Subgroups — C₅₉×#35688 #28447797

Order 15104.

2420 conjugacy classes of subgroups.

The subgroup lattice has 1114 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#2638	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2616	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2600	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2499	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#2485	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#2465	C₂	1	2	yes	maximal, complemented
9	C₅₉×#2463	C₂	1	2	yes	maximal, complemented
10	C₅₉×#2462	C₂	1	2	yes	maximal, complemented
11	C₅₉×#2460	C₂	1	2	yes	maximal, complemented
12	C₅₉×#2440	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₉×#2439	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₉×#2417	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#2415	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₉×#2415	C₂	1	2	yes	maximal, complemented
17	C₅₉×#2392	C₂	1	2	yes	maximal, complemented
18	C₅₉×#2388	C₂	1	1	yes	maximal, characteristic
19	C₅₉×#2362	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₉×#2360	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₉×#2352	C₂	1	1	yes	maximal, characteristic, complemented
22	D₄×C₄⋊C₄×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₉×#2344	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic
25	C₅₉×#554	—	2	8	no	—
26	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
27	C₂×#125×C₅₉	C₂²	1	2	yes	—
28	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	—
32	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	—
34	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	—
35	C₅₉×#520	—	2	8	no	—
36	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
41	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
44	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
45	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
46	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
47	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
48	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
49	C₂×#117×C₅₉	C₂²	1	2	yes	—
50	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
51	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
52	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
53	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
54	C₅₉×#398	C₂²	1	2	yes	—
55	C₅₉×#398	C₂²	1	2	yes	—
56	C₅₉×#397	C₂²	1	2	yes	—
57	C₅₉×#397	C₂²	1	2	yes	—
58	C₅₉×#397	C₂²	1	2	yes	—
59	C₅₉×#397	C₂²	1	2	yes	—
60	C₅₉×#396	C₂²	1	2	yes	—
61	C₅₉×#396	C₂²	1	2	yes	—
62	C₅₉×#395	C₂²	1	2	yes	—
63	C₅₉×#395	C₂²	1	2	yes	—
64	C₅₉×#395	C₂²	1	1	yes	characteristic
65	C₅₉×#394	C₂²	1	2	yes	—
66	C₅₉×#394	C₂²	1	2	yes	—
67	C₅₉×#394	C₂²	1	2	yes	—
68	C₅₉×#394	C₂²	1	2	yes	—
69	C₅₉×#394	C₂²	1	1	yes	characteristic
70	C₅₉×#394	C₂²	1	1	yes	characteristic
71	C₅₉×#394	C₂²	1	1	yes	characteristic
72	C₅₉×#394	C₂²	1	2	yes	—
73	C₅₉×#393	C₂²	1	2	yes	—
74	C₅₉×#393	C₂²	1	1	yes	characteristic
75	C₅₉×#392	C₂²	1	1	yes	characteristic
76	C₅₉×#392	C₂²	1	1	yes	characteristic
77	C₅₉×#392	C₂²	1	1	yes	characteristic
78	C₅₉×#391	C₂²	1	1	yes	characteristic
79	C₅₉×#391	C₂²	1	1	yes	characteristic
80	C₅₉×#391	C₂²	1	2	yes	—
81	C₅₉×#389	C₂²	1	1	yes	characteristic
82	C₅₉×#389	C₂²	1	1	yes	characteristic
83	C₅₉×#389	C₂²	1	1	yes	characteristic
84	C₅₉×#389	C₂²	1	1	yes	characteristic
85	C₅₉×#389	C₂²	1	2	yes	—
86	C₅₉×#389	C₂²	1	2	yes	—
87	C₅₉×#389	C₂²	1	2	yes	—
88	C₅₉×#388	C₂²	1	2	yes	—
89	C₅₉×#388	C₂²	1	2	yes	—
90	C₅₉×#388	C₂²	1	2	yes	—
91	C₅₉×#388	C₂²	1	2	yes	—
92	C₅₉×#388	C₂²	1	2	yes	—
93	C₅₉×#387	C₂²	1	2	yes	—
94	C₅₉×#387	C₂²	1	2	yes	—
95	C₅₉×#387	C₂²	1	2	yes	—
96	C₅₉×#387	C₂²	1	2	yes	—
97	C₅₉×#387	C₂²	1	2	yes	—
98	C₅₉×#387	C₂²	1	2	yes	—
99	C₅₉×#387	C₂²	1	2	yes	—
100	C₅₉×#387	C₂²	1	2	yes	—
101	C₅₉×#387	C₂²	1	2	yes	—
102	C₅₉×#386	C₂²	1	2	yes	—
103	C₅₉×#386	C₂²	1	2	yes	—
104	C₅₉×#385	C₂²	1	2	yes	—
105	C₅₉×#385	C₂²	1	2	yes	—
106	C₅₉×#385	C₂²	1	2	yes	—
107	C₅₉×#385	C₂²	1	2	yes	—
108	C₅₉×#384	C₂²	1	1	yes	characteristic
109	C₅₉×#382	C₂²	1	1	yes	characteristic
110	C₅₉×#381	C₂²	1	2	yes	—
111	C₅₉×#380	C₂²	1	1	yes	characteristic
112	C₅₉×#380	C₂²	1	1	yes	characteristic
113	C₅₉×#380	C₂²	1	1	yes	characteristic
114	C₅₉×#380	C₂²	1	1	yes	characteristic
115	C₅₉×#380	C₂²	1	1	yes	characteristic
116	C₅₉×#380	C₂²	1	2	yes	—
117	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
118	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
119	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
122	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
123	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
124	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
125	C₂×#41×C₅₉	—	2	4	no	—
126	C₂×#41×C₅₉	—	2	4	no	—
127	C₂×#41×C₅₉	—	2	4	no	—
128	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
129	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
130	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
131	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
132	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
135	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
136	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
142	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
143	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
144	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
145	C₄⋊Q₈×C₅₉	—	2	4	no	—
146	#125×C₅₉	—	2	8	no	—
147	C₂²⋊Q₈×C₅₉	—	2	8	no	—
148	C₂²⋊Q₈×C₅₉	—	2	4	no	—
149	C₂²⋊Q₈×C₅₉	—	2	4	no	—
150	C₂²⋊Q₈×C₅₉	—	2	4	no	—
151	C₂²⋊Q₈×C₅₉	—	2	8	no	—
152	C₂²⋊Q₈×C₅₉	—	2	4	no	—
153	C₂²⋊Q₈×C₅₉	—	4	4	no	—
154	C₄×Q₈×C₅₉	—	2	8	no	—
155	C₄×Q₈×C₅₉	—	2	4	no	—
156	C₄×D₄×C₅₉	—	2	8	no	—
157	C₄×D₄×C₅₉	—	2	8	no	—
158	C₄×D₄×C₅₉	—	2	8	no	—
159	C₄×D₄×C₅₉	—	2	4	no	—
160	C₄×D₄×C₅₉	—	2	4	no	—
161	C₄×D₄×C₅₉	—	2	4	no	—
162	C₄×D₄×C₅₉	—	2	8	no	—
163	C₄×D₄×C₅₉	—	4	4	no	—
164	#117×C₅₉	—	2	4	no	—
165	#117×C₅₉	—	2	4	no	—
166	#117×C₅₉	—	2	4	no	—
167	#117×C₅₉	—	4	4	no	—
168	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
169	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
170	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
171	C₂×C₄⋊C₄×C₅₉	D₄	1	8	yes	complemented
172	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
184	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
185	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
192	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
195	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
196	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
197	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
218	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
219	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
221	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
222	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
226	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
227	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
228	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
229	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
230	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
231	#95×C₅₉	C₂³	1	1	yes	characteristic
232	#95×C₅₉	C₂³	1	2	yes	—
233	#95×C₅₉	C₂³	1	2	yes	—
234	#95×C₅₉	C₂³	1	2	yes	—
235	#95×C₅₉	C₂³	1	2	yes	—
236	#95×C₅₉	C₂³	1	1	yes	characteristic
237	#95×C₅₉	C₂³	1	1	yes	characteristic
238	#95×C₅₉	C₂³	1	1	yes	characteristic
239	#95×C₅₉	C₂³	1	1	yes	characteristic
240	#95×C₅₉	C₂³	1	1	yes	characteristic
241	#95×C₅₉	C₂³	1	2	yes	—
242	#95×C₅₉	C₂³	1	2	yes	—
243	#95×C₅₉	C₂³	1	2	yes	—
244	#95×C₅₉	C₂³	1	2	yes	—
245	#95×C₅₉	C₂³	1	2	yes	—
246	#95×C₅₉	C₂³	1	2	yes	—
247	#95×C₅₉	C₂³	1	2	yes	—
248	#95×C₅₉	C₂³	1	2	yes	—
249	#95×C₅₉	C₂³	1	2	yes	—
250	#95×C₅₉	C₂³	1	2	yes	—
251	#95×C₅₉	C₂³	1	2	yes	—
252	#95×C₅₉	C₂³	1	2	yes	—
253	#95×C₅₉	C₂³	1	2	yes	—
254	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
255	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
256	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
257	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
258	#41×C₅₉	—	2	32	no	—
259	C₂×Q₈×C₅₉	—	2	2	no	—
260	C₂×Q₈×C₅₉	—	2	2	no	—
261	C₂×Q₈×C₅₉	—	2	4	no	—
262	C₂×Q₈×C₅₉	—	2	2	no	—
263	C₂×Q₈×C₅₉	—	2	2	no	—
264	C₂×Q₈×C₅₉	—	2	2	no	—
265	C₂×Q₈×C₅₉	—	2	2	no	—
266	C₂×Q₈×C₅₉	—	4	2	no	—
267	C₂×Q₈×C₅₉	—	4	2	no	—
268	C₂×D₄×C₅₉	—	2	2	no	—
269	C₂×D₄×C₅₉	—	2	2	no	—
270	C₂×D₄×C₅₉	—	2	2	no	—
271	C₂×D₄×C₅₉	—	2	2	no	—
272	C₂×D₄×C₅₉	—	2	2	no	—
273	C₂×D₄×C₅₉	—	2	2	no	—
274	C₂×D₄×C₅₉	—	2	2	no	—
275	C₂×D₄×C₅₉	—	2	2	no	—
276	C₂×D₄×C₅₉	—	2	2	no	—
277	C₂×D₄×C₅₉	—	2	2	no	—
278	C₂×D₄×C₅₉	—	2	2	no	—
279	C₂×D₄×C₅₉	—	2	2	no	—
280	C₂×D₄×C₅₉	—	2	2	no	—
281	C₂×D₄×C₅₉	—	2	2	no	—
282	C₂×D₄×C₅₉	—	2	2	no	—
283	C₂×D₄×C₅₉	—	2	2	no	—
284	C₂×D₄×C₅₉	—	2	2	no	—
285	C₂×D₄×C₅₉	—	4	1	no	—
286	C₂²×C₄×C₅₉	—	2	2	no	—
287	C₂²×C₄×C₅₉	—	2	2	no	—
288	C₂²×C₄×C₅₉	—	2	2	no	—
289	C₂²×C₄×C₅₉	—	2	2	no	—
290	C₂²×C₄×C₅₉	—	2	2	no	—
291	C₂²×C₄×C₅₉	—	2	2	no	—
292	C₂²×C₄×C₅₉	—	2	2	no	—
293	C₂²×C₄×C₅₉	—	2	2	no	—
294	C₂²×C₄×C₅₉	—	2	2	no	—
295	C₂²×C₄×C₅₉	—	2	4	no	—
296	C₂²×C₄×C₅₉	—	2	4	no	—
297	C₂²×C₄×C₅₉	—	2	4	no	—
298	C₂²×C₄×C₅₉	—	4	2	no	—
299	C₂²×C₄×C₅₉	—	4	2	no	—
300	C₂²×C₄×C₅₉	—	4	2	no	—
301	C₂²×C₄×C₅₉	—	4	2	no	—
302	C₂²×C₄×C₅₉	—	4	2	no	—
303	C₂²×C₄×C₅₉	—	4	2	no	—
304	C₂²×C₄×C₅₉	—	4	2	no	—
305	C₂²×C₄×C₅₉	—	4	2	no	—
306	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
307	C₂²×C₄×C₅₉	C₂×D₄	1	8	yes	—
308	C₂²×C₄×C₅₉	#41	1	4	yes	—
309	C₂²×C₄×C₅₉	#41	1	4	yes	—
310	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
319	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
324	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
329	C₄⋊C₄×C₅₉	—	2	2	no	—
330	C₄⋊C₄×C₅₉	—	2	4	no	—
331	C₄⋊C₄×C₅₉	—	2	4	no	—
332	C₄⋊C₄×C₅₉	—	2	4	no	—
333	C₄⋊C₄×C₅₉	—	2	2	no	—
334	C₄⋊C₄×C₅₉	—	2	2	no	—
335	C₄⋊C₄×C₅₉	—	2	2	no	—
336	C₄⋊C₄×C₅₉	—	2	4	no	—
337	C₄⋊C₄×C₅₉	—	2	4	no	—
338	C₄⋊C₄×C₅₉	—	2	4	no	—
339	C₄⋊C₄×C₅₉	—	2	4	no	—
340	C₄⋊C₄×C₅₉	—	2	2	no	—
341	C₄⋊C₄×C₅₉	—	2	2	no	—
342	C₄⋊C₄×C₅₉	—	2	2	no	—
343	C₄⋊C₄×C₅₉	—	2	2	no	—
344	C₄⋊C₄×C₅₉	—	2	4	no	—
345	C₄⋊C₄×C₅₉	—	2	4	no	—
346	C₄⋊C₄×C₅₉	—	2	4	no	—
347	C₄⋊C₄×C₅₉	—	2	4	no	—
348	C₄⋊C₄×C₅₉	—	2	4	no	—
349	C₄⋊C₄×C₅₉	—	4	2	no	—
350	C₄⋊C₄×C₅₉	—	4	2	no	—
351	C₄⋊C₄×C₅₉	—	4	2	no	—
352	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
353	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
354	C₄⋊C₄×C₅₉	C₂×D₄	1	8	yes	—
355	C₂²⋊C₄×C₅₉	—	2	4	no	—
356	C₂²⋊C₄×C₅₉	—	2	4	no	—
357	C₂²⋊C₄×C₅₉	—	2	2	no	—
358	C₂²⋊C₄×C₅₉	—	2	2	no	—
359	C₂²⋊C₄×C₅₉	—	2	2	no	—
360	C₂²⋊C₄×C₅₉	—	2	4	no	—
361	C₂²⋊C₄×C₅₉	—	2	4	no	—
362	C₂²⋊C₄×C₅₉	—	2	4	no	—
363	C₂²⋊C₄×C₅₉	—	2	4	no	—
364	C₂²⋊C₄×C₅₉	—	2	4	no	—
365	C₂²⋊C₄×C₅₉	—	2	4	no	—
366	C₂²⋊C₄×C₅₉	—	2	2	no	—
367	C₂²⋊C₄×C₅₉	—	2	2	no	—
368	C₂²⋊C₄×C₅₉	—	2	2	no	—
369	C₂²⋊C₄×C₅₉	—	2	2	no	—
370	C₂²⋊C₄×C₅₉	—	2	2	no	—
371	C₂²⋊C₄×C₅₉	—	2	2	no	—
372	C₂²⋊C₄×C₅₉	—	2	2	no	—
373	C₂²⋊C₄×C₅₉	—	4	1	no	—
374	C₂²⋊C₄×C₅₉	—	4	1	no	—
375	C₂²⋊C₄×C₅₉	—	4	2	no	—
376	C₂²⋊C₄×C₅₉	—	4	2	no	—
377	C₂²⋊C₄×C₅₉	—	4	2	no	—
378	C₂²⋊C₄×C₅₉	—	4	2	no	—
379	C₄²×C₅₉	—	2	4	no	—
380	C₄²×C₅₉	—	2	4	no	—
381	C₄²×C₅₉	—	2	4	no	—
382	C₄²×C₅₉	—	2	4	no	—
383	C₄²×C₅₉	—	2	2	no	—
384	C₄²×C₅₉	—	2	2	no	—
385	C₄²×C₅₉	—	2	2	no	—
386	C₄²×C₅₉	—	2	4	no	—
387	C₄²×C₅₉	—	4	2	no	—
388	C₂³×C₅₉	—	2	1	no	—
389	C₂³×C₅₉	—	2	1	no	—
390	C₂³×C₅₉	—	2	1	no	—
391	C₂³×C₅₉	—	2	1	no	—
392	C₂³×C₅₉	—	2	1	no	—
393	C₂³×C₅₉	—	2	1	no	—
394	C₂³×C₅₉	—	2	1	no	—
395	C₂³×C₅₉	—	2	1	no	—
396	C₂³×C₅₉	—	2	1	no	—
397	C₂³×C₅₉	—	2	1	no	—
398	C₂³×C₅₉	—	2	1	no	—
399	C₂³×C₅₉	—	2	1	no	—
400	C₂³×C₅₉	—	2	1	no	—
401	C₂³×C₅₉	—	2	1	no	—
402	C₂³×C₅₉	—	2	1	no	—
403	C₂³×C₅₉	—	2	1	no	—
404	C₂³×C₅₉	—	2	1	no	—
405	C₂³×C₅₉	—	2	1	no	—
406	C₂³×C₅₉	—	2	1	no	—
407	C₂³×C₅₉	—	2	1	no	—
408	C₂³×C₅₉	—	2	1	no	—
409	C₂³×C₅₉	—	2	1	no	—
410	C₂³×C₅₉	—	2	1	no	—
411	C₂³×C₅₉	—	2	1	no	—
412	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
413	C₂³×C₅₉	C₂×#41	1	2	yes	—
414	C₂³×C₅₉	C₂×#41	1	2	yes	—
415	C₂³×C₅₉	2₋¹⁺⁴	1	2	yes	—
416	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
417	Q₈×C₅₉	—	2	8	no	—
418	Q₈×C₅₉	—	4	4	no	—
419	Q₈×C₅₉	—	8	4	no	—
420	D₄×C₅₉	—	2	8	no	—
421	D₄×C₅₉	—	2	8	no	—
422	D₄×C₅₉	—	2	8	no	—
423	D₄×C₅₉	—	2	8	no	—
424	D₄×C₅₉	—	2	8	no	—
425	D₄×C₅₉	—	4	4	no	—
426	C₂×C₄×C₅₉	—	2	1	no	—
427	C₂×C₄×C₅₉	—	2	1	no	—
428	C₂×C₄×C₅₉	—	2	1	no	—
429	C₂×C₄×C₅₉	—	2	1	no	—
430	C₂×C₄×C₅₉	—	2	1	no	—
431	C₂×C₄×C₅₉	—	2	1	no	—
432	C₂×C₄×C₅₉	—	2	1	no	—
433	C₂×C₄×C₅₉	—	2	1	no	—
434	C₂×C₄×C₅₉	—	2	2	no	—
435	C₂×C₄×C₅₉	—	2	2	no	—
436	C₂×C₄×C₅₉	—	2	1	no	—
437	C₂×C₄×C₅₉	—	2	1	no	—
438	C₂×C₄×C₅₉	—	2	2	no	—
439	C₂×C₄×C₅₉	—	2	2	no	—
440	C₂×C₄×C₅₉	—	2	8	no	—
441	C₂×C₄×C₅₉	—	2	8	no	—
442	C₂×C₄×C₅₉	—	2	8	no	—
443	C₂×C₄×C₅₉	—	2	2	no	—
444	C₂×C₄×C₅₉	—	2	2	no	—
445	C₂×C₄×C₅₉	—	2	1	no	—
446	C₂×C₄×C₅₉	—	2	2	no	—
447	C₂×C₄×C₅₉	—	2	1	no	—
448	C₂×C₄×C₅₉	—	2	2	no	—
449	C₂×C₄×C₅₉	—	2	1	no	—
450	C₂×C₄×C₅₉	—	2	1	no	—
451	C₂×C₄×C₅₉	—	2	1	no	—
452	C₂×C₄×C₅₉	—	2	2	no	—
453	C₂×C₄×C₅₉	—	2	2	no	—
454	C₂×C₄×C₅₉	—	2	1	no	—
455	C₂×C₄×C₅₉	—	2	1	no	—
456	C₂×C₄×C₅₉	—	2	2	no	—
457	C₂×C₄×C₅₉	—	2	2	no	—
458	C₂×C₄×C₅₉	—	2	2	no	—
459	C₂×C₄×C₅₉	—	2	1	no	—
460	C₂×C₄×C₅₉	—	2	2	no	—
461	C₂×C₄×C₅₉	—	2	1	no	—
462	C₂×C₄×C₅₉	—	2	2	no	—
463	C₂×C₄×C₅₉	—	2	2	no	—
464	C₂×C₄×C₅₉	—	2	2	no	—
465	C₂×C₄×C₅₉	—	2	2	no	—
466	C₂×C₄×C₅₉	—	2	1	no	—
467	C₂×C₄×C₅₉	—	2	1	no	—
468	C₂×C₄×C₅₉	—	2	2	no	—
469	C₂×C₄×C₅₉	—	2	2	no	—
470	C₂×C₄×C₅₉	—	2	1	no	—
471	C₂×C₄×C₅₉	—	2	1	no	—
472	C₂×C₄×C₅₉	—	2	1	no	—
473	C₂×C₄×C₅₉	—	2	1	no	—
474	C₂×C₄×C₅₉	—	2	2	no	—
475	C₂×C₄×C₅₉	—	2	2	no	—
476	C₂×C₄×C₅₉	—	4	8	no	—
477	C₂×C₄×C₅₉	—	4	4	no	—
478	C₂×C₄×C₅₉	—	8	4	no	—
479	C₂×C₄×C₅₉	—	8	4	no	—
480	C₂×C₄×C₅₉	—	8	4	no	—
481	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
482	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
483	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
484	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
485	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
486	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
487	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
488	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
489	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
490	C₂×C₄×C₅₉	2₋¹⁺⁴	1	2	yes	—
491	#35688	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
492	C₂²×C₅₉	—	2	2	no	—
493	C₂²×C₅₉	—	2	2	no	—
494	C₂²×C₅₉	—	2	2	no	—
495	C₂²×C₅₉	—	2	2	no	—
496	C₂²×C₅₉	—	2	2	no	—
497	C₂²×C₅₉	—	2	2	no	—
498	C₂²×C₅₉	—	2	2	no	—
499	C₂²×C₅₉	—	2	2	no	—
500	C₂²×C₅₉	—	2	2	no	—
501	C₂²×C₅₉	—	2	2	no	—
502	C₂²×C₅₉	—	2	2	no	—
503	C₂²×C₅₉	—	2	2	no	—
504	C₂²×C₅₉	—	4	1	no	—
505	C₂²×C₅₉	—	4	1	no	—
506	C₂²×C₅₉	—	4	1	no	—
507	C₂²×C₅₉	—	4	1	no	—
508	C₂²×C₅₉	—	4	1	no	—
509	C₂²×C₅₉	—	4	1	no	—
510	C₂²×C₅₉	—	4	1	no	—
511	C₂²×C₅₉	—	4	1	no	—
512	C₂²×C₅₉	—	4	1	no	—
513	C₂²×C₅₉	—	4	1	no	—
514	C₂²×C₅₉	—	4	1	no	—
515	C₂²×C₅₉	—	4	1	no	—
516	C₂²×C₅₉	—	4	1	no	—
517	C₂²×C₅₉	—	4	1	no	—
518	C₂²×C₅₉	—	4	1	no	—
519	C₂²×C₅₉	—	4	1	no	—
520	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
521	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
522	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
523	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
524	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
525	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
526	C₂²×C₅₉	#585	1	1	yes	characteristic
527	C₄×C₅₉	—	2	2	no	—
528	C₄×C₅₉	—	2	2	no	—
529	C₄×C₅₉	—	2	2	no	—
530	C₄×C₅₉	—	2	2	no	—
531	C₄×C₅₉	—	2	2	no	—
532	C₄×C₅₉	—	2	4	no	—
533	C₄×C₅₉	—	2	4	no	—
534	C₄×C₅₉	—	4	1	no	—
535	C₄×C₅₉	—	4	2	no	—
536	C₄×C₅₉	—	4	2	no	—
537	C₄×C₅₉	—	4	2	no	—
538	C₄×C₅₉	—	4	1	no	—
539	C₄×C₅₉	—	4	2	no	—
540	C₄×C₅₉	—	4	2	no	—
541	C₄×C₅₉	—	4	1	no	—
542	C₄×C₅₉	—	4	1	no	—
543	C₄×C₅₉	—	4	1	no	—
544	C₄×C₅₉	—	4	2	no	—
545	C₄×C₅₉	#525	1	4	yes	—
546	C₂×#554	C₂×C₅₉	1	1	yes	characteristic, complemented
547	C₂×#520	C₂×C₅₉	1	1	yes	characteristic, complemented
548	#2638	C₂×C₅₉	1	2	yes	complemented
549	#2616	C₂×C₅₉	1	1	yes	characteristic, complemented
550	#2600	C₂×C₅₉	1	2	yes	complemented
551	#2499	C₂×C₅₉	1	1	yes	characteristic, complemented
552	#2485	C₂×C₅₉	1	1	yes	characteristic, complemented
553	#2465	C₂×C₅₉	1	2	yes	complemented
554	#2463	C₂×C₅₉	1	2	yes	complemented
555	#2462	C₂×C₅₉	1	2	yes	complemented
556	#2460	C₂×C₅₉	1	2	yes	complemented
557	#2440	C₂×C₅₉	1	1	yes	characteristic, complemented
558	#2439	C₂×C₅₉	1	1	yes	characteristic, complemented
559	#2417	C₂×C₅₉	1	1	yes	characteristic, complemented
560	#2415	C₂×C₅₉	1	1	yes	characteristic, complemented
561	#2415	C₂×C₅₉	1	2	yes	complemented
562	#2392	C₂×C₅₉	1	2	yes	complemented
563	#2388	C₂×C₅₉	1	1	yes	characteristic
564	#2362	C₂×C₅₉	1	1	yes	characteristic, complemented
565	#2360	C₂×C₅₉	1	1	yes	characteristic, complemented
566	#2352	C₂×C₅₉	1	1	yes	characteristic, complemented
567	D₄×C₄⋊C₄	C₂×C₅₉	1	1	yes	characteristic, complemented
568	#2344	C₂×C₅₉	1	1	yes	characteristic, complemented
569	C₂×C₅₉	—	4	2	no	—
570	C₂×C₅₉	—	4	2	no	—
571	C₂×C₅₉	—	4	2	no	—
572	C₂×C₅₉	—	4	2	no	—
573	C₂×C₅₉	C₂×#525	1	1	yes	characteristic
574	C₂×C₅₉	#3486	1	1	yes	characteristic
575	C₂×C₅₉	#3492	1	1	yes	characteristic
576	C₂×C₅₉	#3495	1	1	yes	characteristic
577	C₂×C₅₉	#3496	1	1	yes	characteristic
578	C₂×C₅₉	#3507	1	1	yes	characteristic
579	C₂×C₅₉	#3511	1	1	yes	characteristic
580	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic
581	#554	—	2	8	no	—
582	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
583	C₂×#125	C₂²×C₅₉	1	2	yes	—
584	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
585	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
586	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
587	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	—
588	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
589	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	—
590	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	—
591	#520	—	2	8	no	—
592	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
593	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
594	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
595	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
596	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
597	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
598	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
599	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
600	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
601	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
602	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
603	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
604	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
605	C₂×#117	C₂²×C₅₉	1	2	yes	—
606	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
607	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
608	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
609	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
610	#398	C₂²×C₅₉	1	2	yes	—
611	#398	C₂²×C₅₉	1	2	yes	—
612	#397	C₂²×C₅₉	1	2	yes	—
613	#397	C₂²×C₅₉	1	2	yes	—
614	#397	C₂²×C₅₉	1	2	yes	—
615	#397	C₂²×C₅₉	1	2	yes	—
616	#396	C₂²×C₅₉	1	2	yes	—
617	#396	C₂²×C₅₉	1	2	yes	—
618	#395	C₂²×C₅₉	1	2	yes	—
619	#395	C₂²×C₅₉	1	2	yes	—
620	#395	C₂²×C₅₉	1	1	yes	characteristic
621	#394	C₂²×C₅₉	1	2	yes	—
622	#394	C₂²×C₅₉	1	2	yes	—
623	#394	C₂²×C₅₉	1	2	yes	—
624	#394	C₂²×C₅₉	1	2	yes	—
625	#394	C₂²×C₅₉	1	1	yes	characteristic
626	#394	C₂²×C₅₉	1	1	yes	characteristic
627	#394	C₂²×C₅₉	1	1	yes	characteristic
628	#394	C₂²×C₅₉	1	2	yes	—
629	#393	C₂²×C₅₉	1	2	yes	—
630	#393	C₂²×C₅₉	1	1	yes	characteristic
631	#392	C₂²×C₅₉	1	1	yes	characteristic
632	#392	C₂²×C₅₉	1	1	yes	characteristic
633	#392	C₂²×C₅₉	1	1	yes	characteristic
634	#391	C₂²×C₅₉	1	1	yes	characteristic
635	#391	C₂²×C₅₉	1	1	yes	characteristic
636	#391	C₂²×C₅₉	1	2	yes	—
637	#389	C₂²×C₅₉	1	1	yes	characteristic
638	#389	C₂²×C₅₉	1	1	yes	characteristic
639	#389	C₂²×C₅₉	1	2	yes	—
640	#389	C₂²×C₅₉	1	2	yes	—
641	#389	C₂²×C₅₉	1	1	yes	characteristic
642	#389	C₂²×C₅₉	1	1	yes	characteristic
643	#389	C₂²×C₅₉	1	2	yes	—
644	#388	C₂²×C₅₉	1	2	yes	—
645	#388	C₂²×C₅₉	1	2	yes	—
646	#388	C₂²×C₅₉	1	2	yes	—
647	#388	C₂²×C₅₉	1	2	yes	—
648	#388	C₂²×C₅₉	1	2	yes	—
649	#387	C₂²×C₅₉	1	2	yes	—
650	#387	C₂²×C₅₉	1	2	yes	—
651	#387	C₂²×C₅₉	1	2	yes	—
652	#387	C₂²×C₅₉	1	2	yes	—
653	#387	C₂²×C₅₉	1	2	yes	—
654	#387	C₂²×C₅₉	1	2	yes	—
655	#387	C₂²×C₅₉	1	2	yes	—
656	#387	C₂²×C₅₉	1	2	yes	—
657	#387	C₂²×C₅₉	1	2	yes	—
658	#386	C₂²×C₅₉	1	2	yes	—
659	#386	C₂²×C₅₉	1	2	yes	—
660	#385	C₂²×C₅₉	1	2	yes	—
661	#385	C₂²×C₅₉	1	2	yes	—
662	#385	C₂²×C₅₉	1	2	yes	—
663	#385	C₂²×C₅₉	1	2	yes	—
664	#384	C₂²×C₅₉	1	1	yes	characteristic
665	#382	C₂²×C₅₉	1	1	yes	characteristic
666	#381	C₂²×C₅₉	1	2	yes	—
667	#380	C₂²×C₅₉	1	1	yes	characteristic
668	#380	C₂²×C₅₉	1	1	yes	characteristic
669	#380	C₂²×C₅₉	1	1	yes	characteristic
670	#380	C₂²×C₅₉	1	1	yes	characteristic
671	#380	C₂²×C₅₉	1	1	yes	characteristic
672	#380	C₂²×C₅₉	1	2	yes	—
673	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
674	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
675	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
676	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
677	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
678	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
679	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
680	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
681	C₅₉	#35688	1	1	yes	characteristic, direct product factor, Sylow
682	C₂×#41	—	2	4	no	—
683	C₂×#41	—	2	4	no	—
684	C₂×#41	—	2	4	no	—
685	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
686	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
687	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
688	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
689	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
690	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
691	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
692	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
693	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
694	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
695	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
696	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
697	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
698	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
699	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
700	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
701	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
702	C₄⋊Q₈	—	2	4	no	—
703	#125	—	2	8	no	—
704	C₂²⋊Q₈	—	2	8	no	—
705	C₂²⋊Q₈	—	2	4	no	—
706	C₂²⋊Q₈	—	2	4	no	—
707	C₂²⋊Q₈	—	2	4	no	—
708	C₂²⋊Q₈	—	2	8	no	—
709	C₂²⋊Q₈	—	2	4	no	—
710	C₂²⋊Q₈	—	4	4	no	—
711	C₄×Q₈	—	2	8	no	—
712	C₄×Q₈	—	2	4	no	—
713	C₄×D₄	—	2	8	no	—
714	C₄×D₄	—	2	8	no	—
715	C₄×D₄	—	2	8	no	—
716	C₄×D₄	—	2	4	no	—
717	C₄×D₄	—	2	4	no	—
718	C₄×D₄	—	2	4	no	—
719	C₄×D₄	—	2	8	no	—
720	C₄×D₄	—	4	4	no	—
721	#117	—	2	4	no	—
722	#117	—	2	4	no	—
723	#117	—	2	4	no	—
724	#117	—	4	4	no	—
725	C₂×C₄⋊C₄	—	2	4	no	—
726	C₂×C₄⋊C₄	—	2	4	no	—
727	C₂×C₄⋊C₄	—	2	4	no	—
728	C₂×C₄⋊C₄	D₄×C₅₉	1	8	yes	complemented
729	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
730	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
731	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
732	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
733	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
734	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
735	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
736	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
737	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
738	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
739	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
740	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
741	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
742	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
743	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
744	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
745	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
746	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
747	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
748	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
749	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
750	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
751	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
752	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
753	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
754	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
755	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
756	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
757	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
758	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
759	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
760	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
761	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
762	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
763	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
764	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
765	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
766	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
767	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
768	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
769	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
770	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
771	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
772	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
773	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
774	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
775	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
776	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
777	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
778	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
779	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
780	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
781	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
782	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
783	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
784	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
785	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
786	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
787	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
788	#95	C₂³×C₅₉	1	1	yes	characteristic
789	#95	C₂³×C₅₉	1	2	yes	—
790	#95	C₂³×C₅₉	1	2	yes	—
791	#95	C₂³×C₅₉	1	2	yes	—
792	#95	C₂³×C₅₉	1	2	yes	—
793	#95	C₂³×C₅₉	1	1	yes	characteristic
794	#95	C₂³×C₅₉	1	1	yes	characteristic
795	#95	C₂³×C₅₉	1	1	yes	characteristic
796	#95	C₂³×C₅₉	1	1	yes	characteristic
797	#95	C₂³×C₅₉	1	1	yes	characteristic
798	#95	C₂³×C₅₉	1	2	yes	—
799	#95	C₂³×C₅₉	1	2	yes	—
800	#95	C₂³×C₅₉	1	2	yes	—
801	#95	C₂³×C₅₉	1	2	yes	—
802	#95	C₂³×C₅₉	1	2	yes	—
803	#95	C₂³×C₅₉	1	2	yes	—
804	#95	C₂³×C₅₉	1	2	yes	—
805	#95	C₂³×C₅₉	1	2	yes	—
806	#95	C₂³×C₅₉	1	2	yes	—
807	#95	C₂³×C₅₉	1	2	yes	—
808	#95	C₂³×C₅₉	1	2	yes	—
809	#95	C₂³×C₅₉	1	2	yes	—
810	#95	C₂³×C₅₉	1	2	yes	—
811	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
812	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
813	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
814	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
815	#41	—	2	32	no	—
816	C₂×Q₈	—	2	2	no	—
817	C₂×Q₈	—	2	2	no	—
818	C₂×Q₈	—	2	4	no	—
819	C₂×Q₈	—	2	2	no	—
820	C₂×Q₈	—	2	2	no	—
821	C₂×Q₈	—	2	2	no	—
822	C₂×Q₈	—	2	2	no	—
823	C₂×Q₈	—	4	2	no	—
824	C₂×Q₈	—	4	2	no	—
825	C₂×D₄	—	2	2	no	—
826	C₂×D₄	—	2	2	no	—
827	C₂×D₄	—	2	2	no	—
828	C₂×D₄	—	2	2	no	—
829	C₂×D₄	—	2	2	no	—
830	C₂×D₄	—	2	2	no	—
831	C₂×D₄	—	2	2	no	—
832	C₂×D₄	—	2	2	no	—
833	C₂×D₄	—	2	2	no	—
834	C₂×D₄	—	2	2	no	—
835	C₂×D₄	—	2	2	no	—
836	C₂×D₄	—	2	2	no	—
837	C₂×D₄	—	2	2	no	—
838	C₂×D₄	—	2	2	no	—
839	C₂×D₄	—	2	2	no	—
840	C₂×D₄	—	2	2	no	—
841	C₂×D₄	—	2	2	no	—
842	C₂×D₄	—	4	1	no	—
843	C₂²×C₄	—	2	2	no	—
844	C₂²×C₄	—	2	2	no	—
845	C₂²×C₄	—	2	2	no	—
846	C₂²×C₄	—	2	2	no	—
847	C₂²×C₄	—	2	2	no	—
848	C₂²×C₄	—	2	2	no	—
849	C₂²×C₄	—	2	2	no	—
850	C₂²×C₄	—	2	2	no	—
851	C₂²×C₄	—	2	2	no	—
852	C₂²×C₄	—	2	4	no	—
853	C₂²×C₄	—	2	4	no	—
854	C₂²×C₄	—	2	4	no	—
855	C₂²×C₄	—	4	2	no	—
856	C₂²×C₄	—	4	2	no	—
857	C₂²×C₄	—	4	2	no	—
858	C₂²×C₄	—	4	2	no	—
859	C₂²×C₄	—	4	2	no	—
860	C₂²×C₄	—	4	2	no	—
861	C₂²×C₄	—	4	2	no	—
862	C₂²×C₄	—	4	2	no	—
863	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
864	C₂²×C₄	C₂×D₄×C₅₉	1	8	yes	—
865	C₂²×C₄	#41×C₅₉	1	4	yes	—
866	C₂²×C₄	#41×C₅₉	1	4	yes	—
867	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
868	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
869	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
870	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
871	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
872	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
873	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
874	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
875	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
876	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
877	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
878	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
879	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
880	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
881	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
882	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
883	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
884	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
885	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	—	2	4	no	—
888	C₄⋊C₄	—	2	4	no	—
889	C₄⋊C₄	—	2	4	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	4	no	—
894	C₄⋊C₄	—	2	4	no	—
895	C₄⋊C₄	—	2	4	no	—
896	C₄⋊C₄	—	2	4	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	4	no	—
902	C₄⋊C₄	—	2	4	no	—
903	C₄⋊C₄	—	2	4	no	—
904	C₄⋊C₄	—	2	4	no	—
905	C₄⋊C₄	—	2	4	no	—
906	C₄⋊C₄	—	4	2	no	—
907	C₄⋊C₄	—	4	2	no	—
908	C₄⋊C₄	—	4	2	no	—
909	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
910	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
911	C₄⋊C₄	C₂×D₄×C₅₉	1	8	yes	—
912	C₂²⋊C₄	—	2	4	no	—
913	C₂²⋊C₄	—	2	4	no	—
914	C₂²⋊C₄	—	2	2	no	—
915	C₂²⋊C₄	—	2	2	no	—
916	C₂²⋊C₄	—	2	2	no	—
917	C₂²⋊C₄	—	2	4	no	—
918	C₂²⋊C₄	—	2	4	no	—
919	C₂²⋊C₄	—	2	4	no	—
920	C₂²⋊C₄	—	2	4	no	—
921	C₂²⋊C₄	—	2	4	no	—
922	C₂²⋊C₄	—	2	4	no	—
923	C₂²⋊C₄	—	2	2	no	—
924	C₂²⋊C₄	—	2	2	no	—
925	C₂²⋊C₄	—	2	2	no	—
926	C₂²⋊C₄	—	2	2	no	—
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	2	2	no	—
930	C₂²⋊C₄	—	4	2	no	—
931	C₂²⋊C₄	—	4	2	no	—
932	C₂²⋊C₄	—	4	2	no	—
933	C₂²⋊C₄	—	4	2	no	—
934	C₂²⋊C₄	—	4	1	no	—
935	C₂²⋊C₄	—	4	1	no	—
936	C₄²	—	2	4	no	—
937	C₄²	—	2	4	no	—
938	C₄²	—	2	4	no	—
939	C₄²	—	2	4	no	—
940	C₄²	—	2	2	no	—
941	C₄²	—	2	2	no	—
942	C₄²	—	2	2	no	—
943	C₄²	—	2	4	no	—
944	C₄²	—	4	2	no	—
945	C₂³	—	2	1	no	—
946	C₂³	—	2	1	no	—
947	C₂³	—	2	1	no	—
948	C₂³	—	2	1	no	—
949	C₂³	—	2	1	no	—
950	C₂³	—	2	1	no	—
951	C₂³	—	2	1	no	—
952	C₂³	—	2	1	no	—
953	C₂³	—	2	1	no	—
954	C₂³	—	2	1	no	—
955	C₂³	—	2	1	no	—
956	C₂³	—	2	1	no	—
957	C₂³	—	2	1	no	—
958	C₂³	—	2	1	no	—
959	C₂³	—	2	1	no	—
960	C₂³	—	2	1	no	—
961	C₂³	—	2	1	no	—
962	C₂³	—	2	1	no	—
963	C₂³	—	2	1	no	—
964	C₂³	—	2	1	no	—
965	C₂³	—	2	1	no	—
966	C₂³	—	2	1	no	—
967	C₂³	—	2	1	no	—
968	C₂³	—	2	1	no	—
969	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
970	C₂³	C₂×#41×C₅₉	1	2	yes	—
971	C₂³	C₂×#41×C₅₉	1	2	yes	—
972	C₂³	2₋¹⁺⁴×C₅₉	1	2	yes	—
973	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
974	Q₈	—	2	8	no	—
975	Q₈	—	4	4	no	—
976	Q₈	—	8	4	no	—
977	D₄	—	2	8	no	—
978	D₄	—	2	8	no	—
979	D₄	—	2	8	no	—
980	D₄	—	2	8	no	—
981	D₄	—	2	8	no	—
982	D₄	—	4	4	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	1	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	8	no	—
998	C₂×C₄	—	2	8	no	—
999	C₂×C₄	—	2	8	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	2	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	2	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	4	8	no	—
1034	C₂×C₄	—	4	4	no	—
1035	C₂×C₄	—	8	4	no	—
1036	C₂×C₄	—	8	4	no	—
1037	C₂×C₄	—	8	4	no	—
1038	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
1039	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1040	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
1041	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1042	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
1043	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
1044	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
1045	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
1046	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
1047	C₂×C₄	2₋¹⁺⁴×C₅₉	1	2	yes	—
1048	C₂²	—	2	2	no	—
1049	C₂²	—	2	2	no	—
1050	C₂²	—	2	2	no	—
1051	C₂²	—	2	2	no	—
1052	C₂²	—	2	2	no	—
1053	C₂²	—	2	2	no	—
1054	C₂²	—	2	2	no	—
1055	C₂²	—	2	2	no	—
1056	C₂²	—	2	2	no	—
1057	C₂²	—	2	2	no	—
1058	C₂²	—	2	2	no	—
1059	C₂²	—	2	2	no	—
1060	C₂²	—	4	1	no	—
1061	C₂²	—	4	1	no	—
1062	C₂²	—	4	1	no	—
1063	C₂²	—	4	1	no	—
1064	C₂²	—	4	1	no	—
1065	C₂²	—	4	1	no	—
1066	C₂²	—	4	1	no	—
1067	C₂²	—	4	1	no	—
1068	C₂²	—	4	1	no	—
1069	C₂²	—	4	1	no	—
1070	C₂²	—	4	1	no	—
1071	C₂²	—	4	1	no	—
1072	C₂²	—	4	1	no	—
1073	C₂²	—	4	1	no	—
1074	C₂²	—	4	1	no	—
1075	C₂²	—	4	1	no	—
1076	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
1077	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
1078	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
1079	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
1080	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
1081	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
1082	C₂²	C₅₉×#585	1	1	yes	characteristic
1083	C₄	—	2	2	no	—
1084	C₄	—	2	2	no	—
1085	C₄	—	2	2	no	—
1086	C₄	—	2	2	no	—
1087	C₄	—	2	2	no	—
1088	C₄	—	2	4	no	—
1089	C₄	—	2	4	no	—
1090	C₄	—	4	1	no	—
1091	C₄	—	4	1	no	—
1092	C₄	—	4	2	no	—
1093	C₄	—	4	1	no	—
1094	C₄	—	4	2	no	—
1095	C₄	—	4	2	no	—
1096	C₄	—	4	2	no	—
1097	C₄	—	4	1	no	—
1098	C₄	—	4	2	no	—
1099	C₄	—	4	2	no	—
1100	C₄	—	4	1	no	—
1101	C₄	C₅₉×#525	1	4	yes	—
1102	C₂	—	4	2	no	—
1103	C₂	—	4	2	no	—
1104	C₂	—	4	2	no	—
1105	C₂	—	4	2	no	—
1106	C₂	C₂×C₅₉×#525	1	1	yes	characteristic
1107	C₂	C₅₉×#3486	1	1	yes	characteristic
1108	C₂	C₅₉×#3492	1	1	yes	characteristic
1109	C₂	C₅₉×#3495	1	1	yes	characteristic
1110	C₂	C₅₉×#3496	1	1	yes	characteristic
1111	C₂	C₅₉×#3507	1	1	yes	characteristic
1112	C₂	C₅₉×#3511	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₅₉×#2388	C₂
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. C₂×C₅₉×#554	C₂	semidirect
2. C₂×C₅₉×#520	C₂	semidirect
3. C₅₉×#2638	C₂	semidirect
4. C₅₉×#2616	C₂	semidirect
5. C₅₉×#2600	C₂	semidirect
6. C₅₉×#2499	C₂	semidirect
7. C₅₉×#2485	C₂	semidirect
8. C₅₉×#2465	C₂	semidirect
9. C₅₉×#2463	C₂	semidirect
10. C₅₉×#2462	C₂	semidirect
11. C₅₉×#2460	C₂	semidirect
12. C₅₉×#2440	C₂	semidirect
13. C₅₉×#2439	C₂	semidirect
14. C₅₉×#2417	C₂	semidirect
15. C₅₉×#2415	C₂	semidirect
16. C₅₉×#2415	C₂	semidirect
17. C₅₉×#2392	C₂	semidirect
19. C₅₉×#2362	C₂	semidirect
20. C₅₉×#2360	C₂	semidirect
21. C₅₉×#2352	C₂	semidirect
22. D₄×C₄⋊C₄×C₅₉	C₂	semidirect
23. C₅₉×#2344	C₂	semidirect
171. C₂×C₄⋊C₄×C₅₉	D₄	semidirect
491. #35688	C₅₉	direct (N × H)
546. C₂×#554	C₂×C₅₉	semidirect
547. C₂×#520	C₂×C₅₉	semidirect
548. #2638	C₂×C₅₉	semidirect
549. #2616	C₂×C₅₉	semidirect
550. #2600	C₂×C₅₉	semidirect
551. #2499	C₂×C₅₉	semidirect
552. #2485	C₂×C₅₉	semidirect
553. #2465	C₂×C₅₉	semidirect
554. #2463	C₂×C₅₉	semidirect
555. #2462	C₂×C₅₉	semidirect
556. #2460	C₂×C₅₉	semidirect
557. #2440	C₂×C₅₉	semidirect
558. #2439	C₂×C₅₉	semidirect
559. #2417	C₂×C₅₉	semidirect
560. #2415	C₂×C₅₉	semidirect
561. #2415	C₂×C₅₉	semidirect
562. #2392	C₂×C₅₉	semidirect
564. #2362	C₂×C₅₉	semidirect
565. #2360	C₂×C₅₉	semidirect
566. #2352	C₂×C₅₉	semidirect
567. D₄×C₄⋊C₄	C₂×C₅₉	semidirect
568. #2344	C₂×C₅₉	semidirect
681. C₅₉	#35688	direct (N × H)
728. C₂×C₄⋊C₄	D₄×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₉×#554	2
C₂×C₅₉×#520	2
C₅₉×#2638	2
C₅₉×#2616	2
C₅₉×#2600	2
C₅₉×#2499	2
C₅₉×#2485	2
C₅₉×#2465	2
C₅₉×#2463	2
C₅₉×#2462	2
C₅₉×#2460	2
C₅₉×#2440	2
C₅₉×#2439	2
C₅₉×#2417	2
C₅₉×#2415	2
C₅₉×#2392	2
C₅₉×#2388	2
C₅₉×#2362	2
C₅₉×#2360	2
C₅₉×#2352	2
D₄×C₄⋊C₄×C₅₉	2
C₅₉×#2344	2
#35688	59

Subgroups — C59×#35688 #28447797

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35688 #28447797