Subgroups — C₅₉×#35614 #28447723

Order 15104.

1750 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#2597	C₂	1	2	yes	maximal, complemented
2	C₅₉×#2594	C₂	1	2	yes	maximal, complemented
3	C₅₉×#2576	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2554	C₂	1	2	yes	maximal, complemented
5	C₅₉×#2516	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2513	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2512	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#2508	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#2504	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#2494	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2490	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#2486	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₉×#2478	C₂	1	2	yes	maximal, complemented
14	C₅₉×#2471	C₂	1	2	yes	maximal, complemented
15	C₅₉×#2441	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₉×#2414	C₂	1	1	yes	maximal, characteristic
17	C₅₉×#2324	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₉×#2324	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₉×#2314	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#125×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₉×#2293	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₉×#2293	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₉×#2274	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#126×C₅₉	C₂²	1	2	yes	—
25	C₂×#125×C₅₉	C₂²	1	1	yes	characteristic
26	C₂×#123×C₅₉	C₂²	1	2	yes	—
27	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
31	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
32	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
33	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
34	C₂×#117×C₅₉	C₂²	1	2	yes	—
35	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
36	C₅₉×#401	C₂²	1	2	yes	—
37	C₅₉×#400	C₂²	1	2	yes	—
38	C₅₉×#399	C₂²	1	2	yes	—
39	C₅₉×#398	C₂²	1	2	yes	—
40	C₅₉×#398	C₂²	1	2	yes	—
41	C₅₉×#397	C₂²	1	2	yes	—
42	C₅₉×#397	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×#394	C₂²	1	2	yes	—
50	C₅₉×#394	C₂²	1	2	yes	—
51	C₅₉×#392	C₂²	1	2	yes	—
52	C₅₉×#390	C₂²	1	1	yes	characteristic
53	C₅₉×#390	C₂²	1	1	yes	characteristic
54	C₅₉×#390	C₂²	1	2	yes	—
55	C₅₉×#390	C₂²	1	1	yes	characteristic
56	C₅₉×#390	C₂²	1	1	yes	characteristic
57	C₅₉×#390	C₂²	1	2	yes	—
58	C₅₉×#390	C₂²	1	2	yes	—
59	C₅₉×#390	C₂²	1	2	yes	—
60	C₅₉×#390	C₂²	1	1	yes	characteristic
61	C₅₉×#390	C₂²	1	1	yes	characteristic
62	C₅₉×#389	C₂²	1	1	yes	characteristic
63	C₅₉×#389	C₂²	1	1	yes	characteristic
64	C₅₉×#389	C₂²	1	1	yes	characteristic
65	C₅₉×#389	C₂²	1	1	yes	characteristic
66	C₅₉×#389	C₂²	1	1	yes	characteristic
67	C₅₉×#389	C₂²	1	1	yes	characteristic
68	C₅₉×#389	C₂²	1	2	yes	—
69	C₅₉×#389	C₂²	1	1	yes	characteristic
70	C₅₉×#389	C₂²	1	1	yes	characteristic
71	C₅₉×#388	C₂²	1	2	yes	—
72	C₅₉×#388	C₂²	1	2	yes	—
73	C₅₉×#388	C₂²	1	2	yes	—
74	C₅₉×#388	C₂²	1	1	yes	characteristic
75	C₅₉×#388	C₂²	1	2	yes	—
76	C₅₉×#388	C₂²	1	2	yes	—
77	C₅₉×#388	C₂²	1	2	yes	—
78	C₅₉×#388	C₂²	1	1	yes	characteristic
79	C₅₉×#388	C₂²	1	2	yes	—
80	C₅₉×#388	C₂²	1	2	yes	—
81	C₅₉×#388	C₂²	1	1	yes	characteristic
82	C₅₉×#388	C₂²	1	1	yes	characteristic
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	2	yes	—
88	C₅₉×#387	C₂²	1	2	yes	—
89	C₅₉×#387	C₂²	1	2	yes	—
90	C₅₉×#387	C₂²	1	2	yes	—
91	C₅₉×#387	C₂²	1	2	yes	—
92	C₅₉×#386	C₂²	1	2	yes	—
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×#384	C₂²	1	1	yes	characteristic
99	C₅₉×#382	C₂²	1	1	yes	characteristic
100	C₅₉×#382	C₂²	1	1	yes	characteristic
101	C₅₉×#382	C₂²	1	2	yes	—
102	C₅₉×#381	C₂²	1	2	yes	—
103	C₅₉×#380	C₂²	1	1	yes	characteristic
104	C₅₉×#380	C₂²	1	1	yes	characteristic
105	C₅₉×#380	C₂²	1	1	yes	characteristic
106	C₅₉×#380	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
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	2	yes	—
111	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
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×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
116	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
121	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
122	C₄³×C₅₉	C₂²	1	1	yes	characteristic
123	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
126	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
127	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
130	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
131	#126×C₅₉	—	4	4	no	—
132	#125×C₅₉	—	2	4	no	—
133	#123×C₅₉	—	4	4	no	—
134	#121×C₅₉	—	2	4	no	—
135	#121×C₅₉	—	2	4	no	—
136	C₄×D₄×C₅₉	—	2	4	no	—
137	C₄×D₄×C₅₉	—	2	4	no	—
138	#117×C₅₉	—	2	4	no	—
139	#117×C₅₉	—	2	4	no	—
140	#117×C₅₉	—	2	4	no	—
141	#117×C₅₉	—	4	4	no	—
142	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
143	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
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	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	1	yes	characteristic
155	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
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	2	yes	—
159	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
168	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
170	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
172	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
177	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
178	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
180	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
183	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
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	2	yes	—
200	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
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	2	yes	—
207	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
208	C₂×C₄²×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	2	yes	—
213	#95×C₅₉	C₂³	1	2	yes	—
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	1	yes	characteristic
219	#95×C₅₉	C₂³	1	2	yes	—
220	#95×C₅₉	C₂³	1	1	yes	characteristic
221	#95×C₅₉	C₂³	1	2	yes	—
222	#95×C₅₉	C₂³	1	2	yes	—
223	#95×C₅₉	C₂³	1	2	yes	—
224	#95×C₅₉	C₂³	1	2	yes	—
225	#95×C₅₉	C₂³	1	1	yes	characteristic
226	#95×C₅₉	C₂³	1	2	yes	—
227	#95×C₅₉	C₂³	1	2	yes	—
228	#95×C₅₉	C₂³	1	2	yes	—
229	#95×C₅₉	C₂³	1	2	yes	—
230	#95×C₅₉	C₂³	1	2	yes	—
231	#95×C₅₉	C₂³	1	2	yes	—
232	#95×C₅₉	C₂³	1	2	yes	—
233	#95×C₅₉	C₂³	1	2	yes	—
234	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
235	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
236	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
237	C₂×D₄×C₅₉	—	2	2	no	—
238	C₂×D₄×C₅₉	—	2	4	no	—
239	C₂×D₄×C₅₉	—	2	2	no	—
240	C₂×D₄×C₅₉	—	2	2	no	—
241	C₂×D₄×C₅₉	—	2	2	no	—
242	C₂×D₄×C₅₉	—	2	4	no	—
243	C₂×D₄×C₅₉	—	2	2	no	—
244	C₂×D₄×C₅₉	—	4	1	no	—
245	C₂×D₄×C₅₉	—	4	2	no	—
246	C₂×D₄×C₅₉	—	4	2	no	—
247	C₂×D₄×C₅₉	—	4	2	no	—
248	C₂×D₄×C₅₉	—	4	2	no	—
249	C₂²×C₄×C₅₉	—	2	2	no	—
250	C₂²×C₄×C₅₉	—	2	2	no	—
251	C₂²×C₄×C₅₉	—	2	4	no	—
252	C₂²×C₄×C₅₉	—	2	2	no	—
253	C₂²×C₄×C₅₉	—	2	4	no	—
254	C₂²×C₄×C₅₉	—	2	2	no	—
255	C₂²×C₄×C₅₉	—	2	2	no	—
256	C₂²×C₄×C₅₉	—	4	2	no	—
257	C₂²×C₄×C₅₉	—	4	2	no	—
258	C₂²×C₄×C₅₉	—	4	2	no	—
259	C₂²×C₄×C₅₉	—	4	2	no	—
260	C₂²×C₄×C₅₉	#41	1	4	yes	—
261	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
281	C₄⋊C₄×C₅₉	—	2	4	no	—
282	C₄⋊C₄×C₅₉	—	2	2	no	—
283	C₄⋊C₄×C₅₉	—	2	2	no	—
284	C₄⋊C₄×C₅₉	—	2	2	no	—
285	C₄⋊C₄×C₅₉	—	2	2	no	—
286	C₄⋊C₄×C₅₉	—	2	2	no	—
287	C₄⋊C₄×C₅₉	—	2	2	no	—
288	C₄⋊C₄×C₅₉	—	2	2	no	—
289	C₄⋊C₄×C₅₉	—	2	2	no	—
290	C₄⋊C₄×C₅₉	—	2	2	no	—
291	C₄⋊C₄×C₅₉	—	2	2	no	—
292	C₄⋊C₄×C₅₉	—	2	4	no	—
293	C₄⋊C₄×C₅₉	—	2	4	no	—
294	C₄⋊C₄×C₅₉	—	2	2	no	—
295	C₄⋊C₄×C₅₉	—	2	4	no	—
296	C₄⋊C₄×C₅₉	—	2	4	no	—
297	C₄⋊C₄×C₅₉	—	2	2	no	—
298	C₄⋊C₄×C₅₉	—	4	1	no	—
299	C₄⋊C₄×C₅₉	—	4	2	no	—
300	C₄⋊C₄×C₅₉	—	4	2	no	—
301	C₄⋊C₄×C₅₉	—	4	2	no	—
302	C₄⋊C₄×C₅₉	—	4	2	no	—
303	C₄⋊C₄×C₅₉	—	4	2	no	—
304	C₄⋊C₄×C₅₉	—	4	2	no	—
305	C₄⋊C₄×C₅₉	#41	1	4	yes	—
306	C₂²⋊C₄×C₅₉	—	2	2	no	—
307	C₂²⋊C₄×C₅₉	—	2	4	no	—
308	C₂²⋊C₄×C₅₉	—	2	2	no	—
309	C₂²⋊C₄×C₅₉	—	2	2	no	—
310	C₂²⋊C₄×C₅₉	—	2	2	no	—
311	C₂²⋊C₄×C₅₉	—	2	2	no	—
312	C₂²⋊C₄×C₅₉	—	2	2	no	—
313	C₂²⋊C₄×C₅₉	—	2	4	no	—
314	C₂²⋊C₄×C₅₉	—	2	4	no	—
315	C₂²⋊C₄×C₅₉	—	2	4	no	—
316	C₂²⋊C₄×C₅₉	—	2	4	no	—
317	C₂²⋊C₄×C₅₉	—	4	2	no	—
318	C₂²⋊C₄×C₅₉	—	4	1	no	—
319	C₂²⋊C₄×C₅₉	—	4	2	no	—
320	C₂²⋊C₄×C₅₉	—	4	1	no	—
321	C₂²⋊C₄×C₅₉	—	4	1	no	—
322	C₂²⋊C₄×C₅₉	—	4	1	no	—
323	C₂²⋊C₄×C₅₉	—	4	2	no	—
324	C₂²⋊C₄×C₅₉	—	4	2	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	C₄²×C₅₉	—	2	4	no	—
333	C₄²×C₅₉	—	2	2	no	—
334	C₄²×C₅₉	—	2	2	no	—
335	C₄²×C₅₉	—	2	2	no	—
336	C₄²×C₅₉	—	2	2	no	—
337	C₄²×C₅₉	—	2	2	no	—
338	C₄²×C₅₉	—	4	2	no	—
339	C₄²×C₅₉	—	4	1	no	—
340	C₄²×C₅₉	—	4	1	no	—
341	C₄²×C₅₉	—	4	2	no	—
342	C₄²×C₅₉	—	4	2	no	—
343	C₄²×C₅₉	—	4	1	no	—
344	C₄²×C₅₉	—	4	2	no	—
345	C₄²×C₅₉	—	4	2	no	—
346	C₄²×C₅₉	#41	1	4	yes	—
347	C₂³×C₅₉	—	2	1	no	—
348	C₂³×C₅₉	—	2	1	no	—
349	C₂³×C₅₉	—	2	1	no	—
350	C₂³×C₅₉	—	2	1	no	—
351	C₂³×C₅₉	—	2	1	no	—
352	C₂³×C₅₉	—	2	1	no	—
353	C₂³×C₅₉	—	2	1	no	—
354	C₂³×C₅₉	—	2	1	no	—
355	C₂³×C₅₉	—	2	2	no	—
356	C₂³×C₅₉	—	2	2	no	—
357	C₂³×C₅₉	—	2	2	no	—
358	C₂³×C₅₉	—	2	1	no	—
359	C₂³×C₅₉	—	2	2	no	—
360	C₂³×C₅₉	—	2	1	no	—
361	C₂³×C₅₉	—	2	1	no	—
362	C₂³×C₅₉	—	2	2	no	—
363	C₂³×C₅₉	—	2	2	no	—
364	C₂³×C₅₉	—	2	1	no	—
365	C₂³×C₅₉	—	2	2	no	—
366	C₂³×C₅₉	—	2	1	no	—
367	C₂³×C₅₉	C₂×#41	1	2	yes	—
368	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
369	D₄×C₅₉	—	4	4	no	—
370	D₄×C₅₉	—	4	4	no	—
371	D₄×C₅₉	—	8	4	no	—
372	D₄×C₅₉	—	8	4	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	2	no	—
380	C₂×C₄×C₅₉	—	2	1	no	—
381	C₂×C₄×C₅₉	—	2	1	no	—
382	C₂×C₄×C₅₉	—	2	2	no	—
383	C₂×C₄×C₅₉	—	2	8	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	1	no	—
389	C₂×C₄×C₅₉	—	2	2	no	—
390	C₂×C₄×C₅₉	—	2	1	no	—
391	C₂×C₄×C₅₉	—	2	1	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	1	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	2	no	—
402	C₂×C₄×C₅₉	—	2	1	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	1	no	—
407	C₂×C₄×C₅₉	—	2	2	no	—
408	C₂×C₄×C₅₉	—	2	1	no	—
409	C₂×C₄×C₅₉	—	2	1	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	2	no	—
415	C₂×C₄×C₅₉	—	2	2	no	—
416	C₂×C₄×C₅₉	—	2	2	no	—
417	C₂×C₄×C₅₉	—	2	1	no	—
418	C₂×C₄×C₅₉	—	2	1	no	—
419	C₂×C₄×C₅₉	—	2	1	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	—	2	2	no	—
425	C₂×C₄×C₅₉	—	2	2	no	—
426	C₂×C₄×C₅₉	—	4	8	no	—
427	C₂×C₄×C₅₉	—	4	4	no	—
428	C₂×C₄×C₅₉	—	8	4	no	—
429	C₂×C₄×C₅₉	C₂×#41	1	4	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	C₂×#41	1	2	yes	—
436	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
437	#35614	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
438	C₂²×C₅₉	—	2	2	no	—
439	C₂²×C₅₉	—	2	2	no	—
440	C₂²×C₅₉	—	2	2	no	—
441	C₂²×C₅₉	—	4	1	no	—
442	C₂²×C₅₉	—	4	1	no	—
443	C₂²×C₅₉	—	4	1	no	—
444	C₂²×C₅₉	—	4	1	no	—
445	C₂²×C₅₉	—	4	1	no	—
446	C₂²×C₅₉	—	4	2	no	—
447	C₂²×C₅₉	—	4	1	no	—
448	C₂²×C₅₉	—	4	2	no	—
449	C₂²×C₅₉	—	4	2	no	—
450	C₂²×C₅₉	—	4	1	no	—
451	C₂²×C₅₉	—	4	2	no	—
452	C₂²×C₅₉	—	4	1	no	—
453	C₂²×C₅₉	—	4	1	no	—
454	C₂²×C₅₉	—	4	2	no	—
455	C₂²×C₅₉	—	4	2	no	—
456	C₂²×C₅₉	—	4	1	no	—
457	C₂²×C₅₉	—	4	1	no	—
458	C₂²×C₅₉	—	4	2	no	—
459	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
460	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
461	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
462	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
463	C₂²×C₅₉	#585	1	1	yes	characteristic
464	C₂²×C₅₉	#585	1	1	yes	characteristic
465	C₂²×C₅₉	#585	1	1	yes	characteristic
466	C₄×C₅₉	—	2	2	no	—
467	C₄×C₅₉	—	2	2	no	—
468	C₄×C₅₉	—	2	2	no	—
469	C₄×C₅₉	—	2	2	no	—
470	C₄×C₅₉	—	2	4	no	—
471	C₄×C₅₉	—	4	1	no	—
472	C₄×C₅₉	—	4	2	no	—
473	C₄×C₅₉	—	4	2	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	2	no	—
479	C₄×C₅₉	—	4	1	no	—
480	C₄×C₅₉	—	4	1	no	—
481	C₄×C₅₉	—	4	2	no	—
482	C₄×C₅₉	—	4	1	no	—
483	C₄×C₅₉	—	4	2	no	—
484	C₄×C₅₉	—	4	1	no	—
485	C₄×C₅₉	#529	1	4	yes	—
486	#2597	C₂×C₅₉	1	2	yes	complemented
487	#2594	C₂×C₅₉	1	2	yes	complemented
488	#2576	C₂×C₅₉	1	2	yes	complemented
489	#2554	C₂×C₅₉	1	2	yes	complemented
490	#2516	C₂×C₅₉	1	2	yes	complemented
491	#2513	C₂×C₅₉	1	2	yes	complemented
492	#2512	C₂×C₅₉	1	1	yes	characteristic, complemented
493	#2508	C₂×C₅₉	1	1	yes	characteristic, complemented
494	#2504	C₂×C₅₉	1	1	yes	characteristic, complemented
495	#2494	C₂×C₅₉	1	1	yes	characteristic, complemented
496	#2490	C₂×C₅₉	1	1	yes	characteristic, complemented
497	#2486	C₂×C₅₉	1	1	yes	characteristic, complemented
498	#2478	C₂×C₅₉	1	2	yes	complemented
499	#2471	C₂×C₅₉	1	2	yes	complemented
500	#2441	C₂×C₅₉	1	1	yes	characteristic, complemented
501	#2414	C₂×C₅₉	1	1	yes	characteristic
502	#2324	C₂×C₅₉	1	1	yes	characteristic, complemented
503	#2324	C₂×C₅₉	1	1	yes	characteristic, complemented
504	#2314	C₂×C₅₉	1	1	yes	characteristic, complemented
505	C₄×#125	C₂×C₅₉	1	1	yes	characteristic, complemented
506	#2293	C₂×C₅₉	1	1	yes	characteristic, complemented
507	#2293	C₂×C₅₉	1	1	yes	characteristic, complemented
508	#2274	C₂×C₅₉	1	1	yes	characteristic, complemented
509	C₂×C₅₉	—	4	2	no	—
510	C₂×C₅₉	—	8	1	no	—
511	C₂×C₅₉	—	8	2	no	—
512	C₂×C₅₉	C₂×#529	1	1	yes	characteristic
513	C₂×C₅₉	#3494	1	1	yes	characteristic
514	C₂×C₅₉	#3506	1	1	yes	characteristic
515	C₂×C₅₉	#3510	1	1	yes	characteristic
516	C₂×C₅₉	#3512	1	1	yes	characteristic
517	C₂×C₅₉	#3517	1	1	yes	characteristic
518	C₂×C₅₉	#3521	1	1	yes	characteristic
519	C₂×#126	C₂²×C₅₉	1	2	yes	—
520	C₂×#125	C₂²×C₅₉	1	1	yes	characteristic
521	C₂×#123	C₂²×C₅₉	1	2	yes	—
522	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
523	C₂×#121	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×#117	C₂²×C₅₉	1	1	yes	characteristic
527	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
528	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
529	C₂×#117	C₂²×C₅₉	1	2	yes	—
530	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
531	#401	C₂²×C₅₉	1	2	yes	—
532	#400	C₂²×C₅₉	1	2	yes	—
533	#399	C₂²×C₅₉	1	2	yes	—
534	#398	C₂²×C₅₉	1	2	yes	—
535	#398	C₂²×C₅₉	1	2	yes	—
536	#397	C₂²×C₅₉	1	2	yes	—
537	#397	C₂²×C₅₉	1	2	yes	—
538	#397	C₂²×C₅₉	1	2	yes	—
539	#397	C₂²×C₅₉	1	2	yes	—
540	#397	C₂²×C₅₉	1	2	yes	—
541	#397	C₂²×C₅₉	1	2	yes	—
542	#396	C₂²×C₅₉	1	2	yes	—
543	#396	C₂²×C₅₉	1	2	yes	—
544	#394	C₂²×C₅₉	1	2	yes	—
545	#394	C₂²×C₅₉	1	2	yes	—
546	#392	C₂²×C₅₉	1	2	yes	—
547	#390	C₂²×C₅₉	1	1	yes	characteristic
548	#390	C₂²×C₅₉	1	1	yes	characteristic
549	#390	C₂²×C₅₉	1	2	yes	—
550	#390	C₂²×C₅₉	1	2	yes	—
551	#390	C₂²×C₅₉	1	2	yes	—
552	#390	C₂²×C₅₉	1	1	yes	characteristic
553	#390	C₂²×C₅₉	1	1	yes	characteristic
554	#390	C₂²×C₅₉	1	2	yes	—
555	#390	C₂²×C₅₉	1	1	yes	characteristic
556	#390	C₂²×C₅₉	1	1	yes	characteristic
557	#389	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	#389	C₂²×C₅₉	1	1	yes	characteristic
566	#388	C₂²×C₅₉	1	2	yes	—
567	#388	C₂²×C₅₉	1	2	yes	—
568	#388	C₂²×C₅₉	1	1	yes	characteristic
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	#388	C₂²×C₅₉	1	1	yes	characteristic
575	#388	C₂²×C₅₉	1	2	yes	—
576	#388	C₂²×C₅₉	1	2	yes	—
577	#388	C₂²×C₅₉	1	1	yes	characteristic
578	#388	C₂²×C₅₉	1	2	yes	—
579	#388	C₂²×C₅₉	1	1	yes	characteristic
580	#387	C₂²×C₅₉	1	2	yes	—
581	#387	C₂²×C₅₉	1	2	yes	—
582	#387	C₂²×C₅₉	1	2	yes	—
583	#387	C₂²×C₅₉	1	2	yes	—
584	#387	C₂²×C₅₉	1	2	yes	—
585	#387	C₂²×C₅₉	1	2	yes	—
586	#387	C₂²×C₅₉	1	2	yes	—
587	#386	C₂²×C₅₉	1	2	yes	—
588	#386	C₂²×C₅₉	1	2	yes	—
589	#386	C₂²×C₅₉	1	2	yes	—
590	#386	C₂²×C₅₉	1	2	yes	—
591	#385	C₂²×C₅₉	1	2	yes	—
592	#385	C₂²×C₅₉	1	2	yes	—
593	#384	C₂²×C₅₉	1	1	yes	characteristic
594	#382	C₂²×C₅₉	1	1	yes	characteristic
595	#382	C₂²×C₅₉	1	1	yes	characteristic
596	#382	C₂²×C₅₉	1	2	yes	—
597	#381	C₂²×C₅₉	1	2	yes	—
598	#380	C₂²×C₅₉	1	1	yes	characteristic
599	#380	C₂²×C₅₉	1	1	yes	characteristic
600	#380	C₂²×C₅₉	1	1	yes	characteristic
601	#380	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×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
605	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
606	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
607	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
608	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
609	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
610	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
611	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
612	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
613	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
614	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
615	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
616	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
617	C₄³	C₂²×C₅₉	1	1	yes	characteristic
618	C₅₉	#35614	1	1	yes	characteristic, direct product factor, Sylow
619	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
620	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
621	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
622	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
623	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
624	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
625	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
626	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
627	#126	—	4	4	no	—
628	#125	—	2	4	no	—
629	#123	—	4	4	no	—
630	#121	—	2	4	no	—
631	#121	—	2	4	no	—
632	C₄×D₄	—	2	4	no	—
633	C₄×D₄	—	2	4	no	—
634	#117	—	2	4	no	—
635	#117	—	2	4	no	—
636	#117	—	2	4	no	—
637	#117	—	4	4	no	—
638	C₂×C₄⋊C₄	—	2	4	no	—
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	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
651	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
652	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
653	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
654	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
663	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
664	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
666	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
667	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
669	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
670	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
671	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
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	1	yes	characteristic
682	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
683	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
684	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
685	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
686	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
687	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
688	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
689	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
690	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
691	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
692	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
693	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
694	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
695	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
696	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
697	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
698	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
699	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
700	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
701	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
702	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
703	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
704	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
705	#95	C₂³×C₅₉	1	2	yes	—
706	#95	C₂³×C₅₉	1	2	yes	—
707	#95	C₂³×C₅₉	1	2	yes	—
708	#95	C₂³×C₅₉	1	2	yes	—
709	#95	C₂³×C₅₉	1	2	yes	—
710	#95	C₂³×C₅₉	1	1	yes	characteristic
711	#95	C₂³×C₅₉	1	1	yes	characteristic
712	#95	C₂³×C₅₉	1	2	yes	—
713	#95	C₂³×C₅₉	1	1	yes	characteristic
714	#95	C₂³×C₅₉	1	1	yes	characteristic
715	#95	C₂³×C₅₉	1	2	yes	—
716	#95	C₂³×C₅₉	1	1	yes	characteristic
717	#95	C₂³×C₅₉	1	2	yes	—
718	#95	C₂³×C₅₉	1	2	yes	—
719	#95	C₂³×C₅₉	1	2	yes	—
720	#95	C₂³×C₅₉	1	2	yes	—
721	#95	C₂³×C₅₉	1	1	yes	characteristic
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	#95	C₂³×C₅₉	1	2	yes	—
728	#95	C₂³×C₅₉	1	2	yes	—
729	#95	C₂³×C₅₉	1	2	yes	—
730	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
731	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
732	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
733	C₂×D₄	—	2	2	no	—
734	C₂×D₄	—	2	4	no	—
735	C₂×D₄	—	2	2	no	—
736	C₂×D₄	—	2	2	no	—
737	C₂×D₄	—	2	2	no	—
738	C₂×D₄	—	2	4	no	—
739	C₂×D₄	—	2	2	no	—
740	C₂×D₄	—	4	1	no	—
741	C₂×D₄	—	4	2	no	—
742	C₂×D₄	—	4	2	no	—
743	C₂×D₄	—	4	2	no	—
744	C₂×D₄	—	4	2	no	—
745	C₂²×C₄	—	2	2	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	4	no	—
748	C₂²×C₄	—	2	2	no	—
749	C₂²×C₄	—	2	4	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	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	#41×C₅₉	1	4	yes	—
757	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
759	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
760	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
761	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
762	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
763	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
764	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
765	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
766	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
767	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
769	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
770	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
771	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
772	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
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	C₄⋊C₄	—	2	4	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	2	no	—
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	2	no	—
791	C₄⋊C₄	—	2	4	no	—
792	C₄⋊C₄	—	2	4	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	4	2	no	—
795	C₄⋊C₄	—	4	2	no	—
796	C₄⋊C₄	—	4	1	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	#41×C₅₉	1	4	yes	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	4	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	2	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	—	2	2	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	—	4	2	no	—
814	C₂²⋊C₄	—	4	2	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	1	no	—
821	C₂²⋊C₄	—	4	2	no	—
822	C₂²⋊C₄	—	4	1	no	—
823	C₂²⋊C₄	—	4	1	no	—
824	C₂²⋊C₄	—	4	1	no	—
825	C₂²⋊C₄	—	4	2	no	—
826	C₂²⋊C₄	—	4	2	no	—
827	C₂²⋊C₄	—	4	2	no	—
828	C₄²	—	2	4	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	2	no	—
837	C₄²	—	4	1	no	—
838	C₄²	—	4	1	no	—
839	C₄²	—	4	2	no	—
840	C₄²	—	4	2	no	—
841	C₄²	—	4	1	no	—
842	C₄²	#41×C₅₉	1	4	yes	—
843	C₂³	—	2	1	no	—
844	C₂³	—	2	1	no	—
845	C₂³	—	2	1	no	—
846	C₂³	—	2	1	no	—
847	C₂³	—	2	1	no	—
848	C₂³	—	2	1	no	—
849	C₂³	—	2	1	no	—
850	C₂³	—	2	2	no	—
851	C₂³	—	2	1	no	—
852	C₂³	—	2	2	no	—
853	C₂³	—	2	2	no	—
854	C₂³	—	2	1	no	—
855	C₂³	—	2	2	no	—
856	C₂³	—	2	1	no	—
857	C₂³	—	2	1	no	—
858	C₂³	—	2	2	no	—
859	C₂³	—	2	2	no	—
860	C₂³	—	2	1	no	—
861	C₂³	—	2	2	no	—
862	C₂³	—	2	1	no	—
863	C₂³	C₂×#41×C₅₉	1	2	yes	—
864	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
865	D₄	—	4	4	no	—
866	D₄	—	4	4	no	—
867	D₄	—	8	4	no	—
868	D₄	—	8	4	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	2	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	8	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	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	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	4	8	no	—
923	C₂×C₄	—	4	4	no	—
924	C₂×C₄	—	8	4	no	—
925	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
926	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
927	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
928	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
929	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
930	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
931	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
932	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
933	C₂²	—	2	2	no	—
934	C₂²	—	2	2	no	—
935	C₂²	—	2	2	no	—
936	C₂²	—	4	1	no	—
937	C₂²	—	4	1	no	—
938	C₂²	—	4	1	no	—
939	C₂²	—	4	1	no	—
940	C₂²	—	4	2	no	—
941	C₂²	—	4	1	no	—
942	C₂²	—	4	2	no	—
943	C₂²	—	4	1	no	—
944	C₂²	—	4	1	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	1	no	—
948	C₂²	—	4	1	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	4	1	no	—
951	C₂²	—	4	2	no	—
952	C₂²	—	4	1	no	—
953	C₂²	—	4	2	no	—
954	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
955	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
956	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
957	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
958	C₂²	C₅₉×#585	1	1	yes	characteristic
959	C₂²	C₅₉×#585	1	1	yes	characteristic
960	C₂²	C₅₉×#585	1	1	yes	characteristic
961	C₄	—	2	2	no	—
962	C₄	—	2	2	no	—
963	C₄	—	2	4	no	—
964	C₄	—	2	2	no	—
965	C₄	—	2	2	no	—
966	C₄	—	4	2	no	—
967	C₄	—	4	1	no	—
968	C₄	—	4	1	no	—
969	C₄	—	4	2	no	—
970	C₄	—	4	1	no	—
971	C₄	—	4	1	no	—
972	C₄	—	4	1	no	—
973	C₄	—	4	2	no	—
974	C₄	—	4	1	no	—
975	C₄	—	4	2	no	—
976	C₄	—	4	1	no	—
977	C₄	—	4	1	no	—
978	C₄	—	4	2	no	—
979	C₄	—	4	2	no	—
980	C₄	C₅₉×#529	1	4	yes	—
981	C₂	—	4	2	no	—
982	C₂	—	8	2	no	—
983	C₂	—	8	1	no	—
984	C₂	C₂×C₅₉×#529	1	1	yes	characteristic
985	C₂	C₅₉×#3494	1	1	yes	characteristic
986	C₂	C₅₉×#3506	1	1	yes	characteristic
987	C₂	C₅₉×#3510	1	1	yes	characteristic
988	C₂	C₅₉×#3512	1	1	yes	characteristic
989	C₂	C₅₉×#3517	1	1	yes	characteristic
990	C₂	C₅₉×#3521	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₅₉×#2414	C₂
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×#2597	C₂	semidirect
2. C₅₉×#2594	C₂	semidirect
3. C₅₉×#2576	C₂	semidirect
4. C₅₉×#2554	C₂	semidirect
5. C₅₉×#2516	C₂	semidirect
6. C₅₉×#2513	C₂	semidirect
7. C₅₉×#2512	C₂	semidirect
8. C₅₉×#2508	C₂	semidirect
9. C₅₉×#2504	C₂	semidirect
10. C₅₉×#2494	C₂	semidirect
11. C₅₉×#2490	C₂	semidirect
12. C₅₉×#2486	C₂	semidirect
13. C₅₉×#2478	C₂	semidirect
14. C₅₉×#2471	C₂	semidirect
15. C₅₉×#2441	C₂	semidirect
17. C₅₉×#2324	C₂	semidirect
18. C₅₉×#2324	C₂	semidirect
19. C₅₉×#2314	C₂	semidirect
20. C₄×#125×C₅₉	C₂	semidirect
21. C₅₉×#2293	C₂	semidirect
22. C₅₉×#2293	C₂	semidirect
23. C₅₉×#2274	C₂	semidirect
437. #35614	C₅₉	direct (N × H)
486. #2597	C₂×C₅₉	semidirect
487. #2594	C₂×C₅₉	semidirect
488. #2576	C₂×C₅₉	semidirect
489. #2554	C₂×C₅₉	semidirect
490. #2516	C₂×C₅₉	semidirect
491. #2513	C₂×C₅₉	semidirect
492. #2512	C₂×C₅₉	semidirect
493. #2508	C₂×C₅₉	semidirect
494. #2504	C₂×C₅₉	semidirect
495. #2494	C₂×C₅₉	semidirect
496. #2490	C₂×C₅₉	semidirect
497. #2486	C₂×C₅₉	semidirect
498. #2478	C₂×C₅₉	semidirect
499. #2471	C₂×C₅₉	semidirect
500. #2441	C₂×C₅₉	semidirect
502. #2324	C₂×C₅₉	semidirect
503. #2324	C₂×C₅₉	semidirect
504. #2314	C₂×C₅₉	semidirect
505. C₄×#125	C₂×C₅₉	semidirect
506. #2293	C₂×C₅₉	semidirect
507. #2293	C₂×C₅₉	semidirect
508. #2274	C₂×C₅₉	semidirect
618. C₅₉	#35614	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×#2597	2
C₅₉×#2594	2
C₅₉×#2576	2
C₅₉×#2554	2
C₅₉×#2516	2
C₅₉×#2513	2
C₅₉×#2512	2
C₅₉×#2508	2
C₅₉×#2504	2
C₅₉×#2494	2
C₅₉×#2490	2
C₅₉×#2486	2
C₅₉×#2478	2
C₅₉×#2471	2
C₅₉×#2441	2
C₅₉×#2414	2
C₅₉×#2324	2
C₅₉×#2314	2
C₄×#125×C₅₉	2
C₅₉×#2293	2
C₅₉×#2274	2
#35614	59

Subgroups — C59×#35614 #28447723

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35614 #28447723