Subgroups — #35179021

Order 20224.

1606 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23777890	C₂	1	1	yes	maximal, characteristic
2	#23777210	C₂	1	1	yes	maximal, characteristic, complemented
3	#23776367	C₂	1	2	yes	maximal, complemented
4	#23776330	C₂	1	1	yes	maximal, characteristic, complemented
5	#23776308	C₂	1	1	yes	maximal, characteristic, complemented
6	#23776286	C₂	1	2	yes	maximal, complemented
7	Q₁₆×Dic₁₅₈	C₂	1	1	yes	maximal, characteristic, complemented
8	#23776273	C₂	1	1	yes	maximal, characteristic, complemented
9	#23776246	C₂	1	2	yes	maximal, complemented
10	#23776201	C₂	1	1	yes	maximal, characteristic, complemented
11	#23776138	C₂	1	1	yes	maximal, characteristic, complemented
12	#23776083	C₂	1	1	yes	maximal, characteristic, complemented
13	#23776080	C₂	1	2	yes	maximal, complemented
14	#23776076	C₂	1	1	yes	maximal, characteristic, complemented
15	#23774679	C₂	1	2	yes	maximal
16	#23774664	C₂	1	2	yes	maximal, complemented
17	#23774575	C₂	1	1	yes	maximal, characteristic
18	#23774561	C₂	1	1	yes	maximal, characteristic, complemented
19	#23773694	C₂	1	2	yes	maximal, complemented
20	#23773622	C₂	1	2	yes	maximal
21	#23773439	C₂	1	1	yes	maximal, characteristic, complemented
22	#23772501	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇₉×#3108	C₂	1	1	yes	maximal, characteristic
24	#19099316	—	2	2	no	—
25	Q₈×Dic₁₅₈	—	2	1	no	—
26	Q₈×Dic₁₅₈	C₂²	1	1	yes	characteristic
27	Q₈×Dic₁₅₈	C₂²	1	1	yes	characteristic
28	Q₈×Dic₁₅₈	C₂²	1	1	yes	characteristic
29	#19099292	—	2	1	no	—
30	#19099292	C₂²	1	1	yes	characteristic
31	#19099292	C₂²	1	1	yes	characteristic
32	#19099291	C₂²	1	1	yes	characteristic
33	#19099290	C₂²	1	2	yes	—
34	#19099289	—	2	2	no	—
35	#19099289	C₂²	1	2	yes	—
36	#19099289	C₂²	1	2	yes	—
37	#19099283	—	2	1	no	—
38	#19099283	C₂²	1	1	yes	characteristic
39	#19099282	C₂²	1	2	yes	—
40	#19099270	C₂²	1	1	yes	characteristic
41	#19099253	—	2	1	no	—
42	#19099194	—	2	2	no	—
43	#19099194	C₂²	1	2	yes	—
44	#19099191	—	2	1	no	—
45	#19099180	C₂²	1	2	yes	—
46	#19099175	—	2	1	no	—
47	#19099173	C₂²	1	2	yes	—
48	#19099170	—	2	2	no	—
49	#19099120	—	2	1	no	—
50	#19099120	—	2	1	no	—
51	#19099120	C₂²	1	1	yes	characteristic
52	#19099120	C₂²	1	1	yes	characteristic
53	#19099120	C₂²	1	1	yes	characteristic
54	#19099041	C₂²	1	2	yes	—
55	#19098971	C₂²	1	2	yes	—
56	#19098970	C₂²	1	2	yes	—
57	#19098968	C₂²	1	1	yes	characteristic
58	#19098967	C₂²	1	2	yes	—
59	#19098963	C₂²	1	2	yes	—
60	#19098962	C₂²	1	2	yes	—
61	#19098961	C₂²	1	1	yes	characteristic
62	#19098930	C₂²	1	2	yes	—
63	#19098921	C₂²	1	2	yes	—
64	#19098917	C₂²	1	2	yes	—
65	#19098916	C₂²	1	2	yes	—
66	#19098914	C₂²	1	1	yes	characteristic
67	#19098914	C₂²	1	1	yes	characteristic
68	#19098912	C₂²	1	2	yes	—
69	#19098905	C₂²	1	2	yes	—
70	#19098905	C₂²	1	2	yes	—
71	#19098901	C₂²	1	2	yes	—
72	#19098898	C₂²	1	2	yes	—
73	#19098884	C₂²	1	2	yes	—
74	#19098873	C₂²	1	2	yes	—
75	#19098872	C₂²	1	2	yes	—
76	#19098871	C₂²	1	2	yes	—
77	#19098871	C₂²	1	2	yes	—
78	#19098869	C₂²	1	2	yes	—
79	#19098868	C₂²	1	2	yes	—
80	#19098868	C₂²	1	2	yes	—
81	#19098865	C₂²	1	2	yes	—
82	#19098858	C₂²	1	1	yes	characteristic
83	#19098858	C₂²	1	1	yes	characteristic
84	#19098858	C₂²	1	1	yes	characteristic
85	#19098857	C₂²	1	2	yes	—
86	#19098856	C₂²	1	2	yes	—
87	#19098856	C₂²	1	2	yes	—
88	#19098853	C₂²	1	1	yes	characteristic
89	#19098848	C₂²	1	1	yes	characteristic
90	#19098847	C₂²	1	2	yes	—
91	#19098846	C₂²	1	2	yes	—
92	#19098843	C₂²	1	1	yes	characteristic
93	#19098841	C₂²	1	2	yes	—
94	#19098783	C₂²	1	2	yes	—
95	#19098783	C₂²	1	2	yes	—
96	#19098773	C₂²	1	1	yes	characteristic
97	#19098773	C₂²	1	1	yes	characteristic
98	#19098771	C₂²	1	2	yes	—
99	#19098771	C₂²	1	2	yes	—
100	#19098719	C₂²	1	2	yes	—
101	#19098693	C₂²	1	1	yes	characteristic
102	#19098693	C₂²	1	1	yes	characteristic
103	#19098690	C₂²	1	2	yes	—
104	C₈×Dic₁₅₈	C₂²	1	1	yes	characteristic
105	C₈×Dic₁₅₈	C₂²	1	1	yes	characteristic
106	#19098687	C₂²	1	2	yes	—
107	#19098670	C₂²	1	2	yes	—
108	#19098667	C₂²	1	2	yes	—
109	#19098667	C₂²	1	2	yes	—
110	#19098664	C₂²	1	2	yes	—
111	Q₁₆×Dic₇₉	C₂²	1	2	yes	—
112	C₄×#11929614	C₂²	1	2	yes	—
113	C₄×#11929614	C₂²	1	2	yes	—
114	#19098655	C₂²	1	2	yes	—
115	#19098655	C₂²	1	2	yes	—
116	SD₁₆×Dic₇₉	C₂²	1	2	yes	—
117	#19098621	C₂²	1	2	yes	—
118	#19098621	C₂²	1	2	yes	—
119	#19098616	C₂²	1	1	yes	characteristic
120	#529×C₇₉	C₂²	1	1	yes	characteristic
121	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
122	#483×C₇₉	C₂²	1	1	yes	characteristic
123	#480×C₇₉	C₂²	1	1	yes	characteristic
124	#479×C₇₉	C₂²	1	1	yes	characteristic
125	#479×C₇₉	C₂²	1	1	yes	characteristic
126	#464×C₇₉	C₂²	1	1	yes	characteristic
127	#464×C₇₉	C₂²	1	1	yes	characteristic
128	#451×C₇₉	C₂²	1	1	yes	characteristic
129	#448×C₇₉	C₂²	1	1	yes	characteristic
130	C₄×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
131	C₄×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
132	C₄×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
133	C₄×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
134	#431×C₇₉	C₂²	1	1	yes	characteristic
135	C₂×#11929614	C₂³	1	2	yes	—
136	C₂×#11929614	C₂³	1	2	yes	—
137	#14579161	—	2	1	no	—
138	#14579161	—	2	1	no	—
139	#14579161	—	2	1	no	—
140	#14579161	—	2	1	no	—
141	#14579161	—	2	1	no	—
142	#14579161	D₄	1	1	yes	characteristic
143	#14579161	D₄	1	1	yes	characteristic
144	#14579161	C₂³	1	1	yes	characteristic
145	#14579161	C₂³	1	1	yes	characteristic
146	#14579161	C₂³	1	1	yes	characteristic
147	#14579161	C₂³	1	1	yes	characteristic
148	#14579160	—	2	2	no	—
149	#14579160	—	2	2	no	—
150	#14579160	—	2	2	no	—
151	#14579160	—	2	2	no	—
152	#14579160	—	2	2	no	—
153	#14579160	—	2	2	no	—
154	#14579160	—	2	2	no	—
155	#14579160	C₂³	1	2	yes	—
156	#14579160	C₂³	1	2	yes	—
157	#14579160	C₂³	1	2	yes	—
158	#14579159	C₂³	1	2	yes	—
159	#14579154	—	2	2	no	—
160	#14579154	—	2	2	no	—
161	#14579154	—	2	2	no	—
162	#14579154	—	2	2	no	—
163	#14579154	—	2	2	no	—
164	#14579154	—	2	2	no	—
165	#14579153	—	2	1	no	—
166	#14579153	—	2	1	no	—
167	#14579153	—	2	2	no	—
168	#14579153	—	2	2	no	—
169	#14579153	D₄	1	2	yes	—
170	#14579153	C₂³	1	2	yes	—
171	#14579152	—	2	2	no	—
172	#14579152	—	2	2	no	—
173	#14579152	—	2	2	no	—
174	#14579152	—	2	2	no	—
175	#14579152	—	2	2	no	—
176	#14579152	—	2	2	no	—
177	#14579152	C₂³	1	2	yes	—
178	#14579152	C₂³	1	2	yes	—
179	#14579152	C₂³	1	2	yes	—
180	#14579151	—	2	2	no	—
181	#14579151	—	2	2	no	—
182	#14579151	—	2	2	no	—
183	#14579151	—	2	2	no	—
184	#14579148	—	2	2	no	—
185	#14579148	C₂³	1	2	yes	—
186	#14579142	—	2	2	no	—
187	#14579140	—	2	1	no	—
188	#14579140	—	2	1	no	—
189	#14579140	—	2	1	no	—
190	#14579140	—	2	1	no	—
191	#14579140	—	2	1	no	—
192	#14579140	—	2	2	no	—
193	#14579140	—	2	2	no	—
194	#14579140	D₄	1	2	yes	—
195	#14579140	D₄	1	1	yes	characteristic
196	#14579140	D₄	1	1	yes	characteristic
197	#14579140	C₂³	1	2	yes	—
198	#14579138	—	2	2	no	—
199	#14579138	—	2	2	no	—
200	#14579138	—	2	2	no	—
201	Q₈×Dic₇₉	—	2	2	no	—
202	Q₈×Dic₇₉	—	2	2	no	—
203	Q₈×Dic₇₉	C₂³	1	2	yes	—
204	Q₈×Dic₇₉	C₂³	1	2	yes	—
205	Q₈×Dic₇₉	C₂³	1	2	yes	—
206	Q₈×Dic₇₉	C₂³	1	2	yes	—
207	Q₈×Dic₇₉	C₂³	1	2	yes	—
208	C₄×Dic₁₅₈	—	2	1	no	—
209	C₄×Dic₁₅₈	—	2	1	no	—
210	C₄×Dic₁₅₈	—	2	1	no	—
211	C₄×Dic₁₅₈	—	2	1	no	—
212	C₄×Dic₁₅₈	—	2	1	no	—
213	C₄×Dic₁₅₈	—	2	1	no	—
214	C₄×Dic₁₅₈	—	2	1	no	—
215	C₄×Dic₁₅₈	—	2	1	no	—
216	C₄×Dic₁₅₈	—	2	1	no	—
217	C₄×Dic₁₅₈	—	2	2	no	—
218	C₄×Dic₁₅₈	—	2	2	no	—
219	C₄×Dic₁₅₈	C₂³	1	2	yes	—
220	C₄×Dic₁₅₈	C₂³	1	2	yes	—
221	C₄×Dic₁₅₈	C₂³	1	1	yes	characteristic
222	C₄×Dic₁₅₈	C₂³	1	1	yes	characteristic
223	#14579126	—	2	2	no	—
224	#14579126	C₂³	1	2	yes	—
225	#14579126	C₂³	1	2	yes	—
226	D₄×Dic₇₉	C₂³	1	2	yes	—
227	#14579120	—	2	1	no	—
228	#14579120	—	2	1	no	—
229	#14579120	—	2	2	no	—
230	#14579120	—	2	2	no	—
231	#14579120	C₂³	1	2	yes	—
232	#14579120	C₂³	1	2	yes	—
233	#14579117	—	2	2	no	—
234	C₂×C₄⋊Dic₇₉	—	2	1	no	—
235	#14579095	C₂³	1	2	yes	—
236	#14579095	C₂³	1	2	yes	—
237	#14579094	C₂³	1	2	yes	—
238	#14579094	C₂³	1	2	yes	—
239	#14579094	C₂³	1	2	yes	—
240	#14579094	C₂³	1	2	yes	—
241	#14579093	C₂³	1	2	yes	—
242	#14579093	C₂³	1	2	yes	—
243	#14579092	C₂³	1	2	yes	—
244	#14579092	C₂³	1	2	yes	—
245	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
246	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
247	Dic₇₉⋊C₈	C₂³	1	2	yes	—
248	Dic₇₉⋊C₈	C₂³	1	2	yes	—
249	Dic₇₉⋊C₈	C₂³	1	2	yes	—
250	Dic₇₉⋊C₈	C₂³	1	2	yes	—
251	#14579086	C₂³	1	2	yes	—
252	#14579086	C₂³	1	2	yes	—
253	#14579086	C₂³	1	2	yes	—
254	#14579086	C₂³	1	2	yes	—
255	#14579085	C₂³	1	2	yes	—
256	#14579085	C₂³	1	2	yes	—
257	#14579085	C₂³	1	2	yes	—
258	#14579085	C₂³	1	2	yes	—
259	#14579084	C₂³	1	2	yes	—
260	#14579084	C₂³	1	2	yes	—
261	#14579082	C₂³	1	2	yes	—
262	#14579082	C₂³	1	2	yes	—
263	C₂²⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
264	#14579071	C₂³	1	2	yes	—
265	#14579071	C₂³	1	2	yes	—
266	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
267	C₈×Dic₇₉	C₂³	1	2	yes	—
268	C₈×Dic₇₉	C₂³	1	2	yes	—
269	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
270	C₂×Q₁₆×C₇₉	C₂³	1	1	yes	characteristic
271	C₂×Q₁₆×C₇₉	C₂³	1	1	yes	characteristic
272	C₂×SD₁₆×C₇₉	C₂³	1	1	yes	characteristic
273	C₂×SD₁₆×C₇₉	C₂³	1	1	yes	characteristic
274	#126×C₇₉	—	2	1	no	—
275	#125×C₇₉	C₂³	1	1	yes	characteristic
276	#124×C₇₉	C₂³	1	1	yes	characteristic
277	#123×C₇₉	—	2	1	no	—
278	C₂²⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
279	#121×C₇₉	C₂³	1	1	yes	characteristic
280	C₄×Q₈×C₇₉	—	2	1	no	—
281	C₄×Q₈×C₇₉	—	2	1	no	—
282	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
283	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
284	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
285	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
286	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
287	C₄×D₄×C₇₉	—	2	1	no	—
288	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
289	#117×C₇₉	—	2	1	no	—
290	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
291	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
292	C₂×C₄²×C₇₉	—	2	1	no	—
293	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
294	#107×C₇₉	C₂³	1	1	yes	characteristic
295	#107×C₇₉	C₂³	1	1	yes	characteristic
296	#106×C₇₉	C₂³	1	1	yes	characteristic
297	#106×C₇₉	C₂³	1	1	yes	characteristic
298	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
299	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
300	#103×C₇₉	C₂³	1	1	yes	characteristic
301	#103×C₇₉	C₂³	1	1	yes	characteristic
302	#103×C₇₉	C₂³	1	1	yes	characteristic
303	#103×C₇₉	C₂³	1	1	yes	characteristic
304	#103×C₇₉	C₂³	1	1	yes	characteristic
305	#103×C₇₉	C₂³	1	1	yes	characteristic
306	#102×C₇₉	C₂³	1	1	yes	characteristic
307	#102×C₇₉	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
312	C₂×Dic₁₅₈	—	2	2	no	—
313	C₂×Dic₁₅₈	—	2	2	no	—
314	C₂×Dic₁₅₈	—	2	2	no	—
315	C₂×Dic₁₅₈	—	2	1	no	—
316	C₂×Dic₁₅₈	—	2	1	no	—
317	C₂×Dic₁₅₈	—	2	1	no	—
318	C₂×Dic₁₅₈	C₂×D₄	1	1	yes	characteristic
319	C₂×Dic₁₅₈	C₂×D₄	1	1	yes	characteristic
320	C₂×Dic₁₅₈	C₂×D₄	1	2	yes	—
321	C₂×Dic₁₅₈	C₂⁴	1	2	yes	—
322	C₂²×Dic₇₉	—	2	2	no	—
323	#11929614	—	2	4	no	—
324	#11929614	—	2	4	no	—
325	C₂×C₇₉⋊C₈	C₂⁴	1	2	yes	—
326	C₂×C₇₉⋊C₈	C₂⁴	1	2	yes	—
327	C₄⋊Dic₇₉	—	2	2	no	—
328	C₄⋊Dic₇₉	—	2	2	no	—
329	C₄⋊Dic₇₉	—	2	2	no	—
330	C₄⋊Dic₇₉	—	2	2	no	—
331	C₄⋊Dic₇₉	—	2	2	no	—
332	C₄⋊Dic₇₉	—	2	2	no	—
333	C₄⋊Dic₇₉	—	2	2	no	—
334	C₄⋊Dic₇₉	—	2	2	no	—
335	C₄⋊Dic₇₉	—	2	1	no	—
336	C₄⋊Dic₇₉	—	2	1	no	—
337	C₄⋊Dic₇₉	—	2	1	no	—
338	C₄⋊Dic₇₉	—	2	1	no	—
339	C₄⋊Dic₇₉	—	2	1	no	—
340	C₄⋊Dic₇₉	C₂×D₄	1	1	yes	characteristic
341	C₄⋊Dic₇₉	C₂×D₄	1	1	yes	characteristic
342	C₄⋊Dic₇₉	C₂×D₄	1	2	yes	—
343	C₄⋊Dic₇₉	C₂×D₄	1	2	yes	—
344	C₄⋊Dic₇₉	C₂×D₄	1	2	yes	—
345	C₄⋊Dic₇₉	C₂⁴	1	2	yes	—
346	C₄⋊Dic₇₉	C₂⁴	1	2	yes	—
347	C₄⋊Dic₇₉	C₂⁴	1	2	yes	—
348	Dic₇₉⋊C₄	—	2	2	no	—
349	Dic₇₉⋊C₄	—	2	2	no	—
350	Dic₇₉⋊C₄	—	2	2	no	—
351	Dic₇₉⋊C₄	—	2	2	no	—
352	Dic₇₉⋊C₄	—	2	2	no	—
353	Dic₇₉⋊C₄	—	2	2	no	—
354	Dic₇₉⋊C₄	—	2	2	no	—
355	Dic₇₉⋊C₄	—	2	2	no	—
356	Dic₇₉⋊C₄	—	2	2	no	—
357	Dic₇₉⋊C₄	—	2	2	no	—
358	Dic₇₉⋊C₄	—	2	2	no	—
359	Dic₇₉⋊C₄	—	2	2	no	—
360	Dic₇₉⋊C₄	—	2	2	no	—
361	Dic₇₉⋊C₄	—	2	2	no	—
362	Dic₇₉⋊C₄	C₂×D₄	1	2	yes	—
363	Dic₇₉⋊C₄	C₂×D₄	1	2	yes	—
364	Dic₇₉⋊C₄	C₂×D₄	1	2	yes	—
365	Dic₇₉⋊C₄	C₂×D₄	1	2	yes	—
366	C₂²⋊Dic₇₉	—	2	2	no	—
367	C₂²⋊Dic₇₉	—	2	2	no	—
368	C₂²⋊Dic₇₉	—	2	2	no	—
369	C₂²⋊Dic₇₉	—	2	2	no	—
370	C₂²⋊Dic₇₉	—	2	2	no	—
371	C₂²⋊Dic₇₉	C₂×D₄	1	2	yes	—
372	C₂²⋊Dic₇₉	C₂×D₄	1	2	yes	—
373	C₄×Dic₇₉	—	2	2	no	—
374	C₄×Dic₇₉	—	2	2	no	—
375	C₄×Dic₇₉	—	2	2	no	—
376	C₄×Dic₇₉	—	2	2	no	—
377	C₄×Dic₇₉	—	2	2	no	—
378	C₄×Dic₇₉	—	2	2	no	—
379	C₄×Dic₇₉	—	2	2	no	—
380	C₄×Dic₇₉	—	2	2	no	—
381	C₄×Dic₇₉	—	2	2	no	—
382	C₄×Dic₇₉	C₂⁴	1	2	yes	—
383	C₄×Dic₇₉	C₂⁴	1	2	yes	—
384	C₂×Q₈×C₇₉	—	2	2	no	—
385	C₂×Q₈×C₇₉	—	2	2	no	—
386	C₂×Q₈×C₇₉	—	2	1	no	—
387	C₂×Q₈×C₇₉	C₂⁴	1	1	yes	characteristic
388	C₂×Q₈×C₇₉	C₂⁴	1	1	yes	characteristic
389	C₂×Q₈×C₇₉	C₂⁴	1	1	yes	characteristic
390	C₂×D₄×C₇₉	—	2	1	no	—
391	C₂×D₄×C₇₉	C₂⁴	1	1	yes	characteristic
392	C₂²×C₄×C₇₉	—	2	1	no	—
393	C₂²×C₄×C₇₉	—	2	1	no	—
394	C₂²×C₄×C₇₉	—	2	1	no	—
395	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
396	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
397	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
398	Q₁₆×C₇₉	—	2	2	no	—
399	Q₁₆×C₇₉	—	2	2	no	—
400	SD₁₆×C₇₉	—	2	2	no	—
401	SD₁₆×C₇₉	—	2	2	no	—
402	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
403	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
404	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
405	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₇₉	—	2	1	no	—
407	C₄⋊C₄×C₇₉	—	2	1	no	—
408	C₄⋊C₄×C₇₉	—	2	1	no	—
409	C₄⋊C₄×C₇₉	—	2	1	no	—
410	C₄⋊C₄×C₇₉	—	2	1	no	—
411	C₄⋊C₄×C₇₉	—	2	1	no	—
412	C₄⋊C₄×C₇₉	—	2	1	no	—
413	C₄⋊C₄×C₇₉	—	2	1	no	—
414	C₄⋊C₄×C₇₉	—	2	1	no	—
415	C₄⋊C₄×C₇₉	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₇₉	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄×C₇₉	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₇₉	C₂⁴	1	1	yes	characteristic
419	C₂²⋊C₄×C₇₉	—	2	1	no	—
420	C₂²⋊C₄×C₇₉	—	2	1	no	—
421	C₂²⋊C₄×C₇₉	—	2	1	no	—
422	C₂²⋊C₄×C₇₉	—	2	1	no	—
423	C₂²⋊C₄×C₇₉	—	2	1	no	—
424	C₄²×C₇₉	—	2	1	no	—
425	C₄²×C₇₉	—	2	1	no	—
426	C₄²×C₇₉	—	2	1	no	—
427	C₄²×C₇₉	—	2	1	no	—
428	C₄²×C₇₉	—	2	1	no	—
429	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
430	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
431	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
432	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
433	C₂³×C₇₉	—	2	1	no	—
434	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
435	Q₈×C₇₉	—	2	4	no	—
436	Q₈×C₇₉	—	2	1	no	—
437	Q₈×C₇₉	—	2	1	no	—
438	Q₈×C₇₉	—	2	1	no	—
439	Q₈×C₇₉	—	2	1	no	—
440	Q₈×C₇₉	2₋¹⁺⁴	1	2	yes	—
441	Q₈×C₇₉	2₋¹⁺⁴	1	2	yes	—
442	D₄×C₇₉	—	2	1	no	—
443	D₄×C₇₉	—	2	1	no	—
444	D₄×C₇₉	—	8	1	no	—
445	C₂×C₄×C₇₉	—	2	4	no	—
446	C₂×C₄×C₇₉	—	2	1	no	—
447	C₂×C₄×C₇₉	—	2	1	no	—
448	C₂×C₄×C₇₉	—	2	2	no	—
449	C₂×C₄×C₇₉	—	2	1	no	—
450	C₂×C₄×C₇₉	—	2	1	no	—
451	C₂×C₄×C₇₉	—	2	1	no	—
452	C₂×C₄×C₇₉	—	2	1	no	—
453	C₂×C₄×C₇₉	—	2	1	no	—
454	C₂×C₄×C₇₉	—	2	1	no	—
455	C₂×C₄×C₇₉	—	2	1	no	—
456	C₂×C₄×C₇₉	—	4	1	no	—
457	C₂×C₄×C₇₉	—	4	2	no	—
458	C₂×C₄×C₇₉	—	8	1	no	—
459	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
462	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
463	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
465	C₂×Dic₇₉	—	2	2	no	—
466	C₂×Dic₇₉	—	2	2	no	—
467	C₂×Dic₇₉	—	2	2	no	—
468	C₂×Dic₇₉	—	2	2	no	—
469	C₂×Dic₇₉	—	8	2	no	—
470	C₂×Dic₇₉	C₂²×D₄	1	2	yes	—
471	C₂×Dic₇₉	C₂²×D₄	1	2	yes	—
472	C₂×Dic₇₉	C₂²×D₄	1	2	yes	—
473	C₂×Dic₇₉	C₂²×D₄	1	2	yes	—
474	Dic₁₅₈	—	2	2	no	—
475	Dic₁₅₈	—	2	2	no	—
476	Dic₁₅₈	—	2	2	no	—
477	Dic₁₅₈	—	2	2	no	—
478	Dic₁₅₈	—	4	2	no	—
479	Dic₁₅₈	—	4	2	no	—
480	Dic₁₅₈	—	8	2	no	—
481	Dic₁₅₈	—	8	2	no	—
482	Dic₁₅₈	—	8	2	no	—
483	Dic₁₅₈	—	8	1	no	—
484	Dic₁₅₈	—	8	1	no	—
485	C₈×C₇₉	—	2	1	no	—
486	C₈×C₇₉	—	2	1	no	—
487	C₈×C₇₉	—	2	1	no	—
488	C₈×C₇₉	—	2	1	no	—
489	C₇₉⋊C₈	—	2	2	no	—
490	C₇₉⋊C₈	—	2	2	no	—
491	C₂²×C₇₉	—	2	1	no	—
492	C₂²×C₇₉	—	2	1	no	—
493	C₂²×C₇₉	—	2	1	no	—
494	C₂²×C₇₉	—	4	1	no	—
495	C₂²×C₇₉	—	4	1	no	—
496	C₂²×C₇₉	—	4	1	no	—
497	C₂²×C₇₉	C₂³×D₄	1	1	yes	characteristic
498	C₄×C₇₉	—	2	1	no	—
499	C₄×C₇₉	—	2	1	no	—
500	C₄×C₇₉	—	2	2	no	—
501	C₄×C₇₉	—	2	2	no	—
502	C₄×C₇₉	—	2	1	no	—
503	C₄×C₇₉	—	2	1	no	—
504	C₄×C₇₉	—	4	1	no	—
505	C₄×C₇₉	—	4	1	no	—
506	C₄×C₇₉	—	4	1	no	—
507	C₄×C₇₉	—	4	1	no	—
508	C₄×C₇₉	—	4	1	no	—
509	C₄×C₇₉	#578	1	2	yes	—
510	C₄×C₇₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
511	C₄×C₇₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
512	Dic₇₉	—	2	2	no	—
513	Dic₇₉	—	2	2	no	—
514	Dic₇₉	—	2	2	no	—
515	Dic₇₉	—	2	2	no	—
516	Dic₇₉	—	4	2	no	—
517	Dic₇₉	—	4	2	no	—
518	Dic₇₉	—	4	2	no	—
519	Dic₇₉	—	4	2	no	—
520	#61866	—	79	1	no	maximal, Sylow
521	C₂×C₇₉	—	4	1	no	—
522	C₂×C₇₉	—	8	1	no	—
523	C₂×C₇₉	#3486	1	1	yes	characteristic
524	C₂×C₇₉	C₂×#578	1	1	yes	characteristic
525	C₂×C₇₉	#3584	1	1	yes	characteristic
526	#3555	—	79	1	no	—
527	#3502	—	79	1	no	—
528	#3390	—	79	2	no	—
529	#3387	—	79	1	no	—
530	#3385	—	79	1	no	—
531	#3383	—	79	2	no	—
532	Q₈×Q₁₆	—	79	1	no	—
533	#3381	—	79	1	no	—
534	#3377	—	79	2	no	—
535	#3374	—	79	1	no	—
536	#3369	—	79	1	no	—
537	#3364	—	79	2	no	—
538	#3364	—	79	1	no	—
539	#3363	—	79	1	no	—
540	#3243	—	79	2	no	—
541	#3242	—	79	2	no	—
542	#3233	—	79	1	no	—
543	#3231	—	79	1	no	—
544	#3127	—	79	2	no	—
545	#3121	—	79	2	no	—
546	#3108	D₇₉	1	1	yes	characteristic
547	#3104	—	79	1	no	—
548	#2986	—	79	1	no	—
549	C₇₉	#61866	1	1	yes	characteristic, complemented, Sylow
550	#563	—	158	2	no	—
551	Q₈²	—	79	1	no	—
552	Q₈²	—	79	1	no	—
553	Q₈²	—	79	1	no	—
554	Q₈²	—	158	1	no	—
555	#557	—	79	2	no	—
556	#557	—	79	1	no	—
557	#557	—	79	2	no	—
558	#557	—	79	1	no	—
559	#557	—	79	2	no	—
560	#557	—	79	1	no	—
561	#557	—	158	2	no	—
562	#557	—	158	1	no	—
563	#556	—	79	2	no	—
564	#556	—	79	1	no	—
565	#556	—	158	1	no	—
566	#554	—	79	1	no	—
567	#552	—	158	1	no	—
568	#544	—	79	2	no	—
569	#544	—	158	2	no	—
570	#544	—	158	1	no	—
571	#542	—	79	2	no	—
572	#541	—	79	2	no	—
573	#541	—	158	1	no	—
574	#541	—	158	2	no	—
575	#533	—	79	1	no	—
576	#533	—	79	1	no	—
577	#533	—	79	1	no	—
578	#533	—	158	1	no	—
579	#533	—	158	1	no	—
580	#529	C₂×D₇₉	1	1	yes	characteristic
581	#519	—	79	2	no	—
582	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
583	#501	—	79	2	no	—
584	#501	—	79	2	no	—
585	#500	—	79	2	no	—
586	#500	—	79	1	no	—
587	#499	—	79	2	no	—
588	#499	—	79	2	no	—
589	#498	—	79	1	no	—
590	#491	—	79	2	no	—
591	#489	—	79	2	no	—
592	#488	—	79	2	no	—
593	#488	—	79	2	no	—
594	#487	—	79	2	no	—
595	#487	—	79	1	no	—
596	#487	—	79	1	no	—
597	#485	—	79	2	no	—
598	#485	—	79	2	no	—
599	#485	—	79	2	no	—
600	#484	—	79	2	no	—
601	#483	C₂×D₇₉	1	1	yes	characteristic
602	#482	—	79	2	no	—
603	#480	C₂×D₇₉	1	1	yes	characteristic
604	#479	—	79	2	no	—
605	#479	—	79	2	no	—
606	#479	—	79	2	no	—
607	#479	—	79	2	no	—
608	#479	—	79	2	no	—
609	#479	—	79	2	no	—
610	#479	—	79	2	no	—
611	#479	C₂×D₇₉	1	1	yes	characteristic
612	#479	C₂×D₇₉	1	1	yes	characteristic
613	#478	—	79	2	no	—
614	#477	—	79	1	no	—
615	#477	—	79	1	no	—
616	#477	—	79	1	no	—
617	#477	—	79	2	no	—
618	#477	—	79	2	no	—
619	#477	—	79	2	no	—
620	#476	—	79	1	no	—
621	#475	—	79	1	no	—
622	#475	—	79	2	no	—
623	#475	—	79	2	no	—
624	#474	—	79	1	no	—
625	#474	—	79	2	no	—
626	#464	—	79	2	no	—
627	#464	—	79	2	no	—
628	#464	C₂×D₇₉	1	1	yes	characteristic
629	#464	C₂×D₇₉	1	1	yes	characteristic
630	#462	—	79	2	no	—
631	#462	—	79	2	no	—
632	#462	—	79	1	no	—
633	#462	—	79	1	no	—
634	#451	—	79	2	no	—
635	#451	C₂×D₇₉	1	1	yes	characteristic
636	#448	C₂×D₇₉	1	1	yes	characteristic
637	#446	—	79	2	no	—
638	#446	—	79	1	no	—
639	#446	—	79	1	no	—
640	C₈×Q₈	—	79	2	no	—
641	C₈×Q₈	—	79	1	no	—
642	C₈×Q₈	—	79	1	no	—
643	#441	—	79	2	no	—
644	#441	—	79	2	no	—
645	#441	—	79	2	no	—
646	#440	—	79	2	no	—
647	C₄×Q₁₆	—	79	2	no	—
648	C₄×Q₁₆	—	79	2	no	—
649	C₄×Q₁₆	—	79	2	no	—
650	C₄×Q₁₆	—	79	2	no	—
651	C₄×Q₁₆	—	79	2	no	—
652	C₄×Q₁₆	C₂×D₇₉	1	1	yes	characteristic
653	C₄×Q₁₆	C₂×D₇₉	1	1	yes	characteristic
654	C₄×SD₁₆	—	79	2	no	—
655	C₄×SD₁₆	C₂×D₇₉	1	1	yes	characteristic
656	C₄×SD₁₆	C₂×D₇₉	1	1	yes	characteristic
657	#433	—	79	2	no	—
658	#433	—	79	2	no	—
659	#431	—	79	1	no	—
660	#431	C₂×D₇₉	1	1	yes	characteristic
661	C₂²×Q₈	C₂²×D₇₉	1	1	yes	characteristic
662	C₂×Q₁₆	—	79	2	no	—
663	C₂×Q₁₆	—	79	2	no	—
664	C₂×Q₁₆	C₂²×D₇₉	1	1	yes	characteristic
665	C₂×Q₁₆	C₂²×D₇₉	1	1	yes	characteristic
666	C₂×SD₁₆	C₂²×D₇₉	1	1	yes	characteristic
667	C₂×SD₁₆	C₂²×D₇₉	1	1	yes	characteristic
668	C₄⋊Q₈	—	79	2	no	—
669	C₄⋊Q₈	—	79	2	no	—
670	C₄⋊Q₈	—	79	2	no	—
671	C₄⋊Q₈	—	79	2	no	—
672	C₄⋊Q₈	—	79	1	no	—
673	C₄⋊Q₈	—	79	1	no	—
674	C₄⋊Q₈	—	79	1	no	—
675	C₄⋊Q₈	—	79	1	no	—
676	C₄⋊Q₈	—	79	1	no	—
677	C₄⋊Q₈	—	79	1	no	—
678	C₄⋊Q₈	—	158	1	no	—
679	C₄⋊Q₈	—	158	1	no	—
680	C₄⋊Q₈	—	158	1	no	—
681	C₄⋊Q₈	—	158	1	no	—
682	C₄⋊Q₈	—	158	1	no	—
683	C₄⋊Q₈	—	158	2	no	—
684	C₄⋊Q₈	—	158	2	no	—
685	C₄⋊Q₈	—	158	2	no	—
686	C₄⋊Q₈	—	158	2	no	—
687	C₄⋊Q₈	—	158	2	no	—
688	C₄⋊Q₈	—	158	2	no	—
689	C₄⋊Q₈	—	158	2	no	—
690	#126	—	2	1	no	—
691	#126	—	158	2	no	—
692	#126	—	158	2	no	—
693	#126	—	158	2	no	—
694	#126	—	158	2	no	—
695	#126	—	158	2	no	—
696	#126	—	158	2	no	—
697	#125	—	79	2	no	—
698	#125	—	79	2	no	—
699	#125	—	79	2	no	—
700	#125	—	79	2	no	—
701	#125	—	79	2	no	—
702	#125	—	158	2	no	—
703	#125	—	158	2	no	—
704	#125	—	158	1	no	—
705	#125	—	158	2	no	—
706	#125	—	158	2	no	—
707	#125	—	158	2	no	—
708	#125	—	158	2	no	—
709	#125	—	158	2	no	—
710	#125	—	158	2	no	—
711	#125	—	158	2	no	—
712	#125	—	158	2	no	—
713	#125	—	158	2	no	—
714	#125	—	158	2	no	—
715	#125	—	158	1	no	—
716	#125	C₂²×D₇₉	1	1	yes	characteristic
717	#124	—	79	2	no	—
718	#124	—	158	2	no	—
719	#124	C₂²×D₇₉	1	1	yes	characteristic
720	#123	—	2	1	no	—
721	#123	—	158	2	no	—
722	C₂²⋊Q₈	—	79	1	no	—
723	C₂²⋊Q₈	—	79	1	no	—
724	C₂²⋊Q₈	—	79	2	no	—
725	C₂²⋊Q₈	—	79	2	no	—
726	C₂²⋊Q₈	—	158	2	no	—
727	C₂²⋊Q₈	—	158	2	no	—
728	C₂²⋊Q₈	—	158	2	no	—
729	C₂²⋊Q₈	—	158	2	no	—
730	C₂²⋊Q₈	—	158	2	no	—
731	C₂²⋊Q₈	—	158	1	no	—
732	C₂²⋊Q₈	—	158	1	no	—
733	C₂²⋊Q₈	—	158	1	no	—
734	C₂²⋊Q₈	—	158	1	no	—
735	C₂²⋊Q₈	—	158	1	no	—
736	C₂²⋊Q₈	C₂²×D₇₉	1	1	yes	characteristic
737	#121	C₂²×D₇₉	1	1	yes	characteristic
738	C₄×Q₈	—	2	1	no	—
739	C₄×Q₈	—	2	1	no	—
740	C₄×Q₈	—	79	1	no	—
741	C₄×Q₈	—	79	2	no	—
742	C₄×Q₈	—	79	1	no	—
743	C₄×Q₈	—	79	2	no	—
744	C₄×Q₈	—	79	2	no	—
745	C₄×Q₈	—	79	2	no	—
746	C₄×Q₈	—	79	2	no	—
747	C₄×Q₈	—	79	2	no	—
748	C₄×Q₈	—	79	2	no	—
749	C₄×Q₈	—	79	2	no	—
750	C₄×Q₈	—	79	2	no	—
751	C₄×Q₈	—	158	2	no	—
752	C₄×Q₈	—	158	2	no	—
753	C₄×Q₈	—	158	1	no	—
754	C₄×Q₈	—	158	1	no	—
755	C₄×Q₈	—	158	1	no	—
756	C₄×Q₈	—	158	1	no	—
757	C₄×Q₈	—	158	1	no	—
758	C₄×Q₈	—	158	1	no	—
759	C₄×Q₈	—	158	2	no	—
760	C₄×Q₈	—	158	2	no	—
761	C₄×Q₈	—	158	2	no	—
762	C₄×Q₈	—	158	1	no	—
763	C₄×Q₈	—	158	1	no	—
764	C₄×Q₈	—	158	1	no	—
765	C₄×Q₈	C₂²×D₇₉	1	1	yes	characteristic
766	C₄×Q₈	C₂²×D₇₉	1	1	yes	characteristic
767	C₄×Q₈	C₂²×D₇₉	1	1	yes	characteristic
768	C₄×Q₈	C₂²×D₇₉	1	1	yes	characteristic
769	C₄×Q₈	C₂²×D₇₉	1	1	yes	characteristic
770	C₄×D₄	—	2	1	no	—
771	C₄×D₄	—	79	2	no	—
772	C₄×D₄	C₂²×D₇₉	1	1	yes	characteristic
773	#117	—	2	1	no	—
774	#117	—	79	2	no	—
775	#117	—	79	2	no	—
776	#117	—	158	2	no	—
777	#117	—	158	2	no	—
778	#117	—	158	2	no	—
779	#117	—	158	1	no	—
780	#117	—	158	1	no	—
781	C₂×C₄⋊C₄	—	2	1	no	—
782	C₂×C₄⋊C₄	—	158	1	no	—
783	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
784	C₂×C₄²	—	2	1	no	—
785	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
786	#107	—	79	2	no	—
787	#107	—	79	2	no	—
788	#107	—	79	2	no	—
789	#107	—	79	2	no	—
790	#107	—	79	2	no	—
791	#107	—	79	2	no	—
792	#107	C₂²×D₇₉	1	1	yes	characteristic
793	#107	C₂²×D₇₉	1	1	yes	characteristic
794	#106	—	79	2	no	—
795	#106	—	79	2	no	—
796	#106	—	79	2	no	—
797	#106	—	79	2	no	—
798	#106	C₂²×D₇₉	1	1	yes	characteristic
799	#106	C₂²×D₇₉	1	1	yes	characteristic
800	C₄⋊C₈	—	79	2	no	—
801	C₄⋊C₈	—	79	2	no	—
802	C₄⋊C₈	—	79	2	no	—
803	C₄⋊C₈	—	79	2	no	—
804	C₄⋊C₈	—	79	1	no	—
805	C₄⋊C₈	—	79	1	no	—
806	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
807	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
808	#103	—	79	2	no	—
809	#103	—	79	2	no	—
810	#103	—	79	2	no	—
811	#103	—	79	2	no	—
812	#103	—	79	2	no	—
813	#103	—	79	2	no	—
814	#103	—	79	2	no	—
815	#103	—	79	2	no	—
816	#103	—	79	2	no	—
817	#103	—	79	2	no	—
818	#103	C₂²×D₇₉	1	1	yes	characteristic
819	#103	C₂²×D₇₉	1	1	yes	characteristic
820	#103	C₂²×D₇₉	1	1	yes	characteristic
821	#103	C₂²×D₇₉	1	1	yes	characteristic
822	#103	C₂²×D₇₉	1	1	yes	characteristic
823	#103	C₂²×D₇₉	1	1	yes	characteristic
824	#102	—	79	2	no	—
825	#102	—	79	2	no	—
826	#102	C₂²×D₇₉	1	1	yes	characteristic
827	#102	C₂²×D₇₉	1	1	yes	characteristic
828	C₂²⋊C₈	—	79	2	no	—
829	C₂²⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
830	C₂²⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
831	#97	—	79	2	no	—
832	#97	—	79	2	no	—
833	C₄×C₈	—	79	2	no	—
834	C₄×C₈	—	79	2	no	—
835	C₄×C₈	—	79	2	no	—
836	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
837	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
838	C₂×Q₈	—	2	2	no	—
839	C₂×Q₈	—	2	2	no	—
840	C₂×Q₈	—	2	1	no	—
841	C₂×Q₈	—	79	2	no	—
842	C₂×Q₈	—	79	1	no	—
843	C₂×Q₈	—	79	1	no	—
844	C₂×Q₈	—	79	2	no	—
845	C₂×Q₈	—	158	2	no	—
846	C₂×Q₈	—	158	2	no	—
847	C₂×Q₈	—	158	2	no	—
848	C₂×Q₈	—	158	1	no	—
849	C₂×Q₈	—	158	1	no	—
850	C₂×Q₈	—	158	1	no	—
851	C₂×Q₈	C₂³×D₇₉	1	1	yes	characteristic
852	C₂×Q₈	C₂³×D₇₉	1	1	yes	characteristic
853	C₂×Q₈	C₂³×D₇₉	1	1	yes	characteristic
854	C₂×D₄	—	2	1	no	—
855	C₂×D₄	C₂³×D₇₉	1	1	yes	characteristic
856	C₂²×C₄	—	2	1	no	—
857	C₂²×C₄	—	2	1	no	—
858	C₂²×C₄	—	2	1	no	—
859	C₂²×C₄	—	158	2	no	—
860	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
861	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
862	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
863	Q₁₆	—	2	2	no	—
864	Q₁₆	—	2	2	no	—
865	Q₁₆	—	158	4	no	—
866	Q₁₆	—	158	4	no	—
867	SD₁₆	—	2	2	no	—
868	SD₁₆	—	2	2	no	—
869	C₂×C₈	—	79	2	no	—
870	C₂×C₈	—	79	2	no	—
871	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
872	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
873	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
874	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
875	C₄⋊C₄	—	2	1	no	—
876	C₄⋊C₄	—	2	1	no	—
877	C₄⋊C₄	—	2	1	no	—
878	C₄⋊C₄	—	2	1	no	—
879	C₄⋊C₄	—	2	1	no	—
880	C₄⋊C₄	—	2	1	no	—
881	C₄⋊C₄	—	2	1	no	—
882	C₄⋊C₄	—	2	1	no	—
883	C₄⋊C₄	—	2	1	no	—
884	C₄⋊C₄	—	79	2	no	—
885	C₄⋊C₄	—	79	2	no	—
886	C₄⋊C₄	—	79	2	no	—
887	C₄⋊C₄	—	79	2	no	—
888	C₄⋊C₄	—	79	1	no	—
889	C₄⋊C₄	—	79	2	no	—
890	C₄⋊C₄	—	79	2	no	—
891	C₄⋊C₄	—	79	1	no	—
892	C₄⋊C₄	—	79	2	no	—
893	C₄⋊C₄	—	79	2	no	—
894	C₄⋊C₄	—	79	2	no	—
895	C₄⋊C₄	—	79	2	no	—
896	C₄⋊C₄	—	158	2	no	—
897	C₄⋊C₄	—	158	2	no	—
898	C₄⋊C₄	—	158	2	no	—
899	C₄⋊C₄	—	158	2	no	—
900	C₄⋊C₄	—	158	2	no	—
901	C₄⋊C₄	—	158	2	no	—
902	C₄⋊C₄	—	158	2	no	—
903	C₄⋊C₄	—	158	2	no	—
904	C₄⋊C₄	—	158	2	no	—
905	C₄⋊C₄	—	158	2	no	—
906	C₄⋊C₄	—	158	2	no	—
907	C₄⋊C₄	—	158	2	no	—
908	C₄⋊C₄	—	158	2	no	—
909	C₄⋊C₄	—	158	2	no	—
910	C₄⋊C₄	—	158	2	no	—
911	C₄⋊C₄	—	158	2	no	—
912	C₄⋊C₄	—	158	2	no	—
913	C₄⋊C₄	—	158	2	no	—
914	C₄⋊C₄	—	158	2	no	—
915	C₄⋊C₄	—	158	2	no	—
916	C₄⋊C₄	—	158	2	no	—
917	C₄⋊C₄	—	158	2	no	—
918	C₄⋊C₄	—	158	1	no	—
919	C₄⋊C₄	—	158	1	no	—
920	C₄⋊C₄	—	158	1	no	—
921	C₄⋊C₄	—	158	1	no	—
922	C₄⋊C₄	—	158	1	no	—
923	C₄⋊C₄	C₂³×D₇₉	1	1	yes	characteristic
924	C₄⋊C₄	C₂³×D₇₉	1	1	yes	characteristic
925	C₄⋊C₄	C₂³×D₇₉	1	1	yes	characteristic
926	C₄⋊C₄	C₂³×D₇₉	1	1	yes	characteristic
927	C₂²⋊C₄	—	2	1	no	—
928	C₂²⋊C₄	—	2	1	no	—
929	C₂²⋊C₄	—	2	1	no	—
930	C₂²⋊C₄	—	2	1	no	—
931	C₂²⋊C₄	—	2	1	no	—
932	C₂²⋊C₄	—	79	2	no	—
933	C₂²⋊C₄	—	79	2	no	—
934	C₂²⋊C₄	—	158	2	no	—
935	C₂²⋊C₄	—	158	2	no	—
936	C₂²⋊C₄	—	158	2	no	—
937	C₂²⋊C₄	—	158	2	no	—
938	C₂²⋊C₄	—	158	2	no	—
939	C₄²	—	2	1	no	—
940	C₄²	—	2	1	no	—
941	C₄²	—	2	1	no	—
942	C₄²	—	2	1	no	—
943	C₄²	—	2	1	no	—
944	C₄²	—	79	2	no	—
945	C₄²	—	79	2	no	—
946	C₄²	—	158	2	no	—
947	C₄²	—	158	2	no	—
948	C₄²	—	158	2	no	—
949	C₄²	—	158	2	no	—
950	C₄²	—	158	2	no	—
951	C₄²	—	158	2	no	—
952	C₄²	—	158	2	no	—
953	C₄²	—	158	2	no	—
954	C₄²	—	158	2	no	—
955	C₄²	D₄×D₇₉	1	1	yes	characteristic
956	C₄²	D₄×D₇₉	1	1	yes	characteristic
957	C₄²	C₂³×D₇₉	1	1	yes	characteristic
958	C₄²	C₂³×D₇₉	1	1	yes	characteristic
959	C₂³	—	2	1	no	—
960	C₂³	C₂×D₄×D₇₉	1	1	yes	characteristic
961	Q₈	—	2	4	no	—
962	Q₈	—	2	1	no	—
963	Q₈	—	2	1	no	—
964	Q₈	—	2	1	no	—
965	Q₈	—	2	1	no	—
966	Q₈	—	316	2	no	—
967	Q₈	—	316	2	no	—
968	Q₈	—	632	1	no	—
969	Q₈	—	632	1	no	—
970	Q₈	—	632	2	no	—
971	Q₈	—	632	2	no	—
972	Q₈	—	632	2	no	—
973	Q₈	—	158	2	no	—
974	Q₈	—	158	2	no	—
975	Q₈	—	158	2	no	—
976	Q₈	—	158	2	no	—
977	Q₈	#14579208	1	2	yes	—
978	Q₈	#14579208	1	2	yes	—
979	D₄	—	2	1	no	—
980	D₄	—	2	1	no	—
981	D₄	—	8	1	no	—
982	C₂×C₄	—	2	4	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	2	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	1	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	4	1	no	—
994	C₂×C₄	—	4	2	no	—
995	C₂×C₄	—	8	1	no	—
996	C₂×C₄	—	79	2	no	—
997	C₂×C₄	—	79	2	no	—
998	C₂×C₄	—	79	2	no	—
999	C₂×C₄	—	79	2	no	—
1000	C₂×C₄	—	632	2	no	—
1001	C₂×C₄	—	158	2	no	—
1002	C₂×C₄	—	158	2	no	—
1003	C₂×C₄	—	158	2	no	—
1004	C₂×C₄	—	158	2	no	—
1005	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
1006	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
1007	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
1008	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
1009	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
1010	C₂×C₄	C₂⁴×D₇₉	1	1	yes	characteristic
1011	C₈	—	2	1	no	—
1012	C₈	—	2	1	no	—
1013	C₈	—	2	1	no	—
1014	C₈	—	2	1	no	—
1015	C₈	—	158	2	no	—
1016	C₈	—	158	2	no	—
1017	C₂²	—	2	1	no	—
1018	C₂²	—	2	1	no	—
1019	C₂²	—	2	1	no	—
1020	C₂²	—	4	1	no	—
1021	C₂²	—	4	1	no	—
1022	C₂²	—	4	1	no	—
1023	C₂²	C₂²×D₄×D₇₉	1	1	yes	characteristic
1024	C₄	—	2	2	no	—
1025	C₄	—	2	2	no	—
1026	C₄	—	2	1	no	—
1027	C₄	—	2	1	no	—
1028	C₄	—	2	1	no	—
1029	C₄	—	2	1	no	—
1030	C₄	—	4	1	no	—
1031	C₄	—	4	1	no	—
1032	C₄	—	4	1	no	—
1033	C₄	—	4	1	no	—
1034	C₄	—	4	1	no	—
1035	C₄	—	316	2	no	—
1036	C₄	—	316	2	no	—
1037	C₄	—	316	2	no	—
1038	C₄	—	316	2	no	—
1039	C₄	—	158	2	no	—
1040	C₄	—	158	2	no	—
1041	C₄	—	158	2	no	—
1042	C₄	—	158	2	no	—
1043	C₄	#19099379	1	2	yes	—
1044	C₄	C₂×#14579208	1	1	yes	characteristic
1045	C₄	C₂×#14579208	1	1	yes	characteristic
1046	C₂	—	4	1	no	—
1047	C₂	—	8	1	no	—
1048	C₂	#23777047	1	1	yes	characteristic
1049	C₂	C₂×#19099379	1	1	yes	characteristic
1050	C₂	#23778169	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₇₉
commutator, cosocle	C₂×C₄×C₇₉	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₉
Fitting	C₇₉×#3108	C₂
socle	C₂²×C₇₉	C₂³×D₄
prime radical	#121×C₇₉	C₂³
hypercenter	#3108	D₇₉
hypocenter	C₇₉	#61866
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3108

Complements

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

N	H ≅ G/N	type
2. #23777210	C₂	semidirect
3. #23776367	C₂	semidirect
4. #23776330	C₂	semidirect
5. #23776308	C₂	semidirect
6. #23776286	C₂	semidirect
7. Q₁₆×Dic₁₅₈	C₂	semidirect
8. #23776273	C₂	semidirect
9. #23776246	C₂	semidirect
10. #23776201	C₂	semidirect
11. #23776138	C₂	semidirect
12. #23776083	C₂	semidirect
13. #23776080	C₂	semidirect
14. #23776076	C₂	semidirect
16. #23774664	C₂	semidirect
18. #23774561	C₂	semidirect
19. #23773694	C₂	semidirect
21. #23773439	C₂	semidirect
22. #23772501	C₂	semidirect
549. C₇₉	#61866	semidirect

Maximal subgroups

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

subgroup	index
#23777890	2
#23777210	2
#23776367	2
#23776330	2
#23776308	2
#23776286	2
Q₁₆×Dic₁₅₈	2
#23776273	2
#23776246	2
#23776201	2
#23776138	2
#23776083	2
#23776080	2
#23776076	2
#23774679	2
#23774664	2
#23774575	2
#23774561	2
#23773694	2
#23773622	2
#23773439	2
#23772501	2
C₇₉×#3108	2
#61866	79