Subgroups — C₅₉×#62252 #28474361

Order 15104.

1886 conjugacy classes of subgroups.

The subgroup lattice has 766 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	2	yes	maximal, complemented
2	C₅₉×#3342	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#3336	C₂	1	2	yes	maximal, complemented
4	C₅₉×#3334	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#3302	C₂	1	2	yes	maximal, complemented
6	C₅₉×#3300	C₂	1	4	yes	maximal, complemented
7	C₅₉×#3298	C₂	1	2	yes	maximal, complemented
8	D₄×Q₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#3285	C₂	1	2	yes	maximal, complemented
10	C₅₉×#3283	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#3248	C₂	1	2	yes	maximal, complemented
12	C₅₉×#3190	C₂	1	4	yes	maximal, complemented
13	C₅₉×#3170	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₉×#3168	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#3050	C₂	1	2	yes	maximal, complemented
16	C₂×C₅₉×#467	C₂	1	2	yes	maximal, complemented
17	C₂×C₈×D₄×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#135×C₅₉	C₂²	1	2	yes	complemented
19	C₂²×Q₁₆×C₅₉	C₂²	1	2	yes	complemented
20	C₂³×C₈×C₅₉	C₂²	1	2	yes	—
21	C₅₉×#556	C₂²	1	2	yes	—
22	C₅₉×#554	—	2	2	no	—
23	C₅₉×#552	C₂²	1	4	yes	—
24	C₅₉×#551	—	2	4	no	—
25	D₄×Q₈×C₅₉	C₂²	1	2	yes	—
26	C₅₉×#548	C₂²	1	4	yes	—
27	C₅₉×#547	C₂²	1	2	yes	—
28	C₅₉×#547	C₂²	1	2	yes	—
29	C₅₉×#546	—	2	2	no	—
30	C₅₉×#542	—	2	2	no	—
31	C₅₉×#539	—	2	4	no	—
32	C₅₉×#533	C₂²	1	2	yes	—
33	C₅₉×#529	C₂²	1	2	yes	—
34	C₅₉×#525	C₂²	1	4	yes	—
35	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	4	yes	—
36	C₅₉×#520	—	2	2	no	—
37	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
38	C₅₉×#500	C₂²	1	1	yes	characteristic, complemented
39	C₅₉×#499	C₂²	1	1	yes	characteristic, complemented
40	C₅₉×#495	C₂²	1	1	yes	characteristic, complemented
41	C₅₉×#494	C₂²	1	1	yes	characteristic, complemented
42	C₅₉×#488	C₂²	1	2	yes	complemented
43	C₅₉×#487	C₂²	1	2	yes	complemented
44	C₅₉×#485	C₂²	1	4	yes	complemented
45	C₅₉×#485	C₂²	1	4	yes	complemented
46	C₅₉×#483	C₂²	1	4	yes	complemented
47	C₅₉×#480	C₂²	1	4	yes	complemented
48	C₅₉×#479	C₂²	1	4	yes	complemented
49	C₅₉×#475	C₂²	1	2	yes	complemented
50	C₅₉×#474	C₂²	1	2	yes	complemented
51	C₅₉×#467	C₂²	1	1	yes	characteristic
52	C₅₉×#467	C₂²	1	2	yes	—
53	C₅₉×#467	C₂²	1	4	yes	—
54	C₅₉×#467	C₂²	1	2	yes	—
55	C₅₉×#467	C₂²	1	2	yes	complemented
56	C₅₉×#467	C₂²	1	2	yes	complemented
57	C₅₉×#467	C₂²	1	2	yes	complemented
58	C₅₉×#467	C₂²	1	4	yes	complemented
59	C₅₉×#466	C₂²	1	1	yes	characteristic
60	C₅₉×#466	C₂²	1	2	yes	complemented
61	C₅₉×#465	C₂²	1	4	yes	—
62	C₅₉×#465	C₂²	1	2	yes	—
63	C₅₉×#465	C₂²	1	4	yes	complemented
64	C₅₉×#464	C₂²	1	4	yes	complemented
65	C₅₉×#462	C₂²	1	2	yes	complemented
66	C₅₉×#461	C₂²	1	2	yes	complemented
67	C₅₉×#452	C₂²	1	4	yes	complemented
68	C₅₉×#452	C₂²	1	4	yes	complemented
69	C₅₉×#451	C₂²	1	4	yes	complemented
70	C₅₉×#448	C₂²	1	4	yes	complemented
71	C₄×Q₁₆×C₅₉	C₂²	1	2	yes	complemented
72	C₄×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic, complemented
73	C₄×Q₁₆×C₅₉	C₂²	1	2	yes	complemented
74	C₄×SD₁₆×C₅₉	C₂²	1	2	yes	complemented
75	C₄×D₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
76	C₈×D₄×C₅₉	C₂²	1	1	yes	characteristic
77	C₈×D₄×C₅₉	C₂²	1	2	yes	—
78	C₈×D₄×C₅₉	C₂²	1	1	yes	characteristic
79	C₈×D₄×C₅₉	C₂²	1	1	yes	characteristic
80	C₈×D₄×C₅₉	C₂²	1	2	yes	—
81	C₈×D₄×C₅₉	C₂²	1	1	yes	characteristic
82	C₅₉×#427	C₂²	1	2	yes	complemented
83	C₂×#107×C₅₉	C₂²	1	2	yes	complemented
84	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
85	C₅₉×#416	C₂²	1	4	yes	complemented
86	C₂×#103×C₅₉	C₂²	1	4	yes	complemented
87	C₂×C₂²⋊C₈×C₅₉	C₂²	1	2	yes	—
88	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
89	C₂×#41×C₅₉	—	2	2	no	—
90	C₂×#41×C₅₉	C₂³	1	4	yes	—
91	C₂²×Q₈×C₅₉	C₂³	1	4	yes	—
92	C₂²×D₄×C₅₉	D₄	1	1	yes	characteristic
93	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
94	#135×C₅₉	—	4	4	no	—
95	C₂×Q₁₆×C₅₉	—	4	4	no	—
96	C₂×Q₁₆×C₅₉	C₂³	1	2	yes	—
97	C₂×Q₁₆×C₅₉	C₂³	1	1	yes	characteristic
98	C₂×Q₁₆×C₅₉	C₂³	1	2	yes	—
99	C₂×Q₁₆×C₅₉	C₂³	1	4	yes	—
100	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
101	C₂×SD₁₆×C₅₉	C₂³	1	4	yes	—
102	C₂×D₈×C₅₉	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₅₉	—	4	4	no	—
104	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
106	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
107	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
109	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
110	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
111	C₄⋊Q₈×C₅₉	—	2	2	no	—
112	C₄⋊Q₈×C₅₉	C₂³	1	2	yes	—
113	C₄⋊Q₈×C₅₉	C₂³	1	2	yes	—
114	#126×C₅₉	—	2	4	no	—
115	#126×C₅₉	—	2	4	no	—
116	#126×C₅₉	—	2	2	no	—
117	#125×C₅₉	—	2	4	no	—
118	#125×C₅₉	—	2	2	no	—
119	#125×C₅₉	C₂³	1	2	yes	—
120	#124×C₅₉	—	2	2	no	—
121	#124×C₅₉	—	2	4	no	—
122	#124×C₅₉	C₂³	1	2	yes	—
123	#123×C₅₉	—	2	4	no	—
124	#123×C₅₉	—	2	4	no	—
125	#123×C₅₉	—	2	2	no	—
126	#123×C₅₉	—	2	4	no	—
127	#123×C₅₉	—	2	4	no	—
128	C₂²⋊Q₈×C₅₉	—	2	4	no	—
129	C₂²⋊Q₈×C₅₉	—	2	4	no	—
130	C₂²⋊Q₈×C₅₉	—	2	2	no	—
131	C₂²⋊Q₈×C₅₉	—	2	4	no	—
132	C₂²⋊Q₈×C₅₉	—	2	2	no	—
133	C₂²⋊Q₈×C₅₉	—	2	4	no	—
134	C₂²⋊Q₈×C₅₉	C₂³	1	4	yes	—
135	C₂²⋊Q₈×C₅₉	C₂³	1	4	yes	—
136	C₂²⋊Q₈×C₅₉	C₂³	1	4	yes	—
137	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
138	C₂²⋊Q₈×C₅₉	C₂³	1	4	yes	—
139	#121×C₅₉	—	2	4	no	—
140	#121×C₅₉	—	2	2	no	—
141	#121×C₅₉	C₂³	1	4	yes	—
142	#121×C₅₉	C₂³	1	2	yes	—
143	#120×C₅₉	—	2	4	no	—
144	C₄×Q₈×C₅₉	—	2	2	no	—
145	C₄×Q₈×C₅₉	—	2	2	no	—
146	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
147	C₄×Q₈×C₅₉	C₂³	1	4	yes	—
148	C₄×D₄×C₅₉	—	2	2	no	—
149	C₄×D₄×C₅₉	—	2	4	no	—
150	C₄×D₄×C₅₉	—	2	4	no	—
151	C₄×D₄×C₅₉	—	2	2	no	—
152	C₄×D₄×C₅₉	—	2	4	no	—
153	C₄×D₄×C₅₉	D₄	1	1	yes	characteristic
154	C₄×D₄×C₅₉	D₄	1	2	yes	—
155	C₄×D₄×C₅₉	D₄	1	1	yes	characteristic
156	C₄×D₄×C₅₉	C₂³	1	2	yes	—
157	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
158	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
159	C₄×D₄×C₅₉	C₂³	1	2	yes	—
160	#117×C₅₉	—	2	2	no	—
161	#117×C₅₉	—	2	4	no	—
162	#117×C₅₉	—	2	2	no	—
163	#117×C₅₉	C₂³	1	4	yes	—
164	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
165	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
166	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
168	C₂×C₂²⋊C₄×C₅₉	—	2	4	no	—
169	C₂×C₂²⋊C₄×C₅₉	D₄	1	2	yes	—
170	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
171	#107×C₅₉	C₂³	1	1	yes	characteristic
172	#107×C₅₉	C₂³	1	2	yes	—
173	#107×C₅₉	C₂³	1	4	yes	—
174	#107×C₅₉	C₂³	1	1	yes	characteristic
175	#107×C₅₉	C₂³	1	2	yes	—
176	#106×C₅₉	C₂³	1	4	yes	—
177	#106×C₅₉	C₂³	1	2	yes	—
178	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
179	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
180	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
181	#103×C₅₉	C₂³	1	2	yes	—
182	#103×C₅₉	C₂³	1	4	yes	—
183	#103×C₅₉	C₂³	1	4	yes	—
184	#103×C₅₉	C₂³	1	4	yes	—
185	#103×C₅₉	C₂³	1	4	yes	—
186	#103×C₅₉	C₂³	1	4	yes	—
187	#103×C₅₉	C₂³	1	2	yes	—
188	#102×C₅₉	C₂³	1	2	yes	—
189	#102×C₅₉	C₂³	1	4	yes	—
190	#102×C₅₉	C₂³	1	2	yes	—
191	C₂²⋊C₈×C₅₉	C₂³	1	2	yes	—
192	C₂²⋊C₈×C₅₉	C₂³	1	2	yes	—
193	C₂²⋊C₈×C₅₉	C₂³	1	2	yes	—
194	C₂²⋊C₈×C₅₉	C₂³	1	2	yes	—
195	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
198	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
199	C₂⁴×C₅₉	C₂×D₄	1	2	yes	—
200	#41×C₅₉	—	4	4	no	—
201	#41×C₅₉	—	4	4	no	—
202	#41×C₅₉	—	4	8	no	—
203	C₂×Q₈×C₅₉	—	2	2	no	—
204	C₂×Q₈×C₅₉	—	2	4	no	—
205	C₂×Q₈×C₅₉	—	4	4	no	—
206	C₂×Q₈×C₅₉	—	4	4	no	—
207	C₂×Q₈×C₅₉	C₂⁴	1	2	yes	—
208	C₂×Q₈×C₅₉	C₂⁴	1	4	yes	—
209	C₂×D₄×C₅₉	—	2	4	no	—
210	C₂×D₄×C₅₉	—	2	2	no	—
211	C₂×D₄×C₅₉	—	2	4	no	—
212	C₂×D₄×C₅₉	—	2	4	no	—
213	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
214	C₂×D₄×C₅₉	C₂×D₄	1	1	yes	characteristic
215	C₂×D₄×C₅₉	C₂×D₄	1	1	yes	characteristic
216	C₂×D₄×C₅₉	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₅₉	—	2	4	no	—
218	C₂²×C₄×C₅₉	—	2	4	no	—
219	C₂²×C₄×C₅₉	—	2	2	no	—
220	C₂²×C₄×C₅₉	—	2	4	no	—
221	C₂²×C₄×C₅₉	—	4	2	no	—
222	C₂²×C₄×C₅₉	—	4	2	no	—
223	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
226	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
227	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
228	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
231	Q₁₆×C₅₉	—	2	2	no	—
232	Q₁₆×C₅₉	—	2	4	no	—
233	Q₁₆×C₅₉	—	4	4	no	—
234	Q₁₆×C₅₉	—	4	2	no	—
235	SD₁₆×C₅₉	—	4	2	no	—
236	SD₁₆×C₅₉	—	4	4	no	—
237	D₈×C₅₉	—	2	2	no	—
238	C₂×C₈×C₅₉	—	2	2	no	—
239	C₂×C₈×C₅₉	—	2	4	no	—
240	C₂×C₈×C₅₉	—	2	4	no	—
241	C₂×C₈×C₅₉	—	4	2	no	—
242	C₂×C₈×C₅₉	—	4	2	no	—
243	C₂×C₈×C₅₉	—	4	2	no	—
244	C₂×C₈×C₅₉	—	4	1	no	—
245	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
246	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
247	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
248	C₂×C₈×C₅₉	C₂⁴	1	2	yes	—
249	C₂×C₈×C₅₉	C₂⁴	1	2	yes	—
250	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
251	C₄⋊C₄×C₅₉	—	2	2	no	—
252	C₄⋊C₄×C₅₉	—	2	4	no	—
253	C₄⋊C₄×C₅₉	—	2	2	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	—	2	2	no	—
258	C₄⋊C₄×C₅₉	—	2	2	no	—
259	C₄⋊C₄×C₅₉	—	2	2	no	—
260	C₄⋊C₄×C₅₉	—	2	4	no	—
261	C₄⋊C₄×C₅₉	—	2	2	no	—
262	C₄⋊C₄×C₅₉	—	2	4	no	—
263	C₄⋊C₄×C₅₉	—	2	2	no	—
264	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
265	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
266	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
267	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
268	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
269	C₄⋊C₄×C₅₉	C₂⁴	1	4	yes	—
270	C₂²⋊C₄×C₅₉	—	2	2	no	—
271	C₂²⋊C₄×C₅₉	—	2	4	no	—
272	C₂²⋊C₄×C₅₉	—	2	4	no	—
273	C₂²⋊C₄×C₅₉	—	2	4	no	—
274	C₂²⋊C₄×C₅₉	—	2	4	no	—
275	C₂²⋊C₄×C₅₉	—	2	4	no	—
276	C₂²⋊C₄×C₅₉	—	2	2	no	—
277	C₂²⋊C₄×C₅₉	—	2	2	no	—
278	C₂²⋊C₄×C₅₉	—	2	2	no	—
279	C₂²⋊C₄×C₅₉	—	2	4	no	—
280	C₂²⋊C₄×C₅₉	—	2	2	no	—
281	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
282	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
283	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
284	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
285	C₄²×C₅₉	—	2	4	no	—
286	C₄²×C₅₉	—	2	4	no	—
287	C₄²×C₅₉	—	2	2	no	—
288	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
289	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
290	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
291	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
292	C₂³×C₅₉	—	2	4	no	—
293	C₂³×C₅₉	—	2	4	no	—
294	C₂³×C₅₉	—	2	2	no	—
295	C₂³×C₅₉	—	4	2	no	—
296	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
297	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
298	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
299	Q₈×C₅₉	—	2	4	no	—
300	Q₈×C₅₉	—	2	2	no	—
301	Q₈×C₅₉	—	2	2	no	—
302	Q₈×C₅₉	—	2	4	no	—
303	Q₈×C₅₉	—	4	4	no	—
304	Q₈×C₅₉	—	8	4	no	—
305	D₄×C₅₉	—	2	4	no	—
306	D₄×C₅₉	—	2	2	no	—
307	D₄×C₅₉	—	2	2	no	—
308	D₄×C₅₉	—	2	2	no	—
309	D₄×C₅₉	—	4	8	no	—
310	D₄×C₅₉	—	4	4	no	—
311	D₄×C₅₉	—	8	4	no	—
312	D₄×C₅₉	#135	1	4	yes	complemented
313	C₂×C₄×C₅₉	—	2	2	no	—
314	C₂×C₄×C₅₉	—	2	2	no	—
315	C₂×C₄×C₅₉	—	2	1	no	—
316	C₂×C₄×C₅₉	—	2	2	no	—
317	C₂×C₄×C₅₉	—	2	2	no	—
318	C₂×C₄×C₅₉	—	2	1	no	—
319	C₂×C₄×C₅₉	—	2	2	no	—
320	C₂×C₄×C₅₉	—	2	2	no	—
321	C₂×C₄×C₅₉	—	2	2	no	—
322	C₂×C₄×C₅₉	—	2	4	no	—
323	C₂×C₄×C₅₉	—	2	2	no	—
324	C₂×C₄×C₅₉	—	2	4	no	—
325	C₂×C₄×C₅₉	—	2	2	no	—
326	C₂×C₄×C₅₉	—	4	2	no	—
327	C₂×C₄×C₅₉	—	4	2	no	—
328	C₂×C₄×C₅₉	—	4	2	no	—
329	C₂×C₄×C₅₉	—	4	8	no	—
330	C₂×C₄×C₅₉	—	4	4	no	—
331	C₂×C₄×C₅₉	—	8	4	no	—
332	C₂×C₄×C₅₉	—	8	4	no	—
333	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
334	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
339	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₅₉	C₂⁵	1	1	yes	characteristic
341	C₈×C₅₉	—	2	1	no	—
342	C₈×C₅₉	—	2	2	no	—
343	C₈×C₅₉	—	2	2	no	—
344	C₈×C₅₉	—	2	1	no	—
345	C₈×C₅₉	—	2	1	no	—
346	C₈×C₅₉	H(5,𝔽₂)	1	2	yes	—
347	#62252	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
348	C₂²×C₅₉	—	2	1	no	—
349	C₂²×C₅₉	—	2	2	no	—
350	C₂²×C₅₉	—	2	1	no	—
351	C₂²×C₅₉	—	2	2	no	—
352	C₂²×C₅₉	—	2	2	no	—
353	C₂²×C₅₉	—	2	2	no	—
354	C₂²×C₅₉	—	2	2	no	—
355	C₂²×C₅₉	—	4	8	no	—
356	C₂²×C₅₉	—	4	2	no	—
357	C₂²×C₅₉	—	4	2	no	—
358	C₂²×C₅₉	—	4	2	no	—
359	C₂²×C₅₉	C₂×#135	1	4	yes	—
360	C₂²×C₅₉	#578	1	2	yes	—
361	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
362	C₄×C₅₉	—	2	1	no	—
363	C₄×C₅₉	—	2	2	no	—
364	C₄×C₅₉	—	2	2	no	—
365	C₄×C₅₉	—	2	1	no	—
366	C₄×C₅₉	—	2	1	no	—
367	C₄×C₅₉	—	2	1	no	—
368	C₄×C₅₉	—	4	4	no	—
369	C₄×C₅₉	—	4	2	no	—
370	C₄×C₅₉	—	4	2	no	—
371	C₄×C₅₉	—	4	4	no	—
372	C₄×C₅₉	—	4	2	no	—
373	C₄×C₅₉	C₂×#135	1	2	yes	—
374	C₄×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
375	C₄×C₅₉	#585	1	1	yes	characteristic
376	#3520	C₂×C₅₉	1	2	yes	complemented
377	#3342	C₂×C₅₉	1	1	yes	characteristic, complemented
378	#3336	C₂×C₅₉	1	2	yes	complemented
379	#3334	C₂×C₅₉	1	1	yes	characteristic, complemented
380	#3302	C₂×C₅₉	1	2	yes	complemented
381	#3300	C₂×C₅₉	1	4	yes	complemented
382	#3298	C₂×C₅₉	1	2	yes	complemented
383	D₄×Q₁₆	C₂×C₅₉	1	1	yes	characteristic, complemented
384	#3285	C₂×C₅₉	1	2	yes	complemented
385	#3283	C₂×C₅₉	1	1	yes	characteristic, complemented
386	#3248	C₂×C₅₉	1	2	yes	complemented
387	#3190	C₂×C₅₉	1	4	yes	complemented
388	#3170	C₂×C₅₉	1	1	yes	characteristic, complemented
389	#3168	C₂×C₅₉	1	1	yes	characteristic, complemented
390	#3050	C₂×C₅₉	1	2	yes	complemented
391	C₂×#467	C₂×C₅₉	1	2	yes	complemented
392	C₂×C₈×D₄	C₂×C₅₉	1	1	yes	characteristic, complemented
393	C₂×C₅₉	—	2	2	no	—
394	C₂×C₅₉	—	2	4	no	—
395	C₂×C₅₉	—	4	2	no	—
396	C₂×C₅₉	—	8	2	no	—
397	C₂×C₅₉	#3496	1	1	yes	characteristic
398	C₂×C₅₉	C₂²×#135	1	1	yes	characteristic
399	C₂×C₅₉	C₂×#578	1	1	yes	characteristic
400	C₂×#135	C₂²×C₅₉	1	2	yes	complemented
401	C₂²×Q₁₆	C₂²×C₅₉	1	2	yes	complemented
402	C₂³×C₈	C₂²×C₅₉	1	2	yes	—
403	#556	C₂²×C₅₉	1	2	yes	—
404	#554	—	2	2	no	—
405	#552	C₂²×C₅₉	1	4	yes	—
406	#551	—	2	4	no	—
407	D₄×Q₈	C₂²×C₅₉	1	2	yes	—
408	#548	C₂²×C₅₉	1	4	yes	—
409	#547	C₂²×C₅₉	1	2	yes	—
410	#547	C₂²×C₅₉	1	2	yes	—
411	#546	—	2	2	no	—
412	#542	—	2	2	no	—
413	#539	—	2	4	no	—
414	#533	C₂²×C₅₉	1	2	yes	—
415	#529	C₂²×C₅₉	1	2	yes	—
416	#525	C₂²×C₅₉	1	4	yes	—
417	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	4	yes	—
418	#520	—	2	2	no	—
419	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
420	#500	C₂²×C₅₉	1	1	yes	characteristic, complemented
421	#499	C₂²×C₅₉	1	1	yes	characteristic, complemented
422	#495	C₂²×C₅₉	1	1	yes	characteristic, complemented
423	#494	C₂²×C₅₉	1	1	yes	characteristic, complemented
424	#488	C₂²×C₅₉	1	2	yes	complemented
425	#487	C₂²×C₅₉	1	2	yes	complemented
426	#485	C₂²×C₅₉	1	4	yes	complemented
427	#485	C₂²×C₅₉	1	4	yes	complemented
428	#483	C₂²×C₅₉	1	4	yes	complemented
429	#480	C₂²×C₅₉	1	4	yes	complemented
430	#479	C₂²×C₅₉	1	4	yes	complemented
431	#475	C₂²×C₅₉	1	2	yes	complemented
432	#474	C₂²×C₅₉	1	2	yes	complemented
433	#467	C₂²×C₅₉	1	1	yes	characteristic
434	#467	C₂²×C₅₉	1	2	yes	—
435	#467	C₂²×C₅₉	1	2	yes	—
436	#467	C₂²×C₅₉	1	4	yes	—
437	#467	C₂²×C₅₉	1	2	yes	complemented
438	#467	C₂²×C₅₉	1	2	yes	complemented
439	#467	C₂²×C₅₉	1	2	yes	complemented
440	#467	C₂²×C₅₉	1	4	yes	complemented
441	#466	C₂²×C₅₉	1	1	yes	characteristic
442	#466	C₂²×C₅₉	1	2	yes	complemented
443	#465	C₂²×C₅₉	1	2	yes	—
444	#465	C₂²×C₅₉	1	4	yes	—
445	#465	C₂²×C₅₉	1	4	yes	complemented
446	#464	C₂²×C₅₉	1	4	yes	complemented
447	#462	C₂²×C₅₉	1	2	yes	complemented
448	#461	C₂²×C₅₉	1	2	yes	complemented
449	#452	C₂²×C₅₉	1	4	yes	complemented
450	#452	C₂²×C₅₉	1	4	yes	complemented
451	#451	C₂²×C₅₉	1	4	yes	complemented
452	#448	C₂²×C₅₉	1	4	yes	complemented
453	C₄×Q₁₆	C₂²×C₅₉	1	2	yes	complemented
454	C₄×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic, complemented
455	C₄×Q₁₆	C₂²×C₅₉	1	2	yes	complemented
456	C₄×SD₁₆	C₂²×C₅₉	1	2	yes	complemented
457	C₄×D₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
458	C₈×D₄	C₂²×C₅₉	1	1	yes	characteristic
459	C₈×D₄	C₂²×C₅₉	1	2	yes	—
460	C₈×D₄	C₂²×C₅₉	1	1	yes	characteristic
461	C₈×D₄	C₂²×C₅₉	1	1	yes	characteristic
462	C₈×D₄	C₂²×C₅₉	1	2	yes	—
463	C₈×D₄	C₂²×C₅₉	1	1	yes	characteristic
464	#427	C₂²×C₅₉	1	2	yes	complemented
465	C₂×#107	C₂²×C₅₉	1	2	yes	complemented
466	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
467	#416	C₂²×C₅₉	1	4	yes	complemented
468	C₂×#103	C₂²×C₅₉	1	4	yes	complemented
469	C₂×C₂²⋊C₈	C₂²×C₅₉	1	2	yes	—
470	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
471	C₅₉	#62252	1	1	yes	characteristic, direct product factor, Sylow
472	C₂×#41	—	2	2	no	—
473	C₂×#41	C₂³×C₅₉	1	4	yes	—
474	C₂²×Q₈	C₂³×C₅₉	1	4	yes	—
475	C₂²×D₄	D₄×C₅₉	1	1	yes	characteristic
476	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
477	#135	—	4	4	no	—
478	C₂×Q₁₆	—	4	4	no	—
479	C₂×Q₁₆	C₂³×C₅₉	1	1	yes	characteristic
480	C₂×Q₁₆	C₂³×C₅₉	1	2	yes	—
481	C₂×Q₁₆	C₂³×C₅₉	1	4	yes	—
482	C₂×Q₁₆	C₂³×C₅₉	1	2	yes	—
483	C₂×SD₁₆	C₂³×C₅₉	1	4	yes	—
484	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
485	C₂×D₈	C₂³×C₅₉	1	1	yes	characteristic
486	C₂²×C₈	—	4	4	no	—
487	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
488	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
489	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
490	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
491	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
492	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
493	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
494	C₄⋊Q₈	—	2	2	no	—
495	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
496	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
497	#126	—	2	4	no	—
498	#126	—	2	4	no	—
499	#126	—	2	2	no	—
500	#125	—	2	4	no	—
501	#125	—	2	2	no	—
502	#125	C₂³×C₅₉	1	2	yes	—
503	#124	—	2	2	no	—
504	#124	—	2	4	no	—
505	#124	C₂³×C₅₉	1	2	yes	—
506	#123	—	2	4	no	—
507	#123	—	2	4	no	—
508	#123	—	2	2	no	—
509	#123	—	2	4	no	—
510	#123	—	2	4	no	—
511	C₂²⋊Q₈	—	2	4	no	—
512	C₂²⋊Q₈	—	2	4	no	—
513	C₂²⋊Q₈	—	2	2	no	—
514	C₂²⋊Q₈	—	2	4	no	—
515	C₂²⋊Q₈	—	2	2	no	—
516	C₂²⋊Q₈	—	2	4	no	—
517	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
518	C₂²⋊Q₈	C₂³×C₅₉	1	4	yes	—
519	C₂²⋊Q₈	C₂³×C₅₉	1	4	yes	—
520	C₂²⋊Q₈	C₂³×C₅₉	1	4	yes	—
521	C₂²⋊Q₈	C₂³×C₅₉	1	4	yes	—
522	#121	—	2	4	no	—
523	#121	—	2	2	no	—
524	#121	C₂³×C₅₉	1	2	yes	—
525	#121	C₂³×C₅₉	1	4	yes	—
526	#120	—	2	4	no	—
527	C₄×Q₈	—	2	2	no	—
528	C₄×Q₈	—	2	2	no	—
529	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
530	C₄×Q₈	C₂³×C₅₉	1	4	yes	—
531	C₄×D₄	—	2	2	no	—
532	C₄×D₄	—	2	4	no	—
533	C₄×D₄	—	2	4	no	—
534	C₄×D₄	—	2	2	no	—
535	C₄×D₄	—	2	4	no	—
536	C₄×D₄	D₄×C₅₉	1	1	yes	characteristic
537	C₄×D₄	D₄×C₅₉	1	2	yes	—
538	C₄×D₄	D₄×C₅₉	1	1	yes	characteristic
539	C₄×D₄	C₂³×C₅₉	1	2	yes	—
540	C₄×D₄	C₂³×C₅₉	1	1	yes	characteristic
541	C₄×D₄	C₂³×C₅₉	1	1	yes	characteristic
542	C₄×D₄	C₂³×C₅₉	1	2	yes	—
543	#117	—	2	2	no	—
544	#117	—	2	4	no	—
545	#117	—	2	2	no	—
546	#117	C₂³×C₅₉	1	4	yes	—
547	C₂×C₄⋊C₄	—	2	4	no	—
548	C₂×C₄⋊C₄	—	2	2	no	—
549	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
550	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
551	C₂×C₂²⋊C₄	—	2	4	no	—
552	C₂×C₂²⋊C₄	D₄×C₅₉	1	2	yes	—
553	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
554	#107	C₂³×C₅₉	1	1	yes	characteristic
555	#107	C₂³×C₅₉	1	2	yes	—
556	#107	C₂³×C₅₉	1	4	yes	—
557	#107	C₂³×C₅₉	1	1	yes	characteristic
558	#107	C₂³×C₅₉	1	2	yes	—
559	#106	C₂³×C₅₉	1	4	yes	—
560	#106	C₂³×C₅₉	1	2	yes	—
561	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
562	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
563	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
564	#103	C₂³×C₅₉	1	2	yes	—
565	#103	C₂³×C₅₉	1	4	yes	—
566	#103	C₂³×C₅₉	1	4	yes	—
567	#103	C₂³×C₅₉	1	4	yes	—
568	#103	C₂³×C₅₉	1	4	yes	—
569	#103	C₂³×C₅₉	1	4	yes	—
570	#103	C₂³×C₅₉	1	2	yes	—
571	#102	C₂³×C₅₉	1	2	yes	—
572	#102	C₂³×C₅₉	1	4	yes	—
573	#102	C₂³×C₅₉	1	2	yes	—
574	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
575	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
576	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
577	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
578	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
579	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
580	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
581	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
582	C₂⁴	C₂×D₄×C₅₉	1	2	yes	—
583	#41	—	4	4	no	—
584	#41	—	4	4	no	—
585	#41	—	4	8	no	—
586	C₂×Q₈	—	2	2	no	—
587	C₂×Q₈	—	2	4	no	—
588	C₂×Q₈	—	4	4	no	—
589	C₂×Q₈	—	4	4	no	—
590	C₂×Q₈	C₂⁴×C₅₉	1	2	yes	—
591	C₂×Q₈	C₂⁴×C₅₉	1	4	yes	—
592	C₂×D₄	—	2	4	no	—
593	C₂×D₄	—	2	2	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
597	C₂×D₄	C₂×D₄×C₅₉	1	1	yes	characteristic
598	C₂×D₄	C₂×D₄×C₅₉	1	1	yes	characteristic
599	C₂×D₄	C₂⁴×C₅₉	1	2	yes	—
600	C₂²×C₄	—	2	4	no	—
601	C₂²×C₄	—	2	4	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	4	no	—
604	C₂²×C₄	—	4	2	no	—
605	C₂²×C₄	—	4	2	no	—
606	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
607	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
608	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
609	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
610	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
613	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
614	Q₁₆	—	2	2	no	—
615	Q₁₆	—	2	4	no	—
616	Q₁₆	—	4	4	no	—
617	Q₁₆	—	4	2	no	—
618	SD₁₆	—	4	4	no	—
619	SD₁₆	—	4	2	no	—
620	D₈	—	2	2	no	—
621	C₂×C₈	—	2	2	no	—
622	C₂×C₈	—	2	4	no	—
623	C₂×C₈	—	2	4	no	—
624	C₂×C₈	—	4	2	no	—
625	C₂×C₈	—	4	2	no	—
626	C₂×C₈	—	4	2	no	—
627	C₂×C₈	—	4	1	no	—
628	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
629	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
630	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
631	C₂×C₈	C₂⁴×C₅₉	1	2	yes	—
632	C₂×C₈	C₂⁴×C₅₉	1	2	yes	—
633	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	2	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	2	no	—
641	C₄⋊C₄	—	2	2	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	2	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	2	no	—
647	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
648	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
649	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
650	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
651	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
652	C₄⋊C₄	C₂⁴×C₅₉	1	4	yes	—
653	C₂²⋊C₄	—	2	2	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	2	2	no	—
661	C₂²⋊C₄	—	2	2	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	2	no	—
664	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
665	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
666	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
667	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
668	C₄²	—	2	4	no	—
669	C₄²	—	2	4	no	—
670	C₄²	—	2	2	no	—
671	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
672	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
673	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
674	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
675	C₂³	—	2	4	no	—
676	C₂³	—	2	4	no	—
677	C₂³	—	2	2	no	—
678	C₂³	—	4	2	no	—
679	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
680	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
681	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
682	Q₈	—	2	4	no	—
683	Q₈	—	2	2	no	—
684	Q₈	—	2	2	no	—
685	Q₈	—	2	4	no	—
686	Q₈	—	4	4	no	—
687	Q₈	—	8	4	no	—
688	D₄	—	2	4	no	—
689	D₄	—	2	2	no	—
690	D₄	—	2	2	no	—
691	D₄	—	2	2	no	—
692	D₄	—	4	8	no	—
693	D₄	—	4	4	no	—
694	D₄	—	8	4	no	—
695	D₄	#135×C₅₉	1	4	yes	complemented
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	4	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	4	2	no	—
710	C₂×C₄	—	4	2	no	—
711	C₂×C₄	—	4	2	no	—
712	C₂×C₄	—	4	8	no	—
713	C₂×C₄	—	4	4	no	—
714	C₂×C₄	—	8	4	no	—
715	C₂×C₄	—	8	4	no	—
716	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
717	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
718	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
719	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
720	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
721	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
722	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
723	C₂×C₄	C₂⁵×C₅₉	1	1	yes	characteristic
724	C₈	—	2	1	no	—
725	C₈	—	2	2	no	—
726	C₈	—	2	2	no	—
727	C₈	—	2	1	no	—
728	C₈	—	2	1	no	—
729	C₈	H(5,𝔽₂)×C₅₉	1	2	yes	—
730	C₂²	—	2	1	no	—
731	C₂²	—	2	2	no	—
732	C₂²	—	2	1	no	—
733	C₂²	—	2	2	no	—
734	C₂²	—	2	2	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	2	2	no	—
737	C₂²	—	4	8	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	C₂×#135×C₅₉	1	4	yes	—
742	C₂²	C₅₉×#578	1	2	yes	—
743	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
744	C₄	—	2	1	no	—
745	C₄	—	2	1	no	—
746	C₄	—	2	1	no	—
747	C₄	—	2	1	no	—
748	C₄	—	2	2	no	—
749	C₄	—	2	2	no	—
750	C₄	—	4	2	no	—
751	C₄	—	4	4	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	4	no	—
754	C₄	—	4	2	no	—
755	C₄	C₂×#135×C₅₉	1	2	yes	—
756	C₄	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
757	C₄	C₅₉×#585	1	1	yes	characteristic
758	C₂	—	2	2	no	—
759	C₂	—	2	4	no	—
760	C₂	—	4	2	no	—
761	C₂	—	8	2	no	—
762	C₂	C₅₉×#3496	1	1	yes	characteristic
763	C₂	C₂²×#135×C₅₉	1	1	yes	characteristic
764	C₂	C₂×C₅₉×#578	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×#3342	C₂	semidirect
3. C₅₉×#3336	C₂	semidirect
4. C₅₉×#3334	C₂	semidirect
5. C₅₉×#3302	C₂	semidirect
6. C₅₉×#3300	C₂	semidirect
7. C₅₉×#3298	C₂	semidirect
8. D₄×Q₁₆×C₅₉	C₂	semidirect
9. C₅₉×#3285	C₂	semidirect
10. C₅₉×#3283	C₂	semidirect
11. C₅₉×#3248	C₂	semidirect
12. C₅₉×#3190	C₂	semidirect
13. C₅₉×#3170	C₂	semidirect
14. C₅₉×#3168	C₂	semidirect
15. C₅₉×#3050	C₂	semidirect
16. C₂×C₅₉×#467	C₂	semidirect
17. C₂×C₈×D₄×C₅₉	C₂	semidirect
18. C₂×#135×C₅₉	C₂²	semidirect
19. C₂²×Q₁₆×C₅₉	C₂²	semidirect
38. C₅₉×#500	C₂²	semidirect
39. C₅₉×#499	C₂²	semidirect
40. C₅₉×#495	C₂²	semidirect
41. C₅₉×#494	C₂²	semidirect
42. C₅₉×#488	C₂²	semidirect
43. C₅₉×#487	C₂²	semidirect
44. C₅₉×#485	C₂²	semidirect
45. C₅₉×#485	C₂²	semidirect
46. C₅₉×#483	C₂²	semidirect
47. C₅₉×#480	C₂²	semidirect
48. C₅₉×#479	C₂²	semidirect
49. C₅₉×#475	C₂²	semidirect
50. C₅₉×#474	C₂²	semidirect
55. C₅₉×#467	C₂²	semidirect
56. C₅₉×#467	C₂²	semidirect
57. C₅₉×#467	C₂²	semidirect
58. C₅₉×#467	C₂²	semidirect
60. C₅₉×#466	C₂²	semidirect
63. C₅₉×#465	C₂²	semidirect
64. C₅₉×#464	C₂²	semidirect
65. C₅₉×#462	C₂²	semidirect
66. C₅₉×#461	C₂²	semidirect
67. C₅₉×#452	C₂²	semidirect
68. C₅₉×#452	C₂²	semidirect
69. C₅₉×#451	C₂²	semidirect
70. C₅₉×#448	C₂²	semidirect
71. C₄×Q₁₆×C₅₉	C₂²	semidirect
72. C₄×Q₁₆×C₅₉	C₂²	semidirect
73. C₄×Q₁₆×C₅₉	C₂²	semidirect
74. C₄×SD₁₆×C₅₉	C₂²	semidirect
75. C₄×D₈×C₅₉	C₂²	semidirect
82. C₅₉×#427	C₂²	semidirect
83. C₂×#107×C₅₉	C₂²	semidirect
85. C₅₉×#416	C₂²	semidirect
86. C₂×#103×C₅₉	C₂²	semidirect
312. D₄×C₅₉	#135	semidirect
347. #62252	C₅₉	direct (N × H)
376. #3520	C₂×C₅₉	semidirect
377. #3342	C₂×C₅₉	semidirect
378. #3336	C₂×C₅₉	semidirect
379. #3334	C₂×C₅₉	semidirect
380. #3302	C₂×C₅₉	semidirect
381. #3300	C₂×C₅₉	semidirect
382. #3298	C₂×C₅₉	semidirect
383. D₄×Q₁₆	C₂×C₅₉	semidirect
384. #3285	C₂×C₅₉	semidirect
385. #3283	C₂×C₅₉	semidirect
386. #3248	C₂×C₅₉	semidirect
387. #3190	C₂×C₅₉	semidirect
388. #3170	C₂×C₅₉	semidirect
389. #3168	C₂×C₅₉	semidirect
390. #3050	C₂×C₅₉	semidirect
391. C₂×#467	C₂×C₅₉	semidirect
392. C₂×C₈×D₄	C₂×C₅₉	semidirect
400. C₂×#135	C₂²×C₅₉	semidirect
401. C₂²×Q₁₆	C₂²×C₅₉	semidirect
420. #500	C₂²×C₅₉	semidirect
421. #499	C₂²×C₅₉	semidirect
422. #495	C₂²×C₅₉	semidirect
423. #494	C₂²×C₅₉	semidirect
424. #488	C₂²×C₅₉	semidirect
425. #487	C₂²×C₅₉	semidirect
426. #485	C₂²×C₅₉	semidirect
427. #485	C₂²×C₅₉	semidirect
428. #483	C₂²×C₅₉	semidirect
429. #480	C₂²×C₅₉	semidirect
430. #479	C₂²×C₅₉	semidirect
431. #475	C₂²×C₅₉	semidirect
432. #474	C₂²×C₅₉	semidirect
437. #467	C₂²×C₅₉	semidirect
438. #467	C₂²×C₅₉	semidirect
439. #467	C₂²×C₅₉	semidirect
440. #467	C₂²×C₅₉	semidirect
442. #466	C₂²×C₅₉	semidirect
445. #465	C₂²×C₅₉	semidirect
446. #464	C₂²×C₅₉	semidirect
447. #462	C₂²×C₅₉	semidirect
448. #461	C₂²×C₅₉	semidirect
449. #452	C₂²×C₅₉	semidirect
450. #452	C₂²×C₅₉	semidirect
451. #451	C₂²×C₅₉	semidirect
452. #448	C₂²×C₅₉	semidirect
453. C₄×Q₁₆	C₂²×C₅₉	semidirect
454. C₄×Q₁₆	C₂²×C₅₉	semidirect
455. C₄×Q₁₆	C₂²×C₅₉	semidirect
456. C₄×SD₁₆	C₂²×C₅₉	semidirect
457. C₄×D₈	C₂²×C₅₉	semidirect
464. #427	C₂²×C₅₉	semidirect
465. C₂×#107	C₂²×C₅₉	semidirect
467. #416	C₂²×C₅₉	semidirect
468. C₂×#103	C₂²×C₅₉	semidirect
471. C₅₉	#62252	direct (N × H)
695. 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×#3342	2
C₅₉×#3336	2
C₅₉×#3334	2
C₅₉×#3302	2
C₅₉×#3300	2
C₅₉×#3298	2
D₄×Q₁₆×C₅₉	2
C₅₉×#3285	2
C₅₉×#3283	2
C₅₉×#3248	2
C₅₉×#3190	2
C₅₉×#3170	2
C₅₉×#3168	2
C₅₉×#3050	2
C₂×C₅₉×#467	2
C₂×C₈×D₄×C₅₉	2
#62252	59

Subgroups — C59×#62252 #28474361

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#62252 #28474361