Subgroups — C₅₉×#62260 #28474369

Order 15104.

1850 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3506	C₂	1	1	yes	maximal, characteristic
2	C₅₉×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#3357	C₂	1	2	yes	maximal, complemented
4	C₅₉×#3356	C₂	1	2	yes	maximal, complemented
5	C₅₉×#3333	C₂	1	2	yes	maximal, complemented
6	C₅₉×#3331	C₂	1	2	yes	maximal, complemented
7	C₅₉×#3329	C₂	1	2	yes	maximal, complemented
8	C₅₉×#3328	C₂	1	2	yes	maximal, complemented
9	C₅₉×#3278	C₂	1	2	yes	maximal, complemented
10	C₅₉×#3276	C₂	1	2	yes	maximal, complemented
11	C₅₉×#3249	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#3246	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₉×#3190	C₂	1	4	yes	maximal, complemented
14	C₅₉×#3170	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#3167	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₉×#3056	C₂	1	4	yes	maximal, complemented
17	C₂×C₅₉×#436	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#137×C₅₉	C₂²	1	4	yes	complemented
19	C₂²×M₁₆×C₅₉	C₂²	1	2	yes	—
20	C₅₉×#559	—	2	2	no	—
21	C₅₉×#556	C₂²	1	2	yes	—
22	C₅₉×#555	C₂²	1	2	yes	—
23	C₅₉×#554	—	2	2	no	—
24	C₅₉×#554	—	2	2	no	—
25	C₅₉×#554	C₂²	1	2	yes	—
26	C₅₉×#554	C₂²	1	2	yes	—
27	C₅₉×#553	—	2	2	no	—
28	C₅₉×#550	C₂²	1	2	yes	—
29	D₄×Q₈×C₅₉	C₂²	1	2	yes	—
30	D₄×Q₈×C₅₉	C₂²	1	2	yes	—
31	C₅₉×#547	C₂²	1	2	yes	—
32	C₅₉×#544	—	2	1	no	—
33	C₅₉×#543	—	2	2	no	—
34	C₅₉×#538	—	2	2	no	—
35	C₅₉×#535	—	2	1	no	—
36	C₅₉×#533	C₂²	1	1	yes	characteristic
37	C₅₉×#533	C₂²	1	1	yes	characteristic
38	C₅₉×#533	C₂²	1	1	yes	characteristic
39	C₅₉×#532	C₂²	1	1	yes	characteristic
40	C₅₉×#525	C₂²	1	4	yes	—
41	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	4	yes	—
42	C₅₉×#520	—	2	1	no	—
43	C₅₉×#518	—	2	1	no	—
44	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
45	C₅₉×#500	C₂²	1	1	yes	characteristic, complemented
46	C₅₉×#498	C₂²	1	1	yes	characteristic, complemented
47	C₅₉×#494	C₂²	1	1	yes	characteristic, complemented
48	C₅₉×#492	C₂²	1	1	yes	characteristic, complemented
49	C₅₉×#487	C₂²	1	1	yes	characteristic, complemented
50	C₅₉×#487	C₂²	1	1	yes	characteristic, complemented
51	C₅₉×#487	C₂²	1	1	yes	characteristic, complemented
52	C₅₉×#486	C₂²	1	1	yes	characteristic, complemented
53	C₅₉×#485	C₂²	1	4	yes	complemented
54	C₅₉×#485	C₂²	1	4	yes	complemented
55	C₅₉×#483	C₂²	1	4	yes	complemented
56	C₅₉×#480	C₂²	1	4	yes	complemented
57	C₅₉×#477	C₂²	1	2	yes	complemented
58	C₅₉×#477	C₂²	1	2	yes	complemented
59	C₅₉×#476	C₂²	1	2	yes	complemented
60	C₅₉×#475	C₂²	1	2	yes	complemented
61	C₅₉×#470	C₂²	1	4	yes	complemented
62	C₅₉×#470	C₂²	1	4	yes	complemented
63	C₅₉×#468	C₂²	1	4	yes	complemented
64	C₅₉×#468	C₂²	1	4	yes	complemented
65	C₅₉×#467	C₂²	1	2	yes	—
66	C₅₉×#467	C₂²	1	4	yes	—
67	C₅₉×#467	C₂²	1	2	yes	—
68	C₅₉×#465	C₂²	1	2	yes	—
69	C₅₉×#465	C₂²	1	4	yes	—
70	C₅₉×#465	C₂²	1	2	yes	—
71	C₅₉×#462	C₂²	1	2	yes	complemented
72	C₅₉×#462	C₂²	1	2	yes	complemented
73	C₅₉×#461	C₂²	1	2	yes	complemented
74	C₅₉×#460	C₂²	1	2	yes	complemented
75	C₅₉×#452	C₂²	1	4	yes	complemented
76	C₅₉×#452	C₂²	1	4	yes	complemented
77	C₅₉×#451	C₂²	1	4	yes	complemented
78	C₅₉×#448	C₂²	1	4	yes	complemented
79	C₄×Q₁₆×C₅₉	C₂²	1	2	yes	complemented
80	C₄×Q₁₆×C₅₉	C₂²	1	2	yes	complemented
81	C₄×SD₁₆×C₅₉	C₂²	1	2	yes	complemented
82	C₄×SD₁₆×C₅₉	C₂²	1	2	yes	complemented
83	C₅₉×#436	C₂²	1	2	yes	—
84	C₅₉×#436	C₂²	1	2	yes	—
85	C₅₉×#436	C₂²	1	2	yes	—
86	C₅₉×#436	C₂²	1	2	yes	—
87	C₅₉×#428	C₂²	1	4	yes	complemented
88	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
89	C₅₉×#419	C₂²	1	4	yes	complemented
90	C₅₉×#417	C₂²	1	4	yes	complemented
91	C₂×C₂²⋊C₈×C₅₉	C₂²	1	2	yes	—
92	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
93	C₂×#41×C₅₉	—	2	1	no	—
94	C₂×#41×C₅₉	C₂³	1	4	yes	—
95	C₂²×Q₈×C₅₉	C₂³	1	4	yes	—
96	C₂²×D₄×C₅₉	D₄	1	1	yes	characteristic
97	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
98	#137×C₅₉	—	4	8	no	—
99	C₂×Q₁₆×C₅₉	C₂³	1	2	yes	—
100	C₂×Q₁₆×C₅₉	C₂³	1	2	yes	—
101	C₂×Q₁₆×C₅₉	C₂³	1	4	yes	—
102	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
103	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₅₉	C₂³	1	4	yes	—
105	C₂×M₁₆×C₅₉	—	4	4	no	—
106	C₂×M₁₆×C₅₉	C₂³	1	4	yes	—
107	C₂×M₁₆×C₅₉	C₂³	1	4	yes	—
108	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
111	C₄⋊Q₈×C₅₉	—	2	2	no	—
112	C₄⋊Q₈×C₅₉	—	2	2	no	—
113	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
114	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
115	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
116	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
117	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
118	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
119	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
120	#127×C₅₉	—	2	2	no	—
121	#127×C₅₉	C₂³	1	1	yes	characteristic
122	#126×C₅₉	—	2	4	no	—
123	#125×C₅₉	—	2	2	no	—
124	#125×C₅₉	—	2	2	no	—
125	#125×C₅₉	—	2	1	no	—
126	#125×C₅₉	—	2	1	no	—
127	#125×C₅₉	—	2	1	no	—
128	#124×C₅₉	—	2	2	no	—
129	#124×C₅₉	—	2	4	no	—
130	#124×C₅₉	—	2	1	no	—
131	#123×C₅₉	—	2	4	no	—
132	#123×C₅₉	—	2	4	no	—
133	C₂²⋊Q₈×C₅₉	—	2	4	no	—
134	C₂²⋊Q₈×C₅₉	—	2	4	no	—
135	C₂²⋊Q₈×C₅₉	—	2	1	no	—
136	C₂²⋊Q₈×C₅₉	—	2	1	no	—
137	C₂²⋊Q₈×C₅₉	—	2	1	no	—
138	C₂²⋊Q₈×C₅₉	—	2	4	no	—
139	C₂²⋊Q₈×C₅₉	—	2	4	no	—
140	C₂²⋊Q₈×C₅₉	—	2	4	no	—
141	C₂²⋊Q₈×C₅₉	—	2	4	no	—
142	C₂²⋊Q₈×C₅₉	C₂³	1	4	yes	—
143	C₂²⋊Q₈×C₅₉	C₂³	1	4	yes	—
144	C₂²⋊Q₈×C₅₉	C₂³	1	4	yes	—
145	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
146	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
147	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
148	#121×C₅₉	—	2	2	no	—
149	#121×C₅₉	—	2	2	no	—
150	#121×C₅₉	—	2	1	no	—
151	#121×C₅₉	—	2	4	no	—
152	#121×C₅₉	C₂³	1	4	yes	—
153	#121×C₅₉	C₂³	1	2	yes	—
154	#120×C₅₉	—	2	4	no	—
155	C₄×Q₈×C₅₉	—	2	2	no	—
156	C₄×Q₈×C₅₉	—	2	1	no	—
157	C₄×Q₈×C₅₉	—	2	1	no	—
158	C₄×Q₈×C₅₉	—	2	1	no	—
159	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
160	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
161	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
162	C₄×D₄×C₅₉	—	2	2	no	—
163	C₄×D₄×C₅₉	—	2	2	no	—
164	C₄×D₄×C₅₉	—	2	2	no	—
165	C₄×D₄×C₅₉	—	2	2	no	—
166	C₄×D₄×C₅₉	—	2	4	no	—
167	C₄×D₄×C₅₉	—	2	4	no	—
168	C₄×D₄×C₅₉	—	2	2	no	—
169	C₄×D₄×C₅₉	—	2	1	no	—
170	C₄×D₄×C₅₉	D₄	1	2	yes	—
171	C₄×D₄×C₅₉	D₄	1	2	yes	—
172	C₄×D₄×C₅₉	C₂³	1	2	yes	—
173	C₄×D₄×C₅₉	C₂³	1	2	yes	—
174	C₄×D₄×C₅₉	C₂³	1	2	yes	—
175	#117×C₅₉	—	2	1	no	—
176	#117×C₅₉	—	2	1	no	—
177	#117×C₅₉	—	2	1	no	—
178	#117×C₅₉	—	2	2	no	—
179	#117×C₅₉	C₂³	1	4	yes	—
180	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
181	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
182	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
184	C₂×C₂²⋊C₄×C₅₉	—	2	4	no	—
185	C₂×C₂²⋊C₄×C₅₉	D₄	1	2	yes	—
186	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
187	#107×C₅₉	C₂³	1	2	yes	—
188	#107×C₅₉	C₂³	1	4	yes	—
189	#107×C₅₉	C₂³	1	2	yes	—
190	#106×C₅₉	C₂³	1	2	yes	—
191	#106×C₅₉	C₂³	1	4	yes	—
192	#106×C₅₉	C₂³	1	2	yes	—
193	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
194	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
195	#103×C₅₉	C₂³	1	2	yes	—
196	#103×C₅₉	C₂³	1	4	yes	—
197	#103×C₅₉	C₂³	1	2	yes	—
198	#103×C₅₉	C₂³	1	2	yes	—
199	#103×C₅₉	C₂³	1	4	yes	—
200	#103×C₅₉	C₂³	1	4	yes	—
201	#103×C₅₉	C₂³	1	2	yes	—
202	#103×C₅₉	C₂³	1	2	yes	—
203	#103×C₅₉	C₂³	1	2	yes	—
204	#102×C₅₉	C₂³	1	2	yes	—
205	#102×C₅₉	C₂³	1	4	yes	—
206	#102×C₅₉	C₂³	1	2	yes	—
207	C₂²⋊C₈×C₅₉	C₂³	1	4	yes	—
208	C₂²⋊C₈×C₅₉	C₂³	1	4	yes	—
209	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
210	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
211	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
212	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
213	C₂⁴×C₅₉	C₂×D₄	1	2	yes	—
214	#41×C₅₉	—	4	4	no	—
215	#41×C₅₉	—	4	4	no	—
216	#41×C₅₉	—	4	4	no	—
217	C₂×Q₈×C₅₉	—	2	1	no	—
218	C₂×Q₈×C₅₉	—	2	1	no	—
219	C₂×Q₈×C₅₉	—	2	1	no	—
220	C₂×Q₈×C₅₉	—	2	1	no	—
221	C₂×Q₈×C₅₉	—	2	4	no	—
222	C₂×Q₈×C₅₉	—	4	4	no	—
223	C₂×Q₈×C₅₉	—	4	4	no	—
224	C₂×Q₈×C₅₉	C₂⁴	1	2	yes	—
225	C₂×Q₈×C₅₉	C₂⁴	1	2	yes	—
226	C₂×Q₈×C₅₉	C₂⁴	1	2	yes	—
227	C₂×D₄×C₅₉	—	2	2	no	—
228	C₂×D₄×C₅₉	—	2	4	no	—
229	C₂×D₄×C₅₉	—	2	4	no	—
230	C₂×D₄×C₅₉	—	2	4	no	—
231	C₂×D₄×C₅₉	—	2	1	no	—
232	C₂×D₄×C₅₉	—	2	1	no	—
233	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
234	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
235	C₂×D₄×C₅₉	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₅₉	—	2	4	no	—
237	C₂²×C₄×C₅₉	—	2	4	no	—
238	C₂²×C₄×C₅₉	—	2	2	no	—
239	C₂²×C₄×C₅₉	—	2	4	no	—
240	C₂²×C₄×C₅₉	—	4	2	no	—
241	C₂²×C₄×C₅₉	—	4	2	no	—
242	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
244	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
245	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
247	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
248	Q₁₆×C₅₉	—	2	4	no	—
249	Q₁₆×C₅₉	—	4	2	no	—
250	Q₁₆×C₅₉	—	4	4	no	—
251	SD₁₆×C₅₉	—	2	4	no	—
252	SD₁₆×C₅₉	—	4	2	no	—
253	SD₁₆×C₅₉	—	4	4	no	—
254	M₁₆×C₅₉	—	2	8	no	—
255	M₁₆×C₅₉	—	4	4	no	—
256	C₂×C₈×C₅₉	—	2	2	no	—
257	C₂×C₈×C₅₉	—	4	1	no	—
258	C₂×C₈×C₅₉	—	4	2	no	—
259	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
260	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
261	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
262	C₂×C₈×C₅₉	C₂⁴	1	4	yes	—
263	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
264	C₄⋊C₄×C₅₉	—	2	1	no	—
265	C₄⋊C₄×C₅₉	—	2	2	no	—
266	C₄⋊C₄×C₅₉	—	2	2	no	—
267	C₄⋊C₄×C₅₉	—	2	4	no	—
268	C₄⋊C₄×C₅₉	—	2	4	no	—
269	C₄⋊C₄×C₅₉	—	2	4	no	—
270	C₄⋊C₄×C₅₉	—	2	4	no	—
271	C₄⋊C₄×C₅₉	—	2	1	no	—
272	C₄⋊C₄×C₅₉	—	2	1	no	—
273	C₄⋊C₄×C₅₉	—	2	1	no	—
274	C₄⋊C₄×C₅₉	—	2	1	no	—
275	C₄⋊C₄×C₅₉	—	2	1	no	—
276	C₄⋊C₄×C₅₉	—	2	2	no	—
277	C₄⋊C₄×C₅₉	—	2	1	no	—
278	C₄⋊C₄×C₅₉	—	2	1	no	—
279	C₄⋊C₄×C₅₉	—	2	1	no	—
280	C₄⋊C₄×C₅₉	—	2	1	no	—
281	C₄⋊C₄×C₅₉	—	2	2	no	—
282	C₄⋊C₄×C₅₉	—	2	2	no	—
283	C₄⋊C₄×C₅₉	—	2	2	no	—
284	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
285	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
286	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
287	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
288	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
289	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
290	C₂²⋊C₄×C₅₉	—	2	2	no	—
291	C₂²⋊C₄×C₅₉	—	2	2	no	—
292	C₂²⋊C₄×C₅₉	—	2	4	no	—
293	C₂²⋊C₄×C₅₉	—	2	4	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	—	2	2	no	—
299	C₂²⋊C₄×C₅₉	—	2	2	no	—
300	C₂²⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
301	C₂²⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
302	C₄²×C₅₉	—	2	4	no	—
303	C₄²×C₅₉	—	2	2	no	—
304	C₄²×C₅₉	—	2	2	no	—
305	C₄²×C₅₉	—	2	2	no	—
306	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
307	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
309	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
310	C₂³×C₅₉	—	2	4	no	—
311	C₂³×C₅₉	—	2	2	no	—
312	C₂³×C₅₉	—	4	2	no	—
313	C₂³×C₅₉	—	4	2	no	—
314	C₂³×C₅₉	C₂²×D₄	1	4	yes	—
315	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
316	Q₈×C₅₉	—	2	2	no	—
317	Q₈×C₅₉	—	2	2	no	—
318	Q₈×C₅₉	—	2	2	no	—
319	Q₈×C₅₉	—	2	2	no	—
320	Q₈×C₅₉	—	2	2	no	—
321	Q₈×C₅₉	—	2	2	no	—
322	Q₈×C₅₉	—	4	2	no	—
323	Q₈×C₅₉	—	8	1	no	—
324	Q₈×C₅₉	—	8	1	no	—
325	Q₈×C₅₉	—	8	1	no	—
326	Q₈×C₅₉	—	8	4	no	—
327	D₄×C₅₉	—	2	4	no	—
328	D₄×C₅₉	—	2	4	no	—
329	D₄×C₅₉	—	2	2	no	—
330	D₄×C₅₉	—	2	2	no	—
331	D₄×C₅₉	—	4	4	no	—
332	D₄×C₅₉	—	4	2	no	—
333	D₄×C₅₉	—	8	1	no	—
334	D₄×C₅₉	—	8	4	no	—
335	D₄×C₅₉	—	8	4	no	—
336	C₂×C₄×C₅₉	—	2	1	no	—
337	C₂×C₄×C₅₉	—	2	4	no	—
338	C₂×C₄×C₅₉	—	2	1	no	—
339	C₂×C₄×C₅₉	—	2	4	no	—
340	C₂×C₄×C₅₉	—	2	2	no	—
341	C₂×C₄×C₅₉	—	2	2	no	—
342	C₂×C₄×C₅₉	—	2	2	no	—
343	C₂×C₄×C₅₉	—	2	2	no	—
344	C₂×C₄×C₅₉	—	2	2	no	—
345	C₂×C₄×C₅₉	—	2	2	no	—
346	C₂×C₄×C₅₉	—	2	2	no	—
347	C₂×C₄×C₅₉	—	4	4	no	—
348	C₂×C₄×C₅₉	—	4	2	no	—
349	C₂×C₄×C₅₉	—	4	1	no	—
350	C₂×C₄×C₅₉	—	4	4	no	—
351	C₂×C₄×C₅₉	—	8	4	no	—
352	C₂×C₄×C₅₉	—	8	4	no	—
353	C₂×C₄×C₅₉	—	8	4	no	—
354	C₂×C₄×C₅₉	#137	1	4	yes	complemented
355	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
356	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₅₉	C₂⁵	1	1	yes	characteristic
362	C₈×C₅₉	—	2	1	no	—
363	C₈×C₅₉	—	2	4	no	—
364	C₈×C₅₉	—	2	1	no	—
365	C₈×C₅₉	—	2	1	no	—
366	C₈×C₅₉	H(5,𝔽₂)	1	2	yes	—
367	#62260	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
368	C₂²×C₅₉	—	2	1	no	—
369	C₂²×C₅₉	—	2	1	no	—
370	C₂²×C₅₉	—	2	4	no	—
371	C₂²×C₅₉	—	2	4	no	—
372	C₂²×C₅₉	—	2	4	no	—
373	C₂²×C₅₉	—	4	2	no	—
374	C₂²×C₅₉	—	4	2	no	—
375	C₂²×C₅₉	—	4	2	no	—
376	C₂²×C₅₉	—	8	4	no	—
377	C₂²×C₅₉	C₂×#137	1	2	yes	—
378	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
379	C₄×C₅₉	—	2	1	no	—
380	C₄×C₅₉	—	2	1	no	—
381	C₄×C₅₉	—	2	1	no	—
382	C₄×C₅₉	—	2	4	no	—
383	C₄×C₅₉	—	4	2	no	—
384	C₄×C₅₉	—	4	2	no	—
385	C₄×C₅₉	—	4	2	no	—
386	C₄×C₅₉	—	4	2	no	—
387	C₄×C₅₉	—	4	2	no	—
388	C₄×C₅₉	—	4	2	no	—
389	C₄×C₅₉	—	4	2	no	—
390	C₄×C₅₉	C₂×#137	1	2	yes	—
391	C₄×C₅₉	C₂×#137	1	2	yes	—
392	C₄×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
393	C₄×C₅₉	#585	1	1	yes	characteristic
394	#3506	C₂×C₅₉	1	1	yes	characteristic
395	#3501	C₂×C₅₉	1	1	yes	characteristic, complemented
396	#3357	C₂×C₅₉	1	2	yes	complemented
397	#3356	C₂×C₅₉	1	2	yes	complemented
398	#3333	C₂×C₅₉	1	2	yes	complemented
399	#3331	C₂×C₅₉	1	2	yes	complemented
400	#3329	C₂×C₅₉	1	2	yes	complemented
401	#3328	C₂×C₅₉	1	2	yes	complemented
402	#3278	C₂×C₅₉	1	2	yes	complemented
403	#3276	C₂×C₅₉	1	2	yes	complemented
404	#3249	C₂×C₅₉	1	1	yes	characteristic, complemented
405	#3246	C₂×C₅₉	1	1	yes	characteristic, complemented
406	#3190	C₂×C₅₉	1	4	yes	complemented
407	#3170	C₂×C₅₉	1	1	yes	characteristic, complemented
408	#3167	C₂×C₅₉	1	1	yes	characteristic, complemented
409	#3056	C₂×C₅₉	1	4	yes	complemented
410	C₂×#436	C₂×C₅₉	1	1	yes	characteristic, complemented
411	C₂×C₅₉	—	2	2	no	—
412	C₂×C₅₉	—	4	4	no	—
413	C₂×C₅₉	—	8	2	no	—
414	C₂×C₅₉	#3496	1	1	yes	characteristic
415	C₂×C₅₉	C₂²×#137	1	1	yes	characteristic
416	C₂×C₅₉	#3584	1	1	yes	characteristic
417	C₂×#137	C₂²×C₅₉	1	4	yes	complemented
418	C₂²×M₁₆	C₂²×C₅₉	1	2	yes	—
419	#559	—	2	2	no	—
420	#556	C₂²×C₅₉	1	2	yes	—
421	#555	C₂²×C₅₉	1	2	yes	—
422	#554	—	2	2	no	—
423	#554	—	2	2	no	—
424	#554	C₂²×C₅₉	1	2	yes	—
425	#554	C₂²×C₅₉	1	2	yes	—
426	#553	—	2	2	no	—
427	#550	C₂²×C₅₉	1	2	yes	—
428	D₄×Q₈	C₂²×C₅₉	1	2	yes	—
429	D₄×Q₈	C₂²×C₅₉	1	2	yes	—
430	#547	C₂²×C₅₉	1	2	yes	—
431	#544	—	2	1	no	—
432	#543	—	2	2	no	—
433	#538	—	2	2	no	—
434	#535	—	2	1	no	—
435	#533	C₂²×C₅₉	1	1	yes	characteristic
436	#533	C₂²×C₅₉	1	1	yes	characteristic
437	#533	C₂²×C₅₉	1	1	yes	characteristic
438	#532	C₂²×C₅₉	1	1	yes	characteristic
439	#525	C₂²×C₅₉	1	4	yes	—
440	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	4	yes	—
441	#520	—	2	1	no	—
442	#518	—	2	1	no	—
443	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
444	#500	C₂²×C₅₉	1	1	yes	characteristic, complemented
445	#498	C₂²×C₅₉	1	1	yes	characteristic, complemented
446	#494	C₂²×C₅₉	1	1	yes	characteristic, complemented
447	#492	C₂²×C₅₉	1	1	yes	characteristic, complemented
448	#487	C₂²×C₅₉	1	1	yes	characteristic, complemented
449	#487	C₂²×C₅₉	1	1	yes	characteristic, complemented
450	#487	C₂²×C₅₉	1	1	yes	characteristic, complemented
451	#486	C₂²×C₅₉	1	1	yes	characteristic, complemented
452	#485	C₂²×C₅₉	1	4	yes	complemented
453	#485	C₂²×C₅₉	1	4	yes	complemented
454	#483	C₂²×C₅₉	1	4	yes	complemented
455	#480	C₂²×C₅₉	1	4	yes	complemented
456	#477	C₂²×C₅₉	1	2	yes	complemented
457	#477	C₂²×C₅₉	1	2	yes	complemented
458	#476	C₂²×C₅₉	1	2	yes	complemented
459	#475	C₂²×C₅₉	1	2	yes	complemented
460	#470	C₂²×C₅₉	1	4	yes	complemented
461	#470	C₂²×C₅₉	1	4	yes	complemented
462	#468	C₂²×C₅₉	1	4	yes	complemented
463	#468	C₂²×C₅₉	1	4	yes	complemented
464	#467	C₂²×C₅₉	1	2	yes	—
465	#467	C₂²×C₅₉	1	2	yes	—
466	#467	C₂²×C₅₉	1	4	yes	—
467	#465	C₂²×C₅₉	1	2	yes	—
468	#465	C₂²×C₅₉	1	2	yes	—
469	#465	C₂²×C₅₉	1	4	yes	—
470	#462	C₂²×C₅₉	1	2	yes	complemented
471	#462	C₂²×C₅₉	1	2	yes	complemented
472	#461	C₂²×C₅₉	1	2	yes	complemented
473	#460	C₂²×C₅₉	1	2	yes	complemented
474	#452	C₂²×C₅₉	1	4	yes	complemented
475	#452	C₂²×C₅₉	1	4	yes	complemented
476	#451	C₂²×C₅₉	1	4	yes	complemented
477	#448	C₂²×C₅₉	1	4	yes	complemented
478	C₄×Q₁₆	C₂²×C₅₉	1	2	yes	complemented
479	C₄×Q₁₆	C₂²×C₅₉	1	2	yes	complemented
480	C₄×SD₁₆	C₂²×C₅₉	1	2	yes	complemented
481	C₄×SD₁₆	C₂²×C₅₉	1	2	yes	complemented
482	#436	C₂²×C₅₉	1	2	yes	—
483	#436	C₂²×C₅₉	1	2	yes	—
484	#436	C₂²×C₅₉	1	2	yes	—
485	#436	C₂²×C₅₉	1	2	yes	—
486	#428	C₂²×C₅₉	1	4	yes	complemented
487	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
488	#419	C₂²×C₅₉	1	4	yes	complemented
489	#417	C₂²×C₅₉	1	4	yes	complemented
490	C₂×C₂²⋊C₈	C₂²×C₅₉	1	2	yes	—
491	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
492	C₅₉	#62260	1	1	yes	characteristic, direct product factor, Sylow
493	C₂×#41	—	2	1	no	—
494	C₂×#41	C₂³×C₅₉	1	4	yes	—
495	C₂²×Q₈	C₂³×C₅₉	1	4	yes	—
496	C₂²×D₄	D₄×C₅₉	1	1	yes	characteristic
497	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
498	#137	—	4	8	no	—
499	C₂×Q₁₆	C₂³×C₅₉	1	2	yes	—
500	C₂×Q₁₆	C₂³×C₅₉	1	4	yes	—
501	C₂×Q₁₆	C₂³×C₅₉	1	2	yes	—
502	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
503	C₂×SD₁₆	C₂³×C₅₉	1	4	yes	—
504	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
505	C₂×M₁₆	—	4	4	no	—
506	C₂×M₁₆	C₂³×C₅₉	1	4	yes	—
507	C₂×M₁₆	C₂³×C₅₉	1	4	yes	—
508	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
509	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
510	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
511	C₄⋊Q₈	—	2	2	no	—
512	C₄⋊Q₈	—	2	2	no	—
513	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
514	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
515	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
516	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
517	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
518	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
519	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
520	#127	—	2	2	no	—
521	#127	C₂³×C₅₉	1	1	yes	characteristic
522	#126	—	2	4	no	—
523	#125	—	2	2	no	—
524	#125	—	2	2	no	—
525	#125	—	2	1	no	—
526	#125	—	2	1	no	—
527	#125	—	2	1	no	—
528	#124	—	2	2	no	—
529	#124	—	2	4	no	—
530	#124	—	2	1	no	—
531	#123	—	2	4	no	—
532	#123	—	2	4	no	—
533	C₂²⋊Q₈	—	2	4	no	—
534	C₂²⋊Q₈	—	2	4	no	—
535	C₂²⋊Q₈	—	2	1	no	—
536	C₂²⋊Q₈	—	2	1	no	—
537	C₂²⋊Q₈	—	2	1	no	—
538	C₂²⋊Q₈	—	2	4	no	—
539	C₂²⋊Q₈	—	2	4	no	—
540	C₂²⋊Q₈	—	2	4	no	—
541	C₂²⋊Q₈	—	2	4	no	—
542	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
543	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
544	C₂²⋊Q₈	C₂³×C₅₉	1	4	yes	—
545	C₂²⋊Q₈	C₂³×C₅₉	1	4	yes	—
546	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
547	C₂²⋊Q₈	C₂³×C₅₉	1	4	yes	—
548	#121	—	2	2	no	—
549	#121	—	2	2	no	—
550	#121	—	2	1	no	—
551	#121	—	2	4	no	—
552	#121	C₂³×C₅₉	1	2	yes	—
553	#121	C₂³×C₅₉	1	4	yes	—
554	#120	—	2	4	no	—
555	C₄×Q₈	—	2	2	no	—
556	C₄×Q₈	—	2	1	no	—
557	C₄×Q₈	—	2	1	no	—
558	C₄×Q₈	—	2	1	no	—
559	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
560	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
561	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
562	C₄×D₄	—	2	2	no	—
563	C₄×D₄	—	2	2	no	—
564	C₄×D₄	—	2	2	no	—
565	C₄×D₄	—	2	2	no	—
566	C₄×D₄	—	2	4	no	—
567	C₄×D₄	—	2	4	no	—
568	C₄×D₄	—	2	2	no	—
569	C₄×D₄	—	2	1	no	—
570	C₄×D₄	D₄×C₅₉	1	2	yes	—
571	C₄×D₄	D₄×C₅₉	1	2	yes	—
572	C₄×D₄	C₂³×C₅₉	1	2	yes	—
573	C₄×D₄	C₂³×C₅₉	1	2	yes	—
574	C₄×D₄	C₂³×C₅₉	1	2	yes	—
575	#117	—	2	1	no	—
576	#117	—	2	1	no	—
577	#117	—	2	1	no	—
578	#117	—	2	2	no	—
579	#117	C₂³×C₅₉	1	4	yes	—
580	C₂×C₄⋊C₄	—	2	4	no	—
581	C₂×C₄⋊C₄	—	2	2	no	—
582	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
584	C₂×C₂²⋊C₄	—	2	4	no	—
585	C₂×C₂²⋊C₄	D₄×C₅₉	1	2	yes	—
586	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
587	#107	C₂³×C₅₉	1	2	yes	—
588	#107	C₂³×C₅₉	1	4	yes	—
589	#107	C₂³×C₅₉	1	2	yes	—
590	#106	C₂³×C₅₉	1	2	yes	—
591	#106	C₂³×C₅₉	1	4	yes	—
592	#106	C₂³×C₅₉	1	2	yes	—
593	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
594	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
595	#103	C₂³×C₅₉	1	2	yes	—
596	#103	C₂³×C₅₉	1	4	yes	—
597	#103	C₂³×C₅₉	1	2	yes	—
598	#103	C₂³×C₅₉	1	2	yes	—
599	#103	C₂³×C₅₉	1	4	yes	—
600	#103	C₂³×C₅₉	1	4	yes	—
601	#103	C₂³×C₅₉	1	2	yes	—
602	#103	C₂³×C₅₉	1	2	yes	—
603	#103	C₂³×C₅₉	1	2	yes	—
604	#102	C₂³×C₅₉	1	2	yes	—
605	#102	C₂³×C₅₉	1	4	yes	—
606	#102	C₂³×C₅₉	1	2	yes	—
607	C₂²⋊C₈	C₂³×C₅₉	1	4	yes	—
608	C₂²⋊C₈	C₂³×C₅₉	1	4	yes	—
609	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
610	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
611	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
612	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
613	C₂⁴	C₂×D₄×C₅₉	1	2	yes	—
614	#41	—	4	4	no	—
615	#41	—	4	4	no	—
616	#41	—	4	4	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	—	2	1	no	—
619	C₂×Q₈	—	2	1	no	—
620	C₂×Q₈	—	2	1	no	—
621	C₂×Q₈	—	2	4	no	—
622	C₂×Q₈	—	4	4	no	—
623	C₂×Q₈	—	4	4	no	—
624	C₂×Q₈	C₂⁴×C₅₉	1	2	yes	—
625	C₂×Q₈	C₂⁴×C₅₉	1	2	yes	—
626	C₂×Q₈	C₂⁴×C₅₉	1	2	yes	—
627	C₂×D₄	—	2	2	no	—
628	C₂×D₄	—	2	4	no	—
629	C₂×D₄	—	2	4	no	—
630	C₂×D₄	—	2	4	no	—
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	—	2	1	no	—
633	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
634	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
635	C₂×D₄	C₂⁴×C₅₉	1	2	yes	—
636	C₂²×C₄	—	2	4	no	—
637	C₂²×C₄	—	2	4	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	4	2	no	—
641	C₂²×C₄	—	4	2	no	—
642	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
643	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
644	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
645	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
646	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
647	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
648	Q₁₆	—	2	4	no	—
649	Q₁₆	—	4	4	no	—
650	Q₁₆	—	4	2	no	—
651	SD₁₆	—	2	4	no	—
652	SD₁₆	—	4	4	no	—
653	SD₁₆	—	4	2	no	—
654	M₁₆	—	2	8	no	—
655	M₁₆	—	4	4	no	—
656	C₂×C₈	—	2	2	no	—
657	C₂×C₈	—	4	2	no	—
658	C₂×C₈	—	4	1	no	—
659	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
660	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
661	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
662	C₂×C₈	C₂⁴×C₅₉	1	4	yes	—
663	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
664	C₄⋊C₄	—	2	1	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	2	2	no	—
667	C₄⋊C₄	—	2	4	no	—
668	C₄⋊C₄	—	2	4	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	4	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	1	no	—
674	C₄⋊C₄	—	2	1	no	—
675	C₄⋊C₄	—	2	1	no	—
676	C₄⋊C₄	—	2	2	no	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	1	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
685	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
686	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
687	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
688	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
689	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
690	C₂²⋊C₄	—	2	2	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	2	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	2	no	—
699	C₂²⋊C₄	—	2	2	no	—
700	C₂²⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
701	C₂²⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
702	C₄²	—	2	4	no	—
703	C₄²	—	2	2	no	—
704	C₄²	—	2	2	no	—
705	C₄²	—	2	2	no	—
706	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
707	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
708	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
709	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
710	C₂³	—	2	4	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	4	2	no	—
713	C₂³	—	4	2	no	—
714	C₂³	C₂²×D₄×C₅₉	1	4	yes	—
715	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
716	Q₈	—	2	2	no	—
717	Q₈	—	2	2	no	—
718	Q₈	—	2	2	no	—
719	Q₈	—	2	2	no	—
720	Q₈	—	2	2	no	—
721	Q₈	—	2	2	no	—
722	Q₈	—	4	2	no	—
723	Q₈	—	8	1	no	—
724	Q₈	—	8	1	no	—
725	Q₈	—	8	1	no	—
726	Q₈	—	8	4	no	—
727	D₄	—	2	4	no	—
728	D₄	—	2	4	no	—
729	D₄	—	2	2	no	—
730	D₄	—	2	2	no	—
731	D₄	—	4	4	no	—
732	D₄	—	4	2	no	—
733	D₄	—	8	1	no	—
734	D₄	—	8	4	no	—
735	D₄	—	8	4	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	4	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	4	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	4	4	no	—
748	C₂×C₄	—	4	2	no	—
749	C₂×C₄	—	4	1	no	—
750	C₂×C₄	—	4	4	no	—
751	C₂×C₄	—	8	4	no	—
752	C₂×C₄	—	8	4	no	—
753	C₂×C₄	—	8	4	no	—
754	C₂×C₄	#137×C₅₉	1	4	yes	complemented
755	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
756	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
757	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
758	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
759	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
760	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
761	C₂×C₄	C₂⁵×C₅₉	1	1	yes	characteristic
762	C₈	—	2	1	no	—
763	C₈	—	2	4	no	—
764	C₈	—	2	1	no	—
765	C₈	—	2	1	no	—
766	C₈	H(5,𝔽₂)×C₅₉	1	2	yes	—
767	C₂²	—	2	1	no	—
768	C₂²	—	2	1	no	—
769	C₂²	—	2	4	no	—
770	C₂²	—	2	4	no	—
771	C₂²	—	2	4	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	8	4	no	—
776	C₂²	C₂×#137×C₅₉	1	2	yes	—
777	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
778	C₄	—	2	1	no	—
779	C₄	—	2	1	no	—
780	C₄	—	2	1	no	—
781	C₄	—	2	4	no	—
782	C₄	—	4	2	no	—
783	C₄	—	4	2	no	—
784	C₄	—	4	2	no	—
785	C₄	—	4	2	no	—
786	C₄	—	4	2	no	—
787	C₄	—	4	2	no	—
788	C₄	—	4	2	no	—
789	C₄	C₂×#137×C₅₉	1	2	yes	—
790	C₄	C₂×#137×C₅₉	1	2	yes	—
791	C₄	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
792	C₄	C₅₉×#585	1	1	yes	characteristic
793	C₂	—	2	2	no	—
794	C₂	—	4	4	no	—
795	C₂	—	8	2	no	—
796	C₂	C₅₉×#3496	1	1	yes	characteristic
797	C₂	C₂²×#137×C₅₉	1	1	yes	characteristic
798	C₂	C₅₉×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₉
prime radical	C₅₉×#3506	C₂
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
2. C₅₉×#3501	C₂	semidirect
3. C₅₉×#3357	C₂	semidirect
4. C₅₉×#3356	C₂	semidirect
5. C₅₉×#3333	C₂	semidirect
6. C₅₉×#3331	C₂	semidirect
7. C₅₉×#3329	C₂	semidirect
8. C₅₉×#3328	C₂	semidirect
9. C₅₉×#3278	C₂	semidirect
10. C₅₉×#3276	C₂	semidirect
11. C₅₉×#3249	C₂	semidirect
12. C₅₉×#3246	C₂	semidirect
13. C₅₉×#3190	C₂	semidirect
14. C₅₉×#3170	C₂	semidirect
15. C₅₉×#3167	C₂	semidirect
16. C₅₉×#3056	C₂	semidirect
17. C₂×C₅₉×#436	C₂	semidirect
18. C₂×#137×C₅₉	C₂²	semidirect
45. C₅₉×#500	C₂²	semidirect
46. C₅₉×#498	C₂²	semidirect
47. C₅₉×#494	C₂²	semidirect
48. C₅₉×#492	C₂²	semidirect
49. C₅₉×#487	C₂²	semidirect
50. C₅₉×#487	C₂²	semidirect
51. C₅₉×#487	C₂²	semidirect
52. C₅₉×#486	C₂²	semidirect
53. C₅₉×#485	C₂²	semidirect
54. C₅₉×#485	C₂²	semidirect
55. C₅₉×#483	C₂²	semidirect
56. C₅₉×#480	C₂²	semidirect
57. C₅₉×#477	C₂²	semidirect
58. C₅₉×#477	C₂²	semidirect
59. C₅₉×#476	C₂²	semidirect
60. C₅₉×#475	C₂²	semidirect
61. C₅₉×#470	C₂²	semidirect
62. C₅₉×#470	C₂²	semidirect
63. C₅₉×#468	C₂²	semidirect
64. C₅₉×#468	C₂²	semidirect
71. C₅₉×#462	C₂²	semidirect
72. C₅₉×#462	C₂²	semidirect
73. C₅₉×#461	C₂²	semidirect
74. C₅₉×#460	C₂²	semidirect
75. C₅₉×#452	C₂²	semidirect
76. C₅₉×#452	C₂²	semidirect
77. C₅₉×#451	C₂²	semidirect
78. C₅₉×#448	C₂²	semidirect
79. C₄×Q₁₆×C₅₉	C₂²	semidirect
80. C₄×Q₁₆×C₅₉	C₂²	semidirect
81. C₄×SD₁₆×C₅₉	C₂²	semidirect
82. C₄×SD₁₆×C₅₉	C₂²	semidirect
87. C₅₉×#428	C₂²	semidirect
89. C₅₉×#419	C₂²	semidirect
90. C₅₉×#417	C₂²	semidirect
354. C₂×C₄×C₅₉	#137	semidirect
367. #62260	C₅₉	direct (N × H)
395. #3501	C₂×C₅₉	semidirect
396. #3357	C₂×C₅₉	semidirect
397. #3356	C₂×C₅₉	semidirect
398. #3333	C₂×C₅₉	semidirect
399. #3331	C₂×C₅₉	semidirect
400. #3329	C₂×C₅₉	semidirect
401. #3328	C₂×C₅₉	semidirect
402. #3278	C₂×C₅₉	semidirect
403. #3276	C₂×C₅₉	semidirect
404. #3249	C₂×C₅₉	semidirect
405. #3246	C₂×C₅₉	semidirect
406. #3190	C₂×C₅₉	semidirect
407. #3170	C₂×C₅₉	semidirect
408. #3167	C₂×C₅₉	semidirect
409. #3056	C₂×C₅₉	semidirect
410. C₂×#436	C₂×C₅₉	semidirect
417. C₂×#137	C₂²×C₅₉	semidirect
444. #500	C₂²×C₅₉	semidirect
445. #498	C₂²×C₅₉	semidirect
446. #494	C₂²×C₅₉	semidirect
447. #492	C₂²×C₅₉	semidirect
448. #487	C₂²×C₅₉	semidirect
449. #487	C₂²×C₅₉	semidirect
450. #487	C₂²×C₅₉	semidirect
451. #486	C₂²×C₅₉	semidirect
452. #485	C₂²×C₅₉	semidirect
453. #485	C₂²×C₅₉	semidirect
454. #483	C₂²×C₅₉	semidirect
455. #480	C₂²×C₅₉	semidirect
456. #477	C₂²×C₅₉	semidirect
457. #477	C₂²×C₅₉	semidirect
458. #476	C₂²×C₅₉	semidirect
459. #475	C₂²×C₅₉	semidirect
460. #470	C₂²×C₅₉	semidirect
461. #470	C₂²×C₅₉	semidirect
462. #468	C₂²×C₅₉	semidirect
463. #468	C₂²×C₅₉	semidirect
470. #462	C₂²×C₅₉	semidirect
471. #462	C₂²×C₅₉	semidirect
472. #461	C₂²×C₅₉	semidirect
473. #460	C₂²×C₅₉	semidirect
474. #452	C₂²×C₅₉	semidirect
475. #452	C₂²×C₅₉	semidirect
476. #451	C₂²×C₅₉	semidirect
477. #448	C₂²×C₅₉	semidirect
478. C₄×Q₁₆	C₂²×C₅₉	semidirect
479. C₄×Q₁₆	C₂²×C₅₉	semidirect
480. C₄×SD₁₆	C₂²×C₅₉	semidirect
481. C₄×SD₁₆	C₂²×C₅₉	semidirect
486. #428	C₂²×C₅₉	semidirect
488. #419	C₂²×C₅₉	semidirect
489. #417	C₂²×C₅₉	semidirect
492. C₅₉	#62260	direct (N × H)
754. C₂×C₄	#137×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₅₉×#3506	2
C₅₉×#3501	2
C₅₉×#3357	2
C₅₉×#3356	2
C₅₉×#3333	2
C₅₉×#3331	2
C₅₉×#3329	2
C₅₉×#3328	2
C₅₉×#3278	2
C₅₉×#3276	2
C₅₉×#3249	2
C₅₉×#3246	2
C₅₉×#3190	2
C₅₉×#3170	2
C₅₉×#3167	2
C₅₉×#3056	2
C₂×C₅₉×#436	2
#62260	59

Subgroups — C59×#62260 #28474369

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#62260 #28474369