Subgroups — C₇₉×#36519 #34148208

Order 20224.

1776 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#2851	C₂	1	1	yes	maximal, characteristic
2	C₇₉×#2851	C₂	1	2	yes	maximal
3	C₇₉×#2590	C₂	1	2	yes	maximal, complemented
4	C₇₉×#2588	C₂	1	2	yes	maximal, complemented
5	C₇₉×#2584	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₉×#2569	C₂	1	2	yes	maximal
7	C₇₉×#2550	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#2549	C₂	1	2	yes	maximal
9	C₇₉×#2520	C₂	1	2	yes	maximal, complemented
10	C₇₉×#2508	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#2506	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₉×#2462	C₂	1	2	yes	maximal, complemented
13	C₇₉×#2442	C₂	1	1	yes	maximal, characteristic
14	C₇₉×#2440	C₂	1	1	yes	maximal, characteristic
15	C₇₉×#2370	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇₉×#2370	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇₉×#2365	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇₉×#2355	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇₉×#2345	C₂	1	1	yes	maximal, characteristic
20	C₇₉×#2345	C₂	1	1	yes	maximal, characteristic
21	C₄×C₂²⋊Q₈×C₇₉	C₂	1	1	yes	maximal, characteristic
22	C₄×C₂²⋊Q₈×C₇₉	C₂	1	2	yes	maximal
23	C₂×C₄×C₄⋊C₄×C₇₉	C₂	1	1	yes	maximal, characteristic
24	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
25	C₂×#125×C₇₉	C₂²	1	1	yes	characteristic
26	C₂×#125×C₇₉	C₂²	1	1	yes	characteristic
27	C₂×#125×C₇₉	C₂²	1	2	yes	—
28	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	2	yes	—
30	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₇₉	C₂²	1	2	yes	—
32	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₇₉	C₂²	1	2	yes	—
36	#400×C₇₉	C₂²	1	2	yes	—
37	#400×C₇₉	C₂²	1	2	yes	—
38	#400×C₇₉	C₂²	1	2	yes	—
39	#398×C₇₉	C₂²	1	2	yes	—
40	#398×C₇₉	C₂²	1	2	yes	—
41	#398×C₇₉	C₂²	1	2	yes	—
42	#398×C₇₉	C₂²	1	2	yes	—
43	#398×C₇₉	C₂²	1	2	yes	—
44	#398×C₇₉	C₂²	1	2	yes	—
45	#395×C₇₉	C₂²	1	2	yes	—
46	#395×C₇₉	C₂²	1	2	yes	—
47	#395×C₇₉	C₂²	1	2	yes	—
48	#391×C₇₉	C₂²	1	1	yes	characteristic
49	#391×C₇₉	C₂²	1	2	yes	—
50	#391×C₇₉	C₂²	1	2	yes	—
51	#391×C₇₉	C₂²	1	2	yes	—
52	#389×C₇₉	C₂²	1	1	yes	characteristic
53	#389×C₇₉	C₂²	1	1	yes	characteristic
54	#389×C₇₉	C₂²	1	1	yes	characteristic
55	#389×C₇₉	C₂²	1	1	yes	characteristic
56	#389×C₇₉	C₂²	1	1	yes	characteristic
57	#389×C₇₉	C₂²	1	1	yes	characteristic
58	#389×C₇₉	C₂²	1	1	yes	characteristic
59	#389×C₇₉	C₂²	1	1	yes	characteristic
60	#389×C₇₉	C₂²	1	2	yes	—
61	#389×C₇₉	C₂²	1	2	yes	—
62	#389×C₇₉	C₂²	1	2	yes	—
63	#389×C₇₉	C₂²	1	2	yes	—
64	#389×C₇₉	C₂²	1	1	yes	characteristic
65	#389×C₇₉	C₂²	1	2	yes	—
66	#389×C₇₉	C₂²	1	1	yes	characteristic
67	#389×C₇₉	C₂²	1	1	yes	characteristic
68	#387×C₇₉	C₂²	1	2	yes	—
69	#387×C₇₉	C₂²	1	2	yes	—
70	#387×C₇₉	C₂²	1	2	yes	—
71	#387×C₇₉	C₂²	1	2	yes	—
72	#387×C₇₉	C₂²	1	2	yes	—
73	#387×C₇₉	C₂²	1	2	yes	—
74	#387×C₇₉	C₂²	1	2	yes	—
75	#387×C₇₉	C₂²	1	1	yes	characteristic
76	#387×C₇₉	C₂²	1	1	yes	characteristic
77	#387×C₇₉	C₂²	1	2	yes	—
78	#387×C₇₉	C₂²	1	2	yes	—
79	#387×C₇₉	C₂²	1	2	yes	—
80	#387×C₇₉	C₂²	1	2	yes	—
81	#387×C₇₉	C₂²	1	2	yes	—
82	#387×C₇₉	C₂²	1	2	yes	—
83	#387×C₇₉	C₂²	1	2	yes	—
84	#387×C₇₉	C₂²	1	2	yes	—
85	#387×C₇₉	C₂²	1	2	yes	—
86	#385×C₇₉	C₂²	1	2	yes	—
87	#385×C₇₉	C₂²	1	2	yes	—
88	#385×C₇₉	C₂²	1	1	yes	characteristic
89	#385×C₇₉	C₂²	1	1	yes	characteristic
90	#385×C₇₉	C₂²	1	2	yes	—
91	#385×C₇₉	C₂²	1	2	yes	—
92	#384×C₇₉	C₂²	1	1	yes	characteristic
93	#382×C₇₉	C₂²	1	2	yes	—
94	#382×C₇₉	C₂²	1	1	yes	characteristic
95	#382×C₇₉	C₂²	1	1	yes	characteristic
96	#380×C₇₉	C₂²	1	2	yes	—
97	#380×C₇₉	C₂²	1	1	yes	characteristic
98	#380×C₇₉	C₂²	1	2	yes	—
99	#380×C₇₉	C₂²	1	2	yes	—
100	#380×C₇₉	C₂²	1	1	yes	characteristic
101	#380×C₇₉	C₂²	1	1	yes	characteristic
102	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
104	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
106	C₄×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
107	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
109	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
113	C₄×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
114	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
117	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
122	C₂×#95×C₇₉	C₂²	1	2	yes	—
123	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
124	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
127	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
130	C₄⋊Q₈×C₇₉	—	2	4	no	—
131	#125×C₇₉	—	2	4	no	—
132	#125×C₇₉	—	2	4	no	—
133	#125×C₇₉	—	4	4	no	—
134	C₂²⋊Q₈×C₇₉	—	2	4	no	—
135	C₂²⋊Q₈×C₇₉	—	2	8	no	—
136	C₄×Q₈×C₇₉	—	2	4	no	—
137	C₄×Q₈×C₇₉	—	4	4	no	—
138	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
139	C₂×C₄⋊C₄×C₇₉	Q₈	1	8	yes	complemented
140	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
176	C₂×C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
177	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
179	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₇₉	—	2	4	no	—
183	C₂×C₄²×C₇₉	—	4	4	no	—
184	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
185	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
186	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
194	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
195	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
196	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
197	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
198	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
199	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
200	#95×C₇₉	C₂³	1	2	yes	—
201	#95×C₇₉	C₂³	1	2	yes	—
202	#95×C₇₉	C₂³	1	2	yes	—
203	#95×C₇₉	C₂³	1	2	yes	—
204	#95×C₇₉	C₂³	1	1	yes	characteristic
205	#95×C₇₉	C₂³	1	1	yes	characteristic
206	#95×C₇₉	C₂³	1	1	yes	characteristic
207	#95×C₇₉	C₂³	1	1	yes	characteristic
208	#95×C₇₉	C₂³	1	2	yes	—
209	#95×C₇₉	C₂³	1	2	yes	—
210	#95×C₇₉	C₂³	1	2	yes	—
211	#95×C₇₉	C₂³	1	2	yes	—
212	#95×C₇₉	C₂³	1	1	yes	characteristic
213	#95×C₇₉	C₂³	1	1	yes	characteristic
214	#95×C₇₉	C₂³	1	2	yes	—
215	#95×C₇₉	C₂³	1	2	yes	—
216	#95×C₇₉	C₂³	1	2	yes	—
217	#95×C₇₉	C₂³	1	2	yes	—
218	#95×C₇₉	C₂³	1	2	yes	—
219	#95×C₇₉	C₂³	1	1	yes	characteristic
220	#95×C₇₉	C₂³	1	1	yes	characteristic
221	#95×C₇₉	C₂³	1	2	yes	—
222	#95×C₇₉	C₂³	1	1	yes	characteristic
223	#95×C₇₉	C₂³	1	2	yes	—
224	#95×C₇₉	C₂³	1	2	yes	—
225	#95×C₇₉	C₂³	1	1	yes	characteristic
226	#95×C₇₉	C₂³	1	2	yes	—
227	#95×C₇₉	C₂³	1	2	yes	—
228	#95×C₇₉	C₂³	1	2	yes	—
229	#95×C₇₉	C₂³	1	2	yes	—
230	#95×C₇₉	C₂³	1	2	yes	—
231	#95×C₇₉	C₂³	1	2	yes	—
232	#95×C₇₉	C₂³	1	2	yes	—
233	#95×C₇₉	C₂³	1	2	yes	—
234	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
235	C₂×Q₈×C₇₉	—	2	2	no	—
236	C₂×Q₈×C₇₉	—	2	2	no	—
237	C₂×Q₈×C₇₉	—	2	4	no	—
238	C₂×Q₈×C₇₉	—	2	4	no	—
239	C₂×Q₈×C₇₉	—	4	2	no	—
240	C₂×Q₈×C₇₉	—	4	1	no	—
241	C₂²×C₄×C₇₉	—	2	2	no	—
242	C₂²×C₄×C₇₉	—	2	2	no	—
243	C₂²×C₄×C₇₉	—	2	2	no	—
244	C₂²×C₄×C₇₉	—	2	2	no	—
245	C₂²×C₄×C₇₉	—	2	2	no	—
246	C₂²×C₄×C₇₉	—	2	4	no	—
247	C₂²×C₄×C₇₉	—	2	2	no	—
248	C₂²×C₄×C₇₉	—	2	2	no	—
249	C₂²×C₄×C₇₉	—	2	4	no	—
250	C₂²×C₄×C₇₉	—	4	2	no	—
251	C₂²×C₄×C₇₉	—	4	2	no	—
252	C₂²×C₄×C₇₉	—	4	2	no	—
253	C₂²×C₄×C₇₉	—	4	1	no	—
254	C₂²×C₄×C₇₉	C₂×Q₈	1	4	yes	—
255	C₂²×C₄×C₇₉	C₂×Q₈	1	8	yes	—
256	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
278	C₄⋊C₄×C₇₉	—	2	4	no	—
279	C₄⋊C₄×C₇₉	—	2	2	no	—
280	C₄⋊C₄×C₇₉	—	2	2	no	—
281	C₄⋊C₄×C₇₉	—	2	2	no	—
282	C₄⋊C₄×C₇₉	—	2	2	no	—
283	C₄⋊C₄×C₇₉	—	2	4	no	—
284	C₄⋊C₄×C₇₉	—	2	2	no	—
285	C₄⋊C₄×C₇₉	—	2	2	no	—
286	C₄⋊C₄×C₇₉	—	2	4	no	—
287	C₄⋊C₄×C₇₉	—	2	4	no	—
288	C₄⋊C₄×C₇₉	—	2	2	no	—
289	C₄⋊C₄×C₇₉	—	2	4	no	—
290	C₄⋊C₄×C₇₉	—	2	4	no	—
291	C₄⋊C₄×C₇₉	—	2	4	no	—
292	C₄⋊C₄×C₇₉	—	2	4	no	—
293	C₄⋊C₄×C₇₉	—	2	2	no	—
294	C₄⋊C₄×C₇₉	—	2	2	no	—
295	C₄⋊C₄×C₇₉	—	2	2	no	—
296	C₄⋊C₄×C₇₉	—	2	4	no	—
297	C₄⋊C₄×C₇₉	—	2	2	no	—
298	C₄⋊C₄×C₇₉	—	2	2	no	—
299	C₄⋊C₄×C₇₉	—	2	4	no	—
300	C₄⋊C₄×C₇₉	—	2	2	no	—
301	C₄⋊C₄×C₇₉	—	4	2	no	—
302	C₄⋊C₄×C₇₉	—	4	2	no	—
303	C₄⋊C₄×C₇₉	—	4	1	no	—
304	C₄⋊C₄×C₇₉	—	4	2	no	—
305	C₄⋊C₄×C₇₉	—	4	2	no	—
306	C₄⋊C₄×C₇₉	—	4	2	no	—
307	C₄⋊C₄×C₇₉	—	4	2	no	—
308	C₄⋊C₄×C₇₉	—	4	2	no	—
309	C₄⋊C₄×C₇₉	—	4	2	no	—
310	C₄⋊C₄×C₇₉	C₂×Q₈	1	8	yes	—
311	C₄⋊C₄×C₇₉	C₂×Q₈	1	4	yes	—
312	C₄⋊C₄×C₇₉	C₂×Q₈	1	4	yes	—
313	C₄⋊C₄×C₇₉	#41	1	4	yes	—
314	C₂²⋊C₄×C₇₉	—	2	4	no	—
315	C₂²⋊C₄×C₇₉	—	2	2	no	—
316	C₂²⋊C₄×C₇₉	—	2	2	no	—
317	C₂²⋊C₄×C₇₉	—	2	4	no	—
318	C₂²⋊C₄×C₇₉	—	2	2	no	—
319	C₂²⋊C₄×C₇₉	#41	1	4	yes	—
320	C₄²×C₇₉	—	2	2	no	—
321	C₄²×C₇₉	—	2	2	no	—
322	C₄²×C₇₉	—	2	2	no	—
323	C₄²×C₇₉	—	2	2	no	—
324	C₄²×C₇₉	—	2	2	no	—
325	C₄²×C₇₉	—	2	2	no	—
326	C₄²×C₇₉	—	2	2	no	—
327	C₄²×C₇₉	—	2	4	no	—
328	C₄²×C₇₉	—	2	4	no	—
329	C₄²×C₇₉	—	4	2	no	—
330	C₄²×C₇₉	—	4	2	no	—
331	C₄²×C₇₉	—	4	2	no	—
332	C₄²×C₇₉	—	4	2	no	—
333	C₄²×C₇₉	—	4	2	no	—
334	C₄²×C₇₉	—	4	2	no	—
335	C₄²×C₇₉	#41	1	4	yes	—
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	C₂²×Q₈	1	2	yes	—
341	C₂³×C₇₉	C₂×#41	1	2	yes	—
342	C₂³×C₇₉	2₋¹⁺⁴	1	2	yes	—
343	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
344	Q₈×C₇₉	—	4	4	no	—
345	Q₈×C₇₉	—	4	8	no	—
346	C₂×C₄×C₇₉	—	2	8	no	—
347	C₂×C₄×C₇₉	—	2	1	no	—
348	C₂×C₄×C₇₉	—	2	1	no	—
349	C₂×C₄×C₇₉	—	2	1	no	—
350	C₂×C₄×C₇₉	—	2	1	no	—
351	C₂×C₄×C₇₉	—	2	1	no	—
352	C₂×C₄×C₇₉	—	2	1	no	—
353	C₂×C₄×C₇₉	—	2	2	no	—
354	C₂×C₄×C₇₉	—	2	2	no	—
355	C₂×C₄×C₇₉	—	2	2	no	—
356	C₂×C₄×C₇₉	—	2	2	no	—
357	C₂×C₄×C₇₉	—	2	1	no	—
358	C₂×C₄×C₇₉	—	2	1	no	—
359	C₂×C₄×C₇₉	—	2	1	no	—
360	C₂×C₄×C₇₉	—	2	1	no	—
361	C₂×C₄×C₇₉	—	2	2	no	—
362	C₂×C₄×C₇₉	—	2	1	no	—
363	C₂×C₄×C₇₉	—	2	2	no	—
364	C₂×C₄×C₇₉	—	2	1	no	—
365	C₂×C₄×C₇₉	—	2	8	no	—
366	C₂×C₄×C₇₉	—	2	1	no	—
367	C₂×C₄×C₇₉	—	2	1	no	—
368	C₂×C₄×C₇₉	—	2	1	no	—
369	C₂×C₄×C₇₉	—	2	1	no	—
370	C₂×C₄×C₇₉	—	2	1	no	—
371	C₂×C₄×C₇₉	—	2	1	no	—
372	C₂×C₄×C₇₉	—	2	1	no	—
373	C₂×C₄×C₇₉	—	2	2	no	—
374	C₂×C₄×C₇₉	—	2	1	no	—
375	C₂×C₄×C₇₉	—	2	1	no	—
376	C₂×C₄×C₇₉	—	2	2	no	—
377	C₂×C₄×C₇₉	—	2	2	no	—
378	C₂×C₄×C₇₉	—	2	2	no	—
379	C₂×C₄×C₇₉	—	2	2	no	—
380	C₂×C₄×C₇₉	—	2	1	no	—
381	C₂×C₄×C₇₉	—	2	2	no	—
382	C₂×C₄×C₇₉	—	2	2	no	—
383	C₂×C₄×C₇₉	—	2	2	no	—
384	C₂×C₄×C₇₉	—	2	2	no	—
385	C₂×C₄×C₇₉	—	2	1	no	—
386	C₂×C₄×C₇₉	—	2	2	no	—
387	C₂×C₄×C₇₉	—	2	2	no	—
388	C₂×C₄×C₇₉	—	2	1	no	—
389	C₂×C₄×C₇₉	—	2	1	no	—
390	C₂×C₄×C₇₉	—	2	1	no	—
391	C₂×C₄×C₇₉	—	2	1	no	—
392	C₂×C₄×C₇₉	—	2	2	no	—
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	1	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	1	no	—
402	C₂×C₄×C₇₉	—	4	8	no	—
403	C₂×C₄×C₇₉	—	4	4	no	—
404	C₂×C₄×C₇₉	—	4	8	no	—
405	C₂×C₄×C₇₉	C₂²×Q₈	1	2	yes	—
406	C₂×C₄×C₇₉	C₂²×Q₈	1	4	yes	—
407	C₂×C₄×C₇₉	C₂²×Q₈	1	4	yes	—
408	C₂×C₄×C₇₉	C₂²×Q₈	1	2	yes	—
409	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
410	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
411	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
412	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
413	C₂×C₄×C₇₉	C₂×#41	1	4	yes	—
414	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
415	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
416	C₂×C₄×C₇₉	H(5,𝔽₂)	1	2	yes	—
417	C₂²×C₇₉	—	2	2	no	—
418	C₂²×C₇₉	—	2	2	no	—
419	C₂²×C₇₉	—	2	2	no	—
420	C₂²×C₇₉	—	2	2	no	—
421	C₂²×C₇₉	—	2	2	no	—
422	C₂²×C₇₉	—	2	2	no	—
423	C₂²×C₇₉	#557	1	4	yes	—
424	C₂²×C₇₉	C₂³×Q₈	1	1	yes	characteristic
425	C₂²×C₇₉	C₂²×#41	1	1	yes	characteristic
426	C₂²×C₇₉	C₂²×#41	1	1	yes	characteristic
427	C₂²×C₇₉	C₂²×#41	1	1	yes	characteristic
428	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
429	C₂²×C₇₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
430	C₂²×C₇₉	#585	1	1	yes	characteristic
431	C₄×C₇₉	—	2	2	no	—
432	C₄×C₇₉	—	2	2	no	—
433	C₄×C₇₉	—	2	2	no	—
434	C₄×C₇₉	—	2	4	no	—
435	C₄×C₇₉	—	2	2	no	—
436	C₄×C₇₉	—	2	2	no	—
437	C₄×C₇₉	—	2	2	no	—
438	C₄×C₇₉	—	2	4	no	—
439	C₄×C₇₉	—	2	4	no	—
440	C₄×C₇₉	—	4	2	no	—
441	C₄×C₇₉	—	4	1	no	—
442	C₄×C₇₉	—	4	1	no	—
443	C₄×C₇₉	—	4	1	no	—
444	C₄×C₇₉	—	4	2	no	—
445	C₄×C₇₉	—	4	2	no	—
446	C₄×C₇₉	—	4	1	no	—
447	C₄×C₇₉	—	4	1	no	—
448	C₄×C₇₉	—	4	2	no	—
449	C₄×C₇₉	—	4	1	no	—
450	C₄×C₇₉	—	4	1	no	—
451	C₄×C₇₉	—	4	2	no	—
452	C₄×C₇₉	#533	1	4	yes	—
453	#36519	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
454	C₂×C₇₉	—	2	4	no	—
455	C₂×C₇₉	C₂×#533	1	1	yes	characteristic
456	C₂×C₇₉	#3475	1	1	yes	characteristic
457	C₂×C₇₉	C₂×#557	1	1	yes	characteristic
458	C₂×C₇₉	#3481	1	1	yes	characteristic
459	C₂×C₇₉	#3492	1	1	yes	characteristic
460	C₂×C₇₉	#3501	1	1	yes	characteristic
461	C₂×C₇₉	#3516	1	1	yes	characteristic
462	#2851	C₂×C₇₉	1	1	yes	characteristic
463	#2851	C₂×C₇₉	1	2	yes	—
464	#2590	C₂×C₇₉	1	2	yes	complemented
465	#2588	C₂×C₇₉	1	2	yes	complemented
466	#2584	C₂×C₇₉	1	1	yes	characteristic, complemented
467	#2569	C₂×C₇₉	1	2	yes	—
468	#2550	C₂×C₇₉	1	1	yes	characteristic, complemented
469	#2549	C₂×C₇₉	1	2	yes	—
470	#2520	C₂×C₇₉	1	2	yes	complemented
471	#2508	C₂×C₇₉	1	1	yes	characteristic, complemented
472	#2506	C₂×C₇₉	1	1	yes	characteristic, complemented
473	#2462	C₂×C₇₉	1	2	yes	complemented
474	#2442	C₂×C₇₉	1	1	yes	characteristic
475	#2440	C₂×C₇₉	1	1	yes	characteristic
476	#2370	C₂×C₇₉	1	1	yes	characteristic, complemented
477	#2370	C₂×C₇₉	1	1	yes	characteristic, complemented
478	#2365	C₂×C₇₉	1	1	yes	characteristic, complemented
479	#2355	C₂×C₇₉	1	1	yes	characteristic, complemented
480	#2345	C₂×C₇₉	1	1	yes	characteristic
481	#2345	C₂×C₇₉	1	1	yes	characteristic
482	C₄×C₂²⋊Q₈	C₂×C₇₉	1	1	yes	characteristic
483	C₄×C₂²⋊Q₈	C₂×C₇₉	1	2	yes	—
484	C₂×C₄×C₄⋊C₄	C₂×C₇₉	1	1	yes	characteristic
485	C₇₉	#36519	1	1	yes	characteristic, direct product factor, Sylow
486	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
487	C₂×#125	C₂²×C₇₉	1	1	yes	characteristic
488	C₂×#125	C₂²×C₇₉	1	1	yes	characteristic
489	C₂×#125	C₂²×C₇₉	1	2	yes	—
490	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	2	yes	—
491	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
492	C₂×C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
493	C₂×C₄×Q₈	C₂²×C₇₉	1	2	yes	—
494	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
495	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
496	C₂²×C₄²	C₂²×C₇₉	1	1	yes	characteristic
497	C₂²×C₄²	C₂²×C₇₉	1	2	yes	—
498	#400	C₂²×C₇₉	1	2	yes	—
499	#400	C₂²×C₇₉	1	2	yes	—
500	#400	C₂²×C₇₉	1	2	yes	—
501	#398	C₂²×C₇₉	1	2	yes	—
502	#398	C₂²×C₇₉	1	2	yes	—
503	#398	C₂²×C₇₉	1	2	yes	—
504	#398	C₂²×C₇₉	1	2	yes	—
505	#398	C₂²×C₇₉	1	2	yes	—
506	#398	C₂²×C₇₉	1	2	yes	—
507	#395	C₂²×C₇₉	1	2	yes	—
508	#395	C₂²×C₇₉	1	2	yes	—
509	#395	C₂²×C₇₉	1	2	yes	—
510	#391	C₂²×C₇₉	1	2	yes	—
511	#391	C₂²×C₇₉	1	2	yes	—
512	#391	C₂²×C₇₉	1	2	yes	—
513	#391	C₂²×C₇₉	1	1	yes	characteristic
514	#389	C₂²×C₇₉	1	2	yes	—
515	#389	C₂²×C₇₉	1	2	yes	—
516	#389	C₂²×C₇₉	1	1	yes	characteristic
517	#389	C₂²×C₇₉	1	1	yes	characteristic
518	#389	C₂²×C₇₉	1	1	yes	characteristic
519	#389	C₂²×C₇₉	1	1	yes	characteristic
520	#389	C₂²×C₇₉	1	2	yes	—
521	#389	C₂²×C₇₉	1	2	yes	—
522	#389	C₂²×C₇₉	1	1	yes	characteristic
523	#389	C₂²×C₇₉	1	1	yes	characteristic
524	#389	C₂²×C₇₉	1	1	yes	characteristic
525	#389	C₂²×C₇₉	1	1	yes	characteristic
526	#389	C₂²×C₇₉	1	1	yes	characteristic
527	#389	C₂²×C₇₉	1	1	yes	characteristic
528	#389	C₂²×C₇₉	1	2	yes	—
529	#389	C₂²×C₇₉	1	1	yes	characteristic
530	#387	C₂²×C₇₉	1	2	yes	—
531	#387	C₂²×C₇₉	1	2	yes	—
532	#387	C₂²×C₇₉	1	2	yes	—
533	#387	C₂²×C₇₉	1	2	yes	—
534	#387	C₂²×C₇₉	1	1	yes	characteristic
535	#387	C₂²×C₇₉	1	2	yes	—
536	#387	C₂²×C₇₉	1	2	yes	—
537	#387	C₂²×C₇₉	1	2	yes	—
538	#387	C₂²×C₇₉	1	2	yes	—
539	#387	C₂²×C₇₉	1	1	yes	characteristic
540	#387	C₂²×C₇₉	1	2	yes	—
541	#387	C₂²×C₇₉	1	2	yes	—
542	#387	C₂²×C₇₉	1	2	yes	—
543	#387	C₂²×C₇₉	1	2	yes	—
544	#387	C₂²×C₇₉	1	2	yes	—
545	#387	C₂²×C₇₉	1	2	yes	—
546	#387	C₂²×C₇₉	1	2	yes	—
547	#387	C₂²×C₇₉	1	2	yes	—
548	#385	C₂²×C₇₉	1	2	yes	—
549	#385	C₂²×C₇₉	1	2	yes	—
550	#385	C₂²×C₇₉	1	1	yes	characteristic
551	#385	C₂²×C₇₉	1	2	yes	—
552	#385	C₂²×C₇₉	1	2	yes	—
553	#385	C₂²×C₇₉	1	1	yes	characteristic
554	#384	C₂²×C₇₉	1	1	yes	characteristic
555	#382	C₂²×C₇₉	1	1	yes	characteristic
556	#382	C₂²×C₇₉	1	2	yes	—
557	#382	C₂²×C₇₉	1	1	yes	characteristic
558	#380	C₂²×C₇₉	1	1	yes	characteristic
559	#380	C₂²×C₇₉	1	2	yes	—
560	#380	C₂²×C₇₉	1	2	yes	—
561	#380	C₂²×C₇₉	1	1	yes	characteristic
562	#380	C₂²×C₇₉	1	1	yes	characteristic
563	#380	C₂²×C₇₉	1	2	yes	—
564	C₄×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
565	C₄×C₄⋊C₄	C₂²×C₇₉	1	2	yes	—
566	C₄×C₄⋊C₄	C₂²×C₇₉	1	2	yes	—
567	C₄×C₄⋊C₄	C₂²×C₇₉	1	2	yes	—
568	C₄×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
569	C₄×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
570	C₄×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
571	C₄×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
572	C₄×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
573	C₄×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
574	C₄×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
575	C₄×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
576	C₄×C₄⋊C₄	C₂²×C₇₉	1	2	yes	—
577	C₄×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
578	C₄×C₄⋊C₄	C₂²×C₇₉	1	2	yes	—
579	C₄×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
580	C₄×C₂²⋊C₄	C₂²×C₇₉	1	2	yes	—
581	C₄×C₂²⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
582	C₄×C₂²⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
583	C₄×C₂²⋊C₄	C₂²×C₇₉	1	2	yes	—
584	C₂×#95	C₂²×C₇₉	1	2	yes	—
585	C₂²×Q₈	C₂³×C₇₉	1	2	yes	—
586	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
587	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
588	C₂³×C₄	C₂³×C₇₉	1	2	yes	—
589	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
590	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
591	C₂³×C₄	C₂³×C₇₉	1	2	yes	—
592	C₄⋊Q₈	—	2	4	no	—
593	#125	—	2	4	no	—
594	#125	—	2	4	no	—
595	#125	—	4	4	no	—
596	C₂²⋊Q₈	—	2	8	no	—
597	C₂²⋊Q₈	—	2	4	no	—
598	C₄×Q₈	—	2	4	no	—
599	C₄×Q₈	—	4	4	no	—
600	C₂×C₄⋊C₄	—	2	4	no	—
601	C₂×C₄⋊C₄	Q₈×C₇₉	1	8	yes	complemented
602	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
627	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
628	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
638	C₂×C₂²⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
639	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
641	C₂×C₂²⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
642	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
644	C₂×C₄²	—	2	4	no	—
645	C₂×C₄²	—	4	4	no	—
646	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
648	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
649	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
650	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
651	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
653	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
654	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
655	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
656	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
657	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
658	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
659	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
660	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
661	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
662	#95	C₂³×C₇₉	1	2	yes	—
663	#95	C₂³×C₇₉	1	2	yes	—
664	#95	C₂³×C₇₉	1	2	yes	—
665	#95	C₂³×C₇₉	1	2	yes	—
666	#95	C₂³×C₇₉	1	1	yes	characteristic
667	#95	C₂³×C₇₉	1	1	yes	characteristic
668	#95	C₂³×C₇₉	1	1	yes	characteristic
669	#95	C₂³×C₇₉	1	1	yes	characteristic
670	#95	C₂³×C₇₉	1	2	yes	—
671	#95	C₂³×C₇₉	1	2	yes	—
672	#95	C₂³×C₇₉	1	2	yes	—
673	#95	C₂³×C₇₉	1	2	yes	—
674	#95	C₂³×C₇₉	1	1	yes	characteristic
675	#95	C₂³×C₇₉	1	1	yes	characteristic
676	#95	C₂³×C₇₉	1	2	yes	—
677	#95	C₂³×C₇₉	1	2	yes	—
678	#95	C₂³×C₇₉	1	2	yes	—
679	#95	C₂³×C₇₉	1	2	yes	—
680	#95	C₂³×C₇₉	1	2	yes	—
681	#95	C₂³×C₇₉	1	1	yes	characteristic
682	#95	C₂³×C₇₉	1	1	yes	characteristic
683	#95	C₂³×C₇₉	1	2	yes	—
684	#95	C₂³×C₇₉	1	1	yes	characteristic
685	#95	C₂³×C₇₉	1	2	yes	—
686	#95	C₂³×C₇₉	1	2	yes	—
687	#95	C₂³×C₇₉	1	1	yes	characteristic
688	#95	C₂³×C₇₉	1	2	yes	—
689	#95	C₂³×C₇₉	1	2	yes	—
690	#95	C₂³×C₇₉	1	2	yes	—
691	#95	C₂³×C₇₉	1	2	yes	—
692	#95	C₂³×C₇₉	1	2	yes	—
693	#95	C₂³×C₇₉	1	2	yes	—
694	#95	C₂³×C₇₉	1	2	yes	—
695	#95	C₂³×C₇₉	1	2	yes	—
696	C₂⁴	C₂⁴×C₇₉	1	1	yes	characteristic
697	C₂×Q₈	—	2	2	no	—
698	C₂×Q₈	—	2	2	no	—
699	C₂×Q₈	—	2	4	no	—
700	C₂×Q₈	—	2	4	no	—
701	C₂×Q₈	—	4	2	no	—
702	C₂×Q₈	—	4	1	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	2	no	—
705	C₂²×C₄	—	2	2	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	2	2	no	—
708	C₂²×C₄	—	2	4	no	—
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	4	no	—
712	C₂²×C₄	—	4	2	no	—
713	C₂²×C₄	—	4	2	no	—
714	C₂²×C₄	—	4	2	no	—
715	C₂²×C₄	—	4	1	no	—
716	C₂²×C₄	C₂×Q₈×C₇₉	1	4	yes	—
717	C₂²×C₄	C₂×Q₈×C₇₉	1	8	yes	—
718	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
719	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
723	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
730	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
732	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
735	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
736	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
738	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
739	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
740	C₄⋊C₄	—	2	4	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	4	no	—
749	C₄⋊C₄	—	2	4	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	4	no	—
752	C₄⋊C₄	—	2	4	no	—
753	C₄⋊C₄	—	2	4	no	—
754	C₄⋊C₄	—	2	4	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	4	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	4	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	4	2	no	—
764	C₄⋊C₄	—	4	2	no	—
765	C₄⋊C₄	—	4	2	no	—
766	C₄⋊C₄	—	4	2	no	—
767	C₄⋊C₄	—	4	2	no	—
768	C₄⋊C₄	—	4	2	no	—
769	C₄⋊C₄	—	4	2	no	—
770	C₄⋊C₄	—	4	1	no	—
771	C₄⋊C₄	—	4	2	no	—
772	C₄⋊C₄	C₂×Q₈×C₇₉	1	8	yes	—
773	C₄⋊C₄	C₂×Q₈×C₇₉	1	4	yes	—
774	C₄⋊C₄	C₂×Q₈×C₇₉	1	4	yes	—
775	C₄⋊C₄	#41×C₇₉	1	4	yes	—
776	C₂²⋊C₄	—	2	4	no	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	2	no	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	#41×C₇₉	1	4	yes	—
782	C₄²	—	2	2	no	—
783	C₄²	—	2	2	no	—
784	C₄²	—	2	2	no	—
785	C₄²	—	2	2	no	—
786	C₄²	—	2	2	no	—
787	C₄²	—	2	2	no	—
788	C₄²	—	2	2	no	—
789	C₄²	—	2	4	no	—
790	C₄²	—	2	4	no	—
791	C₄²	—	4	2	no	—
792	C₄²	—	4	2	no	—
793	C₄²	—	4	2	no	—
794	C₄²	—	4	2	no	—
795	C₄²	—	4	2	no	—
796	C₄²	—	4	2	no	—
797	C₄²	#41×C₇₉	1	4	yes	—
798	C₂³	—	2	1	no	—
799	C₂³	—	2	1	no	—
800	C₂³	—	2	1	no	—
801	C₂³	—	2	1	no	—
802	C₂³	C₂²×Q₈×C₇₉	1	2	yes	—
803	C₂³	C₂×#41×C₇₉	1	2	yes	—
804	C₂³	2₋¹⁺⁴×C₇₉	1	2	yes	—
805	C₂³	C₂⁵×C₇₉	1	1	yes	characteristic
806	Q₈	—	4	4	no	—
807	Q₈	—	4	8	no	—
808	C₂×C₄	—	2	8	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	8	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	4	8	no	—
865	C₂×C₄	—	4	4	no	—
866	C₂×C₄	—	4	8	no	—
867	C₂×C₄	C₂²×Q₈×C₇₉	1	2	yes	—
868	C₂×C₄	C₂²×Q₈×C₇₉	1	4	yes	—
869	C₂×C₄	C₂²×Q₈×C₇₉	1	4	yes	—
870	C₂×C₄	C₂²×Q₈×C₇₉	1	2	yes	—
871	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
872	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
873	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
874	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
875	C₂×C₄	C₂×#41×C₇₉	1	4	yes	—
876	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
877	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
878	C₂×C₄	H(5,𝔽₂)×C₇₉	1	2	yes	—
879	C₂²	—	2	2	no	—
880	C₂²	—	2	2	no	—
881	C₂²	—	2	2	no	—
882	C₂²	—	2	2	no	—
883	C₂²	—	2	2	no	—
884	C₂²	—	2	2	no	—
885	C₂²	#557×C₇₉	1	4	yes	—
886	C₂²	C₂³×Q₈×C₇₉	1	1	yes	characteristic
887	C₂²	C₂²×#41×C₇₉	1	1	yes	characteristic
888	C₂²	C₂²×#41×C₇₉	1	1	yes	characteristic
889	C₂²	C₂²×#41×C₇₉	1	1	yes	characteristic
890	C₂²	C₂×H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
891	C₂²	C₂×2₋¹⁺⁴×C₇₉	1	1	yes	characteristic
892	C₂²	#585×C₇₉	1	1	yes	characteristic
893	C₄	—	2	2	no	—
894	C₄	—	2	2	no	—
895	C₄	—	2	2	no	—
896	C₄	—	2	4	no	—
897	C₄	—	2	2	no	—
898	C₄	—	2	2	no	—
899	C₄	—	2	2	no	—
900	C₄	—	2	4	no	—
901	C₄	—	2	4	no	—
902	C₄	—	4	1	no	—
903	C₄	—	4	1	no	—
904	C₄	—	4	2	no	—
905	C₄	—	4	2	no	—
906	C₄	—	4	2	no	—
907	C₄	—	4	1	no	—
908	C₄	—	4	1	no	—
909	C₄	—	4	1	no	—
910	C₄	—	4	2	no	—
911	C₄	—	4	1	no	—
912	C₄	—	4	1	no	—
913	C₄	—	4	2	no	—
914	C₄	#533×C₇₉	1	4	yes	—
915	C₂	—	2	4	no	—
916	C₂	C₂×#533×C₇₉	1	1	yes	characteristic
917	C₂	C₇₉×#3475	1	1	yes	characteristic
918	C₂	C₂×#557×C₇₉	1	1	yes	characteristic
919	C₂	C₇₉×#3481	1	1	yes	characteristic
920	C₂	C₇₉×#3492	1	1	yes	characteristic
921	C₂	C₇₉×#3501	1	1	yes	characteristic
922	C₂	C₇₉×#3516	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₉
prime radical	C₂⁴×C₇₉	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₇₉×#2590	C₂	semidirect
4. C₇₉×#2588	C₂	semidirect
5. C₇₉×#2584	C₂	semidirect
7. C₇₉×#2550	C₂	semidirect
9. C₇₉×#2520	C₂	semidirect
10. C₇₉×#2508	C₂	semidirect
11. C₇₉×#2506	C₂	semidirect
12. C₇₉×#2462	C₂	semidirect
15. C₇₉×#2370	C₂	semidirect
16. C₇₉×#2370	C₂	semidirect
17. C₇₉×#2365	C₂	semidirect
18. C₇₉×#2355	C₂	semidirect
139. C₂×C₄⋊C₄×C₇₉	Q₈	semidirect
453. #36519	C₇₉	direct (N × H)
464. #2590	C₂×C₇₉	semidirect
465. #2588	C₂×C₇₉	semidirect
466. #2584	C₂×C₇₉	semidirect
468. #2550	C₂×C₇₉	semidirect
470. #2520	C₂×C₇₉	semidirect
471. #2508	C₂×C₇₉	semidirect
472. #2506	C₂×C₇₉	semidirect
473. #2462	C₂×C₇₉	semidirect
476. #2370	C₂×C₇₉	semidirect
477. #2370	C₂×C₇₉	semidirect
478. #2365	C₂×C₇₉	semidirect
479. #2355	C₂×C₇₉	semidirect
485. C₇₉	#36519	direct (N × H)
601. C₂×C₄⋊C₄	Q₈×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₇₉×#2851	2
C₇₉×#2590	2
C₇₉×#2588	2
C₇₉×#2584	2
C₇₉×#2569	2
C₇₉×#2550	2
C₇₉×#2549	2
C₇₉×#2520	2
C₇₉×#2508	2
C₇₉×#2506	2
C₇₉×#2462	2
C₇₉×#2442	2
C₇₉×#2440	2
C₇₉×#2370	2
C₇₉×#2365	2
C₇₉×#2355	2
C₇₉×#2345	2
C₄×C₂²⋊Q₈×C₇₉	2
C₂×C₄×C₄⋊C₄×C₇₉	2
#36519	79

Subgroups — C79×#36519 #34148208

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#36519 #34148208