Subgroups — #34293288

Order 20224.

1184 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098624	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#19098519	C₂	1	1	yes	maximal, characteristic, complemented
3	#23764341	C₂	1	1	yes	maximal, characteristic, complemented
4	#23764337	C₂	1	1	yes	maximal, characteristic, complemented
5	#23764199	C₂	1	1	yes	maximal, characteristic, complemented
6	#23764195	C₂	1	1	yes	maximal, characteristic, complemented
7	#23763698	C₂	1	1	yes	maximal, characteristic, complemented
8	#23763698	C₂	1	1	yes	maximal, characteristic, complemented
9	#23763693	C₂	1	1	yes	maximal, characteristic, complemented
10	#23763693	C₂	1	1	yes	maximal, characteristic, complemented
11	#23763166	C₂	1	1	yes	maximal, characteristic, complemented
12	#23763166	C₂	1	1	yes	maximal, characteristic, complemented
13	#23763162	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₂²⋊(C₇₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#529×C₇₉	C₂	1	1	yes	maximal, characteristic
16	C₂²×#11929608	C₂²	1	1	yes	characteristic
17	C₂³×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
18	#19098624	—	2	4	no	—
19	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
31	#19098519	—	2	4	no	—
32	C₂×#14579072	C₂²	1	1	yes	characteristic
33	C₂×#14579072	C₂²	1	1	yes	characteristic
34	C₂×#14579072	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
38	#19098318	C₂²	1	1	yes	characteristic
39	#19098318	C₂²	1	1	yes	characteristic
40	#19098318	C₂²	1	1	yes	characteristic
41	#19098318	C₂²	1	1	yes	characteristic
42	#19098318	C₂²	1	1	yes	characteristic
43	#19098318	C₂²	1	1	yes	characteristic
44	#19098318	C₂²	1	1	yes	characteristic
45	#19098318	C₂²	1	1	yes	characteristic
46	#529×C₇₉	—	2	4	no	—
47	#529×C₇₉	—	2	4	no	—
48	C₂×#126×C₇₉	C₄	1	1	yes	characteristic
49	C₂×#126×C₇₉	C₄	1	1	yes	characteristic
50	C₂×#125×C₇₉	C₄	1	1	yes	characteristic
51	C₂×#124×C₇₉	C₄	1	1	yes	characteristic
52	C₂×#123×C₇₉	C₄	1	1	yes	characteristic
53	C₂×#123×C₇₉	C₄	1	1	yes	characteristic
54	C₂×C₂²⋊Q₈×C₇₉	C₄	1	1	yes	characteristic
55	C₂×#121×C₇₉	C₄	1	1	yes	characteristic
56	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
57	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
58	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
59	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
60	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
61	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
62	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
63	C₂×#11929608	—	2	2	no	—
64	C₂×#11929608	—	2	2	no	—
65	C₂×#11929608	—	2	2	no	—
66	C₂²×C₇₉⋊C₈	—	2	2	no	—
67	C₂²×C₇₉⋊C₈	—	2	2	no	—
68	C₂²×C₇₉⋊C₈	—	2	2	no	—
69	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
72	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
73	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
74	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
75	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
76	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
77	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
78	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
79	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
80	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
81	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
82	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
83	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
84	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
85	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
86	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
87	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
88	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
89	#14579072	—	2	2	no	—
90	#14579072	—	2	2	no	—
91	#14579072	—	2	2	no	—
92	C₄×C₇₉⋊C₈	—	2	2	no	—
93	C₄×C₇₉⋊C₈	—	2	2	no	—
94	C₄×C₇₉⋊C₈	—	2	2	no	—
95	C₂²×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
96	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
97	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
98	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
99	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
100	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
101	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
104	#126×C₇₉	—	2	4	no	—
105	#126×C₇₉	—	2	4	no	—
106	#125×C₇₉	—	2	4	no	—
107	#124×C₇₉	—	2	4	no	—
108	#123×C₇₉	—	2	4	no	—
109	#123×C₇₉	—	2	4	no	—
110	C₂²⋊Q₈×C₇₉	—	2	4	no	—
111	#121×C₇₉	—	2	4	no	—
112	C₄×Q₈×C₇₉	—	2	2	no	—
113	C₄×Q₈×C₇₉	—	2	2	no	—
114	C₄×D₄×C₇₉	—	2	2	no	—
115	C₄×D₄×C₇₉	—	2	2	no	—
116	C₄×D₄×C₇₉	—	2	2	no	—
117	C₄×D₄×C₇₉	—	2	2	no	—
118	C₄×D₄×C₇₉	—	2	2	no	—
119	C₄×D₄×C₇₉	—	2	2	no	—
120	#117×C₇₉	—	2	2	no	—
121	#117×C₇₉	—	2	2	no	—
122	#117×C₇₉	D₄	1	4	yes	—
123	#117×C₇₉	D₄	1	4	yes	—
124	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
134	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
135	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
136	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
137	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
138	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
139	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
140	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
141	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
142	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
143	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
144	C₂×C₄²×C₇₉	—	2	2	no	—
145	C₂×C₄²×C₇₉	—	2	2	no	—
146	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
147	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
148	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
149	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
152	#11929608	—	2	8	no	—
153	C₂×C₇₉⋊C₈	—	2	8	no	—
154	C₂×C₇₉⋊C₈	—	2	1	no	—
155	C₂×C₇₉⋊C₈	—	2	1	no	—
156	C₂×C₇₉⋊C₈	—	2	1	no	—
157	C₂×C₇₉⋊C₈	—	2	1	no	—
158	C₂×C₇₉⋊C₈	—	2	1	no	—
159	C₂×C₇₉⋊C₈	—	2	1	no	—
160	C₂×C₇₉⋊C₈	—	2	1	no	—
161	C₂×C₇₉⋊C₈	—	2	1	no	—
162	C₂×C₇₉⋊C₈	—	2	1	no	—
163	C₂×C₇₉⋊C₈	—	2	1	no	—
164	C₂×C₇₉⋊C₈	—	2	1	no	—
165	C₂×C₇₉⋊C₈	—	2	1	no	—
166	C₂×C₇₉⋊C₈	—	2	1	no	—
167	C₂×C₇₉⋊C₈	—	2	1	no	—
168	C₂×C₇₉⋊C₈	—	2	1	no	—
169	C₂×C₇₉⋊C₈	—	2	1	no	—
170	C₂×C₇₉⋊C₈	—	2	1	no	—
171	C₂×C₇₉⋊C₈	—	2	1	no	—
172	C₂×C₇₉⋊C₈	—	2	1	no	—
173	C₂×C₇₉⋊C₈	—	2	1	no	—
174	C₂×C₇₉⋊C₈	#41	1	2	yes	—
175	C₂×C₇₉⋊C₈	#41	1	2	yes	—
176	C₂×C₇₉⋊C₈	#41	1	2	yes	—
177	C₂×C₇₉⋊C₈	#41	1	2	yes	—
178	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
179	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
180	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
181	C₂×Q₈×C₇₉	—	2	2	no	—
182	C₂×Q₈×C₇₉	—	2	2	no	—
183	C₂×Q₈×C₇₉	—	4	1	no	—
184	C₂×D₄×C₇₉	—	2	2	no	—
185	C₂×D₄×C₇₉	—	2	2	no	—
186	C₂×D₄×C₇₉	—	2	2	no	—
187	C₂×D₄×C₇₉	—	2	2	no	—
188	C₂×D₄×C₇₉	—	2	2	no	—
189	C₂×D₄×C₇₉	—	2	2	no	—
190	C₂×D₄×C₇₉	—	4	1	no	—
191	C₂×D₄×C₇₉	—	4	1	no	—
192	C₂×D₄×C₇₉	—	4	1	no	—
193	C₂²×C₄×C₇₉	—	2	1	no	—
194	C₂²×C₄×C₇₉	—	2	1	no	—
195	C₂²×C₄×C₇₉	—	2	1	no	—
196	C₂²×C₄×C₇₉	—	2	1	no	—
197	C₂²×C₄×C₇₉	—	2	2	no	—
198	C₂²×C₄×C₇₉	—	2	2	no	—
199	C₂²×C₄×C₇₉	—	2	2	no	—
200	C₂²×C₄×C₇₉	—	2	2	no	—
201	C₂²×C₄×C₇₉	—	2	1	no	—
202	C₂²×C₄×C₇₉	—	2	1	no	—
203	C₂²×C₄×C₇₉	—	2	1	no	—
204	C₂²×C₄×C₇₉	—	2	1	no	—
205	C₂²×C₄×C₇₉	—	2	1	no	—
206	C₂²×C₄×C₇₉	—	2	1	no	—
207	C₂²×C₄×C₇₉	—	2	1	no	—
208	C₂²×C₄×C₇₉	—	2	1	no	—
209	C₂²×C₄×C₇₉	—	2	1	no	—
210	C₂²×C₄×C₇₉	—	2	1	no	—
211	C₂²×C₄×C₇₉	—	2	1	no	—
212	C₂²×C₄×C₇₉	—	2	1	no	—
213	C₂²×C₄×C₇₉	—	4	1	no	—
214	C₂²×C₄×C₇₉	—	4	1	no	—
215	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
216	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
217	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
218	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
219	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
220	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
221	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
222	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
223	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
224	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
225	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
226	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
227	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
228	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
229	C₄⋊C₄×C₇₉	—	2	2	no	—
230	C₄⋊C₄×C₇₉	—	2	2	no	—
231	C₄⋊C₄×C₇₉	—	2	2	no	—
232	C₄⋊C₄×C₇₉	—	2	2	no	—
233	C₄⋊C₄×C₇₉	—	2	2	no	—
234	C₄⋊C₄×C₇₉	—	2	2	no	—
235	C₄⋊C₄×C₇₉	—	2	2	no	—
236	C₄⋊C₄×C₇₉	—	2	2	no	—
237	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	4	yes	—
238	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	4	yes	—
239	C₂²⋊C₄×C₇₉	—	2	2	no	—
240	C₂²⋊C₄×C₇₉	—	2	2	no	—
241	C₂²⋊C₄×C₇₉	—	2	2	no	—
242	C₂²⋊C₄×C₇₉	—	2	2	no	—
243	C₂²⋊C₄×C₇₉	—	2	2	no	—
244	C₂²⋊C₄×C₇₉	—	2	2	no	—
245	C₂²⋊C₄×C₇₉	—	2	2	no	—
246	C₂²⋊C₄×C₇₉	—	2	2	no	—
247	C₂²⋊C₄×C₇₉	C₂²⋊C₄	1	4	yes	—
248	C₂²⋊C₄×C₇₉	C₂²⋊C₄	1	4	yes	—
249	C₄²×C₇₉	—	2	2	no	—
250	C₄²×C₇₉	—	2	2	no	—
251	C₄²×C₇₉	—	2	1	no	—
252	C₄²×C₇₉	—	2	1	no	—
253	C₄²×C₇₉	—	2	1	no	—
254	C₄²×C₇₉	—	2	1	no	—
255	C₄²×C₇₉	C₂×D₄	1	2	yes	—
256	C₄²×C₇₉	C₂×D₄	1	2	yes	—
257	C₄²×C₇₉	C₂×D₄	1	2	yes	—
258	C₄²×C₇₉	C₂×D₄	1	2	yes	—
259	C₂³×C₇₉	—	2	1	no	—
260	C₂³×C₇₉	—	2	1	no	—
261	C₂³×C₇₉	—	2	1	no	—
262	C₂³×C₇₉	—	2	1	no	—
263	C₂³×C₇₉	—	2	1	no	—
264	C₂³×C₇₉	—	2	1	no	—
265	C₂³×C₇₉	—	2	1	no	—
266	C₂³×C₇₉	—	2	1	no	—
267	C₂³×C₇₉	—	2	1	no	—
268	C₂³×C₇₉	—	2	1	no	—
269	C₂³×C₇₉	—	2	1	no	—
270	C₂³×C₇₉	—	2	1	no	—
271	C₂³×C₇₉	—	2	1	no	—
272	C₂³×C₇₉	—	2	1	no	—
273	C₂³×C₇₉	—	2	1	no	—
274	C₂³×C₇₉	—	2	1	no	—
275	C₂³×C₇₉	—	2	1	no	—
276	C₂³×C₇₉	—	2	1	no	—
277	C₂³×C₇₉	—	2	1	no	—
278	C₂³×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
279	C₂³×C₇₉	#131	1	2	yes	—
280	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
281	Q₈×C₇₉	—	4	4	no	—
282	D₄×C₇₉	—	4	4	no	—
283	D₄×C₇₉	—	4	4	no	—
284	D₄×C₇₉	—	4	4	no	—
285	C₂×C₄×C₇₉	—	2	1	no	—
286	C₂×C₄×C₇₉	—	2	1	no	—
287	C₂×C₄×C₇₉	—	2	1	no	—
288	C₂×C₄×C₇₉	—	2	1	no	—
289	C₂×C₄×C₇₉	—	2	1	no	—
290	C₂×C₄×C₇₉	—	2	1	no	—
291	C₂×C₄×C₇₉	—	2	1	no	—
292	C₂×C₄×C₇₉	—	2	1	no	—
293	C₂×C₄×C₇₉	—	2	1	no	—
294	C₂×C₄×C₇₉	—	2	1	no	—
295	C₂×C₄×C₇₉	—	2	1	no	—
296	C₂×C₄×C₇₉	—	2	1	no	—
297	C₂×C₄×C₇₉	—	2	2	no	—
298	C₂×C₄×C₇₉	—	2	2	no	—
299	C₂×C₄×C₇₉	—	2	2	no	—
300	C₂×C₄×C₇₉	—	2	2	no	—
301	C₂×C₄×C₇₉	—	2	1	no	—
302	C₂×C₄×C₇₉	—	2	1	no	—
303	C₂×C₄×C₇₉	—	2	1	no	—
304	C₂×C₄×C₇₉	—	2	1	no	—
305	C₂×C₄×C₇₉	—	2	1	no	—
306	C₂×C₄×C₇₉	—	2	1	no	—
307	C₂×C₄×C₇₉	—	2	1	no	—
308	C₂×C₄×C₇₉	—	2	1	no	—
309	C₂×C₄×C₇₉	—	2	1	no	—
310	C₂×C₄×C₇₉	—	2	1	no	—
311	C₂×C₄×C₇₉	—	2	1	no	—
312	C₂×C₄×C₇₉	—	2	1	no	—
313	C₂×C₄×C₇₉	—	2	1	no	—
314	C₂×C₄×C₇₉	—	2	1	no	—
315	C₂×C₄×C₇₉	—	2	1	no	—
316	C₂×C₄×C₇₉	—	4	4	no	—
317	C₂×C₄×C₇₉	—	4	4	no	—
318	C₂×C₄×C₇₉	—	4	1	no	—
319	C₂×C₄×C₇₉	—	4	1	no	—
320	C₂×C₄×C₇₉	—	4	1	no	—
321	C₂×C₄×C₇₉	—	4	1	no	—
322	C₂×C₄×C₇₉	—	4	1	no	—
323	C₂×C₄×C₇₉	—	4	1	no	—
324	C₂×C₄×C₇₉	—	4	1	no	—
325	C₂×C₄×C₇₉	—	4	1	no	—
326	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
327	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
328	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
329	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
330	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
331	C₂×C₄×C₇₉	#131	1	2	yes	—
332	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
334	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
335	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
336	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
337	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
338	C₇₉⋊C₈	—	2	2	no	—
339	C₇₉⋊C₈	—	2	2	no	—
340	C₇₉⋊C₈	—	2	2	no	—
341	C₇₉⋊C₈	—	2	2	no	—
342	C₇₉⋊C₈	—	4	1	no	—
343	C₇₉⋊C₈	—	4	1	no	—
344	C₇₉⋊C₈	—	4	1	no	—
345	C₇₉⋊C₈	—	4	1	no	—
346	C₂²×C₇₉	—	2	2	no	—
347	C₂²×C₇₉	—	2	2	no	—
348	C₂²×C₇₉	—	2	2	no	—
349	C₂²×C₇₉	—	2	2	no	—
350	C₂²×C₇₉	—	2	2	no	—
351	C₂²×C₇₉	—	2	2	no	—
352	C₂²×C₇₉	—	4	1	no	—
353	C₂²×C₇₉	—	4	1	no	—
354	C₂²×C₇₉	—	4	1	no	—
355	C₂²×C₇₉	—	4	1	no	—
356	C₂²×C₇₉	—	4	1	no	—
357	C₂²×C₇₉	—	4	1	no	—
358	C₂²×C₇₉	—	4	1	no	—
359	C₂²×C₇₉	—	4	1	no	—
360	C₂²×C₇₉	—	4	1	no	—
361	C₂²×C₇₉	—	4	1	no	—
362	C₂²×C₇₉	—	4	1	no	—
363	C₂²×C₇₉	—	4	1	no	—
364	C₂²×C₇₉	—	4	1	no	—
365	C₂²×C₇₉	—	4	1	no	—
366	C₂²×C₇₉	—	4	1	no	—
367	C₂²×C₇₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
368	C₂²×C₇₉	C₄×#41	1	1	yes	characteristic
369	C₂²×C₇₉	C₄×#41	1	1	yes	characteristic
370	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
371	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
372	C₂²×C₇₉	#568	1	1	yes	characteristic
373	C₂²×C₇₉	#568	1	1	yes	characteristic
374	C₄×C₇₉	—	2	2	no	—
375	C₄×C₇₉	—	2	2	no	—
376	C₄×C₇₉	—	2	2	no	—
377	C₄×C₇₉	—	2	2	no	—
378	C₄×C₇₉	—	2	2	no	—
379	C₄×C₇₉	—	2	2	no	—
380	C₄×C₇₉	—	4	1	no	—
381	C₄×C₇₉	—	4	1	no	—
382	C₄×C₇₉	—	4	1	no	—
383	C₄×C₇₉	—	4	1	no	—
384	C₄×C₇₉	—	4	1	no	—
385	C₄×C₇₉	#525	1	1	yes	characteristic
386	C₄×C₇₉	#525	1	1	yes	characteristic
387	C₄×C₇₉	#532	1	1	yes	characteristic
388	C₄×C₇₉	#532	1	1	yes	characteristic
389	#21381	—	79	1	no	maximal, Sylow
390	C₂×C₇₉	—	4	2	no	—
391	C₂×C₇₉	—	4	2	no	—
392	C₂×C₇₉	—	8	1	no	—
393	C₂×C₇₉	#2297	1	1	yes	characteristic
394	C₂×C₇₉	#2880	1	1	yes	characteristic
395	C₂×C₇₉	#2880	1	1	yes	characteristic
396	C₂×C₇₉	#2966	1	1	yes	characteristic
397	C₂×C₇₉	#2967	1	1	yes	characteristic
398	C₂×C₇₉	#2968	1	1	yes	characteristic
399	C₂×C₇₉	#2969	1	1	yes	characteristic
400	C₂×#529	D₇₉	1	1	yes	characteristic
401	C₂×#433	—	79	1	no	—
402	C₂×#405	—	79	1	no	—
403	#1985	—	79	1	no	—
404	#1984	—	79	1	no	—
405	#1955	—	79	1	no	—
406	#1954	—	79	1	no	—
407	#1870	—	79	1	no	—
408	#1870	—	79	1	no	—
409	#1869	—	79	1	no	—
410	#1869	—	79	1	no	—
411	#1750	—	79	1	no	—
412	#1750	—	79	1	no	—
413	#1749	—	79	1	no	—
414	C₄×C₂²⋊C₈	—	79	1	no	—
415	C₇₉	#21381	1	1	yes	characteristic, complemented, Sylow
416	C₂²×M₁₆	—	79	1	no	—
417	C₂³×C₈	—	79	1	no	—
418	#529	—	2	4	no	—
419	#529	—	2	4	no	—
420	C₂×#126	Dic₇₉	1	1	yes	characteristic
421	C₂×#126	Dic₇₉	1	1	yes	characteristic
422	C₂×#125	Dic₇₉	1	1	yes	characteristic
423	C₂×#124	Dic₇₉	1	1	yes	characteristic
424	C₂×#123	Dic₇₉	1	1	yes	characteristic
425	C₂×#123	Dic₇₉	1	1	yes	characteristic
426	C₂×C₂²⋊Q₈	Dic₇₉	1	1	yes	characteristic
427	C₂×#121	Dic₇₉	1	1	yes	characteristic
428	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
429	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
430	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
431	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
432	C₂×#117	C₂×D₇₉	1	1	yes	characteristic
433	C₂×#117	C₂×D₇₉	1	1	yes	characteristic
434	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
435	#433	—	158	4	no	—
436	C₂×C₄⋊C₈	—	79	1	no	—
437	C₂×C₄⋊C₈	—	79	1	no	—
438	C₂×C₂²⋊C₈	—	79	1	no	—
439	C₂×C₂²⋊C₈	—	79	1	no	—
440	C₂×C₂²⋊C₈	—	79	1	no	—
441	C₂×C₂²⋊C₈	—	79	1	no	—
442	C₂×C₂²⋊C₈	—	79	1	no	—
443	C₂×C₂²⋊C₈	—	79	1	no	—
444	C₂×C₂²⋊C₈	—	79	1	no	—
445	C₂×C₂²⋊C₈	—	79	1	no	—
446	C₂×C₂²⋊C₈	—	79	1	no	—
447	C₂×C₂²⋊C₈	—	79	1	no	—
448	#405	—	158	4	no	—
449	C₂×#97	—	79	1	no	—
450	C₂×#97	—	79	1	no	—
451	C₂×#97	—	79	1	no	—
452	C₂×C₄×C₈	—	79	1	no	—
453	C₂×C₄×C₈	—	79	1	no	—
454	C₂×C₄×C₈	—	79	1	no	—
455	#336	—	79	1	no	—
456	#336	—	79	1	no	—
457	#336	—	79	1	no	—
458	#336	—	79	1	no	—
459	#336	—	79	1	no	—
460	#336	—	79	1	no	—
461	#336	—	79	1	no	—
462	#336	—	79	1	no	—
463	C₂²×Q₈	C₂×Dic₇₉	1	1	yes	characteristic
464	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
465	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
466	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
467	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
468	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
469	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
470	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
471	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
472	C₂×M₁₆	—	158	2	no	—
473	C₂×M₁₆	—	158	2	no	—
474	C₂×M₁₆	—	158	2	no	—
475	C₂²×C₈	—	79	1	no	—
476	C₂²×C₈	—	79	1	no	—
477	C₂²×C₈	—	79	1	no	—
478	C₂²×C₈	—	79	1	no	—
479	C₂²×C₈	—	79	1	no	—
480	C₂²×C₈	—	79	1	no	—
481	C₂²×C₈	—	79	1	no	—
482	C₂²×C₈	—	79	1	no	—
483	C₂²×C₈	—	158	2	no	—
484	C₂²×C₈	—	158	2	no	—
485	C₂²×C₈	—	158	2	no	—
486	#126	—	2	4	no	—
487	#126	—	2	4	no	—
488	#125	—	2	4	no	—
489	#124	—	2	4	no	—
490	#123	—	2	4	no	—
491	#123	—	2	4	no	—
492	C₂²⋊Q₈	—	2	4	no	—
493	#121	—	2	4	no	—
494	C₄×Q₈	—	2	2	no	—
495	C₄×Q₈	—	2	2	no	—
496	C₄×D₄	—	2	2	no	—
497	C₄×D₄	—	2	2	no	—
498	C₄×D₄	—	2	2	no	—
499	C₄×D₄	—	2	2	no	—
500	C₄×D₄	—	2	2	no	—
501	C₄×D₄	—	2	2	no	—
502	#117	—	2	2	no	—
503	#117	—	2	2	no	—
504	#117	C₂²⋊D₇₉	1	4	yes	—
505	#117	C₂²⋊D₇₉	1	4	yes	—
506	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
511	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
512	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
513	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
516	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
517	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
518	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
519	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
520	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
521	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
522	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
523	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
524	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
525	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
526	C₂×C₄²	—	2	2	no	—
527	C₂×C₄²	—	2	2	no	—
528	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
529	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
530	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
531	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
532	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
533	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
534	C₄⋊C₈	—	158	2	no	—
535	C₄⋊C₈	—	158	2	no	—
536	C₂²⋊C₈	—	158	2	no	—
537	C₂²⋊C₈	—	158	2	no	—
538	C₂²⋊C₈	—	158	2	no	—
539	C₂²⋊C₈	—	158	2	no	—
540	C₂²⋊C₈	—	158	2	no	—
541	C₂²⋊C₈	—	158	2	no	—
542	C₂²⋊C₈	—	158	2	no	—
543	C₂²⋊C₈	—	158	2	no	—
544	C₂²⋊C₈	—	158	2	no	—
545	C₂²⋊C₈	—	158	2	no	—
546	#97	—	158	2	no	—
547	#97	—	158	2	no	—
548	#97	—	158	2	no	—
549	C₄×C₈	—	158	2	no	—
550	C₄×C₈	—	158	2	no	—
551	C₄×C₈	—	158	2	no	—
552	C₂⁴	C₂²×Dic₇₉	1	1	yes	characteristic
553	C₂⁴	C₂²×Dic₇₉	1	1	yes	characteristic
554	C₂⁴	C₂²×Dic₇₉	1	1	yes	characteristic
555	C₂×Q₈	—	2	2	no	—
556	C₂×Q₈	—	2	2	no	—
557	C₂×Q₈	—	4	1	no	—
558	C₂×D₄	—	2	2	no	—
559	C₂×D₄	—	2	2	no	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	2	2	no	—
562	C₂×D₄	—	2	2	no	—
563	C₂×D₄	—	2	2	no	—
564	C₂×D₄	—	4	1	no	—
565	C₂×D₄	—	4	1	no	—
566	C₂×D₄	—	4	1	no	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	4	1	no	—
588	C₂²×C₄	—	4	1	no	—
589	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
590	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
591	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
592	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
593	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
594	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
595	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
596	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
597	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
598	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
599	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
600	C₂²×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
601	C₂²×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
602	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
603	M₁₆	—	158	8	no	—
604	C₂×C₈	—	79	2	no	—
605	C₂×C₈	—	79	2	no	—
606	C₂×C₈	—	79	2	no	—
607	C₂×C₈	—	79	2	no	—
608	C₂×C₈	—	158	1	no	—
609	C₂×C₈	—	158	1	no	—
610	C₂×C₈	—	158	1	no	—
611	C₂×C₈	—	158	1	no	—
612	C₂×C₈	—	158	1	no	—
613	C₂×C₈	—	158	1	no	—
614	C₂×C₈	—	158	1	no	—
615	C₂×C₈	—	158	1	no	—
616	C₂×C₈	—	158	1	no	—
617	C₂×C₈	—	158	1	no	—
618	C₂×C₈	—	158	1	no	—
619	C₂×C₈	—	158	1	no	—
620	C₂×C₈	—	158	8	no	—
621	C₂×C₈	—	158	1	no	—
622	C₂×C₈	—	158	1	no	—
623	C₂×C₈	—	158	1	no	—
624	C₂×C₈	—	158	1	no	—
625	C₂×C₈	—	158	1	no	—
626	C₂×C₈	—	158	1	no	—
627	C₂×C₈	—	158	1	no	—
628	C₂×C₈	—	158	1	no	—
629	C₄⋊C₄	—	2	2	no	—
630	C₄⋊C₄	—	2	2	no	—
631	C₄⋊C₄	—	2	2	no	—
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	—	2	2	no	—
637	C₄⋊C₄	C₂²⋊Dic₇₉	1	4	yes	—
638	C₄⋊C₄	C₂²⋊Dic₇₉	1	4	yes	—
639	C₂²⋊C₄	—	2	2	no	—
640	C₂²⋊C₄	—	2	2	no	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	2	2	no	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	2	no	—
647	C₂²⋊C₄	C₂²⋊Dic₇₉	1	4	yes	—
648	C₂²⋊C₄	C₂²⋊Dic₇₉	1	4	yes	—
649	C₄²	—	2	2	no	—
650	C₄²	—	2	2	no	—
651	C₄²	—	2	1	no	—
652	C₄²	—	2	1	no	—
653	C₄²	—	2	1	no	—
654	C₄²	—	2	1	no	—
655	C₄²	C₂×C₂²⋊D₇₉	1	2	yes	—
656	C₄²	C₂×C₂²⋊D₇₉	1	2	yes	—
657	C₄²	C₂×C₂²⋊D₇₉	1	2	yes	—
658	C₄²	C₂×C₂²⋊D₇₉	1	2	yes	—
659	C₂³	—	2	1	no	—
660	C₂³	—	2	1	no	—
661	C₂³	—	2	1	no	—
662	C₂³	—	2	1	no	—
663	C₂³	—	2	1	no	—
664	C₂³	—	2	1	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	2	1	no	—
667	C₂³	—	2	1	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	1	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	1	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	2	1	no	—
675	C₂³	—	2	1	no	—
676	C₂³	—	2	1	no	—
677	C₂³	—	2	1	no	—
678	C₂³	C₂×C₂²⋊Dic₇₉	1	2	yes	—
679	C₂³	#14579168	1	2	yes	—
680	C₂³	C₂³×Dic₇₉	1	1	yes	characteristic
681	Q₈	—	4	4	no	—
682	D₄	—	4	4	no	—
683	D₄	—	4	4	no	—
684	D₄	—	4	4	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	4	4	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	2	yes	—
727	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	2	yes	—
728	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	2	yes	—
729	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	2	yes	—
730	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	2	yes	—
731	C₂×C₄	#14579168	1	2	yes	—
732	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
733	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
734	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
735	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
736	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
737	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
738	C₈	—	316	1	no	—
739	C₈	—	316	1	no	—
740	C₈	—	316	1	no	—
741	C₈	—	316	1	no	—
742	C₈	—	158	2	no	—
743	C₈	—	158	2	no	—
744	C₈	—	158	2	no	—
745	C₈	—	158	2	no	—
746	C₂²	—	2	2	no	—
747	C₂²	—	2	2	no	—
748	C₂²	—	2	2	no	—
749	C₂²	—	2	2	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	2	2	no	—
752	C₂²	—	4	1	no	—
753	C₂²	—	4	1	no	—
754	C₂²	—	4	1	no	—
755	C₂²	—	4	1	no	—
756	C₂²	—	4	1	no	—
757	C₂²	—	4	1	no	—
758	C₂²	—	4	1	no	—
759	C₂²	—	4	1	no	—
760	C₂²	—	4	1	no	—
761	C₂²	—	4	1	no	—
762	C₂²	—	4	1	no	—
763	C₂²	—	4	1	no	—
764	C₂²	—	4	1	no	—
765	C₂²	—	4	1	no	—
766	C₂²	—	4	1	no	—
767	C₂²	C₂²×C₂²⋊Dic₇₉	1	1	yes	characteristic
768	C₂²	#41×Dic₇₉	1	1	yes	characteristic
769	C₂²	#41×Dic₇₉	1	1	yes	characteristic
770	C₂²	C₂×#14579168	1	1	yes	characteristic
771	C₂²	C₂×#14579168	1	1	yes	characteristic
772	C₂²	#19099330	1	1	yes	characteristic
773	C₂²	#19099330	1	1	yes	characteristic
774	C₄	—	2	2	no	—
775	C₄	—	2	2	no	—
776	C₄	—	2	2	no	—
777	C₄	—	2	2	no	—
778	C₄	—	2	2	no	—
779	C₄	—	2	2	no	—
780	C₄	—	4	1	no	—
781	C₄	—	4	1	no	—
782	C₄	—	4	1	no	—
783	C₄	—	4	1	no	—
784	C₄	—	4	1	no	—
785	C₄	#19099070	1	1	yes	characteristic
786	C₄	#19099070	1	1	yes	characteristic
787	C₄	#19099109	1	1	yes	characteristic
788	C₄	#19099109	1	1	yes	characteristic
789	C₂	—	4	2	no	—
790	C₂	—	4	2	no	—
791	C₂	—	8	1	no	—
792	C₂	#23765891	1	1	yes	characteristic
793	C₂	#23771849	1	1	yes	characteristic
794	C₂	#23771849	1	1	yes	characteristic
795	C₂	#23772376	1	1	yes	characteristic
796	C₂	#23772387	1	1	yes	characteristic
797	C₂	#23772396	1	1	yes	characteristic
798	C₂	#23772405	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₉
commutator, socle	C₂³×C₇₉	C₂³×C₄
Fitting	C₂×#529×C₇₉	C₂
prime radical	C₂×#121×C₇₉	C₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₂×#529	D₇₉
hypocenter	C₇₉	#21381
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#529

Complements

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

N	H ≅ G/N	type
1. C₂×#19098624	C₂	semidirect
2. C₂×#19098519	C₂	semidirect
3. #23764341	C₂	semidirect
4. #23764337	C₂	semidirect
5. #23764199	C₂	semidirect
6. #23764195	C₂	semidirect
7. #23763698	C₂	semidirect
8. #23763698	C₂	semidirect
9. #23763693	C₂	semidirect
10. #23763693	C₂	semidirect
11. #23763166	C₂	semidirect
12. #23763166	C₂	semidirect
13. #23763162	C₂	semidirect
14. C₄×C₂²⋊(C₇₉⋊C₈)	C₂	semidirect
415. C₇₉	#21381	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098624	2
C₂×#19098519	2
#23764341	2
#23764337	2
#23764199	2
#23764195	2
#23763698	2
#23763693	2
#23763166	2
#23763162	2
C₄×C₂²⋊(C₇₉⋊C₈)	2
C₂×#529×C₇₉	2
#21381	79