Subgroups — C₅₉×#35505 #28447614

Order 15104.

1930 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#2608	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₉×#2602	C₂	1	2	yes	maximal, complemented
3	C₅₉×#2575	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2558	C₂	1	2	yes	maximal, complemented
5	C₅₉×#2558	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2539	C₂	1	1	yes	maximal, characteristic
7	C₅₉×#2534	C₂	1	2	yes	maximal, complemented
8	C₅₉×#2526	C₂	1	2	yes	maximal, complemented
9	C₅₉×#2500	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#2482	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2471	C₂	1	2	yes	maximal, complemented
12	C₅₉×#2470	C₂	1	2	yes	maximal, complemented
13	C₅₉×#2441	C₂	1	2	yes	maximal, complemented
14	C₅₉×#2411	C₂	1	2	yes	maximal, complemented
15	C₅₉×#2335	C₂	1	2	yes	maximal, complemented
16	C₅₉×#2333	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₉×#2298	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₉×#2293	C₂	1	2	yes	maximal, complemented
19	C₅₉×#2273	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#125×C₅₉	C₂²	1	2	yes	complemented
21	C₂×#123×C₅₉	C₂²	1	2	yes	—
22	C₂×#123×C₅₉	C₂²	1	2	yes	—
23	C₂×#123×C₅₉	C₂²	1	2	yes	—
24	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
25	C₂×#120×C₅₉	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
27	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×#117×C₅₉	C₂²	1	2	yes	—
29	C₂×#117×C₅₉	C₂²	1	2	yes	complemented
30	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
31	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
32	C₅₉×#400	C₂²	1	2	yes	complemented
33	C₅₉×#400	C₂²	1	2	yes	complemented
34	C₅₉×#399	C₂²	1	2	yes	—
35	C₅₉×#399	C₂²	1	2	yes	—
36	C₅₉×#397	C₂²	1	2	yes	—
37	C₅₉×#397	C₂²	1	2	yes	complemented
38	C₅₉×#396	C₂²	1	2	yes	—
39	C₅₉×#396	C₂²	1	2	yes	—
40	C₅₉×#396	C₂²	1	2	yes	—
41	C₅₉×#396	C₂²	1	2	yes	—
42	C₅₉×#396	C₂²	1	2	yes	complemented
43	C₅₉×#394	C₂²	1	2	yes	—
44	C₅₉×#394	C₂²	1	2	yes	—
45	C₅₉×#394	C₂²	1	2	yes	—
46	C₅₉×#394	C₂²	1	2	yes	—
47	C₅₉×#392	C₂²	1	2	yes	—
48	C₅₉×#390	C₂²	1	2	yes	—
49	C₅₉×#390	C₂²	1	2	yes	—
50	C₅₉×#390	C₂²	1	2	yes	—
51	C₅₉×#390	C₂²	1	2	yes	—
52	C₅₉×#390	C₂²	1	1	yes	characteristic, complemented
53	C₅₉×#390	C₂²	1	1	yes	characteristic, complemented
54	C₅₉×#389	C₂²	1	2	yes	complemented
55	C₅₉×#389	C₂²	1	2	yes	complemented
56	C₅₉×#389	C₂²	1	2	yes	complemented
57	C₅₉×#389	C₂²	1	2	yes	complemented
58	C₅₉×#389	C₂²	1	2	yes	complemented
59	C₅₉×#388	C₂²	1	2	yes	—
60	C₅₉×#388	C₂²	1	2	yes	—
61	C₅₉×#388	C₂²	1	2	yes	—
62	C₅₉×#388	C₂²	1	2	yes	—
63	C₅₉×#388	C₂²	1	2	yes	—
64	C₅₉×#388	C₂²	1	2	yes	—
65	C₅₉×#388	C₂²	1	2	yes	complemented
66	C₅₉×#388	C₂²	1	2	yes	complemented
67	C₅₉×#388	C₂²	1	2	yes	complemented
68	C₅₉×#388	C₂²	1	2	yes	complemented
69	C₅₉×#388	C₂²	1	2	yes	complemented
70	C₅₉×#388	C₂²	1	2	yes	complemented
71	C₅₉×#388	C₂²	1	2	yes	complemented
72	C₅₉×#387	C₂²	1	2	yes	complemented
73	C₅₉×#387	C₂²	1	2	yes	complemented
74	C₅₉×#387	C₂²	1	2	yes	complemented
75	C₅₉×#387	C₂²	1	2	yes	complemented
76	C₅₉×#387	C₂²	1	2	yes	complemented
77	C₅₉×#387	C₂²	1	2	yes	complemented
78	C₅₉×#386	C₂²	1	2	yes	—
79	C₅₉×#386	C₂²	1	2	yes	—
80	C₅₉×#386	C₂²	1	2	yes	—
81	C₅₉×#386	C₂²	1	2	yes	complemented
82	C₅₉×#385	C₂²	1	1	yes	characteristic
83	C₅₉×#385	C₂²	1	1	yes	characteristic
84	C₅₉×#385	C₂²	1	2	yes	—
85	C₅₉×#385	C₂²	1	2	yes	complemented
86	C₅₉×#384	C₂²	1	1	yes	characteristic, complemented
87	C₅₉×#382	C₂²	1	1	yes	characteristic, complemented
88	C₅₉×#381	C₂²	1	1	yes	characteristic
89	C₅₉×#381	C₂²	1	2	yes	—
90	C₅₉×#380	C₂²	1	2	yes	—
91	C₅₉×#379	C₂²	1	1	yes	characteristic
92	C₅₉×#379	C₂²	1	1	yes	characteristic
93	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
94	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
95	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
96	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
97	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
100	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
104	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	complemented
105	C₅₉×#376	C₂²	1	1	yes	characteristic, complemented
106	C₄³×C₅₉	C₂²	1	1	yes	characteristic, complemented
107	C₂⁵×C₅₉	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
109	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
110	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
111	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
113	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
115	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
117	#125×C₅₉	—	4	4	no	—
118	#123×C₅₉	—	2	8	no	—
119	#123×C₅₉	—	4	4	no	—
120	#123×C₅₉	—	4	4	no	—
121	#121×C₅₉	—	2	4	no	—
122	#120×C₅₉	—	4	4	no	—
123	C₄×D₄×C₅₉	—	2	8	no	—
124	#117×C₅₉	—	2	4	no	—
125	#117×C₅₉	—	4	4	no	—
126	#117×C₅₉	—	4	4	no	—
127	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₅₉	—	2	4	no	—
146	C₂×C₂²⋊C₄×C₅₉	—	2	8	no	—
147	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
158	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
159	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
166	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
167	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
174	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
176	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
177	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
183	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
186	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
187	#95×C₅₉	C₂³	1	2	yes	—
188	#95×C₅₉	C₂³	1	2	yes	—
189	#95×C₅₉	C₂³	1	2	yes	—
190	#95×C₅₉	C₂³	1	2	yes	—
191	#95×C₅₉	C₂³	1	2	yes	—
192	#95×C₅₉	C₂³	1	2	yes	—
193	#95×C₅₉	C₂³	1	2	yes	—
194	#95×C₅₉	C₂³	1	2	yes	—
195	#95×C₅₉	C₂³	1	2	yes	—
196	#95×C₅₉	C₂³	1	2	yes	—
197	#95×C₅₉	C₂³	1	2	yes	—
198	#95×C₅₉	C₂³	1	2	yes	—
199	#95×C₅₉	C₂³	1	2	yes	—
200	#95×C₅₉	C₂³	1	2	yes	—
201	#95×C₅₉	C₂³	1	2	yes	—
202	#95×C₅₉	C₂³	1	2	yes	—
203	#95×C₅₉	C₂³	1	2	yes	—
204	#95×C₅₉	C₂³	1	2	yes	—
205	#95×C₅₉	C₂³	1	2	yes	—
206	C₂⁴×C₅₉	—	2	2	no	—
207	C₂⁴×C₅₉	—	2	4	no	—
208	C₂⁴×C₅₉	—	4	2	no	—
209	C₂⁴×C₅₉	—	4	1	no	—
210	C₂⁴×C₅₉	—	4	1	no	—
211	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
212	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
213	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
214	C₂×D₄×C₅₉	—	2	4	no	—
215	C₂×D₄×C₅₉	—	2	4	no	—
216	C₂×D₄×C₅₉	—	2	4	no	—
217	C₂×D₄×C₅₉	—	2	2	no	—
218	C₂×D₄×C₅₉	—	2	4	no	—
219	C₂×D₄×C₅₉	—	4	2	no	—
220	C₂×D₄×C₅₉	—	4	2	no	—
221	C₂×D₄×C₅₉	—	4	2	no	—
222	C₂×D₄×C₅₉	—	4	2	no	—
223	C₂×D₄×C₅₉	—	4	1	no	—
224	C₂×D₄×C₅₉	—	4	1	no	—
225	C₂×D₄×C₅₉	—	4	2	no	—
226	C₂²×C₄×C₅₉	—	2	4	no	—
227	C₂²×C₄×C₅₉	—	2	2	no	—
228	C₂²×C₄×C₅₉	—	2	4	no	—
229	C₂²×C₄×C₅₉	—	4	2	no	—
230	C₂²×C₄×C₅₉	—	4	2	no	—
231	C₂²×C₄×C₅₉	—	4	1	no	—
232	C₂²×C₄×C₅₉	—	4	1	no	—
233	C₂²×C₄×C₅₉	—	4	2	no	—
234	C₂²×C₄×C₅₉	—	4	2	no	—
235	C₂²×C₄×C₅₉	—	4	2	no	—
236	C₂²×C₄×C₅₉	—	4	2	no	—
237	C₂²×C₄×C₅₉	—	4	2	no	—
238	C₂²×C₄×C₅₉	#41	1	4	yes	—
239	C₂²×C₄×C₅₉	#41	1	8	yes	—
240	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
256	C₄⋊C₄×C₅₉	—	2	2	no	—
257	C₄⋊C₄×C₅₉	—	2	2	no	—
258	C₄⋊C₄×C₅₉	—	2	4	no	—
259	C₄⋊C₄×C₅₉	—	2	2	no	—
260	C₄⋊C₄×C₅₉	—	2	4	no	—
261	C₄⋊C₄×C₅₉	—	2	4	no	—
262	C₄⋊C₄×C₅₉	—	2	4	no	—
263	C₄⋊C₄×C₅₉	—	2	4	no	—
264	C₄⋊C₄×C₅₉	—	2	4	no	—
265	C₄⋊C₄×C₅₉	—	2	4	no	—
266	C₄⋊C₄×C₅₉	—	4	2	no	—
267	C₄⋊C₄×C₅₉	—	4	2	no	—
268	C₄⋊C₄×C₅₉	—	4	2	no	—
269	C₄⋊C₄×C₅₉	—	4	2	no	—
270	C₄⋊C₄×C₅₉	—	4	2	no	—
271	C₄⋊C₄×C₅₉	—	4	2	no	—
272	C₄⋊C₄×C₅₉	—	4	2	no	—
273	C₄⋊C₄×C₅₉	—	4	2	no	—
274	C₂²⋊C₄×C₅₉	—	2	2	no	—
275	C₂²⋊C₄×C₅₉	—	2	2	no	—
276	C₂²⋊C₄×C₅₉	—	2	4	no	—
277	C₂²⋊C₄×C₅₉	—	2	4	no	—
278	C₂²⋊C₄×C₅₉	—	2	4	no	—
279	C₂²⋊C₄×C₅₉	—	2	4	no	—
280	C₂²⋊C₄×C₅₉	—	2	4	no	—
281	C₂²⋊C₄×C₅₉	—	2	4	no	—
282	C₂²⋊C₄×C₅₉	—	2	4	no	—
283	C₂²⋊C₄×C₅₉	—	2	4	no	—
284	C₂²⋊C₄×C₅₉	—	2	4	no	—
285	C₂²⋊C₄×C₅₉	—	2	4	no	—
286	C₂²⋊C₄×C₅₉	—	2	4	no	—
287	C₂²⋊C₄×C₅₉	—	2	4	no	—
288	C₂²⋊C₄×C₅₉	—	2	4	no	—
289	C₂²⋊C₄×C₅₉	—	2	4	no	—
290	C₂²⋊C₄×C₅₉	—	2	4	no	—
291	C₂²⋊C₄×C₅₉	—	4	2	no	—
292	C₂²⋊C₄×C₅₉	—	4	1	no	—
293	C₂²⋊C₄×C₅₉	—	4	1	no	—
294	C₂²⋊C₄×C₅₉	—	4	2	no	—
295	C₂²⋊C₄×C₅₉	—	4	2	no	—
296	C₂²⋊C₄×C₅₉	—	4	2	no	—
297	C₂²⋊C₄×C₅₉	—	4	2	no	—
298	C₂²⋊C₄×C₅₉	—	4	2	no	—
299	C₂²⋊C₄×C₅₉	—	4	2	no	—
300	C₂²⋊C₄×C₅₉	—	4	2	no	—
301	C₄²×C₅₉	—	2	2	no	—
302	C₄²×C₅₉	—	2	2	no	—
303	C₄²×C₅₉	—	2	4	no	—
304	C₄²×C₅₉	—	2	4	no	—
305	C₄²×C₅₉	—	4	1	no	—
306	C₄²×C₅₉	—	4	1	no	—
307	C₄²×C₅₉	—	4	1	no	—
308	C₄²×C₅₉	—	4	1	no	—
309	C₄²×C₅₉	—	4	1	no	—
310	C₄²×C₅₉	—	4	1	no	—
311	C₄²×C₅₉	—	4	2	no	—
312	C₄²×C₅₉	—	4	2	no	—
313	C₄²×C₅₉	—	4	2	no	—
314	C₂³×C₅₉	—	2	8	no	—
315	C₂³×C₅₉	—	2	2	no	—
316	C₂³×C₅₉	—	2	2	no	—
317	C₂³×C₅₉	—	2	2	no	—
318	C₂³×C₅₉	—	2	2	no	—
319	C₂³×C₅₉	—	2	2	no	—
320	C₂³×C₅₉	—	2	2	no	—
321	C₂³×C₅₉	—	2	1	no	—
322	C₂³×C₅₉	—	2	1	no	—
323	C₂³×C₅₉	—	2	2	no	—
324	C₂³×C₅₉	—	2	2	no	—
325	C₂³×C₅₉	—	2	2	no	—
326	C₂³×C₅₉	—	2	2	no	—
327	C₂³×C₅₉	—	2	2	no	—
328	C₂³×C₅₉	—	2	2	no	—
329	C₂³×C₅₉	—	2	2	no	—
330	C₂³×C₅₉	—	2	2	no	—
331	C₂³×C₅₉	—	2	2	no	—
332	C₂³×C₅₉	—	8	2	no	—
333	C₂³×C₅₉	—	8	4	no	—
334	C₂³×C₅₉	—	8	4	no	—
335	C₂³×C₅₉	—	8	2	no	—
336	C₂³×C₅₉	C₂×#41	1	2	yes	—
337	C₂³×C₅₉	C₂×#41	1	4	yes	—
338	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
339	D₄×C₅₉	—	4	8	no	—
340	D₄×C₅₉	—	8	2	no	—
341	D₄×C₅₉	—	8	4	no	—
342	D₄×C₅₉	—	8	4	no	—
343	C₂×C₄×C₅₉	—	2	2	no	—
344	C₂×C₄×C₅₉	—	2	2	no	—
345	C₂×C₄×C₅₉	—	2	2	no	—
346	C₂×C₄×C₅₉	—	2	1	no	—
347	C₂×C₄×C₅₉	—	2	1	no	—
348	C₂×C₄×C₅₉	—	2	2	no	—
349	C₂×C₄×C₅₉	—	2	2	no	—
350	C₂×C₄×C₅₉	—	2	2	no	—
351	C₂×C₄×C₅₉	—	2	1	no	—
352	C₂×C₄×C₅₉	—	2	1	no	—
353	C₂×C₄×C₅₉	—	2	2	no	—
354	C₂×C₄×C₅₉	—	2	1	no	—
355	C₂×C₄×C₅₉	—	2	1	no	—
356	C₂×C₄×C₅₉	—	2	1	no	—
357	C₂×C₄×C₅₉	—	2	1	no	—
358	C₂×C₄×C₅₉	—	2	2	no	—
359	C₂×C₄×C₅₉	—	2	2	no	—
360	C₂×C₄×C₅₉	—	2	2	no	—
361	C₂×C₄×C₅₉	—	2	2	no	—
362	C₂×C₄×C₅₉	—	2	2	no	—
363	C₂×C₄×C₅₉	—	2	2	no	—
364	C₂×C₄×C₅₉	—	2	2	no	—
365	C₂×C₄×C₅₉	—	2	2	no	—
366	C₂×C₄×C₅₉	—	2	2	no	—
367	C₂×C₄×C₅₉	—	2	2	no	—
368	C₂×C₄×C₅₉	—	2	2	no	—
369	C₂×C₄×C₅₉	—	2	2	no	—
370	C₂×C₄×C₅₉	—	2	2	no	—
371	C₂×C₄×C₅₉	—	2	2	no	—
372	C₂×C₄×C₅₉	—	2	2	no	—
373	C₂×C₄×C₅₉	—	2	2	no	—
374	C₂×C₄×C₅₉	—	2	2	no	—
375	C₂×C₄×C₅₉	—	2	2	no	—
376	C₂×C₄×C₅₉	—	2	2	no	—
377	C₂×C₄×C₅₉	—	2	2	no	—
378	C₂×C₄×C₅₉	—	2	2	no	—
379	C₂×C₄×C₅₉	—	2	2	no	—
380	C₂×C₄×C₅₉	—	2	2	no	—
381	C₂×C₄×C₅₉	—	2	2	no	—
382	C₂×C₄×C₅₉	—	4	4	no	—
383	C₂×C₄×C₅₉	—	4	8	no	—
384	C₂×C₄×C₅₉	—	4	8	no	—
385	C₂×C₄×C₅₉	—	8	4	no	—
386	C₂×C₄×C₅₉	—	8	2	no	—
387	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
388	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
389	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
390	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
391	C₂×C₄×C₅₉	H(5,𝔽₂)	1	4	yes	—
392	#35505	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
393	C₂²×C₅₉	—	2	2	no	—
394	C₂²×C₅₉	—	2	4	no	—
395	C₂²×C₅₉	—	2	2	no	—
396	C₂²×C₅₉	—	2	4	no	—
397	C₂²×C₅₉	—	2	4	no	—
398	C₂²×C₅₉	—	2	2	no	—
399	C₂²×C₅₉	—	4	2	no	—
400	C₂²×C₅₉	—	4	2	no	—
401	C₂²×C₅₉	—	4	2	no	—
402	C₂²×C₅₉	—	4	2	no	—
403	C₂²×C₅₉	—	4	2	no	—
404	C₂²×C₅₉	—	4	2	no	—
405	C₂²×C₅₉	—	4	2	no	—
406	C₂²×C₅₉	—	4	2	no	—
407	C₂²×C₅₉	—	4	2	no	—
408	C₂²×C₅₉	—	4	2	no	—
409	C₂²×C₅₉	—	4	2	no	—
410	C₂²×C₅₉	—	4	2	no	—
411	C₂²×C₅₉	—	4	2	no	—
412	C₂²×C₅₉	—	8	8	no	—
413	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
414	C₂²×C₅₉	C₂²×#41	1	2	yes	—
415	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	2	yes	—
416	C₂²×C₅₉	#585	1	1	yes	characteristic
417	C₂²×C₅₉	#585	1	1	yes	characteristic
418	C₄×C₅₉	—	2	2	no	—
419	C₄×C₅₉	—	2	2	no	—
420	C₄×C₅₉	—	2	4	no	—
421	C₄×C₅₉	—	2	4	no	—
422	C₄×C₅₉	—	2	4	no	—
423	C₄×C₅₉	—	4	1	no	—
424	C₄×C₅₉	—	4	1	no	—
425	C₄×C₅₉	—	4	2	no	—
426	C₄×C₅₉	—	4	2	no	—
427	C₄×C₅₉	—	4	2	no	—
428	C₄×C₅₉	—	4	2	no	—
429	C₄×C₅₉	—	4	2	no	—
430	C₄×C₅₉	—	4	1	no	—
431	C₄×C₅₉	—	4	1	no	—
432	C₄×C₅₉	—	4	2	no	—
433	C₄×C₅₉	—	4	2	no	—
434	#2608	C₂×C₅₉	1	1	yes	characteristic, complemented
435	#2602	C₂×C₅₉	1	2	yes	complemented
436	#2575	C₂×C₅₉	1	2	yes	complemented
437	#2558	C₂×C₅₉	1	2	yes	complemented
438	#2558	C₂×C₅₉	1	2	yes	complemented
439	#2539	C₂×C₅₉	1	1	yes	characteristic
440	#2534	C₂×C₅₉	1	2	yes	complemented
441	#2526	C₂×C₅₉	1	2	yes	complemented
442	#2500	C₂×C₅₉	1	1	yes	characteristic, complemented
443	#2482	C₂×C₅₉	1	1	yes	characteristic, complemented
444	#2471	C₂×C₅₉	1	2	yes	complemented
445	#2470	C₂×C₅₉	1	2	yes	complemented
446	#2441	C₂×C₅₉	1	2	yes	complemented
447	#2411	C₂×C₅₉	1	2	yes	complemented
448	#2335	C₂×C₅₉	1	2	yes	complemented
449	#2333	C₂×C₅₉	1	1	yes	characteristic, complemented
450	#2298	C₂×C₅₉	1	1	yes	characteristic, complemented
451	#2293	C₂×C₅₉	1	2	yes	complemented
452	#2273	C₂×C₅₉	1	1	yes	characteristic, complemented
453	C₂×C₅₉	—	4	2	no	—
454	C₂×C₅₉	—	4	4	no	—
455	C₂×C₅₉	—	8	2	no	—
456	C₂×C₅₉	#3444	1	1	yes	characteristic
457	C₂×C₅₉	#3491	1	1	yes	characteristic
458	C₂×C₅₉	#3494	1	2	yes	—
459	C₂×C₅₉	#3505	1	2	yes	—
460	C₂×C₅₉	#3508	1	1	yes	characteristic
461	C₂×#125	C₂²×C₅₉	1	2	yes	complemented
462	C₂×#123	C₂²×C₅₉	1	2	yes	—
463	C₂×#123	C₂²×C₅₉	1	2	yes	—
464	C₂×#123	C₂²×C₅₉	1	2	yes	—
465	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
466	C₂×#120	C₂²×C₅₉	1	2	yes	—
467	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
468	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
469	C₂×#117	C₂²×C₅₉	1	2	yes	—
470	C₂×#117	C₂²×C₅₉	1	2	yes	complemented
471	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
472	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
473	#400	C₂²×C₅₉	1	2	yes	complemented
474	#400	C₂²×C₅₉	1	2	yes	complemented
475	#399	C₂²×C₅₉	1	2	yes	—
476	#399	C₂²×C₅₉	1	2	yes	—
477	#397	C₂²×C₅₉	1	2	yes	—
478	#397	C₂²×C₅₉	1	2	yes	complemented
479	#396	C₂²×C₅₉	1	2	yes	—
480	#396	C₂²×C₅₉	1	2	yes	—
481	#396	C₂²×C₅₉	1	2	yes	—
482	#396	C₂²×C₅₉	1	2	yes	—
483	#396	C₂²×C₅₉	1	2	yes	complemented
484	#394	C₂²×C₅₉	1	2	yes	—
485	#394	C₂²×C₅₉	1	2	yes	—
486	#394	C₂²×C₅₉	1	2	yes	—
487	#394	C₂²×C₅₉	1	2	yes	—
488	#392	C₂²×C₅₉	1	2	yes	—
489	#390	C₂²×C₅₉	1	2	yes	—
490	#390	C₂²×C₅₉	1	2	yes	—
491	#390	C₂²×C₅₉	1	2	yes	—
492	#390	C₂²×C₅₉	1	2	yes	—
493	#390	C₂²×C₅₉	1	1	yes	characteristic, complemented
494	#390	C₂²×C₅₉	1	1	yes	characteristic, complemented
495	#389	C₂²×C₅₉	1	2	yes	complemented
496	#389	C₂²×C₅₉	1	2	yes	complemented
497	#389	C₂²×C₅₉	1	2	yes	complemented
498	#389	C₂²×C₅₉	1	2	yes	complemented
499	#389	C₂²×C₅₉	1	2	yes	complemented
500	#388	C₂²×C₅₉	1	2	yes	—
501	#388	C₂²×C₅₉	1	2	yes	—
502	#388	C₂²×C₅₉	1	2	yes	—
503	#388	C₂²×C₅₉	1	2	yes	—
504	#388	C₂²×C₅₉	1	2	yes	—
505	#388	C₂²×C₅₉	1	2	yes	—
506	#388	C₂²×C₅₉	1	2	yes	complemented
507	#388	C₂²×C₅₉	1	2	yes	complemented
508	#388	C₂²×C₅₉	1	2	yes	complemented
509	#388	C₂²×C₅₉	1	2	yes	complemented
510	#388	C₂²×C₅₉	1	2	yes	complemented
511	#388	C₂²×C₅₉	1	2	yes	complemented
512	#388	C₂²×C₅₉	1	2	yes	complemented
513	#387	C₂²×C₅₉	1	2	yes	complemented
514	#387	C₂²×C₅₉	1	2	yes	complemented
515	#387	C₂²×C₅₉	1	2	yes	complemented
516	#387	C₂²×C₅₉	1	2	yes	complemented
517	#387	C₂²×C₅₉	1	2	yes	complemented
518	#387	C₂²×C₅₉	1	2	yes	complemented
519	#386	C₂²×C₅₉	1	2	yes	—
520	#386	C₂²×C₅₉	1	2	yes	—
521	#386	C₂²×C₅₉	1	2	yes	—
522	#386	C₂²×C₅₉	1	2	yes	complemented
523	#385	C₂²×C₅₉	1	2	yes	—
524	#385	C₂²×C₅₉	1	1	yes	characteristic
525	#385	C₂²×C₅₉	1	1	yes	characteristic
526	#385	C₂²×C₅₉	1	2	yes	complemented
527	#384	C₂²×C₅₉	1	1	yes	characteristic, complemented
528	#382	C₂²×C₅₉	1	1	yes	characteristic, complemented
529	#381	C₂²×C₅₉	1	2	yes	—
530	#381	C₂²×C₅₉	1	1	yes	characteristic
531	#380	C₂²×C₅₉	1	2	yes	—
532	#379	C₂²×C₅₉	1	1	yes	characteristic
533	#379	C₂²×C₅₉	1	1	yes	characteristic
534	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
535	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
536	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
537	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
538	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
539	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
540	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
541	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
542	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
543	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
544	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
545	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	complemented
546	#376	C₂²×C₅₉	1	1	yes	characteristic, complemented
547	C₄³	C₂²×C₅₉	1	1	yes	characteristic, complemented
548	C₅₉	#35505	1	1	yes	characteristic, direct product factor, Sylow
549	C₂⁵	C₂³×C₅₉	1	1	yes	characteristic
550	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
551	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
552	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
553	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
554	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
555	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
556	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
557	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
558	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
559	#125	—	4	4	no	—
560	#123	—	2	8	no	—
561	#123	—	4	4	no	—
562	#123	—	4	4	no	—
563	#121	—	2	4	no	—
564	#120	—	4	4	no	—
565	C₄×D₄	—	2	8	no	—
566	#117	—	2	4	no	—
567	#117	—	4	4	no	—
568	#117	—	4	4	no	—
569	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
587	C₂×C₂²⋊C₄	—	2	4	no	—
588	C₂×C₂²⋊C₄	—	2	8	no	—
589	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
597	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
598	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
614	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
615	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
616	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
617	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
618	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
619	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
620	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
621	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
622	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
623	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
624	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
625	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
626	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
627	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
628	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
629	#95	C₂³×C₅₉	1	2	yes	—
630	#95	C₂³×C₅₉	1	2	yes	—
631	#95	C₂³×C₅₉	1	2	yes	—
632	#95	C₂³×C₅₉	1	2	yes	—
633	#95	C₂³×C₅₉	1	2	yes	—
634	#95	C₂³×C₅₉	1	2	yes	—
635	#95	C₂³×C₅₉	1	2	yes	—
636	#95	C₂³×C₅₉	1	2	yes	—
637	#95	C₂³×C₅₉	1	2	yes	—
638	#95	C₂³×C₅₉	1	2	yes	—
639	#95	C₂³×C₅₉	1	2	yes	—
640	#95	C₂³×C₅₉	1	2	yes	—
641	#95	C₂³×C₅₉	1	2	yes	—
642	#95	C₂³×C₅₉	1	2	yes	—
643	#95	C₂³×C₅₉	1	2	yes	—
644	#95	C₂³×C₅₉	1	2	yes	—
645	#95	C₂³×C₅₉	1	2	yes	—
646	#95	C₂³×C₅₉	1	2	yes	—
647	#95	C₂³×C₅₉	1	2	yes	—
648	C₂⁴	—	2	2	no	—
649	C₂⁴	—	2	4	no	—
650	C₂⁴	—	4	2	no	—
651	C₂⁴	—	4	1	no	—
652	C₂⁴	—	4	1	no	—
653	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
654	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
655	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
656	C₂×D₄	—	2	4	no	—
657	C₂×D₄	—	2	4	no	—
658	C₂×D₄	—	2	4	no	—
659	C₂×D₄	—	2	2	no	—
660	C₂×D₄	—	2	4	no	—
661	C₂×D₄	—	4	2	no	—
662	C₂×D₄	—	4	2	no	—
663	C₂×D₄	—	4	2	no	—
664	C₂×D₄	—	4	2	no	—
665	C₂×D₄	—	4	1	no	—
666	C₂×D₄	—	4	1	no	—
667	C₂×D₄	—	4	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	4	no	—
670	C₂²×C₄	—	2	4	no	—
671	C₂²×C₄	—	4	2	no	—
672	C₂²×C₄	—	4	2	no	—
673	C₂²×C₄	—	4	1	no	—
674	C₂²×C₄	—	4	1	no	—
675	C₂²×C₄	—	4	2	no	—
676	C₂²×C₄	—	4	2	no	—
677	C₂²×C₄	—	4	2	no	—
678	C₂²×C₄	—	4	2	no	—
679	C₂²×C₄	—	4	2	no	—
680	C₂²×C₄	#41×C₅₉	1	4	yes	—
681	C₂²×C₄	#41×C₅₉	1	8	yes	—
682	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
686	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
687	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
688	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
692	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
693	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
694	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
695	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
696	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	4	no	—
704	C₄⋊C₄	—	2	4	no	—
705	C₄⋊C₄	—	2	4	no	—
706	C₄⋊C₄	—	2	4	no	—
707	C₄⋊C₄	—	2	4	no	—
708	C₄⋊C₄	—	4	2	no	—
709	C₄⋊C₄	—	4	2	no	—
710	C₄⋊C₄	—	4	2	no	—
711	C₄⋊C₄	—	4	2	no	—
712	C₄⋊C₄	—	4	2	no	—
713	C₄⋊C₄	—	4	2	no	—
714	C₄⋊C₄	—	4	2	no	—
715	C₄⋊C₄	—	4	2	no	—
716	C₂²⋊C₄	—	2	2	no	—
717	C₂²⋊C₄	—	2	2	no	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	2	4	no	—
720	C₂²⋊C₄	—	2	4	no	—
721	C₂²⋊C₄	—	2	4	no	—
722	C₂²⋊C₄	—	2	4	no	—
723	C₂²⋊C₄	—	2	4	no	—
724	C₂²⋊C₄	—	2	4	no	—
725	C₂²⋊C₄	—	2	4	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	4	no	—
728	C₂²⋊C₄	—	2	4	no	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	2	4	no	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	4	2	no	—
734	C₂²⋊C₄	—	4	2	no	—
735	C₂²⋊C₄	—	4	2	no	—
736	C₂²⋊C₄	—	4	2	no	—
737	C₂²⋊C₄	—	4	2	no	—
738	C₂²⋊C₄	—	4	2	no	—
739	C₂²⋊C₄	—	4	2	no	—
740	C₂²⋊C₄	—	4	2	no	—
741	C₂²⋊C₄	—	4	1	no	—
742	C₂²⋊C₄	—	4	1	no	—
743	C₄²	—	2	2	no	—
744	C₄²	—	2	2	no	—
745	C₄²	—	2	4	no	—
746	C₄²	—	2	4	no	—
747	C₄²	—	4	2	no	—
748	C₄²	—	4	2	no	—
749	C₄²	—	4	2	no	—
750	C₄²	—	4	1	no	—
751	C₄²	—	4	1	no	—
752	C₄²	—	4	1	no	—
753	C₄²	—	4	1	no	—
754	C₄²	—	4	1	no	—
755	C₄²	—	4	1	no	—
756	C₂³	—	2	8	no	—
757	C₂³	—	2	2	no	—
758	C₂³	—	2	2	no	—
759	C₂³	—	2	2	no	—
760	C₂³	—	2	2	no	—
761	C₂³	—	2	2	no	—
762	C₂³	—	2	2	no	—
763	C₂³	—	2	1	no	—
764	C₂³	—	2	1	no	—
765	C₂³	—	2	2	no	—
766	C₂³	—	2	2	no	—
767	C₂³	—	2	2	no	—
768	C₂³	—	2	2	no	—
769	C₂³	—	2	2	no	—
770	C₂³	—	2	2	no	—
771	C₂³	—	2	2	no	—
772	C₂³	—	2	2	no	—
773	C₂³	—	2	2	no	—
774	C₂³	—	8	2	no	—
775	C₂³	—	8	2	no	—
776	C₂³	—	8	4	no	—
777	C₂³	—	8	4	no	—
778	C₂³	C₂×#41×C₅₉	1	2	yes	—
779	C₂³	C₂×#41×C₅₉	1	4	yes	—
780	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
781	D₄	—	4	8	no	—
782	D₄	—	8	2	no	—
783	D₄	—	8	4	no	—
784	D₄	—	8	4	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	4	4	no	—
825	C₂×C₄	—	4	8	no	—
826	C₂×C₄	—	4	8	no	—
827	C₂×C₄	—	8	2	no	—
828	C₂×C₄	—	8	4	no	—
829	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
830	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
831	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
832	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
833	C₂×C₄	H(5,𝔽₂)×C₅₉	1	4	yes	—
834	C₂²	—	2	2	no	—
835	C₂²	—	2	2	no	—
836	C₂²	—	2	4	no	—
837	C₂²	—	2	2	no	—
838	C₂²	—	2	4	no	—
839	C₂²	—	2	4	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	2	no	—
847	C₂²	—	4	2	no	—
848	C₂²	—	4	2	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	4	2	no	—
851	C₂²	—	4	2	no	—
852	C₂²	—	4	2	no	—
853	C₂²	—	8	8	no	—
854	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
855	C₂²	C₂²×#41×C₅₉	1	2	yes	—
856	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	2	yes	—
857	C₂²	C₅₉×#585	1	1	yes	characteristic
858	C₂²	C₅₉×#585	1	1	yes	characteristic
859	C₄	—	2	2	no	—
860	C₄	—	2	2	no	—
861	C₄	—	2	4	no	—
862	C₄	—	2	4	no	—
863	C₄	—	2	4	no	—
864	C₄	—	4	2	no	—
865	C₄	—	4	2	no	—
866	C₄	—	4	1	no	—
867	C₄	—	4	1	no	—
868	C₄	—	4	1	no	—
869	C₄	—	4	1	no	—
870	C₄	—	4	2	no	—
871	C₄	—	4	2	no	—
872	C₄	—	4	2	no	—
873	C₄	—	4	2	no	—
874	C₄	—	4	2	no	—
875	C₂	—	4	2	no	—
876	C₂	—	4	4	no	—
877	C₂	—	8	2	no	—
878	C₂	C₅₉×#3444	1	1	yes	characteristic
879	C₂	C₅₉×#3491	1	1	yes	characteristic
880	C₂	C₅₉×#3494	1	2	yes	—
881	C₂	C₅₉×#3505	1	2	yes	—
882	C₂	C₅₉×#3508	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₅₉×#2539	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. C₅₉×#2608	C₂	semidirect
2. C₅₉×#2602	C₂	semidirect
3. C₅₉×#2575	C₂	semidirect
4. C₅₉×#2558	C₂	semidirect
5. C₅₉×#2558	C₂	semidirect
7. C₅₉×#2534	C₂	semidirect
8. C₅₉×#2526	C₂	semidirect
9. C₅₉×#2500	C₂	semidirect
10. C₅₉×#2482	C₂	semidirect
11. C₅₉×#2471	C₂	semidirect
12. C₅₉×#2470	C₂	semidirect
13. C₅₉×#2441	C₂	semidirect
14. C₅₉×#2411	C₂	semidirect
15. C₅₉×#2335	C₂	semidirect
16. C₅₉×#2333	C₂	semidirect
17. C₅₉×#2298	C₂	semidirect
18. C₅₉×#2293	C₂	semidirect
19. C₅₉×#2273	C₂	semidirect
20. C₂×#125×C₅₉	C₂²	semidirect
29. C₂×#117×C₅₉	C₂²	semidirect
32. C₅₉×#400	C₂²	semidirect
33. C₅₉×#400	C₂²	semidirect
37. C₅₉×#397	C₂²	semidirect
42. C₅₉×#396	C₂²	semidirect
52. C₅₉×#390	C₂²	semidirect
53. C₅₉×#390	C₂²	semidirect
54. C₅₉×#389	C₂²	semidirect
55. C₅₉×#389	C₂²	semidirect
56. C₅₉×#389	C₂²	semidirect
57. C₅₉×#389	C₂²	semidirect
58. C₅₉×#389	C₂²	semidirect
65. C₅₉×#388	C₂²	semidirect
66. C₅₉×#388	C₂²	semidirect
67. C₅₉×#388	C₂²	semidirect
68. C₅₉×#388	C₂²	semidirect
69. C₅₉×#388	C₂²	semidirect
70. C₅₉×#388	C₂²	semidirect
71. C₅₉×#388	C₂²	semidirect
72. C₅₉×#387	C₂²	semidirect
73. C₅₉×#387	C₂²	semidirect
74. C₅₉×#387	C₂²	semidirect
75. C₅₉×#387	C₂²	semidirect
76. C₅₉×#387	C₂²	semidirect
77. C₅₉×#387	C₂²	semidirect
81. C₅₉×#386	C₂²	semidirect
85. C₅₉×#385	C₂²	semidirect
86. C₅₉×#384	C₂²	semidirect
87. C₅₉×#382	C₂²	semidirect
93. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
94. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
95. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
104. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
105. C₅₉×#376	C₂²	semidirect
106. C₄³×C₅₉	C₂²	semidirect
392. #35505	C₅₉	direct (N × H)
434. #2608	C₂×C₅₉	semidirect
435. #2602	C₂×C₅₉	semidirect
436. #2575	C₂×C₅₉	semidirect
437. #2558	C₂×C₅₉	semidirect
438. #2558	C₂×C₅₉	semidirect
440. #2534	C₂×C₅₉	semidirect
441. #2526	C₂×C₅₉	semidirect
442. #2500	C₂×C₅₉	semidirect
443. #2482	C₂×C₅₉	semidirect
444. #2471	C₂×C₅₉	semidirect
445. #2470	C₂×C₅₉	semidirect
446. #2441	C₂×C₅₉	semidirect
447. #2411	C₂×C₅₉	semidirect
448. #2335	C₂×C₅₉	semidirect
449. #2333	C₂×C₅₉	semidirect
450. #2298	C₂×C₅₉	semidirect
451. #2293	C₂×C₅₉	semidirect
452. #2273	C₂×C₅₉	semidirect
461. C₂×#125	C₂²×C₅₉	semidirect
470. C₂×#117	C₂²×C₅₉	semidirect
473. #400	C₂²×C₅₉	semidirect
474. #400	C₂²×C₅₉	semidirect
478. #397	C₂²×C₅₉	semidirect
483. #396	C₂²×C₅₉	semidirect
493. #390	C₂²×C₅₉	semidirect
494. #390	C₂²×C₅₉	semidirect
495. #389	C₂²×C₅₉	semidirect
496. #389	C₂²×C₅₉	semidirect
497. #389	C₂²×C₅₉	semidirect
498. #389	C₂²×C₅₉	semidirect
499. #389	C₂²×C₅₉	semidirect
506. #388	C₂²×C₅₉	semidirect
507. #388	C₂²×C₅₉	semidirect
508. #388	C₂²×C₅₉	semidirect
509. #388	C₂²×C₅₉	semidirect
510. #388	C₂²×C₅₉	semidirect
511. #388	C₂²×C₅₉	semidirect
512. #388	C₂²×C₅₉	semidirect
513. #387	C₂²×C₅₉	semidirect
514. #387	C₂²×C₅₉	semidirect
515. #387	C₂²×C₅₉	semidirect
516. #387	C₂²×C₅₉	semidirect
517. #387	C₂²×C₅₉	semidirect
518. #387	C₂²×C₅₉	semidirect
522. #386	C₂²×C₅₉	semidirect
526. #385	C₂²×C₅₉	semidirect
527. #384	C₂²×C₅₉	semidirect
528. #382	C₂²×C₅₉	semidirect
534. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
535. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
536. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
545. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
546. #376	C₂²×C₅₉	semidirect
547. C₄³	C₂²×C₅₉	semidirect
548. C₅₉	#35505	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₉×#2608	2
C₅₉×#2602	2
C₅₉×#2575	2
C₅₉×#2558	2
C₅₉×#2539	2
C₅₉×#2534	2
C₅₉×#2526	2
C₅₉×#2500	2
C₅₉×#2482	2
C₅₉×#2471	2
C₅₉×#2470	2
C₅₉×#2441	2
C₅₉×#2411	2
C₅₉×#2335	2
C₅₉×#2333	2
C₅₉×#2298	2
C₅₉×#2293	2
C₅₉×#2273	2
#35505	59

Subgroups — C59×#35505 #28447614

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35505 #28447614