Subgroups — C₇₉×#23857 #34135546

Order 20224.

1852 conjugacy classes of subgroups.

The subgroup lattice has 1010 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×#550×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#452×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#449×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×#2014	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#2011	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#2000	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#1999	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1893	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₉×#1880	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₉×#1878	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×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×D₈×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	#550×C₇₉	—	2	4	no	—
30	#550×C₇₉	—	2	4	no	—
31	C₂×#127×C₇₉	—	2	1	no	—
32	C₂×#127×C₇₉	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
34	C₂×#121×C₇₉	—	2	1	no	—
35	C₂×#121×C₇₉	—	2	1	no	—
36	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
37	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
38	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₇₉	—	2	1	no	—
41	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
42	#452×C₇₉	—	2	4	no	—
43	#449×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×#102×C₇₉	C₂²	1	1	yes	characteristic
49	C₂×#102×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×D₄×C₇₉	—	2	1	no	—
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	—	2	1	no	—
93	C₂²×D₄×C₇₉	—	2	1	no	—
94	C₂²×D₄×C₇₉	—	2	1	no	—
95	C₂²×D₄×C₇₉	D₄	1	1	yes	characteristic
96	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
97	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₇₉	—	2	1	no	—
100	C₂³×C₄×C₇₉	—	2	1	no	—
101	C₂³×C₄×C₇₉	—	2	1	no	—
102	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
104	#135×C₇₉	—	2	32	no	—
105	C₂×Q₁₆×C₇₉	—	2	2	no	—
106	C₂×Q₁₆×C₇₉	—	2	2	no	—
107	C₂×Q₁₆×C₇₉	D₄	1	4	yes	complemented
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	—	2	2	no	—
120	C₂×D₈×C₇₉	—	2	2	no	—
121	C₂×D₈×C₇₉	—	2	2	no	—
122	C₂×D₈×C₇₉	—	4	1	no	—
123	C₂²×C₈×C₇₉	—	2	2	no	—
124	C₂²×C₈×C₇₉	—	2	2	no	—
125	C₂²×C₈×C₇₉	—	2	2	no	—
126	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
127	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
128	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
129	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
130	#127×C₇₉	—	2	8	no	—
131	#127×C₇₉	—	2	2	no	—
132	#127×C₇₉	—	2	2	no	—
133	C₂²⋊Q₈×C₇₉	—	2	2	no	—
134	C₂²⋊Q₈×C₇₉	—	4	1	no	—
135	#121×C₇₉	—	2	8	no	—
136	#121×C₇₉	—	2	8	no	—
137	#121×C₇₉	—	2	2	no	—
138	#121×C₇₉	—	2	2	no	—
139	#121×C₇₉	—	2	2	no	—
140	#121×C₇₉	—	2	2	no	—
141	#121×C₇₉	—	4	1	no	—
142	#121×C₇₉	D₄	1	4	yes	complemented
143	C₄×Q₈×C₇₉	—	2	2	no	—
144	C₄×Q₈×C₇₉	—	2	2	no	—
145	C₄×D₄×C₇₉	—	2	8	no	—
146	C₄×D₄×C₇₉	—	2	2	no	—
147	C₄×D₄×C₇₉	—	2	2	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	D₄	1	1	yes	characteristic
162	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
163	C₂×C₄²×C₇₉	—	2	1	no	—
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	#102×C₇₉	—	2	2	no	—
169	#102×C₇₉	—	2	2	no	—
170	#102×C₇₉	—	2	2	no	—
171	#102×C₇₉	—	4	1	no	—
172	#102×C₇₉	—	4	1	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	—	2	1	no	—
182	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
183	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
184	#41×C₇₉	—	2	8	no	—
185	#41×C₇₉	—	2	8	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	#41×C₇₉	—	4	4	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	C₂×D₄	1	2	yes	—
205	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
206	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
207	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
208	C₂×D₄×C₇₉	—	2	4	no	—
209	C₂×D₄×C₇₉	—	2	4	no	—
210	C₂×D₄×C₇₉	—	2	2	no	—
211	C₂×D₄×C₇₉	—	2	4	no	—
212	C₂×D₄×C₇₉	—	2	4	no	—
213	C₂×D₄×C₇₉	—	2	4	no	—
214	C₂×D₄×C₇₉	—	2	4	no	—
215	C₂×D₄×C₇₉	—	2	2	no	—
216	C₂×D₄×C₇₉	—	2	1	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	—	2	1	no	—
226	C₂×D₄×C₇₉	—	2	1	no	—
227	C₂×D₄×C₇₉	—	2	1	no	—
228	C₂×D₄×C₇₉	—	2	1	no	—
229	C₂×D₄×C₇₉	—	2	1	no	—
230	C₂×D₄×C₇₉	—	2	1	no	—
231	C₂×D₄×C₇₉	—	4	1	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	—	4	2	no	—
236	C₂×D₄×C₇₉	—	4	2	no	—
237	C₂×D₄×C₇₉	—	4	2	no	—
238	C₂×D₄×C₇₉	—	4	2	no	—
239	C₂×D₄×C₇₉	—	4	2	no	—
240	C₂×D₄×C₇₉	—	4	2	no	—
241	C₂×D₄×C₇₉	—	4	2	no	—
242	C₂×D₄×C₇₉	—	4	2	no	—
243	C₂×D₄×C₇₉	—	8	1	no	—
244	C₂×D₄×C₇₉	—	8	1	no	—
245	C₂×D₄×C₇₉	—	8	1	no	—
246	C₂×D₄×C₇₉	—	8	1	no	—
247	C₂×D₄×C₇₉	—	8	1	no	—
248	C₂×D₄×C₇₉	—	8	1	no	—
249	C₂×D₄×C₇₉	—	8	1	no	—
250	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
251	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
252	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
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	4	no	—
259	C₂²×C₄×C₇₉	—	2	1	no	—
260	C₂²×C₄×C₇₉	—	2	1	no	—
261	C₂²×C₄×C₇₉	—	2	4	no	—
262	C₂²×C₄×C₇₉	—	2	1	no	—
263	C₂²×C₄×C₇₉	—	2	1	no	—
264	C₂²×C₄×C₇₉	—	2	1	no	—
265	C₂²×C₄×C₇₉	—	2	1	no	—
266	C₂²×C₄×C₇₉	—	2	1	no	—
267	C₂²×C₄×C₇₉	—	2	1	no	—
268	C₂²×C₄×C₇₉	—	2	1	no	—
269	C₂²×C₄×C₇₉	—	2	1	no	—
270	C₂²×C₄×C₇₉	—	4	2	no	—
271	C₂²×C₄×C₇₉	—	4	2	no	—
272	C₂²×C₄×C₇₉	—	4	2	no	—
273	C₂²×C₄×C₇₉	—	4	2	no	—
274	C₂²×C₄×C₇₉	—	4	2	no	—
275	C₂²×C₄×C₇₉	—	4	2	no	—
276	C₂²×C₄×C₇₉	—	4	2	no	—
277	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
279	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
280	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
281	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
282	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
284	Q₁₆×C₇₉	—	2	8	no	—
285	SD₁₆×C₇₉	—	2	8	no	—
286	SD₁₆×C₇₉	—	2	8	no	—
287	SD₁₆×C₇₉	—	4	4	no	—
288	D₈×C₇₉	—	2	8	no	—
289	D₈×C₇₉	—	4	4	no	—
290	C₂×C₈×C₇₉	—	2	8	no	—
291	C₂×C₈×C₇₉	—	2	1	no	—
292	C₂×C₈×C₇₉	—	2	1	no	—
293	C₂×C₈×C₇₉	—	2	1	no	—
294	C₂×C₈×C₇₉	—	2	1	no	—
295	C₂×C₈×C₇₉	—	2	1	no	—
296	C₂×C₈×C₇₉	—	2	1	no	—
297	C₂×C₈×C₇₉	—	2	1	no	—
298	C₂×C₈×C₇₉	—	2	1	no	—
299	C₂×C₈×C₇₉	—	2	1	no	—
300	C₂×C₈×C₇₉	—	2	1	no	—
301	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
302	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
303	C₄⋊C₄×C₇₉	—	2	4	no	—
304	C₄⋊C₄×C₇₉	—	2	2	no	—
305	C₄⋊C₄×C₇₉	—	2	1	no	—
306	C₄⋊C₄×C₇₉	—	2	1	no	—
307	C₄⋊C₄×C₇₉	—	2	1	no	—
308	C₄⋊C₄×C₇₉	—	2	1	no	—
309	C₄⋊C₄×C₇₉	—	2	1	no	—
310	C₄⋊C₄×C₇₉	—	4	2	no	—
311	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
312	C₂²⋊C₄×C₇₉	—	2	4	no	—
313	C₂²⋊C₄×C₇₉	—	2	2	no	—
314	C₂²⋊C₄×C₇₉	—	2	4	no	—
315	C₂²⋊C₄×C₇₉	—	2	2	no	—
316	C₂²⋊C₄×C₇₉	—	4	2	no	—
317	C₂²⋊C₄×C₇₉	—	4	2	no	—
318	C₂²⋊C₄×C₇₉	—	4	2	no	—
319	C₂²⋊C₄×C₇₉	—	8	1	no	—
320	C₂²⋊C₄×C₇₉	—	8	1	no	—
321	C₄²×C₇₉	—	2	4	no	—
322	C₄²×C₇₉	—	2	1	no	—
323	C₄²×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	1	no	—
330	C₂³×C₇₉	—	2	1	no	—
331	C₂³×C₇₉	—	2	2	no	—
332	C₂³×C₇₉	—	2	2	no	—
333	C₂³×C₇₉	—	2	1	no	—
334	C₂³×C₇₉	—	2	2	no	—
335	C₂³×C₇₉	—	2	1	no	—
336	C₂³×C₇₉	—	2	1	no	—
337	C₂³×C₇₉	—	2	1	no	—
338	C₂³×C₇₉	—	2	1	no	—
339	C₂³×C₇₉	—	2	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	—	4	1	no	—
346	C₂³×C₇₉	—	4	1	no	—
347	C₂³×C₇₉	—	4	1	no	—
348	C₂³×C₇₉	—	4	1	no	—
349	C₂³×C₇₉	—	4	1	no	—
350	C₂³×C₇₉	—	4	1	no	—
351	C₂³×C₇₉	—	4	1	no	—
352	C₂³×C₇₉	—	4	1	no	—
353	C₂³×C₇₉	—	4	1	no	—
354	C₂³×C₇₉	—	4	1	no	—
355	C₂³×C₇₉	—	4	1	no	—
356	C₂³×C₇₉	—	4	1	no	—
357	C₂³×C₇₉	—	4	1	no	—
358	C₂³×C₇₉	#120	1	2	yes	—
359	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
360	Q₈×C₇₉	—	2	2	no	—
361	Q₈×C₇₉	—	2	2	no	—
362	Q₈×C₇₉	—	2	2	no	—
363	Q₈×C₇₉	—	2	2	no	—
364	Q₈×C₇₉	—	2	2	no	—
365	Q₈×C₇₉	—	4	1	no	—
366	Q₈×C₇₉	—	4	1	no	—
367	Q₈×C₇₉	#120	1	4	yes	—
368	D₄×C₇₉	—	2	2	no	—
369	D₄×C₇₉	—	2	2	no	—
370	D₄×C₇₉	—	2	2	no	—
371	D₄×C₇₉	—	2	2	no	—
372	D₄×C₇₉	—	2	2	no	—
373	D₄×C₇₉	—	2	2	no	—
374	D₄×C₇₉	—	4	4	no	—
375	D₄×C₇₉	—	4	8	no	—
376	D₄×C₇₉	—	4	8	no	—
377	D₄×C₇₉	—	4	8	no	—
378	D₄×C₇₉	—	4	8	no	—
379	D₄×C₇₉	—	4	1	no	—
380	D₄×C₇₉	—	4	1	no	—
381	D₄×C₇₉	—	4	1	no	—
382	D₄×C₇₉	—	4	1	no	—
383	D₄×C₇₉	—	4	1	no	—
384	D₄×C₇₉	—	4	1	no	—
385	D₄×C₇₉	—	8	4	no	—
386	D₄×C₇₉	—	8	4	no	—
387	D₄×C₇₉	—	8	4	no	—
388	D₄×C₇₉	—	8	4	no	—
389	C₂×C₄×C₇₉	—	2	1	no	—
390	C₂×C₄×C₇₉	—	2	2	no	—
391	C₂×C₄×C₇₉	—	2	1	no	—
392	C₂×C₄×C₇₉	—	2	1	no	—
393	C₂×C₄×C₇₉	—	2	2	no	—
394	C₂×C₄×C₇₉	—	2	2	no	—
395	C₂×C₄×C₇₉	—	2	1	no	—
396	C₂×C₄×C₇₉	—	2	2	no	—
397	C₂×C₄×C₇₉	—	2	2	no	—
398	C₂×C₄×C₇₉	—	2	2	no	—
399	C₂×C₄×C₇₉	—	2	2	no	—
400	C₂×C₄×C₇₉	—	2	1	no	—
401	C₂×C₄×C₇₉	—	2	2	no	—
402	C₂×C₄×C₇₉	—	2	1	no	—
403	C₂×C₄×C₇₉	—	2	1	no	—
404	C₂×C₄×C₇₉	—	2	2	no	—
405	C₂×C₄×C₇₉	—	2	1	no	—
406	C₂×C₄×C₇₉	—	2	1	no	—
407	C₂×C₄×C₇₉	—	2	1	no	—
408	C₂×C₄×C₇₉	—	4	8	no	—
409	C₂×C₄×C₇₉	—	4	8	no	—
410	C₂×C₄×C₇₉	—	4	8	no	—
411	C₂×C₄×C₇₉	—	4	1	no	—
412	C₂×C₄×C₇₉	—	4	1	no	—
413	C₂×C₄×C₇₉	—	4	1	no	—
414	C₂×C₄×C₇₉	—	4	1	no	—
415	C₂×C₄×C₇₉	—	4	1	no	—
416	C₂×C₄×C₇₉	—	4	1	no	—
417	C₂×C₄×C₇₉	—	4	1	no	—
418	C₂×C₄×C₇₉	—	4	1	no	—
419	C₂×C₄×C₇₉	—	4	1	no	—
420	C₂×C₄×C₇₉	—	4	1	no	—
421	C₂×C₄×C₇₉	—	4	1	no	—
422	C₂×C₄×C₇₉	—	4	1	no	—
423	C₂×C₄×C₇₉	—	4	1	no	—
424	C₂×C₄×C₇₉	—	4	1	no	—
425	C₂×C₄×C₇₉	#120	1	2	yes	—
426	C₂×C₄×C₇₉	#135	1	2	yes	complemented
427	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
430	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
431	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
432	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
433	C₈×C₇₉	—	2	2	no	—
434	C₈×C₇₉	—	2	2	no	—
435	C₈×C₇₉	—	4	1	no	—
436	C₈×C₇₉	—	4	1	no	—
437	C₂²×C₇₉	—	2	2	no	—
438	C₂²×C₇₉	—	2	2	no	—
439	C₂²×C₇₉	—	2	2	no	—
440	C₂²×C₇₉	—	4	1	no	—
441	C₂²×C₇₉	—	4	1	no	—
442	C₂²×C₇₉	—	4	1	no	—
443	C₂²×C₇₉	—	4	1	no	—
444	C₂²×C₇₉	—	4	2	no	—
445	C₂²×C₇₉	—	4	2	no	—
446	C₂²×C₇₉	—	4	2	no	—
447	C₂²×C₇₉	—	4	1	no	—
448	C₂²×C₇₉	—	4	1	no	—
449	C₂²×C₇₉	—	4	2	no	—
450	C₂²×C₇₉	—	4	2	no	—
451	C₂²×C₇₉	—	4	1	no	—
452	C₂²×C₇₉	—	4	2	no	—
453	C₂²×C₇₉	—	4	2	no	—
454	C₂²×C₇₉	—	4	1	no	—
455	C₂²×C₇₉	—	4	2	no	—
456	C₂²×C₇₉	—	4	1	no	—
457	C₂²×C₇₉	—	4	1	no	—
458	C₂²×C₇₉	—	4	2	no	—
459	C₂²×C₇₉	—	4	1	no	—
460	C₂²×C₇₉	—	8	1	no	—
461	C₂²×C₇₉	—	8	1	no	—
462	C₂²×C₇₉	—	8	1	no	—
463	C₂²×C₇₉	—	8	1	no	—
464	C₂²×C₇₉	—	8	1	no	—
465	C₂²×C₇₉	—	8	1	no	—
466	C₂²×C₇₉	—	8	1	no	—
467	C₂²×C₇₉	—	8	1	no	—
468	C₂²×C₇₉	—	8	1	no	—
469	C₂²×C₇₉	—	8	1	no	—
470	C₂²×C₇₉	—	8	1	no	—
471	C₂²×C₇₉	—	8	1	no	—
472	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
473	C₂²×C₇₉	D₄²	1	1	yes	characteristic
474	C₂²×C₇₉	D₄²	1	1	yes	characteristic
475	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
476	C₂²×C₇₉	#575	1	1	yes	characteristic
477	C₂²×C₇₉	#576	1	1	yes	characteristic
478	C₂²×C₇₉	#577	1	1	yes	characteristic
479	C₄×C₇₉	—	2	2	no	—
480	C₄×C₇₉	—	2	4	no	—
481	C₄×C₇₉	—	2	2	no	—
482	C₄×C₇₉	—	4	1	no	—
483	C₄×C₇₉	—	4	2	no	—
484	C₄×C₇₉	—	4	1	no	—
485	C₄×C₇₉	—	4	2	no	—
486	C₄×C₇₉	—	8	1	no	—
487	C₄×C₇₉	—	8	1	no	—
488	C₄×C₇₉	C₂×#120	1	1	yes	characteristic
489	C₄×C₇₉	#534	1	1	yes	characteristic
490	C₄×C₇₉	D₄²	1	1	yes	characteristic
491	C₄×C₇₉	D₄²	1	1	yes	characteristic
492	#23857	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
493	C₂×C₇₉	—	4	2	no	—
494	C₂×C₇₉	—	8	1	no	—
495	C₂×C₇₉	—	8	2	no	—
496	C₂×C₇₉	—	8	2	no	—
497	C₂×C₇₉	—	8	2	no	—
498	C₂×C₇₉	#2403	1	1	yes	characteristic
499	C₂×C₇₉	#3002	1	1	yes	characteristic
500	C₂×C₇₉	#3012	1	1	yes	characteristic
501	C₂×C₇₉	#3268	1	1	yes	characteristic
502	C₂×C₇₉	#3271	1	1	yes	characteristic
503	C₂×C₇₉	#3284	1	1	yes	characteristic
504	C₂×C₇₉	#3287	1	1	yes	characteristic
505	C₂²×#135	C₂×C₇₉	1	1	yes	characteristic, complemented
506	C₂×#550	C₂×C₇₉	1	1	yes	characteristic, complemented
507	C₂×#452	C₂×C₇₉	1	1	yes	characteristic, complemented
508	C₂×#449	C₂×C₇₉	1	1	yes	characteristic, complemented
509	C₂×#449	C₂×C₇₉	1	1	yes	characteristic, complemented
510	#2407	C₂×C₇₉	1	1	yes	characteristic, complemented
511	#2014	C₂×C₇₉	1	1	yes	characteristic, complemented
512	#2011	C₂×C₇₉	1	1	yes	characteristic, complemented
513	#2000	C₂×C₇₉	1	1	yes	characteristic, complemented
514	#1999	C₂×C₇₉	1	1	yes	characteristic, complemented
515	#1893	C₂×C₇₉	1	1	yes	characteristic, complemented
516	#1880	C₂×C₇₉	1	1	yes	characteristic, complemented
517	#1878	C₂×C₇₉	1	1	yes	characteristic, complemented
518	#1869	C₂×C₇₉	1	1	yes	characteristic, complemented
519	#1788	C₂×C₇₉	1	1	yes	characteristic, complemented
520	C₇₉	#23857	1	1	yes	characteristic, direct product factor, Sylow
521	C₂²×#41	C₂²×C₇₉	1	1	yes	characteristic
522	C₂²×#41	C₂²×C₇₉	1	1	yes	characteristic
523	C₂²×#41	C₂²×C₇₉	1	1	yes	characteristic
524	C₂×#135	—	2	4	no	—
525	C₂×#135	—	2	4	no	—
526	C₂×#135	—	2	4	no	—
527	C₂²×Q₁₆	C₂²×C₇₉	1	1	yes	characteristic
528	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
529	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
530	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
531	C₂²×D₈	C₂²×C₇₉	1	1	yes	characteristic
532	C₂²×D₈	C₂²×C₇₉	1	1	yes	characteristic
533	C₂³×C₈	C₂²×C₇₉	1	1	yes	characteristic
534	#550	—	2	4	no	—
535	#550	—	2	4	no	—
536	C₂×#127	—	2	1	no	—
537	C₂×#127	C₂²×C₇₉	1	1	yes	characteristic
538	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
539	C₂×#121	—	2	1	no	—
540	C₂×#121	—	2	1	no	—
541	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
542	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
543	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
544	C₂×C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
545	C₂×C₄×D₄	—	2	1	no	—
546	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
547	#452	—	2	4	no	—
548	#449	—	2	4	no	—
549	#449	—	2	4	no	—
550	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
551	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
552	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
553	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
554	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
555	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
556	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
557	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
558	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
559	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
560	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
561	#394	—	2	1	no	—
562	#392	—	2	1	no	—
563	#391	C₂²×C₇₉	1	1	yes	characteristic
564	#390	C₂²×C₇₉	1	1	yes	characteristic
565	#386	—	2	1	no	—
566	#385	—	2	1	no	—
567	#380	C₂²×C₇₉	1	1	yes	characteristic
568	#340	C₂²×C₇₉	1	1	yes	characteristic
569	#340	C₂²×C₇₉	1	1	yes	characteristic
570	#336	C₂²×C₇₉	1	1	yes	characteristic
571	#336	C₂²×C₇₉	1	1	yes	characteristic
572	C₂×#41	—	2	2	no	—
573	C₂×#41	—	2	2	no	—
574	C₂×#41	—	2	2	no	—
575	C₂×#41	—	2	2	no	—
576	C₂×#41	—	2	2	no	—
577	C₂×#41	—	2	2	no	—
578	C₂×#41	—	2	2	no	—
579	C₂×#41	—	2	2	no	—
580	C₂×#41	—	2	2	no	—
581	C₂×#41	—	2	2	no	—
582	C₂×#41	—	2	2	no	—
583	C₂×#41	—	4	1	no	—
584	C₂×#41	—	4	1	no	—
585	C₂×#41	—	4	1	no	—
586	C₂×#41	—	4	1	no	—
587	C₂×#41	—	4	1	no	—
588	C₂×#41	—	4	1	no	—
589	C₂×#41	D₄×C₇₉	1	4	yes	complemented
590	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
591	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
592	C₂²×D₄	—	2	1	no	—
593	C₂²×D₄	—	2	1	no	—
594	C₂²×D₄	—	2	1	no	—
595	C₂²×D₄	—	2	1	no	—
596	C₂²×D₄	—	2	1	no	—
597	C₂²×D₄	—	2	1	no	—
598	C₂²×D₄	—	2	1	no	—
599	C₂²×D₄	—	2	1	no	—
600	C₂²×D₄	D₄×C₇₉	1	1	yes	characteristic
601	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
602	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
603	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
604	C₂³×C₄	—	2	1	no	—
605	C₂³×C₄	—	2	1	no	—
606	C₂³×C₄	—	2	1	no	—
607	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
608	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
609	#135	—	2	32	no	—
610	C₂×Q₁₆	—	2	2	no	—
611	C₂×Q₁₆	—	2	2	no	—
612	C₂×Q₁₆	D₄×C₇₉	1	4	yes	complemented
613	C₂×SD₁₆	—	2	2	no	—
614	C₂×SD₁₆	—	2	2	no	—
615	C₂×SD₁₆	—	2	2	no	—
616	C₂×SD₁₆	—	2	2	no	—
617	C₂×SD₁₆	—	2	2	no	—
618	C₂×SD₁₆	—	2	2	no	—
619	C₂×SD₁₆	—	2	2	no	—
620	C₂×SD₁₆	—	4	1	no	—
621	C₂×SD₁₆	D₄×C₇₉	1	4	yes	complemented
622	C₂×D₈	—	2	2	no	—
623	C₂×D₈	—	2	2	no	—
624	C₂×D₈	—	2	2	no	—
625	C₂×D₈	—	2	2	no	—
626	C₂×D₈	—	2	2	no	—
627	C₂×D₈	—	4	1	no	—
628	C₂²×C₈	—	2	2	no	—
629	C₂²×C₈	—	2	2	no	—
630	C₂²×C₈	—	2	2	no	—
631	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
632	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
633	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
634	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
635	#127	—	2	8	no	—
636	#127	—	2	2	no	—
637	#127	—	2	2	no	—
638	C₂²⋊Q₈	—	2	2	no	—
639	C₂²⋊Q₈	—	4	1	no	—
640	#121	—	2	8	no	—
641	#121	—	2	8	no	—
642	#121	—	2	2	no	—
643	#121	—	2	2	no	—
644	#121	—	2	2	no	—
645	#121	—	2	2	no	—
646	#121	—	4	1	no	—
647	#121	D₄×C₇₉	1	4	yes	complemented
648	C₄×Q₈	—	2	2	no	—
649	C₄×Q₈	—	2	2	no	—
650	C₄×D₄	—	2	8	no	—
651	C₄×D₄	—	2	2	no	—
652	C₄×D₄	—	2	2	no	—
653	C₂×C₄⋊C₄	—	2	1	no	—
654	C₂×C₄⋊C₄	—	2	1	no	—
655	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
656	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
657	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
658	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
659	C₂×C₂²⋊C₄	—	2	1	no	—
660	C₂×C₂²⋊C₄	—	2	1	no	—
661	C₂×C₂²⋊C₄	—	2	1	no	—
662	C₂×C₂²⋊C₄	—	2	1	no	—
663	C₂×C₂²⋊C₄	—	2	1	no	—
664	C₂×C₂²⋊C₄	—	2	1	no	—
665	C₂×C₂²⋊C₄	—	2	1	no	—
666	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
667	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
668	C₂×C₄²	—	2	1	no	—
669	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
670	#103	—	2	2	no	—
671	#103	—	2	2	no	—
672	#103	—	2	2	no	—
673	#102	—	2	2	no	—
674	#102	—	2	2	no	—
675	#102	—	2	2	no	—
676	#102	—	4	1	no	—
677	#102	—	4	1	no	—
678	C₂²⋊C₈	—	2	2	no	—
679	C₂²⋊C₈	—	2	2	no	—
680	C₂²⋊C₈	—	2	2	no	—
681	#95	—	2	1	no	—
682	#95	—	2	1	no	—
683	#95	—	2	1	no	—
684	C₂⁴	—	2	1	no	—
685	C₂⁴	—	2	1	no	—
686	C₂⁴	—	2	1	no	—
687	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
688	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
689	#41	—	2	8	no	—
690	#41	—	2	8	no	—
691	#41	—	4	4	no	—
692	#41	—	4	4	no	—
693	#41	—	4	4	no	—
694	#41	—	4	4	no	—
695	#41	—	4	4	no	—
696	#41	—	4	4	no	—
697	#41	—	4	4	no	—
698	#41	—	4	4	no	—
699	#41	—	4	4	no	—
700	#41	—	4	4	no	—
701	C₂×Q₈	—	2	1	no	—
702	C₂×Q₈	—	2	1	no	—
703	C₂×Q₈	—	2	1	no	—
704	C₂×Q₈	—	2	1	no	—
705	C₂×Q₈	—	2	1	no	—
706	C₂×Q₈	—	2	1	no	—
707	C₂×Q₈	—	2	1	no	—
708	C₂×Q₈	—	2	1	no	—
709	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
710	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
711	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
712	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
713	C₂×D₄	—	2	4	no	—
714	C₂×D₄	—	2	4	no	—
715	C₂×D₄	—	2	2	no	—
716	C₂×D₄	—	2	4	no	—
717	C₂×D₄	—	2	4	no	—
718	C₂×D₄	—	2	4	no	—
719	C₂×D₄	—	2	4	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	1	no	—
722	C₂×D₄	—	2	1	no	—
723	C₂×D₄	—	2	1	no	—
724	C₂×D₄	—	2	1	no	—
725	C₂×D₄	—	2	1	no	—
726	C₂×D₄	—	2	1	no	—
727	C₂×D₄	—	2	1	no	—
728	C₂×D₄	—	2	1	no	—
729	C₂×D₄	—	2	1	no	—
730	C₂×D₄	—	2	1	no	—
731	C₂×D₄	—	2	1	no	—
732	C₂×D₄	—	2	1	no	—
733	C₂×D₄	—	2	1	no	—
734	C₂×D₄	—	2	1	no	—
735	C₂×D₄	—	2	1	no	—
736	C₂×D₄	—	4	1	no	—
737	C₂×D₄	—	4	2	no	—
738	C₂×D₄	—	4	2	no	—
739	C₂×D₄	—	4	2	no	—
740	C₂×D₄	—	4	2	no	—
741	C₂×D₄	—	4	2	no	—
742	C₂×D₄	—	4	2	no	—
743	C₂×D₄	—	4	2	no	—
744	C₂×D₄	—	4	2	no	—
745	C₂×D₄	—	4	2	no	—
746	C₂×D₄	—	4	2	no	—
747	C₂×D₄	—	4	2	no	—
748	C₂×D₄	—	8	1	no	—
749	C₂×D₄	—	8	1	no	—
750	C₂×D₄	—	8	1	no	—
751	C₂×D₄	—	8	1	no	—
752	C₂×D₄	—	8	1	no	—
753	C₂×D₄	—	8	1	no	—
754	C₂×D₄	—	8	1	no	—
755	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
756	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
757	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
758	C₂²×C₄	—	2	1	no	—
759	C₂²×C₄	—	2	1	no	—
760	C₂²×C₄	—	2	1	no	—
761	C₂²×C₄	—	2	1	no	—
762	C₂²×C₄	—	2	1	no	—
763	C₂²×C₄	—	2	4	no	—
764	C₂²×C₄	—	2	1	no	—
765	C₂²×C₄	—	2	1	no	—
766	C₂²×C₄	—	2	4	no	—
767	C₂²×C₄	—	2	1	no	—
768	C₂²×C₄	—	2	1	no	—
769	C₂²×C₄	—	2	1	no	—
770	C₂²×C₄	—	2	1	no	—
771	C₂²×C₄	—	2	1	no	—
772	C₂²×C₄	—	2	1	no	—
773	C₂²×C₄	—	2	1	no	—
774	C₂²×C₄	—	2	1	no	—
775	C₂²×C₄	—	4	2	no	—
776	C₂²×C₄	—	4	2	no	—
777	C₂²×C₄	—	4	2	no	—
778	C₂²×C₄	—	4	2	no	—
779	C₂²×C₄	—	4	2	no	—
780	C₂²×C₄	—	4	2	no	—
781	C₂²×C₄	—	4	2	no	—
782	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
783	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
784	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
785	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
786	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
787	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
788	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
789	Q₁₆	—	2	8	no	—
790	SD₁₆	—	2	8	no	—
791	SD₁₆	—	2	8	no	—
792	SD₁₆	—	4	4	no	—
793	D₈	—	2	8	no	—
794	D₈	—	4	4	no	—
795	C₂×C₈	—	2	8	no	—
796	C₂×C₈	—	2	1	no	—
797	C₂×C₈	—	2	1	no	—
798	C₂×C₈	—	2	1	no	—
799	C₂×C₈	—	2	1	no	—
800	C₂×C₈	—	2	1	no	—
801	C₂×C₈	—	2	1	no	—
802	C₂×C₈	—	2	1	no	—
803	C₂×C₈	—	2	1	no	—
804	C₂×C₈	—	2	1	no	—
805	C₂×C₈	—	2	1	no	—
806	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
807	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
808	C₄⋊C₄	—	2	4	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	1	no	—
811	C₄⋊C₄	—	2	1	no	—
812	C₄⋊C₄	—	2	1	no	—
813	C₄⋊C₄	—	2	1	no	—
814	C₄⋊C₄	—	2	1	no	—
815	C₄⋊C₄	—	4	2	no	—
816	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
817	C₂²⋊C₄	—	2	4	no	—
818	C₂²⋊C₄	—	2	2	no	—
819	C₂²⋊C₄	—	2	4	no	—
820	C₂²⋊C₄	—	2	2	no	—
821	C₂²⋊C₄	—	4	2	no	—
822	C₂²⋊C₄	—	4	2	no	—
823	C₂²⋊C₄	—	4	2	no	—
824	C₂²⋊C₄	—	8	1	no	—
825	C₂²⋊C₄	—	8	1	no	—
826	C₄²	—	2	4	no	—
827	C₄²	—	2	1	no	—
828	C₄²	—	2	1	no	—
829	C₂³	—	2	1	no	—
830	C₂³	—	2	1	no	—
831	C₂³	—	2	1	no	—
832	C₂³	—	2	1	no	—
833	C₂³	—	2	1	no	—
834	C₂³	—	2	1	no	—
835	C₂³	—	2	1	no	—
836	C₂³	—	2	2	no	—
837	C₂³	—	2	2	no	—
838	C₂³	—	2	1	no	—
839	C₂³	—	2	2	no	—
840	C₂³	—	2	1	no	—
841	C₂³	—	2	1	no	—
842	C₂³	—	2	1	no	—
843	C₂³	—	2	1	no	—
844	C₂³	—	2	1	no	—
845	C₂³	—	4	1	no	—
846	C₂³	—	4	1	no	—
847	C₂³	—	4	1	no	—
848	C₂³	—	4	1	no	—
849	C₂³	—	4	1	no	—
850	C₂³	—	4	1	no	—
851	C₂³	—	4	1	no	—
852	C₂³	—	4	1	no	—
853	C₂³	—	4	1	no	—
854	C₂³	—	4	1	no	—
855	C₂³	—	4	1	no	—
856	C₂³	—	4	1	no	—
857	C₂³	—	4	1	no	—
858	C₂³	—	4	1	no	—
859	C₂³	—	4	1	no	—
860	C₂³	—	4	1	no	—
861	C₂³	—	4	1	no	—
862	C₂³	—	4	1	no	—
863	C₂³	#120×C₇₉	1	2	yes	—
864	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
865	Q₈	—	2	2	no	—
866	Q₈	—	2	2	no	—
867	Q₈	—	2	2	no	—
868	Q₈	—	2	2	no	—
869	Q₈	—	2	2	no	—
870	Q₈	—	4	1	no	—
871	Q₈	—	4	1	no	—
872	Q₈	#120×C₇₉	1	4	yes	—
873	D₄	—	2	2	no	—
874	D₄	—	2	2	no	—
875	D₄	—	2	2	no	—
876	D₄	—	2	2	no	—
877	D₄	—	2	2	no	—
878	D₄	—	2	2	no	—
879	D₄	—	4	4	no	—
880	D₄	—	4	8	no	—
881	D₄	—	4	8	no	—
882	D₄	—	4	8	no	—
883	D₄	—	4	8	no	—
884	D₄	—	4	1	no	—
885	D₄	—	4	1	no	—
886	D₄	—	4	1	no	—
887	D₄	—	4	1	no	—
888	D₄	—	4	1	no	—
889	D₄	—	4	1	no	—
890	D₄	—	8	4	no	—
891	D₄	—	8	4	no	—
892	D₄	—	8	4	no	—
893	D₄	—	8	4	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	4	8	no	—
914	C₂×C₄	—	4	8	no	—
915	C₂×C₄	—	4	8	no	—
916	C₂×C₄	—	4	1	no	—
917	C₂×C₄	—	4	1	no	—
918	C₂×C₄	—	4	1	no	—
919	C₂×C₄	—	4	1	no	—
920	C₂×C₄	—	4	1	no	—
921	C₂×C₄	—	4	1	no	—
922	C₂×C₄	—	4	1	no	—
923	C₂×C₄	—	4	1	no	—
924	C₂×C₄	—	4	1	no	—
925	C₂×C₄	—	4	1	no	—
926	C₂×C₄	—	4	1	no	—
927	C₂×C₄	—	4	1	no	—
928	C₂×C₄	—	4	1	no	—
929	C₂×C₄	—	4	1	no	—
930	C₂×C₄	#120×C₇₉	1	2	yes	—
931	C₂×C₄	#135×C₇₉	1	2	yes	complemented
932	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
933	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
934	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
935	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
936	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
937	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
938	C₈	—	2	2	no	—
939	C₈	—	2	2	no	—
940	C₈	—	4	1	no	—
941	C₈	—	4	1	no	—
942	C₂²	—	2	2	no	—
943	C₂²	—	2	2	no	—
944	C₂²	—	2	2	no	—
945	C₂²	—	4	1	no	—
946	C₂²	—	4	1	no	—
947	C₂²	—	4	1	no	—
948	C₂²	—	4	1	no	—
949	C₂²	—	4	1	no	—
950	C₂²	—	4	2	no	—
951	C₂²	—	4	1	no	—
952	C₂²	—	4	2	no	—
953	C₂²	—	4	2	no	—
954	C₂²	—	4	2	no	—
955	C₂²	—	4	1	no	—
956	C₂²	—	4	1	no	—
957	C₂²	—	4	2	no	—
958	C₂²	—	4	2	no	—
959	C₂²	—	4	1	no	—
960	C₂²	—	4	2	no	—
961	C₂²	—	4	2	no	—
962	C₂²	—	4	1	no	—
963	C₂²	—	4	2	no	—
964	C₂²	—	4	1	no	—
965	C₂²	—	8	1	no	—
966	C₂²	—	8	1	no	—
967	C₂²	—	8	1	no	—
968	C₂²	—	8	1	no	—
969	C₂²	—	8	1	no	—
970	C₂²	—	8	1	no	—
971	C₂²	—	8	1	no	—
972	C₂²	—	8	1	no	—
973	C₂²	—	8	1	no	—
974	C₂²	—	8	1	no	—
975	C₂²	—	8	1	no	—
976	C₂²	—	8	1	no	—
977	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
978	C₂²	D₄²×C₇₉	1	1	yes	characteristic
979	C₂²	D₄²×C₇₉	1	1	yes	characteristic
980	C₂²	C₂×#135×C₇₉	1	1	yes	characteristic
981	C₂²	#575×C₇₉	1	1	yes	characteristic
982	C₂²	#576×C₇₉	1	1	yes	characteristic
983	C₂²	#577×C₇₉	1	1	yes	characteristic
984	C₄	—	2	2	no	—
985	C₄	—	2	4	no	—
986	C₄	—	2	2	no	—
987	C₄	—	4	1	no	—
988	C₄	—	4	2	no	—
989	C₄	—	4	1	no	—
990	C₄	—	4	2	no	—
991	C₄	—	8	1	no	—
992	C₄	—	8	1	no	—
993	C₄	C₂×#120×C₇₉	1	1	yes	characteristic
994	C₄	#534×C₇₉	1	1	yes	characteristic
995	C₄	D₄²×C₇₉	1	1	yes	characteristic
996	C₄	D₄²×C₇₉	1	1	yes	characteristic
997	C₂	—	4	2	no	—
998	C₂	—	8	1	no	—
999	C₂	—	8	2	no	—
1000	C₂	—	8	2	no	—
1001	C₂	—	8	2	no	—
1002	C₂	C₇₉×#2403	1	1	yes	characteristic
1003	C₂	C₇₉×#3002	1	1	yes	characteristic
1004	C₂	C₇₉×#3012	1	1	yes	characteristic
1005	C₂	C₇₉×#3268	1	1	yes	characteristic
1006	C₂	C₇₉×#3271	1	1	yes	characteristic
1007	C₂	C₇₉×#3284	1	1	yes	characteristic
1008	C₂	C₇₉×#3287	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×#550×C₇₉	C₂	semidirect
3. C₂×#452×C₇₉	C₂	semidirect
4. C₂×#449×C₇₉	C₂	semidirect
5. C₂×#449×C₇₉	C₂	semidirect
6. C₇₉×#2407	C₂	semidirect
7. C₇₉×#2014	C₂	semidirect
8. C₇₉×#2011	C₂	semidirect
9. C₇₉×#2000	C₂	semidirect
10. C₇₉×#1999	C₂	semidirect
11. C₇₉×#1893	C₂	semidirect
12. C₇₉×#1880	C₂	semidirect
13. C₇₉×#1878	C₂	semidirect
14. C₇₉×#1869	C₂	semidirect
15. C₇₉×#1788	C₂	semidirect
84. C₂×#41×C₇₉	D₄	semidirect
107. C₂×Q₁₆×C₇₉	D₄	semidirect
116. C₂×SD₁₆×C₇₉	D₄	semidirect
142. #121×C₇₉	D₄	semidirect
426. C₂×C₄×C₇₉	#135	semidirect
492. #23857	C₇₉	direct (N × H)
505. C₂²×#135	C₂×C₇₉	semidirect
506. C₂×#550	C₂×C₇₉	semidirect
507. C₂×#452	C₂×C₇₉	semidirect
508. C₂×#449	C₂×C₇₉	semidirect
509. C₂×#449	C₂×C₇₉	semidirect
510. #2407	C₂×C₇₉	semidirect
511. #2014	C₂×C₇₉	semidirect
512. #2011	C₂×C₇₉	semidirect
513. #2000	C₂×C₇₉	semidirect
514. #1999	C₂×C₇₉	semidirect
515. #1893	C₂×C₇₉	semidirect
516. #1880	C₂×C₇₉	semidirect
517. #1878	C₂×C₇₉	semidirect
518. #1869	C₂×C₇₉	semidirect
519. #1788	C₂×C₇₉	semidirect
520. C₇₉	#23857	direct (N × H)
589. C₂×#41	D₄×C₇₉	semidirect
612. C₂×Q₁₆	D₄×C₇₉	semidirect
621. C₂×SD₁₆	D₄×C₇₉	semidirect
647. #121	D₄×C₇₉	semidirect
931. 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×#550×C₇₉	2
C₂×#452×C₇₉	2
C₂×#449×C₇₉	2
C₇₉×#2407	2
C₇₉×#2014	2
C₇₉×#2011	2
C₇₉×#2000	2
C₇₉×#1999	2
C₇₉×#1893	2
C₇₉×#1880	2
C₇₉×#1878	2
C₇₉×#1869	2
C₇₉×#1788	2
#23857	79

Subgroups — C79×#23857 #34135546

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#23857 #34135546