Subgroups — C₅₉×#62250 #28474359

Order 15104.

1950 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₉×#3519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#3340	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#3337	C₂	1	2	yes	maximal, complemented
5	C₅₉×#3335	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#3304	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#3303	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#3301	C₂	1	2	yes	maximal, complemented
9	C₅₉×#3299	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#3296	C₂	1	2	yes	maximal, complemented
11	C₅₉×#3294	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#3284	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₉×#3282	C₂	1	2	yes	maximal, complemented
14	D₄×SD₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#3248	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₉×#3247	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₉×#3190	C₂	1	2	yes	maximal, complemented
18	C₅₉×#3188	C₂	1	2	yes	maximal, complemented
19	C₅₉×#3168	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₉×#3167	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₉×#3050	C₂	1	2	yes	maximal, complemented
22	C₂×C₅₉×#465	C₂	1	2	yes	maximal, complemented
23	C₂×C₈×D₄×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#135×C₅₉	C₂²	1	2	yes	complemented
25	C₂²×SD₁₆×C₅₉	C₂²	1	2	yes	complemented
26	C₂³×C₈×C₅₉	C₂²	1	2	yes	complemented
27	C₅₉×#556	C₂²	1	1	yes	characteristic, complemented
28	C₅₉×#555	C₂²	1	1	yes	characteristic
29	C₅₉×#554	—	2	1	no	—
30	C₅₉×#554	C₂²	1	1	yes	characteristic
31	C₅₉×#553	—	2	1	no	—
32	C₅₉×#553	C₂²	1	2	yes	—
33	C₅₉×#552	C₂²	1	2	yes	complemented
34	C₅₉×#551	—	2	2	no	—
35	C₅₉×#550	C₂²	1	1	yes	characteristic
36	D₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
37	C₅₉×#548	C₂²	1	2	yes	complemented
38	C₅₉×#547	C₂²	1	1	yes	characteristic
39	C₅₉×#547	C₂²	1	1	yes	characteristic, complemented
40	C₅₉×#546	—	2	1	no	—
41	C₅₉×#546	—	2	2	no	—
42	C₅₉×#546	C₂²	1	2	yes	—
43	D₄²×C₅₉	—	2	1	no	—
44	D₄²×C₅₉	C₂²	1	1	yes	characteristic
45	C₅₉×#542	—	2	1	no	—
46	C₅₉×#540	—	2	1	no	—
47	C₅₉×#539	—	2	2	no	—
48	C₅₉×#538	—	2	2	no	—
49	C₅₉×#533	C₂²	1	1	yes	characteristic, complemented
50	C₅₉×#532	C₂²	1	1	yes	characteristic
51	C₅₉×#529	C₂²	1	1	yes	characteristic
52	C₅₉×#529	C₂²	1	1	yes	characteristic, complemented
53	C₅₉×#525	C₂²	1	2	yes	—
54	C₅₉×#525	C₂²	1	2	yes	complemented
55	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	complemented
56	C₂×#121×C₅₉	C₂²	1	2	yes	—
57	C₅₉×#520	—	2	1	no	—
58	C₅₉×#518	—	2	1	no	—
59	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
60	C₅₉×#499	C₂²	1	1	yes	characteristic, complemented
61	C₅₉×#498	C₂²	1	1	yes	characteristic, complemented
62	C₅₉×#495	C₂²	1	1	yes	characteristic, complemented
63	C₅₉×#492	C₂²	1	1	yes	characteristic, complemented
64	C₅₉×#488	C₂²	1	1	yes	characteristic, complemented
65	C₅₉×#488	C₂²	1	1	yes	characteristic, complemented
66	C₅₉×#487	C₂²	1	1	yes	characteristic, complemented
67	C₅₉×#486	C₂²	1	1	yes	characteristic, complemented
68	C₅₉×#485	C₂²	1	2	yes	complemented
69	C₅₉×#485	C₂²	1	2	yes	complemented
70	C₅₉×#484	C₂²	1	2	yes	complemented
71	C₅₉×#483	C₂²	1	2	yes	complemented
72	C₅₉×#482	C₂²	1	2	yes	complemented
73	C₅₉×#482	C₂²	1	2	yes	complemented
74	C₅₉×#481	C₂²	1	2	yes	complemented
75	C₅₉×#480	C₂²	1	2	yes	complemented
76	C₅₉×#479	C₂²	1	2	yes	complemented
77	C₅₉×#478	C₂²	1	2	yes	complemented
78	C₅₉×#477	C₂²	1	1	yes	characteristic, complemented
79	C₅₉×#476	C₂²	1	1	yes	characteristic, complemented
80	C₅₉×#475	C₂²	1	1	yes	characteristic, complemented
81	C₅₉×#474	C₂²	1	1	yes	characteristic, complemented
82	C₅₉×#467	C₂²	1	2	yes	complemented
83	C₅₉×#467	C₂²	1	2	yes	complemented
84	C₅₉×#467	C₂²	1	1	yes	characteristic, complemented
85	C₅₉×#466	C₂²	1	1	yes	characteristic
86	C₅₉×#466	C₂²	1	2	yes	complemented
87	C₅₉×#466	C₂²	1	2	yes	complemented
88	C₅₉×#465	C₂²	1	1	yes	characteristic
89	C₅₉×#465	C₂²	1	2	yes	—
90	C₅₉×#465	C₂²	1	2	yes	complemented
91	C₅₉×#465	C₂²	1	2	yes	complemented
92	C₅₉×#465	C₂²	1	2	yes	complemented
93	C₅₉×#465	C₂²	1	2	yes	complemented
94	C₅₉×#465	C₂²	1	2	yes	complemented
95	C₅₉×#465	C₂²	1	2	yes	complemented
96	C₅₉×#465	C₂²	1	2	yes	complemented
97	C₅₉×#465	C₂²	1	2	yes	complemented
98	C₅₉×#465	C₂²	1	1	yes	characteristic, complemented
99	C₅₉×#465	C₂²	1	2	yes	complemented
100	C₅₉×#464	C₂²	1	2	yes	complemented
101	C₅₉×#463	C₂²	1	2	yes	complemented
102	C₅₉×#462	C₂²	1	1	yes	characteristic, complemented
103	C₅₉×#461	C₂²	1	1	yes	characteristic, complemented
104	C₅₉×#460	C₂²	1	1	yes	characteristic, complemented
105	C₅₉×#459	C₂²	1	1	yes	characteristic, complemented
106	C₅₉×#452	C₂²	1	2	yes	complemented
107	C₅₉×#452	C₂²	1	2	yes	complemented
108	C₅₉×#451	C₂²	1	2	yes	complemented
109	C₅₉×#450	C₂²	1	2	yes	complemented
110	C₅₉×#449	C₂²	1	2	yes	complemented
111	C₅₉×#449	C₂²	1	2	yes	complemented
112	C₅₉×#448	C₂²	1	2	yes	complemented
113	C₅₉×#447	C₂²	1	2	yes	complemented
114	C₄×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic, complemented
115	C₄×SD₁₆×C₅₉	C₂²	1	1	yes	characteristic, complemented
116	C₄×SD₁₆×C₅₉	C₂²	1	2	yes	complemented
117	C₄×SD₁₆×C₅₉	C₂²	1	1	yes	characteristic, complemented
118	C₄×SD₁₆×C₅₉	C₂²	1	2	yes	complemented
119	C₄×D₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
120	C₈×D₄×C₅₉	C₂²	1	1	yes	characteristic
121	C₈×D₄×C₅₉	C₂²	1	1	yes	characteristic
122	C₈×D₄×C₅₉	C₂²	1	2	yes	complemented
123	C₈×D₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
124	C₈×D₄×C₅₉	C₂²	1	2	yes	complemented
125	C₈×D₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
126	C₅₉×#427	C₂²	1	2	yes	complemented
127	C₂×#106×C₅₉	C₂²	1	2	yes	complemented
128	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
129	C₅₉×#416	C₂²	1	2	yes	complemented
130	C₅₉×#416	C₂²	1	2	yes	complemented
131	C₂×#103×C₅₉	C₂²	1	2	yes	complemented
132	C₂×#102×C₅₉	C₂²	1	2	yes	complemented
133	C₂×C₂²⋊C₈×C₅₉	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₅₉	—	2	1	no	—
136	C₂×#41×C₅₉	—	2	1	no	—
137	C₂×#41×C₅₉	C₂³	1	2	yes	—
138	C₂×#41×C₅₉	C₂³	1	2	yes	—
139	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
140	C₂²×D₄×C₅₉	—	2	2	no	—
141	C₂²×D₄×C₅₉	—	2	1	no	—
142	C₂²×D₄×C₅₉	D₄	1	1	yes	characteristic
143	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
144	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
145	#135×C₅₉	—	4	4	no	—
146	C₂×Q₁₆×C₅₉	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆×C₅₉	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₅₉	—	4	4	no	—
149	C₂×SD₁₆×C₅₉	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₅₉	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
155	C₂×D₈×C₅₉	C₂³	1	1	yes	characteristic
156	C₂×D₈×C₅₉	C₂³	1	2	yes	—
157	C₂²×C₈×C₅₉	—	4	4	no	—
158	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
159	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
160	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
161	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
162	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
163	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
164	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
165	C₄⋊Q₈×C₅₉	—	2	1	no	—
166	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
167	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
168	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
169	#127×C₅₉	—	2	1	no	—
170	#127×C₅₉	C₂³	1	1	yes	characteristic
171	#126×C₅₉	—	2	2	no	—
172	#126×C₅₉	—	2	2	no	—
173	#126×C₅₉	—	2	2	no	—
174	#126×C₅₉	—	2	1	no	—
175	#126×C₅₉	—	2	1	no	—
176	#125×C₅₉	—	2	2	no	—
177	#125×C₅₉	—	2	1	no	—
178	#125×C₅₉	—	2	1	no	—
179	#125×C₅₉	C₂³	1	1	yes	characteristic
180	#125×C₅₉	C₂³	1	1	yes	characteristic
181	#124×C₅₉	—	2	1	no	—
182	#124×C₅₉	—	2	2	no	—
183	#124×C₅₉	—	2	2	no	—
184	#124×C₅₉	—	2	1	no	—
185	#124×C₅₉	C₂³	1	1	yes	characteristic
186	#124×C₅₉	C₂³	1	1	yes	characteristic
187	#123×C₅₉	—	2	2	no	—
188	#123×C₅₉	—	2	2	no	—
189	#123×C₅₉	—	2	2	no	—
190	#123×C₅₉	—	2	1	no	—
191	#123×C₅₉	—	2	1	no	—
192	#123×C₅₉	—	2	2	no	—
193	#123×C₅₉	—	2	2	no	—
194	#123×C₅₉	—	2	2	no	—
195	#123×C₅₉	—	2	2	no	—
196	C₂²⋊Q₈×C₅₉	—	2	2	no	—
197	C₂²⋊Q₈×C₅₉	—	2	2	no	—
198	C₂²⋊Q₈×C₅₉	—	2	1	no	—
199	C₂²⋊Q₈×C₅₉	—	2	2	no	—
200	C₂²⋊Q₈×C₅₉	—	2	1	no	—
201	C₂²⋊Q₈×C₅₉	—	2	2	no	—
202	C₂²⋊Q₈×C₅₉	—	2	2	no	—
203	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
204	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
205	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
206	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
207	C₂²⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
208	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
209	C₂²⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
210	#121×C₅₉	—	2	2	no	—
211	#121×C₅₉	—	2	2	no	—
212	#121×C₅₉	—	2	1	no	—
213	#121×C₅₉	—	2	1	no	—
214	#121×C₅₉	—	2	2	no	—
215	#121×C₅₉	—	2	2	no	—
216	#121×C₅₉	—	2	1	no	—
217	#121×C₅₉	—	2	1	no	—
218	#121×C₅₉	—	2	2	no	—
219	#121×C₅₉	—	2	2	no	—
220	#121×C₅₉	C₂³	1	2	yes	—
221	#121×C₅₉	C₂³	1	2	yes	—
222	#121×C₅₉	C₂³	1	2	yes	—
223	#121×C₅₉	C₂³	1	2	yes	—
224	#121×C₅₉	C₂³	1	1	yes	characteristic
225	#121×C₅₉	C₂³	1	2	yes	—
226	#121×C₅₉	C₂³	1	1	yes	characteristic
227	#120×C₅₉	—	2	2	no	—
228	#120×C₅₉	—	2	2	no	—
229	#120×C₅₉	—	2	2	no	—
230	#120×C₅₉	—	2	2	no	—
231	C₄×Q₈×C₅₉	—	2	1	no	—
232	C₄×Q₈×C₅₉	—	2	1	no	—
233	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
234	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
235	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₅₉	—	2	1	no	—
237	C₄×D₄×C₅₉	—	2	1	no	—
238	C₄×D₄×C₅₉	—	2	2	no	—
239	C₄×D₄×C₅₉	—	2	2	no	—
240	C₄×D₄×C₅₉	—	2	2	no	—
241	C₄×D₄×C₅₉	—	2	2	no	—
242	C₄×D₄×C₅₉	—	2	1	no	—
243	C₄×D₄×C₅₉	—	2	1	no	—
244	C₄×D₄×C₅₉	—	2	1	no	—
245	C₄×D₄×C₅₉	—	2	2	no	—
246	C₄×D₄×C₅₉	—	2	2	no	—
247	C₄×D₄×C₅₉	—	2	1	no	—
248	C₄×D₄×C₅₉	D₄	1	1	yes	characteristic
249	C₄×D₄×C₅₉	D₄	1	2	yes	—
250	C₄×D₄×C₅₉	D₄	1	1	yes	characteristic
251	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₅₉	C₂³	1	2	yes	—
254	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₅₉	C₂³	1	2	yes	—
256	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
257	#117×C₅₉	—	2	1	no	—
258	#117×C₅₉	—	2	1	no	—
259	#117×C₅₉	—	2	2	no	—
260	#117×C₅₉	—	2	1	no	—
261	#117×C₅₉	—	2	1	no	—
262	#117×C₅₉	C₂³	1	2	yes	—
263	#117×C₅₉	C₂³	1	2	yes	—
264	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
265	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
266	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
267	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
268	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
269	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
270	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
271	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
272	C₂×C₂²⋊C₄×C₅₉	D₄	1	2	yes	—
273	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
274	#107×C₅₉	C₂³	1	2	yes	—
275	#107×C₅₉	C₂³	1	2	yes	—
276	#107×C₅₉	C₂³	1	1	yes	characteristic
277	#107×C₅₉	C₂³	1	1	yes	characteristic
278	#106×C₅₉	C₂³	1	1	yes	characteristic
279	#106×C₅₉	C₂³	1	2	yes	—
280	#106×C₅₉	C₂³	1	2	yes	—
281	#106×C₅₉	C₂³	1	2	yes	—
282	#106×C₅₉	C₂³	1	1	yes	characteristic
283	#106×C₅₉	C₂³	1	2	yes	—
284	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
285	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
286	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
287	#103×C₅₉	C₂³	1	1	yes	characteristic
288	#103×C₅₉	C₂³	1	2	yes	—
289	#103×C₅₉	C₂³	1	2	yes	—
290	#103×C₅₉	C₂³	1	2	yes	—
291	#103×C₅₉	C₂³	1	1	yes	characteristic
292	#103×C₅₉	C₂³	1	2	yes	—
293	#103×C₅₉	C₂³	1	2	yes	—
294	#103×C₅₉	C₂³	1	1	yes	characteristic
295	#103×C₅₉	C₂³	1	2	yes	—
296	#103×C₅₉	C₂³	1	1	yes	characteristic
297	#102×C₅₉	C₂³	1	1	yes	characteristic
298	#102×C₅₉	C₂³	1	2	yes	—
299	#102×C₅₉	C₂³	1	2	yes	—
300	#102×C₅₉	C₂³	1	2	yes	—
301	#102×C₅₉	C₂³	1	1	yes	characteristic
302	#102×C₅₉	C₂³	1	2	yes	—
303	#102×C₅₉	C₂³	1	2	yes	—
304	#102×C₅₉	C₂³	1	2	yes	—
305	#102×C₅₉	C₂³	1	1	yes	characteristic
306	#102×C₅₉	C₂³	1	1	yes	characteristic
307	C₂²⋊C₈×C₅₉	C₂³	1	2	yes	—
308	C₂²⋊C₈×C₅₉	C₂³	1	2	yes	—
309	C₂²⋊C₈×C₅₉	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₅₉	C₂³	1	2	yes	—
311	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
315	C₂⁴×C₅₉	—	2	2	no	—
316	C₂⁴×C₅₉	C₂×D₄	1	2	yes	—
317	#41×C₅₉	—	4	2	no	—
318	#41×C₅₉	—	4	2	no	—
319	#41×C₅₉	—	4	2	no	—
320	#41×C₅₉	—	4	2	no	—
321	#41×C₅₉	—	4	4	no	—
322	#41×C₅₉	—	8	2	no	—
323	C₂×Q₈×C₅₉	—	2	1	no	—
324	C₂×Q₈×C₅₉	—	2	2	no	—
325	C₂×Q₈×C₅₉	—	2	1	no	—
326	C₂×Q₈×C₅₉	—	4	2	no	—
327	C₂×Q₈×C₅₉	—	4	2	no	—
328	C₂×Q₈×C₅₉	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₅₉	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₅₉	C₂⁴	1	2	yes	—
331	C₂×D₄×C₅₉	—	2	4	no	—
332	C₂×D₄×C₅₉	—	2	1	no	—
333	C₂×D₄×C₅₉	—	2	2	no	—
334	C₂×D₄×C₅₉	—	2	2	no	—
335	C₂×D₄×C₅₉	—	2	2	no	—
336	C₂×D₄×C₅₉	—	2	1	no	—
337	C₂×D₄×C₅₉	—	2	2	no	—
338	C₂×D₄×C₅₉	—	2	2	no	—
339	C₂×D₄×C₅₉	—	2	2	no	—
340	C₂×D₄×C₅₉	—	2	2	no	—
341	C₂×D₄×C₅₉	—	2	1	no	—
342	C₂×D₄×C₅₉	—	2	1	no	—
343	C₂×D₄×C₅₉	—	2	2	no	—
344	C₂×D₄×C₅₉	—	4	2	no	—
345	C₂×D₄×C₅₉	—	4	2	no	—
346	C₂×D₄×C₅₉	—	4	4	no	—
347	C₂×D₄×C₅₉	—	8	4	no	—
348	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
349	C₂×D₄×C₅₉	C₂×D₄	1	1	yes	characteristic
350	C₂×D₄×C₅₉	C₂×D₄	1	1	yes	characteristic
351	C₂×D₄×C₅₉	C₂⁴	1	1	yes	characteristic
352	C₂×D₄×C₅₉	C₂⁴	1	1	yes	characteristic
353	C₂×D₄×C₅₉	C₂⁴	1	2	yes	—
354	C₂²×C₄×C₅₉	—	2	2	no	—
355	C₂²×C₄×C₅₉	—	2	2	no	—
356	C₂²×C₄×C₅₉	—	2	2	no	—
357	C₂²×C₄×C₅₉	—	2	1	no	—
358	C₂²×C₄×C₅₉	—	2	1	no	—
359	C₂²×C₄×C₅₉	—	2	2	no	—
360	C₂²×C₄×C₅₉	—	2	2	no	—
361	C₂²×C₄×C₅₉	—	2	2	no	—
362	C₂²×C₄×C₅₉	—	4	2	no	—
363	C₂²×C₄×C₅₉	—	4	2	no	—
364	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
365	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
367	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
368	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
369	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
370	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
371	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
372	Q₁₆×C₅₉	—	4	1	no	—
373	Q₁₆×C₅₉	—	4	2	no	—
374	SD₁₆×C₅₉	—	2	2	no	—
375	SD₁₆×C₅₉	—	2	4	no	—
376	SD₁₆×C₅₉	—	2	2	no	—
377	SD₁₆×C₅₉	—	4	2	no	—
378	SD₁₆×C₅₉	—	4	2	no	—
379	SD₁₆×C₅₉	—	4	2	no	—
380	D₈×C₅₉	—	4	1	no	—
381	D₈×C₅₉	—	4	2	no	—
382	C₂×C₈×C₅₉	—	2	2	no	—
383	C₂×C₈×C₅₉	—	2	4	no	—
384	C₂×C₈×C₅₉	—	2	4	no	—
385	C₂×C₈×C₅₉	—	4	2	no	—
386	C₂×C₈×C₅₉	—	4	2	no	—
387	C₂×C₈×C₅₉	—	4	2	no	—
388	C₂×C₈×C₅₉	—	4	1	no	—
389	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
390	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
391	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
392	C₂×C₈×C₅₉	C₂⁴	1	2	yes	—
393	C₂×C₈×C₅₉	C₂⁴	1	2	yes	—
394	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
395	C₄⋊C₄×C₅₉	—	2	1	no	—
396	C₄⋊C₄×C₅₉	—	2	2	no	—
397	C₄⋊C₄×C₅₉	—	2	1	no	—
398	C₄⋊C₄×C₅₉	—	2	2	no	—
399	C₄⋊C₄×C₅₉	—	2	2	no	—
400	C₄⋊C₄×C₅₉	—	2	2	no	—
401	C₄⋊C₄×C₅₉	—	2	2	no	—
402	C₄⋊C₄×C₅₉	—	2	1	no	—
403	C₄⋊C₄×C₅₉	—	2	1	no	—
404	C₄⋊C₄×C₅₉	—	2	1	no	—
405	C₄⋊C₄×C₅₉	—	2	1	no	—
406	C₄⋊C₄×C₅₉	—	2	1	no	—
407	C₄⋊C₄×C₅₉	—	2	1	no	—
408	C₄⋊C₄×C₅₉	—	2	1	no	—
409	C₄⋊C₄×C₅₉	—	2	2	no	—
410	C₄⋊C₄×C₅₉	—	2	2	no	—
411	C₄⋊C₄×C₅₉	—	2	1	no	—
412	C₄⋊C₄×C₅₉	—	2	1	no	—
413	C₄⋊C₄×C₅₉	—	2	2	no	—
414	C₄⋊C₄×C₅₉	—	2	1	no	—
415	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
416	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
417	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
418	C₄⋊C₄×C₅₉	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
420	C₄⋊C₄×C₅₉	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₅₉	C₂⁴	1	1	yes	characteristic
422	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
423	C₄⋊C₄×C₅₉	C₂⁴	1	1	yes	characteristic
424	C₂²⋊C₄×C₅₉	—	2	1	no	—
425	C₂²⋊C₄×C₅₉	—	2	2	no	—
426	C₂²⋊C₄×C₅₉	—	2	2	no	—
427	C₂²⋊C₄×C₅₉	—	2	2	no	—
428	C₂²⋊C₄×C₅₉	—	2	2	no	—
429	C₂²⋊C₄×C₅₉	—	2	2	no	—
430	C₂²⋊C₄×C₅₉	—	2	2	no	—
431	C₂²⋊C₄×C₅₉	—	2	2	no	—
432	C₂²⋊C₄×C₅₉	—	2	1	no	—
433	C₂²⋊C₄×C₅₉	—	2	1	no	—
434	C₂²⋊C₄×C₅₉	—	2	1	no	—
435	C₂²⋊C₄×C₅₉	—	2	2	no	—
436	C₂²⋊C₄×C₅₉	—	2	2	no	—
437	C₂²⋊C₄×C₅₉	—	2	2	no	—
438	C₂²⋊C₄×C₅₉	—	2	1	no	—
439	C₂²⋊C₄×C₅₉	—	2	1	no	—
440	C₂²⋊C₄×C₅₉	—	2	1	no	—
441	C₂²⋊C₄×C₅₉	—	2	2	no	—
442	C₂²⋊C₄×C₅₉	—	2	1	no	—
443	C₂²⋊C₄×C₅₉	—	2	2	no	—
444	C₂²⋊C₄×C₅₉	—	2	1	no	—
445	C₂²⋊C₄×C₅₉	—	2	2	no	—
446	C₂²⋊C₄×C₅₉	—	2	1	no	—
447	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
448	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
449	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
450	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
451	C₄²×C₅₉	—	2	2	no	—
452	C₄²×C₅₉	—	2	2	no	—
453	C₄²×C₅₉	—	2	2	no	—
454	C₄²×C₅₉	—	2	1	no	—
455	C₄²×C₅₉	—	2	1	no	—
456	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
457	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
458	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
459	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
460	C₂³×C₅₉	—	2	4	no	—
461	C₂³×C₅₉	—	2	4	no	—
462	C₂³×C₅₉	—	2	1	no	—
463	C₂³×C₅₉	—	2	1	no	—
464	C₂³×C₅₉	—	2	2	no	—
465	C₂³×C₅₉	—	4	2	no	—
466	C₂³×C₅₉	—	4	4	no	—
467	C₂³×C₅₉	—	8	2	no	—
468	C₂³×C₅₉	—	8	2	no	—
469	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
470	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
471	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
472	Q₈×C₅₉	—	2	1	no	—
473	Q₈×C₅₉	—	2	2	no	—
474	Q₈×C₅₉	—	2	1	no	—
475	Q₈×C₅₉	—	2	2	no	—
476	Q₈×C₅₉	—	2	1	no	—
477	Q₈×C₅₉	—	2	1	no	—
478	Q₈×C₅₉	—	4	2	no	—
479	Q₈×C₅₉	—	8	2	no	—
480	Q₈×C₅₉	—	8	1	no	—
481	D₄×C₅₉	—	2	4	no	—
482	D₄×C₅₉	—	2	2	no	—
483	D₄×C₅₉	—	2	1	no	—
484	D₄×C₅₉	—	2	2	no	—
485	D₄×C₅₉	—	2	1	no	—
486	D₄×C₅₉	—	2	1	no	—
487	D₄×C₅₉	—	2	1	no	—
488	D₄×C₅₉	—	2	2	no	—
489	D₄×C₅₉	—	4	4	no	—
490	D₄×C₅₉	—	4	4	no	—
491	D₄×C₅₉	—	4	2	no	—
492	D₄×C₅₉	—	4	2	no	—
493	D₄×C₅₉	—	4	4	no	—
494	D₄×C₅₉	—	4	2	no	—
495	D₄×C₅₉	—	8	2	no	—
496	D₄×C₅₉	—	8	1	no	—
497	D₄×C₅₉	—	8	2	no	—
498	D₄×C₅₉	—	8	2	no	—
499	D₄×C₅₉	—	8	2	no	—
500	D₄×C₅₉	—	8	2	no	—
501	D₄×C₅₉	#135	1	4	yes	complemented
502	C₂×C₄×C₅₉	—	2	2	no	—
503	C₂×C₄×C₅₉	—	2	2	no	—
504	C₂×C₄×C₅₉	—	2	1	no	—
505	C₂×C₄×C₅₉	—	2	2	no	—
506	C₂×C₄×C₅₉	—	2	2	no	—
507	C₂×C₄×C₅₉	—	2	1	no	—
508	C₂×C₄×C₅₉	—	2	2	no	—
509	C₂×C₄×C₅₉	—	2	2	no	—
510	C₂×C₄×C₅₉	—	2	1	no	—
511	C₂×C₄×C₅₉	—	2	1	no	—
512	C₂×C₄×C₅₉	—	2	2	no	—
513	C₂×C₄×C₅₉	—	2	1	no	—
514	C₂×C₄×C₅₉	—	2	1	no	—
515	C₂×C₄×C₅₉	—	2	2	no	—
516	C₂×C₄×C₅₉	—	2	2	no	—
517	C₂×C₄×C₅₉	—	2	1	no	—
518	C₂×C₄×C₅₉	—	2	1	no	—
519	C₂×C₄×C₅₉	—	4	2	no	—
520	C₂×C₄×C₅₉	—	4	2	no	—
521	C₂×C₄×C₅₉	—	4	2	no	—
522	C₂×C₄×C₅₉	—	4	4	no	—
523	C₂×C₄×C₅₉	—	4	2	no	—
524	C₂×C₄×C₅₉	—	4	2	no	—
525	C₂×C₄×C₅₉	—	8	2	no	—
526	C₂×C₄×C₅₉	—	8	2	no	—
527	C₂×C₄×C₅₉	—	8	2	no	—
528	C₂×C₄×C₅₉	—	8	2	no	—
529	C₂×C₄×C₅₉	—	8	2	no	—
530	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
532	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
536	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
537	C₂×C₄×C₅₉	C₂⁵	1	1	yes	characteristic
538	C₈×C₅₉	—	2	1	no	—
539	C₈×C₅₉	—	2	2	no	—
540	C₈×C₅₉	—	2	2	no	—
541	C₈×C₅₉	—	2	1	no	—
542	C₈×C₅₉	—	2	1	no	—
543	C₈×C₅₉	H(5,𝔽₂)	1	2	yes	—
544	#62250	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
545	C₂²×C₅₉	—	2	1	no	—
546	C₂²×C₅₉	—	2	2	no	—
547	C₂²×C₅₉	—	2	1	no	—
548	C₂²×C₅₉	—	2	2	no	—
549	C₂²×C₅₉	—	2	2	no	—
550	C₂²×C₅₉	—	2	2	no	—
551	C₂²×C₅₉	—	2	2	no	—
552	C₂²×C₅₉	—	4	8	no	—
553	C₂²×C₅₉	—	4	1	no	—
554	C₂²×C₅₉	—	4	2	no	—
555	C₂²×C₅₉	—	4	1	no	—
556	C₂²×C₅₉	—	4	1	no	—
557	C₂²×C₅₉	—	4	1	no	—
558	C₂²×C₅₉	—	4	2	no	—
559	C₂²×C₅₉	—	4	2	no	—
560	C₂²×C₅₉	—	4	1	no	—
561	C₂²×C₅₉	—	4	1	no	—
562	C₂²×C₅₉	—	16	4	no	—
563	C₂²×C₅₉	C₂×#135	1	4	yes	—
564	C₂²×C₅₉	#577	1	2	yes	—
565	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
566	C₄×C₅₉	—	2	1	no	—
567	C₄×C₅₉	—	2	2	no	—
568	C₄×C₅₉	—	2	2	no	—
569	C₄×C₅₉	—	2	1	no	—
570	C₄×C₅₉	—	2	1	no	—
571	C₄×C₅₉	—	2	1	no	—
572	C₄×C₅₉	—	4	1	no	—
573	C₄×C₅₉	—	4	2	no	—
574	C₄×C₅₉	—	4	1	no	—
575	C₄×C₅₉	—	4	1	no	—
576	C₄×C₅₉	—	4	1	no	—
577	C₄×C₅₉	—	4	2	no	—
578	C₄×C₅₉	—	4	1	no	—
579	C₄×C₅₉	—	4	2	no	—
580	C₄×C₅₉	—	4	1	no	—
581	C₄×C₅₉	C₂×#135	1	2	yes	—
582	C₄×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
583	C₄×C₅₉	#585	1	1	yes	characteristic
584	#3520	C₂×C₅₉	1	1	yes	characteristic, complemented
585	#3519	C₂×C₅₉	1	1	yes	characteristic, complemented
586	#3340	C₂×C₅₉	1	1	yes	characteristic, complemented
587	#3337	C₂×C₅₉	1	2	yes	complemented
588	#3335	C₂×C₅₉	1	1	yes	characteristic, complemented
589	#3304	C₂×C₅₉	1	1	yes	characteristic, complemented
590	#3303	C₂×C₅₉	1	1	yes	characteristic, complemented
591	#3301	C₂×C₅₉	1	2	yes	complemented
592	#3299	C₂×C₅₉	1	1	yes	characteristic, complemented
593	#3296	C₂×C₅₉	1	2	yes	complemented
594	#3294	C₂×C₅₉	1	1	yes	characteristic, complemented
595	#3284	C₂×C₅₉	1	1	yes	characteristic, complemented
596	#3282	C₂×C₅₉	1	2	yes	complemented
597	D₄×SD₁₆	C₂×C₅₉	1	1	yes	characteristic, complemented
598	#3248	C₂×C₅₉	1	1	yes	characteristic, complemented
599	#3247	C₂×C₅₉	1	1	yes	characteristic, complemented
600	#3190	C₂×C₅₉	1	2	yes	complemented
601	#3188	C₂×C₅₉	1	2	yes	complemented
602	#3168	C₂×C₅₉	1	1	yes	characteristic, complemented
603	#3167	C₂×C₅₉	1	1	yes	characteristic, complemented
604	#3050	C₂×C₅₉	1	2	yes	complemented
605	C₂×#465	C₂×C₅₉	1	2	yes	complemented
606	C₂×C₈×D₄	C₂×C₅₉	1	1	yes	characteristic, complemented
607	C₂×C₅₉	—	2	2	no	—
608	C₂×C₅₉	—	2	4	no	—
609	C₂×C₅₉	—	4	2	no	—
610	C₂×C₅₉	—	8	1	no	—
611	C₂×C₅₉	—	8	2	no	—
612	C₂×C₅₉	—	8	1	no	—
613	C₂×C₅₉	#3496	1	1	yes	characteristic
614	C₂×C₅₉	C₂²×#135	1	1	yes	characteristic
615	C₂×C₅₉	C₂×#577	1	1	yes	characteristic
616	C₂×#135	C₂²×C₅₉	1	2	yes	complemented
617	C₂²×SD₁₆	C₂²×C₅₉	1	2	yes	complemented
618	C₂³×C₈	C₂²×C₅₉	1	2	yes	complemented
619	#556	C₂²×C₅₉	1	1	yes	characteristic, complemented
620	#555	C₂²×C₅₉	1	1	yes	characteristic
621	#554	—	2	1	no	—
622	#554	C₂²×C₅₉	1	1	yes	characteristic
623	#553	—	2	1	no	—
624	#553	C₂²×C₅₉	1	2	yes	—
625	#552	C₂²×C₅₉	1	2	yes	complemented
626	#551	—	2	2	no	—
627	#550	C₂²×C₅₉	1	1	yes	characteristic
628	D₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
629	#548	C₂²×C₅₉	1	2	yes	complemented
630	#547	C₂²×C₅₉	1	1	yes	characteristic
631	#547	C₂²×C₅₉	1	1	yes	characteristic, complemented
632	#546	—	2	1	no	—
633	#546	—	2	2	no	—
634	#546	C₂²×C₅₉	1	2	yes	—
635	D₄²	—	2	1	no	—
636	D₄²	C₂²×C₅₉	1	1	yes	characteristic
637	#542	—	2	1	no	—
638	#540	—	2	1	no	—
639	#539	—	2	2	no	—
640	#538	—	2	2	no	—
641	#533	C₂²×C₅₉	1	1	yes	characteristic, complemented
642	#532	C₂²×C₅₉	1	1	yes	characteristic
643	#529	C₂²×C₅₉	1	1	yes	characteristic
644	#529	C₂²×C₅₉	1	1	yes	characteristic, complemented
645	#525	C₂²×C₅₉	1	2	yes	—
646	#525	C₂²×C₅₉	1	2	yes	complemented
647	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	complemented
648	C₂×#121	C₂²×C₅₉	1	2	yes	—
649	#520	—	2	1	no	—
650	#518	—	2	1	no	—
651	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
652	#499	C₂²×C₅₉	1	1	yes	characteristic, complemented
653	#498	C₂²×C₅₉	1	1	yes	characteristic, complemented
654	#495	C₂²×C₅₉	1	1	yes	characteristic, complemented
655	#492	C₂²×C₅₉	1	1	yes	characteristic, complemented
656	#488	C₂²×C₅₉	1	1	yes	characteristic, complemented
657	#488	C₂²×C₅₉	1	1	yes	characteristic, complemented
658	#487	C₂²×C₅₉	1	1	yes	characteristic, complemented
659	#486	C₂²×C₅₉	1	1	yes	characteristic, complemented
660	#485	C₂²×C₅₉	1	2	yes	complemented
661	#485	C₂²×C₅₉	1	2	yes	complemented
662	#484	C₂²×C₅₉	1	2	yes	complemented
663	#483	C₂²×C₅₉	1	2	yes	complemented
664	#482	C₂²×C₅₉	1	2	yes	complemented
665	#482	C₂²×C₅₉	1	2	yes	complemented
666	#481	C₂²×C₅₉	1	2	yes	complemented
667	#480	C₂²×C₅₉	1	2	yes	complemented
668	#479	C₂²×C₅₉	1	2	yes	complemented
669	#478	C₂²×C₅₉	1	2	yes	complemented
670	#477	C₂²×C₅₉	1	1	yes	characteristic, complemented
671	#476	C₂²×C₅₉	1	1	yes	characteristic, complemented
672	#475	C₂²×C₅₉	1	1	yes	characteristic, complemented
673	#474	C₂²×C₅₉	1	1	yes	characteristic, complemented
674	#467	C₂²×C₅₉	1	1	yes	characteristic, complemented
675	#467	C₂²×C₅₉	1	2	yes	complemented
676	#467	C₂²×C₅₉	1	2	yes	complemented
677	#466	C₂²×C₅₉	1	1	yes	characteristic
678	#466	C₂²×C₅₉	1	2	yes	complemented
679	#466	C₂²×C₅₉	1	2	yes	complemented
680	#465	C₂²×C₅₉	1	1	yes	characteristic
681	#465	C₂²×C₅₉	1	2	yes	—
682	#465	C₂²×C₅₉	1	2	yes	complemented
683	#465	C₂²×C₅₉	1	2	yes	complemented
684	#465	C₂²×C₅₉	1	2	yes	complemented
685	#465	C₂²×C₅₉	1	2	yes	complemented
686	#465	C₂²×C₅₉	1	2	yes	complemented
687	#465	C₂²×C₅₉	1	2	yes	complemented
688	#465	C₂²×C₅₉	1	1	yes	characteristic, complemented
689	#465	C₂²×C₅₉	1	2	yes	complemented
690	#465	C₂²×C₅₉	1	2	yes	complemented
691	#465	C₂²×C₅₉	1	2	yes	complemented
692	#464	C₂²×C₅₉	1	2	yes	complemented
693	#463	C₂²×C₅₉	1	2	yes	complemented
694	#462	C₂²×C₅₉	1	1	yes	characteristic, complemented
695	#461	C₂²×C₅₉	1	1	yes	characteristic, complemented
696	#460	C₂²×C₅₉	1	1	yes	characteristic, complemented
697	#459	C₂²×C₅₉	1	1	yes	characteristic, complemented
698	#452	C₂²×C₅₉	1	2	yes	complemented
699	#452	C₂²×C₅₉	1	2	yes	complemented
700	#451	C₂²×C₅₉	1	2	yes	complemented
701	#450	C₂²×C₅₉	1	2	yes	complemented
702	#449	C₂²×C₅₉	1	2	yes	complemented
703	#449	C₂²×C₅₉	1	2	yes	complemented
704	#448	C₂²×C₅₉	1	2	yes	complemented
705	#447	C₂²×C₅₉	1	2	yes	complemented
706	C₄×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic, complemented
707	C₄×SD₁₆	C₂²×C₅₉	1	1	yes	characteristic, complemented
708	C₄×SD₁₆	C₂²×C₅₉	1	2	yes	complemented
709	C₄×SD₁₆	C₂²×C₅₉	1	1	yes	characteristic, complemented
710	C₄×SD₁₆	C₂²×C₅₉	1	2	yes	complemented
711	C₄×D₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
712	C₈×D₄	C₂²×C₅₉	1	1	yes	characteristic
713	C₈×D₄	C₂²×C₅₉	1	1	yes	characteristic
714	C₈×D₄	C₂²×C₅₉	1	2	yes	complemented
715	C₈×D₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
716	C₈×D₄	C₂²×C₅₉	1	2	yes	complemented
717	C₈×D₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
718	#427	C₂²×C₅₉	1	2	yes	complemented
719	C₂×#106	C₂²×C₅₉	1	2	yes	complemented
720	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
721	#416	C₂²×C₅₉	1	2	yes	complemented
722	#416	C₂²×C₅₉	1	2	yes	complemented
723	C₂×#103	C₂²×C₅₉	1	2	yes	complemented
724	C₂×#102	C₂²×C₅₉	1	2	yes	complemented
725	C₂×C₂²⋊C₈	C₂²×C₅₉	1	2	yes	complemented
726	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
727	C₅₉	#62250	1	1	yes	characteristic, direct product factor, Sylow
728	C₂×#41	—	2	1	no	—
729	C₂×#41	—	2	1	no	—
730	C₂×#41	C₂³×C₅₉	1	2	yes	—
731	C₂×#41	C₂³×C₅₉	1	2	yes	—
732	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
733	C₂²×D₄	—	2	2	no	—
734	C₂²×D₄	—	2	1	no	—
735	C₂²×D₄	D₄×C₅₉	1	1	yes	characteristic
736	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
737	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
738	#135	—	4	4	no	—
739	C₂×Q₁₆	C₂³×C₅₉	1	2	yes	—
740	C₂×Q₁₆	C₂³×C₅₉	1	1	yes	characteristic
741	C₂×SD₁₆	—	4	4	no	—
742	C₂×SD₁₆	C₂³×C₅₉	1	1	yes	characteristic
743	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
744	C₂×SD₁₆	C₂³×C₅₉	1	1	yes	characteristic
745	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
746	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
747	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
748	C₂×D₈	C₂³×C₅₉	1	2	yes	—
749	C₂×D₈	C₂³×C₅₉	1	1	yes	characteristic
750	C₂²×C₈	—	4	4	no	—
751	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
752	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
753	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
754	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
755	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
756	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
757	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
758	C₄⋊Q₈	—	2	1	no	—
759	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
760	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
761	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
762	#127	—	2	1	no	—
763	#127	C₂³×C₅₉	1	1	yes	characteristic
764	#126	—	2	2	no	—
765	#126	—	2	2	no	—
766	#126	—	2	2	no	—
767	#126	—	2	1	no	—
768	#126	—	2	1	no	—
769	#125	—	2	2	no	—
770	#125	—	2	1	no	—
771	#125	—	2	1	no	—
772	#125	C₂³×C₅₉	1	1	yes	characteristic
773	#125	C₂³×C₅₉	1	1	yes	characteristic
774	#124	—	2	1	no	—
775	#124	—	2	2	no	—
776	#124	—	2	2	no	—
777	#124	—	2	1	no	—
778	#124	C₂³×C₅₉	1	1	yes	characteristic
779	#124	C₂³×C₅₉	1	1	yes	characteristic
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	—	2	2	no	—
783	#123	—	2	1	no	—
784	#123	—	2	1	no	—
785	#123	—	2	2	no	—
786	#123	—	2	2	no	—
787	#123	—	2	2	no	—
788	#123	—	2	2	no	—
789	C₂²⋊Q₈	—	2	2	no	—
790	C₂²⋊Q₈	—	2	2	no	—
791	C₂²⋊Q₈	—	2	1	no	—
792	C₂²⋊Q₈	—	2	2	no	—
793	C₂²⋊Q₈	—	2	1	no	—
794	C₂²⋊Q₈	—	2	2	no	—
795	C₂²⋊Q₈	—	2	2	no	—
796	C₂²⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
797	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
798	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
799	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
800	C₂²⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
801	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
802	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
803	#121	—	2	2	no	—
804	#121	—	2	2	no	—
805	#121	—	2	1	no	—
806	#121	—	2	1	no	—
807	#121	—	2	2	no	—
808	#121	—	2	2	no	—
809	#121	—	2	1	no	—
810	#121	—	2	1	no	—
811	#121	—	2	2	no	—
812	#121	—	2	2	no	—
813	#121	C₂³×C₅₉	1	1	yes	characteristic
814	#121	C₂³×C₅₉	1	2	yes	—
815	#121	C₂³×C₅₉	1	2	yes	—
816	#121	C₂³×C₅₉	1	2	yes	—
817	#121	C₂³×C₅₉	1	2	yes	—
818	#121	C₂³×C₅₉	1	1	yes	characteristic
819	#121	C₂³×C₅₉	1	2	yes	—
820	#120	—	2	2	no	—
821	#120	—	2	2	no	—
822	#120	—	2	2	no	—
823	#120	—	2	2	no	—
824	C₄×Q₈	—	2	1	no	—
825	C₄×Q₈	—	2	1	no	—
826	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
827	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
828	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	—	2	1	no	—
831	C₄×D₄	—	2	2	no	—
832	C₄×D₄	—	2	2	no	—
833	C₄×D₄	—	2	2	no	—
834	C₄×D₄	—	2	2	no	—
835	C₄×D₄	—	2	1	no	—
836	C₄×D₄	—	2	1	no	—
837	C₄×D₄	—	2	1	no	—
838	C₄×D₄	—	2	2	no	—
839	C₄×D₄	—	2	2	no	—
840	C₄×D₄	—	2	1	no	—
841	C₄×D₄	D₄×C₅₉	1	1	yes	characteristic
842	C₄×D₄	D₄×C₅₉	1	2	yes	—
843	C₄×D₄	D₄×C₅₉	1	1	yes	characteristic
844	C₄×D₄	C₂³×C₅₉	1	1	yes	characteristic
845	C₄×D₄	C₂³×C₅₉	1	1	yes	characteristic
846	C₄×D₄	C₂³×C₅₉	1	2	yes	—
847	C₄×D₄	C₂³×C₅₉	1	1	yes	characteristic
848	C₄×D₄	C₂³×C₅₉	1	2	yes	—
849	C₄×D₄	C₂³×C₅₉	1	1	yes	characteristic
850	#117	—	2	1	no	—
851	#117	—	2	1	no	—
852	#117	—	2	2	no	—
853	#117	—	2	1	no	—
854	#117	—	2	1	no	—
855	#117	C₂³×C₅₉	1	2	yes	—
856	#117	C₂³×C₅₉	1	2	yes	—
857	C₂×C₄⋊C₄	—	2	2	no	—
858	C₂×C₄⋊C₄	—	2	1	no	—
859	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
860	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
861	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
862	C₂×C₂²⋊C₄	—	2	2	no	—
863	C₂×C₂²⋊C₄	—	2	2	no	—
864	C₂×C₂²⋊C₄	—	2	2	no	—
865	C₂×C₂²⋊C₄	D₄×C₅₉	1	2	yes	—
866	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
867	#107	C₂³×C₅₉	1	2	yes	—
868	#107	C₂³×C₅₉	1	2	yes	—
869	#107	C₂³×C₅₉	1	1	yes	characteristic
870	#107	C₂³×C₅₉	1	1	yes	characteristic
871	#106	C₂³×C₅₉	1	1	yes	characteristic
872	#106	C₂³×C₅₉	1	2	yes	—
873	#106	C₂³×C₅₉	1	2	yes	—
874	#106	C₂³×C₅₉	1	2	yes	—
875	#106	C₂³×C₅₉	1	1	yes	characteristic
876	#106	C₂³×C₅₉	1	2	yes	—
877	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
878	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
879	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
880	#103	C₂³×C₅₉	1	1	yes	characteristic
881	#103	C₂³×C₅₉	1	2	yes	—
882	#103	C₂³×C₅₉	1	2	yes	—
883	#103	C₂³×C₅₉	1	2	yes	—
884	#103	C₂³×C₅₉	1	1	yes	characteristic
885	#103	C₂³×C₅₉	1	2	yes	—
886	#103	C₂³×C₅₉	1	2	yes	—
887	#103	C₂³×C₅₉	1	1	yes	characteristic
888	#103	C₂³×C₅₉	1	2	yes	—
889	#103	C₂³×C₅₉	1	1	yes	characteristic
890	#102	C₂³×C₅₉	1	1	yes	characteristic
891	#102	C₂³×C₅₉	1	2	yes	—
892	#102	C₂³×C₅₉	1	2	yes	—
893	#102	C₂³×C₅₉	1	2	yes	—
894	#102	C₂³×C₅₉	1	1	yes	characteristic
895	#102	C₂³×C₅₉	1	2	yes	—
896	#102	C₂³×C₅₉	1	2	yes	—
897	#102	C₂³×C₅₉	1	2	yes	—
898	#102	C₂³×C₅₉	1	1	yes	characteristic
899	#102	C₂³×C₅₉	1	1	yes	characteristic
900	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
901	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
902	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
903	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
904	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
905	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
906	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
907	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
908	C₂⁴	—	2	2	no	—
909	C₂⁴	C₂×D₄×C₅₉	1	2	yes	—
910	#41	—	4	2	no	—
911	#41	—	4	2	no	—
912	#41	—	4	2	no	—
913	#41	—	4	2	no	—
914	#41	—	4	4	no	—
915	#41	—	8	2	no	—
916	C₂×Q₈	—	2	1	no	—
917	C₂×Q₈	—	2	2	no	—
918	C₂×Q₈	—	2	1	no	—
919	C₂×Q₈	—	4	2	no	—
920	C₂×Q₈	—	4	2	no	—
921	C₂×Q₈	C₂⁴×C₅₉	1	1	yes	characteristic
922	C₂×Q₈	C₂⁴×C₅₉	1	1	yes	characteristic
923	C₂×Q₈	C₂⁴×C₅₉	1	2	yes	—
924	C₂×D₄	—	2	4	no	—
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	2	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	1	no	—
935	C₂×D₄	—	2	1	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	4	2	no	—
938	C₂×D₄	—	4	2	no	—
939	C₂×D₄	—	4	4	no	—
940	C₂×D₄	—	8	4	no	—
941	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
942	C₂×D₄	C₂×D₄×C₅₉	1	1	yes	characteristic
943	C₂×D₄	C₂×D₄×C₅₉	1	1	yes	characteristic
944	C₂×D₄	C₂⁴×C₅₉	1	1	yes	characteristic
945	C₂×D₄	C₂⁴×C₅₉	1	1	yes	characteristic
946	C₂×D₄	C₂⁴×C₅₉	1	2	yes	—
947	C₂²×C₄	—	2	2	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	2	2	no	—
950	C₂²×C₄	—	2	1	no	—
951	C₂²×C₄	—	2	1	no	—
952	C₂²×C₄	—	2	2	no	—
953	C₂²×C₄	—	2	2	no	—
954	C₂²×C₄	—	2	2	no	—
955	C₂²×C₄	—	4	2	no	—
956	C₂²×C₄	—	4	2	no	—
957	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
958	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
959	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
960	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
961	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
962	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
963	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
964	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
965	Q₁₆	—	4	2	no	—
966	Q₁₆	—	4	1	no	—
967	SD₁₆	—	2	2	no	—
968	SD₁₆	—	2	4	no	—
969	SD₁₆	—	2	2	no	—
970	SD₁₆	—	4	2	no	—
971	SD₁₆	—	4	2	no	—
972	SD₁₆	—	4	2	no	—
973	D₈	—	4	2	no	—
974	D₈	—	4	1	no	—
975	C₂×C₈	—	2	2	no	—
976	C₂×C₈	—	2	4	no	—
977	C₂×C₈	—	2	4	no	—
978	C₂×C₈	—	4	2	no	—
979	C₂×C₈	—	4	2	no	—
980	C₂×C₈	—	4	2	no	—
981	C₂×C₈	—	4	1	no	—
982	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
983	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
984	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
985	C₂×C₈	C₂⁴×C₅₉	1	2	yes	—
986	C₂×C₈	C₂⁴×C₅₉	1	2	yes	—
987	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	2	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	1	no	—
996	C₄⋊C₄	—	2	1	no	—
997	C₄⋊C₄	—	2	1	no	—
998	C₄⋊C₄	—	2	1	no	—
999	C₄⋊C₄	—	2	1	no	—
1000	C₄⋊C₄	—	2	1	no	—
1001	C₄⋊C₄	—	2	1	no	—
1002	C₄⋊C₄	—	2	2	no	—
1003	C₄⋊C₄	—	2	2	no	—
1004	C₄⋊C₄	—	2	1	no	—
1005	C₄⋊C₄	—	2	1	no	—
1006	C₄⋊C₄	—	2	2	no	—
1007	C₄⋊C₄	—	2	1	no	—
1008	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
1009	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
1010	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
1011	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
1012	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
1013	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
1014	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
1015	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
1016	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	1	no	—
1026	C₂²⋊C₄	—	2	1	no	—
1027	C₂²⋊C₄	—	2	1	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	1	no	—
1032	C₂²⋊C₄	—	2	1	no	—
1033	C₂²⋊C₄	—	2	1	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	1	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	1	no	—
1038	C₂²⋊C₄	—	2	2	no	—
1039	C₂²⋊C₄	—	2	1	no	—
1040	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
1041	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
1042	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
1043	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
1044	C₄²	—	2	2	no	—
1045	C₄²	—	2	2	no	—
1046	C₄²	—	2	2	no	—
1047	C₄²	—	2	1	no	—
1048	C₄²	—	2	1	no	—
1049	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
1050	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
1051	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
1052	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
1053	C₂³	—	2	4	no	—
1054	C₂³	—	2	4	no	—
1055	C₂³	—	2	1	no	—
1056	C₂³	—	2	1	no	—
1057	C₂³	—	2	2	no	—
1058	C₂³	—	4	2	no	—
1059	C₂³	—	4	4	no	—
1060	C₂³	—	8	2	no	—
1061	C₂³	—	8	2	no	—
1062	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
1063	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
1064	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
1065	Q₈	—	2	1	no	—
1066	Q₈	—	2	2	no	—
1067	Q₈	—	2	1	no	—
1068	Q₈	—	2	2	no	—
1069	Q₈	—	2	1	no	—
1070	Q₈	—	2	1	no	—
1071	Q₈	—	4	2	no	—
1072	Q₈	—	8	2	no	—
1073	Q₈	—	8	1	no	—
1074	D₄	—	2	4	no	—
1075	D₄	—	2	2	no	—
1076	D₄	—	2	1	no	—
1077	D₄	—	2	2	no	—
1078	D₄	—	2	1	no	—
1079	D₄	—	2	1	no	—
1080	D₄	—	2	1	no	—
1081	D₄	—	2	2	no	—
1082	D₄	—	4	4	no	—
1083	D₄	—	4	4	no	—
1084	D₄	—	4	2	no	—
1085	D₄	—	4	2	no	—
1086	D₄	—	4	4	no	—
1087	D₄	—	4	2	no	—
1088	D₄	—	8	2	no	—
1089	D₄	—	8	1	no	—
1090	D₄	—	8	2	no	—
1091	D₄	—	8	2	no	—
1092	D₄	—	8	2	no	—
1093	D₄	—	8	2	no	—
1094	D₄	#135×C₅₉	1	4	yes	complemented
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	2	no	—
1099	C₂×C₄	—	2	2	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	2	no	—
1102	C₂×C₄	—	2	2	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	2	no	—
1109	C₂×C₄	—	2	2	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	4	2	no	—
1113	C₂×C₄	—	4	2	no	—
1114	C₂×C₄	—	4	2	no	—
1115	C₂×C₄	—	4	4	no	—
1116	C₂×C₄	—	4	2	no	—
1117	C₂×C₄	—	4	2	no	—
1118	C₂×C₄	—	8	2	no	—
1119	C₂×C₄	—	8	2	no	—
1120	C₂×C₄	—	8	2	no	—
1121	C₂×C₄	—	8	2	no	—
1122	C₂×C₄	—	8	2	no	—
1123	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1124	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1125	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1126	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1127	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1128	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1129	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1130	C₂×C₄	C₂⁵×C₅₉	1	1	yes	characteristic
1131	C₈	—	2	1	no	—
1132	C₈	—	2	2	no	—
1133	C₈	—	2	2	no	—
1134	C₈	—	2	1	no	—
1135	C₈	—	2	1	no	—
1136	C₈	H(5,𝔽₂)×C₅₉	1	2	yes	—
1137	C₂²	—	2	1	no	—
1138	C₂²	—	2	2	no	—
1139	C₂²	—	2	1	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	2	no	—
1142	C₂²	—	2	2	no	—
1143	C₂²	—	2	2	no	—
1144	C₂²	—	4	8	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	4	1	no	—
1147	C₂²	—	4	2	no	—
1148	C₂²	—	4	2	no	—
1149	C₂²	—	4	1	no	—
1150	C₂²	—	4	1	no	—
1151	C₂²	—	4	1	no	—
1152	C₂²	—	4	2	no	—
1153	C₂²	—	4	1	no	—
1154	C₂²	—	16	4	no	—
1155	C₂²	C₂×#135×C₅₉	1	4	yes	—
1156	C₂²	C₅₉×#577	1	2	yes	—
1157	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
1158	C₄	—	2	1	no	—
1159	C₄	—	2	1	no	—
1160	C₄	—	2	1	no	—
1161	C₄	—	2	1	no	—
1162	C₄	—	2	2	no	—
1163	C₄	—	2	2	no	—
1164	C₄	—	4	1	no	—
1165	C₄	—	4	1	no	—
1166	C₄	—	4	2	no	—
1167	C₄	—	4	1	no	—
1168	C₄	—	4	2	no	—
1169	C₄	—	4	1	no	—
1170	C₄	—	4	1	no	—
1171	C₄	—	4	2	no	—
1172	C₄	—	4	1	no	—
1173	C₄	C₂×#135×C₅₉	1	2	yes	—
1174	C₄	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
1175	C₄	C₅₉×#585	1	1	yes	characteristic
1176	C₂	—	2	2	no	—
1177	C₂	—	2	4	no	—
1178	C₂	—	4	2	no	—
1179	C₂	—	8	1	no	—
1180	C₂	—	8	2	no	—
1181	C₂	—	8	1	no	—
1182	C₂	C₅₉×#3496	1	1	yes	characteristic
1183	C₂	C₂²×#135×C₅₉	1	1	yes	characteristic
1184	C₂	C₂×C₅₉×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂×C₄×D₄×C₅₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₅₉×#3520	C₂	semidirect
2. C₅₉×#3519	C₂	semidirect
3. C₅₉×#3340	C₂	semidirect
4. C₅₉×#3337	C₂	semidirect
5. C₅₉×#3335	C₂	semidirect
6. C₅₉×#3304	C₂	semidirect
7. C₅₉×#3303	C₂	semidirect
8. C₅₉×#3301	C₂	semidirect
9. C₅₉×#3299	C₂	semidirect
10. C₅₉×#3296	C₂	semidirect
11. C₅₉×#3294	C₂	semidirect
12. C₅₉×#3284	C₂	semidirect
13. C₅₉×#3282	C₂	semidirect
14. D₄×SD₁₆×C₅₉	C₂	semidirect
15. C₅₉×#3248	C₂	semidirect
16. C₅₉×#3247	C₂	semidirect
17. C₅₉×#3190	C₂	semidirect
18. C₅₉×#3188	C₂	semidirect
19. C₅₉×#3168	C₂	semidirect
20. C₅₉×#3167	C₂	semidirect
21. C₅₉×#3050	C₂	semidirect
22. C₂×C₅₉×#465	C₂	semidirect
23. C₂×C₈×D₄×C₅₉	C₂	semidirect
24. C₂×#135×C₅₉	C₂²	semidirect
25. C₂²×SD₁₆×C₅₉	C₂²	semidirect
26. C₂³×C₈×C₅₉	C₂²	semidirect
27. C₅₉×#556	C₂²	semidirect
33. C₅₉×#552	C₂²	semidirect
37. C₅₉×#548	C₂²	semidirect
39. C₅₉×#547	C₂²	semidirect
49. C₅₉×#533	C₂²	semidirect
52. C₅₉×#529	C₂²	semidirect
54. C₅₉×#525	C₂²	semidirect
55. C₂×C₂²⋊Q₈×C₅₉	C₂²	semidirect
60. C₅₉×#499	C₂²	semidirect
61. C₅₉×#498	C₂²	semidirect
62. C₅₉×#495	C₂²	semidirect
63. C₅₉×#492	C₂²	semidirect
64. C₅₉×#488	C₂²	semidirect
65. C₅₉×#488	C₂²	semidirect
66. C₅₉×#487	C₂²	semidirect
67. C₅₉×#486	C₂²	semidirect
68. C₅₉×#485	C₂²	semidirect
69. C₅₉×#485	C₂²	semidirect
70. C₅₉×#484	C₂²	semidirect
71. C₅₉×#483	C₂²	semidirect
72. C₅₉×#482	C₂²	semidirect
73. C₅₉×#482	C₂²	semidirect
74. C₅₉×#481	C₂²	semidirect
75. C₅₉×#480	C₂²	semidirect
76. C₅₉×#479	C₂²	semidirect
77. C₅₉×#478	C₂²	semidirect
78. C₅₉×#477	C₂²	semidirect
79. C₅₉×#476	C₂²	semidirect
80. C₅₉×#475	C₂²	semidirect
81. C₅₉×#474	C₂²	semidirect
82. C₅₉×#467	C₂²	semidirect
83. C₅₉×#467	C₂²	semidirect
84. C₅₉×#467	C₂²	semidirect
86. C₅₉×#466	C₂²	semidirect
87. C₅₉×#466	C₂²	semidirect
90. C₅₉×#465	C₂²	semidirect
91. C₅₉×#465	C₂²	semidirect
92. C₅₉×#465	C₂²	semidirect
93. C₅₉×#465	C₂²	semidirect
94. C₅₉×#465	C₂²	semidirect
95. C₅₉×#465	C₂²	semidirect
96. C₅₉×#465	C₂²	semidirect
97. C₅₉×#465	C₂²	semidirect
98. C₅₉×#465	C₂²	semidirect
99. C₅₉×#465	C₂²	semidirect
100. C₅₉×#464	C₂²	semidirect
101. C₅₉×#463	C₂²	semidirect
102. C₅₉×#462	C₂²	semidirect
103. C₅₉×#461	C₂²	semidirect
104. C₅₉×#460	C₂²	semidirect
105. C₅₉×#459	C₂²	semidirect
106. C₅₉×#452	C₂²	semidirect
107. C₅₉×#452	C₂²	semidirect
108. C₅₉×#451	C₂²	semidirect
109. C₅₉×#450	C₂²	semidirect
110. C₅₉×#449	C₂²	semidirect
111. C₅₉×#449	C₂²	semidirect
112. C₅₉×#448	C₂²	semidirect
113. C₅₉×#447	C₂²	semidirect
114. C₄×Q₁₆×C₅₉	C₂²	semidirect
115. C₄×SD₁₆×C₅₉	C₂²	semidirect
116. C₄×SD₁₆×C₅₉	C₂²	semidirect
117. C₄×SD₁₆×C₅₉	C₂²	semidirect
118. C₄×SD₁₆×C₅₉	C₂²	semidirect
119. C₄×D₈×C₅₉	C₂²	semidirect
122. C₈×D₄×C₅₉	C₂²	semidirect
123. C₈×D₄×C₅₉	C₂²	semidirect
124. C₈×D₄×C₅₉	C₂²	semidirect
125. C₈×D₄×C₅₉	C₂²	semidirect
126. C₅₉×#427	C₂²	semidirect
127. C₂×#106×C₅₉	C₂²	semidirect
128. C₂×C₄⋊C₈×C₅₉	C₂²	semidirect
129. C₅₉×#416	C₂²	semidirect
130. C₅₉×#416	C₂²	semidirect
131. C₂×#103×C₅₉	C₂²	semidirect
132. C₂×#102×C₅₉	C₂²	semidirect
133. C₂×C₂²⋊C₈×C₅₉	C₂²	semidirect
134. C₂×C₄×C₈×C₅₉	C₂²	semidirect
501. D₄×C₅₉	#135	semidirect
544. #62250	C₅₉	direct (N × H)
584. #3520	C₂×C₅₉	semidirect
585. #3519	C₂×C₅₉	semidirect
586. #3340	C₂×C₅₉	semidirect
587. #3337	C₂×C₅₉	semidirect
588. #3335	C₂×C₅₉	semidirect
589. #3304	C₂×C₅₉	semidirect
590. #3303	C₂×C₅₉	semidirect
591. #3301	C₂×C₅₉	semidirect
592. #3299	C₂×C₅₉	semidirect
593. #3296	C₂×C₅₉	semidirect
594. #3294	C₂×C₅₉	semidirect
595. #3284	C₂×C₅₉	semidirect
596. #3282	C₂×C₅₉	semidirect
597. D₄×SD₁₆	C₂×C₅₉	semidirect
598. #3248	C₂×C₅₉	semidirect
599. #3247	C₂×C₅₉	semidirect
600. #3190	C₂×C₅₉	semidirect
601. #3188	C₂×C₅₉	semidirect
602. #3168	C₂×C₅₉	semidirect
603. #3167	C₂×C₅₉	semidirect
604. #3050	C₂×C₅₉	semidirect
605. C₂×#465	C₂×C₅₉	semidirect
606. C₂×C₈×D₄	C₂×C₅₉	semidirect
616. C₂×#135	C₂²×C₅₉	semidirect
617. C₂²×SD₁₆	C₂²×C₅₉	semidirect
618. C₂³×C₈	C₂²×C₅₉	semidirect
619. #556	C₂²×C₅₉	semidirect
625. #552	C₂²×C₅₉	semidirect
629. #548	C₂²×C₅₉	semidirect
631. #547	C₂²×C₅₉	semidirect
641. #533	C₂²×C₅₉	semidirect
644. #529	C₂²×C₅₉	semidirect
646. #525	C₂²×C₅₉	semidirect
647. C₂×C₂²⋊Q₈	C₂²×C₅₉	semidirect
652. #499	C₂²×C₅₉	semidirect
653. #498	C₂²×C₅₉	semidirect
654. #495	C₂²×C₅₉	semidirect
655. #492	C₂²×C₅₉	semidirect
656. #488	C₂²×C₅₉	semidirect
657. #488	C₂²×C₅₉	semidirect
658. #487	C₂²×C₅₉	semidirect
659. #486	C₂²×C₅₉	semidirect
660. #485	C₂²×C₅₉	semidirect
661. #485	C₂²×C₅₉	semidirect
662. #484	C₂²×C₅₉	semidirect
663. #483	C₂²×C₅₉	semidirect
664. #482	C₂²×C₅₉	semidirect
665. #482	C₂²×C₅₉	semidirect
666. #481	C₂²×C₅₉	semidirect
667. #480	C₂²×C₅₉	semidirect
668. #479	C₂²×C₅₉	semidirect
669. #478	C₂²×C₅₉	semidirect
670. #477	C₂²×C₅₉	semidirect
671. #476	C₂²×C₅₉	semidirect
672. #475	C₂²×C₅₉	semidirect
673. #474	C₂²×C₅₉	semidirect
674. #467	C₂²×C₅₉	semidirect
675. #467	C₂²×C₅₉	semidirect
676. #467	C₂²×C₅₉	semidirect
678. #466	C₂²×C₅₉	semidirect
679. #466	C₂²×C₅₉	semidirect
682. #465	C₂²×C₅₉	semidirect
683. #465	C₂²×C₅₉	semidirect
684. #465	C₂²×C₅₉	semidirect
685. #465	C₂²×C₅₉	semidirect
686. #465	C₂²×C₅₉	semidirect
687. #465	C₂²×C₅₉	semidirect
688. #465	C₂²×C₅₉	semidirect
689. #465	C₂²×C₅₉	semidirect
690. #465	C₂²×C₅₉	semidirect
691. #465	C₂²×C₅₉	semidirect
692. #464	C₂²×C₅₉	semidirect
693. #463	C₂²×C₅₉	semidirect
694. #462	C₂²×C₅₉	semidirect
695. #461	C₂²×C₅₉	semidirect
696. #460	C₂²×C₅₉	semidirect
697. #459	C₂²×C₅₉	semidirect
698. #452	C₂²×C₅₉	semidirect
699. #452	C₂²×C₅₉	semidirect
700. #451	C₂²×C₅₉	semidirect
701. #450	C₂²×C₅₉	semidirect
702. #449	C₂²×C₅₉	semidirect
703. #449	C₂²×C₅₉	semidirect
704. #448	C₂²×C₅₉	semidirect
705. #447	C₂²×C₅₉	semidirect
706. C₄×Q₁₆	C₂²×C₅₉	semidirect
707. C₄×SD₁₆	C₂²×C₅₉	semidirect
708. C₄×SD₁₆	C₂²×C₅₉	semidirect
709. C₄×SD₁₆	C₂²×C₅₉	semidirect
710. C₄×SD₁₆	C₂²×C₅₉	semidirect
711. C₄×D₈	C₂²×C₅₉	semidirect
714. C₈×D₄	C₂²×C₅₉	semidirect
715. C₈×D₄	C₂²×C₅₉	semidirect
716. C₈×D₄	C₂²×C₅₉	semidirect
717. C₈×D₄	C₂²×C₅₉	semidirect
718. #427	C₂²×C₅₉	semidirect
719. C₂×#106	C₂²×C₅₉	semidirect
720. C₂×C₄⋊C₈	C₂²×C₅₉	semidirect
721. #416	C₂²×C₅₉	semidirect
722. #416	C₂²×C₅₉	semidirect
723. C₂×#103	C₂²×C₅₉	semidirect
724. C₂×#102	C₂²×C₅₉	semidirect
725. C₂×C₂²⋊C₈	C₂²×C₅₉	semidirect
726. C₂×C₄×C₈	C₂²×C₅₉	semidirect
727. C₅₉	#62250	direct (N × H)
1094. D₄	#135×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₅₉×#3520	2
C₅₉×#3519	2
C₅₉×#3340	2
C₅₉×#3337	2
C₅₉×#3335	2
C₅₉×#3304	2
C₅₉×#3303	2
C₅₉×#3301	2
C₅₉×#3299	2
C₅₉×#3296	2
C₅₉×#3294	2
C₅₉×#3284	2
C₅₉×#3282	2
D₄×SD₁₆×C₅₉	2
C₅₉×#3248	2
C₅₉×#3247	2
C₅₉×#3190	2
C₅₉×#3188	2
C₅₉×#3168	2
C₅₉×#3167	2
C₅₉×#3050	2
C₂×C₅₉×#465	2
C₂×C₈×D₄×C₅₉	2
#62250	59

Subgroups — C59×#62250 #28474359

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#62250 #28474359