Subgroups — C₇₉×#25560 #34137249

Order 20224.

1178 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#552×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#482×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#468×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#2416	C₂	1	1	yes	maximal, characteristic
5	C₇₉×#2059	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₉×#2035	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#2025	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#2000	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#1880	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#1874	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×#1863	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×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
18	#552×C₇₉	—	2	4	no	—
19	#552×C₇₉	—	2	4	no	—
20	C₂×#126×C₇₉	—	2	1	no	—
21	C₂×#125×C₇₉	—	2	1	no	—
22	C₂×#125×C₇₉	C₂²	1	1	yes	characteristic
23	C₂×#123×C₇₉	—	2	1	no	—
24	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
26	C₂×#121×C₇₉	—	2	1	no	—
27	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
28	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
31	C₂×#117×C₇₉	—	2	1	no	—
32	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
34	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
35	#482×C₇₉	—	2	4	no	—
36	#468×C₇₉	—	2	4	no	—
37	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic
38	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic
39	C₂×#106×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×#103×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×#102×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	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
49	#396×C₇₉	—	2	1	no	—
50	#394×C₇₉	—	2	1	no	—
51	#390×C₇₉	C₂²	1	1	yes	characteristic
52	#389×C₇₉	C₂²	1	1	yes	characteristic
53	#386×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	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₇₉	—	2	1	no	—
65	C₂²×D₄×C₇₉	—	2	1	no	—
66	C₂²×D₄×C₇₉	D₄	1	1	yes	characteristic
67	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₇₉	—	2	1	no	—
69	C₂³×C₄×C₇₉	—	2	1	no	—
70	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
72	C₂×SD₁₆×C₇₉	—	2	2	no	—
73	C₂×SD₁₆×C₇₉	—	2	2	no	—
74	C₂×SD₁₆×C₇₉	—	4	1	no	—
75	C₂×M₁₆×C₇₉	—	2	2	no	—
76	C₂×M₁₆×C₇₉	—	2	2	no	—
77	C₂×M₁₆×C₇₉	—	4	1	no	—
78	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
82	#126×C₇₉	—	2	8	no	—
83	#125×C₇₉	—	2	8	no	—
84	#125×C₇₉	—	2	2	no	—
85	#125×C₇₉	—	2	2	no	—
86	#123×C₇₉	—	2	8	no	—
87	C₂²⋊Q₈×C₇₉	—	2	2	no	—
88	C₂²⋊Q₈×C₇₉	—	2	2	no	—
89	C₂²⋊Q₈×C₇₉	—	2	2	no	—
90	C₂²⋊Q₈×C₇₉	D₄	1	4	yes	complemented
91	#121×C₇₉	—	2	2	no	—
92	#121×C₇₉	—	2	2	no	—
93	#121×C₇₉	—	2	2	no	—
94	#121×C₇₉	—	4	1	no	—
95	#121×C₇₉	—	4	4	no	—
96	C₄×Q₈×C₇₉	—	2	2	no	—
97	C₄×Q₈×C₇₉	—	2	2	no	—
98	C₄×D₄×C₇₉	—	2	2	no	—
99	C₄×D₄×C₇₉	—	2	2	no	—
100	#117×C₇₉	—	2	8	no	—
101	#117×C₇₉	—	2	2	no	—
102	#117×C₇₉	D₄	1	4	yes	complemented
103	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
104	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
105	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
106	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
107	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
108	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
109	C₂×C₄⋊C₄×C₇₉	—	2	2	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	—	4	1	no	—
115	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₇₉	—	2	1	no	—
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	—	2	1	no	—
134	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
135	#107×C₇₉	—	2	2	no	—
136	#107×C₇₉	—	2	2	no	—
137	#106×C₇₉	—	2	2	no	—
138	#103×C₇₉	—	2	2	no	—
139	#103×C₇₉	—	2	2	no	—
140	#103×C₇₉	—	4	1	no	—
141	#102×C₇₉	—	2	2	no	—
142	#102×C₇₉	—	2	2	no	—
143	#102×C₇₉	—	2	2	no	—
144	C₂²⋊C₈×C₇₉	—	2	2	no	—
145	C₂²⋊C₈×C₇₉	—	2	2	no	—
146	C₂²⋊C₈×C₇₉	—	4	1	no	—
147	#95×C₇₉	—	2	1	no	—
148	#95×C₇₉	—	2	1	no	—
149	C₂⁴×C₇₉	—	2	1	no	—
150	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
151	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
152	C₂×Q₈×C₇₉	—	2	1	no	—
153	C₂×Q₈×C₇₉	—	2	1	no	—
154	C₂×Q₈×C₇₉	—	2	1	no	—
155	C₂×Q₈×C₇₉	—	2	1	no	—
156	C₂×Q₈×C₇₉	—	2	1	no	—
157	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
158	C₂×D₄×C₇₉	—	2	2	no	—
159	C₂×D₄×C₇₉	—	2	2	no	—
160	C₂×D₄×C₇₉	—	2	1	no	—
161	C₂×D₄×C₇₉	—	2	1	no	—
162	C₂×D₄×C₇₉	—	2	1	no	—
163	C₂×D₄×C₇₉	—	2	1	no	—
164	C₂×D₄×C₇₉	—	2	1	no	—
165	C₂×D₄×C₇₉	—	2	1	no	—
166	C₂×D₄×C₇₉	—	4	1	no	—
167	C₂×D₄×C₇₉	—	4	2	no	—
168	C₂×D₄×C₇₉	—	4	2	no	—
169	C₂×D₄×C₇₉	—	4	2	no	—
170	C₂×D₄×C₇₉	—	4	2	no	—
171	C₂×D₄×C₇₉	—	4	2	no	—
172	C₂×D₄×C₇₉	—	8	1	no	—
173	C₂²×C₄×C₇₉	—	2	1	no	—
174	C₂²×C₄×C₇₉	—	2	1	no	—
175	C₂²×C₄×C₇₉	—	2	1	no	—
176	C₂²×C₄×C₇₉	—	2	1	no	—
177	C₂²×C₄×C₇₉	—	2	4	no	—
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	1	no	—
183	C₂²×C₄×C₇₉	—	2	1	no	—
184	C₂²×C₄×C₇₉	—	2	1	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	—	4	2	no	—
192	C₂²×C₄×C₇₉	—	4	2	no	—
193	C₂²×C₄×C₇₉	—	4	2	no	—
194	C₂²×C₄×C₇₉	—	4	2	no	—
195	C₂²×C₄×C₇₉	—	8	1	no	—
196	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
201	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
202	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
203	SD₁₆×C₇₉	—	4	4	no	—
204	M₁₆×C₇₉	—	4	4	no	—
205	C₂×C₈×C₇₉	—	2	1	no	—
206	C₂×C₈×C₇₉	—	2	1	no	—
207	C₂×C₈×C₇₉	—	2	1	no	—
208	C₂×C₈×C₇₉	—	2	1	no	—
209	C₂×C₈×C₇₉	—	2	1	no	—
210	C₂×C₈×C₇₉	—	2	1	no	—
211	C₂×C₈×C₇₉	—	2	1	no	—
212	C₂×C₈×C₇₉	—	2	1	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	#41	1	2	yes	—
217	C₄⋊C₄×C₇₉	—	2	4	no	—
218	C₄⋊C₄×C₇₉	—	2	4	no	—
219	C₄⋊C₄×C₇₉	—	2	4	no	—
220	C₄⋊C₄×C₇₉	—	2	4	no	—
221	C₄⋊C₄×C₇₉	—	2	4	no	—
222	C₄⋊C₄×C₇₉	—	2	4	no	—
223	C₄⋊C₄×C₇₉	—	2	2	no	—
224	C₄⋊C₄×C₇₉	—	2	1	no	—
225	C₄⋊C₄×C₇₉	—	2	1	no	—
226	C₄⋊C₄×C₇₉	—	2	1	no	—
227	C₄⋊C₄×C₇₉	—	2	1	no	—
228	C₄⋊C₄×C₇₉	—	2	1	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	—	4	2	no	—
233	C₄⋊C₄×C₇₉	—	4	2	no	—
234	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
235	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
236	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
237	C₄⋊C₄×C₇₉	#41	1	2	yes	—
238	C₂²⋊C₄×C₇₉	—	2	4	no	—
239	C₂²⋊C₄×C₇₉	—	2	4	no	—
240	C₂²⋊C₄×C₇₉	—	2	4	no	—
241	C₂²⋊C₄×C₇₉	—	2	2	no	—
242	C₂²⋊C₄×C₇₉	—	2	2	no	—
243	C₂²⋊C₄×C₇₉	—	4	2	no	—
244	C₂²⋊C₄×C₇₉	—	4	2	no	—
245	C₂²⋊C₄×C₇₉	—	4	2	no	—
246	C₂²⋊C₄×C₇₉	—	4	2	no	—
247	C₂²⋊C₄×C₇₉	—	8	1	no	—
248	C₄²×C₇₉	—	2	4	no	—
249	C₄²×C₇₉	—	2	4	no	—
250	C₄²×C₇₉	—	2	1	no	—
251	C₄²×C₇₉	—	2	1	no	—
252	C₂³×C₇₉	—	2	1	no	—
253	C₂³×C₇₉	—	2	1	no	—
254	C₂³×C₇₉	—	2	1	no	—
255	C₂³×C₇₉	—	2	1	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	—	4	1	no	—
265	C₂³×C₇₉	—	4	1	no	—
266	C₂³×C₇₉	—	4	1	no	—
267	C₂³×C₇₉	—	4	1	no	—
268	C₂³×C₇₉	—	4	1	no	—
269	C₂³×C₇₉	—	4	1	no	—
270	C₂³×C₇₉	—	4	1	no	—
271	C₂³×C₇₉	#120	1	2	yes	—
272	C₂³×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
273	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
274	Q₈×C₇₉	—	2	2	no	—
275	Q₈×C₇₉	—	2	2	no	—
276	Q₈×C₇₉	—	4	1	no	—
277	Q₈×C₇₉	—	4	1	no	—
278	D₄×C₇₉	—	4	4	no	—
279	D₄×C₇₉	—	4	1	no	—
280	D₄×C₇₉	—	4	1	no	—
281	D₄×C₇₉	—	4	1	no	—
282	D₄×C₇₉	—	4	1	no	—
283	D₄×C₇₉	—	8	4	no	—
284	D₄×C₇₉	—	8	4	no	—
285	C₂×C₄×C₇₉	—	2	1	no	—
286	C₂×C₄×C₇₉	—	2	1	no	—
287	C₂×C₄×C₇₉	—	2	2	no	—
288	C₂×C₄×C₇₉	—	2	2	no	—
289	C₂×C₄×C₇₉	—	2	2	no	—
290	C₂×C₄×C₇₉	—	2	2	no	—
291	C₂×C₄×C₇₉	—	2	1	no	—
292	C₂×C₄×C₇₉	—	2	2	no	—
293	C₂×C₄×C₇₉	—	2	2	no	—
294	C₂×C₄×C₇₉	—	2	2	no	—
295	C₂×C₄×C₇₉	—	2	1	no	—
296	C₂×C₄×C₇₉	—	2	1	no	—
297	C₂×C₄×C₇₉	—	2	2	no	—
298	C₂×C₄×C₇₉	—	2	1	no	—
299	C₂×C₄×C₇₉	—	2	2	no	—
300	C₂×C₄×C₇₉	—	2	1	no	—
301	C₂×C₄×C₇₉	—	2	1	no	—
302	C₂×C₄×C₇₉	—	2	1	no	—
303	C₂×C₄×C₇₉	—	2	1	no	—
304	C₂×C₄×C₇₉	—	2	1	no	—
305	C₂×C₄×C₇₉	—	4	8	no	—
306	C₂×C₄×C₇₉	—	4	1	no	—
307	C₂×C₄×C₇₉	—	4	1	no	—
308	C₂×C₄×C₇₉	—	4	1	no	—
309	C₂×C₄×C₇₉	—	4	1	no	—
310	C₂×C₄×C₇₉	—	4	1	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	—	8	4	no	—
327	C₂×C₄×C₇₉	#120	1	2	yes	—
328	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
331	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
332	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
333	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
334	C₈×C₇₉	—	2	2	no	—
335	C₈×C₇₉	—	4	1	no	—
336	C₈×C₇₉	—	4	1	no	—
337	C₈×C₇₉	—	4	1	no	—
338	C₂²×C₇₉	—	2	2	no	—
339	C₂²×C₇₉	—	2	2	no	—
340	C₂²×C₇₉	—	2	2	no	—
341	C₂²×C₇₉	—	2	2	no	—
342	C₂²×C₇₉	—	2	2	no	—
343	C₂²×C₇₉	—	2	2	no	—
344	C₂²×C₇₉	—	4	1	no	—
345	C₂²×C₇₉	—	4	1	no	—
346	C₂²×C₇₉	—	4	1	no	—
347	C₂²×C₇₉	—	4	1	no	—
348	C₂²×C₇₉	—	4	1	no	—
349	C₂²×C₇₉	—	4	1	no	—
350	C₂²×C₇₉	—	4	1	no	—
351	C₂²×C₇₉	—	4	1	no	—
352	C₂²×C₇₉	—	8	1	no	—
353	C₂²×C₇₉	—	8	1	no	—
354	C₂²×C₇₉	—	8	1	no	—
355	C₂²×C₇₉	—	8	1	no	—
356	C₂²×C₇₉	—	8	1	no	—
357	C₂²×C₇₉	—	8	1	no	—
358	C₂²×C₇₉	—	8	1	no	—
359	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
360	C₂²×C₇₉	#546	1	1	yes	characteristic
361	C₂²×C₇₉	#547	1	1	yes	characteristic
362	C₂²×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
363	C₂²×C₇₉	#575	1	1	yes	characteristic
364	C₂²×C₇₉	#577	1	1	yes	characteristic
365	C₂²×C₇₉	#578	1	1	yes	characteristic
366	C₄×C₇₉	—	2	2	no	—
367	C₄×C₇₉	—	4	1	no	—
368	C₄×C₇₉	—	4	2	no	—
369	C₄×C₇₉	—	4	1	no	—
370	C₄×C₇₉	—	4	2	no	—
371	C₄×C₇₉	—	4	2	no	—
372	C₄×C₇₉	—	4	1	no	—
373	C₄×C₇₉	—	4	2	no	—
374	C₄×C₇₉	—	4	2	no	—
375	C₄×C₇₉	—	8	1	no	—
376	C₄×C₇₉	—	8	1	no	—
377	C₄×C₇₉	#532	1	1	yes	characteristic
378	C₄×C₇₉	#537	1	1	yes	characteristic
379	C₄×C₇₉	#546	1	1	yes	characteristic
380	C₄×C₇₉	#547	1	1	yes	characteristic
381	#25560	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
382	C₂×C₇₉	—	4	2	no	—
383	C₂×C₇₉	—	4	2	no	—
384	C₂×C₇₉	—	16	1	no	—
385	C₂×C₇₉	#2430	1	1	yes	characteristic
386	C₂×C₇₉	#3006	1	1	yes	characteristic
387	C₂×C₇₉	#3013	1	1	yes	characteristic
388	C₂×C₇₉	#3310	1	1	yes	characteristic
389	C₂×C₇₉	#3327	1	1	yes	characteristic
390	C₂×C₇₉	#3343	1	1	yes	characteristic
391	C₂×C₇₉	#3351	1	1	yes	characteristic
392	C₂×#552	C₂×C₇₉	1	1	yes	characteristic, complemented
393	C₂×#482	C₂×C₇₉	1	1	yes	characteristic, complemented
394	C₂×#468	C₂×C₇₉	1	1	yes	characteristic, complemented
395	#2416	C₂×C₇₉	1	1	yes	characteristic
396	#2059	C₂×C₇₉	1	1	yes	characteristic, complemented
397	#2035	C₂×C₇₉	1	1	yes	characteristic, complemented
398	#2025	C₂×C₇₉	1	1	yes	characteristic, complemented
399	#2000	C₂×C₇₉	1	1	yes	characteristic, complemented
400	#1880	C₂×C₇₉	1	1	yes	characteristic, complemented
401	#1874	C₂×C₇₉	1	1	yes	characteristic, complemented
402	#1872	C₂×C₇₉	1	1	yes	characteristic, complemented
403	#1870	C₂×C₇₉	1	1	yes	characteristic, complemented
404	#1863	C₂×C₇₉	1	1	yes	characteristic, complemented
405	#1852	C₂×C₇₉	1	1	yes	characteristic, complemented
406	#1736	C₂×C₇₉	1	1	yes	characteristic, complemented
407	C₇₉	#25560	1	1	yes	characteristic, direct product factor, Sylow
408	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
409	C₂²×M₁₆	C₂²×C₇₉	1	1	yes	characteristic
410	#552	—	2	4	no	—
411	#552	—	2	4	no	—
412	C₂×#126	—	2	1	no	—
413	C₂×#125	—	2	1	no	—
414	C₂×#125	C₂²×C₇₉	1	1	yes	characteristic
415	C₂×#123	—	2	1	no	—
416	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
417	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
418	C₂×#121	—	2	1	no	—
419	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
420	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
421	C₂×C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
422	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
423	C₂×#117	—	2	1	no	—
424	C₂×#117	C₂²×C₇₉	1	1	yes	characteristic
425	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
426	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
427	#482	—	2	4	no	—
428	#468	—	2	4	no	—
429	C₂×#107	C₂²×C₇₉	1	1	yes	characteristic
430	C₂×#107	C₂²×C₇₉	1	1	yes	characteristic
431	C₂×#106	C₂²×C₇₉	1	1	yes	characteristic
432	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
433	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
434	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
435	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
436	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
437	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
438	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
439	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
440	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
441	#396	—	2	1	no	—
442	#394	—	2	1	no	—
443	#390	C₂²×C₇₉	1	1	yes	characteristic
444	#389	C₂²×C₇₉	1	1	yes	characteristic
445	#386	—	2	1	no	—
446	#380	C₂²×C₇₉	1	1	yes	characteristic
447	#340	C₂²×C₇₉	1	1	yes	characteristic
448	#340	C₂²×C₇₉	1	1	yes	characteristic
449	#340	C₂²×C₇₉	1	1	yes	characteristic
450	#340	C₂²×C₇₉	1	1	yes	characteristic
451	#340	C₂²×C₇₉	1	1	yes	characteristic
452	#340	C₂²×C₇₉	1	1	yes	characteristic
453	#336	C₂²×C₇₉	1	1	yes	characteristic
454	#336	C₂²×C₇₉	1	1	yes	characteristic
455	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
456	C₂²×D₄	—	2	1	no	—
457	C₂²×D₄	—	2	1	no	—
458	C₂²×D₄	D₄×C₇₉	1	1	yes	characteristic
459	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
460	C₂³×C₄	—	2	1	no	—
461	C₂³×C₄	—	2	1	no	—
462	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
463	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
464	C₂×SD₁₆	—	2	2	no	—
465	C₂×SD₁₆	—	2	2	no	—
466	C₂×SD₁₆	—	4	1	no	—
467	C₂×M₁₆	—	2	2	no	—
468	C₂×M₁₆	—	2	2	no	—
469	C₂×M₁₆	—	4	1	no	—
470	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
471	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
472	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
473	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
474	#126	—	2	8	no	—
475	#125	—	2	8	no	—
476	#125	—	2	2	no	—
477	#125	—	2	2	no	—
478	#123	—	2	8	no	—
479	C₂²⋊Q₈	—	2	2	no	—
480	C₂²⋊Q₈	—	2	2	no	—
481	C₂²⋊Q₈	—	2	2	no	—
482	C₂²⋊Q₈	D₄×C₇₉	1	4	yes	complemented
483	#121	—	2	2	no	—
484	#121	—	2	2	no	—
485	#121	—	2	2	no	—
486	#121	—	4	1	no	—
487	#121	—	4	4	no	—
488	C₄×Q₈	—	2	2	no	—
489	C₄×Q₈	—	2	2	no	—
490	C₄×D₄	—	2	2	no	—
491	C₄×D₄	—	2	2	no	—
492	#117	—	2	8	no	—
493	#117	—	2	2	no	—
494	#117	D₄×C₇₉	1	4	yes	complemented
495	C₂×C₄⋊C₄	—	2	1	no	—
496	C₂×C₄⋊C₄	—	2	1	no	—
497	C₂×C₄⋊C₄	—	2	1	no	—
498	C₂×C₄⋊C₄	—	2	1	no	—
499	C₂×C₄⋊C₄	—	2	1	no	—
500	C₂×C₄⋊C₄	—	2	1	no	—
501	C₂×C₄⋊C₄	—	2	2	no	—
502	C₂×C₄⋊C₄	—	2	2	no	—
503	C₂×C₄⋊C₄	—	2	2	no	—
504	C₂×C₄⋊C₄	—	2	1	no	—
505	C₂×C₄⋊C₄	—	2	1	no	—
506	C₂×C₄⋊C₄	—	4	1	no	—
507	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
511	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
512	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
513	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
514	C₂×C₂²⋊C₄	—	2	1	no	—
515	C₂×C₂²⋊C₄	—	2	1	no	—
516	C₂×C₂²⋊C₄	—	2	1	no	—
517	C₂×C₂²⋊C₄	—	2	1	no	—
518	C₂×C₂²⋊C₄	—	2	1	no	—
519	C₂×C₂²⋊C₄	—	2	1	no	—
520	C₂×C₂²⋊C₄	—	2	1	no	—
521	C₂×C₂²⋊C₄	—	2	1	no	—
522	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
523	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
524	C₂×C₄²	—	2	1	no	—
525	C₂×C₄²	—	2	1	no	—
526	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
527	#107	—	2	2	no	—
528	#107	—	2	2	no	—
529	#106	—	2	2	no	—
530	#103	—	2	2	no	—
531	#103	—	2	2	no	—
532	#103	—	4	1	no	—
533	#102	—	2	2	no	—
534	#102	—	2	2	no	—
535	#102	—	2	2	no	—
536	C₂²⋊C₈	—	2	2	no	—
537	C₂²⋊C₈	—	2	2	no	—
538	C₂²⋊C₈	—	4	1	no	—
539	#95	—	2	1	no	—
540	#95	—	2	1	no	—
541	C₂⁴	—	2	1	no	—
542	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
543	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
544	C₂×Q₈	—	2	1	no	—
545	C₂×Q₈	—	2	1	no	—
546	C₂×Q₈	—	2	1	no	—
547	C₂×Q₈	—	2	1	no	—
548	C₂×Q₈	—	2	1	no	—
549	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	—	2	1	no	—
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	—	2	1	no	—
557	C₂×D₄	—	2	1	no	—
558	C₂×D₄	—	4	1	no	—
559	C₂×D₄	—	4	2	no	—
560	C₂×D₄	—	4	2	no	—
561	C₂×D₄	—	4	2	no	—
562	C₂×D₄	—	4	2	no	—
563	C₂×D₄	—	4	2	no	—
564	C₂×D₄	—	8	1	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	4	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
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	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	4	2	no	—
584	C₂²×C₄	—	4	2	no	—
585	C₂²×C₄	—	4	2	no	—
586	C₂²×C₄	—	4	2	no	—
587	C₂²×C₄	—	8	1	no	—
588	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
589	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
590	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
591	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
592	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
593	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
595	SD₁₆	—	4	4	no	—
596	M₁₆	—	4	4	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	—	2	1	no	—
599	C₂×C₈	—	2	1	no	—
600	C₂×C₈	—	2	1	no	—
601	C₂×C₈	—	2	1	no	—
602	C₂×C₈	—	2	1	no	—
603	C₂×C₈	—	2	1	no	—
604	C₂×C₈	—	2	1	no	—
605	C₂×C₈	—	2	1	no	—
606	C₂×C₈	—	2	1	no	—
607	C₂×C₈	—	2	1	no	—
608	C₂×C₈	#41×C₇₉	1	2	yes	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	—	2	1	no	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	4	2	no	—
625	C₄⋊C₄	—	4	2	no	—
626	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
627	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
628	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
629	C₄⋊C₄	#41×C₇₉	1	2	yes	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	2	no	—
634	C₂²⋊C₄	—	2	2	no	—
635	C₂²⋊C₄	—	4	2	no	—
636	C₂²⋊C₄	—	4	2	no	—
637	C₂²⋊C₄	—	4	2	no	—
638	C₂²⋊C₄	—	4	2	no	—
639	C₂²⋊C₄	—	8	1	no	—
640	C₄²	—	2	4	no	—
641	C₄²	—	2	4	no	—
642	C₄²	—	2	1	no	—
643	C₄²	—	2	1	no	—
644	C₂³	—	2	1	no	—
645	C₂³	—	2	1	no	—
646	C₂³	—	2	1	no	—
647	C₂³	—	2	1	no	—
648	C₂³	—	2	1	no	—
649	C₂³	—	2	1	no	—
650	C₂³	—	2	1	no	—
651	C₂³	—	2	1	no	—
652	C₂³	—	2	1	no	—
653	C₂³	—	2	1	no	—
654	C₂³	—	2	1	no	—
655	C₂³	—	2	1	no	—
656	C₂³	—	4	1	no	—
657	C₂³	—	4	1	no	—
658	C₂³	—	4	1	no	—
659	C₂³	—	4	1	no	—
660	C₂³	—	4	1	no	—
661	C₂³	—	4	1	no	—
662	C₂³	—	4	1	no	—
663	C₂³	#120×C₇₉	1	2	yes	—
664	C₂³	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
665	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
666	Q₈	—	2	2	no	—
667	Q₈	—	2	2	no	—
668	Q₈	—	4	1	no	—
669	Q₈	—	4	1	no	—
670	D₄	—	4	4	no	—
671	D₄	—	4	1	no	—
672	D₄	—	4	1	no	—
673	D₄	—	4	1	no	—
674	D₄	—	4	1	no	—
675	D₄	—	8	4	no	—
676	D₄	—	8	4	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	4	8	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	1	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	4	1	no	—
705	C₂×C₄	—	4	1	no	—
706	C₂×C₄	—	4	1	no	—
707	C₂×C₄	—	4	1	no	—
708	C₂×C₄	—	4	1	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	—	8	4	no	—
719	C₂×C₄	#120×C₇₉	1	2	yes	—
720	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
721	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
722	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
723	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
724	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
725	C₂×C₄	2₋¹⁺⁴×C₇₉	1	1	yes	characteristic
726	C₈	—	2	2	no	—
727	C₈	—	4	1	no	—
728	C₈	—	4	1	no	—
729	C₈	—	4	1	no	—
730	C₂²	—	2	2	no	—
731	C₂²	—	2	2	no	—
732	C₂²	—	2	2	no	—
733	C₂²	—	2	2	no	—
734	C₂²	—	2	2	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	4	1	no	—
737	C₂²	—	4	1	no	—
738	C₂²	—	4	1	no	—
739	C₂²	—	4	1	no	—
740	C₂²	—	4	1	no	—
741	C₂²	—	4	1	no	—
742	C₂²	—	4	1	no	—
743	C₂²	—	4	1	no	—
744	C₂²	—	8	1	no	—
745	C₂²	—	8	1	no	—
746	C₂²	—	8	1	no	—
747	C₂²	—	8	1	no	—
748	C₂²	—	8	1	no	—
749	C₂²	—	8	1	no	—
750	C₂²	—	8	1	no	—
751	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
752	C₂²	#546×C₇₉	1	1	yes	characteristic
753	C₂²	#547×C₇₉	1	1	yes	characteristic
754	C₂²	C₂×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
755	C₂²	#575×C₇₉	1	1	yes	characteristic
756	C₂²	#577×C₇₉	1	1	yes	characteristic
757	C₂²	#578×C₇₉	1	1	yes	characteristic
758	C₄	—	2	2	no	—
759	C₄	—	4	2	no	—
760	C₄	—	4	1	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	1	no	—
763	C₄	—	4	2	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	1	no	—
766	C₄	—	4	2	no	—
767	C₄	—	8	1	no	—
768	C₄	—	8	1	no	—
769	C₄	#532×C₇₉	1	1	yes	characteristic
770	C₄	#537×C₇₉	1	1	yes	characteristic
771	C₄	#546×C₇₉	1	1	yes	characteristic
772	C₄	#547×C₇₉	1	1	yes	characteristic
773	C₂	—	4	2	no	—
774	C₂	—	4	2	no	—
775	C₂	—	16	1	no	—
776	C₂	C₇₉×#2430	1	1	yes	characteristic
777	C₂	C₇₉×#3006	1	1	yes	characteristic
778	C₂	C₇₉×#3013	1	1	yes	characteristic
779	C₂	C₇₉×#3310	1	1	yes	characteristic
780	C₂	C₇₉×#3327	1	1	yes	characteristic
781	C₂	C₇₉×#3343	1	1	yes	characteristic
782	C₂	C₇₉×#3351	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₇₉×#2416	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
1. C₂×#552×C₇₉	C₂	semidirect
2. C₂×#482×C₇₉	C₂	semidirect
3. C₂×#468×C₇₉	C₂	semidirect
5. C₇₉×#2059	C₂	semidirect
6. C₇₉×#2035	C₂	semidirect
7. C₇₉×#2025	C₂	semidirect
8. C₇₉×#2000	C₂	semidirect
9. C₇₉×#1880	C₂	semidirect
10. C₇₉×#1874	C₂	semidirect
11. C₇₉×#1872	C₂	semidirect
12. C₇₉×#1870	C₂	semidirect
13. C₇₉×#1863	C₂	semidirect
14. C₇₉×#1852	C₂	semidirect
15. C₇₉×#1736	C₂	semidirect
90. C₂²⋊Q₈×C₇₉	D₄	semidirect
102. #117×C₇₉	D₄	semidirect
381. #25560	C₇₉	direct (N × H)
392. C₂×#552	C₂×C₇₉	semidirect
393. C₂×#482	C₂×C₇₉	semidirect
394. C₂×#468	C₂×C₇₉	semidirect
396. #2059	C₂×C₇₉	semidirect
397. #2035	C₂×C₇₉	semidirect
398. #2025	C₂×C₇₉	semidirect
399. #2000	C₂×C₇₉	semidirect
400. #1880	C₂×C₇₉	semidirect
401. #1874	C₂×C₇₉	semidirect
402. #1872	C₂×C₇₉	semidirect
403. #1870	C₂×C₇₉	semidirect
404. #1863	C₂×C₇₉	semidirect
405. #1852	C₂×C₇₉	semidirect
406. #1736	C₂×C₇₉	semidirect
407. C₇₉	#25560	direct (N × H)
482. C₂²⋊Q₈	D₄×C₇₉	semidirect
494. #117	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×#552×C₇₉	2
C₂×#482×C₇₉	2
C₂×#468×C₇₉	2
C₇₉×#2416	2
C₇₉×#2059	2
C₇₉×#2035	2
C₇₉×#2025	2
C₇₉×#2000	2
C₇₉×#1880	2
C₇₉×#1874	2
C₇₉×#1872	2
C₇₉×#1870	2
C₇₉×#1863	2
C₇₉×#1852	2
C₇₉×#1736	2
#25560	79

Subgroups — C79×#25560 #34137249

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#25560 #34137249