Subgroups — C₅₉×#35706 #28447815

Order 15104.

2038 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#2653	C₂	1	2	yes	maximal, complemented
2	C₅₉×#2617	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2572	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2569	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2557	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2527	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2523	C₂	1	2	yes	maximal, complemented
8	C₅₉×#2510	C₂	1	2	yes	maximal, complemented
9	C₅₉×#2459	C₂	1	2	yes	maximal, complemented
10	C₅₉×#2458	C₂	1	2	yes	maximal, complemented
11	C₅₉×#2436	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#2412	C₂	1	2	yes	maximal, complemented
13	C₅₉×#2398	C₂	1	2	yes	maximal, complemented
14	C₂×C₅₉×#393	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#2364	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₉×#2358	C₂	1	2	yes	maximal, complemented
17	C₅₉×#2353	C₂	1	2	yes	maximal, complemented
18	Q₈×C₂²⋊C₄×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₉×#2273	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂³×Q₈×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×#124×C₅₉	C₂²	1	2	yes	complemented
22	C₂×#123×C₅₉	C₂²	1	2	yes	—
23	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
24	C₂×#120×C₅₉	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	complemented
26	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
28	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
31	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
32	C₅₉×#401	C₂²	1	2	yes	complemented
33	C₅₉×#400	C₂²	1	2	yes	complemented
34	C₅₉×#400	C₂²	1	2	yes	complemented
35	C₅₉×#398	C₂²	1	2	yes	complemented
36	C₅₉×#397	C₂²	1	1	yes	characteristic
37	C₅₉×#397	C₂²	1	2	yes	—
38	C₅₉×#397	C₂²	1	2	yes	—
39	C₅₉×#397	C₂²	1	1	yes	characteristic
40	C₅₉×#397	C₂²	1	2	yes	complemented
41	C₅₉×#397	C₂²	1	2	yes	complemented
42	C₅₉×#394	C₂²	1	2	yes	—
43	C₅₉×#394	C₂²	1	2	yes	—
44	C₅₉×#394	C₂²	1	2	yes	—
45	C₅₉×#394	C₂²	1	2	yes	—
46	C₅₉×#393	C₂²	1	2	yes	—
47	C₅₉×#393	C₂²	1	2	yes	—
48	C₅₉×#393	C₂²	1	1	yes	characteristic
49	C₅₉×#393	C₂²	1	1	yes	characteristic
50	C₅₉×#393	C₂²	1	1	yes	characteristic
51	C₅₉×#393	C₂²	1	1	yes	characteristic
52	C₅₉×#393	C₂²	1	2	yes	complemented
53	C₅₉×#393	C₂²	1	2	yes	complemented
54	C₅₉×#392	C₂²	1	1	yes	characteristic
55	C₅₉×#392	C₂²	1	1	yes	characteristic
56	C₅₉×#391	C₂²	1	2	yes	complemented
57	C₅₉×#391	C₂²	1	2	yes	complemented
58	C₅₉×#391	C₂²	1	2	yes	complemented
59	C₅₉×#391	C₂²	1	2	yes	complemented
60	C₅₉×#390	C₂²	1	2	yes	—
61	C₅₉×#388	C₂²	1	2	yes	—
62	C₅₉×#388	C₂²	1	2	yes	—
63	C₅₉×#388	C₂²	1	2	yes	complemented
64	C₅₉×#388	C₂²	1	2	yes	complemented
65	C₅₉×#388	C₂²	1	2	yes	complemented
66	C₅₉×#388	C₂²	1	2	yes	complemented
67	C₅₉×#388	C₂²	1	2	yes	complemented
68	C₅₉×#387	C₂²	1	2	yes	complemented
69	C₅₉×#387	C₂²	1	2	yes	complemented
70	C₅₉×#387	C₂²	1	2	yes	complemented
71	C₅₉×#387	C₂²	1	2	yes	complemented
72	C₅₉×#387	C₂²	1	2	yes	complemented
73	C₅₉×#387	C₂²	1	2	yes	complemented
74	C₅₉×#386	C₂²	1	2	yes	—
75	C₅₉×#386	C₂²	1	2	yes	—
76	C₅₉×#386	C₂²	1	2	yes	—
77	C₅₉×#386	C₂²	1	2	yes	—
78	C₅₉×#386	C₂²	1	2	yes	—
79	C₅₉×#386	C₂²	1	2	yes	—
80	C₅₉×#386	C₂²	1	2	yes	—
81	C₅₉×#386	C₂²	1	2	yes	complemented
82	C₅₉×#385	C₂²	1	2	yes	—
83	C₅₉×#385	C₂²	1	2	yes	—
84	C₅₉×#385	C₂²	1	2	yes	—
85	C₅₉×#383	C₂²	1	2	yes	complemented
86	C₅₉×#383	C₂²	1	2	yes	complemented
87	C₅₉×#381	C₂²	1	2	yes	—
88	C₅₉×#381	C₂²	1	2	yes	complemented
89	C₅₉×#380	C₂²	1	2	yes	—
90	C₅₉×#380	C₂²	1	1	yes	characteristic
91	C₅₉×#380	C₂²	1	2	yes	—
92	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
93	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
94	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
95	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
96	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
97	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
99	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
100	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	complemented
103	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	complemented
104	C₅₉×#376	C₂²	1	2	yes	complemented
105	C₂×#95×C₅₉	C₂²	1	2	yes	—
106	C₂×#95×C₅₉	C₂²	1	1	yes	characteristic
107	C₂⁵×C₅₉	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₅₉	—	2	4	no	—
109	C₂²×Q₈×C₅₉	—	4	4	no	—
110	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
111	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
112	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
114	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
115	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
116	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
118	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
120	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
121	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
122	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
123	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
124	#124×C₅₉	—	4	4	no	—
125	#123×C₅₉	—	4	4	no	—
126	#121×C₅₉	—	2	4	no	—
127	#120×C₅₉	—	2	8	no	—
128	C₄×Q₈×C₅₉	—	4	4	no	—
129	C₄×D₄×C₅₉	—	2	8	no	—
130	C₄×D₄×C₅₉	—	4	4	no	—
131	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₅₉	—	2	4	no	—
141	C₂×C₂²⋊C₄×C₅₉	—	2	4	no	—
142	C₂×C₂²⋊C₄×C₅₉	—	2	4	no	—
143	C₂×C₂²⋊C₄×C₅₉	—	4	4	no	—
144	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
146	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
150	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
151	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
172	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
173	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
174	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
175	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
176	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
177	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
178	#95×C₅₉	C₂³	1	2	yes	—
179	#95×C₅₉	C₂³	1	1	yes	characteristic
180	#95×C₅₉	C₂³	1	2	yes	—
181	#95×C₅₉	C₂³	1	2	yes	—
182	#95×C₅₉	C₂³	1	2	yes	—
183	#95×C₅₉	C₂³	1	2	yes	—
184	#95×C₅₉	C₂³	1	1	yes	characteristic
185	#95×C₅₉	C₂³	1	2	yes	—
186	#95×C₅₉	C₂³	1	2	yes	—
187	#95×C₅₉	C₂³	1	2	yes	—
188	#95×C₅₉	C₂³	1	2	yes	—
189	#95×C₅₉	C₂³	1	2	yes	—
190	#95×C₅₉	C₂³	1	2	yes	—
191	#95×C₅₉	C₂³	1	2	yes	—
192	#95×C₅₉	C₂³	1	2	yes	—
193	#95×C₅₉	C₂³	1	2	yes	—
194	#95×C₅₉	C₂³	1	2	yes	—
195	#95×C₅₉	C₂³	1	2	yes	—
196	#95×C₅₉	C₂³	1	2	yes	—
197	#95×C₅₉	C₂³	1	2	yes	—
198	#95×C₅₉	C₂³	1	2	yes	—
199	#95×C₅₉	C₂³	1	2	yes	—
200	#95×C₅₉	C₂³	1	1	yes	characteristic
201	#95×C₅₉	C₂³	1	1	yes	characteristic
202	#95×C₅₉	C₂³	1	2	yes	—
203	#95×C₅₉	C₂³	1	2	yes	—
204	#95×C₅₉	C₂³	1	2	yes	—
205	#95×C₅₉	C₂³	1	2	yes	—
206	#95×C₅₉	C₂³	1	2	yes	—
207	C₂⁴×C₅₉	—	2	2	no	—
208	C₂⁴×C₅₉	—	2	2	no	—
209	C₂⁴×C₅₉	—	4	2	no	—
210	C₂⁴×C₅₉	—	4	2	no	—
211	C₂⁴×C₅₉	#41	1	4	yes	—
212	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
213	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
214	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
215	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
216	C₂×Q₈×C₅₉	—	2	2	no	—
217	C₂×Q₈×C₅₉	—	2	4	no	—
218	C₂×Q₈×C₅₉	—	2	2	no	—
219	C₂×Q₈×C₅₉	—	2	4	no	—
220	C₂×Q₈×C₅₉	—	2	4	no	—
221	C₂×Q₈×C₅₉	—	4	2	no	—
222	C₂×Q₈×C₅₉	—	4	2	no	—
223	C₂×Q₈×C₅₉	—	4	16	no	—
224	C₂×D₄×C₅₉	—	2	4	no	—
225	C₂×D₄×C₅₉	—	2	4	no	—
226	C₂×D₄×C₅₉	—	2	4	no	—
227	C₂×D₄×C₅₉	—	2	4	no	—
228	C₂×D₄×C₅₉	—	2	4	no	—
229	C₂×D₄×C₅₉	—	2	2	no	—
230	C₂×D₄×C₅₉	—	4	2	no	—
231	C₂×D₄×C₅₉	—	4	2	no	—
232	C₂×D₄×C₅₉	—	4	2	no	—
233	C₂×D₄×C₅₉	—	4	2	no	—
234	C₂×D₄×C₅₉	—	4	2	no	—
235	C₂²×C₄×C₅₉	—	2	4	no	—
236	C₂²×C₄×C₅₉	—	2	4	no	—
237	C₂²×C₄×C₅₉	—	2	2	no	—
238	C₂²×C₄×C₅₉	—	2	4	no	—
239	C₂²×C₄×C₅₉	—	2	4	no	—
240	C₂²×C₄×C₅₉	—	2	4	no	—
241	C₂²×C₄×C₅₉	—	2	4	no	—
242	C₂²×C₄×C₅₉	—	4	2	no	—
243	C₂²×C₄×C₅₉	—	4	2	no	—
244	C₂²×C₄×C₅₉	—	4	2	no	—
245	C₂²×C₄×C₅₉	—	4	2	no	—
246	C₂²×C₄×C₅₉	—	4	2	no	—
247	C₂²×C₄×C₅₉	—	4	2	no	—
248	C₂²×C₄×C₅₉	—	4	2	no	—
249	C₂²×C₄×C₅₉	—	4	2	no	—
250	C₂²×C₄×C₅₉	—	4	2	no	—
251	C₂²×C₄×C₅₉	—	4	2	no	—
252	C₂²×C₄×C₅₉	—	4	2	no	—
253	C₂²×C₄×C₅₉	#41	1	4	yes	—
254	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
269	C₄⋊C₄×C₅₉	—	2	4	no	—
270	C₄⋊C₄×C₅₉	—	2	2	no	—
271	C₄⋊C₄×C₅₉	—	2	4	no	—
272	C₄⋊C₄×C₅₉	—	4	2	no	—
273	C₄⋊C₄×C₅₉	—	4	2	no	—
274	C₄⋊C₄×C₅₉	—	4	2	no	—
275	C₄⋊C₄×C₅₉	—	4	2	no	—
276	C₄⋊C₄×C₅₉	—	4	2	no	—
277	C₄⋊C₄×C₅₉	—	4	2	no	—
278	C₂²⋊C₄×C₅₉	—	2	4	no	—
279	C₂²⋊C₄×C₅₉	—	2	2	no	—
280	C₂²⋊C₄×C₅₉	—	2	2	no	—
281	C₂²⋊C₄×C₅₉	—	2	2	no	—
282	C₂²⋊C₄×C₅₉	—	2	4	no	—
283	C₂²⋊C₄×C₅₉	—	2	4	no	—
284	C₂²⋊C₄×C₅₉	—	2	4	no	—
285	C₂²⋊C₄×C₅₉	—	2	4	no	—
286	C₂²⋊C₄×C₅₉	—	2	2	no	—
287	C₂²⋊C₄×C₅₉	—	2	2	no	—
288	C₂²⋊C₄×C₅₉	—	2	2	no	—
289	C₂²⋊C₄×C₅₉	—	2	2	no	—
290	C₂²⋊C₄×C₅₉	—	2	4	no	—
291	C₂²⋊C₄×C₅₉	—	2	4	no	—
292	C₂²⋊C₄×C₅₉	—	2	4	no	—
293	C₂²⋊C₄×C₅₉	—	2	4	no	—
294	C₂²⋊C₄×C₅₉	—	2	4	no	—
295	C₂²⋊C₄×C₅₉	—	2	4	no	—
296	C₂²⋊C₄×C₅₉	—	4	2	no	—
297	C₂²⋊C₄×C₅₉	—	4	2	no	—
298	C₂²⋊C₄×C₅₉	—	4	2	no	—
299	C₂²⋊C₄×C₅₉	—	4	2	no	—
300	C₂²⋊C₄×C₅₉	—	4	2	no	—
301	C₂²⋊C₄×C₅₉	—	4	2	no	—
302	C₂²⋊C₄×C₅₉	—	4	2	no	—
303	C₂²⋊C₄×C₅₉	—	4	2	no	—
304	C₂²⋊C₄×C₅₉	#41	1	4	yes	—
305	C₄²×C₅₉	—	2	4	no	—
306	C₄²×C₅₉	—	2	4	no	—
307	C₄²×C₅₉	—	4	2	no	—
308	C₄²×C₅₉	—	4	2	no	—
309	C₄²×C₅₉	—	4	2	no	—
310	C₄²×C₅₉	—	4	2	no	—
311	C₄²×C₅₉	—	4	2	no	—
312	C₂³×C₅₉	—	2	2	no	—
313	C₂³×C₅₉	—	2	2	no	—
314	C₂³×C₅₉	—	2	1	no	—
315	C₂³×C₅₉	—	2	1	no	—
316	C₂³×C₅₉	—	2	1	no	—
317	C₂³×C₅₉	—	2	1	no	—
318	C₂³×C₅₉	—	2	2	no	—
319	C₂³×C₅₉	—	2	2	no	—
320	C₂³×C₅₉	—	2	2	no	—
321	C₂³×C₅₉	—	2	2	no	—
322	C₂³×C₅₉	—	2	8	no	—
323	C₂³×C₅₉	—	2	2	no	—
324	C₂³×C₅₉	—	2	2	no	—
325	C₂³×C₅₉	—	2	2	no	—
326	C₂³×C₅₉	—	2	2	no	—
327	C₂³×C₅₉	—	2	2	no	—
328	C₂³×C₅₉	—	2	2	no	—
329	C₂³×C₅₉	—	2	2	no	—
330	C₂³×C₅₉	—	4	8	no	—
331	C₂³×C₅₉	—	8	2	no	—
332	C₂³×C₅₉	—	8	2	no	—
333	C₂³×C₅₉	—	8	4	no	—
334	C₂³×C₅₉	C₂×#41	1	2	yes	—
335	C₂³×C₅₉	C₂×#41	1	2	yes	—
336	C₂³×C₅₉	C₂×#41	1	2	yes	—
337	C₂³×C₅₉	C₂×#41	1	2	yes	—
338	C₂³×C₅₉	C₂×#41	1	2	yes	—
339	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
340	Q₈×C₅₉	—	2	8	no	—
341	Q₈×C₅₉	—	4	8	no	—
342	Q₈×C₅₉	—	4	4	no	—
343	D₄×C₅₉	—	4	8	no	—
344	D₄×C₅₉	—	4	8	no	—
345	D₄×C₅₉	—	8	2	no	—
346	D₄×C₅₉	—	8	4	no	—
347	C₂×C₄×C₅₉	—	2	2	no	—
348	C₂×C₄×C₅₉	—	2	2	no	—
349	C₂×C₄×C₅₉	—	2	2	no	—
350	C₂×C₄×C₅₉	—	2	2	no	—
351	C₂×C₄×C₅₉	—	2	2	no	—
352	C₂×C₄×C₅₉	—	2	2	no	—
353	C₂×C₄×C₅₉	—	2	2	no	—
354	C₂×C₄×C₅₉	—	2	2	no	—
355	C₂×C₄×C₅₉	—	2	2	no	—
356	C₂×C₄×C₅₉	—	2	2	no	—
357	C₂×C₄×C₅₉	—	2	1	no	—
358	C₂×C₄×C₅₉	—	2	1	no	—
359	C₂×C₄×C₅₉	—	2	2	no	—
360	C₂×C₄×C₅₉	—	2	2	no	—
361	C₂×C₄×C₅₉	—	2	2	no	—
362	C₂×C₄×C₅₉	—	2	2	no	—
363	C₂×C₄×C₅₉	—	2	2	no	—
364	C₂×C₄×C₅₉	—	2	2	no	—
365	C₂×C₄×C₅₉	—	2	2	no	—
366	C₂×C₄×C₅₉	—	2	2	no	—
367	C₂×C₄×C₅₉	—	2	2	no	—
368	C₂×C₄×C₅₉	—	2	2	no	—
369	C₂×C₄×C₅₉	—	2	2	no	—
370	C₂×C₄×C₅₉	—	2	2	no	—
371	C₂×C₄×C₅₉	—	2	2	no	—
372	C₂×C₄×C₅₉	—	2	2	no	—
373	C₂×C₄×C₅₉	—	2	2	no	—
374	C₂×C₄×C₅₉	—	2	2	no	—
375	C₂×C₄×C₅₉	—	2	2	no	—
376	C₂×C₄×C₅₉	—	2	2	no	—
377	C₂×C₄×C₅₉	—	2	2	no	—
378	C₂×C₄×C₅₉	—	2	2	no	—
379	C₂×C₄×C₅₉	—	2	2	no	—
380	C₂×C₄×C₅₉	—	2	2	no	—
381	C₂×C₄×C₅₉	—	2	2	no	—
382	C₂×C₄×C₅₉	—	2	2	no	—
383	C₂×C₄×C₅₉	—	2	2	no	—
384	C₂×C₄×C₅₉	—	4	4	no	—
385	C₂×C₄×C₅₉	—	4	8	no	—
386	C₂×C₄×C₅₉	—	8	4	no	—
387	C₂×C₄×C₅₉	—	8	4	no	—
388	C₂×C₄×C₅₉	—	8	4	no	—
389	C₂×C₄×C₅₉	—	8	2	no	—
390	C₂×C₄×C₅₉	—	8	4	no	—
391	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
392	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
393	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
394	C₂×C₄×C₅₉	H(5,𝔽₂)	1	4	yes	—
395	#35706	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
396	C₂²×C₅₉	—	2	2	no	—
397	C₂²×C₅₉	—	2	4	no	—
398	C₂²×C₅₉	—	2	2	no	—
399	C₂²×C₅₉	—	2	4	no	—
400	C₂²×C₅₉	—	2	2	no	—
401	C₂²×C₅₉	—	2	2	no	—
402	C₂²×C₅₉	—	2	4	no	—
403	C₂²×C₅₉	—	2	4	no	—
404	C₂²×C₅₉	—	4	1	no	—
405	C₂²×C₅₉	—	4	1	no	—
406	C₂²×C₅₉	—	4	1	no	—
407	C₂²×C₅₉	—	4	1	no	—
408	C₂²×C₅₉	—	4	2	no	—
409	C₂²×C₅₉	—	4	2	no	—
410	C₂²×C₅₉	—	4	2	no	—
411	C₂²×C₅₉	—	4	2	no	—
412	C₂²×C₅₉	—	4	2	no	—
413	C₂²×C₅₉	—	4	2	no	—
414	C₂²×C₅₉	—	4	2	no	—
415	C₂²×C₅₉	—	4	2	no	—
416	C₂²×C₅₉	—	4	2	no	—
417	C₂²×C₅₉	—	8	8	no	—
418	C₂²×C₅₉	#529	1	4	yes	—
419	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
420	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
421	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
422	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	2	yes	—
423	C₂²×C₅₉	#585	1	2	yes	—
424	C₄×C₅₉	—	2	2	no	—
425	C₄×C₅₉	—	2	2	no	—
426	C₄×C₅₉	—	2	4	no	—
427	C₄×C₅₉	—	2	4	no	—
428	C₄×C₅₉	—	4	2	no	—
429	C₄×C₅₉	—	4	2	no	—
430	C₄×C₅₉	—	4	2	no	—
431	C₄×C₅₉	—	4	2	no	—
432	C₄×C₅₉	—	4	2	no	—
433	C₄×C₅₉	—	4	2	no	—
434	C₄×C₅₉	—	4	1	no	—
435	C₄×C₅₉	—	4	1	no	—
436	C₄×C₅₉	—	4	2	no	—
437	C₄×C₅₉	—	4	2	no	—
438	C₄×C₅₉	—	4	2	no	—
439	#2653	C₂×C₅₉	1	2	yes	complemented
440	#2617	C₂×C₅₉	1	1	yes	characteristic
441	#2572	C₂×C₅₉	1	2	yes	complemented
442	#2569	C₂×C₅₉	1	1	yes	characteristic, complemented
443	#2557	C₂×C₅₉	1	2	yes	complemented
444	#2527	C₂×C₅₉	1	2	yes	complemented
445	#2523	C₂×C₅₉	1	2	yes	complemented
446	#2510	C₂×C₅₉	1	2	yes	complemented
447	#2459	C₂×C₅₉	1	2	yes	complemented
448	#2458	C₂×C₅₉	1	2	yes	complemented
449	#2436	C₂×C₅₉	1	1	yes	characteristic, complemented
450	#2412	C₂×C₅₉	1	2	yes	complemented
451	#2398	C₂×C₅₉	1	2	yes	complemented
452	C₂×#393	C₂×C₅₉	1	1	yes	characteristic, complemented
453	#2364	C₂×C₅₉	1	1	yes	characteristic, complemented
454	#2358	C₂×C₅₉	1	2	yes	complemented
455	#2353	C₂×C₅₉	1	2	yes	complemented
456	Q₈×C₂²⋊C₄	C₂×C₅₉	1	1	yes	characteristic, complemented
457	#2273	C₂×C₅₉	1	1	yes	characteristic, complemented
458	C₂×C₅₉	—	2	4	no	—
459	C₂×C₅₉	—	4	2	no	—
460	C₂×C₅₉	—	4	2	no	—
461	C₂×C₅₉	—	8	2	no	—
462	C₂×C₅₉	C₂×#529	1	1	yes	characteristic
463	C₂×C₅₉	#3490	1	1	yes	characteristic
464	C₂×C₅₉	#3505	1	2	yes	—
465	C₂×C₅₉	#3510	1	1	yes	characteristic
466	C₂×C₅₉	#3514	1	2	yes	—
467	C₂³×Q₈	C₂²×C₅₉	1	1	yes	characteristic
468	C₂×#124	C₂²×C₅₉	1	2	yes	complemented
469	C₂×#123	C₂²×C₅₉	1	2	yes	—
470	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
471	C₂×#120	C₂²×C₅₉	1	2	yes	—
472	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	complemented
473	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
474	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
475	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
476	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
477	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
478	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
479	#401	C₂²×C₅₉	1	2	yes	complemented
480	#400	C₂²×C₅₉	1	2	yes	complemented
481	#400	C₂²×C₅₉	1	2	yes	complemented
482	#398	C₂²×C₅₉	1	2	yes	complemented
483	#397	C₂²×C₅₉	1	1	yes	characteristic
484	#397	C₂²×C₅₉	1	1	yes	characteristic
485	#397	C₂²×C₅₉	1	2	yes	—
486	#397	C₂²×C₅₉	1	2	yes	—
487	#397	C₂²×C₅₉	1	2	yes	complemented
488	#397	C₂²×C₅₉	1	2	yes	complemented
489	#394	C₂²×C₅₉	1	2	yes	—
490	#394	C₂²×C₅₉	1	2	yes	—
491	#394	C₂²×C₅₉	1	2	yes	—
492	#394	C₂²×C₅₉	1	2	yes	—
493	#393	C₂²×C₅₉	1	1	yes	characteristic
494	#393	C₂²×C₅₉	1	1	yes	characteristic
495	#393	C₂²×C₅₉	1	1	yes	characteristic
496	#393	C₂²×C₅₉	1	1	yes	characteristic
497	#393	C₂²×C₅₉	1	2	yes	—
498	#393	C₂²×C₅₉	1	2	yes	—
499	#393	C₂²×C₅₉	1	2	yes	complemented
500	#393	C₂²×C₅₉	1	2	yes	complemented
501	#392	C₂²×C₅₉	1	1	yes	characteristic
502	#392	C₂²×C₅₉	1	1	yes	characteristic
503	#391	C₂²×C₅₉	1	2	yes	complemented
504	#391	C₂²×C₅₉	1	2	yes	complemented
505	#391	C₂²×C₅₉	1	2	yes	complemented
506	#391	C₂²×C₅₉	1	2	yes	complemented
507	#390	C₂²×C₅₉	1	2	yes	—
508	#388	C₂²×C₅₉	1	2	yes	—
509	#388	C₂²×C₅₉	1	2	yes	—
510	#388	C₂²×C₅₉	1	2	yes	complemented
511	#388	C₂²×C₅₉	1	2	yes	complemented
512	#388	C₂²×C₅₉	1	2	yes	complemented
513	#388	C₂²×C₅₉	1	2	yes	complemented
514	#388	C₂²×C₅₉	1	2	yes	complemented
515	#387	C₂²×C₅₉	1	2	yes	complemented
516	#387	C₂²×C₅₉	1	2	yes	complemented
517	#387	C₂²×C₅₉	1	2	yes	complemented
518	#387	C₂²×C₅₉	1	2	yes	complemented
519	#387	C₂²×C₅₉	1	2	yes	complemented
520	#387	C₂²×C₅₉	1	2	yes	complemented
521	#386	C₂²×C₅₉	1	2	yes	—
522	#386	C₂²×C₅₉	1	2	yes	—
523	#386	C₂²×C₅₉	1	2	yes	—
524	#386	C₂²×C₅₉	1	2	yes	—
525	#386	C₂²×C₅₉	1	2	yes	—
526	#386	C₂²×C₅₉	1	2	yes	—
527	#386	C₂²×C₅₉	1	2	yes	—
528	#386	C₂²×C₅₉	1	2	yes	complemented
529	#385	C₂²×C₅₉	1	2	yes	—
530	#385	C₂²×C₅₉	1	2	yes	—
531	#385	C₂²×C₅₉	1	2	yes	—
532	#383	C₂²×C₅₉	1	2	yes	complemented
533	#383	C₂²×C₅₉	1	2	yes	complemented
534	#381	C₂²×C₅₉	1	2	yes	—
535	#381	C₂²×C₅₉	1	2	yes	complemented
536	#380	C₂²×C₅₉	1	1	yes	characteristic
537	#380	C₂²×C₅₉	1	2	yes	—
538	#380	C₂²×C₅₉	1	2	yes	—
539	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
540	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
541	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
542	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
543	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
544	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
545	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
546	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
547	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
548	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
549	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	complemented
550	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	complemented
551	#376	C₂²×C₅₉	1	2	yes	complemented
552	C₂×#95	C₂²×C₅₉	1	1	yes	characteristic
553	C₂×#95	C₂²×C₅₉	1	2	yes	—
554	C₅₉	#35706	1	1	yes	characteristic, direct product factor, Sylow
555	C₂⁵	C₂³×C₅₉	1	1	yes	characteristic
556	C₂²×Q₈	—	2	4	no	—
557	C₂²×Q₈	—	4	4	no	—
558	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
559	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
560	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
561	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
562	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
563	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
564	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
565	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
566	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
567	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
568	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
569	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
570	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
571	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
572	#124	—	4	4	no	—
573	#123	—	4	4	no	—
574	#121	—	2	4	no	—
575	#120	—	2	8	no	—
576	C₄×Q₈	—	4	4	no	—
577	C₄×D₄	—	2	8	no	—
578	C₄×D₄	—	4	4	no	—
579	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
588	C₂×C₂²⋊C₄	—	2	4	no	—
589	C₂×C₂²⋊C₄	—	2	4	no	—
590	C₂×C₂²⋊C₄	—	2	4	no	—
591	C₂×C₂²⋊C₄	—	4	4	no	—
592	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
595	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
596	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
597	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
599	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
600	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
601	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
602	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
619	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
620	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
621	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
622	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
623	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
624	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
625	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
626	#95	C₂³×C₅₉	1	2	yes	—
627	#95	C₂³×C₅₉	1	1	yes	characteristic
628	#95	C₂³×C₅₉	1	2	yes	—
629	#95	C₂³×C₅₉	1	2	yes	—
630	#95	C₂³×C₅₉	1	2	yes	—
631	#95	C₂³×C₅₉	1	2	yes	—
632	#95	C₂³×C₅₉	1	1	yes	characteristic
633	#95	C₂³×C₅₉	1	2	yes	—
634	#95	C₂³×C₅₉	1	2	yes	—
635	#95	C₂³×C₅₉	1	2	yes	—
636	#95	C₂³×C₅₉	1	2	yes	—
637	#95	C₂³×C₅₉	1	2	yes	—
638	#95	C₂³×C₅₉	1	2	yes	—
639	#95	C₂³×C₅₉	1	2	yes	—
640	#95	C₂³×C₅₉	1	2	yes	—
641	#95	C₂³×C₅₉	1	2	yes	—
642	#95	C₂³×C₅₉	1	2	yes	—
643	#95	C₂³×C₅₉	1	2	yes	—
644	#95	C₂³×C₅₉	1	2	yes	—
645	#95	C₂³×C₅₉	1	2	yes	—
646	#95	C₂³×C₅₉	1	2	yes	—
647	#95	C₂³×C₅₉	1	2	yes	—
648	#95	C₂³×C₅₉	1	1	yes	characteristic
649	#95	C₂³×C₅₉	1	1	yes	characteristic
650	#95	C₂³×C₅₉	1	2	yes	—
651	#95	C₂³×C₅₉	1	2	yes	—
652	#95	C₂³×C₅₉	1	2	yes	—
653	#95	C₂³×C₅₉	1	2	yes	—
654	#95	C₂³×C₅₉	1	2	yes	—
655	C₂⁴	—	2	2	no	—
656	C₂⁴	—	2	2	no	—
657	C₂⁴	—	4	2	no	—
658	C₂⁴	—	4	2	no	—
659	C₂⁴	#41×C₅₉	1	4	yes	—
660	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
661	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
662	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
663	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
664	C₂×Q₈	—	2	2	no	—
665	C₂×Q₈	—	2	4	no	—
666	C₂×Q₈	—	2	2	no	—
667	C₂×Q₈	—	2	4	no	—
668	C₂×Q₈	—	2	4	no	—
669	C₂×Q₈	—	4	2	no	—
670	C₂×Q₈	—	4	2	no	—
671	C₂×Q₈	—	4	16	no	—
672	C₂×D₄	—	2	4	no	—
673	C₂×D₄	—	2	4	no	—
674	C₂×D₄	—	2	4	no	—
675	C₂×D₄	—	2	4	no	—
676	C₂×D₄	—	2	4	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	4	2	no	—
679	C₂×D₄	—	4	2	no	—
680	C₂×D₄	—	4	2	no	—
681	C₂×D₄	—	4	2	no	—
682	C₂×D₄	—	4	2	no	—
683	C₂²×C₄	—	2	4	no	—
684	C₂²×C₄	—	2	4	no	—
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	2	4	no	—
687	C₂²×C₄	—	2	4	no	—
688	C₂²×C₄	—	2	4	no	—
689	C₂²×C₄	—	2	4	no	—
690	C₂²×C₄	—	4	2	no	—
691	C₂²×C₄	—	4	2	no	—
692	C₂²×C₄	—	4	2	no	—
693	C₂²×C₄	—	4	2	no	—
694	C₂²×C₄	—	4	2	no	—
695	C₂²×C₄	—	4	2	no	—
696	C₂²×C₄	—	4	2	no	—
697	C₂²×C₄	—	4	2	no	—
698	C₂²×C₄	—	4	2	no	—
699	C₂²×C₄	—	4	2	no	—
700	C₂²×C₄	—	4	2	no	—
701	C₂²×C₄	#41×C₅₉	1	4	yes	—
702	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
703	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
704	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
706	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
707	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
708	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
709	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
710	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
714	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
716	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	4	2	no	—
721	C₄⋊C₄	—	4	2	no	—
722	C₄⋊C₄	—	4	2	no	—
723	C₄⋊C₄	—	4	2	no	—
724	C₄⋊C₄	—	4	2	no	—
725	C₄⋊C₄	—	4	2	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	2	no	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	2	4	no	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	2	no	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	—	2	2	no	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	2	4	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	4	2	no	—
745	C₂²⋊C₄	—	4	2	no	—
746	C₂²⋊C₄	—	4	2	no	—
747	C₂²⋊C₄	—	4	2	no	—
748	C₂²⋊C₄	—	4	2	no	—
749	C₂²⋊C₄	—	4	2	no	—
750	C₂²⋊C₄	—	4	2	no	—
751	C₂²⋊C₄	—	4	2	no	—
752	C₂²⋊C₄	#41×C₅₉	1	4	yes	—
753	C₄²	—	2	4	no	—
754	C₄²	—	2	4	no	—
755	C₄²	—	4	2	no	—
756	C₄²	—	4	2	no	—
757	C₄²	—	4	2	no	—
758	C₄²	—	4	2	no	—
759	C₄²	—	4	2	no	—
760	C₂³	—	2	2	no	—
761	C₂³	—	2	2	no	—
762	C₂³	—	2	1	no	—
763	C₂³	—	2	1	no	—
764	C₂³	—	2	1	no	—
765	C₂³	—	2	1	no	—
766	C₂³	—	2	2	no	—
767	C₂³	—	2	2	no	—
768	C₂³	—	2	2	no	—
769	C₂³	—	2	2	no	—
770	C₂³	—	2	8	no	—
771	C₂³	—	2	2	no	—
772	C₂³	—	2	2	no	—
773	C₂³	—	2	2	no	—
774	C₂³	—	2	2	no	—
775	C₂³	—	2	2	no	—
776	C₂³	—	2	2	no	—
777	C₂³	—	2	2	no	—
778	C₂³	—	4	8	no	—
779	C₂³	—	8	2	no	—
780	C₂³	—	8	4	no	—
781	C₂³	—	8	2	no	—
782	C₂³	C₂×#41×C₅₉	1	2	yes	—
783	C₂³	C₂×#41×C₅₉	1	2	yes	—
784	C₂³	C₂×#41×C₅₉	1	2	yes	—
785	C₂³	C₂×#41×C₅₉	1	2	yes	—
786	C₂³	C₂×#41×C₅₉	1	2	yes	—
787	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
788	Q₈	—	2	8	no	—
789	Q₈	—	4	8	no	—
790	Q₈	—	4	4	no	—
791	D₄	—	4	8	no	—
792	D₄	—	4	8	no	—
793	D₄	—	8	2	no	—
794	D₄	—	8	4	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	4	4	no	—
833	C₂×C₄	—	4	8	no	—
834	C₂×C₄	—	8	4	no	—
835	C₂×C₄	—	8	4	no	—
836	C₂×C₄	—	8	2	no	—
837	C₂×C₄	—	8	4	no	—
838	C₂×C₄	—	8	4	no	—
839	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
840	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
841	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
842	C₂×C₄	H(5,𝔽₂)×C₅₉	1	4	yes	—
843	C₂²	—	2	2	no	—
844	C₂²	—	2	4	no	—
845	C₂²	—	2	2	no	—
846	C₂²	—	2	4	no	—
847	C₂²	—	2	2	no	—
848	C₂²	—	2	2	no	—
849	C₂²	—	2	4	no	—
850	C₂²	—	2	4	no	—
851	C₂²	—	4	1	no	—
852	C₂²	—	4	1	no	—
853	C₂²	—	4	2	no	—
854	C₂²	—	4	2	no	—
855	C₂²	—	4	1	no	—
856	C₂²	—	4	1	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	4	2	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	2	no	—
863	C₂²	—	4	2	no	—
864	C₂²	—	8	8	no	—
865	C₂²	C₅₉×#529	1	4	yes	—
866	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
867	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
868	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
869	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	2	yes	—
870	C₂²	C₅₉×#585	1	2	yes	—
871	C₄	—	2	4	no	—
872	C₄	—	2	2	no	—
873	C₄	—	2	2	no	—
874	C₄	—	2	4	no	—
875	C₄	—	4	1	no	—
876	C₄	—	4	1	no	—
877	C₄	—	4	2	no	—
878	C₄	—	4	2	no	—
879	C₄	—	4	2	no	—
880	C₄	—	4	2	no	—
881	C₄	—	4	2	no	—
882	C₄	—	4	2	no	—
883	C₄	—	4	2	no	—
884	C₄	—	4	2	no	—
885	C₄	—	4	2	no	—
886	C₂	—	2	4	no	—
887	C₂	—	4	2	no	—
888	C₂	—	4	2	no	—
889	C₂	—	8	2	no	—
890	C₂	C₂×C₅₉×#529	1	1	yes	characteristic
891	C₂	C₅₉×#3490	1	1	yes	characteristic
892	C₂	C₅₉×#3505	1	2	yes	—
893	C₂	C₅₉×#3510	1	1	yes	characteristic
894	C₂	C₅₉×#3514	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₅₉×#2617	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×#2653	C₂	semidirect
3. C₅₉×#2572	C₂	semidirect
4. C₅₉×#2569	C₂	semidirect
5. C₅₉×#2557	C₂	semidirect
6. C₅₉×#2527	C₂	semidirect
7. C₅₉×#2523	C₂	semidirect
8. C₅₉×#2510	C₂	semidirect
9. C₅₉×#2459	C₂	semidirect
10. C₅₉×#2458	C₂	semidirect
11. C₅₉×#2436	C₂	semidirect
12. C₅₉×#2412	C₂	semidirect
13. C₅₉×#2398	C₂	semidirect
14. C₂×C₅₉×#393	C₂	semidirect
15. C₅₉×#2364	C₂	semidirect
16. C₅₉×#2358	C₂	semidirect
17. C₅₉×#2353	C₂	semidirect
18. Q₈×C₂²⋊C₄×C₅₉	C₂	semidirect
19. C₅₉×#2273	C₂	semidirect
21. C₂×#124×C₅₉	C₂²	semidirect
25. C₂×C₄×Q₈×C₅₉	C₂²	semidirect
32. C₅₉×#401	C₂²	semidirect
33. C₅₉×#400	C₂²	semidirect
34. C₅₉×#400	C₂²	semidirect
35. C₅₉×#398	C₂²	semidirect
40. C₅₉×#397	C₂²	semidirect
41. C₅₉×#397	C₂²	semidirect
52. C₅₉×#393	C₂²	semidirect
53. C₅₉×#393	C₂²	semidirect
56. C₅₉×#391	C₂²	semidirect
57. C₅₉×#391	C₂²	semidirect
58. C₅₉×#391	C₂²	semidirect
59. C₅₉×#391	C₂²	semidirect
63. C₅₉×#388	C₂²	semidirect
64. C₅₉×#388	C₂²	semidirect
65. C₅₉×#388	C₂²	semidirect
66. C₅₉×#388	C₂²	semidirect
67. C₅₉×#388	C₂²	semidirect
68. C₅₉×#387	C₂²	semidirect
69. C₅₉×#387	C₂²	semidirect
70. C₅₉×#387	C₂²	semidirect
71. C₅₉×#387	C₂²	semidirect
72. C₅₉×#387	C₂²	semidirect
73. C₅₉×#387	C₂²	semidirect
81. C₅₉×#386	C₂²	semidirect
85. C₅₉×#383	C₂²	semidirect
86. C₅₉×#383	C₂²	semidirect
88. C₅₉×#381	C₂²	semidirect
102. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
103. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
104. C₅₉×#376	C₂²	semidirect
395. #35706	C₅₉	direct (N × H)
439. #2653	C₂×C₅₉	semidirect
441. #2572	C₂×C₅₉	semidirect
442. #2569	C₂×C₅₉	semidirect
443. #2557	C₂×C₅₉	semidirect
444. #2527	C₂×C₅₉	semidirect
445. #2523	C₂×C₅₉	semidirect
446. #2510	C₂×C₅₉	semidirect
447. #2459	C₂×C₅₉	semidirect
448. #2458	C₂×C₅₉	semidirect
449. #2436	C₂×C₅₉	semidirect
450. #2412	C₂×C₅₉	semidirect
451. #2398	C₂×C₅₉	semidirect
452. C₂×#393	C₂×C₅₉	semidirect
453. #2364	C₂×C₅₉	semidirect
454. #2358	C₂×C₅₉	semidirect
455. #2353	C₂×C₅₉	semidirect
456. Q₈×C₂²⋊C₄	C₂×C₅₉	semidirect
457. #2273	C₂×C₅₉	semidirect
468. C₂×#124	C₂²×C₅₉	semidirect
472. C₂×C₄×Q₈	C₂²×C₅₉	semidirect
479. #401	C₂²×C₅₉	semidirect
480. #400	C₂²×C₅₉	semidirect
481. #400	C₂²×C₅₉	semidirect
482. #398	C₂²×C₅₉	semidirect
487. #397	C₂²×C₅₉	semidirect
488. #397	C₂²×C₅₉	semidirect
499. #393	C₂²×C₅₉	semidirect
500. #393	C₂²×C₅₉	semidirect
503. #391	C₂²×C₅₉	semidirect
504. #391	C₂²×C₅₉	semidirect
505. #391	C₂²×C₅₉	semidirect
506. #391	C₂²×C₅₉	semidirect
510. #388	C₂²×C₅₉	semidirect
511. #388	C₂²×C₅₉	semidirect
512. #388	C₂²×C₅₉	semidirect
513. #388	C₂²×C₅₉	semidirect
514. #388	C₂²×C₅₉	semidirect
515. #387	C₂²×C₅₉	semidirect
516. #387	C₂²×C₅₉	semidirect
517. #387	C₂²×C₅₉	semidirect
518. #387	C₂²×C₅₉	semidirect
519. #387	C₂²×C₅₉	semidirect
520. #387	C₂²×C₅₉	semidirect
528. #386	C₂²×C₅₉	semidirect
532. #383	C₂²×C₅₉	semidirect
533. #383	C₂²×C₅₉	semidirect
535. #381	C₂²×C₅₉	semidirect
549. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
550. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
551. #376	C₂²×C₅₉	semidirect
554. C₅₉	#35706	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×#2653	2
C₅₉×#2617	2
C₅₉×#2572	2
C₅₉×#2569	2
C₅₉×#2557	2
C₅₉×#2527	2
C₅₉×#2523	2
C₅₉×#2510	2
C₅₉×#2459	2
C₅₉×#2458	2
C₅₉×#2436	2
C₅₉×#2412	2
C₅₉×#2398	2
C₂×C₅₉×#393	2
C₅₉×#2364	2
C₅₉×#2358	2
C₅₉×#2353	2
Q₈×C₂²⋊C₄×C₅₉	2
C₅₉×#2273	2
#35706	59

Subgroups — C59×#35706 #28447815

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35706 #28447815