Subgroups — #35153304

Order 20224.

1658 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23776978	C₂	1	1	yes	maximal, characteristic
2	#23772503	C₂	1	2	yes	maximal, complemented
3	#23772503	C₂	1	2	yes	maximal, complemented
4	#23772500	C₂	1	2	yes	maximal, complemented
5	#23772493	C₂	1	2	yes	maximal, complemented
6	#23772493	C₂	1	2	yes	maximal, complemented
7	#23772491	C₂	1	2	yes	maximal, complemented
8	#23772486	C₂	1	2	yes	maximal, complemented
9	#23772482	C₂	1	2	yes	maximal, complemented
10	M₁₆×Dic₁₅₈	C₂	1	1	yes	maximal, characteristic, complemented
11	#23772346	C₂	1	1	yes	maximal, characteristic, complemented
12	#23772346	C₂	1	1	yes	maximal, characteristic, complemented
13	#23772341	C₂	1	1	yes	maximal, characteristic, complemented
14	#23772338	C₂	1	1	yes	maximal, characteristic, complemented
15	#23772332	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#19098692	C₂	1	1	yes	maximal, characteristic, complemented
17	#23772065	C₂	1	1	yes	maximal, characteristic
18	#23772064	C₂	1	1	yes	maximal, characteristic
19	#23772064	C₂	1	1	yes	maximal, characteristic
20	#23772052	C₂	1	1	yes	maximal, characteristic
21	#23772050	C₂	1	1	yes	maximal, characteristic
22	#23772043	C₂	1	1	yes	maximal, characteristic
23	C₇₉×#2962	C₂	1	1	yes	maximal, characteristic, complemented
24	#19099293	C₄	1	1	yes	characteristic
25	#19099290	C₄	1	1	yes	characteristic
26	#19099290	C₄	1	1	yes	characteristic
27	#19099288	C₄	1	1	yes	characteristic
28	#19099274	C₄	1	1	yes	characteristic
29	#19099271	C₄	1	2	yes	—
30	#19099269	C₄	1	1	yes	characteristic
31	#19099269	C₄	1	1	yes	characteristic
32	#19099267	C₄	1	2	yes	—
33	#19099267	C₄	1	2	yes	—
34	#19099228	C₄	1	1	yes	characteristic
35	#19099226	C₄	1	2	yes	—
36	#19099117	C₂²	1	2	yes	—
37	#19099117	C₂²	1	2	yes	—
38	#19099117	C₂²	1	2	yes	—
39	#19099116	C₂²	1	1	yes	characteristic
40	#19099116	C₂²	1	1	yes	characteristic
41	C₄×#11929624	C₂²	1	1	yes	characteristic
42	#19099031	C₂²	1	1	yes	characteristic
43	#19099031	C₂²	1	1	yes	characteristic
44	C₂×C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic
45	C₄×Q₈×D₇₉	C₂²	1	2	yes	—
46	#19098694	C₂²	1	2	yes	—
47	#19098694	C₂²	1	2	yes	—
48	#19098694	C₂²	1	2	yes	—
49	#19098694	C₂²	1	2	yes	—
50	#19098693	C₂²	1	2	yes	—
51	#19098693	C₂²	1	2	yes	—
52	#19098693	C₂²	1	2	yes	—
53	#19098692	C₂²	1	1	yes	characteristic
54	#19098692	C₂²	1	2	yes	—
55	#19098692	C₂²	1	1	yes	characteristic
56	#19098692	C₂²	1	2	yes	—
57	#19098692	C₂²	1	1	yes	characteristic
58	#19098692	C₂²	1	1	yes	characteristic
59	#19098692	C₂²	1	1	yes	characteristic
60	#19098692	C₂²	1	2	yes	—
61	#19098692	C₂²	1	2	yes	—
62	#19098692	C₂²	1	1	yes	characteristic
63	#19098692	C₂²	1	1	yes	characteristic
64	#19098692	C₂²	1	1	yes	characteristic
65	#19098691	C₂²	1	2	yes	—
66	#19098691	C₂²	1	2	yes	—
67	#19098691	C₂²	1	2	yes	—
68	#19098691	C₂²	1	2	yes	—
69	#19098691	C₂²	1	2	yes	—
70	#19098691	C₂²	1	2	yes	—
71	#19098690	C₂²	1	2	yes	—
72	#19098690	C₂²	1	2	yes	—
73	C₈×Dic₁₅₈	C₂²	1	2	yes	—
74	C₈×Dic₁₅₈	C₂²	1	2	yes	—
75	C₈×Dic₁₅₈	C₂²	1	2	yes	—
76	#19098687	C₂²	1	2	yes	—
77	#19098687	C₂²	1	2	yes	—
78	#19098625	C₂²	1	2	yes	—
79	#19098625	C₂²	1	2	yes	—
80	#19098623	C₂²	1	2	yes	—
81	#19098623	C₂²	1	2	yes	—
82	#19098623	C₂²	1	2	yes	—
83	#19098623	C₂²	1	2	yes	—
84	#19098623	C₂²	1	2	yes	—
85	#19098623	C₂²	1	2	yes	—
86	#19098622	C₂²	1	2	yes	—
87	#19098622	C₂²	1	2	yes	—
88	#19098622	C₂²	1	2	yes	—
89	#19098622	C₂²	1	2	yes	—
90	#19098619	C₂²	1	2	yes	—
91	#19098619	C₂²	1	2	yes	—
92	#19098619	C₂²	1	2	yes	—
93	#19098618	C₂²	1	2	yes	—
94	#19098618	C₂²	1	2	yes	—
95	#19098618	C₂²	1	2	yes	—
96	#19098618	C₂²	1	2	yes	—
97	#19098615	C₂²	1	2	yes	—
98	#19098615	C₂²	1	2	yes	—
99	#19098615	C₂²	1	2	yes	—
100	#19098614	C₂²	1	2	yes	—
101	#19098614	C₂²	1	2	yes	—
102	#19098591	C₂²	1	1	yes	characteristic
103	#19098591	C₂²	1	1	yes	characteristic
104	#19098590	C₂²	1	1	yes	characteristic
105	#19098590	C₂²	1	1	yes	characteristic
106	#19098587	C₂²	1	1	yes	characteristic
107	#19098586	C₂²	1	1	yes	characteristic
108	#19098586	C₂²	1	1	yes	characteristic
109	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
110	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
111	#19098531	C₂²	1	1	yes	characteristic
112	#19098531	C₂²	1	1	yes	characteristic
113	#19098529	C₂²	1	1	yes	characteristic
114	#19098529	C₂²	1	1	yes	characteristic
115	#19098519	C₂²	1	1	yes	characteristic
116	#19098519	C₂²	1	1	yes	characteristic
117	#19098518	C₂²	1	1	yes	characteristic
118	#19098518	C₂²	1	1	yes	characteristic
119	M₁₆×Dic₇₉	C₂²	1	1	yes	characteristic
120	M₁₆×Dic₇₉	C₂²	1	1	yes	characteristic
121	C₂×#14579072	C₂²	1	1	yes	characteristic
122	C₂×#14579071	C₂²	1	1	yes	characteristic
123	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
124	#533×C₇₉	C₂²	1	1	yes	characteristic
125	#446×C₇₉	C₂²	1	2	yes	—
126	#446×C₇₉	C₂²	1	2	yes	—
127	#446×C₇₉	C₂²	1	2	yes	—
128	C₈×Q₈×C₇₉	C₂²	1	2	yes	—
129	#424×C₇₉	C₂²	1	1	yes	characteristic
130	#424×C₇₉	C₂²	1	1	yes	characteristic
131	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
132	#405×C₇₉	C₂²	1	1	yes	characteristic
133	#405×C₇₉	C₂²	1	1	yes	characteristic
134	C₄×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
135	C₂×#11929624	C₂³	1	1	yes	characteristic
136	C₂²×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
137	C₂×Q₈×D₇₉	C₂×C₄	1	2	yes	—
138	C₂×#11929608	C₂³	1	1	yes	characteristic
139	C₂×#11929608	C₂³	1	1	yes	characteristic
140	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
141	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
142	#14579160	C₂×C₄	1	2	yes	—
143	#14579160	C₂×C₄	1	2	yes	—
144	#14579160	C₂×C₄	1	1	yes	characteristic
145	#14579160	C₂×C₄	1	1	yes	characteristic
146	#14579160	C₂×C₄	1	1	yes	characteristic
147	#14579160	C₂×C₄	1	1	yes	characteristic
148	#14579160	C₂×C₄	1	2	yes	—
149	#14579159	C₂×C₄	1	2	yes	—
150	#14579159	C₂×C₄	1	2	yes	—
151	#14579159	C₂×C₄	1	2	yes	—
152	#14579152	C₂×C₄	1	1	yes	characteristic
153	#14579152	C₂×C₄	1	1	yes	characteristic
154	#14579152	C₂×C₄	1	1	yes	characteristic
155	#14579152	C₂×C₄	1	1	yes	characteristic
156	#14579151	C₂×C₄	1	2	yes	—
157	#14579151	C₂×C₄	1	2	yes	—
158	#14579151	C₂×C₄	1	2	yes	—
159	#14579151	C₂×C₄	1	2	yes	—
160	#14579151	C₂×C₄	1	2	yes	—
161	#14579151	C₂×C₄	1	2	yes	—
162	#14579141	C₂×C₄	1	2	yes	—
163	#14579141	C₂×C₄	1	2	yes	—
164	#14579141	C₂×C₄	1	2	yes	—
165	#14579139	C₂×C₄	1	2	yes	—
166	#14579139	C₂×C₄	1	2	yes	—
167	#14579139	C₂×C₄	1	2	yes	—
168	#14579139	C₂×C₄	1	2	yes	—
169	#14579139	C₂×C₄	1	2	yes	—
170	#14579139	C₂×C₄	1	2	yes	—
171	#14579138	C₂×C₄	1	2	yes	—
172	#14579138	C₂×C₄	1	2	yes	—
173	#14579138	C₂×C₄	1	2	yes	—
174	#14579138	C₂×C₄	1	2	yes	—
175	#14579137	C₂×C₄	1	2	yes	—
176	#14579137	C₂×C₄	1	2	yes	—
177	#14579137	C₂×C₄	1	2	yes	—
178	Q₈×Dic₇₉	C₂×C₄	1	2	yes	—
179	C₄×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
180	C₄×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
181	C₄×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
182	C₄×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
183	C₄×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
184	C₄×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
185	C₄×Dic₁₅₈	C₂³	1	2	yes	—
186	C₄×Dic₁₅₈	C₂³	1	2	yes	—
187	C₄×Dic₁₅₈	C₂³	1	1	yes	characteristic
188	C₄×Dic₁₅₈	C₂³	1	2	yes	—
189	C₄×Dic₁₅₈	C₂³	1	2	yes	—
190	C₄×Dic₁₅₈	C₂³	1	1	yes	characteristic
191	C₄×Dic₁₅₈	C₂³	1	1	yes	characteristic
192	C₄×Dic₁₅₈	C₂³	1	1	yes	characteristic
193	#14579126	C₂×C₄	1	2	yes	—
194	#14579126	C₂×C₄	1	2	yes	—
195	#14579126	C₂×C₄	1	2	yes	—
196	#14579126	C₂×C₄	1	1	yes	characteristic
197	#14579126	C₂×C₄	1	1	yes	characteristic
198	#14579126	C₂×C₄	1	1	yes	characteristic
199	#14579126	C₂×C₄	1	1	yes	characteristic
200	C₄×D₃₁₆	C₂×C₄	1	1	yes	characteristic
201	C₄×D₃₁₆	C₂×C₄	1	1	yes	characteristic
202	#14579123	C₂×C₄	1	1	yes	characteristic
203	#14579123	C₂×C₄	1	1	yes	characteristic
204	#14579123	C₂×C₄	1	1	yes	characteristic
205	#14579123	C₂×C₄	1	1	yes	characteristic
206	C₄×C₂²⋊D₇₉	C₂×C₄	1	2	yes	—
207	C₄×C₂²⋊D₇₉	C₂×C₄	1	2	yes	—
208	(C₂²⋊D₇₉)⋊C₄	C₂×C₄	1	2	yes	—
209	(C₂²⋊D₇₉)⋊C₄	C₂×C₄	1	2	yes	—
210	(C₂²⋊D₇₉)⋊C₄	C₂×C₄	1	2	yes	—
211	(C₂²⋊D₇₉)⋊C₄	C₂×C₄	1	2	yes	—
212	#14579120	C₂³	1	1	yes	characteristic
213	#14579118	C₂³	1	2	yes	—
214	#14579118	C₂³	1	2	yes	—
215	#14579118	C₂³	1	2	yes	—
216	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
217	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
218	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
219	C₄⋊C₄×D₇₉	C₂×C₄	1	2	yes	—
220	C₄⋊C₄×D₇₉	C₂×C₄	1	2	yes	—
221	C₄⋊C₄×D₇₉	C₂×C₄	1	2	yes	—
222	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
223	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
224	C₄²×D₇₉	C₂³	1	2	yes	—
225	C₄²×D₇₉	C₂³	1	2	yes	—
226	C₄²×D₇₉	C₂³	1	2	yes	—
227	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
228	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
229	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
230	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
231	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
232	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
233	Dic₇₉⋊C₈	C₂³	1	1	yes	characteristic
234	Dic₇₉⋊C₈	C₂³	1	1	yes	characteristic
235	Dic₇₉⋊C₈	C₂³	1	2	yes	—
236	Dic₇₉⋊C₈	C₂³	1	2	yes	—
237	Dic₇₉⋊C₈	C₂³	1	1	yes	characteristic
238	Dic₇₉⋊C₈	C₂³	1	1	yes	characteristic
239	Dic₇₉⋊C₈	C₂³	1	2	yes	—
240	Dic₇₉⋊C₈	C₂³	1	2	yes	—
241	Dic₇₉⋊C₈	C₂³	1	2	yes	—
242	Dic₇₉⋊C₈	C₂³	1	2	yes	—
243	Dic₇₉⋊C₈	C₂³	1	2	yes	—
244	Dic₇₉⋊C₈	C₂³	1	1	yes	characteristic
245	Dic₇₉⋊C₈	C₂³	1	1	yes	characteristic
246	Dic₇₉⋊C₈	C₂³	1	2	yes	—
247	Dic₇₉⋊C₈	C₂³	1	1	yes	characteristic
248	Dic₇₉⋊C₈	C₂³	1	1	yes	characteristic
249	(C₂×D₇₉)⋊C₈	C₂³	1	2	yes	—
250	(C₂×D₇₉)⋊C₈	C₂³	1	2	yes	—
251	(C₂×D₇₉)⋊C₈	C₂³	1	2	yes	—
252	(C₂×D₇₉)⋊C₈	C₂³	1	2	yes	—
253	(C₂×D₇₉)⋊C₈	C₂³	1	2	yes	—
254	(C₂×D₇₉)⋊C₈	C₂³	1	2	yes	—
255	(C₂×D₇₉)⋊C₈	C₂³	1	2	yes	—
256	(C₂×D₇₉)⋊C₈	C₂³	1	2	yes	—
257	#14579072	C₂³	1	1	yes	characteristic
258	#14579072	C₂³	1	1	yes	characteristic
259	#14579072	C₂³	1	1	yes	characteristic
260	#14579072	C₂³	1	1	yes	characteristic
261	#14579072	C₂³	1	2	yes	—
262	#14579072	C₂³	1	2	yes	—
263	#14579071	C₂³	1	2	yes	—
264	#14579071	C₂³	1	2	yes	—
265	#14579071	C₂³	1	2	yes	—
266	#14579071	C₂³	1	2	yes	—
267	#14579071	C₂³	1	1	yes	characteristic
268	#14579071	C₂³	1	1	yes	characteristic
269	#14579071	C₂³	1	1	yes	characteristic
270	#14579071	C₂³	1	1	yes	characteristic
271	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
272	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
273	C₈×Dic₇₉	C₂³	1	2	yes	—
274	C₈×Dic₇₉	C₂³	1	2	yes	—
275	C₈×Dic₇₉	C₂³	1	2	yes	—
276	C₈×Dic₇₉	C₂³	1	2	yes	—
277	C₈×Dic₇₉	C₂³	1	1	yes	characteristic
278	C₈×Dic₇₉	C₂³	1	1	yes	characteristic
279	C₈×Dic₇₉	C₂³	1	1	yes	characteristic
280	C₈×Dic₇₉	C₂³	1	1	yes	characteristic
281	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
282	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
283	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
284	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
285	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
286	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
287	#125×C₇₉	C₂×C₄	1	1	yes	characteristic
288	#125×C₇₉	C₂×C₄	1	1	yes	characteristic
289	C₂²⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
290	C₂²⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
291	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
292	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
293	#117×C₇₉	C₂³	1	1	yes	characteristic
294	#117×C₇₉	C₂³	1	1	yes	characteristic
295	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
296	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
297	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
298	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
299	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
300	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
301	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
302	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
303	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
304	#97×C₇₉	C₂³	1	2	yes	—
305	#97×C₇₉	C₂³	1	2	yes	—
306	#97×C₇₉	C₂³	1	2	yes	—
307	C₄×C₈×C₇₉	C₂³	1	2	yes	—
308	C₄×C₈×C₇₉	C₂³	1	2	yes	—
309	C₄×C₈×C₇₉	C₂³	1	2	yes	—
310	#11929624	—	2	2	no	—
311	#11929624	—	2	2	no	—
312	C₂×Dic₁₅₈	—	4	2	no	—
313	C₂×Dic₁₅₈	C₂²×C₄	1	1	yes	characteristic
314	C₂×Dic₁₅₈	C₂²×C₄	1	2	yes	—
315	C₂×Dic₁₅₈	C₂²×C₄	1	1	yes	characteristic
316	C₂×Dic₁₅₈	C₂²×C₄	1	1	yes	characteristic
317	C₂×Dic₁₅₈	C₂²×C₄	1	2	yes	—
318	C₂×Dic₁₅₈	C₂²×C₄	1	1	yes	characteristic
319	C₂×Dic₁₅₈	C₂²×C₄	1	1	yes	characteristic
320	C₂×Dic₁₅₈	C₂²×C₄	1	2	yes	—
321	C₂×Dic₁₅₈	C₂²×C₄	1	2	yes	—
322	Q₈×D₇₉	—	4	4	no	—
323	C₂×D₃₁₆	C₂²×C₄	1	1	yes	characteristic
324	C₂×C₂²⋊D₇₉	C₂²×C₄	1	2	yes	—
325	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
326	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
327	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
328	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
329	C₂×C₄×D₇₉	C₂²×C₄	1	2	yes	—
330	C₂×C₄×D₇₉	C₂²×C₄	1	2	yes	—
331	C₂×C₄×D₇₉	C₂²×C₄	1	2	yes	—
332	C₂×C₄×D₇₉	C₂²×C₄	1	2	yes	—
333	C₂×C₄×D₇₉	C₂²×C₄	1	2	yes	—
334	C₂×C₄×D₇₉	C₂²×C₄	1	2	yes	—
335	C₂×C₄×D₇₉	C₂⁴	1	2	yes	—
336	#11929608	—	2	2	no	—
337	#11929608	—	2	2	no	—
338	C₂×C₇₉⋊C₈	—	2	2	no	—
339	C₂×C₇₉⋊C₈	—	2	2	no	—
340	C₂×C₇₉⋊C₈	C₂⁴	1	2	yes	—
341	C₂×C₇₉⋊C₈	C₂⁴	1	2	yes	—
342	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
343	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
344	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
345	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
346	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
347	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
348	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
349	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
350	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
351	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
352	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
353	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
354	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
355	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
356	Dic₇₉⋊C₄	C₂²×C₄	1	1	yes	characteristic
357	Dic₇₉⋊C₄	C₂²×C₄	1	1	yes	characteristic
358	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
359	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
360	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
361	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
362	Dic₇₉⋊C₄	C₂²×C₄	1	1	yes	characteristic
363	Dic₇₉⋊C₄	C₂²×C₄	1	1	yes	characteristic
364	Dic₇₉⋊C₄	C₂²×C₄	1	1	yes	characteristic
365	Dic₇₉⋊C₄	C₂²×C₄	1	1	yes	characteristic
366	Dic₇₉⋊C₄	C₂²×C₄	1	1	yes	characteristic
367	Dic₇₉⋊C₄	C₂²×C₄	1	1	yes	characteristic
368	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
369	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
370	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
371	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
372	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
373	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
374	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
375	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
376	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
377	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
378	C₂²⋊Dic₇₉	C₂²×C₄	1	2	yes	—
379	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
380	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
381	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
382	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
383	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
384	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
385	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
386	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
387	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
388	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
389	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
390	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
391	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
392	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
393	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
394	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
395	C₄×Dic₇₉	C₂⁴	1	1	yes	characteristic
396	C₄×Dic₇₉	C₂⁴	1	2	yes	—
397	C₄×Dic₇₉	C₂⁴	1	1	yes	characteristic
398	C₄×Dic₇₉	C₂⁴	1	1	yes	characteristic
399	C₄×Dic₇₉	C₂⁴	1	1	yes	characteristic
400	C₂×Q₈×C₇₉	C₂²×C₄	1	2	yes	—
401	C₂×Q₈×C₇₉	C₂²×C₄	1	2	yes	—
402	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
403	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
404	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
405	M₁₆×C₇₉	—	2	2	no	—
406	M₁₆×C₇₉	—	2	2	no	—
407	C₂×C₈×C₇₉	—	2	2	no	—
408	C₂×C₈×C₇₉	—	2	2	no	—
409	C₂×C₈×C₇₉	C₂⁴	1	2	yes	—
410	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
411	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
412	C₂×C₈×C₇₉	C₂⁴	1	2	yes	—
413	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
414	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
416	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
417	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
418	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
419	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
420	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
421	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
422	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
423	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
424	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
425	C₂²⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
426	C₂²⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
427	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
428	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
429	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
430	C₄²×C₇₉	C₂⁴	1	2	yes	—
431	C₄²×C₇₉	C₂⁴	1	2	yes	—
432	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
433	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
434	C₂²×D₇₉	C₂³×C₄	1	2	yes	—
435	Q₈×C₇₉	—	4	2	no	—
436	Q₈×C₇₉	—	4	2	no	—
437	C₂×C₄×C₇₉	—	4	1	no	—
438	C₂×C₄×C₇₉	—	4	1	no	—
439	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
440	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
441	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
442	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
443	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
444	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
445	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
446	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
447	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
448	C₂×C₄×C₇₉	2₋¹⁺⁴	1	2	yes	—
449	C₂×C₄×C₇₉	2₋¹⁺⁴	1	2	yes	—
450	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
451	C₂²⋊D₇₉	—	2	4	no	—
452	C₂×Dic₇₉	—	2	2	no	—
453	C₂×Dic₇₉	—	4	1	no	—
454	C₂×Dic₇₉	—	4	1	no	—
455	C₂×Dic₇₉	—	4	1	no	—
456	C₂×Dic₇₉	C₂³×C₄	1	2	yes	—
457	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
458	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
459	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
460	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
461	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
462	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
463	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
464	C₂×Dic₇₉	C₂³×C₄	1	2	yes	—
465	C₂×Dic₇₉	C₂³×C₄	1	2	yes	—
466	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
467	D₃₁₆	—	2	2	no	—
468	C₄×D₇₉	—	2	2	no	—
469	C₄×D₇₉	—	2	2	no	—
470	C₄×D₇₉	—	2	4	no	—
471	C₄×D₇₉	—	4	2	no	—
472	C₄×D₇₉	—	4	2	no	—
473	C₄×D₇₉	—	4	2	no	—
474	C₄×D₇₉	—	4	2	no	—
475	C₄×D₇₉	—	4	2	no	—
476	Dic₁₅₈	—	2	2	no	—
477	Dic₁₅₈	—	2	2	no	—
478	Dic₁₅₈	—	2	4	no	—
479	Dic₁₅₈	—	2	2	no	—
480	Dic₁₅₈	—	4	2	no	—
481	Dic₁₅₈	—	4	1	no	—
482	Dic₁₅₈	—	4	1	no	—
483	Dic₁₅₈	—	4	2	no	—
484	Dic₁₅₈	—	4	2	no	—
485	C₈×C₇₉	—	2	1	no	—
486	C₈×C₇₉	—	2	1	no	—
487	C₈×C₇₉	—	2	1	no	—
488	C₈×C₇₉	—	2	1	no	—
489	C₈×C₇₉	—	2	2	no	—
490	C₈×C₇₉	—	2	2	no	—
491	C₇₉⋊C₈	—	2	1	no	—
492	C₇₉⋊C₈	—	2	1	no	—
493	C₇₉⋊C₈	—	2	1	no	—
494	C₇₉⋊C₈	—	2	1	no	—
495	C₇₉⋊C₈	—	2	2	no	—
496	C₇₉⋊C₈	—	2	2	no	—
497	C₂²×C₇₉	—	2	1	no	—
498	C₂²×C₇₉	—	2	1	no	—
499	C₂²×C₇₉	#519	1	2	yes	—
500	C₂²×C₇₉	C₂⁴×C₄	1	1	yes	characteristic
501	C₂×D₇₉	—	2	2	no	—
502	C₂×D₇₉	—	2	2	no	—
503	C₂×D₇₉	—	2	2	no	—
504	C₄×C₇₉	—	2	1	no	—
505	C₄×C₇₉	—	2	1	no	—
506	C₄×C₇₉	—	2	2	no	—
507	C₄×C₇₉	—	2	2	no	—
508	C₄×C₇₉	—	2	1	no	—
509	C₄×C₇₉	—	2	1	no	—
510	C₄×C₇₉	—	2	2	no	—
511	C₄×C₇₉	—	2	2	no	—
512	C₄×C₇₉	#519	1	2	yes	—
513	C₄×C₇₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
514	C₄×C₇₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
515	Dic₇₉	—	2	2	no	—
516	Dic₇₉	—	2	1	no	—
517	Dic₇₉	—	2	2	no	—
518	Dic₇₉	—	2	1	no	—
519	Dic₇₉	—	2	1	no	—
520	Dic₇₉	—	2	2	no	—
521	Dic₇₉	—	2	1	no	—
522	Dic₇₉	—	2	1	no	—
523	Dic₇₉	—	2	1	no	—
524	Dic₇₉	—	2	1	no	—
525	Dic₇₉	#568	1	2	yes	—
526	#60254	—	79	1	no	maximal, Sylow
527	C₂×C₇₉	—	2	2	no	—
528	C₂×C₇₉	C₂×#519	1	1	yes	characteristic
529	C₂×C₇₉	C₂×#568	1	1	yes	characteristic
530	C₂×C₇₉	#3573	1	1	yes	characteristic
531	D₇₉	—	4	2	no	—
532	Q₈×#41	—	79	1	no	—
533	#2987	—	79	2	no	—
534	#2987	—	79	2	no	—
535	#2986	—	79	2	no	—
536	#2985	—	79	2	no	—
537	#2985	—	79	2	no	—
538	#2985	—	79	2	no	—
539	#2984	—	79	2	no	—
540	#2983	—	79	2	no	—
541	Q₈×M₁₆	—	79	1	no	—
542	#2962	—	79	1	no	—
543	#2962	—	79	1	no	—
544	#2962	D₇₉	1	1	yes	characteristic, complemented
545	#2961	—	79	1	no	—
546	#2961	—	79	1	no	—
547	#2960	—	79	1	no	—
548	C₂×#446	—	79	1	no	—
549	#2925	—	79	1	no	—
550	#2925	—	79	1	no	—
551	#2925	—	79	1	no	—
552	#2923	—	79	1	no	—
553	#2923	—	79	1	no	—
554	#2922	—	79	1	no	—
555	C₇₉	#60254	1	1	yes	characteristic, complemented, Sylow
556	Q₈²	—	79	1	no	—
557	#557	—	79	1	no	—
558	#557	—	79	1	no	—
559	#557	—	79	1	no	—
560	#554	—	79	1	no	—
561	#554	—	79	1	no	—
562	#554	—	79	1	no	—
563	#554	—	79	2	no	—
564	#554	—	79	2	no	—
565	#554	—	79	2	no	—
566	D₄×Q₈	—	79	1	no	—
567	D₄×Q₈	—	79	2	no	—
568	#533	—	79	2	no	—
569	#533	—	79	2	no	—
570	#533	—	79	2	no	—
571	#533	—	79	1	no	—
572	#533	—	79	1	no	—
573	#533	C₂×D₇₉	1	1	yes	characteristic
574	C₄×#41	—	79	1	no	—
575	C₄×#41	—	79	1	no	—
576	C₄×#41	—	79	1	no	—
577	C₂×C₄×Q₈	—	79	2	no	—
578	C₂×C₄×Q₈	—	79	1	no	—
579	#446	—	79	2	no	—
580	#446	—	79	2	no	—
581	#446	—	79	2	no	—
582	#446	—	79	2	no	—
583	#446	—	79	2	no	—
584	#446	—	79	2	no	—
585	#446	—	79	1	no	—
586	#446	—	79	1	no	—
587	#446	—	79	1	no	—
588	#446	—	79	1	no	—
589	#446	—	79	1	no	—
590	#446	—	79	1	no	—
591	#446	—	79	1	no	—
592	#446	—	79	1	no	—
593	#446	—	79	2	no	—
594	#446	—	79	2	no	—
595	#446	—	79	2	no	—
596	#446	—	79	2	no	—
597	#446	—	79	2	no	—
598	#446	—	79	2	no	—
599	#446	—	79	2	no	—
600	#446	—	79	2	no	—
601	#446	—	79	2	no	—
602	#446	—	79	2	no	—
603	#446	—	79	2	no	—
604	#446	—	79	2	no	—
605	#446	—	79	2	no	—
606	#446	C₂×D₇₉	1	2	yes	—
607	#446	C₂×D₇₉	1	2	yes	—
608	#446	C₂×D₇₉	1	2	yes	—
609	C₈×Q₈	—	79	2	no	—
610	C₈×Q₈	—	79	2	no	—
611	C₈×Q₈	—	79	2	no	—
612	C₈×Q₈	—	79	2	no	—
613	C₈×Q₈	—	79	2	no	—
614	C₈×Q₈	C₂×D₇₉	1	2	yes	—
615	#433	—	79	2	no	—
616	#433	—	79	2	no	—
617	#433	—	79	2	no	—
618	#433	—	79	2	no	—
619	#433	—	79	2	no	—
620	#433	—	79	2	no	—
621	#433	—	79	2	no	—
622	#433	—	79	2	no	—
623	#433	—	79	2	no	—
624	#433	—	79	2	no	—
625	#433	—	79	2	no	—
626	#433	—	79	2	no	—
627	#432	—	79	2	no	—
628	#432	—	79	2	no	—
629	#432	—	79	2	no	—
630	#432	—	79	2	no	—
631	#432	—	79	2	no	—
632	#432	—	79	2	no	—
633	#432	—	79	2	no	—
634	#431	—	79	2	no	—
635	#431	—	79	2	no	—
636	#431	—	79	2	no	—
637	#431	—	79	2	no	—
638	#431	—	79	2	no	—
639	#424	—	79	1	no	—
640	#424	—	79	1	no	—
641	#424	—	79	1	no	—
642	#424	—	79	1	no	—
643	#424	C₂×D₇₉	1	1	yes	characteristic
644	#424	C₂×D₇₉	1	1	yes	characteristic
645	#423	—	79	1	no	—
646	#423	—	79	1	no	—
647	#423	—	79	1	no	—
648	C₂×C₄⋊C₈	—	79	1	no	—
649	C₂×C₄⋊C₈	—	79	1	no	—
650	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
651	#408	—	79	1	no	—
652	#408	—	79	1	no	—
653	#408	—	79	1	no	—
654	#408	—	79	1	no	—
655	#405	—	79	1	no	—
656	#405	—	79	1	no	—
657	#405	—	79	1	no	—
658	#405	—	79	1	no	—
659	#405	C₂×D₇₉	1	1	yes	characteristic
660	#405	C₂×D₇₉	1	1	yes	characteristic
661	C₄×M₁₆	—	79	1	no	—
662	C₄×M₁₆	—	79	1	no	—
663	C₄×M₁₆	C₂×D₇₉	1	1	yes	characteristic
664	C₂×#97	—	79	1	no	—
665	C₂×#97	—	79	1	no	—
666	C₂×C₄×C₈	—	79	1	no	—
667	C₂×#41	—	79	1	no	—
668	C₂²×Q₈	—	79	2	no	—
669	C₂²×Q₈	—	79	1	no	—
670	C₂×M₁₆	—	79	1	no	—
671	C₂×M₁₆	—	79	1	no	—
672	C₂×M₁₆	C₂²×D₇₉	1	1	yes	characteristic
673	C₂×M₁₆	C₂²×D₇₉	1	1	yes	characteristic
674	C₂²×C₈	—	79	1	no	—
675	C₂²×C₈	—	79	1	no	—
676	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
677	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
678	C₄⋊Q₈	—	79	2	no	—
679	C₄⋊Q₈	—	79	2	no	—
680	C₄⋊Q₈	—	79	2	no	—
681	C₄⋊Q₈	—	79	2	no	—
682	C₄⋊Q₈	—	79	2	no	—
683	C₄⋊Q₈	—	79	1	no	—
684	C₄⋊Q₈	—	79	1	no	—
685	C₄⋊Q₈	—	79	1	no	—
686	C₄⋊Q₈	—	79	1	no	—
687	C₄⋊Q₈	—	79	2	no	—
688	C₄⋊Q₈	C₄×D₇₉	1	1	yes	characteristic
689	C₄⋊Q₈	C₄×D₇₉	1	1	yes	characteristic
690	#125	—	79	2	no	—
691	#125	—	79	2	no	—
692	#125	—	79	2	no	—
693	#125	—	79	2	no	—
694	#125	—	79	2	no	—
695	#125	—	79	2	no	—
696	#125	—	79	1	no	—
697	#125	—	79	1	no	—
698	#125	—	79	1	no	—
699	#125	—	79	1	no	—
700	#125	C₄×D₇₉	1	1	yes	characteristic
701	#125	C₄×D₇₉	1	1	yes	characteristic
702	C₂²⋊Q₈	—	79	2	no	—
703	C₂²⋊Q₈	—	79	2	no	—
704	C₂²⋊Q₈	—	79	2	no	—
705	C₂²⋊Q₈	—	79	2	no	—
706	C₂²⋊Q₈	—	79	2	no	—
707	C₂²⋊Q₈	—	79	2	no	—
708	C₂²⋊Q₈	—	79	2	no	—
709	C₂²⋊Q₈	—	79	2	no	—
710	C₂²⋊Q₈	—	79	2	no	—
711	C₂²⋊Q₈	—	79	2	no	—
712	C₂²⋊Q₈	—	79	2	no	—
713	C₂²⋊Q₈	—	79	2	no	—
714	C₂²⋊Q₈	—	79	2	no	—
715	C₂²⋊Q₈	—	79	2	no	—
716	C₂²⋊Q₈	—	79	2	no	—
717	C₂²⋊Q₈	—	79	2	no	—
718	C₂²⋊Q₈	C₄×D₇₉	1	2	yes	—
719	C₂²⋊Q₈	C₄×D₇₉	1	2	yes	—
720	C₄×Q₈	—	79	2	no	—
721	C₄×Q₈	—	79	2	no	—
722	C₄×Q₈	—	79	2	no	—
723	C₄×Q₈	—	79	2	no	—
724	C₄×Q₈	—	79	1	no	—
725	C₄×Q₈	—	79	1	no	—
726	C₄×Q₈	—	79	1	no	—
727	C₄×Q₈	—	79	1	no	—
728	C₄×Q₈	—	79	1	no	—
729	C₄×Q₈	—	79	1	no	—
730	C₄×Q₈	—	79	1	no	—
731	C₄×Q₈	—	79	1	no	—
732	C₄×Q₈	—	79	1	no	—
733	C₄×Q₈	—	79	1	no	—
734	C₄×Q₈	—	79	1	no	—
735	C₄×Q₈	—	79	2	no	—
736	C₄×Q₈	—	79	1	no	—
737	C₄×Q₈	—	79	1	no	—
738	C₄×Q₈	—	79	2	no	—
739	C₄×Q₈	—	79	1	no	—
740	C₄×Q₈	—	79	2	no	—
741	C₄×Q₈	—	79	2	no	—
742	C₄×Q₈	C₂²×D₇₉	1	2	yes	—
743	C₄×Q₈	C₂²×D₇₉	1	2	yes	—
744	C₄×D₄	—	79	2	no	—
745	C₄×D₄	—	79	2	no	—
746	C₄×D₄	—	79	1	no	—
747	C₄×D₄	—	79	1	no	—
748	C₄×D₄	—	79	1	no	—
749	C₄×D₄	—	79	1	no	—
750	C₄×D₄	—	79	2	no	—
751	C₄×D₄	—	79	2	no	—
752	C₄×D₄	—	79	2	no	—
753	C₄×D₄	—	79	2	no	—
754	C₄×D₄	—	79	1	no	—
755	C₄×D₄	—	79	1	no	—
756	#117	—	79	1	no	—
757	#117	—	79	2	no	—
758	#117	—	79	2	no	—
759	#117	—	79	2	no	—
760	#117	C₂²×D₇₉	1	1	yes	characteristic
761	#117	C₂²×D₇₉	1	1	yes	characteristic
762	C₂×C₄⋊C₄	—	79	1	no	—
763	C₂×C₄⋊C₄	—	79	1	no	—
764	C₂×C₄⋊C₄	—	79	1	no	—
765	C₂×C₄⋊C₄	—	79	2	no	—
766	C₂×C₄⋊C₄	—	79	2	no	—
767	C₂×C₄⋊C₄	—	79	2	no	—
768	C₂×C₄²	—	79	1	no	—
769	C₂×C₄²	—	79	1	no	—
770	C₂×C₄²	—	79	2	no	—
771	C₂×C₄²	—	79	2	no	—
772	C₂×C₄²	—	79	2	no	—
773	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
774	C₄⋊C₈	—	79	1	no	—
775	C₄⋊C₈	—	79	1	no	—
776	C₄⋊C₈	—	79	1	no	—
777	C₄⋊C₈	—	79	1	no	—
778	C₄⋊C₈	—	79	1	no	—
779	C₄⋊C₈	—	79	1	no	—
780	C₄⋊C₈	—	79	1	no	—
781	C₄⋊C₈	—	79	1	no	—
782	C₄⋊C₈	—	79	2	no	—
783	C₄⋊C₈	—	79	2	no	—
784	C₄⋊C₈	—	79	2	no	—
785	C₄⋊C₈	—	79	2	no	—
786	C₄⋊C₈	—	79	2	no	—
787	C₄⋊C₈	—	79	2	no	—
788	C₄⋊C₈	—	79	2	no	—
789	C₄⋊C₈	—	79	2	no	—
790	C₄⋊C₈	—	79	2	no	—
791	C₄⋊C₈	—	79	2	no	—
792	C₄⋊C₈	—	79	2	no	—
793	C₄⋊C₈	—	79	2	no	—
794	C₄⋊C₈	—	79	2	no	—
795	C₄⋊C₈	—	79	2	no	—
796	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
797	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
798	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
799	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
800	C₄⋊C₈	C₂²×D₇₉	1	2	yes	—
801	C₄⋊C₈	C₂²×D₇₉	1	2	yes	—
802	C₄⋊C₈	C₂²×D₇₉	1	2	yes	—
803	C₄⋊C₈	C₂²×D₇₉	1	2	yes	—
804	C₂²⋊C₈	—	79	2	no	—
805	C₂²⋊C₈	—	79	2	no	—
806	C₂²⋊C₈	—	79	2	no	—
807	C₂²⋊C₈	—	79	2	no	—
808	C₂²⋊C₈	—	79	2	no	—
809	C₂²⋊C₈	—	79	2	no	—
810	C₂²⋊C₈	—	79	2	no	—
811	C₂²⋊C₈	—	79	2	no	—
812	#97	—	79	1	no	—
813	#97	—	79	1	no	—
814	#97	—	79	1	no	—
815	#97	—	79	1	no	—
816	#97	—	79	2	no	—
817	#97	—	79	2	no	—
818	#97	—	79	2	no	—
819	#97	—	79	2	no	—
820	#97	—	79	1	no	—
821	#97	—	79	1	no	—
822	#97	—	79	1	no	—
823	#97	—	79	1	no	—
824	#97	—	79	2	no	—
825	#97	—	79	2	no	—
826	#97	C₂²×D₇₉	1	2	yes	—
827	#97	C₂²×D₇₉	1	2	yes	—
828	#97	C₂²×D₇₉	1	2	yes	—
829	C₄×C₈	—	79	1	no	—
830	C₄×C₈	—	79	1	no	—
831	C₄×C₈	—	79	1	no	—
832	C₄×C₈	—	79	1	no	—
833	C₄×C₈	—	79	2	no	—
834	C₄×C₈	—	79	2	no	—
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	C₄×C₈	C₂²×D₇₉	1	2	yes	—
840	C₄×C₈	C₂²×D₇₉	1	2	yes	—
841	C₄×C₈	C₂²×D₇₉	1	2	yes	—
842	#41	—	158	2	no	—
843	#41	—	158	2	no	—
844	C₂×Q₈	—	316	2	no	—
845	C₂×Q₈	—	316	4	no	—
846	C₂×Q₈	—	79	2	no	—
847	C₂×Q₈	—	79	1	no	—
848	C₂×Q₈	—	79	1	no	—
849	C₂×Q₈	—	79	2	no	—
850	C₂×Q₈	—	79	2	no	—
851	C₂×Q₈	—	79	1	no	—
852	C₂×Q₈	—	79	1	no	—
853	C₂×Q₈	—	79	2	no	—
854	C₂×Q₈	—	79	1	no	—
855	C₂×Q₈	C₂×C₄×D₇₉	1	2	yes	—
856	C₂×Q₈	C₂×C₄×D₇₉	1	2	yes	—
857	C₂×D₄	—	79	2	no	—
858	C₂×D₄	—	79	1	no	—
859	C₂²×C₄	—	79	1	no	—
860	C₂²×C₄	—	79	1	no	—
861	C₂²×C₄	—	79	1	no	—
862	C₂²×C₄	—	79	2	no	—
863	C₂²×C₄	—	79	2	no	—
864	C₂²×C₄	—	79	2	no	—
865	C₂²×C₄	—	79	2	no	—
866	C₂²×C₄	—	79	2	no	—
867	C₂²×C₄	—	79	1	no	—
868	C₂²×C₄	—	79	2	no	—
869	C₂²×C₄	—	79	2	no	—
870	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
871	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
872	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
873	M₁₆	—	2	2	no	—
874	M₁₆	—	2	2	no	—
875	M₁₆	—	158	2	no	—
876	M₁₆	—	158	2	no	—
877	C₂×C₈	—	2	2	no	—
878	C₂×C₈	—	2	2	no	—
879	C₂×C₈	—	79	2	no	—
880	C₂×C₈	—	79	2	no	—
881	C₂×C₈	—	79	1	no	—
882	C₂×C₈	—	79	1	no	—
883	C₂×C₈	—	79	1	no	—
884	C₂×C₈	—	79	1	no	—
885	C₂×C₈	—	158	2	no	—
886	C₂×C₈	—	158	2	no	—
887	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
888	C₂×C₈	C₂³×D₇₉	1	2	yes	—
889	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
890	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
891	C₂×C₈	C₂³×D₇₉	1	2	yes	—
892	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
893	C₄⋊C₄	—	79	1	no	—
894	C₄⋊C₄	—	79	1	no	—
895	C₄⋊C₄	—	79	2	no	—
896	C₄⋊C₄	—	79	2	no	—
897	C₄⋊C₄	—	79	1	no	—
898	C₄⋊C₄	—	79	1	no	—
899	C₄⋊C₄	—	79	1	no	—
900	C₄⋊C₄	—	79	1	no	—
901	C₄⋊C₄	—	79	2	no	—
902	C₄⋊C₄	—	79	1	no	—
903	C₄⋊C₄	—	79	2	no	—
904	C₄⋊C₄	—	79	1	no	—
905	C₄⋊C₄	—	79	2	no	—
906	C₄⋊C₄	—	79	2	no	—
907	C₄⋊C₄	—	79	2	no	—
908	C₄⋊C₄	—	79	2	no	—
909	C₄⋊C₄	—	79	2	no	—
910	C₄⋊C₄	—	79	2	no	—
911	C₄⋊C₄	—	79	2	no	—
912	C₄⋊C₄	—	79	2	no	—
913	C₄⋊C₄	—	79	2	no	—
914	C₄⋊C₄	—	79	2	no	—
915	C₄⋊C₄	—	79	1	no	—
916	C₄⋊C₄	—	79	2	no	—
917	C₄⋊C₄	—	79	2	no	—
918	C₄⋊C₄	—	79	1	no	—
919	C₄⋊C₄	—	79	1	no	—
920	C₄⋊C₄	—	79	1	no	—
921	C₄⋊C₄	—	79	1	no	—
922	C₄⋊C₄	—	79	1	no	—
923	C₄⋊C₄	—	79	2	no	—
924	C₄⋊C₄	—	79	2	no	—
925	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
926	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
927	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
928	C₄⋊C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
929	C₄⋊C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
930	C₄⋊C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
931	C₄⋊C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
932	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
933	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
934	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
935	C₂²⋊C₄	—	79	2	no	—
936	C₂²⋊C₄	—	79	2	no	—
937	C₂²⋊C₄	—	79	2	no	—
938	C₂²⋊C₄	—	79	2	no	—
939	C₂²⋊C₄	—	79	2	no	—
940	C₂²⋊C₄	—	79	2	no	—
941	C₂²⋊C₄	—	79	2	no	—
942	C₂²⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
943	C₂²⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
944	C₄²	—	79	1	no	—
945	C₄²	—	79	2	no	—
946	C₄²	—	79	1	no	—
947	C₄²	—	79	1	no	—
948	C₄²	—	79	1	no	—
949	C₄²	—	79	2	no	—
950	C₄²	—	79	2	no	—
951	C₄²	—	79	2	no	—
952	C₄²	—	79	1	no	—
953	C₄²	—	79	1	no	—
954	C₄²	—	79	2	no	—
955	C₄²	—	79	1	no	—
956	C₄²	—	79	2	no	—
957	C₄²	—	79	2	no	—
958	C₄²	—	79	1	no	—
959	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
960	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
961	C₄²	C₂³×D₇₉	1	2	yes	—
962	C₄²	C₂³×D₇₉	1	2	yes	—
963	C₄²	C₂³×D₇₉	1	1	yes	characteristic
964	C₄²	C₂³×D₇₉	1	1	yes	characteristic
965	C₂³	—	79	2	no	—
966	C₂³	C₂²×C₄×D₇₉	1	1	yes	characteristic
967	Q₈	—	4	2	no	—
968	Q₈	—	4	2	no	—
969	Q₈	—	316	1	no	—
970	Q₈	—	316	1	no	—
971	Q₈	—	316	2	no	—
972	Q₈	—	316	2	no	—
973	Q₈	—	316	2	no	—
974	Q₈	—	158	2	no	—
975	Q₈	—	158	2	no	—
976	Q₈	—	158	4	no	—
977	Q₈	—	158	2	no	—
978	D₄	—	158	4	no	—
979	D₄	—	158	2	no	—
980	C₂×C₄	—	4	1	no	—
981	C₂×C₄	—	4	1	no	—
982	C₂×C₄	—	316	2	no	—
983	C₂×C₄	—	316	2	no	—
984	C₂×C₄	—	316	2	no	—
985	C₂×C₄	—	316	2	no	—
986	C₂×C₄	—	316	2	no	—
987	C₂×C₄	—	316	1	no	—
988	C₂×C₄	—	316	1	no	—
989	C₂×C₄	—	316	1	no	—
990	C₂×C₄	—	79	1	no	—
991	C₂×C₄	—	79	2	no	—
992	C₂×C₄	—	79	1	no	—
993	C₂×C₄	—	79	1	no	—
994	C₂×C₄	—	79	1	no	—
995	C₂×C₄	—	79	2	no	—
996	C₂×C₄	—	79	1	no	—
997	C₂×C₄	—	79	1	no	—
998	C₂×C₄	—	79	2	no	—
999	C₂×C₄	—	79	1	no	—
1000	C₂×C₄	—	79	1	no	—
1001	C₂×C₄	—	158	4	no	—
1002	C₂×C₄	—	158	2	no	—
1003	C₂×C₄	—	158	2	no	—
1004	C₂×C₄	—	158	2	no	—
1005	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
1006	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
1007	C₂×C₄	C₂²×C₄×D₇₉	1	2	yes	—
1008	C₂×C₄	C₂²×C₄×D₇₉	1	2	yes	—
1009	C₂×C₄	C₂²×C₄×D₇₉	1	2	yes	—
1010	C₂×C₄	C₂²×C₄×D₇₉	1	2	yes	—
1011	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
1012	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
1013	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
1014	C₂×C₄	#14579208	1	2	yes	—
1015	C₂×C₄	#14579209	1	2	yes	—
1016	C₂×C₄	C₂⁴×D₇₉	1	1	yes	characteristic
1017	C₈	—	2	1	no	—
1018	C₈	—	2	1	no	—
1019	C₈	—	2	1	no	—
1020	C₈	—	2	1	no	—
1021	C₈	—	2	2	no	—
1022	C₈	—	2	2	no	—
1023	C₈	—	158	1	no	—
1024	C₈	—	158	1	no	—
1025	C₈	—	158	1	no	—
1026	C₈	—	158	1	no	—
1027	C₈	—	158	2	no	—
1028	C₈	—	158	2	no	—
1029	C₂²	—	2	1	no	—
1030	C₂²	—	2	1	no	—
1031	C₂²	—	158	2	no	—
1032	C₂²	—	158	2	no	—
1033	C₂²	—	158	2	no	—
1034	C₂²	#19099039	1	2	yes	—
1035	C₂²	C₂³×C₄×D₇₉	1	1	yes	characteristic
1036	C₄	—	2	1	no	—
1037	C₄	—	2	1	no	—
1038	C₄	—	2	2	no	—
1039	C₄	—	2	2	no	—
1040	C₄	—	2	1	no	—
1041	C₄	—	2	1	no	—
1042	C₄	—	2	2	no	—
1043	C₄	—	2	2	no	—
1044	C₄	—	79	2	no	—
1045	C₄	—	158	1	no	—
1046	C₄	—	158	2	no	—
1047	C₄	—	158	1	no	—
1048	C₄	—	158	1	no	—
1049	C₄	—	158	1	no	—
1050	C₄	—	158	1	no	—
1051	C₄	—	158	2	no	—
1052	C₄	—	158	1	no	—
1053	C₄	—	158	1	no	—
1054	C₄	—	158	2	no	—
1055	C₄	#19099039	1	2	yes	—
1056	C₄	C₂×#14579208	1	1	yes	characteristic
1057	C₄	C₂×#14579209	1	1	yes	characteristic
1058	C₂	—	2	2	no	—
1059	C₂	—	316	2	no	—
1060	C₂	C₂×#19099039	1	1	yes	characteristic
1061	C₂	#568×D₇₉	1	1	yes	characteristic
1062	C₂	#23778111	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₇₉
commutator, socle	C₂²×C₇₉	C₂⁴×C₄
Fitting	C₇₉×#2962	C₂
prime radical	C₂×#11929624	C₂³
cosocle	C₂×C₄×C₇₉	C₂⁵
hypercenter	#2962	D₇₉
hypocenter	C₇₉	#60254
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ #2962

Complements

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

N	H ≅ G/N	type
2. #23772503	C₂	semidirect
3. #23772503	C₂	semidirect
4. #23772500	C₂	semidirect
5. #23772493	C₂	semidirect
6. #23772493	C₂	semidirect
7. #23772491	C₂	semidirect
8. #23772486	C₂	semidirect
9. #23772482	C₂	semidirect
10. M₁₆×Dic₁₅₈	C₂	semidirect
11. #23772346	C₂	semidirect
12. #23772346	C₂	semidirect
13. #23772341	C₂	semidirect
14. #23772338	C₂	semidirect
15. #23772332	C₂	semidirect
16. C₂×#19098692	C₂	semidirect
23. C₇₉×#2962	C₂	semidirect
544. #2962	D₇₉	semidirect
555. C₇₉	#60254	semidirect

Maximal subgroups

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

subgroup	index
#23776978	2
#23772503	2
#23772500	2
#23772493	2
#23772491	2
#23772486	2
#23772482	2
M₁₆×Dic₁₅₈	2
#23772346	2
#23772341	2
#23772338	2
#23772332	2
C₂×#19098692	2
#23772065	2
#23772064	2
#23772052	2
#23772050	2
#23772043	2
C₇₉×#2962	2
#60254	79