Subgroups — C₅₉×#62046 #28474155

Order 15104.

1822 conjugacy classes of subgroups.

The subgroup lattice has 1150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₉×#3522	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#3396	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#3375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#3363	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#3333	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#3330	C₂	1	2	yes	maximal, complemented
9	C₅₉×#3308	C₂	1	2	yes	maximal, complemented
10	C₅₉×#3299	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#3287	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#3278	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₉×#3277	C₂	1	2	yes	maximal, complemented
14	C₅₉×#3269	C₂	1	2	yes	maximal, complemented
15	C₅₉×#3262	C₂	1	2	yes	maximal, complemented
16	C₅₉×#3254	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₉×#3225	C₂	1	2	yes	maximal, complemented
18	C₅₉×#3207	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₉×#3124	C₂	1	2	yes	maximal, complemented
20	C₅₉×#3104	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₉×#3046	C₂	1	2	yes	maximal, complemented
22	C₅₉×#3037	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₉×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₅₉	C₂²	1	2	yes	—
25	C₂×#137×C₅₉	C₂²	1	2	yes	—
26	C₂×#135×C₅₉	C₂²	1	2	yes	—
27	C₅₉×#562	—	2	2	no	—
28	C₅₉×#559	—	2	1	no	—
29	C₅₉×#559	—	2	1	no	—
30	C₅₉×#559	C₂²	1	1	yes	characteristic
31	C₅₉×#559	C₂²	1	1	yes	characteristic
32	Q₈²×C₅₉	C₂²	1	1	yes	characteristic
33	C₅₉×#557	C₂²	1	1	yes	characteristic
34	C₅₉×#554	—	2	1	no	—
35	C₅₉×#554	—	2	1	no	—
36	C₅₉×#554	C₂²	1	1	yes	characteristic
37	C₅₉×#550	C₂²	1	1	yes	characteristic
38	C₅₉×#550	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
40	C₅₉×#548	C₂²	1	2	yes	—
41	C₅₉×#548	C₂²	1	2	yes	—
42	C₅₉×#547	—	2	2	no	—
43	C₅₉×#547	C₂²	1	2	yes	—
44	C₅₉×#547	C₂²	1	2	yes	—
45	C₅₉×#542	—	2	2	no	—
46	C₅₉×#542	—	2	1	no	—
47	C₅₉×#542	C₂²	1	2	yes	—
48	C₅₉×#542	C₂²	1	2	yes	—
49	C₅₉×#540	—	2	1	no	—
50	C₅₉×#539	—	2	2	no	—
51	C₅₉×#536	C₂²	1	2	yes	—
52	C₅₉×#533	C₂²	1	1	yes	characteristic
53	C₅₉×#532	—	2	1	no	—
54	C₅₉×#532	C₂²	1	1	yes	characteristic
55	C₅₉×#532	C₂²	1	1	yes	characteristic
56	C₅₉×#529	—	2	1	no	—
57	C₅₉×#529	C₂²	1	1	yes	characteristic
58	C₅₉×#520	C₂²	1	2	yes	—
59	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
60	C₅₉×#497	C₂²	1	2	yes	—
61	C₅₉×#495	C₂²	1	2	yes	—
62	C₅₉×#493	C₂²	1	1	yes	characteristic
63	C₅₉×#492	C₂²	1	1	yes	characteristic
64	C₅₉×#489	C₂²	1	2	yes	—
65	C₅₉×#487	C₂²	1	1	yes	characteristic
66	C₅₉×#487	C₂²	1	2	yes	—
67	C₅₉×#486	C₂²	1	1	yes	characteristic
68	C₅₉×#484	C₂²	1	2	yes	—
69	C₅₉×#484	C₂²	1	1	yes	characteristic
70	C₅₉×#484	C₂²	1	1	yes	characteristic
71	C₅₉×#480	C₂²	1	2	yes	—
72	C₅₉×#477	C₂²	1	1	yes	characteristic
73	C₅₉×#477	C₂²	1	1	yes	characteristic
74	C₅₉×#477	C₂²	1	1	yes	characteristic
75	C₅₉×#477	C₂²	1	2	yes	—
76	C₅₉×#477	C₂²	1	1	yes	characteristic
77	C₅₉×#474	C₂²	1	2	yes	—
78	C₅₉×#474	C₂²	1	2	yes	—
79	C₅₉×#468	C₂²	1	2	yes	—
80	C₅₉×#468	C₂²	1	2	yes	—
81	C₅₉×#468	C₂²	1	2	yes	—
82	C₅₉×#468	C₂²	1	2	yes	—
83	C₅₉×#467	C₂²	1	2	yes	—
84	C₅₉×#466	C₂²	1	2	yes	—
85	C₅₉×#464	C₂²	1	2	yes	—
86	C₅₉×#464	C₂²	1	2	yes	—
87	C₅₉×#464	C₂²	1	2	yes	—
88	C₅₉×#464	C₂²	1	2	yes	—
89	C₅₉×#463	C₂²	1	2	yes	—
90	C₅₉×#463	C₂²	1	2	yes	—
91	C₅₉×#463	C₂²	1	2	yes	—
92	C₅₉×#463	C₂²	1	2	yes	—
93	C₅₉×#462	C₂²	1	2	yes	—
94	C₅₉×#462	C₂²	1	1	yes	characteristic
95	C₅₉×#462	C₂²	1	1	yes	characteristic
96	C₅₉×#462	C₂²	1	1	yes	characteristic
97	C₅₉×#462	C₂²	1	1	yes	characteristic
98	C₅₉×#461	C₂²	1	2	yes	—
99	C₅₉×#461	C₂²	1	2	yes	—
100	C₅₉×#460	C₂²	1	1	yes	characteristic
101	C₅₉×#460	C₂²	1	1	yes	characteristic
102	C₅₉×#460	C₂²	1	1	yes	characteristic
103	C₅₉×#460	C₂²	1	1	yes	characteristic
104	C₅₉×#452	C₂²	1	2	yes	—
105	C₅₉×#452	C₂²	1	2	yes	—
106	C₅₉×#451	C₂²	1	1	yes	characteristic
107	C₅₉×#451	C₂²	1	1	yes	characteristic
108	C₅₉×#451	C₂²	1	2	yes	—
109	C₅₉×#449	C₂²	1	2	yes	—
110	C₅₉×#449	C₂²	1	2	yes	—
111	C₅₉×#449	C₂²	1	2	yes	—
112	C₅₉×#449	C₂²	1	2	yes	—
113	C₅₉×#448	C₂²	1	2	yes	—
114	C₅₉×#446	C₂²	1	1	yes	characteristic
115	C₈×Q₈×C₅₉	C₂²	1	1	yes	characteristic
116	C₅₉×#440	C₂²	1	2	yes	—
117	C₅₉×#440	C₂²	1	2	yes	—
118	C₄×Q₁₆×C₅₉	C₂²	1	2	yes	—
119	C₄×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
120	C₄×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
121	C₄×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
122	C₄×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
123	C₄×D₈×C₅₉	C₂²	1	2	yes	—
124	C₅₉×#436	C₂²	1	2	yes	—
125	C₅₉×#436	C₂²	1	1	yes	characteristic
126	C₅₉×#435	C₂²	1	2	yes	—
127	C₈×D₄×C₅₉	C₂²	1	1	yes	characteristic
128	C₅₉×#433	C₂²	1	2	yes	—
129	C₅₉×#431	C₂²	1	1	yes	characteristic
130	C₅₉×#424	C₂²	1	2	yes	—
131	C₅₉×#423	C₂²	1	1	yes	characteristic
132	C₅₉×#417	C₂²	1	2	yes	—
133	C₅₉×#417	C₂²	1	2	yes	—
134	C₂×#103×C₅₉	C₂²	1	2	yes	—
135	C₂×#41×C₅₉	—	2	2	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	C₂×#41×C₅₉	C₂³	1	2	yes	—
140	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
141	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
142	#137×C₅₉	—	4	4	no	—
143	#137×C₅₉	—	4	4	no	—
144	#135×C₅₉	—	4	4	no	—
145	C₂×Q₁₆×C₅₉	C₂³	1	1	yes	characteristic
146	C₂×Q₁₆×C₅₉	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆×C₅₉	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₅₉	C₂³	1	1	yes	characteristic
149	C₂×Q₁₆×C₅₉	C₂³	1	1	yes	characteristic
150	C₂×Q₁₆×C₅₉	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
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×SD₁₆×C₅₉	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
157	C₂×D₈×C₅₉	C₂³	1	2	yes	—
158	C₂×D₈×C₅₉	C₂³	1	2	yes	—
159	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
160	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
161	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
162	C₄⋊Q₈×C₅₉	—	2	1	no	—
163	C₄⋊Q₈×C₅₉	—	2	2	no	—
164	C₄⋊Q₈×C₅₉	—	2	1	no	—
165	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
166	C₄⋊Q₈×C₅₉	C₂³	1	2	yes	—
167	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
168	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
169	C₄⋊Q₈×C₅₉	C₂³	1	2	yes	—
170	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
171	#127×C₅₉	—	2	1	no	—
172	#127×C₅₉	—	2	1	no	—
173	#127×C₅₉	C₂³	1	1	yes	characteristic
174	#127×C₅₉	C₂³	1	1	yes	characteristic
175	#126×C₅₉	—	2	2	no	—
176	#126×C₅₉	—	2	2	no	—
177	#126×C₅₉	D₄	1	2	yes	—
178	#125×C₅₉	—	2	1	no	—
179	#125×C₅₉	—	2	2	no	—
180	#125×C₅₉	—	2	1	no	—
181	#125×C₅₉	—	2	1	no	—
182	#125×C₅₉	D₄	1	1	yes	characteristic
183	#124×C₅₉	—	2	1	no	—
184	#124×C₅₉	—	2	1	no	—
185	#124×C₅₉	—	2	2	no	—
186	#124×C₅₉	—	2	2	no	—
187	#124×C₅₉	—	2	2	no	—
188	#124×C₅₉	—	2	2	no	—
189	#124×C₅₉	—	2	1	no	—
190	#124×C₅₉	D₄	1	1	yes	characteristic
191	#124×C₅₉	C₂³	1	2	yes	—
192	#124×C₅₉	C₂³	1	2	yes	—
193	#124×C₅₉	C₂³	1	2	yes	—
194	#123×C₅₉	—	2	2	no	—
195	#123×C₅₉	—	2	2	no	—
196	#123×C₅₉	—	2	2	no	—
197	#123×C₅₉	—	2	2	no	—
198	#123×C₅₉	—	2	2	no	—
199	#123×C₅₉	—	2	2	no	—
200	#123×C₅₉	—	2	2	no	—
201	#123×C₅₉	—	2	2	no	—
202	#123×C₅₉	—	2	2	no	—
203	#123×C₅₉	—	2	2	no	—
204	#123×C₅₉	D₄	1	2	yes	—
205	C₂²⋊Q₈×C₅₉	—	2	1	no	—
206	C₂²⋊Q₈×C₅₉	—	2	2	no	—
207	C₂²⋊Q₈×C₅₉	—	2	2	no	—
208	C₂²⋊Q₈×C₅₉	—	2	2	no	—
209	C₂²⋊Q₈×C₅₉	—	2	2	no	—
210	C₂²⋊Q₈×C₅₉	—	2	2	no	—
211	C₂²⋊Q₈×C₅₉	—	2	2	no	—
212	C₂²⋊Q₈×C₅₉	—	2	2	no	—
213	C₂²⋊Q₈×C₅₉	—	2	2	no	—
214	C₂²⋊Q₈×C₅₉	—	2	2	no	—
215	C₂²⋊Q₈×C₅₉	D₄	1	1	yes	characteristic
216	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
217	C₂²⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
218	C₂²⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
219	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
220	#121×C₅₉	—	2	2	no	—
221	#121×C₅₉	—	2	2	no	—
222	#121×C₅₉	—	2	2	no	—
223	#121×C₅₉	—	2	1	no	—
224	#121×C₅₉	—	2	1	no	—
225	#121×C₅₉	—	2	1	no	—
226	#121×C₅₉	—	2	2	no	—
227	#121×C₅₉	—	2	2	no	—
228	#121×C₅₉	D₄	1	1	yes	characteristic
229	#121×C₅₉	C₂³	1	2	yes	—
230	#121×C₅₉	C₂³	1	2	yes	—
231	#121×C₅₉	C₂³	1	2	yes	—
232	C₄×Q₈×C₅₉	—	2	1	no	—
233	C₄×Q₈×C₅₉	—	2	1	no	—
234	C₄×Q₈×C₅₉	—	2	1	no	—
235	C₄×Q₈×C₅₉	—	2	1	no	—
236	C₄×Q₈×C₅₉	—	2	1	no	—
237	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
238	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
239	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
240	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
242	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
243	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
244	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
245	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₅₉	—	2	1	no	—
247	C₄×D₄×C₅₉	—	2	1	no	—
248	C₄×D₄×C₅₉	—	2	1	no	—
249	C₄×D₄×C₅₉	—	2	1	no	—
250	C₄×D₄×C₅₉	—	2	1	no	—
251	C₄×D₄×C₅₉	—	2	1	no	—
252	C₄×D₄×C₅₉	—	2	2	no	—
253	C₄×D₄×C₅₉	—	2	2	no	—
254	C₄×D₄×C₅₉	—	2	2	no	—
255	C₄×D₄×C₅₉	—	2	2	no	—
256	C₄×D₄×C₅₉	—	2	1	no	—
257	C₄×D₄×C₅₉	—	2	1	no	—
258	C₄×D₄×C₅₉	—	2	1	no	—
259	C₄×D₄×C₅₉	C₂³	1	2	yes	—
260	C₄×D₄×C₅₉	C₂³	1	2	yes	—
261	C₄×D₄×C₅₉	C₂³	1	2	yes	—
262	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
263	C₄×D₄×C₅₉	C₂³	1	2	yes	—
264	#117×C₅₉	—	2	1	no	—
265	#117×C₅₉	—	2	2	no	—
266	#117×C₅₉	C₂³	1	2	yes	—
267	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
268	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
269	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
270	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
271	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
272	C₂×C₄²×C₅₉	—	2	1	no	—
273	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
274	#107×C₅₉	C₂³	1	1	yes	characteristic
275	#107×C₅₉	C₂³	1	1	yes	characteristic
276	#107×C₅₉	C₂³	1	1	yes	characteristic
277	#107×C₅₉	C₂³	1	1	yes	characteristic
278	#107×C₅₉	C₂³	1	2	yes	—
279	#107×C₅₉	C₂³	1	2	yes	—
280	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
281	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
285	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
286	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
296	#103×C₅₉	C₂³	1	1	yes	characteristic
297	#103×C₅₉	C₂³	1	1	yes	characteristic
298	#103×C₅₉	C₂³	1	2	yes	—
299	#103×C₅₉	C₂³	1	1	yes	characteristic
300	#103×C₅₉	C₂³	1	1	yes	characteristic
301	#102×C₅₉	C₂³	1	2	yes	—
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	2	yes	—
306	#102×C₅₉	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₅₉	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₅₉	C₂³	1	2	yes	—
311	#97×C₅₉	C₂³	1	2	yes	—
312	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₅₉	C₂³	1	2	yes	—
315	#41×C₅₉	—	2	4	no	—
316	#41×C₅₉	—	4	2	no	—
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	—	8	2	no	—
322	#41×C₅₉	—	8	4	no	—
323	C₂×Q₈×C₅₉	—	2	1	no	—
324	C₂×Q₈×C₅₉	—	2	1	no	—
325	C₂×Q₈×C₅₉	—	2	2	no	—
326	C₂×Q₈×C₅₉	—	2	2	no	—
327	C₂×Q₈×C₅₉	—	2	1	no	—
328	C₂×Q₈×C₅₉	—	2	2	no	—
329	C₂×Q₈×C₅₉	—	4	1	no	—
330	C₂×Q₈×C₅₉	—	4	2	no	—
331	C₂×Q₈×C₅₉	—	4	2	no	—
332	C₂×Q₈×C₅₉	C₂×D₄	1	1	yes	characteristic
333	C₂×Q₈×C₅₉	C₂⁴	1	1	yes	characteristic
334	C₂×Q₈×C₅₉	C₂⁴	1	2	yes	—
335	C₂×Q₈×C₅₉	C₂⁴	1	1	yes	characteristic
336	C₂×Q₈×C₅₉	C₂⁴	1	1	yes	characteristic
337	C₂×Q₈×C₅₉	C₂⁴	1	1	yes	characteristic
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	2	no	—
342	C₂×D₄×C₅₉	—	2	2	no	—
343	C₂×D₄×C₅₉	—	2	2	no	—
344	C₂×D₄×C₅₉	—	2	1	no	—
345	C₂×D₄×C₅₉	—	2	1	no	—
346	C₂×D₄×C₅₉	—	2	1	no	—
347	C₂×D₄×C₅₉	—	2	1	no	—
348	C₂×D₄×C₅₉	C₂×D₄	1	1	yes	characteristic
349	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
350	C₂×D₄×C₅₉	C₂⁴	1	2	yes	—
351	C₂×D₄×C₅₉	C₂⁴	1	2	yes	—
352	C₂²×C₄×C₅₉	—	2	1	no	—
353	C₂²×C₄×C₅₉	—	2	1	no	—
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	2	no	—
358	C₂²×C₄×C₅₉	—	2	2	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	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
366	Q₁₆×C₅₉	—	2	2	no	—
367	Q₁₆×C₅₉	—	2	2	no	—
368	Q₁₆×C₅₉	—	2	4	no	—
369	Q₁₆×C₅₉	—	4	1	no	—
370	Q₁₆×C₅₉	—	4	1	no	—
371	Q₁₆×C₅₉	—	4	2	no	—
372	SD₁₆×C₅₉	—	2	4	no	—
373	SD₁₆×C₅₉	—	4	2	no	—
374	SD₁₆×C₅₉	—	4	2	no	—
375	SD₁₆×C₅₉	—	4	2	no	—
376	SD₁₆×C₅₉	—	4	2	no	—
377	SD₁₆×C₅₉	—	4	2	no	—
378	D₈×C₅₉	—	4	2	no	—
379	D₈×C₅₉	—	4	2	no	—
380	M₁₆×C₅₉	—	4	2	no	—
381	M₁₆×C₅₉	—	4	2	no	—
382	C₂×C₈×C₅₉	—	4	2	no	—
383	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₅₉	C₂⁴	1	2	yes	—
387	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₅₉	C₂⁴	1	2	yes	—
389	C₄⋊C₄×C₅₉	—	2	1	no	—
390	C₄⋊C₄×C₅₉	—	2	1	no	—
391	C₄⋊C₄×C₅₉	—	2	2	no	—
392	C₄⋊C₄×C₅₉	—	2	2	no	—
393	C₄⋊C₄×C₅₉	—	2	1	no	—
394	C₄⋊C₄×C₅₉	—	2	1	no	—
395	C₄⋊C₄×C₅₉	—	2	1	no	—
396	C₄⋊C₄×C₅₉	—	2	2	no	—
397	C₄⋊C₄×C₅₉	—	2	2	no	—
398	C₄⋊C₄×C₅₉	—	2	1	no	—
399	C₄⋊C₄×C₅₉	—	2	1	no	—
400	C₄⋊C₄×C₅₉	—	2	1	no	—
401	C₄⋊C₄×C₅₉	—	2	1	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	2	no	—
406	C₄⋊C₄×C₅₉	—	2	1	no	—
407	C₄⋊C₄×C₅₉	—	2	2	no	—
408	C₄⋊C₄×C₅₉	—	2	2	no	—
409	C₄⋊C₄×C₅₉	—	2	1	no	—
410	C₄⋊C₄×C₅₉	—	2	2	no	—
411	C₄⋊C₄×C₅₉	—	2	1	no	—
412	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
413	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
414	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
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	1	yes	characteristic
423	C₂²⋊C₄×C₅₉	—	2	1	no	—
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	2	no	—
433	C₂²⋊C₄×C₅₉	—	2	2	no	—
434	C₂²⋊C₄×C₅₉	—	2	2	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	2	no	—
439	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
440	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
441	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
444	C₄²×C₅₉	—	2	1	no	—
445	C₄²×C₅₉	—	2	1	no	—
446	C₄²×C₅₉	—	2	1	no	—
447	C₄²×C₅₉	—	2	1	no	—
448	C₄²×C₅₉	—	2	2	no	—
449	C₄²×C₅₉	—	2	1	no	—
450	C₄²×C₅₉	—	2	1	no	—
451	C₄²×C₅₉	—	2	2	no	—
452	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
453	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
454	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
455	C₄²×C₅₉	C₂⁴	1	2	yes	—
456	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
457	C₂³×C₅₉	—	2	2	no	—
458	C₂³×C₅₉	—	2	2	no	—
459	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
460	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
461	Q₈×C₅₉	—	2	2	no	—
462	Q₈×C₅₉	—	2	1	no	—
463	Q₈×C₅₉	—	2	1	no	—
464	Q₈×C₅₉	—	2	1	no	—
465	Q₈×C₅₉	—	2	1	no	—
466	Q₈×C₅₉	—	2	2	no	—
467	Q₈×C₅₉	—	2	2	no	—
468	Q₈×C₅₉	—	2	1	no	—
469	Q₈×C₅₉	—	2	1	no	—
470	Q₈×C₅₉	—	2	1	no	—
471	Q₈×C₅₉	—	4	2	no	—
472	Q₈×C₅₉	—	8	1	no	—
473	Q₈×C₅₉	—	8	2	no	—
474	Q₈×C₅₉	—	8	1	no	—
475	Q₈×C₅₉	—	8	2	no	—
476	Q₈×C₅₉	H(5,𝔽₂)	1	2	yes	—
477	D₄×C₅₉	—	2	2	no	—
478	D₄×C₅₉	—	2	2	no	—
479	D₄×C₅₉	—	2	2	no	—
480	D₄×C₅₉	—	2	2	no	—
481	D₄×C₅₉	—	2	2	no	—
482	D₄×C₅₉	—	4	2	no	—
483	D₄×C₅₉	—	4	4	no	—
484	D₄×C₅₉	—	4	4	no	—
485	D₄×C₅₉	—	4	2	no	—
486	D₄×C₅₉	—	4	2	no	—
487	D₄×C₅₉	—	8	1	no	—
488	D₄×C₅₉	—	8	1	no	—
489	D₄×C₅₉	—	8	2	no	—
490	D₄×C₅₉	—	8	2	no	—
491	D₄×C₅₉	—	8	2	no	—
492	D₄×C₅₉	—	8	2	no	—
493	C₂×C₄×C₅₉	—	2	1	no	—
494	C₂×C₄×C₅₉	—	2	2	no	—
495	C₂×C₄×C₅₉	—	2	2	no	—
496	C₂×C₄×C₅₉	—	2	1	no	—
497	C₂×C₄×C₅₉	—	2	2	no	—
498	C₂×C₄×C₅₉	—	2	1	no	—
499	C₂×C₄×C₅₉	—	2	1	no	—
500	C₂×C₄×C₅₉	—	2	1	no	—
501	C₂×C₄×C₅₉	—	2	1	no	—
502	C₂×C₄×C₅₉	—	2	1	no	—
503	C₂×C₄×C₅₉	—	2	1	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	—	4	1	no	—
509	C₂×C₄×C₅₉	—	4	4	no	—
510	C₂×C₄×C₅₉	—	4	2	no	—
511	C₂×C₄×C₅₉	—	4	2	no	—
512	C₂×C₄×C₅₉	—	8	2	no	—
513	C₂×C₄×C₅₉	—	8	2	no	—
514	C₂×C₄×C₅₉	—	8	2	no	—
515	C₂×C₄×C₅₉	—	8	2	no	—
516	C₂×C₄×C₅₉	—	8	2	no	—
517	C₂×C₄×C₅₉	—	8	2	no	—
518	C₂×C₄×C₅₉	—	8	2	no	—
519	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
521	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
525	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
526	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄×C₅₉	C₂⁵	1	1	yes	characteristic
528	C₈×C₅₉	—	2	1	no	—
529	C₈×C₅₉	—	2	2	no	—
530	C₈×C₅₉	—	2	1	no	—
531	C₈×C₅₉	—	2	2	no	—
532	C₈×C₅₉	—	2	1	no	—
533	C₈×C₅₉	—	2	1	no	—
534	#62046	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
535	C₂²×C₅₉	—	2	1	no	—
536	C₂²×C₅₉	—	2	2	no	—
537	C₂²×C₅₉	—	2	1	no	—
538	C₂²×C₅₉	—	2	2	no	—
539	C₂²×C₅₉	—	2	1	no	—
540	C₂²×C₅₉	—	2	2	no	—
541	C₂²×C₅₉	—	4	2	no	—
542	C₂²×C₅₉	—	4	2	no	—
543	C₂²×C₅₉	—	4	2	no	—
544	C₂²×C₅₉	—	4	2	no	—
545	C₂²×C₅₉	—	4	2	no	—
546	C₂²×C₅₉	—	4	2	no	—
547	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
548	C₄×C₅₉	—	2	1	no	—
549	C₄×C₅₉	—	2	1	no	—
550	C₄×C₅₉	—	2	2	no	—
551	C₄×C₅₉	—	2	2	no	—
552	C₄×C₅₉	—	2	1	no	—
553	C₄×C₅₉	—	2	2	no	—
554	C₄×C₅₉	—	2	1	no	—
555	C₄×C₅₉	—	2	2	no	—
556	C₄×C₅₉	—	4	1	no	—
557	C₄×C₅₉	—	4	1	no	—
558	C₄×C₅₉	—	4	2	no	—
559	C₄×C₅₉	—	4	1	no	—
560	C₄×C₅₉	—	4	1	no	—
561	C₄×C₅₉	—	4	1	no	—
562	C₄×C₅₉	—	4	1	no	—
563	C₄×C₅₉	—	4	2	no	—
564	C₄×C₅₉	—	4	1	no	—
565	C₄×C₅₉	#578	1	2	yes	—
566	C₄×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
567	C₄×C₅₉	#585	1	1	yes	characteristic
568	#3554	C₂×C₅₉	1	1	yes	characteristic, complemented
569	#3522	C₂×C₅₉	1	1	yes	characteristic, complemented
570	#3400	C₂×C₅₉	1	1	yes	characteristic, complemented
571	#3396	C₂×C₅₉	1	1	yes	characteristic, complemented
572	#3375	C₂×C₅₉	1	1	yes	characteristic, complemented
573	#3363	C₂×C₅₉	1	1	yes	characteristic, complemented
574	#3333	C₂×C₅₉	1	1	yes	characteristic, complemented
575	#3330	C₂×C₅₉	1	2	yes	complemented
576	#3308	C₂×C₅₉	1	2	yes	complemented
577	#3299	C₂×C₅₉	1	1	yes	characteristic, complemented
578	#3287	C₂×C₅₉	1	1	yes	characteristic, complemented
579	#3278	C₂×C₅₉	1	1	yes	characteristic, complemented
580	#3277	C₂×C₅₉	1	2	yes	complemented
581	#3269	C₂×C₅₉	1	2	yes	complemented
582	#3262	C₂×C₅₉	1	2	yes	complemented
583	#3254	C₂×C₅₉	1	1	yes	characteristic, complemented
584	#3225	C₂×C₅₉	1	2	yes	complemented
585	#3207	C₂×C₅₉	1	1	yes	characteristic, complemented
586	#3124	C₂×C₅₉	1	2	yes	complemented
587	#3104	C₂×C₅₉	1	1	yes	characteristic, complemented
588	#3046	C₂×C₅₉	1	2	yes	complemented
589	#3037	C₂×C₅₉	1	1	yes	characteristic, complemented
590	#2993	C₂×C₅₉	1	1	yes	characteristic, complemented
591	C₂×C₅₉	—	4	1	no	—
592	C₂×C₅₉	—	4	2	no	—
593	C₂×C₅₉	—	8	2	no	—
594	C₂×C₅₉	—	8	2	no	—
595	C₂×C₅₉	#3488	1	1	yes	characteristic
596	C₂×C₅₉	C₂×#578	1	1	yes	characteristic
597	C₂×C₅₉	#3585	1	1	yes	characteristic
598	C₂×#137	C₂²×C₅₉	1	2	yes	—
599	C₂×#137	C₂²×C₅₉	1	2	yes	—
600	C₂×#135	C₂²×C₅₉	1	2	yes	—
601	#562	—	2	2	no	—
602	#559	—	2	1	no	—
603	#559	—	2	1	no	—
604	#559	C₂²×C₅₉	1	1	yes	characteristic
605	#559	C₂²×C₅₉	1	1	yes	characteristic
606	Q₈²	C₂²×C₅₉	1	1	yes	characteristic
607	#557	C₂²×C₅₉	1	1	yes	characteristic
608	#554	—	2	1	no	—
609	#554	—	2	1	no	—
610	#554	C₂²×C₅₉	1	1	yes	characteristic
611	#550	C₂²×C₅₉	1	1	yes	characteristic
612	#550	C₂²×C₅₉	1	1	yes	characteristic
613	D₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
614	#548	C₂²×C₅₉	1	2	yes	—
615	#548	C₂²×C₅₉	1	2	yes	—
616	#547	—	2	2	no	—
617	#547	C₂²×C₅₉	1	2	yes	—
618	#547	C₂²×C₅₉	1	2	yes	—
619	#542	—	2	2	no	—
620	#542	—	2	1	no	—
621	#542	C₂²×C₅₉	1	2	yes	—
622	#542	C₂²×C₅₉	1	2	yes	—
623	#540	—	2	1	no	—
624	#539	—	2	2	no	—
625	#536	C₂²×C₅₉	1	2	yes	—
626	#533	C₂²×C₅₉	1	1	yes	characteristic
627	#532	—	2	1	no	—
628	#532	C₂²×C₅₉	1	1	yes	characteristic
629	#532	C₂²×C₅₉	1	1	yes	characteristic
630	#529	—	2	1	no	—
631	#529	C₂²×C₅₉	1	1	yes	characteristic
632	#520	C₂²×C₅₉	1	2	yes	—
633	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
634	#497	C₂²×C₅₉	1	2	yes	—
635	#495	C₂²×C₅₉	1	2	yes	—
636	#493	C₂²×C₅₉	1	1	yes	characteristic
637	#492	C₂²×C₅₉	1	1	yes	characteristic
638	#489	C₂²×C₅₉	1	2	yes	—
639	#487	C₂²×C₅₉	1	2	yes	—
640	#487	C₂²×C₅₉	1	1	yes	characteristic
641	#486	C₂²×C₅₉	1	1	yes	characteristic
642	#484	C₂²×C₅₉	1	1	yes	characteristic
643	#484	C₂²×C₅₉	1	2	yes	—
644	#484	C₂²×C₅₉	1	1	yes	characteristic
645	#480	C₂²×C₅₉	1	2	yes	—
646	#477	C₂²×C₅₉	1	1	yes	characteristic
647	#477	C₂²×C₅₉	1	1	yes	characteristic
648	#477	C₂²×C₅₉	1	1	yes	characteristic
649	#477	C₂²×C₅₉	1	2	yes	—
650	#477	C₂²×C₅₉	1	1	yes	characteristic
651	#474	C₂²×C₅₉	1	2	yes	—
652	#474	C₂²×C₅₉	1	2	yes	—
653	#468	C₂²×C₅₉	1	2	yes	—
654	#468	C₂²×C₅₉	1	2	yes	—
655	#468	C₂²×C₅₉	1	2	yes	—
656	#468	C₂²×C₅₉	1	2	yes	—
657	#467	C₂²×C₅₉	1	2	yes	—
658	#466	C₂²×C₅₉	1	2	yes	—
659	#464	C₂²×C₅₉	1	2	yes	—
660	#464	C₂²×C₅₉	1	2	yes	—
661	#464	C₂²×C₅₉	1	2	yes	—
662	#464	C₂²×C₅₉	1	2	yes	—
663	#463	C₂²×C₅₉	1	2	yes	—
664	#463	C₂²×C₅₉	1	2	yes	—
665	#463	C₂²×C₅₉	1	2	yes	—
666	#463	C₂²×C₅₉	1	2	yes	—
667	#462	C₂²×C₅₉	1	1	yes	characteristic
668	#462	C₂²×C₅₉	1	1	yes	characteristic
669	#462	C₂²×C₅₉	1	2	yes	—
670	#462	C₂²×C₅₉	1	1	yes	characteristic
671	#462	C₂²×C₅₉	1	1	yes	characteristic
672	#461	C₂²×C₅₉	1	2	yes	—
673	#461	C₂²×C₅₉	1	2	yes	—
674	#460	C₂²×C₅₉	1	1	yes	characteristic
675	#460	C₂²×C₅₉	1	1	yes	characteristic
676	#460	C₂²×C₅₉	1	1	yes	characteristic
677	#460	C₂²×C₅₉	1	1	yes	characteristic
678	#452	C₂²×C₅₉	1	2	yes	—
679	#452	C₂²×C₅₉	1	2	yes	—
680	#451	C₂²×C₅₉	1	1	yes	characteristic
681	#451	C₂²×C₅₉	1	1	yes	characteristic
682	#451	C₂²×C₅₉	1	2	yes	—
683	#449	C₂²×C₅₉	1	2	yes	—
684	#449	C₂²×C₅₉	1	2	yes	—
685	#449	C₂²×C₅₉	1	2	yes	—
686	#449	C₂²×C₅₉	1	2	yes	—
687	#448	C₂²×C₅₉	1	2	yes	—
688	#446	C₂²×C₅₉	1	1	yes	characteristic
689	C₈×Q₈	C₂²×C₅₉	1	1	yes	characteristic
690	#440	C₂²×C₅₉	1	2	yes	—
691	#440	C₂²×C₅₉	1	2	yes	—
692	C₄×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic
693	C₄×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic
694	C₄×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic
695	C₄×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic
696	C₄×Q₁₆	C₂²×C₅₉	1	2	yes	—
697	C₄×D₈	C₂²×C₅₉	1	2	yes	—
698	#436	C₂²×C₅₉	1	2	yes	—
699	#436	C₂²×C₅₉	1	1	yes	characteristic
700	#435	C₂²×C₅₉	1	2	yes	—
701	C₈×D₄	C₂²×C₅₉	1	1	yes	characteristic
702	#433	C₂²×C₅₉	1	2	yes	—
703	#431	C₂²×C₅₉	1	1	yes	characteristic
704	#424	C₂²×C₅₉	1	2	yes	—
705	#423	C₂²×C₅₉	1	1	yes	characteristic
706	#417	C₂²×C₅₉	1	2	yes	—
707	#417	C₂²×C₅₉	1	2	yes	—
708	C₂×#103	C₂²×C₅₉	1	2	yes	—
709	C₅₉	#62046	1	1	yes	characteristic, direct product factor, Sylow
710	C₂×#41	—	2	2	no	—
711	C₂×#41	—	2	1	no	—
712	C₂×#41	C₂³×C₅₉	1	2	yes	—
713	C₂×#41	C₂³×C₅₉	1	2	yes	—
714	C₂×#41	C₂³×C₅₉	1	2	yes	—
715	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
716	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
717	#137	—	4	4	no	—
718	#137	—	4	4	no	—
719	#135	—	4	4	no	—
720	C₂×Q₁₆	C₂³×C₅₉	1	1	yes	characteristic
721	C₂×Q₁₆	C₂³×C₅₉	1	1	yes	characteristic
722	C₂×Q₁₆	C₂³×C₅₉	1	2	yes	—
723	C₂×Q₁₆	C₂³×C₅₉	1	2	yes	—
724	C₂×Q₁₆	C₂³×C₅₉	1	1	yes	characteristic
725	C₂×Q₁₆	C₂³×C₅₉	1	1	yes	characteristic
726	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
727	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
728	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
729	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
730	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
731	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
732	C₂×D₈	C₂³×C₅₉	1	2	yes	—
733	C₂×D₈	C₂³×C₅₉	1	2	yes	—
734	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
735	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
736	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
737	C₄⋊Q₈	—	2	1	no	—
738	C₄⋊Q₈	—	2	2	no	—
739	C₄⋊Q₈	—	2	1	no	—
740	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
741	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
742	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
743	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
744	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
745	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
746	#127	—	2	1	no	—
747	#127	—	2	1	no	—
748	#127	C₂³×C₅₉	1	1	yes	characteristic
749	#127	C₂³×C₅₉	1	1	yes	characteristic
750	#126	—	2	2	no	—
751	#126	—	2	2	no	—
752	#126	D₄×C₅₉	1	2	yes	—
753	#125	—	2	1	no	—
754	#125	—	2	2	no	—
755	#125	—	2	1	no	—
756	#125	—	2	1	no	—
757	#125	D₄×C₅₉	1	1	yes	characteristic
758	#124	—	2	1	no	—
759	#124	—	2	1	no	—
760	#124	—	2	2	no	—
761	#124	—	2	2	no	—
762	#124	—	2	2	no	—
763	#124	—	2	2	no	—
764	#124	—	2	1	no	—
765	#124	D₄×C₅₉	1	1	yes	characteristic
766	#124	C₂³×C₅₉	1	2	yes	—
767	#124	C₂³×C₅₉	1	2	yes	—
768	#124	C₂³×C₅₉	1	2	yes	—
769	#123	—	2	2	no	—
770	#123	—	2	2	no	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	#123	D₄×C₅₉	1	2	yes	—
780	C₂²⋊Q₈	—	2	1	no	—
781	C₂²⋊Q₈	—	2	2	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	—	2	2	no	—
785	C₂²⋊Q₈	—	2	2	no	—
786	C₂²⋊Q₈	—	2	2	no	—
787	C₂²⋊Q₈	—	2	2	no	—
788	C₂²⋊Q₈	—	2	2	no	—
789	C₂²⋊Q₈	—	2	2	no	—
790	C₂²⋊Q₈	D₄×C₅₉	1	1	yes	characteristic
791	C₂²⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
792	C₂²⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
793	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
794	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
795	#121	—	2	2	no	—
796	#121	—	2	2	no	—
797	#121	—	2	2	no	—
798	#121	—	2	1	no	—
799	#121	—	2	1	no	—
800	#121	—	2	1	no	—
801	#121	—	2	2	no	—
802	#121	—	2	2	no	—
803	#121	D₄×C₅₉	1	1	yes	characteristic
804	#121	C₂³×C₅₉	1	2	yes	—
805	#121	C₂³×C₅₉	1	2	yes	—
806	#121	C₂³×C₅₉	1	2	yes	—
807	C₄×Q₈	—	2	1	no	—
808	C₄×Q₈	—	2	1	no	—
809	C₄×Q₈	—	2	1	no	—
810	C₄×Q₈	—	2	1	no	—
811	C₄×Q₈	—	2	1	no	—
812	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
813	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
814	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
815	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
816	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
817	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
818	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
819	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
820	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	—	2	2	no	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	—	2	2	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	—	2	1	no	—
832	C₄×D₄	—	2	1	no	—
833	C₄×D₄	—	2	1	no	—
834	C₄×D₄	C₂³×C₅₉	1	2	yes	—
835	C₄×D₄	C₂³×C₅₉	1	2	yes	—
836	C₄×D₄	C₂³×C₅₉	1	2	yes	—
837	C₄×D₄	C₂³×C₅₉	1	2	yes	—
838	C₄×D₄	C₂³×C₅₉	1	1	yes	characteristic
839	#117	—	2	1	no	—
840	#117	—	2	2	no	—
841	#117	C₂³×C₅₉	1	2	yes	—
842	C₂×C₄⋊C₄	—	2	1	no	—
843	C₂×C₄⋊C₄	—	2	2	no	—
844	C₂×C₄⋊C₄	—	2	2	no	—
845	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
846	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
847	C₂×C₄²	—	2	1	no	—
848	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
849	#107	C₂³×C₅₉	1	1	yes	characteristic
850	#107	C₂³×C₅₉	1	1	yes	characteristic
851	#107	C₂³×C₅₉	1	1	yes	characteristic
852	#107	C₂³×C₅₉	1	1	yes	characteristic
853	#107	C₂³×C₅₉	1	2	yes	—
854	#107	C₂³×C₅₉	1	2	yes	—
855	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
856	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
857	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
858	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
859	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
860	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
861	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
862	#103	C₂³×C₅₉	1	1	yes	characteristic
863	#103	C₂³×C₅₉	1	2	yes	—
864	#103	C₂³×C₅₉	1	2	yes	—
865	#103	C₂³×C₅₉	1	2	yes	—
866	#103	C₂³×C₅₉	1	1	yes	characteristic
867	#103	C₂³×C₅₉	1	2	yes	—
868	#103	C₂³×C₅₉	1	2	yes	—
869	#103	C₂³×C₅₉	1	1	yes	characteristic
870	#103	C₂³×C₅₉	1	1	yes	characteristic
871	#103	C₂³×C₅₉	1	1	yes	characteristic
872	#103	C₂³×C₅₉	1	1	yes	characteristic
873	#103	C₂³×C₅₉	1	2	yes	—
874	#103	C₂³×C₅₉	1	1	yes	characteristic
875	#103	C₂³×C₅₉	1	1	yes	characteristic
876	#102	C₂³×C₅₉	1	2	yes	—
877	#102	C₂³×C₅₉	1	2	yes	—
878	#102	C₂³×C₅₉	1	2	yes	—
879	#102	C₂³×C₅₉	1	2	yes	—
880	#102	C₂³×C₅₉	1	2	yes	—
881	#102	C₂³×C₅₉	1	2	yes	—
882	C₂²⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
883	C₂²⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
884	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
885	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
886	#97	C₂³×C₅₉	1	2	yes	—
887	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
888	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
889	C₄×C₈	C₂³×C₅₉	1	2	yes	—
890	#41	—	2	4	no	—
891	#41	—	4	2	no	—
892	#41	—	4	2	no	—
893	#41	—	4	2	no	—
894	#41	—	4	2	no	—
895	#41	—	4	2	no	—
896	#41	—	8	2	no	—
897	#41	—	8	4	no	—
898	C₂×Q₈	—	2	1	no	—
899	C₂×Q₈	—	2	1	no	—
900	C₂×Q₈	—	2	2	no	—
901	C₂×Q₈	—	2	2	no	—
902	C₂×Q₈	—	2	1	no	—
903	C₂×Q₈	—	2	2	no	—
904	C₂×Q₈	—	4	1	no	—
905	C₂×Q₈	—	4	2	no	—
906	C₂×Q₈	—	4	2	no	—
907	C₂×Q₈	C₂×D₄×C₅₉	1	1	yes	characteristic
908	C₂×Q₈	C₂⁴×C₅₉	1	1	yes	characteristic
909	C₂×Q₈	C₂⁴×C₅₉	1	2	yes	—
910	C₂×Q₈	C₂⁴×C₅₉	1	1	yes	characteristic
911	C₂×Q₈	C₂⁴×C₅₉	1	1	yes	characteristic
912	C₂×Q₈	C₂⁴×C₅₉	1	1	yes	characteristic
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	1	no	—
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	1	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	C₂×D₄×C₅₉	1	1	yes	characteristic
924	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
925	C₂×D₄	C₂⁴×C₅₉	1	2	yes	—
926	C₂×D₄	C₂⁴×C₅₉	1	2	yes	—
927	C₂²×C₄	—	2	1	no	—
928	C₂²×C₄	—	2	1	no	—
929	C₂²×C₄	—	2	2	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	—	2	2	no	—
933	C₂²×C₄	—	2	2	no	—
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	—	2	2	no	—
936	C₂²×C₄	—	2	2	no	—
937	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
938	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
939	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
940	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
941	Q₁₆	—	2	2	no	—
942	Q₁₆	—	2	2	no	—
943	Q₁₆	—	2	4	no	—
944	Q₁₆	—	4	2	no	—
945	Q₁₆	—	4	1	no	—
946	Q₁₆	—	4	1	no	—
947	SD₁₆	—	2	4	no	—
948	SD₁₆	—	4	2	no	—
949	SD₁₆	—	4	2	no	—
950	SD₁₆	—	4	2	no	—
951	SD₁₆	—	4	2	no	—
952	SD₁₆	—	4	2	no	—
953	D₈	—	4	2	no	—
954	D₈	—	4	2	no	—
955	M₁₆	—	4	2	no	—
956	M₁₆	—	4	2	no	—
957	C₂×C₈	—	4	2	no	—
958	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
959	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
960	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
961	C₂×C₈	C₂⁴×C₅₉	1	2	yes	—
962	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
963	C₂×C₈	C₂⁴×C₅₉	1	2	yes	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
988	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
989	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
990	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
991	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
992	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
993	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
994	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
995	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
996	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
997	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
1015	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
1016	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
1017	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
1018	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
1019	C₄²	—	2	1	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	1	no	—
1022	C₄²	—	2	1	no	—
1023	C₄²	—	2	2	no	—
1024	C₄²	—	2	1	no	—
1025	C₄²	—	2	1	no	—
1026	C₄²	—	2	2	no	—
1027	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
1028	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
1029	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
1030	C₄²	C₂⁴×C₅₉	1	2	yes	—
1031	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
1032	C₂³	—	2	2	no	—
1033	C₂³	—	2	2	no	—
1034	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
1035	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
1036	Q₈	—	2	2	no	—
1037	Q₈	—	2	1	no	—
1038	Q₈	—	2	1	no	—
1039	Q₈	—	2	1	no	—
1040	Q₈	—	2	1	no	—
1041	Q₈	—	2	2	no	—
1042	Q₈	—	2	2	no	—
1043	Q₈	—	2	1	no	—
1044	Q₈	—	2	1	no	—
1045	Q₈	—	2	1	no	—
1046	Q₈	—	4	2	no	—
1047	Q₈	—	8	1	no	—
1048	Q₈	—	8	2	no	—
1049	Q₈	—	8	1	no	—
1050	Q₈	—	8	2	no	—
1051	Q₈	H(5,𝔽₂)×C₅₉	1	2	yes	—
1052	D₄	—	2	2	no	—
1053	D₄	—	2	2	no	—
1054	D₄	—	2	2	no	—
1055	D₄	—	2	2	no	—
1056	D₄	—	2	2	no	—
1057	D₄	—	4	2	no	—
1058	D₄	—	4	4	no	—
1059	D₄	—	4	4	no	—
1060	D₄	—	4	2	no	—
1061	D₄	—	4	2	no	—
1062	D₄	—	8	1	no	—
1063	D₄	—	8	1	no	—
1064	D₄	—	8	2	no	—
1065	D₄	—	8	2	no	—
1066	D₄	—	8	2	no	—
1067	D₄	—	8	2	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	4	1	no	—
1084	C₂×C₄	—	4	4	no	—
1085	C₂×C₄	—	4	2	no	—
1086	C₂×C₄	—	4	2	no	—
1087	C₂×C₄	—	8	2	no	—
1088	C₂×C₄	—	8	2	no	—
1089	C₂×C₄	—	8	2	no	—
1090	C₂×C₄	—	8	2	no	—
1091	C₂×C₄	—	8	2	no	—
1092	C₂×C₄	—	8	2	no	—
1093	C₂×C₄	—	8	2	no	—
1094	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1095	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1096	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1097	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1098	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1099	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1100	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1101	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1102	C₂×C₄	C₂⁵×C₅₉	1	1	yes	characteristic
1103	C₈	—	2	1	no	—
1104	C₈	—	2	2	no	—
1105	C₈	—	2	1	no	—
1106	C₈	—	2	2	no	—
1107	C₈	—	2	1	no	—
1108	C₈	—	2	1	no	—
1109	C₂²	—	2	1	no	—
1110	C₂²	—	2	2	no	—
1111	C₂²	—	2	1	no	—
1112	C₂²	—	2	2	no	—
1113	C₂²	—	2	1	no	—
1114	C₂²	—	2	2	no	—
1115	C₂²	—	4	2	no	—
1116	C₂²	—	4	2	no	—
1117	C₂²	—	4	2	no	—
1118	C₂²	—	4	2	no	—
1119	C₂²	—	4	2	no	—
1120	C₂²	—	4	2	no	—
1121	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
1122	C₄	—	2	1	no	—
1123	C₄	—	2	2	no	—
1124	C₄	—	2	1	no	—
1125	C₄	—	2	1	no	—
1126	C₄	—	2	2	no	—
1127	C₄	—	2	2	no	—
1128	C₄	—	2	1	no	—
1129	C₄	—	2	2	no	—
1130	C₄	—	4	1	no	—
1131	C₄	—	4	1	no	—
1132	C₄	—	4	2	no	—
1133	C₄	—	4	1	no	—
1134	C₄	—	4	1	no	—
1135	C₄	—	4	1	no	—
1136	C₄	—	4	1	no	—
1137	C₄	—	4	2	no	—
1138	C₄	—	4	1	no	—
1139	C₄	C₅₉×#578	1	2	yes	—
1140	C₄	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
1141	C₄	C₅₉×#585	1	1	yes	characteristic
1142	C₂	—	4	1	no	—
1143	C₂	—	4	2	no	—
1144	C₂	—	8	2	no	—
1145	C₂	—	8	2	no	—
1146	C₂	C₅₉×#3488	1	1	yes	characteristic
1147	C₂	C₂×C₅₉×#578	1	1	yes	characteristic
1148	C₂	C₅₉×#3585	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 ◁ C₅₉×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₉×#3554	C₂	semidirect
2. C₅₉×#3522	C₂	semidirect
3. C₅₉×#3400	C₂	semidirect
4. C₅₉×#3396	C₂	semidirect
5. C₅₉×#3375	C₂	semidirect
6. C₅₉×#3363	C₂	semidirect
7. C₅₉×#3333	C₂	semidirect
8. C₅₉×#3330	C₂	semidirect
9. C₅₉×#3308	C₂	semidirect
10. C₅₉×#3299	C₂	semidirect
11. C₅₉×#3287	C₂	semidirect
12. C₅₉×#3278	C₂	semidirect
13. C₅₉×#3277	C₂	semidirect
14. C₅₉×#3269	C₂	semidirect
15. C₅₉×#3262	C₂	semidirect
16. C₅₉×#3254	C₂	semidirect
17. C₅₉×#3225	C₂	semidirect
18. C₅₉×#3207	C₂	semidirect
19. C₅₉×#3124	C₂	semidirect
20. C₅₉×#3104	C₂	semidirect
21. C₅₉×#3046	C₂	semidirect
22. C₅₉×#3037	C₂	semidirect
23. C₅₉×#2993	C₂	semidirect
534. #62046	C₅₉	direct (N × H)
568. #3554	C₂×C₅₉	semidirect
569. #3522	C₂×C₅₉	semidirect
570. #3400	C₂×C₅₉	semidirect
571. #3396	C₂×C₅₉	semidirect
572. #3375	C₂×C₅₉	semidirect
573. #3363	C₂×C₅₉	semidirect
574. #3333	C₂×C₅₉	semidirect
575. #3330	C₂×C₅₉	semidirect
576. #3308	C₂×C₅₉	semidirect
577. #3299	C₂×C₅₉	semidirect
578. #3287	C₂×C₅₉	semidirect
579. #3278	C₂×C₅₉	semidirect
580. #3277	C₂×C₅₉	semidirect
581. #3269	C₂×C₅₉	semidirect
582. #3262	C₂×C₅₉	semidirect
583. #3254	C₂×C₅₉	semidirect
584. #3225	C₂×C₅₉	semidirect
585. #3207	C₂×C₅₉	semidirect
586. #3124	C₂×C₅₉	semidirect
587. #3104	C₂×C₅₉	semidirect
588. #3046	C₂×C₅₉	semidirect
589. #3037	C₂×C₅₉	semidirect
590. #2993	C₂×C₅₉	semidirect
709. C₅₉	#62046	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₉×#3554	2
C₅₉×#3522	2
C₅₉×#3400	2
C₅₉×#3396	2
C₅₉×#3375	2
C₅₉×#3363	2
C₅₉×#3333	2
C₅₉×#3330	2
C₅₉×#3308	2
C₅₉×#3299	2
C₅₉×#3287	2
C₅₉×#3278	2
C₅₉×#3277	2
C₅₉×#3269	2
C₅₉×#3262	2
C₅₉×#3254	2
C₅₉×#3225	2
C₅₉×#3207	2
C₅₉×#3124	2
C₅₉×#3104	2
C₅₉×#3046	2
C₅₉×#3037	2
C₅₉×#2993	2
#62046	59

Subgroups — C59×#62046 #28474155

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#62046 #28474155