147	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₂×D₄×C₁₉	—	2	1	no	—
151	C₂×D₄×C₁₉	—	2	1	no	—
152	C₂×D₄×C₁₉	—	2	1	no	—
153	C₂×D₄×C₁₉	—	2	1	no	—
154	C₂×D₄×C₁₉	—	2	1	no	—
155	C₂×D₄×C₁₉	—	2	1	no	—
156	C₂×D₄×C₁₉	—	2	1	no	—
157	C₂×D₄×C₁₉	—	2	1	no	—
158	C₂×D₄×C₁₉	—	2	1	no	—
159	C₂×D₄×C₁₉	—	4	1	no	—
160	C₂×D₄×C₁₉	—	4	1	no	—
161	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₉	—	2	1	no	—
163	C₂²×C₄×C₁₉	—	4	1	no	—
164	C₂²×C₄×C₁₉	—	4	1	no	—
165	C₂²×C₄×C₁₉	—	4	1	no	—
166	Q₁₆×C₁₉	—	4	1	no	—
167	Q₁₆×C₁₉	—	8	1	no	—
168	SD₁₆×C₁₉	—	2	2	no	—
169	SD₁₆×C₁₉	—	4	2	no	—
170	SD₁₆×C₁₉	—	8	1	no	—
171	SD₁₆×C₁₉	—	8	1	no	—
172	SD₁₆×C₁₉	—	8	1	no	—
173	SD₁₆×C₁₉	—	8	1	no	—
174	SD₁₆×C₁₉	—	8	1	no	—
175	D₈×C₁₉	—	4	2	no	—
176	D₈×C₁₉	—	4	2	no	—
177	D₈×C₁₉	—	8	1	no	—
178	D₈×C₁₉	—	8	1	no	—
179	D₈×C₁₉	—	8	1	no	—
180	D₈×C₁₉	—	8	1	no	—
181	D₈×C₁₉	—	8	2	no	—
182	C₂×C₈×C₁₉	—	2	1	no	—
183	C₂×C₈×C₁₉	—	2	1	no	—
184	C₂×C₈×C₁₉	—	2	1	no	—
185	C₂×C₈×C₁₉	—	2	1	no	—
186	C₂×C₈×C₁₉	—	2	1	no	—
187	C₂×C₈×C₁₉	—	8	1	no	—
188	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
190	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
191	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
192	C₄⋊C₄×C₁₉	—	2	1	no	—
193	C₄⋊C₄×C₁₉	—	2	1	no	—
194	C₄⋊C₄×C₁₉	—	2	1	no	—
195	C₄⋊C₄×C₁₉	—	2	1	no	—
196	C₄⋊C₄×C₁₉	—	2	1	no	—
197	C₄⋊C₄×C₁₉	—	4	1	no	—
198	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
199	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
200	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
201	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
202	C₂²⋊C₄×C₁₉	—	2	1	no	—
203	C₂²⋊C₄×C₁₉	—	4	1	no	—
204	C₂²⋊C₄×C₁₉	—	4	1	no	—
205	C₂²⋊C₄×C₁₉	—	4	1	no	—
206	C₂²⋊C₄×C₁₉	—	4	1	no	—
207	C₂²⋊C₄×C₁₉	—	4	1	no	—
208	C₂²⋊C₄×C₁₉	—	4	1	no	—
209	C₂²⋊C₄×C₁₉	—	4	1	no	—
210	C₂²⋊C₄×C₁₉	—	4	1	no	—
211	C₂²⋊C₄×C₁₉	—	4	1	no	—
212	C₄²×C₁₉	—	2	1	no	—
213	C₄²×C₁₉	—	2	1	no	—
214	C₄²×C₁₉	—	2	1	no	—
215	C₄²×C₁₉	—	4	1	no	—
216	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
217	#19871	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂³×C₁₉	—	2	1	no	—
219	C₂³×C₁₉	—	4	1	no	—
220	C₂³×C₁₉	—	4	1	no	—
221	C₂³×C₁₉	—	4	1	no	—
222	Q₈×C₁₉	—	2	1	no	—
223	Q₈×C₁₉	—	2	1	no	—
224	Q₈×C₁₉	—	2	1	no	—
225	Q₈×C₁₉	—	2	1	no	—
226	Q₈×C₁₉	—	2	1	no	—
227	Q₈×C₁₉	—	2	1	no	—
228	Q₈×C₁₉	—	4	1	no	—
229	Q₈×C₁₉	—	4	1	no	—
230	D₄×C₁₉	—	2	1	no	—
231	D₄×C₁₉	—	2	1	no	—
232	D₄×C₁₉	—	4	1	no	—
233	D₄×C₁₉	—	4	1	no	—
234	D₄×C₁₉	—	4	1	no	—
235	D₄×C₁₉	—	4	1	no	—
236	D₄×C₁₉	—	4	1	no	—
237	D₄×C₁₉	—	4	1	no	—
238	D₄×C₁₉	—	4	1	no	—
239	D₄×C₁₉	—	4	1	no	—
240	D₄×C₁₉	—	4	1	no	—
241	D₄×C₁₉	—	4	1	no	—
242	D₄×C₁₉	—	4	1	no	—
243	D₄×C₁₉	—	4	1	no	—
244	D₄×C₁₉	—	8	1	no	—
245	D₄×C₁₉	—	8	1	no	—
246	D₄×C₁₉	—	8	1	no	—
247	D₄×C₁₉	—	8	2	no	—
248	D₄×C₁₉	—	16	1	no	—
249	C₂×C₄×C₁₉	—	2	1	no	—
250	C₂×C₄×C₁₉	—	2	1	no	—
251	C₂×C₄×C₁₉	—	2	1	no	—
252	C₂×C₄×C₁₉	—	2	1	no	—
253	C₂×C₄×C₁₉	—	2	1	no	—
254	C₂×C₄×C₁₉	—	2	1	no	—
255	C₂×C₄×C₁₉	—	2	1	no	—
256	C₂×C₄×C₁₉	—	4	1	no	—
257	C₂×C₄×C₁₉	—	4	1	no	—
258	C₂×C₄×C₁₉	—	4	1	no	—
259	C₂×C₄×C₁₉	—	8	2	no	—
260	C₂×C₄×C₁₉	—	16	1	no	—
261	C₂×C₄×C₁₉	—	16	1	no	—
262	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
265	C₈×C₁₉	—	2	1	no	—
266	C₈×C₁₉	—	2	1	no	—
267	C₈×C₁₉	—	2	1	no	—
268	C₈×C₁₉	—	4	1	no	—
269	C₈×C₁₉	—	4	1	no	—
270	C₈×C₁₉	—	4	1	no	—
271	C₈×C₁₉	—	4	1	no	—
272	C₈×C₁₉	—	4	1	no	—
273	C₈×C₁₉	#135	1	2	yes	—
274	#3399	C₂×C₁₉	1	1	yes	characteristic, complemented
275	#3396	C₂×C₁₉	1	1	yes	characteristic, complemented
276	#3394	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#3304	C₂×C₁₉	1	1	yes	characteristic, complemented
278	#1721	C₂×C₁₉	1	1	yes	characteristic, complemented
279	#1686	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#1682	C₂×C₁₉	1	1	yes	characteristic, complemented
281	#1668	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#1667	C₂×C₁₉	1	1	yes	characteristic, complemented
283	#1640	C₂×C₁₉	1	1	yes	characteristic, complemented
284	#1628	C₂×C₁₉	1	1	yes	characteristic, complemented
285	#1621	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#1620	C₂×C₁₉	1	1	yes	characteristic, complemented
287	#1584	C₂×C₁₉	1	1	yes	characteristic, complemented
288	SD₁₆⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
289	C₂²×C₁₉	—	4	1	no	—
290	C₂²×C₁₉	—	4	1	no	—
291	C₂²×C₁₉	—	4	1	no	—
292	C₂²×C₁₉	—	8	1	no	—
293	C₂²×C₁₉	—	8	1	no	—
294	C₂²×C₁₉	—	8	1	no	—
295	C₂²×C₁₉	—	8	1	no	—
296	C₂²×C₁₉	—	8	1	no	—
297	C₂²×C₁₉	—	8	1	no	—
298	C₂²×C₁₉	—	8	1	no	—
299	C₂²×C₁₉	—	8	1	no	—
300	C₂²×C₁₉	—	8	1	no	—
301	C₂²×C₁₉	D₄²	1	1	yes	characteristic
302	C₄×C₁₉	—	2	1	no	—
303	C₄×C₁₉	—	4	1	no	—
304	C₄×C₁₉	—	4	1	no	—
305	C₄×C₁₉	—	4	1	no	—
306	C₄×C₁₉	—	4	1	no	—
307	C₄×C₁₉	—	4	1	no	—
308	C₄×C₁₉	—	4	1	no	—
309	C₄×C₁₉	—	4	1	no	—
310	C₄×C₁₉	—	8	1	no	—
311	C₄×C₁₉	C₂×#135	1	1	yes	characteristic
312	C₄×C₁₉	#575	1	1	yes	characteristic
313	C₄×C₁₉	#576	1	1	yes	characteristic
314	C₄×C₁₉	#576	1	1	yes	characteristic
315	#559	C₂²×C₁₉	1	1	yes	characteristic
316	#559	C₂²×C₁₉	1	1	yes	characteristic
317	#556	C₂²×C₁₉	1	1	yes	characteristic
318	#550	C₂²×C₁₉	1	1	yes	characteristic
319	#496	—	2	1	no	—
320	#495	—	2	1	no	—
321	#495	—	2	1	no	—
322	#493	C₂²×C₁₉	1	1	yes	characteristic
323	#493	C₂²×C₁₉	1	1	yes	characteristic
324	#493	C₂²×C₁₉	1	1	yes	characteristic
325	#492	C₂²×C₁₉	1	1	yes	characteristic
326	#486	C₂²×C₁₉	1	1	yes	characteristic
327	#486	C₂²×C₁₉	1	1	yes	characteristic
328	#482	—	2	1	no	—
329	#475	C₂²×C₁₉	1	1	yes	characteristic
330	#465	—	2	1	no	—
331	#464	—	2	1	no	—
332	#463	—	2	1	no	—
333	#463	—	2	1	no	—
334	#463	—	2	1	no	—
335	#463	—	2	1	no	—
336	#462	C₂²×C₁₉	1	1	yes	characteristic
337	#460	C₂²×C₁₉	1	1	yes	characteristic
338	#460	C₂²×C₁₉	1	1	yes	characteristic
339	#460	C₂²×C₁₉	1	1	yes	characteristic
340	#460	C₂²×C₁₉	1	1	yes	characteristic
341	#459	—	2	1	no	—
342	#459	C₂²×C₁₉	1	1	yes	characteristic
343	#459	C₂²×C₁₉	1	1	yes	characteristic
344	#452	—	2	1	no	—
345	#446	C₂²×C₁₉	1	1	yes	characteristic
346	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
347	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
348	#442	—	2	1	no	—
349	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
350	C₄×SD₁₆	—	2	1	no	—
351	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
352	C₄×D₈	—	2	1	no	—
353	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
354	#416	—	2	1	no	—
355	#335	C₂²×C₁₉	1	1	yes	characteristic
356	#335	C₂²×C₁₉	1	1	yes	characteristic
357	#332	C₂²×C₁₉	1	1	yes	characteristic
358	#331	C₂²×C₁₉	1	1	yes	characteristic
359	#331	C₂²×C₁₉	1	1	yes	characteristic
360	#331	C₂²×C₁₉	1	1	yes	characteristic
361	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
362	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
363	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
364	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
365	#322	C₂²×C₁₉	1	1	yes	characteristic
366	C₂×C₁₉	—	8	1	no	—
367	C₂×C₁₉	—	16	1	no	—
368	C₂×C₁₉	—	16	1	no	—
369	C₂×C₁₉	—	16	1	no	—
370	C₂×C₁₉	#3268	1	1	yes	characteristic
371	C₂×C₁₉	#3287	1	1	yes	characteristic
372	C₂×C₁₉	#3288	1	1	yes	characteristic
373	C₂×#41	—	2	1	no	—
374	C₂×Q₁₆	—	2	1	no	—
375	C₂×Q₁₆	D₄×C₁₉	1	1	yes	characteristic
376	C₂×SD₁₆	—	2	1	no	—
377	C₂×SD₁₆	—	2	1	no	—
378	C₂×SD₁₆	—	2	1	no	—
379	C₂×SD₁₆	—	2	1	no	—
380	C₂×SD₁₆	—	2	1	no	—
381	C₂×SD₁₆	—	2	1	no	—
382	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
383	C₂×D₈	—	2	1	no	—
384	C₂×D₈	—	2	1	no	—
385	C₂×D₈	—	2	1	no	—
386	C₂×D₈	—	2	1	no	—
387	C₂×D₈	—	2	1	no	—
388	C₂×D₈	—	2	1	no	—
389	C₂×D₈	—	4	1	no	—
390	C₂²×C₈	—	2	1	no	—
391	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
392	#127	—	2	1	no	—
393	#127	C₂³×C₁₉	1	1	yes	characteristic
394	#127	C₂³×C₁₉	1	1	yes	characteristic
395	#127	C₂³×C₁₉	1	1	yes	characteristic
396	#126	—	4	1	no	—
397	#124	—	2	1	no	—
398	#124	—	2	1	no	—
399	#124	—	2	1	no	—
400	#124	—	2	1	no	—
401	#124	—	2	1	no	—
402	#123	—	4	1	no	—
403	#123	—	4	1	no	—
404	C₂²⋊Q₈	—	2	1	no	—
405	#121	—	2	1	no	—
406	#121	—	4	1	no	—
407	C₄×Q₈	—	2	1	no	—
408	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
409	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
410	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
411	C₄×D₄	—	2	1	no	—
412	C₄×D₄	—	2	1	no	—
413	C₄×D₄	—	2	1	no	—
414	C₄×D₄	—	2	1	no	—
415	C₄×D₄	—	2	1	no	—
416	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
417	#117	—	2	1	no	—
418	#107	D₄×C₁₉	1	1	yes	characteristic
419	#106	—	2	1	no	—
420	#106	D₄×C₁₉	1	1	yes	characteristic
421	C₄⋊C₈	—	2	1	no	—
422	C₄⋊C₈	—	2	1	no	—
423	C₄⋊C₈	—	2	1	no	—
424	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
425	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
426	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
427	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
428	#103	—	2	1	no	—
429	#103	—	2	1	no	—
430	#103	D₄×C₁₉	1	1	yes	characteristic
431	#103	D₄×C₁₉	1	1	yes	characteristic
432	#103	D₄×C₁₉	1	1	yes	characteristic
433	#102	—	2	1	no	—
434	#102	—	2	1	no	—
435	#102	—	2	1	no	—
436	#102	—	2	1	no	—
437	#102	—	2	1	no	—
438	#102	—	2	1	no	—
439	#102	—	2	1	no	—
440	#102	—	2	1	no	—
441	#102	—	4	1	no	—
442	#102	D₄×C₁₉	1	1	yes	characteristic
443	C₂²⋊C₈	—	2	1	no	—
444	#97	—	2	1	no	—
445	C₄×C₈	—	2	1	no	—
446	C₄×C₈	—	2	1	no	—
447	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
448	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
449	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
450	C₁₉	#19871	1	1	yes	characteristic, direct product factor, Sylow
451	#41	—	4	2	no	—
452	#41	—	8	1	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
455	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
456	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	4	1	no	—
467	C₂×D₄	—	4	1	no	—
468	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	4	1	no	—
471	C₂²×C₄	—	4	1	no	—
472	C₂²×C₄	—	4	1	no	—
473	Q₁₆	—	4	1	no	—
474	Q₁₆	—	8	1	no	—
475	SD₁₆	—	2	2	no	—
476	SD₁₆	—	4	2	no	—
477	SD₁₆	—	8	1	no	—
478	SD₁₆	—	8	1	no	—
479	SD₁₆	—	8	1	no	—
480	SD₁₆	—	8	1	no	—
481	SD₁₆	—	8	1	no	—
482	D₈	—	4	2	no	—
483	D₈	—	4	2	no	—
484	D₈	—	8	1	no	—
485	D₈	—	8	1	no	—
486	D₈	—	8	1	no	—
487	D₈	—	8	1	no	—
488	D₈	—	8	2	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	8	1	no	—
495	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
496	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
497	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
498	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	4	1	no	—
505	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
506	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
507	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
508	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
509	C₂²⋊C₄	—	2	1	no	—
510	C₂²⋊C₄	—	4	1	no	—
511	C₂²⋊C₄	—	4	1	no	—
512	C₂²⋊C₄	—	4	1	no	—
513	C₂²⋊C₄	—	4	1	no	—
514	C₂²⋊C₄	—	4	1	no	—
515	C₂²⋊C₄	—	4	1	no	—
516	C₂²⋊C₄	—	4	1	no	—
517	C₂²⋊C₄	—	4	1	no	—
518	C₂²⋊C₄	—	4	1	no	—
519	C₄²	—	2	1	no	—
520	C₄²	—	2	1	no	—
521	C₄²	—	2	1	no	—
522	C₄²	—	4	1	no	—
523	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
524	C₂³	—	2	1	no	—
525	C₂³	—	4	1	no	—
526	C₂³	—	4	1	no	—
527	C₂³	—	4	1	no	—
528	Q₈	—	2	1	no	—
529	Q₈	—	2	1	no	—
530	Q₈	—	2	1	no	—
531	Q₈	—	2	1	no	—
532	Q₈	—	2	1	no	—
533	Q₈	—	2	1	no	—
534	Q₈	—	4	1	no	—
535	Q₈	—	4	1	no	—
536	D₄	—	2	1	no	—
537	D₄	—	2	1	no	—
538	D₄	—	4	1	no	—
539	D₄	—	4	1	no	—
540	D₄	—	4	1	no	—
541	D₄	—	4	1	no	—
542	D₄	—	4	1	no	—
543	D₄	—	4	1	no	—
544	D₄	—	4	1	no	—
545	D₄	—	4	1	no	—
546	D₄	—	4	1	no	—
547	D₄	—	4	1	no	—
548	D₄	—	4	1	no	—
549	D₄	—	4	1	no	—
550	D₄	—	8	1	no	—
551	D₄	—	8	1	no	—
552	D₄	—	8	1	no	—
553	D₄	—	8	2	no	—
554	D₄	—	16	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	8	2	no	—
566	C₂×C₄	—	16	1	no	—
567	C₂×C₄	—	16	1	no	—
568	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
569	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
570	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
571	C₈	—	2	1	no	—
572	C₈	—	2	1	no	—
573	C₈	—	2	1	no	—
574	C₈	—	4	1	no	—
575	C₈	—	4	1	no	—
576	C₈	—	4	1	no	—
577	C₈	—	4	1	no	—
578	C₈	—	4	1	no	—
579	C₈	C₁₉×#135	1	2	yes	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	8	1	no	—
584	C₂²	—	8	1	no	—
585	C₂²	—	8	1	no	—
586	C₂²	—	8	1	no	—
587	C₂²	—	8	1	no	—
588	C₂²	—	8	1	no	—
589	C₂²	—	8	1	no	—
590	C₂²	—	8	1	no	—
591	C₂²	—	8	1	no	—
592	C₂²	D₄²×C₁₉	1	1	yes	characteristic
593	C₄	—	2	1	no	—
594	C₄	—	4	1	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	1	no	—
599	C₄	—	4	1	no	—
600	C₄	—	4	1	no	—
601	C₄	—	8	1	no	—
602	C₄	C₂×C₁₉×#135	1	1	yes	characteristic
603	C₄	C₁₉×#575	1	1	yes	characteristic
604	C₄	C₁₉×#576	1	1	yes	characteristic
605	C₄	C₁₉×#576	1	1	yes	characteristic
606	C₂	—	8	1	no	—
607	C₂	—	16	1	no	—
608	C₂	—	16	1	no	—
609	C₂	—	16	1	no	—
610	C₂	C₁₉×#3268	1	1	yes	characteristic
611	C₂	C₁₉×#3287	1	1	yes	characteristic
612	C₂	C₁₉×#3288	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3399	C₂	semidirect
2. C₁₉×#3396	C₂	semidirect
3. C₁₉×#3394	C₂	semidirect
4. C₁₉×#3304	C₂	semidirect
5. C₁₉×#1721	C₂	semidirect
6. C₁₉×#1686	C₂	semidirect
7. C₁₉×#1682	C₂	semidirect
8. C₁₉×#1668	C₂	semidirect
9. C₁₉×#1667	C₂	semidirect
10. C₁₉×#1640	C₂	semidirect
11. C₁₉×#1628	C₂	semidirect
12. C₁₉×#1621	C₂	semidirect
13. C₁₉×#1620	C₂	semidirect
14. C₁₉×#1584	C₂	semidirect
15. C₁₉×SD₁₆⋊C₈	C₂	semidirect
217. #19871	C₁₉	direct (N × H)
274. #3399	C₂×C₁₉	semidirect
275. #3396	C₂×C₁₉	semidirect
276. #3394	C₂×C₁₉	semidirect
277. #3304	C₂×C₁₉	semidirect
278. #1721	C₂×C₁₉	semidirect
279. #1686	C₂×C₁₉	semidirect
280. #1682	C₂×C₁₉	semidirect
281. #1668	C₂×C₁₉	semidirect
282. #1667	C₂×C₁₉	semidirect
283. #1640	C₂×C₁₉	semidirect
284. #1628	C₂×C₁₉	semidirect
285. #1621	C₂×C₁₉	semidirect
286. #1620	C₂×C₁₉	semidirect
287. #1584	C₂×C₁₉	semidirect
288. SD₁₆⋊C₈	C₂×C₁₉	semidirect
450. C₁₉	#19871	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×#3399	2
C₁₉×#3396	2
C₁₉×#3394	2
C₁₉×#3304	2
C₁₉×#1721	2
C₁₉×#1686	2
C₁₉×#1682	2
C₁₉×#1668	2
C₁₉×#1667	2
C₁₉×#1640	2
C₁₉×#1628	2
C₁₉×#1621	2
C₁₉×#1620	2
C₁₉×#1584	2
C₁₉×SD₁₆⋊C₈	2
#19871	19

Subgroups — C19×#19871 #18025830

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19871 #18025830