Subgroups — C₇₉×#25500 #34137189

Order 20224.

1226 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#529×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#466×C₇₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#465×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#2854	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#2059	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₉×#2042	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#2025	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#2012	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#1893	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#1892	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1880	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₉×#1879	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₉×#1864	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₉×#1863	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#336×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
17	C₂²×D₈×C₇₉	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₇₉	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₇₉	C₂²	1	1	yes	characteristic
20	#529×C₇₉	—	2	4	no	—
21	#529×C₇₉	—	2	4	no	—
22	C₂×#126×C₇₉	—	2	1	no	—
23	C₂×#125×C₇₉	C₂²	1	1	yes	characteristic
24	C₂×#124×C₇₉	C₂²	1	1	yes	characteristic
25	C₂×#123×C₇₉	—	2	1	no	—
26	C₂×#123×C₇₉	—	2	1	no	—
27	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
28	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
29	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₇₉	—	2	1	no	—
32	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
33	C₂×#117×C₇₉	—	2	1	no	—
34	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
35	#466×C₇₉	—	2	4	no	—
36	#465×C₇₉	—	2	4	no	—
37	C₂×#107×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×#102×C₇₉	C₂²	1	1	yes	characteristic
46	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
47	#390×C₇₉	C₂²	1	1	yes	characteristic
48	#390×C₇₉	C₂²	1	1	yes	characteristic
49	#389×C₇₉	C₂²	1	1	yes	characteristic
50	#389×C₇₉	C₂²	1	1	yes	characteristic
51	#388×C₇₉	—	2	1	no	—
52	#388×C₇₉	—	2	1	no	—
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	#336×C₇₉	C₂²	1	1	yes	characteristic
60	#336×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	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₇₉	—	2	1	no	—
69	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
70	C₂³×C₄×C₇₉	D₄	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×D₈×C₇₉	—	2	2	no	—
76	C₂×D₈×C₇₉	—	2	2	no	—
77	C₂×D₈×C₇₉	—	4	1	no	—
78	C₂²×C₈×C₇₉	—	2	2	no	—
79	C₂²×C₈×C₇₉	—	2	2	no	—
80	C₂²×C₈×C₇₉	—	2	2	no	—
81	C₂²×C₈×C₇₉	—	2	2	no	—
82	C₂²×C₈×C₇₉	—	4	1	no	—
83	C₂²×C₈×C₇₉	—	4	1	no	—
84	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
88	#126×C₇₉	—	2	8	no	—
89	#125×C₇₉	—	2	2	no	—
90	#125×C₇₉	—	2	2	no	—
91	#124×C₇₉	—	2	2	no	—
92	#124×C₇₉	—	2	2	no	—
93	#123×C₇₉	—	2	8	no	—
94	#123×C₇₉	—	4	4	no	—
95	C₂²⋊Q₈×C₇₉	—	2	2	no	—
96	C₂²⋊Q₈×C₇₉	D₄	1	4	yes	—
97	#121×C₇₉	—	2	2	no	—
98	#121×C₇₉	—	2	2	no	—
99	#121×C₇₉	—	2	2	no	—
100	#121×C₇₉	D₄	1	4	yes	—
101	C₄×Q₈×C₇₉	—	2	2	no	—
102	C₄×Q₈×C₇₉	—	2	2	no	—
103	C₄×D₄×C₇₉	—	2	8	no	—
104	C₄×D₄×C₇₉	—	2	2	no	—
105	C₄×D₄×C₇₉	—	2	2	no	—
106	#117×C₇₉	—	2	8	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	—	2	1	no	—
111	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
112	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
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×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
129	C₂×C₄²×C₇₉	—	2	2	no	—
130	C₂×C₄²×C₇₉	—	2	2	no	—
131	C₂×C₄²×C₇₉	—	2	1	no	—
132	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
133	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
134	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
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	#102×C₇₉	—	2	2	no	—
145	#102×C₇₉	—	4	1	no	—
146	#95×C₇₉	—	2	1	no	—
147	#95×C₇₉	—	2	1	no	—
148	#95×C₇₉	—	2	1	no	—
149	C₂⁴×C₇₉	—	2	1	no	—
150	C₂⁴×C₇₉	—	2	1	no	—
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	4	no	—
159	C₂×D₄×C₇₉	—	2	1	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	—	2	1	no	—
167	C₂×D₄×C₇₉	—	2	1	no	—
168	C₂×D₄×C₇₉	—	2	1	no	—
169	C₂×D₄×C₇₉	—	2	1	no	—
170	C₂×D₄×C₇₉	—	4	2	no	—
171	C₂×D₄×C₇₉	—	4	2	no	—
172	C₂×D₄×C₇₉	—	4	2	no	—
173	C₂×D₄×C₇₉	—	4	2	no	—
174	C₂×D₄×C₇₉	—	4	2	no	—
175	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
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	4	no	—
181	C₂²×C₄×C₇₉	—	2	2	no	—
182	C₂²×C₄×C₇₉	—	2	2	no	—
183	C₂²×C₄×C₇₉	—	2	2	no	—
184	C₂²×C₄×C₇₉	—	2	2	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	2	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	—	4	1	no	—
193	C₂²×C₄×C₇₉	—	4	2	no	—
194	C₂²×C₄×C₇₉	—	4	2	no	—
195	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
200	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
201	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
203	SD₁₆×C₇₉	—	4	4	no	—
204	D₈×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	—	4	4	no	—
216	C₂×C₈×C₇₉	—	4	4	no	—
217	C₂×C₈×C₇₉	#41	1	2	yes	—
218	C₂×C₈×C₇₉	#41	1	2	yes	—
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	1	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	—	4	2	no	—
232	C₄⋊C₄×C₇₉	—	4	2	no	—
233	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
234	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
235	C₂²⋊C₄×C₇₉	—	2	4	no	—
236	C₂²⋊C₄×C₇₉	—	2	4	no	—
237	C₂²⋊C₄×C₇₉	—	2	4	no	—
238	C₂²⋊C₄×C₇₉	—	2	4	no	—
239	C₂²⋊C₄×C₇₉	—	2	4	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	2	no	—
245	C₂²⋊C₄×C₇₉	—	4	2	no	—
246	C₄²×C₇₉	—	2	4	no	—
247	C₄²×C₇₉	—	2	2	no	—
248	C₄²×C₇₉	—	2	2	no	—
249	C₄²×C₇₉	—	2	1	no	—
250	C₄²×C₇₉	—	2	1	no	—
251	C₄²×C₇₉	—	2	1	no	—
252	C₄²×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	2	no	—
258	C₂³×C₇₉	—	4	1	no	—
259	C₂³×C₇₉	—	4	1	no	—
260	C₂³×C₇₉	—	4	1	no	—
261	C₂³×C₇₉	—	4	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	—	4	1	no	—
270	C₂³×C₇₉	—	4	1	no	—
271	C₂³×C₇₉	#120	1	2	yes	—
272	C₂³×C₇₉	#135	1	2	yes	—
273	C₂³×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
274	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
275	Q₈×C₇₉	—	2	2	no	—
276	Q₈×C₇₉	—	2	2	no	—
277	Q₈×C₇₉	—	4	1	no	—
278	Q₈×C₇₉	—	4	1	no	—
279	D₄×C₇₉	—	2	2	no	—
280	D₄×C₇₉	—	2	2	no	—
281	D₄×C₇₉	—	4	8	no	—
282	D₄×C₇₉	—	4	1	no	—
283	D₄×C₇₉	—	4	1	no	—
284	D₄×C₇₉	—	4	1	no	—
285	D₄×C₇₉	—	4	1	no	—
286	D₄×C₇₉	—	4	1	no	—
287	D₄×C₇₉	—	4	1	no	—
288	D₄×C₇₉	—	8	4	no	—
289	C₂×C₄×C₇₉	—	2	1	no	—
290	C₂×C₄×C₇₉	—	2	1	no	—
291	C₂×C₄×C₇₉	—	2	1	no	—
292	C₂×C₄×C₇₉	—	2	1	no	—
293	C₂×C₄×C₇₉	—	2	2	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	1	no	—
298	C₂×C₄×C₇₉	—	2	1	no	—
299	C₂×C₄×C₇₉	—	2	1	no	—
300	C₂×C₄×C₇₉	—	2	2	no	—
301	C₂×C₄×C₇₉	—	2	2	no	—
302	C₂×C₄×C₇₉	—	2	2	no	—
303	C₂×C₄×C₇₉	—	2	1	no	—
304	C₂×C₄×C₇₉	—	2	1	no	—
305	C₂×C₄×C₇₉	—	2	1	no	—
306	C₂×C₄×C₇₉	—	2	1	no	—
307	C₂×C₄×C₇₉	—	2	1	no	—
308	C₂×C₄×C₇₉	—	2	1	no	—
309	C₂×C₄×C₇₉	—	4	4	no	—
310	C₂×C₄×C₇₉	—	4	8	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	4	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	—	4	1	no	—
327	C₂×C₄×C₇₉	#120	1	2	yes	—
328	C₂×C₄×C₇₉	#135	1	2	yes	—
329	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
332	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
333	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
334	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
335	C₈×C₇₉	—	2	2	no	—
336	C₈×C₇₉	—	2	2	no	—
337	C₈×C₇₉	—	4	1	no	—
338	C₈×C₇₉	—	4	1	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	—	2	2	no	—
345	C₂²×C₇₉	—	4	2	no	—
346	C₂²×C₇₉	—	4	2	no	—
347	C₂²×C₇₉	—	4	2	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	—	8	1	no	—
356	C₂²×C₇₉	—	8	1	no	—
357	C₂²×C₇₉	—	8	1	no	—
358	C₂²×C₇₉	—	8	1	no	—
359	C₂²×C₇₉	#449	1	4	yes	—
360	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
361	C₂²×C₇₉	#532	1	1	yes	characteristic
362	C₂²×C₇₉	#537	1	1	yes	characteristic
363	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
364	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
365	C₂²×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
366	C₂²×C₇₉	#575	1	1	yes	characteristic
367	C₄×C₇₉	—	2	2	no	—
368	C₄×C₇₉	—	2	2	no	—
369	C₄×C₇₉	—	4	2	no	—
370	C₄×C₇₉	—	4	1	no	—
371	C₄×C₇₉	—	4	1	no	—
372	C₄×C₇₉	—	4	2	no	—
373	C₄×C₇₉	—	4	1	no	—
374	C₄×C₇₉	—	4	2	no	—
375	C₄×C₇₉	—	8	1	no	—
376	C₄×C₇₉	—	8	1	no	—
377	C₄×C₇₉	—	8	1	no	—
378	C₄×C₇₉	#546	1	1	yes	characteristic
379	C₄×C₇₉	#546	1	1	yes	characteristic
380	C₄×C₇₉	#547	1	1	yes	characteristic
381	C₄×C₇₉	#547	1	1	yes	characteristic
382	#25500	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
383	C₂×C₇₉	—	2	4	no	—
384	C₂×C₇₉	—	8	2	no	—
385	C₂×C₇₉	—	16	1	no	—
386	C₂×C₇₉	#2430	1	1	yes	characteristic
387	C₂×C₇₉	C₂×#449	1	1	yes	characteristic
388	C₂×C₇₉	#3002	1	1	yes	characteristic
389	C₂×C₇₉	#3168	1	1	yes	characteristic
390	C₂×C₇₉	#3180	1	1	yes	characteristic
391	C₂×C₇₉	#3247	1	1	yes	characteristic
392	C₂×C₇₉	#3250	1	1	yes	characteristic
393	C₂×#529	C₂×C₇₉	1	1	yes	characteristic, complemented
394	C₂×#466	C₂×C₇₉	1	1	yes	characteristic
395	C₂×#465	C₂×C₇₉	1	1	yes	characteristic, complemented
396	#2854	C₂×C₇₉	1	1	yes	characteristic, complemented
397	#2059	C₂×C₇₉	1	1	yes	characteristic, complemented
398	#2042	C₂×C₇₉	1	1	yes	characteristic, complemented
399	#2025	C₂×C₇₉	1	1	yes	characteristic, complemented
400	#2012	C₂×C₇₉	1	1	yes	characteristic, complemented
401	#1893	C₂×C₇₉	1	1	yes	characteristic, complemented
402	#1892	C₂×C₇₉	1	1	yes	characteristic, complemented
403	#1880	C₂×C₇₉	1	1	yes	characteristic, complemented
404	#1879	C₂×C₇₉	1	1	yes	characteristic, complemented
405	#1864	C₂×C₇₉	1	1	yes	characteristic, complemented
406	#1863	C₂×C₇₉	1	1	yes	characteristic, complemented
407	C₂×#336	C₂×C₇₉	1	1	yes	characteristic, complemented
408	C₇₉	#25500	1	1	yes	characteristic, direct product factor, Sylow
409	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
410	C₂²×D₈	C₂²×C₇₉	1	1	yes	characteristic
411	C₂³×C₈	C₂²×C₇₉	1	1	yes	characteristic
412	C₂³×C₈	C₂²×C₇₉	1	1	yes	characteristic
413	#529	—	2	4	no	—
414	#529	—	2	4	no	—
415	C₂×#126	—	2	1	no	—
416	C₂×#125	C₂²×C₇₉	1	1	yes	characteristic
417	C₂×#124	C₂²×C₇₉	1	1	yes	characteristic
418	C₂×#123	—	2	1	no	—
419	C₂×#123	—	2	1	no	—
420	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
421	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
422	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
423	C₂×C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
424	C₂×C₄×D₄	—	2	1	no	—
425	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
426	C₂×#117	—	2	1	no	—
427	C₂²×C₄²	C₂²×C₇₉	1	1	yes	characteristic
428	#466	—	2	4	no	—
429	#465	—	2	4	no	—
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×#102	C₂²×C₇₉	1	1	yes	characteristic
439	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
440	#390	C₂²×C₇₉	1	1	yes	characteristic
441	#390	C₂²×C₇₉	1	1	yes	characteristic
442	#389	C₂²×C₇₉	1	1	yes	characteristic
443	#389	C₂²×C₇₉	1	1	yes	characteristic
444	#388	—	2	1	no	—
445	#388	—	2	1	no	—
446	#386	—	2	1	no	—
447	#380	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	#336	C₂²×C₇₉	1	1	yes	characteristic
453	#336	C₂²×C₇₉	1	1	yes	characteristic
454	#336	C₂²×C₇₉	1	1	yes	characteristic
455	#336	C₂²×C₇₉	1	1	yes	characteristic
456	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
457	C₂²×D₄	—	2	1	no	—
458	C₂²×D₄	—	2	1	no	—
459	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
460	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
461	C₂³×C₄	—	2	1	no	—
462	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
463	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
464	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
465	C₂×SD₁₆	—	2	2	no	—
466	C₂×SD₁₆	—	2	2	no	—
467	C₂×SD₁₆	—	4	1	no	—
468	C₂×D₈	—	2	2	no	—
469	C₂×D₈	—	2	2	no	—
470	C₂×D₈	—	4	1	no	—
471	C₂²×C₈	—	2	2	no	—
472	C₂²×C₈	—	2	2	no	—
473	C₂²×C₈	—	2	2	no	—
474	C₂²×C₈	—	2	2	no	—
475	C₂²×C₈	—	4	1	no	—
476	C₂²×C₈	—	4	1	no	—
477	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
478	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
479	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
480	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
481	#126	—	2	8	no	—
482	#125	—	2	2	no	—
483	#125	—	2	2	no	—
484	#124	—	2	2	no	—
485	#124	—	2	2	no	—
486	#123	—	2	8	no	—
487	#123	—	4	4	no	—
488	C₂²⋊Q₈	—	2	2	no	—
489	C₂²⋊Q₈	D₄×C₇₉	1	4	yes	—
490	#121	—	2	2	no	—
491	#121	—	2	2	no	—
492	#121	—	2	2	no	—
493	#121	D₄×C₇₉	1	4	yes	—
494	C₄×Q₈	—	2	2	no	—
495	C₄×Q₈	—	2	2	no	—
496	C₄×D₄	—	2	8	no	—
497	C₄×D₄	—	2	2	no	—
498	C₄×D₄	—	2	2	no	—
499	#117	—	2	8	no	—
500	C₂×C₄⋊C₄	—	2	1	no	—
501	C₂×C₄⋊C₄	—	2	1	no	—
502	C₂×C₄⋊C₄	—	2	1	no	—
503	C₂×C₄⋊C₄	—	2	1	no	—
504	C₂×C₄⋊C₄	—	2	1	no	—
505	C₂×C₄⋊C₄	—	2	1	no	—
506	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂³×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×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	—	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×C₄²	—	2	1	no	—
523	C₂×C₄²	—	2	2	no	—
524	C₂×C₄²	—	2	2	no	—
525	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
526	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
527	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
528	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
529	#107	—	2	2	no	—
530	#106	—	2	2	no	—
531	#103	—	2	2	no	—
532	#103	—	2	2	no	—
533	#103	—	4	1	no	—
534	#102	—	2	2	no	—
535	#102	—	2	2	no	—
536	#102	—	2	2	no	—
537	#102	—	2	2	no	—
538	#102	—	4	1	no	—
539	#95	—	2	1	no	—
540	#95	—	2	1	no	—
541	#95	—	2	1	no	—
542	C₂⁴	—	2	1	no	—
543	C₂⁴	—	2	1	no	—
544	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
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	—	2	1	no	—
550	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
551	C₂×D₄	—	2	4	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	—	2	1	no	—
559	C₂×D₄	—	2	1	no	—
560	C₂×D₄	—	2	1	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	—	4	2	no	—
564	C₂×D₄	—	4	2	no	—
565	C₂×D₄	—	4	2	no	—
566	C₂×D₄	—	4	2	no	—
567	C₂×D₄	—	4	2	no	—
568	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
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	4	no	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	4	1	no	—
586	C₂²×C₄	—	4	2	no	—
587	C₂²×C₄	—	4	2	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	C₂×D₄×C₇₉	1	1	yes	characteristic
595	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
596	SD₁₆	—	4	4	no	—
597	D₈	—	4	4	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	—	4	4	no	—
609	C₂×C₈	—	4	4	no	—
610	C₂×C₈	#41×C₇₉	1	2	yes	—
611	C₂×C₈	#41×C₇₉	1	2	yes	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	4	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	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	4	2	no	—
634	C₂²⋊C₄	—	4	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	C₄²	—	2	4	no	—
640	C₄²	—	2	2	no	—
641	C₄²	—	2	2	no	—
642	C₄²	—	2	1	no	—
643	C₄²	—	2	1	no	—
644	C₄²	—	2	1	no	—
645	C₄²	—	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	2	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	—	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	—	4	1	no	—
664	C₂³	#120×C₇₉	1	2	yes	—
665	C₂³	#135×C₇₉	1	2	yes	—
666	C₂³	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
667	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
668	Q₈	—	2	2	no	—
669	Q₈	—	2	2	no	—
670	Q₈	—	4	1	no	—
671	Q₈	—	4	1	no	—
672	D₄	—	2	2	no	—
673	D₄	—	2	2	no	—
674	D₄	—	4	8	no	—
675	D₄	—	4	1	no	—
676	D₄	—	4	1	no	—
677	D₄	—	4	1	no	—
678	D₄	—	4	1	no	—
679	D₄	—	4	1	no	—
680	D₄	—	4	1	no	—
681	D₄	—	8	4	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	4	4	no	—
703	C₂×C₄	—	4	8	no	—
704	C₂×C₄	—	4	4	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	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	#120×C₇₉	1	2	yes	—
721	C₂×C₄	#135×C₇₉	1	2	yes	—
722	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
723	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
724	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
725	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
726	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
727	C₂×C₄	2₋¹⁺⁴×C₇₉	1	1	yes	characteristic
728	C₈	—	2	2	no	—
729	C₈	—	2	2	no	—
730	C₈	—	4	1	no	—
731	C₈	—	4	1	no	—
732	C₂²	—	2	2	no	—
733	C₂²	—	2	2	no	—
734	C₂²	—	2	2	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	2	2	no	—
737	C₂²	—	2	2	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	8	1	no	—
742	C₂²	—	8	1	no	—
743	C₂²	—	8	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	—	8	1	no	—
752	C₂²	#449×C₇₉	1	4	yes	—
753	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
754	C₂²	#532×C₇₉	1	1	yes	characteristic
755	C₂²	#537×C₇₉	1	1	yes	characteristic
756	C₂²	C₂×#135×C₇₉	1	1	yes	characteristic
757	C₂²	C₂×#135×C₇₉	1	1	yes	characteristic
758	C₂²	C₂×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
759	C₂²	#575×C₇₉	1	1	yes	characteristic
760	C₄	—	2	2	no	—
761	C₄	—	2	2	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	1	no	—
764	C₄	—	4	1	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	1	no	—
767	C₄	—	4	2	no	—
768	C₄	—	8	1	no	—
769	C₄	—	8	1	no	—
770	C₄	—	8	1	no	—
771	C₄	#546×C₇₉	1	1	yes	characteristic
772	C₄	#546×C₇₉	1	1	yes	characteristic
773	C₄	#547×C₇₉	1	1	yes	characteristic
774	C₄	#547×C₇₉	1	1	yes	characteristic
775	C₂	—	2	4	no	—
776	C₂	—	8	2	no	—
777	C₂	—	16	1	no	—
778	C₂	C₇₉×#2430	1	1	yes	characteristic
779	C₂	C₂×#449×C₇₉	1	1	yes	characteristic
780	C₂	C₇₉×#3002	1	1	yes	characteristic
781	C₂	C₇₉×#3168	1	1	yes	characteristic
782	C₂	C₇₉×#3180	1	1	yes	characteristic
783	C₂	C₇₉×#3247	1	1	yes	characteristic
784	C₂	C₇₉×#3250	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₂×#466×C₇₉	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ C₂²×C₄²×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#529×C₇₉	C₂	semidirect
3. C₂×#465×C₇₉	C₂	semidirect
4. C₇₉×#2854	C₂	semidirect
5. C₇₉×#2059	C₂	semidirect
6. C₇₉×#2042	C₂	semidirect
7. C₇₉×#2025	C₂	semidirect
8. C₇₉×#2012	C₂	semidirect
9. C₇₉×#1893	C₂	semidirect
10. C₇₉×#1892	C₂	semidirect
11. C₇₉×#1880	C₂	semidirect
12. C₇₉×#1879	C₂	semidirect
13. C₇₉×#1864	C₂	semidirect
14. C₇₉×#1863	C₂	semidirect
15. C₂×#336×C₇₉	C₂	semidirect
382. #25500	C₇₉	direct (N × H)
393. C₂×#529	C₂×C₇₉	semidirect
395. C₂×#465	C₂×C₇₉	semidirect
396. #2854	C₂×C₇₉	semidirect
397. #2059	C₂×C₇₉	semidirect
398. #2042	C₂×C₇₉	semidirect
399. #2025	C₂×C₇₉	semidirect
400. #2012	C₂×C₇₉	semidirect
401. #1893	C₂×C₇₉	semidirect
402. #1892	C₂×C₇₉	semidirect
403. #1880	C₂×C₇₉	semidirect
404. #1879	C₂×C₇₉	semidirect
405. #1864	C₂×C₇₉	semidirect
406. #1863	C₂×C₇₉	semidirect
407. C₂×#336	C₂×C₇₉	semidirect
408. C₇₉	#25500	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#529×C₇₉	2
C₂×#466×C₇₉	2
C₂×#465×C₇₉	2
C₇₉×#2854	2
C₇₉×#2059	2
C₇₉×#2042	2
C₇₉×#2025	2
C₇₉×#2012	2
C₇₉×#1893	2
C₇₉×#1892	2
C₇₉×#1880	2
C₇₉×#1879	2
C₇₉×#1864	2
C₇₉×#1863	2
C₂×#336×C₇₉	2
#25500	79

Subgroups — C79×#25500 #34137189

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#25500 #34137189