Subgroups — C₅₉×#35589 #28447698

Order 15104.

1864 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#2594	C₂	1	2	yes	maximal, complemented
2	C₅₉×#2576	C₂	1	2	yes	maximal, complemented
3	C₅₉×#2574	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2560	C₂	1	2	yes	maximal, complemented
5	C₅₉×#2512	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#2507	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#2500	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#2494	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#2491	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#2485	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2476	C₂	1	2	yes	maximal, complemented
12	C₅₉×#2474	C₂	1	2	yes	maximal, complemented
13	C₅₉×#2468	C₂	1	2	yes	maximal, complemented
14	C₅₉×#2440	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#2427	C₂	1	2	yes	maximal, complemented
16	C₅₉×#2416	C₂	1	1	yes	maximal, characteristic
17	C₅₉×#2331	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₉×#2324	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₉×#2319	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#121×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₉×#2290	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₉×#2285	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₉×#2274	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
25	C₂×#126×C₅₉	C₂²	1	2	yes	—
26	C₂×#124×C₅₉	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	—
28	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
29	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
30	C₂×#121×C₅₉	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
34	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
35	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
36	C₂×#117×C₅₉	C₂²	1	2	yes	—
37	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
39	C₅₉×#401	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×#397	C₂²	1	2	yes	—
44	C₅₉×#397	C₂²	1	2	yes	—
45	C₅₉×#397	C₂²	1	2	yes	—
46	C₅₉×#396	C₂²	1	2	yes	—
47	C₅₉×#396	C₂²	1	2	yes	—
48	C₅₉×#395	C₂²	1	2	yes	—
49	C₅₉×#394	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	2	yes	—
56	C₅₉×#391	C₂²	1	2	yes	—
57	C₅₉×#390	C₂²	1	1	yes	characteristic
58	C₅₉×#390	C₂²	1	1	yes	characteristic
59	C₅₉×#390	C₂²	1	1	yes	characteristic
60	C₅₉×#390	C₂²	1	1	yes	characteristic
61	C₅₉×#390	C₂²	1	2	yes	—
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×#388	C₂²	1	2	yes	—
70	C₅₉×#388	C₂²	1	2	yes	—
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	2	yes	—
75	C₅₉×#388	C₂²	1	1	yes	characteristic
76	C₅₉×#388	C₂²	1	1	yes	characteristic
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×#387	C₂²	1	2	yes	—
82	C₅₉×#387	C₂²	1	2	yes	—
83	C₅₉×#387	C₂²	1	2	yes	—
84	C₅₉×#387	C₂²	1	1	yes	characteristic
85	C₅₉×#387	C₂²	1	1	yes	characteristic
86	C₅₉×#387	C₂²	1	2	yes	—
87	C₅₉×#387	C₂²	1	2	yes	—
88	C₅₉×#386	C₂²	1	1	yes	characteristic
89	C₅₉×#386	C₂²	1	1	yes	characteristic
90	C₅₉×#386	C₂²	1	2	yes	—
91	C₅₉×#386	C₂²	1	2	yes	—
92	C₅₉×#386	C₂²	1	2	yes	—
93	C₅₉×#385	C₂²	1	1	yes	characteristic
94	C₅₉×#385	C₂²	1	1	yes	characteristic
95	C₅₉×#385	C₂²	1	2	yes	—
96	C₅₉×#385	C₂²	1	2	yes	—
97	C₅₉×#384	C₂²	1	1	yes	characteristic
98	C₅₉×#384	C₂²	1	1	yes	characteristic
99	C₅₉×#382	C₂²	1	1	yes	characteristic
100	C₅₉×#382	C₂²	1	2	yes	—
101	C₅₉×#381	C₂²	1	2	yes	—
102	C₅₉×#380	C₂²	1	1	yes	characteristic
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	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	2	yes	—
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	C₅₉×#376	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
124	C₂²×D₄×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	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
133	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
134	C₄⋊Q₈×C₅₉	—	2	4	no	—
135	#126×C₅₉	—	4	4	no	—
136	#124×C₅₉	—	4	4	no	—
137	C₂²⋊Q₈×C₅₉	—	4	4	no	—
138	#121×C₅₉	—	2	4	no	—
139	#121×C₅₉	—	2	4	no	—
140	#121×C₅₉	—	4	4	no	—
141	C₄×D₄×C₅₉	—	2	4	no	—
142	C₄×D₄×C₅₉	—	2	4	no	—
143	C₄×D₄×C₅₉	—	4	4	no	—
144	#117×C₅₉	—	2	4	no	—
145	#117×C₅₉	—	2	4	no	—
146	#117×C₅₉	—	4	4	no	—
147	C₂×C₄⋊C₄×C₅₉	—	2	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	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	2	yes	—
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	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	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	1	yes	characteristic
172	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
176	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	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	1	yes	characteristic
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×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
196	C₂×C₄²×C₅₉	—	2	4	no	—
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	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	2	yes	—
209	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
210	#95×C₅₉	C₂³	1	1	yes	characteristic
211	#95×C₅₉	C₂³	1	1	yes	characteristic
212	#95×C₅₉	C₂³	1	1	yes	characteristic
213	#95×C₅₉	C₂³	1	1	yes	characteristic
214	#95×C₅₉	C₂³	1	2	yes	—
215	#95×C₅₉	C₂³	1	2	yes	—
216	#95×C₅₉	C₂³	1	2	yes	—
217	#95×C₅₉	C₂³	1	2	yes	—
218	#95×C₅₉	C₂³	1	2	yes	—
219	#95×C₅₉	C₂³	1	2	yes	—
220	#95×C₅₉	C₂³	1	1	yes	characteristic
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	2	yes	—
226	#95×C₅₉	C₂³	1	2	yes	—
227	#95×C₅₉	C₂³	1	1	yes	characteristic
228	#95×C₅₉	C₂³	1	1	yes	characteristic
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	#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	1	yes	characteristic
239	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
240	C₂×Q₈×C₅₉	—	2	4	no	—
241	C₂×Q₈×C₅₉	—	4	2	no	—
242	C₂×Q₈×C₅₉	—	4	2	no	—
243	C₂×D₄×C₅₉	—	2	2	no	—
244	C₂×D₄×C₅₉	—	2	2	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	4	no	—
249	C₂×D₄×C₅₉	—	2	2	no	—
250	C₂×D₄×C₅₉	—	2	2	no	—
251	C₂×D₄×C₅₉	—	4	2	no	—
252	C₂×D₄×C₅₉	—	4	1	no	—
253	C₂×D₄×C₅₉	—	4	2	no	—
254	C₂×D₄×C₅₉	—	4	2	no	—
255	C₂²×C₄×C₅₉	—	2	2	no	—
256	C₂²×C₄×C₅₉	—	2	2	no	—
257	C₂²×C₄×C₅₉	—	2	2	no	—
258	C₂²×C₄×C₅₉	—	2	2	no	—
259	C₂²×C₄×C₅₉	—	2	2	no	—
260	C₂²×C₄×C₅₉	—	2	2	no	—
261	C₂²×C₄×C₅₉	—	2	2	no	—
262	C₂²×C₄×C₅₉	—	2	2	no	—
263	C₂²×C₄×C₅₉	—	2	2	no	—
264	C₂²×C₄×C₅₉	—	2	2	no	—
265	C₂²×C₄×C₅₉	—	2	4	no	—
266	C₂²×C₄×C₅₉	—	2	4	no	—
267	C₂²×C₄×C₅₉	—	4	1	no	—
268	C₂²×C₄×C₅₉	—	4	2	no	—
269	C₂²×C₄×C₅₉	—	4	2	no	—
270	C₂²×C₄×C₅₉	—	4	2	no	—
271	C₂²×C₄×C₅₉	—	4	2	no	—
272	C₂²×C₄×C₅₉	#41	1	4	yes	—
273	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
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	2	yes	—
281	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
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	2	yes	—
290	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
293	C₄⋊C₄×C₅₉	—	2	4	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	2	no	—
299	C₄⋊C₄×C₅₉	—	2	2	no	—
300	C₄⋊C₄×C₅₉	—	2	2	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	4	no	—
305	C₄⋊C₄×C₅₉	—	2	4	no	—
306	C₄⋊C₄×C₅₉	—	2	2	no	—
307	C₄⋊C₄×C₅₉	—	2	2	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	C₄⋊C₄×C₅₉	—	4	2	no	—
316	C₄⋊C₄×C₅₉	#41	1	4	yes	—
317	C₂²⋊C₄×C₅₉	—	2	4	no	—
318	C₂²⋊C₄×C₅₉	—	2	2	no	—
319	C₂²⋊C₄×C₅₉	—	2	4	no	—
320	C₂²⋊C₄×C₅₉	—	2	4	no	—
321	C₂²⋊C₄×C₅₉	—	2	2	no	—
322	C₂²⋊C₄×C₅₉	—	2	2	no	—
323	C₂²⋊C₄×C₅₉	—	2	2	no	—
324	C₂²⋊C₄×C₅₉	—	2	2	no	—
325	C₂²⋊C₄×C₅₉	—	2	4	no	—
326	C₂²⋊C₄×C₅₉	—	2	4	no	—
327	C₂²⋊C₄×C₅₉	—	2	4	no	—
328	C₂²⋊C₄×C₅₉	—	2	4	no	—
329	C₂²⋊C₄×C₅₉	—	2	2	no	—
330	C₂²⋊C₄×C₅₉	—	2	2	no	—
331	C₂²⋊C₄×C₅₉	—	2	4	no	—
332	C₂²⋊C₄×C₅₉	—	4	1	no	—
333	C₂²⋊C₄×C₅₉	—	4	2	no	—
334	C₂²⋊C₄×C₅₉	—	4	2	no	—
335	C₂²⋊C₄×C₅₉	—	4	2	no	—
336	C₂²⋊C₄×C₅₉	—	4	2	no	—
337	C₂²⋊C₄×C₅₉	—	4	2	no	—
338	C₂²⋊C₄×C₅₉	—	4	2	no	—
339	C₂²⋊C₄×C₅₉	—	4	2	no	—
340	C₂²⋊C₄×C₅₉	—	4	2	no	—
341	C₄²×C₅₉	—	2	2	no	—
342	C₄²×C₅₉	—	2	2	no	—
343	C₄²×C₅₉	—	2	2	no	—
344	C₄²×C₅₉	—	2	4	no	—
345	C₄²×C₅₉	—	2	2	no	—
346	C₄²×C₅₉	—	2	2	no	—
347	C₄²×C₅₉	—	2	2	no	—
348	C₄²×C₅₉	—	4	2	no	—
349	C₄²×C₅₉	—	4	2	no	—
350	C₄²×C₅₉	—	4	2	no	—
351	C₄²×C₅₉	—	4	2	no	—
352	C₄²×C₅₉	—	4	2	no	—
353	C₄²×C₅₉	#41	1	4	yes	—
354	C₂³×C₅₉	—	2	1	no	—
355	C₂³×C₅₉	—	2	1	no	—
356	C₂³×C₅₉	—	2	1	no	—
357	C₂³×C₅₉	—	2	1	no	—
358	C₂³×C₅₉	—	2	1	no	—
359	C₂³×C₅₉	—	2	1	no	—
360	C₂³×C₅₉	—	2	1	no	—
361	C₂³×C₅₉	—	2	1	no	—
362	C₂³×C₅₉	—	2	1	no	—
363	C₂³×C₅₉	—	2	1	no	—
364	C₂³×C₅₉	—	2	1	no	—
365	C₂³×C₅₉	—	2	1	no	—
366	C₂³×C₅₉	—	2	2	no	—
367	C₂³×C₅₉	—	2	2	no	—
368	C₂³×C₅₉	—	2	2	no	—
369	C₂³×C₅₉	—	2	2	no	—
370	C₂³×C₅₉	—	2	2	no	—
371	C₂³×C₅₉	—	2	2	no	—
372	C₂³×C₅₉	—	2	2	no	—
373	C₂³×C₅₉	C₂×#41	1	2	yes	—
374	C₂³×C₅₉	H(5,𝔽₂)	1	2	yes	—
375	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
376	Q₈×C₅₉	—	8	4	no	—
377	D₄×C₅₉	—	4	8	no	—
378	D₄×C₅₉	—	4	4	no	—
379	D₄×C₅₉	—	4	4	no	—
380	D₄×C₅₉	—	8	4	no	—
381	C₂×C₄×C₅₉	—	2	8	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	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	8	no	—
395	C₂×C₄×C₅₉	—	2	1	no	—
396	C₂×C₄×C₅₉	—	2	1	no	—
397	C₂×C₄×C₅₉	—	2	1	no	—
398	C₂×C₄×C₅₉	—	2	1	no	—
399	C₂×C₄×C₅₉	—	2	2	no	—
400	C₂×C₄×C₅₉	—	2	2	no	—
401	C₂×C₄×C₅₉	—	2	1	no	—
402	C₂×C₄×C₅₉	—	2	1	no	—
403	C₂×C₄×C₅₉	—	2	1	no	—
404	C₂×C₄×C₅₉	—	2	1	no	—
405	C₂×C₄×C₅₉	—	2	1	no	—
406	C₂×C₄×C₅₉	—	2	2	no	—
407	C₂×C₄×C₅₉	—	2	2	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	2	no	—
412	C₂×C₄×C₅₉	—	2	2	no	—
413	C₂×C₄×C₅₉	—	2	1	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	2	no	—
418	C₂×C₄×C₅₉	—	2	1	no	—
419	C₂×C₄×C₅₉	—	2	1	no	—
420	C₂×C₄×C₅₉	—	2	1	no	—
421	C₂×C₄×C₅₉	—	2	2	no	—
422	C₂×C₄×C₅₉	—	2	2	no	—
423	C₂×C₄×C₅₉	—	2	1	no	—
424	C₂×C₄×C₅₉	—	2	2	no	—
425	C₂×C₄×C₅₉	—	2	1	no	—
426	C₂×C₄×C₅₉	—	2	1	no	—
427	C₂×C₄×C₅₉	—	2	1	no	—
428	C₂×C₄×C₅₉	—	2	1	no	—
429	C₂×C₄×C₅₉	—	2	1	no	—
430	C₂×C₄×C₅₉	—	2	2	no	—
431	C₂×C₄×C₅₉	—	2	2	no	—
432	C₂×C₄×C₅₉	—	2	1	no	—
433	C₂×C₄×C₅₉	—	2	2	no	—
434	C₂×C₄×C₅₉	—	4	4	no	—
435	C₂×C₄×C₅₉	—	4	4	no	—
436	C₂×C₄×C₅₉	—	8	4	no	—
437	C₂×C₄×C₅₉	—	8	4	no	—
438	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
439	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
440	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
441	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
442	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
443	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
444	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
445	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
446	C₂×C₄×C₅₉	2₋¹⁺⁴	1	2	yes	—
447	#35589	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
448	C₂²×C₅₉	—	2	2	no	—
449	C₂²×C₅₉	—	2	2	no	—
450	C₂²×C₅₉	—	2	2	no	—
451	C₂²×C₅₉	—	2	2	no	—
452	C₂²×C₅₉	—	2	2	no	—
453	C₂²×C₅₉	—	2	2	no	—
454	C₂²×C₅₉	—	4	1	no	—
455	C₂²×C₅₉	—	4	1	no	—
456	C₂²×C₅₉	—	4	1	no	—
457	C₂²×C₅₉	—	4	1	no	—
458	C₂²×C₅₉	—	4	1	no	—
459	C₂²×C₅₉	—	4	1	no	—
460	C₂²×C₅₉	—	4	1	no	—
461	C₂²×C₅₉	—	4	1	no	—
462	C₂²×C₅₉	—	4	2	no	—
463	C₂²×C₅₉	—	4	2	no	—
464	C₂²×C₅₉	—	4	2	no	—
465	C₂²×C₅₉	—	4	2	no	—
466	C₂²×C₅₉	—	4	2	no	—
467	C₂²×C₅₉	—	4	2	no	—
468	C₂²×C₅₉	—	4	2	no	—
469	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
470	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
471	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
472	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
473	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
474	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
475	C₂²×C₅₉	#585	1	1	yes	characteristic
476	C₄×C₅₉	—	2	2	no	—
477	C₄×C₅₉	—	2	2	no	—
478	C₄×C₅₉	—	2	2	no	—
479	C₄×C₅₉	—	2	2	no	—
480	C₄×C₅₉	—	2	2	no	—
481	C₄×C₅₉	—	2	4	no	—
482	C₄×C₅₉	—	4	1	no	—
483	C₄×C₅₉	—	4	1	no	—
484	C₄×C₅₉	—	4	1	no	—
485	C₄×C₅₉	—	4	2	no	—
486	C₄×C₅₉	—	4	2	no	—
487	C₄×C₅₉	—	4	1	no	—
488	C₄×C₅₉	—	4	2	no	—
489	C₄×C₅₉	—	4	1	no	—
490	C₄×C₅₉	—	4	2	no	—
491	C₄×C₅₉	—	4	1	no	—
492	C₄×C₅₉	—	4	2	no	—
493	C₄×C₅₉	—	4	2	no	—
494	C₄×C₅₉	—	4	1	no	—
495	C₄×C₅₉	#529	1	4	yes	—
496	#2594	C₂×C₅₉	1	2	yes	complemented
497	#2576	C₂×C₅₉	1	2	yes	complemented
498	#2574	C₂×C₅₉	1	2	yes	complemented
499	#2560	C₂×C₅₉	1	2	yes	complemented
500	#2512	C₂×C₅₉	1	1	yes	characteristic, complemented
501	#2507	C₂×C₅₉	1	1	yes	characteristic, complemented
502	#2500	C₂×C₅₉	1	1	yes	characteristic, complemented
503	#2494	C₂×C₅₉	1	1	yes	characteristic, complemented
504	#2491	C₂×C₅₉	1	1	yes	characteristic, complemented
505	#2485	C₂×C₅₉	1	1	yes	characteristic, complemented
506	#2476	C₂×C₅₉	1	2	yes	complemented
507	#2474	C₂×C₅₉	1	2	yes	complemented
508	#2468	C₂×C₅₉	1	2	yes	complemented
509	#2440	C₂×C₅₉	1	1	yes	characteristic, complemented
510	#2427	C₂×C₅₉	1	2	yes	complemented
511	#2416	C₂×C₅₉	1	1	yes	characteristic
512	#2331	C₂×C₅₉	1	1	yes	characteristic, complemented
513	#2324	C₂×C₅₉	1	1	yes	characteristic, complemented
514	#2319	C₂×C₅₉	1	1	yes	characteristic, complemented
515	C₄×#121	C₂×C₅₉	1	1	yes	characteristic, complemented
516	#2290	C₂×C₅₉	1	1	yes	characteristic, complemented
517	#2285	C₂×C₅₉	1	1	yes	characteristic, complemented
518	#2274	C₂×C₅₉	1	1	yes	characteristic, complemented
519	C₂×C₅₉	—	4	2	no	—
520	C₂×C₅₉	—	4	2	no	—
521	C₂×C₅₉	—	8	2	no	—
522	C₂×C₅₉	C₂×#529	1	1	yes	characteristic
523	C₂×C₅₉	#3492	1	1	yes	characteristic
524	C₂×C₅₉	#3494	1	1	yes	characteristic
525	C₂×C₅₉	#3494	1	1	yes	characteristic
526	C₂×C₅₉	#3511	1	1	yes	characteristic
527	C₂×C₅₉	#3518	1	1	yes	characteristic
528	C₂×C₅₉	#3519	1	1	yes	characteristic
529	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
530	C₂×#126	C₂²×C₅₉	1	2	yes	—
531	C₂×#124	C₂²×C₅₉	1	2	yes	—
532	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	—
533	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
534	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
535	C₂×#121	C₂²×C₅₉	1	2	yes	—
536	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
537	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
538	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
539	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
540	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
541	C₂×#117	C₂²×C₅₉	1	2	yes	—
542	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
543	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
544	#401	C₂²×C₅₉	1	2	yes	—
545	#398	C₂²×C₅₉	1	2	yes	—
546	#398	C₂²×C₅₉	1	2	yes	—
547	#398	C₂²×C₅₉	1	2	yes	—
548	#397	C₂²×C₅₉	1	2	yes	—
549	#397	C₂²×C₅₉	1	2	yes	—
550	#397	C₂²×C₅₉	1	2	yes	—
551	#396	C₂²×C₅₉	1	2	yes	—
552	#396	C₂²×C₅₉	1	2	yes	—
553	#395	C₂²×C₅₉	1	2	yes	—
554	#394	C₂²×C₅₉	1	2	yes	—
555	#394	C₂²×C₅₉	1	2	yes	—
556	#394	C₂²×C₅₉	1	2	yes	—
557	#394	C₂²×C₅₉	1	2	yes	—
558	#394	C₂²×C₅₉	1	2	yes	—
559	#393	C₂²×C₅₉	1	2	yes	—
560	#391	C₂²×C₅₉	1	2	yes	—
561	#391	C₂²×C₅₉	1	2	yes	—
562	#390	C₂²×C₅₉	1	2	yes	—
563	#390	C₂²×C₅₉	1	1	yes	characteristic
564	#390	C₂²×C₅₉	1	1	yes	characteristic
565	#390	C₂²×C₅₉	1	1	yes	characteristic
566	#390	C₂²×C₅₉	1	1	yes	characteristic
567	#389	C₂²×C₅₉	1	1	yes	characteristic
568	#389	C₂²×C₅₉	1	1	yes	characteristic
569	#389	C₂²×C₅₉	1	1	yes	characteristic
570	#389	C₂²×C₅₉	1	1	yes	characteristic
571	#389	C₂²×C₅₉	1	1	yes	characteristic
572	#389	C₂²×C₅₉	1	2	yes	—
573	#389	C₂²×C₅₉	1	1	yes	characteristic
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	2	yes	—
578	#388	C₂²×C₅₉	1	2	yes	—
579	#388	C₂²×C₅₉	1	2	yes	—
580	#388	C₂²×C₅₉	1	1	yes	characteristic
581	#388	C₂²×C₅₉	1	2	yes	—
582	#388	C₂²×C₅₉	1	2	yes	—
583	#388	C₂²×C₅₉	1	2	yes	—
584	#388	C₂²×C₅₉	1	2	yes	—
585	#388	C₂²×C₅₉	1	2	yes	—
586	#387	C₂²×C₅₉	1	2	yes	—
587	#387	C₂²×C₅₉	1	1	yes	characteristic
588	#387	C₂²×C₅₉	1	2	yes	—
589	#387	C₂²×C₅₉	1	2	yes	—
590	#387	C₂²×C₅₉	1	2	yes	—
591	#387	C₂²×C₅₉	1	2	yes	—
592	#387	C₂²×C₅₉	1	1	yes	characteristic
593	#386	C₂²×C₅₉	1	2	yes	—
594	#386	C₂²×C₅₉	1	2	yes	—
595	#386	C₂²×C₅₉	1	1	yes	characteristic
596	#386	C₂²×C₅₉	1	2	yes	—
597	#386	C₂²×C₅₉	1	1	yes	characteristic
598	#385	C₂²×C₅₉	1	2	yes	—
599	#385	C₂²×C₅₉	1	2	yes	—
600	#385	C₂²×C₅₉	1	1	yes	characteristic
601	#385	C₂²×C₅₉	1	1	yes	characteristic
602	#384	C₂²×C₅₉	1	1	yes	characteristic
603	#384	C₂²×C₅₉	1	1	yes	characteristic
604	#382	C₂²×C₅₉	1	2	yes	—
605	#382	C₂²×C₅₉	1	1	yes	characteristic
606	#381	C₂²×C₅₉	1	2	yes	—
607	#380	C₂²×C₅₉	1	2	yes	—
608	#380	C₂²×C₅₉	1	1	yes	characteristic
609	#380	C₂²×C₅₉	1	1	yes	characteristic
610	#380	C₂²×C₅₉	1	2	yes	—
611	#380	C₂²×C₅₉	1	1	yes	characteristic
612	#380	C₂²×C₅₉	1	1	yes	characteristic
613	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
614	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
615	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
616	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
617	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
618	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
619	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
620	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
621	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
622	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
623	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
624	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
625	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
626	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
627	#376	C₂²×C₅₉	1	1	yes	characteristic
628	C₅₉	#35589	1	1	yes	characteristic, direct product factor, Sylow
629	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
630	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
631	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
632	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
633	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
634	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
635	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
636	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
637	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
638	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
639	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
640	C₄⋊Q₈	—	2	4	no	—
641	#126	—	4	4	no	—
642	#124	—	4	4	no	—
643	C₂²⋊Q₈	—	4	4	no	—
644	#121	—	2	4	no	—
645	#121	—	2	4	no	—
646	#121	—	4	4	no	—
647	C₄×D₄	—	2	4	no	—
648	C₄×D₄	—	2	4	no	—
649	C₄×D₄	—	4	4	no	—
650	#117	—	2	4	no	—
651	#117	—	2	4	no	—
652	#117	—	4	4	no	—
653	C₂×C₄⋊C₄	—	2	4	no	—
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	1	yes	characteristic
657	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
658	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
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	1	yes	characteristic
662	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
663	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
665	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
667	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
668	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
669	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
670	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
671	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
672	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
673	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
674	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
675	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
676	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
677	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
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	1	yes	characteristic
681	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
682	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
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	1	yes	characteristic
686	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
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	1	yes	characteristic
690	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
691	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
692	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
693	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
694	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
695	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
696	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
697	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
698	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
699	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
700	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
701	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
702	C₂×C₄²	—	2	4	no	—
703	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
704	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
705	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
706	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
707	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
708	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
709	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
710	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
711	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
712	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
713	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
714	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
715	C₂×C₄²	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	1	yes	characteristic
719	#95	C₂³×C₅₉	1	1	yes	characteristic
720	#95	C₂³×C₅₉	1	2	yes	—
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	1	yes	characteristic
727	#95	C₂³×C₅₉	1	1	yes	characteristic
728	#95	C₂³×C₅₉	1	1	yes	characteristic
729	#95	C₂³×C₅₉	1	1	yes	characteristic
730	#95	C₂³×C₅₉	1	2	yes	—
731	#95	C₂³×C₅₉	1	2	yes	—
732	#95	C₂³×C₅₉	1	2	yes	—
733	#95	C₂³×C₅₉	1	1	yes	characteristic
734	#95	C₂³×C₅₉	1	1	yes	characteristic
735	#95	C₂³×C₅₉	1	2	yes	—
736	#95	C₂³×C₅₉	1	2	yes	—
737	#95	C₂³×C₅₉	1	2	yes	—
738	#95	C₂³×C₅₉	1	2	yes	—
739	#95	C₂³×C₅₉	1	2	yes	—
740	#95	C₂³×C₅₉	1	2	yes	—
741	#95	C₂³×C₅₉	1	2	yes	—
742	#95	C₂³×C₅₉	1	2	yes	—
743	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
744	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
745	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
746	C₂×Q₈	—	2	4	no	—
747	C₂×Q₈	—	4	2	no	—
748	C₂×Q₈	—	4	2	no	—
749	C₂×D₄	—	2	2	no	—
750	C₂×D₄	—	2	2	no	—
751	C₂×D₄	—	2	4	no	—
752	C₂×D₄	—	2	4	no	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	2	4	no	—
755	C₂×D₄	—	2	2	no	—
756	C₂×D₄	—	2	2	no	—
757	C₂×D₄	—	4	2	no	—
758	C₂×D₄	—	4	1	no	—
759	C₂×D₄	—	4	2	no	—
760	C₂×D₄	—	4	2	no	—
761	C₂²×C₄	—	2	2	no	—
762	C₂²×C₄	—	2	2	no	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	—	2	2	no	—
767	C₂²×C₄	—	2	2	no	—
768	C₂²×C₄	—	2	2	no	—
769	C₂²×C₄	—	2	2	no	—
770	C₂²×C₄	—	2	2	no	—
771	C₂²×C₄	—	2	4	no	—
772	C₂²×C₄	—	2	4	no	—
773	C₂²×C₄	—	4	1	no	—
774	C₂²×C₄	—	4	2	no	—
775	C₂²×C₄	—	4	2	no	—
776	C₂²×C₄	—	4	2	no	—
777	C₂²×C₄	—	4	2	no	—
778	C₂²×C₄	#41×C₅₉	1	4	yes	—
779	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
780	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
781	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
782	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
783	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
784	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
786	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
787	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
788	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
789	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
790	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
791	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
792	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
793	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
794	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
795	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
796	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
797	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
798	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
799	C₄⋊C₄	—	2	4	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	4	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	4	no	—
811	C₄⋊C₄	—	2	4	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	4	2	no	—
815	C₄⋊C₄	—	4	2	no	—
816	C₄⋊C₄	—	4	2	no	—
817	C₄⋊C₄	—	4	2	no	—
818	C₄⋊C₄	—	4	2	no	—
819	C₄⋊C₄	—	4	2	no	—
820	C₄⋊C₄	—	4	2	no	—
821	C₄⋊C₄	—	4	2	no	—
822	C₄⋊C₄	#41×C₅₉	1	4	yes	—
823	C₂²⋊C₄	—	2	4	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	4	no	—
826	C₂²⋊C₄	—	2	4	no	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	—	2	2	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	4	no	—
832	C₂²⋊C₄	—	2	4	no	—
833	C₂²⋊C₄	—	2	4	no	—
834	C₂²⋊C₄	—	2	4	no	—
835	C₂²⋊C₄	—	2	2	no	—
836	C₂²⋊C₄	—	2	2	no	—
837	C₂²⋊C₄	—	2	4	no	—
838	C₂²⋊C₄	—	4	2	no	—
839	C₂²⋊C₄	—	4	2	no	—
840	C₂²⋊C₄	—	4	2	no	—
841	C₂²⋊C₄	—	4	2	no	—
842	C₂²⋊C₄	—	4	2	no	—
843	C₂²⋊C₄	—	4	2	no	—
844	C₂²⋊C₄	—	4	2	no	—
845	C₂²⋊C₄	—	4	1	no	—
846	C₂²⋊C₄	—	4	2	no	—
847	C₄²	—	2	2	no	—
848	C₄²	—	2	2	no	—
849	C₄²	—	2	2	no	—
850	C₄²	—	2	4	no	—
851	C₄²	—	2	2	no	—
852	C₄²	—	2	2	no	—
853	C₄²	—	2	2	no	—
854	C₄²	—	4	2	no	—
855	C₄²	—	4	2	no	—
856	C₄²	—	4	2	no	—
857	C₄²	—	4	2	no	—
858	C₄²	—	4	2	no	—
859	C₄²	#41×C₅₉	1	4	yes	—
860	C₂³	—	2	1	no	—
861	C₂³	—	2	1	no	—
862	C₂³	—	2	1	no	—
863	C₂³	—	2	1	no	—
864	C₂³	—	2	1	no	—
865	C₂³	—	2	1	no	—
866	C₂³	—	2	1	no	—
867	C₂³	—	2	1	no	—
868	C₂³	—	2	1	no	—
869	C₂³	—	2	1	no	—
870	C₂³	—	2	1	no	—
871	C₂³	—	2	1	no	—
872	C₂³	—	2	2	no	—
873	C₂³	—	2	2	no	—
874	C₂³	—	2	2	no	—
875	C₂³	—	2	2	no	—
876	C₂³	—	2	2	no	—
877	C₂³	—	2	2	no	—
878	C₂³	—	2	2	no	—
879	C₂³	C₂×#41×C₅₉	1	2	yes	—
880	C₂³	H(5,𝔽₂)×C₅₉	1	2	yes	—
881	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
882	Q₈	—	8	4	no	—
883	D₄	—	4	8	no	—
884	D₄	—	4	4	no	—
885	D₄	—	4	4	no	—
886	D₄	—	8	4	no	—
887	C₂×C₄	—	2	8	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	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	1	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	8	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	2	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	4	4	no	—
941	C₂×C₄	—	4	4	no	—
942	C₂×C₄	—	8	4	no	—
943	C₂×C₄	—	8	4	no	—
944	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
945	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
946	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
947	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
948	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
949	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
950	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
951	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
952	C₂×C₄	2₋¹⁺⁴×C₅₉	1	2	yes	—
953	C₂²	—	2	2	no	—
954	C₂²	—	2	2	no	—
955	C₂²	—	2	2	no	—
956	C₂²	—	2	2	no	—
957	C₂²	—	2	2	no	—
958	C₂²	—	2	2	no	—
959	C₂²	—	4	1	no	—
960	C₂²	—	4	1	no	—
961	C₂²	—	4	1	no	—
962	C₂²	—	4	1	no	—
963	C₂²	—	4	1	no	—
964	C₂²	—	4	1	no	—
965	C₂²	—	4	1	no	—
966	C₂²	—	4	1	no	—
967	C₂²	—	4	2	no	—
968	C₂²	—	4	2	no	—
969	C₂²	—	4	2	no	—
970	C₂²	—	4	2	no	—
971	C₂²	—	4	2	no	—
972	C₂²	—	4	2	no	—
973	C₂²	—	4	2	no	—
974	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
975	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
976	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
977	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
978	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
979	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
980	C₂²	C₅₉×#585	1	1	yes	characteristic
981	C₄	—	2	4	no	—
982	C₄	—	2	2	no	—
983	C₄	—	2	2	no	—
984	C₄	—	2	2	no	—
985	C₄	—	2	2	no	—
986	C₄	—	2	2	no	—
987	C₄	—	4	1	no	—
988	C₄	—	4	2	no	—
989	C₄	—	4	1	no	—
990	C₄	—	4	2	no	—
991	C₄	—	4	1	no	—
992	C₄	—	4	2	no	—
993	C₄	—	4	1	no	—
994	C₄	—	4	1	no	—
995	C₄	—	4	2	no	—
996	C₄	—	4	1	no	—
997	C₄	—	4	2	no	—
998	C₄	—	4	1	no	—
999	C₄	—	4	2	no	—
1000	C₄	C₅₉×#529	1	4	yes	—
1001	C₂	—	4	2	no	—
1002	C₂	—	4	2	no	—
1003	C₂	—	8	2	no	—
1004	C₂	C₂×C₅₉×#529	1	1	yes	characteristic
1005	C₂	C₅₉×#3492	1	1	yes	characteristic
1006	C₂	C₅₉×#3494	1	1	yes	characteristic
1007	C₂	C₅₉×#3494	1	1	yes	characteristic
1008	C₂	C₅₉×#3511	1	1	yes	characteristic
1009	C₂	C₅₉×#3518	1	1	yes	characteristic
1010	C₂	C₅₉×#3519	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₅₉×#2416	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×#2594	C₂	semidirect
2. C₅₉×#2576	C₂	semidirect
3. C₅₉×#2574	C₂	semidirect
4. C₅₉×#2560	C₂	semidirect
5. C₅₉×#2512	C₂	semidirect
6. C₅₉×#2507	C₂	semidirect
7. C₅₉×#2500	C₂	semidirect
8. C₅₉×#2494	C₂	semidirect
9. C₅₉×#2491	C₂	semidirect
10. C₅₉×#2485	C₂	semidirect
11. C₅₉×#2476	C₂	semidirect
12. C₅₉×#2474	C₂	semidirect
13. C₅₉×#2468	C₂	semidirect
14. C₅₉×#2440	C₂	semidirect
15. C₅₉×#2427	C₂	semidirect
17. C₅₉×#2331	C₂	semidirect
18. C₅₉×#2324	C₂	semidirect
19. C₅₉×#2319	C₂	semidirect
20. C₄×#121×C₅₉	C₂	semidirect
21. C₅₉×#2290	C₂	semidirect
22. C₅₉×#2285	C₂	semidirect
23. C₅₉×#2274	C₂	semidirect
447. #35589	C₅₉	direct (N × H)
496. #2594	C₂×C₅₉	semidirect
497. #2576	C₂×C₅₉	semidirect
498. #2574	C₂×C₅₉	semidirect
499. #2560	C₂×C₅₉	semidirect
500. #2512	C₂×C₅₉	semidirect
501. #2507	C₂×C₅₉	semidirect
502. #2500	C₂×C₅₉	semidirect
503. #2494	C₂×C₅₉	semidirect
504. #2491	C₂×C₅₉	semidirect
505. #2485	C₂×C₅₉	semidirect
506. #2476	C₂×C₅₉	semidirect
507. #2474	C₂×C₅₉	semidirect
508. #2468	C₂×C₅₉	semidirect
509. #2440	C₂×C₅₉	semidirect
510. #2427	C₂×C₅₉	semidirect
512. #2331	C₂×C₅₉	semidirect
513. #2324	C₂×C₅₉	semidirect
514. #2319	C₂×C₅₉	semidirect
515. C₄×#121	C₂×C₅₉	semidirect
516. #2290	C₂×C₅₉	semidirect
517. #2285	C₂×C₅₉	semidirect
518. #2274	C₂×C₅₉	semidirect
628. C₅₉	#35589	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×#2594	2
C₅₉×#2576	2
C₅₉×#2574	2
C₅₉×#2560	2
C₅₉×#2512	2
C₅₉×#2507	2
C₅₉×#2500	2
C₅₉×#2494	2
C₅₉×#2491	2
C₅₉×#2485	2
C₅₉×#2476	2
C₅₉×#2474	2
C₅₉×#2468	2
C₅₉×#2440	2
C₅₉×#2427	2
C₅₉×#2416	2
C₅₉×#2331	2
C₅₉×#2324	2
C₅₉×#2319	2
C₄×#121×C₅₉	2
C₅₉×#2290	2
C₅₉×#2285	2
C₅₉×#2274	2
#35589	59

Subgroups — C59×#35589 #28447698

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35589 #28447698