Subgroups — #18075196

Order 4864.

898 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563615	C₂	1	2	yes	maximal, complemented
2	C₂×#11926268	C₂	1	2	yes	maximal
3	#14561478	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
6	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	4	yes	—
7	#11926299	—	2	2	no	—
8	#11926268	—	2	4	no	—
9	C₂⁴×C₄×C₁₉	C₄	1	1	yes	characteristic
10	C₂²×C₂²⋊C₄×C₁₉	C₄	1	1	yes	characteristic
11	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₁₉	C₄	1	1	yes	characteristic
13	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
14	C₄×C₂²⋊C₄×C₁₉	—	2	2	no	—
15	C₄×C₂²⋊C₄×C₁₉	—	2	2	no	—
16	C₂×C₁₉×#95	C₄	1	1	yes	characteristic
17	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
18	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂³×C₄×C₁₉	—	2	1	no	—
20	C₂³×C₄×C₁₉	—	2	1	no	—
21	C₂³×C₄×C₁₉	—	2	2	no	—
22	C₂³×C₄×C₁₉	—	4	2	no	—
23	C₂³×C₄×C₁₉	—	4	2	no	—
24	C₂³×C₄×C₁₉	C₈	1	4	yes	complemented
25	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
32	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
33	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
34	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
35	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
36	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
37	C₂×C₂²⋊C₄×C₁₉	Q₈	1	2	yes	—
38	C₂×C₄²×C₁₉	—	2	1	no	—
39	C₂×C₄²×C₁₉	—	2	1	no	—
40	C₂×C₄²×C₁₉	—	4	2	no	—
41	C₂×C₄²×C₁₉	—	4	2	no	—
42	C₂×C₄²×C₁₉	D₄	1	2	yes	—
43	C₂×C₄²×C₁₉	D₄	1	2	yes	—
44	C₂²×C₁₉⋊C₈	—	2	4	no	—
45	C₁₉×#95	—	2	2	no	—
46	C₁₉×#95	—	2	2	no	—
47	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
48	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
49	C₄⋊(C₁₉⋊C₈)	—	4	4	no	—
50	C₂⁴×C₁₉	—	2	1	no	—
51	C₂⁴×C₁₉	—	2	1	no	—
52	C₂⁴×C₁₉	—	2	1	no	—
53	C₂⁴×C₁₉	—	2	1	no	—
54	C₂⁴×C₁₉	—	4	1	no	—
55	C₂⁴×C₁₉	—	4	1	no	—
56	C₂⁴×C₁₉	—	4	1	no	—
57	C₂⁴×C₁₉	—	4	1	no	—
58	C₂⁴×C₁₉	C₄⋊C₄	1	2	yes	—
59	C₂⁴×C₁₉	C₂×C₈	1	2	yes	—
60	C₂⁴×C₁₉	M₁₆	1	2	yes	—
61	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	—	2	2	no	—
63	C₂²×C₄×C₁₉	—	2	2	no	—
64	C₂²×C₄×C₁₉	—	2	1	no	—
65	C₂²×C₄×C₁₉	—	2	1	no	—
66	C₂²×C₄×C₁₉	—	2	1	no	—
67	C₂²×C₄×C₁₉	—	2	1	no	—
68	C₂²×C₄×C₁₉	—	2	1	no	—
69	C₂²×C₄×C₁₉	—	2	1	no	—
70	C₂²×C₄×C₁₉	—	2	1	no	—
71	C₂²×C₄×C₁₉	—	2	1	no	—
72	C₂²×C₄×C₁₉	—	2	4	no	—
73	C₂²×C₄×C₁₉	—	2	4	no	—
74	C₂²×C₄×C₁₉	—	4	1	no	—
75	C₂²×C₄×C₁₉	—	4	1	no	—
76	C₂²×C₄×C₁₉	—	4	1	no	—
77	C₂²×C₄×C₁₉	—	4	1	no	—
78	C₂²×C₄×C₁₉	—	4	2	no	—
79	C₂²×C₄×C₁₉	—	4	2	no	—
80	C₂²×C₄×C₁₉	—	4	8	no	—
81	C₂²×C₄×C₁₉	—	4	8	no	—
82	C₂²×C₄×C₁₉	—	4	2	no	—
83	C₂²×C₄×C₁₉	—	4	2	no	—
84	C₂²×C₄×C₁₉	—	4	1	no	—
85	C₂²×C₄×C₁₉	—	4	1	no	—
86	C₂²×C₄×C₁₉	—	4	1	no	—
87	C₂²×C₄×C₁₉	—	4	1	no	—
88	C₂²×C₄×C₁₉	—	4	1	no	—
89	C₂²×C₄×C₁₉	—	4	1	no	—
90	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
91	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
94	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
95	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
96	C₂²×C₄×C₁₉	M₁₆	1	2	yes	—
97	C₂²×C₄×C₁₉	M₁₆	1	2	yes	—
98	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	#41	1	2	yes	—
102	C₂²⋊C₄×C₁₉	—	2	8	no	—
103	C₂²⋊C₄×C₁₉	—	2	4	no	—
104	C₂²⋊C₄×C₁₉	—	2	4	no	—
105	C₄²×C₁₉	—	2	4	no	—
106	C₄²×C₁₉	—	4	2	no	—
107	C₄²×C₁₉	—	4	2	no	—
108	C₄²×C₁₉	—	4	2	no	—
109	C₂×C₁₉⋊C₈	—	4	4	no	—
110	C₂×C₁₉⋊C₈	—	4	4	no	—
111	C₂×C₁₉⋊C₈	—	4	4	no	—
112	#8557	—	19	1	no	maximal, Sylow
113	C₂³×C₁₉	—	2	1	no	—
114	C₂³×C₁₉	—	2	1	no	—
115	C₂³×C₁₉	—	2	1	no	—
116	C₂³×C₁₉	—	2	1	no	—
117	C₂³×C₁₉	—	2	2	no	—
118	C₂³×C₁₉	—	2	2	no	—
119	C₂³×C₁₉	—	2	2	no	—
120	C₂³×C₁₉	—	2	2	no	—
121	C₂³×C₁₉	—	2	2	no	—
122	C₂³×C₁₉	—	2	2	no	—
123	C₂³×C₁₉	—	4	2	no	—
124	C₂³×C₁₉	—	4	2	no	—
125	C₂³×C₁₉	—	4	2	no	—
126	C₂³×C₁₉	—	4	2	no	—
127	C₂³×C₁₉	—	4	2	no	—
128	C₂³×C₁₉	—	4	2	no	—
129	C₂³×C₁₉	—	4	2	no	—
130	C₂³×C₁₉	—	4	2	no	—
131	C₂³×C₁₉	—	4	2	no	—
132	C₂³×C₁₉	—	4	2	no	—
133	C₂³×C₁₉	—	4	2	no	—
134	C₂³×C₁₉	—	4	2	no	—
135	C₂³×C₁₉	—	4	1	no	—
136	C₂³×C₁₉	—	4	1	no	—
137	C₂³×C₁₉	—	4	1	no	—
138	C₂³×C₁₉	—	4	1	no	—
139	C₂³×C₁₉	C₄⋊C₈	1	4	yes	complemented
140	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
141	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂³×C₁₉	#117	1	1	yes	characteristic
143	C₂³×C₁₉	C₂²×C₈	1	1	yes	characteristic
144	C₂³×C₁₉	C₂×M₁₆	1	1	yes	characteristic
145	C₂³×C₁₉	C₂×M₁₆	1	1	yes	characteristic
146	C₂³×C₁₉	C₂×M₁₆	1	1	yes	characteristic
147	C₂×C₄×C₁₉	—	2	2	no	—
148	C₂×C₄×C₁₉	—	2	1	no	—
149	C₂×C₄×C₁₉	—	2	2	no	—
150	C₂×C₄×C₁₉	—	2	1	no	—
151	C₂×C₄×C₁₉	—	2	4	no	—
152	C₂×C₄×C₁₉	—	2	4	no	—
153	C₂×C₄×C₁₉	—	2	2	no	—
154	C₂×C₄×C₁₉	—	2	2	no	—
155	C₂×C₄×C₁₉	—	2	2	no	—
156	C₂×C₄×C₁₉	—	2	2	no	—
157	C₂×C₄×C₁₉	—	2	2	no	—
158	C₂×C₄×C₁₉	—	2	2	no	—
159	C₂×C₄×C₁₉	—	4	1	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	8	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	4	2	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	—	4	1	no	—
171	C₂×C₄×C₁₉	—	4	1	no	—
172	C₂×C₄×C₁₉	—	4	1	no	—
173	C₂×C₄×C₁₉	—	4	1	no	—
174	C₂×C₄×C₁₉	—	4	8	no	—
175	C₂×C₄×C₁₉	—	4	2	no	—
176	C₂×C₄×C₁₉	—	4	2	no	—
177	C₂×C₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
179	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
180	C₂×C₄×C₁₉	#99	1	2	yes	—
181	C₂×C₄×C₁₉	#100	1	2	yes	—
182	C₂×C₄×C₁₉	#121	1	2	yes	—
183	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
184	C₁₉⋊C₈	—	8	4	no	—
185	C₂×C₄×C₂²⋊C₄	D₁₉	1	1	yes	characteristic
186	#1797	—	19	2	no	—
187	C₂×#323	—	19	2	no	—
188	#1280	—	19	2	no	—
189	C₂²×C₁₉	—	2	1	no	—
190	C₂²×C₁₉	—	2	1	no	—
191	C₂²×C₁₉	—	2	1	no	—
192	C₂²×C₁₉	—	2	1	no	—
193	C₂²×C₁₉	—	2	1	no	—
194	C₂²×C₁₉	—	2	1	no	—
195	C₂²×C₁₉	—	2	1	no	—
196	C₂²×C₁₉	—	2	1	no	—
197	C₂²×C₁₉	—	2	1	no	—
198	C₂²×C₁₉	—	2	1	no	—
199	C₂²×C₁₉	—	2	1	no	—
200	C₂²×C₁₉	—	2	1	no	—
201	C₂²×C₁₉	—	2	4	no	—
202	C₂²×C₁₉	—	4	4	no	—
203	C₂²×C₁₉	—	4	4	no	—
204	C₂²×C₁₉	—	4	4	no	—
205	C₂²×C₁₉	—	4	4	no	—
206	C₂²×C₁₉	—	4	2	no	—
207	C₂²×C₁₉	—	4	2	no	—
208	C₂²×C₁₉	—	4	2	no	—
209	C₂²×C₁₉	—	4	2	no	—
210	C₂²×C₁₉	—	4	2	no	—
211	C₂²×C₁₉	—	4	2	no	—
212	C₂²×C₁₉	#380	1	1	yes	characteristic
213	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
214	C₂²×C₁₉	#407	1	1	yes	characteristic
215	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
216	C₂²×C₁₉	#410	1	1	yes	characteristic
217	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
218	C₂²×C₁₉	#413	1	1	yes	characteristic
219	C₂²×C₁₉	C₂×C₄⋊C₈	1	1	yes	characteristic
220	C₂²×C₁₉	#423	1	1	yes	characteristic
221	C₂²×C₁₉	#431	1	1	yes	characteristic
222	C₂²×C₁₉	#432	1	1	yes	characteristic
223	C₄×C₁₉	—	2	2	no	—
224	C₄×C₁₉	—	2	2	no	—
225	C₄×C₁₉	—	2	2	no	—
226	C₄×C₁₉	—	4	2	no	—
227	C₄×C₁₉	—	4	2	no	—
228	C₄×C₁₉	—	4	2	no	—
229	C₄×C₁₉	—	4	2	no	—
230	C₄×C₁₉	#323	1	4	yes	complemented
231	C₂⁴×C₄	Dic₁₉	1	1	yes	characteristic
232	C₂²×C₂²⋊C₄	Dic₁₉	1	1	yes	characteristic
233	C₂²×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
234	C₂²×C₄²	Dic₁₉	1	1	yes	characteristic
235	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
236	C₂×C₄⋊C₈	—	38	2	no	—
237	C₂×C₂²⋊C₈	—	19	4	no	—
238	C₄×C₂²⋊C₄	—	2	2	no	—
239	C₄×C₂²⋊C₄	—	2	2	no	—
240	C₂×#95	Dic₁₉	1	1	yes	characteristic
241	C₂×#95	C₂×D₁₉	1	1	yes	characteristic
242	#336	—	38	2	no	—
243	#323	—	38	4	no	—
244	C₂×C₁₉	—	2	1	no	—
245	C₂×C₁₉	—	2	1	no	—
246	C₂×C₁₉	—	2	1	no	—
247	C₂×C₁₉	—	2	1	no	—
248	C₂×C₁₉	—	4	4	no	—
249	C₂×C₁₉	C₂×#323	1	1	yes	characteristic
250	C₂×C₁₉	#1458	1	1	yes	characteristic
251	C₂×C₁₉	#1465	1	1	yes	characteristic
252	C₂×C₁₉	#1466	1	1	yes	characteristic
253	C₂×C₁₉	#1797	1	1	yes	characteristic
254	C₂×C₁₉	#1799	1	1	yes	characteristic
255	C₂×C₁₉	#1800	1	1	yes	characteristic
256	C₂⁵	C₂×Dic₁₉	1	1	yes	characteristic
257	C₂³×C₄	—	2	2	no	—
258	C₂³×C₄	—	2	1	no	—
259	C₂³×C₄	—	2	1	no	—
260	C₂³×C₄	—	4	2	no	—
261	C₂³×C₄	—	4	2	no	—
262	C₂³×C₄	C₁₉⋊C₈	1	4	yes	complemented
263	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
264	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
265	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
266	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
267	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
268	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
269	C₂²×C₈	—	38	4	no	—
270	C₂×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	Dic₃₈	1	2	yes	—
276	C₂×C₂²⋊C₄	D₇₆	1	2	yes	—
277	C₂×C₄²	—	2	1	no	—
278	C₂×C₄²	—	2	1	no	—
279	C₂×C₄²	—	4	2	no	—
280	C₂×C₄²	—	4	2	no	—
281	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
282	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
283	C₄⋊C₈	—	76	4	no	—
284	C₂²⋊C₈	—	38	4	no	—
285	C₂²⋊C₈	—	38	4	no	—
286	#95	—	2	2	no	—
287	#95	—	2	2	no	—
288	C₁₉	#8557	1	1	yes	characteristic, complemented, Sylow
289	C₂⁴	—	2	1	no	—
290	C₂⁴	—	2	1	no	—
291	C₂⁴	—	2	1	no	—
292	C₂⁴	—	2	1	no	—
293	C₂⁴	—	4	1	no	—
294	C₂⁴	—	4	1	no	—
295	C₂⁴	—	4	1	no	—
296	C₂⁴	—	4	1	no	—
297	C₂⁴	C₂×C₁₉⋊C₈	1	2	yes	—
298	C₂⁴	#64520	1	2	yes	—
299	C₂⁴	C₄⋊Dic₁₉	1	2	yes	—
300	C₂⁴	C₂²×Dic₁₉	1	1	yes	characteristic
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	4	1	no	—
314	C₂²×C₄	—	4	1	no	—
315	C₂²×C₄	—	4	1	no	—
316	C₂²×C₄	—	4	1	no	—
317	C₂²×C₄	—	4	2	no	—
318	C₂²×C₄	—	4	2	no	—
319	C₂²×C₄	—	4	8	no	—
320	C₂²×C₄	—	4	8	no	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	—	4	2	no	—
323	C₂²×C₄	—	4	1	no	—
324	C₂²×C₄	—	4	1	no	—
325	C₂²×C₄	—	4	1	no	—
326	C₂²×C₄	—	4	1	no	—
327	C₂²×C₄	—	4	1	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	C₂×C₁₉⋊C₈	1	2	yes	—
330	C₂²×C₄	C₂×C₁₉⋊C₈	1	2	yes	—
331	C₂²×C₄	#64520	1	2	yes	—
332	C₂²×C₄	#64520	1	2	yes	—
333	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
334	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
335	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
336	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
337	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
338	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
339	C₂²×C₄	#64541	1	2	yes	—
340	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
341	C₂×C₈	—	76	4	no	—
342	C₂×C₈	—	76	4	no	—
343	C₂×C₈	—	76	4	no	—
344	C₂²⋊C₄	—	2	8	no	—
345	C₂²⋊C₄	—	2	4	no	—
346	C₂²⋊C₄	—	2	4	no	—
347	C₄²	—	2	4	no	—
348	C₄²	—	4	2	no	—
349	C₄²	—	4	2	no	—
350	C₄²	—	4	2	no	—
351	C₂³	—	2	1	no	—
352	C₂³	—	2	1	no	—
353	C₂³	—	2	1	no	—
354	C₂³	—	2	1	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	2	2	no	—
357	C₂³	—	2	2	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	2	no	—
360	C₂³	—	2	2	no	—
361	C₂³	—	4	2	no	—
362	C₂³	—	4	2	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	4	2	no	—
367	C₂³	—	4	2	no	—
368	C₂³	—	4	2	no	—
369	C₂³	—	4	2	no	—
370	C₂³	—	4	2	no	—
371	C₂³	—	4	2	no	—
372	C₂³	—	4	2	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	1	no	—
375	C₂³	—	4	1	no	—
376	C₂³	—	4	1	no	—
377	C₂³	C₄⋊(C₁₉⋊C₈)	1	4	yes	complemented
378	C₂³	C₂²×C₁₉⋊C₈	1	1	yes	characteristic
379	C₂³	C₂×#64520	1	1	yes	characteristic
380	C₂³	C₂×#64520	1	1	yes	characteristic
381	C₂³	C₂×#64520	1	1	yes	characteristic
382	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
383	C₂³	#10597372	1	1	yes	characteristic
384	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	8	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	8	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
417	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
418	C₂×C₄	#10597290	1	2	yes	—
419	C₂×C₄	#10597291	1	2	yes	—
420	C₂×C₄	#10597370	1	2	yes	—
421	C₂×C₄	#10597376	1	2	yes	—
422	C₈	—	152	4	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	4	no	—
436	C₂²	—	4	4	no	—
437	C₂²	—	4	4	no	—
438	C₂²	—	4	4	no	—
439	C₂²	—	4	4	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	4	2	no	—
446	C₂²	#11926404	1	1	yes	characteristic
447	C₂²	C₂×C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
448	C₂²	#11926508	1	1	yes	characteristic
449	C₂²	C₂×#10597291	1	1	yes	characteristic
450	C₂²	#11926518	1	1	yes	characteristic
451	C₂²	C₂×#10597290	1	1	yes	characteristic
452	C₂²	#11926528	1	1	yes	characteristic
453	C₂²	C₂×C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
454	C₂²	#11926568	1	1	yes	characteristic
455	C₂²	#11926597	1	1	yes	characteristic
456	C₂²	#11926601	1	1	yes	characteristic
457	C₄	—	2	2	no	—
458	C₄	—	2	2	no	—
459	C₄	—	2	2	no	—
460	C₄	—	4	2	no	—
461	C₄	—	4	2	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	2	no	—
464	C₄	#11926268	1	4	yes	complemented
465	C₂	—	2	1	no	—
466	C₂	—	2	1	no	—
467	C₂	—	2	1	no	—
468	C₂	—	2	1	no	—
469	C₂	—	4	4	no	—
470	C₂	C₂×#11926268	1	1	yes	characteristic
471	C₂	#14561949	1	1	yes	characteristic
472	C₂	#14561973	1	1	yes	characteristic
473	C₂	#14561976	1	1	yes	characteristic
474	C₂	#14563615	1	1	yes	characteristic
475	C₂	#14563623	1	1	yes	characteristic
476	C₂	#14563627	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂³×C₁₉	C₂²×C₈
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₄×C₂²⋊C₄×C₁₉	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁵×C₁₉	C₂×C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×C₄×C₂²⋊C₄	D₁₉
hypocenter	C₁₉	#8557
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×C₄×C₂²⋊C₄

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #14563615	C₂	semidirect
3. #14561478	C₂	semidirect
24. C₂³×C₄×C₁₉	C₈	semidirect
139. C₂³×C₁₉	C₄⋊C₈	semidirect
230. C₄×C₁₉	#323	semidirect
262. C₂³×C₄	C₁₉⋊C₈	semidirect
288. C₁₉	#8557	semidirect
377. C₂³	C₄⋊(C₁₉⋊C₈)	semidirect
464. C₄	#11926268	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#14563615	2
C₂×#11926268	2
#14561478	2
C₂×C₄×C₂²⋊C₄×C₁₉	2
#8557	19