Subgroups — C₇₉×#26786 #34138475

Order 20224.

904 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#483×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#476×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#2492	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#2361	C₂	1	1	yes	maximal, characteristic
5	C₇₉×#2066	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₉×#2058	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#2034	C₂	1	1	yes	maximal, characteristic
8	C₇₉×#2000	C₂	1	1	yes	maximal, characteristic
9	C₇₉×#1968	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#1927	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1926	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₉×#1923	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₉×#1877	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₉×#1853	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#106×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
19	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₇₉	—	2	1	no	—
21	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
23	#483×C₇₉	—	2	4	no	—
24	#476×C₇₉	—	2	4	no	—
25	C₂×#106×C₇₉	C₂²	1	1	yes	characteristic
26	C₂×#106×C₇₉	C₂²	1	1	yes	characteristic
27	C₂×#106×C₇₉	C₂²	1	1	yes	characteristic
28	C₂×#106×C₇₉	C₂²	1	1	yes	characteristic
29	C₂×#106×C₇₉	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
31	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
32	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
33	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
34	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
35	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
36	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
40	#400×C₇₉	—	2	1	no	—
41	#393×C₇₉	—	2	1	no	—
42	#391×C₇₉	—	2	1	no	—
43	#391×C₇₉	C₂²	1	1	yes	characteristic
44	#391×C₇₉	C₂²	1	1	yes	characteristic
45	#390×C₇₉	C₂²	1	1	yes	characteristic
46	#389×C₇₉	C₂²	1	1	yes	characteristic
47	#388×C₇₉	—	2	1	no	—
48	#388×C₇₉	—	2	1	no	—
49	#386×C₇₉	—	2	1	no	—
50	#385×C₇₉	—	2	1	no	—
51	#380×C₇₉	C₂²	1	1	yes	characteristic
52	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
53	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊C₄×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	C₂²×Q₈×C₇₉	—	2	1	no	—
62	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₇₉	—	2	1	no	—
64	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₇₉	—	2	1	no	—
66	C₂³×C₄×C₇₉	—	2	1	no	—
67	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
68	C₂×SD₁₆×C₇₉	—	2	2	no	—
69	C₂×SD₁₆×C₇₉	—	2	2	no	—
70	C₂×SD₁₆×C₇₉	—	4	1	no	—
71	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
75	C₄⋊Q₈×C₇₉	—	2	2	no	—
76	C₄⋊Q₈×C₇₉	—	4	1	no	—
77	C₂²⋊Q₈×C₇₉	—	2	2	no	—
78	C₂²⋊Q₈×C₇₉	—	4	1	no	—
79	#121×C₇₉	—	2	2	no	—
80	#121×C₇₉	—	2	2	no	—
81	C₄×D₄×C₇₉	—	2	2	no	—
82	C₄×D₄×C₇₉	—	4	1	no	—
83	C₄×D₄×C₇₉	—	4	4	no	—
84	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
85	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
88	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
89	C₂×C₄⋊C₄×C₇₉	—	4	1	no	—
90	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₇₉	—	2	1	no	—
105	C₂×C₄²×C₇₉	—	2	1	no	—
106	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
108	#106×C₇₉	—	2	2	no	—
109	#106×C₇₉	—	2	2	no	—
110	#106×C₇₉	—	2	2	no	—
111	#106×C₇₉	—	4	1	no	—
112	#106×C₇₉	D₄	1	4	yes	complemented
113	C₄⋊C₈×C₇₉	—	2	2	no	—
114	#103×C₇₉	—	2	2	no	—
115	#103×C₇₉	—	2	2	no	—
116	#103×C₇₉	—	2	2	no	—
117	#102×C₇₉	—	2	2	no	—
118	#102×C₇₉	—	2	2	no	—
119	#102×C₇₉	—	2	2	no	—
120	C₂²⋊C₈×C₇₉	—	2	2	no	—
121	C₂²⋊C₈×C₇₉	—	2	2	no	—
122	C₄×C₈×C₇₉	—	2	2	no	—
123	#95×C₇₉	—	2	1	no	—
124	#95×C₇₉	—	2	1	no	—
125	#95×C₇₉	—	2	1	no	—
126	#95×C₇₉	—	2	1	no	—
127	#95×C₇₉	—	2	1	no	—
128	#95×C₇₉	—	2	1	no	—
129	#95×C₇₉	—	2	1	no	—
130	#95×C₇₉	—	2	1	no	—
131	#95×C₇₉	D₄	1	1	yes	characteristic
132	#95×C₇₉	D₄	1	1	yes	characteristic
133	C₂⁴×C₇₉	—	2	1	no	—
134	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
135	C₂×Q₈×C₇₉	—	2	1	no	—
136	C₂×Q₈×C₇₉	—	2	1	no	—
137	C₂×Q₈×C₇₉	—	2	1	no	—
138	C₂×Q₈×C₇₉	—	2	1	no	—
139	C₂×Q₈×C₇₉	—	2	1	no	—
140	C₂×Q₈×C₇₉	—	2	1	no	—
141	C₂×Q₈×C₇₉	—	4	2	no	—
142	C₂×Q₈×C₇₉	—	4	2	no	—
143	C₂×Q₈×C₇₉	—	8	1	no	—
144	C₂×D₄×C₇₉	—	2	4	no	—
145	C₂×D₄×C₇₉	—	2	1	no	—
146	C₂×D₄×C₇₉	—	2	1	no	—
147	C₂×D₄×C₇₉	—	2	1	no	—
148	C₂×D₄×C₇₉	—	2	1	no	—
149	C₂×D₄×C₇₉	—	2	1	no	—
150	C₂×D₄×C₇₉	—	4	2	no	—
151	C₂×D₄×C₇₉	—	4	2	no	—
152	C₂×D₄×C₇₉	#41	1	2	yes	—
153	C₂²×C₄×C₇₉	—	2	1	no	—
154	C₂²×C₄×C₇₉	—	2	1	no	—
155	C₂²×C₄×C₇₉	—	2	1	no	—
156	C₂²×C₄×C₇₉	—	2	1	no	—
157	C₂²×C₄×C₇₉	—	2	1	no	—
158	C₂²×C₄×C₇₉	—	2	1	no	—
159	C₂²×C₄×C₇₉	—	2	1	no	—
160	C₂²×C₄×C₇₉	—	2	1	no	—
161	C₂²×C₄×C₇₉	—	2	1	no	—
162	C₂²×C₄×C₇₉	—	2	1	no	—
163	C₂²×C₄×C₇₉	—	2	1	no	—
164	C₂²×C₄×C₇₉	—	2	1	no	—
165	C₂²×C₄×C₇₉	—	2	1	no	—
166	C₂²×C₄×C₇₉	—	4	2	no	—
167	C₂²×C₄×C₇₉	—	4	2	no	—
168	C₂²×C₄×C₇₉	—	4	2	no	—
169	C₂²×C₄×C₇₉	—	4	2	no	—
170	C₂²×C₄×C₇₉	—	8	1	no	—
171	C₂²×C₄×C₇₉	—	8	1	no	—
172	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
178	SD₁₆×C₇₉	—	4	4	no	—
179	C₂×C₈×C₇₉	—	2	1	no	—
180	C₂×C₈×C₇₉	—	2	1	no	—
181	C₂×C₈×C₇₉	—	2	1	no	—
182	C₂×C₈×C₇₉	—	2	1	no	—
183	C₂×C₈×C₇₉	—	2	1	no	—
184	C₂×C₈×C₇₉	—	2	1	no	—
185	C₂×C₈×C₇₉	—	2	1	no	—
186	C₂×C₈×C₇₉	—	2	1	no	—
187	C₂×C₈×C₇₉	—	2	1	no	—
188	C₂×C₈×C₇₉	—	2	1	no	—
189	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
190	C₂×C₈×C₇₉	#41	1	2	yes	—
191	C₄⋊C₄×C₇₉	—	2	1	no	—
192	C₄⋊C₄×C₇₉	—	2	1	no	—
193	C₄⋊C₄×C₇₉	—	2	1	no	—
194	C₄⋊C₄×C₇₉	—	2	1	no	—
195	C₄⋊C₄×C₇₉	—	2	1	no	—
196	C₄⋊C₄×C₇₉	—	2	1	no	—
197	C₄⋊C₄×C₇₉	—	2	1	no	—
198	C₄⋊C₄×C₇₉	—	2	1	no	—
199	C₄⋊C₄×C₇₉	—	2	1	no	—
200	C₄⋊C₄×C₇₉	—	4	2	no	—
201	C₄⋊C₄×C₇₉	—	4	2	no	—
202	C₄⋊C₄×C₇₉	—	4	2	no	—
203	C₄⋊C₄×C₇₉	—	4	2	no	—
204	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
205	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
206	C₄⋊C₄×C₇₉	#41	1	2	yes	—
207	C₂²⋊C₄×C₇₉	—	2	4	no	—
208	C₂²⋊C₄×C₇₉	—	4	1	no	—
209	C₂²⋊C₄×C₇₉	—	4	2	no	—
210	C₂²⋊C₄×C₇₉	—	4	2	no	—
211	C₂²⋊C₄×C₇₉	—	4	2	no	—
212	C₂²⋊C₄×C₇₉	—	8	1	no	—
213	C₂²⋊C₄×C₇₉	—	8	1	no	—
214	C₂²⋊C₄×C₇₉	SD₁₆	1	4	yes	complemented
215	C₄²×C₇₉	—	2	1	no	—
216	C₄²×C₇₉	—	2	1	no	—
217	C₄²×C₇₉	—	2	1	no	—
218	C₄²×C₇₉	—	2	1	no	—
219	C₄²×C₇₉	—	4	2	no	—
220	C₄²×C₇₉	—	8	1	no	—
221	C₂³×C₇₉	—	2	1	no	—
222	C₂³×C₇₉	—	2	1	no	—
223	C₂³×C₇₉	—	2	1	no	—
224	C₂³×C₇₉	—	2	1	no	—
225	C₂³×C₇₉	—	2	1	no	—
226	C₂³×C₇₉	—	2	1	no	—
227	C₂³×C₇₉	—	2	2	no	—
228	C₂³×C₇₉	—	4	1	no	—
229	C₂³×C₇₉	—	4	1	no	—
230	C₂³×C₇₉	—	4	1	no	—
231	C₂³×C₇₉	—	4	1	no	—
232	C₂³×C₇₉	—	4	1	no	—
233	C₂³×C₇₉	—	4	1	no	—
234	C₂³×C₇₉	C₂×SD₁₆	1	2	yes	—
235	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
236	Q₈×C₇₉	—	4	1	no	—
237	Q₈×C₇₉	—	4	1	no	—
238	Q₈×C₇₉	—	4	1	no	—
239	Q₈×C₇₉	—	4	1	no	—
240	Q₈×C₇₉	—	8	4	no	—
241	D₄×C₇₉	—	2	2	no	—
242	D₄×C₇₉	—	2	2	no	—
243	D₄×C₇₉	—	4	8	no	—
244	D₄×C₇₉	—	4	1	no	—
245	D₄×C₇₉	—	4	1	no	—
246	C₂×C₄×C₇₉	—	2	1	no	—
247	C₂×C₄×C₇₉	—	2	1	no	—
248	C₂×C₄×C₇₉	—	2	1	no	—
249	C₂×C₄×C₇₉	—	2	1	no	—
250	C₂×C₄×C₇₉	—	2	1	no	—
251	C₂×C₄×C₇₉	—	2	2	no	—
252	C₂×C₄×C₇₉	—	2	1	no	—
253	C₂×C₄×C₇₉	—	2	2	no	—
254	C₂×C₄×C₇₉	—	2	2	no	—
255	C₂×C₄×C₇₉	—	2	1	no	—
256	C₂×C₄×C₇₉	—	2	1	no	—
257	C₂×C₄×C₇₉	—	2	1	no	—
258	C₂×C₄×C₇₉	—	2	1	no	—
259	C₂×C₄×C₇₉	—	2	1	no	—
260	C₂×C₄×C₇₉	—	2	1	no	—
261	C₂×C₄×C₇₉	—	2	1	no	—
262	C₂×C₄×C₇₉	—	4	1	no	—
263	C₂×C₄×C₇₉	—	4	1	no	—
264	C₂×C₄×C₇₉	—	4	1	no	—
265	C₂×C₄×C₇₉	—	4	1	no	—
266	C₂×C₄×C₇₉	—	4	1	no	—
267	C₂×C₄×C₇₉	—	4	1	no	—
268	C₂×C₄×C₇₉	—	4	1	no	—
269	C₂×C₄×C₇₉	—	4	1	no	—
270	C₂×C₄×C₇₉	—	4	1	no	—
271	C₂×C₄×C₇₉	—	4	1	no	—
272	C₂×C₄×C₇₉	—	4	1	no	—
273	C₂×C₄×C₇₉	—	4	1	no	—
274	C₂×C₄×C₇₉	—	4	1	no	—
275	C₂×C₄×C₇₉	—	4	1	no	—
276	C₂×C₄×C₇₉	—	4	1	no	—
277	C₂×C₄×C₇₉	—	4	1	no	—
278	C₂×C₄×C₇₉	—	4	1	no	—
279	C₂×C₄×C₇₉	—	4	1	no	—
280	C₂×C₄×C₇₉	—	4	1	no	—
281	C₂×C₄×C₇₉	—	4	1	no	—
282	C₂×C₄×C₇₉	—	4	1	no	—
283	C₂×C₄×C₇₉	—	4	1	no	—
284	C₂×C₄×C₇₉	—	8	4	no	—
285	C₂×C₄×C₇₉	—	8	4	no	—
286	C₂×C₄×C₇₉	C₂×SD₁₆	1	2	yes	—
287	C₂×C₄×C₇₉	C₂×SD₁₆	1	2	yes	—
288	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
289	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
290	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
291	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
292	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
293	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
294	C₈×C₇₉	—	2	2	no	—
295	C₈×C₇₉	—	2	2	no	—
296	C₈×C₇₉	—	4	1	no	—
297	C₈×C₇₉	—	4	1	no	—
298	C₂²×C₇₉	—	2	2	no	—
299	C₂²×C₇₉	—	2	2	no	—
300	C₂²×C₇₉	—	2	2	no	—
301	C₂²×C₇₉	—	4	1	no	—
302	C₂²×C₇₉	—	4	1	no	—
303	C₂²×C₇₉	—	4	1	no	—
304	C₂²×C₇₉	—	4	1	no	—
305	C₂²×C₇₉	—	4	2	no	—
306	C₂²×C₇₉	—	4	2	no	—
307	C₂²×C₇₉	—	4	2	no	—
308	C₂²×C₇₉	—	8	1	no	—
309	C₂²×C₇₉	—	8	1	no	—
310	C₂²×C₇₉	—	8	1	no	—
311	C₂²×C₇₉	—	8	1	no	—
312	C₂²×C₇₉	#525	1	1	yes	characteristic
313	C₂²×C₇₉	D₄²	1	1	yes	characteristic
314	C₂²×C₇₉	#547	1	1	yes	characteristic
315	C₂²×C₇₉	C₂²×SD₁₆	1	1	yes	characteristic
316	C₂²×C₇₉	#575	1	1	yes	characteristic
317	C₂²×C₇₉	#577	1	1	yes	characteristic
318	C₂²×C₇₉	#577	1	1	yes	characteristic
319	C₄×C₇₉	—	2	2	no	—
320	C₄×C₇₉	—	2	2	no	—
321	C₄×C₇₉	—	4	1	no	—
322	C₄×C₇₉	—	4	2	no	—
323	C₄×C₇₉	—	4	1	no	—
324	C₄×C₇₉	—	4	1	no	—
325	C₄×C₇₉	—	4	2	no	—
326	C₄×C₇₉	—	4	2	no	—
327	C₄×C₇₉	—	8	1	no	—
328	C₄×C₇₉	—	8	1	no	—
329	C₄×C₇₉	—	8	1	no	—
330	C₄×C₇₉	—	8	1	no	—
331	C₄×C₇₉	#532	1	1	yes	characteristic
332	C₄×C₇₉	#542	1	1	yes	characteristic
333	C₄×C₇₉	#548	1	1	yes	characteristic
334	C₄×C₇₉	#551	1	1	yes	characteristic
335	#26786	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
336	C₂×C₇₉	—	4	2	no	—
337	C₂×C₇₉	—	8	2	no	—
338	C₂×C₇₉	#2461	1	1	yes	characteristic
339	C₂×C₇₉	#3101	1	1	yes	characteristic
340	C₂×C₇₉	#3125	1	1	yes	characteristic
341	C₂×C₇₉	#3275	1	1	yes	characteristic
342	C₂×C₇₉	D₄×SD₁₆	1	1	yes	characteristic
343	C₂×C₇₉	#3335	1	1	yes	characteristic
344	C₂×C₇₉	#3350	1	1	yes	characteristic
345	C₂×#483	C₂×C₇₉	1	1	yes	characteristic, complemented
346	C₂×#476	C₂×C₇₉	1	1	yes	characteristic, complemented
347	#2492	C₂×C₇₉	1	1	yes	characteristic, complemented
348	#2361	C₂×C₇₉	1	1	yes	characteristic
349	#2066	C₂×C₇₉	1	1	yes	characteristic, complemented
350	#2058	C₂×C₇₉	1	1	yes	characteristic, complemented
351	#2034	C₂×C₇₉	1	1	yes	characteristic
352	#2000	C₂×C₇₉	1	1	yes	characteristic
353	#1968	C₂×C₇₉	1	1	yes	characteristic, complemented
354	#1927	C₂×C₇₉	1	1	yes	characteristic, complemented
355	#1926	C₂×C₇₉	1	1	yes	characteristic, complemented
356	#1923	C₂×C₇₉	1	1	yes	characteristic, complemented
357	#1877	C₂×C₇₉	1	1	yes	characteristic, complemented
358	#1853	C₂×C₇₉	1	1	yes	characteristic, complemented
359	C₄×#106	C₂×C₇₉	1	1	yes	characteristic, complemented
360	C₇₉	#26786	1	1	yes	characteristic, direct product factor, Sylow
361	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
362	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
363	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
364	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
365	C₂×C₄×D₄	—	2	1	no	—
366	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
367	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
368	#483	—	2	4	no	—
369	#476	—	2	4	no	—
370	C₂×#106	C₂²×C₇₉	1	1	yes	characteristic
371	C₂×#106	C₂²×C₇₉	1	1	yes	characteristic
372	C₂×#106	C₂²×C₇₉	1	1	yes	characteristic
373	C₂×#106	C₂²×C₇₉	1	1	yes	characteristic
374	C₂×#106	C₂²×C₇₉	1	1	yes	characteristic
375	C₂×C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
376	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
377	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
378	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
379	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
380	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
381	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
382	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
383	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
384	C₂×C₄×C₈	C₂²×C₇₉	1	1	yes	characteristic
385	#400	—	2	1	no	—
386	#393	—	2	1	no	—
387	#391	—	2	1	no	—
388	#391	C₂²×C₇₉	1	1	yes	characteristic
389	#391	C₂²×C₇₉	1	1	yes	characteristic
390	#390	C₂²×C₇₉	1	1	yes	characteristic
391	#389	C₂²×C₇₉	1	1	yes	characteristic
392	#388	—	2	1	no	—
393	#388	—	2	1	no	—
394	#386	—	2	1	no	—
395	#385	—	2	1	no	—
396	#380	C₂²×C₇₉	1	1	yes	characteristic
397	C₄×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
398	C₄×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
399	C₄×C₂²⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
400	#340	C₂²×C₇₉	1	1	yes	characteristic
401	#340	C₂²×C₇₉	1	1	yes	characteristic
402	#340	C₂²×C₇₉	1	1	yes	characteristic
403	#340	C₂²×C₇₉	1	1	yes	characteristic
404	#336	C₂²×C₇₉	1	1	yes	characteristic
405	#336	C₂²×C₇₉	1	1	yes	characteristic
406	C₂²×Q₈	—	2	1	no	—
407	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
408	C₂²×D₄	—	2	1	no	—
409	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
410	C₂³×C₄	—	2	1	no	—
411	C₂³×C₄	—	2	1	no	—
412	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
413	C₂×SD₁₆	—	2	2	no	—
414	C₂×SD₁₆	—	2	2	no	—
415	C₂×SD₁₆	—	4	1	no	—
416	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
417	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
418	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
419	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
420	C₄⋊Q₈	—	2	2	no	—
421	C₄⋊Q₈	—	4	1	no	—
422	C₂²⋊Q₈	—	2	2	no	—
423	C₂²⋊Q₈	—	4	1	no	—
424	#121	—	2	2	no	—
425	#121	—	2	2	no	—
426	C₄×D₄	—	2	2	no	—
427	C₄×D₄	—	4	1	no	—
428	C₄×D₄	—	4	4	no	—
429	C₂×C₄⋊C₄	—	2	2	no	—
430	C₂×C₄⋊C₄	—	2	1	no	—
431	C₂×C₄⋊C₄	—	2	1	no	—
432	C₂×C₄⋊C₄	—	2	1	no	—
433	C₂×C₄⋊C₄	—	2	1	no	—
434	C₂×C₄⋊C₄	—	4	1	no	—
435	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
439	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
440	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
441	C₂×C₂²⋊C₄	—	2	1	no	—
442	C₂×C₂²⋊C₄	—	2	1	no	—
443	C₂×C₂²⋊C₄	—	2	1	no	—
444	C₂×C₂²⋊C₄	—	2	1	no	—
445	C₂×C₂²⋊C₄	—	2	1	no	—
446	C₂×C₂²⋊C₄	—	2	1	no	—
447	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
448	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
449	C₂×C₄²	—	2	1	no	—
450	C₂×C₄²	—	2	1	no	—
451	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
452	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
453	#106	—	2	2	no	—
454	#106	—	2	2	no	—
455	#106	—	2	2	no	—
456	#106	—	4	1	no	—
457	#106	D₄×C₇₉	1	4	yes	complemented
458	C₄⋊C₈	—	2	2	no	—
459	#103	—	2	2	no	—
460	#103	—	2	2	no	—
461	#103	—	2	2	no	—
462	#102	—	2	2	no	—
463	#102	—	2	2	no	—
464	#102	—	2	2	no	—
465	C₂²⋊C₈	—	2	2	no	—
466	C₂²⋊C₈	—	2	2	no	—
467	C₄×C₈	—	2	2	no	—
468	#95	—	2	1	no	—
469	#95	—	2	1	no	—
470	#95	—	2	1	no	—
471	#95	—	2	1	no	—
472	#95	—	2	1	no	—
473	#95	—	2	1	no	—
474	#95	—	2	1	no	—
475	#95	—	2	1	no	—
476	#95	D₄×C₇₉	1	1	yes	characteristic
477	#95	D₄×C₇₉	1	1	yes	characteristic
478	C₂⁴	—	2	1	no	—
479	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×Q₈	—	2	1	no	—
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	2	1	no	—
486	C₂×Q₈	—	4	2	no	—
487	C₂×Q₈	—	4	2	no	—
488	C₂×Q₈	—	8	1	no	—
489	C₂×D₄	—	2	4	no	—
490	C₂×D₄	—	2	1	no	—
491	C₂×D₄	—	2	1	no	—
492	C₂×D₄	—	2	1	no	—
493	C₂×D₄	—	2	1	no	—
494	C₂×D₄	—	2	1	no	—
495	C₂×D₄	—	4	2	no	—
496	C₂×D₄	—	4	2	no	—
497	C₂×D₄	#41×C₇₉	1	2	yes	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	4	2	no	—
512	C₂²×C₄	—	4	2	no	—
513	C₂²×C₄	—	4	2	no	—
514	C₂²×C₄	—	4	2	no	—
515	C₂²×C₄	—	8	1	no	—
516	C₂²×C₄	—	8	1	no	—
517	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
518	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
519	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
520	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
521	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
522	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
523	SD₁₆	—	4	4	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	—	2	1	no	—
534	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
535	C₂×C₈	#41×C₇₉	1	2	yes	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	1	no	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	4	2	no	—
546	C₄⋊C₄	—	4	2	no	—
547	C₄⋊C₄	—	4	2	no	—
548	C₄⋊C₄	—	4	2	no	—
549	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
550	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
551	C₄⋊C₄	#41×C₇₉	1	2	yes	—
552	C₂²⋊C₄	—	2	4	no	—
553	C₂²⋊C₄	—	4	1	no	—
554	C₂²⋊C₄	—	4	2	no	—
555	C₂²⋊C₄	—	4	2	no	—
556	C₂²⋊C₄	—	4	2	no	—
557	C₂²⋊C₄	—	8	1	no	—
558	C₂²⋊C₄	—	8	1	no	—
559	C₂²⋊C₄	SD₁₆×C₇₉	1	4	yes	complemented
560	C₄²	—	2	1	no	—
561	C₄²	—	2	1	no	—
562	C₄²	—	2	1	no	—
563	C₄²	—	2	1	no	—
564	C₄²	—	4	2	no	—
565	C₄²	—	8	1	no	—
566	C₂³	—	2	1	no	—
567	C₂³	—	2	1	no	—
568	C₂³	—	2	1	no	—
569	C₂³	—	2	1	no	—
570	C₂³	—	2	1	no	—
571	C₂³	—	2	1	no	—
572	C₂³	—	2	2	no	—
573	C₂³	—	4	1	no	—
574	C₂³	—	4	1	no	—
575	C₂³	—	4	1	no	—
576	C₂³	—	4	1	no	—
577	C₂³	—	4	1	no	—
578	C₂³	—	4	1	no	—
579	C₂³	C₂×SD₁₆×C₇₉	1	2	yes	—
580	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
581	Q₈	—	4	1	no	—
582	Q₈	—	4	1	no	—
583	Q₈	—	4	1	no	—
584	Q₈	—	4	1	no	—
585	Q₈	—	8	4	no	—
586	D₄	—	2	2	no	—
587	D₄	—	2	2	no	—
588	D₄	—	4	8	no	—
589	D₄	—	4	1	no	—
590	D₄	—	4	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	8	4	no	—
630	C₂×C₄	—	8	4	no	—
631	C₂×C₄	C₂×SD₁₆×C₇₉	1	2	yes	—
632	C₂×C₄	C₂×SD₁₆×C₇₉	1	2	yes	—
633	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
634	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
635	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
636	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
637	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
638	C₂×C₄	2₋¹⁺⁴×C₇₉	1	1	yes	characteristic
639	C₈	—	2	2	no	—
640	C₈	—	2	2	no	—
641	C₈	—	4	1	no	—
642	C₈	—	4	1	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	4	1	no	—
647	C₂²	—	4	1	no	—
648	C₂²	—	4	1	no	—
649	C₂²	—	4	1	no	—
650	C₂²	—	4	2	no	—
651	C₂²	—	4	2	no	—
652	C₂²	—	4	2	no	—
653	C₂²	—	8	1	no	—
654	C₂²	—	8	1	no	—
655	C₂²	—	8	1	no	—
656	C₂²	—	8	1	no	—
657	C₂²	#525×C₇₉	1	1	yes	characteristic
658	C₂²	D₄²×C₇₉	1	1	yes	characteristic
659	C₂²	#547×C₇₉	1	1	yes	characteristic
660	C₂²	C₂²×SD₁₆×C₇₉	1	1	yes	characteristic
661	C₂²	#575×C₇₉	1	1	yes	characteristic
662	C₂²	#577×C₇₉	1	1	yes	characteristic
663	C₂²	#577×C₇₉	1	1	yes	characteristic
664	C₄	—	2	2	no	—
665	C₄	—	2	2	no	—
666	C₄	—	4	1	no	—
667	C₄	—	4	2	no	—
668	C₄	—	4	2	no	—
669	C₄	—	4	1	no	—
670	C₄	—	4	2	no	—
671	C₄	—	4	1	no	—
672	C₄	—	8	1	no	—
673	C₄	—	8	1	no	—
674	C₄	—	8	1	no	—
675	C₄	—	8	1	no	—
676	C₄	#532×C₇₉	1	1	yes	characteristic
677	C₄	#542×C₇₉	1	1	yes	characteristic
678	C₄	#548×C₇₉	1	1	yes	characteristic
679	C₄	#551×C₇₉	1	1	yes	characteristic
680	C₂	—	4	2	no	—
681	C₂	—	8	2	no	—
682	C₂	C₇₉×#2461	1	1	yes	characteristic
683	C₂	C₇₉×#3101	1	1	yes	characteristic
684	C₂	C₇₉×#3125	1	1	yes	characteristic
685	C₂	C₇₉×#3275	1	1	yes	characteristic
686	C₂	D₄×SD₁₆×C₇₉	1	1	yes	characteristic
687	C₂	C₇₉×#3335	1	1	yes	characteristic
688	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	C₂×#121×C₇₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ C₄×C₂²⋊C₄×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#483×C₇₉	C₂	semidirect
2. C₂×#476×C₇₉	C₂	semidirect
3. C₇₉×#2492	C₂	semidirect
5. C₇₉×#2066	C₂	semidirect
6. C₇₉×#2058	C₂	semidirect
9. C₇₉×#1968	C₂	semidirect
10. C₇₉×#1927	C₂	semidirect
11. C₇₉×#1926	C₂	semidirect
12. C₇₉×#1923	C₂	semidirect
13. C₇₉×#1877	C₂	semidirect
14. C₇₉×#1853	C₂	semidirect
15. C₄×#106×C₇₉	C₂	semidirect
112. #106×C₇₉	D₄	semidirect
214. C₂²⋊C₄×C₇₉	SD₁₆	semidirect
335. #26786	C₇₉	direct (N × H)
345. C₂×#483	C₂×C₇₉	semidirect
346. C₂×#476	C₂×C₇₉	semidirect
347. #2492	C₂×C₇₉	semidirect
349. #2066	C₂×C₇₉	semidirect
350. #2058	C₂×C₇₉	semidirect
353. #1968	C₂×C₇₉	semidirect
354. #1927	C₂×C₇₉	semidirect
355. #1926	C₂×C₇₉	semidirect
356. #1923	C₂×C₇₉	semidirect
357. #1877	C₂×C₇₉	semidirect
358. #1853	C₂×C₇₉	semidirect
359. C₄×#106	C₂×C₇₉	semidirect
360. C₇₉	#26786	direct (N × H)
457. #106	D₄×C₇₉	semidirect
559. C₂²⋊C₄	SD₁₆×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#483×C₇₉	2
C₂×#476×C₇₉	2
C₇₉×#2492	2
C₇₉×#2361	2
C₇₉×#2066	2
C₇₉×#2058	2
C₇₉×#2034	2
C₇₉×#2000	2
C₇₉×#1968	2
C₇₉×#1927	2
C₇₉×#1926	2
C₇₉×#1923	2
C₇₉×#1877	2
C₇₉×#1853	2
C₄×#106×C₇₉	2
#26786	79

Subgroups — C79×#26786 #34138475

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#26786 #34138475