Subgroups — #18077066

Order 4864.

628 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926597	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂²⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₈⋊(C₁₉⋊C₈)	C₂	1	2	yes	maximal, complemented
4	#14561476	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
6	#11926597	—	2	4	no	—
7	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
8	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
9	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
10	C₂×C₄×C₁₉⋊C₈	—	2	1	no	—
11	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
12	#11926299	—	2	1	no	—
13	Q₈⋊(C₁₉⋊C₈)	—	2	4	no	—
14	C₂×C₁₉×C₂²⋊Q₈	C₄	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#391	C₄	1	1	yes	characteristic
18	C₁₉×#389	C₄	1	1	yes	characteristic
19	C₁₉×#387	—	2	1	no	—
20	C₁₉×#385	—	2	1	no	—
21	C₁₉×#380	C₄	1	1	yes	characteristic
22	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
23	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
25	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
29	C₁₉×C₂²⋊Q₈	—	2	2	no	—
30	C₁₉×C₂²⋊Q₈	C₈	1	4	yes	complemented
31	C₄×Q₈×C₁₉	—	2	2	no	—
32	C₄×Q₈×C₁₉	—	2	2	no	—
33	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
36	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
40	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
41	C₂×C₄²×C₁₉	—	2	2	no	—
42	C₂×C₄²×C₁₉	—	2	2	no	—
43	C₂×C₄²×C₁₉	—	2	1	no	—
44	C₂×C₄²×C₁₉	—	2	1	no	—
45	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
49	C₂²×C₁₉⋊C₈	—	2	2	no	—
50	C₂²×C₁₉⋊C₈	—	2	2	no	—
51	C₁₉×#95	—	2	1	no	—
52	C₁₉×#95	—	2	1	no	—
53	C₁₉×#95	—	2	1	no	—
54	C₁₉×#95	—	2	1	no	—
55	C₁₉×#95	—	2	1	no	—
56	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
57	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
58	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
59	C₄⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
60	C₄×C₁₉⋊C₈	—	2	4	no	—
61	C₄×C₁₉⋊C₈	—	2	2	no	—
62	C₄×C₁₉⋊C₈	—	2	2	no	—
63	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
64	C₂×Q₈×C₁₉	—	2	1	no	—
65	C₂×Q₈×C₁₉	—	2	2	no	—
66	C₂×Q₈×C₁₉	—	2	2	no	—
67	C₂×Q₈×C₁₉	C₂×C₈	1	2	yes	—
68	C₂²×C₄×C₁₉	—	2	2	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	2	no	—
75	C₂²×C₄×C₁₉	—	2	1	no	—
76	C₂²×C₄×C₁₉	—	2	2	no	—
77	C₂²×C₄×C₁₉	—	2	2	no	—
78	C₂²×C₄×C₁₉	—	2	1	no	—
79	C₂²×C₄×C₁₉	—	2	1	no	—
80	C₂²×C₄×C₁₉	—	4	1	no	—
81	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
85	C₂²×C₄×C₁₉	M₁₆	1	2	yes	—
86	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
89	C₄⋊C₄×C₁₉	—	2	4	no	—
90	C₄⋊C₄×C₁₉	—	2	1	no	—
91	C₄⋊C₄×C₁₉	—	2	2	no	—
92	C₄⋊C₄×C₁₉	—	2	2	no	—
93	C₄⋊C₄×C₁₉	—	4	2	no	—
94	C₄⋊C₄×C₁₉	—	4	2	no	—
95	C₄⋊C₄×C₁₉	C₂×C₈	1	2	yes	—
96	C₂²⋊C₄×C₁₉	—	2	4	no	—
97	C₂²⋊C₄×C₁₉	—	4	2	no	—
98	C₄²×C₁₉	—	2	2	no	—
99	C₄²×C₁₉	—	2	1	no	—
100	C₄²×C₁₉	—	2	2	no	—
101	C₄²×C₁₉	—	2	1	no	—
102	C₄²×C₁₉	—	4	1	no	—
103	C₄²×C₁₉	—	4	1	no	—
104	C₄²×C₁₉	—	4	2	no	—
105	C₄²×C₁₉	C₂×D₄	1	2	yes	—
106	C₄²×C₁₉	#41	1	2	yes	—
107	C₂×C₁₉⋊C₈	—	2	4	no	—
108	C₂×C₁₉⋊C₈	—	2	4	no	—
109	C₂×C₁₉⋊C₈	—	4	2	no	—
110	C₂×C₁₉⋊C₈	—	4	2	no	—
111	C₂×C₁₉⋊C₈	—	4	2	no	—
112	C₂×C₁₉⋊C₈	—	4	2	no	—
113	#8938	—	19	1	no	maximal, Sylow
114	C₂³×C₁₉	—	2	1	no	—
115	C₂³×C₁₉	—	2	1	no	—
116	C₂³×C₁₉	—	2	1	no	—
117	C₂³×C₁₉	—	2	1	no	—
118	C₂³×C₁₉	—	2	1	no	—
119	C₂³×C₁₉	—	2	1	no	—
120	C₂³×C₁₉	C₂²⋊C₈	1	2	yes	—
121	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
122	Q₈×C₁₉	—	2	4	no	—
123	Q₈×C₁₉	—	4	2	no	—
124	C₂×C₄×C₁₉	—	2	1	no	—
125	C₂×C₄×C₁₉	—	2	1	no	—
126	C₂×C₄×C₁₉	—	2	1	no	—
127	C₂×C₄×C₁₉	—	2	1	no	—
128	C₂×C₄×C₁₉	—	2	1	no	—
129	C₂×C₄×C₁₉	—	2	1	no	—
130	C₂×C₄×C₁₉	—	2	4	no	—
131	C₂×C₄×C₁₉	—	2	4	no	—
132	C₂×C₄×C₁₉	—	2	1	no	—
133	C₂×C₄×C₁₉	—	2	2	no	—
134	C₂×C₄×C₁₉	—	2	2	no	—
135	C₂×C₄×C₁₉	—	2	1	no	—
136	C₂×C₄×C₁₉	—	2	1	no	—
137	C₂×C₄×C₁₉	—	4	4	no	—
138	C₂×C₄×C₁₉	—	4	1	no	—
139	C₂×C₄×C₁₉	—	4	1	no	—
140	C₂×C₄×C₁₉	—	4	1	no	—
141	C₂×C₄×C₁₉	—	4	1	no	—
142	C₂×C₄×C₁₉	—	4	2	no	—
143	C₂×C₄×C₁₉	—	4	2	no	—
144	C₂×C₄×C₁₉	—	4	1	no	—
145	C₂×C₄×C₁₉	—	4	1	no	—
146	C₂×C₄×C₁₉	—	4	1	no	—
147	C₂×C₄×C₁₉	—	4	1	no	—
148	C₂×C₄×C₁₉	—	4	1	no	—
149	C₂×C₄×C₁₉	—	4	1	no	—
150	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
151	C₂×C₄×C₁₉	#104	1	2	yes	—
152	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
153	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
154	C₂×C₄×C₁₉	#121	1	2	yes	—
155	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
156	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
157	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
158	C₂×C₄×C₁₉	#131	1	2	yes	—
159	C₂×C₄×C₁₉	#135	1	2	yes	—
160	C₂×C₄×C₁₉	#137	1	2	yes	—
161	C₁₉⋊C₈	—	4	4	no	—
162	C₁₉⋊C₈	—	4	4	no	—
163	C₂×#431	—	19	1	no	—
164	C₄×C₂²⋊Q₈	D₁₉	1	1	yes	characteristic
165	C₄×C₂²⋊C₈	—	19	1	no	—
166	C₂×Q₈⋊C₈	—	19	2	no	—
167	#1279	—	19	2	no	—
168	C₂²×C₁₉	—	2	2	no	—
169	C₂²×C₁₉	—	2	2	no	—
170	C₂²×C₁₉	—	2	2	no	—
171	C₂²×C₁₉	—	4	1	no	—
172	C₂²×C₁₉	—	4	1	no	—
173	C₂²×C₁₉	—	4	1	no	—
174	C₂²×C₁₉	—	4	1	no	—
175	C₂²×C₁₉	#386	1	1	yes	characteristic
176	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
177	C₂²×C₁₉	#408	1	1	yes	characteristic
178	C₂²×C₁₉	#416	1	1	yes	characteristic
179	C₂²×C₁₉	#419	1	1	yes	characteristic
180	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
181	C₂²×C₁₉	#421	1	1	yes	characteristic
182	C₄×C₁₉	—	2	2	no	—
183	C₄×C₁₉	—	2	2	no	—
184	C₄×C₁₉	—	2	2	no	—
185	C₄×C₁₉	—	4	2	no	—
186	C₄×C₁₉	—	4	1	no	—
187	C₄×C₁₉	—	4	2	no	—
188	C₄×C₁₉	—	8	1	no	—
189	C₄×C₁₉	—	8	1	no	—
190	C₄×C₁₉	C₈×D₄	1	2	yes	—
191	C₄×C₁₉	#435	1	2	yes	—
192	C₄×C₁₉	#452	1	2	yes	—
193	C₄×C₁₉	#485	1	2	yes	—
194	C₂×C₂²⋊Q₈	Dic₁₉	1	1	yes	characteristic
195	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
196	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
197	#431	—	38	4	no	—
198	C₂×C₄⋊C₈	—	19	2	no	—
199	C₂×C₂²⋊C₈	—	38	1	no	—
200	C₂×C₂²⋊C₈	—	38	1	no	—
201	C₂×C₄×C₈	—	19	2	no	—
202	C₂×C₄×C₈	—	38	1	no	—
203	#391	Dic₁₉	1	1	yes	characteristic
204	#389	Dic₁₉	1	1	yes	characteristic
205	#387	—	2	1	no	—
206	#385	—	2	1	no	—
207	#380	Dic₁₉	1	1	yes	characteristic
208	C₄×C₄⋊C₄	—	2	1	no	—
209	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
210	C₄×C₂²⋊C₄	—	2	1	no	—
211	#336	—	38	1	no	—
212	Q₈⋊C₈	—	38	4	no	—
213	C₂×C₁₉	—	4	2	no	—
214	C₂×C₁₉	#1476	1	1	yes	characteristic
215	C₂×C₁₉	#1479	1	1	yes	characteristic
216	C₂×C₁₉	#1482	1	1	yes	characteristic
217	C₂×C₁₉	#1485	1	1	yes	characteristic
218	C₂×C₁₉	#1869	1	1	yes	characteristic
219	C₂×C₁₉	#1871	1	1	yes	characteristic
220	C₂×C₁₉	#1873	1	1	yes	characteristic
221	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
222	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
223	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
224	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
225	C₂²×C₈	—	38	2	no	—
226	C₂²×C₈	—	38	2	no	—
227	C₂²⋊Q₈	—	2	2	no	—
228	C₂²⋊Q₈	C₁₉⋊C₈	1	4	yes	complemented
229	C₄×Q₈	—	2	2	no	—
230	C₄×Q₈	—	2	2	no	—
231	C₂×C₄⋊C₄	—	2	1	no	—
232	C₂×C₄⋊C₄	—	2	1	no	—
233	C₂×C₄⋊C₄	—	2	1	no	—
234	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
235	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
236	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
237	C₂×C₂²⋊C₄	—	2	1	no	—
238	C₂×C₂²⋊C₄	—	2	1	no	—
239	C₂×C₄²	—	2	2	no	—
240	C₂×C₄²	—	2	2	no	—
241	C₂×C₄²	—	2	1	no	—
242	C₂×C₄²	—	2	1	no	—
243	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
244	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
245	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
246	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
247	C₄⋊C₈	—	19	4	no	—
248	C₄⋊C₈	—	38	2	no	—
249	C₂²⋊C₈	—	38	4	no	—
250	C₂²⋊C₈	—	38	4	no	—
251	C₄×C₈	—	38	4	no	—
252	C₄×C₈	—	38	2	no	—
253	C₄×C₈	—	38	2	no	—
254	#95	—	2	1	no	—
255	#95	—	2	1	no	—
256	#95	—	2	1	no	—
257	#95	—	2	1	no	—
258	#95	—	2	1	no	—
259	C₁₉	#8938	1	1	yes	characteristic, complemented, Sylow
260	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
261	C₂×Q₈	—	2	1	no	—
262	C₂×Q₈	—	2	2	no	—
263	C₂×Q₈	—	2	2	no	—
264	C₂×Q₈	C₂×C₁₉⋊C₈	1	2	yes	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	2	1	no	—
269	C₂²×C₄	—	2	1	no	—
270	C₂²×C₄	—	2	1	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	4	1	no	—
278	C₂²×C₄	C₂×C₁₉⋊C₈	1	2	yes	—
279	C₂²×C₄	#64520	1	2	yes	—
280	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
281	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
282	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
283	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
284	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
285	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
286	C₂×C₈	—	38	4	no	—
287	C₂×C₈	—	38	4	no	—
288	C₂×C₈	—	76	2	no	—
289	C₂×C₈	—	76	2	no	—
290	C₂×C₈	—	76	2	no	—
291	C₂×C₈	—	76	2	no	—
292	C₄⋊C₄	—	2	4	no	—
293	C₄⋊C₄	—	2	1	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	4	2	no	—
297	C₄⋊C₄	—	4	2	no	—
298	C₄⋊C₄	C₂×C₁₉⋊C₈	1	2	yes	—
299	C₂²⋊C₄	—	2	4	no	—
300	C₂²⋊C₄	—	4	2	no	—
301	C₄²	—	2	2	no	—
302	C₄²	—	2	1	no	—
303	C₄²	—	2	1	no	—
304	C₄²	—	2	2	no	—
305	C₄²	—	4	1	no	—
306	C₄²	—	4	1	no	—
307	C₄²	—	4	2	no	—
308	C₄²	D₄×D₁₉	1	2	yes	—
309	C₄²	#64543	1	2	yes	—
310	C₂³	—	2	1	no	—
311	C₂³	—	2	1	no	—
312	C₂³	—	2	1	no	—
313	C₂³	—	2	1	no	—
314	C₂³	—	2	1	no	—
315	C₂³	—	2	1	no	—
316	C₂³	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
317	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
318	Q₈	—	2	4	no	—
319	Q₈	—	4	2	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
347	C₂×C₄	#10597294	1	2	yes	—
348	C₂×C₄	C₂²×C₁₉⋊C₈	1	1	yes	characteristic
349	C₂×C₄	C₂×#64520	1	1	yes	characteristic
350	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
351	C₂×C₄	#10597381	1	1	yes	characteristic
352	C₂×C₄	#10597383	1	1	yes	characteristic
353	C₂×C₄	#10597385	1	2	yes	—
354	C₂×C₄	#10597388	1	2	yes	—
355	C₂×C₄	#10597394	1	2	yes	—
356	C₂×C₄	#10597396	1	2	yes	—
357	C₈	—	76	4	no	—
358	C₈	—	76	4	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	4	1	no	—
363	C₂²	—	4	1	no	—
364	C₂²	—	4	1	no	—
365	C₂²	—	4	1	no	—
366	C₂²	#11926424	1	1	yes	characteristic
367	C₂²	C₂×C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
368	C₂²	#11926511	1	1	yes	characteristic
369	C₂²	#11926540	1	1	yes	characteristic
370	C₂²	#11926553	1	1	yes	characteristic
371	C₂²	C₂×#10597294	1	1	yes	characteristic
372	C₂²	#11926561	1	1	yes	characteristic
373	C₄	—	2	2	no	—
374	C₄	—	2	2	no	—
375	C₄	—	2	2	no	—
376	C₄	—	4	2	no	—
377	C₄	—	4	1	no	—
378	C₄	—	4	2	no	—
379	C₄	—	8	1	no	—
380	C₄	—	8	1	no	—
381	C₄	D₄×C₁₉⋊C₈	1	2	yes	—
382	C₄	#11926616	1	2	yes	—
383	C₄	#11926704	1	2	yes	—
384	C₄	#11926882	1	2	yes	—
385	C₂	—	4	2	no	—
386	C₂	#14562017	1	1	yes	characteristic
387	C₂	#14562030	1	1	yes	characteristic
388	C₂	#14562043	1	1	yes	characteristic
389	C₂	#14562056	1	1	yes	characteristic
390	C₂	#14563928	1	1	yes	characteristic
391	C₂	#14563938	1	1	yes	characteristic
392	C₂	#14563948	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄×C₁₉×C₂²⋊Q₈	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×C₂²⋊Q₈	D₁₉
hypocenter	C₁₉	#8938
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₄×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
3. C₂×Q₈⋊(C₁₉⋊C₈)	C₂	semidirect
4. #14561476	C₂	semidirect
30. C₁₉×C₂²⋊Q₈	C₈	semidirect
228. C₂²⋊Q₈	C₁₉⋊C₈	semidirect
259. C₁₉	#8938	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926597	2
C₄×C₂²⋊(C₁₉⋊C₈)	2
C₂×Q₈⋊(C₁₉⋊C₈)	2
#14561476	2
C₄×C₁₉×C₂²⋊Q₈	2
#8938	19