Subgroups — C₇₉×#25540 #34137229

Order 20224.

1142 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#556×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#482×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#465×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#2414	C₂	1	1	yes	maximal, characteristic
5	C₇₉×#2058	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₉×#2035	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#2023	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×#1875	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1873	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₉×#1869	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₉×#1863	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₉×#1854	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#1735	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₇₉	C₂²	1	1	yes	characteristic
18	#556×C₇₉	—	2	4	no	—
19	#556×C₇₉	—	2	4	no	—
20	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
21	C₂×#126×C₇₉	—	2	1	no	—
22	C₂×#126×C₇₉	—	2	1	no	—
23	C₂×#124×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	C₂²	1	1	yes	characteristic
27	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₇₉	—	2	1	no	—
29	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
31	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
32	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
33	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
34	#482×C₇₉	—	2	4	no	—
35	#465×C₇₉	—	2	4	no	—
36	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic
37	C₂×#106×C₇₉	C₂²	1	1	yes	characteristic
38	C₂×#106×C₇₉	C₂²	1	1	yes	characteristic
39	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
40	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
41	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
42	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
43	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
44	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
48	#394×C₇₉	—	2	1	no	—
49	#392×C₇₉	—	2	1	no	—
50	#390×C₇₉	—	2	1	no	—
51	#390×C₇₉	C₂²	1	1	yes	characteristic
52	#389×C₇₉	C₂²	1	1	yes	characteristic
53	#388×C₇₉	—	2	1	no	—
54	#380×C₇₉	C₂²	1	1	yes	characteristic
55	#340×C₇₉	C₂²	1	1	yes	characteristic
56	#340×C₇₉	C₂²	1	1	yes	characteristic
57	#340×C₇₉	C₂²	1	1	yes	characteristic
58	#340×C₇₉	C₂²	1	1	yes	characteristic
59	#340×C₇₉	C₂²	1	1	yes	characteristic
60	#340×C₇₉	C₂²	1	1	yes	characteristic
61	#336×C₇₉	C₂²	1	1	yes	characteristic
62	#336×C₇₉	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₇₉	—	2	1	no	—
64	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₇₉	—	2	1	no	—
66	C₂²×D₄×C₇₉	—	2	1	no	—
67	C₂²×D₄×C₇₉	D₄	1	1	yes	characteristic
68	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
71	C₂×SD₁₆×C₇₉	—	2	2	no	—
72	C₂×SD₁₆×C₇₉	—	2	2	no	—
73	C₂×SD₁₆×C₇₉	—	4	1	no	—
74	C₂²×C₈×C₇₉	—	2	2	no	—
75	C₂²×C₈×C₇₉	—	2	2	no	—
76	C₂²×C₈×C₇₉	—	4	1	no	—
77	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
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	C₄⋊Q₈×C₇₉	—	2	2	no	—
82	C₄⋊Q₈×C₇₉	—	2	2	no	—
83	#126×C₇₉	—	2	8	no	—
84	#126×C₇₉	—	2	8	no	—
85	#124×C₇₉	—	2	8	no	—
86	C₂²⋊Q₈×C₇₉	—	2	2	no	—
87	C₂²⋊Q₈×C₇₉	—	2	2	no	—
88	C₂²⋊Q₈×C₇₉	—	2	2	no	—
89	C₂²⋊Q₈×C₇₉	D₄	1	4	yes	complemented
90	#121×C₇₉	—	2	2	no	—
91	#121×C₇₉	—	2	2	no	—
92	#121×C₇₉	—	2	2	no	—
93	#121×C₇₉	—	4	1	no	—
94	C₄×Q₈×C₇₉	—	2	8	no	—
95	C₄×Q₈×C₇₉	—	2	2	no	—
96	C₄×Q₈×C₇₉	—	2	2	no	—
97	C₄×D₄×C₇₉	—	2	2	no	—
98	C₄×D₄×C₇₉	—	2	2	no	—
99	#117×C₇₉	—	2	2	no	—
100	#117×C₇₉	—	2	2	no	—
101	#117×C₇₉	—	2	2	no	—
102	#117×C₇₉	—	2	2	no	—
103	#117×C₇₉	—	4	1	no	—
104	#117×C₇₉	D₄	1	4	yes	complemented
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	1	no	—
110	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
117	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
118	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
119	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
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	D₄	1	1	yes	characteristic
128	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
129	C₂×C₄²×C₇₉	—	2	1	no	—
130	C₂×C₄²×C₇₉	—	2	1	no	—
131	C₂×C₄²×C₇₉	—	2	1	no	—
132	C₂×C₄²×C₇₉	—	2	1	no	—
133	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
134	#107×C₇₉	—	2	2	no	—
135	#106×C₇₉	—	2	2	no	—
136	#106×C₇₉	—	2	2	no	—
137	#103×C₇₉	—	2	2	no	—
138	#103×C₇₉	—	2	2	no	—
139	#103×C₇₉	—	4	1	no	—
140	#102×C₇₉	—	2	2	no	—
141	#102×C₇₉	—	2	2	no	—
142	#102×C₇₉	—	2	2	no	—
143	C₂²⋊C₈×C₇₉	—	2	2	no	—
144	C₂²⋊C₈×C₇₉	—	2	2	no	—
145	C₂²⋊C₈×C₇₉	—	4	1	no	—
146	#95×C₇₉	—	2	1	no	—
147	#95×C₇₉	—	2	1	no	—
148	C₂⁴×C₇₉	—	2	1	no	—
149	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
150	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
151	C₂×Q₈×C₇₉	—	2	4	no	—
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	—	4	2	no	—
158	C₂×Q₈×C₇₉	—	4	2	no	—
159	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
160	C₂×D₄×C₇₉	—	2	2	no	—
161	C₂×D₄×C₇₉	—	2	2	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	—	2	1	no	—
167	C₂×D₄×C₇₉	—	2	1	no	—
168	C₂×D₄×C₇₉	—	4	1	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	C₂×D₄×C₇₉	—	8	1	no	—
174	C₂×D₄×C₇₉	—	8	1	no	—
175	C₂²×C₄×C₇₉	—	2	1	no	—
176	C₂²×C₄×C₇₉	—	2	1	no	—
177	C₂²×C₄×C₇₉	—	2	1	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	—	2	1	no	—
192	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
196	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
197	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
199	SD₁₆×C₇₉	—	4	4	no	—
200	C₂×C₈×C₇₉	—	2	1	no	—
201	C₂×C₈×C₇₉	—	2	1	no	—
202	C₂×C₈×C₇₉	—	2	1	no	—
203	C₂×C₈×C₇₉	—	2	1	no	—
204	C₂×C₈×C₇₉	—	2	1	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	—	4	4	no	—
212	C₂×C₈×C₇₉	#41	1	2	yes	—
213	C₄⋊C₄×C₇₉	—	2	4	no	—
214	C₄⋊C₄×C₇₉	—	2	4	no	—
215	C₄⋊C₄×C₇₉	—	2	4	no	—
216	C₄⋊C₄×C₇₉	—	2	4	no	—
217	C₄⋊C₄×C₇₉	—	2	2	no	—
218	C₄⋊C₄×C₇₉	—	2	1	no	—
219	C₄⋊C₄×C₇₉	—	2	1	no	—
220	C₄⋊C₄×C₇₉	—	2	1	no	—
221	C₄⋊C₄×C₇₉	—	2	1	no	—
222	C₄⋊C₄×C₇₉	—	2	1	no	—
223	C₄⋊C₄×C₇₉	—	2	1	no	—
224	C₄⋊C₄×C₇₉	—	2	1	no	—
225	C₄⋊C₄×C₇₉	—	2	1	no	—
226	C₄⋊C₄×C₇₉	—	8	1	no	—
227	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
228	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
229	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
230	C₄⋊C₄×C₇₉	#41	1	2	yes	—
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	2	no	—
236	C₂²⋊C₄×C₇₉	—	2	2	no	—
237	C₂²⋊C₄×C₇₉	—	4	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	—	8	1	no	—
242	C₂²⋊C₄×C₇₉	—	8	1	no	—
243	C₄²×C₇₉	—	2	4	no	—
244	C₄²×C₇₉	—	2	4	no	—
245	C₄²×C₇₉	—	2	4	no	—
246	C₄²×C₇₉	—	2	1	no	—
247	C₄²×C₇₉	—	2	1	no	—
248	C₄²×C₇₉	—	4	2	no	—
249	C₂³×C₇₉	—	2	1	no	—
250	C₂³×C₇₉	—	2	1	no	—
251	C₂³×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	—	4	1	no	—
263	C₂³×C₇₉	—	4	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	#120	1	2	yes	—
270	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
271	Q₈×C₇₉	—	2	2	no	—
272	Q₈×C₇₉	—	2	2	no	—
273	Q₈×C₇₉	—	4	8	no	—
274	Q₈×C₇₉	—	4	1	no	—
275	Q₈×C₇₉	—	4	1	no	—
276	D₄×C₇₉	—	4	4	no	—
277	D₄×C₇₉	—	4	1	no	—
278	D₄×C₇₉	—	4	1	no	—
279	D₄×C₇₉	—	4	1	no	—
280	D₄×C₇₉	—	4	1	no	—
281	D₄×C₇₉	—	8	4	no	—
282	D₄×C₇₉	—	8	4	no	—
283	C₂×C₄×C₇₉	—	2	1	no	—
284	C₂×C₄×C₇₉	—	2	1	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	2	no	—
292	C₂×C₄×C₇₉	—	2	1	no	—
293	C₂×C₄×C₇₉	—	2	1	no	—
294	C₂×C₄×C₇₉	—	2	2	no	—
295	C₂×C₄×C₇₉	—	2	2	no	—
296	C₂×C₄×C₇₉	—	2	2	no	—
297	C₂×C₄×C₇₉	—	2	2	no	—
298	C₂×C₄×C₇₉	—	2	1	no	—
299	C₂×C₄×C₇₉	—	2	1	no	—
300	C₂×C₄×C₇₉	—	2	1	no	—
301	C₂×C₄×C₇₉	—	2	1	no	—
302	C₂×C₄×C₇₉	—	4	1	no	—
303	C₂×C₄×C₇₉	—	4	1	no	—
304	C₂×C₄×C₇₉	—	4	1	no	—
305	C₂×C₄×C₇₉	—	4	1	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	#120	1	2	yes	—
323	C₂×C₄×C₇₉	#135	1	2	yes	—
324	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
327	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
328	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
329	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
330	C₈×C₇₉	—	2	2	no	—
331	C₈×C₇₉	—	4	1	no	—
332	C₈×C₇₉	—	4	1	no	—
333	C₈×C₇₉	—	4	1	no	—
334	C₂²×C₇₉	—	2	2	no	—
335	C₂²×C₇₉	—	2	2	no	—
336	C₂²×C₇₉	—	2	2	no	—
337	C₂²×C₇₉	—	4	1	no	—
338	C₂²×C₇₉	—	4	1	no	—
339	C₂²×C₇₉	—	4	1	no	—
340	C₂²×C₇₉	—	4	1	no	—
341	C₂²×C₇₉	—	4	1	no	—
342	C₂²×C₇₉	—	4	1	no	—
343	C₂²×C₇₉	—	4	1	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	—	8	1	no	—
349	C₂²×C₇₉	—	8	1	no	—
350	C₂²×C₇₉	—	8	1	no	—
351	C₂²×C₇₉	—	8	1	no	—
352	C₂²×C₇₉	—	8	1	no	—
353	C₂²×C₇₉	—	8	1	no	—
354	C₂²×C₇₉	—	8	1	no	—
355	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
356	C₂²×C₇₉	#546	1	1	yes	characteristic
357	C₂²×C₇₉	#547	1	1	yes	characteristic
358	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
359	C₂²×C₇₉	#575	1	1	yes	characteristic
360	C₂²×C₇₉	#577	1	1	yes	characteristic
361	C₂²×C₇₉	#577	1	1	yes	characteristic
362	C₄×C₇₉	—	2	2	no	—
363	C₄×C₇₉	—	2	2	no	—
364	C₄×C₇₉	—	4	1	no	—
365	C₄×C₇₉	—	4	2	no	—
366	C₄×C₇₉	—	4	2	no	—
367	C₄×C₇₉	—	4	2	no	—
368	C₄×C₇₉	—	4	1	no	—
369	C₄×C₇₉	—	4	2	no	—
370	C₄×C₇₉	—	4	2	no	—
371	C₄×C₇₉	—	8	1	no	—
372	C₄×C₇₉	—	8	1	no	—
373	C₄×C₇₉	#532	1	1	yes	characteristic
374	C₄×C₇₉	#537	1	1	yes	characteristic
375	C₄×C₇₉	#546	1	1	yes	characteristic
376	C₄×C₇₉	#547	1	1	yes	characteristic
377	#25540	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
378	C₂×C₇₉	—	4	2	no	—
379	C₂×C₇₉	—	8	1	no	—
380	C₂×C₇₉	—	16	1	no	—
381	C₂×C₇₉	#2430	1	1	yes	characteristic
382	C₂×C₇₉	#3002	1	1	yes	characteristic
383	C₂×C₇₉	#3010	1	1	yes	characteristic
384	C₂×C₇₉	#3304	1	1	yes	characteristic
385	C₂×C₇₉	#3311	1	1	yes	characteristic
386	C₂×C₇₉	#3340	1	1	yes	characteristic
387	C₂×C₇₉	#3350	1	1	yes	characteristic
388	C₂×#556	C₂×C₇₉	1	1	yes	characteristic, complemented
389	C₂×#482	C₂×C₇₉	1	1	yes	characteristic, complemented
390	C₂×#465	C₂×C₇₉	1	1	yes	characteristic, complemented
391	#2414	C₂×C₇₉	1	1	yes	characteristic
392	#2058	C₂×C₇₉	1	1	yes	characteristic, complemented
393	#2035	C₂×C₇₉	1	1	yes	characteristic, complemented
394	#2023	C₂×C₇₉	1	1	yes	characteristic, complemented
395	#2000	C₂×C₇₉	1	1	yes	characteristic, complemented
396	#1880	C₂×C₇₉	1	1	yes	characteristic, complemented
397	#1875	C₂×C₇₉	1	1	yes	characteristic, complemented
398	#1873	C₂×C₇₉	1	1	yes	characteristic, complemented
399	#1869	C₂×C₇₉	1	1	yes	characteristic, complemented
400	#1863	C₂×C₇₉	1	1	yes	characteristic, complemented
401	#1854	C₂×C₇₉	1	1	yes	characteristic, complemented
402	#1735	C₂×C₇₉	1	1	yes	characteristic, complemented
403	C₇₉	#25540	1	1	yes	characteristic, direct product factor, Sylow
404	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
405	C₂³×C₈	C₂²×C₇₉	1	1	yes	characteristic
406	#556	—	2	4	no	—
407	#556	—	2	4	no	—
408	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
409	C₂×#126	—	2	1	no	—
410	C₂×#126	—	2	1	no	—
411	C₂×#124	—	2	1	no	—
412	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
413	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
414	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
415	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
416	C₂×C₄×Q₈	—	2	1	no	—
417	C₂×C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
418	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
419	C₂×#117	C₂²×C₇₉	1	1	yes	characteristic
420	C₂×#117	C₂²×C₇₉	1	1	yes	characteristic
421	C₂×#117	C₂²×C₇₉	1	1	yes	characteristic
422	#482	—	2	4	no	—
423	#465	—	2	4	no	—
424	C₂×#107	C₂²×C₇₉	1	1	yes	characteristic
425	C₂×#106	C₂²×C₇₉	1	1	yes	characteristic
426	C₂×#106	C₂²×C₇₉	1	1	yes	characteristic
427	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
428	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
429	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
430	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
431	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
432	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
433	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
434	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
435	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
436	#394	—	2	1	no	—
437	#392	—	2	1	no	—
438	#390	—	2	1	no	—
439	#390	C₂²×C₇₉	1	1	yes	characteristic
440	#389	C₂²×C₇₉	1	1	yes	characteristic
441	#388	—	2	1	no	—
442	#380	C₂²×C₇₉	1	1	yes	characteristic
443	#340	C₂²×C₇₉	1	1	yes	characteristic
444	#340	C₂²×C₇₉	1	1	yes	characteristic
445	#340	C₂²×C₇₉	1	1	yes	characteristic
446	#340	C₂²×C₇₉	1	1	yes	characteristic
447	#340	C₂²×C₇₉	1	1	yes	characteristic
448	#340	C₂²×C₇₉	1	1	yes	characteristic
449	#336	C₂²×C₇₉	1	1	yes	characteristic
450	#336	C₂²×C₇₉	1	1	yes	characteristic
451	C₂²×Q₈	—	2	1	no	—
452	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
453	C₂²×D₄	—	2	1	no	—
454	C₂²×D₄	—	2	1	no	—
455	C₂²×D₄	D₄×C₇₉	1	1	yes	characteristic
456	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
457	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
458	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
459	C₂×SD₁₆	—	2	2	no	—
460	C₂×SD₁₆	—	2	2	no	—
461	C₂×SD₁₆	—	4	1	no	—
462	C₂²×C₈	—	2	2	no	—
463	C₂²×C₈	—	2	2	no	—
464	C₂²×C₈	—	4	1	no	—
465	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
466	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
467	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
468	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
469	C₄⋊Q₈	—	2	2	no	—
470	C₄⋊Q₈	—	2	2	no	—
471	#126	—	2	8	no	—
472	#126	—	2	8	no	—
473	#124	—	2	8	no	—
474	C₂²⋊Q₈	—	2	2	no	—
475	C₂²⋊Q₈	—	2	2	no	—
476	C₂²⋊Q₈	—	2	2	no	—
477	C₂²⋊Q₈	D₄×C₇₉	1	4	yes	complemented
478	#121	—	2	2	no	—
479	#121	—	2	2	no	—
480	#121	—	2	2	no	—
481	#121	—	4	1	no	—
482	C₄×Q₈	—	2	8	no	—
483	C₄×Q₈	—	2	2	no	—
484	C₄×Q₈	—	2	2	no	—
485	C₄×D₄	—	2	2	no	—
486	C₄×D₄	—	2	2	no	—
487	#117	—	2	2	no	—
488	#117	—	2	2	no	—
489	#117	—	2	2	no	—
490	#117	—	2	2	no	—
491	#117	—	4	1	no	—
492	#117	D₄×C₇₉	1	4	yes	complemented
493	C₂×C₄⋊C₄	—	2	1	no	—
494	C₂×C₄⋊C₄	—	2	1	no	—
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	D₄×C₇₉	1	1	yes	characteristic
499	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
500	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
501	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
502	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
505	C₂×C₂²⋊C₄	—	2	1	no	—
506	C₂×C₂²⋊C₄	—	2	1	no	—
507	C₂×C₂²⋊C₄	—	2	1	no	—
508	C₂×C₂²⋊C₄	—	2	1	no	—
509	C₂×C₂²⋊C₄	—	2	1	no	—
510	C₂×C₂²⋊C₄	—	2	1	no	—
511	C₂×C₂²⋊C₄	—	2	1	no	—
512	C₂×C₂²⋊C₄	—	2	1	no	—
513	C₂×C₂²⋊C₄	—	2	1	no	—
514	C₂×C₂²⋊C₄	—	2	1	no	—
515	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
516	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
517	C₂×C₄²	—	2	1	no	—
518	C₂×C₄²	—	2	1	no	—
519	C₂×C₄²	—	2	1	no	—
520	C₂×C₄²	—	2	1	no	—
521	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
522	#107	—	2	2	no	—
523	#106	—	2	2	no	—
524	#106	—	2	2	no	—
525	#103	—	2	2	no	—
526	#103	—	2	2	no	—
527	#103	—	4	1	no	—
528	#102	—	2	2	no	—
529	#102	—	2	2	no	—
530	#102	—	2	2	no	—
531	C₂²⋊C₈	—	2	2	no	—
532	C₂²⋊C₈	—	2	2	no	—
533	C₂²⋊C₈	—	4	1	no	—
534	#95	—	2	1	no	—
535	#95	—	2	1	no	—
536	C₂⁴	—	2	1	no	—
537	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
538	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
539	C₂×Q₈	—	2	4	no	—
540	C₂×Q₈	—	2	1	no	—
541	C₂×Q₈	—	2	1	no	—
542	C₂×Q₈	—	2	1	no	—
543	C₂×Q₈	—	2	1	no	—
544	C₂×Q₈	—	2	1	no	—
545	C₂×Q₈	—	4	2	no	—
546	C₂×Q₈	—	4	2	no	—
547	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
548	C₂×D₄	—	2	2	no	—
549	C₂×D₄	—	2	2	no	—
550	C₂×D₄	—	2	1	no	—
551	C₂×D₄	—	2	1	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	—	4	1	no	—
557	C₂×D₄	—	4	2	no	—
558	C₂×D₄	—	4	2	no	—
559	C₂×D₄	—	4	2	no	—
560	C₂×D₄	—	8	1	no	—
561	C₂×D₄	—	8	1	no	—
562	C₂×D₄	—	8	1	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	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	1	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	C₂×D₄×C₇₉	1	1	yes	characteristic
581	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
582	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
583	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
584	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
585	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
586	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
587	SD₁₆	—	4	4	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	2	1	no	—
591	C₂×C₈	—	2	1	no	—
592	C₂×C₈	—	2	1	no	—
593	C₂×C₈	—	2	1	no	—
594	C₂×C₈	—	2	1	no	—
595	C₂×C₈	—	2	1	no	—
596	C₂×C₈	—	2	1	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	—	2	1	no	—
599	C₂×C₈	—	4	4	no	—
600	C₂×C₈	#41×C₇₉	1	2	yes	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	2	2	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	—	2	1	no	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	8	1	no	—
615	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
616	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
617	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
618	C₄⋊C₄	#41×C₇₉	1	2	yes	—
619	C₂²⋊C₄	—	2	4	no	—
620	C₂²⋊C₄	—	2	4	no	—
621	C₂²⋊C₄	—	2	4	no	—
622	C₂²⋊C₄	—	2	4	no	—
623	C₂²⋊C₄	—	2	2	no	—
624	C₂²⋊C₄	—	2	2	no	—
625	C₂²⋊C₄	—	4	2	no	—
626	C₂²⋊C₄	—	4	2	no	—
627	C₂²⋊C₄	—	4	2	no	—
628	C₂²⋊C₄	—	4	2	no	—
629	C₂²⋊C₄	—	8	1	no	—
630	C₂²⋊C₄	—	8	1	no	—
631	C₄²	—	2	4	no	—
632	C₄²	—	2	4	no	—
633	C₄²	—	2	4	no	—
634	C₄²	—	2	1	no	—
635	C₄²	—	2	1	no	—
636	C₄²	—	4	2	no	—
637	C₂³	—	2	1	no	—
638	C₂³	—	2	1	no	—
639	C₂³	—	2	1	no	—
640	C₂³	—	2	1	no	—
641	C₂³	—	2	1	no	—
642	C₂³	—	2	1	no	—
643	C₂³	—	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	—	4	1	no	—
651	C₂³	—	4	1	no	—
652	C₂³	—	4	1	no	—
653	C₂³	—	4	1	no	—
654	C₂³	—	4	1	no	—
655	C₂³	—	4	1	no	—
656	C₂³	—	4	1	no	—
657	C₂³	#120×C₇₉	1	2	yes	—
658	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
659	Q₈	—	2	2	no	—
660	Q₈	—	2	2	no	—
661	Q₈	—	4	8	no	—
662	Q₈	—	4	1	no	—
663	Q₈	—	4	1	no	—
664	D₄	—	4	4	no	—
665	D₄	—	4	1	no	—
666	D₄	—	4	1	no	—
667	D₄	—	4	1	no	—
668	D₄	—	4	1	no	—
669	D₄	—	8	4	no	—
670	D₄	—	8	4	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	1	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	#120×C₇₉	1	2	yes	—
711	C₂×C₄	#135×C₇₉	1	2	yes	—
712	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
713	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
714	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
715	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
716	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
717	C₂×C₄	2₋¹⁺⁴×C₇₉	1	1	yes	characteristic
718	C₈	—	2	2	no	—
719	C₈	—	4	1	no	—
720	C₈	—	4	1	no	—
721	C₈	—	4	1	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	2	no	—
725	C₂²	—	4	1	no	—
726	C₂²	—	4	1	no	—
727	C₂²	—	4	1	no	—
728	C₂²	—	4	1	no	—
729	C₂²	—	4	1	no	—
730	C₂²	—	4	1	no	—
731	C₂²	—	4	1	no	—
732	C₂²	—	4	1	no	—
733	C₂²	—	4	1	no	—
734	C₂²	—	4	1	no	—
735	C₂²	—	4	1	no	—
736	C₂²	—	8	1	no	—
737	C₂²	—	8	1	no	—
738	C₂²	—	8	1	no	—
739	C₂²	—	8	1	no	—
740	C₂²	—	8	1	no	—
741	C₂²	—	8	1	no	—
742	C₂²	—	8	1	no	—
743	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
744	C₂²	#546×C₇₉	1	1	yes	characteristic
745	C₂²	#547×C₇₉	1	1	yes	characteristic
746	C₂²	C₂×#135×C₇₉	1	1	yes	characteristic
747	C₂²	#575×C₇₉	1	1	yes	characteristic
748	C₂²	#577×C₇₉	1	1	yes	characteristic
749	C₂²	#577×C₇₉	1	1	yes	characteristic
750	C₄	—	2	2	no	—
751	C₄	—	2	2	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	1	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	1	no	—
758	C₄	—	4	2	no	—
759	C₄	—	8	1	no	—
760	C₄	—	8	1	no	—
761	C₄	#532×C₇₉	1	1	yes	characteristic
762	C₄	#537×C₇₉	1	1	yes	characteristic
763	C₄	#546×C₇₉	1	1	yes	characteristic
764	C₄	#547×C₇₉	1	1	yes	characteristic
765	C₂	—	4	2	no	—
766	C₂	—	8	1	no	—
767	C₂	—	16	1	no	—
768	C₂	C₇₉×#2430	1	1	yes	characteristic
769	C₂	C₇₉×#3002	1	1	yes	characteristic
770	C₂	C₇₉×#3010	1	1	yes	characteristic
771	C₂	C₇₉×#3304	1	1	yes	characteristic
772	C₂	C₇₉×#3311	1	1	yes	characteristic
773	C₂	C₇₉×#3340	1	1	yes	characteristic
774	C₂	C₇₉×#3350	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₇₉×#2414	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×#556×C₇₉	C₂	semidirect
2. C₂×#482×C₇₉	C₂	semidirect
3. C₂×#465×C₇₉	C₂	semidirect
5. C₇₉×#2058	C₂	semidirect
6. C₇₉×#2035	C₂	semidirect
7. C₇₉×#2023	C₂	semidirect
8. C₇₉×#2000	C₂	semidirect
9. C₇₉×#1880	C₂	semidirect
10. C₇₉×#1875	C₂	semidirect
11. C₇₉×#1873	C₂	semidirect
12. C₇₉×#1869	C₂	semidirect
13. C₇₉×#1863	C₂	semidirect
14. C₇₉×#1854	C₂	semidirect
15. C₇₉×#1735	C₂	semidirect
89. C₂²⋊Q₈×C₇₉	D₄	semidirect
104. #117×C₇₉	D₄	semidirect
377. #25540	C₇₉	direct (N × H)
388. C₂×#556	C₂×C₇₉	semidirect
389. C₂×#482	C₂×C₇₉	semidirect
390. C₂×#465	C₂×C₇₉	semidirect
392. #2058	C₂×C₇₉	semidirect
393. #2035	C₂×C₇₉	semidirect
394. #2023	C₂×C₇₉	semidirect
395. #2000	C₂×C₇₉	semidirect
396. #1880	C₂×C₇₉	semidirect
397. #1875	C₂×C₇₉	semidirect
398. #1873	C₂×C₇₉	semidirect
399. #1869	C₂×C₇₉	semidirect
400. #1863	C₂×C₇₉	semidirect
401. #1854	C₂×C₇₉	semidirect
402. #1735	C₂×C₇₉	semidirect
403. C₇₉	#25540	direct (N × H)
477. C₂²⋊Q₈	D₄×C₇₉	semidirect
492. #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×#556×C₇₉	2
C₂×#482×C₇₉	2
C₂×#465×C₇₉	2
C₇₉×#2414	2
C₇₉×#2058	2
C₇₉×#2035	2
C₇₉×#2023	2
C₇₉×#2000	2
C₇₉×#1880	2
C₇₉×#1875	2
C₇₉×#1873	2
C₇₉×#1869	2
C₇₉×#1863	2
C₇₉×#1854	2
C₇₉×#1735	2
#25540	79

Subgroups — C79×#25540 #34137229

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#25540 #34137229