Subgroups — C₄×#11926268 #18073041

Order 4864.

946 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₂²⋊(C₁₉⋊C₈)	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×C₂²⋊(C₁₉⋊C₈)	C₂²	1	4	yes	—
6	C₂×C₄×C₁₉⋊C₈	—	2	2	no	—
7	#11926299	—	2	2	no	—
8	#11926268	C₄	1	8	yes	direct product factor
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	C₈	1	4	yes	complemented
36	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
37	C₂×C₄²×C₁₉	—	2	1	no	—
38	C₂×C₄²×C₁₉	—	2	1	no	—
39	C₂×C₄²×C₁₉	—	4	2	no	—
40	C₂×C₄²×C₁₉	—	4	2	no	—
41	C₂×C₄²×C₁₉	D₄	1	2	yes	—
42	C₂×C₄²×C₁₉	D₄	1	2	yes	—
43	C₂²×C₁₉⋊C₈	—	2	4	no	—
44	C₁₉×#95	—	2	2	no	—
45	C₁₉×#95	—	2	2	no	—
46	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
47	C₂²⋊(C₁₉⋊C₈)	C₂×C₄	1	8	yes	complemented
48	C₄×C₁₉⋊C₈	—	4	4	no	—
49	C₂⁴×C₁₉	—	2	1	no	—
50	C₂⁴×C₁₉	—	2	1	no	—
51	C₂⁴×C₁₉	—	2	1	no	—
52	C₂⁴×C₁₉	—	2	1	no	—
53	C₂⁴×C₁₉	—	4	1	no	—
54	C₂⁴×C₁₉	—	4	1	no	—
55	C₂⁴×C₁₉	—	4	1	no	—
56	C₂⁴×C₁₉	—	4	1	no	—
57	C₂⁴×C₁₉	C₄²	1	2	yes	—
58	C₂⁴×C₁₉	C₂×C₈	1	2	yes	—
59	C₂⁴×C₁₉	C₂×C₈	1	2	yes	—
60	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	—	2	2	no	—
62	C₂²×C₄×C₁₉	—	2	2	no	—
63	C₂²×C₄×C₁₉	—	2	1	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	4	no	—
70	C₂²×C₄×C₁₉	—	2	4	no	—
71	C₂²×C₄×C₁₉	—	4	1	no	—
72	C₂²×C₄×C₁₉	—	4	1	no	—
73	C₂²×C₄×C₁₉	—	4	1	no	—
74	C₂²×C₄×C₁₉	—	4	1	no	—
75	C₂²×C₄×C₁₉	—	4	2	no	—
76	C₂²×C₄×C₁₉	—	4	2	no	—
77	C₂²×C₄×C₁₉	—	4	8	no	—
78	C₂²×C₄×C₁₉	—	4	8	no	—
79	C₂²×C₄×C₁₉	—	4	2	no	—
80	C₂²×C₄×C₁₉	—	4	2	no	—
81	C₂²×C₄×C₁₉	—	4	1	no	—
82	C₂²×C₄×C₁₉	—	4	1	no	—
83	C₂²×C₄×C₁₉	—	4	1	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	C₄²	1	2	yes	—
88	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
90	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
92	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
93	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
94	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
95	C₂²×C₄×C₁₉	M₁₆	1	2	yes	—
96	C₂²×C₄×C₁₉	M₁₆	1	2	yes	—
97	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₁₉	#41	1	2	yes	—
100	C₂²⋊C₄×C₁₉	—	2	8	no	—
101	C₂²⋊C₄×C₁₉	—	2	8	no	—
102	C₄²×C₁₉	—	2	4	no	—
103	C₄²×C₁₉	—	4	2	no	—
104	C₄²×C₁₉	—	4	2	no	—
105	C₄²×C₁₉	—	4	2	no	—
106	C₂×C₁₉⋊C₈	—	2	8	no	—
107	C₂×C₁₉⋊C₈	—	4	4	no	—
108	C₂×C₁₉⋊C₈	—	4	4	no	—
109	C₄×#323	—	19	1	no	maximal, Sylow
110	C₂³×C₁₉	—	2	1	no	—
111	C₂³×C₁₉	—	2	1	no	—
112	C₂³×C₁₉	—	2	1	no	—
113	C₂³×C₁₉	—	2	1	no	—
114	C₂³×C₁₉	—	2	2	no	—
115	C₂³×C₁₉	—	2	2	no	—
116	C₂³×C₁₉	—	2	2	no	—
117	C₂³×C₁₉	—	2	2	no	—
118	C₂³×C₁₉	—	2	2	no	—
119	C₂³×C₁₉	—	2	2	no	—
120	C₂³×C₁₉	—	4	2	no	—
121	C₂³×C₁₉	—	4	2	no	—
122	C₂³×C₁₉	—	4	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	1	no	—
133	C₂³×C₁₉	—	4	1	no	—
134	C₂³×C₁₉	—	4	1	no	—
135	C₂³×C₁₉	—	4	1	no	—
136	C₂³×C₁₉	C₄×C₈	1	4	yes	complemented
137	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
138	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
139	C₂³×C₁₉	#117	1	1	yes	characteristic
140	C₂³×C₁₉	C₂²×C₈	1	1	yes	characteristic
141	C₂³×C₁₉	C₂²×C₈	1	1	yes	characteristic
142	C₂³×C₁₉	C₂×M₁₆	1	1	yes	characteristic
143	C₂³×C₁₉	C₂×M₁₆	1	1	yes	characteristic
144	C₂×C₄×C₁₉	—	2	2	no	—
145	C₂×C₄×C₁₉	—	2	2	no	—
146	C₂×C₄×C₁₉	—	2	1	no	—
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	4	no	—
151	C₂×C₄×C₁₉	—	2	4	no	—
152	C₂×C₄×C₁₉	—	2	2	no	—
153	C₂×C₄×C₁₉	—	2	2	no	—
154	C₂×C₄×C₁₉	—	2	2	no	—
155	C₂×C₄×C₁₉	—	4	2	no	—
156	C₂×C₄×C₁₉	—	4	2	no	—
157	C₂×C₄×C₁₉	—	4	2	no	—
158	C₂×C₄×C₁₉	—	4	2	no	—
159	C₂×C₄×C₁₉	—	4	8	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	4	8	no	—
170	C₂×C₄×C₁₉	—	4	2	no	—
171	C₂×C₄×C₁₉	—	4	2	no	—
172	C₂×C₄×C₁₉	—	4	2	no	—
173	C₂×C₄×C₁₉	C₂²⋊C₈	1	4	yes	—
174	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
175	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
176	C₂×C₄×C₁₉	#99	1	2	yes	—
177	C₂×C₄×C₁₉	#100	1	2	yes	—
178	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
179	C₁₉⋊C₈	—	4	8	no	—
180	C₂×C₄×C₂²⋊C₄	D₁₉	1	1	yes	characteristic
181	C₄×C₂²⋊C₈	—	19	2	no	—
182	C₂×#323	—	19	2	no	—
183	#1280	—	19	2	no	—
184	C₂²×C₁₉	—	2	1	no	—
185	C₂²×C₁₉	—	2	1	no	—
186	C₂²×C₁₉	—	2	1	no	—
187	C₂²×C₁₉	—	2	1	no	—
188	C₂²×C₁₉	—	2	1	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	4	no	—
197	C₂²×C₁₉	—	4	4	no	—
198	C₂²×C₁₉	—	4	4	no	—
199	C₂²×C₁₉	—	4	4	no	—
200	C₂²×C₁₉	—	4	4	no	—
201	C₂²×C₁₉	—	4	2	no	—
202	C₂²×C₁₉	—	4	2	no	—
203	C₂²×C₁₉	—	4	2	no	—
204	C₂²×C₁₉	—	4	2	no	—
205	C₂²×C₁₉	—	4	2	no	—
206	C₂²×C₁₉	—	4	2	no	—
207	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
208	C₂²×C₁₉	C₂×C₄×C₈	1	1	yes	characteristic
209	C₂²×C₁₉	C₄×M₁₆	1	1	yes	characteristic
210	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
211	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
212	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
213	C₂²×C₁₉	#410	1	1	yes	characteristic
214	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
215	C₂²×C₁₉	#413	1	1	yes	characteristic
216	C₂²×C₁₉	#431	1	1	yes	characteristic
217	C₂²×C₁₉	#431	1	1	yes	characteristic
218	C₄×C₁₉	—	2	2	no	—
219	C₄×C₁₉	—	2	4	no	—
220	C₄×C₁₉	—	2	4	no	—
221	C₄×C₁₉	—	4	2	no	—
222	C₄×C₁₉	—	4	2	no	—
223	C₄×C₁₉	—	4	2	no	—
224	C₄×C₁₉	#323	1	4	yes	complemented
225	C₂⁴×C₄	Dic₁₉	1	1	yes	characteristic
226	C₂²×C₂²⋊C₄	Dic₁₉	1	1	yes	characteristic
227	C₂²×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
228	C₂²×C₄²	Dic₁₉	1	1	yes	characteristic
229	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
230	C₂×C₂²⋊C₈	—	19	4	no	—
231	C₂×C₄×C₈	—	38	2	no	—
232	C₄×C₂²⋊C₄	—	2	2	no	—
233	C₄×C₂²⋊C₄	—	2	2	no	—
234	C₂×#95	Dic₁₉	1	1	yes	characteristic
235	C₂×#95	C₂×D₁₉	1	1	yes	characteristic
236	#336	—	38	2	no	—
237	#323	—	19	8	no	—
238	C₂×C₁₉	—	2	1	no	—
239	C₂×C₁₉	—	2	1	no	—
240	C₂×C₁₉	—	2	1	no	—
241	C₂×C₁₉	—	2	1	no	—
242	C₂×C₁₉	—	4	4	no	—
243	C₂×C₁₉	C₂×#323	1	1	yes	characteristic
244	C₂×C₁₉	#1458	1	1	yes	characteristic
245	C₂×C₁₉	#1459	1	1	yes	characteristic
246	C₂×C₁₉	#1460	1	1	yes	characteristic
247	C₂×C₁₉	C₄×C₂²⋊C₈	1	1	yes	characteristic
248	C₂×C₁₉	C₄×#99	1	1	yes	characteristic
249	C₂×C₁₉	C₄×#100	1	1	yes	characteristic
250	C₂⁵	C₂×Dic₁₉	1	1	yes	characteristic
251	C₂³×C₄	—	2	2	no	—
252	C₂³×C₄	—	2	1	no	—
253	C₂³×C₄	—	2	1	no	—
254	C₂³×C₄	—	4	2	no	—
255	C₂³×C₄	—	4	2	no	—
256	C₂³×C₄	C₁₉⋊C₈	1	4	yes	complemented
257	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
258	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
259	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
260	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
261	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
262	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
263	C₂²×C₈	—	38	4	no	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₂²⋊C₄	C₁₉⋊C₈	1	4	yes	complemented
269	C₂×C₂²⋊C₄	C₄×D₁₉	1	4	yes	—
270	C₂×C₄²	—	2	1	no	—
271	C₂×C₄²	—	2	1	no	—
272	C₂×C₄²	—	4	2	no	—
273	C₂×C₄²	—	4	2	no	—
274	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
275	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
276	C₂²⋊C₈	—	19	8	no	—
277	C₂²⋊C₈	—	38	4	no	—
278	C₄×C₈	—	76	4	no	—
279	#95	—	2	2	no	—
280	#95	—	2	2	no	—
281	C₁₉	C₄×#323	1	1	yes	characteristic, complemented, Sylow
282	C₂⁴	—	2	1	no	—
283	C₂⁴	—	2	1	no	—
284	C₂⁴	—	2	1	no	—
285	C₂⁴	—	2	1	no	—
286	C₂⁴	—	4	1	no	—
287	C₂⁴	—	4	1	no	—
288	C₂⁴	—	4	1	no	—
289	C₂⁴	—	4	1	no	—
290	C₂⁴	C₂×C₁₉⋊C₈	1	2	yes	—
291	C₂⁴	C₂×C₁₉⋊C₈	1	2	yes	—
292	C₂⁴	C₄×Dic₁₉	1	2	yes	—
293	C₂⁴	C₂²×Dic₁₉	1	1	yes	characteristic
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	4	1	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	—	4	1	no	—
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	—	4	2	no	—
309	C₂²×C₄	—	4	2	no	—
310	C₂²×C₄	—	4	8	no	—
311	C₂²×C₄	—	4	8	no	—
312	C₂²×C₄	—	4	2	no	—
313	C₂²×C₄	—	4	2	no	—
314	C₂²×C₄	—	4	1	no	—
315	C₂²×C₄	—	4	1	no	—
316	C₂²×C₄	—	4	1	no	—
317	C₂²×C₄	—	4	1	no	—
318	C₂²×C₄	—	4	1	no	—
319	C₂²×C₄	—	4	1	no	—
320	C₂²×C₄	C₂×C₁₉⋊C₈	1	2	yes	—
321	C₂²×C₄	C₂×C₁₉⋊C₈	1	2	yes	—
322	C₂²×C₄	C₂×C₁₉⋊C₈	1	2	yes	—
323	C₂²×C₄	C₂×C₁₉⋊C₈	1	2	yes	—
324	C₂²×C₄	#64520	1	2	yes	—
325	C₂²×C₄	#64520	1	2	yes	—
326	C₂²×C₄	C₄×Dic₁₉	1	2	yes	—
327	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
328	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
329	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
330	C₂²×C₄	C₂×C₄×D₁₉	1	2	yes	—
331	C₂²×C₄	#64541	1	2	yes	—
332	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
333	C₂×C₈	—	38	8	no	—
334	C₂×C₈	—	76	4	no	—
335	C₂×C₈	—	76	4	no	—
336	C₂²⋊C₄	—	2	8	no	—
337	C₂²⋊C₄	—	2	8	no	—
338	C₄²	—	2	4	no	—
339	C₄²	—	4	2	no	—
340	C₄²	—	4	2	no	—
341	C₄²	—	4	2	no	—
342	C₂³	—	2	1	no	—
343	C₂³	—	2	1	no	—
344	C₂³	—	2	1	no	—
345	C₂³	—	2	1	no	—
346	C₂³	—	2	2	no	—
347	C₂³	—	2	2	no	—
348	C₂³	—	2	2	no	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	4	2	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	4	2	no	—
360	C₂³	—	4	2	no	—
361	C₂³	—	4	2	no	—
362	C₂³	—	4	2	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	1	no	—
365	C₂³	—	4	1	no	—
366	C₂³	—	4	1	no	—
367	C₂³	—	4	1	no	—
368	C₂³	C₄×C₁₉⋊C₈	1	4	yes	complemented
369	C₂³	C₂²×C₁₉⋊C₈	1	1	yes	characteristic
370	C₂³	C₂²×C₁₉⋊C₈	1	1	yes	characteristic
371	C₂³	C₂×#64520	1	1	yes	characteristic
372	C₂³	C₂×#64520	1	1	yes	characteristic
373	C₂³	C₂×C₄×Dic₁₉	1	1	yes	characteristic
374	C₂³	#10597372	1	1	yes	characteristic
375	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	8	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	8	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	4	yes	—
406	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
407	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
408	C₂×C₄	#10597290	1	2	yes	—
409	C₂×C₄	#10597291	1	2	yes	—
410	C₂×C₄	C₄×C₂²⋊D₁₉	1	4	yes	—
411	C₈	—	76	8	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	4	no	—
425	C₂²	—	4	4	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	4	4	no	—
428	C₂²	—	4	4	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	2	no	—
435	C₂²	C₄×C₂²⋊Dic₁₉	1	1	yes	characteristic
436	C₂²	C₂×C₄×C₁₉⋊C₈	1	1	yes	characteristic
437	C₂²	C₄×#64520	1	1	yes	characteristic
438	C₂²	C₂×C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
439	C₂²	C₂×C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
440	C₂²	C₂×#10597291	1	1	yes	characteristic
441	C₂²	#11926518	1	1	yes	characteristic
442	C₂²	C₂×#10597290	1	1	yes	characteristic
443	C₂²	#11926528	1	1	yes	characteristic
444	C₂²	#11926597	1	1	yes	characteristic
445	C₂²	#11926597	1	1	yes	characteristic
446	C₄	—	2	4	no	—
447	C₄	—	2	2	no	—
448	C₄	—	2	4	no	—
449	C₄	—	4	2	no	—
450	C₄	—	4	2	no	—
451	C₄	—	4	2	no	—
452	C₄	#11926268	1	4	yes	direct product factor
453	C₂	—	2	1	no	—
454	C₂	—	2	1	no	—
455	C₂	—	2	1	no	—
456	C₂	—	2	1	no	—
457	C₂	—	4	4	no	—
458	C₂	C₂×#11926268	1	1	yes	characteristic
459	C₂	#14561949	1	1	yes	characteristic
460	C₂	#14561953	1	1	yes	characteristic
461	C₂	#14561956	1	1	yes	characteristic
462	C₂	C₄×C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
463	C₂	C₄×#10597291	1	1	yes	characteristic
464	C₂	C₄×#10597290	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²⋊Dic₁₉
commutator	C₂²×C₁₉	C₂×C₄×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	C₄×#323
LCS	G ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×C₄×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₄×C₂²⋊(C₁₉⋊C₈)	C₂	semidirect
3. #14561478	C₂	semidirect
8. #11926268	C₄	direct (N × H)
24. C₂³×C₄×C₁₉	C₈	semidirect
35. C₂×C₂²⋊C₄×C₁₉	C₈	semidirect
47. C₂²⋊(C₁₉⋊C₈)	C₂×C₄	semidirect
136. C₂³×C₁₉	C₄×C₈	semidirect
224. C₄×C₁₉	#323	semidirect
256. C₂³×C₄	C₁₉⋊C₈	semidirect
268. C₂×C₂²⋊C₄	C₁₉⋊C₈	semidirect
281. C₁₉	C₄×#323	semidirect
368. C₂³	C₄×C₁₉⋊C₈	semidirect
452. C₄	#11926268	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₂²⋊(C₁₉⋊C₈)	2
C₂×#11926268	2
#14561478	2
C₂×C₄×C₂²⋊C₄×C₁₉	2
C₄×#323	19

Subgroups — C4×#11926268 #18073041

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11926268 #18073041