Subgroups — C₅₉×#35288 #28447397

Order 15104.

1978 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#2859	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₉×#2858	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2856	C₂	1	1	yes	maximal, characteristic
5	C₅₉×#2644	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2624	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2513	C₂	1	2	yes	maximal, complemented
8	C₅₉×#2490	C₂	1	2	yes	maximal, complemented
9	C₅₉×#2454	C₂	1	2	yes	maximal, complemented
10	C₅₉×#2448	C₂	1	2	yes	maximal, complemented
11	C₅₉×#2447	C₂	1	2	yes	maximal, complemented
12	C₅₉×#2427	C₂	1	2	yes	maximal, complemented
13	C₅₉×#2426	C₂	1	2	yes	maximal, complemented
14	C₅₉×#2420	C₂	1	2	yes	maximal, complemented
15	C₅₉×#2324	C₂	1	2	yes	maximal, complemented
16	C₅₉×#2319	C₂	1	2	yes	maximal, complemented
17	C₄×C₄⋊Q₈×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×#127×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#117×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×#127×C₅₉	C₂²	1	1	yes	characteristic
22	C₂×#125×C₅₉	C₂²	1	2	yes	—
23	C₂×#124×C₅₉	C₂²	1	2	yes	—
24	C₂×#124×C₅₉	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	—
26	C₂×#121×C₅₉	C₂²	1	2	yes	—
27	C₂×#121×C₅₉	C₂²	1	2	yes	—
28	C₂×#121×C₅₉	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
33	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
34	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
36	C₅₉×#399	C₂²	1	4	yes	—
37	C₅₉×#397	C₂²	1	4	yes	—
38	C₅₉×#397	C₂²	1	4	yes	—
39	C₅₉×#397	C₂²	1	4	yes	—
40	C₅₉×#397	C₂²	1	4	yes	—
41	C₅₉×#396	C₂²	1	4	yes	—
42	C₅₉×#394	C₂²	1	4	yes	—
43	C₅₉×#394	C₂²	1	4	yes	—
44	C₅₉×#391	C₂²	1	2	yes	—
45	C₅₉×#391	C₂²	1	2	yes	—
46	C₅₉×#390	C₂²	1	2	yes	—
47	C₅₉×#390	C₂²	1	4	yes	—
48	C₅₉×#390	C₂²	1	2	yes	—
49	C₅₉×#390	C₂²	1	2	yes	—
50	C₅₉×#390	C₂²	1	2	yes	—
51	C₅₉×#390	C₂²	1	2	yes	—
52	C₅₉×#390	C₂²	1	2	yes	—
53	C₅₉×#390	C₂²	1	2	yes	—
54	C₅₉×#390	C₂²	1	2	yes	—
55	C₅₉×#390	C₂²	1	2	yes	—
56	C₅₉×#390	C₂²	1	2	yes	—
57	C₅₉×#389	C₂²	1	2	yes	—
58	C₅₉×#389	C₂²	1	2	yes	—
59	C₅₉×#389	C₂²	1	2	yes	—
60	C₅₉×#389	C₂²	1	2	yes	—
61	C₅₉×#389	C₂²	1	2	yes	—
62	C₅₉×#389	C₂²	1	2	yes	—
63	C₅₉×#389	C₂²	1	2	yes	—
64	C₅₉×#389	C₂²	1	2	yes	—
65	C₅₉×#388	C₂²	1	4	yes	—
66	C₅₉×#388	C₂²	1	4	yes	—
67	C₅₉×#388	C₂²	1	4	yes	—
68	C₅₉×#386	C₂²	1	4	yes	—
69	C₅₉×#385	C₂²	1	4	yes	—
70	C₅₉×#384	C₂²	1	1	yes	characteristic
71	C₅₉×#384	C₂²	1	1	yes	characteristic
72	C₅₉×#382	C₂²	1	2	yes	—
73	C₅₉×#381	C₂²	1	4	yes	—
74	C₅₉×#380	C₂²	1	2	yes	—
75	C₅₉×#380	C₂²	1	4	yes	—
76	C₅₉×#380	C₂²	1	2	yes	—
77	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
78	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
79	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
80	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
81	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
82	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
83	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
84	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
85	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
86	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
87	C₅₉×#376	C₂²	1	1	yes	characteristic
88	C₅₉×#376	C₂²	1	1	yes	characteristic
89	C₄³×C₅₉	C₂²	1	1	yes	characteristic
90	C₄³×C₅₉	C₂²	1	1	yes	characteristic
91	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
92	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
93	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
94	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
95	C₂²×D₄×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	4	yes	—
100	C₄⋊Q₈×C₅₉	—	2	4	no	—
101	#127×C₅₉	—	2	4	no	—
102	#125×C₅₉	—	4	4	no	—
103	#124×C₅₉	—	4	4	no	—
104	#124×C₅₉	—	4	4	no	—
105	C₂²⋊Q₈×C₅₉	—	4	4	no	—
106	#121×C₅₉	—	2	8	no	—
107	#121×C₅₉	—	4	4	no	—
108	#121×C₅₉	—	4	4	no	—
109	C₄×Q₈×C₅₉	—	4	4	no	—
110	C₄×D₄×C₅₉	—	2	8	no	—
111	C₄×D₄×C₅₉	—	4	4	no	—
112	C₄×D₄×C₅₉	—	4	4	no	—
113	#117×C₅₉	—	2	4	no	—
114	#117×C₅₉	—	2	4	no	—
115	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
128	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
129	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
130	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
139	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
142	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
146	C₂×C₄²×C₅₉	—	2	4	no	—
147	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
148	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
149	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
152	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
155	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
156	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
162	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
164	#95×C₅₉	C₂³	1	1	yes	characteristic
165	#95×C₅₉	C₂³	1	1	yes	characteristic
166	#95×C₅₉	C₂³	1	1	yes	characteristic
167	#95×C₅₉	C₂³	1	1	yes	characteristic
168	#95×C₅₉	C₂³	1	1	yes	characteristic
169	#95×C₅₉	C₂³	1	1	yes	characteristic
170	#95×C₅₉	C₂³	1	1	yes	characteristic
171	#95×C₅₉	C₂³	1	1	yes	characteristic
172	#95×C₅₉	C₂³	1	4	yes	—
173	#95×C₅₉	C₂³	1	4	yes	—
174	#95×C₅₉	C₂³	1	4	yes	—
175	#95×C₅₉	C₂³	1	4	yes	—
176	#95×C₅₉	C₂³	1	4	yes	—
177	#95×C₅₉	C₂³	1	4	yes	—
178	C₂⁴×C₅₉	C₂⁴	1	4	yes	—
179	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
180	C₂×Q₈×C₅₉	—	2	4	no	—
181	C₂×Q₈×C₅₉	—	2	4	no	—
182	C₂×Q₈×C₅₉	—	2	4	no	—
183	C₂×D₄×C₅₉	—	2	8	no	—
184	C₂×D₄×C₅₉	—	2	4	no	—
185	C₂×D₄×C₅₉	—	2	4	no	—
186	C₂×D₄×C₅₉	—	2	4	no	—
187	C₂×D₄×C₅₉	—	2	4	no	—
188	C₂×D₄×C₅₉	—	2	4	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	4	no	—
193	C₂×D₄×C₅₉	—	4	4	no	—
194	C₂×D₄×C₅₉	—	4	4	no	—
195	C₂²×C₄×C₅₉	—	2	2	no	—
196	C₂²×C₄×C₅₉	—	2	2	no	—
197	C₂²×C₄×C₅₉	—	2	2	no	—
198	C₂²×C₄×C₅₉	—	2	2	no	—
199	C₂²×C₄×C₅₉	—	2	2	no	—
200	C₂²×C₄×C₅₉	—	2	2	no	—
201	C₂²×C₄×C₅₉	—	2	2	no	—
202	C₂²×C₄×C₅₉	—	2	2	no	—
203	C₂²×C₄×C₅₉	—	2	8	no	—
204	C₂²×C₄×C₅₉	—	4	4	no	—
205	C₂²×C₄×C₅₉	—	4	4	no	—
206	C₂²×C₄×C₅₉	#41	1	4	yes	—
207	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
208	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
210	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
213	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
214	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
215	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
217	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
218	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
224	C₄⋊C₄×C₅₉	—	2	2	no	—
225	C₄⋊C₄×C₅₉	—	2	2	no	—
226	C₄⋊C₄×C₅₉	—	2	2	no	—
227	C₄⋊C₄×C₅₉	—	2	2	no	—
228	C₄⋊C₄×C₅₉	—	2	4	no	—
229	C₄⋊C₄×C₅₉	—	2	4	no	—
230	C₄⋊C₄×C₅₉	—	2	4	no	—
231	C₄⋊C₄×C₅₉	—	2	4	no	—
232	C₄⋊C₄×C₅₉	—	2	4	no	—
233	C₄⋊C₄×C₅₉	—	2	4	no	—
234	C₄⋊C₄×C₅₉	—	2	4	no	—
235	C₄⋊C₄×C₅₉	—	2	4	no	—
236	C₄⋊C₄×C₅₉	—	4	4	no	—
237	C₄⋊C₄×C₅₉	—	4	4	no	—
238	C₄⋊C₄×C₅₉	—	4	4	no	—
239	C₄⋊C₄×C₅₉	—	4	4	no	—
240	C₂²⋊C₄×C₅₉	—	2	2	no	—
241	C₂²⋊C₄×C₅₉	—	2	2	no	—
242	C₂²⋊C₄×C₅₉	—	2	2	no	—
243	C₂²⋊C₄×C₅₉	—	2	2	no	—
244	C₂²⋊C₄×C₅₉	—	2	8	no	—
245	C₂²⋊C₄×C₅₉	—	2	8	no	—
246	C₂²⋊C₄×C₅₉	—	4	4	no	—
247	C₂²⋊C₄×C₅₉	—	4	4	no	—
248	C₂²⋊C₄×C₅₉	—	4	4	no	—
249	C₂²⋊C₄×C₅₉	—	4	4	no	—
250	C₂²⋊C₄×C₅₉	—	4	4	no	—
251	C₂²⋊C₄×C₅₉	—	4	4	no	—
252	C₂²⋊C₄×C₅₉	—	4	4	no	—
253	C₂²⋊C₄×C₅₉	—	4	4	no	—
254	C₂²⋊C₄×C₅₉	—	4	4	no	—
255	C₄²×C₅₉	—	2	2	no	—
256	C₄²×C₅₉	—	2	2	no	—
257	C₄²×C₅₉	—	2	2	no	—
258	C₄²×C₅₉	—	2	2	no	—
259	C₄²×C₅₉	—	2	2	no	—
260	C₄²×C₅₉	—	2	2	no	—
261	C₄²×C₅₉	—	2	2	no	—
262	C₄²×C₅₉	—	2	2	no	—
263	C₄²×C₅₉	—	2	2	no	—
264	C₄²×C₅₉	—	2	2	no	—
265	C₄²×C₅₉	—	2	2	no	—
266	C₄²×C₅₉	—	2	2	no	—
267	C₄²×C₅₉	—	2	2	no	—
268	C₄²×C₅₉	—	2	2	no	—
269	C₄²×C₅₉	—	4	4	no	—
270	C₄²×C₅₉	#41	1	4	yes	—
271	C₄²×C₅₉	#41	1	4	yes	—
272	C₂³×C₅₉	—	2	1	no	—
273	C₂³×C₅₉	—	2	1	no	—
274	C₂³×C₅₉	—	2	1	no	—
275	C₂³×C₅₉	—	2	1	no	—
276	C₂³×C₅₉	—	2	1	no	—
277	C₂³×C₅₉	—	2	1	no	—
278	C₂³×C₅₉	—	2	4	no	—
279	C₂³×C₅₉	—	2	4	no	—
280	C₂³×C₅₉	—	2	4	no	—
281	C₂³×C₅₉	—	2	4	no	—
282	C₂³×C₅₉	—	2	4	no	—
283	C₂³×C₅₉	—	2	4	no	—
284	C₂³×C₅₉	—	2	4	no	—
285	C₂³×C₅₉	C₂×#41	1	2	yes	—
286	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
287	Q₈×C₅₉	—	4	8	no	—
288	D₄×C₅₉	—	4	8	no	—
289	D₄×C₅₉	—	4	8	no	—
290	D₄×C₅₉	—	4	8	no	—
291	D₄×C₅₉	—	8	8	no	—
292	C₂×C₄×C₅₉	—	2	1	no	—
293	C₂×C₄×C₅₉	—	2	1	no	—
294	C₂×C₄×C₅₉	—	2	1	no	—
295	C₂×C₄×C₅₉	—	2	1	no	—
296	C₂×C₄×C₅₉	—	2	1	no	—
297	C₂×C₄×C₅₉	—	2	1	no	—
298	C₂×C₄×C₅₉	—	2	8	no	—
299	C₂×C₄×C₅₉	—	2	1	no	—
300	C₂×C₄×C₅₉	—	2	1	no	—
301	C₂×C₄×C₅₉	—	2	1	no	—
302	C₂×C₄×C₅₉	—	2	1	no	—
303	C₂×C₄×C₅₉	—	2	1	no	—
304	C₂×C₄×C₅₉	—	2	1	no	—
305	C₂×C₄×C₅₉	—	2	1	no	—
306	C₂×C₄×C₅₉	—	2	1	no	—
307	C₂×C₄×C₅₉	—	2	4	no	—
308	C₂×C₄×C₅₉	—	2	4	no	—
309	C₂×C₄×C₅₉	—	2	4	no	—
310	C₂×C₄×C₅₉	—	2	1	no	—
311	C₂×C₄×C₅₉	—	2	1	no	—
312	C₂×C₄×C₅₉	—	2	1	no	—
313	C₂×C₄×C₅₉	—	2	1	no	—
314	C₂×C₄×C₅₉	—	2	1	no	—
315	C₂×C₄×C₅₉	—	2	1	no	—
316	C₂×C₄×C₅₉	—	2	1	no	—
317	C₂×C₄×C₅₉	—	2	1	no	—
318	C₂×C₄×C₅₉	—	2	1	no	—
319	C₂×C₄×C₅₉	—	2	4	no	—
320	C₂×C₄×C₅₉	—	2	4	no	—
321	C₂×C₄×C₅₉	—	2	1	no	—
322	C₂×C₄×C₅₉	—	2	1	no	—
323	C₂×C₄×C₅₉	—	2	4	no	—
324	C₂×C₄×C₅₉	—	2	4	no	—
325	C₂×C₄×C₅₉	—	2	4	no	—
326	C₂×C₄×C₅₉	—	2	4	no	—
327	C₂×C₄×C₅₉	—	2	1	no	—
328	C₂×C₄×C₅₉	—	2	1	no	—
329	C₂×C₄×C₅₉	—	2	1	no	—
330	C₂×C₄×C₅₉	—	2	1	no	—
331	C₂×C₄×C₅₉	—	2	1	no	—
332	C₂×C₄×C₅₉	—	4	4	no	—
333	C₂×C₄×C₅₉	—	4	4	no	—
334	C₂×C₄×C₅₉	—	8	8	no	—
335	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
336	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
337	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
338	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
339	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
340	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
341	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
342	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
343	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
344	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
345	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
346	C₂×C₄×C₅₉	2₋¹⁺⁴	1	2	yes	—
347	#35288	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
348	C₂²×C₅₉	—	2	2	no	—
349	C₂²×C₅₉	—	2	2	no	—
350	C₂²×C₅₉	—	2	2	no	—
351	C₂²×C₅₉	—	4	1	no	—
352	C₂²×C₅₉	—	4	1	no	—
353	C₂²×C₅₉	—	4	1	no	—
354	C₂²×C₅₉	—	4	1	no	—
355	C₂²×C₅₉	—	4	4	no	—
356	C₂²×C₅₉	—	4	4	no	—
357	C₂²×C₅₉	—	4	4	no	—
358	C₂²×C₅₉	—	4	4	no	—
359	C₂²×C₅₉	—	4	4	no	—
360	C₂²×C₅₉	—	4	4	no	—
361	C₂²×C₅₉	—	4	4	no	—
362	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
363	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
364	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
365	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
366	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
367	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
368	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
369	C₄×C₅₉	—	2	2	no	—
370	C₄×C₅₉	—	2	2	no	—
371	C₄×C₅₉	—	2	2	no	—
372	C₄×C₅₉	—	4	1	no	—
373	C₄×C₅₉	—	4	4	no	—
374	C₄×C₅₉	—	4	1	no	—
375	C₄×C₅₉	—	4	1	no	—
376	C₄×C₅₉	—	4	1	no	—
377	C₄×C₅₉	—	4	1	no	—
378	C₄×C₅₉	—	4	4	no	—
379	C₄×C₅₉	—	4	4	no	—
380	C₄×C₅₉	—	4	1	no	—
381	C₄×C₅₉	—	4	1	no	—
382	C₄×C₅₉	—	4	1	no	—
383	C₄×C₅₉	#529	1	4	yes	—
384	C₄×C₅₉	#540	1	4	yes	—
385	C₄×C₅₉	#542	1	4	yes	—
386	#2859	C₂×C₅₉	1	1	yes	characteristic, complemented
387	#2858	C₂×C₅₉	1	1	yes	characteristic, complemented
388	#2857	C₂×C₅₉	1	1	yes	characteristic, complemented
389	#2856	C₂×C₅₉	1	1	yes	characteristic
390	#2644	C₂×C₅₉	1	2	yes	complemented
391	#2624	C₂×C₅₉	1	2	yes	complemented
392	#2513	C₂×C₅₉	1	2	yes	complemented
393	#2490	C₂×C₅₉	1	2	yes	complemented
394	#2454	C₂×C₅₉	1	2	yes	complemented
395	#2448	C₂×C₅₉	1	2	yes	complemented
396	#2447	C₂×C₅₉	1	2	yes	complemented
397	#2427	C₂×C₅₉	1	2	yes	complemented
398	#2426	C₂×C₅₉	1	2	yes	complemented
399	#2420	C₂×C₅₉	1	2	yes	complemented
400	#2324	C₂×C₅₉	1	2	yes	complemented
401	#2319	C₂×C₅₉	1	2	yes	complemented
402	C₄×C₄⋊Q₈	C₂×C₅₉	1	1	yes	characteristic, complemented
403	C₄×#127	C₂×C₅₉	1	1	yes	characteristic, complemented
404	C₄×#117	C₂×C₅₉	1	1	yes	characteristic, complemented
405	C₂×C₅₉	—	4	2	no	—
406	C₂×C₅₉	—	8	4	no	—
407	C₂×C₅₉	C₂×#529	1	1	yes	characteristic
408	C₂×C₅₉	C₂×#540	1	1	yes	characteristic
409	C₂×C₅₉	C₂×#542	1	1	yes	characteristic
410	C₂×C₅₉	#3508	1	1	yes	characteristic
411	C₂×C₅₉	#3508	1	1	yes	characteristic
412	C₂×C₅₉	#3511	1	1	yes	characteristic
413	C₂×C₅₉	#3511	1	1	yes	characteristic
414	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
415	C₂×#127	C₂²×C₅₉	1	1	yes	characteristic
416	C₂×#125	C₂²×C₅₉	1	2	yes	—
417	C₂×#124	C₂²×C₅₉	1	2	yes	—
418	C₂×#124	C₂²×C₅₉	1	2	yes	—
419	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	—
420	C₂×#121	C₂²×C₅₉	1	2	yes	—
421	C₂×#121	C₂²×C₅₉	1	2	yes	—
422	C₂×#121	C₂²×C₅₉	1	2	yes	—
423	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
424	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
425	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
426	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
427	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
428	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
429	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
430	#399	C₂²×C₅₉	1	4	yes	—
431	#397	C₂²×C₅₉	1	4	yes	—
432	#397	C₂²×C₅₉	1	4	yes	—
433	#397	C₂²×C₅₉	1	4	yes	—
434	#397	C₂²×C₅₉	1	4	yes	—
435	#396	C₂²×C₅₉	1	4	yes	—
436	#394	C₂²×C₅₉	1	4	yes	—
437	#394	C₂²×C₅₉	1	4	yes	—
438	#391	C₂²×C₅₉	1	2	yes	—
439	#391	C₂²×C₅₉	1	2	yes	—
440	#390	C₂²×C₅₉	1	2	yes	—
441	#390	C₂²×C₅₉	1	2	yes	—
442	#390	C₂²×C₅₉	1	2	yes	—
443	#390	C₂²×C₅₉	1	2	yes	—
444	#390	C₂²×C₅₉	1	2	yes	—
445	#390	C₂²×C₅₉	1	2	yes	—
446	#390	C₂²×C₅₉	1	4	yes	—
447	#390	C₂²×C₅₉	1	2	yes	—
448	#390	C₂²×C₅₉	1	2	yes	—
449	#390	C₂²×C₅₉	1	2	yes	—
450	#390	C₂²×C₅₉	1	2	yes	—
451	#389	C₂²×C₅₉	1	2	yes	—
452	#389	C₂²×C₅₉	1	2	yes	—
453	#389	C₂²×C₅₉	1	2	yes	—
454	#389	C₂²×C₅₉	1	2	yes	—
455	#389	C₂²×C₅₉	1	2	yes	—
456	#389	C₂²×C₅₉	1	2	yes	—
457	#389	C₂²×C₅₉	1	2	yes	—
458	#389	C₂²×C₅₉	1	2	yes	—
459	#388	C₂²×C₅₉	1	4	yes	—
460	#388	C₂²×C₅₉	1	4	yes	—
461	#388	C₂²×C₅₉	1	4	yes	—
462	#386	C₂²×C₅₉	1	4	yes	—
463	#385	C₂²×C₅₉	1	4	yes	—
464	#384	C₂²×C₅₉	1	1	yes	characteristic
465	#384	C₂²×C₅₉	1	1	yes	characteristic
466	#382	C₂²×C₅₉	1	2	yes	—
467	#381	C₂²×C₅₉	1	4	yes	—
468	#380	C₂²×C₅₉	1	4	yes	—
469	#380	C₂²×C₅₉	1	2	yes	—
470	#380	C₂²×C₅₉	1	2	yes	—
471	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
472	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
473	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
474	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
475	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
476	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
477	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
478	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
479	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
480	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
481	#376	C₂²×C₅₉	1	1	yes	characteristic
482	#376	C₂²×C₅₉	1	1	yes	characteristic
483	C₄³	C₂²×C₅₉	1	1	yes	characteristic
484	C₄³	C₂²×C₅₉	1	1	yes	characteristic
485	C₅₉	#35288	1	1	yes	characteristic, direct product factor, Sylow
486	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
487	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
488	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
489	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
490	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
491	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
492	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
493	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
494	C₂³×C₄	C₂³×C₅₉	1	4	yes	—
495	C₄⋊Q₈	—	2	4	no	—
496	#127	—	2	4	no	—
497	#125	—	4	4	no	—
498	#124	—	4	4	no	—
499	#124	—	4	4	no	—
500	C₂²⋊Q₈	—	4	4	no	—
501	#121	—	2	8	no	—
502	#121	—	4	4	no	—
503	#121	—	4	4	no	—
504	C₄×Q₈	—	4	4	no	—
505	C₄×D₄	—	2	8	no	—
506	C₄×D₄	—	4	4	no	—
507	C₄×D₄	—	4	4	no	—
508	#117	—	2	4	no	—
509	#117	—	2	4	no	—
510	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
511	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
512	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
513	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
523	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
524	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
525	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
527	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
528	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
529	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
530	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
541	C₂×C₄²	—	2	4	no	—
542	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
543	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
544	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
545	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
546	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
547	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
548	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
549	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
550	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
551	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
552	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
553	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
554	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
555	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
556	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
557	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
558	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
559	#95	C₂³×C₅₉	1	1	yes	characteristic
560	#95	C₂³×C₅₉	1	1	yes	characteristic
561	#95	C₂³×C₅₉	1	1	yes	characteristic
562	#95	C₂³×C₅₉	1	1	yes	characteristic
563	#95	C₂³×C₅₉	1	1	yes	characteristic
564	#95	C₂³×C₅₉	1	1	yes	characteristic
565	#95	C₂³×C₅₉	1	1	yes	characteristic
566	#95	C₂³×C₅₉	1	1	yes	characteristic
567	#95	C₂³×C₅₉	1	4	yes	—
568	#95	C₂³×C₅₉	1	4	yes	—
569	#95	C₂³×C₅₉	1	4	yes	—
570	#95	C₂³×C₅₉	1	4	yes	—
571	#95	C₂³×C₅₉	1	4	yes	—
572	#95	C₂³×C₅₉	1	4	yes	—
573	C₂⁴	C₂⁴×C₅₉	1	4	yes	—
574	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
575	C₂×Q₈	—	2	4	no	—
576	C₂×Q₈	—	2	4	no	—
577	C₂×Q₈	—	2	4	no	—
578	C₂×D₄	—	2	8	no	—
579	C₂×D₄	—	2	4	no	—
580	C₂×D₄	—	2	4	no	—
581	C₂×D₄	—	2	4	no	—
582	C₂×D₄	—	2	4	no	—
583	C₂×D₄	—	2	4	no	—
584	C₂×D₄	—	2	4	no	—
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	—	2	4	no	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	4	4	no	—
589	C₂×D₄	—	4	4	no	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	2	no	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	2	2	no	—
595	C₂²×C₄	—	2	2	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	2	no	—
598	C₂²×C₄	—	2	8	no	—
599	C₂²×C₄	—	4	4	no	—
600	C₂²×C₄	—	4	4	no	—
601	C₂²×C₄	#41×C₅₉	1	4	yes	—
602	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
603	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
604	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
605	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
606	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
608	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
609	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
610	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
611	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
612	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
613	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
614	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
615	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
616	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
617	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
618	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	4	4	no	—
632	C₄⋊C₄	—	4	4	no	—
633	C₄⋊C₄	—	4	4	no	—
634	C₄⋊C₄	—	4	4	no	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	2	2	no	—
637	C₂²⋊C₄	—	2	2	no	—
638	C₂²⋊C₄	—	2	2	no	—
639	C₂²⋊C₄	—	2	8	no	—
640	C₂²⋊C₄	—	2	8	no	—
641	C₂²⋊C₄	—	4	4	no	—
642	C₂²⋊C₄	—	4	4	no	—
643	C₂²⋊C₄	—	4	4	no	—
644	C₂²⋊C₄	—	4	4	no	—
645	C₂²⋊C₄	—	4	4	no	—
646	C₂²⋊C₄	—	4	4	no	—
647	C₂²⋊C₄	—	4	4	no	—
648	C₂²⋊C₄	—	4	4	no	—
649	C₂²⋊C₄	—	4	4	no	—
650	C₄²	—	2	2	no	—
651	C₄²	—	2	2	no	—
652	C₄²	—	2	2	no	—
653	C₄²	—	2	2	no	—
654	C₄²	—	2	2	no	—
655	C₄²	—	2	2	no	—
656	C₄²	—	2	2	no	—
657	C₄²	—	2	2	no	—
658	C₄²	—	2	2	no	—
659	C₄²	—	2	2	no	—
660	C₄²	—	2	2	no	—
661	C₄²	—	2	2	no	—
662	C₄²	—	2	2	no	—
663	C₄²	—	2	2	no	—
664	C₄²	—	4	4	no	—
665	C₄²	#41×C₅₉	1	4	yes	—
666	C₄²	#41×C₅₉	1	4	yes	—
667	C₂³	—	2	1	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	1	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	1	no	—
673	C₂³	—	2	4	no	—
674	C₂³	—	2	4	no	—
675	C₂³	—	2	4	no	—
676	C₂³	—	2	4	no	—
677	C₂³	—	2	4	no	—
678	C₂³	—	2	4	no	—
679	C₂³	—	2	4	no	—
680	C₂³	C₂×#41×C₅₉	1	2	yes	—
681	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
682	Q₈	—	4	8	no	—
683	D₄	—	4	8	no	—
684	D₄	—	4	8	no	—
685	D₄	—	4	8	no	—
686	D₄	—	8	8	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	8	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	4	no	—
703	C₂×C₄	—	2	4	no	—
704	C₂×C₄	—	2	4	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	4	no	—
715	C₂×C₄	—	2	4	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	4	no	—
719	C₂×C₄	—	2	4	no	—
720	C₂×C₄	—	2	4	no	—
721	C₂×C₄	—	2	4	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	1	no	—
727	C₂×C₄	—	4	4	no	—
728	C₂×C₄	—	4	4	no	—
729	C₂×C₄	—	8	8	no	—
730	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
731	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
732	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
733	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
734	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
735	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
736	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
737	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
738	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
739	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
740	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
741	C₂×C₄	2₋¹⁺⁴×C₅₉	1	2	yes	—
742	C₂²	—	2	2	no	—
743	C₂²	—	2	2	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	4	1	no	—
746	C₂²	—	4	1	no	—
747	C₂²	—	4	1	no	—
748	C₂²	—	4	1	no	—
749	C₂²	—	4	4	no	—
750	C₂²	—	4	4	no	—
751	C₂²	—	4	4	no	—
752	C₂²	—	4	4	no	—
753	C₂²	—	4	4	no	—
754	C₂²	—	4	4	no	—
755	C₂²	—	4	4	no	—
756	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
757	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
758	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
759	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
760	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
761	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
762	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
763	C₄	—	2	2	no	—
764	C₄	—	2	2	no	—
765	C₄	—	2	2	no	—
766	C₄	—	4	4	no	—
767	C₄	—	4	4	no	—
768	C₄	—	4	1	no	—
769	C₄	—	4	1	no	—
770	C₄	—	4	1	no	—
771	C₄	—	4	1	no	—
772	C₄	—	4	1	no	—
773	C₄	—	4	1	no	—
774	C₄	—	4	1	no	—
775	C₄	—	4	4	no	—
776	C₄	—	4	1	no	—
777	C₄	C₅₉×#529	1	4	yes	—
778	C₄	C₅₉×#540	1	4	yes	—
779	C₄	C₅₉×#542	1	4	yes	—
780	C₂	—	4	2	no	—
781	C₂	—	8	4	no	—
782	C₂	C₂×C₅₉×#529	1	1	yes	characteristic
783	C₂	C₂×C₅₉×#540	1	1	yes	characteristic
784	C₂	C₂×C₅₉×#542	1	1	yes	characteristic
785	C₂	C₅₉×#3508	1	1	yes	characteristic
786	C₂	C₅₉×#3508	1	1	yes	characteristic
787	C₂	C₅₉×#3511	1	1	yes	characteristic
788	C₂	C₅₉×#3511	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₅₉×#2856	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₅₉×#2859	C₂	semidirect
2. C₅₉×#2858	C₂	semidirect
3. C₅₉×#2857	C₂	semidirect
5. C₅₉×#2644	C₂	semidirect
6. C₅₉×#2624	C₂	semidirect
7. C₅₉×#2513	C₂	semidirect
8. C₅₉×#2490	C₂	semidirect
9. C₅₉×#2454	C₂	semidirect
10. C₅₉×#2448	C₂	semidirect
11. C₅₉×#2447	C₂	semidirect
12. C₅₉×#2427	C₂	semidirect
13. C₅₉×#2426	C₂	semidirect
14. C₅₉×#2420	C₂	semidirect
15. C₅₉×#2324	C₂	semidirect
16. C₅₉×#2319	C₂	semidirect
17. C₄×C₄⋊Q₈×C₅₉	C₂	semidirect
18. C₄×#127×C₅₉	C₂	semidirect
19. C₄×#117×C₅₉	C₂	semidirect
347. #35288	C₅₉	direct (N × H)
386. #2859	C₂×C₅₉	semidirect
387. #2858	C₂×C₅₉	semidirect
388. #2857	C₂×C₅₉	semidirect
390. #2644	C₂×C₅₉	semidirect
391. #2624	C₂×C₅₉	semidirect
392. #2513	C₂×C₅₉	semidirect
393. #2490	C₂×C₅₉	semidirect
394. #2454	C₂×C₅₉	semidirect
395. #2448	C₂×C₅₉	semidirect
396. #2447	C₂×C₅₉	semidirect
397. #2427	C₂×C₅₉	semidirect
398. #2426	C₂×C₅₉	semidirect
399. #2420	C₂×C₅₉	semidirect
400. #2324	C₂×C₅₉	semidirect
401. #2319	C₂×C₅₉	semidirect
402. C₄×C₄⋊Q₈	C₂×C₅₉	semidirect
403. C₄×#127	C₂×C₅₉	semidirect
404. C₄×#117	C₂×C₅₉	semidirect
485. C₅₉	#35288	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₉×#2859	2
C₅₉×#2858	2
C₅₉×#2857	2
C₅₉×#2856	2
C₅₉×#2644	2
C₅₉×#2624	2
C₅₉×#2513	2
C₅₉×#2490	2
C₅₉×#2454	2
C₅₉×#2448	2
C₅₉×#2447	2
C₅₉×#2427	2
C₅₉×#2426	2
C₅₉×#2420	2
C₅₉×#2324	2
C₅₉×#2319	2
C₄×C₄⋊Q₈×C₅₉	2
C₄×#127×C₅₉	2
C₄×#117×C₅₉	2
#35288	59

Subgroups — C59×#35288 #28447397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35288 #28447397