Subgroups — C₁₉×#19765 #18025724

Order 4864.

668 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3385	C₂	1	1	yes	maximal, characteristic, complemented
2	Q₈×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3295	C₂	1	1	yes	maximal, characteristic
4	D₄×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1714	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1686	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1678	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1675	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×#1637	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1629	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1623	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1582	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₁₉	—	2	1	no	—
17	Q₈²×C₁₉	C₂²	1	1	yes	characteristic, complemented
18	C₁₉×#554	C₂²	1	1	yes	characteristic
19	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
20	D₄²×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#501	—	2	1	no	—
22	C₁₉×#500	C₂²	1	1	yes	characteristic, complemented
23	C₁₉×#498	—	2	1	no	—
24	C₁₉×#498	C₂²	1	1	yes	characteristic, complemented
25	C₁₉×#492	C₂²	1	1	yes	characteristic
26	C₁₉×#492	C₂²	1	1	yes	characteristic
27	C₁₉×#487	C₂²	1	1	yes	characteristic, complemented
28	C₁₉×#486	C₂²	1	1	yes	characteristic
29	C₁₉×#481	—	2	1	no	—
30	C₁₉×#479	—	2	1	no	—
31	C₁₉×#477	C₂²	1	1	yes	characteristic, complemented
32	C₁₉×#476	—	2	1	no	—
33	C₁₉×#476	C₂²	1	1	yes	characteristic
34	C₁₉×#476	C₂²	1	1	yes	characteristic
35	C₁₉×#476	C₂²	1	1	yes	characteristic
36	C₁₉×#475	—	2	1	no	—
37	C₁₉×#475	C₂²	1	1	yes	characteristic, complemented
38	C₁₉×#474	—	2	1	no	—
39	C₁₉×#465	—	2	1	no	—
40	C₁₉×#465	—	2	1	no	—
41	C₁₉×#461	C₂²	1	1	yes	characteristic
42	C₁₉×#460	C₂²	1	1	yes	characteristic
43	C₁₉×#460	C₂²	1	1	yes	characteristic
44	C₁₉×#450	—	2	1	no	—
45	C₁₉×#450	—	2	1	no	—
46	C₁₉×#448	—	2	1	no	—
47	C₁₉×#446	C₂²	1	1	yes	characteristic, complemented
48	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
49	C₁₉×#440	—	2	1	no	—
50	C₄×SD₁₆×C₁₉	—	2	1	no	—
51	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
52	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
53	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
54	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
55	C₂×C₁₉×#102	—	2	1	no	—
56	C₁₉×#335	C₂²	1	1	yes	characteristic, complemented
57	C₁₉×#334	C₂²	1	1	yes	characteristic, complemented
58	C₁₉×#333	C₂²	1	1	yes	characteristic, complemented
59	C₁₉×#333	C₂²	1	1	yes	characteristic, complemented
60	C₁₉×#332	C₂²	1	1	yes	characteristic, complemented
61	C₁₉×#331	C₂²	1	1	yes	characteristic
62	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
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, complemented
67	C₂²×Q₈×C₁₉	—	2	1	no	—
68	C₂²×D₄×C₁₉	—	2	1	no	—
69	C₂²×D₄×C₁₉	—	2	1	no	—
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	—	4	1	no	—
76	C₂×SD₁₆×C₁₉	—	4	4	no	—
77	C₂×SD₁₆×C₁₉	D₄	1	1	yes	characteristic
78	C₂×SD₁₆×C₁₉	D₄	1	1	yes	characteristic
79	C₂²×C₈×C₁₉	—	2	1	no	—
80	C₂²×C₈×C₁₉	—	2	1	no	—
81	C₁₉×C₄⋊Q₈	—	2	1	no	—
82	C₁₉×C₄⋊Q₈	—	2	1	no	—
83	C₁₉×C₄⋊Q₈	—	2	1	no	—
84	C₁₉×C₄⋊Q₈	—	4	1	no	—
85	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
87	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
88	C₁₉×#127	C₂³	1	1	yes	characteristic
89	C₁₉×#125	—	2	1	no	—
90	C₁₉×C₂²⋊Q₈	—	2	1	no	—
91	C₁₉×C₂²⋊Q₈	—	2	1	no	—
92	C₁₉×C₂²⋊Q₈	—	4	1	no	—
93	C₁₉×C₂²⋊Q₈	—	4	1	no	—
94	C₁₉×#121	—	2	1	no	—
95	C₁₉×#121	—	2	1	no	—
96	C₁₉×#120	—	4	1	no	—
97	C₄×Q₈×C₁₉	—	2	1	no	—
98	C₄×Q₈×C₁₉	—	2	1	no	—
99	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
100	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
101	C₄×D₄×C₁₉	—	2	1	no	—
102	C₄×D₄×C₁₉	—	2	1	no	—
103	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
104	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
106	C₁₉×#107	—	2	1	no	—
107	C₁₉×#107	—	2	1	no	—
108	C₁₉×#107	—	2	1	no	—
109	C₁₉×#106	—	2	1	no	—
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	D₄	1	1	yes	characteristic
116	C₁₉×#106	D₄	1	1	yes	characteristic
117	C₁₉×C₄⋊C₈	—	2	1	no	—
118	C₁₉×C₄⋊C₈	—	2	1	no	—
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×C₄⋊C₈	C₂³	1	1	yes	characteristic
123	C₁₉×#103	—	2	1	no	—
124	C₁₉×#103	—	2	1	no	—
125	C₁₉×#103	—	2	1	no	—
126	C₁₉×#103	—	4	1	no	—
127	C₁₉×#103	D₄	1	1	yes	characteristic
128	C₁₉×#103	D₄	1	1	yes	characteristic
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	—	2	1	no	—
136	C₁₉×#102	D₄	1	1	yes	characteristic
137	C₁₉×#102	D₄	1	1	yes	characteristic
138	C₁₉×C₂²⋊C₈	—	2	1	no	—
139	C₁₉×C₂²⋊C₈	—	2	1	no	—
140	C₁₉×#97	—	2	1	no	—
141	C₄×C₈×C₁₉	—	2	1	no	—
142	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
145	C₂⁴×C₁₉	—	4	1	no	—
146	C₂×Q₈×C₁₉	—	2	1	no	—
147	C₂×Q₈×C₁₉	—	2	1	no	—
148	C₂×Q₈×C₁₉	—	2	1	no	—
149	C₂×Q₈×C₁₉	—	4	1	no	—
150	C₂×Q₈×C₁₉	—	4	1	no	—
151	C₂×Q₈×C₁₉	—	4	2	no	—
152	C₂×Q₈×C₁₉	—	8	1	no	—
153	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	4	1	no	—
159	C₂×D₄×C₁₉	—	4	1	no	—
160	C₂×D₄×C₁₉	—	4	2	no	—
161	C₂×D₄×C₁₉	—	4	2	no	—
162	C₂×D₄×C₁₉	—	8	1	no	—
163	C₂×D₄×C₁₉	—	8	1	no	—
164	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₉	—	2	1	no	—
167	C₂²×C₄×C₁₉	—	2	1	no	—
168	C₂²×C₄×C₁₉	—	4	1	no	—
169	C₂²×C₄×C₁₉	—	4	1	no	—
170	SD₁₆×C₁₉	—	2	2	no	—
171	SD₁₆×C₁₉	—	4	2	no	—
172	SD₁₆×C₁₉	—	4	2	no	—
173	SD₁₆×C₁₉	—	4	2	no	—
174	SD₁₆×C₁₉	—	8	1	no	—
175	SD₁₆×C₁₉	—	8	1	no	—
176	SD₁₆×C₁₉	—	8	2	no	—
177	SD₁₆×C₁₉	SD₁₆	1	4	yes	complemented
178	C₂×C₈×C₁₉	—	2	1	no	—
179	C₂×C₈×C₁₉	—	2	1	no	—
180	C₂×C₈×C₁₉	—	2	1	no	—
181	C₂×C₈×C₁₉	—	2	1	no	—
182	C₂×C₈×C₁₉	—	2	1	no	—
183	C₂×C₈×C₁₉	—	4	2	no	—
184	C₂×C₈×C₁₉	—	8	1	no	—
185	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
186	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
187	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
188	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₄⋊C₄×C₁₉	—	2	1	no	—
190	C₄⋊C₄×C₁₉	—	2	1	no	—
191	C₄⋊C₄×C₁₉	—	2	1	no	—
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	—	4	1	no	—
199	C₄⋊C₄×C₁₉	—	4	1	no	—
200	C₄⋊C₄×C₁₉	—	4	1	no	—
201	C₄⋊C₄×C₁₉	—	4	1	no	—
202	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
204	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
205	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
206	C₂²⋊C₄×C₁₉	—	2	1	no	—
207	C₂²⋊C₄×C₁₉	—	2	1	no	—
208	C₂²⋊C₄×C₁₉	—	4	1	no	—
209	C₂²⋊C₄×C₁₉	—	4	1	no	—
210	C₂²⋊C₄×C₁₉	—	4	1	no	—
211	C₄²×C₁₉	—	2	1	no	—
212	C₄²×C₁₉	—	2	1	no	—
213	C₄²×C₁₉	—	4	1	no	—
214	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
215	#19765	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂³×C₁₉	—	2	1	no	—
217	C₂³×C₁₉	—	2	1	no	—
218	C₂³×C₁₉	—	4	1	no	—
219	C₂³×C₁₉	—	8	2	no	—
220	C₂³×C₁₉	—	8	2	no	—
221	C₂³×C₁₉	—	16	1	no	—
222	Q₈×C₁₉	—	2	1	no	—
223	Q₈×C₁₉	—	2	1	no	—
224	Q₈×C₁₉	—	2	1	no	—
225	Q₈×C₁₉	—	4	1	no	—
226	Q₈×C₁₉	—	4	1	no	—
227	Q₈×C₁₉	—	8	2	no	—
228	Q₈×C₁₉	—	8	1	no	—
229	Q₈×C₁₉	—	8	1	no	—
230	Q₈×C₁₉	—	16	1	no	—
231	Q₈×C₁₉	C₂×SD₁₆	1	2	yes	—
232	D₄×C₁₉	—	2	1	no	—
233	D₄×C₁₉	—	2	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	—	8	1	no	—
239	D₄×C₁₉	—	8	2	no	—
240	D₄×C₁₉	—	8	2	no	—
241	D₄×C₁₉	C₂×SD₁₆	1	2	yes	—
242	D₄×C₁₉	#137	1	2	yes	—
243	C₂×C₄×C₁₉	—	2	1	no	—
244	C₂×C₄×C₁₉	—	2	1	no	—
245	C₂×C₄×C₁₉	—	2	1	no	—
246	C₂×C₄×C₁₉	—	2	1	no	—
247	C₂×C₄×C₁₉	—	2	1	no	—
248	C₂×C₄×C₁₉	—	2	1	no	—
249	C₂×C₄×C₁₉	—	4	1	no	—
250	C₂×C₄×C₁₉	—	4	1	no	—
251	C₂×C₄×C₁₉	—	4	1	no	—
252	C₂×C₄×C₁₉	—	4	1	no	—
253	C₂×C₄×C₁₉	—	4	1	no	—
254	C₂×C₄×C₁₉	—	4	1	no	—
255	C₂×C₄×C₁₉	—	4	1	no	—
256	C₂×C₄×C₁₉	—	8	2	no	—
257	C₂×C₄×C₁₉	—	16	1	no	—
258	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
261	C₈×C₁₉	—	2	1	no	—
262	C₈×C₁₉	—	2	1	no	—
263	C₈×C₁₉	—	2	1	no	—
264	C₈×C₁₉	—	4	1	no	—
265	C₈×C₁₉	—	4	1	no	—
266	C₈×C₁₉	—	4	1	no	—
267	C₈×C₁₉	—	4	1	no	—
268	C₈×C₁₉	—	4	1	no	—
269	C₈×C₁₉	C₂×SD₁₆	1	2	yes	—
270	#3385	C₂×C₁₉	1	1	yes	characteristic, complemented
271	Q₈×SD₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
272	#3295	C₂×C₁₉	1	1	yes	characteristic
273	D₄×SD₁₆	C₂×C₁₉	1	1	yes	characteristic
274	#1714	C₂×C₁₉	1	1	yes	characteristic, complemented
275	#1686	C₂×C₁₉	1	1	yes	characteristic, complemented
276	#1678	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#1675	C₂×C₁₉	1	1	yes	characteristic, complemented
278	#1671	C₂×C₁₉	1	1	yes	characteristic, complemented
279	#1643	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#1637	C₂×C₁₉	1	1	yes	characteristic, complemented
281	#1629	C₂×C₁₉	1	1	yes	characteristic
282	#1623	C₂×C₁₉	1	1	yes	characteristic, complemented
283	#1582	C₂×C₁₉	1	1	yes	characteristic, complemented
284	SD₁₆⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
285	C₂²×C₁₉	—	2	2	no	—
286	C₂²×C₁₉	—	2	2	no	—
287	C₂²×C₁₉	—	4	1	no	—
288	C₂²×C₁₉	—	4	1	no	—
289	C₂²×C₁₉	—	4	1	no	—
290	C₂²×C₁₉	—	4	1	no	—
291	C₂²×C₁₉	—	8	1	no	—
292	C₂²×C₁₉	—	8	1	no	—
293	C₂²×C₁₉	—	8	1	no	—
294	C₂²×C₁₉	—	16	4	no	—
295	C₂²×C₁₉	D₄²	1	1	yes	characteristic
296	C₄×C₁₉	—	2	2	no	—
297	C₄×C₁₉	—	2	1	no	—
298	C₄×C₁₉	—	4	1	no	—
299	C₄×C₁₉	—	4	1	no	—
300	C₄×C₁₉	—	4	1	no	—
301	C₄×C₁₉	—	4	1	no	—
302	C₄×C₁₉	—	4	1	no	—
303	C₄×C₁₉	—	8	1	no	—
304	C₄×C₁₉	—	8	1	no	—
305	C₄×C₁₉	—	8	1	no	—
306	C₄×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
307	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
308	C₄×C₁₉	#577	1	1	yes	characteristic
309	C₄×C₁₉	#577	1	1	yes	characteristic
310	C₂²×SD₁₆	—	2	1	no	—
311	Q₈²	C₂²×C₁₉	1	1	yes	characteristic, complemented
312	#554	C₂²×C₁₉	1	1	yes	characteristic
313	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
314	D₄²	C₂²×C₁₉	1	1	yes	characteristic
315	#501	—	2	1	no	—
316	#500	C₂²×C₁₉	1	1	yes	characteristic, complemented
317	#498	—	2	1	no	—
318	#498	C₂²×C₁₉	1	1	yes	characteristic, complemented
319	#492	C₂²×C₁₉	1	1	yes	characteristic
320	#492	C₂²×C₁₉	1	1	yes	characteristic
321	#487	C₂²×C₁₉	1	1	yes	characteristic, complemented
322	#486	C₂²×C₁₉	1	1	yes	characteristic
323	#481	—	2	1	no	—
324	#479	—	2	1	no	—
325	#477	C₂²×C₁₉	1	1	yes	characteristic, complemented
326	#476	—	2	1	no	—
327	#476	C₂²×C₁₉	1	1	yes	characteristic
328	#476	C₂²×C₁₉	1	1	yes	characteristic
329	#476	C₂²×C₁₉	1	1	yes	characteristic
330	#475	—	2	1	no	—
331	#475	C₂²×C₁₉	1	1	yes	characteristic, complemented
332	#474	—	2	1	no	—
333	#465	—	2	1	no	—
334	#465	—	2	1	no	—
335	#461	C₂²×C₁₉	1	1	yes	characteristic
336	#460	C₂²×C₁₉	1	1	yes	characteristic
337	#460	C₂²×C₁₉	1	1	yes	characteristic
338	#450	—	2	1	no	—
339	#450	—	2	1	no	—
340	#448	—	2	1	no	—
341	#446	C₂²×C₁₉	1	1	yes	characteristic, complemented
342	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
343	#440	—	2	1	no	—
344	C₄×SD₁₆	—	2	1	no	—
345	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
346	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
347	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
348	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
349	C₂×#102	—	2	1	no	—
350	#335	C₂²×C₁₉	1	1	yes	characteristic, complemented
351	#334	C₂²×C₁₉	1	1	yes	characteristic, complemented
352	#333	C₂²×C₁₉	1	1	yes	characteristic, complemented
353	#333	C₂²×C₁₉	1	1	yes	characteristic, complemented
354	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
355	#331	C₂²×C₁₉	1	1	yes	characteristic
356	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
357	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
358	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
359	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
360	#322	C₂²×C₁₉	1	1	yes	characteristic, complemented
361	C₂×C₁₉	—	4	2	no	—
362	C₂×C₁₉	—	4	2	no	—
363	C₂×C₁₉	—	16	1	no	—
364	C₂×C₁₉	#3266	1	1	yes	characteristic
365	C₂×C₁₉	D₄×SD₁₆	1	1	yes	characteristic
366	C₂×C₁₉	#3288	1	1	yes	characteristic
367	C₂²×Q₈	—	2	1	no	—
368	C₂²×D₄	—	2	1	no	—
369	C₂²×D₄	—	2	1	no	—
370	C₂×SD₁₆	—	2	1	no	—
371	C₂×SD₁₆	—	2	1	no	—
372	C₂×SD₁₆	—	2	1	no	—
373	C₂×SD₁₆	—	2	1	no	—
374	C₂×SD₁₆	—	2	1	no	—
375	C₂×SD₁₆	—	4	1	no	—
376	C₂×SD₁₆	—	4	4	no	—
377	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
378	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
379	C₂²×C₈	—	2	1	no	—
380	C₂²×C₈	—	2	1	no	—
381	C₄⋊Q₈	—	2	1	no	—
382	C₄⋊Q₈	—	2	1	no	—
383	C₄⋊Q₈	—	2	1	no	—
384	C₄⋊Q₈	—	4	1	no	—
385	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
386	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
387	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
388	#127	C₂³×C₁₉	1	1	yes	characteristic
389	#125	—	2	1	no	—
390	C₂²⋊Q₈	—	2	1	no	—
391	C₂²⋊Q₈	—	2	1	no	—
392	C₂²⋊Q₈	—	4	1	no	—
393	C₂²⋊Q₈	—	4	1	no	—
394	#121	—	2	1	no	—
395	#121	—	2	1	no	—
396	#120	—	4	1	no	—
397	C₄×Q₈	—	2	1	no	—
398	C₄×Q₈	—	2	1	no	—
399	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
400	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
401	C₄×D₄	—	2	1	no	—
402	C₄×D₄	—	2	1	no	—
403	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
404	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
405	C₂×C₄⋊C₄	—	2	1	no	—
406	#107	—	2	1	no	—
407	#107	—	2	1	no	—
408	#107	—	2	1	no	—
409	#106	—	2	1	no	—
410	#106	—	2	1	no	—
411	#106	—	2	1	no	—
412	#106	—	2	1	no	—
413	#106	—	2	1	no	—
414	#106	—	2	1	no	—
415	#106	D₄×C₁₉	1	1	yes	characteristic
416	#106	D₄×C₁₉	1	1	yes	characteristic
417	C₄⋊C₈	—	2	1	no	—
418	C₄⋊C₈	—	2	1	no	—
419	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
420	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
421	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
422	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
423	#103	—	2	1	no	—
424	#103	—	2	1	no	—
425	#103	—	2	1	no	—
426	#103	—	4	1	no	—
427	#103	D₄×C₁₉	1	1	yes	characteristic
428	#103	D₄×C₁₉	1	1	yes	characteristic
429	#102	—	2	1	no	—
430	#102	—	2	1	no	—
431	#102	—	2	1	no	—
432	#102	—	2	1	no	—
433	#102	—	2	1	no	—
434	#102	—	2	1	no	—
435	#102	—	2	1	no	—
436	#102	D₄×C₁₉	1	1	yes	characteristic
437	#102	D₄×C₁₉	1	1	yes	characteristic
438	C₂²⋊C₈	—	2	1	no	—
439	C₂²⋊C₈	—	2	1	no	—
440	#97	—	2	1	no	—
441	C₄×C₈	—	2	1	no	—
442	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
443	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
444	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
445	C₁₉	#19765	1	1	yes	characteristic, direct product factor, Sylow
446	C₂⁴	—	4	1	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	—	2	1	no	—
450	C₂×Q₈	—	4	1	no	—
451	C₂×Q₈	—	4	1	no	—
452	C₂×Q₈	—	4	2	no	—
453	C₂×Q₈	—	8	1	no	—
454	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
455	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	4	1	no	—
460	C₂×D₄	—	4	1	no	—
461	C₂×D₄	—	4	2	no	—
462	C₂×D₄	—	4	2	no	—
463	C₂×D₄	—	8	1	no	—
464	C₂×D₄	—	8	1	no	—
465	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
466	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	4	1	no	—
470	C₂²×C₄	—	4	1	no	—
471	SD₁₆	—	2	2	no	—
472	SD₁₆	—	4	2	no	—
473	SD₁₆	—	4	2	no	—
474	SD₁₆	—	4	2	no	—
475	SD₁₆	—	8	1	no	—
476	SD₁₆	—	8	1	no	—
477	SD₁₆	—	8	2	no	—
478	SD₁₆	SD₁₆×C₁₉	1	4	yes	complemented
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	4	2	no	—
485	C₂×C₈	—	8	1	no	—
486	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
487	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
488	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
489	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	4	1	no	—
499	C₄⋊C₄	—	4	1	no	—
500	C₄⋊C₄	—	4	1	no	—
501	C₄⋊C₄	—	4	1	no	—
502	C₄⋊C₄	—	4	1	no	—
503	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
504	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
505	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
506	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
507	C₂²⋊C₄	—	2	1	no	—
508	C₂²⋊C₄	—	2	1	no	—
509	C₂²⋊C₄	—	4	1	no	—
510	C₂²⋊C₄	—	4	1	no	—
511	C₂²⋊C₄	—	4	1	no	—
512	C₄²	—	2	1	no	—
513	C₄²	—	2	1	no	—
514	C₄²	—	4	1	no	—
515	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
516	C₂³	—	2	1	no	—
517	C₂³	—	2	1	no	—
518	C₂³	—	4	1	no	—
519	C₂³	—	8	2	no	—
520	C₂³	—	8	2	no	—
521	C₂³	—	16	1	no	—
522	Q₈	—	2	1	no	—
523	Q₈	—	2	1	no	—
524	Q₈	—	2	1	no	—
525	Q₈	—	4	1	no	—
526	Q₈	—	4	1	no	—
527	Q₈	—	8	2	no	—
528	Q₈	—	8	1	no	—
529	Q₈	—	8	1	no	—
530	Q₈	—	16	1	no	—
531	Q₈	C₂×SD₁₆×C₁₉	1	2	yes	—
532	D₄	—	2	1	no	—
533	D₄	—	2	1	no	—
534	D₄	—	4	1	no	—
535	D₄	—	4	1	no	—
536	D₄	—	4	1	no	—
537	D₄	—	4	1	no	—
538	D₄	—	8	1	no	—
539	D₄	—	8	2	no	—
540	D₄	—	8	2	no	—
541	D₄	C₂×SD₁₆×C₁₉	1	2	yes	—
542	D₄	C₁₉×#137	1	2	yes	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	8	2	no	—
557	C₂×C₄	—	16	1	no	—
558	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
559	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
560	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
561	C₈	—	2	1	no	—
562	C₈	—	2	1	no	—
563	C₈	—	2	1	no	—
564	C₈	—	4	1	no	—
565	C₈	—	4	1	no	—
566	C₈	—	4	1	no	—
567	C₈	—	4	1	no	—
568	C₈	—	4	1	no	—
569	C₈	C₂×SD₁₆×C₁₉	1	2	yes	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	8	1	no	—
577	C₂²	—	8	1	no	—
578	C₂²	—	8	1	no	—
579	C₂²	—	16	4	no	—
580	C₂²	D₄²×C₁₉	1	1	yes	characteristic
581	C₄	—	2	2	no	—
582	C₄	—	2	1	no	—
583	C₄	—	4	1	no	—
584	C₄	—	4	1	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	1	no	—
587	C₄	—	4	1	no	—
588	C₄	—	8	1	no	—
589	C₄	—	8	1	no	—
590	C₄	—	8	1	no	—
591	C₄	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
592	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
593	C₄	C₁₉×#577	1	1	yes	characteristic
594	C₄	C₁₉×#577	1	1	yes	characteristic
595	C₂	—	4	2	no	—
596	C₂	—	4	2	no	—
597	C₂	—	16	1	no	—
598	C₂	C₁₉×#3266	1	1	yes	characteristic
599	C₂	D₄×SD₁₆×C₁₉	1	1	yes	characteristic
600	C₂	C₁₉×#3288	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	D₄²×C₁₉	C₂²
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×#3385	C₂	semidirect
2. Q₈×SD₁₆×C₁₉	C₂	semidirect
5. C₁₉×#1714	C₂	semidirect
6. C₁₉×#1686	C₂	semidirect
7. C₁₉×#1678	C₂	semidirect
8. C₁₉×#1675	C₂	semidirect
9. C₁₉×#1671	C₂	semidirect
10. C₁₉×#1643	C₂	semidirect
11. C₁₉×#1637	C₂	semidirect
13. C₁₉×#1623	C₂	semidirect
14. C₁₉×#1582	C₂	semidirect
15. C₁₉×SD₁₆⋊C₈	C₂	semidirect
17. Q₈²×C₁₉	C₂²	semidirect
22. C₁₉×#500	C₂²	semidirect
24. C₁₉×#498	C₂²	semidirect
27. C₁₉×#487	C₂²	semidirect
31. C₁₉×#477	C₂²	semidirect
37. C₁₉×#475	C₂²	semidirect
47. C₁₉×#446	C₂²	semidirect
48. C₈×Q₈×C₁₉	C₂²	semidirect
56. C₁₉×#335	C₂²	semidirect
57. C₁₉×#334	C₂²	semidirect
58. C₁₉×#333	C₂²	semidirect
59. C₁₉×#333	C₂²	semidirect
60. C₁₉×#332	C₂²	semidirect
62. C₁₉×Q₈⋊C₈	C₂²	semidirect
63. C₁₉×Q₈⋊C₈	C₂²	semidirect
66. C₁₉×#322	C₂²	semidirect
177. SD₁₆×C₁₉	SD₁₆	semidirect
215. #19765	C₁₉	direct (N × H)
270. #3385	C₂×C₁₉	semidirect
271. Q₈×SD₁₆	C₂×C₁₉	semidirect
274. #1714	C₂×C₁₉	semidirect
275. #1686	C₂×C₁₉	semidirect
276. #1678	C₂×C₁₉	semidirect
277. #1675	C₂×C₁₉	semidirect
278. #1671	C₂×C₁₉	semidirect
279. #1643	C₂×C₁₉	semidirect
280. #1637	C₂×C₁₉	semidirect
282. #1623	C₂×C₁₉	semidirect
283. #1582	C₂×C₁₉	semidirect
284. SD₁₆⋊C₈	C₂×C₁₉	semidirect
311. Q₈²	C₂²×C₁₉	semidirect
316. #500	C₂²×C₁₉	semidirect
318. #498	C₂²×C₁₉	semidirect
321. #487	C₂²×C₁₉	semidirect
325. #477	C₂²×C₁₉	semidirect
331. #475	C₂²×C₁₉	semidirect
341. #446	C₂²×C₁₉	semidirect
342. C₈×Q₈	C₂²×C₁₉	semidirect
350. #335	C₂²×C₁₉	semidirect
351. #334	C₂²×C₁₉	semidirect
352. #333	C₂²×C₁₉	semidirect
353. #333	C₂²×C₁₉	semidirect
354. #332	C₂²×C₁₉	semidirect
356. Q₈⋊C₈	C₂²×C₁₉	semidirect
357. Q₈⋊C₈	C₂²×C₁₉	semidirect
360. #322	C₂²×C₁₉	semidirect
445. C₁₉	#19765	direct (N × H)
478. SD₁₆	SD₁₆×C₁₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₉×#3385	2
Q₈×SD₁₆×C₁₉	2
C₁₉×#3295	2
D₄×SD₁₆×C₁₉	2
C₁₉×#1714	2
C₁₉×#1686	2
C₁₉×#1678	2
C₁₉×#1675	2
C₁₉×#1671	2
C₁₉×#1643	2
C₁₉×#1637	2
C₁₉×#1629	2
C₁₉×#1623	2
C₁₉×#1582	2
C₁₉×SD₁₆⋊C₈	2
#19765	19

Subgroups — C19×#19765 #18025724

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19765 #18025724