Subgroups — C₁₉×#18624 #18024583

Order 4864.

1152 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3208	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#493	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3038	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1621	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1620	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1545	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1493	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1476	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
11	C₂²×D₈×C₁₉	—	2	2	no	—
12	C₁₉×#559	—	2	1	no	—
13	C₁₉×#559	C₂²	1	2	yes	complemented
14	C₁₉×#550	—	2	1	no	—
15	C₁₉×#550	C₂²	1	2	yes	complemented
16	C₁₉×#546	—	2	2	no	—
17	C₁₉×#546	—	2	2	no	—
18	C₁₉×#540	—	2	2	no	—
19	C₁₉×#535	—	2	1	no	—
20	C₁₉×#533	C₂²	1	1	yes	characteristic
21	C₁₉×#532	—	2	1	no	—
22	C₁₉×#532	—	2	1	no	—
23	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
25	C₁₉×#518	—	2	1	no	—
26	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#493	—	2	2	no	—
28	C₁₉×#493	C₂²	1	4	yes	—
29	C₁₉×#492	—	2	1	no	—
30	C₁₉×#486	—	2	1	no	—
31	C₁₉×#460	—	2	1	no	—
32	C₁₉×#460	C₂²	1	4	yes	complemented
33	C₁₉×#460	C₂²	1	2	yes	complemented
34	C₁₉×#459	—	2	1	no	—
35	C₁₉×#459	C₂²	1	2	yes	complemented
36	C₁₉×#450	—	2	2	no	—
37	C₁₉×#431	C₂²	1	1	yes	characteristic
38	C₁₉×#423	C₂²	1	1	yes	characteristic
39	C₁₉×#418	—	2	1	no	—
40	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
41	C₁₉×#331	C₂²	1	4	yes	complemented
42	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	complemented
43	C₁₉×Q₈⋊C₈	C₂²	1	4	yes	complemented
44	C₁₉×D₄⋊C₈	C₂²	1	2	yes	complemented
45	C₂×#41×C₁₉	—	2	2	no	—
46	C₂×#41×C₁₉	—	2	2	no	—
47	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
48	C₂²×D₄×C₁₉	—	2	1	no	—
49	C₂²×D₄×C₁₉	—	2	1	no	—
50	C₂²×D₄×C₁₉	—	2	1	no	—
51	C₂²×D₄×C₁₉	—	2	1	no	—
52	C₂²×D₄×C₁₉	—	2	1	no	—
53	C₂²×D₄×C₁₉	D₄	1	2	yes	—
54	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
55	C₂×SD₁₆×C₁₉	—	2	2	no	—
56	C₂×SD₁₆×C₁₉	—	2	4	no	—
57	C₂×D₈×C₁₉	—	2	2	no	—
58	C₂×D₈×C₁₉	—	2	8	no	—
59	C₂×D₈×C₁₉	—	4	8	no	—
60	C₂×M₁₆×C₁₉	—	2	1	no	—
61	C₂²×C₈×C₁₉	—	2	1	no	—
62	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
63	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
64	C₁₉×#127	—	2	2	no	—
65	C₁₉×#127	—	2	1	no	—
66	C₁₉×#127	—	2	1	no	—
67	C₁₉×#127	—	2	1	no	—
68	C₁₉×#127	—	2	1	no	—
69	C₁₉×#127	—	2	1	no	—
70	C₁₉×#127	D₄	1	2	yes	—
71	C₁₉×#127	C₂³	1	2	yes	—
72	C₁₉×#127	C₂³	1	2	yes	—
73	C₁₉×#125	—	2	1	no	—
74	C₁₉×#124	—	2	2	no	—
75	C₁₉×#124	—	2	2	no	—
76	C₁₉×#124	—	2	2	no	—
77	C₁₉×#123	—	2	4	no	—
78	C₁₉×#123	—	2	4	no	—
79	C₁₉×C₂²⋊Q₈	—	2	1	no	—
80	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
81	C₁₉×#121	—	2	2	no	—
82	C₁₉×#121	—	2	2	no	—
83	C₁₉×#121	—	2	2	no	—
84	C₁₉×#121	—	2	4	no	—
85	C₁₉×#121	—	2	4	no	—
86	C₁₉×#121	—	2	2	no	—
87	C₁₉×#120	—	2	4	no	—
88	C₄×Q₈×C₁₉	—	2	1	no	—
89	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
90	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
91	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
92	C₄×D₄×C₁₉	—	2	2	no	—
93	C₄×D₄×C₁₉	—	2	2	no	—
94	C₄×D₄×C₁₉	—	2	2	no	—
95	C₄×D₄×C₁₉	—	2	1	no	—
96	C₄×D₄×C₁₉	—	2	1	no	—
97	C₄×D₄×C₁₉	—	2	2	no	—
98	C₄×D₄×C₁₉	—	2	2	no	—
99	C₄×D₄×C₁₉	—	2	2	no	—
100	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
101	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
102	C₁₉×#117	—	2	1	no	—
103	C₁₉×#117	—	2	1	no	—
104	C₁₉×#117	D₄	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
106	C₂×C₄²×C₁₉	—	2	1	no	—
107	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
108	C₁₉×C₄⋊C₈	—	2	1	no	—
109	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
110	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
111	C₁₉×#102	—	2	2	no	—
112	C₁₉×#102	—	2	2	no	—
113	C₁₉×#102	—	2	4	no	—
114	C₁₉×C₂²⋊C₈	—	2	1	no	—
115	C₄×C₈×C₁₉	—	2	1	no	—
116	C₄×C₈×C₁₉	—	2	1	no	—
117	C₄×C₈×C₁₉	C₂³	1	2	yes	—
118	C₂⁴×C₁₉	—	2	2	no	—
119	C₂⁴×C₁₉	—	4	1	no	—
120	#41×C₁₉	—	2	2	no	—
121	#41×C₁₉	—	2	2	no	—
122	#41×C₁₉	—	8	4	no	—
123	#41×C₁₉	—	8	4	no	—
124	C₂×Q₈×C₁₉	—	2	1	no	—
125	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
127	C₂×D₄×C₁₉	—	2	1	no	—
128	C₂×D₄×C₁₉	—	2	4	no	—
129	C₂×D₄×C₁₉	—	2	4	no	—
130	C₂×D₄×C₁₉	—	2	2	no	—
131	C₂×D₄×C₁₉	—	2	2	no	—
132	C₂×D₄×C₁₉	—	2	2	no	—
133	C₂×D₄×C₁₉	—	2	2	no	—
134	C₂×D₄×C₁₉	—	2	2	no	—
135	C₂×D₄×C₁₉	—	2	2	no	—
136	C₂×D₄×C₁₉	—	2	2	no	—
137	C₂×D₄×C₁₉	—	2	2	no	—
138	C₂×D₄×C₁₉	—	4	4	no	—
139	C₂×D₄×C₁₉	—	4	4	no	—
140	C₂×D₄×C₁₉	—	4	1	no	—
141	C₂×D₄×C₁₉	—	4	1	no	—
142	C₂×D₄×C₁₉	—	4	1	no	—
143	C₂×D₄×C₁₉	—	4	2	no	—
144	C₂×D₄×C₁₉	—	4	2	no	—
145	C₂×D₄×C₁₉	—	4	2	no	—
146	C₂×D₄×C₁₉	—	4	2	no	—
147	C₂×D₄×C₁₉	—	8	2	no	—
148	C₂×D₄×C₁₉	—	8	2	no	—
149	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
151	C₂²×C₄×C₁₉	—	2	4	no	—
152	C₂²×C₄×C₁₉	—	2	4	no	—
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	C₂²×C₄×C₁₉	—	2	1	no	—
155	C₂²×C₄×C₁₉	—	2	1	no	—
156	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
159	SD₁₆×C₁₉	—	4	4	no	—
160	SD₁₆×C₁₉	—	8	4	no	—
161	D₈×C₁₉	—	4	16	no	—
162	D₈×C₁₉	—	4	4	no	—
163	M₁₆×C₁₉	—	4	2	no	—
164	C₂×C₈×C₁₉	—	2	4	no	—
165	C₂×C₈×C₁₉	—	2	2	no	—
166	C₂×C₈×C₁₉	—	2	2	no	—
167	C₂×C₈×C₁₉	—	2	2	no	—
168	C₄⋊C₄×C₁₉	—	2	1	no	—
169	C₄⋊C₄×C₁₉	—	2	1	no	—
170	C₄⋊C₄×C₁₉	—	2	1	no	—
171	C₄⋊C₄×C₁₉	—	2	1	no	—
172	C₄⋊C₄×C₁₉	—	2	2	no	—
173	C₄⋊C₄×C₁₉	—	2	1	no	—
174	C₄⋊C₄×C₁₉	—	2	2	no	—
175	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
176	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
177	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
178	C₂²⋊C₄×C₁₉	—	2	4	no	—
179	C₂²⋊C₄×C₁₉	—	2	4	no	—
180	C₂²⋊C₄×C₁₉	—	2	4	no	—
181	C₂²⋊C₄×C₁₉	—	2	4	no	—
182	C₂²⋊C₄×C₁₉	—	2	1	no	—
183	C₂²⋊C₄×C₁₉	—	2	2	no	—
184	C₂²⋊C₄×C₁₉	—	2	1	no	—
185	C₂²⋊C₄×C₁₉	—	2	1	no	—
186	C₄²×C₁₉	—	2	1	no	—
187	C₄²×C₁₉	—	2	1	no	—
188	C₄²×C₁₉	—	2	1	no	—
189	C₄²×C₁₉	—	2	2	no	—
190	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
192	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
193	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
194	#18624	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂³×C₁₉	—	2	4	no	—
196	C₂³×C₁₉	—	2	1	no	—
197	C₂³×C₁₉	—	4	4	no	—
198	C₂³×C₁₉	—	4	2	no	—
199	C₂³×C₁₉	—	8	2	no	—
200	C₂³×C₁₉	—	8	2	no	—
201	C₂³×C₁₉	—	8	2	no	—
202	C₂³×C₁₉	—	8	2	no	—
203	C₂³×C₁₉	—	8	2	no	—
204	C₂³×C₁₉	#120	1	1	yes	characteristic
205	Q₈×C₁₉	—	2	1	no	—
206	Q₈×C₁₉	—	2	1	no	—
207	Q₈×C₁₉	—	2	4	no	—
208	Q₈×C₁₉	—	4	2	no	—
209	D₄×C₁₉	—	2	1	no	—
210	D₄×C₁₉	—	2	1	no	—
211	D₄×C₁₉	—	4	4	no	—
212	D₄×C₁₉	—	4	4	no	—
213	D₄×C₁₉	—	4	2	no	—
214	D₄×C₁₉	—	4	2	no	—
215	D₄×C₁₉	—	4	2	no	—
216	D₄×C₁₉	—	4	2	no	—
217	D₄×C₁₉	—	4	2	no	—
218	D₄×C₁₉	—	4	4	no	—
219	D₄×C₁₉	—	4	4	no	—
220	D₄×C₁₉	—	4	4	no	—
221	D₄×C₁₉	—	4	4	no	—
222	D₄×C₁₉	—	8	2	no	—
223	D₄×C₁₉	—	8	2	no	—
224	D₄×C₁₉	—	8	4	no	—
225	D₄×C₁₉	—	8	4	no	—
226	D₄×C₁₉	—	8	2	no	—
227	D₄×C₁₉	—	8	2	no	—
228	C₂×C₄×C₁₉	—	2	2	no	—
229	C₂×C₄×C₁₉	—	2	2	no	—
230	C₂×C₄×C₁₉	—	2	1	no	—
231	C₂×C₄×C₁₉	—	2	1	no	—
232	C₂×C₄×C₁₉	—	2	1	no	—
233	C₂×C₄×C₁₉	—	2	2	no	—
234	C₂×C₄×C₁₉	—	2	2	no	—
235	C₂×C₄×C₁₉	—	4	2	no	—
236	C₂×C₄×C₁₉	—	4	2	no	—
237	C₂×C₄×C₁₉	—	4	2	no	—
238	C₂×C₄×C₁₉	—	8	4	no	—
239	C₂×C₄×C₁₉	—	8	4	no	—
240	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
241	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
242	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
243	C₂×C₄×C₁₉	#135	1	2	yes	—
244	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
245	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
248	C₈×C₁₉	—	2	4	no	—
249	C₈×C₁₉	—	4	2	no	—
250	C₈×C₁₉	—	4	2	no	—
251	#3508	C₂×C₁₉	1	1	yes	characteristic, complemented
252	#3208	C₂×C₁₉	1	1	yes	characteristic, complemented
253	C₂×#493	C₂×C₁₉	1	1	yes	characteristic, complemented
254	#3038	C₂×C₁₉	1	1	yes	characteristic, complemented
255	#1621	C₂×C₁₉	1	4	yes	complemented
256	#1620	C₂×C₁₉	1	4	yes	complemented
257	#1545	C₂×C₁₉	1	1	yes	characteristic, complemented
258	#1493	C₂×C₁₉	1	1	yes	characteristic, complemented
259	#1476	C₂×C₁₉	1	1	yes	characteristic, complemented
260	C₂²×C₁₉	—	2	1	no	—
261	C₂²×C₁₉	—	2	1	no	—
262	C₂²×C₁₉	—	4	1	no	—
263	C₂²×C₁₉	—	4	4	no	—
264	C₂²×C₁₉	—	4	1	no	—
265	C₂²×C₁₉	—	4	4	no	—
266	C₂²×C₁₉	—	4	1	no	—
267	C₂²×C₁₉	—	4	4	no	—
268	C₂²×C₁₉	—	8	2	no	—
269	C₂²×C₁₉	—	8	2	no	—
270	C₂²×C₁₉	—	8	2	no	—
271	C₂²×C₁₉	—	16	4	no	—
272	C₂²×C₁₉	—	16	4	no	—
273	C₂²×C₁₉	#449	1	2	yes	—
274	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
275	C₄×C₁₉	—	2	1	no	—
276	C₄×C₁₉	—	2	1	no	—
277	C₄×C₁₉	—	4	1	no	—
278	C₄×C₁₉	—	4	1	no	—
279	C₄×C₁₉	—	4	2	no	—
280	C₄×C₁₉	—	4	1	no	—
281	C₄×C₁₉	—	4	2	no	—
282	C₄×C₁₉	#449	1	2	yes	—
283	C₄×C₁₉	#453	1	2	yes	—
284	C₄×C₁₉	C₂×#135	1	1	yes	characteristic
285	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
286	C₄×C₁₉	#576	1	2	yes	—
287	C₂×AGL(1,ℤ/8)	—	2	1	no	—
288	C₂²×D₈	—	2	2	no	—
289	#559	—	2	1	no	—
290	#559	C₂²×C₁₉	1	2	yes	complemented
291	#550	—	2	1	no	—
292	#550	C₂²×C₁₉	1	2	yes	complemented
293	#546	—	2	2	no	—
294	#546	—	2	2	no	—
295	#540	—	2	2	no	—
296	#535	—	2	1	no	—
297	#533	C₂²×C₁₉	1	1	yes	characteristic
298	#532	—	2	1	no	—
299	#532	—	2	1	no	—
300	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
301	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
302	#518	—	2	1	no	—
303	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
304	#493	—	2	2	no	—
305	#493	C₂²×C₁₉	1	4	yes	—
306	#492	—	2	1	no	—
307	#486	—	2	1	no	—
308	#460	—	2	1	no	—
309	#460	C₂²×C₁₉	1	2	yes	complemented
310	#460	C₂²×C₁₉	1	4	yes	complemented
311	#459	—	2	1	no	—
312	#459	C₂²×C₁₉	1	2	yes	complemented
313	#450	—	2	2	no	—
314	#431	C₂²×C₁₉	1	1	yes	characteristic
315	#423	C₂²×C₁₉	1	1	yes	characteristic
316	#418	—	2	1	no	—
317	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
318	#331	C₂²×C₁₉	1	4	yes	complemented
319	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	complemented
320	Q₈⋊C₈	C₂²×C₁₉	1	4	yes	complemented
321	D₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
322	C₂×C₁₉	—	2	2	no	—
323	C₂×C₁₉	—	8	1	no	—
324	C₂×C₁₉	—	8	4	no	—
325	C₂×C₁₉	—	16	2	no	—
326	C₂×C₁₉	C₂×#449	1	1	yes	characteristic
327	C₂×C₁₉	#3008	1	1	yes	characteristic
328	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
329	C₂×#41	—	2	2	no	—
330	C₂×#41	—	2	2	no	—
331	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
332	C₂²×D₄	—	2	1	no	—
333	C₂²×D₄	—	2	1	no	—
334	C₂²×D₄	—	2	1	no	—
335	C₂²×D₄	—	2	1	no	—
336	C₂²×D₄	—	2	1	no	—
337	C₂²×D₄	D₄×C₁₉	1	2	yes	—
338	AGL(1,ℤ/8)	—	4	4	no	—
339	C₂×SD₁₆	—	2	2	no	—
340	C₂×SD₁₆	—	2	4	no	—
341	C₂×D₈	—	2	8	no	—
342	C₂×D₈	—	2	2	no	—
343	C₂×D₈	—	4	8	no	—
344	C₂×M₁₆	—	2	1	no	—
345	C₂²×C₈	—	2	1	no	—
346	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
347	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
348	#127	—	2	2	no	—
349	#127	—	2	1	no	—
350	#127	—	2	1	no	—
351	#127	—	2	1	no	—
352	#127	—	2	1	no	—
353	#127	—	2	1	no	—
354	#127	D₄×C₁₉	1	2	yes	—
355	#127	C₂³×C₁₉	1	2	yes	—
356	#127	C₂³×C₁₉	1	2	yes	—
357	#125	—	2	1	no	—
358	#124	—	2	2	no	—
359	#124	—	2	2	no	—
360	#124	—	2	2	no	—
361	#123	—	2	4	no	—
362	#123	—	2	4	no	—
363	C₂²⋊Q₈	—	2	1	no	—
364	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
365	#121	—	2	2	no	—
366	#121	—	2	2	no	—
367	#121	—	2	2	no	—
368	#121	—	2	4	no	—
369	#121	—	2	4	no	—
370	#121	—	2	2	no	—
371	#120	—	2	4	no	—
372	C₄×Q₈	—	2	1	no	—
373	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
374	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
375	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
376	C₄×D₄	—	2	2	no	—
377	C₄×D₄	—	2	2	no	—
378	C₄×D₄	—	2	2	no	—
379	C₄×D₄	—	2	1	no	—
380	C₄×D₄	—	2	1	no	—
381	C₄×D₄	—	2	2	no	—
382	C₄×D₄	—	2	2	no	—
383	C₄×D₄	—	2	2	no	—
384	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
385	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
386	#117	—	2	1	no	—
387	#117	—	2	1	no	—
388	#117	D₄×C₁₉	1	1	yes	characteristic
389	C₂×C₂²⋊C₄	—	2	4	no	—
390	C₂×C₄²	—	2	1	no	—
391	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
392	C₄⋊C₈	—	2	1	no	—
393	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
394	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
395	#102	—	2	2	no	—
396	#102	—	2	2	no	—
397	#102	—	2	4	no	—
398	C₂²⋊C₈	—	2	1	no	—
399	C₄×C₈	—	2	1	no	—
400	C₄×C₈	—	2	1	no	—
401	C₄×C₈	C₂³×C₁₉	1	2	yes	—
402	C₁₉	#18624	1	1	yes	characteristic, direct product factor, Sylow
403	C₂⁴	—	2	2	no	—
404	C₂⁴	—	4	1	no	—
405	#41	—	2	2	no	—
406	#41	—	2	2	no	—
407	#41	—	8	4	no	—
408	#41	—	8	4	no	—
409	C₂×Q₈	—	2	1	no	—
410	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
411	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
412	C₂×D₄	—	2	1	no	—
413	C₂×D₄	—	2	4	no	—
414	C₂×D₄	—	2	4	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	2	no	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	4	4	no	—
424	C₂×D₄	—	4	4	no	—
425	C₂×D₄	—	4	1	no	—
426	C₂×D₄	—	4	1	no	—
427	C₂×D₄	—	4	1	no	—
428	C₂×D₄	—	4	2	no	—
429	C₂×D₄	—	4	2	no	—
430	C₂×D₄	—	4	2	no	—
431	C₂×D₄	—	4	2	no	—
432	C₂×D₄	—	8	2	no	—
433	C₂×D₄	—	8	2	no	—
434	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
435	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	4	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
442	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
443	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
444	SD₁₆	—	4	4	no	—
445	SD₁₆	—	8	4	no	—
446	D₈	—	4	16	no	—
447	D₈	—	4	4	no	—
448	M₁₆	—	4	2	no	—
449	C₂×C₈	—	2	4	no	—
450	C₂×C₈	—	2	2	no	—
451	C₂×C₈	—	2	2	no	—
452	C₂×C₈	—	2	2	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	2	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
461	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
462	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
463	C₂²⋊C₄	—	2	4	no	—
464	C₂²⋊C₄	—	2	4	no	—
465	C₂²⋊C₄	—	2	4	no	—
466	C₂²⋊C₄	—	2	4	no	—
467	C₂²⋊C₄	—	2	1	no	—
468	C₂²⋊C₄	—	2	2	no	—
469	C₂²⋊C₄	—	2	1	no	—
470	C₂²⋊C₄	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	2	1	no	—
473	C₄²	—	2	1	no	—
474	C₄²	—	2	2	no	—
475	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
476	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
477	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
478	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
479	C₂³	—	2	4	no	—
480	C₂³	—	2	1	no	—
481	C₂³	—	4	4	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	8	2	no	—
484	C₂³	—	8	2	no	—
485	C₂³	—	8	2	no	—
486	C₂³	—	8	2	no	—
487	C₂³	—	8	2	no	—
488	C₂³	C₁₉×#120	1	1	yes	characteristic
489	Q₈	—	2	1	no	—
490	Q₈	—	2	1	no	—
491	Q₈	—	2	4	no	—
492	Q₈	—	4	2	no	—
493	D₄	—	2	1	no	—
494	D₄	—	2	1	no	—
495	D₄	—	4	4	no	—
496	D₄	—	4	4	no	—
497	D₄	—	4	2	no	—
498	D₄	—	4	4	no	—
499	D₄	—	4	4	no	—
500	D₄	—	4	2	no	—
501	D₄	—	4	2	no	—
502	D₄	—	4	2	no	—
503	D₄	—	4	2	no	—
504	D₄	—	4	4	no	—
505	D₄	—	4	4	no	—
506	D₄	—	8	2	no	—
507	D₄	—	8	2	no	—
508	D₄	—	8	4	no	—
509	D₄	—	8	4	no	—
510	D₄	—	8	2	no	—
511	D₄	—	8	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	8	4	no	—
523	C₂×C₄	—	8	4	no	—
524	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
525	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
526	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
527	C₂×C₄	C₁₉×#135	1	2	yes	—
528	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
529	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
530	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
531	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
532	C₈	—	2	4	no	—
533	C₈	—	4	2	no	—
534	C₈	—	4	2	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	4	1	no	—
538	C₂²	—	4	4	no	—
539	C₂²	—	4	1	no	—
540	C₂²	—	4	4	no	—
541	C₂²	—	4	1	no	—
542	C₂²	—	4	4	no	—
543	C₂²	—	8	2	no	—
544	C₂²	—	8	2	no	—
545	C₂²	—	8	2	no	—
546	C₂²	—	16	4	no	—
547	C₂²	—	16	4	no	—
548	C₂²	C₁₉×#449	1	2	yes	—
549	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	1	no	—
554	C₄	—	4	2	no	—
555	C₄	—	4	1	no	—
556	C₄	—	4	2	no	—
557	C₄	C₁₉×#449	1	2	yes	—
558	C₄	C₁₉×#453	1	2	yes	—
559	C₄	C₂×C₁₉×#135	1	1	yes	characteristic
560	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
561	C₄	C₁₉×#576	1	2	yes	—
562	C₂	—	2	2	no	—
563	C₂	—	8	4	no	—
564	C₂	—	8	1	no	—
565	C₂	—	16	2	no	—
566	C₂	C₂×C₁₉×#449	1	1	yes	characteristic
567	C₂	C₁₉×#3008	1	1	yes	characteristic
568	C₂	C₂×C₁₉×#453	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×#3508	C₂	semidirect
2. C₁₉×#3208	C₂	semidirect
3. C₂×C₁₉×#493	C₂	semidirect
4. C₁₉×#3038	C₂	semidirect
5. C₁₉×#1621	C₂	semidirect
6. C₁₉×#1620	C₂	semidirect
7. C₁₉×#1545	C₂	semidirect
8. C₁₉×#1493	C₂	semidirect
9. C₁₉×#1476	C₂	semidirect
13. C₁₉×#559	C₂²	semidirect
15. C₁₉×#550	C₂²	semidirect
32. C₁₉×#460	C₂²	semidirect
33. C₁₉×#460	C₂²	semidirect
35. C₁₉×#459	C₂²	semidirect
41. C₁₉×#331	C₂²	semidirect
42. C₁₉×Q₈⋊C₈	C₂²	semidirect
43. C₁₉×Q₈⋊C₈	C₂²	semidirect
44. C₁₉×D₄⋊C₈	C₂²	semidirect
194. #18624	C₁₉	direct (N × H)
251. #3508	C₂×C₁₉	semidirect
252. #3208	C₂×C₁₉	semidirect
253. C₂×#493	C₂×C₁₉	semidirect
254. #3038	C₂×C₁₉	semidirect
255. #1621	C₂×C₁₉	semidirect
256. #1620	C₂×C₁₉	semidirect
257. #1545	C₂×C₁₉	semidirect
258. #1493	C₂×C₁₉	semidirect
259. #1476	C₂×C₁₉	semidirect
290. #559	C₂²×C₁₉	semidirect
292. #550	C₂²×C₁₉	semidirect
309. #460	C₂²×C₁₉	semidirect
310. #460	C₂²×C₁₉	semidirect
312. #459	C₂²×C₁₉	semidirect
318. #331	C₂²×C₁₉	semidirect
319. Q₈⋊C₈	C₂²×C₁₉	semidirect
320. Q₈⋊C₈	C₂²×C₁₉	semidirect
321. D₄⋊C₈	C₂²×C₁₉	semidirect
402. C₁₉	#18624	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×#3508	2
C₁₉×#3208	2
C₂×C₁₉×#493	2
C₁₉×#3038	2
C₁₉×#1621	2
C₁₉×#1620	2
C₁₉×#1545	2
C₁₉×#1493	2
C₁₉×#1476	2
#18624	19

Subgroups — C19×#18624 #18024583

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18624 #18024583