Subgroups — C₇₉×#26789 #34138478

Order 20224.

804 conjugacy classes of subgroups.

The subgroup lattice has 644 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
2	C₂×#479×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#2489	C₂	1	1	yes	maximal, characteristic
4	C₇₉×#2360	C₂	1	1	yes	maximal, characteristic
5	C₇₉×#2066	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₉×#2059	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#2035	C₂	1	1	yes	maximal, characteristic
8	C₇₉×#2001	C₂	1	1	yes	maximal, characteristic
9	C₇₉×#1969	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#1928	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1927	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₉×#1923	C₂	1	1	yes	maximal, characteristic
13	C₇₉×#1878	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₉×#1852	C₂	1	1	yes	maximal, characteristic
15	C₄×#106×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×#125×C₇₉	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
22	#483×C₇₉	—	2	4	no	—
23	#479×C₇₉	—	2	4	no	—
24	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic
25	C₂×#107×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×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
30	C₂×#103×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×#103×C₇₉	C₂²	1	1	yes	characteristic
35	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
39	#400×C₇₉	—	2	1	no	—
40	#397×C₇₉	—	2	1	no	—
41	#391×C₇₉	C₂²	1	1	yes	characteristic
42	#391×C₇₉	C₂²	1	1	yes	characteristic
43	#391×C₇₉	C₂²	1	1	yes	characteristic
44	#389×C₇₉	—	2	1	no	—
45	#389×C₇₉	C₂²	1	1	yes	characteristic
46	#388×C₇₉	—	2	1	no	—
47	#387×C₇₉	—	2	1	no	—
48	#385×C₇₉	—	2	1	no	—
49	#382×C₇₉	—	2	1	no	—
50	#380×C₇₉	C₂²	1	1	yes	characteristic
51	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
52	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
53	C₄×C₂²⋊C₄×C₇₉	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
62	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₇₉	—	2	1	no	—
64	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
65	C₂×Q₁₆×C₇₉	—	2	2	no	—
66	C₂×Q₁₆×C₇₉	—	2	2	no	—
67	C₂×Q₁₆×C₇₉	—	4	1	no	—
68	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
72	#125×C₇₉	—	2	2	no	—
73	#125×C₇₉	—	4	1	no	—
74	C₂²⋊Q₈×C₇₉	—	2	2	no	—
75	C₂²⋊Q₈×C₇₉	—	2	2	no	—
76	C₂²⋊Q₈×C₇₉	—	2	2	no	—
77	C₂²⋊Q₈×C₇₉	—	4	1	no	—
78	C₄×Q₈×C₇₉	—	2	2	no	—
79	C₄×Q₈×C₇₉	—	4	1	no	—
80	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
82	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₇₉	—	2	1	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	—	4	1	no	—
89	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₇₉	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₇₉	—	2	1	no	—
101	C₂×C₄²×C₇₉	—	2	1	no	—
102	C₂×C₄²×C₇₉	—	2	1	no	—
103	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
105	#107×C₇₉	—	2	2	no	—
106	#107×C₇₉	—	4	1	no	—
107	#106×C₇₉	—	2	2	no	—
108	#106×C₇₉	—	2	2	no	—
109	#106×C₇₉	D₄	1	4	yes	—
110	C₄⋊C₈×C₇₉	—	2	2	no	—
111	#103×C₇₉	—	2	2	no	—
112	#103×C₇₉	—	2	2	no	—
113	#103×C₇₉	—	2	2	no	—
114	#103×C₇₉	—	2	2	no	—
115	#103×C₇₉	—	2	2	no	—
116	#103×C₇₉	—	2	2	no	—
117	C₂²⋊C₈×C₇₉	—	2	2	no	—
118	C₂²⋊C₈×C₇₉	—	2	2	no	—
119	C₄×C₈×C₇₉	—	2	2	no	—
120	#95×C₇₉	—	2	1	no	—
121	#95×C₇₉	—	2	1	no	—
122	#95×C₇₉	—	2	1	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	D₄	1	1	yes	characteristic
131	#95×C₇₉	D₄	1	1	yes	characteristic
132	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
133	C₂×Q₈×C₇₉	—	2	1	no	—
134	C₂×Q₈×C₇₉	—	2	1	no	—
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	—	2	1	no	—
142	C₂×Q₈×C₇₉	—	2	1	no	—
143	C₂×Q₈×C₇₉	—	2	1	no	—
144	C₂×Q₈×C₇₉	#41	1	2	yes	—
145	C₂²×C₄×C₇₉	—	2	1	no	—
146	C₂²×C₄×C₇₉	—	2	1	no	—
147	C₂²×C₄×C₇₉	—	2	1	no	—
148	C₂²×C₄×C₇₉	—	2	1	no	—
149	C₂²×C₄×C₇₉	—	2	1	no	—
150	C₂²×C₄×C₇₉	—	2	1	no	—
151	C₂²×C₄×C₇₉	—	2	1	no	—
152	C₂²×C₄×C₇₉	—	2	1	no	—
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	—	4	2	no	—
160	C₂²×C₄×C₇₉	—	4	2	no	—
161	C₂²×C₄×C₇₉	—	8	1	no	—
162	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
168	Q₁₆×C₇₉	—	4	4	no	—
169	C₂×C₈×C₇₉	—	2	1	no	—
170	C₂×C₈×C₇₉	—	2	1	no	—
171	C₂×C₈×C₇₉	—	2	1	no	—
172	C₂×C₈×C₇₉	—	2	1	no	—
173	C₂×C₈×C₇₉	—	2	1	no	—
174	C₂×C₈×C₇₉	—	2	1	no	—
175	C₂×C₈×C₇₉	—	2	1	no	—
176	C₂×C₈×C₇₉	—	2	1	no	—
177	C₂×C₈×C₇₉	—	2	1	no	—
178	C₂×C₈×C₇₉	—	2	1	no	—
179	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
180	C₂×C₈×C₇₉	#41	1	2	yes	—
181	C₄⋊C₄×C₇₉	—	2	4	no	—
182	C₄⋊C₄×C₇₉	—	2	1	no	—
183	C₄⋊C₄×C₇₉	—	2	1	no	—
184	C₄⋊C₄×C₇₉	—	2	1	no	—
185	C₄⋊C₄×C₇₉	—	2	1	no	—
186	C₄⋊C₄×C₇₉	—	2	1	no	—
187	C₄⋊C₄×C₇₉	—	2	1	no	—
188	C₄⋊C₄×C₇₉	—	2	1	no	—
189	C₄⋊C₄×C₇₉	—	2	1	no	—
190	C₄⋊C₄×C₇₉	—	2	1	no	—
191	C₄⋊C₄×C₇₉	—	4	2	no	—
192	C₄⋊C₄×C₇₉	—	4	2	no	—
193	C₄⋊C₄×C₇₉	—	4	2	no	—
194	C₄⋊C₄×C₇₉	—	4	2	no	—
195	C₄⋊C₄×C₇₉	—	4	2	no	—
196	C₄⋊C₄×C₇₉	—	8	1	no	—
197	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
198	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
199	C₄⋊C₄×C₇₉	#41	1	2	yes	—
200	C₂²⋊C₄×C₇₉	—	2	4	no	—
201	C₂²⋊C₄×C₇₉	—	2	2	no	—
202	C₂²⋊C₄×C₇₉	—	2	2	no	—
203	C₂²⋊C₄×C₇₉	—	4	2	no	—
204	C₂²⋊C₄×C₇₉	—	4	2	no	—
205	C₄²×C₇₉	—	2	1	no	—
206	C₄²×C₇₉	—	2	1	no	—
207	C₄²×C₇₉	—	2	1	no	—
208	C₄²×C₇₉	—	2	1	no	—
209	C₄²×C₇₉	—	4	2	no	—
210	C₄²×C₇₉	—	4	2	no	—
211	C₄²×C₇₉	—	8	1	no	—
212	C₂³×C₇₉	—	2	1	no	—
213	C₂³×C₇₉	—	2	1	no	—
214	C₂³×C₇₉	—	2	1	no	—
215	C₂³×C₇₉	—	2	1	no	—
216	C₂³×C₇₉	—	2	1	no	—
217	C₂³×C₇₉	—	2	1	no	—
218	C₂³×C₇₉	#135	1	2	yes	—
219	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
220	Q₈×C₇₉	—	2	2	no	—
221	Q₈×C₇₉	—	2	2	no	—
222	Q₈×C₇₉	—	4	1	no	—
223	Q₈×C₇₉	—	4	1	no	—
224	Q₈×C₇₉	—	4	1	no	—
225	Q₈×C₇₉	—	4	1	no	—
226	Q₈×C₇₉	—	4	1	no	—
227	Q₈×C₇₉	—	4	1	no	—
228	C₂×C₄×C₇₉	—	2	1	no	—
229	C₂×C₄×C₇₉	—	2	1	no	—
230	C₂×C₄×C₇₉	—	2	2	no	—
231	C₂×C₄×C₇₉	—	2	2	no	—
232	C₂×C₄×C₇₉	—	2	1	no	—
233	C₂×C₄×C₇₉	—	2	1	no	—
234	C₂×C₄×C₇₉	—	2	1	no	—
235	C₂×C₄×C₇₉	—	2	2	no	—
236	C₂×C₄×C₇₉	—	2	2	no	—
237	C₂×C₄×C₇₉	—	2	1	no	—
238	C₂×C₄×C₇₉	—	2	1	no	—
239	C₂×C₄×C₇₉	—	2	1	no	—
240	C₂×C₄×C₇₉	—	2	1	no	—
241	C₂×C₄×C₇₉	—	2	1	no	—
242	C₂×C₄×C₇₉	—	2	1	no	—
243	C₂×C₄×C₇₉	—	2	1	no	—
244	C₂×C₄×C₇₉	—	2	1	no	—
245	C₂×C₄×C₇₉	—	2	1	no	—
246	C₂×C₄×C₇₉	—	4	1	no	—
247	C₂×C₄×C₇₉	—	4	1	no	—
248	C₂×C₄×C₇₉	—	4	1	no	—
249	C₂×C₄×C₇₉	—	4	1	no	—
250	C₂×C₄×C₇₉	—	4	1	no	—
251	C₂×C₄×C₇₉	—	4	1	no	—
252	C₂×C₄×C₇₉	—	4	1	no	—
253	C₂×C₄×C₇₉	—	4	1	no	—
254	C₂×C₄×C₇₉	—	4	1	no	—
255	C₂×C₄×C₇₉	—	4	1	no	—
256	C₂×C₄×C₇₉	—	4	1	no	—
257	C₂×C₄×C₇₉	—	4	1	no	—
258	C₂×C₄×C₇₉	—	4	1	no	—
259	C₂×C₄×C₇₉	—	4	1	no	—
260	C₂×C₄×C₇₉	—	4	1	no	—
261	C₂×C₄×C₇₉	—	4	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	—	8	4	no	—
271	C₂×C₄×C₇₉	#137	1	2	yes	—
272	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
274	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
275	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
276	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
277	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
278	C₈×C₇₉	—	2	2	no	—
279	C₈×C₇₉	—	2	2	no	—
280	C₈×C₇₉	—	4	1	no	—
281	C₈×C₇₉	—	4	1	no	—
282	C₂²×C₇₉	—	2	2	no	—
283	C₂²×C₇₉	—	2	2	no	—
284	C₂²×C₇₉	—	2	2	no	—
285	C₂²×C₇₉	—	4	1	no	—
286	C₂²×C₇₉	—	4	1	no	—
287	C₂²×C₇₉	—	4	1	no	—
288	C₂²×C₇₉	—	4	1	no	—
289	C₂²×C₇₉	#525	1	1	yes	characteristic
290	C₂²×C₇₉	D₄²	1	1	yes	characteristic
291	C₂²×C₇₉	#547	1	1	yes	characteristic
292	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
293	C₂²×C₇₉	C₂×#137	1	1	yes	characteristic
294	C₂²×C₇₉	#577	1	1	yes	characteristic
295	C₂²×C₇₉	#578	1	1	yes	characteristic
296	C₄×C₇₉	—	2	2	no	—
297	C₄×C₇₉	—	4	1	no	—
298	C₄×C₇₉	—	4	2	no	—
299	C₄×C₇₉	—	4	1	no	—
300	C₄×C₇₉	—	4	2	no	—
301	C₄×C₇₉	—	4	1	no	—
302	C₄×C₇₉	—	4	2	no	—
303	C₄×C₇₉	—	4	1	no	—
304	C₄×C₇₉	—	4	2	no	—
305	C₄×C₇₉	—	8	1	no	—
306	C₄×C₇₉	—	8	1	no	—
307	C₄×C₇₉	—	8	1	no	—
308	C₄×C₇₉	—	8	1	no	—
309	C₄×C₇₉	#532	1	1	yes	characteristic
310	C₄×C₇₉	#542	1	1	yes	characteristic
311	C₄×C₇₉	#548	1	1	yes	characteristic
312	C₄×C₇₉	#551	1	1	yes	characteristic
313	#26789	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
314	C₂×C₇₉	—	4	2	no	—
315	C₂×C₇₉	#2461	1	1	yes	characteristic
316	C₂×C₇₉	#3108	1	1	yes	characteristic
317	C₂×C₇₉	#3120	1	1	yes	characteristic
318	C₂×C₇₉	#3276	1	1	yes	characteristic
319	C₂×C₇₉	#3282	1	1	yes	characteristic
320	C₂×C₇₉	#3336	1	1	yes	characteristic
321	C₂×C₇₉	#3344	1	1	yes	characteristic
322	C₂×#483	C₂×C₇₉	1	1	yes	characteristic
323	C₂×#479	C₂×C₇₉	1	1	yes	characteristic, complemented
324	#2489	C₂×C₇₉	1	1	yes	characteristic
325	#2360	C₂×C₇₉	1	1	yes	characteristic
326	#2066	C₂×C₇₉	1	1	yes	characteristic, complemented
327	#2059	C₂×C₇₉	1	1	yes	characteristic, complemented
328	#2035	C₂×C₇₉	1	1	yes	characteristic
329	#2001	C₂×C₇₉	1	1	yes	characteristic
330	#1969	C₂×C₇₉	1	1	yes	characteristic, complemented
331	#1928	C₂×C₇₉	1	1	yes	characteristic, complemented
332	#1927	C₂×C₇₉	1	1	yes	characteristic, complemented
333	#1923	C₂×C₇₉	1	1	yes	characteristic
334	#1878	C₂×C₇₉	1	1	yes	characteristic, complemented
335	#1852	C₂×C₇₉	1	1	yes	characteristic
336	C₄×#106	C₂×C₇₉	1	1	yes	characteristic, complemented
337	C₇₉	#26789	1	1	yes	characteristic, direct product factor, Sylow
338	C₂²×Q₁₆	C₂²×C₇₉	1	1	yes	characteristic
339	C₂×#125	C₂²×C₇₉	1	1	yes	characteristic
340	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
341	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
342	C₂×C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
343	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
344	#483	—	2	4	no	—
345	#479	—	2	4	no	—
346	C₂×#107	C₂²×C₇₉	1	1	yes	characteristic
347	C₂×#107	C₂²×C₇₉	1	1	yes	characteristic
348	C₂×#106	C₂²×C₇₉	1	1	yes	characteristic
349	C₂×#106	C₂²×C₇₉	1	1	yes	characteristic
350	C₂×#106	C₂²×C₇₉	1	1	yes	characteristic
351	C₂×C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
352	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
353	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
354	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
355	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
356	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
357	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
358	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
359	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
360	C₂×C₄×C₈	C₂²×C₇₉	1	1	yes	characteristic
361	#400	—	2	1	no	—
362	#397	—	2	1	no	—
363	#391	C₂²×C₇₉	1	1	yes	characteristic
364	#391	C₂²×C₇₉	1	1	yes	characteristic
365	#391	C₂²×C₇₉	1	1	yes	characteristic
366	#389	—	2	1	no	—
367	#389	C₂²×C₇₉	1	1	yes	characteristic
368	#388	—	2	1	no	—
369	#387	—	2	1	no	—
370	#385	—	2	1	no	—
371	#382	—	2	1	no	—
372	#380	C₂²×C₇₉	1	1	yes	characteristic
373	C₄×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
374	C₄×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
375	C₄×C₂²⋊C₄	—	2	1	no	—
376	C₄×C₂²⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
377	#340	C₂²×C₇₉	1	1	yes	characteristic
378	#340	C₂²×C₇₉	1	1	yes	characteristic
379	#340	C₂²×C₇₉	1	1	yes	characteristic
380	#340	C₂²×C₇₉	1	1	yes	characteristic
381	#336	C₂²×C₇₉	1	1	yes	characteristic
382	#336	C₂²×C₇₉	1	1	yes	characteristic
383	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
384	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
385	C₂³×C₄	—	2	1	no	—
386	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
387	C₂×Q₁₆	—	2	2	no	—
388	C₂×Q₁₆	—	2	2	no	—
389	C₂×Q₁₆	—	4	1	no	—
390	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
391	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
392	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
393	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
394	#125	—	2	2	no	—
395	#125	—	4	1	no	—
396	C₂²⋊Q₈	—	2	2	no	—
397	C₂²⋊Q₈	—	2	2	no	—
398	C₂²⋊Q₈	—	2	2	no	—
399	C₂²⋊Q₈	—	4	1	no	—
400	C₄×Q₈	—	2	2	no	—
401	C₄×Q₈	—	4	1	no	—
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	—	2	2	no	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	—	2	1	no	—
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	—	2	1	no	—
409	C₂×C₄⋊C₄	—	2	1	no	—
410	C₂×C₄⋊C₄	—	4	1	no	—
411	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
412	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
413	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
417	C₂×C₂²⋊C₄	—	2	1	no	—
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₂²⋊C₄	—	2	1	no	—
420	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
421	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
422	C₂×C₄²	—	2	1	no	—
423	C₂×C₄²	—	2	1	no	—
424	C₂×C₄²	—	2	1	no	—
425	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
426	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
427	#107	—	2	2	no	—
428	#107	—	4	1	no	—
429	#106	—	2	2	no	—
430	#106	—	2	2	no	—
431	#106	D₄×C₇₉	1	4	yes	—
432	C₄⋊C₈	—	2	2	no	—
433	#103	—	2	2	no	—
434	#103	—	2	2	no	—
435	#103	—	2	2	no	—
436	#103	—	2	2	no	—
437	#103	—	2	2	no	—
438	#103	—	2	2	no	—
439	C₂²⋊C₈	—	2	2	no	—
440	C₂²⋊C₈	—	2	2	no	—
441	C₄×C₈	—	2	2	no	—
442	#95	—	2	1	no	—
443	#95	—	2	1	no	—
444	#95	—	2	1	no	—
445	#95	—	2	1	no	—
446	#95	—	2	1	no	—
447	#95	—	2	1	no	—
448	#95	—	2	1	no	—
449	#95	—	2	1	no	—
450	#95	—	2	1	no	—
451	#95	—	2	1	no	—
452	#95	D₄×C₇₉	1	1	yes	characteristic
453	#95	D₄×C₇₉	1	1	yes	characteristic
454	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	—	2	1	no	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	2	1	no	—
463	C₂×Q₈	—	2	1	no	—
464	C₂×Q₈	—	2	1	no	—
465	C₂×Q₈	—	2	1	no	—
466	C₂×Q₈	#41×C₇₉	1	2	yes	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	4	2	no	—
482	C₂²×C₄	—	4	2	no	—
483	C₂²×C₄	—	8	1	no	—
484	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
485	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
486	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
487	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
488	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
489	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
490	Q₁₆	—	4	4	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
502	C₂×C₈	#41×C₇₉	1	2	yes	—
503	C₄⋊C₄	—	2	4	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	4	2	no	—
514	C₄⋊C₄	—	4	2	no	—
515	C₄⋊C₄	—	4	2	no	—
516	C₄⋊C₄	—	4	2	no	—
517	C₄⋊C₄	—	4	2	no	—
518	C₄⋊C₄	—	8	1	no	—
519	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
520	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
521	C₄⋊C₄	#41×C₇₉	1	2	yes	—
522	C₂²⋊C₄	—	2	4	no	—
523	C₂²⋊C₄	—	2	2	no	—
524	C₂²⋊C₄	—	2	2	no	—
525	C₂²⋊C₄	—	4	2	no	—
526	C₂²⋊C₄	—	4	2	no	—
527	C₄²	—	2	1	no	—
528	C₄²	—	2	1	no	—
529	C₄²	—	2	1	no	—
530	C₄²	—	2	1	no	—
531	C₄²	—	4	2	no	—
532	C₄²	—	4	2	no	—
533	C₄²	—	8	1	no	—
534	C₂³	—	2	1	no	—
535	C₂³	—	2	1	no	—
536	C₂³	—	2	1	no	—
537	C₂³	—	2	1	no	—
538	C₂³	—	2	1	no	—
539	C₂³	—	2	1	no	—
540	C₂³	#135×C₇₉	1	2	yes	—
541	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
542	Q₈	—	2	2	no	—
543	Q₈	—	2	2	no	—
544	Q₈	—	4	1	no	—
545	Q₈	—	4	1	no	—
546	Q₈	—	4	1	no	—
547	Q₈	—	4	1	no	—
548	Q₈	—	4	1	no	—
549	Q₈	—	4	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	8	4	no	—
593	C₂×C₄	#137×C₇₉	1	2	yes	—
594	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
595	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
596	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
597	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
598	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
599	C₂×C₄	2₋¹⁺⁴×C₇₉	1	1	yes	characteristic
600	C₈	—	2	2	no	—
601	C₈	—	2	2	no	—
602	C₈	—	4	1	no	—
603	C₈	—	4	1	no	—
604	C₂²	—	2	2	no	—
605	C₂²	—	2	2	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	1	no	—
609	C₂²	—	4	1	no	—
610	C₂²	—	4	1	no	—
611	C₂²	#525×C₇₉	1	1	yes	characteristic
612	C₂²	D₄²×C₇₉	1	1	yes	characteristic
613	C₂²	#547×C₇₉	1	1	yes	characteristic
614	C₂²	C₂×#135×C₇₉	1	1	yes	characteristic
615	C₂²	C₂×#137×C₇₉	1	1	yes	characteristic
616	C₂²	#577×C₇₉	1	1	yes	characteristic
617	C₂²	#578×C₇₉	1	1	yes	characteristic
618	C₄	—	2	2	no	—
619	C₄	—	4	1	no	—
620	C₄	—	4	2	no	—
621	C₄	—	4	1	no	—
622	C₄	—	4	2	no	—
623	C₄	—	4	1	no	—
624	C₄	—	4	2	no	—
625	C₄	—	4	1	no	—
626	C₄	—	4	2	no	—
627	C₄	—	8	1	no	—
628	C₄	—	8	1	no	—
629	C₄	—	8	1	no	—
630	C₄	—	8	1	no	—
631	C₄	#532×C₇₉	1	1	yes	characteristic
632	C₄	#542×C₇₉	1	1	yes	characteristic
633	C₄	#548×C₇₉	1	1	yes	characteristic
634	C₄	#551×C₇₉	1	1	yes	characteristic
635	C₂	—	4	2	no	—
636	C₂	C₇₉×#2461	1	1	yes	characteristic
637	C₂	C₇₉×#3108	1	1	yes	characteristic
638	C₂	C₇₉×#3120	1	1	yes	characteristic
639	C₂	C₇₉×#3276	1	1	yes	characteristic
640	C₂	C₇₉×#3282	1	1	yes	characteristic
641	C₂	C₇₉×#3336	1	1	yes	characteristic
642	C₂	C₇₉×#3344	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₂⁴×C₇₉	C₂×D₄
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
2. C₂×#479×C₇₉	C₂	semidirect
5. C₇₉×#2066	C₂	semidirect
6. C₇₉×#2059	C₂	semidirect
9. C₇₉×#1969	C₂	semidirect
10. C₇₉×#1928	C₂	semidirect
11. C₇₉×#1927	C₂	semidirect
13. C₇₉×#1878	C₂	semidirect
15. C₄×#106×C₇₉	C₂	semidirect
313. #26789	C₇₉	direct (N × H)
323. C₂×#479	C₂×C₇₉	semidirect
326. #2066	C₂×C₇₉	semidirect
327. #2059	C₂×C₇₉	semidirect
330. #1969	C₂×C₇₉	semidirect
331. #1928	C₂×C₇₉	semidirect
332. #1927	C₂×C₇₉	semidirect
334. #1878	C₂×C₇₉	semidirect
336. C₄×#106	C₂×C₇₉	semidirect
337. C₇₉	#26789	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×#483×C₇₉	2
C₂×#479×C₇₉	2
C₇₉×#2489	2
C₇₉×#2360	2
C₇₉×#2066	2
C₇₉×#2059	2
C₇₉×#2035	2
C₇₉×#2001	2
C₇₉×#1969	2
C₇₉×#1928	2
C₇₉×#1927	2
C₇₉×#1923	2
C₇₉×#1878	2
C₇₉×#1852	2
C₄×#106×C₇₉	2
#26789	79

Subgroups — C79×#26789 #34138478

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#26789 #34138478