Subgroups — C₁₉×#18582 #18024541

Order 4864.

1124 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3499	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3253	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3141	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3106	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1637	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1635	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1627	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1625	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1549	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1489	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1484	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×2₋¹⁺⁴	—	2	1	no	—
13	D₄×Q₈×C₁₉	—	2	1	no	—
14	D₄×Q₈×C₁₉	C₂²	1	2	yes	—
15	C₁₉×#547	—	2	2	no	—
16	C₁₉×#547	—	2	1	no	—
17	C₁₉×#547	—	2	2	no	—
18	C₁₉×#547	C₂²	1	2	yes	—
19	C₁₉×#536	—	2	2	no	—
20	C₁₉×#536	—	2	1	no	—
21	C₁₉×#532	—	2	1	no	—
22	C₁₉×#532	C₂²	1	1	yes	characteristic
23	C₁₉×#532	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
25	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#489	—	2	2	no	—
28	C₁₉×#487	C₂²	1	2	yes	—
29	C₁₉×#486	C₂²	1	2	yes	—
30	C₁₉×#482	—	2	1	no	—
31	C₁₉×#477	C₂²	1	1	yes	characteristic
32	C₁₉×#476	—	2	1	no	—
33	C₁₉×#476	C₂²	1	1	yes	characteristic
34	C₁₉×#476	C₂²	1	2	yes	—
35	C₁₉×#469	—	2	2	no	—
36	C₁₉×#460	C₂²	1	1	yes	characteristic
37	C₁₉×#459	—	2	1	no	—
38	C₁₉×#459	C₂²	1	2	yes	—
39	C₁₉×#459	C₂²	1	1	yes	characteristic
40	C₁₉×#449	—	2	1	no	—
41	C₄×SD₁₆×C₁₉	—	2	1	no	—
42	C₄×D₈×C₁₉	—	2	1	no	—
43	C₁₉×#431	C₂²	1	1	yes	characteristic
44	C₁₉×#423	C₂²	1	1	yes	characteristic
45	C₁₉×#417	—	2	2	no	—
46	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
47	C₁₉×#332	C₂²	1	2	yes	—
48	C₁₉×#332	C₂²	1	2	yes	—
49	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
50	C₁₉×D₄⋊C₈	C₂²	1	2	yes	—
51	C₁₉×D₄⋊C₈	C₂²	1	2	yes	—
52	C₁₉×D₄⋊C₈	C₂²	1	2	yes	—
53	C₁₉×2₋¹⁺⁴	—	4	4	no	—
54	C₁₉×2₋¹⁺⁴	—	4	4	no	—
55	C₂×#41×C₁₉	—	2	2	no	—
56	C₂×#41×C₁₉	—	2	4	no	—
57	C₂×#41×C₁₉	—	2	2	no	—
58	C₂×#41×C₁₉	—	2	1	no	—
59	C₂×#41×C₁₉	—	2	1	no	—
60	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
61	C₂²×Q₈×C₁₉	—	2	2	no	—
62	C₂²×Q₈×C₁₉	—	2	2	no	—
63	C₂²×Q₈×C₁₉	—	2	1	no	—
64	C₂×SD₁₆×C₁₉	—	2	1	no	—
65	C₂×D₈×C₁₉	—	2	1	no	—
66	C₂×D₈×C₁₉	—	2	2	no	—
67	C₂×M₁₆×C₁₉	—	2	1	no	—
68	C₂×M₁₆×C₁₉	—	2	1	no	—
69	C₁₉×C₄⋊Q₈	—	2	2	no	—
70	C₁₉×C₄⋊Q₈	—	2	2	no	—
71	C₁₉×C₄⋊Q₈	—	2	2	no	—
72	C₁₉×C₄⋊Q₈	—	2	1	no	—
73	C₁₉×C₄⋊Q₈	—	2	1	no	—
74	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
75	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
76	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
77	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
78	C₁₉×#127	D₄	1	1	yes	characteristic
79	C₁₉×#127	C₂³	1	1	yes	characteristic
80	C₁₉×#124	—	2	2	no	—
81	C₁₉×#124	—	2	1	no	—
82	C₁₉×#124	—	2	1	no	—
83	C₁₉×#123	—	2	4	no	—
84	C₁₉×#123	—	2	4	no	—
85	C₁₉×#123	—	2	4	no	—
86	C₁₉×C₂²⋊Q₈	—	2	4	no	—
87	C₁₉×C₂²⋊Q₈	—	2	2	no	—
88	C₁₉×C₂²⋊Q₈	—	2	4	no	—
89	C₁₉×C₂²⋊Q₈	—	2	2	no	—
90	C₁₉×#121	—	2	2	no	—
91	C₁₉×#121	—	2	2	no	—
92	C₁₉×#121	—	2	1	no	—
93	C₁₉×#121	—	2	1	no	—
94	C₁₉×#121	—	2	1	no	—
95	C₁₉×#121	D₄	1	2	yes	—
96	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
97	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
98	C₄×D₄×C₁₉	—	2	2	no	—
99	C₄×D₄×C₁₉	—	2	2	no	—
100	C₄×D₄×C₁₉	—	2	1	no	—
101	C₄×D₄×C₁₉	—	2	1	no	—
102	C₄×D₄×C₁₉	—	2	1	no	—
103	C₄×D₄×C₁₉	—	2	1	no	—
104	C₄×D₄×C₁₉	—	2	1	no	—
105	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
106	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
107	C₄×D₄×C₁₉	C₂³	1	2	yes	—
108	C₁₉×#117	—	2	1	no	—
109	C₁₉×#117	D₄	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
111	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
112	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
113	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
114	C₂×C₄²×C₁₉	—	2	1	no	—
115	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
116	C₁₉×#107	—	2	1	no	—
117	C₁₉×#106	—	2	1	no	—
118	C₁₉×#106	—	2	2	no	—
119	C₁₉×C₄⋊C₈	—	2	1	no	—
120	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
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	4	no	—
125	C₁₉×#102	—	2	1	no	—
126	C₁₉×#102	—	2	2	no	—
127	C₁₉×#102	—	2	4	no	—
128	C₁₉×#102	—	2	1	no	—
129	C₁₉×#102	—	2	1	no	—
130	C₁₉×#102	—	2	2	no	—
131	C₁₉×C₂²⋊C₈	—	2	1	no	—
132	C₁₉×#97	—	2	1	no	—
133	C₄×C₈×C₁₉	—	2	1	no	—
134	C₄×C₈×C₁₉	C₂³	1	2	yes	—
135	#41×C₁₉	—	2	2	no	—
136	#41×C₁₉	—	2	2	no	—
137	#41×C₁₉	—	4	8	no	—
138	#41×C₁₉	—	4	2	no	—
139	#41×C₁₉	—	4	2	no	—
140	#41×C₁₉	—	4	4	no	—
141	#41×C₁₉	—	4	16	no	—
142	#41×C₁₉	—	4	4	no	—
143	#41×C₁₉	—	4	4	no	—
144	C₂×Q₈×C₁₉	—	2	4	no	—
145	C₂×Q₈×C₁₉	—	2	2	no	—
146	C₂×Q₈×C₁₉	—	2	1	no	—
147	C₂×Q₈×C₁₉	—	2	2	no	—
148	C₂×Q₈×C₁₉	—	2	1	no	—
149	C₂×Q₈×C₁₉	—	4	8	no	—
150	C₂×Q₈×C₁₉	—	4	2	no	—
151	C₂×Q₈×C₁₉	—	4	2	no	—
152	C₂×Q₈×C₁₉	—	4	4	no	—
153	C₂×Q₈×C₁₉	—	4	4	no	—
154	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂×D₄×C₁₉	—	2	1	no	—
156	C₂×D₄×C₁₉	—	2	4	no	—
157	C₂×D₄×C₁₉	—	2	2	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	—	2	1	no	—
162	C₂×D₄×C₁₉	—	2	1	no	—
163	C₂×D₄×C₁₉	—	4	1	no	—
164	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
165	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₉	—	2	1	no	—
167	C₂²×C₄×C₁₉	—	2	4	no	—
168	C₂²×C₄×C₁₉	—	2	4	no	—
169	C₂²×C₄×C₁₉	—	2	2	no	—
170	C₂²×C₄×C₁₉	—	2	1	no	—
171	C₂²×C₄×C₁₉	—	2	1	no	—
172	C₂²×C₄×C₁₉	—	2	2	no	—
173	C₂²×C₄×C₁₉	—	4	1	no	—
174	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
177	SD₁₆×C₁₉	—	4	2	no	—
178	D₈×C₁₉	—	4	2	no	—
179	D₈×C₁₉	—	8	2	no	—
180	M₁₆×C₁₉	—	4	2	no	—
181	M₁₆×C₁₉	—	8	1	no	—
182	C₂×C₈×C₁₉	—	2	2	no	—
183	C₂×C₈×C₁₉	—	2	2	no	—
184	C₂×C₈×C₁₉	—	2	1	no	—
185	C₂×C₈×C₁₉	—	2	1	no	—
186	C₄⋊C₄×C₁₉	—	2	4	no	—
187	C₄⋊C₄×C₁₉	—	2	4	no	—
188	C₄⋊C₄×C₁₉	—	2	1	no	—
189	C₄⋊C₄×C₁₉	—	2	2	no	—
190	C₄⋊C₄×C₁₉	—	2	2	no	—
191	C₄⋊C₄×C₁₉	—	2	1	no	—
192	C₄⋊C₄×C₁₉	—	2	2	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	C₂×D₄	1	2	yes	—
197	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
198	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
199	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
200	C₂²⋊C₄×C₁₉	—	2	4	no	—
201	C₂²⋊C₄×C₁₉	—	2	4	no	—
202	C₂²⋊C₄×C₁₉	—	2	1	no	—
203	C₂²⋊C₄×C₁₉	—	2	1	no	—
204	C₂²⋊C₄×C₁₉	—	2	2	no	—
205	C₂²⋊C₄×C₁₉	—	2	1	no	—
206	C₂²⋊C₄×C₁₉	—	2	2	no	—
207	C₂²⋊C₄×C₁₉	—	4	1	no	—
208	C₂²⋊C₄×C₁₉	—	4	1	no	—
209	C₄²×C₁₉	—	2	1	no	—
210	C₄²×C₁₉	—	2	1	no	—
211	C₄²×C₁₉	—	2	1	no	—
212	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
213	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
214	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
215	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
216	#18582	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
217	C₂³×C₁₉	—	2	1	no	—
218	C₂³×C₁₉	—	2	2	no	—
219	C₂³×C₁₉	—	4	1	no	—
220	C₂³×C₁₉	#120	1	1	yes	characteristic
221	Q₈×C₁₉	—	2	1	no	—
222	Q₈×C₁₉	—	4	4	no	—
223	Q₈×C₁₉	—	4	2	no	—
224	Q₈×C₁₉	—	4	8	no	—
225	Q₈×C₁₉	—	4	2	no	—
226	Q₈×C₁₉	—	4	2	no	—
227	Q₈×C₁₉	—	4	2	no	—
228	Q₈×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
229	D₄×C₁₉	—	2	4	no	—
230	D₄×C₁₉	—	2	1	no	—
231	D₄×C₁₉	—	2	2	no	—
232	D₄×C₁₉	—	2	2	no	—
233	D₄×C₁₉	—	4	2	no	—
234	D₄×C₁₉	—	4	2	no	—
235	D₄×C₁₉	—	4	4	no	—
236	D₄×C₁₉	—	4	8	no	—
237	D₄×C₁₉	—	4	1	no	—
238	D₄×C₁₉	—	4	1	no	—
239	D₄×C₁₉	—	4	1	no	—
240	D₄×C₁₉	—	4	1	no	—
241	D₄×C₁₉	—	4	2	no	—
242	D₄×C₁₉	—	8	2	no	—
243	D₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
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	1	no	—
248	C₂×C₄×C₁₉	—	2	1	no	—
249	C₂×C₄×C₁₉	—	2	1	no	—
250	C₂×C₄×C₁₉	—	2	2	no	—
251	C₂×C₄×C₁₉	—	2	1	no	—
252	C₂×C₄×C₁₉	—	2	1	no	—
253	C₂×C₄×C₁₉	—	2	4	no	—
254	C₂×C₄×C₁₉	—	2	2	no	—
255	C₂×C₄×C₁₉	—	4	8	no	—
256	C₂×C₄×C₁₉	—	4	4	no	—
257	C₂×C₄×C₁₉	—	4	8	no	—
258	C₂×C₄×C₁₉	—	4	2	no	—
259	C₂×C₄×C₁₉	—	4	2	no	—
260	C₂×C₄×C₁₉	—	4	1	no	—
261	C₂×C₄×C₁₉	—	4	1	no	—
262	C₂×C₄×C₁₉	—	4	2	no	—
263	C₂×C₄×C₁₉	—	4	1	no	—
264	C₂×C₄×C₁₉	—	8	2	no	—
265	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
266	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
267	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
268	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
271	C₈×C₁₉	—	4	2	no	—
272	C₈×C₁₉	—	4	1	no	—
273	C₈×C₁₉	—	4	1	no	—
274	C₈×C₁₉	—	4	2	no	—
275	#3499	C₂×C₁₉	1	1	yes	characteristic, complemented
276	#3253	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#3141	C₂×C₁₉	1	1	yes	characteristic, complemented
278	#3106	C₂×C₁₉	1	1	yes	characteristic, complemented
279	#1637	C₂×C₁₉	1	2	yes	complemented
280	#1635	C₂×C₁₉	1	2	yes	complemented
281	#1627	C₂×C₁₉	1	2	yes	complemented
282	#1625	C₂×C₁₉	1	2	yes	complemented
283	#1549	C₂×C₁₉	1	1	yes	characteristic, complemented
284	#1489	C₂×C₁₉	1	1	yes	characteristic, complemented
285	#1484	C₂×C₁₉	1	1	yes	characteristic, complemented
286	C₂²×C₁₉	—	2	1	no	—
287	C₂²×C₁₉	—	2	2	no	—
288	C₂²×C₁₉	—	2	1	no	—
289	C₂²×C₁₉	—	2	1	no	—
290	C₂²×C₁₉	—	4	1	no	—
291	C₂²×C₁₉	—	4	1	no	—
292	C₂²×C₁₉	—	4	2	no	—
293	C₂²×C₁₉	—	4	2	no	—
294	C₂²×C₁₉	—	4	2	no	—
295	C₂²×C₁₉	—	8	1	no	—
296	C₂²×C₁₉	—	8	1	no	—
297	C₂²×C₁₉	—	8	1	no	—
298	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
299	C₄×C₁₉	—	2	1	no	—
300	C₄×C₁₉	—	2	2	no	—
301	C₄×C₁₉	—	2	1	no	—
302	C₄×C₁₉	—	2	1	no	—
303	C₄×C₁₉	—	4	4	no	—
304	C₄×C₁₉	—	4	2	no	—
305	C₄×C₁₉	—	4	1	no	—
306	C₄×C₁₉	—	4	1	no	—
307	C₄×C₁₉	—	8	1	no	—
308	C₄×C₁₉	#454	1	2	yes	—
309	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
310	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
311	C₄×C₁₉	#577	1	1	yes	characteristic
312	C₄×C₁₉	#578	1	1	yes	characteristic
313	C₂×2₋¹⁺⁴	—	2	1	no	—
314	D₄×Q₈	—	2	1	no	—
315	D₄×Q₈	C₂²×C₁₉	1	2	yes	—
316	#547	—	2	2	no	—
317	#547	—	2	1	no	—
318	#547	—	2	2	no	—
319	#547	C₂²×C₁₉	1	2	yes	—
320	#536	—	2	2	no	—
321	#536	—	2	1	no	—
322	#532	—	2	1	no	—
323	#532	C₂²×C₁₉	1	1	yes	characteristic
324	#532	C₂²×C₁₉	1	1	yes	characteristic
325	C₂×C₄⋊Q₈	—	2	1	no	—
326	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
327	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
328	#489	—	2	2	no	—
329	#487	C₂²×C₁₉	1	2	yes	—
330	#486	C₂²×C₁₉	1	2	yes	—
331	#482	—	2	1	no	—
332	#477	C₂²×C₁₉	1	1	yes	characteristic
333	#476	—	2	1	no	—
334	#476	C₂²×C₁₉	1	1	yes	characteristic
335	#476	C₂²×C₁₉	1	2	yes	—
336	#469	—	2	2	no	—
337	#460	C₂²×C₁₉	1	1	yes	characteristic
338	#459	—	2	1	no	—
339	#459	C₂²×C₁₉	1	1	yes	characteristic
340	#459	C₂²×C₁₉	1	2	yes	—
341	#449	—	2	1	no	—
342	C₄×SD₁₆	—	2	1	no	—
343	C₄×D₈	—	2	1	no	—
344	#431	C₂²×C₁₉	1	1	yes	characteristic
345	#423	C₂²×C₁₉	1	1	yes	characteristic
346	#417	—	2	2	no	—
347	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
348	#332	C₂²×C₁₉	1	2	yes	—
349	#332	C₂²×C₁₉	1	2	yes	—
350	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
351	D₄⋊C₈	C₂²×C₁₉	1	2	yes	—
352	D₄⋊C₈	C₂²×C₁₉	1	2	yes	—
353	D₄⋊C₈	C₂²×C₁₉	1	2	yes	—
354	C₂×C₁₉	—	4	1	no	—
355	C₂×C₁₉	—	4	2	no	—
356	C₂×C₁₉	—	8	2	no	—
357	C₂×C₁₉	—	16	1	no	—
358	C₂×C₁₉	#3003	1	1	yes	characteristic
359	C₂×C₁₉	#3013	1	1	yes	characteristic
360	C₂×C₁₉	C₂×#454	1	1	yes	characteristic
361	2₋¹⁺⁴	—	4	4	no	—
362	2₋¹⁺⁴	—	4	4	no	—
363	C₂×#41	—	2	2	no	—
364	C₂×#41	—	2	4	no	—
365	C₂×#41	—	2	2	no	—
366	C₂×#41	—	2	1	no	—
367	C₂×#41	—	2	1	no	—
368	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
369	C₂²×Q₈	—	2	2	no	—
370	C₂²×Q₈	—	2	2	no	—
371	C₂²×Q₈	—	2	1	no	—
372	C₂×SD₁₆	—	2	1	no	—
373	C₂×D₈	—	2	1	no	—
374	C₂×D₈	—	2	2	no	—
375	C₂×M₁₆	—	2	1	no	—
376	C₂×M₁₆	—	2	1	no	—
377	C₄⋊Q₈	—	2	2	no	—
378	C₄⋊Q₈	—	2	2	no	—
379	C₄⋊Q₈	—	2	2	no	—
380	C₄⋊Q₈	—	2	1	no	—
381	C₄⋊Q₈	—	2	1	no	—
382	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
383	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
384	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
385	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
386	#127	D₄×C₁₉	1	1	yes	characteristic
387	#127	C₂³×C₁₉	1	1	yes	characteristic
388	#124	—	2	2	no	—
389	#124	—	2	1	no	—
390	#124	—	2	1	no	—
391	#123	—	2	4	no	—
392	#123	—	2	4	no	—
393	#123	—	2	4	no	—
394	C₂²⋊Q₈	—	2	4	no	—
395	C₂²⋊Q₈	—	2	2	no	—
396	C₂²⋊Q₈	—	2	4	no	—
397	C₂²⋊Q₈	—	2	2	no	—
398	#121	—	2	2	no	—
399	#121	—	2	2	no	—
400	#121	—	2	1	no	—
401	#121	—	2	1	no	—
402	#121	—	2	1	no	—
403	#121	D₄×C₁₉	1	2	yes	—
404	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
405	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
406	C₄×D₄	—	2	2	no	—
407	C₄×D₄	—	2	2	no	—
408	C₄×D₄	—	2	1	no	—
409	C₄×D₄	—	2	1	no	—
410	C₄×D₄	—	2	1	no	—
411	C₄×D₄	—	2	1	no	—
412	C₄×D₄	—	2	1	no	—
413	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
414	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
415	C₄×D₄	C₂³×C₁₉	1	2	yes	—
416	#117	—	2	1	no	—
417	#117	D₄×C₁₉	1	1	yes	characteristic
418	C₂×C₄⋊C₄	—	2	2	no	—
419	C₂×C₄⋊C₄	—	2	1	no	—
420	C₂×C₄⋊C₄	—	2	2	no	—
421	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
422	C₂×C₄²	—	2	1	no	—
423	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
424	#107	—	2	1	no	—
425	#106	—	2	1	no	—
426	#106	—	2	2	no	—
427	C₄⋊C₈	—	2	1	no	—
428	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
429	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
430	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
431	#103	—	2	1	no	—
432	#103	—	2	4	no	—
433	#102	—	2	1	no	—
434	#102	—	2	2	no	—
435	#102	—	2	4	no	—
436	#102	—	2	1	no	—
437	#102	—	2	1	no	—
438	#102	—	2	2	no	—
439	C₂²⋊C₈	—	2	1	no	—
440	#97	—	2	1	no	—
441	C₄×C₈	—	2	1	no	—
442	C₄×C₈	C₂³×C₁₉	1	2	yes	—
443	C₁₉	#18582	1	1	yes	characteristic, direct product factor, Sylow
444	#41	—	2	2	no	—
445	#41	—	2	2	no	—
446	#41	—	4	8	no	—
447	#41	—	4	2	no	—
448	#41	—	4	2	no	—
449	#41	—	4	4	no	—
450	#41	—	4	16	no	—
451	#41	—	4	4	no	—
452	#41	—	4	4	no	—
453	C₂×Q₈	—	2	4	no	—
454	C₂×Q₈	—	2	2	no	—
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	—	2	2	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	4	8	no	—
459	C₂×Q₈	—	4	2	no	—
460	C₂×Q₈	—	4	2	no	—
461	C₂×Q₈	—	4	4	no	—
462	C₂×Q₈	—	4	4	no	—
463	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	2	4	no	—
466	C₂×D₄	—	2	2	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	—	4	1	no	—
473	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
474	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	4	no	—
477	C₂²×C₄	—	2	4	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	4	1	no	—
483	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
484	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
485	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
486	SD₁₆	—	4	2	no	—
487	D₈	—	4	2	no	—
488	D₈	—	8	2	no	—
489	M₁₆	—	4	2	no	—
490	M₁₆	—	8	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	2	no	—
494	C₂×C₈	—	2	2	no	—
495	C₄⋊C₄	—	2	4	no	—
496	C₄⋊C₄	—	2	4	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
506	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
507	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
508	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
509	C₂²⋊C₄	—	2	4	no	—
510	C₂²⋊C₄	—	2	4	no	—
511	C₂²⋊C₄	—	2	1	no	—
512	C₂²⋊C₄	—	2	1	no	—
513	C₂²⋊C₄	—	2	2	no	—
514	C₂²⋊C₄	—	2	1	no	—
515	C₂²⋊C₄	—	2	2	no	—
516	C₂²⋊C₄	—	4	1	no	—
517	C₂²⋊C₄	—	4	1	no	—
518	C₄²	—	2	1	no	—
519	C₄²	—	2	1	no	—
520	C₄²	—	2	1	no	—
521	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
522	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
523	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
524	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
525	C₂³	—	2	1	no	—
526	C₂³	—	2	2	no	—
527	C₂³	—	4	1	no	—
528	C₂³	C₁₉×#120	1	1	yes	characteristic
529	Q₈	—	2	1	no	—
530	Q₈	—	4	4	no	—
531	Q₈	—	4	2	no	—
532	Q₈	—	4	8	no	—
533	Q₈	—	4	2	no	—
534	Q₈	—	4	2	no	—
535	Q₈	—	4	2	no	—
536	Q₈	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
537	D₄	—	2	4	no	—
538	D₄	—	2	1	no	—
539	D₄	—	2	2	no	—
540	D₄	—	2	2	no	—
541	D₄	—	4	2	no	—
542	D₄	—	4	2	no	—
543	D₄	—	4	4	no	—
544	D₄	—	4	8	no	—
545	D₄	—	4	2	no	—
546	D₄	—	4	1	no	—
547	D₄	—	4	1	no	—
548	D₄	—	4	1	no	—
549	D₄	—	4	1	no	—
550	D₄	—	8	2	no	—
551	D₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	4	8	no	—
564	C₂×C₄	—	4	4	no	—
565	C₂×C₄	—	4	8	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	4	2	no	—
568	C₂×C₄	—	4	2	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	8	2	no	—
573	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
574	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
575	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
576	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
577	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
578	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
579	C₈	—	4	2	no	—
580	C₈	—	4	1	no	—
581	C₈	—	4	1	no	—
582	C₈	—	4	2	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	2	2	no	—
585	C₂²	—	2	1	no	—
586	C₂²	—	2	1	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	4	2	no	—
590	C₂²	—	4	2	no	—
591	C₂²	—	4	2	no	—
592	C₂²	—	8	1	no	—
593	C₂²	—	8	1	no	—
594	C₂²	—	8	1	no	—
595	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
596	C₄	—	2	1	no	—
597	C₄	—	2	2	no	—
598	C₄	—	2	1	no	—
599	C₄	—	2	1	no	—
600	C₄	—	4	4	no	—
601	C₄	—	4	2	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	1	no	—
604	C₄	—	8	1	no	—
605	C₄	C₁₉×#454	1	2	yes	—
606	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
607	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
608	C₄	C₁₉×#577	1	1	yes	characteristic
609	C₄	C₁₉×#578	1	1	yes	characteristic
610	C₂	—	4	1	no	—
611	C₂	—	4	2	no	—
612	C₂	—	8	2	no	—
613	C₂	—	16	1	no	—
614	C₂	C₁₉×#3003	1	1	yes	characteristic
615	C₂	C₁₉×#3013	1	1	yes	characteristic
616	C₂	C₂×C₁₉×#454	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×#3499	C₂	semidirect
2. C₁₉×#3253	C₂	semidirect
3. C₁₉×#3141	C₂	semidirect
4. C₁₉×#3106	C₂	semidirect
5. C₁₉×#1637	C₂	semidirect
6. C₁₉×#1635	C₂	semidirect
7. C₁₉×#1627	C₂	semidirect
8. C₁₉×#1625	C₂	semidirect
9. C₁₉×#1549	C₂	semidirect
10. C₁₉×#1489	C₂	semidirect
11. C₁₉×#1484	C₂	semidirect
216. #18582	C₁₉	direct (N × H)
275. #3499	C₂×C₁₉	semidirect
276. #3253	C₂×C₁₉	semidirect
277. #3141	C₂×C₁₉	semidirect
278. #3106	C₂×C₁₉	semidirect
279. #1637	C₂×C₁₉	semidirect
280. #1635	C₂×C₁₉	semidirect
281. #1627	C₂×C₁₉	semidirect
282. #1625	C₂×C₁₉	semidirect
283. #1549	C₂×C₁₉	semidirect
284. #1489	C₂×C₁₉	semidirect
285. #1484	C₂×C₁₉	semidirect
443. C₁₉	#18582	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×#3499	2
C₁₉×#3253	2
C₁₉×#3141	2
C₁₉×#3106	2
C₁₉×#1637	2
C₁₉×#1635	2
C₁₉×#1627	2
C₁₉×#1625	2
C₁₉×#1549	2
C₁₉×#1489	2
C₁₉×#1484	2
#18582	19

Subgroups — C19×#18582 #18024541

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18582 #18024541