Subgroups — C₅₉×#35561 #28447670

Order 15104.

1856 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#2592	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₉×#2560	C₂	1	2	yes	maximal, complemented
3	C₅₉×#2558	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2552	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2544	C₂	1	1	yes	maximal, characteristic
6	C₅₉×#2538	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#2531	C₂	1	2	yes	maximal, complemented
8	C₅₉×#2526	C₂	1	2	yes	maximal, complemented
9	C₅₉×#2512	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#2511	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2466	C₂	1	2	yes	maximal, complemented
12	C₅₉×#2460	C₂	1	2	yes	maximal, complemented
13	C₅₉×#2450	C₂	1	2	yes	maximal, complemented
14	C₅₉×#2447	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#2445	C₂	1	1	yes	maximal, characteristic
16	C₅₉×#2419	C₂	1	2	yes	maximal, complemented
17	C₅₉×#2326	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₉×#2326	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₉×#2319	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#127×C₅₉	C₂	1	1	yes	maximal, characteristic
21	C₅₉×#2295	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₉×#2295	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₉×#2275	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#127×C₅₉	C₂²	1	1	yes	characteristic
25	C₂×#126×C₅₉	C₂²	1	2	yes	—
26	C₂×#125×C₅₉	C₂²	1	2	yes	—
27	C₂×#124×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×#124×C₅₉	C₂²	1	1	yes	characteristic
29	C₂×#123×C₅₉	C₂²	1	2	yes	—
30	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	—
31	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
39	C₅₉×#400	C₂²	1	2	yes	—
40	C₅₉×#400	C₂²	1	2	yes	—
41	C₅₉×#398	C₂²	1	2	yes	—
42	C₅₉×#398	C₂²	1	2	yes	—
43	C₅₉×#397	C₂²	1	2	yes	—
44	C₅₉×#397	C₂²	1	2	yes	—
45	C₅₉×#397	C₂²	1	2	yes	—
46	C₅₉×#397	C₂²	1	2	yes	—
47	C₅₉×#396	C₂²	1	2	yes	—
48	C₅₉×#396	C₂²	1	2	yes	—
49	C₅₉×#396	C₂²	1	2	yes	—
50	C₅₉×#394	C₂²	1	2	yes	—
51	C₅₉×#394	C₂²	1	2	yes	—
52	C₅₉×#394	C₂²	1	2	yes	—
53	C₅₉×#394	C₂²	1	2	yes	—
54	C₅₉×#393	C₂²	1	2	yes	—
55	C₅₉×#391	C₂²	1	1	yes	characteristic
56	C₅₉×#391	C₂²	1	1	yes	characteristic
57	C₅₉×#391	C₂²	1	1	yes	characteristic
58	C₅₉×#391	C₂²	1	1	yes	characteristic
59	C₅₉×#391	C₂²	1	1	yes	characteristic
60	C₅₉×#391	C₂²	1	1	yes	characteristic
61	C₅₉×#390	C₂²	1	1	yes	characteristic
62	C₅₉×#390	C₂²	1	1	yes	characteristic
63	C₅₉×#390	C₂²	1	1	yes	characteristic
64	C₅₉×#390	C₂²	1	2	yes	—
65	C₅₉×#390	C₂²	1	1	yes	characteristic
66	C₅₉×#390	C₂²	1	1	yes	characteristic
67	C₅₉×#390	C₂²	1	2	yes	—
68	C₅₉×#390	C₂²	1	1	yes	characteristic
69	C₅₉×#389	C₂²	1	1	yes	characteristic
70	C₅₉×#389	C₂²	1	1	yes	characteristic
71	C₅₉×#389	C₂²	1	2	yes	—
72	C₅₉×#389	C₂²	1	1	yes	characteristic
73	C₅₉×#389	C₂²	1	1	yes	characteristic
74	C₅₉×#389	C₂²	1	1	yes	characteristic
75	C₅₉×#389	C₂²	1	1	yes	characteristic
76	C₅₉×#388	C₂²	1	2	yes	—
77	C₅₉×#388	C₂²	1	2	yes	—
78	C₅₉×#388	C₂²	1	2	yes	—
79	C₅₉×#388	C₂²	1	2	yes	—
80	C₅₉×#388	C₂²	1	2	yes	—
81	C₅₉×#388	C₂²	1	2	yes	—
82	C₅₉×#388	C₂²	1	2	yes	—
83	C₅₉×#388	C₂²	1	2	yes	—
84	C₅₉×#388	C₂²	1	2	yes	—
85	C₅₉×#387	C₂²	1	2	yes	—
86	C₅₉×#387	C₂²	1	2	yes	—
87	C₅₉×#387	C₂²	1	1	yes	characteristic
88	C₅₉×#387	C₂²	1	1	yes	characteristic
89	C₅₉×#387	C₂²	1	1	yes	characteristic
90	C₅₉×#387	C₂²	1	2	yes	—
91	C₅₉×#387	C₂²	1	2	yes	—
92	C₅₉×#387	C₂²	1	1	yes	characteristic
93	C₅₉×#386	C₂²	1	2	yes	—
94	C₅₉×#386	C₂²	1	2	yes	—
95	C₅₉×#386	C₂²	1	2	yes	—
96	C₅₉×#385	C₂²	1	2	yes	—
97	C₅₉×#385	C₂²	1	2	yes	—
98	C₅₉×#385	C₂²	1	2	yes	—
99	C₅₉×#385	C₂²	1	2	yes	—
100	C₅₉×#385	C₂²	1	2	yes	—
101	C₅₉×#384	C₂²	1	1	yes	characteristic
102	C₅₉×#384	C₂²	1	1	yes	characteristic
103	C₅₉×#384	C₂²	1	1	yes	characteristic
104	C₅₉×#381	C₂²	1	2	yes	—
105	C₅₉×#381	C₂²	1	2	yes	—
106	C₅₉×#380	C₂²	1	2	yes	—
107	C₅₉×#380	C₂²	1	2	yes	—
108	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
115	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
116	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
118	C₅₉×#376	C₂²	1	2	yes	—
119	C₅₉×#376	C₂²	1	1	yes	characteristic
120	C₅₉×#376	C₂²	1	1	yes	characteristic
121	C₂×#95×C₅₉	C₂²	1	2	yes	—
122	C₄³×C₅₉	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
127	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
128	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
130	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
131	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
132	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
133	#127×C₅₉	—	2	4	no	—
134	#126×C₅₉	—	4	4	no	—
135	#125×C₅₉	—	4	4	no	—
136	#124×C₅₉	—	2	4	no	—
137	#124×C₅₉	—	2	4	no	—
138	#123×C₅₉	—	4	4	no	—
139	C₂²⋊Q₈×C₅₉	—	4	4	no	—
140	C₄×Q₈×C₅₉	—	2	4	no	—
141	C₄×Q₈×C₅₉	—	2	4	no	—
142	C₄×D₄×C₅₉	—	2	4	no	—
143	C₄×D₄×C₅₉	—	2	4	no	—
144	C₄×D₄×C₅₉	—	2	4	no	—
145	C₄×D₄×C₅₉	—	2	4	no	—
146	C₄×D₄×C₅₉	—	4	4	no	—
147	C₄×D₄×C₅₉	—	4	4	no	—
148	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
157	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
164	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
193	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
201	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
204	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
205	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
206	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
208	#95×C₅₉	C₂³	1	1	yes	characteristic
209	#95×C₅₉	C₂³	1	2	yes	—
210	#95×C₅₉	C₂³	1	2	yes	—
211	#95×C₅₉	C₂³	1	2	yes	—
212	#95×C₅₉	C₂³	1	1	yes	characteristic
213	#95×C₅₉	C₂³	1	1	yes	characteristic
214	#95×C₅₉	C₂³	1	1	yes	characteristic
215	#95×C₅₉	C₂³	1	1	yes	characteristic
216	#95×C₅₉	C₂³	1	2	yes	—
217	#95×C₅₉	C₂³	1	1	yes	characteristic
218	#95×C₅₉	C₂³	1	2	yes	—
219	#95×C₅₉	C₂³	1	2	yes	—
220	#95×C₅₉	C₂³	1	2	yes	—
221	#95×C₅₉	C₂³	1	1	yes	characteristic
222	#95×C₅₉	C₂³	1	1	yes	characteristic
223	#95×C₅₉	C₂³	1	1	yes	characteristic
224	#95×C₅₉	C₂³	1	2	yes	—
225	#95×C₅₉	C₂³	1	1	yes	characteristic
226	#95×C₅₉	C₂³	1	1	yes	characteristic
227	#95×C₅₉	C₂³	1	1	yes	characteristic
228	#95×C₅₉	C₂³	1	2	yes	—
229	#95×C₅₉	C₂³	1	1	yes	characteristic
230	#95×C₅₉	C₂³	1	1	yes	characteristic
231	#95×C₅₉	C₂³	1	2	yes	—
232	#95×C₅₉	C₂³	1	2	yes	—
233	#95×C₅₉	C₂³	1	2	yes	—
234	#95×C₅₉	C₂³	1	2	yes	—
235	#95×C₅₉	C₂³	1	2	yes	—
236	#95×C₅₉	C₂³	1	2	yes	—
237	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
238	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
239	C₂×Q₈×C₅₉	—	2	2	no	—
240	C₂×Q₈×C₅₉	—	2	2	no	—
241	C₂×Q₈×C₅₉	—	2	2	no	—
242	C₂×Q₈×C₅₉	—	2	2	no	—
243	C₂×Q₈×C₅₉	—	2	2	no	—
244	C₂×Q₈×C₅₉	—	4	1	no	—
245	C₂×D₄×C₅₉	—	2	4	no	—
246	C₂×D₄×C₅₉	—	2	4	no	—
247	C₂×D₄×C₅₉	—	2	2	no	—
248	C₂×D₄×C₅₉	—	2	2	no	—
249	C₂×D₄×C₅₉	—	2	2	no	—
250	C₂×D₄×C₅₉	—	2	2	no	—
251	C₂×D₄×C₅₉	—	2	2	no	—
252	C₂×D₄×C₅₉	—	2	4	no	—
253	C₂×D₄×C₅₉	—	2	4	no	—
254	C₂×D₄×C₅₉	—	4	2	no	—
255	C₂×D₄×C₅₉	—	4	2	no	—
256	C₂×D₄×C₅₉	#41	1	4	yes	—
257	C₂²×C₄×C₅₉	—	2	4	no	—
258	C₂²×C₄×C₅₉	—	2	4	no	—
259	C₂²×C₄×C₅₉	—	2	4	no	—
260	C₂²×C₄×C₅₉	—	2	4	no	—
261	C₂²×C₄×C₅₉	—	4	2	no	—
262	C₂²×C₄×C₅₉	—	4	2	no	—
263	C₂²×C₄×C₅₉	—	4	2	no	—
264	C₂²×C₄×C₅₉	—	4	2	no	—
265	C₂²×C₄×C₅₉	—	4	2	no	—
266	C₂²×C₄×C₅₉	—	4	2	no	—
267	C₂²×C₄×C₅₉	—	4	2	no	—
268	C₂²×C₄×C₅₉	—	4	2	no	—
269	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
290	C₄⋊C₄×C₅₉	—	2	2	no	—
291	C₄⋊C₄×C₅₉	—	2	2	no	—
292	C₄⋊C₄×C₅₉	—	2	2	no	—
293	C₄⋊C₄×C₅₉	—	2	2	no	—
294	C₄⋊C₄×C₅₉	—	2	2	no	—
295	C₄⋊C₄×C₅₉	—	2	2	no	—
296	C₄⋊C₄×C₅₉	—	2	2	no	—
297	C₄⋊C₄×C₅₉	—	2	2	no	—
298	C₄⋊C₄×C₅₉	—	2	4	no	—
299	C₄⋊C₄×C₅₉	—	2	4	no	—
300	C₄⋊C₄×C₅₉	—	2	4	no	—
301	C₄⋊C₄×C₅₉	—	2	2	no	—
302	C₄⋊C₄×C₅₉	—	2	4	no	—
303	C₄⋊C₄×C₅₉	—	2	2	no	—
304	C₄⋊C₄×C₅₉	—	2	2	no	—
305	C₄⋊C₄×C₅₉	—	2	2	no	—
306	C₄⋊C₄×C₅₉	—	2	2	no	—
307	C₄⋊C₄×C₅₉	—	4	1	no	—
308	C₄⋊C₄×C₅₉	—	4	2	no	—
309	C₄⋊C₄×C₅₉	—	4	2	no	—
310	C₄⋊C₄×C₅₉	—	4	2	no	—
311	C₄⋊C₄×C₅₉	—	4	2	no	—
312	C₄⋊C₄×C₅₉	—	4	2	no	—
313	C₄⋊C₄×C₅₉	—	4	2	no	—
314	C₄⋊C₄×C₅₉	—	4	2	no	—
315	C₂²⋊C₄×C₅₉	—	2	4	no	—
316	C₂²⋊C₄×C₅₉	—	2	4	no	—
317	C₂²⋊C₄×C₅₉	—	2	4	no	—
318	C₂²⋊C₄×C₅₉	—	2	4	no	—
319	C₂²⋊C₄×C₅₉	—	2	4	no	—
320	C₂²⋊C₄×C₅₉	—	2	4	no	—
321	C₂²⋊C₄×C₅₉	—	2	4	no	—
322	C₂²⋊C₄×C₅₉	—	2	4	no	—
323	C₂²⋊C₄×C₅₉	—	2	4	no	—
324	C₂²⋊C₄×C₅₉	—	2	4	no	—
325	C₂²⋊C₄×C₅₉	—	4	2	no	—
326	C₂²⋊C₄×C₅₉	—	4	2	no	—
327	C₂²⋊C₄×C₅₉	—	4	2	no	—
328	C₂²⋊C₄×C₅₉	—	4	2	no	—
329	C₂²⋊C₄×C₅₉	—	4	2	no	—
330	C₂²⋊C₄×C₅₉	—	4	2	no	—
331	C₂²⋊C₄×C₅₉	—	4	2	no	—
332	C₂²⋊C₄×C₅₉	—	4	2	no	—
333	C₂²⋊C₄×C₅₉	—	4	2	no	—
334	C₂²⋊C₄×C₅₉	—	4	2	no	—
335	C₄²×C₅₉	—	2	2	no	—
336	C₄²×C₅₉	—	2	2	no	—
337	C₄²×C₅₉	—	2	4	no	—
338	C₄²×C₅₉	—	2	2	no	—
339	C₄²×C₅₉	—	2	2	no	—
340	C₄²×C₅₉	—	2	2	no	—
341	C₄²×C₅₉	—	2	2	no	—
342	C₄²×C₅₉	—	2	2	no	—
343	C₄²×C₅₉	—	2	2	no	—
344	C₄²×C₅₉	—	4	1	no	—
345	C₄²×C₅₉	—	4	2	no	—
346	C₄²×C₅₉	—	4	2	no	—
347	C₄²×C₅₉	—	4	2	no	—
348	C₄²×C₅₉	#41	1	4	yes	—
349	C₄²×C₅₉	#41	1	4	yes	—
350	C₂³×C₅₉	—	2	2	no	—
351	C₂³×C₅₉	—	2	2	no	—
352	C₂³×C₅₉	—	2	2	no	—
353	C₂³×C₅₉	—	2	2	no	—
354	C₂³×C₅₉	—	2	2	no	—
355	C₂³×C₅₉	—	2	2	no	—
356	C₂³×C₅₉	—	2	2	no	—
357	C₂³×C₅₉	—	2	2	no	—
358	C₂³×C₅₉	—	2	2	no	—
359	C₂³×C₅₉	—	2	2	no	—
360	C₂³×C₅₉	—	2	2	no	—
361	C₂³×C₅₉	—	2	2	no	—
362	C₂³×C₅₉	—	2	2	no	—
363	C₂³×C₅₉	C₂×#41	1	4	yes	—
364	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
365	Q₈×C₅₉	—	4	4	no	—
366	Q₈×C₅₉	—	4	4	no	—
367	D₄×C₅₉	—	2	8	no	—
368	D₄×C₅₉	—	4	8	no	—
369	D₄×C₅₉	—	4	8	no	—
370	D₄×C₅₉	—	4	4	no	—
371	C₂×C₄×C₅₉	—	2	1	no	—
372	C₂×C₄×C₅₉	—	2	1	no	—
373	C₂×C₄×C₅₉	—	2	1	no	—
374	C₂×C₄×C₅₉	—	2	1	no	—
375	C₂×C₄×C₅₉	—	2	1	no	—
376	C₂×C₄×C₅₉	—	2	1	no	—
377	C₂×C₄×C₅₉	—	2	1	no	—
378	C₂×C₄×C₅₉	—	2	1	no	—
379	C₂×C₄×C₅₉	—	2	1	no	—
380	C₂×C₄×C₅₉	—	2	1	no	—
381	C₂×C₄×C₅₉	—	2	1	no	—
382	C₂×C₄×C₅₉	—	2	1	no	—
383	C₂×C₄×C₅₉	—	2	1	no	—
384	C₂×C₄×C₅₉	—	2	1	no	—
385	C₂×C₄×C₅₉	—	2	1	no	—
386	C₂×C₄×C₅₉	—	2	1	no	—
387	C₂×C₄×C₅₉	—	2	1	no	—
388	C₂×C₄×C₅₉	—	2	2	no	—
389	C₂×C₄×C₅₉	—	2	1	no	—
390	C₂×C₄×C₅₉	—	2	1	no	—
391	C₂×C₄×C₅₉	—	2	2	no	—
392	C₂×C₄×C₅₉	—	2	1	no	—
393	C₂×C₄×C₅₉	—	2	1	no	—
394	C₂×C₄×C₅₉	—	2	2	no	—
395	C₂×C₄×C₅₉	—	2	2	no	—
396	C₂×C₄×C₅₉	—	2	2	no	—
397	C₂×C₄×C₅₉	—	2	2	no	—
398	C₂×C₄×C₅₉	—	2	2	no	—
399	C₂×C₄×C₅₉	—	2	2	no	—
400	C₂×C₄×C₅₉	—	2	1	no	—
401	C₂×C₄×C₅₉	—	2	1	no	—
402	C₂×C₄×C₅₉	—	2	2	no	—
403	C₂×C₄×C₅₉	—	2	2	no	—
404	C₂×C₄×C₅₉	—	2	2	no	—
405	C₂×C₄×C₅₉	—	2	2	no	—
406	C₂×C₄×C₅₉	—	2	2	no	—
407	C₂×C₄×C₅₉	—	2	1	no	—
408	C₂×C₄×C₅₉	—	2	2	no	—
409	C₂×C₄×C₅₉	—	2	2	no	—
410	C₂×C₄×C₅₉	—	2	1	no	—
411	C₂×C₄×C₅₉	—	2	1	no	—
412	C₂×C₄×C₅₉	—	2	1	no	—
413	C₂×C₄×C₅₉	—	2	2	no	—
414	C₂×C₄×C₅₉	—	2	1	no	—
415	C₂×C₄×C₅₉	—	2	1	no	—
416	C₂×C₄×C₅₉	—	2	1	no	—
417	C₂×C₄×C₅₉	—	2	1	no	—
418	C₂×C₄×C₅₉	—	2	1	no	—
419	C₂×C₄×C₅₉	—	2	2	no	—
420	C₂×C₄×C₅₉	—	2	2	no	—
421	C₂×C₄×C₅₉	—	2	1	no	—
422	C₂×C₄×C₅₉	—	2	1	no	—
423	C₂×C₄×C₅₉	—	2	1	no	—
424	C₂×C₄×C₅₉	—	8	4	no	—
425	C₂×C₄×C₅₉	—	8	4	no	—
426	C₂×C₄×C₅₉	—	8	4	no	—
427	C₂×C₄×C₅₉	—	8	4	no	—
428	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
429	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
430	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
431	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
432	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
433	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
434	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
435	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
436	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
437	C₂×C₄×C₅₉	2₋¹⁺⁴	1	2	yes	—
438	#35561	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
439	C₂²×C₅₉	—	2	4	no	—
440	C₂²×C₅₉	—	2	4	no	—
441	C₂²×C₅₉	—	2	4	no	—
442	C₂²×C₅₉	—	4	2	no	—
443	C₂²×C₅₉	—	4	2	no	—
444	C₂²×C₅₉	—	4	2	no	—
445	C₂²×C₅₉	—	4	2	no	—
446	C₂²×C₅₉	—	4	2	no	—
447	C₂²×C₅₉	—	4	2	no	—
448	C₂²×C₅₉	—	4	2	no	—
449	C₂²×C₅₉	—	4	2	no	—
450	C₂²×C₅₉	—	4	2	no	—
451	C₂²×C₅₉	—	4	2	no	—
452	C₂²×C₅₉	—	4	2	no	—
453	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
454	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
455	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
456	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
457	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
458	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
459	C₂²×C₅₉	#585	1	1	yes	characteristic
460	C₄×C₅₉	—	2	2	no	—
461	C₄×C₅₉	—	2	2	no	—
462	C₄×C₅₉	—	2	2	no	—
463	C₄×C₅₉	—	2	2	no	—
464	C₄×C₅₉	—	2	2	no	—
465	C₄×C₅₉	—	2	2	no	—
466	C₄×C₅₉	—	2	2	no	—
467	C₄×C₅₉	—	4	2	no	—
468	C₄×C₅₉	—	4	2	no	—
469	C₄×C₅₉	—	4	1	no	—
470	C₄×C₅₉	—	4	2	no	—
471	C₄×C₅₉	—	4	2	no	—
472	C₄×C₅₉	—	4	2	no	—
473	C₄×C₅₉	—	4	1	no	—
474	C₄×C₅₉	—	4	1	no	—
475	C₄×C₅₉	—	4	1	no	—
476	C₄×C₅₉	—	4	2	no	—
477	C₄×C₅₉	—	4	1	no	—
478	C₄×C₅₉	—	4	1	no	—
479	C₄×C₅₉	—	4	1	no	—
480	C₄×C₅₉	#529	1	4	yes	—
481	#2592	C₂×C₅₉	1	1	yes	characteristic, complemented
482	#2560	C₂×C₅₉	1	2	yes	complemented
483	#2558	C₂×C₅₉	1	2	yes	complemented
484	#2552	C₂×C₅₉	1	1	yes	characteristic, complemented
485	#2544	C₂×C₅₉	1	1	yes	characteristic
486	#2538	C₂×C₅₉	1	1	yes	characteristic, complemented
487	#2531	C₂×C₅₉	1	2	yes	complemented
488	#2526	C₂×C₅₉	1	2	yes	complemented
489	#2512	C₂×C₅₉	1	1	yes	characteristic, complemented
490	#2511	C₂×C₅₉	1	1	yes	characteristic, complemented
491	#2466	C₂×C₅₉	1	2	yes	complemented
492	#2460	C₂×C₅₉	1	2	yes	complemented
493	#2450	C₂×C₅₉	1	2	yes	complemented
494	#2447	C₂×C₅₉	1	1	yes	characteristic, complemented
495	#2445	C₂×C₅₉	1	1	yes	characteristic
496	#2419	C₂×C₅₉	1	2	yes	complemented
497	#2326	C₂×C₅₉	1	1	yes	characteristic, complemented
498	#2326	C₂×C₅₉	1	1	yes	characteristic, complemented
499	#2319	C₂×C₅₉	1	1	yes	characteristic, complemented
500	C₄×#127	C₂×C₅₉	1	1	yes	characteristic
501	#2295	C₂×C₅₉	1	1	yes	characteristic, complemented
502	#2295	C₂×C₅₉	1	1	yes	characteristic, complemented
503	#2275	C₂×C₅₉	1	1	yes	characteristic, complemented
504	C₂×C₅₉	—	4	4	no	—
505	C₂×C₅₉	—	8	2	no	—
506	C₂×C₅₉	C₂×#529	1	1	yes	characteristic
507	C₂×C₅₉	#3494	1	1	yes	characteristic
508	C₂×C₅₉	#3507	1	1	yes	characteristic
509	C₂×C₅₉	#3508	1	1	yes	characteristic
510	C₂×C₅₉	#3511	1	1	yes	characteristic
511	C₂×C₅₉	#3513	1	1	yes	characteristic
512	C₂×C₅₉	#3520	1	1	yes	characteristic
513	C₂×#127	C₂²×C₅₉	1	1	yes	characteristic
514	C₂×#126	C₂²×C₅₉	1	2	yes	—
515	C₂×#125	C₂²×C₅₉	1	2	yes	—
516	C₂×#124	C₂²×C₅₉	1	1	yes	characteristic
517	C₂×#124	C₂²×C₅₉	1	1	yes	characteristic
518	C₂×#123	C₂²×C₅₉	1	2	yes	—
519	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	—
520	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
521	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
522	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
523	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
524	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
525	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
526	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
527	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
528	#400	C₂²×C₅₉	1	2	yes	—
529	#400	C₂²×C₅₉	1	2	yes	—
530	#398	C₂²×C₅₉	1	2	yes	—
531	#398	C₂²×C₅₉	1	2	yes	—
532	#397	C₂²×C₅₉	1	2	yes	—
533	#397	C₂²×C₅₉	1	2	yes	—
534	#397	C₂²×C₅₉	1	2	yes	—
535	#397	C₂²×C₅₉	1	2	yes	—
536	#396	C₂²×C₅₉	1	2	yes	—
537	#396	C₂²×C₅₉	1	2	yes	—
538	#396	C₂²×C₅₉	1	2	yes	—
539	#394	C₂²×C₅₉	1	2	yes	—
540	#394	C₂²×C₅₉	1	2	yes	—
541	#394	C₂²×C₅₉	1	2	yes	—
542	#394	C₂²×C₅₉	1	2	yes	—
543	#393	C₂²×C₅₉	1	2	yes	—
544	#391	C₂²×C₅₉	1	1	yes	characteristic
545	#391	C₂²×C₅₉	1	1	yes	characteristic
546	#391	C₂²×C₅₉	1	1	yes	characteristic
547	#391	C₂²×C₅₉	1	1	yes	characteristic
548	#391	C₂²×C₅₉	1	1	yes	characteristic
549	#391	C₂²×C₅₉	1	1	yes	characteristic
550	#390	C₂²×C₅₉	1	2	yes	—
551	#390	C₂²×C₅₉	1	1	yes	characteristic
552	#390	C₂²×C₅₉	1	1	yes	characteristic
553	#390	C₂²×C₅₉	1	2	yes	—
554	#390	C₂²×C₅₉	1	1	yes	characteristic
555	#390	C₂²×C₅₉	1	1	yes	characteristic
556	#390	C₂²×C₅₉	1	1	yes	characteristic
557	#390	C₂²×C₅₉	1	1	yes	characteristic
558	#389	C₂²×C₅₉	1	1	yes	characteristic
559	#389	C₂²×C₅₉	1	1	yes	characteristic
560	#389	C₂²×C₅₉	1	1	yes	characteristic
561	#389	C₂²×C₅₉	1	1	yes	characteristic
562	#389	C₂²×C₅₉	1	2	yes	—
563	#389	C₂²×C₅₉	1	1	yes	characteristic
564	#389	C₂²×C₅₉	1	1	yes	characteristic
565	#388	C₂²×C₅₉	1	2	yes	—
566	#388	C₂²×C₅₉	1	2	yes	—
567	#388	C₂²×C₅₉	1	2	yes	—
568	#388	C₂²×C₅₉	1	2	yes	—
569	#388	C₂²×C₅₉	1	2	yes	—
570	#388	C₂²×C₅₉	1	2	yes	—
571	#388	C₂²×C₅₉	1	2	yes	—
572	#388	C₂²×C₅₉	1	2	yes	—
573	#388	C₂²×C₅₉	1	2	yes	—
574	#387	C₂²×C₅₉	1	2	yes	—
575	#387	C₂²×C₅₉	1	1	yes	characteristic
576	#387	C₂²×C₅₉	1	2	yes	—
577	#387	C₂²×C₅₉	1	2	yes	—
578	#387	C₂²×C₅₉	1	1	yes	characteristic
579	#387	C₂²×C₅₉	1	2	yes	—
580	#387	C₂²×C₅₉	1	1	yes	characteristic
581	#387	C₂²×C₅₉	1	1	yes	characteristic
582	#386	C₂²×C₅₉	1	2	yes	—
583	#386	C₂²×C₅₉	1	2	yes	—
584	#386	C₂²×C₅₉	1	2	yes	—
585	#385	C₂²×C₅₉	1	2	yes	—
586	#385	C₂²×C₅₉	1	2	yes	—
587	#385	C₂²×C₅₉	1	2	yes	—
588	#385	C₂²×C₅₉	1	2	yes	—
589	#385	C₂²×C₅₉	1	2	yes	—
590	#384	C₂²×C₅₉	1	1	yes	characteristic
591	#384	C₂²×C₅₉	1	1	yes	characteristic
592	#384	C₂²×C₅₉	1	1	yes	characteristic
593	#381	C₂²×C₅₉	1	2	yes	—
594	#381	C₂²×C₅₉	1	2	yes	—
595	#380	C₂²×C₅₉	1	2	yes	—
596	#380	C₂²×C₅₉	1	2	yes	—
597	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
598	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
599	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
600	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
601	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
602	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
603	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
604	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
605	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
606	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
607	#376	C₂²×C₅₉	1	1	yes	characteristic
608	#376	C₂²×C₅₉	1	1	yes	characteristic
609	#376	C₂²×C₅₉	1	2	yes	—
610	C₂×#95	C₂²×C₅₉	1	2	yes	—
611	C₄³	C₂²×C₅₉	1	1	yes	characteristic
612	C₅₉	#35561	1	1	yes	characteristic, direct product factor, Sylow
613	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
614	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
615	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
616	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
617	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
618	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
619	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
620	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
621	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
622	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
623	#127	—	2	4	no	—
624	#126	—	4	4	no	—
625	#125	—	4	4	no	—
626	#124	—	2	4	no	—
627	#124	—	2	4	no	—
628	#123	—	4	4	no	—
629	C₂²⋊Q₈	—	4	4	no	—
630	C₄×Q₈	—	2	4	no	—
631	C₄×Q₈	—	2	4	no	—
632	C₄×D₄	—	2	4	no	—
633	C₄×D₄	—	2	4	no	—
634	C₄×D₄	—	2	4	no	—
635	C₄×D₄	—	2	4	no	—
636	C₄×D₄	—	4	4	no	—
637	C₄×D₄	—	4	4	no	—
638	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
645	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
649	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
651	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
652	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
653	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
654	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
655	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
660	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
663	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
683	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
684	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
685	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
686	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
687	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
688	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
689	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
690	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
691	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
692	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
693	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
694	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
695	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
696	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
697	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
698	#95	C₂³×C₅₉	1	1	yes	characteristic
699	#95	C₂³×C₅₉	1	2	yes	—
700	#95	C₂³×C₅₉	1	2	yes	—
701	#95	C₂³×C₅₉	1	2	yes	—
702	#95	C₂³×C₅₉	1	1	yes	characteristic
703	#95	C₂³×C₅₉	1	1	yes	characteristic
704	#95	C₂³×C₅₉	1	1	yes	characteristic
705	#95	C₂³×C₅₉	1	1	yes	characteristic
706	#95	C₂³×C₅₉	1	2	yes	—
707	#95	C₂³×C₅₉	1	1	yes	characteristic
708	#95	C₂³×C₅₉	1	2	yes	—
709	#95	C₂³×C₅₉	1	2	yes	—
710	#95	C₂³×C₅₉	1	2	yes	—
711	#95	C₂³×C₅₉	1	1	yes	characteristic
712	#95	C₂³×C₅₉	1	1	yes	characteristic
713	#95	C₂³×C₅₉	1	1	yes	characteristic
714	#95	C₂³×C₅₉	1	2	yes	—
715	#95	C₂³×C₅₉	1	1	yes	characteristic
716	#95	C₂³×C₅₉	1	1	yes	characteristic
717	#95	C₂³×C₅₉	1	1	yes	characteristic
718	#95	C₂³×C₅₉	1	2	yes	—
719	#95	C₂³×C₅₉	1	1	yes	characteristic
720	#95	C₂³×C₅₉	1	1	yes	characteristic
721	#95	C₂³×C₅₉	1	2	yes	—
722	#95	C₂³×C₅₉	1	2	yes	—
723	#95	C₂³×C₅₉	1	2	yes	—
724	#95	C₂³×C₅₉	1	2	yes	—
725	#95	C₂³×C₅₉	1	2	yes	—
726	#95	C₂³×C₅₉	1	2	yes	—
727	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
728	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
729	C₂×Q₈	—	2	2	no	—
730	C₂×Q₈	—	2	2	no	—
731	C₂×Q₈	—	2	2	no	—
732	C₂×Q₈	—	2	2	no	—
733	C₂×Q₈	—	2	2	no	—
734	C₂×Q₈	—	4	1	no	—
735	C₂×D₄	—	2	4	no	—
736	C₂×D₄	—	2	4	no	—
737	C₂×D₄	—	2	2	no	—
738	C₂×D₄	—	2	2	no	—
739	C₂×D₄	—	2	2	no	—
740	C₂×D₄	—	2	2	no	—
741	C₂×D₄	—	2	2	no	—
742	C₂×D₄	—	2	4	no	—
743	C₂×D₄	—	2	4	no	—
744	C₂×D₄	—	4	2	no	—
745	C₂×D₄	—	4	2	no	—
746	C₂×D₄	#41×C₅₉	1	4	yes	—
747	C₂²×C₄	—	2	4	no	—
748	C₂²×C₄	—	2	4	no	—
749	C₂²×C₄	—	2	4	no	—
750	C₂²×C₄	—	2	4	no	—
751	C₂²×C₄	—	4	2	no	—
752	C₂²×C₄	—	4	2	no	—
753	C₂²×C₄	—	4	2	no	—
754	C₂²×C₄	—	4	2	no	—
755	C₂²×C₄	—	4	2	no	—
756	C₂²×C₄	—	4	2	no	—
757	C₂²×C₄	—	4	2	no	—
758	C₂²×C₄	—	4	2	no	—
759	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
760	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
761	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
762	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
763	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
764	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
765	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
766	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
769	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
770	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
771	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
772	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
773	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
774	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
775	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
776	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
777	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
778	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
779	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	4	no	—
789	C₄⋊C₄	—	2	4	no	—
790	C₄⋊C₄	—	2	4	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	4	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	2	no	—
795	C₄⋊C₄	—	2	2	no	—
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	4	2	no	—
798	C₄⋊C₄	—	4	2	no	—
799	C₄⋊C₄	—	4	2	no	—
800	C₄⋊C₄	—	4	2	no	—
801	C₄⋊C₄	—	4	2	no	—
802	C₄⋊C₄	—	4	2	no	—
803	C₄⋊C₄	—	4	2	no	—
804	C₄⋊C₄	—	4	1	no	—
805	C₂²⋊C₄	—	2	4	no	—
806	C₂²⋊C₄	—	2	4	no	—
807	C₂²⋊C₄	—	2	4	no	—
808	C₂²⋊C₄	—	2	4	no	—
809	C₂²⋊C₄	—	2	4	no	—
810	C₂²⋊C₄	—	2	4	no	—
811	C₂²⋊C₄	—	2	4	no	—
812	C₂²⋊C₄	—	2	4	no	—
813	C₂²⋊C₄	—	2	4	no	—
814	C₂²⋊C₄	—	2	4	no	—
815	C₂²⋊C₄	—	4	2	no	—
816	C₂²⋊C₄	—	4	2	no	—
817	C₂²⋊C₄	—	4	2	no	—
818	C₂²⋊C₄	—	4	2	no	—
819	C₂²⋊C₄	—	4	2	no	—
820	C₂²⋊C₄	—	4	2	no	—
821	C₂²⋊C₄	—	4	2	no	—
822	C₂²⋊C₄	—	4	2	no	—
823	C₂²⋊C₄	—	4	2	no	—
824	C₂²⋊C₄	—	4	2	no	—
825	C₄²	—	2	2	no	—
826	C₄²	—	2	2	no	—
827	C₄²	—	2	4	no	—
828	C₄²	—	2	2	no	—
829	C₄²	—	2	2	no	—
830	C₄²	—	2	2	no	—
831	C₄²	—	2	2	no	—
832	C₄²	—	2	2	no	—
833	C₄²	—	2	2	no	—
834	C₄²	—	4	2	no	—
835	C₄²	—	4	2	no	—
836	C₄²	—	4	1	no	—
837	C₄²	—	4	2	no	—
838	C₄²	#41×C₅₉	1	4	yes	—
839	C₄²	#41×C₅₉	1	4	yes	—
840	C₂³	—	2	2	no	—
841	C₂³	—	2	2	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	2	2	no	—
844	C₂³	—	2	2	no	—
845	C₂³	—	2	2	no	—
846	C₂³	—	2	2	no	—
847	C₂³	—	2	2	no	—
848	C₂³	—	2	2	no	—
849	C₂³	—	2	2	no	—
850	C₂³	—	2	2	no	—
851	C₂³	—	2	2	no	—
852	C₂³	—	2	2	no	—
853	C₂³	C₂×#41×C₅₉	1	4	yes	—
854	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
855	Q₈	—	4	4	no	—
856	Q₈	—	4	4	no	—
857	D₄	—	2	8	no	—
858	D₄	—	4	8	no	—
859	D₄	—	4	8	no	—
860	D₄	—	4	4	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	8	4	no	—
915	C₂×C₄	—	8	4	no	—
916	C₂×C₄	—	8	4	no	—
917	C₂×C₄	—	8	4	no	—
918	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
919	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
920	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
921	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
922	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
923	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
924	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
925	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
926	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
927	C₂×C₄	2₋¹⁺⁴×C₅₉	1	2	yes	—
928	C₂²	—	2	4	no	—
929	C₂²	—	2	4	no	—
930	C₂²	—	2	4	no	—
931	C₂²	—	4	2	no	—
932	C₂²	—	4	2	no	—
933	C₂²	—	4	2	no	—
934	C₂²	—	4	2	no	—
935	C₂²	—	4	2	no	—
936	C₂²	—	4	2	no	—
937	C₂²	—	4	2	no	—
938	C₂²	—	4	2	no	—
939	C₂²	—	4	2	no	—
940	C₂²	—	4	2	no	—
941	C₂²	—	4	2	no	—
942	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
943	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
944	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
945	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
946	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
947	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
948	C₂²	C₅₉×#585	1	1	yes	characteristic
949	C₄	—	2	2	no	—
950	C₄	—	2	2	no	—
951	C₄	—	2	2	no	—
952	C₄	—	2	2	no	—
953	C₄	—	2	2	no	—
954	C₄	—	2	2	no	—
955	C₄	—	2	2	no	—
956	C₄	—	4	2	no	—
957	C₄	—	4	2	no	—
958	C₄	—	4	2	no	—
959	C₄	—	4	1	no	—
960	C₄	—	4	1	no	—
961	C₄	—	4	1	no	—
962	C₄	—	4	2	no	—
963	C₄	—	4	1	no	—
964	C₄	—	4	1	no	—
965	C₄	—	4	1	no	—
966	C₄	—	4	2	no	—
967	C₄	—	4	2	no	—
968	C₄	—	4	1	no	—
969	C₄	C₅₉×#529	1	4	yes	—
970	C₂	—	4	4	no	—
971	C₂	—	8	2	no	—
972	C₂	C₂×C₅₉×#529	1	1	yes	characteristic
973	C₂	C₅₉×#3494	1	1	yes	characteristic
974	C₂	C₅₉×#3507	1	1	yes	characteristic
975	C₂	C₅₉×#3508	1	1	yes	characteristic
976	C₂	C₅₉×#3511	1	1	yes	characteristic
977	C₂	C₅₉×#3513	1	1	yes	characteristic
978	C₂	C₅₉×#3520	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₂×#127×C₅₉	C₂²
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×#2592	C₂	semidirect
2. C₅₉×#2560	C₂	semidirect
3. C₅₉×#2558	C₂	semidirect
4. C₅₉×#2552	C₂	semidirect
6. C₅₉×#2538	C₂	semidirect
7. C₅₉×#2531	C₂	semidirect
8. C₅₉×#2526	C₂	semidirect
9. C₅₉×#2512	C₂	semidirect
10. C₅₉×#2511	C₂	semidirect
11. C₅₉×#2466	C₂	semidirect
12. C₅₉×#2460	C₂	semidirect
13. C₅₉×#2450	C₂	semidirect
14. C₅₉×#2447	C₂	semidirect
16. C₅₉×#2419	C₂	semidirect
17. C₅₉×#2326	C₂	semidirect
18. C₅₉×#2326	C₂	semidirect
19. C₅₉×#2319	C₂	semidirect
21. C₅₉×#2295	C₂	semidirect
22. C₅₉×#2295	C₂	semidirect
23. C₅₉×#2275	C₂	semidirect
438. #35561	C₅₉	direct (N × H)
481. #2592	C₂×C₅₉	semidirect
482. #2560	C₂×C₅₉	semidirect
483. #2558	C₂×C₅₉	semidirect
484. #2552	C₂×C₅₉	semidirect
486. #2538	C₂×C₅₉	semidirect
487. #2531	C₂×C₅₉	semidirect
488. #2526	C₂×C₅₉	semidirect
489. #2512	C₂×C₅₉	semidirect
490. #2511	C₂×C₅₉	semidirect
491. #2466	C₂×C₅₉	semidirect
492. #2460	C₂×C₅₉	semidirect
493. #2450	C₂×C₅₉	semidirect
494. #2447	C₂×C₅₉	semidirect
496. #2419	C₂×C₅₉	semidirect
497. #2326	C₂×C₅₉	semidirect
498. #2326	C₂×C₅₉	semidirect
499. #2319	C₂×C₅₉	semidirect
501. #2295	C₂×C₅₉	semidirect
502. #2295	C₂×C₅₉	semidirect
503. #2275	C₂×C₅₉	semidirect
612. C₅₉	#35561	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₉×#2592	2
C₅₉×#2560	2
C₅₉×#2558	2
C₅₉×#2552	2
C₅₉×#2544	2
C₅₉×#2538	2
C₅₉×#2531	2
C₅₉×#2526	2
C₅₉×#2512	2
C₅₉×#2511	2
C₅₉×#2466	2
C₅₉×#2460	2
C₅₉×#2450	2
C₅₉×#2447	2
C₅₉×#2445	2
C₅₉×#2419	2
C₅₉×#2326	2
C₅₉×#2319	2
C₄×#127×C₅₉	2
C₅₉×#2295	2
C₅₉×#2275	2
#35561	59

Subgroups — C59×#35561 #28447670

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35561 #28447670