Subgroups — C₇₉×#25819 #34137508

Order 20224.

1078 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#125×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#501×C₇₉	C₂	1	2	yes	maximal, complemented
3	C₇₉×#2857	C₂	1	1	yes	maximal, characteristic
4	C₇₉×#2059	C₂	1	4	yes	maximal, complemented
5	C₇₉×#1992	C₂	1	2	yes	maximal, complemented
6	C₇₉×#1853	C₂	1	2	yes	maximal
7	C₇₉×#1852	C₂	1	2	yes	maximal
8	C₇₉×#1749	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
10	C₂×#125×C₇₉	—	2	8	no	—
11	C₂×#125×C₇₉	—	2	1	no	—
12	C₂×#125×C₇₉	—	2	1	no	—
13	C₂×#125×C₇₉	C₂²	1	2	yes	—
14	C₂×#125×C₇₉	C₂²	1	2	yes	—
15	C₂×C₂²⋊Q₈×C₇₉	—	2	1	no	—
16	C₂²×C₄⋊C₄×C₇₉	—	2	1	no	—
17	C₂²×C₄⋊C₄×C₇₉	—	2	1	no	—
18	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
21	#501×C₇₉	—	2	8	no	—
22	C₂×#107×C₇₉	C₂²	1	4	yes	—
23	C₂×#106×C₇₉	C₂²	1	4	yes	—
24	C₂×C₂²⋊C₈×C₇₉	C₂²	1	2	yes	—
25	C₂×#97×C₇₉	C₂²	1	2	yes	—
26	#391×C₇₉	—	2	1	no	—
27	#389×C₇₉	—	2	1	no	—
28	#389×C₇₉	C₂²	1	2	yes	—
29	#384×C₇₉	C₂²	1	1	yes	characteristic
30	#380×C₇₉	—	2	1	no	—
31	#380×C₇₉	C₂²	1	2	yes	—
32	#340×C₇₉	C₂²	1	4	yes	—
33	#340×C₇₉	C₂²	1	4	yes	—
34	#336×C₇₉	C₂²	1	2	yes	—
35	C₂²×Q₈×C₇₉	—	2	1	no	—
36	C₂³×C₄×C₇₉	—	2	1	no	—
37	C₂³×C₄×C₇₉	—	2	1	no	—
38	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
41	C₂²×C₈×C₇₉	C₂³	1	4	yes	—
42	C₄⋊Q₈×C₇₉	—	2	4	no	—
43	#125×C₇₉	—	2	8	no	—
44	#125×C₇₉	—	2	8	no	—
45	#125×C₇₉	—	2	4	no	—
46	#125×C₇₉	—	2	4	no	—
47	#125×C₇₉	—	2	4	no	—
48	#125×C₇₉	D₄	1	8	yes	—
49	C₂²⋊Q₈×C₇₉	—	4	4	no	—
50	C₂×C₄⋊C₄×C₇₉	—	2	8	no	—
51	C₂×C₄⋊C₄×C₇₉	—	2	8	no	—
52	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
53	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
55	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
56	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
59	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
60	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
62	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
68	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
69	C₂×C₄²×C₇₉	—	2	4	no	—
70	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
74	#107×C₇₉	—	2	8	no	—
75	#106×C₇₉	—	2	8	no	—
76	C₂²⋊C₈×C₇₉	Q₈	1	8	yes	complemented
77	#97×C₇₉	—	2	4	no	—
78	#95×C₇₉	—	2	2	no	—
79	#95×C₇₉	—	2	2	no	—
80	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
81	C₂×Q₈×C₇₉	—	4	2	no	—
82	C₂×Q₈×C₇₉	—	4	2	no	—
83	C₂×Q₈×C₇₉	—	4	2	no	—
84	C₂²×C₄×C₇₉	—	2	2	no	—
85	C₂²×C₄×C₇₉	—	2	2	no	—
86	C₂²×C₄×C₇₉	—	2	4	no	—
87	C₂²×C₄×C₇₉	—	2	4	no	—
88	C₂²×C₄×C₇₉	—	2	2	no	—
89	C₂²×C₄×C₇₉	—	2	2	no	—
90	C₂²×C₄×C₇₉	—	2	2	no	—
91	C₂²×C₄×C₇₉	—	2	2	no	—
92	C₂²×C₄×C₇₉	—	2	2	no	—
93	C₂²×C₄×C₇₉	—	2	2	no	—
94	C₂²×C₄×C₇₉	—	2	2	no	—
95	C₂²×C₄×C₇₉	—	2	2	no	—
96	C₂²×C₄×C₇₉	—	4	1	no	—
97	C₂²×C₄×C₇₉	—	4	1	no	—
98	C₂²×C₄×C₇₉	—	4	2	no	—
99	C₂²×C₄×C₇₉	—	4	2	no	—
100	C₂²×C₄×C₇₉	—	4	2	no	—
101	C₂²×C₄×C₇₉	—	4	2	no	—
102	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₇₉	C₂×Q₈	1	4	yes	—
108	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
109	C₂×C₈×C₇₉	—	2	4	no	—
110	C₂×C₈×C₇₉	—	2	4	no	—
111	C₂×C₈×C₇₉	C₂×Q₈	1	8	yes	—
112	C₄⋊C₄×C₇₉	—	2	4	no	—
113	C₄⋊C₄×C₇₉	—	2	4	no	—
114	C₄⋊C₄×C₇₉	—	2	8	no	—
115	C₄⋊C₄×C₇₉	—	2	8	no	—
116	C₄⋊C₄×C₇₉	—	2	8	no	—
117	C₄⋊C₄×C₇₉	—	2	8	no	—
118	C₄⋊C₄×C₇₉	—	2	2	no	—
119	C₄⋊C₄×C₇₉	—	2	2	no	—
120	C₄⋊C₄×C₇₉	—	2	4	no	—
121	C₄⋊C₄×C₇₉	—	2	4	no	—
122	C₄⋊C₄×C₇₉	—	4	2	no	—
123	C₄⋊C₄×C₇₉	—	4	2	no	—
124	C₄⋊C₄×C₇₉	—	4	4	no	—
125	C₄⋊C₄×C₇₉	—	4	2	no	—
126	C₄⋊C₄×C₇₉	C₂×D₄	1	4	yes	—
127	C₄⋊C₄×C₇₉	C₂×D₄	1	4	yes	—
128	C₂²⋊C₄×C₇₉	—	4	4	no	—
129	C₄²×C₇₉	—	2	2	no	—
130	C₄²×C₇₉	—	2	2	no	—
131	C₄²×C₇₉	—	2	2	no	—
132	C₄²×C₇₉	C₂×D₄	1	4	yes	—
133	C₂³×C₇₉	—	2	1	no	—
134	C₂³×C₇₉	—	2	1	no	—
135	C₂³×C₇₉	—	2	1	no	—
136	C₂³×C₇₉	—	2	1	no	—
137	C₂³×C₇₉	C₄⋊Q₈	1	2	yes	—
138	C₂³×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
139	C₂³×C₇₉	#137	1	2	yes	—
140	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
141	Q₈×C₇₉	—	8	4	no	—
142	C₂×C₄×C₇₉	—	2	1	no	—
143	C₂×C₄×C₇₉	—	2	1	no	—
144	C₂×C₄×C₇₉	—	2	1	no	—
145	C₂×C₄×C₇₉	—	2	1	no	—
146	C₂×C₄×C₇₉	—	2	1	no	—
147	C₂×C₄×C₇₉	—	2	1	no	—
148	C₂×C₄×C₇₉	—	2	8	no	—
149	C₂×C₄×C₇₉	—	2	1	no	—
150	C₂×C₄×C₇₉	—	2	1	no	—
151	C₂×C₄×C₇₉	—	2	4	no	—
152	C₂×C₄×C₇₉	—	2	4	no	—
153	C₂×C₄×C₇₉	—	2	1	no	—
154	C₂×C₄×C₇₉	—	2	1	no	—
155	C₂×C₄×C₇₉	—	2	1	no	—
156	C₂×C₄×C₇₉	—	2	1	no	—
157	C₂×C₄×C₇₉	—	4	4	no	—
158	C₂×C₄×C₇₉	—	4	4	no	—
159	C₂×C₄×C₇₉	—	4	8	no	—
160	C₂×C₄×C₇₉	—	4	8	no	—
161	C₂×C₄×C₇₉	—	4	2	no	—
162	C₂×C₄×C₇₉	—	4	2	no	—
163	C₂×C₄×C₇₉	—	4	2	no	—
164	C₂×C₄×C₇₉	—	4	2	no	—
165	C₂×C₄×C₇₉	—	4	2	no	—
166	C₂×C₄×C₇₉	—	4	2	no	—
167	C₂×C₄×C₇₉	—	4	2	no	—
168	C₂×C₄×C₇₉	—	4	2	no	—
169	C₂×C₄×C₇₉	—	4	2	no	—
170	C₂×C₄×C₇₉	—	4	2	no	—
171	C₂×C₄×C₇₉	#120	1	2	yes	—
172	C₂×C₄×C₇₉	#120	1	2	yes	—
173	C₂×C₄×C₇₉	C₄⋊Q₈	1	2	yes	—
174	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
175	C₂×C₄×C₇₉	C₂²×Q₈	1	2	yes	—
176	C₂×C₄×C₇₉	2₋¹⁺⁴	1	2	yes	—
177	C₈×C₇₉	—	2	8	no	—
178	C₂²×C₇₉	—	2	2	no	—
179	C₂²×C₇₉	—	2	2	no	—
180	C₂²×C₇₉	—	2	2	no	—
181	C₂²×C₇₉	—	2	2	no	—
182	C₂²×C₇₉	—	2	2	no	—
183	C₂²×C₇₉	—	2	2	no	—
184	C₂²×C₇₉	#501	1	4	yes	complemented
185	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
186	C₂²×C₇₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
187	C₂²×C₇₉	#536	1	1	yes	characteristic
188	C₂²×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
189	C₂²×C₇₉	C₂×#137	1	1	yes	characteristic
190	C₂²×C₇₉	#575	1	1	yes	characteristic
191	C₂²×C₇₉	#575	1	1	yes	characteristic
192	C₄×C₇₉	—	2	2	no	—
193	C₄×C₇₉	—	2	2	no	—
194	C₄×C₇₉	—	2	2	no	—
195	C₄×C₇₉	—	4	1	no	—
196	C₄×C₇₉	—	4	4	no	—
197	C₄×C₇₉	—	4	1	no	—
198	C₄×C₇₉	—	4	4	no	—
199	C₄×C₇₉	—	8	2	no	—
200	C₄×C₇₉	—	8	2	no	—
201	C₄×C₇₉	D₄×Q₈	1	4	yes	—
202	#25819	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₂×C₇₉	—	2	4	no	—
204	C₂×C₇₉	#2434	1	1	yes	characteristic
205	C₂×C₇₉	#3006	1	1	yes	characteristic
206	C₂×C₇₉	#3007	1	1	yes	characteristic
207	C₂×C₇₉	C₂×#501	1	1	yes	characteristic
208	C₂×C₇₉	#3166	1	1	yes	characteristic
209	C₂×C₇₉	#3234	1	1	yes	characteristic
210	C₂×C₇₉	#3236	1	1	yes	characteristic
211	C₂²×#125	C₂×C₇₉	1	1	yes	characteristic
212	C₂×#501	C₂×C₇₉	1	2	yes	complemented
213	#2857	C₂×C₇₉	1	1	yes	characteristic
214	#2059	C₂×C₇₉	1	4	yes	complemented
215	#1992	C₂×C₇₉	1	2	yes	complemented
216	#1853	C₂×C₇₉	1	2	yes	—
217	#1852	C₂×C₇₉	1	2	yes	—
218	#1749	C₂×C₇₉	1	1	yes	characteristic
219	C₇₉	#25819	1	1	yes	characteristic, direct product factor, Sylow
220	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
221	C₂×#125	—	2	8	no	—
222	C₂×#125	—	2	1	no	—
223	C₂×#125	—	2	1	no	—
224	C₂×#125	C₂²×C₇₉	1	2	yes	—
225	C₂×#125	C₂²×C₇₉	1	2	yes	—
226	C₂×C₂²⋊Q₈	—	2	1	no	—
227	C₂²×C₄⋊C₄	—	2	1	no	—
228	C₂²×C₄⋊C₄	—	2	1	no	—
229	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
230	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
231	C₂²×C₄²	C₂²×C₇₉	1	1	yes	characteristic
232	#501	—	2	8	no	—
233	C₂×#107	C₂²×C₇₉	1	4	yes	—
234	C₂×#106	C₂²×C₇₉	1	4	yes	—
235	C₂×C₂²⋊C₈	C₂²×C₇₉	1	2	yes	—
236	C₂×#97	C₂²×C₇₉	1	2	yes	—
237	#391	—	2	1	no	—
238	#389	—	2	1	no	—
239	#389	C₂²×C₇₉	1	2	yes	—
240	#384	C₂²×C₇₉	1	1	yes	characteristic
241	#380	—	2	1	no	—
242	#380	C₂²×C₇₉	1	2	yes	—
243	#340	C₂²×C₇₉	1	4	yes	—
244	#340	C₂²×C₇₉	1	4	yes	—
245	#336	C₂²×C₇₉	1	2	yes	—
246	C₂²×Q₈	—	2	1	no	—
247	C₂³×C₄	—	2	1	no	—
248	C₂³×C₄	—	2	1	no	—
249	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
250	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
251	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
252	C₂²×C₈	C₂³×C₇₉	1	4	yes	—
253	C₄⋊Q₈	—	2	4	no	—
254	#125	—	2	8	no	—
255	#125	—	2	8	no	—
256	#125	—	2	4	no	—
257	#125	—	2	4	no	—
258	#125	—	2	4	no	—
259	#125	D₄×C₇₉	1	8	yes	—
260	C₂²⋊Q₈	—	4	4	no	—
261	C₂×C₄⋊C₄	—	2	8	no	—
262	C₂×C₄⋊C₄	—	2	8	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	4	no	—
270	C₂×C₄⋊C₄	—	2	4	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	2	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
276	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
277	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
278	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₄²	—	2	4	no	—
281	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
282	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
283	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
284	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
285	#107	—	2	8	no	—
286	#106	—	2	8	no	—
287	C₂²⋊C₈	Q₈×C₇₉	1	8	yes	complemented
288	#97	—	2	4	no	—
289	#95	—	2	2	no	—
290	#95	—	2	2	no	—
291	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
292	C₂×Q₈	—	4	2	no	—
293	C₂×Q₈	—	4	2	no	—
294	C₂×Q₈	—	4	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	—	4	1	no	—
309	C₂²×C₄	—	4	2	no	—
310	C₂²×C₄	—	4	2	no	—
311	C₂²×C₄	—	4	2	no	—
312	C₂²×C₄	—	4	2	no	—
313	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
314	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
318	C₂²×C₄	C₂×Q₈×C₇₉	1	4	yes	—
319	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
320	C₂×C₈	—	2	4	no	—
321	C₂×C₈	—	2	4	no	—
322	C₂×C₈	C₂×Q₈×C₇₉	1	8	yes	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	2	8	no	—
326	C₄⋊C₄	—	2	8	no	—
327	C₄⋊C₄	—	2	8	no	—
328	C₄⋊C₄	—	2	8	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	4	2	no	—
334	C₄⋊C₄	—	4	4	no	—
335	C₄⋊C₄	—	4	2	no	—
336	C₄⋊C₄	—	4	2	no	—
337	C₄⋊C₄	C₂×D₄×C₇₉	1	4	yes	—
338	C₄⋊C₄	C₂×D₄×C₇₉	1	4	yes	—
339	C₂²⋊C₄	—	4	4	no	—
340	C₄²	—	2	2	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	2	2	no	—
343	C₄²	C₂×D₄×C₇₉	1	4	yes	—
344	C₂³	—	2	1	no	—
345	C₂³	—	2	1	no	—
346	C₂³	—	2	1	no	—
347	C₂³	—	2	1	no	—
348	C₂³	C₄⋊Q₈×C₇₉	1	2	yes	—
349	C₂³	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
350	C₂³	#137×C₇₉	1	2	yes	—
351	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
352	Q₈	—	8	4	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	8	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	8	no	—
371	C₂×C₄	—	4	8	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	#120×C₇₉	1	2	yes	—
383	C₂×C₄	#120×C₇₉	1	2	yes	—
384	C₂×C₄	C₄⋊Q₈×C₇₉	1	2	yes	—
385	C₂×C₄	C₂²×D₄×C₇₉	1	2	yes	—
386	C₂×C₄	C₂²×Q₈×C₇₉	1	2	yes	—
387	C₂×C₄	2₋¹⁺⁴×C₇₉	1	2	yes	—
388	C₈	—	2	8	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	2	2	no	—
395	C₂²	#501×C₇₉	1	4	yes	complemented
396	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
397	C₂²	C₂×C₄⋊Q₈×C₇₉	1	1	yes	characteristic
398	C₂²	#536×C₇₉	1	1	yes	characteristic
399	C₂²	C₂×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
400	C₂²	C₂×#137×C₇₉	1	1	yes	characteristic
401	C₂²	#575×C₇₉	1	1	yes	characteristic
402	C₂²	#575×C₇₉	1	1	yes	characteristic
403	C₄	—	2	2	no	—
404	C₄	—	2	2	no	—
405	C₄	—	2	2	no	—
406	C₄	—	4	1	no	—
407	C₄	—	4	4	no	—
408	C₄	—	4	1	no	—
409	C₄	—	4	4	no	—
410	C₄	—	8	2	no	—
411	C₄	—	8	2	no	—
412	C₄	D₄×Q₈×C₇₉	1	4	yes	—
413	C₂	—	2	4	no	—
414	C₂	C₇₉×#2434	1	1	yes	characteristic
415	C₂	C₇₉×#3006	1	1	yes	characteristic
416	C₂	C₇₉×#3007	1	1	yes	characteristic
417	C₂	C₂×#501×C₇₉	1	1	yes	characteristic
418	C₂	C₇₉×#3166	1	1	yes	characteristic
419	C₂	C₇₉×#3234	1	1	yes	characteristic
420	C₂	C₇₉×#3236	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 ◁ C₂²×C₄²×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#501×C₇₉	C₂	semidirect
4. C₇₉×#2059	C₂	semidirect
5. C₇₉×#1992	C₂	semidirect
76. C₂²⋊C₈×C₇₉	Q₈	semidirect
184. C₂²×C₇₉	#501	semidirect
202. #25819	C₇₉	direct (N × H)
212. C₂×#501	C₂×C₇₉	semidirect
214. #2059	C₂×C₇₉	semidirect
215. #1992	C₂×C₇₉	semidirect
219. C₇₉	#25819	direct (N × H)
287. C₂²⋊C₈	Q₈×C₇₉	semidirect
395. C₂²	#501×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#125×C₇₉	2
C₂×#501×C₇₉	2
C₇₉×#2857	2
C₇₉×#2059	2
C₇₉×#1992	2
C₇₉×#1853	2
C₇₉×#1852	2
C₇₉×#1749	2
#25819	79

Subgroups — C79×#25819 #34137508

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#25819 #34137508