Subgroups — C₅₉×#35821 #28447930

Order 15104.

3252 conjugacy classes of subgroups.

The subgroup lattice has 1256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#546	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅₉×#546	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅₉×#520	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2620	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#2618	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2545	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#2538	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#2534	C₂	1	2	yes	maximal, complemented
10	C₅₉×#2429	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2426	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#2425	C₂	1	2	yes	maximal, complemented
13	C₅₉×#2424	C₂	1	2	yes	maximal, complemented
14	C₅₉×#2417	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#2416	C₂	1	2	yes	maximal, complemented
16	C₅₉×#2416	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₉×#2413	C₂	1	2	yes	maximal, complemented
18	C₅₉×#2411	C₂	1	2	yes	maximal, complemented
19	C₅₉×#2392	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₅₉×#396	C₂	1	2	yes	maximal, complemented
21	D₄×C₄⋊C₄×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₉×#2339	C₂	1	1	yes	maximal, characteristic, complemented
23	D₄×C₂²⋊C₄×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic
26	C₂³×D₄×C₅₉	C₂²	1	1	yes	characteristic
27	C₅₉×#547	—	2	8	no	—
28	C₅₉×#546	—	2	8	no	—
29	C₅₉×#546	—	2	8	no	—
30	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
31	C₂×#124×C₅₉	C₂²	1	1	yes	characteristic
32	C₂×#124×C₅₉	C₂²	1	1	yes	characteristic
33	C₂×#123×C₅₉	C₂²	1	2	yes	—
34	C₂×#123×C₅₉	C₂²	1	2	yes	—
35	C₂×#123×C₅₉	C₂²	1	2	yes	complemented
36	C₂×#123×C₅₉	C₂²	1	2	yes	complemented
37	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
41	C₂×#121×C₅₉	C₂²	1	2	yes	—
42	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
43	C₂×#121×C₅₉	C₂²	1	2	yes	—
44	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
45	C₂×#121×C₅₉	C₂²	1	2	yes	complemented
46	C₂×#121×C₅₉	C₂²	1	2	yes	complemented
47	C₂×#120×C₅₉	C₂²	1	2	yes	—
48	C₂×#120×C₅₉	C₂²	1	2	yes	—
49	C₅₉×#520	—	2	8	no	—
50	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
53	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
54	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
56	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
57	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
58	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	complemented
59	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	complemented
61	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic, complemented
62	C₂×#117×C₅₉	C₂²	1	2	yes	complemented
63	C₂²×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
64	C₂²×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
65	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
66	C₂²×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
67	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
68	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
69	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
70	C₅₉×#398	C₂²	1	2	yes	complemented
71	C₅₉×#398	C₂²	1	2	yes	complemented
72	C₅₉×#398	C₂²	1	1	yes	characteristic, complemented
73	C₅₉×#397	C₂²	1	1	yes	characteristic, complemented
74	C₅₉×#396	C₂²	1	2	yes	—
75	C₅₉×#396	C₂²	1	1	yes	characteristic
76	C₅₉×#396	C₂²	1	2	yes	—
77	C₅₉×#396	C₂²	1	2	yes	—
78	C₅₉×#396	C₂²	1	2	yes	complemented
79	C₅₉×#396	C₂²	1	2	yes	complemented
80	C₅₉×#396	C₂²	1	2	yes	complemented
81	C₅₉×#396	C₂²	1	1	yes	characteristic, complemented
82	C₅₉×#396	C₂²	1	2	yes	complemented
83	C₅₉×#396	C₂²	1	2	yes	complemented
84	C₅₉×#396	C₂²	1	2	yes	complemented
85	C₅₉×#396	C₂²	1	2	yes	complemented
86	C₅₉×#394	C₂²	1	1	yes	characteristic
87	C₅₉×#394	C₂²	1	1	yes	characteristic
88	C₅₉×#394	C₂²	1	2	yes	complemented
89	C₅₉×#394	C₂²	1	2	yes	complemented
90	C₅₉×#394	C₂²	1	2	yes	complemented
91	C₅₉×#394	C₂²	1	2	yes	complemented
92	C₅₉×#394	C₂²	1	1	yes	characteristic, complemented
93	C₅₉×#392	C₂²	1	1	yes	characteristic
94	C₅₉×#391	C₂²	1	1	yes	characteristic, complemented
95	C₅₉×#391	C₂²	1	1	yes	characteristic, complemented
96	C₅₉×#390	C₂²	1	2	yes	—
97	C₅₉×#390	C₂²	1	1	yes	characteristic
98	C₅₉×#390	C₂²	1	1	yes	characteristic
99	C₅₉×#390	C₂²	1	2	yes	complemented
100	C₅₉×#389	C₂²	1	2	yes	complemented
101	C₅₉×#389	C₂²	1	1	yes	characteristic, complemented
102	C₅₉×#389	C₂²	1	1	yes	characteristic, complemented
103	C₅₉×#389	C₂²	1	2	yes	complemented
104	C₅₉×#388	C₂²	1	2	yes	—
105	C₅₉×#388	C₂²	1	2	yes	complemented
106	C₅₉×#388	C₂²	1	2	yes	complemented
107	C₅₉×#388	C₂²	1	2	yes	complemented
108	C₅₉×#386	C₂²	1	2	yes	—
109	C₅₉×#386	C₂²	1	2	yes	—
110	C₅₉×#386	C₂²	1	2	yes	—
111	C₅₉×#386	C₂²	1	2	yes	complemented
112	C₅₉×#386	C₂²	1	2	yes	complemented
113	C₅₉×#386	C₂²	1	2	yes	complemented
114	C₅₉×#385	C₂²	1	2	yes	complemented
115	C₅₉×#385	C₂²	1	2	yes	complemented
116	C₅₉×#384	C₂²	1	1	yes	characteristic, complemented
117	C₅₉×#381	C₂²	1	2	yes	complemented
118	C₅₉×#380	C₂²	1	1	yes	characteristic
119	C₅₉×#380	C₂²	1	2	yes	complemented
120	C₅₉×#380	C₂²	1	1	yes	characteristic, complemented
121	C₅₉×#380	C₂²	1	2	yes	complemented
122	C₅₉×#379	C₂²	1	2	yes	—
123	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
124	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
125	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
126	C₂×#95×C₅₉	C₂²	1	2	yes	complemented
127	C₂⁵×C₅₉	C₂³	1	2	yes	—
128	C₂×#41×C₅₉	—	2	4	no	—
129	C₂×#41×C₅₉	—	2	4	no	—
130	C₂×#41×C₅₉	—	2	4	no	—
131	C₂×#41×C₅₉	—	2	4	no	—
132	C₂×#41×C₅₉	—	2	4	no	—
133	C₂×#41×C₅₉	D₄	1	8	yes	complemented
134	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
135	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
136	C₂²×D₄×C₅₉	—	2	4	no	—
137	C₂²×D₄×C₅₉	—	2	4	no	—
138	C₂²×D₄×C₅₉	—	2	4	no	—
139	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
140	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
141	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
142	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
144	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
145	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
146	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
147	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
148	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
149	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
150	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
151	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
152	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
153	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
154	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
155	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
156	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
157	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
158	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
159	C₄⋊Q₈×C₅₉	—	2	4	no	—
160	#124×C₅₉	—	2	4	no	—
161	#124×C₅₉	—	2	4	no	—
162	#123×C₅₉	—	2	8	no	—
163	#123×C₅₉	—	2	8	no	—
164	#123×C₅₉	—	2	8	no	—
165	#123×C₅₉	—	2	8	no	—
166	C₂²⋊Q₈×C₅₉	—	2	4	no	—
167	C₂²⋊Q₈×C₅₉	—	2	4	no	—
168	C₂²⋊Q₈×C₅₉	—	2	4	no	—
169	C₂²⋊Q₈×C₅₉	—	2	4	no	—
170	#121×C₅₉	—	2	8	no	—
171	#121×C₅₉	—	2	8	no	—
172	#121×C₅₉	—	2	4	no	—
173	#121×C₅₉	—	2	8	no	—
174	#121×C₅₉	—	2	4	no	—
175	#121×C₅₉	—	4	4	no	—
176	#120×C₅₉	—	2	8	no	—
177	#120×C₅₉	—	2	8	no	—
178	C₄×Q₈×C₅₉	—	2	4	no	—
179	C₄×Q₈×C₅₉	—	2	4	no	—
180	C₄×D₄×C₅₉	—	2	4	no	—
181	C₄×D₄×C₅₉	—	2	4	no	—
182	C₄×D₄×C₅₉	—	2	4	no	—
183	C₄×D₄×C₅₉	—	2	4	no	—
184	C₄×D₄×C₅₉	—	2	8	no	—
185	C₄×D₄×C₅₉	—	2	4	no	—
186	C₄×D₄×C₅₉	—	2	8	no	—
187	C₄×D₄×C₅₉	—	2	4	no	—
188	C₄×D₄×C₅₉	D₄	1	8	yes	complemented
189	#117×C₅₉	—	2	8	no	—
190	#117×C₅₉	—	2	4	no	—
191	C₂×C₄⋊C₄×C₅₉	—	2	8	no	—
192	C₂×C₄⋊C₄×C₅₉	—	2	8	no	—
193	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
194	C₂×C₄⋊C₄×C₅₉	—	4	4	no	—
195	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
196	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
197	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
198	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
199	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
200	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
201	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
202	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
203	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
204	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
205	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
206	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
207	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
208	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
209	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
210	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
211	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
212	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
213	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
214	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
215	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
216	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
217	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
218	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
219	C₂×C₂²⋊C₄×C₅₉	—	2	8	no	—
220	C₂×C₂²⋊C₄×C₅₉	—	2	8	no	—
221	C₂×C₂²⋊C₄×C₅₉	—	4	4	no	—
222	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
223	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
224	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
225	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
226	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
227	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
228	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
229	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
230	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
231	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
232	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
233	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
234	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
235	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
236	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
237	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
238	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
239	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
240	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
241	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
242	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
243	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
244	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
245	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
246	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
247	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
248	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
249	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
250	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
251	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
252	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
253	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
254	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
255	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
256	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
257	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
258	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
259	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
260	#95×C₅₉	C₂³	1	1	yes	characteristic
261	#95×C₅₉	C₂³	1	2	yes	—
262	#95×C₅₉	C₂³	1	2	yes	—
263	#95×C₅₉	C₂³	1	2	yes	—
264	#95×C₅₉	C₂³	1	1	yes	characteristic
265	#95×C₅₉	C₂³	1	1	yes	characteristic
266	#95×C₅₉	C₂³	1	1	yes	characteristic
267	#95×C₅₉	C₂³	1	1	yes	characteristic
268	#95×C₅₉	C₂³	1	1	yes	characteristic
269	#95×C₅₉	C₂³	1	2	yes	—
270	#95×C₅₉	C₂³	1	2	yes	—
271	#95×C₅₉	C₂³	1	2	yes	—
272	#95×C₅₉	C₂³	1	2	yes	—
273	#95×C₅₉	C₂³	1	2	yes	—
274	C₂⁴×C₅₉	—	2	4	no	—
275	C₂⁴×C₅₉	—	2	4	no	—
276	C₂⁴×C₅₉	—	2	4	no	—
277	C₂⁴×C₅₉	—	2	4	no	—
278	C₂⁴×C₅₉	—	4	2	no	—
279	C₂⁴×C₅₉	—	4	2	no	—
280	C₂⁴×C₅₉	—	4	2	no	—
281	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
282	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
283	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
284	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
285	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
286	#41×C₅₉	—	2	32	no	—
287	#41×C₅₉	—	4	16	no	—
288	C₂×Q₈×C₅₉	—	2	2	no	—
289	C₂×Q₈×C₅₉	—	2	2	no	—
290	C₂×Q₈×C₅₉	—	2	2	no	—
291	C₂×Q₈×C₅₉	—	2	2	no	—
292	C₂×Q₈×C₅₉	—	2	2	no	—
293	C₂×Q₈×C₅₉	C₂×D₄	1	4	yes	—
294	C₂×D₄×C₅₉	—	2	4	no	—
295	C₂×D₄×C₅₉	—	2	4	no	—
296	C₂×D₄×C₅₉	—	2	2	no	—
297	C₂×D₄×C₅₉	—	2	2	no	—
298	C₂×D₄×C₅₉	—	2	4	no	—
299	C₂×D₄×C₅₉	—	2	4	no	—
300	C₂×D₄×C₅₉	—	2	4	no	—
301	C₂×D₄×C₅₉	—	2	4	no	—
302	C₂×D₄×C₅₉	—	2	4	no	—
303	C₂×D₄×C₅₉	—	2	4	no	—
304	C₂×D₄×C₅₉	—	2	2	no	—
305	C₂×D₄×C₅₉	—	2	2	no	—
306	C₂×D₄×C₅₉	—	2	4	no	—
307	C₂×D₄×C₅₉	—	2	2	no	—
308	C₂×D₄×C₅₉	—	2	2	no	—
309	C₂×D₄×C₅₉	—	2	2	no	—
310	C₂×D₄×C₅₉	—	2	4	no	—
311	C₂×D₄×C₅₉	—	2	2	no	—
312	C₂×D₄×C₅₉	—	2	2	no	—
313	C₂×D₄×C₅₉	—	4	1	no	—
314	C₂×D₄×C₅₉	—	4	1	no	—
315	C₂×D₄×C₅₉	—	4	1	no	—
316	C₂×D₄×C₅₉	—	4	2	no	—
317	C₂×D₄×C₅₉	—	4	2	no	—
318	C₂×D₄×C₅₉	—	4	2	no	—
319	C₂×D₄×C₅₉	—	4	2	no	—
320	C₂×D₄×C₅₉	—	4	16	no	—
321	C₂×D₄×C₅₉	C₂×D₄	1	8	yes	—
322	C₂×D₄×C₅₉	C₂×D₄	1	4	yes	—
323	C₂×D₄×C₅₉	C₂×D₄	1	4	yes	—
324	C₂×D₄×C₅₉	#41	1	4	yes	—
325	C₂²×C₄×C₅₉	—	2	4	no	—
326	C₂²×C₄×C₅₉	—	2	4	no	—
327	C₂²×C₄×C₅₉	—	2	2	no	—
328	C₂²×C₄×C₅₉	—	2	2	no	—
329	C₂²×C₄×C₅₉	—	2	4	no	—
330	C₂²×C₄×C₅₉	—	2	4	no	—
331	C₂²×C₄×C₅₉	—	2	4	no	—
332	C₂²×C₄×C₅₉	—	2	4	no	—
333	C₂²×C₄×C₅₉	—	2	4	no	—
334	C₂²×C₄×C₅₉	—	2	4	no	—
335	C₂²×C₄×C₅₉	—	2	2	no	—
336	C₂²×C₄×C₅₉	—	2	2	no	—
337	C₂²×C₄×C₅₉	—	2	2	no	—
338	C₂²×C₄×C₅₉	—	2	2	no	—
339	C₂²×C₄×C₅₉	—	2	2	no	—
340	C₂²×C₄×C₅₉	—	2	2	no	—
341	C₂²×C₄×C₅₉	—	2	4	no	—
342	C₂²×C₄×C₅₉	—	2	4	no	—
343	C₂²×C₄×C₅₉	—	4	2	no	—
344	C₂²×C₄×C₅₉	—	4	2	no	—
345	C₂²×C₄×C₅₉	—	4	2	no	—
346	C₂²×C₄×C₅₉	—	4	2	no	—
347	C₂²×C₄×C₅₉	—	4	2	no	—
348	C₂²×C₄×C₅₉	—	4	2	no	—
349	C₂²×C₄×C₅₉	—	4	2	no	—
350	C₂²×C₄×C₅₉	—	4	2	no	—
351	C₂²×C₄×C₅₉	—	4	2	no	—
352	C₂²×C₄×C₅₉	C₂×D₄	1	8	yes	—
353	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
354	C₂²×C₄×C₅₉	C₂×D₄	1	8	yes	—
355	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
361	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
362	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
363	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
364	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
366	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
368	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
369	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
370	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
371	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
373	C₄⋊C₄×C₅₉	—	2	4	no	—
374	C₄⋊C₄×C₅₉	—	2	2	no	—
375	C₄⋊C₄×C₅₉	—	2	2	no	—
376	C₄⋊C₄×C₅₉	—	2	4	no	—
377	C₄⋊C₄×C₅₉	—	2	4	no	—
378	C₄⋊C₄×C₅₉	—	2	2	no	—
379	C₄⋊C₄×C₅₉	—	2	4	no	—
380	C₄⋊C₄×C₅₉	—	2	4	no	—
381	C₄⋊C₄×C₅₉	—	2	4	no	—
382	C₄⋊C₄×C₅₉	—	2	2	no	—
383	C₄⋊C₄×C₅₉	—	2	2	no	—
384	C₄⋊C₄×C₅₉	—	2	2	no	—
385	C₄⋊C₄×C₅₉	—	2	2	no	—
386	C₄⋊C₄×C₅₉	—	2	2	no	—
387	C₄⋊C₄×C₅₉	—	2	4	no	—
388	C₄⋊C₄×C₅₉	—	2	4	no	—
389	C₄⋊C₄×C₅₉	—	2	4	no	—
390	C₄⋊C₄×C₅₉	—	2	2	no	—
391	C₄⋊C₄×C₅₉	—	2	4	no	—
392	C₄⋊C₄×C₅₉	—	4	2	no	—
393	C₄⋊C₄×C₅₉	—	4	2	no	—
394	C₄⋊C₄×C₅₉	—	4	2	no	—
395	C₄⋊C₄×C₅₉	—	4	1	no	—
396	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
397	C₂²⋊C₄×C₅₉	—	2	4	no	—
398	C₂²⋊C₄×C₅₉	—	2	4	no	—
399	C₂²⋊C₄×C₅₉	—	2	2	no	—
400	C₂²⋊C₄×C₅₉	—	2	4	no	—
401	C₂²⋊C₄×C₅₉	—	2	2	no	—
402	C₂²⋊C₄×C₅₉	—	2	4	no	—
403	C₂²⋊C₄×C₅₉	—	2	2	no	—
404	C₂²⋊C₄×C₅₉	—	2	2	no	—
405	C₂²⋊C₄×C₅₉	—	2	2	no	—
406	C₂²⋊C₄×C₅₉	—	2	4	no	—
407	C₂²⋊C₄×C₅₉	—	2	4	no	—
408	C₂²⋊C₄×C₅₉	—	2	4	no	—
409	C₂²⋊C₄×C₅₉	—	2	4	no	—
410	C₂²⋊C₄×C₅₉	—	2	4	no	—
411	C₂²⋊C₄×C₅₉	—	2	4	no	—
412	C₂²⋊C₄×C₅₉	—	2	2	no	—
413	C₂²⋊C₄×C₅₉	—	2	2	no	—
414	C₂²⋊C₄×C₅₉	—	2	2	no	—
415	C₂²⋊C₄×C₅₉	—	2	2	no	—
416	C₂²⋊C₄×C₅₉	—	2	4	no	—
417	C₂²⋊C₄×C₅₉	—	2	4	no	—
418	C₂²⋊C₄×C₅₉	—	2	4	no	—
419	C₂²⋊C₄×C₅₉	—	2	2	no	—
420	C₂²⋊C₄×C₅₉	—	2	4	no	—
421	C₂²⋊C₄×C₅₉	—	4	2	no	—
422	C₂²⋊C₄×C₅₉	—	4	2	no	—
423	C₂²⋊C₄×C₅₉	—	4	2	no	—
424	C₂²⋊C₄×C₅₉	—	4	1	no	—
425	C₂²⋊C₄×C₅₉	—	4	2	no	—
426	C₂²⋊C₄×C₅₉	—	4	1	no	—
427	C₂²⋊C₄×C₅₉	—	4	2	no	—
428	C₂²⋊C₄×C₅₉	C₂×D₄	1	8	yes	—
429	C₄²×C₅₉	—	2	4	no	—
430	C₄²×C₅₉	—	2	4	no	—
431	C₄²×C₅₉	—	2	2	no	—
432	C₄²×C₅₉	—	2	2	no	—
433	C₄²×C₅₉	—	2	2	no	—
434	C₄²×C₅₉	C₂×D₄	1	4	yes	—
435	C₂³×C₅₉	—	2	2	no	—
436	C₂³×C₅₉	—	2	2	no	—
437	C₂³×C₅₉	—	2	2	no	—
438	C₂³×C₅₉	—	2	2	no	—
439	C₂³×C₅₉	—	2	1	no	—
440	C₂³×C₅₉	—	2	1	no	—
441	C₂³×C₅₉	—	2	1	no	—
442	C₂³×C₅₉	—	2	1	no	—
443	C₂³×C₅₉	—	2	1	no	—
444	C₂³×C₅₉	—	2	1	no	—
445	C₂³×C₅₉	—	2	1	no	—
446	C₂³×C₅₉	—	2	1	no	—
447	C₂³×C₅₉	—	2	1	no	—
448	C₂³×C₅₉	—	2	1	no	—
449	C₂³×C₅₉	—	2	1	no	—
450	C₂³×C₅₉	—	2	1	no	—
451	C₂³×C₅₉	—	2	1	no	—
452	C₂³×C₅₉	—	2	2	no	—
453	C₂³×C₅₉	—	2	2	no	—
454	C₂³×C₅₉	—	2	1	no	—
455	C₂³×C₅₉	—	2	1	no	—
456	C₂³×C₅₉	—	2	2	no	—
457	C₂³×C₅₉	—	2	2	no	—
458	C₂³×C₅₉	—	2	1	no	—
459	C₂³×C₅₉	—	2	1	no	—
460	C₂³×C₅₉	—	2	2	no	—
461	C₂³×C₅₉	—	2	1	no	—
462	C₂³×C₅₉	—	2	1	no	—
463	C₂³×C₅₉	—	2	2	no	—
464	C₂³×C₅₉	—	2	2	no	—
465	C₂³×C₅₉	—	4	8	no	—
466	C₂³×C₅₉	—	4	8	no	—
467	C₂³×C₅₉	—	4	8	no	—
468	C₂³×C₅₉	—	4	8	no	—
469	C₂³×C₅₉	—	8	4	no	—
470	C₂³×C₅₉	—	8	4	no	—
471	C₂³×C₅₉	—	8	4	no	—
472	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
473	C₂³×C₅₉	C₂²×D₄	1	4	yes	—
474	C₂³×C₅₉	C₂²×D₄	1	4	yes	—
475	C₂³×C₅₉	C₂×#41	1	4	yes	—
476	C₂³×C₅₉	2₋¹⁺⁴	1	2	yes	—
477	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
478	Q₈×C₅₉	—	2	8	no	—
479	Q₈×C₅₉	—	4	4	no	—
480	D₄×C₅₉	—	2	16	no	—
481	D₄×C₅₉	—	4	4	no	—
482	D₄×C₅₉	—	4	4	no	—
483	D₄×C₅₉	—	4	4	no	—
484	D₄×C₅₉	—	4	8	no	—
485	D₄×C₅₉	—	4	8	no	—
486	D₄×C₅₉	—	4	4	no	—
487	D₄×C₅₉	—	8	4	no	—
488	D₄×C₅₉	—	8	4	no	—
489	D₄×C₅₉	#121	1	16	yes	complemented
490	C₂×C₄×C₅₉	—	2	16	no	—
491	C₂×C₄×C₅₉	—	2	2	no	—
492	C₂×C₄×C₅₉	—	2	1	no	—
493	C₂×C₄×C₅₉	—	2	1	no	—
494	C₂×C₄×C₅₉	—	2	1	no	—
495	C₂×C₄×C₅₉	—	2	2	no	—
496	C₂×C₄×C₅₉	—	2	1	no	—
497	C₂×C₄×C₅₉	—	2	2	no	—
498	C₂×C₄×C₅₉	—	2	1	no	—
499	C₂×C₄×C₅₉	—	2	1	no	—
500	C₂×C₄×C₅₉	—	2	1	no	—
501	C₂×C₄×C₅₉	—	2	1	no	—
502	C₂×C₄×C₅₉	—	2	2	no	—
503	C₂×C₄×C₅₉	—	2	8	no	—
504	C₂×C₄×C₅₉	—	2	1	no	—
505	C₂×C₄×C₅₉	—	2	1	no	—
506	C₂×C₄×C₅₉	—	2	1	no	—
507	C₂×C₄×C₅₉	—	2	1	no	—
508	C₂×C₄×C₅₉	—	2	2	no	—
509	C₂×C₄×C₅₉	—	2	1	no	—
510	C₂×C₄×C₅₉	—	2	2	no	—
511	C₂×C₄×C₅₉	—	2	2	no	—
512	C₂×C₄×C₅₉	—	2	1	no	—
513	C₂×C₄×C₅₉	—	2	2	no	—
514	C₂×C₄×C₅₉	—	2	1	no	—
515	C₂×C₄×C₅₉	—	2	1	no	—
516	C₂×C₄×C₅₉	—	2	1	no	—
517	C₂×C₄×C₅₉	—	2	2	no	—
518	C₂×C₄×C₅₉	—	2	1	no	—
519	C₂×C₄×C₅₉	—	2	1	no	—
520	C₂×C₄×C₅₉	—	2	2	no	—
521	C₂×C₄×C₅₉	—	2	1	no	—
522	C₂×C₄×C₅₉	—	2	2	no	—
523	C₂×C₄×C₅₉	—	2	2	no	—
524	C₂×C₄×C₅₉	—	2	2	no	—
525	C₂×C₄×C₅₉	—	2	1	no	—
526	C₂×C₄×C₅₉	—	2	1	no	—
527	C₂×C₄×C₅₉	—	2	1	no	—
528	C₂×C₄×C₅₉	—	2	1	no	—
529	C₂×C₄×C₅₉	—	2	1	no	—
530	C₂×C₄×C₅₉	—	2	1	no	—
531	C₂×C₄×C₅₉	—	2	2	no	—
532	C₂×C₄×C₅₉	—	2	1	no	—
533	C₂×C₄×C₅₉	—	2	1	no	—
534	C₂×C₄×C₅₉	—	2	2	no	—
535	C₂×C₄×C₅₉	—	2	1	no	—
536	C₂×C₄×C₅₉	—	2	2	no	—
537	C₂×C₄×C₅₉	—	4	8	no	—
538	C₂×C₄×C₅₉	—	4	8	no	—
539	C₂×C₄×C₅₉	—	4	8	no	—
540	C₂×C₄×C₅₉	—	4	4	no	—
541	C₂×C₄×C₅₉	—	4	4	no	—
542	C₂×C₄×C₅₉	—	8	4	no	—
543	C₂×C₄×C₅₉	—	8	4	no	—
544	C₂×C₄×C₅₉	—	8	4	no	—
545	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
546	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
547	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
548	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
549	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
550	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
551	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
552	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
553	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
554	#35821	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
555	C₂²×C₅₉	—	2	4	no	—
556	C₂²×C₅₉	—	2	4	no	—
557	C₂²×C₅₉	—	2	4	no	—
558	C₂²×C₅₉	—	2	4	no	—
559	C₂²×C₅₉	—	2	4	no	—
560	C₂²×C₅₉	—	2	4	no	—
561	C₂²×C₅₉	—	2	2	no	—
562	C₂²×C₅₉	—	2	2	no	—
563	C₂²×C₅₉	—	2	2	no	—
564	C₂²×C₅₉	—	2	2	no	—
565	C₂²×C₅₉	—	2	2	no	—
566	C₂²×C₅₉	—	2	2	no	—
567	C₂²×C₅₉	—	4	1	no	—
568	C₂²×C₅₉	—	4	1	no	—
569	C₂²×C₅₉	—	4	1	no	—
570	C₂²×C₅₉	—	4	1	no	—
571	C₂²×C₅₉	—	4	1	no	—
572	C₂²×C₅₉	—	4	1	no	—
573	C₂²×C₅₉	—	4	1	no	—
574	C₂²×C₅₉	—	4	1	no	—
575	C₂²×C₅₉	—	4	1	no	—
576	C₂²×C₅₉	—	4	2	no	—
577	C₂²×C₅₉	—	4	1	no	—
578	C₂²×C₅₉	—	4	2	no	—
579	C₂²×C₅₉	—	4	1	no	—
580	C₂²×C₅₉	—	4	1	no	—
581	C₂²×C₅₉	—	4	2	no	—
582	C₂²×C₅₉	—	4	2	no	—
583	C₂²×C₅₉	—	4	1	no	—
584	C₂²×C₅₉	—	4	2	no	—
585	C₂²×C₅₉	—	4	1	no	—
586	C₂²×C₅₉	—	4	2	no	—
587	C₂²×C₅₉	—	4	1	no	—
588	C₂²×C₅₉	—	4	2	no	—
589	C₂²×C₅₉	—	8	16	no	—
590	C₂²×C₅₉	C₂×#121	1	8	yes	—
591	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
592	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
593	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
594	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
595	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
596	C₂²×C₅₉	#585	1	1	yes	characteristic
597	C₂²×C₅₉	#585	1	1	yes	characteristic
598	C₄×C₅₉	—	2	2	no	—
599	C₄×C₅₉	—	2	4	no	—
600	C₄×C₅₉	—	2	2	no	—
601	C₄×C₅₉	—	2	2	no	—
602	C₄×C₅₉	—	2	2	no	—
603	C₄×C₅₉	—	2	4	no	—
604	C₄×C₅₉	—	4	1	no	—
605	C₄×C₅₉	—	4	1	no	—
606	C₄×C₅₉	—	4	2	no	—
607	C₄×C₅₉	—	4	2	no	—
608	C₄×C₅₉	—	4	1	no	—
609	C₄×C₅₉	—	4	2	no	—
610	C₄×C₅₉	—	4	1	no	—
611	C₄×C₅₉	—	4	1	no	—
612	C₄×C₅₉	—	4	1	no	—
613	C₄×C₅₉	—	4	2	no	—
614	C₄×C₅₉	—	4	1	no	—
615	C₄×C₅₉	C₂×#121	1	4	yes	—
616	C₂×#547	C₂×C₅₉	1	1	yes	characteristic, complemented
617	C₂×#546	C₂×C₅₉	1	1	yes	characteristic, complemented
618	C₂×#546	C₂×C₅₉	1	1	yes	characteristic, complemented
619	C₂×#520	C₂×C₅₉	1	1	yes	characteristic, complemented
620	#2620	C₂×C₅₉	1	1	yes	characteristic, complemented
621	#2618	C₂×C₅₉	1	2	yes	complemented
622	#2545	C₂×C₅₉	1	1	yes	characteristic, complemented
623	#2538	C₂×C₅₉	1	1	yes	characteristic, complemented
624	#2534	C₂×C₅₉	1	2	yes	complemented
625	#2429	C₂×C₅₉	1	1	yes	characteristic, complemented
626	#2426	C₂×C₅₉	1	1	yes	characteristic, complemented
627	#2425	C₂×C₅₉	1	2	yes	complemented
628	#2424	C₂×C₅₉	1	2	yes	complemented
629	#2417	C₂×C₅₉	1	1	yes	characteristic, complemented
630	#2416	C₂×C₅₉	1	2	yes	complemented
631	#2416	C₂×C₅₉	1	1	yes	characteristic, complemented
632	#2413	C₂×C₅₉	1	2	yes	complemented
633	#2411	C₂×C₅₉	1	2	yes	complemented
634	#2392	C₂×C₅₉	1	1	yes	characteristic, complemented
635	C₂×#396	C₂×C₅₉	1	2	yes	complemented
636	D₄×C₄⋊C₄	C₂×C₅₉	1	1	yes	characteristic, complemented
637	#2339	C₂×C₅₉	1	1	yes	characteristic, complemented
638	D₄×C₂²⋊C₄	C₂×C₅₉	1	1	yes	characteristic, complemented
639	C₂×C₅₉	—	2	8	no	—
640	C₂×C₅₉	—	4	2	no	—
641	C₂×C₅₉	—	4	2	no	—
642	C₂×C₅₉	—	8	1	no	—
643	C₂×C₅₉	—	8	2	no	—
644	C₂×C₅₉	C₂²×#121	1	1	yes	characteristic
645	C₂×C₅₉	#3488	1	1	yes	characteristic
646	C₂×C₅₉	#3489	1	1	yes	characteristic
647	C₂×C₅₉	#3489	1	1	yes	characteristic
648	C₂×C₅₉	#3496	1	1	yes	characteristic
649	C₂×C₅₉	#3520	1	1	yes	characteristic
650	C₂×C₅₉	#3521	1	1	yes	characteristic
651	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic
652	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic
653	C₂³×D₄	C₂²×C₅₉	1	1	yes	characteristic
654	#547	—	2	8	no	—
655	#546	—	2	8	no	—
656	#546	—	2	8	no	—
657	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
658	C₂×#124	C₂²×C₅₉	1	1	yes	characteristic
659	C₂×#124	C₂²×C₅₉	1	1	yes	characteristic
660	C₂×#123	C₂²×C₅₉	1	2	yes	—
661	C₂×#123	C₂²×C₅₉	1	2	yes	—
662	C₂×#123	C₂²×C₅₉	1	2	yes	complemented
663	C₂×#123	C₂²×C₅₉	1	2	yes	complemented
664	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
665	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
666	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
667	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
668	C₂×#121	C₂²×C₅₉	1	2	yes	—
669	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
670	C₂×#121	C₂²×C₅₉	1	2	yes	—
671	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
672	C₂×#121	C₂²×C₅₉	1	2	yes	complemented
673	C₂×#121	C₂²×C₅₉	1	2	yes	complemented
674	C₂×#120	C₂²×C₅₉	1	2	yes	—
675	C₂×#120	C₂²×C₅₉	1	2	yes	—
676	#520	—	2	8	no	—
677	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
678	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
679	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
680	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
681	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
682	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
683	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
684	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
685	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
686	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	complemented
687	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	complemented
688	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic, complemented
689	C₂×#117	C₂²×C₅₉	1	2	yes	complemented
690	C₂²×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
691	C₂²×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
692	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
693	C₂²×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
694	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
695	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
696	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
697	#398	C₂²×C₅₉	1	2	yes	complemented
698	#398	C₂²×C₅₉	1	2	yes	complemented
699	#398	C₂²×C₅₉	1	1	yes	characteristic, complemented
700	#397	C₂²×C₅₉	1	1	yes	characteristic, complemented
701	#396	C₂²×C₅₉	1	1	yes	characteristic
702	#396	C₂²×C₅₉	1	2	yes	—
703	#396	C₂²×C₅₉	1	2	yes	—
704	#396	C₂²×C₅₉	1	2	yes	—
705	#396	C₂²×C₅₉	1	1	yes	characteristic, complemented
706	#396	C₂²×C₅₉	1	2	yes	complemented
707	#396	C₂²×C₅₉	1	2	yes	complemented
708	#396	C₂²×C₅₉	1	2	yes	complemented
709	#396	C₂²×C₅₉	1	2	yes	complemented
710	#396	C₂²×C₅₉	1	2	yes	complemented
711	#396	C₂²×C₅₉	1	2	yes	complemented
712	#396	C₂²×C₅₉	1	2	yes	complemented
713	#394	C₂²×C₅₉	1	1	yes	characteristic
714	#394	C₂²×C₅₉	1	1	yes	characteristic
715	#394	C₂²×C₅₉	1	2	yes	complemented
716	#394	C₂²×C₅₉	1	2	yes	complemented
717	#394	C₂²×C₅₉	1	2	yes	complemented
718	#394	C₂²×C₅₉	1	2	yes	complemented
719	#394	C₂²×C₅₉	1	1	yes	characteristic, complemented
720	#392	C₂²×C₅₉	1	1	yes	characteristic
721	#391	C₂²×C₅₉	1	1	yes	characteristic, complemented
722	#391	C₂²×C₅₉	1	1	yes	characteristic, complemented
723	#390	C₂²×C₅₉	1	1	yes	characteristic
724	#390	C₂²×C₅₉	1	1	yes	characteristic
725	#390	C₂²×C₅₉	1	2	yes	—
726	#390	C₂²×C₅₉	1	2	yes	complemented
727	#389	C₂²×C₅₉	1	1	yes	characteristic, complemented
728	#389	C₂²×C₅₉	1	1	yes	characteristic, complemented
729	#389	C₂²×C₅₉	1	2	yes	complemented
730	#389	C₂²×C₅₉	1	2	yes	complemented
731	#388	C₂²×C₅₉	1	2	yes	—
732	#388	C₂²×C₅₉	1	2	yes	complemented
733	#388	C₂²×C₅₉	1	2	yes	complemented
734	#388	C₂²×C₅₉	1	2	yes	complemented
735	#386	C₂²×C₅₉	1	2	yes	—
736	#386	C₂²×C₅₉	1	2	yes	—
737	#386	C₂²×C₅₉	1	2	yes	—
738	#386	C₂²×C₅₉	1	2	yes	complemented
739	#386	C₂²×C₅₉	1	2	yes	complemented
740	#386	C₂²×C₅₉	1	2	yes	complemented
741	#385	C₂²×C₅₉	1	2	yes	complemented
742	#385	C₂²×C₅₉	1	2	yes	complemented
743	#384	C₂²×C₅₉	1	1	yes	characteristic, complemented
744	#381	C₂²×C₅₉	1	2	yes	complemented
745	#380	C₂²×C₅₉	1	1	yes	characteristic
746	#380	C₂²×C₅₉	1	1	yes	characteristic, complemented
747	#380	C₂²×C₅₉	1	2	yes	complemented
748	#380	C₂²×C₅₉	1	2	yes	complemented
749	#379	C₂²×C₅₉	1	2	yes	—
750	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
751	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
752	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
753	C₂×#95	C₂²×C₅₉	1	2	yes	complemented
754	C₅₉	#35821	1	1	yes	characteristic, direct product factor, Sylow
755	C₂⁵	C₂³×C₅₉	1	2	yes	—
756	C₂×#41	—	2	4	no	—
757	C₂×#41	—	2	4	no	—
758	C₂×#41	—	2	4	no	—
759	C₂×#41	—	2	4	no	—
760	C₂×#41	—	2	4	no	—
761	C₂×#41	D₄×C₅₉	1	8	yes	complemented
762	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
763	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
764	C₂²×D₄	—	2	4	no	—
765	C₂²×D₄	—	2	4	no	—
766	C₂²×D₄	—	2	4	no	—
767	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
768	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
769	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
770	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
771	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
772	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
773	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
774	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
775	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
776	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
777	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
778	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
779	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
780	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
781	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
782	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
783	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
784	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
785	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
786	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
787	C₄⋊Q₈	—	2	4	no	—
788	#124	—	2	4	no	—
789	#124	—	2	4	no	—
790	#123	—	2	8	no	—
791	#123	—	2	8	no	—
792	#123	—	2	8	no	—
793	#123	—	2	8	no	—
794	C₂²⋊Q₈	—	2	4	no	—
795	C₂²⋊Q₈	—	2	4	no	—
796	C₂²⋊Q₈	—	2	4	no	—
797	C₂²⋊Q₈	—	2	4	no	—
798	#121	—	2	8	no	—
799	#121	—	2	8	no	—
800	#121	—	2	4	no	—
801	#121	—	2	8	no	—
802	#121	—	2	4	no	—
803	#121	—	4	4	no	—
804	#120	—	2	8	no	—
805	#120	—	2	8	no	—
806	C₄×Q₈	—	2	4	no	—
807	C₄×Q₈	—	2	4	no	—
808	C₄×D₄	—	2	4	no	—
809	C₄×D₄	—	2	4	no	—
810	C₄×D₄	—	2	4	no	—
811	C₄×D₄	—	2	4	no	—
812	C₄×D₄	—	2	8	no	—
813	C₄×D₄	—	2	4	no	—
814	C₄×D₄	—	2	8	no	—
815	C₄×D₄	—	2	4	no	—
816	C₄×D₄	D₄×C₅₉	1	8	yes	complemented
817	#117	—	2	8	no	—
818	#117	—	2	4	no	—
819	C₂×C₄⋊C₄	—	2	8	no	—
820	C₂×C₄⋊C₄	—	2	8	no	—
821	C₂×C₄⋊C₄	—	2	4	no	—
822	C₂×C₄⋊C₄	—	4	4	no	—
823	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
824	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
825	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
826	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
827	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
828	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
829	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
830	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
831	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
832	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
833	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
834	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
835	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
836	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
837	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
838	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
839	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
840	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
841	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
842	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
843	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
844	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
845	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
846	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
847	C₂×C₂²⋊C₄	—	2	8	no	—
848	C₂×C₂²⋊C₄	—	2	8	no	—
849	C₂×C₂²⋊C₄	—	4	4	no	—
850	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
851	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
852	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
853	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
854	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
855	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
856	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
857	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
858	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
859	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
860	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
861	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
862	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
863	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
864	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
865	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
866	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
867	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
868	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
869	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
870	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
871	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
872	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
873	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
874	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
875	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
876	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
877	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
878	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
879	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
880	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
881	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
882	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
883	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
884	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
885	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
886	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
887	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
888	#95	C₂³×C₅₉	1	1	yes	characteristic
889	#95	C₂³×C₅₉	1	2	yes	—
890	#95	C₂³×C₅₉	1	2	yes	—
891	#95	C₂³×C₅₉	1	2	yes	—
892	#95	C₂³×C₅₉	1	1	yes	characteristic
893	#95	C₂³×C₅₉	1	1	yes	characteristic
894	#95	C₂³×C₅₉	1	1	yes	characteristic
895	#95	C₂³×C₅₉	1	1	yes	characteristic
896	#95	C₂³×C₅₉	1	1	yes	characteristic
897	#95	C₂³×C₅₉	1	2	yes	—
898	#95	C₂³×C₅₉	1	2	yes	—
899	#95	C₂³×C₅₉	1	2	yes	—
900	#95	C₂³×C₅₉	1	2	yes	—
901	#95	C₂³×C₅₉	1	2	yes	—
902	C₂⁴	—	2	4	no	—
903	C₂⁴	—	2	4	no	—
904	C₂⁴	—	2	4	no	—
905	C₂⁴	—	2	4	no	—
906	C₂⁴	—	4	2	no	—
907	C₂⁴	—	4	2	no	—
908	C₂⁴	—	4	2	no	—
909	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
910	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
911	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
912	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
913	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
914	#41	—	2	32	no	—
915	#41	—	4	16	no	—
916	C₂×Q₈	—	2	2	no	—
917	C₂×Q₈	—	2	2	no	—
918	C₂×Q₈	—	2	2	no	—
919	C₂×Q₈	—	2	2	no	—
920	C₂×Q₈	—	2	2	no	—
921	C₂×Q₈	C₂×D₄×C₅₉	1	4	yes	—
922	C₂×D₄	—	2	4	no	—
923	C₂×D₄	—	2	4	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	4	no	—
927	C₂×D₄	—	2	4	no	—
928	C₂×D₄	—	2	4	no	—
929	C₂×D₄	—	2	4	no	—
930	C₂×D₄	—	2	4	no	—
931	C₂×D₄	—	2	4	no	—
932	C₂×D₄	—	2	2	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	4	no	—
935	C₂×D₄	—	2	2	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	2	4	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	4	1	no	—
942	C₂×D₄	—	4	1	no	—
943	C₂×D₄	—	4	1	no	—
944	C₂×D₄	—	4	2	no	—
945	C₂×D₄	—	4	2	no	—
946	C₂×D₄	—	4	2	no	—
947	C₂×D₄	—	4	2	no	—
948	C₂×D₄	—	4	16	no	—
949	C₂×D₄	C₂×D₄×C₅₉	1	8	yes	—
950	C₂×D₄	C₂×D₄×C₅₉	1	4	yes	—
951	C₂×D₄	C₂×D₄×C₅₉	1	4	yes	—
952	C₂×D₄	#41×C₅₉	1	4	yes	—
953	C₂²×C₄	—	2	4	no	—
954	C₂²×C₄	—	2	4	no	—
955	C₂²×C₄	—	2	2	no	—
956	C₂²×C₄	—	2	2	no	—
957	C₂²×C₄	—	2	4	no	—
958	C₂²×C₄	—	2	4	no	—
959	C₂²×C₄	—	2	4	no	—
960	C₂²×C₄	—	2	4	no	—
961	C₂²×C₄	—	2	4	no	—
962	C₂²×C₄	—	2	4	no	—
963	C₂²×C₄	—	2	2	no	—
964	C₂²×C₄	—	2	2	no	—
965	C₂²×C₄	—	2	2	no	—
966	C₂²×C₄	—	2	2	no	—
967	C₂²×C₄	—	2	2	no	—
968	C₂²×C₄	—	2	2	no	—
969	C₂²×C₄	—	2	4	no	—
970	C₂²×C₄	—	2	4	no	—
971	C₂²×C₄	—	4	2	no	—
972	C₂²×C₄	—	4	2	no	—
973	C₂²×C₄	—	4	2	no	—
974	C₂²×C₄	—	4	2	no	—
975	C₂²×C₄	—	4	2	no	—
976	C₂²×C₄	—	4	2	no	—
977	C₂²×C₄	—	4	2	no	—
978	C₂²×C₄	—	4	2	no	—
979	C₂²×C₄	—	4	2	no	—
980	C₂²×C₄	C₂×D₄×C₅₉	1	8	yes	—
981	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
982	C₂²×C₄	C₂×D₄×C₅₉	1	8	yes	—
983	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
984	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
985	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
986	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
987	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
988	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
989	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
990	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
991	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
992	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
993	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
994	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
995	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
996	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
997	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
998	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
999	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
1000	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
1001	C₄⋊C₄	—	2	4	no	—
1002	C₄⋊C₄	—	2	2	no	—
1003	C₄⋊C₄	—	2	2	no	—
1004	C₄⋊C₄	—	2	4	no	—
1005	C₄⋊C₄	—	2	4	no	—
1006	C₄⋊C₄	—	2	2	no	—
1007	C₄⋊C₄	—	2	4	no	—
1008	C₄⋊C₄	—	2	4	no	—
1009	C₄⋊C₄	—	2	4	no	—
1010	C₄⋊C₄	—	2	2	no	—
1011	C₄⋊C₄	—	2	2	no	—
1012	C₄⋊C₄	—	2	2	no	—
1013	C₄⋊C₄	—	2	2	no	—
1014	C₄⋊C₄	—	2	2	no	—
1015	C₄⋊C₄	—	2	4	no	—
1016	C₄⋊C₄	—	2	4	no	—
1017	C₄⋊C₄	—	2	4	no	—
1018	C₄⋊C₄	—	2	2	no	—
1019	C₄⋊C₄	—	2	4	no	—
1020	C₄⋊C₄	—	4	2	no	—
1021	C₄⋊C₄	—	4	2	no	—
1022	C₄⋊C₄	—	4	2	no	—
1023	C₄⋊C₄	—	4	1	no	—
1024	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
1025	C₂²⋊C₄	—	2	4	no	—
1026	C₂²⋊C₄	—	2	4	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	2	4	no	—
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	4	no	—
1031	C₂²⋊C₄	—	2	2	no	—
1032	C₂²⋊C₄	—	2	2	no	—
1033	C₂²⋊C₄	—	2	2	no	—
1034	C₂²⋊C₄	—	2	4	no	—
1035	C₂²⋊C₄	—	2	4	no	—
1036	C₂²⋊C₄	—	2	4	no	—
1037	C₂²⋊C₄	—	2	4	no	—
1038	C₂²⋊C₄	—	2	4	no	—
1039	C₂²⋊C₄	—	2	4	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	2	no	—
1044	C₂²⋊C₄	—	2	4	no	—
1045	C₂²⋊C₄	—	2	4	no	—
1046	C₂²⋊C₄	—	2	4	no	—
1047	C₂²⋊C₄	—	2	2	no	—
1048	C₂²⋊C₄	—	2	4	no	—
1049	C₂²⋊C₄	—	4	2	no	—
1050	C₂²⋊C₄	—	4	2	no	—
1051	C₂²⋊C₄	—	4	2	no	—
1052	C₂²⋊C₄	—	4	2	no	—
1053	C₂²⋊C₄	—	4	1	no	—
1054	C₂²⋊C₄	—	4	2	no	—
1055	C₂²⋊C₄	—	4	1	no	—
1056	C₂²⋊C₄	C₂×D₄×C₅₉	1	8	yes	—
1057	C₄²	—	2	4	no	—
1058	C₄²	—	2	4	no	—
1059	C₄²	—	2	2	no	—
1060	C₄²	—	2	2	no	—
1061	C₄²	—	2	2	no	—
1062	C₄²	C₂×D₄×C₅₉	1	4	yes	—
1063	C₂³	—	2	2	no	—
1064	C₂³	—	2	2	no	—
1065	C₂³	—	2	2	no	—
1066	C₂³	—	2	2	no	—
1067	C₂³	—	2	1	no	—
1068	C₂³	—	2	1	no	—
1069	C₂³	—	2	1	no	—
1070	C₂³	—	2	1	no	—
1071	C₂³	—	2	1	no	—
1072	C₂³	—	2	1	no	—
1073	C₂³	—	2	1	no	—
1074	C₂³	—	2	1	no	—
1075	C₂³	—	2	1	no	—
1076	C₂³	—	2	1	no	—
1077	C₂³	—	2	1	no	—
1078	C₂³	—	2	1	no	—
1079	C₂³	—	2	1	no	—
1080	C₂³	—	2	2	no	—
1081	C₂³	—	2	2	no	—
1082	C₂³	—	2	1	no	—
1083	C₂³	—	2	1	no	—
1084	C₂³	—	2	2	no	—
1085	C₂³	—	2	2	no	—
1086	C₂³	—	2	1	no	—
1087	C₂³	—	2	1	no	—
1088	C₂³	—	2	2	no	—
1089	C₂³	—	2	1	no	—
1090	C₂³	—	2	1	no	—
1091	C₂³	—	2	2	no	—
1092	C₂³	—	2	2	no	—
1093	C₂³	—	4	8	no	—
1094	C₂³	—	4	8	no	—
1095	C₂³	—	4	8	no	—
1096	C₂³	—	4	8	no	—
1097	C₂³	—	8	4	no	—
1098	C₂³	—	8	4	no	—
1099	C₂³	—	8	4	no	—
1100	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
1101	C₂³	C₂²×D₄×C₅₉	1	4	yes	—
1102	C₂³	C₂²×D₄×C₅₉	1	4	yes	—
1103	C₂³	C₂×#41×C₅₉	1	4	yes	—
1104	C₂³	2₋¹⁺⁴×C₅₉	1	2	yes	—
1105	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
1106	Q₈	—	2	8	no	—
1107	Q₈	—	4	4	no	—
1108	D₄	—	2	16	no	—
1109	D₄	—	4	4	no	—
1110	D₄	—	4	4	no	—
1111	D₄	—	4	4	no	—
1112	D₄	—	4	8	no	—
1113	D₄	—	4	8	no	—
1114	D₄	—	4	4	no	—
1115	D₄	—	8	4	no	—
1116	D₄	—	8	4	no	—
1117	D₄	#121×C₅₉	1	16	yes	complemented
1118	C₂×C₄	—	2	16	no	—
1119	C₂×C₄	—	2	2	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	2	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	2	2	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	1	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	2	no	—
1131	C₂×C₄	—	2	8	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	2	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	2	no	—
1139	C₂×C₄	—	2	2	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	2	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	2	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	2	no	—
1149	C₂×C₄	—	2	1	no	—
1150	C₂×C₄	—	2	2	no	—
1151	C₂×C₄	—	2	2	no	—
1152	C₂×C₄	—	2	2	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	2	1	no	—
1155	C₂×C₄	—	2	1	no	—
1156	C₂×C₄	—	2	1	no	—
1157	C₂×C₄	—	2	1	no	—
1158	C₂×C₄	—	2	1	no	—
1159	C₂×C₄	—	2	2	no	—
1160	C₂×C₄	—	2	1	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	2	2	no	—
1163	C₂×C₄	—	2	1	no	—
1164	C₂×C₄	—	2	2	no	—
1165	C₂×C₄	—	4	8	no	—
1166	C₂×C₄	—	4	8	no	—
1167	C₂×C₄	—	4	8	no	—
1168	C₂×C₄	—	4	4	no	—
1169	C₂×C₄	—	4	4	no	—
1170	C₂×C₄	—	8	4	no	—
1171	C₂×C₄	—	8	4	no	—
1172	C₂×C₄	—	8	4	no	—
1173	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1174	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
1175	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1176	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1177	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
1178	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1179	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1180	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
1181	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
1182	C₂²	—	2	4	no	—
1183	C₂²	—	2	4	no	—
1184	C₂²	—	2	4	no	—
1185	C₂²	—	2	4	no	—
1186	C₂²	—	2	4	no	—
1187	C₂²	—	2	4	no	—
1188	C₂²	—	2	2	no	—
1189	C₂²	—	2	2	no	—
1190	C₂²	—	2	2	no	—
1191	C₂²	—	2	2	no	—
1192	C₂²	—	2	2	no	—
1193	C₂²	—	2	2	no	—
1194	C₂²	—	4	1	no	—
1195	C₂²	—	4	1	no	—
1196	C₂²	—	4	1	no	—
1197	C₂²	—	4	1	no	—
1198	C₂²	—	4	1	no	—
1199	C₂²	—	4	1	no	—
1200	C₂²	—	4	1	no	—
1201	C₂²	—	4	1	no	—
1202	C₂²	—	4	2	no	—
1203	C₂²	—	4	1	no	—
1204	C₂²	—	4	2	no	—
1205	C₂²	—	4	1	no	—
1206	C₂²	—	4	1	no	—
1207	C₂²	—	4	2	no	—
1208	C₂²	—	4	1	no	—
1209	C₂²	—	4	2	no	—
1210	C₂²	—	4	1	no	—
1211	C₂²	—	4	2	no	—
1212	C₂²	—	4	2	no	—
1213	C₂²	—	4	1	no	—
1214	C₂²	—	4	1	no	—
1215	C₂²	—	4	2	no	—
1216	C₂²	—	8	16	no	—
1217	C₂²	C₂×#121×C₅₉	1	8	yes	—
1218	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
1219	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
1220	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
1221	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
1222	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
1223	C₂²	C₅₉×#585	1	1	yes	characteristic
1224	C₂²	C₅₉×#585	1	1	yes	characteristic
1225	C₄	—	2	2	no	—
1226	C₄	—	2	4	no	—
1227	C₄	—	2	2	no	—
1228	C₄	—	2	2	no	—
1229	C₄	—	2	2	no	—
1230	C₄	—	2	4	no	—
1231	C₄	—	4	1	no	—
1232	C₄	—	4	1	no	—
1233	C₄	—	4	2	no	—
1234	C₄	—	4	2	no	—
1235	C₄	—	4	1	no	—
1236	C₄	—	4	2	no	—
1237	C₄	—	4	1	no	—
1238	C₄	—	4	1	no	—
1239	C₄	—	4	1	no	—
1240	C₄	—	4	2	no	—
1241	C₄	—	4	1	no	—
1242	C₄	C₂×#121×C₅₉	1	4	yes	—
1243	C₂	—	2	8	no	—
1244	C₂	—	4	2	no	—
1245	C₂	—	4	2	no	—
1246	C₂	—	8	2	no	—
1247	C₂	—	8	1	no	—
1248	C₂	C₂²×#121×C₅₉	1	1	yes	characteristic
1249	C₂	C₅₉×#3488	1	1	yes	characteristic
1250	C₂	C₅₉×#3489	1	1	yes	characteristic
1251	C₂	C₅₉×#3489	1	1	yes	characteristic
1252	C₂	C₅₉×#3496	1	1	yes	characteristic
1253	C₂	C₅₉×#3520	1	1	yes	characteristic
1254	C₂	C₅₉×#3521	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
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×#547	C₂	semidirect
2. C₂×C₅₉×#546	C₂	semidirect
3. C₂×C₅₉×#546	C₂	semidirect
4. C₂×C₅₉×#520	C₂	semidirect
5. C₅₉×#2620	C₂	semidirect
6. C₅₉×#2618	C₂	semidirect
7. C₅₉×#2545	C₂	semidirect
8. C₅₉×#2538	C₂	semidirect
9. C₅₉×#2534	C₂	semidirect
10. C₅₉×#2429	C₂	semidirect
11. C₅₉×#2426	C₂	semidirect
12. C₅₉×#2425	C₂	semidirect
13. C₅₉×#2424	C₂	semidirect
14. C₅₉×#2417	C₂	semidirect
15. C₅₉×#2416	C₂	semidirect
16. C₅₉×#2416	C₂	semidirect
17. C₅₉×#2413	C₂	semidirect
18. C₅₉×#2411	C₂	semidirect
19. C₅₉×#2392	C₂	semidirect
20. C₂×C₅₉×#396	C₂	semidirect
21. D₄×C₄⋊C₄×C₅₉	C₂	semidirect
22. C₅₉×#2339	C₂	semidirect
23. D₄×C₂²⋊C₄×C₅₉	C₂	semidirect
30. C₂×C₄⋊Q₈×C₅₉	C₂²	semidirect
35. C₂×#123×C₅₉	C₂²	semidirect
36. C₂×#123×C₅₉	C₂²	semidirect
39. C₂×C₂²⋊Q₈×C₅₉	C₂²	semidirect
40. C₂×C₂²⋊Q₈×C₅₉	C₂²	semidirect
45. C₂×#121×C₅₉	C₂²	semidirect
46. C₂×#121×C₅₉	C₂²	semidirect
50. C₂×C₄×Q₈×C₅₉	C₂²	semidirect
51. C₂×C₄×Q₈×C₅₉	C₂²	semidirect
58. C₂×C₄×D₄×C₅₉	C₂²	semidirect
59. C₂×C₄×D₄×C₅₉	C₂²	semidirect
60. C₂×C₄×D₄×C₅₉	C₂²	semidirect
61. C₂×#117×C₅₉	C₂²	semidirect
62. C₂×#117×C₅₉	C₂²	semidirect
63. C₂²×C₄⋊C₄×C₅₉	C₂²	semidirect
64. C₂²×C₄⋊C₄×C₅₉	C₂²	semidirect
65. C₂²×C₄⋊C₄×C₅₉	C₂²	semidirect
66. C₂²×C₄⋊C₄×C₅₉	C₂²	semidirect
70. C₅₉×#398	C₂²	semidirect
71. C₅₉×#398	C₂²	semidirect
72. C₅₉×#398	C₂²	semidirect
73. C₅₉×#397	C₂²	semidirect
78. C₅₉×#396	C₂²	semidirect
79. C₅₉×#396	C₂²	semidirect
80. C₅₉×#396	C₂²	semidirect
81. C₅₉×#396	C₂²	semidirect
82. C₅₉×#396	C₂²	semidirect
83. C₅₉×#396	C₂²	semidirect
84. C₅₉×#396	C₂²	semidirect
85. C₅₉×#396	C₂²	semidirect
88. C₅₉×#394	C₂²	semidirect
89. C₅₉×#394	C₂²	semidirect
90. C₅₉×#394	C₂²	semidirect
91. C₅₉×#394	C₂²	semidirect
92. C₅₉×#394	C₂²	semidirect
94. C₅₉×#391	C₂²	semidirect
95. C₅₉×#391	C₂²	semidirect
99. C₅₉×#390	C₂²	semidirect
100. C₅₉×#389	C₂²	semidirect
101. C₅₉×#389	C₂²	semidirect
102. C₅₉×#389	C₂²	semidirect
103. C₅₉×#389	C₂²	semidirect
105. C₅₉×#388	C₂²	semidirect
106. C₅₉×#388	C₂²	semidirect
107. C₅₉×#388	C₂²	semidirect
111. C₅₉×#386	C₂²	semidirect
112. C₅₉×#386	C₂²	semidirect
113. C₅₉×#386	C₂²	semidirect
114. C₅₉×#385	C₂²	semidirect
115. C₅₉×#385	C₂²	semidirect
116. C₅₉×#384	C₂²	semidirect
117. C₅₉×#381	C₂²	semidirect
119. C₅₉×#380	C₂²	semidirect
120. C₅₉×#380	C₂²	semidirect
121. C₅₉×#380	C₂²	semidirect
123. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
125. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
126. C₂×#95×C₅₉	C₂²	semidirect
133. C₂×#41×C₅₉	D₄	semidirect
188. C₄×D₄×C₅₉	D₄	semidirect
489. D₄×C₅₉	#121	semidirect
554. #35821	C₅₉	direct (N × H)
616. C₂×#547	C₂×C₅₉	semidirect
617. C₂×#546	C₂×C₅₉	semidirect
618. C₂×#546	C₂×C₅₉	semidirect
619. C₂×#520	C₂×C₅₉	semidirect
620. #2620	C₂×C₅₉	semidirect
621. #2618	C₂×C₅₉	semidirect
622. #2545	C₂×C₅₉	semidirect
623. #2538	C₂×C₅₉	semidirect
624. #2534	C₂×C₅₉	semidirect
625. #2429	C₂×C₅₉	semidirect
626. #2426	C₂×C₅₉	semidirect
627. #2425	C₂×C₅₉	semidirect
628. #2424	C₂×C₅₉	semidirect
629. #2417	C₂×C₅₉	semidirect
630. #2416	C₂×C₅₉	semidirect
631. #2416	C₂×C₅₉	semidirect
632. #2413	C₂×C₅₉	semidirect
633. #2411	C₂×C₅₉	semidirect
634. #2392	C₂×C₅₉	semidirect
635. C₂×#396	C₂×C₅₉	semidirect
636. D₄×C₄⋊C₄	C₂×C₅₉	semidirect
637. #2339	C₂×C₅₉	semidirect
638. D₄×C₂²⋊C₄	C₂×C₅₉	semidirect
657. C₂×C₄⋊Q₈	C₂²×C₅₉	semidirect
662. C₂×#123	C₂²×C₅₉	semidirect
663. C₂×#123	C₂²×C₅₉	semidirect
666. C₂×C₂²⋊Q₈	C₂²×C₅₉	semidirect
667. C₂×C₂²⋊Q₈	C₂²×C₅₉	semidirect
672. C₂×#121	C₂²×C₅₉	semidirect
673. C₂×#121	C₂²×C₅₉	semidirect
677. C₂×C₄×Q₈	C₂²×C₅₉	semidirect
678. C₂×C₄×Q₈	C₂²×C₅₉	semidirect
685. C₂×C₄×D₄	C₂²×C₅₉	semidirect
686. C₂×C₄×D₄	C₂²×C₅₉	semidirect
687. C₂×C₄×D₄	C₂²×C₅₉	semidirect
688. C₂×#117	C₂²×C₅₉	semidirect
689. C₂×#117	C₂²×C₅₉	semidirect
690. C₂²×C₄⋊C₄	C₂²×C₅₉	semidirect
691. C₂²×C₄⋊C₄	C₂²×C₅₉	semidirect
692. C₂²×C₄⋊C₄	C₂²×C₅₉	semidirect
693. C₂²×C₄⋊C₄	C₂²×C₅₉	semidirect
697. #398	C₂²×C₅₉	semidirect
698. #398	C₂²×C₅₉	semidirect
699. #398	C₂²×C₅₉	semidirect
700. #397	C₂²×C₅₉	semidirect
705. #396	C₂²×C₅₉	semidirect
706. #396	C₂²×C₅₉	semidirect
707. #396	C₂²×C₅₉	semidirect
708. #396	C₂²×C₅₉	semidirect
709. #396	C₂²×C₅₉	semidirect
710. #396	C₂²×C₅₉	semidirect
711. #396	C₂²×C₅₉	semidirect
712. #396	C₂²×C₅₉	semidirect
715. #394	C₂²×C₅₉	semidirect
716. #394	C₂²×C₅₉	semidirect
717. #394	C₂²×C₅₉	semidirect
718. #394	C₂²×C₅₉	semidirect
719. #394	C₂²×C₅₉	semidirect
721. #391	C₂²×C₅₉	semidirect
722. #391	C₂²×C₅₉	semidirect
726. #390	C₂²×C₅₉	semidirect
727. #389	C₂²×C₅₉	semidirect
728. #389	C₂²×C₅₉	semidirect
729. #389	C₂²×C₅₉	semidirect
730. #389	C₂²×C₅₉	semidirect
732. #388	C₂²×C₅₉	semidirect
733. #388	C₂²×C₅₉	semidirect
734. #388	C₂²×C₅₉	semidirect
738. #386	C₂²×C₅₉	semidirect
739. #386	C₂²×C₅₉	semidirect
740. #386	C₂²×C₅₉	semidirect
741. #385	C₂²×C₅₉	semidirect
742. #385	C₂²×C₅₉	semidirect
743. #384	C₂²×C₅₉	semidirect
744. #381	C₂²×C₅₉	semidirect
746. #380	C₂²×C₅₉	semidirect
747. #380	C₂²×C₅₉	semidirect
748. #380	C₂²×C₅₉	semidirect
750. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
752. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
753. C₂×#95	C₂²×C₅₉	semidirect
754. C₅₉	#35821	direct (N × H)
761. C₂×#41	D₄×C₅₉	semidirect
816. C₄×D₄	D₄×C₅₉	semidirect
1117. D₄	#121×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×#547	2
C₂×C₅₉×#546	2
C₂×C₅₉×#520	2
C₅₉×#2620	2
C₅₉×#2618	2
C₅₉×#2545	2
C₅₉×#2538	2
C₅₉×#2534	2
C₅₉×#2429	2
C₅₉×#2426	2
C₅₉×#2425	2
C₅₉×#2424	2
C₅₉×#2417	2
C₅₉×#2416	2
C₅₉×#2413	2
C₅₉×#2411	2
C₅₉×#2392	2
C₂×C₅₉×#396	2
D₄×C₄⋊C₄×C₅₉	2
C₅₉×#2339	2
D₄×C₂²⋊C₄×C₅₉	2
#35821	59

Subgroups — C59×#35821 #28447930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35821 #28447930