Subgroups — C₅₉×#35631 #28447740

Order 15104.

1636 conjugacy classes of subgroups.

The subgroup lattice has 936 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×#2573	C₂	1	2	yes	maximal, complemented
3	C₅₉×#2518	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2517	C₂	1	2	yes	maximal, complemented
5	C₅₉×#2516	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2514	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#2510	C₂	1	2	yes	maximal, complemented
8	C₅₉×#2509	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#2494	C₂	1	2	yes	maximal, complemented
10	C₅₉×#2494	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2493	C₂	1	2	yes	maximal, complemented
12	C₅₉×#2489	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₉×#2454	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₉×#2447	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#2427	C₂	1	1	yes	maximal, characteristic
16	C₅₉×#2420	C₂	1	1	yes	maximal, characteristic
17	C₅₉×#2324	C₂	1	1	yes	maximal, characteristic
18	C₅₉×#2323	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₉×#2320	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#125×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#124×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₉×#2298	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₉×#2275	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#125×C₅₉	C₂²	1	1	yes	characteristic
25	C₂×#124×C₅₉	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
27	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×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×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
32	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
33	C₅₉×#401	C₂²	1	2	yes	—
34	C₅₉×#401	C₂²	1	2	yes	—
35	C₅₉×#400	C₂²	1	2	yes	—
36	C₅₉×#400	C₂²	1	2	yes	—
37	C₅₉×#400	C₂²	1	2	yes	—
38	C₅₉×#400	C₂²	1	2	yes	—
39	C₅₉×#399	C₂²	1	2	yes	—
40	C₅₉×#397	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×#396	C₂²	1	2	yes	—
47	C₅₉×#394	C₂²	1	2	yes	—
48	C₅₉×#394	C₂²	1	2	yes	—
49	C₅₉×#391	C₂²	1	1	yes	characteristic
50	C₅₉×#391	C₂²	1	1	yes	characteristic
51	C₅₉×#391	C₂²	1	1	yes	characteristic
52	C₅₉×#391	C₂²	1	1	yes	characteristic
53	C₅₉×#390	C₂²	1	2	yes	—
54	C₅₉×#390	C₂²	1	1	yes	characteristic
55	C₅₉×#390	C₂²	1	1	yes	characteristic
56	C₅₉×#389	C₂²	1	2	yes	—
57	C₅₉×#389	C₂²	1	1	yes	characteristic
58	C₅₉×#389	C₂²	1	2	yes	—
59	C₅₉×#389	C₂²	1	1	yes	characteristic
60	C₅₉×#389	C₂²	1	1	yes	characteristic
61	C₅₉×#389	C₂²	1	1	yes	characteristic
62	C₅₉×#389	C₂²	1	1	yes	characteristic
63	C₅₉×#389	C₂²	1	1	yes	characteristic
64	C₅₉×#388	C₂²	1	2	yes	—
65	C₅₉×#388	C₂²	1	2	yes	—
66	C₅₉×#388	C₂²	1	2	yes	—
67	C₅₉×#388	C₂²	1	2	yes	—
68	C₅₉×#388	C₂²	1	1	yes	characteristic
69	C₅₉×#388	C₂²	1	2	yes	—
70	C₅₉×#388	C₂²	1	1	yes	characteristic
71	C₅₉×#388	C₂²	1	2	yes	—
72	C₅₉×#388	C₂²	1	1	yes	characteristic
73	C₅₉×#388	C₂²	1	1	yes	characteristic
74	C₅₉×#388	C₂²	1	2	yes	—
75	C₅₉×#387	C₂²	1	1	yes	characteristic
76	C₅₉×#387	C₂²	1	2	yes	—
77	C₅₉×#387	C₂²	1	2	yes	—
78	C₅₉×#387	C₂²	1	1	yes	characteristic
79	C₅₉×#387	C₂²	1	2	yes	—
80	C₅₉×#387	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	2	yes	—
85	C₅₉×#387	C₂²	1	1	yes	characteristic
86	C₅₉×#387	C₂²	1	1	yes	characteristic
87	C₅₉×#386	C₂²	1	2	yes	—
88	C₅₉×#386	C₂²	1	2	yes	—
89	C₅₉×#386	C₂²	1	2	yes	—
90	C₅₉×#385	C₂²	1	2	yes	—
91	C₅₉×#385	C₂²	1	2	yes	—
92	C₅₉×#385	C₂²	1	2	yes	—
93	C₅₉×#383	C₂²	1	2	yes	—
94	C₅₉×#383	C₂²	1	2	yes	—
95	C₅₉×#382	C₂²	1	2	yes	—
96	C₅₉×#382	C₂²	1	1	yes	characteristic
97	C₅₉×#382	C₂²	1	1	yes	characteristic
98	C₅₉×#382	C₂²	1	2	yes	—
99	C₅₉×#381	C₂²	1	2	yes	—
100	C₅₉×#381	C₂²	1	2	yes	—
101	C₅₉×#380	C₂²	1	1	yes	characteristic
102	C₅₉×#380	C₂²	1	2	yes	—
103	C₅₉×#380	C₂²	1	2	yes	—
104	C₅₉×#380	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₅₉	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	2	yes	—
112	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
113	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
114	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
115	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
116	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
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×D₄×C₅₉	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
126	C₂³×C₄×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	#125×C₅₉	—	2	4	no	—
131	#124×C₅₉	—	2	4	no	—
132	C₂²⋊Q₈×C₅₉	—	2	4	no	—
133	#121×C₅₉	—	2	4	no	—
134	C₄×Q₈×C₅₉	—	2	4	no	—
135	C₄×D₄×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	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
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	2	yes	—
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	2	yes	—
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	1	yes	characteristic
161	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
168	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
176	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
180	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
185	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
191	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
192	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
193	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
194	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
195	#95×C₅₉	C₂³	1	1	yes	characteristic
196	#95×C₅₉	C₂³	1	2	yes	—
197	#95×C₅₉	C₂³	1	2	yes	—
198	#95×C₅₉	C₂³	1	2	yes	—
199	#95×C₅₉	C₂³	1	1	yes	characteristic
200	#95×C₅₉	C₂³	1	1	yes	characteristic
201	#95×C₅₉	C₂³	1	1	yes	characteristic
202	#95×C₅₉	C₂³	1	1	yes	characteristic
203	#95×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	2	yes	—
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	2	yes	—
213	#95×C₅₉	C₂³	1	2	yes	—
214	#95×C₅₉	C₂³	1	2	yes	—
215	#95×C₅₉	C₂³	1	2	yes	—
216	#95×C₅₉	C₂³	1	1	yes	characteristic
217	#95×C₅₉	C₂³	1	2	yes	—
218	#95×C₅₉	C₂³	1	1	yes	characteristic
219	#95×C₅₉	C₂³	1	2	yes	—
220	#95×C₅₉	C₂³	1	2	yes	—
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	2	yes	—
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	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
232	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
233	C₂×Q₈×C₅₉	—	2	2	no	—
234	C₂×Q₈×C₅₉	—	2	2	no	—
235	C₂×Q₈×C₅₉	—	2	2	no	—
236	C₂×D₄×C₅₉	—	2	4	no	—
237	C₂×D₄×C₅₉	—	2	2	no	—
238	C₂×D₄×C₅₉	—	2	2	no	—
239	C₂×D₄×C₅₉	—	4	2	no	—
240	C₂×D₄×C₅₉	—	4	2	no	—
241	C₂×D₄×C₅₉	#41	1	4	yes	—
242	C₂²×C₄×C₅₉	—	2	4	no	—
243	C₂²×C₄×C₅₉	—	2	2	no	—
244	C₂²×C₄×C₅₉	—	2	2	no	—
245	C₂²×C₄×C₅₉	—	2	2	no	—
246	C₂²×C₄×C₅₉	—	2	4	no	—
247	C₂²×C₄×C₅₉	—	2	4	no	—
248	C₂²×C₄×C₅₉	—	4	2	no	—
249	C₂²×C₄×C₅₉	—	4	2	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	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
267	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
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	2	yes	—
273	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
275	C₄⋊C₄×C₅₉	—	2	2	no	—
276	C₄⋊C₄×C₅₉	—	2	2	no	—
277	C₄⋊C₄×C₅₉	—	2	2	no	—
278	C₄⋊C₄×C₅₉	—	2	2	no	—
279	C₄⋊C₄×C₅₉	—	2	2	no	—
280	C₄⋊C₄×C₅₉	—	2	4	no	—
281	C₄⋊C₄×C₅₉	—	2	2	no	—
282	C₄⋊C₄×C₅₉	—	2	4	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	—	4	2	no	—
287	C₄⋊C₄×C₅₉	—	4	2	no	—
288	C₄⋊C₄×C₅₉	—	4	1	no	—
289	C₄⋊C₄×C₅₉	—	4	1	no	—
290	C₄⋊C₄×C₅₉	—	4	2	no	—
291	C₄⋊C₄×C₅₉	—	4	1	no	—
292	C₄⋊C₄×C₅₉	—	4	1	no	—
293	C₄⋊C₄×C₅₉	—	4	2	no	—
294	C₄⋊C₄×C₅₉	—	4	2	no	—
295	C₄⋊C₄×C₅₉	—	4	2	no	—
296	C₄⋊C₄×C₅₉	#41	1	4	yes	—
297	C₂²⋊C₄×C₅₉	—	2	4	no	—
298	C₂²⋊C₄×C₅₉	—	2	4	no	—
299	C₂²⋊C₄×C₅₉	—	2	4	no	—
300	C₂²⋊C₄×C₅₉	—	2	4	no	—
301	C₂²⋊C₄×C₅₉	—	2	2	no	—
302	C₂²⋊C₄×C₅₉	—	2	2	no	—
303	C₂²⋊C₄×C₅₉	—	2	4	no	—
304	C₂²⋊C₄×C₅₉	—	2	4	no	—
305	C₂²⋊C₄×C₅₉	—	2	4	no	—
306	C₂²⋊C₄×C₅₉	—	4	1	no	—
307	C₂²⋊C₄×C₅₉	—	4	2	no	—
308	C₂²⋊C₄×C₅₉	—	4	2	no	—
309	C₂²⋊C₄×C₅₉	—	4	2	no	—
310	C₂²⋊C₄×C₅₉	—	4	1	no	—
311	C₂²⋊C₄×C₅₉	—	4	1	no	—
312	C₂²⋊C₄×C₅₉	—	4	1	no	—
313	C₂²⋊C₄×C₅₉	—	4	2	no	—
314	C₂²⋊C₄×C₅₉	—	4	2	no	—
315	C₂²⋊C₄×C₅₉	—	4	2	no	—
316	C₄²×C₅₉	—	2	2	no	—
317	C₄²×C₅₉	—	2	2	no	—
318	C₄²×C₅₉	—	2	2	no	—
319	C₄²×C₅₉	—	2	4	no	—
320	C₄²×C₅₉	—	2	2	no	—
321	C₄²×C₅₉	—	2	2	no	—
322	C₄²×C₅₉	—	4	2	no	—
323	C₄²×C₅₉	—	4	1	no	—
324	C₄²×C₅₉	—	4	1	no	—
325	C₄²×C₅₉	—	4	2	no	—
326	C₄²×C₅₉	—	4	2	no	—
327	C₄²×C₅₉	—	4	1	no	—
328	C₄²×C₅₉	—	4	1	no	—
329	C₄²×C₅₉	—	4	2	no	—
330	C₄²×C₅₉	#41	1	4	yes	—
331	C₂³×C₅₉	—	2	2	no	—
332	C₂³×C₅₉	—	2	2	no	—
333	C₂³×C₅₉	—	2	2	no	—
334	C₂³×C₅₉	—	2	2	no	—
335	C₂³×C₅₉	—	2	2	no	—
336	C₂³×C₅₉	—	2	2	no	—
337	C₂³×C₅₉	—	2	1	no	—
338	C₂³×C₅₉	—	2	1	no	—
339	C₂³×C₅₉	—	2	1	no	—
340	C₂³×C₅₉	—	2	1	no	—
341	C₂³×C₅₉	—	2	1	no	—
342	C₂³×C₅₉	—	2	1	no	—
343	C₂³×C₅₉	—	2	1	no	—
344	C₂³×C₅₉	C₂×#41	1	4	yes	—
345	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
346	Q₈×C₅₉	—	4	4	no	—
347	D₄×C₅₉	—	2	8	no	—
348	D₄×C₅₉	—	8	4	no	—
349	C₂×C₄×C₅₉	—	2	1	no	—
350	C₂×C₄×C₅₉	—	2	1	no	—
351	C₂×C₄×C₅₉	—	2	2	no	—
352	C₂×C₄×C₅₉	—	2	2	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	1	no	—
360	C₂×C₄×C₅₉	—	2	1	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	2	no	—
365	C₂×C₄×C₅₉	—	2	1	no	—
366	C₂×C₄×C₅₉	—	2	1	no	—
367	C₂×C₄×C₅₉	—	2	1	no	—
368	C₂×C₄×C₅₉	—	2	2	no	—
369	C₂×C₄×C₅₉	—	2	2	no	—
370	C₂×C₄×C₅₉	—	2	2	no	—
371	C₂×C₄×C₅₉	—	2	2	no	—
372	C₂×C₄×C₅₉	—	2	2	no	—
373	C₂×C₄×C₅₉	—	2	2	no	—
374	C₂×C₄×C₅₉	—	2	1	no	—
375	C₂×C₄×C₅₉	—	2	1	no	—
376	C₂×C₄×C₅₉	—	2	1	no	—
377	C₂×C₄×C₅₉	—	2	1	no	—
378	C₂×C₄×C₅₉	—	2	1	no	—
379	C₂×C₄×C₅₉	—	2	1	no	—
380	C₂×C₄×C₅₉	—	2	1	no	—
381	C₂×C₄×C₅₉	—	2	1	no	—
382	C₂×C₄×C₅₉	—	2	1	no	—
383	C₂×C₄×C₅₉	—	2	1	no	—
384	C₂×C₄×C₅₉	—	2	2	no	—
385	C₂×C₄×C₅₉	—	2	2	no	—
386	C₂×C₄×C₅₉	—	2	2	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	2	no	—
391	C₂×C₄×C₅₉	—	2	2	no	—
392	C₂×C₄×C₅₉	—	2	1	no	—
393	C₂×C₄×C₅₉	—	2	2	no	—
394	C₂×C₄×C₅₉	—	2	1	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	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	1	no	—
403	C₂×C₄×C₅₉	—	2	2	no	—
404	C₂×C₄×C₅₉	—	2	1	no	—
405	C₂×C₄×C₅₉	—	2	1	no	—
406	C₂×C₄×C₅₉	—	4	4	no	—
407	C₂×C₄×C₅₉	—	8	4	no	—
408	C₂×C₄×C₅₉	—	8	4	no	—
409	C₂×C₄×C₅₉	—	8	4	no	—
410	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
411	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
412	C₂×C₄×C₅₉	C₂×#41	1	4	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	2	yes	—
416	#35631	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
417	C₂²×C₅₉	—	2	4	no	—
418	C₂²×C₅₉	—	2	4	no	—
419	C₂²×C₅₉	—	2	4	no	—
420	C₂²×C₅₉	—	4	2	no	—
421	C₂²×C₅₉	—	4	2	no	—
422	C₂²×C₅₉	—	4	2	no	—
423	C₂²×C₅₉	—	4	2	no	—
424	C₂²×C₅₉	—	4	1	no	—
425	C₂²×C₅₉	—	4	1	no	—
426	C₂²×C₅₉	—	4	1	no	—
427	C₂²×C₅₉	—	4	1	no	—
428	C₂²×C₅₉	—	4	1	no	—
429	C₂²×C₅₉	—	4	1	no	—
430	C₂²×C₅₉	—	4	1	no	—
431	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
432	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
433	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
434	C₂²×C₅₉	#585	1	1	yes	characteristic
435	C₂²×C₅₉	#585	1	1	yes	characteristic
436	C₂²×C₅₉	#585	1	1	yes	characteristic
437	C₂²×C₅₉	#585	1	1	yes	characteristic
438	C₄×C₅₉	—	2	2	no	—
439	C₄×C₅₉	—	2	2	no	—
440	C₄×C₅₉	—	2	4	no	—
441	C₄×C₅₉	—	4	1	no	—
442	C₄×C₅₉	—	4	2	no	—
443	C₄×C₅₉	—	4	1	no	—
444	C₄×C₅₉	—	4	2	no	—
445	C₄×C₅₉	—	4	1	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	1	no	—
451	C₄×C₅₉	—	4	2	no	—
452	C₄×C₅₉	—	4	1	no	—
453	C₄×C₅₉	—	4	1	no	—
454	C₄×C₅₉	—	4	2	no	—
455	C₄×C₅₉	—	4	1	no	—
456	C₄×C₅₉	—	4	1	no	—
457	C₄×C₅₉	—	4	2	no	—
458	C₄×C₅₉	#529	1	4	yes	—
459	#2597	C₂×C₅₉	1	2	yes	complemented
460	#2573	C₂×C₅₉	1	2	yes	complemented
461	#2518	C₂×C₅₉	1	2	yes	complemented
462	#2517	C₂×C₅₉	1	2	yes	complemented
463	#2516	C₂×C₅₉	1	2	yes	complemented
464	#2514	C₂×C₅₉	1	1	yes	characteristic, complemented
465	#2510	C₂×C₅₉	1	2	yes	complemented
466	#2509	C₂×C₅₉	1	1	yes	characteristic, complemented
467	#2494	C₂×C₅₉	1	2	yes	complemented
468	#2494	C₂×C₅₉	1	1	yes	characteristic, complemented
469	#2493	C₂×C₅₉	1	2	yes	complemented
470	#2489	C₂×C₅₉	1	1	yes	characteristic, complemented
471	#2454	C₂×C₅₉	1	1	yes	characteristic, complemented
472	#2447	C₂×C₅₉	1	1	yes	characteristic, complemented
473	#2427	C₂×C₅₉	1	1	yes	characteristic
474	#2420	C₂×C₅₉	1	1	yes	characteristic
475	#2324	C₂×C₅₉	1	1	yes	characteristic
476	#2323	C₂×C₅₉	1	1	yes	characteristic, complemented
477	#2320	C₂×C₅₉	1	1	yes	characteristic, complemented
478	C₄×#125	C₂×C₅₉	1	1	yes	characteristic, complemented
479	C₄×#124	C₂×C₅₉	1	1	yes	characteristic, complemented
480	#2298	C₂×C₅₉	1	1	yes	characteristic, complemented
481	#2275	C₂×C₅₉	1	1	yes	characteristic, complemented
482	C₂×C₅₉	—	4	4	no	—
483	C₂×C₅₉	—	8	1	no	—
484	C₂×C₅₉	C₂×#529	1	1	yes	characteristic
485	C₂×C₅₉	#3510	1	1	yes	characteristic
486	C₂×C₅₉	#3512	1	1	yes	characteristic
487	C₂×C₅₉	#3521	1	1	yes	characteristic
488	C₂×C₅₉	#3521	1	1	yes	characteristic
489	C₂×C₅₉	#3521	1	1	yes	characteristic
490	C₂×C₅₉	#3524	1	1	yes	characteristic
491	C₂×#125	C₂²×C₅₉	1	1	yes	characteristic
492	C₂×#124	C₂²×C₅₉	1	1	yes	characteristic
493	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
494	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
495	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
496	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
497	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
498	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
499	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
500	#401	C₂²×C₅₉	1	2	yes	—
501	#401	C₂²×C₅₉	1	2	yes	—
502	#400	C₂²×C₅₉	1	2	yes	—
503	#400	C₂²×C₅₉	1	2	yes	—
504	#400	C₂²×C₅₉	1	2	yes	—
505	#400	C₂²×C₅₉	1	2	yes	—
506	#399	C₂²×C₅₉	1	2	yes	—
507	#397	C₂²×C₅₉	1	2	yes	—
508	#397	C₂²×C₅₉	1	2	yes	—
509	#397	C₂²×C₅₉	1	2	yes	—
510	#397	C₂²×C₅₉	1	2	yes	—
511	#397	C₂²×C₅₉	1	2	yes	—
512	#397	C₂²×C₅₉	1	2	yes	—
513	#396	C₂²×C₅₉	1	2	yes	—
514	#394	C₂²×C₅₉	1	2	yes	—
515	#394	C₂²×C₅₉	1	2	yes	—
516	#391	C₂²×C₅₉	1	1	yes	characteristic
517	#391	C₂²×C₅₉	1	1	yes	characteristic
518	#391	C₂²×C₅₉	1	1	yes	characteristic
519	#391	C₂²×C₅₉	1	1	yes	characteristic
520	#390	C₂²×C₅₉	1	2	yes	—
521	#390	C₂²×C₅₉	1	1	yes	characteristic
522	#390	C₂²×C₅₉	1	1	yes	characteristic
523	#389	C₂²×C₅₉	1	1	yes	characteristic
524	#389	C₂²×C₅₉	1	1	yes	characteristic
525	#389	C₂²×C₅₉	1	2	yes	—
526	#389	C₂²×C₅₉	1	1	yes	characteristic
527	#389	C₂²×C₅₉	1	1	yes	characteristic
528	#389	C₂²×C₅₉	1	1	yes	characteristic
529	#389	C₂²×C₅₉	1	1	yes	characteristic
530	#389	C₂²×C₅₉	1	2	yes	—
531	#388	C₂²×C₅₉	1	2	yes	—
532	#388	C₂²×C₅₉	1	2	yes	—
533	#388	C₂²×C₅₉	1	2	yes	—
534	#388	C₂²×C₅₉	1	2	yes	—
535	#388	C₂²×C₅₉	1	1	yes	characteristic
536	#388	C₂²×C₅₉	1	2	yes	—
537	#388	C₂²×C₅₉	1	2	yes	—
538	#388	C₂²×C₅₉	1	2	yes	—
539	#388	C₂²×C₅₉	1	1	yes	characteristic
540	#388	C₂²×C₅₉	1	1	yes	characteristic
541	#388	C₂²×C₅₉	1	1	yes	characteristic
542	#387	C₂²×C₅₉	1	2	yes	—
543	#387	C₂²×C₅₉	1	2	yes	—
544	#387	C₂²×C₅₉	1	1	yes	characteristic
545	#387	C₂²×C₅₉	1	2	yes	—
546	#387	C₂²×C₅₉	1	2	yes	—
547	#387	C₂²×C₅₉	1	2	yes	—
548	#387	C₂²×C₅₉	1	2	yes	—
549	#387	C₂²×C₅₉	1	2	yes	—
550	#387	C₂²×C₅₉	1	1	yes	characteristic
551	#387	C₂²×C₅₉	1	1	yes	characteristic
552	#387	C₂²×C₅₉	1	2	yes	—
553	#387	C₂²×C₅₉	1	1	yes	characteristic
554	#386	C₂²×C₅₉	1	2	yes	—
555	#386	C₂²×C₅₉	1	2	yes	—
556	#386	C₂²×C₅₉	1	2	yes	—
557	#385	C₂²×C₅₉	1	2	yes	—
558	#385	C₂²×C₅₉	1	2	yes	—
559	#385	C₂²×C₅₉	1	2	yes	—
560	#383	C₂²×C₅₉	1	2	yes	—
561	#383	C₂²×C₅₉	1	2	yes	—
562	#382	C₂²×C₅₉	1	1	yes	characteristic
563	#382	C₂²×C₅₉	1	2	yes	—
564	#382	C₂²×C₅₉	1	2	yes	—
565	#382	C₂²×C₅₉	1	1	yes	characteristic
566	#381	C₂²×C₅₉	1	2	yes	—
567	#381	C₂²×C₅₉	1	2	yes	—
568	#380	C₂²×C₅₉	1	1	yes	characteristic
569	#380	C₂²×C₅₉	1	1	yes	characteristic
570	#380	C₂²×C₅₉	1	2	yes	—
571	#380	C₂²×C₅₉	1	2	yes	—
572	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
583	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
584	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
585	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
586	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
587	#376	C₂²×C₅₉	1	1	yes	characteristic
588	C₂×#95	C₂²×C₅₉	1	2	yes	—
589	C₄³	C₂²×C₅₉	1	1	yes	characteristic
590	C₅₉	#35631	1	1	yes	characteristic, direct product factor, Sylow
591	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
592	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
593	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
594	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
595	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
596	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
597	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
598	#125	—	2	4	no	—
599	#124	—	2	4	no	—
600	C₂²⋊Q₈	—	2	4	no	—
601	#121	—	2	4	no	—
602	C₄×Q₈	—	2	4	no	—
603	C₄×D₄	—	2	4	no	—
604	C₄×D₄	—	2	4	no	—
605	C₄×D₄	—	2	4	no	—
606	#117	—	2	4	no	—
607	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
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	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
628	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
629	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
630	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
631	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
641	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
642	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
643	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
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×C₄²	C₂³×C₅₉	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
650	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
652	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
653	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
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	2	yes	—
659	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
660	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
661	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
662	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
663	#95	C₂³×C₅₉	1	1	yes	characteristic
664	#95	C₂³×C₅₉	1	2	yes	—
665	#95	C₂³×C₅₉	1	2	yes	—
666	#95	C₂³×C₅₉	1	2	yes	—
667	#95	C₂³×C₅₉	1	1	yes	characteristic
668	#95	C₂³×C₅₉	1	1	yes	characteristic
669	#95	C₂³×C₅₉	1	1	yes	characteristic
670	#95	C₂³×C₅₉	1	1	yes	characteristic
671	#95	C₂³×C₅₉	1	1	yes	characteristic
672	#95	C₂³×C₅₉	1	1	yes	characteristic
673	#95	C₂³×C₅₉	1	2	yes	—
674	#95	C₂³×C₅₉	1	2	yes	—
675	#95	C₂³×C₅₉	1	2	yes	—
676	#95	C₂³×C₅₉	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
685	#95	C₂³×C₅₉	1	2	yes	—
686	#95	C₂³×C₅₉	1	1	yes	characteristic
687	#95	C₂³×C₅₉	1	2	yes	—
688	#95	C₂³×C₅₉	1	2	yes	—
689	#95	C₂³×C₅₉	1	2	yes	—
690	#95	C₂³×C₅₉	1	2	yes	—
691	#95	C₂³×C₅₉	1	2	yes	—
692	#95	C₂³×C₅₉	1	2	yes	—
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	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
700	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
701	C₂×Q₈	—	2	2	no	—
702	C₂×Q₈	—	2	2	no	—
703	C₂×Q₈	—	2	2	no	—
704	C₂×D₄	—	2	4	no	—
705	C₂×D₄	—	2	2	no	—
706	C₂×D₄	—	2	2	no	—
707	C₂×D₄	—	4	2	no	—
708	C₂×D₄	—	4	2	no	—
709	C₂×D₄	#41×C₅₉	1	4	yes	—
710	C₂²×C₄	—	2	4	no	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	2	no	—
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	C₂⁴×C₅₉	1	1	yes	characteristic
723	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
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	1	yes	characteristic
733	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
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	2	yes	—
739	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
740	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
741	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
742	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	4	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	4	no	—
751	C₄⋊C₄	—	2	4	no	—
752	C₄⋊C₄	—	2	4	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	4	2	no	—
755	C₄⋊C₄	—	4	2	no	—
756	C₄⋊C₄	—	4	1	no	—
757	C₄⋊C₄	—	4	1	no	—
758	C₄⋊C₄	—	4	2	no	—
759	C₄⋊C₄	—	4	1	no	—
760	C₄⋊C₄	—	4	1	no	—
761	C₄⋊C₄	—	4	2	no	—
762	C₄⋊C₄	—	4	2	no	—
763	C₄⋊C₄	—	4	2	no	—
764	C₄⋊C₄	#41×C₅₉	1	4	yes	—
765	C₂²⋊C₄	—	2	4	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	2	4	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	—	2	4	no	—
774	C₂²⋊C₄	—	4	1	no	—
775	C₂²⋊C₄	—	4	2	no	—
776	C₂²⋊C₄	—	4	2	no	—
777	C₂²⋊C₄	—	4	2	no	—
778	C₂²⋊C₄	—	4	1	no	—
779	C₂²⋊C₄	—	4	1	no	—
780	C₂²⋊C₄	—	4	1	no	—
781	C₂²⋊C₄	—	4	2	no	—
782	C₂²⋊C₄	—	4	2	no	—
783	C₂²⋊C₄	—	4	2	no	—
784	C₄²	—	2	2	no	—
785	C₄²	—	2	2	no	—
786	C₄²	—	2	2	no	—
787	C₄²	—	2	4	no	—
788	C₄²	—	2	2	no	—
789	C₄²	—	2	2	no	—
790	C₄²	—	4	2	no	—
791	C₄²	—	4	1	no	—
792	C₄²	—	4	1	no	—
793	C₄²	—	4	2	no	—
794	C₄²	—	4	2	no	—
795	C₄²	—	4	1	no	—
796	C₄²	—	4	1	no	—
797	C₄²	—	4	2	no	—
798	C₄²	#41×C₅₉	1	4	yes	—
799	C₂³	—	2	2	no	—
800	C₂³	—	2	2	no	—
801	C₂³	—	2	2	no	—
802	C₂³	—	2	2	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	1	no	—
806	C₂³	—	2	1	no	—
807	C₂³	—	2	1	no	—
808	C₂³	—	2	1	no	—
809	C₂³	—	2	1	no	—
810	C₂³	—	2	1	no	—
811	C₂³	—	2	1	no	—
812	C₂³	C₂×#41×C₅₉	1	4	yes	—
813	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
814	Q₈	—	4	4	no	—
815	D₄	—	2	8	no	—
816	D₄	—	8	4	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	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	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	2	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	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	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	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	4	4	no	—
875	C₂×C₄	—	8	4	no	—
876	C₂×C₄	—	8	4	no	—
877	C₂×C₄	—	8	4	no	—
878	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
879	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
880	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
881	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
882	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
883	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
884	C₂²	—	2	4	no	—
885	C₂²	—	2	4	no	—
886	C₂²	—	2	4	no	—
887	C₂²	—	4	2	no	—
888	C₂²	—	4	2	no	—
889	C₂²	—	4	2	no	—
890	C₂²	—	4	2	no	—
891	C₂²	—	4	1	no	—
892	C₂²	—	4	1	no	—
893	C₂²	—	4	1	no	—
894	C₂²	—	4	1	no	—
895	C₂²	—	4	1	no	—
896	C₂²	—	4	1	no	—
897	C₂²	—	4	1	no	—
898	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
899	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
900	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
901	C₂²	C₅₉×#585	1	1	yes	characteristic
902	C₂²	C₅₉×#585	1	1	yes	characteristic
903	C₂²	C₅₉×#585	1	1	yes	characteristic
904	C₂²	C₅₉×#585	1	1	yes	characteristic
905	C₄	—	2	2	no	—
906	C₄	—	2	2	no	—
907	C₄	—	2	4	no	—
908	C₄	—	4	2	no	—
909	C₄	—	4	1	no	—
910	C₄	—	4	1	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	1	no	—
913	C₄	—	4	1	no	—
914	C₄	—	4	2	no	—
915	C₄	—	4	2	no	—
916	C₄	—	4	1	no	—
917	C₄	—	4	1	no	—
918	C₄	—	4	1	no	—
919	C₄	—	4	1	no	—
920	C₄	—	4	1	no	—
921	C₄	—	4	1	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	1	no	—
924	C₄	—	4	2	no	—
925	C₄	C₅₉×#529	1	4	yes	—
926	C₂	—	4	4	no	—
927	C₂	—	8	1	no	—
928	C₂	C₂×C₅₉×#529	1	1	yes	characteristic
929	C₂	C₅₉×#3510	1	1	yes	characteristic
930	C₂	C₅₉×#3512	1	1	yes	characteristic
931	C₂	C₅₉×#3521	1	1	yes	characteristic
932	C₂	C₅₉×#3521	1	1	yes	characteristic
933	C₂	C₅₉×#3521	1	1	yes	characteristic
934	C₂	C₅₉×#3524	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₂×#121×C₅₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₉×#2597	C₂	semidirect
2. C₅₉×#2573	C₂	semidirect
3. C₅₉×#2518	C₂	semidirect
4. C₅₉×#2517	C₂	semidirect
5. C₅₉×#2516	C₂	semidirect
6. C₅₉×#2514	C₂	semidirect
7. C₅₉×#2510	C₂	semidirect
8. C₅₉×#2509	C₂	semidirect
9. C₅₉×#2494	C₂	semidirect
10. C₅₉×#2494	C₂	semidirect
11. C₅₉×#2493	C₂	semidirect
12. C₅₉×#2489	C₂	semidirect
13. C₅₉×#2454	C₂	semidirect
14. C₅₉×#2447	C₂	semidirect
18. C₅₉×#2323	C₂	semidirect
19. C₅₉×#2320	C₂	semidirect
20. C₄×#125×C₅₉	C₂	semidirect
21. C₄×#124×C₅₉	C₂	semidirect
22. C₅₉×#2298	C₂	semidirect
23. C₅₉×#2275	C₂	semidirect
416. #35631	C₅₉	direct (N × H)
459. #2597	C₂×C₅₉	semidirect
460. #2573	C₂×C₅₉	semidirect
461. #2518	C₂×C₅₉	semidirect
462. #2517	C₂×C₅₉	semidirect
463. #2516	C₂×C₅₉	semidirect
464. #2514	C₂×C₅₉	semidirect
465. #2510	C₂×C₅₉	semidirect
466. #2509	C₂×C₅₉	semidirect
467. #2494	C₂×C₅₉	semidirect
468. #2494	C₂×C₅₉	semidirect
469. #2493	C₂×C₅₉	semidirect
470. #2489	C₂×C₅₉	semidirect
471. #2454	C₂×C₅₉	semidirect
472. #2447	C₂×C₅₉	semidirect
476. #2323	C₂×C₅₉	semidirect
477. #2320	C₂×C₅₉	semidirect
478. C₄×#125	C₂×C₅₉	semidirect
479. C₄×#124	C₂×C₅₉	semidirect
480. #2298	C₂×C₅₉	semidirect
481. #2275	C₂×C₅₉	semidirect
590. C₅₉	#35631	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×#2573	2
C₅₉×#2518	2
C₅₉×#2517	2
C₅₉×#2516	2
C₅₉×#2514	2
C₅₉×#2510	2
C₅₉×#2509	2
C₅₉×#2494	2
C₅₉×#2493	2
C₅₉×#2489	2
C₅₉×#2454	2
C₅₉×#2447	2
C₅₉×#2427	2
C₅₉×#2420	2
C₅₉×#2324	2
C₅₉×#2323	2
C₅₉×#2320	2
C₄×#125×C₅₉	2
C₄×#124×C₅₉	2
C₅₉×#2298	2
C₅₉×#2275	2
#35631	59

Subgroups — C59×#35631 #28447740

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35631 #28447740