Subgroups — C₇₉×#25787 #34137476

Order 20224.

1568 conjugacy classes of subgroups.

The subgroup lattice has 828 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×#497×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#496×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#465×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#452×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#449×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#2432	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#2431	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#2015	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#2014	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#2013	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₉×#2012	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₉×#1972	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₉×#1971	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#1752	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	C₂×#135×C₇₉	—	2	4	no	—
19	C₂×#135×C₇₉	—	2	4	no	—
20	C₂×#135×C₇₉	—	2	4	no	—
21	C₂²×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
22	C₂²×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
23	C₂²×SD₁₆×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×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
28	C₂²×D₈×C₇₉	C₂²	1	1	yes	characteristic
29	C₂²×D₈×C₇₉	C₂²	1	1	yes	characteristic
30	C₂³×C₈×C₇₉	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
32	C₂×#127×C₇₉	C₂²	1	1	yes	characteristic
33	C₂×#124×C₇₉	C₂²	1	1	yes	characteristic
34	C₂×#124×C₇₉	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
36	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
37	#497×C₇₉	—	2	4	no	—
38	#496×C₇₉	—	2	4	no	—
39	#465×C₇₉	—	2	4	no	—
40	#452×C₇₉	—	2	4	no	—
41	#449×C₇₉	—	2	4	no	—
42	C₂×#106×C₇₉	C₂²	1	1	yes	characteristic
43	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
44	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
45	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
46	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
47	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
48	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
49	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
50	C₂×#97×C₇₉	C₂²	1	1	yes	characteristic
51	C₂×#97×C₇₉	C₂²	1	1	yes	characteristic
52	#394×C₇₉	—	2	2	no	—
53	#392×C₇₉	—	2	2	no	—
54	#391×C₇₉	C₂²	1	1	yes	characteristic
55	#391×C₇₉	C₂²	1	1	yes	characteristic
56	#390×C₇₉	C₂²	1	1	yes	characteristic
57	#390×C₇₉	C₂²	1	1	yes	characteristic
58	#386×C₇₉	—	2	2	no	—
59	#385×C₇₉	—	2	2	no	—
60	C₄×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
61	#336×C₇₉	C₂²	1	1	yes	characteristic
62	#336×C₇₉	C₂²	1	1	yes	characteristic
63	C₂×#41×C₇₉	—	2	2	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	—	2	2	no	—
69	C₂×#41×C₇₉	—	2	2	no	—
70	C₂×#41×C₇₉	—	2	2	no	—
71	C₂×#41×C₇₉	—	4	1	no	—
72	C₂×#41×C₇₉	—	4	1	no	—
73	C₂×#41×C₇₉	—	4	1	no	—
74	C₂×#41×C₇₉	—	4	1	no	—
75	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
76	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
77	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
78	C₂²×D₄×C₇₉	—	2	1	no	—
79	C₂²×D₄×C₇₉	—	2	1	no	—
80	C₂²×D₄×C₇₉	—	2	1	no	—
81	C₂²×D₄×C₇₉	—	2	2	no	—
82	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₇₉	—	2	1	no	—
86	C₂³×C₄×C₇₉	—	2	1	no	—
87	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
88	#135×C₇₉	—	2	32	no	—
89	C₂×Q₁₆×C₇₉	—	2	2	no	—
90	C₂×Q₁₆×C₇₉	—	2	2	no	—
91	C₂×Q₁₆×C₇₉	—	2	2	no	—
92	C₂×Q₁₆×C₇₉	—	2	2	no	—
93	C₂×Q₁₆×C₇₉	—	4	1	no	—
94	C₂×Q₁₆×C₇₉	D₄	1	4	yes	complemented
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	—	2	2	no	—
100	C₂×SD₁₆×C₇₉	—	2	2	no	—
101	C₂×SD₁₆×C₇₉	—	2	2	no	—
102	C₂×SD₁₆×C₇₉	—	2	2	no	—
103	C₂×SD₁₆×C₇₉	—	2	2	no	—
104	C₂×SD₁₆×C₇₉	—	2	2	no	—
105	C₂×SD₁₆×C₇₉	—	2	2	no	—
106	C₂×SD₁₆×C₇₉	—	2	2	no	—
107	C₂×SD₁₆×C₇₉	—	2	2	no	—
108	C₂×SD₁₆×C₇₉	—	4	1	no	—
109	C₂×SD₁₆×C₇₉	—	4	1	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	—	4	1	no	—
115	C₂×D₈×C₇₉	D₄	1	4	yes	complemented
116	C₂²×C₈×C₇₉	—	2	2	no	—
117	C₂²×C₈×C₇₉	—	2	2	no	—
118	C₂²×C₈×C₇₉	D₄	1	4	yes	complemented
119	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
121	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
122	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
123	C₄⋊Q₈×C₇₉	—	2	2	no	—
124	C₄⋊Q₈×C₇₉	—	4	1	no	—
125	#127×C₇₉	—	2	2	no	—
126	#127×C₇₉	—	4	1	no	—
127	#124×C₇₉	—	2	2	no	—
128	#124×C₇₉	—	2	2	no	—
129	#124×C₇₉	—	4	1	no	—
130	#124×C₇₉	—	4	1	no	—
131	C₂²⋊Q₈×C₇₉	—	2	2	no	—
132	C₂²⋊Q₈×C₇₉	—	2	2	no	—
133	#121×C₇₉	—	2	2	no	—
134	#121×C₇₉	—	2	2	no	—
135	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
136	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
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	2	no	—
142	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
143	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
144	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
145	C₂×C₂²⋊C₄×C₇₉	D₄	1	2	yes	—
146	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
147	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
148	#106×C₇₉	—	2	2	no	—
149	#103×C₇₉	—	2	2	no	—
150	#103×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	C₂²⋊C₈×C₇₉	D₄	1	4	yes	complemented
156	#97×C₇₉	—	2	2	no	—
157	#97×C₇₉	—	2	2	no	—
158	#95×C₇₉	—	2	2	no	—
159	#95×C₇₉	—	2	2	no	—
160	#95×C₇₉	D₄	1	2	yes	—
161	C₂⁴×C₇₉	—	2	1	no	—
162	C₂⁴×C₇₉	—	2	1	no	—
163	C₂⁴×C₇₉	—	2	1	no	—
164	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
165	#41×C₇₉	—	2	8	no	—
166	#41×C₇₉	—	2	8	no	—
167	#41×C₇₉	—	4	4	no	—
168	#41×C₇₉	—	4	4	no	—
169	#41×C₇₉	—	4	4	no	—
170	#41×C₇₉	—	4	4	no	—
171	#41×C₇₉	—	4	4	no	—
172	#41×C₇₉	—	4	4	no	—
173	C₂×Q₈×C₇₉	—	2	1	no	—
174	C₂×Q₈×C₇₉	—	2	1	no	—
175	C₂×Q₈×C₇₉	—	2	1	no	—
176	C₂×Q₈×C₇₉	—	2	1	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	—	2	1	no	—
183	C₂×Q₈×C₇₉	—	2	1	no	—
184	C₂×Q₈×C₇₉	—	2	1	no	—
185	C₂×Q₈×C₇₉	—	2	1	no	—
186	C₂×Q₈×C₇₉	—	2	1	no	—
187	C₂×Q₈×C₇₉	—	2	1	no	—
188	C₂×Q₈×C₇₉	—	2	1	no	—
189	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
190	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
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	—	4	2	no	—
208	C₂×D₄×C₇₉	—	4	2	no	—
209	C₂×D₄×C₇₉	—	4	4	no	—
210	C₂×D₄×C₇₉	—	4	4	no	—
211	C₂×D₄×C₇₉	—	4	2	no	—
212	C₂×D₄×C₇₉	—	4	2	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	—	8	2	no	—
217	C₂×D₄×C₇₉	—	8	2	no	—
218	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
219	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
220	C₂²×C₄×C₇₉	—	2	1	no	—
221	C₂²×C₄×C₇₉	—	2	1	no	—
222	C₂²×C₄×C₇₉	—	2	1	no	—
223	C₂²×C₄×C₇₉	—	2	1	no	—
224	C₂²×C₄×C₇₉	—	2	1	no	—
225	C₂²×C₄×C₇₉	—	2	1	no	—
226	C₂²×C₄×C₇₉	—	2	1	no	—
227	C₂²×C₄×C₇₉	—	2	1	no	—
228	C₂²×C₄×C₇₉	—	2	1	no	—
229	C₂²×C₄×C₇₉	—	4	2	no	—
230	C₂²×C₄×C₇₉	—	4	2	no	—
231	C₂²×C₄×C₇₉	—	4	2	no	—
232	C₂²×C₄×C₇₉	—	4	2	no	—
233	C₂²×C₄×C₇₉	—	4	2	no	—
234	C₂²×C₄×C₇₉	—	4	2	no	—
235	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
236	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
237	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
239	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
240	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
241	Q₁₆×C₇₉	—	2	8	no	—
242	Q₁₆×C₇₉	—	4	4	no	—
243	SD₁₆×C₇₉	—	2	8	no	—
244	SD₁₆×C₇₉	—	2	8	no	—
245	SD₁₆×C₇₉	—	4	4	no	—
246	SD₁₆×C₇₉	—	4	4	no	—
247	SD₁₆×C₇₉	—	4	4	no	—
248	D₈×C₇₉	—	2	8	no	—
249	D₈×C₇₉	—	4	4	no	—
250	C₂×C₈×C₇₉	—	2	8	no	—
251	C₂×C₈×C₇₉	—	2	1	no	—
252	C₂×C₈×C₇₉	—	2	1	no	—
253	C₂×C₈×C₇₉	—	2	1	no	—
254	C₂×C₈×C₇₉	—	2	1	no	—
255	C₂×C₈×C₇₉	—	2	1	no	—
256	C₂×C₈×C₇₉	—	2	1	no	—
257	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
258	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
259	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
260	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
261	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
262	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
263	C₄⋊C₄×C₇₉	—	2	1	no	—
264	C₄⋊C₄×C₇₉	—	2	1	no	—
265	C₄⋊C₄×C₇₉	—	2	1	no	—
266	C₄⋊C₄×C₇₉	—	2	1	no	—
267	C₄⋊C₄×C₇₉	—	4	4	no	—
268	C₄⋊C₄×C₇₉	—	4	2	no	—
269	C₂²⋊C₄×C₇₉	—	4	2	no	—
270	C₂²⋊C₄×C₇₉	—	4	4	no	—
271	C₂²⋊C₄×C₇₉	—	4	4	no	—
272	C₂²⋊C₄×C₇₉	—	4	4	no	—
273	C₂²⋊C₄×C₇₉	—	4	2	no	—
274	C₂²⋊C₄×C₇₉	—	4	2	no	—
275	C₂²⋊C₄×C₇₉	—	8	2	no	—
276	C₄²×C₇₉	—	2	1	no	—
277	C₄²×C₇₉	—	2	1	no	—
278	C₄²×C₇₉	—	2	1	no	—
279	C₄²×C₇₉	—	2	1	no	—
280	C₂³×C₇₉	—	2	1	no	—
281	C₂³×C₇₉	—	2	1	no	—
282	C₂³×C₇₉	—	2	2	no	—
283	C₂³×C₇₉	—	2	2	no	—
284	C₂³×C₇₉	—	2	2	no	—
285	C₂³×C₇₉	—	2	2	no	—
286	C₂³×C₇₉	—	4	1	no	—
287	C₂³×C₇₉	—	4	1	no	—
288	C₂³×C₇₉	—	4	1	no	—
289	C₂³×C₇₉	—	4	1	no	—
290	C₂³×C₇₉	—	4	2	no	—
291	C₂³×C₇₉	—	4	2	no	—
292	C₂³×C₇₉	—	4	2	no	—
293	C₂³×C₇₉	—	4	2	no	—
294	C₂³×C₇₉	—	4	1	no	—
295	C₂³×C₇₉	—	4	1	no	—
296	C₂³×C₇₉	—	4	1	no	—
297	C₂³×C₇₉	—	4	2	no	—
298	C₂³×C₇₉	—	4	2	no	—
299	C₂³×C₇₉	#127	1	2	yes	—
300	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
301	Q₈×C₇₉	—	2	2	no	—
302	Q₈×C₇₉	—	2	2	no	—
303	Q₈×C₇₉	—	2	2	no	—
304	Q₈×C₇₉	—	2	2	no	—
305	Q₈×C₇₉	—	4	1	no	—
306	Q₈×C₇₉	—	4	1	no	—
307	Q₈×C₇₉	—	4	1	no	—
308	Q₈×C₇₉	—	4	1	no	—
309	Q₈×C₇₉	—	4	1	no	—
310	Q₈×C₇₉	—	4	1	no	—
311	Q₈×C₇₉	—	4	1	no	—
312	Q₈×C₇₉	—	4	1	no	—
313	D₄×C₇₉	—	2	2	no	—
314	D₄×C₇₉	—	2	2	no	—
315	D₄×C₇₉	—	2	2	no	—
316	D₄×C₇₉	—	2	2	no	—
317	D₄×C₇₉	—	4	8	no	—
318	D₄×C₇₉	—	4	8	no	—
319	D₄×C₇₉	—	4	1	no	—
320	D₄×C₇₉	—	4	1	no	—
321	D₄×C₇₉	—	4	1	no	—
322	D₄×C₇₉	—	4	1	no	—
323	D₄×C₇₉	—	4	1	no	—
324	D₄×C₇₉	—	4	1	no	—
325	D₄×C₇₉	—	4	1	no	—
326	D₄×C₇₉	—	4	1	no	—
327	D₄×C₇₉	—	8	8	no	—
328	D₄×C₇₉	—	8	4	no	—
329	C₂×C₄×C₇₉	—	2	1	no	—
330	C₂×C₄×C₇₉	—	2	1	no	—
331	C₂×C₄×C₇₉	—	2	2	no	—
332	C₂×C₄×C₇₉	—	2	2	no	—
333	C₂×C₄×C₇₉	—	2	2	no	—
334	C₂×C₄×C₇₉	—	2	2	no	—
335	C₂×C₄×C₇₉	—	2	2	no	—
336	C₂×C₄×C₇₉	—	2	2	no	—
337	C₂×C₄×C₇₉	—	2	2	no	—
338	C₂×C₄×C₇₉	—	2	2	no	—
339	C₂×C₄×C₇₉	—	2	2	no	—
340	C₂×C₄×C₇₉	—	2	2	no	—
341	C₂×C₄×C₇₉	—	2	2	no	—
342	C₂×C₄×C₇₉	—	2	2	no	—
343	C₂×C₄×C₇₉	—	4	8	no	—
344	C₂×C₄×C₇₉	—	4	8	no	—
345	C₂×C₄×C₇₉	—	4	1	no	—
346	C₂×C₄×C₇₉	—	4	1	no	—
347	C₂×C₄×C₇₉	—	4	1	no	—
348	C₂×C₄×C₇₉	—	4	1	no	—
349	C₂×C₄×C₇₉	—	4	1	no	—
350	C₂×C₄×C₇₉	—	4	1	no	—
351	C₂×C₄×C₇₉	—	4	1	no	—
352	C₂×C₄×C₇₉	—	4	1	no	—
353	C₂×C₄×C₇₉	—	4	1	no	—
354	C₂×C₄×C₇₉	—	4	2	no	—
355	C₂×C₄×C₇₉	—	4	2	no	—
356	C₂×C₄×C₇₉	#127	1	2	yes	—
357	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
362	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
363	C₈×C₇₉	—	2	2	no	—
364	C₈×C₇₉	—	2	2	no	—
365	C₈×C₇₉	—	2	2	no	—
366	C₈×C₇₉	#120	1	4	yes	—
367	C₂²×C₇₉	—	2	2	no	—
368	C₂²×C₇₉	—	2	2	no	—
369	C₂²×C₇₉	—	2	2	no	—
370	C₂²×C₇₉	—	4	2	no	—
371	C₂²×C₇₉	—	4	2	no	—
372	C₂²×C₇₉	—	4	2	no	—
373	C₂²×C₇₉	—	4	2	no	—
374	C₂²×C₇₉	—	4	4	no	—
375	C₂²×C₇₉	—	4	4	no	—
376	C₂²×C₇₉	—	8	1	no	—
377	C₂²×C₇₉	—	8	1	no	—
378	C₂²×C₇₉	—	8	1	no	—
379	C₂²×C₇₉	—	8	1	no	—
380	C₂²×C₇₉	—	8	2	no	—
381	C₂²×C₇₉	—	8	2	no	—
382	C₂²×C₇₉	—	8	1	no	—
383	C₂²×C₇₉	—	8	1	no	—
384	C₂²×C₇₉	—	8	1	no	—
385	C₂²×C₇₉	—	8	2	no	—
386	C₂²×C₇₉	—	8	2	no	—
387	C₂²×C₇₉	C₂×#127	1	1	yes	characteristic
388	C₂²×C₇₉	D₄²	1	1	yes	characteristic
389	C₂²×C₇₉	D₄²	1	1	yes	characteristic
390	C₂²×C₇₉	#575	1	2	yes	—
391	C₂²×C₇₉	#577	1	2	yes	—
392	C₄×C₇₉	—	2	2	no	—
393	C₄×C₇₉	—	4	2	no	—
394	C₄×C₇₉	—	4	2	no	—
395	C₄×C₇₉	—	4	2	no	—
396	C₄×C₇₉	—	4	2	no	—
397	C₄×C₇₉	—	8	1	no	—
398	C₄×C₇₉	—	8	1	no	—
399	C₄×C₇₉	—	8	1	no	—
400	C₄×C₇₉	C₂×#120	1	1	yes	characteristic
401	C₄×C₇₉	#535	1	1	yes	characteristic
402	C₄×C₇₉	D₄²	1	1	yes	characteristic
403	C₄×C₇₉	D₄²	1	1	yes	characteristic
404	#25787	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
405	C₂×C₇₉	—	4	2	no	—
406	C₂×C₇₉	—	8	2	no	—
407	C₂×C₇₉	—	8	2	no	—
408	C₂×C₇₉	—	16	1	no	—
409	C₂×C₇₉	#2433	1	1	yes	characteristic
410	C₂×C₇₉	#3150	1	1	yes	characteristic
411	C₂×C₇₉	#3154	1	1	yes	characteristic
412	C₂×C₇₉	#3267	1	2	yes	—
413	C₂×C₇₉	#3271	1	2	yes	—
414	C₂²×#135	C₂×C₇₉	1	1	yes	characteristic, complemented
415	C₂×#497	C₂×C₇₉	1	1	yes	characteristic, complemented
416	C₂×#496	C₂×C₇₉	1	1	yes	characteristic, complemented
417	C₂×#465	C₂×C₇₉	1	1	yes	characteristic, complemented
418	C₂×#452	C₂×C₇₉	1	1	yes	characteristic, complemented
419	C₂×#449	C₂×C₇₉	1	1	yes	characteristic, complemented
420	#2432	C₂×C₇₉	1	1	yes	characteristic, complemented
421	#2431	C₂×C₇₉	1	1	yes	characteristic, complemented
422	#2015	C₂×C₇₉	1	1	yes	characteristic, complemented
423	#2014	C₂×C₇₉	1	1	yes	characteristic, complemented
424	#2013	C₂×C₇₉	1	1	yes	characteristic, complemented
425	#2012	C₂×C₇₉	1	1	yes	characteristic, complemented
426	#1972	C₂×C₇₉	1	1	yes	characteristic, complemented
427	#1971	C₂×C₇₉	1	1	yes	characteristic, complemented
428	#1752	C₂×C₇₉	1	1	yes	characteristic, complemented
429	C₇₉	#25787	1	1	yes	characteristic, direct product factor, Sylow
430	C₂²×#41	C₂²×C₇₉	1	1	yes	characteristic
431	C₂²×#41	C₂²×C₇₉	1	1	yes	characteristic
432	C₂×#135	—	2	4	no	—
433	C₂×#135	—	2	4	no	—
434	C₂×#135	—	2	4	no	—
435	C₂²×Q₁₆	C₂²×C₇₉	1	1	yes	characteristic
436	C₂²×Q₁₆	C₂²×C₇₉	1	1	yes	characteristic
437	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
438	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
439	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
440	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
441	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
442	C₂²×D₈	C₂²×C₇₉	1	1	yes	characteristic
443	C₂²×D₈	C₂²×C₇₉	1	1	yes	characteristic
444	C₂³×C₈	C₂²×C₇₉	1	1	yes	characteristic
445	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
446	C₂×#127	C₂²×C₇₉	1	1	yes	characteristic
447	C₂×#124	C₂²×C₇₉	1	1	yes	characteristic
448	C₂×#124	C₂²×C₇₉	1	1	yes	characteristic
449	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
450	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
451	#497	—	2	4	no	—
452	#496	—	2	4	no	—
453	#465	—	2	4	no	—
454	#452	—	2	4	no	—
455	#449	—	2	4	no	—
456	C₂×#106	C₂²×C₇₉	1	1	yes	characteristic
457	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
458	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
459	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
460	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
461	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
462	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
463	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
464	C₂×#97	C₂²×C₇₉	1	1	yes	characteristic
465	C₂×#97	C₂²×C₇₉	1	1	yes	characteristic
466	#394	—	2	2	no	—
467	#392	—	2	2	no	—
468	#391	C₂²×C₇₉	1	1	yes	characteristic
469	#391	C₂²×C₇₉	1	1	yes	characteristic
470	#390	C₂²×C₇₉	1	1	yes	characteristic
471	#390	C₂²×C₇₉	1	1	yes	characteristic
472	#386	—	2	2	no	—
473	#385	—	2	2	no	—
474	C₄×C₂²⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
475	#336	C₂²×C₇₉	1	1	yes	characteristic
476	#336	C₂²×C₇₉	1	1	yes	characteristic
477	C₂×#41	—	2	2	no	—
478	C₂×#41	—	2	2	no	—
479	C₂×#41	—	2	2	no	—
480	C₂×#41	—	2	2	no	—
481	C₂×#41	—	2	2	no	—
482	C₂×#41	—	2	2	no	—
483	C₂×#41	—	2	2	no	—
484	C₂×#41	—	2	2	no	—
485	C₂×#41	—	4	1	no	—
486	C₂×#41	—	4	1	no	—
487	C₂×#41	—	4	1	no	—
488	C₂×#41	—	4	1	no	—
489	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
490	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
491	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
492	C₂²×D₄	—	2	1	no	—
493	C₂²×D₄	—	2	1	no	—
494	C₂²×D₄	—	2	1	no	—
495	C₂²×D₄	—	2	2	no	—
496	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
497	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
498	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
499	C₂³×C₄	—	2	1	no	—
500	C₂³×C₄	—	2	1	no	—
501	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
502	#135	—	2	32	no	—
503	C₂×Q₁₆	—	2	2	no	—
504	C₂×Q₁₆	—	2	2	no	—
505	C₂×Q₁₆	—	2	2	no	—
506	C₂×Q₁₆	—	2	2	no	—
507	C₂×Q₁₆	—	4	1	no	—
508	C₂×Q₁₆	D₄×C₇₉	1	4	yes	complemented
509	C₂×SD₁₆	—	2	2	no	—
510	C₂×SD₁₆	—	2	2	no	—
511	C₂×SD₁₆	—	2	2	no	—
512	C₂×SD₁₆	—	2	2	no	—
513	C₂×SD₁₆	—	2	2	no	—
514	C₂×SD₁₆	—	2	2	no	—
515	C₂×SD₁₆	—	2	2	no	—
516	C₂×SD₁₆	—	2	2	no	—
517	C₂×SD₁₆	—	2	2	no	—
518	C₂×SD₁₆	—	2	2	no	—
519	C₂×SD₁₆	—	2	2	no	—
520	C₂×SD₁₆	—	2	2	no	—
521	C₂×SD₁₆	—	2	2	no	—
522	C₂×SD₁₆	—	4	1	no	—
523	C₂×SD₁₆	—	4	1	no	—
524	C₂×D₈	—	2	2	no	—
525	C₂×D₈	—	2	2	no	—
526	C₂×D₈	—	2	2	no	—
527	C₂×D₈	—	2	2	no	—
528	C₂×D₈	—	4	1	no	—
529	C₂×D₈	D₄×C₇₉	1	4	yes	complemented
530	C₂²×C₈	—	2	2	no	—
531	C₂²×C₈	—	2	2	no	—
532	C₂²×C₈	D₄×C₇₉	1	4	yes	complemented
533	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
534	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
535	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
536	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
537	C₄⋊Q₈	—	2	2	no	—
538	C₄⋊Q₈	—	4	1	no	—
539	#127	—	2	2	no	—
540	#127	—	4	1	no	—
541	#124	—	2	2	no	—
542	#124	—	2	2	no	—
543	#124	—	4	1	no	—
544	#124	—	4	1	no	—
545	C₂²⋊Q₈	—	2	2	no	—
546	C₂²⋊Q₈	—	2	2	no	—
547	#121	—	2	2	no	—
548	#121	—	2	2	no	—
549	C₂×C₄⋊C₄	—	2	1	no	—
550	C₂×C₄⋊C₄	—	2	2	no	—
551	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
552	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
553	C₂×C₂²⋊C₄	—	2	1	no	—
554	C₂×C₂²⋊C₄	—	2	1	no	—
555	C₂×C₂²⋊C₄	—	2	2	no	—
556	C₂×C₂²⋊C₄	—	2	2	no	—
557	C₂×C₂²⋊C₄	—	2	2	no	—
558	C₂×C₂²⋊C₄	—	2	2	no	—
559	C₂×C₂²⋊C₄	D₄×C₇₉	1	2	yes	—
560	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
561	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
562	#106	—	2	2	no	—
563	#103	—	2	2	no	—
564	#103	—	2	2	no	—
565	#103	—	2	2	no	—
566	#102	—	2	2	no	—
567	#102	—	2	2	no	—
568	#102	—	2	2	no	—
569	C₂²⋊C₈	D₄×C₇₉	1	4	yes	complemented
570	#97	—	2	2	no	—
571	#97	—	2	2	no	—
572	#95	—	2	2	no	—
573	#95	—	2	2	no	—
574	#95	D₄×C₇₉	1	2	yes	—
575	C₂⁴	—	2	1	no	—
576	C₂⁴	—	2	1	no	—
577	C₂⁴	—	2	1	no	—
578	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
579	#41	—	2	8	no	—
580	#41	—	2	8	no	—
581	#41	—	4	4	no	—
582	#41	—	4	4	no	—
583	#41	—	4	4	no	—
584	#41	—	4	4	no	—
585	#41	—	4	4	no	—
586	#41	—	4	4	no	—
587	C₂×Q₈	—	2	1	no	—
588	C₂×Q₈	—	2	1	no	—
589	C₂×Q₈	—	2	1	no	—
590	C₂×Q₈	—	2	1	no	—
591	C₂×Q₈	—	2	1	no	—
592	C₂×Q₈	—	2	1	no	—
593	C₂×Q₈	—	2	1	no	—
594	C₂×Q₈	—	2	1	no	—
595	C₂×Q₈	—	2	1	no	—
596	C₂×Q₈	—	2	1	no	—
597	C₂×Q₈	—	2	1	no	—
598	C₂×Q₈	—	2	1	no	—
599	C₂×Q₈	—	2	1	no	—
600	C₂×Q₈	—	2	1	no	—
601	C₂×Q₈	—	2	1	no	—
602	C₂×Q₈	—	2	1	no	—
603	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
604	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
605	C₂×D₄	—	2	1	no	—
606	C₂×D₄	—	2	1	no	—
607	C₂×D₄	—	2	1	no	—
608	C₂×D₄	—	2	1	no	—
609	C₂×D₄	—	2	1	no	—
610	C₂×D₄	—	2	1	no	—
611	C₂×D₄	—	2	1	no	—
612	C₂×D₄	—	2	1	no	—
613	C₂×D₄	—	2	1	no	—
614	C₂×D₄	—	2	1	no	—
615	C₂×D₄	—	2	1	no	—
616	C₂×D₄	—	2	1	no	—
617	C₂×D₄	—	2	1	no	—
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	4	2	no	—
622	C₂×D₄	—	4	2	no	—
623	C₂×D₄	—	4	4	no	—
624	C₂×D₄	—	4	4	no	—
625	C₂×D₄	—	4	2	no	—
626	C₂×D₄	—	4	2	no	—
627	C₂×D₄	—	4	2	no	—
628	C₂×D₄	—	4	2	no	—
629	C₂×D₄	—	4	2	no	—
630	C₂×D₄	—	8	2	no	—
631	C₂×D₄	—	8	2	no	—
632	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
633	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	—	2	1	no	—
638	C₂²×C₄	—	2	1	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	4	2	no	—
644	C₂²×C₄	—	4	2	no	—
645	C₂²×C₄	—	4	2	no	—
646	C₂²×C₄	—	4	2	no	—
647	C₂²×C₄	—	4	2	no	—
648	C₂²×C₄	—	4	2	no	—
649	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
650	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
651	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
652	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
653	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
654	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
655	Q₁₆	—	2	8	no	—
656	Q₁₆	—	4	4	no	—
657	SD₁₆	—	2	8	no	—
658	SD₁₆	—	2	8	no	—
659	SD₁₆	—	4	4	no	—
660	SD₁₆	—	4	4	no	—
661	SD₁₆	—	4	4	no	—
662	D₈	—	2	8	no	—
663	D₈	—	4	4	no	—
664	C₂×C₈	—	2	1	no	—
665	C₂×C₈	—	2	1	no	—
666	C₂×C₈	—	2	1	no	—
667	C₂×C₈	—	2	1	no	—
668	C₂×C₈	—	2	1	no	—
669	C₂×C₈	—	2	1	no	—
670	C₂×C₈	—	2	8	no	—
671	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
672	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
673	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
674	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
675	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
676	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	1	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	4	4	no	—
682	C₄⋊C₄	—	4	2	no	—
683	C₂²⋊C₄	—	4	2	no	—
684	C₂²⋊C₄	—	4	4	no	—
685	C₂²⋊C₄	—	4	4	no	—
686	C₂²⋊C₄	—	4	4	no	—
687	C₂²⋊C₄	—	4	2	no	—
688	C₂²⋊C₄	—	4	2	no	—
689	C₂²⋊C₄	—	8	2	no	—
690	C₄²	—	2	1	no	—
691	C₄²	—	2	1	no	—
692	C₄²	—	2	1	no	—
693	C₄²	—	2	1	no	—
694	C₂³	—	2	1	no	—
695	C₂³	—	2	1	no	—
696	C₂³	—	2	2	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	4	1	no	—
701	C₂³	—	4	1	no	—
702	C₂³	—	4	1	no	—
703	C₂³	—	4	1	no	—
704	C₂³	—	4	2	no	—
705	C₂³	—	4	2	no	—
706	C₂³	—	4	2	no	—
707	C₂³	—	4	2	no	—
708	C₂³	—	4	1	no	—
709	C₂³	—	4	1	no	—
710	C₂³	—	4	1	no	—
711	C₂³	—	4	2	no	—
712	C₂³	—	4	2	no	—
713	C₂³	#127×C₇₉	1	2	yes	—
714	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
715	Q₈	—	2	2	no	—
716	Q₈	—	2	2	no	—
717	Q₈	—	2	2	no	—
718	Q₈	—	2	2	no	—
719	Q₈	—	4	1	no	—
720	Q₈	—	4	1	no	—
721	Q₈	—	4	1	no	—
722	Q₈	—	4	1	no	—
723	Q₈	—	4	1	no	—
724	Q₈	—	4	1	no	—
725	Q₈	—	4	1	no	—
726	Q₈	—	4	1	no	—
727	D₄	—	2	2	no	—
728	D₄	—	2	2	no	—
729	D₄	—	2	2	no	—
730	D₄	—	2	2	no	—
731	D₄	—	4	8	no	—
732	D₄	—	4	8	no	—
733	D₄	—	4	1	no	—
734	D₄	—	4	1	no	—
735	D₄	—	4	1	no	—
736	D₄	—	4	1	no	—
737	D₄	—	4	1	no	—
738	D₄	—	4	1	no	—
739	D₄	—	4	1	no	—
740	D₄	—	4	1	no	—
741	D₄	—	8	8	no	—
742	D₄	—	8	4	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	4	8	no	—
758	C₂×C₄	—	4	8	no	—
759	C₂×C₄	—	4	1	no	—
760	C₂×C₄	—	4	1	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	—	4	1	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	2	no	—
769	C₂×C₄	—	4	2	no	—
770	C₂×C₄	#127×C₇₉	1	2	yes	—
771	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
772	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
773	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
774	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
775	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
776	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
777	C₈	—	2	2	no	—
778	C₈	—	2	2	no	—
779	C₈	—	2	2	no	—
780	C₈	#120×C₇₉	1	4	yes	—
781	C₂²	—	2	2	no	—
782	C₂²	—	2	2	no	—
783	C₂²	—	2	2	no	—
784	C₂²	—	4	2	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	4	2	no	—
787	C₂²	—	4	2	no	—
788	C₂²	—	4	4	no	—
789	C₂²	—	4	4	no	—
790	C₂²	—	8	1	no	—
791	C₂²	—	8	1	no	—
792	C₂²	—	8	1	no	—
793	C₂²	—	8	1	no	—
794	C₂²	—	8	2	no	—
795	C₂²	—	8	2	no	—
796	C₂²	—	8	1	no	—
797	C₂²	—	8	1	no	—
798	C₂²	—	8	1	no	—
799	C₂²	—	8	2	no	—
800	C₂²	—	8	2	no	—
801	C₂²	C₂×#127×C₇₉	1	1	yes	characteristic
802	C₂²	D₄²×C₇₉	1	1	yes	characteristic
803	C₂²	D₄²×C₇₉	1	1	yes	characteristic
804	C₂²	#575×C₇₉	1	2	yes	—
805	C₂²	#577×C₇₉	1	2	yes	—
806	C₄	—	2	2	no	—
807	C₄	—	4	2	no	—
808	C₄	—	4	2	no	—
809	C₄	—	4	2	no	—
810	C₄	—	4	2	no	—
811	C₄	—	8	1	no	—
812	C₄	—	8	1	no	—
813	C₄	—	8	1	no	—
814	C₄	C₂×#120×C₇₉	1	1	yes	characteristic
815	C₄	#535×C₇₉	1	1	yes	characteristic
816	C₄	D₄²×C₇₉	1	1	yes	characteristic
817	C₄	D₄²×C₇₉	1	1	yes	characteristic
818	C₂	—	4	2	no	—
819	C₂	—	8	2	no	—
820	C₂	—	8	2	no	—
821	C₂	—	16	1	no	—
822	C₂	C₇₉×#2433	1	1	yes	characteristic
823	C₂	C₇₉×#3150	1	1	yes	characteristic
824	C₂	C₇₉×#3154	1	1	yes	characteristic
825	C₂	C₇₉×#3267	1	2	yes	—
826	C₂	C₇₉×#3271	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×#135×C₇₉	C₂	semidirect
2. C₂×#497×C₇₉	C₂	semidirect
3. C₂×#496×C₇₉	C₂	semidirect
4. C₂×#465×C₇₉	C₂	semidirect
5. C₂×#452×C₇₉	C₂	semidirect
6. C₂×#449×C₇₉	C₂	semidirect
7. C₇₉×#2432	C₂	semidirect
8. C₇₉×#2431	C₂	semidirect
9. C₇₉×#2015	C₂	semidirect
10. C₇₉×#2014	C₂	semidirect
11. C₇₉×#2013	C₂	semidirect
12. C₇₉×#2012	C₂	semidirect
13. C₇₉×#1972	C₂	semidirect
14. C₇₉×#1971	C₂	semidirect
15. C₇₉×#1752	C₂	semidirect
94. C₂×Q₁₆×C₇₉	D₄	semidirect
115. C₂×D₈×C₇₉	D₄	semidirect
118. C₂²×C₈×C₇₉	D₄	semidirect
155. C₂²⋊C₈×C₇₉	D₄	semidirect
404. #25787	C₇₉	direct (N × H)
414. C₂²×#135	C₂×C₇₉	semidirect
415. C₂×#497	C₂×C₇₉	semidirect
416. C₂×#496	C₂×C₇₉	semidirect
417. C₂×#465	C₂×C₇₉	semidirect
418. C₂×#452	C₂×C₇₉	semidirect
419. C₂×#449	C₂×C₇₉	semidirect
420. #2432	C₂×C₇₉	semidirect
421. #2431	C₂×C₇₉	semidirect
422. #2015	C₂×C₇₉	semidirect
423. #2014	C₂×C₇₉	semidirect
424. #2013	C₂×C₇₉	semidirect
425. #2012	C₂×C₇₉	semidirect
426. #1972	C₂×C₇₉	semidirect
427. #1971	C₂×C₇₉	semidirect
428. #1752	C₂×C₇₉	semidirect
429. C₇₉	#25787	direct (N × H)
508. C₂×Q₁₆	D₄×C₇₉	semidirect
529. C₂×D₈	D₄×C₇₉	semidirect
532. C₂²×C₈	D₄×C₇₉	semidirect
569. C₂²⋊C₈	D₄×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×#497×C₇₉	2
C₂×#496×C₇₉	2
C₂×#465×C₇₉	2
C₂×#452×C₇₉	2
C₂×#449×C₇₉	2
C₇₉×#2432	2
C₇₉×#2431	2
C₇₉×#2015	2
C₇₉×#2014	2
C₇₉×#2013	2
C₇₉×#2012	2
C₇₉×#1972	2
C₇₉×#1971	2
C₇₉×#1752	2
#25787	79

Subgroups — C79×#25787 #34137476

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#25787 #34137476