Subgroups — #34450981

Order 20224.

2024 conjugacy classes of subgroups.

The subgroup lattice has 1380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19099314	C₂	1	1	yes	maximal, characteristic
2	#23766591	C₂	1	1	yes	maximal, characteristic, complemented
3	#23766590	C₂	1	1	yes	maximal, characteristic, complemented
4	#23766587	C₂	1	1	yes	maximal, characteristic, complemented
5	#23766587	C₂	1	1	yes	maximal, characteristic, complemented
6	#23766584	C₂	1	1	yes	maximal, characteristic, complemented
7	#23766583	C₂	1	1	yes	maximal, characteristic, complemented
8	#23766579	C₂	1	1	yes	maximal, characteristic, complemented
9	#23766578	C₂	1	1	yes	maximal, characteristic, complemented
10	#23766569	C₂	1	1	yes	maximal, characteristic
11	#23766568	C₂	1	1	yes	maximal, characteristic, complemented
12	#23766562	C₂	1	1	yes	maximal, characteristic, complemented
13	#23766561	C₂	1	1	yes	maximal, characteristic, complemented
14	#23766544	C₂	1	1	yes	maximal, characteristic
15	#23766542	C₂	1	1	yes	maximal, characteristic
16	#23765971	C₂	1	1	yes	maximal, characteristic, complemented
17	#23765969	C₂	1	1	yes	maximal, characteristic, complemented
18	#23765959	C₂	1	1	yes	maximal, characteristic, complemented
19	#23765957	C₂	1	1	yes	maximal, characteristic, complemented
20	#23765954	C₂	1	1	yes	maximal, characteristic, complemented
21	#23765954	C₂	1	1	yes	maximal, characteristic, complemented
22	#23765950	C₂	1	1	yes	maximal, characteristic, complemented
23	#23765950	C₂	1	1	yes	maximal, characteristic, complemented
24	#23765941	C₂	1	1	yes	maximal, characteristic
25	#23765938	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂²⋊Q₈×Dic₇₉	C₂	1	1	yes	maximal, characteristic, complemented
27	#23765934	C₂	1	1	yes	maximal, characteristic, complemented
28	#23765928	C₂	1	1	yes	maximal, characteristic, complemented
29	#23765927	C₂	1	1	yes	maximal, characteristic
30	#23765917	C₂	1	1	yes	maximal, characteristic
31	C₇₉×#2378	C₂	1	1	yes	maximal, characteristic, complemented
32	#19099314	C₄	1	16	yes	complemented
33	C₂×#14579160	C₂²	1	1	yes	characteristic
34	C₂×#14579159	C₂²	1	1	yes	characteristic
35	C₂×#14579156	C₂²	1	1	yes	characteristic
36	C₂×#14579156	C₂²	1	1	yes	characteristic
37	C₂×#14579154	C₂²	1	1	yes	characteristic
38	C₂×#14579154	C₂²	1	1	yes	characteristic
39	C₂×#14579152	C₂²	1	1	yes	characteristic
40	C₂×#14579151	C₂²	1	1	yes	characteristic
41	C₂×#14579147	C₂²	1	1	yes	characteristic
42	C₂×#14579144	C₂²	1	1	yes	characteristic
43	C₂×#14579143	C₂²	1	1	yes	characteristic
44	C₂×#14579140	C₂²	1	1	yes	characteristic
45	C₂×#14579139	C₂²	1	1	yes	characteristic
46	C₂×#14579137	C₂²	1	1	yes	characteristic
47	C₂×Q₈×Dic₇₉	C₂²	1	1	yes	characteristic
48	C₂×#14579126	C₂²	1	1	yes	characteristic
49	C₂×#14579126	C₂²	1	1	yes	characteristic
50	C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	1	1	yes	characteristic
51	C₂²×C₄×Dic₇₉	C₂²	1	1	yes	characteristic
52	C₂×C₄²×D₇₉	C₂²	1	1	yes	characteristic
53	#19098470	C₂²	1	1	yes	characteristic
54	#19098469	C₂²	1	1	yes	characteristic
55	#19098468	C₂²	1	1	yes	characteristic
56	#19098467	C₂²	1	1	yes	characteristic
57	#19098467	C₂²	1	1	yes	characteristic
58	#19098467	C₂²	1	1	yes	characteristic
59	#19098467	C₂²	1	1	yes	characteristic
60	#19098463	C₂²	1	1	yes	characteristic
61	#19098462	C₂²	1	1	yes	characteristic
62	#19098461	C₂²	1	1	yes	characteristic
63	#19098461	C₂²	1	1	yes	characteristic
64	#19098461	C₂²	1	1	yes	characteristic
65	#19098460	C₂²	1	1	yes	characteristic
66	#19098460	C₂²	1	1	yes	characteristic
67	#19098460	C₂²	1	1	yes	characteristic
68	#19098460	C₂²	1	1	yes	characteristic
69	#19098460	C₂²	1	1	yes	characteristic
70	#19098460	C₂²	1	1	yes	characteristic
71	#19098459	C₂²	1	1	yes	characteristic
72	#19098458	C₂²	1	1	yes	characteristic
73	#19098458	C₂²	1	1	yes	characteristic
74	#19098458	C₂²	1	1	yes	characteristic
75	#19098457	C₂²	1	1	yes	characteristic
76	#19098457	C₂²	1	1	yes	characteristic
77	#19098457	C₂²	1	1	yes	characteristic
78	#19098455	C₂²	1	1	yes	characteristic
79	#19098455	C₂²	1	1	yes	characteristic
80	#19098454	C₂²	1	1	yes	characteristic
81	#19098454	C₂²	1	1	yes	characteristic
82	#19098454	C₂²	1	1	yes	characteristic
83	#19098453	C₂²	1	1	yes	characteristic
84	#19098453	C₂²	1	1	yes	characteristic
85	#19098453	C₂²	1	1	yes	characteristic
86	#19098452	C₂²	1	1	yes	characteristic
87	#19098452	C₂²	1	1	yes	characteristic
88	#19098451	C₂²	1	1	yes	characteristic
89	#19098451	C₂²	1	1	yes	characteristic
90	#19098451	C₂²	1	1	yes	characteristic
91	#19098450	C₂²	1	1	yes	characteristic
92	#19098450	C₂²	1	1	yes	characteristic
93	#19098450	C₂²	1	1	yes	characteristic
94	#19098450	C₂²	1	1	yes	characteristic
95	#19098450	C₂²	1	1	yes	characteristic
96	#19098449	C₂²	1	1	yes	characteristic
97	#19098449	C₂²	1	1	yes	characteristic
98	#19098448	C₂²	1	1	yes	characteristic
99	#19098448	C₂²	1	1	yes	characteristic
100	#19098448	C₂²	1	1	yes	characteristic
101	#19098448	C₂²	1	1	yes	characteristic
102	#19098448	C₂²	1	1	yes	characteristic
103	#19098447	C₂²	1	1	yes	characteristic
104	#19098447	C₂²	1	1	yes	characteristic
105	#19098447	C₂²	1	1	yes	characteristic
106	#19098447	C₂²	1	1	yes	characteristic
107	#19098447	C₂²	1	1	yes	characteristic
108	#19098446	C₂²	1	1	yes	characteristic
109	#19098446	C₂²	1	1	yes	characteristic
110	#19098446	C₂²	1	1	yes	characteristic
111	#19098445	C₂²	1	1	yes	characteristic
112	#19098445	C₂²	1	1	yes	characteristic
113	#19098445	C₂²	1	1	yes	characteristic
114	#19098445	C₂²	1	1	yes	characteristic
115	#19098444	C₂²	1	1	yes	characteristic
116	#19098444	C₂²	1	1	yes	characteristic
117	#19098444	C₂²	1	1	yes	characteristic
118	#19098444	C₂²	1	1	yes	characteristic
119	#19098440	C₂²	1	1	yes	characteristic
120	#19098439	C₂²	1	1	yes	characteristic
121	#19098438	C₂²	1	1	yes	characteristic
122	#19098438	C₂²	1	1	yes	characteristic
123	#19098437	C₂²	1	1	yes	characteristic
124	#19098437	C₂²	1	1	yes	characteristic
125	#19098437	C₂²	1	1	yes	characteristic
126	#19098435	C₂²	1	1	yes	characteristic
127	#19098435	C₂²	1	1	yes	characteristic
128	#19098435	C₂²	1	1	yes	characteristic
129	#19098434	C₂²	1	1	yes	characteristic
130	#19098434	C₂²	1	1	yes	characteristic
131	#19098432	C₂²	1	1	yes	characteristic
132	#19098432	C₂²	1	1	yes	characteristic
133	#19098430	C₂²	1	1	yes	characteristic
134	#19098430	C₂²	1	1	yes	characteristic
135	#19098430	C₂²	1	1	yes	characteristic
136	#19098430	C₂²	1	1	yes	characteristic
137	#19098428	C₂²	1	1	yes	characteristic
138	#19098427	C₂²	1	1	yes	characteristic
139	#19098427	C₂²	1	1	yes	characteristic
140	#19098425	C₂²	1	1	yes	characteristic
141	#19098423	C₂²	1	1	yes	characteristic
142	#19098422	C₂²	1	1	yes	characteristic
143	#19098420	C₂²	1	1	yes	characteristic
144	C₄⋊C₄×Dic₇₉	C₂²	1	1	yes	characteristic
145	C₄⋊C₄×Dic₇₉	C₂²	1	1	yes	characteristic
146	C₄⋊C₄×Dic₇₉	C₂²	1	1	yes	characteristic
147	C₄⋊C₄×Dic₇₉	C₂²	1	1	yes	characteristic
148	C₄⋊C₄×Dic₇₉	C₂²	1	1	yes	characteristic
149	C₄⋊C₄×Dic₇₉	C₂²	1	1	yes	characteristic
150	C₄⋊C₄×Dic₇₉	C₂²	1	1	yes	characteristic
151	#19098414	C₂²	1	1	yes	characteristic
152	#19098414	C₂²	1	1	yes	characteristic
153	#19098414	C₂²	1	1	yes	characteristic
154	#19098414	C₂²	1	1	yes	characteristic
155	#19098414	C₂²	1	1	yes	characteristic
156	#19098414	C₂²	1	1	yes	characteristic
157	#19098414	C₂²	1	1	yes	characteristic
158	#19098414	C₂²	1	1	yes	characteristic
159	#19098414	C₂²	1	1	yes	characteristic
160	C₂²⋊C₄×Dic₇₉	C₂²	1	1	yes	characteristic
161	C₂²⋊C₄×Dic₇₉	C₂²	1	1	yes	characteristic
162	C₂²⋊C₄×Dic₇₉	C₂²	1	1	yes	characteristic
163	C₂²⋊C₄×Dic₇₉	C₂²	1	1	yes	characteristic
164	C₂²⋊C₄×Dic₇₉	C₂²	1	1	yes	characteristic
165	#19098410	C₂²	1	1	yes	characteristic
166	#19098410	C₂²	1	1	yes	characteristic
167	#19098410	C₂²	1	1	yes	characteristic
168	#19098410	C₂²	1	1	yes	characteristic
169	#19098410	C₂²	1	1	yes	characteristic
170	C₄²×Dic₇₉	C₂²	1	1	yes	characteristic
171	C₄²×Dic₇₉	C₂²	1	1	yes	characteristic
172	C₄²×Dic₇₉	C₂²	1	1	yes	characteristic
173	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
174	#391×C₇₉	C₂²	1	1	yes	characteristic
175	#391×C₇₉	C₂²	1	1	yes	characteristic
176	#389×C₇₉	C₂²	1	1	yes	characteristic
177	#389×C₇₉	C₂²	1	1	yes	characteristic
178	#388×C₇₉	C₂²	1	1	yes	characteristic
179	#388×C₇₉	C₂²	1	1	yes	characteristic
180	#388×C₇₉	C₂²	1	1	yes	characteristic
181	#388×C₇₉	C₂²	1	1	yes	characteristic
182	#387×C₇₉	C₂²	1	1	yes	characteristic
183	#387×C₇₉	C₂²	1	1	yes	characteristic
184	#387×C₇₉	C₂²	1	1	yes	characteristic
185	#387×C₇₉	C₂²	1	1	yes	characteristic
186	#381×C₇₉	C₂²	1	1	yes	characteristic
187	#380×C₇₉	C₂²	1	1	yes	characteristic
188	C₂²×Dic₁₅₈	C₂³	1	1	yes	characteristic
189	C₂²×Dic₁₅₈	C₂³	1	1	yes	characteristic
190	C₂²×C₂²⋊D₇₉	C₂³	1	1	yes	characteristic
191	C₂³×Dic₇₉	C₂³	1	1	yes	characteristic
192	C₂³×Dic₇₉	C₂³	1	1	yes	characteristic
193	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
194	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
195	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
196	#14579160	C₂×C₄	1	8	yes	complemented
197	#14579159	C₂×C₄	1	8	yes	complemented
198	#14579156	C₂×C₄	1	8	yes	complemented
199	#14579156	C₂×C₄	1	8	yes	complemented
200	#14579154	C₂×C₄	1	8	yes	complemented
201	#14579154	C₂×C₄	1	8	yes	complemented
202	#14579152	C₂×C₄	1	8	yes	complemented
203	#14579151	C₂×C₄	1	8	yes	complemented
204	#14579147	C₂×C₄	1	8	yes	—
205	#14579144	C₂×C₄	1	8	yes	—
206	#14579143	C₂×C₄	1	8	yes	—
207	#14579140	C₂×C₄	1	8	yes	complemented
208	#14579139	C₂×C₄	1	8	yes	complemented
209	#14579137	C₂×C₄	1	8	yes	complemented
210	Q₈×Dic₇₉	—	4	2	no	—
211	#14579126	—	4	2	no	—
212	#14579126	—	4	2	no	—
213	(C₂²⋊D₇₉)⋊C₄	—	4	2	no	—
214	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
215	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
216	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
217	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
218	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
219	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
224	C₂×Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
225	C₂×Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
226	C₂×Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
227	C₂×Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
228	C₂×Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
229	C₂×Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
230	C₂×Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
231	C₂×Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
232	C₂×Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
233	C₂×Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
234	C₂×Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
235	C₂×Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
236	C₂×Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
237	C₂×Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
238	C₂×Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
239	C₂×Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
240	C₂×Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
241	C₂×Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
242	C₂×Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
243	C₂×Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
244	C₂×Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
245	C₂×Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
246	C₂×Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
247	C₂×C₂²⋊Dic₇₉	C₂³	1	1	yes	characteristic
248	C₂×C₂²⋊Dic₇₉	C₂³	1	1	yes	characteristic
249	C₂×C₂²⋊Dic₇₉	C₂³	1	1	yes	characteristic
250	C₂×C₂²⋊Dic₇₉	C₂³	1	1	yes	characteristic
251	C₂×C₂²⋊Dic₇₉	C₂³	1	1	yes	characteristic
252	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
253	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
254	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
255	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
256	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
257	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
258	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
259	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
260	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
261	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
262	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
263	C₂×C₄×Dic₇₉	—	4	2	no	—
264	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
265	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
266	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
267	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
268	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
269	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
270	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
271	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
272	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
273	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
274	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
275	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
276	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
277	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
278	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
279	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
280	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
281	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
282	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
283	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
284	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
285	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
286	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
287	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
288	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
289	C₄²×D₇₉	—	4	2	no	—
290	C₇₉⋊#95	C₂³	1	1	yes	characteristic
291	C₇₉⋊#95	C₂³	1	1	yes	characteristic
292	C₇₉⋊#95	C₂³	1	1	yes	characteristic
293	C₇₉⋊#95	C₂³	1	1	yes	characteristic
294	C₇₉⋊#95	C₂³	1	1	yes	characteristic
295	C₇₉⋊#95	C₂³	1	1	yes	characteristic
296	C₇₉⋊#95	C₂³	1	1	yes	characteristic
297	C₇₉⋊#95	C₂³	1	1	yes	characteristic
298	C₇₉⋊#95	C₂³	1	1	yes	characteristic
299	C₇₉⋊#95	C₂³	1	1	yes	characteristic
300	C₇₉⋊#95	C₂³	1	1	yes	characteristic
301	C₇₉⋊#95	C₂³	1	1	yes	characteristic
302	C₇₉⋊#95	C₂³	1	1	yes	characteristic
303	C₇₉⋊#95	C₂³	1	1	yes	characteristic
304	C₇₉⋊#95	C₂³	1	1	yes	characteristic
305	C₇₉⋊#95	C₂³	1	1	yes	characteristic
306	C₇₉⋊#95	C₂³	1	1	yes	characteristic
307	C₇₉⋊#95	C₂³	1	1	yes	characteristic
308	C₇₉⋊#95	C₂³	1	1	yes	characteristic
309	C₇₉⋊#95	C₂³	1	1	yes	characteristic
310	C₇₉⋊#95	C₂³	1	1	yes	characteristic
311	C₇₉⋊#95	C₂³	1	1	yes	characteristic
312	C₇₉⋊#95	C₂³	1	1	yes	characteristic
313	C₇₉⋊#95	C₂³	1	1	yes	characteristic
314	C₇₉⋊#95	C₂³	1	1	yes	characteristic
315	C₇₉⋊#95	C₂³	1	1	yes	characteristic
316	C₇₉⋊#95	C₂³	1	1	yes	characteristic
317	C₇₉⋊#95	C₂³	1	1	yes	characteristic
318	C₇₉⋊#95	C₂³	1	1	yes	characteristic
319	C₇₉⋊#95	C₂³	1	1	yes	characteristic
320	C₇₉⋊#95	C₂³	1	1	yes	characteristic
321	C₇₉⋊#95	C₂³	1	1	yes	characteristic
322	C₇₉⋊#95	C₂³	1	1	yes	characteristic
323	C₇₉⋊#95	C₂³	1	1	yes	characteristic
324	C₇₉⋊#95	C₂³	1	1	yes	characteristic
325	C₇₉⋊#95	C₂³	1	1	yes	characteristic
326	C₇₉⋊#95	C₂³	1	1	yes	characteristic
327	C₇₉⋊#95	C₂³	1	1	yes	characteristic
328	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
329	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
330	C₂²⋊Q₈×C₇₉	C₂×C₄	1	8	yes	complemented
331	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
332	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
333	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
334	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
335	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
336	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
337	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
338	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
339	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
340	C₂×C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
341	C₂×C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
342	C₂×C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
343	C₂×C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
344	C₂×C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
345	C₂×C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
346	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
347	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
348	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
349	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
350	#95×C₇₉	C₂³	1	1	yes	characteristic
351	#95×C₇₉	C₂³	1	1	yes	characteristic
352	#95×C₇₉	C₂³	1	1	yes	characteristic
353	#95×C₇₉	C₂³	1	1	yes	characteristic
354	#95×C₇₉	C₂³	1	1	yes	characteristic
355	#95×C₇₉	C₂³	1	1	yes	characteristic
356	#95×C₇₉	C₂³	1	1	yes	characteristic
357	#95×C₇₉	C₂³	1	1	yes	characteristic
358	#95×C₇₉	C₂³	1	1	yes	characteristic
359	#95×C₇₉	C₂³	1	1	yes	characteristic
360	#95×C₇₉	C₂³	1	1	yes	characteristic
361	#95×C₇₉	C₂³	1	1	yes	characteristic
362	#95×C₇₉	C₂³	1	1	yes	characteristic
363	#95×C₇₉	C₂³	1	1	yes	characteristic
364	C₂³×D₇₉	C₂⁴	1	1	yes	characteristic
365	C₂×Dic₁₅₈	—	4	1	no	—
366	C₂×Dic₁₅₈	—	4	1	no	—
367	C₂×Dic₁₅₈	—	4	1	no	—
368	C₂×Dic₁₅₈	—	4	1	no	—
369	C₂×Dic₁₅₈	C₂²×C₄	1	4	yes	—
370	C₂×Dic₁₅₈	C₂²×C₄	1	4	yes	—
371	C₂×C₂²⋊D₇₉	—	4	1	no	—
372	C₂×C₂²⋊D₇₉	—	4	1	no	—
373	C₂×C₂²⋊D₇₉	C₂²×C₄	1	4	yes	—
374	C₂²×Dic₇₉	—	2	2	no	—
375	C₂²×Dic₇₉	—	2	2	no	—
376	C₂²×Dic₇₉	—	2	2	no	—
377	C₂²×Dic₇₉	—	4	1	no	—
378	C₂²×Dic₇₉	—	4	1	no	—
379	C₂²×Dic₇₉	—	4	1	no	—
380	C₂²×Dic₇₉	C₂⁴	1	1	yes	characteristic
381	C₂²×Dic₇₉	C₂⁴	1	1	yes	characteristic
382	C₂²×Dic₇₉	C₂⁴	1	1	yes	characteristic
383	C₂²×Dic₇₉	C₂⁴	1	1	yes	characteristic
384	C₂²×Dic₇₉	C₂⁴	1	1	yes	characteristic
385	C₂²×Dic₇₉	C₂⁴	1	1	yes	characteristic
386	C₂²×Dic₇₉	C₂⁴	1	1	yes	characteristic
387	C₂²×Dic₇₉	C₂⁴	1	1	yes	characteristic
388	C₂²×Dic₇₉	C₂⁴	1	1	yes	characteristic
389	C₂²×Dic₇₉	C₂⁴	1	1	yes	characteristic
390	C₂²×Dic₇₉	C₂⁴	1	1	yes	characteristic
391	C₂²×Dic₇₉	C₂⁴	1	1	yes	characteristic
392	C₂²×Dic₇₉	C₂⁴	1	1	yes	characteristic
393	C₂²×Dic₇₉	C₂⁴	1	1	yes	characteristic
394	C₂²×Dic₇₉	C₂⁴	1	1	yes	characteristic
395	C₂×C₄×D₇₉	—	2	2	no	—
396	C₂×C₄×D₇₉	—	2	2	no	—
397	C₂×C₄×D₇₉	—	2	2	no	—
398	C₂×C₄×D₇₉	—	4	1	no	—
399	C₂×C₄×D₇₉	—	4	1	no	—
400	C₂×C₄×D₇₉	—	4	1	no	—
401	C₂×C₄×D₇₉	—	4	1	no	—
402	C₂×C₄×D₇₉	—	4	1	no	—
403	C₂×C₄×D₇₉	C₂²×C₄	1	4	yes	—
404	C₄⋊Dic₇₉	—	4	1	no	—
405	C₄⋊Dic₇₉	—	4	1	no	—
406	C₄⋊Dic₇₉	—	4	1	no	—
407	C₄⋊Dic₇₉	—	4	1	no	—
408	C₄⋊Dic₇₉	—	4	1	no	—
409	C₄⋊Dic₇₉	—	4	1	no	—
410	C₄⋊Dic₇₉	C₂²×C₄	1	4	yes	—
411	C₄⋊Dic₇₉	C₂²×C₄	1	4	yes	—
412	C₄⋊Dic₇₉	C₂²×C₄	1	4	yes	—
413	C₄⋊Dic₇₉	C₂²×C₄	1	4	yes	—
414	Dic₇₉⋊C₄	—	4	1	no	—
415	Dic₇₉⋊C₄	—	4	1	no	—
416	Dic₇₉⋊C₄	—	4	1	no	—
417	Dic₇₉⋊C₄	—	4	1	no	—
418	Dic₇₉⋊C₄	—	4	1	no	—
419	Dic₇₉⋊C₄	—	4	1	no	—
420	Dic₇₉⋊C₄	—	4	1	no	—
421	Dic₇₉⋊C₄	—	4	1	no	—
422	Dic₇₉⋊C₄	—	4	1	no	—
423	Dic₇₉⋊C₄	—	4	1	no	—
424	Dic₇₉⋊C₄	—	4	1	no	—
425	Dic₇₉⋊C₄	—	4	1	no	—
426	Dic₇₉⋊C₄	—	4	1	no	—
427	Dic₇₉⋊C₄	—	4	1	no	—
428	Dic₇₉⋊C₄	C₂²×C₄	1	4	yes	—
429	Dic₇₉⋊C₄	C₂²×C₄	1	4	yes	—
430	Dic₇₉⋊C₄	C₂²×C₄	1	4	yes	—
431	Dic₇₉⋊C₄	C₂²×C₄	1	4	yes	—
432	Dic₇₉⋊C₄	C₂²×C₄	1	4	yes	—
433	Dic₇₉⋊C₄	C₂²×C₄	1	4	yes	—
434	Dic₇₉⋊C₄	C₂²×C₄	1	4	yes	—
435	Dic₇₉⋊C₄	C₂²×C₄	1	4	yes	—
436	Dic₇₉⋊C₄	C₂²×C₄	1	4	yes	—
437	C₂²⋊Dic₇₉	—	4	1	no	—
438	C₂²⋊Dic₇₉	—	4	1	no	—
439	C₂²⋊Dic₇₉	C₂²×C₄	1	4	yes	—
440	C₂²⋊Dic₇₉	C₂²×C₄	1	4	yes	—
441	C₂²⋊Dic₇₉	C₂²×C₄	1	4	yes	—
442	(C₂×D₇₉)⋊C₄	—	4	1	no	—
443	(C₂×D₇₉)⋊C₄	—	4	1	no	—
444	(C₂×D₇₉)⋊C₄	—	4	1	no	—
445	(C₂×D₇₉)⋊C₄	—	4	1	no	—
446	(C₂×D₇₉)⋊C₄	—	4	1	no	—
447	(C₂×D₇₉)⋊C₄	—	4	1	no	—
448	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	4	yes	—
449	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	4	yes	—
450	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	4	yes	—
451	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	4	yes	—
452	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	4	yes	—
453	C₄×Dic₇₉	—	2	2	no	—
454	C₄×Dic₇₉	—	2	2	no	—
455	C₄×Dic₇₉	—	2	2	no	—
456	C₄×Dic₇₉	—	2	2	no	—
457	C₄×Dic₇₉	—	2	2	no	—
458	C₄×Dic₇₉	—	2	2	no	—
459	C₄×Dic₇₉	—	2	2	no	—
460	C₄×Dic₇₉	—	2	2	no	—
461	C₄×Dic₇₉	—	2	2	no	—
462	C₄×Dic₇₉	—	2	2	no	—
463	C₄×Dic₇₉	—	2	2	no	—
464	C₄×Dic₇₉	—	2	2	no	—
465	C₄×Dic₇₉	—	2	2	no	—
466	C₄×Dic₇₉	—	4	1	no	—
467	C₄×Dic₇₉	—	4	1	no	—
468	C₄×Dic₇₉	—	4	1	no	—
469	C₄×Dic₇₉	—	4	1	no	—
470	C₄×Dic₇₉	—	4	1	no	—
471	C₄×Dic₇₉	—	4	1	no	—
472	C₄×Dic₇₉	—	4	1	no	—
473	C₄×Dic₇₉	—	4	1	no	—
474	C₄×Dic₇₉	—	4	1	no	—
475	C₄×Dic₇₉	C₂²×C₄	1	4	yes	—
476	C₄×Dic₇₉	C₂²×C₄	1	4	yes	—
477	C₄×Dic₇₉	C₂²×C₄	1	4	yes	—
478	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
479	C₂×Q₈×C₇₉	—	4	1	no	—
480	C₂×Q₈×C₇₉	—	4	1	no	—
481	C₂×Q₈×C₇₉	C₂²×C₄	1	4	yes	—
482	C₂²×C₄×C₇₉	—	4	1	no	—
483	C₂²×C₄×C₇₉	—	4	1	no	—
484	C₂²×C₄×C₇₉	C₂²×C₄	1	4	yes	—
485	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
486	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
487	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
488	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
489	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
490	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
491	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
492	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
493	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
494	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
495	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
496	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
497	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
498	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
499	C₄⋊C₄×C₇₉	—	4	1	no	—
500	C₄⋊C₄×C₇₉	—	4	1	no	—
501	C₄⋊C₄×C₇₉	—	4	1	no	—
502	C₄⋊C₄×C₇₉	—	4	1	no	—
503	C₄⋊C₄×C₇₉	—	4	1	no	—
504	C₄⋊C₄×C₇₉	—	4	1	no	—
505	C₄⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
506	C₄⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
507	C₄⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
508	C₂²⋊C₄×C₇₉	—	4	1	no	—
509	C₂²⋊C₄×C₇₉	—	4	1	no	—
510	C₂²⋊C₄×C₇₉	—	4	1	no	—
511	C₂²⋊C₄×C₇₉	—	4	1	no	—
512	C₂²⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
513	C₂²⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
514	C₄²×C₇₉	—	4	1	no	—
515	C₄²×C₇₉	—	4	1	no	—
516	C₄²×C₇₉	—	4	1	no	—
517	C₄²×C₇₉	—	4	1	no	—
518	C₂³×C₇₉	—	2	1	no	—
519	C₂³×C₇₉	—	2	1	no	—
520	C₂³×C₇₉	—	2	1	no	—
521	C₂³×C₇₉	—	2	1	no	—
522	C₂³×C₇₉	—	2	1	no	—
523	C₂³×C₇₉	—	2	1	no	—
524	C₂³×C₇₉	C₂³×C₄	1	2	yes	—
525	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
526	C₂²×D₇₉	—	2	1	no	—
527	C₂²×D₇₉	—	2	1	no	—
528	C₂²×D₇₉	—	2	1	no	—
529	C₂²×D₇₉	—	2	1	no	—
530	C₂²×D₇₉	—	2	1	no	—
531	C₂²×D₇₉	—	2	1	no	—
532	C₂²×D₇₉	C₂³×C₄	1	2	yes	—
533	Q₈×C₇₉	—	4	4	no	—
534	C₂×C₄×C₇₉	—	2	1	no	—
535	C₂×C₄×C₇₉	—	2	1	no	—
536	C₂×C₄×C₇₉	—	2	1	no	—
537	C₂×C₄×C₇₉	—	2	1	no	—
538	C₂×C₄×C₇₉	—	2	1	no	—
539	C₂×C₄×C₇₉	—	2	1	no	—
540	C₂×C₄×C₇₉	—	2	1	no	—
541	C₂×C₄×C₇₉	—	2	1	no	—
542	C₂×C₄×C₇₉	—	2	1	no	—
543	C₂×C₄×C₇₉	—	2	1	no	—
544	C₂×C₄×C₇₉	—	2	1	no	—
545	C₂×C₄×C₇₉	—	2	1	no	—
546	C₂×C₄×C₇₉	—	2	1	no	—
547	C₂×C₄×C₇₉	—	2	1	no	—
548	C₂×C₄×C₇₉	—	2	1	no	—
549	C₂×C₄×C₇₉	—	2	1	no	—
550	C₂×C₄×C₇₉	—	2	1	no	—
551	C₂×C₄×C₇₉	—	2	1	no	—
552	C₂×C₄×C₇₉	—	2	1	no	—
553	C₂×C₄×C₇₉	—	2	1	no	—
554	C₂×C₄×C₇₉	—	2	1	no	—
555	C₂×C₄×C₇₉	—	2	1	no	—
556	C₂×C₄×C₇₉	—	2	1	no	—
557	C₂×C₄×C₇₉	—	2	1	no	—
558	C₂×C₄×C₇₉	—	2	1	no	—
559	C₂×C₄×C₇₉	—	2	1	no	—
560	C₂×C₄×C₇₉	—	2	1	no	—
561	C₂×C₄×C₇₉	—	2	1	no	—
562	C₂×C₄×C₇₉	—	2	1	no	—
563	C₂×C₄×C₇₉	—	2	1	no	—
564	C₂×C₄×C₇₉	—	2	1	no	—
565	C₂×C₄×C₇₉	—	2	1	no	—
566	C₂×C₄×C₇₉	—	2	1	no	—
567	C₂×C₄×C₇₉	—	2	1	no	—
568	C₂×C₄×C₇₉	—	2	1	no	—
569	C₂×C₄×C₇₉	—	2	1	no	—
570	C₂×C₄×C₇₉	—	4	4	no	—
571	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
572	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
573	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
574	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
575	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
576	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
577	C₂²⋊D₇₉	—	4	4	no	—
578	C₂×Dic₇₉	—	2	1	no	—
579	C₂×Dic₇₉	—	2	1	no	—
580	C₂×Dic₇₉	—	2	1	no	—
581	C₂×Dic₇₉	—	2	1	no	—
582	C₂×Dic₇₉	—	2	1	no	—
583	C₂×Dic₇₉	—	2	1	no	—
584	C₂×Dic₇₉	—	2	1	no	—
585	C₂×Dic₇₉	—	2	1	no	—
586	C₂×Dic₇₉	—	2	1	no	—
587	C₂×Dic₇₉	—	2	1	no	—
588	C₂×Dic₇₉	—	2	1	no	—
589	C₂×Dic₇₉	—	2	1	no	—
590	C₂×Dic₇₉	—	2	1	no	—
591	C₂×Dic₇₉	—	2	1	no	—
592	C₂×Dic₇₉	—	2	1	no	—
593	C₂×Dic₇₉	—	2	1	no	—
594	C₂×Dic₇₉	—	2	1	no	—
595	C₂×Dic₇₉	—	2	1	no	—
596	C₂×Dic₇₉	—	2	1	no	—
597	C₂×Dic₇₉	—	2	1	no	—
598	C₂×Dic₇₉	—	2	1	no	—
599	C₂×Dic₇₉	—	2	1	no	—
600	C₂×Dic₇₉	—	2	1	no	—
601	C₂×Dic₇₉	—	2	1	no	—
602	C₂×Dic₇₉	—	2	1	no	—
603	C₂×Dic₇₉	—	2	1	no	—
604	C₂×Dic₇₉	—	2	1	no	—
605	C₂×Dic₇₉	—	2	1	no	—
606	C₂×Dic₇₉	—	2	1	no	—
607	C₂×Dic₇₉	—	2	1	no	—
608	C₂×Dic₇₉	—	2	1	no	—
609	C₂×Dic₇₉	—	2	1	no	—
610	C₂×Dic₇₉	—	2	1	no	—
611	C₂×Dic₇₉	—	2	1	no	—
612	C₂×Dic₇₉	—	2	1	no	—
613	C₂×Dic₇₉	—	4	4	no	—
614	C₂×Dic₇₉	—	4	4	no	—
615	C₂×Dic₇₉	C₂³×C₄	1	2	yes	—
616	C₂×Dic₇₉	C₂³×C₄	1	2	yes	—
617	C₂×Dic₇₉	C₂³×C₄	1	2	yes	—
618	C₂×Dic₇₉	C₂³×C₄	1	2	yes	—
619	C₂×Dic₇₉	C₂³×C₄	1	2	yes	—
620	C₂×Dic₇₉	C₂³×C₄	1	2	yes	—
621	C₂×Dic₇₉	C₂³×C₄	1	2	yes	—
622	C₂×Dic₇₉	H(5,𝔽₂)	1	2	yes	—
623	C₂×Dic₇₉	2₋¹⁺⁴	1	2	yes	—
624	C₂×Dic₇₉	2₋¹⁺⁴	1	2	yes	—
625	C₄×D₇₉	—	4	4	no	—
626	C₄×D₇₉	—	4	4	no	—
627	C₄×D₇₉	—	4	4	no	—
628	Dic₁₅₈	—	4	4	no	—
629	Dic₁₅₈	—	4	4	no	—
630	C₂²×C₇₉	—	2	2	no	—
631	C₂²×C₇₉	—	2	2	no	—
632	C₂²×C₇₉	—	2	2	no	—
633	C₂²×C₇₉	—	4	1	no	—
634	C₂²×C₇₉	—	4	1	no	—
635	C₂²×C₇₉	—	4	1	no	—
636	C₂²×C₇₉	—	4	1	no	—
637	C₂²×C₇₉	C₂⁴×C₄	1	1	yes	characteristic
638	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
639	C₂²×C₇₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
640	C₂²×C₇₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
641	C₂²×C₇₉	#585	1	1	yes	characteristic
642	C₂²×C₇₉	#585	1	1	yes	characteristic
643	C₂²×C₇₉	#585	1	1	yes	characteristic
644	C₂×D₇₉	—	2	2	no	—
645	C₂×D₇₉	—	2	2	no	—
646	C₂×D₇₉	—	2	2	no	—
647	C₂×D₇₉	—	4	1	no	—
648	C₂×D₇₉	—	4	1	no	—
649	C₂×D₇₉	—	4	1	no	—
650	C₂×D₇₉	—	4	1	no	—
651	C₄×C₇₉	—	2	2	no	—
652	C₄×C₇₉	—	2	2	no	—
653	C₄×C₇₉	—	2	2	no	—
654	C₄×C₇₉	—	2	2	no	—
655	C₄×C₇₉	—	2	2	no	—
656	C₄×C₇₉	—	2	2	no	—
657	C₄×C₇₉	—	4	1	no	—
658	C₄×C₇₉	—	4	1	no	—
659	C₄×C₇₉	—	4	1	no	—
660	C₄×C₇₉	—	4	1	no	—
661	C₄×C₇₉	—	4	1	no	—
662	C₄×C₇₉	—	4	1	no	—
663	C₄×C₇₉	—	4	1	no	—
664	C₄×C₇₉	—	4	1	no	—
665	Dic₇₉	—	2	2	no	—
666	Dic₇₉	—	2	2	no	—
667	Dic₇₉	—	2	2	no	—
668	Dic₇₉	—	2	2	no	—
669	Dic₇₉	—	2	2	no	—
670	Dic₇₉	—	2	2	no	—
671	Dic₇₉	—	2	2	no	—
672	Dic₇₉	—	4	1	no	—
673	Dic₇₉	—	4	1	no	—
674	Dic₇₉	—	4	1	no	—
675	Dic₇₉	—	4	1	no	—
676	Dic₇₉	—	4	1	no	—
677	Dic₇₉	—	4	1	no	—
678	Dic₇₉	—	4	1	no	—
679	Dic₇₉	#563	1	4	yes	complemented
680	C₄×#563	—	79	1	no	maximal, Sylow
681	C₂×C₇₉	—	4	2	no	—
682	C₂×C₇₉	C₄×H(5,𝔽₂)	1	1	yes	characteristic
683	C₂×C₇₉	C₄×2₋¹⁺⁴	1	1	yes	characteristic
684	C₂×C₇₉	C₄×2₋¹⁺⁴	1	1	yes	characteristic
685	C₂×C₇₉	C₂×#563	1	1	yes	characteristic
686	C₂×C₇₉	#3529	1	1	yes	characteristic
687	C₂×C₇₉	#3531	1	1	yes	characteristic
688	C₂×C₇₉	#3531	1	1	yes	characteristic
689	D₇₉	—	4	2	no	—
690	C₂×#563	—	79	1	no	—
691	#2383	—	79	1	no	—
692	#2383	—	79	1	no	—
693	#2383	—	79	1	no	—
694	#2383	—	79	1	no	—
695	#2382	—	79	1	no	—
696	#2382	—	79	1	no	—
697	#2381	—	79	1	no	—
698	#2381	—	79	1	no	—
699	#2379	—	79	1	no	—
700	#2378	—	79	1	no	—
701	#2378	—	79	1	no	—
702	#2378	—	79	1	no	—
703	#2378	D₇₉	1	1	yes	characteristic, complemented
704	#2376	—	79	1	no	—
705	#2376	—	79	1	no	—
706	C₄×C₄⋊Q₈	—	79	1	no	—
707	C₄×C₄⋊Q₈	—	79	1	no	—
708	C₄×#125	—	79	1	no	—
709	C₄×#125	—	79	1	no	—
710	C₄×#126	—	79	1	no	—
711	C₄×#126	—	79	1	no	—
712	C₄×#126	—	79	1	no	—
713	C₄×#126	—	79	1	no	—
714	C₄×#124	—	79	1	no	—
715	C₄×C₂²⋊Q₈	—	79	1	no	—
716	C₄×C₂²⋊Q₈	—	79	1	no	—
717	C₄×C₂²⋊Q₈	—	79	1	no	—
718	C₄×C₂²⋊Q₈	—	79	1	no	—
719	C₄×#123	—	79	1	no	—
720	C₄×#123	—	79	1	no	—
721	C₇₉	C₄×#563	1	1	yes	characteristic, complemented, Sylow
722	#563	—	79	16	no	—
723	C₂×C₄⋊Q₈	—	79	1	no	—
724	C₂×C₄⋊Q₈	—	79	1	no	—
725	C₂×#126	—	79	1	no	—
726	C₂×#126	—	79	1	no	—
727	C₂×#126	—	79	1	no	—
728	C₂×#126	—	79	1	no	—
729	C₂×#125	—	79	1	no	—
730	C₂×#125	—	79	1	no	—
731	C₂×#124	—	79	1	no	—
732	C₂×#123	—	79	1	no	—
733	C₂×#123	—	79	1	no	—
734	C₂×C₂²⋊Q₈	—	79	1	no	—
735	C₂×C₂²⋊Q₈	—	79	1	no	—
736	C₂×C₂²⋊Q₈	—	79	1	no	—
737	C₂×C₂²⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
738	C₂×C₄×Q₈	—	79	1	no	—
739	C₂×C₄×Q₈	—	79	1	no	—
740	C₂×C₄×Q₈	—	79	1	no	—
741	C₂×C₄×D₄	—	79	1	no	—
742	C₂²×C₄²	—	79	1	no	—
743	C₂²×C₄²	—	79	1	no	—
744	#391	—	79	1	no	—
745	#391	—	79	1	no	—
746	#391	—	79	1	no	—
747	#391	—	79	1	no	—
748	#391	—	79	1	no	—
749	#391	—	79	1	no	—
750	#391	—	79	1	no	—
751	#391	C₂×D₇₉	1	1	yes	characteristic
752	#391	C₂×D₇₉	1	1	yes	characteristic
753	#390	—	79	1	no	—
754	#389	—	79	1	no	—
755	#389	—	79	1	no	—
756	#389	—	79	1	no	—
757	#389	—	79	1	no	—
758	#389	—	79	1	no	—
759	#389	—	79	1	no	—
760	#389	—	79	1	no	—
761	#389	—	79	1	no	—
762	#389	—	79	1	no	—
763	#389	—	79	1	no	—
764	#389	—	79	1	no	—
765	#389	—	79	1	no	—
766	#389	—	79	1	no	—
767	#389	—	79	1	no	—
768	#389	C₂×D₇₉	1	1	yes	characteristic
769	#389	C₂×D₇₉	1	1	yes	characteristic
770	#388	—	79	1	no	—
771	#388	—	79	1	no	—
772	#388	—	79	1	no	—
773	#388	—	79	1	no	—
774	#388	—	79	1	no	—
775	#388	—	79	1	no	—
776	#388	—	79	1	no	—
777	#388	—	79	1	no	—
778	#388	—	79	1	no	—
779	#388	—	79	1	no	—
780	#388	—	79	1	no	—
781	#388	—	79	1	no	—
782	#388	—	79	1	no	—
783	#388	—	79	1	no	—
784	#388	—	79	1	no	—
785	#388	—	79	1	no	—
786	#388	C₂×D₇₉	1	1	yes	characteristic
787	#388	C₂×D₇₉	1	1	yes	characteristic
788	#388	C₂×D₇₉	1	1	yes	characteristic
789	#388	C₂×D₇₉	1	1	yes	characteristic
790	#387	—	79	1	no	—
791	#387	—	79	1	no	—
792	#387	—	79	1	no	—
793	#387	—	79	1	no	—
794	#387	—	79	1	no	—
795	#387	—	79	1	no	—
796	#387	—	79	1	no	—
797	#387	—	79	1	no	—
798	#387	—	79	1	no	—
799	#387	—	79	1	no	—
800	#387	—	79	1	no	—
801	#387	—	79	1	no	—
802	#387	—	79	1	no	—
803	#387	—	79	1	no	—
804	#387	—	79	1	no	—
805	#387	—	79	1	no	—
806	#387	—	79	1	no	—
807	#387	—	79	1	no	—
808	#387	—	79	1	no	—
809	#387	—	79	1	no	—
810	#387	—	79	1	no	—
811	#387	—	79	1	no	—
812	#387	—	79	1	no	—
813	#387	—	79	1	no	—
814	#387	—	79	1	no	—
815	#387	—	79	1	no	—
816	#387	—	79	1	no	—
817	#387	—	79	1	no	—
818	#387	C₂×D₇₉	1	1	yes	characteristic
819	#387	C₂×D₇₉	1	1	yes	characteristic
820	#387	C₂×D₇₉	1	1	yes	characteristic
821	#387	C₂×D₇₉	1	1	yes	characteristic
822	#386	—	79	1	no	—
823	#386	—	79	1	no	—
824	#385	—	79	1	no	—
825	#385	—	79	1	no	—
826	#385	—	79	1	no	—
827	#385	—	79	1	no	—
828	#385	—	79	1	no	—
829	#385	—	79	1	no	—
830	#385	—	79	1	no	—
831	#385	—	79	1	no	—
832	#385	—	79	1	no	—
833	#385	—	79	1	no	—
834	#384	—	79	1	no	—
835	#384	—	79	1	no	—
836	#383	—	79	1	no	—
837	#383	—	79	1	no	—
838	#383	—	79	1	no	—
839	#383	—	79	1	no	—
840	#382	—	79	1	no	—
841	#382	—	79	1	no	—
842	#382	—	79	1	no	—
843	#381	—	79	1	no	—
844	#381	C₂×D₇₉	1	1	yes	characteristic
845	#380	—	79	1	no	—
846	#380	—	79	1	no	—
847	#380	—	79	1	no	—
848	#380	C₂×D₇₉	1	1	yes	characteristic
849	C₄×C₄⋊C₄	—	79	1	no	—
850	C₄×C₄⋊C₄	—	79	1	no	—
851	C₄×C₄⋊C₄	—	79	1	no	—
852	C₄×C₄⋊C₄	—	79	1	no	—
853	C₄×C₄⋊C₄	—	79	1	no	—
854	C₄×C₄⋊C₄	—	79	1	no	—
855	C₄×C₄⋊C₄	—	79	1	no	—
856	C₄×C₄⋊C₄	—	79	1	no	—
857	C₄×C₄⋊C₄	—	79	1	no	—
858	C₄×C₄⋊C₄	—	79	1	no	—
859	C₄×C₄⋊C₄	—	79	1	no	—
860	C₄×C₄⋊C₄	—	79	1	no	—
861	C₄×C₄⋊C₄	—	79	1	no	—
862	C₄×C₄⋊C₄	—	79	1	no	—
863	C₄×C₄⋊C₄	—	79	1	no	—
864	C₄×C₄⋊C₄	—	79	1	no	—
865	C₄×C₂²⋊C₄	—	79	1	no	—
866	C₄×C₂²⋊C₄	—	79	1	no	—
867	C₄×C₂²⋊C₄	—	79	1	no	—
868	C₄×C₂²⋊C₄	—	79	1	no	—
869	C₄×C₂²⋊C₄	—	79	1	no	—
870	C₄×C₂²⋊C₄	—	79	1	no	—
871	C₄×C₂²⋊C₄	—	79	1	no	—
872	C₄×C₂²⋊C₄	—	79	1	no	—
873	C₄×C₂²⋊C₄	—	79	1	no	—
874	C₄×C₂²⋊C₄	—	79	1	no	—
875	C₄³	—	79	1	no	—
876	C₄³	—	79	1	no	—
877	C₄³	—	79	1	no	—
878	C₂²×Q₈	—	79	1	no	—
879	C₂²×Q₈	—	79	1	no	—
880	C₂²×Q₈	C₂²×D₇₉	1	1	yes	characteristic
881	C₂²×D₄	—	79	1	no	—
882	C₂³×C₄	—	79	1	no	—
883	C₂³×C₄	—	79	1	no	—
884	C₂³×C₄	—	79	1	no	—
885	C₂³×C₄	—	79	1	no	—
886	C₂³×C₄	—	79	1	no	—
887	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
888	C₄⋊Q₈	—	79	8	no	—
889	C₄⋊Q₈	—	79	8	no	—
890	#126	—	79	8	no	—
891	#126	—	79	8	no	—
892	#126	—	79	8	no	—
893	#126	—	79	8	no	—
894	#125	—	79	8	no	—
895	#125	—	79	8	no	—
896	#124	—	79	8	no	—
897	#123	—	79	8	no	—
898	#123	—	79	8	no	—
899	C₂²⋊Q₈	—	79	8	no	—
900	C₂²⋊Q₈	—	79	8	no	—
901	C₂²⋊Q₈	—	79	8	no	—
902	C₂²⋊Q₈	C₄×D₇₉	1	8	yes	complemented
903	C₄×Q₈	—	316	2	no	—
904	C₄×Q₈	—	316	2	no	—
905	C₄×Q₈	—	316	2	no	—
906	C₄×D₄	—	316	2	no	—
907	C₂×C₄⋊C₄	—	79	1	no	—
908	C₂×C₄⋊C₄	—	79	1	no	—
909	C₂×C₄⋊C₄	—	79	1	no	—
910	C₂×C₄⋊C₄	—	79	1	no	—
911	C₂×C₄⋊C₄	—	79	1	no	—
912	C₂×C₄⋊C₄	—	79	1	no	—
913	C₂×C₄⋊C₄	—	79	1	no	—
914	C₂×C₄⋊C₄	—	79	1	no	—
915	C₂×C₄⋊C₄	—	79	1	no	—
916	C₂×C₄⋊C₄	—	79	1	no	—
917	C₂×C₄⋊C₄	—	79	1	no	—
918	C₂×C₄⋊C₄	—	79	1	no	—
919	C₂×C₄⋊C₄	—	79	1	no	—
920	C₂×C₄⋊C₄	—	79	1	no	—
921	C₂×C₄⋊C₄	—	79	1	no	—
922	C₂×C₄⋊C₄	—	79	1	no	—
923	C₂×C₄⋊C₄	—	79	1	no	—
924	C₂×C₄⋊C₄	—	79	1	no	—
925	C₂×C₄⋊C₄	—	79	1	no	—
926	C₂×C₄⋊C₄	—	79	1	no	—
927	C₂×C₄⋊C₄	—	79	1	no	—
928	C₂×C₄⋊C₄	—	79	1	no	—
929	C₂×C₄⋊C₄	—	79	1	no	—
930	C₂×C₄⋊C₄	—	79	1	no	—
931	C₂×C₄⋊C₄	—	79	1	no	—
932	C₂×C₄⋊C₄	—	79	1	no	—
933	C₂×C₄⋊C₄	—	79	1	no	—
934	C₂×C₄⋊C₄	—	79	1	no	—
935	C₂×C₄⋊C₄	—	79	1	no	—
936	C₂×C₄⋊C₄	—	79	1	no	—
937	C₂×C₄⋊C₄	—	79	1	no	—
938	C₂×C₄⋊C₄	—	79	1	no	—
939	C₂×C₄⋊C₄	—	79	1	no	—
940	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
941	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
942	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
943	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
944	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
945	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
946	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
947	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
948	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
949	C₂×C₂²⋊C₄	—	79	1	no	—
950	C₂×C₂²⋊C₄	—	79	1	no	—
951	C₂×C₂²⋊C₄	—	79	1	no	—
952	C₂×C₂²⋊C₄	—	79	1	no	—
953	C₂×C₂²⋊C₄	—	79	1	no	—
954	C₂×C₂²⋊C₄	—	79	1	no	—
955	C₂×C₂²⋊C₄	—	79	1	no	—
956	C₂×C₂²⋊C₄	—	79	1	no	—
957	C₂×C₂²⋊C₄	—	79	1	no	—
958	C₂×C₂²⋊C₄	—	79	1	no	—
959	C₂×C₂²⋊C₄	—	79	1	no	—
960	C₂×C₂²⋊C₄	—	79	1	no	—
961	C₂×C₂²⋊C₄	—	79	1	no	—
962	C₂×C₂²⋊C₄	—	79	1	no	—
963	C₂×C₂²⋊C₄	—	79	1	no	—
964	C₂×C₂²⋊C₄	—	79	1	no	—
965	C₂×C₂²⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
966	C₂×C₂²⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
967	C₂×C₂²⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
968	C₂×C₂²⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
969	C₂×C₂²⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
970	C₂×C₂²⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
971	C₂×C₄²	—	316	2	no	—
972	C₂×C₄²	—	316	2	no	—
973	C₂×C₄²	—	79	1	no	—
974	C₂×C₄²	—	79	1	no	—
975	C₂×C₄²	—	79	1	no	—
976	C₂×C₄²	—	79	1	no	—
977	C₂×C₄²	—	79	1	no	—
978	C₂×C₄²	—	79	1	no	—
979	C₂×C₄²	—	79	1	no	—
980	C₂×C₄²	—	79	1	no	—
981	C₂×C₄²	—	79	1	no	—
982	C₂×C₄²	—	79	1	no	—
983	C₂×C₄²	—	79	1	no	—
984	C₂×C₄²	—	79	1	no	—
985	C₂×C₄²	—	79	1	no	—
986	C₂×C₄²	—	79	1	no	—
987	C₂×C₄²	—	79	1	no	—
988	C₂×C₄²	—	79	1	no	—
989	C₂×C₄²	—	79	1	no	—
990	C₂×C₄²	—	79	1	no	—
991	C₂×C₄²	—	79	1	no	—
992	C₂×C₄²	—	79	1	no	—
993	C₂×C₄²	—	79	1	no	—
994	C₂×C₄²	—	79	1	no	—
995	C₂×C₄²	—	79	1	no	—
996	C₂×C₄²	—	79	1	no	—
997	C₂×C₄²	—	79	1	no	—
998	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
999	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
1000	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
1001	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
1002	#95	—	79	1	no	—
1003	#95	—	79	1	no	—
1004	#95	—	79	1	no	—
1005	#95	—	79	1	no	—
1006	#95	—	79	1	no	—
1007	#95	—	79	1	no	—
1008	#95	—	79	1	no	—
1009	#95	—	79	1	no	—
1010	#95	—	79	1	no	—
1011	#95	—	79	1	no	—
1012	#95	—	79	1	no	—
1013	#95	—	79	1	no	—
1014	#95	—	79	1	no	—
1015	#95	—	79	1	no	—
1016	#95	—	79	1	no	—
1017	#95	—	79	1	no	—
1018	#95	—	79	1	no	—
1019	#95	—	79	1	no	—
1020	#95	—	79	1	no	—
1021	#95	—	79	1	no	—
1022	#95	—	79	1	no	—
1023	#95	—	79	1	no	—
1024	#95	—	79	1	no	—
1025	#95	—	79	1	no	—
1026	#95	—	79	1	no	—
1027	#95	—	79	1	no	—
1028	#95	—	79	1	no	—
1029	#95	—	79	1	no	—
1030	#95	—	79	1	no	—
1031	#95	—	79	1	no	—
1032	#95	—	79	1	no	—
1033	#95	—	79	1	no	—
1034	#95	—	79	1	no	—
1035	#95	—	79	1	no	—
1036	#95	—	79	1	no	—
1037	#95	—	79	1	no	—
1038	#95	—	79	1	no	—
1039	#95	—	79	1	no	—
1040	#95	C₂²×D₇₉	1	1	yes	characteristic
1041	#95	C₂²×D₇₉	1	1	yes	characteristic
1042	#95	C₂²×D₇₉	1	1	yes	characteristic
1043	#95	C₂²×D₇₉	1	1	yes	characteristic
1044	#95	C₂²×D₇₉	1	1	yes	characteristic
1045	#95	C₂²×D₇₉	1	1	yes	characteristic
1046	#95	C₂²×D₇₉	1	1	yes	characteristic
1047	#95	C₂²×D₇₉	1	1	yes	characteristic
1048	#95	C₂²×D₇₉	1	1	yes	characteristic
1049	#95	C₂²×D₇₉	1	1	yes	characteristic
1050	#95	C₂²×D₇₉	1	1	yes	characteristic
1051	#95	C₂²×D₇₉	1	1	yes	characteristic
1052	#95	C₂²×D₇₉	1	1	yes	characteristic
1053	#95	C₂²×D₇₉	1	1	yes	characteristic
1054	C₂⁴	—	79	1	no	—
1055	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
1056	C₂×Q₈	—	4	1	no	—
1057	C₂×Q₈	—	4	1	no	—
1058	C₂×Q₈	—	316	1	no	—
1059	C₂×Q₈	—	316	1	no	—
1060	C₂×Q₈	—	316	1	no	—
1061	C₂×Q₈	—	316	1	no	—
1062	C₂×Q₈	—	79	4	no	—
1063	C₂×Q₈	—	79	4	no	—
1064	C₂×Q₈	C₂×C₄×D₇₉	1	4	yes	—
1065	C₂×D₄	—	316	1	no	—
1066	C₂×D₄	—	316	1	no	—
1067	C₂×D₄	—	79	4	no	—
1068	C₂²×C₄	—	4	1	no	—
1069	C₂²×C₄	—	4	1	no	—
1070	C₂²×C₄	—	316	1	no	—
1071	C₂²×C₄	—	316	1	no	—
1072	C₂²×C₄	—	316	1	no	—
1073	C₂²×C₄	—	316	1	no	—
1074	C₂²×C₄	—	316	1	no	—
1075	C₂²×C₄	—	316	1	no	—
1076	C₂²×C₄	—	316	1	no	—
1077	C₂²×C₄	—	316	1	no	—
1078	C₂²×C₄	—	79	4	no	—
1079	C₂²×C₄	—	79	1	no	—
1080	C₂²×C₄	—	79	1	no	—
1081	C₂²×C₄	—	79	1	no	—
1082	C₂²×C₄	—	79	1	no	—
1083	C₂²×C₄	—	79	1	no	—
1084	C₂²×C₄	—	79	1	no	—
1085	C₂²×C₄	—	79	1	no	—
1086	C₂²×C₄	—	79	1	no	—
1087	C₂²×C₄	—	79	1	no	—
1088	C₂²×C₄	—	79	1	no	—
1089	C₂²×C₄	—	79	1	no	—
1090	C₂²×C₄	—	79	1	no	—
1091	C₂²×C₄	—	79	1	no	—
1092	C₂²×C₄	—	79	1	no	—
1093	C₂²×C₄	—	79	1	no	—
1094	C₂²×C₄	—	158	2	no	—
1095	C₂²×C₄	—	158	2	no	—
1096	C₂²×C₄	—	158	2	no	—
1097	C₂²×C₄	—	158	2	no	—
1098	C₂²×C₄	—	158	2	no	—
1099	C₂²×C₄	—	158	2	no	—
1100	C₂²×C₄	C₂×C₄×D₇₉	1	4	yes	—
1101	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
1102	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
1103	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
1104	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
1105	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
1106	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
1107	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
1108	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
1109	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
1110	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
1111	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
1112	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
1113	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
1114	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
1115	C₄⋊C₄	—	4	1	no	—
1116	C₄⋊C₄	—	4	1	no	—
1117	C₄⋊C₄	—	4	1	no	—
1118	C₄⋊C₄	—	4	1	no	—
1119	C₄⋊C₄	—	4	1	no	—
1120	C₄⋊C₄	—	4	1	no	—
1121	C₄⋊C₄	—	316	1	no	—
1122	C₄⋊C₄	—	316	1	no	—
1123	C₄⋊C₄	—	316	1	no	—
1124	C₄⋊C₄	—	316	1	no	—
1125	C₄⋊C₄	—	316	1	no	—
1126	C₄⋊C₄	—	316	1	no	—
1127	C₄⋊C₄	—	316	1	no	—
1128	C₄⋊C₄	—	316	1	no	—
1129	C₄⋊C₄	—	316	1	no	—
1130	C₄⋊C₄	—	316	1	no	—
1131	C₄⋊C₄	—	316	1	no	—
1132	C₄⋊C₄	—	316	1	no	—
1133	C₄⋊C₄	—	316	1	no	—
1134	C₄⋊C₄	—	316	1	no	—
1135	C₄⋊C₄	—	316	1	no	—
1136	C₄⋊C₄	—	316	1	no	—
1137	C₄⋊C₄	—	316	1	no	—
1138	C₄⋊C₄	—	316	1	no	—
1139	C₄⋊C₄	—	316	1	no	—
1140	C₄⋊C₄	—	316	1	no	—
1141	C₄⋊C₄	—	79	4	no	—
1142	C₄⋊C₄	—	79	4	no	—
1143	C₄⋊C₄	—	79	4	no	—
1144	C₄⋊C₄	—	79	4	no	—
1145	C₄⋊C₄	—	79	4	no	—
1146	C₄⋊C₄	—	79	4	no	—
1147	C₄⋊C₄	—	79	4	no	—
1148	C₄⋊C₄	—	79	4	no	—
1149	C₄⋊C₄	—	79	4	no	—
1150	C₄⋊C₄	—	79	4	no	—
1151	C₄⋊C₄	—	79	4	no	—
1152	C₄⋊C₄	—	79	4	no	—
1153	C₄⋊C₄	—	79	4	no	—
1154	C₄⋊C₄	C₂×C₄×D₇₉	1	4	yes	—
1155	C₄⋊C₄	C₂×C₄×D₇₉	1	4	yes	—
1156	C₄⋊C₄	C₂×C₄×D₇₉	1	4	yes	—
1157	C₂²⋊C₄	—	4	1	no	—
1158	C₂²⋊C₄	—	4	1	no	—
1159	C₂²⋊C₄	—	4	1	no	—
1160	C₂²⋊C₄	—	4	1	no	—
1161	C₂²⋊C₄	—	316	1	no	—
1162	C₂²⋊C₄	—	316	1	no	—
1163	C₂²⋊C₄	—	316	1	no	—
1164	C₂²⋊C₄	—	316	1	no	—
1165	C₂²⋊C₄	—	316	1	no	—
1166	C₂²⋊C₄	—	316	1	no	—
1167	C₂²⋊C₄	—	316	1	no	—
1168	C₂²⋊C₄	—	316	1	no	—
1169	C₂²⋊C₄	—	79	4	no	—
1170	C₂²⋊C₄	—	79	4	no	—
1171	C₂²⋊C₄	—	79	4	no	—
1172	C₂²⋊C₄	—	79	4	no	—
1173	C₂²⋊C₄	—	79	4	no	—
1174	C₂²⋊C₄	—	79	4	no	—
1175	C₂²⋊C₄	—	79	4	no	—
1176	C₂²⋊C₄	—	79	4	no	—
1177	C₂²⋊C₄	C₂×C₄×D₇₉	1	4	yes	—
1178	C₂²⋊C₄	C₂×C₄×D₇₉	1	4	yes	—
1179	C₄²	—	4	1	no	—
1180	C₄²	—	4	1	no	—
1181	C₄²	—	4	1	no	—
1182	C₄²	—	4	1	no	—
1183	C₄²	—	316	1	no	—
1184	C₄²	—	316	1	no	—
1185	C₄²	—	316	1	no	—
1186	C₄²	—	316	1	no	—
1187	C₄²	—	316	1	no	—
1188	C₄²	—	316	1	no	—
1189	C₄²	—	316	1	no	—
1190	C₄²	—	316	1	no	—
1191	C₄²	—	316	1	no	—
1192	C₄²	—	79	4	no	—
1193	C₄²	—	79	4	no	—
1194	C₄²	—	79	4	no	—
1195	C₄²	—	158	2	no	—
1196	C₄²	—	158	2	no	—
1197	C₄²	—	158	2	no	—
1198	C₄²	—	158	2	no	—
1199	C₄²	—	158	2	no	—
1200	C₄²	—	158	2	no	—
1201	C₄²	—	158	2	no	—
1202	C₄²	—	158	2	no	—
1203	C₄²	—	158	2	no	—
1204	C₄²	—	158	2	no	—
1205	C₄²	—	158	2	no	—
1206	C₄²	—	158	2	no	—
1207	C₄²	—	158	2	no	—
1208	C₂³	—	2	1	no	—
1209	C₂³	—	2	1	no	—
1210	C₂³	—	2	1	no	—
1211	C₂³	—	2	1	no	—
1212	C₂³	—	2	1	no	—
1213	C₂³	—	2	1	no	—
1214	C₂³	—	79	2	no	—
1215	C₂³	—	158	1	no	—
1216	C₂³	—	158	1	no	—
1217	C₂³	—	158	1	no	—
1218	C₂³	—	158	1	no	—
1219	C₂³	—	158	1	no	—
1220	C₂³	—	158	1	no	—
1221	C₂³	C₂²×C₄×D₇₉	1	2	yes	—
1222	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
1223	Q₈	—	4	4	no	—
1224	Q₈	—	316	4	no	—
1225	Q₈	—	316	4	no	—
1226	D₄	—	316	4	no	—
1227	C₂×C₄	—	2	1	no	—
1228	C₂×C₄	—	2	1	no	—
1229	C₂×C₄	—	2	1	no	—
1230	C₂×C₄	—	2	1	no	—
1231	C₂×C₄	—	2	1	no	—
1232	C₂×C₄	—	2	1	no	—
1233	C₂×C₄	—	2	1	no	—
1234	C₂×C₄	—	2	1	no	—
1235	C₂×C₄	—	2	1	no	—
1236	C₂×C₄	—	2	1	no	—
1237	C₂×C₄	—	2	1	no	—
1238	C₂×C₄	—	2	1	no	—
1239	C₂×C₄	—	2	1	no	—
1240	C₂×C₄	—	2	1	no	—
1241	C₂×C₄	—	2	1	no	—
1242	C₂×C₄	—	2	1	no	—
1243	C₂×C₄	—	2	1	no	—
1244	C₂×C₄	—	2	1	no	—
1245	C₂×C₄	—	2	1	no	—
1246	C₂×C₄	—	2	1	no	—
1247	C₂×C₄	—	2	1	no	—
1248	C₂×C₄	—	2	1	no	—
1249	C₂×C₄	—	2	1	no	—
1250	C₂×C₄	—	2	1	no	—
1251	C₂×C₄	—	2	1	no	—
1252	C₂×C₄	—	2	1	no	—
1253	C₂×C₄	—	2	1	no	—
1254	C₂×C₄	—	2	1	no	—
1255	C₂×C₄	—	2	1	no	—
1256	C₂×C₄	—	2	1	no	—
1257	C₂×C₄	—	2	1	no	—
1258	C₂×C₄	—	2	1	no	—
1259	C₂×C₄	—	2	1	no	—
1260	C₂×C₄	—	2	1	no	—
1261	C₂×C₄	—	2	1	no	—
1262	C₂×C₄	—	2	1	no	—
1263	C₂×C₄	—	4	4	no	—
1264	C₂×C₄	—	316	4	no	—
1265	C₂×C₄	—	316	4	no	—
1266	C₂×C₄	—	316	4	no	—
1267	C₂×C₄	—	316	4	no	—
1268	C₂×C₄	—	316	4	no	—
1269	C₂×C₄	—	79	2	no	—
1270	C₂×C₄	—	79	2	no	—
1271	C₂×C₄	—	79	2	no	—
1272	C₂×C₄	—	79	2	no	—
1273	C₂×C₄	—	79	2	no	—
1274	C₂×C₄	—	79	2	no	—
1275	C₂×C₄	—	79	2	no	—
1276	C₂×C₄	—	79	2	no	—
1277	C₂×C₄	—	79	2	no	—
1278	C₂×C₄	—	79	2	no	—
1279	C₂×C₄	—	158	1	no	—
1280	C₂×C₄	—	158	1	no	—
1281	C₂×C₄	—	158	1	no	—
1282	C₂×C₄	—	158	1	no	—
1283	C₂×C₄	—	158	1	no	—
1284	C₂×C₄	—	158	1	no	—
1285	C₂×C₄	—	158	1	no	—
1286	C₂×C₄	—	158	1	no	—
1287	C₂×C₄	—	158	1	no	—
1288	C₂×C₄	—	158	1	no	—
1289	C₂×C₄	—	158	1	no	—
1290	C₂×C₄	—	158	1	no	—
1291	C₂×C₄	—	158	1	no	—
1292	C₂×C₄	—	158	1	no	—
1293	C₂×C₄	—	158	1	no	—
1294	C₂×C₄	—	158	1	no	—
1295	C₂×C₄	—	158	1	no	—
1296	C₂×C₄	—	158	1	no	—
1297	C₂×C₄	—	158	1	no	—
1298	C₂×C₄	—	158	1	no	—
1299	C₂×C₄	—	158	1	no	—
1300	C₂×C₄	—	158	1	no	—
1301	C₂×C₄	—	158	1	no	—
1302	C₂×C₄	—	158	1	no	—
1303	C₂×C₄	—	158	1	no	—
1304	C₂×C₄	—	158	1	no	—
1305	C₂×C₄	—	158	1	no	—
1306	C₂×C₄	—	158	1	no	—
1307	C₂×C₄	—	158	1	no	—
1308	C₂×C₄	—	158	1	no	—
1309	C₂×C₄	—	158	1	no	—
1310	C₂×C₄	—	158	1	no	—
1311	C₂×C₄	—	158	1	no	—
1312	C₂×C₄	—	158	1	no	—
1313	C₂×C₄	—	158	1	no	—
1314	C₂×C₄	C₂²×C₄×D₇₉	1	2	yes	—
1315	C₂×C₄	C₂²×C₄×D₇₉	1	2	yes	—
1316	C₂×C₄	C₂²×C₄×D₇₉	1	2	yes	—
1317	C₂×C₄	C₂²×C₄×D₇₉	1	2	yes	—
1318	C₂×C₄	C₂²×C₄×D₇₉	1	2	yes	—
1319	C₂×C₄	C₂²×C₄×D₇₉	1	2	yes	—
1320	C₂²	—	2	2	no	—
1321	C₂²	—	2	2	no	—
1322	C₂²	—	2	2	no	—
1323	C₂²	—	4	1	no	—
1324	C₂²	—	4	1	no	—
1325	C₂²	—	4	1	no	—
1326	C₂²	—	4	1	no	—
1327	C₂²	—	316	1	no	—
1328	C₂²	—	316	1	no	—
1329	C₂²	—	316	1	no	—
1330	C₂²	—	316	1	no	—
1331	C₂²	—	158	2	no	—
1332	C₂²	—	158	2	no	—
1333	C₂²	—	158	2	no	—
1334	C₂²	C₂³×C₄×D₇₉	1	1	yes	characteristic
1335	C₂²	H(5,𝔽₂)×D₇₉	1	1	yes	characteristic
1336	C₂²	2₋¹⁺⁴×D₇₉	1	1	yes	characteristic
1337	C₂²	2₋¹⁺⁴×D₇₉	1	1	yes	characteristic
1338	C₂²	#19099398	1	1	yes	characteristic
1339	C₂²	#19099398	1	1	yes	characteristic
1340	C₂²	#19099400	1	1	yes	characteristic
1341	C₄	—	2	2	no	—
1342	C₄	—	2	2	no	—
1343	C₄	—	2	2	no	—
1344	C₄	—	2	2	no	—
1345	C₄	—	2	2	no	—
1346	C₄	—	2	2	no	—
1347	C₄	—	4	1	no	—
1348	C₄	—	4	1	no	—
1349	C₄	—	4	1	no	—
1350	C₄	—	4	1	no	—
1351	C₄	—	4	1	no	—
1352	C₄	—	4	1	no	—
1353	C₄	—	4	1	no	—
1354	C₄	—	4	1	no	—
1355	C₄	—	316	1	no	—
1356	C₄	—	316	1	no	—
1357	C₄	—	316	1	no	—
1358	C₄	—	316	1	no	—
1359	C₄	—	316	1	no	—
1360	C₄	—	316	1	no	—
1361	C₄	—	316	1	no	—
1362	C₄	—	79	4	no	—
1363	C₄	—	158	2	no	—
1364	C₄	—	158	2	no	—
1365	C₄	—	158	2	no	—
1366	C₄	—	158	2	no	—
1367	C₄	—	158	2	no	—
1368	C₄	—	158	2	no	—
1369	C₄	—	158	2	no	—
1370	C₂	—	4	2	no	—
1371	C₂	—	316	2	no	—
1372	C₂	#23776604	1	1	yes	characteristic
1373	C₂	#23776609	1	1	yes	characteristic
1374	C₂	#23776611	1	1	yes	characteristic
1375	C₂	#563×D₇₉	1	1	yes	characteristic
1376	C₂	#23777537	1	1	yes	characteristic
1377	C₂	#23777544	1	1	yes	characteristic
1378	C₂	#23777546	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₇₉
commutator	C₂²×C₇₉	C₂⁴×C₄
Fitting	C₇₉×#2378	C₂
socle, cosocle	C₂³×C₇₉	C₂⁵
prime radical	C₂²×C₂²⋊D₇₉	C₂³
hypercenter	#2378	D₇₉
hypocenter	C₇₉	C₄×#563
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ #2378

Complements

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

N	H ≅ G/N	type
2. #23766591	C₂	semidirect
3. #23766590	C₂	semidirect
4. #23766587	C₂	semidirect
5. #23766587	C₂	semidirect
6. #23766584	C₂	semidirect
7. #23766583	C₂	semidirect
8. #23766579	C₂	semidirect
9. #23766578	C₂	semidirect
11. #23766568	C₂	semidirect
12. #23766562	C₂	semidirect
13. #23766561	C₂	semidirect
16. #23765971	C₂	semidirect
17. #23765969	C₂	semidirect
18. #23765959	C₂	semidirect
19. #23765957	C₂	semidirect
20. #23765954	C₂	semidirect
21. #23765954	C₂	semidirect
22. #23765950	C₂	semidirect
23. #23765950	C₂	semidirect
25. #23765938	C₂	semidirect
26. C₂²⋊Q₈×Dic₇₉	C₂	semidirect
27. #23765934	C₂	semidirect
28. #23765928	C₂	semidirect
31. C₇₉×#2378	C₂	semidirect
32. #19099314	C₄	semidirect
196. #14579160	C₂×C₄	semidirect
197. #14579159	C₂×C₄	semidirect
198. #14579156	C₂×C₄	semidirect
199. #14579156	C₂×C₄	semidirect
200. #14579154	C₂×C₄	semidirect
201. #14579154	C₂×C₄	semidirect
202. #14579152	C₂×C₄	semidirect
203. #14579151	C₂×C₄	semidirect
207. #14579140	C₂×C₄	semidirect
208. #14579139	C₂×C₄	semidirect
209. #14579137	C₂×C₄	semidirect
330. C₂²⋊Q₈×C₇₉	C₂×C₄	semidirect
679. Dic₇₉	#563	semidirect
703. #2378	D₇₉	semidirect
721. C₇₉	C₄×#563	semidirect
902. C₂²⋊Q₈	C₄×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19099314	2
#23766591	2
#23766590	2
#23766587	2
#23766584	2
#23766583	2
#23766579	2
#23766578	2
#23766569	2
#23766568	2
#23766562	2
#23766561	2
#23766544	2
#23766542	2
#23765971	2
#23765969	2
#23765959	2
#23765957	2
#23765954	2
#23765950	2
#23765941	2
#23765938	2
C₂²⋊Q₈×Dic₇₉	2
#23765934	2
#23765928	2
#23765927	2
#23765917	2
C₇₉×#2378	2
C₄×#563	79