Subgroups — C₇₉×#25557 #34137246

Order 20224.

1086 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#552×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#484×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#470×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#2415	C₂	1	1	yes	maximal, characteristic
5	C₇₉×#2059	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₉×#2036	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#2026	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#2001	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#1878	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#1873	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1873	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₉×#1870	C₂	1	1	yes	maximal, characteristic
13	C₇₉×#1863	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₉×#1854	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#1736	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
18	#552×C₇₉	—	2	4	no	—
19	#552×C₇₉	—	2	4	no	—
20	C₂×#126×C₇₉	—	2	1	no	—
21	C₂×#125×C₇₉	—	2	1	no	—
22	C₂×#125×C₇₉	C₂²	1	1	yes	characteristic
23	C₂×#123×C₇₉	—	2	1	no	—
24	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
30	C₂×#117×C₇₉	—	2	1	no	—
31	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
32	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
34	#484×C₇₉	—	2	4	no	—
35	#470×C₇₉	—	2	4	no	—
36	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic
37	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic
38	C₂×#106×C₇₉	C₂²	1	1	yes	characteristic
39	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
40	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
41	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
42	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
43	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
44	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
48	#397×C₇₉	—	2	1	no	—
49	#394×C₇₉	—	2	1	no	—
50	#391×C₇₉	C₂²	1	1	yes	characteristic
51	#389×C₇₉	—	2	1	no	—
52	#389×C₇₉	C₂²	1	1	yes	characteristic
53	#388×C₇₉	—	2	1	no	—
54	#380×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	#340×C₇₉	C₂²	1	1	yes	characteristic
60	#340×C₇₉	C₂²	1	1	yes	characteristic
61	#336×C₇₉	C₂²	1	1	yes	characteristic
62	#336×C₇₉	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
64	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₇₉	D₄	1	1	yes	characteristic
66	C₂³×C₄×C₇₉	—	2	1	no	—
67	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
69	C₂×Q₁₆×C₇₉	—	2	2	no	—
70	C₂×Q₁₆×C₇₉	—	2	2	no	—
71	C₂×Q₁₆×C₇₉	—	4	1	no	—
72	C₂×M₁₆×C₇₉	—	2	2	no	—
73	C₂×M₁₆×C₇₉	—	2	2	no	—
74	C₂×M₁₆×C₇₉	—	4	1	no	—
75	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
79	#126×C₇₉	—	2	8	no	—
80	#125×C₇₉	—	2	8	no	—
81	#125×C₇₉	—	2	2	no	—
82	#125×C₇₉	—	2	2	no	—
83	#123×C₇₉	—	2	8	no	—
84	C₂²⋊Q₈×C₇₉	—	2	2	no	—
85	C₂²⋊Q₈×C₇₉	—	2	2	no	—
86	C₂²⋊Q₈×C₇₉	—	2	2	no	—
87	C₂²⋊Q₈×C₇₉	—	2	2	no	—
88	C₂²⋊Q₈×C₇₉	—	2	2	no	—
89	C₂²⋊Q₈×C₇₉	—	2	2	no	—
90	C₂²⋊Q₈×C₇₉	—	4	1	no	—
91	C₂²⋊Q₈×C₇₉	D₄	1	4	yes	—
92	C₄×Q₈×C₇₉	—	2	2	no	—
93	C₄×Q₈×C₇₉	—	2	2	no	—
94	C₄×D₄×C₇₉	—	2	2	no	—
95	C₄×D₄×C₇₉	—	2	2	no	—
96	#117×C₇₉	—	2	8	no	—
97	#117×C₇₉	—	2	2	no	—
98	#117×C₇₉	—	2	2	no	—
99	#117×C₇₉	—	2	2	no	—
100	#117×C₇₉	—	4	1	no	—
101	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
102	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
103	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
104	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
105	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
106	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
107	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
108	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
109	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
110	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
111	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₇₉	D₄	1	4	yes	—
113	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
119	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
127	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
128	C₂×C₄²×C₇₉	—	2	1	no	—
129	C₂×C₄²×C₇₉	—	2	1	no	—
130	C₂×C₄²×C₇₉	—	2	1	no	—
131	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
132	#107×C₇₉	—	2	2	no	—
133	#107×C₇₉	—	2	2	no	—
134	#106×C₇₉	—	2	2	no	—
135	#103×C₇₉	—	2	2	no	—
136	#103×C₇₉	—	2	2	no	—
137	#103×C₇₉	—	2	2	no	—
138	#103×C₇₉	—	2	2	no	—
139	#103×C₇₉	—	2	2	no	—
140	#103×C₇₉	—	4	1	no	—
141	C₂²⋊C₈×C₇₉	—	2	2	no	—
142	C₂²⋊C₈×C₇₉	—	2	2	no	—
143	C₂²⋊C₈×C₇₉	—	4	1	no	—
144	#95×C₇₉	—	2	1	no	—
145	#95×C₇₉	—	2	1	no	—
146	#95×C₇₉	—	2	1	no	—
147	#95×C₇₉	—	2	1	no	—
148	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
149	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
150	C₂×Q₈×C₇₉	—	2	1	no	—
151	C₂×Q₈×C₇₉	—	2	1	no	—
152	C₂×Q₈×C₇₉	—	2	1	no	—
153	C₂×Q₈×C₇₉	—	2	1	no	—
154	C₂×Q₈×C₇₉	—	2	1	no	—
155	C₂×Q₈×C₇₉	—	2	1	no	—
156	C₂×Q₈×C₇₉	—	2	1	no	—
157	C₂×Q₈×C₇₉	—	2	1	no	—
158	C₂×Q₈×C₇₉	—	2	1	no	—
159	C₂×Q₈×C₇₉	—	2	1	no	—
160	C₂×Q₈×C₇₉	—	2	1	no	—
161	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
162	C₂×D₄×C₇₉	—	2	2	no	—
163	C₂×D₄×C₇₉	—	4	1	no	—
164	C₂×D₄×C₇₉	—	4	1	no	—
165	C₂²×C₄×C₇₉	—	2	1	no	—
166	C₂²×C₄×C₇₉	—	2	1	no	—
167	C₂²×C₄×C₇₉	—	2	1	no	—
168	C₂²×C₄×C₇₉	—	2	1	no	—
169	C₂²×C₄×C₇₉	—	2	4	no	—
170	C₂²×C₄×C₇₉	—	2	1	no	—
171	C₂²×C₄×C₇₉	—	2	1	no	—
172	C₂²×C₄×C₇₉	—	2	1	no	—
173	C₂²×C₄×C₇₉	—	2	1	no	—
174	C₂²×C₄×C₇₉	—	2	1	no	—
175	C₂²×C₄×C₇₉	—	2	1	no	—
176	C₂²×C₄×C₇₉	—	2	1	no	—
177	C₂²×C₄×C₇₉	—	2	1	no	—
178	C₂²×C₄×C₇₉	—	2	1	no	—
179	C₂²×C₄×C₇₉	—	2	1	no	—
180	C₂²×C₄×C₇₉	—	2	1	no	—
181	C₂²×C₄×C₇₉	—	2	1	no	—
182	C₂²×C₄×C₇₉	—	2	1	no	—
183	C₂²×C₄×C₇₉	—	2	1	no	—
184	C₂²×C₄×C₇₉	—	4	2	no	—
185	C₂²×C₄×C₇₉	—	4	2	no	—
186	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
191	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
192	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
193	Q₁₆×C₇₉	—	4	4	no	—
194	M₁₆×C₇₉	—	4	4	no	—
195	C₂×C₈×C₇₉	—	2	1	no	—
196	C₂×C₈×C₇₉	—	2	1	no	—
197	C₂×C₈×C₇₉	—	2	1	no	—
198	C₂×C₈×C₇₉	—	2	1	no	—
199	C₂×C₈×C₇₉	—	2	1	no	—
200	C₂×C₈×C₇₉	—	2	1	no	—
201	C₂×C₈×C₇₉	—	2	1	no	—
202	C₂×C₈×C₇₉	—	2	1	no	—
203	C₂×C₈×C₇₉	—	2	1	no	—
204	C₂×C₈×C₇₉	—	2	1	no	—
205	C₂×C₈×C₇₉	—	2	1	no	—
206	C₂×C₈×C₇₉	#41	1	2	yes	—
207	C₄⋊C₄×C₇₉	—	2	4	no	—
208	C₄⋊C₄×C₇₉	—	2	4	no	—
209	C₄⋊C₄×C₇₉	—	2	4	no	—
210	C₄⋊C₄×C₇₉	—	2	4	no	—
211	C₄⋊C₄×C₇₉	—	2	4	no	—
212	C₄⋊C₄×C₇₉	—	2	4	no	—
213	C₄⋊C₄×C₇₉	—	2	2	no	—
214	C₄⋊C₄×C₇₉	—	2	1	no	—
215	C₄⋊C₄×C₇₉	—	2	1	no	—
216	C₄⋊C₄×C₇₉	—	2	1	no	—
217	C₄⋊C₄×C₇₉	—	2	1	no	—
218	C₄⋊C₄×C₇₉	—	2	1	no	—
219	C₄⋊C₄×C₇₉	—	2	1	no	—
220	C₄⋊C₄×C₇₉	—	2	1	no	—
221	C₄⋊C₄×C₇₉	—	2	1	no	—
222	C₄⋊C₄×C₇₉	—	4	2	no	—
223	C₄⋊C₄×C₇₉	—	4	2	no	—
224	C₄⋊C₄×C₇₉	—	4	2	no	—
225	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
226	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
227	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
228	C₄⋊C₄×C₇₉	#41	1	2	yes	—
229	C₂²⋊C₄×C₇₉	—	2	4	no	—
230	C₂²⋊C₄×C₇₉	—	2	4	no	—
231	C₂²⋊C₄×C₇₉	—	2	4	no	—
232	C₂²⋊C₄×C₇₉	—	2	2	no	—
233	C₂²⋊C₄×C₇₉	—	2	2	no	—
234	C₂²⋊C₄×C₇₉	—	4	2	no	—
235	C₂²⋊C₄×C₇₉	—	4	2	no	—
236	C₂²⋊C₄×C₇₉	—	4	2	no	—
237	C₂²⋊C₄×C₇₉	—	4	2	no	—
238	C₄²×C₇₉	—	2	4	no	—
239	C₄²×C₇₉	—	2	4	no	—
240	C₄²×C₇₉	—	2	1	no	—
241	C₄²×C₇₉	—	2	1	no	—
242	C₄²×C₇₉	—	4	2	no	—
243	C₂³×C₇₉	—	2	1	no	—
244	C₂³×C₇₉	—	2	1	no	—
245	C₂³×C₇₉	—	2	1	no	—
246	C₂³×C₇₉	—	2	1	no	—
247	C₂³×C₇₉	—	2	1	no	—
248	C₂³×C₇₉	—	2	1	no	—
249	C₂³×C₇₉	—	2	1	no	—
250	C₂³×C₇₉	—	2	1	no	—
251	C₂³×C₇₉	—	2	1	no	—
252	C₂³×C₇₉	—	2	1	no	—
253	C₂³×C₇₉	—	2	1	no	—
254	C₂³×C₇₉	—	2	1	no	—
255	C₂³×C₇₉	—	2	1	no	—
256	C₂³×C₇₉	#120	1	2	yes	—
257	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
258	Q₈×C₇₉	—	2	2	no	—
259	Q₈×C₇₉	—	2	2	no	—
260	Q₈×C₇₉	—	4	1	no	—
261	Q₈×C₇₉	—	4	1	no	—
262	Q₈×C₇₉	—	4	1	no	—
263	Q₈×C₇₉	—	4	1	no	—
264	Q₈×C₇₉	—	4	1	no	—
265	Q₈×C₇₉	—	4	1	no	—
266	D₄×C₇₉	—	4	4	no	—
267	C₂×C₄×C₇₉	—	2	1	no	—
268	C₂×C₄×C₇₉	—	2	1	no	—
269	C₂×C₄×C₇₉	—	2	2	no	—
270	C₂×C₄×C₇₉	—	2	2	no	—
271	C₂×C₄×C₇₉	—	2	2	no	—
272	C₂×C₄×C₇₉	—	2	2	no	—
273	C₂×C₄×C₇₉	—	2	1	no	—
274	C₂×C₄×C₇₉	—	2	1	no	—
275	C₂×C₄×C₇₉	—	2	2	no	—
276	C₂×C₄×C₇₉	—	2	2	no	—
277	C₂×C₄×C₇₉	—	2	2	no	—
278	C₂×C₄×C₇₉	—	2	1	no	—
279	C₂×C₄×C₇₉	—	2	2	no	—
280	C₂×C₄×C₇₉	—	2	2	no	—
281	C₂×C₄×C₇₉	—	2	1	no	—
282	C₂×C₄×C₇₉	—	2	1	no	—
283	C₂×C₄×C₇₉	—	2	1	no	—
284	C₂×C₄×C₇₉	—	2	1	no	—
285	C₂×C₄×C₇₉	—	2	1	no	—
286	C₂×C₄×C₇₉	—	2	1	no	—
287	C₂×C₄×C₇₉	—	4	8	no	—
288	C₂×C₄×C₇₉	—	4	1	no	—
289	C₂×C₄×C₇₉	—	4	1	no	—
290	C₂×C₄×C₇₉	—	4	1	no	—
291	C₂×C₄×C₇₉	—	4	1	no	—
292	C₂×C₄×C₇₉	—	4	1	no	—
293	C₂×C₄×C₇₉	—	4	1	no	—
294	C₂×C₄×C₇₉	—	4	1	no	—
295	C₂×C₄×C₇₉	—	4	1	no	—
296	C₂×C₄×C₇₉	—	4	1	no	—
297	C₂×C₄×C₇₉	—	4	1	no	—
298	C₂×C₄×C₇₉	—	4	1	no	—
299	C₂×C₄×C₇₉	—	4	1	no	—
300	C₂×C₄×C₇₉	—	4	1	no	—
301	C₂×C₄×C₇₉	—	4	1	no	—
302	C₂×C₄×C₇₉	—	4	1	no	—
303	C₂×C₄×C₇₉	—	4	1	no	—
304	C₂×C₄×C₇₉	—	4	1	no	—
305	C₂×C₄×C₇₉	—	4	1	no	—
306	C₂×C₄×C₇₉	—	4	1	no	—
307	C₂×C₄×C₇₉	—	4	1	no	—
308	C₂×C₄×C₇₉	—	4	1	no	—
309	C₂×C₄×C₇₉	—	4	1	no	—
310	C₂×C₄×C₇₉	—	4	1	no	—
311	C₂×C₄×C₇₉	#120	1	2	yes	—
312	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
313	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
314	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
315	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
316	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
317	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
318	C₈×C₇₉	—	2	2	no	—
319	C₈×C₇₉	—	4	1	no	—
320	C₈×C₇₉	—	4	1	no	—
321	C₈×C₇₉	—	4	1	no	—
322	C₂²×C₇₉	—	2	2	no	—
323	C₂²×C₇₉	—	2	2	no	—
324	C₂²×C₇₉	—	2	2	no	—
325	C₂²×C₇₉	—	4	1	no	—
326	C₂²×C₇₉	—	4	1	no	—
327	C₂²×C₇₉	—	4	1	no	—
328	C₂²×C₇₉	—	4	1	no	—
329	C₂²×C₇₉	—	4	1	no	—
330	C₂²×C₇₉	—	4	1	no	—
331	C₂²×C₇₉	—	4	1	no	—
332	C₂²×C₇₉	—	4	1	no	—
333	C₂²×C₇₉	—	4	1	no	—
334	C₂²×C₇₉	—	4	1	no	—
335	C₂²×C₇₉	—	4	1	no	—
336	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
337	C₂²×C₇₉	#546	1	1	yes	characteristic
338	C₂²×C₇₉	#547	1	1	yes	characteristic
339	C₂²×C₇₉	#575	1	1	yes	characteristic
340	C₂²×C₇₉	#575	1	1	yes	characteristic
341	C₂²×C₇₉	#578	1	1	yes	characteristic
342	C₂²×C₇₉	#578	1	1	yes	characteristic
343	C₄×C₇₉	—	2	2	no	—
344	C₄×C₇₉	—	4	1	no	—
345	C₄×C₇₉	—	4	2	no	—
346	C₄×C₇₉	—	4	1	no	—
347	C₄×C₇₉	—	4	2	no	—
348	C₄×C₇₉	—	4	2	no	—
349	C₄×C₇₉	—	4	1	no	—
350	C₄×C₇₉	—	4	2	no	—
351	C₄×C₇₉	—	4	2	no	—
352	C₄×C₇₉	—	8	1	no	—
353	C₄×C₇₉	—	8	1	no	—
354	C₄×C₇₉	—	8	1	no	—
355	C₄×C₇₉	#532	1	1	yes	characteristic
356	C₄×C₇₉	#537	1	1	yes	characteristic
357	C₄×C₇₉	#546	1	1	yes	characteristic
358	C₄×C₇₉	#547	1	1	yes	characteristic
359	#25557	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
360	C₂×C₇₉	—	4	2	no	—
361	C₂×C₇₉	—	8	1	no	—
362	C₂×C₇₉	#2430	1	1	yes	characteristic
363	C₂×C₇₉	#3005	1	1	yes	characteristic
364	C₂×C₇₉	#3011	1	1	yes	characteristic
365	C₂×C₇₉	#3315	1	1	yes	characteristic
366	C₂×C₇₉	#3327	1	1	yes	characteristic
367	C₂×C₇₉	#3349	1	1	yes	characteristic
368	C₂×C₇₉	#3352	1	1	yes	characteristic
369	C₂×#552	C₂×C₇₉	1	1	yes	characteristic
370	C₂×#484	C₂×C₇₉	1	1	yes	characteristic, complemented
371	C₂×#470	C₂×C₇₉	1	1	yes	characteristic, complemented
372	#2415	C₂×C₇₉	1	1	yes	characteristic
373	#2059	C₂×C₇₉	1	1	yes	characteristic, complemented
374	#2036	C₂×C₇₉	1	1	yes	characteristic, complemented
375	#2026	C₂×C₇₉	1	1	yes	characteristic, complemented
376	#2001	C₂×C₇₉	1	1	yes	characteristic, complemented
377	#1878	C₂×C₇₉	1	1	yes	characteristic, complemented
378	#1873	C₂×C₇₉	1	1	yes	characteristic, complemented
379	#1873	C₂×C₇₉	1	1	yes	characteristic, complemented
380	#1870	C₂×C₇₉	1	1	yes	characteristic
381	#1863	C₂×C₇₉	1	1	yes	characteristic, complemented
382	#1854	C₂×C₇₉	1	1	yes	characteristic, complemented
383	#1736	C₂×C₇₉	1	1	yes	characteristic, complemented
384	C₇₉	#25557	1	1	yes	characteristic, direct product factor, Sylow
385	C₂²×Q₁₆	C₂²×C₇₉	1	1	yes	characteristic
386	C₂²×M₁₆	C₂²×C₇₉	1	1	yes	characteristic
387	#552	—	2	4	no	—
388	#552	—	2	4	no	—
389	C₂×#126	—	2	1	no	—
390	C₂×#125	—	2	1	no	—
391	C₂×#125	C₂²×C₇₉	1	1	yes	characteristic
392	C₂×#123	—	2	1	no	—
393	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
394	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
395	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
396	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
397	C₂×C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
398	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
399	C₂×#117	—	2	1	no	—
400	C₂×#117	C₂²×C₇₉	1	1	yes	characteristic
401	C₂×#117	C₂²×C₇₉	1	1	yes	characteristic
402	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
403	#484	—	2	4	no	—
404	#470	—	2	4	no	—
405	C₂×#107	C₂²×C₇₉	1	1	yes	characteristic
406	C₂×#107	C₂²×C₇₉	1	1	yes	characteristic
407	C₂×#106	C₂²×C₇₉	1	1	yes	characteristic
408	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
409	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
410	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
411	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
412	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
413	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
414	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
415	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
416	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
417	#397	—	2	1	no	—
418	#394	—	2	1	no	—
419	#391	C₂²×C₇₉	1	1	yes	characteristic
420	#389	—	2	1	no	—
421	#389	C₂²×C₇₉	1	1	yes	characteristic
422	#388	—	2	1	no	—
423	#380	C₂²×C₇₉	1	1	yes	characteristic
424	#340	C₂²×C₇₉	1	1	yes	characteristic
425	#340	C₂²×C₇₉	1	1	yes	characteristic
426	#340	C₂²×C₇₉	1	1	yes	characteristic
427	#340	C₂²×C₇₉	1	1	yes	characteristic
428	#340	C₂²×C₇₉	1	1	yes	characteristic
429	#340	C₂²×C₇₉	1	1	yes	characteristic
430	#336	C₂²×C₇₉	1	1	yes	characteristic
431	#336	C₂²×C₇₉	1	1	yes	characteristic
432	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
433	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
434	C₂²×D₄	D₄×C₇₉	1	1	yes	characteristic
435	C₂³×C₄	—	2	1	no	—
436	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
437	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
438	C₂×Q₁₆	—	2	2	no	—
439	C₂×Q₁₆	—	2	2	no	—
440	C₂×Q₁₆	—	4	1	no	—
441	C₂×M₁₆	—	2	2	no	—
442	C₂×M₁₆	—	2	2	no	—
443	C₂×M₁₆	—	4	1	no	—
444	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
445	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
446	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
447	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
448	#126	—	2	8	no	—
449	#125	—	2	8	no	—
450	#125	—	2	2	no	—
451	#125	—	2	2	no	—
452	#123	—	2	8	no	—
453	C₂²⋊Q₈	—	2	2	no	—
454	C₂²⋊Q₈	—	2	2	no	—
455	C₂²⋊Q₈	—	2	2	no	—
456	C₂²⋊Q₈	—	2	2	no	—
457	C₂²⋊Q₈	—	2	2	no	—
458	C₂²⋊Q₈	—	2	2	no	—
459	C₂²⋊Q₈	—	4	1	no	—
460	C₂²⋊Q₈	D₄×C₇₉	1	4	yes	—
461	C₄×Q₈	—	2	2	no	—
462	C₄×Q₈	—	2	2	no	—
463	C₄×D₄	—	2	2	no	—
464	C₄×D₄	—	2	2	no	—
465	#117	—	2	8	no	—
466	#117	—	2	2	no	—
467	#117	—	2	2	no	—
468	#117	—	2	2	no	—
469	#117	—	4	1	no	—
470	C₂×C₄⋊C₄	—	2	1	no	—
471	C₂×C₄⋊C₄	—	2	2	no	—
472	C₂×C₄⋊C₄	—	2	1	no	—
473	C₂×C₄⋊C₄	—	2	1	no	—
474	C₂×C₄⋊C₄	—	2	1	no	—
475	C₂×C₄⋊C₄	—	2	1	no	—
476	C₂×C₄⋊C₄	—	2	1	no	—
477	C₂×C₄⋊C₄	—	2	1	no	—
478	C₂×C₄⋊C₄	—	2	1	no	—
479	C₂×C₄⋊C₄	—	2	1	no	—
480	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
481	C₂×C₄⋊C₄	D₄×C₇₉	1	4	yes	—
482	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
483	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
484	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
485	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
486	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
487	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
488	C₂×C₂²⋊C₄	—	2	1	no	—
489	C₂×C₂²⋊C₄	—	2	1	no	—
490	C₂×C₂²⋊C₄	—	2	1	no	—
491	C₂×C₂²⋊C₄	—	2	1	no	—
492	C₂×C₂²⋊C₄	—	2	1	no	—
493	C₂×C₂²⋊C₄	—	2	1	no	—
494	C₂×C₂²⋊C₄	—	2	1	no	—
495	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
496	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
497	C₂×C₄²	—	2	1	no	—
498	C₂×C₄²	—	2	1	no	—
499	C₂×C₄²	—	2	1	no	—
500	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
501	#107	—	2	2	no	—
502	#107	—	2	2	no	—
503	#106	—	2	2	no	—
504	#103	—	2	2	no	—
505	#103	—	2	2	no	—
506	#103	—	2	2	no	—
507	#103	—	2	2	no	—
508	#103	—	2	2	no	—
509	#103	—	4	1	no	—
510	C₂²⋊C₈	—	2	2	no	—
511	C₂²⋊C₈	—	2	2	no	—
512	C₂²⋊C₈	—	4	1	no	—
513	#95	—	2	1	no	—
514	#95	—	2	1	no	—
515	#95	—	2	1	no	—
516	#95	—	2	1	no	—
517	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
518	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
519	C₂×Q₈	—	2	1	no	—
520	C₂×Q₈	—	2	1	no	—
521	C₂×Q₈	—	2	1	no	—
522	C₂×Q₈	—	2	1	no	—
523	C₂×Q₈	—	2	1	no	—
524	C₂×Q₈	—	2	1	no	—
525	C₂×Q₈	—	2	1	no	—
526	C₂×Q₈	—	2	1	no	—
527	C₂×Q₈	—	2	1	no	—
528	C₂×Q₈	—	2	1	no	—
529	C₂×Q₈	—	2	1	no	—
530	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
531	C₂×D₄	—	2	2	no	—
532	C₂×D₄	—	4	1	no	—
533	C₂×D₄	—	4	1	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	4	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	4	2	no	—
554	C₂²×C₄	—	4	2	no	—
555	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
556	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
557	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
558	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
559	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
560	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
561	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
562	Q₁₆	—	4	4	no	—
563	M₁₆	—	4	4	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	—	2	1	no	—
567	C₂×C₈	—	2	1	no	—
568	C₂×C₈	—	2	1	no	—
569	C₂×C₈	—	2	1	no	—
570	C₂×C₈	—	2	1	no	—
571	C₂×C₈	—	2	1	no	—
572	C₂×C₈	—	2	1	no	—
573	C₂×C₈	—	2	1	no	—
574	C₂×C₈	—	2	1	no	—
575	C₂×C₈	#41×C₇₉	1	2	yes	—
576	C₄⋊C₄	—	2	4	no	—
577	C₄⋊C₄	—	2	4	no	—
578	C₄⋊C₄	—	2	4	no	—
579	C₄⋊C₄	—	2	4	no	—
580	C₄⋊C₄	—	2	4	no	—
581	C₄⋊C₄	—	2	4	no	—
582	C₄⋊C₄	—	2	2	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	4	2	no	—
592	C₄⋊C₄	—	4	2	no	—
593	C₄⋊C₄	—	4	2	no	—
594	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
595	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
596	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
597	C₄⋊C₄	#41×C₇₉	1	2	yes	—
598	C₂²⋊C₄	—	2	4	no	—
599	C₂²⋊C₄	—	2	4	no	—
600	C₂²⋊C₄	—	2	4	no	—
601	C₂²⋊C₄	—	2	2	no	—
602	C₂²⋊C₄	—	2	2	no	—
603	C₂²⋊C₄	—	4	2	no	—
604	C₂²⋊C₄	—	4	2	no	—
605	C₂²⋊C₄	—	4	2	no	—
606	C₂²⋊C₄	—	4	2	no	—
607	C₄²	—	2	4	no	—
608	C₄²	—	2	4	no	—
609	C₄²	—	2	1	no	—
610	C₄²	—	2	1	no	—
611	C₄²	—	4	2	no	—
612	C₂³	—	2	1	no	—
613	C₂³	—	2	1	no	—
614	C₂³	—	2	1	no	—
615	C₂³	—	2	1	no	—
616	C₂³	—	2	1	no	—
617	C₂³	—	2	1	no	—
618	C₂³	—	2	1	no	—
619	C₂³	—	2	1	no	—
620	C₂³	—	2	1	no	—
621	C₂³	—	2	1	no	—
622	C₂³	—	2	1	no	—
623	C₂³	—	2	1	no	—
624	C₂³	—	2	1	no	—
625	C₂³	#120×C₇₉	1	2	yes	—
626	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
627	Q₈	—	2	2	no	—
628	Q₈	—	2	2	no	—
629	Q₈	—	4	1	no	—
630	Q₈	—	4	1	no	—
631	Q₈	—	4	1	no	—
632	Q₈	—	4	1	no	—
633	Q₈	—	4	1	no	—
634	Q₈	—	4	1	no	—
635	D₄	—	4	4	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	4	8	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	4	1	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	4	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	—	4	1	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	1	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	#120×C₇₉	1	2	yes	—
681	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
682	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
683	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
684	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
685	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
686	C₂×C₄	2₋¹⁺⁴×C₇₉	1	1	yes	characteristic
687	C₈	—	2	2	no	—
688	C₈	—	4	1	no	—
689	C₈	—	4	1	no	—
690	C₈	—	4	1	no	—
691	C₂²	—	2	2	no	—
692	C₂²	—	2	2	no	—
693	C₂²	—	2	2	no	—
694	C₂²	—	4	1	no	—
695	C₂²	—	4	1	no	—
696	C₂²	—	4	1	no	—
697	C₂²	—	4	1	no	—
698	C₂²	—	4	1	no	—
699	C₂²	—	4	1	no	—
700	C₂²	—	4	1	no	—
701	C₂²	—	4	1	no	—
702	C₂²	—	4	1	no	—
703	C₂²	—	4	1	no	—
704	C₂²	—	4	1	no	—
705	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
706	C₂²	#546×C₇₉	1	1	yes	characteristic
707	C₂²	#547×C₇₉	1	1	yes	characteristic
708	C₂²	#575×C₇₉	1	1	yes	characteristic
709	C₂²	#575×C₇₉	1	1	yes	characteristic
710	C₂²	#578×C₇₉	1	1	yes	characteristic
711	C₂²	#578×C₇₉	1	1	yes	characteristic
712	C₄	—	2	2	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	1	no	—
715	C₄	—	4	2	no	—
716	C₄	—	4	1	no	—
717	C₄	—	4	2	no	—
718	C₄	—	4	2	no	—
719	C₄	—	4	1	no	—
720	C₄	—	4	2	no	—
721	C₄	—	8	1	no	—
722	C₄	—	8	1	no	—
723	C₄	—	8	1	no	—
724	C₄	#532×C₇₉	1	1	yes	characteristic
725	C₄	#537×C₇₉	1	1	yes	characteristic
726	C₄	#546×C₇₉	1	1	yes	characteristic
727	C₄	#547×C₇₉	1	1	yes	characteristic
728	C₂	—	4	2	no	—
729	C₂	—	8	1	no	—
730	C₂	C₇₉×#2430	1	1	yes	characteristic
731	C₂	C₇₉×#3005	1	1	yes	characteristic
732	C₂	C₇₉×#3011	1	1	yes	characteristic
733	C₂	C₇₉×#3315	1	1	yes	characteristic
734	C₂	C₇₉×#3327	1	1	yes	characteristic
735	C₂	C₇₉×#3349	1	1	yes	characteristic
736	C₂	C₇₉×#3352	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₂²×D₄×C₇₉	D₄
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×#484×C₇₉	C₂	semidirect
3. C₂×#470×C₇₉	C₂	semidirect
5. C₇₉×#2059	C₂	semidirect
6. C₇₉×#2036	C₂	semidirect
7. C₇₉×#2026	C₂	semidirect
8. C₇₉×#2001	C₂	semidirect
9. C₇₉×#1878	C₂	semidirect
10. C₇₉×#1873	C₂	semidirect
11. C₇₉×#1873	C₂	semidirect
13. C₇₉×#1863	C₂	semidirect
14. C₇₉×#1854	C₂	semidirect
15. C₇₉×#1736	C₂	semidirect
359. #25557	C₇₉	direct (N × H)
370. C₂×#484	C₂×C₇₉	semidirect
371. C₂×#470	C₂×C₇₉	semidirect
373. #2059	C₂×C₇₉	semidirect
374. #2036	C₂×C₇₉	semidirect
375. #2026	C₂×C₇₉	semidirect
376. #2001	C₂×C₇₉	semidirect
377. #1878	C₂×C₇₉	semidirect
378. #1873	C₂×C₇₉	semidirect
379. #1873	C₂×C₇₉	semidirect
381. #1863	C₂×C₇₉	semidirect
382. #1854	C₂×C₇₉	semidirect
383. #1736	C₂×C₇₉	semidirect
384. C₇₉	#25557	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×#552×C₇₉	2
C₂×#484×C₇₉	2
C₂×#470×C₇₉	2
C₇₉×#2415	2
C₇₉×#2059	2
C₇₉×#2036	2
C₇₉×#2026	2
C₇₉×#2001	2
C₇₉×#1878	2
C₇₉×#1873	2
C₇₉×#1870	2
C₇₉×#1863	2
C₇₉×#1854	2
C₇₉×#1736	2
#25557	79

Subgroups — C79×#25557 #34137246

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#25557 #34137246