Subgroups — C₅₉×#35581 #28447690

Order 15104.

1772 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#2608	C₂	1	2	yes	maximal, complemented
2	C₅₉×#2587	C₂	1	2	yes	maximal, complemented
3	C₅₉×#2584	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2574	C₂	1	2	yes	maximal, complemented
5	C₅₉×#2566	C₂	1	1	yes	maximal, characteristic
6	C₅₉×#2551	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#2549	C₂	1	2	yes	maximal, complemented
8	C₅₉×#2538	C₂	1	1	yes	maximal, characteristic
9	C₅₉×#2508	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#2507	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2465	C₂	1	2	yes	maximal, complemented
12	C₅₉×#2452	C₂	1	1	yes	maximal, characteristic
13	C₅₉×#2452	C₂	1	1	yes	maximal, characteristic
14	C₅₉×#2439	C₂	1	2	yes	maximal, complemented
15	C₅₉×#2438	C₂	1	2	yes	maximal, complemented
16	C₅₉×#2429	C₂	1	2	yes	maximal, complemented
17	C₅₉×#2331	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₉×#2330	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₉×#2319	C₂	1	1	yes	maximal, characteristic
20	C₄×C₄⋊Q₈×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₉×#2295	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₉×#2293	C₂	1	1	yes	maximal, characteristic
23	C₅₉×#2275	C₂	1	1	yes	maximal, characteristic
24	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊Q₈×C₅₉	C₂²	1	2	yes	—
27	C₂×#125×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×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	2	yes	—
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×#117×C₅₉	C₂²	1	2	yes	—
37	C₅₉×#400	C₂²	1	2	yes	—
38	C₅₉×#398	C₂²	1	2	yes	—
39	C₅₉×#398	C₂²	1	2	yes	—
40	C₅₉×#398	C₂²	1	2	yes	—
41	C₅₉×#398	C₂²	1	2	yes	—
42	C₅₉×#396	C₂²	1	2	yes	—
43	C₅₉×#396	C₂²	1	2	yes	—
44	C₅₉×#396	C₂²	1	2	yes	—
45	C₅₉×#396	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×#395	C₂²	1	2	yes	—
50	C₅₉×#395	C₂²	1	2	yes	—
51	C₅₉×#393	C₂²	1	2	yes	—
52	C₅₉×#393	C₂²	1	2	yes	—
53	C₅₉×#391	C₂²	1	1	yes	characteristic
54	C₅₉×#391	C₂²	1	2	yes	—
55	C₅₉×#391	C₂²	1	1	yes	characteristic
56	C₅₉×#391	C₂²	1	2	yes	—
57	C₅₉×#391	C₂²	1	2	yes	—
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	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	2	yes	—
67	C₅₉×#389	C₂²	1	1	yes	characteristic
68	C₅₉×#389	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	2	yes	—
73	C₅₉×#389	C₂²	1	1	yes	characteristic
74	C₅₉×#389	C₂²	1	1	yes	characteristic
75	C₅₉×#389	C₂²	1	2	yes	—
76	C₅₉×#389	C₂²	1	1	yes	characteristic
77	C₅₉×#389	C₂²	1	1	yes	characteristic
78	C₅₉×#389	C₂²	1	2	yes	—
79	C₅₉×#389	C₂²	1	2	yes	—
80	C₅₉×#389	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	1	yes	characteristic
91	C₅₉×#387	C₂²	1	2	yes	—
92	C₅₉×#387	C₂²	1	2	yes	—
93	C₅₉×#387	C₂²	1	2	yes	—
94	C₅₉×#387	C₂²	1	2	yes	—
95	C₅₉×#385	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×#384	C₂²	1	1	yes	characteristic
100	C₅₉×#384	C₂²	1	1	yes	characteristic
101	C₅₉×#382	C₂²	1	1	yes	characteristic
102	C₅₉×#382	C₂²	1	2	yes	—
103	C₅₉×#381	C₂²	1	2	yes	—
104	C₅₉×#380	C₂²	1	2	yes	—
105	C₅₉×#380	C₂²	1	2	yes	—
106	C₄×C₄⋊C₄×C₅₉	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	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	1	yes	characteristic
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	C₄×C₂²⋊C₄×C₅₉	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	2	yes	—
125	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
126	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
128	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
129	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
130	C₄⋊Q₈×C₅₉	—	2	4	no	—
131	C₄⋊Q₈×C₅₉	—	2	4	no	—
132	C₄⋊Q₈×C₅₉	—	4	4	no	—
133	#125×C₅₉	—	2	4	no	—
134	C₂²⋊Q₈×C₅₉	—	4	4	no	—
135	C₂²⋊Q₈×C₅₉	—	4	4	no	—
136	C₂²⋊Q₈×C₅₉	—	4	4	no	—
137	C₄×Q₈×C₅₉	—	2	4	no	—
138	C₄×Q₈×C₅₉	—	4	4	no	—
139	C₄×D₄×C₅₉	—	2	4	no	—
140	C₄×D₄×C₅₉	—	2	4	no	—
141	C₄×D₄×C₅₉	Q₈	1	8	yes	complemented
142	#117×C₅₉	—	4	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	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	1	yes	characteristic
155	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
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	2	yes	—
159	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
172	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊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	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×C₄²×C₅₉	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
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	2	yes	—
198	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
199	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
200	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
201	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
202	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
204	#95×C₅₉	C₂³	1	1	yes	characteristic
205	#95×C₅₉	C₂³	1	2	yes	—
206	#95×C₅₉	C₂³	1	2	yes	—
207	#95×C₅₉	C₂³	1	2	yes	—
208	#95×C₅₉	C₂³	1	1	yes	characteristic
209	#95×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	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
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	#95×C₅₉	C₂³	1	2	yes	—
235	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
236	C₂×Q₈×C₅₉	—	2	2	no	—
237	C₂×Q₈×C₅₉	—	2	4	no	—
238	C₂×Q₈×C₅₉	—	2	4	no	—
239	C₂×Q₈×C₅₉	—	2	2	no	—
240	C₂×Q₈×C₅₉	—	2	4	no	—
241	C₂×Q₈×C₅₉	—	4	2	no	—
242	C₂×Q₈×C₅₉	—	4	1	no	—
243	C₂×Q₈×C₅₉	—	4	2	no	—
244	C₂×Q₈×C₅₉	—	4	2	no	—
245	C₂×D₄×C₅₉	—	2	2	no	—
246	C₂×D₄×C₅₉	—	2	2	no	—
247	C₂×D₄×C₅₉	C₂×Q₈	1	4	yes	—
248	C₂²×C₄×C₅₉	—	2	4	no	—
249	C₂²×C₄×C₅₉	—	2	4	no	—
250	C₂²×C₄×C₅₉	—	4	2	no	—
251	C₂²×C₄×C₅₉	—	4	2	no	—
252	C₂²×C₄×C₅₉	—	4	2	no	—
253	C₂²×C₄×C₅₉	—	4	2	no	—
254	C₂²×C₄×C₅₉	—	4	2	no	—
255	C₂²×C₄×C₅₉	—	4	2	no	—
256	C₂²×C₄×C₅₉	C₂×Q₈	1	8	yes	—
257	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
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	2	yes	—
269	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
279	C₄⋊C₄×C₅₉	—	2	2	no	—
280	C₄⋊C₄×C₅₉	—	2	2	no	—
281	C₄⋊C₄×C₅₉	—	2	2	no	—
282	C₄⋊C₄×C₅₉	—	2	2	no	—
283	C₄⋊C₄×C₅₉	—	2	4	no	—
284	C₄⋊C₄×C₅₉	—	2	4	no	—
285	C₄⋊C₄×C₅₉	—	2	2	no	—
286	C₄⋊C₄×C₅₉	—	2	2	no	—
287	C₄⋊C₄×C₅₉	—	2	4	no	—
288	C₄⋊C₄×C₅₉	—	2	4	no	—
289	C₄⋊C₄×C₅₉	—	2	2	no	—
290	C₄⋊C₄×C₅₉	—	2	2	no	—
291	C₄⋊C₄×C₅₉	—	2	4	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	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	—	4	2	no	—
300	C₄⋊C₄×C₅₉	—	4	2	no	—
301	C₄⋊C₄×C₅₉	—	4	1	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	—	4	2	no	—
306	C₄⋊C₄×C₅₉	—	4	2	no	—
307	C₄⋊C₄×C₅₉	—	4	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	C₂×Q₈	1	4	yes	—
312	C₄⋊C₄×C₅₉	#41	1	4	yes	—
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	—	2	4	no	—
318	C₂²⋊C₄×C₅₉	—	4	2	no	—
319	C₂²⋊C₄×C₅₉	—	4	2	no	—
320	C₂²⋊C₄×C₅₉	—	4	2	no	—
321	C₂²⋊C₄×C₅₉	—	4	2	no	—
322	C₂²⋊C₄×C₅₉	—	4	2	no	—
323	C₂²⋊C₄×C₅₉	C₂×Q₈	1	8	yes	—
324	C₄²×C₅₉	—	2	2	no	—
325	C₄²×C₅₉	—	2	2	no	—
326	C₄²×C₅₉	—	2	2	no	—
327	C₄²×C₅₉	—	2	2	no	—
328	C₄²×C₅₉	—	2	2	no	—
329	C₄²×C₅₉	—	2	2	no	—
330	C₄²×C₅₉	—	2	2	no	—
331	C₄²×C₅₉	—	2	2	no	—
332	C₄²×C₅₉	—	4	1	no	—
333	C₄²×C₅₉	—	4	2	no	—
334	C₄²×C₅₉	—	4	2	no	—
335	C₄²×C₅₉	—	4	2	no	—
336	C₄²×C₅₉	—	4	2	no	—
337	C₄²×C₅₉	—	4	2	no	—
338	C₄²×C₅₉	C₂×Q₈	1	4	yes	—
339	C₄²×C₅₉	#41	1	4	yes	—
340	C₂³×C₅₉	—	2	2	no	—
341	C₂³×C₅₉	—	2	2	no	—
342	C₂³×C₅₉	—	2	2	no	—
343	C₂³×C₅₉	—	2	2	no	—
344	C₂³×C₅₉	—	2	2	no	—
345	C₂³×C₅₉	—	2	2	no	—
346	C₂³×C₅₉	C₂²×Q₈	1	4	yes	—
347	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
348	Q₈×C₅₉	—	4	4	no	—
349	Q₈×C₅₉	—	4	8	no	—
350	Q₈×C₅₉	—	8	4	no	—
351	D₄×C₅₉	—	2	8	no	—
352	C₂×C₄×C₅₉	—	2	1	no	—
353	C₂×C₄×C₅₉	—	2	1	no	—
354	C₂×C₄×C₅₉	—	2	1	no	—
355	C₂×C₄×C₅₉	—	2	1	no	—
356	C₂×C₄×C₅₉	—	2	1	no	—
357	C₂×C₄×C₅₉	—	2	1	no	—
358	C₂×C₄×C₅₉	—	2	1	no	—
359	C₂×C₄×C₅₉	—	2	2	no	—
360	C₂×C₄×C₅₉	—	2	2	no	—
361	C₂×C₄×C₅₉	—	2	2	no	—
362	C₂×C₄×C₅₉	—	2	1	no	—
363	C₂×C₄×C₅₉	—	2	1	no	—
364	C₂×C₄×C₅₉	—	2	1	no	—
365	C₂×C₄×C₅₉	—	2	1	no	—
366	C₂×C₄×C₅₉	—	2	2	no	—
367	C₂×C₄×C₅₉	—	2	1	no	—
368	C₂×C₄×C₅₉	—	2	1	no	—
369	C₂×C₄×C₅₉	—	2	1	no	—
370	C₂×C₄×C₅₉	—	2	1	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	2	no	—
378	C₂×C₄×C₅₉	—	2	2	no	—
379	C₂×C₄×C₅₉	—	2	2	no	—
380	C₂×C₄×C₅₉	—	2	2	no	—
381	C₂×C₄×C₅₉	—	2	2	no	—
382	C₂×C₄×C₅₉	—	2	1	no	—
383	C₂×C₄×C₅₉	—	2	2	no	—
384	C₂×C₄×C₅₉	—	2	2	no	—
385	C₂×C₄×C₅₉	—	2	2	no	—
386	C₂×C₄×C₅₉	—	2	2	no	—
387	C₂×C₄×C₅₉	—	2	2	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	1	no	—
392	C₂×C₄×C₅₉	—	2	2	no	—
393	C₂×C₄×C₅₉	—	2	1	no	—
394	C₂×C₄×C₅₉	—	2	1	no	—
395	C₂×C₄×C₅₉	—	2	1	no	—
396	C₂×C₄×C₅₉	—	2	1	no	—
397	C₂×C₄×C₅₉	—	2	2	no	—
398	C₂×C₄×C₅₉	—	2	1	no	—
399	C₂×C₄×C₅₉	—	2	1	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	1	no	—
404	C₂×C₄×C₅₉	—	2	2	no	—
405	C₂×C₄×C₅₉	—	2	1	no	—
406	C₂×C₄×C₅₉	—	4	8	no	—
407	C₂×C₄×C₅₉	—	8	4	no	—
408	C₂×C₄×C₅₉	—	8	4	no	—
409	C₂×C₄×C₅₉	C₂²×Q₈	1	2	yes	—
410	C₂×C₄×C₅₉	C₂²×Q₈	1	2	yes	—
411	C₂×C₄×C₅₉	C₂²×Q₈	1	4	yes	—
412	C₂×C₄×C₅₉	C₂²×Q₈	1	2	yes	—
413	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
414	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
415	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
416	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
417	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
418	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
419	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
420	C₂×C₄×C₅₉	2₋¹⁺⁴	1	2	yes	—
421	#35581	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
422	C₂²×C₅₉	—	2	4	no	—
423	C₂²×C₅₉	—	2	4	no	—
424	C₂²×C₅₉	—	2	4	no	—
425	C₂²×C₅₉	—	4	2	no	—
426	C₂²×C₅₉	—	4	2	no	—
427	C₂²×C₅₉	—	4	2	no	—
428	C₂²×C₅₉	—	4	2	no	—
429	C₂²×C₅₉	C₂³×Q₈	1	1	yes	characteristic
430	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
431	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
432	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
433	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
434	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
435	C₂²×C₅₉	#585	1	1	yes	characteristic
436	C₄×C₅₉	—	2	2	no	—
437	C₄×C₅₉	—	2	2	no	—
438	C₄×C₅₉	—	2	2	no	—
439	C₄×C₅₉	—	2	4	no	—
440	C₄×C₅₉	—	2	2	no	—
441	C₄×C₅₉	—	2	2	no	—
442	C₄×C₅₉	—	2	2	no	—
443	C₄×C₅₉	—	2	4	no	—
444	C₄×C₅₉	—	2	2	no	—
445	C₄×C₅₉	—	4	2	no	—
446	C₄×C₅₉	—	4	2	no	—
447	C₄×C₅₉	—	4	1	no	—
448	C₄×C₅₉	—	4	1	no	—
449	C₄×C₅₉	—	4	1	no	—
450	C₄×C₅₉	—	4	2	no	—
451	C₄×C₅₉	—	4	1	no	—
452	C₄×C₅₉	—	4	1	no	—
453	C₄×C₅₉	—	4	1	no	—
454	C₄×C₅₉	—	4	2	no	—
455	C₄×C₅₉	—	4	2	no	—
456	C₄×C₅₉	—	4	1	no	—
457	C₄×C₅₉	#533	1	4	yes	—
458	#2608	C₂×C₅₉	1	2	yes	complemented
459	#2587	C₂×C₅₉	1	2	yes	complemented
460	#2584	C₂×C₅₉	1	1	yes	characteristic, complemented
461	#2574	C₂×C₅₉	1	2	yes	complemented
462	#2566	C₂×C₅₉	1	1	yes	characteristic
463	#2551	C₂×C₅₉	1	1	yes	characteristic, complemented
464	#2549	C₂×C₅₉	1	2	yes	complemented
465	#2538	C₂×C₅₉	1	1	yes	characteristic
466	#2508	C₂×C₅₉	1	1	yes	characteristic, complemented
467	#2507	C₂×C₅₉	1	1	yes	characteristic, complemented
468	#2465	C₂×C₅₉	1	2	yes	complemented
469	#2452	C₂×C₅₉	1	1	yes	characteristic
470	#2452	C₂×C₅₉	1	1	yes	characteristic
471	#2439	C₂×C₅₉	1	2	yes	complemented
472	#2438	C₂×C₅₉	1	2	yes	complemented
473	#2429	C₂×C₅₉	1	2	yes	complemented
474	#2331	C₂×C₅₉	1	1	yes	characteristic, complemented
475	#2330	C₂×C₅₉	1	1	yes	characteristic, complemented
476	#2319	C₂×C₅₉	1	1	yes	characteristic
477	C₄×C₄⋊Q₈	C₂×C₅₉	1	1	yes	characteristic, complemented
478	#2295	C₂×C₅₉	1	1	yes	characteristic, complemented
479	#2293	C₂×C₅₉	1	1	yes	characteristic
480	#2275	C₂×C₅₉	1	1	yes	characteristic
481	C₂×C₅₉	—	4	4	no	—
482	C₂×C₅₉	C₂×#533	1	1	yes	characteristic
483	C₂×C₅₉	#3494	1	1	yes	characteristic
484	C₂×C₅₉	#3501	1	1	yes	characteristic
485	C₂×C₅₉	#3503	1	1	yes	characteristic
486	C₂×C₅₉	#3511	1	1	yes	characteristic
487	C₂×C₅₉	#3516	1	1	yes	characteristic
488	C₂×C₅₉	#3519	1	1	yes	characteristic
489	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
490	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
491	C₂×C₄⋊Q₈	C₂²×C₅₉	1	2	yes	—
492	C₂×#125	C₂²×C₅₉	1	1	yes	characteristic
493	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	—
494	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	—
495	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	—
496	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
497	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
498	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
499	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
500	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
501	C₂×#117	C₂²×C₅₉	1	2	yes	—
502	#400	C₂²×C₅₉	1	2	yes	—
503	#398	C₂²×C₅₉	1	2	yes	—
504	#398	C₂²×C₅₉	1	2	yes	—
505	#398	C₂²×C₅₉	1	2	yes	—
506	#398	C₂²×C₅₉	1	2	yes	—
507	#396	C₂²×C₅₉	1	2	yes	—
508	#396	C₂²×C₅₉	1	2	yes	—
509	#396	C₂²×C₅₉	1	2	yes	—
510	#396	C₂²×C₅₉	1	2	yes	—
511	#396	C₂²×C₅₉	1	2	yes	—
512	#396	C₂²×C₅₉	1	2	yes	—
513	#395	C₂²×C₅₉	1	2	yes	—
514	#395	C₂²×C₅₉	1	2	yes	—
515	#395	C₂²×C₅₉	1	2	yes	—
516	#393	C₂²×C₅₉	1	2	yes	—
517	#393	C₂²×C₅₉	1	2	yes	—
518	#391	C₂²×C₅₉	1	2	yes	—
519	#391	C₂²×C₅₉	1	2	yes	—
520	#391	C₂²×C₅₉	1	2	yes	—
521	#391	C₂²×C₅₉	1	1	yes	characteristic
522	#391	C₂²×C₅₉	1	1	yes	characteristic
523	#390	C₂²×C₅₉	1	1	yes	characteristic
524	#390	C₂²×C₅₉	1	1	yes	characteristic
525	#390	C₂²×C₅₉	1	1	yes	characteristic
526	#390	C₂²×C₅₉	1	1	yes	characteristic
527	#389	C₂²×C₅₉	1	1	yes	characteristic
528	#389	C₂²×C₅₉	1	2	yes	—
529	#389	C₂²×C₅₉	1	1	yes	characteristic
530	#389	C₂²×C₅₉	1	1	yes	characteristic
531	#389	C₂²×C₅₉	1	1	yes	characteristic
532	#389	C₂²×C₅₉	1	1	yes	characteristic
533	#389	C₂²×C₅₉	1	2	yes	—
534	#389	C₂²×C₅₉	1	2	yes	—
535	#389	C₂²×C₅₉	1	1	yes	characteristic
536	#389	C₂²×C₅₉	1	2	yes	—
537	#389	C₂²×C₅₉	1	2	yes	—
538	#389	C₂²×C₅₉	1	1	yes	characteristic
539	#389	C₂²×C₅₉	1	1	yes	characteristic
540	#389	C₂²×C₅₉	1	1	yes	characteristic
541	#389	C₂²×C₅₉	1	2	yes	—
542	#389	C₂²×C₅₉	1	1	yes	characteristic
543	#389	C₂²×C₅₉	1	1	yes	characteristic
544	#389	C₂²×C₅₉	1	2	yes	—
545	#389	C₂²×C₅₉	1	1	yes	characteristic
546	#388	C₂²×C₅₉	1	2	yes	—
547	#388	C₂²×C₅₉	1	2	yes	—
548	#388	C₂²×C₅₉	1	2	yes	—
549	#388	C₂²×C₅₉	1	2	yes	—
550	#387	C₂²×C₅₉	1	1	yes	characteristic
551	#387	C₂²×C₅₉	1	2	yes	—
552	#387	C₂²×C₅₉	1	2	yes	—
553	#387	C₂²×C₅₉	1	2	yes	—
554	#387	C₂²×C₅₉	1	2	yes	—
555	#387	C₂²×C₅₉	1	2	yes	—
556	#387	C₂²×C₅₉	1	1	yes	characteristic
557	#387	C₂²×C₅₉	1	2	yes	—
558	#387	C₂²×C₅₉	1	1	yes	characteristic
559	#387	C₂²×C₅₉	1	1	yes	characteristic
560	#385	C₂²×C₅₉	1	2	yes	—
561	#385	C₂²×C₅₉	1	2	yes	—
562	#385	C₂²×C₅₉	1	2	yes	—
563	#385	C₂²×C₅₉	1	2	yes	—
564	#384	C₂²×C₅₉	1	1	yes	characteristic
565	#384	C₂²×C₅₉	1	1	yes	characteristic
566	#382	C₂²×C₅₉	1	1	yes	characteristic
567	#382	C₂²×C₅₉	1	2	yes	—
568	#381	C₂²×C₅₉	1	2	yes	—
569	#380	C₂²×C₅₉	1	2	yes	—
570	#380	C₂²×C₅₉	1	2	yes	—
571	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
572	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
573	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
574	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
575	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
576	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
577	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
578	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
579	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
580	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
581	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
582	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
583	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
584	#376	C₂²×C₅₉	1	1	yes	characteristic
585	#376	C₂²×C₅₉	1	1	yes	characteristic
586	C₂×#95	C₂²×C₅₉	1	2	yes	—
587	C₄³	C₂²×C₅₉	1	1	yes	characteristic
588	C₅₉	#35581	1	1	yes	characteristic, direct product factor, Sylow
589	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
590	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
591	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
592	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
593	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
594	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
595	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
596	C₄⋊Q₈	—	2	4	no	—
597	C₄⋊Q₈	—	2	4	no	—
598	C₄⋊Q₈	—	4	4	no	—
599	#125	—	2	4	no	—
600	C₂²⋊Q₈	—	4	4	no	—
601	C₂²⋊Q₈	—	4	4	no	—
602	C₂²⋊Q₈	—	4	4	no	—
603	C₄×Q₈	—	2	4	no	—
604	C₄×Q₈	—	4	4	no	—
605	C₄×D₄	—	2	4	no	—
606	C₄×D₄	—	2	4	no	—
607	C₄×D₄	Q₈×C₅₉	1	8	yes	complemented
608	#117	—	4	4	no	—
609	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
627	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
629	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
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	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
643	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
654	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
655	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
656	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
657	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
658	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
659	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
660	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
661	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
662	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
663	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
664	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
665	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
666	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
667	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
668	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
669	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
670	#95	C₂³×C₅₉	1	1	yes	characteristic
671	#95	C₂³×C₅₉	1	2	yes	—
672	#95	C₂³×C₅₉	1	2	yes	—
673	#95	C₂³×C₅₉	1	2	yes	—
674	#95	C₂³×C₅₉	1	1	yes	characteristic
675	#95	C₂³×C₅₉	1	1	yes	characteristic
676	#95	C₂³×C₅₉	1	1	yes	characteristic
677	#95	C₂³×C₅₉	1	1	yes	characteristic
678	#95	C₂³×C₅₉	1	1	yes	characteristic
679	#95	C₂³×C₅₉	1	1	yes	characteristic
680	#95	C₂³×C₅₉	1	1	yes	characteristic
681	#95	C₂³×C₅₉	1	2	yes	—
682	#95	C₂³×C₅₉	1	2	yes	—
683	#95	C₂³×C₅₉	1	2	yes	—
684	#95	C₂³×C₅₉	1	2	yes	—
685	#95	C₂³×C₅₉	1	1	yes	characteristic
686	#95	C₂³×C₅₉	1	1	yes	characteristic
687	#95	C₂³×C₅₉	1	1	yes	characteristic
688	#95	C₂³×C₅₉	1	1	yes	characteristic
689	#95	C₂³×C₅₉	1	1	yes	characteristic
690	#95	C₂³×C₅₉	1	2	yes	—
691	#95	C₂³×C₅₉	1	2	yes	—
692	#95	C₂³×C₅₉	1	1	yes	characteristic
693	#95	C₂³×C₅₉	1	2	yes	—
694	#95	C₂³×C₅₉	1	2	yes	—
695	#95	C₂³×C₅₉	1	2	yes	—
696	#95	C₂³×C₅₉	1	2	yes	—
697	#95	C₂³×C₅₉	1	2	yes	—
698	#95	C₂³×C₅₉	1	2	yes	—
699	#95	C₂³×C₅₉	1	2	yes	—
700	#95	C₂³×C₅₉	1	2	yes	—
701	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
702	C₂×Q₈	—	2	2	no	—
703	C₂×Q₈	—	2	4	no	—
704	C₂×Q₈	—	2	4	no	—
705	C₂×Q₈	—	2	2	no	—
706	C₂×Q₈	—	2	4	no	—
707	C₂×Q₈	—	4	2	no	—
708	C₂×Q₈	—	4	1	no	—
709	C₂×Q₈	—	4	2	no	—
710	C₂×Q₈	—	4	2	no	—
711	C₂×D₄	—	2	2	no	—
712	C₂×D₄	—	2	2	no	—
713	C₂×D₄	C₂×Q₈×C₅₉	1	4	yes	—
714	C₂²×C₄	—	2	4	no	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	4	2	no	—
717	C₂²×C₄	—	4	2	no	—
718	C₂²×C₄	—	4	2	no	—
719	C₂²×C₄	—	4	2	no	—
720	C₂²×C₄	—	4	2	no	—
721	C₂²×C₄	—	4	2	no	—
722	C₂²×C₄	C₂×Q₈×C₅₉	1	8	yes	—
723	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
730	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
736	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
738	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
739	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
740	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
741	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
742	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
743	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
744	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	4	no	—
750	C₄⋊C₄	—	2	4	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	4	no	—
754	C₄⋊C₄	—	2	4	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	4	no	—
758	C₄⋊C₄	—	2	4	no	—
759	C₄⋊C₄	—	2	4	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	4	2	no	—
766	C₄⋊C₄	—	4	2	no	—
767	C₄⋊C₄	—	4	2	no	—
768	C₄⋊C₄	—	4	2	no	—
769	C₄⋊C₄	—	4	2	no	—
770	C₄⋊C₄	—	4	2	no	—
771	C₄⋊C₄	—	4	2	no	—
772	C₄⋊C₄	—	4	2	no	—
773	C₄⋊C₄	—	4	2	no	—
774	C₄⋊C₄	—	4	2	no	—
775	C₄⋊C₄	—	4	2	no	—
776	C₄⋊C₄	—	4	1	no	—
777	C₄⋊C₄	C₂×Q₈×C₅₉	1	4	yes	—
778	C₄⋊C₄	#41×C₅₉	1	4	yes	—
779	C₂²⋊C₄	—	2	4	no	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	2	4	no	—
783	C₂²⋊C₄	—	2	4	no	—
784	C₂²⋊C₄	—	4	2	no	—
785	C₂²⋊C₄	—	4	2	no	—
786	C₂²⋊C₄	—	4	2	no	—
787	C₂²⋊C₄	—	4	2	no	—
788	C₂²⋊C₄	—	4	2	no	—
789	C₂²⋊C₄	C₂×Q₈×C₅₉	1	8	yes	—
790	C₄²	—	2	2	no	—
791	C₄²	—	2	2	no	—
792	C₄²	—	2	2	no	—
793	C₄²	—	2	2	no	—
794	C₄²	—	2	2	no	—
795	C₄²	—	2	2	no	—
796	C₄²	—	2	2	no	—
797	C₄²	—	2	2	no	—
798	C₄²	—	4	2	no	—
799	C₄²	—	4	2	no	—
800	C₄²	—	4	2	no	—
801	C₄²	—	4	2	no	—
802	C₄²	—	4	1	no	—
803	C₄²	—	4	2	no	—
804	C₄²	C₂×Q₈×C₅₉	1	4	yes	—
805	C₄²	#41×C₅₉	1	4	yes	—
806	C₂³	—	2	2	no	—
807	C₂³	—	2	2	no	—
808	C₂³	—	2	2	no	—
809	C₂³	—	2	2	no	—
810	C₂³	—	2	2	no	—
811	C₂³	—	2	2	no	—
812	C₂³	C₂²×Q₈×C₅₉	1	4	yes	—
813	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
814	Q₈	—	4	8	no	—
815	Q₈	—	4	4	no	—
816	Q₈	—	8	4	no	—
817	D₄	—	2	8	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	2	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	2	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	4	8	no	—
873	C₂×C₄	—	8	4	no	—
874	C₂×C₄	—	8	4	no	—
875	C₂×C₄	C₂²×Q₈×C₅₉	1	2	yes	—
876	C₂×C₄	C₂²×Q₈×C₅₉	1	2	yes	—
877	C₂×C₄	C₂²×Q₈×C₅₉	1	4	yes	—
878	C₂×C₄	C₂²×Q₈×C₅₉	1	2	yes	—
879	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
880	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
881	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
882	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
883	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
884	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
885	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
886	C₂×C₄	2₋¹⁺⁴×C₅₉	1	2	yes	—
887	C₂²	—	2	4	no	—
888	C₂²	—	2	4	no	—
889	C₂²	—	2	4	no	—
890	C₂²	—	4	2	no	—
891	C₂²	—	4	2	no	—
892	C₂²	—	4	2	no	—
893	C₂²	—	4	2	no	—
894	C₂²	C₂³×Q₈×C₅₉	1	1	yes	characteristic
895	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
896	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
897	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
898	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
899	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
900	C₂²	C₅₉×#585	1	1	yes	characteristic
901	C₄	—	2	2	no	—
902	C₄	—	2	2	no	—
903	C₄	—	2	4	no	—
904	C₄	—	2	2	no	—
905	C₄	—	2	2	no	—
906	C₄	—	2	2	no	—
907	C₄	—	2	2	no	—
908	C₄	—	2	4	no	—
909	C₄	—	2	2	no	—
910	C₄	—	4	1	no	—
911	C₄	—	4	1	no	—
912	C₄	—	4	2	no	—
913	C₄	—	4	1	no	—
914	C₄	—	4	1	no	—
915	C₄	—	4	1	no	—
916	C₄	—	4	2	no	—
917	C₄	—	4	1	no	—
918	C₄	—	4	2	no	—
919	C₄	—	4	2	no	—
920	C₄	—	4	1	no	—
921	C₄	—	4	2	no	—
922	C₄	C₅₉×#533	1	4	yes	—
923	C₂	—	4	4	no	—
924	C₂	C₂×C₅₉×#533	1	1	yes	characteristic
925	C₂	C₅₉×#3494	1	1	yes	characteristic
926	C₂	C₅₉×#3501	1	1	yes	characteristic
927	C₂	C₅₉×#3503	1	1	yes	characteristic
928	C₂	C₅₉×#3511	1	1	yes	characteristic
929	C₂	C₅₉×#3516	1	1	yes	characteristic
930	C₂	C₅₉×#3519	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₂²×D₄×C₅₉	C₂³
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×#2608	C₂	semidirect
2. C₅₉×#2587	C₂	semidirect
3. C₅₉×#2584	C₂	semidirect
4. C₅₉×#2574	C₂	semidirect
6. C₅₉×#2551	C₂	semidirect
7. C₅₉×#2549	C₂	semidirect
9. C₅₉×#2508	C₂	semidirect
10. C₅₉×#2507	C₂	semidirect
11. C₅₉×#2465	C₂	semidirect
14. C₅₉×#2439	C₂	semidirect
15. C₅₉×#2438	C₂	semidirect
16. C₅₉×#2429	C₂	semidirect
17. C₅₉×#2331	C₂	semidirect
18. C₅₉×#2330	C₂	semidirect
20. C₄×C₄⋊Q₈×C₅₉	C₂	semidirect
21. C₅₉×#2295	C₂	semidirect
141. C₄×D₄×C₅₉	Q₈	semidirect
421. #35581	C₅₉	direct (N × H)
458. #2608	C₂×C₅₉	semidirect
459. #2587	C₂×C₅₉	semidirect
460. #2584	C₂×C₅₉	semidirect
461. #2574	C₂×C₅₉	semidirect
463. #2551	C₂×C₅₉	semidirect
464. #2549	C₂×C₅₉	semidirect
466. #2508	C₂×C₅₉	semidirect
467. #2507	C₂×C₅₉	semidirect
468. #2465	C₂×C₅₉	semidirect
471. #2439	C₂×C₅₉	semidirect
472. #2438	C₂×C₅₉	semidirect
473. #2429	C₂×C₅₉	semidirect
474. #2331	C₂×C₅₉	semidirect
475. #2330	C₂×C₅₉	semidirect
477. C₄×C₄⋊Q₈	C₂×C₅₉	semidirect
478. #2295	C₂×C₅₉	semidirect
588. C₅₉	#35581	direct (N × H)
607. C₄×D₄	Q₈×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₅₉×#2608	2
C₅₉×#2587	2
C₅₉×#2584	2
C₅₉×#2574	2
C₅₉×#2566	2
C₅₉×#2551	2
C₅₉×#2549	2
C₅₉×#2538	2
C₅₉×#2508	2
C₅₉×#2507	2
C₅₉×#2465	2
C₅₉×#2452	2
C₅₉×#2439	2
C₅₉×#2438	2
C₅₉×#2429	2
C₅₉×#2331	2
C₅₉×#2330	2
C₅₉×#2319	2
C₄×C₄⋊Q₈×C₅₉	2
C₅₉×#2295	2
C₅₉×#2293	2
C₅₉×#2275	2
#35581	59

Subgroups — C59×#35581 #28447690

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35581 #28447690