Subgroups — C₇₉×#36529 #34148218

Order 20224.

3132 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#553×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#2854	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#2847	C₂	1	2	yes	maximal, complemented
5	C₇₉×#2539	C₂	1	2	yes	maximal, complemented
6	C₇₉×#2534	C₂	1	2	yes	maximal, complemented
7	C₇₉×#2467	C₂	1	4	yes	maximal, complemented
8	C₇₉×#2456	C₂	1	4	yes	maximal, complemented
9	C₇₉×#2454	C₂	1	2	yes	maximal, complemented
10	C₇₉×#2433	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#2428	C₂	1	2	yes	maximal, complemented
12	C₇₉×#2408	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₉×#2366	C₂	1	2	yes	maximal, complemented
14	C₇₉×#2363	C₂	1	2	yes	maximal, complemented
15	C₇₉×#2345	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#123×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#120×C₇₉	C₂	1	2	yes	maximal, complemented
18	C₂³×D₄×C₇₉	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₇₉	C₂²	1	2	yes	—
20	#553×C₇₉	—	2	8	no	—
21	C₂×#127×C₇₉	C₂²	1	2	yes	—
22	C₂×#126×C₇₉	C₂²	1	2	yes	complemented
23	C₂×#125×C₇₉	C₂²	1	1	yes	characteristic, complemented
24	C₂×#123×C₇₉	C₂²	1	1	yes	characteristic
25	C₂×#123×C₇₉	C₂²	1	2	yes	—
26	C₂×#123×C₇₉	C₂²	1	2	yes	complemented
27	C₂×#121×C₇₉	C₂²	1	2	yes	—
28	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
29	C₂×#121×C₇₉	C₂²	1	2	yes	—
30	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic, complemented
31	C₂×#121×C₇₉	C₂²	1	4	yes	complemented
32	C₂×#120×C₇₉	C₂²	1	2	yes	—
33	C₂×#120×C₇₉	C₂²	1	2	yes	—
34	C₂×#120×C₇₉	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₇₉	—	2	8	no	—
36	C₂×C₄×D₄×C₇₉	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₇₉	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₇₉	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₇₉	C₂²	1	4	yes	—
41	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₄×D₄×C₇₉	C₂²	1	4	yes	complemented
43	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic, complemented
44	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
45	C₂²×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	—
46	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
47	#399×C₇₉	C₂²	1	4	yes	complemented
48	#396×C₇₉	C₂²	1	4	yes	complemented
49	#394×C₇₉	C₂²	1	2	yes	—
50	#394×C₇₉	C₂²	1	4	yes	complemented
51	#392×C₇₉	C₂²	1	2	yes	—
52	#392×C₇₉	C₂²	1	4	yes	—
53	#392×C₇₉	C₂²	1	4	yes	complemented
54	#390×C₇₉	C₂²	1	2	yes	—
55	#390×C₇₉	C₂²	1	2	yes	—
56	#390×C₇₉	C₂²	1	4	yes	complemented
57	#390×C₇₉	C₂²	1	4	yes	complemented
58	#390×C₇₉	C₂²	1	2	yes	complemented
59	#389×C₇₉	C₂²	1	2	yes	complemented
60	#389×C₇₉	C₂²	1	2	yes	complemented
61	#388×C₇₉	C₂²	1	4	yes	complemented
62	#388×C₇₉	C₂²	1	2	yes	complemented
63	#388×C₇₉	C₂²	1	4	yes	complemented
64	#387×C₇₉	C₂²	1	2	yes	complemented
65	#387×C₇₉	C₂²	1	4	yes	complemented
66	#386×C₇₉	C₂²	1	2	yes	—
67	#386×C₇₉	C₂²	1	1	yes	characteristic
68	#386×C₇₉	C₂²	1	4	yes	complemented
69	#386×C₇₉	C₂²	1	4	yes	complemented
70	#386×C₇₉	C₂²	1	4	yes	complemented
71	#386×C₇₉	C₂²	1	4	yes	complemented
72	#385×C₇₉	C₂²	1	1	yes	characteristic
73	#385×C₇₉	C₂²	1	4	yes	complemented
74	#381×C₇₉	C₂²	1	1	yes	characteristic
75	#380×C₇₉	C₂²	1	2	yes	—
76	#380×C₇₉	C₂²	1	1	yes	characteristic
77	#380×C₇₉	C₂²	1	4	yes	complemented
78	#379×C₇₉	C₂²	1	2	yes	—
79	C₄×C₄⋊C₄×C₇₉	C₂²	1	2	yes	complemented
80	C₄×C₄⋊C₄×C₇₉	C₂²	1	2	yes	complemented
81	C₄×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
83	C₄×C₂²⋊C₄×C₇₉	C₂²	1	4	yes	complemented
84	C₄×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	complemented
85	C₂⁵×C₇₉	C₂³	1	2	yes	—
86	C₂²×D₄×C₇₉	—	2	8	no	—
87	C₂²×D₄×C₇₉	—	2	4	no	—
88	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
89	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
90	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₇₉	C₂³	1	4	yes	—
93	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
94	C₂²×D₄×C₇₉	C₂³	1	4	yes	—
95	C₂²×D₄×C₇₉	C₂³	1	4	yes	—
96	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
97	C₂³×C₄×C₇₉	—	2	8	no	—
98	C₂³×C₄×C₇₉	—	4	8	no	—
99	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₇₉	C₂³	1	4	yes	—
103	C₂³×C₄×C₇₉	C₂³	1	4	yes	—
104	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
106	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
107	#127×C₇₉	—	2	8	no	—
108	#126×C₇₉	—	2	8	no	—
109	#125×C₇₉	—	2	4	no	—
110	#123×C₇₉	—	2	8	no	—
111	#123×C₇₉	—	2	4	no	—
112	#123×C₇₉	—	4	4	no	—
113	#121×C₇₉	—	2	8	no	—
114	#121×C₇₉	—	2	8	no	—
115	#121×C₇₉	—	2	4	no	—
116	#121×C₇₉	—	2	4	no	—
117	#121×C₇₉	—	4	8	no	—
118	#120×C₇₉	—	2	8	no	—
119	#120×C₇₉	—	4	4	no	—
120	#120×C₇₉	—	4	4	no	—
121	C₄×D₄×C₇₉	—	2	8	no	—
122	C₄×D₄×C₇₉	—	2	4	no	—
123	C₄×D₄×C₇₉	—	2	8	no	—
124	C₄×D₄×C₇₉	—	2	8	no	—
125	C₄×D₄×C₇₉	—	2	16	no	—
126	C₄×D₄×C₇₉	—	2	4	no	—
127	C₄×D₄×C₇₉	—	4	8	no	—
128	#117×C₇₉	—	2	4	no	—
129	C₂×C₄⋊C₄×C₇₉	D₄	1	8	yes	complemented
130	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
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	4	yes	—
138	C₂×C₄⋊C₄×C₇₉	C₂³	1	4	yes	—
139	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₇₉	—	2	8	no	—
143	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
154	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	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	4	yes	—
159	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
160	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
161	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
162	C₂×C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₇₉	—	2	4	no	—
164	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
165	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
166	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
167	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
169	C₂×C₄²×C₇₉	C₂³	1	4	yes	—
170	#95×C₇₉	C₂³	1	4	yes	—
171	#95×C₇₉	C₂³	1	2	yes	—
172	#95×C₇₉	C₂³	1	2	yes	—
173	#95×C₇₉	C₂³	1	4	yes	—
174	#95×C₇₉	C₂³	1	2	yes	—
175	#95×C₇₉	C₂³	1	4	yes	—
176	#95×C₇₉	C₂³	1	2	yes	—
177	#95×C₇₉	C₂³	1	2	yes	—
178	#95×C₇₉	C₂³	1	2	yes	—
179	C₂⁴×C₇₉	—	2	4	no	—
180	C₂⁴×C₇₉	—	2	8	no	—
181	C₂⁴×C₇₉	—	2	4	no	—
182	C₂⁴×C₇₉	—	2	4	no	—
183	C₂⁴×C₇₉	—	4	4	no	—
184	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
185	C₂⁴×C₇₉	C₂⁴	1	2	yes	—
186	C₂⁴×C₇₉	C₂⁴	1	4	yes	—
187	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
188	C₂×D₄×C₇₉	—	2	32	no	—
189	C₂×D₄×C₇₉	—	2	8	no	—
190	C₂×D₄×C₇₉	—	2	4	no	—
191	C₂×D₄×C₇₉	—	2	2	no	—
192	C₂×D₄×C₇₉	—	2	4	no	—
193	C₂×D₄×C₇₉	—	2	2	no	—
194	C₂×D₄×C₇₉	—	2	8	no	—
195	C₂×D₄×C₇₉	—	2	2	no	—
196	C₂×D₄×C₇₉	—	2	4	no	—
197	C₂×D₄×C₇₉	—	2	8	no	—
198	C₂×D₄×C₇₉	—	2	8	no	—
199	C₂×D₄×C₇₉	—	2	4	no	—
200	C₂×D₄×C₇₉	—	2	4	no	—
201	C₂×D₄×C₇₉	—	2	2	no	—
202	C₂×D₄×C₇₉	—	2	4	no	—
203	C₂×D₄×C₇₉	—	2	4	no	—
204	C₂×D₄×C₇₉	—	2	8	no	—
205	C₂×D₄×C₇₉	—	2	4	no	—
206	C₂×D₄×C₇₉	—	4	4	no	—
207	C₂×D₄×C₇₉	—	4	4	no	—
208	C₂×D₄×C₇₉	—	4	4	no	—
209	C₂×D₄×C₇₉	—	4	4	no	—
210	C₂×D₄×C₇₉	—	4	4	no	—
211	C₂×D₄×C₇₉	—	4	4	no	—
212	C₂×D₄×C₇₉	#41	1	8	yes	—
213	C₂²×C₄×C₇₉	—	2	2	no	—
214	C₂²×C₄×C₇₉	—	2	4	no	—
215	C₂²×C₄×C₇₉	—	2	4	no	—
216	C₂²×C₄×C₇₉	—	2	2	no	—
217	C₂²×C₄×C₇₉	—	2	2	no	—
218	C₂²×C₄×C₇₉	—	2	2	no	—
219	C₂²×C₄×C₇₉	—	2	2	no	—
220	C₂²×C₄×C₇₉	—	2	8	no	—
221	C₂²×C₄×C₇₉	—	2	8	no	—
222	C₂²×C₄×C₇₉	—	2	4	no	—
223	C₂²×C₄×C₇₉	—	2	8	no	—
224	C₂²×C₄×C₇₉	—	2	8	no	—
225	C₂²×C₄×C₇₉	—	2	4	no	—
226	C₂²×C₄×C₇₉	—	4	4	no	—
227	C₂²×C₄×C₇₉	—	4	4	no	—
228	C₂²×C₄×C₇₉	—	4	4	no	—
229	C₂²×C₄×C₇₉	—	4	4	no	—
230	C₂²×C₄×C₇₉	—	4	32	no	—
231	C₂²×C₄×C₇₉	C₂×D₄	1	4	yes	—
232	C₂²×C₄×C₇₉	C₂×D₄	1	8	yes	—
233	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
236	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
239	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
246	C₄⋊C₄×C₇₉	—	2	2	no	—
247	C₄⋊C₄×C₇₉	—	2	4	no	—
248	C₄⋊C₄×C₇₉	—	2	2	no	—
249	C₄⋊C₄×C₇₉	—	2	4	no	—
250	C₄⋊C₄×C₇₉	—	2	4	no	—
251	C₄⋊C₄×C₇₉	—	2	4	no	—
252	C₄⋊C₄×C₇₉	—	2	4	no	—
253	C₄⋊C₄×C₇₉	—	4	4	no	—
254	C₄⋊C₄×C₇₉	—	4	4	no	—
255	C₄⋊C₄×C₇₉	C₂×D₄	1	4	yes	—
256	C₄⋊C₄×C₇₉	C₂×D₄	1	4	yes	—
257	C₄⋊C₄×C₇₉	C₂×D₄	1	8	yes	—
258	C₂²⋊C₄×C₇₉	—	2	2	no	—
259	C₂²⋊C₄×C₇₉	—	2	8	no	—
260	C₂²⋊C₄×C₇₉	—	2	2	no	—
261	C₂²⋊C₄×C₇₉	—	2	4	no	—
262	C₂²⋊C₄×C₇₉	—	2	8	no	—
263	C₂²⋊C₄×C₇₉	—	2	8	no	—
264	C₂²⋊C₄×C₇₉	—	2	4	no	—
265	C₂²⋊C₄×C₇₉	—	2	4	no	—
266	C₂²⋊C₄×C₇₉	—	2	4	no	—
267	C₂²⋊C₄×C₇₉	—	2	2	no	—
268	C₂²⋊C₄×C₇₉	—	2	4	no	—
269	C₂²⋊C₄×C₇₉	—	2	8	no	—
270	C₂²⋊C₄×C₇₉	—	2	4	no	—
271	C₂²⋊C₄×C₇₉	—	2	8	no	—
272	C₂²⋊C₄×C₇₉	—	2	4	no	—
273	C₂²⋊C₄×C₇₉	—	4	4	no	—
274	C₂²⋊C₄×C₇₉	—	4	4	no	—
275	C₂²⋊C₄×C₇₉	—	4	4	no	—
276	C₂²⋊C₄×C₇₉	—	4	4	no	—
277	C₂²⋊C₄×C₇₉	#41	1	4	yes	—
278	C₄²×C₇₉	—	2	4	no	—
279	C₄²×C₇₉	—	2	4	no	—
280	C₄²×C₇₉	—	2	4	no	—
281	C₄²×C₇₉	—	2	2	no	—
282	C₄²×C₇₉	—	2	4	no	—
283	C₄²×C₇₉	—	4	4	no	—
284	C₂³×C₇₉	—	2	2	no	—
285	C₂³×C₇₉	—	2	2	no	—
286	C₂³×C₇₉	—	2	16	no	—
287	C₂³×C₇₉	—	2	4	no	—
288	C₂³×C₇₉	—	2	4	no	—
289	C₂³×C₇₉	—	2	4	no	—
290	C₂³×C₇₉	—	2	4	no	—
291	C₂³×C₇₉	—	2	4	no	—
292	C₂³×C₇₉	—	2	4	no	—
293	C₂³×C₇₉	—	2	1	no	—
294	C₂³×C₇₉	—	2	2	no	—
295	C₂³×C₇₉	—	2	1	no	—
296	C₂³×C₇₉	—	2	2	no	—
297	C₂³×C₇₉	—	2	4	no	—
298	C₂³×C₇₉	—	2	2	no	—
299	C₂³×C₇₉	—	2	4	no	—
300	C₂³×C₇₉	—	2	2	no	—
301	C₂³×C₇₉	—	2	2	no	—
302	C₂³×C₇₉	—	2	1	no	—
303	C₂³×C₇₉	—	4	16	no	—
304	C₂³×C₇₉	—	4	16	no	—
305	C₂³×C₇₉	—	4	8	no	—
306	C₂³×C₇₉	—	4	8	no	—
307	C₂³×C₇₉	C₂²×D₄	1	2	yes	—
308	C₂³×C₇₉	C₂×#41	1	8	yes	—
309	C₂³×C₇₉	C₂×#41	1	2	yes	—
310	C₂³×C₇₉	H(5,𝔽₂)	1	2	yes	—
311	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
312	D₄×C₇₉	—	2	16	no	—
313	D₄×C₇₉	—	2	16	no	—
314	D₄×C₇₉	—	4	16	no	—
315	D₄×C₇₉	—	4	8	no	—
316	D₄×C₇₉	—	4	4	no	—
317	D₄×C₇₉	—	4	4	no	—
318	D₄×C₇₉	—	8	4	no	—
319	D₄×C₇₉	—	8	8	no	—
320	D₄×C₇₉	—	8	8	no	—
321	C₂×C₄×C₇₉	—	2	8	no	—
322	C₂×C₄×C₇₉	—	2	2	no	—
323	C₂×C₄×C₇₉	—	2	2	no	—
324	C₂×C₄×C₇₉	—	2	2	no	—
325	C₂×C₄×C₇₉	—	2	2	no	—
326	C₂×C₄×C₇₉	—	2	4	no	—
327	C₂×C₄×C₇₉	—	2	4	no	—
328	C₂×C₄×C₇₉	—	2	2	no	—
329	C₂×C₄×C₇₉	—	2	8	no	—
330	C₂×C₄×C₇₉	—	2	2	no	—
331	C₂×C₄×C₇₉	—	2	1	no	—
332	C₂×C₄×C₇₉	—	2	2	no	—
333	C₂×C₄×C₇₉	—	2	1	no	—
334	C₂×C₄×C₇₉	—	2	1	no	—
335	C₂×C₄×C₇₉	—	2	2	no	—
336	C₂×C₄×C₇₉	—	2	2	no	—
337	C₂×C₄×C₇₉	—	2	2	no	—
338	C₂×C₄×C₇₉	—	2	2	no	—
339	C₂×C₄×C₇₉	—	2	4	no	—
340	C₂×C₄×C₇₉	—	2	1	no	—
341	C₂×C₄×C₇₉	—	2	4	no	—
342	C₂×C₄×C₇₉	—	2	4	no	—
343	C₂×C₄×C₇₉	—	2	2	no	—
344	C₂×C₄×C₇₉	—	2	2	no	—
345	C₂×C₄×C₇₉	—	2	1	no	—
346	C₂×C₄×C₇₉	—	2	2	no	—
347	C₂×C₄×C₇₉	—	2	2	no	—
348	C₂×C₄×C₇₉	—	2	2	no	—
349	C₂×C₄×C₇₉	—	4	8	no	—
350	C₂×C₄×C₇₉	—	4	16	no	—
351	C₂×C₄×C₇₉	—	4	16	no	—
352	C₂×C₄×C₇₉	—	4	4	no	—
353	C₂×C₄×C₇₉	—	4	4	no	—
354	C₂×C₄×C₇₉	—	8	4	no	—
355	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
356	C₂×C₄×C₇₉	C₂²×D₄	1	4	yes	—
357	C₂×C₄×C₇₉	C₂²×D₄	1	4	yes	—
358	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
359	C₂×C₄×C₇₉	C₂×#41	1	4	yes	—
360	C₂×C₄×C₇₉	C₂×#41	1	4	yes	—
361	C₂×C₄×C₇₉	H(5,𝔽₂)	1	4	yes	—
362	C₂²×C₇₉	—	2	2	no	—
363	C₂²×C₇₉	—	2	4	no	—
364	C₂²×C₇₉	—	2	2	no	—
365	C₂²×C₇₉	—	2	4	no	—
366	C₂²×C₇₉	—	2	8	no	—
367	C₂²×C₇₉	—	2	8	no	—
368	C₂²×C₇₉	—	2	8	no	—
369	C₂²×C₇₉	—	4	32	no	—
370	C₂²×C₇₉	—	4	4	no	—
371	C₂²×C₇₉	—	4	4	no	—
372	C₂²×C₇₉	—	4	4	no	—
373	C₂²×C₇₉	—	4	4	no	—
374	C₂²×C₇₉	—	4	1	no	—
375	C₂²×C₇₉	—	4	2	no	—
376	C₂²×C₇₉	—	4	1	no	—
377	C₂²×C₇₉	—	4	2	no	—
378	C₂²×C₇₉	—	4	4	no	—
379	C₂²×C₇₉	—	4	2	no	—
380	C₂²×C₇₉	—	4	2	no	—
381	C₂²×C₇₉	—	4	1	no	—
382	C₂²×C₇₉	—	4	2	no	—
383	C₂²×C₇₉	—	4	4	no	—
384	C₂²×C₇₉	#550	1	4	yes	—
385	C₂²×C₇₉	C₂³×D₄	1	1	yes	characteristic
386	C₂²×C₇₉	C₂²×#41	1	2	yes	—
387	C₂²×C₇₉	C₂²×#41	1	1	yes	characteristic
388	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
389	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	2	yes	—
390	C₄×C₇₉	—	2	2	no	—
391	C₄×C₇₉	—	2	4	no	—
392	C₄×C₇₉	—	2	4	no	—
393	C₄×C₇₉	—	2	4	no	—
394	C₄×C₇₉	—	2	4	no	—
395	C₄×C₇₉	—	4	1	no	—
396	C₄×C₇₉	—	4	2	no	—
397	C₄×C₇₉	—	4	2	no	—
398	C₄×C₇₉	—	4	1	no	—
399	C₄×C₇₉	—	4	1	no	—
400	C₄×C₇₉	—	4	4	no	—
401	C₄×C₇₉	—	4	2	no	—
402	C₄×C₇₉	#525	1	4	yes	—
403	#36529	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
404	C₂×C₇₉	—	2	4	no	—
405	C₂×C₇₉	—	4	8	no	—
406	C₂×C₇₉	—	8	1	no	—
407	C₂×C₇₉	—	8	2	no	—
408	C₂×C₇₉	C₂×#525	1	1	yes	characteristic
409	C₂×C₇₉	C₂×#550	1	1	yes	characteristic
410	C₂×C₇₉	#3481	1	2	yes	—
411	C₂×C₇₉	#3484	1	1	yes	characteristic
412	C₂×C₇₉	#3519	1	2	yes	—
413	C₂×#553	C₂×C₇₉	1	1	yes	characteristic, complemented
414	C₂²×C₄×D₄	C₂×C₇₉	1	1	yes	characteristic, complemented
415	#2854	C₂×C₇₉	1	1	yes	characteristic, complemented
416	#2847	C₂×C₇₉	1	2	yes	complemented
417	#2539	C₂×C₇₉	1	2	yes	complemented
418	#2534	C₂×C₇₉	1	2	yes	complemented
419	#2467	C₂×C₇₉	1	4	yes	complemented
420	#2456	C₂×C₇₉	1	4	yes	complemented
421	#2454	C₂×C₇₉	1	2	yes	complemented
422	#2433	C₂×C₇₉	1	1	yes	characteristic, complemented
423	#2428	C₂×C₇₉	1	2	yes	complemented
424	#2408	C₂×C₇₉	1	1	yes	characteristic, complemented
425	#2366	C₂×C₇₉	1	2	yes	complemented
426	#2363	C₂×C₇₉	1	2	yes	complemented
427	#2345	C₂×C₇₉	1	1	yes	characteristic, complemented
428	C₄×#123	C₂×C₇₉	1	1	yes	characteristic, complemented
429	C₄×#120	C₂×C₇₉	1	2	yes	complemented
430	C₇₉	#36529	1	1	yes	characteristic, direct product factor, Sylow
431	C₂³×D₄	C₂²×C₇₉	1	1	yes	characteristic
432	C₂⁴×C₄	C₂²×C₇₉	1	2	yes	—
433	#553	—	2	8	no	—
434	C₂×#127	C₂²×C₇₉	1	2	yes	—
435	C₂×#126	C₂²×C₇₉	1	2	yes	complemented
436	C₂×#125	C₂²×C₇₉	1	1	yes	characteristic, complemented
437	C₂×#123	C₂²×C₇₉	1	1	yes	characteristic
438	C₂×#123	C₂²×C₇₉	1	2	yes	—
439	C₂×#123	C₂²×C₇₉	1	2	yes	complemented
440	C₂×#121	C₂²×C₇₉	1	2	yes	—
441	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
442	C₂×#121	C₂²×C₇₉	1	2	yes	—
443	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic, complemented
444	C₂×#121	C₂²×C₇₉	1	4	yes	complemented
445	C₂×#120	C₂²×C₇₉	1	2	yes	—
446	C₂×#120	C₂²×C₇₉	1	2	yes	—
447	C₂×#120	C₂²×C₇₉	1	2	yes	—
448	C₂×C₄×D₄	—	2	8	no	—
449	C₂×C₄×D₄	C₂²×C₇₉	1	2	yes	—
450	C₂×C₄×D₄	C₂²×C₇₉	1	2	yes	—
451	C₂×C₄×D₄	C₂²×C₇₉	1	4	yes	—
452	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
453	C₂×C₄×D₄	C₂²×C₇₉	1	2	yes	—
454	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic, complemented
455	C₂×C₄×D₄	C₂²×C₇₉	1	4	yes	complemented
456	C₂×#117	C₂²×C₇₉	1	1	yes	characteristic, complemented
457	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
458	C₂²×C₂²⋊C₄	C₂²×C₇₉	1	2	yes	—
459	C₂²×C₄²	C₂²×C₇₉	1	1	yes	characteristic
460	#399	C₂²×C₇₉	1	4	yes	complemented
461	#396	C₂²×C₇₉	1	4	yes	complemented
462	#394	C₂²×C₇₉	1	2	yes	—
463	#394	C₂²×C₇₉	1	4	yes	complemented
464	#392	C₂²×C₇₉	1	2	yes	—
465	#392	C₂²×C₇₉	1	4	yes	—
466	#392	C₂²×C₇₉	1	4	yes	complemented
467	#390	C₂²×C₇₉	1	2	yes	—
468	#390	C₂²×C₇₉	1	2	yes	—
469	#390	C₂²×C₇₉	1	2	yes	complemented
470	#390	C₂²×C₇₉	1	4	yes	complemented
471	#390	C₂²×C₇₉	1	4	yes	complemented
472	#389	C₂²×C₇₉	1	2	yes	complemented
473	#389	C₂²×C₇₉	1	2	yes	complemented
474	#388	C₂²×C₇₉	1	4	yes	complemented
475	#388	C₂²×C₇₉	1	4	yes	complemented
476	#388	C₂²×C₇₉	1	2	yes	complemented
477	#387	C₂²×C₇₉	1	4	yes	complemented
478	#387	C₂²×C₇₉	1	2	yes	complemented
479	#386	C₂²×C₇₉	1	1	yes	characteristic
480	#386	C₂²×C₇₉	1	2	yes	—
481	#386	C₂²×C₇₉	1	4	yes	complemented
482	#386	C₂²×C₇₉	1	4	yes	complemented
483	#386	C₂²×C₇₉	1	4	yes	complemented
484	#386	C₂²×C₇₉	1	4	yes	complemented
485	#385	C₂²×C₇₉	1	1	yes	characteristic
486	#385	C₂²×C₇₉	1	4	yes	complemented
487	#381	C₂²×C₇₉	1	1	yes	characteristic
488	#380	C₂²×C₇₉	1	2	yes	—
489	#380	C₂²×C₇₉	1	1	yes	characteristic
490	#380	C₂²×C₇₉	1	4	yes	complemented
491	#379	C₂²×C₇₉	1	2	yes	—
492	C₄×C₄⋊C₄	C₂²×C₇₉	1	2	yes	complemented
493	C₄×C₄⋊C₄	C₂²×C₇₉	1	2	yes	complemented
494	C₄×C₂²⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
495	C₄×C₂²⋊C₄	C₂²×C₇₉	1	2	yes	—
496	C₄×C₂²⋊C₄	C₂²×C₇₉	1	2	yes	complemented
497	C₄×C₂²⋊C₄	C₂²×C₇₉	1	4	yes	complemented
498	C₂⁵	C₂³×C₇₉	1	2	yes	—
499	C₂²×D₄	—	2	8	no	—
500	C₂²×D₄	—	2	4	no	—
501	C₂²×D₄	C₂³×C₇₉	1	2	yes	—
502	C₂²×D₄	C₂³×C₇₉	1	2	yes	—
503	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
504	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
505	C₂²×D₄	C₂³×C₇₉	1	4	yes	—
506	C₂²×D₄	C₂³×C₇₉	1	2	yes	—
507	C₂²×D₄	C₂³×C₇₉	1	4	yes	—
508	C₂²×D₄	C₂³×C₇₉	1	4	yes	—
509	C₂²×D₄	C₂³×C₇₉	1	2	yes	—
510	C₂³×C₄	—	2	8	no	—
511	C₂³×C₄	—	4	8	no	—
512	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
513	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
514	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
515	C₂³×C₄	C₂³×C₇₉	1	4	yes	—
516	C₂³×C₄	C₂³×C₇₉	1	4	yes	—
517	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
518	C₂³×C₄	C₂³×C₇₉	1	2	yes	—
519	C₂³×C₄	C₂³×C₇₉	1	2	yes	—
520	#127	—	2	8	no	—
521	#126	—	2	8	no	—
522	#125	—	2	4	no	—
523	#123	—	2	8	no	—
524	#123	—	2	4	no	—
525	#123	—	4	4	no	—
526	#121	—	2	8	no	—
527	#121	—	2	8	no	—
528	#121	—	2	4	no	—
529	#121	—	2	4	no	—
530	#121	—	4	8	no	—
531	#120	—	2	8	no	—
532	#120	—	4	4	no	—
533	#120	—	4	4	no	—
534	C₄×D₄	—	2	8	no	—
535	C₄×D₄	—	2	4	no	—
536	C₄×D₄	—	2	8	no	—
537	C₄×D₄	—	2	8	no	—
538	C₄×D₄	—	2	16	no	—
539	C₄×D₄	—	2	4	no	—
540	C₄×D₄	—	4	8	no	—
541	#117	—	2	4	no	—
542	C₂×C₄⋊C₄	D₄×C₇₉	1	8	yes	complemented
543	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
544	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
546	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
548	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₇₉	1	4	yes	—
551	C₂×C₄⋊C₄	C₂³×C₇₉	1	4	yes	—
552	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
553	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
554	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
555	C₂×C₂²⋊C₄	—	2	8	no	—
556	C₂×C₂²⋊C₄	C₂³×C₇₉	1	4	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₇₉	1	4	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
560	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
562	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₇₉	1	4	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
565	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₇₉	1	4	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₇₉	1	4	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₇₉	1	4	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₇₉	1	4	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₇₉	1	4	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₇₉	1	4	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
576	C₂×C₄²	—	2	4	no	—
577	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
578	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
579	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
580	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
581	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
582	C₂×C₄²	C₂³×C₇₉	1	4	yes	—
583	#95	C₂³×C₇₉	1	4	yes	—
584	#95	C₂³×C₇₉	1	2	yes	—
585	#95	C₂³×C₇₉	1	2	yes	—
586	#95	C₂³×C₇₉	1	4	yes	—
587	#95	C₂³×C₇₉	1	2	yes	—
588	#95	C₂³×C₇₉	1	4	yes	—
589	#95	C₂³×C₇₉	1	2	yes	—
590	#95	C₂³×C₇₉	1	2	yes	—
591	#95	C₂³×C₇₉	1	2	yes	—
592	C₂⁴	—	2	4	no	—
593	C₂⁴	—	2	8	no	—
594	C₂⁴	—	2	4	no	—
595	C₂⁴	—	2	4	no	—
596	C₂⁴	—	4	4	no	—
597	C₂⁴	C₂⁴×C₇₉	1	1	yes	characteristic
598	C₂⁴	C₂⁴×C₇₉	1	2	yes	—
599	C₂⁴	C₂⁴×C₇₉	1	4	yes	—
600	C₂⁴	C₂⁴×C₇₉	1	1	yes	characteristic
601	C₂×D₄	—	2	32	no	—
602	C₂×D₄	—	2	8	no	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	2	no	—
605	C₂×D₄	—	2	4	no	—
606	C₂×D₄	—	2	2	no	—
607	C₂×D₄	—	2	8	no	—
608	C₂×D₄	—	2	2	no	—
609	C₂×D₄	—	2	4	no	—
610	C₂×D₄	—	2	8	no	—
611	C₂×D₄	—	2	8	no	—
612	C₂×D₄	—	2	4	no	—
613	C₂×D₄	—	2	4	no	—
614	C₂×D₄	—	2	2	no	—
615	C₂×D₄	—	2	4	no	—
616	C₂×D₄	—	2	4	no	—
617	C₂×D₄	—	2	8	no	—
618	C₂×D₄	—	2	4	no	—
619	C₂×D₄	—	4	4	no	—
620	C₂×D₄	—	4	4	no	—
621	C₂×D₄	—	4	4	no	—
622	C₂×D₄	—	4	4	no	—
623	C₂×D₄	—	4	4	no	—
624	C₂×D₄	—	4	4	no	—
625	C₂×D₄	#41×C₇₉	1	8	yes	—
626	C₂²×C₄	—	2	2	no	—
627	C₂²×C₄	—	2	4	no	—
628	C₂²×C₄	—	2	4	no	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	2	2	no	—
631	C₂²×C₄	—	2	2	no	—
632	C₂²×C₄	—	2	2	no	—
633	C₂²×C₄	—	2	8	no	—
634	C₂²×C₄	—	2	8	no	—
635	C₂²×C₄	—	2	4	no	—
636	C₂²×C₄	—	2	8	no	—
637	C₂²×C₄	—	2	8	no	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	4	4	no	—
640	C₂²×C₄	—	4	4	no	—
641	C₂²×C₄	—	4	4	no	—
642	C₂²×C₄	—	4	4	no	—
643	C₂²×C₄	—	4	32	no	—
644	C₂²×C₄	C₂×D₄×C₇₉	1	4	yes	—
645	C₂²×C₄	C₂×D₄×C₇₉	1	8	yes	—
646	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
647	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
648	C₂²×C₄	C₂⁴×C₇₉	1	4	yes	—
649	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
650	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
651	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
652	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
653	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
654	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
655	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
656	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
657	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
658	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	—	2	2	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	4	no	—
666	C₄⋊C₄	—	4	4	no	—
667	C₄⋊C₄	—	4	4	no	—
668	C₄⋊C₄	C₂×D₄×C₇₉	1	4	yes	—
669	C₄⋊C₄	C₂×D₄×C₇₉	1	4	yes	—
670	C₄⋊C₄	C₂×D₄×C₇₉	1	8	yes	—
671	C₂²⋊C₄	—	2	2	no	—
672	C₂²⋊C₄	—	2	8	no	—
673	C₂²⋊C₄	—	2	2	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	8	no	—
676	C₂²⋊C₄	—	2	8	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	2	no	—
681	C₂²⋊C₄	—	2	4	no	—
682	C₂²⋊C₄	—	2	8	no	—
683	C₂²⋊C₄	—	2	4	no	—
684	C₂²⋊C₄	—	2	8	no	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	—	4	4	no	—
687	C₂²⋊C₄	—	4	4	no	—
688	C₂²⋊C₄	—	4	4	no	—
689	C₂²⋊C₄	—	4	4	no	—
690	C₂²⋊C₄	#41×C₇₉	1	4	yes	—
691	C₄²	—	2	4	no	—
692	C₄²	—	2	4	no	—
693	C₄²	—	2	4	no	—
694	C₄²	—	2	2	no	—
695	C₄²	—	2	4	no	—
696	C₄²	—	4	4	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	16	no	—
700	C₂³	—	2	4	no	—
701	C₂³	—	2	4	no	—
702	C₂³	—	2	4	no	—
703	C₂³	—	2	4	no	—
704	C₂³	—	2	4	no	—
705	C₂³	—	2	4	no	—
706	C₂³	—	2	1	no	—
707	C₂³	—	2	2	no	—
708	C₂³	—	2	1	no	—
709	C₂³	—	2	2	no	—
710	C₂³	—	2	4	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	2	4	no	—
713	C₂³	—	2	2	no	—
714	C₂³	—	2	2	no	—
715	C₂³	—	2	1	no	—
716	C₂³	—	4	16	no	—
717	C₂³	—	4	16	no	—
718	C₂³	—	4	8	no	—
719	C₂³	—	4	8	no	—
720	C₂³	C₂²×D₄×C₇₉	1	2	yes	—
721	C₂³	C₂×#41×C₇₉	1	8	yes	—
722	C₂³	C₂×#41×C₇₉	1	2	yes	—
723	C₂³	H(5,𝔽₂)×C₇₉	1	2	yes	—
724	C₂³	C₂⁵×C₇₉	1	1	yes	characteristic
725	D₄	—	2	16	no	—
726	D₄	—	2	16	no	—
727	D₄	—	4	16	no	—
728	D₄	—	4	8	no	—
729	D₄	—	4	4	no	—
730	D₄	—	4	4	no	—
731	D₄	—	8	4	no	—
732	D₄	—	8	8	no	—
733	D₄	—	8	8	no	—
734	C₂×C₄	—	2	8	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	4	no	—
740	C₂×C₄	—	2	4	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	8	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	4	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	4	no	—
755	C₂×C₄	—	2	4	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	4	8	no	—
763	C₂×C₄	—	4	16	no	—
764	C₂×C₄	—	4	16	no	—
765	C₂×C₄	—	4	4	no	—
766	C₂×C₄	—	4	4	no	—
767	C₂×C₄	—	8	4	no	—
768	C₂×C₄	C₂²×D₄×C₇₉	1	2	yes	—
769	C₂×C₄	C₂²×D₄×C₇₉	1	4	yes	—
770	C₂×C₄	C₂²×D₄×C₇₉	1	4	yes	—
771	C₂×C₄	C₂²×D₄×C₇₉	1	2	yes	—
772	C₂×C₄	C₂×#41×C₇₉	1	4	yes	—
773	C₂×C₄	C₂×#41×C₇₉	1	4	yes	—
774	C₂×C₄	H(5,𝔽₂)×C₇₉	1	4	yes	—
775	C₂²	—	2	2	no	—
776	C₂²	—	2	4	no	—
777	C₂²	—	2	2	no	—
778	C₂²	—	2	4	no	—
779	C₂²	—	2	8	no	—
780	C₂²	—	2	8	no	—
781	C₂²	—	2	8	no	—
782	C₂²	—	4	32	no	—
783	C₂²	—	4	4	no	—
784	C₂²	—	4	4	no	—
785	C₂²	—	4	4	no	—
786	C₂²	—	4	4	no	—
787	C₂²	—	4	1	no	—
788	C₂²	—	4	2	no	—
789	C₂²	—	4	1	no	—
790	C₂²	—	4	2	no	—
791	C₂²	—	4	4	no	—
792	C₂²	—	4	2	no	—
793	C₂²	—	4	2	no	—
794	C₂²	—	4	1	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	4	4	no	—
797	C₂²	#550×C₇₉	1	4	yes	—
798	C₂²	C₂³×D₄×C₇₉	1	1	yes	characteristic
799	C₂²	C₂²×#41×C₇₉	1	2	yes	—
800	C₂²	C₂²×#41×C₇₉	1	1	yes	characteristic
801	C₂²	C₂×H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
802	C₂²	C₂×H(5,𝔽₂)×C₇₉	1	2	yes	—
803	C₄	—	2	2	no	—
804	C₄	—	2	4	no	—
805	C₄	—	2	4	no	—
806	C₄	—	2	4	no	—
807	C₄	—	2	4	no	—
808	C₄	—	4	1	no	—
809	C₄	—	4	2	no	—
810	C₄	—	4	2	no	—
811	C₄	—	4	1	no	—
812	C₄	—	4	1	no	—
813	C₄	—	4	2	no	—
814	C₄	—	4	4	no	—
815	C₄	#525×C₇₉	1	4	yes	—
816	C₂	—	2	4	no	—
817	C₂	—	4	8	no	—
818	C₂	—	8	1	no	—
819	C₂	—	8	2	no	—
820	C₂	C₂×#525×C₇₉	1	1	yes	characteristic
821	C₂	C₂×#550×C₇₉	1	1	yes	characteristic
822	C₂	C₇₉×#3481	1	2	yes	—
823	C₂	C₇₉×#3484	1	1	yes	characteristic
824	C₂	C₇₉×#3519	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₉
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. C₂×#553×C₇₉	C₂	semidirect
2. C₂²×C₄×D₄×C₇₉	C₂	semidirect
3. C₇₉×#2854	C₂	semidirect
4. C₇₉×#2847	C₂	semidirect
5. C₇₉×#2539	C₂	semidirect
6. C₇₉×#2534	C₂	semidirect
7. C₇₉×#2467	C₂	semidirect
8. C₇₉×#2456	C₂	semidirect
9. C₇₉×#2454	C₂	semidirect
10. C₇₉×#2433	C₂	semidirect
11. C₇₉×#2428	C₂	semidirect
12. C₇₉×#2408	C₂	semidirect
13. C₇₉×#2366	C₂	semidirect
14. C₇₉×#2363	C₂	semidirect
15. C₇₉×#2345	C₂	semidirect
16. C₄×#123×C₇₉	C₂	semidirect
17. C₄×#120×C₇₉	C₂	semidirect
22. C₂×#126×C₇₉	C₂²	semidirect
23. C₂×#125×C₇₉	C₂²	semidirect
26. C₂×#123×C₇₉	C₂²	semidirect
30. C₂×#121×C₇₉	C₂²	semidirect
31. C₂×#121×C₇₉	C₂²	semidirect
41. C₂×C₄×D₄×C₇₉	C₂²	semidirect
42. C₂×C₄×D₄×C₇₉	C₂²	semidirect
43. C₂×#117×C₇₉	C₂²	semidirect
47. #399×C₇₉	C₂²	semidirect
48. #396×C₇₉	C₂²	semidirect
50. #394×C₇₉	C₂²	semidirect
53. #392×C₇₉	C₂²	semidirect
56. #390×C₇₉	C₂²	semidirect
57. #390×C₇₉	C₂²	semidirect
58. #390×C₇₉	C₂²	semidirect
59. #389×C₇₉	C₂²	semidirect
60. #389×C₇₉	C₂²	semidirect
61. #388×C₇₉	C₂²	semidirect
62. #388×C₇₉	C₂²	semidirect
63. #388×C₇₉	C₂²	semidirect
64. #387×C₇₉	C₂²	semidirect
65. #387×C₇₉	C₂²	semidirect
68. #386×C₇₉	C₂²	semidirect
69. #386×C₇₉	C₂²	semidirect
70. #386×C₇₉	C₂²	semidirect
71. #386×C₇₉	C₂²	semidirect
73. #385×C₇₉	C₂²	semidirect
77. #380×C₇₉	C₂²	semidirect
79. C₄×C₄⋊C₄×C₇₉	C₂²	semidirect
80. C₄×C₄⋊C₄×C₇₉	C₂²	semidirect
83. C₄×C₂²⋊C₄×C₇₉	C₂²	semidirect
84. C₄×C₂²⋊C₄×C₇₉	C₂²	semidirect
129. C₂×C₄⋊C₄×C₇₉	D₄	semidirect
403. #36529	C₇₉	direct (N × H)
413. C₂×#553	C₂×C₇₉	semidirect
414. C₂²×C₄×D₄	C₂×C₇₉	semidirect
415. #2854	C₂×C₇₉	semidirect
416. #2847	C₂×C₇₉	semidirect
417. #2539	C₂×C₇₉	semidirect
418. #2534	C₂×C₇₉	semidirect
419. #2467	C₂×C₇₉	semidirect
420. #2456	C₂×C₇₉	semidirect
421. #2454	C₂×C₇₉	semidirect
422. #2433	C₂×C₇₉	semidirect
423. #2428	C₂×C₇₉	semidirect
424. #2408	C₂×C₇₉	semidirect
425. #2366	C₂×C₇₉	semidirect
426. #2363	C₂×C₇₉	semidirect
427. #2345	C₂×C₇₉	semidirect
428. C₄×#123	C₂×C₇₉	semidirect
429. C₄×#120	C₂×C₇₉	semidirect
430. C₇₉	#36529	direct (N × H)
435. C₂×#126	C₂²×C₇₉	semidirect
436. C₂×#125	C₂²×C₇₉	semidirect
439. C₂×#123	C₂²×C₇₉	semidirect
443. C₂×#121	C₂²×C₇₉	semidirect
444. C₂×#121	C₂²×C₇₉	semidirect
454. C₂×C₄×D₄	C₂²×C₇₉	semidirect
455. C₂×C₄×D₄	C₂²×C₇₉	semidirect
456. C₂×#117	C₂²×C₇₉	semidirect
460. #399	C₂²×C₇₉	semidirect
461. #396	C₂²×C₇₉	semidirect
463. #394	C₂²×C₇₉	semidirect
466. #392	C₂²×C₇₉	semidirect
469. #390	C₂²×C₇₉	semidirect
470. #390	C₂²×C₇₉	semidirect
471. #390	C₂²×C₇₉	semidirect
472. #389	C₂²×C₇₉	semidirect
473. #389	C₂²×C₇₉	semidirect
474. #388	C₂²×C₇₉	semidirect
475. #388	C₂²×C₇₉	semidirect
476. #388	C₂²×C₇₉	semidirect
477. #387	C₂²×C₇₉	semidirect
478. #387	C₂²×C₇₉	semidirect
481. #386	C₂²×C₇₉	semidirect
482. #386	C₂²×C₇₉	semidirect
483. #386	C₂²×C₇₉	semidirect
484. #386	C₂²×C₇₉	semidirect
486. #385	C₂²×C₇₉	semidirect
490. #380	C₂²×C₇₉	semidirect
492. C₄×C₄⋊C₄	C₂²×C₇₉	semidirect
493. C₄×C₄⋊C₄	C₂²×C₇₉	semidirect
496. C₄×C₂²⋊C₄	C₂²×C₇₉	semidirect
497. C₄×C₂²⋊C₄	C₂²×C₇₉	semidirect
542. C₂×C₄⋊C₄	D₄×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#553×C₇₉	2
C₂²×C₄×D₄×C₇₉	2
C₇₉×#2854	2
C₇₉×#2847	2
C₇₉×#2539	2
C₇₉×#2534	2
C₇₉×#2467	2
C₇₉×#2456	2
C₇₉×#2454	2
C₇₉×#2433	2
C₇₉×#2428	2
C₇₉×#2408	2
C₇₉×#2366	2
C₇₉×#2363	2
C₇₉×#2345	2
C₄×#123×C₇₉	2
C₄×#120×C₇₉	2
#36529	79

Subgroups — C79×#36529 #34148218

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#36529 #34148218