Subgroups — C₁₉×#8499 #18014458

Order 4864.

676 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3552	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1993	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1556	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1532	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1532	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1512	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1512	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#563	—	2	2	no	—
9	C₁₉×#557	C₄	1	1	yes	characteristic, complemented
10	C₁₉×#556	C₄	1	1	yes	characteristic, complemented
11	C₁₉×#554	—	2	1	no	—
12	C₁₉×#553	—	2	1	no	—
13	D₄×Q₈×C₁₉	—	2	1	no	—
14	D₄×Q₈×C₁₉	C₄	1	1	yes	characteristic, complemented
15	C₁₉×#548	—	2	1	no	—
16	C₁₉×#547	C₄	1	1	yes	characteristic, complemented
17	C₁₉×#544	—	2	1	no	—
18	C₁₉×#542	—	2	1	no	—
19	C₁₉×#541	—	2	1	no	—
20	C₁₉×#539	—	2	2	no	—
21	C₁₉×#536	—	2	1	no	—
22	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₁₉×#529	C₂²	1	1	yes	characteristic
24	C₁₉×#529	C₂²	1	1	yes	characteristic
25	C₁₉×#432	C₂²	1	1	yes	characteristic
26	C₁₉×#432	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
28	C₁₉×#382	C₂²	1	1	yes	characteristic
29	C₁₉×#340	—	2	2	no	—
30	C₁₉×#332	—	2	2	no	—
31	C₁₉×#330	—	2	1	no	—
32	C₁₉×#330	—	2	1	no	—
33	C₁₉×#329	—	2	1	no	—
34	C₁₉×#329	—	2	1	no	—
35	C₁₉×#328	—	2	1	no	—
36	C₁₉×#328	—	2	1	no	—
37	C₁₉×#327	—	2	1	no	—
38	C₁₉×#327	—	2	1	no	—
39	C₂×#41×C₁₉	—	2	1	no	—
40	C₂²×Q₈×C₁₉	—	2	1	no	—
41	C₂²×Q₈×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	—	2	1	no	—
48	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
49	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
50	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
51	C₁₉×#126	—	2	2	no	—
52	C₁₉×#126	—	2	2	no	—
53	C₁₉×#126	—	2	2	no	—
54	C₁₉×#126	—	2	1	no	—
55	C₁₉×#126	—	2	1	no	—
56	C₁₉×#125	—	2	2	no	—
57	C₁₉×#125	—	2	2	no	—
58	C₁₉×#125	—	2	2	no	—
59	C₁₉×#125	—	2	1	no	—
60	C₁₉×#125	D₄	1	1	yes	characteristic
61	C₁₉×#125	D₄	1	1	yes	characteristic
62	C₁₉×#124	—	2	2	no	—
63	C₁₉×#124	—	2	1	no	—
64	C₁₉×#124	D₄	1	1	yes	characteristic
65	C₁₉×#124	D₄	1	1	yes	characteristic
66	C₁₉×#123	—	2	2	no	—
67	C₁₉×#123	—	2	2	no	—
68	C₁₉×#123	—	2	1	no	—
69	C₁₉×#123	—	2	1	no	—
70	C₁₉×#123	—	2	2	no	—
71	C₁₉×C₂²⋊Q₈	—	2	2	no	—
72	C₁₉×C₂²⋊Q₈	—	2	2	no	—
73	C₁₉×C₂²⋊Q₈	—	2	2	no	—
74	C₁₉×C₂²⋊Q₈	—	2	2	no	—
75	C₁₉×C₂²⋊Q₈	—	2	2	no	—
76	C₁₉×C₂²⋊Q₈	—	2	1	no	—
77	C₁₉×C₂²⋊Q₈	—	2	2	no	—
78	C₁₉×C₂²⋊Q₈	—	2	1	no	—
79	C₁₉×C₂²⋊Q₈	—	2	1	no	—
80	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
81	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
82	C₁₉×#121	—	2	2	no	—
83	C₁₉×#121	—	2	1	no	—
84	C₁₉×#121	D₄	1	1	yes	characteristic
85	C₁₉×#121	D₄	1	1	yes	characteristic
86	C₄×Q₈×C₁₉	—	2	1	no	—
87	C₄×Q₈×C₁₉	—	2	1	no	—
88	C₄×Q₈×C₁₉	—	2	1	no	—
89	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
90	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
91	C₄×D₄×C₁₉	—	2	2	no	—
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	—	2	1	no	—
96	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
97	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
98	C₁₉×#117	—	2	1	no	—
99	C₁₉×#117	—	2	1	no	—
100	C₁₉×#117	—	2	1	no	—
101	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
102	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
103	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
104	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
105	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
106	C₁₉×C₄⋊C₈	—	2	1	no	—
107	C₁₉×C₄⋊C₈	—	2	1	no	—
108	C₁₉×C₂²⋊C₈	—	2	1	no	—
109	C₁₉×C₂²⋊C₈	—	2	1	no	—
110	C₁₉×#97	—	2	1	no	—
111	C₁₉×#97	—	2	1	no	—
112	C₁₉×#97	—	2	1	no	—
113	C₁₉×#97	—	2	1	no	—
114	C₁₉×#95	—	2	1	no	—
115	C₁₉×#95	—	2	1	no	—
116	#41×C₁₉	—	8	2	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	2	no	—
121	C₂×Q₈×C₁₉	—	8	2	no	—
122	C₂×Q₈×C₁₉	—	8	2	no	—
123	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
124	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
125	C₂×D₄×C₁₉	—	2	1	no	—
126	C₂×D₄×C₁₉	—	2	1	no	—
127	C₂×D₄×C₁₉	—	2	2	no	—
128	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
129	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	—	2	1	no	—
134	C₂²×C₄×C₁₉	—	2	1	no	—
135	C₂²×C₄×C₁₉	—	4	1	no	—
136	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₁₉	—	2	2	no	—
140	C₂×C₈×C₁₉	—	4	1	no	—
141	C₂×C₈×C₁₉	—	4	1	no	—
142	C₂×C₈×C₁₉	—	4	1	no	—
143	C₂×C₈×C₁₉	—	4	1	no	—
144	C₄⋊C₄×C₁₉	—	2	2	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	1	no	—
151	C₄⋊C₄×C₁₉	—	2	1	no	—
152	C₄⋊C₄×C₁₉	—	2	1	no	—
153	C₄⋊C₄×C₁₉	—	2	1	no	—
154	C₄⋊C₄×C₁₉	—	2	2	no	—
155	C₄⋊C₄×C₁₉	—	2	2	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	1	no	—
162	C₄⋊C₄×C₁₉	—	4	2	no	—
163	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
164	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
165	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
166	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
167	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
168	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
169	C₂²⋊C₄×C₁₉	—	2	2	no	—
170	C₂²⋊C₄×C₁₉	—	2	2	no	—
171	C₂²⋊C₄×C₁₉	—	2	2	no	—
172	C₂²⋊C₄×C₁₉	—	2	2	no	—
173	C₂²⋊C₄×C₁₉	—	2	1	no	—
174	C₂²⋊C₄×C₁₉	—	2	1	no	—
175	C₂²⋊C₄×C₁₉	—	2	1	no	—
176	C₂²⋊C₄×C₁₉	—	2	1	no	—
177	C₂²⋊C₄×C₁₉	—	2	1	no	—
178	C₂²⋊C₄×C₁₉	—	2	1	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	1	no	—
186	C₄²×C₁₉	—	2	1	no	—
187	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
188	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
191	#8499	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂³×C₁₉	—	2	1	no	—
193	C₂³×C₁₉	—	2	1	no	—
194	C₂³×C₁₉	#120	1	1	yes	characteristic
195	Q₈×C₁₉	—	4	1	no	—
196	Q₈×C₁₉	—	4	1	no	—
197	Q₈×C₁₉	—	4	2	no	—
198	Q₈×C₁₉	—	4	2	no	—
199	Q₈×C₁₉	—	8	2	no	—
200	Q₈×C₁₉	—	8	2	no	—
201	D₄×C₁₉	—	4	1	no	—
202	D₄×C₁₉	—	4	1	no	—
203	D₄×C₁₉	—	4	1	no	—
204	D₄×C₁₉	—	4	1	no	—
205	D₄×C₁₉	—	4	1	no	—
206	D₄×C₁₉	—	4	1	no	—
207	D₄×C₁₉	—	8	2	no	—
208	C₂×C₄×C₁₉	—	2	1	no	—
209	C₂×C₄×C₁₉	—	2	1	no	—
210	C₂×C₄×C₁₉	—	2	1	no	—
211	C₂×C₄×C₁₉	—	2	1	no	—
212	C₂×C₄×C₁₉	—	2	1	no	—
213	C₂×C₄×C₁₉	—	2	1	no	—
214	C₂×C₄×C₁₉	—	2	1	no	—
215	C₂×C₄×C₁₉	—	2	2	no	—
216	C₂×C₄×C₁₉	—	2	2	no	—
217	C₂×C₄×C₁₉	—	2	1	no	—
218	C₂×C₄×C₁₉	—	4	1	no	—
219	C₂×C₄×C₁₉	—	4	1	no	—
220	C₂×C₄×C₁₉	—	4	2	no	—
221	C₂×C₄×C₁₉	—	4	2	no	—
222	C₂×C₄×C₁₉	—	8	2	no	—
223	C₂×C₄×C₁₉	—	8	2	no	—
224	C₂×C₄×C₁₉	—	8	2	no	—
225	C₂×C₄×C₁₉	—	8	1	no	—
226	C₂×C₄×C₁₉	—	8	1	no	—
227	C₂×C₄×C₁₉	—	8	1	no	—
228	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
232	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
233	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
234	C₈×C₁₉	—	4	2	no	—
235	C₈×C₁₉	—	8	1	no	—
236	C₈×C₁₉	—	8	1	no	—
237	#3552	C₂×C₁₉	1	1	yes	characteristic
238	#1993	C₂×C₁₉	1	1	yes	characteristic, complemented
239	#1556	C₂×C₁₉	1	1	yes	characteristic, complemented
240	#1532	C₂×C₁₉	1	1	yes	characteristic, complemented
241	#1532	C₂×C₁₉	1	1	yes	characteristic, complemented
242	#1512	C₂×C₁₉	1	1	yes	characteristic, complemented
243	#1512	C₂×C₁₉	1	1	yes	characteristic, complemented
244	C₂²×C₁₉	—	2	1	no	—
245	C₂²×C₁₉	—	2	1	no	—
246	C₂²×C₁₉	—	4	1	no	—
247	C₂²×C₁₉	—	4	1	no	—
248	C₂²×C₁₉	—	4	1	no	—
249	C₂²×C₁₉	—	4	1	no	—
250	C₂²×C₁₉	—	4	1	no	—
251	C₂²×C₁₉	—	4	1	no	—
252	C₂²×C₁₉	#379	1	1	yes	characteristic
253	C₂²×C₁₉	#454	1	1	yes	characteristic
254	C₂²×C₁₉	#456	1	1	yes	characteristic
255	C₄×C₁₉	—	2	1	no	—
256	C₄×C₁₉	—	2	1	no	—
257	C₄×C₁₉	—	2	1	no	—
258	C₄×C₁₉	—	2	1	no	—
259	C₄×C₁₉	—	2	1	no	—
260	C₄×C₁₉	—	2	1	no	—
261	C₄×C₁₉	—	4	1	no	—
262	C₄×C₁₉	—	4	1	no	—
263	C₄×C₁₉	—	4	1	no	—
264	C₄×C₁₉	—	4	2	no	—
265	C₄×C₁₉	—	4	2	no	—
266	C₄×C₁₉	—	4	1	no	—
267	C₄×C₁₉	—	4	1	no	—
268	C₄×C₁₉	—	4	1	no	—
269	C₄×C₁₉	—	16	1	no	—
270	#563	—	2	2	no	—
271	#557	C₄×C₁₉	1	1	yes	characteristic, complemented
272	#556	C₄×C₁₉	1	1	yes	characteristic, complemented
273	#554	—	2	1	no	—
274	#553	—	2	1	no	—
275	D₄×Q₈	—	2	1	no	—
276	D₄×Q₈	C₄×C₁₉	1	1	yes	characteristic, complemented
277	#548	—	2	1	no	—
278	#547	C₄×C₁₉	1	1	yes	characteristic, complemented
279	#544	—	2	1	no	—
280	#542	—	2	1	no	—
281	#541	—	2	1	no	—
282	#539	—	2	2	no	—
283	#536	—	2	1	no	—
284	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
285	#529	C₂²×C₁₉	1	1	yes	characteristic
286	#529	C₂²×C₁₉	1	1	yes	characteristic
287	#432	C₂²×C₁₉	1	1	yes	characteristic
288	#432	C₂²×C₁₉	1	1	yes	characteristic
289	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
290	#382	C₂²×C₁₉	1	1	yes	characteristic
291	#340	—	2	2	no	—
292	#332	—	2	2	no	—
293	#330	—	2	1	no	—
294	#330	—	2	1	no	—
295	#329	—	2	1	no	—
296	#329	—	2	1	no	—
297	#328	—	2	1	no	—
298	#328	—	2	1	no	—
299	#327	—	2	1	no	—
300	#327	—	2	1	no	—
301	C₂×C₁₉	—	2	1	no	—
302	C₂×C₁₉	—	2	1	no	—
303	C₂×C₁₉	—	8	1	no	—
304	C₂×C₁₉	—	8	1	no	—
305	C₂×C₁₉	#1793	1	1	yes	characteristic
306	C₂×C₁₉	#1795	1	1	yes	characteristic
307	C₂×C₁₉	#1796	1	1	yes	characteristic
308	C₂×#41	—	2	1	no	—
309	C₂²×Q₈	—	2	1	no	—
310	C₂²×Q₈	—	2	1	no	—
311	C₂²×C₈	—	2	1	no	—
312	C₄⋊Q₈	—	2	2	no	—
313	C₄⋊Q₈	—	2	1	no	—
314	C₄⋊Q₈	—	2	1	no	—
315	C₄⋊Q₈	—	2	1	no	—
316	C₄⋊Q₈	—	2	1	no	—
317	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
318	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
319	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
320	#126	—	2	2	no	—
321	#126	—	2	2	no	—
322	#126	—	2	2	no	—
323	#126	—	2	1	no	—
324	#126	—	2	1	no	—
325	#125	—	2	2	no	—
326	#125	—	2	2	no	—
327	#125	—	2	2	no	—
328	#125	—	2	1	no	—
329	#125	D₄×C₁₉	1	1	yes	characteristic
330	#125	D₄×C₁₉	1	1	yes	characteristic
331	#124	—	2	2	no	—
332	#124	—	2	1	no	—
333	#124	D₄×C₁₉	1	1	yes	characteristic
334	#124	D₄×C₁₉	1	1	yes	characteristic
335	#123	—	2	2	no	—
336	#123	—	2	2	no	—
337	#123	—	2	1	no	—
338	#123	—	2	1	no	—
339	#123	—	2	2	no	—
340	C₂²⋊Q₈	—	2	2	no	—
341	C₂²⋊Q₈	—	2	2	no	—
342	C₂²⋊Q₈	—	2	2	no	—
343	C₂²⋊Q₈	—	2	2	no	—
344	C₂²⋊Q₈	—	2	2	no	—
345	C₂²⋊Q₈	—	2	1	no	—
346	C₂²⋊Q₈	—	2	2	no	—
347	C₂²⋊Q₈	—	2	1	no	—
348	C₂²⋊Q₈	—	2	1	no	—
349	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
350	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
351	#121	—	2	2	no	—
352	#121	—	2	1	no	—
353	#121	D₄×C₁₉	1	1	yes	characteristic
354	#121	D₄×C₁₉	1	1	yes	characteristic
355	C₄×Q₈	—	2	1	no	—
356	C₄×Q₈	—	2	1	no	—
357	C₄×Q₈	—	2	1	no	—
358	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
359	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
360	C₄×D₄	—	2	2	no	—
361	C₄×D₄	—	2	2	no	—
362	C₄×D₄	—	2	1	no	—
363	C₄×D₄	—	2	1	no	—
364	C₄×D₄	—	2	1	no	—
365	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
366	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
367	#117	—	2	1	no	—
368	#117	—	2	1	no	—
369	#117	—	2	1	no	—
370	C₂×C₄⋊C₄	—	2	1	no	—
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	—	2	1	no	—
373	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
374	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
375	C₄⋊C₈	—	2	1	no	—
376	C₄⋊C₈	—	2	1	no	—
377	C₂²⋊C₈	—	2	1	no	—
378	C₂²⋊C₈	—	2	1	no	—
379	#97	—	2	1	no	—
380	#97	—	2	1	no	—
381	#97	—	2	1	no	—
382	#97	—	2	1	no	—
383	#95	—	2	1	no	—
384	#95	—	2	1	no	—
385	C₁₉	#8499	1	1	yes	characteristic, direct product factor, Sylow
386	#41	—	8	2	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	—	2	1	no	—
389	C₂×Q₈	—	2	1	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	8	2	no	—
392	C₂×Q₈	—	8	2	no	—
393	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
394	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
399	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	4	1	no	—
406	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
407	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
408	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	4	1	no	—
411	C₂×C₈	—	4	1	no	—
412	C₂×C₈	—	4	1	no	—
413	C₂×C₈	—	4	1	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	4	2	no	—
433	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
434	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
435	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
436	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
437	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
438	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
439	C₂²⋊C₄	—	2	2	no	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	2	2	no	—
443	C₂²⋊C₄	—	2	1	no	—
444	C₂²⋊C₄	—	2	1	no	—
445	C₂²⋊C₄	—	2	1	no	—
446	C₂²⋊C₄	—	2	1	no	—
447	C₂²⋊C₄	—	2	1	no	—
448	C₂²⋊C₄	—	2	1	no	—
449	C₂²⋊C₄	—	2	1	no	—
450	C₂²⋊C₄	—	2	1	no	—
451	C₂²⋊C₄	—	2	1	no	—
452	C₂²⋊C₄	—	2	1	no	—
453	C₄²	—	2	2	no	—
454	C₄²	—	2	2	no	—
455	C₄²	—	2	1	no	—
456	C₄²	—	2	1	no	—
457	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
458	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
459	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
460	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
461	C₂³	—	2	1	no	—
462	C₂³	—	2	1	no	—
463	C₂³	C₁₉×#120	1	1	yes	characteristic
464	Q₈	—	4	1	no	—
465	Q₈	—	4	1	no	—
466	Q₈	—	4	2	no	—
467	Q₈	—	4	2	no	—
468	Q₈	—	8	2	no	—
469	Q₈	—	8	2	no	—
470	D₄	—	4	1	no	—
471	D₄	—	4	1	no	—
472	D₄	—	4	1	no	—
473	D₄	—	4	1	no	—
474	D₄	—	4	1	no	—
475	D₄	—	4	1	no	—
476	D₄	—	8	2	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	8	2	no	—
492	C₂×C₄	—	8	2	no	—
493	C₂×C₄	—	8	2	no	—
494	C₂×C₄	—	8	1	no	—
495	C₂×C₄	—	8	1	no	—
496	C₂×C₄	—	8	1	no	—
497	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
498	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
499	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
500	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
501	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
502	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
503	C₈	—	4	2	no	—
504	C₈	—	8	1	no	—
505	C₈	—	8	1	no	—
506	C₂²	—	2	1	no	—
507	C₂²	—	2	1	no	—
508	C₂²	—	4	1	no	—
509	C₂²	—	4	1	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	1	no	—
512	C₂²	—	4	1	no	—
513	C₂²	—	4	1	no	—
514	C₂²	C₁₉×#379	1	1	yes	characteristic
515	C₂²	C₁₉×#454	1	1	yes	characteristic
516	C₂²	C₁₉×#456	1	1	yes	characteristic
517	C₄	—	2	1	no	—
518	C₄	—	2	1	no	—
519	C₄	—	2	1	no	—
520	C₄	—	2	1	no	—
521	C₄	—	2	1	no	—
522	C₄	—	2	1	no	—
523	C₄	—	4	1	no	—
524	C₄	—	4	1	no	—
525	C₄	—	4	1	no	—
526	C₄	—	4	2	no	—
527	C₄	—	4	2	no	—
528	C₄	—	4	1	no	—
529	C₄	—	4	1	no	—
530	C₄	—	4	1	no	—
531	C₄	—	16	1	no	—
532	C₂	—	2	1	no	—
533	C₂	—	2	1	no	—
534	C₂	—	8	1	no	—
535	C₂	—	8	1	no	—
536	C₂	C₁₉×#1793	1	1	yes	characteristic
537	C₂	C₁₉×#1795	1	1	yes	characteristic
538	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×#3552	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×#1993	C₂	semidirect
3. C₁₉×#1556	C₂	semidirect
4. C₁₉×#1532	C₂	semidirect
5. C₁₉×#1532	C₂	semidirect
6. C₁₉×#1512	C₂	semidirect
7. C₁₉×#1512	C₂	semidirect
9. C₁₉×#557	C₄	semidirect
10. C₁₉×#556	C₄	semidirect
14. D₄×Q₈×C₁₉	C₄	semidirect
16. C₁₉×#547	C₄	semidirect
191. #8499	C₁₉	direct (N × H)
238. #1993	C₂×C₁₉	semidirect
239. #1556	C₂×C₁₉	semidirect
240. #1532	C₂×C₁₉	semidirect
241. #1532	C₂×C₁₉	semidirect
242. #1512	C₂×C₁₉	semidirect
243. #1512	C₂×C₁₉	semidirect
271. #557	C₄×C₁₉	semidirect
272. #556	C₄×C₁₉	semidirect
276. D₄×Q₈	C₄×C₁₉	semidirect
278. #547	C₄×C₁₉	semidirect
385. C₁₉	#8499	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×#3552	2
C₁₉×#1993	2
C₁₉×#1556	2
C₁₉×#1532	2
C₁₉×#1512	2
#8499	19

Subgroups — C19×#8499 #18014458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8499 #18014458