Subgroups — #35153253

Order 20224.

1748 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#533×D₇₉	C₂	1	1	yes	maximal, characteristic
2	#23772500	C₂	1	2	yes	maximal, complemented
3	#23772498	C₂	1	2	yes	maximal, complemented
4	#23772496	C₂	1	2	yes	maximal, complemented
5	#23772491	C₂	1	2	yes	maximal, complemented
6	#23772488	C₂	1	2	yes	maximal, complemented
7	#23772486	C₂	1	2	yes	maximal, complemented
8	#23772482	C₂	1	2	yes	maximal, complemented
9	#23772479	C₂	1	2	yes	maximal, complemented
10	#23772346	C₂	1	2	yes	maximal, complemented
11	#23772344	C₂	1	2	yes	maximal, complemented
12	#23772335	C₂	1	1	yes	maximal, characteristic, complemented
13	#23772334	C₂	1	1	yes	maximal, characteristic, complemented
14	#23772330	C₂	1	1	yes	maximal, characteristic, complemented
15	#23772057	C₂	1	2	yes	maximal
16	#23772055	C₂	1	2	yes	maximal
17	#23772032	C₂	1	1	yes	maximal, characteristic
18	C₂×#19098614	C₂	1	1	yes	maximal, characteristic
19	C₇₉×#2960	C₂	1	1	yes	maximal, characteristic, complemented
20	#19099120	C₂²	1	1	yes	characteristic
21	#19099119	C₄	1	2	yes	—
22	#19099118	C₄	1	1	yes	characteristic
23	#19099118	C₄	1	1	yes	characteristic
24	#19099117	C₂²	1	2	yes	—
25	#19099117	C₂²	1	2	yes	—
26	#19099116	C₂²	1	2	yes	—
27	#19099115	C₄	1	2	yes	—
28	#19099115	C₄	1	2	yes	—
29	C₄⋊Q₈×D₇₉	C₄	1	1	yes	characteristic
30	C₄⋊Q₈×D₇₉	C₄	1	1	yes	characteristic
31	#125×D₇₉	C₄	1	2	yes	—
32	C₂²⋊Q₈×D₇₉	C₄	1	2	yes	—
33	C₂²⋊Q₈×D₇₉	C₄	1	2	yes	—
34	C₄×Q₈×D₇₉	C₂²	1	2	yes	—
35	C₄×Q₈×D₇₉	C₂²	1	2	yes	—
36	#117×D₇₉	C₂²	1	2	yes	—
37	C₂×C₄²×D₇₉	C₂²	1	1	yes	characteristic
38	#19098694	C₂²	1	2	yes	complemented
39	#19098694	C₂²	1	2	yes	complemented
40	#19098693	C₂²	1	2	yes	complemented
41	#19098693	C₂²	1	4	yes	complemented
42	#19098693	C₂²	1	2	yes	complemented
43	#19098692	C₂²	1	4	yes	complemented
44	#19098692	C₂²	1	4	yes	complemented
45	#19098691	C₂²	1	4	yes	complemented
46	#19098691	C₂²	1	4	yes	complemented
47	#19098690	C₂²	1	2	yes	complemented
48	#19098690	C₂²	1	4	yes	complemented
49	#19098690	C₂²	1	2	yes	complemented
50	Q₈×C₇₉⋊C₈	C₂²	1	2	yes	complemented
51	Q₈×C₇₉⋊C₈	C₂²	1	2	yes	complemented
52	C₈×Dic₁₅₈	C₂²	1	2	yes	complemented
53	C₈×Dic₁₅₈	C₂²	1	4	yes	complemented
54	C₈×Dic₁₅₈	C₂²	1	2	yes	complemented
55	#19098687	C₂²	1	2	yes	complemented
56	#19098687	C₂²	1	4	yes	complemented
57	#19098687	C₂²	1	2	yes	complemented
58	#19098625	C₂²	1	4	yes	—
59	#19098623	C₂²	1	4	yes	—
60	#19098623	C₂²	1	4	yes	—
61	#19098622	C₂²	1	4	yes	—
62	#19098619	C₂²	1	4	yes	—
63	#19098619	C₂²	1	2	yes	—
64	#19098619	C₂²	1	2	yes	—
65	#19098618	C₂²	1	4	yes	—
66	#19098615	C₂²	1	2	yes	—
67	#19098615	C₂²	1	4	yes	—
68	#19098615	C₂²	1	2	yes	—
69	#19098614	C₂²	1	1	yes	characteristic
70	#19098614	C₂²	1	4	yes	—
71	#19098614	C₂²	1	1	yes	characteristic
72	#19098614	C₂²	1	1	yes	characteristic
73	#19098614	C₂²	1	1	yes	characteristic
74	#19098614	C₂²	1	1	yes	characteristic
75	#19098614	C₂²	1	1	yes	characteristic
76	#19098614	C₂²	1	1	yes	characteristic
77	#19098614	C₂²	1	1	yes	characteristic
78	#19098591	C₂²	1	2	yes	—
79	#19098590	C₂²	1	2	yes	—
80	#19098589	C₂²	1	2	yes	—
81	#19098587	C₂²	1	1	yes	characteristic
82	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
83	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
84	#19098526	C₂²	1	2	yes	—
85	C₂×(C₂×D₇₉)⋊C₈	C₂²	1	1	yes	characteristic
86	C₂×(C₂×D₇₉)⋊C₈	C₂²	1	1	yes	characteristic
87	#19098521	C₂²	1	2	yes	—
88	#19098519	C₂²	1	2	yes	—
89	#19098518	C₂²	1	2	yes	—
90	M₁₆×Dic₇₉	C₂²	1	2	yes	—
91	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
92	#533×C₇₉	C₂²	1	1	yes	characteristic
93	#446×C₇₉	C₂²	1	2	yes	complemented
94	#446×C₇₉	C₂²	1	2	yes	complemented
95	C₈×Q₈×C₇₉	C₂²	1	2	yes	complemented
96	C₈×Q₈×C₇₉	C₂²	1	2	yes	complemented
97	#424×C₇₉	C₂²	1	2	yes	—
98	#423×C₇₉	C₂²	1	1	yes	characteristic
99	#405×C₇₉	C₂²	1	2	yes	—
100	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
101	C₂×Q₈×D₇₉	C₂×C₄	1	2	yes	—
102	C₂×Q₈×D₇₉	C₂×C₄	1	2	yes	—
103	C₂²×C₄×D₇₉	C₂×C₄	1	1	yes	characteristic
104	C₂²×C₄×D₇₉	C₂×C₄	1	1	yes	characteristic
105	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
106	C₂×#11929608	C₂³	1	2	yes	—
107	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
108	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
109	#14579161	C₂×C₄	1	1	yes	characteristic
110	#14579161	C₂×C₄	1	1	yes	characteristic
111	#14579160	C₂×C₄	1	2	yes	—
112	#14579160	C₂×C₄	1	2	yes	—
113	#14579160	C₂×C₄	1	2	yes	—
114	#14579160	C₂×C₄	1	2	yes	—
115	#14579159	C₂×C₄	1	2	yes	—
116	#14579159	C₂×C₄	1	2	yes	—
117	#14579153	C₂×C₄	1	2	yes	—
118	#14579152	C₂×C₄	1	2	yes	—
119	#14579152	C₂×C₄	1	2	yes	—
120	#14579151	C₂×C₄	1	4	yes	—
121	#14579151	C₂×C₄	1	4	yes	—
122	#14579141	C₂×C₄	1	2	yes	—
123	#14579141	C₂×C₄	1	2	yes	—
124	#14579140	C₂×C₄	1	2	yes	—
125	#14579140	C₂×C₄	1	2	yes	—
126	#14579139	C₂×C₄	1	4	yes	—
127	#14579139	C₂×C₄	1	4	yes	—
128	#14579138	C₂×C₄	1	4	yes	—
129	#14579138	C₂×C₄	1	4	yes	—
130	#14579137	C₂×C₄	1	2	yes	—
131	#14579137	C₂×C₄	1	2	yes	—
132	Q₈×Dic₇₉	C₂×C₄	1	2	yes	—
133	Q₈×Dic₇₉	C₂×C₄	1	2	yes	—
134	C₄×Dic₁₅₈	C₂³	1	2	yes	—
135	C₄×Dic₁₅₈	C₂³	1	2	yes	—
136	C₄×Dic₁₅₈	C₂³	1	4	yes	—
137	C₄×Dic₁₅₈	C₂³	1	4	yes	—
138	#14579126	C₂×C₄	1	2	yes	—
139	#14579126	C₂×C₄	1	2	yes	—
140	#14579126	C₂×C₄	1	4	yes	—
141	#14579126	C₂×C₄	1	4	yes	—
142	#14579120	C₂³	1	2	yes	—
143	#14579119	C₂×C₄	1	2	yes	—
144	#14579119	C₂×C₄	1	2	yes	—
145	#14579118	C₂³	1	4	yes	—
146	#14579117	C₂×C₄	1	4	yes	—
147	C₄⋊C₄×D₇₉	C₂×C₄	1	2	yes	—
148	C₄⋊C₄×D₇₉	C₂×C₄	1	2	yes	—
149	C₄⋊C₄×D₇₉	C₂×C₄	1	4	yes	—
150	C₄⋊C₄×D₇₉	C₂×C₄	1	4	yes	—
151	C₄⋊C₄×D₇₉	C₂×C₄	1	2	yes	—
152	C₄⋊C₄×D₇₉	C₂×C₄	1	2	yes	—
153	C₂²⋊C₄×D₇₉	C₂×C₄	1	4	yes	—
154	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
155	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
156	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
157	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
158	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
159	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
160	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
161	C₄²×D₇₉	C₂³	1	1	yes	characteristic
162	C₄²×D₇₉	C₂³	1	1	yes	characteristic
163	C₄²×D₇₉	C₂³	1	1	yes	characteristic
164	C₄²×D₇₉	C₂³	1	1	yes	characteristic
165	C₄²×D₇₉	C₂³	1	4	yes	—
166	C₄⋊(C₇₉⋊C₈)	C₂³	1	4	yes	—
167	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
168	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
169	C₄⋊(C₇₉⋊C₈)	C₂³	1	4	yes	—
170	Dic₇₉⋊C₈	C₂³	1	4	yes	—
171	Dic₇₉⋊C₈	C₂³	1	4	yes	—
172	Dic₇₉⋊C₈	C₂³	1	1	yes	characteristic
173	Dic₇₉⋊C₈	C₂³	1	4	yes	—
174	Dic₇₉⋊C₈	C₂³	1	1	yes	characteristic
175	Dic₇₉⋊C₈	C₂³	1	4	yes	—
176	Dic₇₉⋊C₈	C₂³	1	1	yes	characteristic
177	Dic₇₉⋊C₈	C₂³	1	1	yes	characteristic
178	Dic₇₉⋊C₈	C₂³	1	1	yes	characteristic
179	Dic₇₉⋊C₈	C₂³	1	1	yes	characteristic
180	Dic₇₉⋊C₈	C₂³	1	1	yes	characteristic
181	Dic₇₉⋊C₈	C₂³	1	1	yes	characteristic
182	(C₂×D₇₉)⋊C₈	C₂³	1	1	yes	characteristic
183	(C₂×D₇₉)⋊C₈	C₂³	1	4	yes	—
184	(C₂×D₇₉)⋊C₈	C₂³	1	1	yes	characteristic
185	(C₂×D₇₉)⋊C₈	C₂³	1	1	yes	characteristic
186	(C₂×D₇₉)⋊C₈	C₂³	1	1	yes	characteristic
187	(C₂×D₇₉)⋊C₈	C₂³	1	1	yes	characteristic
188	(C₂×D₇₉)⋊C₈	C₂³	1	1	yes	characteristic
189	(C₂×D₇₉)⋊C₈	C₂³	1	1	yes	characteristic
190	(C₂×D₇₉)⋊C₈	C₂³	1	1	yes	characteristic
191	(C₂×D₇₉)⋊C₈	C₂³	1	4	yes	—
192	#14579072	C₂³	1	4	yes	—
193	#14579071	C₂³	1	4	yes	—
194	#14579071	C₂³	1	4	yes	—
195	#14579071	C₂³	1	4	yes	—
196	C₄×C₇₉⋊C₈	C₂³	1	4	yes	—
197	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
198	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
199	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
200	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
201	C₈×Dic₇₉	C₂³	1	4	yes	—
202	C₈×Dic₇₉	C₂³	1	4	yes	—
203	C₈×Dic₇₉	C₂³	1	4	yes	—
204	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
205	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
206	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
207	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
208	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
209	#125×C₇₉	C₂×C₄	1	2	yes	—
210	C₂²⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
211	C₂²⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
212	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
213	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
214	#117×C₇₉	C₂³	1	2	yes	—
215	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
216	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
217	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
218	C₄⋊C₈×C₇₉	C₂³	1	4	yes	—
219	C₄⋊C₈×C₇₉	C₂³	1	4	yes	—
220	#97×C₇₉	C₂³	1	4	yes	—
221	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
222	C₄×C₈×C₇₉	C₂³	1	4	yes	—
223	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
224	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
225	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
226	C₂³×D₇₉	C₂²×C₄	1	1	yes	characteristic
227	C₂×Dic₁₅₈	C₂²×C₄	1	4	yes	—
228	C₂×Dic₁₅₈	C₂²×C₄	1	2	yes	—
229	C₂×Dic₁₅₈	C₂²×C₄	1	2	yes	—
230	C₂×Dic₁₅₈	C₂²×C₄	1	4	yes	—
231	Q₈×D₇₉	—	2	8	no	—
232	Q₈×D₇₉	—	4	4	no	—
233	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
234	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
235	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
236	C₂×C₄×D₇₉	—	2	4	no	—
237	C₂×C₄×D₇₉	—	2	2	no	—
238	C₂×C₄×D₇₉	—	2	2	no	—
239	C₂×C₄×D₇₉	—	4	2	no	—
240	C₂×C₄×D₇₉	C₂²×C₄	1	1	yes	characteristic
241	C₂×C₄×D₇₉	C₂²×C₄	1	4	yes	—
242	C₂×C₄×D₇₉	C₂²×C₄	1	1	yes	characteristic
243	C₂×C₄×D₇₉	C₂²×C₄	1	1	yes	characteristic
244	C₂×C₄×D₇₉	C₂²×C₄	1	1	yes	characteristic
245	C₂×C₄×D₇₉	C₂²×C₄	1	1	yes	characteristic
246	C₂×C₄×D₇₉	C₂²×C₄	1	1	yes	characteristic
247	C₂×C₄×D₇₉	C₂²×C₄	1	1	yes	characteristic
248	C₂×C₄×D₇₉	C₂²×C₄	1	4	yes	—
249	C₂×C₄×D₇₉	C₂²×C₄	1	1	yes	characteristic
250	C₂×C₄×D₇₉	C₂²×C₄	1	1	yes	characteristic
251	C₂×C₄×D₇₉	C₂²×C₄	1	1	yes	characteristic
252	C₂×C₄×D₇₉	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×D₇₉	C₂⁴	1	1	yes	characteristic
254	#11929608	—	2	4	no	—
255	C₂×C₇₉⋊C₈	—	2	2	no	—
256	C₂×C₇₉⋊C₈	—	2	2	no	—
257	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
258	C₂×C₇₉⋊C₈	C₂⁴	1	4	yes	—
259	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
260	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
261	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
262	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
263	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
264	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
265	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
266	C₄⋊Dic₇₉	C₂²×C₄	1	4	yes	—
267	C₄⋊Dic₇₉	C₂²×C₄	1	4	yes	—
268	Dic₇₉⋊C₄	C₂²×C₄	1	4	yes	—
269	Dic₇₉⋊C₄	C₂²×C₄	1	4	yes	—
270	Dic₇₉⋊C₄	C₂²×C₄	1	4	yes	—
271	Dic₇₉⋊C₄	C₂²×C₄	1	4	yes	—
272	Dic₇₉⋊C₄	C₂²×C₄	1	4	yes	—
273	Dic₇₉⋊C₄	C₂²×C₄	1	4	yes	—
274	Dic₇₉⋊C₄	C₂²×C₄	1	4	yes	—
275	Dic₇₉⋊C₄	C₂²×C₄	1	4	yes	—
276	C₂²⋊Dic₇₉	C₂²×C₄	1	4	yes	—
277	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	4	yes	—
278	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	4	yes	—
279	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
280	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
281	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
282	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
283	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
284	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
285	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
286	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
287	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
288	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
289	C₄×Dic₇₉	C₂²×C₄	1	4	yes	—
290	C₄×Dic₇₉	C₂²×C₄	1	4	yes	—
291	C₄×Dic₇₉	C₂⁴	1	1	yes	characteristic
292	C₄×Dic₇₉	C₂⁴	1	4	yes	—
293	C₄×Dic₇₉	C₂⁴	1	1	yes	characteristic
294	C₂×Q₈×C₇₉	C₂²×C₄	1	2	yes	—
295	C₂×Q₈×C₇₉	C₂²×C₄	1	2	yes	—
296	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
297	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
298	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
299	M₁₆×C₇₉	—	2	4	no	—
300	C₂×C₈×C₇₉	—	2	2	no	—
301	C₂×C₈×C₇₉	—	2	2	no	—
302	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
303	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
304	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
305	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
306	C₂×C₈×C₇₉	C₂⁴	1	4	yes	—
307	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
308	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
309	C₄⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
310	C₄⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
311	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
312	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
313	C₂²⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
314	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
315	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
316	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
317	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
318	C₄²×C₇₉	C₂⁴	1	4	yes	—
319	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
320	C₂²×D₇₉	—	2	2	no	—
321	C₂²×D₇₉	—	2	2	no	—
322	C₂²×D₇₉	—	4	1	no	—
323	C₂²×D₇₉	C₂³×C₄	1	1	yes	characteristic
324	C₂²×D₇₉	C₂³×C₄	1	1	yes	characteristic
325	Q₈×C₇₉	—	2	4	no	—
326	Q₈×C₇₉	—	2	4	no	—
327	C₂×C₄×C₇₉	—	2	2	no	—
328	C₂×C₄×C₇₉	—	2	2	no	—
329	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
330	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
331	C₂×C₄×C₇₉	C₂³×C₄	1	4	yes	—
332	C₂×C₄×C₇₉	C₂³×C₄	1	4	yes	—
333	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
334	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
335	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
336	C₂×C₄×C₇₉	2₋¹⁺⁴	1	2	yes	—
337	C₂×C₄×C₇₉	2₋¹⁺⁴	1	2	yes	—
338	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
339	C₂×Dic₇₉	—	2	2	no	—
340	C₂×Dic₇₉	—	2	2	no	—
341	C₂×Dic₇₉	—	4	1	no	—
342	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
343	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
344	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
345	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
346	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
347	C₂×Dic₇₉	C₂³×C₄	1	4	yes	—
348	C₂×Dic₇₉	C₂³×C₄	1	4	yes	—
349	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
350	C₄×D₇₉	—	2	2	no	—
351	C₄×D₇₉	—	2	8	no	—
352	C₄×D₇₉	—	2	2	no	—
353	C₄×D₇₉	—	2	2	no	—
354	C₄×D₇₉	—	2	2	no	—
355	C₄×D₇₉	—	2	2	no	—
356	C₄×D₇₉	—	2	2	no	—
357	C₄×D₇₉	—	2	1	no	—
358	C₄×D₇₉	—	2	1	no	—
359	C₄×D₇₉	—	2	1	no	—
360	C₄×D₇₉	—	2	1	no	—
361	C₄×D₇₉	—	2	2	no	—
362	C₄×D₇₉	—	4	1	no	—
363	C₄×D₇₉	—	4	1	no	—
364	C₄×D₇₉	—	4	4	no	—
365	C₄×D₇₉	#131	1	4	yes	—
366	Dic₁₅₈	—	2	4	no	—
367	Dic₁₅₈	—	2	4	no	—
368	Dic₁₅₈	—	2	8	no	—
369	Dic₁₅₈	—	4	4	no	—
370	C₈×C₇₉	—	2	1	no	—
371	C₈×C₇₉	—	2	1	no	—
372	C₈×C₇₉	—	2	1	no	—
373	C₈×C₇₉	—	2	1	no	—
374	C₈×C₇₉	—	2	4	no	—
375	C₇₉⋊C₈	—	2	1	no	—
376	C₇₉⋊C₈	—	2	1	no	—
377	C₇₉⋊C₈	—	2	1	no	—
378	C₇₉⋊C₈	—	2	1	no	—
379	C₇₉⋊C₈	—	2	4	no	—
380	C₂²×C₇₉	—	2	1	no	—
381	C₂²×C₇₉	—	2	1	no	—
382	C₂²×C₇₉	#519	1	2	yes	—
383	C₂²×C₇₉	C₂⁴×C₄	1	1	yes	characteristic
384	C₂×D₇₉	—	2	1	no	—
385	C₂×D₇₉	—	2	1	no	—
386	C₂×D₇₉	—	2	1	no	—
387	C₂×D₇₉	—	2	1	no	—
388	C₂×D₇₉	—	2	1	no	—
389	C₂×D₇₉	—	4	4	no	—
390	C₂×D₇₉	C₂×#131	1	2	yes	—
391	C₄×C₇₉	—	2	1	no	—
392	C₄×C₇₉	—	2	4	no	—
393	C₄×C₇₉	—	2	1	no	—
394	C₄×C₇₉	—	2	4	no	—
395	C₄×C₇₉	#519	1	2	yes	—
396	C₄×C₇₉	C₂×#131	1	2	yes	—
397	C₄×C₇₉	#568	1	2	yes	—
398	C₄×C₇₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
399	C₄×C₇₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
400	Dic₇₉	—	2	1	no	—
401	Dic₇₉	—	2	1	no	—
402	Dic₇₉	—	2	4	no	—
403	Dic₇₉	—	2	1	no	—
404	Dic₇₉	—	2	4	no	—
405	Dic₇₉	—	2	1	no	—
406	Dic₇₉	—	2	1	no	—
407	Dic₇₉	C₂×#131	1	2	yes	—
408	#60250	—	79	1	no	maximal, Sylow
409	C₂×C₇₉	—	2	2	no	—
410	C₂×C₇₉	C₂×#519	1	1	yes	characteristic
411	C₂×C₇₉	C₂²×#131	1	1	yes	characteristic
412	C₂×C₇₉	C₂×#568	1	1	yes	characteristic
413	D₇₉	—	2	2	no	—
414	D₇₉	—	4	1	no	—
415	C₂×#533	—	79	1	no	—
416	#2986	—	79	2	no	—
417	#2986	—	79	2	no	—
418	#2985	—	79	2	no	—
419	#2985	—	79	2	no	—
420	#2984	—	79	2	no	—
421	#2984	—	79	2	no	—
422	#2983	—	79	2	no	—
423	#2982	—	79	2	no	—
424	#2962	—	79	2	no	—
425	#2962	—	79	2	no	—
426	#2960	—	79	1	no	—
427	#2960	—	79	1	no	—
428	#2960	—	79	1	no	—
429	#2960	D₇₉	1	1	yes	characteristic, complemented
430	#2924	—	79	2	no	—
431	#2924	—	79	2	no	—
432	#2920	—	79	1	no	—
433	C₂×#431	—	79	1	no	—
434	C₇₉	#60250	1	1	yes	characteristic, complemented, Sylow
435	#533	—	79	1	no	—
436	#533	—	79	1	no	—
437	#533	—	79	2	no	—
438	#533	—	79	2	no	—
439	#533	—	79	2	no	—
440	#533	—	79	2	no	—
441	#533	—	79	2	no	—
442	#533	—	79	2	no	—
443	#533	—	79	1	no	—
444	#533	C₂×D₇₉	1	1	yes	characteristic
445	C₂×C₄⋊Q₈	—	79	1	no	—
446	C₂×C₄⋊Q₈	—	79	1	no	—
447	C₂×#125	—	79	2	no	—
448	C₂×C₂²⋊Q₈	—	79	2	no	—
449	C₂×C₂²⋊Q₈	—	79	2	no	—
450	C₂×C₄×Q₈	—	79	2	no	—
451	C₂×C₄×Q₈	—	79	2	no	—
452	C₂×#117	—	79	2	no	—
453	C₂²×C₄²	—	79	1	no	—
454	#446	—	79	2	no	—
455	#446	—	79	2	no	—
456	#446	—	79	2	no	—
457	#446	—	79	2	no	—
458	#446	—	79	4	no	—
459	#446	—	79	4	no	—
460	#446	—	79	4	no	—
461	#446	—	79	4	no	—
462	#446	—	79	4	no	—
463	#446	—	79	2	no	—
464	#446	—	79	2	no	—
465	#446	—	79	4	no	—
466	#446	C₂×D₇₉	1	2	yes	complemented
467	#446	C₂×D₇₉	1	2	yes	complemented
468	C₈×Q₈	—	79	2	no	—
469	C₈×Q₈	—	79	2	no	—
470	C₈×Q₈	—	79	2	no	—
471	C₈×Q₈	—	79	2	no	—
472	C₈×Q₈	—	79	4	no	—
473	C₈×Q₈	—	79	2	no	—
474	C₈×Q₈	—	79	2	no	—
475	C₈×Q₈	—	79	4	no	—
476	C₈×Q₈	C₂×D₇₉	1	2	yes	complemented
477	C₈×Q₈	C₂×D₇₉	1	2	yes	complemented
478	#433	—	79	4	no	—
479	#433	—	79	4	no	—
480	#433	—	79	4	no	—
481	#433	—	79	4	no	—
482	#432	—	79	2	no	—
483	#432	—	79	2	no	—
484	#432	—	79	4	no	—
485	#432	—	79	4	no	—
486	#431	—	79	2	no	—
487	#431	—	79	2	no	—
488	#431	—	79	4	no	—
489	#431	—	79	1	no	—
490	#431	—	79	1	no	—
491	#431	—	79	1	no	—
492	#431	—	79	1	no	—
493	#431	—	79	1	no	—
494	#431	—	79	1	no	—
495	#431	—	79	1	no	—
496	#431	—	79	1	no	—
497	#431	—	79	4	no	—
498	#424	—	79	2	no	—
499	#424	—	79	2	no	—
500	#424	—	79	2	no	—
501	#424	C₂×D₇₉	1	2	yes	—
502	#423	—	79	1	no	—
503	#423	C₂×D₇₉	1	1	yes	characteristic
504	C₂×C₄⋊C₈	—	79	1	no	—
505	C₂×C₄⋊C₈	—	79	1	no	—
506	#407	—	79	2	no	—
507	C₂×C₂²⋊C₈	—	79	1	no	—
508	C₂×C₂²⋊C₈	—	79	1	no	—
509	#405	—	79	2	no	—
510	#405	—	79	2	no	—
511	#405	—	79	2	no	—
512	#405	C₂×D₇₉	1	2	yes	—
513	C₄×M₁₆	—	79	2	no	—
514	C₂×C₄×C₈	—	79	1	no	—
515	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
516	C₂²×Q₈	—	79	2	no	—
517	C₂²×Q₈	—	79	2	no	—
518	C₂³×C₄	—	79	1	no	—
519	C₂³×C₄	—	79	1	no	—
520	C₂³×C₄	—	79	1	no	—
521	C₂×M₁₆	—	79	2	no	—
522	C₂×M₁₆	C₂²×D₇₉	1	2	yes	—
523	C₂²×C₈	—	79	1	no	—
524	C₂²×C₈	—	79	1	no	—
525	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
526	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
527	C₄⋊Q₈	—	79	2	no	—
528	C₄⋊Q₈	—	79	2	no	—
529	C₄⋊Q₈	—	79	2	no	—
530	C₄⋊Q₈	—	79	2	no	—
531	C₄⋊Q₈	—	79	2	no	—
532	C₄⋊Q₈	—	79	2	no	—
533	C₄⋊Q₈	—	79	1	no	—
534	C₄⋊Q₈	—	79	1	no	—
535	C₄⋊Q₈	C₄×D₇₉	1	1	yes	characteristic
536	C₄⋊Q₈	C₄×D₇₉	1	1	yes	characteristic
537	#125	—	79	4	no	—
538	#125	—	79	4	no	—
539	#125	—	79	2	no	—
540	#125	—	79	2	no	—
541	#125	—	79	2	no	—
542	#125	C₄×D₇₉	1	2	yes	—
543	C₂²⋊Q₈	—	79	2	no	—
544	C₂²⋊Q₈	—	79	2	no	—
545	C₂²⋊Q₈	—	79	2	no	—
546	C₂²⋊Q₈	—	79	2	no	—
547	C₂²⋊Q₈	—	79	4	no	—
548	C₂²⋊Q₈	—	79	4	no	—
549	C₂²⋊Q₈	—	79	2	no	—
550	C₂²⋊Q₈	—	79	2	no	—
551	C₂²⋊Q₈	—	79	4	no	—
552	C₂²⋊Q₈	—	79	4	no	—
553	C₂²⋊Q₈	C₄×D₇₉	1	2	yes	—
554	C₂²⋊Q₈	C₄×D₇₉	1	2	yes	—
555	C₄×Q₈	—	79	2	no	—
556	C₄×Q₈	—	79	2	no	—
557	C₄×Q₈	—	79	2	no	—
558	C₄×Q₈	—	79	2	no	—
559	C₄×Q₈	—	79	4	no	—
560	C₄×Q₈	—	79	4	no	—
561	C₄×Q₈	—	79	4	no	—
562	C₄×Q₈	—	79	2	no	—
563	C₄×Q₈	—	79	2	no	—
564	C₄×Q₈	—	79	4	no	—
565	C₄×Q₈	C₂²×D₇₉	1	2	yes	—
566	C₄×Q₈	C₂²×D₇₉	1	2	yes	—
567	#117	—	79	2	no	—
568	#117	—	79	2	no	—
569	#117	—	79	2	no	—
570	#117	—	79	4	no	—
571	#117	—	79	4	no	—
572	#117	C₂²×D₇₉	1	2	yes	—
573	C₂×C₄⋊C₄	—	79	2	no	—
574	C₂×C₄⋊C₄	—	79	2	no	—
575	C₂×C₄⋊C₄	—	79	4	no	—
576	C₂×C₄⋊C₄	—	79	4	no	—
577	C₂×C₄⋊C₄	—	79	2	no	—
578	C₂×C₄⋊C₄	—	79	2	no	—
579	C₂×C₂²⋊C₄	—	79	4	no	—
580	C₂×C₄²	—	79	1	no	—
581	C₂×C₄²	—	79	1	no	—
582	C₂×C₄²	—	79	1	no	—
583	C₂×C₄²	—	79	1	no	—
584	C₂×C₄²	—	79	1	no	—
585	C₂×C₄²	—	79	1	no	—
586	C₂×C₄²	—	79	1	no	—
587	C₂×C₄²	—	79	4	no	—
588	C₂×C₄²	—	79	1	no	—
589	C₂×C₄²	—	79	1	no	—
590	C₂×C₄²	—	79	1	no	—
591	C₂×C₄²	—	79	1	no	—
592	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
593	C₄⋊C₈	—	79	1	no	—
594	C₄⋊C₈	—	79	1	no	—
595	C₄⋊C₈	—	79	1	no	—
596	C₄⋊C₈	—	79	1	no	—
597	C₄⋊C₈	—	79	1	no	—
598	C₄⋊C₈	—	79	1	no	—
599	C₄⋊C₈	—	79	1	no	—
600	C₄⋊C₈	—	79	1	no	—
601	C₄⋊C₈	—	79	4	no	—
602	C₄⋊C₈	—	79	4	no	—
603	C₄⋊C₈	—	79	4	no	—
604	C₄⋊C₈	—	79	4	no	—
605	C₄⋊C₈	—	79	2	no	—
606	C₄⋊C₈	—	79	2	no	—
607	C₄⋊C₈	—	79	4	no	—
608	C₄⋊C₈	—	79	4	no	—
609	C₄⋊C₈	C₂²×D₇₉	1	2	yes	—
610	C₄⋊C₈	C₂²×D₇₉	1	2	yes	—
611	C₄⋊C₈	C₂²×D₇₉	1	4	yes	—
612	C₄⋊C₈	C₂²×D₇₉	1	4	yes	—
613	C₂²⋊C₈	—	79	1	no	—
614	C₂²⋊C₈	—	79	1	no	—
615	C₂²⋊C₈	—	79	1	no	—
616	C₂²⋊C₈	—	79	1	no	—
617	C₂²⋊C₈	—	79	1	no	—
618	C₂²⋊C₈	—	79	1	no	—
619	C₂²⋊C₈	—	79	1	no	—
620	C₂²⋊C₈	—	79	1	no	—
621	C₂²⋊C₈	—	79	4	no	—
622	C₂²⋊C₈	—	79	4	no	—
623	#97	—	79	4	no	—
624	#97	—	79	4	no	—
625	#97	—	79	4	no	—
626	#97	—	79	4	no	—
627	#97	C₂²×D₇₉	1	4	yes	—
628	C₄×C₈	—	79	4	no	—
629	C₄×C₈	—	79	4	no	—
630	C₄×C₈	—	79	4	no	—
631	C₄×C₈	—	79	1	no	—
632	C₄×C₈	—	79	1	no	—
633	C₄×C₈	—	79	1	no	—
634	C₄×C₈	—	79	1	no	—
635	C₄×C₈	—	79	4	no	—
636	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
637	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
638	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
639	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
640	C₄×C₈	C₂²×D₇₉	1	4	yes	—
641	C₂⁴	—	79	1	no	—
642	C₂×Q₈	—	316	4	no	—
643	C₂×Q₈	—	79	4	no	—
644	C₂×Q₈	—	79	4	no	—
645	C₂×Q₈	—	79	2	no	—
646	C₂×Q₈	—	79	2	no	—
647	C₂×Q₈	—	158	8	no	—
648	C₂×Q₈	C₂×C₄×D₇₉	1	2	yes	—
649	C₂×Q₈	C₂×C₄×D₇₉	1	2	yes	—
650	C₂²×C₄	—	316	2	no	—
651	C₂²×C₄	—	79	1	no	—
652	C₂²×C₄	—	79	1	no	—
653	C₂²×C₄	—	79	1	no	—
654	C₂²×C₄	—	79	4	no	—
655	C₂²×C₄	—	79	1	no	—
656	C₂²×C₄	—	79	1	no	—
657	C₂²×C₄	—	79	1	no	—
658	C₂²×C₄	—	79	1	no	—
659	C₂²×C₄	—	79	1	no	—
660	C₂²×C₄	—	79	1	no	—
661	C₂²×C₄	—	79	1	no	—
662	C₂²×C₄	—	79	1	no	—
663	C₂²×C₄	—	79	1	no	—
664	C₂²×C₄	—	79	1	no	—
665	C₂²×C₄	—	79	1	no	—
666	C₂²×C₄	—	79	1	no	—
667	C₂²×C₄	—	79	4	no	—
668	C₂²×C₄	—	158	4	no	—
669	C₂²×C₄	—	158	2	no	—
670	C₂²×C₄	—	158	2	no	—
671	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
672	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
673	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
674	M₁₆	—	2	4	no	—
675	M₁₆	—	158	4	no	—
676	C₂×C₈	—	2	2	no	—
677	C₂×C₈	—	2	2	no	—
678	C₂×C₈	—	79	1	no	—
679	C₂×C₈	—	79	1	no	—
680	C₂×C₈	—	79	4	no	—
681	C₂×C₈	—	79	1	no	—
682	C₂×C₈	—	79	1	no	—
683	C₂×C₈	—	158	2	no	—
684	C₂×C₈	—	158	2	no	—
685	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
686	C₂×C₈	C₂³×D₇₉	1	4	yes	—
687	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
688	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
689	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
690	C₄⋊C₄	—	79	4	no	—
691	C₄⋊C₄	—	79	4	no	—
692	C₄⋊C₄	—	79	4	no	—
693	C₄⋊C₄	—	79	4	no	—
694	C₄⋊C₄	—	79	4	no	—
695	C₄⋊C₄	—	79	4	no	—
696	C₄⋊C₄	—	79	4	no	—
697	C₄⋊C₄	—	79	4	no	—
698	C₄⋊C₄	—	79	2	no	—
699	C₄⋊C₄	—	79	2	no	—
700	C₄⋊C₄	—	79	4	no	—
701	C₄⋊C₄	—	79	4	no	—
702	C₄⋊C₄	—	79	2	no	—
703	C₄⋊C₄	—	79	2	no	—
704	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
705	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
706	C₄⋊C₄	C₂×C₄×D₇₉	1	4	yes	—
707	C₄⋊C₄	C₂×C₄×D₇₉	1	4	yes	—
708	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
709	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
710	C₂²⋊C₄	—	79	4	no	—
711	C₂²⋊C₄	—	79	4	no	—
712	C₂²⋊C₄	—	79	4	no	—
713	C₂²⋊C₄	C₂×C₄×D₇₉	1	4	yes	—
714	C₄²	—	79	1	no	—
715	C₄²	—	79	4	no	—
716	C₄²	—	79	1	no	—
717	C₄²	—	79	1	no	—
718	C₄²	—	79	1	no	—
719	C₄²	—	79	1	no	—
720	C₄²	—	79	1	no	—
721	C₄²	—	79	1	no	—
722	C₄²	—	79	1	no	—
723	C₄²	—	79	1	no	—
724	C₄²	—	79	1	no	—
725	C₄²	—	79	1	no	—
726	C₄²	—	79	1	no	—
727	C₄²	—	79	4	no	—
728	C₄²	—	79	4	no	—
729	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
730	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
731	C₄²	C₂³×D₇₉	1	1	yes	characteristic
732	C₄²	C₂³×D₇₉	1	1	yes	characteristic
733	C₄²	C₂³×D₇₉	1	4	yes	—
734	C₂³	—	316	1	no	—
735	C₂³	—	79	1	no	—
736	C₂³	—	79	1	no	—
737	C₂³	—	158	2	no	—
738	C₂³	—	158	2	no	—
739	C₂³	C₂²×C₄×D₇₉	1	1	yes	characteristic
740	Q₈	—	2	4	no	—
741	Q₈	—	2	4	no	—
742	Q₈	—	316	4	no	—
743	Q₈	—	158	8	no	—
744	Q₈	—	158	4	no	—
745	Q₈	—	158	4	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	316	1	no	—
749	C₂×C₄	—	316	1	no	—
750	C₂×C₄	—	316	4	no	—
751	C₂×C₄	—	316	1	no	—
752	C₂×C₄	—	79	1	no	—
753	C₂×C₄	—	79	4	no	—
754	C₂×C₄	—	79	1	no	—
755	C₂×C₄	—	79	1	no	—
756	C₂×C₄	—	79	1	no	—
757	C₂×C₄	—	79	1	no	—
758	C₂×C₄	—	79	1	no	—
759	C₂×C₄	—	79	4	no	—
760	C₂×C₄	—	79	4	no	—
761	C₂×C₄	—	158	2	no	—
762	C₂×C₄	—	158	2	no	—
763	C₂×C₄	—	158	8	no	—
764	C₂×C₄	—	158	2	no	—
765	C₂×C₄	—	158	2	no	—
766	C₂×C₄	—	158	1	no	—
767	C₂×C₄	—	158	1	no	—
768	C₂×C₄	—	158	1	no	—
769	C₂×C₄	—	158	1	no	—
770	C₂×C₄	—	158	2	no	—
771	C₂×C₄	—	158	2	no	—
772	C₂×C₄	—	158	2	no	—
773	C₂×C₄	—	158	2	no	—
774	C₂×C₄	—	158	2	no	—
775	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
776	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
777	C₂×C₄	C₂²×C₄×D₇₉	1	4	yes	—
778	C₂×C₄	C₂²×C₄×D₇₉	1	4	yes	—
779	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
780	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
781	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
782	C₂×C₄	#14579208	1	2	yes	—
783	C₂×C₄	#14579209	1	2	yes	—
784	C₂×C₄	C₂⁴×D₇₉	1	1	yes	characteristic
785	C₈	—	2	1	no	—
786	C₈	—	2	1	no	—
787	C₈	—	2	4	no	—
788	C₈	—	2	1	no	—
789	C₈	—	2	1	no	—
790	C₈	—	158	1	no	—
791	C₈	—	158	1	no	—
792	C₈	—	158	1	no	—
793	C₈	—	158	1	no	—
794	C₈	—	158	4	no	—
795	C₂²	—	2	1	no	—
796	C₂²	—	2	1	no	—
797	C₂²	—	316	4	no	—
798	C₂²	—	79	2	no	—
799	C₂²	—	158	1	no	—
800	C₂²	—	158	1	no	—
801	C₂²	—	158	1	no	—
802	C₂²	—	158	1	no	—
803	C₂²	—	158	1	no	—
804	C₂²	#19099039	1	2	yes	—
805	C₂²	C₂³×C₄×D₇₉	1	1	yes	characteristic
806	C₄	—	2	1	no	—
807	C₄	—	2	4	no	—
808	C₄	—	2	1	no	—
809	C₄	—	2	4	no	—
810	C₄	—	79	2	no	—
811	C₄	—	158	1	no	—
812	C₄	—	158	4	no	—
813	C₄	—	158	1	no	—
814	C₄	—	158	1	no	—
815	C₄	—	158	4	no	—
816	C₄	—	158	1	no	—
817	C₄	—	158	1	no	—
818	C₄	#19099039	1	2	yes	—
819	C₄	#131×D₇₉	1	2	yes	—
820	C₄	#19099328	1	2	yes	—
821	C₄	C₂×#14579208	1	1	yes	characteristic
822	C₄	C₂×#14579209	1	1	yes	characteristic
823	C₂	—	2	2	no	—
824	C₂	—	316	1	no	—
825	C₂	—	158	2	no	—
826	C₂	C₂×#19099039	1	1	yes	characteristic
827	C₂	C₂×#131×D₇₉	1	1	yes	characteristic
828	C₂	C₂×#19099328	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₇₉
commutator, socle	C₂²×C₇₉	C₂⁴×C₄
Fitting	C₇₉×#2960	C₂
prime radical	C₂³×D₇₉	C₂²×C₄
cosocle	C₂×C₄×C₇₉	C₂⁵
hypercenter	#2960	D₇₉
hypocenter	C₇₉	#60250
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ #2960

Complements

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

N	H ≅ G/N	type
2. #23772500	C₂	semidirect
3. #23772498	C₂	semidirect
4. #23772496	C₂	semidirect
5. #23772491	C₂	semidirect
6. #23772488	C₂	semidirect
7. #23772486	C₂	semidirect
8. #23772482	C₂	semidirect
9. #23772479	C₂	semidirect
10. #23772346	C₂	semidirect
11. #23772344	C₂	semidirect
12. #23772335	C₂	semidirect
13. #23772334	C₂	semidirect
14. #23772330	C₂	semidirect
19. C₇₉×#2960	C₂	semidirect
38. #19098694	C₂²	semidirect
39. #19098694	C₂²	semidirect
40. #19098693	C₂²	semidirect
41. #19098693	C₂²	semidirect
42. #19098693	C₂²	semidirect
43. #19098692	C₂²	semidirect
44. #19098692	C₂²	semidirect
45. #19098691	C₂²	semidirect
46. #19098691	C₂²	semidirect
47. #19098690	C₂²	semidirect
48. #19098690	C₂²	semidirect
49. #19098690	C₂²	semidirect
50. Q₈×C₇₉⋊C₈	C₂²	semidirect
51. Q₈×C₇₉⋊C₈	C₂²	semidirect
52. C₈×Dic₁₅₈	C₂²	semidirect
53. C₈×Dic₁₅₈	C₂²	semidirect
54. C₈×Dic₁₅₈	C₂²	semidirect
55. #19098687	C₂²	semidirect
56. #19098687	C₂²	semidirect
57. #19098687	C₂²	semidirect
93. #446×C₇₉	C₂²	semidirect
94. #446×C₇₉	C₂²	semidirect
95. C₈×Q₈×C₇₉	C₂²	semidirect
96. C₈×Q₈×C₇₉	C₂²	semidirect
429. #2960	D₇₉	semidirect
434. C₇₉	#60250	semidirect
466. #446	C₂×D₇₉	semidirect
467. #446	C₂×D₇₉	semidirect
476. C₈×Q₈	C₂×D₇₉	semidirect
477. C₈×Q₈	C₂×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
#533×D₇₉	2
#23772500	2
#23772498	2
#23772496	2
#23772491	2
#23772488	2
#23772486	2
#23772482	2
#23772479	2
#23772346	2
#23772344	2
#23772335	2
#23772334	2
#23772330	2
#23772057	2
#23772055	2
#23772032	2
C₂×#19098614	2
C₇₉×#2960	2
#60250	79