Subgroups — C₇₉×#25761 #34137450

Order 20224.

1582 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#548×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#495×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#464×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#452×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#449×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#451×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#448×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#2540	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#2001	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#2000	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#2000	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₉×#1999	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₉×#1983	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₉×#1954	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#103×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₇₉	C₂²	1	1	yes	characteristic
17	C₂³×Q₈×C₇₉	C₂²	1	1	yes	characteristic
18	C₂²×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
19	C₂²×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
21	C₂²×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
22	C₂²×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
23	C₂²×D₈×C₇₉	C₂²	1	1	yes	characteristic
24	#548×C₇₉	—	2	4	no	—
25	#548×C₇₉	—	2	4	no	—
26	C₂×#124×C₇₉	—	2	1	no	—
27	C₂×#124×C₇₉	C₂²	1	1	yes	characteristic
28	C₂×#124×C₇₉	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊Q₈×C₇₉	—	2	1	no	—
30	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
33	C₂×#121×C₇₉	—	2	1	no	—
34	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
35	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
36	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₇₉	—	2	1	no	—
39	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
40	#495×C₇₉	—	2	4	no	—
41	#464×C₇₉	—	2	4	no	—
42	#452×C₇₉	—	2	4	no	—
43	#451×C₇₉	—	2	4	no	—
44	#449×C₇₉	—	2	4	no	—
45	#448×C₇₉	—	2	4	no	—
46	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
47	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
48	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
49	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
50	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
51	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
52	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
53	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
54	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
55	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
56	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
57	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
58	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
59	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
60	#399×C₇₉	—	2	1	no	—
61	#392×C₇₉	—	2	1	no	—
62	#390×C₇₉	—	2	1	no	—
63	#390×C₇₉	—	2	1	no	—
64	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
65	#340×C₇₉	C₂²	1	1	yes	characteristic
66	#340×C₇₉	C₂²	1	1	yes	characteristic
67	C₂×#41×C₇₉	—	2	2	no	—
68	C₂×#41×C₇₉	—	2	2	no	—
69	C₂×#41×C₇₉	—	2	2	no	—
70	C₂×#41×C₇₉	—	2	2	no	—
71	C₂×#41×C₇₉	—	4	1	no	—
72	C₂×#41×C₇₉	—	4	1	no	—
73	C₂²×Q₈×C₇₉	—	2	2	no	—
74	C₂²×Q₈×C₇₉	—	2	2	no	—
75	C₂²×Q₈×C₇₉	—	2	1	no	—
76	C₂²×Q₈×C₇₉	—	2	2	no	—
77	C₂²×Q₈×C₇₉	—	2	2	no	—
78	C₂²×Q₈×C₇₉	—	4	1	no	—
79	C₂²×Q₈×C₇₉	—	4	1	no	—
80	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
81	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
82	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₇₉	—	2	1	no	—
84	C₂²×D₄×C₇₉	—	2	1	no	—
85	C₂²×D₄×C₇₉	—	2	1	no	—
86	C₂²×D₄×C₇₉	—	2	1	no	—
87	C₂²×D₄×C₇₉	D₄	1	1	yes	characteristic
88	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₇₉	—	2	1	no	—
91	C₂³×C₄×C₇₉	—	2	1	no	—
92	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
94	C₂×Q₁₆×C₇₉	—	2	2	no	—
95	C₂×Q₁₆×C₇₉	—	2	2	no	—
96	C₂×Q₁₆×C₇₉	—	2	2	no	—
97	C₂×Q₁₆×C₇₉	—	2	2	no	—
98	C₂×Q₁₆×C₇₉	—	2	2	no	—
99	C₂×Q₁₆×C₇₉	—	4	1	no	—
100	C₂×SD₁₆×C₇₉	—	2	2	no	—
101	C₂×SD₁₆×C₇₉	—	2	2	no	—
102	C₂×SD₁₆×C₇₉	—	2	2	no	—
103	C₂×SD₁₆×C₇₉	—	2	2	no	—
104	C₂×SD₁₆×C₇₉	—	2	2	no	—
105	C₂×SD₁₆×C₇₉	—	2	2	no	—
106	C₂×SD₁₆×C₇₉	—	2	2	no	—
107	C₂×SD₁₆×C₇₉	—	4	1	no	—
108	C₂×SD₁₆×C₇₉	—	4	1	no	—
109	C₂×D₈×C₇₉	—	2	2	no	—
110	C₂×D₈×C₇₉	—	2	2	no	—
111	C₂×D₈×C₇₉	—	4	1	no	—
112	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
116	#124×C₇₉	—	2	8	no	—
117	#124×C₇₉	—	2	2	no	—
118	#124×C₇₉	—	2	2	no	—
119	#124×C₇₉	—	2	2	no	—
120	#124×C₇₉	D₄	1	4	yes	complemented
121	C₂²⋊Q₈×C₇₉	—	2	8	no	—
122	C₂²⋊Q₈×C₇₉	—	2	2	no	—
123	C₂²⋊Q₈×C₇₉	—	2	2	no	—
124	C₂²⋊Q₈×C₇₉	—	2	2	no	—
125	C₂²⋊Q₈×C₇₉	—	2	2	no	—
126	C₂²⋊Q₈×C₇₉	—	4	1	no	—
127	C₂²⋊Q₈×C₇₉	—	4	1	no	—
128	#121×C₇₉	—	2	8	no	—
129	#121×C₇₉	—	2	2	no	—
130	#121×C₇₉	—	2	2	no	—
131	#121×C₇₉	—	2	2	no	—
132	#121×C₇₉	—	2	2	no	—
133	#121×C₇₉	—	4	1	no	—
134	#121×C₇₉	—	4	1	no	—
135	C₄×Q₈×C₇₉	—	2	2	no	—
136	C₄×Q₈×C₇₉	D₄	1	4	yes	complemented
137	C₄×D₄×C₇₉	—	2	8	no	—
138	C₄×D₄×C₇₉	—	2	2	no	—
139	C₄×D₄×C₇₉	—	2	2	no	—
140	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
141	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
142	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
143	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
144	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
149	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
150	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
151	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
152	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
153	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
154	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
155	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
156	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
157	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
158	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
159	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
160	C₂×C₄²×C₇₉	—	2	1	no	—
161	C₂×C₄²×C₇₉	—	2	1	no	—
162	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
163	C₄⋊C₈×C₇₉	—	2	2	no	—
164	#103×C₇₉	—	2	2	no	—
165	#103×C₇₉	—	2	2	no	—
166	#103×C₇₉	—	2	2	no	—
167	#103×C₇₉	D₄	1	4	yes	complemented
168	#103×C₇₉	D₄	1	4	yes	complemented
169	#102×C₇₉	—	2	2	no	—
170	#102×C₇₉	—	2	2	no	—
171	#102×C₇₉	—	2	2	no	—
172	C₂²⋊C₈×C₇₉	—	2	2	no	—
173	C₂²⋊C₈×C₇₉	—	2	2	no	—
174	C₂²⋊C₈×C₇₉	—	2	2	no	—
175	C₂²⋊C₈×C₇₉	—	2	2	no	—
176	C₄×C₈×C₇₉	—	2	2	no	—
177	#95×C₇₉	—	2	1	no	—
178	C₂⁴×C₇₉	—	2	1	no	—
179	C₂⁴×C₇₉	—	2	1	no	—
180	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
181	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
182	#41×C₇₉	—	4	4	no	—
183	#41×C₇₉	—	4	4	no	—
184	#41×C₇₉	—	4	4	no	—
185	#41×C₇₉	—	4	4	no	—
186	C₂×Q₈×C₇₉	—	2	4	no	—
187	C₂×Q₈×C₇₉	—	2	1	no	—
188	C₂×Q₈×C₇₉	—	2	1	no	—
189	C₂×Q₈×C₇₉	—	2	1	no	—
190	C₂×Q₈×C₇₉	—	2	1	no	—
191	C₂×Q₈×C₇₉	—	2	1	no	—
192	C₂×Q₈×C₇₉	—	2	1	no	—
193	C₂×Q₈×C₇₉	—	2	1	no	—
194	C₂×Q₈×C₇₉	—	2	1	no	—
195	C₂×Q₈×C₇₉	—	2	1	no	—
196	C₂×Q₈×C₇₉	—	2	1	no	—
197	C₂×Q₈×C₇₉	—	2	1	no	—
198	C₂×Q₈×C₇₉	—	2	1	no	—
199	C₂×Q₈×C₇₉	—	2	1	no	—
200	C₂×Q₈×C₇₉	—	2	1	no	—
201	C₂×Q₈×C₇₉	—	4	2	no	—
202	C₂×Q₈×C₇₉	—	4	2	no	—
203	C₂×Q₈×C₇₉	—	4	4	no	—
204	C₂×Q₈×C₇₉	—	4	4	no	—
205	C₂×Q₈×C₇₉	—	4	4	no	—
206	C₂×Q₈×C₇₉	—	4	4	no	—
207	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
208	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
209	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
210	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
211	C₂×D₄×C₇₉	—	2	4	no	—
212	C₂×D₄×C₇₉	—	2	4	no	—
213	C₂×D₄×C₇₉	—	2	2	no	—
214	C₂×D₄×C₇₉	—	2	2	no	—
215	C₂×D₄×C₇₉	—	2	1	no	—
216	C₂×D₄×C₇₉	—	2	1	no	—
217	C₂×D₄×C₇₉	—	2	1	no	—
218	C₂×D₄×C₇₉	—	2	1	no	—
219	C₂×D₄×C₇₉	—	2	1	no	—
220	C₂×D₄×C₇₉	—	2	1	no	—
221	C₂×D₄×C₇₉	—	2	1	no	—
222	C₂×D₄×C₇₉	—	2	1	no	—
223	C₂×D₄×C₇₉	—	2	1	no	—
224	C₂×D₄×C₇₉	—	2	1	no	—
225	C₂×D₄×C₇₉	—	2	1	no	—
226	C₂×D₄×C₇₉	—	4	1	no	—
227	C₂×D₄×C₇₉	—	4	2	no	—
228	C₂×D₄×C₇₉	—	4	2	no	—
229	C₂×D₄×C₇₉	—	4	2	no	—
230	C₂×D₄×C₇₉	—	4	2	no	—
231	C₂×D₄×C₇₉	—	4	2	no	—
232	C₂×D₄×C₇₉	—	4	2	no	—
233	C₂×D₄×C₇₉	—	4	2	no	—
234	C₂×D₄×C₇₉	—	4	2	no	—
235	C₂×D₄×C₇₉	—	8	1	no	—
236	C₂×D₄×C₇₉	—	8	1	no	—
237	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
238	C₂²×C₄×C₇₉	—	2	1	no	—
239	C₂²×C₄×C₇₉	—	2	4	no	—
240	C₂²×C₄×C₇₉	—	2	4	no	—
241	C₂²×C₄×C₇₉	—	2	1	no	—
242	C₂²×C₄×C₇₉	—	2	1	no	—
243	C₂²×C₄×C₇₉	—	2	1	no	—
244	C₂²×C₄×C₇₉	—	2	1	no	—
245	C₂²×C₄×C₇₉	—	2	1	no	—
246	C₂²×C₄×C₇₉	—	2	1	no	—
247	C₂²×C₄×C₇₉	—	2	1	no	—
248	C₂²×C₄×C₇₉	—	2	1	no	—
249	C₂²×C₄×C₇₉	—	2	1	no	—
250	C₂²×C₄×C₇₉	—	2	1	no	—
251	C₂²×C₄×C₇₉	—	2	1	no	—
252	C₂²×C₄×C₇₉	—	2	1	no	—
253	C₂²×C₄×C₇₉	—	2	1	no	—
254	C₂²×C₄×C₇₉	—	2	1	no	—
255	C₂²×C₄×C₇₉	—	2	1	no	—
256	C₂²×C₄×C₇₉	—	2	1	no	—
257	C₂²×C₄×C₇₉	—	2	1	no	—
258	C₂²×C₄×C₇₉	—	4	2	no	—
259	C₂²×C₄×C₇₉	—	4	2	no	—
260	C₂²×C₄×C₇₉	—	4	2	no	—
261	C₂²×C₄×C₇₉	—	4	2	no	—
262	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
267	Q₁₆×C₇₉	—	4	4	no	—
268	Q₁₆×C₇₉	—	4	4	no	—
269	SD₁₆×C₇₉	—	4	4	no	—
270	SD₁₆×C₇₉	—	4	4	no	—
271	SD₁₆×C₇₉	—	4	4	no	—
272	D₈×C₇₉	—	4	4	no	—
273	C₂×C₈×C₇₉	—	2	1	no	—
274	C₂×C₈×C₇₉	—	2	1	no	—
275	C₂×C₈×C₇₉	—	2	1	no	—
276	C₂×C₈×C₇₉	—	2	1	no	—
277	C₂×C₈×C₇₉	—	2	1	no	—
278	C₂×C₈×C₇₉	—	2	1	no	—
279	C₂×C₈×C₇₉	—	2	1	no	—
280	C₂×C₈×C₇₉	—	2	1	no	—
281	C₂×C₈×C₇₉	—	2	1	no	—
282	C₂×C₈×C₇₉	—	2	1	no	—
283	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
284	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
285	C₄⋊C₄×C₇₉	—	2	4	no	—
286	C₄⋊C₄×C₇₉	—	2	4	no	—
287	C₄⋊C₄×C₇₉	—	2	2	no	—
288	C₄⋊C₄×C₇₉	—	2	1	no	—
289	C₄⋊C₄×C₇₉	—	2	1	no	—
290	C₄⋊C₄×C₇₉	—	2	1	no	—
291	C₄⋊C₄×C₇₉	—	4	2	no	—
292	C₄⋊C₄×C₇₉	—	4	2	no	—
293	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
294	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
295	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
296	C₂²⋊C₄×C₇₉	—	2	4	no	—
297	C₂²⋊C₄×C₇₉	—	2	4	no	—
298	C₂²⋊C₄×C₇₉	—	2	4	no	—
299	C₂²⋊C₄×C₇₉	—	2	4	no	—
300	C₂²⋊C₄×C₇₉	—	2	2	no	—
301	C₂²⋊C₄×C₇₉	—	2	2	no	—
302	C₂²⋊C₄×C₇₉	—	4	2	no	—
303	C₂²⋊C₄×C₇₉	—	4	2	no	—
304	C₂²⋊C₄×C₇₉	—	4	2	no	—
305	C₂²⋊C₄×C₇₉	—	4	2	no	—
306	C₂²⋊C₄×C₇₉	—	4	2	no	—
307	C₂²⋊C₄×C₇₉	—	4	2	no	—
308	C₄²×C₇₉	—	2	4	no	—
309	C₄²×C₇₉	—	8	1	no	—
310	C₄²×C₇₉	C₂×D₄	1	2	yes	—
311	C₄²×C₇₉	C₂×D₄	1	2	yes	—
312	C₂³×C₇₉	—	2	1	no	—
313	C₂³×C₇₉	—	2	1	no	—
314	C₂³×C₇₉	—	2	1	no	—
315	C₂³×C₇₉	—	2	1	no	—
316	C₂³×C₇₉	—	2	1	no	—
317	C₂³×C₇₉	—	2	1	no	—
318	C₂³×C₇₉	—	2	1	no	—
319	C₂³×C₇₉	—	2	2	no	—
320	C₂³×C₇₉	—	2	1	no	—
321	C₂³×C₇₉	—	2	1	no	—
322	C₂³×C₇₉	—	2	1	no	—
323	C₂³×C₇₉	—	2	1	no	—
324	C₂³×C₇₉	—	2	1	no	—
325	C₂³×C₇₉	—	2	1	no	—
326	C₂³×C₇₉	—	4	1	no	—
327	C₂³×C₇₉	—	4	1	no	—
328	C₂³×C₇₉	—	4	1	no	—
329	C₂³×C₇₉	—	4	1	no	—
330	C₂³×C₇₉	—	4	1	no	—
331	C₂³×C₇₉	—	4	1	no	—
332	C₂³×C₇₉	—	4	1	no	—
333	C₂³×C₇₉	—	4	1	no	—
334	C₂³×C₇₉	—	4	1	no	—
335	C₂³×C₇₉	—	4	1	no	—
336	C₂³×C₇₉	—	4	1	no	—
337	C₂³×C₇₉	—	4	1	no	—
338	C₂³×C₇₉	—	4	1	no	—
339	C₂³×C₇₉	#135	1	2	yes	—
340	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
341	Q₈×C₇₉	—	2	2	no	—
342	Q₈×C₇₉	—	2	2	no	—
343	Q₈×C₇₉	—	2	2	no	—
344	Q₈×C₇₉	—	2	2	no	—
345	Q₈×C₇₉	—	2	2	no	—
346	Q₈×C₇₉	—	4	8	no	—
347	Q₈×C₇₉	—	4	1	no	—
348	Q₈×C₇₉	—	4	1	no	—
349	Q₈×C₇₉	—	4	1	no	—
350	Q₈×C₇₉	—	4	1	no	—
351	Q₈×C₇₉	—	4	1	no	—
352	Q₈×C₇₉	—	4	1	no	—
353	Q₈×C₇₉	#127	1	4	yes	—
354	D₄×C₇₉	—	2	2	no	—
355	D₄×C₇₉	—	2	2	no	—
356	D₄×C₇₉	—	4	4	no	—
357	D₄×C₇₉	—	4	8	no	—
358	D₄×C₇₉	—	4	8	no	—
359	D₄×C₇₉	—	4	1	no	—
360	D₄×C₇₉	—	4	1	no	—
361	D₄×C₇₉	—	4	1	no	—
362	D₄×C₇₉	—	4	1	no	—
363	D₄×C₇₉	—	4	1	no	—
364	D₄×C₇₉	—	4	1	no	—
365	D₄×C₇₉	—	8	4	no	—
366	D₄×C₇₉	—	8	4	no	—
367	C₂×C₄×C₇₉	—	2	2	no	—
368	C₂×C₄×C₇₉	—	2	2	no	—
369	C₂×C₄×C₇₉	—	2	2	no	—
370	C₂×C₄×C₇₉	—	2	1	no	—
371	C₂×C₄×C₇₉	—	2	1	no	—
372	C₂×C₄×C₇₉	—	2	1	no	—
373	C₂×C₄×C₇₉	—	2	1	no	—
374	C₂×C₄×C₇₉	—	2	2	no	—
375	C₂×C₄×C₇₉	—	2	2	no	—
376	C₂×C₄×C₇₉	—	2	1	no	—
377	C₂×C₄×C₇₉	—	2	1	no	—
378	C₂×C₄×C₇₉	—	2	2	no	—
379	C₂×C₄×C₇₉	—	2	2	no	—
380	C₂×C₄×C₇₉	—	2	1	no	—
381	C₂×C₄×C₇₉	—	2	1	no	—
382	C₂×C₄×C₇₉	—	2	1	no	—
383	C₂×C₄×C₇₉	—	2	1	no	—
384	C₂×C₄×C₇₉	—	4	8	no	—
385	C₂×C₄×C₇₉	—	4	8	no	—
386	C₂×C₄×C₇₉	—	4	1	no	—
387	C₂×C₄×C₇₉	—	4	1	no	—
388	C₂×C₄×C₇₉	—	4	1	no	—
389	C₂×C₄×C₇₉	—	4	1	no	—
390	C₂×C₄×C₇₉	—	4	1	no	—
391	C₂×C₄×C₇₉	—	4	1	no	—
392	C₂×C₄×C₇₉	—	4	1	no	—
393	C₂×C₄×C₇₉	—	4	1	no	—
394	C₂×C₄×C₇₉	—	4	1	no	—
395	C₂×C₄×C₇₉	—	4	1	no	—
396	C₂×C₄×C₇₉	—	4	1	no	—
397	C₂×C₄×C₇₉	—	4	1	no	—
398	C₂×C₄×C₇₉	—	4	1	no	—
399	C₂×C₄×C₇₉	—	4	1	no	—
400	C₂×C₄×C₇₉	—	4	1	no	—
401	C₂×C₄×C₇₉	—	4	1	no	—
402	C₂×C₄×C₇₉	—	4	1	no	—
403	C₂×C₄×C₇₉	—	4	1	no	—
404	C₂×C₄×C₇₉	—	4	1	no	—
405	C₂×C₄×C₇₉	#120	1	2	yes	—
406	C₂×C₄×C₇₉	#120	1	2	yes	—
407	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
412	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
413	C₈×C₇₉	—	2	2	no	—
414	C₈×C₇₉	—	2	2	no	—
415	C₈×C₇₉	—	4	1	no	—
416	C₈×C₇₉	—	4	1	no	—
417	C₂²×C₇₉	—	2	2	no	—
418	C₂²×C₇₉	—	2	2	no	—
419	C₂²×C₇₉	—	2	2	no	—
420	C₂²×C₇₉	—	4	1	no	—
421	C₂²×C₇₉	—	4	1	no	—
422	C₂²×C₇₉	—	4	1	no	—
423	C₂²×C₇₉	—	4	1	no	—
424	C₂²×C₇₉	—	4	2	no	—
425	C₂²×C₇₉	—	4	1	no	—
426	C₂²×C₇₉	—	4	1	no	—
427	C₂²×C₇₉	—	4	2	no	—
428	C₂²×C₇₉	—	4	1	no	—
429	C₂²×C₇₉	—	4	2	no	—
430	C₂²×C₇₉	—	4	1	no	—
431	C₂²×C₇₉	—	4	1	no	—
432	C₂²×C₇₉	—	4	1	no	—
433	C₂²×C₇₉	—	4	1	no	—
434	C₂²×C₇₉	—	8	1	no	—
435	C₂²×C₇₉	—	8	1	no	—
436	C₂²×C₇₉	—	8	1	no	—
437	C₂²×C₇₉	—	8	1	no	—
438	C₂²×C₇₉	—	8	1	no	—
439	C₂²×C₇₉	—	8	1	no	—
440	C₂²×C₇₉	—	8	1	no	—
441	C₂²×C₇₉	—	8	1	no	—
442	C₂²×C₇₉	—	8	1	no	—
443	C₂²×C₇₉	—	8	1	no	—
444	C₂²×C₇₉	—	8	1	no	—
445	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
446	C₂²×C₇₉	D₄²	1	1	yes	characteristic
447	C₂²×C₇₉	D₄²	1	1	yes	characteristic
448	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
449	C₂²×C₇₉	#575	1	1	yes	characteristic
450	C₂²×C₇₉	#577	1	1	yes	characteristic
451	C₂²×C₇₉	#578	1	1	yes	characteristic
452	C₄×C₇₉	—	2	4	no	—
453	C₄×C₇₉	—	2	2	no	—
454	C₄×C₇₉	—	2	2	no	—
455	C₄×C₇₉	—	4	1	no	—
456	C₄×C₇₉	—	4	1	no	—
457	C₄×C₇₉	—	4	2	no	—
458	C₄×C₇₉	—	4	2	no	—
459	C₄×C₇₉	—	4	2	no	—
460	C₄×C₇₉	—	4	2	no	—
461	C₄×C₇₉	—	8	1	no	—
462	C₄×C₇₉	C₂×#127	1	1	yes	characteristic
463	C₄×C₇₉	#535	1	1	yes	characteristic
464	C₄×C₇₉	D₄²	1	1	yes	characteristic
465	C₄×C₇₉	D₄²	1	1	yes	characteristic
466	#25761	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
467	C₂×C₇₉	—	4	2	no	—
468	C₂×C₇₉	—	8	1	no	—
469	C₂×C₇₉	—	8	2	no	—
470	C₂×C₇₉	—	16	1	no	—
471	C₂×C₇₉	#2433	1	1	yes	characteristic
472	C₂×C₇₉	#3002	1	1	yes	characteristic
473	C₂×C₇₉	#3013	1	1	yes	characteristic
474	C₂×C₇₉	#3275	1	1	yes	characteristic
475	C₂×C₇₉	#3277	1	1	yes	characteristic
476	C₂×C₇₉	#3282	1	1	yes	characteristic
477	C₂×C₇₉	#3285	1	1	yes	characteristic
478	C₂×#548	C₂×C₇₉	1	1	yes	characteristic, complemented
479	C₂×#495	C₂×C₇₉	1	1	yes	characteristic, complemented
480	C₂×#464	C₂×C₇₉	1	1	yes	characteristic, complemented
481	C₂×#452	C₂×C₇₉	1	1	yes	characteristic, complemented
482	C₂×#449	C₂×C₇₉	1	1	yes	characteristic, complemented
483	C₂×#451	C₂×C₇₉	1	1	yes	characteristic, complemented
484	C₂×#448	C₂×C₇₉	1	1	yes	characteristic, complemented
485	#2540	C₂×C₇₉	1	1	yes	characteristic, complemented
486	#2001	C₂×C₇₉	1	1	yes	characteristic, complemented
487	#2000	C₂×C₇₉	1	1	yes	characteristic, complemented
488	#2000	C₂×C₇₉	1	1	yes	characteristic, complemented
489	#1999	C₂×C₇₉	1	1	yes	characteristic, complemented
490	#1983	C₂×C₇₉	1	1	yes	characteristic, complemented
491	#1954	C₂×C₇₉	1	1	yes	characteristic, complemented
492	C₄×#103	C₂×C₇₉	1	1	yes	characteristic, complemented
493	C₇₉	#25761	1	1	yes	characteristic, direct product factor, Sylow
494	C₂²×#41	C₂²×C₇₉	1	1	yes	characteristic
495	C₂³×Q₈	C₂²×C₇₉	1	1	yes	characteristic
496	C₂²×Q₁₆	C₂²×C₇₉	1	1	yes	characteristic
497	C₂²×Q₁₆	C₂²×C₇₉	1	1	yes	characteristic
498	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
499	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
500	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
501	C₂²×D₈	C₂²×C₇₉	1	1	yes	characteristic
502	#548	—	2	4	no	—
503	#548	—	2	4	no	—
504	C₂×#124	—	2	1	no	—
505	C₂×#124	C₂²×C₇₉	1	1	yes	characteristic
506	C₂×#124	C₂²×C₇₉	1	1	yes	characteristic
507	C₂×C₂²⋊Q₈	—	2	1	no	—
508	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
509	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
510	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
511	C₂×#121	—	2	1	no	—
512	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
513	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
514	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
515	C₂×C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
516	C₂×C₄×D₄	—	2	1	no	—
517	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
518	#495	—	2	4	no	—
519	#464	—	2	4	no	—
520	#452	—	2	4	no	—
521	#451	—	2	4	no	—
522	#449	—	2	4	no	—
523	#448	—	2	4	no	—
524	C₂×C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
525	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
526	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
527	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
528	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
529	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
530	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
531	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
532	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
533	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
534	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
535	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
536	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
537	C₂×C₄×C₈	C₂²×C₇₉	1	1	yes	characteristic
538	#399	—	2	1	no	—
539	#392	—	2	1	no	—
540	#390	—	2	1	no	—
541	#390	—	2	1	no	—
542	C₄×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
543	#340	C₂²×C₇₉	1	1	yes	characteristic
544	#340	C₂²×C₇₉	1	1	yes	characteristic
545	C₂×#41	—	2	2	no	—
546	C₂×#41	—	2	2	no	—
547	C₂×#41	—	2	2	no	—
548	C₂×#41	—	2	2	no	—
549	C₂×#41	—	4	1	no	—
550	C₂×#41	—	4	1	no	—
551	C₂²×Q₈	—	2	2	no	—
552	C₂²×Q₈	—	2	2	no	—
553	C₂²×Q₈	—	2	1	no	—
554	C₂²×Q₈	—	2	2	no	—
555	C₂²×Q₈	—	2	2	no	—
556	C₂²×Q₈	—	4	1	no	—
557	C₂²×Q₈	—	4	1	no	—
558	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
559	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
560	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
561	C₂²×D₄	—	2	1	no	—
562	C₂²×D₄	—	2	1	no	—
563	C₂²×D₄	—	2	1	no	—
564	C₂²×D₄	—	2	1	no	—
565	C₂²×D₄	D₄×C₇₉	1	1	yes	characteristic
566	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
567	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
568	C₂³×C₄	—	2	1	no	—
569	C₂³×C₄	—	2	1	no	—
570	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
571	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
572	C₂×Q₁₆	—	2	2	no	—
573	C₂×Q₁₆	—	2	2	no	—
574	C₂×Q₁₆	—	2	2	no	—
575	C₂×Q₁₆	—	2	2	no	—
576	C₂×Q₁₆	—	2	2	no	—
577	C₂×Q₁₆	—	4	1	no	—
578	C₂×SD₁₆	—	2	2	no	—
579	C₂×SD₁₆	—	2	2	no	—
580	C₂×SD₁₆	—	2	2	no	—
581	C₂×SD₁₆	—	2	2	no	—
582	C₂×SD₁₆	—	2	2	no	—
583	C₂×SD₁₆	—	2	2	no	—
584	C₂×SD₁₆	—	2	2	no	—
585	C₂×SD₁₆	—	4	1	no	—
586	C₂×SD₁₆	—	4	1	no	—
587	C₂×D₈	—	2	2	no	—
588	C₂×D₈	—	2	2	no	—
589	C₂×D₈	—	4	1	no	—
590	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
591	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
592	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
593	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
594	#124	—	2	8	no	—
595	#124	—	2	2	no	—
596	#124	—	2	2	no	—
597	#124	—	2	2	no	—
598	#124	D₄×C₇₉	1	4	yes	complemented
599	C₂²⋊Q₈	—	2	8	no	—
600	C₂²⋊Q₈	—	2	2	no	—
601	C₂²⋊Q₈	—	2	2	no	—
602	C₂²⋊Q₈	—	2	2	no	—
603	C₂²⋊Q₈	—	2	2	no	—
604	C₂²⋊Q₈	—	4	1	no	—
605	C₂²⋊Q₈	—	4	1	no	—
606	#121	—	2	8	no	—
607	#121	—	2	2	no	—
608	#121	—	2	2	no	—
609	#121	—	2	2	no	—
610	#121	—	2	2	no	—
611	#121	—	4	1	no	—
612	#121	—	4	1	no	—
613	C₄×Q₈	—	2	2	no	—
614	C₄×Q₈	D₄×C₇₉	1	4	yes	complemented
615	C₄×D₄	—	2	8	no	—
616	C₄×D₄	—	2	2	no	—
617	C₄×D₄	—	2	2	no	—
618	C₂×C₄⋊C₄	—	2	1	no	—
619	C₂×C₄⋊C₄	—	2	1	no	—
620	C₂×C₄⋊C₄	—	2	1	no	—
621	C₂×C₄⋊C₄	—	2	1	no	—
622	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
626	C₂×C₂²⋊C₄	—	2	1	no	—
627	C₂×C₂²⋊C₄	—	2	1	no	—
628	C₂×C₂²⋊C₄	—	2	1	no	—
629	C₂×C₂²⋊C₄	—	2	1	no	—
630	C₂×C₂²⋊C₄	—	2	1	no	—
631	C₂×C₂²⋊C₄	—	2	1	no	—
632	C₂×C₂²⋊C₄	—	2	1	no	—
633	C₂×C₂²⋊C₄	—	2	1	no	—
634	C₂×C₂²⋊C₄	—	2	1	no	—
635	C₂×C₂²⋊C₄	—	2	1	no	—
636	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
637	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
638	C₂×C₄²	—	2	1	no	—
639	C₂×C₄²	—	2	1	no	—
640	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
641	C₄⋊C₈	—	2	2	no	—
642	#103	—	2	2	no	—
643	#103	—	2	2	no	—
644	#103	—	2	2	no	—
645	#103	D₄×C₇₉	1	4	yes	complemented
646	#103	D₄×C₇₉	1	4	yes	complemented
647	#102	—	2	2	no	—
648	#102	—	2	2	no	—
649	#102	—	2	2	no	—
650	C₂²⋊C₈	—	2	2	no	—
651	C₂²⋊C₈	—	2	2	no	—
652	C₂²⋊C₈	—	2	2	no	—
653	C₂²⋊C₈	—	2	2	no	—
654	C₄×C₈	—	2	2	no	—
655	#95	—	2	1	no	—
656	C₂⁴	—	2	1	no	—
657	C₂⁴	—	2	1	no	—
658	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
659	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
660	#41	—	4	4	no	—
661	#41	—	4	4	no	—
662	#41	—	4	4	no	—
663	#41	—	4	4	no	—
664	C₂×Q₈	—	2	4	no	—
665	C₂×Q₈	—	2	1	no	—
666	C₂×Q₈	—	2	1	no	—
667	C₂×Q₈	—	2	1	no	—
668	C₂×Q₈	—	2	1	no	—
669	C₂×Q₈	—	2	1	no	—
670	C₂×Q₈	—	2	1	no	—
671	C₂×Q₈	—	2	1	no	—
672	C₂×Q₈	—	2	1	no	—
673	C₂×Q₈	—	2	1	no	—
674	C₂×Q₈	—	2	1	no	—
675	C₂×Q₈	—	2	1	no	—
676	C₂×Q₈	—	2	1	no	—
677	C₂×Q₈	—	2	1	no	—
678	C₂×Q₈	—	2	1	no	—
679	C₂×Q₈	—	4	2	no	—
680	C₂×Q₈	—	4	2	no	—
681	C₂×Q₈	—	4	4	no	—
682	C₂×Q₈	—	4	4	no	—
683	C₂×Q₈	—	4	4	no	—
684	C₂×Q₈	—	4	4	no	—
685	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
686	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
687	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
688	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
689	C₂×D₄	—	2	4	no	—
690	C₂×D₄	—	2	4	no	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	1	no	—
694	C₂×D₄	—	2	1	no	—
695	C₂×D₄	—	2	1	no	—
696	C₂×D₄	—	2	1	no	—
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	—	2	1	no	—
699	C₂×D₄	—	2	1	no	—
700	C₂×D₄	—	2	1	no	—
701	C₂×D₄	—	2	1	no	—
702	C₂×D₄	—	2	1	no	—
703	C₂×D₄	—	2	1	no	—
704	C₂×D₄	—	4	1	no	—
705	C₂×D₄	—	4	2	no	—
706	C₂×D₄	—	4	2	no	—
707	C₂×D₄	—	4	2	no	—
708	C₂×D₄	—	4	2	no	—
709	C₂×D₄	—	4	2	no	—
710	C₂×D₄	—	4	2	no	—
711	C₂×D₄	—	4	2	no	—
712	C₂×D₄	—	4	2	no	—
713	C₂×D₄	—	8	1	no	—
714	C₂×D₄	—	8	1	no	—
715	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
716	C₂²×C₄	—	2	1	no	—
717	C₂²×C₄	—	2	4	no	—
718	C₂²×C₄	—	2	4	no	—
719	C₂²×C₄	—	2	1	no	—
720	C₂²×C₄	—	2	1	no	—
721	C₂²×C₄	—	2	1	no	—
722	C₂²×C₄	—	2	1	no	—
723	C₂²×C₄	—	2	1	no	—
724	C₂²×C₄	—	2	1	no	—
725	C₂²×C₄	—	2	1	no	—
726	C₂²×C₄	—	2	1	no	—
727	C₂²×C₄	—	2	1	no	—
728	C₂²×C₄	—	2	1	no	—
729	C₂²×C₄	—	2	1	no	—
730	C₂²×C₄	—	2	1	no	—
731	C₂²×C₄	—	2	1	no	—
732	C₂²×C₄	—	2	1	no	—
733	C₂²×C₄	—	2	1	no	—
734	C₂²×C₄	—	2	1	no	—
735	C₂²×C₄	—	2	1	no	—
736	C₂²×C₄	—	4	2	no	—
737	C₂²×C₄	—	4	2	no	—
738	C₂²×C₄	—	4	2	no	—
739	C₂²×C₄	—	4	2	no	—
740	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
741	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
742	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
743	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
744	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
745	Q₁₆	—	4	4	no	—
746	Q₁₆	—	4	4	no	—
747	SD₁₆	—	4	4	no	—
748	SD₁₆	—	4	4	no	—
749	SD₁₆	—	4	4	no	—
750	D₈	—	4	4	no	—
751	C₂×C₈	—	2	1	no	—
752	C₂×C₈	—	2	1	no	—
753	C₂×C₈	—	2	1	no	—
754	C₂×C₈	—	2	1	no	—
755	C₂×C₈	—	2	1	no	—
756	C₂×C₈	—	2	1	no	—
757	C₂×C₈	—	2	1	no	—
758	C₂×C₈	—	2	1	no	—
759	C₂×C₈	—	2	1	no	—
760	C₂×C₈	—	2	1	no	—
761	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
762	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
763	C₄⋊C₄	—	2	4	no	—
764	C₄⋊C₄	—	2	4	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	1	no	—
767	C₄⋊C₄	—	2	1	no	—
768	C₄⋊C₄	—	2	1	no	—
769	C₄⋊C₄	—	4	2	no	—
770	C₄⋊C₄	—	4	2	no	—
771	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
772	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
773	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
774	C₂²⋊C₄	—	2	4	no	—
775	C₂²⋊C₄	—	2	4	no	—
776	C₂²⋊C₄	—	2	4	no	—
777	C₂²⋊C₄	—	2	4	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	2	no	—
780	C₂²⋊C₄	—	4	2	no	—
781	C₂²⋊C₄	—	4	2	no	—
782	C₂²⋊C₄	—	4	2	no	—
783	C₂²⋊C₄	—	4	2	no	—
784	C₂²⋊C₄	—	4	2	no	—
785	C₂²⋊C₄	—	4	2	no	—
786	C₄²	—	2	4	no	—
787	C₄²	—	8	1	no	—
788	C₄²	C₂×D₄×C₇₉	1	2	yes	—
789	C₄²	C₂×D₄×C₇₉	1	2	yes	—
790	C₂³	—	2	1	no	—
791	C₂³	—	2	1	no	—
792	C₂³	—	2	1	no	—
793	C₂³	—	2	1	no	—
794	C₂³	—	2	1	no	—
795	C₂³	—	2	1	no	—
796	C₂³	—	2	1	no	—
797	C₂³	—	2	2	no	—
798	C₂³	—	2	1	no	—
799	C₂³	—	2	1	no	—
800	C₂³	—	2	1	no	—
801	C₂³	—	2	1	no	—
802	C₂³	—	2	1	no	—
803	C₂³	—	2	1	no	—
804	C₂³	—	4	1	no	—
805	C₂³	—	4	1	no	—
806	C₂³	—	4	1	no	—
807	C₂³	—	4	1	no	—
808	C₂³	—	4	1	no	—
809	C₂³	—	4	1	no	—
810	C₂³	—	4	1	no	—
811	C₂³	—	4	1	no	—
812	C₂³	—	4	1	no	—
813	C₂³	—	4	1	no	—
814	C₂³	—	4	1	no	—
815	C₂³	—	4	1	no	—
816	C₂³	—	4	1	no	—
817	C₂³	#135×C₇₉	1	2	yes	—
818	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
819	Q₈	—	2	2	no	—
820	Q₈	—	2	2	no	—
821	Q₈	—	2	2	no	—
822	Q₈	—	2	2	no	—
823	Q₈	—	2	2	no	—
824	Q₈	—	4	8	no	—
825	Q₈	—	4	1	no	—
826	Q₈	—	4	1	no	—
827	Q₈	—	4	1	no	—
828	Q₈	—	4	1	no	—
829	Q₈	—	4	1	no	—
830	Q₈	—	4	1	no	—
831	Q₈	#127×C₇₉	1	4	yes	—
832	D₄	—	2	2	no	—
833	D₄	—	2	2	no	—
834	D₄	—	4	4	no	—
835	D₄	—	4	8	no	—
836	D₄	—	4	8	no	—
837	D₄	—	4	1	no	—
838	D₄	—	4	1	no	—
839	D₄	—	4	1	no	—
840	D₄	—	4	1	no	—
841	D₄	—	4	1	no	—
842	D₄	—	4	1	no	—
843	D₄	—	8	4	no	—
844	D₄	—	8	4	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	4	8	no	—
863	C₂×C₄	—	4	8	no	—
864	C₂×C₄	—	4	1	no	—
865	C₂×C₄	—	4	1	no	—
866	C₂×C₄	—	4	1	no	—
867	C₂×C₄	—	4	1	no	—
868	C₂×C₄	—	4	1	no	—
869	C₂×C₄	—	4	1	no	—
870	C₂×C₄	—	4	1	no	—
871	C₂×C₄	—	4	1	no	—
872	C₂×C₄	—	4	1	no	—
873	C₂×C₄	—	4	1	no	—
874	C₂×C₄	—	4	1	no	—
875	C₂×C₄	—	4	1	no	—
876	C₂×C₄	—	4	1	no	—
877	C₂×C₄	—	4	1	no	—
878	C₂×C₄	—	4	1	no	—
879	C₂×C₄	—	4	1	no	—
880	C₂×C₄	—	4	1	no	—
881	C₂×C₄	—	4	1	no	—
882	C₂×C₄	—	4	1	no	—
883	C₂×C₄	#120×C₇₉	1	2	yes	—
884	C₂×C₄	#120×C₇₉	1	2	yes	—
885	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
886	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
887	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
888	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
889	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
890	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
891	C₈	—	2	2	no	—
892	C₈	—	2	2	no	—
893	C₈	—	4	1	no	—
894	C₈	—	4	1	no	—
895	C₂²	—	2	2	no	—
896	C₂²	—	2	2	no	—
897	C₂²	—	2	2	no	—
898	C₂²	—	4	1	no	—
899	C₂²	—	4	1	no	—
900	C₂²	—	4	1	no	—
901	C₂²	—	4	1	no	—
902	C₂²	—	4	1	no	—
903	C₂²	—	4	1	no	—
904	C₂²	—	4	1	no	—
905	C₂²	—	4	1	no	—
906	C₂²	—	4	2	no	—
907	C₂²	—	4	1	no	—
908	C₂²	—	4	1	no	—
909	C₂²	—	4	2	no	—
910	C₂²	—	4	1	no	—
911	C₂²	—	4	2	no	—
912	C₂²	—	8	1	no	—
913	C₂²	—	8	1	no	—
914	C₂²	—	8	1	no	—
915	C₂²	—	8	1	no	—
916	C₂²	—	8	1	no	—
917	C₂²	—	8	1	no	—
918	C₂²	—	8	1	no	—
919	C₂²	—	8	1	no	—
920	C₂²	—	8	1	no	—
921	C₂²	—	8	1	no	—
922	C₂²	—	8	1	no	—
923	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
924	C₂²	D₄²×C₇₉	1	1	yes	characteristic
925	C₂²	D₄²×C₇₉	1	1	yes	characteristic
926	C₂²	C₂×#135×C₇₉	1	1	yes	characteristic
927	C₂²	#575×C₇₉	1	1	yes	characteristic
928	C₂²	#577×C₇₉	1	1	yes	characteristic
929	C₂²	#578×C₇₉	1	1	yes	characteristic
930	C₄	—	2	4	no	—
931	C₄	—	2	2	no	—
932	C₄	—	2	2	no	—
933	C₄	—	4	2	no	—
934	C₄	—	4	2	no	—
935	C₄	—	4	1	no	—
936	C₄	—	4	1	no	—
937	C₄	—	4	2	no	—
938	C₄	—	4	2	no	—
939	C₄	—	8	1	no	—
940	C₄	C₂×#127×C₇₉	1	1	yes	characteristic
941	C₄	#535×C₇₉	1	1	yes	characteristic
942	C₄	D₄²×C₇₉	1	1	yes	characteristic
943	C₄	D₄²×C₇₉	1	1	yes	characteristic
944	C₂	—	4	2	no	—
945	C₂	—	8	1	no	—
946	C₂	—	8	2	no	—
947	C₂	—	16	1	no	—
948	C₂	C₇₉×#2433	1	1	yes	characteristic
949	C₂	C₇₉×#3002	1	1	yes	characteristic
950	C₂	C₇₉×#3013	1	1	yes	characteristic
951	C₂	C₇₉×#3275	1	1	yes	characteristic
952	C₂	C₇₉×#3277	1	1	yes	characteristic
953	C₂	C₇₉×#3282	1	1	yes	characteristic
954	C₂	C₇₉×#3285	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ C₂×C₄×D₄×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#548×C₇₉	C₂	semidirect
2. C₂×#495×C₇₉	C₂	semidirect
3. C₂×#464×C₇₉	C₂	semidirect
4. C₂×#452×C₇₉	C₂	semidirect
5. C₂×#449×C₇₉	C₂	semidirect
6. C₂×#451×C₇₉	C₂	semidirect
7. C₂×#448×C₇₉	C₂	semidirect
8. C₇₉×#2540	C₂	semidirect
9. C₇₉×#2001	C₂	semidirect
10. C₇₉×#2000	C₂	semidirect
11. C₇₉×#2000	C₂	semidirect
12. C₇₉×#1999	C₂	semidirect
13. C₇₉×#1983	C₂	semidirect
14. C₇₉×#1954	C₂	semidirect
15. C₄×#103×C₇₉	C₂	semidirect
120. #124×C₇₉	D₄	semidirect
136. C₄×Q₈×C₇₉	D₄	semidirect
167. #103×C₇₉	D₄	semidirect
168. #103×C₇₉	D₄	semidirect
466. #25761	C₇₉	direct (N × H)
478. C₂×#548	C₂×C₇₉	semidirect
479. C₂×#495	C₂×C₇₉	semidirect
480. C₂×#464	C₂×C₇₉	semidirect
481. C₂×#452	C₂×C₇₉	semidirect
482. C₂×#449	C₂×C₇₉	semidirect
483. C₂×#451	C₂×C₇₉	semidirect
484. C₂×#448	C₂×C₇₉	semidirect
485. #2540	C₂×C₇₉	semidirect
486. #2001	C₂×C₇₉	semidirect
487. #2000	C₂×C₇₉	semidirect
488. #2000	C₂×C₇₉	semidirect
489. #1999	C₂×C₇₉	semidirect
490. #1983	C₂×C₇₉	semidirect
491. #1954	C₂×C₇₉	semidirect
492. C₄×#103	C₂×C₇₉	semidirect
493. C₇₉	#25761	direct (N × H)
598. #124	D₄×C₇₉	semidirect
614. C₄×Q₈	D₄×C₇₉	semidirect
645. #103	D₄×C₇₉	semidirect
646. #103	D₄×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#548×C₇₉	2
C₂×#495×C₇₉	2
C₂×#464×C₇₉	2
C₂×#452×C₇₉	2
C₂×#449×C₇₉	2
C₂×#451×C₇₉	2
C₂×#448×C₇₉	2
C₇₉×#2540	2
C₇₉×#2001	2
C₇₉×#2000	2
C₇₉×#1999	2
C₇₉×#1983	2
C₇₉×#1954	2
C₄×#103×C₇₉	2
#25761	79

Subgroups — C79×#25761 #34137450

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#25761 #34137450