Subgroups — #35160739

Order 20224.

1700 conjugacy classes of subgroups.

The subgroup lattice has 1114 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23777137	C₂	1	1	yes	maximal, characteristic
2	#23776805	C₂	1	1	yes	maximal, characteristic, complemented
3	#23774702	C₂	1	2	yes	maximal, complemented
4	#23774687	C₂	1	2	yes	maximal, complemented
5	#23774657	C₂	1	2	yes	maximal, complemented
6	#23774649	C₂	1	2	yes	maximal, complemented
7	#23774644	C₂	1	2	yes	maximal, complemented
8	#23774595	C₂	1	2	yes	maximal, complemented
9	#23774582	C₂	1	2	yes	maximal, complemented
10	#23774534	C₂	1	2	yes	maximal, complemented
11	#23773940	C₂	1	1	yes	maximal, characteristic, complemented
12	#23773932	C₂	1	1	yes	maximal, characteristic, complemented
13	#23773758	C₂	1	1	yes	maximal, characteristic, complemented
14	#23773758	C₂	1	1	yes	maximal, characteristic, complemented
15	#23773340	C₂	1	1	yes	maximal, characteristic, complemented
16	#23773329	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#19098888	C₂	1	1	yes	maximal, characteristic, complemented
18	#23773260	C₂	1	1	yes	maximal, characteristic, complemented
19	#23773249	C₂	1	1	yes	maximal, characteristic, complemented
20	#23773234	C₂	1	1	yes	maximal, characteristic, complemented
21	#23773234	C₂	1	1	yes	maximal, characteristic, complemented
22	#23772054	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇₉×#3091	C₂	1	1	yes	maximal, characteristic, complemented
24	#19099278	—	2	1	no	—
25	#19099259	—	2	1	no	—
26	#19099259	—	2	1	no	—
27	#19099236	—	2	2	no	—
28	#19099217	—	2	1	no	—
29	#19099200	—	2	2	no	—
30	#19099194	C₂²	1	2	yes	complemented
31	#19099194	C₂²	1	2	yes	complemented
32	#19099191	—	2	1	no	—
33	#19099191	—	2	1	no	—
34	#19099191	C₂²	1	1	yes	characteristic
35	#19099191	C₂²	1	1	yes	characteristic
36	#19099191	C₂²	1	1	yes	characteristic
37	#19099191	C₂²	1	1	yes	characteristic
38	#19099191	C₂²	1	1	yes	characteristic
39	#19099189	—	2	2	no	—
40	#19099186	C₂²	1	2	yes	—
41	#19099166	C₂²	1	2	yes	—
42	#19099127	C₂²	1	1	yes	characteristic
43	#19099120	—	2	1	no	—
44	#19099120	—	2	1	no	—
45	#19099116	—	2	2	no	—
46	#19099116	C₂²	1	2	yes	complemented
47	#19099116	C₂²	1	2	yes	complemented
48	#19099108	C₂²	1	2	yes	—
49	#19099099	C₂²	1	2	yes	—
50	C₂×#14579135	C₂²	1	1	yes	characteristic
51	#19099046	C₂²	1	1	yes	characteristic
52	#19099037	C₂²	1	1	yes	characteristic
53	C₂×#14579120	C₂²	1	1	yes	characteristic
54	C₂×#14579120	C₂²	1	1	yes	characteristic
55	#19098971	C₂²	1	2	yes	complemented
56	#19098971	C₂²	1	2	yes	complemented
57	#19098970	C₂²	1	2	yes	complemented
58	#19098970	C₂²	1	2	yes	complemented
59	#19098967	C₂²	1	2	yes	complemented
60	#19098964	C₂²	1	2	yes	complemented
61	#19098963	C₂²	1	2	yes	complemented
62	#19098960	C₂²	1	2	yes	complemented
63	#19098926	C₂²	1	2	yes	complemented
64	#19098926	C₂²	1	2	yes	complemented
65	#19098924	C₂²	1	2	yes	complemented
66	#19098924	C₂²	1	2	yes	complemented
67	#19098919	C₂²	1	2	yes	complemented
68	#19098919	C₂²	1	2	yes	complemented
69	#19098908	C₂²	1	2	yes	complemented
70	#19098908	C₂²	1	2	yes	complemented
71	#19098901	C₂²	1	2	yes	complemented
72	#19098901	C₂²	1	2	yes	complemented
73	#19098888	C₂²	1	2	yes	—
74	#19098888	C₂²	1	2	yes	—
75	#19098888	C₂²	1	2	yes	—
76	#19098888	C₂²	1	2	yes	—
77	#19098887	C₂²	1	2	yes	—
78	#19098887	C₂²	1	2	yes	—
79	#19098884	C₂²	1	2	yes	complemented
80	#19098884	C₂²	1	2	yes	complemented
81	#19098881	C₂²	1	2	yes	—
82	#19098876	C₂²	1	2	yes	—
83	#19098872	C₂²	1	2	yes	complemented
84	#19098868	C₂²	1	2	yes	complemented
85	#19098866	C₂²	1	2	yes	complemented
86	#19098866	C₂²	1	2	yes	complemented
87	#19098865	C₂²	1	2	yes	complemented
88	#19098862	C₂²	1	2	yes	complemented
89	#19098862	C₂²	1	2	yes	complemented
90	#19098861	C₂²	1	2	yes	complemented
91	#19098856	C₂²	1	2	yes	complemented
92	#19098852	C₂²	1	2	yes	complemented
93	#19098852	C₂²	1	2	yes	complemented
94	#19098851	C₂²	1	2	yes	complemented
95	#19098846	C₂²	1	2	yes	complemented
96	#19098842	C₂²	1	2	yes	complemented
97	#19098842	C₂²	1	2	yes	complemented
98	#19098841	C₂²	1	2	yes	complemented
99	#19098621	C₂²	1	2	yes	complemented
100	#19098621	C₂²	1	2	yes	complemented
101	#19098617	C₂²	1	2	yes	complemented
102	#19098613	C₂²	1	2	yes	complemented
103	#19098606	C₂²	1	1	yes	characteristic
104	#19098606	C₂²	1	1	yes	characteristic
105	#19098606	C₂²	1	1	yes	characteristic
106	#19098606	C₂²	1	1	yes	characteristic
107	C₂×#14579095	C₂²	1	1	yes	characteristic
108	C₂×#14579093	C₂²	1	1	yes	characteristic
109	#19098589	C₂²	1	1	yes	characteristic
110	#19098589	C₂²	1	1	yes	characteristic
111	#19098567	C₂²	1	1	yes	characteristic
112	#19098567	C₂²	1	1	yes	characteristic
113	#19098564	C₂²	1	1	yes	characteristic
114	#19098564	C₂²	1	1	yes	characteristic
115	C₂×#14579083	C₂²	1	1	yes	characteristic
116	C₂×#14579083	C₂²	1	1	yes	characteristic
117	#19098527	C₂²	1	1	yes	characteristic
118	#19098518	C₂²	1	1	yes	characteristic
119	#19098518	C₂²	1	1	yes	characteristic
120	#525×C₇₉	C₂²	1	1	yes	characteristic
121	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
122	#485×C₇₉	C₂²	1	1	yes	characteristic, complemented
123	#485×C₇₉	C₂²	1	1	yes	characteristic, complemented
124	#484×C₇₉	C₂²	1	1	yes	characteristic, complemented
125	#483×C₇₉	C₂²	1	1	yes	characteristic, complemented
126	#482×C₇₉	C₂²	1	1	yes	characteristic, complemented
127	#482×C₇₉	C₂²	1	1	yes	characteristic, complemented
128	#481×C₇₉	C₂²	1	1	yes	characteristic, complemented
129	#480×C₇₉	C₂²	1	1	yes	characteristic, complemented
130	#427×C₇₉	C₂²	1	1	yes	characteristic
131	#427×C₇₉	C₂²	1	1	yes	characteristic
132	#416×C₇₉	C₂²	1	1	yes	characteristic
133	#416×C₇₉	C₂²	1	1	yes	characteristic
134	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
135	C₂×#11929623	—	2	2	no	—
136	C₂²×D₃₁₆	C₂³	1	1	yes	characteristic
137	C₂²×C₂²⋊D₇₉	—	2	1	no	—
138	C₂×#11929608	C₂³	1	1	yes	characteristic
139	C₂×#11929608	C₂³	1	1	yes	characteristic
140	#14579161	—	2	1	no	—
141	#14579161	—	2	1	no	—
142	#14579161	—	2	1	no	—
143	#14579161	—	2	1	no	—
144	#14579161	—	2	1	no	—
145	#14579160	—	2	2	no	—
146	#14579160	—	2	2	no	—
147	#14579160	C₂³	1	2	yes	—
148	#14579160	C₂³	1	2	yes	—
149	#14579160	C₂³	1	2	yes	—
150	#14579160	C₂³	1	2	yes	—
151	#14579160	C₂³	1	2	yes	—
152	#14579157	C₂³	1	2	yes	—
153	#14579156	—	2	2	no	—
154	#14579156	—	2	2	no	—
155	#14579153	—	2	1	no	—
156	#14579153	—	2	1	no	—
157	#14579153	—	2	1	no	—
158	#14579153	—	2	1	no	—
159	#14579153	—	2	1	no	—
160	#14579152	—	2	2	no	—
161	#14579152	—	2	2	no	—
162	#14579152	C₂³	1	2	yes	—
163	#14579152	C₂³	1	2	yes	—
164	#14579152	C₂³	1	2	yes	—
165	#14579152	C₂³	1	2	yes	—
166	#14579152	C₂³	1	2	yes	—
167	#14579150	C₂³	1	2	yes	—
168	#14579147	—	2	2	no	—
169	#14579147	—	2	2	no	—
170	#14579145	—	2	2	no	—
171	#14579145	—	2	2	no	—
172	#14579143	—	2	2	no	—
173	#14579143	—	2	2	no	—
174	#14579141	—	2	2	no	—
175	#14579140	—	2	2	no	—
176	#14579140	—	2	2	no	—
177	#14579140	—	2	2	no	—
178	#14579140	—	2	2	no	—
179	#14579138	—	2	2	no	—
180	#14579138	—	2	2	no	—
181	#14579138	—	2	2	no	—
182	#14579138	—	2	2	no	—
183	#14579138	—	2	2	no	—
184	#14579138	—	2	2	no	—
185	#14579138	—	2	2	no	—
186	#14579138	—	2	2	no	—
187	#14579138	—	2	2	no	—
188	#14579135	—	2	1	no	—
189	#14579135	—	2	1	no	—
190	#14579135	—	2	1	no	—
191	#14579135	—	2	1	no	—
192	#14579135	C₂³	1	2	yes	—
193	#14579135	C₂³	1	2	yes	—
194	#14579133	—	2	2	no	—
195	#14579133	—	2	2	no	—
196	#14579132	—	2	2	no	—
197	#14579129	—	2	2	no	—
198	Q₈×Dic₇₉	C₂³	1	2	yes	—
199	C₄×Dic₁₅₈	—	2	2	no	—
200	C₄×Dic₁₅₈	—	2	2	no	—
201	C₄×Dic₁₅₈	—	2	2	no	—
202	C₄×Dic₁₅₈	—	2	2	no	—
203	C₄×D₃₁₆	—	2	1	no	—
204	C₄×D₃₁₆	—	2	1	no	—
205	D₄×Dic₇₉	—	2	2	no	—
206	D₄×Dic₇₉	C₂³	1	2	yes	—
207	#14579123	C₂³	1	2	yes	—
208	#14579123	C₂³	1	2	yes	—
209	(C₂²⋊D₇₉)⋊C₄	—	2	2	no	—
210	(C₂²⋊D₇₉)⋊C₄	—	2	2	no	—
211	#14579120	—	2	1	no	—
212	#14579120	—	2	1	no	—
213	#14579120	—	2	1	no	—
214	#14579120	D₄	1	2	yes	—
215	#14579120	D₄	1	1	yes	characteristic
216	#14579120	D₄	1	1	yes	characteristic
217	#14579120	C₂³	1	2	yes	—
218	#14579120	C₂³	1	2	yes	—
219	#14579120	C₂³	1	2	yes	—
220	#14579120	C₂³	1	1	yes	characteristic
221	#14579120	C₂³	1	1	yes	characteristic
222	#14579119	—	2	2	no	—
223	C₂×C₄⋊Dic₇₉	—	2	1	no	—
224	C₂×C₄⋊Dic₇₉	D₄	1	1	yes	characteristic
225	C₂×C₄⋊Dic₇₉	D₄	1	1	yes	characteristic
226	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
229	C₂×C₂²⋊Dic₇₉	—	2	1	no	—
230	C₂×C₂²⋊Dic₇₉	D₄	1	2	yes	—
231	C₂×(C₂×D₇₉)⋊C₄	—	2	1	no	—
232	C₂²⋊C₄×D₇₉	—	2	2	no	—
233	C₂×C₄×Dic₇₉	—	2	1	no	—
234	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
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	#14579092	C₂³	1	2	yes	—
246	#14579092	C₂³	1	2	yes	—
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	#14579085	C₂³	1	2	yes	—
252	#14579085	C₂³	1	2	yes	—
253	#14579083	C₂³	1	2	yes	—
254	#14579083	C₂³	1	2	yes	—
255	#14579083	C₂³	1	2	yes	—
256	#14579083	C₂³	1	2	yes	—
257	#14579082	C₂³	1	2	yes	—
258	#14579082	C₂³	1	2	yes	—
259	#14579081	C₂³	1	2	yes	—
260	#14579081	C₂³	1	2	yes	—
261	#14579081	C₂³	1	2	yes	—
262	#14579081	C₂³	1	2	yes	—
263	C₂²⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
264	C₂²⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
265	#14579071	C₂³	1	2	yes	—
266	#14579071	C₂³	1	2	yes	—
267	C₈×Dic₇₉	C₂³	1	2	yes	—
268	C₈×Dic₇₉	C₂³	1	2	yes	—
269	C₂×#41×C₇₉	C₂³	1	1	yes	characteristic
270	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
271	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
272	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
273	#123×C₇₉	—	2	1	no	—
274	C₂²⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
275	C₂²⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
276	#121×C₇₉	C₂³	1	1	yes	characteristic
277	#121×C₇₉	C₂³	1	1	yes	characteristic
278	#120×C₇₉	—	2	1	no	—
279	C₄×D₄×C₇₉	—	2	1	no	—
280	C₄×D₄×C₇₉	—	2	1	no	—
281	#117×C₇₉	—	2	1	no	—
282	#117×C₇₉	—	2	1	no	—
283	#117×C₇₉	C₂³	1	1	yes	characteristic
284	#117×C₇₉	C₂³	1	1	yes	characteristic
285	#117×C₇₉	C₂³	1	1	yes	characteristic
286	#117×C₇₉	C₂³	1	1	yes	characteristic
287	#117×C₇₉	C₂³	1	1	yes	characteristic
288	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
289	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
290	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
291	C₂×C₄²×C₇₉	—	2	1	no	—
292	#107×C₇₉	C₂³	1	1	yes	characteristic
293	#107×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	#106×C₇₉	C₂³	1	1	yes	characteristic
299	#106×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	#102×C₇₉	C₂³	1	1	yes	characteristic
305	#102×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	C₂²⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
311	C₂²⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
312	C₂³×D₇₉	—	2	1	no	—
313	#11929623	—	8	4	no	—
314	C₂×Dic₁₅₈	—	2	2	no	—
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×D₃₁₆	—	2	1	no	—
320	C₂×D₃₁₆	—	2	2	no	—
321	C₂×D₃₁₆	—	2	2	no	—
322	C₂×D₃₁₆	C₂⁴	1	2	yes	—
323	C₂×C₂²⋊D₇₉	—	2	2	no	—
324	C₂×C₂²⋊D₇₉	—	2	2	no	—
325	C₂×C₂²⋊D₇₉	—	2	2	no	—
326	C₂×C₂²⋊D₇₉	—	2	2	no	—
327	C₂×C₂²⋊D₇₉	—	8	2	no	—
328	C₂²×Dic₇₉	—	2	2	no	—
329	C₂²×Dic₇₉	—	2	1	no	—
330	C₂²×Dic₇₉	—	2	1	no	—
331	C₂²×Dic₇₉	—	2	1	no	—
332	C₂²×Dic₇₉	C₂×D₄	1	2	yes	—
333	C₂²×Dic₇₉	C₂×D₄	1	2	yes	—
334	C₂×C₄×D₇₉	—	2	2	no	—
335	C₂×C₄×D₇₉	—	2	2	no	—
336	#11929608	—	2	2	no	—
337	#11929608	—	2	2	no	—
338	C₂×C₇₉⋊C₈	C₂⁴	1	2	yes	—
339	C₂×C₇₉⋊C₈	C₂⁴	1	2	yes	—
340	C₄⋊Dic₇₉	—	2	2	no	—
341	C₄⋊Dic₇₉	—	2	2	no	—
342	C₄⋊Dic₇₉	—	2	2	no	—
343	C₄⋊Dic₇₉	—	2	2	no	—
344	C₄⋊Dic₇₉	—	2	2	no	—
345	C₄⋊Dic₇₉	—	2	2	no	—
346	C₄⋊Dic₇₉	—	2	1	no	—
347	C₄⋊Dic₇₉	—	2	1	no	—
348	C₄⋊Dic₇₉	—	2	1	no	—
349	C₄⋊Dic₇₉	C₂×D₄	1	1	yes	characteristic
350	C₄⋊Dic₇₉	C₂×D₄	1	1	yes	characteristic
351	C₄⋊Dic₇₉	C₂×D₄	1	1	yes	characteristic
352	C₄⋊Dic₇₉	C₂×D₄	1	1	yes	characteristic
353	C₄⋊Dic₇₉	C₂×D₄	1	2	yes	—
354	C₄⋊Dic₇₉	C₂×D₄	1	2	yes	—
355	C₄⋊Dic₇₉	C₂⁴	1	2	yes	—
356	C₄⋊Dic₇₉	C₂⁴	1	2	yes	—
357	C₄⋊Dic₇₉	C₂⁴	1	2	yes	—
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	—	2	2	no	—
363	Dic₇₉⋊C₄	—	2	2	no	—
364	Dic₇₉⋊C₄	—	2	2	no	—
365	Dic₇₉⋊C₄	—	2	2	no	—
366	Dic₇₉⋊C₄	—	2	2	no	—
367	Dic₇₉⋊C₄	—	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	C₂²⋊Dic₇₉	C₂×D₄	1	2	yes	—
374	C₂²⋊Dic₇₉	C₂×D₄	1	2	yes	—
375	(C₂×D₇₉)⋊C₄	—	2	2	no	—
376	(C₂×D₇₉)⋊C₄	—	2	2	no	—
377	(C₂×D₇₉)⋊C₄	—	2	2	no	—
378	(C₂×D₇₉)⋊C₄	—	2	2	no	—
379	(C₂×D₇₉)⋊C₄	—	2	2	no	—
380	(C₂×D₇₉)⋊C₄	—	2	2	no	—
381	C₄×Dic₇₉	—	2	2	no	—
382	C₄×Dic₇₉	—	2	2	no	—
383	C₄×Dic₇₉	—	2	2	no	—
384	C₄×Dic₇₉	C₂×D₄	1	2	yes	—
385	C₄×Dic₇₉	C₂×D₄	1	2	yes	—
386	C₄×Dic₇₉	C₂⁴	1	2	yes	—
387	C₄×Dic₇₉	C₂⁴	1	2	yes	—
388	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
389	#41×C₇₉	—	2	2	no	—
390	#41×C₇₉	—	2	2	no	—
391	C₂×Q₈×C₇₉	C₂⁴	1	1	yes	characteristic
392	C₂×D₄×C₇₉	—	2	1	no	—
393	C₂×D₄×C₇₉	—	2	1	no	—
394	C₂×D₄×C₇₉	—	2	1	no	—
395	C₂×D₄×C₇₉	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄×C₇₉	—	2	2	no	—
397	C₂²×C₄×C₇₉	—	2	2	no	—
398	C₂²×C₄×C₇₉	—	2	1	no	—
399	C₂²×C₄×C₇₉	—	2	1	no	—
400	C₂²×C₄×C₇₉	—	2	1	no	—
401	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
402	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
403	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
404	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
406	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
407	C₂×C₈×C₇₉	—	2	2	no	—
408	C₂×C₈×C₇₉	—	2	2	no	—
409	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
410	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
411	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
412	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₇₉	—	2	1	no	—
414	C₄⋊C₄×C₇₉	—	2	1	no	—
415	C₄⋊C₄×C₇₉	—	2	1	no	—
416	C₄⋊C₄×C₇₉	—	2	1	no	—
417	C₄⋊C₄×C₇₉	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₇₉	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₇₉	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₇₉	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₇₉	C₂⁴	1	1	yes	characteristic
422	C₄⋊C₄×C₇₉	C₂⁴	1	1	yes	characteristic
423	C₂²⋊C₄×C₇₉	—	2	1	no	—
424	C₂²⋊C₄×C₇₉	—	2	1	no	—
425	C₂²⋊C₄×C₇₉	—	2	1	no	—
426	C₂²⋊C₄×C₇₉	—	2	1	no	—
427	C₂²⋊C₄×C₇₉	—	2	1	no	—
428	C₂²⋊C₄×C₇₉	—	2	1	no	—
429	C₂²⋊C₄×C₇₉	—	2	1	no	—
430	C₂²⋊C₄×C₇₉	—	2	1	no	—
431	C₂²⋊C₄×C₇₉	—	2	1	no	—
432	C₄²×C₇₉	—	2	1	no	—
433	C₄²×C₇₉	—	2	1	no	—
434	C₄²×C₇₉	—	2	1	no	—
435	C₄²×C₇₉	—	2	1	no	—
436	C₄²×C₇₉	—	2	1	no	—
437	C₂³×C₇₉	—	2	2	no	—
438	C₂³×C₇₉	—	2	1	no	—
439	C₂³×C₇₉	—	4	1	no	—
440	C₂³×C₇₉	—	4	1	no	—
441	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
442	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
443	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
444	C₂²×D₇₉	—	2	2	no	—
445	C₂²×D₇₉	—	4	2	no	—
446	C₂²×D₇₉	—	8	1	no	—
447	C₂²×D₇₉	—	8	1	no	—
448	Q₈×C₇₉	—	2	1	no	—
449	Q₈×C₇₉	—	2	1	no	—
450	D₄×C₇₉	—	2	1	no	—
451	D₄×C₇₉	—	2	1	no	—
452	D₄×C₇₉	—	4	2	no	—
453	D₄×C₇₉	—	4	2	no	—
454	D₄×C₇₉	—	8	1	no	—
455	C₂×C₄×C₇₉	—	2	2	no	—
456	C₂×C₄×C₇₉	—	2	2	no	—
457	C₂×C₄×C₇₉	—	2	2	no	—
458	C₂×C₄×C₇₉	—	2	1	no	—
459	C₂×C₄×C₇₉	—	2	1	no	—
460	C₂×C₄×C₇₉	—	2	1	no	—
461	C₂×C₄×C₇₉	—	2	1	no	—
462	C₂×C₄×C₇₉	—	2	1	no	—
463	C₂×C₄×C₇₉	—	2	1	no	—
464	C₂×C₄×C₇₉	—	2	1	no	—
465	C₂×C₄×C₇₉	—	2	1	no	—
466	C₂×C₄×C₇₉	—	2	1	no	—
467	C₂×C₄×C₇₉	—	2	1	no	—
468	C₂×C₄×C₇₉	—	2	1	no	—
469	C₂×C₄×C₇₉	—	4	2	no	—
470	C₂×C₄×C₇₉	—	8	1	no	—
471	C₂×C₄×C₇₉	—	8	1	no	—
472	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
473	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
474	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
475	C₂×C₄×C₇₉	2₋¹⁺⁴	1	2	yes	—
476	C₂×C₄×C₇₉	2₋¹⁺⁴	1	2	yes	—
477	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
478	C₂²⋊D₇₉	—	4	4	no	—
479	C₂²⋊D₇₉	—	8	2	no	—
480	C₂²⋊D₇₉	—	8	2	no	—
481	C₂²⋊D₇₉	—	8	2	no	—
482	C₂×Dic₇₉	—	2	2	no	—
483	C₂×Dic₇₉	—	2	2	no	—
484	C₂×Dic₇₉	—	2	2	no	—
485	C₂×Dic₇₉	—	4	2	no	—
486	C₂×Dic₇₉	—	4	2	no	—
487	C₂×Dic₇₉	—	8	2	no	—
488	C₂×Dic₇₉	—	8	1	no	—
489	C₂×Dic₇₉	—	8	1	no	—
490	C₂×Dic₇₉	—	8	1	no	—
491	C₂×Dic₇₉	C₂²×D₄	1	2	yes	—
492	C₂×Dic₇₉	C₂²×D₄	1	2	yes	—
493	C₂×Dic₇₉	C₂²×D₄	1	2	yes	—
494	C₂×Dic₇₉	C₂²×D₄	1	2	yes	—
495	D₃₁₆	—	2	2	no	—
496	D₃₁₆	—	2	2	no	—
497	D₃₁₆	—	4	2	no	—
498	C₄×D₇₉	—	8	2	no	—
499	C₄×D₇₉	—	8	2	no	—
500	Dic₁₅₈	—	8	2	no	—
501	Dic₁₅₈	—	8	2	no	—
502	Dic₁₅₈	—	8	2	no	—
503	Dic₁₅₈	—	8	2	no	—
504	Dic₁₅₈	—	8	2	no	—
505	C₈×C₇₉	—	2	1	no	—
506	C₈×C₇₉	—	2	1	no	—
507	C₈×C₇₉	—	2	1	no	—
508	C₈×C₇₉	—	2	1	no	—
509	C₇₉⋊C₈	—	2	2	no	—
510	C₇₉⋊C₈	—	2	2	no	—
511	C₂²×C₇₉	—	2	1	no	—
512	C₂²×C₇₉	—	2	1	no	—
513	C₂²×C₇₉	—	2	1	no	—
514	C₂²×C₇₉	—	2	1	no	—
515	C₂²×C₇₉	—	2	1	no	—
516	C₂²×C₇₉	—	2	1	no	—
517	C₂²×C₇₉	—	2	1	no	—
518	C₂²×C₇₉	—	2	1	no	—
519	C₂²×C₇₉	—	4	1	no	—
520	C₂²×C₇₉	—	4	1	no	—
521	C₂²×C₇₉	—	4	1	no	—
522	C₂²×C₇₉	—	8	2	no	—
523	C₂²×C₇₉	#536	1	2	yes	—
524	C₂²×C₇₉	C₂³×D₄	1	1	yes	characteristic
525	C₂×D₇₉	—	4	2	no	—
526	C₂×D₇₉	—	4	2	no	—
527	C₂×D₇₉	—	4	2	no	—
528	C₂×D₇₉	—	16	2	no	—
529	C₄×C₇₉	—	2	1	no	—
530	C₄×C₇₉	—	2	1	no	—
531	C₄×C₇₉	—	4	1	no	—
532	C₄×C₇₉	—	4	1	no	—
533	C₄×C₇₉	—	4	1	no	—
534	C₄×C₇₉	—	4	1	no	—
535	C₄×C₇₉	—	4	1	no	—
536	C₄×C₇₉	—	4	1	no	—
537	C₄×C₇₉	—	4	1	no	—
538	C₄×C₇₉	#536	1	2	yes	—
539	C₄×C₇₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
540	C₄×C₇₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
541	Dic₇₉	—	2	2	no	—
542	Dic₇₉	—	2	2	no	—
543	Dic₇₉	—	2	2	no	—
544	Dic₇₉	—	2	2	no	—
545	Dic₇₉	—	4	2	no	—
546	Dic₇₉	—	4	2	no	—
547	Dic₇₉	—	4	2	no	—
548	#60875	—	79	1	no	maximal, Sylow
549	C₂×C₇₉	—	2	2	no	—
550	C₂×C₇₉	—	4	1	no	—
551	C₂×C₇₉	—	4	1	no	—
552	C₂×C₇₉	—	8	1	no	—
553	C₂×C₇₉	C₂×#536	1	1	yes	characteristic
554	C₂×C₇₉	#3584	1	1	yes	characteristic
555	C₂×C₇₉	#3585	1	1	yes	characteristic
556	D₇₉	—	8	2	no	—
557	#3494	—	79	1	no	—
558	#3458	—	79	1	no	—
559	#3244	—	79	2	no	—
560	#3243	—	79	2	no	—
561	#3241	—	79	2	no	—
562	#3241	—	79	2	no	—
563	#3240	—	79	2	no	—
564	#3235	—	79	2	no	—
565	#3233	—	79	2	no	—
566	#3228	—	79	2	no	—
567	#3164	—	79	1	no	—
568	#3163	—	79	1	no	—
569	#3136	—	79	1	no	—
570	#3136	—	79	1	no	—
571	#3094	—	79	1	no	—
572	#3093	—	79	1	no	—
573	#3091	D₇₉	1	1	yes	characteristic, complemented
574	C₂×#482	—	79	1	no	—
575	#3084	—	79	1	no	—
576	#3083	—	79	1	no	—
577	#3081	—	79	1	no	—
578	#3081	—	79	1	no	—
579	#2924	—	79	1	no	—
580	C₇₉	#60875	1	1	yes	characteristic, complemented, Sylow
581	#555	—	158	1	no	—
582	#553	—	158	1	no	—
583	#553	—	158	1	no	—
584	#551	—	158	2	no	—
585	#547	—	158	1	no	—
586	#546	—	158	2	no	—
587	#544	—	79	1	no	—
588	#544	—	79	1	no	—
589	#544	—	79	1	no	—
590	#544	—	79	1	no	—
591	#544	—	79	1	no	—
592	#544	—	79	2	no	—
593	#544	—	79	2	no	—
594	#544	—	158	1	no	—
595	#544	—	158	1	no	—
596	#543	—	158	2	no	—
597	#542	—	79	2	no	—
598	#540	—	79	2	no	—
599	#535	—	79	1	no	—
600	#533	—	79	2	no	—
601	#533	—	79	2	no	—
602	#533	—	158	1	no	—
603	#533	—	158	1	no	—
604	#533	—	158	2	no	—
605	#532	—	79	2	no	—
606	#529	—	79	2	no	—
607	#525	C₂×D₇₉	1	1	yes	characteristic
608	C₂×#121	—	79	1	no	—
609	#520	—	79	1	no	—
610	#518	—	79	1	no	—
611	C₂×#117	—	79	1	no	—
612	C₂×#117	—	79	1	no	—
613	C₂×#117	C₂×D₇₉	1	1	yes	characteristic
614	#501	—	79	2	no	—
615	#501	—	79	2	no	—
616	#501	—	79	2	no	—
617	#501	—	79	2	no	—
618	#500	—	79	2	no	—
619	#499	—	79	2	no	—
620	#499	—	79	2	no	—
621	#498	—	79	2	no	—
622	#490	—	79	2	no	—
623	#490	—	79	2	no	—
624	#489	—	79	2	no	—
625	#489	—	79	2	no	—
626	#488	—	79	2	no	—
627	#488	—	79	2	no	—
628	#486	—	79	2	no	—
629	#486	—	79	2	no	—
630	#485	—	79	2	no	—
631	#485	—	79	2	no	—
632	#485	C₂×D₇₉	1	1	yes	characteristic, complemented
633	#485	C₂×D₇₉	1	1	yes	characteristic, complemented
634	#484	C₂×D₇₉	1	1	yes	characteristic, complemented
635	#483	C₂×D₇₉	1	1	yes	characteristic, complemented
636	#482	—	79	2	no	—
637	#482	—	79	2	no	—
638	#482	—	79	2	no	—
639	#482	—	79	2	no	—
640	#482	—	79	2	no	—
641	#482	—	79	2	no	—
642	#482	—	79	2	no	—
643	#482	—	79	2	no	—
644	#482	C₂×D₇₉	1	1	yes	characteristic, complemented
645	#482	C₂×D₇₉	1	1	yes	characteristic, complemented
646	#481	—	79	2	no	—
647	#481	C₂×D₇₉	1	1	yes	characteristic, complemented
648	#480	—	79	2	no	—
649	#480	C₂×D₇₉	1	1	yes	characteristic, complemented
650	#479	—	79	2	no	—
651	#479	—	79	2	no	—
652	#478	—	79	2	no	—
653	#478	—	79	2	no	—
654	#478	—	79	2	no	—
655	#478	—	79	2	no	—
656	#478	—	79	2	no	—
657	#478	—	79	2	no	—
658	#477	—	79	2	no	—
659	#476	—	79	2	no	—
660	#476	—	79	2	no	—
661	#476	—	79	2	no	—
662	#475	—	79	2	no	—
663	#474	—	79	2	no	—
664	#474	—	79	2	no	—
665	#474	—	79	2	no	—
666	#433	—	79	2	no	—
667	#433	—	79	2	no	—
668	#432	—	79	2	no	—
669	#431	—	79	2	no	—
670	#428	—	79	1	no	—
671	#428	—	79	1	no	—
672	#428	—	79	1	no	—
673	#428	—	79	1	no	—
674	#427	C₂×D₇₉	1	1	yes	characteristic
675	#427	C₂×D₇₉	1	1	yes	characteristic
676	C₂×#107	—	79	1	no	—
677	C₂×#106	—	79	1	no	—
678	#424	—	79	1	no	—
679	#424	—	79	1	no	—
680	#418	—	79	1	no	—
681	#418	—	79	1	no	—
682	#417	—	79	1	no	—
683	#417	—	79	1	no	—
684	#416	C₂×D₇₉	1	1	yes	characteristic
685	#416	C₂×D₇₉	1	1	yes	characteristic
686	C₂×#102	—	79	1	no	—
687	C₂×#102	—	79	1	no	—
688	#407	—	79	1	no	—
689	C₂×C₂²⋊C₈	C₂×D₇₉	1	1	yes	characteristic
690	#405	—	79	1	no	—
691	#405	—	79	1	no	—
692	C₂×#41	—	158	2	no	—
693	C₂×#41	C₂²×D₇₉	1	1	yes	characteristic
694	C₂²×D₄	—	79	1	no	—
695	C₂²×D₄	—	158	1	no	—
696	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
697	C₂×M₁₆	—	79	1	no	—
698	C₂×M₁₆	—	79	1	no	—
699	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
700	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
701	C₄⋊Q₈	—	79	2	no	—
702	C₄⋊Q₈	—	79	2	no	—
703	C₄⋊Q₈	—	79	2	no	—
704	C₄⋊Q₈	—	79	2	no	—
705	C₄⋊Q₈	—	79	2	no	—
706	C₄⋊Q₈	—	158	1	no	—
707	C₄⋊Q₈	—	158	1	no	—
708	C₄⋊Q₈	—	158	1	no	—
709	C₄⋊Q₈	—	158	1	no	—
710	C₄⋊Q₈	—	158	1	no	—
711	C₄⋊Q₈	—	158	2	no	—
712	C₄⋊Q₈	—	158	2	no	—
713	#127	—	79	2	no	—
714	#126	—	158	2	no	—
715	#126	—	158	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	1	no	—
724	#125	—	158	1	no	—
725	#125	—	158	1	no	—
726	#125	—	158	2	no	—
727	#125	—	158	2	no	—
728	#124	—	79	2	no	—
729	#124	—	158	2	no	—
730	#124	—	158	2	no	—
731	#123	—	2	1	no	—
732	#123	—	158	2	no	—
733	#123	—	158	2	no	—
734	#123	—	158	2	no	—
735	#123	—	158	2	no	—
736	C₂²⋊Q₈	—	158	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	C₂²×D₇₉	1	1	yes	characteristic
751	C₂²⋊Q₈	C₂²×D₇₉	1	1	yes	characteristic
752	#121	—	79	2	no	—
753	#121	—	79	2	no	—
754	#121	—	158	2	no	—
755	#121	—	158	2	no	—
756	#121	—	158	1	no	—
757	#121	—	158	1	no	—
758	#121	—	158	2	no	—
759	#121	—	158	1	no	—
760	#121	—	158	1	no	—
761	#121	C₂²×D₇₉	1	1	yes	characteristic
762	#121	C₂²×D₇₉	1	1	yes	characteristic
763	#120	—	2	1	no	—
764	#120	—	158	2	no	—
765	C₄×Q₈	—	79	2	no	—
766	C₄×Q₈	—	158	2	no	—
767	C₄×Q₈	—	158	2	no	—
768	C₄×Q₈	—	158	2	no	—
769	C₄×Q₈	—	158	2	no	—
770	C₄×D₄	—	2	1	no	—
771	C₄×D₄	—	2	1	no	—
772	C₄×D₄	—	79	2	no	—
773	C₄×D₄	—	79	2	no	—
774	C₄×D₄	—	79	2	no	—
775	C₄×D₄	—	158	1	no	—
776	C₄×D₄	—	158	1	no	—
777	C₄×D₄	—	158	2	no	—
778	C₄×D₄	—	158	2	no	—
779	C₄×D₄	—	158	2	no	—
780	#117	—	2	1	no	—
781	#117	—	2	1	no	—
782	#117	—	79	2	no	—
783	#117	—	79	1	no	—
784	#117	—	79	1	no	—
785	#117	—	79	1	no	—
786	#117	—	79	1	no	—
787	#117	—	79	2	no	—
788	#117	—	79	2	no	—
789	#117	—	79	2	no	—
790	#117	—	158	2	no	—
791	#117	—	158	1	no	—
792	#117	—	158	1	no	—
793	#117	—	158	1	no	—
794	#117	C₂²×D₇₉	1	1	yes	characteristic
795	#117	C₂²×D₇₉	1	1	yes	characteristic
796	#117	C₂²×D₇₉	1	1	yes	characteristic
797	#117	C₂²×D₇₉	1	1	yes	characteristic
798	#117	C₂²×D₇₉	1	1	yes	characteristic
799	C₂×C₄⋊C₄	—	79	1	no	—
800	C₂×C₄⋊C₄	—	79	1	no	—
801	C₂×C₄⋊C₄	—	79	1	no	—
802	C₂×C₄⋊C₄	—	79	1	no	—
803	C₂×C₄⋊C₄	—	79	1	no	—
804	C₂×C₄⋊C₄	—	158	1	no	—
805	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
806	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
807	C₂×C₂²⋊C₄	—	2	1	no	—
808	C₂×C₂²⋊C₄	—	79	2	no	—
809	C₂×C₂²⋊C₄	—	158	2	no	—
810	C₂×C₂²⋊C₄	—	158	1	no	—
811	C₂×C₂²⋊C₄	—	158	1	no	—
812	C₂×C₄²	—	2	1	no	—
813	C₂×C₄²	—	79	2	no	—
814	C₂×C₄²	—	158	1	no	—
815	#107	—	79	2	no	—
816	#107	—	79	2	no	—
817	#107	—	79	2	no	—
818	#107	—	79	2	no	—
819	#107	—	79	2	no	—
820	#107	—	79	2	no	—
821	#107	C₂²×D₇₉	1	1	yes	characteristic
822	#107	C₂²×D₇₉	1	1	yes	characteristic
823	#107	C₂²×D₇₉	1	1	yes	characteristic
824	#107	C₂²×D₇₉	1	1	yes	characteristic
825	#106	—	79	2	no	—
826	#106	—	79	2	no	—
827	#106	—	79	2	no	—
828	#106	—	79	2	no	—
829	#106	—	79	2	no	—
830	#106	—	79	2	no	—
831	#106	C₂²×D₇₉	1	1	yes	characteristic
832	#106	C₂²×D₇₉	1	1	yes	characteristic
833	#106	C₂²×D₇₉	1	1	yes	characteristic
834	#106	C₂²×D₇₉	1	1	yes	characteristic
835	C₄⋊C₈	—	79	2	no	—
836	C₄⋊C₈	—	79	2	no	—
837	C₄⋊C₈	—	79	2	no	—
838	C₄⋊C₈	—	79	2	no	—
839	#103	—	79	2	no	—
840	#103	—	79	2	no	—
841	#103	C₂²×D₇₉	1	1	yes	characteristic
842	#103	C₂²×D₇₉	1	1	yes	characteristic
843	#103	C₂²×D₇₉	1	1	yes	characteristic
844	#103	C₂²×D₇₉	1	1	yes	characteristic
845	#102	—	79	2	no	—
846	#102	—	79	2	no	—
847	#102	—	79	2	no	—
848	#102	—	79	2	no	—
849	#102	—	79	2	no	—
850	#102	—	79	2	no	—
851	#102	—	79	2	no	—
852	#102	—	79	2	no	—
853	#102	—	79	2	no	—
854	#102	—	79	2	no	—
855	#102	C₂²×D₇₉	1	1	yes	characteristic
856	#102	C₂²×D₇₉	1	1	yes	characteristic
857	#102	C₂²×D₇₉	1	1	yes	characteristic
858	#102	C₂²×D₇₉	1	1	yes	characteristic
859	C₂²⋊C₈	—	79	2	no	—
860	C₂²⋊C₈	—	79	2	no	—
861	C₂²⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
862	C₂²⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
863	C₂²⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
864	C₂²⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
865	#97	—	79	2	no	—
866	#97	—	79	2	no	—
867	C₄×C₈	—	79	2	no	—
868	C₄×C₈	—	79	2	no	—
869	C₂⁴	—	158	1	no	—
870	C₂⁴	D₄×D₇₉	1	1	yes	characteristic
871	#41	—	2	2	no	—
872	#41	—	2	2	no	—
873	#41	—	632	4	no	—
874	C₂×Q₈	—	158	2	no	—
875	C₂×Q₈	—	158	2	no	—
876	C₂×Q₈	—	158	2	no	—
877	C₂×Q₈	—	158	2	no	—
878	C₂×Q₈	—	158	2	no	—
879	C₂×Q₈	C₂³×D₇₉	1	1	yes	characteristic
880	C₂×D₄	—	2	1	no	—
881	C₂×D₄	—	2	1	no	—
882	C₂×D₄	—	2	1	no	—
883	C₂×D₄	—	79	2	no	—
884	C₂×D₄	—	632	2	no	—
885	C₂×D₄	—	158	2	no	—
886	C₂×D₄	—	158	2	no	—
887	C₂×D₄	—	158	2	no	—
888	C₂×D₄	—	158	2	no	—
889	C₂×D₄	—	158	2	no	—
890	C₂×D₄	—	158	2	no	—
891	C₂×D₄	—	158	1	no	—
892	C₂×D₄	C₂³×D₇₉	1	1	yes	characteristic
893	C₂²×C₄	—	2	2	no	—
894	C₂²×C₄	—	2	2	no	—
895	C₂²×C₄	—	2	1	no	—
896	C₂²×C₄	—	2	1	no	—
897	C₂²×C₄	—	2	1	no	—
898	C₂²×C₄	—	79	2	no	—
899	C₂²×C₄	—	79	2	no	—
900	C₂²×C₄	—	158	2	no	—
901	C₂²×C₄	—	158	2	no	—
902	C₂²×C₄	—	158	2	no	—
903	C₂²×C₄	—	158	1	no	—
904	C₂²×C₄	—	158	1	no	—
905	C₂²×C₄	—	158	1	no	—
906	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
907	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
908	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
909	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
910	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
911	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
912	M₁₆	—	158	2	no	—
913	M₁₆	—	158	2	no	—
914	C₂×C₈	—	2	2	no	—
915	C₂×C₈	—	2	2	no	—
916	C₂×C₈	—	79	2	no	—
917	C₂×C₈	—	79	2	no	—
918	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
919	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
920	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
921	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	79	1	no	—
927	C₄⋊C₄	—	79	1	no	—
928	C₄⋊C₄	—	79	1	no	—
929	C₄⋊C₄	—	79	1	no	—
930	C₄⋊C₄	—	79	2	no	—
931	C₄⋊C₄	—	79	2	no	—
932	C₄⋊C₄	—	79	2	no	—
933	C₄⋊C₄	—	79	2	no	—
934	C₄⋊C₄	—	79	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	2	no	—
943	C₄⋊C₄	—	158	2	no	—
944	C₄⋊C₄	—	158	2	no	—
945	C₄⋊C₄	—	158	2	no	—
946	C₄⋊C₄	—	158	2	no	—
947	C₄⋊C₄	—	158	2	no	—
948	C₄⋊C₄	—	158	2	no	—
949	C₄⋊C₄	—	158	2	no	—
950	C₄⋊C₄	—	158	2	no	—
951	C₄⋊C₄	—	158	1	no	—
952	C₄⋊C₄	—	158	1	no	—
953	C₄⋊C₄	—	158	1	no	—
954	C₄⋊C₄	C₂³×D₇₉	1	1	yes	characteristic
955	C₄⋊C₄	C₂³×D₇₉	1	1	yes	characteristic
956	C₄⋊C₄	C₂³×D₇₉	1	1	yes	characteristic
957	C₄⋊C₄	C₂³×D₇₉	1	1	yes	characteristic
958	C₄⋊C₄	C₂³×D₇₉	1	1	yes	characteristic
959	C₄⋊C₄	C₂³×D₇₉	1	1	yes	characteristic
960	C₂²⋊C₄	—	2	1	no	—
961	C₂²⋊C₄	—	2	1	no	—
962	C₂²⋊C₄	—	2	1	no	—
963	C₂²⋊C₄	—	2	1	no	—
964	C₂²⋊C₄	—	2	1	no	—
965	C₂²⋊C₄	—	2	1	no	—
966	C₂²⋊C₄	—	2	1	no	—
967	C₂²⋊C₄	—	2	1	no	—
968	C₂²⋊C₄	—	2	1	no	—
969	C₂²⋊C₄	—	79	2	no	—
970	C₂²⋊C₄	—	79	2	no	—
971	C₂²⋊C₄	—	79	2	no	—
972	C₂²⋊C₄	—	79	2	no	—
973	C₂²⋊C₄	—	158	2	no	—
974	C₂²⋊C₄	—	158	2	no	—
975	C₂²⋊C₄	—	158	2	no	—
976	C₂²⋊C₄	—	158	2	no	—
977	C₂²⋊C₄	—	158	2	no	—
978	C₂²⋊C₄	—	158	2	no	—
979	C₂²⋊C₄	—	158	2	no	—
980	C₂²⋊C₄	—	158	2	no	—
981	C₂²⋊C₄	—	158	2	no	—
982	C₄²	—	2	1	no	—
983	C₄²	—	2	1	no	—
984	C₄²	—	2	1	no	—
985	C₄²	—	2	1	no	—
986	C₄²	—	2	1	no	—
987	C₄²	—	79	2	no	—
988	C₄²	—	79	2	no	—
989	C₄²	—	79	2	no	—
990	C₄²	—	79	2	no	—
991	C₄²	—	158	2	no	—
992	C₄²	—	158	2	no	—
993	C₄²	—	158	2	no	—
994	C₂³	—	2	2	no	—
995	C₂³	—	2	1	no	—
996	C₂³	—	4	1	no	—
997	C₂³	—	4	1	no	—
998	C₂³	—	316	2	no	—
999	C₂³	—	632	1	no	—
1000	C₂³	—	632	1	no	—
1001	C₂³	—	158	2	no	—
1002	C₂³	C₂×D₄×D₇₉	1	1	yes	characteristic
1003	C₂³	C₂×D₄×D₇₉	1	1	yes	characteristic
1004	C₂³	C₂×D₄×D₇₉	1	1	yes	characteristic
1005	Q₈	—	2	1	no	—
1006	Q₈	—	2	1	no	—
1007	Q₈	—	632	2	no	—
1008	Q₈	—	632	2	no	—
1009	Q₈	—	632	2	no	—
1010	Q₈	—	632	2	no	—
1011	Q₈	—	632	2	no	—
1012	D₄	—	2	1	no	—
1013	D₄	—	2	1	no	—
1014	D₄	—	4	2	no	—
1015	D₄	—	4	2	no	—
1016	D₄	—	8	1	no	—
1017	D₄	—	316	4	no	—
1018	D₄	—	316	2	no	—
1019	D₄	—	632	2	no	—
1020	D₄	—	632	2	no	—
1021	D₄	—	632	2	no	—
1022	D₄	—	158	2	no	—
1023	D₄	—	158	2	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	4	2	no	—
1039	C₂×C₄	—	8	1	no	—
1040	C₂×C₄	—	8	1	no	—
1041	C₂×C₄	—	316	2	no	—
1042	C₂×C₄	—	316	2	no	—
1043	C₂×C₄	—	79	2	no	—
1044	C₂×C₄	—	79	2	no	—
1045	C₂×C₄	—	79	2	no	—
1046	C₂×C₄	—	79	2	no	—
1047	C₂×C₄	—	632	2	no	—
1048	C₂×C₄	—	632	2	no	—
1049	C₂×C₄	—	632	1	no	—
1050	C₂×C₄	—	632	1	no	—
1051	C₂×C₄	—	632	1	no	—
1052	C₂×C₄	—	632	2	no	—
1053	C₂×C₄	—	158	2	no	—
1054	C₂×C₄	—	158	2	no	—
1055	C₂×C₄	—	158	2	no	—
1056	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
1057	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
1058	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
1059	C₂×C₄	#14579208	1	2	yes	—
1060	C₂×C₄	#14579208	1	2	yes	—
1061	C₂×C₄	C₂⁴×D₇₉	1	1	yes	characteristic
1062	C₈	—	2	1	no	—
1063	C₈	—	2	1	no	—
1064	C₈	—	2	1	no	—
1065	C₈	—	2	1	no	—
1066	C₈	—	158	2	no	—
1067	C₈	—	158	2	no	—
1068	C₂²	—	2	1	no	—
1069	C₂²	—	2	1	no	—
1070	C₂²	—	2	1	no	—
1071	C₂²	—	2	1	no	—
1072	C₂²	—	2	1	no	—
1073	C₂²	—	2	1	no	—
1074	C₂²	—	2	1	no	—
1075	C₂²	—	2	1	no	—
1076	C₂²	—	4	1	no	—
1077	C₂²	—	4	1	no	—
1078	C₂²	—	4	1	no	—
1079	C₂²	—	8	2	no	—
1080	C₂²	—	316	2	no	—
1081	C₂²	—	316	2	no	—
1082	C₂²	—	316	2	no	—
1083	C₂²	—	1264	2	no	—
1084	C₂²	#19099135	1	2	yes	—
1085	C₂²	C₂²×D₄×D₇₉	1	1	yes	characteristic
1086	C₄	—	2	1	no	—
1087	C₄	—	2	1	no	—
1088	C₄	—	4	1	no	—
1089	C₄	—	4	1	no	—
1090	C₄	—	4	1	no	—
1091	C₄	—	4	1	no	—
1092	C₄	—	4	1	no	—
1093	C₄	—	4	1	no	—
1094	C₄	—	4	1	no	—
1095	C₄	—	316	2	no	—
1096	C₄	—	316	2	no	—
1097	C₄	—	316	2	no	—
1098	C₄	—	158	2	no	—
1099	C₄	—	158	2	no	—
1100	C₄	—	158	2	no	—
1101	C₄	—	158	2	no	—
1102	C₄	#19099135	1	2	yes	—
1103	C₄	C₂×#14579208	1	1	yes	characteristic
1104	C₄	C₂×#14579208	1	1	yes	characteristic
1105	C₂	—	2	2	no	—
1106	C₂	—	4	1	no	—
1107	C₂	—	4	1	no	—
1108	C₂	—	8	1	no	—
1109	C₂	—	632	2	no	—
1110	C₂	C₂×#19099135	1	1	yes	characteristic
1111	C₂	#23778169	1	1	yes	characteristic
1112	C₂	#23778177	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×#3091	C₂
socle	C₂²×C₇₉	C₂³×D₄
prime radical	#23777137	C₂
hypercenter	#3091	D₇₉
hypocenter	C₇₉	#60875
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #3091

Complements

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

N	H ≅ G/N	type
2. #23776805	C₂	semidirect
3. #23774702	C₂	semidirect
4. #23774687	C₂	semidirect
5. #23774657	C₂	semidirect
6. #23774649	C₂	semidirect
7. #23774644	C₂	semidirect
8. #23774595	C₂	semidirect
9. #23774582	C₂	semidirect
10. #23774534	C₂	semidirect
11. #23773940	C₂	semidirect
12. #23773932	C₂	semidirect
13. #23773758	C₂	semidirect
14. #23773758	C₂	semidirect
15. #23773340	C₂	semidirect
16. #23773329	C₂	semidirect
17. C₂×#19098888	C₂	semidirect
18. #23773260	C₂	semidirect
19. #23773249	C₂	semidirect
20. #23773234	C₂	semidirect
21. #23773234	C₂	semidirect
22. #23772054	C₂	semidirect
23. C₇₉×#3091	C₂	semidirect
30. #19099194	C₂²	semidirect
31. #19099194	C₂²	semidirect
46. #19099116	C₂²	semidirect
47. #19099116	C₂²	semidirect
55. #19098971	C₂²	semidirect
56. #19098971	C₂²	semidirect
57. #19098970	C₂²	semidirect
58. #19098970	C₂²	semidirect
59. #19098967	C₂²	semidirect
60. #19098964	C₂²	semidirect
61. #19098963	C₂²	semidirect
62. #19098960	C₂²	semidirect
63. #19098926	C₂²	semidirect
64. #19098926	C₂²	semidirect
65. #19098924	C₂²	semidirect
66. #19098924	C₂²	semidirect
67. #19098919	C₂²	semidirect
68. #19098919	C₂²	semidirect
69. #19098908	C₂²	semidirect
70. #19098908	C₂²	semidirect
71. #19098901	C₂²	semidirect
72. #19098901	C₂²	semidirect
79. #19098884	C₂²	semidirect
80. #19098884	C₂²	semidirect
83. #19098872	C₂²	semidirect
84. #19098868	C₂²	semidirect
85. #19098866	C₂²	semidirect
86. #19098866	C₂²	semidirect
87. #19098865	C₂²	semidirect
88. #19098862	C₂²	semidirect
89. #19098862	C₂²	semidirect
90. #19098861	C₂²	semidirect
91. #19098856	C₂²	semidirect
92. #19098852	C₂²	semidirect
93. #19098852	C₂²	semidirect
94. #19098851	C₂²	semidirect
95. #19098846	C₂²	semidirect
96. #19098842	C₂²	semidirect
97. #19098842	C₂²	semidirect
98. #19098841	C₂²	semidirect
99. #19098621	C₂²	semidirect
100. #19098621	C₂²	semidirect
101. #19098617	C₂²	semidirect
102. #19098613	C₂²	semidirect
122. #485×C₇₉	C₂²	semidirect
123. #485×C₇₉	C₂²	semidirect
124. #484×C₇₉	C₂²	semidirect
125. #483×C₇₉	C₂²	semidirect
126. #482×C₇₉	C₂²	semidirect
127. #482×C₇₉	C₂²	semidirect
128. #481×C₇₉	C₂²	semidirect
129. #480×C₇₉	C₂²	semidirect
573. #3091	D₇₉	semidirect
580. C₇₉	#60875	semidirect
632. #485	C₂×D₇₉	semidirect
633. #485	C₂×D₇₉	semidirect
634. #484	C₂×D₇₉	semidirect
635. #483	C₂×D₇₉	semidirect
644. #482	C₂×D₇₉	semidirect
645. #482	C₂×D₇₉	semidirect
647. #481	C₂×D₇₉	semidirect
649. #480	C₂×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
#23777137	2
#23776805	2
#23774702	2
#23774687	2
#23774657	2
#23774649	2
#23774644	2
#23774595	2
#23774582	2
#23774534	2
#23773940	2
#23773932	2
#23773758	2
#23773340	2
#23773329	2
C₂×#19098888	2
#23773260	2
#23773249	2
#23773234	2
#23772054	2
C₇₉×#3091	2
#60875	79