Subgroups — C₁₉×#19890 #18025849

Order 4864.

718 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3384	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3335	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3272	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1705	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1691	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1686	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1671	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1665	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1654	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1651	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1629	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1622	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1590	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×D₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
17	C₂²×SD₁₆×C₁₉	—	2	1	no	—
18	C₁₉×#554	C₂²	1	1	yes	characteristic, complemented
19	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#547	C₂²	1	1	yes	characteristic
21	D₄²×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#501	—	2	1	no	—
23	C₁₉×#498	C₂²	1	1	yes	characteristic, complemented
24	C₁₉×#498	C₂²	1	1	yes	characteristic, complemented
25	C₁₉×#498	C₂²	1	1	yes	characteristic, complemented
26	C₁₉×#492	C₂²	1	1	yes	characteristic
27	C₁₉×#492	C₂²	1	1	yes	characteristic
28	C₁₉×#492	C₂²	1	1	yes	characteristic
29	C₁₉×#483	—	2	1	no	—
30	C₁₉×#481	—	2	1	no	—
31	C₁₉×#478	—	2	1	no	—
32	C₁₉×#476	—	2	1	no	—
33	C₁₉×#476	C₂²	1	1	yes	characteristic
34	C₁₉×#476	C₂²	1	1	yes	characteristic
35	C₁₉×#475	C₂²	1	1	yes	characteristic, complemented
36	C₁₉×#474	C₂²	1	1	yes	characteristic, complemented
37	C₁₉×#468	—	2	1	no	—
38	C₁₉×#465	—	2	1	no	—
39	C₁₉×#465	—	2	1	no	—
40	C₁₉×#461	C₂²	1	1	yes	characteristic
41	C₁₉×#461	C₂²	1	1	yes	characteristic
42	C₁₉×#460	C₂²	1	1	yes	characteristic
43	C₁₉×#459	C₂²	1	1	yes	characteristic
44	C₁₉×#450	—	2	1	no	—
45	C₁₉×#450	—	2	1	no	—
46	C₁₉×#449	—	2	1	no	—
47	C₁₉×#448	—	2	1	no	—
48	C₁₉×#446	C₂²	1	1	yes	characteristic, complemented
49	C₁₉×#442	—	2	1	no	—
50	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
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	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₁₉×#106	—	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×#332	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×D₄⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
66	C₈²×C₁₉	C₂²	1	1	yes	characteristic, complemented
67	C₂×#41×C₁₉	—	2	1	no	—
68	C₂²×Q₈×C₁₉	—	2	1	no	—
69	C₂²×D₄×C₁₉	—	2	1	no	—
70	C₂²×D₄×C₁₉	—	2	1	no	—
71	C₁₉×AGL(1,ℤ/8)	—	4	4	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	—	2	1	no	—
77	C₂×SD₁₆×C₁₉	—	2	1	no	—
78	C₂×SD₁₆×C₁₉	—	2	1	no	—
79	C₂×SD₁₆×C₁₉	—	4	1	no	—
80	C₂×SD₁₆×C₁₉	—	4	4	no	—
81	C₂×SD₁₆×C₁₉	D₄	1	1	yes	characteristic
82	C₂×D₈×C₁₉	—	2	1	no	—
83	C₂×D₈×C₁₉	D₄	1	1	yes	characteristic
84	C₂×M₁₆×C₁₉	—	2	1	no	—
85	C₂²×C₈×C₁₉	—	2	1	no	—
86	C₂²×C₈×C₁₉	—	2	1	no	—
87	C₁₉×C₄⋊Q₈	—	2	1	no	—
88	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
89	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
90	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
91	C₁₉×#127	C₂³	1	1	yes	characteristic
92	C₁₉×#125	—	2	1	no	—
93	C₁₉×#123	—	4	1	no	—
94	C₁₉×C₂²⋊Q₈	—	2	1	no	—
95	C₁₉×C₂²⋊Q₈	—	2	1	no	—
96	C₁₉×C₂²⋊Q₈	—	2	1	no	—
97	C₁₉×C₂²⋊Q₈	—	4	1	no	—
98	C₁₉×C₂²⋊Q₈	—	4	1	no	—
99	C₁₉×#121	—	2	1	no	—
100	C₁₉×#121	—	2	1	no	—
101	C₁₉×#121	—	2	1	no	—
102	C₁₉×#120	—	4	1	no	—
103	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
104	C₄×D₄×C₁₉	—	2	1	no	—
105	C₄×D₄×C₁₉	—	2	1	no	—
106	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
107	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
108	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
111	C₁₉×#107	—	2	1	no	—
112	C₁₉×#107	D₄	1	1	yes	characteristic
113	C₁₉×#106	—	2	1	no	—
114	C₁₉×#106	—	2	1	no	—
115	C₁₉×#106	—	2	1	no	—
116	C₁₉×#106	—	2	1	no	—
117	C₁₉×#106	—	2	1	no	—
118	C₁₉×#106	—	2	1	no	—
119	C₁₉×#106	—	2	1	no	—
120	C₁₉×#106	—	4	1	no	—
121	C₁₉×#106	D₄	1	1	yes	characteristic
122	C₁₉×C₄⋊C₈	—	2	1	no	—
123	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
124	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
125	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
126	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
127	C₁₉×#103	—	2	1	no	—
128	C₁₉×#103	—	2	1	no	—
129	C₁₉×#103	—	2	1	no	—
130	C₁₉×#103	D₄	1	1	yes	characteristic
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×#102	D₄	1	1	yes	characteristic
139	C₁₉×C₂²⋊C₈	—	2	1	no	—
140	C₁₉×C₂²⋊C₈	—	2	1	no	—
141	C₁₉×C₂²⋊C₈	—	2	1	no	—
142	C₁₉×#97	—	2	1	no	—
143	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
145	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
146	C₂⁴×C₁₉	—	4	1	no	—
147	#41×C₁₉	—	4	2	no	—
148	#41×C₁₉	—	8	1	no	—
149	C₂×Q₈×C₁₉	—	2	1	no	—
150	C₂×Q₈×C₁₉	—	2	1	no	—
151	C₂×Q₈×C₁₉	—	2	1	no	—
152	C₂×Q₈×C₁₉	—	4	1	no	—
153	C₂×Q₈×C₁₉	—	4	2	no	—
154	C₂×Q₈×C₁₉	—	8	1	no	—
155	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	4	2	no	—
162	C₂×D₄×C₁₉	—	4	2	no	—
163	C₂×D₄×C₁₉	—	4	1	no	—
164	C₂×D₄×C₁₉	—	8	1	no	—
165	C₂×D₄×C₁₉	—	8	1	no	—
166	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₉	—	2	1	no	—
170	C₂²×C₄×C₁₉	—	2	1	no	—
171	C₂²×C₄×C₁₉	—	2	1	no	—
172	C₂²×C₄×C₁₉	—	4	1	no	—
173	C₂²×C₄×C₁₉	—	4	1	no	—
174	C₂²×C₄×C₁₉	—	4	1	no	—
175	SD₁₆×C₁₉	—	2	2	no	—
176	SD₁₆×C₁₉	—	4	2	no	—
177	SD₁₆×C₁₉	—	4	2	no	—
178	SD₁₆×C₁₉	—	4	2	no	—
179	SD₁₆×C₁₉	—	4	2	no	—
180	SD₁₆×C₁₉	—	4	2	no	—
181	SD₁₆×C₁₉	—	8	1	no	—
182	SD₁₆×C₁₉	—	8	1	no	—
183	SD₁₆×C₁₉	—	8	2	no	—
184	D₈×C₁₉	—	4	2	no	—
185	D₈×C₁₉	SD₁₆	1	4	yes	complemented
186	M₁₆×C₁₉	—	4	2	no	—
187	C₂×C₈×C₁₉	—	2	1	no	—
188	C₂×C₈×C₁₉	—	2	1	no	—
189	C₂×C₈×C₁₉	—	2	1	no	—
190	C₂×C₈×C₁₉	—	2	1	no	—
191	C₂×C₈×C₁₉	—	2	1	no	—
192	C₂×C₈×C₁₉	—	4	2	no	—
193	C₂×C₈×C₁₉	—	4	2	no	—
194	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
195	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
196	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
197	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
198	C₄⋊C₄×C₁₉	—	2	1	no	—
199	C₄⋊C₄×C₁₉	—	2	1	no	—
200	C₄⋊C₄×C₁₉	—	2	1	no	—
201	C₄⋊C₄×C₁₉	—	2	1	no	—
202	C₄⋊C₄×C₁₉	—	2	1	no	—
203	C₄⋊C₄×C₁₉	—	2	1	no	—
204	C₄⋊C₄×C₁₉	—	2	1	no	—
205	C₄⋊C₄×C₁₉	—	4	1	no	—
206	C₄⋊C₄×C₁₉	—	4	1	no	—
207	C₄⋊C₄×C₁₉	—	4	1	no	—
208	C₄⋊C₄×C₁₉	—	4	1	no	—
209	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
210	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
211	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
212	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
213	C₂²⋊C₄×C₁₉	—	2	1	no	—
214	C₂²⋊C₄×C₁₉	—	2	1	no	—
215	C₂²⋊C₄×C₁₉	—	2	1	no	—
216	C₂²⋊C₄×C₁₉	—	4	1	no	—
217	C₂²⋊C₄×C₁₉	—	4	1	no	—
218	C₂²⋊C₄×C₁₉	—	4	1	no	—
219	C₂²⋊C₄×C₁₉	—	4	1	no	—
220	C₄²×C₁₉	—	2	1	no	—
221	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
222	#19890	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
223	C₂³×C₁₉	—	2	1	no	—
224	C₂³×C₁₉	—	2	1	no	—
225	C₂³×C₁₉	—	2	1	no	—
226	C₂³×C₁₉	—	4	1	no	—
227	C₂³×C₁₉	—	8	2	no	—
228	C₂³×C₁₉	—	8	2	no	—
229	C₂³×C₁₉	—	16	1	no	—
230	Q₈×C₁₉	—	2	1	no	—
231	Q₈×C₁₉	—	2	1	no	—
232	Q₈×C₁₉	—	4	1	no	—
233	Q₈×C₁₉	—	4	1	no	—
234	Q₈×C₁₉	—	4	1	no	—
235	Q₈×C₁₉	—	4	1	no	—
236	Q₈×C₁₉	—	8	1	no	—
237	Q₈×C₁₉	—	8	2	no	—
238	D₄×C₁₉	—	2	1	no	—
239	D₄×C₁₉	—	2	1	no	—
240	D₄×C₁₉	—	2	1	no	—
241	D₄×C₁₉	—	2	1	no	—
242	D₄×C₁₉	—	4	1	no	—
243	D₄×C₁₉	—	4	1	no	—
244	D₄×C₁₉	—	4	1	no	—
245	D₄×C₁₉	—	4	1	no	—
246	D₄×C₁₉	—	8	1	no	—
247	D₄×C₁₉	—	8	2	no	—
248	D₄×C₁₉	—	8	2	no	—
249	D₄×C₁₉	—	8	2	no	—
250	D₄×C₁₉	C₂×SD₁₆	1	2	yes	—
251	D₄×C₁₉	C₂×SD₁₆	1	2	yes	complemented
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	—	2	1	no	—
257	C₂×C₄×C₁₉	—	4	1	no	—
258	C₂×C₄×C₁₉	—	4	1	no	—
259	C₂×C₄×C₁₉	—	4	1	no	—
260	C₂×C₄×C₁₉	—	4	1	no	—
261	C₂×C₄×C₁₉	—	4	1	no	—
262	C₂×C₄×C₁₉	—	4	1	no	—
263	C₂×C₄×C₁₉	—	4	1	no	—
264	C₂×C₄×C₁₉	—	4	1	no	—
265	C₂×C₄×C₁₉	—	4	1	no	—
266	C₂×C₄×C₁₉	—	8	2	no	—
267	C₂×C₄×C₁₉	—	8	2	no	—
268	C₂×C₄×C₁₉	—	16	1	no	—
269	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
272	C₈×C₁₉	—	2	2	no	—
273	C₈×C₁₉	—	2	1	no	—
274	C₈×C₁₉	—	2	1	no	—
275	C₈×C₁₉	—	4	1	no	—
276	C₈×C₁₉	—	4	1	no	—
277	C₈×C₁₉	—	4	1	no	—
278	C₈×C₁₉	—	4	1	no	—
279	C₈×C₁₉	C₂×SD₁₆	1	2	yes	complemented
280	C₈×C₁₉	AGL(1,ℤ/8)	1	2	yes	complemented
281	#3384	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#3335	C₂×C₁₉	1	1	yes	characteristic, complemented
283	D₄×SD₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
284	#3272	C₂×C₁₉	1	1	yes	characteristic
285	#1705	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#1691	C₂×C₁₉	1	1	yes	characteristic, complemented
287	#1686	C₂×C₁₉	1	1	yes	characteristic, complemented
288	#1671	C₂×C₁₉	1	1	yes	characteristic, complemented
289	#1665	C₂×C₁₉	1	1	yes	characteristic, complemented
290	#1654	C₂×C₁₉	1	1	yes	characteristic, complemented
291	#1651	C₂×C₁₉	1	1	yes	characteristic, complemented
292	#1629	C₂×C₁₉	1	1	yes	characteristic, complemented
293	#1622	C₂×C₁₉	1	1	yes	characteristic, complemented
294	#1590	C₂×C₁₉	1	1	yes	characteristic, complemented
295	C₈×D₈	C₂×C₁₉	1	1	yes	characteristic, complemented
296	C₂²×C₁₉	—	2	2	no	—
297	C₂²×C₁₉	—	2	2	no	—
298	C₂²×C₁₉	—	4	1	no	—
299	C₂²×C₁₉	—	4	1	no	—
300	C₂²×C₁₉	—	4	1	no	—
301	C₂²×C₁₉	—	4	1	no	—
302	C₂²×C₁₉	—	4	1	no	—
303	C₂²×C₁₉	—	4	1	no	—
304	C₂²×C₁₉	—	4	1	no	—
305	C₂²×C₁₉	—	8	1	no	—
306	C₂²×C₁₉	—	8	1	no	—
307	C₂²×C₁₉	—	8	1	no	—
308	C₂²×C₁₉	—	16	4	no	—
309	C₂²×C₁₉	D₄²	1	1	yes	characteristic
310	C₄×C₁₉	—	2	1	no	—
311	C₄×C₁₉	—	4	1	no	—
312	C₄×C₁₉	—	4	1	no	—
313	C₄×C₁₉	—	4	1	no	—
314	C₄×C₁₉	—	4	1	no	—
315	C₄×C₁₉	—	4	1	no	—
316	C₄×C₁₉	—	8	1	no	—
317	C₄×C₁₉	—	8	1	no	—
318	C₄×C₁₉	—	8	1	no	—
319	C₄×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
320	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
321	C₄×C₁₉	#577	1	1	yes	characteristic
322	C₄×C₁₉	#577	1	1	yes	characteristic
323	C₂×AGL(1,ℤ/8)	—	2	1	no	—
324	C₂²×SD₁₆	—	2	1	no	—
325	#554	C₂²×C₁₉	1	1	yes	characteristic, complemented
326	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
327	#547	C₂²×C₁₉	1	1	yes	characteristic
328	D₄²	C₂²×C₁₉	1	1	yes	characteristic
329	#501	—	2	1	no	—
330	#498	C₂²×C₁₉	1	1	yes	characteristic, complemented
331	#498	C₂²×C₁₉	1	1	yes	characteristic, complemented
332	#498	C₂²×C₁₉	1	1	yes	characteristic, complemented
333	#492	C₂²×C₁₉	1	1	yes	characteristic
334	#492	C₂²×C₁₉	1	1	yes	characteristic
335	#492	C₂²×C₁₉	1	1	yes	characteristic
336	#483	—	2	1	no	—
337	#481	—	2	1	no	—
338	#478	—	2	1	no	—
339	#476	—	2	1	no	—
340	#476	C₂²×C₁₉	1	1	yes	characteristic
341	#476	C₂²×C₁₉	1	1	yes	characteristic
342	#475	C₂²×C₁₉	1	1	yes	characteristic, complemented
343	#474	C₂²×C₁₉	1	1	yes	characteristic, complemented
344	#468	—	2	1	no	—
345	#465	—	2	1	no	—
346	#465	—	2	1	no	—
347	#461	C₂²×C₁₉	1	1	yes	characteristic
348	#461	C₂²×C₁₉	1	1	yes	characteristic
349	#460	C₂²×C₁₉	1	1	yes	characteristic
350	#459	C₂²×C₁₉	1	1	yes	characteristic
351	#450	—	2	1	no	—
352	#450	—	2	1	no	—
353	#449	—	2	1	no	—
354	#448	—	2	1	no	—
355	#446	C₂²×C₁₉	1	1	yes	characteristic, complemented
356	#442	—	2	1	no	—
357	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
358	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
359	#436	C₂²×C₁₉	1	1	yes	characteristic
360	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
361	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
362	C₂×#106	—	2	1	no	—
363	#335	C₂²×C₁₉	1	1	yes	characteristic, complemented
364	#334	C₂²×C₁₉	1	1	yes	characteristic, complemented
365	#333	C₂²×C₁₉	1	1	yes	characteristic, complemented
366	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
367	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
368	#331	C₂²×C₁₉	1	1	yes	characteristic
369	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
370	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
371	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
372	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
373	C₈²	C₂²×C₁₉	1	1	yes	characteristic, complemented
374	C₂×C₁₉	—	4	2	no	—
375	C₂×C₁₉	—	4	2	no	—
376	C₂×C₁₉	—	8	1	no	—
377	C₂×C₁₉	—	16	1	no	—
378	C₂×C₁₉	#3272	1	1	yes	characteristic
379	C₂×C₁₉	D₄×SD₁₆	1	1	yes	characteristic
380	C₂×C₁₉	#3291	1	1	yes	characteristic
381	C₂×#41	—	2	1	no	—
382	C₂²×Q₈	—	2	1	no	—
383	C₂²×D₄	—	2	1	no	—
384	C₂²×D₄	—	2	1	no	—
385	AGL(1,ℤ/8)	—	4	4	no	—
386	C₂×SD₁₆	—	2	1	no	—
387	C₂×SD₁₆	—	2	1	no	—
388	C₂×SD₁₆	—	2	1	no	—
389	C₂×SD₁₆	—	2	1	no	—
390	C₂×SD₁₆	—	2	1	no	—
391	C₂×SD₁₆	—	2	1	no	—
392	C₂×SD₁₆	—	2	1	no	—
393	C₂×SD₁₆	—	4	1	no	—
394	C₂×SD₁₆	—	4	4	no	—
395	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
396	C₂×D₈	—	2	1	no	—
397	C₂×D₈	D₄×C₁₉	1	1	yes	characteristic
398	C₂×M₁₆	—	2	1	no	—
399	C₂²×C₈	—	2	1	no	—
400	C₂²×C₈	—	2	1	no	—
401	C₄⋊Q₈	—	2	1	no	—
402	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
403	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
404	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
405	#127	C₂³×C₁₉	1	1	yes	characteristic
406	#125	—	2	1	no	—
407	#123	—	4	1	no	—
408	C₂²⋊Q₈	—	2	1	no	—
409	C₂²⋊Q₈	—	2	1	no	—
410	C₂²⋊Q₈	—	2	1	no	—
411	C₂²⋊Q₈	—	4	1	no	—
412	C₂²⋊Q₈	—	4	1	no	—
413	#121	—	2	1	no	—
414	#121	—	2	1	no	—
415	#121	—	2	1	no	—
416	#120	—	4	1	no	—
417	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
418	C₄×D₄	—	2	1	no	—
419	C₄×D₄	—	2	1	no	—
420	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
421	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
422	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
423	C₂×C₄⋊C₄	—	2	1	no	—
424	C₂×C₄⋊C₄	—	2	1	no	—
425	#107	—	2	1	no	—
426	#107	D₄×C₁₉	1	1	yes	characteristic
427	#106	—	2	1	no	—
428	#106	—	2	1	no	—
429	#106	—	2	1	no	—
430	#106	—	2	1	no	—
431	#106	—	2	1	no	—
432	#106	—	2	1	no	—
433	#106	—	2	1	no	—
434	#106	—	4	1	no	—
435	#106	D₄×C₁₉	1	1	yes	characteristic
436	C₄⋊C₈	—	2	1	no	—
437	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
438	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
439	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
440	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
441	#103	—	2	1	no	—
442	#103	—	2	1	no	—
443	#103	—	2	1	no	—
444	#103	D₄×C₁₉	1	1	yes	characteristic
445	#102	—	2	1	no	—
446	#102	—	2	1	no	—
447	#102	—	2	1	no	—
448	#102	—	2	1	no	—
449	#102	—	2	1	no	—
450	#102	D₄×C₁₉	1	1	yes	characteristic
451	#102	D₄×C₁₉	1	1	yes	characteristic
452	#102	D₄×C₁₉	1	1	yes	characteristic
453	C₂²⋊C₈	—	2	1	no	—
454	C₂²⋊C₈	—	2	1	no	—
455	C₂²⋊C₈	—	2	1	no	—
456	#97	—	2	1	no	—
457	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
458	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
459	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
460	C₁₉	#19890	1	1	yes	characteristic, direct product factor, Sylow
461	C₂⁴	—	4	1	no	—
462	#41	—	4	2	no	—
463	#41	—	8	1	no	—
464	C₂×Q₈	—	2	1	no	—
465	C₂×Q₈	—	2	1	no	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	—	4	1	no	—
468	C₂×Q₈	—	4	2	no	—
469	C₂×Q₈	—	8	1	no	—
470	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	—	2	1	no	—
474	C₂×D₄	—	4	1	no	—
475	C₂×D₄	—	4	1	no	—
476	C₂×D₄	—	4	2	no	—
477	C₂×D₄	—	4	2	no	—
478	C₂×D₄	—	4	1	no	—
479	C₂×D₄	—	8	1	no	—
480	C₂×D₄	—	8	1	no	—
481	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
482	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
483	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	4	1	no	—
488	C₂²×C₄	—	4	1	no	—
489	C₂²×C₄	—	4	1	no	—
490	SD₁₆	—	2	2	no	—
491	SD₁₆	—	4	2	no	—
492	SD₁₆	—	4	2	no	—
493	SD₁₆	—	4	2	no	—
494	SD₁₆	—	4	2	no	—
495	SD₁₆	—	4	2	no	—
496	SD₁₆	—	8	1	no	—
497	SD₁₆	—	8	1	no	—
498	SD₁₆	—	8	2	no	—
499	D₈	—	4	2	no	—
500	D₈	SD₁₆×C₁₉	1	4	yes	complemented
501	M₁₆	—	4	2	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	4	2	no	—
508	C₂×C₈	—	4	2	no	—
509	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
510	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
511	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
512	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	4	1	no	—
521	C₄⋊C₄	—	4	1	no	—
522	C₄⋊C₄	—	4	1	no	—
523	C₄⋊C₄	—	4	1	no	—
524	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
525	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
526	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
527	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
528	C₂²⋊C₄	—	2	1	no	—
529	C₂²⋊C₄	—	2	1	no	—
530	C₂²⋊C₄	—	2	1	no	—
531	C₂²⋊C₄	—	4	1	no	—
532	C₂²⋊C₄	—	4	1	no	—
533	C₂²⋊C₄	—	4	1	no	—
534	C₂²⋊C₄	—	4	1	no	—
535	C₄²	—	2	1	no	—
536	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
537	C₂³	—	2	1	no	—
538	C₂³	—	2	1	no	—
539	C₂³	—	2	1	no	—
540	C₂³	—	4	1	no	—
541	C₂³	—	8	2	no	—
542	C₂³	—	8	2	no	—
543	C₂³	—	16	1	no	—
544	Q₈	—	2	1	no	—
545	Q₈	—	2	1	no	—
546	Q₈	—	4	1	no	—
547	Q₈	—	4	1	no	—
548	Q₈	—	4	1	no	—
549	Q₈	—	4	1	no	—
550	Q₈	—	8	1	no	—
551	Q₈	—	8	2	no	—
552	D₄	—	2	1	no	—
553	D₄	—	2	1	no	—
554	D₄	—	2	1	no	—
555	D₄	—	2	1	no	—
556	D₄	—	4	1	no	—
557	D₄	—	4	1	no	—
558	D₄	—	4	1	no	—
559	D₄	—	4	1	no	—
560	D₄	—	8	1	no	—
561	D₄	—	8	2	no	—
562	D₄	—	8	2	no	—
563	D₄	—	8	2	no	—
564	D₄	C₂×SD₁₆×C₁₉	1	2	yes	—
565	D₄	C₂×SD₁₆×C₁₉	1	2	yes	complemented
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	8	2	no	—
581	C₂×C₄	—	8	2	no	—
582	C₂×C₄	—	16	1	no	—
583	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
584	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
585	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
586	C₈	—	2	2	no	—
587	C₈	—	2	1	no	—
588	C₈	—	2	1	no	—
589	C₈	—	4	1	no	—
590	C₈	—	4	1	no	—
591	C₈	—	4	1	no	—
592	C₈	—	4	1	no	—
593	C₈	C₂×SD₁₆×C₁₉	1	2	yes	complemented
594	C₈	C₁₉×AGL(1,ℤ/8)	1	2	yes	complemented
595	C₂²	—	2	2	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	4	1	no	—
598	C₂²	—	4	1	no	—
599	C₂²	—	4	1	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	8	1	no	—
605	C₂²	—	8	1	no	—
606	C₂²	—	8	1	no	—
607	C₂²	—	16	4	no	—
608	C₂²	D₄²×C₁₉	1	1	yes	characteristic
609	C₄	—	2	1	no	—
610	C₄	—	4	1	no	—
611	C₄	—	4	1	no	—
612	C₄	—	4	1	no	—
613	C₄	—	4	1	no	—
614	C₄	—	4	1	no	—
615	C₄	—	8	1	no	—
616	C₄	—	8	1	no	—
617	C₄	—	8	1	no	—
618	C₄	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
619	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
620	C₄	C₁₉×#577	1	1	yes	characteristic
621	C₄	C₁₉×#577	1	1	yes	characteristic
622	C₂	—	4	2	no	—
623	C₂	—	4	2	no	—
624	C₂	—	8	1	no	—
625	C₂	—	16	1	no	—
626	C₂	C₁₉×#3272	1	1	yes	characteristic
627	C₂	D₄×SD₁₆×C₁₉	1	1	yes	characteristic
628	C₂	C₁₉×#3291	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3272	C₂
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×#3384	C₂	semidirect
2. C₁₉×#3335	C₂	semidirect
3. D₄×SD₁₆×C₁₉	C₂	semidirect
5. C₁₉×#1705	C₂	semidirect
6. C₁₉×#1691	C₂	semidirect
7. C₁₉×#1686	C₂	semidirect
8. C₁₉×#1671	C₂	semidirect
9. C₁₉×#1665	C₂	semidirect
10. C₁₉×#1654	C₂	semidirect
11. C₁₉×#1651	C₂	semidirect
12. C₁₉×#1629	C₂	semidirect
13. C₁₉×#1622	C₂	semidirect
14. C₁₉×#1590	C₂	semidirect
15. C₈×D₈×C₁₉	C₂	semidirect
18. C₁₉×#554	C₂²	semidirect
23. C₁₉×#498	C₂²	semidirect
24. C₁₉×#498	C₂²	semidirect
25. C₁₉×#498	C₂²	semidirect
35. C₁₉×#475	C₂²	semidirect
36. C₁₉×#474	C₂²	semidirect
48. C₁₉×#446	C₂²	semidirect
54. C₈×D₄×C₁₉	C₂²	semidirect
56. C₁₉×#335	C₂²	semidirect
57. C₁₉×#334	C₂²	semidirect
58. C₁₉×#333	C₂²	semidirect
59. C₁₉×#332	C₂²	semidirect
60. C₁₉×#332	C₂²	semidirect
62. C₁₉×Q₈⋊C₈	C₂²	semidirect
65. C₁₉×D₄⋊C₈	C₂²	semidirect
66. C₈²×C₁₉	C₂²	semidirect
185. D₈×C₁₉	SD₁₆	semidirect
222. #19890	C₁₉	direct (N × H)
251. D₄×C₁₉	C₂×SD₁₆	semidirect
279. C₈×C₁₉	C₂×SD₁₆	semidirect
280. C₈×C₁₉	AGL(1,ℤ/8)	semidirect
281. #3384	C₂×C₁₉	semidirect
282. #3335	C₂×C₁₉	semidirect
283. D₄×SD₁₆	C₂×C₁₉	semidirect
285. #1705	C₂×C₁₉	semidirect
286. #1691	C₂×C₁₉	semidirect
287. #1686	C₂×C₁₉	semidirect
288. #1671	C₂×C₁₉	semidirect
289. #1665	C₂×C₁₉	semidirect
290. #1654	C₂×C₁₉	semidirect
291. #1651	C₂×C₁₉	semidirect
292. #1629	C₂×C₁₉	semidirect
293. #1622	C₂×C₁₉	semidirect
294. #1590	C₂×C₁₉	semidirect
295. C₈×D₈	C₂×C₁₉	semidirect
325. #554	C₂²×C₁₉	semidirect
330. #498	C₂²×C₁₉	semidirect
331. #498	C₂²×C₁₉	semidirect
332. #498	C₂²×C₁₉	semidirect
342. #475	C₂²×C₁₉	semidirect
343. #474	C₂²×C₁₉	semidirect
355. #446	C₂²×C₁₉	semidirect
361. C₈×D₄	C₂²×C₁₉	semidirect
363. #335	C₂²×C₁₉	semidirect
364. #334	C₂²×C₁₉	semidirect
365. #333	C₂²×C₁₉	semidirect
366. #332	C₂²×C₁₉	semidirect
367. #332	C₂²×C₁₉	semidirect
369. Q₈⋊C₈	C₂²×C₁₉	semidirect
372. D₄⋊C₈	C₂²×C₁₉	semidirect
373. C₈²	C₂²×C₁₉	semidirect
460. C₁₉	#19890	direct (N × H)
500. D₈	SD₁₆×C₁₉	semidirect
565. D₄	C₂×SD₁₆×C₁₉	semidirect
593. C₈	C₂×SD₁₆×C₁₉	semidirect
594. C₈	C₁₉×AGL(1,ℤ/8)	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3384	2
C₁₉×#3335	2
D₄×SD₁₆×C₁₉	2
C₁₉×#3272	2
C₁₉×#1705	2
C₁₉×#1691	2
C₁₉×#1686	2
C₁₉×#1671	2
C₁₉×#1665	2
C₁₉×#1654	2
C₁₉×#1651	2
C₁₉×#1629	2
C₁₉×#1622	2
C₁₉×#1590	2
C₈×D₈×C₁₉	2
#19890	19

Subgroups — C19×#19890 #18025849

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19890 #18025849