Subgroups — C₇₉×#24448 #34136137

Order 20224.

1888 conjugacy classes of subgroups.

The subgroup lattice has 990 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
2	C₂×#468×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#450×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#450×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#418×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₉×#2415	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#2041	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#2033	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#2014	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#2000	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1877	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×#1862	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×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic, complemented
21	C₂²×SD₁₆×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×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
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×#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	#468×C₇₉	—	2	4	no	—
37	#450×C₇₉	—	2	4	no	—
38	#450×C₇₉	—	2	4	no	—
39	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic, complemented
40	#418×C₇₉	—	2	4	no	—
41	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic, complemented
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
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	#397×C₇₉	—	2	1	no	—
55	#394×C₇₉	—	2	1	no	—
56	#391×C₇₉	C₂²	1	1	yes	characteristic, complemented
57	#389×C₇₉	—	2	1	no	—
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×Q₈×C₇₉	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₇₉	—	2	2	no	—
69	C₂²×D₄×C₇₉	—	2	2	no	—
70	C₂²×D₄×C₇₉	—	2	8	no	—
71	C₂²×D₄×C₇₉	—	2	1	no	—
72	C₂²×D₄×C₇₉	—	2	1	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	2	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	2	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	—	4	1	no	—
85	C₂²×D₄×C₇₉	—	4	1	no	—
86	C₂²×D₄×C₇₉	—	4	4	no	—
87	C₂²×D₄×C₇₉	—	4	4	no	—
88	C₂²×D₄×C₇₉	D₄	1	1	yes	characteristic
89	C₂²×D₄×C₇₉	D₄	1	4	yes	—
90	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₇₉	—	2	1	no	—
94	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
96	C₂×SD₁₆×C₇₉	—	2	2	no	—
97	C₂×SD₁₆×C₇₉	—	2	2	no	—
98	C₂×SD₁₆×C₇₉	—	2	2	no	—
99	C₂×SD₁₆×C₇₉	—	2	2	no	—
100	C₂×SD₁₆×C₇₉	—	2	2	no	—
101	C₂×SD₁₆×C₇₉	—	2	2	no	—
102	C₂×SD₁₆×C₇₉	—	4	1	no	—
103	C₂×SD₁₆×C₇₉	—	4	1	no	—
104	C₂×SD₁₆×C₇₉	—	4	1	no	—
105	C₂×M₁₆×C₇₉	—	2	2	no	—
106	C₂×M₁₆×C₇₉	—	2	2	no	—
107	C₂×M₁₆×C₇₉	—	4	1	no	—
108	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
112	#127×C₇₉	—	2	2	no	—
113	#127×C₇₉	—	2	2	no	—
114	C₂²⋊Q₈×C₇₉	—	2	2	no	—
115	C₂²⋊Q₈×C₇₉	—	2	2	no	—
116	C₂²⋊Q₈×C₇₉	—	2	2	no	—
117	C₂²⋊Q₈×C₇₉	—	4	1	no	—
118	#121×C₇₉	—	2	8	no	—
119	#121×C₇₉	—	2	2	no	—
120	#121×C₇₉	—	2	2	no	—
121	#121×C₇₉	—	2	2	no	—
122	#121×C₇₉	D₄	1	4	yes	—
123	#120×C₇₉	—	2	8	no	—
124	#120×C₇₉	—	2	8	no	—
125	C₄×D₄×C₇₉	—	2	2	no	—
126	C₄×D₄×C₇₉	—	2	2	no	—
127	C₄×D₄×C₇₉	—	2	2	no	—
128	C₄×D₄×C₇₉	—	2	2	no	—
129	#117×C₇₉	—	2	2	no	—
130	#117×C₇₉	—	4	1	no	—
131	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
132	C₂×C₄⋊C₄×C₇₉	—	2	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	D₄	1	1	yes	characteristic
147	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
148	C₂×C₄²×C₇₉	—	2	1	no	—
149	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
150	#107×C₇₉	—	2	2	no	—
151	#103×C₇₉	—	2	2	no	—
152	#102×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	—	4	1	no	—
160	#102×C₇₉	D₄	1	4	yes	complemented
161	C₂²⋊C₈×C₇₉	—	2	2	no	—
162	C₂²⋊C₈×C₇₉	—	2	2	no	—
163	C₂²⋊C₈×C₇₉	—	4	1	no	—
164	#95×C₇₉	—	2	1	no	—
165	#95×C₇₉	—	2	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	—	4	2	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	—	8	1	no	—
182	C₂⁴×C₇₉	—	8	1	no	—
183	C₂⁴×C₇₉	—	8	1	no	—
184	C₂⁴×C₇₉	—	8	1	no	—
185	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
186	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
187	C₂×Q₈×C₇₉	—	2	1	no	—
188	C₂×Q₈×C₇₉	—	2	1	no	—
189	C₂×Q₈×C₇₉	—	2	1	no	—
190	C₂×Q₈×C₇₉	—	2	1	no	—
191	C₂×Q₈×C₇₉	—	2	1	no	—
192	C₂×Q₈×C₇₉	—	2	1	no	—
193	C₂×D₄×C₇₉	—	2	2	no	—
194	C₂×D₄×C₇₉	—	2	2	no	—
195	C₂×D₄×C₇₉	—	2	8	no	—
196	C₂×D₄×C₇₉	—	2	4	no	—
197	C₂×D₄×C₇₉	—	2	4	no	—
198	C₂×D₄×C₇₉	—	2	4	no	—
199	C₂×D₄×C₇₉	—	2	4	no	—
200	C₂×D₄×C₇₉	—	2	4	no	—
201	C₂×D₄×C₇₉	—	2	4	no	—
202	C₂×D₄×C₇₉	—	2	2	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	—	4	4	no	—
217	C₂×D₄×C₇₉	—	4	4	no	—
218	C₂×D₄×C₇₉	—	4	4	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	—	4	2	no	—
223	C₂×D₄×C₇₉	—	4	2	no	—
224	C₂×D₄×C₇₉	—	4	4	no	—
225	C₂×D₄×C₇₉	—	4	4	no	—
226	C₂×D₄×C₇₉	—	4	32	no	—
227	C₂×D₄×C₇₉	—	4	4	no	—
228	C₂×D₄×C₇₉	—	4	2	no	—
229	C₂×D₄×C₇₉	—	4	2	no	—
230	C₂×D₄×C₇₉	—	4	2	no	—
231	C₂×D₄×C₇₉	—	4	2	no	—
232	C₂×D₄×C₇₉	—	4	4	no	—
233	C₂×D₄×C₇₉	—	4	2	no	—
234	C₂×D₄×C₇₉	—	8	1	no	—
235	C₂×D₄×C₇₉	—	8	1	no	—
236	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
237	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
238	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
239	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
240	C₂×D₄×C₇₉	#41	1	2	yes	—
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	4	no	—
246	C₂²×C₄×C₇₉	—	2	1	no	—
247	C₂²×C₄×C₇₉	—	2	1	no	—
248	C₂²×C₄×C₇₉	—	2	1	no	—
249	C₂²×C₄×C₇₉	—	2	1	no	—
250	C₂²×C₄×C₇₉	—	2	1	no	—
251	C₂²×C₄×C₇₉	—	2	1	no	—
252	C₂²×C₄×C₇₉	—	2	1	no	—
253	C₂²×C₄×C₇₉	—	2	1	no	—
254	C₂²×C₄×C₇₉	—	2	1	no	—
255	C₂²×C₄×C₇₉	—	2	1	no	—
256	C₂²×C₄×C₇₉	—	2	1	no	—
257	C₂²×C₄×C₇₉	—	4	2	no	—
258	C₂²×C₄×C₇₉	—	4	2	no	—
259	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
263	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
264	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
266	SD₁₆×C₇₉	—	4	4	no	—
267	SD₁₆×C₇₉	—	4	4	no	—
268	SD₁₆×C₇₉	—	4	4	no	—
269	M₁₆×C₇₉	—	4	4	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	—	2	1	no	—
276	C₂×C₈×C₇₉	—	2	1	no	—
277	C₂×C₈×C₇₉	—	2	1	no	—
278	C₂×C₈×C₇₉	—	2	1	no	—
279	C₂×C₈×C₇₉	—	2	1	no	—
280	C₂×C₈×C₇₉	—	2	1	no	—
281	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	complemented
282	C₄⋊C₄×C₇₉	—	2	2	no	—
283	C₄⋊C₄×C₇₉	—	2	1	no	—
284	C₄⋊C₄×C₇₉	—	2	1	no	—
285	C₄⋊C₄×C₇₉	—	2	1	no	—
286	C₄⋊C₄×C₇₉	—	2	1	no	—
287	C₄⋊C₄×C₇₉	—	2	1	no	—
288	C₄⋊C₄×C₇₉	—	2	1	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	C₂×D₄	1	2	yes	—
293	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	complemented
294	C₂²⋊C₄×C₇₉	—	2	4	no	—
295	C₂²⋊C₄×C₇₉	—	2	4	no	—
296	C₂²⋊C₄×C₇₉	—	2	2	no	—
297	C₂²⋊C₄×C₇₉	—	2	4	no	—
298	C₂²⋊C₄×C₇₉	—	2	2	no	—
299	C₂²⋊C₄×C₇₉	—	4	2	no	—
300	C₂²⋊C₄×C₇₉	—	4	2	no	—
301	C₂²⋊C₄×C₇₉	—	4	2	no	—
302	C₂²⋊C₄×C₇₉	—	4	2	no	—
303	C₄²×C₇₉	—	2	1	no	—
304	C₄²×C₇₉	—	2	1	no	—
305	C₄²×C₇₉	—	4	2	no	—
306	C₂³×C₇₉	—	2	1	no	—
307	C₂³×C₇₉	—	2	2	no	—
308	C₂³×C₇₉	—	2	1	no	—
309	C₂³×C₇₉	—	2	1	no	—
310	C₂³×C₇₉	—	2	2	no	—
311	C₂³×C₇₉	—	2	1	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	1	no	—
317	C₂³×C₇₉	—	2	1	no	—
318	C₂³×C₇₉	—	2	1	no	—
319	C₂³×C₇₉	—	2	1	no	—
320	C₂³×C₇₉	—	2	1	no	—
321	C₂³×C₇₉	—	2	2	no	—
322	C₂³×C₇₉	—	2	2	no	—
323	C₂³×C₇₉	—	4	8	no	—
324	C₂³×C₇₉	—	4	8	no	—
325	C₂³×C₇₉	—	4	8	no	—
326	C₂³×C₇₉	—	4	8	no	—
327	C₂³×C₇₉	—	4	1	no	—
328	C₂³×C₇₉	—	4	1	no	—
329	C₂³×C₇₉	—	4	1	no	—
330	C₂³×C₇₉	—	4	1	no	—
331	C₂³×C₇₉	—	4	1	no	—
332	C₂³×C₇₉	—	4	1	no	—
333	C₂³×C₇₉	—	4	1	no	—
334	C₂³×C₇₉	—	4	1	no	—
335	C₂³×C₇₉	—	4	1	no	—
336	C₂³×C₇₉	—	4	1	no	—
337	C₂³×C₇₉	—	4	1	no	—
338	C₂³×C₇₉	—	4	1	no	—
339	C₂³×C₇₉	—	4	1	no	—
340	C₂³×C₇₉	—	4	1	no	—
341	C₂³×C₇₉	—	4	1	no	—
342	C₂³×C₇₉	—	4	1	no	—
343	C₂³×C₇₉	—	8	4	no	—
344	C₂³×C₇₉	—	8	4	no	—
345	C₂³×C₇₉	—	8	4	no	—
346	C₂³×C₇₉	—	8	4	no	—
347	C₂³×C₇₉	—	8	4	no	—
348	C₂³×C₇₉	—	8	4	no	—
349	C₂³×C₇₉	—	8	4	no	—
350	C₂³×C₇₉	—	8	4	no	—
351	C₂³×C₇₉	—	8	4	no	—
352	C₂³×C₇₉	—	8	4	no	—
353	C₂³×C₇₉	#120	1	2	yes	—
354	C₂³×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
355	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
356	Q₈×C₇₉	—	4	1	no	—
357	Q₈×C₇₉	—	4	1	no	—
358	Q₈×C₇₉	—	4	1	no	—
359	Q₈×C₇₉	—	4	1	no	—
360	D₄×C₇₉	—	2	8	no	—
361	D₄×C₇₉	—	2	2	no	—
362	D₄×C₇₉	—	2	2	no	—
363	D₄×C₇₉	—	2	2	no	—
364	D₄×C₇₉	—	2	2	no	—
365	D₄×C₇₉	—	2	2	no	—
366	D₄×C₇₉	—	2	2	no	—
367	D₄×C₇₉	—	2	2	no	—
368	D₄×C₇₉	—	4	8	no	—
369	D₄×C₇₉	—	4	8	no	—
370	D₄×C₇₉	—	4	8	no	—
371	D₄×C₇₉	—	4	8	no	—
372	D₄×C₇₉	—	4	8	no	—
373	D₄×C₇₉	—	4	1	no	—
374	D₄×C₇₉	—	4	1	no	—
375	D₄×C₇₉	—	4	1	no	—
376	D₄×C₇₉	—	4	1	no	—
377	D₄×C₇₉	—	8	4	no	—
378	D₄×C₇₉	#121	1	4	yes	—
379	C₂×C₄×C₇₉	—	2	1	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	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	1	no	—
388	C₂×C₄×C₇₉	—	2	1	no	—
389	C₂×C₄×C₇₉	—	2	2	no	—
390	C₂×C₄×C₇₉	—	2	2	no	—
391	C₂×C₄×C₇₉	—	2	1	no	—
392	C₂×C₄×C₇₉	—	2	1	no	—
393	C₂×C₄×C₇₉	—	2	1	no	—
394	C₂×C₄×C₇₉	—	2	1	no	—
395	C₂×C₄×C₇₉	—	4	8	no	—
396	C₂×C₄×C₇₉	—	4	1	no	—
397	C₂×C₄×C₇₉	—	4	1	no	—
398	C₂×C₄×C₇₉	—	4	1	no	—
399	C₂×C₄×C₇₉	—	4	1	no	—
400	C₂×C₄×C₇₉	—	4	1	no	—
401	C₂×C₄×C₇₉	—	4	1	no	—
402	C₂×C₄×C₇₉	—	4	1	no	—
403	C₂×C₄×C₇₉	—	4	1	no	—
404	C₂×C₄×C₇₉	—	4	1	no	—
405	C₂×C₄×C₇₉	—	4	1	no	—
406	C₂×C₄×C₇₉	—	4	1	no	—
407	C₂×C₄×C₇₉	—	4	1	no	—
408	C₂×C₄×C₇₉	—	4	1	no	—
409	C₂×C₄×C₇₉	—	4	1	no	—
410	C₂×C₄×C₇₉	—	4	1	no	—
411	C₂×C₄×C₇₉	—	4	1	no	—
412	C₂×C₄×C₇₉	—	4	1	no	—
413	C₂×C₄×C₇₉	#120	1	2	yes	—
414	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
415	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
419	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
420	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
421	C₈×C₇₉	—	2	2	no	—
422	C₈×C₇₉	—	4	1	no	—
423	C₈×C₇₉	—	4	1	no	—
424	C₈×C₇₉	—	4	1	no	—
425	C₂²×C₇₉	—	2	2	no	—
426	C₂²×C₇₉	—	2	4	no	—
427	C₂²×C₇₉	—	2	2	no	—
428	C₂²×C₇₉	—	2	2	no	—
429	C₂²×C₇₉	—	2	2	no	—
430	C₂²×C₇₉	—	2	2	no	—
431	C₂²×C₇₉	—	2	2	no	—
432	C₂²×C₇₉	—	4	1	no	—
433	C₂²×C₇₉	—	4	2	no	—
434	C₂²×C₇₉	—	4	1	no	—
435	C₂²×C₇₉	—	4	2	no	—
436	C₂²×C₇₉	—	4	1	no	—
437	C₂²×C₇₉	—	4	2	no	—
438	C₂²×C₇₉	—	4	1	no	—
439	C₂²×C₇₉	—	4	1	no	—
440	C₂²×C₇₉	—	4	2	no	—
441	C₂²×C₇₉	—	4	1	no	—
442	C₂²×C₇₉	—	4	2	no	—
443	C₂²×C₇₉	—	4	1	no	—
444	C₂²×C₇₉	—	4	1	no	—
445	C₂²×C₇₉	—	4	2	no	—
446	C₂²×C₇₉	—	4	2	no	—
447	C₂²×C₇₉	—	4	2	no	—
448	C₂²×C₇₉	—	4	2	no	—
449	C₂²×C₇₉	—	4	2	no	—
450	C₂²×C₇₉	—	4	2	no	—
451	C₂²×C₇₉	—	4	2	no	—
452	C₂²×C₇₉	—	8	16	no	—
453	C₂²×C₇₉	—	8	16	no	—
454	C₂²×C₇₉	—	8	1	no	—
455	C₂²×C₇₉	—	8	1	no	—
456	C₂²×C₇₉	—	8	1	no	—
457	C₂²×C₇₉	—	8	1	no	—
458	C₂²×C₇₉	—	8	1	no	—
459	C₂²×C₇₉	—	8	1	no	—
460	C₂²×C₇₉	—	8	1	no	—
461	C₂²×C₇₉	—	8	1	no	—
462	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
463	C₂²×C₇₉	D₄²	1	1	yes	characteristic
464	C₂²×C₇₉	#546	1	1	yes	characteristic
465	C₂²×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
466	C₂²×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
467	C₂²×C₇₉	#577	1	1	yes	characteristic
468	C₂²×C₇₉	#577	1	1	yes	characteristic
469	C₄×C₇₉	—	2	2	no	—
470	C₄×C₇₉	—	2	2	no	—
471	C₄×C₇₉	—	4	1	no	—
472	C₄×C₇₉	—	4	2	no	—
473	C₄×C₇₉	—	4	1	no	—
474	C₄×C₇₉	—	4	2	no	—
475	C₄×C₇₉	—	8	1	no	—
476	C₄×C₇₉	—	8	1	no	—
477	C₄×C₇₉	—	8	1	no	—
478	C₄×C₇₉	C₂×#121	1	1	yes	characteristic
479	C₄×C₇₉	#534	1	1	yes	characteristic
480	C₄×C₇₉	D₄²	1	1	yes	characteristic
481	C₄×C₇₉	#546	1	1	yes	characteristic
482	#24448	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
483	C₂×C₇₉	—	4	2	no	—
484	C₂×C₇₉	—	4	2	no	—
485	C₂×C₇₉	—	4	4	no	—
486	C₂×C₇₉	—	8	2	no	—
487	C₂×C₇₉	—	8	2	no	—
488	C₂×C₇₉	#2410	1	1	yes	characteristic
489	C₂×C₇₉	#3003	1	1	yes	characteristic
490	C₂×C₇₉	#3009	1	1	yes	characteristic
491	C₂×C₇₉	#3265	1	1	yes	characteristic
492	C₂×C₇₉	#3272	1	1	yes	characteristic
493	C₂×C₇₉	#3310	1	1	yes	characteristic
494	C₂×C₇₉	#3324	1	1	yes	characteristic
495	C₂×D₄²	C₂×C₇₉	1	1	yes	characteristic
496	C₂×#468	C₂×C₇₉	1	1	yes	characteristic, complemented
497	C₂×#450	C₂×C₇₉	1	1	yes	characteristic, complemented
498	C₂×#450	C₂×C₇₉	1	1	yes	characteristic, complemented
499	C₂×#418	C₂×C₇₉	1	1	yes	characteristic, complemented
500	#2415	C₂×C₇₉	1	1	yes	characteristic, complemented
501	#2041	C₂×C₇₉	1	1	yes	characteristic, complemented
502	#2033	C₂×C₇₉	1	1	yes	characteristic, complemented
503	#2014	C₂×C₇₉	1	1	yes	characteristic, complemented
504	#2000	C₂×C₇₉	1	1	yes	characteristic, complemented
505	#1877	C₂×C₇₉	1	1	yes	characteristic, complemented
506	#1875	C₂×C₇₉	1	1	yes	characteristic, complemented
507	#1870	C₂×C₇₉	1	1	yes	characteristic, complemented
508	#1862	C₂×C₇₉	1	1	yes	characteristic, complemented
509	#1786	C₂×C₇₉	1	1	yes	characteristic, complemented
510	C₇₉	#24448	1	1	yes	characteristic, direct product factor, Sylow
511	C₂³×D₄	—	2	1	no	—
512	C₂³×D₄	C₂²×C₇₉	1	1	yes	characteristic
513	C₂³×D₄	C₂²×C₇₉	1	1	yes	characteristic
514	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
515	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic, complemented
516	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic, complemented
517	C₂²×M₁₆	C₂²×C₇₉	1	1	yes	characteristic, complemented
518	D₄²	—	2	4	no	—
519	D₄²	—	2	4	no	—
520	C₂×#127	C₂²×C₇₉	1	1	yes	characteristic
521	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
522	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
523	C₂×#121	—	2	1	no	—
524	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
525	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
526	C₂×#120	—	2	1	no	—
527	C₂×#120	—	2	1	no	—
528	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
529	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
530	C₂×#117	C₂²×C₇₉	1	1	yes	characteristic, complemented
531	#468	—	2	4	no	—
532	#450	—	2	4	no	—
533	#450	—	2	4	no	—
534	C₂×#107	C₂²×C₇₉	1	1	yes	characteristic, complemented
535	#418	—	2	4	no	—
536	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic, complemented
537	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
538	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
539	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
540	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic, complemented
541	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic, complemented
542	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic, complemented
543	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic, complemented
544	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic, complemented
545	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic, complemented
546	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
547	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
548	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
549	#397	—	2	1	no	—
550	#394	—	2	1	no	—
551	#391	C₂²×C₇₉	1	1	yes	characteristic, complemented
552	#389	—	2	1	no	—
553	#389	C₂²×C₇₉	1	1	yes	characteristic, complemented
554	#388	—	2	1	no	—
555	#380	C₂²×C₇₉	1	1	yes	characteristic, complemented
556	#340	C₂²×C₇₉	1	1	yes	characteristic, complemented
557	#340	C₂²×C₇₉	1	1	yes	characteristic, complemented
558	#336	C₂²×C₇₉	1	1	yes	characteristic, complemented
559	#336	C₂²×C₇₉	1	1	yes	characteristic, complemented
560	C₂⁵	—	2	1	no	—
561	C₂⁵	—	2	1	no	—
562	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
563	C₂²×D₄	—	2	2	no	—
564	C₂²×D₄	—	2	2	no	—
565	C₂²×D₄	—	2	8	no	—
566	C₂²×D₄	—	2	1	no	—
567	C₂²×D₄	—	2	1	no	—
568	C₂²×D₄	—	2	2	no	—
569	C₂²×D₄	—	2	2	no	—
570	C₂²×D₄	—	2	2	no	—
571	C₂²×D₄	—	2	2	no	—
572	C₂²×D₄	—	2	1	no	—
573	C₂²×D₄	—	2	1	no	—
574	C₂²×D₄	—	2	1	no	—
575	C₂²×D₄	—	2	2	no	—
576	C₂²×D₄	—	2	1	no	—
577	C₂²×D₄	—	4	1	no	—
578	C₂²×D₄	—	4	1	no	—
579	C₂²×D₄	—	4	1	no	—
580	C₂²×D₄	—	4	1	no	—
581	C₂²×D₄	—	4	4	no	—
582	C₂²×D₄	—	4	4	no	—
583	C₂²×D₄	D₄×C₇₉	1	1	yes	characteristic
584	C₂²×D₄	D₄×C₇₉	1	4	yes	—
585	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
586	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
587	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
588	C₂³×C₄	—	2	1	no	—
589	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
590	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
591	C₂×SD₁₆	—	2	2	no	—
592	C₂×SD₁₆	—	2	2	no	—
593	C₂×SD₁₆	—	2	2	no	—
594	C₂×SD₁₆	—	2	2	no	—
595	C₂×SD₁₆	—	2	2	no	—
596	C₂×SD₁₆	—	2	2	no	—
597	C₂×SD₁₆	—	4	1	no	—
598	C₂×SD₁₆	—	4	1	no	—
599	C₂×SD₁₆	—	4	1	no	—
600	C₂×M₁₆	—	2	2	no	—
601	C₂×M₁₆	—	2	2	no	—
602	C₂×M₁₆	—	4	1	no	—
603	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
604	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
605	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
606	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
607	#127	—	2	2	no	—
608	#127	—	2	2	no	—
609	C₂²⋊Q₈	—	2	2	no	—
610	C₂²⋊Q₈	—	2	2	no	—
611	C₂²⋊Q₈	—	2	2	no	—
612	C₂²⋊Q₈	—	4	1	no	—
613	#121	—	2	8	no	—
614	#121	—	2	2	no	—
615	#121	—	2	2	no	—
616	#121	—	2	2	no	—
617	#121	D₄×C₇₉	1	4	yes	—
618	#120	—	2	8	no	—
619	#120	—	2	8	no	—
620	C₄×D₄	—	2	2	no	—
621	C₄×D₄	—	2	2	no	—
622	C₄×D₄	—	2	2	no	—
623	C₄×D₄	—	2	2	no	—
624	#117	—	2	2	no	—
625	#117	—	4	1	no	—
626	C₂×C₄⋊C₄	—	2	1	no	—
627	C₂×C₄⋊C₄	—	2	1	no	—
628	C₂×C₄⋊C₄	—	2	1	no	—
629	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
634	C₂×C₂²⋊C₄	—	2	1	no	—
635	C₂×C₂²⋊C₄	—	2	1	no	—
636	C₂×C₂²⋊C₄	—	2	1	no	—
637	C₂×C₂²⋊C₄	—	2	1	no	—
638	C₂×C₂²⋊C₄	—	2	1	no	—
639	C₂×C₂²⋊C₄	—	2	1	no	—
640	C₂×C₂²⋊C₄	—	2	1	no	—
641	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
642	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
643	C₂×C₄²	—	2	1	no	—
644	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
645	#107	—	2	2	no	—
646	#103	—	2	2	no	—
647	#102	—	2	2	no	—
648	#102	—	2	2	no	—
649	#102	—	2	2	no	—
650	#102	—	2	2	no	—
651	#102	—	2	2	no	—
652	#102	—	2	2	no	—
653	#102	—	2	2	no	—
654	#102	—	4	1	no	—
655	#102	D₄×C₇₉	1	4	yes	complemented
656	C₂²⋊C₈	—	2	2	no	—
657	C₂²⋊C₈	—	2	2	no	—
658	C₂²⋊C₈	—	4	1	no	—
659	#95	—	2	1	no	—
660	#95	—	2	1	no	—
661	#95	—	2	1	no	—
662	#95	—	2	1	no	—
663	C₂⁴	—	2	1	no	—
664	C₂⁴	—	2	4	no	—
665	C₂⁴	—	2	1	no	—
666	C₂⁴	—	2	1	no	—
667	C₂⁴	—	2	4	no	—
668	C₂⁴	—	4	2	no	—
669	C₂⁴	—	4	2	no	—
670	C₂⁴	—	4	2	no	—
671	C₂⁴	—	4	2	no	—
672	C₂⁴	—	4	2	no	—
673	C₂⁴	—	4	2	no	—
674	C₂⁴	—	4	2	no	—
675	C₂⁴	—	4	2	no	—
676	C₂⁴	—	8	1	no	—
677	C₂⁴	—	8	1	no	—
678	C₂⁴	—	8	1	no	—
679	C₂⁴	—	8	1	no	—
680	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
681	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
682	C₂×Q₈	—	2	1	no	—
683	C₂×Q₈	—	2	1	no	—
684	C₂×Q₈	—	2	1	no	—
685	C₂×Q₈	—	2	1	no	—
686	C₂×Q₈	—	2	1	no	—
687	C₂×Q₈	—	2	1	no	—
688	C₂×D₄	—	2	2	no	—
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	—	2	8	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	2	no	—
698	C₂×D₄	—	2	1	no	—
699	C₂×D₄	—	2	1	no	—
700	C₂×D₄	—	2	1	no	—
701	C₂×D₄	—	2	1	no	—
702	C₂×D₄	—	2	1	no	—
703	C₂×D₄	—	2	1	no	—
704	C₂×D₄	—	2	1	no	—
705	C₂×D₄	—	2	1	no	—
706	C₂×D₄	—	2	1	no	—
707	C₂×D₄	—	2	1	no	—
708	C₂×D₄	—	2	1	no	—
709	C₂×D₄	—	2	1	no	—
710	C₂×D₄	—	2	1	no	—
711	C₂×D₄	—	4	4	no	—
712	C₂×D₄	—	4	4	no	—
713	C₂×D₄	—	4	4	no	—
714	C₂×D₄	—	4	2	no	—
715	C₂×D₄	—	4	2	no	—
716	C₂×D₄	—	4	2	no	—
717	C₂×D₄	—	4	2	no	—
718	C₂×D₄	—	4	2	no	—
719	C₂×D₄	—	4	4	no	—
720	C₂×D₄	—	4	4	no	—
721	C₂×D₄	—	4	32	no	—
722	C₂×D₄	—	4	4	no	—
723	C₂×D₄	—	4	2	no	—
724	C₂×D₄	—	4	2	no	—
725	C₂×D₄	—	4	2	no	—
726	C₂×D₄	—	4	2	no	—
727	C₂×D₄	—	4	4	no	—
728	C₂×D₄	—	4	2	no	—
729	C₂×D₄	—	8	1	no	—
730	C₂×D₄	—	8	1	no	—
731	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
732	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
733	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
734	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
735	C₂×D₄	#41×C₇₉	1	2	yes	—
736	C₂²×C₄	—	2	1	no	—
737	C₂²×C₄	—	2	1	no	—
738	C₂²×C₄	—	2	1	no	—
739	C₂²×C₄	—	2	1	no	—
740	C₂²×C₄	—	2	4	no	—
741	C₂²×C₄	—	2	1	no	—
742	C₂²×C₄	—	2	1	no	—
743	C₂²×C₄	—	2	1	no	—
744	C₂²×C₄	—	2	1	no	—
745	C₂²×C₄	—	2	1	no	—
746	C₂²×C₄	—	2	1	no	—
747	C₂²×C₄	—	2	1	no	—
748	C₂²×C₄	—	2	1	no	—
749	C₂²×C₄	—	2	1	no	—
750	C₂²×C₄	—	2	1	no	—
751	C₂²×C₄	—	2	1	no	—
752	C₂²×C₄	—	4	2	no	—
753	C₂²×C₄	—	4	2	no	—
754	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
755	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
756	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
757	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
758	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
759	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
760	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
761	SD₁₆	—	4	4	no	—
762	SD₁₆	—	4	4	no	—
763	SD₁₆	—	4	4	no	—
764	M₁₆	—	4	4	no	—
765	C₂×C₈	—	2	1	no	—
766	C₂×C₈	—	2	1	no	—
767	C₂×C₈	—	2	1	no	—
768	C₂×C₈	—	2	1	no	—
769	C₂×C₈	—	2	1	no	—
770	C₂×C₈	—	2	1	no	—
771	C₂×C₈	—	2	1	no	—
772	C₂×C₈	—	2	1	no	—
773	C₂×C₈	—	2	1	no	—
774	C₂×C₈	—	2	1	no	—
775	C₂×C₈	—	2	1	no	—
776	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	complemented
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	1	no	—
779	C₄⋊C₄	—	2	1	no	—
780	C₄⋊C₄	—	2	1	no	—
781	C₄⋊C₄	—	2	1	no	—
782	C₄⋊C₄	—	2	1	no	—
783	C₄⋊C₄	—	2	1	no	—
784	C₄⋊C₄	—	4	2	no	—
785	C₄⋊C₄	—	4	2	no	—
786	C₄⋊C₄	—	4	2	no	—
787	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
788	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	complemented
789	C₂²⋊C₄	—	2	4	no	—
790	C₂²⋊C₄	—	2	4	no	—
791	C₂²⋊C₄	—	2	2	no	—
792	C₂²⋊C₄	—	2	4	no	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	4	2	no	—
795	C₂²⋊C₄	—	4	2	no	—
796	C₂²⋊C₄	—	4	2	no	—
797	C₂²⋊C₄	—	4	2	no	—
798	C₄²	—	2	1	no	—
799	C₄²	—	2	1	no	—
800	C₄²	—	4	2	no	—
801	C₂³	—	2	1	no	—
802	C₂³	—	2	2	no	—
803	C₂³	—	2	1	no	—
804	C₂³	—	2	1	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	2	1	no	—
807	C₂³	—	2	1	no	—
808	C₂³	—	2	2	no	—
809	C₂³	—	2	1	no	—
810	C₂³	—	2	1	no	—
811	C₂³	—	2	1	no	—
812	C₂³	—	2	1	no	—
813	C₂³	—	2	1	no	—
814	C₂³	—	2	1	no	—
815	C₂³	—	2	1	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	2	2	no	—
818	C₂³	—	4	8	no	—
819	C₂³	—	4	8	no	—
820	C₂³	—	4	8	no	—
821	C₂³	—	4	8	no	—
822	C₂³	—	4	1	no	—
823	C₂³	—	4	1	no	—
824	C₂³	—	4	1	no	—
825	C₂³	—	4	1	no	—
826	C₂³	—	4	1	no	—
827	C₂³	—	4	1	no	—
828	C₂³	—	4	1	no	—
829	C₂³	—	4	1	no	—
830	C₂³	—	4	1	no	—
831	C₂³	—	4	1	no	—
832	C₂³	—	4	1	no	—
833	C₂³	—	4	1	no	—
834	C₂³	—	4	1	no	—
835	C₂³	—	4	1	no	—
836	C₂³	—	4	1	no	—
837	C₂³	—	4	1	no	—
838	C₂³	—	8	4	no	—
839	C₂³	—	8	4	no	—
840	C₂³	—	8	4	no	—
841	C₂³	—	8	4	no	—
842	C₂³	—	8	4	no	—
843	C₂³	—	8	4	no	—
844	C₂³	—	8	4	no	—
845	C₂³	—	8	4	no	—
846	C₂³	—	8	4	no	—
847	C₂³	—	8	4	no	—
848	C₂³	#120×C₇₉	1	2	yes	—
849	C₂³	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
850	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
851	Q₈	—	4	1	no	—
852	Q₈	—	4	1	no	—
853	Q₈	—	4	1	no	—
854	Q₈	—	4	1	no	—
855	D₄	—	2	8	no	—
856	D₄	—	2	2	no	—
857	D₄	—	2	2	no	—
858	D₄	—	2	2	no	—
859	D₄	—	2	2	no	—
860	D₄	—	2	2	no	—
861	D₄	—	2	2	no	—
862	D₄	—	2	2	no	—
863	D₄	—	4	8	no	—
864	D₄	—	4	8	no	—
865	D₄	—	4	8	no	—
866	D₄	—	4	8	no	—
867	D₄	—	4	8	no	—
868	D₄	—	4	1	no	—
869	D₄	—	4	1	no	—
870	D₄	—	4	1	no	—
871	D₄	—	4	1	no	—
872	D₄	—	8	4	no	—
873	D₄	#121×C₇₉	1	4	yes	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	4	8	no	—
891	C₂×C₄	—	4	1	no	—
892	C₂×C₄	—	4	1	no	—
893	C₂×C₄	—	4	1	no	—
894	C₂×C₄	—	4	1	no	—
895	C₂×C₄	—	4	1	no	—
896	C₂×C₄	—	4	1	no	—
897	C₂×C₄	—	4	1	no	—
898	C₂×C₄	—	4	1	no	—
899	C₂×C₄	—	4	1	no	—
900	C₂×C₄	—	4	1	no	—
901	C₂×C₄	—	4	1	no	—
902	C₂×C₄	—	4	1	no	—
903	C₂×C₄	—	4	1	no	—
904	C₂×C₄	—	4	1	no	—
905	C₂×C₄	—	4	1	no	—
906	C₂×C₄	—	4	1	no	—
907	C₂×C₄	—	4	1	no	—
908	C₂×C₄	#120×C₇₉	1	2	yes	—
909	C₂×C₄	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
910	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
911	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
912	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
913	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
914	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
915	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
916	C₈	—	2	2	no	—
917	C₈	—	4	1	no	—
918	C₈	—	4	1	no	—
919	C₈	—	4	1	no	—
920	C₂²	—	2	2	no	—
921	C₂²	—	2	2	no	—
922	C₂²	—	2	4	no	—
923	C₂²	—	2	2	no	—
924	C₂²	—	2	2	no	—
925	C₂²	—	2	2	no	—
926	C₂²	—	2	2	no	—
927	C₂²	—	4	1	no	—
928	C₂²	—	4	2	no	—
929	C₂²	—	4	1	no	—
930	C₂²	—	4	1	no	—
931	C₂²	—	4	2	no	—
932	C₂²	—	4	1	no	—
933	C₂²	—	4	2	no	—
934	C₂²	—	4	1	no	—
935	C₂²	—	4	2	no	—
936	C₂²	—	4	1	no	—
937	C₂²	—	4	2	no	—
938	C₂²	—	4	1	no	—
939	C₂²	—	4	1	no	—
940	C₂²	—	4	2	no	—
941	C₂²	—	4	2	no	—
942	C₂²	—	4	2	no	—
943	C₂²	—	4	2	no	—
944	C₂²	—	4	2	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	8	16	no	—
948	C₂²	—	8	16	no	—
949	C₂²	—	8	1	no	—
950	C₂²	—	8	1	no	—
951	C₂²	—	8	1	no	—
952	C₂²	—	8	1	no	—
953	C₂²	—	8	1	no	—
954	C₂²	—	8	1	no	—
955	C₂²	—	8	1	no	—
956	C₂²	—	8	1	no	—
957	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
958	C₂²	D₄²×C₇₉	1	1	yes	characteristic
959	C₂²	#546×C₇₉	1	1	yes	characteristic
960	C₂²	C₂×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
961	C₂²	C₂×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
962	C₂²	#577×C₇₉	1	1	yes	characteristic
963	C₂²	#577×C₇₉	1	1	yes	characteristic
964	C₄	—	2	2	no	—
965	C₄	—	2	2	no	—
966	C₄	—	4	1	no	—
967	C₄	—	4	2	no	—
968	C₄	—	4	1	no	—
969	C₄	—	4	2	no	—
970	C₄	—	8	1	no	—
971	C₄	—	8	1	no	—
972	C₄	—	8	1	no	—
973	C₄	C₂×#121×C₇₉	1	1	yes	characteristic
974	C₄	#534×C₇₉	1	1	yes	characteristic
975	C₄	D₄²×C₇₉	1	1	yes	characteristic
976	C₄	#546×C₇₉	1	1	yes	characteristic
977	C₂	—	4	2	no	—
978	C₂	—	4	2	no	—
979	C₂	—	4	4	no	—
980	C₂	—	8	2	no	—
981	C₂	—	8	2	no	—
982	C₂	C₇₉×#2410	1	1	yes	characteristic
983	C₂	C₇₉×#3003	1	1	yes	characteristic
984	C₂	C₇₉×#3009	1	1	yes	characteristic
985	C₂	C₇₉×#3265	1	1	yes	characteristic
986	C₂	C₇₉×#3272	1	1	yes	characteristic
987	C₂	C₇₉×#3310	1	1	yes	characteristic
988	C₂	C₇₉×#3324	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₂×D₄²×C₇₉	C₂
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
2. C₂×#468×C₇₉	C₂	semidirect
3. C₂×#450×C₇₉	C₂	semidirect
4. C₂×#450×C₇₉	C₂	semidirect
5. C₂×#418×C₇₉	C₂	semidirect
6. C₇₉×#2415	C₂	semidirect
7. C₇₉×#2041	C₂	semidirect
8. C₇₉×#2033	C₂	semidirect
9. C₇₉×#2014	C₂	semidirect
10. C₇₉×#2000	C₂	semidirect
11. C₇₉×#1877	C₂	semidirect
12. C₇₉×#1875	C₂	semidirect
13. C₇₉×#1870	C₂	semidirect
14. C₇₉×#1862	C₂	semidirect
15. C₇₉×#1786	C₂	semidirect
20. C₂²×SD₁₆×C₇₉	C₂²	semidirect
21. C₂²×SD₁₆×C₇₉	C₂²	semidirect
22. C₂²×M₁₆×C₇₉	C₂²	semidirect
26. C₂×C₂²⋊Q₈×C₇₉	C₂²	semidirect
27. C₂×C₂²⋊Q₈×C₇₉	C₂²	semidirect
35. C₂×#117×C₇₉	C₂²	semidirect
39. C₂×#107×C₇₉	C₂²	semidirect
41. C₂×#103×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
56. #391×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
160. #102×C₇₉	D₄	semidirect
281. C₂×C₈×C₇₉	C₂×D₄	semidirect
293. C₄⋊C₄×C₇₉	C₂×D₄	semidirect
482. #24448	C₇₉	direct (N × H)
496. C₂×#468	C₂×C₇₉	semidirect
497. C₂×#450	C₂×C₇₉	semidirect
498. C₂×#450	C₂×C₇₉	semidirect
499. C₂×#418	C₂×C₇₉	semidirect
500. #2415	C₂×C₇₉	semidirect
501. #2041	C₂×C₇₉	semidirect
502. #2033	C₂×C₇₉	semidirect
503. #2014	C₂×C₇₉	semidirect
504. #2000	C₂×C₇₉	semidirect
505. #1877	C₂×C₇₉	semidirect
506. #1875	C₂×C₇₉	semidirect
507. #1870	C₂×C₇₉	semidirect
508. #1862	C₂×C₇₉	semidirect
509. #1786	C₂×C₇₉	semidirect
510. C₇₉	#24448	direct (N × H)
515. C₂²×SD₁₆	C₂²×C₇₉	semidirect
516. C₂²×SD₁₆	C₂²×C₇₉	semidirect
517. C₂²×M₁₆	C₂²×C₇₉	semidirect
521. C₂×C₂²⋊Q₈	C₂²×C₇₉	semidirect
522. C₂×C₂²⋊Q₈	C₂²×C₇₉	semidirect
530. C₂×#117	C₂²×C₇₉	semidirect
534. C₂×#107	C₂²×C₇₉	semidirect
536. C₂×#103	C₂²×C₇₉	semidirect
540. C₂×#102	C₂²×C₇₉	semidirect
541. C₂×#102	C₂²×C₇₉	semidirect
542. C₂×#102	C₂²×C₇₉	semidirect
543. C₂×#102	C₂²×C₇₉	semidirect
544. C₂×#102	C₂²×C₇₉	semidirect
545. C₂×#102	C₂²×C₇₉	semidirect
546. C₂×C₂²⋊C₈	C₂²×C₇₉	semidirect
547. C₂×C₂²⋊C₈	C₂²×C₇₉	semidirect
548. C₂×C₂²⋊C₈	C₂²×C₇₉	semidirect
551. #391	C₂²×C₇₉	semidirect
553. #389	C₂²×C₇₉	semidirect
555. #380	C₂²×C₇₉	semidirect
556. #340	C₂²×C₇₉	semidirect
557. #340	C₂²×C₇₉	semidirect
558. #336	C₂²×C₇₉	semidirect
559. #336	C₂²×C₇₉	semidirect
655. #102	D₄×C₇₉	semidirect
776. C₂×C₈	C₂×D₄×C₇₉	semidirect
788. 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×#468×C₇₉	2
C₂×#450×C₇₉	2
C₂×#418×C₇₉	2
C₇₉×#2415	2
C₇₉×#2041	2
C₇₉×#2033	2
C₇₉×#2014	2
C₇₉×#2000	2
C₇₉×#1877	2
C₇₉×#1875	2
C₇₉×#1870	2
C₇₉×#1862	2
C₇₉×#1786	2
#24448	79

Subgroups — C79×#24448 #34136137

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#24448 #34136137