Subgroups — C₅₉×#35602 #28447711

Order 15104.

1688 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#2607	C₂	1	2	yes	maximal, complemented
2	C₅₉×#2589	C₂	1	2	yes	maximal, complemented
3	C₅₉×#2580	C₂	1	1	yes	maximal, characteristic
4	C₅₉×#2574	C₂	1	2	yes	maximal, complemented
5	C₅₉×#2569	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2563	C₂	1	1	yes	maximal, characteristic
7	C₅₉×#2550	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#2546	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#2522	C₂	1	2	yes	maximal, complemented
10	C₅₉×#2509	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2508	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#2492	C₂	1	2	yes	maximal, complemented
13	C₅₉×#2454	C₂	1	1	yes	maximal, characteristic
14	C₅₉×#2452	C₂	1	1	yes	maximal, characteristic
15	C₅₉×#2439	C₂	1	2	yes	maximal, complemented
16	C₅₉×#2438	C₂	1	2	yes	maximal, complemented
17	C₅₉×#2331	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₉×#2331	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₉×#2319	C₂	1	1	yes	maximal, characteristic
20	C₄×#125×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₉×#2295	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₉×#2293	C₂	1	1	yes	maximal, characteristic
23	C₅₉×#2275	C₂	1	1	yes	maximal, characteristic
24	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊Q₈×C₅₉	C₂²	1	2	yes	—
27	C₂×#125×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
33	C₂×#117×C₅₉	C₂²	1	2	yes	—
34	C₅₉×#400	C₂²	1	2	yes	—
35	C₅₉×#400	C₂²	1	2	yes	—
36	C₅₉×#400	C₂²	1	2	yes	—
37	C₅₉×#399	C₂²	1	2	yes	—
38	C₅₉×#399	C₂²	1	2	yes	—
39	C₅₉×#398	C₂²	1	2	yes	—
40	C₅₉×#398	C₂²	1	2	yes	—
41	C₅₉×#398	C₂²	1	2	yes	—
42	C₅₉×#398	C₂²	1	2	yes	—
43	C₅₉×#396	C₂²	1	2	yes	—
44	C₅₉×#396	C₂²	1	2	yes	—
45	C₅₉×#395	C₂²	1	2	yes	—
46	C₅₉×#393	C₂²	1	2	yes	—
47	C₅₉×#393	C₂²	1	2	yes	—
48	C₅₉×#393	C₂²	1	2	yes	—
49	C₅₉×#393	C₂²	1	2	yes	—
50	C₅₉×#391	C₂²	1	1	yes	characteristic
51	C₅₉×#391	C₂²	1	2	yes	—
52	C₅₉×#391	C₂²	1	2	yes	—
53	C₅₉×#391	C₂²	1	2	yes	—
54	C₅₉×#391	C₂²	1	2	yes	—
55	C₅₉×#391	C₂²	1	1	yes	characteristic
56	C₅₉×#391	C₂²	1	2	yes	—
57	C₅₉×#391	C₂²	1	2	yes	—
58	C₅₉×#390	C₂²	1	1	yes	characteristic
59	C₅₉×#390	C₂²	1	1	yes	characteristic
60	C₅₉×#390	C₂²	1	1	yes	characteristic
61	C₅₉×#390	C₂²	1	1	yes	characteristic
62	C₅₉×#389	C₂²	1	1	yes	characteristic
63	C₅₉×#389	C₂²	1	1	yes	characteristic
64	C₅₉×#389	C₂²	1	1	yes	characteristic
65	C₅₉×#389	C₂²	1	1	yes	characteristic
66	C₅₉×#389	C₂²	1	2	yes	—
67	C₅₉×#389	C₂²	1	1	yes	characteristic
68	C₅₉×#389	C₂²	1	1	yes	characteristic
69	C₅₉×#389	C₂²	1	1	yes	characteristic
70	C₅₉×#389	C₂²	1	1	yes	characteristic
71	C₅₉×#389	C₂²	1	1	yes	characteristic
72	C₅₉×#389	C₂²	1	1	yes	characteristic
73	C₅₉×#389	C₂²	1	1	yes	characteristic
74	C₅₉×#389	C₂²	1	2	yes	—
75	C₅₉×#389	C₂²	1	1	yes	characteristic
76	C₅₉×#388	C₂²	1	2	yes	—
77	C₅₉×#388	C₂²	1	2	yes	—
78	C₅₉×#388	C₂²	1	2	yes	—
79	C₅₉×#388	C₂²	1	2	yes	—
80	C₅₉×#387	C₂²	1	2	yes	—
81	C₅₉×#387	C₂²	1	2	yes	—
82	C₅₉×#387	C₂²	1	2	yes	—
83	C₅₉×#387	C₂²	1	2	yes	—
84	C₅₉×#387	C₂²	1	1	yes	characteristic
85	C₅₉×#387	C₂²	1	1	yes	characteristic
86	C₅₉×#387	C₂²	1	1	yes	characteristic
87	C₅₉×#387	C₂²	1	1	yes	characteristic
88	C₅₉×#387	C₂²	1	2	yes	—
89	C₅₉×#387	C₂²	1	2	yes	—
90	C₅₉×#387	C₂²	1	2	yes	—
91	C₅₉×#387	C₂²	1	2	yes	—
92	C₅₉×#385	C₂²	1	2	yes	—
93	C₅₉×#385	C₂²	1	2	yes	—
94	C₅₉×#385	C₂²	1	2	yes	—
95	C₅₉×#385	C₂²	1	2	yes	—
96	C₅₉×#382	C₂²	1	1	yes	characteristic
97	C₅₉×#382	C₂²	1	2	yes	—
98	C₅₉×#382	C₂²	1	1	yes	characteristic
99	C₅₉×#382	C₂²	1	1	yes	characteristic
100	C₅₉×#381	C₂²	1	2	yes	—
101	C₅₉×#380	C₂²	1	2	yes	—
102	C₅₉×#380	C₂²	1	2	yes	—
103	C₅₉×#380	C₂²	1	2	yes	—
104	C₅₉×#380	C₂²	1	2	yes	—
105	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
106	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
114	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
116	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
119	C₅₉×#376	C₂²	1	1	yes	characteristic
120	C₅₉×#376	C₂²	1	1	yes	characteristic
121	C₂×#95×C₅₉	C₂²	1	2	yes	—
122	C₄³×C₅₉	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
125	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
126	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
128	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
129	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
130	C₄⋊Q₈×C₅₉	—	2	4	no	—
131	C₄⋊Q₈×C₅₉	—	2	4	no	—
132	C₄⋊Q₈×C₅₉	—	4	4	no	—
133	#125×C₅₉	—	2	4	no	—
134	C₂²⋊Q₈×C₅₉	—	4	4	no	—
135	C₄×Q₈×C₅₉	—	2	4	no	—
136	C₄×D₄×C₅₉	—	2	4	no	—
137	C₄×D₄×C₅₉	—	2	4	no	—
138	C₄×D₄×C₅₉	Q₈	1	8	yes	complemented
139	#117×C₅₉	—	4	4	no	—
140	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
181	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
191	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
192	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
193	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
194	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
195	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
197	#95×C₅₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
202	#95×C₅₉	C₂³	1	1	yes	characteristic
203	#95×C₅₉	C₂³	1	1	yes	characteristic
204	#95×C₅₉	C₂³	1	1	yes	characteristic
205	#95×C₅₉	C₂³	1	1	yes	characteristic
206	#95×C₅₉	C₂³	1	1	yes	characteristic
207	#95×C₅₉	C₂³	1	1	yes	characteristic
208	#95×C₅₉	C₂³	1	2	yes	—
209	#95×C₅₉	C₂³	1	2	yes	—
210	#95×C₅₉	C₂³	1	1	yes	characteristic
211	#95×C₅₉	C₂³	1	2	yes	—
212	#95×C₅₉	C₂³	1	2	yes	—
213	#95×C₅₉	C₂³	1	2	yes	—
214	#95×C₅₉	C₂³	1	1	yes	characteristic
215	#95×C₅₉	C₂³	1	1	yes	characteristic
216	#95×C₅₉	C₂³	1	2	yes	—
217	#95×C₅₉	C₂³	1	2	yes	—
218	#95×C₅₉	C₂³	1	1	yes	characteristic
219	#95×C₅₉	C₂³	1	2	yes	—
220	#95×C₅₉	C₂³	1	1	yes	characteristic
221	#95×C₅₉	C₂³	1	1	yes	characteristic
222	#95×C₅₉	C₂³	1	2	yes	—
223	#95×C₅₉	C₂³	1	2	yes	—
224	#95×C₅₉	C₂³	1	2	yes	—
225	#95×C₅₉	C₂³	1	2	yes	—
226	#95×C₅₉	C₂³	1	2	yes	—
227	#95×C₅₉	C₂³	1	2	yes	—
228	#95×C₅₉	C₂³	1	2	yes	—
229	#95×C₅₉	C₂³	1	2	yes	—
230	#95×C₅₉	C₂³	1	2	yes	—
231	#95×C₅₉	C₂³	1	2	yes	—
232	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
233	C₂×Q₈×C₅₉	—	2	2	no	—
234	C₂×Q₈×C₅₉	—	2	4	no	—
235	C₂×Q₈×C₅₉	—	2	4	no	—
236	C₂×Q₈×C₅₉	—	2	2	no	—
237	C₂×Q₈×C₅₉	—	4	1	no	—
238	C₂×Q₈×C₅₉	—	4	2	no	—
239	C₂×Q₈×C₅₉	—	4	2	no	—
240	C₂×Q₈×C₅₉	—	4	2	no	—
241	C₂×Q₈×C₅₉	—	4	2	no	—
242	C₂×D₄×C₅₉	—	2	2	no	—
243	C₂×D₄×C₅₉	—	2	2	no	—
244	C₂×D₄×C₅₉	C₂×Q₈	1	4	yes	—
245	C₂²×C₄×C₅₉	—	2	4	no	—
246	C₂²×C₄×C₅₉	—	2	4	no	—
247	C₂²×C₄×C₅₉	—	4	2	no	—
248	C₂²×C₄×C₅₉	—	4	2	no	—
249	C₂²×C₄×C₅₉	—	4	2	no	—
250	C₂²×C₄×C₅₉	—	4	2	no	—
251	C₂²×C₄×C₅₉	—	4	2	no	—
252	C₂²×C₄×C₅₉	—	4	2	no	—
253	C₂²×C₄×C₅₉	C₂×Q₈	1	8	yes	—
254	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
276	C₄⋊C₄×C₅₉	—	2	2	no	—
277	C₄⋊C₄×C₅₉	—	2	2	no	—
278	C₄⋊C₄×C₅₉	—	2	2	no	—
279	C₄⋊C₄×C₅₉	—	2	2	no	—
280	C₄⋊C₄×C₅₉	—	2	4	no	—
281	C₄⋊C₄×C₅₉	—	2	4	no	—
282	C₄⋊C₄×C₅₉	—	2	2	no	—
283	C₄⋊C₄×C₅₉	—	2	4	no	—
284	C₄⋊C₄×C₅₉	—	2	4	no	—
285	C₄⋊C₄×C₅₉	—	2	2	no	—
286	C₄⋊C₄×C₅₉	—	2	2	no	—
287	C₄⋊C₄×C₅₉	—	2	2	no	—
288	C₄⋊C₄×C₅₉	—	2	4	no	—
289	C₄⋊C₄×C₅₉	—	2	2	no	—
290	C₄⋊C₄×C₅₉	—	2	4	no	—
291	C₄⋊C₄×C₅₉	—	4	2	no	—
292	C₄⋊C₄×C₅₉	—	4	1	no	—
293	C₄⋊C₄×C₅₉	—	4	1	no	—
294	C₄⋊C₄×C₅₉	—	4	1	no	—
295	C₄⋊C₄×C₅₉	—	4	1	no	—
296	C₄⋊C₄×C₅₉	—	4	2	no	—
297	C₄⋊C₄×C₅₉	—	4	2	no	—
298	C₄⋊C₄×C₅₉	—	4	1	no	—
299	C₄⋊C₄×C₅₉	—	4	2	no	—
300	C₄⋊C₄×C₅₉	—	4	2	no	—
301	C₄⋊C₄×C₅₉	—	4	2	no	—
302	C₄⋊C₄×C₅₉	—	4	2	no	—
303	C₄⋊C₄×C₅₉	—	4	2	no	—
304	C₄⋊C₄×C₅₉	C₂×Q₈	1	4	yes	—
305	C₄⋊C₄×C₅₉	#41	1	4	yes	—
306	C₂²⋊C₄×C₅₉	—	2	4	no	—
307	C₂²⋊C₄×C₅₉	—	2	4	no	—
308	C₂²⋊C₄×C₅₉	—	2	4	no	—
309	C₂²⋊C₄×C₅₉	—	4	2	no	—
310	C₂²⋊C₄×C₅₉	—	4	2	no	—
311	C₂²⋊C₄×C₅₉	—	4	2	no	—
312	C₂²⋊C₄×C₅₉	—	4	2	no	—
313	C₂²⋊C₄×C₅₉	—	4	2	no	—
314	C₂²⋊C₄×C₅₉	—	4	2	no	—
315	C₂²⋊C₄×C₅₉	—	4	2	no	—
316	C₂²⋊C₄×C₅₉	C₂×Q₈	1	8	yes	—
317	C₄²×C₅₉	—	2	2	no	—
318	C₄²×C₅₉	—	2	2	no	—
319	C₄²×C₅₉	—	2	2	no	—
320	C₄²×C₅₉	—	2	2	no	—
321	C₄²×C₅₉	—	2	2	no	—
322	C₄²×C₅₉	—	2	2	no	—
323	C₄²×C₅₉	—	4	1	no	—
324	C₄²×C₅₉	—	4	2	no	—
325	C₄²×C₅₉	—	4	1	no	—
326	C₄²×C₅₉	—	4	2	no	—
327	C₄²×C₅₉	—	4	2	no	—
328	C₄²×C₅₉	—	4	1	no	—
329	C₄²×C₅₉	—	4	2	no	—
330	C₄²×C₅₉	—	4	2	no	—
331	C₄²×C₅₉	C₂×Q₈	1	4	yes	—
332	C₄²×C₅₉	#41	1	4	yes	—
333	C₂³×C₅₉	—	2	2	no	—
334	C₂³×C₅₉	—	2	2	no	—
335	C₂³×C₅₉	—	2	2	no	—
336	C₂³×C₅₉	—	2	2	no	—
337	C₂³×C₅₉	—	2	2	no	—
338	C₂³×C₅₉	—	2	2	no	—
339	C₂³×C₅₉	C₂²×Q₈	1	4	yes	—
340	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
341	Q₈×C₅₉	—	4	4	no	—
342	Q₈×C₅₉	—	8	4	no	—
343	Q₈×C₅₉	—	8	4	no	—
344	D₄×C₅₉	—	2	8	no	—
345	C₂×C₄×C₅₉	—	2	1	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	1	no	—
351	C₂×C₄×C₅₉	—	2	1	no	—
352	C₂×C₄×C₅₉	—	2	2	no	—
353	C₂×C₄×C₅₉	—	2	1	no	—
354	C₂×C₄×C₅₉	—	2	1	no	—
355	C₂×C₄×C₅₉	—	2	2	no	—
356	C₂×C₄×C₅₉	—	2	1	no	—
357	C₂×C₄×C₅₉	—	2	1	no	—
358	C₂×C₄×C₅₉	—	2	1	no	—
359	C₂×C₄×C₅₉	—	2	1	no	—
360	C₂×C₄×C₅₉	—	2	1	no	—
361	C₂×C₄×C₅₉	—	2	1	no	—
362	C₂×C₄×C₅₉	—	2	1	no	—
363	C₂×C₄×C₅₉	—	2	1	no	—
364	C₂×C₄×C₅₉	—	2	1	no	—
365	C₂×C₄×C₅₉	—	2	1	no	—
366	C₂×C₄×C₅₉	—	2	1	no	—
367	C₂×C₄×C₅₉	—	2	1	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	1	no	—
374	C₂×C₄×C₅₉	—	2	2	no	—
375	C₂×C₄×C₅₉	—	2	2	no	—
376	C₂×C₄×C₅₉	—	2	1	no	—
377	C₂×C₄×C₅₉	—	2	2	no	—
378	C₂×C₄×C₅₉	—	2	1	no	—
379	C₂×C₄×C₅₉	—	2	1	no	—
380	C₂×C₄×C₅₉	—	2	1	no	—
381	C₂×C₄×C₅₉	—	2	1	no	—
382	C₂×C₄×C₅₉	—	2	1	no	—
383	C₂×C₄×C₅₉	—	2	2	no	—
384	C₂×C₄×C₅₉	—	2	2	no	—
385	C₂×C₄×C₅₉	—	2	1	no	—
386	C₂×C₄×C₅₉	—	2	1	no	—
387	C₂×C₄×C₅₉	—	2	1	no	—
388	C₂×C₄×C₅₉	—	2	2	no	—
389	C₂×C₄×C₅₉	—	2	2	no	—
390	C₂×C₄×C₅₉	—	2	1	no	—
391	C₂×C₄×C₅₉	—	2	1	no	—
392	C₂×C₄×C₅₉	—	2	1	no	—
393	C₂×C₄×C₅₉	—	2	2	no	—
394	C₂×C₄×C₅₉	—	2	2	no	—
395	C₂×C₄×C₅₉	—	2	2	no	—
396	C₂×C₄×C₅₉	—	2	1	no	—
397	C₂×C₄×C₅₉	—	2	1	no	—
398	C₂×C₄×C₅₉	—	2	1	no	—
399	C₂×C₄×C₅₉	—	2	1	no	—
400	C₂×C₄×C₅₉	—	2	1	no	—
401	C₂×C₄×C₅₉	—	4	8	no	—
402	C₂×C₄×C₅₉	—	8	4	no	—
403	C₂×C₄×C₅₉	—	8	4	no	—
404	C₂×C₄×C₅₉	C₂²×Q₈	1	2	yes	—
405	C₂×C₄×C₅₉	C₂²×Q₈	1	2	yes	—
406	C₂×C₄×C₅₉	C₂²×Q₈	1	4	yes	—
407	C₂×C₄×C₅₉	C₂²×Q₈	1	2	yes	—
408	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
409	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
410	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
411	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
412	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
413	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
414	#35602	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
415	C₂²×C₅₉	—	2	4	no	—
416	C₂²×C₅₉	—	2	4	no	—
417	C₂²×C₅₉	—	2	4	no	—
418	C₂²×C₅₉	—	4	2	no	—
419	C₂²×C₅₉	—	4	2	no	—
420	C₂²×C₅₉	—	4	2	no	—
421	C₂²×C₅₉	—	4	2	no	—
422	C₂²×C₅₉	C₂³×Q₈	1	1	yes	characteristic
423	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
424	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
425	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
426	C₂²×C₅₉	#585	1	1	yes	characteristic
427	C₂²×C₅₉	#585	1	1	yes	characteristic
428	C₂²×C₅₉	#585	1	1	yes	characteristic
429	C₄×C₅₉	—	2	2	no	—
430	C₄×C₅₉	—	2	2	no	—
431	C₄×C₅₉	—	2	2	no	—
432	C₄×C₅₉	—	2	4	no	—
433	C₄×C₅₉	—	2	2	no	—
434	C₄×C₅₉	—	2	2	no	—
435	C₄×C₅₉	—	2	4	no	—
436	C₄×C₅₉	—	4	1	no	—
437	C₄×C₅₉	—	4	2	no	—
438	C₄×C₅₉	—	4	2	no	—
439	C₄×C₅₉	—	4	1	no	—
440	C₄×C₅₉	—	4	1	no	—
441	C₄×C₅₉	—	4	2	no	—
442	C₄×C₅₉	—	4	1	no	—
443	C₄×C₅₉	—	4	1	no	—
444	C₄×C₅₉	—	4	2	no	—
445	C₄×C₅₉	—	4	1	no	—
446	C₄×C₅₉	—	4	1	no	—
447	C₄×C₅₉	—	4	1	no	—
448	C₄×C₅₉	—	4	1	no	—
449	C₄×C₅₉	—	4	2	no	—
450	C₄×C₅₉	#533	1	4	yes	—
451	#2607	C₂×C₅₉	1	2	yes	complemented
452	#2589	C₂×C₅₉	1	2	yes	complemented
453	#2580	C₂×C₅₉	1	1	yes	characteristic
454	#2574	C₂×C₅₉	1	2	yes	complemented
455	#2569	C₂×C₅₉	1	2	yes	complemented
456	#2563	C₂×C₅₉	1	1	yes	characteristic
457	#2550	C₂×C₅₉	1	1	yes	characteristic, complemented
458	#2546	C₂×C₅₉	1	1	yes	characteristic, complemented
459	#2522	C₂×C₅₉	1	2	yes	complemented
460	#2509	C₂×C₅₉	1	1	yes	characteristic, complemented
461	#2508	C₂×C₅₉	1	1	yes	characteristic, complemented
462	#2492	C₂×C₅₉	1	2	yes	complemented
463	#2454	C₂×C₅₉	1	1	yes	characteristic
464	#2452	C₂×C₅₉	1	1	yes	characteristic
465	#2439	C₂×C₅₉	1	2	yes	complemented
466	#2438	C₂×C₅₉	1	2	yes	complemented
467	#2331	C₂×C₅₉	1	1	yes	characteristic, complemented
468	#2331	C₂×C₅₉	1	1	yes	characteristic, complemented
469	#2319	C₂×C₅₉	1	1	yes	characteristic
470	C₄×#125	C₂×C₅₉	1	1	yes	characteristic, complemented
471	#2295	C₂×C₅₉	1	1	yes	characteristic, complemented
472	#2293	C₂×C₅₉	1	1	yes	characteristic
473	#2275	C₂×C₅₉	1	1	yes	characteristic
474	C₂×C₅₉	—	4	4	no	—
475	C₂×C₅₉	C₂×#533	1	1	yes	characteristic
476	C₂×C₅₉	#3494	1	1	yes	characteristic
477	C₂×C₅₉	#3501	1	1	yes	characteristic
478	C₂×C₅₉	#3504	1	1	yes	characteristic
479	C₂×C₅₉	#3510	1	1	yes	characteristic
480	C₂×C₅₉	#3514	1	1	yes	characteristic
481	C₂×C₅₉	#3524	1	1	yes	characteristic
482	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
483	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
484	C₂×C₄⋊Q₈	C₂²×C₅₉	1	2	yes	—
485	C₂×#125	C₂²×C₅₉	1	1	yes	characteristic
486	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	—
487	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
488	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
489	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
490	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
491	C₂×#117	C₂²×C₅₉	1	2	yes	—
492	#400	C₂²×C₅₉	1	2	yes	—
493	#400	C₂²×C₅₉	1	2	yes	—
494	#400	C₂²×C₅₉	1	2	yes	—
495	#399	C₂²×C₅₉	1	2	yes	—
496	#399	C₂²×C₅₉	1	2	yes	—
497	#398	C₂²×C₅₉	1	2	yes	—
498	#398	C₂²×C₅₉	1	2	yes	—
499	#398	C₂²×C₅₉	1	2	yes	—
500	#398	C₂²×C₅₉	1	2	yes	—
501	#396	C₂²×C₅₉	1	2	yes	—
502	#396	C₂²×C₅₉	1	2	yes	—
503	#395	C₂²×C₅₉	1	2	yes	—
504	#393	C₂²×C₅₉	1	2	yes	—
505	#393	C₂²×C₅₉	1	2	yes	—
506	#393	C₂²×C₅₉	1	2	yes	—
507	#393	C₂²×C₅₉	1	2	yes	—
508	#391	C₂²×C₅₉	1	2	yes	—
509	#391	C₂²×C₅₉	1	2	yes	—
510	#391	C₂²×C₅₉	1	2	yes	—
511	#391	C₂²×C₅₉	1	2	yes	—
512	#391	C₂²×C₅₉	1	2	yes	—
513	#391	C₂²×C₅₉	1	2	yes	—
514	#391	C₂²×C₅₉	1	1	yes	characteristic
515	#391	C₂²×C₅₉	1	1	yes	characteristic
516	#390	C₂²×C₅₉	1	1	yes	characteristic
517	#390	C₂²×C₅₉	1	1	yes	characteristic
518	#390	C₂²×C₅₉	1	1	yes	characteristic
519	#390	C₂²×C₅₉	1	1	yes	characteristic
520	#389	C₂²×C₅₉	1	1	yes	characteristic
521	#389	C₂²×C₅₉	1	1	yes	characteristic
522	#389	C₂²×C₅₉	1	1	yes	characteristic
523	#389	C₂²×C₅₉	1	1	yes	characteristic
524	#389	C₂²×C₅₉	1	1	yes	characteristic
525	#389	C₂²×C₅₉	1	1	yes	characteristic
526	#389	C₂²×C₅₉	1	1	yes	characteristic
527	#389	C₂²×C₅₉	1	1	yes	characteristic
528	#389	C₂²×C₅₉	1	2	yes	—
529	#389	C₂²×C₅₉	1	1	yes	characteristic
530	#389	C₂²×C₅₉	1	2	yes	—
531	#389	C₂²×C₅₉	1	1	yes	characteristic
532	#389	C₂²×C₅₉	1	1	yes	characteristic
533	#389	C₂²×C₅₉	1	1	yes	characteristic
534	#388	C₂²×C₅₉	1	2	yes	—
535	#388	C₂²×C₅₉	1	2	yes	—
536	#388	C₂²×C₅₉	1	2	yes	—
537	#388	C₂²×C₅₉	1	2	yes	—
538	#387	C₂²×C₅₉	1	2	yes	—
539	#387	C₂²×C₅₉	1	2	yes	—
540	#387	C₂²×C₅₉	1	1	yes	characteristic
541	#387	C₂²×C₅₉	1	2	yes	—
542	#387	C₂²×C₅₉	1	2	yes	—
543	#387	C₂²×C₅₉	1	1	yes	characteristic
544	#387	C₂²×C₅₉	1	2	yes	—
545	#387	C₂²×C₅₉	1	2	yes	—
546	#387	C₂²×C₅₉	1	2	yes	—
547	#387	C₂²×C₅₉	1	1	yes	characteristic
548	#387	C₂²×C₅₉	1	1	yes	characteristic
549	#387	C₂²×C₅₉	1	2	yes	—
550	#385	C₂²×C₅₉	1	2	yes	—
551	#385	C₂²×C₅₉	1	2	yes	—
552	#385	C₂²×C₅₉	1	2	yes	—
553	#385	C₂²×C₅₉	1	2	yes	—
554	#382	C₂²×C₅₉	1	1	yes	characteristic
555	#382	C₂²×C₅₉	1	1	yes	characteristic
556	#382	C₂²×C₅₉	1	2	yes	—
557	#382	C₂²×C₅₉	1	1	yes	characteristic
558	#381	C₂²×C₅₉	1	2	yes	—
559	#380	C₂²×C₅₉	1	2	yes	—
560	#380	C₂²×C₅₉	1	2	yes	—
561	#380	C₂²×C₅₉	1	2	yes	—
562	#380	C₂²×C₅₉	1	2	yes	—
563	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
564	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
565	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
566	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
567	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
568	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
569	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
570	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
571	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
572	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
573	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
574	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
575	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
576	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
577	#376	C₂²×C₅₉	1	1	yes	characteristic
578	#376	C₂²×C₅₉	1	1	yes	characteristic
579	C₂×#95	C₂²×C₅₉	1	2	yes	—
580	C₄³	C₂²×C₅₉	1	1	yes	characteristic
581	C₅₉	#35602	1	1	yes	characteristic, direct product factor, Sylow
582	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
583	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
584	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
585	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
586	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
587	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
588	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
589	C₄⋊Q₈	—	2	4	no	—
590	C₄⋊Q₈	—	2	4	no	—
591	C₄⋊Q₈	—	4	4	no	—
592	#125	—	2	4	no	—
593	C₂²⋊Q₈	—	4	4	no	—
594	C₄×Q₈	—	2	4	no	—
595	C₄×D₄	—	2	4	no	—
596	C₄×D₄	—	2	4	no	—
597	C₄×D₄	Q₈×C₅₉	1	8	yes	complemented
598	#117	—	4	4	no	—
599	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
627	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
629	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
640	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
641	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
642	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
643	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
644	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
645	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
646	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
647	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
648	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
650	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
652	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
653	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
654	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
655	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
656	#95	C₂³×C₅₉	1	1	yes	characteristic
657	#95	C₂³×C₅₉	1	2	yes	—
658	#95	C₂³×C₅₉	1	2	yes	—
659	#95	C₂³×C₅₉	1	2	yes	—
660	#95	C₂³×C₅₉	1	1	yes	characteristic
661	#95	C₂³×C₅₉	1	1	yes	characteristic
662	#95	C₂³×C₅₉	1	1	yes	characteristic
663	#95	C₂³×C₅₉	1	1	yes	characteristic
664	#95	C₂³×C₅₉	1	1	yes	characteristic
665	#95	C₂³×C₅₉	1	1	yes	characteristic
666	#95	C₂³×C₅₉	1	1	yes	characteristic
667	#95	C₂³×C₅₉	1	2	yes	—
668	#95	C₂³×C₅₉	1	2	yes	—
669	#95	C₂³×C₅₉	1	1	yes	characteristic
670	#95	C₂³×C₅₉	1	2	yes	—
671	#95	C₂³×C₅₉	1	2	yes	—
672	#95	C₂³×C₅₉	1	2	yes	—
673	#95	C₂³×C₅₉	1	1	yes	characteristic
674	#95	C₂³×C₅₉	1	1	yes	characteristic
675	#95	C₂³×C₅₉	1	2	yes	—
676	#95	C₂³×C₅₉	1	2	yes	—
677	#95	C₂³×C₅₉	1	1	yes	characteristic
678	#95	C₂³×C₅₉	1	2	yes	—
679	#95	C₂³×C₅₉	1	1	yes	characteristic
680	#95	C₂³×C₅₉	1	1	yes	characteristic
681	#95	C₂³×C₅₉	1	2	yes	—
682	#95	C₂³×C₅₉	1	2	yes	—
683	#95	C₂³×C₅₉	1	2	yes	—
684	#95	C₂³×C₅₉	1	2	yes	—
685	#95	C₂³×C₅₉	1	2	yes	—
686	#95	C₂³×C₅₉	1	2	yes	—
687	#95	C₂³×C₅₉	1	2	yes	—
688	#95	C₂³×C₅₉	1	2	yes	—
689	#95	C₂³×C₅₉	1	2	yes	—
690	#95	C₂³×C₅₉	1	2	yes	—
691	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
692	C₂×Q₈	—	2	2	no	—
693	C₂×Q₈	—	2	4	no	—
694	C₂×Q₈	—	2	4	no	—
695	C₂×Q₈	—	2	2	no	—
696	C₂×Q₈	—	4	1	no	—
697	C₂×Q₈	—	4	2	no	—
698	C₂×Q₈	—	4	2	no	—
699	C₂×Q₈	—	4	2	no	—
700	C₂×Q₈	—	4	2	no	—
701	C₂×D₄	—	2	2	no	—
702	C₂×D₄	—	2	2	no	—
703	C₂×D₄	C₂×Q₈×C₅₉	1	4	yes	—
704	C₂²×C₄	—	2	4	no	—
705	C₂²×C₄	—	2	4	no	—
706	C₂²×C₄	—	4	2	no	—
707	C₂²×C₄	—	4	2	no	—
708	C₂²×C₄	—	4	2	no	—
709	C₂²×C₄	—	4	2	no	—
710	C₂²×C₄	—	4	2	no	—
711	C₂²×C₄	—	4	2	no	—
712	C₂²×C₄	C₂×Q₈×C₅₉	1	8	yes	—
713	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
715	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
716	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
717	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
719	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
723	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
729	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	4	no	—
740	C₄⋊C₄	—	2	4	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	4	no	—
743	C₄⋊C₄	—	2	4	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	4	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	4	no	—
750	C₄⋊C₄	—	4	2	no	—
751	C₄⋊C₄	—	4	2	no	—
752	C₄⋊C₄	—	4	2	no	—
753	C₄⋊C₄	—	4	2	no	—
754	C₄⋊C₄	—	4	2	no	—
755	C₄⋊C₄	—	4	1	no	—
756	C₄⋊C₄	—	4	1	no	—
757	C₄⋊C₄	—	4	1	no	—
758	C₄⋊C₄	—	4	1	no	—
759	C₄⋊C₄	—	4	2	no	—
760	C₄⋊C₄	—	4	2	no	—
761	C₄⋊C₄	—	4	1	no	—
762	C₄⋊C₄	—	4	2	no	—
763	C₄⋊C₄	C₂×Q₈×C₅₉	1	4	yes	—
764	C₄⋊C₄	#41×C₅₉	1	4	yes	—
765	C₂²⋊C₄	—	2	4	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	4	2	no	—
769	C₂²⋊C₄	—	4	2	no	—
770	C₂²⋊C₄	—	4	2	no	—
771	C₂²⋊C₄	—	4	2	no	—
772	C₂²⋊C₄	—	4	2	no	—
773	C₂²⋊C₄	—	4	2	no	—
774	C₂²⋊C₄	—	4	2	no	—
775	C₂²⋊C₄	C₂×Q₈×C₅₉	1	8	yes	—
776	C₄²	—	2	2	no	—
777	C₄²	—	2	2	no	—
778	C₄²	—	2	2	no	—
779	C₄²	—	2	2	no	—
780	C₄²	—	2	2	no	—
781	C₄²	—	2	2	no	—
782	C₄²	—	4	2	no	—
783	C₄²	—	4	2	no	—
784	C₄²	—	4	1	no	—
785	C₄²	—	4	2	no	—
786	C₄²	—	4	1	no	—
787	C₄²	—	4	2	no	—
788	C₄²	—	4	2	no	—
789	C₄²	—	4	1	no	—
790	C₄²	C₂×Q₈×C₅₉	1	4	yes	—
791	C₄²	#41×C₅₉	1	4	yes	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	2	2	no	—
797	C₂³	—	2	2	no	—
798	C₂³	C₂²×Q₈×C₅₉	1	4	yes	—
799	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
800	Q₈	—	4	4	no	—
801	Q₈	—	8	4	no	—
802	Q₈	—	8	4	no	—
803	D₄	—	2	8	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	4	8	no	—
861	C₂×C₄	—	8	4	no	—
862	C₂×C₄	—	8	4	no	—
863	C₂×C₄	C₂²×Q₈×C₅₉	1	2	yes	—
864	C₂×C₄	C₂²×Q₈×C₅₉	1	2	yes	—
865	C₂×C₄	C₂²×Q₈×C₅₉	1	4	yes	—
866	C₂×C₄	C₂²×Q₈×C₅₉	1	2	yes	—
867	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
868	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
869	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
870	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
871	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
872	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
873	C₂²	—	2	4	no	—
874	C₂²	—	2	4	no	—
875	C₂²	—	2	4	no	—
876	C₂²	—	4	2	no	—
877	C₂²	—	4	2	no	—
878	C₂²	—	4	2	no	—
879	C₂²	—	4	2	no	—
880	C₂²	C₂³×Q₈×C₅₉	1	1	yes	characteristic
881	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
882	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
883	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
884	C₂²	C₅₉×#585	1	1	yes	characteristic
885	C₂²	C₅₉×#585	1	1	yes	characteristic
886	C₂²	C₅₉×#585	1	1	yes	characteristic
887	C₄	—	2	2	no	—
888	C₄	—	2	4	no	—
889	C₄	—	2	2	no	—
890	C₄	—	2	2	no	—
891	C₄	—	2	2	no	—
892	C₄	—	2	4	no	—
893	C₄	—	2	2	no	—
894	C₄	—	4	2	no	—
895	C₄	—	4	1	no	—
896	C₄	—	4	1	no	—
897	C₄	—	4	1	no	—
898	C₄	—	4	1	no	—
899	C₄	—	4	2	no	—
900	C₄	—	4	1	no	—
901	C₄	—	4	1	no	—
902	C₄	—	4	1	no	—
903	C₄	—	4	1	no	—
904	C₄	—	4	2	no	—
905	C₄	—	4	1	no	—
906	C₄	—	4	2	no	—
907	C₄	—	4	2	no	—
908	C₄	C₅₉×#533	1	4	yes	—
909	C₂	—	4	4	no	—
910	C₂	C₂×C₅₉×#533	1	1	yes	characteristic
911	C₂	C₅₉×#3494	1	1	yes	characteristic
912	C₂	C₅₉×#3501	1	1	yes	characteristic
913	C₂	C₅₉×#3504	1	1	yes	characteristic
914	C₂	C₅₉×#3510	1	1	yes	characteristic
915	C₂	C₅₉×#3514	1	1	yes	characteristic
916	C₂	C₅₉×#3524	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₂²×D₄×C₅₉	C₂³
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×#2607	C₂	semidirect
2. C₅₉×#2589	C₂	semidirect
4. C₅₉×#2574	C₂	semidirect
5. C₅₉×#2569	C₂	semidirect
7. C₅₉×#2550	C₂	semidirect
8. C₅₉×#2546	C₂	semidirect
9. C₅₉×#2522	C₂	semidirect
10. C₅₉×#2509	C₂	semidirect
11. C₅₉×#2508	C₂	semidirect
12. C₅₉×#2492	C₂	semidirect
15. C₅₉×#2439	C₂	semidirect
16. C₅₉×#2438	C₂	semidirect
17. C₅₉×#2331	C₂	semidirect
18. C₅₉×#2331	C₂	semidirect
20. C₄×#125×C₅₉	C₂	semidirect
21. C₅₉×#2295	C₂	semidirect
138. C₄×D₄×C₅₉	Q₈	semidirect
414. #35602	C₅₉	direct (N × H)
451. #2607	C₂×C₅₉	semidirect
452. #2589	C₂×C₅₉	semidirect
454. #2574	C₂×C₅₉	semidirect
455. #2569	C₂×C₅₉	semidirect
457. #2550	C₂×C₅₉	semidirect
458. #2546	C₂×C₅₉	semidirect
459. #2522	C₂×C₅₉	semidirect
460. #2509	C₂×C₅₉	semidirect
461. #2508	C₂×C₅₉	semidirect
462. #2492	C₂×C₅₉	semidirect
465. #2439	C₂×C₅₉	semidirect
466. #2438	C₂×C₅₉	semidirect
467. #2331	C₂×C₅₉	semidirect
468. #2331	C₂×C₅₉	semidirect
470. C₄×#125	C₂×C₅₉	semidirect
471. #2295	C₂×C₅₉	semidirect
581. C₅₉	#35602	direct (N × H)
597. C₄×D₄	Q₈×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₅₉×#2607	2
C₅₉×#2589	2
C₅₉×#2580	2
C₅₉×#2574	2
C₅₉×#2569	2
C₅₉×#2563	2
C₅₉×#2550	2
C₅₉×#2546	2
C₅₉×#2522	2
C₅₉×#2509	2
C₅₉×#2508	2
C₅₉×#2492	2
C₅₉×#2454	2
C₅₉×#2452	2
C₅₉×#2439	2
C₅₉×#2438	2
C₅₉×#2331	2
C₅₉×#2319	2
C₄×#125×C₅₉	2
C₅₉×#2295	2
C₅₉×#2293	2
C₅₉×#2275	2
#35602	59

Subgroups — C59×#35602 #28447711

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35602 #28447711