Subgroups — C₅₉×#35434 #28447543

Order 15104.

1650 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×#2611	C₂	1	1	yes	maximal, characteristic
2	C₅₉×#2605	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#2599	C₂	1	1	yes	maximal, characteristic
4	C₅₉×#2588	C₂	1	2	yes	maximal, complemented
5	C₅₉×#2584	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#2577	C₂	1	2	yes	maximal
7	C₅₉×#2556	C₂	1	2	yes	maximal
8	C₅₉×#2533	C₂	1	2	yes	maximal, complemented
9	C₅₉×#2530	C₂	1	2	yes	maximal
10	C₅₉×#2475	C₂	1	2	yes	maximal
11	C₅₉×#2465	C₂	1	2	yes	maximal
12	C₅₉×#2462	C₂	1	2	yes	maximal, complemented
13	C₅₉×#2462	C₂	1	2	yes	maximal, complemented
14	C₅₉×#2453	C₂	1	2	yes	maximal, complemented
15	C₅₉×#2336	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₉×#2336	C₂	1	2	yes	maximal, complemented
17	C₄×C₂²⋊Q₈×C₅₉	C₂	1	2	yes	maximal
18	C₅₉×#2296	C₂	1	1	yes	maximal, characteristic
19	C₅₉×#2276	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#125×C₅₉	C₂²	1	2	yes	—
21	C₂×#125×C₅₉	C₂²	1	1	yes	characteristic
22	C₂×#125×C₅₉	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
27	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
30	C₅₉×#400	C₂²	1	2	yes	—
31	C₅₉×#400	C₂²	1	2	yes	—
32	C₅₉×#400	C₂²	1	1	yes	characteristic
33	C₅₉×#400	C₂²	1	2	yes	—
34	C₅₉×#400	C₂²	1	2	yes	—
35	C₅₉×#399	C₂²	1	1	yes	characteristic
36	C₅₉×#398	C₂²	1	2	yes	—
37	C₅₉×#398	C₂²	1	2	yes	—
38	C₅₉×#398	C₂²	1	1	yes	characteristic
39	C₅₉×#398	C₂²	1	1	yes	characteristic
40	C₅₉×#398	C₂²	1	2	yes	—
41	C₅₉×#397	C₂²	1	1	yes	characteristic
42	C₅₉×#397	C₂²	1	2	yes	—
43	C₅₉×#397	C₂²	1	1	yes	characteristic
44	C₅₉×#396	C₂²	1	2	yes	—
45	C₅₉×#395	C₂²	1	2	yes	—
46	C₅₉×#395	C₂²	1	2	yes	—
47	C₅₉×#395	C₂²	1	2	yes	—
48	C₅₉×#395	C₂²	1	1	yes	characteristic
49	C₅₉×#393	C₂²	1	1	yes	characteristic
50	C₅₉×#391	C₂²	1	2	yes	—
51	C₅₉×#391	C₂²	1	2	yes	—
52	C₅₉×#391	C₂²	1	2	yes	—
53	C₅₉×#389	C₂²	1	2	yes	—
54	C₅₉×#389	C₂²	1	2	yes	—
55	C₅₉×#389	C₂²	1	2	yes	—
56	C₅₉×#389	C₂²	1	2	yes	—
57	C₅₉×#389	C₂²	1	2	yes	—
58	C₅₉×#389	C₂²	1	2	yes	—
59	C₅₉×#389	C₂²	1	2	yes	—
60	C₅₉×#389	C₂²	1	2	yes	—
61	C₅₉×#389	C₂²	1	2	yes	—
62	C₅₉×#388	C₂²	1	2	yes	—
63	C₅₉×#388	C₂²	1	2	yes	—
64	C₅₉×#388	C₂²	1	2	yes	—
65	C₅₉×#388	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×#387	C₂²	1	2	yes	—
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	2	yes	—
86	C₅₉×#385	C₂²	1	2	yes	—
87	C₅₉×#385	C₂²	1	2	yes	—
88	C₅₉×#385	C₂²	1	2	yes	—
89	C₅₉×#385	C₂²	1	2	yes	—
90	C₅₉×#383	C₂²	1	2	yes	—
91	C₅₉×#383	C₂²	1	1	yes	characteristic
92	C₅₉×#380	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
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	2	yes	—
98	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
99	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
100	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
101	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
102	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
105	C₅₉×#376	C₂²	1	2	yes	—
106	C₅₉×#376	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
109	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
111	#125×C₅₉	—	2	8	no	—
112	#125×C₅₉	—	2	4	no	—
113	#125×C₅₉	—	4	4	no	—
114	C₂²⋊Q₈×C₅₉	—	2	8	no	—
115	C₄×Q₈×C₅₉	—	2	8	no	—
116	C₄×Q₈×C₅₉	—	2	4	no	—
117	C₄×Q₈×C₅₉	—	4	4	no	—
118	#117×C₅₉	—	2	4	no	—
119	#117×C₅₉	—	4	2	no	—
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	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	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×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
143	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
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	2	yes	—
147	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
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×C₄²×C₅₉	—	4	2	no	—
156	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
157	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
158	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
159	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
160	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
161	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
163	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
164	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
165	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
168	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
171	#95×C₅₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
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	#95×C₅₉	C₂³	1	2	yes	—
201	#95×C₅₉	C₂³	1	2	yes	—
202	#95×C₅₉	C₂³	1	2	yes	—
203	#95×C₅₉	C₂³	1	2	yes	—
204	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
205	C₂×Q₈×C₅₉	—	2	4	no	—
206	C₂×Q₈×C₅₉	—	2	2	no	—
207	C₂×Q₈×C₅₉	—	2	4	no	—
208	C₂×Q₈×C₅₉	—	2	4	no	—
209	C₂×Q₈×C₅₉	—	4	2	no	—
210	C₂²×C₄×C₅₉	—	2	2	no	—
211	C₂²×C₄×C₅₉	—	2	2	no	—
212	C₂²×C₄×C₅₉	—	2	2	no	—
213	C₂²×C₄×C₅₉	—	2	4	no	—
214	C₂²×C₄×C₅₉	—	2	4	no	—
215	C₂²×C₄×C₅₉	—	4	2	no	—
216	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
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	2	yes	—
222	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
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	1	yes	characteristic
229	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
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	2	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	2	no	—
247	C₄⋊C₄×C₅₉	—	2	2	no	—
248	C₄⋊C₄×C₅₉	—	2	4	no	—
249	C₄⋊C₄×C₅₉	—	2	4	no	—
250	C₄⋊C₄×C₅₉	—	2	4	no	—
251	C₄⋊C₄×C₅₉	—	2	4	no	—
252	C₄⋊C₄×C₅₉	—	2	4	no	—
253	C₄⋊C₄×C₅₉	—	2	4	no	—
254	C₄⋊C₄×C₅₉	—	2	4	no	—
255	C₄⋊C₄×C₅₉	—	2	4	no	—
256	C₄⋊C₄×C₅₉	—	2	4	no	—
257	C₄⋊C₄×C₅₉	—	4	2	no	—
258	C₄⋊C₄×C₅₉	—	4	2	no	—
259	C₄⋊C₄×C₅₉	—	4	2	no	—
260	C₄⋊C₄×C₅₉	—	4	2	no	—
261	C₄⋊C₄×C₅₉	#41	1	8	yes	—
262	C₂²⋊C₄×C₅₉	—	2	4	no	—
263	C₂²⋊C₄×C₅₉	—	2	4	no	—
264	C₂²⋊C₄×C₅₉	—	2	2	no	—
265	C₂²⋊C₄×C₅₉	—	2	2	no	—
266	C₂²⋊C₄×C₅₉	—	2	4	no	—
267	C₂²⋊C₄×C₅₉	—	2	4	no	—
268	C₂²⋊C₄×C₅₉	—	4	2	no	—
269	C₄²×C₅₉	—	2	2	no	—
270	C₄²×C₅₉	—	2	4	no	—
271	C₄²×C₅₉	—	2	4	no	—
272	C₄²×C₅₉	—	2	4	no	—
273	C₄²×C₅₉	—	2	4	no	—
274	C₄²×C₅₉	—	2	4	no	—
275	C₄²×C₅₉	—	2	4	no	—
276	C₄²×C₅₉	—	4	1	no	—
277	C₄²×C₅₉	—	4	1	no	—
278	C₄²×C₅₉	—	4	1	no	—
279	C₄²×C₅₉	—	4	1	no	—
280	C₄²×C₅₉	—	4	2	no	—
281	C₄²×C₅₉	—	4	2	no	—
282	C₄²×C₅₉	—	4	2	no	—
283	C₄²×C₅₉	#41	1	4	yes	—
284	C₂³×C₅₉	—	2	1	no	—
285	C₂³×C₅₉	—	2	2	no	—
286	C₂³×C₅₉	—	2	1	no	—
287	C₂³×C₅₉	—	2	2	no	—
288	C₂³×C₅₉	2₋¹⁺⁴	1	2	yes	—
289	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
290	Q₈×C₅₉	—	2	8	no	—
291	Q₈×C₅₉	—	4	8	no	—
292	C₂×C₄×C₅₉	—	2	8	no	—
293	C₂×C₄×C₅₉	—	2	2	no	—
294	C₂×C₄×C₅₉	—	2	2	no	—
295	C₂×C₄×C₅₉	—	2	2	no	—
296	C₂×C₄×C₅₉	—	2	1	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	1	no	—
301	C₂×C₄×C₅₉	—	2	2	no	—
302	C₂×C₄×C₅₉	—	2	2	no	—
303	C₂×C₄×C₅₉	—	2	1	no	—
304	C₂×C₄×C₅₉	—	2	1	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	1	no	—
309	C₂×C₄×C₅₉	—	2	1	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	—	2	2	no	—
333	C₂×C₄×C₅₉	—	2	2	no	—
334	C₂×C₄×C₅₉	—	2	2	no	—
335	C₂×C₄×C₅₉	—	4	8	no	—
336	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
337	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
338	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
339	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
340	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
341	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
342	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
343	C₂×C₄×C₅₉	2₋¹⁺⁴	1	4	yes	—
344	#35434	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
345	C₂²×C₅₉	—	2	2	no	—
346	C₂²×C₅₉	—	2	4	no	—
347	C₂²×C₅₉	—	4	1	no	—
348	C₂²×C₅₉	—	4	1	no	—
349	C₂²×C₅₉	—	4	2	no	—
350	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
351	C₂²×C₅₉	C₂²×#41	1	2	yes	—
352	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
353	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
354	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	2	yes	—
355	C₄×C₅₉	—	2	4	no	—
356	C₄×C₅₉	—	2	2	no	—
357	C₄×C₅₉	—	2	2	no	—
358	C₄×C₅₉	—	2	2	no	—
359	C₄×C₅₉	—	2	2	no	—
360	C₄×C₅₉	—	2	4	no	—
361	C₄×C₅₉	—	2	4	no	—
362	C₄×C₅₉	—	2	4	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	1	no	—
368	C₄×C₅₉	—	4	2	no	—
369	C₄×C₅₉	—	4	2	no	—
370	C₄×C₅₉	—	4	2	no	—
371	C₄×C₅₉	—	4	2	no	—
372	C₄×C₅₉	—	4	2	no	—
373	#2611	C₂×C₅₉	1	1	yes	characteristic
374	#2605	C₂×C₅₉	1	1	yes	characteristic, complemented
375	#2599	C₂×C₅₉	1	1	yes	characteristic
376	#2588	C₂×C₅₉	1	2	yes	complemented
377	#2584	C₂×C₅₉	1	1	yes	characteristic, complemented
378	#2577	C₂×C₅₉	1	2	yes	—
379	#2556	C₂×C₅₉	1	2	yes	—
380	#2533	C₂×C₅₉	1	2	yes	complemented
381	#2530	C₂×C₅₉	1	2	yes	—
382	#2475	C₂×C₅₉	1	2	yes	—
383	#2465	C₂×C₅₉	1	2	yes	—
384	#2462	C₂×C₅₉	1	2	yes	complemented
385	#2462	C₂×C₅₉	1	2	yes	complemented
386	#2453	C₂×C₅₉	1	2	yes	complemented
387	#2336	C₂×C₅₉	1	1	yes	characteristic, complemented
388	#2336	C₂×C₅₉	1	2	yes	complemented
389	C₄×C₂²⋊Q₈	C₂×C₅₉	1	2	yes	—
390	#2296	C₂×C₅₉	1	1	yes	characteristic
391	#2276	C₂×C₅₉	1	1	yes	characteristic, complemented
392	C₂×C₅₉	—	4	2	no	—
393	C₂×C₅₉	#3444	1	1	yes	characteristic
394	C₂×C₅₉	#3492	1	1	yes	characteristic
395	C₂×C₅₉	#3509	1	1	yes	characteristic
396	C₂×C₅₉	#3520	1	2	yes	—
397	C₂×C₅₉	#3523	1	2	yes	—
398	C₂×#125	C₂²×C₅₉	1	1	yes	characteristic
399	C₂×#125	C₂²×C₅₉	1	2	yes	—
400	C₂×#125	C₂²×C₅₉	1	2	yes	—
401	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	—
402	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
403	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
404	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
405	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
406	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
407	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
408	#400	C₂²×C₅₉	1	2	yes	—
409	#400	C₂²×C₅₉	1	2	yes	—
410	#400	C₂²×C₅₉	1	2	yes	—
411	#400	C₂²×C₅₉	1	1	yes	characteristic
412	#400	C₂²×C₅₉	1	2	yes	—
413	#399	C₂²×C₅₉	1	1	yes	characteristic
414	#398	C₂²×C₅₉	1	2	yes	—
415	#398	C₂²×C₅₉	1	2	yes	—
416	#398	C₂²×C₅₉	1	1	yes	characteristic
417	#398	C₂²×C₅₉	1	1	yes	characteristic
418	#398	C₂²×C₅₉	1	2	yes	—
419	#397	C₂²×C₅₉	1	1	yes	characteristic
420	#397	C₂²×C₅₉	1	2	yes	—
421	#397	C₂²×C₅₉	1	1	yes	characteristic
422	#396	C₂²×C₅₉	1	2	yes	—
423	#395	C₂²×C₅₉	1	2	yes	—
424	#395	C₂²×C₅₉	1	2	yes	—
425	#395	C₂²×C₅₉	1	1	yes	characteristic
426	#395	C₂²×C₅₉	1	2	yes	—
427	#393	C₂²×C₅₉	1	1	yes	characteristic
428	#391	C₂²×C₅₉	1	2	yes	—
429	#391	C₂²×C₅₉	1	2	yes	—
430	#391	C₂²×C₅₉	1	2	yes	—
431	#389	C₂²×C₅₉	1	2	yes	—
432	#389	C₂²×C₅₉	1	2	yes	—
433	#389	C₂²×C₅₉	1	2	yes	—
434	#389	C₂²×C₅₉	1	2	yes	—
435	#389	C₂²×C₅₉	1	2	yes	—
436	#389	C₂²×C₅₉	1	2	yes	—
437	#389	C₂²×C₅₉	1	2	yes	—
438	#389	C₂²×C₅₉	1	2	yes	—
439	#389	C₂²×C₅₉	1	2	yes	—
440	#388	C₂²×C₅₉	1	2	yes	—
441	#388	C₂²×C₅₉	1	2	yes	—
442	#388	C₂²×C₅₉	1	2	yes	—
443	#388	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	#387	C₂²×C₅₉	1	2	yes	—
453	#387	C₂²×C₅₉	1	2	yes	—
454	#387	C₂²×C₅₉	1	2	yes	—
455	#387	C₂²×C₅₉	1	2	yes	—
456	#387	C₂²×C₅₉	1	2	yes	—
457	#387	C₂²×C₅₉	1	2	yes	—
458	#387	C₂²×C₅₉	1	2	yes	—
459	#387	C₂²×C₅₉	1	2	yes	—
460	#387	C₂²×C₅₉	1	2	yes	—
461	#387	C₂²×C₅₉	1	2	yes	—
462	#387	C₂²×C₅₉	1	2	yes	—
463	#387	C₂²×C₅₉	1	2	yes	—
464	#385	C₂²×C₅₉	1	2	yes	—
465	#385	C₂²×C₅₉	1	2	yes	—
466	#385	C₂²×C₅₉	1	2	yes	—
467	#385	C₂²×C₅₉	1	2	yes	—
468	#383	C₂²×C₅₉	1	2	yes	—
469	#383	C₂²×C₅₉	1	1	yes	characteristic
470	#380	C₂²×C₅₉	1	2	yes	—
471	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
472	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
473	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
474	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
475	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
476	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
477	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
478	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
479	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
480	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
481	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
482	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
483	#376	C₂²×C₅₉	1	1	yes	characteristic
484	#376	C₂²×C₅₉	1	2	yes	—
485	C₅₉	#35434	1	1	yes	characteristic, direct product factor, Sylow
486	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
487	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
488	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
489	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
490	#125	—	2	8	no	—
491	#125	—	2	4	no	—
492	#125	—	4	4	no	—
493	C₂²⋊Q₈	—	2	8	no	—
494	C₄×Q₈	—	2	8	no	—
495	C₄×Q₈	—	2	4	no	—
496	C₄×Q₈	—	4	4	no	—
497	#117	—	2	4	no	—
498	#117	—	4	2	no	—
499	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
501	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
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×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
528	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
529	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
534	C₂×C₄²	—	4	2	no	—
535	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
536	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
537	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
538	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
539	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
540	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
541	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
542	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
543	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
544	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
545	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
546	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
547	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
548	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
549	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
550	#95	C₂³×C₅₉	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
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	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
584	C₂×Q₈	—	2	4	no	—
585	C₂×Q₈	—	2	2	no	—
586	C₂×Q₈	—	2	4	no	—
587	C₂×Q₈	—	2	4	no	—
588	C₂×Q₈	—	4	2	no	—
589	C₂²×C₄	—	2	2	no	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	4	no	—
593	C₂²×C₄	—	2	4	no	—
594	C₂²×C₄	—	4	2	no	—
595	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
598	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
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	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
606	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
607	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
609	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
610	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
612	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
613	C₄⋊C₄	—	2	2	no	—
614	C₄⋊C₄	—	2	2	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	2	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	—	2	2	no	—
626	C₄⋊C₄	—	2	2	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	4	2	no	—
637	C₄⋊C₄	—	4	2	no	—
638	C₄⋊C₄	—	4	2	no	—
639	C₄⋊C₄	—	4	2	no	—
640	C₄⋊C₄	#41×C₅₉	1	8	yes	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	4	2	no	—
648	C₄²	—	2	2	no	—
649	C₄²	—	2	4	no	—
650	C₄²	—	2	4	no	—
651	C₄²	—	2	4	no	—
652	C₄²	—	2	4	no	—
653	C₄²	—	2	4	no	—
654	C₄²	—	2	4	no	—
655	C₄²	—	4	1	no	—
656	C₄²	—	4	1	no	—
657	C₄²	—	4	1	no	—
658	C₄²	—	4	1	no	—
659	C₄²	—	4	2	no	—
660	C₄²	—	4	2	no	—
661	C₄²	—	4	2	no	—
662	C₄²	#41×C₅₉	1	4	yes	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	1	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	2	2	no	—
667	C₂³	2₋¹⁺⁴×C₅₉	1	2	yes	—
668	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
669	Q₈	—	2	8	no	—
670	Q₈	—	4	8	no	—
671	C₂×C₄	—	2	8	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	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	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	4	8	no	—
715	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
716	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
717	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
718	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
719	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
720	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
721	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
722	C₂×C₄	2₋¹⁺⁴×C₅₉	1	4	yes	—
723	C₂²	—	2	4	no	—
724	C₂²	—	2	2	no	—
725	C₂²	—	4	1	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	4	1	no	—
728	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
729	C₂²	C₂²×#41×C₅₉	1	2	yes	—
730	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
731	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	2	yes	—
732	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
733	C₄	—	2	2	no	—
734	C₄	—	2	4	no	—
735	C₄	—	2	4	no	—
736	C₄	—	2	4	no	—
737	C₄	—	2	4	no	—
738	C₄	—	2	2	no	—
739	C₄	—	2	2	no	—
740	C₄	—	2	2	no	—
741	C₄	—	4	1	no	—
742	C₄	—	4	2	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	2	no	—
745	C₄	—	4	2	no	—
746	C₄	—	4	2	no	—
747	C₄	—	4	1	no	—
748	C₄	—	4	2	no	—
749	C₄	—	4	2	no	—
750	C₄	—	4	2	no	—
751	C₂	—	4	2	no	—
752	C₂	C₅₉×#3444	1	1	yes	characteristic
753	C₂	C₅₉×#3492	1	1	yes	characteristic
754	C₂	C₅₉×#3509	1	1	yes	characteristic
755	C₂	C₅₉×#3520	1	2	yes	—
756	C₂	C₅₉×#3523	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×#2605	C₂	semidirect
4. C₅₉×#2588	C₂	semidirect
5. C₅₉×#2584	C₂	semidirect
8. C₅₉×#2533	C₂	semidirect
12. C₅₉×#2462	C₂	semidirect
13. C₅₉×#2462	C₂	semidirect
14. C₅₉×#2453	C₂	semidirect
15. C₅₉×#2336	C₂	semidirect
16. C₅₉×#2336	C₂	semidirect
19. C₅₉×#2276	C₂	semidirect
344. #35434	C₅₉	direct (N × H)
374. #2605	C₂×C₅₉	semidirect
376. #2588	C₂×C₅₉	semidirect
377. #2584	C₂×C₅₉	semidirect
380. #2533	C₂×C₅₉	semidirect
384. #2462	C₂×C₅₉	semidirect
385. #2462	C₂×C₅₉	semidirect
386. #2453	C₂×C₅₉	semidirect
387. #2336	C₂×C₅₉	semidirect
388. #2336	C₂×C₅₉	semidirect
391. #2276	C₂×C₅₉	semidirect
485. C₅₉	#35434	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×#2611	2
C₅₉×#2605	2
C₅₉×#2599	2
C₅₉×#2588	2
C₅₉×#2584	2
C₅₉×#2577	2
C₅₉×#2556	2
C₅₉×#2533	2
C₅₉×#2530	2
C₅₉×#2475	2
C₅₉×#2465	2
C₅₉×#2462	2
C₅₉×#2453	2
C₅₉×#2336	2
C₄×C₂²⋊Q₈×C₅₉	2
C₅₉×#2296	2
C₅₉×#2276	2
#35434	59

Subgroups — C59×#35434 #28447543

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35434 #28447543