Subgroups — C₅₉×#35702 #28447811

Order 15104.

2774 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#518	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2628	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2626	C₂	1	2	yes	maximal, complemented
5	C₅₉×#2580	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#2564	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2563	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#2452	C₂	1	2	yes	maximal, complemented
9	C₅₉×#2450	C₂	1	4	yes	maximal, complemented
10	C₅₉×#2439	C₂	1	2	yes	maximal, complemented
11	C₅₉×#2437	C₂	1	4	yes	maximal, complemented
12	C₅₉×#2409	C₂	1	2	yes	maximal, complemented
13	C₅₉×#2396	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅₉×#393	C₂	1	2	yes	maximal, complemented
15	C₅₉×#2349	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₉×#2349	C₂	1	2	yes	maximal, complemented
17	D₄×C₂²⋊C₄×C₅₉	C₂	1	2	yes	maximal
18	C₂³×Q₈×C₅₉	C₂²	1	2	yes	complemented
19	C₂³×D₄×C₅₉	C₂²	1	1	yes	characteristic
20	D₄×Q₈×C₅₉	—	2	8	no	—
21	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₄⋊Q₈×C₅₉	C₂²	1	2	yes	complemented
23	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	complemented
24	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	4	yes	complemented
25	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	4	yes	complemented
26	C₅₉×#518	—	2	8	no	—
27	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×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	1	yes	characteristic
33	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
36	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
37	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
39	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
40	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	4	yes	—
41	C₅₉×#400	C₂²	1	1	yes	characteristic, complemented
42	C₅₉×#400	C₂²	1	2	yes	complemented
43	C₅₉×#399	C₂²	1	1	yes	characteristic
44	C₅₉×#399	C₂²	1	2	yes	—
45	C₅₉×#399	C₂²	1	2	yes	complemented
46	C₅₉×#398	C₂²	1	2	yes	complemented
47	C₅₉×#396	C₂²	1	4	yes	—
48	C₅₉×#396	C₂²	1	2	yes	—
49	C₅₉×#396	C₂²	1	4	yes	complemented
50	C₅₉×#395	C₂²	1	2	yes	complemented
51	C₅₉×#395	C₂²	1	1	yes	characteristic, complemented
52	C₅₉×#393	C₂²	1	2	yes	—
53	C₅₉×#393	C₂²	1	1	yes	characteristic
54	C₅₉×#393	C₂²	1	4	yes	—
55	C₅₉×#393	C₂²	1	2	yes	complemented
56	C₅₉×#393	C₂²	1	2	yes	complemented
57	C₅₉×#393	C₂²	1	2	yes	complemented
58	C₅₉×#393	C₂²	1	4	yes	complemented
59	C₅₉×#391	C₂²	1	4	yes	complemented
60	C₅₉×#390	C₂²	1	2	yes	—
61	C₅₉×#390	C₂²	1	2	yes	—
62	C₅₉×#389	C₂²	1	2	yes	complemented
63	C₅₉×#389	C₂²	1	2	yes	complemented
64	C₅₉×#389	C₂²	1	2	yes	complemented
65	C₅₉×#387	C₂²	1	4	yes	complemented
66	C₅₉×#386	C₂²	1	4	yes	—
67	C₅₉×#386	C₂²	1	4	yes	—
68	C₅₉×#385	C₂²	1	4	yes	complemented
69	C₅₉×#385	C₂²	1	4	yes	complemented
70	C₅₉×#385	C₂²	1	4	yes	complemented
71	C₅₉×#385	C₂²	1	4	yes	complemented
72	C₅₉×#385	C₂²	1	4	yes	complemented
73	C₅₉×#382	C₂²	1	2	yes	complemented
74	C₅₉×#382	C₂²	1	1	yes	characteristic, complemented
75	C₅₉×#380	C₂²	1	2	yes	—
76	C₅₉×#380	C₂²	1	4	yes	complemented
77	C₅₉×#380	C₂²	1	4	yes	complemented
78	C₅₉×#380	C₂²	1	2	yes	complemented
79	C₅₉×#379	C₂²	1	4	yes	—
80	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
81	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
82	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
83	C₂×#95×C₅₉	C₂²	1	2	yes	complemented
84	C₂×#95×C₅₉	C₂²	1	4	yes	complemented
85	C₂⁵×C₅₉	C₂³	1	2	yes	—
86	C₂²×Q₈×C₅₉	—	2	8	no	—
87	C₂²×Q₈×C₅₉	—	4	8	no	—
88	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
89	C₂²×Q₈×C₅₉	C₂³	1	4	yes	—
90	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
91	C₂²×D₄×C₅₉	—	2	4	no	—
92	C₂²×D₄×C₅₉	—	2	4	no	—
93	C₂²×D₄×C₅₉	Q₈	1	8	yes	complemented
94	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
95	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
96	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₅₉	C₂³	1	4	yes	—
98	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₅₉	C₂³	1	4	yes	—
100	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
101	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
102	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
103	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
104	C₄⋊Q₈×C₅₉	—	2	8	no	—
105	C₄⋊Q₈×C₅₉	—	2	4	no	—
106	C₂²⋊Q₈×C₅₉	—	2	8	no	—
107	C₂²⋊Q₈×C₅₉	—	2	16	no	—
108	C₂²⋊Q₈×C₅₉	—	4	8	no	—
109	C₄×Q₈×C₅₉	—	2	4	no	—
110	C₄×D₄×C₅₉	—	2	4	no	—
111	C₄×D₄×C₅₉	—	2	8	no	—
112	C₄×D₄×C₅₉	—	2	8	no	—
113	C₄×D₄×C₅₉	—	2	8	no	—
114	C₄×D₄×C₅₉	—	2	4	no	—
115	C₄×D₄×C₅₉	—	2	8	no	—
116	C₄×D₄×C₅₉	—	2	4	no	—
117	C₄×D₄×C₅₉	D₄	1	8	yes	—
118	#117×C₅₉	—	2	4	no	—
119	#117×C₅₉	—	2	4	no	—
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	1	yes	characteristic
125	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
127	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
133	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
134	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
135	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊C₄×C₅₉	—	2	8	no	—
137	C₂×C₂²⋊C₄×C₅₉	—	2	8	no	—
138	C₂×C₂²⋊C₄×C₅₉	—	4	8	no	—
139	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	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	2	yes	—
143	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
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	2	yes	—
150	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
152	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
153	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
154	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
155	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
156	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
157	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
159	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
160	#95×C₅₉	C₂³	1	2	yes	—
161	#95×C₅₉	C₂³	1	1	yes	characteristic
162	#95×C₅₉	C₂³	1	4	yes	—
163	#95×C₅₉	C₂³	1	2	yes	—
164	#95×C₅₉	C₂³	1	4	yes	—
165	#95×C₅₉	C₂³	1	4	yes	—
166	#95×C₅₉	C₂³	1	4	yes	—
167	#95×C₅₉	C₂³	1	2	yes	—
168	#95×C₅₉	C₂³	1	2	yes	—
169	#95×C₅₉	C₂³	1	2	yes	—
170	#95×C₅₉	C₂³	1	1	yes	characteristic
171	#95×C₅₉	C₂³	1	4	yes	—
172	#95×C₅₉	C₂³	1	4	yes	—
173	#95×C₅₉	C₂³	1	2	yes	—
174	C₂⁴×C₅₉	—	2	4	no	—
175	C₂⁴×C₅₉	—	2	4	no	—
176	C₂⁴×C₅₉	—	4	4	no	—
177	C₂⁴×C₅₉	—	4	4	no	—
178	C₂⁴×C₅₉	C₂×Q₈	1	8	yes	complemented
179	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
180	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
181	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
182	C₂×Q₈×C₅₉	—	2	2	no	—
183	C₂×Q₈×C₅₉	—	2	8	no	—
184	C₂×Q₈×C₅₉	—	2	4	no	—
185	C₂×Q₈×C₅₉	—	2	4	no	—
186	C₂×Q₈×C₅₉	—	2	8	no	—
187	C₂×Q₈×C₅₉	—	4	4	no	—
188	C₂×Q₈×C₅₉	—	4	4	no	—
189	C₂×Q₈×C₅₉	—	4	32	no	—
190	C₂×D₄×C₅₉	—	2	4	no	—
191	C₂×D₄×C₅₉	—	2	4	no	—
192	C₂×D₄×C₅₉	—	2	32	no	—
193	C₂×D₄×C₅₉	—	2	2	no	—
194	C₂×D₄×C₅₉	—	2	2	no	—
195	C₂×D₄×C₅₉	C₂×D₄	1	4	yes	—
196	C₂×D₄×C₅₉	C₂×Q₈	1	4	yes	—
197	C₂×D₄×C₅₉	C₂×Q₈	1	8	yes	complemented
198	C₂×D₄×C₅₉	C₂×Q₈	1	4	yes	complemented
199	C₂×D₄×C₅₉	#41	1	4	yes	—
200	C₂²×C₄×C₅₉	—	2	2	no	—
201	C₂²×C₄×C₅₉	—	2	2	no	—
202	C₂²×C₄×C₅₉	—	2	8	no	—
203	C₂²×C₄×C₅₉	—	2	4	no	—
204	C₂²×C₄×C₅₉	—	2	8	no	—
205	C₂²×C₄×C₅₉	—	2	8	no	—
206	C₂²×C₄×C₅₉	—	2	4	no	—
207	C₂²×C₄×C₅₉	—	2	4	no	—
208	C₂²×C₄×C₅₉	—	4	4	no	—
209	C₂²×C₄×C₅₉	—	4	4	no	—
210	C₂²×C₄×C₅₉	—	4	4	no	—
211	C₂²×C₄×C₅₉	—	4	4	no	—
212	C₂²×C₄×C₅₉	—	4	4	no	—
213	C₂²×C₄×C₅₉	—	4	4	no	—
214	C₂²×C₄×C₅₉	—	4	4	no	—
215	C₂²×C₄×C₅₉	C₂×D₄	1	8	yes	—
216	C₂²×C₄×C₅₉	C₂×Q₈	1	4	yes	complemented
217	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
221	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
223	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
231	C₄⋊C₄×C₅₉	—	2	2	no	—
232	C₄⋊C₄×C₅₉	—	2	2	no	—
233	C₄⋊C₄×C₅₉	—	2	2	no	—
234	C₄⋊C₄×C₅₉	—	2	4	no	—
235	C₄⋊C₄×C₅₉	—	2	4	no	—
236	C₄⋊C₄×C₅₉	—	2	2	no	—
237	C₄⋊C₄×C₅₉	—	2	8	no	—
238	C₄⋊C₄×C₅₉	—	2	4	no	—
239	C₄⋊C₄×C₅₉	—	2	4	no	—
240	C₄⋊C₄×C₅₉	—	2	4	no	—
241	C₄⋊C₄×C₅₉	—	4	2	no	—
242	C₄⋊C₄×C₅₉	—	4	2	no	—
243	C₄⋊C₄×C₅₉	—	4	4	no	—
244	C₄⋊C₄×C₅₉	—	4	4	no	—
245	C₄⋊C₄×C₅₉	—	4	4	no	—
246	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
247	C₂²⋊C₄×C₅₉	—	2	4	no	—
248	C₂²⋊C₄×C₅₉	—	2	8	no	—
249	C₂²⋊C₄×C₅₉	—	2	8	no	—
250	C₂²⋊C₄×C₅₉	—	2	4	no	—
251	C₂²⋊C₄×C₅₉	—	2	2	no	—
252	C₂²⋊C₄×C₅₉	—	2	2	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	—	4	4	no	—
258	C₂²⋊C₄×C₅₉	—	4	4	no	—
259	C₂²⋊C₄×C₅₉	—	4	4	no	—
260	C₂²⋊C₄×C₅₉	—	4	2	no	—
261	C₂²⋊C₄×C₅₉	—	4	4	no	—
262	C₂²⋊C₄×C₅₉	C₂×D₄	1	8	yes	—
263	C₄²×C₅₉	—	2	4	no	—
264	C₄²×C₅₉	—	2	2	no	—
265	C₄²×C₅₉	—	2	4	no	—
266	C₄²×C₅₉	—	2	4	no	—
267	C₄²×C₅₉	C₂×D₄	1	4	yes	—
268	C₂³×C₅₉	—	2	4	no	—
269	C₂³×C₅₉	—	2	4	no	—
270	C₂³×C₅₉	—	2	1	no	—
271	C₂³×C₅₉	—	2	2	no	—
272	C₂³×C₅₉	—	2	1	no	—
273	C₂³×C₅₉	—	2	2	no	—
274	C₂³×C₅₉	—	2	4	no	—
275	C₂³×C₅₉	—	2	2	no	—
276	C₂³×C₅₉	—	2	4	no	—
277	C₂³×C₅₉	—	2	2	no	—
278	C₂³×C₅₉	—	2	16	no	—
279	C₂³×C₅₉	—	4	16	no	—
280	C₂³×C₅₉	—	8	4	no	—
281	C₂³×C₅₉	—	8	4	no	—
282	C₂³×C₅₉	—	8	8	no	—
283	C₂³×C₅₉	C₂²×D₄	1	4	yes	—
284	C₂³×C₅₉	C₂²×Q₈	1	2	yes	—
285	C₂³×C₅₉	C₂²×Q₈	1	4	yes	—
286	C₂³×C₅₉	C₂²×Q₈	1	4	yes	—
287	C₂³×C₅₉	C₂×#41	1	4	yes	—
288	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
289	Q₈×C₅₉	—	2	8	no	—
290	Q₈×C₅₉	—	4	16	no	—
291	Q₈×C₅₉	—	4	8	no	—
292	D₄×C₅₉	—	2	16	no	—
293	D₄×C₅₉	—	2	8	no	—
294	D₄×C₅₉	C₂²⋊Q₈	1	16	yes	complemented
295	C₂×C₄×C₅₉	—	2	1	no	—
296	C₂×C₄×C₅₉	—	2	2	no	—
297	C₂×C₄×C₅₉	—	2	1	no	—
298	C₂×C₄×C₅₉	—	2	4	no	—
299	C₂×C₄×C₅₉	—	2	2	no	—
300	C₂×C₄×C₅₉	—	2	2	no	—
301	C₂×C₄×C₅₉	—	2	2	no	—
302	C₂×C₄×C₅₉	—	2	8	no	—
303	C₂×C₄×C₅₉	—	2	1	no	—
304	C₂×C₄×C₅₉	—	2	2	no	—
305	C₂×C₄×C₅₉	—	2	1	no	—
306	C₂×C₄×C₅₉	—	2	2	no	—
307	C₂×C₄×C₅₉	—	2	4	no	—
308	C₂×C₄×C₅₉	—	2	2	no	—
309	C₂×C₄×C₅₉	—	2	2	no	—
310	C₂×C₄×C₅₉	—	2	4	no	—
311	C₂×C₄×C₅₉	—	2	2	no	—
312	C₂×C₄×C₅₉	—	2	4	no	—
313	C₂×C₄×C₅₉	—	2	2	no	—
314	C₂×C₄×C₅₉	—	2	4	no	—
315	C₂×C₄×C₅₉	—	2	4	no	—
316	C₂×C₄×C₅₉	—	2	2	no	—
317	C₂×C₄×C₅₉	—	2	2	no	—
318	C₂×C₄×C₅₉	—	2	2	no	—
319	C₂×C₄×C₅₉	—	2	2	no	—
320	C₂×C₄×C₅₉	—	2	4	no	—
321	C₂×C₄×C₅₉	—	2	4	no	—
322	C₂×C₄×C₅₉	—	2	2	no	—
323	C₂×C₄×C₅₉	—	2	2	no	—
324	C₂×C₄×C₅₉	—	4	8	no	—
325	C₂×C₄×C₅₉	—	4	16	no	—
326	C₂×C₄×C₅₉	—	8	4	no	—
327	C₂×C₄×C₅₉	—	8	4	no	—
328	C₂×C₄×C₅₉	—	8	4	no	—
329	C₂×C₄×C₅₉	—	8	8	no	—
330	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
331	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
332	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
333	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₅₉	C₂²×Q₈	1	2	yes	—
335	C₂×C₄×C₅₉	C₂²×Q₈	1	2	yes	—
336	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
337	C₂×C₄×C₅₉	H(5,𝔽₂)	1	4	yes	—
338	#35702	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
339	C₂²×C₅₉	—	2	4	no	—
340	C₂²×C₅₉	—	2	4	no	—
341	C₂²×C₅₉	—	2	8	no	—
342	C₂²×C₅₉	—	2	8	no	—
343	C₂²×C₅₉	—	2	2	no	—
344	C₂²×C₅₉	—	2	4	no	—
345	C₂²×C₅₉	—	2	4	no	—
346	C₂²×C₅₉	—	2	8	no	—
347	C₂²×C₅₉	—	4	2	no	—
348	C₂²×C₅₉	—	4	1	no	—
349	C₂²×C₅₉	—	4	2	no	—
350	C₂²×C₅₉	—	4	1	no	—
351	C₂²×C₅₉	—	4	4	no	—
352	C₂²×C₅₉	—	4	2	no	—
353	C₂²×C₅₉	—	8	16	no	—
354	C₂²×C₅₉	C₂×C₂²⋊Q₈	1	8	yes	—
355	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
356	C₂²×C₅₉	C₂³×Q₈	1	1	yes	characteristic
357	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
358	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	2	yes	—
359	C₂²×C₅₉	#585	1	2	yes	—
360	C₄×C₅₉	—	2	2	no	—
361	C₄×C₅₉	—	2	2	no	—
362	C₄×C₅₉	—	2	4	no	—
363	C₄×C₅₉	—	2	4	no	—
364	C₄×C₅₉	—	2	2	no	—
365	C₄×C₅₉	—	4	4	no	—
366	C₄×C₅₉	—	4	1	no	—
367	C₄×C₅₉	—	4	2	no	—
368	C₄×C₅₉	—	4	2	no	—
369	C₄×C₅₉	—	4	1	no	—
370	C₄×C₅₉	—	4	2	no	—
371	C₄×C₅₉	—	4	4	no	—
372	C₄×C₅₉	—	4	2	no	—
373	C₄×C₅₉	C₂×C₂²⋊Q₈	1	4	yes	—
374	C₂×D₄×Q₈	C₂×C₅₉	1	1	yes	characteristic, complemented
375	C₂×#518	C₂×C₅₉	1	1	yes	characteristic
376	#2628	C₂×C₅₉	1	1	yes	characteristic, complemented
377	#2626	C₂×C₅₉	1	2	yes	complemented
378	#2580	C₂×C₅₉	1	1	yes	characteristic, complemented
379	#2564	C₂×C₅₉	1	2	yes	complemented
380	#2563	C₂×C₅₉	1	1	yes	characteristic, complemented
381	#2452	C₂×C₅₉	1	2	yes	complemented
382	#2450	C₂×C₅₉	1	4	yes	complemented
383	#2439	C₂×C₅₉	1	2	yes	complemented
384	#2437	C₂×C₅₉	1	4	yes	complemented
385	#2409	C₂×C₅₉	1	2	yes	complemented
386	#2396	C₂×C₅₉	1	1	yes	characteristic, complemented
387	C₂×#393	C₂×C₅₉	1	2	yes	complemented
388	#2349	C₂×C₅₉	1	1	yes	characteristic, complemented
389	#2349	C₂×C₅₉	1	2	yes	complemented
390	D₄×C₂²⋊C₄	C₂×C₅₉	1	2	yes	—
391	C₂×C₅₉	—	2	8	no	—
392	C₂×C₅₉	—	4	4	no	—
393	C₂×C₅₉	—	4	2	no	—
394	C₂×C₅₉	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
395	C₂×C₅₉	#3484	1	1	yes	characteristic
396	C₂×C₅₉	#3500	1	1	yes	characteristic
397	C₂×C₅₉	#3501	1	2	yes	—
398	C₂×C₅₉	#3514	1	2	yes	—
399	C₂³×Q₈	C₂²×C₅₉	1	2	yes	complemented
400	C₂³×D₄	C₂²×C₅₉	1	1	yes	characteristic
401	D₄×Q₈	—	2	8	no	—
402	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
403	C₂×C₄⋊Q₈	C₂²×C₅₉	1	2	yes	complemented
404	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	complemented
405	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	4	yes	complemented
406	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	4	yes	complemented
407	#518	—	2	8	no	—
408	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
409	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
410	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
411	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
412	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
413	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
414	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
415	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
416	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
417	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
418	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
419	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
420	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
421	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	4	yes	—
422	#400	C₂²×C₅₉	1	1	yes	characteristic, complemented
423	#400	C₂²×C₅₉	1	2	yes	complemented
424	#399	C₂²×C₅₉	1	1	yes	characteristic
425	#399	C₂²×C₅₉	1	2	yes	—
426	#399	C₂²×C₅₉	1	2	yes	complemented
427	#398	C₂²×C₅₉	1	2	yes	complemented
428	#396	C₂²×C₅₉	1	4	yes	—
429	#396	C₂²×C₅₉	1	2	yes	—
430	#396	C₂²×C₅₉	1	4	yes	complemented
431	#395	C₂²×C₅₉	1	2	yes	complemented
432	#395	C₂²×C₅₉	1	1	yes	characteristic, complemented
433	#393	C₂²×C₅₉	1	2	yes	—
434	#393	C₂²×C₅₉	1	1	yes	characteristic
435	#393	C₂²×C₅₉	1	4	yes	—
436	#393	C₂²×C₅₉	1	2	yes	complemented
437	#393	C₂²×C₅₉	1	2	yes	complemented
438	#393	C₂²×C₅₉	1	2	yes	complemented
439	#393	C₂²×C₅₉	1	4	yes	complemented
440	#391	C₂²×C₅₉	1	4	yes	complemented
441	#390	C₂²×C₅₉	1	2	yes	—
442	#390	C₂²×C₅₉	1	2	yes	—
443	#389	C₂²×C₅₉	1	2	yes	complemented
444	#389	C₂²×C₅₉	1	2	yes	complemented
445	#389	C₂²×C₅₉	1	2	yes	complemented
446	#387	C₂²×C₅₉	1	4	yes	complemented
447	#386	C₂²×C₅₉	1	4	yes	—
448	#386	C₂²×C₅₉	1	4	yes	—
449	#385	C₂²×C₅₉	1	4	yes	complemented
450	#385	C₂²×C₅₉	1	4	yes	complemented
451	#385	C₂²×C₅₉	1	4	yes	complemented
452	#385	C₂²×C₅₉	1	4	yes	complemented
453	#385	C₂²×C₅₉	1	4	yes	complemented
454	#382	C₂²×C₅₉	1	2	yes	complemented
455	#382	C₂²×C₅₉	1	1	yes	characteristic, complemented
456	#380	C₂²×C₅₉	1	2	yes	—
457	#380	C₂²×C₅₉	1	4	yes	complemented
458	#380	C₂²×C₅₉	1	4	yes	complemented
459	#380	C₂²×C₅₉	1	2	yes	complemented
460	#379	C₂²×C₅₉	1	4	yes	—
461	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
462	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
463	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
464	C₂×#95	C₂²×C₅₉	1	2	yes	complemented
465	C₂×#95	C₂²×C₅₉	1	4	yes	complemented
466	C₅₉	#35702	1	1	yes	characteristic, direct product factor, Sylow
467	C₂⁵	C₂³×C₅₉	1	2	yes	—
468	C₂²×Q₈	—	2	8	no	—
469	C₂²×Q₈	—	4	8	no	—
470	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
471	C₂²×Q₈	C₂³×C₅₉	1	4	yes	—
472	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
473	C₂²×D₄	—	2	4	no	—
474	C₂²×D₄	—	2	4	no	—
475	C₂²×D₄	Q₈×C₅₉	1	8	yes	complemented
476	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
477	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
478	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
479	C₂³×C₄	C₂³×C₅₉	1	4	yes	—
480	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
481	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
482	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
483	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
484	C₂³×C₄	C₂³×C₅₉	1	4	yes	—
485	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
486	C₄⋊Q₈	—	2	8	no	—
487	C₄⋊Q₈	—	2	4	no	—
488	C₂²⋊Q₈	—	2	8	no	—
489	C₂²⋊Q₈	—	2	16	no	—
490	C₂²⋊Q₈	—	4	8	no	—
491	C₄×Q₈	—	2	4	no	—
492	C₄×D₄	—	2	4	no	—
493	C₄×D₄	—	2	8	no	—
494	C₄×D₄	—	2	8	no	—
495	C₄×D₄	—	2	8	no	—
496	C₄×D₄	—	2	4	no	—
497	C₄×D₄	—	2	8	no	—
498	C₄×D₄	—	2	4	no	—
499	C₄×D₄	D₄×C₅₉	1	8	yes	—
500	#117	—	2	4	no	—
501	#117	—	2	4	no	—
502	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
511	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
513	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
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	4	yes	—
517	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
518	C₂×C₂²⋊C₄	—	2	8	no	—
519	C₂×C₂²⋊C₄	—	2	8	no	—
520	C₂×C₂²⋊C₄	—	4	8	no	—
521	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
522	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
524	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
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	2	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
537	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
538	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
539	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
540	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
541	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
542	#95	C₂³×C₅₉	1	2	yes	—
543	#95	C₂³×C₅₉	1	1	yes	characteristic
544	#95	C₂³×C₅₉	1	4	yes	—
545	#95	C₂³×C₅₉	1	2	yes	—
546	#95	C₂³×C₅₉	1	4	yes	—
547	#95	C₂³×C₅₉	1	4	yes	—
548	#95	C₂³×C₅₉	1	4	yes	—
549	#95	C₂³×C₅₉	1	2	yes	—
550	#95	C₂³×C₅₉	1	2	yes	—
551	#95	C₂³×C₅₉	1	2	yes	—
552	#95	C₂³×C₅₉	1	1	yes	characteristic
553	#95	C₂³×C₅₉	1	4	yes	—
554	#95	C₂³×C₅₉	1	4	yes	—
555	#95	C₂³×C₅₉	1	2	yes	—
556	C₂⁴	—	2	4	no	—
557	C₂⁴	—	2	4	no	—
558	C₂⁴	—	4	4	no	—
559	C₂⁴	—	4	4	no	—
560	C₂⁴	C₂×Q₈×C₅₉	1	8	yes	complemented
561	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
562	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
563	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
564	C₂×Q₈	—	2	2	no	—
565	C₂×Q₈	—	2	8	no	—
566	C₂×Q₈	—	2	4	no	—
567	C₂×Q₈	—	2	4	no	—
568	C₂×Q₈	—	2	8	no	—
569	C₂×Q₈	—	4	4	no	—
570	C₂×Q₈	—	4	4	no	—
571	C₂×Q₈	—	4	32	no	—
572	C₂×D₄	—	2	4	no	—
573	C₂×D₄	—	2	4	no	—
574	C₂×D₄	—	2	32	no	—
575	C₂×D₄	—	2	2	no	—
576	C₂×D₄	—	2	2	no	—
577	C₂×D₄	C₂×D₄×C₅₉	1	4	yes	—
578	C₂×D₄	C₂×Q₈×C₅₉	1	4	yes	—
579	C₂×D₄	C₂×Q₈×C₅₉	1	8	yes	complemented
580	C₂×D₄	C₂×Q₈×C₅₉	1	4	yes	complemented
581	C₂×D₄	#41×C₅₉	1	4	yes	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	8	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	8	no	—
587	C₂²×C₄	—	2	8	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	4	no	—
590	C₂²×C₄	—	4	4	no	—
591	C₂²×C₄	—	4	4	no	—
592	C₂²×C₄	—	4	4	no	—
593	C₂²×C₄	—	4	4	no	—
594	C₂²×C₄	—	4	4	no	—
595	C₂²×C₄	—	4	4	no	—
596	C₂²×C₄	—	4	4	no	—
597	C₂²×C₄	C₂×D₄×C₅₉	1	8	yes	—
598	C₂²×C₄	C₂×Q₈×C₅₉	1	4	yes	complemented
599	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
600	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
601	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
603	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
605	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
606	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
611	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
613	C₄⋊C₄	—	2	2	no	—
614	C₄⋊C₄	—	2	2	no	—
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	8	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	4	4	no	—
624	C₄⋊C₄	—	4	4	no	—
625	C₄⋊C₄	—	4	2	no	—
626	C₄⋊C₄	—	4	2	no	—
627	C₄⋊C₄	—	4	4	no	—
628	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	8	no	—
631	C₂²⋊C₄	—	2	8	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	2	no	—
634	C₂²⋊C₄	—	2	2	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	2	8	no	—
639	C₂²⋊C₄	—	4	4	no	—
640	C₂²⋊C₄	—	4	4	no	—
641	C₂²⋊C₄	—	4	4	no	—
642	C₂²⋊C₄	—	4	4	no	—
643	C₂²⋊C₄	—	4	2	no	—
644	C₂²⋊C₄	C₂×D₄×C₅₉	1	8	yes	—
645	C₄²	—	2	4	no	—
646	C₄²	—	2	2	no	—
647	C₄²	—	2	4	no	—
648	C₄²	—	2	4	no	—
649	C₄²	C₂×D₄×C₅₉	1	4	yes	—
650	C₂³	—	2	4	no	—
651	C₂³	—	2	4	no	—
652	C₂³	—	2	1	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	1	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	2	4	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	4	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	16	no	—
661	C₂³	—	4	16	no	—
662	C₂³	—	8	8	no	—
663	C₂³	—	8	4	no	—
664	C₂³	—	8	4	no	—
665	C₂³	C₂²×D₄×C₅₉	1	4	yes	—
666	C₂³	C₂²×Q₈×C₅₉	1	2	yes	—
667	C₂³	C₂²×Q₈×C₅₉	1	4	yes	—
668	C₂³	C₂²×Q₈×C₅₉	1	4	yes	—
669	C₂³	C₂×#41×C₅₉	1	4	yes	—
670	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
671	Q₈	—	2	8	no	—
672	Q₈	—	4	16	no	—
673	Q₈	—	4	8	no	—
674	D₄	—	2	16	no	—
675	D₄	—	2	8	no	—
676	D₄	C₂²⋊Q₈×C₅₉	1	16	yes	complemented
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	8	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	4	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	4	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	4	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	4	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	4	8	no	—
707	C₂×C₄	—	4	16	no	—
708	C₂×C₄	—	8	4	no	—
709	C₂×C₄	—	8	4	no	—
710	C₂×C₄	—	8	8	no	—
711	C₂×C₄	—	8	4	no	—
712	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
713	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
714	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
715	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
716	C₂×C₄	C₂²×Q₈×C₅₉	1	2	yes	—
717	C₂×C₄	C₂²×Q₈×C₅₉	1	2	yes	—
718	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
719	C₂×C₄	H(5,𝔽₂)×C₅₉	1	4	yes	—
720	C₂²	—	2	8	no	—
721	C₂²	—	2	4	no	—
722	C₂²	—	2	4	no	—
723	C₂²	—	2	8	no	—
724	C₂²	—	2	2	no	—
725	C₂²	—	2	4	no	—
726	C₂²	—	2	4	no	—
727	C₂²	—	2	8	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	4	4	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	1	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	1	no	—
734	C₂²	—	8	16	no	—
735	C₂²	C₂×C₂²⋊Q₈×C₅₉	1	8	yes	—
736	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
737	C₂²	C₂³×Q₈×C₅₉	1	1	yes	characteristic
738	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
739	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	2	yes	—
740	C₂²	C₅₉×#585	1	2	yes	—
741	C₄	—	2	2	no	—
742	C₄	—	2	2	no	—
743	C₄	—	2	4	no	—
744	C₄	—	2	4	no	—
745	C₄	—	2	2	no	—
746	C₄	—	4	2	no	—
747	C₄	—	4	4	no	—
748	C₄	—	4	2	no	—
749	C₄	—	4	4	no	—
750	C₄	—	4	1	no	—
751	C₄	—	4	2	no	—
752	C₄	—	4	1	no	—
753	C₄	—	4	2	no	—
754	C₄	C₂×C₂²⋊Q₈×C₅₉	1	4	yes	—
755	C₂	—	2	8	no	—
756	C₂	—	4	2	no	—
757	C₂	—	4	4	no	—
758	C₂	C₂²×C₂²⋊Q₈×C₅₉	1	1	yes	characteristic
759	C₂	C₅₉×#3484	1	1	yes	characteristic
760	C₂	C₅₉×#3500	1	1	yes	characteristic
761	C₂	C₅₉×#3501	1	2	yes	—
762	C₂	C₅₉×#3514	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₂³×D₄×C₅₉	C₂²
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×D₄×Q₈×C₅₉	C₂	semidirect
3. C₅₉×#2628	C₂	semidirect
4. C₅₉×#2626	C₂	semidirect
5. C₅₉×#2580	C₂	semidirect
6. C₅₉×#2564	C₂	semidirect
7. C₅₉×#2563	C₂	semidirect
8. C₅₉×#2452	C₂	semidirect
9. C₅₉×#2450	C₂	semidirect
10. C₅₉×#2439	C₂	semidirect
11. C₅₉×#2437	C₂	semidirect
12. C₅₉×#2409	C₂	semidirect
13. C₅₉×#2396	C₂	semidirect
14. C₂×C₅₉×#393	C₂	semidirect
15. C₅₉×#2349	C₂	semidirect
16. C₅₉×#2349	C₂	semidirect
18. C₂³×Q₈×C₅₉	C₂²	semidirect
21. C₂×C₄⋊Q₈×C₅₉	C₂²	semidirect
22. C₂×C₄⋊Q₈×C₅₉	C₂²	semidirect
23. C₂×C₂²⋊Q₈×C₅₉	C₂²	semidirect
24. C₂×C₂²⋊Q₈×C₅₉	C₂²	semidirect
25. C₂×C₂²⋊Q₈×C₅₉	C₂²	semidirect
27. C₂×C₄×Q₈×C₅₉	C₂²	semidirect
41. C₅₉×#400	C₂²	semidirect
42. C₅₉×#400	C₂²	semidirect
45. C₅₉×#399	C₂²	semidirect
46. C₅₉×#398	C₂²	semidirect
49. C₅₉×#396	C₂²	semidirect
50. C₅₉×#395	C₂²	semidirect
51. C₅₉×#395	C₂²	semidirect
55. C₅₉×#393	C₂²	semidirect
56. C₅₉×#393	C₂²	semidirect
57. C₅₉×#393	C₂²	semidirect
58. C₅₉×#393	C₂²	semidirect
59. C₅₉×#391	C₂²	semidirect
62. C₅₉×#389	C₂²	semidirect
63. C₅₉×#389	C₂²	semidirect
64. C₅₉×#389	C₂²	semidirect
65. C₅₉×#387	C₂²	semidirect
68. C₅₉×#385	C₂²	semidirect
69. C₅₉×#385	C₂²	semidirect
70. C₅₉×#385	C₂²	semidirect
71. C₅₉×#385	C₂²	semidirect
72. C₅₉×#385	C₂²	semidirect
73. C₅₉×#382	C₂²	semidirect
74. C₅₉×#382	C₂²	semidirect
76. C₅₉×#380	C₂²	semidirect
77. C₅₉×#380	C₂²	semidirect
78. C₅₉×#380	C₂²	semidirect
80. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
81. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
83. C₂×#95×C₅₉	C₂²	semidirect
84. C₂×#95×C₅₉	C₂²	semidirect
93. C₂²×D₄×C₅₉	Q₈	semidirect
178. C₂⁴×C₅₉	C₂×Q₈	semidirect
197. C₂×D₄×C₅₉	C₂×Q₈	semidirect
198. C₂×D₄×C₅₉	C₂×Q₈	semidirect
216. C₂²×C₄×C₅₉	C₂×Q₈	semidirect
294. D₄×C₅₉	C₂²⋊Q₈	semidirect
338. #35702	C₅₉	direct (N × H)
374. C₂×D₄×Q₈	C₂×C₅₉	semidirect
376. #2628	C₂×C₅₉	semidirect
377. #2626	C₂×C₅₉	semidirect
378. #2580	C₂×C₅₉	semidirect
379. #2564	C₂×C₅₉	semidirect
380. #2563	C₂×C₅₉	semidirect
381. #2452	C₂×C₅₉	semidirect
382. #2450	C₂×C₅₉	semidirect
383. #2439	C₂×C₅₉	semidirect
384. #2437	C₂×C₅₉	semidirect
385. #2409	C₂×C₅₉	semidirect
386. #2396	C₂×C₅₉	semidirect
387. C₂×#393	C₂×C₅₉	semidirect
388. #2349	C₂×C₅₉	semidirect
389. #2349	C₂×C₅₉	semidirect
399. C₂³×Q₈	C₂²×C₅₉	semidirect
402. C₂×C₄⋊Q₈	C₂²×C₅₉	semidirect
403. C₂×C₄⋊Q₈	C₂²×C₅₉	semidirect
404. C₂×C₂²⋊Q₈	C₂²×C₅₉	semidirect
405. C₂×C₂²⋊Q₈	C₂²×C₅₉	semidirect
406. C₂×C₂²⋊Q₈	C₂²×C₅₉	semidirect
408. C₂×C₄×Q₈	C₂²×C₅₉	semidirect
422. #400	C₂²×C₅₉	semidirect
423. #400	C₂²×C₅₉	semidirect
426. #399	C₂²×C₅₉	semidirect
427. #398	C₂²×C₅₉	semidirect
430. #396	C₂²×C₅₉	semidirect
431. #395	C₂²×C₅₉	semidirect
432. #395	C₂²×C₅₉	semidirect
436. #393	C₂²×C₅₉	semidirect
437. #393	C₂²×C₅₉	semidirect
438. #393	C₂²×C₅₉	semidirect
439. #393	C₂²×C₅₉	semidirect
440. #391	C₂²×C₅₉	semidirect
443. #389	C₂²×C₅₉	semidirect
444. #389	C₂²×C₅₉	semidirect
445. #389	C₂²×C₅₉	semidirect
446. #387	C₂²×C₅₉	semidirect
449. #385	C₂²×C₅₉	semidirect
450. #385	C₂²×C₅₉	semidirect
451. #385	C₂²×C₅₉	semidirect
452. #385	C₂²×C₅₉	semidirect
453. #385	C₂²×C₅₉	semidirect
454. #382	C₂²×C₅₉	semidirect
455. #382	C₂²×C₅₉	semidirect
457. #380	C₂²×C₅₉	semidirect
458. #380	C₂²×C₅₉	semidirect
459. #380	C₂²×C₅₉	semidirect
461. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
462. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
464. C₂×#95	C₂²×C₅₉	semidirect
465. C₂×#95	C₂²×C₅₉	semidirect
466. C₅₉	#35702	direct (N × H)
475. C₂²×D₄	Q₈×C₅₉	semidirect
560. C₂⁴	C₂×Q₈×C₅₉	semidirect
579. C₂×D₄	C₂×Q₈×C₅₉	semidirect
580. C₂×D₄	C₂×Q₈×C₅₉	semidirect
598. C₂²×C₄	C₂×Q₈×C₅₉	semidirect
676. D₄	C₂²⋊Q₈×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×Q₈×C₅₉	2
C₂×C₅₉×#518	2
C₅₉×#2628	2
C₅₉×#2626	2
C₅₉×#2580	2
C₅₉×#2564	2
C₅₉×#2563	2
C₅₉×#2452	2
C₅₉×#2450	2
C₅₉×#2439	2
C₅₉×#2437	2
C₅₉×#2409	2
C₅₉×#2396	2
C₂×C₅₉×#393	2
C₅₉×#2349	2
D₄×C₂²⋊C₄×C₅₉	2
#35702	59

Subgroups — C59×#35702 #28447811

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35702 #28447811