Subgroups — #18090424

Order 4864.

934 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926299	C₂	1	2	yes	maximal
3	C₂×#11926299	C₂	1	2	yes	maximal
4	C₂×#11926299	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₁₉⋊C₈	C₂²	1	2	yes	—
7	C₂³×C₁₉⋊C₈	C₂²	1	2	yes	—
8	C₂×C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
9	C₂×C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
10	#11926299	—	2	4	no	—
11	#11926299	—	2	2	no	—
12	#11926299	—	2	4	no	—
13	C₂²×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
15	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
18	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
19	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
20	C₂×C₁₉×#95	C₄	1	1	yes	characteristic
21	C₂×C₁₉×#95	C₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
29	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
30	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
31	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
32	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
33	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
34	C₂×C₄⋊C₄×C₁₉	C₈	1	4	yes	complemented
35	C₂×C₄²×C₁₉	—	2	2	no	—
36	C₂×C₄²×C₁₉	—	2	1	no	—
37	C₂×C₄²×C₁₉	—	2	1	no	—
38	C₂×C₄²×C₁₉	—	2	1	no	—
39	C₂×C₄²×C₁₉	—	2	1	no	—
40	C₂×C₄²×C₁₉	—	2	2	no	—
41	C₂×C₄²×C₁₉	—	2	2	no	—
42	C₂×C₄²×C₁₉	—	2	1	no	—
43	C₂×C₄²×C₁₉	—	2	1	no	—
44	C₂×C₄²×C₁₉	—	2	2	no	—
45	C₂×C₄²×C₁₉	D₄	1	2	yes	—
46	C₂×C₄²×C₁₉	D₄	1	2	yes	—
47	C₂×C₄²×C₁₉	D₄	1	2	yes	—
48	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
49	C₂²×C₁₉⋊C₈	—	2	2	no	—
50	C₂²×C₁₉⋊C₈	—	2	2	no	—
51	C₂²×C₁₉⋊C₈	—	2	2	no	—
52	C₂²×C₁₉⋊C₈	—	2	2	no	—
53	C₂²×C₁₉⋊C₈	—	2	2	no	—
54	C₂²×C₁₉⋊C₈	—	2	2	no	—
55	C₂²×C₁₉⋊C₈	—	2	2	no	—
56	C₂²×C₁₉⋊C₈	—	2	2	no	—
57	C₂²×C₁₉⋊C₈	—	2	2	no	—
58	C₂²×C₁₉⋊C₈	—	2	2	no	—
59	C₂²×C₁₉⋊C₈	—	2	2	no	—
60	C₂²×C₁₉⋊C₈	—	2	2	no	—
61	C₂²×C₁₉⋊C₈	D₄	1	4	yes	—
62	C₂²×C₁₉⋊C₈	Q₈	1	4	yes	—
63	C₁₉×#95	—	2	2	no	—
64	C₁₉×#95	—	2	2	no	—
65	C₄⋊(C₁₉⋊C₈)	—	2	8	no	—
66	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₉	—	2	1	no	—
68	C₂²×C₄×C₁₉	—	2	1	no	—
69	C₂²×C₄×C₁₉	—	2	2	no	—
70	C₂²×C₄×C₁₉	—	2	1	no	—
71	C₂²×C₄×C₁₉	—	2	1	no	—
72	C₂²×C₄×C₁₉	—	2	2	no	—
73	C₂²×C₄×C₁₉	—	2	1	no	—
74	C₂²×C₄×C₁₉	—	2	1	no	—
75	C₂²×C₄×C₁₉	—	2	1	no	—
76	C₂²×C₄×C₁₉	—	2	1	no	—
77	C₂²×C₄×C₁₉	—	2	2	no	—
78	C₂²×C₄×C₁₉	—	2	2	no	—
79	C₂²×C₄×C₁₉	—	2	2	no	—
80	C₂²×C₄×C₁₉	—	2	1	no	—
81	C₂²×C₄×C₁₉	—	2	1	no	—
82	C₂²×C₄×C₁₉	—	2	1	no	—
83	C₂²×C₄×C₁₉	—	2	1	no	—
84	C₂²×C₄×C₁₉	—	2	2	no	—
85	C₂²×C₄×C₁₉	—	2	2	no	—
86	C₂²×C₄×C₁₉	—	2	2	no	—
87	C₂²×C₄×C₁₉	—	2	2	no	—
88	C₂²×C₄×C₁₉	—	2	2	no	—
89	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
90	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
91	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
92	C₂²×C₄×C₁₉	C₄⋊C₄	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	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	M₁₆	1	2	yes	—
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
105	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	#41	1	2	yes	—
108	C₂²×C₄×C₁₉	#41	1	2	yes	—
109	C₄⋊C₄×C₁₉	—	2	8	no	—
110	C₄⋊C₄×C₁₉	—	2	8	no	—
111	C₄²×C₁₉	—	2	2	no	—
112	C₄²×C₁₉	—	2	2	no	—
113	C₄²×C₁₉	—	2	2	no	—
114	C₄²×C₁₉	—	2	4	no	—
115	C₄²×C₁₉	—	2	2	no	—
116	C₄²×C₁₉	—	2	2	no	—
117	C₄²×C₁₉	—	2	2	no	—
118	C₄²×C₁₉	—	4	1	no	—
119	C₄²×C₁₉	—	4	2	no	—
120	C₄²×C₁₉	—	4	1	no	—
121	C₂×C₁₉⋊C₈	—	2	4	no	—
122	C₂×C₁₉⋊C₈	—	2	4	no	—
123	C₂×C₁₉⋊C₈	—	2	4	no	—
124	C₂×C₁₉⋊C₈	—	2	4	no	—
125	C₂×C₁₉⋊C₈	—	2	4	no	—
126	C₂×C₁₉⋊C₈	—	2	4	no	—
127	C₂×C₁₉⋊C₈	—	4	2	no	—
128	C₂×C₁₉⋊C₈	—	4	2	no	—
129	C₂×C₁₉⋊C₈	—	4	2	no	—
130	C₂×C₁₉⋊C₈	—	4	2	no	—
131	C₂×C₁₉⋊C₈	—	4	2	no	—
132	C₂×C₁₉⋊C₈	—	4	2	no	—
133	C₂×C₁₉⋊C₈	—	4	2	no	—
134	C₂×C₁₉⋊C₈	—	4	2	no	—
135	#11202	—	19	1	no	maximal, Sylow
136	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
137	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂³×C₁₉	#117	1	1	yes	characteristic
139	C₂³×C₁₉	C₄×D₄	1	2	yes	—
140	C₂³×C₁₉	C₄×Q₈	1	2	yes	—
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	C₂³×C₁₉	C₂×M₁₆	1	1	yes	characteristic
145	C₂³×C₁₉	#131	1	2	yes	—
146	C₂³×C₁₉	#131	1	2	yes	—
147	C₂×C₄×C₁₉	—	2	2	no	—
148	C₂×C₄×C₁₉	—	2	2	no	—
149	C₂×C₄×C₁₉	—	2	2	no	—
150	C₂×C₄×C₁₉	—	2	2	no	—
151	C₂×C₄×C₁₉	—	2	2	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	—	2	4	no	—
156	C₂×C₄×C₁₉	—	2	4	no	—
157	C₂×C₄×C₁₉	—	2	2	no	—
158	C₂×C₄×C₁₉	—	2	2	no	—
159	C₂×C₄×C₁₉	—	2	2	no	—
160	C₂×C₄×C₁₉	—	2	2	no	—
161	C₂×C₄×C₁₉	—	2	2	no	—
162	C₂×C₄×C₁₉	—	2	2	no	—
163	C₂×C₄×C₁₉	—	2	4	no	—
164	C₂×C₄×C₁₉	—	2	4	no	—
165	C₂×C₄×C₁₉	—	2	4	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	1	no	—
170	C₂×C₄×C₁₉	—	4	1	no	—
171	C₂×C₄×C₁₉	—	4	1	no	—
172	C₂×C₄×C₁₉	—	4	2	no	—
173	C₂×C₄×C₁₉	—	4	2	no	—
174	C₂×C₄×C₁₉	—	4	2	no	—
175	C₂×C₄×C₁₉	—	4	2	no	—
176	C₂×C₄×C₁₉	—	4	2	no	—
177	C₂×C₄×C₁₉	C₂²⋊C₈	1	4	yes	—
178	C₂×C₄×C₁₉	C₄⋊C₈	1	4	yes	complemented
179	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
182	C₂×C₄×C₁₉	#121	1	2	yes	—
183	C₂×C₄×C₁₉	#121	1	2	yes	—
184	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
185	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
186	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
187	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
188	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
189	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
190	C₂×C₄×C₁₉	#123	1	2	yes	—
191	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
192	C₂×C₄×C₁₉	#125	1	2	yes	—
193	C₂×C₄×C₁₉	#125	1	2	yes	—
194	C₂×C₄×C₁₉	#126	1	2	yes	—
195	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
197	C₁₉⋊C₈	—	4	4	no	—
198	C₁₉⋊C₈	—	4	4	no	—
199	C₂²×C₄⋊C₈	—	19	1	no	—
200	C₂×C₄×C₄⋊C₄	D₁₉	1	1	yes	characteristic
201	C₂×#336	—	19	2	no	—
202	C₂×#336	—	19	2	no	—
203	C₂×#336	—	19	1	no	—
204	C₂²×C₁₉	#380	1	1	yes	characteristic
205	C₂²×C₁₉	#386	1	1	yes	characteristic
206	C₂²×C₁₉	#387	1	2	yes	—
207	C₂²×C₁₉	#389	1	2	yes	—
208	C₂²×C₁₉	#391	1	1	yes	characteristic
209	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
210	C₂²×C₁₉	#407	1	1	yes	characteristic
211	C₂²×C₁₉	#408	1	1	yes	characteristic
212	C₂²×C₁₉	#408	1	1	yes	characteristic
213	C₂²×C₁₉	C₂×C₄⋊C₈	1	1	yes	characteristic
214	C₂²×C₁₉	#423	1	1	yes	characteristic
215	C₂²×C₁₉	#424	1	2	yes	—
216	C₂²×C₁₉	#431	1	1	yes	characteristic
217	C₂²×C₁₉	#432	1	1	yes	characteristic
218	C₂²×C₁₉	#433	1	2	yes	—
219	C₂²×C₁₉	C₈×D₄	1	2	yes	—
220	C₂²×C₁₉	#435	1	2	yes	—
221	C₂²×C₁₉	#435	1	2	yes	—
222	C₂²×C₁₉	#436	1	2	yes	—
223	C₂²×C₁₉	C₈×Q₈	1	2	yes	—
224	C₂²×C₁₉	#446	1	2	yes	—
225	C₂²×C₁₉	#446	1	2	yes	—
226	C₂²×C₁₉	#446	1	2	yes	—
227	C₄×C₁₉	—	2	4	no	—
228	C₄×C₁₉	—	2	4	no	—
229	C₄×C₁₉	—	4	2	no	—
230	C₄×C₁₉	—	4	2	no	—
231	C₄×C₁₉	—	4	2	no	—
232	C₄×C₁₉	—	4	2	no	—
233	C₄×C₁₉	#394	1	1	yes	characteristic
234	C₄×C₁₉	#395	1	1	yes	characteristic
235	C₄×C₁₉	#396	1	2	yes	—
236	C₄×C₁₉	#398	1	1	yes	characteristic
237	C₄×C₁₉	#398	1	2	yes	—
238	C₄×C₁₉	#400	1	1	yes	characteristic
239	C₂³×C₈	—	19	2	no	—
240	C₂³×C₈	—	19	2	no	—
241	C₂²×C₄⋊C₄	Dic₁₉	1	1	yes	characteristic
242	C₂²×C₄⋊C₄	Dic₁₉	1	1	yes	characteristic
243	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
244	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
245	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
246	C₂×C₄⋊C₈	—	38	4	no	—
247	C₂×C₄⋊C₈	—	38	2	no	—
248	C₄×C₄⋊C₄	—	2	2	no	—
249	C₄×C₄⋊C₄	—	2	2	no	—
250	C₂×#95	Dic₁₉	1	1	yes	characteristic
251	C₂×#95	Dic₁₉	1	1	yes	characteristic
252	#336	—	38	4	no	—
253	#336	—	38	4	no	—
254	#336	—	38	2	no	—
255	C₂×C₁₉	#1441	1	1	yes	characteristic
256	C₂×C₁₉	#1797	1	1	yes	characteristic
257	C₂×C₁₉	#1798	1	1	yes	characteristic
258	C₂×C₁₉	#1869	1	1	yes	characteristic
259	C₂×C₁₉	#1870	1	1	yes	characteristic
260	C₂×C₁₉	#1916	1	2	yes	—
261	C₂×C₁₉	#1917	1	2	yes	—
262	C₂×C₁₉	#1939	1	2	yes	—
263	C₂×C₁₉	#1940	1	2	yes	—
264	C₂×C₁₉	#1984	1	1	yes	characteristic
265	C₂×C₁₉	#1985	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	C₂×Dic₁₉	1	1	yes	characteristic
269	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
270	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
271	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
272	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
273	C₂²×C₈	—	19	4	no	—
274	C₂²×C₈	—	19	4	no	—
275	C₂²×C₈	—	38	2	no	—
276	C₂²×C₈	—	38	2	no	—
277	C₂²×C₈	—	38	2	no	—
278	C₂²×C₈	—	38	2	no	—
279	C₂²×C₈	—	38	2	no	—
280	C₂²×C₈	—	38	2	no	—
281	C₂²×C₈	—	38	2	no	—
282	C₂²×C₈	—	38	2	no	—
283	C₂²×C₈	—	38	2	no	—
284	C₂²×C₈	—	38	2	no	—
285	C₂²×C₈	—	38	2	no	—
286	C₂²×C₈	—	38	2	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	C₁₉⋊C₈	1	4	yes	complemented
293	C₂×C₄²	—	2	1	no	—
294	C₂×C₄²	—	2	1	no	—
295	C₂×C₄²	—	2	2	no	—
296	C₂×C₄²	—	2	2	no	—
297	C₂×C₄²	—	2	1	no	—
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	—	2	2	no	—
300	C₂×C₄²	—	2	2	no	—
301	C₂×C₄²	—	2	1	no	—
302	C₂×C₄²	—	2	1	no	—
303	C₂×C₄²	Dic₃₈	1	2	yes	—
304	C₂×C₄²	D₇₆	1	2	yes	—
305	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
306	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
307	C₄⋊C₈	—	38	8	no	—
308	#95	—	2	2	no	—
309	#95	—	2	2	no	—
310	C₁₉	#11202	1	1	yes	characteristic, complemented, Sylow
311	C₂⁴	C₂²×Dic₁₉	1	1	yes	characteristic
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	C₂×C₁₉⋊C₈	1	2	yes	—
335	C₂²×C₄	C₂×C₁₉⋊C₈	1	2	yes	—
336	C₂²×C₄	C₂×C₁₉⋊C₈	1	2	yes	—
337	C₂²×C₄	#64520	1	2	yes	—
338	C₂²×C₄	#64520	1	2	yes	—
339	C₂²×C₄	#64520	1	2	yes	—
340	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
341	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
342	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
343	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
344	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
345	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
346	C₂²×C₄	#64541	1	1	yes	characteristic
347	C₂²×C₄	#64541	1	1	yes	characteristic
348	C₂²×C₄	D₄×D₁₉	1	2	yes	—
349	C₂²×C₄	#64543	1	2	yes	—
350	C₂²×C₄	Q₈×D₁₉	1	2	yes	—
351	C₂²×C₄	#64545	1	2	yes	—
352	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
353	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
354	C₂×C₈	—	38	4	no	—
355	C₂×C₈	—	38	4	no	—
356	C₂×C₈	—	38	4	no	—
357	C₂×C₈	—	38	4	no	—
358	C₂×C₈	—	38	4	no	—
359	C₂×C₈	—	38	4	no	—
360	C₂×C₈	—	76	2	no	—
361	C₂×C₈	—	76	2	no	—
362	C₂×C₈	—	76	2	no	—
363	C₂×C₈	—	76	2	no	—
364	C₂×C₈	—	76	2	no	—
365	C₂×C₈	—	76	2	no	—
366	C₂×C₈	—	76	2	no	—
367	C₂×C₈	—	76	2	no	—
368	C₄⋊C₄	—	2	8	no	—
369	C₄⋊C₄	—	2	8	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	4	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	4	1	no	—
378	C₄²	—	4	1	no	—
379	C₄²	—	4	2	no	—
380	C₂³	C₂²×C₁₉⋊C₈	1	1	yes	characteristic
381	C₂³	C₂×#64520	1	1	yes	characteristic
382	C₂³	C₂×#64520	1	1	yes	characteristic
383	C₂³	C₂×#64520	1	1	yes	characteristic
384	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
385	C₂³	#10597372	1	1	yes	characteristic
386	C₂³	D₄×Dic₁₉	1	2	yes	—
387	C₂³	Q₈×Dic₁₉	1	2	yes	—
388	C₂³	#10597394	1	2	yes	—
389	C₂³	#10597394	1	2	yes	—
390	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	C₄⋊(C₁₉⋊C₈)	1	4	yes	complemented
422	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	4	yes	—
423	C₂×C₄	#10597334	1	2	yes	—
424	C₂×C₄	#10597335	1	2	yes	—
425	C₂×C₄	#10597336	1	2	yes	—
426	C₂×C₄	#10597340	1	2	yes	—
427	C₂×C₄	#10597341	1	2	yes	—
428	C₂×C₄	#10597342	1	2	yes	—
429	C₂×C₄	#10597343	1	2	yes	—
430	C₂×C₄	#10597344	1	2	yes	—
431	C₂×C₄	#10597370	1	1	yes	characteristic
432	C₂×C₄	#10597370	1	1	yes	characteristic
433	C₂×C₄	#10597376	1	1	yes	characteristic
434	C₂×C₄	#10597376	1	1	yes	characteristic
435	C₂×C₄	#10597381	1	1	yes	characteristic
436	C₂×C₄	#10597383	1	1	yes	characteristic
437	C₂×C₄	#10597385	1	2	yes	—
438	C₂×C₄	#10597390	1	1	yes	characteristic
439	C₂×C₄	#10597392	1	2	yes	—
440	C₂×C₄	#10597393	1	1	yes	characteristic
441	C₈	—	76	4	no	—
442	C₈	—	76	4	no	—
443	C₂²	#11926404	1	1	yes	characteristic
444	C₂²	#11926424	1	1	yes	characteristic
445	C₂²	#11926430	1	2	yes	—
446	C₂²	#11926443	1	2	yes	—
447	C₂²	#11926451	1	1	yes	characteristic
448	C₂²	C₂×C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
449	C₂²	#11926508	1	1	yes	characteristic
450	C₂²	#11926511	1	1	yes	characteristic
451	C₂²	#11926511	1	1	yes	characteristic
452	C₂²	C₂×C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
453	C₂²	#11926568	1	1	yes	characteristic
454	C₂²	#11926571	1	2	yes	—
455	C₂²	#11926597	1	1	yes	characteristic
456	C₂²	#11926601	1	1	yes	characteristic
457	C₂²	#11926605	1	2	yes	—
458	C₂²	D₄×C₁₉⋊C₈	1	2	yes	—
459	C₂²	#11926616	1	2	yes	—
460	C₂²	#11926616	1	2	yes	—
461	C₂²	#11926622	1	2	yes	—
462	C₂²	Q₈×C₁₉⋊C₈	1	2	yes	—
463	C₂²	#11926675	1	2	yes	—
464	C₂²	#11926675	1	2	yes	—
465	C₂²	#11926675	1	2	yes	—
466	C₄	—	2	4	no	—
467	C₄	—	2	4	no	—
468	C₄	—	4	2	no	—
469	C₄	—	4	2	no	—
470	C₄	—	4	2	no	—
471	C₄	—	4	2	no	—
472	C₄	#11926461	1	1	yes	characteristic
473	C₄	#11926464	1	1	yes	characteristic
474	C₄	#11926466	1	2	yes	—
475	C₄	#11926474	1	1	yes	characteristic
476	C₄	#11926477	1	2	yes	—
477	C₄	#11926483	1	1	yes	characteristic
478	C₂	#14561888	1	1	yes	characteristic
479	C₂	#14563615	1	1	yes	characteristic
480	C₂	#14563619	1	1	yes	characteristic
481	C₂	#14563928	1	1	yes	characteristic
482	C₂	#14563933	1	1	yes	characteristic
483	C₂	#14564194	1	2	yes	—
484	C₂	#14564201	1	2	yes	—
485	C₂	#14564354	1	2	yes	—
486	C₂	#14564359	1	2	yes	—
487	C₂	#14564572	1	1	yes	characteristic
488	C₂	#14564576	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³×C₄	C₂²×D₁₉
commutator	C₂³×C₁₉	C₂²×C₈
Fitting	C₂×C₄×C₄⋊C₄×C₁₉	C₂
socle, prime radical	C₂⁴×C₁₉	C₂²×C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×C₄×C₄⋊C₄	D₁₉
hypocenter	C₁₉	#11202
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³×C₄ ◁ C₂×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
34. C₂×C₄⋊C₄×C₁₉	C₈	semidirect
178. C₂×C₄×C₁₉	C₄⋊C₈	semidirect
292. C₂×C₄⋊C₄	C₁₉⋊C₈	semidirect
310. C₁₉	#11202	semidirect
421. C₂×C₄	C₄⋊(C₁₉⋊C₈)	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊(C₁₉⋊C₈)	2
C₂×#11926299	2
C₂×C₄×C₄⋊C₄×C₁₉	2
#11202	19