Subgroups — C₅₉×#35728 #28447837

Order 15104.

3614 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#546	C₂	1	2	yes	maximal, complemented
2	C₂×D₄²×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅₉×#520	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2619	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2618	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2548	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#2543	C₂	1	2	yes	maximal, complemented
8	C₅₉×#2536	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#2426	C₂	1	2	yes	maximal, complemented
10	C₅₉×#2424	C₂	1	4	yes	maximal, complemented
11	C₅₉×#2416	C₂	1	2	yes	maximal, complemented
12	C₅₉×#2411	C₂	1	4	yes	maximal, complemented
13	C₅₉×#2408	C₂	1	2	yes	maximal, complemented
14	C₅₉×#2392	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅₉×#394	C₂	1	2	yes	maximal, complemented
16	C₅₉×#2349	C₂	1	1	yes	maximal, characteristic, complemented
17	D₄×C₂²⋊C₄×C₅₉	C₂	1	2	yes	maximal, complemented
18	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₅₉	C₂²	1	2	yes	—
20	C₂³×D₄×C₅₉	C₂²	1	2	yes	—
21	C₅₉×#546	—	2	16	no	—
22	D₄²×C₅₉	—	2	8	no	—
23	C₂×#127×C₅₉	C₂²	1	1	yes	characteristic
24	C₂×#124×C₅₉	C₂²	1	2	yes	complemented
25	C₂×#123×C₅₉	C₂²	1	4	yes	complemented
26	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	complemented
27	C₂×#121×C₅₉	C₂²	1	2	yes	—
28	C₂×#121×C₅₉	C₂²	1	2	yes	—
29	C₂×#121×C₅₉	C₂²	1	4	yes	complemented
30	C₂×#121×C₅₉	C₂²	1	2	yes	complemented
31	C₂×#121×C₅₉	C₂²	1	4	yes	complemented
32	C₂×#120×C₅₉	C₂²	1	4	yes	—
33	C₂×#120×C₅₉	C₂²	1	4	yes	complemented
34	C₅₉×#520	—	2	8	no	—
35	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	complemented
42	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	complemented
43	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	complemented
44	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic, complemented
45	C₂×#117×C₅₉	C₂²	1	2	yes	complemented
46	C₂²×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
47	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
48	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	4	yes	complemented
49	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	4	yes	complemented
50	C₅₉×#398	C₂²	1	2	yes	complemented
51	C₅₉×#398	C₂²	1	1	yes	characteristic, complemented
52	C₅₉×#397	C₂²	1	1	yes	characteristic, complemented
53	C₅₉×#396	C₂²	1	4	yes	complemented
54	C₅₉×#396	C₂²	1	4	yes	complemented
55	C₅₉×#396	C₂²	1	2	yes	complemented
56	C₅₉×#394	C₂²	1	2	yes	—
57	C₅₉×#394	C₂²	1	1	yes	characteristic
58	C₅₉×#394	C₂²	1	2	yes	complemented
59	C₅₉×#394	C₂²	1	2	yes	complemented
60	C₅₉×#394	C₂²	1	2	yes	complemented
61	C₅₉×#394	C₂²	1	2	yes	complemented
62	C₅₉×#394	C₂²	1	4	yes	complemented
63	C₅₉×#394	C₂²	1	4	yes	complemented
64	C₅₉×#394	C₂²	1	2	yes	complemented
65	C₅₉×#392	C₂²	1	1	yes	characteristic
66	C₅₉×#392	C₂²	1	2	yes	complemented
67	C₅₉×#392	C₂²	1	2	yes	complemented
68	C₅₉×#390	C₂²	1	2	yes	complemented
69	C₅₉×#390	C₂²	1	4	yes	complemented
70	C₅₉×#390	C₂²	1	2	yes	complemented
71	C₅₉×#390	C₂²	1	4	yes	complemented
72	C₅₉×#389	C₂²	1	2	yes	complemented
73	C₅₉×#388	C₂²	1	4	yes	complemented
74	C₅₉×#388	C₂²	1	4	yes	complemented
75	C₅₉×#386	C₂²	1	4	yes	complemented
76	C₅₉×#386	C₂²	1	4	yes	complemented
77	C₅₉×#386	C₂²	1	4	yes	complemented
78	C₅₉×#385	C₂²	1	4	yes	complemented
79	C₅₉×#382	C₂²	1	1	yes	characteristic, complemented
80	C₅₉×#380	C₂²	1	2	yes	complemented
81	C₅₉×#380	C₂²	1	2	yes	complemented
82	C₅₉×#379	C₂²	1	4	yes	complemented
83	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
84	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	complemented
85	C₂×#95×C₅₉	C₂²	1	2	yes	complemented
86	C₂⁵×C₅₉	C₂³	1	4	yes	—
87	C₂×#41×C₅₉	—	2	4	no	—
88	C₂×#41×C₅₉	—	2	4	no	—
89	C₂×#41×C₅₉	D₄	1	8	yes	complemented
90	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₅₉	—	2	8	no	—
92	C₂²×D₄×C₅₉	—	2	8	no	—
93	C₂²×D₄×C₅₉	—	2	8	no	—
94	C₂²×D₄×C₅₉	—	2	8	no	—
95	C₂²×D₄×C₅₉	—	4	8	no	—
96	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
97	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
98	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
100	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
101	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
102	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
103	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
104	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
105	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
107	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
108	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₅₉	C₂³	1	4	yes	—
110	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
111	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
112	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
113	#127×C₅₉	—	2	4	no	—
114	#124×C₅₉	—	2	8	no	—
115	#123×C₅₉	—	2	16	no	—
116	C₂²⋊Q₈×C₅₉	—	2	8	no	—
117	#121×C₅₉	—	2	16	no	—
118	#121×C₅₉	—	2	8	no	—
119	#121×C₅₉	—	2	8	no	—
120	#121×C₅₉	—	2	8	no	—
121	#121×C₅₉	—	4	8	no	—
122	#120×C₅₉	—	2	16	no	—
123	#120×C₅₉	—	2	16	no	—
124	C₄×Q₈×C₅₉	—	2	4	no	—
125	C₄×Q₈×C₅₉	—	2	4	no	—
126	C₄×D₄×C₅₉	—	2	4	no	—
127	C₄×D₄×C₅₉	—	2	8	no	—
128	C₄×D₄×C₅₉	—	2	8	no	—
129	C₄×D₄×C₅₉	—	2	8	no	—
130	C₄×D₄×C₅₉	—	2	8	no	—
131	C₄×D₄×C₅₉	—	2	4	no	—
132	C₄×D₄×C₅₉	D₄	1	8	yes	complemented
133	#117×C₅₉	—	2	8	no	—
134	#117×C₅₉	—	2	4	no	—
135	C₂×C₄⋊C₄×C₅₉	—	2	8	no	—
136	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
137	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
140	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
149	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
150	C₂×C₂²⋊C₄×C₅₉	—	2	16	no	—
151	C₂×C₂²⋊C₄×C₅₉	—	4	8	no	—
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	4	yes	—
155	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
156	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
158	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
160	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
161	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
162	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
163	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
164	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
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	2	yes	—
172	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
177	#95×C₅₉	C₂³	1	1	yes	characteristic
178	#95×C₅₉	C₂³	1	2	yes	—
179	#95×C₅₉	C₂³	1	4	yes	—
180	#95×C₅₉	C₂³	1	2	yes	—
181	#95×C₅₉	C₂³	1	2	yes	—
182	#95×C₅₉	C₂³	1	1	yes	characteristic
183	#95×C₅₉	C₂³	1	4	yes	—
184	#95×C₅₉	C₂³	1	2	yes	—
185	C₂⁴×C₅₉	—	2	8	no	—
186	C₂⁴×C₅₉	—	2	8	no	—
187	C₂⁴×C₅₉	—	2	8	no	—
188	C₂⁴×C₅₉	—	2	8	no	—
189	C₂⁴×C₅₉	—	4	4	no	—
190	C₂⁴×C₅₉	—	4	4	no	—
191	C₂⁴×C₅₉	—	4	4	no	—
192	C₂⁴×C₅₉	C₂⁴	1	4	yes	—
193	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
194	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
195	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
196	#41×C₅₉	—	2	32	no	—
197	C₂×Q₈×C₅₉	—	2	2	no	—
198	C₂×Q₈×C₅₉	—	2	2	no	—
199	C₂×Q₈×C₅₉	C₂×D₄	1	4	yes	complemented
200	C₂×D₄×C₅₉	—	2	4	no	—
201	C₂×D₄×C₅₉	—	2	4	no	—
202	C₂×D₄×C₅₉	—	2	4	no	—
203	C₂×D₄×C₅₉	—	2	4	no	—
204	C₂×D₄×C₅₉	—	2	8	no	—
205	C₂×D₄×C₅₉	—	2	8	no	—
206	C₂×D₄×C₅₉	—	2	8	no	—
207	C₂×D₄×C₅₉	—	2	4	no	—
208	C₂×D₄×C₅₉	—	2	8	no	—
209	C₂×D₄×C₅₉	—	2	8	no	—
210	C₂×D₄×C₅₉	—	2	2	no	—
211	C₂×D₄×C₅₉	—	2	8	no	—
212	C₂×D₄×C₅₉	—	2	4	no	—
213	C₂×D₄×C₅₉	—	2	4	no	—
214	C₂×D₄×C₅₉	—	2	4	no	—
215	C₂×D₄×C₅₉	—	2	4	no	—
216	C₂×D₄×C₅₉	—	2	4	no	—
217	C₂×D₄×C₅₉	—	4	4	no	—
218	C₂×D₄×C₅₉	—	4	4	no	—
219	C₂×D₄×C₅₉	—	4	2	no	—
220	C₂×D₄×C₅₉	—	4	4	no	—
221	C₂×D₄×C₅₉	—	4	4	no	—
222	C₂×D₄×C₅₉	—	4	4	no	—
223	C₂×D₄×C₅₉	—	4	32	no	—
224	C₂×D₄×C₅₉	—	4	32	no	—
225	C₂×D₄×C₅₉	C₂×D₄	1	4	yes	—
226	C₂×D₄×C₅₉	C₂×D₄	1	4	yes	—
227	C₂×D₄×C₅₉	C₂×D₄	1	8	yes	complemented
228	C₂×D₄×C₅₉	#41	1	4	yes	—
229	C₂²×C₄×C₅₉	—	2	4	no	—
230	C₂²×C₄×C₅₉	—	2	4	no	—
231	C₂²×C₄×C₅₉	—	2	2	no	—
232	C₂²×C₄×C₅₉	—	2	2	no	—
233	C₂²×C₄×C₅₉	—	2	8	no	—
234	C₂²×C₄×C₅₉	—	2	4	no	—
235	C₂²×C₄×C₅₉	—	2	4	no	—
236	C₂²×C₄×C₅₉	—	2	4	no	—
237	C₂²×C₄×C₅₉	—	2	4	no	—
238	C₂²×C₄×C₅₉	—	2	4	no	—
239	C₂²×C₄×C₅₉	—	4	4	no	—
240	C₂²×C₄×C₅₉	—	4	4	no	—
241	C₂²×C₄×C₅₉	—	4	4	no	—
242	C₂²×C₄×C₅₉	—	4	4	no	—
243	C₂²×C₄×C₅₉	—	4	4	no	—
244	C₂²×C₄×C₅₉	C₂×D₄	1	8	yes	—
245	C₂²×C₄×C₅₉	C₂×D₄	1	8	yes	complemented
246	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	complemented
247	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
249	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₅₉	C₂⁴	1	2	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	1	yes	characteristic
259	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
260	C₄⋊C₄×C₅₉	—	2	4	no	—
261	C₄⋊C₄×C₅₉	—	2	2	no	—
262	C₄⋊C₄×C₅₉	—	2	4	no	—
263	C₄⋊C₄×C₅₉	—	2	4	no	—
264	C₄⋊C₄×C₅₉	—	2	2	no	—
265	C₄⋊C₄×C₅₉	—	2	2	no	—
266	C₄⋊C₄×C₅₉	—	2	2	no	—
267	C₄⋊C₄×C₅₉	—	2	4	no	—
268	C₄⋊C₄×C₅₉	—	2	4	no	—
269	C₄⋊C₄×C₅₉	—	2	8	no	—
270	C₄⋊C₄×C₅₉	—	4	2	no	—
271	C₄⋊C₄×C₅₉	—	4	4	no	—
272	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
273	C₂²⋊C₄×C₅₉	—	2	4	no	—
274	C₂²⋊C₄×C₅₉	—	2	8	no	—
275	C₂²⋊C₄×C₅₉	—	2	4	no	—
276	C₂²⋊C₄×C₅₉	—	2	4	no	—
277	C₂²⋊C₄×C₅₉	—	2	8	no	—
278	C₂²⋊C₄×C₅₉	—	2	4	no	—
279	C₂²⋊C₄×C₅₉	—	2	8	no	—
280	C₂²⋊C₄×C₅₉	—	2	8	no	—
281	C₂²⋊C₄×C₅₉	—	2	8	no	—
282	C₂²⋊C₄×C₅₉	—	2	2	no	—
283	C₂²⋊C₄×C₅₉	—	2	2	no	—
284	C₂²⋊C₄×C₅₉	—	2	4	no	—
285	C₂²⋊C₄×C₅₉	—	2	8	no	—
286	C₂²⋊C₄×C₅₉	—	2	8	no	—
287	C₂²⋊C₄×C₅₉	—	4	4	no	—
288	C₂²⋊C₄×C₅₉	—	4	4	no	—
289	C₂²⋊C₄×C₅₉	—	4	2	no	—
290	C₂²⋊C₄×C₅₉	—	4	4	no	—
291	C₂²⋊C₄×C₅₉	—	4	4	no	—
292	C₂²⋊C₄×C₅₉	C₂×D₄	1	8	yes	—
293	C₄²×C₅₉	—	2	4	no	—
294	C₄²×C₅₉	—	2	4	no	—
295	C₄²×C₅₉	—	2	2	no	—
296	C₄²×C₅₉	—	2	4	no	—
297	C₄²×C₅₉	C₂×D₄	1	4	yes	—
298	C₂³×C₅₉	—	2	4	no	—
299	C₂³×C₅₉	—	2	4	no	—
300	C₂³×C₅₉	—	2	2	no	—
301	C₂³×C₅₉	—	2	1	no	—
302	C₂³×C₅₉	—	2	2	no	—
303	C₂³×C₅₉	—	2	1	no	—
304	C₂³×C₅₉	—	2	2	no	—
305	C₂³×C₅₉	—	2	2	no	—
306	C₂³×C₅₉	—	2	2	no	—
307	C₂³×C₅₉	—	2	2	no	—
308	C₂³×C₅₉	—	2	2	no	—
309	C₂³×C₅₉	—	2	2	no	—
310	C₂³×C₅₉	—	2	4	no	—
311	C₂³×C₅₉	—	2	4	no	—
312	C₂³×C₅₉	—	2	4	no	—
313	C₂³×C₅₉	—	2	4	no	—
314	C₂³×C₅₉	—	2	4	no	—
315	C₂³×C₅₉	—	2	4	no	—
316	C₂³×C₅₉	—	2	4	no	—
317	C₂³×C₅₉	—	4	16	no	—
318	C₂³×C₅₉	—	4	16	no	—
319	C₂³×C₅₉	—	4	16	no	—
320	C₂³×C₅₉	—	4	16	no	—
321	C₂³×C₅₉	—	8	8	no	—
322	C₂³×C₅₉	—	8	8	no	—
323	C₂³×C₅₉	—	8	8	no	—
324	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
325	C₂³×C₅₉	C₂²×D₄	1	4	yes	—
326	C₂³×C₅₉	C₂²×D₄	1	4	yes	—
327	C₂³×C₅₉	C₂×#41	1	4	yes	—
328	C₂³×C₅₉	H(5,𝔽₂)	1	4	yes	—
329	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
330	Q₈×C₅₉	—	2	8	no	—
331	D₄×C₅₉	—	2	8	no	—
332	D₄×C₅₉	—	2	16	no	—
333	D₄×C₅₉	—	4	16	no	—
334	D₄×C₅₉	—	4	8	no	—
335	D₄×C₅₉	—	4	8	no	—
336	D₄×C₅₉	—	4	16	no	—
337	D₄×C₅₉	—	4	8	no	—
338	D₄×C₅₉	—	8	4	no	—
339	D₄×C₅₉	—	8	8	no	—
340	D₄×C₅₉	#121	1	16	yes	complemented
341	C₂×C₄×C₅₉	—	2	16	no	—
342	C₂×C₄×C₅₉	—	2	2	no	—
343	C₂×C₄×C₅₉	—	2	1	no	—
344	C₂×C₄×C₅₉	—	2	1	no	—
345	C₂×C₄×C₅₉	—	2	2	no	—
346	C₂×C₄×C₅₉	—	2	4	no	—
347	C₂×C₄×C₅₉	—	2	2	no	—
348	C₂×C₄×C₅₉	—	2	2	no	—
349	C₂×C₄×C₅₉	—	2	8	no	—
350	C₂×C₄×C₅₉	—	2	1	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	1	no	—
355	C₂×C₄×C₅₉	—	2	4	no	—
356	C₂×C₄×C₅₉	—	2	2	no	—
357	C₂×C₄×C₅₉	—	2	2	no	—
358	C₂×C₄×C₅₉	—	2	2	no	—
359	C₂×C₄×C₅₉	—	2	2	no	—
360	C₂×C₄×C₅₉	—	2	4	no	—
361	C₂×C₄×C₅₉	—	2	2	no	—
362	C₂×C₄×C₅₉	—	2	4	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	4	no	—
367	C₂×C₄×C₅₉	—	2	2	no	—
368	C₂×C₄×C₅₉	—	4	8	no	—
369	C₂×C₄×C₅₉	—	4	8	no	—
370	C₂×C₄×C₅₉	—	8	4	no	—
371	C₂×C₄×C₅₉	—	8	4	no	—
372	C₂×C₄×C₅₉	—	8	8	no	—
373	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
374	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
375	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
376	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
377	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
378	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
379	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
380	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
381	#35728	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
382	C₂²×C₅₉	—	2	4	no	—
383	C₂²×C₅₉	—	2	8	no	—
384	C₂²×C₅₉	—	2	4	no	—
385	C₂²×C₅₉	—	2	8	no	—
386	C₂²×C₅₉	—	2	2	no	—
387	C₂²×C₅₉	—	2	4	no	—
388	C₂²×C₅₉	—	2	4	no	—
389	C₂²×C₅₉	—	2	4	no	—
390	C₂²×C₅₉	—	2	4	no	—
391	C₂²×C₅₉	—	4	2	no	—
392	C₂²×C₅₉	—	4	1	no	—
393	C₂²×C₅₉	—	4	2	no	—
394	C₂²×C₅₉	—	4	1	no	—
395	C₂²×C₅₉	—	4	2	no	—
396	C₂²×C₅₉	—	4	2	no	—
397	C₂²×C₅₉	—	4	2	no	—
398	C₂²×C₅₉	—	4	4	no	—
399	C₂²×C₅₉	—	4	4	no	—
400	C₂²×C₅₉	—	4	4	no	—
401	C₂²×C₅₉	—	4	4	no	—
402	C₂²×C₅₉	—	4	4	no	—
403	C₂²×C₅₉	—	4	4	no	—
404	C₂²×C₅₉	—	4	4	no	—
405	C₂²×C₅₉	—	8	32	no	—
406	C₂²×C₅₉	C₂×#121	1	8	yes	—
407	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
408	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
409	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
410	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	2	yes	—
411	C₂²×C₅₉	#585	1	2	yes	—
412	C₄×C₅₉	—	2	2	no	—
413	C₄×C₅₉	—	2	4	no	—
414	C₄×C₅₉	—	2	2	no	—
415	C₄×C₅₉	—	2	4	no	—
416	C₄×C₅₉	—	2	2	no	—
417	C₄×C₅₉	—	4	2	no	—
418	C₄×C₅₉	—	4	2	no	—
419	C₄×C₅₉	—	4	1	no	—
420	C₄×C₅₉	—	4	2	no	—
421	C₄×C₅₉	—	4	4	no	—
422	C₄×C₅₉	—	4	2	no	—
423	C₄×C₅₉	—	4	1	no	—
424	C₄×C₅₉	C₂×#121	1	4	yes	—
425	C₂×#546	C₂×C₅₉	1	2	yes	complemented
426	C₂×D₄²	C₂×C₅₉	1	1	yes	characteristic, complemented
427	C₂×#520	C₂×C₅₉	1	1	yes	characteristic, complemented
428	#2619	C₂×C₅₉	1	1	yes	characteristic, complemented
429	#2618	C₂×C₅₉	1	2	yes	complemented
430	#2548	C₂×C₅₉	1	1	yes	characteristic, complemented
431	#2543	C₂×C₅₉	1	2	yes	complemented
432	#2536	C₂×C₅₉	1	1	yes	characteristic, complemented
433	#2426	C₂×C₅₉	1	2	yes	complemented
434	#2424	C₂×C₅₉	1	4	yes	complemented
435	#2416	C₂×C₅₉	1	2	yes	complemented
436	#2411	C₂×C₅₉	1	4	yes	complemented
437	#2408	C₂×C₅₉	1	2	yes	complemented
438	#2392	C₂×C₅₉	1	1	yes	characteristic, complemented
439	C₂×#394	C₂×C₅₉	1	2	yes	complemented
440	#2349	C₂×C₅₉	1	1	yes	characteristic, complemented
441	D₄×C₂²⋊C₄	C₂×C₅₉	1	2	yes	complemented
442	C₂×C₅₉	—	2	8	no	—
443	C₂×C₅₉	—	4	2	no	—
444	C₂×C₅₉	—	4	4	no	—
445	C₂×C₅₉	—	8	4	no	—
446	C₂×C₅₉	C₂²×#121	1	1	yes	characteristic
447	C₂×C₅₉	#3484	1	1	yes	characteristic
448	C₂×C₅₉	#3488	1	2	yes	—
449	C₂×C₅₉	#3500	1	1	yes	characteristic
450	C₂×C₅₉	#3513	1	2	yes	—
451	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic
452	C₂³×D₄	C₂²×C₅₉	1	2	yes	—
453	C₂³×D₄	C₂²×C₅₉	1	2	yes	—
454	#546	—	2	16	no	—
455	D₄²	—	2	8	no	—
456	C₂×#127	C₂²×C₅₉	1	1	yes	characteristic
457	C₂×#124	C₂²×C₅₉	1	2	yes	complemented
458	C₂×#123	C₂²×C₅₉	1	4	yes	complemented
459	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	complemented
460	C₂×#121	C₂²×C₅₉	1	2	yes	—
461	C₂×#121	C₂²×C₅₉	1	2	yes	—
462	C₂×#121	C₂²×C₅₉	1	2	yes	complemented
463	C₂×#121	C₂²×C₅₉	1	4	yes	complemented
464	C₂×#121	C₂²×C₅₉	1	4	yes	complemented
465	C₂×#120	C₂²×C₅₉	1	4	yes	—
466	C₂×#120	C₂²×C₅₉	1	4	yes	complemented
467	#520	—	2	8	no	—
468	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
469	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
470	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
471	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
472	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
473	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
474	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	complemented
475	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	complemented
476	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	complemented
477	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic, complemented
478	C₂×#117	C₂²×C₅₉	1	2	yes	complemented
479	C₂²×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
480	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
481	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	4	yes	complemented
482	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	4	yes	complemented
483	#398	C₂²×C₅₉	1	1	yes	characteristic, complemented
484	#398	C₂²×C₅₉	1	2	yes	complemented
485	#397	C₂²×C₅₉	1	1	yes	characteristic, complemented
486	#396	C₂²×C₅₉	1	4	yes	complemented
487	#396	C₂²×C₅₉	1	4	yes	complemented
488	#396	C₂²×C₅₉	1	2	yes	complemented
489	#394	C₂²×C₅₉	1	1	yes	characteristic
490	#394	C₂²×C₅₉	1	2	yes	—
491	#394	C₂²×C₅₉	1	2	yes	complemented
492	#394	C₂²×C₅₉	1	2	yes	complemented
493	#394	C₂²×C₅₉	1	2	yes	complemented
494	#394	C₂²×C₅₉	1	4	yes	complemented
495	#394	C₂²×C₅₉	1	4	yes	complemented
496	#394	C₂²×C₅₉	1	2	yes	complemented
497	#394	C₂²×C₅₉	1	2	yes	complemented
498	#392	C₂²×C₅₉	1	1	yes	characteristic
499	#392	C₂²×C₅₉	1	2	yes	complemented
500	#392	C₂²×C₅₉	1	2	yes	complemented
501	#390	C₂²×C₅₉	1	2	yes	complemented
502	#390	C₂²×C₅₉	1	2	yes	complemented
503	#390	C₂²×C₅₉	1	4	yes	complemented
504	#390	C₂²×C₅₉	1	4	yes	complemented
505	#389	C₂²×C₅₉	1	2	yes	complemented
506	#388	C₂²×C₅₉	1	4	yes	complemented
507	#388	C₂²×C₅₉	1	4	yes	complemented
508	#386	C₂²×C₅₉	1	4	yes	complemented
509	#386	C₂²×C₅₉	1	4	yes	complemented
510	#386	C₂²×C₅₉	1	4	yes	complemented
511	#385	C₂²×C₅₉	1	4	yes	complemented
512	#382	C₂²×C₅₉	1	1	yes	characteristic, complemented
513	#380	C₂²×C₅₉	1	2	yes	complemented
514	#380	C₂²×C₅₉	1	2	yes	complemented
515	#379	C₂²×C₅₉	1	4	yes	complemented
516	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
517	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	complemented
518	C₂×#95	C₂²×C₅₉	1	2	yes	complemented
519	C₅₉	#35728	1	1	yes	characteristic, direct product factor, Sylow
520	C₂⁵	C₂³×C₅₉	1	4	yes	—
521	C₂×#41	—	2	4	no	—
522	C₂×#41	—	2	4	no	—
523	C₂×#41	D₄×C₅₉	1	8	yes	complemented
524	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
525	C₂²×D₄	—	2	8	no	—
526	C₂²×D₄	—	2	8	no	—
527	C₂²×D₄	—	2	8	no	—
528	C₂²×D₄	—	2	8	no	—
529	C₂²×D₄	—	4	8	no	—
530	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
531	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
532	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
533	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
534	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
535	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
536	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
537	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
538	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
539	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
540	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
541	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
542	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
543	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
544	C₂³×C₄	C₂³×C₅₉	1	4	yes	—
545	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
546	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
547	#127	—	2	4	no	—
548	#124	—	2	8	no	—
549	#123	—	2	16	no	—
550	C₂²⋊Q₈	—	2	8	no	—
551	#121	—	2	16	no	—
552	#121	—	2	8	no	—
553	#121	—	2	8	no	—
554	#121	—	2	8	no	—
555	#121	—	4	8	no	—
556	#120	—	2	16	no	—
557	#120	—	2	16	no	—
558	C₄×Q₈	—	2	4	no	—
559	C₄×Q₈	—	2	4	no	—
560	C₄×D₄	—	2	4	no	—
561	C₄×D₄	—	2	8	no	—
562	C₄×D₄	—	2	8	no	—
563	C₄×D₄	—	2	8	no	—
564	C₄×D₄	—	2	8	no	—
565	C₄×D₄	—	2	4	no	—
566	C₄×D₄	D₄×C₅₉	1	8	yes	complemented
567	#117	—	2	8	no	—
568	#117	—	2	4	no	—
569	C₂×C₄⋊C₄	—	2	8	no	—
570	C₂×C₄⋊C₄	—	2	4	no	—
571	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
574	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
578	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
581	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
582	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
584	C₂×C₂²⋊C₄	—	2	16	no	—
585	C₂×C₂²⋊C₄	—	4	8	no	—
586	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
594	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
595	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
606	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
607	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
608	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
609	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
610	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
611	#95	C₂³×C₅₉	1	1	yes	characteristic
612	#95	C₂³×C₅₉	1	2	yes	—
613	#95	C₂³×C₅₉	1	4	yes	—
614	#95	C₂³×C₅₉	1	2	yes	—
615	#95	C₂³×C₅₉	1	2	yes	—
616	#95	C₂³×C₅₉	1	1	yes	characteristic
617	#95	C₂³×C₅₉	1	4	yes	—
618	#95	C₂³×C₅₉	1	2	yes	—
619	C₂⁴	—	2	8	no	—
620	C₂⁴	—	2	8	no	—
621	C₂⁴	—	2	8	no	—
622	C₂⁴	—	2	8	no	—
623	C₂⁴	—	4	4	no	—
624	C₂⁴	—	4	4	no	—
625	C₂⁴	—	4	4	no	—
626	C₂⁴	C₂⁴×C₅₉	1	4	yes	—
627	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
628	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
629	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
630	#41	—	2	32	no	—
631	C₂×Q₈	—	2	2	no	—
632	C₂×Q₈	—	2	2	no	—
633	C₂×Q₈	C₂×D₄×C₅₉	1	4	yes	complemented
634	C₂×D₄	—	2	4	no	—
635	C₂×D₄	—	2	4	no	—
636	C₂×D₄	—	2	4	no	—
637	C₂×D₄	—	2	4	no	—
638	C₂×D₄	—	2	8	no	—
639	C₂×D₄	—	2	8	no	—
640	C₂×D₄	—	2	8	no	—
641	C₂×D₄	—	2	4	no	—
642	C₂×D₄	—	2	8	no	—
643	C₂×D₄	—	2	8	no	—
644	C₂×D₄	—	2	2	no	—
645	C₂×D₄	—	2	8	no	—
646	C₂×D₄	—	2	4	no	—
647	C₂×D₄	—	2	4	no	—
648	C₂×D₄	—	2	4	no	—
649	C₂×D₄	—	2	4	no	—
650	C₂×D₄	—	2	4	no	—
651	C₂×D₄	—	4	4	no	—
652	C₂×D₄	—	4	4	no	—
653	C₂×D₄	—	4	2	no	—
654	C₂×D₄	—	4	4	no	—
655	C₂×D₄	—	4	4	no	—
656	C₂×D₄	—	4	4	no	—
657	C₂×D₄	—	4	32	no	—
658	C₂×D₄	—	4	32	no	—
659	C₂×D₄	C₂×D₄×C₅₉	1	4	yes	—
660	C₂×D₄	C₂×D₄×C₅₉	1	4	yes	—
661	C₂×D₄	C₂×D₄×C₅₉	1	8	yes	complemented
662	C₂×D₄	#41×C₅₉	1	4	yes	—
663	C₂²×C₄	—	2	4	no	—
664	C₂²×C₄	—	2	4	no	—
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	8	no	—
668	C₂²×C₄	—	2	4	no	—
669	C₂²×C₄	—	2	4	no	—
670	C₂²×C₄	—	2	4	no	—
671	C₂²×C₄	—	2	4	no	—
672	C₂²×C₄	—	2	4	no	—
673	C₂²×C₄	—	4	4	no	—
674	C₂²×C₄	—	4	4	no	—
675	C₂²×C₄	—	4	4	no	—
676	C₂²×C₄	—	4	4	no	—
677	C₂²×C₄	—	4	4	no	—
678	C₂²×C₄	C₂×D₄×C₅₉	1	8	yes	—
679	C₂²×C₄	C₂×D₄×C₅₉	1	8	yes	complemented
680	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	complemented
681	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
683	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
685	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
686	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
687	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
688	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
689	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
690	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
692	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
693	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	2	4	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	8	no	—
704	C₄⋊C₄	—	4	4	no	—
705	C₄⋊C₄	—	4	2	no	—
706	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	8	no	—
709	C₂²⋊C₄	—	2	4	no	—
710	C₂²⋊C₄	—	2	4	no	—
711	C₂²⋊C₄	—	2	8	no	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	2	8	no	—
714	C₂²⋊C₄	—	2	8	no	—
715	C₂²⋊C₄	—	2	8	no	—
716	C₂²⋊C₄	—	2	2	no	—
717	C₂²⋊C₄	—	2	2	no	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	2	8	no	—
720	C₂²⋊C₄	—	2	8	no	—
721	C₂²⋊C₄	—	4	4	no	—
722	C₂²⋊C₄	—	4	4	no	—
723	C₂²⋊C₄	—	4	4	no	—
724	C₂²⋊C₄	—	4	2	no	—
725	C₂²⋊C₄	—	4	4	no	—
726	C₂²⋊C₄	C₂×D₄×C₅₉	1	8	yes	—
727	C₄²	—	2	4	no	—
728	C₄²	—	2	4	no	—
729	C₄²	—	2	2	no	—
730	C₄²	—	2	4	no	—
731	C₄²	C₂×D₄×C₅₉	1	4	yes	—
732	C₂³	—	2	4	no	—
733	C₂³	—	2	4	no	—
734	C₂³	—	2	2	no	—
735	C₂³	—	2	1	no	—
736	C₂³	—	2	2	no	—
737	C₂³	—	2	1	no	—
738	C₂³	—	2	2	no	—
739	C₂³	—	2	2	no	—
740	C₂³	—	2	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	2	2	no	—
744	C₂³	—	2	4	no	—
745	C₂³	—	2	4	no	—
746	C₂³	—	2	4	no	—
747	C₂³	—	2	4	no	—
748	C₂³	—	2	4	no	—
749	C₂³	—	2	4	no	—
750	C₂³	—	2	4	no	—
751	C₂³	—	4	16	no	—
752	C₂³	—	4	16	no	—
753	C₂³	—	4	16	no	—
754	C₂³	—	4	16	no	—
755	C₂³	—	8	8	no	—
756	C₂³	—	8	8	no	—
757	C₂³	—	8	8	no	—
758	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
759	C₂³	C₂²×D₄×C₅₉	1	4	yes	—
760	C₂³	C₂²×D₄×C₅₉	1	4	yes	—
761	C₂³	C₂×#41×C₅₉	1	4	yes	—
762	C₂³	H(5,𝔽₂)×C₅₉	1	4	yes	—
763	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
764	Q₈	—	2	8	no	—
765	D₄	—	2	8	no	—
766	D₄	—	2	16	no	—
767	D₄	—	4	16	no	—
768	D₄	—	4	8	no	—
769	D₄	—	4	8	no	—
770	D₄	—	4	16	no	—
771	D₄	—	4	8	no	—
772	D₄	—	8	4	no	—
773	D₄	—	8	8	no	—
774	D₄	#121×C₅₉	1	16	yes	complemented
775	C₂×C₄	—	2	16	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	4	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	8	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	4	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	4	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	4	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	4	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	4	8	no	—
803	C₂×C₄	—	4	8	no	—
804	C₂×C₄	—	8	4	no	—
805	C₂×C₄	—	8	4	no	—
806	C₂×C₄	—	8	8	no	—
807	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
808	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
809	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
810	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
811	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
812	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
813	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
814	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
815	C₂²	—	2	8	no	—
816	C₂²	—	2	4	no	—
817	C₂²	—	2	8	no	—
818	C₂²	—	2	4	no	—
819	C₂²	—	2	4	no	—
820	C₂²	—	2	2	no	—
821	C₂²	—	2	4	no	—
822	C₂²	—	2	4	no	—
823	C₂²	—	2	4	no	—
824	C₂²	—	4	2	no	—
825	C₂²	—	4	2	no	—
826	C₂²	—	4	2	no	—
827	C₂²	—	4	1	no	—
828	C₂²	—	4	2	no	—
829	C₂²	—	4	2	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	4	no	—
832	C₂²	—	4	4	no	—
833	C₂²	—	4	4	no	—
834	C₂²	—	4	4	no	—
835	C₂²	—	4	4	no	—
836	C₂²	—	4	4	no	—
837	C₂²	—	4	4	no	—
838	C₂²	—	8	32	no	—
839	C₂²	C₂×#121×C₅₉	1	8	yes	—
840	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
841	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
842	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
843	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	2	yes	—
844	C₂²	C₅₉×#585	1	2	yes	—
845	C₄	—	2	2	no	—
846	C₄	—	2	4	no	—
847	C₄	—	2	2	no	—
848	C₄	—	2	4	no	—
849	C₄	—	2	2	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	2	no	—
852	C₄	—	4	1	no	—
853	C₄	—	4	2	no	—
854	C₄	—	4	4	no	—
855	C₄	—	4	2	no	—
856	C₄	—	4	1	no	—
857	C₄	C₂×#121×C₅₉	1	4	yes	—
858	C₂	—	2	8	no	—
859	C₂	—	4	4	no	—
860	C₂	—	4	2	no	—
861	C₂	—	8	4	no	—
862	C₂	C₂²×#121×C₅₉	1	1	yes	characteristic
863	C₂	C₅₉×#3484	1	1	yes	characteristic
864	C₂	C₅₉×#3488	1	2	yes	—
865	C₂	C₅₉×#3500	1	1	yes	characteristic
866	C₂	C₅₉×#3513	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₉×#546	C₂	semidirect
2. C₂×D₄²×C₅₉	C₂	semidirect
3. C₂×C₅₉×#520	C₂	semidirect
4. C₅₉×#2619	C₂	semidirect
5. C₅₉×#2618	C₂	semidirect
6. C₅₉×#2548	C₂	semidirect
7. C₅₉×#2543	C₂	semidirect
8. C₅₉×#2536	C₂	semidirect
9. C₅₉×#2426	C₂	semidirect
10. C₅₉×#2424	C₂	semidirect
11. C₅₉×#2416	C₂	semidirect
12. C₅₉×#2411	C₂	semidirect
13. C₅₉×#2408	C₂	semidirect
14. C₅₉×#2392	C₂	semidirect
15. C₂×C₅₉×#394	C₂	semidirect
16. C₅₉×#2349	C₂	semidirect
17. D₄×C₂²⋊C₄×C₅₉	C₂	semidirect
24. C₂×#124×C₅₉	C₂²	semidirect
25. C₂×#123×C₅₉	C₂²	semidirect
26. C₂×C₂²⋊Q₈×C₅₉	C₂²	semidirect
29. C₂×#121×C₅₉	C₂²	semidirect
30. C₂×#121×C₅₉	C₂²	semidirect
31. C₂×#121×C₅₉	C₂²	semidirect
33. C₂×#120×C₅₉	C₂²	semidirect
35. C₂×C₄×Q₈×C₅₉	C₂²	semidirect
36. C₂×C₄×Q₈×C₅₉	C₂²	semidirect
41. C₂×C₄×D₄×C₅₉	C₂²	semidirect
42. C₂×C₄×D₄×C₅₉	C₂²	semidirect
43. C₂×C₄×D₄×C₅₉	C₂²	semidirect
44. C₂×#117×C₅₉	C₂²	semidirect
45. C₂×#117×C₅₉	C₂²	semidirect
46. C₂²×C₄⋊C₄×C₅₉	C₂²	semidirect
47. C₂²×C₄⋊C₄×C₅₉	C₂²	semidirect
48. C₂²×C₂²⋊C₄×C₅₉	C₂²	semidirect
49. C₂²×C₂²⋊C₄×C₅₉	C₂²	semidirect
50. C₅₉×#398	C₂²	semidirect
51. C₅₉×#398	C₂²	semidirect
52. C₅₉×#397	C₂²	semidirect
53. C₅₉×#396	C₂²	semidirect
54. C₅₉×#396	C₂²	semidirect
55. C₅₉×#396	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×#394	C₂²	semidirect
64. C₅₉×#394	C₂²	semidirect
66. C₅₉×#392	C₂²	semidirect
67. C₅₉×#392	C₂²	semidirect
68. C₅₉×#390	C₂²	semidirect
69. C₅₉×#390	C₂²	semidirect
70. C₅₉×#390	C₂²	semidirect
71. C₅₉×#390	C₂²	semidirect
72. C₅₉×#389	C₂²	semidirect
73. C₅₉×#388	C₂²	semidirect
74. C₅₉×#388	C₂²	semidirect
75. C₅₉×#386	C₂²	semidirect
76. C₅₉×#386	C₂²	semidirect
77. C₅₉×#386	C₂²	semidirect
78. C₅₉×#385	C₂²	semidirect
79. C₅₉×#382	C₂²	semidirect
80. C₅₉×#380	C₂²	semidirect
81. C₅₉×#380	C₂²	semidirect
82. C₅₉×#379	C₂²	semidirect
83. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
84. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
85. C₂×#95×C₅₉	C₂²	semidirect
89. C₂×#41×C₅₉	D₄	semidirect
132. C₄×D₄×C₅₉	D₄	semidirect
199. C₂×Q₈×C₅₉	C₂×D₄	semidirect
227. C₂×D₄×C₅₉	C₂×D₄	semidirect
245. C₂²×C₄×C₅₉	C₂×D₄	semidirect
246. C₂²×C₄×C₅₉	C₂×D₄	semidirect
340. D₄×C₅₉	#121	semidirect
381. #35728	C₅₉	direct (N × H)
425. C₂×#546	C₂×C₅₉	semidirect
426. C₂×D₄²	C₂×C₅₉	semidirect
427. C₂×#520	C₂×C₅₉	semidirect
428. #2619	C₂×C₅₉	semidirect
429. #2618	C₂×C₅₉	semidirect
430. #2548	C₂×C₅₉	semidirect
431. #2543	C₂×C₅₉	semidirect
432. #2536	C₂×C₅₉	semidirect
433. #2426	C₂×C₅₉	semidirect
434. #2424	C₂×C₅₉	semidirect
435. #2416	C₂×C₅₉	semidirect
436. #2411	C₂×C₅₉	semidirect
437. #2408	C₂×C₅₉	semidirect
438. #2392	C₂×C₅₉	semidirect
439. C₂×#394	C₂×C₅₉	semidirect
440. #2349	C₂×C₅₉	semidirect
441. D₄×C₂²⋊C₄	C₂×C₅₉	semidirect
457. C₂×#124	C₂²×C₅₉	semidirect
458. C₂×#123	C₂²×C₅₉	semidirect
459. C₂×C₂²⋊Q₈	C₂²×C₅₉	semidirect
462. C₂×#121	C₂²×C₅₉	semidirect
463. C₂×#121	C₂²×C₅₉	semidirect
464. C₂×#121	C₂²×C₅₉	semidirect
466. C₂×#120	C₂²×C₅₉	semidirect
468. C₂×C₄×Q₈	C₂²×C₅₉	semidirect
469. C₂×C₄×Q₈	C₂²×C₅₉	semidirect
474. C₂×C₄×D₄	C₂²×C₅₉	semidirect
475. C₂×C₄×D₄	C₂²×C₅₉	semidirect
476. C₂×C₄×D₄	C₂²×C₅₉	semidirect
477. C₂×#117	C₂²×C₅₉	semidirect
478. C₂×#117	C₂²×C₅₉	semidirect
479. C₂²×C₄⋊C₄	C₂²×C₅₉	semidirect
480. C₂²×C₄⋊C₄	C₂²×C₅₉	semidirect
481. C₂²×C₂²⋊C₄	C₂²×C₅₉	semidirect
482. C₂²×C₂²⋊C₄	C₂²×C₅₉	semidirect
483. #398	C₂²×C₅₉	semidirect
484. #398	C₂²×C₅₉	semidirect
485. #397	C₂²×C₅₉	semidirect
486. #396	C₂²×C₅₉	semidirect
487. #396	C₂²×C₅₉	semidirect
488. #396	C₂²×C₅₉	semidirect
491. #394	C₂²×C₅₉	semidirect
492. #394	C₂²×C₅₉	semidirect
493. #394	C₂²×C₅₉	semidirect
494. #394	C₂²×C₅₉	semidirect
495. #394	C₂²×C₅₉	semidirect
496. #394	C₂²×C₅₉	semidirect
497. #394	C₂²×C₅₉	semidirect
499. #392	C₂²×C₅₉	semidirect
500. #392	C₂²×C₅₉	semidirect
501. #390	C₂²×C₅₉	semidirect
502. #390	C₂²×C₅₉	semidirect
503. #390	C₂²×C₅₉	semidirect
504. #390	C₂²×C₅₉	semidirect
505. #389	C₂²×C₅₉	semidirect
506. #388	C₂²×C₅₉	semidirect
507. #388	C₂²×C₅₉	semidirect
508. #386	C₂²×C₅₉	semidirect
509. #386	C₂²×C₅₉	semidirect
510. #386	C₂²×C₅₉	semidirect
511. #385	C₂²×C₅₉	semidirect
512. #382	C₂²×C₅₉	semidirect
513. #380	C₂²×C₅₉	semidirect
514. #380	C₂²×C₅₉	semidirect
515. #379	C₂²×C₅₉	semidirect
516. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
517. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
518. C₂×#95	C₂²×C₅₉	semidirect
519. C₅₉	#35728	direct (N × H)
523. C₂×#41	D₄×C₅₉	semidirect
566. C₄×D₄	D₄×C₅₉	semidirect
633. C₂×Q₈	C₂×D₄×C₅₉	semidirect
661. C₂×D₄	C₂×D₄×C₅₉	semidirect
679. C₂²×C₄	C₂×D₄×C₅₉	semidirect
680. C₂²×C₄	C₂×D₄×C₅₉	semidirect
774. D₄	#121×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₉×#546	2
C₂×D₄²×C₅₉	2
C₂×C₅₉×#520	2
C₅₉×#2619	2
C₅₉×#2618	2
C₅₉×#2548	2
C₅₉×#2543	2
C₅₉×#2536	2
C₅₉×#2426	2
C₅₉×#2424	2
C₅₉×#2416	2
C₅₉×#2411	2
C₅₉×#2408	2
C₅₉×#2392	2
C₂×C₅₉×#394	2
C₅₉×#2349	2
D₄×C₂²⋊C₄×C₅₉	2
#35728	59

Subgroups — C59×#35728 #28447837

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35728 #28447837