Subgroups — C₅₉×#35695 #28447804

Order 15104.

2490 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#2648	C₂	1	2	yes	maximal, complemented
2	C₅₉×#2626	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#2569	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2557	C₂	1	2	yes	maximal, complemented
5	C₅₉×#2554	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2480	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2471	C₂	1	2	yes	maximal, complemented
8	C₅₉×#2467	C₂	1	2	yes	maximal, complemented
9	C₅₉×#2459	C₂	1	2	yes	maximal, complemented
10	C₅₉×#2457	C₂	1	2	yes	maximal, complemented
11	C₅₉×#2435	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#2405	C₂	1	2	yes	maximal, complemented
13	C₅₉×#2392	C₂	1	2	yes	maximal, complemented
14	C₂×C₅₉×#392	C₂	1	1	yes	maximal, characteristic
15	C₅₉×#2368	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₉×#2342	C₂	1	2	yes	maximal, complemented
17	D₄×C₂²⋊C₄×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
18	D₄×C₂²⋊C₄×C₅₉	C₂	1	2	yes	maximal, complemented
19	C₅₉×#2273	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂³×D₄×C₅₉	C₂²	1	2	yes	—
21	C₂³×D₄×C₅₉	C₂²	1	1	yes	characteristic
22	C₂×#126×C₅₉	C₂²	1	2	yes	complemented
23	C₂×#124×C₅₉	C₂²	1	2	yes	complemented
24	C₂×#123×C₅₉	C₂²	1	2	yes	complemented
25	C₂×#123×C₅₉	C₂²	1	2	yes	complemented
26	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	complemented
28	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	complemented
29	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	complemented
30	C₂×#117×C₅₉	C₂²	1	2	yes	complemented
31	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
32	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
33	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
35	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
36	C₅₉×#400	C₂²	1	2	yes	complemented
37	C₅₉×#399	C₂²	1	1	yes	characteristic, complemented
38	C₅₉×#399	C₂²	1	1	yes	characteristic, complemented
39	C₅₉×#398	C₂²	1	2	yes	complemented
40	C₅₉×#397	C₂²	1	2	yes	complemented
41	C₅₉×#397	C₂²	1	2	yes	complemented
42	C₅₉×#397	C₂²	1	2	yes	complemented
43	C₅₉×#396	C₂²	1	2	yes	complemented
44	C₅₉×#396	C₂²	1	2	yes	complemented
45	C₅₉×#396	C₂²	1	2	yes	complemented
46	C₅₉×#394	C₂²	1	2	yes	complemented
47	C₅₉×#394	C₂²	1	2	yes	complemented
48	C₅₉×#394	C₂²	1	2	yes	complemented
49	C₅₉×#394	C₂²	1	2	yes	complemented
50	C₅₉×#394	C₂²	1	2	yes	complemented
51	C₅₉×#394	C₂²	1	2	yes	complemented
52	C₅₉×#393	C₂²	1	1	yes	characteristic, complemented
53	C₅₉×#393	C₂²	1	1	yes	characteristic, complemented
54	C₅₉×#392	C₂²	1	1	yes	characteristic
55	C₅₉×#392	C₂²	1	2	yes	—
56	C₅₉×#392	C₂²	1	1	yes	characteristic
57	C₅₉×#392	C₂²	1	1	yes	characteristic
58	C₅₉×#392	C₂²	1	1	yes	characteristic
59	C₅₉×#392	C₂²	1	2	yes	—
60	C₅₉×#391	C₂²	1	2	yes	complemented
61	C₅₉×#390	C₂²	1	2	yes	complemented
62	C₅₉×#390	C₂²	1	2	yes	complemented
63	C₅₉×#390	C₂²	1	2	yes	complemented
64	C₅₉×#390	C₂²	1	2	yes	complemented
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×#386	C₂²	1	2	yes	complemented
77	C₅₉×#386	C₂²	1	2	yes	complemented
78	C₅₉×#386	C₂²	1	2	yes	complemented
79	C₅₉×#386	C₂²	1	2	yes	complemented
80	C₅₉×#386	C₂²	1	2	yes	complemented
81	C₅₉×#386	C₂²	1	2	yes	complemented
82	C₅₉×#386	C₂²	1	2	yes	complemented
83	C₅₉×#386	C₂²	1	2	yes	complemented
84	C₅₉×#385	C₂²	1	2	yes	—
85	C₅₉×#385	C₂²	1	2	yes	—
86	C₅₉×#385	C₂²	1	2	yes	—
87	C₅₉×#381	C₂²	1	2	yes	complemented
88	C₅₉×#380	C₂²	1	1	yes	characteristic
89	C₅₉×#380	C₂²	1	2	yes	—
90	C₅₉×#380	C₂²	1	2	yes	complemented
91	C₅₉×#379	C₂²	1	2	yes	—
92	C₅₉×#379	C₂²	1	2	yes	—
93	C₅₉×#379	C₂²	1	2	yes	—
94	C₅₉×#379	C₂²	1	2	yes	—
95	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
96	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
97	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
98	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
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	complemented
102	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	complemented
103	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	complemented
104	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	complemented
105	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	complemented
106	C₂×#95×C₅₉	C₂²	1	1	yes	characteristic
107	C₂⁵×C₅₉	C₂³	1	2	yes	—
108	C₂⁵×C₅₉	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₅₉	—	2	8	no	—
111	C₂²×D₄×C₅₉	—	2	4	no	—
112	C₂²×D₄×C₅₉	—	4	4	no	—
113	C₂²×D₄×C₅₉	—	4	4	no	—
114	C₂²×D₄×C₅₉	—	4	4	no	—
115	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
116	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
117	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
118	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
119	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
120	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
121	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
123	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
124	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
126	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
127	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
128	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
129	#126×C₅₉	—	4	4	no	—
130	#124×C₅₉	—	4	4	no	—
131	#123×C₅₉	—	4	4	no	—
132	#123×C₅₉	—	4	4	no	—
133	C₂²⋊Q₈×C₅₉	—	2	4	no	—
134	C₄×D₄×C₅₉	—	4	4	no	—
135	C₄×D₄×C₅₉	—	4	4	no	—
136	C₄×D₄×C₅₉	—	4	4	no	—
137	#117×C₅₉	—	4	4	no	—
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	1	yes	characteristic
143	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
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	2	yes	—
149	C₂×C₂²⋊C₄×C₅₉	—	2	4	no	—
150	C₂×C₂²⋊C₄×C₅₉	—	2	4	no	—
151	C₂×C₂²⋊C₄×C₅₉	—	2	8	no	—
152	C₂×C₂²⋊C₄×C₅₉	—	2	4	no	—
153	C₂×C₂²⋊C₄×C₅₉	—	4	4	no	—
154	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
155	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
156	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
157	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
160	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
161	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
162	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
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	2	yes	—
166	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
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×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×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
189	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
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	#95×C₅₉	C₂³	1	1	yes	characteristic
195	#95×C₅₉	C₂³	1	2	yes	—
196	#95×C₅₉	C₂³	1	1	yes	characteristic
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	#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	2	yes	—
211	#95×C₅₉	C₂³	1	2	yes	—
212	#95×C₅₉	C₂³	1	2	yes	—
213	C₂⁴×C₅₉	—	2	2	no	—
214	C₂⁴×C₅₉	—	2	2	no	—
215	C₂⁴×C₅₉	—	2	4	no	—
216	C₂⁴×C₅₉	—	2	4	no	—
217	C₂⁴×C₅₉	—	2	4	no	—
218	C₂⁴×C₅₉	—	2	4	no	—
219	C₂⁴×C₅₉	—	4	2	no	—
220	C₂⁴×C₅₉	—	4	2	no	—
221	C₂⁴×C₅₉	—	4	2	no	—
222	C₂⁴×C₅₉	—	4	2	no	—
223	C₂⁴×C₅₉	—	4	2	no	—
224	C₂⁴×C₅₉	#41	1	4	yes	—
225	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
226	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
227	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
228	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
229	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
230	C₂×Q₈×C₅₉	—	2	2	no	—
231	C₂×Q₈×C₅₉	—	4	2	no	—
232	C₂×D₄×C₅₉	—	2	4	no	—
233	C₂×D₄×C₅₉	—	2	4	no	—
234	C₂×D₄×C₅₉	—	2	4	no	—
235	C₂×D₄×C₅₉	—	2	4	no	—
236	C₂×D₄×C₅₉	—	2	4	no	—
237	C₂×D₄×C₅₉	—	2	4	no	—
238	C₂×D₄×C₅₉	—	2	4	no	—
239	C₂×D₄×C₅₉	—	2	4	no	—
240	C₂×D₄×C₅₉	—	2	2	no	—
241	C₂×D₄×C₅₉	—	2	2	no	—
242	C₂×D₄×C₅₉	—	2	4	no	—
243	C₂×D₄×C₅₉	—	2	4	no	—
244	C₂×D₄×C₅₉	—	2	4	no	—
245	C₂×D₄×C₅₉	—	4	2	no	—
246	C₂×D₄×C₅₉	—	4	2	no	—
247	C₂×D₄×C₅₉	—	4	2	no	—
248	C₂×D₄×C₅₉	—	4	2	no	—
249	C₂×D₄×C₅₉	—	4	2	no	—
250	C₂×D₄×C₅₉	—	4	2	no	—
251	C₂×D₄×C₅₉	—	4	16	no	—
252	C₂×D₄×C₅₉	—	4	32	no	—
253	C₂²×C₄×C₅₉	—	2	4	no	—
254	C₂²×C₄×C₅₉	—	2	4	no	—
255	C₂²×C₄×C₅₉	—	2	4	no	—
256	C₂²×C₄×C₅₉	—	2	2	no	—
257	C₂²×C₄×C₅₉	—	2	4	no	—
258	C₂²×C₄×C₅₉	—	2	4	no	—
259	C₂²×C₄×C₅₉	—	2	4	no	—
260	C₂²×C₄×C₅₉	—	2	4	no	—
261	C₂²×C₄×C₅₉	—	4	2	no	—
262	C₂²×C₄×C₅₉	—	4	2	no	—
263	C₂²×C₄×C₅₉	—	4	2	no	—
264	C₂²×C₄×C₅₉	—	4	2	no	—
265	C₂²×C₄×C₅₉	—	4	2	no	—
266	C₂²×C₄×C₅₉	—	4	2	no	—
267	C₂²×C₄×C₅₉	—	4	2	no	—
268	C₂²×C₄×C₅₉	—	4	2	no	—
269	C₂²×C₄×C₅₉	—	4	2	no	—
270	C₂²×C₄×C₅₉	—	4	2	no	—
271	C₂²×C₄×C₅₉	#41	1	4	yes	—
272	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
286	C₄⋊C₄×C₅₉	—	2	2	no	—
287	C₄⋊C₄×C₅₉	—	2	4	no	—
288	C₄⋊C₄×C₅₉	—	2	4	no	—
289	C₄⋊C₄×C₅₉	—	2	4	no	—
290	C₄⋊C₄×C₅₉	—	2	4	no	—
291	C₄⋊C₄×C₅₉	—	4	2	no	—
292	C₄⋊C₄×C₅₉	—	4	2	no	—
293	C₄⋊C₄×C₅₉	—	4	2	no	—
294	C₄⋊C₄×C₅₉	—	4	2	no	—
295	C₄⋊C₄×C₅₉	—	4	2	no	—
296	C₄⋊C₄×C₅₉	—	4	2	no	—
297	C₂²⋊C₄×C₅₉	—	2	4	no	—
298	C₂²⋊C₄×C₅₉	—	2	2	no	—
299	C₂²⋊C₄×C₅₉	—	2	4	no	—
300	C₂²⋊C₄×C₅₉	—	2	2	no	—
301	C₂²⋊C₄×C₅₉	—	2	2	no	—
302	C₂²⋊C₄×C₅₉	—	2	4	no	—
303	C₂²⋊C₄×C₅₉	—	2	4	no	—
304	C₂²⋊C₄×C₅₉	—	2	4	no	—
305	C₂²⋊C₄×C₅₉	—	2	4	no	—
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	—	2	2	no	—
310	C₂²⋊C₄×C₅₉	—	2	2	no	—
311	C₂²⋊C₄×C₅₉	—	2	2	no	—
312	C₂²⋊C₄×C₅₉	—	2	2	no	—
313	C₂²⋊C₄×C₅₉	—	2	4	no	—
314	C₂²⋊C₄×C₅₉	—	2	4	no	—
315	C₂²⋊C₄×C₅₉	—	4	2	no	—
316	C₂²⋊C₄×C₅₉	—	4	2	no	—
317	C₂²⋊C₄×C₅₉	—	4	2	no	—
318	C₂²⋊C₄×C₅₉	—	4	2	no	—
319	C₂²⋊C₄×C₅₉	—	4	2	no	—
320	C₂²⋊C₄×C₅₉	—	4	2	no	—
321	C₂²⋊C₄×C₅₉	—	4	2	no	—
322	C₂²⋊C₄×C₅₉	—	4	2	no	—
323	C₂²⋊C₄×C₅₉	—	4	2	no	—
324	C₂²⋊C₄×C₅₉	—	4	2	no	—
325	C₂²⋊C₄×C₅₉	—	4	2	no	—
326	C₂²⋊C₄×C₅₉	—	4	2	no	—
327	C₂²⋊C₄×C₅₉	—	4	2	no	—
328	C₂²⋊C₄×C₅₉	—	4	2	no	—
329	C₂²⋊C₄×C₅₉	—	4	2	no	—
330	C₂²⋊C₄×C₅₉	#41	1	4	yes	—
331	C₄²×C₅₉	—	2	4	no	—
332	C₄²×C₅₉	—	4	2	no	—
333	C₄²×C₅₉	—	4	2	no	—
334	C₄²×C₅₉	—	4	2	no	—
335	C₄²×C₅₉	—	4	2	no	—
336	C₄²×C₅₉	—	4	2	no	—
337	C₂³×C₅₉	—	2	2	no	—
338	C₂³×C₅₉	—	2	2	no	—
339	C₂³×C₅₉	—	2	1	no	—
340	C₂³×C₅₉	—	2	1	no	—
341	C₂³×C₅₉	—	2	1	no	—
342	C₂³×C₅₉	—	2	1	no	—
343	C₂³×C₅₉	—	2	2	no	—
344	C₂³×C₅₉	—	2	2	no	—
345	C₂³×C₅₉	—	2	2	no	—
346	C₂³×C₅₉	—	2	2	no	—
347	C₂³×C₅₉	—	2	2	no	—
348	C₂³×C₅₉	—	2	2	no	—
349	C₂³×C₅₉	—	2	2	no	—
350	C₂³×C₅₉	—	2	2	no	—
351	C₂³×C₅₉	—	2	2	no	—
352	C₂³×C₅₉	—	2	2	no	—
353	C₂³×C₅₉	—	2	8	no	—
354	C₂³×C₅₉	—	2	2	no	—
355	C₂³×C₅₉	—	2	2	no	—
356	C₂³×C₅₉	—	2	2	no	—
357	C₂³×C₅₉	—	2	2	no	—
358	C₂³×C₅₉	—	2	2	no	—
359	C₂³×C₅₉	—	2	2	no	—
360	C₂³×C₅₉	—	2	2	no	—
361	C₂³×C₅₉	—	4	8	no	—
362	C₂³×C₅₉	—	4	8	no	—
363	C₂³×C₅₉	—	4	8	no	—
364	C₂³×C₅₉	—	4	8	no	—
365	C₂³×C₅₉	—	4	8	no	—
366	C₂³×C₅₉	—	8	2	no	—
367	C₂³×C₅₉	—	8	4	no	—
368	C₂³×C₅₉	—	8	2	no	—
369	C₂³×C₅₉	—	8	4	no	—
370	C₂³×C₅₉	—	8	4	no	—
371	C₂³×C₅₉	—	8	4	no	—
372	C₂³×C₅₉	C₂×#41	1	2	yes	—
373	C₂³×C₅₉	C₂×#41	1	2	yes	—
374	C₂³×C₅₉	C₂×#41	1	2	yes	—
375	C₂³×C₅₉	C₂×#41	1	2	yes	—
376	C₂³×C₅₉	C₂×#41	1	2	yes	—
377	C₂³×C₅₉	H(5,𝔽₂)	1	4	yes	—
378	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
379	Q₈×C₅₉	—	8	2	no	—
380	D₄×C₅₉	—	2	8	no	—
381	D₄×C₅₉	—	2	16	no	—
382	D₄×C₅₉	—	4	8	no	—
383	D₄×C₅₉	—	4	8	no	—
384	D₄×C₅₉	—	4	4	no	—
385	D₄×C₅₉	—	4	8	no	—
386	D₄×C₅₉	—	4	8	no	—
387	C₂×C₄×C₅₉	—	2	2	no	—
388	C₂×C₄×C₅₉	—	2	2	no	—
389	C₂×C₄×C₅₉	—	2	2	no	—
390	C₂×C₄×C₅₉	—	2	2	no	—
391	C₂×C₄×C₅₉	—	2	2	no	—
392	C₂×C₄×C₅₉	—	2	2	no	—
393	C₂×C₄×C₅₉	—	2	2	no	—
394	C₂×C₄×C₅₉	—	2	2	no	—
395	C₂×C₄×C₅₉	—	2	1	no	—
396	C₂×C₄×C₅₉	—	2	1	no	—
397	C₂×C₄×C₅₉	—	2	2	no	—
398	C₂×C₄×C₅₉	—	2	2	no	—
399	C₂×C₄×C₅₉	—	2	2	no	—
400	C₂×C₄×C₅₉	—	2	2	no	—
401	C₂×C₄×C₅₉	—	2	2	no	—
402	C₂×C₄×C₅₉	—	2	2	no	—
403	C₂×C₄×C₅₉	—	2	2	no	—
404	C₂×C₄×C₅₉	—	2	2	no	—
405	C₂×C₄×C₅₉	—	2	2	no	—
406	C₂×C₄×C₅₉	—	2	2	no	—
407	C₂×C₄×C₅₉	—	2	2	no	—
408	C₂×C₄×C₅₉	—	2	2	no	—
409	C₂×C₄×C₅₉	—	2	2	no	—
410	C₂×C₄×C₅₉	—	2	2	no	—
411	C₂×C₄×C₅₉	—	2	2	no	—
412	C₂×C₄×C₅₉	—	2	2	no	—
413	C₂×C₄×C₅₉	—	2	2	no	—
414	C₂×C₄×C₅₉	—	2	2	no	—
415	C₂×C₄×C₅₉	—	2	2	no	—
416	C₂×C₄×C₅₉	—	2	2	no	—
417	C₂×C₄×C₅₉	—	2	2	no	—
418	C₂×C₄×C₅₉	—	2	2	no	—
419	C₂×C₄×C₅₉	—	2	2	no	—
420	C₂×C₄×C₅₉	—	2	2	no	—
421	C₂×C₄×C₅₉	—	4	4	no	—
422	C₂×C₄×C₅₉	—	4	8	no	—
423	C₂×C₄×C₅₉	—	4	8	no	—
424	C₂×C₄×C₅₉	—	8	4	no	—
425	C₂×C₄×C₅₉	—	8	4	no	—
426	C₂×C₄×C₅₉	—	8	4	no	—
427	C₂×C₄×C₅₉	—	8	2	no	—
428	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
429	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
430	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
431	C₂×C₄×C₅₉	H(5,𝔽₂)	1	4	yes	—
432	#35695	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
433	C₂²×C₅₉	—	2	2	no	—
434	C₂²×C₅₉	—	2	4	no	—
435	C₂²×C₅₉	—	2	2	no	—
436	C₂²×C₅₉	—	2	4	no	—
437	C₂²×C₅₉	—	2	2	no	—
438	C₂²×C₅₉	—	2	2	no	—
439	C₂²×C₅₉	—	2	4	no	—
440	C₂²×C₅₉	—	2	4	no	—
441	C₂²×C₅₉	—	2	4	no	—
442	C₂²×C₅₉	—	2	4	no	—
443	C₂²×C₅₉	—	2	4	no	—
444	C₂²×C₅₉	—	4	2	no	—
445	C₂²×C₅₉	—	4	1	no	—
446	C₂²×C₅₉	—	4	1	no	—
447	C₂²×C₅₉	—	4	2	no	—
448	C₂²×C₅₉	—	4	1	no	—
449	C₂²×C₅₉	—	4	1	no	—
450	C₂²×C₅₉	—	4	2	no	—
451	C₂²×C₅₉	—	4	2	no	—
452	C₂²×C₅₉	—	4	2	no	—
453	C₂²×C₅₉	—	4	2	no	—
454	C₂²×C₅₉	—	4	2	no	—
455	C₂²×C₅₉	—	4	2	no	—
456	C₂²×C₅₉	—	4	2	no	—
457	C₂²×C₅₉	—	4	2	no	—
458	C₂²×C₅₉	—	4	2	no	—
459	C₂²×C₅₉	—	4	2	no	—
460	C₂²×C₅₉	—	4	2	no	—
461	C₂²×C₅₉	—	8	8	no	—
462	C₂²×C₅₉	—	8	16	no	—
463	C₂²×C₅₉	#529	1	4	yes	—
464	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
465	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
466	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
467	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	2	yes	—
468	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	2	yes	—
469	C₄×C₅₉	—	2	2	no	—
470	C₄×C₅₉	—	2	2	no	—
471	C₄×C₅₉	—	2	4	no	—
472	C₄×C₅₉	—	2	4	no	—
473	C₄×C₅₉	—	4	2	no	—
474	C₄×C₅₉	—	4	2	no	—
475	C₄×C₅₉	—	4	2	no	—
476	C₄×C₅₉	—	4	2	no	—
477	C₄×C₅₉	—	4	2	no	—
478	C₄×C₅₉	—	4	1	no	—
479	C₄×C₅₉	—	4	1	no	—
480	C₄×C₅₉	—	4	2	no	—
481	C₄×C₅₉	—	4	2	no	—
482	C₄×C₅₉	—	4	2	no	—
483	#2648	C₂×C₅₉	1	2	yes	complemented
484	#2626	C₂×C₅₉	1	1	yes	characteristic, complemented
485	#2569	C₂×C₅₉	1	1	yes	characteristic, complemented
486	#2557	C₂×C₅₉	1	2	yes	complemented
487	#2554	C₂×C₅₉	1	2	yes	complemented
488	#2480	C₂×C₅₉	1	2	yes	complemented
489	#2471	C₂×C₅₉	1	2	yes	complemented
490	#2467	C₂×C₅₉	1	2	yes	complemented
491	#2459	C₂×C₅₉	1	2	yes	complemented
492	#2457	C₂×C₅₉	1	2	yes	complemented
493	#2435	C₂×C₅₉	1	1	yes	characteristic, complemented
494	#2405	C₂×C₅₉	1	2	yes	complemented
495	#2392	C₂×C₅₉	1	2	yes	complemented
496	C₂×#392	C₂×C₅₉	1	1	yes	characteristic
497	#2368	C₂×C₅₉	1	1	yes	characteristic, complemented
498	#2342	C₂×C₅₉	1	2	yes	complemented
499	D₄×C₂²⋊C₄	C₂×C₅₉	1	1	yes	characteristic, complemented
500	D₄×C₂²⋊C₄	C₂×C₅₉	1	2	yes	complemented
501	#2273	C₂×C₅₉	1	1	yes	characteristic, complemented
502	C₂×C₅₉	—	2	4	no	—
503	C₂×C₅₉	—	4	2	no	—
504	C₂×C₅₉	—	4	2	no	—
505	C₂×C₅₉	—	4	4	no	—
506	C₂×C₅₉	—	8	2	no	—
507	C₂×C₅₉	C₂×#529	1	1	yes	characteristic
508	C₂×C₅₉	#3490	1	1	yes	characteristic
509	C₂×C₅₉	#3490	1	2	yes	—
510	C₂×C₅₉	#3508	1	1	yes	characteristic
511	C₂×C₅₉	#3519	1	2	yes	—
512	C₂³×D₄	C₂²×C₅₉	1	2	yes	—
513	C₂³×D₄	C₂²×C₅₉	1	1	yes	characteristic
514	C₂×#126	C₂²×C₅₉	1	2	yes	complemented
515	C₂×#124	C₂²×C₅₉	1	2	yes	complemented
516	C₂×#123	C₂²×C₅₉	1	2	yes	complemented
517	C₂×#123	C₂²×C₅₉	1	2	yes	complemented
518	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
519	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	complemented
520	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	complemented
521	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	complemented
522	C₂×#117	C₂²×C₅₉	1	2	yes	complemented
523	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
524	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
525	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
526	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
527	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
528	#400	C₂²×C₅₉	1	2	yes	complemented
529	#399	C₂²×C₅₉	1	1	yes	characteristic, complemented
530	#399	C₂²×C₅₉	1	1	yes	characteristic, complemented
531	#398	C₂²×C₅₉	1	2	yes	complemented
532	#397	C₂²×C₅₉	1	2	yes	complemented
533	#397	C₂²×C₅₉	1	2	yes	complemented
534	#397	C₂²×C₅₉	1	2	yes	complemented
535	#396	C₂²×C₅₉	1	2	yes	complemented
536	#396	C₂²×C₅₉	1	2	yes	complemented
537	#396	C₂²×C₅₉	1	2	yes	complemented
538	#394	C₂²×C₅₉	1	2	yes	complemented
539	#394	C₂²×C₅₉	1	2	yes	complemented
540	#394	C₂²×C₅₉	1	2	yes	complemented
541	#394	C₂²×C₅₉	1	2	yes	complemented
542	#394	C₂²×C₅₉	1	2	yes	complemented
543	#394	C₂²×C₅₉	1	2	yes	complemented
544	#393	C₂²×C₅₉	1	1	yes	characteristic, complemented
545	#393	C₂²×C₅₉	1	1	yes	characteristic, complemented
546	#392	C₂²×C₅₉	1	1	yes	characteristic
547	#392	C₂²×C₅₉	1	1	yes	characteristic
548	#392	C₂²×C₅₉	1	1	yes	characteristic
549	#392	C₂²×C₅₉	1	2	yes	—
550	#392	C₂²×C₅₉	1	2	yes	—
551	#392	C₂²×C₅₉	1	1	yes	characteristic
552	#391	C₂²×C₅₉	1	2	yes	complemented
553	#390	C₂²×C₅₉	1	2	yes	complemented
554	#390	C₂²×C₅₉	1	2	yes	complemented
555	#390	C₂²×C₅₉	1	2	yes	complemented
556	#390	C₂²×C₅₉	1	2	yes	complemented
557	#388	C₂²×C₅₉	1	2	yes	complemented
558	#388	C₂²×C₅₉	1	2	yes	complemented
559	#388	C₂²×C₅₉	1	2	yes	complemented
560	#388	C₂²×C₅₉	1	2	yes	complemented
561	#388	C₂²×C₅₉	1	2	yes	complemented
562	#388	C₂²×C₅₉	1	2	yes	complemented
563	#388	C₂²×C₅₉	1	2	yes	complemented
564	#387	C₂²×C₅₉	1	2	yes	complemented
565	#387	C₂²×C₅₉	1	2	yes	complemented
566	#387	C₂²×C₅₉	1	2	yes	complemented
567	#387	C₂²×C₅₉	1	2	yes	complemented
568	#386	C₂²×C₅₉	1	2	yes	complemented
569	#386	C₂²×C₅₉	1	2	yes	complemented
570	#386	C₂²×C₅₉	1	2	yes	complemented
571	#386	C₂²×C₅₉	1	2	yes	complemented
572	#386	C₂²×C₅₉	1	2	yes	complemented
573	#386	C₂²×C₅₉	1	2	yes	complemented
574	#386	C₂²×C₅₉	1	2	yes	complemented
575	#386	C₂²×C₅₉	1	2	yes	complemented
576	#385	C₂²×C₅₉	1	2	yes	—
577	#385	C₂²×C₅₉	1	2	yes	—
578	#385	C₂²×C₅₉	1	2	yes	—
579	#381	C₂²×C₅₉	1	2	yes	complemented
580	#380	C₂²×C₅₉	1	1	yes	characteristic
581	#380	C₂²×C₅₉	1	2	yes	—
582	#380	C₂²×C₅₉	1	2	yes	complemented
583	#379	C₂²×C₅₉	1	2	yes	—
584	#379	C₂²×C₅₉	1	2	yes	—
585	#379	C₂²×C₅₉	1	2	yes	—
586	#379	C₂²×C₅₉	1	2	yes	—
587	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
588	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
589	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
590	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
591	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
592	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
593	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	complemented
594	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	complemented
595	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	complemented
596	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	complemented
597	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	complemented
598	C₂×#95	C₂²×C₅₉	1	1	yes	characteristic
599	C₅₉	#35695	1	1	yes	characteristic, direct product factor, Sylow
600	C₂⁵	C₂³×C₅₉	1	2	yes	—
601	C₂⁵	C₂³×C₅₉	1	1	yes	characteristic
602	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
603	C₂²×D₄	—	2	8	no	—
604	C₂²×D₄	—	2	4	no	—
605	C₂²×D₄	—	4	4	no	—
606	C₂²×D₄	—	4	4	no	—
607	C₂²×D₄	—	4	4	no	—
608	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
609	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
610	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
611	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
612	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
613	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
614	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
615	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
616	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
617	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
618	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
619	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
620	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
621	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
622	#126	—	4	4	no	—
623	#124	—	4	4	no	—
624	#123	—	4	4	no	—
625	#123	—	4	4	no	—
626	C₂²⋊Q₈	—	2	4	no	—
627	C₄×D₄	—	4	4	no	—
628	C₄×D₄	—	4	4	no	—
629	C₄×D₄	—	4	4	no	—
630	#117	—	4	4	no	—
631	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
642	C₂×C₂²⋊C₄	—	2	4	no	—
643	C₂×C₂²⋊C₄	—	2	4	no	—
644	C₂×C₂²⋊C₄	—	2	8	no	—
645	C₂×C₂²⋊C₄	—	2	4	no	—
646	C₂×C₂²⋊C₄	—	4	4	no	—
647	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
650	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
651	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
652	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
654	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
655	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
656	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
657	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
681	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
682	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
683	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
684	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
685	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
686	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
687	#95	C₂³×C₅₉	1	1	yes	characteristic
688	#95	C₂³×C₅₉	1	2	yes	—
689	#95	C₂³×C₅₉	1	1	yes	characteristic
690	#95	C₂³×C₅₉	1	2	yes	—
691	#95	C₂³×C₅₉	1	2	yes	—
692	#95	C₂³×C₅₉	1	2	yes	—
693	#95	C₂³×C₅₉	1	2	yes	—
694	#95	C₂³×C₅₉	1	2	yes	—
695	#95	C₂³×C₅₉	1	2	yes	—
696	#95	C₂³×C₅₉	1	2	yes	—
697	#95	C₂³×C₅₉	1	2	yes	—
698	#95	C₂³×C₅₉	1	2	yes	—
699	#95	C₂³×C₅₉	1	1	yes	characteristic
700	#95	C₂³×C₅₉	1	1	yes	characteristic
701	#95	C₂³×C₅₉	1	2	yes	—
702	#95	C₂³×C₅₉	1	2	yes	—
703	#95	C₂³×C₅₉	1	2	yes	—
704	#95	C₂³×C₅₉	1	2	yes	—
705	#95	C₂³×C₅₉	1	2	yes	—
706	C₂⁴	—	2	2	no	—
707	C₂⁴	—	2	2	no	—
708	C₂⁴	—	2	4	no	—
709	C₂⁴	—	2	4	no	—
710	C₂⁴	—	2	4	no	—
711	C₂⁴	—	2	4	no	—
712	C₂⁴	—	4	2	no	—
713	C₂⁴	—	4	2	no	—
714	C₂⁴	—	4	2	no	—
715	C₂⁴	—	4	2	no	—
716	C₂⁴	—	4	2	no	—
717	C₂⁴	#41×C₅₉	1	4	yes	—
718	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
719	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
720	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
721	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
722	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
723	C₂×Q₈	—	2	2	no	—
724	C₂×Q₈	—	4	2	no	—
725	C₂×D₄	—	2	4	no	—
726	C₂×D₄	—	2	4	no	—
727	C₂×D₄	—	2	4	no	—
728	C₂×D₄	—	2	4	no	—
729	C₂×D₄	—	2	4	no	—
730	C₂×D₄	—	2	4	no	—
731	C₂×D₄	—	2	4	no	—
732	C₂×D₄	—	2	4	no	—
733	C₂×D₄	—	2	2	no	—
734	C₂×D₄	—	2	2	no	—
735	C₂×D₄	—	2	4	no	—
736	C₂×D₄	—	2	4	no	—
737	C₂×D₄	—	2	4	no	—
738	C₂×D₄	—	4	2	no	—
739	C₂×D₄	—	4	2	no	—
740	C₂×D₄	—	4	2	no	—
741	C₂×D₄	—	4	2	no	—
742	C₂×D₄	—	4	2	no	—
743	C₂×D₄	—	4	2	no	—
744	C₂×D₄	—	4	16	no	—
745	C₂×D₄	—	4	32	no	—
746	C₂²×C₄	—	2	4	no	—
747	C₂²×C₄	—	2	4	no	—
748	C₂²×C₄	—	2	4	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	4	no	—
751	C₂²×C₄	—	2	4	no	—
752	C₂²×C₄	—	2	4	no	—
753	C₂²×C₄	—	2	4	no	—
754	C₂²×C₄	—	4	2	no	—
755	C₂²×C₄	—	4	2	no	—
756	C₂²×C₄	—	4	2	no	—
757	C₂²×C₄	—	4	2	no	—
758	C₂²×C₄	—	4	2	no	—
759	C₂²×C₄	—	4	2	no	—
760	C₂²×C₄	—	4	2	no	—
761	C₂²×C₄	—	4	2	no	—
762	C₂²×C₄	—	4	2	no	—
763	C₂²×C₄	—	4	2	no	—
764	C₂²×C₄	#41×C₅₉	1	4	yes	—
765	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
766	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
769	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
770	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
771	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
772	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
773	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
774	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
775	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
776	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
777	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
778	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	4	no	—
781	C₄⋊C₄	—	2	4	no	—
782	C₄⋊C₄	—	2	4	no	—
783	C₄⋊C₄	—	2	4	no	—
784	C₄⋊C₄	—	4	2	no	—
785	C₄⋊C₄	—	4	2	no	—
786	C₄⋊C₄	—	4	2	no	—
787	C₄⋊C₄	—	4	2	no	—
788	C₄⋊C₄	—	4	2	no	—
789	C₄⋊C₄	—	4	2	no	—
790	C₂²⋊C₄	—	2	4	no	—
791	C₂²⋊C₄	—	2	2	no	—
792	C₂²⋊C₄	—	2	4	no	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	2	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	—	2	4	no	—
798	C₂²⋊C₄	—	2	4	no	—
799	C₂²⋊C₄	—	2	4	no	—
800	C₂²⋊C₄	—	2	4	no	—
801	C₂²⋊C₄	—	2	4	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	4	no	—
807	C₂²⋊C₄	—	2	4	no	—
808	C₂²⋊C₄	—	4	2	no	—
809	C₂²⋊C₄	—	4	2	no	—
810	C₂²⋊C₄	—	4	2	no	—
811	C₂²⋊C₄	—	4	2	no	—
812	C₂²⋊C₄	—	4	2	no	—
813	C₂²⋊C₄	—	4	2	no	—
814	C₂²⋊C₄	—	4	2	no	—
815	C₂²⋊C₄	—	4	2	no	—
816	C₂²⋊C₄	—	4	2	no	—
817	C₂²⋊C₄	—	4	2	no	—
818	C₂²⋊C₄	—	4	2	no	—
819	C₂²⋊C₄	—	4	2	no	—
820	C₂²⋊C₄	—	4	2	no	—
821	C₂²⋊C₄	—	4	2	no	—
822	C₂²⋊C₄	—	4	2	no	—
823	C₂²⋊C₄	#41×C₅₉	1	4	yes	—
824	C₄²	—	2	4	no	—
825	C₄²	—	4	2	no	—
826	C₄²	—	4	2	no	—
827	C₄²	—	4	2	no	—
828	C₄²	—	4	2	no	—
829	C₄²	—	4	2	no	—
830	C₂³	—	2	2	no	—
831	C₂³	—	2	2	no	—
832	C₂³	—	2	1	no	—
833	C₂³	—	2	1	no	—
834	C₂³	—	2	1	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	1	no	—
837	C₂³	—	2	2	no	—
838	C₂³	—	2	2	no	—
839	C₂³	—	2	2	no	—
840	C₂³	—	2	2	no	—
841	C₂³	—	2	2	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	2	2	no	—
844	C₂³	—	2	2	no	—
845	C₂³	—	2	2	no	—
846	C₂³	—	2	8	no	—
847	C₂³	—	2	2	no	—
848	C₂³	—	2	2	no	—
849	C₂³	—	2	2	no	—
850	C₂³	—	2	2	no	—
851	C₂³	—	2	2	no	—
852	C₂³	—	2	2	no	—
853	C₂³	—	2	2	no	—
854	C₂³	—	4	8	no	—
855	C₂³	—	4	8	no	—
856	C₂³	—	4	8	no	—
857	C₂³	—	4	8	no	—
858	C₂³	—	4	8	no	—
859	C₂³	—	8	2	no	—
860	C₂³	—	8	4	no	—
861	C₂³	—	8	4	no	—
862	C₂³	—	8	4	no	—
863	C₂³	—	8	2	no	—
864	C₂³	—	8	4	no	—
865	C₂³	C₂×#41×C₅₉	1	2	yes	—
866	C₂³	C₂×#41×C₅₉	1	2	yes	—
867	C₂³	C₂×#41×C₅₉	1	2	yes	—
868	C₂³	C₂×#41×C₅₉	1	2	yes	—
869	C₂³	C₂×#41×C₅₉	1	2	yes	—
870	C₂³	H(5,𝔽₂)×C₅₉	1	4	yes	—
871	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
872	Q₈	—	8	2	no	—
873	D₄	—	2	8	no	—
874	D₄	—	2	16	no	—
875	D₄	—	4	8	no	—
876	D₄	—	4	8	no	—
877	D₄	—	4	4	no	—
878	D₄	—	4	8	no	—
879	D₄	—	4	8	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	4	4	no	—
915	C₂×C₄	—	4	8	no	—
916	C₂×C₄	—	4	8	no	—
917	C₂×C₄	—	8	4	no	—
918	C₂×C₄	—	8	4	no	—
919	C₂×C₄	—	8	2	no	—
920	C₂×C₄	—	8	4	no	—
921	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
922	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
923	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
924	C₂×C₄	H(5,𝔽₂)×C₅₉	1	4	yes	—
925	C₂²	—	2	2	no	—
926	C₂²	—	2	4	no	—
927	C₂²	—	2	2	no	—
928	C₂²	—	2	4	no	—
929	C₂²	—	2	4	no	—
930	C₂²	—	2	2	no	—
931	C₂²	—	2	2	no	—
932	C₂²	—	2	4	no	—
933	C₂²	—	2	4	no	—
934	C₂²	—	2	4	no	—
935	C₂²	—	2	4	no	—
936	C₂²	—	4	1	no	—
937	C₂²	—	4	1	no	—
938	C₂²	—	4	2	no	—
939	C₂²	—	4	2	no	—
940	C₂²	—	4	2	no	—
941	C₂²	—	4	2	no	—
942	C₂²	—	4	2	no	—
943	C₂²	—	4	1	no	—
944	C₂²	—	4	1	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	4	2	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	4	2	no	—
951	C₂²	—	4	2	no	—
952	C₂²	—	4	2	no	—
953	C₂²	—	8	8	no	—
954	C₂²	—	8	16	no	—
955	C₂²	C₅₉×#529	1	4	yes	—
956	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
957	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
958	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
959	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	2	yes	—
960	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	2	yes	—
961	C₄	—	2	4	no	—
962	C₄	—	2	2	no	—
963	C₄	—	2	2	no	—
964	C₄	—	2	4	no	—
965	C₄	—	4	1	no	—
966	C₄	—	4	1	no	—
967	C₄	—	4	2	no	—
968	C₄	—	4	2	no	—
969	C₄	—	4	2	no	—
970	C₄	—	4	2	no	—
971	C₄	—	4	2	no	—
972	C₄	—	4	2	no	—
973	C₄	—	4	2	no	—
974	C₄	—	4	2	no	—
975	C₂	—	2	4	no	—
976	C₂	—	4	4	no	—
977	C₂	—	4	2	no	—
978	C₂	—	4	2	no	—
979	C₂	—	8	2	no	—
980	C₂	C₂×C₅₉×#529	1	1	yes	characteristic
981	C₂	C₅₉×#3490	1	1	yes	characteristic
982	C₂	C₅₉×#3490	1	2	yes	—
983	C₂	C₅₉×#3508	1	1	yes	characteristic
984	C₂	C₅₉×#3519	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₂×C₅₉×#392	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×#2648	C₂	semidirect
2. C₅₉×#2626	C₂	semidirect
3. C₅₉×#2569	C₂	semidirect
4. C₅₉×#2557	C₂	semidirect
5. C₅₉×#2554	C₂	semidirect
6. C₅₉×#2480	C₂	semidirect
7. C₅₉×#2471	C₂	semidirect
8. C₅₉×#2467	C₂	semidirect
9. C₅₉×#2459	C₂	semidirect
10. C₅₉×#2457	C₂	semidirect
11. C₅₉×#2435	C₂	semidirect
12. C₅₉×#2405	C₂	semidirect
13. C₅₉×#2392	C₂	semidirect
15. C₅₉×#2368	C₂	semidirect
16. C₅₉×#2342	C₂	semidirect
17. D₄×C₂²⋊C₄×C₅₉	C₂	semidirect
18. D₄×C₂²⋊C₄×C₅₉	C₂	semidirect
19. C₅₉×#2273	C₂	semidirect
22. C₂×#126×C₅₉	C₂²	semidirect
23. C₂×#124×C₅₉	C₂²	semidirect
24. C₂×#123×C₅₉	C₂²	semidirect
25. C₂×#123×C₅₉	C₂²	semidirect
27. C₂×C₄×D₄×C₅₉	C₂²	semidirect
28. C₂×C₄×D₄×C₅₉	C₂²	semidirect
29. C₂×C₄×D₄×C₅₉	C₂²	semidirect
30. C₂×#117×C₅₉	C₂²	semidirect
36. C₅₉×#400	C₂²	semidirect
37. C₅₉×#399	C₂²	semidirect
38. C₅₉×#399	C₂²	semidirect
39. C₅₉×#398	C₂²	semidirect
40. C₅₉×#397	C₂²	semidirect
41. C₅₉×#397	C₂²	semidirect
42. C₅₉×#397	C₂²	semidirect
43. C₅₉×#396	C₂²	semidirect
44. C₅₉×#396	C₂²	semidirect
45. C₅₉×#396	C₂²	semidirect
46. C₅₉×#394	C₂²	semidirect
47. C₅₉×#394	C₂²	semidirect
48. C₅₉×#394	C₂²	semidirect
49. C₅₉×#394	C₂²	semidirect
50. C₅₉×#394	C₂²	semidirect
51. C₅₉×#394	C₂²	semidirect
52. C₅₉×#393	C₂²	semidirect
53. C₅₉×#393	C₂²	semidirect
60. C₅₉×#391	C₂²	semidirect
61. C₅₉×#390	C₂²	semidirect
62. C₅₉×#390	C₂²	semidirect
63. C₅₉×#390	C₂²	semidirect
64. C₅₉×#390	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×#386	C₂²	semidirect
77. C₅₉×#386	C₂²	semidirect
78. C₅₉×#386	C₂²	semidirect
79. C₅₉×#386	C₂²	semidirect
80. C₅₉×#386	C₂²	semidirect
81. C₅₉×#386	C₂²	semidirect
82. C₅₉×#386	C₂²	semidirect
83. C₅₉×#386	C₂²	semidirect
87. C₅₉×#381	C₂²	semidirect
90. C₅₉×#380	C₂²	semidirect
95. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
101. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
102. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
103. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
104. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
105. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
432. #35695	C₅₉	direct (N × H)
483. #2648	C₂×C₅₉	semidirect
484. #2626	C₂×C₅₉	semidirect
485. #2569	C₂×C₅₉	semidirect
486. #2557	C₂×C₅₉	semidirect
487. #2554	C₂×C₅₉	semidirect
488. #2480	C₂×C₅₉	semidirect
489. #2471	C₂×C₅₉	semidirect
490. #2467	C₂×C₅₉	semidirect
491. #2459	C₂×C₅₉	semidirect
492. #2457	C₂×C₅₉	semidirect
493. #2435	C₂×C₅₉	semidirect
494. #2405	C₂×C₅₉	semidirect
495. #2392	C₂×C₅₉	semidirect
497. #2368	C₂×C₅₉	semidirect
498. #2342	C₂×C₅₉	semidirect
499. D₄×C₂²⋊C₄	C₂×C₅₉	semidirect
500. D₄×C₂²⋊C₄	C₂×C₅₉	semidirect
501. #2273	C₂×C₅₉	semidirect
514. C₂×#126	C₂²×C₅₉	semidirect
515. C₂×#124	C₂²×C₅₉	semidirect
516. C₂×#123	C₂²×C₅₉	semidirect
517. C₂×#123	C₂²×C₅₉	semidirect
519. C₂×C₄×D₄	C₂²×C₅₉	semidirect
520. C₂×C₄×D₄	C₂²×C₅₉	semidirect
521. C₂×C₄×D₄	C₂²×C₅₉	semidirect
522. C₂×#117	C₂²×C₅₉	semidirect
528. #400	C₂²×C₅₉	semidirect
529. #399	C₂²×C₅₉	semidirect
530. #399	C₂²×C₅₉	semidirect
531. #398	C₂²×C₅₉	semidirect
532. #397	C₂²×C₅₉	semidirect
533. #397	C₂²×C₅₉	semidirect
534. #397	C₂²×C₅₉	semidirect
535. #396	C₂²×C₅₉	semidirect
536. #396	C₂²×C₅₉	semidirect
537. #396	C₂²×C₅₉	semidirect
538. #394	C₂²×C₅₉	semidirect
539. #394	C₂²×C₅₉	semidirect
540. #394	C₂²×C₅₉	semidirect
541. #394	C₂²×C₅₉	semidirect
542. #394	C₂²×C₅₉	semidirect
543. #394	C₂²×C₅₉	semidirect
544. #393	C₂²×C₅₉	semidirect
545. #393	C₂²×C₅₉	semidirect
552. #391	C₂²×C₅₉	semidirect
553. #390	C₂²×C₅₉	semidirect
554. #390	C₂²×C₅₉	semidirect
555. #390	C₂²×C₅₉	semidirect
556. #390	C₂²×C₅₉	semidirect
557. #388	C₂²×C₅₉	semidirect
558. #388	C₂²×C₅₉	semidirect
559. #388	C₂²×C₅₉	semidirect
560. #388	C₂²×C₅₉	semidirect
561. #388	C₂²×C₅₉	semidirect
562. #388	C₂²×C₅₉	semidirect
563. #388	C₂²×C₅₉	semidirect
564. #387	C₂²×C₅₉	semidirect
565. #387	C₂²×C₅₉	semidirect
566. #387	C₂²×C₅₉	semidirect
567. #387	C₂²×C₅₉	semidirect
568. #386	C₂²×C₅₉	semidirect
569. #386	C₂²×C₅₉	semidirect
570. #386	C₂²×C₅₉	semidirect
571. #386	C₂²×C₅₉	semidirect
572. #386	C₂²×C₅₉	semidirect
573. #386	C₂²×C₅₉	semidirect
574. #386	C₂²×C₅₉	semidirect
575. #386	C₂²×C₅₉	semidirect
579. #381	C₂²×C₅₉	semidirect
582. #380	C₂²×C₅₉	semidirect
587. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
593. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
594. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
595. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
596. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
597. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
599. C₅₉	#35695	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×#2648	2
C₅₉×#2626	2
C₅₉×#2569	2
C₅₉×#2557	2
C₅₉×#2554	2
C₅₉×#2480	2
C₅₉×#2471	2
C₅₉×#2467	2
C₅₉×#2459	2
C₅₉×#2457	2
C₅₉×#2435	2
C₅₉×#2405	2
C₅₉×#2392	2
C₂×C₅₉×#392	2
C₅₉×#2368	2
C₅₉×#2342	2
D₄×C₂²⋊C₄×C₅₉	2
C₅₉×#2273	2
#35695	59

Subgroups — C59×#35695 #28447804

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35695 #28447804