Subgroups — C₇₉×#36530 #34148219

Order 20224.

2314 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#2852	C₂	1	2	yes	maximal, complemented
2	C₇₉×#2847	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#2578	C₂	1	2	yes	maximal, complemented
4	C₇₉×#2569	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#2559	C₂	1	2	yes	maximal, complemented
6	C₇₉×#2543	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#2522	C₂	1	2	yes	maximal, complemented
8	C₇₉×#2518	C₂	1	2	yes	maximal, complemented
9	C₇₉×#2467	C₂	1	2	yes	maximal, complemented
10	C₇₉×#2464	C₂	1	2	yes	maximal, complemented
11	C₇₉×#2424	C₂	1	2	yes	maximal, complemented
12	C₇₉×#2418	C₂	1	2	yes	maximal, complemented
13	C₇₉×#2374	C₂	1	2	yes	maximal, complemented
14	C₇₉×#2364	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#2364	C₂	1	2	yes	maximal, complemented
16	C₇₉×#2349	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#121×C₇₉	C₂	1	2	yes	maximal, complemented
18	C₄×#120×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₄×C₂²⋊C₄×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×C₄×C₇₉	C₂²	1	1	yes	characteristic
21	C₂×#126×C₇₉	C₂²	1	2	yes	complemented
22	C₂×#123×C₇₉	C₂²	1	2	yes	—
23	C₂×#121×C₇₉	C₂²	1	2	yes	—
24	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
25	C₂×#121×C₇₉	C₂²	1	2	yes	—
26	C₂×#121×C₇₉	C₂²	1	2	yes	—
27	C₂×#120×C₇₉	C₂²	1	1	yes	characteristic
28	C₂×#120×C₇₉	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₇₉	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₇₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₇₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₇₉	C₂²	1	2	yes	complemented
34	C₂²×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	—
35	C₂²×C₄²×C₇₉	C₂²	1	2	yes	—
36	#400×C₇₉	C₂²	1	2	yes	complemented
37	#399×C₇₉	C₂²	1	2	yes	—
38	#398×C₇₉	C₂²	1	1	yes	characteristic, complemented
39	#398×C₇₉	C₂²	1	2	yes	complemented
40	#397×C₇₉	C₂²	1	2	yes	—
41	#397×C₇₉	C₂²	1	1	yes	characteristic, complemented
42	#396×C₇₉	C₂²	1	2	yes	—
43	#394×C₇₉	C₂²	1	2	yes	—
44	#394×C₇₉	C₂²	1	2	yes	—
45	#394×C₇₉	C₂²	1	2	yes	—
46	#394×C₇₉	C₂²	1	2	yes	—
47	#394×C₇₉	C₂²	1	1	yes	characteristic, complemented
48	#392×C₇₉	C₂²	1	2	yes	—
49	#392×C₇₉	C₂²	1	1	yes	characteristic, complemented
50	#390×C₇₉	C₂²	1	2	yes	—
51	#390×C₇₉	C₂²	1	2	yes	complemented
52	#389×C₇₉	C₂²	1	2	yes	complemented
53	#389×C₇₉	C₂²	1	2	yes	complemented
54	#388×C₇₉	C₂²	1	2	yes	—
55	#388×C₇₉	C₂²	1	2	yes	—
56	#388×C₇₉	C₂²	1	2	yes	—
57	#388×C₇₉	C₂²	1	2	yes	complemented
58	#388×C₇₉	C₂²	1	2	yes	complemented
59	#388×C₇₉	C₂²	1	2	yes	complemented
60	#388×C₇₉	C₂²	1	2	yes	complemented
61	#388×C₇₉	C₂²	1	2	yes	complemented
62	#388×C₇₉	C₂²	1	2	yes	complemented
63	#388×C₇₉	C₂²	1	2	yes	complemented
64	#387×C₇₉	C₂²	1	2	yes	complemented
65	#387×C₇₉	C₂²	1	2	yes	complemented
66	#387×C₇₉	C₂²	1	2	yes	complemented
67	#387×C₇₉	C₂²	1	2	yes	complemented
68	#387×C₇₉	C₂²	1	2	yes	complemented
69	#387×C₇₉	C₂²	1	2	yes	complemented
70	#386×C₇₉	C₂²	1	2	yes	—
71	#386×C₇₉	C₂²	1	2	yes	—
72	#386×C₇₉	C₂²	1	1	yes	characteristic
73	#386×C₇₉	C₂²	1	2	yes	—
74	#386×C₇₉	C₂²	1	2	yes	—
75	#386×C₇₉	C₂²	1	2	yes	—
76	#386×C₇₉	C₂²	1	2	yes	—
77	#386×C₇₉	C₂²	1	2	yes	—
78	#386×C₇₉	C₂²	1	2	yes	—
79	#386×C₇₉	C₂²	1	2	yes	complemented
80	#386×C₇₉	C₂²	1	2	yes	complemented
81	#385×C₇₉	C₂²	1	2	yes	—
82	#385×C₇₉	C₂²	1	1	yes	characteristic
83	#385×C₇₉	C₂²	1	2	yes	—
84	#385×C₇₉	C₂²	1	2	yes	—
85	#385×C₇₉	C₂²	1	2	yes	complemented
86	#383×C₇₉	C₂²	1	2	yes	complemented
87	#382×C₇₉	C₂²	1	1	yes	characteristic, complemented
88	#380×C₇₉	C₂²	1	2	yes	—
89	#380×C₇₉	C₂²	1	2	yes	—
90	#380×C₇₉	C₂²	1	1	yes	characteristic
91	#380×C₇₉	C₂²	1	1	yes	characteristic, complemented
92	#379×C₇₉	C₂²	1	1	yes	characteristic
93	C₄×C₄⋊C₄×C₇₉	C₂²	1	2	yes	complemented
94	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
95	C₄×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	—
96	C₄×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	—
97	C₄×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
101	C₄×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	complemented
102	C₄×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	complemented
103	C₄×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	complemented
104	C₂×#95×C₇₉	C₂²	1	1	yes	characteristic
105	C₂×#95×C₇₉	C₂²	1	1	yes	characteristic
106	C₂×#95×C₇₉	C₂²	1	1	yes	characteristic, complemented
107	C₂⁵×C₇₉	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
109	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
110	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
111	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
113	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
114	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₇₉	—	2	4	no	—
116	C₂³×C₄×C₇₉	—	4	4	no	—
117	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
119	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
120	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
121	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
122	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
124	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
125	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
126	#126×C₇₉	—	4	4	no	—
127	#123×C₇₉	—	2	8	no	—
128	#121×C₇₉	—	2	8	no	—
129	#121×C₇₉	—	2	4	no	—
130	#121×C₇₉	—	2	8	no	—
131	#121×C₇₉	—	4	4	no	—
132	#120×C₇₉	—	2	4	no	—
133	#120×C₇₉	—	4	4	no	—
134	C₄×D₄×C₇₉	—	2	4	no	—
135	C₄×D₄×C₇₉	—	4	4	no	—
136	C₄×D₄×C₇₉	—	4	4	no	—
137	C₄×D₄×C₇₉	—	4	4	no	—
138	C₄×D₄×C₇₉	—	4	4	no	—
139	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₇₉	—	2	8	no	—
153	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
157	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
160	C₂×C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
161	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
163	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
179	C₂×C₄²×C₇₉	—	4	4	no	—
180	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
181	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
182	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
184	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
185	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
186	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
187	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
188	#95×C₇₉	C₂³	1	1	yes	characteristic
189	#95×C₇₉	C₂³	1	1	yes	characteristic
190	#95×C₇₉	C₂³	1	2	yes	—
191	#95×C₇₉	C₂³	1	2	yes	—
192	#95×C₇₉	C₂³	1	1	yes	characteristic
193	#95×C₇₉	C₂³	1	1	yes	characteristic
194	#95×C₇₉	C₂³	1	1	yes	characteristic
195	#95×C₇₉	C₂³	1	2	yes	—
196	#95×C₇₉	C₂³	1	2	yes	—
197	#95×C₇₉	C₂³	1	2	yes	—
198	#95×C₇₉	C₂³	1	2	yes	—
199	#95×C₇₉	C₂³	1	2	yes	—
200	#95×C₇₉	C₂³	1	2	yes	—
201	#95×C₇₉	C₂³	1	2	yes	—
202	#95×C₇₉	C₂³	1	2	yes	—
203	#95×C₇₉	C₂³	1	1	yes	characteristic
204	#95×C₇₉	C₂³	1	2	yes	—
205	#95×C₇₉	C₂³	1	2	yes	—
206	#95×C₇₉	C₂³	1	2	yes	—
207	#95×C₇₉	C₂³	1	2	yes	—
208	#95×C₇₉	C₂³	1	2	yes	—
209	#95×C₇₉	C₂³	1	2	yes	—
210	#95×C₇₉	C₂³	1	2	yes	—
211	C₂⁴×C₇₉	—	2	4	no	—
212	C₂⁴×C₇₉	—	2	2	no	—
213	C₂⁴×C₇₉	—	2	2	no	—
214	C₂⁴×C₇₉	—	2	2	no	—
215	C₂⁴×C₇₉	—	4	2	no	—
216	C₂⁴×C₇₉	C₂⁴	1	2	yes	—
217	C₂⁴×C₇₉	C₂⁴	1	2	yes	—
218	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
219	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
220	C₂×D₄×C₇₉	—	2	2	no	—
221	C₂×D₄×C₇₉	—	2	2	no	—
222	C₂×D₄×C₇₉	—	2	4	no	—
223	C₂×D₄×C₇₉	—	2	4	no	—
224	C₂×D₄×C₇₉	—	2	4	no	—
225	C₂×D₄×C₇₉	—	2	4	no	—
226	C₂×D₄×C₇₉	—	2	4	no	—
227	C₂×D₄×C₇₉	—	2	4	no	—
228	C₂×D₄×C₇₉	—	2	4	no	—
229	C₂×D₄×C₇₉	—	2	4	no	—
230	C₂×D₄×C₇₉	—	2	4	no	—
231	C₂×D₄×C₇₉	—	2	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	—	4	2	no	—
236	C₂×D₄×C₇₉	—	4	2	no	—
237	C₂×D₄×C₇₉	—	4	2	no	—
238	C₂×D₄×C₇₉	—	4	2	no	—
239	C₂×D₄×C₇₉	#41	1	4	yes	—
240	C₂²×C₄×C₇₉	—	2	2	no	—
241	C₂²×C₄×C₇₉	—	2	4	no	—
242	C₂²×C₄×C₇₉	—	2	4	no	—
243	C₂²×C₄×C₇₉	—	2	4	no	—
244	C₂²×C₄×C₇₉	—	2	4	no	—
245	C₂²×C₄×C₇₉	—	2	4	no	—
246	C₂²×C₄×C₇₉	—	2	4	no	—
247	C₂²×C₄×C₇₉	—	2	4	no	—
248	C₂²×C₄×C₇₉	—	2	4	no	—
249	C₂²×C₄×C₇₉	—	2	4	no	—
250	C₂²×C₄×C₇₉	—	2	2	no	—
251	C₂²×C₄×C₇₉	—	2	4	no	—
252	C₂²×C₄×C₇₉	—	2	4	no	—
253	C₂²×C₄×C₇₉	—	4	2	no	—
254	C₂²×C₄×C₇₉	—	4	2	no	—
255	C₂²×C₄×C₇₉	—	4	2	no	—
256	C₂²×C₄×C₇₉	—	4	2	no	—
257	C₂²×C₄×C₇₉	—	4	2	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	—	4	2	no	—
263	C₂²×C₄×C₇₉	—	4	16	no	—
264	C₂²×C₄×C₇₉	#41	1	4	yes	—
265	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
280	C₄⋊C₄×C₇₉	—	2	2	no	—
281	C₄⋊C₄×C₇₉	—	2	4	no	—
282	C₄⋊C₄×C₇₉	—	2	2	no	—
283	C₄⋊C₄×C₇₉	—	2	4	no	—
284	C₄⋊C₄×C₇₉	—	2	4	no	—
285	C₄⋊C₄×C₇₉	—	2	4	no	—
286	C₄⋊C₄×C₇₉	—	2	4	no	—
287	C₄⋊C₄×C₇₉	—	4	2	no	—
288	C₄⋊C₄×C₇₉	—	4	2	no	—
289	C₄⋊C₄×C₇₉	—	4	2	no	—
290	C₄⋊C₄×C₇₉	—	4	2	no	—
291	C₄⋊C₄×C₇₉	—	4	2	no	—
292	C₄⋊C₄×C₇₉	—	4	2	no	—
293	C₂²⋊C₄×C₇₉	—	2	4	no	—
294	C₂²⋊C₄×C₇₉	—	2	2	no	—
295	C₂²⋊C₄×C₇₉	—	2	2	no	—
296	C₂²⋊C₄×C₇₉	—	2	4	no	—
297	C₂²⋊C₄×C₇₉	—	2	4	no	—
298	C₂²⋊C₄×C₇₉	—	2	2	no	—
299	C₂²⋊C₄×C₇₉	—	2	4	no	—
300	C₂²⋊C₄×C₇₉	—	2	4	no	—
301	C₂²⋊C₄×C₇₉	—	2	4	no	—
302	C₂²⋊C₄×C₇₉	—	2	2	no	—
303	C₂²⋊C₄×C₇₉	—	2	4	no	—
304	C₂²⋊C₄×C₇₉	—	2	4	no	—
305	C₂²⋊C₄×C₇₉	—	2	4	no	—
306	C₂²⋊C₄×C₇₉	—	2	4	no	—
307	C₂²⋊C₄×C₇₉	—	2	4	no	—
308	C₂²⋊C₄×C₇₉	—	2	4	no	—
309	C₂²⋊C₄×C₇₉	—	2	4	no	—
310	C₂²⋊C₄×C₇₉	—	2	4	no	—
311	C₂²⋊C₄×C₇₉	—	4	2	no	—
312	C₂²⋊C₄×C₇₉	—	4	2	no	—
313	C₂²⋊C₄×C₇₉	—	4	2	no	—
314	C₂²⋊C₄×C₇₉	—	4	2	no	—
315	C₂²⋊C₄×C₇₉	—	4	2	no	—
316	C₂²⋊C₄×C₇₉	—	4	2	no	—
317	C₂²⋊C₄×C₇₉	—	4	2	no	—
318	C₂²⋊C₄×C₇₉	#41	1	8	yes	—
319	C₄²×C₇₉	—	2	2	no	—
320	C₄²×C₇₉	—	2	4	no	—
321	C₄²×C₇₉	—	2	4	no	—
322	C₄²×C₇₉	—	4	2	no	—
323	C₄²×C₇₉	—	4	2	no	—
324	C₄²×C₇₉	—	4	2	no	—
325	C₄²×C₇₉	—	4	2	no	—
326	C₄²×C₇₉	—	4	2	no	—
327	C₂³×C₇₉	—	2	2	no	—
328	C₂³×C₇₉	—	2	2	no	—
329	C₂³×C₇₉	—	2	8	no	—
330	C₂³×C₇₉	—	2	2	no	—
331	C₂³×C₇₉	—	2	1	no	—
332	C₂³×C₇₉	—	2	2	no	—
333	C₂³×C₇₉	—	2	2	no	—
334	C₂³×C₇₉	—	2	2	no	—
335	C₂³×C₇₉	—	2	2	no	—
336	C₂³×C₇₉	—	2	1	no	—
337	C₂³×C₇₉	—	2	2	no	—
338	C₂³×C₇₉	—	2	2	no	—
339	C₂³×C₇₉	—	2	2	no	—
340	C₂³×C₇₉	—	2	2	no	—
341	C₂³×C₇₉	—	2	2	no	—
342	C₂³×C₇₉	—	2	2	no	—
343	C₂³×C₇₉	—	2	2	no	—
344	C₂³×C₇₉	—	2	2	no	—
345	C₂³×C₇₉	—	2	2	no	—
346	C₂³×C₇₉	—	2	2	no	—
347	C₂³×C₇₉	—	4	8	no	—
348	C₂³×C₇₉	—	4	8	no	—
349	C₂³×C₇₉	—	4	4	no	—
350	C₂³×C₇₉	—	4	4	no	—
351	C₂³×C₇₉	C₂×#41	1	4	yes	—
352	C₂³×C₇₉	C₂×#41	1	2	yes	—
353	C₂³×C₇₉	C₂×#41	1	2	yes	—
354	C₂³×C₇₉	C₂×#41	1	2	yes	—
355	C₂³×C₇₉	H(5,𝔽₂)	1	2	yes	—
356	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
357	D₄×C₇₉	—	2	8	no	—
358	D₄×C₇₉	—	4	8	no	—
359	D₄×C₇₉	—	4	8	no	—
360	D₄×C₇₉	—	4	8	no	—
361	D₄×C₇₉	—	8	2	no	—
362	D₄×C₇₉	—	8	4	no	—
363	D₄×C₇₉	—	8	4	no	—
364	C₂×C₄×C₇₉	—	2	8	no	—
365	C₂×C₄×C₇₉	—	2	1	no	—
366	C₂×C₄×C₇₉	—	2	2	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	2	no	—
372	C₂×C₄×C₇₉	—	2	2	no	—
373	C₂×C₄×C₇₉	—	2	2	no	—
374	C₂×C₄×C₇₉	—	2	2	no	—
375	C₂×C₄×C₇₉	—	2	1	no	—
376	C₂×C₄×C₇₉	—	2	2	no	—
377	C₂×C₄×C₇₉	—	2	2	no	—
378	C₂×C₄×C₇₉	—	2	2	no	—
379	C₂×C₄×C₇₉	—	2	2	no	—
380	C₂×C₄×C₇₉	—	2	2	no	—
381	C₂×C₄×C₇₉	—	2	1	no	—
382	C₂×C₄×C₇₉	—	2	2	no	—
383	C₂×C₄×C₇₉	—	2	2	no	—
384	C₂×C₄×C₇₉	—	2	2	no	—
385	C₂×C₄×C₇₉	—	2	2	no	—
386	C₂×C₄×C₇₉	—	2	2	no	—
387	C₂×C₄×C₇₉	—	2	2	no	—
388	C₂×C₄×C₇₉	—	2	2	no	—
389	C₂×C₄×C₇₉	—	2	2	no	—
390	C₂×C₄×C₇₉	—	2	2	no	—
391	C₂×C₄×C₇₉	—	2	2	no	—
392	C₂×C₄×C₇₉	—	2	2	no	—
393	C₂×C₄×C₇₉	—	2	2	no	—
394	C₂×C₄×C₇₉	—	2	2	no	—
395	C₂×C₄×C₇₉	—	2	2	no	—
396	C₂×C₄×C₇₉	—	2	2	no	—
397	C₂×C₄×C₇₉	—	2	2	no	—
398	C₂×C₄×C₇₉	—	2	2	no	—
399	C₂×C₄×C₇₉	—	2	2	no	—
400	C₂×C₄×C₇₉	—	4	4	no	—
401	C₂×C₄×C₇₉	—	4	8	no	—
402	C₂×C₄×C₇₉	—	4	8	no	—
403	C₂×C₄×C₇₉	—	4	8	no	—
404	C₂×C₄×C₇₉	—	4	8	no	—
405	C₂×C₄×C₇₉	—	8	2	no	—
406	C₂×C₄×C₇₉	—	8	4	no	—
407	C₂×C₄×C₇₉	—	8	4	no	—
408	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
409	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
410	C₂×C₄×C₇₉	C₂×#41	1	4	yes	—
411	C₂×C₄×C₇₉	C₂×#41	1	4	yes	—
412	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
413	C₂×C₄×C₇₉	H(5,𝔽₂)	1	4	yes	—
414	C₂²×C₇₉	—	2	2	no	—
415	C₂²×C₇₉	—	2	4	no	—
416	C₂²×C₇₉	—	2	2	no	—
417	C₂²×C₇₉	—	2	4	no	—
418	C₂²×C₇₉	—	2	4	no	—
419	C₂²×C₇₉	—	2	2	no	—
420	C₂²×C₇₉	—	2	4	no	—
421	C₂²×C₇₉	—	2	4	no	—
422	C₂²×C₇₉	—	2	4	no	—
423	C₂²×C₇₉	—	4	16	no	—
424	C₂²×C₇₉	—	4	1	no	—
425	C₂²×C₇₉	—	4	2	no	—
426	C₂²×C₇₉	—	4	2	no	—
427	C₂²×C₇₉	—	4	2	no	—
428	C₂²×C₇₉	—	4	1	no	—
429	C₂²×C₇₉	—	4	2	no	—
430	C₂²×C₇₉	—	4	2	no	—
431	C₂²×C₇₉	—	4	2	no	—
432	C₂²×C₇₉	—	4	2	no	—
433	C₂²×C₇₉	—	4	2	no	—
434	C₂²×C₇₉	—	4	2	no	—
435	C₂²×C₇₉	—	4	2	no	—
436	C₂²×C₇₉	—	4	2	no	—
437	C₂²×C₇₉	—	4	2	no	—
438	C₂²×C₇₉	#553	1	4	yes	—
439	C₂²×C₇₉	C₂²×#41	1	1	yes	characteristic
440	C₂²×C₇₉	C₂²×#41	1	2	yes	—
441	C₂²×C₇₉	C₂²×#41	1	1	yes	characteristic
442	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
443	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	2	yes	—
444	C₄×C₇₉	—	2	2	no	—
445	C₄×C₇₉	—	2	4	no	—
446	C₄×C₇₉	—	2	4	no	—
447	C₄×C₇₉	—	2	2	no	—
448	C₄×C₇₉	—	2	2	no	—
449	C₄×C₇₉	—	2	4	no	—
450	C₄×C₇₉	—	4	1	no	—
451	C₄×C₇₉	—	4	2	no	—
452	C₄×C₇₉	—	4	2	no	—
453	C₄×C₇₉	—	4	2	no	—
454	C₄×C₇₉	—	4	1	no	—
455	C₄×C₇₉	—	4	2	no	—
456	C₄×C₇₉	—	4	2	no	—
457	C₄×C₇₉	—	4	2	no	—
458	C₄×C₇₉	—	4	2	no	—
459	#36530	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
460	C₂×C₇₉	—	2	4	no	—
461	C₂×C₇₉	—	4	2	no	—
462	C₂×C₇₉	—	4	4	no	—
463	C₂×C₇₉	—	8	2	no	—
464	C₂×C₇₉	#3444	1	1	yes	characteristic
465	C₂×C₇₉	C₂×#553	1	1	yes	characteristic
466	C₂×C₇₉	#3481	1	2	yes	—
467	C₂×C₇₉	#3490	1	1	yes	characteristic
468	C₂×C₇₉	#3519	1	2	yes	—
469	#2852	C₂×C₇₉	1	2	yes	complemented
470	#2847	C₂×C₇₉	1	1	yes	characteristic, complemented
471	#2578	C₂×C₇₉	1	2	yes	complemented
472	#2569	C₂×C₇₉	1	1	yes	characteristic, complemented
473	#2559	C₂×C₇₉	1	2	yes	complemented
474	#2543	C₂×C₇₉	1	1	yes	characteristic, complemented
475	#2522	C₂×C₇₉	1	2	yes	complemented
476	#2518	C₂×C₇₉	1	2	yes	complemented
477	#2467	C₂×C₇₉	1	2	yes	complemented
478	#2464	C₂×C₇₉	1	2	yes	complemented
479	#2424	C₂×C₇₉	1	2	yes	complemented
480	#2418	C₂×C₇₉	1	2	yes	complemented
481	#2374	C₂×C₇₉	1	2	yes	complemented
482	#2364	C₂×C₇₉	1	1	yes	characteristic, complemented
483	#2364	C₂×C₇₉	1	2	yes	complemented
484	#2349	C₂×C₇₉	1	1	yes	characteristic, complemented
485	C₄×#121	C₂×C₇₉	1	2	yes	complemented
486	C₄×#120	C₂×C₇₉	1	1	yes	characteristic, complemented
487	C₂×C₄×C₂²⋊C₄	C₂×C₇₉	1	1	yes	characteristic, complemented
488	C₇₉	#36530	1	1	yes	characteristic, direct product factor, Sylow
489	C₂⁴×C₄	C₂²×C₇₉	1	1	yes	characteristic
490	C₂×#126	C₂²×C₇₉	1	2	yes	complemented
491	C₂×#123	C₂²×C₇₉	1	2	yes	—
492	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
493	C₂×#121	C₂²×C₇₉	1	2	yes	—
494	C₂×#121	C₂²×C₇₉	1	2	yes	—
495	C₂×#121	C₂²×C₇₉	1	2	yes	—
496	C₂×#120	C₂²×C₇₉	1	1	yes	characteristic
497	C₂×#120	C₂²×C₇₉	1	2	yes	—
498	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
499	C₂×C₄×D₄	C₂²×C₇₉	1	2	yes	—
500	C₂×C₄×D₄	C₂²×C₇₉	1	2	yes	—
501	C₂×C₄×D₄	C₂²×C₇₉	1	2	yes	—
502	C₂×C₄×D₄	C₂²×C₇₉	1	2	yes	complemented
503	C₂²×C₂²⋊C₄	C₂²×C₇₉	1	2	yes	—
504	C₂²×C₄²	C₂²×C₇₉	1	2	yes	—
505	#400	C₂²×C₇₉	1	2	yes	complemented
506	#399	C₂²×C₇₉	1	2	yes	—
507	#398	C₂²×C₇₉	1	2	yes	complemented
508	#398	C₂²×C₇₉	1	1	yes	characteristic, complemented
509	#397	C₂²×C₇₉	1	2	yes	—
510	#397	C₂²×C₇₉	1	1	yes	characteristic, complemented
511	#396	C₂²×C₇₉	1	2	yes	—
512	#394	C₂²×C₇₉	1	2	yes	—
513	#394	C₂²×C₇₉	1	2	yes	—
514	#394	C₂²×C₇₉	1	2	yes	—
515	#394	C₂²×C₇₉	1	2	yes	—
516	#394	C₂²×C₇₉	1	1	yes	characteristic, complemented
517	#392	C₂²×C₇₉	1	2	yes	—
518	#392	C₂²×C₇₉	1	1	yes	characteristic, complemented
519	#390	C₂²×C₇₉	1	2	yes	—
520	#390	C₂²×C₇₉	1	2	yes	complemented
521	#389	C₂²×C₇₉	1	2	yes	complemented
522	#389	C₂²×C₇₉	1	2	yes	complemented
523	#388	C₂²×C₇₉	1	2	yes	—
524	#388	C₂²×C₇₉	1	2	yes	—
525	#388	C₂²×C₇₉	1	2	yes	—
526	#388	C₂²×C₇₉	1	2	yes	complemented
527	#388	C₂²×C₇₉	1	2	yes	complemented
528	#388	C₂²×C₇₉	1	2	yes	complemented
529	#388	C₂²×C₇₉	1	2	yes	complemented
530	#388	C₂²×C₇₉	1	2	yes	complemented
531	#388	C₂²×C₇₉	1	2	yes	complemented
532	#388	C₂²×C₇₉	1	2	yes	complemented
533	#387	C₂²×C₇₉	1	2	yes	complemented
534	#387	C₂²×C₇₉	1	2	yes	complemented
535	#387	C₂²×C₇₉	1	2	yes	complemented
536	#387	C₂²×C₇₉	1	2	yes	complemented
537	#387	C₂²×C₇₉	1	2	yes	complemented
538	#387	C₂²×C₇₉	1	2	yes	complemented
539	#386	C₂²×C₇₉	1	2	yes	—
540	#386	C₂²×C₇₉	1	2	yes	—
541	#386	C₂²×C₇₉	1	2	yes	—
542	#386	C₂²×C₇₉	1	2	yes	—
543	#386	C₂²×C₇₉	1	2	yes	—
544	#386	C₂²×C₇₉	1	2	yes	—
545	#386	C₂²×C₇₉	1	2	yes	—
546	#386	C₂²×C₇₉	1	2	yes	—
547	#386	C₂²×C₇₉	1	1	yes	characteristic
548	#386	C₂²×C₇₉	1	2	yes	complemented
549	#386	C₂²×C₇₉	1	2	yes	complemented
550	#385	C₂²×C₇₉	1	2	yes	—
551	#385	C₂²×C₇₉	1	1	yes	characteristic
552	#385	C₂²×C₇₉	1	2	yes	—
553	#385	C₂²×C₇₉	1	2	yes	—
554	#385	C₂²×C₇₉	1	2	yes	complemented
555	#383	C₂²×C₇₉	1	2	yes	complemented
556	#382	C₂²×C₇₉	1	1	yes	characteristic, complemented
557	#380	C₂²×C₇₉	1	1	yes	characteristic
558	#380	C₂²×C₇₉	1	2	yes	—
559	#380	C₂²×C₇₉	1	2	yes	—
560	#380	C₂²×C₇₉	1	1	yes	characteristic, complemented
561	#379	C₂²×C₇₉	1	1	yes	characteristic
562	C₄×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic, complemented
563	C₄×C₄⋊C₄	C₂²×C₇₉	1	2	yes	complemented
564	C₄×C₂²⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
565	C₄×C₂²⋊C₄	C₂²×C₇₉	1	2	yes	—
566	C₄×C₂²⋊C₄	C₂²×C₇₉	1	2	yes	—
567	C₄×C₂²⋊C₄	C₂²×C₇₉	1	2	yes	—
568	C₄×C₂²⋊C₄	C₂²×C₇₉	1	2	yes	—
569	C₄×C₂²⋊C₄	C₂²×C₇₉	1	2	yes	—
570	C₄×C₂²⋊C₄	C₂²×C₇₉	1	2	yes	complemented
571	C₄×C₂²⋊C₄	C₂²×C₇₉	1	2	yes	complemented
572	C₄×C₂²⋊C₄	C₂²×C₇₉	1	2	yes	complemented
573	C₂×#95	C₂²×C₇₉	1	1	yes	characteristic
574	C₂×#95	C₂²×C₇₉	1	1	yes	characteristic
575	C₂×#95	C₂²×C₇₉	1	1	yes	characteristic, complemented
576	C₂⁵	C₂³×C₇₉	1	1	yes	characteristic
577	C₂²×D₄	C₂³×C₇₉	1	2	yes	—
578	C₂²×D₄	C₂³×C₇₉	1	2	yes	—
579	C₂²×D₄	C₂³×C₇₉	1	2	yes	—
580	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
581	C₂²×D₄	C₂³×C₇₉	1	2	yes	—
582	C₂²×D₄	C₂³×C₇₉	1	2	yes	—
583	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
584	C₂³×C₄	—	2	4	no	—
585	C₂³×C₄	—	4	4	no	—
586	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
587	C₂³×C₄	C₂³×C₇₉	1	2	yes	—
588	C₂³×C₄	C₂³×C₇₉	1	2	yes	—
589	C₂³×C₄	C₂³×C₇₉	1	2	yes	—
590	C₂³×C₄	C₂³×C₇₉	1	2	yes	—
591	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
592	C₂³×C₄	C₂³×C₇₉	1	2	yes	—
593	C₂³×C₄	C₂³×C₇₉	1	2	yes	—
594	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
595	#126	—	4	4	no	—
596	#123	—	2	8	no	—
597	#121	—	2	8	no	—
598	#121	—	2	4	no	—
599	#121	—	2	8	no	—
600	#121	—	4	4	no	—
601	#120	—	2	4	no	—
602	#120	—	4	4	no	—
603	C₄×D₄	—	2	4	no	—
604	C₄×D₄	—	4	4	no	—
605	C₄×D₄	—	4	4	no	—
606	C₄×D₄	—	4	4	no	—
607	C₄×D₄	—	4	4	no	—
608	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
620	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
621	C₂×C₂²⋊C₄	—	2	8	no	—
622	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
626	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
629	C₂×C₂²⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
630	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
632	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
648	C₂×C₄²	—	4	4	no	—
649	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
650	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
651	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
652	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
653	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
654	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
655	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
656	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
657	#95	C₂³×C₇₉	1	1	yes	characteristic
658	#95	C₂³×C₇₉	1	1	yes	characteristic
659	#95	C₂³×C₇₉	1	2	yes	—
660	#95	C₂³×C₇₉	1	2	yes	—
661	#95	C₂³×C₇₉	1	1	yes	characteristic
662	#95	C₂³×C₇₉	1	1	yes	characteristic
663	#95	C₂³×C₇₉	1	1	yes	characteristic
664	#95	C₂³×C₇₉	1	2	yes	—
665	#95	C₂³×C₇₉	1	2	yes	—
666	#95	C₂³×C₇₉	1	2	yes	—
667	#95	C₂³×C₇₉	1	2	yes	—
668	#95	C₂³×C₇₉	1	2	yes	—
669	#95	C₂³×C₇₉	1	2	yes	—
670	#95	C₂³×C₇₉	1	2	yes	—
671	#95	C₂³×C₇₉	1	2	yes	—
672	#95	C₂³×C₇₉	1	1	yes	characteristic
673	#95	C₂³×C₇₉	1	2	yes	—
674	#95	C₂³×C₇₉	1	2	yes	—
675	#95	C₂³×C₇₉	1	2	yes	—
676	#95	C₂³×C₇₉	1	2	yes	—
677	#95	C₂³×C₇₉	1	2	yes	—
678	#95	C₂³×C₇₉	1	2	yes	—
679	#95	C₂³×C₇₉	1	2	yes	—
680	C₂⁴	—	2	4	no	—
681	C₂⁴	—	2	2	no	—
682	C₂⁴	—	2	2	no	—
683	C₂⁴	—	2	2	no	—
684	C₂⁴	—	4	2	no	—
685	C₂⁴	C₂⁴×C₇₉	1	2	yes	—
686	C₂⁴	C₂⁴×C₇₉	1	2	yes	—
687	C₂⁴	C₂⁴×C₇₉	1	1	yes	characteristic
688	C₂⁴	C₂⁴×C₇₉	1	1	yes	characteristic
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	—	2	2	no	—
691	C₂×D₄	—	2	4	no	—
692	C₂×D₄	—	2	4	no	—
693	C₂×D₄	—	2	4	no	—
694	C₂×D₄	—	2	4	no	—
695	C₂×D₄	—	2	4	no	—
696	C₂×D₄	—	2	4	no	—
697	C₂×D₄	—	2	4	no	—
698	C₂×D₄	—	2	4	no	—
699	C₂×D₄	—	2	4	no	—
700	C₂×D₄	—	2	2	no	—
701	C₂×D₄	—	4	2	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	—	4	2	no	—
707	C₂×D₄	—	4	2	no	—
708	C₂×D₄	#41×C₇₉	1	4	yes	—
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	—	2	4	no	—
711	C₂²×C₄	—	2	4	no	—
712	C₂²×C₄	—	2	4	no	—
713	C₂²×C₄	—	2	4	no	—
714	C₂²×C₄	—	2	4	no	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	2	4	no	—
717	C₂²×C₄	—	2	4	no	—
718	C₂²×C₄	—	2	4	no	—
719	C₂²×C₄	—	2	2	no	—
720	C₂²×C₄	—	2	4	no	—
721	C₂²×C₄	—	2	4	no	—
722	C₂²×C₄	—	4	2	no	—
723	C₂²×C₄	—	4	2	no	—
724	C₂²×C₄	—	4	2	no	—
725	C₂²×C₄	—	4	2	no	—
726	C₂²×C₄	—	4	2	no	—
727	C₂²×C₄	—	4	2	no	—
728	C₂²×C₄	—	4	2	no	—
729	C₂²×C₄	—	4	2	no	—
730	C₂²×C₄	—	4	2	no	—
731	C₂²×C₄	—	4	2	no	—
732	C₂²×C₄	—	4	16	no	—
733	C₂²×C₄	#41×C₇₉	1	4	yes	—
734	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
736	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
737	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
738	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
740	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
741	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
742	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
743	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
744	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
746	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
748	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	4	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	4	no	—
753	C₄⋊C₄	—	2	4	no	—
754	C₄⋊C₄	—	2	4	no	—
755	C₄⋊C₄	—	2	4	no	—
756	C₄⋊C₄	—	4	2	no	—
757	C₄⋊C₄	—	4	2	no	—
758	C₄⋊C₄	—	4	2	no	—
759	C₄⋊C₄	—	4	2	no	—
760	C₄⋊C₄	—	4	2	no	—
761	C₄⋊C₄	—	4	2	no	—
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	4	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	2	4	no	—
771	C₂²⋊C₄	—	2	2	no	—
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	4	no	—
777	C₂²⋊C₄	—	2	4	no	—
778	C₂²⋊C₄	—	2	4	no	—
779	C₂²⋊C₄	—	2	4	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	C₂²⋊C₄	—	4	2	no	—
787	C₂²⋊C₄	#41×C₇₉	1	8	yes	—
788	C₄²	—	2	2	no	—
789	C₄²	—	2	4	no	—
790	C₄²	—	2	4	no	—
791	C₄²	—	4	2	no	—
792	C₄²	—	4	2	no	—
793	C₄²	—	4	2	no	—
794	C₄²	—	4	2	no	—
795	C₄²	—	4	2	no	—
796	C₂³	—	2	2	no	—
797	C₂³	—	2	2	no	—
798	C₂³	—	2	8	no	—
799	C₂³	—	2	2	no	—
800	C₂³	—	2	1	no	—
801	C₂³	—	2	2	no	—
802	C₂³	—	2	2	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	1	no	—
806	C₂³	—	2	2	no	—
807	C₂³	—	2	2	no	—
808	C₂³	—	2	2	no	—
809	C₂³	—	2	2	no	—
810	C₂³	—	2	2	no	—
811	C₂³	—	2	2	no	—
812	C₂³	—	2	2	no	—
813	C₂³	—	2	2	no	—
814	C₂³	—	2	2	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	4	8	no	—
817	C₂³	—	4	8	no	—
818	C₂³	—	4	4	no	—
819	C₂³	—	4	4	no	—
820	C₂³	C₂×#41×C₇₉	1	4	yes	—
821	C₂³	C₂×#41×C₇₉	1	2	yes	—
822	C₂³	C₂×#41×C₇₉	1	2	yes	—
823	C₂³	C₂×#41×C₇₉	1	2	yes	—
824	C₂³	H(5,𝔽₂)×C₇₉	1	2	yes	—
825	C₂³	C₂⁵×C₇₉	1	1	yes	characteristic
826	D₄	—	2	8	no	—
827	D₄	—	4	8	no	—
828	D₄	—	4	8	no	—
829	D₄	—	4	8	no	—
830	D₄	—	8	2	no	—
831	D₄	—	8	4	no	—
832	D₄	—	8	4	no	—
833	C₂×C₄	—	2	8	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	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	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	4	4	no	—
870	C₂×C₄	—	4	8	no	—
871	C₂×C₄	—	4	8	no	—
872	C₂×C₄	—	4	8	no	—
873	C₂×C₄	—	4	8	no	—
874	C₂×C₄	—	8	2	no	—
875	C₂×C₄	—	8	4	no	—
876	C₂×C₄	—	8	4	no	—
877	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
878	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
879	C₂×C₄	C₂×#41×C₇₉	1	4	yes	—
880	C₂×C₄	C₂×#41×C₇₉	1	4	yes	—
881	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
882	C₂×C₄	H(5,𝔽₂)×C₇₉	1	4	yes	—
883	C₂²	—	2	2	no	—
884	C₂²	—	2	4	no	—
885	C₂²	—	2	2	no	—
886	C₂²	—	2	4	no	—
887	C₂²	—	2	4	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	2	4	no	—
890	C₂²	—	2	4	no	—
891	C₂²	—	2	4	no	—
892	C₂²	—	4	16	no	—
893	C₂²	—	4	1	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	4	2	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	4	1	no	—
898	C₂²	—	4	2	no	—
899	C₂²	—	4	2	no	—
900	C₂²	—	4	2	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	4	2	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	2	no	—
906	C₂²	—	4	2	no	—
907	C₂²	#553×C₇₉	1	4	yes	—
908	C₂²	C₂²×#41×C₇₉	1	1	yes	characteristic
909	C₂²	C₂²×#41×C₇₉	1	2	yes	—
910	C₂²	C₂²×#41×C₇₉	1	1	yes	characteristic
911	C₂²	C₂×H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
912	C₂²	C₂×H(5,𝔽₂)×C₇₉	1	2	yes	—
913	C₄	—	2	2	no	—
914	C₄	—	2	4	no	—
915	C₄	—	2	4	no	—
916	C₄	—	2	2	no	—
917	C₄	—	2	2	no	—
918	C₄	—	2	4	no	—
919	C₄	—	4	1	no	—
920	C₄	—	4	2	no	—
921	C₄	—	4	2	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	1	no	—
924	C₄	—	4	2	no	—
925	C₄	—	4	2	no	—
926	C₄	—	4	2	no	—
927	C₄	—	4	2	no	—
928	C₂	—	2	4	no	—
929	C₂	—	4	4	no	—
930	C₂	—	4	2	no	—
931	C₂	—	8	2	no	—
932	C₂	C₇₉×#3444	1	1	yes	characteristic
933	C₂	C₂×#553×C₇₉	1	1	yes	characteristic
934	C₂	C₇₉×#3481	1	2	yes	—
935	C₂	C₇₉×#3490	1	1	yes	characteristic
936	C₂	C₇₉×#3519	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₉×#2852	C₂	semidirect
2. C₇₉×#2847	C₂	semidirect
3. C₇₉×#2578	C₂	semidirect
4. C₇₉×#2569	C₂	semidirect
5. C₇₉×#2559	C₂	semidirect
6. C₇₉×#2543	C₂	semidirect
7. C₇₉×#2522	C₂	semidirect
8. C₇₉×#2518	C₂	semidirect
9. C₇₉×#2467	C₂	semidirect
10. C₇₉×#2464	C₂	semidirect
11. C₇₉×#2424	C₂	semidirect
12. C₇₉×#2418	C₂	semidirect
13. C₇₉×#2374	C₂	semidirect
14. C₇₉×#2364	C₂	semidirect
15. C₇₉×#2364	C₂	semidirect
16. C₇₉×#2349	C₂	semidirect
17. C₄×#121×C₇₉	C₂	semidirect
18. C₄×#120×C₇₉	C₂	semidirect
19. C₂×C₄×C₂²⋊C₄×C₇₉	C₂	semidirect
21. C₂×#126×C₇₉	C₂²	semidirect
33. C₂×C₄×D₄×C₇₉	C₂²	semidirect
36. #400×C₇₉	C₂²	semidirect
38. #398×C₇₉	C₂²	semidirect
39. #398×C₇₉	C₂²	semidirect
41. #397×C₇₉	C₂²	semidirect
47. #394×C₇₉	C₂²	semidirect
49. #392×C₇₉	C₂²	semidirect
51. #390×C₇₉	C₂²	semidirect
52. #389×C₇₉	C₂²	semidirect
53. #389×C₇₉	C₂²	semidirect
57. #388×C₇₉	C₂²	semidirect
58. #388×C₇₉	C₂²	semidirect
59. #388×C₇₉	C₂²	semidirect
60. #388×C₇₉	C₂²	semidirect
61. #388×C₇₉	C₂²	semidirect
62. #388×C₇₉	C₂²	semidirect
63. #388×C₇₉	C₂²	semidirect
64. #387×C₇₉	C₂²	semidirect
65. #387×C₇₉	C₂²	semidirect
66. #387×C₇₉	C₂²	semidirect
67. #387×C₇₉	C₂²	semidirect
68. #387×C₇₉	C₂²	semidirect
69. #387×C₇₉	C₂²	semidirect
79. #386×C₇₉	C₂²	semidirect
80. #386×C₇₉	C₂²	semidirect
85. #385×C₇₉	C₂²	semidirect
86. #383×C₇₉	C₂²	semidirect
87. #382×C₇₉	C₂²	semidirect
91. #380×C₇₉	C₂²	semidirect
93. C₄×C₄⋊C₄×C₇₉	C₂²	semidirect
94. C₄×C₄⋊C₄×C₇₉	C₂²	semidirect
101. C₄×C₂²⋊C₄×C₇₉	C₂²	semidirect
102. C₄×C₂²⋊C₄×C₇₉	C₂²	semidirect
103. C₄×C₂²⋊C₄×C₇₉	C₂²	semidirect
106. C₂×#95×C₇₉	C₂²	semidirect
459. #36530	C₇₉	direct (N × H)
469. #2852	C₂×C₇₉	semidirect
470. #2847	C₂×C₇₉	semidirect
471. #2578	C₂×C₇₉	semidirect
472. #2569	C₂×C₇₉	semidirect
473. #2559	C₂×C₇₉	semidirect
474. #2543	C₂×C₇₉	semidirect
475. #2522	C₂×C₇₉	semidirect
476. #2518	C₂×C₇₉	semidirect
477. #2467	C₂×C₇₉	semidirect
478. #2464	C₂×C₇₉	semidirect
479. #2424	C₂×C₇₉	semidirect
480. #2418	C₂×C₇₉	semidirect
481. #2374	C₂×C₇₉	semidirect
482. #2364	C₂×C₇₉	semidirect
483. #2364	C₂×C₇₉	semidirect
484. #2349	C₂×C₇₉	semidirect
485. C₄×#121	C₂×C₇₉	semidirect
486. C₄×#120	C₂×C₇₉	semidirect
487. C₂×C₄×C₂²⋊C₄	C₂×C₇₉	semidirect
488. C₇₉	#36530	direct (N × H)
490. C₂×#126	C₂²×C₇₉	semidirect
502. C₂×C₄×D₄	C₂²×C₇₉	semidirect
505. #400	C₂²×C₇₉	semidirect
507. #398	C₂²×C₇₉	semidirect
508. #398	C₂²×C₇₉	semidirect
510. #397	C₂²×C₇₉	semidirect
516. #394	C₂²×C₇₉	semidirect
518. #392	C₂²×C₇₉	semidirect
520. #390	C₂²×C₇₉	semidirect
521. #389	C₂²×C₇₉	semidirect
522. #389	C₂²×C₇₉	semidirect
526. #388	C₂²×C₇₉	semidirect
527. #388	C₂²×C₇₉	semidirect
528. #388	C₂²×C₇₉	semidirect
529. #388	C₂²×C₇₉	semidirect
530. #388	C₂²×C₇₉	semidirect
531. #388	C₂²×C₇₉	semidirect
532. #388	C₂²×C₇₉	semidirect
533. #387	C₂²×C₇₉	semidirect
534. #387	C₂²×C₇₉	semidirect
535. #387	C₂²×C₇₉	semidirect
536. #387	C₂²×C₇₉	semidirect
537. #387	C₂²×C₇₉	semidirect
538. #387	C₂²×C₇₉	semidirect
548. #386	C₂²×C₇₉	semidirect
549. #386	C₂²×C₇₉	semidirect
554. #385	C₂²×C₇₉	semidirect
555. #383	C₂²×C₇₉	semidirect
556. #382	C₂²×C₇₉	semidirect
560. #380	C₂²×C₇₉	semidirect
562. C₄×C₄⋊C₄	C₂²×C₇₉	semidirect
563. C₄×C₄⋊C₄	C₂²×C₇₉	semidirect
570. C₄×C₂²⋊C₄	C₂²×C₇₉	semidirect
571. C₄×C₂²⋊C₄	C₂²×C₇₉	semidirect
572. C₄×C₂²⋊C₄	C₂²×C₇₉	semidirect
575. C₂×#95	C₂²×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₇₉×#2852	2
C₇₉×#2847	2
C₇₉×#2578	2
C₇₉×#2569	2
C₇₉×#2559	2
C₇₉×#2543	2
C₇₉×#2522	2
C₇₉×#2518	2
C₇₉×#2467	2
C₇₉×#2464	2
C₇₉×#2424	2
C₇₉×#2418	2
C₇₉×#2374	2
C₇₉×#2364	2
C₇₉×#2349	2
C₄×#121×C₇₉	2
C₄×#120×C₇₉	2
C₂×C₄×C₂²⋊C₄×C₇₉	2
#36530	79

Subgroups — C79×#36530 #34148219

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#36530 #34148219