Subgroups — C₅₉×#35542 #28447651

Order 15104.

2518 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#525	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2563	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2562	C₂	1	2	yes	maximal, complemented
5	C₅₉×#2562	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2547	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2492	C₂	1	2	yes	maximal, complemented
8	C₅₉×#2491	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×#2311	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₉×#2311	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#2280	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅₉×#380	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₉×#2274	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₅₉	C₂²	1	1	yes	characteristic
20	C₅₉×#544	—	2	8	no	—
21	C₂×C₄⋊Q₈×C₅₉	C₂²	1	2	yes	complemented
22	C₂×C₄⋊Q₈×C₅₉	C₂²	1	2	yes	complemented
23	C₂×#125×C₅₉	C₂²	1	2	yes	complemented
24	C₂×#125×C₅₉	C₂²	1	2	yes	complemented
25	C₂×#124×C₅₉	C₂²	1	4	yes	—
26	C₅₉×#525	—	2	8	no	—
27	C₂×#123×C₅₉	C₂²	1	2	yes	—
28	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	4	yes	—
29	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
31	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
32	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
33	C₂×#120×C₅₉	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
36	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
37	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
38	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
39	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
40	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
41	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
42	C₅₉×#400	C₂²	1	4	yes	complemented
43	C₅₉×#400	C₂²	1	4	yes	complemented
44	C₅₉×#397	C₂²	1	4	yes	—
45	C₅₉×#397	C₂²	1	4	yes	complemented
46	C₅₉×#394	C₂²	1	4	yes	—
47	C₅₉×#394	C₂²	1	4	yes	—
48	C₅₉×#393	C₂²	1	4	yes	—
49	C₅₉×#393	C₂²	1	4	yes	complemented
50	C₅₉×#391	C₂²	1	4	yes	complemented
51	C₅₉×#391	C₂²	1	2	yes	complemented
52	C₅₉×#391	C₂²	1	2	yes	complemented
53	C₅₉×#390	C₂²	1	4	yes	—
54	C₅₉×#390	C₂²	1	2	yes	complemented
55	C₅₉×#390	C₂²	1	2	yes	complemented
56	C₅₉×#388	C₂²	1	4	yes	—
57	C₅₉×#388	C₂²	1	4	yes	—
58	C₅₉×#388	C₂²	1	4	yes	complemented
59	C₅₉×#388	C₂²	1	4	yes	complemented
60	C₅₉×#386	C₂²	1	4	yes	—
61	C₅₉×#386	C₂²	1	4	yes	—
62	C₅₉×#382	C₂²	1	4	yes	complemented
63	C₅₉×#381	C₂²	1	2	yes	—
64	C₅₉×#380	C₂²	1	2	yes	—
65	C₅₉×#380	C₂²	1	2	yes	—
66	C₅₉×#380	C₂²	1	2	yes	—
67	C₅₉×#380	C₂²	1	2	yes	—
68	C₅₉×#380	C₂²	1	1	yes	characteristic
69	C₅₉×#380	C₂²	1	1	yes	characteristic
70	C₅₉×#380	C₂²	1	1	yes	characteristic
71	C₅₉×#380	C₂²	1	1	yes	characteristic
72	C₅₉×#380	C₂²	1	2	yes	complemented
73	C₅₉×#380	C₂²	1	2	yes	complemented
74	C₅₉×#380	C₂²	1	2	yes	complemented
75	C₅₉×#380	C₂²	1	2	yes	complemented
76	C₅₉×#379	C₂²	1	2	yes	—
77	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
78	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
79	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
80	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
81	C₄×C₂²⋊C₄×C₅₉	C₂²	1	4	yes	—
82	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
83	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
84	C₂×#95×C₅₉	C₂²	1	2	yes	—
85	C₂⁵×C₅₉	C₂³	1	1	yes	characteristic
86	C₂×#41×C₅₉	—	2	4	no	—
87	C₂×#41×C₅₉	—	2	4	no	—
88	C₂×#41×C₅₉	—	2	4	no	—
89	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
90	C₂²×Q₈×C₅₉	C₂³	1	4	yes	—
91	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
92	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
94	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
95	C₂³×C₄×C₅₉	—	2	4	no	—
96	C₂³×C₄×C₅₉	—	2	4	no	—
97	C₂³×C₄×C₅₉	—	2	4	no	—
98	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
104	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
105	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
106	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
107	C₄⋊Q₈×C₅₉	—	2	8	no	—
108	C₄⋊Q₈×C₅₉	—	2	8	no	—
109	#125×C₅₉	—	2	8	no	—
110	#125×C₅₉	—	2	8	no	—
111	#124×C₅₉	—	4	8	no	—
112	#123×C₅₉	—	2	8	no	—
113	C₂²⋊Q₈×C₅₉	—	2	4	no	—
114	C₂²⋊Q₈×C₅₉	—	2	4	no	—
115	C₂²⋊Q₈×C₅₉	—	2	16	no	—
116	#121×C₅₉	—	2	4	no	—
117	#121×C₅₉	—	2	4	no	—
118	#120×C₅₉	—	2	8	no	—
119	C₄×D₄×C₅₉	—	2	8	no	—
120	C₄×D₄×C₅₉	—	2	8	no	—
121	#117×C₅₉	—	2	4	no	—
122	#117×C₅₉	—	2	4	no	—
123	#117×C₅₉	D₄	1	8	yes	—
124	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
125	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
126	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
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	4	yes	—
136	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
137	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
138	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊C₄×C₅₉	—	4	4	no	—
142	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
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	4	yes	—
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	4	yes	—
154	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
155	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
156	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
157	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
158	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
159	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
160	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
161	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
162	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
163	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
164	#95×C₅₉	C₂³	1	4	yes	—
165	#95×C₅₉	C₂³	1	4	yes	—
166	#95×C₅₉	C₂³	1	4	yes	—
167	#95×C₅₉	C₂³	1	4	yes	—
168	#95×C₅₉	C₂³	1	2	yes	—
169	#95×C₅₉	C₂³	1	2	yes	—
170	#95×C₅₉	C₂³	1	2	yes	—
171	#95×C₅₉	C₂³	1	2	yes	—
172	#95×C₅₉	C₂³	1	4	yes	—
173	#95×C₅₉	C₂³	1	4	yes	—
174	#95×C₅₉	C₂³	1	4	yes	—
175	#95×C₅₉	C₂³	1	4	yes	—
176	C₂⁴×C₅₉	—	2	2	no	—
177	C₂⁴×C₅₉	—	2	2	no	—
178	C₂⁴×C₅₉	—	2	2	no	—
179	C₂⁴×C₅₉	—	2	2	no	—
180	C₂⁴×C₅₉	—	2	2	no	—
181	C₂⁴×C₅₉	—	4	1	no	—
182	C₂⁴×C₅₉	—	4	1	no	—
183	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
184	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
185	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
186	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
187	#41×C₅₉	—	4	16	no	—
188	C₂×Q₈×C₅₉	—	2	2	no	—
189	C₂×Q₈×C₅₉	—	2	8	no	—
190	C₂×Q₈×C₅₉	—	2	2	no	—
191	C₂×Q₈×C₅₉	—	2	2	no	—
192	C₂×Q₈×C₅₉	—	4	4	no	—
193	C₂×Q₈×C₅₉	—	4	4	no	—
194	C₂×D₄×C₅₉	—	2	4	no	—
195	C₂×D₄×C₅₉	—	2	4	no	—
196	C₂×D₄×C₅₉	—	2	4	no	—
197	C₂×D₄×C₅₉	—	2	4	no	—
198	C₂×D₄×C₅₉	—	2	4	no	—
199	C₂×D₄×C₅₉	—	2	4	no	—
200	C₂×D₄×C₅₉	—	2	4	no	—
201	C₂×D₄×C₅₉	—	2	2	no	—
202	C₂×D₄×C₅₉	—	2	2	no	—
203	C₂×D₄×C₅₉	—	2	2	no	—
204	C₂×D₄×C₅₉	—	4	2	no	—
205	C₂×D₄×C₅₉	—	4	2	no	—
206	C₂²×C₄×C₅₉	—	2	2	no	—
207	C₂²×C₄×C₅₉	—	2	2	no	—
208	C₂²×C₄×C₅₉	—	2	2	no	—
209	C₂²×C₄×C₅₉	—	2	4	no	—
210	C₂²×C₄×C₅₉	—	2	4	no	—
211	C₂²×C₄×C₅₉	—	2	2	no	—
212	C₂²×C₄×C₅₉	—	2	2	no	—
213	C₂²×C₄×C₅₉	—	2	4	no	—
214	C₂²×C₄×C₅₉	—	2	2	no	—
215	C₂²×C₄×C₅₉	—	2	2	no	—
216	C₂²×C₄×C₅₉	—	2	2	no	—
217	C₂²×C₄×C₅₉	—	2	2	no	—
218	C₂²×C₄×C₅₉	—	2	2	no	—
219	C₂²×C₄×C₅₉	—	2	2	no	—
220	C₂²×C₄×C₅₉	—	2	2	no	—
221	C₂²×C₄×C₅₉	—	2	2	no	—
222	C₂²×C₄×C₅₉	—	2	2	no	—
223	C₂²×C₄×C₅₉	—	2	2	no	—
224	C₂²×C₄×C₅₉	—	2	4	no	—
225	C₂²×C₄×C₅₉	—	2	4	no	—
226	C₂²×C₄×C₅₉	—	4	2	no	—
227	C₂²×C₄×C₅₉	—	4	2	no	—
228	C₂²×C₄×C₅₉	—	4	2	no	—
229	C₂²×C₄×C₅₉	—	4	2	no	—
230	C₂²×C₄×C₅₉	—	4	16	no	—
231	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
232	C₂²×C₄×C₅₉	#41	1	4	yes	—
233	C₂²×C₄×C₅₉	#41	1	4	yes	—
234	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
240	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
243	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
247	C₄⋊C₄×C₅₉	—	2	4	no	—
248	C₄⋊C₄×C₅₉	—	2	4	no	—
249	C₄⋊C₄×C₅₉	—	2	2	no	—
250	C₄⋊C₄×C₅₉	—	2	2	no	—
251	C₄⋊C₄×C₅₉	—	2	4	no	—
252	C₄⋊C₄×C₅₉	—	2	4	no	—
253	C₄⋊C₄×C₅₉	—	2	8	no	—
254	C₄⋊C₄×C₅₉	—	2	8	no	—
255	C₄⋊C₄×C₅₉	—	2	8	no	—
256	C₄⋊C₄×C₅₉	—	2	4	no	—
257	C₄⋊C₄×C₅₉	—	2	4	no	—
258	C₄⋊C₄×C₅₉	—	2	2	no	—
259	C₄⋊C₄×C₅₉	—	2	2	no	—
260	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
261	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
262	C₂²⋊C₄×C₅₉	—	2	4	no	—
263	C₂²⋊C₄×C₅₉	—	2	4	no	—
264	C₂²⋊C₄×C₅₉	—	2	8	no	—
265	C₂²⋊C₄×C₅₉	—	2	4	no	—
266	C₂²⋊C₄×C₅₉	—	2	4	no	—
267	C₂²⋊C₄×C₅₉	—	2	4	no	—
268	C₂²⋊C₄×C₅₉	—	2	4	no	—
269	C₂²⋊C₄×C₅₉	—	2	4	no	—
270	C₂²⋊C₄×C₅₉	—	2	4	no	—
271	C₂²⋊C₄×C₅₉	—	4	4	no	—
272	C₂²⋊C₄×C₅₉	—	4	2	no	—
273	C₂²⋊C₄×C₅₉	—	4	4	no	—
274	C₂²⋊C₄×C₅₉	—	4	4	no	—
275	C₂²⋊C₄×C₅₉	—	4	2	no	—
276	C₂²⋊C₄×C₅₉	—	4	4	no	—
277	C₂²⋊C₄×C₅₉	—	4	4	no	—
278	C₂²⋊C₄×C₅₉	C₂×D₄	1	8	yes	—
279	C₄²×C₅₉	—	2	4	no	—
280	C₄²×C₅₉	—	2	4	no	—
281	C₄²×C₅₉	—	4	4	no	—
282	C₄²×C₅₉	—	4	4	no	—
283	C₄²×C₅₉	C₂×D₄	1	8	yes	—
284	C₂³×C₅₉	—	2	1	no	—
285	C₂³×C₅₉	—	2	1	no	—
286	C₂³×C₅₉	—	2	1	no	—
287	C₂³×C₅₉	—	2	1	no	—
288	C₂³×C₅₉	—	2	8	no	—
289	C₂³×C₅₉	—	2	1	no	—
290	C₂³×C₅₉	—	2	1	no	—
291	C₂³×C₅₉	—	2	1	no	—
292	C₂³×C₅₉	—	2	1	no	—
293	C₂³×C₅₉	—	2	1	no	—
294	C₂³×C₅₉	—	2	1	no	—
295	C₂³×C₅₉	—	2	1	no	—
296	C₂³×C₅₉	—	2	1	no	—
297	C₂³×C₅₉	—	2	1	no	—
298	C₂³×C₅₉	—	2	1	no	—
299	C₂³×C₅₉	—	2	1	no	—
300	C₂³×C₅₉	—	2	1	no	—
301	C₂³×C₅₉	—	2	2	no	—
302	C₂³×C₅₉	—	2	2	no	—
303	C₂³×C₅₉	—	2	2	no	—
304	C₂³×C₅₉	—	2	2	no	—
305	C₂³×C₅₉	—	2	2	no	—
306	C₂³×C₅₉	—	2	2	no	—
307	C₂³×C₅₉	—	2	2	no	—
308	C₂³×C₅₉	—	4	4	no	—
309	C₂³×C₅₉	—	4	4	no	—
310	C₂³×C₅₉	—	4	4	no	—
311	C₂³×C₅₉	—	4	4	no	—
312	C₂³×C₅₉	—	4	4	no	—
313	C₂³×C₅₉	—	4	4	no	—
314	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
315	C₂³×C₅₉	C₂×#41	1	2	yes	—
316	C₂³×C₅₉	C₂×#41	1	2	yes	—
317	C₂³×C₅₉	H(5,𝔽₂)	1	2	yes	—
318	C₂³×C₅₉	2₋¹⁺⁴	1	2	yes	—
319	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
320	Q₈×C₅₉	—	4	4	no	—
321	Q₈×C₅₉	—	8	8	no	—
322	D₄×C₅₉	—	4	8	no	—
323	D₄×C₅₉	—	4	8	no	—
324	D₄×C₅₉	—	4	8	no	—
325	D₄×C₅₉	—	4	4	no	—
326	C₂×C₄×C₅₉	—	2	2	no	—
327	C₂×C₄×C₅₉	—	2	2	no	—
328	C₂×C₄×C₅₉	—	2	2	no	—
329	C₂×C₄×C₅₉	—	2	2	no	—
330	C₂×C₄×C₅₉	—	2	2	no	—
331	C₂×C₄×C₅₉	—	2	2	no	—
332	C₂×C₄×C₅₉	—	2	1	no	—
333	C₂×C₄×C₅₉	—	2	1	no	—
334	C₂×C₄×C₅₉	—	2	2	no	—
335	C₂×C₄×C₅₉	—	2	4	no	—
336	C₂×C₄×C₅₉	—	2	2	no	—
337	C₂×C₄×C₅₉	—	2	2	no	—
338	C₂×C₄×C₅₉	—	2	4	no	—
339	C₂×C₄×C₅₉	—	2	1	no	—
340	C₂×C₄×C₅₉	—	2	1	no	—
341	C₂×C₄×C₅₉	—	2	1	no	—
342	C₂×C₄×C₅₉	—	2	1	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	4	no	—
347	C₂×C₄×C₅₉	—	2	4	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	2	no	—
352	C₂×C₄×C₅₉	—	2	4	no	—
353	C₂×C₄×C₅₉	—	2	2	no	—
354	C₂×C₄×C₅₉	—	2	2	no	—
355	C₂×C₄×C₅₉	—	2	4	no	—
356	C₂×C₄×C₅₉	—	2	2	no	—
357	C₂×C₄×C₅₉	—	4	4	no	—
358	C₂×C₄×C₅₉	—	4	4	no	—
359	C₂×C₄×C₅₉	—	4	4	no	—
360	C₂×C₄×C₅₉	—	4	4	no	—
361	C₂×C₄×C₅₉	—	4	4	no	—
362	C₂×C₄×C₅₉	—	4	8	no	—
363	C₂×C₄×C₅₉	—	8	4	no	—
364	C₂×C₄×C₅₉	—	8	4	no	—
365	C₂×C₄×C₅₉	#124	1	16	yes	complemented
366	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
367	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
368	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
369	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
370	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
371	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
372	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
373	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
374	#35542	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
375	C₂²×C₅₉	—	2	2	no	—
376	C₂²×C₅₉	—	2	2	no	—
377	C₂²×C₅₉	—	2	2	no	—
378	C₂²×C₅₉	—	2	2	no	—
379	C₂²×C₅₉	—	2	2	no	—
380	C₂²×C₅₉	—	2	2	no	—
381	C₂²×C₅₉	—	2	2	no	—
382	C₂²×C₅₉	—	2	2	no	—
383	C₂²×C₅₉	—	2	2	no	—
384	C₂²×C₅₉	—	2	2	no	—
385	C₂²×C₅₉	—	2	2	no	—
386	C₂²×C₅₉	—	2	2	no	—
387	C₂²×C₅₉	—	4	16	no	—
388	C₂²×C₅₉	—	4	1	no	—
389	C₂²×C₅₉	—	4	1	no	—
390	C₂²×C₅₉	—	4	1	no	—
391	C₂²×C₅₉	—	4	1	no	—
392	C₂²×C₅₉	—	4	1	no	—
393	C₂²×C₅₉	—	4	1	no	—
394	C₂²×C₅₉	—	4	1	no	—
395	C₂²×C₅₉	—	4	1	no	—
396	C₂²×C₅₉	—	4	2	no	—
397	C₂²×C₅₉	—	4	2	no	—
398	C₂²×C₅₉	—	4	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	C₂×#124	1	4	yes	—
404	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
405	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
406	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
407	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
408	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
409	C₂²×C₅₉	#585	1	1	yes	characteristic
410	C₂²×C₅₉	#585	1	1	yes	characteristic
411	C₄×C₅₉	—	2	4	no	—
412	C₄×C₅₉	—	2	4	no	—
413	C₄×C₅₉	—	4	1	no	—
414	C₄×C₅₉	—	4	1	no	—
415	C₄×C₅₉	—	4	2	no	—
416	C₄×C₅₉	—	4	4	no	—
417	C₄×C₅₉	—	4	2	no	—
418	C₄×C₅₉	—	4	2	no	—
419	C₄×C₅₉	—	4	2	no	—
420	C₄×C₅₉	—	4	2	no	—
421	C₄×C₅₉	—	4	4	no	—
422	C₄×C₅₉	C₂×#124	1	4	yes	—
423	C₄×C₅₉	C₂×#124	1	4	yes	—
424	C₂×#544	C₂×C₅₉	1	1	yes	characteristic, complemented
425	C₂×#525	C₂×C₅₉	1	1	yes	characteristic
426	#2563	C₂×C₅₉	1	2	yes	complemented
427	#2562	C₂×C₅₉	1	2	yes	complemented
428	#2562	C₂×C₅₉	1	2	yes	complemented
429	#2547	C₂×C₅₉	1	2	yes	complemented
430	#2492	C₂×C₅₉	1	2	yes	complemented
431	#2491	C₂×C₅₉	1	2	yes	complemented
432	#2490	C₂×C₅₉	1	2	yes	complemented
433	#2489	C₂×C₅₉	1	2	yes	complemented
434	#2488	C₂×C₅₉	1	4	yes	complemented
435	#2472	C₂×C₅₉	1	4	yes	complemented
436	#2311	C₂×C₅₉	1	1	yes	characteristic, complemented
437	#2311	C₂×C₅₉	1	1	yes	characteristic, complemented
438	#2280	C₂×C₅₉	1	1	yes	characteristic, complemented
439	C₂×#380	C₂×C₅₉	1	1	yes	characteristic, complemented
440	#2274	C₂×C₅₉	1	1	yes	characteristic, complemented
441	C₂×C₅₉	—	2	4	no	—
442	C₂×C₅₉	—	4	2	no	—
443	C₂×C₅₉	—	4	2	no	—
444	C₂×C₅₉	—	8	2	no	—
445	C₂×C₅₉	C₂²×#124	1	1	yes	characteristic
446	C₂×C₅₉	#3488	1	1	yes	characteristic
447	C₂×C₅₉	#3489	1	1	yes	characteristic
448	C₂×C₅₉	#3492	1	1	yes	characteristic
449	C₂×C₅₉	#3493	1	1	yes	characteristic
450	C₂×C₅₉	#3494	1	1	yes	characteristic
451	C₂×C₅₉	#3495	1	1	yes	characteristic
452	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic
453	C₂⁴×C₄	C₂²×C₅₉	1	1	yes	characteristic
454	#544	—	2	8	no	—
455	C₂×C₄⋊Q₈	C₂²×C₅₉	1	2	yes	complemented
456	C₂×C₄⋊Q₈	C₂²×C₅₉	1	2	yes	complemented
457	C₂×#125	C₂²×C₅₉	1	2	yes	complemented
458	C₂×#125	C₂²×C₅₉	1	2	yes	complemented
459	C₂×#124	C₂²×C₅₉	1	4	yes	—
460	#525	—	2	8	no	—
461	C₂×#123	C₂²×C₅₉	1	2	yes	—
462	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
463	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
464	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	4	yes	—
465	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
466	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
467	C₂×#120	C₂²×C₅₉	1	2	yes	—
468	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
469	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
470	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
471	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
472	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
473	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
474	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
475	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
476	#400	C₂²×C₅₉	1	4	yes	complemented
477	#400	C₂²×C₅₉	1	4	yes	complemented
478	#397	C₂²×C₅₉	1	4	yes	—
479	#397	C₂²×C₅₉	1	4	yes	complemented
480	#394	C₂²×C₅₉	1	4	yes	—
481	#394	C₂²×C₅₉	1	4	yes	—
482	#393	C₂²×C₅₉	1	4	yes	—
483	#393	C₂²×C₅₉	1	4	yes	complemented
484	#391	C₂²×C₅₉	1	2	yes	complemented
485	#391	C₂²×C₅₉	1	2	yes	complemented
486	#391	C₂²×C₅₉	1	4	yes	complemented
487	#390	C₂²×C₅₉	1	4	yes	—
488	#390	C₂²×C₅₉	1	2	yes	complemented
489	#390	C₂²×C₅₉	1	2	yes	complemented
490	#388	C₂²×C₅₉	1	4	yes	—
491	#388	C₂²×C₅₉	1	4	yes	—
492	#388	C₂²×C₅₉	1	4	yes	complemented
493	#388	C₂²×C₅₉	1	4	yes	complemented
494	#386	C₂²×C₅₉	1	4	yes	—
495	#386	C₂²×C₅₉	1	4	yes	—
496	#382	C₂²×C₅₉	1	4	yes	complemented
497	#381	C₂²×C₅₉	1	2	yes	—
498	#380	C₂²×C₅₉	1	1	yes	characteristic
499	#380	C₂²×C₅₉	1	1	yes	characteristic
500	#380	C₂²×C₅₉	1	2	yes	—
501	#380	C₂²×C₅₉	1	2	yes	—
502	#380	C₂²×C₅₉	1	1	yes	characteristic
503	#380	C₂²×C₅₉	1	2	yes	—
504	#380	C₂²×C₅₉	1	2	yes	—
505	#380	C₂²×C₅₉	1	1	yes	characteristic
506	#380	C₂²×C₅₉	1	2	yes	complemented
507	#380	C₂²×C₅₉	1	2	yes	complemented
508	#380	C₂²×C₅₉	1	2	yes	complemented
509	#380	C₂²×C₅₉	1	2	yes	complemented
510	#379	C₂²×C₅₉	1	2	yes	—
511	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
512	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
513	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
514	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
515	C₄×C₂²⋊C₄	C₂²×C₅₉	1	4	yes	—
516	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
517	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
518	C₂×#95	C₂²×C₅₉	1	2	yes	—
519	C₅₉	#35542	1	1	yes	characteristic, direct product factor, Sylow
520	C₂⁵	C₂³×C₅₉	1	1	yes	characteristic
521	C₂×#41	—	2	4	no	—
522	C₂×#41	—	2	4	no	—
523	C₂×#41	—	2	4	no	—
524	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
525	C₂²×Q₈	C₂³×C₅₉	1	4	yes	—
526	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
527	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
528	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
529	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
530	C₂³×C₄	—	2	4	no	—
531	C₂³×C₄	—	2	4	no	—
532	C₂³×C₄	—	2	4	no	—
533	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
534	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
535	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
536	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
537	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
538	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
539	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
540	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
541	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
542	C₄⋊Q₈	—	2	8	no	—
543	C₄⋊Q₈	—	2	8	no	—
544	#125	—	2	8	no	—
545	#125	—	2	8	no	—
546	#124	—	4	8	no	—
547	#123	—	2	8	no	—
548	C₂²⋊Q₈	—	2	4	no	—
549	C₂²⋊Q₈	—	2	4	no	—
550	C₂²⋊Q₈	—	2	16	no	—
551	#121	—	2	4	no	—
552	#121	—	2	4	no	—
553	#120	—	2	8	no	—
554	C₄×D₄	—	2	8	no	—
555	C₄×D₄	—	2	8	no	—
556	#117	—	2	4	no	—
557	#117	—	2	4	no	—
558	#117	D₄×C₅₉	1	8	yes	—
559	C₂×C₄⋊C₄	—	2	4	no	—
560	C₂×C₄⋊C₄	—	2	4	no	—
561	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
566	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
567	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
568	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
572	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
573	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
574	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
576	C₂×C₂²⋊C₄	—	4	4	no	—
577	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
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	4	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
594	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
595	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
596	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
597	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
598	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
599	#95	C₂³×C₅₉	1	4	yes	—
600	#95	C₂³×C₅₉	1	4	yes	—
601	#95	C₂³×C₅₉	1	4	yes	—
602	#95	C₂³×C₅₉	1	4	yes	—
603	#95	C₂³×C₅₉	1	2	yes	—
604	#95	C₂³×C₅₉	1	2	yes	—
605	#95	C₂³×C₅₉	1	2	yes	—
606	#95	C₂³×C₅₉	1	2	yes	—
607	#95	C₂³×C₅₉	1	4	yes	—
608	#95	C₂³×C₅₉	1	4	yes	—
609	#95	C₂³×C₅₉	1	4	yes	—
610	#95	C₂³×C₅₉	1	4	yes	—
611	C₂⁴	—	2	2	no	—
612	C₂⁴	—	2	2	no	—
613	C₂⁴	—	2	2	no	—
614	C₂⁴	—	2	2	no	—
615	C₂⁴	—	2	2	no	—
616	C₂⁴	—	4	1	no	—
617	C₂⁴	—	4	1	no	—
618	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
619	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
620	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
621	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
622	#41	—	4	16	no	—
623	C₂×Q₈	—	2	2	no	—
624	C₂×Q₈	—	2	8	no	—
625	C₂×Q₈	—	2	2	no	—
626	C₂×Q₈	—	2	2	no	—
627	C₂×Q₈	—	4	4	no	—
628	C₂×Q₈	—	4	4	no	—
629	C₂×D₄	—	2	4	no	—
630	C₂×D₄	—	2	4	no	—
631	C₂×D₄	—	2	4	no	—
632	C₂×D₄	—	2	4	no	—
633	C₂×D₄	—	2	4	no	—
634	C₂×D₄	—	2	4	no	—
635	C₂×D₄	—	2	4	no	—
636	C₂×D₄	—	2	2	no	—
637	C₂×D₄	—	2	2	no	—
638	C₂×D₄	—	2	2	no	—
639	C₂×D₄	—	4	2	no	—
640	C₂×D₄	—	4	2	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	2	no	—
644	C₂²×C₄	—	2	4	no	—
645	C₂²×C₄	—	2	4	no	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	2	4	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	2	2	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	2	2	no	—
656	C₂²×C₄	—	2	2	no	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	2	4	no	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	4	2	no	—
662	C₂²×C₄	—	4	2	no	—
663	C₂²×C₄	—	4	2	no	—
664	C₂²×C₄	—	4	2	no	—
665	C₂²×C₄	—	4	16	no	—
666	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
667	C₂²×C₄	#41×C₅₉	1	4	yes	—
668	C₂²×C₄	#41×C₅₉	1	4	yes	—
669	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
670	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
671	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
675	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
678	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
681	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	4	no	—
684	C₄⋊C₄	—	2	2	no	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	—	2	4	no	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	8	no	—
689	C₄⋊C₄	—	2	8	no	—
690	C₄⋊C₄	—	2	8	no	—
691	C₄⋊C₄	—	2	4	no	—
692	C₄⋊C₄	—	2	4	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	2	2	no	—
695	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
696	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	8	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	4	4	no	—
707	C₂²⋊C₄	—	4	4	no	—
708	C₂²⋊C₄	—	4	4	no	—
709	C₂²⋊C₄	—	4	2	no	—
710	C₂²⋊C₄	—	4	4	no	—
711	C₂²⋊C₄	—	4	4	no	—
712	C₂²⋊C₄	—	4	2	no	—
713	C₂²⋊C₄	C₂×D₄×C₅₉	1	8	yes	—
714	C₄²	—	2	4	no	—
715	C₄²	—	2	4	no	—
716	C₄²	—	4	4	no	—
717	C₄²	—	4	4	no	—
718	C₄²	C₂×D₄×C₅₉	1	8	yes	—
719	C₂³	—	2	1	no	—
720	C₂³	—	2	1	no	—
721	C₂³	—	2	1	no	—
722	C₂³	—	2	1	no	—
723	C₂³	—	2	8	no	—
724	C₂³	—	2	1	no	—
725	C₂³	—	2	1	no	—
726	C₂³	—	2	1	no	—
727	C₂³	—	2	1	no	—
728	C₂³	—	2	1	no	—
729	C₂³	—	2	1	no	—
730	C₂³	—	2	1	no	—
731	C₂³	—	2	1	no	—
732	C₂³	—	2	1	no	—
733	C₂³	—	2	1	no	—
734	C₂³	—	2	1	no	—
735	C₂³	—	2	1	no	—
736	C₂³	—	2	2	no	—
737	C₂³	—	2	2	no	—
738	C₂³	—	2	2	no	—
739	C₂³	—	2	2	no	—
740	C₂³	—	2	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	4	4	no	—
744	C₂³	—	4	4	no	—
745	C₂³	—	4	4	no	—
746	C₂³	—	4	4	no	—
747	C₂³	—	4	4	no	—
748	C₂³	—	4	4	no	—
749	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
750	C₂³	C₂×#41×C₅₉	1	2	yes	—
751	C₂³	C₂×#41×C₅₉	1	2	yes	—
752	C₂³	H(5,𝔽₂)×C₅₉	1	2	yes	—
753	C₂³	2₋¹⁺⁴×C₅₉	1	2	yes	—
754	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
755	Q₈	—	4	4	no	—
756	Q₈	—	8	8	no	—
757	D₄	—	4	8	no	—
758	D₄	—	4	8	no	—
759	D₄	—	4	8	no	—
760	D₄	—	4	4	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	4	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	4	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	4	no	—
782	C₂×C₄	—	2	4	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	4	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	4	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	4	4	no	—
793	C₂×C₄	—	4	4	no	—
794	C₂×C₄	—	4	4	no	—
795	C₂×C₄	—	4	4	no	—
796	C₂×C₄	—	4	4	no	—
797	C₂×C₄	—	4	8	no	—
798	C₂×C₄	—	8	4	no	—
799	C₂×C₄	—	8	4	no	—
800	C₂×C₄	#124×C₅₉	1	16	yes	complemented
801	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
802	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
803	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
804	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
805	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
806	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
807	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
808	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
809	C₂²	—	2	2	no	—
810	C₂²	—	2	2	no	—
811	C₂²	—	2	2	no	—
812	C₂²	—	2	2	no	—
813	C₂²	—	2	2	no	—
814	C₂²	—	2	2	no	—
815	C₂²	—	2	2	no	—
816	C₂²	—	2	2	no	—
817	C₂²	—	2	2	no	—
818	C₂²	—	2	2	no	—
819	C₂²	—	2	2	no	—
820	C₂²	—	2	2	no	—
821	C₂²	—	4	16	no	—
822	C₂²	—	4	1	no	—
823	C₂²	—	4	1	no	—
824	C₂²	—	4	1	no	—
825	C₂²	—	4	1	no	—
826	C₂²	—	4	1	no	—
827	C₂²	—	4	1	no	—
828	C₂²	—	4	1	no	—
829	C₂²	—	4	1	no	—
830	C₂²	—	4	2	no	—
831	C₂²	—	4	2	no	—
832	C₂²	—	4	2	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	2	no	—
837	C₂²	C₂×#124×C₅₉	1	4	yes	—
838	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
839	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
840	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
841	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
842	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
843	C₂²	C₅₉×#585	1	1	yes	characteristic
844	C₂²	C₅₉×#585	1	1	yes	characteristic
845	C₄	—	2	4	no	—
846	C₄	—	2	4	no	—
847	C₄	—	4	1	no	—
848	C₄	—	4	1	no	—
849	C₄	—	4	2	no	—
850	C₄	—	4	4	no	—
851	C₄	—	4	2	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	2	no	—
854	C₄	—	4	2	no	—
855	C₄	—	4	4	no	—
856	C₄	C₂×#124×C₅₉	1	4	yes	—
857	C₄	C₂×#124×C₅₉	1	4	yes	—
858	C₂	—	2	4	no	—
859	C₂	—	4	2	no	—
860	C₂	—	4	2	no	—
861	C₂	—	8	2	no	—
862	C₂	C₂²×#124×C₅₉	1	1	yes	characteristic
863	C₂	C₅₉×#3488	1	1	yes	characteristic
864	C₂	C₅₉×#3489	1	1	yes	characteristic
865	C₂	C₅₉×#3492	1	1	yes	characteristic
866	C₂	C₅₉×#3493	1	1	yes	characteristic
867	C₂	C₅₉×#3494	1	1	yes	characteristic
868	C₂	C₅₉×#3495	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₂×C₅₉×#525	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×#544	C₂	semidirect
3. C₅₉×#2563	C₂	semidirect
4. C₅₉×#2562	C₂	semidirect
5. C₅₉×#2562	C₂	semidirect
6. C₅₉×#2547	C₂	semidirect
7. C₅₉×#2492	C₂	semidirect
8. C₅₉×#2491	C₂	semidirect
9. C₅₉×#2490	C₂	semidirect
10. C₅₉×#2489	C₂	semidirect
11. C₅₉×#2488	C₂	semidirect
12. C₅₉×#2472	C₂	semidirect
13. C₅₉×#2311	C₂	semidirect
14. C₅₉×#2311	C₂	semidirect
15. C₅₉×#2280	C₂	semidirect
16. C₂×C₅₉×#380	C₂	semidirect
17. C₅₉×#2274	C₂	semidirect
21. C₂×C₄⋊Q₈×C₅₉	C₂²	semidirect
22. C₂×C₄⋊Q₈×C₅₉	C₂²	semidirect
23. C₂×#125×C₅₉	C₂²	semidirect
24. C₂×#125×C₅₉	C₂²	semidirect
42. C₅₉×#400	C₂²	semidirect
43. C₅₉×#400	C₂²	semidirect
45. C₅₉×#397	C₂²	semidirect
49. C₅₉×#393	C₂²	semidirect
50. C₅₉×#391	C₂²	semidirect
51. C₅₉×#391	C₂²	semidirect
52. C₅₉×#391	C₂²	semidirect
54. C₅₉×#390	C₂²	semidirect
55. C₅₉×#390	C₂²	semidirect
58. C₅₉×#388	C₂²	semidirect
59. C₅₉×#388	C₂²	semidirect
62. C₅₉×#382	C₂²	semidirect
72. C₅₉×#380	C₂²	semidirect
73. C₅₉×#380	C₂²	semidirect
74. C₅₉×#380	C₂²	semidirect
75. C₅₉×#380	C₂²	semidirect
77. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
78. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
79. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
80. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
365. C₂×C₄×C₅₉	#124	semidirect
374. #35542	C₅₉	direct (N × H)
424. C₂×#544	C₂×C₅₉	semidirect
426. #2563	C₂×C₅₉	semidirect
427. #2562	C₂×C₅₉	semidirect
428. #2562	C₂×C₅₉	semidirect
429. #2547	C₂×C₅₉	semidirect
430. #2492	C₂×C₅₉	semidirect
431. #2491	C₂×C₅₉	semidirect
432. #2490	C₂×C₅₉	semidirect
433. #2489	C₂×C₅₉	semidirect
434. #2488	C₂×C₅₉	semidirect
435. #2472	C₂×C₅₉	semidirect
436. #2311	C₂×C₅₉	semidirect
437. #2311	C₂×C₅₉	semidirect
438. #2280	C₂×C₅₉	semidirect
439. C₂×#380	C₂×C₅₉	semidirect
440. #2274	C₂×C₅₉	semidirect
455. C₂×C₄⋊Q₈	C₂²×C₅₉	semidirect
456. C₂×C₄⋊Q₈	C₂²×C₅₉	semidirect
457. C₂×#125	C₂²×C₅₉	semidirect
458. C₂×#125	C₂²×C₅₉	semidirect
476. #400	C₂²×C₅₉	semidirect
477. #400	C₂²×C₅₉	semidirect
479. #397	C₂²×C₅₉	semidirect
483. #393	C₂²×C₅₉	semidirect
484. #391	C₂²×C₅₉	semidirect
485. #391	C₂²×C₅₉	semidirect
486. #391	C₂²×C₅₉	semidirect
488. #390	C₂²×C₅₉	semidirect
489. #390	C₂²×C₅₉	semidirect
492. #388	C₂²×C₅₉	semidirect
493. #388	C₂²×C₅₉	semidirect
496. #382	C₂²×C₅₉	semidirect
506. #380	C₂²×C₅₉	semidirect
507. #380	C₂²×C₅₉	semidirect
508. #380	C₂²×C₅₉	semidirect
509. #380	C₂²×C₅₉	semidirect
511. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
512. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
513. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
514. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
519. C₅₉	#35542	direct (N × H)
800. C₂×C₄	#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×#544	2
C₂×C₅₉×#525	2
C₅₉×#2563	2
C₅₉×#2562	2
C₅₉×#2547	2
C₅₉×#2492	2
C₅₉×#2491	2
C₅₉×#2490	2
C₅₉×#2489	2
C₅₉×#2488	2
C₅₉×#2472	2
C₅₉×#2311	2
C₅₉×#2280	2
C₂×C₅₉×#380	2
C₅₉×#2274	2
#35542	59

Subgroups — C59×#35542 #28447651

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35542 #28447651