Subgroups — C₅₉×#35496 #28447605

Order 15104.

1542 conjugacy classes of subgroups.

The subgroup lattice has 750 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
2	C₅₉×#2590	C₂	1	2	yes	maximal, complemented
3	C₅₉×#2588	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2583	C₂	1	1	yes	maximal, characteristic
5	C₅₉×#2573	C₂	1	2	yes	maximal
6	C₅₉×#2533	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2524	C₂	1	2	yes	maximal, complemented
8	C₅₉×#2520	C₂	1	2	yes	maximal, complemented
9	C₅₉×#2515	C₂	1	2	yes	maximal
10	C₅₉×#2506	C₂	1	2	yes	maximal, complemented
11	C₅₉×#2499	C₂	1	1	yes	maximal, characteristic
12	C₅₉×#2484	C₂	1	1	yes	maximal, characteristic
13	C₅₉×#2475	C₂	1	2	yes	maximal
14	C₅₉×#2475	C₂	1	2	yes	maximal
15	C₅₉×#2336	C₂	1	2	yes	maximal, complemented
16	C₅₉×#2332	C₂	1	1	yes	maximal, characteristic
17	C₄×#125×C₅₉	C₂	1	2	yes	maximal, complemented
18	C₅₉×#2298	C₂	1	1	yes	maximal, characteristic
19	C₅₉×#2274	C₂	1	1	yes	maximal, characteristic
20	C₂×#125×C₅₉	C₂²	1	2	yes	—
21	C₂×#125×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	C₂×#117×C₅₉	C₂²	1	2	yes	—
25	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
26	C₅₉×#400	C₂²	1	2	yes	—
27	C₅₉×#400	C₂²	1	2	yes	—
28	C₅₉×#400	C₂²	1	2	yes	—
29	C₅₉×#400	C₂²	1	2	yes	—
30	C₅₉×#400	C₂²	1	2	yes	—
31	C₅₉×#400	C₂²	1	2	yes	—
32	C₅₉×#398	C₂²	1	2	yes	—
33	C₅₉×#398	C₂²	1	2	yes	—
34	C₅₉×#398	C₂²	1	2	yes	—
35	C₅₉×#398	C₂²	1	2	yes	—
36	C₅₉×#398	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×#395	C₂²	1	2	yes	—
42	C₅₉×#391	C₂²	1	1	yes	characteristic
43	C₅₉×#391	C₂²	1	1	yes	characteristic
44	C₅₉×#391	C₂²	1	2	yes	—
45	C₅₉×#389	C₂²	1	2	yes	—
46	C₅₉×#389	C₂²	1	2	yes	—
47	C₅₉×#389	C₂²	1	2	yes	—
48	C₅₉×#389	C₂²	1	2	yes	—
49	C₅₉×#389	C₂²	1	2	yes	—
50	C₅₉×#389	C₂²	1	2	yes	—
51	C₅₉×#389	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×#387	C₂²	1	2	yes	—
57	C₅₉×#387	C₂²	1	2	yes	—
58	C₅₉×#387	C₂²	1	2	yes	—
59	C₅₉×#387	C₂²	1	2	yes	—
60	C₅₉×#387	C₂²	1	2	yes	—
61	C₅₉×#387	C₂²	1	2	yes	—
62	C₅₉×#387	C₂²	1	2	yes	—
63	C₅₉×#387	C₂²	1	2	yes	—
64	C₅₉×#387	C₂²	1	2	yes	—
65	C₅₉×#387	C₂²	1	2	yes	—
66	C₅₉×#387	C₂²	1	2	yes	—
67	C₅₉×#387	C₂²	1	2	yes	—
68	C₅₉×#387	C₂²	1	2	yes	—
69	C₅₉×#387	C₂²	1	2	yes	—
70	C₅₉×#387	C₂²	1	2	yes	—
71	C₅₉×#387	C₂²	1	2	yes	—
72	C₅₉×#387	C₂²	1	2	yes	—
73	C₅₉×#387	C₂²	1	2	yes	—
74	C₅₉×#387	C₂²	1	2	yes	—
75	C₅₉×#387	C₂²	1	2	yes	—
76	C₅₉×#387	C₂²	1	2	yes	—
77	C₅₉×#387	C₂²	1	2	yes	—
78	C₅₉×#385	C₂²	1	1	yes	characteristic
79	C₅₉×#385	C₂²	1	1	yes	characteristic
80	C₅₉×#385	C₂²	1	2	yes	—
81	C₅₉×#385	C₂²	1	2	yes	—
82	C₅₉×#384	C₂²	1	1	yes	characteristic
83	C₅₉×#383	C₂²	1	2	yes	—
84	C₅₉×#383	C₂²	1	2	yes	—
85	C₅₉×#382	C₂²	1	1	yes	characteristic
86	C₅₉×#382	C₂²	1	2	yes	—
87	C₅₉×#381	C₂²	1	1	yes	characteristic
88	C₅₉×#381	C₂²	1	1	yes	characteristic
89	C₅₉×#381	C₂²	1	1	yes	characteristic
90	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
92	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
95	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
97	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
98	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
99	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
100	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
104	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
105	C₅₉×#376	C₂²	1	1	yes	characteristic
106	C₄³×C₅₉	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
111	#125×C₅₉	—	2	8	no	—
112	#125×C₅₉	—	2	8	no	—
113	C₂²⋊Q₈×C₅₉	—	2	4	no	—
114	#117×C₅₉	—	2	4	no	—
115	#117×C₅₉	—	2	8	no	—
116	C₂×C₄⋊C₄×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	2	yes	—
124	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
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	1	yes	characteristic
131	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
142	C₂×C₄⋊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	1	yes	characteristic
147	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
150	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
152	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
153	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
154	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
155	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
156	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
158	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
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	2	yes	—
165	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
167	#95×C₅₉	C₂³	1	2	yes	—
168	#95×C₅₉	C₂³	1	2	yes	—
169	#95×C₅₉	C₂³	1	2	yes	—
170	#95×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	C₂⁴	1	1	yes	characteristic
201	C₂×Q₈×C₅₉	—	2	2	no	—
202	C₂×Q₈×C₅₉	—	4	1	no	—
203	C₂×Q₈×C₅₉	—	4	1	no	—
204	C₂²×C₄×C₅₉	—	2	2	no	—
205	C₂²×C₄×C₅₉	—	2	4	no	—
206	C₂²×C₄×C₅₉	—	2	2	no	—
207	C₂²×C₄×C₅₉	—	4	1	no	—
208	C₂²×C₄×C₅₉	—	4	1	no	—
209	C₂²×C₄×C₅₉	—	4	1	no	—
210	C₂²×C₄×C₅₉	—	4	1	no	—
211	C₂²×C₄×C₅₉	#41	1	4	yes	—
212	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
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	2	yes	—
230	C₄⋊C₄×C₅₉	—	2	4	no	—
231	C₄⋊C₄×C₅₉	—	2	4	no	—
232	C₄⋊C₄×C₅₉	—	2	4	no	—
233	C₄⋊C₄×C₅₉	—	2	2	no	—
234	C₄⋊C₄×C₅₉	—	2	2	no	—
235	C₄⋊C₄×C₅₉	—	2	2	no	—
236	C₄⋊C₄×C₅₉	—	2	4	no	—
237	C₄⋊C₄×C₅₉	—	2	4	no	—
238	C₄⋊C₄×C₅₉	—	2	4	no	—
239	C₄⋊C₄×C₅₉	—	2	4	no	—
240	C₄⋊C₄×C₅₉	—	2	4	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	—	2	4	no	—
249	C₄⋊C₄×C₅₉	—	2	4	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	#41	1	8	yes	—
256	C₂²⋊C₄×C₅₉	—	2	2	no	—
257	C₂²⋊C₄×C₅₉	—	2	2	no	—
258	C₂²⋊C₄×C₅₉	—	2	4	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	—	4	1	no	—
263	C₂²⋊C₄×C₅₉	—	4	1	no	—
264	C₄²×C₅₉	—	2	4	no	—
265	C₄²×C₅₉	—	2	4	no	—
266	C₄²×C₅₉	—	2	2	no	—
267	C₄²×C₅₉	—	2	2	no	—
268	C₄²×C₅₉	—	2	4	no	—
269	C₄²×C₅₉	—	2	4	no	—
270	C₄²×C₅₉	—	2	4	no	—
271	C₄²×C₅₉	—	4	1	no	—
272	C₄²×C₅₉	—	4	2	no	—
273	C₄²×C₅₉	—	4	2	no	—
274	C₄²×C₅₉	—	4	1	no	—
275	C₄²×C₅₉	—	4	1	no	—
276	C₄²×C₅₉	—	4	1	no	—
277	C₄²×C₅₉	—	4	1	no	—
278	C₄²×C₅₉	—	4	1	no	—
279	C₄²×C₅₉	—	4	2	no	—
280	C₂³×C₅₉	—	2	2	no	—
281	C₂³×C₅₉	—	2	2	no	—
282	C₂³×C₅₉	—	2	1	no	—
283	C₂³×C₅₉	—	2	1	no	—
284	C₂³×C₅₉	C₂×#41	1	2	yes	—
285	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
286	Q₈×C₅₉	—	8	2	no	—
287	C₂×C₄×C₅₉	—	2	8	no	—
288	C₂×C₄×C₅₉	—	2	2	no	—
289	C₂×C₄×C₅₉	—	2	2	no	—
290	C₂×C₄×C₅₉	—	2	2	no	—
291	C₂×C₄×C₅₉	—	2	2	no	—
292	C₂×C₄×C₅₉	—	2	2	no	—
293	C₂×C₄×C₅₉	—	2	2	no	—
294	C₂×C₄×C₅₉	—	2	2	no	—
295	C₂×C₄×C₅₉	—	2	1	no	—
296	C₂×C₄×C₅₉	—	2	1	no	—
297	C₂×C₄×C₅₉	—	2	2	no	—
298	C₂×C₄×C₅₉	—	2	1	no	—
299	C₂×C₄×C₅₉	—	2	1	no	—
300	C₂×C₄×C₅₉	—	2	1	no	—
301	C₂×C₄×C₅₉	—	2	1	no	—
302	C₂×C₄×C₅₉	—	2	1	no	—
303	C₂×C₄×C₅₉	—	2	1	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	2	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	2	no	—
316	C₂×C₄×C₅₉	—	2	2	no	—
317	C₂×C₄×C₅₉	—	2	2	no	—
318	C₂×C₄×C₅₉	—	2	2	no	—
319	C₂×C₄×C₅₉	—	2	2	no	—
320	C₂×C₄×C₅₉	—	2	2	no	—
321	C₂×C₄×C₅₉	—	2	2	no	—
322	C₂×C₄×C₅₉	—	2	2	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	—	4	4	no	—
333	C₂×C₄×C₅₉	—	8	2	no	—
334	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
335	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
336	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
337	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
338	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
339	C₂×C₄×C₅₉	2₋¹⁺⁴	1	4	yes	—
340	#35496	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
341	C₂²×C₅₉	—	2	2	no	—
342	C₂²×C₅₉	—	2	2	no	—
343	C₂²×C₅₉	—	2	2	no	—
344	C₂²×C₅₉	—	4	2	no	—
345	C₂²×C₅₉	—	4	2	no	—
346	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
347	C₂²×C₅₉	C₂²×#41	1	2	yes	—
348	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	2	yes	—
349	C₂²×C₅₉	#585	1	1	yes	characteristic
350	C₂²×C₅₉	#585	1	1	yes	characteristic
351	C₄×C₅₉	—	2	4	no	—
352	C₄×C₅₉	—	2	2	no	—
353	C₄×C₅₉	—	2	2	no	—
354	C₄×C₅₉	—	2	4	no	—
355	C₄×C₅₉	—	2	4	no	—
356	C₄×C₅₉	—	2	4	no	—
357	C₄×C₅₉	—	4	1	no	—
358	C₄×C₅₉	—	4	1	no	—
359	C₄×C₅₉	—	4	2	no	—
360	C₄×C₅₉	—	4	2	no	—
361	C₄×C₅₉	—	4	2	no	—
362	C₄×C₅₉	—	4	1	no	—
363	C₄×C₅₉	—	4	1	no	—
364	C₄×C₅₉	—	4	2	no	—
365	C₄×C₅₉	—	4	2	no	—
366	C₄×C₅₉	—	4	2	no	—
367	C₄×C₅₉	—	4	2	no	—
368	C₄×C₅₉	—	4	2	no	—
369	#2608	C₂×C₅₉	1	1	yes	characteristic
370	#2590	C₂×C₅₉	1	2	yes	complemented
371	#2588	C₂×C₅₉	1	2	yes	complemented
372	#2583	C₂×C₅₉	1	1	yes	characteristic
373	#2573	C₂×C₅₉	1	2	yes	—
374	#2533	C₂×C₅₉	1	2	yes	complemented
375	#2524	C₂×C₅₉	1	2	yes	complemented
376	#2520	C₂×C₅₉	1	2	yes	complemented
377	#2515	C₂×C₅₉	1	2	yes	—
378	#2506	C₂×C₅₉	1	2	yes	complemented
379	#2499	C₂×C₅₉	1	1	yes	characteristic
380	#2484	C₂×C₅₉	1	1	yes	characteristic
381	#2475	C₂×C₅₉	1	2	yes	—
382	#2475	C₂×C₅₉	1	2	yes	—
383	#2336	C₂×C₅₉	1	2	yes	complemented
384	#2332	C₂×C₅₉	1	1	yes	characteristic
385	C₄×#125	C₂×C₅₉	1	2	yes	complemented
386	#2298	C₂×C₅₉	1	1	yes	characteristic
387	#2274	C₂×C₅₉	1	1	yes	characteristic
388	C₂×C₅₉	—	4	2	no	—
389	C₂×C₅₉	#3444	1	1	yes	characteristic
390	C₂×C₅₉	#3491	1	1	yes	characteristic
391	C₂×C₅₉	#3509	1	1	yes	characteristic
392	C₂×C₅₉	#3515	1	2	yes	—
393	C₂×C₅₉	#3516	1	2	yes	—
394	C₂×#125	C₂²×C₅₉	1	2	yes	—
395	C₂×#125	C₂²×C₅₉	1	2	yes	—
396	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
397	C₂×#117	C₂²×C₅₉	1	2	yes	—
398	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
399	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
400	#400	C₂²×C₅₉	1	2	yes	—
401	#400	C₂²×C₅₉	1	2	yes	—
402	#400	C₂²×C₅₉	1	2	yes	—
403	#400	C₂²×C₅₉	1	2	yes	—
404	#400	C₂²×C₅₉	1	2	yes	—
405	#400	C₂²×C₅₉	1	2	yes	—
406	#398	C₂²×C₅₉	1	2	yes	—
407	#398	C₂²×C₅₉	1	2	yes	—
408	#398	C₂²×C₅₉	1	2	yes	—
409	#398	C₂²×C₅₉	1	2	yes	—
410	#398	C₂²×C₅₉	1	2	yes	—
411	#397	C₂²×C₅₉	1	2	yes	—
412	#397	C₂²×C₅₉	1	2	yes	—
413	#396	C₂²×C₅₉	1	2	yes	—
414	#396	C₂²×C₅₉	1	2	yes	—
415	#395	C₂²×C₅₉	1	2	yes	—
416	#391	C₂²×C₅₉	1	2	yes	—
417	#391	C₂²×C₅₉	1	1	yes	characteristic
418	#391	C₂²×C₅₉	1	1	yes	characteristic
419	#389	C₂²×C₅₉	1	2	yes	—
420	#389	C₂²×C₅₉	1	2	yes	—
421	#389	C₂²×C₅₉	1	2	yes	—
422	#389	C₂²×C₅₉	1	2	yes	—
423	#389	C₂²×C₅₉	1	2	yes	—
424	#389	C₂²×C₅₉	1	2	yes	—
425	#389	C₂²×C₅₉	1	2	yes	—
426	#388	C₂²×C₅₉	1	2	yes	—
427	#388	C₂²×C₅₉	1	2	yes	—
428	#388	C₂²×C₅₉	1	2	yes	—
429	#388	C₂²×C₅₉	1	2	yes	—
430	#387	C₂²×C₅₉	1	2	yes	—
431	#387	C₂²×C₅₉	1	2	yes	—
432	#387	C₂²×C₅₉	1	2	yes	—
433	#387	C₂²×C₅₉	1	2	yes	—
434	#387	C₂²×C₅₉	1	2	yes	—
435	#387	C₂²×C₅₉	1	2	yes	—
436	#387	C₂²×C₅₉	1	2	yes	—
437	#387	C₂²×C₅₉	1	2	yes	—
438	#387	C₂²×C₅₉	1	2	yes	—
439	#387	C₂²×C₅₉	1	2	yes	—
440	#387	C₂²×C₅₉	1	2	yes	—
441	#387	C₂²×C₅₉	1	2	yes	—
442	#387	C₂²×C₅₉	1	2	yes	—
443	#387	C₂²×C₅₉	1	2	yes	—
444	#387	C₂²×C₅₉	1	2	yes	—
445	#387	C₂²×C₅₉	1	2	yes	—
446	#387	C₂²×C₅₉	1	2	yes	—
447	#387	C₂²×C₅₉	1	2	yes	—
448	#387	C₂²×C₅₉	1	2	yes	—
449	#387	C₂²×C₅₉	1	2	yes	—
450	#387	C₂²×C₅₉	1	2	yes	—
451	#387	C₂²×C₅₉	1	2	yes	—
452	#385	C₂²×C₅₉	1	2	yes	—
453	#385	C₂²×C₅₉	1	2	yes	—
454	#385	C₂²×C₅₉	1	1	yes	characteristic
455	#385	C₂²×C₅₉	1	1	yes	characteristic
456	#384	C₂²×C₅₉	1	1	yes	characteristic
457	#383	C₂²×C₅₉	1	2	yes	—
458	#383	C₂²×C₅₉	1	2	yes	—
459	#382	C₂²×C₅₉	1	2	yes	—
460	#382	C₂²×C₅₉	1	1	yes	characteristic
461	#381	C₂²×C₅₉	1	1	yes	characteristic
462	#381	C₂²×C₅₉	1	1	yes	characteristic
463	#381	C₂²×C₅₉	1	1	yes	characteristic
464	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
465	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
466	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
467	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
468	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
469	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
470	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
471	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
472	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
473	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
474	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
475	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
476	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
477	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
478	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
479	#376	C₂²×C₅₉	1	1	yes	characteristic
480	C₄³	C₂²×C₅₉	1	1	yes	characteristic
481	C₅₉	#35496	1	1	yes	characteristic, direct product factor, Sylow
482	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
483	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
484	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
485	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
486	#125	—	2	8	no	—
487	#125	—	2	8	no	—
488	C₂²⋊Q₈	—	2	4	no	—
489	#117	—	2	4	no	—
490	#117	—	2	8	no	—
491	C₂×C₄⋊C₄	—	2	4	no	—
492	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
493	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
497	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
498	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
499	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
502	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
514	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
521	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
522	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
525	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
526	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
527	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
528	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
529	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
530	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
531	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
532	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
533	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
534	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
535	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
536	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
537	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
538	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
539	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
540	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
541	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
542	#95	C₂³×C₅₉	1	2	yes	—
543	#95	C₂³×C₅₉	1	2	yes	—
544	#95	C₂³×C₅₉	1	2	yes	—
545	#95	C₂³×C₅₉	1	2	yes	—
546	#95	C₂³×C₅₉	1	2	yes	—
547	#95	C₂³×C₅₉	1	2	yes	—
548	#95	C₂³×C₅₉	1	2	yes	—
549	#95	C₂³×C₅₉	1	2	yes	—
550	#95	C₂³×C₅₉	1	2	yes	—
551	#95	C₂³×C₅₉	1	2	yes	—
552	#95	C₂³×C₅₉	1	2	yes	—
553	#95	C₂³×C₅₉	1	2	yes	—
554	#95	C₂³×C₅₉	1	2	yes	—
555	#95	C₂³×C₅₉	1	2	yes	—
556	#95	C₂³×C₅₉	1	2	yes	—
557	#95	C₂³×C₅₉	1	2	yes	—
558	#95	C₂³×C₅₉	1	2	yes	—
559	#95	C₂³×C₅₉	1	2	yes	—
560	#95	C₂³×C₅₉	1	2	yes	—
561	#95	C₂³×C₅₉	1	2	yes	—
562	#95	C₂³×C₅₉	1	2	yes	—
563	#95	C₂³×C₅₉	1	2	yes	—
564	#95	C₂³×C₅₉	1	2	yes	—
565	#95	C₂³×C₅₉	1	2	yes	—
566	#95	C₂³×C₅₉	1	2	yes	—
567	#95	C₂³×C₅₉	1	2	yes	—
568	#95	C₂³×C₅₉	1	2	yes	—
569	#95	C₂³×C₅₉	1	2	yes	—
570	#95	C₂³×C₅₉	1	2	yes	—
571	#95	C₂³×C₅₉	1	2	yes	—
572	#95	C₂³×C₅₉	1	2	yes	—
573	#95	C₂³×C₅₉	1	2	yes	—
574	#95	C₂³×C₅₉	1	2	yes	—
575	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
576	C₂×Q₈	—	2	2	no	—
577	C₂×Q₈	—	4	1	no	—
578	C₂×Q₈	—	4	1	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	4	1	no	—
583	C₂²×C₄	—	4	1	no	—
584	C₂²×C₄	—	4	1	no	—
585	C₂²×C₄	—	4	1	no	—
586	C₂²×C₄	#41×C₅₉	1	4	yes	—
587	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
588	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
589	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
590	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
591	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
592	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
593	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
598	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
600	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
602	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
603	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	2	no	—
609	C₄⋊C₄	—	2	2	no	—
610	C₄⋊C₄	—	2	2	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	4	2	no	—
626	C₄⋊C₄	—	4	2	no	—
627	C₄⋊C₄	—	4	2	no	—
628	C₄⋊C₄	—	4	2	no	—
629	C₄⋊C₄	—	4	2	no	—
630	C₄⋊C₄	#41×C₅₉	1	8	yes	—
631	C₂²⋊C₄	—	2	2	no	—
632	C₂²⋊C₄	—	2	2	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	4	1	no	—
638	C₂²⋊C₄	—	4	1	no	—
639	C₄²	—	2	4	no	—
640	C₄²	—	2	4	no	—
641	C₄²	—	2	2	no	—
642	C₄²	—	2	2	no	—
643	C₄²	—	2	4	no	—
644	C₄²	—	2	4	no	—
645	C₄²	—	2	4	no	—
646	C₄²	—	4	1	no	—
647	C₄²	—	4	2	no	—
648	C₄²	—	4	2	no	—
649	C₄²	—	4	1	no	—
650	C₄²	—	4	1	no	—
651	C₄²	—	4	1	no	—
652	C₄²	—	4	1	no	—
653	C₄²	—	4	1	no	—
654	C₄²	—	4	2	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	1	no	—
658	C₂³	—	2	1	no	—
659	C₂³	C₂×#41×C₅₉	1	2	yes	—
660	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
661	Q₈	—	8	2	no	—
662	C₂×C₄	—	2	8	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	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	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	4	4	no	—
708	C₂×C₄	—	8	2	no	—
709	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
710	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
711	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
712	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
713	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
714	C₂×C₄	2₋¹⁺⁴×C₅₉	1	4	yes	—
715	C₂²	—	2	2	no	—
716	C₂²	—	2	2	no	—
717	C₂²	—	2	2	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	2	no	—
720	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
721	C₂²	C₂²×#41×C₅₉	1	2	yes	—
722	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	2	yes	—
723	C₂²	C₅₉×#585	1	1	yes	characteristic
724	C₂²	C₅₉×#585	1	1	yes	characteristic
725	C₄	—	2	4	no	—
726	C₄	—	2	4	no	—
727	C₄	—	2	4	no	—
728	C₄	—	2	4	no	—
729	C₄	—	2	2	no	—
730	C₄	—	2	2	no	—
731	C₄	—	4	1	no	—
732	C₄	—	4	1	no	—
733	C₄	—	4	2	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	2	no	—
738	C₄	—	4	1	no	—
739	C₄	—	4	1	no	—
740	C₄	—	4	2	no	—
741	C₄	—	4	2	no	—
742	C₄	—	4	2	no	—
743	C₂	—	4	2	no	—
744	C₂	C₅₉×#3444	1	1	yes	characteristic
745	C₂	C₅₉×#3491	1	1	yes	characteristic
746	C₂	C₅₉×#3509	1	1	yes	characteristic
747	C₂	C₅₉×#3515	1	2	yes	—
748	C₂	C₅₉×#3516	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₂⁴×C₅₉	C₂⁴
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
2. C₅₉×#2590	C₂	semidirect
3. C₅₉×#2588	C₂	semidirect
6. C₅₉×#2533	C₂	semidirect
7. C₅₉×#2524	C₂	semidirect
8. C₅₉×#2520	C₂	semidirect
10. C₅₉×#2506	C₂	semidirect
15. C₅₉×#2336	C₂	semidirect
17. C₄×#125×C₅₉	C₂	semidirect
340. #35496	C₅₉	direct (N × H)
370. #2590	C₂×C₅₉	semidirect
371. #2588	C₂×C₅₉	semidirect
374. #2533	C₂×C₅₉	semidirect
375. #2524	C₂×C₅₉	semidirect
376. #2520	C₂×C₅₉	semidirect
378. #2506	C₂×C₅₉	semidirect
383. #2336	C₂×C₅₉	semidirect
385. C₄×#125	C₂×C₅₉	semidirect
481. C₅₉	#35496	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×#2590	2
C₅₉×#2588	2
C₅₉×#2583	2
C₅₉×#2573	2
C₅₉×#2533	2
C₅₉×#2524	2
C₅₉×#2520	2
C₅₉×#2515	2
C₅₉×#2506	2
C₅₉×#2499	2
C₅₉×#2484	2
C₅₉×#2475	2
C₅₉×#2336	2
C₅₉×#2332	2
C₄×#125×C₅₉	2
C₅₉×#2298	2
C₅₉×#2274	2
#35496	59

Subgroups — C59×#35496 #28447605

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35496 #28447605