Subgroups — C₇₉×#25547 #34137236

Order 20224.

1340 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#547×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#484×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#468×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#2415	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#2057	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₉×#2033	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#2024	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#2000	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#1877	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#1875	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1872	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₉×#1870	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₉×#1862	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₉×#1852	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#1736	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₇₉	—	2	1	no	—
17	C₂²×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
19	#547×C₇₉	—	2	4	no	—
20	#547×C₇₉	—	2	4	no	—
21	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
22	C₂×#123×C₇₉	—	2	1	no	—
23	C₂×#123×C₇₉	—	2	1	no	—
24	C₂×C₂²⋊Q₈×C₇₉	—	2	1	no	—
25	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
27	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
28	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
31	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
34	#484×C₇₉	—	2	4	no	—
35	#468×C₇₉	—	2	4	no	—
36	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic
37	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic
38	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic
39	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
40	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
41	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
42	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
43	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
44	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
48	#397×C₇₉	—	2	1	no	—
49	#394×C₇₉	—	2	1	no	—
50	#391×C₇₉	C₂²	1	1	yes	characteristic
51	#389×C₇₉	—	2	1	no	—
52	#389×C₇₉	C₂²	1	1	yes	characteristic
53	#388×C₇₉	—	2	1	no	—
54	#380×C₇₉	C₂²	1	1	yes	characteristic
55	#340×C₇₉	C₂²	1	1	yes	characteristic
56	#340×C₇₉	C₂²	1	1	yes	characteristic
57	#340×C₇₉	C₂²	1	1	yes	characteristic
58	#340×C₇₉	C₂²	1	1	yes	characteristic
59	#340×C₇₉	C₂²	1	1	yes	characteristic
60	#340×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	8	no	—
64	C₂×#41×C₇₉	—	4	4	no	—
65	C₂×#41×C₇₉	—	4	4	no	—
66	C₂²×Q₈×C₇₉	—	2	1	no	—
67	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₇₉	—	2	1	no	—
69	C₂²×D₄×C₇₉	—	2	1	no	—
70	C₂²×D₄×C₇₉	D₄	1	1	yes	characteristic
71	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₇₉	—	2	1	no	—
73	C₂³×C₄×C₇₉	—	2	1	no	—
74	C₂³×C₄×C₇₉	—	2	1	no	—
75	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
77	C₂×SD₁₆×C₇₉	—	2	2	no	—
78	C₂×SD₁₆×C₇₉	—	2	2	no	—
79	C₂×SD₁₆×C₇₉	—	4	1	no	—
80	C₂×M₁₆×C₇₉	—	2	2	no	—
81	C₂×M₁₆×C₇₉	—	2	2	no	—
82	C₂×M₁₆×C₇₉	—	4	1	no	—
83	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
87	C₄⋊Q₈×C₇₉	—	2	2	no	—
88	C₄⋊Q₈×C₇₉	—	2	2	no	—
89	#123×C₇₉	—	2	8	no	—
90	#123×C₇₉	—	2	8	no	—
91	C₂²⋊Q₈×C₇₉	—	2	8	no	—
92	C₂²⋊Q₈×C₇₉	—	2	2	no	—
93	C₂²⋊Q₈×C₇₉	—	2	2	no	—
94	C₂²⋊Q₈×C₇₉	—	2	2	no	—
95	C₂²⋊Q₈×C₇₉	—	4	1	no	—
96	#121×C₇₉	—	2	2	no	—
97	#121×C₇₉	—	2	2	no	—
98	#121×C₇₉	—	2	2	no	—
99	#121×C₇₉	D₄	1	4	yes	—
100	C₄×D₄×C₇₉	—	2	2	no	—
101	C₄×D₄×C₇₉	—	2	2	no	—
102	C₄×D₄×C₇₉	—	2	2	no	—
103	C₄×D₄×C₇₉	—	2	2	no	—
104	#117×C₇₉	—	2	2	no	—
105	#117×C₇₉	—	4	1	no	—
106	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
107	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
108	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
109	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
110	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
111	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
112	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
113	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
114	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
115	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₇₉	D₄	1	4	yes	—
117	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
123	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
129	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
130	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
131	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
132	C₂×C₄²×C₇₉	—	2	1	no	—
133	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
134	#107×C₇₉	—	2	2	no	—
135	#107×C₇₉	—	2	2	no	—
136	#107×C₇₉	—	2	2	no	—
137	#103×C₇₉	—	2	2	no	—
138	#103×C₇₉	—	2	2	no	—
139	#103×C₇₉	—	2	2	no	—
140	#102×C₇₉	—	2	2	no	—
141	#102×C₇₉	—	2	2	no	—
142	#102×C₇₉	—	4	1	no	—
143	C₂²⋊C₈×C₇₉	—	2	2	no	—
144	C₂²⋊C₈×C₇₉	—	2	2	no	—
145	C₂²⋊C₈×C₇₉	—	4	1	no	—
146	#95×C₇₉	—	2	1	no	—
147	#95×C₇₉	—	2	1	no	—
148	#95×C₇₉	—	2	1	no	—
149	#95×C₇₉	—	2	1	no	—
150	C₂⁴×C₇₉	—	2	1	no	—
151	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
152	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
153	#41×C₇₉	—	4	32	no	—
154	C₂×Q₈×C₇₉	—	2	4	no	—
155	C₂×Q₈×C₇₉	—	2	1	no	—
156	C₂×Q₈×C₇₉	—	2	1	no	—
157	C₂×Q₈×C₇₉	—	2	1	no	—
158	C₂×Q₈×C₇₉	—	2	1	no	—
159	C₂×Q₈×C₇₉	—	2	1	no	—
160	C₂×Q₈×C₇₉	—	2	1	no	—
161	C₂×Q₈×C₇₉	—	4	2	no	—
162	C₂×Q₈×C₇₉	—	4	2	no	—
163	C₂×D₄×C₇₉	—	2	2	no	—
164	C₂×D₄×C₇₉	—	2	2	no	—
165	C₂×D₄×C₇₉	—	2	4	no	—
166	C₂×D₄×C₇₉	—	2	4	no	—
167	C₂×D₄×C₇₉	—	2	2	no	—
168	C₂×D₄×C₇₉	—	2	1	no	—
169	C₂×D₄×C₇₉	—	2	1	no	—
170	C₂×D₄×C₇₉	—	2	1	no	—
171	C₂×D₄×C₇₉	—	2	1	no	—
172	C₂×D₄×C₇₉	—	2	1	no	—
173	C₂×D₄×C₇₉	—	4	2	no	—
174	C₂×D₄×C₇₉	—	4	2	no	—
175	C₂×D₄×C₇₉	—	4	2	no	—
176	C₂×D₄×C₇₉	—	4	2	no	—
177	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
178	C₂²×C₄×C₇₉	—	2	1	no	—
179	C₂²×C₄×C₇₉	—	2	1	no	—
180	C₂²×C₄×C₇₉	—	2	1	no	—
181	C₂²×C₄×C₇₉	—	2	1	no	—
182	C₂²×C₄×C₇₉	—	2	4	no	—
183	C₂²×C₄×C₇₉	—	2	4	no	—
184	C₂²×C₄×C₇₉	—	2	4	no	—
185	C₂²×C₄×C₇₉	—	2	1	no	—
186	C₂²×C₄×C₇₉	—	2	1	no	—
187	C₂²×C₄×C₇₉	—	2	1	no	—
188	C₂²×C₄×C₇₉	—	2	1	no	—
189	C₂²×C₄×C₇₉	—	2	1	no	—
190	C₂²×C₄×C₇₉	—	2	1	no	—
191	C₂²×C₄×C₇₉	—	2	1	no	—
192	C₂²×C₄×C₇₉	—	2	1	no	—
193	C₂²×C₄×C₇₉	—	2	1	no	—
194	C₂²×C₄×C₇₉	—	2	1	no	—
195	C₂²×C₄×C₇₉	—	2	1	no	—
196	C₂²×C₄×C₇₉	—	2	1	no	—
197	C₂²×C₄×C₇₉	—	2	1	no	—
198	C₂²×C₄×C₇₉	—	4	2	no	—
199	C₂²×C₄×C₇₉	—	4	2	no	—
200	C₂²×C₄×C₇₉	—	4	2	no	—
201	C₂²×C₄×C₇₉	—	4	2	no	—
202	C₂²×C₄×C₇₉	—	4	2	no	—
203	C₂²×C₄×C₇₉	—	4	2	no	—
204	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
208	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
209	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
211	SD₁₆×C₇₉	—	4	4	no	—
212	M₁₆×C₇₉	—	4	4	no	—
213	C₂×C₈×C₇₉	—	2	1	no	—
214	C₂×C₈×C₇₉	—	2	1	no	—
215	C₂×C₈×C₇₉	—	2	1	no	—
216	C₂×C₈×C₇₉	—	2	1	no	—
217	C₂×C₈×C₇₉	—	2	1	no	—
218	C₂×C₈×C₇₉	—	2	1	no	—
219	C₂×C₈×C₇₉	—	2	1	no	—
220	C₂×C₈×C₇₉	—	2	1	no	—
221	C₂×C₈×C₇₉	—	2	1	no	—
222	C₂×C₈×C₇₉	—	2	1	no	—
223	C₂×C₈×C₇₉	—	2	1	no	—
224	C₂×C₈×C₇₉	#41	1	2	yes	complemented
225	C₄⋊C₄×C₇₉	—	2	4	no	—
226	C₄⋊C₄×C₇₉	—	2	4	no	—
227	C₄⋊C₄×C₇₉	—	2	4	no	—
228	C₄⋊C₄×C₇₉	—	2	2	no	—
229	C₄⋊C₄×C₇₉	—	2	1	no	—
230	C₄⋊C₄×C₇₉	—	2	1	no	—
231	C₄⋊C₄×C₇₉	—	2	1	no	—
232	C₄⋊C₄×C₇₉	—	2	1	no	—
233	C₄⋊C₄×C₇₉	—	2	1	no	—
234	C₄⋊C₄×C₇₉	—	2	1	no	—
235	C₄⋊C₄×C₇₉	—	2	1	no	—
236	C₄⋊C₄×C₇₉	—	2	1	no	—
237	C₄⋊C₄×C₇₉	—	4	2	no	—
238	C₄⋊C₄×C₇₉	—	4	2	no	—
239	C₄⋊C₄×C₇₉	—	4	2	no	—
240	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
241	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
242	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
243	C₄⋊C₄×C₇₉	#41	1	2	yes	complemented
244	C₂²⋊C₄×C₇₉	—	2	4	no	—
245	C₂²⋊C₄×C₇₉	—	2	4	no	—
246	C₂²⋊C₄×C₇₉	—	2	2	no	—
247	C₂²⋊C₄×C₇₉	—	2	4	no	—
248	C₂²⋊C₄×C₇₉	—	2	2	no	—
249	C₂²⋊C₄×C₇₉	—	4	2	no	—
250	C₂²⋊C₄×C₇₉	—	4	2	no	—
251	C₂²⋊C₄×C₇₉	—	4	2	no	—
252	C₂²⋊C₄×C₇₉	—	4	2	no	—
253	C₄²×C₇₉	—	2	1	no	—
254	C₄²×C₇₉	—	2	1	no	—
255	C₄²×C₇₉	—	4	2	no	—
256	C₂³×C₇₉	—	2	1	no	—
257	C₂³×C₇₉	—	2	1	no	—
258	C₂³×C₇₉	—	2	1	no	—
259	C₂³×C₇₉	—	2	1	no	—
260	C₂³×C₇₉	—	2	1	no	—
261	C₂³×C₇₉	—	2	1	no	—
262	C₂³×C₇₉	—	2	1	no	—
263	C₂³×C₇₉	—	2	1	no	—
264	C₂³×C₇₉	—	2	1	no	—
265	C₂³×C₇₉	—	2	1	no	—
266	C₂³×C₇₉	—	2	1	no	—
267	C₂³×C₇₉	—	2	1	no	—
268	C₂³×C₇₉	—	2	2	no	—
269	C₂³×C₇₉	—	4	1	no	—
270	C₂³×C₇₉	—	4	1	no	—
271	C₂³×C₇₉	—	4	1	no	—
272	C₂³×C₇₉	—	4	1	no	—
273	C₂³×C₇₉	—	4	1	no	—
274	C₂³×C₇₉	—	4	1	no	—
275	C₂³×C₇₉	#120	1	2	yes	—
276	C₂³×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
277	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
278	Q₈×C₇₉	—	4	8	no	—
279	Q₈×C₇₉	—	4	1	no	—
280	Q₈×C₇₉	—	4	1	no	—
281	Q₈×C₇₉	—	4	1	no	—
282	Q₈×C₇₉	—	4	1	no	—
283	D₄×C₇₉	—	2	8	no	—
284	D₄×C₇₉	—	2	2	no	—
285	D₄×C₇₉	—	2	2	no	—
286	D₄×C₇₉	—	4	8	no	—
287	D₄×C₇₉	—	4	8	no	—
288	D₄×C₇₉	—	4	1	no	—
289	D₄×C₇₉	—	4	1	no	—
290	C₂×C₄×C₇₉	—	2	1	no	—
291	C₂×C₄×C₇₉	—	2	1	no	—
292	C₂×C₄×C₇₉	—	2	1	no	—
293	C₂×C₄×C₇₉	—	2	1	no	—
294	C₂×C₄×C₇₉	—	2	2	no	—
295	C₂×C₄×C₇₉	—	2	2	no	—
296	C₂×C₄×C₇₉	—	2	2	no	—
297	C₂×C₄×C₇₉	—	2	2	no	—
298	C₂×C₄×C₇₉	—	2	1	no	—
299	C₂×C₄×C₇₉	—	2	1	no	—
300	C₂×C₄×C₇₉	—	2	2	no	—
301	C₂×C₄×C₇₉	—	2	2	no	—
302	C₂×C₄×C₇₉	—	2	2	no	—
303	C₂×C₄×C₇₉	—	2	2	no	—
304	C₂×C₄×C₇₉	—	2	1	no	—
305	C₂×C₄×C₇₉	—	2	1	no	—
306	C₂×C₄×C₇₉	—	2	1	no	—
307	C₂×C₄×C₇₉	—	2	1	no	—
308	C₂×C₄×C₇₉	—	4	8	no	—
309	C₂×C₄×C₇₉	—	4	8	no	—
310	C₂×C₄×C₇₉	—	4	8	no	—
311	C₂×C₄×C₇₉	—	4	1	no	—
312	C₂×C₄×C₇₉	—	4	1	no	—
313	C₂×C₄×C₇₉	—	4	1	no	—
314	C₂×C₄×C₇₉	—	4	1	no	—
315	C₂×C₄×C₇₉	—	4	1	no	—
316	C₂×C₄×C₇₉	—	4	1	no	—
317	C₂×C₄×C₇₉	—	4	1	no	—
318	C₂×C₄×C₇₉	—	4	1	no	—
319	C₂×C₄×C₇₉	—	4	1	no	—
320	C₂×C₄×C₇₉	—	4	1	no	—
321	C₂×C₄×C₇₉	—	4	1	no	—
322	C₂×C₄×C₇₉	—	4	1	no	—
323	C₂×C₄×C₇₉	—	4	1	no	—
324	C₂×C₄×C₇₉	—	4	1	no	—
325	C₂×C₄×C₇₉	—	4	1	no	—
326	C₂×C₄×C₇₉	—	4	1	no	—
327	C₂×C₄×C₇₉	—	4	1	no	—
328	C₂×C₄×C₇₉	—	4	1	no	—
329	C₂×C₄×C₇₉	—	4	1	no	—
330	C₂×C₄×C₇₉	—	4	1	no	—
331	C₂×C₄×C₇₉	—	4	1	no	—
332	C₂×C₄×C₇₉	#120	1	2	yes	—
333	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
334	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
337	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
338	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
339	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
340	C₈×C₇₉	—	2	2	no	—
341	C₈×C₇₉	—	4	1	no	—
342	C₈×C₇₉	—	4	1	no	—
343	C₈×C₇₉	—	4	1	no	—
344	C₂²×C₇₉	—	2	2	no	—
345	C₂²×C₇₉	—	2	2	no	—
346	C₂²×C₇₉	—	2	2	no	—
347	C₂²×C₇₉	—	2	2	no	—
348	C₂²×C₇₉	—	2	2	no	—
349	C₂²×C₇₉	—	2	2	no	—
350	C₂²×C₇₉	—	4	1	no	—
351	C₂²×C₇₉	—	4	1	no	—
352	C₂²×C₇₉	—	4	1	no	—
353	C₂²×C₇₉	—	4	1	no	—
354	C₂²×C₇₉	—	4	1	no	—
355	C₂²×C₇₉	—	4	1	no	—
356	C₂²×C₇₉	—	4	1	no	—
357	C₂²×C₇₉	—	4	1	no	—
358	C₂²×C₇₉	—	4	2	no	—
359	C₂²×C₇₉	—	4	2	no	—
360	C₂²×C₇₉	—	4	2	no	—
361	C₂²×C₇₉	—	8	1	no	—
362	C₂²×C₇₉	—	8	1	no	—
363	C₂²×C₇₉	—	8	1	no	—
364	C₂²×C₇₉	—	8	1	no	—
365	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
366	C₂²×C₇₉	#546	1	1	yes	characteristic
367	C₂²×C₇₉	#547	1	1	yes	characteristic
368	C₂²×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
369	C₂²×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
370	C₂²×C₇₉	#578	1	1	yes	characteristic
371	C₂²×C₇₉	#578	1	1	yes	characteristic
372	C₄×C₇₉	—	2	2	no	—
373	C₄×C₇₉	—	2	2	no	—
374	C₄×C₇₉	—	4	2	no	—
375	C₄×C₇₉	—	4	1	no	—
376	C₄×C₇₉	—	4	2	no	—
377	C₄×C₇₉	—	4	2	no	—
378	C₄×C₇₉	—	4	2	no	—
379	C₄×C₇₉	—	4	1	no	—
380	C₄×C₇₉	—	8	1	no	—
381	C₄×C₇₉	—	8	1	no	—
382	C₄×C₇₉	—	8	1	no	—
383	C₄×C₇₉	#532	1	1	yes	characteristic
384	C₄×C₇₉	#537	1	1	yes	characteristic
385	C₄×C₇₉	#546	1	1	yes	characteristic
386	C₄×C₇₉	#547	1	1	yes	characteristic
387	#25547	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
388	C₂×C₇₉	—	4	2	no	—
389	C₂×C₇₉	—	4	2	no	—
390	C₂×C₇₉	—	8	2	no	—
391	C₂×C₇₉	#2430	1	1	yes	characteristic
392	C₂×C₇₉	#3003	1	1	yes	characteristic
393	C₂×C₇₉	#3011	1	1	yes	characteristic
394	C₂×C₇₉	#3308	1	1	yes	characteristic
395	C₂×C₇₉	#3330	1	1	yes	characteristic
396	C₂×C₇₉	#3343	1	1	yes	characteristic
397	C₂×C₇₉	#3353	1	1	yes	characteristic
398	C₂×#547	C₂×C₇₉	1	1	yes	characteristic
399	C₂×#484	C₂×C₇₉	1	1	yes	characteristic, complemented
400	C₂×#468	C₂×C₇₉	1	1	yes	characteristic, complemented
401	#2415	C₂×C₇₉	1	1	yes	characteristic, complemented
402	#2057	C₂×C₇₉	1	1	yes	characteristic, complemented
403	#2033	C₂×C₇₉	1	1	yes	characteristic, complemented
404	#2024	C₂×C₇₉	1	1	yes	characteristic, complemented
405	#2000	C₂×C₇₉	1	1	yes	characteristic, complemented
406	#1877	C₂×C₇₉	1	1	yes	characteristic, complemented
407	#1875	C₂×C₇₉	1	1	yes	characteristic, complemented
408	#1872	C₂×C₇₉	1	1	yes	characteristic, complemented
409	#1870	C₂×C₇₉	1	1	yes	characteristic, complemented
410	#1862	C₂×C₇₉	1	1	yes	characteristic, complemented
411	#1852	C₂×C₇₉	1	1	yes	characteristic, complemented
412	#1736	C₂×C₇₉	1	1	yes	characteristic, complemented
413	C₇₉	#25547	1	1	yes	characteristic, direct product factor, Sylow
414	C₂²×#41	—	2	1	no	—
415	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
416	C₂²×M₁₆	C₂²×C₇₉	1	1	yes	characteristic
417	#547	—	2	4	no	—
418	#547	—	2	4	no	—
419	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
420	C₂×#123	—	2	1	no	—
421	C₂×#123	—	2	1	no	—
422	C₂×C₂²⋊Q₈	—	2	1	no	—
423	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
424	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
425	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
426	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
427	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
428	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
429	C₂×#117	C₂²×C₇₉	1	1	yes	characteristic
430	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
431	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
432	#484	—	2	4	no	—
433	#468	—	2	4	no	—
434	C₂×#107	C₂²×C₇₉	1	1	yes	characteristic
435	C₂×#107	C₂²×C₇₉	1	1	yes	characteristic
436	C₂×#107	C₂²×C₇₉	1	1	yes	characteristic
437	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
438	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
439	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
440	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
441	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
442	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
443	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
444	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
445	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
446	#397	—	2	1	no	—
447	#394	—	2	1	no	—
448	#391	C₂²×C₇₉	1	1	yes	characteristic
449	#389	—	2	1	no	—
450	#389	C₂²×C₇₉	1	1	yes	characteristic
451	#388	—	2	1	no	—
452	#380	C₂²×C₇₉	1	1	yes	characteristic
453	#340	C₂²×C₇₉	1	1	yes	characteristic
454	#340	C₂²×C₇₉	1	1	yes	characteristic
455	#340	C₂²×C₇₉	1	1	yes	characteristic
456	#340	C₂²×C₇₉	1	1	yes	characteristic
457	#340	C₂²×C₇₉	1	1	yes	characteristic
458	#340	C₂²×C₇₉	1	1	yes	characteristic
459	#336	C₂²×C₇₉	1	1	yes	characteristic
460	#336	C₂²×C₇₉	1	1	yes	characteristic
461	C₂×#41	—	2	8	no	—
462	C₂×#41	—	4	4	no	—
463	C₂×#41	—	4	4	no	—
464	C₂²×Q₈	—	2	1	no	—
465	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
466	C₂²×D₄	—	2	1	no	—
467	C₂²×D₄	—	2	1	no	—
468	C₂²×D₄	D₄×C₇₉	1	1	yes	characteristic
469	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
470	C₂³×C₄	—	2	1	no	—
471	C₂³×C₄	—	2	1	no	—
472	C₂³×C₄	—	2	1	no	—
473	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
474	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
475	C₂×SD₁₆	—	2	2	no	—
476	C₂×SD₁₆	—	2	2	no	—
477	C₂×SD₁₆	—	4	1	no	—
478	C₂×M₁₆	—	2	2	no	—
479	C₂×M₁₆	—	2	2	no	—
480	C₂×M₁₆	—	4	1	no	—
481	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
482	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
483	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
484	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
485	C₄⋊Q₈	—	2	2	no	—
486	C₄⋊Q₈	—	2	2	no	—
487	#123	—	2	8	no	—
488	#123	—	2	8	no	—
489	C₂²⋊Q₈	—	2	8	no	—
490	C₂²⋊Q₈	—	2	2	no	—
491	C₂²⋊Q₈	—	2	2	no	—
492	C₂²⋊Q₈	—	2	2	no	—
493	C₂²⋊Q₈	—	4	1	no	—
494	#121	—	2	2	no	—
495	#121	—	2	2	no	—
496	#121	—	2	2	no	—
497	#121	D₄×C₇₉	1	4	yes	—
498	C₄×D₄	—	2	2	no	—
499	C₄×D₄	—	2	2	no	—
500	C₄×D₄	—	2	2	no	—
501	C₄×D₄	—	2	2	no	—
502	#117	—	2	2	no	—
503	#117	—	4	1	no	—
504	C₂×C₄⋊C₄	—	2	1	no	—
505	C₂×C₄⋊C₄	—	2	1	no	—
506	C₂×C₄⋊C₄	—	2	2	no	—
507	C₂×C₄⋊C₄	—	2	1	no	—
508	C₂×C₄⋊C₄	—	2	2	no	—
509	C₂×C₄⋊C₄	—	2	2	no	—
510	C₂×C₄⋊C₄	—	2	1	no	—
511	C₂×C₄⋊C₄	—	2	1	no	—
512	C₂×C₄⋊C₄	—	2	1	no	—
513	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
514	C₂×C₄⋊C₄	D₄×C₇₉	1	4	yes	—
515	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
518	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
519	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
520	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
521	C₂×C₂²⋊C₄	—	2	1	no	—
522	C₂×C₂²⋊C₄	—	2	1	no	—
523	C₂×C₂²⋊C₄	—	2	1	no	—
524	C₂×C₂²⋊C₄	—	2	1	no	—
525	C₂×C₂²⋊C₄	—	2	1	no	—
526	C₂×C₂²⋊C₄	—	2	1	no	—
527	C₂×C₂²⋊C₄	—	2	1	no	—
528	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
529	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
530	C₂×C₄²	—	2	1	no	—
531	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
532	#107	—	2	2	no	—
533	#107	—	2	2	no	—
534	#107	—	2	2	no	—
535	#103	—	2	2	no	—
536	#103	—	2	2	no	—
537	#103	—	2	2	no	—
538	#102	—	2	2	no	—
539	#102	—	2	2	no	—
540	#102	—	4	1	no	—
541	C₂²⋊C₈	—	2	2	no	—
542	C₂²⋊C₈	—	2	2	no	—
543	C₂²⋊C₈	—	4	1	no	—
544	#95	—	2	1	no	—
545	#95	—	2	1	no	—
546	#95	—	2	1	no	—
547	#95	—	2	1	no	—
548	C₂⁴	—	2	1	no	—
549	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
550	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
551	#41	—	4	32	no	—
552	C₂×Q₈	—	2	4	no	—
553	C₂×Q₈	—	2	1	no	—
554	C₂×Q₈	—	2	1	no	—
555	C₂×Q₈	—	2	1	no	—
556	C₂×Q₈	—	2	1	no	—
557	C₂×Q₈	—	2	1	no	—
558	C₂×Q₈	—	2	1	no	—
559	C₂×Q₈	—	4	2	no	—
560	C₂×Q₈	—	4	2	no	—
561	C₂×D₄	—	2	2	no	—
562	C₂×D₄	—	2	2	no	—
563	C₂×D₄	—	2	4	no	—
564	C₂×D₄	—	2	4	no	—
565	C₂×D₄	—	2	2	no	—
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	2	1	no	—
568	C₂×D₄	—	2	1	no	—
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	2	1	no	—
571	C₂×D₄	—	4	2	no	—
572	C₂×D₄	—	4	2	no	—
573	C₂×D₄	—	4	2	no	—
574	C₂×D₄	—	4	2	no	—
575	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	4	2	no	—
597	C₂²×C₄	—	4	2	no	—
598	C₂²×C₄	—	4	2	no	—
599	C₂²×C₄	—	4	2	no	—
600	C₂²×C₄	—	4	2	no	—
601	C₂²×C₄	—	4	2	no	—
602	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
603	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
604	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
605	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
606	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
607	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
609	SD₁₆	—	4	4	no	—
610	M₁₆	—	4	4	no	—
611	C₂×C₈	—	2	1	no	—
612	C₂×C₈	—	2	1	no	—
613	C₂×C₈	—	2	1	no	—
614	C₂×C₈	—	2	1	no	—
615	C₂×C₈	—	2	1	no	—
616	C₂×C₈	—	2	1	no	—
617	C₂×C₈	—	2	1	no	—
618	C₂×C₈	—	2	1	no	—
619	C₂×C₈	—	2	1	no	—
620	C₂×C₈	—	2	1	no	—
621	C₂×C₈	—	2	1	no	—
622	C₂×C₈	#41×C₇₉	1	2	yes	complemented
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	2	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	1	no	—
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	—	2	1	no	—
635	C₄⋊C₄	—	4	2	no	—
636	C₄⋊C₄	—	4	2	no	—
637	C₄⋊C₄	—	4	2	no	—
638	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
639	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
640	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
641	C₄⋊C₄	#41×C₇₉	1	2	yes	complemented
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	—	2	2	no	—
647	C₂²⋊C₄	—	4	2	no	—
648	C₂²⋊C₄	—	4	2	no	—
649	C₂²⋊C₄	—	4	2	no	—
650	C₂²⋊C₄	—	4	2	no	—
651	C₄²	—	2	1	no	—
652	C₄²	—	2	1	no	—
653	C₄²	—	4	2	no	—
654	C₂³	—	2	1	no	—
655	C₂³	—	2	1	no	—
656	C₂³	—	2	1	no	—
657	C₂³	—	2	1	no	—
658	C₂³	—	2	1	no	—
659	C₂³	—	2	1	no	—
660	C₂³	—	2	1	no	—
661	C₂³	—	2	1	no	—
662	C₂³	—	2	1	no	—
663	C₂³	—	2	1	no	—
664	C₂³	—	2	1	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	4	1	no	—
668	C₂³	—	4	1	no	—
669	C₂³	—	4	1	no	—
670	C₂³	—	4	1	no	—
671	C₂³	—	4	1	no	—
672	C₂³	—	4	1	no	—
673	C₂³	#120×C₇₉	1	2	yes	—
674	C₂³	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
675	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
676	Q₈	—	4	8	no	—
677	Q₈	—	4	1	no	—
678	Q₈	—	4	1	no	—
679	Q₈	—	4	1	no	—
680	Q₈	—	4	1	no	—
681	D₄	—	2	8	no	—
682	D₄	—	2	2	no	—
683	D₄	—	2	2	no	—
684	D₄	—	4	8	no	—
685	D₄	—	4	8	no	—
686	D₄	—	4	1	no	—
687	D₄	—	4	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	4	8	no	—
707	C₂×C₄	—	4	8	no	—
708	C₂×C₄	—	4	8	no	—
709	C₂×C₄	—	4	1	no	—
710	C₂×C₄	—	4	1	no	—
711	C₂×C₄	—	4	1	no	—
712	C₂×C₄	—	4	1	no	—
713	C₂×C₄	—	4	1	no	—
714	C₂×C₄	—	4	1	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	#120×C₇₉	1	2	yes	—
731	C₂×C₄	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
732	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
733	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
734	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
735	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
736	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
737	C₂×C₄	2₋¹⁺⁴×C₇₉	1	1	yes	characteristic
738	C₈	—	2	2	no	—
739	C₈	—	4	1	no	—
740	C₈	—	4	1	no	—
741	C₈	—	4	1	no	—
742	C₂²	—	2	2	no	—
743	C₂²	—	2	2	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	2	2	no	—
746	C₂²	—	2	2	no	—
747	C₂²	—	2	2	no	—
748	C₂²	—	4	1	no	—
749	C₂²	—	4	1	no	—
750	C₂²	—	4	1	no	—
751	C₂²	—	4	1	no	—
752	C₂²	—	4	1	no	—
753	C₂²	—	4	1	no	—
754	C₂²	—	4	1	no	—
755	C₂²	—	4	1	no	—
756	C₂²	—	4	2	no	—
757	C₂²	—	4	2	no	—
758	C₂²	—	4	2	no	—
759	C₂²	—	8	1	no	—
760	C₂²	—	8	1	no	—
761	C₂²	—	8	1	no	—
762	C₂²	—	8	1	no	—
763	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
764	C₂²	#546×C₇₉	1	1	yes	characteristic
765	C₂²	#547×C₇₉	1	1	yes	characteristic
766	C₂²	C₂×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
767	C₂²	C₂×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
768	C₂²	#578×C₇₉	1	1	yes	characteristic
769	C₂²	#578×C₇₉	1	1	yes	characteristic
770	C₄	—	2	2	no	—
771	C₄	—	2	2	no	—
772	C₄	—	4	2	no	—
773	C₄	—	4	1	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	2	no	—
776	C₄	—	4	2	no	—
777	C₄	—	4	1	no	—
778	C₄	—	8	1	no	—
779	C₄	—	8	1	no	—
780	C₄	—	8	1	no	—
781	C₄	#532×C₇₉	1	1	yes	characteristic
782	C₄	#537×C₇₉	1	1	yes	characteristic
783	C₄	#546×C₇₉	1	1	yes	characteristic
784	C₄	#547×C₇₉	1	1	yes	characteristic
785	C₂	—	4	2	no	—
786	C₂	—	4	2	no	—
787	C₂	—	8	2	no	—
788	C₂	C₇₉×#2430	1	1	yes	characteristic
789	C₂	C₇₉×#3003	1	1	yes	characteristic
790	C₂	C₇₉×#3011	1	1	yes	characteristic
791	C₂	C₇₉×#3308	1	1	yes	characteristic
792	C₂	C₇₉×#3330	1	1	yes	characteristic
793	C₂	C₇₉×#3343	1	1	yes	characteristic
794	C₂	C₇₉×#3353	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₂×#547×C₇₉	C₂
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
2. C₂×#484×C₇₉	C₂	semidirect
3. C₂×#468×C₇₉	C₂	semidirect
4. C₇₉×#2415	C₂	semidirect
5. C₇₉×#2057	C₂	semidirect
6. C₇₉×#2033	C₂	semidirect
7. C₇₉×#2024	C₂	semidirect
8. C₇₉×#2000	C₂	semidirect
9. C₇₉×#1877	C₂	semidirect
10. C₇₉×#1875	C₂	semidirect
11. C₇₉×#1872	C₂	semidirect
12. C₇₉×#1870	C₂	semidirect
13. C₇₉×#1862	C₂	semidirect
14. C₇₉×#1852	C₂	semidirect
15. C₇₉×#1736	C₂	semidirect
224. C₂×C₈×C₇₉	#41	semidirect
243. C₄⋊C₄×C₇₉	#41	semidirect
387. #25547	C₇₉	direct (N × H)
399. C₂×#484	C₂×C₇₉	semidirect
400. C₂×#468	C₂×C₇₉	semidirect
401. #2415	C₂×C₇₉	semidirect
402. #2057	C₂×C₇₉	semidirect
403. #2033	C₂×C₇₉	semidirect
404. #2024	C₂×C₇₉	semidirect
405. #2000	C₂×C₇₉	semidirect
406. #1877	C₂×C₇₉	semidirect
407. #1875	C₂×C₇₉	semidirect
408. #1872	C₂×C₇₉	semidirect
409. #1870	C₂×C₇₉	semidirect
410. #1862	C₂×C₇₉	semidirect
411. #1852	C₂×C₇₉	semidirect
412. #1736	C₂×C₇₉	semidirect
413. C₇₉	#25547	direct (N × H)
622. C₂×C₈	#41×C₇₉	semidirect
641. C₄⋊C₄	#41×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#547×C₇₉	2
C₂×#484×C₇₉	2
C₂×#468×C₇₉	2
C₇₉×#2415	2
C₇₉×#2057	2
C₇₉×#2033	2
C₇₉×#2024	2
C₇₉×#2000	2
C₇₉×#1877	2
C₇₉×#1875	2
C₇₉×#1872	2
C₇₉×#1870	2
C₇₉×#1862	2
C₇₉×#1852	2
C₇₉×#1736	2
#25547	79

Subgroups — C79×#25547 #34137236

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#25547 #34137236