Subgroups — #34182895

Order 20224.

566 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23772511	C₂	1	1	yes	maximal, characteristic, complemented
2	#23764195	C₂	1	1	yes	maximal, characteristic, complemented
3	#23761791	C₂	1	1	yes	maximal, characteristic, complemented
4	#23761782	C₂	1	1	yes	maximal, characteristic, complemented
5	#23761251	C₂	1	1	yes	maximal, characteristic, complemented
6	#23761238	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×AGL(1,ℤ/8)×C₇₉	C₂	1	1	yes	maximal, characteristic
8	Q₈×C₇₉⋊C₈	—	2	1	no	—
9	D₄×C₇₉⋊C₈	—	2	2	no	—
10	D₄×C₇₉⋊C₈	—	2	1	no	—
11	#19098616	—	2	1	no	—
12	#19098616	C₂²	1	1	yes	characteristic
13	#19098616	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
15	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
17	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
18	Q₈⋊(C₇₉⋊C₈)	—	2	1	no	—
19	D₄⋊(C₇₉⋊C₈)	—	2	1	no	—
20	D₄⋊(C₇₉⋊C₈)	—	2	1	no	—
21	D₄⋊(C₇₉⋊C₈)	—	2	1	no	—
22	C₂×AGL(1,ℤ/8)×C₇₉	C₄	1	1	yes	characteristic
23	C₄×#41×C₇₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
25	#442×C₇₉	—	2	1	no	—
26	#440×C₇₉	—	2	1	no	—
27	C₄×SD₁₆×C₇₉	—	2	1	no	—
28	C₄×D₈×C₇₉	—	2	1	no	—
29	#428×C₇₉	C₄	1	1	yes	characteristic
30	#418×C₇₉	C₄	1	1	yes	characteristic
31	#417×C₇₉	C₄	1	1	yes	characteristic
32	C₄×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
33	C₂²×C₇₉⋊C₈	—	2	1	no	—
34	C₂²×C₇₉⋊C₈	—	2	2	no	—
35	C₂²×C₇₉⋊C₈	D₄	1	2	yes	—
36	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
37	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
38	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
39	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
40	C₄⋊(C₇₉⋊C₈)	D₄	1	1	yes	characteristic
41	C₄⋊(C₇₉⋊C₈)	D₄	1	1	yes	characteristic
42	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
43	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
44	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
45	C₂²⋊(C₇₉⋊C₈)	—	4	4	no	—
46	C₄×C₇₉⋊C₈	—	2	2	no	—
47	C₄×C₇₉⋊C₈	—	2	1	no	—
48	C₄×C₇₉⋊C₈	—	2	1	no	—
49	C₄×C₇₉⋊C₈	—	2	1	no	—
50	C₄×C₇₉⋊C₈	—	2	1	no	—
51	C₂×#41×C₇₉	C₂×C₄	1	1	yes	characteristic
52	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
53	C₂³×C₄×C₇₉	—	2	1	no	—
54	AGL(1,ℤ/8)×C₇₉	—	2	2	no	—
55	AGL(1,ℤ/8)×C₇₉	C₈	1	4	yes	complemented
56	C₂×SD₁₆×C₇₉	—	2	1	no	—
57	C₂×D₈×C₇₉	—	2	1	no	—
58	C₂×M₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
59	C₂×M₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
60	C₄×Q₈×C₇₉	D₄	1	1	yes	characteristic
61	C₄×Q₈×C₇₉	D₄	1	1	yes	characteristic
62	C₄×D₄×C₇₉	—	2	1	no	—
63	C₄×D₄×C₇₉	—	2	1	no	—
64	C₄×D₄×C₇₉	—	2	1	no	—
65	C₄×D₄×C₇₉	—	2	1	no	—
66	C₄×D₄×C₇₉	—	2	1	no	—
67	C₄×D₄×C₇₉	—	2	1	no	—
68	C₄×D₄×C₇₉	D₄	1	1	yes	characteristic
69	C₄×D₄×C₇₉	D₄	1	1	yes	characteristic
70	#117×C₇₉	—	2	1	no	—
71	#117×C₇₉	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
74	C₂×C₄²×C₇₉	—	2	1	no	—
75	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
76	#107×C₇₉	—	2	1	no	—
77	#106×C₇₉	—	2	1	no	—
78	#103×C₇₉	—	2	1	no	—
79	#102×C₇₉	—	2	1	no	—
80	#102×C₇₉	—	2	1	no	—
81	#102×C₇₉	—	2	1	no	—
82	#97×C₇₉	—	2	1	no	—
83	C₄×C₈×C₇₉	—	2	1	no	—
84	C₂×C₇₉⋊C₈	—	2	2	no	—
85	C₂×C₇₉⋊C₈	—	2	1	no	—
86	C₂×C₇₉⋊C₈	—	2	2	no	—
87	C₂×C₇₉⋊C₈	—	2	1	no	—
88	C₂×C₇₉⋊C₈	—	4	2	no	—
89	C₂×C₇₉⋊C₈	—	4	1	no	—
90	C₂×C₇₉⋊C₈	—	4	1	no	—
91	C₂×C₇₉⋊C₈	—	4	1	no	—
92	C₂×C₇₉⋊C₈	—	8	2	no	—
93	C₂⁴×C₇₉	—	2	1	no	—
94	#41×C₇₉	—	2	1	no	—
95	#41×C₇₉	—	2	1	no	—
96	#41×C₇₉	C₂×C₈	1	2	yes	—
97	#41×C₇₉	M₁₆	1	2	yes	—
98	C₂×Q₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
99	C₂×D₄×C₇₉	—	2	1	no	—
100	C₂×D₄×C₇₉	—	2	1	no	—
101	C₂×D₄×C₇₉	—	2	1	no	—
102	C₂×D₄×C₇₉	—	2	1	no	—
103	C₂×D₄×C₇₉	—	2	1	no	—
104	C₂×D₄×C₇₉	—	2	1	no	—
105	C₂×D₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
106	C₂×D₄×C₇₉	C₂×C₈	1	2	yes	complemented
107	C₂²×C₄×C₇₉	—	2	1	no	—
108	C₂²×C₄×C₇₉	—	2	1	no	—
109	C₂²×C₄×C₇₉	—	2	1	no	—
110	C₂²×C₄×C₇₉	—	2	1	no	—
111	C₂²×C₄×C₇₉	—	4	2	no	—
112	C₂²×C₄×C₇₉	—	4	2	no	—
113	C₂²×C₄×C₇₉	—	4	1	no	—
114	C₂²×C₄×C₇₉	—	4	1	no	—
115	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
118	SD₁₆×C₇₉	—	2	4	no	—
119	D₈×C₇₉	—	2	4	no	—
120	M₁₆×C₇₉	—	2	1	no	—
121	M₁₆×C₇₉	—	2	1	no	—
122	M₁₆×C₇₉	—	2	1	no	—
123	M₁₆×C₇₉	C₂×C₈	1	2	yes	complemented
124	C₂×C₈×C₇₉	—	2	1	no	—
125	C₂×C₈×C₇₉	—	2	1	no	—
126	C₄⋊C₄×C₇₉	—	2	1	no	—
127	C₄⋊C₄×C₇₉	—	2	1	no	—
128	C₄⋊C₄×C₇₉	—	2	1	no	—
129	C₄⋊C₄×C₇₉	—	2	1	no	—
130	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
131	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
132	C₂²⋊C₄×C₇₉	—	2	1	no	—
133	C₂²⋊C₄×C₇₉	—	2	1	no	—
134	C₂²⋊C₄×C₇₉	—	2	1	no	—
135	C₂²⋊C₄×C₇₉	—	4	1	no	—
136	C₂²⋊C₄×C₇₉	—	4	1	no	—
137	C₄²×C₇₉	—	2	1	no	—
138	C₄²×C₇₉	—	2	1	no	—
139	C₄²×C₇₉	—	2	1	no	—
140	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₇₉	#41	1	1	yes	characteristic
144	C₂³×C₇₉	—	2	1	no	—
145	C₂³×C₇₉	—	2	2	no	—
146	C₂³×C₇₉	—	4	2	no	—
147	C₂³×C₇₉	—	4	2	no	—
148	C₂³×C₇₉	—	4	1	no	—
149	C₂³×C₇₉	—	4	1	no	—
150	C₂³×C₇₉	C₄×D₄	1	1	yes	characteristic
151	Q₈×C₇₉	—	2	1	no	—
152	Q₈×C₇₉	C₂²⋊C₈	1	2	yes	complemented
153	D₄×C₇₉	—	2	2	no	—
154	D₄×C₇₉	—	2	2	no	—
155	D₄×C₇₉	—	2	2	no	—
156	D₄×C₇₉	—	2	1	no	—
157	D₄×C₇₉	—	2	2	no	—
158	D₄×C₇₉	—	4	1	no	—
159	D₄×C₇₉	—	4	1	no	—
160	D₄×C₇₉	C₂²⋊C₈	1	2	yes	complemented
161	C₂×C₄×C₇₉	—	2	1	no	—
162	C₂×C₄×C₇₉	—	2	2	no	—
163	C₂×C₄×C₇₉	—	2	2	no	—
164	C₂×C₄×C₇₉	—	2	1	no	—
165	C₂×C₄×C₇₉	—	2	1	no	—
166	C₂×C₄×C₇₉	—	2	1	no	—
167	C₂×C₄×C₇₉	—	2	1	no	—
168	C₂×C₄×C₇₉	—	4	1	no	—
169	C₂×C₄×C₇₉	—	4	1	no	—
170	C₂×C₄×C₇₉	—	4	1	no	—
171	C₂×C₄×C₇₉	—	4	2	no	—
172	C₂×C₄×C₇₉	—	4	1	no	—
173	C₂×C₄×C₇₉	—	8	1	no	—
174	C₂×C₄×C₇₉	—	8	2	no	—
175	C₂×C₄×C₇₉	—	8	1	no	—
176	C₂×C₄×C₇₉	—	8	1	no	—
177	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
179	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
180	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
181	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
182	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
183	C₂×C₄×C₇₉	C₂²×C₈	1	1	yes	characteristic
184	C₂×C₄×C₇₉	C₂×M₁₆	1	1	yes	characteristic
185	C₂×C₄×C₇₉	#131	1	1	yes	characteristic
186	C₂×C₄×C₇₉	#131	1	1	yes	characteristic
187	C₈×C₇₉	—	2	2	no	—
188	C₈×C₇₉	—	4	1	no	—
189	C₇₉⋊C₈	—	4	2	no	—
190	C₇₉⋊C₈	—	4	2	no	—
191	C₇₉⋊C₈	—	4	1	no	—
192	C₇₉⋊C₈	—	4	1	no	—
193	C₇₉⋊C₈	—	8	1	no	—
194	C₂²×C₇₉	—	2	1	no	—
195	C₂²×C₇₉	—	2	1	no	—
196	C₂²×C₇₉	—	2	2	no	—
197	C₂²×C₇₉	—	4	4	no	—
198	C₂²×C₇₉	—	4	1	no	—
199	C₂²×C₇₉	—	4	1	no	—
200	C₂²×C₇₉	—	4	2	no	—
201	C₂²×C₇₉	—	8	2	no	—
202	C₂²×C₇₉	—	8	1	no	—
203	C₂²×C₇₉	—	8	1	no	—
204	C₂²×C₇₉	#386	1	1	yes	characteristic
205	C₂²×C₇₉	C₈×D₄	1	1	yes	characteristic
206	C₂²×C₇₉	#435	1	1	yes	characteristic
207	C₄×C₇₉	—	2	2	no	—
208	C₄×C₇₉	—	2	1	no	—
209	C₄×C₇₉	—	2	1	no	—
210	C₄×C₇₉	—	2	1	no	—
211	C₄×C₇₉	—	4	1	no	—
212	C₄×C₇₉	—	4	1	no	—
213	C₄×C₇₉	—	8	1	no	—
214	C₄×C₇₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
215	C₄×C₇₉	#408	1	1	yes	characteristic
216	C₄×C₇₉	C₈×D₄	1	1	yes	characteristic
217	C₄×C₇₉	#435	1	1	yes	characteristic
218	C₄×C₇₉	#453	1	1	yes	characteristic
219	C₄×C₇₉	#454	1	1	yes	characteristic
220	#8954	—	79	1	no	maximal, Sylow
221	C₂×C₇₉	—	2	1	no	—
222	C₂×C₇₉	—	2	1	no	—
223	C₂×C₇₉	—	4	2	no	—
224	C₂×C₇₉	—	8	2	no	—
225	C₂×C₇₉	#1869	1	1	yes	characteristic
226	C₂×C₇₉	#1881	1	1	yes	characteristic
227	C₂×C₇₉	#1883	1	1	yes	characteristic
228	#2988	—	79	1	no	—
229	C₄×AGL(1,ℤ/8)	D₇₉	1	1	yes	characteristic
230	#1954	—	79	1	no	—
231	#1478	—	79	1	no	—
232	#1476	—	79	1	no	—
233	#1283	—	79	1	no	—
234	#1278	—	79	1	no	—
235	C₇₉	#8954	1	1	yes	characteristic, complemented, Sylow
236	C₂×AGL(1,ℤ/8)	Dic₇₉	1	1	yes	characteristic
237	C₄×#41	C₂×D₇₉	1	1	yes	characteristic
238	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
239	C₈×Q₈	—	158	1	no	—
240	#442	—	2	1	no	—
241	#440	—	2	1	no	—
242	C₄×SD₁₆	—	2	1	no	—
243	C₄×D₈	—	2	1	no	—
244	C₈×D₄	—	158	2	no	—
245	C₈×D₄	—	158	1	no	—
246	#431	—	79	1	no	—
247	#431	—	79	1	no	—
248	#431	—	158	1	no	—
249	#428	Dic₇₉	1	1	yes	characteristic
250	C₂×C₄⋊C₈	—	79	1	no	—
251	C₂×C₄⋊C₈	—	158	1	no	—
252	#418	Dic₇₉	1	1	yes	characteristic
253	#417	Dic₇₉	1	1	yes	characteristic
254	C₂×C₂²⋊C₈	—	158	2	no	—
255	C₄×M₁₆	C₂×D₇₉	1	1	yes	characteristic
256	C₂×C₄×C₈	—	79	1	no	—
257	Q₈⋊C₈	—	158	1	no	—
258	D₄⋊C₈	—	158	1	no	—
259	D₄⋊C₈	—	158	1	no	—
260	D₄⋊C₈	—	158	1	no	—
261	C₂×#41	C₂×Dic₇₉	1	1	yes	characteristic
262	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
263	C₂³×C₄	—	2	1	no	—
264	AGL(1,ℤ/8)	—	2	2	no	—
265	AGL(1,ℤ/8)	C₇₉⋊C₈	1	4	yes	complemented
266	C₂×SD₁₆	—	2	1	no	—
267	C₂×D₈	—	2	1	no	—
268	C₂×M₁₆	C₂×Dic₇₉	1	1	yes	characteristic
269	C₂×M₁₆	C₂×Dic₇₉	1	1	yes	characteristic
270	C₂²×C₈	—	79	2	no	—
271	C₂²×C₈	—	158	1	no	—
272	C₂²×C₈	—	158	2	no	—
273	C₄×Q₈	C₂²⋊D₇₉	1	1	yes	characteristic
274	C₄×Q₈	C₂²⋊D₇₉	1	1	yes	characteristic
275	C₄×D₄	—	2	1	no	—
276	C₄×D₄	—	2	1	no	—
277	C₄×D₄	—	2	1	no	—
278	C₄×D₄	—	2	1	no	—
279	C₄×D₄	—	2	1	no	—
280	C₄×D₄	—	2	1	no	—
281	C₄×D₄	C₂²⋊D₇₉	1	1	yes	characteristic
282	C₄×D₄	C₂²⋊D₇₉	1	1	yes	characteristic
283	#117	—	2	1	no	—
284	#117	C₂×Dic₇₉	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
286	C₂×C₂²⋊C₄	—	2	1	no	—
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
289	#107	—	2	1	no	—
290	#106	—	2	1	no	—
291	C₄⋊C₈	—	79	1	no	—
292	C₄⋊C₈	—	79	1	no	—
293	C₄⋊C₈	—	158	2	no	—
294	C₄⋊C₈	—	158	1	no	—
295	C₄⋊C₈	—	158	1	no	—
296	C₄⋊C₈	—	158	1	no	—
297	#103	—	2	1	no	—
298	#102	—	2	1	no	—
299	#102	—	2	1	no	—
300	#102	—	2	1	no	—
301	C₂²⋊C₈	—	316	4	no	—
302	C₂²⋊C₈	—	158	1	no	—
303	C₂²⋊C₈	—	158	2	no	—
304	C₂²⋊C₈	—	158	1	no	—
305	#97	—	2	1	no	—
306	C₄×C₈	—	2	1	no	—
307	C₄×C₈	—	158	2	no	—
308	C₄×C₈	—	158	1	no	—
309	C₄×C₈	—	158	1	no	—
310	C₄×C₈	—	158	1	no	—
311	C₄×C₈	—	158	1	no	—
312	C₂⁴	—	2	1	no	—
313	#41	—	2	1	no	—
314	#41	—	2	1	no	—
315	#41	C₂×C₇₉⋊C₈	1	2	yes	—
316	#41	#11929608	1	2	yes	—
317	C₂×Q₈	C₂²⋊Dic₇₉	1	1	yes	characteristic
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
325	C₂×D₄	C₂×C₇₉⋊C₈	1	2	yes	complemented
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	—	4	2	no	—
331	C₂²×C₄	—	4	2	no	—
332	C₂²×C₄	—	4	1	no	—
333	C₂²×C₄	—	4	1	no	—
334	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
335	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
336	C₂²×C₄	#11929623	1	1	yes	characteristic
337	SD₁₆	—	2	4	no	—
338	D₈	—	2	4	no	—
339	M₁₆	—	2	1	no	—
340	M₁₆	—	2	1	no	—
341	M₁₆	—	2	1	no	—
342	M₁₆	C₂×C₇₉⋊C₈	1	2	yes	complemented
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	316	1	no	—
346	C₂×C₈	—	316	1	no	—
347	C₂×C₈	—	316	2	no	—
348	C₂×C₈	—	316	1	no	—
349	C₂×C₈	—	632	2	no	—
350	C₂×C₈	—	158	2	no	—
351	C₂×C₈	—	158	1	no	—
352	C₂×C₈	—	158	1	no	—
353	C₂×C₈	—	158	2	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
359	C₄⋊C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
360	C₂²⋊C₄	—	2	1	no	—
361	C₂²⋊C₄	—	2	1	no	—
362	C₂²⋊C₄	—	2	1	no	—
363	C₂²⋊C₄	—	4	1	no	—
364	C₂²⋊C₄	—	4	1	no	—
365	C₄²	—	2	1	no	—
366	C₄²	—	2	1	no	—
367	C₄²	—	2	1	no	—
368	C₄²	D₄×D₇₉	1	1	yes	characteristic
369	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
370	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
371	C₄²	#11929623	1	1	yes	characteristic
372	C₂³	—	2	1	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	4	2	no	—
375	C₂³	—	4	2	no	—
376	C₂³	—	4	1	no	—
377	C₂³	—	4	1	no	—
378	C₂³	D₄×Dic₇₉	1	1	yes	characteristic
379	Q₈	—	2	1	no	—
380	Q₈	C₂²⋊(C₇₉⋊C₈)	1	2	yes	complemented
381	D₄	—	2	2	no	—
382	D₄	—	2	2	no	—
383	D₄	—	2	2	no	—
384	D₄	—	2	2	no	—
385	D₄	—	2	1	no	—
386	D₄	—	4	1	no	—
387	D₄	—	4	1	no	—
388	D₄	C₂²⋊(C₇₉⋊C₈)	1	2	yes	complemented
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	8	1	no	—
402	C₂×C₄	—	8	2	no	—
403	C₂×C₄	—	8	1	no	—
404	C₂×C₄	—	8	1	no	—
405	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
406	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
407	C₂×C₄	#14579129	1	1	yes	characteristic
408	C₂×C₄	#14579133	1	1	yes	characteristic
409	C₂×C₄	#14579133	1	1	yes	characteristic
410	C₂×C₄	#14579142	1	1	yes	characteristic
411	C₂×C₄	C₂²×C₇₉⋊C₈	1	1	yes	characteristic
412	C₂×C₄	C₂×#11929608	1	1	yes	characteristic
413	C₂×C₄	#14579168	1	1	yes	characteristic
414	C₂×C₄	#14579168	1	1	yes	characteristic
415	C₈	—	2	2	no	—
416	C₈	—	4	1	no	—
417	C₈	—	316	2	no	—
418	C₈	—	316	2	no	—
419	C₈	—	316	1	no	—
420	C₈	—	316	1	no	—
421	C₈	—	632	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	4	4	no	—
426	C₂²	—	4	1	no	—
427	C₂²	—	4	1	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	8	2	no	—
430	C₂²	—	8	1	no	—
431	C₂²	—	8	1	no	—
432	C₂²	#19098443	1	1	yes	characteristic
433	C₂²	D₄×C₇₉⋊C₈	1	1	yes	characteristic
434	C₂²	#19098635	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	2	no	—
439	C₄	—	4	1	no	—
440	C₄	—	4	1	no	—
441	C₄	—	8	1	no	—
442	C₄	C₂×C₂²⋊(C₇₉⋊C₈)	1	1	yes	characteristic
443	C₄	#19098530	1	1	yes	characteristic
444	C₄	D₄×C₇₉⋊C₈	1	1	yes	characteristic
445	C₄	#19098635	1	1	yes	characteristic
446	C₄	#19098729	1	1	yes	characteristic
447	C₄	#19098734	1	1	yes	characteristic
448	C₂	—	2	1	no	—
449	C₂	—	2	1	no	—
450	C₂	—	4	2	no	—
451	C₂	—	8	2	no	—
452	C₂	#23763693	1	1	yes	characteristic
453	C₂	#23763764	1	1	yes	characteristic
454	C₂	#23763778	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14579129
commutator	C₂×C₄×C₇₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₄×AGL(1,ℤ/8)×C₇₉	C₂
socle	C₂²×C₇₉	#386
prime radical	C₂×AGL(1,ℤ/8)×C₇₉	C₄
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	C₄×AGL(1,ℤ/8)	D₇₉
hypocenter	C₇₉	#8954
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. #23772511	C₂	semidirect
2. #23764195	C₂	semidirect
3. #23761791	C₂	semidirect
4. #23761782	C₂	semidirect
5. #23761251	C₂	semidirect
6. #23761238	C₂	semidirect
55. AGL(1,ℤ/8)×C₇₉	C₈	semidirect
106. C₂×D₄×C₇₉	C₂×C₈	semidirect
123. M₁₆×C₇₉	C₂×C₈	semidirect
152. Q₈×C₇₉	C₂²⋊C₈	semidirect
160. D₄×C₇₉	C₂²⋊C₈	semidirect
235. C₇₉	#8954	semidirect
265. AGL(1,ℤ/8)	C₇₉⋊C₈	semidirect
325. C₂×D₄	C₂×C₇₉⋊C₈	semidirect
342. M₁₆	C₂×C₇₉⋊C₈	semidirect
380. Q₈	C₂²⋊(C₇₉⋊C₈)	semidirect
388. D₄	C₂²⋊(C₇₉⋊C₈)	semidirect

Maximal subgroups

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

subgroup	index
#23772511	2
#23764195	2
#23761791	2
#23761782	2
#23761251	2
#23761238	2
C₄×AGL(1,ℤ/8)×C₇₉	2
#8954	79