Subgroups — C₁₉×#19049 #18025008

Order 4864.

886 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3561	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3215	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3181	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3162	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1664	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1661	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1661	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1660	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1532	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1531	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₉×#329	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#563	C₂²	1	2	yes	—
13	C₁₉×#562	C₂²	1	2	yes	—
14	C₁₉×#556	—	2	1	no	—
15	C₁₉×#551	—	2	2	no	—
16	D₄×Q₈×C₁₉	—	2	1	no	—
17	C₁₉×#548	—	2	1	no	—
18	C₁₉×#546	—	2	1	no	—
19	C₁₉×#543	—	2	1	no	—
20	C₁₉×#542	—	2	1	no	—
21	C₁₉×#542	—	2	2	no	—
22	C₁₉×#538	—	2	1	no	—
23	C₁₉×#536	—	2	1	no	—
24	C₁₉×#533	C₂²	1	1	yes	characteristic
25	C₁₉×#533	C₂²	1	1	yes	characteristic
26	C₁₉×#529	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
28	C₁₉×#501	—	2	1	no	—
29	C₁₉×#501	—	2	1	no	—
30	C₁₉×#501	C₂²	1	1	yes	characteristic, complemented
31	C₁₉×#501	C₂²	1	2	yes	complemented
32	C₁₉×#501	C₂²	1	2	yes	complemented
33	C₁₉×#497	C₂²	1	2	yes	—
34	C₁₉×#497	C₂²	1	1	yes	characteristic, complemented
35	C₁₉×#491	C₂²	1	1	yes	characteristic, complemented
36	C₁₉×#489	C₂²	1	2	yes	—
37	C₁₉×#489	C₂²	1	1	yes	characteristic, complemented
38	C₁₉×#467	—	2	1	no	—
39	C₁₉×#465	—	2	1	no	—
40	C₁₉×#464	—	2	2	no	—
41	C₁₉×#451	—	2	1	no	—
42	C₁₉×#450	—	2	1	no	—
43	C₁₉×#441	—	2	1	no	—
44	C₁₉×#440	—	2	1	no	—
45	C₁₉×#432	C₂²	1	1	yes	characteristic
46	C₁₉×#427	—	2	2	no	—
47	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
48	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
49	C₁₉×#330	C₂²	1	2	yes	complemented
50	C₁₉×#330	C₂²	1	2	yes	complemented
51	C₁₉×#330	C₂²	1	2	yes	complemented
52	C₁₉×#329	C₂²	1	2	yes	—
53	C₁₉×#329	C₂²	1	2	yes	—
54	C₁₉×#329	C₂²	1	2	yes	complemented
55	C₂×#41×C₁₉	—	2	1	no	—
56	C₂²×Q₈×C₁₉	—	2	1	no	—
57	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
58	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
59	C₂×Q₁₆×C₁₉	—	2	1	no	—
60	C₂×Q₁₆×C₁₉	—	2	2	no	—
61	C₂×SD₁₆×C₁₉	—	2	1	no	—
62	C₂×SD₁₆×C₁₉	—	2	2	no	—
63	C₂²×C₈×C₁₉	—	2	1	no	—
64	C₂²×C₈×C₁₉	—	2	1	no	—
65	C₁₉×C₄⋊Q₈	—	2	1	no	—
66	C₁₉×C₄⋊Q₈	—	2	2	no	—
67	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
68	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
69	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
70	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
71	C₁₉×#126	—	2	2	no	—
72	C₁₉×#126	—	2	2	no	—
73	C₁₉×#126	—	2	2	no	—
74	C₁₉×#126	—	2	1	no	—
75	C₁₉×#125	—	2	1	no	—
76	C₁₉×#125	C₂³	1	1	yes	characteristic
77	C₁₉×#125	C₂³	1	2	yes	—
78	C₁₉×#124	—	2	1	no	—
79	C₁₉×#124	—	2	2	no	—
80	C₁₉×#124	—	2	2	no	—
81	C₁₉×#124	—	2	1	no	—
82	C₁₉×#124	—	2	1	no	—
83	C₁₉×#124	D₄	1	2	yes	—
84	C₁₉×#124	C₂³	1	2	yes	—
85	C₁₉×#124	C₂³	1	1	yes	characteristic
86	C₁₉×#123	—	2	2	no	—
87	C₁₉×#123	—	2	2	no	—
88	C₁₉×#123	—	2	1	no	—
89	C₁₉×#123	—	2	2	no	—
90	C₁₉×#123	—	2	2	no	—
91	C₁₉×C₂²⋊Q₈	—	2	2	no	—
92	C₁₉×C₂²⋊Q₈	—	2	2	no	—
93	C₁₉×C₂²⋊Q₈	—	2	1	no	—
94	C₁₉×C₂²⋊Q₈	—	2	2	no	—
95	C₁₉×C₂²⋊Q₈	—	2	2	no	—
96	C₁₉×C₂²⋊Q₈	—	2	2	no	—
97	C₁₉×C₂²⋊Q₈	—	2	1	no	—
98	C₁₉×C₂²⋊Q₈	—	2	1	no	—
99	C₁₉×C₂²⋊Q₈	—	2	2	no	—
100	C₁₉×C₂²⋊Q₈	—	2	2	no	—
101	C₁₉×C₂²⋊Q₈	—	2	1	no	—
102	C₁₉×C₂²⋊Q₈	—	2	1	no	—
103	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
104	C₁₉×#121	—	2	1	no	—
105	C₁₉×#121	—	2	2	no	—
106	C₁₉×#121	—	2	2	no	—
107	C₁₉×#121	D₄	1	1	yes	characteristic
108	C₁₉×#120	—	2	2	no	—
109	C₄×Q₈×C₁₉	—	2	1	no	—
110	C₄×Q₈×C₁₉	—	2	1	no	—
111	C₄×Q₈×C₁₉	—	2	1	no	—
112	C₄×Q₈×C₁₉	—	2	1	no	—
113	C₄×Q₈×C₁₉	—	2	1	no	—
114	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
115	C₄×D₄×C₁₉	—	2	2	no	—
116	C₄×D₄×C₁₉	—	2	1	no	—
117	C₄×D₄×C₁₉	—	2	2	no	—
118	C₄×D₄×C₁₉	—	2	1	no	—
119	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
120	C₁₉×#117	—	2	2	no	—
121	C₁₉×#117	—	2	1	no	—
122	C₁₉×#117	—	2	1	no	—
123	C₁₉×#117	D₄	1	2	yes	—
124	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
125	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
127	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
128	C₁₉×#107	—	2	2	no	—
129	C₁₉×#107	—	2	2	no	—
130	C₁₉×#107	—	2	1	no	—
131	C₁₉×#106	—	2	2	no	—
132	C₁₉×#106	—	2	2	no	—
133	C₁₉×#106	—	2	1	no	—
134	C₁₉×C₄⋊C₈	—	2	1	no	—
135	C₁₉×#103	—	2	1	no	—
136	C₁₉×#103	—	2	2	no	—
137	C₁₉×#103	—	2	1	no	—
138	C₁₉×#103	—	2	1	no	—
139	C₁₉×#102	—	2	1	no	—
140	C₁₉×#102	—	2	2	no	—
141	C₁₉×C₂²⋊C₈	—	2	1	no	—
142	C₁₉×#97	—	2	1	no	—
143	C₁₉×#97	—	2	1	no	—
144	C₁₉×#97	C₂³	1	1	yes	characteristic
145	C₁₉×#97	C₂³	1	1	yes	characteristic
146	C₁₉×#97	C₂³	1	2	yes	—
147	C₁₉×#97	C₂³	1	2	yes	—
148	C₂⁴×C₁₉	—	2	1	no	—
149	#41×C₁₉	—	8	2	no	—
150	C₂×Q₈×C₁₉	—	2	2	no	—
151	C₂×Q₈×C₁₉	—	2	1	no	—
152	C₂×Q₈×C₁₉	—	2	1	no	—
153	C₂×Q₈×C₁₉	—	2	1	no	—
154	C₂×Q₈×C₁₉	—	2	1	no	—
155	C₂×Q₈×C₁₉	—	2	1	no	—
156	C₂×Q₈×C₁₉	—	8	2	no	—
157	C₂×Q₈×C₁₉	—	8	1	no	—
158	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
159	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
160	C₂×D₄×C₁₉	—	2	1	no	—
161	C₂×D₄×C₁₉	—	2	2	no	—
162	C₂×D₄×C₁₉	—	2	2	no	—
163	C₂×D₄×C₁₉	—	2	1	no	—
164	C₂×D₄×C₁₉	—	8	1	no	—
165	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
167	C₂²×C₄×C₁₉	—	2	2	no	—
168	C₂²×C₄×C₁₉	—	2	2	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	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
175	Q₁₆×C₁₉	—	4	2	no	—
176	Q₁₆×C₁₉	—	8	2	no	—
177	SD₁₆×C₁₉	—	4	2	no	—
178	SD₁₆×C₁₉	—	8	2	no	—
179	C₂×C₈×C₁₉	—	2	4	no	—
180	C₂×C₈×C₁₉	—	2	1	no	—
181	C₂×C₈×C₁₉	—	2	2	no	—
182	C₂×C₈×C₁₉	—	2	1	no	—
183	C₂×C₈×C₁₉	—	2	2	no	—
184	C₂×C₈×C₁₉	—	4	2	no	—
185	C₄⋊C₄×C₁₉	—	2	2	no	—
186	C₄⋊C₄×C₁₉	—	2	2	no	—
187	C₄⋊C₄×C₁₉	—	2	2	no	—
188	C₄⋊C₄×C₁₉	—	2	2	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	2	no	—
196	C₄⋊C₄×C₁₉	—	2	2	no	—
197	C₄⋊C₄×C₁₉	—	2	1	no	—
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	—	4	1	no	—
202	C₄⋊C₄×C₁₉	—	4	1	no	—
203	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
204	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
205	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
206	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
207	C₂²⋊C₄×C₁₉	—	2	2	no	—
208	C₂²⋊C₄×C₁₉	—	2	2	no	—
209	C₂²⋊C₄×C₁₉	—	2	2	no	—
210	C₂²⋊C₄×C₁₉	—	2	2	no	—
211	C₂²⋊C₄×C₁₉	—	2	2	no	—
212	C₂²⋊C₄×C₁₉	—	2	1	no	—
213	C₂²⋊C₄×C₁₉	—	2	2	no	—
214	C₂²⋊C₄×C₁₉	—	2	2	no	—
215	C₂²⋊C₄×C₁₉	—	2	2	no	—
216	C₂²⋊C₄×C₁₉	—	2	1	no	—
217	C₂²⋊C₄×C₁₉	—	2	1	no	—
218	C₂²⋊C₄×C₁₉	—	2	2	no	—
219	C₂²⋊C₄×C₁₉	—	2	2	no	—
220	C₂²⋊C₄×C₁₉	—	2	1	no	—
221	C₂²⋊C₄×C₁₉	—	2	1	no	—
222	C₂²⋊C₄×C₁₉	—	4	1	no	—
223	C₄²×C₁₉	—	2	2	no	—
224	C₄²×C₁₉	—	2	2	no	—
225	C₄²×C₁₉	—	2	1	no	—
226	C₄²×C₁₉	—	4	1	no	—
227	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
228	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
229	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
230	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
231	#19049	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂³×C₁₉	—	2	2	no	—
233	C₂³×C₁₉	—	2	1	no	—
234	C₂³×C₁₉	—	4	2	no	—
235	C₂³×C₁₉	—	8	1	no	—
236	C₂³×C₁₉	—	8	1	no	—
237	C₂³×C₁₉	#120	1	1	yes	characteristic
238	Q₈×C₁₉	—	4	1	no	—
239	Q₈×C₁₉	—	4	2	no	—
240	Q₈×C₁₉	—	4	2	no	—
241	Q₈×C₁₉	—	4	2	no	—
242	Q₈×C₁₉	—	4	1	no	—
243	Q₈×C₁₉	—	4	2	no	—
244	Q₈×C₁₉	—	4	1	no	—
245	Q₈×C₁₉	—	8	1	no	—
246	Q₈×C₁₉	—	8	2	no	—
247	D₄×C₁₉	—	4	1	no	—
248	D₄×C₁₉	—	4	2	no	—
249	D₄×C₁₉	—	4	2	no	—
250	D₄×C₁₉	—	4	2	no	—
251	D₄×C₁₉	—	8	2	no	—
252	D₄×C₁₉	—	8	2	no	—
253	C₂×C₄×C₁₉	—	2	2	no	—
254	C₂×C₄×C₁₉	—	2	1	no	—
255	C₂×C₄×C₁₉	—	2	2	no	—
256	C₂×C₄×C₁₉	—	2	1	no	—
257	C₂×C₄×C₁₉	—	2	2	no	—
258	C₂×C₄×C₁₉	—	2	2	no	—
259	C₂×C₄×C₁₉	—	2	1	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	—	4	1	no	—
265	C₂×C₄×C₁₉	—	8	1	no	—
266	C₂×C₄×C₁₉	—	8	2	no	—
267	C₂×C₄×C₁₉	—	8	2	no	—
268	C₂×C₄×C₁₉	—	8	2	no	—
269	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
270	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
271	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
272	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
275	C₈×C₁₉	—	2	4	no	—
276	C₈×C₁₉	—	2	2	no	—
277	C₈×C₁₉	—	4	1	no	—
278	C₈×C₁₉	—	4	2	no	—
279	#3561	C₂×C₁₉	1	1	yes	characteristic
280	#3215	C₂×C₁₉	1	1	yes	characteristic, complemented
281	#3181	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#3162	C₂×C₁₉	1	1	yes	characteristic, complemented
283	#1664	C₂×C₁₉	1	2	yes	complemented
284	#1661	C₂×C₁₉	1	2	yes	complemented
285	#1661	C₂×C₁₉	1	2	yes	complemented
286	#1660	C₂×C₁₉	1	2	yes	complemented
287	#1532	C₂×C₁₉	1	1	yes	characteristic, complemented
288	#1531	C₂×C₁₉	1	1	yes	characteristic, complemented
289	C₂×#329	C₂×C₁₉	1	1	yes	characteristic, complemented
290	C₂²×C₁₉	—	2	1	no	—
291	C₂²×C₁₉	—	2	1	no	—
292	C₂²×C₁₉	—	4	1	no	—
293	C₂²×C₁₉	—	4	2	no	—
294	C₂²×C₁₉	—	4	2	no	—
295	C₂²×C₁₉	—	4	1	no	—
296	C₂²×C₁₉	—	4	1	no	—
297	C₂²×C₁₉	—	4	2	no	—
298	C₂²×C₁₉	—	16	2	no	—
299	C₂²×C₁₉	#456	1	2	yes	—
300	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
301	C₄×C₁₉	—	2	1	no	—
302	C₄×C₁₉	—	2	1	no	—
303	C₄×C₁₉	—	2	1	no	—
304	C₄×C₁₉	—	2	1	no	—
305	C₄×C₁₉	—	2	1	no	—
306	C₄×C₁₉	—	2	1	no	—
307	C₄×C₁₉	—	4	1	no	—
308	C₄×C₁₉	—	4	1	no	—
309	C₄×C₁₉	—	4	2	no	—
310	C₄×C₁₉	—	4	1	no	—
311	C₄×C₁₉	—	4	2	no	—
312	C₄×C₁₉	—	4	2	no	—
313	C₄×C₁₉	—	8	1	no	—
314	C₄×C₁₉	—	8	1	no	—
315	#563	C₂²×C₁₉	1	2	yes	—
316	#562	C₂²×C₁₉	1	2	yes	—
317	#556	—	2	1	no	—
318	#551	—	2	2	no	—
319	D₄×Q₈	—	2	1	no	—
320	#548	—	2	1	no	—
321	#546	—	2	1	no	—
322	#543	—	2	1	no	—
323	#542	—	2	1	no	—
324	#542	—	2	2	no	—
325	#538	—	2	1	no	—
326	#536	—	2	1	no	—
327	#533	C₂²×C₁₉	1	1	yes	characteristic
328	#533	C₂²×C₁₉	1	1	yes	characteristic
329	#529	C₂²×C₁₉	1	1	yes	characteristic
330	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
331	#501	—	2	1	no	—
332	#501	—	2	1	no	—
333	#501	C₂²×C₁₉	1	2	yes	complemented
334	#501	C₂²×C₁₉	1	2	yes	complemented
335	#501	C₂²×C₁₉	1	1	yes	characteristic, complemented
336	#497	C₂²×C₁₉	1	2	yes	—
337	#497	C₂²×C₁₉	1	1	yes	characteristic, complemented
338	#491	C₂²×C₁₉	1	1	yes	characteristic, complemented
339	#489	C₂²×C₁₉	1	2	yes	—
340	#489	C₂²×C₁₉	1	1	yes	characteristic, complemented
341	#467	—	2	1	no	—
342	#465	—	2	1	no	—
343	#464	—	2	2	no	—
344	#451	—	2	1	no	—
345	#450	—	2	1	no	—
346	#441	—	2	1	no	—
347	#440	—	2	1	no	—
348	#432	C₂²×C₁₉	1	1	yes	characteristic
349	#427	—	2	2	no	—
350	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
351	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
352	#330	C₂²×C₁₉	1	2	yes	complemented
353	#330	C₂²×C₁₉	1	2	yes	complemented
354	#330	C₂²×C₁₉	1	2	yes	complemented
355	#329	C₂²×C₁₉	1	2	yes	—
356	#329	C₂²×C₁₉	1	2	yes	—
357	#329	C₂²×C₁₉	1	2	yes	complemented
358	C₂×C₁₉	—	2	2	no	—
359	C₂×C₁₉	—	8	1	no	—
360	C₂×C₁₉	—	8	2	no	—
361	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
362	C₂×C₁₉	#3018	1	1	yes	characteristic
363	C₂×C₁₉	#3019	1	1	yes	characteristic
364	C₂×#41	—	2	1	no	—
365	C₂²×Q₈	—	2	1	no	—
366	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
367	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
368	C₂×Q₁₆	—	2	1	no	—
369	C₂×Q₁₆	—	2	2	no	—
370	C₂×SD₁₆	—	2	1	no	—
371	C₂×SD₁₆	—	2	2	no	—
372	C₂²×C₈	—	2	1	no	—
373	C₂²×C₈	—	2	1	no	—
374	C₄⋊Q₈	—	2	1	no	—
375	C₄⋊Q₈	—	2	2	no	—
376	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
377	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
378	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
379	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
380	#126	—	2	2	no	—
381	#126	—	2	2	no	—
382	#126	—	2	2	no	—
383	#126	—	2	1	no	—
384	#125	—	2	1	no	—
385	#125	C₂³×C₁₉	1	1	yes	characteristic
386	#125	C₂³×C₁₉	1	2	yes	—
387	#124	—	2	1	no	—
388	#124	—	2	2	no	—
389	#124	—	2	2	no	—
390	#124	—	2	1	no	—
391	#124	—	2	1	no	—
392	#124	D₄×C₁₉	1	2	yes	—
393	#124	C₂³×C₁₉	1	2	yes	—
394	#124	C₂³×C₁₉	1	1	yes	characteristic
395	#123	—	2	2	no	—
396	#123	—	2	2	no	—
397	#123	—	2	1	no	—
398	#123	—	2	2	no	—
399	#123	—	2	2	no	—
400	C₂²⋊Q₈	—	2	2	no	—
401	C₂²⋊Q₈	—	2	2	no	—
402	C₂²⋊Q₈	—	2	1	no	—
403	C₂²⋊Q₈	—	2	2	no	—
404	C₂²⋊Q₈	—	2	2	no	—
405	C₂²⋊Q₈	—	2	2	no	—
406	C₂²⋊Q₈	—	2	1	no	—
407	C₂²⋊Q₈	—	2	1	no	—
408	C₂²⋊Q₈	—	2	2	no	—
409	C₂²⋊Q₈	—	2	2	no	—
410	C₂²⋊Q₈	—	2	1	no	—
411	C₂²⋊Q₈	—	2	1	no	—
412	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
413	#121	—	2	1	no	—
414	#121	—	2	2	no	—
415	#121	—	2	2	no	—
416	#121	D₄×C₁₉	1	1	yes	characteristic
417	#120	—	2	2	no	—
418	C₄×Q₈	—	2	1	no	—
419	C₄×Q₈	—	2	1	no	—
420	C₄×Q₈	—	2	1	no	—
421	C₄×Q₈	—	2	1	no	—
422	C₄×Q₈	—	2	1	no	—
423	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
424	C₄×D₄	—	2	2	no	—
425	C₄×D₄	—	2	1	no	—
426	C₄×D₄	—	2	2	no	—
427	C₄×D₄	—	2	1	no	—
428	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
429	#117	—	2	2	no	—
430	#117	—	2	1	no	—
431	#117	—	2	1	no	—
432	#117	D₄×C₁₉	1	2	yes	—
433	C₂×C₂²⋊C₄	—	2	2	no	—
434	C₂×C₂²⋊C₄	—	2	1	no	—
435	C₂×C₂²⋊C₄	—	2	1	no	—
436	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
437	#107	—	2	2	no	—
438	#107	—	2	2	no	—
439	#107	—	2	1	no	—
440	#106	—	2	2	no	—
441	#106	—	2	2	no	—
442	#106	—	2	1	no	—
443	C₄⋊C₈	—	2	1	no	—
444	#103	—	2	1	no	—
445	#103	—	2	2	no	—
446	#103	—	2	1	no	—
447	#103	—	2	1	no	—
448	#102	—	2	1	no	—
449	#102	—	2	2	no	—
450	C₂²⋊C₈	—	2	1	no	—
451	#97	—	2	1	no	—
452	#97	—	2	1	no	—
453	#97	C₂³×C₁₉	1	2	yes	—
454	#97	C₂³×C₁₉	1	1	yes	characteristic
455	#97	C₂³×C₁₉	1	1	yes	characteristic
456	#97	C₂³×C₁₉	1	2	yes	—
457	C₁₉	#19049	1	1	yes	characteristic, direct product factor, Sylow
458	C₂⁴	—	2	1	no	—
459	#41	—	8	2	no	—
460	C₂×Q₈	—	2	2	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	2	1	no	—
463	C₂×Q₈	—	2	1	no	—
464	C₂×Q₈	—	2	1	no	—
465	C₂×Q₈	—	2	1	no	—
466	C₂×Q₈	—	8	2	no	—
467	C₂×Q₈	—	8	1	no	—
468	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
469	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	—	2	2	no	—
472	C₂×D₄	—	2	2	no	—
473	C₂×D₄	—	2	1	no	—
474	C₂×D₄	—	8	1	no	—
475	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
476	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
483	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
484	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
485	Q₁₆	—	4	2	no	—
486	Q₁₆	—	8	2	no	—
487	SD₁₆	—	4	2	no	—
488	SD₁₆	—	8	2	no	—
489	C₂×C₈	—	2	4	no	—
490	C₂×C₈	—	2	2	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	2	no	—
494	C₂×C₈	—	4	2	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	2	2	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	2	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	4	1	no	—
512	C₄⋊C₄	—	4	1	no	—
513	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
514	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
515	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
516	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	—	2	2	no	—
519	C₂²⋊C₄	—	2	2	no	—
520	C₂²⋊C₄	—	2	2	no	—
521	C₂²⋊C₄	—	2	2	no	—
522	C₂²⋊C₄	—	2	1	no	—
523	C₂²⋊C₄	—	2	2	no	—
524	C₂²⋊C₄	—	2	2	no	—
525	C₂²⋊C₄	—	2	2	no	—
526	C₂²⋊C₄	—	2	1	no	—
527	C₂²⋊C₄	—	2	1	no	—
528	C₂²⋊C₄	—	2	2	no	—
529	C₂²⋊C₄	—	2	2	no	—
530	C₂²⋊C₄	—	2	1	no	—
531	C₂²⋊C₄	—	2	1	no	—
532	C₂²⋊C₄	—	4	1	no	—
533	C₄²	—	2	2	no	—
534	C₄²	—	2	2	no	—
535	C₄²	—	2	1	no	—
536	C₄²	—	4	1	no	—
537	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
538	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
539	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
540	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
541	C₂³	—	2	2	no	—
542	C₂³	—	2	1	no	—
543	C₂³	—	4	2	no	—
544	C₂³	—	8	1	no	—
545	C₂³	—	8	1	no	—
546	C₂³	C₁₉×#120	1	1	yes	characteristic
547	Q₈	—	4	1	no	—
548	Q₈	—	4	2	no	—
549	Q₈	—	4	2	no	—
550	Q₈	—	4	2	no	—
551	Q₈	—	4	1	no	—
552	Q₈	—	4	2	no	—
553	Q₈	—	4	1	no	—
554	Q₈	—	8	1	no	—
555	Q₈	—	8	2	no	—
556	D₄	—	4	1	no	—
557	D₄	—	4	2	no	—
558	D₄	—	4	2	no	—
559	D₄	—	4	2	no	—
560	D₄	—	8	2	no	—
561	D₄	—	8	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	8	1	no	—
575	C₂×C₄	—	8	2	no	—
576	C₂×C₄	—	8	2	no	—
577	C₂×C₄	—	8	2	no	—
578	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
579	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
580	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
581	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
582	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
583	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
584	C₈	—	2	4	no	—
585	C₈	—	2	2	no	—
586	C₈	—	4	1	no	—
587	C₈	—	4	2	no	—
588	C₂²	—	2	1	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	4	2	no	—
592	C₂²	—	4	2	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	4	2	no	—
596	C₂²	—	16	2	no	—
597	C₂²	C₁₉×#456	1	2	yes	—
598	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
599	C₄	—	2	1	no	—
600	C₄	—	2	1	no	—
601	C₄	—	2	1	no	—
602	C₄	—	2	1	no	—
603	C₄	—	2	1	no	—
604	C₄	—	2	1	no	—
605	C₄	—	4	1	no	—
606	C₄	—	4	1	no	—
607	C₄	—	4	2	no	—
608	C₄	—	4	1	no	—
609	C₄	—	4	2	no	—
610	C₄	—	4	2	no	—
611	C₄	—	8	1	no	—
612	C₄	—	8	1	no	—
613	C₂	—	2	2	no	—
614	C₂	—	8	2	no	—
615	C₂	—	8	1	no	—
616	C₂	C₂×C₁₉×#456	1	1	yes	characteristic
617	C₂	C₁₉×#3018	1	1	yes	characteristic
618	C₂	C₁₉×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3561	C₂
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×#3215	C₂	semidirect
3. C₁₉×#3181	C₂	semidirect
4. C₁₉×#3162	C₂	semidirect
5. C₁₉×#1664	C₂	semidirect
6. C₁₉×#1661	C₂	semidirect
7. C₁₉×#1661	C₂	semidirect
8. C₁₉×#1660	C₂	semidirect
9. C₁₉×#1532	C₂	semidirect
10. C₁₉×#1531	C₂	semidirect
11. C₂×C₁₉×#329	C₂	semidirect
30. C₁₉×#501	C₂²	semidirect
31. C₁₉×#501	C₂²	semidirect
32. C₁₉×#501	C₂²	semidirect
34. C₁₉×#497	C₂²	semidirect
35. C₁₉×#491	C₂²	semidirect
37. C₁₉×#489	C₂²	semidirect
49. C₁₉×#330	C₂²	semidirect
50. C₁₉×#330	C₂²	semidirect
51. C₁₉×#330	C₂²	semidirect
54. C₁₉×#329	C₂²	semidirect
231. #19049	C₁₉	direct (N × H)
280. #3215	C₂×C₁₉	semidirect
281. #3181	C₂×C₁₉	semidirect
282. #3162	C₂×C₁₉	semidirect
283. #1664	C₂×C₁₉	semidirect
284. #1661	C₂×C₁₉	semidirect
285. #1661	C₂×C₁₉	semidirect
286. #1660	C₂×C₁₉	semidirect
287. #1532	C₂×C₁₉	semidirect
288. #1531	C₂×C₁₉	semidirect
289. C₂×#329	C₂×C₁₉	semidirect
333. #501	C₂²×C₁₉	semidirect
334. #501	C₂²×C₁₉	semidirect
335. #501	C₂²×C₁₉	semidirect
337. #497	C₂²×C₁₉	semidirect
338. #491	C₂²×C₁₉	semidirect
340. #489	C₂²×C₁₉	semidirect
352. #330	C₂²×C₁₉	semidirect
353. #330	C₂²×C₁₉	semidirect
354. #330	C₂²×C₁₉	semidirect
357. #329	C₂²×C₁₉	semidirect
457. C₁₉	#19049	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×#3561	2
C₁₉×#3215	2
C₁₉×#3181	2
C₁₉×#3162	2
C₁₉×#1664	2
C₁₉×#1661	2
C₁₉×#1660	2
C₁₉×#1532	2
C₁₉×#1531	2
C₂×C₁₉×#329	2
#19049	19

Subgroups — C19×#19049 #18025008

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19049 #18025008