Subgroups — C₇₉×#23853 #34135542

Order 20224.

1800 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#135×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#547×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#452×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#452×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#449×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₉×#2407	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#2016	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#2013	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#2001	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#2000	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1892	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₉×#1879	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₉×#1877	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₉×#1869	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#1788	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₇₉	C₂²	1	1	yes	characteristic
17	C₂²×#41×C₇₉	C₂²	1	1	yes	characteristic
18	C₂²×#41×C₇₉	C₂²	1	1	yes	characteristic
19	C₂×#135×C₇₉	—	2	4	no	—
20	C₂×#135×C₇₉	—	2	4	no	—
21	C₂×#135×C₇₉	—	2	4	no	—
22	C₂²×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
23	C₂²×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
24	C₂²×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
25	C₂²×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
26	C₂²×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
27	C₂²×D₈×C₇₉	C₂²	1	1	yes	characteristic
28	C₂³×C₈×C₇₉	C₂²	1	1	yes	characteristic
29	#547×C₇₉	—	2	4	no	—
30	#547×C₇₉	—	2	4	no	—
31	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
32	C₂×#123×C₇₉	—	2	1	no	—
33	C₂×#123×C₇₉	—	2	1	no	—
34	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
37	C₂×#121×C₇₉	—	2	1	no	—
38	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
41	C₂²×C₄⋊C₄×C₇₉	—	2	1	no	—
42	#452×C₇₉	—	2	4	no	—
43	#452×C₇₉	—	2	4	no	—
44	#449×C₇₉	—	2	4	no	—
45	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
46	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
47	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
48	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
49	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
50	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
51	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
52	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
54	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
55	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
56	#394×C₇₉	—	2	1	no	—
57	#392×C₇₉	—	2	1	no	—
58	#391×C₇₉	C₂²	1	1	yes	characteristic
59	#390×C₇₉	C₂²	1	1	yes	characteristic
60	#386×C₇₉	—	2	1	no	—
61	#385×C₇₉	—	2	1	no	—
62	#380×C₇₉	C₂²	1	1	yes	characteristic
63	#340×C₇₉	C₂²	1	1	yes	characteristic
64	#340×C₇₉	C₂²	1	1	yes	characteristic
65	#336×C₇₉	C₂²	1	1	yes	characteristic
66	#336×C₇₉	C₂²	1	1	yes	characteristic
67	C₂×#41×C₇₉	—	2	2	no	—
68	C₂×#41×C₇₉	—	2	2	no	—
69	C₂×#41×C₇₉	—	2	2	no	—
70	C₂×#41×C₇₉	—	2	2	no	—
71	C₂×#41×C₇₉	—	2	2	no	—
72	C₂×#41×C₇₉	—	2	2	no	—
73	C₂×#41×C₇₉	—	2	2	no	—
74	C₂×#41×C₇₉	—	2	2	no	—
75	C₂×#41×C₇₉	—	2	2	no	—
76	C₂×#41×C₇₉	—	2	2	no	—
77	C₂×#41×C₇₉	—	2	2	no	—
78	C₂×#41×C₇₉	—	4	1	no	—
79	C₂×#41×C₇₉	—	4	1	no	—
80	C₂×#41×C₇₉	—	4	1	no	—
81	C₂×#41×C₇₉	—	4	1	no	—
82	C₂×#41×C₇₉	—	4	1	no	—
83	C₂×#41×C₇₉	—	4	1	no	—
84	C₂×#41×C₇₉	D₄	1	4	yes	complemented
85	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
87	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₇₉	—	2	1	no	—
89	C₂²×D₄×C₇₉	—	2	1	no	—
90	C₂²×D₄×C₇₉	—	2	1	no	—
91	C₂²×D₄×C₇₉	—	2	1	no	—
92	C₂²×D₄×C₇₉	D₄	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	—	2	1	no	—
97	C₂³×C₄×C₇₉	—	2	1	no	—
98	C₂³×C₄×C₇₉	—	2	1	no	—
99	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
101	#135×C₇₉	—	2	32	no	—
102	C₂×Q₁₆×C₇₉	—	2	2	no	—
103	C₂×Q₁₆×C₇₉	—	2	2	no	—
104	C₂×Q₁₆×C₇₉	—	2	2	no	—
105	C₂×Q₁₆×C₇₉	—	2	2	no	—
106	C₂×Q₁₆×C₇₉	—	2	2	no	—
107	C₂×Q₁₆×C₇₉	—	4	1	no	—
108	C₂×SD₁₆×C₇₉	—	2	2	no	—
109	C₂×SD₁₆×C₇₉	—	2	2	no	—
110	C₂×SD₁₆×C₇₉	—	2	2	no	—
111	C₂×SD₁₆×C₇₉	—	2	2	no	—
112	C₂×SD₁₆×C₇₉	—	2	2	no	—
113	C₂×SD₁₆×C₇₉	—	2	2	no	—
114	C₂×SD₁₆×C₇₉	—	2	2	no	—
115	C₂×SD₁₆×C₇₉	—	4	1	no	—
116	C₂×SD₁₆×C₇₉	D₄	1	4	yes	complemented
117	C₂×D₈×C₇₉	—	2	2	no	—
118	C₂×D₈×C₇₉	—	2	2	no	—
119	C₂×D₈×C₇₉	D₄	1	4	yes	complemented
120	C₂²×C₈×C₇₉	—	2	2	no	—
121	C₂²×C₈×C₇₉	—	2	2	no	—
122	C₂²×C₈×C₇₉	—	2	2	no	—
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	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
127	C₄⋊Q₈×C₇₉	—	2	2	no	—
128	C₄⋊Q₈×C₇₉	—	2	2	no	—
129	#123×C₇₉	—	2	8	no	—
130	#123×C₇₉	—	2	8	no	—
131	C₂²⋊Q₈×C₇₉	—	2	2	no	—
132	C₂²⋊Q₈×C₇₉	—	2	2	no	—
133	C₂²⋊Q₈×C₇₉	—	2	2	no	—
134	C₂²⋊Q₈×C₇₉	—	2	2	no	—
135	C₂²⋊Q₈×C₇₉	—	4	1	no	—
136	C₂²⋊Q₈×C₇₉	D₄	1	4	yes	complemented
137	#121×C₇₉	—	2	8	no	—
138	#121×C₇₉	—	2	2	no	—
139	#121×C₇₉	—	4	1	no	—
140	C₄×D₄×C₇₉	—	2	2	no	—
141	C₄×D₄×C₇₉	—	2	2	no	—
142	C₄×D₄×C₇₉	—	2	2	no	—
143	C₄×D₄×C₇₉	—	2	2	no	—
144	C₂×C₄⋊C₄×C₇₉	—	2	8	no	—
145	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
146	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
147	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
148	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
149	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
150	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
154	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
155	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
156	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
157	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
158	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
159	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
160	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
161	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
162	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
163	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
164	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
165	#103×C₇₉	—	2	2	no	—
166	#103×C₇₉	—	2	2	no	—
167	#103×C₇₉	—	2	2	no	—
168	#103×C₇₉	—	4	1	no	—
169	#103×C₇₉	—	4	1	no	—
170	#102×C₇₉	—	2	2	no	—
171	#102×C₇₉	—	2	2	no	—
172	#102×C₇₉	—	2	2	no	—
173	C₂²⋊C₈×C₇₉	—	2	2	no	—
174	C₂²⋊C₈×C₇₉	—	2	2	no	—
175	C₂²⋊C₈×C₇₉	—	2	2	no	—
176	#95×C₇₉	—	2	1	no	—
177	#95×C₇₉	—	2	1	no	—
178	#95×C₇₉	—	2	1	no	—
179	C₂⁴×C₇₉	—	2	1	no	—
180	C₂⁴×C₇₉	—	2	1	no	—
181	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
182	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
183	#41×C₇₉	—	2	8	no	—
184	#41×C₇₉	—	2	8	no	—
185	#41×C₇₉	—	4	4	no	—
186	#41×C₇₉	—	4	4	no	—
187	#41×C₇₉	—	4	4	no	—
188	#41×C₇₉	—	4	4	no	—
189	#41×C₇₉	—	4	4	no	—
190	#41×C₇₉	—	4	4	no	—
191	#41×C₇₉	—	4	4	no	—
192	#41×C₇₉	—	4	4	no	—
193	#41×C₇₉	—	4	4	no	—
194	#41×C₇₉	—	4	4	no	—
195	C₂×Q₈×C₇₉	—	2	1	no	—
196	C₂×Q₈×C₇₉	—	2	1	no	—
197	C₂×Q₈×C₇₉	—	2	1	no	—
198	C₂×Q₈×C₇₉	—	2	1	no	—
199	C₂×Q₈×C₇₉	—	2	1	no	—
200	C₂×Q₈×C₇₉	—	2	1	no	—
201	C₂×Q₈×C₇₉	—	2	1	no	—
202	C₂×Q₈×C₇₉	—	2	1	no	—
203	C₂×Q₈×C₇₉	—	2	1	no	—
204	C₂×Q₈×C₇₉	—	2	1	no	—
205	C₂×Q₈×C₇₉	—	2	1	no	—
206	C₂×Q₈×C₇₉	—	2	1	no	—
207	C₂×Q₈×C₇₉	—	2	1	no	—
208	C₂×Q₈×C₇₉	—	2	1	no	—
209	C₂×Q₈×C₇₉	—	2	1	no	—
210	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
211	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
212	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
213	C₂×D₄×C₇₉	—	2	4	no	—
214	C₂×D₄×C₇₉	—	2	2	no	—
215	C₂×D₄×C₇₉	—	2	4	no	—
216	C₂×D₄×C₇₉	—	2	2	no	—
217	C₂×D₄×C₇₉	—	2	1	no	—
218	C₂×D₄×C₇₉	—	2	1	no	—
219	C₂×D₄×C₇₉	—	2	1	no	—
220	C₂×D₄×C₇₉	—	2	1	no	—
221	C₂×D₄×C₇₉	—	2	1	no	—
222	C₂×D₄×C₇₉	—	2	1	no	—
223	C₂×D₄×C₇₉	—	2	1	no	—
224	C₂×D₄×C₇₉	—	2	1	no	—
225	C₂×D₄×C₇₉	—	4	1	no	—
226	C₂×D₄×C₇₉	—	4	2	no	—
227	C₂×D₄×C₇₉	—	4	2	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	2	no	—
233	C₂×D₄×C₇₉	—	4	2	no	—
234	C₂×D₄×C₇₉	—	4	2	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	C₂²×C₄×C₇₉	—	2	1	no	—
241	C₂²×C₄×C₇₉	—	2	1	no	—
242	C₂²×C₄×C₇₉	—	2	1	no	—
243	C₂²×C₄×C₇₉	—	2	1	no	—
244	C₂²×C₄×C₇₉	—	2	4	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	4	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	—	2	1	no	—
258	C₂²×C₄×C₇₉	—	2	1	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	2	no	—
264	C₂²×C₄×C₇₉	—	4	2	no	—
265	C₂²×C₄×C₇₉	—	4	2	no	—
266	C₂²×C₄×C₇₉	—	4	2	no	—
267	C₂²×C₄×C₇₉	—	4	2	no	—
268	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
272	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
273	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
275	Q₁₆×C₇₉	—	2	8	no	—
276	Q₁₆×C₇₉	—	4	4	no	—
277	SD₁₆×C₇₉	—	2	8	no	—
278	SD₁₆×C₇₉	—	2	8	no	—
279	SD₁₆×C₇₉	—	4	4	no	—
280	D₈×C₇₉	—	2	8	no	—
281	C₂×C₈×C₇₉	—	2	8	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	—	2	1	no	—
288	C₂×C₈×C₇₉	—	2	1	no	—
289	C₂×C₈×C₇₉	—	2	1	no	—
290	C₂×C₈×C₇₉	—	2	1	no	—
291	C₂×C₈×C₇₉	—	2	1	no	—
292	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
293	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
294	C₄⋊C₄×C₇₉	—	2	4	no	—
295	C₄⋊C₄×C₇₉	—	2	4	no	—
296	C₄⋊C₄×C₇₉	—	2	4	no	—
297	C₄⋊C₄×C₇₉	—	2	2	no	—
298	C₄⋊C₄×C₇₉	—	2	4	no	—
299	C₄⋊C₄×C₇₉	—	2	1	no	—
300	C₄⋊C₄×C₇₉	—	2	1	no	—
301	C₄⋊C₄×C₇₉	—	2	1	no	—
302	C₄⋊C₄×C₇₉	—	2	1	no	—
303	C₄⋊C₄×C₇₉	—	2	1	no	—
304	C₄⋊C₄×C₇₉	—	4	2	no	—
305	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
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	2	no	—
310	C₂²⋊C₄×C₇₉	—	2	2	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	—	8	1	no	—
315	C₂²⋊C₄×C₇₉	—	8	1	no	—
316	C₄²×C₇₉	—	2	1	no	—
317	C₄²×C₇₉	—	2	1	no	—
318	C₂³×C₇₉	—	2	2	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	—	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	1	no	—
328	C₂³×C₇₉	—	2	1	no	—
329	C₂³×C₇₉	—	2	2	no	—
330	C₂³×C₇₉	—	2	1	no	—
331	C₂³×C₇₉	—	2	1	no	—
332	C₂³×C₇₉	—	2	1	no	—
333	C₂³×C₇₉	—	2	1	no	—
334	C₂³×C₇₉	—	2	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	#120	1	2	yes	—
346	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
347	Q₈×C₇₉	—	2	2	no	—
348	Q₈×C₇₉	—	2	2	no	—
349	Q₈×C₇₉	—	2	2	no	—
350	Q₈×C₇₉	—	2	2	no	—
351	Q₈×C₇₉	—	2	2	no	—
352	Q₈×C₇₉	—	2	2	no	—
353	Q₈×C₇₉	—	4	1	no	—
354	Q₈×C₇₉	—	4	1	no	—
355	Q₈×C₇₉	—	4	1	no	—
356	Q₈×C₇₉	—	4	1	no	—
357	Q₈×C₇₉	—	4	1	no	—
358	Q₈×C₇₉	—	4	1	no	—
359	D₄×C₇₉	—	2	2	no	—
360	D₄×C₇₉	—	2	2	no	—
361	D₄×C₇₉	—	2	2	no	—
362	D₄×C₇₉	—	2	2	no	—
363	D₄×C₇₉	—	2	2	no	—
364	D₄×C₇₉	—	4	4	no	—
365	D₄×C₇₉	—	4	8	no	—
366	D₄×C₇₉	—	4	8	no	—
367	D₄×C₇₉	—	4	8	no	—
368	D₄×C₇₉	—	4	1	no	—
369	D₄×C₇₉	—	4	1	no	—
370	D₄×C₇₉	—	8	4	no	—
371	D₄×C₇₉	#120	1	4	yes	—
372	C₂×C₄×C₇₉	—	2	1	no	—
373	C₂×C₄×C₇₉	—	2	1	no	—
374	C₂×C₄×C₇₉	—	2	1	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	1	no	—
381	C₂×C₄×C₇₉	—	2	2	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	1	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	1	no	—
390	C₂×C₄×C₇₉	—	4	8	no	—
391	C₂×C₄×C₇₉	—	4	8	no	—
392	C₂×C₄×C₇₉	—	4	8	no	—
393	C₂×C₄×C₇₉	—	4	8	no	—
394	C₂×C₄×C₇₉	—	4	1	no	—
395	C₂×C₄×C₇₉	—	4	1	no	—
396	C₂×C₄×C₇₉	—	4	1	no	—
397	C₂×C₄×C₇₉	—	4	1	no	—
398	C₂×C₄×C₇₉	—	4	1	no	—
399	C₂×C₄×C₇₉	—	4	1	no	—
400	C₂×C₄×C₇₉	—	4	1	no	—
401	C₂×C₄×C₇₉	—	4	1	no	—
402	C₂×C₄×C₇₉	—	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	#120	1	2	yes	—
413	C₂×C₄×C₇₉	#135	1	2	yes	complemented
414	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
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	H(5,𝔽₂)	1	1	yes	characteristic
419	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
420	C₈×C₇₉	—	2	2	no	—
421	C₈×C₇₉	—	2	2	no	—
422	C₈×C₇₉	—	4	1	no	—
423	C₈×C₇₉	—	4	1	no	—
424	C₂²×C₇₉	—	2	2	no	—
425	C₂²×C₇₉	—	2	4	no	—
426	C₂²×C₇₉	—	2	2	no	—
427	C₂²×C₇₉	—	2	2	no	—
428	C₂²×C₇₉	—	4	2	no	—
429	C₂²×C₇₉	—	4	1	no	—
430	C₂²×C₇₉	—	4	2	no	—
431	C₂²×C₇₉	—	4	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	2	no	—
439	C₂²×C₇₉	—	4	1	no	—
440	C₂²×C₇₉	—	4	1	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	1	no	—
446	C₂²×C₇₉	—	4	2	no	—
447	C₂²×C₇₉	—	4	1	no	—
448	C₂²×C₇₉	—	8	1	no	—
449	C₂²×C₇₉	—	8	1	no	—
450	C₂²×C₇₉	—	8	1	no	—
451	C₂²×C₇₉	—	8	1	no	—
452	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
453	C₂²×C₇₉	D₄²	1	1	yes	characteristic
454	C₂²×C₇₉	D₄²	1	1	yes	characteristic
455	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
456	C₂²×C₇₉	#575	1	1	yes	characteristic
457	C₂²×C₇₉	#577	1	1	yes	characteristic
458	C₂²×C₇₉	#578	1	1	yes	characteristic
459	C₄×C₇₉	—	2	2	no	—
460	C₄×C₇₉	—	2	2	no	—
461	C₄×C₇₉	—	4	1	no	—
462	C₄×C₇₉	—	4	2	no	—
463	C₄×C₇₉	—	4	2	no	—
464	C₄×C₇₉	—	4	2	no	—
465	C₄×C₇₉	—	4	2	no	—
466	C₄×C₇₉	—	4	1	no	—
467	C₄×C₇₉	—	8	1	no	—
468	C₄×C₇₉	—	8	1	no	—
469	C₄×C₇₉	C₂×#120	1	1	yes	characteristic
470	C₄×C₇₉	#534	1	1	yes	characteristic
471	C₄×C₇₉	D₄²	1	1	yes	characteristic
472	C₄×C₇₉	D₄²	1	1	yes	characteristic
473	#23853	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
474	C₂×C₇₉	—	4	2	no	—
475	C₂×C₇₉	—	4	4	no	—
476	C₂×C₇₉	—	8	1	no	—
477	C₂×C₇₉	—	8	2	no	—
478	C₂×C₇₉	#2403	1	1	yes	characteristic
479	C₂×C₇₉	#3002	1	1	yes	characteristic
480	C₂×C₇₉	#3013	1	1	yes	characteristic
481	C₂×C₇₉	#3267	1	1	yes	characteristic
482	C₂×C₇₉	#3269	1	1	yes	characteristic
483	C₂×C₇₉	#3283	1	1	yes	characteristic
484	C₂×C₇₉	#3284	1	1	yes	characteristic
485	C₂²×#135	C₂×C₇₉	1	1	yes	characteristic, complemented
486	C₂×#547	C₂×C₇₉	1	1	yes	characteristic, complemented
487	C₂×#452	C₂×C₇₉	1	1	yes	characteristic, complemented
488	C₂×#452	C₂×C₇₉	1	1	yes	characteristic, complemented
489	C₂×#449	C₂×C₇₉	1	1	yes	characteristic, complemented
490	#2407	C₂×C₇₉	1	1	yes	characteristic, complemented
491	#2016	C₂×C₇₉	1	1	yes	characteristic, complemented
492	#2013	C₂×C₇₉	1	1	yes	characteristic, complemented
493	#2001	C₂×C₇₉	1	1	yes	characteristic, complemented
494	#2000	C₂×C₇₉	1	1	yes	characteristic, complemented
495	#1892	C₂×C₇₉	1	1	yes	characteristic, complemented
496	#1879	C₂×C₇₉	1	1	yes	characteristic, complemented
497	#1877	C₂×C₇₉	1	1	yes	characteristic, complemented
498	#1869	C₂×C₇₉	1	1	yes	characteristic, complemented
499	#1788	C₂×C₇₉	1	1	yes	characteristic, complemented
500	C₇₉	#23853	1	1	yes	characteristic, direct product factor, Sylow
501	C₂²×#41	C₂²×C₇₉	1	1	yes	characteristic
502	C₂²×#41	C₂²×C₇₉	1	1	yes	characteristic
503	C₂²×#41	C₂²×C₇₉	1	1	yes	characteristic
504	C₂×#135	—	2	4	no	—
505	C₂×#135	—	2	4	no	—
506	C₂×#135	—	2	4	no	—
507	C₂²×Q₁₆	C₂²×C₇₉	1	1	yes	characteristic
508	C₂²×Q₁₆	C₂²×C₇₉	1	1	yes	characteristic
509	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
510	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
511	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
512	C₂²×D₈	C₂²×C₇₉	1	1	yes	characteristic
513	C₂³×C₈	C₂²×C₇₉	1	1	yes	characteristic
514	#547	—	2	4	no	—
515	#547	—	2	4	no	—
516	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
517	C₂×#123	—	2	1	no	—
518	C₂×#123	—	2	1	no	—
519	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
520	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
521	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
522	C₂×#121	—	2	1	no	—
523	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
524	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
525	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
526	C₂²×C₄⋊C₄	—	2	1	no	—
527	#452	—	2	4	no	—
528	#452	—	2	4	no	—
529	#449	—	2	4	no	—
530	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
531	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
532	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
533	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
534	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
535	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
536	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
537	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
538	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
539	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
540	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
541	#394	—	2	1	no	—
542	#392	—	2	1	no	—
543	#391	C₂²×C₇₉	1	1	yes	characteristic
544	#390	C₂²×C₇₉	1	1	yes	characteristic
545	#386	—	2	1	no	—
546	#385	—	2	1	no	—
547	#380	C₂²×C₇₉	1	1	yes	characteristic
548	#340	C₂²×C₇₉	1	1	yes	characteristic
549	#340	C₂²×C₇₉	1	1	yes	characteristic
550	#336	C₂²×C₇₉	1	1	yes	characteristic
551	#336	C₂²×C₇₉	1	1	yes	characteristic
552	C₂×#41	—	2	2	no	—
553	C₂×#41	—	2	2	no	—
554	C₂×#41	—	2	2	no	—
555	C₂×#41	—	2	2	no	—
556	C₂×#41	—	2	2	no	—
557	C₂×#41	—	2	2	no	—
558	C₂×#41	—	2	2	no	—
559	C₂×#41	—	2	2	no	—
560	C₂×#41	—	2	2	no	—
561	C₂×#41	—	2	2	no	—
562	C₂×#41	—	2	2	no	—
563	C₂×#41	—	4	1	no	—
564	C₂×#41	—	4	1	no	—
565	C₂×#41	—	4	1	no	—
566	C₂×#41	—	4	1	no	—
567	C₂×#41	—	4	1	no	—
568	C₂×#41	—	4	1	no	—
569	C₂×#41	D₄×C₇₉	1	4	yes	complemented
570	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
571	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
572	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
573	C₂²×D₄	—	2	1	no	—
574	C₂²×D₄	—	2	1	no	—
575	C₂²×D₄	—	2	1	no	—
576	C₂²×D₄	—	2	1	no	—
577	C₂²×D₄	D₄×C₇₉	1	1	yes	characteristic
578	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
579	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
580	C₂³×C₄	—	2	1	no	—
581	C₂³×C₄	—	2	1	no	—
582	C₂³×C₄	—	2	1	no	—
583	C₂³×C₄	—	2	1	no	—
584	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
585	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
586	#135	—	2	32	no	—
587	C₂×Q₁₆	—	2	2	no	—
588	C₂×Q₁₆	—	2	2	no	—
589	C₂×Q₁₆	—	2	2	no	—
590	C₂×Q₁₆	—	2	2	no	—
591	C₂×Q₁₆	—	2	2	no	—
592	C₂×Q₁₆	—	4	1	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	—	2	2	no	—
598	C₂×SD₁₆	—	2	2	no	—
599	C₂×SD₁₆	—	2	2	no	—
600	C₂×SD₁₆	—	4	1	no	—
601	C₂×SD₁₆	D₄×C₇₉	1	4	yes	complemented
602	C₂×D₈	—	2	2	no	—
603	C₂×D₈	—	2	2	no	—
604	C₂×D₈	D₄×C₇₉	1	4	yes	complemented
605	C₂²×C₈	—	2	2	no	—
606	C₂²×C₈	—	2	2	no	—
607	C₂²×C₈	—	2	2	no	—
608	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
609	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
610	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
611	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
612	C₄⋊Q₈	—	2	2	no	—
613	C₄⋊Q₈	—	2	2	no	—
614	#123	—	2	8	no	—
615	#123	—	2	8	no	—
616	C₂²⋊Q₈	—	2	2	no	—
617	C₂²⋊Q₈	—	2	2	no	—
618	C₂²⋊Q₈	—	2	2	no	—
619	C₂²⋊Q₈	—	2	2	no	—
620	C₂²⋊Q₈	—	4	1	no	—
621	C₂²⋊Q₈	D₄×C₇₉	1	4	yes	complemented
622	#121	—	2	8	no	—
623	#121	—	2	2	no	—
624	#121	—	4	1	no	—
625	C₄×D₄	—	2	2	no	—
626	C₄×D₄	—	2	2	no	—
627	C₄×D₄	—	2	2	no	—
628	C₄×D₄	—	2	2	no	—
629	C₂×C₄⋊C₄	—	2	8	no	—
630	C₂×C₄⋊C₄	—	2	1	no	—
631	C₂×C₄⋊C₄	—	2	1	no	—
632	C₂×C₄⋊C₄	—	2	1	no	—
633	C₂×C₄⋊C₄	—	2	1	no	—
634	C₂×C₄⋊C₄	—	2	1	no	—
635	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
636	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
638	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
639	C₂×C₂²⋊C₄	—	2	1	no	—
640	C₂×C₂²⋊C₄	—	2	1	no	—
641	C₂×C₂²⋊C₄	—	2	1	no	—
642	C₂×C₂²⋊C₄	—	2	1	no	—
643	C₂×C₂²⋊C₄	—	2	1	no	—
644	C₂×C₂²⋊C₄	—	2	1	no	—
645	C₂×C₂²⋊C₄	—	2	1	no	—
646	C₂×C₂²⋊C₄	—	2	1	no	—
647	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
648	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
650	#103	—	2	2	no	—
651	#103	—	2	2	no	—
652	#103	—	2	2	no	—
653	#103	—	4	1	no	—
654	#103	—	4	1	no	—
655	#102	—	2	2	no	—
656	#102	—	2	2	no	—
657	#102	—	2	2	no	—
658	C₂²⋊C₈	—	2	2	no	—
659	C₂²⋊C₈	—	2	2	no	—
660	C₂²⋊C₈	—	2	2	no	—
661	#95	—	2	1	no	—
662	#95	—	2	1	no	—
663	#95	—	2	1	no	—
664	C₂⁴	—	2	1	no	—
665	C₂⁴	—	2	1	no	—
666	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
667	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
668	#41	—	2	8	no	—
669	#41	—	2	8	no	—
670	#41	—	4	4	no	—
671	#41	—	4	4	no	—
672	#41	—	4	4	no	—
673	#41	—	4	4	no	—
674	#41	—	4	4	no	—
675	#41	—	4	4	no	—
676	#41	—	4	4	no	—
677	#41	—	4	4	no	—
678	#41	—	4	4	no	—
679	#41	—	4	4	no	—
680	C₂×Q₈	—	2	1	no	—
681	C₂×Q₈	—	2	1	no	—
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×Q₈	—	2	1	no	—
689	C₂×Q₈	—	2	1	no	—
690	C₂×Q₈	—	2	1	no	—
691	C₂×Q₈	—	2	1	no	—
692	C₂×Q₈	—	2	1	no	—
693	C₂×Q₈	—	2	1	no	—
694	C₂×Q₈	—	2	1	no	—
695	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
696	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
697	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
698	C₂×D₄	—	2	4	no	—
699	C₂×D₄	—	2	2	no	—
700	C₂×D₄	—	2	4	no	—
701	C₂×D₄	—	2	2	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	—	4	1	no	—
711	C₂×D₄	—	4	2	no	—
712	C₂×D₄	—	4	2	no	—
713	C₂×D₄	—	4	2	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	2	no	—
720	C₂×D₄	—	8	1	no	—
721	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
722	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
723	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
724	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
725	C₂²×C₄	—	2	1	no	—
726	C₂²×C₄	—	2	1	no	—
727	C₂²×C₄	—	2	1	no	—
728	C₂²×C₄	—	2	1	no	—
729	C₂²×C₄	—	2	4	no	—
730	C₂²×C₄	—	2	4	no	—
731	C₂²×C₄	—	2	1	no	—
732	C₂²×C₄	—	2	1	no	—
733	C₂²×C₄	—	2	1	no	—
734	C₂²×C₄	—	2	1	no	—
735	C₂²×C₄	—	2	4	no	—
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	1	no	—
741	C₂²×C₄	—	2	1	no	—
742	C₂²×C₄	—	2	1	no	—
743	C₂²×C₄	—	2	1	no	—
744	C₂²×C₄	—	4	2	no	—
745	C₂²×C₄	—	4	2	no	—
746	C₂²×C₄	—	4	2	no	—
747	C₂²×C₄	—	4	2	no	—
748	C₂²×C₄	—	4	2	no	—
749	C₂²×C₄	—	4	2	no	—
750	C₂²×C₄	—	4	2	no	—
751	C₂²×C₄	—	4	2	no	—
752	C₂²×C₄	—	4	2	no	—
753	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
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	2	yes	—
757	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
758	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
759	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
760	Q₁₆	—	2	8	no	—
761	Q₁₆	—	4	4	no	—
762	SD₁₆	—	2	8	no	—
763	SD₁₆	—	2	8	no	—
764	SD₁₆	—	4	4	no	—
765	D₈	—	2	8	no	—
766	C₂×C₈	—	2	8	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	—	2	1	no	—
777	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
778	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
779	C₄⋊C₄	—	2	4	no	—
780	C₄⋊C₄	—	2	4	no	—
781	C₄⋊C₄	—	2	4	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	4	no	—
784	C₄⋊C₄	—	2	1	no	—
785	C₄⋊C₄	—	2	1	no	—
786	C₄⋊C₄	—	2	1	no	—
787	C₄⋊C₄	—	2	1	no	—
788	C₄⋊C₄	—	2	1	no	—
789	C₄⋊C₄	—	4	2	no	—
790	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
791	C₂²⋊C₄	—	2	4	no	—
792	C₂²⋊C₄	—	2	4	no	—
793	C₂²⋊C₄	—	2	4	no	—
794	C₂²⋊C₄	—	2	2	no	—
795	C₂²⋊C₄	—	2	2	no	—
796	C₂²⋊C₄	—	4	2	no	—
797	C₂²⋊C₄	—	4	2	no	—
798	C₂²⋊C₄	—	4	2	no	—
799	C₂²⋊C₄	—	8	1	no	—
800	C₂²⋊C₄	—	8	1	no	—
801	C₄²	—	2	1	no	—
802	C₄²	—	2	1	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	1	no	—
805	C₂³	—	2	1	no	—
806	C₂³	—	2	2	no	—
807	C₂³	—	2	2	no	—
808	C₂³	—	2	1	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	2	no	—
815	C₂³	—	2	1	no	—
816	C₂³	—	2	1	no	—
817	C₂³	—	2	1	no	—
818	C₂³	—	2	1	no	—
819	C₂³	—	2	1	no	—
820	C₂³	—	4	1	no	—
821	C₂³	—	4	1	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	#120×C₇₉	1	2	yes	—
831	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
832	Q₈	—	2	2	no	—
833	Q₈	—	2	2	no	—
834	Q₈	—	2	2	no	—
835	Q₈	—	2	2	no	—
836	Q₈	—	2	2	no	—
837	Q₈	—	2	2	no	—
838	Q₈	—	4	1	no	—
839	Q₈	—	4	1	no	—
840	Q₈	—	4	1	no	—
841	Q₈	—	4	1	no	—
842	Q₈	—	4	1	no	—
843	Q₈	—	4	1	no	—
844	D₄	—	2	2	no	—
845	D₄	—	2	2	no	—
846	D₄	—	2	2	no	—
847	D₄	—	2	2	no	—
848	D₄	—	2	2	no	—
849	D₄	—	4	4	no	—
850	D₄	—	4	8	no	—
851	D₄	—	4	8	no	—
852	D₄	—	4	8	no	—
853	D₄	—	4	1	no	—
854	D₄	—	4	1	no	—
855	D₄	—	8	4	no	—
856	D₄	#120×C₇₉	1	4	yes	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	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	1	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	4	8	no	—
876	C₂×C₄	—	4	8	no	—
877	C₂×C₄	—	4	8	no	—
878	C₂×C₄	—	4	8	no	—
879	C₂×C₄	—	4	1	no	—
880	C₂×C₄	—	4	1	no	—
881	C₂×C₄	—	4	1	no	—
882	C₂×C₄	—	4	1	no	—
883	C₂×C₄	—	4	1	no	—
884	C₂×C₄	—	4	1	no	—
885	C₂×C₄	—	4	1	no	—
886	C₂×C₄	—	4	1	no	—
887	C₂×C₄	—	4	1	no	—
888	C₂×C₄	—	4	1	no	—
889	C₂×C₄	—	4	1	no	—
890	C₂×C₄	—	4	1	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	#120×C₇₉	1	2	yes	—
898	C₂×C₄	#135×C₇₉	1	2	yes	complemented
899	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
900	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
901	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
902	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
903	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
904	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
905	C₈	—	2	2	no	—
906	C₈	—	2	2	no	—
907	C₈	—	4	1	no	—
908	C₈	—	4	1	no	—
909	C₂²	—	2	2	no	—
910	C₂²	—	2	4	no	—
911	C₂²	—	2	2	no	—
912	C₂²	—	2	2	no	—
913	C₂²	—	4	1	no	—
914	C₂²	—	4	2	no	—
915	C₂²	—	4	1	no	—
916	C₂²	—	4	2	no	—
917	C₂²	—	4	2	no	—
918	C₂²	—	4	1	no	—
919	C₂²	—	4	2	no	—
920	C₂²	—	4	2	no	—
921	C₂²	—	4	1	no	—
922	C₂²	—	4	2	no	—
923	C₂²	—	4	1	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	4	1	no	—
926	C₂²	—	4	2	no	—
927	C₂²	—	4	1	no	—
928	C₂²	—	4	1	no	—
929	C₂²	—	4	1	no	—
930	C₂²	—	4	2	no	—
931	C₂²	—	4	1	no	—
932	C₂²	—	4	1	no	—
933	C₂²	—	8	1	no	—
934	C₂²	—	8	1	no	—
935	C₂²	—	8	1	no	—
936	C₂²	—	8	1	no	—
937	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
938	C₂²	D₄²×C₇₉	1	1	yes	characteristic
939	C₂²	D₄²×C₇₉	1	1	yes	characteristic
940	C₂²	C₂×#135×C₇₉	1	1	yes	characteristic
941	C₂²	#575×C₇₉	1	1	yes	characteristic
942	C₂²	#577×C₇₉	1	1	yes	characteristic
943	C₂²	#578×C₇₉	1	1	yes	characteristic
944	C₄	—	2	2	no	—
945	C₄	—	2	2	no	—
946	C₄	—	4	1	no	—
947	C₄	—	4	2	no	—
948	C₄	—	4	2	no	—
949	C₄	—	4	2	no	—
950	C₄	—	4	2	no	—
951	C₄	—	4	1	no	—
952	C₄	—	8	1	no	—
953	C₄	—	8	1	no	—
954	C₄	C₂×#120×C₇₉	1	1	yes	characteristic
955	C₄	#534×C₇₉	1	1	yes	characteristic
956	C₄	D₄²×C₇₉	1	1	yes	characteristic
957	C₄	D₄²×C₇₉	1	1	yes	characteristic
958	C₂	—	4	2	no	—
959	C₂	—	4	4	no	—
960	C₂	—	8	1	no	—
961	C₂	—	8	2	no	—
962	C₂	C₇₉×#2403	1	1	yes	characteristic
963	C₂	C₇₉×#3002	1	1	yes	characteristic
964	C₂	C₇₉×#3013	1	1	yes	characteristic
965	C₂	C₇₉×#3267	1	1	yes	characteristic
966	C₂	C₇₉×#3269	1	1	yes	characteristic
967	C₂	C₇₉×#3283	1	1	yes	characteristic
968	C₂	C₇₉×#3284	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. C₂²×#135×C₇₉	C₂	semidirect
2. C₂×#547×C₇₉	C₂	semidirect
3. C₂×#452×C₇₉	C₂	semidirect
4. C₂×#452×C₇₉	C₂	semidirect
5. C₂×#449×C₇₉	C₂	semidirect
6. C₇₉×#2407	C₂	semidirect
7. C₇₉×#2016	C₂	semidirect
8. C₇₉×#2013	C₂	semidirect
9. C₇₉×#2001	C₂	semidirect
10. C₇₉×#2000	C₂	semidirect
11. C₇₉×#1892	C₂	semidirect
12. C₇₉×#1879	C₂	semidirect
13. C₇₉×#1877	C₂	semidirect
14. C₇₉×#1869	C₂	semidirect
15. C₇₉×#1788	C₂	semidirect
84. C₂×#41×C₇₉	D₄	semidirect
116. C₂×SD₁₆×C₇₉	D₄	semidirect
119. C₂×D₈×C₇₉	D₄	semidirect
136. C₂²⋊Q₈×C₇₉	D₄	semidirect
413. C₂×C₄×C₇₉	#135	semidirect
473. #23853	C₇₉	direct (N × H)
485. C₂²×#135	C₂×C₇₉	semidirect
486. C₂×#547	C₂×C₇₉	semidirect
487. C₂×#452	C₂×C₇₉	semidirect
488. C₂×#452	C₂×C₇₉	semidirect
489. C₂×#449	C₂×C₇₉	semidirect
490. #2407	C₂×C₇₉	semidirect
491. #2016	C₂×C₇₉	semidirect
492. #2013	C₂×C₇₉	semidirect
493. #2001	C₂×C₇₉	semidirect
494. #2000	C₂×C₇₉	semidirect
495. #1892	C₂×C₇₉	semidirect
496. #1879	C₂×C₇₉	semidirect
497. #1877	C₂×C₇₉	semidirect
498. #1869	C₂×C₇₉	semidirect
499. #1788	C₂×C₇₉	semidirect
500. C₇₉	#23853	direct (N × H)
569. C₂×#41	D₄×C₇₉	semidirect
601. C₂×SD₁₆	D₄×C₇₉	semidirect
604. C₂×D₈	D₄×C₇₉	semidirect
621. C₂²⋊Q₈	D₄×C₇₉	semidirect
898. C₂×C₄	#135×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#135×C₇₉	2
C₂×#547×C₇₉	2
C₂×#452×C₇₉	2
C₂×#449×C₇₉	2
C₇₉×#2407	2
C₇₉×#2016	2
C₇₉×#2013	2
C₇₉×#2001	2
C₇₉×#2000	2
C₇₉×#1892	2
C₇₉×#1879	2
C₇₉×#1877	2
C₇₉×#1869	2
C₇₉×#1788	2
#23853	79

Subgroups — C79×#23853 #34135542

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#23853 #34135542