Subgroups — C₅₉×#35252 #28447361

Order 15104.

3602 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#535	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#525	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#121×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#117×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2856	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2850	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2620	C₂	1	2	yes	maximal, complemented
8	C₅₉×#2619	C₂	1	2	yes	maximal, complemented
9	C₅₉×#2416	C₂	1	4	yes	maximal, complemented
10	C₅₉×#2414	C₂	1	4	yes	maximal, complemented
11	C₅₉×#2411	C₂	1	4	yes	maximal, complemented
12	C₅₉×#2410	C₂	1	4	yes	maximal, complemented
13	C₅₉×#2317	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₉×#2311	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#2309	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₅₉	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₅₉	C₂²	1	2	yes	—
19	C₂⁴×C₄×C₅₉	C₂²	1	1	yes	characteristic
20	C₅₉×#535	—	2	8	no	—
21	C₂×#127×C₅₉	C₂²	1	2	yes	complemented
22	C₂×#124×C₅₉	C₂²	1	2	yes	complemented
23	C₅₉×#525	—	2	8	no	—
24	C₂×#123×C₅₉	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
27	C₂×#121×C₅₉	—	2	8	no	—
28	C₂×#121×C₅₉	C₂²	1	2	yes	—
29	C₂×#121×C₅₉	C₂²	1	2	yes	—
30	C₂×#121×C₅₉	C₂²	1	2	yes	—
31	C₂×#121×C₅₉	C₂²	1	2	yes	—
32	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic, complemented
33	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic, complemented
34	C₂×#121×C₅₉	C₂²	1	4	yes	complemented
35	C₂×#121×C₅₉	C₂²	1	8	yes	complemented
36	C₂×#120×C₅₉	C₂²	1	2	yes	—
37	C₂×#120×C₅₉	C₂²	1	4	yes	—
38	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	complemented
39	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	complemented
40	C₂×#117×C₅₉	—	2	8	no	—
41	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
42	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
43	C₂×#117×C₅₉	C₂²	1	2	yes	—
44	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
45	C₂×#117×C₅₉	C₂²	1	2	yes	complemented
46	C₂×#117×C₅₉	C₂²	1	2	yes	complemented
47	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
48	C₂²×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
49	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
50	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
51	C₂²×C₄²×C₅₉	C₂²	1	2	yes	complemented
52	C₅₉×#396	C₂²	1	8	yes	complemented
53	C₅₉×#394	C₂²	1	8	yes	complemented
54	C₅₉×#394	C₂²	1	8	yes	complemented
55	C₅₉×#392	C₂²	1	8	yes	complemented
56	C₅₉×#391	C₂²	1	2	yes	complemented
57	C₅₉×#390	C₂²	1	2	yes	complemented
58	C₅₉×#390	C₂²	1	2	yes	complemented
59	C₅₉×#390	C₂²	1	4	yes	complemented
60	C₅₉×#390	C₂²	1	2	yes	complemented
61	C₅₉×#390	C₂²	1	8	yes	complemented
62	C₅₉×#389	C₂²	1	4	yes	complemented
63	C₅₉×#388	C₂²	1	8	yes	complemented
64	C₅₉×#386	C₂²	1	4	yes	—
65	C₅₉×#386	C₂²	1	8	yes	complemented
66	C₅₉×#385	C₂²	1	4	yes	—
67	C₅₉×#384	C₂²	1	2	yes	complemented
68	C₅₉×#382	C₂²	1	2	yes	complemented
69	C₅₉×#380	C₂²	1	4	yes	complemented
70	C₅₉×#379	C₂²	1	4	yes	—
71	C₂⁵×C₅₉	C₂³	1	1	yes	characteristic
72	C₂⁵×C₅₉	C₂³	1	2	yes	—
73	C₂×#41×C₅₉	—	2	4	no	—
74	C₂×#41×C₅₉	—	2	4	no	—
75	C₂×#41×C₅₉	—	2	4	no	—
76	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₅₉	—	2	8	no	—
78	C₂²×D₄×C₅₉	—	2	4	no	—
79	C₂²×D₄×C₅₉	—	2	4	no	—
80	C₂²×D₄×C₅₉	—	2	4	no	—
81	C₂²×D₄×C₅₉	—	4	8	no	—
82	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
83	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
84	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
85	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
86	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
88	C₂²×D₄×C₅₉	C₂³	1	8	yes	—
89	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
90	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
91	C₂³×C₄×C₅₉	—	2	4	no	—
92	C₂³×C₄×C₅₉	—	2	4	no	—
93	C₂³×C₄×C₅₉	D₄	1	8	yes	complemented
94	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
95	C₂³×C₄×C₅₉	C₂³	1	4	yes	—
96	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
102	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
103	#127×C₅₉	—	2	8	no	—
104	#124×C₅₉	—	2	8	no	—
105	#123×C₅₉	—	2	8	no	—
106	C₂²⋊Q₈×C₅₉	—	2	4	no	—
107	C₂²⋊Q₈×C₅₉	—	2	4	no	—
108	#121×C₅₉	—	2	8	no	—
109	#121×C₅₉	—	2	8	no	—
110	#121×C₅₉	—	2	8	no	—
111	#121×C₅₉	—	2	8	no	—
112	#121×C₅₉	—	2	4	no	—
113	#121×C₅₉	—	2	4	no	—
114	#121×C₅₉	—	2	16	no	—
115	#121×C₅₉	—	4	16	no	—
116	#120×C₅₉	—	2	8	no	—
117	#120×C₅₉	—	2	16	no	—
118	C₄×D₄×C₅₉	—	2	8	no	—
119	C₄×D₄×C₅₉	—	2	8	no	—
120	#117×C₅₉	—	2	4	no	—
121	#117×C₅₉	—	2	4	no	—
122	#117×C₅₉	—	2	8	no	—
123	#117×C₅₉	—	2	8	no	—
124	#117×C₅₉	—	2	8	no	—
125	#117×C₅₉	D₄	1	8	yes	complemented
126	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
127	C₂×C₄⋊C₄×C₅₉	—	2	8	no	—
128	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
135	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
137	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₅₉	—	2	8	no	—
139	C₂×C₂²⋊C₄×C₅₉	—	2	8	no	—
140	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
144	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
151	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
152	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
153	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
154	C₂×C₄²×C₅₉	—	2	8	no	—
155	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
156	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
157	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
158	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
159	#95×C₅₉	C₂³	1	8	yes	—
160	#95×C₅₉	C₂³	1	8	yes	—
161	C₂⁴×C₅₉	—	2	2	no	—
162	C₂⁴×C₅₉	—	2	2	no	—
163	C₂⁴×C₅₉	—	2	4	no	—
164	C₂⁴×C₅₉	—	2	4	no	—
165	C₂⁴×C₅₉	—	2	4	no	—
166	C₂⁴×C₅₉	—	2	4	no	—
167	C₂⁴×C₅₉	—	4	2	no	—
168	C₂⁴×C₅₉	—	4	4	no	—
169	C₂⁴×C₅₉	—	4	4	no	—
170	C₂⁴×C₅₉	C₂×D₄	1	4	yes	—
171	C₂⁴×C₅₉	C₂⁴	1	4	yes	—
172	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
173	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
174	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
175	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
176	#41×C₅₉	—	4	16	no	—
177	C₂×Q₈×C₅₉	—	2	2	no	—
178	C₂×Q₈×C₅₉	—	2	2	no	—
179	C₂×Q₈×C₅₉	—	2	2	no	—
180	C₂×D₄×C₅₉	—	2	4	no	—
181	C₂×D₄×C₅₉	—	2	4	no	—
182	C₂×D₄×C₅₉	—	2	4	no	—
183	C₂×D₄×C₅₉	—	2	4	no	—
184	C₂×D₄×C₅₉	—	2	8	no	—
185	C₂×D₄×C₅₉	—	2	8	no	—
186	C₂×D₄×C₅₉	—	2	4	no	—
187	C₂×D₄×C₅₉	—	2	8	no	—
188	C₂×D₄×C₅₉	—	2	16	no	—
189	C₂×D₄×C₅₉	—	2	4	no	—
190	C₂×D₄×C₅₉	—	2	4	no	—
191	C₂×D₄×C₅₉	—	2	4	no	—
192	C₂×D₄×C₅₉	—	2	2	no	—
193	C₂×D₄×C₅₉	—	2	4	no	—
194	C₂×D₄×C₅₉	—	2	2	no	—
195	C₂×D₄×C₅₉	—	2	16	no	—
196	C₂×D₄×C₅₉	—	2	4	no	—
197	C₂×D₄×C₅₉	—	2	4	no	—
198	C₂×D₄×C₅₉	—	2	2	no	—
199	C₂×D₄×C₅₉	—	4	8	no	—
200	C₂×D₄×C₅₉	—	4	4	no	—
201	C₂×D₄×C₅₉	—	4	8	no	—
202	C₂×D₄×C₅₉	—	4	8	no	—
203	C₂×D₄×C₅₉	—	4	32	no	—
204	C₂×D₄×C₅₉	—	4	16	no	—
205	C₂²×C₄×C₅₉	—	2	2	no	—
206	C₂²×C₄×C₅₉	—	2	2	no	—
207	C₂²×C₄×C₅₉	—	2	32	no	—
208	C₂²×C₄×C₅₉	—	2	2	no	—
209	C₂²×C₄×C₅₉	—	2	2	no	—
210	C₂²×C₄×C₅₉	—	2	2	no	—
211	C₂²×C₄×C₅₉	—	2	2	no	—
212	C₂²×C₄×C₅₉	—	2	2	no	—
213	C₂²×C₄×C₅₉	—	2	2	no	—
214	C₂²×C₄×C₅₉	—	2	2	no	—
215	C₂²×C₄×C₅₉	—	2	2	no	—
216	C₂²×C₄×C₅₉	—	2	4	no	—
217	C₂²×C₄×C₅₉	—	2	8	no	—
218	C₂²×C₄×C₅₉	—	2	8	no	—
219	C₂²×C₄×C₅₉	—	2	4	no	—
220	C₂²×C₄×C₅₉	—	2	4	no	—
221	C₂²×C₄×C₅₉	—	2	4	no	—
222	C₂²×C₄×C₅₉	—	4	4	no	—
223	C₂²×C₄×C₅₉	—	4	4	no	—
224	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
225	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
226	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
227	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
228	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
229	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
230	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
231	C₂²×C₄×C₅₉	#41	1	4	yes	—
232	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
235	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
236	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
238	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
239	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
242	C₄⋊C₄×C₅₉	—	2	8	no	—
243	C₄⋊C₄×C₅₉	—	2	4	no	—
244	C₄⋊C₄×C₅₉	—	2	4	no	—
245	C₄⋊C₄×C₅₉	—	2	4	no	—
246	C₄⋊C₄×C₅₉	—	2	2	no	—
247	C₄⋊C₄×C₅₉	—	2	2	no	—
248	C₄⋊C₄×C₅₉	—	2	4	no	—
249	C₄⋊C₄×C₅₉	—	2	4	no	—
250	C₄⋊C₄×C₅₉	—	4	8	no	—
251	C₄⋊C₄×C₅₉	C₂×D₄	1	8	yes	complemented
252	C₂²⋊C₄×C₅₉	—	2	4	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	8	no	—
257	C₂²⋊C₄×C₅₉	—	2	8	no	—
258	C₂²⋊C₄×C₅₉	—	2	8	no	—
259	C₂²⋊C₄×C₅₉	—	2	4	no	—
260	C₂²⋊C₄×C₅₉	—	2	4	no	—
261	C₂²⋊C₄×C₅₉	—	2	16	no	—
262	C₂²⋊C₄×C₅₉	—	4	8	no	—
263	C₂²⋊C₄×C₅₉	—	4	8	no	—
264	C₂²⋊C₄×C₅₉	—	4	8	no	—
265	C₂²⋊C₄×C₅₉	C₂×D₄	1	8	yes	—
266	C₄²×C₅₉	—	2	8	no	—
267	C₄²×C₅₉	—	2	4	no	—
268	C₄²×C₅₉	—	2	4	no	—
269	C₄²×C₅₉	C₂×D₄	1	8	yes	complemented
270	C₂³×C₅₉	—	2	1	no	—
271	C₂³×C₅₉	—	2	1	no	—
272	C₂³×C₅₉	—	2	2	no	—
273	C₂³×C₅₉	—	2	2	no	—
274	C₂³×C₅₉	—	2	2	no	—
275	C₂³×C₅₉	—	2	8	no	—
276	C₂³×C₅₉	—	2	8	no	—
277	C₂³×C₅₉	—	2	1	no	—
278	C₂³×C₅₉	—	2	1	no	—
279	C₂³×C₅₉	—	2	2	no	—
280	C₂³×C₅₉	—	2	2	no	—
281	C₂³×C₅₉	—	2	2	no	—
282	C₂³×C₅₉	—	2	4	no	—
283	C₂³×C₅₉	—	2	4	no	—
284	C₂³×C₅₉	—	2	2	no	—
285	C₂³×C₅₉	—	2	2	no	—
286	C₂³×C₅₉	—	2	4	no	—
287	C₂³×C₅₉	—	2	4	no	—
288	C₂³×C₅₉	—	2	8	no	—
289	C₂³×C₅₉	—	2	8	no	—
290	C₂³×C₅₉	—	2	4	no	—
291	C₂³×C₅₉	—	4	4	no	—
292	C₂³×C₅₉	—	4	8	no	—
293	C₂³×C₅₉	—	4	8	no	—
294	C₂³×C₅₉	—	4	8	no	—
295	C₂³×C₅₉	—	4	8	no	—
296	C₂³×C₅₉	—	4	8	no	—
297	C₂³×C₅₉	—	8	8	no	—
298	C₂³×C₅₉	—	8	8	no	—
299	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
300	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
301	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
302	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
303	C₂³×C₅₉	C₂×#41	1	2	yes	—
304	C₂³×C₅₉	H(5,𝔽₂)	1	4	yes	—
305	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
306	Q₈×C₅₉	—	4	4	no	—
307	D₄×C₅₉	—	4	8	no	—
308	D₄×C₅₉	—	4	16	no	—
309	D₄×C₅₉	—	4	8	no	—
310	D₄×C₅₉	—	4	8	no	—
311	D₄×C₅₉	—	4	16	no	—
312	D₄×C₅₉	—	4	8	no	—
313	D₄×C₅₉	—	4	8	no	—
314	D₄×C₅₉	—	4	4	no	—
315	D₄×C₅₉	—	8	16	no	—
316	C₂×C₄×C₅₉	—	2	8	no	—
317	C₂×C₄×C₅₉	—	2	1	no	—
318	C₂×C₄×C₅₉	—	2	1	no	—
319	C₂×C₄×C₅₉	—	2	1	no	—
320	C₂×C₄×C₅₉	—	2	1	no	—
321	C₂×C₄×C₅₉	—	2	4	no	—
322	C₂×C₄×C₅₉	—	2	4	no	—
323	C₂×C₄×C₅₉	—	2	8	no	—
324	C₂×C₄×C₅₉	—	2	8	no	—
325	C₂×C₄×C₅₉	—	2	8	no	—
326	C₂×C₄×C₅₉	—	2	8	no	—
327	C₂×C₄×C₅₉	—	2	4	no	—
328	C₂×C₄×C₅₉	—	2	2	no	—
329	C₂×C₄×C₅₉	—	2	2	no	—
330	C₂×C₄×C₅₉	—	2	2	no	—
331	C₂×C₄×C₅₉	—	2	4	no	—
332	C₂×C₄×C₅₉	—	2	2	no	—
333	C₂×C₄×C₅₉	—	2	2	no	—
334	C₂×C₄×C₅₉	—	2	4	no	—
335	C₂×C₄×C₅₉	—	2	4	no	—
336	C₂×C₄×C₅₉	—	2	8	no	—
337	C₂×C₄×C₅₉	—	2	4	no	—
338	C₂×C₄×C₅₉	—	2	4	no	—
339	C₂×C₄×C₅₉	—	4	16	no	—
340	C₂×C₄×C₅₉	—	4	8	no	—
341	C₂×C₄×C₅₉	—	4	8	no	—
342	C₂×C₄×C₅₉	#121	1	16	yes	complemented
343	C₂×C₄×C₅₉	C₂²×D₄	1	8	yes	—
344	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
345	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
346	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
347	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
348	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
349	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
350	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
351	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
352	#35252	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
353	C₂²×C₅₉	—	2	2	no	—
354	C₂²×C₅₉	—	2	2	no	—
355	C₂²×C₅₉	—	2	2	no	—
356	C₂²×C₅₉	—	2	2	no	—
357	C₂²×C₅₉	—	2	4	no	—
358	C₂²×C₅₉	—	2	4	no	—
359	C₂²×C₅₉	—	2	4	no	—
360	C₂²×C₅₉	—	2	4	no	—
361	C₂²×C₅₉	—	2	2	no	—
362	C₂²×C₅₉	—	2	2	no	—
363	C₂²×C₅₉	—	2	2	no	—
364	C₂²×C₅₉	—	4	16	no	—
365	C₂²×C₅₉	—	4	2	no	—
366	C₂²×C₅₉	—	4	2	no	—
367	C₂²×C₅₉	—	4	2	no	—
368	C₂²×C₅₉	—	4	4	no	—
369	C₂²×C₅₉	—	4	4	no	—
370	C₂²×C₅₉	—	4	2	no	—
371	C₂²×C₅₉	—	4	2	no	—
372	C₂²×C₅₉	—	4	4	no	—
373	C₂²×C₅₉	—	4	4	no	—
374	C₂²×C₅₉	—	4	8	no	—
375	C₂²×C₅₉	—	4	4	no	—
376	C₂²×C₅₉	—	4	8	no	—
377	C₂²×C₅₉	—	8	16	no	—
378	C₂²×C₅₉	C₂×#121	1	4	yes	—
379	C₂²×C₅₉	#535	1	4	yes	complemented
380	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
381	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
382	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
383	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	2	yes	—
384	C₂²×C₅₉	#585	1	2	yes	—
385	C₄×C₅₉	—	2	2	no	—
386	C₄×C₅₉	—	2	2	no	—
387	C₄×C₅₉	—	2	8	no	—
388	C₄×C₅₉	—	4	2	no	—
389	C₄×C₅₉	—	4	4	no	—
390	C₄×C₅₉	—	4	2	no	—
391	C₄×C₅₉	—	4	2	no	—
392	C₄×C₅₉	—	4	4	no	—
393	C₄×C₅₉	C₂×#121	1	4	yes	—
394	C₄×C₅₉	C₂×#121	1	4	yes	—
395	C₂×#535	C₂×C₅₉	1	1	yes	characteristic, complemented
396	C₂×#525	C₂×C₅₉	1	1	yes	characteristic, complemented
397	C₂²×#121	C₂×C₅₉	1	1	yes	characteristic, complemented
398	C₂²×#117	C₂×C₅₉	1	1	yes	characteristic, complemented
399	#2856	C₂×C₅₉	1	2	yes	complemented
400	#2850	C₂×C₅₉	1	2	yes	complemented
401	#2620	C₂×C₅₉	1	2	yes	complemented
402	#2619	C₂×C₅₉	1	2	yes	complemented
403	#2416	C₂×C₅₉	1	4	yes	complemented
404	#2414	C₂×C₅₉	1	4	yes	complemented
405	#2411	C₂×C₅₉	1	4	yes	complemented
406	#2410	C₂×C₅₉	1	4	yes	complemented
407	#2317	C₂×C₅₉	1	1	yes	characteristic, complemented
408	#2311	C₂×C₅₉	1	1	yes	characteristic, complemented
409	#2309	C₂×C₅₉	1	1	yes	characteristic, complemented
410	C₂×C₅₉	—	2	4	no	—
411	C₂×C₅₉	—	2	4	no	—
412	C₂×C₅₉	—	4	2	no	—
413	C₂×C₅₉	—	8	2	no	—
414	C₂×C₅₉	—	8	4	no	—
415	C₂×C₅₉	C₂²×#121	1	1	yes	characteristic
416	C₂×C₅₉	C₂×#535	1	1	yes	characteristic
417	C₂×C₅₉	#3449	1	1	yes	characteristic
418	C₂×C₅₉	#3488	1	2	yes	—
419	C₂×C₅₉	#3494	1	2	yes	—
420	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic
421	C₂³×D₄	C₂²×C₅₉	1	1	yes	characteristic
422	C₂³×D₄	C₂²×C₅₉	1	2	yes	—
423	C₂⁴×C₄	C₂²×C₅₉	1	1	yes	characteristic
424	#535	—	2	8	no	—
425	C₂×#127	C₂²×C₅₉	1	2	yes	complemented
426	C₂×#124	C₂²×C₅₉	1	2	yes	complemented
427	#525	—	2	8	no	—
428	C₂×#123	C₂²×C₅₉	1	2	yes	—
429	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
430	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
431	C₂×#121	—	2	8	no	—
432	C₂×#121	C₂²×C₅₉	1	2	yes	—
433	C₂×#121	C₂²×C₅₉	1	2	yes	—
434	C₂×#121	C₂²×C₅₉	1	2	yes	—
435	C₂×#121	C₂²×C₅₉	1	2	yes	—
436	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic, complemented
437	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic, complemented
438	C₂×#121	C₂²×C₅₉	1	4	yes	complemented
439	C₂×#121	C₂²×C₅₉	1	8	yes	complemented
440	C₂×#120	C₂²×C₅₉	1	2	yes	—
441	C₂×#120	C₂²×C₅₉	1	4	yes	—
442	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	complemented
443	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	complemented
444	C₂×#117	—	2	8	no	—
445	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
446	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
447	C₂×#117	C₂²×C₅₉	1	2	yes	—
448	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
449	C₂×#117	C₂²×C₅₉	1	2	yes	complemented
450	C₂×#117	C₂²×C₅₉	1	2	yes	complemented
451	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
452	C₂²×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
453	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
454	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
455	C₂²×C₄²	C₂²×C₅₉	1	2	yes	complemented
456	#396	C₂²×C₅₉	1	8	yes	complemented
457	#394	C₂²×C₅₉	1	8	yes	complemented
458	#394	C₂²×C₅₉	1	8	yes	complemented
459	#392	C₂²×C₅₉	1	8	yes	complemented
460	#391	C₂²×C₅₉	1	2	yes	complemented
461	#390	C₂²×C₅₉	1	2	yes	complemented
462	#390	C₂²×C₅₉	1	2	yes	complemented
463	#390	C₂²×C₅₉	1	4	yes	complemented
464	#390	C₂²×C₅₉	1	2	yes	complemented
465	#390	C₂²×C₅₉	1	8	yes	complemented
466	#389	C₂²×C₅₉	1	4	yes	complemented
467	#388	C₂²×C₅₉	1	8	yes	complemented
468	#386	C₂²×C₅₉	1	4	yes	—
469	#386	C₂²×C₅₉	1	8	yes	complemented
470	#385	C₂²×C₅₉	1	4	yes	—
471	#384	C₂²×C₅₉	1	2	yes	complemented
472	#382	C₂²×C₅₉	1	2	yes	complemented
473	#380	C₂²×C₅₉	1	4	yes	complemented
474	#379	C₂²×C₅₉	1	4	yes	—
475	C₅₉	#35252	1	1	yes	characteristic, direct product factor, Sylow
476	C₂⁵	C₂³×C₅₉	1	1	yes	characteristic
477	C₂⁵	C₂³×C₅₉	1	2	yes	—
478	C₂×#41	—	2	4	no	—
479	C₂×#41	—	2	4	no	—
480	C₂×#41	—	2	4	no	—
481	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
482	C₂²×D₄	—	2	8	no	—
483	C₂²×D₄	—	2	4	no	—
484	C₂²×D₄	—	2	4	no	—
485	C₂²×D₄	—	2	4	no	—
486	C₂²×D₄	—	4	8	no	—
487	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
488	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
489	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
490	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
491	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
492	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
493	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
494	C₂²×D₄	C₂³×C₅₉	1	8	yes	—
495	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
496	C₂³×C₄	—	2	4	no	—
497	C₂³×C₄	—	2	4	no	—
498	C₂³×C₄	D₄×C₅₉	1	8	yes	complemented
499	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
500	C₂³×C₄	C₂³×C₅₉	1	4	yes	—
501	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
502	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
503	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
504	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
505	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
506	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
507	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
508	#127	—	2	8	no	—
509	#124	—	2	8	no	—
510	#123	—	2	8	no	—
511	C₂²⋊Q₈	—	2	4	no	—
512	C₂²⋊Q₈	—	2	4	no	—
513	#121	—	2	8	no	—
514	#121	—	2	8	no	—
515	#121	—	2	8	no	—
516	#121	—	2	8	no	—
517	#121	—	2	4	no	—
518	#121	—	2	4	no	—
519	#121	—	2	16	no	—
520	#121	—	4	16	no	—
521	#120	—	2	8	no	—
522	#120	—	2	16	no	—
523	C₄×D₄	—	2	8	no	—
524	C₄×D₄	—	2	8	no	—
525	#117	—	2	4	no	—
526	#117	—	2	4	no	—
527	#117	—	2	8	no	—
528	#117	—	2	8	no	—
529	#117	—	2	8	no	—
530	#117	D₄×C₅₉	1	8	yes	complemented
531	C₂×C₄⋊C₄	—	2	4	no	—
532	C₂×C₄⋊C₄	—	2	8	no	—
533	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
537	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
538	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
539	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
542	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
543	C₂×C₂²⋊C₄	—	2	8	no	—
544	C₂×C₂²⋊C₄	—	2	8	no	—
545	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
559	C₂×C₄²	—	2	8	no	—
560	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
561	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
562	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
563	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
564	#95	C₂³×C₅₉	1	8	yes	—
565	#95	C₂³×C₅₉	1	8	yes	—
566	C₂⁴	—	2	2	no	—
567	C₂⁴	—	2	2	no	—
568	C₂⁴	—	2	4	no	—
569	C₂⁴	—	2	4	no	—
570	C₂⁴	—	2	4	no	—
571	C₂⁴	—	2	4	no	—
572	C₂⁴	—	4	2	no	—
573	C₂⁴	—	4	4	no	—
574	C₂⁴	—	4	4	no	—
575	C₂⁴	C₂×D₄×C₅₉	1	4	yes	—
576	C₂⁴	C₂⁴×C₅₉	1	4	yes	—
577	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
578	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
579	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
580	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
581	#41	—	4	16	no	—
582	C₂×Q₈	—	2	2	no	—
583	C₂×Q₈	—	2	2	no	—
584	C₂×Q₈	—	2	2	no	—
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	—	2	4	no	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	2	4	no	—
589	C₂×D₄	—	2	8	no	—
590	C₂×D₄	—	2	8	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	8	no	—
593	C₂×D₄	—	2	16	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	—	2	4	no	—
597	C₂×D₄	—	2	2	no	—
598	C₂×D₄	—	2	4	no	—
599	C₂×D₄	—	2	2	no	—
600	C₂×D₄	—	2	16	no	—
601	C₂×D₄	—	2	4	no	—
602	C₂×D₄	—	2	4	no	—
603	C₂×D₄	—	2	2	no	—
604	C₂×D₄	—	4	8	no	—
605	C₂×D₄	—	4	4	no	—
606	C₂×D₄	—	4	8	no	—
607	C₂×D₄	—	4	8	no	—
608	C₂×D₄	—	4	32	no	—
609	C₂×D₄	—	4	16	no	—
610	C₂²×C₄	—	2	2	no	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	2	32	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	8	no	—
623	C₂²×C₄	—	2	8	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	—	2	4	no	—
626	C₂²×C₄	—	2	4	no	—
627	C₂²×C₄	—	4	4	no	—
628	C₂²×C₄	—	4	4	no	—
629	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
630	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
631	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
632	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
633	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
634	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
635	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
636	C₂²×C₄	#41×C₅₉	1	4	yes	—
637	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
639	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
640	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
641	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
642	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
643	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
644	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
645	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
646	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
647	C₄⋊C₄	—	2	8	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	4	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	2	no	—
652	C₄⋊C₄	—	2	2	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	4	8	no	—
656	C₄⋊C₄	C₂×D₄×C₅₉	1	8	yes	complemented
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	8	no	—
662	C₂²⋊C₄	—	2	8	no	—
663	C₂²⋊C₄	—	2	8	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	16	no	—
667	C₂²⋊C₄	—	4	8	no	—
668	C₂²⋊C₄	—	4	8	no	—
669	C₂²⋊C₄	—	4	8	no	—
670	C₂²⋊C₄	C₂×D₄×C₅₉	1	8	yes	—
671	C₄²	—	2	8	no	—
672	C₄²	—	2	4	no	—
673	C₄²	—	2	4	no	—
674	C₄²	C₂×D₄×C₅₉	1	8	yes	complemented
675	C₂³	—	2	1	no	—
676	C₂³	—	2	1	no	—
677	C₂³	—	2	2	no	—
678	C₂³	—	2	2	no	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	8	no	—
681	C₂³	—	2	8	no	—
682	C₂³	—	2	1	no	—
683	C₂³	—	2	1	no	—
684	C₂³	—	2	2	no	—
685	C₂³	—	2	2	no	—
686	C₂³	—	2	2	no	—
687	C₂³	—	2	4	no	—
688	C₂³	—	2	4	no	—
689	C₂³	—	2	2	no	—
690	C₂³	—	2	2	no	—
691	C₂³	—	2	4	no	—
692	C₂³	—	2	4	no	—
693	C₂³	—	2	8	no	—
694	C₂³	—	2	8	no	—
695	C₂³	—	2	4	no	—
696	C₂³	—	4	4	no	—
697	C₂³	—	4	8	no	—
698	C₂³	—	4	8	no	—
699	C₂³	—	4	8	no	—
700	C₂³	—	4	8	no	—
701	C₂³	—	4	8	no	—
702	C₂³	—	8	8	no	—
703	C₂³	—	8	8	no	—
704	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
705	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
706	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
707	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
708	C₂³	C₂×#41×C₅₉	1	2	yes	—
709	C₂³	H(5,𝔽₂)×C₅₉	1	4	yes	—
710	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
711	Q₈	—	4	4	no	—
712	D₄	—	4	8	no	—
713	D₄	—	4	16	no	—
714	D₄	—	4	8	no	—
715	D₄	—	4	8	no	—
716	D₄	—	4	16	no	—
717	D₄	—	4	8	no	—
718	D₄	—	4	8	no	—
719	D₄	—	4	4	no	—
720	D₄	—	8	16	no	—
721	C₂×C₄	—	2	8	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	4	no	—
727	C₂×C₄	—	2	4	no	—
728	C₂×C₄	—	2	8	no	—
729	C₂×C₄	—	2	8	no	—
730	C₂×C₄	—	2	8	no	—
731	C₂×C₄	—	2	8	no	—
732	C₂×C₄	—	2	4	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	4	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	4	no	—
740	C₂×C₄	—	2	4	no	—
741	C₂×C₄	—	2	8	no	—
742	C₂×C₄	—	2	4	no	—
743	C₂×C₄	—	2	4	no	—
744	C₂×C₄	—	4	16	no	—
745	C₂×C₄	—	4	8	no	—
746	C₂×C₄	—	4	8	no	—
747	C₂×C₄	#121×C₅₉	1	16	yes	complemented
748	C₂×C₄	C₂²×D₄×C₅₉	1	8	yes	—
749	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
750	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
751	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
752	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
753	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
754	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
755	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
756	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
757	C₂²	—	2	2	no	—
758	C₂²	—	2	2	no	—
759	C₂²	—	2	2	no	—
760	C₂²	—	2	2	no	—
761	C₂²	—	2	4	no	—
762	C₂²	—	2	4	no	—
763	C₂²	—	2	4	no	—
764	C₂²	—	2	4	no	—
765	C₂²	—	2	2	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	2	2	no	—
768	C₂²	—	4	16	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	4	no	—
773	C₂²	—	4	4	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	4	2	no	—
776	C₂²	—	4	4	no	—
777	C₂²	—	4	4	no	—
778	C₂²	—	4	8	no	—
779	C₂²	—	4	8	no	—
780	C₂²	—	4	4	no	—
781	C₂²	—	8	16	no	—
782	C₂²	C₂×#121×C₅₉	1	4	yes	—
783	C₂²	C₅₉×#535	1	4	yes	complemented
784	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
785	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
786	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
787	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	2	yes	—
788	C₂²	C₅₉×#585	1	2	yes	—
789	C₄	—	2	2	no	—
790	C₄	—	2	2	no	—
791	C₄	—	2	8	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	4	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	4	no	—
797	C₄	C₂×#121×C₅₉	1	4	yes	—
798	C₄	C₂×#121×C₅₉	1	4	yes	—
799	C₂	—	2	4	no	—
800	C₂	—	2	4	no	—
801	C₂	—	4	2	no	—
802	C₂	—	8	4	no	—
803	C₂	—	8	2	no	—
804	C₂	C₂²×#121×C₅₉	1	1	yes	characteristic
805	C₂	C₂×C₅₉×#535	1	1	yes	characteristic
806	C₂	C₅₉×#3449	1	1	yes	characteristic
807	C₂	C₅₉×#3488	1	2	yes	—
808	C₂	C₅₉×#3494	1	2	yes	—

	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×#535	C₂	semidirect
2. C₂×C₅₉×#525	C₂	semidirect
3. C₂²×#121×C₅₉	C₂	semidirect
4. C₂²×#117×C₅₉	C₂	semidirect
5. C₅₉×#2856	C₂	semidirect
6. C₅₉×#2850	C₂	semidirect
7. C₅₉×#2620	C₂	semidirect
8. C₅₉×#2619	C₂	semidirect
9. C₅₉×#2416	C₂	semidirect
10. C₅₉×#2414	C₂	semidirect
11. C₅₉×#2411	C₂	semidirect
12. C₅₉×#2410	C₂	semidirect
13. C₅₉×#2317	C₂	semidirect
14. C₅₉×#2311	C₂	semidirect
15. C₅₉×#2309	C₂	semidirect
21. C₂×#127×C₅₉	C₂²	semidirect
22. C₂×#124×C₅₉	C₂²	semidirect
25. C₂×C₂²⋊Q₈×C₅₉	C₂²	semidirect
26. C₂×C₂²⋊Q₈×C₅₉	C₂²	semidirect
32. C₂×#121×C₅₉	C₂²	semidirect
33. C₂×#121×C₅₉	C₂²	semidirect
34. C₂×#121×C₅₉	C₂²	semidirect
35. C₂×#121×C₅₉	C₂²	semidirect
38. C₂×C₄×D₄×C₅₉	C₂²	semidirect
39. C₂×C₄×D₄×C₅₉	C₂²	semidirect
45. C₂×#117×C₅₉	C₂²	semidirect
46. C₂×#117×C₅₉	C₂²	semidirect
48. C₂²×C₄⋊C₄×C₅₉	C₂²	semidirect
51. C₂²×C₄²×C₅₉	C₂²	semidirect
52. C₅₉×#396	C₂²	semidirect
53. C₅₉×#394	C₂²	semidirect
54. C₅₉×#394	C₂²	semidirect
55. C₅₉×#392	C₂²	semidirect
56. C₅₉×#391	C₂²	semidirect
57. C₅₉×#390	C₂²	semidirect
58. C₅₉×#390	C₂²	semidirect
59. C₅₉×#390	C₂²	semidirect
60. C₅₉×#390	C₂²	semidirect
61. C₅₉×#390	C₂²	semidirect
62. C₅₉×#389	C₂²	semidirect
63. C₅₉×#388	C₂²	semidirect
65. C₅₉×#386	C₂²	semidirect
67. C₅₉×#384	C₂²	semidirect
68. C₅₉×#382	C₂²	semidirect
69. C₅₉×#380	C₂²	semidirect
93. C₂³×C₄×C₅₉	D₄	semidirect
125. #117×C₅₉	D₄	semidirect
251. C₄⋊C₄×C₅₉	C₂×D₄	semidirect
269. C₄²×C₅₉	C₂×D₄	semidirect
342. C₂×C₄×C₅₉	#121	semidirect
352. #35252	C₅₉	direct (N × H)
379. C₂²×C₅₉	#535	semidirect
395. C₂×#535	C₂×C₅₉	semidirect
396. C₂×#525	C₂×C₅₉	semidirect
397. C₂²×#121	C₂×C₅₉	semidirect
398. C₂²×#117	C₂×C₅₉	semidirect
399. #2856	C₂×C₅₉	semidirect
400. #2850	C₂×C₅₉	semidirect
401. #2620	C₂×C₅₉	semidirect
402. #2619	C₂×C₅₉	semidirect
403. #2416	C₂×C₅₉	semidirect
404. #2414	C₂×C₅₉	semidirect
405. #2411	C₂×C₅₉	semidirect
406. #2410	C₂×C₅₉	semidirect
407. #2317	C₂×C₅₉	semidirect
408. #2311	C₂×C₅₉	semidirect
409. #2309	C₂×C₅₉	semidirect
425. C₂×#127	C₂²×C₅₉	semidirect
426. C₂×#124	C₂²×C₅₉	semidirect
429. C₂×C₂²⋊Q₈	C₂²×C₅₉	semidirect
430. C₂×C₂²⋊Q₈	C₂²×C₅₉	semidirect
436. C₂×#121	C₂²×C₅₉	semidirect
437. C₂×#121	C₂²×C₅₉	semidirect
438. C₂×#121	C₂²×C₅₉	semidirect
439. C₂×#121	C₂²×C₅₉	semidirect
442. C₂×C₄×D₄	C₂²×C₅₉	semidirect
443. C₂×C₄×D₄	C₂²×C₅₉	semidirect
449. C₂×#117	C₂²×C₅₉	semidirect
450. C₂×#117	C₂²×C₅₉	semidirect
452. C₂²×C₄⋊C₄	C₂²×C₅₉	semidirect
455. C₂²×C₄²	C₂²×C₅₉	semidirect
456. #396	C₂²×C₅₉	semidirect
457. #394	C₂²×C₅₉	semidirect
458. #394	C₂²×C₅₉	semidirect
459. #392	C₂²×C₅₉	semidirect
460. #391	C₂²×C₅₉	semidirect
461. #390	C₂²×C₅₉	semidirect
462. #390	C₂²×C₅₉	semidirect
463. #390	C₂²×C₅₉	semidirect
464. #390	C₂²×C₅₉	semidirect
465. #390	C₂²×C₅₉	semidirect
466. #389	C₂²×C₅₉	semidirect
467. #388	C₂²×C₅₉	semidirect
469. #386	C₂²×C₅₉	semidirect
471. #384	C₂²×C₅₉	semidirect
472. #382	C₂²×C₅₉	semidirect
473. #380	C₂²×C₅₉	semidirect
475. C₅₉	#35252	direct (N × H)
498. C₂³×C₄	D₄×C₅₉	semidirect
530. #117	D₄×C₅₉	semidirect
656. C₄⋊C₄	C₂×D₄×C₅₉	semidirect
674. C₄²	C₂×D₄×C₅₉	semidirect
747. C₂×C₄	#121×C₅₉	semidirect
783. C₂²	C₅₉×#535	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅₉×#535	2
C₂×C₅₉×#525	2
C₂²×#121×C₅₉	2
C₂²×#117×C₅₉	2
C₅₉×#2856	2
C₅₉×#2850	2
C₅₉×#2620	2
C₅₉×#2619	2
C₅₉×#2416	2
C₅₉×#2414	2
C₅₉×#2411	2
C₅₉×#2410	2
C₅₉×#2317	2
C₅₉×#2311	2
C₅₉×#2309	2
#35252	59

Subgroups — C59×#35252 #28447361

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35252 #28447361