Subgroups — #34176379

Order 20224.

504 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23763468	C₂	1	1	yes	maximal, characteristic
2	#23763380	C₂	1	1	yes	maximal, characteristic
3	#23761226	C₂	1	2	yes	maximal, complemented
4	#23761223	C₂	1	2	yes	maximal, complemented
5	C₄×C₂²⋊Q₈×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
7	C₂×C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
8	C₂×C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
9	#19098318	—	2	1	no	—
10	#19098318	C₂²	1	2	yes	—
11	#19098318	C₂²	1	2	yes	—
12	C₂×C₂²⋊Q₈×C₇₉	C₄	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₇₉	C₄	1	1	yes	characteristic
14	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
15	#391×C₇₉	C₂²	1	1	yes	characteristic
16	#389×C₇₉	C₂²	1	1	yes	characteristic
17	#387×C₇₉	—	2	1	no	—
18	#385×C₇₉	—	2	1	no	—
19	#380×C₇₉	C₄	1	1	yes	characteristic
20	C₄×C₄⋊C₄×C₇₉	—	2	1	no	—
21	C₄×C₄⋊C₄×C₇₉	C₄	1	1	yes	characteristic
22	C₄×C₂²⋊C₄×C₇₉	—	2	1	no	—
23	C₂²×C₇₉⋊C₈	—	2	2	no	—
24	C₂²×C₇₉⋊C₈	—	2	2	no	—
25	C₄⋊(C₇₉⋊C₈)	—	4	2	no	—
26	C₂²⋊(C₇₉⋊C₈)	—	4	2	no	—
27	C₂²⋊(C₇₉⋊C₈)	—	4	2	no	—
28	C₂²×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
31	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
32	C₂²⋊Q₈×C₇₉	—	2	2	no	—
33	C₂²⋊Q₈×C₇₉	C₈	1	4	yes	complemented
34	C₄×Q₈×C₇₉	—	4	2	no	—
35	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
36	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
41	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
42	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
43	C₂×C₄²×C₇₉	—	2	1	no	—
44	C₂×C₄²×C₇₉	—	2	1	no	—
45	C₂×C₄²×C₇₉	—	4	2	no	—
46	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
50	#95×C₇₉	—	2	1	no	—
51	#95×C₇₉	—	2	1	no	—
52	#95×C₇₉	—	2	1	no	—
53	#95×C₇₉	—	2	1	no	—
54	#95×C₇₉	—	2	1	no	—
55	C₂×C₇₉⋊C₈	—	4	2	no	—
56	C₂×C₇₉⋊C₈	—	4	2	no	—
57	C₂×C₇₉⋊C₈	—	4	2	no	—
58	C₂×C₇₉⋊C₈	—	4	2	no	—
59	C₂×C₇₉⋊C₈	—	4	2	no	—
60	C₂×C₇₉⋊C₈	—	4	2	no	—
61	C₂⁴×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
62	C₂×Q₈×C₇₉	—	2	1	no	—
63	C₂×Q₈×C₇₉	—	4	1	no	—
64	C₂×Q₈×C₇₉	—	4	1	no	—
65	C₂×Q₈×C₇₉	C₂×C₈	1	2	yes	—
66	C₂²×C₄×C₇₉	—	2	1	no	—
67	C₂²×C₄×C₇₉	—	2	1	no	—
68	C₂²×C₄×C₇₉	—	2	2	no	—
69	C₂²×C₄×C₇₉	—	2	1	no	—
70	C₂²×C₄×C₇₉	—	2	2	no	—
71	C₂²×C₄×C₇₉	—	2	1	no	—
72	C₂²×C₄×C₇₉	—	2	1	no	—
73	C₂²×C₄×C₇₉	—	2	1	no	—
74	C₂²×C₄×C₇₉	—	4	1	no	—
75	C₂²×C₄×C₇₉	—	4	1	no	—
76	C₂²×C₄×C₇₉	—	4	1	no	—
77	C₂²×C₄×C₇₉	—	4	1	no	—
78	C₂²×C₄×C₇₉	—	4	1	no	—
79	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₇₉	C₂×C₈	1	2	yes	—
83	C₂²×C₄×C₇₉	M₁₆	1	2	yes	—
84	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
87	C₄⋊C₄×C₇₉	—	2	4	no	—
88	C₄⋊C₄×C₇₉	—	2	1	no	—
89	C₄⋊C₄×C₇₉	—	4	2	no	—
90	C₄⋊C₄×C₇₉	—	4	1	no	—
91	C₄⋊C₄×C₇₉	—	4	1	no	—
92	C₄⋊C₄×C₇₉	—	4	1	no	—
93	C₄⋊C₄×C₇₉	—	4	1	no	—
94	C₄⋊C₄×C₇₉	C₂×C₈	1	2	yes	—
95	C₂²⋊C₄×C₇₉	—	2	4	no	—
96	C₂²⋊C₄×C₇₉	—	4	2	no	—
97	C₄²×C₇₉	—	2	2	no	—
98	C₄²×C₇₉	—	2	2	no	—
99	C₄²×C₇₉	—	4	1	no	—
100	C₄²×C₇₉	—	4	1	no	—
101	C₄²×C₇₉	—	4	2	no	—
102	C₄²×C₇₉	—	4	2	no	—
103	C₂³×C₇₉	—	2	1	no	—
104	C₂³×C₇₉	—	2	1	no	—
105	C₂³×C₇₉	—	2	1	no	—
106	C₂³×C₇₉	—	2	1	no	—
107	C₂³×C₇₉	—	2	1	no	—
108	C₂³×C₇₉	—	2	1	no	—
109	C₂³×C₇₉	C₂²⋊C₈	1	2	yes	—
110	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
111	Q₈×C₇₉	—	4	2	no	—
112	Q₈×C₇₉	—	4	2	no	—
113	C₂×C₄×C₇₉	—	2	1	no	—
114	C₂×C₄×C₇₉	—	2	1	no	—
115	C₂×C₄×C₇₉	—	2	1	no	—
116	C₂×C₄×C₇₉	—	2	1	no	—
117	C₂×C₄×C₇₉	—	2	1	no	—
118	C₂×C₄×C₇₉	—	2	1	no	—
119	C₂×C₄×C₇₉	—	2	1	no	—
120	C₂×C₄×C₇₉	—	2	1	no	—
121	C₂×C₄×C₇₉	—	2	1	no	—
122	C₂×C₄×C₇₉	—	2	1	no	—
123	C₂×C₄×C₇₉	—	2	2	no	—
124	C₂×C₄×C₇₉	—	2	2	no	—
125	C₂×C₄×C₇₉	—	2	1	no	—
126	C₂×C₄×C₇₉	—	2	1	no	—
127	C₂×C₄×C₇₉	—	2	1	no	—
128	C₂×C₄×C₇₉	—	4	2	no	—
129	C₂×C₄×C₇₉	—	4	2	no	—
130	C₂×C₄×C₇₉	—	4	4	no	—
131	C₂×C₄×C₇₉	—	4	2	no	—
132	C₂×C₄×C₇₉	—	4	2	no	—
133	C₂×C₄×C₇₉	—	4	1	no	—
134	C₂×C₄×C₇₉	—	4	1	no	—
135	C₂×C₄×C₇₉	—	4	1	no	—
136	C₂×C₄×C₇₉	—	4	1	no	—
137	C₂×C₄×C₇₉	—	4	1	no	—
138	C₂×C₄×C₇₉	—	4	1	no	—
139	C₂×C₄×C₇₉	—	4	1	no	—
140	C₂×C₄×C₇₉	—	4	1	no	—
141	C₂×C₄×C₇₉	—	4	1	no	—
142	C₂×C₄×C₇₉	—	4	1	no	—
143	C₂×C₄×C₇₉	C₂²⋊C₈	1	2	yes	—
144	C₂×C₄×C₇₉	#99	1	2	yes	—
145	C₂×C₄×C₇₉	C₂²×C₈	1	1	yes	characteristic
146	C₂×C₄×C₇₉	C₂×M₁₆	1	1	yes	characteristic
147	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
148	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
149	C₂×C₄×C₇₉	#137	1	2	yes	—
150	C₇₉⋊C₈	—	8	2	no	—
151	C₇₉⋊C₈	—	8	2	no	—
152	C₂²×C₇₉	—	2	2	no	—
153	C₂²×C₇₉	—	2	2	no	—
154	C₂²×C₇₉	—	2	2	no	—
155	C₂²×C₇₉	—	4	1	no	—
156	C₂²×C₇₉	—	4	1	no	—
157	C₂²×C₇₉	—	4	1	no	—
158	C₂²×C₇₉	—	4	1	no	—
159	C₂²×C₇₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
160	C₂²×C₇₉	C₂×#99	1	1	yes	characteristic
161	C₂²×C₇₉	#413	1	1	yes	characteristic
162	C₂²×C₇₉	#417	1	1	yes	characteristic
163	C₂²×C₇₉	#419	1	1	yes	characteristic
164	C₂²×C₇₉	#421	1	1	yes	characteristic
165	C₂²×C₇₉	#421	1	1	yes	characteristic
166	C₄×C₇₉	—	2	2	no	—
167	C₄×C₇₉	—	2	1	no	—
168	C₄×C₇₉	—	2	1	no	—
169	C₄×C₇₉	—	2	2	no	—
170	C₄×C₇₉	—	2	2	no	—
171	C₄×C₇₉	—	2	1	no	—
172	C₄×C₇₉	—	2	1	no	—
173	C₄×C₇₉	—	4	2	no	—
174	C₄×C₇₉	—	4	2	no	—
175	C₄×C₇₉	—	4	1	no	—
176	C₄×C₇₉	—	8	1	no	—
177	C₄×C₇₉	—	8	1	no	—
178	#7600	—	79	1	no	maximal, Sylow
179	C₂×C₇₉	—	4	2	no	—
180	C₂×C₇₉	#1459	1	1	yes	characteristic
181	C₂×C₇₉	#1477	1	1	yes	characteristic
182	C₂×C₇₉	#1479	1	1	yes	characteristic
183	C₂×C₇₉	#1511	1	1	yes	characteristic
184	C₂×C₇₉	#1513	1	1	yes	characteristic
185	C₂×C₇₉	#1535	1	1	yes	characteristic
186	C₂×C₇₉	#1559	1	1	yes	characteristic
187	C₄×C₂²⋊Q₈	D₇₉	1	1	yes	characteristic
188	#1817	—	79	1	no	—
189	#1797	—	79	1	no	—
190	#1272	—	79	2	no	—
191	#1271	—	79	2	no	—
192	C₇₉	#7600	1	1	yes	characteristic, complemented, Sylow
193	C₂×C₂²⋊Q₈	Dic₇₉	1	1	yes	characteristic
194	C₂×C₄×Q₈	Dic₇₉	1	1	yes	characteristic
195	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
196	C₂×C₄⋊C₈	—	158	1	no	—
197	C₂×C₂²⋊C₈	—	158	1	no	—
198	C₂×C₂²⋊C₈	—	158	1	no	—
199	#391	C₂×D₇₉	1	1	yes	characteristic
200	#389	C₂×D₇₉	1	1	yes	characteristic
201	#387	—	2	1	no	—
202	#385	—	2	1	no	—
203	#380	Dic₇₉	1	1	yes	characteristic
204	C₄×C₄⋊C₄	—	2	1	no	—
205	C₄×C₄⋊C₄	Dic₇₉	1	1	yes	characteristic
206	C₄×C₂²⋊C₄	—	2	1	no	—
207	#336	—	79	2	no	—
208	#336	—	79	2	no	—
209	#336	—	158	1	no	—
210	C₂²×Q₈	C₂×Dic₇₉	1	1	yes	characteristic
211	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
212	C₂³×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
213	C₂³×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
214	C₂²×C₈	—	158	2	no	—
215	C₂²×C₈	—	158	2	no	—
216	C₂²⋊Q₈	—	2	2	no	—
217	C₂²⋊Q₈	C₇₉⋊C₈	1	4	yes	complemented
218	C₄×Q₈	—	4	2	no	—
219	C₂×C₄⋊C₄	—	2	1	no	—
220	C₂×C₄⋊C₄	—	2	1	no	—
221	C₂×C₄⋊C₄	—	2	1	no	—
222	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
223	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
224	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
225	C₂×C₂²⋊C₄	—	2	1	no	—
226	C₂×C₂²⋊C₄	—	2	1	no	—
227	C₂×C₄²	—	2	1	no	—
228	C₂×C₄²	—	2	1	no	—
229	C₂×C₄²	—	4	2	no	—
230	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
231	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
232	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
233	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
234	C₄⋊C₈	—	316	2	no	—
235	C₂²⋊C₈	—	316	2	no	—
236	C₂²⋊C₈	—	316	2	no	—
237	#95	—	2	1	no	—
238	#95	—	2	1	no	—
239	#95	—	2	1	no	—
240	#95	—	2	1	no	—
241	#95	—	2	1	no	—
242	C₂⁴	C₂²⋊Dic₇₉	1	1	yes	characteristic
243	C₂×Q₈	—	2	1	no	—
244	C₂×Q₈	—	4	1	no	—
245	C₂×Q₈	—	4	1	no	—
246	C₂×Q₈	C₂×C₇₉⋊C₈	1	2	yes	—
247	C₂²×C₄	—	2	1	no	—
248	C₂²×C₄	—	2	1	no	—
249	C₂²×C₄	—	2	2	no	—
250	C₂²×C₄	—	2	1	no	—
251	C₂²×C₄	—	2	1	no	—
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	2	1	no	—
254	C₂²×C₄	—	2	1	no	—
255	C₂²×C₄	—	4	1	no	—
256	C₂²×C₄	—	4	1	no	—
257	C₂²×C₄	—	4	1	no	—
258	C₂²×C₄	—	4	1	no	—
259	C₂²×C₄	—	4	1	no	—
260	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
261	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
262	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
263	C₂²×C₄	C₂×C₇₉⋊C₈	1	2	yes	—
264	C₂²×C₄	#11929608	1	2	yes	—
265	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
266	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
267	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
268	C₂×C₈	—	316	2	no	—
269	C₂×C₈	—	316	2	no	—
270	C₂×C₈	—	316	2	no	—
271	C₂×C₈	—	316	2	no	—
272	C₂×C₈	—	316	2	no	—
273	C₂×C₈	—	316	2	no	—
274	C₄⋊C₄	—	2	4	no	—
275	C₄⋊C₄	—	2	1	no	—
276	C₄⋊C₄	—	4	1	no	—
277	C₄⋊C₄	—	4	1	no	—
278	C₄⋊C₄	—	4	2	no	—
279	C₄⋊C₄	—	4	1	no	—
280	C₄⋊C₄	—	4	1	no	—
281	C₄⋊C₄	C₂×C₇₉⋊C₈	1	2	yes	—
282	C₂²⋊C₄	—	2	4	no	—
283	C₂²⋊C₄	—	4	2	no	—
284	C₄²	—	2	2	no	—
285	C₄²	—	2	2	no	—
286	C₄²	—	4	1	no	—
287	C₄²	—	4	1	no	—
288	C₄²	—	4	2	no	—
289	C₄²	—	4	2	no	—
290	C₂³	—	2	1	no	—
291	C₂³	—	2	1	no	—
292	C₂³	—	2	1	no	—
293	C₂³	—	2	1	no	—
294	C₂³	—	2	1	no	—
295	C₂³	—	2	1	no	—
296	C₂³	C₂²⋊(C₇₉⋊C₈)	1	2	yes	—
297	C₂³	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
298	Q₈	—	4	2	no	—
299	Q₈	—	4	2	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	4	4	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	C₂²⋊(C₇₉⋊C₈)	1	2	yes	—
331	C₂×C₄	#14579076	1	2	yes	—
332	C₂×C₄	C₂²×C₇₉⋊C₈	1	1	yes	characteristic
333	C₂×C₄	C₂×#11929608	1	1	yes	characteristic
334	C₂×C₄	#14579186	1	1	yes	characteristic
335	C₂×C₄	#14579191	1	1	yes	characteristic
336	C₂×C₄	#14579192	1	2	yes	—
337	C₈	—	632	2	no	—
338	C₈	—	632	2	no	—
339	C₂²	—	2	2	no	—
340	C₂²	—	2	2	no	—
341	C₂²	—	2	2	no	—
342	C₂²	—	4	1	no	—
343	C₂²	—	4	1	no	—
344	C₂²	—	4	1	no	—
345	C₂²	—	4	1	no	—
346	C₂²	C₂×C₂²⋊(C₇₉⋊C₈)	1	1	yes	characteristic
347	C₂²	C₂×#14579076	1	1	yes	characteristic
348	C₂²	#19098547	1	1	yes	characteristic
349	C₂²	#19098564	1	1	yes	characteristic
350	C₂²	#19098572	1	1	yes	characteristic
351	C₂²	#19098580	1	1	yes	characteristic
352	C₂²	#19098580	1	1	yes	characteristic
353	C₄	—	2	2	no	—
354	C₄	—	2	2	no	—
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	2	2	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	4	1	no	—
361	C₄	—	4	2	no	—
362	C₄	—	4	2	no	—
363	C₄	—	8	1	no	—
364	C₄	—	8	1	no	—
365	C₂	—	4	2	no	—
366	C₂	#23761718	1	1	yes	characteristic
367	C₂	#23761787	1	1	yes	characteristic
368	C₂	#23761795	1	1	yes	characteristic
369	C₂	#23761933	1	1	yes	characteristic
370	C₂	#23761943	1	1	yes	characteristic
371	C₂	#23762031	1	1	yes	characteristic
372	C₂	#23762130	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₇₉
commutator	C₂×C₄×C₇₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₄×C₂²⋊Q₈×C₇₉	C₂
socle	C₂³×C₇₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₇₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	C₄×C₂²⋊Q₈	D₇₉
hypocenter	C₇₉	#7600
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₄×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
3. #23761226	C₂	semidirect
4. #23761223	C₂	semidirect
33. C₂²⋊Q₈×C₇₉	C₈	semidirect
192. C₇₉	#7600	semidirect
217. C₂²⋊Q₈	C₇₉⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
#23763468	2
#23763380	2
#23761226	2
#23761223	2
C₄×C₂²⋊Q₈×C₇₉	2
#7600	79