Subgroups — C₇₉×#23850 #34135539

Order 20224.

1934 conjugacy classes of subgroups.

The subgroup lattice has 1020 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×#546×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#449×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#450×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#447×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₉×#2407	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#2015	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#2012	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×#1893	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, complemented
18	C₂³×D₄×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, complemented
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, complemented
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, complemented
29	#546×C₇₉	—	2	4	no	—
30	#546×C₇₉	—	2	4	no	—
31	C₂×#124×C₇₉	C₂²	1	1	yes	characteristic
32	C₂×#123×C₇₉	—	2	1	no	—
33	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
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×#120×C₇₉	—	2	1	no	—
39	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
41	C₂²×C₂²⋊C₄×C₇₉	—	2	1	no	—
42	#450×C₇₉	—	2	4	no	—
43	#449×C₇₉	—	2	4	no	—
44	#447×C₇₉	—	2	4	no	—
45	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic, complemented
46	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic, complemented
47	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic, complemented
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, complemented
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, complemented
56	#394×C₇₉	—	2	1	no	—
57	#392×C₇₉	—	2	1	no	—
58	#391×C₇₉	C₂²	1	1	yes	characteristic, complemented
59	#390×C₇₉	C₂²	1	1	yes	characteristic, complemented
60	#386×C₇₉	—	2	1	no	—
61	#385×C₇₉	—	2	1	no	—
62	#380×C₇₉	C₂²	1	1	yes	characteristic, complemented
63	#340×C₇₉	C₂²	1	1	yes	characteristic, complemented
64	#340×C₇₉	C₂²	1	1	yes	characteristic, complemented
65	#336×C₇₉	C₂²	1	1	yes	characteristic, complemented
66	#336×C₇₉	C₂²	1	1	yes	characteristic, complemented
67	C₂⁵×C₇₉	—	2	1	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	—	4	1	no	—
76	C₂×#41×C₇₉	—	4	1	no	—
77	C₂×#41×C₇₉	—	4	1	no	—
78	C₂×#41×C₇₉	—	4	1	no	—
79	C₂×#41×C₇₉	D₄	1	4	yes	complemented
80	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
81	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₇₉	—	2	1	no	—
83	C₂²×D₄×C₇₉	—	2	1	no	—
84	C₂²×D₄×C₇₉	—	2	2	no	—
85	C₂²×D₄×C₇₉	—	2	2	no	—
86	C₂²×D₄×C₇₉	—	2	2	no	—
87	C₂²×D₄×C₇₉	—	2	2	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	—	4	1	no	—
92	C₂²×D₄×C₇₉	—	4	1	no	—
93	C₂²×D₄×C₇₉	D₄	1	1	yes	characteristic
94	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
96	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₇₉	—	2	1	no	—
98	C₂³×C₄×C₇₉	—	2	1	no	—
99	C₂³×C₄×C₇₉	—	2	1	no	—
100	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
102	#135×C₇₉	—	2	32	no	—
103	C₂×Q₁₆×C₇₉	—	2	2	no	—
104	C₂×Q₁₆×C₇₉	—	2	2	no	—
105	C₂×Q₁₆×C₇₉	—	2	2	no	—
106	C₂×SD₁₆×C₇₉	—	2	2	no	—
107	C₂×SD₁₆×C₇₉	—	2	2	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	—	4	1	no	—
114	C₂×SD₁₆×C₇₉	D₄	1	4	yes	complemented
115	C₂×D₈×C₇₉	—	2	2	no	—
116	C₂×D₈×C₇₉	—	2	2	no	—
117	C₂×D₈×C₇₉	—	2	2	no	—
118	C₂×D₈×C₇₉	—	2	2	no	—
119	C₂×D₈×C₇₉	—	4	1	no	—
120	C₂×D₈×C₇₉	D₄	1	4	yes	complemented
121	C₂²×C₈×C₇₉	—	2	2	no	—
122	C₂²×C₈×C₇₉	—	2	2	no	—
123	C₂²×C₈×C₇₉	—	2	2	no	—
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	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
128	#124×C₇₉	—	2	2	no	—
129	#124×C₇₉	—	2	2	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	—	4	1	no	—
135	#121×C₇₉	—	2	8	no	—
136	#121×C₇₉	—	2	2	no	—
137	#121×C₇₉	—	2	2	no	—
138	#121×C₇₉	—	4	1	no	—
139	#121×C₇₉	D₄	1	4	yes	complemented
140	#120×C₇₉	—	2	8	no	—
141	C₄×D₄×C₇₉	—	2	2	no	—
142	C₄×D₄×C₇₉	—	2	2	no	—
143	C₄×D₄×C₇₉	—	2	2	no	—
144	C₄×D₄×C₇₉	—	2	2	no	—
145	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
146	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
147	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
151	C₂×C₂²⋊C₄×C₇₉	—	2	8	no	—
152	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
153	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
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	—	4	1	no	—
167	#103×C₇₉	—	4	1	no	—
168	#102×C₇₉	—	2	2	no	—
169	#102×C₇₉	—	2	2	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	4	no	—
181	C₂⁴×C₇₉	—	2	1	no	—
182	C₂⁴×C₇₉	—	2	1	no	—
183	C₂⁴×C₇₉	—	4	2	no	—
184	C₂⁴×C₇₉	—	4	2	no	—
185	C₂⁴×C₇₉	—	4	2	no	—
186	C₂⁴×C₇₉	—	4	2	no	—
187	C₂⁴×C₇₉	—	8	1	no	—
188	C₂⁴×C₇₉	—	8	1	no	—
189	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
190	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
191	#41×C₇₉	—	2	8	no	—
192	#41×C₇₉	—	2	8	no	—
193	#41×C₇₉	—	4	4	no	—
194	#41×C₇₉	—	4	4	no	—
195	#41×C₇₉	—	4	4	no	—
196	#41×C₇₉	—	4	4	no	—
197	#41×C₇₉	—	4	4	no	—
198	#41×C₇₉	—	4	4	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	C₂×D₄	1	2	yes	—
210	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
211	C₂×D₄×C₇₉	—	2	4	no	—
212	C₂×D₄×C₇₉	—	2	2	no	—
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	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	—	4	1	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	4	no	—
234	C₂×D₄×C₇₉	—	4	4	no	—
235	C₂×D₄×C₇₉	—	4	4	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	4	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	C₂×D₄	1	2	yes	—
247	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
248	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
249	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
250	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
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	4	no	—
259	C₂²×C₄×C₇₉	—	2	4	no	—
260	C₂²×C₄×C₇₉	—	2	1	no	—
261	C₂²×C₄×C₇₉	—	2	1	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	—	4	2	no	—
269	C₂²×C₄×C₇₉	—	4	2	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	—	8	1	no	—
274	C₂²×C₄×C₇₉	—	8	1	no	—
275	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
280	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
281	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
282	Q₁₆×C₇₉	—	2	8	no	—
283	SD₁₆×C₇₉	—	2	8	no	—
284	SD₁₆×C₇₉	—	2	8	no	—
285	SD₁₆×C₇₉	—	4	4	no	—
286	D₈×C₇₉	—	2	8	no	—
287	D₈×C₇₉	—	4	4	no	—
288	C₂×C₈×C₇₉	—	2	8	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	—	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	C₂×D₄	1	2	yes	—
300	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
301	C₄⋊C₄×C₇₉	—	2	4	no	—
302	C₄⋊C₄×C₇₉	—	2	2	no	—
303	C₄⋊C₄×C₇₉	—	2	1	no	—
304	C₄⋊C₄×C₇₉	—	2	1	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	—	4	2	no	—
309	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
310	C₂²⋊C₄×C₇₉	—	2	4	no	—
311	C₂²⋊C₄×C₇₉	—	2	4	no	—
312	C₂²⋊C₄×C₇₉	—	2	4	no	—
313	C₂²⋊C₄×C₇₉	—	2	4	no	—
314	C₂²⋊C₄×C₇₉	—	2	2	no	—
315	C₂²⋊C₄×C₇₉	—	2	2	no	—
316	C₂²⋊C₄×C₇₉	—	2	4	no	—
317	C₂²⋊C₄×C₇₉	—	4	2	no	—
318	C₂²⋊C₄×C₇₉	—	4	2	no	—
319	C₂²⋊C₄×C₇₉	—	4	2	no	—
320	C₂²⋊C₄×C₇₉	—	8	1	no	—
321	C₂²⋊C₄×C₇₉	—	8	1	no	—
322	C₄²×C₇₉	—	2	1	no	—
323	C₄²×C₇₉	—	2	1	no	—
324	C₂³×C₇₉	—	2	1	no	—
325	C₂³×C₇₉	—	2	2	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	2	no	—
331	C₂³×C₇₉	—	2	2	no	—
332	C₂³×C₇₉	—	2	1	no	—
333	C₂³×C₇₉	—	2	1	no	—
334	C₂³×C₇₉	—	2	1	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	2	no	—
340	C₂³×C₇₉	—	2	2	no	—
341	C₂³×C₇₉	—	4	8	no	—
342	C₂³×C₇₉	—	4	8	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	—	4	1	no	—
359	C₂³×C₇₉	—	8	4	no	—
360	C₂³×C₇₉	—	8	4	no	—
361	C₂³×C₇₉	—	8	4	no	—
362	C₂³×C₇₉	—	8	4	no	—
363	C₂³×C₇₉	—	8	4	no	—
364	C₂³×C₇₉	#120	1	2	yes	—
365	C₂³×C₇₉	#135	1	2	yes	complemented
366	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
367	Q₈×C₇₉	—	2	2	no	—
368	Q₈×C₇₉	—	2	2	no	—
369	Q₈×C₇₉	—	2	2	no	—
370	Q₈×C₇₉	—	2	2	no	—
371	Q₈×C₇₉	—	4	1	no	—
372	Q₈×C₇₉	—	4	1	no	—
373	Q₈×C₇₉	—	4	1	no	—
374	Q₈×C₇₉	—	4	1	no	—
375	D₄×C₇₉	—	2	2	no	—
376	D₄×C₇₉	—	2	2	no	—
377	D₄×C₇₉	—	2	2	no	—
378	D₄×C₇₉	—	2	2	no	—
379	D₄×C₇₉	—	2	2	no	—
380	D₄×C₇₉	—	2	2	no	—
381	D₄×C₇₉	—	2	2	no	—
382	D₄×C₇₉	—	4	4	no	—
383	D₄×C₇₉	—	4	8	no	—
384	D₄×C₇₉	—	4	8	no	—
385	D₄×C₇₉	—	4	8	no	—
386	D₄×C₇₉	—	4	1	no	—
387	D₄×C₇₉	—	4	1	no	—
388	D₄×C₇₉	—	4	1	no	—
389	D₄×C₇₉	—	4	1	no	—
390	D₄×C₇₉	—	8	4	no	—
391	D₄×C₇₉	—	8	4	no	—
392	D₄×C₇₉	#120	1	4	yes	—
393	C₂×C₄×C₇₉	—	2	1	no	—
394	C₂×C₄×C₇₉	—	2	1	no	—
395	C₂×C₄×C₇₉	—	2	2	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	1	no	—
400	C₂×C₄×C₇₉	—	2	1	no	—
401	C₂×C₄×C₇₉	—	2	2	no	—
402	C₂×C₄×C₇₉	—	2	2	no	—
403	C₂×C₄×C₇₉	—	2	1	no	—
404	C₂×C₄×C₇₉	—	2	1	no	—
405	C₂×C₄×C₇₉	—	2	2	no	—
406	C₂×C₄×C₇₉	—	2	1	no	—
407	C₂×C₄×C₇₉	—	2	1	no	—
408	C₂×C₄×C₇₉	—	2	1	no	—
409	C₂×C₄×C₇₉	—	2	1	no	—
410	C₂×C₄×C₇₉	—	2	1	no	—
411	C₂×C₄×C₇₉	—	4	8	no	—
412	C₂×C₄×C₇₉	—	4	8	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	—	4	1	no	—
426	C₂×C₄×C₇₉	—	4	1	no	—
427	C₂×C₄×C₇₉	—	4	1	no	—
428	C₂×C₄×C₇₉	—	4	1	no	—
429	C₂×C₄×C₇₉	—	8	4	no	—
430	C₂×C₄×C₇₉	#120	1	2	yes	—
431	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
432	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
433	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
434	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
435	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
436	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
437	C₈×C₇₉	—	2	2	no	—
438	C₈×C₇₉	—	2	2	no	—
439	C₈×C₇₉	—	4	1	no	—
440	C₈×C₇₉	—	4	1	no	—
441	C₂²×C₇₉	—	2	2	no	—
442	C₂²×C₇₉	—	2	4	no	—
443	C₂²×C₇₉	—	2	2	no	—
444	C₂²×C₇₉	—	2	2	no	—
445	C₂²×C₇₉	—	2	2	no	—
446	C₂²×C₇₉	—	2	2	no	—
447	C₂²×C₇₉	—	2	2	no	—
448	C₂²×C₇₉	—	4	1	no	—
449	C₂²×C₇₉	—	4	2	no	—
450	C₂²×C₇₉	—	4	1	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	1	no	—
456	C₂²×C₇₉	—	4	1	no	—
457	C₂²×C₇₉	—	4	2	no	—
458	C₂²×C₇₉	—	4	1	no	—
459	C₂²×C₇₉	—	4	2	no	—
460	C₂²×C₇₉	—	4	1	no	—
461	C₂²×C₇₉	—	4	2	no	—
462	C₂²×C₇₉	—	4	2	no	—
463	C₂²×C₇₉	—	4	2	no	—
464	C₂²×C₇₉	—	4	2	no	—
465	C₂²×C₇₉	—	4	2	no	—
466	C₂²×C₇₉	—	4	2	no	—
467	C₂²×C₇₉	—	4	2	no	—
468	C₂²×C₇₉	—	8	16	no	—
469	C₂²×C₇₉	—	8	1	no	—
470	C₂²×C₇₉	—	8	1	no	—
471	C₂²×C₇₉	—	8	1	no	—
472	C₂²×C₇₉	—	8	1	no	—
473	C₂²×C₇₉	—	8	1	no	—
474	C₂²×C₇₉	—	8	1	no	—
475	C₂²×C₇₉	—	8	1	no	—
476	C₂²×C₇₉	—	8	1	no	—
477	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
478	C₂²×C₇₉	D₄²	1	1	yes	characteristic
479	C₂²×C₇₉	D₄²	1	1	yes	characteristic
480	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
481	C₂²×C₇₉	#575	1	1	yes	characteristic
482	C₂²×C₇₉	#576	1	1	yes	characteristic
483	C₂²×C₇₉	#577	1	1	yes	characteristic
484	C₄×C₇₉	—	2	2	no	—
485	C₄×C₇₉	—	4	1	no	—
486	C₄×C₇₉	—	4	2	no	—
487	C₄×C₇₉	—	4	2	no	—
488	C₄×C₇₉	—	4	1	no	—
489	C₄×C₇₉	—	4	1	no	—
490	C₄×C₇₉	—	4	2	no	—
491	C₄×C₇₉	—	8	1	no	—
492	C₄×C₇₉	—	8	1	no	—
493	C₄×C₇₉	C₂×#120	1	1	yes	characteristic
494	C₄×C₇₉	#534	1	1	yes	characteristic
495	C₄×C₇₉	D₄²	1	1	yes	characteristic
496	C₄×C₇₉	D₄²	1	1	yes	characteristic
497	#23850	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
498	C₂×C₇₉	—	4	2	no	—
499	C₂×C₇₉	—	4	2	no	—
500	C₂×C₇₉	—	4	4	no	—
501	C₂×C₇₉	—	8	2	no	—
502	C₂×C₇₉	—	8	2	no	—
503	C₂×C₇₉	#2403	1	1	yes	characteristic
504	C₂×C₇₉	#3002	1	1	yes	characteristic
505	C₂×C₇₉	#3012	1	1	yes	characteristic
506	C₂×C₇₉	#3267	1	1	yes	characteristic
507	C₂×C₇₉	#3268	1	1	yes	characteristic
508	C₂×C₇₉	#3280	1	1	yes	characteristic
509	C₂×C₇₉	#3282	1	1	yes	characteristic
510	C₂²×#135	C₂×C₇₉	1	1	yes	characteristic, complemented
511	C₂×#546	C₂×C₇₉	1	1	yes	characteristic, complemented
512	C₂×#449	C₂×C₇₉	1	1	yes	characteristic, complemented
513	C₂×#450	C₂×C₇₉	1	1	yes	characteristic, complemented
514	C₂×#447	C₂×C₇₉	1	1	yes	characteristic, complemented
515	#2407	C₂×C₇₉	1	1	yes	characteristic, complemented
516	#2015	C₂×C₇₉	1	1	yes	characteristic, complemented
517	#2012	C₂×C₇₉	1	1	yes	characteristic, complemented
518	#2001	C₂×C₇₉	1	1	yes	characteristic, complemented
519	#2000	C₂×C₇₉	1	1	yes	characteristic, complemented
520	#1893	C₂×C₇₉	1	1	yes	characteristic, complemented
521	#1879	C₂×C₇₉	1	1	yes	characteristic, complemented
522	#1877	C₂×C₇₉	1	1	yes	characteristic, complemented
523	#1869	C₂×C₇₉	1	1	yes	characteristic, complemented
524	#1788	C₂×C₇₉	1	1	yes	characteristic, complemented
525	C₇₉	#23850	1	1	yes	characteristic, direct product factor, Sylow
526	C₂²×#41	C₂²×C₇₉	1	1	yes	characteristic
527	C₂²×#41	C₂²×C₇₉	1	1	yes	characteristic, complemented
528	C₂³×D₄	C₂²×C₇₉	1	1	yes	characteristic
529	C₂×#135	—	2	4	no	—
530	C₂×#135	—	2	4	no	—
531	C₂×#135	—	2	4	no	—
532	C₂²×Q₁₆	C₂²×C₇₉	1	1	yes	characteristic, complemented
533	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
534	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
535	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic, complemented
536	C₂²×D₈	C₂²×C₇₉	1	1	yes	characteristic
537	C₂²×D₈	C₂²×C₇₉	1	1	yes	characteristic
538	C₂³×C₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
539	#546	—	2	4	no	—
540	#546	—	2	4	no	—
541	C₂×#124	C₂²×C₇₉	1	1	yes	characteristic
542	C₂×#123	—	2	1	no	—
543	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
544	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
545	C₂×#121	—	2	1	no	—
546	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
547	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
548	C₂×#120	—	2	1	no	—
549	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
550	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
551	C₂²×C₂²⋊C₄	—	2	1	no	—
552	#450	—	2	4	no	—
553	#449	—	2	4	no	—
554	#447	—	2	4	no	—
555	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic, complemented
556	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic, complemented
557	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic, complemented
558	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
559	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
560	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
561	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
562	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic, complemented
563	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
564	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
565	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
566	#394	—	2	1	no	—
567	#392	—	2	1	no	—
568	#391	C₂²×C₇₉	1	1	yes	characteristic, complemented
569	#390	C₂²×C₇₉	1	1	yes	characteristic, complemented
570	#386	—	2	1	no	—
571	#385	—	2	1	no	—
572	#380	C₂²×C₇₉	1	1	yes	characteristic, complemented
573	#340	C₂²×C₇₉	1	1	yes	characteristic, complemented
574	#340	C₂²×C₇₉	1	1	yes	characteristic, complemented
575	#336	C₂²×C₇₉	1	1	yes	characteristic, complemented
576	#336	C₂²×C₇₉	1	1	yes	characteristic, complemented
577	C₂⁵	—	2	1	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	—	2	2	no	—
584	C₂×#41	—	2	2	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	2	no	—
595	C₂²×D₄	—	2	2	no	—
596	C₂²×D₄	—	2	2	no	—
597	C₂²×D₄	—	2	2	no	—
598	C₂²×D₄	—	2	1	no	—
599	C₂²×D₄	—	2	1	no	—
600	C₂²×D₄	—	2	1	no	—
601	C₂²×D₄	—	4	1	no	—
602	C₂²×D₄	—	4	1	no	—
603	C₂²×D₄	D₄×C₇₉	1	1	yes	characteristic
604	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
605	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
606	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
607	C₂³×C₄	—	2	1	no	—
608	C₂³×C₄	—	2	1	no	—
609	C₂³×C₄	—	2	1	no	—
610	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
611	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
612	#135	—	2	32	no	—
613	C₂×Q₁₆	—	2	2	no	—
614	C₂×Q₁₆	—	2	2	no	—
615	C₂×Q₁₆	—	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	—	2	2	no	—
621	C₂×SD₁₆	—	2	2	no	—
622	C₂×SD₁₆	—	2	2	no	—
623	C₂×SD₁₆	—	4	1	no	—
624	C₂×SD₁₆	D₄×C₇₉	1	4	yes	complemented
625	C₂×D₈	—	2	2	no	—
626	C₂×D₈	—	2	2	no	—
627	C₂×D₈	—	2	2	no	—
628	C₂×D₈	—	2	2	no	—
629	C₂×D₈	—	4	1	no	—
630	C₂×D₈	D₄×C₇₉	1	4	yes	complemented
631	C₂²×C₈	—	2	2	no	—
632	C₂²×C₈	—	2	2	no	—
633	C₂²×C₈	—	2	2	no	—
634	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
635	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
636	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
637	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
638	#124	—	2	2	no	—
639	#124	—	2	2	no	—
640	#123	—	2	8	no	—
641	C₂²⋊Q₈	—	2	2	no	—
642	C₂²⋊Q₈	—	2	2	no	—
643	C₂²⋊Q₈	—	2	2	no	—
644	C₂²⋊Q₈	—	4	1	no	—
645	#121	—	2	8	no	—
646	#121	—	2	2	no	—
647	#121	—	2	2	no	—
648	#121	—	4	1	no	—
649	#121	D₄×C₇₉	1	4	yes	complemented
650	#120	—	2	8	no	—
651	C₄×D₄	—	2	2	no	—
652	C₄×D₄	—	2	2	no	—
653	C₄×D₄	—	2	2	no	—
654	C₄×D₄	—	2	2	no	—
655	C₂×C₄⋊C₄	—	2	1	no	—
656	C₂×C₄⋊C₄	—	2	1	no	—
657	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
658	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
659	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
660	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
661	C₂×C₂²⋊C₄	—	2	8	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	—	2	1	no	—
667	C₂×C₂²⋊C₄	—	2	1	no	—
668	C₂×C₂²⋊C₄	—	2	1	no	—
669	C₂×C₂²⋊C₄	—	2	1	no	—
670	C₂×C₂²⋊C₄	—	2	1	no	—
671	C₂×C₂²⋊C₄	—	2	1	no	—
672	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
673	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
674	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
675	#103	—	2	2	no	—
676	#103	—	4	1	no	—
677	#103	—	4	1	no	—
678	#102	—	2	2	no	—
679	#102	—	2	2	no	—
680	#102	—	2	2	no	—
681	#102	—	2	2	no	—
682	#102	—	2	2	no	—
683	C₂²⋊C₈	—	2	2	no	—
684	C₂²⋊C₈	—	2	2	no	—
685	C₂²⋊C₈	—	2	2	no	—
686	#95	—	2	1	no	—
687	#95	—	2	1	no	—
688	#95	—	2	1	no	—
689	C₂⁴	—	2	1	no	—
690	C₂⁴	—	2	4	no	—
691	C₂⁴	—	2	1	no	—
692	C₂⁴	—	2	1	no	—
693	C₂⁴	—	4	2	no	—
694	C₂⁴	—	4	2	no	—
695	C₂⁴	—	4	2	no	—
696	C₂⁴	—	4	2	no	—
697	C₂⁴	—	8	1	no	—
698	C₂⁴	—	8	1	no	—
699	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
700	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
701	#41	—	2	8	no	—
702	#41	—	2	8	no	—
703	#41	—	4	4	no	—
704	#41	—	4	4	no	—
705	#41	—	4	4	no	—
706	#41	—	4	4	no	—
707	#41	—	4	4	no	—
708	#41	—	4	4	no	—
709	C₂×Q₈	—	2	1	no	—
710	C₂×Q₈	—	2	1	no	—
711	C₂×Q₈	—	2	1	no	—
712	C₂×Q₈	—	2	1	no	—
713	C₂×Q₈	—	2	1	no	—
714	C₂×Q₈	—	2	1	no	—
715	C₂×Q₈	—	2	1	no	—
716	C₂×Q₈	—	2	1	no	—
717	C₂×Q₈	—	2	1	no	—
718	C₂×Q₈	—	2	1	no	—
719	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
720	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
721	C₂×D₄	—	2	4	no	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	2	4	no	—
724	C₂×D₄	—	2	2	no	—
725	C₂×D₄	—	2	4	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	—	2	1	no	—
737	C₂×D₄	—	2	1	no	—
738	C₂×D₄	—	2	1	no	—
739	C₂×D₄	—	4	1	no	—
740	C₂×D₄	—	4	2	no	—
741	C₂×D₄	—	4	2	no	—
742	C₂×D₄	—	4	2	no	—
743	C₂×D₄	—	4	4	no	—
744	C₂×D₄	—	4	4	no	—
745	C₂×D₄	—	4	4	no	—
746	C₂×D₄	—	4	2	no	—
747	C₂×D₄	—	4	2	no	—
748	C₂×D₄	—	4	2	no	—
749	C₂×D₄	—	4	2	no	—
750	C₂×D₄	—	4	4	no	—
751	C₂×D₄	—	4	2	no	—
752	C₂×D₄	—	4	2	no	—
753	C₂×D₄	—	8	1	no	—
754	C₂×D₄	—	8	1	no	—
755	C₂×D₄	—	8	1	no	—
756	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
757	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
758	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
759	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
760	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
761	C₂²×C₄	—	2	1	no	—
762	C₂²×C₄	—	2	1	no	—
763	C₂²×C₄	—	2	1	no	—
764	C₂²×C₄	—	2	1	no	—
765	C₂²×C₄	—	2	1	no	—
766	C₂²×C₄	—	2	1	no	—
767	C₂²×C₄	—	2	1	no	—
768	C₂²×C₄	—	2	4	no	—
769	C₂²×C₄	—	2	4	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	—	2	1	no	—
776	C₂²×C₄	—	2	1	no	—
777	C₂²×C₄	—	2	1	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	—	4	2	no	—
783	C₂²×C₄	—	8	1	no	—
784	C₂²×C₄	—	8	1	no	—
785	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
786	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
787	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
788	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
789	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
790	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
791	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
792	Q₁₆	—	2	8	no	—
793	SD₁₆	—	2	8	no	—
794	SD₁₆	—	2	8	no	—
795	SD₁₆	—	4	4	no	—
796	D₈	—	2	8	no	—
797	D₈	—	4	4	no	—
798	C₂×C₈	—	2	8	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	—	2	1	no	—
807	C₂×C₈	—	2	1	no	—
808	C₂×C₈	—	2	1	no	—
809	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
810	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
811	C₄⋊C₄	—	2	4	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	1	no	—
814	C₄⋊C₄	—	2	1	no	—
815	C₄⋊C₄	—	2	1	no	—
816	C₄⋊C₄	—	2	1	no	—
817	C₄⋊C₄	—	2	1	no	—
818	C₄⋊C₄	—	4	2	no	—
819	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
820	C₂²⋊C₄	—	2	4	no	—
821	C₂²⋊C₄	—	2	4	no	—
822	C₂²⋊C₄	—	2	4	no	—
823	C₂²⋊C₄	—	2	4	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	4	no	—
827	C₂²⋊C₄	—	4	2	no	—
828	C₂²⋊C₄	—	4	2	no	—
829	C₂²⋊C₄	—	4	2	no	—
830	C₂²⋊C₄	—	8	1	no	—
831	C₂²⋊C₄	—	8	1	no	—
832	C₄²	—	2	1	no	—
833	C₄²	—	2	1	no	—
834	C₂³	—	2	1	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	1	no	—
837	C₂³	—	2	1	no	—
838	C₂³	—	2	1	no	—
839	C₂³	—	2	1	no	—
840	C₂³	—	2	2	no	—
841	C₂³	—	2	2	no	—
842	C₂³	—	2	1	no	—
843	C₂³	—	2	1	no	—
844	C₂³	—	2	1	no	—
845	C₂³	—	2	1	no	—
846	C₂³	—	2	1	no	—
847	C₂³	—	2	1	no	—
848	C₂³	—	2	1	no	—
849	C₂³	—	2	2	no	—
850	C₂³	—	2	2	no	—
851	C₂³	—	4	8	no	—
852	C₂³	—	4	8	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	—	4	1	no	—
864	C₂³	—	4	1	no	—
865	C₂³	—	4	1	no	—
866	C₂³	—	4	1	no	—
867	C₂³	—	4	1	no	—
868	C₂³	—	4	1	no	—
869	C₂³	—	8	4	no	—
870	C₂³	—	8	4	no	—
871	C₂³	—	8	4	no	—
872	C₂³	—	8	4	no	—
873	C₂³	—	8	4	no	—
874	C₂³	#120×C₇₉	1	2	yes	—
875	C₂³	#135×C₇₉	1	2	yes	complemented
876	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
877	Q₈	—	2	2	no	—
878	Q₈	—	2	2	no	—
879	Q₈	—	2	2	no	—
880	Q₈	—	2	2	no	—
881	Q₈	—	4	1	no	—
882	Q₈	—	4	1	no	—
883	Q₈	—	4	1	no	—
884	Q₈	—	4	1	no	—
885	D₄	—	2	2	no	—
886	D₄	—	2	2	no	—
887	D₄	—	2	2	no	—
888	D₄	—	2	2	no	—
889	D₄	—	2	2	no	—
890	D₄	—	2	2	no	—
891	D₄	—	2	2	no	—
892	D₄	—	4	4	no	—
893	D₄	—	4	8	no	—
894	D₄	—	4	8	no	—
895	D₄	—	4	8	no	—
896	D₄	—	4	1	no	—
897	D₄	—	4	1	no	—
898	D₄	—	4	1	no	—
899	D₄	—	4	1	no	—
900	D₄	—	8	4	no	—
901	D₄	—	8	4	no	—
902	D₄	#120×C₇₉	1	4	yes	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	4	8	no	—
922	C₂×C₄	—	4	8	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	—	4	1	no	—
931	C₂×C₄	—	4	1	no	—
932	C₂×C₄	—	4	1	no	—
933	C₂×C₄	—	4	1	no	—
934	C₂×C₄	—	4	1	no	—
935	C₂×C₄	—	4	1	no	—
936	C₂×C₄	—	4	1	no	—
937	C₂×C₄	—	4	1	no	—
938	C₂×C₄	—	4	1	no	—
939	C₂×C₄	—	8	4	no	—
940	C₂×C₄	#120×C₇₉	1	2	yes	—
941	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
942	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
943	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
944	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
945	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
946	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
947	C₈	—	2	2	no	—
948	C₈	—	2	2	no	—
949	C₈	—	4	1	no	—
950	C₈	—	4	1	no	—
951	C₂²	—	2	2	no	—
952	C₂²	—	2	2	no	—
953	C₂²	—	2	2	no	—
954	C₂²	—	2	4	no	—
955	C₂²	—	2	2	no	—
956	C₂²	—	2	2	no	—
957	C₂²	—	2	2	no	—
958	C₂²	—	4	1	no	—
959	C₂²	—	4	2	no	—
960	C₂²	—	4	1	no	—
961	C₂²	—	4	2	no	—
962	C₂²	—	4	1	no	—
963	C₂²	—	4	2	no	—
964	C₂²	—	4	1	no	—
965	C₂²	—	4	1	no	—
966	C₂²	—	4	2	no	—
967	C₂²	—	4	2	no	—
968	C₂²	—	4	1	no	—
969	C₂²	—	4	1	no	—
970	C₂²	—	4	1	no	—
971	C₂²	—	4	2	no	—
972	C₂²	—	4	2	no	—
973	C₂²	—	4	2	no	—
974	C₂²	—	4	2	no	—
975	C₂²	—	4	2	no	—
976	C₂²	—	4	2	no	—
977	C₂²	—	4	2	no	—
978	C₂²	—	8	16	no	—
979	C₂²	—	8	1	no	—
980	C₂²	—	8	1	no	—
981	C₂²	—	8	1	no	—
982	C₂²	—	8	1	no	—
983	C₂²	—	8	1	no	—
984	C₂²	—	8	1	no	—
985	C₂²	—	8	1	no	—
986	C₂²	—	8	1	no	—
987	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
988	C₂²	D₄²×C₇₉	1	1	yes	characteristic
989	C₂²	D₄²×C₇₉	1	1	yes	characteristic
990	C₂²	C₂×#135×C₇₉	1	1	yes	characteristic
991	C₂²	#575×C₇₉	1	1	yes	characteristic
992	C₂²	#576×C₇₉	1	1	yes	characteristic
993	C₂²	#577×C₇₉	1	1	yes	characteristic
994	C₄	—	2	2	no	—
995	C₄	—	4	1	no	—
996	C₄	—	4	2	no	—
997	C₄	—	4	2	no	—
998	C₄	—	4	1	no	—
999	C₄	—	4	1	no	—
1000	C₄	—	4	2	no	—
1001	C₄	—	8	1	no	—
1002	C₄	—	8	1	no	—
1003	C₄	C₂×#120×C₇₉	1	1	yes	characteristic
1004	C₄	#534×C₇₉	1	1	yes	characteristic
1005	C₄	D₄²×C₇₉	1	1	yes	characteristic
1006	C₄	D₄²×C₇₉	1	1	yes	characteristic
1007	C₂	—	4	2	no	—
1008	C₂	—	4	2	no	—
1009	C₂	—	4	4	no	—
1010	C₂	—	8	2	no	—
1011	C₂	—	8	2	no	—
1012	C₂	C₇₉×#2403	1	1	yes	characteristic
1013	C₂	C₇₉×#3002	1	1	yes	characteristic
1014	C₂	C₇₉×#3012	1	1	yes	characteristic
1015	C₂	C₇₉×#3267	1	1	yes	characteristic
1016	C₂	C₇₉×#3268	1	1	yes	characteristic
1017	C₂	C₇₉×#3280	1	1	yes	characteristic
1018	C₂	C₇₉×#3282	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×#546×C₇₉	C₂	semidirect
3. C₂×#449×C₇₉	C₂	semidirect
4. C₂×#450×C₇₉	C₂	semidirect
5. C₂×#447×C₇₉	C₂	semidirect
6. C₇₉×#2407	C₂	semidirect
7. C₇₉×#2015	C₂	semidirect
8. C₇₉×#2012	C₂	semidirect
9. C₇₉×#2001	C₂	semidirect
10. C₇₉×#2000	C₂	semidirect
11. C₇₉×#1893	C₂	semidirect
12. C₇₉×#1879	C₂	semidirect
13. C₇₉×#1877	C₂	semidirect
14. C₇₉×#1869	C₂	semidirect
15. C₇₉×#1788	C₂	semidirect
17. C₂²×#41×C₇₉	C₂²	semidirect
22. C₂²×Q₁₆×C₇₉	C₂²	semidirect
25. C₂²×SD₁₆×C₇₉	C₂²	semidirect
28. C₂³×C₈×C₇₉	C₂²	semidirect
45. C₂×#103×C₇₉	C₂²	semidirect
46. C₂×#103×C₇₉	C₂²	semidirect
47. C₂×#103×C₇₉	C₂²	semidirect
52. C₂×#102×C₇₉	C₂²	semidirect
55. C₂×C₂²⋊C₈×C₇₉	C₂²	semidirect
58. #391×C₇₉	C₂²	semidirect
59. #390×C₇₉	C₂²	semidirect
62. #380×C₇₉	C₂²	semidirect
63. #340×C₇₉	C₂²	semidirect
64. #340×C₇₉	C₂²	semidirect
65. #336×C₇₉	C₂²	semidirect
66. #336×C₇₉	C₂²	semidirect
79. C₂×#41×C₇₉	D₄	semidirect
114. C₂×SD₁₆×C₇₉	D₄	semidirect
120. C₂×D₈×C₇₉	D₄	semidirect
139. #121×C₇₉	D₄	semidirect
365. C₂³×C₇₉	#135	semidirect
497. #23850	C₇₉	direct (N × H)
510. C₂²×#135	C₂×C₇₉	semidirect
511. C₂×#546	C₂×C₇₉	semidirect
512. C₂×#449	C₂×C₇₉	semidirect
513. C₂×#450	C₂×C₇₉	semidirect
514. C₂×#447	C₂×C₇₉	semidirect
515. #2407	C₂×C₇₉	semidirect
516. #2015	C₂×C₇₉	semidirect
517. #2012	C₂×C₇₉	semidirect
518. #2001	C₂×C₇₉	semidirect
519. #2000	C₂×C₇₉	semidirect
520. #1893	C₂×C₇₉	semidirect
521. #1879	C₂×C₇₉	semidirect
522. #1877	C₂×C₇₉	semidirect
523. #1869	C₂×C₇₉	semidirect
524. #1788	C₂×C₇₉	semidirect
525. C₇₉	#23850	direct (N × H)
527. C₂²×#41	C₂²×C₇₉	semidirect
532. C₂²×Q₁₆	C₂²×C₇₉	semidirect
535. C₂²×SD₁₆	C₂²×C₇₉	semidirect
538. C₂³×C₈	C₂²×C₇₉	semidirect
555. C₂×#103	C₂²×C₇₉	semidirect
556. C₂×#103	C₂²×C₇₉	semidirect
557. C₂×#103	C₂²×C₇₉	semidirect
562. C₂×#102	C₂²×C₇₉	semidirect
565. C₂×C₂²⋊C₈	C₂²×C₇₉	semidirect
568. #391	C₂²×C₇₉	semidirect
569. #390	C₂²×C₇₉	semidirect
572. #380	C₂²×C₇₉	semidirect
573. #340	C₂²×C₇₉	semidirect
574. #340	C₂²×C₇₉	semidirect
575. #336	C₂²×C₇₉	semidirect
576. #336	C₂²×C₇₉	semidirect
589. C₂×#41	D₄×C₇₉	semidirect
624. C₂×SD₁₆	D₄×C₇₉	semidirect
630. C₂×D₈	D₄×C₇₉	semidirect
649. #121	D₄×C₇₉	semidirect
875. C₂³	#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×#546×C₇₉	2
C₂×#449×C₇₉	2
C₂×#450×C₇₉	2
C₂×#447×C₇₉	2
C₇₉×#2407	2
C₇₉×#2015	2
C₇₉×#2012	2
C₇₉×#2001	2
C₇₉×#2000	2
C₇₉×#1893	2
C₇₉×#1879	2
C₇₉×#1877	2
C₇₉×#1869	2
C₇₉×#1788	2
#23850	79

Subgroups — C79×#23850 #34135539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#23850 #34135539