Subgroups — C₁₉×#19865 #18025824

Order 4864.

572 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3380	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3360	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3356	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3338	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1723	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1695	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1684	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1676	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1671	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1643	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1638	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1632	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1632	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1581	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#1579	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#556	C₂²	1	1	yes	characteristic
17	C₁₉×#554	C₂²	1	1	yes	characteristic
18	C₁₉×#554	C₂²	1	1	yes	characteristic
19	C₁₉×#554	C₂²	1	1	yes	characteristic
20	C₁₉×#500	C₂²	1	1	yes	characteristic
21	C₁₉×#500	C₂²	1	1	yes	characteristic
22	C₁₉×#499	—	2	1	no	—
23	C₁₉×#498	C₂²	1	1	yes	characteristic
24	C₁₉×#494	C₂²	1	1	yes	characteristic
25	C₁₉×#488	—	2	1	no	—
26	C₁₉×#487	C₂²	1	1	yes	characteristic
27	C₁₉×#487	C₂²	1	1	yes	characteristic
28	C₁₉×#485	—	2	1	no	—
29	C₁₉×#484	—	2	1	no	—
30	C₁₉×#484	—	2	1	no	—
31	C₁₉×#483	—	2	1	no	—
32	C₁₉×#479	—	2	1	no	—
33	C₁₉×#478	—	2	1	no	—
34	C₁₉×#478	—	2	1	no	—
35	C₁₉×#477	C₂²	1	1	yes	characteristic
36	C₁₉×#477	C₂²	1	1	yes	characteristic
37	C₁₉×#477	C₂²	1	1	yes	characteristic
38	C₁₉×#476	C₂²	1	1	yes	characteristic
39	C₁₉×#476	C₂²	1	1	yes	characteristic
40	C₁₉×#476	C₂²	1	1	yes	characteristic
41	C₁₉×#475	C₂²	1	1	yes	characteristic
42	C₁₉×#470	—	2	1	no	—
43	C₁₉×#467	—	2	1	no	—
44	C₁₉×#463	—	2	1	no	—
45	C₁₉×#461	C₂²	1	1	yes	characteristic
46	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
47	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
48	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
49	C₄×SD₁₆×C₁₉	—	2	1	no	—
50	C₄×D₈×C₁₉	—	2	1	no	—
51	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
52	C₁₉×#436	C₂²	1	1	yes	characteristic
53	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
54	C₁₉×#428	—	2	1	no	—
55	C₂×C₁₉×#107	—	2	1	no	—
56	C₁₉×#335	C₂²	1	1	yes	characteristic
57	C₁₉×#334	C₂²	1	1	yes	characteristic
58	C₁₉×#333	C₂²	1	1	yes	characteristic
59	C₁₉×#333	C₂²	1	1	yes	characteristic
60	C₁₉×#333	C₂²	1	1	yes	characteristic
61	C₁₉×#332	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×D₄⋊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×Q₁₆×C₁₉	—	4	1	no	—
68	C₂×Q₁₆×C₁₉	D₄	1	1	yes	characteristic
69	C₂×SD₁₆×C₁₉	—	2	1	no	—
70	C₂×D₈×C₁₉	D₄	1	1	yes	characteristic
71	C₂×M₁₆×C₁₉	—	2	1	no	—
72	C₂²×C₈×C₁₉	—	2	1	no	—
73	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
74	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
75	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
76	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
77	C₁₉×#126	—	4	1	no	—
78	C₁₉×#125	—	2	1	no	—
79	C₁₉×#125	—	2	1	no	—
80	C₁₉×#125	—	2	1	no	—
81	C₁₉×#124	—	2	1	no	—
82	C₁₉×C₂²⋊Q₈	—	2	1	no	—
83	C₁₉×C₂²⋊Q₈	—	2	1	no	—
84	C₁₉×C₂²⋊Q₈	—	2	1	no	—
85	C₁₉×C₂²⋊Q₈	—	2	1	no	—
86	C₁₉×C₂²⋊Q₈	—	4	1	no	—
87	C₁₉×C₂²⋊Q₈	—	4	1	no	—
88	C₁₉×C₂²⋊Q₈	—	4	1	no	—
89	C₄×Q₈×C₁₉	—	2	1	no	—
90	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
91	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
92	C₄×D₄×C₁₉	—	2	1	no	—
93	C₄×D₄×C₁₉	—	2	1	no	—
94	C₄×D₄×C₁₉	—	2	1	no	—
95	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
96	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
97	C₁₉×#117	—	2	1	no	—
98	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
99	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
101	C₁₉×#107	—	2	1	no	—
102	C₁₉×#107	—	2	1	no	—
103	C₁₉×#107	—	2	1	no	—
104	C₁₉×#107	—	2	1	no	—
105	C₁₉×#107	—	2	1	no	—
106	C₁₉×#107	—	2	1	no	—
107	C₁₉×#107	—	2	1	no	—
108	C₁₉×#107	D₄	1	1	yes	characteristic
109	C₁₉×#107	D₄	1	1	yes	characteristic
110	C₁₉×#106	—	2	1	no	—
111	C₁₉×#106	—	2	1	no	—
112	C₁₉×#106	—	2	1	no	—
113	C₁₉×#106	—	2	1	no	—
114	C₁₉×#106	—	2	1	no	—
115	C₁₉×#106	—	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	—	2	1	no	—
125	C₁₉×#103	—	2	1	no	—
126	C₁₉×#103	—	2	1	no	—
127	C₁₉×#103	—	2	1	no	—
128	C₁₉×#103	—	2	1	no	—
129	C₁₉×#103	—	4	1	no	—
130	C₁₉×#103	D₄	1	1	yes	characteristic
131	C₁₉×#103	D₄	1	1	yes	characteristic
132	C₁₉×#102	—	2	1	no	—
133	C₁₉×#102	—	2	1	no	—
134	C₁₉×#102	—	2	1	no	—
135	C₁₉×#102	D₄	1	1	yes	characteristic
136	C₁₉×#102	D₄	1	1	yes	characteristic
137	C₁₉×C₂²⋊C₈	—	2	1	no	—
138	C₁₉×C₂²⋊C₈	—	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	C₂×Q₈×C₁₉	—	2	1	no	—
145	C₂×Q₈×C₁₉	—	2	1	no	—
146	C₂×Q₈×C₁₉	—	2	1	no	—
147	C₂×Q₈×C₁₉	—	2	1	no	—
148	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₉	—	2	1	no	—
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	C₂²×C₄×C₁₉	—	4	1	no	—
155	C₂²×C₄×C₁₉	—	4	1	no	—
156	C₂²×C₄×C₁₉	—	4	1	no	—
157	Q₁₆×C₁₉	—	2	2	no	—
158	Q₁₆×C₁₉	—	8	2	no	—
159	SD₁₆×C₁₉	—	4	2	no	—
160	D₈×C₁₉	—	2	2	no	—
161	M₁₆×C₁₉	—	4	2	no	—
162	C₂×C₈×C₁₉	—	2	1	no	—
163	C₂×C₈×C₁₉	—	2	1	no	—
164	C₂×C₈×C₁₉	—	2	1	no	—
165	C₂×C₈×C₁₉	—	2	1	no	—
166	C₂×C₈×C₁₉	—	2	1	no	—
167	C₂×C₈×C₁₉	—	4	2	no	—
168	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
171	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₄⋊C₄×C₁₉	—	2	1	no	—
173	C₄⋊C₄×C₁₉	—	2	1	no	—
174	C₄⋊C₄×C₁₉	—	2	1	no	—
175	C₄⋊C₄×C₁₉	—	2	1	no	—
176	C₄⋊C₄×C₁₉	—	2	1	no	—
177	C₄⋊C₄×C₁₉	—	2	1	no	—
178	C₄⋊C₄×C₁₉	—	2	1	no	—
179	C₄⋊C₄×C₁₉	—	2	1	no	—
180	C₄⋊C₄×C₁₉	—	2	1	no	—
181	C₄⋊C₄×C₁₉	—	2	1	no	—
182	C₄⋊C₄×C₁₉	—	4	1	no	—
183	C₄⋊C₄×C₁₉	—	4	1	no	—
184	C₄⋊C₄×C₁₉	—	4	1	no	—
185	C₄⋊C₄×C₁₉	—	4	1	no	—
186	C₄⋊C₄×C₁₉	—	4	1	no	—
187	C₄⋊C₄×C₁₉	—	4	1	no	—
188	C₄⋊C₄×C₁₉	—	4	1	no	—
189	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
190	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
191	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
192	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
193	C₂²⋊C₄×C₁₉	—	2	1	no	—
194	C₂²⋊C₄×C₁₉	—	2	1	no	—
195	C₂²⋊C₄×C₁₉	—	4	1	no	—
196	C₂²⋊C₄×C₁₉	—	4	1	no	—
197	C₂²⋊C₄×C₁₉	—	4	1	no	—
198	C₂²⋊C₄×C₁₉	—	4	1	no	—
199	C₂²⋊C₄×C₁₉	—	4	1	no	—
200	C₄²×C₁₉	—	2	1	no	—
201	C₄²×C₁₉	—	2	1	no	—
202	C₄²×C₁₉	—	4	1	no	—
203	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
204	#19865	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂³×C₁₉	—	2	1	no	—
206	C₂³×C₁₉	—	2	1	no	—
207	Q₈×C₁₉	—	2	1	no	—
208	Q₈×C₁₉	—	2	1	no	—
209	Q₈×C₁₉	—	2	1	no	—
210	Q₈×C₁₉	—	2	1	no	—
211	Q₈×C₁₉	—	4	1	no	—
212	Q₈×C₁₉	—	4	1	no	—
213	Q₈×C₁₉	—	8	1	no	—
214	Q₈×C₁₉	—	8	1	no	—
215	Q₈×C₁₉	—	8	1	no	—
216	D₄×C₁₉	—	2	1	no	—
217	D₄×C₁₉	—	2	1	no	—
218	D₄×C₁₉	—	2	1	no	—
219	D₄×C₁₉	#137	1	2	yes	—
220	C₂×C₄×C₁₉	—	2	1	no	—
221	C₂×C₄×C₁₉	—	2	1	no	—
222	C₂×C₄×C₁₉	—	2	1	no	—
223	C₂×C₄×C₁₉	—	2	1	no	—
224	C₂×C₄×C₁₉	—	2	1	no	—
225	C₂×C₄×C₁₉	—	2	1	no	—
226	C₂×C₄×C₁₉	—	4	1	no	—
227	C₂×C₄×C₁₉	—	4	1	no	—
228	C₂×C₄×C₁₉	—	4	1	no	—
229	C₂×C₄×C₁₉	—	4	1	no	—
230	C₂×C₄×C₁₉	—	4	1	no	—
231	C₂×C₄×C₁₉	—	4	1	no	—
232	C₂×C₄×C₁₉	—	4	1	no	—
233	C₂×C₄×C₁₉	—	4	1	no	—
234	C₂×C₄×C₁₉	—	16	1	no	—
235	C₂×C₄×C₁₉	—	16	1	no	—
236	C₂×C₄×C₁₉	—	16	1	no	—
237	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
240	C₈×C₁₉	—	2	1	no	—
241	C₈×C₁₉	—	2	1	no	—
242	C₈×C₁₉	—	2	1	no	—
243	C₈×C₁₉	—	4	1	no	—
244	C₈×C₁₉	—	4	1	no	—
245	C₈×C₁₉	—	4	1	no	—
246	C₈×C₁₉	—	4	1	no	—
247	C₈×C₁₉	—	4	1	no	—
248	C₈×C₁₉	#135	1	2	yes	—
249	#3380	C₂×C₁₉	1	1	yes	characteristic
250	#3360	C₂×C₁₉	1	1	yes	characteristic
251	#3356	C₂×C₁₉	1	1	yes	characteristic, complemented
252	#3338	C₂×C₁₉	1	1	yes	characteristic, complemented
253	#1723	C₂×C₁₉	1	1	yes	characteristic, complemented
254	#1695	C₂×C₁₉	1	1	yes	characteristic, complemented
255	#1684	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#1676	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#1671	C₂×C₁₉	1	1	yes	characteristic, complemented
258	#1643	C₂×C₁₉	1	1	yes	characteristic, complemented
259	#1638	C₂×C₁₉	1	1	yes	characteristic, complemented
260	#1632	C₂×C₁₉	1	1	yes	characteristic, complemented
261	#1632	C₂×C₁₉	1	1	yes	characteristic, complemented
262	#1581	C₂×C₁₉	1	1	yes	characteristic
263	#1579	C₂×C₁₉	1	1	yes	characteristic, complemented
264	C₂²×C₁₉	—	2	2	no	—
265	C₂²×C₁₉	—	4	1	no	—
266	C₂²×C₁₉	—	4	1	no	—
267	C₂²×C₁₉	—	4	1	no	—
268	C₂²×C₁₉	—	4	1	no	—
269	C₂²×C₁₉	—	4	1	no	—
270	C₂²×C₁₉	D₄²	1	1	yes	characteristic
271	C₄×C₁₉	—	2	1	no	—
272	C₄×C₁₉	—	4	1	no	—
273	C₄×C₁₉	—	4	1	no	—
274	C₄×C₁₉	—	4	1	no	—
275	C₄×C₁₉	—	4	1	no	—
276	C₄×C₁₉	—	4	1	no	—
277	C₄×C₁₉	—	4	1	no	—
278	C₄×C₁₉	—	8	1	no	—
279	C₄×C₁₉	—	8	1	no	—
280	C₄×C₁₉	—	8	1	no	—
281	C₄×C₁₉	—	8	1	no	—
282	C₄×C₁₉	C₂×#135	1	1	yes	characteristic
283	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
284	C₄×C₁₉	#578	1	1	yes	characteristic
285	C₄×C₁₉	#578	1	1	yes	characteristic
286	#556	C₂²×C₁₉	1	1	yes	characteristic
287	#554	C₂²×C₁₉	1	1	yes	characteristic
288	#554	C₂²×C₁₉	1	1	yes	characteristic
289	#554	C₂²×C₁₉	1	1	yes	characteristic
290	#500	C₂²×C₁₉	1	1	yes	characteristic
291	#500	C₂²×C₁₉	1	1	yes	characteristic
292	#499	—	2	1	no	—
293	#498	C₂²×C₁₉	1	1	yes	characteristic
294	#494	C₂²×C₁₉	1	1	yes	characteristic
295	#488	—	2	1	no	—
296	#487	C₂²×C₁₉	1	1	yes	characteristic
297	#487	C₂²×C₁₉	1	1	yes	characteristic
298	#485	—	2	1	no	—
299	#484	—	2	1	no	—
300	#484	—	2	1	no	—
301	#483	—	2	1	no	—
302	#479	—	2	1	no	—
303	#478	—	2	1	no	—
304	#478	—	2	1	no	—
305	#477	C₂²×C₁₉	1	1	yes	characteristic
306	#477	C₂²×C₁₉	1	1	yes	characteristic
307	#477	C₂²×C₁₉	1	1	yes	characteristic
308	#476	C₂²×C₁₉	1	1	yes	characteristic
309	#476	C₂²×C₁₉	1	1	yes	characteristic
310	#476	C₂²×C₁₉	1	1	yes	characteristic
311	#475	C₂²×C₁₉	1	1	yes	characteristic
312	#470	—	2	1	no	—
313	#467	—	2	1	no	—
314	#463	—	2	1	no	—
315	#461	C₂²×C₁₉	1	1	yes	characteristic
316	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
317	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
318	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
319	C₄×SD₁₆	—	2	1	no	—
320	C₄×D₈	—	2	1	no	—
321	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
322	#436	C₂²×C₁₉	1	1	yes	characteristic
323	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
324	#428	—	2	1	no	—
325	C₂×#107	—	2	1	no	—
326	#335	C₂²×C₁₉	1	1	yes	characteristic
327	#334	C₂²×C₁₉	1	1	yes	characteristic
328	#333	C₂²×C₁₉	1	1	yes	characteristic
329	#333	C₂²×C₁₉	1	1	yes	characteristic
330	#333	C₂²×C₁₉	1	1	yes	characteristic
331	#332	C₂²×C₁₉	1	1	yes	characteristic
332	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
333	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
334	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
335	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
336	#322	C₂²×C₁₉	1	1	yes	characteristic
337	C₂×C₁₉	—	4	2	no	—
338	C₂×C₁₉	—	8	1	no	—
339	C₂×C₁₉	#3270	1	1	yes	characteristic
340	C₂×C₁₉	#3283	1	1	yes	characteristic
341	C₂×C₁₉	#3288	1	1	yes	characteristic
342	C₂×Q₁₆	—	4	1	no	—
343	C₂×Q₁₆	D₄×C₁₉	1	1	yes	characteristic
344	C₂×SD₁₆	—	2	1	no	—
345	C₂×D₈	D₄×C₁₉	1	1	yes	characteristic
346	C₂×M₁₆	—	2	1	no	—
347	C₂²×C₈	—	2	1	no	—
348	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
349	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
350	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
351	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
352	#126	—	4	1	no	—
353	#125	—	2	1	no	—
354	#125	—	2	1	no	—
355	#125	—	2	1	no	—
356	#124	—	2	1	no	—
357	C₂²⋊Q₈	—	2	1	no	—
358	C₂²⋊Q₈	—	2	1	no	—
359	C₂²⋊Q₈	—	2	1	no	—
360	C₂²⋊Q₈	—	2	1	no	—
361	C₂²⋊Q₈	—	4	1	no	—
362	C₂²⋊Q₈	—	4	1	no	—
363	C₂²⋊Q₈	—	4	1	no	—
364	C₄×Q₈	—	2	1	no	—
365	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
366	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
367	C₄×D₄	—	2	1	no	—
368	C₄×D₄	—	2	1	no	—
369	C₄×D₄	—	2	1	no	—
370	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
371	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
372	#117	—	2	1	no	—
373	C₂×C₄⋊C₄	—	2	1	no	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	#107	—	2	1	no	—
377	#107	—	2	1	no	—
378	#107	—	2	1	no	—
379	#107	—	2	1	no	—
380	#107	—	2	1	no	—
381	#107	—	2	1	no	—
382	#107	—	2	1	no	—
383	#107	D₄×C₁₉	1	1	yes	characteristic
384	#107	D₄×C₁₉	1	1	yes	characteristic
385	#106	—	2	1	no	—
386	#106	—	2	1	no	—
387	#106	—	2	1	no	—
388	#106	—	2	1	no	—
389	#106	—	2	1	no	—
390	#106	—	2	1	no	—
391	C₄⋊C₈	—	2	1	no	—
392	C₄⋊C₈	—	2	1	no	—
393	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
394	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
395	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
396	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
397	#103	—	2	1	no	—
398	#103	—	2	1	no	—
399	#103	—	2	1	no	—
400	#103	—	2	1	no	—
401	#103	—	2	1	no	—
402	#103	—	2	1	no	—
403	#103	—	2	1	no	—
404	#103	—	4	1	no	—
405	#103	D₄×C₁₉	1	1	yes	characteristic
406	#103	D₄×C₁₉	1	1	yes	characteristic
407	#102	—	2	1	no	—
408	#102	—	2	1	no	—
409	#102	—	2	1	no	—
410	#102	D₄×C₁₉	1	1	yes	characteristic
411	#102	D₄×C₁₉	1	1	yes	characteristic
412	C₂²⋊C₈	—	2	1	no	—
413	C₂²⋊C₈	—	2	1	no	—
414	C₄×C₈	—	2	1	no	—
415	C₄×C₈	—	2	1	no	—
416	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
417	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
418	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
419	C₁₉	#19865	1	1	yes	characteristic, direct product factor, Sylow
420	C₂×Q₈	—	2	1	no	—
421	C₂×Q₈	—	2	1	no	—
422	C₂×Q₈	—	2	1	no	—
423	C₂×Q₈	—	2	1	no	—
424	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
425	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
426	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
427	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	4	1	no	—
431	C₂²×C₄	—	4	1	no	—
432	C₂²×C₄	—	4	1	no	—
433	Q₁₆	—	2	2	no	—
434	Q₁₆	—	8	2	no	—
435	SD₁₆	—	4	2	no	—
436	D₈	—	2	2	no	—
437	M₁₆	—	4	2	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	4	2	no	—
444	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
445	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
446	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
447	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	4	1	no	—
459	C₄⋊C₄	—	4	1	no	—
460	C₄⋊C₄	—	4	1	no	—
461	C₄⋊C₄	—	4	1	no	—
462	C₄⋊C₄	—	4	1	no	—
463	C₄⋊C₄	—	4	1	no	—
464	C₄⋊C₄	—	4	1	no	—
465	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
466	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
467	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
468	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
469	C₂²⋊C₄	—	2	1	no	—
470	C₂²⋊C₄	—	2	1	no	—
471	C₂²⋊C₄	—	4	1	no	—
472	C₂²⋊C₄	—	4	1	no	—
473	C₂²⋊C₄	—	4	1	no	—
474	C₂²⋊C₄	—	4	1	no	—
475	C₂²⋊C₄	—	4	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	4	1	no	—
479	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
480	C₂³	—	2	1	no	—
481	C₂³	—	2	1	no	—
482	Q₈	—	2	1	no	—
483	Q₈	—	2	1	no	—
484	Q₈	—	2	1	no	—
485	Q₈	—	2	1	no	—
486	Q₈	—	4	1	no	—
487	Q₈	—	4	1	no	—
488	Q₈	—	8	1	no	—
489	Q₈	—	8	1	no	—
490	Q₈	—	8	1	no	—
491	D₄	—	2	1	no	—
492	D₄	—	2	1	no	—
493	D₄	—	2	1	no	—
494	D₄	C₁₉×#137	1	2	yes	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	16	1	no	—
510	C₂×C₄	—	16	1	no	—
511	C₂×C₄	—	16	1	no	—
512	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
513	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
514	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
515	C₈	—	2	1	no	—
516	C₈	—	2	1	no	—
517	C₈	—	2	1	no	—
518	C₈	—	4	1	no	—
519	C₈	—	4	1	no	—
520	C₈	—	4	1	no	—
521	C₈	—	4	1	no	—
522	C₈	—	4	1	no	—
523	C₈	C₁₉×#135	1	2	yes	—
524	C₂²	—	2	2	no	—
525	C₂²	—	4	1	no	—
526	C₂²	—	4	1	no	—
527	C₂²	—	4	1	no	—
528	C₂²	—	4	1	no	—
529	C₂²	—	4	1	no	—
530	C₂²	D₄²×C₁₉	1	1	yes	characteristic
531	C₄	—	2	1	no	—
532	C₄	—	4	1	no	—
533	C₄	—	4	1	no	—
534	C₄	—	4	1	no	—
535	C₄	—	4	1	no	—
536	C₄	—	4	1	no	—
537	C₄	—	4	1	no	—
538	C₄	—	8	1	no	—
539	C₄	—	8	1	no	—
540	C₄	—	8	1	no	—
541	C₄	—	8	1	no	—
542	C₄	C₂×C₁₉×#135	1	1	yes	characteristic
543	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
544	C₄	C₁₉×#578	1	1	yes	characteristic
545	C₄	C₁₉×#578	1	1	yes	characteristic
546	C₂	—	4	2	no	—
547	C₂	—	8	1	no	—
548	C₂	C₁₉×#3270	1	1	yes	characteristic
549	C₂	C₁₉×#3283	1	1	yes	characteristic
550	C₂	C₁₉×#3288	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂×D₈×C₁₉	D₄
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
3. C₁₉×#3356	C₂	semidirect
4. C₁₉×#3338	C₂	semidirect
5. C₁₉×#1723	C₂	semidirect
6. C₁₉×#1695	C₂	semidirect
7. C₁₉×#1684	C₂	semidirect
8. C₁₉×#1676	C₂	semidirect
9. C₁₉×#1671	C₂	semidirect
10. C₁₉×#1643	C₂	semidirect
11. C₁₉×#1638	C₂	semidirect
12. C₁₉×#1632	C₂	semidirect
13. C₁₉×#1632	C₂	semidirect
15. C₁₉×#1579	C₂	semidirect
204. #19865	C₁₉	direct (N × H)
251. #3356	C₂×C₁₉	semidirect
252. #3338	C₂×C₁₉	semidirect
253. #1723	C₂×C₁₉	semidirect
254. #1695	C₂×C₁₉	semidirect
255. #1684	C₂×C₁₉	semidirect
256. #1676	C₂×C₁₉	semidirect
257. #1671	C₂×C₁₉	semidirect
258. #1643	C₂×C₁₉	semidirect
259. #1638	C₂×C₁₉	semidirect
260. #1632	C₂×C₁₉	semidirect
261. #1632	C₂×C₁₉	semidirect
263. #1579	C₂×C₁₉	semidirect
419. C₁₉	#19865	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×#3380	2
C₁₉×#3360	2
C₁₉×#3356	2
C₁₉×#3338	2
C₁₉×#1723	2
C₁₉×#1695	2
C₁₉×#1684	2
C₁₉×#1676	2
C₁₉×#1671	2
C₁₉×#1643	2
C₁₉×#1638	2
C₁₉×#1632	2
C₁₉×#1581	2
C₁₉×#1579	2
#19865	19

Subgroups — C19×#19865 #18025824

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19865 #18025824