Subgroups — #35157935

Order 20224.

1798 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23776804	C₂	1	1	yes	maximal, characteristic
2	#544×D₇₉	C₂	1	1	yes	maximal, characteristic
3	#23773951	C₂	1	2	yes	maximal, complemented
4	#23773948	C₂	1	2	yes	maximal, complemented
5	#23773945	C₂	1	2	yes	maximal, complemented
6	#23773941	C₂	1	2	yes	maximal, complemented
7	#23773940	C₂	1	1	yes	maximal, characteristic, complemented
8	#23773939	C₂	1	1	yes	maximal, characteristic, complemented
9	#23773938	C₂	1	1	yes	maximal, characteristic, complemented
10	#23773937	C₂	1	2	yes	maximal, complemented
11	#23773935	C₂	1	2	yes	maximal, complemented
12	#23773934	C₂	1	1	yes	maximal, characteristic, complemented
13	#23773930	C₂	1	1	yes	maximal, characteristic, complemented
14	#23773928	C₂	1	1	yes	maximal, characteristic, complemented
15	#23773927	C₂	1	2	yes	maximal, complemented
16	#23773926	C₂	1	1	yes	maximal, characteristic, complemented
17	#23773925	C₂	1	2	yes	maximal, complemented
18	#23771988	C₂	1	1	yes	maximal, characteristic
19	#23771987	C₂	1	1	yes	maximal, characteristic
20	C₂×#19098602	C₂	1	1	yes	maximal, characteristic
21	#428×D₇₉	C₂	1	1	yes	maximal, characteristic
22	#23771816	C₂	1	1	yes	maximal, characteristic
23	C₇₉×#3163	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#11929607	C₂²	1	1	yes	characteristic
25	C₂×M₁₆×D₇₉	C₂²	1	1	yes	characteristic
26	#19099194	C₂²	1	1	yes	characteristic
27	#19099194	C₂²	1	1	yes	characteristic
28	#19099193	—	2	1	no	—
29	#19099193	—	2	1	no	—
30	#19099193	C₂²	1	2	yes	—
31	#19099193	C₂²	1	2	yes	—
32	#19099192	—	2	2	no	—
33	#19099191	C₂²	1	1	yes	characteristic
34	#19099191	C₂²	1	1	yes	characteristic
35	#19099191	C₂²	1	1	yes	characteristic
36	#19099191	C₂²	1	1	yes	characteristic
37	#19099190	—	2	1	no	—
38	#19099190	—	2	1	no	—
39	#19099190	C₂²	1	2	yes	—
40	#19099190	C₂²	1	2	yes	—
41	#19099188	—	2	2	no	—
42	#19099119	—	2	1	no	—
43	#19099119	C₂²	1	2	yes	—
44	#19099118	—	2	1	no	—
45	#19099118	C₂²	1	2	yes	—
46	#19099115	—	2	2	no	—
47	C₄⋊Q₈×D₇₉	—	2	1	no	—
48	C₄⋊Q₈×D₇₉	C₂²	1	2	yes	—
49	#125×D₇₉	—	2	1	no	—
50	#125×D₇₉	C₂²	1	2	yes	—
51	C₂²⋊Q₈×D₇₉	—	2	2	no	—
52	C₂×#14579119	C₂²	1	1	yes	characteristic
53	#117×D₇₉	C₂²	1	1	yes	characteristic
54	#117×D₇₉	C₂²	1	1	yes	characteristic
55	#117×D₇₉	C₂²	1	1	yes	characteristic
56	C₂×C₄⋊C₄×D₇₉	C₂²	1	1	yes	characteristic
57	#19098973	C₂²	1	2	yes	complemented
58	#19098973	C₂²	1	2	yes	complemented
59	#19098972	C₂²	1	2	yes	complemented
60	#19098972	C₂²	1	2	yes	complemented
61	#19098971	C₂²	1	2	yes	complemented
62	#19098971	C₂²	1	2	yes	complemented
63	#19098970	C₂²	1	2	yes	complemented
64	#19098970	C₂²	1	2	yes	complemented
65	#19098970	C₂²	1	2	yes	complemented
66	#19098970	C₂²	1	2	yes	complemented
67	#19098970	C₂²	1	2	yes	complemented
68	#19098970	C₂²	1	2	yes	complemented
69	#19098969	C₂²	1	2	yes	complemented
70	#19098969	C₂²	1	2	yes	complemented
71	#19098968	C₂²	1	2	yes	complemented
72	#19098967	C₂²	1	2	yes	complemented
73	#19098967	C₂²	1	2	yes	complemented
74	#19098966	C₂²	1	2	yes	complemented
75	#19098965	C₂²	1	2	yes	complemented
76	#19098964	C₂²	1	2	yes	complemented
77	#19098964	C₂²	1	2	yes	complemented
78	#19098963	C₂²	1	2	yes	complemented
79	#19098963	C₂²	1	2	yes	complemented
80	#19098962	C₂²	1	2	yes	complemented
81	#19098962	C₂²	1	2	yes	complemented
82	#19098960	C₂²	1	2	yes	complemented
83	#19098960	C₂²	1	2	yes	complemented
84	#19098959	C₂²	1	2	yes	complemented
85	#19098606	C₂²	1	1	yes	characteristic
86	#19098606	C₂²	1	1	yes	characteristic
87	#19098605	C₂²	1	1	yes	characteristic
88	#19098605	C₂²	1	1	yes	characteristic
89	#19098604	C₂²	1	2	yes	—
90	#19098604	C₂²	1	2	yes	—
91	#19098604	C₂²	1	1	yes	characteristic
92	#19098604	C₂²	1	1	yes	characteristic
93	#19098604	C₂²	1	1	yes	characteristic
94	#19098604	C₂²	1	1	yes	characteristic
95	#19098603	C₂²	1	1	yes	characteristic
96	#19098603	C₂²	1	1	yes	characteristic
97	#19098602	C₂²	1	2	yes	—
98	#19098602	C₂²	1	2	yes	—
99	#19098602	C₂²	1	2	yes	—
100	#19098602	C₂²	1	2	yes	—
101	#19098602	C₂²	1	2	yes	—
102	#19098602	C₂²	1	2	yes	—
103	#19098602	C₂²	1	1	yes	characteristic
104	#19098602	C₂²	1	1	yes	characteristic
105	#19098602	C₂²	1	1	yes	characteristic
106	#19098602	C₂²	1	1	yes	characteristic
107	#19098601	C₂²	1	1	yes	characteristic
108	#19098600	C₂²	1	2	yes	—
109	#19098599	C₂²	1	1	yes	characteristic
110	#19098599	C₂²	1	1	yes	characteristic
111	#19098598	C₂²	1	2	yes	—
112	C₂×#14579095	C₂²	1	1	yes	characteristic
113	C₂×#14579094	C₂²	1	1	yes	characteristic
114	#107×D₇₉	C₂²	1	2	yes	—
115	C₂×#14579092	C₂²	1	1	yes	characteristic
116	#106×D₇₉	C₂²	1	2	yes	—
117	#19098521	C₂²	1	1	yes	characteristic
118	#19098520	C₂²	1	2	yes	—
119	#19098519	C₂²	1	1	yes	characteristic
120	#19098518	C₂²	1	1	yes	characteristic
121	#19098517	C₂²	1	2	yes	—
122	#19098515	C₂²	1	2	yes	—
123	C₄×#11929607	C₂²	1	2	yes	—
124	#544×C₇₉	C₂²	1	1	yes	characteristic
125	#544×C₇₉	C₂²	1	1	yes	characteristic
126	#501×C₇₉	C₂²	1	2	yes	complemented
127	#501×C₇₉	C₂²	1	2	yes	complemented
128	#499×C₇₉	C₂²	1	2	yes	complemented
129	#498×C₇₉	C₂²	1	2	yes	complemented
130	#428×C₇₉	C₂²	1	1	yes	characteristic
131	#428×C₇₉	C₂²	1	1	yes	characteristic
132	#427×C₇₉	C₂²	1	1	yes	characteristic
133	C₂×#106×C₇₉	C₂²	1	1	yes	characteristic
134	#405×C₇₉	C₂²	1	1	yes	characteristic
135	C₂×Q₈×D₇₉	—	2	2	no	—
136	C₂²×C₄×D₇₉	—	2	1	no	—
137	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
138	C₂×#11929608	C₂³	1	1	yes	characteristic
139	C₂×#11929607	Q₈	1	8	yes	complemented
140	C₂×#11929607	C₂³	1	1	yes	characteristic
141	C₂×#11929607	C₂³	1	2	yes	—
142	C₂×#11929607	C₂³	1	1	yes	characteristic
143	C₂×#11929607	C₂³	1	1	yes	characteristic
144	C₂×#11929607	C₂³	1	1	yes	characteristic
145	M₁₆×D₇₉	Q₈	1	8	yes	complemented
146	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
147	C₂×C₈×D₇₉	C₂³	1	2	yes	—
148	#14579161	—	2	1	no	—
149	#14579161	—	2	1	no	—
150	#14579161	C₂³	1	2	yes	—
151	#14579161	C₂³	1	2	yes	—
152	#14579160	—	2	1	no	—
153	#14579160	—	2	1	no	—
154	#14579160	—	2	1	no	—
155	#14579160	—	2	1	no	—
156	#14579160	—	2	2	no	—
157	#14579160	—	2	2	no	—
158	#14579160	—	2	2	no	—
159	#14579160	C₂³	1	2	yes	—
160	#14579160	C₂³	1	2	yes	—
161	#14579160	C₂³	1	2	yes	—
162	#14579160	C₂³	1	2	yes	—
163	#14579159	—	2	2	no	—
164	#14579159	—	2	2	no	—
165	#14579159	—	2	2	no	—
166	#14579153	—	2	1	no	—
167	#14579153	—	2	1	no	—
168	#14579153	C₂³	1	2	yes	—
169	#14579153	C₂³	1	2	yes	—
170	#14579152	—	2	1	no	—
171	#14579152	—	2	1	no	—
172	#14579152	—	2	1	no	—
173	#14579152	—	2	1	no	—
174	#14579152	C₂³	1	2	yes	—
175	#14579152	C₂³	1	2	yes	—
176	#14579152	C₂³	1	2	yes	—
177	#14579152	C₂³	1	2	yes	—
178	#14579151	—	2	2	no	—
179	#14579151	—	2	2	no	—
180	#14579151	—	2	2	no	—
181	#14579151	—	2	2	no	—
182	#14579151	—	2	2	no	—
183	#14579151	—	2	2	no	—
184	#14579141	—	2	2	no	—
185	#14579141	—	2	2	no	—
186	#14579141	—	2	2	no	—
187	#14579140	—	2	2	no	—
188	#14579140	—	2	2	no	—
189	#14579139	—	2	2	no	—
190	#14579139	—	2	2	no	—
191	#14579139	—	2	2	no	—
192	#14579139	—	2	2	no	—
193	#14579139	—	2	2	no	—
194	#14579139	—	2	2	no	—
195	#14579138	—	2	2	no	—
196	#14579138	—	2	2	no	—
197	#14579138	—	2	2	no	—
198	#14579138	—	2	2	no	—
199	#14579137	—	2	2	no	—
200	#14579137	—	2	2	no	—
201	#14579137	—	2	2	no	—
202	Q₈×Dic₇₉	—	2	2	no	—
203	#14579126	—	2	2	no	—
204	#14579126	—	2	2	no	—
205	#14579126	—	2	2	no	—
206	#14579120	C₂³	1	1	yes	characteristic
207	#14579120	C₂³	1	1	yes	characteristic
208	#14579120	C₂³	1	1	yes	characteristic
209	#14579119	—	2	1	no	—
210	#14579119	—	2	1	no	—
211	#14579119	D₄	1	1	yes	characteristic
212	#14579119	D₄	1	1	yes	characteristic
213	#14579119	C₂³	1	1	yes	characteristic
214	#14579119	C₂³	1	2	yes	—
215	#14579119	C₂³	1	1	yes	characteristic
216	#14579119	C₂³	1	1	yes	characteristic
217	#14579119	C₂³	1	1	yes	characteristic
218	#14579119	C₂³	1	2	yes	—
219	#14579118	—	2	1	no	—
220	#14579118	—	2	1	no	—
221	#14579118	C₂³	1	2	yes	—
222	#14579117	—	2	1	no	—
223	#14579117	—	2	1	no	—
224	#14579117	D₄	1	2	yes	—
225	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
227	C₂×Dic₇₉⋊C₄	—	2	1	no	—
228	C₄⋊C₄×D₇₉	—	2	1	no	—
229	C₄⋊C₄×D₇₉	—	2	1	no	—
230	C₄⋊C₄×D₇₉	—	2	2	no	—
231	C₄⋊C₄×D₇₉	—	2	2	no	—
232	C₄⋊C₄×D₇₉	—	2	2	no	—
233	C₄⋊C₄×D₇₉	D₄	1	1	yes	characteristic
234	C₄⋊C₄×D₇₉	D₄	1	1	yes	characteristic
235	C₄⋊C₄×D₇₉	C₂³	1	1	yes	characteristic
236	C₄⋊C₄×D₇₉	C₂³	1	2	yes	—
237	C₄⋊C₄×D₇₉	C₂³	1	1	yes	characteristic
238	C₄⋊C₄×D₇₉	C₂³	1	2	yes	—
239	C₄⋊C₄×D₇₉	C₂³	1	1	yes	characteristic
240	C₄⋊C₄×D₇₉	C₂³	1	1	yes	characteristic
241	C₂×(C₂×D₇₉)⋊C₄	—	2	1	no	—
242	C₂²⋊C₄×D₇₉	—	2	1	no	—
243	C₂²⋊C₄×D₇₉	—	2	1	no	—
244	C₂²⋊C₄×D₇₉	D₄	1	2	yes	—
245	C₂×C₄×Dic₇₉	—	2	1	no	—
246	C₄²×D₇₉	—	2	1	no	—
247	C₄²×D₇₉	—	2	1	no	—
248	C₄²×D₇₉	C₂³	1	2	yes	—
249	#14579095	C₂³	1	2	yes	—
250	#14579095	C₂³	1	2	yes	—
251	#14579095	C₂³	1	1	yes	characteristic
252	#14579095	C₂³	1	2	yes	—
253	#14579095	C₂³	1	2	yes	—
254	#14579095	C₂³	1	1	yes	characteristic
255	#14579094	C₂³	1	1	yes	characteristic
256	#14579094	C₂³	1	2	yes	—
257	#14579094	C₂³	1	2	yes	—
258	#14579094	C₂³	1	2	yes	—
259	#14579094	C₂³	1	1	yes	characteristic
260	#14579094	C₂³	1	2	yes	—
261	#14579094	C₂³	1	2	yes	—
262	#14579094	C₂³	1	1	yes	characteristic
263	#14579094	C₂³	1	2	yes	—
264	#14579094	C₂³	1	1	yes	characteristic
265	#14579093	C₂³	1	1	yes	characteristic
266	#14579093	C₂³	1	2	yes	—
267	#14579093	C₂³	1	1	yes	characteristic
268	#14579093	C₂³	1	2	yes	—
269	#14579092	C₂³	1	1	yes	characteristic
270	#14579092	C₂³	1	2	yes	—
271	#14579092	C₂³	1	2	yes	—
272	#14579092	C₂³	1	2	yes	—
273	#14579092	C₂³	1	1	yes	characteristic
274	#14579092	C₂³	1	2	yes	—
275	#14579092	C₂³	1	2	yes	—
276	#14579092	C₂³	1	1	yes	characteristic
277	#14579092	C₂³	1	2	yes	—
278	#14579092	C₂³	1	1	yes	characteristic
279	#14579072	C₂³	1	2	yes	—
280	#14579071	C₂³	1	2	yes	—
281	#14579071	C₂³	1	2	yes	—
282	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
283	C₈×Dic₇₉	C₂³	1	2	yes	—
284	C₈×Dic₇₉	C₂³	1	2	yes	—
285	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
286	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
287	C₄⋊Q₈×C₇₉	—	2	1	no	—
288	C₄⋊Q₈×C₇₉	—	2	1	no	—
289	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
290	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
291	#125×C₇₉	—	2	1	no	—
292	#125×C₇₉	—	2	1	no	—
293	#125×C₇₉	C₂³	1	2	yes	—
294	#125×C₇₉	C₂³	1	2	yes	—
295	C₂²⋊Q₈×C₇₉	—	2	2	no	—
296	C₂²⋊Q₈×C₇₉	—	2	2	no	—
297	#117×C₇₉	C₂³	1	1	yes	characteristic
298	#117×C₇₉	C₂³	1	1	yes	characteristic
299	#117×C₇₉	C₂³	1	1	yes	characteristic
300	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
301	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
302	#107×C₇₉	C₂³	1	1	yes	characteristic
303	#107×C₇₉	C₂³	1	1	yes	characteristic
304	#107×C₇₉	C₂³	1	2	yes	—
305	#107×C₇₉	C₂³	1	2	yes	—
306	#106×C₇₉	C₂³	1	2	yes	—
307	#106×C₇₉	C₂³	1	2	yes	—
308	#106×C₇₉	C₂³	1	1	yes	characteristic
309	#106×C₇₉	C₂³	1	1	yes	characteristic
310	#106×C₇₉	C₂³	1	2	yes	—
311	#106×C₇₉	C₂³	1	2	yes	—
312	#97×C₇₉	C₂³	1	2	yes	—
313	C₄×C₈×C₇₉	C₂³	1	2	yes	—
314	C₂³×D₇₉	C₂×D₄	1	1	yes	characteristic
315	C₂×Dic₁₅₈	—	2	2	no	—
316	C₂×Dic₁₅₈	—	2	2	no	—
317	C₂×Dic₁₅₈	—	2	2	no	—
318	C₂×Dic₁₅₈	—	2	2	no	—
319	C₂×Dic₁₅₈	—	2	2	no	—
320	C₂×Dic₁₅₈	—	2	2	no	—
321	Q₈×D₇₉	—	8	4	no	—
322	C₂²×Dic₇₉	—	2	1	no	—
323	C₂²×Dic₇₉	—	2	1	no	—
324	C₂²×Dic₇₉	C₂×D₄	1	1	yes	characteristic
325	C₂×C₄×D₇₉	—	2	1	no	—
326	C₂×C₄×D₇₉	—	2	2	no	—
327	C₂×C₄×D₇₉	—	2	1	no	—
328	C₂×C₄×D₇₉	—	2	1	no	—
329	C₂×C₄×D₇₉	—	2	1	no	—
330	C₂×C₄×D₇₉	—	2	2	no	—
331	C₂×C₄×D₇₉	—	8	2	no	—
332	C₂×C₄×D₇₉	C₂×D₄	1	2	yes	—
333	C₂×C₄×D₇₉	C₂×D₄	1	2	yes	—
334	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
335	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
336	C₂×C₄×D₇₉	C₂×Q₈	1	4	yes	—
337	C₂×C₄×D₇₉	C₂×Q₈	1	4	yes	—
338	C₂×C₄×D₇₉	C₂⁴	1	1	yes	characteristic
339	C₂×C₄×D₇₉	C₂⁴	1	1	yes	characteristic
340	#11929608	C₂×Q₈	1	4	yes	complemented
341	#11929607	C₂×Q₈	1	8	yes	—
342	#11929607	C₂×Q₈	1	4	yes	—
343	#11929607	C₂×Q₈	1	4	yes	—
344	#11929607	C₂×Q₈	1	4	yes	complemented
345	#11929607	C₂×Q₈	1	4	yes	complemented
346	C₂×C₇₉⋊C₈	C₂×Q₈	1	4	yes	complemented
347	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
348	C₂×C₇₉⋊C₈	C₂⁴	1	2	yes	—
349	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
350	C₈×D₇₉	C₂×Q₈	1	8	yes	complemented
351	C₄⋊Dic₇₉	—	2	2	no	—
352	C₄⋊Dic₇₉	—	2	2	no	—
353	C₄⋊Dic₇₉	—	2	2	no	—
354	C₄⋊Dic₇₉	—	2	2	no	—
355	C₄⋊Dic₇₉	—	2	1	no	—
356	C₄⋊Dic₇₉	—	2	2	no	—
357	C₄⋊Dic₇₉	—	2	1	no	—
358	C₄⋊Dic₇₉	—	2	2	no	—
359	C₄⋊Dic₇₉	C₂×D₄	1	1	yes	characteristic
360	C₄⋊Dic₇₉	C₂×D₄	1	1	yes	characteristic
361	C₄⋊Dic₇₉	C₂⁴	1	1	yes	characteristic
362	C₄⋊Dic₇₉	C₂⁴	1	2	yes	—
363	C₄⋊Dic₇₉	C₂⁴	1	1	yes	characteristic
364	C₄⋊Dic₇₉	C₂⁴	1	1	yes	characteristic
365	C₄⋊Dic₇₉	C₂⁴	1	1	yes	characteristic
366	C₄⋊Dic₇₉	C₂⁴	1	2	yes	—
367	Dic₇₉⋊C₄	—	2	2	no	—
368	Dic₇₉⋊C₄	—	2	2	no	—
369	Dic₇₉⋊C₄	—	2	2	no	—
370	Dic₇₉⋊C₄	—	2	2	no	—
371	Dic₇₉⋊C₄	—	2	2	no	—
372	Dic₇₉⋊C₄	—	2	2	no	—
373	Dic₇₉⋊C₄	—	2	1	no	—
374	Dic₇₉⋊C₄	—	2	1	no	—
375	Dic₇₉⋊C₄	—	2	1	no	—
376	Dic₇₉⋊C₄	—	2	1	no	—
377	Dic₇₉⋊C₄	—	2	2	no	—
378	Dic₇₉⋊C₄	—	2	2	no	—
379	Dic₇₉⋊C₄	—	2	2	no	—
380	Dic₇₉⋊C₄	—	2	2	no	—
381	Dic₇₉⋊C₄	—	2	2	no	—
382	Dic₇₉⋊C₄	—	2	2	no	—
383	Dic₇₉⋊C₄	—	2	2	no	—
384	Dic₇₉⋊C₄	—	2	2	no	—
385	Dic₇₉⋊C₄	C₂×D₄	1	2	yes	—
386	Dic₇₉⋊C₄	C₂×D₄	1	2	yes	—
387	C₂²⋊Dic₇₉	—	2	1	no	—
388	C₂²⋊Dic₇₉	—	2	1	no	—
389	C₂²⋊Dic₇₉	C₂×D₄	1	2	yes	—
390	(C₂×D₇₉)⋊C₄	—	2	1	no	—
391	(C₂×D₇₉)⋊C₄	—	2	1	no	—
392	(C₂×D₇₉)⋊C₄	—	2	1	no	—
393	(C₂×D₇₉)⋊C₄	—	2	1	no	—
394	(C₂×D₇₉)⋊C₄	—	2	2	no	—
395	(C₂×D₇₉)⋊C₄	—	2	2	no	—
396	(C₂×D₇₉)⋊C₄	C₂×D₄	1	2	yes	—
397	(C₂×D₇₉)⋊C₄	C₂×D₄	1	2	yes	—
398	C₄×Dic₇₉	—	2	1	no	—
399	C₄×Dic₇₉	—	2	1	no	—
400	C₄×Dic₇₉	—	2	1	no	—
401	C₄×Dic₇₉	—	2	1	no	—
402	C₄×Dic₇₉	—	2	2	no	—
403	C₄×Dic₇₉	—	2	2	no	—
404	C₄×Dic₇₉	—	2	1	no	—
405	C₄×Dic₇₉	—	2	1	no	—
406	C₄×Dic₇₉	C₂×D₄	1	2	yes	—
407	C₄×Dic₇₉	C₂×D₄	1	2	yes	—
408	C₄×Dic₇₉	C₂⁴	1	2	yes	—
409	C₂×Q₈×C₇₉	—	2	2	no	—
410	C₂×Q₈×C₇₉	—	2	2	no	—
411	C₂²×C₄×C₇₉	—	2	1	no	—
412	C₂²×C₄×C₇₉	—	2	1	no	—
413	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
414	M₁₆×C₇₉	C₂×Q₈	1	4	yes	complemented
415	C₂×C₈×C₇₉	C₂×Q₈	1	4	yes	complemented
416	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
417	C₂×C₈×C₇₉	C₂⁴	1	2	yes	—
418	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₇₉	—	2	1	no	—
420	C₄⋊C₄×C₇₉	—	2	1	no	—
421	C₄⋊C₄×C₇₉	—	2	2	no	—
422	C₄⋊C₄×C₇₉	—	2	2	no	—
423	C₄⋊C₄×C₇₉	—	2	2	no	—
424	C₄⋊C₄×C₇₉	—	2	2	no	—
425	C₄⋊C₄×C₇₉	—	2	2	no	—
426	C₄⋊C₄×C₇₉	—	2	2	no	—
427	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
428	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
429	C₄⋊C₄×C₇₉	C₂⁴	1	2	yes	—
430	C₄⋊C₄×C₇₉	C₂⁴	1	2	yes	—
431	C₄⋊C₄×C₇₉	C₂⁴	1	1	yes	characteristic
432	C₄⋊C₄×C₇₉	C₂⁴	1	1	yes	characteristic
433	C₄⋊C₄×C₇₉	C₂⁴	1	1	yes	characteristic
434	C₄⋊C₄×C₇₉	C₂⁴	1	1	yes	characteristic
435	C₂²⋊C₄×C₇₉	—	2	1	no	—
436	C₂²⋊C₄×C₇₉	—	2	1	no	—
437	C₂²⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
438	C₄²×C₇₉	—	2	1	no	—
439	C₄²×C₇₉	—	2	1	no	—
440	C₄²×C₇₉	C₂⁴	1	2	yes	—
441	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
442	C₂²×D₇₉	—	4	1	no	—
443	C₂²×D₇₉	—	4	1	no	—
444	C₂²×D₇₉	C₄⋊Q₈	1	4	yes	—
445	C₂²×D₇₉	C₂²×D₄	1	1	yes	characteristic
446	C₂²×D₇₉	C₂²×D₄	1	1	yes	characteristic
447	Q₈×C₇₉	—	8	2	no	—
448	Q₈×C₇₉	—	8	2	no	—
449	C₂×C₄×C₇₉	—	2	2	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	2	no	—
455	C₂×C₄×C₇₉	—	8	1	no	—
456	C₂×C₄×C₇₉	—	8	1	no	—
457	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
458	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
459	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₇₉	C₂²×Q₈	1	2	yes	—
461	C₂×C₄×C₇₉	C₂²×Q₈	1	2	yes	—
462	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
463	C₂×Dic₇₉	—	2	2	no	—
464	C₂×Dic₇₉	—	2	1	no	—
465	C₂×Dic₇₉	—	2	1	no	—
466	C₂×Dic₇₉	—	2	1	no	—
467	C₂×Dic₇₉	—	2	1	no	—
468	C₂×Dic₇₉	—	2	2	no	—
469	C₂×Dic₇₉	—	8	1	no	—
470	C₂×Dic₇₉	—	8	1	no	—
471	C₂×Dic₇₉	C₄⋊Q₈	1	4	yes	—
472	C₂×Dic₇₉	C₂²×D₄	1	2	yes	—
473	C₂×Dic₇₉	C₂²×D₄	1	2	yes	—
474	C₂×Dic₇₉	C₂²×D₄	1	1	yes	characteristic
475	C₂×Dic₇₉	C₂²×D₄	1	1	yes	characteristic
476	C₄×D₇₉	—	4	2	no	—
477	C₄×D₇₉	—	4	2	no	—
478	C₄×D₇₉	—	4	2	no	—
479	C₄×D₇₉	—	4	4	no	—
480	C₄×D₇₉	—	4	2	no	—
481	C₄×D₇₉	—	8	1	no	—
482	C₄×D₇₉	—	8	1	no	—
483	C₄×D₇₉	—	8	2	no	—
484	C₄×D₇₉	C₄⋊Q₈	1	4	yes	—
485	C₄×D₇₉	C₄⋊Q₈	1	4	yes	—
486	C₄×D₇₉	C₂²×Q₈	1	2	yes	—
487	C₄×D₇₉	C₂²×Q₈	1	2	yes	—
488	C₄×D₇₉	C₂²×Q₈	1	2	yes	—
489	C₄×D₇₉	C₂²×Q₈	1	2	yes	—
490	Dic₁₅₈	—	8	2	no	—
491	Dic₁₅₈	—	8	2	no	—
492	Dic₁₅₈	—	8	2	no	—
493	Dic₁₅₈	—	8	2	no	—
494	Dic₁₅₈	—	8	2	no	—
495	Dic₁₅₈	—	8	2	no	—
496	C₈×C₇₉	C₂²×Q₈	1	4	yes	—
497	C₈×C₇₉	C₂²×Q₈	1	2	yes	—
498	C₈×C₇₉	C₂²×Q₈	1	2	yes	—
499	C₇₉⋊C₈	C₂²×Q₈	1	4	yes	—
500	C₇₉⋊C₈	C₂²×Q₈	1	2	yes	—
501	C₇₉⋊C₈	C₂²×Q₈	1	2	yes	—
502	C₂²×C₇₉	—	2	1	no	—
503	C₂²×C₇₉	—	2	1	no	—
504	C₂²×C₇₉	C₂×C₄⋊Q₈	1	2	yes	—
505	C₂²×C₇₉	C₂³×D₄	1	1	yes	characteristic
506	C₂×D₇₉	—	2	1	no	—
507	C₂×D₇₉	—	2	1	no	—
508	C₂×D₇₉	—	2	1	no	—
509	C₂×D₇₉	—	2	1	no	—
510	C₂×D₇₉	—	4	4	no	—
511	C₂×D₇₉	C₂×C₄⋊Q₈	1	2	yes	—
512	C₂×D₇₉	C₂×C₄⋊Q₈	1	2	yes	—
513	C₄×C₇₉	—	2	2	no	—
514	C₄×C₇₉	—	2	2	no	—
515	C₄×C₇₉	—	4	2	no	—
516	C₄×C₇₉	—	4	1	no	—
517	C₄×C₇₉	—	4	1	no	—
518	C₄×C₇₉	—	4	2	no	—
519	C₄×C₇₉	—	4	1	no	—
520	C₄×C₇₉	—	4	1	no	—
521	C₄×C₇₉	C₂×C₄⋊Q₈	1	2	yes	—
522	C₄×C₇₉	C₂³×Q₈	1	1	yes	characteristic
523	C₄×C₇₉	C₂³×Q₈	1	1	yes	characteristic
524	Dic₇₉	—	2	2	no	—
525	Dic₇₉	—	2	2	no	—
526	Dic₇₉	—	4	1	no	—
527	Dic₇₉	—	4	2	no	—
528	Dic₇₉	—	4	1	no	—
529	Dic₇₉	—	4	2	no	—
530	Dic₇₉	—	4	1	no	—
531	Dic₇₉	—	4	1	no	—
532	Dic₇₉	C₂×C₄⋊Q₈	1	2	yes	—
533	Dic₇₉	C₂×C₄⋊Q₈	1	2	yes	—
534	#60664	—	79	1	no	maximal, Sylow
535	C₂×C₇₉	—	2	2	no	—
536	C₂×C₇₉	C₂²×C₄⋊Q₈	1	1	yes	characteristic
537	C₂×C₇₉	#3585	1	1	yes	characteristic
538	C₂×C₇₉	#3586	1	1	yes	characteristic
539	D₇₉	—	2	2	no	—
540	D₇₉	—	2	2	no	—
541	#3458	—	79	1	no	—
542	C₂×#544	—	79	1	no	—
543	#3166	—	79	2	no	—
544	#3166	—	79	2	no	—
545	#3165	—	79	2	no	—
546	#3165	—	79	2	no	—
547	#3164	—	79	2	no	—
548	#3164	—	79	2	no	—
549	#3164	—	79	1	no	—
550	#3164	—	79	1	no	—
551	#3164	—	79	1	no	—
552	#3164	—	79	1	no	—
553	#3163	—	79	2	no	—
554	#3163	—	79	2	no	—
555	#3163	—	79	1	no	—
556	#3163	—	79	1	no	—
557	#3163	—	79	1	no	—
558	#3163	D₇₉	1	1	yes	characteristic, complemented
559	#2911	—	79	1	no	—
560	#2911	—	79	1	no	—
561	C₂×#428	—	79	1	no	—
562	C₂×#428	—	79	1	no	—
563	#2873	—	79	1	no	—
564	C₇₉	#60664	1	1	yes	characteristic, complemented, Sylow
565	C₂²×M₁₆	—	79	1	no	—
566	C₂²×M₁₆	—	79	1	no	—
567	#544	—	79	2	no	—
568	#544	—	79	2	no	—
569	#544	—	79	2	no	—
570	#544	—	79	2	no	—
571	#544	—	79	1	no	—
572	#544	—	79	1	no	—
573	#544	—	79	1	no	—
574	#544	—	79	1	no	—
575	#544	—	79	1	no	—
576	#544	—	79	1	no	—
577	#544	—	158	1	no	—
578	#544	—	158	1	no	—
579	#544	—	158	2	no	—
580	#544	—	158	1	no	—
581	#544	—	158	1	no	—
582	#544	C₂×D₇₉	1	1	yes	characteristic
583	#544	C₂×D₇₉	1	1	yes	characteristic
584	#543	—	158	2	no	—
585	#533	—	79	2	no	—
586	#533	—	79	2	no	—
587	#533	—	158	2	no	—
588	#533	—	158	1	no	—
589	#533	—	158	1	no	—
590	C₂×C₄⋊Q₈	—	79	2	no	—
591	C₂×C₄⋊Q₈	—	158	1	no	—
592	C₂×#125	—	79	2	no	—
593	C₂×#125	—	158	1	no	—
594	C₂×C₂²⋊Q₈	—	158	2	no	—
595	C₂×#117	—	79	1	no	—
596	C₂×#117	—	79	1	no	—
597	C₂×#117	—	79	1	no	—
598	C₂×#117	—	79	1	no	—
599	C₂²×C₄⋊C₄	—	79	1	no	—
600	#501	—	79	2	no	—
601	#501	—	79	2	no	—
602	#501	—	79	2	no	—
603	#501	—	79	2	no	—
604	#501	—	79	2	no	—
605	#501	—	79	2	no	—
606	#501	—	79	2	no	—
607	#501	—	79	2	no	—
608	#501	—	79	2	no	—
609	#501	—	79	2	no	—
610	#501	—	79	2	no	—
611	#501	—	79	2	no	—
612	#501	—	79	2	no	—
613	#501	—	79	2	no	—
614	#501	C₂×D₇₉	1	2	yes	complemented
615	#501	C₂×D₇₉	1	2	yes	complemented
616	#500	—	79	2	no	—
617	#500	—	79	2	no	—
618	#500	—	79	2	no	—
619	#500	—	79	2	no	—
620	#499	—	79	2	no	—
621	#499	—	79	2	no	—
622	#499	—	79	2	no	—
623	#499	—	79	2	no	—
624	#499	—	79	2	no	—
625	#499	—	79	2	no	—
626	#499	—	79	2	no	—
627	#499	C₂×D₇₉	1	2	yes	complemented
628	#498	—	79	2	no	—
629	#498	—	79	2	no	—
630	#498	—	79	2	no	—
631	#498	C₂×D₇₉	1	2	yes	complemented
632	#428	—	79	1	no	—
633	#428	—	79	1	no	—
634	#428	—	79	1	no	—
635	#428	—	79	1	no	—
636	#428	—	79	1	no	—
637	#428	—	79	1	no	—
638	#428	—	79	1	no	—
639	#428	—	79	1	no	—
640	#428	—	79	1	no	—
641	#428	—	79	2	no	—
642	#428	—	79	2	no	—
643	#428	—	79	1	no	—
644	#428	—	79	1	no	—
645	#428	—	79	2	no	—
646	#428	—	79	2	no	—
647	#428	—	79	1	no	—
648	#428	—	79	2	no	—
649	#428	—	79	1	no	—
650	#428	—	79	2	no	—
651	#428	—	79	2	no	—
652	#428	—	79	2	no	—
653	#428	—	79	1	no	—
654	#428	C₂×D₇₉	1	1	yes	characteristic
655	#428	C₂×D₇₉	1	1	yes	characteristic
656	#427	—	79	1	no	—
657	#427	—	79	1	no	—
658	#427	—	79	1	no	—
659	#427	—	79	2	no	—
660	#427	—	79	2	no	—
661	#427	C₂×D₇₉	1	1	yes	characteristic
662	C₂×#107	—	79	1	no	—
663	C₂×#107	—	79	1	no	—
664	C₂×#107	—	79	2	no	—
665	C₂×#106	—	79	1	no	—
666	C₂×#106	—	79	2	no	—
667	C₂×#106	C₂×D₇₉	1	1	yes	characteristic
668	#405	—	79	1	no	—
669	#405	—	79	1	no	—
670	#405	—	79	1	no	—
671	#405	—	79	2	no	—
672	#405	—	79	2	no	—
673	#405	C₂×D₇₉	1	1	yes	characteristic
674	C₄×M₁₆	—	79	2	no	—
675	C₄×M₁₆	—	79	2	no	—
676	C₂²×Q₈	—	158	2	no	—
677	C₂³×C₄	—	79	1	no	—
678	C₂³×C₄	—	158	1	no	—
679	C₂×M₁₆	—	79	1	no	—
680	C₂×M₁₆	—	79	8	no	—
681	C₂×M₁₆	—	79	8	no	—
682	C₂×M₁₆	—	79	1	no	—
683	C₂×M₁₆	—	79	2	no	—
684	C₂×M₁₆	—	79	1	no	—
685	C₂×M₁₆	—	79	1	no	—
686	C₂×M₁₆	—	79	1	no	—
687	C₂×M₁₆	C₂²×D₇₉	1	1	yes	characteristic
688	C₂²×C₈	—	79	1	no	—
689	C₂²×C₈	—	79	2	no	—
690	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
691	C₄⋊Q₈	—	2	1	no	—
692	C₄⋊Q₈	—	2	1	no	—
693	C₄⋊Q₈	—	79	2	no	—
694	C₄⋊Q₈	—	79	2	no	—
695	C₄⋊Q₈	—	79	2	no	—
696	C₄⋊Q₈	—	79	2	no	—
697	C₄⋊Q₈	—	79	2	no	—
698	C₄⋊Q₈	—	79	2	no	—
699	C₄⋊Q₈	—	158	1	no	—
700	C₄⋊Q₈	—	158	1	no	—
701	C₄⋊Q₈	—	158	2	no	—
702	C₄⋊Q₈	—	158	2	no	—
703	C₄⋊Q₈	—	158	2	no	—
704	C₄⋊Q₈	—	158	1	no	—
705	C₄⋊Q₈	—	158	2	no	—
706	C₄⋊Q₈	—	158	1	no	—
707	C₄⋊Q₈	—	158	2	no	—
708	C₄⋊Q₈	—	158	2	no	—
709	C₄⋊Q₈	—	158	1	no	—
710	C₄⋊Q₈	—	158	1	no	—
711	C₄⋊Q₈	C₂²×D₇₉	1	2	yes	—
712	C₄⋊Q₈	C₂²×D₇₉	1	2	yes	—
713	#125	—	2	1	no	—
714	#125	—	2	1	no	—
715	#125	—	79	2	no	—
716	#125	—	79	2	no	—
717	#125	—	79	2	no	—
718	#125	—	79	2	no	—
719	#125	—	79	2	no	—
720	#125	—	79	2	no	—
721	#125	—	158	1	no	—
722	#125	—	158	1	no	—
723	#125	—	158	2	no	—
724	#125	—	158	2	no	—
725	#125	—	158	2	no	—
726	#125	—	158	2	no	—
727	#125	—	158	1	no	—
728	#125	—	158	2	no	—
729	#125	—	158	2	no	—
730	#125	—	158	1	no	—
731	#125	—	158	1	no	—
732	#125	—	158	1	no	—
733	#125	C₂²×D₇₉	1	2	yes	—
734	#125	C₂²×D₇₉	1	2	yes	—
735	C₂²⋊Q₈	—	2	2	no	—
736	C₂²⋊Q₈	—	2	2	no	—
737	C₂²⋊Q₈	—	158	2	no	—
738	C₂²⋊Q₈	—	158	2	no	—
739	C₂²⋊Q₈	—	158	2	no	—
740	C₂²⋊Q₈	—	158	2	no	—
741	C₂²⋊Q₈	—	158	2	no	—
742	C₂²⋊Q₈	—	158	2	no	—
743	C₂²⋊Q₈	—	158	2	no	—
744	C₂²⋊Q₈	—	158	2	no	—
745	C₂²⋊Q₈	—	158	2	no	—
746	C₂²⋊Q₈	—	158	2	no	—
747	C₂²⋊Q₈	—	158	2	no	—
748	C₂²⋊Q₈	—	158	2	no	—
749	C₂²⋊Q₈	—	158	2	no	—
750	C₂²⋊Q₈	—	158	2	no	—
751	C₂²⋊Q₈	—	158	2	no	—
752	C₂²⋊Q₈	—	158	2	no	—
753	C₂²⋊Q₈	—	158	2	no	—
754	C₂²⋊Q₈	—	158	2	no	—
755	C₄×Q₈	—	158	2	no	—
756	C₄×Q₈	—	158	2	no	—
757	C₄×Q₈	—	158	2	no	—
758	C₄×Q₈	—	158	2	no	—
759	#117	—	79	1	no	—
760	#117	—	79	1	no	—
761	#117	—	79	1	no	—
762	#117	—	79	2	no	—
763	#117	—	79	2	no	—
764	#117	—	79	1	no	—
765	#117	—	79	1	no	—
766	#117	—	79	1	no	—
767	#117	—	79	1	no	—
768	#117	—	79	2	no	—
769	#117	—	79	1	no	—
770	#117	—	79	1	no	—
771	#117	—	79	2	no	—
772	#117	—	158	1	no	—
773	#117	—	158	1	no	—
774	#117	—	158	1	no	—
775	#117	—	158	1	no	—
776	#117	—	158	1	no	—
777	#117	—	158	1	no	—
778	#117	C₂²×D₇₉	1	1	yes	characteristic
779	#117	C₂²×D₇₉	1	1	yes	characteristic
780	#117	C₂²×D₇₉	1	1	yes	characteristic
781	C₂×C₄⋊C₄	—	79	1	no	—
782	C₂×C₄⋊C₄	—	79	1	no	—
783	C₂×C₄⋊C₄	—	79	1	no	—
784	C₂×C₄⋊C₄	—	79	1	no	—
785	C₂×C₄⋊C₄	—	79	2	no	—
786	C₂×C₄⋊C₄	—	79	2	no	—
787	C₂×C₄⋊C₄	—	79	1	no	—
788	C₂×C₄⋊C₄	—	79	1	no	—
789	C₂×C₄⋊C₄	—	79	1	no	—
790	C₂×C₄⋊C₄	—	79	1	no	—
791	C₂×C₄⋊C₄	—	158	1	no	—
792	C₂×C₄⋊C₄	—	158	1	no	—
793	C₂×C₄⋊C₄	—	158	2	no	—
794	C₂×C₄⋊C₄	—	158	2	no	—
795	C₂×C₄⋊C₄	—	158	2	no	—
796	C₂×C₄⋊C₄	—	158	1	no	—
797	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
798	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
799	C₂×C₂²⋊C₄	—	79	2	no	—
800	C₂×C₂²⋊C₄	—	158	1	no	—
801	C₂×C₂²⋊C₄	—	158	1	no	—
802	C₂×C₂²⋊C₄	—	158	1	no	—
803	C₂×C₄²	—	79	2	no	—
804	C₂×C₄²	—	158	1	no	—
805	C₂×C₄²	—	158	1	no	—
806	C₂×C₄²	—	158	1	no	—
807	#107	—	79	2	no	—
808	#107	—	79	2	no	—
809	#107	—	79	2	no	—
810	#107	—	79	1	no	—
811	#107	—	79	2	no	—
812	#107	—	79	1	no	—
813	#107	—	79	2	no	—
814	#107	—	79	2	no	—
815	#107	—	79	2	no	—
816	#107	—	79	2	no	—
817	#107	—	79	1	no	—
818	#107	—	79	1	no	—
819	#107	—	79	2	no	—
820	#107	—	79	1	no	—
821	#107	—	79	1	no	—
822	#107	—	79	2	no	—
823	#107	C₂²×D₇₉	1	2	yes	—
824	#107	C₂²×D₇₉	1	2	yes	—
825	#107	C₂²×D₇₉	1	1	yes	characteristic
826	#107	C₂²×D₇₉	1	1	yes	characteristic
827	#106	—	79	2	no	—
828	#106	—	79	1	no	—
829	#106	—	79	1	no	—
830	#106	—	79	2	no	—
831	#106	—	79	2	no	—
832	#106	—	79	2	no	—
833	#106	—	79	2	no	—
834	#106	—	79	2	no	—
835	#106	—	79	1	no	—
836	#106	—	79	1	no	—
837	#106	—	79	2	no	—
838	#106	—	79	1	no	—
839	#106	—	79	2	no	—
840	#106	—	79	1	no	—
841	#106	C₂²×D₇₉	1	2	yes	—
842	#106	C₂²×D₇₉	1	2	yes	—
843	#106	C₂²×D₇₉	1	2	yes	—
844	#106	C₂²×D₇₉	1	2	yes	—
845	#106	C₂²×D₇₉	1	1	yes	characteristic
846	#106	C₂²×D₇₉	1	1	yes	characteristic
847	#97	—	79	2	no	—
848	#97	—	79	2	no	—
849	#97	—	79	2	no	—
850	#97	C₂²×D₇₉	1	2	yes	—
851	C₄×C₈	—	79	2	no	—
852	C₄×C₈	—	79	2	no	—
853	C₄×C₈	—	79	2	no	—
854	C₄×C₈	C₂²×D₇₉	1	2	yes	—
855	C₂⁴	—	79	1	no	—
856	C₂×Q₈	—	2	2	no	—
857	C₂×Q₈	—	2	2	no	—
858	C₂×Q₈	—	632	4	no	—
859	C₂×Q₈	—	158	2	no	—
860	C₂×Q₈	—	158	2	no	—
861	C₂×Q₈	—	158	2	no	—
862	C₂×Q₈	—	158	2	no	—
863	C₂×Q₈	—	158	2	no	—
864	C₂×Q₈	—	158	2	no	—
865	C₂²×C₄	—	2	1	no	—
866	C₂²×C₄	—	2	1	no	—
867	C₂²×C₄	—	79	2	no	—
868	C₂²×C₄	—	79	2	no	—
869	C₂²×C₄	—	79	1	no	—
870	C₂²×C₄	—	79	4	no	—
871	C₂²×C₄	—	79	4	no	—
872	C₂²×C₄	—	79	1	no	—
873	C₂²×C₄	—	79	1	no	—
874	C₂²×C₄	—	79	1	no	—
875	C₂²×C₄	—	79	1	no	—
876	C₂²×C₄	—	632	2	no	—
877	C₂²×C₄	—	158	1	no	—
878	C₂²×C₄	—	158	1	no	—
879	C₂²×C₄	—	158	2	no	—
880	C₂²×C₄	—	158	1	no	—
881	C₂²×C₄	—	158	1	no	—
882	C₂²×C₄	—	158	2	no	—
883	C₂²×C₄	—	158	1	no	—
884	C₂²×C₄	—	158	1	no	—
885	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
886	M₁₆	—	79	4	no	—
887	M₁₆	—	79	8	no	—
888	M₁₆	—	79	4	no	—
889	M₁₆	—	79	4	no	—
890	M₁₆	—	79	4	no	—
891	M₁₆	—	79	4	no	—
892	M₁₆	Q₈×D₇₉	1	4	yes	complemented
893	C₂×C₈	—	79	4	no	—
894	C₂×C₈	—	79	1	no	—
895	C₂×C₈	—	79	2	no	—
896	C₂×C₈	—	79	1	no	—
897	C₂×C₈	—	79	8	no	—
898	C₂×C₈	Q₈×D₇₉	1	4	yes	complemented
899	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
900	C₂×C₈	C₂³×D₇₉	1	2	yes	—
901	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
902	C₄⋊C₄	—	2	1	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	79	2	no	—
911	C₄⋊C₄	—	79	2	no	—
912	C₄⋊C₄	—	79	1	no	—
913	C₄⋊C₄	—	79	1	no	—
914	C₄⋊C₄	—	79	1	no	—
915	C₄⋊C₄	—	79	2	no	—
916	C₄⋊C₄	—	79	1	no	—
917	C₄⋊C₄	—	79	1	no	—
918	C₄⋊C₄	—	79	1	no	—
919	C₄⋊C₄	—	79	2	no	—
920	C₄⋊C₄	—	158	2	no	—
921	C₄⋊C₄	—	158	2	no	—
922	C₄⋊C₄	—	158	1	no	—
923	C₄⋊C₄	—	158	1	no	—
924	C₄⋊C₄	—	158	1	no	—
925	C₄⋊C₄	—	158	1	no	—
926	C₄⋊C₄	—	158	2	no	—
927	C₄⋊C₄	—	158	2	no	—
928	C₄⋊C₄	—	158	2	no	—
929	C₄⋊C₄	—	158	2	no	—
930	C₄⋊C₄	—	158	2	no	—
931	C₄⋊C₄	—	158	2	no	—
932	C₄⋊C₄	—	158	2	no	—
933	C₄⋊C₄	—	158	2	no	—
934	C₄⋊C₄	—	158	2	no	—
935	C₄⋊C₄	—	158	2	no	—
936	C₄⋊C₄	—	158	2	no	—
937	C₄⋊C₄	—	158	2	no	—
938	C₄⋊C₄	—	158	2	no	—
939	C₄⋊C₄	—	158	2	no	—
940	C₄⋊C₄	—	158	2	no	—
941	C₄⋊C₄	—	158	2	no	—
942	C₄⋊C₄	—	158	1	no	—
943	C₄⋊C₄	—	158	1	no	—
944	C₄⋊C₄	—	158	2	no	—
945	C₄⋊C₄	—	158	2	no	—
946	C₄⋊C₄	D₄×D₇₉	1	1	yes	characteristic
947	C₄⋊C₄	D₄×D₇₉	1	1	yes	characteristic
948	C₄⋊C₄	C₂³×D₇₉	1	1	yes	characteristic
949	C₄⋊C₄	C₂³×D₇₉	1	2	yes	—
950	C₄⋊C₄	C₂³×D₇₉	1	1	yes	characteristic
951	C₄⋊C₄	C₂³×D₇₉	1	2	yes	—
952	C₄⋊C₄	C₂³×D₇₉	1	1	yes	characteristic
953	C₄⋊C₄	C₂³×D₇₉	1	1	yes	characteristic
954	C₂²⋊C₄	—	2	1	no	—
955	C₂²⋊C₄	—	2	1	no	—
956	C₂²⋊C₄	—	79	2	no	—
957	C₂²⋊C₄	—	79	2	no	—
958	C₂²⋊C₄	—	79	2	no	—
959	C₂²⋊C₄	—	158	1	no	—
960	C₂²⋊C₄	—	158	1	no	—
961	C₂²⋊C₄	—	158	1	no	—
962	C₂²⋊C₄	—	158	1	no	—
963	C₂²⋊C₄	—	158	2	no	—
964	C₂²⋊C₄	—	158	2	no	—
965	C₂²⋊C₄	—	158	1	no	—
966	C₂²⋊C₄	—	158	1	no	—
967	C₂²⋊C₄	D₄×D₇₉	1	2	yes	—
968	C₄²	—	2	1	no	—
969	C₄²	—	2	1	no	—
970	C₄²	—	79	2	no	—
971	C₄²	—	79	2	no	—
972	C₄²	—	79	2	no	—
973	C₄²	—	158	1	no	—
974	C₄²	—	158	1	no	—
975	C₄²	—	158	2	no	—
976	C₄²	—	158	1	no	—
977	C₄²	—	158	1	no	—
978	C₄²	—	158	2	no	—
979	C₄²	—	158	1	no	—
980	C₄²	—	158	1	no	—
981	C₄²	C₂³×D₇₉	1	2	yes	—
982	C₂³	—	316	1	no	—
983	C₂³	—	316	1	no	—
984	C₂³	—	79	4	no	—
985	C₂³	—	79	1	no	—
986	C₂³	—	79	1	no	—
987	C₂³	C₂×D₄×D₇₉	1	1	yes	characteristic
988	Q₈	—	8	2	no	—
989	Q₈	—	8	2	no	—
990	Q₈	—	632	2	no	—
991	Q₈	—	632	2	no	—
992	Q₈	—	632	2	no	—
993	Q₈	—	632	2	no	—
994	Q₈	—	632	2	no	—
995	Q₈	—	632	2	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	8	1	no	—
1003	C₂×C₄	—	8	1	no	—
1004	C₂×C₄	—	316	2	no	—
1005	C₂×C₄	—	316	2	no	—
1006	C₂×C₄	—	316	4	no	—
1007	C₂×C₄	—	316	2	no	—
1008	C₂×C₄	—	316	2	no	—
1009	C₂×C₄	—	79	4	no	—
1010	C₂×C₄	—	79	1	no	—
1011	C₂×C₄	—	79	1	no	—
1012	C₂×C₄	—	79	4	no	—
1013	C₂×C₄	—	79	4	no	—
1014	C₂×C₄	—	79	2	no	—
1015	C₂×C₄	—	79	2	no	—
1016	C₂×C₄	—	79	2	no	—
1017	C₂×C₄	—	79	2	no	—
1018	C₂×C₄	—	79	2	no	—
1019	C₂×C₄	—	79	2	no	—
1020	C₂×C₄	—	632	2	no	—
1021	C₂×C₄	—	632	1	no	—
1022	C₂×C₄	—	632	1	no	—
1023	C₂×C₄	—	632	1	no	—
1024	C₂×C₄	—	632	1	no	—
1025	C₂×C₄	—	158	1	no	—
1026	C₂×C₄	—	158	2	no	—
1027	C₂×C₄	—	158	1	no	—
1028	C₂×C₄	—	158	1	no	—
1029	C₂×C₄	—	158	1	no	—
1030	C₂×C₄	—	158	2	no	—
1031	C₂×C₄	C₂×D₄×D₇₉	1	2	yes	—
1032	C₂×C₄	C₂×D₄×D₇₉	1	2	yes	—
1033	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
1034	C₂×C₄	C₂×Q₈×D₇₉	1	2	yes	—
1035	C₂×C₄	C₂×Q₈×D₇₉	1	2	yes	—
1036	C₂×C₄	C₂⁴×D₇₉	1	1	yes	characteristic
1037	C₈	—	79	2	no	—
1038	C₈	—	79	2	no	—
1039	C₈	—	79	4	no	—
1040	C₈	C₂×Q₈×D₇₉	1	4	yes	—
1041	C₈	C₂×Q₈×D₇₉	1	2	yes	—
1042	C₈	C₂×Q₈×D₇₉	1	2	yes	—
1043	C₂²	—	2	1	no	—
1044	C₂²	—	2	1	no	—
1045	C₂²	—	316	4	no	—
1046	C₂²	—	79	2	no	—
1047	C₂²	—	79	2	no	—
1048	C₂²	—	158	1	no	—
1049	C₂²	—	158	1	no	—
1050	C₂²	—	158	1	no	—
1051	C₂²	—	158	1	no	—
1052	C₂²	C₄⋊Q₈×D₇₉	1	2	yes	—
1053	C₂²	C₂²×D₄×D₇₉	1	1	yes	characteristic
1054	C₄	—	2	2	no	—
1055	C₄	—	2	2	no	—
1056	C₄	—	4	2	no	—
1057	C₄	—	4	1	no	—
1058	C₄	—	4	1	no	—
1059	C₄	—	4	2	no	—
1060	C₄	—	4	1	no	—
1061	C₄	—	4	1	no	—
1062	C₄	—	316	2	no	—
1063	C₄	—	316	1	no	—
1064	C₄	—	316	1	no	—
1065	C₄	—	316	2	no	—
1066	C₄	—	316	1	no	—
1067	C₄	—	316	1	no	—
1068	C₄	—	79	2	no	—
1069	C₄	—	79	2	no	—
1070	C₄	—	158	2	no	—
1071	C₄	—	158	2	no	—
1072	C₄	C₄⋊Q₈×D₇₉	1	2	yes	—
1073	C₄	C₂²×Q₈×D₇₉	1	1	yes	characteristic
1074	C₄	C₂²×Q₈×D₇₉	1	1	yes	characteristic
1075	C₂	—	2	2	no	—
1076	C₂	—	158	2	no	—
1077	C₂	—	158	2	no	—
1078	C₂	C₂×C₄⋊Q₈×D₇₉	1	1	yes	characteristic
1079	C₂	#23778178	1	1	yes	characteristic
1080	C₂	#23778182	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×#3163	C₂
socle	C₂²×C₇₉	C₂³×D₄
prime radical	C₂³×D₇₉	C₂×D₄
hypercenter	#3163	D₇₉
hypocenter	C₇₉	#60664
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3163

Complements

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

N	H ≅ G/N	type
3. #23773951	C₂	semidirect
4. #23773948	C₂	semidirect
5. #23773945	C₂	semidirect
6. #23773941	C₂	semidirect
7. #23773940	C₂	semidirect
8. #23773939	C₂	semidirect
9. #23773938	C₂	semidirect
10. #23773937	C₂	semidirect
11. #23773935	C₂	semidirect
12. #23773934	C₂	semidirect
13. #23773930	C₂	semidirect
14. #23773928	C₂	semidirect
15. #23773927	C₂	semidirect
16. #23773926	C₂	semidirect
17. #23773925	C₂	semidirect
23. C₇₉×#3163	C₂	semidirect
57. #19098973	C₂²	semidirect
58. #19098973	C₂²	semidirect
59. #19098972	C₂²	semidirect
60. #19098972	C₂²	semidirect
61. #19098971	C₂²	semidirect
62. #19098971	C₂²	semidirect
63. #19098970	C₂²	semidirect
64. #19098970	C₂²	semidirect
65. #19098970	C₂²	semidirect
66. #19098970	C₂²	semidirect
67. #19098970	C₂²	semidirect
68. #19098970	C₂²	semidirect
69. #19098969	C₂²	semidirect
70. #19098969	C₂²	semidirect
71. #19098968	C₂²	semidirect
72. #19098967	C₂²	semidirect
73. #19098967	C₂²	semidirect
74. #19098966	C₂²	semidirect
75. #19098965	C₂²	semidirect
76. #19098964	C₂²	semidirect
77. #19098964	C₂²	semidirect
78. #19098963	C₂²	semidirect
79. #19098963	C₂²	semidirect
80. #19098962	C₂²	semidirect
81. #19098962	C₂²	semidirect
82. #19098960	C₂²	semidirect
83. #19098960	C₂²	semidirect
84. #19098959	C₂²	semidirect
126. #501×C₇₉	C₂²	semidirect
127. #501×C₇₉	C₂²	semidirect
128. #499×C₇₉	C₂²	semidirect
129. #498×C₇₉	C₂²	semidirect
139. C₂×#11929607	Q₈	semidirect
145. M₁₆×D₇₉	Q₈	semidirect
340. #11929608	C₂×Q₈	semidirect
344. #11929607	C₂×Q₈	semidirect
345. #11929607	C₂×Q₈	semidirect
346. C₂×C₇₉⋊C₈	C₂×Q₈	semidirect
350. C₈×D₇₉	C₂×Q₈	semidirect
414. M₁₆×C₇₉	C₂×Q₈	semidirect
415. C₂×C₈×C₇₉	C₂×Q₈	semidirect
558. #3163	D₇₉	semidirect
564. C₇₉	#60664	semidirect
614. #501	C₂×D₇₉	semidirect
615. #501	C₂×D₇₉	semidirect
627. #499	C₂×D₇₉	semidirect
631. #498	C₂×D₇₉	semidirect
892. M₁₆	Q₈×D₇₉	semidirect
898. C₂×C₈	Q₈×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
#23776804	2
#544×D₇₉	2
#23773951	2
#23773948	2
#23773945	2
#23773941	2
#23773940	2
#23773939	2
#23773938	2
#23773937	2
#23773935	2
#23773934	2
#23773930	2
#23773928	2
#23773927	2
#23773926	2
#23773925	2
#23771988	2
#23771987	2
C₂×#19098602	2
#428×D₇₉	2
#23771816	2
C₇₉×#3163	2
#60664	79