Subgroups — C₇₉×#25709 #34137398

Order 20224.

1276 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#547×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#501×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#478×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#2562	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#2034	C₂	1	2	yes	maximal, complemented
6	C₇₉×#2033	C₂	1	2	yes	maximal, complemented
7	C₇₉×#1987	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#1955	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#1853	C₂	1	2	yes	maximal, complemented
10	C₇₉×#1852	C₂	1	2	yes	maximal, complemented
11	C₇₉×#1762	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₇₉	—	2	1	no	—
13	#547×C₇₉	—	2	4	no	—
14	#547×C₇₉	—	2	4	no	—
15	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
16	C₂×#125×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×#123×C₇₉	—	2	2	no	—
18	C₂×C₂²⋊Q₈×C₇₉	—	2	1	no	—
19	C₂×#121×C₇₉	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
23	#501×C₇₉	—	2	4	no	—
24	#478×C₇₉	—	2	4	no	—
25	C₂×#107×C₇₉	C₂²	1	2	yes	—
26	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic
27	C₂×#106×C₇₉	C₂²	1	2	yes	—
28	C₂×#106×C₇₉	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
30	C₂×#102×C₇₉	C₂²	1	2	yes	—
31	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
32	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₈×C₇₉	C₂²	1	2	yes	—
34	C₂×C₂²⋊C₈×C₇₉	C₂²	1	2	yes	—
35	C₂×#97×C₇₉	C₂²	1	1	yes	characteristic
36	#400×C₇₉	—	2	1	no	—
37	#394×C₇₉	—	2	1	no	—
38	#388×C₇₉	—	2	2	no	—
39	#380×C₇₉	C₂²	1	2	yes	—
40	#380×C₇₉	C₂²	1	2	yes	—
41	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
42	#340×C₇₉	C₂²	1	2	yes	—
43	#340×C₇₉	C₂²	1	2	yes	—
44	#340×C₇₉	C₂²	1	2	yes	—
45	C₂×#41×C₇₉	—	2	8	no	—
46	C₂×#41×C₇₉	—	4	8	no	—
47	C₂²×Q₈×C₇₉	—	2	1	no	—
48	C₂²×D₄×C₇₉	—	2	2	no	—
49	C₂²×D₄×C₇₉	D₄	1	1	yes	characteristic
50	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₇₉	—	2	2	no	—
52	C₂³×C₄×C₇₉	—	2	1	no	—
53	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
54	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
57	C₄⋊Q₈×C₇₉	—	2	2	no	—
58	C₄⋊Q₈×C₇₉	D₄	1	4	yes	—
59	#125×C₇₉	—	2	2	no	—
60	#125×C₇₉	—	2	2	no	—
61	#123×C₇₉	—	2	16	no	—
62	C₂²⋊Q₈×C₇₉	—	2	8	no	—
63	#121×C₇₉	—	2	4	no	—
64	#121×C₇₉	—	2	4	no	—
65	C₄×D₄×C₇₉	—	2	2	no	—
66	C₄×D₄×C₇₉	—	2	2	no	—
67	C₄×D₄×C₇₉	—	2	2	no	—
68	C₄×D₄×C₇₉	D₄	1	4	yes	—
69	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
70	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
72	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
73	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
79	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
81	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
82	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
83	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₇₉	D₄	1	2	yes	—
86	C₂×C₄²×C₇₉	—	2	1	no	—
87	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
88	#107×C₇₉	—	2	2	no	—
89	#107×C₇₉	—	2	4	no	—
90	#106×C₇₉	—	2	2	no	—
91	#106×C₇₉	—	2	4	no	—
92	C₄⋊C₈×C₇₉	—	2	2	no	—
93	#102×C₇₉	—	2	2	no	—
94	#102×C₇₉	—	2	2	no	—
95	#102×C₇₉	—	2	4	no	—
96	C₂²⋊C₈×C₇₉	—	2	4	no	—
97	C₂²⋊C₈×C₇₉	—	2	4	no	—
98	#97×C₇₉	—	2	2	no	—
99	#95×C₇₉	—	2	1	no	—
100	#95×C₇₉	—	2	2	no	—
101	#95×C₇₉	—	2	2	no	—
102	C₂⁴×C₇₉	—	2	1	no	—
103	C₂⁴×C₇₉	C₂×D₄	1	2	yes	—
104	#41×C₇₉	—	4	32	no	—
105	C₂×Q₈×C₇₉	—	2	4	no	—
106	C₂×Q₈×C₇₉	—	4	4	no	—
107	C₂×D₄×C₇₉	—	2	4	no	—
108	C₂×D₄×C₇₉	—	2	8	no	—
109	C₂×D₄×C₇₉	—	2	2	no	—
110	C₂×D₄×C₇₉	—	2	1	no	—
111	C₂×D₄×C₇₉	—	2	2	no	—
112	C₂×D₄×C₇₉	—	2	2	no	—
113	C₂×D₄×C₇₉	—	4	4	no	—
114	C₂×D₄×C₇₉	—	4	4	no	—
115	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₇₉	—	2	8	no	—
117	C₂²×C₄×C₇₉	—	2	1	no	—
118	C₂²×C₄×C₇₉	—	2	2	no	—
119	C₂²×C₄×C₇₉	—	2	4	no	—
120	C₂²×C₄×C₇₉	—	2	2	no	—
121	C₂²×C₄×C₇₉	—	2	2	no	—
122	C₂²×C₄×C₇₉	—	2	2	no	—
123	C₂²×C₄×C₇₉	—	2	2	no	—
124	C₂²×C₄×C₇₉	—	2	2	no	—
125	C₂²×C₄×C₇₉	—	2	2	no	—
126	C₂²×C₄×C₇₉	—	2	2	no	—
127	C₂²×C₄×C₇₉	—	2	1	no	—
128	C₂²×C₄×C₇₉	—	2	1	no	—
129	C₂²×C₄×C₇₉	—	4	4	no	—
130	C₂²×C₄×C₇₉	—	4	4	no	—
131	C₂²×C₄×C₇₉	—	4	4	no	—
132	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
136	C₂×C₈×C₇₉	—	2	2	no	—
137	C₂×C₈×C₇₉	—	2	1	no	—
138	C₂×C₈×C₇₉	—	2	1	no	—
139	C₂×C₈×C₇₉	—	2	2	no	—
140	C₂×C₈×C₇₉	—	2	2	no	—
141	C₂×C₈×C₇₉	—	2	2	no	—
142	C₂×C₈×C₇₉	#41	1	4	yes	complemented
143	C₄⋊C₄×C₇₉	—	2	8	no	—
144	C₄⋊C₄×C₇₉	—	2	4	no	—
145	C₄⋊C₄×C₇₉	—	2	2	no	—
146	C₄⋊C₄×C₇₉	—	2	1	no	—
147	C₄⋊C₄×C₇₉	—	2	2	no	—
148	C₄⋊C₄×C₇₉	—	2	1	no	—
149	C₄⋊C₄×C₇₉	—	2	1	no	—
150	C₄⋊C₄×C₇₉	—	2	1	no	—
151	C₄⋊C₄×C₇₉	—	2	1	no	—
152	C₄⋊C₄×C₇₉	—	2	2	no	—
153	C₄⋊C₄×C₇₉	—	2	2	no	—
154	C₄⋊C₄×C₇₉	—	4	2	no	—
155	C₄⋊C₄×C₇₉	—	4	2	no	—
156	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
157	C₄⋊C₄×C₇₉	C₂×D₄	1	4	yes	—
158	C₂²⋊C₄×C₇₉	—	2	8	no	—
159	C₂²⋊C₄×C₇₉	—	2	4	no	—
160	C₂²⋊C₄×C₇₉	—	2	4	no	—
161	C₂²⋊C₄×C₇₉	—	4	4	no	—
162	C₂²⋊C₄×C₇₉	—	8	2	no	—
163	C₄²×C₇₉	—	8	1	no	—
164	C₄²×C₇₉	C₂×D₄	1	2	yes	—
165	C₄²×C₇₉	C₂×D₄	1	2	yes	—
166	C₂³×C₇₉	—	2	2	no	—
167	C₂³×C₇₉	—	2	2	no	—
168	C₂³×C₇₉	—	2	2	no	—
169	C₂³×C₇₉	—	2	2	no	—
170	C₂³×C₇₉	—	2	2	no	—
171	C₂³×C₇₉	—	2	2	no	—
172	C₂³×C₇₉	—	2	2	no	—
173	C₂³×C₇₉	—	4	2	no	—
174	C₂³×C₇₉	—	4	2	no	—
175	C₂³×C₇₉	—	4	1	no	—
176	C₂³×C₇₉	—	4	1	no	—
177	C₂³×C₇₉	AGL(1,ℤ/8)	1	4	yes	—
178	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
179	Q₈×C₇₉	—	4	8	no	—
180	D₄×C₇₉	—	2	8	no	—
181	D₄×C₇₉	—	2	2	no	—
182	D₄×C₇₉	—	2	2	no	—
183	D₄×C₇₉	—	4	16	no	—
184	D₄×C₇₉	—	4	2	no	—
185	C₂×C₄×C₇₉	—	2	2	no	—
186	C₂×C₄×C₇₉	—	2	1	no	—
187	C₂×C₄×C₇₉	—	2	1	no	—
188	C₂×C₄×C₇₉	—	2	2	no	—
189	C₂×C₄×C₇₉	—	2	2	no	—
190	C₂×C₄×C₇₉	—	2	4	no	—
191	C₂×C₄×C₇₉	—	2	2	no	—
192	C₂×C₄×C₇₉	—	2	2	no	—
193	C₂×C₄×C₇₉	—	4	8	no	—
194	C₂×C₄×C₇₉	—	4	16	no	—
195	C₂×C₄×C₇₉	—	4	2	no	—
196	C₂×C₄×C₇₉	—	4	2	no	—
197	C₂×C₄×C₇₉	—	4	2	no	—
198	C₂×C₄×C₇₉	—	4	2	no	—
199	C₂×C₄×C₇₉	—	4	2	no	—
200	C₂×C₄×C₇₉	—	4	2	no	—
201	C₂×C₄×C₇₉	—	4	2	no	—
202	C₂×C₄×C₇₉	—	4	1	no	—
203	C₂×C₄×C₇₉	—	4	1	no	—
204	C₂×C₄×C₇₉	—	4	2	no	—
205	C₂×C₄×C₇₉	—	4	2	no	—
206	C₂×C₄×C₇₉	—	4	2	no	—
207	C₂×C₄×C₇₉	—	4	2	no	—
208	C₂×C₄×C₇₉	—	4	1	no	—
209	C₂×C₄×C₇₉	—	4	1	no	—
210	C₂×C₄×C₇₉	#120	1	2	yes	—
211	C₂×C₄×C₇₉	#120	1	2	yes	—
212	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
215	C₂×C₄×C₇₉	2₋¹⁺⁴	1	2	yes	—
216	C₈×C₇₉	—	2	4	no	—
217	C₈×C₇₉	—	4	1	no	—
218	C₈×C₇₉	—	4	1	no	—
219	C₂²×C₇₉	—	2	4	no	—
220	C₂²×C₇₉	—	2	4	no	—
221	C₂²×C₇₉	—	2	4	no	—
222	C₂²×C₇₉	—	4	2	no	—
223	C₂²×C₇₉	—	4	2	no	—
224	C₂²×C₇₉	—	4	2	no	—
225	C₂²×C₇₉	—	4	2	no	—
226	C₂²×C₇₉	—	4	2	no	—
227	C₂²×C₇₉	—	4	2	no	—
228	C₂²×C₇₉	—	4	2	no	—
229	C₂²×C₇₉	—	8	2	no	—
230	C₂²×C₇₉	—	8	2	no	—
231	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
232	C₂²×C₇₉	#547	1	2	yes	—
233	C₂²×C₇₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
234	C₂²×C₇₉	#577	1	1	yes	characteristic
235	C₂²×C₇₉	#578	1	1	yes	characteristic
236	C₄×C₇₉	—	2	2	no	—
237	C₄×C₇₉	—	2	2	no	—
238	C₄×C₇₉	—	4	2	no	—
239	C₄×C₇₉	—	4	2	no	—
240	C₄×C₇₉	—	4	4	no	—
241	C₄×C₇₉	—	8	2	no	—
242	C₄×C₇₉	—	8	1	no	—
243	C₄×C₇₉	—	8	1	no	—
244	C₄×C₇₉	#532	1	1	yes	characteristic
245	C₄×C₇₉	#536	1	1	yes	characteristic
246	C₄×C₇₉	#548	1	2	yes	—
247	#25709	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
248	C₂×C₇₉	—	4	4	no	—
249	C₂×C₇₉	—	8	2	no	—
250	C₂×C₇₉	#2432	1	1	yes	characteristic
251	C₂×C₇₉	#3003	1	1	yes	characteristic
252	C₂×C₇₉	#3013	1	1	yes	characteristic
253	C₂×C₇₉	#3343	1	2	yes	—
254	C₂×C₇₉	#3345	1	2	yes	—
255	C₂×#547	C₂×C₇₉	1	1	yes	characteristic
256	C₂×#501	C₂×C₇₉	1	1	yes	characteristic, complemented
257	C₂×#478	C₂×C₇₉	1	1	yes	characteristic, complemented
258	#2562	C₂×C₇₉	1	1	yes	characteristic, complemented
259	#2034	C₂×C₇₉	1	2	yes	complemented
260	#2033	C₂×C₇₉	1	2	yes	complemented
261	#1987	C₂×C₇₉	1	1	yes	characteristic, complemented
262	#1955	C₂×C₇₉	1	1	yes	characteristic, complemented
263	#1853	C₂×C₇₉	1	2	yes	complemented
264	#1852	C₂×C₇₉	1	2	yes	complemented
265	#1762	C₂×C₇₉	1	1	yes	characteristic, complemented
266	C₇₉	#25709	1	1	yes	characteristic, direct product factor, Sylow
267	C₂²×#41	—	2	1	no	—
268	#547	—	2	4	no	—
269	#547	—	2	4	no	—
270	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
271	C₂×#125	C₂²×C₇₉	1	1	yes	characteristic
272	C₂×#123	—	2	2	no	—
273	C₂×C₂²⋊Q₈	—	2	1	no	—
274	C₂×#121	C₂²×C₇₉	1	2	yes	—
275	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
276	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
277	C₂²×C₄⋊C₄	C₂²×C₇₉	1	2	yes	—
278	#501	—	2	4	no	—
279	#478	—	2	4	no	—
280	C₂×#107	C₂²×C₇₉	1	1	yes	characteristic
281	C₂×#107	C₂²×C₇₉	1	2	yes	—
282	C₂×#106	C₂²×C₇₉	1	1	yes	characteristic
283	C₂×#106	C₂²×C₇₉	1	2	yes	—
284	C₂×C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
285	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
286	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
287	C₂×#102	C₂²×C₇₉	1	2	yes	—
288	C₂×C₂²⋊C₈	C₂²×C₇₉	1	2	yes	—
289	C₂×C₂²⋊C₈	C₂²×C₇₉	1	2	yes	—
290	C₂×#97	C₂²×C₇₉	1	1	yes	characteristic
291	#400	—	2	1	no	—
292	#394	—	2	1	no	—
293	#388	—	2	2	no	—
294	#380	C₂²×C₇₉	1	2	yes	—
295	#380	C₂²×C₇₉	1	2	yes	—
296	C₄×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
297	#340	C₂²×C₇₉	1	2	yes	—
298	#340	C₂²×C₇₉	1	2	yes	—
299	#340	C₂²×C₇₉	1	2	yes	—
300	C₂×#41	—	2	8	no	—
301	C₂×#41	—	4	8	no	—
302	C₂²×Q₈	—	2	1	no	—
303	C₂²×D₄	—	2	2	no	—
304	C₂²×D₄	D₄×C₇₉	1	1	yes	characteristic
305	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
306	C₂³×C₄	—	2	2	no	—
307	C₂³×C₄	—	2	1	no	—
308	C₂³×C₄	C₂³×C₇₉	1	2	yes	—
309	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
310	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
311	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
312	C₄⋊Q₈	—	2	2	no	—
313	C₄⋊Q₈	D₄×C₇₉	1	4	yes	—
314	#125	—	2	2	no	—
315	#125	—	2	2	no	—
316	#123	—	2	16	no	—
317	C₂²⋊Q₈	—	2	8	no	—
318	#121	—	2	4	no	—
319	#121	—	2	4	no	—
320	C₄×D₄	—	2	2	no	—
321	C₄×D₄	—	2	2	no	—
322	C₄×D₄	—	2	2	no	—
323	C₄×D₄	D₄×C₇₉	1	4	yes	—
324	C₂×C₄⋊C₄	—	2	2	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	4	no	—
327	C₂×C₄⋊C₄	—	2	4	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
331	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
332	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
333	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
334	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
335	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
336	C₂×C₂²⋊C₄	—	2	1	no	—
337	C₂×C₂²⋊C₄	—	2	2	no	—
338	C₂×C₂²⋊C₄	—	2	2	no	—
339	C₂×C₂²⋊C₄	—	2	2	no	—
340	C₂×C₂²⋊C₄	D₄×C₇₉	1	2	yes	—
341	C₂×C₄²	—	2	1	no	—
342	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
343	#107	—	2	2	no	—
344	#107	—	2	4	no	—
345	#106	—	2	2	no	—
346	#106	—	2	4	no	—
347	C₄⋊C₈	—	2	2	no	—
348	#102	—	2	2	no	—
349	#102	—	2	2	no	—
350	#102	—	2	4	no	—
351	C₂²⋊C₈	—	2	4	no	—
352	C₂²⋊C₈	—	2	4	no	—
353	#97	—	2	2	no	—
354	#95	—	2	1	no	—
355	#95	—	2	2	no	—
356	#95	—	2	2	no	—
357	C₂⁴	—	2	1	no	—
358	C₂⁴	C₂×D₄×C₇₉	1	2	yes	—
359	#41	—	4	32	no	—
360	C₂×Q₈	—	2	4	no	—
361	C₂×Q₈	—	4	4	no	—
362	C₂×D₄	—	2	4	no	—
363	C₂×D₄	—	2	8	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	4	4	no	—
369	C₂×D₄	—	4	4	no	—
370	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
371	C₂²×C₄	—	2	8	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	4	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	4	4	no	—
385	C₂²×C₄	—	4	4	no	—
386	C₂²×C₄	—	4	4	no	—
387	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
388	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
390	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	#41×C₇₉	1	4	yes	complemented
398	C₄⋊C₄	—	2	8	no	—
399	C₄⋊C₄	—	2	4	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	4	2	no	—
410	C₄⋊C₄	—	4	2	no	—
411	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
412	C₄⋊C₄	C₂×D₄×C₇₉	1	4	yes	—
413	C₂²⋊C₄	—	2	8	no	—
414	C₂²⋊C₄	—	2	4	no	—
415	C₂²⋊C₄	—	2	4	no	—
416	C₂²⋊C₄	—	4	4	no	—
417	C₂²⋊C₄	—	8	2	no	—
418	C₄²	—	8	1	no	—
419	C₄²	C₂×D₄×C₇₉	1	2	yes	—
420	C₄²	C₂×D₄×C₇₉	1	2	yes	—
421	C₂³	—	2	2	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	2	2	no	—
427	C₂³	—	2	2	no	—
428	C₂³	—	4	2	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	4	1	no	—
431	C₂³	—	4	1	no	—
432	C₂³	AGL(1,ℤ/8)×C₇₉	1	4	yes	—
433	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
434	Q₈	—	4	8	no	—
435	D₄	—	2	8	no	—
436	D₄	—	2	2	no	—
437	D₄	—	2	2	no	—
438	D₄	—	4	16	no	—
439	D₄	—	4	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	4	8	no	—
449	C₂×C₄	—	4	16	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	#120×C₇₉	1	2	yes	—
466	C₂×C₄	#120×C₇₉	1	2	yes	—
467	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
468	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
469	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
470	C₂×C₄	2₋¹⁺⁴×C₇₉	1	2	yes	—
471	C₈	—	2	4	no	—
472	C₈	—	4	1	no	—
473	C₈	—	4	1	no	—
474	C₂²	—	2	4	no	—
475	C₂²	—	2	4	no	—
476	C₂²	—	2	4	no	—
477	C₂²	—	4	2	no	—
478	C₂²	—	4	2	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	4	2	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	8	2	no	—
485	C₂²	—	8	2	no	—
486	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
487	C₂²	#547×C₇₉	1	2	yes	—
488	C₂²	C₂×AGL(1,ℤ/8)×C₇₉	1	2	yes	—
489	C₂²	#577×C₇₉	1	1	yes	characteristic
490	C₂²	#578×C₇₉	1	1	yes	characteristic
491	C₄	—	2	2	no	—
492	C₄	—	2	2	no	—
493	C₄	—	4	2	no	—
494	C₄	—	4	2	no	—
495	C₄	—	4	4	no	—
496	C₄	—	8	2	no	—
497	C₄	—	8	1	no	—
498	C₄	—	8	1	no	—
499	C₄	#532×C₇₉	1	1	yes	characteristic
500	C₄	#536×C₇₉	1	1	yes	characteristic
501	C₄	#548×C₇₉	1	2	yes	—
502	C₂	—	4	4	no	—
503	C₂	—	8	2	no	—
504	C₂	C₇₉×#2432	1	1	yes	characteristic
505	C₂	C₇₉×#3003	1	1	yes	characteristic
506	C₂	C₇₉×#3013	1	1	yes	characteristic
507	C₂	C₇₉×#3343	1	2	yes	—
508	C₂	C₇₉×#3345	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₂×#547×C₇₉	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
2. C₂×#501×C₇₉	C₂	semidirect
3. C₂×#478×C₇₉	C₂	semidirect
4. C₇₉×#2562	C₂	semidirect
5. C₇₉×#2034	C₂	semidirect
6. C₇₉×#2033	C₂	semidirect
7. C₇₉×#1987	C₂	semidirect
8. C₇₉×#1955	C₂	semidirect
9. C₇₉×#1853	C₂	semidirect
10. C₇₉×#1852	C₂	semidirect
11. C₇₉×#1762	C₂	semidirect
142. C₂×C₈×C₇₉	#41	semidirect
247. #25709	C₇₉	direct (N × H)
256. C₂×#501	C₂×C₇₉	semidirect
257. C₂×#478	C₂×C₇₉	semidirect
258. #2562	C₂×C₇₉	semidirect
259. #2034	C₂×C₇₉	semidirect
260. #2033	C₂×C₇₉	semidirect
261. #1987	C₂×C₇₉	semidirect
262. #1955	C₂×C₇₉	semidirect
263. #1853	C₂×C₇₉	semidirect
264. #1852	C₂×C₇₉	semidirect
265. #1762	C₂×C₇₉	semidirect
266. C₇₉	#25709	direct (N × H)
397. C₂×C₈	#41×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#547×C₇₉	2
C₂×#501×C₇₉	2
C₂×#478×C₇₉	2
C₇₉×#2562	2
C₇₉×#2034	2
C₇₉×#2033	2
C₇₉×#1987	2
C₇₉×#1955	2
C₇₉×#1853	2
C₇₉×#1852	2
C₇₉×#1762	2
#25709	79

Subgroups — C79×#25709 #34137398

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#25709 #34137398