Subgroups — C₇₉×#36531 #34148220

Order 20224.

2120 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#2852	C₂	1	2	yes	maximal, complemented
2	C₇₉×#2848	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#2577	C₂	1	2	yes	maximal, complemented
4	C₇₉×#2564	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#2560	C₂	1	2	yes	maximal, complemented
6	C₇₉×#2549	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#2523	C₂	1	2	yes	maximal, complemented
8	C₇₉×#2521	C₂	1	2	yes	maximal, complemented
9	C₇₉×#2480	C₂	1	2	yes	maximal, complemented
10	C₇₉×#2472	C₂	1	2	yes	maximal
11	C₇₉×#2466	C₂	1	2	yes	maximal, complemented
12	C₇₉×#2465	C₂	1	2	yes	maximal, complemented
13	C₇₉×#2373	C₂	1	2	yes	maximal, complemented
14	C₇₉×#2368	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#2367	C₂	1	2	yes	maximal, complemented
16	C₇₉×#2353	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₂²⋊Q₈×C₇₉	C₂	1	2	yes	maximal, complemented
18	C₄×#120×C₇₉	C₂	1	1	yes	maximal, characteristic
19	C₂×C₄×C₂²⋊C₄×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×C₄×C₇₉	C₂²	1	1	yes	characteristic
21	C₂×#126×C₇₉	C₂²	1	2	yes	—
22	C₂×#126×C₇₉	C₂²	1	2	yes	complemented
23	C₂×#124×C₇₉	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	2	yes	—
27	C₂×#120×C₇₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₇₉	C₂²	1	2	yes	complemented
29	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₇₉	C₂²	1	2	yes	—
31	C₂²×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	—
32	C₂²×C₄²×C₇₉	C₂²	1	2	yes	—
33	#400×C₇₉	C₂²	1	1	yes	characteristic, complemented
34	#399×C₇₉	C₂²	1	1	yes	characteristic, complemented
35	#398×C₇₉	C₂²	1	2	yes	complemented
36	#397×C₇₉	C₂²	1	2	yes	—
37	#397×C₇₉	C₂²	1	2	yes	—
38	#397×C₇₉	C₂²	1	2	yes	—
39	#397×C₇₉	C₂²	1	2	yes	—
40	#396×C₇₉	C₂²	1	2	yes	—
41	#395×C₇₉	C₂²	1	2	yes	complemented
42	#395×C₇₉	C₂²	1	1	yes	characteristic, complemented
43	#394×C₇₉	C₂²	1	2	yes	—
44	#394×C₇₉	C₂²	1	2	yes	—
45	#393×C₇₉	C₂²	1	2	yes	—
46	#393×C₇₉	C₂²	1	1	yes	characteristic, complemented
47	#391×C₇₉	C₂²	1	2	yes	complemented
48	#391×C₇₉	C₂²	1	2	yes	complemented
49	#391×C₇₉	C₂²	1	2	yes	complemented
50	#390×C₇₉	C₂²	1	2	yes	—
51	#389×C₇₉	C₂²	1	2	yes	complemented
52	#389×C₇₉	C₂²	1	2	yes	complemented
53	#388×C₇₉	C₂²	1	2	yes	—
54	#388×C₇₉	C₂²	1	2	yes	—
55	#388×C₇₉	C₂²	1	2	yes	—
56	#388×C₇₉	C₂²	1	2	yes	—
57	#388×C₇₉	C₂²	1	2	yes	—
58	#388×C₇₉	C₂²	1	2	yes	complemented
59	#388×C₇₉	C₂²	1	2	yes	complemented
60	#388×C₇₉	C₂²	1	2	yes	complemented
61	#388×C₇₉	C₂²	1	2	yes	complemented
62	#387×C₇₉	C₂²	1	2	yes	complemented
63	#387×C₇₉	C₂²	1	2	yes	complemented
64	#387×C₇₉	C₂²	1	2	yes	complemented
65	#387×C₇₉	C₂²	1	2	yes	complemented
66	#387×C₇₉	C₂²	1	2	yes	complemented
67	#387×C₇₉	C₂²	1	2	yes	complemented
68	#387×C₇₉	C₂²	1	2	yes	complemented
69	#387×C₇₉	C₂²	1	2	yes	complemented
70	#387×C₇₉	C₂²	1	2	yes	complemented
71	#386×C₇₉	C₂²	1	2	yes	—
72	#386×C₇₉	C₂²	1	1	yes	characteristic
73	#386×C₇₉	C₂²	1	2	yes	—
74	#386×C₇₉	C₂²	1	2	yes	—
75	#385×C₇₉	C₂²	1	2	yes	—
76	#385×C₇₉	C₂²	1	2	yes	—
77	#385×C₇₉	C₂²	1	1	yes	characteristic
78	#385×C₇₉	C₂²	1	2	yes	—
79	#385×C₇₉	C₂²	1	2	yes	—
80	#385×C₇₉	C₂²	1	2	yes	—
81	#385×C₇₉	C₂²	1	2	yes	—
82	#385×C₇₉	C₂²	1	2	yes	complemented
83	#383×C₇₉	C₂²	1	1	yes	characteristic, complemented
84	#383×C₇₉	C₂²	1	2	yes	complemented
85	#381×C₇₉	C₂²	1	1	yes	characteristic, complemented
86	#380×C₇₉	C₂²	1	2	yes	—
87	#380×C₇₉	C₂²	1	1	yes	characteristic
88	#380×C₇₉	C₂²	1	2	yes	—
89	#379×C₇₉	C₂²	1	1	yes	characteristic
90	#379×C₇₉	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₇₉	C₂²	1	2	yes	complemented
92	C₄×C₄⋊C₄×C₇₉	C₂²	1	2	yes	complemented
93	C₄×C₄⋊C₄×C₇₉	C₂²	1	2	yes	complemented
94	C₄×C₄⋊C₄×C₇₉	C₂²	1	2	yes	complemented
95	C₄×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	—
96	C₄×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	—
97	C₄×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
101	C₄×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
104	#376×C₇₉	C₂²	1	1	yes	characteristic, complemented
105	C₂×#95×C₇₉	C₂²	1	1	yes	characteristic
106	C₂×#95×C₇₉	C₂²	1	1	yes	characteristic
107	C₂⁵×C₇₉	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
109	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
111	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
112	C₂³×C₄×C₇₉	—	2	4	no	—
113	C₂³×C₄×C₇₉	—	4	4	no	—
114	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
116	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
117	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
118	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
119	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
121	#126×C₇₉	—	2	8	no	—
122	#126×C₇₉	—	4	4	no	—
123	#124×C₇₉	—	2	8	no	—
124	C₂²⋊Q₈×C₇₉	—	2	4	no	—
125	C₂²⋊Q₈×C₇₉	—	2	8	no	—
126	C₂²⋊Q₈×C₇₉	—	4	4	no	—
127	#120×C₇₉	—	2	4	no	—
128	C₄×Q₈×C₇₉	—	4	4	no	—
129	C₄×D₄×C₇₉	—	2	4	no	—
130	C₄×D₄×C₇₉	—	4	4	no	—
131	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₇₉	—	2	8	no	—
148	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
153	C₂×C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
154	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
163	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₇₉	—	4	4	no	—
171	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
172	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
173	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
175	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
176	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
177	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
178	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
179	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
180	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
181	#95×C₇₉	C₂³	1	1	yes	characteristic
182	#95×C₇₉	C₂³	1	1	yes	characteristic
183	#95×C₇₉	C₂³	1	2	yes	—
184	#95×C₇₉	C₂³	1	2	yes	—
185	#95×C₇₉	C₂³	1	1	yes	characteristic
186	#95×C₇₉	C₂³	1	1	yes	characteristic
187	#95×C₇₉	C₂³	1	1	yes	characteristic
188	#95×C₇₉	C₂³	1	2	yes	—
189	#95×C₇₉	C₂³	1	2	yes	—
190	#95×C₇₉	C₂³	1	2	yes	—
191	#95×C₇₉	C₂³	1	2	yes	—
192	#95×C₇₉	C₂³	1	2	yes	—
193	#95×C₇₉	C₂³	1	2	yes	—
194	#95×C₇₉	C₂³	1	2	yes	—
195	#95×C₇₉	C₂³	1	2	yes	—
196	#95×C₇₉	C₂³	1	1	yes	characteristic
197	#95×C₇₉	C₂³	1	2	yes	—
198	#95×C₇₉	C₂³	1	2	yes	—
199	#95×C₇₉	C₂³	1	2	yes	—
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	2	yes	—
205	#95×C₇₉	C₂³	1	2	yes	—
206	#95×C₇₉	C₂³	1	2	yes	—
207	#95×C₇₉	C₂³	1	2	yes	—
208	C₂⁴×C₇₉	—	2	4	no	—
209	C₂⁴×C₇₉	—	2	2	no	—
210	C₂⁴×C₇₉	—	2	2	no	—
211	C₂⁴×C₇₉	—	2	2	no	—
212	C₂⁴×C₇₉	—	4	2	no	—
213	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
214	C₂⁴×C₇₉	C₂⁴	1	2	yes	—
215	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
216	C₂×Q₈×C₇₉	—	2	4	no	—
217	C₂×Q₈×C₇₉	—	2	4	no	—
218	C₂×Q₈×C₇₉	—	2	2	no	—
219	C₂×Q₈×C₇₉	—	4	2	no	—
220	C₂×Q₈×C₇₉	—	4	2	no	—
221	C₂×D₄×C₇₉	—	2	2	no	—
222	C₂×D₄×C₇₉	—	2	2	no	—
223	C₂×D₄×C₇₉	—	2	4	no	—
224	C₂×D₄×C₇₉	—	2	2	no	—
225	C₂×D₄×C₇₉	—	2	4	no	—
226	C₂×D₄×C₇₉	—	4	2	no	—
227	C₂²×C₄×C₇₉	—	2	2	no	—
228	C₂²×C₄×C₇₉	—	2	4	no	—
229	C₂²×C₄×C₇₉	—	2	4	no	—
230	C₂²×C₄×C₇₉	—	2	4	no	—
231	C₂²×C₄×C₇₉	—	2	4	no	—
232	C₂²×C₄×C₇₉	—	2	4	no	—
233	C₂²×C₄×C₇₉	—	2	4	no	—
234	C₂²×C₄×C₇₉	—	2	4	no	—
235	C₂²×C₄×C₇₉	—	2	4	no	—
236	C₂²×C₄×C₇₉	—	2	4	no	—
237	C₂²×C₄×C₇₉	—	2	2	no	—
238	C₂²×C₄×C₇₉	—	4	2	no	—
239	C₂²×C₄×C₇₉	—	4	2	no	—
240	C₂²×C₄×C₇₉	—	4	2	no	—
241	C₂²×C₄×C₇₉	—	4	2	no	—
242	C₂²×C₄×C₇₉	—	4	2	no	—
243	C₂²×C₄×C₇₉	—	4	2	no	—
244	C₂²×C₄×C₇₉	—	4	16	no	—
245	C₂²×C₄×C₇₉	#41	1	4	yes	—
246	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₇₉	C₂⁴	1	2	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	2	yes	—
259	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
262	C₄⋊C₄×C₇₉	—	2	2	no	—
263	C₄⋊C₄×C₇₉	—	2	4	no	—
264	C₄⋊C₄×C₇₉	—	2	2	no	—
265	C₄⋊C₄×C₇₉	—	2	4	no	—
266	C₄⋊C₄×C₇₉	—	2	4	no	—
267	C₄⋊C₄×C₇₉	—	2	4	no	—
268	C₄⋊C₄×C₇₉	—	2	4	no	—
269	C₄⋊C₄×C₇₉	—	2	4	no	—
270	C₄⋊C₄×C₇₉	—	2	4	no	—
271	C₄⋊C₄×C₇₉	—	2	4	no	—
272	C₄⋊C₄×C₇₉	—	2	4	no	—
273	C₄⋊C₄×C₇₉	—	2	4	no	—
274	C₄⋊C₄×C₇₉	—	4	2	no	—
275	C₄⋊C₄×C₇₉	—	4	2	no	—
276	C₄⋊C₄×C₇₉	—	4	2	no	—
277	C₄⋊C₄×C₇₉	—	4	2	no	—
278	C₂²⋊C₄×C₇₉	—	2	4	no	—
279	C₂²⋊C₄×C₇₉	—	2	2	no	—
280	C₂²⋊C₄×C₇₉	—	2	4	no	—
281	C₂²⋊C₄×C₇₉	—	2	4	no	—
282	C₂²⋊C₄×C₇₉	—	2	4	no	—
283	C₂²⋊C₄×C₇₉	—	2	4	no	—
284	C₂²⋊C₄×C₇₉	—	2	4	no	—
285	C₂²⋊C₄×C₇₉	—	2	2	no	—
286	C₂²⋊C₄×C₇₉	—	2	4	no	—
287	C₂²⋊C₄×C₇₉	—	2	4	no	—
288	C₂²⋊C₄×C₇₉	—	2	2	no	—
289	C₂²⋊C₄×C₇₉	—	2	4	no	—
290	C₂²⋊C₄×C₇₉	—	2	4	no	—
291	C₂²⋊C₄×C₇₉	—	2	4	no	—
292	C₂²⋊C₄×C₇₉	—	2	4	no	—
293	C₂²⋊C₄×C₇₉	—	4	2	no	—
294	C₂²⋊C₄×C₇₉	—	4	2	no	—
295	C₂²⋊C₄×C₇₉	—	4	2	no	—
296	C₂²⋊C₄×C₇₉	—	4	2	no	—
297	C₂²⋊C₄×C₇₉	—	4	2	no	—
298	C₂²⋊C₄×C₇₉	#41	1	8	yes	—
299	C₂²⋊C₄×C₇₉	#41	1	4	yes	—
300	C₄²×C₇₉	—	2	2	no	—
301	C₄²×C₇₉	—	2	4	no	—
302	C₄²×C₇₉	—	2	4	no	—
303	C₄²×C₇₉	—	2	4	no	—
304	C₄²×C₇₉	—	2	4	no	—
305	C₄²×C₇₉	—	4	2	no	—
306	C₄²×C₇₉	—	4	2	no	—
307	C₄²×C₇₉	—	4	2	no	—
308	C₄²×C₇₉	—	4	2	no	—
309	C₄²×C₇₉	—	4	2	no	—
310	C₂³×C₇₉	—	2	2	no	—
311	C₂³×C₇₉	—	2	2	no	—
312	C₂³×C₇₉	—	2	8	no	—
313	C₂³×C₇₉	—	2	2	no	—
314	C₂³×C₇₉	—	2	2	no	—
315	C₂³×C₇₉	—	2	2	no	—
316	C₂³×C₇₉	—	2	2	no	—
317	C₂³×C₇₉	—	2	2	no	—
318	C₂³×C₇₉	—	2	2	no	—
319	C₂³×C₇₉	—	2	2	no	—
320	C₂³×C₇₉	—	2	1	no	—
321	C₂³×C₇₉	—	2	1	no	—
322	C₂³×C₇₉	—	2	2	no	—
323	C₂³×C₇₉	—	2	1	no	—
324	C₂³×C₇₉	—	4	8	no	—
325	C₂³×C₇₉	—	4	8	no	—
326	C₂³×C₇₉	—	4	4	no	—
327	C₂³×C₇₉	—	4	4	no	—
328	C₂³×C₇₉	C₂×#41	1	4	yes	—
329	C₂³×C₇₉	C₂×#41	1	2	yes	—
330	C₂³×C₇₉	C₂×#41	1	2	yes	—
331	C₂³×C₇₉	2₋¹⁺⁴	1	2	yes	—
332	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
333	Q₈×C₇₉	—	4	8	no	—
334	Q₈×C₇₉	—	8	2	no	—
335	D₄×C₇₉	—	4	8	no	—
336	D₄×C₇₉	—	4	4	no	—
337	C₂×C₄×C₇₉	—	2	8	no	—
338	C₂×C₄×C₇₉	—	2	2	no	—
339	C₂×C₄×C₇₉	—	2	2	no	—
340	C₂×C₄×C₇₉	—	2	2	no	—
341	C₂×C₄×C₇₉	—	2	2	no	—
342	C₂×C₄×C₇₉	—	2	2	no	—
343	C₂×C₄×C₇₉	—	2	2	no	—
344	C₂×C₄×C₇₉	—	2	2	no	—
345	C₂×C₄×C₇₉	—	2	2	no	—
346	C₂×C₄×C₇₉	—	2	2	no	—
347	C₂×C₄×C₇₉	—	2	2	no	—
348	C₂×C₄×C₇₉	—	2	1	no	—
349	C₂×C₄×C₇₉	—	2	2	no	—
350	C₂×C₄×C₇₉	—	2	2	no	—
351	C₂×C₄×C₇₉	—	2	2	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	1	no	—
356	C₂×C₄×C₇₉	—	2	2	no	—
357	C₂×C₄×C₇₉	—	2	2	no	—
358	C₂×C₄×C₇₉	—	2	2	no	—
359	C₂×C₄×C₇₉	—	2	2	no	—
360	C₂×C₄×C₇₉	—	2	2	no	—
361	C₂×C₄×C₇₉	—	2	1	no	—
362	C₂×C₄×C₇₉	—	2	2	no	—
363	C₂×C₄×C₇₉	—	2	2	no	—
364	C₂×C₄×C₇₉	—	2	2	no	—
365	C₂×C₄×C₇₉	—	2	2	no	—
366	C₂×C₄×C₇₉	—	2	2	no	—
367	C₂×C₄×C₇₉	—	2	2	no	—
368	C₂×C₄×C₇₉	—	2	2	no	—
369	C₂×C₄×C₇₉	—	2	2	no	—
370	C₂×C₄×C₇₉	—	2	2	no	—
371	C₂×C₄×C₇₉	—	2	2	no	—
372	C₂×C₄×C₇₉	—	2	2	no	—
373	C₂×C₄×C₇₉	—	2	2	no	—
374	C₂×C₄×C₇₉	—	2	2	no	—
375	C₂×C₄×C₇₉	—	2	1	no	—
376	C₂×C₄×C₇₉	—	4	4	no	—
377	C₂×C₄×C₇₉	—	4	8	no	—
378	C₂×C₄×C₇₉	—	4	8	no	—
379	C₂×C₄×C₇₉	—	4	8	no	—
380	C₂×C₄×C₇₉	—	4	8	no	—
381	C₂×C₄×C₇₉	—	8	2	no	—
382	C₂×C₄×C₇₉	C₂×#41	1	4	yes	—
383	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
384	C₂×C₄×C₇₉	C₂×#41	1	4	yes	—
385	C₂×C₄×C₇₉	C₂×#41	1	4	yes	—
386	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
387	C₂×C₄×C₇₉	H(5,𝔽₂)	1	4	yes	—
388	C₂²×C₇₉	—	2	2	no	—
389	C₂²×C₇₉	—	2	4	no	—
390	C₂²×C₇₉	—	2	2	no	—
391	C₂²×C₇₉	—	2	4	no	—
392	C₂²×C₇₉	—	2	4	no	—
393	C₂²×C₇₉	—	2	4	no	—
394	C₂²×C₇₉	—	2	4	no	—
395	C₂²×C₇₉	—	4	16	no	—
396	C₂²×C₇₉	—	4	2	no	—
397	C₂²×C₇₉	—	4	2	no	—
398	C₂²×C₇₉	—	4	2	no	—
399	C₂²×C₇₉	—	4	2	no	—
400	C₂²×C₇₉	—	4	1	no	—
401	C₂²×C₇₉	—	4	1	no	—
402	C₂²×C₇₉	—	4	2	no	—
403	C₂²×C₇₉	—	4	1	no	—
404	C₂²×C₇₉	—	4	2	no	—
405	C₂²×C₇₉	#556	1	4	yes	—
406	C₂²×C₇₉	C₂²×#41	1	1	yes	characteristic
407	C₂²×C₇₉	C₂²×#41	1	2	yes	—
408	C₂²×C₇₉	C₂²×#41	1	1	yes	characteristic
409	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	2	yes	—
410	C₂²×C₇₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
411	C₄×C₇₉	—	2	4	no	—
412	C₄×C₇₉	—	2	4	no	—
413	C₄×C₇₉	—	2	4	no	—
414	C₄×C₇₉	—	2	2	no	—
415	C₄×C₇₉	—	2	2	no	—
416	C₄×C₇₉	—	2	4	no	—
417	C₄×C₇₉	—	4	1	no	—
418	C₄×C₇₉	—	4	2	no	—
419	C₄×C₇₉	—	4	1	no	—
420	C₄×C₇₉	—	4	2	no	—
421	C₄×C₇₉	—	4	2	no	—
422	C₄×C₇₉	—	4	2	no	—
423	C₄×C₇₉	—	4	1	no	—
424	C₄×C₇₉	—	4	2	no	—
425	C₄×C₇₉	—	4	2	no	—
426	C₄×C₇₉	—	4	2	no	—
427	#36531	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
428	C₂×C₇₉	—	2	4	no	—
429	C₂×C₇₉	—	4	4	no	—
430	C₂×C₇₉	—	8	1	no	—
431	C₂×C₇₉	#3444	1	1	yes	characteristic
432	C₂×C₇₉	C₂×#556	1	1	yes	characteristic
433	C₂×C₇₉	#3481	1	2	yes	—
434	C₂×C₇₉	#3490	1	1	yes	characteristic
435	C₂×C₇₉	#3520	1	2	yes	—
436	#2852	C₂×C₇₉	1	2	yes	complemented
437	#2848	C₂×C₇₉	1	1	yes	characteristic, complemented
438	#2577	C₂×C₇₉	1	2	yes	complemented
439	#2564	C₂×C₇₉	1	1	yes	characteristic, complemented
440	#2560	C₂×C₇₉	1	2	yes	complemented
441	#2549	C₂×C₇₉	1	1	yes	characteristic, complemented
442	#2523	C₂×C₇₉	1	2	yes	complemented
443	#2521	C₂×C₇₉	1	2	yes	complemented
444	#2480	C₂×C₇₉	1	2	yes	complemented
445	#2472	C₂×C₇₉	1	2	yes	—
446	#2466	C₂×C₇₉	1	2	yes	complemented
447	#2465	C₂×C₇₉	1	2	yes	complemented
448	#2373	C₂×C₇₉	1	2	yes	complemented
449	#2368	C₂×C₇₉	1	1	yes	characteristic, complemented
450	#2367	C₂×C₇₉	1	2	yes	complemented
451	#2353	C₂×C₇₉	1	1	yes	characteristic, complemented
452	C₄×C₂²⋊Q₈	C₂×C₇₉	1	2	yes	complemented
453	C₄×#120	C₂×C₇₉	1	1	yes	characteristic
454	C₂×C₄×C₂²⋊C₄	C₂×C₇₉	1	1	yes	characteristic, complemented
455	C₇₉	#36531	1	1	yes	characteristic, direct product factor, Sylow
456	C₂⁴×C₄	C₂²×C₇₉	1	1	yes	characteristic
457	C₂×#126	C₂²×C₇₉	1	2	yes	—
458	C₂×#126	C₂²×C₇₉	1	2	yes	complemented
459	C₂×#124	C₂²×C₇₉	1	2	yes	—
460	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
461	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	2	yes	—
462	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	2	yes	—
463	C₂×#120	C₂²×C₇₉	1	1	yes	characteristic
464	C₂×C₄×Q₈	C₂²×C₇₉	1	2	yes	complemented
465	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
466	C₂×C₄×D₄	C₂²×C₇₉	1	2	yes	—
467	C₂²×C₂²⋊C₄	C₂²×C₇₉	1	2	yes	—
468	C₂²×C₄²	C₂²×C₇₉	1	2	yes	—
469	#400	C₂²×C₇₉	1	1	yes	characteristic, complemented
470	#399	C₂²×C₇₉	1	1	yes	characteristic, complemented
471	#398	C₂²×C₇₉	1	2	yes	complemented
472	#397	C₂²×C₇₉	1	2	yes	—
473	#397	C₂²×C₇₉	1	2	yes	—
474	#397	C₂²×C₇₉	1	2	yes	—
475	#397	C₂²×C₇₉	1	2	yes	—
476	#396	C₂²×C₇₉	1	2	yes	—
477	#395	C₂²×C₇₉	1	1	yes	characteristic, complemented
478	#395	C₂²×C₇₉	1	2	yes	complemented
479	#394	C₂²×C₇₉	1	2	yes	—
480	#394	C₂²×C₇₉	1	2	yes	—
481	#393	C₂²×C₇₉	1	2	yes	—
482	#393	C₂²×C₇₉	1	1	yes	characteristic, complemented
483	#391	C₂²×C₇₉	1	2	yes	complemented
484	#391	C₂²×C₇₉	1	2	yes	complemented
485	#391	C₂²×C₇₉	1	2	yes	complemented
486	#390	C₂²×C₇₉	1	2	yes	—
487	#389	C₂²×C₇₉	1	2	yes	complemented
488	#389	C₂²×C₇₉	1	2	yes	complemented
489	#388	C₂²×C₇₉	1	2	yes	—
490	#388	C₂²×C₇₉	1	2	yes	—
491	#388	C₂²×C₇₉	1	2	yes	—
492	#388	C₂²×C₇₉	1	2	yes	—
493	#388	C₂²×C₇₉	1	2	yes	—
494	#388	C₂²×C₇₉	1	2	yes	complemented
495	#388	C₂²×C₇₉	1	2	yes	complemented
496	#388	C₂²×C₇₉	1	2	yes	complemented
497	#388	C₂²×C₇₉	1	2	yes	complemented
498	#387	C₂²×C₇₉	1	2	yes	complemented
499	#387	C₂²×C₇₉	1	2	yes	complemented
500	#387	C₂²×C₇₉	1	2	yes	complemented
501	#387	C₂²×C₇₉	1	2	yes	complemented
502	#387	C₂²×C₇₉	1	2	yes	complemented
503	#387	C₂²×C₇₉	1	2	yes	complemented
504	#387	C₂²×C₇₉	1	2	yes	complemented
505	#387	C₂²×C₇₉	1	2	yes	complemented
506	#387	C₂²×C₇₉	1	2	yes	complemented
507	#386	C₂²×C₇₉	1	2	yes	—
508	#386	C₂²×C₇₉	1	2	yes	—
509	#386	C₂²×C₇₉	1	1	yes	characteristic
510	#386	C₂²×C₇₉	1	2	yes	—
511	#385	C₂²×C₇₉	1	2	yes	—
512	#385	C₂²×C₇₉	1	2	yes	—
513	#385	C₂²×C₇₉	1	2	yes	—
514	#385	C₂²×C₇₉	1	2	yes	—
515	#385	C₂²×C₇₉	1	2	yes	—
516	#385	C₂²×C₇₉	1	2	yes	—
517	#385	C₂²×C₇₉	1	1	yes	characteristic
518	#385	C₂²×C₇₉	1	2	yes	complemented
519	#383	C₂²×C₇₉	1	2	yes	complemented
520	#383	C₂²×C₇₉	1	1	yes	characteristic, complemented
521	#381	C₂²×C₇₉	1	1	yes	characteristic, complemented
522	#380	C₂²×C₇₉	1	2	yes	—
523	#380	C₂²×C₇₉	1	2	yes	—
524	#380	C₂²×C₇₉	1	1	yes	characteristic
525	#379	C₂²×C₇₉	1	2	yes	—
526	#379	C₂²×C₇₉	1	1	yes	characteristic
527	C₄×C₄⋊C₄	C₂²×C₇₉	1	2	yes	complemented
528	C₄×C₄⋊C₄	C₂²×C₇₉	1	2	yes	complemented
529	C₄×C₄⋊C₄	C₂²×C₇₉	1	2	yes	complemented
530	C₄×C₄⋊C₄	C₂²×C₇₉	1	2	yes	complemented
531	C₄×C₂²⋊C₄	C₂²×C₇₉	1	2	yes	—
532	C₄×C₂²⋊C₄	C₂²×C₇₉	1	2	yes	—
533	C₄×C₂²⋊C₄	C₂²×C₇₉	1	2	yes	—
534	C₄×C₂²⋊C₄	C₂²×C₇₉	1	2	yes	—
535	C₄×C₂²⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
536	C₄×C₂²⋊C₄	C₂²×C₇₉	1	2	yes	—
537	C₄×C₂²⋊C₄	C₂²×C₇₉	1	2	yes	—
538	C₄×C₂²⋊C₄	C₂²×C₇₉	1	2	yes	—
539	C₄×C₂²⋊C₄	C₂²×C₇₉	1	1	yes	characteristic, complemented
540	#376	C₂²×C₇₉	1	1	yes	characteristic, complemented
541	C₂×#95	C₂²×C₇₉	1	1	yes	characteristic
542	C₂×#95	C₂²×C₇₉	1	1	yes	characteristic
543	C₂⁵	C₂³×C₇₉	1	1	yes	characteristic
544	C₂²×Q₈	C₂³×C₇₉	1	2	yes	—
545	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
546	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
547	C₂²×D₄	C₂³×C₇₉	1	2	yes	—
548	C₂³×C₄	—	2	4	no	—
549	C₂³×C₄	—	4	4	no	—
550	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
551	C₂³×C₄	C₂³×C₇₉	1	2	yes	—
552	C₂³×C₄	C₂³×C₇₉	1	2	yes	—
553	C₂³×C₄	C₂³×C₇₉	1	2	yes	—
554	C₂³×C₄	C₂³×C₇₉	1	2	yes	—
555	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
556	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
557	#126	—	2	8	no	—
558	#126	—	4	4	no	—
559	#124	—	2	8	no	—
560	C₂²⋊Q₈	—	2	4	no	—
561	C₂²⋊Q₈	—	2	8	no	—
562	C₂²⋊Q₈	—	4	4	no	—
563	#120	—	2	4	no	—
564	C₄×Q₈	—	4	4	no	—
565	C₄×D₄	—	2	4	no	—
566	C₄×D₄	—	4	4	no	—
567	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
583	C₂×C₂²⋊C₄	—	2	8	no	—
584	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
589	C₂×C₂²⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
590	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
599	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
606	C₂×C₄²	—	4	4	no	—
607	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
608	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
609	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
610	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
611	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
612	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
613	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
614	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
615	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
616	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
617	#95	C₂³×C₇₉	1	1	yes	characteristic
618	#95	C₂³×C₇₉	1	1	yes	characteristic
619	#95	C₂³×C₇₉	1	2	yes	—
620	#95	C₂³×C₇₉	1	2	yes	—
621	#95	C₂³×C₇₉	1	1	yes	characteristic
622	#95	C₂³×C₇₉	1	1	yes	characteristic
623	#95	C₂³×C₇₉	1	1	yes	characteristic
624	#95	C₂³×C₇₉	1	2	yes	—
625	#95	C₂³×C₇₉	1	2	yes	—
626	#95	C₂³×C₇₉	1	2	yes	—
627	#95	C₂³×C₇₉	1	2	yes	—
628	#95	C₂³×C₇₉	1	2	yes	—
629	#95	C₂³×C₇₉	1	2	yes	—
630	#95	C₂³×C₇₉	1	2	yes	—
631	#95	C₂³×C₇₉	1	2	yes	—
632	#95	C₂³×C₇₉	1	1	yes	characteristic
633	#95	C₂³×C₇₉	1	2	yes	—
634	#95	C₂³×C₇₉	1	2	yes	—
635	#95	C₂³×C₇₉	1	2	yes	—
636	#95	C₂³×C₇₉	1	2	yes	—
637	#95	C₂³×C₇₉	1	2	yes	—
638	#95	C₂³×C₇₉	1	2	yes	—
639	#95	C₂³×C₇₉	1	2	yes	—
640	#95	C₂³×C₇₉	1	2	yes	—
641	#95	C₂³×C₇₉	1	2	yes	—
642	#95	C₂³×C₇₉	1	2	yes	—
643	#95	C₂³×C₇₉	1	2	yes	—
644	C₂⁴	—	2	4	no	—
645	C₂⁴	—	2	2	no	—
646	C₂⁴	—	2	2	no	—
647	C₂⁴	—	2	2	no	—
648	C₂⁴	—	4	2	no	—
649	C₂⁴	C₂⁴×C₇₉	1	1	yes	characteristic
650	C₂⁴	C₂⁴×C₇₉	1	2	yes	—
651	C₂⁴	C₂⁴×C₇₉	1	1	yes	characteristic
652	C₂×Q₈	—	2	4	no	—
653	C₂×Q₈	—	2	4	no	—
654	C₂×Q₈	—	2	2	no	—
655	C₂×Q₈	—	4	2	no	—
656	C₂×Q₈	—	4	2	no	—
657	C₂×D₄	—	2	2	no	—
658	C₂×D₄	—	2	2	no	—
659	C₂×D₄	—	2	4	no	—
660	C₂×D₄	—	2	2	no	—
661	C₂×D₄	—	2	4	no	—
662	C₂×D₄	—	4	2	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	2	4	no	—
665	C₂²×C₄	—	2	4	no	—
666	C₂²×C₄	—	2	4	no	—
667	C₂²×C₄	—	2	4	no	—
668	C₂²×C₄	—	2	4	no	—
669	C₂²×C₄	—	2	4	no	—
670	C₂²×C₄	—	2	4	no	—
671	C₂²×C₄	—	2	4	no	—
672	C₂²×C₄	—	2	4	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	4	2	no	—
675	C₂²×C₄	—	4	2	no	—
676	C₂²×C₄	—	4	2	no	—
677	C₂²×C₄	—	4	2	no	—
678	C₂²×C₄	—	4	2	no	—
679	C₂²×C₄	—	4	2	no	—
680	C₂²×C₄	—	4	16	no	—
681	C₂²×C₄	#41×C₇₉	1	4	yes	—
682	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
685	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
686	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
687	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
688	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
690	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
692	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
693	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
694	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
695	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
696	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	4	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	4	no	—
704	C₄⋊C₄	—	2	4	no	—
705	C₄⋊C₄	—	2	4	no	—
706	C₄⋊C₄	—	2	4	no	—
707	C₄⋊C₄	—	2	4	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	4	2	no	—
711	C₄⋊C₄	—	4	2	no	—
712	C₄⋊C₄	—	4	2	no	—
713	C₄⋊C₄	—	4	2	no	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	2	2	no	—
716	C₂²⋊C₄	—	2	4	no	—
717	C₂²⋊C₄	—	2	4	no	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	2	4	no	—
720	C₂²⋊C₄	—	2	4	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	4	no	—
723	C₂²⋊C₄	—	2	4	no	—
724	C₂²⋊C₄	—	2	2	no	—
725	C₂²⋊C₄	—	2	4	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	4	no	—
728	C₂²⋊C₄	—	2	4	no	—
729	C₂²⋊C₄	—	4	2	no	—
730	C₂²⋊C₄	—	4	2	no	—
731	C₂²⋊C₄	—	4	2	no	—
732	C₂²⋊C₄	—	4	2	no	—
733	C₂²⋊C₄	—	4	2	no	—
734	C₂²⋊C₄	#41×C₇₉	1	8	yes	—
735	C₂²⋊C₄	#41×C₇₉	1	4	yes	—
736	C₄²	—	2	2	no	—
737	C₄²	—	2	4	no	—
738	C₄²	—	2	4	no	—
739	C₄²	—	2	4	no	—
740	C₄²	—	2	4	no	—
741	C₄²	—	4	2	no	—
742	C₄²	—	4	2	no	—
743	C₄²	—	4	2	no	—
744	C₄²	—	4	2	no	—
745	C₄²	—	4	2	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	2	8	no	—
749	C₂³	—	2	2	no	—
750	C₂³	—	2	2	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	2	no	—
756	C₂³	—	2	1	no	—
757	C₂³	—	2	1	no	—
758	C₂³	—	2	2	no	—
759	C₂³	—	2	1	no	—
760	C₂³	—	4	8	no	—
761	C₂³	—	4	8	no	—
762	C₂³	—	4	4	no	—
763	C₂³	—	4	4	no	—
764	C₂³	C₂×#41×C₇₉	1	4	yes	—
765	C₂³	C₂×#41×C₇₉	1	2	yes	—
766	C₂³	C₂×#41×C₇₉	1	2	yes	—
767	C₂³	2₋¹⁺⁴×C₇₉	1	2	yes	—
768	C₂³	C₂⁵×C₇₉	1	1	yes	characteristic
769	Q₈	—	4	8	no	—
770	Q₈	—	8	2	no	—
771	D₄	—	4	8	no	—
772	D₄	—	4	4	no	—
773	C₂×C₄	—	2	8	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	4	4	no	—
813	C₂×C₄	—	4	8	no	—
814	C₂×C₄	—	4	8	no	—
815	C₂×C₄	—	4	8	no	—
816	C₂×C₄	—	4	8	no	—
817	C₂×C₄	—	8	2	no	—
818	C₂×C₄	C₂×#41×C₇₉	1	4	yes	—
819	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
820	C₂×C₄	C₂×#41×C₇₉	1	4	yes	—
821	C₂×C₄	C₂×#41×C₇₉	1	4	yes	—
822	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
823	C₂×C₄	H(5,𝔽₂)×C₇₉	1	4	yes	—
824	C₂²	—	2	2	no	—
825	C₂²	—	2	4	no	—
826	C₂²	—	2	2	no	—
827	C₂²	—	2	4	no	—
828	C₂²	—	2	4	no	—
829	C₂²	—	2	4	no	—
830	C₂²	—	2	4	no	—
831	C₂²	—	4	16	no	—
832	C₂²	—	4	2	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	1	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	1	no	—
840	C₂²	—	4	2	no	—
841	C₂²	#556×C₇₉	1	4	yes	—
842	C₂²	C₂²×#41×C₇₉	1	1	yes	characteristic
843	C₂²	C₂²×#41×C₇₉	1	2	yes	—
844	C₂²	C₂²×#41×C₇₉	1	1	yes	characteristic
845	C₂²	C₂×H(5,𝔽₂)×C₇₉	1	2	yes	—
846	C₂²	C₂×2₋¹⁺⁴×C₇₉	1	1	yes	characteristic
847	C₄	—	2	4	no	—
848	C₄	—	2	4	no	—
849	C₄	—	2	4	no	—
850	C₄	—	2	2	no	—
851	C₄	—	2	2	no	—
852	C₄	—	2	4	no	—
853	C₄	—	4	1	no	—
854	C₄	—	4	2	no	—
855	C₄	—	4	1	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	2	no	—
861	C₄	—	4	2	no	—
862	C₄	—	4	2	no	—
863	C₂	—	2	4	no	—
864	C₂	—	4	4	no	—
865	C₂	—	8	1	no	—
866	C₂	C₇₉×#3444	1	1	yes	characteristic
867	C₂	C₂×#556×C₇₉	1	1	yes	characteristic
868	C₂	C₇₉×#3481	1	2	yes	—
869	C₂	C₇₉×#3490	1	1	yes	characteristic
870	C₂	C₇₉×#3520	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₉
prime radical	C₂×#120×C₇₉	C₂²
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
1. C₇₉×#2852	C₂	semidirect
2. C₇₉×#2848	C₂	semidirect
3. C₇₉×#2577	C₂	semidirect
4. C₇₉×#2564	C₂	semidirect
5. C₇₉×#2560	C₂	semidirect
6. C₇₉×#2549	C₂	semidirect
7. C₇₉×#2523	C₂	semidirect
8. C₇₉×#2521	C₂	semidirect
9. C₇₉×#2480	C₂	semidirect
11. C₇₉×#2466	C₂	semidirect
12. C₇₉×#2465	C₂	semidirect
13. C₇₉×#2373	C₂	semidirect
14. C₇₉×#2368	C₂	semidirect
15. C₇₉×#2367	C₂	semidirect
16. C₇₉×#2353	C₂	semidirect
17. C₄×C₂²⋊Q₈×C₇₉	C₂	semidirect
19. C₂×C₄×C₂²⋊C₄×C₇₉	C₂	semidirect
22. C₂×#126×C₇₉	C₂²	semidirect
28. C₂×C₄×Q₈×C₇₉	C₂²	semidirect
33. #400×C₇₉	C₂²	semidirect
34. #399×C₇₉	C₂²	semidirect
35. #398×C₇₉	C₂²	semidirect
41. #395×C₇₉	C₂²	semidirect
42. #395×C₇₉	C₂²	semidirect
46. #393×C₇₉	C₂²	semidirect
47. #391×C₇₉	C₂²	semidirect
48. #391×C₇₉	C₂²	semidirect
49. #391×C₇₉	C₂²	semidirect
51. #389×C₇₉	C₂²	semidirect
52. #389×C₇₉	C₂²	semidirect
58. #388×C₇₉	C₂²	semidirect
59. #388×C₇₉	C₂²	semidirect
60. #388×C₇₉	C₂²	semidirect
61. #388×C₇₉	C₂²	semidirect
62. #387×C₇₉	C₂²	semidirect
63. #387×C₇₉	C₂²	semidirect
64. #387×C₇₉	C₂²	semidirect
65. #387×C₇₉	C₂²	semidirect
66. #387×C₇₉	C₂²	semidirect
67. #387×C₇₉	C₂²	semidirect
68. #387×C₇₉	C₂²	semidirect
69. #387×C₇₉	C₂²	semidirect
70. #387×C₇₉	C₂²	semidirect
82. #385×C₇₉	C₂²	semidirect
83. #383×C₇₉	C₂²	semidirect
84. #383×C₇₉	C₂²	semidirect
85. #381×C₇₉	C₂²	semidirect
91. C₄×C₄⋊C₄×C₇₉	C₂²	semidirect
92. C₄×C₄⋊C₄×C₇₉	C₂²	semidirect
93. C₄×C₄⋊C₄×C₇₉	C₂²	semidirect
94. C₄×C₄⋊C₄×C₇₉	C₂²	semidirect
103. C₄×C₂²⋊C₄×C₇₉	C₂²	semidirect
104. #376×C₇₉	C₂²	semidirect
427. #36531	C₇₉	direct (N × H)
436. #2852	C₂×C₇₉	semidirect
437. #2848	C₂×C₇₉	semidirect
438. #2577	C₂×C₇₉	semidirect
439. #2564	C₂×C₇₉	semidirect
440. #2560	C₂×C₇₉	semidirect
441. #2549	C₂×C₇₉	semidirect
442. #2523	C₂×C₇₉	semidirect
443. #2521	C₂×C₇₉	semidirect
444. #2480	C₂×C₇₉	semidirect
446. #2466	C₂×C₇₉	semidirect
447. #2465	C₂×C₇₉	semidirect
448. #2373	C₂×C₇₉	semidirect
449. #2368	C₂×C₇₉	semidirect
450. #2367	C₂×C₇₉	semidirect
451. #2353	C₂×C₇₉	semidirect
452. C₄×C₂²⋊Q₈	C₂×C₇₉	semidirect
454. C₂×C₄×C₂²⋊C₄	C₂×C₇₉	semidirect
455. C₇₉	#36531	direct (N × H)
458. C₂×#126	C₂²×C₇₉	semidirect
464. C₂×C₄×Q₈	C₂²×C₇₉	semidirect
469. #400	C₂²×C₇₉	semidirect
470. #399	C₂²×C₇₉	semidirect
471. #398	C₂²×C₇₉	semidirect
477. #395	C₂²×C₇₉	semidirect
478. #395	C₂²×C₇₉	semidirect
482. #393	C₂²×C₇₉	semidirect
483. #391	C₂²×C₇₉	semidirect
484. #391	C₂²×C₇₉	semidirect
485. #391	C₂²×C₇₉	semidirect
487. #389	C₂²×C₇₉	semidirect
488. #389	C₂²×C₇₉	semidirect
494. #388	C₂²×C₇₉	semidirect
495. #388	C₂²×C₇₉	semidirect
496. #388	C₂²×C₇₉	semidirect
497. #388	C₂²×C₇₉	semidirect
498. #387	C₂²×C₇₉	semidirect
499. #387	C₂²×C₇₉	semidirect
500. #387	C₂²×C₇₉	semidirect
501. #387	C₂²×C₇₉	semidirect
502. #387	C₂²×C₇₉	semidirect
503. #387	C₂²×C₇₉	semidirect
504. #387	C₂²×C₇₉	semidirect
505. #387	C₂²×C₇₉	semidirect
506. #387	C₂²×C₇₉	semidirect
518. #385	C₂²×C₇₉	semidirect
519. #383	C₂²×C₇₉	semidirect
520. #383	C₂²×C₇₉	semidirect
521. #381	C₂²×C₇₉	semidirect
527. C₄×C₄⋊C₄	C₂²×C₇₉	semidirect
528. C₄×C₄⋊C₄	C₂²×C₇₉	semidirect
529. C₄×C₄⋊C₄	C₂²×C₇₉	semidirect
530. C₄×C₄⋊C₄	C₂²×C₇₉	semidirect
539. C₄×C₂²⋊C₄	C₂²×C₇₉	semidirect
540. #376	C₂²×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₇₉×#2852	2
C₇₉×#2848	2
C₇₉×#2577	2
C₇₉×#2564	2
C₇₉×#2560	2
C₇₉×#2549	2
C₇₉×#2523	2
C₇₉×#2521	2
C₇₉×#2480	2
C₇₉×#2472	2
C₇₉×#2466	2
C₇₉×#2465	2
C₇₉×#2373	2
C₇₉×#2368	2
C₇₉×#2367	2
C₇₉×#2353	2
C₄×C₂²⋊Q₈×C₇₉	2
C₄×#120×C₇₉	2
C₂×C₄×C₂²⋊C₄×C₇₉	2
#36531	79

Subgroups — C79×#36531 #34148220

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#36531 #34148220