Subgroups — C₇₉×#62020 #34173709

Order 20224.

1772 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3561	C₂	1	1	yes	maximal, characteristic
2	C₇₉×#3523	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#3398	C₂	1	2	yes	maximal, complemented
4	C₇₉×#3377	C₂	1	2	yes	maximal, complemented
5	C₇₉×#3313	C₂	1	2	yes	maximal, complemented
6	C₇₉×#3312	C₂	1	2	yes	maximal, complemented
7	C₇₉×#3296	C₂	1	2	yes	maximal, complemented
8	D₄×Q₁₆×C₇₉	C₂	1	2	yes	maximal, complemented
9	C₇₉×#3270	C₂	1	2	yes	maximal, complemented
10	C₇₉×#3266	C₂	1	2	yes	maximal, complemented
11	C₇₉×#3258	C₂	1	2	yes	maximal, complemented
12	C₇₉×#3249	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₉×#3223	C₂	1	2	yes	maximal, complemented
14	C₇₉×#3215	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#3121	C₂	1	2	yes	maximal, complemented
16	C₇₉×#3113	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇₉×#3044	C₂	1	2	yes	maximal, complemented
18	C₂×#464×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇₉×#2992	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#137×C₇₉	C₂²	1	2	yes	—
21	C₂²×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
22	C₂²×Q₁₆×C₇₉	C₂²	1	2	yes	complemented
23	C₂²×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
24	#563×C₇₉	—	2	1	no	—
25	#562×C₇₉	—	2	1	no	—
26	#557×C₇₉	—	2	1	no	—
27	#557×C₇₉	C₂²	1	1	yes	characteristic, complemented
28	#557×C₇₉	C₂²	1	1	yes	characteristic, complemented
29	#556×C₇₉	—	2	1	no	—
30	#556×C₇₉	C₂²	1	2	yes	—
31	#556×C₇₉	C₂²	1	1	yes	characteristic, complemented
32	#552×C₇₉	—	2	2	no	—
33	#552×C₇₉	C₂²	1	2	yes	—
34	#551×C₇₉	—	2	2	no	—
35	D₄×Q₈×C₇₉	C₂²	1	2	yes	—
36	D₄×Q₈×C₇₉	C₂²	1	2	yes	—
37	D₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
38	#548×C₇₉	C₂²	1	2	yes	—
39	#546×C₇₉	C₂²	1	2	yes	—
40	#543×C₇₉	—	2	1	no	—
41	#542×C₇₉	—	2	2	no	—
42	#542×C₇₉	C₂²	1	2	yes	—
43	#541×C₇₉	—	2	2	no	—
44	#541×C₇₉	C₂²	1	2	yes	complemented
45	#538×C₇₉	—	2	1	no	—
46	#536×C₇₉	C₂²	1	2	yes	—
47	#533×C₇₉	—	2	1	no	—
48	#533×C₇₉	C₂²	1	1	yes	characteristic
49	#533×C₇₉	C₂²	1	1	yes	characteristic
50	#529×C₇₉	—	2	1	no	—
51	#529×C₇₉	C₂²	1	1	yes	characteristic
52	C₂×#124×C₇₉	C₂²	1	1	yes	characteristic
53	#519×C₇₉	C₂²	1	2	yes	complemented
54	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
55	#497×C₇₉	C₂²	1	2	yes	—
56	#497×C₇₉	C₂²	1	2	yes	—
57	#494×C₇₉	C₂²	1	2	yes	complemented
58	#491×C₇₉	C₂²	1	2	yes	complemented
59	#489×C₇₉	C₂²	1	2	yes	—
60	#488×C₇₉	C₂²	1	2	yes	—
61	#485×C₇₉	C₂²	1	2	yes	complemented
62	#483×C₇₉	C₂²	1	2	yes	—
63	#482×C₇₉	C₂²	1	2	yes	—
64	#479×C₇₉	C₂²	1	2	yes	complemented
65	#478×C₇₉	C₂²	1	2	yes	—
66	#477×C₇₉	C₂²	1	2	yes	complemented
67	#477×C₇₉	C₂²	1	2	yes	complemented
68	#475×C₇₉	C₂²	1	1	yes	characteristic, complemented
69	#475×C₇₉	C₂²	1	1	yes	characteristic, complemented
70	#470×C₇₉	C₂²	1	2	yes	complemented
71	#468×C₇₉	C₂²	1	2	yes	—
72	#467×C₇₉	C₂²	1	2	yes	—
73	#467×C₇₉	C₂²	1	2	yes	—
74	#467×C₇₉	C₂²	1	2	yes	complemented
75	#465×C₇₉	C₂²	1	2	yes	—
76	#464×C₇₉	C₂²	1	2	yes	—
77	#464×C₇₉	C₂²	1	2	yes	—
78	#464×C₇₉	C₂²	1	2	yes	—
79	#464×C₇₉	C₂²	1	2	yes	—
80	#464×C₇₉	C₂²	1	2	yes	—
81	#464×C₇₉	C₂²	1	2	yes	—
82	#464×C₇₉	C₂²	1	2	yes	—
83	#464×C₇₉	C₂²	1	2	yes	—
84	#462×C₇₉	C₂²	1	2	yes	complemented
85	#462×C₇₉	C₂²	1	2	yes	complemented
86	#462×C₇₉	C₂²	1	1	yes	characteristic, complemented
87	#462×C₇₉	C₂²	1	2	yes	complemented
88	#462×C₇₉	C₂²	1	2	yes	complemented
89	#462×C₇₉	C₂²	1	1	yes	characteristic, complemented
90	#462×C₇₉	C₂²	1	2	yes	complemented
91	#461×C₇₉	C₂²	1	2	yes	—
92	#452×C₇₉	C₂²	1	2	yes	—
93	#452×C₇₉	C₂²	1	2	yes	—
94	#451×C₇₉	C₂²	1	2	yes	—
95	#451×C₇₉	C₂²	1	2	yes	—
96	#451×C₇₉	C₂²	1	2	yes	complemented
97	#451×C₇₉	C₂²	1	2	yes	complemented
98	#451×C₇₉	C₂²	1	2	yes	complemented
99	#450×C₇₉	C₂²	1	2	yes	—
100	#448×C₇₉	C₂²	1	2	yes	—
101	#446×C₇₉	C₂²	1	2	yes	complemented
102	#441×C₇₉	C₂²	1	2	yes	complemented
103	#441×C₇₉	C₂²	1	2	yes	complemented
104	#441×C₇₉	C₂²	1	2	yes	complemented
105	#440×C₇₉	C₂²	1	2	yes	—
106	C₄×Q₁₆×C₇₉	C₂²	1	2	yes	complemented
107	C₄×SD₁₆×C₇₉	C₂²	1	2	yes	—
108	#435×C₇₉	C₂²	1	2	yes	—
109	#435×C₇₉	C₂²	1	2	yes	complemented
110	C₈×D₄×C₇₉	C₂²	1	2	yes	—
111	#433×C₇₉	C₂²	1	2	yes	complemented
112	#432×C₇₉	C₂²	1	1	yes	characteristic
113	#424×C₇₉	C₂²	1	2	yes	complemented
114	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
115	#419×C₇₉	C₂²	1	2	yes	complemented
116	#416×C₇₉	C₂²	1	2	yes	—
117	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
118	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
119	C₂×#41×C₇₉	C₂³	1	2	yes	—
120	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
121	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
122	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
123	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
125	#137×C₇₉	—	4	4	no	—
126	C₂×Q₁₆×C₇₉	—	4	2	no	—
127	C₂×Q₁₆×C₇₉	—	4	4	no	—
128	C₂×Q₁₆×C₇₉	C₂³	1	2	yes	—
129	C₂×Q₁₆×C₇₉	C₂³	1	2	yes	—
130	C₂×Q₁₆×C₇₉	C₂³	1	2	yes	—
131	C₂×Q₁₆×C₇₉	C₂³	1	2	yes	—
132	C₂×Q₁₆×C₇₉	C₂³	1	2	yes	—
133	C₂×Q₁₆×C₇₉	C₂³	1	2	yes	—
134	C₂×Q₁₆×C₇₉	C₂³	1	2	yes	—
135	C₂×Q₁₆×C₇₉	C₂³	1	2	yes	—
136	C₂×SD₁₆×C₇₉	—	4	2	no	—
137	C₂×SD₁₆×C₇₉	C₂³	1	2	yes	—
138	C₂×SD₁₆×C₇₉	C₂³	1	2	yes	—
139	C₂×SD₁₆×C₇₉	C₂³	1	2	yes	—
140	C₂×SD₁₆×C₇₉	C₂³	1	2	yes	—
141	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
142	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
143	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
144	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
145	C₄⋊Q₈×C₇₉	—	2	1	no	—
146	C₄⋊Q₈×C₇₉	—	2	1	no	—
147	C₄⋊Q₈×C₇₉	—	2	2	no	—
148	C₄⋊Q₈×C₇₉	—	2	2	no	—
149	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
150	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
151	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
152	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
153	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
154	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
155	#126×C₇₉	—	2	2	no	—
156	#126×C₇₉	—	2	2	no	—
157	#126×C₇₉	—	2	2	no	—
158	#126×C₇₉	—	2	2	no	—
159	#126×C₇₉	—	2	2	no	—
160	#126×C₇₉	—	2	2	no	—
161	#126×C₇₉	—	2	2	no	—
162	#126×C₇₉	D₄	1	2	yes	—
163	#125×C₇₉	—	2	1	no	—
164	#125×C₇₉	—	2	2	no	—
165	#125×C₇₉	—	2	2	no	—
166	#125×C₇₉	—	2	2	no	—
167	#125×C₇₉	—	2	2	no	—
168	#125×C₇₉	—	2	2	no	—
169	#125×C₇₉	—	2	1	no	—
170	#125×C₇₉	—	2	1	no	—
171	#125×C₇₉	D₄	1	1	yes	characteristic
172	#125×C₇₉	C₂³	1	2	yes	—
173	#124×C₇₉	—	2	1	no	—
174	#124×C₇₉	—	2	2	no	—
175	#124×C₇₉	—	2	2	no	—
176	#124×C₇₉	—	2	1	no	—
177	#124×C₇₉	—	2	1	no	—
178	#124×C₇₉	D₄	1	1	yes	characteristic
179	#124×C₇₉	C₂³	1	2	yes	—
180	#124×C₇₉	C₂³	1	2	yes	—
181	#124×C₇₉	C₂³	1	2	yes	—
182	#123×C₇₉	—	2	2	no	—
183	#123×C₇₉	—	2	2	no	—
184	#123×C₇₉	—	2	2	no	—
185	#123×C₇₉	—	2	2	no	—
186	#123×C₇₉	—	2	2	no	—
187	#123×C₇₉	D₄	1	2	yes	—
188	C₂²⋊Q₈×C₇₉	—	2	2	no	—
189	C₂²⋊Q₈×C₇₉	—	2	1	no	—
190	C₂²⋊Q₈×C₇₉	—	2	1	no	—
191	C₂²⋊Q₈×C₇₉	—	2	2	no	—
192	C₂²⋊Q₈×C₇₉	—	2	2	no	—
193	C₂²⋊Q₈×C₇₉	—	2	2	no	—
194	C₂²⋊Q₈×C₇₉	—	2	2	no	—
195	C₂²⋊Q₈×C₇₉	—	2	2	no	—
196	C₂²⋊Q₈×C₇₉	—	2	2	no	—
197	C₂²⋊Q₈×C₇₉	—	2	2	no	—
198	C₂²⋊Q₈×C₇₉	—	2	2	no	—
199	C₂²⋊Q₈×C₇₉	—	2	2	no	—
200	C₂²⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
201	C₂²⋊Q₈×C₇₉	C₂³	1	2	yes	—
202	C₂²⋊Q₈×C₇₉	C₂³	1	2	yes	—
203	C₂²⋊Q₈×C₇₉	C₂³	1	2	yes	—
204	C₂²⋊Q₈×C₇₉	C₂³	1	2	yes	—
205	C₂²⋊Q₈×C₇₉	C₂³	1	2	yes	—
206	#121×C₇₉	—	2	2	no	—
207	#121×C₇₉	—	2	2	no	—
208	#121×C₇₉	D₄	1	1	yes	characteristic
209	#121×C₇₉	C₂³	1	2	yes	—
210	#120×C₇₉	—	2	2	no	—
211	C₄×Q₈×C₇₉	—	2	1	no	—
212	C₄×Q₈×C₇₉	—	2	2	no	—
213	C₄×Q₈×C₇₉	—	2	2	no	—
214	C₄×Q₈×C₇₉	—	2	1	no	—
215	C₄×Q₈×C₇₉	—	2	1	no	—
216	C₄×Q₈×C₇₉	—	2	1	no	—
217	C₄×Q₈×C₇₉	—	2	1	no	—
218	C₄×Q₈×C₇₉	—	2	1	no	—
219	C₄×Q₈×C₇₉	—	2	1	no	—
220	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
221	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
222	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
223	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
224	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
229	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
230	C₄×D₄×C₇₉	—	2	2	no	—
231	C₄×D₄×C₇₉	—	2	1	no	—
232	C₄×D₄×C₇₉	—	2	2	no	—
233	C₄×D₄×C₇₉	—	2	2	no	—
234	C₄×D₄×C₇₉	C₂³	1	2	yes	—
235	C₄×D₄×C₇₉	C₂³	1	2	yes	—
236	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
237	#117×C₇₉	—	2	1	no	—
238	#117×C₇₉	—	2	1	no	—
239	#117×C₇₉	—	2	2	no	—
240	#117×C₇₉	—	2	2	no	—
241	#117×C₇₉	—	2	2	no	—
242	#117×C₇₉	—	2	2	no	—
243	#117×C₇₉	C₂³	1	2	yes	—
244	#117×C₇₉	C₂³	1	2	yes	—
245	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
246	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
247	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
248	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
249	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
250	C₂×C₄²×C₇₉	—	2	1	no	—
251	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
252	#107×C₇₉	C₂³	1	2	yes	—
253	#107×C₇₉	C₂³	1	2	yes	—
254	#106×C₇₉	C₂³	1	2	yes	—
255	#106×C₇₉	C₂³	1	2	yes	—
256	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
257	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
258	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
259	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
260	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
261	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
262	#103×C₇₉	C₂³	1	2	yes	—
263	#103×C₇₉	C₂³	1	2	yes	—
264	#103×C₇₉	C₂³	1	2	yes	—
265	#103×C₇₉	C₂³	1	2	yes	—
266	#103×C₇₉	C₂³	1	2	yes	—
267	#103×C₇₉	C₂³	1	2	yes	—
268	#103×C₇₉	C₂³	1	2	yes	—
269	#103×C₇₉	C₂³	1	2	yes	—
270	#103×C₇₉	C₂³	1	2	yes	—
271	#103×C₇₉	C₂³	1	2	yes	—
272	#103×C₇₉	C₂³	1	2	yes	—
273	#103×C₇₉	C₂³	1	2	yes	—
274	#102×C₇₉	C₂³	1	2	yes	—
275	#102×C₇₉	C₂³	1	2	yes	—
276	#102×C₇₉	C₂³	1	2	yes	—
277	#102×C₇₉	C₂³	1	2	yes	—
278	C₂²⋊C₈×C₇₉	C₂³	1	2	yes	—
279	C₂²⋊C₈×C₇₉	C₂³	1	2	yes	—
280	C₂²⋊C₈×C₇₉	C₂³	1	2	yes	—
281	#97×C₇₉	C₂³	1	2	yes	—
282	#97×C₇₉	C₂³	1	2	yes	—
283	C₄×C₈×C₇₉	C₂³	1	2	yes	—
284	C₂⁴×C₇₉	—	2	1	no	—
285	#41×C₇₉	—	4	2	no	—
286	#41×C₇₉	—	4	2	no	—
287	C₂×Q₈×C₇₉	—	2	1	no	—
288	C₂×Q₈×C₇₉	—	2	2	no	—
289	C₂×Q₈×C₇₉	—	2	1	no	—
290	C₂×Q₈×C₇₉	—	2	1	no	—
291	C₂×Q₈×C₇₉	—	2	2	no	—
292	C₂×Q₈×C₇₉	—	2	1	no	—
293	C₂×Q₈×C₇₉	—	2	2	no	—
294	C₂×Q₈×C₇₉	—	2	4	no	—
295	C₂×Q₈×C₇₉	—	4	1	no	—
296	C₂×Q₈×C₇₉	—	4	2	no	—
297	C₂×Q₈×C₇₉	—	4	1	no	—
298	C₂×Q₈×C₇₉	—	4	2	no	—
299	C₂×Q₈×C₇₉	—	4	1	no	—
300	C₂×Q₈×C₇₉	—	4	2	no	—
301	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
302	C₂×Q₈×C₇₉	C₂⁴	1	2	yes	—
303	C₂×Q₈×C₇₉	C₂⁴	1	2	yes	—
304	C₂×Q₈×C₇₉	C₂⁴	1	1	yes	characteristic
305	C₂×Q₈×C₇₉	C₂⁴	1	2	yes	—
306	C₂×Q₈×C₇₉	C₂⁴	1	1	yes	characteristic
307	C₂×D₄×C₇₉	—	2	2	no	—
308	C₂×D₄×C₇₉	—	2	2	no	—
309	C₂×D₄×C₇₉	—	2	1	no	—
310	C₂×D₄×C₇₉	—	4	1	no	—
311	C₂×D₄×C₇₉	—	4	1	no	—
312	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
313	C₂×D₄×C₇₉	C₂×D₄	1	1	yes	characteristic
314	C₂×D₄×C₇₉	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₇₉	—	2	1	no	—
316	C₂²×C₄×C₇₉	—	2	1	no	—
317	C₂²×C₄×C₇₉	—	2	2	no	—
318	C₂²×C₄×C₇₉	—	2	1	no	—
319	C₂²×C₄×C₇₉	—	2	2	no	—
320	C₂²×C₄×C₇₉	—	2	2	no	—
321	C₂²×C₄×C₇₉	—	2	2	no	—
322	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
323	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
324	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
326	Q₁₆×C₇₉	—	2	4	no	—
327	Q₁₆×C₇₉	—	2	4	no	—
328	Q₁₆×C₇₉	—	4	2	no	—
329	Q₁₆×C₇₉	—	4	2	no	—
330	Q₁₆×C₇₉	—	4	2	no	—
331	Q₁₆×C₇₉	—	4	2	no	—
332	Q₁₆×C₇₉	—	4	2	no	—
333	Q₁₆×C₇₉	—	4	2	no	—
334	SD₁₆×C₇₉	—	2	4	no	—
335	SD₁₆×C₇₉	—	4	2	no	—
336	SD₁₆×C₇₉	—	4	2	no	—
337	SD₁₆×C₇₉	—	4	2	no	—
338	M₁₆×C₇₉	—	4	2	no	—
339	C₂×C₈×C₇₉	—	4	1	no	—
340	C₂×C₈×C₇₉	—	4	1	no	—
341	C₂×C₈×C₇₉	—	4	2	no	—
342	C₂×C₈×C₇₉	C₂⁴	1	2	yes	—
343	C₂×C₈×C₇₉	C₂⁴	1	2	yes	—
344	C₂×C₈×C₇₉	C₂⁴	1	2	yes	—
345	C₂×C₈×C₇₉	C₂⁴	1	2	yes	—
346	C₄⋊C₄×C₇₉	—	2	1	no	—
347	C₄⋊C₄×C₇₉	—	2	1	no	—
348	C₄⋊C₄×C₇₉	—	2	1	no	—
349	C₄⋊C₄×C₇₉	—	2	1	no	—
350	C₄⋊C₄×C₇₉	—	2	1	no	—
351	C₄⋊C₄×C₇₉	—	2	2	no	—
352	C₄⋊C₄×C₇₉	—	2	2	no	—
353	C₄⋊C₄×C₇₉	—	2	2	no	—
354	C₄⋊C₄×C₇₉	—	2	2	no	—
355	C₄⋊C₄×C₇₉	—	2	1	no	—
356	C₄⋊C₄×C₇₉	—	2	1	no	—
357	C₄⋊C₄×C₇₉	—	2	2	no	—
358	C₄⋊C₄×C₇₉	—	2	1	no	—
359	C₄⋊C₄×C₇₉	—	2	1	no	—
360	C₄⋊C₄×C₇₉	—	2	2	no	—
361	C₄⋊C₄×C₇₉	—	2	1	no	—
362	C₄⋊C₄×C₇₉	—	2	2	no	—
363	C₄⋊C₄×C₇₉	—	2	2	no	—
364	C₄⋊C₄×C₇₉	—	2	2	no	—
365	C₄⋊C₄×C₇₉	—	2	2	no	—
366	C₄⋊C₄×C₇₉	—	2	1	no	—
367	C₄⋊C₄×C₇₉	—	2	2	no	—
368	C₄⋊C₄×C₇₉	—	2	2	no	—
369	C₄⋊C₄×C₇₉	—	2	2	no	—
370	C₄⋊C₄×C₇₉	—	2	2	no	—
371	C₄⋊C₄×C₇₉	—	2	2	no	—
372	C₄⋊C₄×C₇₉	—	2	2	no	—
373	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
374	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
375	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
376	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
377	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
378	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
379	C₄⋊C₄×C₇₉	C₂⁴	1	1	yes	characteristic
380	C₄⋊C₄×C₇₉	C₂⁴	1	1	yes	characteristic
381	C₄⋊C₄×C₇₉	C₂⁴	1	2	yes	—
382	C₄⋊C₄×C₇₉	C₂⁴	1	2	yes	—
383	C₂²⋊C₄×C₇₉	—	2	2	no	—
384	C₂²⋊C₄×C₇₉	—	2	2	no	—
385	C₂²⋊C₄×C₇₉	—	2	2	no	—
386	C₂²⋊C₄×C₇₉	—	2	2	no	—
387	C₂²⋊C₄×C₇₉	—	2	2	no	—
388	C₂²⋊C₄×C₇₉	—	2	2	no	—
389	C₂²⋊C₄×C₇₉	—	2	2	no	—
390	C₂²⋊C₄×C₇₉	—	2	2	no	—
391	C₂²⋊C₄×C₇₉	—	2	2	no	—
392	C₂²⋊C₄×C₇₉	—	2	2	no	—
393	C₂²⋊C₄×C₇₉	—	2	2	no	—
394	C₂²⋊C₄×C₇₉	—	2	2	no	—
395	C₂²⋊C₄×C₇₉	—	2	2	no	—
396	C₂²⋊C₄×C₇₉	—	2	2	no	—
397	C₂²⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
398	C₂²⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
399	C₂²⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
400	C₂²⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
401	C₂²⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
402	C₄²×C₇₉	—	2	1	no	—
403	C₄²×C₇₉	—	2	1	no	—
404	C₄²×C₇₉	—	2	1	no	—
405	C₄²×C₇₉	—	2	1	no	—
406	C₄²×C₇₉	—	2	2	no	—
407	C₄²×C₇₉	—	2	2	no	—
408	C₄²×C₇₉	—	2	2	no	—
409	C₄²×C₇₉	—	2	2	no	—
410	C₄²×C₇₉	—	2	2	no	—
411	C₄²×C₇₉	—	2	2	no	—
412	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
413	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
414	C₄²×C₇₉	C₂⁴	1	2	yes	—
415	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
416	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
417	C₂³×C₇₉	—	2	2	no	—
418	C₂³×C₇₉	—	4	2	no	—
419	C₂³×C₇₉	—	8	1	no	—
420	C₂³×C₇₉	—	8	1	no	—
421	C₂³×C₇₉	C₂²×D₄	1	2	yes	—
422	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
423	Q₈×C₇₉	—	2	1	no	—
424	Q₈×C₇₉	—	2	1	no	—
425	Q₈×C₇₉	—	2	2	no	—
426	Q₈×C₇₉	—	2	2	no	—
427	Q₈×C₇₉	—	2	2	no	—
428	Q₈×C₇₉	—	2	2	no	—
429	Q₈×C₇₉	—	2	1	no	—
430	Q₈×C₇₉	—	2	2	no	—
431	Q₈×C₇₉	—	2	2	no	—
432	Q₈×C₇₉	—	4	1	no	—
433	Q₈×C₇₉	—	4	4	no	—
434	Q₈×C₇₉	—	4	2	no	—
435	Q₈×C₇₉	—	4	2	no	—
436	Q₈×C₇₉	—	8	1	no	—
437	Q₈×C₇₉	—	8	2	no	—
438	Q₈×C₇₉	—	8	1	no	—
439	Q₈×C₇₉	H(5,𝔽₂)	1	2	yes	—
440	D₄×C₇₉	—	2	4	no	—
441	D₄×C₇₉	—	2	2	no	—
442	D₄×C₇₉	—	2	2	no	—
443	D₄×C₇₉	—	4	1	no	—
444	D₄×C₇₉	—	8	1	no	—
445	D₄×C₇₉	—	8	2	no	—
446	D₄×C₇₉	—	8	2	no	—
447	C₂×C₄×C₇₉	—	2	2	no	—
448	C₂×C₄×C₇₉	—	2	1	no	—
449	C₂×C₄×C₇₉	—	2	1	no	—
450	C₂×C₄×C₇₉	—	2	2	no	—
451	C₂×C₄×C₇₉	—	2	1	no	—
452	C₂×C₄×C₇₉	—	2	2	no	—
453	C₂×C₄×C₇₉	—	2	1	no	—
454	C₂×C₄×C₇₉	—	2	2	no	—
455	C₂×C₄×C₇₉	—	2	2	no	—
456	C₂×C₄×C₇₉	—	2	1	no	—
457	C₂×C₄×C₇₉	—	2	1	no	—
458	C₂×C₄×C₇₉	—	2	2	no	—
459	C₂×C₄×C₇₉	—	2	2	no	—
460	C₂×C₄×C₇₉	—	2	2	no	—
461	C₂×C₄×C₇₉	—	4	1	no	—
462	C₂×C₄×C₇₉	—	4	2	no	—
463	C₂×C₄×C₇₉	—	4	4	no	—
464	C₂×C₄×C₇₉	—	4	2	no	—
465	C₂×C₄×C₇₉	—	8	2	no	—
466	C₂×C₄×C₇₉	—	8	2	no	—
467	C₂×C₄×C₇₉	—	8	2	no	—
468	C₂×C₄×C₇₉	—	8	1	no	—
469	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
470	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
471	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
472	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
473	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
474	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
475	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
476	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
478	C₈×C₇₉	—	2	2	no	—
479	C₈×C₇₉	—	2	2	no	—
480	C₈×C₇₉	—	2	2	no	—
481	C₈×C₇₉	—	2	2	no	—
482	C₂²×C₇₉	—	2	1	no	—
483	C₂²×C₇₉	—	2	1	no	—
484	C₂²×C₇₉	—	2	2	no	—
485	C₂²×C₇₉	—	2	2	no	—
486	C₂²×C₇₉	—	2	2	no	—
487	C₂²×C₇₉	—	4	2	no	—
488	C₂²×C₇₉	—	4	2	no	—
489	C₂²×C₇₉	—	4	2	no	—
490	C₂²×C₇₉	—	16	2	no	—
491	C₂²×C₇₉	#578	1	2	yes	—
492	C₂²×C₇₉	C₂³×D₄	1	1	yes	characteristic
493	C₄×C₇₉	—	2	1	no	—
494	C₄×C₇₉	—	2	1	no	—
495	C₄×C₇₉	—	2	2	no	—
496	C₄×C₇₉	—	2	2	no	—
497	C₄×C₇₉	—	2	1	no	—
498	C₄×C₇₉	—	2	2	no	—
499	C₄×C₇₉	—	2	1	no	—
500	C₄×C₇₉	—	2	1	no	—
501	C₄×C₇₉	—	2	2	no	—
502	C₄×C₇₉	—	4	2	no	—
503	C₄×C₇₉	—	4	2	no	—
504	C₄×C₇₉	—	4	1	no	—
505	C₄×C₇₉	—	4	2	no	—
506	C₄×C₇₉	—	4	2	no	—
507	C₄×C₇₉	—	4	2	no	—
508	C₄×C₇₉	—	4	1	no	—
509	C₄×C₇₉	—	4	1	no	—
510	C₄×C₇₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
511	C₄×C₇₉	#585	1	1	yes	characteristic
512	#62020	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
513	C₂×C₇₉	—	2	2	no	—
514	C₂×C₇₉	—	4	2	no	—
515	C₂×C₇₉	—	8	2	no	—
516	C₂×C₇₉	#3488	1	1	yes	characteristic
517	C₂×C₇₉	C₂×#578	1	1	yes	characteristic
518	C₂×C₇₉	#3586	1	1	yes	characteristic
519	#3561	C₂×C₇₉	1	1	yes	characteristic
520	#3523	C₂×C₇₉	1	1	yes	characteristic, complemented
521	#3398	C₂×C₇₉	1	2	yes	complemented
522	#3377	C₂×C₇₉	1	2	yes	complemented
523	#3313	C₂×C₇₉	1	2	yes	complemented
524	#3312	C₂×C₇₉	1	2	yes	complemented
525	#3296	C₂×C₇₉	1	2	yes	complemented
526	D₄×Q₁₆	C₂×C₇₉	1	2	yes	complemented
527	#3270	C₂×C₇₉	1	2	yes	complemented
528	#3266	C₂×C₇₉	1	2	yes	complemented
529	#3258	C₂×C₇₉	1	2	yes	complemented
530	#3249	C₂×C₇₉	1	1	yes	characteristic, complemented
531	#3223	C₂×C₇₉	1	2	yes	complemented
532	#3215	C₂×C₇₉	1	1	yes	characteristic, complemented
533	#3121	C₂×C₇₉	1	2	yes	complemented
534	#3113	C₂×C₇₉	1	1	yes	characteristic, complemented
535	#3044	C₂×C₇₉	1	2	yes	complemented
536	C₂×#464	C₂×C₇₉	1	1	yes	characteristic, complemented
537	#2992	C₂×C₇₉	1	1	yes	characteristic, complemented
538	C₇₉	#62020	1	1	yes	characteristic, direct product factor, Sylow
539	C₂×#137	C₂²×C₇₉	1	2	yes	—
540	C₂²×Q₁₆	C₂²×C₇₉	1	1	yes	characteristic
541	C₂²×Q₁₆	C₂²×C₇₉	1	2	yes	complemented
542	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
543	#563	—	2	1	no	—
544	#562	—	2	1	no	—
545	#557	—	2	1	no	—
546	#557	C₂²×C₇₉	1	1	yes	characteristic, complemented
547	#557	C₂²×C₇₉	1	1	yes	characteristic, complemented
548	#556	—	2	1	no	—
549	#556	C₂²×C₇₉	1	2	yes	—
550	#556	C₂²×C₇₉	1	1	yes	characteristic, complemented
551	#552	—	2	2	no	—
552	#552	C₂²×C₇₉	1	2	yes	—
553	#551	—	2	2	no	—
554	D₄×Q₈	C₂²×C₇₉	1	2	yes	—
555	D₄×Q₈	C₂²×C₇₉	1	2	yes	—
556	D₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
557	#548	C₂²×C₇₉	1	2	yes	—
558	#546	C₂²×C₇₉	1	2	yes	—
559	#543	—	2	1	no	—
560	#542	—	2	2	no	—
561	#542	C₂²×C₇₉	1	2	yes	—
562	#541	—	2	2	no	—
563	#541	C₂²×C₇₉	1	2	yes	complemented
564	#538	—	2	1	no	—
565	#536	C₂²×C₇₉	1	2	yes	—
566	#533	—	2	1	no	—
567	#533	C₂²×C₇₉	1	1	yes	characteristic
568	#533	C₂²×C₇₉	1	1	yes	characteristic
569	#529	—	2	1	no	—
570	#529	C₂²×C₇₉	1	1	yes	characteristic
571	C₂×#124	C₂²×C₇₉	1	1	yes	characteristic
572	#519	C₂²×C₇₉	1	2	yes	complemented
573	C₂×C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
574	#497	C₂²×C₇₉	1	2	yes	—
575	#497	C₂²×C₇₉	1	2	yes	—
576	#494	C₂²×C₇₉	1	2	yes	complemented
577	#491	C₂²×C₇₉	1	2	yes	complemented
578	#489	C₂²×C₇₉	1	2	yes	—
579	#488	C₂²×C₇₉	1	2	yes	—
580	#485	C₂²×C₇₉	1	2	yes	complemented
581	#483	C₂²×C₇₉	1	2	yes	—
582	#482	C₂²×C₇₉	1	2	yes	—
583	#479	C₂²×C₇₉	1	2	yes	complemented
584	#478	C₂²×C₇₉	1	2	yes	—
585	#477	C₂²×C₇₉	1	2	yes	complemented
586	#477	C₂²×C₇₉	1	2	yes	complemented
587	#475	C₂²×C₇₉	1	1	yes	characteristic, complemented
588	#475	C₂²×C₇₉	1	1	yes	characteristic, complemented
589	#470	C₂²×C₇₉	1	2	yes	complemented
590	#468	C₂²×C₇₉	1	2	yes	—
591	#467	C₂²×C₇₉	1	2	yes	—
592	#467	C₂²×C₇₉	1	2	yes	—
593	#467	C₂²×C₇₉	1	2	yes	complemented
594	#465	C₂²×C₇₉	1	2	yes	—
595	#464	C₂²×C₇₉	1	2	yes	—
596	#464	C₂²×C₇₉	1	2	yes	—
597	#464	C₂²×C₇₉	1	2	yes	—
598	#464	C₂²×C₇₉	1	2	yes	—
599	#464	C₂²×C₇₉	1	2	yes	—
600	#464	C₂²×C₇₉	1	2	yes	—
601	#464	C₂²×C₇₉	1	2	yes	—
602	#464	C₂²×C₇₉	1	2	yes	—
603	#462	C₂²×C₇₉	1	1	yes	characteristic, complemented
604	#462	C₂²×C₇₉	1	1	yes	characteristic, complemented
605	#462	C₂²×C₇₉	1	2	yes	complemented
606	#462	C₂²×C₇₉	1	2	yes	complemented
607	#462	C₂²×C₇₉	1	2	yes	complemented
608	#462	C₂²×C₇₉	1	2	yes	complemented
609	#462	C₂²×C₇₉	1	2	yes	complemented
610	#461	C₂²×C₇₉	1	2	yes	—
611	#452	C₂²×C₇₉	1	2	yes	—
612	#452	C₂²×C₇₉	1	2	yes	—
613	#451	C₂²×C₇₉	1	2	yes	—
614	#451	C₂²×C₇₉	1	2	yes	—
615	#451	C₂²×C₇₉	1	2	yes	complemented
616	#451	C₂²×C₇₉	1	2	yes	complemented
617	#451	C₂²×C₇₉	1	2	yes	complemented
618	#450	C₂²×C₇₉	1	2	yes	—
619	#448	C₂²×C₇₉	1	2	yes	—
620	#446	C₂²×C₇₉	1	2	yes	complemented
621	#441	C₂²×C₇₉	1	2	yes	complemented
622	#441	C₂²×C₇₉	1	2	yes	complemented
623	#441	C₂²×C₇₉	1	2	yes	complemented
624	#440	C₂²×C₇₉	1	2	yes	—
625	C₄×Q₁₆	C₂²×C₇₉	1	2	yes	complemented
626	C₄×SD₁₆	C₂²×C₇₉	1	2	yes	—
627	#435	C₂²×C₇₉	1	2	yes	—
628	#435	C₂²×C₇₉	1	2	yes	complemented
629	C₈×D₄	C₂²×C₇₉	1	2	yes	—
630	#433	C₂²×C₇₉	1	2	yes	complemented
631	#432	C₂²×C₇₉	1	1	yes	characteristic
632	#424	C₂²×C₇₉	1	2	yes	complemented
633	C₂×C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
634	#419	C₂²×C₇₉	1	2	yes	complemented
635	#416	C₂²×C₇₉	1	2	yes	—
636	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
637	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
638	C₂×#41	C₂³×C₇₉	1	2	yes	—
639	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
640	C₂²×Q₈	C₂³×C₇₉	1	2	yes	—
641	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
642	C₂²×Q₈	C₂³×C₇₉	1	2	yes	—
643	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
644	#137	—	4	4	no	—
645	C₂×Q₁₆	—	4	2	no	—
646	C₂×Q₁₆	—	4	4	no	—
647	C₂×Q₁₆	C₂³×C₇₉	1	2	yes	—
648	C₂×Q₁₆	C₂³×C₇₉	1	2	yes	—
649	C₂×Q₁₆	C₂³×C₇₉	1	2	yes	—
650	C₂×Q₁₆	C₂³×C₇₉	1	2	yes	—
651	C₂×Q₁₆	C₂³×C₇₉	1	2	yes	—
652	C₂×Q₁₆	C₂³×C₇₉	1	2	yes	—
653	C₂×Q₁₆	C₂³×C₇₉	1	2	yes	—
654	C₂×Q₁₆	C₂³×C₇₉	1	2	yes	—
655	C₂×SD₁₆	—	4	2	no	—
656	C₂×SD₁₆	C₂³×C₇₉	1	2	yes	—
657	C₂×SD₁₆	C₂³×C₇₉	1	2	yes	—
658	C₂×SD₁₆	C₂³×C₇₉	1	2	yes	—
659	C₂×SD₁₆	C₂³×C₇₉	1	2	yes	—
660	C₂×M₁₆	C₂³×C₇₉	1	2	yes	—
661	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
662	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
663	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
664	C₄⋊Q₈	—	2	1	no	—
665	C₄⋊Q₈	—	2	1	no	—
666	C₄⋊Q₈	—	2	2	no	—
667	C₄⋊Q₈	—	2	2	no	—
668	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
669	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
670	C₄⋊Q₈	C₂³×C₇₉	1	2	yes	—
671	C₄⋊Q₈	C₂³×C₇₉	1	2	yes	—
672	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
673	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
674	#126	—	2	2	no	—
675	#126	—	2	2	no	—
676	#126	—	2	2	no	—
677	#126	—	2	2	no	—
678	#126	—	2	2	no	—
679	#126	—	2	2	no	—
680	#126	—	2	2	no	—
681	#126	D₄×C₇₉	1	2	yes	—
682	#125	—	2	1	no	—
683	#125	—	2	2	no	—
684	#125	—	2	2	no	—
685	#125	—	2	2	no	—
686	#125	—	2	2	no	—
687	#125	—	2	2	no	—
688	#125	—	2	1	no	—
689	#125	—	2	1	no	—
690	#125	D₄×C₇₉	1	1	yes	characteristic
691	#125	C₂³×C₇₉	1	2	yes	—
692	#124	—	2	1	no	—
693	#124	—	2	2	no	—
694	#124	—	2	2	no	—
695	#124	—	2	1	no	—
696	#124	—	2	1	no	—
697	#124	D₄×C₇₉	1	1	yes	characteristic
698	#124	C₂³×C₇₉	1	2	yes	—
699	#124	C₂³×C₇₉	1	2	yes	—
700	#124	C₂³×C₇₉	1	2	yes	—
701	#123	—	2	2	no	—
702	#123	—	2	2	no	—
703	#123	—	2	2	no	—
704	#123	—	2	2	no	—
705	#123	—	2	2	no	—
706	#123	D₄×C₇₉	1	2	yes	—
707	C₂²⋊Q₈	—	2	2	no	—
708	C₂²⋊Q₈	—	2	1	no	—
709	C₂²⋊Q₈	—	2	1	no	—
710	C₂²⋊Q₈	—	2	2	no	—
711	C₂²⋊Q₈	—	2	2	no	—
712	C₂²⋊Q₈	—	2	2	no	—
713	C₂²⋊Q₈	—	2	2	no	—
714	C₂²⋊Q₈	—	2	2	no	—
715	C₂²⋊Q₈	—	2	2	no	—
716	C₂²⋊Q₈	—	2	2	no	—
717	C₂²⋊Q₈	—	2	2	no	—
718	C₂²⋊Q₈	—	2	2	no	—
719	C₂²⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
720	C₂²⋊Q₈	C₂³×C₇₉	1	2	yes	—
721	C₂²⋊Q₈	C₂³×C₇₉	1	2	yes	—
722	C₂²⋊Q₈	C₂³×C₇₉	1	2	yes	—
723	C₂²⋊Q₈	C₂³×C₇₉	1	2	yes	—
724	C₂²⋊Q₈	C₂³×C₇₉	1	2	yes	—
725	#121	—	2	2	no	—
726	#121	—	2	2	no	—
727	#121	D₄×C₇₉	1	1	yes	characteristic
728	#121	C₂³×C₇₉	1	2	yes	—
729	#120	—	2	2	no	—
730	C₄×Q₈	—	2	1	no	—
731	C₄×Q₈	—	2	2	no	—
732	C₄×Q₈	—	2	2	no	—
733	C₄×Q₈	—	2	1	no	—
734	C₄×Q₈	—	2	1	no	—
735	C₄×Q₈	—	2	1	no	—
736	C₄×Q₈	—	2	1	no	—
737	C₄×Q₈	—	2	1	no	—
738	C₄×Q₈	—	2	1	no	—
739	C₄×Q₈	C₂³×C₇₉	1	1	yes	characteristic
740	C₄×Q₈	C₂³×C₇₉	1	1	yes	characteristic
741	C₄×Q₈	C₂³×C₇₉	1	1	yes	characteristic
742	C₄×Q₈	C₂³×C₇₉	1	1	yes	characteristic
743	C₄×Q₈	C₂³×C₇₉	1	2	yes	—
744	C₄×Q₈	C₂³×C₇₉	1	2	yes	—
745	C₄×Q₈	C₂³×C₇₉	1	2	yes	—
746	C₄×Q₈	C₂³×C₇₉	1	2	yes	—
747	C₄×Q₈	C₂³×C₇₉	1	2	yes	—
748	C₄×Q₈	C₂³×C₇₉	1	1	yes	characteristic
749	C₄×D₄	—	2	2	no	—
750	C₄×D₄	—	2	1	no	—
751	C₄×D₄	—	2	2	no	—
752	C₄×D₄	—	2	2	no	—
753	C₄×D₄	C₂³×C₇₉	1	2	yes	—
754	C₄×D₄	C₂³×C₇₉	1	2	yes	—
755	C₄×D₄	C₂³×C₇₉	1	1	yes	characteristic
756	#117	—	2	1	no	—
757	#117	—	2	1	no	—
758	#117	—	2	2	no	—
759	#117	—	2	2	no	—
760	#117	—	2	2	no	—
761	#117	—	2	2	no	—
762	#117	C₂³×C₇₉	1	2	yes	—
763	#117	C₂³×C₇₉	1	2	yes	—
764	C₂×C₄⋊C₄	—	2	1	no	—
765	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
766	C₂×C₂²⋊C₄	—	2	1	no	—
767	C₂×C₂²⋊C₄	—	2	1	no	—
768	C₂×C₂²⋊C₄	—	2	2	no	—
769	C₂×C₄²	—	2	1	no	—
770	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
771	#107	C₂³×C₇₉	1	2	yes	—
772	#107	C₂³×C₇₉	1	2	yes	—
773	#106	C₂³×C₇₉	1	2	yes	—
774	#106	C₂³×C₇₉	1	2	yes	—
775	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
776	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
777	C₄⋊C₈	C₂³×C₇₉	1	1	yes	characteristic
778	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
779	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
780	C₄⋊C₈	C₂³×C₇₉	1	1	yes	characteristic
781	#103	C₂³×C₇₉	1	2	yes	—
782	#103	C₂³×C₇₉	1	2	yes	—
783	#103	C₂³×C₇₉	1	2	yes	—
784	#103	C₂³×C₇₉	1	2	yes	—
785	#103	C₂³×C₇₉	1	2	yes	—
786	#103	C₂³×C₇₉	1	2	yes	—
787	#103	C₂³×C₇₉	1	2	yes	—
788	#103	C₂³×C₇₉	1	2	yes	—
789	#103	C₂³×C₇₉	1	2	yes	—
790	#103	C₂³×C₇₉	1	2	yes	—
791	#103	C₂³×C₇₉	1	2	yes	—
792	#103	C₂³×C₇₉	1	2	yes	—
793	#102	C₂³×C₇₉	1	2	yes	—
794	#102	C₂³×C₇₉	1	2	yes	—
795	#102	C₂³×C₇₉	1	2	yes	—
796	#102	C₂³×C₇₉	1	2	yes	—
797	C₂²⋊C₈	C₂³×C₇₉	1	2	yes	—
798	C₂²⋊C₈	C₂³×C₇₉	1	2	yes	—
799	C₂²⋊C₈	C₂³×C₇₉	1	2	yes	—
800	#97	C₂³×C₇₉	1	2	yes	—
801	#97	C₂³×C₇₉	1	2	yes	—
802	C₄×C₈	C₂³×C₇₉	1	2	yes	—
803	C₂⁴	—	2	1	no	—
804	#41	—	4	2	no	—
805	#41	—	4	2	no	—
806	C₂×Q₈	—	2	1	no	—
807	C₂×Q₈	—	2	2	no	—
808	C₂×Q₈	—	2	1	no	—
809	C₂×Q₈	—	2	1	no	—
810	C₂×Q₈	—	2	2	no	—
811	C₂×Q₈	—	2	1	no	—
812	C₂×Q₈	—	2	2	no	—
813	C₂×Q₈	—	2	4	no	—
814	C₂×Q₈	—	4	1	no	—
815	C₂×Q₈	—	4	2	no	—
816	C₂×Q₈	—	4	1	no	—
817	C₂×Q₈	—	4	2	no	—
818	C₂×Q₈	—	4	1	no	—
819	C₂×Q₈	—	4	2	no	—
820	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
821	C₂×Q₈	C₂⁴×C₇₉	1	2	yes	—
822	C₂×Q₈	C₂⁴×C₇₉	1	2	yes	—
823	C₂×Q₈	C₂⁴×C₇₉	1	1	yes	characteristic
824	C₂×Q₈	C₂⁴×C₇₉	1	2	yes	—
825	C₂×Q₈	C₂⁴×C₇₉	1	1	yes	characteristic
826	C₂×D₄	—	2	2	no	—
827	C₂×D₄	—	2	2	no	—
828	C₂×D₄	—	2	1	no	—
829	C₂×D₄	—	4	1	no	—
830	C₂×D₄	—	4	1	no	—
831	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
832	C₂×D₄	C₂×D₄×C₇₉	1	1	yes	characteristic
833	C₂×D₄	C₂⁴×C₇₉	1	2	yes	—
834	C₂²×C₄	—	2	1	no	—
835	C₂²×C₄	—	2	1	no	—
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	—	2	1	no	—
838	C₂²×C₄	—	2	2	no	—
839	C₂²×C₄	—	2	2	no	—
840	C₂²×C₄	—	2	2	no	—
841	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
842	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
843	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
844	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
845	Q₁₆	—	2	4	no	—
846	Q₁₆	—	2	4	no	—
847	Q₁₆	—	4	2	no	—
848	Q₁₆	—	4	2	no	—
849	Q₁₆	—	4	2	no	—
850	Q₁₆	—	4	2	no	—
851	Q₁₆	—	4	2	no	—
852	Q₁₆	—	4	2	no	—
853	SD₁₆	—	2	4	no	—
854	SD₁₆	—	4	2	no	—
855	SD₁₆	—	4	2	no	—
856	SD₁₆	—	4	2	no	—
857	M₁₆	—	4	2	no	—
858	C₂×C₈	—	4	1	no	—
859	C₂×C₈	—	4	1	no	—
860	C₂×C₈	—	4	2	no	—
861	C₂×C₈	C₂⁴×C₇₉	1	2	yes	—
862	C₂×C₈	C₂⁴×C₇₉	1	2	yes	—
863	C₂×C₈	C₂⁴×C₇₉	1	2	yes	—
864	C₂×C₈	C₂⁴×C₇₉	1	2	yes	—
865	C₄⋊C₄	—	2	1	no	—
866	C₄⋊C₄	—	2	1	no	—
867	C₄⋊C₄	—	2	1	no	—
868	C₄⋊C₄	—	2	1	no	—
869	C₄⋊C₄	—	2	1	no	—
870	C₄⋊C₄	—	2	2	no	—
871	C₄⋊C₄	—	2	2	no	—
872	C₄⋊C₄	—	2	2	no	—
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	—	2	1	no	—
875	C₄⋊C₄	—	2	1	no	—
876	C₄⋊C₄	—	2	2	no	—
877	C₄⋊C₄	—	2	1	no	—
878	C₄⋊C₄	—	2	1	no	—
879	C₄⋊C₄	—	2	2	no	—
880	C₄⋊C₄	—	2	1	no	—
881	C₄⋊C₄	—	2	2	no	—
882	C₄⋊C₄	—	2	2	no	—
883	C₄⋊C₄	—	2	2	no	—
884	C₄⋊C₄	—	2	2	no	—
885	C₄⋊C₄	—	2	1	no	—
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
893	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
894	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
895	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
896	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
897	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
898	C₄⋊C₄	C₂⁴×C₇₉	1	1	yes	characteristic
899	C₄⋊C₄	C₂⁴×C₇₉	1	1	yes	characteristic
900	C₄⋊C₄	C₂⁴×C₇₉	1	2	yes	—
901	C₄⋊C₄	C₂⁴×C₇₉	1	2	yes	—
902	C₂²⋊C₄	—	2	2	no	—
903	C₂²⋊C₄	—	2	2	no	—
904	C₂²⋊C₄	—	2	2	no	—
905	C₂²⋊C₄	—	2	2	no	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	2	no	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	—	2	2	no	—
910	C₂²⋊C₄	—	2	2	no	—
911	C₂²⋊C₄	—	2	2	no	—
912	C₂²⋊C₄	—	2	2	no	—
913	C₂²⋊C₄	—	2	2	no	—
914	C₂²⋊C₄	—	2	2	no	—
915	C₂²⋊C₄	—	2	2	no	—
916	C₂²⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
917	C₂²⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
918	C₂²⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
919	C₂²⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
920	C₂²⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
921	C₄²	—	2	1	no	—
922	C₄²	—	2	1	no	—
923	C₄²	—	2	1	no	—
924	C₄²	—	2	1	no	—
925	C₄²	—	2	2	no	—
926	C₄²	—	2	2	no	—
927	C₄²	—	2	2	no	—
928	C₄²	—	2	2	no	—
929	C₄²	—	2	2	no	—
930	C₄²	—	2	2	no	—
931	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
932	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
933	C₄²	C₂⁴×C₇₉	1	2	yes	—
934	C₄²	C₂⁴×C₇₉	1	1	yes	characteristic
935	C₄²	C₂⁴×C₇₉	1	1	yes	characteristic
936	C₂³	—	2	2	no	—
937	C₂³	—	4	2	no	—
938	C₂³	—	8	1	no	—
939	C₂³	—	8	1	no	—
940	C₂³	C₂²×D₄×C₇₉	1	2	yes	—
941	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
942	Q₈	—	2	1	no	—
943	Q₈	—	2	1	no	—
944	Q₈	—	2	2	no	—
945	Q₈	—	2	2	no	—
946	Q₈	—	2	2	no	—
947	Q₈	—	2	2	no	—
948	Q₈	—	2	1	no	—
949	Q₈	—	2	2	no	—
950	Q₈	—	2	2	no	—
951	Q₈	—	4	1	no	—
952	Q₈	—	4	4	no	—
953	Q₈	—	4	2	no	—
954	Q₈	—	4	2	no	—
955	Q₈	—	8	1	no	—
956	Q₈	—	8	2	no	—
957	Q₈	—	8	1	no	—
958	Q₈	H(5,𝔽₂)×C₇₉	1	2	yes	—
959	D₄	—	2	4	no	—
960	D₄	—	2	2	no	—
961	D₄	—	2	2	no	—
962	D₄	—	4	1	no	—
963	D₄	—	8	1	no	—
964	D₄	—	8	2	no	—
965	D₄	—	8	2	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	1	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	4	1	no	—
981	C₂×C₄	—	4	2	no	—
982	C₂×C₄	—	4	4	no	—
983	C₂×C₄	—	4	2	no	—
984	C₂×C₄	—	8	2	no	—
985	C₂×C₄	—	8	2	no	—
986	C₂×C₄	—	8	2	no	—
987	C₂×C₄	—	8	1	no	—
988	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
989	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
990	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
991	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
992	C₂×C₄	C₂²×D₄×C₇₉	1	2	yes	—
993	C₂×C₄	C₂²×D₄×C₇₉	1	2	yes	—
994	C₂×C₄	C₂²×D₄×C₇₉	1	2	yes	—
995	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
996	C₂×C₄	C₂⁵×C₇₉	1	1	yes	characteristic
997	C₈	—	2	2	no	—
998	C₈	—	2	2	no	—
999	C₈	—	2	2	no	—
1000	C₈	—	2	2	no	—
1001	C₂²	—	2	1	no	—
1002	C₂²	—	2	1	no	—
1003	C₂²	—	2	2	no	—
1004	C₂²	—	2	2	no	—
1005	C₂²	—	2	2	no	—
1006	C₂²	—	4	2	no	—
1007	C₂²	—	4	2	no	—
1008	C₂²	—	4	2	no	—
1009	C₂²	—	16	2	no	—
1010	C₂²	#578×C₇₉	1	2	yes	—
1011	C₂²	C₂³×D₄×C₇₉	1	1	yes	characteristic
1012	C₄	—	2	1	no	—
1013	C₄	—	2	1	no	—
1014	C₄	—	2	2	no	—
1015	C₄	—	2	1	no	—
1016	C₄	—	2	1	no	—
1017	C₄	—	2	2	no	—
1018	C₄	—	2	2	no	—
1019	C₄	—	2	1	no	—
1020	C₄	—	2	2	no	—
1021	C₄	—	4	1	no	—
1022	C₄	—	4	1	no	—
1023	C₄	—	4	2	no	—
1024	C₄	—	4	2	no	—
1025	C₄	—	4	1	no	—
1026	C₄	—	4	2	no	—
1027	C₄	—	4	2	no	—
1028	C₄	—	4	2	no	—
1029	C₄	C₂×H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
1030	C₄	#585×C₇₉	1	1	yes	characteristic
1031	C₂	—	2	2	no	—
1032	C₂	—	4	2	no	—
1033	C₂	—	8	2	no	—
1034	C₂	C₇₉×#3488	1	1	yes	characteristic
1035	C₂	C₂×#578×C₇₉	1	1	yes	characteristic
1036	C₂	C₇₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₉
prime radical	C₇₉×#3561	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₉ ◁ #529×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇₉×#3523	C₂	semidirect
3. C₇₉×#3398	C₂	semidirect
4. C₇₉×#3377	C₂	semidirect
5. C₇₉×#3313	C₂	semidirect
6. C₇₉×#3312	C₂	semidirect
7. C₇₉×#3296	C₂	semidirect
8. D₄×Q₁₆×C₇₉	C₂	semidirect
9. C₇₉×#3270	C₂	semidirect
10. C₇₉×#3266	C₂	semidirect
11. C₇₉×#3258	C₂	semidirect
12. C₇₉×#3249	C₂	semidirect
13. C₇₉×#3223	C₂	semidirect
14. C₇₉×#3215	C₂	semidirect
15. C₇₉×#3121	C₂	semidirect
16. C₇₉×#3113	C₂	semidirect
17. C₇₉×#3044	C₂	semidirect
18. C₂×#464×C₇₉	C₂	semidirect
19. C₇₉×#2992	C₂	semidirect
22. C₂²×Q₁₆×C₇₉	C₂²	semidirect
27. #557×C₇₉	C₂²	semidirect
28. #557×C₇₉	C₂²	semidirect
31. #556×C₇₉	C₂²	semidirect
37. D₄×Q₈×C₇₉	C₂²	semidirect
44. #541×C₇₉	C₂²	semidirect
53. #519×C₇₉	C₂²	semidirect
57. #494×C₇₉	C₂²	semidirect
58. #491×C₇₉	C₂²	semidirect
61. #485×C₇₉	C₂²	semidirect
64. #479×C₇₉	C₂²	semidirect
66. #477×C₇₉	C₂²	semidirect
67. #477×C₇₉	C₂²	semidirect
68. #475×C₇₉	C₂²	semidirect
69. #475×C₇₉	C₂²	semidirect
70. #470×C₇₉	C₂²	semidirect
74. #467×C₇₉	C₂²	semidirect
84. #462×C₇₉	C₂²	semidirect
85. #462×C₇₉	C₂²	semidirect
86. #462×C₇₉	C₂²	semidirect
87. #462×C₇₉	C₂²	semidirect
88. #462×C₇₉	C₂²	semidirect
89. #462×C₇₉	C₂²	semidirect
90. #462×C₇₉	C₂²	semidirect
96. #451×C₇₉	C₂²	semidirect
97. #451×C₇₉	C₂²	semidirect
98. #451×C₇₉	C₂²	semidirect
101. #446×C₇₉	C₂²	semidirect
102. #441×C₇₉	C₂²	semidirect
103. #441×C₇₉	C₂²	semidirect
104. #441×C₇₉	C₂²	semidirect
106. C₄×Q₁₆×C₇₉	C₂²	semidirect
109. #435×C₇₉	C₂²	semidirect
111. #433×C₇₉	C₂²	semidirect
113. #424×C₇₉	C₂²	semidirect
115. #419×C₇₉	C₂²	semidirect
512. #62020	C₇₉	direct (N × H)
520. #3523	C₂×C₇₉	semidirect
521. #3398	C₂×C₇₉	semidirect
522. #3377	C₂×C₇₉	semidirect
523. #3313	C₂×C₇₉	semidirect
524. #3312	C₂×C₇₉	semidirect
525. #3296	C₂×C₇₉	semidirect
526. D₄×Q₁₆	C₂×C₇₉	semidirect
527. #3270	C₂×C₇₉	semidirect
528. #3266	C₂×C₇₉	semidirect
529. #3258	C₂×C₇₉	semidirect
530. #3249	C₂×C₇₉	semidirect
531. #3223	C₂×C₇₉	semidirect
532. #3215	C₂×C₇₉	semidirect
533. #3121	C₂×C₇₉	semidirect
534. #3113	C₂×C₇₉	semidirect
535. #3044	C₂×C₇₉	semidirect
536. C₂×#464	C₂×C₇₉	semidirect
537. #2992	C₂×C₇₉	semidirect
538. C₇₉	#62020	direct (N × H)
541. C₂²×Q₁₆	C₂²×C₇₉	semidirect
546. #557	C₂²×C₇₉	semidirect
547. #557	C₂²×C₇₉	semidirect
550. #556	C₂²×C₇₉	semidirect
556. D₄×Q₈	C₂²×C₇₉	semidirect
563. #541	C₂²×C₇₉	semidirect
572. #519	C₂²×C₇₉	semidirect
576. #494	C₂²×C₇₉	semidirect
577. #491	C₂²×C₇₉	semidirect
580. #485	C₂²×C₇₉	semidirect
583. #479	C₂²×C₇₉	semidirect
585. #477	C₂²×C₇₉	semidirect
586. #477	C₂²×C₇₉	semidirect
587. #475	C₂²×C₇₉	semidirect
588. #475	C₂²×C₇₉	semidirect
589. #470	C₂²×C₇₉	semidirect
593. #467	C₂²×C₇₉	semidirect
603. #462	C₂²×C₇₉	semidirect
604. #462	C₂²×C₇₉	semidirect
605. #462	C₂²×C₇₉	semidirect
606. #462	C₂²×C₇₉	semidirect
607. #462	C₂²×C₇₉	semidirect
608. #462	C₂²×C₇₉	semidirect
609. #462	C₂²×C₇₉	semidirect
615. #451	C₂²×C₇₉	semidirect
616. #451	C₂²×C₇₉	semidirect
617. #451	C₂²×C₇₉	semidirect
620. #446	C₂²×C₇₉	semidirect
621. #441	C₂²×C₇₉	semidirect
622. #441	C₂²×C₇₉	semidirect
623. #441	C₂²×C₇₉	semidirect
625. C₄×Q₁₆	C₂²×C₇₉	semidirect
628. #435	C₂²×C₇₉	semidirect
630. #433	C₂²×C₇₉	semidirect
632. #424	C₂²×C₇₉	semidirect
634. #419	C₂²×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₇₉×#3561	2
C₇₉×#3523	2
C₇₉×#3398	2
C₇₉×#3377	2
C₇₉×#3313	2
C₇₉×#3312	2
C₇₉×#3296	2
D₄×Q₁₆×C₇₉	2
C₇₉×#3270	2
C₇₉×#3266	2
C₇₉×#3258	2
C₇₉×#3249	2
C₇₉×#3223	2
C₇₉×#3215	2
C₇₉×#3121	2
C₇₉×#3113	2
C₇₉×#3044	2
C₂×#464×C₇₉	2
C₇₉×#2992	2
#62020	79

Subgroups — C79×#62020 #34173709

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#62020 #34173709