Subgroups — C₅₉×#35572 #28447681

Order 15104.

2346 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#529	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#2610	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2603	C₂	1	2	yes	maximal, complemented
5	C₅₉×#2601	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2560	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2554	C₂	1	2	yes	maximal, complemented
8	C₅₉×#2550	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#2548	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#2544	C₂	1	2	yes	maximal, complemented
11	C₅₉×#2541	C₂	1	1	yes	maximal, characteristic
12	C₅₉×#2536	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₉×#2491	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₉×#2490	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#2461	C₂	1	2	yes	maximal, complemented
16	C₅₉×#2445	C₂	1	2	yes	maximal, complemented
17	C₅₉×#2426	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₉×#2426	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₉×#2328	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₉×#2324	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#121×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₉×#2290	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₉×#2276	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₉×#542	—	2	8	no	—
25	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
26	C₂×#127×C₅₉	C₂²	1	1	yes	characteristic
27	C₂×#127×C₅₉	C₂²	1	2	yes	—
28	C₅₉×#529	—	2	8	no	—
29	C₂×#126×C₅₉	C₂²	1	2	yes	—
30	C₂×#126×C₅₉	C₂²	1	2	yes	—
31	C₂×#125×C₅₉	C₂²	1	1	yes	characteristic
32	C₂×#124×C₅₉	C₂²	1	2	yes	—
33	C₂×#124×C₅₉	C₂²	1	1	yes	characteristic
34	C₂×#124×C₅₉	C₂²	1	1	yes	characteristic
35	C₂×#124×C₅₉	C₂²	1	2	yes	—
36	C₂×#123×C₅₉	C₂²	1	2	yes	—
37	C₂×#123×C₅₉	C₂²	1	2	yes	—
38	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	—
41	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
42	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
43	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
44	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
47	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
50	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
52	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
53	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
54	C₂×#117×C₅₉	C₂²	1	2	yes	—
55	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
56	C₅₉×#398	C₂²	1	2	yes	—
57	C₅₉×#398	C₂²	1	2	yes	—
58	C₅₉×#397	C₂²	1	2	yes	—
59	C₅₉×#396	C₂²	1	2	yes	—
60	C₅₉×#396	C₂²	1	2	yes	—
61	C₅₉×#395	C₂²	1	2	yes	—
62	C₅₉×#394	C₂²	1	2	yes	—
63	C₅₉×#394	C₂²	1	2	yes	—
64	C₅₉×#394	C₂²	1	2	yes	—
65	C₅₉×#394	C₂²	1	2	yes	—
66	C₅₉×#394	C₂²	1	2	yes	—
67	C₅₉×#394	C₂²	1	2	yes	—
68	C₅₉×#394	C₂²	1	2	yes	—
69	C₅₉×#393	C₂²	1	2	yes	—
70	C₅₉×#392	C₂²	1	2	yes	—
71	C₅₉×#392	C₂²	1	2	yes	—
72	C₅₉×#391	C₂²	1	2	yes	—
73	C₅₉×#390	C₂²	1	2	yes	—
74	C₅₉×#390	C₂²	1	1	yes	characteristic
75	C₅₉×#390	C₂²	1	1	yes	characteristic
76	C₅₉×#390	C₂²	1	1	yes	characteristic
77	C₅₉×#390	C₂²	1	1	yes	characteristic
78	C₅₉×#390	C₂²	1	2	yes	—
79	C₅₉×#390	C₂²	1	2	yes	—
80	C₅₉×#390	C₂²	1	2	yes	—
81	C₅₉×#390	C₂²	1	2	yes	—
82	C₅₉×#390	C₂²	1	2	yes	—
83	C₅₉×#390	C₂²	1	2	yes	—
84	C₅₉×#389	C₂²	1	1	yes	characteristic
85	C₅₉×#389	C₂²	1	1	yes	characteristic
86	C₅₉×#389	C₂²	1	2	yes	—
87	C₅₉×#388	C₂²	1	2	yes	—
88	C₅₉×#388	C₂²	1	2	yes	—
89	C₅₉×#388	C₂²	1	2	yes	—
90	C₅₉×#388	C₂²	1	2	yes	—
91	C₅₉×#388	C₂²	1	1	yes	characteristic
92	C₅₉×#388	C₂²	1	1	yes	characteristic
93	C₅₉×#388	C₂²	1	2	yes	—
94	C₅₉×#388	C₂²	1	2	yes	—
95	C₅₉×#388	C₂²	1	2	yes	—
96	C₅₉×#388	C₂²	1	2	yes	—
97	C₅₉×#387	C₂²	1	1	yes	characteristic
98	C₅₉×#387	C₂²	1	1	yes	characteristic
99	C₅₉×#386	C₂²	1	1	yes	characteristic
100	C₅₉×#386	C₂²	1	2	yes	—
101	C₅₉×#386	C₂²	1	2	yes	—
102	C₅₉×#386	C₂²	1	2	yes	—
103	C₅₉×#386	C₂²	1	1	yes	characteristic
104	C₅₉×#386	C₂²	1	2	yes	—
105	C₅₉×#386	C₂²	1	2	yes	—
106	C₅₉×#386	C₂²	1	2	yes	—
107	C₅₉×#385	C₂²	1	1	yes	characteristic
108	C₅₉×#385	C₂²	1	1	yes	characteristic
109	C₅₉×#385	C₂²	1	2	yes	—
110	C₅₉×#382	C₂²	1	1	yes	characteristic
111	C₅₉×#380	C₂²	1	1	yes	characteristic
112	C₅₉×#380	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
116	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
117	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
118	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
119	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
122	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
123	C₅₉×#376	C₂²	1	1	yes	characteristic
124	C₅₉×#376	C₂²	1	2	yes	—
125	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
126	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
127	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
128	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
131	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
132	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
133	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
134	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
135	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
136	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
140	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
142	C₄⋊Q₈×C₅₉	—	2	4	no	—
143	#127×C₅₉	—	2	4	no	—
144	#127×C₅₉	—	4	4	no	—
145	#126×C₅₉	—	2	8	no	—
146	#126×C₅₉	—	2	8	no	—
147	#125×C₅₉	—	2	4	no	—
148	#124×C₅₉	—	2	4	no	—
149	#124×C₅₉	—	2	4	no	—
150	#124×C₅₉	—	2	8	no	—
151	#124×C₅₉	—	4	4	no	—
152	#123×C₅₉	—	2	8	no	—
153	#123×C₅₉	—	2	8	no	—
154	C₂²⋊Q₈×C₅₉	—	2	4	no	—
155	C₂²⋊Q₈×C₅₉	—	2	4	no	—
156	C₂²⋊Q₈×C₅₉	—	2	8	no	—
157	#121×C₅₉	—	2	4	no	—
158	#121×C₅₉	—	2	4	no	—
159	#121×C₅₉	—	2	4	no	—
160	#121×C₅₉	—	2	4	no	—
161	C₄×Q₈×C₅₉	—	2	4	no	—
162	C₄×Q₈×C₅₉	—	2	4	no	—
163	C₄×Q₈×C₅₉	D₄	1	8	yes	complemented
164	C₄×D₄×C₅₉	—	2	4	no	—
165	C₄×D₄×C₅₉	—	2	8	no	—
166	C₄×D₄×C₅₉	—	2	4	no	—
167	C₄×D₄×C₅₉	—	2	4	no	—
168	C₄×D₄×C₅₉	—	4	4	no	—
169	#117×C₅₉	—	2	8	no	—
170	#117×C₅₉	—	2	4	no	—
171	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
184	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
189	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
191	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
192	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
195	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
197	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
217	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
219	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
221	C₂×C₄²×C₅₉	—	2	4	no	—
222	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
224	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
225	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
230	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
231	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
232	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
234	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
235	#95×C₅₉	C₂³	1	1	yes	characteristic
236	#95×C₅₉	C₂³	1	2	yes	—
237	#95×C₅₉	C₂³	1	1	yes	characteristic
238	#95×C₅₉	C₂³	1	1	yes	characteristic
239	#95×C₅₉	C₂³	1	1	yes	characteristic
240	#95×C₅₉	C₂³	1	2	yes	—
241	#95×C₅₉	C₂³	1	2	yes	—
242	#95×C₅₉	C₂³	1	2	yes	—
243	#95×C₅₉	C₂³	1	1	yes	characteristic
244	#95×C₅₉	C₂³	1	1	yes	characteristic
245	#95×C₅₉	C₂³	1	2	yes	—
246	#95×C₅₉	C₂³	1	1	yes	characteristic
247	#95×C₅₉	C₂³	1	1	yes	characteristic
248	#95×C₅₉	C₂³	1	1	yes	characteristic
249	#95×C₅₉	C₂³	1	1	yes	characteristic
250	#95×C₅₉	C₂³	1	2	yes	—
251	#95×C₅₉	C₂³	1	2	yes	—
252	#95×C₅₉	C₂³	1	2	yes	—
253	#95×C₅₉	C₂³	1	2	yes	—
254	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
255	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
256	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
257	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
258	C₂×Q₈×C₅₉	—	2	4	no	—
259	C₂×Q₈×C₅₉	—	2	2	no	—
260	C₂×Q₈×C₅₉	—	2	2	no	—
261	C₂×Q₈×C₅₉	—	4	2	no	—
262	C₂×Q₈×C₅₉	—	4	2	no	—
263	C₂×Q₈×C₅₉	C₂×D₄	1	4	yes	—
264	C₂×D₄×C₅₉	—	2	4	no	—
265	C₂×D₄×C₅₉	—	2	4	no	—
266	C₂×D₄×C₅₉	—	2	2	no	—
267	C₂×D₄×C₅₉	—	2	4	no	—
268	C₂×D₄×C₅₉	—	2	2	no	—
269	C₂×D₄×C₅₉	—	2	2	no	—
270	C₂×D₄×C₅₉	—	2	4	no	—
271	C₂×D₄×C₅₉	—	2	2	no	—
272	C₂×D₄×C₅₉	—	2	4	no	—
273	C₂×D₄×C₅₉	—	2	2	no	—
274	C₂×D₄×C₅₉	—	2	2	no	—
275	C₂×D₄×C₅₉	—	2	2	no	—
276	C₂×D₄×C₅₉	—	2	2	no	—
277	C₂×D₄×C₅₉	—	2	4	no	—
278	C₂×D₄×C₅₉	—	2	4	no	—
279	C₂×D₄×C₅₉	—	2	4	no	—
280	C₂×D₄×C₅₉	—	4	2	no	—
281	C₂×D₄×C₅₉	—	4	1	no	—
282	C₂×D₄×C₅₉	—	4	2	no	—
283	C₂×D₄×C₅₉	—	4	2	no	—
284	C₂×D₄×C₅₉	—	4	2	no	—
285	C₂×D₄×C₅₉	—	4	2	no	—
286	C₂×D₄×C₅₉	—	4	2	no	—
287	C₂×D₄×C₅₉	—	4	2	no	—
288	C₂×D₄×C₅₉	—	4	2	no	—
289	C₂×D₄×C₅₉	—	4	2	no	—
290	C₂×D₄×C₅₉	—	4	2	no	—
291	C₂²×C₄×C₅₉	—	2	2	no	—
292	C₂²×C₄×C₅₉	—	2	2	no	—
293	C₂²×C₄×C₅₉	—	2	2	no	—
294	C₂²×C₄×C₅₉	—	2	2	no	—
295	C₂²×C₄×C₅₉	—	2	4	no	—
296	C₂²×C₄×C₅₉	—	2	2	no	—
297	C₂²×C₄×C₅₉	—	2	2	no	—
298	C₂²×C₄×C₅₉	—	2	2	no	—
299	C₂²×C₄×C₅₉	—	2	2	no	—
300	C₂²×C₄×C₅₉	—	2	2	no	—
301	C₂²×C₄×C₅₉	—	2	4	no	—
302	C₂²×C₄×C₅₉	—	4	1	no	—
303	C₂²×C₄×C₅₉	—	4	2	no	—
304	C₂²×C₄×C₅₉	—	4	1	no	—
305	C₂²×C₄×C₅₉	—	4	1	no	—
306	C₂²×C₄×C₅₉	—	4	2	no	—
307	C₂²×C₄×C₅₉	—	4	2	no	—
308	C₂²×C₄×C₅₉	—	4	2	no	—
309	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
324	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
327	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
328	C₄⋊C₄×C₅₉	—	2	2	no	—
329	C₄⋊C₄×C₅₉	—	2	4	no	—
330	C₄⋊C₄×C₅₉	—	2	4	no	—
331	C₄⋊C₄×C₅₉	—	2	2	no	—
332	C₄⋊C₄×C₅₉	—	2	2	no	—
333	C₄⋊C₄×C₅₉	—	2	2	no	—
334	C₄⋊C₄×C₅₉	—	2	4	no	—
335	C₄⋊C₄×C₅₉	—	2	4	no	—
336	C₄⋊C₄×C₅₉	—	2	4	no	—
337	C₄⋊C₄×C₅₉	—	2	2	no	—
338	C₄⋊C₄×C₅₉	—	2	4	no	—
339	C₄⋊C₄×C₅₉	—	2	4	no	—
340	C₄⋊C₄×C₅₉	—	2	2	no	—
341	C₄⋊C₄×C₅₉	—	4	1	no	—
342	C₄⋊C₄×C₅₉	—	4	2	no	—
343	C₄⋊C₄×C₅₉	—	4	1	no	—
344	C₄⋊C₄×C₅₉	—	4	2	no	—
345	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
346	C₄⋊C₄×C₅₉	C₂×D₄	1	8	yes	—
347	C₄⋊C₄×C₅₉	#41	1	4	yes	—
348	C₂²⋊C₄×C₅₉	—	2	4	no	—
349	C₂²⋊C₄×C₅₉	—	2	2	no	—
350	C₂²⋊C₄×C₅₉	—	2	4	no	—
351	C₂²⋊C₄×C₅₉	—	2	2	no	—
352	C₂²⋊C₄×C₅₉	—	2	4	no	—
353	C₂²⋊C₄×C₅₉	—	2	2	no	—
354	C₂²⋊C₄×C₅₉	—	2	4	no	—
355	C₂²⋊C₄×C₅₉	—	2	4	no	—
356	C₂²⋊C₄×C₅₉	—	2	4	no	—
357	C₂²⋊C₄×C₅₉	—	2	4	no	—
358	C₂²⋊C₄×C₅₉	—	2	4	no	—
359	C₂²⋊C₄×C₅₉	—	2	4	no	—
360	C₂²⋊C₄×C₅₉	—	2	4	no	—
361	C₂²⋊C₄×C₅₉	—	2	4	no	—
362	C₂²⋊C₄×C₅₉	—	2	2	no	—
363	C₂²⋊C₄×C₅₉	—	2	2	no	—
364	C₂²⋊C₄×C₅₉	—	2	4	no	—
365	C₂²⋊C₄×C₅₉	—	2	4	no	—
366	C₂²⋊C₄×C₅₉	—	4	1	no	—
367	C₂²⋊C₄×C₅₉	—	4	2	no	—
368	C₂²⋊C₄×C₅₉	—	4	2	no	—
369	C₂²⋊C₄×C₅₉	—	4	2	no	—
370	C₂²⋊C₄×C₅₉	—	4	2	no	—
371	C₂²⋊C₄×C₅₉	—	4	1	no	—
372	C₂²⋊C₄×C₅₉	—	4	1	no	—
373	C₂²⋊C₄×C₅₉	—	4	2	no	—
374	C₂²⋊C₄×C₅₉	—	4	2	no	—
375	C₂²⋊C₄×C₅₉	—	4	2	no	—
376	C₂²⋊C₄×C₅₉	—	4	2	no	—
377	C₂²⋊C₄×C₅₉	—	4	2	no	—
378	C₄²×C₅₉	—	2	2	no	—
379	C₄²×C₅₉	—	2	2	no	—
380	C₄²×C₅₉	—	2	2	no	—
381	C₄²×C₅₉	—	2	2	no	—
382	C₄²×C₅₉	—	2	4	no	—
383	C₄²×C₅₉	—	2	4	no	—
384	C₄²×C₅₉	—	2	2	no	—
385	C₄²×C₅₉	—	4	2	no	—
386	C₄²×C₅₉	—	4	2	no	—
387	C₄²×C₅₉	—	4	2	no	—
388	C₄²×C₅₉	C₂×D₄	1	4	yes	—
389	C₄²×C₅₉	C₂×D₄	1	8	yes	—
390	C₄²×C₅₉	#41	1	4	yes	—
391	C₂³×C₅₉	—	2	1	no	—
392	C₂³×C₅₉	—	2	1	no	—
393	C₂³×C₅₉	—	2	1	no	—
394	C₂³×C₅₉	—	2	1	no	—
395	C₂³×C₅₉	—	2	1	no	—
396	C₂³×C₅₉	—	2	1	no	—
397	C₂³×C₅₉	—	2	1	no	—
398	C₂³×C₅₉	—	2	2	no	—
399	C₂³×C₅₉	—	2	2	no	—
400	C₂³×C₅₉	—	2	1	no	—
401	C₂³×C₅₉	—	2	2	no	—
402	C₂³×C₅₉	—	2	2	no	—
403	C₂³×C₅₉	—	2	1	no	—
404	C₂³×C₅₉	—	2	2	no	—
405	C₂³×C₅₉	—	2	2	no	—
406	C₂³×C₅₉	—	2	2	no	—
407	C₂³×C₅₉	—	2	2	no	—
408	C₂³×C₅₉	—	2	1	no	—
409	C₂³×C₅₉	—	2	1	no	—
410	C₂³×C₅₉	—	2	2	no	—
411	C₂³×C₅₉	—	2	2	no	—
412	C₂³×C₅₉	—	2	2	no	—
413	C₂³×C₅₉	—	2	1	no	—
414	C₂³×C₅₉	—	2	2	no	—
415	C₂³×C₅₉	—	2	1	no	—
416	C₂³×C₅₉	—	2	2	no	—
417	C₂³×C₅₉	—	2	2	no	—
418	C₂³×C₅₉	H(5,𝔽₂)	1	2	yes	—
419	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
420	Q₈×C₅₉	—	2	8	no	—
421	Q₈×C₅₉	—	8	4	no	—
422	D₄×C₅₉	—	4	8	no	—
423	D₄×C₅₉	—	4	4	no	—
424	D₄×C₅₉	—	4	8	no	—
425	D₄×C₅₉	—	4	4	no	—
426	D₄×C₅₉	—	4	4	no	—
427	D₄×C₅₉	—	8	4	no	—
428	D₄×C₅₉	—	8	4	no	—
429	D₄×C₅₉	—	8	4	no	—
430	D₄×C₅₉	—	8	4	no	—
431	C₂×C₄×C₅₉	—	2	2	no	—
432	C₂×C₄×C₅₉	—	2	2	no	—
433	C₂×C₄×C₅₉	—	2	2	no	—
434	C₂×C₄×C₅₉	—	2	1	no	—
435	C₂×C₄×C₅₉	—	2	1	no	—
436	C₂×C₄×C₅₉	—	2	2	no	—
437	C₂×C₄×C₅₉	—	2	1	no	—
438	C₂×C₄×C₅₉	—	2	1	no	—
439	C₂×C₄×C₅₉	—	2	2	no	—
440	C₂×C₄×C₅₉	—	2	1	no	—
441	C₂×C₄×C₅₉	—	2	1	no	—
442	C₂×C₄×C₅₉	—	2	1	no	—
443	C₂×C₄×C₅₉	—	2	1	no	—
444	C₂×C₄×C₅₉	—	2	2	no	—
445	C₂×C₄×C₅₉	—	2	1	no	—
446	C₂×C₄×C₅₉	—	2	1	no	—
447	C₂×C₄×C₅₉	—	2	1	no	—
448	C₂×C₄×C₅₉	—	2	1	no	—
449	C₂×C₄×C₅₉	—	2	1	no	—
450	C₂×C₄×C₅₉	—	2	1	no	—
451	C₂×C₄×C₅₉	—	2	2	no	—
452	C₂×C₄×C₅₉	—	2	2	no	—
453	C₂×C₄×C₅₉	—	2	1	no	—
454	C₂×C₄×C₅₉	—	2	2	no	—
455	C₂×C₄×C₅₉	—	2	1	no	—
456	C₂×C₄×C₅₉	—	2	1	no	—
457	C₂×C₄×C₅₉	—	2	1	no	—
458	C₂×C₄×C₅₉	—	2	1	no	—
459	C₂×C₄×C₅₉	—	2	1	no	—
460	C₂×C₄×C₅₉	—	2	2	no	—
461	C₂×C₄×C₅₉	—	2	1	no	—
462	C₂×C₄×C₅₉	—	2	1	no	—
463	C₂×C₄×C₅₉	—	2	2	no	—
464	C₂×C₄×C₅₉	—	2	1	no	—
465	C₂×C₄×C₅₉	—	2	1	no	—
466	C₂×C₄×C₅₉	—	2	2	no	—
467	C₂×C₄×C₅₉	—	2	1	no	—
468	C₂×C₄×C₅₉	—	2	1	no	—
469	C₂×C₄×C₅₉	—	2	1	no	—
470	C₂×C₄×C₅₉	—	2	1	no	—
471	C₂×C₄×C₅₉	—	2	2	no	—
472	C₂×C₄×C₅₉	—	2	1	no	—
473	C₂×C₄×C₅₉	—	2	2	no	—
474	C₂×C₄×C₅₉	—	2	1	no	—
475	C₂×C₄×C₅₉	—	2	2	no	—
476	C₂×C₄×C₅₉	—	2	1	no	—
477	C₂×C₄×C₅₉	—	2	1	no	—
478	C₂×C₄×C₅₉	—	4	4	no	—
479	C₂×C₄×C₅₉	—	4	4	no	—
480	C₂×C₄×C₅₉	—	4	8	no	—
481	C₂×C₄×C₅₉	—	4	4	no	—
482	C₂×C₄×C₅₉	—	4	4	no	—
483	C₂×C₄×C₅₉	—	8	4	no	—
484	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
485	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
486	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
487	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
488	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
489	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
490	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
491	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
492	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
493	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
494	#35572	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
495	C₂²×C₅₉	—	2	2	no	—
496	C₂²×C₅₉	—	2	2	no	—
497	C₂²×C₅₉	—	2	2	no	—
498	C₂²×C₅₉	—	4	1	no	—
499	C₂²×C₅₉	—	4	1	no	—
500	C₂²×C₅₉	—	4	1	no	—
501	C₂²×C₅₉	—	4	1	no	—
502	C₂²×C₅₉	—	4	1	no	—
503	C₂²×C₅₉	—	4	2	no	—
504	C₂²×C₅₉	—	4	2	no	—
505	C₂²×C₅₉	—	4	2	no	—
506	C₂²×C₅₉	—	4	1	no	—
507	C₂²×C₅₉	—	4	2	no	—
508	C₂²×C₅₉	—	4	2	no	—
509	C₂²×C₅₉	—	4	2	no	—
510	C₂²×C₅₉	—	4	1	no	—
511	C₂²×C₅₉	—	4	1	no	—
512	C₂²×C₅₉	—	4	2	no	—
513	C₂²×C₅₉	—	4	2	no	—
514	C₂²×C₅₉	—	4	2	no	—
515	C₂²×C₅₉	—	4	2	no	—
516	C₂²×C₅₉	—	4	1	no	—
517	C₂²×C₅₉	—	4	2	no	—
518	C₂²×C₅₉	—	4	1	no	—
519	C₂²×C₅₉	—	4	2	no	—
520	C₂²×C₅₉	—	4	2	no	—
521	C₂²×C₅₉	—	4	2	no	—
522	C₂²×C₅₉	—	4	1	no	—
523	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
524	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
525	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
526	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
527	C₂²×C₅₉	#585	1	1	yes	characteristic
528	C₂²×C₅₉	#585	1	1	yes	characteristic
529	C₂²×C₅₉	#585	1	1	yes	characteristic
530	C₄×C₅₉	—	2	4	no	—
531	C₄×C₅₉	—	2	2	no	—
532	C₄×C₅₉	—	2	2	no	—
533	C₄×C₅₉	—	2	4	no	—
534	C₄×C₅₉	—	2	2	no	—
535	C₄×C₅₉	—	2	2	no	—
536	C₄×C₅₉	—	2	4	no	—
537	C₄×C₅₉	—	4	1	no	—
538	C₄×C₅₉	—	4	1	no	—
539	C₄×C₅₉	—	4	1	no	—
540	C₄×C₅₉	—	4	1	no	—
541	C₄×C₅₉	—	4	2	no	—
542	C₄×C₅₉	—	4	1	no	—
543	C₄×C₅₉	—	4	2	no	—
544	C₄×C₅₉	—	4	1	no	—
545	C₄×C₅₉	—	4	2	no	—
546	C₄×C₅₉	—	4	1	no	—
547	C₄×C₅₉	—	4	1	no	—
548	C₄×C₅₉	#532	1	4	yes	—
549	C₂×#542	C₂×C₅₉	1	1	yes	characteristic, complemented
550	C₂×#529	C₂×C₅₉	1	1	yes	characteristic, complemented
551	#2610	C₂×C₅₉	1	2	yes	complemented
552	#2603	C₂×C₅₉	1	2	yes	complemented
553	#2601	C₂×C₅₉	1	2	yes	complemented
554	#2560	C₂×C₅₉	1	2	yes	complemented
555	#2554	C₂×C₅₉	1	2	yes	complemented
556	#2550	C₂×C₅₉	1	1	yes	characteristic, complemented
557	#2548	C₂×C₅₉	1	1	yes	characteristic, complemented
558	#2544	C₂×C₅₉	1	2	yes	complemented
559	#2541	C₂×C₅₉	1	1	yes	characteristic
560	#2536	C₂×C₅₉	1	1	yes	characteristic, complemented
561	#2491	C₂×C₅₉	1	1	yes	characteristic, complemented
562	#2490	C₂×C₅₉	1	1	yes	characteristic, complemented
563	#2461	C₂×C₅₉	1	2	yes	complemented
564	#2445	C₂×C₅₉	1	2	yes	complemented
565	#2426	C₂×C₅₉	1	1	yes	characteristic, complemented
566	#2426	C₂×C₅₉	1	1	yes	characteristic, complemented
567	#2328	C₂×C₅₉	1	1	yes	characteristic, complemented
568	#2324	C₂×C₅₉	1	1	yes	characteristic, complemented
569	C₄×#121	C₂×C₅₉	1	1	yes	characteristic, complemented
570	#2290	C₂×C₅₉	1	1	yes	characteristic, complemented
571	#2276	C₂×C₅₉	1	1	yes	characteristic, complemented
572	C₂×C₅₉	—	4	2	no	—
573	C₂×C₅₉	—	8	1	no	—
574	C₂×C₅₉	—	8	2	no	—
575	C₂×C₅₉	—	8	2	no	—
576	C₂×C₅₉	C₂×#532	1	1	yes	characteristic
577	C₂×C₅₉	#3487	1	1	yes	characteristic
578	C₂×C₅₉	#3488	1	1	yes	characteristic
579	C₂×C₅₉	#3494	1	1	yes	characteristic
580	C₂×C₅₉	#3510	1	1	yes	characteristic
581	C₂×C₅₉	#3513	1	1	yes	characteristic
582	C₂×C₅₉	#3524	1	1	yes	characteristic
583	#542	—	2	8	no	—
584	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
585	C₂×#127	C₂²×C₅₉	1	1	yes	characteristic
586	C₂×#127	C₂²×C₅₉	1	2	yes	—
587	#529	—	2	8	no	—
588	C₂×#126	C₂²×C₅₉	1	2	yes	—
589	C₂×#126	C₂²×C₅₉	1	2	yes	—
590	C₂×#125	C₂²×C₅₉	1	1	yes	characteristic
591	C₂×#124	C₂²×C₅₉	1	2	yes	—
592	C₂×#124	C₂²×C₅₉	1	1	yes	characteristic
593	C₂×#124	C₂²×C₅₉	1	1	yes	characteristic
594	C₂×#124	C₂²×C₅₉	1	2	yes	—
595	C₂×#123	C₂²×C₅₉	1	2	yes	—
596	C₂×#123	C₂²×C₅₉	1	2	yes	—
597	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	—
598	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
599	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
600	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
601	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
602	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
603	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
604	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
605	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
606	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
607	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
608	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
609	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
610	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
611	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
612	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
613	C₂×#117	C₂²×C₅₉	1	2	yes	—
614	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
615	#398	C₂²×C₅₉	1	2	yes	—
616	#398	C₂²×C₅₉	1	2	yes	—
617	#397	C₂²×C₅₉	1	2	yes	—
618	#396	C₂²×C₅₉	1	2	yes	—
619	#396	C₂²×C₅₉	1	2	yes	—
620	#395	C₂²×C₅₉	1	2	yes	—
621	#394	C₂²×C₅₉	1	2	yes	—
622	#394	C₂²×C₅₉	1	2	yes	—
623	#394	C₂²×C₅₉	1	2	yes	—
624	#394	C₂²×C₅₉	1	2	yes	—
625	#394	C₂²×C₅₉	1	2	yes	—
626	#394	C₂²×C₅₉	1	2	yes	—
627	#394	C₂²×C₅₉	1	2	yes	—
628	#393	C₂²×C₅₉	1	2	yes	—
629	#392	C₂²×C₅₉	1	2	yes	—
630	#392	C₂²×C₅₉	1	2	yes	—
631	#391	C₂²×C₅₉	1	2	yes	—
632	#390	C₂²×C₅₉	1	2	yes	—
633	#390	C₂²×C₅₉	1	2	yes	—
634	#390	C₂²×C₅₉	1	1	yes	characteristic
635	#390	C₂²×C₅₉	1	1	yes	characteristic
636	#390	C₂²×C₅₉	1	1	yes	characteristic
637	#390	C₂²×C₅₉	1	2	yes	—
638	#390	C₂²×C₅₉	1	2	yes	—
639	#390	C₂²×C₅₉	1	2	yes	—
640	#390	C₂²×C₅₉	1	2	yes	—
641	#390	C₂²×C₅₉	1	2	yes	—
642	#390	C₂²×C₅₉	1	1	yes	characteristic
643	#389	C₂²×C₅₉	1	1	yes	characteristic
644	#389	C₂²×C₅₉	1	2	yes	—
645	#389	C₂²×C₅₉	1	1	yes	characteristic
646	#388	C₂²×C₅₉	1	2	yes	—
647	#388	C₂²×C₅₉	1	2	yes	—
648	#388	C₂²×C₅₉	1	2	yes	—
649	#388	C₂²×C₅₉	1	2	yes	—
650	#388	C₂²×C₅₉	1	2	yes	—
651	#388	C₂²×C₅₉	1	2	yes	—
652	#388	C₂²×C₅₉	1	2	yes	—
653	#388	C₂²×C₅₉	1	1	yes	characteristic
654	#388	C₂²×C₅₉	1	2	yes	—
655	#388	C₂²×C₅₉	1	1	yes	characteristic
656	#387	C₂²×C₅₉	1	1	yes	characteristic
657	#387	C₂²×C₅₉	1	1	yes	characteristic
658	#386	C₂²×C₅₉	1	2	yes	—
659	#386	C₂²×C₅₉	1	2	yes	—
660	#386	C₂²×C₅₉	1	2	yes	—
661	#386	C₂²×C₅₉	1	2	yes	—
662	#386	C₂²×C₅₉	1	2	yes	—
663	#386	C₂²×C₅₉	1	2	yes	—
664	#386	C₂²×C₅₉	1	1	yes	characteristic
665	#386	C₂²×C₅₉	1	1	yes	characteristic
666	#385	C₂²×C₅₉	1	2	yes	—
667	#385	C₂²×C₅₉	1	1	yes	characteristic
668	#385	C₂²×C₅₉	1	1	yes	characteristic
669	#382	C₂²×C₅₉	1	1	yes	characteristic
670	#380	C₂²×C₅₉	1	1	yes	characteristic
671	#380	C₂²×C₅₉	1	1	yes	characteristic
672	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
673	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
674	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
675	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
676	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
677	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
678	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
679	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
680	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
681	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
682	#376	C₂²×C₅₉	1	1	yes	characteristic
683	#376	C₂²×C₅₉	1	2	yes	—
684	C₅₉	#35572	1	1	yes	characteristic, direct product factor, Sylow
685	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
686	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
687	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
688	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
689	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
690	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
691	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
692	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
693	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
694	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
695	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
696	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
697	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
698	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
699	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
700	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
701	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
702	C₄⋊Q₈	—	2	4	no	—
703	#127	—	2	4	no	—
704	#127	—	4	4	no	—
705	#126	—	2	8	no	—
706	#126	—	2	8	no	—
707	#125	—	2	4	no	—
708	#124	—	2	4	no	—
709	#124	—	2	4	no	—
710	#124	—	2	8	no	—
711	#124	—	4	4	no	—
712	#123	—	2	8	no	—
713	#123	—	2	8	no	—
714	C₂²⋊Q₈	—	2	4	no	—
715	C₂²⋊Q₈	—	2	4	no	—
716	C₂²⋊Q₈	—	2	8	no	—
717	#121	—	2	4	no	—
718	#121	—	2	4	no	—
719	#121	—	2	4	no	—
720	#121	—	2	4	no	—
721	C₄×Q₈	—	2	4	no	—
722	C₄×Q₈	—	2	4	no	—
723	C₄×Q₈	D₄×C₅₉	1	8	yes	complemented
724	C₄×D₄	—	2	4	no	—
725	C₄×D₄	—	2	8	no	—
726	C₄×D₄	—	2	4	no	—
727	C₄×D₄	—	2	4	no	—
728	C₄×D₄	—	4	4	no	—
729	#117	—	2	8	no	—
730	#117	—	2	4	no	—
731	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
732	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
733	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
734	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
735	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
736	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
737	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
738	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
739	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
740	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
741	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
742	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
743	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
744	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
745	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
746	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
747	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
748	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
749	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
750	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
751	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
752	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
753	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
754	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
755	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
756	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
757	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
758	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
759	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
760	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
761	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
762	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
763	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
764	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
765	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
766	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
767	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
768	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
769	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
770	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
771	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
772	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
773	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
774	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
775	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
776	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
777	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
778	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
779	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
780	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
781	C₂×C₄²	—	2	4	no	—
782	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
783	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
784	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
785	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
786	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
787	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
788	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
789	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
790	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
791	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
792	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
793	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
794	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
795	#95	C₂³×C₅₉	1	1	yes	characteristic
796	#95	C₂³×C₅₉	1	2	yes	—
797	#95	C₂³×C₅₉	1	1	yes	characteristic
798	#95	C₂³×C₅₉	1	1	yes	characteristic
799	#95	C₂³×C₅₉	1	1	yes	characteristic
800	#95	C₂³×C₅₉	1	2	yes	—
801	#95	C₂³×C₅₉	1	2	yes	—
802	#95	C₂³×C₅₉	1	2	yes	—
803	#95	C₂³×C₅₉	1	1	yes	characteristic
804	#95	C₂³×C₅₉	1	1	yes	characteristic
805	#95	C₂³×C₅₉	1	2	yes	—
806	#95	C₂³×C₅₉	1	1	yes	characteristic
807	#95	C₂³×C₅₉	1	1	yes	characteristic
808	#95	C₂³×C₅₉	1	1	yes	characteristic
809	#95	C₂³×C₅₉	1	1	yes	characteristic
810	#95	C₂³×C₅₉	1	2	yes	—
811	#95	C₂³×C₅₉	1	2	yes	—
812	#95	C₂³×C₅₉	1	2	yes	—
813	#95	C₂³×C₅₉	1	2	yes	—
814	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
815	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
816	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
817	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
818	C₂×Q₈	—	2	4	no	—
819	C₂×Q₈	—	2	2	no	—
820	C₂×Q₈	—	2	2	no	—
821	C₂×Q₈	—	4	2	no	—
822	C₂×Q₈	—	4	2	no	—
823	C₂×Q₈	C₂×D₄×C₅₉	1	4	yes	—
824	C₂×D₄	—	2	4	no	—
825	C₂×D₄	—	2	4	no	—
826	C₂×D₄	—	2	2	no	—
827	C₂×D₄	—	2	4	no	—
828	C₂×D₄	—	2	2	no	—
829	C₂×D₄	—	2	2	no	—
830	C₂×D₄	—	2	4	no	—
831	C₂×D₄	—	2	2	no	—
832	C₂×D₄	—	2	4	no	—
833	C₂×D₄	—	2	2	no	—
834	C₂×D₄	—	2	2	no	—
835	C₂×D₄	—	2	2	no	—
836	C₂×D₄	—	2	2	no	—
837	C₂×D₄	—	2	4	no	—
838	C₂×D₄	—	2	4	no	—
839	C₂×D₄	—	2	4	no	—
840	C₂×D₄	—	4	2	no	—
841	C₂×D₄	—	4	1	no	—
842	C₂×D₄	—	4	2	no	—
843	C₂×D₄	—	4	2	no	—
844	C₂×D₄	—	4	2	no	—
845	C₂×D₄	—	4	2	no	—
846	C₂×D₄	—	4	2	no	—
847	C₂×D₄	—	4	2	no	—
848	C₂×D₄	—	4	2	no	—
849	C₂×D₄	—	4	2	no	—
850	C₂×D₄	—	4	2	no	—
851	C₂²×C₄	—	2	2	no	—
852	C₂²×C₄	—	2	2	no	—
853	C₂²×C₄	—	2	2	no	—
854	C₂²×C₄	—	2	2	no	—
855	C₂²×C₄	—	2	4	no	—
856	C₂²×C₄	—	2	2	no	—
857	C₂²×C₄	—	2	2	no	—
858	C₂²×C₄	—	2	2	no	—
859	C₂²×C₄	—	2	2	no	—
860	C₂²×C₄	—	2	2	no	—
861	C₂²×C₄	—	2	4	no	—
862	C₂²×C₄	—	4	1	no	—
863	C₂²×C₄	—	4	2	no	—
864	C₂²×C₄	—	4	1	no	—
865	C₂²×C₄	—	4	1	no	—
866	C₂²×C₄	—	4	2	no	—
867	C₂²×C₄	—	4	2	no	—
868	C₂²×C₄	—	4	2	no	—
869	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
870	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
871	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
872	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
873	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
874	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
875	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
876	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
877	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
878	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
879	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
880	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
881	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
882	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
883	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
884	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
885	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
886	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
887	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	4	no	—
890	C₄⋊C₄	—	2	4	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	4	no	—
895	C₄⋊C₄	—	2	4	no	—
896	C₄⋊C₄	—	2	4	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	4	no	—
899	C₄⋊C₄	—	2	4	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	4	2	no	—
902	C₄⋊C₄	—	4	1	no	—
903	C₄⋊C₄	—	4	2	no	—
904	C₄⋊C₄	—	4	1	no	—
905	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
906	C₄⋊C₄	C₂×D₄×C₅₉	1	8	yes	—
907	C₄⋊C₄	#41×C₅₉	1	4	yes	—
908	C₂²⋊C₄	—	2	4	no	—
909	C₂²⋊C₄	—	2	2	no	—
910	C₂²⋊C₄	—	2	4	no	—
911	C₂²⋊C₄	—	2	2	no	—
912	C₂²⋊C₄	—	2	4	no	—
913	C₂²⋊C₄	—	2	2	no	—
914	C₂²⋊C₄	—	2	4	no	—
915	C₂²⋊C₄	—	2	4	no	—
916	C₂²⋊C₄	—	2	4	no	—
917	C₂²⋊C₄	—	2	4	no	—
918	C₂²⋊C₄	—	2	4	no	—
919	C₂²⋊C₄	—	2	4	no	—
920	C₂²⋊C₄	—	2	4	no	—
921	C₂²⋊C₄	—	2	4	no	—
922	C₂²⋊C₄	—	2	2	no	—
923	C₂²⋊C₄	—	2	2	no	—
924	C₂²⋊C₄	—	2	4	no	—
925	C₂²⋊C₄	—	2	4	no	—
926	C₂²⋊C₄	—	4	2	no	—
927	C₂²⋊C₄	—	4	2	no	—
928	C₂²⋊C₄	—	4	2	no	—
929	C₂²⋊C₄	—	4	1	no	—
930	C₂²⋊C₄	—	4	2	no	—
931	C₂²⋊C₄	—	4	2	no	—
932	C₂²⋊C₄	—	4	2	no	—
933	C₂²⋊C₄	—	4	2	no	—
934	C₂²⋊C₄	—	4	1	no	—
935	C₂²⋊C₄	—	4	1	no	—
936	C₂²⋊C₄	—	4	2	no	—
937	C₂²⋊C₄	—	4	2	no	—
938	C₄²	—	2	2	no	—
939	C₄²	—	2	2	no	—
940	C₄²	—	2	2	no	—
941	C₄²	—	2	2	no	—
942	C₄²	—	2	4	no	—
943	C₄²	—	2	4	no	—
944	C₄²	—	2	2	no	—
945	C₄²	—	4	2	no	—
946	C₄²	—	4	2	no	—
947	C₄²	—	4	2	no	—
948	C₄²	C₂×D₄×C₅₉	1	4	yes	—
949	C₄²	C₂×D₄×C₅₉	1	8	yes	—
950	C₄²	#41×C₅₉	1	4	yes	—
951	C₂³	—	2	1	no	—
952	C₂³	—	2	1	no	—
953	C₂³	—	2	1	no	—
954	C₂³	—	2	1	no	—
955	C₂³	—	2	1	no	—
956	C₂³	—	2	1	no	—
957	C₂³	—	2	1	no	—
958	C₂³	—	2	2	no	—
959	C₂³	—	2	2	no	—
960	C₂³	—	2	1	no	—
961	C₂³	—	2	2	no	—
962	C₂³	—	2	2	no	—
963	C₂³	—	2	1	no	—
964	C₂³	—	2	2	no	—
965	C₂³	—	2	2	no	—
966	C₂³	—	2	2	no	—
967	C₂³	—	2	2	no	—
968	C₂³	—	2	1	no	—
969	C₂³	—	2	1	no	—
970	C₂³	—	2	2	no	—
971	C₂³	—	2	2	no	—
972	C₂³	—	2	2	no	—
973	C₂³	—	2	2	no	—
974	C₂³	—	2	1	no	—
975	C₂³	—	2	1	no	—
976	C₂³	—	2	2	no	—
977	C₂³	—	2	2	no	—
978	C₂³	H(5,𝔽₂)×C₅₉	1	2	yes	—
979	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
980	Q₈	—	2	8	no	—
981	Q₈	—	8	4	no	—
982	D₄	—	4	8	no	—
983	D₄	—	4	8	no	—
984	D₄	—	4	4	no	—
985	D₄	—	4	4	no	—
986	D₄	—	4	4	no	—
987	D₄	—	8	4	no	—
988	D₄	—	8	4	no	—
989	D₄	—	8	4	no	—
990	D₄	—	8	4	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	2	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	4	4	no	—
1039	C₂×C₄	—	4	4	no	—
1040	C₂×C₄	—	4	8	no	—
1041	C₂×C₄	—	4	4	no	—
1042	C₂×C₄	—	4	4	no	—
1043	C₂×C₄	—	8	4	no	—
1044	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1045	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1046	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
1047	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
1048	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1049	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
1050	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
1051	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
1052	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
1053	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
1054	C₂²	—	2	2	no	—
1055	C₂²	—	2	2	no	—
1056	C₂²	—	2	2	no	—
1057	C₂²	—	4	1	no	—
1058	C₂²	—	4	1	no	—
1059	C₂²	—	4	1	no	—
1060	C₂²	—	4	1	no	—
1061	C₂²	—	4	2	no	—
1062	C₂²	—	4	2	no	—
1063	C₂²	—	4	1	no	—
1064	C₂²	—	4	2	no	—
1065	C₂²	—	4	1	no	—
1066	C₂²	—	4	2	no	—
1067	C₂²	—	4	2	no	—
1068	C₂²	—	4	2	no	—
1069	C₂²	—	4	1	no	—
1070	C₂²	—	4	1	no	—
1071	C₂²	—	4	2	no	—
1072	C₂²	—	4	2	no	—
1073	C₂²	—	4	2	no	—
1074	C₂²	—	4	2	no	—
1075	C₂²	—	4	1	no	—
1076	C₂²	—	4	2	no	—
1077	C₂²	—	4	2	no	—
1078	C₂²	—	4	1	no	—
1079	C₂²	—	4	1	no	—
1080	C₂²	—	4	2	no	—
1081	C₂²	—	4	2	no	—
1082	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
1083	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
1084	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
1085	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
1086	C₂²	C₅₉×#585	1	1	yes	characteristic
1087	C₂²	C₅₉×#585	1	1	yes	characteristic
1088	C₂²	C₅₉×#585	1	1	yes	characteristic
1089	C₄	—	2	2	no	—
1090	C₄	—	2	4	no	—
1091	C₄	—	2	4	no	—
1092	C₄	—	2	2	no	—
1093	C₄	—	2	2	no	—
1094	C₄	—	2	4	no	—
1095	C₄	—	2	2	no	—
1096	C₄	—	4	1	no	—
1097	C₄	—	4	1	no	—
1098	C₄	—	4	1	no	—
1099	C₄	—	4	1	no	—
1100	C₄	—	4	1	no	—
1101	C₄	—	4	2	no	—
1102	C₄	—	4	1	no	—
1103	C₄	—	4	1	no	—
1104	C₄	—	4	2	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	2	no	—
1107	C₄	C₅₉×#532	1	4	yes	—
1108	C₂	—	4	2	no	—
1109	C₂	—	8	2	no	—
1110	C₂	—	8	2	no	—
1111	C₂	—	8	1	no	—
1112	C₂	C₂×C₅₉×#532	1	1	yes	characteristic
1113	C₂	C₅₉×#3487	1	1	yes	characteristic
1114	C₂	C₅₉×#3488	1	1	yes	characteristic
1115	C₂	C₅₉×#3494	1	1	yes	characteristic
1116	C₂	C₅₉×#3510	1	1	yes	characteristic
1117	C₂	C₅₉×#3513	1	1	yes	characteristic
1118	C₂	C₅₉×#3524	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₅₉×#2541	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₉×#542	C₂	semidirect
2. C₂×C₅₉×#529	C₂	semidirect
3. C₅₉×#2610	C₂	semidirect
4. C₅₉×#2603	C₂	semidirect
5. C₅₉×#2601	C₂	semidirect
6. C₅₉×#2560	C₂	semidirect
7. C₅₉×#2554	C₂	semidirect
8. C₅₉×#2550	C₂	semidirect
9. C₅₉×#2548	C₂	semidirect
10. C₅₉×#2544	C₂	semidirect
12. C₅₉×#2536	C₂	semidirect
13. C₅₉×#2491	C₂	semidirect
14. C₅₉×#2490	C₂	semidirect
15. C₅₉×#2461	C₂	semidirect
16. C₅₉×#2445	C₂	semidirect
17. C₅₉×#2426	C₂	semidirect
18. C₅₉×#2426	C₂	semidirect
19. C₅₉×#2328	C₂	semidirect
20. C₅₉×#2324	C₂	semidirect
21. C₄×#121×C₅₉	C₂	semidirect
22. C₅₉×#2290	C₂	semidirect
23. C₅₉×#2276	C₂	semidirect
163. C₄×Q₈×C₅₉	D₄	semidirect
494. #35572	C₅₉	direct (N × H)
549. C₂×#542	C₂×C₅₉	semidirect
550. C₂×#529	C₂×C₅₉	semidirect
551. #2610	C₂×C₅₉	semidirect
552. #2603	C₂×C₅₉	semidirect
553. #2601	C₂×C₅₉	semidirect
554. #2560	C₂×C₅₉	semidirect
555. #2554	C₂×C₅₉	semidirect
556. #2550	C₂×C₅₉	semidirect
557. #2548	C₂×C₅₉	semidirect
558. #2544	C₂×C₅₉	semidirect
560. #2536	C₂×C₅₉	semidirect
561. #2491	C₂×C₅₉	semidirect
562. #2490	C₂×C₅₉	semidirect
563. #2461	C₂×C₅₉	semidirect
564. #2445	C₂×C₅₉	semidirect
565. #2426	C₂×C₅₉	semidirect
566. #2426	C₂×C₅₉	semidirect
567. #2328	C₂×C₅₉	semidirect
568. #2324	C₂×C₅₉	semidirect
569. C₄×#121	C₂×C₅₉	semidirect
570. #2290	C₂×C₅₉	semidirect
571. #2276	C₂×C₅₉	semidirect
684. C₅₉	#35572	direct (N × H)
723. C₄×Q₈	D₄×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₉×#542	2
C₂×C₅₉×#529	2
C₅₉×#2610	2
C₅₉×#2603	2
C₅₉×#2601	2
C₅₉×#2560	2
C₅₉×#2554	2
C₅₉×#2550	2
C₅₉×#2548	2
C₅₉×#2544	2
C₅₉×#2541	2
C₅₉×#2536	2
C₅₉×#2491	2
C₅₉×#2490	2
C₅₉×#2461	2
C₅₉×#2445	2
C₅₉×#2426	2
C₅₉×#2328	2
C₅₉×#2324	2
C₄×#121×C₅₉	2
C₅₉×#2290	2
C₅₉×#2276	2
#35572	59

Subgroups — C59×#35572 #28447681

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35572 #28447681