Subgroups — C₅₉×#35750 #28447859

Order 15104.

5482 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×H(5,𝔽₂)×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅₉×#546	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2616	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2613	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2435	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#2432	C₂	1	2	yes	maximal, complemented
8	C₅₉×#2430	C₂	1	2	yes	maximal, complemented
9	C₅₉×#2410	C₂	1	4	yes	maximal, complemented
10	C₅₉×#2408	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2407	C₂	1	2	yes	maximal, complemented
12	C₅₉×#2406	C₂	1	2	yes	maximal, complemented
13	C₅₉×#2405	C₂	1	4	yes	maximal, complemented
14	C₅₉×#2388	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅₉×#394	C₂	1	2	yes	maximal, complemented
16	C₅₉×#2339	C₂	1	1	yes	maximal, characteristic, complemented
17	D₄×C₂²⋊C₄×C₅₉	C₂	1	2	yes	maximal, complemented
18	C₂×H(5,𝔽₂)×C₅₉	—	2	8	no	—
19	C₂×H(5,𝔽₂)×C₅₉	—	2	16	no	—
20	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic
21	C₂²×#41×C₅₉	C₂²	1	2	yes	—
22	C₂²×#41×C₅₉	C₂²	1	2	yes	—
23	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic
24	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic, complemented
25	C₂³×D₄×C₅₉	C₂²	1	2	yes	—
26	C₂³×D₄×C₅₉	C₂²	1	4	yes	—
27	C₂³×D₄×C₅₉	C₂²	1	1	yes	characteristic
28	C₂³×D₄×C₅₉	C₂²	1	2	yes	—
29	C₅₉×#547	—	2	8	no	—
30	C₅₉×#546	—	2	16	no	—
31	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
32	C₂×#124×C₅₉	C₂²	1	2	yes	complemented
33	C₂×#123×C₅₉	C₂²	1	2	yes	complemented
34	C₂×#123×C₅₉	C₂²	1	2	yes	complemented
35	C₂×#123×C₅₉	C₂²	1	4	yes	complemented
36	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	complemented
37	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
39	C₂×#121×C₅₉	C₂²	1	2	yes	complemented
40	C₂×#121×C₅₉	C₂²	1	2	yes	complemented
41	C₂×#121×C₅₉	C₂²	1	4	yes	complemented
42	C₂×#120×C₅₉	C₂²	1	4	yes	complemented
43	C₂×#120×C₅₉	C₂²	1	2	yes	complemented
44	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	complemented
46	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	complemented
47	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
48	C₂²×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
49	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	4	yes	complemented
50	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	4	yes	complemented
51	C₅₉×#395	C₂²	1	2	yes	complemented
52	C₅₉×#395	C₂²	1	1	yes	characteristic, complemented
53	C₅₉×#394	C₂²	1	2	yes	complemented
54	C₅₉×#394	C₂²	1	4	yes	complemented
55	C₅₉×#394	C₂²	1	2	yes	complemented
56	C₅₉×#394	C₂²	1	4	yes	complemented
57	C₅₉×#394	C₂²	1	1	yes	characteristic, complemented
58	C₅₉×#394	C₂²	1	4	yes	complemented
59	C₅₉×#394	C₂²	1	2	yes	complemented
60	C₅₉×#394	C₂²	1	4	yes	complemented
61	C₅₉×#394	C₂²	1	2	yes	complemented
62	C₅₉×#394	C₂²	1	2	yes	complemented
63	C₅₉×#393	C₂²	1	1	yes	characteristic, complemented
64	C₅₉×#392	C₂²	1	1	yes	characteristic, complemented
65	C₅₉×#392	C₂²	1	4	yes	complemented
66	C₅₉×#392	C₂²	1	2	yes	complemented
67	C₅₉×#392	C₂²	1	2	yes	complemented
68	C₅₉×#391	C₂²	1	2	yes	complemented
69	C₅₉×#390	C₂²	1	2	yes	complemented
70	C₅₉×#390	C₂²	1	2	yes	complemented
71	C₅₉×#386	C₂²	1	4	yes	complemented
72	C₅₉×#386	C₂²	1	4	yes	complemented
73	C₅₉×#386	C₂²	1	4	yes	complemented
74	C₅₉×#386	C₂²	1	4	yes	complemented
75	C₅₉×#385	C₂²	1	4	yes	complemented
76	C₅₉×#385	C₂²	1	4	yes	complemented
77	C₅₉×#385	C₂²	1	4	yes	complemented
78	C₅₉×#381	C₂²	1	2	yes	complemented
79	C₅₉×#380	C₂²	1	2	yes	complemented
80	C₅₉×#380	C₂²	1	1	yes	characteristic, complemented
81	C₅₉×#379	C₂²	1	4	yes	complemented
82	C₅₉×#379	C₂²	1	2	yes	complemented
83	C₅₉×#379	C₂²	1	4	yes	complemented
84	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	complemented
85	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
86	C₂×#95×C₅₉	C₂²	1	2	yes	complemented
87	C₂⁵×C₅₉	C₂³	1	2	yes	—
88	C₂⁵×C₅₉	C₂³	1	4	yes	—
89	H(5,𝔽₂)×C₅₉	—	2	128	no	—
90	C₂×#41×C₅₉	—	2	8	no	—
91	C₂×#41×C₅₉	—	2	16	no	—
92	C₂×#41×C₅₉	—	2	8	no	—
93	C₂×#41×C₅₉	—	2	8	no	—
94	C₂×#41×C₅₉	—	2	8	no	—
95	C₂×#41×C₅₉	—	2	4	no	—
96	C₂×#41×C₅₉	—	2	8	no	—
97	C₂×#41×C₅₉	—	2	4	no	—
98	C₂×#41×C₅₉	—	2	8	no	—
99	C₂×#41×C₅₉	—	2	8	no	—
100	C₂×#41×C₅₉	D₄	1	8	yes	complemented
101	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
102	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
103	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
104	C₂²×D₄×C₅₉	—	2	16	no	—
105	C₂²×D₄×C₅₉	—	2	16	no	—
106	C₂²×D₄×C₅₉	—	2	16	no	—
107	C₂²×D₄×C₅₉	—	2	16	no	—
108	C₂²×D₄×C₅₉	—	2	8	no	—
109	C₂²×D₄×C₅₉	—	2	8	no	—
110	C₂²×D₄×C₅₉	—	2	8	no	—
111	C₂²×D₄×C₅₉	—	2	8	no	—
112	C₂²×D₄×C₅₉	—	2	4	no	—
113	C₂²×D₄×C₅₉	D₄	1	16	yes	complemented
114	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
115	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
116	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
117	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
118	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
119	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
120	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
121	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
122	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
123	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
124	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
125	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₅₉	C₂³	1	4	yes	—
127	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
128	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
130	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
131	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
133	C₂³×C₄×C₅₉	C₂³	1	4	yes	—
134	C₄⋊Q₈×C₅₉	—	2	4	no	—
135	#124×C₅₉	—	2	8	no	—
136	#123×C₅₉	—	2	16	no	—
137	#123×C₅₉	—	2	8	no	—
138	#123×C₅₉	—	2	8	no	—
139	C₂²⋊Q₈×C₅₉	—	2	4	no	—
140	C₂²⋊Q₈×C₅₉	—	2	8	no	—
141	C₂²⋊Q₈×C₅₉	—	2	4	no	—
142	#121×C₅₉	—	2	8	no	—
143	#121×C₅₉	—	2	16	no	—
144	#121×C₅₉	—	2	8	no	—
145	#120×C₅₉	—	2	16	no	—
146	#120×C₅₉	—	4	4	no	—
147	C₄×D₄×C₅₉	—	2	8	no	—
148	C₄×D₄×C₅₉	—	2	4	no	—
149	C₄×D₄×C₅₉	—	2	8	no	—
150	C₄×D₄×C₅₉	—	2	4	no	—
151	C₂×C₄⋊C₄×C₅₉	—	2	8	no	—
152	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
159	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₅₉	—	2	16	no	—
162	C₂×C₂²⋊C₄×C₅₉	—	4	8	no	—
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	1	yes	characteristic
166	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
168	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
169	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
170	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
171	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
172	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
177	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
180	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
181	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
183	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
184	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
186	#95×C₅₉	C₂³	1	1	yes	characteristic
187	#95×C₅₉	C₂³	1	2	yes	—
188	#95×C₅₉	C₂³	1	4	yes	—
189	#95×C₅₉	C₂³	1	1	yes	characteristic
190	#95×C₅₉	C₂³	1	2	yes	—
191	#95×C₅₉	C₂³	1	2	yes	—
192	#95×C₅₉	C₂³	1	4	yes	—
193	#95×C₅₉	C₂³	1	4	yes	—
194	C₂⁴×C₅₉	—	2	8	no	—
195	C₂⁴×C₅₉	—	2	4	no	—
196	C₂⁴×C₅₉	—	2	8	no	—
197	C₂⁴×C₅₉	—	2	8	no	—
198	C₂⁴×C₅₉	—	4	4	no	—
199	C₂⁴×C₅₉	—	4	4	no	—
200	C₂⁴×C₅₉	—	4	4	no	—
201	C₂⁴×C₅₉	—	4	4	no	—
202	C₂⁴×C₅₉	—	4	2	no	—
203	C₂⁴×C₅₉	—	4	2	no	—
204	C₂⁴×C₅₉	—	4	4	no	—
205	C₂⁴×C₅₉	C₂×D₄	1	16	yes	—
206	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
207	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
208	C₂⁴×C₅₉	C₂⁴	1	4	yes	—
209	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
210	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
211	#41×C₅₉	—	2	64	no	—
212	#41×C₅₉	—	2	64	no	—
213	#41×C₅₉	—	2	32	no	—
214	#41×C₅₉	—	2	32	no	—
215	#41×C₅₉	—	4	16	no	—
216	C₂×Q₈×C₅₉	—	2	4	no	—
217	C₂×Q₈×C₅₉	—	2	2	no	—
218	C₂×Q₈×C₅₉	—	2	4	no	—
219	C₂×Q₈×C₅₉	—	2	4	no	—
220	C₂×Q₈×C₅₉	—	2	2	no	—
221	C₂×Q₈×C₅₉	C₂×D₄	1	4	yes	—
222	C₂×D₄×C₅₉	—	2	128	no	—
223	C₂×D₄×C₅₉	—	2	64	no	—
224	C₂×D₄×C₅₉	—	2	32	no	—
225	C₂×D₄×C₅₉	—	2	8	no	—
226	C₂×D₄×C₅₉	—	2	8	no	—
227	C₂×D₄×C₅₉	—	2	4	no	—
228	C₂×D₄×C₅₉	—	2	8	no	—
229	C₂×D₄×C₅₉	—	2	4	no	—
230	C₂×D₄×C₅₉	—	2	4	no	—
231	C₂×D₄×C₅₉	—	2	8	no	—
232	C₂×D₄×C₅₉	—	2	8	no	—
233	C₂×D₄×C₅₉	—	2	8	no	—
234	C₂×D₄×C₅₉	—	2	64	no	—
235	C₂×D₄×C₅₉	—	2	4	no	—
236	C₂×D₄×C₅₉	—	2	2	no	—
237	C₂×D₄×C₅₉	—	2	8	no	—
238	C₂×D₄×C₅₉	—	2	4	no	—
239	C₂×D₄×C₅₉	—	2	8	no	—
240	C₂×D₄×C₅₉	—	2	8	no	—
241	C₂×D₄×C₅₉	—	2	4	no	—
242	C₂×D₄×C₅₉	—	2	2	no	—
243	C₂×D₄×C₅₉	—	2	4	no	—
244	C₂×D₄×C₅₉	—	2	4	no	—
245	C₂×D₄×C₅₉	—	2	4	no	—
246	C₂×D₄×C₅₉	—	2	2	no	—
247	C₂×D₄×C₅₉	—	4	1	no	—
248	C₂×D₄×C₅₉	—	4	2	no	—
249	C₂×D₄×C₅₉	—	4	2	no	—
250	C₂×D₄×C₅₉	—	4	4	no	—
251	C₂×D₄×C₅₉	—	4	4	no	—
252	C₂×D₄×C₅₉	C₂×D₄	1	8	yes	—
253	C₂×D₄×C₅₉	C₂×D₄	1	16	yes	—
254	C₂×D₄×C₅₉	C₂×D₄	1	8	yes	—
255	C₂×D₄×C₅₉	C₂×D₄	1	4	yes	—
256	C₂×D₄×C₅₉	C₂×D₄	1	8	yes	—
257	C₂²×C₄×C₅₉	—	2	8	no	—
258	C₂²×C₄×C₅₉	—	2	8	no	—
259	C₂²×C₄×C₅₉	—	2	8	no	—
260	C₂²×C₄×C₅₉	—	2	8	no	—
261	C₂²×C₄×C₅₉	—	2	4	no	—
262	C₂²×C₄×C₅₉	—	2	4	no	—
263	C₂²×C₄×C₅₉	—	2	4	no	—
264	C₂²×C₄×C₅₉	—	2	8	no	—
265	C₂²×C₄×C₅₉	—	2	4	no	—
266	C₂²×C₄×C₅₉	—	2	4	no	—
267	C₂²×C₄×C₅₉	—	2	8	no	—
268	C₂²×C₄×C₅₉	—	2	4	no	—
269	C₂²×C₄×C₅₉	—	2	2	no	—
270	C₂²×C₄×C₅₉	—	2	4	no	—
271	C₂²×C₄×C₅₉	—	4	2	no	—
272	C₂²×C₄×C₅₉	—	4	4	no	—
273	C₂²×C₄×C₅₉	—	4	4	no	—
274	C₂²×C₄×C₅₉	C₂×D₄	1	8	yes	—
275	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
276	C₂²×C₄×C₅₉	C₂×D₄	1	8	yes	—
277	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
280	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
289	C₄⋊C₄×C₅₉	—	2	2	no	—
290	C₄⋊C₄×C₅₉	—	2	4	no	—
291	C₄⋊C₄×C₅₉	—	2	4	no	—
292	C₄⋊C₄×C₅₉	—	2	4	no	—
293	C₄⋊C₄×C₅₉	—	2	4	no	—
294	C₄⋊C₄×C₅₉	—	2	2	no	—
295	C₄⋊C₄×C₅₉	—	2	4	no	—
296	C₄⋊C₄×C₅₉	—	2	8	no	—
297	C₄⋊C₄×C₅₉	—	2	4	no	—
298	C₂²⋊C₄×C₅₉	—	2	4	no	—
299	C₂²⋊C₄×C₅₉	—	2	8	no	—
300	C₂²⋊C₄×C₅₉	—	2	8	no	—
301	C₂²⋊C₄×C₅₉	—	2	8	no	—
302	C₂²⋊C₄×C₅₉	—	2	8	no	—
303	C₂²⋊C₄×C₅₉	—	2	4	no	—
304	C₂²⋊C₄×C₅₉	—	2	2	no	—
305	C₂²⋊C₄×C₅₉	—	2	8	no	—
306	C₂²⋊C₄×C₅₉	—	2	4	no	—
307	C₂²⋊C₄×C₅₉	—	2	4	no	—
308	C₂²⋊C₄×C₅₉	—	2	2	no	—
309	C₂²⋊C₄×C₅₉	—	2	4	no	—
310	C₂²⋊C₄×C₅₉	—	2	4	no	—
311	C₂²⋊C₄×C₅₉	—	2	8	no	—
312	C₂²⋊C₄×C₅₉	—	4	4	no	—
313	C₂²⋊C₄×C₅₉	—	4	4	no	—
314	C₂²⋊C₄×C₅₉	—	4	2	no	—
315	C₂²⋊C₄×C₅₉	—	4	4	no	—
316	C₂²⋊C₄×C₅₉	—	4	4	no	—
317	C₂²⋊C₄×C₅₉	—	4	2	no	—
318	C₂²⋊C₄×C₅₉	—	4	2	no	—
319	C₄²×C₅₉	—	2	4	no	—
320	C₄²×C₅₉	—	2	2	no	—
321	C₂³×C₅₉	—	2	2	no	—
322	C₂³×C₅₉	—	2	2	no	—
323	C₂³×C₅₉	—	2	4	no	—
324	C₂³×C₅₉	—	2	16	no	—
325	C₂³×C₅₉	—	2	4	no	—
326	C₂³×C₅₉	—	2	2	no	—
327	C₂³×C₅₉	—	2	2	no	—
328	C₂³×C₅₉	—	2	4	no	—
329	C₂³×C₅₉	—	2	2	no	—
330	C₂³×C₅₉	—	2	2	no	—
331	C₂³×C₅₉	—	2	4	no	—
332	C₂³×C₅₉	—	2	1	no	—
333	C₂³×C₅₉	—	2	4	no	—
334	C₂³×C₅₉	—	2	4	no	—
335	C₂³×C₅₉	—	2	2	no	—
336	C₂³×C₅₉	—	2	2	no	—
337	C₂³×C₅₉	—	2	2	no	—
338	C₂³×C₅₉	—	2	2	no	—
339	C₂³×C₅₉	—	2	1	no	—
340	C₂³×C₅₉	—	2	4	no	—
341	C₂³×C₅₉	—	2	32	no	—
342	C₂³×C₅₉	—	2	1	no	—
343	C₂³×C₅₉	—	2	2	no	—
344	C₂³×C₅₉	—	2	1	no	—
345	C₂³×C₅₉	—	2	1	no	—
346	C₂³×C₅₉	—	2	2	no	—
347	C₂³×C₅₉	—	4	16	no	—
348	C₂³×C₅₉	—	4	16	no	—
349	C₂³×C₅₉	—	8	8	no	—
350	C₂³×C₅₉	—	8	8	no	—
351	C₂³×C₅₉	—	8	8	no	—
352	C₂³×C₅₉	—	8	8	no	—
353	C₂³×C₅₉	—	8	8	no	—
354	C₂³×C₅₉	—	8	4	no	—
355	C₂³×C₅₉	—	8	8	no	—
356	C₂³×C₅₉	—	8	4	no	—
357	C₂³×C₅₉	C₂²×D₄	1	8	yes	—
358	C₂³×C₅₉	C₂²×D₄	1	4	yes	—
359	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
360	C₂³×C₅₉	C₂²×D₄	1	8	yes	—
361	C₂³×C₅₉	C₂²×D₄	1	4	yes	—
362	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
363	Q₈×C₅₉	—	2	8	no	—
364	Q₈×C₅₉	—	2	8	no	—
365	Q₈×C₅₉	—	4	4	no	—
366	D₄×C₅₉	—	2	32	no	—
367	D₄×C₅₉	—	2	16	no	—
368	D₄×C₅₉	—	2	16	no	—
369	D₄×C₅₉	—	2	8	no	—
370	D₄×C₅₉	—	2	16	no	—
371	D₄×C₅₉	—	2	32	no	—
372	D₄×C₅₉	—	2	16	no	—
373	D₄×C₅₉	—	4	4	no	—
374	D₄×C₅₉	—	4	8	no	—
375	D₄×C₅₉	—	4	8	no	—
376	D₄×C₅₉	—	8	8	no	—
377	D₄×C₅₉	#120	1	16	yes	complemented
378	C₂×C₄×C₅₉	—	2	32	no	—
379	C₂×C₄×C₅₉	—	2	16	no	—
380	C₂×C₄×C₅₉	—	2	1	no	—
381	C₂×C₄×C₅₉	—	2	4	no	—
382	C₂×C₄×C₅₉	—	2	2	no	—
383	C₂×C₄×C₅₉	—	2	2	no	—
384	C₂×C₄×C₅₉	—	2	2	no	—
385	C₂×C₄×C₅₉	—	2	1	no	—
386	C₂×C₄×C₅₉	—	2	8	no	—
387	C₂×C₄×C₅₉	—	2	16	no	—
388	C₂×C₄×C₅₉	—	2	1	no	—
389	C₂×C₄×C₅₉	—	2	2	no	—
390	C₂×C₄×C₅₉	—	2	2	no	—
391	C₂×C₄×C₅₉	—	2	2	no	—
392	C₂×C₄×C₅₉	—	2	4	no	—
393	C₂×C₄×C₅₉	—	2	2	no	—
394	C₂×C₄×C₅₉	—	2	4	no	—
395	C₂×C₄×C₅₉	—	2	1	no	—
396	C₂×C₄×C₅₉	—	2	2	no	—
397	C₂×C₄×C₅₉	—	2	2	no	—
398	C₂×C₄×C₅₉	—	2	4	no	—
399	C₂×C₄×C₅₉	—	2	2	no	—
400	C₂×C₄×C₅₉	—	2	2	no	—
401	C₂×C₄×C₅₉	—	2	2	no	—
402	C₂×C₄×C₅₉	—	2	2	no	—
403	C₂×C₄×C₅₉	—	2	2	no	—
404	C₂×C₄×C₅₉	—	2	2	no	—
405	C₂×C₄×C₅₉	—	2	4	no	—
406	C₂×C₄×C₅₉	—	4	8	no	—
407	C₂×C₄×C₅₉	—	4	8	no	—
408	C₂×C₄×C₅₉	—	4	4	no	—
409	C₂×C₄×C₅₉	—	8	8	no	—
410	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
411	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
412	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
413	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
414	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
415	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	complemented
416	#35750	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
417	C₂²×C₅₉	—	2	8	no	—
418	C₂²×C₅₉	—	2	4	no	—
419	C₂²×C₅₉	—	2	8	no	—
420	C₂²×C₅₉	—	2	4	no	—
421	C₂²×C₅₉	—	2	8	no	—
422	C₂²×C₅₉	—	2	4	no	—
423	C₂²×C₅₉	—	2	2	no	—
424	C₂²×C₅₉	—	2	4	no	—
425	C₂²×C₅₉	—	2	8	no	—
426	C₂²×C₅₉	—	2	2	no	—
427	C₂²×C₅₉	—	2	8	no	—
428	C₂²×C₅₉	—	2	4	no	—
429	C₂²×C₅₉	—	2	2	no	—
430	C₂²×C₅₉	—	4	2	no	—
431	C₂²×C₅₉	—	4	4	no	—
432	C₂²×C₅₉	—	4	2	no	—
433	C₂²×C₅₉	—	4	2	no	—
434	C₂²×C₅₉	—	4	4	no	—
435	C₂²×C₅₉	—	4	2	no	—
436	C₂²×C₅₉	—	4	4	no	—
437	C₂²×C₅₉	—	4	2	no	—
438	C₂²×C₅₉	—	4	2	no	—
439	C₂²×C₅₉	—	4	4	no	—
440	C₂²×C₅₉	—	4	1	no	—
441	C₂²×C₅₉	—	4	2	no	—
442	C₂²×C₅₉	—	4	1	no	—
443	C₂²×C₅₉	—	4	2	no	—
444	C₂²×C₅₉	—	4	1	no	—
445	C₂²×C₅₉	—	8	32	no	—
446	C₂²×C₅₉	—	8	16	no	—
447	C₂²×C₅₉	C₂×#120	1	8	yes	—
448	C₂²×C₅₉	C₂³×D₄	1	2	yes	—
449	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
450	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
451	C₂²×C₅₉	#585	1	1	yes	characteristic
452	C₂²×C₅₉	#585	1	2	yes	—
453	C₄×C₅₉	—	2	4	no	—
454	C₄×C₅₉	—	2	4	no	—
455	C₄×C₅₉	—	2	2	no	—
456	C₄×C₅₉	—	2	2	no	—
457	C₄×C₅₉	—	4	1	no	—
458	C₄×C₅₉	—	4	2	no	—
459	C₄×C₅₉	—	4	2	no	—
460	C₄×C₅₉	—	4	2	no	—
461	C₄×C₅₉	—	4	2	no	—
462	C₄×C₅₉	—	4	4	no	—
463	C₄×C₅₉	—	4	1	no	—
464	C₄×C₅₉	C₂×#120	1	4	yes	—
465	C₂²×H(5,𝔽₂)	C₂×C₅₉	1	1	yes	characteristic, complemented
466	C₂×#547	C₂×C₅₉	1	1	yes	characteristic, complemented
467	C₂×#546	C₂×C₅₉	1	2	yes	complemented
468	#2616	C₂×C₅₉	1	1	yes	characteristic, complemented
469	#2613	C₂×C₅₉	1	2	yes	complemented
470	#2435	C₂×C₅₉	1	1	yes	characteristic, complemented
471	#2432	C₂×C₅₉	1	2	yes	complemented
472	#2430	C₂×C₅₉	1	2	yes	complemented
473	#2410	C₂×C₅₉	1	4	yes	complemented
474	#2408	C₂×C₅₉	1	1	yes	characteristic, complemented
475	#2407	C₂×C₅₉	1	2	yes	complemented
476	#2406	C₂×C₅₉	1	2	yes	complemented
477	#2405	C₂×C₅₉	1	4	yes	complemented
478	#2388	C₂×C₅₉	1	1	yes	characteristic, complemented
479	C₂×#394	C₂×C₅₉	1	2	yes	complemented
480	#2339	C₂×C₅₉	1	1	yes	characteristic, complemented
481	D₄×C₂²⋊C₄	C₂×C₅₉	1	2	yes	complemented
482	C₂×C₅₉	—	2	8	no	—
483	C₂×C₅₉	—	4	4	no	—
484	C₂×C₅₉	—	4	8	no	—
485	C₂×C₅₉	—	4	2	no	—
486	C₂×C₅₉	—	8	1	no	—
487	C₂×C₅₉	C₂²×#120	1	1	yes	characteristic
488	C₂×C₅₉	#3485	1	2	yes	—
489	C₂×C₅₉	#3488	1	1	yes	characteristic
490	C₂×C₅₉	#3496	1	2	yes	—
491	C₂×C₅₉	#3500	1	1	yes	characteristic
492	C₂×H(5,𝔽₂)	—	2	8	no	—
493	C₂×H(5,𝔽₂)	—	2	16	no	—
494	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic
495	C₂²×#41	C₂²×C₅₉	1	2	yes	—
496	C₂²×#41	C₂²×C₅₉	1	2	yes	—
497	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic
498	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic, complemented
499	C₂³×D₄	C₂²×C₅₉	1	2	yes	—
500	C₂³×D₄	C₂²×C₅₉	1	4	yes	—
501	C₂³×D₄	C₂²×C₅₉	1	1	yes	characteristic
502	C₂³×D₄	C₂²×C₅₉	1	2	yes	—
503	#547	—	2	8	no	—
504	#546	—	2	16	no	—
505	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
506	C₂×#124	C₂²×C₅₉	1	2	yes	complemented
507	C₂×#123	C₂²×C₅₉	1	2	yes	complemented
508	C₂×#123	C₂²×C₅₉	1	2	yes	complemented
509	C₂×#123	C₂²×C₅₉	1	4	yes	complemented
510	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	complemented
511	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
512	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
513	C₂×#121	C₂²×C₅₉	1	2	yes	complemented
514	C₂×#121	C₂²×C₅₉	1	2	yes	complemented
515	C₂×#121	C₂²×C₅₉	1	4	yes	complemented
516	C₂×#120	C₂²×C₅₉	1	4	yes	complemented
517	C₂×#120	C₂²×C₅₉	1	2	yes	complemented
518	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
519	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	complemented
520	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	complemented
521	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
522	C₂²×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
523	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	4	yes	complemented
524	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	4	yes	complemented
525	#395	C₂²×C₅₉	1	2	yes	complemented
526	#395	C₂²×C₅₉	1	1	yes	characteristic, complemented
527	#394	C₂²×C₅₉	1	2	yes	complemented
528	#394	C₂²×C₅₉	1	4	yes	complemented
529	#394	C₂²×C₅₉	1	2	yes	complemented
530	#394	C₂²×C₅₉	1	4	yes	complemented
531	#394	C₂²×C₅₉	1	1	yes	characteristic, complemented
532	#394	C₂²×C₅₉	1	4	yes	complemented
533	#394	C₂²×C₅₉	1	2	yes	complemented
534	#394	C₂²×C₅₉	1	4	yes	complemented
535	#394	C₂²×C₅₉	1	2	yes	complemented
536	#394	C₂²×C₅₉	1	2	yes	complemented
537	#393	C₂²×C₅₉	1	1	yes	characteristic, complemented
538	#392	C₂²×C₅₉	1	1	yes	characteristic, complemented
539	#392	C₂²×C₅₉	1	4	yes	complemented
540	#392	C₂²×C₅₉	1	2	yes	complemented
541	#392	C₂²×C₅₉	1	2	yes	complemented
542	#391	C₂²×C₅₉	1	2	yes	complemented
543	#390	C₂²×C₅₉	1	2	yes	complemented
544	#390	C₂²×C₅₉	1	2	yes	complemented
545	#386	C₂²×C₅₉	1	4	yes	complemented
546	#386	C₂²×C₅₉	1	4	yes	complemented
547	#386	C₂²×C₅₉	1	4	yes	complemented
548	#386	C₂²×C₅₉	1	4	yes	complemented
549	#385	C₂²×C₅₉	1	4	yes	complemented
550	#385	C₂²×C₅₉	1	4	yes	complemented
551	#385	C₂²×C₅₉	1	4	yes	complemented
552	#381	C₂²×C₅₉	1	2	yes	complemented
553	#380	C₂²×C₅₉	1	2	yes	complemented
554	#380	C₂²×C₅₉	1	1	yes	characteristic, complemented
555	#379	C₂²×C₅₉	1	4	yes	complemented
556	#379	C₂²×C₅₉	1	2	yes	complemented
557	#379	C₂²×C₅₉	1	4	yes	complemented
558	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	complemented
559	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
560	C₂×#95	C₂²×C₅₉	1	2	yes	complemented
561	C₅₉	#35750	1	1	yes	characteristic, direct product factor, Sylow
562	C₂⁵	C₂³×C₅₉	1	2	yes	—
563	C₂⁵	C₂³×C₅₉	1	4	yes	—
564	H(5,𝔽₂)	—	2	128	no	—
565	C₂×#41	—	2	8	no	—
566	C₂×#41	—	2	16	no	—
567	C₂×#41	—	2	8	no	—
568	C₂×#41	—	2	8	no	—
569	C₂×#41	—	2	8	no	—
570	C₂×#41	—	2	4	no	—
571	C₂×#41	—	2	8	no	—
572	C₂×#41	—	2	4	no	—
573	C₂×#41	—	2	8	no	—
574	C₂×#41	—	2	8	no	—
575	C₂×#41	D₄×C₅₉	1	8	yes	complemented
576	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
577	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
578	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
579	C₂²×D₄	—	2	16	no	—
580	C₂²×D₄	—	2	16	no	—
581	C₂²×D₄	—	2	16	no	—
582	C₂²×D₄	—	2	16	no	—
583	C₂²×D₄	—	2	8	no	—
584	C₂²×D₄	—	2	8	no	—
585	C₂²×D₄	—	2	8	no	—
586	C₂²×D₄	—	2	8	no	—
587	C₂²×D₄	—	2	4	no	—
588	C₂²×D₄	D₄×C₅₉	1	16	yes	complemented
589	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
590	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
591	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
592	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
593	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
594	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
595	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
596	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
597	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
598	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
599	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
600	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
601	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
602	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
603	C₂³×C₄	C₂³×C₅₉	1	4	yes	—
604	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
605	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
606	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
607	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
608	C₂³×C₄	C₂³×C₅₉	1	4	yes	—
609	C₄⋊Q₈	—	2	4	no	—
610	#124	—	2	8	no	—
611	#123	—	2	16	no	—
612	#123	—	2	8	no	—
613	#123	—	2	8	no	—
614	C₂²⋊Q₈	—	2	4	no	—
615	C₂²⋊Q₈	—	2	8	no	—
616	C₂²⋊Q₈	—	2	4	no	—
617	#121	—	2	8	no	—
618	#121	—	2	16	no	—
619	#121	—	2	8	no	—
620	#120	—	2	16	no	—
621	#120	—	4	4	no	—
622	C₄×D₄	—	2	8	no	—
623	C₄×D₄	—	2	4	no	—
624	C₄×D₄	—	2	8	no	—
625	C₄×D₄	—	2	4	no	—
626	C₂×C₄⋊C₄	—	2	8	no	—
627	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
635	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
636	C₂×C₂²⋊C₄	—	2	16	no	—
637	C₂×C₂²⋊C₄	—	4	8	no	—
638	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
648	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
649	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
659	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
660	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
661	#95	C₂³×C₅₉	1	1	yes	characteristic
662	#95	C₂³×C₅₉	1	2	yes	—
663	#95	C₂³×C₅₉	1	4	yes	—
664	#95	C₂³×C₅₉	1	1	yes	characteristic
665	#95	C₂³×C₅₉	1	2	yes	—
666	#95	C₂³×C₅₉	1	2	yes	—
667	#95	C₂³×C₅₉	1	4	yes	—
668	#95	C₂³×C₅₉	1	4	yes	—
669	C₂⁴	—	2	8	no	—
670	C₂⁴	—	2	4	no	—
671	C₂⁴	—	2	8	no	—
672	C₂⁴	—	2	8	no	—
673	C₂⁴	—	4	4	no	—
674	C₂⁴	—	4	4	no	—
675	C₂⁴	—	4	4	no	—
676	C₂⁴	—	4	4	no	—
677	C₂⁴	—	4	2	no	—
678	C₂⁴	—	4	2	no	—
679	C₂⁴	—	4	4	no	—
680	C₂⁴	C₂×D₄×C₅₉	1	16	yes	—
681	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
682	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
683	C₂⁴	C₂⁴×C₅₉	1	4	yes	—
684	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
685	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
686	#41	—	2	64	no	—
687	#41	—	2	64	no	—
688	#41	—	2	32	no	—
689	#41	—	2	32	no	—
690	#41	—	4	16	no	—
691	C₂×Q₈	—	2	4	no	—
692	C₂×Q₈	—	2	2	no	—
693	C₂×Q₈	—	2	4	no	—
694	C₂×Q₈	—	2	4	no	—
695	C₂×Q₈	—	2	2	no	—
696	C₂×Q₈	C₂×D₄×C₅₉	1	4	yes	—
697	C₂×D₄	—	2	128	no	—
698	C₂×D₄	—	2	64	no	—
699	C₂×D₄	—	2	32	no	—
700	C₂×D₄	—	2	8	no	—
701	C₂×D₄	—	2	8	no	—
702	C₂×D₄	—	2	4	no	—
703	C₂×D₄	—	2	8	no	—
704	C₂×D₄	—	2	4	no	—
705	C₂×D₄	—	2	4	no	—
706	C₂×D₄	—	2	8	no	—
707	C₂×D₄	—	2	8	no	—
708	C₂×D₄	—	2	8	no	—
709	C₂×D₄	—	2	64	no	—
710	C₂×D₄	—	2	4	no	—
711	C₂×D₄	—	2	2	no	—
712	C₂×D₄	—	2	8	no	—
713	C₂×D₄	—	2	4	no	—
714	C₂×D₄	—	2	8	no	—
715	C₂×D₄	—	2	8	no	—
716	C₂×D₄	—	2	4	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	2	4	no	—
719	C₂×D₄	—	2	4	no	—
720	C₂×D₄	—	2	4	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	4	1	no	—
723	C₂×D₄	—	4	2	no	—
724	C₂×D₄	—	4	2	no	—
725	C₂×D₄	—	4	4	no	—
726	C₂×D₄	—	4	4	no	—
727	C₂×D₄	C₂×D₄×C₅₉	1	8	yes	—
728	C₂×D₄	C₂×D₄×C₅₉	1	16	yes	—
729	C₂×D₄	C₂×D₄×C₅₉	1	8	yes	—
730	C₂×D₄	C₂×D₄×C₅₉	1	4	yes	—
731	C₂×D₄	C₂×D₄×C₅₉	1	8	yes	—
732	C₂²×C₄	—	2	8	no	—
733	C₂²×C₄	—	2	8	no	—
734	C₂²×C₄	—	2	8	no	—
735	C₂²×C₄	—	2	8	no	—
736	C₂²×C₄	—	2	4	no	—
737	C₂²×C₄	—	2	4	no	—
738	C₂²×C₄	—	2	4	no	—
739	C₂²×C₄	—	2	8	no	—
740	C₂²×C₄	—	2	4	no	—
741	C₂²×C₄	—	2	4	no	—
742	C₂²×C₄	—	2	8	no	—
743	C₂²×C₄	—	2	4	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	2	4	no	—
746	C₂²×C₄	—	4	2	no	—
747	C₂²×C₄	—	4	4	no	—
748	C₂²×C₄	—	4	4	no	—
749	C₂²×C₄	C₂×D₄×C₅₉	1	8	yes	—
750	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
751	C₂²×C₄	C₂×D₄×C₅₉	1	8	yes	—
752	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
753	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
754	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
755	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
756	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
757	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
758	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
759	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
760	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
761	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
762	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
763	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	4	no	—
766	C₄⋊C₄	—	2	4	no	—
767	C₄⋊C₄	—	2	4	no	—
768	C₄⋊C₄	—	2	4	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	4	no	—
771	C₄⋊C₄	—	2	8	no	—
772	C₄⋊C₄	—	2	4	no	—
773	C₂²⋊C₄	—	2	4	no	—
774	C₂²⋊C₄	—	2	8	no	—
775	C₂²⋊C₄	—	2	8	no	—
776	C₂²⋊C₄	—	2	8	no	—
777	C₂²⋊C₄	—	2	8	no	—
778	C₂²⋊C₄	—	2	4	no	—
779	C₂²⋊C₄	—	2	2	no	—
780	C₂²⋊C₄	—	2	8	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	2	4	no	—
783	C₂²⋊C₄	—	2	2	no	—
784	C₂²⋊C₄	—	2	4	no	—
785	C₂²⋊C₄	—	2	4	no	—
786	C₂²⋊C₄	—	2	8	no	—
787	C₂²⋊C₄	—	4	4	no	—
788	C₂²⋊C₄	—	4	4	no	—
789	C₂²⋊C₄	—	4	2	no	—
790	C₂²⋊C₄	—	4	2	no	—
791	C₂²⋊C₄	—	4	4	no	—
792	C₂²⋊C₄	—	4	4	no	—
793	C₂²⋊C₄	—	4	2	no	—
794	C₄²	—	2	4	no	—
795	C₄²	—	2	2	no	—
796	C₂³	—	2	2	no	—
797	C₂³	—	2	2	no	—
798	C₂³	—	2	4	no	—
799	C₂³	—	2	16	no	—
800	C₂³	—	2	4	no	—
801	C₂³	—	2	2	no	—
802	C₂³	—	2	2	no	—
803	C₂³	—	2	4	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	2	4	no	—
807	C₂³	—	2	1	no	—
808	C₂³	—	2	4	no	—
809	C₂³	—	2	4	no	—
810	C₂³	—	2	2	no	—
811	C₂³	—	2	2	no	—
812	C₂³	—	2	2	no	—
813	C₂³	—	2	2	no	—
814	C₂³	—	2	1	no	—
815	C₂³	—	2	4	no	—
816	C₂³	—	2	32	no	—
817	C₂³	—	2	1	no	—
818	C₂³	—	2	2	no	—
819	C₂³	—	2	1	no	—
820	C₂³	—	2	1	no	—
821	C₂³	—	2	2	no	—
822	C₂³	—	4	16	no	—
823	C₂³	—	4	16	no	—
824	C₂³	—	8	8	no	—
825	C₂³	—	8	8	no	—
826	C₂³	—	8	8	no	—
827	C₂³	—	8	8	no	—
828	C₂³	—	8	8	no	—
829	C₂³	—	8	4	no	—
830	C₂³	—	8	8	no	—
831	C₂³	—	8	4	no	—
832	C₂³	C₂²×D₄×C₅₉	1	8	yes	—
833	C₂³	C₂²×D₄×C₅₉	1	4	yes	—
834	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
835	C₂³	C₂²×D₄×C₅₉	1	8	yes	—
836	C₂³	C₂²×D₄×C₅₉	1	4	yes	—
837	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
838	Q₈	—	2	8	no	—
839	Q₈	—	2	8	no	—
840	Q₈	—	4	4	no	—
841	D₄	—	2	32	no	—
842	D₄	—	2	16	no	—
843	D₄	—	2	16	no	—
844	D₄	—	2	8	no	—
845	D₄	—	2	16	no	—
846	D₄	—	2	32	no	—
847	D₄	—	2	16	no	—
848	D₄	—	4	4	no	—
849	D₄	—	4	8	no	—
850	D₄	—	4	8	no	—
851	D₄	—	8	8	no	—
852	D₄	#120×C₅₉	1	16	yes	complemented
853	C₂×C₄	—	2	32	no	—
854	C₂×C₄	—	2	16	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	4	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	8	no	—
862	C₂×C₄	—	2	16	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	4	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	4	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	4	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	4	no	—
881	C₂×C₄	—	4	8	no	—
882	C₂×C₄	—	4	8	no	—
883	C₂×C₄	—	4	4	no	—
884	C₂×C₄	—	8	8	no	—
885	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
886	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
887	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
888	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
889	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
890	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	complemented
891	C₂²	—	2	8	no	—
892	C₂²	—	2	4	no	—
893	C₂²	—	2	8	no	—
894	C₂²	—	2	4	no	—
895	C₂²	—	2	8	no	—
896	C₂²	—	2	4	no	—
897	C₂²	—	2	2	no	—
898	C₂²	—	2	4	no	—
899	C₂²	—	2	8	no	—
900	C₂²	—	2	2	no	—
901	C₂²	—	2	8	no	—
902	C₂²	—	2	4	no	—
903	C₂²	—	2	2	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	4	no	—
906	C₂²	—	4	2	no	—
907	C₂²	—	4	2	no	—
908	C₂²	—	4	4	no	—
909	C₂²	—	4	2	no	—
910	C₂²	—	4	4	no	—
911	C₂²	—	4	2	no	—
912	C₂²	—	4	2	no	—
913	C₂²	—	4	4	no	—
914	C₂²	—	4	1	no	—
915	C₂²	—	4	2	no	—
916	C₂²	—	4	1	no	—
917	C₂²	—	4	2	no	—
918	C₂²	—	4	1	no	—
919	C₂²	—	8	32	no	—
920	C₂²	—	8	16	no	—
921	C₂²	C₂×#120×C₅₉	1	8	yes	—
922	C₂²	C₂³×D₄×C₅₉	1	2	yes	—
923	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
924	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
925	C₂²	C₅₉×#585	1	1	yes	characteristic
926	C₂²	C₅₉×#585	1	2	yes	—
927	C₄	—	2	4	no	—
928	C₄	—	2	4	no	—
929	C₄	—	2	2	no	—
930	C₄	—	2	2	no	—
931	C₄	—	4	1	no	—
932	C₄	—	4	2	no	—
933	C₄	—	4	2	no	—
934	C₄	—	4	2	no	—
935	C₄	—	4	2	no	—
936	C₄	—	4	4	no	—
937	C₄	—	4	1	no	—
938	C₄	C₂×#120×C₅₉	1	4	yes	—
939	C₂	—	2	8	no	—
940	C₂	—	4	4	no	—
941	C₂	—	4	8	no	—
942	C₂	—	4	2	no	—
943	C₂	—	8	1	no	—
944	C₂	C₂²×#120×C₅₉	1	1	yes	characteristic
945	C₂	C₅₉×#3485	1	2	yes	—
946	C₂	C₅₉×#3488	1	1	yes	characteristic
947	C₂	C₅₉×#3496	1	2	yes	—
948	C₂	C₅₉×#3500	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×H(5,𝔽₂)×C₅₉	C₂	semidirect
2. C₂×C₅₉×#547	C₂	semidirect
3. C₂×C₅₉×#546	C₂	semidirect
4. C₅₉×#2616	C₂	semidirect
5. C₅₉×#2613	C₂	semidirect
6. C₅₉×#2435	C₂	semidirect
7. C₅₉×#2432	C₂	semidirect
8. C₅₉×#2430	C₂	semidirect
9. C₅₉×#2410	C₂	semidirect
10. C₅₉×#2408	C₂	semidirect
11. C₅₉×#2407	C₂	semidirect
12. C₅₉×#2406	C₂	semidirect
13. C₅₉×#2405	C₂	semidirect
14. C₅₉×#2388	C₂	semidirect
15. C₂×C₅₉×#394	C₂	semidirect
16. C₅₉×#2339	C₂	semidirect
17. D₄×C₂²⋊C₄×C₅₉	C₂	semidirect
24. C₂²×#41×C₅₉	C₂²	semidirect
31. C₂×C₄⋊Q₈×C₅₉	C₂²	semidirect
32. C₂×#124×C₅₉	C₂²	semidirect
33. C₂×#123×C₅₉	C₂²	semidirect
34. C₂×#123×C₅₉	C₂²	semidirect
35. C₂×#123×C₅₉	C₂²	semidirect
36. C₂×C₂²⋊Q₈×C₅₉	C₂²	semidirect
37. C₂×C₂²⋊Q₈×C₅₉	C₂²	semidirect
38. C₂×C₂²⋊Q₈×C₅₉	C₂²	semidirect
39. C₂×#121×C₅₉	C₂²	semidirect
40. C₂×#121×C₅₉	C₂²	semidirect
41. C₂×#121×C₅₉	C₂²	semidirect
42. C₂×#120×C₅₉	C₂²	semidirect
43. C₂×#120×C₅₉	C₂²	semidirect
44. C₂×C₄×D₄×C₅₉	C₂²	semidirect
45. C₂×C₄×D₄×C₅₉	C₂²	semidirect
46. C₂×C₄×D₄×C₅₉	C₂²	semidirect
47. C₂×C₄×D₄×C₅₉	C₂²	semidirect
48. C₂²×C₄⋊C₄×C₅₉	C₂²	semidirect
49. C₂²×C₂²⋊C₄×C₅₉	C₂²	semidirect
50. C₂²×C₂²⋊C₄×C₅₉	C₂²	semidirect
51. C₅₉×#395	C₂²	semidirect
52. C₅₉×#395	C₂²	semidirect
53. C₅₉×#394	C₂²	semidirect
54. C₅₉×#394	C₂²	semidirect
55. C₅₉×#394	C₂²	semidirect
56. C₅₉×#394	C₂²	semidirect
57. C₅₉×#394	C₂²	semidirect
58. C₅₉×#394	C₂²	semidirect
59. C₅₉×#394	C₂²	semidirect
60. C₅₉×#394	C₂²	semidirect
61. C₅₉×#394	C₂²	semidirect
62. C₅₉×#394	C₂²	semidirect
63. C₅₉×#393	C₂²	semidirect
64. C₅₉×#392	C₂²	semidirect
65. C₅₉×#392	C₂²	semidirect
66. C₅₉×#392	C₂²	semidirect
67. C₅₉×#392	C₂²	semidirect
68. C₅₉×#391	C₂²	semidirect
69. C₅₉×#390	C₂²	semidirect
70. C₅₉×#390	C₂²	semidirect
71. C₅₉×#386	C₂²	semidirect
72. C₅₉×#386	C₂²	semidirect
73. C₅₉×#386	C₂²	semidirect
74. C₅₉×#386	C₂²	semidirect
75. C₅₉×#385	C₂²	semidirect
76. C₅₉×#385	C₂²	semidirect
77. C₅₉×#385	C₂²	semidirect
78. C₅₉×#381	C₂²	semidirect
79. C₅₉×#380	C₂²	semidirect
80. C₅₉×#380	C₂²	semidirect
81. C₅₉×#379	C₂²	semidirect
82. C₅₉×#379	C₂²	semidirect
83. C₅₉×#379	C₂²	semidirect
84. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
85. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
86. C₂×#95×C₅₉	C₂²	semidirect
100. C₂×#41×C₅₉	D₄	semidirect
113. C₂²×D₄×C₅₉	D₄	semidirect
377. D₄×C₅₉	#120	semidirect
415. C₂×C₄×C₅₉	H(5,𝔽₂)	semidirect
416. #35750	C₅₉	direct (N × H)
465. C₂²×H(5,𝔽₂)	C₂×C₅₉	semidirect
466. C₂×#547	C₂×C₅₉	semidirect
467. C₂×#546	C₂×C₅₉	semidirect
468. #2616	C₂×C₅₉	semidirect
469. #2613	C₂×C₅₉	semidirect
470. #2435	C₂×C₅₉	semidirect
471. #2432	C₂×C₅₉	semidirect
472. #2430	C₂×C₅₉	semidirect
473. #2410	C₂×C₅₉	semidirect
474. #2408	C₂×C₅₉	semidirect
475. #2407	C₂×C₅₉	semidirect
476. #2406	C₂×C₅₉	semidirect
477. #2405	C₂×C₅₉	semidirect
478. #2388	C₂×C₅₉	semidirect
479. C₂×#394	C₂×C₅₉	semidirect
480. #2339	C₂×C₅₉	semidirect
481. D₄×C₂²⋊C₄	C₂×C₅₉	semidirect
498. C₂²×#41	C₂²×C₅₉	semidirect
505. C₂×C₄⋊Q₈	C₂²×C₅₉	semidirect
506. C₂×#124	C₂²×C₅₉	semidirect
507. C₂×#123	C₂²×C₅₉	semidirect
508. C₂×#123	C₂²×C₅₉	semidirect
509. C₂×#123	C₂²×C₅₉	semidirect
510. C₂×C₂²⋊Q₈	C₂²×C₅₉	semidirect
511. C₂×C₂²⋊Q₈	C₂²×C₅₉	semidirect
512. C₂×C₂²⋊Q₈	C₂²×C₅₉	semidirect
513. C₂×#121	C₂²×C₅₉	semidirect
514. C₂×#121	C₂²×C₅₉	semidirect
515. C₂×#121	C₂²×C₅₉	semidirect
516. C₂×#120	C₂²×C₅₉	semidirect
517. C₂×#120	C₂²×C₅₉	semidirect
518. C₂×C₄×D₄	C₂²×C₅₉	semidirect
519. C₂×C₄×D₄	C₂²×C₅₉	semidirect
520. C₂×C₄×D₄	C₂²×C₅₉	semidirect
521. C₂×C₄×D₄	C₂²×C₅₉	semidirect
522. C₂²×C₄⋊C₄	C₂²×C₅₉	semidirect
523. C₂²×C₂²⋊C₄	C₂²×C₅₉	semidirect
524. C₂²×C₂²⋊C₄	C₂²×C₅₉	semidirect
525. #395	C₂²×C₅₉	semidirect
526. #395	C₂²×C₅₉	semidirect
527. #394	C₂²×C₅₉	semidirect
528. #394	C₂²×C₅₉	semidirect
529. #394	C₂²×C₅₉	semidirect
530. #394	C₂²×C₅₉	semidirect
531. #394	C₂²×C₅₉	semidirect
532. #394	C₂²×C₅₉	semidirect
533. #394	C₂²×C₅₉	semidirect
534. #394	C₂²×C₅₉	semidirect
535. #394	C₂²×C₅₉	semidirect
536. #394	C₂²×C₅₉	semidirect
537. #393	C₂²×C₅₉	semidirect
538. #392	C₂²×C₅₉	semidirect
539. #392	C₂²×C₅₉	semidirect
540. #392	C₂²×C₅₉	semidirect
541. #392	C₂²×C₅₉	semidirect
542. #391	C₂²×C₅₉	semidirect
543. #390	C₂²×C₅₉	semidirect
544. #390	C₂²×C₅₉	semidirect
545. #386	C₂²×C₅₉	semidirect
546. #386	C₂²×C₅₉	semidirect
547. #386	C₂²×C₅₉	semidirect
548. #386	C₂²×C₅₉	semidirect
549. #385	C₂²×C₅₉	semidirect
550. #385	C₂²×C₅₉	semidirect
551. #385	C₂²×C₅₉	semidirect
552. #381	C₂²×C₅₉	semidirect
553. #380	C₂²×C₅₉	semidirect
554. #380	C₂²×C₅₉	semidirect
555. #379	C₂²×C₅₉	semidirect
556. #379	C₂²×C₅₉	semidirect
557. #379	C₂²×C₅₉	semidirect
558. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
559. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
560. C₂×#95	C₂²×C₅₉	semidirect
561. C₅₉	#35750	direct (N × H)
575. C₂×#41	D₄×C₅₉	semidirect
588. C₂²×D₄	D₄×C₅₉	semidirect
852. D₄	#120×C₅₉	semidirect
890. C₂×C₄	H(5,𝔽₂)×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×H(5,𝔽₂)×C₅₉	2
C₂×C₅₉×#547	2
C₂×C₅₉×#546	2
C₅₉×#2616	2
C₅₉×#2613	2
C₅₉×#2435	2
C₅₉×#2432	2
C₅₉×#2430	2
C₅₉×#2410	2
C₅₉×#2408	2
C₅₉×#2407	2
C₅₉×#2406	2
C₅₉×#2405	2
C₅₉×#2388	2
C₂×C₅₉×#394	2
C₅₉×#2339	2
D₄×C₂²⋊C₄×C₅₉	2
#35750	59

Subgroups — C59×#35750 #28447859

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35750 #28447859