Subgroups — C₇₉×#25519 #34137208

Order 20224.

1092 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3492	C₂	1	1	yes	maximal, characteristic
2	C₇₉×#3056	C₂	1	2	yes	maximal, complemented
3	C₇₉×#2502	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#2060	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#2039	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₉×#2028	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#2007	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#1882	C₂	1	2	yes	maximal, complemented
9	C₇₉×#1871	C₂	1	2	yes	maximal, complemented
10	C₇₉×#1859	C₂	1	2	yes	maximal, complemented
11	C₂×#343×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₇₉	C₂²	1	2	yes	—
13	C₂²×M₁₆×C₇₉	C₂²	1	2	yes	—
14	#554×C₇₉	—	2	2	no	—
15	#553×C₇₉	—	2	2	no	—
16	#552×C₇₉	—	2	2	no	—
17	#547×C₇₉	—	2	2	no	—
18	#544×C₇₉	C₂²	1	1	yes	characteristic
19	#539×C₇₉	—	2	2	no	—
20	#537×C₇₉	C₂²	1	1	yes	characteristic
21	#525×C₇₉	—	2	2	no	—
22	#525×C₇₉	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
24	#520×C₇₉	C₂²	1	2	yes	—
25	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
26	#470×C₇₉	—	2	2	no	—
27	#468×C₇₉	—	2	2	no	—
28	#467×C₇₉	—	2	2	no	—
29	#465×C₇₉	—	2	2	no	—
30	#428×C₇₉	C₂²	1	2	yes	—
31	C₂×#104×C₇₉	C₂²	1	2	yes	—
32	C₂×#104×C₇₉	C₂²	1	2	yes	—
33	#419×C₇₉	C₂²	1	2	yes	—
34	#417×C₇₉	C₂²	1	2	yes	—
35	#398×C₇₉	—	2	2	no	—
36	#391×C₇₉	C₂²	1	1	yes	characteristic
37	#391×C₇₉	C₂²	1	1	yes	characteristic
38	#385×C₇₉	—	2	2	no	—
39	#384×C₇₉	C₂²	1	1	yes	characteristic
40	#384×C₇₉	C₂²	1	1	yes	characteristic
41	C₄×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
42	#343×C₇₉	C₂²	1	1	yes	characteristic
43	#343×C₇₉	C₂²	1	1	yes	characteristic
44	#343×C₇₉	C₂²	1	2	yes	—
45	#339×C₇₉	C₂²	1	2	yes	—
46	#339×C₇₉	C₂²	1	2	yes	—
47	C₂×#41×C₇₉	—	2	2	no	—
48	C₂×#41×C₇₉	C₂³	1	2	yes	—
49	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₇₉	D₄	1	2	yes	—
51	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
52	#137×C₇₉	—	2	4	no	—
53	#137×C₇₉	—	4	2	no	—
54	C₂×Q₁₆×C₇₉	—	2	2	no	—
55	C₂×SD₁₆×C₇₉	—	2	2	no	—
56	C₂×M₁₆×C₇₉	—	2	2	no	—
57	C₂×M₁₆×C₇₉	—	2	4	no	—
58	C₂×M₁₆×C₇₉	—	4	2	no	—
59	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
60	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
61	C₂²×C₈×C₇₉	—	2	2	no	—
62	C₄⋊Q₈×C₇₉	—	2	2	no	—
63	#126×C₇₉	—	2	4	no	—
64	#125×C₇₉	—	2	4	no	—
65	#125×C₇₉	—	2	2	no	—
66	#123×C₇₉	—	2	4	no	—
67	#123×C₇₉	—	2	4	no	—
68	#123×C₇₉	—	2	2	no	—
69	C₂²⋊Q₈×C₇₉	—	2	2	no	—
70	C₂²⋊Q₈×C₇₉	—	2	4	no	—
71	C₂²⋊Q₈×C₇₉	—	2	2	no	—
72	C₂²⋊Q₈×C₇₉	—	2	2	no	—
73	C₂²⋊Q₈×C₇₉	—	2	2	no	—
74	C₂²⋊Q₈×C₇₉	—	2	2	no	—
75	C₂²⋊Q₈×C₇₉	D₄	1	2	yes	—
76	C₂²⋊Q₈×C₇₉	D₄	1	2	yes	—
77	#121×C₇₉	—	2	2	no	—
78	#121×C₇₉	—	2	2	no	—
79	#121×C₇₉	—	2	2	no	—
80	#121×C₇₉	D₄	1	2	yes	—
81	#121×C₇₉	D₄	1	2	yes	—
82	#120×C₇₉	—	2	2	no	—
83	C₄×Q₈×C₇₉	—	2	2	no	—
84	C₄×D₄×C₇₉	—	2	4	no	—
85	C₄×D₄×C₇₉	—	2	2	no	—
86	C₄×D₄×C₇₉	—	2	4	no	—
87	C₄×D₄×C₇₉	—	2	2	no	—
88	C₄×D₄×C₇₉	—	2	2	no	—
89	#117×C₇₉	—	2	2	no	—
90	#117×C₇₉	—	2	2	no	—
91	#117×C₇₉	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
93	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
94	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
95	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
96	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
97	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
98	C₂×C₄⋊C₄×C₇₉	D₄	1	2	yes	—
99	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
102	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
104	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
106	#107×C₇₉	—	2	2	no	—
107	#106×C₇₉	—	2	2	no	—
108	#104×C₇₉	—	2	4	no	—
109	#104×C₇₉	—	4	2	no	—
110	#103×C₇₉	—	2	2	no	—
111	#103×C₇₉	—	2	2	no	—
112	#103×C₇₉	—	2	2	no	—
113	#102×C₇₉	—	2	2	no	—
114	#95×C₇₉	—	2	1	no	—
115	#95×C₇₉	—	2	2	no	—
116	#95×C₇₉	—	2	2	no	—
117	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
118	#41×C₇₉	—	2	2	no	—
119	#41×C₇₉	—	2	2	no	—
120	#41×C₇₉	—	2	2	no	—
121	#41×C₇₉	—	2	2	no	—
122	#41×C₇₉	—	8	4	no	—
123	C₂×Q₈×C₇₉	—	2	2	no	—
124	C₂×Q₈×C₇₉	—	2	2	no	—
125	C₂×Q₈×C₇₉	—	2	2	no	—
126	C₂×Q₈×C₇₉	—	2	1	no	—
127	C₂×Q₈×C₇₉	—	2	1	no	—
128	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
129	C₂×D₄×C₇₉	—	2	2	no	—
130	C₂×D₄×C₇₉	—	2	2	no	—
131	C₂×D₄×C₇₉	—	2	2	no	—
132	C₂×D₄×C₇₉	—	2	2	no	—
133	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₇₉	—	2	2	no	—
135	C₂²×C₄×C₇₉	—	2	1	no	—
136	C₂²×C₄×C₇₉	—	2	1	no	—
137	C₂²×C₄×C₇₉	—	2	2	no	—
138	C₂²×C₄×C₇₉	—	2	1	no	—
139	C₂²×C₄×C₇₉	—	2	1	no	—
140	C₂²×C₄×C₇₉	—	2	4	no	—
141	C₂²×C₄×C₇₉	—	2	2	no	—
142	C₂²×C₄×C₇₉	—	2	2	no	—
143	C₂²×C₄×C₇₉	—	2	1	no	—
144	C₂²×C₄×C₇₉	—	2	1	no	—
145	C₂²×C₄×C₇₉	—	8	2	no	—
146	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
152	Q₁₆×C₇₉	—	4	4	no	—
153	SD₁₆×C₇₉	—	4	4	no	—
154	M₁₆×C₇₉	—	2	2	no	—
155	M₁₆×C₇₉	—	2	2	no	—
156	M₁₆×C₇₉	—	2	2	no	—
157	M₁₆×C₇₉	—	4	4	no	—
158	M₁₆×C₇₉	#41	1	4	yes	complemented
159	C₂×C₈×C₇₉	—	2	2	no	—
160	C₂×C₈×C₇₉	—	2	2	no	—
161	C₂×C₈×C₇₉	—	4	4	no	—
162	C₄⋊C₄×C₇₉	—	2	4	no	—
163	C₄⋊C₄×C₇₉	—	2	2	no	—
164	C₄⋊C₄×C₇₉	—	2	2	no	—
165	C₄⋊C₄×C₇₉	—	2	4	no	—
166	C₄⋊C₄×C₇₉	—	2	4	no	—
167	C₄⋊C₄×C₇₉	—	2	2	no	—
168	C₄⋊C₄×C₇₉	—	2	2	no	—
169	C₄⋊C₄×C₇₉	—	2	2	no	—
170	C₄⋊C₄×C₇₉	—	2	2	no	—
171	C₄⋊C₄×C₇₉	—	2	2	no	—
172	C₄⋊C₄×C₇₉	—	4	2	no	—
173	C₄⋊C₄×C₇₉	—	8	2	no	—
174	C₄⋊C₄×C₇₉	—	8	2	no	—
175	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
176	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
177	C₂²⋊C₄×C₇₉	—	2	4	no	—
178	C₂²⋊C₄×C₇₉	—	2	4	no	—
179	C₂²⋊C₄×C₇₉	—	2	4	no	—
180	C₂²⋊C₄×C₇₉	—	2	2	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	—	4	1	no	—
186	C₂²⋊C₄×C₇₉	—	4	1	no	—
187	C₄²×C₇₉	—	2	4	no	—
188	C₄²×C₇₉	—	2	2	no	—
189	C₄²×C₇₉	—	2	2	no	—
190	C₄²×C₇₉	—	2	1	no	—
191	C₄²×C₇₉	—	2	1	no	—
192	C₂³×C₇₉	—	2	1	no	—
193	C₂³×C₇₉	—	2	1	no	—
194	C₂³×C₇₉	—	2	2	no	—
195	C₂³×C₇₉	—	2	2	no	—
196	C₂³×C₇₉	—	4	1	no	—
197	C₂³×C₇₉	#120	1	1	yes	characteristic
198	C₂³×C₇₉	#120	1	1	yes	characteristic
199	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
200	Q₈×C₇₉	—	2	2	no	—
201	Q₈×C₇₉	—	2	2	no	—
202	Q₈×C₇₉	—	4	2	no	—
203	Q₈×C₇₉	—	4	2	no	—
204	Q₈×C₇₉	—	8	2	no	—
205	D₄×C₇₉	—	2	2	no	—
206	D₄×C₇₉	—	2	2	no	—
207	D₄×C₇₉	—	4	4	no	—
208	D₄×C₇₉	—	4	2	no	—
209	D₄×C₇₉	—	4	2	no	—
210	D₄×C₇₉	—	4	4	no	—
211	D₄×C₇₉	—	8	2	no	—
212	C₂×C₄×C₇₉	—	2	1	no	—
213	C₂×C₄×C₇₉	—	2	1	no	—
214	C₂×C₄×C₇₉	—	2	2	no	—
215	C₂×C₄×C₇₉	—	2	2	no	—
216	C₂×C₄×C₇₉	—	2	2	no	—
217	C₂×C₄×C₇₉	—	2	2	no	—
218	C₂×C₄×C₇₉	—	2	2	no	—
219	C₂×C₄×C₇₉	—	2	2	no	—
220	C₂×C₄×C₇₉	—	2	2	no	—
221	C₂×C₄×C₇₉	—	2	2	no	—
222	C₂×C₄×C₇₉	—	2	2	no	—
223	C₂×C₄×C₇₉	—	2	2	no	—
224	C₂×C₄×C₇₉	—	2	2	no	—
225	C₂×C₄×C₇₉	—	4	1	no	—
226	C₂×C₄×C₇₉	—	4	1	no	—
227	C₂×C₄×C₇₉	—	4	4	no	—
228	C₂×C₄×C₇₉	—	4	1	no	—
229	C₂×C₄×C₇₉	—	4	1	no	—
230	C₂×C₄×C₇₉	—	4	2	no	—
231	C₂×C₄×C₇₉	—	4	2	no	—
232	C₂×C₄×C₇₉	—	4	2	no	—
233	C₂×C₄×C₇₉	—	4	2	no	—
234	C₂×C₄×C₇₉	—	4	2	no	—
235	C₂×C₄×C₇₉	—	4	1	no	—
236	C₂×C₄×C₇₉	—	4	1	no	—
237	C₂×C₄×C₇₉	—	4	1	no	—
238	C₂×C₄×C₇₉	—	4	1	no	—
239	C₂×C₄×C₇₉	—	8	2	no	—
240	C₂×C₄×C₇₉	—	8	4	no	—
241	C₂×C₄×C₇₉	#120	1	2	yes	—
242	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
243	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
244	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
245	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
246	C₈×C₇₉	—	2	4	no	—
247	C₈×C₇₉	—	4	2	no	—
248	C₂²×C₇₉	—	2	1	no	—
249	C₂²×C₇₉	—	2	1	no	—
250	C₂²×C₇₉	—	2	1	no	—
251	C₂²×C₇₉	—	2	1	no	—
252	C₂²×C₇₉	—	2	1	no	—
253	C₂²×C₇₉	—	2	1	no	—
254	C₂²×C₇₉	—	2	1	no	—
255	C₂²×C₇₉	—	4	2	no	—
256	C₂²×C₇₉	—	4	2	no	—
257	C₂²×C₇₉	—	4	2	no	—
258	C₂²×C₇₉	—	4	2	no	—
259	C₂²×C₇₉	—	4	2	no	—
260	C₂²×C₇₉	#456	1	2	yes	—
261	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
262	C₂²×C₇₉	#532	1	1	yes	characteristic
263	C₂²×C₇₉	#537	1	1	yes	characteristic
264	C₄×C₇₉	—	2	2	no	—
265	C₄×C₇₉	—	4	2	no	—
266	C₄×C₇₉	—	4	2	no	—
267	C₄×C₇₉	—	4	2	no	—
268	C₄×C₇₉	—	4	2	no	—
269	C₄×C₇₉	—	4	2	no	—
270	C₄×C₇₉	—	4	2	no	—
271	C₄×C₇₉	—	4	2	no	—
272	C₄×C₇₉	—	8	1	no	—
273	C₄×C₇₉	—	8	1	no	—
274	C₄×C₇₉	#546	1	2	yes	—
275	C₄×C₇₉	#547	1	2	yes	—
276	#25519	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
277	C₂×C₇₉	—	2	1	no	—
278	C₂×C₇₉	—	2	1	no	—
279	C₂×C₇₉	—	2	2	no	—
280	C₂×C₇₉	—	4	1	no	—
281	C₂×C₇₉	—	8	2	no	—
282	C₂×C₇₉	#2430	1	1	yes	characteristic
283	C₂×C₇₉	C₂×#456	1	1	yes	characteristic
284	C₂×C₇₉	#3019	1	1	yes	characteristic
285	#3492	C₂×C₇₉	1	1	yes	characteristic
286	#3056	C₂×C₇₉	1	2	yes	complemented
287	#2502	C₂×C₇₉	1	1	yes	characteristic, complemented
288	#2060	C₂×C₇₉	1	1	yes	characteristic, complemented
289	#2039	C₂×C₇₉	1	1	yes	characteristic, complemented
290	#2028	C₂×C₇₉	1	1	yes	characteristic, complemented
291	#2007	C₂×C₇₉	1	1	yes	characteristic, complemented
292	#1882	C₂×C₇₉	1	2	yes	complemented
293	#1871	C₂×C₇₉	1	2	yes	complemented
294	#1859	C₂×C₇₉	1	2	yes	complemented
295	C₂×#343	C₂×C₇₉	1	1	yes	characteristic, complemented
296	C₇₉	#25519	1	1	yes	characteristic, direct product factor, Sylow
297	C₂×#137	C₂²×C₇₉	1	2	yes	—
298	C₂²×M₁₆	C₂²×C₇₉	1	2	yes	—
299	#554	—	2	2	no	—
300	#553	—	2	2	no	—
301	#552	—	2	2	no	—
302	#547	—	2	2	no	—
303	#544	C₂²×C₇₉	1	1	yes	characteristic
304	#539	—	2	2	no	—
305	#537	C₂²×C₇₉	1	1	yes	characteristic
306	#525	—	2	2	no	—
307	#525	C₂²×C₇₉	1	2	yes	—
308	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
309	#520	C₂²×C₇₉	1	2	yes	—
310	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
311	#470	—	2	2	no	—
312	#468	—	2	2	no	—
313	#467	—	2	2	no	—
314	#465	—	2	2	no	—
315	#428	C₂²×C₇₉	1	2	yes	—
316	C₂×#104	C₂²×C₇₉	1	2	yes	—
317	C₂×#104	C₂²×C₇₉	1	2	yes	—
318	#419	C₂²×C₇₉	1	2	yes	—
319	#417	C₂²×C₇₉	1	2	yes	—
320	#398	—	2	2	no	—
321	#391	C₂²×C₇₉	1	1	yes	characteristic
322	#391	C₂²×C₇₉	1	1	yes	characteristic
323	#385	—	2	2	no	—
324	#384	C₂²×C₇₉	1	1	yes	characteristic
325	#384	C₂²×C₇₉	1	1	yes	characteristic
326	C₄×C₂²⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
327	#343	C₂²×C₇₉	1	1	yes	characteristic
328	#343	C₂²×C₇₉	1	2	yes	—
329	#343	C₂²×C₇₉	1	1	yes	characteristic
330	#339	C₂²×C₇₉	1	2	yes	—
331	#339	C₂²×C₇₉	1	2	yes	—
332	C₂×#41	—	2	2	no	—
333	C₂×#41	C₂³×C₇₉	1	2	yes	—
334	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
335	C₂³×C₄	D₄×C₇₉	1	2	yes	—
336	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
337	#137	—	2	4	no	—
338	#137	—	4	2	no	—
339	C₂×Q₁₆	—	2	2	no	—
340	C₂×SD₁₆	—	2	2	no	—
341	C₂×M₁₆	—	2	2	no	—
342	C₂×M₁₆	—	2	4	no	—
343	C₂×M₁₆	—	4	2	no	—
344	C₂×M₁₆	C₂³×C₇₉	1	2	yes	—
345	C₂×M₁₆	C₂³×C₇₉	1	2	yes	—
346	C₂²×C₈	—	2	2	no	—
347	C₄⋊Q₈	—	2	2	no	—
348	#126	—	2	4	no	—
349	#125	—	2	4	no	—
350	#125	—	2	2	no	—
351	#123	—	2	4	no	—
352	#123	—	2	4	no	—
353	#123	—	2	2	no	—
354	C₂²⋊Q₈	—	2	2	no	—
355	C₂²⋊Q₈	—	2	4	no	—
356	C₂²⋊Q₈	—	2	2	no	—
357	C₂²⋊Q₈	—	2	2	no	—
358	C₂²⋊Q₈	—	2	2	no	—
359	C₂²⋊Q₈	—	2	2	no	—
360	C₂²⋊Q₈	D₄×C₇₉	1	2	yes	—
361	C₂²⋊Q₈	D₄×C₇₉	1	2	yes	—
362	#121	—	2	2	no	—
363	#121	—	2	2	no	—
364	#121	—	2	2	no	—
365	#121	D₄×C₇₉	1	2	yes	—
366	#121	D₄×C₇₉	1	2	yes	—
367	#120	—	2	2	no	—
368	C₄×Q₈	—	2	2	no	—
369	C₄×D₄	—	2	4	no	—
370	C₄×D₄	—	2	2	no	—
371	C₄×D₄	—	2	4	no	—
372	C₄×D₄	—	2	2	no	—
373	C₄×D₄	—	2	2	no	—
374	#117	—	2	2	no	—
375	#117	—	2	2	no	—
376	#117	C₂³×C₇₉	1	2	yes	—
377	C₂×C₄⋊C₄	—	2	2	no	—
378	C₂×C₄⋊C₄	—	2	2	no	—
379	C₂×C₄⋊C₄	—	2	2	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	—	2	2	no	—
382	C₂×C₄⋊C₄	—	2	2	no	—
383	C₂×C₄⋊C₄	D₄×C₇₉	1	2	yes	—
384	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
387	C₂×C₂²⋊C₄	—	2	1	no	—
388	C₂×C₂²⋊C₄	—	2	1	no	—
389	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
390	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
391	#107	—	2	2	no	—
392	#106	—	2	2	no	—
393	#104	—	2	4	no	—
394	#104	—	4	2	no	—
395	#103	—	2	2	no	—
396	#103	—	2	2	no	—
397	#103	—	2	2	no	—
398	#102	—	2	2	no	—
399	#95	—	2	1	no	—
400	#95	—	2	2	no	—
401	#95	—	2	2	no	—
402	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
403	#41	—	2	2	no	—
404	#41	—	2	2	no	—
405	#41	—	2	2	no	—
406	#41	—	2	2	no	—
407	#41	—	8	4	no	—
408	C₂×Q₈	—	2	2	no	—
409	C₂×Q₈	—	2	2	no	—
410	C₂×Q₈	—	2	2	no	—
411	C₂×Q₈	—	2	1	no	—
412	C₂×Q₈	—	2	1	no	—
413	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	4	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	8	2	no	—
431	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
432	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
433	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
434	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
435	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
436	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
437	Q₁₆	—	4	4	no	—
438	SD₁₆	—	4	4	no	—
439	M₁₆	—	2	2	no	—
440	M₁₆	—	2	2	no	—
441	M₁₆	—	2	2	no	—
442	M₁₆	—	4	4	no	—
443	M₁₆	#41×C₇₉	1	4	yes	complemented
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	—	2	2	no	—
446	C₂×C₈	—	4	4	no	—
447	C₄⋊C₄	—	2	4	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	4	no	—
451	C₄⋊C₄	—	2	4	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	4	2	no	—
458	C₄⋊C₄	—	8	2	no	—
459	C₄⋊C₄	—	8	2	no	—
460	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
461	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
462	C₂²⋊C₄	—	2	4	no	—
463	C₂²⋊C₄	—	2	4	no	—
464	C₂²⋊C₄	—	2	4	no	—
465	C₂²⋊C₄	—	2	2	no	—
466	C₂²⋊C₄	—	2	2	no	—
467	C₂²⋊C₄	—	2	2	no	—
468	C₂²⋊C₄	—	2	2	no	—
469	C₂²⋊C₄	—	2	2	no	—
470	C₂²⋊C₄	—	4	1	no	—
471	C₂²⋊C₄	—	4	1	no	—
472	C₄²	—	2	4	no	—
473	C₄²	—	2	2	no	—
474	C₄²	—	2	2	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	2	1	no	—
479	C₂³	—	2	1	no	—
480	C₂³	—	2	2	no	—
481	C₂³	—	4	1	no	—
482	C₂³	#120×C₇₉	1	1	yes	characteristic
483	C₂³	#120×C₇₉	1	1	yes	characteristic
484	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
485	Q₈	—	2	2	no	—
486	Q₈	—	2	2	no	—
487	Q₈	—	4	2	no	—
488	Q₈	—	4	2	no	—
489	Q₈	—	8	2	no	—
490	D₄	—	2	2	no	—
491	D₄	—	2	2	no	—
492	D₄	—	4	4	no	—
493	D₄	—	4	4	no	—
494	D₄	—	4	2	no	—
495	D₄	—	4	2	no	—
496	D₄	—	8	2	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	4	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	8	2	no	—
525	C₂×C₄	—	8	4	no	—
526	C₂×C₄	#120×C₇₉	1	2	yes	—
527	C₂×C₄	C₂²×D₄×C₇₉	1	2	yes	—
528	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
529	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
530	C₂×C₄	2₋¹⁺⁴×C₇₉	1	1	yes	characteristic
531	C₈	—	2	4	no	—
532	C₈	—	4	2	no	—
533	C₂²	—	2	1	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	2	1	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	4	2	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	4	2	no	—
545	C₂²	#456×C₇₉	1	2	yes	—
546	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
547	C₂²	#532×C₇₉	1	1	yes	characteristic
548	C₂²	#537×C₇₉	1	1	yes	characteristic
549	C₄	—	2	2	no	—
550	C₄	—	4	2	no	—
551	C₄	—	4	2	no	—
552	C₄	—	4	2	no	—
553	C₄	—	4	2	no	—
554	C₄	—	4	2	no	—
555	C₄	—	4	2	no	—
556	C₄	—	4	2	no	—
557	C₄	—	8	1	no	—
558	C₄	—	8	1	no	—
559	C₄	#546×C₇₉	1	2	yes	—
560	C₄	#547×C₇₉	1	2	yes	—
561	C₂	—	2	1	no	—
562	C₂	—	2	1	no	—
563	C₂	—	2	2	no	—
564	C₂	—	4	1	no	—
565	C₂	—	8	2	no	—
566	C₂	C₇₉×#2430	1	1	yes	characteristic
567	C₂	C₂×#456×C₇₉	1	1	yes	characteristic
568	C₂	C₇₉×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₇₉×#3492	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₉ ◁ C₂³×C₄×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇₉×#3056	C₂	semidirect
3. C₇₉×#2502	C₂	semidirect
4. C₇₉×#2060	C₂	semidirect
5. C₇₉×#2039	C₂	semidirect
6. C₇₉×#2028	C₂	semidirect
7. C₇₉×#2007	C₂	semidirect
8. C₇₉×#1882	C₂	semidirect
9. C₇₉×#1871	C₂	semidirect
10. C₇₉×#1859	C₂	semidirect
11. C₂×#343×C₇₉	C₂	semidirect
158. M₁₆×C₇₉	#41	semidirect
276. #25519	C₇₉	direct (N × H)
286. #3056	C₂×C₇₉	semidirect
287. #2502	C₂×C₇₉	semidirect
288. #2060	C₂×C₇₉	semidirect
289. #2039	C₂×C₇₉	semidirect
290. #2028	C₂×C₇₉	semidirect
291. #2007	C₂×C₇₉	semidirect
292. #1882	C₂×C₇₉	semidirect
293. #1871	C₂×C₇₉	semidirect
294. #1859	C₂×C₇₉	semidirect
295. C₂×#343	C₂×C₇₉	semidirect
296. C₇₉	#25519	direct (N × H)
443. M₁₆	#41×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₇₉×#3492	2
C₇₉×#3056	2
C₇₉×#2502	2
C₇₉×#2060	2
C₇₉×#2039	2
C₇₉×#2028	2
C₇₉×#2007	2
C₇₉×#1882	2
C₇₉×#1871	2
C₇₉×#1859	2
C₂×#343×C₇₉	2
#25519	79

Subgroups — C79×#25519 #34137208

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#25519 #34137208