Subgroups — C₁₉×#19308 #18025267

Order 4864.

632 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3182	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3113	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3037	C₂	1	1	yes	maximal, characteristic
4	Q₈×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1702	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1700	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1694	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1686	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1682	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1680	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1674	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1666	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1569	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1561	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1557	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₉×#137	—	2	1	no	—
17	C₁₉×#533	C₂²	1	1	yes	characteristic
18	C₁₉×#532	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#500	C₂²	1	1	yes	characteristic
21	C₁₉×#492	C₂²	1	1	yes	characteristic
22	C₁₉×#487	C₂²	1	1	yes	characteristic
23	C₁₉×#486	C₂²	1	1	yes	characteristic
24	C₁₉×#483	—	2	1	no	—
25	C₁₉×#475	C₂²	1	1	yes	characteristic
26	C₁₉×#475	C₂²	1	1	yes	characteristic
27	C₁₉×#468	—	2	1	no	—
28	C₁₉×#468	—	2	1	no	—
29	C₁₉×#464	—	2	1	no	—
30	C₁₉×#464	—	2	1	no	—
31	C₁₉×#462	C₂²	1	1	yes	characteristic
32	C₁₉×#462	C₂²	1	1	yes	characteristic
33	C₁₉×#462	C₂²	1	1	yes	characteristic
34	C₁₉×#462	C₂²	1	1	yes	characteristic
35	C₁₉×#460	C₂²	1	1	yes	characteristic
36	C₁₉×#460	C₂²	1	1	yes	characteristic
37	C₁₉×#451	—	2	1	no	—
38	C₁₉×#446	—	2	1	no	—
39	C₁₉×#446	—	2	1	no	—
40	C₁₉×#446	C₂²	1	1	yes	characteristic
41	C₁₉×#446	C₂²	1	1	yes	characteristic
42	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
43	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
44	C₁₉×#441	—	2	1	no	—
45	C₁₉×#441	—	2	1	no	—
46	C₁₉×#440	—	2	1	no	—
47	C₁₉×#440	—	2	1	no	—
48	C₁₉×#432	C₂²	1	1	yes	characteristic
49	C₁₉×#423	—	2	1	no	—
50	C₁₉×#423	C₂²	1	1	yes	characteristic
51	C₁₉×#423	C₂²	1	1	yes	characteristic
52	C₁₉×#417	—	2	1	no	—
53	C₄×M₁₆×C₁₉	—	2	1	no	—
54	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
55	C₁₉×#335	C₂²	1	1	yes	characteristic
56	C₁₉×#335	C₂²	1	1	yes	characteristic
57	C₁₉×#334	C₂²	1	1	yes	characteristic
58	C₁₉×#334	C₂²	1	1	yes	characteristic
59	C₁₉×#332	C₂²	1	1	yes	characteristic
60	C₁₉×#332	C₂²	1	1	yes	characteristic
61	C₁₉×#332	C₂²	1	1	yes	characteristic
62	C₁₉×#332	C₂²	1	1	yes	characteristic
63	C₁₉×#332	C₂²	1	1	yes	characteristic
64	C₁₉×#332	C₂²	1	1	yes	characteristic
65	C₁₉×#331	C₂²	1	1	yes	characteristic
66	C₁₉×#331	C₂²	1	1	yes	characteristic
67	C₂×#41×C₁₉	—	2	1	no	—
68	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
69	C₁₉×#137	—	4	4	no	—
70	C₂×Q₁₆×C₁₉	—	2	1	no	—
71	C₂×Q₁₆×C₁₉	—	2	1	no	—
72	C₂×Q₁₆×C₁₉	—	2	1	no	—
73	C₂×Q₁₆×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×M₁₆×C₁₉	—	2	1	no	—
79	C₂×M₁₆×C₁₉	—	2	1	no	—
80	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
81	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
82	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₁₉×#127	C₂³	1	1	yes	characteristic
86	C₁₉×#125	—	2	1	no	—
87	C₁₉×#124	—	2	1	no	—
88	C₁₉×C₂²⋊Q₈	—	2	1	no	—
89	C₁₉×C₂²⋊Q₈	—	2	1	no	—
90	C₁₉×#121	—	2	1	no	—
91	C₁₉×#121	—	2	1	no	—
92	C₄×Q₈×C₁₉	—	2	1	no	—
93	C₄×Q₈×C₁₉	—	2	1	no	—
94	C₄×Q₈×C₁₉	—	2	1	no	—
95	C₄×Q₈×C₁₉	—	2	1	no	—
96	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
97	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
98	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
99	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
100	C₄×D₄×C₁₉	—	2	1	no	—
101	C₄×D₄×C₁₉	—	2	1	no	—
102	C₁₉×#117	—	2	1	no	—
103	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
104	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
105	C₂×C₄²×C₁₉	—	2	1	no	—
106	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
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×C₄⋊C₈	—	2	1	no	—
112	C₁₉×C₄⋊C₈	—	2	1	no	—
113	C₁₉×C₄⋊C₈	—	2	1	no	—
114	C₁₉×C₄⋊C₈	—	2	1	no	—
115	C₁₉×C₄⋊C₈	—	2	1	no	—
116	C₁₉×C₄⋊C₈	—	2	1	no	—
117	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
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×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	—	2	1	no	—
127	C₁₉×#103	—	2	1	no	—
128	C₁₉×#103	—	2	1	no	—
129	C₁₉×#103	—	2	1	no	—
130	C₁₉×#103	—	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×C₂²⋊C₈	—	2	1	no	—
136	C₁₉×#97	—	2	1	no	—
137	C₁₉×#97	—	2	1	no	—
138	C₁₉×#97	—	2	1	no	—
139	C₁₉×#97	D₄	1	1	yes	characteristic
140	C₁₉×#97	D₄	1	1	yes	characteristic
141	C₄×C₈×C₁₉	—	2	1	no	—
142	C₄×C₈×C₁₉	—	2	1	no	—
143	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
145	#41×C₁₉	—	4	2	no	—
146	#41×C₁₉	—	4	2	no	—
147	C₂×Q₈×C₁₉	—	2	1	no	—
148	C₂×Q₈×C₁₉	—	2	2	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	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	C₂²×C₄×C₁₉	—	2	1	no	—
160	C₂²×C₄×C₁₉	—	2	1	no	—
161	C₂²×C₄×C₁₉	—	4	1	no	—
162	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
165	Q₁₆×C₁₉	—	4	2	no	—
166	Q₁₆×C₁₉	—	4	2	no	—
167	Q₁₆×C₁₉	—	4	2	no	—
168	Q₁₆×C₁₉	—	4	2	no	—
169	SD₁₆×C₁₉	—	4	2	no	—
170	SD₁₆×C₁₉	—	4	2	no	—
171	SD₁₆×C₁₉	—	4	2	no	—
172	SD₁₆×C₁₉	—	4	2	no	—
173	M₁₆×C₁₉	—	2	2	no	—
174	M₁₆×C₁₉	—	4	1	no	—
175	M₁₆×C₁₉	—	4	2	no	—
176	M₁₆×C₁₉	—	4	2	no	—
177	C₂×C₈×C₁₉	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
184	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
185	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
186	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
187	C₄⋊C₄×C₁₉	—	2	1	no	—
188	C₄⋊C₄×C₁₉	—	2	1	no	—
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	—	2	1	no	—
198	C₄⋊C₄×C₁₉	—	4	1	no	—
199	C₄⋊C₄×C₁₉	—	4	1	no	—
200	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
201	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
202	C₂²⋊C₄×C₁₉	—	4	1	no	—
203	C₂²⋊C₄×C₁₉	—	4	1	no	—
204	C₂²⋊C₄×C₁₉	—	4	1	no	—
205	C₄²×C₁₉	—	2	1	no	—
206	C₄²×C₁₉	—	2	1	no	—
207	C₄²×C₁₉	—	2	1	no	—
208	C₄²×C₁₉	—	2	1	no	—
209	C₄²×C₁₉	—	4	1	no	—
210	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
211	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
212	C₄²×C₁₉	#41	1	1	yes	characteristic
213	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
214	#19308	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₂³×C₁₉	—	4	1	no	—
216	C₂³×C₁₉	#121	1	1	yes	characteristic
217	Q₈×C₁₉	—	2	1	no	—
218	Q₈×C₁₉	—	2	1	no	—
219	Q₈×C₁₉	—	2	1	no	—
220	Q₈×C₁₉	—	4	2	no	—
221	Q₈×C₁₉	—	4	1	no	—
222	Q₈×C₁₉	—	4	1	no	—
223	Q₈×C₁₉	—	4	1	no	—
224	Q₈×C₁₉	—	4	1	no	—
225	Q₈×C₁₉	—	4	1	no	—
226	Q₈×C₁₉	—	4	1	no	—
227	Q₈×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
228	D₄×C₁₉	—	4	1	no	—
229	D₄×C₁₉	—	4	1	no	—
230	D₄×C₁₉	—	4	1	no	—
231	D₄×C₁₉	—	4	1	no	—
232	D₄×C₁₉	—	8	1	no	—
233	D₄×C₁₉	—	8	2	no	—
234	C₂×C₄×C₁₉	—	2	1	no	—
235	C₂×C₄×C₁₉	—	2	1	no	—
236	C₂×C₄×C₁₉	—	2	1	no	—
237	C₂×C₄×C₁₉	—	2	1	no	—
238	C₂×C₄×C₁₉	—	2	1	no	—
239	C₂×C₄×C₁₉	—	2	1	no	—
240	C₂×C₄×C₁₉	—	2	1	no	—
241	C₂×C₄×C₁₉	—	2	1	no	—
242	C₂×C₄×C₁₉	—	4	1	no	—
243	C₂×C₄×C₁₉	—	4	2	no	—
244	C₂×C₄×C₁₉	—	4	1	no	—
245	C₂×C₄×C₁₉	—	4	1	no	—
246	C₂×C₄×C₁₉	—	4	1	no	—
247	C₂×C₄×C₁₉	—	8	2	no	—
248	C₂×C₄×C₁₉	—	8	1	no	—
249	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
250	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
251	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
252	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
255	C₈×C₁₉	—	2	1	no	—
256	C₈×C₁₉	—	2	1	no	—
257	C₈×C₁₉	—	2	1	no	—
258	C₈×C₁₉	—	4	1	no	—
259	C₈×C₁₉	—	4	1	no	—
260	C₈×C₁₉	—	4	1	no	—
261	C₈×C₁₉	—	4	1	no	—
262	C₈×C₁₉	—	4	1	no	—
263	C₈×C₁₉	—	4	1	no	—
264	C₈×C₁₉	#137	1	2	yes	complemented
265	#3182	C₂×C₁₉	1	1	yes	characteristic
266	#3113	C₂×C₁₉	1	1	yes	characteristic, complemented
267	#3037	C₂×C₁₉	1	1	yes	characteristic
268	Q₈×M₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
269	#1702	C₂×C₁₉	1	1	yes	characteristic, complemented
270	#1700	C₂×C₁₉	1	1	yes	characteristic, complemented
271	#1694	C₂×C₁₉	1	1	yes	characteristic, complemented
272	#1686	C₂×C₁₉	1	1	yes	characteristic, complemented
273	#1682	C₂×C₁₉	1	1	yes	characteristic, complemented
274	#1680	C₂×C₁₉	1	1	yes	characteristic, complemented
275	#1674	C₂×C₁₉	1	1	yes	characteristic, complemented
276	#1666	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#1569	C₂×C₁₉	1	1	yes	characteristic, complemented
278	#1561	C₂×C₁₉	1	1	yes	characteristic, complemented
279	#1557	C₂×C₁₉	1	1	yes	characteristic
280	C₂²×C₁₉	—	2	1	no	—
281	C₂²×C₁₉	—	2	1	no	—
282	C₂²×C₁₉	—	2	1	no	—
283	C₂²×C₁₉	—	8	1	no	—
284	C₂²×C₁₉	—	8	1	no	—
285	C₂²×C₁₉	—	8	1	no	—
286	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
287	C₄×C₁₉	—	2	1	no	—
288	C₄×C₁₉	—	2	1	no	—
289	C₄×C₁₉	—	2	2	no	—
290	C₄×C₁₉	—	2	1	no	—
291	C₄×C₁₉	—	2	1	no	—
292	C₄×C₁₉	—	4	1	no	—
293	C₄×C₁₉	—	4	1	no	—
294	C₄×C₁₉	—	4	1	no	—
295	C₄×C₁₉	—	8	1	no	—
296	C₄×C₁₉	—	8	1	no	—
297	C₄×C₁₉	—	8	1	no	—
298	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
299	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
300	C₄×C₁₉	#575	1	1	yes	characteristic
301	C₄×C₁₉	#575	1	1	yes	characteristic
302	C₂×#137	—	2	1	no	—
303	#533	C₂²×C₁₉	1	1	yes	characteristic
304	#532	C₂²×C₁₉	1	1	yes	characteristic
305	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
306	#500	C₂²×C₁₉	1	1	yes	characteristic
307	#492	C₂²×C₁₉	1	1	yes	characteristic
308	#487	C₂²×C₁₉	1	1	yes	characteristic
309	#486	C₂²×C₁₉	1	1	yes	characteristic
310	#483	—	2	1	no	—
311	#475	C₂²×C₁₉	1	1	yes	characteristic
312	#475	C₂²×C₁₉	1	1	yes	characteristic
313	#468	—	2	1	no	—
314	#468	—	2	1	no	—
315	#464	—	2	1	no	—
316	#464	—	2	1	no	—
317	#462	C₂²×C₁₉	1	1	yes	characteristic
318	#462	C₂²×C₁₉	1	1	yes	characteristic
319	#462	C₂²×C₁₉	1	1	yes	characteristic
320	#462	C₂²×C₁₉	1	1	yes	characteristic
321	#460	C₂²×C₁₉	1	1	yes	characteristic
322	#460	C₂²×C₁₉	1	1	yes	characteristic
323	#451	—	2	1	no	—
324	#446	—	2	1	no	—
325	#446	—	2	1	no	—
326	#446	C₂²×C₁₉	1	1	yes	characteristic
327	#446	C₂²×C₁₉	1	1	yes	characteristic
328	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
329	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
330	#441	—	2	1	no	—
331	#441	—	2	1	no	—
332	#440	—	2	1	no	—
333	#440	—	2	1	no	—
334	#432	C₂²×C₁₉	1	1	yes	characteristic
335	#423	—	2	1	no	—
336	#423	C₂²×C₁₉	1	1	yes	characteristic
337	#423	C₂²×C₁₉	1	1	yes	characteristic
338	#417	—	2	1	no	—
339	C₄×M₁₆	—	2	1	no	—
340	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
341	#335	C₂²×C₁₉	1	1	yes	characteristic
342	#335	C₂²×C₁₉	1	1	yes	characteristic
343	#334	C₂²×C₁₉	1	1	yes	characteristic
344	#334	C₂²×C₁₉	1	1	yes	characteristic
345	#332	C₂²×C₁₉	1	1	yes	characteristic
346	#332	C₂²×C₁₉	1	1	yes	characteristic
347	#332	C₂²×C₁₉	1	1	yes	characteristic
348	#332	C₂²×C₁₉	1	1	yes	characteristic
349	#332	C₂²×C₁₉	1	1	yes	characteristic
350	#332	C₂²×C₁₉	1	1	yes	characteristic
351	#331	C₂²×C₁₉	1	1	yes	characteristic
352	#331	C₂²×C₁₉	1	1	yes	characteristic
353	C₂×C₁₉	—	4	1	no	—
354	C₂×C₁₉	—	16	1	no	—
355	C₂×C₁₉	#3037	1	1	yes	characteristic
356	C₂×C₁₉	#3055	1	1	yes	characteristic
357	C₂×C₁₉	#3069	1	1	yes	characteristic
358	C₂×#41	—	2	1	no	—
359	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
360	#137	—	4	4	no	—
361	C₂×Q₁₆	—	2	1	no	—
362	C₂×Q₁₆	—	2	1	no	—
363	C₂×Q₁₆	—	2	1	no	—
364	C₂×Q₁₆	—	2	1	no	—
365	C₂×SD₁₆	—	2	1	no	—
366	C₂×SD₁₆	—	2	1	no	—
367	C₂×SD₁₆	—	2	1	no	—
368	C₂×SD₁₆	—	2	1	no	—
369	C₂×M₁₆	—	2	1	no	—
370	C₂×M₁₆	—	2	1	no	—
371	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
372	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
373	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
374	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
375	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
376	#127	C₂³×C₁₉	1	1	yes	characteristic
377	#125	—	2	1	no	—
378	#124	—	2	1	no	—
379	C₂²⋊Q₈	—	2	1	no	—
380	C₂²⋊Q₈	—	2	1	no	—
381	#121	—	2	1	no	—
382	#121	—	2	1	no	—
383	C₄×Q₈	—	2	1	no	—
384	C₄×Q₈	—	2	1	no	—
385	C₄×Q₈	—	2	1	no	—
386	C₄×Q₈	—	2	1	no	—
387	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
388	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
389	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
390	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
391	C₄×D₄	—	2	1	no	—
392	C₄×D₄	—	2	1	no	—
393	#117	—	2	1	no	—
394	C₂×C₄⋊C₄	—	2	1	no	—
395	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
396	C₂×C₄²	—	2	1	no	—
397	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
398	#107	—	2	1	no	—
399	#107	—	2	1	no	—
400	#106	—	2	1	no	—
401	#106	—	2	1	no	—
402	C₄⋊C₈	—	2	1	no	—
403	C₄⋊C₈	—	2	1	no	—
404	C₄⋊C₈	—	2	1	no	—
405	C₄⋊C₈	—	2	1	no	—
406	C₄⋊C₈	—	2	1	no	—
407	C₄⋊C₈	—	2	1	no	—
408	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
409	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
410	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
411	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
412	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
413	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
414	#103	—	2	1	no	—
415	#103	—	2	1	no	—
416	#103	—	2	1	no	—
417	#103	—	2	1	no	—
418	#103	—	2	1	no	—
419	#103	—	2	1	no	—
420	#103	—	2	1	no	—
421	#103	—	2	1	no	—
422	#102	—	2	1	no	—
423	#102	—	2	1	no	—
424	#102	—	2	1	no	—
425	#102	—	2	1	no	—
426	C₂²⋊C₈	—	2	1	no	—
427	#97	—	2	1	no	—
428	#97	—	2	1	no	—
429	#97	—	2	1	no	—
430	#97	D₄×C₁₉	1	1	yes	characteristic
431	#97	D₄×C₁₉	1	1	yes	characteristic
432	C₄×C₈	—	2	1	no	—
433	C₄×C₈	—	2	1	no	—
434	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
435	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
436	C₁₉	#19308	1	1	yes	characteristic, direct product factor, Sylow
437	#41	—	4	2	no	—
438	#41	—	4	2	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	2	2	no	—
441	C₂×Q₈	—	2	1	no	—
442	C₂×Q₈	—	2	1	no	—
443	C₂×Q₈	—	2	1	no	—
444	C₂×Q₈	—	4	1	no	—
445	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
446	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	4	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	4	1	no	—
454	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
456	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
457	Q₁₆	—	4	2	no	—
458	Q₁₆	—	4	2	no	—
459	Q₁₆	—	4	2	no	—
460	Q₁₆	—	4	2	no	—
461	SD₁₆	—	4	2	no	—
462	SD₁₆	—	4	2	no	—
463	SD₁₆	—	4	2	no	—
464	SD₁₆	—	4	2	no	—
465	M₁₆	—	2	2	no	—
466	M₁₆	—	4	1	no	—
467	M₁₆	—	4	2	no	—
468	M₁₆	—	4	2	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
476	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
477	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
478	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	4	1	no	—
491	C₄⋊C₄	—	4	1	no	—
492	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
493	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
494	C₂²⋊C₄	—	4	1	no	—
495	C₂²⋊C₄	—	4	1	no	—
496	C₂²⋊C₄	—	4	1	no	—
497	C₄²	—	2	1	no	—
498	C₄²	—	2	1	no	—
499	C₄²	—	2	1	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	4	1	no	—
502	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
503	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
504	C₄²	#41×C₁₉	1	1	yes	characteristic
505	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
506	C₂³	—	4	1	no	—
507	C₂³	C₁₉×#121	1	1	yes	characteristic
508	Q₈	—	2	1	no	—
509	Q₈	—	2	1	no	—
510	Q₈	—	2	1	no	—
511	Q₈	—	4	2	no	—
512	Q₈	—	4	1	no	—
513	Q₈	—	4	1	no	—
514	Q₈	—	4	1	no	—
515	Q₈	—	4	1	no	—
516	Q₈	—	4	1	no	—
517	Q₈	—	4	1	no	—
518	Q₈	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
519	D₄	—	4	1	no	—
520	D₄	—	4	1	no	—
521	D₄	—	4	1	no	—
522	D₄	—	4	1	no	—
523	D₄	—	8	1	no	—
524	D₄	—	8	2	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	8	2	no	—
539	C₂×C₄	—	8	1	no	—
540	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
541	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
542	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
543	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
544	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
545	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
546	C₈	—	2	1	no	—
547	C₈	—	2	1	no	—
548	C₈	—	2	1	no	—
549	C₈	—	4	1	no	—
550	C₈	—	4	1	no	—
551	C₈	—	4	1	no	—
552	C₈	—	4	1	no	—
553	C₈	—	4	1	no	—
554	C₈	—	4	1	no	—
555	C₈	C₁₉×#137	1	2	yes	complemented
556	C₂²	—	2	1	no	—
557	C₂²	—	2	1	no	—
558	C₂²	—	2	1	no	—
559	C₂²	—	8	1	no	—
560	C₂²	—	8	1	no	—
561	C₂²	—	8	1	no	—
562	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
563	C₄	—	2	1	no	—
564	C₄	—	2	1	no	—
565	C₄	—	2	2	no	—
566	C₄	—	2	1	no	—
567	C₄	—	2	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	1	no	—
571	C₄	—	8	1	no	—
572	C₄	—	8	1	no	—
573	C₄	—	8	1	no	—
574	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
575	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
576	C₄	C₁₉×#575	1	1	yes	characteristic
577	C₄	C₁₉×#575	1	1	yes	characteristic
578	C₂	—	4	1	no	—
579	C₂	—	16	1	no	—
580	C₂	C₁₉×#3037	1	1	yes	characteristic
581	C₂	C₁₉×#3055	1	1	yes	characteristic
582	C₂	C₁₉×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3113	C₂	semidirect
4. Q₈×M₁₆×C₁₉	C₂	semidirect
5. C₁₉×#1702	C₂	semidirect
6. C₁₉×#1700	C₂	semidirect
7. C₁₉×#1694	C₂	semidirect
8. C₁₉×#1686	C₂	semidirect
9. C₁₉×#1682	C₂	semidirect
10. C₁₉×#1680	C₂	semidirect
11. C₁₉×#1674	C₂	semidirect
12. C₁₉×#1666	C₂	semidirect
13. C₁₉×#1569	C₂	semidirect
14. C₁₉×#1561	C₂	semidirect
214. #19308	C₁₉	direct (N × H)
264. C₈×C₁₉	#137	semidirect
266. #3113	C₂×C₁₉	semidirect
268. Q₈×M₁₆	C₂×C₁₉	semidirect
269. #1702	C₂×C₁₉	semidirect
270. #1700	C₂×C₁₉	semidirect
271. #1694	C₂×C₁₉	semidirect
272. #1686	C₂×C₁₉	semidirect
273. #1682	C₂×C₁₉	semidirect
274. #1680	C₂×C₁₉	semidirect
275. #1674	C₂×C₁₉	semidirect
276. #1666	C₂×C₁₉	semidirect
277. #1569	C₂×C₁₉	semidirect
278. #1561	C₂×C₁₉	semidirect
436. C₁₉	#19308	direct (N × H)
555. C₈	C₁₉×#137	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3182	2
C₁₉×#3113	2
C₁₉×#3037	2
Q₈×M₁₆×C₁₉	2
C₁₉×#1702	2
C₁₉×#1700	2
C₁₉×#1694	2
C₁₉×#1686	2
C₁₉×#1682	2
C₁₉×#1680	2
C₁₉×#1674	2
C₁₉×#1666	2
C₁₉×#1569	2
C₁₉×#1561	2
C₁₉×#1557	2
#19308	19

Subgroups — C19×#19308 #18025267

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19308 #18025267