Subgroups — C₅₉×#35488 #28447597

Order 15104.

1666 conjugacy classes of subgroups.

The subgroup lattice has 806 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	1	yes	maximal, characteristic, complemented
2	C₅₉×#2589	C₂	1	2	yes	maximal, complemented
3	C₅₉×#2577	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2573	C₂	1	2	yes	maximal, complemented
5	C₅₉×#2561	C₂	1	1	yes	maximal, characteristic
6	C₅₉×#2530	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2523	C₂	1	2	yes	maximal, complemented
8	C₅₉×#2517	C₂	1	2	yes	maximal, complemented
9	C₅₉×#2515	C₂	1	2	yes	maximal, complemented
10	C₅₉×#2499	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2496	C₂	1	2	yes	maximal, complemented
12	C₅₉×#2482	C₂	1	1	yes	maximal, characteristic
13	C₅₉×#2480	C₂	1	2	yes	maximal
14	C₅₉×#2480	C₂	1	2	yes	maximal
15	C₅₉×#2334	C₂	1	2	yes	maximal, complemented
16	C₅₉×#2332	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#126×C₅₉	C₂	1	2	yes	maximal, complemented
18	C₅₉×#2298	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₉×#2273	C₂	1	1	yes	maximal, characteristic
20	C₂×#126×C₅₉	C₂²	1	2	yes	—
21	C₂×#126×C₅₉	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
23	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
26	C₅₉×#400	C₂²	1	2	yes	complemented
27	C₅₉×#400	C₂²	1	2	yes	complemented
28	C₅₉×#400	C₂²	1	2	yes	complemented
29	C₅₉×#399	C₂²	1	2	yes	—
30	C₅₉×#398	C₂²	1	2	yes	complemented
31	C₅₉×#397	C₂²	1	2	yes	—
32	C₅₉×#397	C₂²	1	2	yes	—
33	C₅₉×#397	C₂²	1	2	yes	—
34	C₅₉×#397	C₂²	1	2	yes	—
35	C₅₉×#397	C₂²	1	2	yes	—
36	C₅₉×#397	C₂²	1	2	yes	—
37	C₅₉×#397	C₂²	1	2	yes	—
38	C₅₉×#397	C₂²	1	2	yes	—
39	C₅₉×#396	C₂²	1	2	yes	—
40	C₅₉×#396	C₂²	1	2	yes	—
41	C₅₉×#393	C₂²	1	2	yes	—
42	C₅₉×#391	C₂²	1	1	yes	characteristic, complemented
43	C₅₉×#391	C₂²	1	1	yes	characteristic, complemented
44	C₅₉×#391	C₂²	1	2	yes	complemented
45	C₅₉×#389	C₂²	1	2	yes	complemented
46	C₅₉×#389	C₂²	1	2	yes	complemented
47	C₅₉×#389	C₂²	1	2	yes	complemented
48	C₅₉×#388	C₂²	1	2	yes	—
49	C₅₉×#388	C₂²	1	2	yes	—
50	C₅₉×#388	C₂²	1	2	yes	—
51	C₅₉×#388	C₂²	1	2	yes	—
52	C₅₉×#388	C₂²	1	2	yes	—
53	C₅₉×#388	C₂²	1	2	yes	—
54	C₅₉×#388	C₂²	1	2	yes	—
55	C₅₉×#388	C₂²	1	2	yes	—
56	C₅₉×#388	C₂²	1	2	yes	—
57	C₅₉×#388	C₂²	1	2	yes	—
58	C₅₉×#387	C₂²	1	2	yes	complemented
59	C₅₉×#387	C₂²	1	2	yes	complemented
60	C₅₉×#387	C₂²	1	2	yes	complemented
61	C₅₉×#387	C₂²	1	2	yes	complemented
62	C₅₉×#387	C₂²	1	2	yes	complemented
63	C₅₉×#387	C₂²	1	2	yes	complemented
64	C₅₉×#387	C₂²	1	2	yes	complemented
65	C₅₉×#387	C₂²	1	2	yes	complemented
66	C₅₉×#387	C₂²	1	2	yes	complemented
67	C₅₉×#387	C₂²	1	2	yes	complemented
68	C₅₉×#387	C₂²	1	2	yes	complemented
69	C₅₉×#387	C₂²	1	2	yes	complemented
70	C₅₉×#387	C₂²	1	2	yes	complemented
71	C₅₉×#387	C₂²	1	2	yes	complemented
72	C₅₉×#385	C₂²	1	1	yes	characteristic
73	C₅₉×#385	C₂²	1	1	yes	characteristic
74	C₅₉×#385	C₂²	1	2	yes	—
75	C₅₉×#385	C₂²	1	2	yes	—
76	C₅₉×#385	C₂²	1	2	yes	—
77	C₅₉×#385	C₂²	1	2	yes	—
78	C₅₉×#384	C₂²	1	1	yes	characteristic, complemented
79	C₅₉×#383	C₂²	1	2	yes	complemented
80	C₅₉×#383	C₂²	1	2	yes	complemented
81	C₅₉×#382	C₂²	1	1	yes	characteristic, complemented
82	C₅₉×#382	C₂²	1	2	yes	complemented
83	C₅₉×#381	C₂²	1	1	yes	characteristic
84	C₅₉×#381	C₂²	1	2	yes	—
85	C₅₉×#380	C₂²	1	2	yes	—
86	C₅₉×#380	C₂²	1	2	yes	—
87	C₅₉×#379	C₂²	1	1	yes	characteristic
88	C₅₉×#379	C₂²	1	1	yes	characteristic
89	C₅₉×#379	C₂²	1	2	yes	—
90	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
91	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
92	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
93	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
94	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
95	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
96	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
97	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
103	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
105	C₅₉×#376	C₂²	1	1	yes	characteristic, complemented
106	C₄³×C₅₉	C₂²	1	1	yes	characteristic, complemented
107	C₂⁵×C₅₉	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
110	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
111	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
113	#126×C₅₉	—	2	8	no	—
114	#126×C₅₉	—	2	8	no	—
115	C₂²⋊Q₈×C₅₉	—	2	4	no	—
116	#117×C₅₉	—	2	4	no	—
117	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
135	C₂×C₂²⋊C₄×C₅₉	—	2	4	no	—
136	C₂×C₂²⋊C₄×C₅₉	—	2	8	no	—
137	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
153	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
154	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
157	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
159	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
160	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
163	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
167	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
169	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
171	#95×C₅₉	C₂³	1	2	yes	—
172	#95×C₅₉	C₂³	1	2	yes	—
173	#95×C₅₉	C₂³	1	2	yes	—
174	#95×C₅₉	C₂³	1	2	yes	—
175	#95×C₅₉	C₂³	1	2	yes	—
176	#95×C₅₉	C₂³	1	2	yes	—
177	#95×C₅₉	C₂³	1	2	yes	—
178	#95×C₅₉	C₂³	1	2	yes	—
179	#95×C₅₉	C₂³	1	2	yes	—
180	#95×C₅₉	C₂³	1	2	yes	—
181	#95×C₅₉	C₂³	1	2	yes	—
182	#95×C₅₉	C₂³	1	2	yes	—
183	#95×C₅₉	C₂³	1	2	yes	—
184	#95×C₅₉	C₂³	1	2	yes	—
185	#95×C₅₉	C₂³	1	2	yes	—
186	#95×C₅₉	C₂³	1	2	yes	—
187	#95×C₅₉	C₂³	1	2	yes	—
188	#95×C₅₉	C₂³	1	2	yes	—
189	#95×C₅₉	C₂³	1	2	yes	—
190	#95×C₅₉	C₂³	1	2	yes	—
191	#95×C₅₉	C₂³	1	2	yes	—
192	#95×C₅₉	C₂³	1	2	yes	—
193	#95×C₅₉	C₂³	1	2	yes	—
194	#95×C₅₉	C₂³	1	2	yes	—
195	#95×C₅₉	C₂³	1	2	yes	—
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	2	yes	—
200	C₂⁴×C₅₉	—	2	2	no	—
201	C₂⁴×C₅₉	—	2	4	no	—
202	C₂⁴×C₅₉	—	4	1	no	—
203	C₂⁴×C₅₉	—	4	1	no	—
204	C₂⁴×C₅₉	—	4	2	no	—
205	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
206	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
207	C₂×Q₈×C₅₉	—	2	2	no	—
208	C₂×Q₈×C₅₉	—	4	1	no	—
209	C₂×Q₈×C₅₉	—	4	1	no	—
210	C₂²×C₄×C₅₉	—	2	2	no	—
211	C₂²×C₄×C₅₉	—	2	4	no	—
212	C₂²×C₄×C₅₉	—	2	4	no	—
213	C₂²×C₄×C₅₉	—	4	1	no	—
214	C₂²×C₄×C₅₉	—	4	1	no	—
215	C₂²×C₄×C₅₉	—	4	2	no	—
216	C₂²×C₄×C₅₉	—	4	2	no	—
217	C₂²×C₄×C₅₉	—	4	2	no	—
218	C₂²×C₄×C₅₉	—	4	2	no	—
219	C₂²×C₄×C₅₉	—	4	2	no	—
220	C₂²×C₄×C₅₉	#41	1	4	yes	—
221	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
238	C₄⋊C₄×C₅₉	—	2	2	no	—
239	C₄⋊C₄×C₅₉	—	2	2	no	—
240	C₄⋊C₄×C₅₉	—	2	2	no	—
241	C₄⋊C₄×C₅₉	—	2	4	no	—
242	C₄⋊C₄×C₅₉	—	2	4	no	—
243	C₄⋊C₄×C₅₉	—	2	4	no	—
244	C₄⋊C₄×C₅₉	—	2	4	no	—
245	C₄⋊C₄×C₅₉	—	2	4	no	—
246	C₄⋊C₄×C₅₉	—	2	4	no	—
247	C₄⋊C₄×C₅₉	—	2	4	no	—
248	C₄⋊C₄×C₅₉	—	4	2	no	—
249	C₄⋊C₄×C₅₉	—	4	2	no	—
250	C₄⋊C₄×C₅₉	—	4	2	no	—
251	C₄⋊C₄×C₅₉	—	4	2	no	—
252	C₄⋊C₄×C₅₉	—	4	2	no	—
253	C₄⋊C₄×C₅₉	—	4	2	no	—
254	C₄⋊C₄×C₅₉	—	4	2	no	—
255	C₄⋊C₄×C₅₉	—	4	2	no	—
256	C₂²⋊C₄×C₅₉	—	2	4	no	—
257	C₂²⋊C₄×C₅₉	—	2	2	no	—
258	C₂²⋊C₄×C₅₉	—	2	2	no	—
259	C₂²⋊C₄×C₅₉	—	2	4	no	—
260	C₂²⋊C₄×C₅₉	—	2	4	no	—
261	C₂²⋊C₄×C₅₉	—	2	4	no	—
262	C₂²⋊C₄×C₅₉	—	2	4	no	—
263	C₂²⋊C₄×C₅₉	—	2	4	no	—
264	C₂²⋊C₄×C₅₉	—	2	4	no	—
265	C₂²⋊C₄×C₅₉	—	2	4	no	—
266	C₂²⋊C₄×C₅₉	—	2	4	no	—
267	C₂²⋊C₄×C₅₉	—	2	4	no	—
268	C₂²⋊C₄×C₅₉	—	4	1	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	—	4	2	no	—
273	C₂²⋊C₄×C₅₉	—	4	1	no	—
274	C₂²⋊C₄×C₅₉	—	4	2	no	—
275	C₂²⋊C₄×C₅₉	#41	1	8	yes	—
276	C₄²×C₅₉	—	2	2	no	—
277	C₄²×C₅₉	—	2	2	no	—
278	C₄²×C₅₉	—	2	4	no	—
279	C₄²×C₅₉	—	2	4	no	—
280	C₄²×C₅₉	—	4	1	no	—
281	C₄²×C₅₉	—	4	2	no	—
282	C₄²×C₅₉	—	4	1	no	—
283	C₄²×C₅₉	—	4	2	no	—
284	C₄²×C₅₉	—	4	1	no	—
285	C₄²×C₅₉	—	4	2	no	—
286	C₄²×C₅₉	—	4	1	no	—
287	C₄²×C₅₉	—	4	1	no	—
288	C₄²×C₅₉	—	4	1	no	—
289	C₄²×C₅₉	—	4	2	no	—
290	C₂³×C₅₉	—	2	8	no	—
291	C₂³×C₅₉	—	2	2	no	—
292	C₂³×C₅₉	—	2	2	no	—
293	C₂³×C₅₉	—	2	2	no	—
294	C₂³×C₅₉	—	2	1	no	—
295	C₂³×C₅₉	—	2	1	no	—
296	C₂³×C₅₉	—	2	2	no	—
297	C₂³×C₅₉	—	2	2	no	—
298	C₂³×C₅₉	—	2	2	no	—
299	C₂³×C₅₉	—	2	2	no	—
300	C₂³×C₅₉	—	2	2	no	—
301	C₂³×C₅₉	—	8	2	no	—
302	C₂³×C₅₉	—	8	2	no	—
303	C₂³×C₅₉	—	8	4	no	—
304	C₂³×C₅₉	—	8	4	no	—
305	C₂³×C₅₉	C₂×#41	1	4	yes	—
306	C₂³×C₅₉	C₂×#41	1	2	yes	—
307	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
308	Q₈×C₅₉	—	8	2	no	—
309	C₂×C₄×C₅₉	—	2	1	no	—
310	C₂×C₄×C₅₉	—	2	1	no	—
311	C₂×C₄×C₅₉	—	2	2	no	—
312	C₂×C₄×C₅₉	—	2	2	no	—
313	C₂×C₄×C₅₉	—	2	2	no	—
314	C₂×C₄×C₅₉	—	2	2	no	—
315	C₂×C₄×C₅₉	—	2	1	no	—
316	C₂×C₄×C₅₉	—	2	1	no	—
317	C₂×C₄×C₅₉	—	2	1	no	—
318	C₂×C₄×C₅₉	—	2	1	no	—
319	C₂×C₄×C₅₉	—	2	2	no	—
320	C₂×C₄×C₅₉	—	2	2	no	—
321	C₂×C₄×C₅₉	—	2	1	no	—
322	C₂×C₄×C₅₉	—	2	1	no	—
323	C₂×C₄×C₅₉	—	2	2	no	—
324	C₂×C₄×C₅₉	—	2	2	no	—
325	C₂×C₄×C₅₉	—	2	2	no	—
326	C₂×C₄×C₅₉	—	2	2	no	—
327	C₂×C₄×C₅₉	—	2	2	no	—
328	C₂×C₄×C₅₉	—	2	2	no	—
329	C₂×C₄×C₅₉	—	2	2	no	—
330	C₂×C₄×C₅₉	—	2	2	no	—
331	C₂×C₄×C₅₉	—	2	2	no	—
332	C₂×C₄×C₅₉	—	2	2	no	—
333	C₂×C₄×C₅₉	—	2	2	no	—
334	C₂×C₄×C₅₉	—	2	2	no	—
335	C₂×C₄×C₅₉	—	2	2	no	—
336	C₂×C₄×C₅₉	—	2	2	no	—
337	C₂×C₄×C₅₉	—	2	2	no	—
338	C₂×C₄×C₅₉	—	2	2	no	—
339	C₂×C₄×C₅₉	—	2	2	no	—
340	C₂×C₄×C₅₉	—	2	2	no	—
341	C₂×C₄×C₅₉	—	2	2	no	—
342	C₂×C₄×C₅₉	—	2	2	no	—
343	C₂×C₄×C₅₉	—	2	2	no	—
344	C₂×C₄×C₅₉	—	2	2	no	—
345	C₂×C₄×C₅₉	—	2	2	no	—
346	C₂×C₄×C₅₉	—	2	2	no	—
347	C₂×C₄×C₅₉	—	2	2	no	—
348	C₂×C₄×C₅₉	—	2	2	no	—
349	C₂×C₄×C₅₉	—	2	2	no	—
350	C₂×C₄×C₅₉	—	2	2	no	—
351	C₂×C₄×C₅₉	—	2	2	no	—
352	C₂×C₄×C₅₉	—	4	4	no	—
353	C₂×C₄×C₅₉	—	8	4	no	—
354	C₂×C₄×C₅₉	—	8	4	no	—
355	C₂×C₄×C₅₉	—	8	2	no	—
356	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
357	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
358	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
359	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
360	#35488	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
361	C₂²×C₅₉	—	2	2	no	—
362	C₂²×C₅₉	—	2	4	no	—
363	C₂²×C₅₉	—	2	2	no	—
364	C₂²×C₅₉	—	2	2	no	—
365	C₂²×C₅₉	—	2	4	no	—
366	C₂²×C₅₉	—	2	4	no	—
367	C₂²×C₅₉	—	4	2	no	—
368	C₂²×C₅₉	—	4	2	no	—
369	C₂²×C₅₉	—	4	2	no	—
370	C₂²×C₅₉	—	4	2	no	—
371	C₂²×C₅₉	—	4	2	no	—
372	C₂²×C₅₉	—	4	2	no	—
373	C₂²×C₅₉	—	8	8	no	—
374	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
375	C₂²×C₅₉	C₂²×#41	1	2	yes	—
376	C₂²×C₅₉	#585	1	1	yes	characteristic
377	C₂²×C₅₉	#585	1	1	yes	characteristic
378	C₂²×C₅₉	#585	1	2	yes	—
379	C₄×C₅₉	—	2	2	no	—
380	C₄×C₅₉	—	2	2	no	—
381	C₄×C₅₉	—	2	4	no	—
382	C₄×C₅₉	—	2	4	no	—
383	C₄×C₅₉	—	4	1	no	—
384	C₄×C₅₉	—	4	1	no	—
385	C₄×C₅₉	—	4	2	no	—
386	C₄×C₅₉	—	4	2	no	—
387	C₄×C₅₉	—	4	1	no	—
388	C₄×C₅₉	—	4	1	no	—
389	C₄×C₅₉	—	4	2	no	—
390	C₄×C₅₉	—	4	2	no	—
391	C₄×C₅₉	—	4	2	no	—
392	C₄×C₅₉	—	4	2	no	—
393	C₄×C₅₉	—	4	2	no	—
394	C₄×C₅₉	—	4	2	no	—
395	C₄×C₅₉	—	4	2	no	—
396	#2608	C₂×C₅₉	1	1	yes	characteristic, complemented
397	#2589	C₂×C₅₉	1	2	yes	complemented
398	#2577	C₂×C₅₉	1	2	yes	complemented
399	#2573	C₂×C₅₉	1	2	yes	complemented
400	#2561	C₂×C₅₉	1	1	yes	characteristic
401	#2530	C₂×C₅₉	1	2	yes	complemented
402	#2523	C₂×C₅₉	1	2	yes	complemented
403	#2517	C₂×C₅₉	1	2	yes	complemented
404	#2515	C₂×C₅₉	1	2	yes	complemented
405	#2499	C₂×C₅₉	1	1	yes	characteristic, complemented
406	#2496	C₂×C₅₉	1	2	yes	complemented
407	#2482	C₂×C₅₉	1	1	yes	characteristic
408	#2480	C₂×C₅₉	1	2	yes	—
409	#2480	C₂×C₅₉	1	2	yes	—
410	#2334	C₂×C₅₉	1	2	yes	complemented
411	#2332	C₂×C₅₉	1	1	yes	characteristic, complemented
412	C₄×#126	C₂×C₅₉	1	2	yes	complemented
413	#2298	C₂×C₅₉	1	1	yes	characteristic, complemented
414	#2273	C₂×C₅₉	1	1	yes	characteristic
415	C₂×C₅₉	—	4	2	no	—
416	C₂×C₅₉	—	4	4	no	—
417	C₂×C₅₉	#3444	1	1	yes	characteristic
418	C₂×C₅₉	#3491	1	1	yes	characteristic
419	C₂×C₅₉	#3510	1	1	yes	characteristic
420	C₂×C₅₉	#3521	1	2	yes	—
421	C₂×C₅₉	#3521	1	2	yes	—
422	C₂×#126	C₂²×C₅₉	1	2	yes	—
423	C₂×#126	C₂²×C₅₉	1	2	yes	—
424	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
425	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
426	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
427	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
428	#400	C₂²×C₅₉	1	2	yes	complemented
429	#400	C₂²×C₅₉	1	2	yes	complemented
430	#400	C₂²×C₅₉	1	2	yes	complemented
431	#399	C₂²×C₅₉	1	2	yes	—
432	#398	C₂²×C₅₉	1	2	yes	complemented
433	#397	C₂²×C₅₉	1	2	yes	—
434	#397	C₂²×C₅₉	1	2	yes	—
435	#397	C₂²×C₅₉	1	2	yes	—
436	#397	C₂²×C₅₉	1	2	yes	—
437	#397	C₂²×C₅₉	1	2	yes	—
438	#397	C₂²×C₅₉	1	2	yes	—
439	#397	C₂²×C₅₉	1	2	yes	—
440	#397	C₂²×C₅₉	1	2	yes	—
441	#396	C₂²×C₅₉	1	2	yes	—
442	#396	C₂²×C₅₉	1	2	yes	—
443	#393	C₂²×C₅₉	1	2	yes	—
444	#391	C₂²×C₅₉	1	2	yes	complemented
445	#391	C₂²×C₅₉	1	1	yes	characteristic, complemented
446	#391	C₂²×C₅₉	1	1	yes	characteristic, complemented
447	#389	C₂²×C₅₉	1	2	yes	complemented
448	#389	C₂²×C₅₉	1	2	yes	complemented
449	#389	C₂²×C₅₉	1	2	yes	complemented
450	#388	C₂²×C₅₉	1	2	yes	—
451	#388	C₂²×C₅₉	1	2	yes	—
452	#388	C₂²×C₅₉	1	2	yes	—
453	#388	C₂²×C₅₉	1	2	yes	—
454	#388	C₂²×C₅₉	1	2	yes	—
455	#388	C₂²×C₅₉	1	2	yes	—
456	#388	C₂²×C₅₉	1	2	yes	—
457	#388	C₂²×C₅₉	1	2	yes	—
458	#388	C₂²×C₅₉	1	2	yes	—
459	#388	C₂²×C₅₉	1	2	yes	—
460	#387	C₂²×C₅₉	1	2	yes	complemented
461	#387	C₂²×C₅₉	1	2	yes	complemented
462	#387	C₂²×C₅₉	1	2	yes	complemented
463	#387	C₂²×C₅₉	1	2	yes	complemented
464	#387	C₂²×C₅₉	1	2	yes	complemented
465	#387	C₂²×C₅₉	1	2	yes	complemented
466	#387	C₂²×C₅₉	1	2	yes	complemented
467	#387	C₂²×C₅₉	1	2	yes	complemented
468	#387	C₂²×C₅₉	1	2	yes	complemented
469	#387	C₂²×C₅₉	1	2	yes	complemented
470	#387	C₂²×C₅₉	1	2	yes	complemented
471	#387	C₂²×C₅₉	1	2	yes	complemented
472	#387	C₂²×C₅₉	1	2	yes	complemented
473	#387	C₂²×C₅₉	1	2	yes	complemented
474	#385	C₂²×C₅₉	1	1	yes	characteristic
475	#385	C₂²×C₅₉	1	2	yes	—
476	#385	C₂²×C₅₉	1	2	yes	—
477	#385	C₂²×C₅₉	1	2	yes	—
478	#385	C₂²×C₅₉	1	2	yes	—
479	#385	C₂²×C₅₉	1	1	yes	characteristic
480	#384	C₂²×C₅₉	1	1	yes	characteristic, complemented
481	#383	C₂²×C₅₉	1	2	yes	complemented
482	#383	C₂²×C₅₉	1	2	yes	complemented
483	#382	C₂²×C₅₉	1	2	yes	complemented
484	#382	C₂²×C₅₉	1	1	yes	characteristic, complemented
485	#381	C₂²×C₅₉	1	2	yes	—
486	#381	C₂²×C₅₉	1	1	yes	characteristic
487	#380	C₂²×C₅₉	1	2	yes	—
488	#380	C₂²×C₅₉	1	2	yes	—
489	#379	C₂²×C₅₉	1	2	yes	—
490	#379	C₂²×C₅₉	1	1	yes	characteristic
491	#379	C₂²×C₅₉	1	1	yes	characteristic
492	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
493	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
494	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
495	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
496	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
497	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
498	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
499	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
500	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
501	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
502	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
503	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
504	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
505	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
506	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
507	#376	C₂²×C₅₉	1	1	yes	characteristic, complemented
508	C₄³	C₂²×C₅₉	1	1	yes	characteristic, complemented
509	C₅₉	#35488	1	1	yes	characteristic, direct product factor, Sylow
510	C₂⁵	C₂³×C₅₉	1	1	yes	characteristic
511	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
512	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
513	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
514	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
515	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
516	#126	—	2	8	no	—
517	#126	—	2	8	no	—
518	C₂²⋊Q₈	—	2	4	no	—
519	#117	—	2	4	no	—
520	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
521	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
522	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
524	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
528	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
538	C₂×C₂²⋊C₄	—	2	4	no	—
539	C₂×C₂²⋊C₄	—	2	8	no	—
540	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
546	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
547	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
556	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
557	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
560	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
561	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
562	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
563	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
564	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
565	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
566	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
567	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
568	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
569	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
570	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
571	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
572	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
573	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
574	#95	C₂³×C₅₉	1	2	yes	—
575	#95	C₂³×C₅₉	1	2	yes	—
576	#95	C₂³×C₅₉	1	2	yes	—
577	#95	C₂³×C₅₉	1	2	yes	—
578	#95	C₂³×C₅₉	1	2	yes	—
579	#95	C₂³×C₅₉	1	2	yes	—
580	#95	C₂³×C₅₉	1	2	yes	—
581	#95	C₂³×C₅₉	1	2	yes	—
582	#95	C₂³×C₅₉	1	2	yes	—
583	#95	C₂³×C₅₉	1	2	yes	—
584	#95	C₂³×C₅₉	1	2	yes	—
585	#95	C₂³×C₅₉	1	2	yes	—
586	#95	C₂³×C₅₉	1	2	yes	—
587	#95	C₂³×C₅₉	1	2	yes	—
588	#95	C₂³×C₅₉	1	2	yes	—
589	#95	C₂³×C₅₉	1	2	yes	—
590	#95	C₂³×C₅₉	1	2	yes	—
591	#95	C₂³×C₅₉	1	2	yes	—
592	#95	C₂³×C₅₉	1	2	yes	—
593	#95	C₂³×C₅₉	1	2	yes	—
594	#95	C₂³×C₅₉	1	2	yes	—
595	#95	C₂³×C₅₉	1	2	yes	—
596	#95	C₂³×C₅₉	1	2	yes	—
597	#95	C₂³×C₅₉	1	2	yes	—
598	#95	C₂³×C₅₉	1	2	yes	—
599	#95	C₂³×C₅₉	1	2	yes	—
600	#95	C₂³×C₅₉	1	2	yes	—
601	#95	C₂³×C₅₉	1	2	yes	—
602	#95	C₂³×C₅₉	1	2	yes	—
603	C₂⁴	—	2	2	no	—
604	C₂⁴	—	2	4	no	—
605	C₂⁴	—	4	2	no	—
606	C₂⁴	—	4	1	no	—
607	C₂⁴	—	4	1	no	—
608	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
609	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
610	C₂×Q₈	—	2	2	no	—
611	C₂×Q₈	—	4	1	no	—
612	C₂×Q₈	—	4	1	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	—	4	1	no	—
617	C₂²×C₄	—	4	1	no	—
618	C₂²×C₄	—	4	2	no	—
619	C₂²×C₄	—	4	2	no	—
620	C₂²×C₄	—	4	2	no	—
621	C₂²×C₄	—	4	2	no	—
622	C₂²×C₄	—	4	2	no	—
623	C₂²×C₄	#41×C₅₉	1	4	yes	—
624	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
625	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
626	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
627	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
628	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
629	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
630	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
631	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
632	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
633	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
635	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
638	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
639	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
640	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
641	C₄⋊C₄	—	2	2	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	2	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	4	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	4	2	no	—
652	C₄⋊C₄	—	4	2	no	—
653	C₄⋊C₄	—	4	2	no	—
654	C₄⋊C₄	—	4	2	no	—
655	C₄⋊C₄	—	4	2	no	—
656	C₄⋊C₄	—	4	2	no	—
657	C₄⋊C₄	—	4	2	no	—
658	C₄⋊C₄	—	4	2	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	2	no	—
661	C₂²⋊C₄	—	2	2	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	4	1	no	—
672	C₂²⋊C₄	—	4	2	no	—
673	C₂²⋊C₄	—	4	2	no	—
674	C₂²⋊C₄	—	4	2	no	—
675	C₂²⋊C₄	—	4	2	no	—
676	C₂²⋊C₄	—	4	1	no	—
677	C₂²⋊C₄	—	4	2	no	—
678	C₂²⋊C₄	#41×C₅₉	1	8	yes	—
679	C₄²	—	2	2	no	—
680	C₄²	—	2	2	no	—
681	C₄²	—	2	4	no	—
682	C₄²	—	2	4	no	—
683	C₄²	—	4	1	no	—
684	C₄²	—	4	2	no	—
685	C₄²	—	4	2	no	—
686	C₄²	—	4	1	no	—
687	C₄²	—	4	1	no	—
688	C₄²	—	4	2	no	—
689	C₄²	—	4	1	no	—
690	C₄²	—	4	1	no	—
691	C₄²	—	4	1	no	—
692	C₄²	—	4	2	no	—
693	C₂³	—	2	8	no	—
694	C₂³	—	2	2	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	2	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	1	no	—
703	C₂³	—	2	1	no	—
704	C₂³	—	8	2	no	—
705	C₂³	—	8	4	no	—
706	C₂³	—	8	4	no	—
707	C₂³	—	8	2	no	—
708	C₂³	C₂×#41×C₅₉	1	4	yes	—
709	C₂³	C₂×#41×C₅₉	1	2	yes	—
710	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
711	Q₈	—	8	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	4	4	no	—
756	C₂×C₄	—	8	4	no	—
757	C₂×C₄	—	8	4	no	—
758	C₂×C₄	—	8	2	no	—
759	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
760	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
761	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
762	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
763	C₂²	—	2	2	no	—
764	C₂²	—	2	4	no	—
765	C₂²	—	2	4	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	2	4	no	—
768	C₂²	—	2	2	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	8	8	no	—
776	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
777	C₂²	C₂²×#41×C₅₉	1	2	yes	—
778	C₂²	C₅₉×#585	1	2	yes	—
779	C₂²	C₅₉×#585	1	1	yes	characteristic
780	C₂²	C₅₉×#585	1	1	yes	characteristic
781	C₄	—	2	4	no	—
782	C₄	—	2	4	no	—
783	C₄	—	2	2	no	—
784	C₄	—	2	2	no	—
785	C₄	—	4	2	no	—
786	C₄	—	4	1	no	—
787	C₄	—	4	1	no	—
788	C₄	—	4	2	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	2	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	2	no	—
794	C₄	—	4	1	no	—
795	C₄	—	4	1	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	2	no	—
798	C₂	—	4	2	no	—
799	C₂	—	4	4	no	—
800	C₂	C₅₉×#3444	1	1	yes	characteristic
801	C₂	C₅₉×#3491	1	1	yes	characteristic
802	C₂	C₅₉×#3510	1	1	yes	characteristic
803	C₂	C₅₉×#3521	1	2	yes	—
804	C₂	C₅₉×#3521	1	2	yes	—

	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×#2608	C₂	semidirect
2. C₅₉×#2589	C₂	semidirect
3. C₅₉×#2577	C₂	semidirect
4. C₅₉×#2573	C₂	semidirect
6. C₅₉×#2530	C₂	semidirect
7. C₅₉×#2523	C₂	semidirect
8. C₅₉×#2517	C₂	semidirect
9. C₅₉×#2515	C₂	semidirect
10. C₅₉×#2499	C₂	semidirect
11. C₅₉×#2496	C₂	semidirect
15. C₅₉×#2334	C₂	semidirect
16. C₅₉×#2332	C₂	semidirect
17. C₄×#126×C₅₉	C₂	semidirect
18. C₅₉×#2298	C₂	semidirect
26. C₅₉×#400	C₂²	semidirect
27. C₅₉×#400	C₂²	semidirect
28. C₅₉×#400	C₂²	semidirect
30. C₅₉×#398	C₂²	semidirect
42. C₅₉×#391	C₂²	semidirect
43. C₅₉×#391	C₂²	semidirect
44. C₅₉×#391	C₂²	semidirect
45. C₅₉×#389	C₂²	semidirect
46. C₅₉×#389	C₂²	semidirect
47. C₅₉×#389	C₂²	semidirect
58. C₅₉×#387	C₂²	semidirect
59. C₅₉×#387	C₂²	semidirect
60. C₅₉×#387	C₂²	semidirect
61. C₅₉×#387	C₂²	semidirect
62. C₅₉×#387	C₂²	semidirect
63. C₅₉×#387	C₂²	semidirect
64. C₅₉×#387	C₂²	semidirect
65. C₅₉×#387	C₂²	semidirect
66. C₅₉×#387	C₂²	semidirect
67. C₅₉×#387	C₂²	semidirect
68. C₅₉×#387	C₂²	semidirect
69. C₅₉×#387	C₂²	semidirect
70. C₅₉×#387	C₂²	semidirect
71. C₅₉×#387	C₂²	semidirect
78. C₅₉×#384	C₂²	semidirect
79. C₅₉×#383	C₂²	semidirect
80. C₅₉×#383	C₂²	semidirect
81. C₅₉×#382	C₂²	semidirect
82. C₅₉×#382	C₂²	semidirect
90. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
91. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
92. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
93. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
94. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
105. C₅₉×#376	C₂²	semidirect
106. C₄³×C₅₉	C₂²	semidirect
360. #35488	C₅₉	direct (N × H)
396. #2608	C₂×C₅₉	semidirect
397. #2589	C₂×C₅₉	semidirect
398. #2577	C₂×C₅₉	semidirect
399. #2573	C₂×C₅₉	semidirect
401. #2530	C₂×C₅₉	semidirect
402. #2523	C₂×C₅₉	semidirect
403. #2517	C₂×C₅₉	semidirect
404. #2515	C₂×C₅₉	semidirect
405. #2499	C₂×C₅₉	semidirect
406. #2496	C₂×C₅₉	semidirect
410. #2334	C₂×C₅₉	semidirect
411. #2332	C₂×C₅₉	semidirect
412. C₄×#126	C₂×C₅₉	semidirect
413. #2298	C₂×C₅₉	semidirect
428. #400	C₂²×C₅₉	semidirect
429. #400	C₂²×C₅₉	semidirect
430. #400	C₂²×C₅₉	semidirect
432. #398	C₂²×C₅₉	semidirect
444. #391	C₂²×C₅₉	semidirect
445. #391	C₂²×C₅₉	semidirect
446. #391	C₂²×C₅₉	semidirect
447. #389	C₂²×C₅₉	semidirect
448. #389	C₂²×C₅₉	semidirect
449. #389	C₂²×C₅₉	semidirect
460. #387	C₂²×C₅₉	semidirect
461. #387	C₂²×C₅₉	semidirect
462. #387	C₂²×C₅₉	semidirect
463. #387	C₂²×C₅₉	semidirect
464. #387	C₂²×C₅₉	semidirect
465. #387	C₂²×C₅₉	semidirect
466. #387	C₂²×C₅₉	semidirect
467. #387	C₂²×C₅₉	semidirect
468. #387	C₂²×C₅₉	semidirect
469. #387	C₂²×C₅₉	semidirect
470. #387	C₂²×C₅₉	semidirect
471. #387	C₂²×C₅₉	semidirect
472. #387	C₂²×C₅₉	semidirect
473. #387	C₂²×C₅₉	semidirect
480. #384	C₂²×C₅₉	semidirect
481. #383	C₂²×C₅₉	semidirect
482. #383	C₂²×C₅₉	semidirect
483. #382	C₂²×C₅₉	semidirect
484. #382	C₂²×C₅₉	semidirect
492. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
493. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
494. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
495. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
496. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
507. #376	C₂²×C₅₉	semidirect
508. C₄³	C₂²×C₅₉	semidirect
509. C₅₉	#35488	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×#2608	2
C₅₉×#2589	2
C₅₉×#2577	2
C₅₉×#2573	2
C₅₉×#2561	2
C₅₉×#2530	2
C₅₉×#2523	2
C₅₉×#2517	2
C₅₉×#2515	2
C₅₉×#2499	2
C₅₉×#2496	2
C₅₉×#2482	2
C₅₉×#2480	2
C₅₉×#2334	2
C₅₉×#2332	2
C₄×#126×C₅₉	2
C₅₉×#2298	2
C₅₉×#2273	2
#35488	59

Subgroups — C59×#35488 #28447597

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35488 #28447597