Subgroups — C₅₉×#35847 #28447956

Order 15104.

2590 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#546	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2640	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2639	C₂	1	2	yes	maximal, complemented
5	C₅₉×#2592	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#2561	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2547	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#2504	C₂	1	2	yes	maximal, complemented
9	C₅₉×#2490	C₂	1	2	yes	maximal, complemented
10	C₅₉×#2489	C₂	1	2	yes	maximal, complemented
11	C₅₉×#2488	C₂	1	4	yes	maximal, complemented
12	C₅₉×#2472	C₂	1	4	yes	maximal, complemented
13	C₅₉×#2398	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅₉×#397	C₂	1	2	yes	maximal, complemented
15	C₅₉×#2339	C₂	1	2	yes	maximal, complemented
16	D₄×C₂²⋊C₄×C₅₉	C₂	1	2	yes	maximal, complemented
17	C₅₉×#2275	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₅₉	C₂²	1	1	yes	characteristic
20	C₅₉×#554	—	2	8	no	—
21	C₅₉×#546	—	2	8	no	—
22	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
23	C₂×#125×C₅₉	C₂²	1	2	yes	complemented
24	C₂×#124×C₅₉	C₂²	1	1	yes	characteristic
25	C₂×#124×C₅₉	C₂²	1	2	yes	—
26	C₂×#123×C₅₉	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	4	yes	complemented
29	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	complemented
30	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
31	C₂×#121×C₅₉	C₂²	1	2	yes	—
32	C₂×#120×C₅₉	C₂²	1	2	yes	—
33	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
38	C₂²×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
39	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
40	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	4	yes	—
41	C₅₉×#400	C₂²	1	2	yes	complemented
42	C₅₉×#400	C₂²	1	4	yes	complemented
43	C₅₉×#397	C₂²	1	4	yes	—
44	C₅₉×#397	C₂²	1	2	yes	—
45	C₅₉×#397	C₂²	1	1	yes	characteristic
46	C₅₉×#397	C₂²	1	4	yes	complemented
47	C₅₉×#397	C₂²	1	1	yes	characteristic, complemented
48	C₅₉×#397	C₂²	1	2	yes	complemented
49	C₅₉×#397	C₂²	1	2	yes	complemented
50	C₅₉×#397	C₂²	1	2	yes	complemented
51	C₅₉×#397	C₂²	1	2	yes	complemented
52	C₅₉×#394	C₂²	1	2	yes	—
53	C₅₉×#394	C₂²	1	4	yes	complemented
54	C₅₉×#393	C₂²	1	1	yes	characteristic
55	C₅₉×#393	C₂²	1	4	yes	complemented
56	C₅₉×#393	C₂²	1	2	yes	complemented
57	C₅₉×#393	C₂²	1	1	yes	characteristic, complemented
58	C₅₉×#391	C₂²	1	2	yes	complemented
59	C₅₉×#391	C₂²	1	2	yes	complemented
60	C₅₉×#391	C₂²	1	2	yes	complemented
61	C₅₉×#390	C₂²	1	2	yes	—
62	C₅₉×#390	C₂²	1	2	yes	—
63	C₅₉×#390	C₂²	1	4	yes	complemented
64	C₅₉×#388	C₂²	1	4	yes	—
65	C₅₉×#388	C₂²	1	4	yes	complemented
66	C₅₉×#388	C₂²	1	4	yes	complemented
67	C₅₉×#386	C₂²	1	4	yes	—
68	C₅₉×#386	C₂²	1	4	yes	—
69	C₅₉×#386	C₂²	1	4	yes	complemented
70	C₅₉×#386	C₂²	1	4	yes	complemented
71	C₅₉×#382	C₂²	1	4	yes	complemented
72	C₅₉×#381	C₂²	1	4	yes	complemented
73	C₅₉×#380	C₂²	1	2	yes	—
74	C₅₉×#380	C₂²	1	2	yes	complemented
75	C₅₉×#379	C₂²	1	4	yes	—
76	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
77	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
78	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
79	C₄×C₂²⋊C₄×C₅₉	C₂²	1	4	yes	complemented
80	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	complemented
81	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	complemented
82	C₅₉×#376	C₂²	1	1	yes	characteristic, complemented
83	C₂×#95×C₅₉	C₂²	1	4	yes	complemented
84	C₂×#95×C₅₉	C₂²	1	2	yes	complemented
85	C₂⁵×C₅₉	C₂³	1	2	yes	—
86	C₂×#41×C₅₉	—	2	4	no	—
87	C₂×#41×C₅₉	—	2	8	no	—
88	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
89	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
90	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₅₉	—	2	4	no	—
92	C₂²×D₄×C₅₉	—	2	8	no	—
93	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
94	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
95	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
96	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
97	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
98	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
100	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₅₉	C₂³	1	4	yes	—
103	C₂³×C₄×C₅₉	C₂³	1	4	yes	—
104	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
105	C₄⋊Q₈×C₅₉	—	2	4	no	—
106	#125×C₅₉	—	2	8	no	—
107	#124×C₅₉	—	2	4	no	—
108	#124×C₅₉	—	4	4	no	—
109	#123×C₅₉	—	2	8	no	—
110	C₂²⋊Q₈×C₅₉	—	2	8	no	—
111	C₂²⋊Q₈×C₅₉	—	2	4	no	—
112	C₂²⋊Q₈×C₅₉	—	2	16	no	—
113	#121×C₅₉	—	2	8	no	—
114	#121×C₅₉	—	2	4	no	—
115	#120×C₅₉	—	2	8	no	—
116	C₄×Q₈×C₅₉	—	2	4	no	—
117	C₄×D₄×C₅₉	—	2	8	no	—
118	C₄×D₄×C₅₉	—	2	8	no	—
119	C₄×D₄×C₅₉	—	2	4	no	—
120	C₄×D₄×C₅₉	D₄	1	8	yes	—
121	C₂×C₄⋊C₄×C₅₉	—	2	8	no	—
122	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
126	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
127	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊C₄×C₅₉	—	2	8	no	—
133	C₂×C₂²⋊C₄×C₅₉	—	4	8	no	—
134	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
135	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
152	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
153	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
154	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
155	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
156	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
157	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
158	#95×C₅₉	C₂³	1	1	yes	characteristic
159	#95×C₅₉	C₂³	1	2	yes	—
160	#95×C₅₉	C₂³	1	2	yes	—
161	#95×C₅₉	C₂³	1	4	yes	—
162	#95×C₅₉	C₂³	1	4	yes	—
163	#95×C₅₉	C₂³	1	4	yes	—
164	#95×C₅₉	C₂³	1	4	yes	—
165	#95×C₅₉	C₂³	1	1	yes	characteristic
166	#95×C₅₉	C₂³	1	2	yes	—
167	#95×C₅₉	C₂³	1	2	yes	—
168	#95×C₅₉	C₂³	1	2	yes	—
169	#95×C₅₉	C₂³	1	2	yes	—
170	#95×C₅₉	C₂³	1	4	yes	—
171	#95×C₅₉	C₂³	1	4	yes	—
172	#95×C₅₉	C₂³	1	4	yes	—
173	C₂⁴×C₅₉	—	2	4	no	—
174	C₂⁴×C₅₉	—	2	4	no	—
175	C₂⁴×C₅₉	—	2	8	no	—
176	C₂⁴×C₅₉	—	4	4	no	—
177	C₂⁴×C₅₉	—	4	2	no	—
178	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
179	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
180	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
181	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
182	#41×C₅₉	—	4	16	no	—
183	C₂×Q₈×C₅₉	—	2	2	no	—
184	C₂×Q₈×C₅₉	—	2	2	no	—
185	C₂×Q₈×C₅₉	—	2	4	no	—
186	C₂×Q₈×C₅₉	—	2	4	no	—
187	C₂×Q₈×C₅₉	—	4	2	no	—
188	C₂×Q₈×C₅₉	—	4	2	no	—
189	C₂×Q₈×C₅₉	—	4	2	no	—
190	C₂×D₄×C₅₉	—	2	4	no	—
191	C₂×D₄×C₅₉	—	2	4	no	—
192	C₂×D₄×C₅₉	—	2	8	no	—
193	C₂×D₄×C₅₉	—	2	8	no	—
194	C₂×D₄×C₅₉	—	2	2	no	—
195	C₂×D₄×C₅₉	—	2	2	no	—
196	C₂×D₄×C₅₉	—	2	2	no	—
197	C₂×D₄×C₅₉	—	2	4	no	—
198	C₂×D₄×C₅₉	—	2	4	no	—
199	C₂×D₄×C₅₉	—	4	1	no	—
200	C₂×D₄×C₅₉	—	4	4	no	—
201	C₂×D₄×C₅₉	—	4	16	no	—
202	C₂×D₄×C₅₉	C₂×D₄	1	4	yes	—
203	C₂×D₄×C₅₉	#41	1	8	yes	—
204	C₂²×C₄×C₅₉	—	2	4	no	—
205	C₂²×C₄×C₅₉	—	2	8	no	—
206	C₂²×C₄×C₅₉	—	2	8	no	—
207	C₂²×C₄×C₅₉	—	2	8	no	—
208	C₂²×C₄×C₅₉	—	2	2	no	—
209	C₂²×C₄×C₅₉	—	2	2	no	—
210	C₂²×C₄×C₅₉	—	2	4	no	—
211	C₂²×C₄×C₅₉	—	2	4	no	—
212	C₂²×C₄×C₅₉	—	4	4	no	—
213	C₂²×C₄×C₅₉	—	4	4	no	—
214	C₂²×C₄×C₅₉	—	4	4	no	—
215	C₂²×C₄×C₅₉	—	4	4	no	—
216	C₂²×C₄×C₅₉	—	4	4	no	—
217	C₂²×C₄×C₅₉	C₂×D₄	1	8	yes	—
218	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
224	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
227	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
231	C₄⋊C₄×C₅₉	—	2	2	no	—
232	C₄⋊C₄×C₅₉	—	2	8	no	—
233	C₄⋊C₄×C₅₉	—	2	4	no	—
234	C₄⋊C₄×C₅₉	—	2	2	no	—
235	C₄⋊C₄×C₅₉	—	2	4	no	—
236	C₄⋊C₄×C₅₉	—	2	4	no	—
237	C₄⋊C₄×C₅₉	—	2	4	no	—
238	C₄⋊C₄×C₅₉	—	2	8	no	—
239	C₄⋊C₄×C₅₉	—	2	4	no	—
240	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
241	C₂²⋊C₄×C₅₉	—	2	8	no	—
242	C₂²⋊C₄×C₅₉	—	2	8	no	—
243	C₂²⋊C₄×C₅₉	—	2	4	no	—
244	C₂²⋊C₄×C₅₉	—	2	8	no	—
245	C₂²⋊C₄×C₅₉	—	2	2	no	—
246	C₂²⋊C₄×C₅₉	—	2	4	no	—
247	C₂²⋊C₄×C₅₉	—	2	4	no	—
248	C₂²⋊C₄×C₅₉	—	2	4	no	—
249	C₂²⋊C₄×C₅₉	—	2	2	no	—
250	C₂²⋊C₄×C₅₉	—	2	4	no	—
251	C₂²⋊C₄×C₅₉	—	4	4	no	—
252	C₂²⋊C₄×C₅₉	—	4	4	no	—
253	C₂²⋊C₄×C₅₉	—	4	2	no	—
254	C₂²⋊C₄×C₅₉	—	4	4	no	—
255	C₂²⋊C₄×C₅₉	—	4	2	no	—
256	C₂²⋊C₄×C₅₉	—	4	4	no	—
257	C₂²⋊C₄×C₅₉	—	4	2	no	—
258	C₂²⋊C₄×C₅₉	—	4	4	no	—
259	C₂²⋊C₄×C₅₉	C₂×D₄	1	8	yes	—
260	C₄²×C₅₉	—	2	4	no	—
261	C₄²×C₅₉	—	2	4	no	—
262	C₄²×C₅₉	—	4	4	no	—
263	C₄²×C₅₉	—	4	2	no	—
264	C₄²×C₅₉	C₂×D₄	1	4	yes	—
265	C₂³×C₅₉	—	2	2	no	—
266	C₂³×C₅₉	—	2	4	no	—
267	C₂³×C₅₉	—	2	2	no	—
268	C₂³×C₅₉	—	2	1	no	—
269	C₂³×C₅₉	—	2	2	no	—
270	C₂³×C₅₉	—	2	2	no	—
271	C₂³×C₅₉	—	2	1	no	—
272	C₂³×C₅₉	—	2	2	no	—
273	C₂³×C₅₉	—	2	1	no	—
274	C₂³×C₅₉	—	2	2	no	—
275	C₂³×C₅₉	—	2	4	no	—
276	C₂³×C₅₉	—	2	1	no	—
277	C₂³×C₅₉	—	2	2	no	—
278	C₂³×C₅₉	—	2	1	no	—
279	C₂³×C₅₉	—	2	2	no	—
280	C₂³×C₅₉	—	2	2	no	—
281	C₂³×C₅₉	—	2	4	no	—
282	C₂³×C₅₉	—	4	8	no	—
283	C₂³×C₅₉	—	4	16	no	—
284	C₂³×C₅₉	—	4	8	no	—
285	C₂³×C₅₉	—	8	4	no	—
286	C₂³×C₅₉	—	8	8	no	—
287	C₂³×C₅₉	C₂²×D₄	1	4	yes	—
288	C₂³×C₅₉	C₂×#41	1	8	yes	—
289	C₂³×C₅₉	H(5,𝔽₂)	1	2	yes	—
290	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
291	Q₈×C₅₉	—	4	4	no	—
292	Q₈×C₅₉	—	4	4	no	—
293	Q₈×C₅₉	—	8	4	no	—
294	D₄×C₅₉	—	4	4	no	—
295	D₄×C₅₉	—	4	8	no	—
296	D₄×C₅₉	—	4	8	no	—
297	D₄×C₅₉	—	4	4	no	—
298	D₄×C₅₉	—	8	4	no	—
299	D₄×C₅₉	#124	1	16	yes	complemented
300	C₂×C₄×C₅₉	—	2	1	no	—
301	C₂×C₄×C₅₉	—	2	4	no	—
302	C₂×C₄×C₅₉	—	2	2	no	—
303	C₂×C₄×C₅₉	—	2	1	no	—
304	C₂×C₄×C₅₉	—	2	2	no	—
305	C₂×C₄×C₅₉	—	2	2	no	—
306	C₂×C₄×C₅₉	—	2	1	no	—
307	C₂×C₄×C₅₉	—	2	2	no	—
308	C₂×C₄×C₅₉	—	2	4	no	—
309	C₂×C₄×C₅₉	—	2	1	no	—
310	C₂×C₄×C₅₉	—	2	2	no	—
311	C₂×C₄×C₅₉	—	2	2	no	—
312	C₂×C₄×C₅₉	—	2	4	no	—
313	C₂×C₄×C₅₉	—	2	2	no	—
314	C₂×C₄×C₅₉	—	2	2	no	—
315	C₂×C₄×C₅₉	—	2	4	no	—
316	C₂×C₄×C₅₉	—	2	4	no	—
317	C₂×C₄×C₅₉	—	2	2	no	—
318	C₂×C₄×C₅₉	—	2	2	no	—
319	C₂×C₄×C₅₉	—	2	4	no	—
320	C₂×C₄×C₅₉	—	2	2	no	—
321	C₂×C₄×C₅₉	—	2	4	no	—
322	C₂×C₄×C₅₉	—	2	2	no	—
323	C₂×C₄×C₅₉	—	2	2	no	—
324	C₂×C₄×C₅₉	—	2	2	no	—
325	C₂×C₄×C₅₉	—	2	2	no	—
326	C₂×C₄×C₅₉	—	2	2	no	—
327	C₂×C₄×C₅₉	—	2	4	no	—
328	C₂×C₄×C₅₉	—	4	8	no	—
329	C₂×C₄×C₅₉	—	4	8	no	—
330	C₂×C₄×C₅₉	—	4	4	no	—
331	C₂×C₄×C₅₉	—	4	4	no	—
332	C₂×C₄×C₅₉	—	8	8	no	—
333	C₂×C₄×C₅₉	—	8	8	no	—
334	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
336	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
337	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
338	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
339	#35847	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
340	C₂²×C₅₉	—	2	4	no	—
341	C₂²×C₅₉	—	2	4	no	—
342	C₂²×C₅₉	—	2	8	no	—
343	C₂²×C₅₉	—	2	8	no	—
344	C₂²×C₅₉	—	2	2	no	—
345	C₂²×C₅₉	—	2	4	no	—
346	C₂²×C₅₉	—	4	1	no	—
347	C₂²×C₅₉	—	4	1	no	—
348	C₂²×C₅₉	—	4	2	no	—
349	C₂²×C₅₉	—	4	1	no	—
350	C₂²×C₅₉	—	4	2	no	—
351	C₂²×C₅₉	—	4	1	no	—
352	C₂²×C₅₉	—	4	2	no	—
353	C₂²×C₅₉	—	4	1	no	—
354	C₂²×C₅₉	—	4	2	no	—
355	C₂²×C₅₉	—	4	2	no	—
356	C₂²×C₅₉	—	4	4	no	—
357	C₂²×C₅₉	—	4	2	no	—
358	C₂²×C₅₉	—	4	4	no	—
359	C₂²×C₅₉	—	8	16	no	—
360	C₂²×C₅₉	C₂×#124	1	8	yes	—
361	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
362	C₂²×C₅₉	C₂²×#41	1	2	yes	—
363	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
364	C₂²×C₅₉	#585	1	2	yes	—
365	C₂²×C₅₉	#585	1	1	yes	characteristic
366	C₄×C₅₉	—	2	2	no	—
367	C₄×C₅₉	—	2	4	no	—
368	C₄×C₅₉	—	2	2	no	—
369	C₄×C₅₉	—	4	1	no	—
370	C₄×C₅₉	—	4	1	no	—
371	C₄×C₅₉	—	4	2	no	—
372	C₄×C₅₉	—	4	2	no	—
373	C₄×C₅₉	—	4	2	no	—
374	C₄×C₅₉	—	4	4	no	—
375	C₄×C₅₉	—	4	4	no	—
376	C₄×C₅₉	—	4	2	no	—
377	C₄×C₅₉	—	4	2	no	—
378	C₄×C₅₉	C₂×#124	1	4	yes	—
379	C₂×#554	C₂×C₅₉	1	1	yes	characteristic, complemented
380	C₂×#546	C₂×C₅₉	1	1	yes	characteristic
381	#2640	C₂×C₅₉	1	1	yes	characteristic, complemented
382	#2639	C₂×C₅₉	1	2	yes	complemented
383	#2592	C₂×C₅₉	1	1	yes	characteristic, complemented
384	#2561	C₂×C₅₉	1	2	yes	complemented
385	#2547	C₂×C₅₉	1	1	yes	characteristic, complemented
386	#2504	C₂×C₅₉	1	2	yes	complemented
387	#2490	C₂×C₅₉	1	2	yes	complemented
388	#2489	C₂×C₅₉	1	2	yes	complemented
389	#2488	C₂×C₅₉	1	4	yes	complemented
390	#2472	C₂×C₅₉	1	4	yes	complemented
391	#2398	C₂×C₅₉	1	1	yes	characteristic, complemented
392	C₂×#397	C₂×C₅₉	1	2	yes	complemented
393	#2339	C₂×C₅₉	1	2	yes	complemented
394	D₄×C₂²⋊C₄	C₂×C₅₉	1	2	yes	complemented
395	#2275	C₂×C₅₉	1	1	yes	characteristic, complemented
396	C₂×C₅₉	—	2	8	no	—
397	C₂×C₅₉	—	4	2	no	—
398	C₂×C₅₉	—	8	1	no	—
399	C₂×C₅₉	—	8	2	no	—
400	C₂×C₅₉	C₂²×#124	1	1	yes	characteristic
401	C₂×C₅₉	#3485	1	1	yes	characteristic
402	C₂×C₅₉	#3488	1	1	yes	characteristic
403	C₂×C₅₉	#3513	1	2	yes	—
404	C₂×C₅₉	#3521	1	2	yes	—
405	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic
406	C₂³×D₄	C₂²×C₅₉	1	1	yes	characteristic
407	#554	—	2	8	no	—
408	#546	—	2	8	no	—
409	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
410	C₂×#125	C₂²×C₅₉	1	2	yes	complemented
411	C₂×#124	C₂²×C₅₉	1	1	yes	characteristic
412	C₂×#124	C₂²×C₅₉	1	2	yes	—
413	C₂×#123	C₂²×C₅₉	1	2	yes	—
414	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
415	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	complemented
416	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	4	yes	complemented
417	C₂×#121	C₂²×C₅₉	1	2	yes	—
418	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
419	C₂×#120	C₂²×C₅₉	1	2	yes	—
420	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
421	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
422	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
423	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
424	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
425	C₂²×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
426	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
427	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	4	yes	—
428	#400	C₂²×C₅₉	1	4	yes	complemented
429	#400	C₂²×C₅₉	1	2	yes	complemented
430	#397	C₂²×C₅₉	1	2	yes	—
431	#397	C₂²×C₅₉	1	1	yes	characteristic
432	#397	C₂²×C₅₉	1	4	yes	—
433	#397	C₂²×C₅₉	1	2	yes	complemented
434	#397	C₂²×C₅₉	1	2	yes	complemented
435	#397	C₂²×C₅₉	1	2	yes	complemented
436	#397	C₂²×C₅₉	1	2	yes	complemented
437	#397	C₂²×C₅₉	1	4	yes	complemented
438	#397	C₂²×C₅₉	1	1	yes	characteristic, complemented
439	#394	C₂²×C₅₉	1	2	yes	—
440	#394	C₂²×C₅₉	1	4	yes	complemented
441	#393	C₂²×C₅₉	1	1	yes	characteristic
442	#393	C₂²×C₅₉	1	2	yes	complemented
443	#393	C₂²×C₅₉	1	1	yes	characteristic, complemented
444	#393	C₂²×C₅₉	1	4	yes	complemented
445	#391	C₂²×C₅₉	1	2	yes	complemented
446	#391	C₂²×C₅₉	1	2	yes	complemented
447	#391	C₂²×C₅₉	1	2	yes	complemented
448	#390	C₂²×C₅₉	1	2	yes	—
449	#390	C₂²×C₅₉	1	2	yes	—
450	#390	C₂²×C₅₉	1	4	yes	complemented
451	#388	C₂²×C₅₉	1	4	yes	—
452	#388	C₂²×C₅₉	1	4	yes	complemented
453	#388	C₂²×C₅₉	1	4	yes	complemented
454	#386	C₂²×C₅₉	1	4	yes	—
455	#386	C₂²×C₅₉	1	4	yes	—
456	#386	C₂²×C₅₉	1	4	yes	complemented
457	#386	C₂²×C₅₉	1	4	yes	complemented
458	#382	C₂²×C₅₉	1	4	yes	complemented
459	#381	C₂²×C₅₉	1	4	yes	complemented
460	#380	C₂²×C₅₉	1	2	yes	—
461	#380	C₂²×C₅₉	1	2	yes	complemented
462	#379	C₂²×C₅₉	1	4	yes	—
463	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
464	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
465	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
466	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	complemented
467	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	complemented
468	C₄×C₂²⋊C₄	C₂²×C₅₉	1	4	yes	complemented
469	#376	C₂²×C₅₉	1	1	yes	characteristic, complemented
470	C₂×#95	C₂²×C₅₉	1	4	yes	complemented
471	C₂×#95	C₂²×C₅₉	1	2	yes	complemented
472	C₅₉	#35847	1	1	yes	characteristic, direct product factor, Sylow
473	C₂⁵	C₂³×C₅₉	1	2	yes	—
474	C₂×#41	—	2	4	no	—
475	C₂×#41	—	2	8	no	—
476	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
477	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
478	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
479	C₂²×D₄	—	2	4	no	—
480	C₂²×D₄	—	2	8	no	—
481	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
482	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
483	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
484	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
485	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
486	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
487	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
488	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
489	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
490	C₂³×C₄	C₂³×C₅₉	1	4	yes	—
491	C₂³×C₄	C₂³×C₅₉	1	4	yes	—
492	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
493	C₄⋊Q₈	—	2	4	no	—
494	#125	—	2	8	no	—
495	#124	—	2	4	no	—
496	#124	—	4	4	no	—
497	#123	—	2	8	no	—
498	C₂²⋊Q₈	—	2	8	no	—
499	C₂²⋊Q₈	—	2	4	no	—
500	C₂²⋊Q₈	—	2	16	no	—
501	#121	—	2	8	no	—
502	#121	—	2	4	no	—
503	#120	—	2	8	no	—
504	C₄×Q₈	—	2	4	no	—
505	C₄×D₄	—	2	8	no	—
506	C₄×D₄	—	2	8	no	—
507	C₄×D₄	—	2	4	no	—
508	C₄×D₄	D₄×C₅₉	1	8	yes	—
509	C₂×C₄⋊C₄	—	2	8	no	—
510	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
511	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
512	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
519	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
520	C₂×C₂²⋊C₄	—	2	8	no	—
521	C₂×C₂²⋊C₄	—	4	8	no	—
522	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
523	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
529	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
541	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
542	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
543	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
544	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
545	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
546	#95	C₂³×C₅₉	1	1	yes	characteristic
547	#95	C₂³×C₅₉	1	2	yes	—
548	#95	C₂³×C₅₉	1	2	yes	—
549	#95	C₂³×C₅₉	1	4	yes	—
550	#95	C₂³×C₅₉	1	4	yes	—
551	#95	C₂³×C₅₉	1	4	yes	—
552	#95	C₂³×C₅₉	1	4	yes	—
553	#95	C₂³×C₅₉	1	1	yes	characteristic
554	#95	C₂³×C₅₉	1	2	yes	—
555	#95	C₂³×C₅₉	1	2	yes	—
556	#95	C₂³×C₅₉	1	2	yes	—
557	#95	C₂³×C₅₉	1	2	yes	—
558	#95	C₂³×C₅₉	1	4	yes	—
559	#95	C₂³×C₅₉	1	4	yes	—
560	#95	C₂³×C₅₉	1	4	yes	—
561	C₂⁴	—	2	4	no	—
562	C₂⁴	—	2	4	no	—
563	C₂⁴	—	2	8	no	—
564	C₂⁴	—	4	4	no	—
565	C₂⁴	—	4	2	no	—
566	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
567	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
568	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
569	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
570	#41	—	4	16	no	—
571	C₂×Q₈	—	2	2	no	—
572	C₂×Q₈	—	2	2	no	—
573	C₂×Q₈	—	2	4	no	—
574	C₂×Q₈	—	2	4	no	—
575	C₂×Q₈	—	4	2	no	—
576	C₂×Q₈	—	4	2	no	—
577	C₂×Q₈	—	4	2	no	—
578	C₂×D₄	—	2	4	no	—
579	C₂×D₄	—	2	4	no	—
580	C₂×D₄	—	2	8	no	—
581	C₂×D₄	—	2	8	no	—
582	C₂×D₄	—	2	2	no	—
583	C₂×D₄	—	2	2	no	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	—	2	4	no	—
587	C₂×D₄	—	4	1	no	—
588	C₂×D₄	—	4	4	no	—
589	C₂×D₄	—	4	16	no	—
590	C₂×D₄	C₂×D₄×C₅₉	1	4	yes	—
591	C₂×D₄	#41×C₅₉	1	8	yes	—
592	C₂²×C₄	—	2	4	no	—
593	C₂²×C₄	—	2	8	no	—
594	C₂²×C₄	—	2	8	no	—
595	C₂²×C₄	—	2	8	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	2	no	—
598	C₂²×C₄	—	2	4	no	—
599	C₂²×C₄	—	2	4	no	—
600	C₂²×C₄	—	4	4	no	—
601	C₂²×C₄	—	4	4	no	—
602	C₂²×C₄	—	4	4	no	—
603	C₂²×C₄	—	4	4	no	—
604	C₂²×C₄	—	4	4	no	—
605	C₂²×C₄	C₂×D₄×C₅₉	1	8	yes	—
606	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
607	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
609	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
610	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
612	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
613	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
614	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
615	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
616	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
617	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	8	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	8	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
629	C₂²⋊C₄	—	2	8	no	—
630	C₂²⋊C₄	—	2	8	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	8	no	—
633	C₂²⋊C₄	—	2	2	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	2	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	4	4	no	—
640	C₂²⋊C₄	—	4	4	no	—
641	C₂²⋊C₄	—	4	4	no	—
642	C₂²⋊C₄	—	4	2	no	—
643	C₂²⋊C₄	—	4	4	no	—
644	C₂²⋊C₄	—	4	2	no	—
645	C₂²⋊C₄	—	4	4	no	—
646	C₂²⋊C₄	—	4	2	no	—
647	C₂²⋊C₄	C₂×D₄×C₅₉	1	8	yes	—
648	C₄²	—	2	4	no	—
649	C₄²	—	2	4	no	—
650	C₄²	—	4	2	no	—
651	C₄²	—	4	4	no	—
652	C₄²	C₂×D₄×C₅₉	1	4	yes	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	4	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	2	1	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	1	no	—
660	C₂³	—	2	2	no	—
661	C₂³	—	2	1	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	4	no	—
664	C₂³	—	2	1	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	1	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	4	no	—
670	C₂³	—	4	16	no	—
671	C₂³	—	4	8	no	—
672	C₂³	—	4	8	no	—
673	C₂³	—	8	8	no	—
674	C₂³	—	8	4	no	—
675	C₂³	C₂²×D₄×C₅₉	1	4	yes	—
676	C₂³	C₂×#41×C₅₉	1	8	yes	—
677	C₂³	H(5,𝔽₂)×C₅₉	1	2	yes	—
678	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
679	Q₈	—	4	4	no	—
680	Q₈	—	4	4	no	—
681	Q₈	—	8	4	no	—
682	D₄	—	4	4	no	—
683	D₄	—	4	8	no	—
684	D₄	—	4	8	no	—
685	D₄	—	4	4	no	—
686	D₄	—	8	4	no	—
687	D₄	#124×C₅₉	1	16	yes	complemented
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	4	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	4	no	—
704	C₂×C₄	—	2	4	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	4	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	4	no	—
716	C₂×C₄	—	4	8	no	—
717	C₂×C₄	—	4	8	no	—
718	C₂×C₄	—	4	4	no	—
719	C₂×C₄	—	4	4	no	—
720	C₂×C₄	—	8	8	no	—
721	C₂×C₄	—	8	8	no	—
722	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
723	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
724	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
725	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
726	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
727	C₂²	—	2	8	no	—
728	C₂²	—	2	8	no	—
729	C₂²	—	2	4	no	—
730	C₂²	—	2	4	no	—
731	C₂²	—	2	4	no	—
732	C₂²	—	2	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	1	no	—
735	C₂²	—	4	1	no	—
736	C₂²	—	4	4	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	4	4	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	1	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	1	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	1	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	8	16	no	—
747	C₂²	C₂×#124×C₅₉	1	8	yes	—
748	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
749	C₂²	C₂²×#41×C₅₉	1	2	yes	—
750	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
751	C₂²	C₅₉×#585	1	2	yes	—
752	C₂²	C₅₉×#585	1	1	yes	characteristic
753	C₄	—	2	2	no	—
754	C₄	—	2	4	no	—
755	C₄	—	2	2	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	4	no	—
758	C₄	—	4	2	no	—
759	C₄	—	4	1	no	—
760	C₄	—	4	1	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	2	no	—
764	C₄	—	4	4	no	—
765	C₄	C₂×#124×C₅₉	1	4	yes	—
766	C₂	—	2	8	no	—
767	C₂	—	4	2	no	—
768	C₂	—	8	2	no	—
769	C₂	—	8	1	no	—
770	C₂	C₂²×#124×C₅₉	1	1	yes	characteristic
771	C₂	C₅₉×#3485	1	1	yes	characteristic
772	C₂	C₅₉×#3488	1	1	yes	characteristic
773	C₂	C₅₉×#3513	1	2	yes	—
774	C₂	C₅₉×#3521	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₂×C₅₉×#546	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×#554	C₂	semidirect
3. C₅₉×#2640	C₂	semidirect
4. C₅₉×#2639	C₂	semidirect
5. C₅₉×#2592	C₂	semidirect
6. C₅₉×#2561	C₂	semidirect
7. C₅₉×#2547	C₂	semidirect
8. C₅₉×#2504	C₂	semidirect
9. C₅₉×#2490	C₂	semidirect
10. C₅₉×#2489	C₂	semidirect
11. C₅₉×#2488	C₂	semidirect
12. C₅₉×#2472	C₂	semidirect
13. C₅₉×#2398	C₂	semidirect
14. C₂×C₅₉×#397	C₂	semidirect
15. C₅₉×#2339	C₂	semidirect
16. D₄×C₂²⋊C₄×C₅₉	C₂	semidirect
17. C₅₉×#2275	C₂	semidirect
22. C₂×C₄⋊Q₈×C₅₉	C₂²	semidirect
23. C₂×#125×C₅₉	C₂²	semidirect
28. C₂×C₂²⋊Q₈×C₅₉	C₂²	semidirect
29. C₂×C₂²⋊Q₈×C₅₉	C₂²	semidirect
33. C₂×C₄×Q₈×C₅₉	C₂²	semidirect
38. C₂²×C₄⋊C₄×C₅₉	C₂²	semidirect
41. C₅₉×#400	C₂²	semidirect
42. C₅₉×#400	C₂²	semidirect
46. C₅₉×#397	C₂²	semidirect
47. C₅₉×#397	C₂²	semidirect
48. C₅₉×#397	C₂²	semidirect
49. C₅₉×#397	C₂²	semidirect
50. C₅₉×#397	C₂²	semidirect
51. C₅₉×#397	C₂²	semidirect
53. C₅₉×#394	C₂²	semidirect
55. C₅₉×#393	C₂²	semidirect
56. C₅₉×#393	C₂²	semidirect
57. C₅₉×#393	C₂²	semidirect
58. C₅₉×#391	C₂²	semidirect
59. C₅₉×#391	C₂²	semidirect
60. C₅₉×#391	C₂²	semidirect
63. C₅₉×#390	C₂²	semidirect
65. C₅₉×#388	C₂²	semidirect
66. C₅₉×#388	C₂²	semidirect
69. C₅₉×#386	C₂²	semidirect
70. C₅₉×#386	C₂²	semidirect
71. C₅₉×#382	C₂²	semidirect
72. C₅₉×#381	C₂²	semidirect
74. C₅₉×#380	C₂²	semidirect
76. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
77. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
79. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
80. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
81. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
82. C₅₉×#376	C₂²	semidirect
83. C₂×#95×C₅₉	C₂²	semidirect
84. C₂×#95×C₅₉	C₂²	semidirect
299. D₄×C₅₉	#124	semidirect
339. #35847	C₅₉	direct (N × H)
379. C₂×#554	C₂×C₅₉	semidirect
381. #2640	C₂×C₅₉	semidirect
382. #2639	C₂×C₅₉	semidirect
383. #2592	C₂×C₅₉	semidirect
384. #2561	C₂×C₅₉	semidirect
385. #2547	C₂×C₅₉	semidirect
386. #2504	C₂×C₅₉	semidirect
387. #2490	C₂×C₅₉	semidirect
388. #2489	C₂×C₅₉	semidirect
389. #2488	C₂×C₅₉	semidirect
390. #2472	C₂×C₅₉	semidirect
391. #2398	C₂×C₅₉	semidirect
392. C₂×#397	C₂×C₅₉	semidirect
393. #2339	C₂×C₅₉	semidirect
394. D₄×C₂²⋊C₄	C₂×C₅₉	semidirect
395. #2275	C₂×C₅₉	semidirect
409. C₂×C₄⋊Q₈	C₂²×C₅₉	semidirect
410. C₂×#125	C₂²×C₅₉	semidirect
415. C₂×C₂²⋊Q₈	C₂²×C₅₉	semidirect
416. C₂×C₂²⋊Q₈	C₂²×C₅₉	semidirect
420. C₂×C₄×Q₈	C₂²×C₅₉	semidirect
425. C₂²×C₄⋊C₄	C₂²×C₅₉	semidirect
428. #400	C₂²×C₅₉	semidirect
429. #400	C₂²×C₅₉	semidirect
433. #397	C₂²×C₅₉	semidirect
434. #397	C₂²×C₅₉	semidirect
435. #397	C₂²×C₅₉	semidirect
436. #397	C₂²×C₅₉	semidirect
437. #397	C₂²×C₅₉	semidirect
438. #397	C₂²×C₅₉	semidirect
440. #394	C₂²×C₅₉	semidirect
442. #393	C₂²×C₅₉	semidirect
443. #393	C₂²×C₅₉	semidirect
444. #393	C₂²×C₅₉	semidirect
445. #391	C₂²×C₅₉	semidirect
446. #391	C₂²×C₅₉	semidirect
447. #391	C₂²×C₅₉	semidirect
450. #390	C₂²×C₅₉	semidirect
452. #388	C₂²×C₅₉	semidirect
453. #388	C₂²×C₅₉	semidirect
456. #386	C₂²×C₅₉	semidirect
457. #386	C₂²×C₅₉	semidirect
458. #382	C₂²×C₅₉	semidirect
459. #381	C₂²×C₅₉	semidirect
461. #380	C₂²×C₅₉	semidirect
463. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
464. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
466. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
467. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
468. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
469. #376	C₂²×C₅₉	semidirect
470. C₂×#95	C₂²×C₅₉	semidirect
471. C₂×#95	C₂²×C₅₉	semidirect
472. C₅₉	#35847	direct (N × H)
687. D₄	#124×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×#554	2
C₂×C₅₉×#546	2
C₅₉×#2640	2
C₅₉×#2639	2
C₅₉×#2592	2
C₅₉×#2561	2
C₅₉×#2547	2
C₅₉×#2504	2
C₅₉×#2490	2
C₅₉×#2489	2
C₅₉×#2488	2
C₅₉×#2472	2
C₅₉×#2398	2
C₂×C₅₉×#397	2
C₅₉×#2339	2
D₄×C₂²⋊C₄×C₅₉	2
C₅₉×#2275	2
#35847	59

Subgroups — C59×#35847 #28447956

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35847 #28447956