Subgroups — C₇₉×#25794 #34137483

Order 20224.

1818 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×AGL(1,ℤ/8)×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#496×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#493×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#469×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#449×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#447×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#2433	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#2431	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#2014	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#2012	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#2011	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₉×#2011	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₉×#1972	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₉×#1968	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#1753	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₇₉	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₇₉	C₂²	1	1	yes	characteristic
18	C₂×AGL(1,ℤ/8)×C₇₉	—	2	4	no	—
19	C₂×AGL(1,ℤ/8)×C₇₉	—	2	4	no	—
20	C₂×AGL(1,ℤ/8)×C₇₉	—	2	4	no	—
21	C₂²×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
22	C₂²×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
23	C₂²×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic, complemented
24	C₂²×D₈×C₇₉	C₂²	1	1	yes	characteristic
25	C₂²×D₈×C₇₉	C₂²	1	1	yes	characteristic
26	C₂²×D₈×C₇₉	C₂²	1	1	yes	characteristic
27	C₂²×D₈×C₇₉	C₂²	1	1	yes	characteristic
28	C₂²×D₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
29	C₂²×D₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
30	C₂²×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
31	C₂×#127×C₇₉	C₂²	1	1	yes	characteristic
32	C₂×#127×C₇₉	C₂²	1	1	yes	characteristic
33	C₂×#127×C₇₉	C₂²	1	1	yes	characteristic, complemented
34	C₂×#124×C₇₉	C₂²	1	1	yes	characteristic, complemented
35	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
36	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
37	C₂×#120×C₇₉	—	2	2	no	—
38	#496×C₇₉	—	2	4	no	—
39	#493×C₇₉	—	2	4	no	—
40	#469×C₇₉	—	2	4	no	—
41	#449×C₇₉	—	2	4	no	—
42	#447×C₇₉	—	2	4	no	—
43	C₂×#106×C₇₉	C₂²	1	1	yes	characteristic, complemented
44	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic, complemented
45	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
46	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
47	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic, complemented
48	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic, complemented
49	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
51	C₂×#97×C₇₉	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
53	#392×C₇₉	—	2	2	no	—
54	#392×C₇₉	—	2	2	no	—
55	#391×C₇₉	C₂²	1	1	yes	characteristic, complemented
56	#390×C₇₉	C₂²	1	1	yes	characteristic
57	#390×C₇₉	C₂²	1	1	yes	characteristic
58	#390×C₇₉	C₂²	1	1	yes	characteristic, complemented
59	#386×C₇₉	—	2	2	no	—
60	C₄×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
61	#336×C₇₉	C₂²	1	1	yes	characteristic, complemented
62	#336×C₇₉	C₂²	1	1	yes	characteristic, complemented
63	C₂⁵×C₇₉	—	2	1	no	—
64	C₂×#41×C₇₉	—	2	2	no	—
65	C₂×#41×C₇₉	—	2	2	no	—
66	C₂×#41×C₇₉	—	2	2	no	—
67	C₂×#41×C₇₉	—	2	2	no	—
68	C₂×#41×C₇₉	—	4	1	no	—
69	C₂×#41×C₇₉	—	4	1	no	—
70	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₇₉	—	2	2	no	—
72	C₂²×D₄×C₇₉	—	2	2	no	—
73	C₂²×D₄×C₇₉	—	2	1	no	—
74	C₂²×D₄×C₇₉	—	2	1	no	—
75	C₂²×D₄×C₇₉	—	2	1	no	—
76	C₂²×D₄×C₇₉	—	2	2	no	—
77	C₂²×D₄×C₇₉	—	2	2	no	—
78	C₂²×D₄×C₇₉	—	2	1	no	—
79	C₂²×D₄×C₇₉	—	2	2	no	—
80	C₂²×D₄×C₇₉	—	2	2	no	—
81	C₂²×D₄×C₇₉	—	2	2	no	—
82	C₂²×D₄×C₇₉	—	4	1	no	—
83	C₂²×D₄×C₇₉	—	4	1	no	—
84	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₇₉	—	2	1	no	—
90	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
91	AGL(1,ℤ/8)×C₇₉	—	2	32	no	—
92	C₂×SD₁₆×C₇₉	—	2	2	no	—
93	C₂×SD₁₆×C₇₉	—	2	2	no	—
94	C₂×SD₁₆×C₇₉	—	2	2	no	—
95	C₂×SD₁₆×C₇₉	—	2	2	no	—
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	—	4	1	no	—
100	C₂×SD₁₆×C₇₉	D₄	1	4	yes	complemented
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	—	2	2	no	—
105	C₂×D₈×C₇₉	—	2	2	no	—
106	C₂×D₈×C₇₉	—	2	2	no	—
107	C₂×D₈×C₇₉	—	2	2	no	—
108	C₂×D₈×C₇₉	—	2	2	no	—
109	C₂×D₈×C₇₉	—	2	2	no	—
110	C₂×D₈×C₇₉	—	2	2	no	—
111	C₂×D₈×C₇₉	—	2	2	no	—
112	C₂×D₈×C₇₉	—	2	2	no	—
113	C₂×D₈×C₇₉	—	2	2	no	—
114	C₂×D₈×C₇₉	—	2	2	no	—
115	C₂×D₈×C₇₉	—	4	1	no	—
116	C₂×D₈×C₇₉	—	4	1	no	—
117	C₂×D₈×C₇₉	—	4	1	no	—
118	C₂×D₈×C₇₉	D₄	1	4	yes	complemented
119	C₂×M₁₆×C₇₉	—	2	2	no	—
120	C₂×M₁₆×C₇₉	—	2	2	no	—
121	C₂×M₁₆×C₇₉	D₄	1	4	yes	complemented
122	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
123	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
124	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
125	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
126	#127×C₇₉	—	2	2	no	—
127	#127×C₇₉	—	2	2	no	—
128	#127×C₇₉	—	2	2	no	—
129	#127×C₇₉	—	4	1	no	—
130	#127×C₇₉	—	4	1	no	—
131	#127×C₇₉	—	4	1	no	—
132	#124×C₇₉	—	2	2	no	—
133	#124×C₇₉	—	4	1	no	—
134	#121×C₇₉	—	2	2	no	—
135	#121×C₇₉	—	2	2	no	—
136	#121×C₇₉	—	2	2	no	—
137	#121×C₇₉	—	2	2	no	—
138	#120×C₇₉	—	4	8	no	—
139	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
142	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
143	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
144	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
145	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
146	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
147	C₂×C₂²⋊C₄×C₇₉	D₄	1	2	yes	—
148	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
149	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
150	#106×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	C₂²⋊C₈×C₇₉	D₄	1	4	yes	complemented
158	#97×C₇₉	—	2	2	no	—
159	C₄×C₈×C₇₉	—	2	2	no	—
160	#95×C₇₉	—	2	2	no	—
161	#95×C₇₉	D₄	1	2	yes	—
162	C₂⁴×C₇₉	—	2	1	no	—
163	C₂⁴×C₇₉	—	2	1	no	—
164	C₂⁴×C₇₉	—	2	1	no	—
165	C₂⁴×C₇₉	—	2	1	no	—
166	C₂⁴×C₇₉	—	2	1	no	—
167	C₂⁴×C₇₉	—	4	2	no	—
168	C₂⁴×C₇₉	—	4	2	no	—
169	C₂⁴×C₇₉	—	4	4	no	—
170	C₂⁴×C₇₉	—	4	2	no	—
171	C₂⁴×C₇₉	—	8	2	no	—
172	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
173	#41×C₇₉	—	2	8	no	—
174	#41×C₇₉	—	4	4	no	—
175	#41×C₇₉	—	4	4	no	—
176	#41×C₇₉	—	4	4	no	—
177	C₂×Q₈×C₇₉	—	2	1	no	—
178	C₂×Q₈×C₇₉	—	2	1	no	—
179	C₂×Q₈×C₇₉	—	2	1	no	—
180	C₂×Q₈×C₇₉	—	2	1	no	—
181	C₂×Q₈×C₇₉	—	2	1	no	—
182	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
183	C₂×D₄×C₇₉	—	2	8	no	—
184	C₂×D₄×C₇₉	—	2	1	no	—
185	C₂×D₄×C₇₉	—	2	1	no	—
186	C₂×D₄×C₇₉	—	2	1	no	—
187	C₂×D₄×C₇₉	—	2	1	no	—
188	C₂×D₄×C₇₉	—	2	1	no	—
189	C₂×D₄×C₇₉	—	2	1	no	—
190	C₂×D₄×C₇₉	—	2	1	no	—
191	C₂×D₄×C₇₉	—	2	1	no	—
192	C₂×D₄×C₇₉	—	2	1	no	—
193	C₂×D₄×C₇₉	—	2	1	no	—
194	C₂×D₄×C₇₉	—	2	1	no	—
195	C₂×D₄×C₇₉	—	2	1	no	—
196	C₂×D₄×C₇₉	—	2	1	no	—
197	C₂×D₄×C₇₉	—	2	1	no	—
198	C₂×D₄×C₇₉	—	2	1	no	—
199	C₂×D₄×C₇₉	—	2	1	no	—
200	C₂×D₄×C₇₉	—	2	1	no	—
201	C₂×D₄×C₇₉	—	2	1	no	—
202	C₂×D₄×C₇₉	—	2	1	no	—
203	C₂×D₄×C₇₉	—	2	1	no	—
204	C₂×D₄×C₇₉	—	2	1	no	—
205	C₂×D₄×C₇₉	—	2	1	no	—
206	C₂×D₄×C₇₉	—	2	1	no	—
207	C₂×D₄×C₇₉	—	2	1	no	—
208	C₂×D₄×C₇₉	—	2	1	no	—
209	C₂×D₄×C₇₉	—	2	1	no	—
210	C₂×D₄×C₇₉	—	2	1	no	—
211	C₂×D₄×C₇₉	—	4	4	no	—
212	C₂×D₄×C₇₉	—	4	4	no	—
213	C₂×D₄×C₇₉	—	4	2	no	—
214	C₂×D₄×C₇₉	—	4	2	no	—
215	C₂×D₄×C₇₉	—	4	2	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	4	no	—
220	C₂×D₄×C₇₉	—	4	4	no	—
221	C₂×D₄×C₇₉	—	4	2	no	—
222	C₂×D₄×C₇₉	—	4	2	no	—
223	C₂×D₄×C₇₉	—	4	4	no	—
224	C₂×D₄×C₇₉	—	4	2	no	—
225	C₂×D₄×C₇₉	—	4	2	no	—
226	C₂×D₄×C₇₉	—	4	2	no	—
227	C₂×D₄×C₇₉	—	4	4	no	—
228	C₂×D₄×C₇₉	—	4	4	no	—
229	C₂×D₄×C₇₉	—	8	2	no	—
230	C₂×D₄×C₇₉	—	8	2	no	—
231	C₂×D₄×C₇₉	—	8	2	no	—
232	C₂×D₄×C₇₉	—	8	2	no	—
233	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
234	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
235	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
236	C₂²×C₄×C₇₉	—	2	1	no	—
237	C₂²×C₄×C₇₉	—	2	1	no	—
238	C₂²×C₄×C₇₉	—	2	1	no	—
239	C₂²×C₄×C₇₉	—	2	1	no	—
240	C₂²×C₄×C₇₉	—	2	1	no	—
241	C₂²×C₄×C₇₉	—	2	1	no	—
242	C₂²×C₄×C₇₉	—	2	1	no	—
243	C₂²×C₄×C₇₉	—	4	2	no	—
244	C₂²×C₄×C₇₉	—	4	2	no	—
245	C₂²×C₄×C₇₉	—	4	2	no	—
246	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
247	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
249	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
250	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
251	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
252	SD₁₆×C₇₉	—	2	8	no	—
253	SD₁₆×C₇₉	—	2	8	no	—
254	SD₁₆×C₇₉	—	4	4	no	—
255	D₈×C₇₉	—	2	8	no	—
256	D₈×C₇₉	—	2	8	no	—
257	D₈×C₇₉	—	4	4	no	—
258	D₈×C₇₉	—	4	4	no	—
259	D₈×C₇₉	—	4	4	no	—
260	D₈×C₇₉	—	4	4	no	—
261	M₁₆×C₇₉	—	2	8	no	—
262	C₂×C₈×C₇₉	—	2	1	no	—
263	C₂×C₈×C₇₉	—	2	1	no	—
264	C₂×C₈×C₇₉	—	2	1	no	—
265	C₂×C₈×C₇₉	—	2	1	no	—
266	C₂×C₈×C₇₉	—	2	1	no	—
267	C₂×C₈×C₇₉	—	2	1	no	—
268	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
269	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
270	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
271	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
272	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
273	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
274	C₄⋊C₄×C₇₉	—	2	1	no	—
275	C₄⋊C₄×C₇₉	—	2	1	no	—
276	C₄⋊C₄×C₇₉	—	2	1	no	—
277	C₄⋊C₄×C₇₉	—	2	1	no	—
278	C₂²⋊C₄×C₇₉	—	2	4	no	—
279	C₂²⋊C₄×C₇₉	—	4	4	no	—
280	C₂²⋊C₄×C₇₉	—	4	4	no	—
281	C₂²⋊C₄×C₇₉	—	4	2	no	—
282	C₂²⋊C₄×C₇₉	—	4	2	no	—
283	C₂²⋊C₄×C₇₉	—	4	4	no	—
284	C₂²⋊C₄×C₇₉	—	8	2	no	—
285	C₄²×C₇₉	—	2	1	no	—
286	C₄²×C₇₉	—	2	1	no	—
287	C₄²×C₇₉	—	2	1	no	—
288	C₄²×C₇₉	—	2	1	no	—
289	C₂³×C₇₉	—	2	1	no	—
290	C₂³×C₇₉	—	2	1	no	—
291	C₂³×C₇₉	—	2	2	no	—
292	C₂³×C₇₉	—	2	2	no	—
293	C₂³×C₇₉	—	2	2	no	—
294	C₂³×C₇₉	—	2	2	no	—
295	C₂³×C₇₉	—	2	2	no	—
296	C₂³×C₇₉	—	4	8	no	—
297	C₂³×C₇₉	—	4	1	no	—
298	C₂³×C₇₉	—	4	1	no	—
299	C₂³×C₇₉	—	4	1	no	—
300	C₂³×C₇₉	—	4	1	no	—
301	C₂³×C₇₉	—	4	1	no	—
302	C₂³×C₇₉	—	4	1	no	—
303	C₂³×C₇₉	—	4	2	no	—
304	C₂³×C₇₉	—	4	2	no	—
305	C₂³×C₇₉	—	4	2	no	—
306	C₂³×C₇₉	—	4	2	no	—
307	C₂³×C₇₉	—	4	2	no	—
308	C₂³×C₇₉	—	4	2	no	—
309	C₂³×C₇₉	—	4	1	no	—
310	C₂³×C₇₉	—	4	1	no	—
311	C₂³×C₇₉	—	4	1	no	—
312	C₂³×C₇₉	—	4	1	no	—
313	C₂³×C₇₉	—	4	1	no	—
314	C₂³×C₇₉	—	4	1	no	—
315	C₂³×C₇₉	—	4	2	no	—
316	C₂³×C₇₉	—	4	2	no	—
317	C₂³×C₇₉	—	4	2	no	—
318	C₂³×C₇₉	—	4	2	no	—
319	C₂³×C₇₉	—	8	4	no	—
320	C₂³×C₇₉	—	8	4	no	—
321	C₂³×C₇₉	—	8	8	no	—
322	C₂³×C₇₉	—	8	8	no	—
323	C₂³×C₇₉	#127	1	2	yes	—
324	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
325	Q₈×C₇₉	—	2	2	no	—
326	Q₈×C₇₉	—	2	2	no	—
327	Q₈×C₇₉	—	4	1	no	—
328	Q₈×C₇₉	—	4	1	no	—
329	D₄×C₇₉	—	2	2	no	—
330	D₄×C₇₉	—	2	2	no	—
331	D₄×C₇₉	—	2	2	no	—
332	D₄×C₇₉	—	2	2	no	—
333	D₄×C₇₉	—	2	2	no	—
334	D₄×C₇₉	—	2	2	no	—
335	D₄×C₇₉	—	4	8	no	—
336	D₄×C₇₉	—	4	8	no	—
337	D₄×C₇₉	—	4	1	no	—
338	D₄×C₇₉	—	4	1	no	—
339	D₄×C₇₉	—	4	1	no	—
340	D₄×C₇₉	—	4	1	no	—
341	D₄×C₇₉	—	4	1	no	—
342	D₄×C₇₉	—	4	1	no	—
343	D₄×C₇₉	—	4	1	no	—
344	D₄×C₇₉	—	4	1	no	—
345	D₄×C₇₉	—	4	1	no	—
346	D₄×C₇₉	—	4	1	no	—
347	D₄×C₇₉	—	4	1	no	—
348	D₄×C₇₉	—	4	1	no	—
349	D₄×C₇₉	—	4	1	no	—
350	D₄×C₇₉	—	4	1	no	—
351	D₄×C₇₉	—	8	8	no	—
352	D₄×C₇₉	—	8	8	no	—
353	D₄×C₇₉	—	8	8	no	—
354	D₄×C₇₉	—	8	4	no	—
355	D₄×C₇₉	—	8	4	no	—
356	C₂×C₄×C₇₉	—	2	2	no	—
357	C₂×C₄×C₇₉	—	2	1	no	—
358	C₂×C₄×C₇₉	—	2	1	no	—
359	C₂×C₄×C₇₉	—	2	2	no	—
360	C₂×C₄×C₇₉	—	2	2	no	—
361	C₂×C₄×C₇₉	—	2	2	no	—
362	C₂×C₄×C₇₉	—	2	2	no	—
363	C₂×C₄×C₇₉	—	2	2	no	—
364	C₂×C₄×C₇₉	—	2	2	no	—
365	C₂×C₄×C₇₉	—	2	2	no	—
366	C₂×C₄×C₇₉	—	2	2	no	—
367	C₂×C₄×C₇₉	—	2	2	no	—
368	C₂×C₄×C₇₉	—	4	8	no	—
369	C₂×C₄×C₇₉	—	4	1	no	—
370	C₂×C₄×C₇₉	—	4	1	no	—
371	C₂×C₄×C₇₉	—	4	1	no	—
372	C₂×C₄×C₇₉	—	4	1	no	—
373	C₂×C₄×C₇₉	—	4	2	no	—
374	C₂×C₄×C₇₉	—	4	2	no	—
375	C₂×C₄×C₇₉	#127	1	2	yes	—
376	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	4	yes	complemented
377	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
382	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
383	C₈×C₇₉	—	2	2	no	—
384	C₈×C₇₉	—	2	2	no	—
385	C₈×C₇₉	—	2	2	no	—
386	C₈×C₇₉	#120	1	4	yes	complemented
387	C₂²×C₇₉	—	2	2	no	—
388	C₂²×C₇₉	—	2	2	no	—
389	C₂²×C₇₉	—	2	2	no	—
390	C₂²×C₇₉	—	4	2	no	—
391	C₂²×C₇₉	—	4	2	no	—
392	C₂²×C₇₉	—	4	2	no	—
393	C₂²×C₇₉	—	4	2	no	—
394	C₂²×C₇₉	—	4	2	no	—
395	C₂²×C₇₉	—	4	4	no	—
396	C₂²×C₇₉	—	4	4	no	—
397	C₂²×C₇₉	—	4	4	no	—
398	C₂²×C₇₉	—	8	16	no	—
399	C₂²×C₇₉	—	8	1	no	—
400	C₂²×C₇₉	—	8	1	no	—
401	C₂²×C₇₉	—	8	1	no	—
402	C₂²×C₇₉	—	8	1	no	—
403	C₂²×C₇₉	—	8	1	no	—
404	C₂²×C₇₉	—	8	1	no	—
405	C₂²×C₇₉	—	8	2	no	—
406	C₂²×C₇₉	—	8	2	no	—
407	C₂²×C₇₉	—	8	2	no	—
408	C₂²×C₇₉	—	8	1	no	—
409	C₂²×C₇₉	—	8	1	no	—
410	C₂²×C₇₉	—	8	1	no	—
411	C₂²×C₇₉	—	8	1	no	—
412	C₂²×C₇₉	—	8	1	no	—
413	C₂²×C₇₉	—	8	1	no	—
414	C₂²×C₇₉	—	8	2	no	—
415	C₂²×C₇₉	—	8	2	no	—
416	C₂²×C₇₉	—	8	2	no	—
417	C₂²×C₇₉	—	8	2	no	—
418	C₂²×C₇₉	C₂×#127	1	1	yes	characteristic
419	C₂²×C₇₉	D₄²	1	1	yes	characteristic
420	C₂²×C₇₉	D₄²	1	1	yes	characteristic
421	C₂²×C₇₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
422	C₂²×C₇₉	#576	1	2	yes	—
423	C₄×C₇₉	—	2	2	no	—
424	C₄×C₇₉	—	2	4	no	—
425	C₄×C₇₉	—	4	2	no	—
426	C₄×C₇₉	—	4	2	no	—
427	C₄×C₇₉	—	8	1	no	—
428	C₄×C₇₉	—	8	1	no	—
429	C₄×C₇₉	C₂×#120	1	1	yes	characteristic
430	C₄×C₇₉	#535	1	1	yes	characteristic
431	C₄×C₇₉	D₄²	1	1	yes	characteristic
432	C₄×C₇₉	D₄²	1	1	yes	characteristic
433	#25794	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
434	C₂×C₇₉	—	4	2	no	—
435	C₂×C₇₉	—	8	2	no	—
436	C₂×C₇₉	—	8	2	no	—
437	C₂×C₇₉	—	8	2	no	—
438	C₂×C₇₉	—	16	1	no	—
439	C₂×C₇₉	—	16	1	no	—
440	C₂×C₇₉	#2433	1	1	yes	characteristic
441	C₂×C₇₉	#3151	1	1	yes	characteristic
442	C₂×C₇₉	#3155	1	1	yes	characteristic
443	C₂×C₇₉	#3264	1	2	yes	—
444	C₂×C₇₉	#3274	1	2	yes	—
445	C₂²×AGL(1,ℤ/8)	C₂×C₇₉	1	1	yes	characteristic, complemented
446	C₂×#496	C₂×C₇₉	1	1	yes	characteristic, complemented
447	C₂×#493	C₂×C₇₉	1	1	yes	characteristic, complemented
448	C₂×#469	C₂×C₇₉	1	1	yes	characteristic, complemented
449	C₂×#449	C₂×C₇₉	1	1	yes	characteristic, complemented
450	C₂×#447	C₂×C₇₉	1	1	yes	characteristic, complemented
451	#2433	C₂×C₇₉	1	1	yes	characteristic, complemented
452	#2431	C₂×C₇₉	1	1	yes	characteristic, complemented
453	#2014	C₂×C₇₉	1	1	yes	characteristic, complemented
454	#2012	C₂×C₇₉	1	1	yes	characteristic, complemented
455	#2011	C₂×C₇₉	1	1	yes	characteristic, complemented
456	#2011	C₂×C₇₉	1	1	yes	characteristic, complemented
457	#1972	C₂×C₇₉	1	1	yes	characteristic, complemented
458	#1968	C₂×C₇₉	1	1	yes	characteristic, complemented
459	#1753	C₂×C₇₉	1	1	yes	characteristic, complemented
460	C₇₉	#25794	1	1	yes	characteristic, direct product factor, Sylow
461	C₂²×#41	C₂²×C₇₉	1	1	yes	characteristic
462	C₂³×D₄	C₂²×C₇₉	1	1	yes	characteristic
463	C₂×AGL(1,ℤ/8)	—	2	4	no	—
464	C₂×AGL(1,ℤ/8)	—	2	4	no	—
465	C₂×AGL(1,ℤ/8)	—	2	4	no	—
466	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
467	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
468	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic, complemented
469	C₂²×D₈	C₂²×C₇₉	1	1	yes	characteristic
470	C₂²×D₈	C₂²×C₇₉	1	1	yes	characteristic
471	C₂²×D₈	C₂²×C₇₉	1	1	yes	characteristic
472	C₂²×D₈	C₂²×C₇₉	1	1	yes	characteristic
473	C₂²×D₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
474	C₂²×D₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
475	C₂²×M₁₆	C₂²×C₇₉	1	1	yes	characteristic
476	C₂×#127	C₂²×C₇₉	1	1	yes	characteristic
477	C₂×#127	C₂²×C₇₉	1	1	yes	characteristic
478	C₂×#127	C₂²×C₇₉	1	1	yes	characteristic, complemented
479	C₂×#124	C₂²×C₇₉	1	1	yes	characteristic, complemented
480	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
481	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
482	C₂×#120	—	2	2	no	—
483	#496	—	2	4	no	—
484	#493	—	2	4	no	—
485	#469	—	2	4	no	—
486	#449	—	2	4	no	—
487	#447	—	2	4	no	—
488	C₂×#106	C₂²×C₇₉	1	1	yes	characteristic, complemented
489	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic, complemented
490	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
491	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
492	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic, complemented
493	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic, complemented
494	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic, complemented
495	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
496	C₂×#97	C₂²×C₇₉	1	1	yes	characteristic, complemented
497	C₂×C₄×C₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
498	#392	—	2	2	no	—
499	#392	—	2	2	no	—
500	#391	C₂²×C₇₉	1	1	yes	characteristic, complemented
501	#390	C₂²×C₇₉	1	1	yes	characteristic
502	#390	C₂²×C₇₉	1	1	yes	characteristic
503	#390	C₂²×C₇₉	1	1	yes	characteristic, complemented
504	#386	—	2	2	no	—
505	C₄×C₂²⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
506	#336	C₂²×C₇₉	1	1	yes	characteristic, complemented
507	#336	C₂²×C₇₉	1	1	yes	characteristic, complemented
508	C₂⁵	—	2	1	no	—
509	C₂×#41	—	2	2	no	—
510	C₂×#41	—	2	2	no	—
511	C₂×#41	—	2	2	no	—
512	C₂×#41	—	2	2	no	—
513	C₂×#41	—	4	1	no	—
514	C₂×#41	—	4	1	no	—
515	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
516	C₂²×D₄	—	2	2	no	—
517	C₂²×D₄	—	2	2	no	—
518	C₂²×D₄	—	2	1	no	—
519	C₂²×D₄	—	2	1	no	—
520	C₂²×D₄	—	2	1	no	—
521	C₂²×D₄	—	2	2	no	—
522	C₂²×D₄	—	2	2	no	—
523	C₂²×D₄	—	2	1	no	—
524	C₂²×D₄	—	2	2	no	—
525	C₂²×D₄	—	2	2	no	—
526	C₂²×D₄	—	2	2	no	—
527	C₂²×D₄	—	4	1	no	—
528	C₂²×D₄	—	4	1	no	—
529	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
530	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
531	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
532	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
533	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
534	C₂³×C₄	—	2	1	no	—
535	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
536	AGL(1,ℤ/8)	—	2	32	no	—
537	C₂×SD₁₆	—	2	2	no	—
538	C₂×SD₁₆	—	2	2	no	—
539	C₂×SD₁₆	—	2	2	no	—
540	C₂×SD₁₆	—	2	2	no	—
541	C₂×SD₁₆	—	2	2	no	—
542	C₂×SD₁₆	—	2	2	no	—
543	C₂×SD₁₆	—	2	2	no	—
544	C₂×SD₁₆	—	4	1	no	—
545	C₂×SD₁₆	D₄×C₇₉	1	4	yes	complemented
546	C₂×D₈	—	2	2	no	—
547	C₂×D₈	—	2	2	no	—
548	C₂×D₈	—	2	2	no	—
549	C₂×D₈	—	2	2	no	—
550	C₂×D₈	—	2	2	no	—
551	C₂×D₈	—	2	2	no	—
552	C₂×D₈	—	2	2	no	—
553	C₂×D₈	—	2	2	no	—
554	C₂×D₈	—	2	2	no	—
555	C₂×D₈	—	2	2	no	—
556	C₂×D₈	—	2	2	no	—
557	C₂×D₈	—	2	2	no	—
558	C₂×D₈	—	2	2	no	—
559	C₂×D₈	—	2	2	no	—
560	C₂×D₈	—	4	1	no	—
561	C₂×D₈	—	4	1	no	—
562	C₂×D₈	—	4	1	no	—
563	C₂×D₈	D₄×C₇₉	1	4	yes	complemented
564	C₂×M₁₆	—	2	2	no	—
565	C₂×M₁₆	—	2	2	no	—
566	C₂×M₁₆	D₄×C₇₉	1	4	yes	complemented
567	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
568	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
569	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
570	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
571	#127	—	2	2	no	—
572	#127	—	2	2	no	—
573	#127	—	2	2	no	—
574	#127	—	4	1	no	—
575	#127	—	4	1	no	—
576	#127	—	4	1	no	—
577	#124	—	2	2	no	—
578	#124	—	4	1	no	—
579	#121	—	2	2	no	—
580	#121	—	2	2	no	—
581	#121	—	2	2	no	—
582	#121	—	2	2	no	—
583	#120	—	4	8	no	—
584	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
586	C₂×C₂²⋊C₄	—	2	2	no	—
587	C₂×C₂²⋊C₄	—	2	2	no	—
588	C₂×C₂²⋊C₄	—	2	1	no	—
589	C₂×C₂²⋊C₄	—	2	1	no	—
590	C₂×C₂²⋊C₄	—	2	2	no	—
591	C₂×C₂²⋊C₄	—	2	2	no	—
592	C₂×C₂²⋊C₄	D₄×C₇₉	1	2	yes	—
593	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
594	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
595	#106	—	2	2	no	—
596	#103	—	2	2	no	—
597	#102	—	2	2	no	—
598	#102	—	2	2	no	—
599	#102	—	2	2	no	—
600	#102	—	2	2	no	—
601	#102	—	2	2	no	—
602	C₂²⋊C₈	D₄×C₇₉	1	4	yes	complemented
603	#97	—	2	2	no	—
604	C₄×C₈	—	2	2	no	—
605	#95	—	2	2	no	—
606	#95	D₄×C₇₉	1	2	yes	—
607	C₂⁴	—	2	1	no	—
608	C₂⁴	—	2	1	no	—
609	C₂⁴	—	2	1	no	—
610	C₂⁴	—	2	1	no	—
611	C₂⁴	—	2	1	no	—
612	C₂⁴	—	4	2	no	—
613	C₂⁴	—	4	2	no	—
614	C₂⁴	—	4	4	no	—
615	C₂⁴	—	4	2	no	—
616	C₂⁴	—	8	2	no	—
617	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
618	#41	—	2	8	no	—
619	#41	—	4	4	no	—
620	#41	—	4	4	no	—
621	#41	—	4	4	no	—
622	C₂×Q₈	—	2	1	no	—
623	C₂×Q₈	—	2	1	no	—
624	C₂×Q₈	—	2	1	no	—
625	C₂×Q₈	—	2	1	no	—
626	C₂×Q₈	—	2	1	no	—
627	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
628	C₂×D₄	—	2	8	no	—
629	C₂×D₄	—	2	1	no	—
630	C₂×D₄	—	2	1	no	—
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	—	2	1	no	—
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	2	1	no	—
635	C₂×D₄	—	2	1	no	—
636	C₂×D₄	—	2	1	no	—
637	C₂×D₄	—	2	1	no	—
638	C₂×D₄	—	2	1	no	—
639	C₂×D₄	—	2	1	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	2	1	no	—
642	C₂×D₄	—	2	1	no	—
643	C₂×D₄	—	2	1	no	—
644	C₂×D₄	—	2	1	no	—
645	C₂×D₄	—	2	1	no	—
646	C₂×D₄	—	2	1	no	—
647	C₂×D₄	—	2	1	no	—
648	C₂×D₄	—	2	1	no	—
649	C₂×D₄	—	2	1	no	—
650	C₂×D₄	—	2	1	no	—
651	C₂×D₄	—	2	1	no	—
652	C₂×D₄	—	2	1	no	—
653	C₂×D₄	—	2	1	no	—
654	C₂×D₄	—	2	1	no	—
655	C₂×D₄	—	2	1	no	—
656	C₂×D₄	—	4	4	no	—
657	C₂×D₄	—	4	4	no	—
658	C₂×D₄	—	4	2	no	—
659	C₂×D₄	—	4	2	no	—
660	C₂×D₄	—	4	2	no	—
661	C₂×D₄	—	4	4	no	—
662	C₂×D₄	—	4	4	no	—
663	C₂×D₄	—	4	4	no	—
664	C₂×D₄	—	4	4	no	—
665	C₂×D₄	—	4	4	no	—
666	C₂×D₄	—	4	2	no	—
667	C₂×D₄	—	4	2	no	—
668	C₂×D₄	—	4	4	no	—
669	C₂×D₄	—	4	2	no	—
670	C₂×D₄	—	4	2	no	—
671	C₂×D₄	—	4	2	no	—
672	C₂×D₄	—	4	4	no	—
673	C₂×D₄	—	4	4	no	—
674	C₂×D₄	—	8	2	no	—
675	C₂×D₄	—	8	2	no	—
676	C₂×D₄	—	8	2	no	—
677	C₂×D₄	—	8	2	no	—
678	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
679	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
680	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
681	C₂²×C₄	—	2	1	no	—
682	C₂²×C₄	—	2	1	no	—
683	C₂²×C₄	—	2	1	no	—
684	C₂²×C₄	—	2	1	no	—
685	C₂²×C₄	—	2	1	no	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	1	no	—
688	C₂²×C₄	—	4	2	no	—
689	C₂²×C₄	—	4	2	no	—
690	C₂²×C₄	—	4	2	no	—
691	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
692	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
693	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
694	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
695	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
696	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
697	SD₁₆	—	2	8	no	—
698	SD₁₆	—	2	8	no	—
699	SD₁₆	—	4	4	no	—
700	D₈	—	2	8	no	—
701	D₈	—	2	8	no	—
702	D₈	—	4	4	no	—
703	D₈	—	4	4	no	—
704	D₈	—	4	4	no	—
705	D₈	—	4	4	no	—
706	M₁₆	—	2	8	no	—
707	C₂×C₈	—	2	1	no	—
708	C₂×C₈	—	2	1	no	—
709	C₂×C₈	—	2	1	no	—
710	C₂×C₈	—	2	1	no	—
711	C₂×C₈	—	2	1	no	—
712	C₂×C₈	—	2	1	no	—
713	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
714	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
715	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
716	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
717	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
718	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₂²⋊C₄	—	2	4	no	—
724	C₂²⋊C₄	—	4	4	no	—
725	C₂²⋊C₄	—	4	4	no	—
726	C₂²⋊C₄	—	4	2	no	—
727	C₂²⋊C₄	—	4	2	no	—
728	C₂²⋊C₄	—	4	4	no	—
729	C₂²⋊C₄	—	8	2	no	—
730	C₄²	—	2	1	no	—
731	C₄²	—	2	1	no	—
732	C₄²	—	2	1	no	—
733	C₄²	—	2	1	no	—
734	C₂³	—	2	1	no	—
735	C₂³	—	2	1	no	—
736	C₂³	—	2	2	no	—
737	C₂³	—	2	2	no	—
738	C₂³	—	2	2	no	—
739	C₂³	—	2	2	no	—
740	C₂³	—	2	2	no	—
741	C₂³	—	4	8	no	—
742	C₂³	—	4	1	no	—
743	C₂³	—	4	1	no	—
744	C₂³	—	4	1	no	—
745	C₂³	—	4	1	no	—
746	C₂³	—	4	1	no	—
747	C₂³	—	4	1	no	—
748	C₂³	—	4	2	no	—
749	C₂³	—	4	2	no	—
750	C₂³	—	4	2	no	—
751	C₂³	—	4	2	no	—
752	C₂³	—	4	2	no	—
753	C₂³	—	4	2	no	—
754	C₂³	—	4	1	no	—
755	C₂³	—	4	1	no	—
756	C₂³	—	4	1	no	—
757	C₂³	—	4	1	no	—
758	C₂³	—	4	1	no	—
759	C₂³	—	4	1	no	—
760	C₂³	—	4	2	no	—
761	C₂³	—	4	2	no	—
762	C₂³	—	4	2	no	—
763	C₂³	—	4	2	no	—
764	C₂³	—	8	4	no	—
765	C₂³	—	8	4	no	—
766	C₂³	—	8	8	no	—
767	C₂³	—	8	8	no	—
768	C₂³	#127×C₇₉	1	2	yes	—
769	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
770	Q₈	—	2	2	no	—
771	Q₈	—	2	2	no	—
772	Q₈	—	4	1	no	—
773	Q₈	—	4	1	no	—
774	D₄	—	2	2	no	—
775	D₄	—	2	2	no	—
776	D₄	—	2	2	no	—
777	D₄	—	2	2	no	—
778	D₄	—	2	2	no	—
779	D₄	—	2	2	no	—
780	D₄	—	4	8	no	—
781	D₄	—	4	8	no	—
782	D₄	—	4	1	no	—
783	D₄	—	4	1	no	—
784	D₄	—	4	1	no	—
785	D₄	—	4	1	no	—
786	D₄	—	4	1	no	—
787	D₄	—	4	1	no	—
788	D₄	—	4	1	no	—
789	D₄	—	4	1	no	—
790	D₄	—	4	1	no	—
791	D₄	—	4	1	no	—
792	D₄	—	4	1	no	—
793	D₄	—	4	1	no	—
794	D₄	—	4	1	no	—
795	D₄	—	4	1	no	—
796	D₄	—	8	8	no	—
797	D₄	—	8	8	no	—
798	D₄	—	8	8	no	—
799	D₄	—	8	4	no	—
800	D₄	—	8	4	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	4	8	no	—
814	C₂×C₄	—	4	1	no	—
815	C₂×C₄	—	4	1	no	—
816	C₂×C₄	—	4	1	no	—
817	C₂×C₄	—	4	1	no	—
818	C₂×C₄	—	4	2	no	—
819	C₂×C₄	—	4	2	no	—
820	C₂×C₄	#127×C₇₉	1	2	yes	—
821	C₂×C₄	AGL(1,ℤ/8)×C₇₉	1	4	yes	complemented
822	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
823	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
824	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
825	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
826	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
827	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
828	C₈	—	2	2	no	—
829	C₈	—	2	2	no	—
830	C₈	—	2	2	no	—
831	C₈	#120×C₇₉	1	4	yes	complemented
832	C₂²	—	2	2	no	—
833	C₂²	—	2	2	no	—
834	C₂²	—	2	2	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	4	4	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	4	4	no	—
842	C₂²	—	4	4	no	—
843	C₂²	—	8	16	no	—
844	C₂²	—	8	2	no	—
845	C₂²	—	8	2	no	—
846	C₂²	—	8	1	no	—
847	C₂²	—	8	1	no	—
848	C₂²	—	8	1	no	—
849	C₂²	—	8	1	no	—
850	C₂²	—	8	1	no	—
851	C₂²	—	8	1	no	—
852	C₂²	—	8	2	no	—
853	C₂²	—	8	2	no	—
854	C₂²	—	8	2	no	—
855	C₂²	—	8	1	no	—
856	C₂²	—	8	1	no	—
857	C₂²	—	8	1	no	—
858	C₂²	—	8	1	no	—
859	C₂²	—	8	1	no	—
860	C₂²	—	8	1	no	—
861	C₂²	—	8	2	no	—
862	C₂²	—	8	2	no	—
863	C₂²	C₂×#127×C₇₉	1	1	yes	characteristic
864	C₂²	D₄²×C₇₉	1	1	yes	characteristic
865	C₂²	D₄²×C₇₉	1	1	yes	characteristic
866	C₂²	C₂×AGL(1,ℤ/8)×C₇₉	1	2	yes	—
867	C₂²	#576×C₇₉	1	2	yes	—
868	C₄	—	2	2	no	—
869	C₄	—	2	4	no	—
870	C₄	—	4	2	no	—
871	C₄	—	4	2	no	—
872	C₄	—	8	1	no	—
873	C₄	—	8	1	no	—
874	C₄	C₂×#120×C₇₉	1	1	yes	characteristic
875	C₄	#535×C₇₉	1	1	yes	characteristic
876	C₄	D₄²×C₇₉	1	1	yes	characteristic
877	C₄	D₄²×C₇₉	1	1	yes	characteristic
878	C₂	—	4	2	no	—
879	C₂	—	8	2	no	—
880	C₂	—	8	2	no	—
881	C₂	—	8	2	no	—
882	C₂	—	16	1	no	—
883	C₂	—	16	1	no	—
884	C₂	C₇₉×#2433	1	1	yes	characteristic
885	C₂	C₇₉×#3151	1	1	yes	characteristic
886	C₂	C₇₉×#3155	1	1	yes	characteristic
887	C₂	C₇₉×#3264	1	2	yes	—
888	C₂	C₇₉×#3274	1	2	yes	—

	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 ◁ C₄×C₂²⋊C₄×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×AGL(1,ℤ/8)×C₇₉	C₂	semidirect
2. C₂×#496×C₇₉	C₂	semidirect
3. C₂×#493×C₇₉	C₂	semidirect
4. C₂×#469×C₇₉	C₂	semidirect
5. C₂×#449×C₇₉	C₂	semidirect
6. C₂×#447×C₇₉	C₂	semidirect
7. C₇₉×#2433	C₂	semidirect
8. C₇₉×#2431	C₂	semidirect
9. C₇₉×#2014	C₂	semidirect
10. C₇₉×#2012	C₂	semidirect
11. C₇₉×#2011	C₂	semidirect
12. C₇₉×#2011	C₂	semidirect
13. C₇₉×#1972	C₂	semidirect
14. C₇₉×#1968	C₂	semidirect
15. C₇₉×#1753	C₂	semidirect
23. C₂²×SD₁₆×C₇₉	C₂²	semidirect
28. C₂²×D₈×C₇₉	C₂²	semidirect
29. C₂²×D₈×C₇₉	C₂²	semidirect
33. C₂×#127×C₇₉	C₂²	semidirect
34. C₂×#124×C₇₉	C₂²	semidirect
43. C₂×#106×C₇₉	C₂²	semidirect
44. C₂×#103×C₇₉	C₂²	semidirect
47. C₂×#102×C₇₉	C₂²	semidirect
48. C₂×#102×C₇₉	C₂²	semidirect
49. C₂×#102×C₇₉	C₂²	semidirect
51. C₂×#97×C₇₉	C₂²	semidirect
52. C₂×C₄×C₈×C₇₉	C₂²	semidirect
55. #391×C₇₉	C₂²	semidirect
58. #390×C₇₉	C₂²	semidirect
61. #336×C₇₉	C₂²	semidirect
62. #336×C₇₉	C₂²	semidirect
100. C₂×SD₁₆×C₇₉	D₄	semidirect
118. C₂×D₈×C₇₉	D₄	semidirect
121. C₂×M₁₆×C₇₉	D₄	semidirect
157. C₂²⋊C₈×C₇₉	D₄	semidirect
376. C₂×C₄×C₇₉	AGL(1,ℤ/8)	semidirect
386. C₈×C₇₉	#120	semidirect
433. #25794	C₇₉	direct (N × H)
445. C₂²×AGL(1,ℤ/8)	C₂×C₇₉	semidirect
446. C₂×#496	C₂×C₇₉	semidirect
447. C₂×#493	C₂×C₇₉	semidirect
448. C₂×#469	C₂×C₇₉	semidirect
449. C₂×#449	C₂×C₇₉	semidirect
450. C₂×#447	C₂×C₇₉	semidirect
451. #2433	C₂×C₇₉	semidirect
452. #2431	C₂×C₇₉	semidirect
453. #2014	C₂×C₇₉	semidirect
454. #2012	C₂×C₇₉	semidirect
455. #2011	C₂×C₇₉	semidirect
456. #2011	C₂×C₇₉	semidirect
457. #1972	C₂×C₇₉	semidirect
458. #1968	C₂×C₇₉	semidirect
459. #1753	C₂×C₇₉	semidirect
460. C₇₉	#25794	direct (N × H)
468. C₂²×SD₁₆	C₂²×C₇₉	semidirect
473. C₂²×D₈	C₂²×C₇₉	semidirect
474. C₂²×D₈	C₂²×C₇₉	semidirect
478. C₂×#127	C₂²×C₇₉	semidirect
479. C₂×#124	C₂²×C₇₉	semidirect
488. C₂×#106	C₂²×C₇₉	semidirect
489. C₂×#103	C₂²×C₇₉	semidirect
492. C₂×#102	C₂²×C₇₉	semidirect
493. C₂×#102	C₂²×C₇₉	semidirect
494. C₂×#102	C₂²×C₇₉	semidirect
496. C₂×#97	C₂²×C₇₉	semidirect
497. C₂×C₄×C₈	C₂²×C₇₉	semidirect
500. #391	C₂²×C₇₉	semidirect
503. #390	C₂²×C₇₉	semidirect
506. #336	C₂²×C₇₉	semidirect
507. #336	C₂²×C₇₉	semidirect
545. C₂×SD₁₆	D₄×C₇₉	semidirect
563. C₂×D₈	D₄×C₇₉	semidirect
566. C₂×M₁₆	D₄×C₇₉	semidirect
602. C₂²⋊C₈	D₄×C₇₉	semidirect
821. C₂×C₄	AGL(1,ℤ/8)×C₇₉	semidirect
831. C₈	#120×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×AGL(1,ℤ/8)×C₇₉	2
C₂×#496×C₇₉	2
C₂×#493×C₇₉	2
C₂×#469×C₇₉	2
C₂×#449×C₇₉	2
C₂×#447×C₇₉	2
C₇₉×#2433	2
C₇₉×#2431	2
C₇₉×#2014	2
C₇₉×#2012	2
C₇₉×#2011	2
C₇₉×#1972	2
C₇₉×#1968	2
C₇₉×#1753	2
#25794	79

Subgroups — C79×#25794 #34137483

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#25794 #34137483