Subgroups — C₅₉×#35753 #28447862

Order 15104.

2590 conjugacy classes of subgroups.

The subgroup lattice has 1094 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#2636	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2633	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2613	C₂	1	1	yes	maximal, characteristic
6	C₅₉×#2603	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#2598	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#2562	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#2536	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#2498	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2484	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#2467	C₂	1	2	yes	maximal, complemented
13	C₅₉×#2463	C₂	1	2	yes	maximal, complemented
14	C₅₉×#2460	C₂	1	2	yes	maximal, complemented
15	C₅₉×#2460	C₂	1	2	yes	maximal, complemented
16	C₅₉×#2437	C₂	1	2	yes	maximal, complemented
17	C₅₉×#2412	C₂	1	2	yes	maximal, complemented
18	C₅₉×#2398	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₉×#2392	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₅₉×#394	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₉×#2358	C₂	1	2	yes	maximal, complemented
22	C₅₉×#2343	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₉×#2342	C₂	1	2	yes	maximal, complemented
24	C₂³×D₄×C₅₉	C₂²	1	1	yes	characteristic
25	C₅₉×#552	—	2	8	no	—
26	C₂×#126×C₅₉	C₂²	1	1	yes	characteristic, complemented
27	C₂×#126×C₅₉	C₂²	1	1	yes	characteristic, complemented
28	C₂×#125×C₅₉	C₂²	1	1	yes	characteristic, complemented
29	C₂×#125×C₅₉	C₂²	1	1	yes	characteristic, complemented
30	C₂×#125×C₅₉	C₂²	1	1	yes	characteristic, complemented
31	C₂×#123×C₅₉	C₂²	1	1	yes	characteristic
32	C₂×#123×C₅₉	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	complemented
36	C₂×#120×C₅₉	C₂²	1	2	yes	—
37	C₅₉×#518	—	2	8	no	—
38	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
45	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
46	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	complemented
47	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
48	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
49	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
50	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic, complemented
51	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
52	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
53	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
54	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
55	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
56	C₅₉×#400	C₂²	1	1	yes	characteristic, complemented
57	C₅₉×#400	C₂²	1	1	yes	characteristic, complemented
58	C₅₉×#400	C₂²	1	1	yes	characteristic, complemented
59	C₅₉×#399	C₂²	1	1	yes	characteristic, complemented
60	C₅₉×#399	C₂²	1	2	yes	complemented
61	C₅₉×#398	C₂²	1	1	yes	characteristic, complemented
62	C₅₉×#398	C₂²	1	1	yes	characteristic, complemented
63	C₅₉×#398	C₂²	1	1	yes	characteristic, complemented
64	C₅₉×#397	C₂²	1	1	yes	characteristic, complemented
65	C₅₉×#397	C₂²	1	2	yes	complemented
66	C₅₉×#397	C₂²	1	2	yes	complemented
67	C₅₉×#396	C₂²	1	2	yes	complemented
68	C₅₉×#396	C₂²	1	2	yes	complemented
69	C₅₉×#394	C₂²	1	1	yes	characteristic
70	C₅₉×#394	C₂²	1	1	yes	characteristic
71	C₅₉×#394	C₂²	1	1	yes	characteristic
72	C₅₉×#394	C₂²	1	1	yes	characteristic
73	C₅₉×#394	C₂²	1	2	yes	—
74	C₅₉×#394	C₂²	1	1	yes	characteristic
75	C₅₉×#394	C₂²	1	1	yes	characteristic
76	C₅₉×#394	C₂²	1	2	yes	—
77	C₅₉×#394	C₂²	1	2	yes	—
78	C₅₉×#394	C₂²	1	2	yes	complemented
79	C₅₉×#394	C₂²	1	2	yes	complemented
80	C₅₉×#393	C₂²	1	2	yes	complemented
81	C₅₉×#392	C₂²	1	1	yes	characteristic
82	C₅₉×#392	C₂²	1	1	yes	characteristic
83	C₅₉×#392	C₂²	1	2	yes	—
84	C₅₉×#390	C₂²	1	2	yes	complemented
85	C₅₉×#388	C₂²	1	2	yes	complemented
86	C₅₉×#388	C₂²	1	2	yes	complemented
87	C₅₉×#388	C₂²	1	2	yes	complemented
88	C₅₉×#388	C₂²	1	2	yes	complemented
89	C₅₉×#388	C₂²	1	2	yes	complemented
90	C₅₉×#388	C₂²	1	2	yes	complemented
91	C₅₉×#388	C₂²	1	2	yes	complemented
92	C₅₉×#387	C₂²	1	2	yes	complemented
93	C₅₉×#387	C₂²	1	2	yes	complemented
94	C₅₉×#387	C₂²	1	2	yes	complemented
95	C₅₉×#387	C₂²	1	2	yes	complemented
96	C₅₉×#387	C₂²	1	2	yes	complemented
97	C₅₉×#386	C₂²	1	2	yes	—
98	C₅₉×#386	C₂²	1	2	yes	complemented
99	C₅₉×#386	C₂²	1	2	yes	complemented
100	C₅₉×#386	C₂²	1	2	yes	complemented
101	C₅₉×#386	C₂²	1	2	yes	complemented
102	C₅₉×#385	C₂²	1	2	yes	—
103	C₅₉×#385	C₂²	1	2	yes	—
104	C₅₉×#385	C₂²	1	2	yes	complemented
105	C₅₉×#385	C₂²	1	2	yes	complemented
106	C₅₉×#385	C₂²	1	2	yes	complemented
107	C₅₉×#385	C₂²	1	2	yes	complemented
108	C₅₉×#385	C₂²	1	2	yes	complemented
109	C₅₉×#383	C₂²	1	1	yes	characteristic, complemented
110	C₅₉×#382	C₂²	1	1	yes	characteristic, complemented
111	C₅₉×#381	C₂²	1	2	yes	—
112	C₅₉×#381	C₂²	1	1	yes	characteristic
113	C₅₉×#380	C₂²	1	2	yes	—
114	C₅₉×#380	C₂²	1	2	yes	complemented
115	C₅₉×#380	C₂²	1	2	yes	complemented
116	C₅₉×#380	C₂²	1	2	yes	complemented
117	C₅₉×#379	C₂²	1	2	yes	—
118	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	complemented
121	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	complemented
122	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	complemented
123	C₅₉×#376	C₂²	1	1	yes	characteristic, complemented
124	C₂×#95×C₅₉	C₂²	1	1	yes	characteristic
125	C₂⁵×C₅₉	C₂³	1	2	yes	—
126	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₅₉	—	2	8	no	—
128	C₂²×D₄×C₅₉	—	2	4	no	—
129	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
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	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
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	2	yes	—
141	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
142	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
143	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
144	#126×C₅₉	—	2	4	no	—
145	#126×C₅₉	—	2	4	no	—
146	#125×C₅₉	—	2	4	no	—
147	#125×C₅₉	—	2	4	no	—
148	#125×C₅₉	—	2	4	no	—
149	#123×C₅₉	—	2	4	no	—
150	#123×C₅₉	—	2	4	no	—
151	C₂²⋊Q₈×C₅₉	—	2	4	no	—
152	C₂²⋊Q₈×C₅₉	—	2	4	no	—
153	C₂²⋊Q₈×C₅₉	—	4	4	no	—
154	#120×C₅₉	—	2	8	no	—
155	C₄×Q₈×C₅₉	—	2	4	no	—
156	C₄×D₄×C₅₉	—	2	8	no	—
157	C₄×D₄×C₅₉	—	2	8	no	—
158	C₄×D₄×C₅₉	—	2	4	no	—
159	C₄×D₄×C₅₉	—	2	4	no	—
160	C₄×D₄×C₅₉	—	2	4	no	—
161	C₄×D₄×C₅₉	—	2	4	no	—
162	C₄×D₄×C₅₉	—	2	4	no	—
163	C₄×D₄×C₅₉	—	4	4	no	—
164	#117×C₅₉	—	2	4	no	—
165	#117×C₅₉	—	2	4	no	—
166	#117×C₅₉	—	2	4	no	—
167	#117×C₅₉	D₄	1	8	yes	complemented
168	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
169	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
180	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
192	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊C₄×C₅₉	—	2	8	no	—
194	C₂×C₂²⋊C₄×C₅₉	—	2	8	no	—
195	C₂×C₂²⋊C₄×C₅₉	—	2	8	no	—
196	C₂×C₂²⋊C₄×C₅₉	—	4	4	no	—
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	2	yes	—
200	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
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	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	1	yes	characteristic
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	1	yes	characteristic
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×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
222	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
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	1	yes	characteristic
226	C₂×C₂²⋊C₄×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	1	yes	characteristic
230	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
231	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
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	#95×C₅₉	C₂³	1	1	yes	characteristic
236	#95×C₅₉	C₂³	1	1	yes	characteristic
237	#95×C₅₉	C₂³	1	2	yes	—
238	#95×C₅₉	C₂³	1	1	yes	characteristic
239	#95×C₅₉	C₂³	1	2	yes	—
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	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	2	yes	—
251	#95×C₅₉	C₂³	1	2	yes	—
252	#95×C₅₉	C₂³	1	2	yes	—
253	#95×C₅₉	C₂³	1	2	yes	—
254	#95×C₅₉	C₂³	1	2	yes	—
255	C₂⁴×C₅₉	—	2	4	no	—
256	C₂⁴×C₅₉	—	2	4	no	—
257	C₂⁴×C₅₉	—	4	2	no	—
258	C₂⁴×C₅₉	—	4	2	no	—
259	C₂⁴×C₅₉	—	4	2	no	—
260	C₂⁴×C₅₉	—	4	2	no	—
261	C₂⁴×C₅₉	#41	1	8	yes	—
262	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
263	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
264	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
265	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
266	C₂×Q₈×C₅₉	—	2	2	no	—
267	C₂×Q₈×C₅₉	—	2	2	no	—
268	C₂×Q₈×C₅₉	—	4	1	no	—
269	C₂×D₄×C₅₉	—	2	32	no	—
270	C₂×D₄×C₅₉	—	2	4	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	4	no	—
276	C₂×D₄×C₅₉	—	2	4	no	—
277	C₂×D₄×C₅₉	—	2	4	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	—	4	2	no	—
282	C₂×D₄×C₅₉	—	4	2	no	—
283	C₂×D₄×C₅₉	—	4	2	no	—
284	C₂×D₄×C₅₉	—	4	2	no	—
285	C₂²×C₄×C₅₉	—	2	4	no	—
286	C₂²×C₄×C₅₉	—	2	2	no	—
287	C₂²×C₄×C₅₉	—	2	2	no	—
288	C₂²×C₄×C₅₉	—	2	4	no	—
289	C₂²×C₄×C₅₉	—	2	4	no	—
290	C₂²×C₄×C₅₉	—	2	2	no	—
291	C₂²×C₄×C₅₉	—	2	2	no	—
292	C₂²×C₄×C₅₉	—	2	2	no	—
293	C₂²×C₄×C₅₉	—	2	4	no	—
294	C₂²×C₄×C₅₉	—	2	4	no	—
295	C₂²×C₄×C₅₉	—	2	4	no	—
296	C₂²×C₄×C₅₉	—	2	4	no	—
297	C₂²×C₄×C₅₉	—	4	1	no	—
298	C₂²×C₄×C₅₉	—	4	1	no	—
299	C₂²×C₄×C₅₉	—	4	2	no	—
300	C₂²×C₄×C₅₉	—	4	2	no	—
301	C₂²×C₄×C₅₉	—	4	2	no	—
302	C₂²×C₄×C₅₉	—	4	2	no	—
303	C₂²×C₄×C₅₉	—	4	2	no	—
304	C₂²×C₄×C₅₉	—	4	2	no	—
305	C₂²×C₄×C₅₉	—	4	2	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	C₂×D₄	1	4	yes	—
310	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
311	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
323	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
329	C₄⋊C₄×C₅₉	—	2	2	no	—
330	C₄⋊C₄×C₅₉	—	2	2	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	2	no	—
335	C₄⋊C₄×C₅₉	—	2	2	no	—
336	C₄⋊C₄×C₅₉	—	2	2	no	—
337	C₄⋊C₄×C₅₉	—	2	2	no	—
338	C₄⋊C₄×C₅₉	—	2	2	no	—
339	C₄⋊C₄×C₅₉	—	2	2	no	—
340	C₄⋊C₄×C₅₉	—	2	2	no	—
341	C₄⋊C₄×C₅₉	—	2	2	no	—
342	C₄⋊C₄×C₅₉	—	2	2	no	—
343	C₄⋊C₄×C₅₉	—	2	2	no	—
344	C₄⋊C₄×C₅₉	—	2	2	no	—
345	C₄⋊C₄×C₅₉	—	2	4	no	—
346	C₄⋊C₄×C₅₉	—	4	2	no	—
347	C₄⋊C₄×C₅₉	—	4	2	no	—
348	C₄⋊C₄×C₅₉	—	4	2	no	—
349	C₄⋊C₄×C₅₉	—	4	2	no	—
350	C₄⋊C₄×C₅₉	—	4	2	no	—
351	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
352	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
353	C₂²⋊C₄×C₅₉	—	2	4	no	—
354	C₂²⋊C₄×C₅₉	—	2	2	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	4	no	—
363	C₂²⋊C₄×C₅₉	—	2	4	no	—
364	C₂²⋊C₄×C₅₉	—	2	4	no	—
365	C₂²⋊C₄×C₅₉	—	2	4	no	—
366	C₂²⋊C₄×C₅₉	—	2	2	no	—
367	C₂²⋊C₄×C₅₉	—	2	2	no	—
368	C₂²⋊C₄×C₅₉	—	2	2	no	—
369	C₂²⋊C₄×C₅₉	—	2	2	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	—	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	C₂²⋊C₄×C₅₉	—	4	2	no	—
379	C₂²⋊C₄×C₅₉	—	4	2	no	—
380	C₂²⋊C₄×C₅₉	—	4	2	no	—
381	C₂²⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
382	C₂²⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
383	C₄²×C₅₉	—	2	2	no	—
384	C₄²×C₅₉	—	2	4	no	—
385	C₄²×C₅₉	—	2	2	no	—
386	C₄²×C₅₉	—	2	2	no	—
387	C₄²×C₅₉	—	4	2	no	—
388	C₄²×C₅₉	—	4	2	no	—
389	C₄²×C₅₉	C₂×D₄	1	4	yes	—
390	C₄²×C₅₉	C₂×D₄	1	4	yes	—
391	C₂³×C₅₉	—	2	1	no	—
392	C₂³×C₅₉	—	2	1	no	—
393	C₂³×C₅₉	—	2	2	no	—
394	C₂³×C₅₉	—	2	2	no	—
395	C₂³×C₅₉	—	2	2	no	—
396	C₂³×C₅₉	—	2	2	no	—
397	C₂³×C₅₉	—	2	2	no	—
398	C₂³×C₅₉	—	2	2	no	—
399	C₂³×C₅₉	—	2	2	no	—
400	C₂³×C₅₉	—	2	2	no	—
401	C₂³×C₅₉	—	2	2	no	—
402	C₂³×C₅₉	—	2	2	no	—
403	C₂³×C₅₉	—	2	2	no	—
404	C₂³×C₅₉	—	2	2	no	—
405	C₂³×C₅₉	—	2	2	no	—
406	C₂³×C₅₉	—	2	16	no	—
407	C₂³×C₅₉	—	2	1	no	—
408	C₂³×C₅₉	—	2	2	no	—
409	C₂³×C₅₉	—	2	1	no	—
410	C₂³×C₅₉	—	2	2	no	—
411	C₂³×C₅₉	—	2	1	no	—
412	C₂³×C₅₉	—	4	8	no	—
413	C₂³×C₅₉	—	4	8	no	—
414	C₂³×C₅₉	—	8	4	no	—
415	C₂³×C₅₉	—	8	4	no	—
416	C₂³×C₅₉	—	8	4	no	—
417	C₂³×C₅₉	—	8	4	no	—
418	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
419	C₂³×C₅₉	C₂×#41	1	4	yes	—
420	C₂³×C₅₉	C₂×#41	1	4	yes	—
421	C₂³×C₅₉	C₂×#41	1	4	yes	—
422	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
423	Q₈×C₅₉	—	4	4	no	—
424	D₄×C₅₉	—	2	16	no	—
425	D₄×C₅₉	—	2	8	no	—
426	D₄×C₅₉	—	2	8	no	—
427	D₄×C₅₉	—	4	8	no	—
428	D₄×C₅₉	—	4	4	no	—
429	D₄×C₅₉	—	8	4	no	—
430	C₂×C₄×C₅₉	—	2	8	no	—
431	C₂×C₄×C₅₉	—	2	1	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	2	no	—
438	C₂×C₄×C₅₉	—	2	1	no	—
439	C₂×C₄×C₅₉	—	2	1	no	—
440	C₂×C₄×C₅₉	—	2	1	no	—
441	C₂×C₄×C₅₉	—	2	1	no	—
442	C₂×C₄×C₅₉	—	2	2	no	—
443	C₂×C₄×C₅₉	—	2	2	no	—
444	C₂×C₄×C₅₉	—	2	1	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	2	no	—
450	C₂×C₄×C₅₉	—	2	2	no	—
451	C₂×C₄×C₅₉	—	2	2	no	—
452	C₂×C₄×C₅₉	—	2	2	no	—
453	C₂×C₄×C₅₉	—	2	2	no	—
454	C₂×C₄×C₅₉	—	2	2	no	—
455	C₂×C₄×C₅₉	—	2	2	no	—
456	C₂×C₄×C₅₉	—	2	2	no	—
457	C₂×C₄×C₅₉	—	2	2	no	—
458	C₂×C₄×C₅₉	—	2	2	no	—
459	C₂×C₄×C₅₉	—	2	1	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	2	no	—
465	C₂×C₄×C₅₉	—	2	1	no	—
466	C₂×C₄×C₅₉	—	2	2	no	—
467	C₂×C₄×C₅₉	—	2	2	no	—
468	C₂×C₄×C₅₉	—	2	2	no	—
469	C₂×C₄×C₅₉	—	2	2	no	—
470	C₂×C₄×C₅₉	—	2	1	no	—
471	C₂×C₄×C₅₉	—	2	2	no	—
472	C₂×C₄×C₅₉	—	2	2	no	—
473	C₂×C₄×C₅₉	—	4	4	no	—
474	C₂×C₄×C₅₉	—	4	4	no	—
475	C₂×C₄×C₅₉	—	4	4	no	—
476	C₂×C₄×C₅₉	—	8	4	no	—
477	C₂×C₄×C₅₉	—	8	4	no	—
478	C₂×C₄×C₅₉	—	8	4	no	—
479	C₂×C₄×C₅₉	—	8	4	no	—
480	C₂×C₄×C₅₉	—	8	4	no	—
481	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
482	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
483	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
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	2	yes	—
487	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
488	#35753	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
489	C₂²×C₅₉	—	2	2	no	—
490	C₂²×C₅₉	—	2	4	no	—
491	C₂²×C₅₉	—	2	2	no	—
492	C₂²×C₅₉	—	2	4	no	—
493	C₂²×C₅₉	—	2	4	no	—
494	C₂²×C₅₉	—	2	4	no	—
495	C₂²×C₅₉	—	2	4	no	—
496	C₂²×C₅₉	—	2	4	no	—
497	C₂²×C₅₉	—	2	4	no	—
498	C₂²×C₅₉	—	2	4	no	—
499	C₂²×C₅₉	—	4	2	no	—
500	C₂²×C₅₉	—	4	2	no	—
501	C₂²×C₅₉	—	4	2	no	—
502	C₂²×C₅₉	—	4	2	no	—
503	C₂²×C₅₉	—	4	2	no	—
504	C₂²×C₅₉	—	4	2	no	—
505	C₂²×C₅₉	—	4	2	no	—
506	C₂²×C₅₉	—	4	2	no	—
507	C₂²×C₅₉	—	4	1	no	—
508	C₂²×C₅₉	—	4	1	no	—
509	C₂²×C₅₉	—	4	2	no	—
510	C₂²×C₅₉	—	4	1	no	—
511	C₂²×C₅₉	—	4	2	no	—
512	C₂²×C₅₉	—	8	16	no	—
513	C₂²×C₅₉	#525	1	4	yes	—
514	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
515	C₂²×C₅₉	C₂²×#41	1	2	yes	—
516	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
517	C₂²×C₅₉	#585	1	1	yes	characteristic
518	C₂²×C₅₉	#585	1	2	yes	—
519	C₄×C₅₉	—	2	2	no	—
520	C₄×C₅₉	—	2	2	no	—
521	C₄×C₅₉	—	2	2	no	—
522	C₄×C₅₉	—	2	2	no	—
523	C₄×C₅₉	—	2	2	no	—
524	C₄×C₅₉	—	2	2	no	—
525	C₄×C₅₉	—	2	2	no	—
526	C₄×C₅₉	—	4	1	no	—
527	C₄×C₅₉	—	4	1	no	—
528	C₄×C₅₉	—	4	1	no	—
529	C₄×C₅₉	—	4	1	no	—
530	C₄×C₅₉	—	4	2	no	—
531	C₄×C₅₉	—	4	1	no	—
532	C₄×C₅₉	—	4	2	no	—
533	C₄×C₅₉	—	4	1	no	—
534	C₄×C₅₉	—	4	2	no	—
535	C₄×C₅₉	—	4	2	no	—
536	C₄×C₅₉	—	4	2	no	—
537	C₄×C₅₉	—	4	2	no	—
538	C₂×#552	C₂×C₅₉	1	1	yes	characteristic, complemented
539	C₂×#518	C₂×C₅₉	1	1	yes	characteristic, complemented
540	#2636	C₂×C₅₉	1	1	yes	characteristic, complemented
541	#2633	C₂×C₅₉	1	1	yes	characteristic, complemented
542	#2613	C₂×C₅₉	1	1	yes	characteristic
543	#2603	C₂×C₅₉	1	1	yes	characteristic, complemented
544	#2598	C₂×C₅₉	1	1	yes	characteristic, complemented
545	#2562	C₂×C₅₉	1	1	yes	characteristic, complemented
546	#2536	C₂×C₅₉	1	1	yes	characteristic, complemented
547	#2498	C₂×C₅₉	1	1	yes	characteristic, complemented
548	#2484	C₂×C₅₉	1	1	yes	characteristic, complemented
549	#2467	C₂×C₅₉	1	2	yes	complemented
550	#2463	C₂×C₅₉	1	2	yes	complemented
551	#2460	C₂×C₅₉	1	2	yes	complemented
552	#2460	C₂×C₅₉	1	2	yes	complemented
553	#2437	C₂×C₅₉	1	2	yes	complemented
554	#2412	C₂×C₅₉	1	2	yes	complemented
555	#2398	C₂×C₅₉	1	1	yes	characteristic, complemented
556	#2392	C₂×C₅₉	1	1	yes	characteristic, complemented
557	C₂×#394	C₂×C₅₉	1	1	yes	characteristic, complemented
558	#2358	C₂×C₅₉	1	2	yes	complemented
559	#2343	C₂×C₅₉	1	1	yes	characteristic, complemented
560	#2342	C₂×C₅₉	1	2	yes	complemented
561	C₂×C₅₉	—	2	4	no	—
562	C₂×C₅₉	—	4	4	no	—
563	C₂×C₅₉	—	4	4	no	—
564	C₂×C₅₉	—	8	1	no	—
565	C₂×C₅₉	C₂×#525	1	1	yes	characteristic
566	C₂×C₅₉	#3488	1	1	yes	characteristic
567	C₂×C₅₉	#3491	1	2	yes	—
568	C₂×C₅₉	#3500	1	1	yes	characteristic
569	C₂×C₅₉	#3505	1	2	yes	—
570	C₂³×D₄	C₂²×C₅₉	1	1	yes	characteristic
571	#552	—	2	8	no	—
572	C₂×#126	C₂²×C₅₉	1	1	yes	characteristic, complemented
573	C₂×#126	C₂²×C₅₉	1	1	yes	characteristic, complemented
574	C₂×#125	C₂²×C₅₉	1	1	yes	characteristic, complemented
575	C₂×#125	C₂²×C₅₉	1	1	yes	characteristic, complemented
576	C₂×#125	C₂²×C₅₉	1	1	yes	characteristic, complemented
577	C₂×#123	C₂²×C₅₉	1	1	yes	characteristic
578	C₂×#123	C₂²×C₅₉	1	1	yes	characteristic
579	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
580	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
581	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	complemented
582	C₂×#120	C₂²×C₅₉	1	2	yes	—
583	#518	—	2	8	no	—
584	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
585	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
586	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
587	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
588	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
589	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
590	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
591	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
592	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	complemented
593	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
594	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
595	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
596	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic, complemented
597	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
598	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
599	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
600	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
601	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
602	#400	C₂²×C₅₉	1	1	yes	characteristic, complemented
603	#400	C₂²×C₅₉	1	1	yes	characteristic, complemented
604	#400	C₂²×C₅₉	1	1	yes	characteristic, complemented
605	#399	C₂²×C₅₉	1	1	yes	characteristic, complemented
606	#399	C₂²×C₅₉	1	2	yes	complemented
607	#398	C₂²×C₅₉	1	1	yes	characteristic, complemented
608	#398	C₂²×C₅₉	1	1	yes	characteristic, complemented
609	#398	C₂²×C₅₉	1	1	yes	characteristic, complemented
610	#397	C₂²×C₅₉	1	1	yes	characteristic, complemented
611	#397	C₂²×C₅₉	1	2	yes	complemented
612	#397	C₂²×C₅₉	1	2	yes	complemented
613	#396	C₂²×C₅₉	1	2	yes	complemented
614	#396	C₂²×C₅₉	1	2	yes	complemented
615	#394	C₂²×C₅₉	1	1	yes	characteristic
616	#394	C₂²×C₅₉	1	1	yes	characteristic
617	#394	C₂²×C₅₉	1	1	yes	characteristic
618	#394	C₂²×C₅₉	1	1	yes	characteristic
619	#394	C₂²×C₅₉	1	2	yes	—
620	#394	C₂²×C₅₉	1	1	yes	characteristic
621	#394	C₂²×C₅₉	1	1	yes	characteristic
622	#394	C₂²×C₅₉	1	2	yes	—
623	#394	C₂²×C₅₉	1	2	yes	—
624	#394	C₂²×C₅₉	1	2	yes	complemented
625	#394	C₂²×C₅₉	1	2	yes	complemented
626	#393	C₂²×C₅₉	1	2	yes	complemented
627	#392	C₂²×C₅₉	1	1	yes	characteristic
628	#392	C₂²×C₅₉	1	1	yes	characteristic
629	#392	C₂²×C₅₉	1	2	yes	—
630	#390	C₂²×C₅₉	1	2	yes	complemented
631	#388	C₂²×C₅₉	1	2	yes	complemented
632	#388	C₂²×C₅₉	1	2	yes	complemented
633	#388	C₂²×C₅₉	1	2	yes	complemented
634	#388	C₂²×C₅₉	1	2	yes	complemented
635	#388	C₂²×C₅₉	1	2	yes	complemented
636	#388	C₂²×C₅₉	1	2	yes	complemented
637	#388	C₂²×C₅₉	1	2	yes	complemented
638	#387	C₂²×C₅₉	1	2	yes	complemented
639	#387	C₂²×C₅₉	1	2	yes	complemented
640	#387	C₂²×C₅₉	1	2	yes	complemented
641	#387	C₂²×C₅₉	1	2	yes	complemented
642	#387	C₂²×C₅₉	1	2	yes	complemented
643	#386	C₂²×C₅₉	1	2	yes	—
644	#386	C₂²×C₅₉	1	2	yes	complemented
645	#386	C₂²×C₅₉	1	2	yes	complemented
646	#386	C₂²×C₅₉	1	2	yes	complemented
647	#386	C₂²×C₅₉	1	2	yes	complemented
648	#385	C₂²×C₅₉	1	2	yes	—
649	#385	C₂²×C₅₉	1	2	yes	—
650	#385	C₂²×C₅₉	1	2	yes	complemented
651	#385	C₂²×C₅₉	1	2	yes	complemented
652	#385	C₂²×C₅₉	1	2	yes	complemented
653	#385	C₂²×C₅₉	1	2	yes	complemented
654	#385	C₂²×C₅₉	1	2	yes	complemented
655	#383	C₂²×C₅₉	1	1	yes	characteristic, complemented
656	#382	C₂²×C₅₉	1	1	yes	characteristic, complemented
657	#381	C₂²×C₅₉	1	2	yes	—
658	#381	C₂²×C₅₉	1	1	yes	characteristic
659	#380	C₂²×C₅₉	1	2	yes	—
660	#380	C₂²×C₅₉	1	2	yes	complemented
661	#380	C₂²×C₅₉	1	2	yes	complemented
662	#380	C₂²×C₅₉	1	2	yes	complemented
663	#379	C₂²×C₅₉	1	2	yes	—
664	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
665	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
666	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	complemented
667	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	complemented
668	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	complemented
669	#376	C₂²×C₅₉	1	1	yes	characteristic, complemented
670	C₂×#95	C₂²×C₅₉	1	1	yes	characteristic
671	C₅₉	#35753	1	1	yes	characteristic, direct product factor, Sylow
672	C₂⁵	C₂³×C₅₉	1	2	yes	—
673	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
674	C₂²×D₄	—	2	8	no	—
675	C₂²×D₄	—	2	4	no	—
676	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
677	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
678	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
679	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
680	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
681	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
682	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
683	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
684	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
685	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
686	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
687	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
688	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
689	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
690	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
691	#126	—	2	4	no	—
692	#126	—	2	4	no	—
693	#125	—	2	4	no	—
694	#125	—	2	4	no	—
695	#125	—	2	4	no	—
696	#123	—	2	4	no	—
697	#123	—	2	4	no	—
698	C₂²⋊Q₈	—	2	4	no	—
699	C₂²⋊Q₈	—	2	4	no	—
700	C₂²⋊Q₈	—	4	4	no	—
701	#120	—	2	8	no	—
702	C₄×Q₈	—	2	4	no	—
703	C₄×D₄	—	2	8	no	—
704	C₄×D₄	—	2	8	no	—
705	C₄×D₄	—	2	4	no	—
706	C₄×D₄	—	2	4	no	—
707	C₄×D₄	—	2	4	no	—
708	C₄×D₄	—	2	4	no	—
709	C₄×D₄	—	2	4	no	—
710	C₄×D₄	—	4	4	no	—
711	#117	—	2	4	no	—
712	#117	—	2	4	no	—
713	#117	—	2	4	no	—
714	#117	D₄×C₅₉	1	8	yes	complemented
715	C₂×C₄⋊C₄	—	2	4	no	—
716	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
717	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
718	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
719	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
720	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
721	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
722	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
723	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
724	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
725	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
726	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
727	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
728	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
729	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
730	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
731	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
732	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
733	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
734	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
735	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
736	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
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×C₂²⋊C₄	—	2	8	no	—
741	C₂×C₂²⋊C₄	—	2	8	no	—
742	C₂×C₂²⋊C₄	—	2	8	no	—
743	C₂×C₂²⋊C₄	—	4	4	no	—
744	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
745	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
746	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
747	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
748	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
749	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
750	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
751	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
752	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
753	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
754	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
755	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
756	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
757	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
758	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
759	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
760	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
761	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
762	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
763	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
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	2	yes	—
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×C₄²	C₂³×C₅₉	1	1	yes	characteristic
775	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
776	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
777	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
778	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
779	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
780	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
781	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
782	#95	C₂³×C₅₉	1	1	yes	characteristic
783	#95	C₂³×C₅₉	1	1	yes	characteristic
784	#95	C₂³×C₅₉	1	2	yes	—
785	#95	C₂³×C₅₉	1	1	yes	characteristic
786	#95	C₂³×C₅₉	1	2	yes	—
787	#95	C₂³×C₅₉	1	2	yes	—
788	#95	C₂³×C₅₉	1	2	yes	—
789	#95	C₂³×C₅₉	1	2	yes	—
790	#95	C₂³×C₅₉	1	2	yes	—
791	#95	C₂³×C₅₉	1	2	yes	—
792	#95	C₂³×C₅₉	1	2	yes	—
793	#95	C₂³×C₅₉	1	2	yes	—
794	#95	C₂³×C₅₉	1	2	yes	—
795	#95	C₂³×C₅₉	1	1	yes	characteristic
796	#95	C₂³×C₅₉	1	2	yes	—
797	#95	C₂³×C₅₉	1	2	yes	—
798	#95	C₂³×C₅₉	1	2	yes	—
799	#95	C₂³×C₅₉	1	2	yes	—
800	#95	C₂³×C₅₉	1	2	yes	—
801	#95	C₂³×C₅₉	1	2	yes	—
802	C₂⁴	—	2	4	no	—
803	C₂⁴	—	2	4	no	—
804	C₂⁴	—	4	2	no	—
805	C₂⁴	—	4	2	no	—
806	C₂⁴	—	4	2	no	—
807	C₂⁴	—	4	2	no	—
808	C₂⁴	#41×C₅₉	1	8	yes	—
809	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
810	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
811	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
812	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
813	C₂×Q₈	—	2	2	no	—
814	C₂×Q₈	—	2	2	no	—
815	C₂×Q₈	—	4	1	no	—
816	C₂×D₄	—	2	32	no	—
817	C₂×D₄	—	2	4	no	—
818	C₂×D₄	—	2	4	no	—
819	C₂×D₄	—	2	4	no	—
820	C₂×D₄	—	2	4	no	—
821	C₂×D₄	—	2	2	no	—
822	C₂×D₄	—	2	4	no	—
823	C₂×D₄	—	2	4	no	—
824	C₂×D₄	—	2	4	no	—
825	C₂×D₄	—	2	4	no	—
826	C₂×D₄	—	2	2	no	—
827	C₂×D₄	—	2	2	no	—
828	C₂×D₄	—	4	2	no	—
829	C₂×D₄	—	4	2	no	—
830	C₂×D₄	—	4	2	no	—
831	C₂×D₄	—	4	2	no	—
832	C₂²×C₄	—	2	4	no	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	—	2	2	no	—
835	C₂²×C₄	—	2	4	no	—
836	C₂²×C₄	—	2	4	no	—
837	C₂²×C₄	—	2	2	no	—
838	C₂²×C₄	—	2	2	no	—
839	C₂²×C₄	—	2	2	no	—
840	C₂²×C₄	—	2	4	no	—
841	C₂²×C₄	—	2	4	no	—
842	C₂²×C₄	—	2	4	no	—
843	C₂²×C₄	—	2	4	no	—
844	C₂²×C₄	—	4	1	no	—
845	C₂²×C₄	—	4	1	no	—
846	C₂²×C₄	—	4	2	no	—
847	C₂²×C₄	—	4	2	no	—
848	C₂²×C₄	—	4	2	no	—
849	C₂²×C₄	—	4	2	no	—
850	C₂²×C₄	—	4	2	no	—
851	C₂²×C₄	—	4	2	no	—
852	C₂²×C₄	—	4	2	no	—
853	C₂²×C₄	—	4	2	no	—
854	C₂²×C₄	—	4	2	no	—
855	C₂²×C₄	—	4	2	no	—
856	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
857	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
858	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
859	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
860	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
861	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
862	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
863	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
864	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
865	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
866	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
867	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
868	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
869	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
870	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
871	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
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	C₄⋊C₄	—	2	2	no	—
877	C₄⋊C₄	—	2	2	no	—
878	C₄⋊C₄	—	2	2	no	—
879	C₄⋊C₄	—	2	2	no	—
880	C₄⋊C₄	—	2	2	no	—
881	C₄⋊C₄	—	2	2	no	—
882	C₄⋊C₄	—	2	2	no	—
883	C₄⋊C₄	—	2	2	no	—
884	C₄⋊C₄	—	2	2	no	—
885	C₄⋊C₄	—	2	2	no	—
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	4	no	—
893	C₄⋊C₄	—	4	2	no	—
894	C₄⋊C₄	—	4	2	no	—
895	C₄⋊C₄	—	4	2	no	—
896	C₄⋊C₄	—	4	2	no	—
897	C₄⋊C₄	—	4	2	no	—
898	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
899	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
900	C₂²⋊C₄	—	2	4	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	—	2	4	no	—
907	C₂²⋊C₄	—	2	4	no	—
908	C₂²⋊C₄	—	2	4	no	—
909	C₂²⋊C₄	—	2	4	no	—
910	C₂²⋊C₄	—	2	4	no	—
911	C₂²⋊C₄	—	2	4	no	—
912	C₂²⋊C₄	—	2	4	no	—
913	C₂²⋊C₄	—	2	2	no	—
914	C₂²⋊C₄	—	2	2	no	—
915	C₂²⋊C₄	—	2	2	no	—
916	C₂²⋊C₄	—	2	2	no	—
917	C₂²⋊C₄	—	2	2	no	—
918	C₂²⋊C₄	—	2	4	no	—
919	C₂²⋊C₄	—	2	4	no	—
920	C₂²⋊C₄	—	4	2	no	—
921	C₂²⋊C₄	—	4	2	no	—
922	C₂²⋊C₄	—	4	2	no	—
923	C₂²⋊C₄	—	4	2	no	—
924	C₂²⋊C₄	—	4	2	no	—
925	C₂²⋊C₄	—	4	2	no	—
926	C₂²⋊C₄	—	4	2	no	—
927	C₂²⋊C₄	—	4	2	no	—
928	C₂²⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
929	C₂²⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
930	C₄²	—	2	2	no	—
931	C₄²	—	2	4	no	—
932	C₄²	—	2	2	no	—
933	C₄²	—	2	2	no	—
934	C₄²	—	4	2	no	—
935	C₄²	—	4	2	no	—
936	C₄²	C₂×D₄×C₅₉	1	4	yes	—
937	C₄²	C₂×D₄×C₅₉	1	4	yes	—
938	C₂³	—	2	1	no	—
939	C₂³	—	2	1	no	—
940	C₂³	—	2	2	no	—
941	C₂³	—	2	2	no	—
942	C₂³	—	2	2	no	—
943	C₂³	—	2	2	no	—
944	C₂³	—	2	2	no	—
945	C₂³	—	2	2	no	—
946	C₂³	—	2	2	no	—
947	C₂³	—	2	2	no	—
948	C₂³	—	2	2	no	—
949	C₂³	—	2	2	no	—
950	C₂³	—	2	2	no	—
951	C₂³	—	2	2	no	—
952	C₂³	—	2	2	no	—
953	C₂³	—	2	16	no	—
954	C₂³	—	2	1	no	—
955	C₂³	—	2	2	no	—
956	C₂³	—	2	1	no	—
957	C₂³	—	2	2	no	—
958	C₂³	—	2	1	no	—
959	C₂³	—	4	8	no	—
960	C₂³	—	4	8	no	—
961	C₂³	—	8	4	no	—
962	C₂³	—	8	4	no	—
963	C₂³	—	8	4	no	—
964	C₂³	—	8	4	no	—
965	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
966	C₂³	C₂×#41×C₅₉	1	4	yes	—
967	C₂³	C₂×#41×C₅₉	1	4	yes	—
968	C₂³	C₂×#41×C₅₉	1	4	yes	—
969	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
970	Q₈	—	4	4	no	—
971	D₄	—	2	16	no	—
972	D₄	—	2	8	no	—
973	D₄	—	2	8	no	—
974	D₄	—	4	8	no	—
975	D₄	—	4	4	no	—
976	D₄	—	8	4	no	—
977	C₂×C₄	—	2	8	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	2	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	2	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	2	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	4	4	no	—
1021	C₂×C₄	—	4	4	no	—
1022	C₂×C₄	—	4	4	no	—
1023	C₂×C₄	—	8	4	no	—
1024	C₂×C₄	—	8	4	no	—
1025	C₂×C₄	—	8	4	no	—
1026	C₂×C₄	—	8	4	no	—
1027	C₂×C₄	—	8	4	no	—
1028	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1029	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1030	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1031	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1032	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1033	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1034	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
1035	C₂²	—	2	2	no	—
1036	C₂²	—	2	4	no	—
1037	C₂²	—	2	2	no	—
1038	C₂²	—	2	4	no	—
1039	C₂²	—	2	4	no	—
1040	C₂²	—	2	4	no	—
1041	C₂²	—	2	4	no	—
1042	C₂²	—	2	4	no	—
1043	C₂²	—	2	4	no	—
1044	C₂²	—	2	4	no	—
1045	C₂²	—	4	2	no	—
1046	C₂²	—	4	2	no	—
1047	C₂²	—	4	2	no	—
1048	C₂²	—	4	2	no	—
1049	C₂²	—	4	2	no	—
1050	C₂²	—	4	2	no	—
1051	C₂²	—	4	2	no	—
1052	C₂²	—	4	2	no	—
1053	C₂²	—	4	1	no	—
1054	C₂²	—	4	1	no	—
1055	C₂²	—	4	2	no	—
1056	C₂²	—	4	1	no	—
1057	C₂²	—	4	2	no	—
1058	C₂²	—	8	16	no	—
1059	C₂²	C₅₉×#525	1	4	yes	—
1060	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
1061	C₂²	C₂²×#41×C₅₉	1	2	yes	—
1062	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
1063	C₂²	C₅₉×#585	1	1	yes	characteristic
1064	C₂²	C₅₉×#585	1	2	yes	—
1065	C₄	—	2	2	no	—
1066	C₄	—	2	2	no	—
1067	C₄	—	2	2	no	—
1068	C₄	—	2	2	no	—
1069	C₄	—	2	2	no	—
1070	C₄	—	2	2	no	—
1071	C₄	—	2	2	no	—
1072	C₄	—	4	1	no	—
1073	C₄	—	4	1	no	—
1074	C₄	—	4	1	no	—
1075	C₄	—	4	1	no	—
1076	C₄	—	4	2	no	—
1077	C₄	—	4	1	no	—
1078	C₄	—	4	2	no	—
1079	C₄	—	4	2	no	—
1080	C₄	—	4	1	no	—
1081	C₄	—	4	2	no	—
1082	C₄	—	4	2	no	—
1083	C₄	—	4	2	no	—
1084	C₂	—	2	4	no	—
1085	C₂	—	4	4	no	—
1086	C₂	—	4	4	no	—
1087	C₂	—	8	1	no	—
1088	C₂	C₂×C₅₉×#525	1	1	yes	characteristic
1089	C₂	C₅₉×#3488	1	1	yes	characteristic
1090	C₂	C₅₉×#3491	1	2	yes	—
1091	C₂	C₅₉×#3500	1	1	yes	characteristic
1092	C₂	C₅₉×#3505	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₅₉×#2613	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×#552	C₂	semidirect
2. C₂×C₅₉×#518	C₂	semidirect
3. C₅₉×#2636	C₂	semidirect
4. C₅₉×#2633	C₂	semidirect
6. C₅₉×#2603	C₂	semidirect
7. C₅₉×#2598	C₂	semidirect
8. C₅₉×#2562	C₂	semidirect
9. C₅₉×#2536	C₂	semidirect
10. C₅₉×#2498	C₂	semidirect
11. C₅₉×#2484	C₂	semidirect
12. C₅₉×#2467	C₂	semidirect
13. C₅₉×#2463	C₂	semidirect
14. C₅₉×#2460	C₂	semidirect
15. C₅₉×#2460	C₂	semidirect
16. C₅₉×#2437	C₂	semidirect
17. C₅₉×#2412	C₂	semidirect
18. C₅₉×#2398	C₂	semidirect
19. C₅₉×#2392	C₂	semidirect
20. C₂×C₅₉×#394	C₂	semidirect
21. C₅₉×#2358	C₂	semidirect
22. C₅₉×#2343	C₂	semidirect
23. C₅₉×#2342	C₂	semidirect
26. C₂×#126×C₅₉	C₂²	semidirect
27. C₂×#126×C₅₉	C₂²	semidirect
28. C₂×#125×C₅₉	C₂²	semidirect
29. C₂×#125×C₅₉	C₂²	semidirect
30. C₂×#125×C₅₉	C₂²	semidirect
34. C₂×C₂²⋊Q₈×C₅₉	C₂²	semidirect
35. C₂×C₂²⋊Q₈×C₅₉	C₂²	semidirect
38. C₂×C₄×Q₈×C₅₉	C₂²	semidirect
46. C₂×C₄×D₄×C₅₉	C₂²	semidirect
50. C₂×#117×C₅₉	C₂²	semidirect
56. C₅₉×#400	C₂²	semidirect
57. C₅₉×#400	C₂²	semidirect
58. C₅₉×#400	C₂²	semidirect
59. C₅₉×#399	C₂²	semidirect
60. C₅₉×#399	C₂²	semidirect
61. C₅₉×#398	C₂²	semidirect
62. C₅₉×#398	C₂²	semidirect
63. C₅₉×#398	C₂²	semidirect
64. C₅₉×#397	C₂²	semidirect
65. C₅₉×#397	C₂²	semidirect
66. C₅₉×#397	C₂²	semidirect
67. C₅₉×#396	C₂²	semidirect
68. C₅₉×#396	C₂²	semidirect
78. C₅₉×#394	C₂²	semidirect
79. C₅₉×#394	C₂²	semidirect
80. C₅₉×#393	C₂²	semidirect
84. C₅₉×#390	C₂²	semidirect
85. C₅₉×#388	C₂²	semidirect
86. C₅₉×#388	C₂²	semidirect
87. C₅₉×#388	C₂²	semidirect
88. C₅₉×#388	C₂²	semidirect
89. C₅₉×#388	C₂²	semidirect
90. C₅₉×#388	C₂²	semidirect
91. C₅₉×#388	C₂²	semidirect
92. C₅₉×#387	C₂²	semidirect
93. C₅₉×#387	C₂²	semidirect
94. C₅₉×#387	C₂²	semidirect
95. C₅₉×#387	C₂²	semidirect
96. C₅₉×#387	C₂²	semidirect
98. C₅₉×#386	C₂²	semidirect
99. C₅₉×#386	C₂²	semidirect
100. C₅₉×#386	C₂²	semidirect
101. C₅₉×#386	C₂²	semidirect
104. C₅₉×#385	C₂²	semidirect
105. C₅₉×#385	C₂²	semidirect
106. C₅₉×#385	C₂²	semidirect
107. C₅₉×#385	C₂²	semidirect
108. C₅₉×#385	C₂²	semidirect
109. C₅₉×#383	C₂²	semidirect
110. C₅₉×#382	C₂²	semidirect
114. C₅₉×#380	C₂²	semidirect
115. C₅₉×#380	C₂²	semidirect
116. C₅₉×#380	C₂²	semidirect
118. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
120. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
121. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
122. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
123. C₅₉×#376	C₂²	semidirect
167. #117×C₅₉	D₄	semidirect
488. #35753	C₅₉	direct (N × H)
538. C₂×#552	C₂×C₅₉	semidirect
539. C₂×#518	C₂×C₅₉	semidirect
540. #2636	C₂×C₅₉	semidirect
541. #2633	C₂×C₅₉	semidirect
543. #2603	C₂×C₅₉	semidirect
544. #2598	C₂×C₅₉	semidirect
545. #2562	C₂×C₅₉	semidirect
546. #2536	C₂×C₅₉	semidirect
547. #2498	C₂×C₅₉	semidirect
548. #2484	C₂×C₅₉	semidirect
549. #2467	C₂×C₅₉	semidirect
550. #2463	C₂×C₅₉	semidirect
551. #2460	C₂×C₅₉	semidirect
552. #2460	C₂×C₅₉	semidirect
553. #2437	C₂×C₅₉	semidirect
554. #2412	C₂×C₅₉	semidirect
555. #2398	C₂×C₅₉	semidirect
556. #2392	C₂×C₅₉	semidirect
557. C₂×#394	C₂×C₅₉	semidirect
558. #2358	C₂×C₅₉	semidirect
559. #2343	C₂×C₅₉	semidirect
560. #2342	C₂×C₅₉	semidirect
572. C₂×#126	C₂²×C₅₉	semidirect
573. C₂×#126	C₂²×C₅₉	semidirect
574. C₂×#125	C₂²×C₅₉	semidirect
575. C₂×#125	C₂²×C₅₉	semidirect
576. C₂×#125	C₂²×C₅₉	semidirect
580. C₂×C₂²⋊Q₈	C₂²×C₅₉	semidirect
581. C₂×C₂²⋊Q₈	C₂²×C₅₉	semidirect
584. C₂×C₄×Q₈	C₂²×C₅₉	semidirect
592. C₂×C₄×D₄	C₂²×C₅₉	semidirect
596. C₂×#117	C₂²×C₅₉	semidirect
602. #400	C₂²×C₅₉	semidirect
603. #400	C₂²×C₅₉	semidirect
604. #400	C₂²×C₅₉	semidirect
605. #399	C₂²×C₅₉	semidirect
606. #399	C₂²×C₅₉	semidirect
607. #398	C₂²×C₅₉	semidirect
608. #398	C₂²×C₅₉	semidirect
609. #398	C₂²×C₅₉	semidirect
610. #397	C₂²×C₅₉	semidirect
611. #397	C₂²×C₅₉	semidirect
612. #397	C₂²×C₅₉	semidirect
613. #396	C₂²×C₅₉	semidirect
614. #396	C₂²×C₅₉	semidirect
624. #394	C₂²×C₅₉	semidirect
625. #394	C₂²×C₅₉	semidirect
626. #393	C₂²×C₅₉	semidirect
630. #390	C₂²×C₅₉	semidirect
631. #388	C₂²×C₅₉	semidirect
632. #388	C₂²×C₅₉	semidirect
633. #388	C₂²×C₅₉	semidirect
634. #388	C₂²×C₅₉	semidirect
635. #388	C₂²×C₅₉	semidirect
636. #388	C₂²×C₅₉	semidirect
637. #388	C₂²×C₅₉	semidirect
638. #387	C₂²×C₅₉	semidirect
639. #387	C₂²×C₅₉	semidirect
640. #387	C₂²×C₅₉	semidirect
641. #387	C₂²×C₅₉	semidirect
642. #387	C₂²×C₅₉	semidirect
644. #386	C₂²×C₅₉	semidirect
645. #386	C₂²×C₅₉	semidirect
646. #386	C₂²×C₅₉	semidirect
647. #386	C₂²×C₅₉	semidirect
650. #385	C₂²×C₅₉	semidirect
651. #385	C₂²×C₅₉	semidirect
652. #385	C₂²×C₅₉	semidirect
653. #385	C₂²×C₅₉	semidirect
654. #385	C₂²×C₅₉	semidirect
655. #383	C₂²×C₅₉	semidirect
656. #382	C₂²×C₅₉	semidirect
660. #380	C₂²×C₅₉	semidirect
661. #380	C₂²×C₅₉	semidirect
662. #380	C₂²×C₅₉	semidirect
664. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
666. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
667. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
668. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
669. #376	C₂²×C₅₉	semidirect
671. C₅₉	#35753	direct (N × H)
714. #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×#552	2
C₂×C₅₉×#518	2
C₅₉×#2636	2
C₅₉×#2633	2
C₅₉×#2613	2
C₅₉×#2603	2
C₅₉×#2598	2
C₅₉×#2562	2
C₅₉×#2536	2
C₅₉×#2498	2
C₅₉×#2484	2
C₅₉×#2467	2
C₅₉×#2463	2
C₅₉×#2460	2
C₅₉×#2437	2
C₅₉×#2412	2
C₅₉×#2398	2
C₅₉×#2392	2
C₂×C₅₉×#394	2
C₅₉×#2358	2
C₅₉×#2343	2
C₅₉×#2342	2
#35753	59

Subgroups — C59×#35753 #28447862

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35753 #28447862