Subgroups — C₁₉×#18674 #18024633

Order 4864.

1176 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3497	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3245	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3169	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3037	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1649	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1641	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1627	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1621	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1547	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1492	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₉×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×2₋¹⁺⁴	—	2	1	no	—
13	C₂×C₁₉×#137	—	2	1	no	—
14	C₁₉×#550	—	2	1	no	—
15	C₁₉×#550	C₂²	1	2	yes	—
16	D₄×Q₈×C₁₉	—	2	1	no	—
17	D₄×Q₈×C₁₉	C₂²	1	2	yes	—
18	C₁₉×#548	—	2	2	no	—
19	C₁₉×#548	—	2	2	no	—
20	C₁₉×#537	—	2	2	no	—
21	C₁₉×#537	—	2	1	no	—
22	C₁₉×#532	—	2	2	no	—
23	C₁₉×#532	C₂²	1	1	yes	characteristic
24	C₁₉×#532	C₂²	1	1	yes	characteristic
25	C₁₉×#532	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#500	C₂²	1	1	yes	characteristic
28	C₁₉×#493	C₂²	1	1	yes	characteristic
29	C₁₉×#486	C₂²	1	1	yes	characteristic
30	C₁₉×#486	C₂²	1	1	yes	characteristic
31	C₁₉×#474	—	2	1	no	—
32	C₁₉×#474	C₂²	1	2	yes	—
33	C₁₉×#466	—	2	2	no	—
34	C₁₉×#466	—	2	2	no	—
35	C₁₉×#464	—	2	2	no	—
36	C₁₉×#462	C₂²	1	2	yes	—
37	C₁₉×#460	C₂²	1	2	yes	—
38	C₁₉×#459	—	2	1	no	—
39	C₁₉×#459	C₂²	1	2	yes	—
40	C₄×D₈×C₁₉	—	2	2	no	—
41	C₁₉×#423	C₂²	1	1	yes	characteristic
42	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
43	C₁₉×#417	—	2	1	no	—
44	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
45	C₁₉×#332	C₂²	1	2	yes	—
46	C₁₉×#331	C₂²	1	2	yes	—
47	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
48	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
49	C₁₉×D₄⋊C₈	C₂²	1	2	yes	—
50	C₁₉×D₄⋊C₈	C₂²	1	2	yes	—
51	C₁₉×2₋¹⁺⁴	—	4	4	no	—
52	C₁₉×2₋¹⁺⁴	—	4	4	no	—
53	C₂×#41×C₁₉	—	2	4	no	—
54	C₂×#41×C₁₉	—	2	2	no	—
55	C₂×#41×C₁₉	—	2	2	no	—
56	C₂×#41×C₁₉	—	2	1	no	—
57	C₂×#41×C₁₉	—	2	1	no	—
58	C₂×#41×C₁₉	—	2	1	no	—
59	C₂²×Q₈×C₁₉	—	2	2	no	—
60	C₂²×Q₈×C₁₉	—	2	2	no	—
61	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
62	C₁₉×#137	—	4	4	no	—
63	C₂×Q₁₆×C₁₉	—	2	2	no	—
64	C₂×SD₁₆×C₁₉	—	2	2	no	—
65	C₂×D₈×C₁₉	—	2	2	no	—
66	C₂×D₈×C₁₉	—	2	2	no	—
67	C₂×M₁₆×C₁₉	—	2	1	no	—
68	C₂²×C₈×C₁₉	—	2	1	no	—
69	C₂²×C₈×C₁₉	—	2	1	no	—
70	C₁₉×C₄⋊Q₈	—	2	2	no	—
71	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
72	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
73	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
74	C₁₉×#127	—	2	2	no	—
75	C₁₉×#127	D₄	1	1	yes	characteristic
76	C₁₉×#127	C₂³	1	1	yes	characteristic
77	C₁₉×#127	C₂³	1	1	yes	characteristic
78	C₁₉×#124	—	2	4	no	—
79	C₁₉×#124	—	2	1	no	—
80	C₁₉×#124	—	2	1	no	—
81	C₁₉×#124	—	2	1	no	—
82	C₁₉×C₂²⋊Q₈	—	2	2	no	—
83	C₁₉×C₂²⋊Q₈	—	2	4	no	—
84	C₁₉×C₂²⋊Q₈	—	2	2	no	—
85	C₁₉×C₂²⋊Q₈	—	2	4	no	—
86	C₁₉×#121	—	2	4	no	—
87	C₁₉×#121	—	2	2	no	—
88	C₁₉×#121	—	2	4	no	—
89	C₁₉×#121	—	2	4	no	—
90	C₁₉×#121	—	2	1	no	—
91	C₁₉×#121	—	2	1	no	—
92	C₁₉×#121	—	2	2	no	—
93	C₁₉×#121	—	2	1	no	—
94	C₁₉×#121	—	2	1	no	—
95	C₁₉×#121	D₄	1	2	yes	—
96	C₁₉×#121	D₄	1	2	yes	—
97	C₄×Q₈×C₁₉	—	2	1	no	—
98	C₄×Q₈×C₁₉	—	2	1	no	—
99	C₄×Q₈×C₁₉	D₄	1	2	yes	—
100	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
101	C₄×D₄×C₁₉	—	2	4	no	—
102	C₄×D₄×C₁₉	—	2	2	no	—
103	C₄×D₄×C₁₉	—	2	2	no	—
104	C₄×D₄×C₁₉	—	2	1	no	—
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	D₄	1	2	yes	—
109	C₄×D₄×C₁₉	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
111	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
112	C₂×C₄²×C₁₉	—	2	1	no	—
113	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
114	C₁₉×#107	—	2	2	no	—
115	C₁₉×#107	—	2	2	no	—
116	C₁₉×C₄⋊C₈	—	2	1	no	—
117	C₁₉×C₄⋊C₈	—	2	1	no	—
118	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
119	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
120	C₁₉×#103	—	2	2	no	—
121	C₁₉×#102	—	2	2	no	—
122	C₁₉×#102	—	2	2	no	—
123	C₁₉×#102	—	2	2	no	—
124	C₁₉×#102	—	2	2	no	—
125	C₁₉×#102	—	2	2	no	—
126	C₄×C₈×C₁₉	—	2	1	no	—
127	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
128	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
129	#41×C₁₉	—	4	16	no	—
130	#41×C₁₉	—	4	4	no	—
131	#41×C₁₉	—	4	8	no	—
132	#41×C₁₉	—	4	4	no	—
133	#41×C₁₉	—	4	2	no	—
134	#41×C₁₉	—	4	2	no	—
135	#41×C₁₉	—	4	2	no	—
136	#41×C₁₉	—	4	2	no	—
137	#41×C₁₉	—	4	2	no	—
138	#41×C₁₉	—	4	2	no	—
139	C₂×Q₈×C₁₉	—	2	4	no	—
140	C₂×Q₈×C₁₉	—	2	1	no	—
141	C₂×Q₈×C₁₉	—	2	1	no	—
142	C₂×Q₈×C₁₉	—	2	2	no	—
143	C₂×Q₈×C₁₉	—	2	1	no	—
144	C₂×Q₈×C₁₉	—	2	1	no	—
145	C₂×Q₈×C₁₉	—	4	4	no	—
146	C₂×Q₈×C₁₉	—	4	8	no	—
147	C₂×Q₈×C₁₉	—	4	4	no	—
148	C₂×Q₈×C₁₉	D₈	1	4	yes	complemented
149	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
150	C₂×D₄×C₁₉	—	2	4	no	—
151	C₂×D₄×C₁₉	—	2	2	no	—
152	C₂×D₄×C₁₉	—	2	2	no	—
153	C₂×D₄×C₁₉	—	2	4	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	—	2	1	no	—
160	C₂×D₄×C₁₉	—	2	1	no	—
161	C₂×D₄×C₁₉	—	4	1	no	—
162	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
163	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
164	C₂²×C₄×C₁₉	—	2	1	no	—
165	C₂²×C₄×C₁₉	—	2	4	no	—
166	C₂²×C₄×C₁₉	—	2	4	no	—
167	C₂²×C₄×C₁₉	—	2	1	no	—
168	C₂²×C₄×C₁₉	—	2	2	no	—
169	C₂²×C₄×C₁₉	—	2	2	no	—
170	C₂²×C₄×C₁₉	—	4	1	no	—
171	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
174	Q₁₆×C₁₉	—	4	4	no	—
175	SD₁₆×C₁₉	—	4	4	no	—
176	D₈×C₁₉	—	4	4	no	—
177	D₈×C₁₉	—	8	2	no	—
178	M₁₆×C₁₉	—	4	2	no	—
179	C₂×C₈×C₁₉	—	2	1	no	—
180	C₂×C₈×C₁₉	—	2	2	no	—
181	C₂×C₈×C₁₉	—	2	1	no	—
182	C₂×C₈×C₁₉	—	2	2	no	—
183	C₂×C₈×C₁₉	—	4	2	no	—
184	C₂×C₈×C₁₉	—	8	1	no	—
185	C₄⋊C₄×C₁₉	—	2	4	no	—
186	C₄⋊C₄×C₁₉	—	2	2	no	—
187	C₄⋊C₄×C₁₉	—	2	1	no	—
188	C₄⋊C₄×C₁₉	—	2	1	no	—
189	C₄⋊C₄×C₁₉	—	2	2	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	C₂×D₄	1	2	yes	—
194	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
195	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
196	C₂²⋊C₄×C₁₉	—	2	4	no	—
197	C₂²⋊C₄×C₁₉	—	2	4	no	—
198	C₂²⋊C₄×C₁₉	—	2	2	no	—
199	C₂²⋊C₄×C₁₉	—	2	2	no	—
200	C₂²⋊C₄×C₁₉	—	2	2	no	—
201	C₂²⋊C₄×C₁₉	—	2	2	no	—
202	C₂²⋊C₄×C₁₉	—	4	1	no	—
203	C₂²⋊C₄×C₁₉	—	4	1	no	—
204	C₄²×C₁₉	—	2	2	no	—
205	C₄²×C₁₉	—	2	2	no	—
206	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
210	#18674	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂³×C₁₉	—	2	2	no	—
212	C₂³×C₁₉	—	2	2	no	—
213	C₂³×C₁₉	—	4	1	no	—
214	C₂³×C₁₉	#120	1	1	yes	characteristic
215	Q₈×C₁₉	—	2	2	no	—
216	Q₈×C₁₉	—	2	4	no	—
217	Q₈×C₁₉	—	4	8	no	—
218	Q₈×C₁₉	—	4	1	no	—
219	Q₈×C₁₉	—	4	1	no	—
220	Q₈×C₁₉	—	4	2	no	—
221	Q₈×C₁₉	—	4	1	no	—
222	Q₈×C₁₉	—	4	1	no	—
223	Q₈×C₁₉	C₂×D₈	1	4	yes	—
224	D₄×C₁₉	—	2	2	no	—
225	D₄×C₁₉	—	2	2	no	—
226	D₄×C₁₉	—	4	2	no	—
227	D₄×C₁₉	—	4	8	no	—
228	D₄×C₁₉	—	4	2	no	—
229	D₄×C₁₉	—	4	4	no	—
230	D₄×C₁₉	—	4	4	no	—
231	D₄×C₁₉	—	4	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	2	no	—
240	D₄×C₁₉	—	8	1	no	—
241	D₄×C₁₉	—	8	4	no	—
242	D₄×C₁₉	—	8	2	no	—
243	C₂×C₄×C₁₉	—	2	2	no	—
244	C₂×C₄×C₁₉	—	2	4	no	—
245	C₂×C₄×C₁₉	—	2	1	no	—
246	C₂×C₄×C₁₉	—	2	1	no	—
247	C₂×C₄×C₁₉	—	2	2	no	—
248	C₂×C₄×C₁₉	—	2	2	no	—
249	C₂×C₄×C₁₉	—	2	2	no	—
250	C₂×C₄×C₁₉	—	4	1	no	—
251	C₂×C₄×C₁₉	—	4	8	no	—
252	C₂×C₄×C₁₉	—	4	8	no	—
253	C₂×C₄×C₁₉	—	4	2	no	—
254	C₂×C₄×C₁₉	—	4	2	no	—
255	C₂×C₄×C₁₉	—	4	4	no	—
256	C₂×C₄×C₁₉	—	4	1	no	—
257	C₂×C₄×C₁₉	—	8	1	no	—
258	C₂×C₄×C₁₉	—	8	2	no	—
259	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
260	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
261	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
262	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
263	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
264	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
267	C₈×C₁₉	—	2	2	no	—
268	C₈×C₁₉	—	4	1	no	—
269	C₈×C₁₉	—	4	2	no	—
270	C₈×C₁₉	—	4	2	no	—
271	#3497	C₂×C₁₉	1	1	yes	characteristic, complemented
272	#3245	C₂×C₁₉	1	1	yes	characteristic, complemented
273	#3169	C₂×C₁₉	1	1	yes	characteristic, complemented
274	#3037	C₂×C₁₉	1	1	yes	characteristic, complemented
275	#1649	C₂×C₁₉	1	2	yes	complemented
276	#1641	C₂×C₁₉	1	2	yes	complemented
277	#1627	C₂×C₁₉	1	2	yes	complemented
278	#1621	C₂×C₁₉	1	2	yes	complemented
279	#1547	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#1492	C₂×C₁₉	1	1	yes	characteristic, complemented
281	C₂×Q₈⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
282	C₂²×C₁₉	—	2	1	no	—
283	C₂²×C₁₉	—	2	1	no	—
284	C₂²×C₁₉	—	4	2	no	—
285	C₂²×C₁₉	—	4	2	no	—
286	C₂²×C₁₉	—	4	2	no	—
287	C₂²×C₁₉	—	4	2	no	—
288	C₂²×C₁₉	—	4	2	no	—
289	C₂²×C₁₉	—	4	2	no	—
290	C₂²×C₁₉	—	8	1	no	—
291	C₂²×C₁₉	—	8	1	no	—
292	C₂²×C₁₉	—	8	1	no	—
293	C₂²×C₁₉	#447	1	2	yes	—
294	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
295	C₄×C₁₉	—	2	4	no	—
296	C₄×C₁₉	—	2	1	no	—
297	C₄×C₁₉	—	2	1	no	—
298	C₄×C₁₉	—	2	1	no	—
299	C₄×C₁₉	—	4	2	no	—
300	C₄×C₁₉	—	4	2	no	—
301	C₄×C₁₉	—	4	2	no	—
302	C₄×C₁₉	—	8	1	no	—
303	C₄×C₁₉	#447	1	2	yes	—
304	C₄×C₁₉	C₂²×D₈	1	1	yes	characteristic
305	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
306	C₄×C₁₉	#577	1	1	yes	characteristic
307	C₄×C₁₉	#578	1	1	yes	characteristic
308	C₂×2₋¹⁺⁴	—	2	1	no	—
309	C₂×#137	—	2	1	no	—
310	#550	—	2	1	no	—
311	#550	C₂²×C₁₉	1	2	yes	—
312	D₄×Q₈	—	2	1	no	—
313	D₄×Q₈	C₂²×C₁₉	1	2	yes	—
314	#548	—	2	2	no	—
315	#548	—	2	2	no	—
316	#537	—	2	2	no	—
317	#537	—	2	1	no	—
318	#532	—	2	2	no	—
319	#532	C₂²×C₁₉	1	1	yes	characteristic
320	#532	C₂²×C₁₉	1	1	yes	characteristic
321	#532	C₂²×C₁₉	1	1	yes	characteristic
322	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
323	#500	C₂²×C₁₉	1	1	yes	characteristic
324	#493	C₂²×C₁₉	1	1	yes	characteristic
325	#486	C₂²×C₁₉	1	1	yes	characteristic
326	#486	C₂²×C₁₉	1	1	yes	characteristic
327	#474	—	2	1	no	—
328	#474	C₂²×C₁₉	1	2	yes	—
329	#466	—	2	2	no	—
330	#466	—	2	2	no	—
331	#464	—	2	2	no	—
332	#462	C₂²×C₁₉	1	2	yes	—
333	#460	C₂²×C₁₉	1	2	yes	—
334	#459	—	2	1	no	—
335	#459	C₂²×C₁₉	1	2	yes	—
336	C₄×D₈	—	2	2	no	—
337	#423	C₂²×C₁₉	1	1	yes	characteristic
338	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
339	#417	—	2	1	no	—
340	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
341	#332	C₂²×C₁₉	1	2	yes	—
342	#331	C₂²×C₁₉	1	2	yes	—
343	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
344	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
345	D₄⋊C₈	C₂²×C₁₉	1	2	yes	—
346	D₄⋊C₈	C₂²×C₁₉	1	2	yes	—
347	C₂×C₁₉	—	2	2	no	—
348	C₂×C₁₉	—	8	2	no	—
349	C₂×C₁₉	—	8	2	no	—
350	C₂×C₁₉	—	16	1	no	—
351	C₂×C₁₉	C₂×#447	1	1	yes	characteristic
352	C₂×C₁₉	#3013	1	1	yes	characteristic
353	C₂×C₁₉	#3018	1	1	yes	characteristic
354	2₋¹⁺⁴	—	4	4	no	—
355	2₋¹⁺⁴	—	4	4	no	—
356	C₂×#41	—	2	4	no	—
357	C₂×#41	—	2	2	no	—
358	C₂×#41	—	2	2	no	—
359	C₂×#41	—	2	1	no	—
360	C₂×#41	—	2	1	no	—
361	C₂×#41	—	2	1	no	—
362	C₂²×Q₈	—	2	2	no	—
363	C₂²×Q₈	—	2	2	no	—
364	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
365	#137	—	4	4	no	—
366	C₂×Q₁₆	—	2	2	no	—
367	C₂×SD₁₆	—	2	2	no	—
368	C₂×D₈	—	2	2	no	—
369	C₂×D₈	—	2	2	no	—
370	C₂×M₁₆	—	2	1	no	—
371	C₂²×C₈	—	2	1	no	—
372	C₂²×C₈	—	2	1	no	—
373	C₄⋊Q₈	—	2	2	no	—
374	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
375	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
376	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
377	#127	—	2	2	no	—
378	#127	D₄×C₁₉	1	1	yes	characteristic
379	#127	C₂³×C₁₉	1	1	yes	characteristic
380	#127	C₂³×C₁₉	1	1	yes	characteristic
381	#124	—	2	4	no	—
382	#124	—	2	1	no	—
383	#124	—	2	1	no	—
384	#124	—	2	1	no	—
385	C₂²⋊Q₈	—	2	2	no	—
386	C₂²⋊Q₈	—	2	4	no	—
387	C₂²⋊Q₈	—	2	2	no	—
388	C₂²⋊Q₈	—	2	4	no	—
389	#121	—	2	4	no	—
390	#121	—	2	2	no	—
391	#121	—	2	4	no	—
392	#121	—	2	4	no	—
393	#121	—	2	1	no	—
394	#121	—	2	1	no	—
395	#121	—	2	2	no	—
396	#121	—	2	1	no	—
397	#121	—	2	1	no	—
398	#121	D₄×C₁₉	1	2	yes	—
399	#121	D₄×C₁₉	1	2	yes	—
400	C₄×Q₈	—	2	1	no	—
401	C₄×Q₈	—	2	1	no	—
402	C₄×Q₈	D₄×C₁₉	1	2	yes	—
403	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
404	C₄×D₄	—	2	4	no	—
405	C₄×D₄	—	2	2	no	—
406	C₄×D₄	—	2	2	no	—
407	C₄×D₄	—	2	1	no	—
408	C₄×D₄	—	2	1	no	—
409	C₄×D₄	—	2	1	no	—
410	C₄×D₄	—	2	1	no	—
411	C₄×D₄	D₄×C₁₉	1	2	yes	—
412	C₄×D₄	C₂³×C₁₉	1	2	yes	—
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
415	C₂×C₄²	—	2	1	no	—
416	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
417	#107	—	2	2	no	—
418	#107	—	2	2	no	—
419	C₄⋊C₈	—	2	1	no	—
420	C₄⋊C₈	—	2	1	no	—
421	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
422	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
423	#103	—	2	2	no	—
424	#102	—	2	2	no	—
425	#102	—	2	2	no	—
426	#102	—	2	2	no	—
427	#102	—	2	2	no	—
428	#102	—	2	2	no	—
429	C₄×C₈	—	2	1	no	—
430	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
431	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
432	C₁₉	#18674	1	1	yes	characteristic, direct product factor, Sylow
433	#41	—	4	16	no	—
434	#41	—	4	8	no	—
435	#41	—	4	4	no	—
436	#41	—	4	4	no	—
437	#41	—	4	2	no	—
438	#41	—	4	2	no	—
439	#41	—	4	2	no	—
440	#41	—	4	2	no	—
441	#41	—	4	2	no	—
442	#41	—	4	2	no	—
443	C₂×Q₈	—	2	4	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	2	2	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	—	4	8	no	—
450	C₂×Q₈	—	4	4	no	—
451	C₂×Q₈	—	4	4	no	—
452	C₂×Q₈	D₈×C₁₉	1	4	yes	complemented
453	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
454	C₂×D₄	—	2	4	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	—	2	2	no	—
457	C₂×D₄	—	2	4	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	—	4	1	no	—
466	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
467	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	4	no	—
470	C₂²×C₄	—	2	4	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	4	1	no	—
475	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
476	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
478	Q₁₆	—	4	4	no	—
479	SD₁₆	—	4	4	no	—
480	D₈	—	4	4	no	—
481	D₈	—	8	2	no	—
482	M₁₆	—	4	2	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	2	no	—
486	C₂×C₈	—	2	2	no	—
487	C₂×C₈	—	4	2	no	—
488	C₂×C₈	—	8	1	no	—
489	C₄⋊C₄	—	2	4	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
498	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
499	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
500	C₂²⋊C₄	—	2	4	no	—
501	C₂²⋊C₄	—	2	4	no	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	2	2	no	—
506	C₂²⋊C₄	—	4	1	no	—
507	C₂²⋊C₄	—	4	1	no	—
508	C₄²	—	2	2	no	—
509	C₄²	—	2	2	no	—
510	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
511	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
512	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
513	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
514	C₂³	—	2	2	no	—
515	C₂³	—	2	2	no	—
516	C₂³	—	4	1	no	—
517	C₂³	C₁₉×#120	1	1	yes	characteristic
518	Q₈	—	2	4	no	—
519	Q₈	—	2	2	no	—
520	Q₈	—	4	8	no	—
521	Q₈	—	4	2	no	—
522	Q₈	—	4	1	no	—
523	Q₈	—	4	1	no	—
524	Q₈	—	4	1	no	—
525	Q₈	—	4	1	no	—
526	Q₈	C₂×D₈×C₁₉	1	4	yes	—
527	D₄	—	2	2	no	—
528	D₄	—	2	2	no	—
529	D₄	—	4	2	no	—
530	D₄	—	4	8	no	—
531	D₄	—	4	2	no	—
532	D₄	—	4	4	no	—
533	D₄	—	4	4	no	—
534	D₄	—	4	2	no	—
535	D₄	—	4	1	no	—
536	D₄	—	4	1	no	—
537	D₄	—	4	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	—	8	1	no	—
544	D₄	—	8	4	no	—
545	D₄	—	8	2	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	8	no	—
555	C₂×C₄	—	4	8	no	—
556	C₂×C₄	—	4	4	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	8	1	no	—
561	C₂×C₄	—	8	2	no	—
562	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
563	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
564	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
565	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
566	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
567	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
568	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
569	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
570	C₈	—	2	2	no	—
571	C₈	—	4	1	no	—
572	C₈	—	4	2	no	—
573	C₈	—	4	2	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	4	2	no	—
577	C₂²	—	4	2	no	—
578	C₂²	—	4	2	no	—
579	C₂²	—	4	2	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	8	1	no	—
583	C₂²	—	8	1	no	—
584	C₂²	—	8	1	no	—
585	C₂²	C₁₉×#447	1	2	yes	—
586	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
587	C₄	—	2	4	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	4	2	no	—
592	C₄	—	4	2	no	—
593	C₄	—	4	2	no	—
594	C₄	—	8	1	no	—
595	C₄	C₁₉×#447	1	2	yes	—
596	C₄	C₂²×D₈×C₁₉	1	1	yes	characteristic
597	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
598	C₄	C₁₉×#577	1	1	yes	characteristic
599	C₄	C₁₉×#578	1	1	yes	characteristic
600	C₂	—	2	2	no	—
601	C₂	—	8	2	no	—
602	C₂	—	8	2	no	—
603	C₂	—	16	1	no	—
604	C₂	C₂×C₁₉×#447	1	1	yes	characteristic
605	C₂	C₁₉×#3013	1	1	yes	characteristic
606	C₂	C₁₉×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
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
1. C₁₉×#3497	C₂	semidirect
2. C₁₉×#3245	C₂	semidirect
3. C₁₉×#3169	C₂	semidirect
4. C₁₉×#3037	C₂	semidirect
5. C₁₉×#1649	C₂	semidirect
6. C₁₉×#1641	C₂	semidirect
7. C₁₉×#1627	C₂	semidirect
8. C₁₉×#1621	C₂	semidirect
9. C₁₉×#1547	C₂	semidirect
10. C₁₉×#1492	C₂	semidirect
11. C₂×C₁₉×Q₈⋊C₈	C₂	semidirect
148. C₂×Q₈×C₁₉	D₈	semidirect
210. #18674	C₁₉	direct (N × H)
271. #3497	C₂×C₁₉	semidirect
272. #3245	C₂×C₁₉	semidirect
273. #3169	C₂×C₁₉	semidirect
274. #3037	C₂×C₁₉	semidirect
275. #1649	C₂×C₁₉	semidirect
276. #1641	C₂×C₁₉	semidirect
277. #1627	C₂×C₁₉	semidirect
278. #1621	C₂×C₁₉	semidirect
279. #1547	C₂×C₁₉	semidirect
280. #1492	C₂×C₁₉	semidirect
281. C₂×Q₈⋊C₈	C₂×C₁₉	semidirect
432. C₁₉	#18674	direct (N × H)
452. C₂×Q₈	D₈×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3497	2
C₁₉×#3245	2
C₁₉×#3169	2
C₁₉×#3037	2
C₁₉×#1649	2
C₁₉×#1641	2
C₁₉×#1627	2
C₁₉×#1621	2
C₁₉×#1547	2
C₁₉×#1492	2
C₂×C₁₉×Q₈⋊C₈	2
#18674	19

Subgroups — C19×#18674 #18024633

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18674 #18024633