Subgroups — C₅₉×#35830 #28447939

Order 15104.

2496 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#553	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#2662	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2619	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2601	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2557	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2555	C₂	1	2	yes	maximal, complemented
8	C₅₉×#2550	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#2544	C₂	1	2	yes	maximal, complemented
10	C₅₉×#2541	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2491	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#2490	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₉×#2464	C₂	1	2	yes	maximal, complemented
14	C₅₉×#2428	C₂	1	2	yes	maximal, complemented
15	C₅₉×#2416	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₉×#2416	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₉×#2392	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₉×#2392	C₂	1	2	yes	maximal, complemented
19	C₅₉×#2366	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₉×#2363	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₉×#2361	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₉×#2352	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₉×#2274	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₉×#555	—	2	8	no	—
25	C₅₉×#553	—	2	8	no	—
26	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
27	C₂×#127×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×#127×C₅₉	C₂²	1	2	yes	—
29	C₂×#126×C₅₉	C₂²	1	2	yes	—
30	C₂×#125×C₅₉	C₂²	1	1	yes	characteristic
31	C₂×#124×C₅₉	C₂²	1	2	yes	—
32	C₂×#124×C₅₉	C₂²	1	2	yes	—
33	C₂×#124×C₅₉	C₂²	1	2	yes	—
34	C₂×#123×C₅₉	C₂²	1	2	yes	—
35	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
36	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
37	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
38	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
39	C₂×#121×C₅₉	C₂²	1	2	yes	—
40	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
41	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
42	C₂×#121×C₅₉	C₂²	1	2	yes	—
43	C₂×#121×C₅₉	C₂²	1	2	yes	—
44	C₂×#121×C₅₉	C₂²	1	2	yes	—
45	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
47	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
50	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
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	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
56	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
57	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
58	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
59	C₅₉×#398	C₂²	1	2	yes	—
60	C₅₉×#398	C₂²	1	1	yes	characteristic
61	C₅₉×#397	C₂²	1	2	yes	—
62	C₅₉×#397	C₂²	1	1	yes	characteristic
63	C₅₉×#396	C₂²	1	2	yes	—
64	C₅₉×#396	C₂²	1	2	yes	—
65	C₅₉×#396	C₂²	1	1	yes	characteristic
66	C₅₉×#396	C₂²	1	1	yes	characteristic
67	C₅₉×#395	C₂²	1	2	yes	—
68	C₅₉×#394	C₂²	1	2	yes	—
69	C₅₉×#394	C₂²	1	2	yes	—
70	C₅₉×#394	C₂²	1	1	yes	characteristic
71	C₅₉×#394	C₂²	1	2	yes	—
72	C₅₉×#394	C₂²	1	2	yes	—
73	C₅₉×#394	C₂²	1	2	yes	—
74	C₅₉×#394	C₂²	1	1	yes	characteristic
75	C₅₉×#394	C₂²	1	2	yes	—
76	C₅₉×#394	C₂²	1	1	yes	characteristic
77	C₅₉×#393	C₂²	1	2	yes	—
78	C₅₉×#392	C₂²	1	2	yes	—
79	C₅₉×#392	C₂²	1	2	yes	—
80	C₅₉×#392	C₂²	1	2	yes	—
81	C₅₉×#392	C₂²	1	2	yes	—
82	C₅₉×#392	C₂²	1	1	yes	characteristic
83	C₅₉×#391	C₂²	1	2	yes	—
84	C₅₉×#390	C₂²	1	2	yes	—
85	C₅₉×#390	C₂²	1	1	yes	characteristic
86	C₅₉×#390	C₂²	1	1	yes	characteristic
87	C₅₉×#390	C₂²	1	1	yes	characteristic
88	C₅₉×#390	C₂²	1	1	yes	characteristic
89	C₅₉×#390	C₂²	1	2	yes	—
90	C₅₉×#390	C₂²	1	2	yes	—
91	C₅₉×#390	C₂²	1	2	yes	—
92	C₅₉×#389	C₂²	1	2	yes	—
93	C₅₉×#389	C₂²	1	1	yes	characteristic
94	C₅₉×#389	C₂²	1	1	yes	characteristic
95	C₅₉×#388	C₂²	1	2	yes	—
96	C₅₉×#388	C₂²	1	2	yes	—
97	C₅₉×#388	C₂²	1	2	yes	—
98	C₅₉×#388	C₂²	1	2	yes	—
99	C₅₉×#388	C₂²	1	2	yes	—
100	C₅₉×#387	C₂²	1	2	yes	—
101	C₅₉×#386	C₂²	1	2	yes	—
102	C₅₉×#386	C₂²	1	2	yes	—
103	C₅₉×#386	C₂²	1	2	yes	—
104	C₅₉×#386	C₂²	1	2	yes	—
105	C₅₉×#386	C₂²	1	2	yes	—
106	C₅₉×#386	C₂²	1	2	yes	—
107	C₅₉×#386	C₂²	1	2	yes	—
108	C₅₉×#385	C₂²	1	2	yes	—
109	C₅₉×#382	C₂²	1	1	yes	characteristic
110	C₅₉×#380	C₂²	1	1	yes	characteristic
111	C₅₉×#380	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
115	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
117	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
118	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
122	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
123	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
124	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
125	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
126	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
128	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
130	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
131	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
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	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
137	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
138	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
139	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
142	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
144	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
145	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
146	C₄⋊Q₈×C₅₉	—	2	4	no	—
147	#127×C₅₉	—	2	4	no	—
148	#127×C₅₉	—	4	4	no	—
149	#126×C₅₉	—	2	8	no	—
150	#125×C₅₉	—	2	4	no	—
151	#124×C₅₉	—	2	8	no	—
152	#124×C₅₉	—	2	8	no	—
153	#124×C₅₉	—	4	4	no	—
154	#123×C₅₉	—	2	8	no	—
155	#121×C₅₉	—	2	4	no	—
156	#121×C₅₉	—	2	4	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	#121×C₅₉	—	2	8	no	—
162	#121×C₅₉	—	2	8	no	—
163	#121×C₅₉	—	4	4	no	—
164	#121×C₅₉	—	4	4	no	—
165	C₄×D₄×C₅₉	—	2	4	no	—
166	C₄×D₄×C₅₉	—	2	4	no	—
167	C₄×D₄×C₅₉	—	2	4	no	—
168	C₄×D₄×C₅₉	—	2	4	no	—
169	C₄×D₄×C₅₉	—	2	8	no	—
170	C₄×D₄×C₅₉	—	2	4	no	—
171	C₄×D₄×C₅₉	—	4	4	no	—
172	C₄×D₄×C₅₉	—	4	4	no	—
173	#117×C₅₉	—	2	4	no	—
174	#117×C₅₉	—	2	8	no	—
175	#117×C₅₉	—	2	4	no	—
176	#117×C₅₉	D₄	1	8	yes	complemented
177	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
178	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
179	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
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	2	yes	—
191	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
192	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
193	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
194	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
195	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
197	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
198	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
202	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
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	2	yes	—
212	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
218	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
219	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
220	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
221	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
222	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
223	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
224	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
225	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
226	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
227	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
228	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
229	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
230	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
231	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
233	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
236	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
237	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
238	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
239	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
240	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
241	#95×C₅₉	C₂³	1	1	yes	characteristic
242	#95×C₅₉	C₂³	1	2	yes	—
243	#95×C₅₉	C₂³	1	2	yes	—
244	#95×C₅₉	C₂³	1	2	yes	—
245	#95×C₅₉	C₂³	1	2	yes	—
246	#95×C₅₉	C₂³	1	2	yes	—
247	#95×C₅₉	C₂³	1	2	yes	—
248	#95×C₅₉	C₂³	1	1	yes	characteristic
249	#95×C₅₉	C₂³	1	2	yes	—
250	#95×C₅₉	C₂³	1	1	yes	characteristic
251	#95×C₅₉	C₂³	1	1	yes	characteristic
252	#95×C₅₉	C₂³	1	1	yes	characteristic
253	#95×C₅₉	C₂³	1	1	yes	characteristic
254	#95×C₅₉	C₂³	1	2	yes	—
255	#95×C₅₉	C₂³	1	2	yes	—
256	#95×C₅₉	C₂³	1	2	yes	—
257	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
258	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
259	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
260	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
261	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
262	C₂×Q₈×C₅₉	—	2	4	no	—
263	C₂×Q₈×C₅₉	—	4	2	no	—
264	C₂×Q₈×C₅₉	—	4	2	no	—
265	C₂×D₄×C₅₉	—	2	2	no	—
266	C₂×D₄×C₅₉	—	2	2	no	—
267	C₂×D₄×C₅₉	—	2	2	no	—
268	C₂×D₄×C₅₉	—	2	4	no	—
269	C₂×D₄×C₅₉	—	2	4	no	—
270	C₂×D₄×C₅₉	—	2	2	no	—
271	C₂×D₄×C₅₉	—	2	4	no	—
272	C₂×D₄×C₅₉	—	2	4	no	—
273	C₂×D₄×C₅₉	—	2	4	no	—
274	C₂×D₄×C₅₉	—	2	2	no	—
275	C₂×D₄×C₅₉	—	2	2	no	—
276	C₂×D₄×C₅₉	—	2	4	no	—
277	C₂×D₄×C₅₉	—	2	2	no	—
278	C₂×D₄×C₅₉	—	2	4	no	—
279	C₂×D₄×C₅₉	—	2	2	no	—
280	C₂×D₄×C₅₉	—	2	2	no	—
281	C₂×D₄×C₅₉	—	2	4	no	—
282	C₂×D₄×C₅₉	—	2	2	no	—
283	C₂×D₄×C₅₉	—	2	2	no	—
284	C₂×D₄×C₅₉	—	2	4	no	—
285	C₂×D₄×C₅₉	—	2	4	no	—
286	C₂×D₄×C₅₉	—	2	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	1	no	—
291	C₂×D₄×C₅₉	—	4	1	no	—
292	C₂×D₄×C₅₉	—	4	2	no	—
293	C₂×D₄×C₅₉	—	4	1	no	—
294	C₂×D₄×C₅₉	—	4	2	no	—
295	C₂×D₄×C₅₉	—	4	2	no	—
296	C₂×D₄×C₅₉	—	4	2	no	—
297	C₂×D₄×C₅₉	—	4	2	no	—
298	C₂×D₄×C₅₉	—	4	2	no	—
299	C₂×D₄×C₅₉	—	4	2	no	—
300	C₂×D₄×C₅₉	—	4	2	no	—
301	C₂×D₄×C₅₉	—	4	2	no	—
302	C₂×D₄×C₅₉	—	4	2	no	—
303	C₂×D₄×C₅₉	—	4	2	no	—
304	C₂²×C₄×C₅₉	—	2	2	no	—
305	C₂²×C₄×C₅₉	—	2	2	no	—
306	C₂²×C₄×C₅₉	—	2	2	no	—
307	C₂²×C₄×C₅₉	—	2	4	no	—
308	C₂²×C₄×C₅₉	—	2	2	no	—
309	C₂²×C₄×C₅₉	—	2	2	no	—
310	C₂²×C₄×C₅₉	—	2	2	no	—
311	C₂²×C₄×C₅₉	—	2	2	no	—
312	C₂²×C₄×C₅₉	—	2	2	no	—
313	C₂²×C₄×C₅₉	—	2	4	no	—
314	C₂²×C₄×C₅₉	—	2	4	no	—
315	C₂²×C₄×C₅₉	—	2	4	no	—
316	C₂²×C₄×C₅₉	—	2	4	no	—
317	C₂²×C₄×C₅₉	—	4	2	no	—
318	C₂²×C₄×C₅₉	—	4	2	no	—
319	C₂²×C₄×C₅₉	—	4	2	no	—
320	C₂²×C₄×C₅₉	—	4	2	no	—
321	C₂²×C₄×C₅₉	—	4	2	no	—
322	C₂²×C₄×C₅₉	—	4	2	no	—
323	C₂²×C₄×C₅₉	—	4	2	no	—
324	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
325	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
329	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
332	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
334	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
336	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
337	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
341	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
343	C₄⋊C₄×C₅₉	—	2	2	no	—
344	C₄⋊C₄×C₅₉	—	2	4	no	—
345	C₄⋊C₄×C₅₉	—	2	2	no	—
346	C₄⋊C₄×C₅₉	—	2	4	no	—
347	C₄⋊C₄×C₅₉	—	2	2	no	—
348	C₄⋊C₄×C₅₉	—	2	4	no	—
349	C₄⋊C₄×C₅₉	—	2	2	no	—
350	C₄⋊C₄×C₅₉	—	2	4	no	—
351	C₄⋊C₄×C₅₉	—	2	4	no	—
352	C₄⋊C₄×C₅₉	—	2	2	no	—
353	C₄⋊C₄×C₅₉	—	2	2	no	—
354	C₄⋊C₄×C₅₉	—	2	2	no	—
355	C₄⋊C₄×C₅₉	—	2	2	no	—
356	C₄⋊C₄×C₅₉	—	2	2	no	—
357	C₄⋊C₄×C₅₉	—	2	4	no	—
358	C₄⋊C₄×C₅₉	—	4	1	no	—
359	C₄⋊C₄×C₅₉	—	4	2	no	—
360	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
361	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
362	C₄⋊C₄×C₅₉	#41	1	4	yes	—
363	C₂²⋊C₄×C₅₉	—	2	2	no	—
364	C₂²⋊C₄×C₅₉	—	2	2	no	—
365	C₂²⋊C₄×C₅₉	—	2	4	no	—
366	C₂²⋊C₄×C₅₉	—	2	2	no	—
367	C₂²⋊C₄×C₅₉	—	2	4	no	—
368	C₂²⋊C₄×C₅₉	—	2	4	no	—
369	C₂²⋊C₄×C₅₉	—	2	4	no	—
370	C₂²⋊C₄×C₅₉	—	2	2	no	—
371	C₂²⋊C₄×C₅₉	—	2	4	no	—
372	C₂²⋊C₄×C₅₉	—	2	4	no	—
373	C₂²⋊C₄×C₅₉	—	2	4	no	—
374	C₂²⋊C₄×C₅₉	—	2	2	no	—
375	C₂²⋊C₄×C₅₉	—	2	4	no	—
376	C₂²⋊C₄×C₅₉	—	2	2	no	—
377	C₂²⋊C₄×C₅₉	—	2	2	no	—
378	C₂²⋊C₄×C₅₉	—	2	2	no	—
379	C₂²⋊C₄×C₅₉	—	2	2	no	—
380	C₂²⋊C₄×C₅₉	—	2	4	no	—
381	C₂²⋊C₄×C₅₉	—	2	4	no	—
382	C₂²⋊C₄×C₅₉	—	2	2	no	—
383	C₂²⋊C₄×C₅₉	—	2	4	no	—
384	C₂²⋊C₄×C₅₉	—	4	1	no	—
385	C₂²⋊C₄×C₅₉	—	4	1	no	—
386	C₂²⋊C₄×C₅₉	—	4	2	no	—
387	C₂²⋊C₄×C₅₉	—	4	2	no	—
388	C₂²⋊C₄×C₅₉	—	4	2	no	—
389	C₂²⋊C₄×C₅₉	—	4	2	no	—
390	C₂²⋊C₄×C₅₉	—	4	2	no	—
391	C₂²⋊C₄×C₅₉	—	4	2	no	—
392	C₂²⋊C₄×C₅₉	—	4	2	no	—
393	C₂²⋊C₄×C₅₉	—	4	2	no	—
394	C₂²⋊C₄×C₅₉	C₂×D₄	1	8	yes	—
395	C₄²×C₅₉	—	2	4	no	—
396	C₄²×C₅₉	—	2	2	no	—
397	C₄²×C₅₉	—	2	2	no	—
398	C₄²×C₅₉	—	2	2	no	—
399	C₄²×C₅₉	—	4	2	no	—
400	C₄²×C₅₉	—	4	2	no	—
401	C₄²×C₅₉	—	4	2	no	—
402	C₄²×C₅₉	—	4	2	no	—
403	C₄²×C₅₉	C₂×D₄	1	8	yes	—
404	C₄²×C₅₉	#41	1	4	yes	—
405	C₂³×C₅₉	—	2	1	no	—
406	C₂³×C₅₉	—	2	1	no	—
407	C₂³×C₅₉	—	2	1	no	—
408	C₂³×C₅₉	—	2	1	no	—
409	C₂³×C₅₉	—	2	1	no	—
410	C₂³×C₅₉	—	2	1	no	—
411	C₂³×C₅₉	—	2	1	no	—
412	C₂³×C₅₉	—	2	1	no	—
413	C₂³×C₅₉	—	2	1	no	—
414	C₂³×C₅₉	—	2	1	no	—
415	C₂³×C₅₉	—	2	1	no	—
416	C₂³×C₅₉	—	2	1	no	—
417	C₂³×C₅₉	—	2	1	no	—
418	C₂³×C₅₉	—	2	2	no	—
419	C₂³×C₅₉	—	2	2	no	—
420	C₂³×C₅₉	—	2	1	no	—
421	C₂³×C₅₉	—	2	2	no	—
422	C₂³×C₅₉	—	2	2	no	—
423	C₂³×C₅₉	—	2	1	no	—
424	C₂³×C₅₉	—	2	2	no	—
425	C₂³×C₅₉	—	2	2	no	—
426	C₂³×C₅₉	—	2	2	no	—
427	C₂³×C₅₉	—	2	2	no	—
428	C₂³×C₅₉	—	2	2	no	—
429	C₂³×C₅₉	—	2	1	no	—
430	C₂³×C₅₉	—	2	2	no	—
431	C₂³×C₅₉	—	2	1	no	—
432	C₂³×C₅₉	—	2	2	no	—
433	C₂³×C₅₉	—	2	1	no	—
434	C₂³×C₅₉	—	2	2	no	—
435	C₂³×C₅₉	—	2	1	no	—
436	C₂³×C₅₉	—	2	2	no	—
437	C₂³×C₅₉	—	2	2	no	—
438	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
439	C₂³×C₅₉	H(5,𝔽₂)	1	2	yes	—
440	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
441	Q₈×C₅₉	—	8	4	no	—
442	D₄×C₅₉	—	4	4	no	—
443	D₄×C₅₉	—	4	8	no	—
444	D₄×C₅₉	—	4	4	no	—
445	D₄×C₅₉	—	4	8	no	—
446	D₄×C₅₉	—	4	8	no	—
447	D₄×C₅₉	—	4	4	no	—
448	D₄×C₅₉	—	4	4	no	—
449	D₄×C₅₉	—	4	4	no	—
450	D₄×C₅₉	—	8	4	no	—
451	D₄×C₅₉	—	8	4	no	—
452	D₄×C₅₉	—	8	4	no	—
453	D₄×C₅₉	—	8	4	no	—
454	D₄×C₅₉	—	8	4	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	2	no	—
460	C₂×C₄×C₅₉	—	2	1	no	—
461	C₂×C₄×C₅₉	—	2	2	no	—
462	C₂×C₄×C₅₉	—	2	2	no	—
463	C₂×C₄×C₅₉	—	2	2	no	—
464	C₂×C₄×C₅₉	—	2	1	no	—
465	C₂×C₄×C₅₉	—	2	2	no	—
466	C₂×C₄×C₅₉	—	2	1	no	—
467	C₂×C₄×C₅₉	—	2	1	no	—
468	C₂×C₄×C₅₉	—	2	2	no	—
469	C₂×C₄×C₅₉	—	2	8	no	—
470	C₂×C₄×C₅₉	—	2	1	no	—
471	C₂×C₄×C₅₉	—	2	1	no	—
472	C₂×C₄×C₅₉	—	2	1	no	—
473	C₂×C₄×C₅₉	—	2	1	no	—
474	C₂×C₄×C₅₉	—	2	2	no	—
475	C₂×C₄×C₅₉	—	2	1	no	—
476	C₂×C₄×C₅₉	—	2	2	no	—
477	C₂×C₄×C₅₉	—	2	1	no	—
478	C₂×C₄×C₅₉	—	2	1	no	—
479	C₂×C₄×C₅₉	—	2	1	no	—
480	C₂×C₄×C₅₉	—	2	1	no	—
481	C₂×C₄×C₅₉	—	2	1	no	—
482	C₂×C₄×C₅₉	—	2	1	no	—
483	C₂×C₄×C₅₉	—	2	2	no	—
484	C₂×C₄×C₅₉	—	2	1	no	—
485	C₂×C₄×C₅₉	—	2	1	no	—
486	C₂×C₄×C₅₉	—	2	2	no	—
487	C₂×C₄×C₅₉	—	2	2	no	—
488	C₂×C₄×C₅₉	—	2	1	no	—
489	C₂×C₄×C₅₉	—	2	2	no	—
490	C₂×C₄×C₅₉	—	2	1	no	—
491	C₂×C₄×C₅₉	—	2	2	no	—
492	C₂×C₄×C₅₉	—	2	1	no	—
493	C₂×C₄×C₅₉	—	2	1	no	—
494	C₂×C₄×C₅₉	—	2	1	no	—
495	C₂×C₄×C₅₉	—	2	1	no	—
496	C₂×C₄×C₅₉	—	2	1	no	—
497	C₂×C₄×C₅₉	—	2	2	no	—
498	C₂×C₄×C₅₉	—	2	2	no	—
499	C₂×C₄×C₅₉	—	2	1	no	—
500	C₂×C₄×C₅₉	—	4	8	no	—
501	C₂×C₄×C₅₉	—	4	4	no	—
502	C₂×C₄×C₅₉	—	4	4	no	—
503	C₂×C₄×C₅₉	—	8	4	no	—
504	C₂×C₄×C₅₉	—	8	4	no	—
505	C₂×C₄×C₅₉	—	8	4	no	—
506	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
507	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
508	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
509	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
510	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
511	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
512	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
513	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
514	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
515	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
516	#35830	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
517	C₂²×C₅₉	—	2	2	no	—
518	C₂²×C₅₉	—	2	2	no	—
519	C₂²×C₅₉	—	2	2	no	—
520	C₂²×C₅₉	—	2	2	no	—
521	C₂²×C₅₉	—	2	2	no	—
522	C₂²×C₅₉	—	2	2	no	—
523	C₂²×C₅₉	—	4	1	no	—
524	C₂²×C₅₉	—	4	1	no	—
525	C₂²×C₅₉	—	4	1	no	—
526	C₂²×C₅₉	—	4	1	no	—
527	C₂²×C₅₉	—	4	1	no	—
528	C₂²×C₅₉	—	4	1	no	—
529	C₂²×C₅₉	—	4	1	no	—
530	C₂²×C₅₉	—	4	1	no	—
531	C₂²×C₅₉	—	4	1	no	—
532	C₂²×C₅₉	—	4	2	no	—
533	C₂²×C₅₉	—	4	2	no	—
534	C₂²×C₅₉	—	4	2	no	—
535	C₂²×C₅₉	—	4	2	no	—
536	C₂²×C₅₉	—	4	1	no	—
537	C₂²×C₅₉	—	4	2	no	—
538	C₂²×C₅₉	—	4	1	no	—
539	C₂²×C₅₉	—	4	2	no	—
540	C₂²×C₅₉	—	4	1	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	1	no	—
546	C₂²×C₅₉	—	4	2	no	—
547	C₂²×C₅₉	—	4	1	no	—
548	C₂²×C₅₉	—	4	2	no	—
549	C₂²×C₅₉	—	4	2	no	—
550	C₂²×C₅₉	—	4	2	no	—
551	C₂²×C₅₉	—	4	1	no	—
552	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
553	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
554	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
555	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
556	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
557	C₂²×C₅₉	#585	1	1	yes	characteristic
558	C₂²×C₅₉	#585	1	1	yes	characteristic
559	C₄×C₅₉	—	2	2	no	—
560	C₄×C₅₉	—	2	2	no	—
561	C₄×C₅₉	—	2	4	no	—
562	C₄×C₅₉	—	2	4	no	—
563	C₄×C₅₉	—	2	2	no	—
564	C₄×C₅₉	—	2	2	no	—
565	C₄×C₅₉	—	2	4	no	—
566	C₄×C₅₉	—	4	1	no	—
567	C₄×C₅₉	—	4	1	no	—
568	C₄×C₅₉	—	4	1	no	—
569	C₄×C₅₉	—	4	2	no	—
570	C₄×C₅₉	—	4	1	no	—
571	C₄×C₅₉	—	4	2	no	—
572	C₄×C₅₉	—	4	1	no	—
573	C₄×C₅₉	—	4	1	no	—
574	C₄×C₅₉	—	4	1	no	—
575	C₄×C₅₉	—	4	2	no	—
576	C₄×C₅₉	#532	1	4	yes	—
577	C₂×#555	C₂×C₅₉	1	1	yes	characteristic, complemented
578	C₂×#553	C₂×C₅₉	1	1	yes	characteristic, complemented
579	#2662	C₂×C₅₉	1	2	yes	complemented
580	#2619	C₂×C₅₉	1	1	yes	characteristic, complemented
581	#2601	C₂×C₅₉	1	2	yes	complemented
582	#2557	C₂×C₅₉	1	2	yes	complemented
583	#2555	C₂×C₅₉	1	2	yes	complemented
584	#2550	C₂×C₅₉	1	1	yes	characteristic, complemented
585	#2544	C₂×C₅₉	1	2	yes	complemented
586	#2541	C₂×C₅₉	1	1	yes	characteristic, complemented
587	#2491	C₂×C₅₉	1	1	yes	characteristic, complemented
588	#2490	C₂×C₅₉	1	1	yes	characteristic, complemented
589	#2464	C₂×C₅₉	1	2	yes	complemented
590	#2428	C₂×C₅₉	1	2	yes	complemented
591	#2416	C₂×C₅₉	1	1	yes	characteristic, complemented
592	#2416	C₂×C₅₉	1	1	yes	characteristic, complemented
593	#2392	C₂×C₅₉	1	2	yes	complemented
594	#2392	C₂×C₅₉	1	1	yes	characteristic, complemented
595	#2366	C₂×C₅₉	1	1	yes	characteristic, complemented
596	#2363	C₂×C₅₉	1	1	yes	characteristic, complemented
597	#2361	C₂×C₅₉	1	1	yes	characteristic, complemented
598	#2352	C₂×C₅₉	1	1	yes	characteristic, complemented
599	#2274	C₂×C₅₉	1	1	yes	characteristic, complemented
600	C₂×C₅₉	—	4	2	no	—
601	C₂×C₅₉	—	4	2	no	—
602	C₂×C₅₉	—	8	1	no	—
603	C₂×C₅₉	—	8	2	no	—
604	C₂×C₅₉	—	8	2	no	—
605	C₂×C₅₉	C₂×#532	1	1	yes	characteristic
606	C₂×C₅₉	#3488	1	1	yes	characteristic
607	C₂×C₅₉	#3488	1	1	yes	characteristic
608	C₂×C₅₉	#3494	1	1	yes	characteristic
609	C₂×C₅₉	#3506	1	1	yes	characteristic
610	C₂×C₅₉	#3519	1	1	yes	characteristic
611	C₂×C₅₉	#3524	1	1	yes	characteristic
612	#555	—	2	8	no	—
613	#553	—	2	8	no	—
614	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
615	C₂×#127	C₂²×C₅₉	1	1	yes	characteristic
616	C₂×#127	C₂²×C₅₉	1	2	yes	—
617	C₂×#126	C₂²×C₅₉	1	2	yes	—
618	C₂×#125	C₂²×C₅₉	1	1	yes	characteristic
619	C₂×#124	C₂²×C₅₉	1	2	yes	—
620	C₂×#124	C₂²×C₅₉	1	2	yes	—
621	C₂×#124	C₂²×C₅₉	1	2	yes	—
622	C₂×#123	C₂²×C₅₉	1	2	yes	—
623	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
624	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
625	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
626	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
627	C₂×#121	C₂²×C₅₉	1	2	yes	—
628	C₂×#121	C₂²×C₅₉	1	2	yes	—
629	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
630	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
631	C₂×#121	C₂²×C₅₉	1	2	yes	—
632	C₂×#121	C₂²×C₅₉	1	2	yes	—
633	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
634	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
635	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
636	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
637	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
638	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
639	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
640	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
641	C₂×#117	C₂²×C₅₉	1	2	yes	—
642	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
643	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
644	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
645	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
646	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
647	#398	C₂²×C₅₉	1	1	yes	characteristic
648	#398	C₂²×C₅₉	1	2	yes	—
649	#397	C₂²×C₅₉	1	2	yes	—
650	#397	C₂²×C₅₉	1	1	yes	characteristic
651	#396	C₂²×C₅₉	1	2	yes	—
652	#396	C₂²×C₅₉	1	2	yes	—
653	#396	C₂²×C₅₉	1	1	yes	characteristic
654	#396	C₂²×C₅₉	1	1	yes	characteristic
655	#395	C₂²×C₅₉	1	2	yes	—
656	#394	C₂²×C₅₉	1	2	yes	—
657	#394	C₂²×C₅₉	1	2	yes	—
658	#394	C₂²×C₅₉	1	2	yes	—
659	#394	C₂²×C₅₉	1	2	yes	—
660	#394	C₂²×C₅₉	1	1	yes	characteristic
661	#394	C₂²×C₅₉	1	1	yes	characteristic
662	#394	C₂²×C₅₉	1	1	yes	characteristic
663	#394	C₂²×C₅₉	1	2	yes	—
664	#394	C₂²×C₅₉	1	2	yes	—
665	#393	C₂²×C₅₉	1	2	yes	—
666	#392	C₂²×C₅₉	1	2	yes	—
667	#392	C₂²×C₅₉	1	2	yes	—
668	#392	C₂²×C₅₉	1	1	yes	characteristic
669	#392	C₂²×C₅₉	1	2	yes	—
670	#392	C₂²×C₅₉	1	2	yes	—
671	#391	C₂²×C₅₉	1	2	yes	—
672	#390	C₂²×C₅₉	1	2	yes	—
673	#390	C₂²×C₅₉	1	1	yes	characteristic
674	#390	C₂²×C₅₉	1	1	yes	characteristic
675	#390	C₂²×C₅₉	1	2	yes	—
676	#390	C₂²×C₅₉	1	2	yes	—
677	#390	C₂²×C₅₉	1	1	yes	characteristic
678	#390	C₂²×C₅₉	1	1	yes	characteristic
679	#390	C₂²×C₅₉	1	2	yes	—
680	#389	C₂²×C₅₉	1	2	yes	—
681	#389	C₂²×C₅₉	1	1	yes	characteristic
682	#389	C₂²×C₅₉	1	1	yes	characteristic
683	#388	C₂²×C₅₉	1	2	yes	—
684	#388	C₂²×C₅₉	1	2	yes	—
685	#388	C₂²×C₅₉	1	2	yes	—
686	#388	C₂²×C₅₉	1	2	yes	—
687	#388	C₂²×C₅₉	1	2	yes	—
688	#387	C₂²×C₅₉	1	2	yes	—
689	#386	C₂²×C₅₉	1	2	yes	—
690	#386	C₂²×C₅₉	1	2	yes	—
691	#386	C₂²×C₅₉	1	2	yes	—
692	#386	C₂²×C₅₉	1	2	yes	—
693	#386	C₂²×C₅₉	1	2	yes	—
694	#386	C₂²×C₅₉	1	2	yes	—
695	#386	C₂²×C₅₉	1	2	yes	—
696	#385	C₂²×C₅₉	1	2	yes	—
697	#382	C₂²×C₅₉	1	1	yes	characteristic
698	#380	C₂²×C₅₉	1	1	yes	characteristic
699	#380	C₂²×C₅₉	1	1	yes	characteristic
700	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
701	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
702	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
703	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
704	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
705	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
706	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
707	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
708	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
709	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
710	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
711	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
712	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
713	C₅₉	#35830	1	1	yes	characteristic, direct product factor, Sylow
714	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
715	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
716	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
717	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
718	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
719	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
720	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
721	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
722	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
723	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
724	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
725	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
726	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
727	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
728	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
729	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
730	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
731	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
732	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
733	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
734	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
735	C₄⋊Q₈	—	2	4	no	—
736	#127	—	2	4	no	—
737	#127	—	4	4	no	—
738	#126	—	2	8	no	—
739	#125	—	2	4	no	—
740	#124	—	2	8	no	—
741	#124	—	2	8	no	—
742	#124	—	4	4	no	—
743	#123	—	2	8	no	—
744	#121	—	2	4	no	—
745	#121	—	2	4	no	—
746	#121	—	2	4	no	—
747	#121	—	2	4	no	—
748	#121	—	2	4	no	—
749	#121	—	2	4	no	—
750	#121	—	2	8	no	—
751	#121	—	2	8	no	—
752	#121	—	4	4	no	—
753	#121	—	4	4	no	—
754	C₄×D₄	—	2	4	no	—
755	C₄×D₄	—	2	4	no	—
756	C₄×D₄	—	2	4	no	—
757	C₄×D₄	—	2	4	no	—
758	C₄×D₄	—	2	8	no	—
759	C₄×D₄	—	2	4	no	—
760	C₄×D₄	—	4	4	no	—
761	C₄×D₄	—	4	4	no	—
762	#117	—	2	4	no	—
763	#117	—	2	8	no	—
764	#117	—	2	4	no	—
765	#117	D₄×C₅₉	1	8	yes	complemented
766	C₂×C₄⋊C₄	—	2	4	no	—
767	C₂×C₄⋊C₄	—	2	4	no	—
768	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
769	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
770	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
771	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
772	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
773	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
774	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
775	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
776	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
777	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
778	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
779	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
780	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
781	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
782	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
783	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
784	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
785	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
786	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
787	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
788	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
789	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
790	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
791	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
792	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
793	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
794	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
795	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
796	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
797	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
798	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
799	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
800	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
801	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
802	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
803	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
804	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
805	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
806	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
807	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
808	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
809	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
810	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
811	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
812	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
813	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
814	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
815	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
816	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
817	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
818	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
819	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
820	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
821	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
822	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
823	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
824	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
825	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
826	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
827	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
828	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
829	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
830	#95	C₂³×C₅₉	1	1	yes	characteristic
831	#95	C₂³×C₅₉	1	2	yes	—
832	#95	C₂³×C₅₉	1	2	yes	—
833	#95	C₂³×C₅₉	1	2	yes	—
834	#95	C₂³×C₅₉	1	2	yes	—
835	#95	C₂³×C₅₉	1	2	yes	—
836	#95	C₂³×C₅₉	1	2	yes	—
837	#95	C₂³×C₅₉	1	1	yes	characteristic
838	#95	C₂³×C₅₉	1	2	yes	—
839	#95	C₂³×C₅₉	1	1	yes	characteristic
840	#95	C₂³×C₅₉	1	1	yes	characteristic
841	#95	C₂³×C₅₉	1	1	yes	characteristic
842	#95	C₂³×C₅₉	1	1	yes	characteristic
843	#95	C₂³×C₅₉	1	2	yes	—
844	#95	C₂³×C₅₉	1	2	yes	—
845	#95	C₂³×C₅₉	1	2	yes	—
846	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
847	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
848	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
849	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
850	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
851	C₂×Q₈	—	2	4	no	—
852	C₂×Q₈	—	4	2	no	—
853	C₂×Q₈	—	4	2	no	—
854	C₂×D₄	—	2	2	no	—
855	C₂×D₄	—	2	2	no	—
856	C₂×D₄	—	2	2	no	—
857	C₂×D₄	—	2	4	no	—
858	C₂×D₄	—	2	4	no	—
859	C₂×D₄	—	2	2	no	—
860	C₂×D₄	—	2	4	no	—
861	C₂×D₄	—	2	4	no	—
862	C₂×D₄	—	2	4	no	—
863	C₂×D₄	—	2	2	no	—
864	C₂×D₄	—	2	2	no	—
865	C₂×D₄	—	2	4	no	—
866	C₂×D₄	—	2	2	no	—
867	C₂×D₄	—	2	4	no	—
868	C₂×D₄	—	2	2	no	—
869	C₂×D₄	—	2	2	no	—
870	C₂×D₄	—	2	4	no	—
871	C₂×D₄	—	2	2	no	—
872	C₂×D₄	—	2	2	no	—
873	C₂×D₄	—	2	4	no	—
874	C₂×D₄	—	2	4	no	—
875	C₂×D₄	—	2	2	no	—
876	C₂×D₄	—	4	2	no	—
877	C₂×D₄	—	4	2	no	—
878	C₂×D₄	—	4	2	no	—
879	C₂×D₄	—	4	1	no	—
880	C₂×D₄	—	4	1	no	—
881	C₂×D₄	—	4	2	no	—
882	C₂×D₄	—	4	1	no	—
883	C₂×D₄	—	4	2	no	—
884	C₂×D₄	—	4	2	no	—
885	C₂×D₄	—	4	2	no	—
886	C₂×D₄	—	4	2	no	—
887	C₂×D₄	—	4	2	no	—
888	C₂×D₄	—	4	2	no	—
889	C₂×D₄	—	4	2	no	—
890	C₂×D₄	—	4	2	no	—
891	C₂×D₄	—	4	2	no	—
892	C₂×D₄	—	4	2	no	—
893	C₂²×C₄	—	2	2	no	—
894	C₂²×C₄	—	2	2	no	—
895	C₂²×C₄	—	2	2	no	—
896	C₂²×C₄	—	2	4	no	—
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	—	2	2	no	—
899	C₂²×C₄	—	2	2	no	—
900	C₂²×C₄	—	2	2	no	—
901	C₂²×C₄	—	2	2	no	—
902	C₂²×C₄	—	2	4	no	—
903	C₂²×C₄	—	2	4	no	—
904	C₂²×C₄	—	2	4	no	—
905	C₂²×C₄	—	2	4	no	—
906	C₂²×C₄	—	4	2	no	—
907	C₂²×C₄	—	4	2	no	—
908	C₂²×C₄	—	4	2	no	—
909	C₂²×C₄	—	4	2	no	—
910	C₂²×C₄	—	4	2	no	—
911	C₂²×C₄	—	4	2	no	—
912	C₂²×C₄	—	4	2	no	—
913	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
914	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
915	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
916	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
917	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
918	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
919	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
920	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
921	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
922	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
923	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
924	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
925	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
926	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
927	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
928	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
929	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
930	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
931	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	4	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	4	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	4	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	4	no	—
940	C₄⋊C₄	—	2	4	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	4	no	—
947	C₄⋊C₄	—	4	2	no	—
948	C₄⋊C₄	—	4	1	no	—
949	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
950	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
951	C₄⋊C₄	#41×C₅₉	1	4	yes	—
952	C₂²⋊C₄	—	2	2	no	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	4	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	4	no	—
957	C₂²⋊C₄	—	2	4	no	—
958	C₂²⋊C₄	—	2	4	no	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	4	no	—
961	C₂²⋊C₄	—	2	4	no	—
962	C₂²⋊C₄	—	2	4	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	4	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	4	no	—
970	C₂²⋊C₄	—	2	4	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	4	no	—
973	C₂²⋊C₄	—	4	2	no	—
974	C₂²⋊C₄	—	4	2	no	—
975	C₂²⋊C₄	—	4	2	no	—
976	C₂²⋊C₄	—	4	2	no	—
977	C₂²⋊C₄	—	4	2	no	—
978	C₂²⋊C₄	—	4	2	no	—
979	C₂²⋊C₄	—	4	1	no	—
980	C₂²⋊C₄	—	4	1	no	—
981	C₂²⋊C₄	—	4	2	no	—
982	C₂²⋊C₄	—	4	2	no	—
983	C₂²⋊C₄	C₂×D₄×C₅₉	1	8	yes	—
984	C₄²	—	2	4	no	—
985	C₄²	—	2	2	no	—
986	C₄²	—	2	2	no	—
987	C₄²	—	2	2	no	—
988	C₄²	—	4	2	no	—
989	C₄²	—	4	2	no	—
990	C₄²	—	4	2	no	—
991	C₄²	—	4	2	no	—
992	C₄²	C₂×D₄×C₅₉	1	8	yes	—
993	C₄²	#41×C₅₉	1	4	yes	—
994	C₂³	—	2	1	no	—
995	C₂³	—	2	1	no	—
996	C₂³	—	2	1	no	—
997	C₂³	—	2	1	no	—
998	C₂³	—	2	1	no	—
999	C₂³	—	2	1	no	—
1000	C₂³	—	2	1	no	—
1001	C₂³	—	2	1	no	—
1002	C₂³	—	2	1	no	—
1003	C₂³	—	2	1	no	—
1004	C₂³	—	2	1	no	—
1005	C₂³	—	2	1	no	—
1006	C₂³	—	2	1	no	—
1007	C₂³	—	2	2	no	—
1008	C₂³	—	2	2	no	—
1009	C₂³	—	2	1	no	—
1010	C₂³	—	2	2	no	—
1011	C₂³	—	2	2	no	—
1012	C₂³	—	2	1	no	—
1013	C₂³	—	2	2	no	—
1014	C₂³	—	2	2	no	—
1015	C₂³	—	2	2	no	—
1016	C₂³	—	2	2	no	—
1017	C₂³	—	2	1	no	—
1018	C₂³	—	2	2	no	—
1019	C₂³	—	2	2	no	—
1020	C₂³	—	2	1	no	—
1021	C₂³	—	2	2	no	—
1022	C₂³	—	2	2	no	—
1023	C₂³	—	2	1	no	—
1024	C₂³	—	2	1	no	—
1025	C₂³	—	2	2	no	—
1026	C₂³	—	2	2	no	—
1027	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
1028	C₂³	H(5,𝔽₂)×C₅₉	1	2	yes	—
1029	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
1030	Q₈	—	8	4	no	—
1031	D₄	—	4	8	no	—
1032	D₄	—	4	4	no	—
1033	D₄	—	4	8	no	—
1034	D₄	—	4	4	no	—
1035	D₄	—	4	8	no	—
1036	D₄	—	4	4	no	—
1037	D₄	—	4	4	no	—
1038	D₄	—	4	4	no	—
1039	D₄	—	8	4	no	—
1040	D₄	—	8	4	no	—
1041	D₄	—	8	4	no	—
1042	D₄	—	8	4	no	—
1043	D₄	—	8	4	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	8	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	1	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	2	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	4	8	no	—
1090	C₂×C₄	—	4	4	no	—
1091	C₂×C₄	—	4	4	no	—
1092	C₂×C₄	—	8	4	no	—
1093	C₂×C₄	—	8	4	no	—
1094	C₂×C₄	—	8	4	no	—
1095	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
1096	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1097	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
1098	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1099	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
1100	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
1101	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
1102	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
1103	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
1104	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
1105	C₂²	—	2	2	no	—
1106	C₂²	—	2	2	no	—
1107	C₂²	—	2	2	no	—
1108	C₂²	—	2	2	no	—
1109	C₂²	—	2	2	no	—
1110	C₂²	—	2	2	no	—
1111	C₂²	—	4	1	no	—
1112	C₂²	—	4	1	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	—	4	1	no	—
1115	C₂²	—	4	1	no	—
1116	C₂²	—	4	1	no	—
1117	C₂²	—	4	1	no	—
1118	C₂²	—	4	1	no	—
1119	C₂²	—	4	2	no	—
1120	C₂²	—	4	2	no	—
1121	C₂²	—	4	1	no	—
1122	C₂²	—	4	2	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	2	no	—
1125	C₂²	—	4	2	no	—
1126	C₂²	—	4	2	no	—
1127	C₂²	—	4	1	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	—	4	2	no	—
1130	C₂²	—	4	2	no	—
1131	C₂²	—	4	2	no	—
1132	C₂²	—	4	2	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	4	2	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	2	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	4	2	no	—
1139	C₂²	—	4	2	no	—
1140	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
1141	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
1142	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
1143	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
1144	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
1145	C₂²	C₅₉×#585	1	1	yes	characteristic
1146	C₂²	C₅₉×#585	1	1	yes	characteristic
1147	C₄	—	2	2	no	—
1148	C₄	—	2	4	no	—
1149	C₄	—	2	2	no	—
1150	C₄	—	2	2	no	—
1151	C₄	—	2	4	no	—
1152	C₄	—	2	4	no	—
1153	C₄	—	2	2	no	—
1154	C₄	—	4	1	no	—
1155	C₄	—	4	2	no	—
1156	C₄	—	4	1	no	—
1157	C₄	—	4	1	no	—
1158	C₄	—	4	1	no	—
1159	C₄	—	4	2	no	—
1160	C₄	—	4	1	no	—
1161	C₄	—	4	2	no	—
1162	C₄	—	4	1	no	—
1163	C₄	—	4	1	no	—
1164	C₄	C₅₉×#532	1	4	yes	—
1165	C₂	—	4	2	no	—
1166	C₂	—	4	2	no	—
1167	C₂	—	8	2	no	—
1168	C₂	—	8	2	no	—
1169	C₂	—	8	1	no	—
1170	C₂	C₂×C₅₉×#532	1	1	yes	characteristic
1171	C₂	C₅₉×#3488	1	1	yes	characteristic
1172	C₂	C₅₉×#3488	1	1	yes	characteristic
1173	C₂	C₅₉×#3494	1	1	yes	characteristic
1174	C₂	C₅₉×#3506	1	1	yes	characteristic
1175	C₂	C₅₉×#3519	1	1	yes	characteristic
1176	C₂	C₅₉×#3524	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
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×#555	C₂	semidirect
2. C₂×C₅₉×#553	C₂	semidirect
3. C₅₉×#2662	C₂	semidirect
4. C₅₉×#2619	C₂	semidirect
5. C₅₉×#2601	C₂	semidirect
6. C₅₉×#2557	C₂	semidirect
7. C₅₉×#2555	C₂	semidirect
8. C₅₉×#2550	C₂	semidirect
9. C₅₉×#2544	C₂	semidirect
10. C₅₉×#2541	C₂	semidirect
11. C₅₉×#2491	C₂	semidirect
12. C₅₉×#2490	C₂	semidirect
13. C₅₉×#2464	C₂	semidirect
14. C₅₉×#2428	C₂	semidirect
15. C₅₉×#2416	C₂	semidirect
16. C₅₉×#2416	C₂	semidirect
17. C₅₉×#2392	C₂	semidirect
18. C₅₉×#2392	C₂	semidirect
19. C₅₉×#2366	C₂	semidirect
20. C₅₉×#2363	C₂	semidirect
21. C₅₉×#2361	C₂	semidirect
22. C₅₉×#2352	C₂	semidirect
23. C₅₉×#2274	C₂	semidirect
176. #117×C₅₉	D₄	semidirect
516. #35830	C₅₉	direct (N × H)
577. C₂×#555	C₂×C₅₉	semidirect
578. C₂×#553	C₂×C₅₉	semidirect
579. #2662	C₂×C₅₉	semidirect
580. #2619	C₂×C₅₉	semidirect
581. #2601	C₂×C₅₉	semidirect
582. #2557	C₂×C₅₉	semidirect
583. #2555	C₂×C₅₉	semidirect
584. #2550	C₂×C₅₉	semidirect
585. #2544	C₂×C₅₉	semidirect
586. #2541	C₂×C₅₉	semidirect
587. #2491	C₂×C₅₉	semidirect
588. #2490	C₂×C₅₉	semidirect
589. #2464	C₂×C₅₉	semidirect
590. #2428	C₂×C₅₉	semidirect
591. #2416	C₂×C₅₉	semidirect
592. #2416	C₂×C₅₉	semidirect
593. #2392	C₂×C₅₉	semidirect
594. #2392	C₂×C₅₉	semidirect
595. #2366	C₂×C₅₉	semidirect
596. #2363	C₂×C₅₉	semidirect
597. #2361	C₂×C₅₉	semidirect
598. #2352	C₂×C₅₉	semidirect
599. #2274	C₂×C₅₉	semidirect
713. C₅₉	#35830	direct (N × H)
765. #117	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×#555	2
C₂×C₅₉×#553	2
C₅₉×#2662	2
C₅₉×#2619	2
C₅₉×#2601	2
C₅₉×#2557	2
C₅₉×#2555	2
C₅₉×#2550	2
C₅₉×#2544	2
C₅₉×#2541	2
C₅₉×#2491	2
C₅₉×#2490	2
C₅₉×#2464	2
C₅₉×#2428	2
C₅₉×#2416	2
C₅₉×#2392	2
C₅₉×#2366	2
C₅₉×#2363	2
C₅₉×#2361	2
C₅₉×#2352	2
C₅₉×#2274	2
#35830	59

Subgroups — C59×#35830 #28447939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35830 #28447939