Subgroups — C₇₉×#24440 #34136129

Order 20224.

1938 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄²×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#469×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#447×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#447×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#418×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₉×#2414	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#2041	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#2034	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#2011	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#1999	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1879	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₉×#1875	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	C₂³×D₄×C₇₉	—	2	1	no	—
17	C₂³×D₄×C₇₉	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₇₉	C₂²	1	1	yes	characteristic
19	C₂²×D₈×C₇₉	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
21	C₂²×D₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
22	C₂²×M₁₆×C₇₉	C₂²	1	1	yes	characteristic, complemented
23	D₄²×C₇₉	—	2	4	no	—
24	D₄²×C₇₉	—	2	4	no	—
25	C₂×#127×C₇₉	C₂²	1	1	yes	characteristic
26	C₂×#121×C₇₉	—	2	1	no	—
27	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
28	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
29	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic, complemented
30	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic, complemented
31	C₂×#120×C₇₉	—	2	1	no	—
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	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic, complemented
36	#469×C₇₉	—	2	4	no	—
37	#447×C₇₉	—	2	4	no	—
38	#447×C₇₉	—	2	4	no	—
39	C₂×#106×C₇₉	C₂²	1	1	yes	characteristic, complemented
40	#418×C₇₉	—	2	4	no	—
41	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
42	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
43	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
44	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic, complemented
45	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic, complemented
46	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic, complemented
47	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic, complemented
48	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic, complemented
49	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic, complemented
50	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
54	#394×C₇₉	—	2	1	no	—
55	#392×C₇₉	—	2	1	no	—
56	#390×C₇₉	—	2	1	no	—
57	#390×C₇₉	C₂²	1	1	yes	characteristic, complemented
58	#389×C₇₉	C₂²	1	1	yes	characteristic, complemented
59	#388×C₇₉	—	2	1	no	—
60	#380×C₇₉	C₂²	1	1	yes	characteristic, complemented
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	C₂⁵×C₇₉	—	2	1	no	—
67	C₂²×D₄×C₇₉	—	2	2	no	—
68	C₂²×D₄×C₇₉	—	2	2	no	—
69	C₂²×D₄×C₇₉	—	2	8	no	—
70	C₂²×D₄×C₇₉	—	2	1	no	—
71	C₂²×D₄×C₇₉	—	2	1	no	—
72	C₂²×D₄×C₇₉	—	2	2	no	—
73	C₂²×D₄×C₇₉	—	2	2	no	—
74	C₂²×D₄×C₇₉	—	2	2	no	—
75	C₂²×D₄×C₇₉	—	2	2	no	—
76	C₂²×D₄×C₇₉	—	2	1	no	—
77	C₂²×D₄×C₇₉	—	2	1	no	—
78	C₂²×D₄×C₇₉	—	2	1	no	—
79	C₂²×D₄×C₇₉	—	2	1	no	—
80	C₂²×D₄×C₇₉	—	2	1	no	—
81	C₂²×D₄×C₇₉	—	2	2	no	—
82	C₂²×D₄×C₇₉	—	2	1	no	—
83	C₂²×D₄×C₇₉	—	4	1	no	—
84	C₂²×D₄×C₇₉	—	4	1	no	—
85	C₂²×D₄×C₇₉	—	4	1	no	—
86	C₂²×D₄×C₇₉	—	4	1	no	—
87	C₂²×D₄×C₇₉	—	4	4	no	—
88	C₂²×D₄×C₇₉	—	4	4	no	—
89	C₂²×D₄×C₇₉	D₄	1	1	yes	characteristic
90	C₂²×D₄×C₇₉	D₄	1	4	yes	complemented
91	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₇₉	—	2	1	no	—
96	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
102	C₂×D₈×C₇₉	—	2	2	no	—
103	C₂×D₈×C₇₉	—	2	2	no	—
104	C₂×D₈×C₇₉	—	4	1	no	—
105	C₂×D₈×C₇₉	—	4	1	no	—
106	C₂×D₈×C₇₉	—	4	1	no	—
107	C₂×M₁₆×C₇₉	—	2	2	no	—
108	C₂×M₁₆×C₇₉	—	2	2	no	—
109	C₂×M₁₆×C₇₉	—	4	1	no	—
110	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
114	#127×C₇₉	—	2	2	no	—
115	#127×C₇₉	—	2	2	no	—
116	#121×C₇₉	—	2	8	no	—
117	#121×C₇₉	—	2	2	no	—
118	#121×C₇₉	—	2	2	no	—
119	#121×C₇₉	—	2	2	no	—
120	#121×C₇₉	—	2	2	no	—
121	#121×C₇₉	—	2	2	no	—
122	#121×C₇₉	—	2	2	no	—
123	#121×C₇₉	—	4	1	no	—
124	#121×C₇₉	D₄	1	4	yes	complemented
125	#120×C₇₉	—	2	8	no	—
126	#120×C₇₉	—	2	8	no	—
127	C₄×D₄×C₇₉	—	2	2	no	—
128	C₄×D₄×C₇₉	—	2	2	no	—
129	C₄×D₄×C₇₉	—	2	2	no	—
130	C₄×D₄×C₇₉	—	2	2	no	—
131	#117×C₇₉	—	2	2	no	—
132	#117×C₇₉	—	4	1	no	—
133	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
134	C₂×C₄⋊C₄×C₇₉	D₄	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×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
151	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
152	#106×C₇₉	—	2	2	no	—
153	#102×C₇₉	—	2	2	no	—
154	#102×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	—	2	2	no	—
161	#102×C₇₉	—	4	1	no	—
162	#102×C₇₉	D₄	1	4	yes	complemented
163	C₂²⋊C₈×C₇₉	—	2	2	no	—
164	C₂²⋊C₈×C₇₉	—	2	2	no	—
165	C₂²⋊C₈×C₇₉	—	4	1	no	—
166	#95×C₇₉	—	2	1	no	—
167	#95×C₇₉	—	2	1	no	—
168	C₂⁴×C₇₉	—	2	1	no	—
169	C₂⁴×C₇₉	—	2	4	no	—
170	C₂⁴×C₇₉	—	2	1	no	—
171	C₂⁴×C₇₉	—	2	1	no	—
172	C₂⁴×C₇₉	—	2	4	no	—
173	C₂⁴×C₇₉	—	2	1	no	—
174	C₂⁴×C₇₉	—	4	2	no	—
175	C₂⁴×C₇₉	—	4	2	no	—
176	C₂⁴×C₇₉	—	4	2	no	—
177	C₂⁴×C₇₉	—	4	2	no	—
178	C₂⁴×C₇₉	—	4	2	no	—
179	C₂⁴×C₇₉	—	4	2	no	—
180	C₂⁴×C₇₉	—	4	2	no	—
181	C₂⁴×C₇₉	—	4	2	no	—
182	C₂⁴×C₇₉	—	8	1	no	—
183	C₂⁴×C₇₉	—	8	1	no	—
184	C₂⁴×C₇₉	—	8	1	no	—
185	C₂⁴×C₇₉	—	8	1	no	—
186	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
187	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
188	C₂×D₄×C₇₉	—	2	2	no	—
189	C₂×D₄×C₇₉	—	2	2	no	—
190	C₂×D₄×C₇₉	—	2	8	no	—
191	C₂×D₄×C₇₉	—	2	4	no	—
192	C₂×D₄×C₇₉	—	2	4	no	—
193	C₂×D₄×C₇₉	—	2	4	no	—
194	C₂×D₄×C₇₉	—	2	4	no	—
195	C₂×D₄×C₇₉	—	2	4	no	—
196	C₂×D₄×C₇₉	—	2	4	no	—
197	C₂×D₄×C₇₉	—	2	2	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	—	2	1	no	—
209	C₂×D₄×C₇₉	—	2	1	no	—
210	C₂×D₄×C₇₉	—	2	1	no	—
211	C₂×D₄×C₇₉	—	2	1	no	—
212	C₂×D₄×C₇₉	—	2	1	no	—
213	C₂×D₄×C₇₉	—	2	1	no	—
214	C₂×D₄×C₇₉	—	2	1	no	—
215	C₂×D₄×C₇₉	—	2	1	no	—
216	C₂×D₄×C₇₉	—	2	1	no	—
217	C₂×D₄×C₇₉	—	4	4	no	—
218	C₂×D₄×C₇₉	—	4	4	no	—
219	C₂×D₄×C₇₉	—	4	4	no	—
220	C₂×D₄×C₇₉	—	4	2	no	—
221	C₂×D₄×C₇₉	—	4	2	no	—
222	C₂×D₄×C₇₉	—	4	2	no	—
223	C₂×D₄×C₇₉	—	4	2	no	—
224	C₂×D₄×C₇₉	—	4	2	no	—
225	C₂×D₄×C₇₉	—	4	2	no	—
226	C₂×D₄×C₇₉	—	4	4	no	—
227	C₂×D₄×C₇₉	—	4	4	no	—
228	C₂×D₄×C₇₉	—	4	32	no	—
229	C₂×D₄×C₇₉	—	4	4	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	4	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	—	8	1	no	—
239	C₂×D₄×C₇₉	—	8	1	no	—
240	C₂×D₄×C₇₉	—	8	1	no	—
241	C₂×D₄×C₇₉	—	8	1	no	—
242	C₂×D₄×C₇₉	—	8	1	no	—
243	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
244	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
245	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
246	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
247	C₂×D₄×C₇₉	#41	1	2	yes	—
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	4	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	—	2	1	no	—
259	C₂²×C₄×C₇₉	—	2	1	no	—
260	C₂²×C₄×C₇₉	—	2	1	no	—
261	C₂²×C₄×C₇₉	—	2	1	no	—
262	C₂²×C₄×C₇₉	—	2	1	no	—
263	C₂²×C₄×C₇₉	—	4	2	no	—
264	C₂²×C₄×C₇₉	—	4	2	no	—
265	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
269	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
270	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
272	D₈×C₇₉	—	4	4	no	—
273	D₈×C₇₉	—	4	4	no	—
274	D₈×C₇₉	—	4	4	no	—
275	M₁₆×C₇₉	—	4	4	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	—	2	1	no	—
284	C₂×C₈×C₇₉	—	2	1	no	—
285	C₂×C₈×C₇₉	—	2	1	no	—
286	C₂×C₈×C₇₉	—	2	1	no	—
287	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	complemented
288	C₄⋊C₄×C₇₉	—	2	2	no	—
289	C₄⋊C₄×C₇₉	—	2	1	no	—
290	C₄⋊C₄×C₇₉	—	2	1	no	—
291	C₄⋊C₄×C₇₉	—	2	1	no	—
292	C₄⋊C₄×C₇₉	—	2	1	no	—
293	C₄⋊C₄×C₇₉	—	2	1	no	—
294	C₄⋊C₄×C₇₉	—	2	1	no	—
295	C₄⋊C₄×C₇₉	—	8	1	no	—
296	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
297	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	complemented
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	4	no	—
302	C₂²⋊C₄×C₇₉	—	2	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	—	8	1	no	—
308	C₂²⋊C₄×C₇₉	—	8	1	no	—
309	C₄²×C₇₉	—	2	1	no	—
310	C₄²×C₇₉	—	2	1	no	—
311	C₄²×C₇₉	—	4	2	no	—
312	C₂³×C₇₉	—	2	1	no	—
313	C₂³×C₇₉	—	2	2	no	—
314	C₂³×C₇₉	—	2	1	no	—
315	C₂³×C₇₉	—	2	1	no	—
316	C₂³×C₇₉	—	2	2	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	—	2	1	no	—
327	C₂³×C₇₉	—	2	2	no	—
328	C₂³×C₇₉	—	2	2	no	—
329	C₂³×C₇₉	—	4	8	no	—
330	C₂³×C₇₉	—	4	8	no	—
331	C₂³×C₇₉	—	4	8	no	—
332	C₂³×C₇₉	—	4	8	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	—	4	1	no	—
340	C₂³×C₇₉	—	4	1	no	—
341	C₂³×C₇₉	—	4	1	no	—
342	C₂³×C₇₉	—	4	1	no	—
343	C₂³×C₇₉	—	4	1	no	—
344	C₂³×C₇₉	—	4	1	no	—
345	C₂³×C₇₉	—	4	1	no	—
346	C₂³×C₇₉	—	4	1	no	—
347	C₂³×C₇₉	—	4	1	no	—
348	C₂³×C₇₉	—	4	1	no	—
349	C₂³×C₇₉	—	4	1	no	—
350	C₂³×C₇₉	—	4	1	no	—
351	C₂³×C₇₉	—	4	1	no	—
352	C₂³×C₇₉	—	4	1	no	—
353	C₂³×C₇₉	—	4	1	no	—
354	C₂³×C₇₉	—	4	1	no	—
355	C₂³×C₇₉	—	4	1	no	—
356	C₂³×C₇₉	—	8	4	no	—
357	C₂³×C₇₉	—	8	4	no	—
358	C₂³×C₇₉	—	8	4	no	—
359	C₂³×C₇₉	—	8	4	no	—
360	C₂³×C₇₉	—	8	4	no	—
361	C₂³×C₇₉	—	8	4	no	—
362	C₂³×C₇₉	—	8	4	no	—
363	C₂³×C₇₉	—	8	4	no	—
364	C₂³×C₇₉	—	8	4	no	—
365	C₂³×C₇₉	—	8	4	no	—
366	C₂³×C₇₉	#120	1	2	yes	—
367	C₂³×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
368	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
369	D₄×C₇₉	—	2	8	no	—
370	D₄×C₇₉	—	2	2	no	—
371	D₄×C₇₉	—	2	2	no	—
372	D₄×C₇₉	—	2	2	no	—
373	D₄×C₇₉	—	2	2	no	—
374	D₄×C₇₉	—	2	2	no	—
375	D₄×C₇₉	—	2	2	no	—
376	D₄×C₇₉	—	2	2	no	—
377	D₄×C₇₉	—	4	8	no	—
378	D₄×C₇₉	—	4	8	no	—
379	D₄×C₇₉	—	4	8	no	—
380	D₄×C₇₉	—	4	8	no	—
381	D₄×C₇₉	—	4	8	no	—
382	D₄×C₇₉	—	4	1	no	—
383	D₄×C₇₉	—	4	1	no	—
384	D₄×C₇₉	—	4	1	no	—
385	D₄×C₇₉	—	4	1	no	—
386	D₄×C₇₉	—	4	1	no	—
387	D₄×C₇₉	—	4	1	no	—
388	D₄×C₇₉	—	4	1	no	—
389	D₄×C₇₉	—	4	1	no	—
390	D₄×C₇₉	—	8	4	no	—
391	D₄×C₇₉	—	8	4	no	—
392	D₄×C₇₉	—	8	4	no	—
393	D₄×C₇₉	#121	1	4	yes	—
394	C₂×C₄×C₇₉	—	2	1	no	—
395	C₂×C₄×C₇₉	—	2	1	no	—
396	C₂×C₄×C₇₉	—	2	1	no	—
397	C₂×C₄×C₇₉	—	2	1	no	—
398	C₂×C₄×C₇₉	—	2	2	no	—
399	C₂×C₄×C₇₉	—	2	2	no	—
400	C₂×C₄×C₇₉	—	2	2	no	—
401	C₂×C₄×C₇₉	—	2	2	no	—
402	C₂×C₄×C₇₉	—	2	1	no	—
403	C₂×C₄×C₇₉	—	2	1	no	—
404	C₂×C₄×C₇₉	—	2	2	no	—
405	C₂×C₄×C₇₉	—	2	2	no	—
406	C₂×C₄×C₇₉	—	2	1	no	—
407	C₂×C₄×C₇₉	—	2	1	no	—
408	C₂×C₄×C₇₉	—	2	1	no	—
409	C₂×C₄×C₇₉	—	2	1	no	—
410	C₂×C₄×C₇₉	—	4	8	no	—
411	C₂×C₄×C₇₉	—	4	1	no	—
412	C₂×C₄×C₇₉	—	4	1	no	—
413	C₂×C₄×C₇₉	—	4	1	no	—
414	C₂×C₄×C₇₉	—	4	1	no	—
415	C₂×C₄×C₇₉	—	4	1	no	—
416	C₂×C₄×C₇₉	—	4	1	no	—
417	C₂×C₄×C₇₉	—	4	1	no	—
418	C₂×C₄×C₇₉	—	4	1	no	—
419	C₂×C₄×C₇₉	—	4	1	no	—
420	C₂×C₄×C₇₉	—	4	1	no	—
421	C₂×C₄×C₇₉	—	4	1	no	—
422	C₂×C₄×C₇₉	—	4	1	no	—
423	C₂×C₄×C₇₉	—	4	1	no	—
424	C₂×C₄×C₇₉	—	4	1	no	—
425	C₂×C₄×C₇₉	#120	1	2	yes	—
426	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
427	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
430	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
431	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
432	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
433	C₈×C₇₉	—	2	2	no	—
434	C₈×C₇₉	—	4	1	no	—
435	C₈×C₇₉	—	4	1	no	—
436	C₈×C₇₉	—	4	1	no	—
437	C₂²×C₇₉	—	2	2	no	—
438	C₂²×C₇₉	—	2	4	no	—
439	C₂²×C₇₉	—	2	2	no	—
440	C₂²×C₇₉	—	2	2	no	—
441	C₂²×C₇₉	—	2	2	no	—
442	C₂²×C₇₉	—	2	2	no	—
443	C₂²×C₇₉	—	2	2	no	—
444	C₂²×C₇₉	—	4	1	no	—
445	C₂²×C₇₉	—	4	2	no	—
446	C₂²×C₇₉	—	4	1	no	—
447	C₂²×C₇₉	—	4	2	no	—
448	C₂²×C₇₉	—	4	1	no	—
449	C₂²×C₇₉	—	4	2	no	—
450	C₂²×C₇₉	—	4	1	no	—
451	C₂²×C₇₉	—	4	1	no	—
452	C₂²×C₇₉	—	4	2	no	—
453	C₂²×C₇₉	—	4	1	no	—
454	C₂²×C₇₉	—	4	2	no	—
455	C₂²×C₇₉	—	4	1	no	—
456	C₂²×C₇₉	—	4	1	no	—
457	C₂²×C₇₉	—	4	2	no	—
458	C₂²×C₇₉	—	4	2	no	—
459	C₂²×C₇₉	—	4	2	no	—
460	C₂²×C₇₉	—	4	2	no	—
461	C₂²×C₇₉	—	4	2	no	—
462	C₂²×C₇₉	—	4	2	no	—
463	C₂²×C₇₉	—	4	2	no	—
464	C₂²×C₇₉	—	8	16	no	—
465	C₂²×C₇₉	—	8	16	no	—
466	C₂²×C₇₉	—	8	1	no	—
467	C₂²×C₇₉	—	8	1	no	—
468	C₂²×C₇₉	—	8	1	no	—
469	C₂²×C₇₉	—	8	1	no	—
470	C₂²×C₇₉	—	8	1	no	—
471	C₂²×C₇₉	—	8	1	no	—
472	C₂²×C₇₉	—	8	1	no	—
473	C₂²×C₇₉	—	8	1	no	—
474	C₂²×C₇₉	—	8	1	no	—
475	C₂²×C₇₉	—	8	1	no	—
476	C₂²×C₇₉	—	8	1	no	—
477	C₂²×C₇₉	—	8	1	no	—
478	C₂²×C₇₉	—	8	1	no	—
479	C₂²×C₇₉	—	8	1	no	—
480	C₂²×C₇₉	—	8	1	no	—
481	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
482	C₂²×C₇₉	D₄²	1	1	yes	characteristic
483	C₂²×C₇₉	#546	1	1	yes	characteristic
484	C₂²×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
485	C₂²×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
486	C₂²×C₇₉	#576	1	1	yes	characteristic
487	C₂²×C₇₉	#576	1	1	yes	characteristic
488	C₄×C₇₉	—	2	2	no	—
489	C₄×C₇₉	—	2	2	no	—
490	C₄×C₇₉	—	4	1	no	—
491	C₄×C₇₉	—	4	2	no	—
492	C₄×C₇₉	—	4	1	no	—
493	C₄×C₇₉	—	4	2	no	—
494	C₄×C₇₉	—	8	1	no	—
495	C₄×C₇₉	—	8	1	no	—
496	C₄×C₇₉	C₂×#121	1	1	yes	characteristic
497	C₄×C₇₉	#534	1	1	yes	characteristic
498	C₄×C₇₉	D₄²	1	1	yes	characteristic
499	C₄×C₇₉	#546	1	1	yes	characteristic
500	#24440	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
501	C₂×C₇₉	—	4	2	no	—
502	C₂×C₇₉	—	4	2	no	—
503	C₂×C₇₉	—	4	4	no	—
504	C₂×C₇₉	—	8	2	no	—
505	C₂×C₇₉	—	8	2	no	—
506	C₂×C₇₉	—	16	1	no	—
507	C₂×C₇₉	#2410	1	1	yes	characteristic
508	C₂×C₇₉	#3003	1	1	yes	characteristic
509	C₂×C₇₉	#3008	1	1	yes	characteristic
510	C₂×C₇₉	#3264	1	1	yes	characteristic
511	C₂×C₇₉	#3274	1	1	yes	characteristic
512	C₂×C₇₉	#3318	1	1	yes	characteristic
513	C₂×C₇₉	#3325	1	1	yes	characteristic
514	C₂×D₄²	C₂×C₇₉	1	1	yes	characteristic, complemented
515	C₂×#469	C₂×C₇₉	1	1	yes	characteristic, complemented
516	C₂×#447	C₂×C₇₉	1	1	yes	characteristic, complemented
517	C₂×#447	C₂×C₇₉	1	1	yes	characteristic, complemented
518	C₂×#418	C₂×C₇₉	1	1	yes	characteristic, complemented
519	#2414	C₂×C₇₉	1	1	yes	characteristic, complemented
520	#2041	C₂×C₇₉	1	1	yes	characteristic, complemented
521	#2034	C₂×C₇₉	1	1	yes	characteristic, complemented
522	#2011	C₂×C₇₉	1	1	yes	characteristic, complemented
523	#1999	C₂×C₇₉	1	1	yes	characteristic, complemented
524	#1879	C₂×C₇₉	1	1	yes	characteristic, complemented
525	#1875	C₂×C₇₉	1	1	yes	characteristic, complemented
526	#1870	C₂×C₇₉	1	1	yes	characteristic, complemented
527	#1864	C₂×C₇₉	1	1	yes	characteristic, complemented
528	#1786	C₂×C₇₉	1	1	yes	characteristic, complemented
529	C₇₉	#24440	1	1	yes	characteristic, direct product factor, Sylow
530	C₂³×D₄	—	2	1	no	—
531	C₂³×D₄	C₂²×C₇₉	1	1	yes	characteristic
532	C₂³×D₄	C₂²×C₇₉	1	1	yes	characteristic
533	C₂²×D₈	C₂²×C₇₉	1	1	yes	characteristic
534	C₂²×D₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
535	C₂²×D₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
536	C₂²×M₁₆	C₂²×C₇₉	1	1	yes	characteristic, complemented
537	D₄²	—	2	4	no	—
538	D₄²	—	2	4	no	—
539	C₂×#127	C₂²×C₇₉	1	1	yes	characteristic
540	C₂×#121	—	2	1	no	—
541	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
542	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
543	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic, complemented
544	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic, complemented
545	C₂×#120	—	2	1	no	—
546	C₂×#120	—	2	1	no	—
547	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
548	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
549	C₂×#117	C₂²×C₇₉	1	1	yes	characteristic, complemented
550	#469	—	2	4	no	—
551	#447	—	2	4	no	—
552	#447	—	2	4	no	—
553	C₂×#106	C₂²×C₇₉	1	1	yes	characteristic, complemented
554	#418	—	2	4	no	—
555	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
556	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
557	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
558	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic, complemented
559	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic, complemented
560	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic, complemented
561	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic, complemented
562	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic, complemented
563	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic, complemented
564	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic, complemented
565	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
566	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
567	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
568	#394	—	2	1	no	—
569	#392	—	2	1	no	—
570	#390	—	2	1	no	—
571	#390	C₂²×C₇₉	1	1	yes	characteristic, complemented
572	#389	C₂²×C₇₉	1	1	yes	characteristic, complemented
573	#388	—	2	1	no	—
574	#380	C₂²×C₇₉	1	1	yes	characteristic, complemented
575	#340	C₂²×C₇₉	1	1	yes	characteristic, complemented
576	#340	C₂²×C₇₉	1	1	yes	characteristic, complemented
577	#336	C₂²×C₇₉	1	1	yes	characteristic, complemented
578	#336	C₂²×C₇₉	1	1	yes	characteristic, complemented
579	C₂⁵	—	2	1	no	—
580	C₂⁵	—	2	1	no	—
581	C₂²×D₄	—	2	2	no	—
582	C₂²×D₄	—	2	2	no	—
583	C₂²×D₄	—	2	8	no	—
584	C₂²×D₄	—	2	1	no	—
585	C₂²×D₄	—	2	1	no	—
586	C₂²×D₄	—	2	2	no	—
587	C₂²×D₄	—	2	2	no	—
588	C₂²×D₄	—	2	2	no	—
589	C₂²×D₄	—	2	2	no	—
590	C₂²×D₄	—	2	1	no	—
591	C₂²×D₄	—	2	1	no	—
592	C₂²×D₄	—	2	1	no	—
593	C₂²×D₄	—	2	1	no	—
594	C₂²×D₄	—	2	1	no	—
595	C₂²×D₄	—	2	2	no	—
596	C₂²×D₄	—	2	1	no	—
597	C₂²×D₄	—	4	1	no	—
598	C₂²×D₄	—	4	1	no	—
599	C₂²×D₄	—	4	1	no	—
600	C₂²×D₄	—	4	1	no	—
601	C₂²×D₄	—	4	4	no	—
602	C₂²×D₄	—	4	4	no	—
603	C₂²×D₄	D₄×C₇₉	1	1	yes	characteristic
604	C₂²×D₄	D₄×C₇₉	1	4	yes	complemented
605	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
606	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
607	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
608	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
609	C₂³×C₄	—	2	1	no	—
610	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
611	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
612	C₂×D₈	—	2	2	no	—
613	C₂×D₈	—	2	2	no	—
614	C₂×D₈	—	2	2	no	—
615	C₂×D₈	—	2	2	no	—
616	C₂×D₈	—	2	2	no	—
617	C₂×D₈	—	2	2	no	—
618	C₂×D₈	—	4	1	no	—
619	C₂×D₈	—	4	1	no	—
620	C₂×D₈	—	4	1	no	—
621	C₂×M₁₆	—	2	2	no	—
622	C₂×M₁₆	—	2	2	no	—
623	C₂×M₁₆	—	4	1	no	—
624	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
625	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
626	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
627	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
628	#127	—	2	2	no	—
629	#127	—	2	2	no	—
630	#121	—	2	8	no	—
631	#121	—	2	2	no	—
632	#121	—	2	2	no	—
633	#121	—	2	2	no	—
634	#121	—	2	2	no	—
635	#121	—	2	2	no	—
636	#121	—	2	2	no	—
637	#121	—	4	1	no	—
638	#121	D₄×C₇₉	1	4	yes	complemented
639	#120	—	2	8	no	—
640	#120	—	2	8	no	—
641	C₄×D₄	—	2	2	no	—
642	C₄×D₄	—	2	2	no	—
643	C₄×D₄	—	2	2	no	—
644	C₄×D₄	—	2	2	no	—
645	#117	—	2	2	no	—
646	#117	—	4	1	no	—
647	C₂×C₄⋊C₄	—	2	1	no	—
648	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
651	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
652	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
653	C₂×C₂²⋊C₄	—	2	1	no	—
654	C₂×C₂²⋊C₄	—	2	1	no	—
655	C₂×C₂²⋊C₄	—	2	1	no	—
656	C₂×C₂²⋊C₄	—	2	1	no	—
657	C₂×C₂²⋊C₄	—	2	1	no	—
658	C₂×C₂²⋊C₄	—	2	1	no	—
659	C₂×C₂²⋊C₄	—	2	1	no	—
660	C₂×C₂²⋊C₄	—	2	1	no	—
661	C₂×C₂²⋊C₄	—	2	1	no	—
662	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
663	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
664	C₂×C₄²	—	2	1	no	—
665	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
666	#106	—	2	2	no	—
667	#102	—	2	2	no	—
668	#102	—	2	2	no	—
669	#102	—	2	2	no	—
670	#102	—	2	2	no	—
671	#102	—	2	2	no	—
672	#102	—	2	2	no	—
673	#102	—	2	2	no	—
674	#102	—	2	2	no	—
675	#102	—	4	1	no	—
676	#102	D₄×C₇₉	1	4	yes	complemented
677	C₂²⋊C₈	—	2	2	no	—
678	C₂²⋊C₈	—	2	2	no	—
679	C₂²⋊C₈	—	4	1	no	—
680	#95	—	2	1	no	—
681	#95	—	2	1	no	—
682	C₂⁴	—	2	1	no	—
683	C₂⁴	—	2	4	no	—
684	C₂⁴	—	2	1	no	—
685	C₂⁴	—	2	1	no	—
686	C₂⁴	—	2	4	no	—
687	C₂⁴	—	2	1	no	—
688	C₂⁴	—	4	2	no	—
689	C₂⁴	—	4	2	no	—
690	C₂⁴	—	4	2	no	—
691	C₂⁴	—	4	2	no	—
692	C₂⁴	—	4	2	no	—
693	C₂⁴	—	4	2	no	—
694	C₂⁴	—	4	2	no	—
695	C₂⁴	—	4	2	no	—
696	C₂⁴	—	8	1	no	—
697	C₂⁴	—	8	1	no	—
698	C₂⁴	—	8	1	no	—
699	C₂⁴	—	8	1	no	—
700	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
701	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
702	C₂×D₄	—	2	2	no	—
703	C₂×D₄	—	2	2	no	—
704	C₂×D₄	—	2	8	no	—
705	C₂×D₄	—	2	4	no	—
706	C₂×D₄	—	2	4	no	—
707	C₂×D₄	—	2	4	no	—
708	C₂×D₄	—	2	4	no	—
709	C₂×D₄	—	2	4	no	—
710	C₂×D₄	—	2	4	no	—
711	C₂×D₄	—	2	2	no	—
712	C₂×D₄	—	2	1	no	—
713	C₂×D₄	—	2	1	no	—
714	C₂×D₄	—	2	1	no	—
715	C₂×D₄	—	2	1	no	—
716	C₂×D₄	—	2	1	no	—
717	C₂×D₄	—	2	1	no	—
718	C₂×D₄	—	2	1	no	—
719	C₂×D₄	—	2	1	no	—
720	C₂×D₄	—	2	1	no	—
721	C₂×D₄	—	2	1	no	—
722	C₂×D₄	—	2	1	no	—
723	C₂×D₄	—	2	1	no	—
724	C₂×D₄	—	2	1	no	—
725	C₂×D₄	—	2	1	no	—
726	C₂×D₄	—	2	1	no	—
727	C₂×D₄	—	2	1	no	—
728	C₂×D₄	—	2	1	no	—
729	C₂×D₄	—	2	1	no	—
730	C₂×D₄	—	2	1	no	—
731	C₂×D₄	—	4	4	no	—
732	C₂×D₄	—	4	4	no	—
733	C₂×D₄	—	4	4	no	—
734	C₂×D₄	—	4	2	no	—
735	C₂×D₄	—	4	2	no	—
736	C₂×D₄	—	4	2	no	—
737	C₂×D₄	—	4	2	no	—
738	C₂×D₄	—	4	2	no	—
739	C₂×D₄	—	4	2	no	—
740	C₂×D₄	—	4	4	no	—
741	C₂×D₄	—	4	4	no	—
742	C₂×D₄	—	4	32	no	—
743	C₂×D₄	—	4	4	no	—
744	C₂×D₄	—	4	2	no	—
745	C₂×D₄	—	4	2	no	—
746	C₂×D₄	—	4	2	no	—
747	C₂×D₄	—	4	2	no	—
748	C₂×D₄	—	4	4	no	—
749	C₂×D₄	—	4	2	no	—
750	C₂×D₄	—	4	2	no	—
751	C₂×D₄	—	4	2	no	—
752	C₂×D₄	—	8	1	no	—
753	C₂×D₄	—	8	1	no	—
754	C₂×D₄	—	8	1	no	—
755	C₂×D₄	—	8	1	no	—
756	C₂×D₄	—	8	1	no	—
757	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
758	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
759	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
760	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
761	C₂×D₄	#41×C₇₉	1	2	yes	—
762	C₂²×C₄	—	2	1	no	—
763	C₂²×C₄	—	2	1	no	—
764	C₂²×C₄	—	2	1	no	—
765	C₂²×C₄	—	2	1	no	—
766	C₂²×C₄	—	2	4	no	—
767	C₂²×C₄	—	2	1	no	—
768	C₂²×C₄	—	2	1	no	—
769	C₂²×C₄	—	2	1	no	—
770	C₂²×C₄	—	2	1	no	—
771	C₂²×C₄	—	2	1	no	—
772	C₂²×C₄	—	2	1	no	—
773	C₂²×C₄	—	2	1	no	—
774	C₂²×C₄	—	2	1	no	—
775	C₂²×C₄	—	2	1	no	—
776	C₂²×C₄	—	2	1	no	—
777	C₂²×C₄	—	4	2	no	—
778	C₂²×C₄	—	4	2	no	—
779	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
780	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
781	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
782	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
783	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
784	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
786	D₈	—	4	4	no	—
787	D₈	—	4	4	no	—
788	D₈	—	4	4	no	—
789	M₁₆	—	4	4	no	—
790	C₂×C₈	—	2	1	no	—
791	C₂×C₈	—	2	1	no	—
792	C₂×C₈	—	2	1	no	—
793	C₂×C₈	—	2	1	no	—
794	C₂×C₈	—	2	1	no	—
795	C₂×C₈	—	2	1	no	—
796	C₂×C₈	—	2	1	no	—
797	C₂×C₈	—	2	1	no	—
798	C₂×C₈	—	2	1	no	—
799	C₂×C₈	—	2	1	no	—
800	C₂×C₈	—	2	1	no	—
801	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	complemented
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	1	no	—
804	C₄⋊C₄	—	2	1	no	—
805	C₄⋊C₄	—	2	1	no	—
806	C₄⋊C₄	—	2	1	no	—
807	C₄⋊C₄	—	2	1	no	—
808	C₄⋊C₄	—	2	1	no	—
809	C₄⋊C₄	—	8	1	no	—
810	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
811	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	complemented
812	C₂²⋊C₄	—	2	4	no	—
813	C₂²⋊C₄	—	2	4	no	—
814	C₂²⋊C₄	—	2	2	no	—
815	C₂²⋊C₄	—	2	4	no	—
816	C₂²⋊C₄	—	2	2	no	—
817	C₂²⋊C₄	—	4	2	no	—
818	C₂²⋊C₄	—	4	2	no	—
819	C₂²⋊C₄	—	4	2	no	—
820	C₂²⋊C₄	—	4	2	no	—
821	C₂²⋊C₄	—	8	1	no	—
822	C₂²⋊C₄	—	8	1	no	—
823	C₄²	—	2	1	no	—
824	C₄²	—	2	1	no	—
825	C₄²	—	4	2	no	—
826	C₂³	—	2	1	no	—
827	C₂³	—	2	2	no	—
828	C₂³	—	2	1	no	—
829	C₂³	—	2	1	no	—
830	C₂³	—	2	2	no	—
831	C₂³	—	2	1	no	—
832	C₂³	—	2	1	no	—
833	C₂³	—	2	2	no	—
834	C₂³	—	2	1	no	—
835	C₂³	—	2	1	no	—
836	C₂³	—	2	1	no	—
837	C₂³	—	2	1	no	—
838	C₂³	—	2	1	no	—
839	C₂³	—	2	1	no	—
840	C₂³	—	2	1	no	—
841	C₂³	—	2	2	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	4	8	no	—
844	C₂³	—	4	8	no	—
845	C₂³	—	4	8	no	—
846	C₂³	—	4	8	no	—
847	C₂³	—	4	1	no	—
848	C₂³	—	4	1	no	—
849	C₂³	—	4	1	no	—
850	C₂³	—	4	1	no	—
851	C₂³	—	4	1	no	—
852	C₂³	—	4	1	no	—
853	C₂³	—	4	1	no	—
854	C₂³	—	4	1	no	—
855	C₂³	—	4	1	no	—
856	C₂³	—	4	1	no	—
857	C₂³	—	4	1	no	—
858	C₂³	—	4	1	no	—
859	C₂³	—	4	1	no	—
860	C₂³	—	4	1	no	—
861	C₂³	—	4	1	no	—
862	C₂³	—	4	1	no	—
863	C₂³	—	4	1	no	—
864	C₂³	—	4	1	no	—
865	C₂³	—	4	1	no	—
866	C₂³	—	4	1	no	—
867	C₂³	—	4	1	no	—
868	C₂³	—	4	1	no	—
869	C₂³	—	4	1	no	—
870	C₂³	—	8	4	no	—
871	C₂³	—	8	4	no	—
872	C₂³	—	8	4	no	—
873	C₂³	—	8	4	no	—
874	C₂³	—	8	4	no	—
875	C₂³	—	8	4	no	—
876	C₂³	—	8	4	no	—
877	C₂³	—	8	4	no	—
878	C₂³	—	8	4	no	—
879	C₂³	—	8	4	no	—
880	C₂³	#120×C₇₉	1	2	yes	—
881	C₂³	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
882	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
883	D₄	—	2	8	no	—
884	D₄	—	2	2	no	—
885	D₄	—	2	2	no	—
886	D₄	—	2	2	no	—
887	D₄	—	2	2	no	—
888	D₄	—	2	2	no	—
889	D₄	—	2	2	no	—
890	D₄	—	2	2	no	—
891	D₄	—	4	8	no	—
892	D₄	—	4	8	no	—
893	D₄	—	4	8	no	—
894	D₄	—	4	8	no	—
895	D₄	—	4	8	no	—
896	D₄	—	4	1	no	—
897	D₄	—	4	1	no	—
898	D₄	—	4	1	no	—
899	D₄	—	4	1	no	—
900	D₄	—	4	1	no	—
901	D₄	—	4	1	no	—
902	D₄	—	4	1	no	—
903	D₄	—	4	1	no	—
904	D₄	—	8	4	no	—
905	D₄	—	8	4	no	—
906	D₄	—	8	4	no	—
907	D₄	#121×C₇₉	1	4	yes	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	4	8	no	—
925	C₂×C₄	—	4	1	no	—
926	C₂×C₄	—	4	1	no	—
927	C₂×C₄	—	4	1	no	—
928	C₂×C₄	—	4	1	no	—
929	C₂×C₄	—	4	1	no	—
930	C₂×C₄	—	4	1	no	—
931	C₂×C₄	—	4	1	no	—
932	C₂×C₄	—	4	1	no	—
933	C₂×C₄	—	4	1	no	—
934	C₂×C₄	—	4	1	no	—
935	C₂×C₄	—	4	1	no	—
936	C₂×C₄	—	4	1	no	—
937	C₂×C₄	—	4	1	no	—
938	C₂×C₄	—	4	1	no	—
939	C₂×C₄	#120×C₇₉	1	2	yes	—
940	C₂×C₄	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
941	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
942	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
943	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
944	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
945	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
946	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
947	C₈	—	2	2	no	—
948	C₈	—	4	1	no	—
949	C₈	—	4	1	no	—
950	C₈	—	4	1	no	—
951	C₂²	—	2	2	no	—
952	C₂²	—	2	2	no	—
953	C₂²	—	2	4	no	—
954	C₂²	—	2	2	no	—
955	C₂²	—	2	2	no	—
956	C₂²	—	2	2	no	—
957	C₂²	—	2	2	no	—
958	C₂²	—	4	1	no	—
959	C₂²	—	4	1	no	—
960	C₂²	—	4	2	no	—
961	C₂²	—	4	1	no	—
962	C₂²	—	4	2	no	—
963	C₂²	—	4	1	no	—
964	C₂²	—	4	1	no	—
965	C₂²	—	4	2	no	—
966	C₂²	—	4	1	no	—
967	C₂²	—	4	2	no	—
968	C₂²	—	4	1	no	—
969	C₂²	—	4	2	no	—
970	C₂²	—	4	1	no	—
971	C₂²	—	4	2	no	—
972	C₂²	—	4	2	no	—
973	C₂²	—	4	2	no	—
974	C₂²	—	4	2	no	—
975	C₂²	—	4	2	no	—
976	C₂²	—	4	2	no	—
977	C₂²	—	4	2	no	—
978	C₂²	—	8	16	no	—
979	C₂²	—	8	16	no	—
980	C₂²	—	8	1	no	—
981	C₂²	—	8	1	no	—
982	C₂²	—	8	1	no	—
983	C₂²	—	8	1	no	—
984	C₂²	—	8	1	no	—
985	C₂²	—	8	1	no	—
986	C₂²	—	8	1	no	—
987	C₂²	—	8	1	no	—
988	C₂²	—	8	1	no	—
989	C₂²	—	8	1	no	—
990	C₂²	—	8	1	no	—
991	C₂²	—	8	1	no	—
992	C₂²	—	8	1	no	—
993	C₂²	—	8	1	no	—
994	C₂²	—	8	1	no	—
995	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
996	C₂²	D₄²×C₇₉	1	1	yes	characteristic
997	C₂²	#546×C₇₉	1	1	yes	characteristic
998	C₂²	C₂×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
999	C₂²	C₂×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
1000	C₂²	#576×C₇₉	1	1	yes	characteristic
1001	C₂²	#576×C₇₉	1	1	yes	characteristic
1002	C₄	—	2	2	no	—
1003	C₄	—	2	2	no	—
1004	C₄	—	4	1	no	—
1005	C₄	—	4	2	no	—
1006	C₄	—	4	1	no	—
1007	C₄	—	4	2	no	—
1008	C₄	—	8	1	no	—
1009	C₄	—	8	1	no	—
1010	C₄	C₂×#121×C₇₉	1	1	yes	characteristic
1011	C₄	#534×C₇₉	1	1	yes	characteristic
1012	C₄	D₄²×C₇₉	1	1	yes	characteristic
1013	C₄	#546×C₇₉	1	1	yes	characteristic
1014	C₂	—	4	2	no	—
1015	C₂	—	4	2	no	—
1016	C₂	—	4	4	no	—
1017	C₂	—	8	2	no	—
1018	C₂	—	8	2	no	—
1019	C₂	—	16	1	no	—
1020	C₂	C₇₉×#2410	1	1	yes	characteristic
1021	C₂	C₇₉×#3003	1	1	yes	characteristic
1022	C₂	C₇₉×#3008	1	1	yes	characteristic
1023	C₂	C₇₉×#3264	1	1	yes	characteristic
1024	C₂	C₇₉×#3274	1	1	yes	characteristic
1025	C₂	C₇₉×#3318	1	1	yes	characteristic
1026	C₂	C₇₉×#3325	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×D₄²×C₇₉	C₂	semidirect
2. C₂×#469×C₇₉	C₂	semidirect
3. C₂×#447×C₇₉	C₂	semidirect
4. C₂×#447×C₇₉	C₂	semidirect
5. C₂×#418×C₇₉	C₂	semidirect
6. C₇₉×#2414	C₂	semidirect
7. C₇₉×#2041	C₂	semidirect
8. C₇₉×#2034	C₂	semidirect
9. C₇₉×#2011	C₂	semidirect
10. C₇₉×#1999	C₂	semidirect
11. C₇₉×#1879	C₂	semidirect
12. C₇₉×#1875	C₂	semidirect
13. C₇₉×#1870	C₂	semidirect
14. C₇₉×#1864	C₂	semidirect
15. C₇₉×#1786	C₂	semidirect
20. C₂²×D₈×C₇₉	C₂²	semidirect
21. C₂²×D₈×C₇₉	C₂²	semidirect
22. C₂²×M₁₆×C₇₉	C₂²	semidirect
29. C₂×#121×C₇₉	C₂²	semidirect
30. C₂×#121×C₇₉	C₂²	semidirect
35. C₂×#117×C₇₉	C₂²	semidirect
39. C₂×#106×C₇₉	C₂²	semidirect
44. C₂×#102×C₇₉	C₂²	semidirect
45. C₂×#102×C₇₉	C₂²	semidirect
46. C₂×#102×C₇₉	C₂²	semidirect
47. C₂×#102×C₇₉	C₂²	semidirect
48. C₂×#102×C₇₉	C₂²	semidirect
49. C₂×#102×C₇₉	C₂²	semidirect
50. C₂×#102×C₇₉	C₂²	semidirect
51. C₂×C₂²⋊C₈×C₇₉	C₂²	semidirect
52. C₂×C₂²⋊C₈×C₇₉	C₂²	semidirect
53. C₂×C₂²⋊C₈×C₇₉	C₂²	semidirect
57. #390×C₇₉	C₂²	semidirect
58. #389×C₇₉	C₂²	semidirect
60. #380×C₇₉	C₂²	semidirect
61. #340×C₇₉	C₂²	semidirect
62. #340×C₇₉	C₂²	semidirect
63. #336×C₇₉	C₂²	semidirect
64. #336×C₇₉	C₂²	semidirect
90. C₂²×D₄×C₇₉	D₄	semidirect
124. #121×C₇₉	D₄	semidirect
162. #102×C₇₉	D₄	semidirect
287. C₂×C₈×C₇₉	C₂×D₄	semidirect
297. C₄⋊C₄×C₇₉	C₂×D₄	semidirect
500. #24440	C₇₉	direct (N × H)
514. C₂×D₄²	C₂×C₇₉	semidirect
515. C₂×#469	C₂×C₇₉	semidirect
516. C₂×#447	C₂×C₇₉	semidirect
517. C₂×#447	C₂×C₇₉	semidirect
518. C₂×#418	C₂×C₇₉	semidirect
519. #2414	C₂×C₇₉	semidirect
520. #2041	C₂×C₇₉	semidirect
521. #2034	C₂×C₇₉	semidirect
522. #2011	C₂×C₇₉	semidirect
523. #1999	C₂×C₇₉	semidirect
524. #1879	C₂×C₇₉	semidirect
525. #1875	C₂×C₇₉	semidirect
526. #1870	C₂×C₇₉	semidirect
527. #1864	C₂×C₇₉	semidirect
528. #1786	C₂×C₇₉	semidirect
529. C₇₉	#24440	direct (N × H)
534. C₂²×D₈	C₂²×C₇₉	semidirect
535. C₂²×D₈	C₂²×C₇₉	semidirect
536. C₂²×M₁₆	C₂²×C₇₉	semidirect
543. C₂×#121	C₂²×C₇₉	semidirect
544. C₂×#121	C₂²×C₇₉	semidirect
549. C₂×#117	C₂²×C₇₉	semidirect
553. C₂×#106	C₂²×C₇₉	semidirect
558. C₂×#102	C₂²×C₇₉	semidirect
559. C₂×#102	C₂²×C₇₉	semidirect
560. C₂×#102	C₂²×C₇₉	semidirect
561. C₂×#102	C₂²×C₇₉	semidirect
562. C₂×#102	C₂²×C₇₉	semidirect
563. C₂×#102	C₂²×C₇₉	semidirect
564. C₂×#102	C₂²×C₇₉	semidirect
565. C₂×C₂²⋊C₈	C₂²×C₇₉	semidirect
566. C₂×C₂²⋊C₈	C₂²×C₇₉	semidirect
567. C₂×C₂²⋊C₈	C₂²×C₇₉	semidirect
571. #390	C₂²×C₇₉	semidirect
572. #389	C₂²×C₇₉	semidirect
574. #380	C₂²×C₇₉	semidirect
575. #340	C₂²×C₇₉	semidirect
576. #340	C₂²×C₇₉	semidirect
577. #336	C₂²×C₇₉	semidirect
578. #336	C₂²×C₇₉	semidirect
604. C₂²×D₄	D₄×C₇₉	semidirect
638. #121	D₄×C₇₉	semidirect
676. #102	D₄×C₇₉	semidirect
801. C₂×C₈	C₂×D₄×C₇₉	semidirect
811. C₄⋊C₄	C₂×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×D₄²×C₇₉	2
C₂×#469×C₇₉	2
C₂×#447×C₇₉	2
C₂×#418×C₇₉	2
C₇₉×#2414	2
C₇₉×#2041	2
C₇₉×#2034	2
C₇₉×#2011	2
C₇₉×#1999	2
C₇₉×#1879	2
C₇₉×#1875	2
C₇₉×#1870	2
C₇₉×#1864	2
C₇₉×#1786	2
#24440	79

Subgroups — C79×#24440 #34136129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#24440 #34136129