Subgroups — C₅₉×#35611 #28447720

Order 15104.

2546 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#2602	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2561	C₂	1	2	yes	maximal, complemented
5	C₅₉×#2480	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2472	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2466	C₂	1	2	yes	maximal, complemented
8	C₅₉×#2459	C₂	1	2	yes	maximal, complemented
9	C₅₉×#2452	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#2447	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2439	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#2435	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₉×#2427	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₉×#2420	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#2415	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₉×#2415	C₂	1	2	yes	maximal, complemented
17	C₅₉×#2411	C₂	1	2	yes	maximal, complemented
18	C₅₉×#2408	C₂	1	1	yes	maximal, characteristic
19	C₅₉×#2324	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₉×#2323	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#124×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₉×#2293	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₉×#2293	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×D₄×C₅₉	C₂²	1	1	yes	characteristic
25	C₅₉×#542	—	2	8	no	—
26	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
27	C₂×#126×C₅₉	C₂²	1	2	yes	complemented
28	C₂×#124×C₅₉	C₂²	1	1	yes	characteristic
29	C₂×#124×C₅₉	C₂²	1	1	yes	characteristic
30	C₂×#124×C₅₉	C₂²	1	2	yes	complemented
31	C₂×#123×C₅₉	C₂²	1	2	yes	complemented
32	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	complemented
34	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	complemented
36	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
37	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
38	C₂×#120×C₅₉	C₂²	1	2	yes	—
39	C₅₉×#518	—	2	8	no	—
40	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
44	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
47	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
48	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
49	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
50	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic, complemented
51	C₂×#117×C₅₉	C₂²	1	2	yes	complemented
52	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
53	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
54	C₅₉×#397	C₂²	1	2	yes	—
55	C₅₉×#397	C₂²	1	2	yes	complemented
56	C₅₉×#397	C₂²	1	2	yes	complemented
57	C₅₉×#397	C₂²	1	2	yes	complemented
58	C₅₉×#397	C₂²	1	2	yes	complemented
59	C₅₉×#396	C₂²	1	2	yes	—
60	C₅₉×#396	C₂²	1	2	yes	complemented
61	C₅₉×#394	C₂²	1	2	yes	—
62	C₅₉×#394	C₂²	1	2	yes	—
63	C₅₉×#394	C₂²	1	2	yes	—
64	C₅₉×#394	C₂²	1	2	yes	—
65	C₅₉×#394	C₂²	1	2	yes	complemented
66	C₅₉×#394	C₂²	1	2	yes	complemented
67	C₅₉×#393	C₂²	1	2	yes	—
68	C₅₉×#393	C₂²	1	2	yes	complemented
69	C₅₉×#392	C₂²	1	2	yes	—
70	C₅₉×#391	C₂²	1	1	yes	characteristic, complemented
71	C₅₉×#391	C₂²	1	1	yes	characteristic, complemented
72	C₅₉×#391	C₂²	1	2	yes	complemented
73	C₅₉×#390	C₂²	1	1	yes	characteristic
74	C₅₉×#390	C₂²	1	1	yes	characteristic
75	C₅₉×#390	C₂²	1	1	yes	characteristic
76	C₅₉×#390	C₂²	1	1	yes	characteristic
77	C₅₉×#390	C₂²	1	1	yes	characteristic
78	C₅₉×#390	C₂²	1	1	yes	characteristic
79	C₅₉×#390	C₂²	1	2	yes	complemented
80	C₅₉×#389	C₂²	1	1	yes	characteristic, complemented
81	C₅₉×#389	C₂²	1	1	yes	characteristic, complemented
82	C₅₉×#389	C₂²	1	1	yes	characteristic, complemented
83	C₅₉×#389	C₂²	1	1	yes	characteristic, complemented
84	C₅₉×#389	C₂²	1	2	yes	complemented
85	C₅₉×#389	C₂²	1	1	yes	characteristic, complemented
86	C₅₉×#389	C₂²	1	1	yes	characteristic, complemented
87	C₅₉×#389	C₂²	1	2	yes	complemented
88	C₅₉×#388	C₂²	1	1	yes	characteristic
89	C₅₉×#388	C₂²	1	1	yes	characteristic
90	C₅₉×#388	C₂²	1	2	yes	—
91	C₅₉×#388	C₂²	1	2	yes	—
92	C₅₉×#388	C₂²	1	1	yes	characteristic, complemented
93	C₅₉×#388	C₂²	1	1	yes	characteristic, complemented
94	C₅₉×#388	C₂²	1	2	yes	complemented
95	C₅₉×#388	C₂²	1	2	yes	complemented
96	C₅₉×#388	C₂²	1	2	yes	complemented
97	C₅₉×#388	C₂²	1	2	yes	complemented
98	C₅₉×#388	C₂²	1	2	yes	complemented
99	C₅₉×#388	C₂²	1	2	yes	complemented
100	C₅₉×#387	C₂²	1	2	yes	complemented
101	C₅₉×#387	C₂²	1	2	yes	complemented
102	C₅₉×#386	C₂²	1	2	yes	complemented
103	C₅₉×#386	C₂²	1	2	yes	complemented
104	C₅₉×#386	C₂²	1	2	yes	complemented
105	C₅₉×#385	C₂²	1	2	yes	complemented
106	C₅₉×#385	C₂²	1	2	yes	complemented
107	C₅₉×#385	C₂²	1	2	yes	complemented
108	C₅₉×#382	C₂²	1	1	yes	characteristic, complemented
109	C₅₉×#381	C₂²	1	2	yes	complemented
110	C₅₉×#381	C₂²	1	2	yes	complemented
111	C₅₉×#380	C₂²	1	1	yes	characteristic
112	C₅₉×#380	C₂²	1	1	yes	characteristic, complemented
113	C₅₉×#380	C₂²	1	2	yes	complemented
114	C₅₉×#379	C₂²	1	2	yes	—
115	C₅₉×#379	C₂²	1	2	yes	—
116	C₅₉×#379	C₂²	1	2	yes	—
117	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
118	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	complemented
121	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
122	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	complemented
123	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	complemented
124	C₄³×C₅₉	C₂²	1	1	yes	characteristic, complemented
125	C₂⁵×C₅₉	C₂³	1	2	yes	—
126	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
127	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
128	C₂²×D₄×C₅₉	—	2	4	no	—
129	C₂²×D₄×C₅₉	—	2	4	no	—
130	C₂²×D₄×C₅₉	—	2	4	no	—
131	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
132	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
135	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
136	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
137	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
140	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
141	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
142	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
143	C₄⋊Q₈×C₅₉	—	2	4	no	—
144	#126×C₅₉	—	2	8	no	—
145	#124×C₅₉	—	2	4	no	—
146	#124×C₅₉	—	2	4	no	—
147	#124×C₅₉	—	2	8	no	—
148	#123×C₅₉	—	2	8	no	—
149	C₂²⋊Q₈×C₅₉	—	2	8	no	—
150	C₂²⋊Q₈×C₅₉	—	2	4	no	—
151	C₂²⋊Q₈×C₅₉	—	2	4	no	—
152	C₂²⋊Q₈×C₅₉	—	4	4	no	—
153	#121×C₅₉	—	2	4	no	—
154	#121×C₅₉	—	2	4	no	—
155	#120×C₅₉	—	4	4	no	—
156	C₄×Q₈×C₅₉	—	2	4	no	—
157	C₄×D₄×C₅₉	—	2	4	no	—
158	C₄×D₄×C₅₉	—	2	8	no	—
159	C₄×D₄×C₅₉	—	2	4	no	—
160	C₄×D₄×C₅₉	—	2	4	no	—
161	C₄×D₄×C₅₉	—	2	8	no	—
162	C₄×D₄×C₅₉	—	2	4	no	—
163	C₄×D₄×C₅₉	D₄	1	8	yes	complemented
164	#117×C₅₉	—	2	4	no	—
165	#117×C₅₉	—	2	4	no	—
166	#117×C₅₉	—	2	4	no	—
167	#117×C₅₉	—	4	4	no	—
168	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
185	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
188	C₂×C₂²⋊C₄×C₅₉	—	2	8	no	—
189	C₂×C₂²⋊C₄×C₅₉	—	2	8	no	—
190	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
195	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
216	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
219	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
221	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
222	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
223	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
228	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
230	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
234	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
235	#95×C₅₉	C₂³	1	1	yes	characteristic
236	#95×C₅₉	C₂³	1	1	yes	characteristic
237	#95×C₅₉	C₂³	1	1	yes	characteristic
238	#95×C₅₉	C₂³	1	1	yes	characteristic
239	#95×C₅₉	C₂³	1	2	yes	—
240	#95×C₅₉	C₂³	1	2	yes	—
241	#95×C₅₉	C₂³	1	2	yes	—
242	#95×C₅₉	C₂³	1	2	yes	—
243	#95×C₅₉	C₂³	1	2	yes	—
244	#95×C₅₉	C₂³	1	2	yes	—
245	#95×C₅₉	C₂³	1	1	yes	characteristic
246	#95×C₅₉	C₂³	1	1	yes	characteristic
247	#95×C₅₉	C₂³	1	2	yes	—
248	#95×C₅₉	C₂³	1	2	yes	—
249	#95×C₅₉	C₂³	1	2	yes	—
250	#95×C₅₉	C₂³	1	2	yes	—
251	#95×C₅₉	C₂³	1	2	yes	—
252	#95×C₅₉	C₂³	1	2	yes	—
253	#95×C₅₉	C₂³	1	2	yes	—
254	C₂⁴×C₅₉	—	2	4	no	—
255	C₂⁴×C₅₉	—	2	4	no	—
256	C₂⁴×C₅₉	—	2	4	no	—
257	C₂⁴×C₅₉	—	4	2	no	—
258	C₂⁴×C₅₉	—	4	2	no	—
259	C₂⁴×C₅₉	—	4	2	no	—
260	C₂⁴×C₅₉	—	4	2	no	—
261	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
262	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
263	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
264	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
265	C₂×Q₈×C₅₉	—	2	2	no	—
266	C₂×Q₈×C₅₉	—	2	4	no	—
267	C₂×Q₈×C₅₉	—	2	2	no	—
268	C₂×Q₈×C₅₉	—	2	2	no	—
269	C₂×Q₈×C₅₉	—	4	2	no	—
270	C₂×Q₈×C₅₉	—	4	2	no	—
271	C₂×D₄×C₅₉	—	2	32	no	—
272	C₂×D₄×C₅₉	—	2	4	no	—
273	C₂×D₄×C₅₉	—	2	4	no	—
274	C₂×D₄×C₅₉	—	2	2	no	—
275	C₂×D₄×C₅₉	—	2	4	no	—
276	C₂×D₄×C₅₉	—	2	4	no	—
277	C₂×D₄×C₅₉	—	2	2	no	—
278	C₂×D₄×C₅₉	—	2	4	no	—
279	C₂×D₄×C₅₉	—	2	2	no	—
280	C₂×D₄×C₅₉	—	2	2	no	—
281	C₂×D₄×C₅₉	—	2	2	no	—
282	C₂×D₄×C₅₉	—	2	2	no	—
283	C₂×D₄×C₅₉	—	4	1	no	—
284	C₂×D₄×C₅₉	—	4	2	no	—
285	C₂×D₄×C₅₉	—	4	2	no	—
286	C₂×D₄×C₅₉	—	4	2	no	—
287	C₂×D₄×C₅₉	—	4	2	no	—
288	C₂×D₄×C₅₉	C₂×D₄	1	4	yes	—
289	C₂×D₄×C₅₉	#41	1	4	yes	—
290	C₂²×C₄×C₅₉	—	2	2	no	—
291	C₂²×C₄×C₅₉	—	2	2	no	—
292	C₂²×C₄×C₅₉	—	2	4	no	—
293	C₂²×C₄×C₅₉	—	2	2	no	—
294	C₂²×C₄×C₅₉	—	2	2	no	—
295	C₂²×C₄×C₅₉	—	2	2	no	—
296	C₂²×C₄×C₅₉	—	2	4	no	—
297	C₂²×C₄×C₅₉	—	2	4	no	—
298	C₂²×C₄×C₅₉	—	4	2	no	—
299	C₂²×C₄×C₅₉	—	4	2	no	—
300	C₂²×C₄×C₅₉	—	4	2	no	—
301	C₂²×C₄×C₅₉	—	4	2	no	—
302	C₂²×C₄×C₅₉	—	4	2	no	—
303	C₂²×C₄×C₅₉	—	4	2	no	—
304	C₂²×C₄×C₅₉	—	4	2	no	—
305	C₂²×C₄×C₅₉	—	4	2	no	—
306	C₂²×C₄×C₅₉	C₂×D₄	1	8	yes	—
307	C₂²×C₄×C₅₉	#41	1	4	yes	—
308	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
311	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
319	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
327	C₄⋊C₄×C₅₉	—	2	2	no	—
328	C₄⋊C₄×C₅₉	—	2	2	no	—
329	C₄⋊C₄×C₅₉	—	2	2	no	—
330	C₄⋊C₄×C₅₉	—	2	2	no	—
331	C₄⋊C₄×C₅₉	—	2	2	no	—
332	C₄⋊C₄×C₅₉	—	2	2	no	—
333	C₄⋊C₄×C₅₉	—	2	4	no	—
334	C₄⋊C₄×C₅₉	—	2	4	no	—
335	C₄⋊C₄×C₅₉	—	2	4	no	—
336	C₄⋊C₄×C₅₉	—	2	2	no	—
337	C₄⋊C₄×C₅₉	—	2	2	no	—
338	C₄⋊C₄×C₅₉	—	2	2	no	—
339	C₄⋊C₄×C₅₉	—	2	4	no	—
340	C₄⋊C₄×C₅₉	—	2	4	no	—
341	C₄⋊C₄×C₅₉	—	2	2	no	—
342	C₄⋊C₄×C₅₉	—	4	1	no	—
343	C₄⋊C₄×C₅₉	—	4	2	no	—
344	C₄⋊C₄×C₅₉	—	4	2	no	—
345	C₄⋊C₄×C₅₉	—	4	2	no	—
346	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
347	C₂²⋊C₄×C₅₉	—	2	4	no	—
348	C₂²⋊C₄×C₅₉	—	2	4	no	—
349	C₂²⋊C₄×C₅₉	—	2	4	no	—
350	C₂²⋊C₄×C₅₉	—	2	4	no	—
351	C₂²⋊C₄×C₅₉	—	2	2	no	—
352	C₂²⋊C₄×C₅₉	—	2	4	no	—
353	C₂²⋊C₄×C₅₉	—	2	4	no	—
354	C₂²⋊C₄×C₅₉	—	2	4	no	—
355	C₂²⋊C₄×C₅₉	—	2	4	no	—
356	C₂²⋊C₄×C₅₉	—	2	2	no	—
357	C₂²⋊C₄×C₅₉	—	2	4	no	—
358	C₂²⋊C₄×C₅₉	—	2	2	no	—
359	C₂²⋊C₄×C₅₉	—	2	4	no	—
360	C₂²⋊C₄×C₅₉	—	2	4	no	—
361	C₂²⋊C₄×C₅₉	—	2	2	no	—
362	C₂²⋊C₄×C₅₉	—	2	2	no	—
363	C₂²⋊C₄×C₅₉	—	2	4	no	—
364	C₂²⋊C₄×C₅₉	—	2	2	no	—
365	C₂²⋊C₄×C₅₉	—	2	4	no	—
366	C₂²⋊C₄×C₅₉	—	2	4	no	—
367	C₂²⋊C₄×C₅₉	—	4	2	no	—
368	C₂²⋊C₄×C₅₉	—	4	1	no	—
369	C₂²⋊C₄×C₅₉	—	4	2	no	—
370	C₂²⋊C₄×C₅₉	—	4	1	no	—
371	C₂²⋊C₄×C₅₉	—	4	1	no	—
372	C₂²⋊C₄×C₅₉	—	4	2	no	—
373	C₂²⋊C₄×C₅₉	—	4	1	no	—
374	C₂²⋊C₄×C₅₉	—	4	2	no	—
375	C₂²⋊C₄×C₅₉	—	4	2	no	—
376	C₂²⋊C₄×C₅₉	—	4	2	no	—
377	C₂²⋊C₄×C₅₉	—	4	2	no	—
378	C₂²⋊C₄×C₅₉	—	4	2	no	—
379	C₂²⋊C₄×C₅₉	C₂×D₄	1	8	yes	—
380	C₄²×C₅₉	—	2	4	no	—
381	C₄²×C₅₉	—	2	2	no	—
382	C₄²×C₅₉	—	2	2	no	—
383	C₄²×C₅₉	—	2	4	no	—
384	C₄²×C₅₉	—	2	2	no	—
385	C₄²×C₅₉	—	2	2	no	—
386	C₄²×C₅₉	—	2	2	no	—
387	C₄²×C₅₉	—	4	1	no	—
388	C₄²×C₅₉	—	4	1	no	—
389	C₄²×C₅₉	—	4	1	no	—
390	C₄²×C₅₉	—	4	2	no	—
391	C₄²×C₅₉	C₂×D₄	1	4	yes	—
392	C₂³×C₅₉	—	2	16	no	—
393	C₂³×C₅₉	—	2	1	no	—
394	C₂³×C₅₉	—	2	2	no	—
395	C₂³×C₅₉	—	2	1	no	—
396	C₂³×C₅₉	—	2	2	no	—
397	C₂³×C₅₉	—	2	2	no	—
398	C₂³×C₅₉	—	2	2	no	—
399	C₂³×C₅₉	—	2	2	no	—
400	C₂³×C₅₉	—	2	2	no	—
401	C₂³×C₅₉	—	2	1	no	—
402	C₂³×C₅₉	—	2	2	no	—
403	C₂³×C₅₉	—	2	2	no	—
404	C₂³×C₅₉	—	2	2	no	—
405	C₂³×C₅₉	—	2	2	no	—
406	C₂³×C₅₉	—	2	1	no	—
407	C₂³×C₅₉	—	2	1	no	—
408	C₂³×C₅₉	—	2	2	no	—
409	C₂³×C₅₉	—	2	2	no	—
410	C₂³×C₅₉	—	2	1	no	—
411	C₂³×C₅₉	—	2	1	no	—
412	C₂³×C₅₉	—	2	1	no	—
413	C₂³×C₅₉	—	2	1	no	—
414	C₂³×C₅₉	—	2	1	no	—
415	C₂³×C₅₉	—	2	1	no	—
416	C₂³×C₅₉	—	2	1	no	—
417	C₂³×C₅₉	—	2	1	no	—
418	C₂³×C₅₉	—	8	4	no	—
419	C₂³×C₅₉	—	8	4	no	—
420	C₂³×C₅₉	—	8	4	no	—
421	C₂³×C₅₉	—	8	4	no	—
422	C₂³×C₅₉	—	8	4	no	—
423	C₂³×C₅₉	—	8	4	no	—
424	C₂³×C₅₉	C₂²×D₄	1	4	yes	—
425	C₂³×C₅₉	C₂×#41	1	2	yes	—
426	C₂³×C₅₉	C₂×#41	1	4	yes	—
427	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
428	Q₈×C₅₉	—	4	4	no	—
429	Q₈×C₅₉	—	8	4	no	—
430	D₄×C₅₉	—	2	16	no	—
431	D₄×C₅₉	—	2	8	no	—
432	D₄×C₅₉	—	2	8	no	—
433	D₄×C₅₉	—	4	4	no	—
434	D₄×C₅₉	—	8	4	no	—
435	D₄×C₅₉	—	8	4	no	—
436	C₂×C₄×C₅₉	—	2	1	no	—
437	C₂×C₄×C₅₉	—	2	1	no	—
438	C₂×C₄×C₅₉	—	2	1	no	—
439	C₂×C₄×C₅₉	—	2	1	no	—
440	C₂×C₄×C₅₉	—	2	2	no	—
441	C₂×C₄×C₅₉	—	2	1	no	—
442	C₂×C₄×C₅₉	—	2	1	no	—
443	C₂×C₄×C₅₉	—	2	1	no	—
444	C₂×C₄×C₅₉	—	2	1	no	—
445	C₂×C₄×C₅₉	—	2	2	no	—
446	C₂×C₄×C₅₉	—	2	8	no	—
447	C₂×C₄×C₅₉	—	2	1	no	—
448	C₂×C₄×C₅₉	—	2	2	no	—
449	C₂×C₄×C₅₉	—	2	1	no	—
450	C₂×C₄×C₅₉	—	2	2	no	—
451	C₂×C₄×C₅₉	—	2	1	no	—
452	C₂×C₄×C₅₉	—	2	1	no	—
453	C₂×C₄×C₅₉	—	2	2	no	—
454	C₂×C₄×C₅₉	—	2	1	no	—
455	C₂×C₄×C₅₉	—	2	1	no	—
456	C₂×C₄×C₅₉	—	2	1	no	—
457	C₂×C₄×C₅₉	—	2	1	no	—
458	C₂×C₄×C₅₉	—	2	1	no	—
459	C₂×C₄×C₅₉	—	2	2	no	—
460	C₂×C₄×C₅₉	—	2	2	no	—
461	C₂×C₄×C₅₉	—	2	1	no	—
462	C₂×C₄×C₅₉	—	2	2	no	—
463	C₂×C₄×C₅₉	—	2	2	no	—
464	C₂×C₄×C₅₉	—	2	1	no	—
465	C₂×C₄×C₅₉	—	2	2	no	—
466	C₂×C₄×C₅₉	—	2	2	no	—
467	C₂×C₄×C₅₉	—	2	2	no	—
468	C₂×C₄×C₅₉	—	2	1	no	—
469	C₂×C₄×C₅₉	—	2	1	no	—
470	C₂×C₄×C₅₉	—	2	1	no	—
471	C₂×C₄×C₅₉	—	2	1	no	—
472	C₂×C₄×C₅₉	—	2	1	no	—
473	C₂×C₄×C₅₉	—	2	1	no	—
474	C₂×C₄×C₅₉	—	2	1	no	—
475	C₂×C₄×C₅₉	—	2	2	no	—
476	C₂×C₄×C₅₉	—	2	1	no	—
477	C₂×C₄×C₅₉	—	2	1	no	—
478	C₂×C₄×C₅₉	—	2	2	no	—
479	C₂×C₄×C₅₉	—	2	1	no	—
480	C₂×C₄×C₅₉	—	2	2	no	—
481	C₂×C₄×C₅₉	—	2	1	no	—
482	C₂×C₄×C₅₉	—	2	2	no	—
483	C₂×C₄×C₅₉	—	2	1	no	—
484	C₂×C₄×C₅₉	—	2	1	no	—
485	C₂×C₄×C₅₉	—	2	2	no	—
486	C₂×C₄×C₅₉	—	4	8	no	—
487	C₂×C₄×C₅₉	—	4	4	no	—
488	C₂×C₄×C₅₉	—	8	4	no	—
489	C₂×C₄×C₅₉	—	8	4	no	—
490	C₂×C₄×C₅₉	—	8	4	no	—
491	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
492	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
493	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
494	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
495	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
496	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
497	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
498	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
499	#35611	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
500	C₂²×C₅₉	—	2	2	no	—
501	C₂²×C₅₉	—	2	4	no	—
502	C₂²×C₅₉	—	2	4	no	—
503	C₂²×C₅₉	—	2	2	no	—
504	C₂²×C₅₉	—	2	4	no	—
505	C₂²×C₅₉	—	2	4	no	—
506	C₂²×C₅₉	—	2	2	no	—
507	C₂²×C₅₉	—	2	4	no	—
508	C₂²×C₅₉	—	2	4	no	—
509	C₂²×C₅₉	—	4	2	no	—
510	C₂²×C₅₉	—	4	2	no	—
511	C₂²×C₅₉	—	4	2	no	—
512	C₂²×C₅₉	—	4	1	no	—
513	C₂²×C₅₉	—	4	2	no	—
514	C₂²×C₅₉	—	4	1	no	—
515	C₂²×C₅₉	—	4	2	no	—
516	C₂²×C₅₉	—	4	2	no	—
517	C₂²×C₅₉	—	4	2	no	—
518	C₂²×C₅₉	—	4	1	no	—
519	C₂²×C₅₉	—	4	2	no	—
520	C₂²×C₅₉	—	4	1	no	—
521	C₂²×C₅₉	—	4	1	no	—
522	C₂²×C₅₉	—	4	1	no	—
523	C₂²×C₅₉	—	4	1	no	—
524	C₂²×C₅₉	—	4	1	no	—
525	C₂²×C₅₉	—	4	1	no	—
526	C₂²×C₅₉	—	4	1	no	—
527	C₂²×C₅₉	—	4	1	no	—
528	C₂²×C₅₉	—	8	16	no	—
529	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
530	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
531	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
532	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
533	C₂²×C₅₉	#585	1	1	yes	characteristic
534	C₂²×C₅₉	#585	1	1	yes	characteristic
535	C₂²×C₅₉	#585	1	1	yes	characteristic
536	C₄×C₅₉	—	2	2	no	—
537	C₄×C₅₉	—	2	2	no	—
538	C₄×C₅₉	—	2	2	no	—
539	C₄×C₅₉	—	2	4	no	—
540	C₄×C₅₉	—	2	2	no	—
541	C₄×C₅₉	—	4	1	no	—
542	C₄×C₅₉	—	4	2	no	—
543	C₄×C₅₉	—	4	2	no	—
544	C₄×C₅₉	—	4	1	no	—
545	C₄×C₅₉	—	4	2	no	—
546	C₄×C₅₉	—	4	1	no	—
547	C₄×C₅₉	—	4	1	no	—
548	C₄×C₅₉	—	4	2	no	—
549	C₄×C₅₉	—	4	1	no	—
550	C₄×C₅₉	—	4	1	no	—
551	C₄×C₅₉	—	4	1	no	—
552	C₄×C₅₉	—	4	2	no	—
553	C₄×C₅₉	—	4	1	no	—
554	C₄×C₅₉	#525	1	4	yes	—
555	C₂×#542	C₂×C₅₉	1	1	yes	characteristic, complemented
556	C₂×#518	C₂×C₅₉	1	1	yes	characteristic, complemented
557	#2602	C₂×C₅₉	1	2	yes	complemented
558	#2561	C₂×C₅₉	1	2	yes	complemented
559	#2480	C₂×C₅₉	1	2	yes	complemented
560	#2472	C₂×C₅₉	1	2	yes	complemented
561	#2466	C₂×C₅₉	1	2	yes	complemented
562	#2459	C₂×C₅₉	1	2	yes	complemented
563	#2452	C₂×C₅₉	1	1	yes	characteristic, complemented
564	#2447	C₂×C₅₉	1	1	yes	characteristic, complemented
565	#2439	C₂×C₅₉	1	1	yes	characteristic, complemented
566	#2435	C₂×C₅₉	1	1	yes	characteristic, complemented
567	#2427	C₂×C₅₉	1	1	yes	characteristic, complemented
568	#2420	C₂×C₅₉	1	1	yes	characteristic, complemented
569	#2415	C₂×C₅₉	1	1	yes	characteristic, complemented
570	#2415	C₂×C₅₉	1	2	yes	complemented
571	#2411	C₂×C₅₉	1	2	yes	complemented
572	#2408	C₂×C₅₉	1	1	yes	characteristic
573	#2324	C₂×C₅₉	1	1	yes	characteristic, complemented
574	#2323	C₂×C₅₉	1	1	yes	characteristic, complemented
575	C₄×#124	C₂×C₅₉	1	1	yes	characteristic, complemented
576	#2293	C₂×C₅₉	1	1	yes	characteristic, complemented
577	#2293	C₂×C₅₉	1	1	yes	characteristic, complemented
578	C₂×C₅₉	—	4	4	no	—
579	C₂×C₅₉	—	4	4	no	—
580	C₂×C₅₉	—	4	2	no	—
581	C₂×C₅₉	—	8	1	no	—
582	C₂×C₅₉	C₂×#525	1	1	yes	characteristic
583	C₂×C₅₉	#3494	1	1	yes	characteristic
584	C₂×C₅₉	#3496	1	1	yes	characteristic
585	C₂×C₅₉	#3500	1	1	yes	characteristic
586	C₂×C₅₉	#3510	1	1	yes	characteristic
587	C₂×C₅₉	#3514	1	1	yes	characteristic
588	C₂×C₅₉	#3521	1	1	yes	characteristic
589	C₂³×D₄	C₂²×C₅₉	1	1	yes	characteristic
590	#542	—	2	8	no	—
591	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
592	C₂×#126	C₂²×C₅₉	1	2	yes	complemented
593	C₂×#124	C₂²×C₅₉	1	1	yes	characteristic
594	C₂×#124	C₂²×C₅₉	1	1	yes	characteristic
595	C₂×#124	C₂²×C₅₉	1	2	yes	complemented
596	C₂×#123	C₂²×C₅₉	1	2	yes	complemented
597	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
598	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	complemented
599	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
600	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	complemented
601	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
602	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
603	C₂×#120	C₂²×C₅₉	1	2	yes	—
604	#518	—	2	8	no	—
605	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
606	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
607	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
608	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
609	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
610	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
611	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
612	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
613	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
614	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
615	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic, complemented
616	C₂×#117	C₂²×C₅₉	1	2	yes	complemented
617	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
618	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
619	#397	C₂²×C₅₉	1	2	yes	—
620	#397	C₂²×C₅₉	1	2	yes	complemented
621	#397	C₂²×C₅₉	1	2	yes	complemented
622	#397	C₂²×C₅₉	1	2	yes	complemented
623	#397	C₂²×C₅₉	1	2	yes	complemented
624	#396	C₂²×C₅₉	1	2	yes	—
625	#396	C₂²×C₅₉	1	2	yes	complemented
626	#394	C₂²×C₅₉	1	2	yes	—
627	#394	C₂²×C₅₉	1	2	yes	—
628	#394	C₂²×C₅₉	1	2	yes	—
629	#394	C₂²×C₅₉	1	2	yes	—
630	#394	C₂²×C₅₉	1	2	yes	complemented
631	#394	C₂²×C₅₉	1	2	yes	complemented
632	#393	C₂²×C₅₉	1	2	yes	—
633	#393	C₂²×C₅₉	1	2	yes	complemented
634	#392	C₂²×C₅₉	1	2	yes	—
635	#391	C₂²×C₅₉	1	1	yes	characteristic, complemented
636	#391	C₂²×C₅₉	1	2	yes	complemented
637	#391	C₂²×C₅₉	1	1	yes	characteristic, complemented
638	#390	C₂²×C₅₉	1	1	yes	characteristic
639	#390	C₂²×C₅₉	1	1	yes	characteristic
640	#390	C₂²×C₅₉	1	1	yes	characteristic
641	#390	C₂²×C₅₉	1	1	yes	characteristic
642	#390	C₂²×C₅₉	1	1	yes	characteristic
643	#390	C₂²×C₅₉	1	1	yes	characteristic
644	#390	C₂²×C₅₉	1	2	yes	complemented
645	#389	C₂²×C₅₉	1	2	yes	complemented
646	#389	C₂²×C₅₉	1	1	yes	characteristic, complemented
647	#389	C₂²×C₅₉	1	1	yes	characteristic, complemented
648	#389	C₂²×C₅₉	1	2	yes	complemented
649	#389	C₂²×C₅₉	1	1	yes	characteristic, complemented
650	#389	C₂²×C₅₉	1	1	yes	characteristic, complemented
651	#389	C₂²×C₅₉	1	1	yes	characteristic, complemented
652	#389	C₂²×C₅₉	1	1	yes	characteristic, complemented
653	#388	C₂²×C₅₉	1	1	yes	characteristic
654	#388	C₂²×C₅₉	1	2	yes	—
655	#388	C₂²×C₅₉	1	2	yes	—
656	#388	C₂²×C₅₉	1	1	yes	characteristic
657	#388	C₂²×C₅₉	1	2	yes	complemented
658	#388	C₂²×C₅₉	1	2	yes	complemented
659	#388	C₂²×C₅₉	1	1	yes	characteristic, complemented
660	#388	C₂²×C₅₉	1	2	yes	complemented
661	#388	C₂²×C₅₉	1	2	yes	complemented
662	#388	C₂²×C₅₉	1	1	yes	characteristic, complemented
663	#388	C₂²×C₅₉	1	2	yes	complemented
664	#388	C₂²×C₅₉	1	2	yes	complemented
665	#387	C₂²×C₅₉	1	2	yes	complemented
666	#387	C₂²×C₅₉	1	2	yes	complemented
667	#386	C₂²×C₅₉	1	2	yes	complemented
668	#386	C₂²×C₅₉	1	2	yes	complemented
669	#386	C₂²×C₅₉	1	2	yes	complemented
670	#385	C₂²×C₅₉	1	2	yes	complemented
671	#385	C₂²×C₅₉	1	2	yes	complemented
672	#385	C₂²×C₅₉	1	2	yes	complemented
673	#382	C₂²×C₅₉	1	1	yes	characteristic, complemented
674	#381	C₂²×C₅₉	1	2	yes	complemented
675	#381	C₂²×C₅₉	1	2	yes	complemented
676	#380	C₂²×C₅₉	1	1	yes	characteristic
677	#380	C₂²×C₅₉	1	1	yes	characteristic, complemented
678	#380	C₂²×C₅₉	1	2	yes	complemented
679	#379	C₂²×C₅₉	1	2	yes	—
680	#379	C₂²×C₅₉	1	2	yes	—
681	#379	C₂²×C₅₉	1	2	yes	—
682	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
683	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
684	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
685	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	complemented
686	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
687	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	complemented
688	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	complemented
689	C₄³	C₂²×C₅₉	1	1	yes	characteristic, complemented
690	C₅₉	#35611	1	1	yes	characteristic, direct product factor, Sylow
691	C₂⁵	C₂³×C₅₉	1	2	yes	—
692	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
693	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
694	C₂²×D₄	—	2	4	no	—
695	C₂²×D₄	—	2	4	no	—
696	C₂²×D₄	—	2	4	no	—
697	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
698	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
699	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
700	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
701	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
702	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
703	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
704	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
705	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
706	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
707	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
708	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
709	C₄⋊Q₈	—	2	4	no	—
710	#126	—	2	8	no	—
711	#124	—	2	4	no	—
712	#124	—	2	4	no	—
713	#124	—	2	8	no	—
714	#123	—	2	8	no	—
715	C₂²⋊Q₈	—	2	8	no	—
716	C₂²⋊Q₈	—	2	4	no	—
717	C₂²⋊Q₈	—	2	4	no	—
718	C₂²⋊Q₈	—	4	4	no	—
719	#121	—	2	4	no	—
720	#121	—	2	4	no	—
721	#120	—	4	4	no	—
722	C₄×Q₈	—	2	4	no	—
723	C₄×D₄	—	2	4	no	—
724	C₄×D₄	—	2	8	no	—
725	C₄×D₄	—	2	4	no	—
726	C₄×D₄	—	2	4	no	—
727	C₄×D₄	—	2	8	no	—
728	C₄×D₄	—	2	4	no	—
729	C₄×D₄	D₄×C₅₉	1	8	yes	complemented
730	#117	—	2	4	no	—
731	#117	—	2	4	no	—
732	#117	—	2	4	no	—
733	#117	—	4	4	no	—
734	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
735	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
736	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
737	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
738	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
739	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
740	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
741	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
742	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
743	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
744	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
745	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
746	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
747	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
748	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
749	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
750	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
751	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
752	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
753	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
754	C₂×C₂²⋊C₄	—	2	8	no	—
755	C₂×C₂²⋊C₄	—	2	8	no	—
756	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
757	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
758	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
759	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
760	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
761	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
762	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
763	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
764	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
765	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
766	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
767	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
768	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
769	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
770	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
771	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
772	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
773	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
774	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
775	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
776	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
777	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
778	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
779	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
780	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
781	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
782	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
783	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
784	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
785	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
786	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
787	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
788	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
789	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
790	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
791	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
792	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
793	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
794	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
795	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
796	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
797	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
798	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
799	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
800	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
801	#95	C₂³×C₅₉	1	1	yes	characteristic
802	#95	C₂³×C₅₉	1	1	yes	characteristic
803	#95	C₂³×C₅₉	1	1	yes	characteristic
804	#95	C₂³×C₅₉	1	1	yes	characteristic
805	#95	C₂³×C₅₉	1	2	yes	—
806	#95	C₂³×C₅₉	1	2	yes	—
807	#95	C₂³×C₅₉	1	2	yes	—
808	#95	C₂³×C₅₉	1	2	yes	—
809	#95	C₂³×C₅₉	1	2	yes	—
810	#95	C₂³×C₅₉	1	2	yes	—
811	#95	C₂³×C₅₉	1	1	yes	characteristic
812	#95	C₂³×C₅₉	1	1	yes	characteristic
813	#95	C₂³×C₅₉	1	2	yes	—
814	#95	C₂³×C₅₉	1	2	yes	—
815	#95	C₂³×C₅₉	1	2	yes	—
816	#95	C₂³×C₅₉	1	2	yes	—
817	#95	C₂³×C₅₉	1	2	yes	—
818	#95	C₂³×C₅₉	1	2	yes	—
819	#95	C₂³×C₅₉	1	2	yes	—
820	C₂⁴	—	2	4	no	—
821	C₂⁴	—	2	4	no	—
822	C₂⁴	—	2	4	no	—
823	C₂⁴	—	4	2	no	—
824	C₂⁴	—	4	2	no	—
825	C₂⁴	—	4	2	no	—
826	C₂⁴	—	4	2	no	—
827	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
828	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
829	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
830	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
831	C₂×Q₈	—	2	2	no	—
832	C₂×Q₈	—	2	4	no	—
833	C₂×Q₈	—	2	2	no	—
834	C₂×Q₈	—	2	2	no	—
835	C₂×Q₈	—	4	2	no	—
836	C₂×Q₈	—	4	2	no	—
837	C₂×D₄	—	2	32	no	—
838	C₂×D₄	—	2	4	no	—
839	C₂×D₄	—	2	4	no	—
840	C₂×D₄	—	2	2	no	—
841	C₂×D₄	—	2	4	no	—
842	C₂×D₄	—	2	4	no	—
843	C₂×D₄	—	2	2	no	—
844	C₂×D₄	—	2	4	no	—
845	C₂×D₄	—	2	2	no	—
846	C₂×D₄	—	2	2	no	—
847	C₂×D₄	—	2	2	no	—
848	C₂×D₄	—	2	2	no	—
849	C₂×D₄	—	4	1	no	—
850	C₂×D₄	—	4	2	no	—
851	C₂×D₄	—	4	2	no	—
852	C₂×D₄	—	4	2	no	—
853	C₂×D₄	—	4	2	no	—
854	C₂×D₄	C₂×D₄×C₅₉	1	4	yes	—
855	C₂×D₄	#41×C₅₉	1	4	yes	—
856	C₂²×C₄	—	2	2	no	—
857	C₂²×C₄	—	2	2	no	—
858	C₂²×C₄	—	2	4	no	—
859	C₂²×C₄	—	2	2	no	—
860	C₂²×C₄	—	2	2	no	—
861	C₂²×C₄	—	2	2	no	—
862	C₂²×C₄	—	2	4	no	—
863	C₂²×C₄	—	2	4	no	—
864	C₂²×C₄	—	4	2	no	—
865	C₂²×C₄	—	4	2	no	—
866	C₂²×C₄	—	4	2	no	—
867	C₂²×C₄	—	4	2	no	—
868	C₂²×C₄	—	4	2	no	—
869	C₂²×C₄	—	4	2	no	—
870	C₂²×C₄	—	4	2	no	—
871	C₂²×C₄	—	4	2	no	—
872	C₂²×C₄	C₂×D₄×C₅₉	1	8	yes	—
873	C₂²×C₄	#41×C₅₉	1	4	yes	—
874	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
875	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
876	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
877	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
878	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
879	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
880	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
881	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
882	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
883	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
884	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
885	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
886	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
887	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
888	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
889	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
890	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
891	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
892	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	4	no	—
900	C₄⋊C₄	—	2	4	no	—
901	C₄⋊C₄	—	2	4	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	4	no	—
906	C₄⋊C₄	—	2	4	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	4	2	no	—
909	C₄⋊C₄	—	4	2	no	—
910	C₄⋊C₄	—	4	1	no	—
911	C₄⋊C₄	—	4	2	no	—
912	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
913	C₂²⋊C₄	—	2	4	no	—
914	C₂²⋊C₄	—	2	4	no	—
915	C₂²⋊C₄	—	2	4	no	—
916	C₂²⋊C₄	—	2	4	no	—
917	C₂²⋊C₄	—	2	2	no	—
918	C₂²⋊C₄	—	2	4	no	—
919	C₂²⋊C₄	—	2	4	no	—
920	C₂²⋊C₄	—	2	4	no	—
921	C₂²⋊C₄	—	2	4	no	—
922	C₂²⋊C₄	—	2	2	no	—
923	C₂²⋊C₄	—	2	4	no	—
924	C₂²⋊C₄	—	2	2	no	—
925	C₂²⋊C₄	—	2	4	no	—
926	C₂²⋊C₄	—	2	4	no	—
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	2	4	no	—
930	C₂²⋊C₄	—	2	2	no	—
931	C₂²⋊C₄	—	2	4	no	—
932	C₂²⋊C₄	—	2	4	no	—
933	C₂²⋊C₄	—	4	2	no	—
934	C₂²⋊C₄	—	4	2	no	—
935	C₂²⋊C₄	—	4	2	no	—
936	C₂²⋊C₄	—	4	2	no	—
937	C₂²⋊C₄	—	4	1	no	—
938	C₂²⋊C₄	—	4	2	no	—
939	C₂²⋊C₄	—	4	1	no	—
940	C₂²⋊C₄	—	4	1	no	—
941	C₂²⋊C₄	—	4	2	no	—
942	C₂²⋊C₄	—	4	1	no	—
943	C₂²⋊C₄	—	4	2	no	—
944	C₂²⋊C₄	—	4	2	no	—
945	C₂²⋊C₄	C₂×D₄×C₅₉	1	8	yes	—
946	C₄²	—	2	4	no	—
947	C₄²	—	2	2	no	—
948	C₄²	—	2	2	no	—
949	C₄²	—	2	4	no	—
950	C₄²	—	2	2	no	—
951	C₄²	—	2	2	no	—
952	C₄²	—	2	2	no	—
953	C₄²	—	4	2	no	—
954	C₄²	—	4	1	no	—
955	C₄²	—	4	1	no	—
956	C₄²	—	4	1	no	—
957	C₄²	C₂×D₄×C₅₉	1	4	yes	—
958	C₂³	—	2	16	no	—
959	C₂³	—	2	1	no	—
960	C₂³	—	2	2	no	—
961	C₂³	—	2	1	no	—
962	C₂³	—	2	2	no	—
963	C₂³	—	2	2	no	—
964	C₂³	—	2	2	no	—
965	C₂³	—	2	2	no	—
966	C₂³	—	2	2	no	—
967	C₂³	—	2	1	no	—
968	C₂³	—	2	2	no	—
969	C₂³	—	2	2	no	—
970	C₂³	—	2	2	no	—
971	C₂³	—	2	2	no	—
972	C₂³	—	2	1	no	—
973	C₂³	—	2	1	no	—
974	C₂³	—	2	2	no	—
975	C₂³	—	2	2	no	—
976	C₂³	—	2	1	no	—
977	C₂³	—	2	1	no	—
978	C₂³	—	2	1	no	—
979	C₂³	—	2	1	no	—
980	C₂³	—	2	1	no	—
981	C₂³	—	2	1	no	—
982	C₂³	—	2	1	no	—
983	C₂³	—	2	1	no	—
984	C₂³	—	8	4	no	—
985	C₂³	—	8	4	no	—
986	C₂³	—	8	4	no	—
987	C₂³	—	8	4	no	—
988	C₂³	—	8	4	no	—
989	C₂³	—	8	4	no	—
990	C₂³	C₂²×D₄×C₅₉	1	4	yes	—
991	C₂³	C₂×#41×C₅₉	1	2	yes	—
992	C₂³	C₂×#41×C₅₉	1	4	yes	—
993	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
994	Q₈	—	4	4	no	—
995	Q₈	—	8	4	no	—
996	D₄	—	2	16	no	—
997	D₄	—	2	8	no	—
998	D₄	—	2	8	no	—
999	D₄	—	4	4	no	—
1000	D₄	—	8	4	no	—
1001	D₄	—	8	4	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	8	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	2	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	2	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	4	8	no	—
1053	C₂×C₄	—	4	4	no	—
1054	C₂×C₄	—	8	4	no	—
1055	C₂×C₄	—	8	4	no	—
1056	C₂×C₄	—	8	4	no	—
1057	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1058	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
1059	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1060	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1061	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
1062	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
1063	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
1064	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
1065	C₂²	—	2	2	no	—
1066	C₂²	—	2	4	no	—
1067	C₂²	—	2	4	no	—
1068	C₂²	—	2	2	no	—
1069	C₂²	—	2	4	no	—
1070	C₂²	—	2	4	no	—
1071	C₂²	—	2	2	no	—
1072	C₂²	—	2	4	no	—
1073	C₂²	—	2	4	no	—
1074	C₂²	—	4	2	no	—
1075	C₂²	—	4	2	no	—
1076	C₂²	—	4	1	no	—
1077	C₂²	—	4	2	no	—
1078	C₂²	—	4	1	no	—
1079	C₂²	—	4	2	no	—
1080	C₂²	—	4	2	no	—
1081	C₂²	—	4	2	no	—
1082	C₂²	—	4	2	no	—
1083	C₂²	—	4	1	no	—
1084	C₂²	—	4	2	no	—
1085	C₂²	—	4	1	no	—
1086	C₂²	—	4	1	no	—
1087	C₂²	—	4	1	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	4	1	no	—
1091	C₂²	—	4	1	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	8	16	no	—
1094	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
1095	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
1096	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
1097	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
1098	C₂²	C₅₉×#585	1	1	yes	characteristic
1099	C₂²	C₅₉×#585	1	1	yes	characteristic
1100	C₂²	C₅₉×#585	1	1	yes	characteristic
1101	C₄	—	2	2	no	—
1102	C₄	—	2	2	no	—
1103	C₄	—	2	2	no	—
1104	C₄	—	2	4	no	—
1105	C₄	—	2	2	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	2	no	—
1108	C₄	—	4	1	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	2	no	—
1112	C₄	—	4	2	no	—
1113	C₄	—	4	1	no	—
1114	C₄	—	4	2	no	—
1115	C₄	—	4	1	no	—
1116	C₄	—	4	2	no	—
1117	C₄	—	4	1	no	—
1118	C₄	—	4	1	no	—
1119	C₄	C₅₉×#525	1	4	yes	—
1120	C₂	—	4	2	no	—
1121	C₂	—	4	4	no	—
1122	C₂	—	4	4	no	—
1123	C₂	—	8	1	no	—
1124	C₂	C₂×C₅₉×#525	1	1	yes	characteristic
1125	C₂	C₅₉×#3494	1	1	yes	characteristic
1126	C₂	C₅₉×#3496	1	1	yes	characteristic
1127	C₂	C₅₉×#3500	1	1	yes	characteristic
1128	C₂	C₅₉×#3510	1	1	yes	characteristic
1129	C₂	C₅₉×#3514	1	1	yes	characteristic
1130	C₂	C₅₉×#3521	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₅₉×#2408	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×#542	C₂	semidirect
2. C₂×C₅₉×#518	C₂	semidirect
3. C₅₉×#2602	C₂	semidirect
4. C₅₉×#2561	C₂	semidirect
5. C₅₉×#2480	C₂	semidirect
6. C₅₉×#2472	C₂	semidirect
7. C₅₉×#2466	C₂	semidirect
8. C₅₉×#2459	C₂	semidirect
9. C₅₉×#2452	C₂	semidirect
10. C₅₉×#2447	C₂	semidirect
11. C₅₉×#2439	C₂	semidirect
12. C₅₉×#2435	C₂	semidirect
13. C₅₉×#2427	C₂	semidirect
14. C₅₉×#2420	C₂	semidirect
15. C₅₉×#2415	C₂	semidirect
16. C₅₉×#2415	C₂	semidirect
17. C₅₉×#2411	C₂	semidirect
19. C₅₉×#2324	C₂	semidirect
20. C₅₉×#2323	C₂	semidirect
21. C₄×#124×C₅₉	C₂	semidirect
22. C₅₉×#2293	C₂	semidirect
23. C₅₉×#2293	C₂	semidirect
26. C₂×C₄⋊Q₈×C₅₉	C₂²	semidirect
27. C₂×#126×C₅₉	C₂²	semidirect
30. C₂×#124×C₅₉	C₂²	semidirect
31. C₂×#123×C₅₉	C₂²	semidirect
33. C₂×C₂²⋊Q₈×C₅₉	C₂²	semidirect
34. C₂×C₂²⋊Q₈×C₅₉	C₂²	semidirect
35. C₂×C₂²⋊Q₈×C₅₉	C₂²	semidirect
40. C₂×C₄×Q₈×C₅₉	C₂²	semidirect
50. C₂×#117×C₅₉	C₂²	semidirect
51. C₂×#117×C₅₉	C₂²	semidirect
55. C₅₉×#397	C₂²	semidirect
56. C₅₉×#397	C₂²	semidirect
57. C₅₉×#397	C₂²	semidirect
58. C₅₉×#397	C₂²	semidirect
60. C₅₉×#396	C₂²	semidirect
65. C₅₉×#394	C₂²	semidirect
66. C₅₉×#394	C₂²	semidirect
68. C₅₉×#393	C₂²	semidirect
70. C₅₉×#391	C₂²	semidirect
71. C₅₉×#391	C₂²	semidirect
72. C₅₉×#391	C₂²	semidirect
79. C₅₉×#390	C₂²	semidirect
80. C₅₉×#389	C₂²	semidirect
81. C₅₉×#389	C₂²	semidirect
82. C₅₉×#389	C₂²	semidirect
83. C₅₉×#389	C₂²	semidirect
84. C₅₉×#389	C₂²	semidirect
85. C₅₉×#389	C₂²	semidirect
86. C₅₉×#389	C₂²	semidirect
87. C₅₉×#389	C₂²	semidirect
92. C₅₉×#388	C₂²	semidirect
93. C₅₉×#388	C₂²	semidirect
94. C₅₉×#388	C₂²	semidirect
95. C₅₉×#388	C₂²	semidirect
96. C₅₉×#388	C₂²	semidirect
97. C₅₉×#388	C₂²	semidirect
98. C₅₉×#388	C₂²	semidirect
99. C₅₉×#388	C₂²	semidirect
100. C₅₉×#387	C₂²	semidirect
101. C₅₉×#387	C₂²	semidirect
102. C₅₉×#386	C₂²	semidirect
103. C₅₉×#386	C₂²	semidirect
104. C₅₉×#386	C₂²	semidirect
105. C₅₉×#385	C₂²	semidirect
106. C₅₉×#385	C₂²	semidirect
107. C₅₉×#385	C₂²	semidirect
108. C₅₉×#382	C₂²	semidirect
109. C₅₉×#381	C₂²	semidirect
110. C₅₉×#381	C₂²	semidirect
112. C₅₉×#380	C₂²	semidirect
113. C₅₉×#380	C₂²	semidirect
117. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
118. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
120. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
121. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
122. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
123. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
124. C₄³×C₅₉	C₂²	semidirect
163. C₄×D₄×C₅₉	D₄	semidirect
499. #35611	C₅₉	direct (N × H)
555. C₂×#542	C₂×C₅₉	semidirect
556. C₂×#518	C₂×C₅₉	semidirect
557. #2602	C₂×C₅₉	semidirect
558. #2561	C₂×C₅₉	semidirect
559. #2480	C₂×C₅₉	semidirect
560. #2472	C₂×C₅₉	semidirect
561. #2466	C₂×C₅₉	semidirect
562. #2459	C₂×C₅₉	semidirect
563. #2452	C₂×C₅₉	semidirect
564. #2447	C₂×C₅₉	semidirect
565. #2439	C₂×C₅₉	semidirect
566. #2435	C₂×C₅₉	semidirect
567. #2427	C₂×C₅₉	semidirect
568. #2420	C₂×C₅₉	semidirect
569. #2415	C₂×C₅₉	semidirect
570. #2415	C₂×C₅₉	semidirect
571. #2411	C₂×C₅₉	semidirect
573. #2324	C₂×C₅₉	semidirect
574. #2323	C₂×C₅₉	semidirect
575. C₄×#124	C₂×C₅₉	semidirect
576. #2293	C₂×C₅₉	semidirect
577. #2293	C₂×C₅₉	semidirect
591. C₂×C₄⋊Q₈	C₂²×C₅₉	semidirect
592. C₂×#126	C₂²×C₅₉	semidirect
595. C₂×#124	C₂²×C₅₉	semidirect
596. C₂×#123	C₂²×C₅₉	semidirect
598. C₂×C₂²⋊Q₈	C₂²×C₅₉	semidirect
599. C₂×C₂²⋊Q₈	C₂²×C₅₉	semidirect
600. C₂×C₂²⋊Q₈	C₂²×C₅₉	semidirect
605. C₂×C₄×Q₈	C₂²×C₅₉	semidirect
615. C₂×#117	C₂²×C₅₉	semidirect
616. C₂×#117	C₂²×C₅₉	semidirect
620. #397	C₂²×C₅₉	semidirect
621. #397	C₂²×C₅₉	semidirect
622. #397	C₂²×C₅₉	semidirect
623. #397	C₂²×C₅₉	semidirect
625. #396	C₂²×C₅₉	semidirect
630. #394	C₂²×C₅₉	semidirect
631. #394	C₂²×C₅₉	semidirect
633. #393	C₂²×C₅₉	semidirect
635. #391	C₂²×C₅₉	semidirect
636. #391	C₂²×C₅₉	semidirect
637. #391	C₂²×C₅₉	semidirect
644. #390	C₂²×C₅₉	semidirect
645. #389	C₂²×C₅₉	semidirect
646. #389	C₂²×C₅₉	semidirect
647. #389	C₂²×C₅₉	semidirect
648. #389	C₂²×C₅₉	semidirect
649. #389	C₂²×C₅₉	semidirect
650. #389	C₂²×C₅₉	semidirect
651. #389	C₂²×C₅₉	semidirect
652. #389	C₂²×C₅₉	semidirect
657. #388	C₂²×C₅₉	semidirect
658. #388	C₂²×C₅₉	semidirect
659. #388	C₂²×C₅₉	semidirect
660. #388	C₂²×C₅₉	semidirect
661. #388	C₂²×C₅₉	semidirect
662. #388	C₂²×C₅₉	semidirect
663. #388	C₂²×C₅₉	semidirect
664. #388	C₂²×C₅₉	semidirect
665. #387	C₂²×C₅₉	semidirect
666. #387	C₂²×C₅₉	semidirect
667. #386	C₂²×C₅₉	semidirect
668. #386	C₂²×C₅₉	semidirect
669. #386	C₂²×C₅₉	semidirect
670. #385	C₂²×C₅₉	semidirect
671. #385	C₂²×C₅₉	semidirect
672. #385	C₂²×C₅₉	semidirect
673. #382	C₂²×C₅₉	semidirect
674. #381	C₂²×C₅₉	semidirect
675. #381	C₂²×C₅₉	semidirect
677. #380	C₂²×C₅₉	semidirect
678. #380	C₂²×C₅₉	semidirect
682. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
683. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
685. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
686. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
687. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
688. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
689. C₄³	C₂²×C₅₉	semidirect
690. C₅₉	#35611	direct (N × H)
729. C₄×D₄	D₄×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×#542	2
C₂×C₅₉×#518	2
C₅₉×#2602	2
C₅₉×#2561	2
C₅₉×#2480	2
C₅₉×#2472	2
C₅₉×#2466	2
C₅₉×#2459	2
C₅₉×#2452	2
C₅₉×#2447	2
C₅₉×#2439	2
C₅₉×#2435	2
C₅₉×#2427	2
C₅₉×#2420	2
C₅₉×#2415	2
C₅₉×#2411	2
C₅₉×#2408	2
C₅₉×#2324	2
C₅₉×#2323	2
C₄×#124×C₅₉	2
C₅₉×#2293	2
#35611	59

Subgroups — C59×#35611 #28447720

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35611 #28447720