Subgroups — C₁₉×#8417 #18014376

Order 4864.

706 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3523	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1986	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1763	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1531	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1524	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1509	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1491	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#557	—	2	1	no	—
9	C₁₉×#557	C₄	1	1	yes	characteristic, complemented
10	C₁₉×#557	C₄	1	1	yes	characteristic, complemented
11	C₁₉×#556	—	2	1	no	—
12	C₁₉×#556	C₄	1	1	yes	characteristic, complemented
13	C₁₉×#552	—	2	2	no	—
14	C₁₉×#552	—	2	1	no	—
15	D₄×Q₈×C₁₉	—	2	1	no	—
16	D₄×Q₈×C₁₉	C₄	1	1	yes	characteristic, complemented
17	C₁₉×#541	—	2	2	no	—
18	C₁₉×#541	—	2	1	no	—
19	C₁₉×#533	—	2	1	no	—
20	C₁₉×#533	C₂²	1	1	yes	characteristic
21	C₁₉×#529	—	2	1	no	—
22	C₁₉×#529	C₂²	1	1	yes	characteristic
23	C₁₉×#519	—	2	1	no	—
24	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#432	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#103	—	2	1	no	—
27	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
29	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
30	C₁₉×#340	—	2	1	no	—
31	C₁₉×#339	—	2	2	no	—
32	C₁₉×#330	—	2	1	no	—
33	C₁₉×#330	—	2	2	no	—
34	C₁₉×#329	—	2	1	no	—
35	C₁₉×#328	—	2	1	no	—
36	C₁₉×#327	—	2	1	no	—
37	C₁₉×Q₈⋊C₈	—	2	1	no	—
38	C₁₉×Q₈⋊C₈	—	2	1	no	—
39	C₂²×Q₈×C₁₉	—	2	1	no	—
40	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
41	C₂×M₁₆×C₁₉	—	2	1	no	—
42	C₂²×C₈×C₁₉	—	2	1	no	—
43	C₁₉×C₄⋊Q₈	—	2	2	no	—
44	C₁₉×C₄⋊Q₈	—	2	1	no	—
45	C₁₉×C₄⋊Q₈	—	2	1	no	—
46	C₁₉×C₄⋊Q₈	—	2	1	no	—
47	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
48	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
49	C₁₉×#126	—	2	2	no	—
50	C₁₉×#126	—	2	2	no	—
51	C₁₉×#126	—	2	2	no	—
52	C₁₉×#126	—	2	2	no	—
53	C₁₉×#126	—	2	1	no	—
54	C₁₉×#125	—	2	2	no	—
55	C₁₉×#125	—	2	2	no	—
56	C₁₉×#125	—	2	2	no	—
57	C₁₉×#125	—	2	1	no	—
58	C₁₉×#125	—	2	2	no	—
59	C₁₉×#125	—	2	2	no	—
60	C₁₉×#125	—	2	1	no	—
61	C₁₉×#125	D₄	1	1	yes	characteristic
62	C₁₉×#125	D₄	1	2	yes	—
63	C₁₉×#124	—	2	1	no	—
64	C₁₉×#124	D₄	1	1	yes	characteristic
65	C₁₉×#123	—	2	2	no	—
66	C₁₉×#123	—	2	1	no	—
67	C₁₉×C₂²⋊Q₈	—	2	2	no	—
68	C₁₉×C₂²⋊Q₈	—	2	2	no	—
69	C₁₉×C₂²⋊Q₈	—	2	1	no	—
70	C₁₉×C₂²⋊Q₈	—	2	1	no	—
71	C₁₉×C₂²⋊Q₈	—	2	1	no	—
72	C₁₉×C₂²⋊Q₈	—	2	1	no	—
73	C₁₉×C₂²⋊Q₈	—	2	2	no	—
74	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
75	C₁₉×#121	D₄	1	1	yes	characteristic
76	C₄×Q₈×C₁₉	—	2	2	no	—
77	C₄×Q₈×C₁₉	—	2	2	no	—
78	C₄×Q₈×C₁₉	—	2	1	no	—
79	C₄×Q₈×C₁₉	—	2	1	no	—
80	C₄×Q₈×C₁₉	—	2	1	no	—
81	C₄×Q₈×C₁₉	—	2	1	no	—
82	C₄×Q₈×C₁₉	—	2	1	no	—
83	C₄×Q₈×C₁₉	—	2	1	no	—
84	C₄×Q₈×C₁₉	—	2	1	no	—
85	C₄×Q₈×C₁₉	—	2	1	no	—
86	C₄×Q₈×C₁₉	—	2	1	no	—
87	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
88	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
89	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
90	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
91	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
92	C₄×D₄×C₁₉	—	2	2	no	—
93	C₄×D₄×C₁₉	—	2	1	no	—
94	C₄×D₄×C₁₉	—	2	1	no	—
95	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
96	C₁₉×#117	—	2	2	no	—
97	C₁₉×#117	—	2	2	no	—
98	C₁₉×#117	—	2	2	no	—
99	C₁₉×#117	—	2	1	no	—
100	C₁₉×#117	—	2	1	no	—
101	C₁₉×#117	D₄	1	2	yes	—
102	C₂×C₄⋊C₄×C₁₉	—	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	—	2	1	no	—
107	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
108	C₁₉×C₄⋊C₈	—	2	1	no	—
109	C₁₉×#103	—	2	4	no	—
110	C₁₉×C₂²⋊C₈	—	2	1	no	—
111	C₁₉×#97	—	2	1	no	—
112	C₁₉×#97	—	2	1	no	—
113	C₁₉×#97	—	2	1	no	—
114	C₁₉×#97	—	2	1	no	—
115	C₄×C₈×C₁₉	—	2	1	no	—
116	C₁₉×#95	—	2	1	no	—
117	C₂×Q₈×C₁₉	—	2	2	no	—
118	C₂×Q₈×C₁₉	—	2	1	no	—
119	C₂×Q₈×C₁₉	—	2	1	no	—
120	C₂×Q₈×C₁₉	—	2	1	no	—
121	C₂×Q₈×C₁₉	—	2	2	no	—
122	C₂×Q₈×C₁₉	—	4	1	no	—
123	C₂×Q₈×C₁₉	—	4	2	no	—
124	C₂×Q₈×C₁₉	—	4	2	no	—
125	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
126	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
127	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
128	C₂×D₄×C₁₉	—	2	1	no	—
129	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	1	no	—
132	C₂²×C₄×C₁₉	—	2	1	no	—
133	C₂²×C₄×C₁₉	—	2	1	no	—
134	C₂²×C₄×C₁₉	—	4	1	no	—
135	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
138	M₁₆×C₁₉	—	2	2	no	—
139	M₁₆×C₁₉	—	4	1	no	—
140	C₂×C₈×C₁₉	—	2	2	no	—
141	C₂×C₈×C₁₉	—	4	1	no	—
142	C₂×C₈×C₁₉	—	4	1	no	—
143	C₂×C₈×C₁₉	—	4	1	no	—
144	C₂×C₈×C₁₉	—	4	1	no	—
145	C₄⋊C₄×C₁₉	—	2	2	no	—
146	C₄⋊C₄×C₁₉	—	2	2	no	—
147	C₄⋊C₄×C₁₉	—	2	2	no	—
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	—	2	2	no	—
150	C₄⋊C₄×C₁₉	—	2	2	no	—
151	C₄⋊C₄×C₁₉	—	2	2	no	—
152	C₄⋊C₄×C₁₉	—	2	2	no	—
153	C₄⋊C₄×C₁₉	—	2	1	no	—
154	C₄⋊C₄×C₁₉	—	2	1	no	—
155	C₄⋊C₄×C₁₉	—	2	1	no	—
156	C₄⋊C₄×C₁₉	—	2	1	no	—
157	C₄⋊C₄×C₁₉	—	2	1	no	—
158	C₄⋊C₄×C₁₉	—	2	1	no	—
159	C₄⋊C₄×C₁₉	—	2	1	no	—
160	C₄⋊C₄×C₁₉	—	2	1	no	—
161	C₄⋊C₄×C₁₉	—	2	2	no	—
162	C₄⋊C₄×C₁₉	—	2	1	no	—
163	C₄⋊C₄×C₁₉	—	2	1	no	—
164	C₄⋊C₄×C₁₉	—	2	1	no	—
165	C₄⋊C₄×C₁₉	—	2	2	no	—
166	C₄⋊C₄×C₁₉	—	2	2	no	—
167	C₄⋊C₄×C₁₉	—	4	1	no	—
168	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
169	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
170	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
171	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
172	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
173	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
174	C₂²⋊C₄×C₁₉	—	2	2	no	—
175	C₂²⋊C₄×C₁₉	—	2	2	no	—
176	C₂²⋊C₄×C₁₉	—	2	2	no	—
177	C₂²⋊C₄×C₁₉	—	2	1	no	—
178	C₂²⋊C₄×C₁₉	—	2	2	no	—
179	C₂²⋊C₄×C₁₉	—	2	1	no	—
180	C₂²⋊C₄×C₁₉	—	2	1	no	—
181	C₂²⋊C₄×C₁₉	—	2	1	no	—
182	C₂²⋊C₄×C₁₉	—	2	1	no	—
183	C₄²×C₁₉	—	2	2	no	—
184	C₄²×C₁₉	—	2	2	no	—
185	C₄²×C₁₉	—	2	2	no	—
186	C₄²×C₁₉	—	2	1	no	—
187	C₄²×C₁₉	—	2	1	no	—
188	C₄²×C₁₉	—	2	1	no	—
189	C₄²×C₁₉	—	2	1	no	—
190	C₄²×C₁₉	—	2	1	no	—
191	C₄²×C₁₉	—	2	2	no	—
192	C₄²×C₁₉	—	4	2	no	—
193	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
194	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
195	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
196	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
197	#8417	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₂³×C₁₉	—	2	1	no	—
199	C₂³×C₁₉	#120	1	1	yes	characteristic
200	Q₈×C₁₉	—	2	1	no	—
201	Q₈×C₁₉	—	2	1	no	—
202	Q₈×C₁₉	—	2	1	no	—
203	Q₈×C₁₉	—	4	2	no	—
204	Q₈×C₁₉	—	4	1	no	—
205	Q₈×C₁₉	—	4	2	no	—
206	Q₈×C₁₉	—	4	4	no	—
207	Q₈×C₁₉	—	4	1	no	—
208	Q₈×C₁₉	—	4	1	no	—
209	Q₈×C₁₉	#104	1	2	yes	—
210	D₄×C₁₉	—	4	1	no	—
211	D₄×C₁₉	—	4	1	no	—
212	D₄×C₁₉	—	4	1	no	—
213	C₂×C₄×C₁₉	—	2	1	no	—
214	C₂×C₄×C₁₉	—	2	1	no	—
215	C₂×C₄×C₁₉	—	2	1	no	—
216	C₂×C₄×C₁₉	—	2	1	no	—
217	C₂×C₄×C₁₉	—	2	1	no	—
218	C₂×C₄×C₁₉	—	2	1	no	—
219	C₂×C₄×C₁₉	—	2	1	no	—
220	C₂×C₄×C₁₉	—	2	2	no	—
221	C₂×C₄×C₁₉	—	2	1	no	—
222	C₂×C₄×C₁₉	—	2	1	no	—
223	C₂×C₄×C₁₉	—	2	1	no	—
224	C₂×C₄×C₁₉	—	2	1	no	—
225	C₂×C₄×C₁₉	—	2	2	no	—
226	C₂×C₄×C₁₉	—	4	1	no	—
227	C₂×C₄×C₁₉	—	4	2	no	—
228	C₂×C₄×C₁₉	—	4	4	no	—
229	C₂×C₄×C₁₉	—	4	1	no	—
230	C₂×C₄×C₁₉	—	4	1	no	—
231	C₂×C₄×C₁₉	—	4	1	no	—
232	C₂×C₄×C₁₉	—	4	1	no	—
233	C₂×C₄×C₁₉	—	4	2	no	—
234	C₂×C₄×C₁₉	—	8	1	no	—
235	C₂×C₄×C₁₉	—	8	1	no	—
236	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
237	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
238	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
239	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
240	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
241	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
242	C₈×C₁₉	—	4	2	no	—
243	C₈×C₁₉	—	4	2	no	—
244	C₈×C₁₉	—	8	1	no	—
245	#3523	C₂×C₁₉	1	1	yes	characteristic
246	#1986	C₂×C₁₉	1	1	yes	characteristic, complemented
247	#1763	C₂×C₁₉	1	1	yes	characteristic, complemented
248	#1531	C₂×C₁₉	1	1	yes	characteristic, complemented
249	#1524	C₂×C₁₉	1	1	yes	characteristic
250	#1509	C₂×C₁₉	1	1	yes	characteristic
251	#1491	C₂×C₁₉	1	1	yes	characteristic, complemented
252	C₂²×C₁₉	—	2	1	no	—
253	C₂²×C₁₉	—	2	1	no	—
254	C₂²×C₁₉	—	4	1	no	—
255	C₂²×C₁₉	—	4	1	no	—
256	C₂²×C₁₉	—	4	1	no	—
257	C₂²×C₁₉	#379	1	1	yes	characteristic
258	C₂²×C₁₉	#454	1	1	yes	characteristic
259	C₂²×C₁₉	#456	1	1	yes	characteristic
260	C₄×C₁₉	—	2	1	no	—
261	C₄×C₁₉	—	2	1	no	—
262	C₄×C₁₉	—	2	1	no	—
263	C₄×C₁₉	—	2	1	no	—
264	C₄×C₁₉	—	2	1	no	—
265	C₄×C₁₉	—	2	2	no	—
266	C₄×C₁₉	—	4	1	no	—
267	C₄×C₁₉	—	4	1	no	—
268	C₄×C₁₉	—	4	1	no	—
269	C₄×C₁₉	—	4	1	no	—
270	C₄×C₁₉	—	4	2	no	—
271	C₄×C₁₉	—	4	1	no	—
272	C₄×C₁₉	—	4	2	no	—
273	C₄×C₁₉	—	4	1	no	—
274	C₄×C₁₉	—	8	2	no	—
275	C₄×C₁₉	C₂×#104	1	1	yes	characteristic
276	C₄×C₁₉	#421	1	1	yes	characteristic
277	#557	—	2	1	no	—
278	#557	C₄×C₁₉	1	1	yes	characteristic, complemented
279	#557	C₄×C₁₉	1	1	yes	characteristic, complemented
280	#556	—	2	1	no	—
281	#556	C₄×C₁₉	1	1	yes	characteristic, complemented
282	#552	—	2	2	no	—
283	#552	—	2	1	no	—
284	D₄×Q₈	—	2	1	no	—
285	D₄×Q₈	C₄×C₁₉	1	1	yes	characteristic, complemented
286	#541	—	2	2	no	—
287	#541	—	2	1	no	—
288	#533	—	2	1	no	—
289	#533	C₂²×C₁₉	1	1	yes	characteristic
290	#529	—	2	1	no	—
291	#529	C₂²×C₁₉	1	1	yes	characteristic
292	#519	—	2	1	no	—
293	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
294	#432	C₂²×C₁₉	1	1	yes	characteristic
295	C₂×#103	—	2	1	no	—
296	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
297	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
298	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
299	#340	—	2	1	no	—
300	#339	—	2	2	no	—
301	#330	—	2	1	no	—
302	#330	—	2	2	no	—
303	#329	—	2	1	no	—
304	#328	—	2	1	no	—
305	#327	—	2	1	no	—
306	Q₈⋊C₈	—	2	1	no	—
307	Q₈⋊C₈	—	2	1	no	—
308	C₂×C₁₉	—	2	1	no	—
309	C₂×C₁₉	—	2	1	no	—
310	C₂×C₁₉	—	8	1	no	—
311	C₂×C₁₉	#1789	1	1	yes	characteristic
312	C₂×C₁₉	#1793	1	1	yes	characteristic
313	C₂×C₁₉	#1796	1	1	yes	characteristic
314	C₂²×Q₈	—	2	1	no	—
315	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
316	C₂×M₁₆	—	2	1	no	—
317	C₂²×C₈	—	2	1	no	—
318	C₄⋊Q₈	—	2	2	no	—
319	C₄⋊Q₈	—	2	1	no	—
320	C₄⋊Q₈	—	2	1	no	—
321	C₄⋊Q₈	—	2	1	no	—
322	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
323	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
324	#126	—	2	2	no	—
325	#126	—	2	2	no	—
326	#126	—	2	2	no	—
327	#126	—	2	2	no	—
328	#126	—	2	1	no	—
329	#125	—	2	2	no	—
330	#125	—	2	2	no	—
331	#125	—	2	2	no	—
332	#125	—	2	1	no	—
333	#125	—	2	2	no	—
334	#125	—	2	2	no	—
335	#125	—	2	1	no	—
336	#125	D₄×C₁₉	1	1	yes	characteristic
337	#125	D₄×C₁₉	1	2	yes	—
338	#124	—	2	1	no	—
339	#124	D₄×C₁₉	1	1	yes	characteristic
340	#123	—	2	2	no	—
341	#123	—	2	1	no	—
342	C₂²⋊Q₈	—	2	2	no	—
343	C₂²⋊Q₈	—	2	2	no	—
344	C₂²⋊Q₈	—	2	1	no	—
345	C₂²⋊Q₈	—	2	1	no	—
346	C₂²⋊Q₈	—	2	1	no	—
347	C₂²⋊Q₈	—	2	1	no	—
348	C₂²⋊Q₈	—	2	2	no	—
349	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
350	#121	D₄×C₁₉	1	1	yes	characteristic
351	C₄×Q₈	—	2	2	no	—
352	C₄×Q₈	—	2	2	no	—
353	C₄×Q₈	—	2	1	no	—
354	C₄×Q₈	—	2	1	no	—
355	C₄×Q₈	—	2	1	no	—
356	C₄×Q₈	—	2	1	no	—
357	C₄×Q₈	—	2	1	no	—
358	C₄×Q₈	—	2	1	no	—
359	C₄×Q₈	—	2	1	no	—
360	C₄×Q₈	—	2	1	no	—
361	C₄×Q₈	—	2	1	no	—
362	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
363	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
364	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
365	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
366	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
367	C₄×D₄	—	2	2	no	—
368	C₄×D₄	—	2	1	no	—
369	C₄×D₄	—	2	1	no	—
370	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
371	#117	—	2	2	no	—
372	#117	—	2	2	no	—
373	#117	—	2	2	no	—
374	#117	—	2	1	no	—
375	#117	—	2	1	no	—
376	#117	D₄×C₁₉	1	2	yes	—
377	C₂×C₄⋊C₄	—	2	1	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
380	C₂×C₄²	—	2	1	no	—
381	C₂×C₄²	—	2	1	no	—
382	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
383	C₄⋊C₈	—	2	1	no	—
384	#103	—	2	4	no	—
385	C₂²⋊C₈	—	2	1	no	—
386	#97	—	2	1	no	—
387	#97	—	2	1	no	—
388	#97	—	2	1	no	—
389	#97	—	2	1	no	—
390	C₄×C₈	—	2	1	no	—
391	#95	—	2	1	no	—
392	C₁₉	#8417	1	1	yes	characteristic, direct product factor, Sylow
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	2	1	no	—
395	C₂×Q₈	—	2	1	no	—
396	C₂×Q₈	—	2	1	no	—
397	C₂×Q₈	—	2	2	no	—
398	C₂×Q₈	—	4	1	no	—
399	C₂×Q₈	—	4	2	no	—
400	C₂×Q₈	—	4	2	no	—
401	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
402	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
403	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	4	1	no	—
411	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
412	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
413	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
414	M₁₆	—	2	2	no	—
415	M₁₆	—	4	1	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	4	1	no	—
418	C₂×C₈	—	4	1	no	—
419	C₂×C₈	—	4	1	no	—
420	C₂×C₈	—	4	1	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	4	1	no	—
444	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
445	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
446	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
447	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
448	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
449	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
450	C₂²⋊C₄	—	2	2	no	—
451	C₂²⋊C₄	—	2	2	no	—
452	C₂²⋊C₄	—	2	2	no	—
453	C₂²⋊C₄	—	2	1	no	—
454	C₂²⋊C₄	—	2	2	no	—
455	C₂²⋊C₄	—	2	1	no	—
456	C₂²⋊C₄	—	2	1	no	—
457	C₂²⋊C₄	—	2	1	no	—
458	C₂²⋊C₄	—	2	1	no	—
459	C₄²	—	2	2	no	—
460	C₄²	—	2	2	no	—
461	C₄²	—	2	2	no	—
462	C₄²	—	2	1	no	—
463	C₄²	—	2	1	no	—
464	C₄²	—	2	1	no	—
465	C₄²	—	2	1	no	—
466	C₄²	—	2	1	no	—
467	C₄²	—	2	2	no	—
468	C₄²	—	4	2	no	—
469	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
470	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
471	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
472	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
473	C₂³	—	2	1	no	—
474	C₂³	C₁₉×#120	1	1	yes	characteristic
475	Q₈	—	2	1	no	—
476	Q₈	—	2	1	no	—
477	Q₈	—	2	1	no	—
478	Q₈	—	4	2	no	—
479	Q₈	—	4	1	no	—
480	Q₈	—	4	4	no	—
481	Q₈	—	4	2	no	—
482	Q₈	—	4	1	no	—
483	Q₈	—	4	1	no	—
484	Q₈	C₁₉×#104	1	2	yes	—
485	D₄	—	4	1	no	—
486	D₄	—	4	1	no	—
487	D₄	—	4	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	4	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	8	1	no	—
510	C₂×C₄	—	8	1	no	—
511	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
512	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
513	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
514	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
515	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
516	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
517	C₈	—	4	2	no	—
518	C₈	—	4	2	no	—
519	C₈	—	8	1	no	—
520	C₂²	—	2	1	no	—
521	C₂²	—	2	1	no	—
522	C₂²	—	4	1	no	—
523	C₂²	—	4	1	no	—
524	C₂²	—	4	1	no	—
525	C₂²	C₁₉×#379	1	1	yes	characteristic
526	C₂²	C₁₉×#454	1	1	yes	characteristic
527	C₂²	C₁₉×#456	1	1	yes	characteristic
528	C₄	—	2	1	no	—
529	C₄	—	2	2	no	—
530	C₄	—	2	1	no	—
531	C₄	—	2	1	no	—
532	C₄	—	2	1	no	—
533	C₄	—	2	1	no	—
534	C₄	—	4	1	no	—
535	C₄	—	4	2	no	—
536	C₄	—	4	1	no	—
537	C₄	—	4	1	no	—
538	C₄	—	4	1	no	—
539	C₄	—	4	1	no	—
540	C₄	—	4	2	no	—
541	C₄	—	4	1	no	—
542	C₄	—	8	2	no	—
543	C₄	C₂×C₁₉×#104	1	1	yes	characteristic
544	C₄	C₁₉×#421	1	1	yes	characteristic
545	C₂	—	2	1	no	—
546	C₂	—	2	1	no	—
547	C₂	—	8	1	no	—
548	C₂	C₁₉×#1789	1	1	yes	characteristic
549	C₂	C₁₉×#1793	1	1	yes	characteristic
550	C₂	C₁₉×#1796	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#379
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#121	D₄
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×#1986	C₂	semidirect
3. C₁₉×#1763	C₂	semidirect
4. C₁₉×#1531	C₂	semidirect
7. C₁₉×#1491	C₂	semidirect
9. C₁₉×#557	C₄	semidirect
10. C₁₉×#557	C₄	semidirect
12. C₁₉×#556	C₄	semidirect
16. D₄×Q₈×C₁₉	C₄	semidirect
197. #8417	C₁₉	direct (N × H)
246. #1986	C₂×C₁₉	semidirect
247. #1763	C₂×C₁₉	semidirect
248. #1531	C₂×C₁₉	semidirect
251. #1491	C₂×C₁₉	semidirect
278. #557	C₄×C₁₉	semidirect
279. #557	C₄×C₁₉	semidirect
281. #556	C₄×C₁₉	semidirect
285. D₄×Q₈	C₄×C₁₉	semidirect
392. C₁₉	#8417	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×#3523	2
C₁₉×#1986	2
C₁₉×#1763	2
C₁₉×#1531	2
C₁₉×#1524	2
C₁₉×#1509	2
C₁₉×#1491	2
#8417	19

Subgroups — C19×#8417 #18014376

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8417 #18014376