Subgroups — C₅₉×#35544 #28447653

Order 15104.

1882 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#2497	C₂	1	2	yes	maximal, complemented
2	C₅₉×#2497	C₂	1	2	yes	maximal, complemented
3	C₅₉×#2496	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2496	C₂	1	2	yes	maximal, complemented
5	C₅₉×#2495	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2495	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2494	C₂	1	2	yes	maximal, complemented
8	C₅₉×#2494	C₂	1	2	yes	maximal, complemented
9	C₅₉×#2493	C₂	1	4	yes	maximal, complemented
10	C₅₉×#2480	C₂	1	4	yes	maximal
11	C₅₉×#2317	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#2317	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₉×#2316	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₉×#2280	C₂	1	1	yes	maximal, characteristic
15	C₅₉×#2280	C₂	1	1	yes	maximal, characteristic
16	C₂×C₅₉×#380	C₂	1	1	yes	maximal, characteristic
17	C₅₉×#2274	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂⁴×C₄×C₅₉	C₂²	1	1	yes	characteristic
19	C₂×#126×C₅₉	C₂²	1	4	yes	—
20	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
22	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
23	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
27	C₅₉×#401	C₂²	1	4	yes	complemented
28	C₅₉×#400	C₂²	1	4	yes	complemented
29	C₅₉×#400	C₂²	1	4	yes	complemented
30	C₅₉×#400	C₂²	1	4	yes	complemented
31	C₅₉×#397	C₂²	1	4	yes	—
32	C₅₉×#397	C₂²	1	4	yes	—
33	C₅₉×#397	C₂²	1	4	yes	—
34	C₅₉×#396	C₂²	1	4	yes	—
35	C₅₉×#389	C₂²	1	2	yes	complemented
36	C₅₉×#389	C₂²	1	2	yes	complemented
37	C₅₉×#389	C₂²	1	2	yes	complemented
38	C₅₉×#389	C₂²	1	2	yes	complemented
39	C₅₉×#389	C₂²	1	2	yes	complemented
40	C₅₉×#389	C₂²	1	2	yes	complemented
41	C₅₉×#389	C₂²	1	2	yes	complemented
42	C₅₉×#389	C₂²	1	2	yes	complemented
43	C₅₉×#388	C₂²	1	4	yes	—
44	C₅₉×#388	C₂²	1	4	yes	—
45	C₅₉×#388	C₂²	1	4	yes	—
46	C₅₉×#387	C₂²	1	4	yes	complemented
47	C₅₉×#387	C₂²	1	4	yes	complemented
48	C₅₉×#387	C₂²	1	4	yes	complemented
49	C₅₉×#385	C₂²	1	4	yes	—
50	C₅₉×#385	C₂²	1	4	yes	—
51	C₅₉×#384	C₂²	1	2	yes	complemented
52	C₅₉×#384	C₂²	1	2	yes	complemented
53	C₅₉×#383	C₂²	1	4	yes	complemented
54	C₅₉×#382	C₂²	1	2	yes	complemented
55	C₅₉×#382	C₂²	1	2	yes	complemented
56	C₅₉×#381	C₂²	1	2	yes	—
57	C₅₉×#381	C₂²	1	2	yes	—
58	C₅₉×#380	C₂²	1	4	yes	—
59	C₅₉×#380	C₂²	1	1	yes	characteristic
60	C₅₉×#380	C₂²	1	1	yes	characteristic
61	C₅₉×#380	C₂²	1	2	yes	—
62	C₅₉×#380	C₂²	1	2	yes	—
63	C₅₉×#380	C₂²	1	1	yes	characteristic
64	C₅₉×#380	C₂²	1	1	yes	characteristic
65	C₅₉×#380	C₂²	1	2	yes	—
66	C₅₉×#380	C₂²	1	2	yes	—
67	C₅₉×#380	C₂²	1	1	yes	characteristic
68	C₅₉×#380	C₂²	1	1	yes	characteristic
69	C₅₉×#380	C₂²	1	1	yes	characteristic
70	C₅₉×#380	C₂²	1	1	yes	characteristic
71	C₅₉×#379	C₂²	1	2	yes	—
72	C₅₉×#379	C₂²	1	2	yes	—
73	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
74	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
75	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
76	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
77	C₄×C₂²⋊C₄×C₅₉	C₂²	1	4	yes	—
78	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
79	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
80	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
81	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
82	C₂×#95×C₅₉	C₂²	1	2	yes	—
83	C₂⁵×C₅₉	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₅₉	—	2	4	no	—
85	C₂³×C₄×C₅₉	—	2	4	no	—
86	C₂³×C₄×C₅₉	—	2	4	no	—
87	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
93	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
94	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
95	#126×C₅₉	—	4	8	no	—
96	#117×C₅₉	—	2	4	no	—
97	#117×C₅₉	—	2	4	no	—
98	#117×C₅₉	—	2	4	no	—
99	#117×C₅₉	—	2	4	no	—
100	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
101	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
102	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
118	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
120	C₂×C₂²⋊C₄×C₅₉	—	4	4	no	—
121	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
122	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
125	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
127	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
131	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
132	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
133	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
135	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
136	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
137	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
138	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
139	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
140	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
141	#95×C₅₉	C₂³	1	4	yes	—
142	#95×C₅₉	C₂³	1	4	yes	—
143	#95×C₅₉	C₂³	1	4	yes	—
144	#95×C₅₉	C₂³	1	4	yes	—
145	#95×C₅₉	C₂³	1	2	yes	—
146	#95×C₅₉	C₂³	1	2	yes	—
147	#95×C₅₉	C₂³	1	2	yes	—
148	#95×C₅₉	C₂³	1	2	yes	—
149	#95×C₅₉	C₂³	1	2	yes	—
150	#95×C₅₉	C₂³	1	2	yes	—
151	#95×C₅₉	C₂³	1	2	yes	—
152	#95×C₅₉	C₂³	1	2	yes	—
153	#95×C₅₉	C₂³	1	4	yes	—
154	#95×C₅₉	C₂³	1	4	yes	—
155	#95×C₅₉	C₂³	1	4	yes	—
156	#95×C₅₉	C₂³	1	4	yes	—
157	#95×C₅₉	C₂³	1	4	yes	—
158	#95×C₅₉	C₂³	1	4	yes	—
159	C₂⁴×C₅₉	—	2	2	no	—
160	C₂⁴×C₅₉	—	2	2	no	—
161	C₂⁴×C₅₉	—	2	2	no	—
162	C₂⁴×C₅₉	—	2	2	no	—
163	C₂⁴×C₅₉	—	2	2	no	—
164	C₂⁴×C₅₉	—	4	1	no	—
165	C₂⁴×C₅₉	—	4	1	no	—
166	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
167	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
168	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
169	C₂²×C₄×C₅₉	—	2	2	no	—
170	C₂²×C₄×C₅₉	—	2	2	no	—
171	C₂²×C₄×C₅₉	—	2	2	no	—
172	C₂²×C₄×C₅₉	—	2	4	no	—
173	C₂²×C₄×C₅₉	—	2	4	no	—
174	C₂²×C₄×C₅₉	—	2	2	no	—
175	C₂²×C₄×C₅₉	—	2	2	no	—
176	C₂²×C₄×C₅₉	—	2	2	no	—
177	C₂²×C₄×C₅₉	—	2	2	no	—
178	C₂²×C₄×C₅₉	—	2	2	no	—
179	C₂²×C₄×C₅₉	—	2	2	no	—
180	C₂²×C₄×C₅₉	—	2	2	no	—
181	C₂²×C₄×C₅₉	—	2	2	no	—
182	C₂²×C₄×C₅₉	—	2	2	no	—
183	C₂²×C₄×C₅₉	—	2	2	no	—
184	C₂²×C₄×C₅₉	—	2	2	no	—
185	C₂²×C₄×C₅₉	—	2	2	no	—
186	C₂²×C₄×C₅₉	—	4	2	no	—
187	C₂²×C₄×C₅₉	—	4	2	no	—
188	C₂²×C₄×C₅₉	—	4	2	no	—
189	C₂²×C₄×C₅₉	—	4	2	no	—
190	C₂²×C₄×C₅₉	—	4	16	no	—
191	C₂²×C₄×C₅₉	#41	1	4	yes	—
192	C₂²×C₄×C₅₉	#41	1	4	yes	—
193	C₂²×C₄×C₅₉	#41	1	4	yes	—
194	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
195	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
201	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
204	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
207	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
208	C₄⋊C₄×C₅₉	—	2	4	no	—
209	C₄⋊C₄×C₅₉	—	2	4	no	—
210	C₄⋊C₄×C₅₉	—	2	4	no	—
211	C₄⋊C₄×C₅₉	—	2	4	no	—
212	C₄⋊C₄×C₅₉	—	2	2	no	—
213	C₄⋊C₄×C₅₉	—	2	2	no	—
214	C₄⋊C₄×C₅₉	—	2	2	no	—
215	C₄⋊C₄×C₅₉	—	2	2	no	—
216	C₄⋊C₄×C₅₉	—	2	2	no	—
217	C₄⋊C₄×C₅₉	—	2	2	no	—
218	C₄⋊C₄×C₅₉	—	2	2	no	—
219	C₄⋊C₄×C₅₉	—	2	2	no	—
220	C₄⋊C₄×C₅₉	—	4	4	no	—
221	C₄⋊C₄×C₅₉	—	4	4	no	—
222	C₄⋊C₄×C₅₉	—	4	4	no	—
223	C₄⋊C₄×C₅₉	—	4	4	no	—
224	C₄⋊C₄×C₅₉	—	4	4	no	—
225	C₄⋊C₄×C₅₉	—	4	4	no	—
226	C₂²⋊C₄×C₅₉	—	2	4	no	—
227	C₂²⋊C₄×C₅₉	—	2	4	no	—
228	C₂²⋊C₄×C₅₉	—	2	4	no	—
229	C₂²⋊C₄×C₅₉	—	2	4	no	—
230	C₂²⋊C₄×C₅₉	—	2	8	no	—
231	C₂²⋊C₄×C₅₉	—	2	4	no	—
232	C₂²⋊C₄×C₅₉	—	2	4	no	—
233	C₂²⋊C₄×C₅₉	—	2	4	no	—
234	C₂²⋊C₄×C₅₉	—	2	4	no	—
235	C₂²⋊C₄×C₅₉	—	4	4	no	—
236	C₂²⋊C₄×C₅₉	—	4	2	no	—
237	C₂²⋊C₄×C₅₉	—	4	2	no	—
238	C₂²⋊C₄×C₅₉	—	4	2	no	—
239	C₂²⋊C₄×C₅₉	—	4	2	no	—
240	C₄²×C₅₉	—	2	4	no	—
241	C₄²×C₅₉	—	2	4	no	—
242	C₄²×C₅₉	—	2	4	no	—
243	C₄²×C₅₉	—	2	4	no	—
244	C₄²×C₅₉	—	4	4	no	—
245	C₄²×C₅₉	—	4	4	no	—
246	C₂³×C₅₉	—	2	1	no	—
247	C₂³×C₅₉	—	2	1	no	—
248	C₂³×C₅₉	—	2	1	no	—
249	C₂³×C₅₉	—	2	1	no	—
250	C₂³×C₅₉	—	2	8	no	—
251	C₂³×C₅₉	—	2	1	no	—
252	C₂³×C₅₉	—	2	1	no	—
253	C₂³×C₅₉	—	2	1	no	—
254	C₂³×C₅₉	—	2	1	no	—
255	C₂³×C₅₉	—	2	1	no	—
256	C₂³×C₅₉	—	2	1	no	—
257	C₂³×C₅₉	—	2	1	no	—
258	C₂³×C₅₉	—	2	1	no	—
259	C₂³×C₅₉	—	2	1	no	—
260	C₂³×C₅₉	—	2	1	no	—
261	C₂³×C₅₉	—	2	1	no	—
262	C₂³×C₅₉	—	2	1	no	—
263	C₂³×C₅₉	—	4	4	no	—
264	C₂³×C₅₉	—	4	4	no	—
265	C₂³×C₅₉	—	4	4	no	—
266	C₂³×C₅₉	—	4	4	no	—
267	C₂³×C₅₉	—	4	4	no	—
268	C₂³×C₅₉	—	4	4	no	—
269	C₂³×C₅₉	C₂×#41	1	2	yes	—
270	C₂³×C₅₉	C₂×#41	1	2	yes	—
271	C₂³×C₅₉	C₂×#41	1	2	yes	—
272	C₂³×C₅₉	H(5,𝔽₂)	1	2	yes	—
273	C₂³×C₅₉	2₋¹⁺⁴	1	2	yes	—
274	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
275	C₂×C₄×C₅₉	—	2	2	no	—
276	C₂×C₄×C₅₉	—	2	2	no	—
277	C₂×C₄×C₅₉	—	2	2	no	—
278	C₂×C₄×C₅₉	—	2	2	no	—
279	C₂×C₄×C₅₉	—	2	2	no	—
280	C₂×C₄×C₅₉	—	2	2	no	—
281	C₂×C₄×C₅₉	—	2	2	no	—
282	C₂×C₄×C₅₉	—	2	2	no	—
283	C₂×C₄×C₅₉	—	2	4	no	—
284	C₂×C₄×C₅₉	—	2	4	no	—
285	C₂×C₄×C₅₉	—	2	1	no	—
286	C₂×C₄×C₅₉	—	2	1	no	—
287	C₂×C₄×C₅₉	—	2	1	no	—
288	C₂×C₄×C₅₉	—	2	1	no	—
289	C₂×C₄×C₅₉	—	2	1	no	—
290	C₂×C₄×C₅₉	—	2	1	no	—
291	C₂×C₄×C₅₉	—	2	2	no	—
292	C₂×C₄×C₅₉	—	2	2	no	—
293	C₂×C₄×C₅₉	—	2	4	no	—
294	C₂×C₄×C₅₉	—	2	4	no	—
295	C₂×C₄×C₅₉	—	2	2	no	—
296	C₂×C₄×C₅₉	—	2	2	no	—
297	C₂×C₄×C₅₉	—	2	2	no	—
298	C₂×C₄×C₅₉	—	2	2	no	—
299	C₂×C₄×C₅₉	—	2	2	no	—
300	C₂×C₄×C₅₉	—	2	2	no	—
301	C₂×C₄×C₅₉	—	2	2	no	—
302	C₂×C₄×C₅₉	—	2	2	no	—
303	C₂×C₄×C₅₉	—	2	4	no	—
304	C₂×C₄×C₅₉	—	2	2	no	—
305	C₂×C₄×C₅₉	—	2	2	no	—
306	C₂×C₄×C₅₉	—	2	2	no	—
307	C₂×C₄×C₅₉	—	2	2	no	—
308	C₂×C₄×C₅₉	—	2	2	no	—
309	C₂×C₄×C₅₉	—	2	2	no	—
310	C₂×C₄×C₅₉	—	2	4	no	—
311	C₂×C₄×C₅₉	—	4	4	no	—
312	C₂×C₄×C₅₉	—	4	4	no	—
313	C₂×C₄×C₅₉	—	4	4	no	—
314	C₂×C₄×C₅₉	—	4	4	no	—
315	C₂×C₄×C₅₉	—	4	4	no	—
316	C₂×C₄×C₅₉	—	8	4	no	—
317	C₂×C₄×C₅₉	—	8	4	no	—
318	C₂×C₄×C₅₉	#126	1	16	yes	complemented
319	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
320	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
321	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
322	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
323	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
324	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
325	#35544	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
326	C₂²×C₅₉	—	2	2	no	—
327	C₂²×C₅₉	—	2	2	no	—
328	C₂²×C₅₉	—	2	2	no	—
329	C₂²×C₅₉	—	2	2	no	—
330	C₂²×C₅₉	—	2	2	no	—
331	C₂²×C₅₉	—	2	2	no	—
332	C₂²×C₅₉	—	2	2	no	—
333	C₂²×C₅₉	—	2	2	no	—
334	C₂²×C₅₉	—	2	2	no	—
335	C₂²×C₅₉	—	2	2	no	—
336	C₂²×C₅₉	—	2	2	no	—
337	C₂²×C₅₉	—	2	2	no	—
338	C₂²×C₅₉	—	4	16	no	—
339	C₂²×C₅₉	—	4	1	no	—
340	C₂²×C₅₉	—	4	1	no	—
341	C₂²×C₅₉	—	4	1	no	—
342	C₂²×C₅₉	—	4	1	no	—
343	C₂²×C₅₉	—	4	1	no	—
344	C₂²×C₅₉	—	4	1	no	—
345	C₂²×C₅₉	—	4	1	no	—
346	C₂²×C₅₉	—	4	1	no	—
347	C₂²×C₅₉	C₂×#126	1	4	yes	—
348	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
349	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
350	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
351	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
352	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
353	C₂²×C₅₉	#585	1	1	yes	characteristic
354	C₂²×C₅₉	#585	1	1	yes	characteristic
355	C₄×C₅₉	—	4	1	no	—
356	C₄×C₅₉	—	4	1	no	—
357	C₄×C₅₉	—	4	2	no	—
358	C₄×C₅₉	—	4	2	no	—
359	C₄×C₅₉	—	4	2	no	—
360	C₄×C₅₉	—	4	2	no	—
361	C₄×C₅₉	—	4	2	no	—
362	C₄×C₅₉	—	4	2	no	—
363	C₄×C₅₉	—	4	4	no	—
364	C₄×C₅₉	—	4	4	no	—
365	C₄×C₅₉	—	4	2	no	—
366	C₄×C₅₉	—	4	2	no	—
367	C₄×C₅₉	C₂×#126	1	4	yes	—
368	C₄×C₅₉	C₂×#126	1	4	yes	—
369	#2497	C₂×C₅₉	1	2	yes	complemented
370	#2497	C₂×C₅₉	1	2	yes	complemented
371	#2496	C₂×C₅₉	1	2	yes	complemented
372	#2496	C₂×C₅₉	1	2	yes	complemented
373	#2495	C₂×C₅₉	1	2	yes	complemented
374	#2495	C₂×C₅₉	1	2	yes	complemented
375	#2494	C₂×C₅₉	1	2	yes	complemented
376	#2494	C₂×C₅₉	1	2	yes	complemented
377	#2493	C₂×C₅₉	1	4	yes	complemented
378	#2480	C₂×C₅₉	1	4	yes	—
379	#2317	C₂×C₅₉	1	1	yes	characteristic, complemented
380	#2317	C₂×C₅₉	1	1	yes	characteristic, complemented
381	#2316	C₂×C₅₉	1	1	yes	characteristic, complemented
382	#2280	C₂×C₅₉	1	1	yes	characteristic
383	#2280	C₂×C₅₉	1	1	yes	characteristic
384	C₂×#380	C₂×C₅₉	1	1	yes	characteristic
385	#2274	C₂×C₅₉	1	1	yes	characteristic, complemented
386	C₂×C₅₉	—	2	4	no	—
387	C₂×C₅₉	—	4	2	no	—
388	C₂×C₅₉	—	4	2	no	—
389	C₂×C₅₉	C₂²×#126	1	1	yes	characteristic
390	C₂×C₅₉	#3492	1	1	yes	characteristic
391	C₂×C₅₉	#3493	1	1	yes	characteristic
392	C₂×C₅₉	#3494	1	1	yes	characteristic
393	C₂×C₅₉	#3494	1	1	yes	characteristic
394	C₂×C₅₉	#3495	1	1	yes	characteristic
395	C₂×C₅₉	#3495	1	1	yes	characteristic
396	C₂⁴×C₄	C₂²×C₅₉	1	1	yes	characteristic
397	C₂×#126	C₂²×C₅₉	1	4	yes	—
398	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
399	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
400	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
401	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
402	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
403	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
404	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
405	#401	C₂²×C₅₉	1	4	yes	complemented
406	#400	C₂²×C₅₉	1	4	yes	complemented
407	#400	C₂²×C₅₉	1	4	yes	complemented
408	#400	C₂²×C₅₉	1	4	yes	complemented
409	#397	C₂²×C₅₉	1	4	yes	—
410	#397	C₂²×C₅₉	1	4	yes	—
411	#397	C₂²×C₅₉	1	4	yes	—
412	#396	C₂²×C₅₉	1	4	yes	—
413	#389	C₂²×C₅₉	1	2	yes	complemented
414	#389	C₂²×C₅₉	1	2	yes	complemented
415	#389	C₂²×C₅₉	1	2	yes	complemented
416	#389	C₂²×C₅₉	1	2	yes	complemented
417	#389	C₂²×C₅₉	1	2	yes	complemented
418	#389	C₂²×C₅₉	1	2	yes	complemented
419	#389	C₂²×C₅₉	1	2	yes	complemented
420	#389	C₂²×C₅₉	1	2	yes	complemented
421	#388	C₂²×C₅₉	1	4	yes	—
422	#388	C₂²×C₅₉	1	4	yes	—
423	#388	C₂²×C₅₉	1	4	yes	—
424	#387	C₂²×C₅₉	1	4	yes	complemented
425	#387	C₂²×C₅₉	1	4	yes	complemented
426	#387	C₂²×C₅₉	1	4	yes	complemented
427	#385	C₂²×C₅₉	1	4	yes	—
428	#385	C₂²×C₅₉	1	4	yes	—
429	#384	C₂²×C₅₉	1	2	yes	complemented
430	#384	C₂²×C₅₉	1	2	yes	complemented
431	#383	C₂²×C₅₉	1	4	yes	complemented
432	#382	C₂²×C₅₉	1	2	yes	complemented
433	#382	C₂²×C₅₉	1	2	yes	complemented
434	#381	C₂²×C₅₉	1	2	yes	—
435	#381	C₂²×C₅₉	1	2	yes	—
436	#380	C₂²×C₅₉	1	4	yes	—
437	#380	C₂²×C₅₉	1	1	yes	characteristic
438	#380	C₂²×C₅₉	1	1	yes	characteristic
439	#380	C₂²×C₅₉	1	2	yes	—
440	#380	C₂²×C₅₉	1	2	yes	—
441	#380	C₂²×C₅₉	1	1	yes	characteristic
442	#380	C₂²×C₅₉	1	1	yes	characteristic
443	#380	C₂²×C₅₉	1	2	yes	—
444	#380	C₂²×C₅₉	1	2	yes	—
445	#380	C₂²×C₅₉	1	1	yes	characteristic
446	#380	C₂²×C₅₉	1	1	yes	characteristic
447	#380	C₂²×C₅₉	1	1	yes	characteristic
448	#380	C₂²×C₅₉	1	1	yes	characteristic
449	#379	C₂²×C₅₉	1	2	yes	—
450	#379	C₂²×C₅₉	1	2	yes	—
451	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
452	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
453	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
454	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
455	C₄×C₂²⋊C₄	C₂²×C₅₉	1	4	yes	—
456	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
457	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
458	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
459	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
460	C₂×#95	C₂²×C₅₉	1	2	yes	—
461	C₅₉	#35544	1	1	yes	characteristic, direct product factor, Sylow
462	C₂⁵	C₂³×C₅₉	1	1	yes	characteristic
463	C₂³×C₄	—	2	4	no	—
464	C₂³×C₄	—	2	4	no	—
465	C₂³×C₄	—	2	4	no	—
466	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
467	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
468	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
469	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
470	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
471	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
472	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
473	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
474	#126	—	4	8	no	—
475	#117	—	2	4	no	—
476	#117	—	2	4	no	—
477	#117	—	2	4	no	—
478	#117	—	2	4	no	—
479	C₂×C₄⋊C₄	—	2	4	no	—
480	C₂×C₄⋊C₄	—	2	4	no	—
481	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
482	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
483	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
484	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
485	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
486	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
487	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
489	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
490	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
491	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
493	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
494	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
495	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
496	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
497	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
498	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
499	C₂×C₂²⋊C₄	—	4	4	no	—
500	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
501	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
514	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
515	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
516	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
517	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
518	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
519	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
520	#95	C₂³×C₅₉	1	4	yes	—
521	#95	C₂³×C₅₉	1	4	yes	—
522	#95	C₂³×C₅₉	1	4	yes	—
523	#95	C₂³×C₅₉	1	4	yes	—
524	#95	C₂³×C₅₉	1	2	yes	—
525	#95	C₂³×C₅₉	1	2	yes	—
526	#95	C₂³×C₅₉	1	2	yes	—
527	#95	C₂³×C₅₉	1	2	yes	—
528	#95	C₂³×C₅₉	1	2	yes	—
529	#95	C₂³×C₅₉	1	2	yes	—
530	#95	C₂³×C₅₉	1	2	yes	—
531	#95	C₂³×C₅₉	1	2	yes	—
532	#95	C₂³×C₅₉	1	4	yes	—
533	#95	C₂³×C₅₉	1	4	yes	—
534	#95	C₂³×C₅₉	1	4	yes	—
535	#95	C₂³×C₅₉	1	4	yes	—
536	#95	C₂³×C₅₉	1	4	yes	—
537	#95	C₂³×C₅₉	1	4	yes	—
538	C₂⁴	—	2	2	no	—
539	C₂⁴	—	2	2	no	—
540	C₂⁴	—	2	2	no	—
541	C₂⁴	—	2	2	no	—
542	C₂⁴	—	2	2	no	—
543	C₂⁴	—	4	1	no	—
544	C₂⁴	—	4	1	no	—
545	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
546	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
547	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	4	no	—
552	C₂²×C₄	—	2	4	no	—
553	C₂²×C₄	—	2	2	no	—
554	C₂²×C₄	—	2	2	no	—
555	C₂²×C₄	—	2	2	no	—
556	C₂²×C₄	—	2	2	no	—
557	C₂²×C₄	—	2	2	no	—
558	C₂²×C₄	—	2	2	no	—
559	C₂²×C₄	—	2	2	no	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	—	2	2	no	—
565	C₂²×C₄	—	4	2	no	—
566	C₂²×C₄	—	4	2	no	—
567	C₂²×C₄	—	4	2	no	—
568	C₂²×C₄	—	4	2	no	—
569	C₂²×C₄	—	4	16	no	—
570	C₂²×C₄	#41×C₅₉	1	4	yes	—
571	C₂²×C₄	#41×C₅₉	1	4	yes	—
572	C₂²×C₄	#41×C₅₉	1	4	yes	—
573	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
574	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
575	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
576	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
577	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
578	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
579	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
580	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
581	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
582	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
583	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
584	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
586	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
587	C₄⋊C₄	—	2	4	no	—
588	C₄⋊C₄	—	2	4	no	—
589	C₄⋊C₄	—	2	4	no	—
590	C₄⋊C₄	—	2	4	no	—
591	C₄⋊C₄	—	2	2	no	—
592	C₄⋊C₄	—	2	2	no	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	2	2	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	—	4	4	no	—
600	C₄⋊C₄	—	4	4	no	—
601	C₄⋊C₄	—	4	4	no	—
602	C₄⋊C₄	—	4	4	no	—
603	C₄⋊C₄	—	4	4	no	—
604	C₄⋊C₄	—	4	4	no	—
605	C₂²⋊C₄	—	2	4	no	—
606	C₂²⋊C₄	—	2	4	no	—
607	C₂²⋊C₄	—	2	4	no	—
608	C₂²⋊C₄	—	2	4	no	—
609	C₂²⋊C₄	—	2	8	no	—
610	C₂²⋊C₄	—	2	4	no	—
611	C₂²⋊C₄	—	2	4	no	—
612	C₂²⋊C₄	—	2	4	no	—
613	C₂²⋊C₄	—	2	4	no	—
614	C₂²⋊C₄	—	4	4	no	—
615	C₂²⋊C₄	—	4	2	no	—
616	C₂²⋊C₄	—	4	2	no	—
617	C₂²⋊C₄	—	4	2	no	—
618	C₂²⋊C₄	—	4	2	no	—
619	C₄²	—	2	4	no	—
620	C₄²	—	2	4	no	—
621	C₄²	—	2	4	no	—
622	C₄²	—	2	4	no	—
623	C₄²	—	4	4	no	—
624	C₄²	—	4	4	no	—
625	C₂³	—	2	1	no	—
626	C₂³	—	2	1	no	—
627	C₂³	—	2	1	no	—
628	C₂³	—	2	1	no	—
629	C₂³	—	2	8	no	—
630	C₂³	—	2	1	no	—
631	C₂³	—	2	1	no	—
632	C₂³	—	2	1	no	—
633	C₂³	—	2	1	no	—
634	C₂³	—	2	1	no	—
635	C₂³	—	2	1	no	—
636	C₂³	—	2	1	no	—
637	C₂³	—	2	1	no	—
638	C₂³	—	2	1	no	—
639	C₂³	—	2	1	no	—
640	C₂³	—	2	1	no	—
641	C₂³	—	2	1	no	—
642	C₂³	—	4	4	no	—
643	C₂³	—	4	4	no	—
644	C₂³	—	4	4	no	—
645	C₂³	—	4	4	no	—
646	C₂³	—	4	4	no	—
647	C₂³	—	4	4	no	—
648	C₂³	C₂×#41×C₅₉	1	2	yes	—
649	C₂³	C₂×#41×C₅₉	1	2	yes	—
650	C₂³	C₂×#41×C₅₉	1	2	yes	—
651	C₂³	H(5,𝔽₂)×C₅₉	1	2	yes	—
652	C₂³	2₋¹⁺⁴×C₅₉	1	2	yes	—
653	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	4	no	—
663	C₂×C₄	—	2	4	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	4	no	—
673	C₂×C₄	—	2	4	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	4	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	4	no	—
690	C₂×C₄	—	4	4	no	—
691	C₂×C₄	—	4	4	no	—
692	C₂×C₄	—	4	4	no	—
693	C₂×C₄	—	4	4	no	—
694	C₂×C₄	—	4	4	no	—
695	C₂×C₄	—	8	4	no	—
696	C₂×C₄	—	8	4	no	—
697	C₂×C₄	#126×C₅₉	1	16	yes	complemented
698	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
699	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
700	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
701	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
702	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
703	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
704	C₂²	—	2	2	no	—
705	C₂²	—	2	2	no	—
706	C₂²	—	2	2	no	—
707	C₂²	—	2	2	no	—
708	C₂²	—	2	2	no	—
709	C₂²	—	2	2	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	2	2	no	—
712	C₂²	—	2	2	no	—
713	C₂²	—	2	2	no	—
714	C₂²	—	2	2	no	—
715	C₂²	—	2	2	no	—
716	C₂²	—	4	16	no	—
717	C₂²	—	4	1	no	—
718	C₂²	—	4	1	no	—
719	C₂²	—	4	1	no	—
720	C₂²	—	4	1	no	—
721	C₂²	—	4	1	no	—
722	C₂²	—	4	1	no	—
723	C₂²	—	4	1	no	—
724	C₂²	—	4	1	no	—
725	C₂²	C₂×#126×C₅₉	1	4	yes	—
726	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
727	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
728	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
729	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
730	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
731	C₂²	C₅₉×#585	1	1	yes	characteristic
732	C₂²	C₅₉×#585	1	1	yes	characteristic
733	C₄	—	4	1	no	—
734	C₄	—	4	1	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	2	no	—
738	C₄	—	4	2	no	—
739	C₄	—	4	4	no	—
740	C₄	—	4	4	no	—
741	C₄	—	4	2	no	—
742	C₄	—	4	2	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	2	no	—
745	C₄	C₂×#126×C₅₉	1	4	yes	—
746	C₄	C₂×#126×C₅₉	1	4	yes	—
747	C₂	—	2	4	no	—
748	C₂	—	4	2	no	—
749	C₂	—	4	2	no	—
750	C₂	C₂²×#126×C₅₉	1	1	yes	characteristic
751	C₂	C₅₉×#3492	1	1	yes	characteristic
752	C₂	C₅₉×#3493	1	1	yes	characteristic
753	C₂	C₅₉×#3494	1	1	yes	characteristic
754	C₂	C₅₉×#3494	1	1	yes	characteristic
755	C₂	C₅₉×#3495	1	1	yes	characteristic
756	C₂	C₅₉×#3495	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₂⁵×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×#2497	C₂	semidirect
2. C₅₉×#2497	C₂	semidirect
3. C₅₉×#2496	C₂	semidirect
4. C₅₉×#2496	C₂	semidirect
5. C₅₉×#2495	C₂	semidirect
6. C₅₉×#2495	C₂	semidirect
7. C₅₉×#2494	C₂	semidirect
8. C₅₉×#2494	C₂	semidirect
9. C₅₉×#2493	C₂	semidirect
11. C₅₉×#2317	C₂	semidirect
12. C₅₉×#2317	C₂	semidirect
13. C₅₉×#2316	C₂	semidirect
17. C₅₉×#2274	C₂	semidirect
27. C₅₉×#401	C₂²	semidirect
28. C₅₉×#400	C₂²	semidirect
29. C₅₉×#400	C₂²	semidirect
30. C₅₉×#400	C₂²	semidirect
35. C₅₉×#389	C₂²	semidirect
36. C₅₉×#389	C₂²	semidirect
37. C₅₉×#389	C₂²	semidirect
38. C₅₉×#389	C₂²	semidirect
39. C₅₉×#389	C₂²	semidirect
40. C₅₉×#389	C₂²	semidirect
41. C₅₉×#389	C₂²	semidirect
42. C₅₉×#389	C₂²	semidirect
46. C₅₉×#387	C₂²	semidirect
47. C₅₉×#387	C₂²	semidirect
48. C₅₉×#387	C₂²	semidirect
51. C₅₉×#384	C₂²	semidirect
52. C₅₉×#384	C₂²	semidirect
53. C₅₉×#383	C₂²	semidirect
54. C₅₉×#382	C₂²	semidirect
55. C₅₉×#382	C₂²	semidirect
73. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
74. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
75. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
76. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
318. C₂×C₄×C₅₉	#126	semidirect
325. #35544	C₅₉	direct (N × H)
369. #2497	C₂×C₅₉	semidirect
370. #2497	C₂×C₅₉	semidirect
371. #2496	C₂×C₅₉	semidirect
372. #2496	C₂×C₅₉	semidirect
373. #2495	C₂×C₅₉	semidirect
374. #2495	C₂×C₅₉	semidirect
375. #2494	C₂×C₅₉	semidirect
376. #2494	C₂×C₅₉	semidirect
377. #2493	C₂×C₅₉	semidirect
379. #2317	C₂×C₅₉	semidirect
380. #2317	C₂×C₅₉	semidirect
381. #2316	C₂×C₅₉	semidirect
385. #2274	C₂×C₅₉	semidirect
405. #401	C₂²×C₅₉	semidirect
406. #400	C₂²×C₅₉	semidirect
407. #400	C₂²×C₅₉	semidirect
408. #400	C₂²×C₅₉	semidirect
413. #389	C₂²×C₅₉	semidirect
414. #389	C₂²×C₅₉	semidirect
415. #389	C₂²×C₅₉	semidirect
416. #389	C₂²×C₅₉	semidirect
417. #389	C₂²×C₅₉	semidirect
418. #389	C₂²×C₅₉	semidirect
419. #389	C₂²×C₅₉	semidirect
420. #389	C₂²×C₅₉	semidirect
424. #387	C₂²×C₅₉	semidirect
425. #387	C₂²×C₅₉	semidirect
426. #387	C₂²×C₅₉	semidirect
429. #384	C₂²×C₅₉	semidirect
430. #384	C₂²×C₅₉	semidirect
431. #383	C₂²×C₅₉	semidirect
432. #382	C₂²×C₅₉	semidirect
433. #382	C₂²×C₅₉	semidirect
451. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
452. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
453. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
454. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
461. C₅₉	#35544	direct (N × H)
697. C₂×C₄	#126×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₅₉×#2497	2
C₅₉×#2496	2
C₅₉×#2495	2
C₅₉×#2494	2
C₅₉×#2493	2
C₅₉×#2480	2
C₅₉×#2317	2
C₅₉×#2316	2
C₅₉×#2280	2
C₂×C₅₉×#380	2
C₅₉×#2274	2
#35544	59

Subgroups — C59×#35544 #28447653

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35544 #28447653