Subgroups — C₅₉×#35743 #28447852

Order 15104.

1822 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#2666	C₂	1	2	yes	maximal, complemented
2	C₅₉×#2627	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2605	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2588	C₂	1	2	yes	maximal, complemented
5	C₅₉×#2586	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2550	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2549	C₂	1	1	yes	maximal, characteristic
8	C₅₉×#2473	C₂	1	2	yes	maximal
9	C₅₉×#2462	C₂	1	2	yes	maximal, complemented
10	C₅₉×#2451	C₂	1	2	yes	maximal, complemented
11	C₅₉×#2438	C₂	1	2	yes	maximal
12	C₅₉×#2434	C₂	1	1	yes	maximal, characteristic
13	C₅₉×#2399	C₂	1	2	yes	maximal, complemented
14	C₂×C₅₉×#395	C₂	1	1	yes	maximal, characteristic
15	C₅₉×#2368	C₂	1	1	yes	maximal, characteristic
16	C₅₉×#2360	C₂	1	2	yes	maximal
17	C₅₉×#2343	C₂	1	2	yes	maximal
18	Q₈×C₂²⋊C₄×C₅₉	C₂	1	1	yes	maximal, characteristic
19	C₅₉×#2274	C₂	1	1	yes	maximal, characteristic
20	C₂³×Q₈×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₅₉	C₂²	1	2	yes	—
22	C₂×#125×C₅₉	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
27	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
30	C₂²×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
31	C₅₉×#400	C₂²	1	1	yes	characteristic
32	C₅₉×#400	C₂²	1	2	yes	—
33	C₅₉×#400	C₂²	1	1	yes	characteristic
34	C₅₉×#400	C₂²	1	2	yes	—
35	C₅₉×#398	C₂²	1	2	yes	—
36	C₅₉×#398	C₂²	1	2	yes	—
37	C₅₉×#398	C₂²	1	2	yes	—
38	C₅₉×#398	C₂²	1	2	yes	—
39	C₅₉×#398	C₂²	1	2	yes	—
40	C₅₉×#398	C₂²	1	2	yes	—
41	C₅₉×#398	C₂²	1	2	yes	—
42	C₅₉×#398	C₂²	1	2	yes	—
43	C₅₉×#395	C₂²	1	2	yes	—
44	C₅₉×#395	C₂²	1	1	yes	characteristic
45	C₅₉×#395	C₂²	1	2	yes	—
46	C₅₉×#395	C₂²	1	1	yes	characteristic
47	C₅₉×#395	C₂²	1	2	yes	—
48	C₅₉×#395	C₂²	1	2	yes	—
49	C₅₉×#395	C₂²	1	2	yes	—
50	C₅₉×#395	C₂²	1	1	yes	characteristic
51	C₅₉×#395	C₂²	1	1	yes	characteristic
52	C₅₉×#395	C₂²	1	1	yes	characteristic
53	C₅₉×#395	C₂²	1	1	yes	characteristic
54	C₅₉×#395	C₂²	1	2	yes	—
55	C₅₉×#391	C₂²	1	2	yes	—
56	C₅₉×#391	C₂²	1	2	yes	—
57	C₅₉×#391	C₂²	1	2	yes	—
58	C₅₉×#391	C₂²	1	2	yes	—
59	C₅₉×#391	C₂²	1	2	yes	—
60	C₅₉×#391	C₂²	1	2	yes	—
61	C₅₉×#391	C₂²	1	2	yes	—
62	C₅₉×#391	C₂²	1	2	yes	—
63	C₅₉×#389	C₂²	1	2	yes	—
64	C₅₉×#389	C₂²	1	2	yes	—
65	C₅₉×#389	C₂²	1	2	yes	—
66	C₅₉×#389	C₂²	1	2	yes	—
67	C₅₉×#389	C₂²	1	2	yes	—
68	C₅₉×#389	C₂²	1	2	yes	—
69	C₅₉×#387	C₂²	1	2	yes	—
70	C₅₉×#387	C₂²	1	2	yes	—
71	C₅₉×#387	C₂²	1	2	yes	—
72	C₅₉×#387	C₂²	1	2	yes	—
73	C₅₉×#387	C₂²	1	2	yes	—
74	C₅₉×#387	C₂²	1	2	yes	—
75	C₅₉×#387	C₂²	1	2	yes	—
76	C₅₉×#387	C₂²	1	2	yes	—
77	C₅₉×#387	C₂²	1	2	yes	—
78	C₅₉×#387	C₂²	1	2	yes	—
79	C₅₉×#387	C₂²	1	2	yes	—
80	C₅₉×#387	C₂²	1	2	yes	—
81	C₅₉×#385	C₂²	1	2	yes	—
82	C₅₉×#385	C₂²	1	2	yes	—
83	C₅₉×#385	C₂²	1	2	yes	—
84	C₅₉×#385	C₂²	1	2	yes	—
85	C₅₉×#385	C₂²	1	2	yes	—
86	C₅₉×#383	C₂²	1	2	yes	—
87	C₅₉×#382	C₂²	1	2	yes	—
88	C₅₉×#381	C₂²	1	2	yes	—
89	C₅₉×#380	C₂²	1	1	yes	characteristic
90	C₅₉×#380	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
92	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
95	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
97	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
99	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
100	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
101	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
104	C₅₉×#376	C₂²	1	2	yes	—
105	C₂×#95×C₅₉	C₂²	1	1	yes	characteristic
106	C₂×#95×C₅₉	C₂²	1	2	yes	—
107	C₂²×Q₈×C₅₉	—	2	4	no	—
108	C₂²×Q₈×C₅₉	—	4	4	no	—
109	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
110	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
111	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
112	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
113	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
115	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
116	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
119	C₄⋊Q₈×C₅₉	—	4	4	no	—
120	#125×C₅₉	—	4	4	no	—
121	C₂²⋊Q₈×C₅₉	—	2	4	no	—
122	C₂²⋊Q₈×C₅₉	—	2	8	no	—
123	C₄×Q₈×C₅₉	—	4	4	no	—
124	C₄×Q₈×C₅₉	—	4	4	no	—
125	#117×C₅₉	—	2	4	no	—
126	#117×C₅₉	Q₈	1	8	yes	complemented
127	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
128	C₂×C₄⋊C₄×C₅₉	—	4	4	no	—
129	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
158	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
161	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
162	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
164	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
165	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
166	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
167	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
168	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
169	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
170	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
171	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
172	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
173	#95×C₅₉	C₂³	1	2	yes	—
174	#95×C₅₉	C₂³	1	1	yes	characteristic
175	#95×C₅₉	C₂³	1	2	yes	—
176	#95×C₅₉	C₂³	1	2	yes	—
177	#95×C₅₉	C₂³	1	2	yes	—
178	#95×C₅₉	C₂³	1	1	yes	characteristic
179	#95×C₅₉	C₂³	1	2	yes	—
180	#95×C₅₉	C₂³	1	2	yes	—
181	#95×C₅₉	C₂³	1	2	yes	—
182	#95×C₅₉	C₂³	1	2	yes	—
183	#95×C₅₉	C₂³	1	2	yes	—
184	#95×C₅₉	C₂³	1	2	yes	—
185	#95×C₅₉	C₂³	1	2	yes	—
186	#95×C₅₉	C₂³	1	2	yes	—
187	#95×C₅₉	C₂³	1	2	yes	—
188	#95×C₅₉	C₂³	1	2	yes	—
189	#95×C₅₉	C₂³	1	2	yes	—
190	#95×C₅₉	C₂³	1	2	yes	—
191	#95×C₅₉	C₂³	1	2	yes	—
192	#95×C₅₉	C₂³	1	2	yes	—
193	#95×C₅₉	C₂³	1	2	yes	—
194	#95×C₅₉	C₂³	1	2	yes	—
195	#95×C₅₉	C₂³	1	2	yes	—
196	#95×C₅₉	C₂³	1	2	yes	—
197	#95×C₅₉	C₂³	1	1	yes	characteristic
198	#95×C₅₉	C₂³	1	1	yes	characteristic
199	#95×C₅₉	C₂³	1	2	yes	—
200	#95×C₅₉	C₂³	1	2	yes	—
201	#95×C₅₉	C₂³	1	2	yes	—
202	#95×C₅₉	C₂³	1	2	yes	—
203	#95×C₅₉	C₂³	1	2	yes	—
204	#95×C₅₉	C₂³	1	2	yes	—
205	#95×C₅₉	C₂³	1	2	yes	—
206	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
207	C₂×Q₈×C₅₉	—	2	2	no	—
208	C₂×Q₈×C₅₉	—	2	4	no	—
209	C₂×Q₈×C₅₉	—	2	4	no	—
210	C₂×Q₈×C₅₉	—	2	2	no	—
211	C₂×Q₈×C₅₉	—	2	2	no	—
212	C₂×Q₈×C₅₉	—	2	4	no	—
213	C₂×Q₈×C₅₉	—	2	4	no	—
214	C₂×Q₈×C₅₉	—	2	4	no	—
215	C₂×Q₈×C₅₉	—	4	2	no	—
216	C₂×Q₈×C₅₉	—	4	2	no	—
217	C₂×Q₈×C₅₉	—	4	2	no	—
218	C₂×Q₈×C₅₉	—	4	2	no	—
219	C₂×Q₈×C₅₉	—	4	16	no	—
220	C₂²×C₄×C₅₉	—	2	2	no	—
221	C₂²×C₄×C₅₉	—	2	2	no	—
222	C₂²×C₄×C₅₉	—	2	4	no	—
223	C₂²×C₄×C₅₉	—	2	4	no	—
224	C₂²×C₄×C₅₉	—	2	2	no	—
225	C₂²×C₄×C₅₉	—	2	4	no	—
226	C₂²×C₄×C₅₉	—	2	4	no	—
227	C₂²×C₄×C₅₉	—	4	2	no	—
228	C₂²×C₄×C₅₉	—	4	2	no	—
229	C₂²×C₄×C₅₉	—	4	2	no	—
230	C₂²×C₄×C₅₉	—	4	2	no	—
231	C₂²×C₄×C₅₉	C₂×Q₈	1	4	yes	—
232	C₂²×C₄×C₅₉	#41	1	4	yes	—
233	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
251	C₄⋊C₄×C₅₉	—	2	2	no	—
252	C₄⋊C₄×C₅₉	—	2	2	no	—
253	C₄⋊C₄×C₅₉	—	2	2	no	—
254	C₄⋊C₄×C₅₉	—	2	2	no	—
255	C₄⋊C₄×C₅₉	—	2	4	no	—
256	C₄⋊C₄×C₅₉	—	2	4	no	—
257	C₄⋊C₄×C₅₉	—	2	2	no	—
258	C₄⋊C₄×C₅₉	—	2	4	no	—
259	C₄⋊C₄×C₅₉	—	2	4	no	—
260	C₄⋊C₄×C₅₉	—	2	4	no	—
261	C₄⋊C₄×C₅₉	—	2	4	no	—
262	C₄⋊C₄×C₅₉	—	2	4	no	—
263	C₄⋊C₄×C₅₉	—	2	4	no	—
264	C₄⋊C₄×C₅₉	—	2	4	no	—
265	C₄⋊C₄×C₅₉	—	2	4	no	—
266	C₄⋊C₄×C₅₉	—	2	4	no	—
267	C₄⋊C₄×C₅₉	—	2	4	no	—
268	C₄⋊C₄×C₅₉	—	4	2	no	—
269	C₄⋊C₄×C₅₉	—	4	2	no	—
270	C₄⋊C₄×C₅₉	—	4	2	no	—
271	C₄⋊C₄×C₅₉	—	4	2	no	—
272	C₄⋊C₄×C₅₉	—	4	2	no	—
273	C₄⋊C₄×C₅₉	—	4	2	no	—
274	C₄⋊C₄×C₅₉	—	4	2	no	—
275	C₄⋊C₄×C₅₉	—	4	2	no	—
276	C₄⋊C₄×C₅₉	—	4	2	no	—
277	C₄⋊C₄×C₅₉	—	4	2	no	—
278	C₄⋊C₄×C₅₉	C₂×Q₈	1	8	yes	complemented
279	C₂²⋊C₄×C₅₉	—	2	2	no	—
280	C₂²⋊C₄×C₅₉	—	2	4	no	—
281	C₂²⋊C₄×C₅₉	—	2	4	no	—
282	C₂²⋊C₄×C₅₉	C₂×Q₈	1	4	yes	—
283	C₂²⋊C₄×C₅₉	C₂×Q₈	1	4	yes	—
284	C₂²⋊C₄×C₅₉	#41	1	4	yes	—
285	C₄²×C₅₉	—	2	4	no	—
286	C₄²×C₅₉	—	2	4	no	—
287	C₄²×C₅₉	—	2	4	no	—
288	C₄²×C₅₉	—	4	2	no	—
289	C₄²×C₅₉	—	4	2	no	—
290	C₄²×C₅₉	—	4	2	no	—
291	C₄²×C₅₉	—	4	2	no	—
292	C₄²×C₅₉	—	4	2	no	—
293	C₄²×C₅₉	—	4	2	no	—
294	C₄²×C₅₉	C₂×Q₈	1	8	yes	complemented
295	C₂³×C₅₉	—	2	2	no	—
296	C₂³×C₅₉	—	2	2	no	—
297	C₂³×C₅₉	C₂²×Q₈	1	2	yes	—
298	C₂³×C₅₉	C₂×#41	1	2	yes	—
299	C₂³×C₅₉	C₂×#41	1	2	yes	—
300	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
301	Q₈×C₅₉	—	2	8	no	—
302	Q₈×C₅₉	—	4	8	no	—
303	Q₈×C₅₉	—	4	8	no	—
304	Q₈×C₅₉	—	4	4	no	—
305	Q₈×C₅₉	—	8	2	no	—
306	C₂×C₄×C₅₉	—	2	8	no	—
307	C₂×C₄×C₅₉	—	2	1	no	—
308	C₂×C₄×C₅₉	—	2	1	no	—
309	C₂×C₄×C₅₉	—	2	1	no	—
310	C₂×C₄×C₅₉	—	2	1	no	—
311	C₂×C₄×C₅₉	—	2	2	no	—
312	C₂×C₄×C₅₉	—	2	2	no	—
313	C₂×C₄×C₅₉	—	2	2	no	—
314	C₂×C₄×C₅₉	—	2	2	no	—
315	C₂×C₄×C₅₉	—	2	2	no	—
316	C₂×C₄×C₅₉	—	2	2	no	—
317	C₂×C₄×C₅₉	—	2	2	no	—
318	C₂×C₄×C₅₉	—	2	2	no	—
319	C₂×C₄×C₅₉	—	2	2	no	—
320	C₂×C₄×C₅₉	—	2	2	no	—
321	C₂×C₄×C₅₉	—	2	2	no	—
322	C₂×C₄×C₅₉	—	2	2	no	—
323	C₂×C₄×C₅₉	—	2	2	no	—
324	C₂×C₄×C₅₉	—	2	2	no	—
325	C₂×C₄×C₅₉	—	2	2	no	—
326	C₂×C₄×C₅₉	—	2	2	no	—
327	C₂×C₄×C₅₉	—	2	2	no	—
328	C₂×C₄×C₅₉	—	2	1	no	—
329	C₂×C₄×C₅₉	—	2	1	no	—
330	C₂×C₄×C₅₉	—	2	2	no	—
331	C₂×C₄×C₅₉	—	2	2	no	—
332	C₂×C₄×C₅₉	—	2	2	no	—
333	C₂×C₄×C₅₉	—	2	2	no	—
334	C₂×C₄×C₅₉	—	2	2	no	—
335	C₂×C₄×C₅₉	—	2	2	no	—
336	C₂×C₄×C₅₉	—	2	2	no	—
337	C₂×C₄×C₅₉	—	2	2	no	—
338	C₂×C₄×C₅₉	—	2	2	no	—
339	C₂×C₄×C₅₉	—	2	2	no	—
340	C₂×C₄×C₅₉	—	2	2	no	—
341	C₂×C₄×C₅₉	—	2	2	no	—
342	C₂×C₄×C₅₉	—	2	2	no	—
343	C₂×C₄×C₅₉	—	2	2	no	—
344	C₂×C₄×C₅₉	—	2	2	no	—
345	C₂×C₄×C₅₉	—	2	2	no	—
346	C₂×C₄×C₅₉	—	2	2	no	—
347	C₂×C₄×C₅₉	—	2	2	no	—
348	C₂×C₄×C₅₉	—	4	4	no	—
349	C₂×C₄×C₅₉	—	4	8	no	—
350	C₂×C₄×C₅₉	—	4	8	no	—
351	C₂×C₄×C₅₉	—	8	2	no	—
352	C₂×C₄×C₅₉	C₂²×Q₈	1	2	yes	—
353	C₂×C₄×C₅₉	C₂²×Q₈	1	4	yes	—
354	C₂×C₄×C₅₉	C₂²×Q₈	1	4	yes	—
355	C₂×C₄×C₅₉	C₂²×Q₈	1	2	yes	—
356	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
357	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
358	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
359	C₂×C₄×C₅₉	H(5,𝔽₂)	1	4	yes	—
360	C₂×C₄×C₅₉	2₋¹⁺⁴	1	4	yes	—
361	#35743	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
362	C₂²×C₅₉	—	2	2	no	—
363	C₂²×C₅₉	—	2	4	no	—
364	C₂²×C₅₉	—	2	2	no	—
365	C₂²×C₅₉	—	2	4	no	—
366	C₂²×C₅₉	#533	1	4	yes	—
367	C₂²×C₅₉	C₂³×Q₈	1	1	yes	characteristic
368	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
369	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
370	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	2	yes	—
371	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	2	yes	—
372	C₄×C₅₉	—	2	2	no	—
373	C₄×C₅₉	—	2	2	no	—
374	C₄×C₅₉	—	2	2	no	—
375	C₄×C₅₉	—	2	2	no	—
376	C₄×C₅₉	—	2	4	no	—
377	C₄×C₅₉	—	2	4	no	—
378	C₄×C₅₉	—	2	4	no	—
379	C₄×C₅₉	—	2	4	no	—
380	C₄×C₅₉	—	2	4	no	—
381	C₄×C₅₉	—	4	2	no	—
382	C₄×C₅₉	—	4	1	no	—
383	C₄×C₅₉	—	4	1	no	—
384	C₄×C₅₉	—	4	2	no	—
385	C₄×C₅₉	—	4	2	no	—
386	C₄×C₅₉	—	4	2	no	—
387	C₄×C₅₉	—	4	2	no	—
388	C₄×C₅₉	—	4	2	no	—
389	C₄×C₅₉	—	4	2	no	—
390	#2666	C₂×C₅₉	1	2	yes	complemented
391	#2627	C₂×C₅₉	1	1	yes	characteristic
392	#2605	C₂×C₅₉	1	2	yes	complemented
393	#2588	C₂×C₅₉	1	2	yes	complemented
394	#2586	C₂×C₅₉	1	2	yes	complemented
395	#2550	C₂×C₅₉	1	2	yes	complemented
396	#2549	C₂×C₅₉	1	1	yes	characteristic
397	#2473	C₂×C₅₉	1	2	yes	—
398	#2462	C₂×C₅₉	1	2	yes	complemented
399	#2451	C₂×C₅₉	1	2	yes	complemented
400	#2438	C₂×C₅₉	1	2	yes	—
401	#2434	C₂×C₅₉	1	1	yes	characteristic
402	#2399	C₂×C₅₉	1	2	yes	complemented
403	C₂×#395	C₂×C₅₉	1	1	yes	characteristic
404	#2368	C₂×C₅₉	1	1	yes	characteristic
405	#2360	C₂×C₅₉	1	2	yes	—
406	#2343	C₂×C₅₉	1	2	yes	—
407	Q₈×C₂²⋊C₄	C₂×C₅₉	1	1	yes	characteristic
408	#2274	C₂×C₅₉	1	1	yes	characteristic
409	C₂×C₅₉	—	2	4	no	—
410	C₂×C₅₉	C₂×#533	1	1	yes	characteristic
411	C₂×C₅₉	#3490	1	1	yes	characteristic
412	C₂×C₅₉	#3503	1	2	yes	—
413	C₂×C₅₉	#3509	1	1	yes	characteristic
414	C₂×C₅₉	#3520	1	2	yes	—
415	C₂³×Q₈	C₂²×C₅₉	1	1	yes	characteristic
416	C₂×C₄⋊Q₈	C₂²×C₅₉	1	2	yes	—
417	C₂×#125	C₂²×C₅₉	1	2	yes	—
418	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	—
419	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
420	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
421	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
422	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
423	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
424	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
425	C₂²×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
426	#400	C₂²×C₅₉	1	1	yes	characteristic
427	#400	C₂²×C₅₉	1	2	yes	—
428	#400	C₂²×C₅₉	1	1	yes	characteristic
429	#400	C₂²×C₅₉	1	2	yes	—
430	#398	C₂²×C₅₉	1	2	yes	—
431	#398	C₂²×C₅₉	1	2	yes	—
432	#398	C₂²×C₅₉	1	2	yes	—
433	#398	C₂²×C₅₉	1	2	yes	—
434	#398	C₂²×C₅₉	1	2	yes	—
435	#398	C₂²×C₅₉	1	2	yes	—
436	#398	C₂²×C₅₉	1	2	yes	—
437	#398	C₂²×C₅₉	1	2	yes	—
438	#395	C₂²×C₅₉	1	1	yes	characteristic
439	#395	C₂²×C₅₉	1	2	yes	—
440	#395	C₂²×C₅₉	1	2	yes	—
441	#395	C₂²×C₅₉	1	2	yes	—
442	#395	C₂²×C₅₉	1	2	yes	—
443	#395	C₂²×C₅₉	1	2	yes	—
444	#395	C₂²×C₅₉	1	1	yes	characteristic
445	#395	C₂²×C₅₉	1	1	yes	characteristic
446	#395	C₂²×C₅₉	1	1	yes	characteristic
447	#395	C₂²×C₅₉	1	1	yes	characteristic
448	#395	C₂²×C₅₉	1	1	yes	characteristic
449	#395	C₂²×C₅₉	1	2	yes	—
450	#391	C₂²×C₅₉	1	2	yes	—
451	#391	C₂²×C₅₉	1	2	yes	—
452	#391	C₂²×C₅₉	1	2	yes	—
453	#391	C₂²×C₅₉	1	2	yes	—
454	#391	C₂²×C₅₉	1	2	yes	—
455	#391	C₂²×C₅₉	1	2	yes	—
456	#391	C₂²×C₅₉	1	2	yes	—
457	#391	C₂²×C₅₉	1	2	yes	—
458	#389	C₂²×C₅₉	1	2	yes	—
459	#389	C₂²×C₅₉	1	2	yes	—
460	#389	C₂²×C₅₉	1	2	yes	—
461	#389	C₂²×C₅₉	1	2	yes	—
462	#389	C₂²×C₅₉	1	2	yes	—
463	#389	C₂²×C₅₉	1	2	yes	—
464	#387	C₂²×C₅₉	1	2	yes	—
465	#387	C₂²×C₅₉	1	2	yes	—
466	#387	C₂²×C₅₉	1	2	yes	—
467	#387	C₂²×C₅₉	1	2	yes	—
468	#387	C₂²×C₅₉	1	2	yes	—
469	#387	C₂²×C₅₉	1	2	yes	—
470	#387	C₂²×C₅₉	1	2	yes	—
471	#387	C₂²×C₅₉	1	2	yes	—
472	#387	C₂²×C₅₉	1	2	yes	—
473	#387	C₂²×C₅₉	1	2	yes	—
474	#387	C₂²×C₅₉	1	2	yes	—
475	#387	C₂²×C₅₉	1	2	yes	—
476	#385	C₂²×C₅₉	1	2	yes	—
477	#385	C₂²×C₅₉	1	2	yes	—
478	#385	C₂²×C₅₉	1	2	yes	—
479	#385	C₂²×C₅₉	1	2	yes	—
480	#385	C₂²×C₅₉	1	2	yes	—
481	#383	C₂²×C₅₉	1	2	yes	—
482	#382	C₂²×C₅₉	1	2	yes	—
483	#381	C₂²×C₅₉	1	2	yes	—
484	#380	C₂²×C₅₉	1	1	yes	characteristic
485	#380	C₂²×C₅₉	1	2	yes	—
486	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
487	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
488	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
489	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
490	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
491	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
492	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
493	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
494	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
495	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
496	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
497	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
498	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
499	#376	C₂²×C₅₉	1	2	yes	—
500	C₂×#95	C₂²×C₅₉	1	2	yes	—
501	C₂×#95	C₂²×C₅₉	1	1	yes	characteristic
502	C₅₉	#35743	1	1	yes	characteristic, direct product factor, Sylow
503	C₂²×Q₈	—	2	4	no	—
504	C₂²×Q₈	—	4	4	no	—
505	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
506	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
507	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
508	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
509	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
510	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
511	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
512	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
513	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
514	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
515	C₄⋊Q₈	—	4	4	no	—
516	#125	—	4	4	no	—
517	C₂²⋊Q₈	—	2	4	no	—
518	C₂²⋊Q₈	—	2	8	no	—
519	C₄×Q₈	—	4	4	no	—
520	C₄×Q₈	—	4	4	no	—
521	#117	—	2	4	no	—
522	#117	Q₈×C₅₉	1	8	yes	complemented
523	C₂×C₄⋊C₄	—	2	4	no	—
524	C₂×C₄⋊C₄	—	4	4	no	—
525	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
529	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
531	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
538	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
544	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
548	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
554	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
557	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
558	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
559	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
560	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
561	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
562	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
563	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
564	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
565	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
566	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
567	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
568	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
569	#95	C₂³×C₅₉	1	2	yes	—
570	#95	C₂³×C₅₉	1	1	yes	characteristic
571	#95	C₂³×C₅₉	1	2	yes	—
572	#95	C₂³×C₅₉	1	2	yes	—
573	#95	C₂³×C₅₉	1	2	yes	—
574	#95	C₂³×C₅₉	1	1	yes	characteristic
575	#95	C₂³×C₅₉	1	2	yes	—
576	#95	C₂³×C₅₉	1	2	yes	—
577	#95	C₂³×C₅₉	1	2	yes	—
578	#95	C₂³×C₅₉	1	2	yes	—
579	#95	C₂³×C₅₉	1	2	yes	—
580	#95	C₂³×C₅₉	1	2	yes	—
581	#95	C₂³×C₅₉	1	2	yes	—
582	#95	C₂³×C₅₉	1	2	yes	—
583	#95	C₂³×C₅₉	1	2	yes	—
584	#95	C₂³×C₅₉	1	2	yes	—
585	#95	C₂³×C₅₉	1	2	yes	—
586	#95	C₂³×C₅₉	1	2	yes	—
587	#95	C₂³×C₅₉	1	2	yes	—
588	#95	C₂³×C₅₉	1	2	yes	—
589	#95	C₂³×C₅₉	1	2	yes	—
590	#95	C₂³×C₅₉	1	2	yes	—
591	#95	C₂³×C₅₉	1	2	yes	—
592	#95	C₂³×C₅₉	1	2	yes	—
593	#95	C₂³×C₅₉	1	1	yes	characteristic
594	#95	C₂³×C₅₉	1	1	yes	characteristic
595	#95	C₂³×C₅₉	1	2	yes	—
596	#95	C₂³×C₅₉	1	2	yes	—
597	#95	C₂³×C₅₉	1	2	yes	—
598	#95	C₂³×C₅₉	1	2	yes	—
599	#95	C₂³×C₅₉	1	2	yes	—
600	#95	C₂³×C₅₉	1	2	yes	—
601	#95	C₂³×C₅₉	1	2	yes	—
602	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
603	C₂×Q₈	—	2	2	no	—
604	C₂×Q₈	—	2	4	no	—
605	C₂×Q₈	—	2	4	no	—
606	C₂×Q₈	—	2	2	no	—
607	C₂×Q₈	—	2	2	no	—
608	C₂×Q₈	—	2	4	no	—
609	C₂×Q₈	—	2	4	no	—
610	C₂×Q₈	—	2	4	no	—
611	C₂×Q₈	—	4	2	no	—
612	C₂×Q₈	—	4	2	no	—
613	C₂×Q₈	—	4	2	no	—
614	C₂×Q₈	—	4	2	no	—
615	C₂×Q₈	—	4	16	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	4	no	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	4	2	no	—
624	C₂²×C₄	—	4	2	no	—
625	C₂²×C₄	—	4	2	no	—
626	C₂²×C₄	—	4	2	no	—
627	C₂²×C₄	C₂×Q₈×C₅₉	1	4	yes	—
628	C₂²×C₄	#41×C₅₉	1	4	yes	—
629	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
630	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
631	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
632	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
636	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
637	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
639	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
640	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
641	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
642	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
643	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
644	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
645	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
646	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	—	2	2	no	—
649	C₄⋊C₄	—	2	2	no	—
650	C₄⋊C₄	—	2	2	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	2	2	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	4	2	no	—
665	C₄⋊C₄	—	4	2	no	—
666	C₄⋊C₄	—	4	2	no	—
667	C₄⋊C₄	—	4	2	no	—
668	C₄⋊C₄	—	4	2	no	—
669	C₄⋊C₄	—	4	2	no	—
670	C₄⋊C₄	—	4	2	no	—
671	C₄⋊C₄	—	4	2	no	—
672	C₄⋊C₄	—	4	2	no	—
673	C₄⋊C₄	—	4	2	no	—
674	C₄⋊C₄	C₂×Q₈×C₅₉	1	8	yes	complemented
675	C₂²⋊C₄	—	2	2	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	C₂×Q₈×C₅₉	1	4	yes	—
679	C₂²⋊C₄	C₂×Q₈×C₅₉	1	4	yes	—
680	C₂²⋊C₄	#41×C₅₉	1	4	yes	—
681	C₄²	—	2	4	no	—
682	C₄²	—	2	4	no	—
683	C₄²	—	2	4	no	—
684	C₄²	—	4	2	no	—
685	C₄²	—	4	2	no	—
686	C₄²	—	4	2	no	—
687	C₄²	—	4	2	no	—
688	C₄²	—	4	2	no	—
689	C₄²	—	4	2	no	—
690	C₄²	C₂×Q₈×C₅₉	1	8	yes	complemented
691	C₂³	—	2	2	no	—
692	C₂³	—	2	2	no	—
693	C₂³	C₂²×Q₈×C₅₉	1	2	yes	—
694	C₂³	C₂×#41×C₅₉	1	2	yes	—
695	C₂³	C₂×#41×C₅₉	1	2	yes	—
696	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
697	Q₈	—	2	8	no	—
698	Q₈	—	4	8	no	—
699	Q₈	—	4	8	no	—
700	Q₈	—	4	4	no	—
701	Q₈	—	8	2	no	—
702	C₂×C₄	—	2	8	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	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	4	4	no	—
745	C₂×C₄	—	4	8	no	—
746	C₂×C₄	—	4	8	no	—
747	C₂×C₄	—	8	2	no	—
748	C₂×C₄	C₂²×Q₈×C₅₉	1	2	yes	—
749	C₂×C₄	C₂²×Q₈×C₅₉	1	4	yes	—
750	C₂×C₄	C₂²×Q₈×C₅₉	1	4	yes	—
751	C₂×C₄	C₂²×Q₈×C₅₉	1	2	yes	—
752	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
753	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
754	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
755	C₂×C₄	H(5,𝔽₂)×C₅₉	1	4	yes	—
756	C₂×C₄	2₋¹⁺⁴×C₅₉	1	4	yes	—
757	C₂²	—	2	2	no	—
758	C₂²	—	2	4	no	—
759	C₂²	—	2	2	no	—
760	C₂²	—	2	4	no	—
761	C₂²	C₅₉×#533	1	4	yes	—
762	C₂²	C₂³×Q₈×C₅₉	1	1	yes	characteristic
763	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
764	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
765	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	2	yes	—
766	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	2	yes	—
767	C₄	—	2	4	no	—
768	C₄	—	2	4	no	—
769	C₄	—	2	2	no	—
770	C₄	—	2	2	no	—
771	C₄	—	2	2	no	—
772	C₄	—	2	2	no	—
773	C₄	—	2	4	no	—
774	C₄	—	2	4	no	—
775	C₄	—	2	4	no	—
776	C₄	—	4	2	no	—
777	C₄	—	4	2	no	—
778	C₄	—	4	2	no	—
779	C₄	—	4	2	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	2	no	—
782	C₄	—	4	1	no	—
783	C₄	—	4	1	no	—
784	C₄	—	4	2	no	—
785	C₂	—	2	4	no	—
786	C₂	C₂×C₅₉×#533	1	1	yes	characteristic
787	C₂	C₅₉×#3490	1	1	yes	characteristic
788	C₂	C₅₉×#3503	1	2	yes	—
789	C₂	C₅₉×#3509	1	1	yes	characteristic
790	C₂	C₅₉×#3520	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₂⁴×C₅₉	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₉×#2666	C₂	semidirect
3. C₅₉×#2605	C₂	semidirect
4. C₅₉×#2588	C₂	semidirect
5. C₅₉×#2586	C₂	semidirect
6. C₅₉×#2550	C₂	semidirect
9. C₅₉×#2462	C₂	semidirect
10. C₅₉×#2451	C₂	semidirect
13. C₅₉×#2399	C₂	semidirect
126. #117×C₅₉	Q₈	semidirect
278. C₄⋊C₄×C₅₉	C₂×Q₈	semidirect
294. C₄²×C₅₉	C₂×Q₈	semidirect
361. #35743	C₅₉	direct (N × H)
390. #2666	C₂×C₅₉	semidirect
392. #2605	C₂×C₅₉	semidirect
393. #2588	C₂×C₅₉	semidirect
394. #2586	C₂×C₅₉	semidirect
395. #2550	C₂×C₅₉	semidirect
398. #2462	C₂×C₅₉	semidirect
399. #2451	C₂×C₅₉	semidirect
402. #2399	C₂×C₅₉	semidirect
502. C₅₉	#35743	direct (N × H)
522. #117	Q₈×C₅₉	semidirect
674. C₄⋊C₄	C₂×Q₈×C₅₉	semidirect
690. C₄²	C₂×Q₈×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₅₉×#2666	2
C₅₉×#2627	2
C₅₉×#2605	2
C₅₉×#2588	2
C₅₉×#2586	2
C₅₉×#2550	2
C₅₉×#2549	2
C₅₉×#2473	2
C₅₉×#2462	2
C₅₉×#2451	2
C₅₉×#2438	2
C₅₉×#2434	2
C₅₉×#2399	2
C₂×C₅₉×#395	2
C₅₉×#2368	2
C₅₉×#2360	2
C₅₉×#2343	2
Q₈×C₂²⋊C₄×C₅₉	2
C₅₉×#2274	2
#35743	59

Subgroups — C59×#35743 #28447852

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35743 #28447852