Subgroups — C₇₉×#24444 #34136133

Order 20224.

1662 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#546×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#469×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#449×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#447×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#417×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₉×#2416	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#2042	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#2035	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#2012	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#2000	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1879	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₉×#1874	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₉×#1870	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₉×#1864	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#1786	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₇₉	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₇₉	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic, complemented
19	C₂²×D₈×C₇₉	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₇₉	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₇₉	C₂²	1	1	yes	characteristic, complemented
22	#546×C₇₉	—	2	4	no	—
23	#546×C₇₉	—	2	4	no	—
24	C₂×#124×C₇₉	C₂²	1	1	yes	characteristic
25	C₂×#123×C₇₉	—	2	1	no	—
26	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
27	C₂×#121×C₇₉	—	2	1	no	—
28	C₂×#121×C₇₉	—	2	1	no	—
29	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
30	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
31	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic, complemented
32	C₂×#120×C₇₉	—	2	1	no	—
33	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
36	C₂²×C₂²⋊C₄×C₇₉	—	2	1	no	—
37	#469×C₇₉	—	2	4	no	—
38	#449×C₇₉	—	2	4	no	—
39	#447×C₇₉	—	2	4	no	—
40	C₂×#106×C₇₉	C₂²	1	1	yes	characteristic, complemented
41	#417×C₇₉	—	2	4	no	—
42	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic, complemented
43	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic, complemented
44	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic, complemented
45	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
46	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
47	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
48	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
49	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
50	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
51	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
54	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
55	#396×C₇₉	—	2	1	no	—
56	#394×C₇₉	—	2	1	no	—
57	#390×C₇₉	C₂²	1	1	yes	characteristic, complemented
58	#389×C₇₉	C₂²	1	1	yes	characteristic, complemented
59	#386×C₇₉	—	2	1	no	—
60	#380×C₇₉	C₂²	1	1	yes	characteristic
61	#340×C₇₉	C₂²	1	1	yes	characteristic, complemented
62	#340×C₇₉	C₂²	1	1	yes	characteristic, complemented
63	#336×C₇₉	C₂²	1	1	yes	characteristic, complemented
64	#336×C₇₉	C₂²	1	1	yes	characteristic, complemented
65	C₂⁵×C₇₉	—	2	1	no	—
66	C₂×#41×C₇₉	—	2	2	no	—
67	C₂×#41×C₇₉	—	2	2	no	—
68	C₂×#41×C₇₉	—	2	2	no	—
69	C₂×#41×C₇₉	—	4	1	no	—
70	C₂×#41×C₇₉	—	4	1	no	—
71	C₂×#41×C₇₉	D₄	1	4	yes	complemented
72	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
73	C₂²×D₄×C₇₉	—	2	1	no	—
74	C₂²×D₄×C₇₉	—	2	1	no	—
75	C₂²×D₄×C₇₉	—	2	2	no	—
76	C₂²×D₄×C₇₉	—	2	2	no	—
77	C₂²×D₄×C₇₉	—	2	2	no	—
78	C₂²×D₄×C₇₉	—	2	2	no	—
79	C₂²×D₄×C₇₉	—	2	1	no	—
80	C₂²×D₄×C₇₉	—	2	1	no	—
81	C₂²×D₄×C₇₉	—	2	1	no	—
82	C₂²×D₄×C₇₉	—	4	1	no	—
83	C₂²×D₄×C₇₉	—	4	1	no	—
84	C₂²×D₄×C₇₉	D₄	1	1	yes	characteristic
85	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₇₉	—	2	1	no	—
89	C₂³×C₄×C₇₉	—	2	1	no	—
90	C₂³×C₄×C₇₉	—	2	1	no	—
91	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
93	C₂×SD₁₆×C₇₉	—	2	2	no	—
94	C₂×SD₁₆×C₇₉	—	4	1	no	—
95	C₂×SD₁₆×C₇₉	—	4	1	no	—
96	C₂×D₈×C₇₉	—	2	2	no	—
97	C₂×D₈×C₇₉	—	2	2	no	—
98	C₂×D₈×C₇₉	—	2	2	no	—
99	C₂×D₈×C₇₉	—	2	2	no	—
100	C₂×D₈×C₇₉	—	2	2	no	—
101	C₂×D₈×C₇₉	—	4	1	no	—
102	C₂×M₁₆×C₇₉	—	2	2	no	—
103	C₂×M₁₆×C₇₉	—	2	2	no	—
104	C₂×M₁₆×C₇₉	—	4	1	no	—
105	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
109	#124×C₇₉	—	2	2	no	—
110	#124×C₇₉	—	2	2	no	—
111	#123×C₇₉	—	2	8	no	—
112	C₂²⋊Q₈×C₇₉	—	2	2	no	—
113	C₂²⋊Q₈×C₇₉	—	2	2	no	—
114	#121×C₇₉	—	2	8	no	—
115	#121×C₇₉	—	2	2	no	—
116	#121×C₇₉	—	2	2	no	—
117	#121×C₇₉	—	2	2	no	—
118	#121×C₇₉	—	2	2	no	—
119	#121×C₇₉	—	4	1	no	—
120	#121×C₇₉	—	4	4	no	—
121	#121×C₇₉	D₄	1	4	yes	complemented
122	#120×C₇₉	—	2	8	no	—
123	C₄×D₄×C₇₉	—	2	2	no	—
124	C₄×D₄×C₇₉	—	2	2	no	—
125	C₄×D₄×C₇₉	—	2	2	no	—
126	C₄×D₄×C₇₉	—	2	2	no	—
127	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
128	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
129	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
130	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
131	C₂×C₄⋊C₄×C₇₉	—	4	1	no	—
132	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊C₄×C₇₉	—	2	8	no	—
138	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
139	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
140	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
141	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
142	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
143	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
144	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
145	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
146	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
147	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
148	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
149	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
150	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
151	#106×C₇₉	—	2	2	no	—
152	#103×C₇₉	—	2	2	no	—
153	#103×C₇₉	—	2	2	no	—
154	#103×C₇₉	—	2	2	no	—
155	#102×C₇₉	—	2	2	no	—
156	#102×C₇₉	—	2	2	no	—
157	#102×C₇₉	—	2	2	no	—
158	#102×C₇₉	—	2	2	no	—
159	#102×C₇₉	—	2	2	no	—
160	#102×C₇₉	—	4	1	no	—
161	#102×C₇₉	D₄	1	4	yes	complemented
162	C₂²⋊C₈×C₇₉	—	2	2	no	—
163	C₂²⋊C₈×C₇₉	—	2	2	no	—
164	C₂²⋊C₈×C₇₉	—	4	1	no	—
165	#95×C₇₉	—	2	1	no	—
166	#95×C₇₉	—	2	1	no	—
167	C₂⁴×C₇₉	—	2	1	no	—
168	C₂⁴×C₇₉	—	2	4	no	—
169	C₂⁴×C₇₉	—	2	1	no	—
170	C₂⁴×C₇₉	—	2	1	no	—
171	C₂⁴×C₇₉	—	4	2	no	—
172	C₂⁴×C₇₉	—	4	2	no	—
173	C₂⁴×C₇₉	—	4	2	no	—
174	C₂⁴×C₇₉	—	4	2	no	—
175	C₂⁴×C₇₉	—	8	1	no	—
176	C₂⁴×C₇₉	—	8	1	no	—
177	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
178	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
179	#41×C₇₉	—	2	8	no	—
180	#41×C₇₉	—	4	4	no	—
181	#41×C₇₉	—	4	4	no	—
182	#41×C₇₉	—	4	4	no	—
183	C₂×Q₈×C₇₉	—	2	1	no	—
184	C₂×Q₈×C₇₉	—	2	1	no	—
185	C₂×Q₈×C₇₉	—	2	1	no	—
186	C₂×Q₈×C₇₉	—	2	1	no	—
187	C₂×Q₈×C₇₉	—	2	1	no	—
188	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
189	C₂×D₄×C₇₉	—	2	4	no	—
190	C₂×D₄×C₇₉	—	2	2	no	—
191	C₂×D₄×C₇₉	—	2	4	no	—
192	C₂×D₄×C₇₉	—	2	2	no	—
193	C₂×D₄×C₇₉	—	2	4	no	—
194	C₂×D₄×C₇₉	—	2	1	no	—
195	C₂×D₄×C₇₉	—	2	1	no	—
196	C₂×D₄×C₇₉	—	2	1	no	—
197	C₂×D₄×C₇₉	—	2	1	no	—
198	C₂×D₄×C₇₉	—	2	1	no	—
199	C₂×D₄×C₇₉	—	2	1	no	—
200	C₂×D₄×C₇₉	—	2	1	no	—
201	C₂×D₄×C₇₉	—	2	1	no	—
202	C₂×D₄×C₇₉	—	2	1	no	—
203	C₂×D₄×C₇₉	—	2	1	no	—
204	C₂×D₄×C₇₉	—	2	1	no	—
205	C₂×D₄×C₇₉	—	2	1	no	—
206	C₂×D₄×C₇₉	—	2	1	no	—
207	C₂×D₄×C₇₉	—	2	1	no	—
208	C₂×D₄×C₇₉	—	4	1	no	—
209	C₂×D₄×C₇₉	—	4	2	no	—
210	C₂×D₄×C₇₉	—	4	2	no	—
211	C₂×D₄×C₇₉	—	4	2	no	—
212	C₂×D₄×C₇₉	—	4	4	no	—
213	C₂×D₄×C₇₉	—	4	4	no	—
214	C₂×D₄×C₇₉	—	4	4	no	—
215	C₂×D₄×C₇₉	—	4	2	no	—
216	C₂×D₄×C₇₉	—	4	2	no	—
217	C₂×D₄×C₇₉	—	4	4	no	—
218	C₂×D₄×C₇₉	—	4	2	no	—
219	C₂×D₄×C₇₉	—	4	2	no	—
220	C₂×D₄×C₇₉	—	4	2	no	—
221	C₂×D₄×C₇₉	—	4	2	no	—
222	C₂×D₄×C₇₉	—	8	1	no	—
223	C₂×D₄×C₇₉	—	8	1	no	—
224	C₂×D₄×C₇₉	—	8	1	no	—
225	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
226	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
227	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
228	C₂×D₄×C₇₉	#41	1	2	yes	—
229	C₂²×C₄×C₇₉	—	2	1	no	—
230	C₂²×C₄×C₇₉	—	2	1	no	—
231	C₂²×C₄×C₇₉	—	2	1	no	—
232	C₂²×C₄×C₇₉	—	2	1	no	—
233	C₂²×C₄×C₇₉	—	2	1	no	—
234	C₂²×C₄×C₇₉	—	2	1	no	—
235	C₂²×C₄×C₇₉	—	2	1	no	—
236	C₂²×C₄×C₇₉	—	2	4	no	—
237	C₂²×C₄×C₇₉	—	2	4	no	—
238	C₂²×C₄×C₇₉	—	2	1	no	—
239	C₂²×C₄×C₇₉	—	2	1	no	—
240	C₂²×C₄×C₇₉	—	2	1	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	—	4	2	no	—
247	C₂²×C₄×C₇₉	—	4	2	no	—
248	C₂²×C₄×C₇₉	—	4	2	no	—
249	C₂²×C₄×C₇₉	—	4	2	no	—
250	C₂²×C₄×C₇₉	—	8	1	no	—
251	C₂²×C₄×C₇₉	—	8	1	no	—
252	C₂²×C₄×C₇₉	—	8	1	no	—
253	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
258	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
259	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
260	SD₁₆×C₇₉	—	4	4	no	—
261	D₈×C₇₉	—	4	4	no	—
262	D₈×C₇₉	—	4	4	no	—
263	M₁₆×C₇₉	—	4	4	no	—
264	C₂×C₈×C₇₉	—	2	1	no	—
265	C₂×C₈×C₇₉	—	2	1	no	—
266	C₂×C₈×C₇₉	—	2	1	no	—
267	C₂×C₈×C₇₉	—	2	1	no	—
268	C₂×C₈×C₇₉	—	2	1	no	—
269	C₂×C₈×C₇₉	—	2	1	no	—
270	C₂×C₈×C₇₉	—	2	1	no	—
271	C₂×C₈×C₇₉	—	2	1	no	—
272	C₂×C₈×C₇₉	—	2	1	no	—
273	C₂×C₈×C₇₉	—	2	1	no	—
274	C₂×C₈×C₇₉	—	2	1	no	—
275	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
276	C₄⋊C₄×C₇₉	—	2	4	no	—
277	C₄⋊C₄×C₇₉	—	2	2	no	—
278	C₄⋊C₄×C₇₉	—	2	1	no	—
279	C₄⋊C₄×C₇₉	—	2	1	no	—
280	C₄⋊C₄×C₇₉	—	2	1	no	—
281	C₄⋊C₄×C₇₉	—	2	1	no	—
282	C₄⋊C₄×C₇₉	—	2	1	no	—
283	C₄⋊C₄×C₇₉	—	2	1	no	—
284	C₄⋊C₄×C₇₉	—	4	2	no	—
285	C₄⋊C₄×C₇₉	—	4	2	no	—
286	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
287	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
288	C₂²⋊C₄×C₇₉	—	2	4	no	—
289	C₂²⋊C₄×C₇₉	—	2	4	no	—
290	C₂²⋊C₄×C₇₉	—	2	4	no	—
291	C₂²⋊C₄×C₇₉	—	2	4	no	—
292	C₂²⋊C₄×C₇₉	—	2	2	no	—
293	C₂²⋊C₄×C₇₉	—	2	2	no	—
294	C₂²⋊C₄×C₇₉	—	2	4	no	—
295	C₂²⋊C₄×C₇₉	—	4	2	no	—
296	C₂²⋊C₄×C₇₉	—	4	2	no	—
297	C₂²⋊C₄×C₇₉	—	4	2	no	—
298	C₂²⋊C₄×C₇₉	—	4	2	no	—
299	C₂²⋊C₄×C₇₉	—	8	1	no	—
300	C₄²×C₇₉	—	2	1	no	—
301	C₄²×C₇₉	—	2	1	no	—
302	C₂³×C₇₉	—	2	1	no	—
303	C₂³×C₇₉	—	2	2	no	—
304	C₂³×C₇₉	—	2	1	no	—
305	C₂³×C₇₉	—	2	1	no	—
306	C₂³×C₇₉	—	2	2	no	—
307	C₂³×C₇₉	—	2	1	no	—
308	C₂³×C₇₉	—	2	1	no	—
309	C₂³×C₇₉	—	2	2	no	—
310	C₂³×C₇₉	—	2	1	no	—
311	C₂³×C₇₉	—	2	1	no	—
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	2	no	—
318	C₂³×C₇₉	—	4	8	no	—
319	C₂³×C₇₉	—	4	8	no	—
320	C₂³×C₇₉	—	4	1	no	—
321	C₂³×C₇₉	—	4	1	no	—
322	C₂³×C₇₉	—	4	1	no	—
323	C₂³×C₇₉	—	4	1	no	—
324	C₂³×C₇₉	—	4	1	no	—
325	C₂³×C₇₉	—	4	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	—	8	4	no	—
338	C₂³×C₇₉	—	8	4	no	—
339	C₂³×C₇₉	—	8	4	no	—
340	C₂³×C₇₉	—	8	4	no	—
341	C₂³×C₇₉	—	8	4	no	—
342	C₂³×C₇₉	#120	1	2	yes	—
343	C₂³×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
344	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
345	Q₈×C₇₉	—	2	2	no	—
346	Q₈×C₇₉	—	2	2	no	—
347	Q₈×C₇₉	—	4	1	no	—
348	Q₈×C₇₉	—	4	1	no	—
349	D₄×C₇₉	—	2	2	no	—
350	D₄×C₇₉	—	2	2	no	—
351	D₄×C₇₉	—	2	2	no	—
352	D₄×C₇₉	—	2	2	no	—
353	D₄×C₇₉	—	2	2	no	—
354	D₄×C₇₉	—	4	4	no	—
355	D₄×C₇₉	—	4	8	no	—
356	D₄×C₇₉	—	4	8	no	—
357	D₄×C₇₉	—	4	1	no	—
358	D₄×C₇₉	—	4	1	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	—	8	4	no	—
364	D₄×C₇₉	—	8	4	no	—
365	D₄×C₇₉	—	8	4	no	—
366	D₄×C₇₉	#121	1	4	yes	complemented
367	C₂×C₄×C₇₉	—	2	1	no	—
368	C₂×C₄×C₇₉	—	2	1	no	—
369	C₂×C₄×C₇₉	—	2	2	no	—
370	C₂×C₄×C₇₉	—	2	2	no	—
371	C₂×C₄×C₇₉	—	2	2	no	—
372	C₂×C₄×C₇₉	—	2	2	no	—
373	C₂×C₄×C₇₉	—	2	1	no	—
374	C₂×C₄×C₇₉	—	2	1	no	—
375	C₂×C₄×C₇₉	—	2	2	no	—
376	C₂×C₄×C₇₉	—	2	2	no	—
377	C₂×C₄×C₇₉	—	2	1	no	—
378	C₂×C₄×C₇₉	—	2	1	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	—	2	1	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	—	8	4	no	—
403	C₂×C₄×C₇₉	—	8	4	no	—
404	C₂×C₄×C₇₉	#120	1	2	yes	—
405	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
409	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
410	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
411	C₈×C₇₉	—	2	2	no	—
412	C₈×C₇₉	—	4	1	no	—
413	C₈×C₇₉	—	4	1	no	—
414	C₈×C₇₉	—	4	1	no	—
415	C₂²×C₇₉	—	2	2	no	—
416	C₂²×C₇₉	—	2	4	no	—
417	C₂²×C₇₉	—	2	2	no	—
418	C₂²×C₇₉	—	2	2	no	—
419	C₂²×C₇₉	—	2	2	no	—
420	C₂²×C₇₉	—	2	2	no	—
421	C₂²×C₇₉	—	2	2	no	—
422	C₂²×C₇₉	—	4	1	no	—
423	C₂²×C₇₉	—	4	2	no	—
424	C₂²×C₇₉	—	4	1	no	—
425	C₂²×C₇₉	—	4	2	no	—
426	C₂²×C₇₉	—	4	2	no	—
427	C₂²×C₇₉	—	4	1	no	—
428	C₂²×C₇₉	—	4	1	no	—
429	C₂²×C₇₉	—	4	1	no	—
430	C₂²×C₇₉	—	4	2	no	—
431	C₂²×C₇₉	—	4	1	no	—
432	C₂²×C₇₉	—	4	2	no	—
433	C₂²×C₇₉	—	4	1	no	—
434	C₂²×C₇₉	—	4	1	no	—
435	C₂²×C₇₉	—	4	2	no	—
436	C₂²×C₇₉	—	4	2	no	—
437	C₂²×C₇₉	—	4	2	no	—
438	C₂²×C₇₉	—	4	2	no	—
439	C₂²×C₇₉	—	8	16	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	—	8	1	no	—
446	C₂²×C₇₉	—	8	1	no	—
447	C₂²×C₇₉	—	8	1	no	—
448	C₂²×C₇₉	—	8	1	no	—
449	C₂²×C₇₉	—	8	1	no	—
450	C₂²×C₇₉	—	8	1	no	—
451	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
452	C₂²×C₇₉	D₄²	1	1	yes	characteristic
453	C₂²×C₇₉	#546	1	1	yes	characteristic
454	C₂²×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
455	C₂²×C₇₉	#575	1	1	yes	characteristic
456	C₂²×C₇₉	#576	1	1	yes	characteristic
457	C₂²×C₇₉	#577	1	1	yes	characteristic
458	C₄×C₇₉	—	2	2	no	—
459	C₄×C₇₉	—	4	1	no	—
460	C₄×C₇₉	—	4	2	no	—
461	C₄×C₇₉	—	4	1	no	—
462	C₄×C₇₉	—	4	2	no	—
463	C₄×C₇₉	—	4	1	no	—
464	C₄×C₇₉	—	4	2	no	—
465	C₄×C₇₉	—	8	1	no	—
466	C₄×C₇₉	—	8	1	no	—
467	C₄×C₇₉	C₂×#121	1	1	yes	characteristic
468	C₄×C₇₉	#534	1	1	yes	characteristic
469	C₄×C₇₉	D₄²	1	1	yes	characteristic
470	C₄×C₇₉	#546	1	1	yes	characteristic
471	#24444	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
472	C₂×C₇₉	—	4	2	no	—
473	C₂×C₇₉	—	4	2	no	—
474	C₂×C₇₉	—	4	4	no	—
475	C₂×C₇₉	—	8	2	no	—
476	C₂×C₇₉	—	16	1	no	—
477	C₂×C₇₉	#2410	1	1	yes	characteristic
478	C₂×C₇₉	#3006	1	1	yes	characteristic
479	C₂×C₇₉	#3012	1	1	yes	characteristic
480	C₂×C₇₉	#3264	1	1	yes	characteristic
481	C₂×C₇₉	#3275	1	1	yes	characteristic
482	C₂×C₇₉	#3306	1	1	yes	characteristic
483	C₂×C₇₉	#3322	1	1	yes	characteristic
484	C₂×#546	C₂×C₇₉	1	1	yes	characteristic, complemented
485	C₂×#469	C₂×C₇₉	1	1	yes	characteristic, complemented
486	C₂×#449	C₂×C₇₉	1	1	yes	characteristic, complemented
487	C₂×#447	C₂×C₇₉	1	1	yes	characteristic, complemented
488	C₂×#417	C₂×C₇₉	1	1	yes	characteristic, complemented
489	#2416	C₂×C₇₉	1	1	yes	characteristic, complemented
490	#2042	C₂×C₇₉	1	1	yes	characteristic, complemented
491	#2035	C₂×C₇₉	1	1	yes	characteristic, complemented
492	#2012	C₂×C₇₉	1	1	yes	characteristic, complemented
493	#2000	C₂×C₇₉	1	1	yes	characteristic, complemented
494	#1879	C₂×C₇₉	1	1	yes	characteristic, complemented
495	#1874	C₂×C₇₉	1	1	yes	characteristic, complemented
496	#1870	C₂×C₇₉	1	1	yes	characteristic, complemented
497	#1864	C₂×C₇₉	1	1	yes	characteristic, complemented
498	#1786	C₂×C₇₉	1	1	yes	characteristic, complemented
499	C₇₉	#24444	1	1	yes	characteristic, direct product factor, Sylow
500	C₂²×#41	C₂²×C₇₉	1	1	yes	characteristic
501	C₂³×D₄	C₂²×C₇₉	1	1	yes	characteristic
502	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic, complemented
503	C₂²×D₈	C₂²×C₇₉	1	1	yes	characteristic
504	C₂²×D₈	C₂²×C₇₉	1	1	yes	characteristic
505	C₂²×M₁₆	C₂²×C₇₉	1	1	yes	characteristic, complemented
506	#546	—	2	4	no	—
507	#546	—	2	4	no	—
508	C₂×#124	C₂²×C₇₉	1	1	yes	characteristic
509	C₂×#123	—	2	1	no	—
510	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
511	C₂×#121	—	2	1	no	—
512	C₂×#121	—	2	1	no	—
513	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
514	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
515	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic, complemented
516	C₂×#120	—	2	1	no	—
517	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
518	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
519	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic, complemented
520	C₂²×C₂²⋊C₄	—	2	1	no	—
521	#469	—	2	4	no	—
522	#449	—	2	4	no	—
523	#447	—	2	4	no	—
524	C₂×#106	C₂²×C₇₉	1	1	yes	characteristic, complemented
525	#417	—	2	4	no	—
526	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic, complemented
527	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic, complemented
528	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic, complemented
529	C₂×#102	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×#102	C₂²×C₇₉	1	1	yes	characteristic
534	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
535	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic, complemented
536	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
537	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
538	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
539	#396	—	2	1	no	—
540	#394	—	2	1	no	—
541	#390	C₂²×C₇₉	1	1	yes	characteristic, complemented
542	#389	C₂²×C₇₉	1	1	yes	characteristic, complemented
543	#386	—	2	1	no	—
544	#380	C₂²×C₇₉	1	1	yes	characteristic
545	#340	C₂²×C₇₉	1	1	yes	characteristic, complemented
546	#340	C₂²×C₇₉	1	1	yes	characteristic, complemented
547	#336	C₂²×C₇₉	1	1	yes	characteristic, complemented
548	#336	C₂²×C₇₉	1	1	yes	characteristic, complemented
549	C₂⁵	—	2	1	no	—
550	C₂×#41	—	2	2	no	—
551	C₂×#41	—	2	2	no	—
552	C₂×#41	—	2	2	no	—
553	C₂×#41	—	4	1	no	—
554	C₂×#41	—	4	1	no	—
555	C₂×#41	D₄×C₇₉	1	4	yes	complemented
556	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
557	C₂²×D₄	—	2	1	no	—
558	C₂²×D₄	—	2	1	no	—
559	C₂²×D₄	—	2	2	no	—
560	C₂²×D₄	—	2	2	no	—
561	C₂²×D₄	—	2	2	no	—
562	C₂²×D₄	—	2	2	no	—
563	C₂²×D₄	—	2	1	no	—
564	C₂²×D₄	—	2	1	no	—
565	C₂²×D₄	—	2	1	no	—
566	C₂²×D₄	—	4	1	no	—
567	C₂²×D₄	—	4	1	no	—
568	C₂²×D₄	D₄×C₇₉	1	1	yes	characteristic
569	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
570	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
571	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
572	C₂³×C₄	—	2	1	no	—
573	C₂³×C₄	—	2	1	no	—
574	C₂³×C₄	—	2	1	no	—
575	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
576	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
577	C₂×SD₁₆	—	2	2	no	—
578	C₂×SD₁₆	—	4	1	no	—
579	C₂×SD₁₆	—	4	1	no	—
580	C₂×D₈	—	2	2	no	—
581	C₂×D₈	—	2	2	no	—
582	C₂×D₈	—	2	2	no	—
583	C₂×D₈	—	2	2	no	—
584	C₂×D₈	—	2	2	no	—
585	C₂×D₈	—	4	1	no	—
586	C₂×M₁₆	—	2	2	no	—
587	C₂×M₁₆	—	2	2	no	—
588	C₂×M₁₆	—	4	1	no	—
589	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
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	#124	—	2	2	no	—
594	#124	—	2	2	no	—
595	#123	—	2	8	no	—
596	C₂²⋊Q₈	—	2	2	no	—
597	C₂²⋊Q₈	—	2	2	no	—
598	#121	—	2	8	no	—
599	#121	—	2	2	no	—
600	#121	—	2	2	no	—
601	#121	—	2	2	no	—
602	#121	—	2	2	no	—
603	#121	—	4	1	no	—
604	#121	—	4	4	no	—
605	#121	D₄×C₇₉	1	4	yes	complemented
606	#120	—	2	8	no	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	2	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	—	2	2	no	—
611	C₂×C₄⋊C₄	—	2	1	no	—
612	C₂×C₄⋊C₄	—	2	2	no	—
613	C₂×C₄⋊C₄	—	2	1	no	—
614	C₂×C₄⋊C₄	—	2	1	no	—
615	C₂×C₄⋊C₄	—	4	1	no	—
616	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
621	C₂×C₂²⋊C₄	—	2	8	no	—
622	C₂×C₂²⋊C₄	—	2	1	no	—
623	C₂×C₂²⋊C₄	—	2	1	no	—
624	C₂×C₂²⋊C₄	—	2	1	no	—
625	C₂×C₂²⋊C₄	—	2	1	no	—
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	D₄×C₇₉	1	1	yes	characteristic
633	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
634	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
635	#106	—	2	2	no	—
636	#103	—	2	2	no	—
637	#103	—	2	2	no	—
638	#103	—	2	2	no	—
639	#102	—	2	2	no	—
640	#102	—	2	2	no	—
641	#102	—	2	2	no	—
642	#102	—	2	2	no	—
643	#102	—	2	2	no	—
644	#102	—	4	1	no	—
645	#102	D₄×C₇₉	1	4	yes	complemented
646	C₂²⋊C₈	—	2	2	no	—
647	C₂²⋊C₈	—	2	2	no	—
648	C₂²⋊C₈	—	4	1	no	—
649	#95	—	2	1	no	—
650	#95	—	2	1	no	—
651	C₂⁴	—	2	1	no	—
652	C₂⁴	—	2	4	no	—
653	C₂⁴	—	2	1	no	—
654	C₂⁴	—	2	1	no	—
655	C₂⁴	—	4	2	no	—
656	C₂⁴	—	4	2	no	—
657	C₂⁴	—	4	2	no	—
658	C₂⁴	—	4	2	no	—
659	C₂⁴	—	8	1	no	—
660	C₂⁴	—	8	1	no	—
661	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
662	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
663	#41	—	2	8	no	—
664	#41	—	4	4	no	—
665	#41	—	4	4	no	—
666	#41	—	4	4	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	C₂×D₄×C₇₉	1	2	yes	—
673	C₂×D₄	—	2	4	no	—
674	C₂×D₄	—	2	2	no	—
675	C₂×D₄	—	2	4	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	4	no	—
678	C₂×D₄	—	2	1	no	—
679	C₂×D₄	—	2	1	no	—
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	1	no	—
683	C₂×D₄	—	2	1	no	—
684	C₂×D₄	—	2	1	no	—
685	C₂×D₄	—	2	1	no	—
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	2	1	no	—
688	C₂×D₄	—	2	1	no	—
689	C₂×D₄	—	2	1	no	—
690	C₂×D₄	—	2	1	no	—
691	C₂×D₄	—	2	1	no	—
692	C₂×D₄	—	4	1	no	—
693	C₂×D₄	—	4	2	no	—
694	C₂×D₄	—	4	2	no	—
695	C₂×D₄	—	4	2	no	—
696	C₂×D₄	—	4	4	no	—
697	C₂×D₄	—	4	4	no	—
698	C₂×D₄	—	4	4	no	—
699	C₂×D₄	—	4	2	no	—
700	C₂×D₄	—	4	2	no	—
701	C₂×D₄	—	4	4	no	—
702	C₂×D₄	—	4	2	no	—
703	C₂×D₄	—	4	2	no	—
704	C₂×D₄	—	4	2	no	—
705	C₂×D₄	—	4	2	no	—
706	C₂×D₄	—	8	1	no	—
707	C₂×D₄	—	8	1	no	—
708	C₂×D₄	—	8	1	no	—
709	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
710	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
711	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
712	C₂×D₄	#41×C₇₉	1	2	yes	—
713	C₂²×C₄	—	2	1	no	—
714	C₂²×C₄	—	2	1	no	—
715	C₂²×C₄	—	2	1	no	—
716	C₂²×C₄	—	2	1	no	—
717	C₂²×C₄	—	2	1	no	—
718	C₂²×C₄	—	2	1	no	—
719	C₂²×C₄	—	2	1	no	—
720	C₂²×C₄	—	2	4	no	—
721	C₂²×C₄	—	2	4	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	—	4	2	no	—
731	C₂²×C₄	—	4	2	no	—
732	C₂²×C₄	—	4	2	no	—
733	C₂²×C₄	—	4	2	no	—
734	C₂²×C₄	—	8	1	no	—
735	C₂²×C₄	—	8	1	no	—
736	C₂²×C₄	—	8	1	no	—
737	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
738	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
739	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
740	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
741	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
742	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
743	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
744	SD₁₆	—	4	4	no	—
745	D₈	—	4	4	no	—
746	D₈	—	4	4	no	—
747	M₁₆	—	4	4	no	—
748	C₂×C₈	—	2	1	no	—
749	C₂×C₈	—	2	1	no	—
750	C₂×C₈	—	2	1	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	C₂×D₄×C₇₉	1	2	yes	—
760	C₄⋊C₄	—	2	4	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	1	no	—
763	C₄⋊C₄	—	2	1	no	—
764	C₄⋊C₄	—	2	1	no	—
765	C₄⋊C₄	—	2	1	no	—
766	C₄⋊C₄	—	2	1	no	—
767	C₄⋊C₄	—	2	1	no	—
768	C₄⋊C₄	—	4	2	no	—
769	C₄⋊C₄	—	4	2	no	—
770	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
771	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
772	C₂²⋊C₄	—	2	4	no	—
773	C₂²⋊C₄	—	2	4	no	—
774	C₂²⋊C₄	—	2	4	no	—
775	C₂²⋊C₄	—	2	4	no	—
776	C₂²⋊C₄	—	2	2	no	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	—	2	4	no	—
779	C₂²⋊C₄	—	4	2	no	—
780	C₂²⋊C₄	—	4	2	no	—
781	C₂²⋊C₄	—	4	2	no	—
782	C₂²⋊C₄	—	4	2	no	—
783	C₂²⋊C₄	—	8	1	no	—
784	C₄²	—	2	1	no	—
785	C₄²	—	2	1	no	—
786	C₂³	—	2	1	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	2	1	no	—
789	C₂³	—	2	1	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	2	1	no	—
792	C₂³	—	2	1	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	2	1	no	—
795	C₂³	—	2	1	no	—
796	C₂³	—	2	1	no	—
797	C₂³	—	2	1	no	—
798	C₂³	—	2	1	no	—
799	C₂³	—	2	1	no	—
800	C₂³	—	2	1	no	—
801	C₂³	—	2	2	no	—
802	C₂³	—	4	8	no	—
803	C₂³	—	4	8	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	—	4	1	no	—
818	C₂³	—	4	1	no	—
819	C₂³	—	4	1	no	—
820	C₂³	—	4	1	no	—
821	C₂³	—	8	4	no	—
822	C₂³	—	8	4	no	—
823	C₂³	—	8	4	no	—
824	C₂³	—	8	4	no	—
825	C₂³	—	8	4	no	—
826	C₂³	#120×C₇₉	1	2	yes	—
827	C₂³	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
828	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
829	Q₈	—	2	2	no	—
830	Q₈	—	2	2	no	—
831	Q₈	—	4	1	no	—
832	Q₈	—	4	1	no	—
833	D₄	—	2	2	no	—
834	D₄	—	2	2	no	—
835	D₄	—	2	2	no	—
836	D₄	—	2	2	no	—
837	D₄	—	2	2	no	—
838	D₄	—	4	4	no	—
839	D₄	—	4	8	no	—
840	D₄	—	4	8	no	—
841	D₄	—	4	1	no	—
842	D₄	—	4	1	no	—
843	D₄	—	4	1	no	—
844	D₄	—	4	1	no	—
845	D₄	—	4	1	no	—
846	D₄	—	4	1	no	—
847	D₄	—	8	4	no	—
848	D₄	—	8	4	no	—
849	D₄	—	8	4	no	—
850	D₄	#121×C₇₉	1	4	yes	complemented
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	4	8	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	—	4	1	no	—
884	C₂×C₄	—	4	1	no	—
885	C₂×C₄	—	4	1	no	—
886	C₂×C₄	—	8	4	no	—
887	C₂×C₄	—	8	4	no	—
888	C₂×C₄	#120×C₇₉	1	2	yes	—
889	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
890	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
891	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
892	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
893	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
894	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
895	C₈	—	2	2	no	—
896	C₈	—	4	1	no	—
897	C₈	—	4	1	no	—
898	C₈	—	4	1	no	—
899	C₂²	—	2	2	no	—
900	C₂²	—	2	2	no	—
901	C₂²	—	2	4	no	—
902	C₂²	—	2	2	no	—
903	C₂²	—	2	2	no	—
904	C₂²	—	2	2	no	—
905	C₂²	—	2	2	no	—
906	C₂²	—	4	1	no	—
907	C₂²	—	4	1	no	—
908	C₂²	—	4	2	no	—
909	C₂²	—	4	1	no	—
910	C₂²	—	4	2	no	—
911	C₂²	—	4	1	no	—
912	C₂²	—	4	1	no	—
913	C₂²	—	4	2	no	—
914	C₂²	—	4	1	no	—
915	C₂²	—	4	2	no	—
916	C₂²	—	4	1	no	—
917	C₂²	—	4	2	no	—
918	C₂²	—	4	2	no	—
919	C₂²	—	4	1	no	—
920	C₂²	—	4	2	no	—
921	C₂²	—	4	2	no	—
922	C₂²	—	4	2	no	—
923	C₂²	—	8	16	no	—
924	C₂²	—	8	1	no	—
925	C₂²	—	8	1	no	—
926	C₂²	—	8	1	no	—
927	C₂²	—	8	1	no	—
928	C₂²	—	8	1	no	—
929	C₂²	—	8	1	no	—
930	C₂²	—	8	1	no	—
931	C₂²	—	8	1	no	—
932	C₂²	—	8	1	no	—
933	C₂²	—	8	1	no	—
934	C₂²	—	8	1	no	—
935	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
936	C₂²	D₄²×C₇₉	1	1	yes	characteristic
937	C₂²	#546×C₇₉	1	1	yes	characteristic
938	C₂²	C₂×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
939	C₂²	#575×C₇₉	1	1	yes	characteristic
940	C₂²	#576×C₇₉	1	1	yes	characteristic
941	C₂²	#577×C₇₉	1	1	yes	characteristic
942	C₄	—	2	2	no	—
943	C₄	—	4	1	no	—
944	C₄	—	4	2	no	—
945	C₄	—	4	1	no	—
946	C₄	—	4	2	no	—
947	C₄	—	4	1	no	—
948	C₄	—	4	2	no	—
949	C₄	—	8	1	no	—
950	C₄	—	8	1	no	—
951	C₄	C₂×#121×C₇₉	1	1	yes	characteristic
952	C₄	#534×C₇₉	1	1	yes	characteristic
953	C₄	D₄²×C₇₉	1	1	yes	characteristic
954	C₄	#546×C₇₉	1	1	yes	characteristic
955	C₂	—	4	2	no	—
956	C₂	—	4	2	no	—
957	C₂	—	4	4	no	—
958	C₂	—	8	2	no	—
959	C₂	—	16	1	no	—
960	C₂	C₇₉×#2410	1	1	yes	characteristic
961	C₂	C₇₉×#3006	1	1	yes	characteristic
962	C₂	C₇₉×#3012	1	1	yes	characteristic
963	C₂	C₇₉×#3264	1	1	yes	characteristic
964	C₂	C₇₉×#3275	1	1	yes	characteristic
965	C₂	C₇₉×#3306	1	1	yes	characteristic
966	C₂	C₇₉×#3322	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×#546×C₇₉	C₂	semidirect
2. C₂×#469×C₇₉	C₂	semidirect
3. C₂×#449×C₇₉	C₂	semidirect
4. C₂×#447×C₇₉	C₂	semidirect
5. C₂×#417×C₇₉	C₂	semidirect
6. C₇₉×#2416	C₂	semidirect
7. C₇₉×#2042	C₂	semidirect
8. C₇₉×#2035	C₂	semidirect
9. C₇₉×#2012	C₂	semidirect
10. C₇₉×#2000	C₂	semidirect
11. C₇₉×#1879	C₂	semidirect
12. C₇₉×#1874	C₂	semidirect
13. C₇₉×#1870	C₂	semidirect
14. C₇₉×#1864	C₂	semidirect
15. C₇₉×#1786	C₂	semidirect
18. C₂²×SD₁₆×C₇₉	C₂²	semidirect
21. C₂²×M₁₆×C₇₉	C₂²	semidirect
31. C₂×#121×C₇₉	C₂²	semidirect
35. C₂²×C₄⋊C₄×C₇₉	C₂²	semidirect
40. C₂×#106×C₇₉	C₂²	semidirect
42. C₂×#103×C₇₉	C₂²	semidirect
43. C₂×#103×C₇₉	C₂²	semidirect
44. C₂×#103×C₇₉	C₂²	semidirect
51. C₂×#102×C₇₉	C₂²	semidirect
54. C₂×C₂²⋊C₈×C₇₉	C₂²	semidirect
57. #390×C₇₉	C₂²	semidirect
58. #389×C₇₉	C₂²	semidirect
61. #340×C₇₉	C₂²	semidirect
62. #340×C₇₉	C₂²	semidirect
63. #336×C₇₉	C₂²	semidirect
64. #336×C₇₉	C₂²	semidirect
71. C₂×#41×C₇₉	D₄	semidirect
121. #121×C₇₉	D₄	semidirect
161. #102×C₇₉	D₄	semidirect
366. D₄×C₇₉	#121	semidirect
471. #24444	C₇₉	direct (N × H)
484. C₂×#546	C₂×C₇₉	semidirect
485. C₂×#469	C₂×C₇₉	semidirect
486. C₂×#449	C₂×C₇₉	semidirect
487. C₂×#447	C₂×C₇₉	semidirect
488. C₂×#417	C₂×C₇₉	semidirect
489. #2416	C₂×C₇₉	semidirect
490. #2042	C₂×C₇₉	semidirect
491. #2035	C₂×C₇₉	semidirect
492. #2012	C₂×C₇₉	semidirect
493. #2000	C₂×C₇₉	semidirect
494. #1879	C₂×C₇₉	semidirect
495. #1874	C₂×C₇₉	semidirect
496. #1870	C₂×C₇₉	semidirect
497. #1864	C₂×C₇₉	semidirect
498. #1786	C₂×C₇₉	semidirect
499. C₇₉	#24444	direct (N × H)
502. C₂²×SD₁₆	C₂²×C₇₉	semidirect
505. C₂²×M₁₆	C₂²×C₇₉	semidirect
515. C₂×#121	C₂²×C₇₉	semidirect
519. C₂²×C₄⋊C₄	C₂²×C₇₉	semidirect
524. C₂×#106	C₂²×C₇₉	semidirect
526. C₂×#103	C₂²×C₇₉	semidirect
527. C₂×#103	C₂²×C₇₉	semidirect
528. C₂×#103	C₂²×C₇₉	semidirect
535. C₂×#102	C₂²×C₇₉	semidirect
538. C₂×C₂²⋊C₈	C₂²×C₇₉	semidirect
541. #390	C₂²×C₇₉	semidirect
542. #389	C₂²×C₇₉	semidirect
545. #340	C₂²×C₇₉	semidirect
546. #340	C₂²×C₇₉	semidirect
547. #336	C₂²×C₇₉	semidirect
548. #336	C₂²×C₇₉	semidirect
555. C₂×#41	D₄×C₇₉	semidirect
605. #121	D₄×C₇₉	semidirect
645. #102	D₄×C₇₉	semidirect
850. D₄	#121×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#546×C₇₉	2
C₂×#469×C₇₉	2
C₂×#449×C₇₉	2
C₂×#447×C₇₉	2
C₂×#417×C₇₉	2
C₇₉×#2416	2
C₇₉×#2042	2
C₇₉×#2035	2
C₇₉×#2012	2
C₇₉×#2000	2
C₇₉×#1879	2
C₇₉×#1874	2
C₇₉×#1870	2
C₇₉×#1864	2
C₇₉×#1786	2
#24444	79

Subgroups — C79×#24444 #34136133

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#24444 #34136133