Subgroups — C₅₉×#35691 #28447800

Order 15104.

4194 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄²×C₅₉	C₂	1	2	yes	maximal, complemented
2	C₂×D₄²×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅₉×#518	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2619	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2617	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2543	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2541	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#2535	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#2428	C₂	1	2	yes	maximal, complemented
10	C₅₉×#2424	C₂	1	4	yes	maximal, complemented
11	C₅₉×#2414	C₂	1	2	yes	maximal, complemented
12	C₅₉×#2410	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×#392	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	C₂³×D₄×C₅₉	C₂²	1	2	yes	—
19	C₂³×D₄×C₅₉	C₂²	1	1	yes	characteristic
20	C₂³×D₄×C₅₉	C₂²	1	2	yes	complemented
21	C₂³×D₄×C₅₉	C₂²	1	4	yes	complemented
22	D₄²×C₅₉	—	2	16	no	—
23	D₄²×C₅₉	—	2	8	no	—
24	C₂×#127×C₅₉	C₂²	1	1	yes	characteristic, complemented
25	C₂×#127×C₅₉	C₂²	1	2	yes	complemented
26	C₂×#121×C₅₉	C₂²	1	2	yes	complemented
27	C₂×#121×C₅₉	C₂²	1	2	yes	complemented
28	C₂×#121×C₅₉	C₂²	1	4	yes	complemented
29	C₂×#121×C₅₉	C₂²	1	2	yes	complemented
30	C₂×#121×C₅₉	C₂²	1	2	yes	complemented
31	C₂×#121×C₅₉	C₂²	1	4	yes	complemented
32	C₂×#121×C₅₉	C₂²	1	4	yes	complemented
33	C₂×#120×C₅₉	C₂²	1	4	yes	complemented
34	C₂×#120×C₅₉	C₂²	1	4	yes	complemented
35	C₂×#120×C₅₉	C₂²	1	4	yes	complemented
36	C₅₉×#518	—	2	8	no	—
37	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	complemented
43	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	complemented
44	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	complemented
45	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
46	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic, complemented
47	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic, complemented
48	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	complemented
49	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	complemented
50	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	4	yes	complemented
51	C₅₉×#398	C₂²	1	1	yes	characteristic, complemented
52	C₅₉×#397	C₂²	1	2	yes	complemented
53	C₅₉×#397	C₂²	1	1	yes	characteristic, complemented
54	C₅₉×#396	C₂²	1	2	yes	complemented
55	C₅₉×#394	C₂²	1	2	yes	complemented
56	C₅₉×#394	C₂²	1	4	yes	complemented
57	C₅₉×#394	C₂²	1	4	yes	complemented
58	C₅₉×#394	C₂²	1	2	yes	complemented
59	C₅₉×#394	C₂²	1	1	yes	characteristic, complemented
60	C₅₉×#394	C₂²	1	2	yes	complemented
61	C₅₉×#392	C₂²	1	1	yes	characteristic
62	C₅₉×#392	C₂²	1	2	yes	complemented
63	C₅₉×#392	C₂²	1	2	yes	complemented
64	C₅₉×#392	C₂²	1	2	yes	complemented
65	C₅₉×#392	C₂²	1	2	yes	complemented
66	C₅₉×#392	C₂²	1	2	yes	complemented
67	C₅₉×#392	C₂²	1	4	yes	complemented
68	C₅₉×#392	C₂²	1	4	yes	complemented
69	C₅₉×#390	C₂²	1	2	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×#386	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	C₂⁵×C₅₉	C₂³	1	2	yes	—
88	C₂²×D₄×C₅₉	—	2	4	no	—
89	C₂²×D₄×C₅₉	—	2	4	no	—
90	C₂²×D₄×C₅₉	—	2	16	no	—
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	—	4	8	no	—
97	C₂²×D₄×C₅₉	—	4	8	no	—
98	C₂²×D₄×C₅₉	D₄	1	8	yes	complemented
99	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
100	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
101	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
102	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
103	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
104	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
105	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
106	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
107	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
109	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
110	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
111	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
112	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
114	C₂³×C₄×C₅₉	C₂³	1	4	yes	—
115	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
117	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
118	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
119	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
120	#127×C₅₉	—	2	8	no	—
121	#127×C₅₉	—	2	4	no	—
122	#121×C₅₉	—	2	8	no	—
123	#121×C₅₉	—	2	16	no	—
124	#121×C₅₉	—	2	8	no	—
125	#121×C₅₉	—	2	8	no	—
126	#121×C₅₉	—	2	8	no	—
127	#121×C₅₉	—	4	8	no	—
128	#121×C₅₉	—	4	8	no	—
129	#120×C₅₉	—	2	16	no	—
130	#120×C₅₉	—	2	16	no	—
131	#120×C₅₉	—	2	16	no	—
132	C₄×D₄×C₅₉	—	2	4	no	—
133	C₄×D₄×C₅₉	—	2	8	no	—
134	C₄×D₄×C₅₉	—	2	8	no	—
135	C₄×D₄×C₅₉	—	2	8	no	—
136	C₄×D₄×C₅₉	—	2	4	no	—
137	C₄×D₄×C₅₉	—	2	8	no	—
138	C₄×D₄×C₅₉	—	2	4	no	—
139	C₄×D₄×C₅₉	—	2	4	no	—
140	C₄×D₄×C₅₉	D₄	1	8	yes	complemented
141	#117×C₅₉	—	2	4	no	—
142	#117×C₅₉	—	2	4	no	—
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	2	yes	—
147	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
151	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊C₄×C₅₉	—	2	8	no	—
153	C₂×C₂²⋊C₄×C₅₉	—	2	8	no	—
154	C₂×C₂²⋊C₄×C₅₉	—	4	8	no	—
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	4	yes	—
159	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	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	4	yes	—
163	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	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	1	yes	characteristic
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	2	yes	—
171	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
172	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
173	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
174	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
175	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
176	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
178	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
179	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
180	#95×C₅₉	C₂³	1	1	yes	characteristic
181	#95×C₅₉	C₂³	1	2	yes	—
182	#95×C₅₉	C₂³	1	4	yes	—
183	#95×C₅₉	C₂³	1	2	yes	—
184	#95×C₅₉	C₂³	1	2	yes	—
185	#95×C₅₉	C₂³	1	1	yes	characteristic
186	#95×C₅₉	C₂³	1	4	yes	—
187	#95×C₅₉	C₂³	1	2	yes	—
188	C₂⁴×C₅₉	—	2	4	no	—
189	C₂⁴×C₅₉	—	2	4	no	—
190	C₂⁴×C₅₉	—	2	8	no	—
191	C₂⁴×C₅₉	—	2	8	no	—
192	C₂⁴×C₅₉	—	2	8	no	—
193	C₂⁴×C₅₉	—	2	8	no	—
194	C₂⁴×C₅₉	—	4	4	no	—
195	C₂⁴×C₅₉	—	4	4	no	—
196	C₂⁴×C₅₉	—	4	4	no	—
197	C₂⁴×C₅₉	—	4	4	no	—
198	C₂⁴×C₅₉	—	4	4	no	—
199	C₂⁴×C₅₉	C₂×D₄	1	8	yes	complemented
200	C₂⁴×C₅₉	C₂⁴	1	4	yes	—
201	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
202	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
203	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
204	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
205	C₂×D₄×C₅₉	—	2	4	no	—
206	C₂×D₄×C₅₉	—	2	4	no	—
207	C₂×D₄×C₅₉	—	2	4	no	—
208	C₂×D₄×C₅₉	—	2	4	no	—
209	C₂×D₄×C₅₉	—	2	4	no	—
210	C₂×D₄×C₅₉	—	2	32	no	—
211	C₂×D₄×C₅₉	—	2	8	no	—
212	C₂×D₄×C₅₉	—	2	8	no	—
213	C₂×D₄×C₅₉	—	2	8	no	—
214	C₂×D₄×C₅₉	—	2	8	no	—
215	C₂×D₄×C₅₉	—	2	8	no	—
216	C₂×D₄×C₅₉	—	2	8	no	—
217	C₂×D₄×C₅₉	—	2	8	no	—
218	C₂×D₄×C₅₉	—	2	8	no	—
219	C₂×D₄×C₅₉	—	2	8	no	—
220	C₂×D₄×C₅₉	—	2	2	no	—
221	C₂×D₄×C₅₉	—	2	2	no	—
222	C₂×D₄×C₅₉	—	2	8	no	—
223	C₂×D₄×C₅₉	—	2	4	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	2	no	—
228	C₂×D₄×C₅₉	—	2	4	no	—
229	C₂×D₄×C₅₉	—	2	4	no	—
230	C₂×D₄×C₅₉	—	2	8	no	—
231	C₂×D₄×C₅₉	—	4	4	no	—
232	C₂×D₄×C₅₉	—	4	4	no	—
233	C₂×D₄×C₅₉	—	4	4	no	—
234	C₂×D₄×C₅₉	—	4	4	no	—
235	C₂×D₄×C₅₉	—	4	4	no	—
236	C₂×D₄×C₅₉	—	4	4	no	—
237	C₂×D₄×C₅₉	—	4	4	no	—
238	C₂×D₄×C₅₉	—	4	4	no	—
239	C₂×D₄×C₅₉	—	4	4	no	—
240	C₂×D₄×C₅₉	—	4	32	no	—
241	C₂×D₄×C₅₉	—	4	64	no	—
242	C₂×D₄×C₅₉	—	4	32	no	—
243	C₂×D₄×C₅₉	C₂×D₄	1	4	yes	—
244	C₂×D₄×C₅₉	C₂×D₄	1	4	yes	—
245	C₂×D₄×C₅₉	C₂×D₄	1	8	yes	complemented
246	C₂×D₄×C₅₉	C₂×D₄	1	4	yes	complemented
247	C₂×D₄×C₅₉	#41	1	4	yes	—
248	C₂²×C₄×C₅₉	—	2	2	no	—
249	C₂²×C₄×C₅₉	—	2	2	no	—
250	C₂²×C₄×C₅₉	—	2	8	no	—
251	C₂²×C₄×C₅₉	—	2	4	no	—
252	C₂²×C₄×C₅₉	—	2	4	no	—
253	C₂²×C₄×C₅₉	—	2	4	no	—
254	C₂²×C₄×C₅₉	—	2	4	no	—
255	C₂²×C₄×C₅₉	—	2	8	no	—
256	C₂²×C₄×C₅₉	—	2	4	no	—
257	C₂²×C₄×C₅₉	—	2	4	no	—
258	C₂²×C₄×C₅₉	—	4	4	no	—
259	C₂²×C₄×C₅₉	—	4	4	no	—
260	C₂²×C₄×C₅₉	—	4	4	no	—
261	C₂²×C₄×C₅₉	—	4	4	no	—
262	C₂²×C₄×C₅₉	—	4	4	no	—
263	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	complemented
264	C₂²×C₄×C₅₉	C₂×D₄	1	8	yes	complemented
265	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
267	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
277	C₄⋊C₄×C₅₉	—	2	2	no	—
278	C₄⋊C₄×C₅₉	—	2	2	no	—
279	C₄⋊C₄×C₅₉	—	2	2	no	—
280	C₄⋊C₄×C₅₉	—	2	4	no	—
281	C₄⋊C₄×C₅₉	—	2	2	no	—
282	C₄⋊C₄×C₅₉	—	2	4	no	—
283	C₄⋊C₄×C₅₉	—	2	4	no	—
284	C₄⋊C₄×C₅₉	—	4	4	no	—
285	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	complemented
286	C₂²⋊C₄×C₅₉	—	2	4	no	—
287	C₂²⋊C₄×C₅₉	—	2	4	no	—
288	C₂²⋊C₄×C₅₉	—	2	8	no	—
289	C₂²⋊C₄×C₅₉	—	2	8	no	—
290	C₂²⋊C₄×C₅₉	—	2	4	no	—
291	C₂²⋊C₄×C₅₉	—	2	4	no	—
292	C₂²⋊C₄×C₅₉	—	2	2	no	—
293	C₂²⋊C₄×C₅₉	—	2	2	no	—
294	C₂²⋊C₄×C₅₉	—	2	4	no	—
295	C₂²⋊C₄×C₅₉	—	2	4	no	—
296	C₂²⋊C₄×C₅₉	—	2	4	no	—
297	C₂²⋊C₄×C₅₉	—	2	4	no	—
298	C₂²⋊C₄×C₅₉	—	2	8	no	—
299	C₂²⋊C₄×C₅₉	—	2	8	no	—
300	C₂²⋊C₄×C₅₉	—	2	4	no	—
301	C₂²⋊C₄×C₅₉	—	2	8	no	—
302	C₂²⋊C₄×C₅₉	—	4	4	no	—
303	C₂²⋊C₄×C₅₉	—	4	4	no	—
304	C₂²⋊C₄×C₅₉	—	4	4	no	—
305	C₂²⋊C₄×C₅₉	—	4	4	no	—
306	C₂²⋊C₄×C₅₉	C₂×D₄	1	8	yes	complemented
307	C₄²×C₅₉	—	2	4	no	—
308	C₄²×C₅₉	—	2	2	no	—
309	C₄²×C₅₉	—	2	4	no	—
310	C₄²×C₅₉	C₂×D₄	1	4	yes	complemented
311	C₂³×C₅₉	—	2	4	no	—
312	C₂³×C₅₉	—	2	4	no	—
313	C₂³×C₅₉	—	2	1	no	—
314	C₂³×C₅₉	—	2	2	no	—
315	C₂³×C₅₉	—	2	2	no	—
316	C₂³×C₅₉	—	2	2	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	4	no	—
322	C₂³×C₅₉	—	2	4	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	16	no	—
328	C₂³×C₅₉	—	2	4	no	—
329	C₂³×C₅₉	—	2	4	no	—
330	C₂³×C₅₉	—	2	4	no	—
331	C₂³×C₅₉	—	2	4	no	—
332	C₂³×C₅₉	—	2	4	no	—
333	C₂³×C₅₉	—	2	4	no	—
334	C₂³×C₅₉	—	2	4	no	—
335	C₂³×C₅₉	—	4	16	no	—
336	C₂³×C₅₉	—	4	16	no	—
337	C₂³×C₅₉	—	4	16	no	—
338	C₂³×C₅₉	—	4	16	no	—
339	C₂³×C₅₉	—	4	16	no	—
340	C₂³×C₅₉	—	8	4	no	—
341	C₂³×C₅₉	—	8	8	no	—
342	C₂³×C₅₉	—	8	4	no	—
343	C₂³×C₅₉	—	8	8	no	—
344	C₂³×C₅₉	—	8	8	no	—
345	C₂³×C₅₉	—	8	8	no	—
346	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
347	C₂³×C₅₉	C₂²×D₄	1	4	yes	—
348	C₂³×C₅₉	C₂²×D₄	1	4	yes	—
349	C₂³×C₅₉	C₂²×D₄	1	4	yes	—
350	C₂³×C₅₉	C₂×#41	1	4	yes	—
351	C₂³×C₅₉	H(5,𝔽₂)	1	4	yes	—
352	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
353	D₄×C₅₉	—	2	8	no	—
354	D₄×C₅₉	—	2	16	no	—
355	D₄×C₅₉	—	2	16	no	—
356	D₄×C₅₉	—	2	8	no	—
357	D₄×C₅₉	—	4	16	no	—
358	D₄×C₅₉	—	4	16	no	—
359	D₄×C₅₉	—	4	8	no	—
360	D₄×C₅₉	—	4	16	no	—
361	D₄×C₅₉	—	4	16	no	—
362	D₄×C₅₉	—	4	16	no	—
363	D₄×C₅₉	—	4	8	no	—
364	D₄×C₅₉	—	8	4	no	—
365	D₄×C₅₉	—	8	8	no	—
366	D₄×C₅₉	#121	1	16	yes	complemented
367	C₂×C₄×C₅₉	—	2	1	no	—
368	C₂×C₄×C₅₉	—	2	2	no	—
369	C₂×C₄×C₅₉	—	2	1	no	—
370	C₂×C₄×C₅₉	—	2	2	no	—
371	C₂×C₄×C₅₉	—	2	4	no	—
372	C₂×C₄×C₅₉	—	2	2	no	—
373	C₂×C₄×C₅₉	—	2	2	no	—
374	C₂×C₄×C₅₉	—	2	8	no	—
375	C₂×C₄×C₅₉	—	2	2	no	—
376	C₂×C₄×C₅₉	—	2	1	no	—
377	C₂×C₄×C₅₉	—	2	2	no	—
378	C₂×C₄×C₅₉	—	2	1	no	—
379	C₂×C₄×C₅₉	—	2	2	no	—
380	C₂×C₄×C₅₉	—	2	2	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	4	no	—
386	C₂×C₄×C₅₉	—	2	2	no	—
387	C₂×C₄×C₅₉	—	2	2	no	—
388	C₂×C₄×C₅₉	—	2	4	no	—
389	C₂×C₄×C₅₉	—	2	4	no	—
390	C₂×C₄×C₅₉	—	4	8	no	—
391	C₂×C₄×C₅₉	—	4	16	no	—
392	C₂×C₄×C₅₉	—	4	8	no	—
393	C₂×C₄×C₅₉	—	8	4	no	—
394	C₂×C₄×C₅₉	—	8	4	no	—
395	C₂×C₄×C₅₉	—	8	4	no	—
396	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
397	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
398	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
399	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
400	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
401	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
402	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
403	C₂×C₄×C₅₉	H(5,𝔽₂)	1	4	yes	—
404	#35691	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
405	C₂²×C₅₉	—	2	4	no	—
406	C₂²×C₅₉	—	2	8	no	—
407	C₂²×C₅₉	—	2	4	no	—
408	C₂²×C₅₉	—	2	8	no	—
409	C₂²×C₅₉	—	2	2	no	—
410	C₂²×C₅₉	—	2	4	no	—
411	C₂²×C₅₉	—	2	4	no	—
412	C₂²×C₅₉	—	2	4	no	—
413	C₂²×C₅₉	—	2	4	no	—
414	C₂²×C₅₉	—	2	8	no	—
415	C₂²×C₅₉	—	2	4	no	—
416	C₂²×C₅₉	—	4	2	no	—
417	C₂²×C₅₉	—	4	2	no	—
418	C₂²×C₅₉	—	4	1	no	—
419	C₂²×C₅₉	—	4	2	no	—
420	C₂²×C₅₉	—	4	2	no	—
421	C₂²×C₅₉	—	4	1	no	—
422	C₂²×C₅₉	—	4	2	no	—
423	C₂²×C₅₉	—	4	4	no	—
424	C₂²×C₅₉	—	4	2	no	—
425	C₂²×C₅₉	—	4	2	no	—
426	C₂²×C₅₉	—	4	4	no	—
427	C₂²×C₅₉	—	4	4	no	—
428	C₂²×C₅₉	—	4	4	no	—
429	C₂²×C₅₉	—	4	4	no	—
430	C₂²×C₅₉	—	4	4	no	—
431	C₂²×C₅₉	—	4	4	no	—
432	C₂²×C₅₉	—	4	4	no	—
433	C₂²×C₅₉	—	8	16	no	—
434	C₂²×C₅₉	—	8	32	no	—
435	C₂²×C₅₉	C₂×#121	1	8	yes	—
436	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
437	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
438	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
439	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	2	yes	—
440	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	2	yes	—
441	C₄×C₅₉	—	2	2	no	—
442	C₄×C₅₉	—	2	2	no	—
443	C₄×C₅₉	—	2	4	no	—
444	C₄×C₅₉	—	2	4	no	—
445	C₄×C₅₉	—	2	2	no	—
446	C₄×C₅₉	—	4	2	no	—
447	C₄×C₅₉	—	4	4	no	—
448	C₄×C₅₉	—	4	1	no	—
449	C₄×C₅₉	—	4	2	no	—
450	C₄×C₅₉	—	4	2	no	—
451	C₄×C₅₉	—	4	1	no	—
452	C₄×C₅₉	C₂×#121	1	4	yes	—
453	C₂×D₄²	C₂×C₅₉	1	2	yes	complemented
454	C₂×D₄²	C₂×C₅₉	1	1	yes	characteristic, complemented
455	C₂×#518	C₂×C₅₉	1	1	yes	characteristic, complemented
456	#2619	C₂×C₅₉	1	1	yes	characteristic, complemented
457	#2617	C₂×C₅₉	1	2	yes	complemented
458	#2543	C₂×C₅₉	1	2	yes	complemented
459	#2541	C₂×C₅₉	1	1	yes	characteristic, complemented
460	#2535	C₂×C₅₉	1	1	yes	characteristic, complemented
461	#2428	C₂×C₅₉	1	2	yes	complemented
462	#2424	C₂×C₅₉	1	4	yes	complemented
463	#2414	C₂×C₅₉	1	2	yes	complemented
464	#2410	C₂×C₅₉	1	4	yes	complemented
465	#2408	C₂×C₅₉	1	2	yes	complemented
466	#2392	C₂×C₅₉	1	1	yes	characteristic, complemented
467	C₂×#392	C₂×C₅₉	1	2	yes	complemented
468	#2349	C₂×C₅₉	1	1	yes	characteristic, complemented
469	D₄×C₂²⋊C₄	C₂×C₅₉	1	2	yes	complemented
470	C₂×C₅₉	—	2	8	no	—
471	C₂×C₅₉	—	4	4	no	—
472	C₂×C₅₉	—	4	2	no	—
473	C₂×C₅₉	—	4	4	no	—
474	C₂×C₅₉	—	8	4	no	—
475	C₂×C₅₉	C₂²×#121	1	1	yes	characteristic
476	C₂×C₅₉	#3484	1	1	yes	characteristic
477	C₂×C₅₉	#3484	1	2	yes	—
478	C₂×C₅₉	#3498	1	1	yes	characteristic
479	C₂×C₅₉	#3519	1	2	yes	—
480	C₂³×D₄	C₂²×C₅₉	1	2	yes	—
481	C₂³×D₄	C₂²×C₅₉	1	1	yes	characteristic
482	C₂³×D₄	C₂²×C₅₉	1	2	yes	complemented
483	C₂³×D₄	C₂²×C₅₉	1	4	yes	complemented
484	D₄²	—	2	16	no	—
485	D₄²	—	2	8	no	—
486	C₂×#127	C₂²×C₅₉	1	1	yes	characteristic, complemented
487	C₂×#127	C₂²×C₅₉	1	2	yes	complemented
488	C₂×#121	C₂²×C₅₉	1	2	yes	complemented
489	C₂×#121	C₂²×C₅₉	1	2	yes	complemented
490	C₂×#121	C₂²×C₅₉	1	2	yes	complemented
491	C₂×#121	C₂²×C₅₉	1	4	yes	complemented
492	C₂×#121	C₂²×C₅₉	1	2	yes	complemented
493	C₂×#121	C₂²×C₅₉	1	4	yes	complemented
494	C₂×#121	C₂²×C₅₉	1	4	yes	complemented
495	C₂×#120	C₂²×C₅₉	1	4	yes	complemented
496	C₂×#120	C₂²×C₅₉	1	4	yes	complemented
497	C₂×#120	C₂²×C₅₉	1	4	yes	complemented
498	#518	—	2	8	no	—
499	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
500	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
501	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
502	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	complemented
503	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
504	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	complemented
505	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	complemented
506	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
507	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
508	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic, complemented
509	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic, complemented
510	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	complemented
511	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	complemented
512	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	4	yes	complemented
513	#398	C₂²×C₅₉	1	1	yes	characteristic, complemented
514	#397	C₂²×C₅₉	1	1	yes	characteristic, complemented
515	#397	C₂²×C₅₉	1	2	yes	complemented
516	#396	C₂²×C₅₉	1	2	yes	complemented
517	#394	C₂²×C₅₉	1	4	yes	complemented
518	#394	C₂²×C₅₉	1	4	yes	complemented
519	#394	C₂²×C₅₉	1	2	yes	complemented
520	#394	C₂²×C₅₉	1	2	yes	complemented
521	#394	C₂²×C₅₉	1	1	yes	characteristic, complemented
522	#394	C₂²×C₅₉	1	2	yes	complemented
523	#392	C₂²×C₅₉	1	1	yes	characteristic
524	#392	C₂²×C₅₉	1	2	yes	complemented
525	#392	C₂²×C₅₉	1	2	yes	complemented
526	#392	C₂²×C₅₉	1	2	yes	complemented
527	#392	C₂²×C₅₉	1	2	yes	complemented
528	#392	C₂²×C₅₉	1	4	yes	complemented
529	#392	C₂²×C₅₉	1	4	yes	complemented
530	#392	C₂²×C₅₉	1	2	yes	complemented
531	#390	C₂²×C₅₉	1	2	yes	complemented
532	#390	C₂²×C₅₉	1	2	yes	complemented
533	#390	C₂²×C₅₉	1	4	yes	complemented
534	#389	C₂²×C₅₉	1	2	yes	complemented
535	#388	C₂²×C₅₉	1	4	yes	complemented
536	#386	C₂²×C₅₉	1	4	yes	complemented
537	#386	C₂²×C₅₉	1	4	yes	complemented
538	#386	C₂²×C₅₉	1	4	yes	complemented
539	#386	C₂²×C₅₉	1	4	yes	complemented
540	#385	C₂²×C₅₉	1	4	yes	complemented
541	#382	C₂²×C₅₉	1	1	yes	characteristic, complemented
542	#380	C₂²×C₅₉	1	2	yes	complemented
543	#380	C₂²×C₅₉	1	2	yes	complemented
544	#379	C₂²×C₅₉	1	4	yes	complemented
545	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
546	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	complemented
547	C₂×#95	C₂²×C₅₉	1	2	yes	complemented
548	C₅₉	#35691	1	1	yes	characteristic, direct product factor, Sylow
549	C₂⁵	C₂³×C₅₉	1	4	yes	—
550	C₂⁵	C₂³×C₅₉	1	2	yes	—
551	C₂²×D₄	—	2	4	no	—
552	C₂²×D₄	—	2	4	no	—
553	C₂²×D₄	—	2	16	no	—
554	C₂²×D₄	—	2	8	no	—
555	C₂²×D₄	—	2	8	no	—
556	C₂²×D₄	—	2	8	no	—
557	C₂²×D₄	—	2	8	no	—
558	C₂²×D₄	—	4	8	no	—
559	C₂²×D₄	—	4	8	no	—
560	C₂²×D₄	—	4	8	no	—
561	C₂²×D₄	D₄×C₅₉	1	8	yes	complemented
562	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
563	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
564	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
565	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
566	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
567	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
568	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
569	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
570	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
571	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
572	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
573	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
574	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
575	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
576	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
577	C₂³×C₄	C₂³×C₅₉	1	4	yes	—
578	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
579	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
580	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
581	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
582	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
583	#127	—	2	8	no	—
584	#127	—	2	4	no	—
585	#121	—	2	8	no	—
586	#121	—	2	16	no	—
587	#121	—	2	8	no	—
588	#121	—	2	8	no	—
589	#121	—	2	8	no	—
590	#121	—	4	8	no	—
591	#121	—	4	8	no	—
592	#120	—	2	16	no	—
593	#120	—	2	16	no	—
594	#120	—	2	16	no	—
595	C₄×D₄	—	2	4	no	—
596	C₄×D₄	—	2	8	no	—
597	C₄×D₄	—	2	8	no	—
598	C₄×D₄	—	2	8	no	—
599	C₄×D₄	—	2	4	no	—
600	C₄×D₄	—	2	8	no	—
601	C₄×D₄	—	2	4	no	—
602	C₄×D₄	—	2	4	no	—
603	C₄×D₄	D₄×C₅₉	1	8	yes	complemented
604	#117	—	2	4	no	—
605	#117	—	2	4	no	—
606	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
614	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
615	C₂×C₂²⋊C₄	—	2	8	no	—
616	C₂×C₂²⋊C₄	—	2	8	no	—
617	C₂×C₂²⋊C₄	—	4	8	no	—
618	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
619	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
621	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
639	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
640	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
641	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
642	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
643	#95	C₂³×C₅₉	1	1	yes	characteristic
644	#95	C₂³×C₅₉	1	2	yes	—
645	#95	C₂³×C₅₉	1	4	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	4	yes	—
650	#95	C₂³×C₅₉	1	2	yes	—
651	C₂⁴	—	2	4	no	—
652	C₂⁴	—	2	4	no	—
653	C₂⁴	—	2	8	no	—
654	C₂⁴	—	2	8	no	—
655	C₂⁴	—	2	8	no	—
656	C₂⁴	—	2	8	no	—
657	C₂⁴	—	4	4	no	—
658	C₂⁴	—	4	4	no	—
659	C₂⁴	—	4	4	no	—
660	C₂⁴	—	4	4	no	—
661	C₂⁴	—	4	4	no	—
662	C₂⁴	C₂×D₄×C₅₉	1	8	yes	complemented
663	C₂⁴	C₂⁴×C₅₉	1	4	yes	—
664	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
665	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
666	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
667	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
668	C₂×D₄	—	2	4	no	—
669	C₂×D₄	—	2	4	no	—
670	C₂×D₄	—	2	4	no	—
671	C₂×D₄	—	2	4	no	—
672	C₂×D₄	—	2	4	no	—
673	C₂×D₄	—	2	32	no	—
674	C₂×D₄	—	2	8	no	—
675	C₂×D₄	—	2	8	no	—
676	C₂×D₄	—	2	8	no	—
677	C₂×D₄	—	2	8	no	—
678	C₂×D₄	—	2	8	no	—
679	C₂×D₄	—	2	8	no	—
680	C₂×D₄	—	2	8	no	—
681	C₂×D₄	—	2	8	no	—
682	C₂×D₄	—	2	8	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	8	no	—
686	C₂×D₄	—	2	4	no	—
687	C₂×D₄	—	2	4	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	—	2	4	no	—
690	C₂×D₄	—	2	2	no	—
691	C₂×D₄	—	2	4	no	—
692	C₂×D₄	—	2	4	no	—
693	C₂×D₄	—	2	8	no	—
694	C₂×D₄	—	4	4	no	—
695	C₂×D₄	—	4	4	no	—
696	C₂×D₄	—	4	4	no	—
697	C₂×D₄	—	4	4	no	—
698	C₂×D₄	—	4	4	no	—
699	C₂×D₄	—	4	4	no	—
700	C₂×D₄	—	4	4	no	—
701	C₂×D₄	—	4	4	no	—
702	C₂×D₄	—	4	4	no	—
703	C₂×D₄	—	4	32	no	—
704	C₂×D₄	—	4	64	no	—
705	C₂×D₄	—	4	32	no	—
706	C₂×D₄	C₂×D₄×C₅₉	1	4	yes	—
707	C₂×D₄	C₂×D₄×C₅₉	1	4	yes	—
708	C₂×D₄	C₂×D₄×C₅₉	1	8	yes	complemented
709	C₂×D₄	C₂×D₄×C₅₉	1	4	yes	complemented
710	C₂×D₄	#41×C₅₉	1	4	yes	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	8	no	—
714	C₂²×C₄	—	2	4	no	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	2	4	no	—
717	C₂²×C₄	—	2	4	no	—
718	C₂²×C₄	—	2	8	no	—
719	C₂²×C₄	—	2	4	no	—
720	C₂²×C₄	—	2	4	no	—
721	C₂²×C₄	—	4	4	no	—
722	C₂²×C₄	—	4	4	no	—
723	C₂²×C₄	—	4	4	no	—
724	C₂²×C₄	—	4	4	no	—
725	C₂²×C₄	—	4	4	no	—
726	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	complemented
727	C₂²×C₄	C₂×D₄×C₅₉	1	8	yes	complemented
728	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
730	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
735	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
736	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
737	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	4	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	—	2	4	no	—
747	C₄⋊C₄	—	4	4	no	—
748	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	complemented
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	8	no	—
752	C₂²⋊C₄	—	2	8	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	4	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	4	no	—
761	C₂²⋊C₄	—	2	8	no	—
762	C₂²⋊C₄	—	2	8	no	—
763	C₂²⋊C₄	—	2	4	no	—
764	C₂²⋊C₄	—	2	8	no	—
765	C₂²⋊C₄	—	4	4	no	—
766	C₂²⋊C₄	—	4	4	no	—
767	C₂²⋊C₄	—	4	4	no	—
768	C₂²⋊C₄	—	4	4	no	—
769	C₂²⋊C₄	C₂×D₄×C₅₉	1	8	yes	complemented
770	C₄²	—	2	4	no	—
771	C₄²	—	2	2	no	—
772	C₄²	—	2	4	no	—
773	C₄²	C₂×D₄×C₅₉	1	4	yes	complemented
774	C₂³	—	2	4	no	—
775	C₂³	—	2	4	no	—
776	C₂³	—	2	1	no	—
777	C₂³	—	2	2	no	—
778	C₂³	—	2	2	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	2	1	no	—
782	C₂³	—	2	2	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	4	no	—
785	C₂³	—	2	4	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	2	16	no	—
791	C₂³	—	2	4	no	—
792	C₂³	—	2	4	no	—
793	C₂³	—	2	4	no	—
794	C₂³	—	2	4	no	—
795	C₂³	—	2	4	no	—
796	C₂³	—	2	4	no	—
797	C₂³	—	2	4	no	—
798	C₂³	—	4	16	no	—
799	C₂³	—	4	16	no	—
800	C₂³	—	4	16	no	—
801	C₂³	—	4	16	no	—
802	C₂³	—	4	16	no	—
803	C₂³	—	8	8	no	—
804	C₂³	—	8	8	no	—
805	C₂³	—	8	4	no	—
806	C₂³	—	8	8	no	—
807	C₂³	—	8	4	no	—
808	C₂³	—	8	8	no	—
809	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
810	C₂³	C₂²×D₄×C₅₉	1	4	yes	—
811	C₂³	C₂²×D₄×C₅₉	1	4	yes	—
812	C₂³	C₂²×D₄×C₅₉	1	4	yes	—
813	C₂³	C₂×#41×C₅₉	1	4	yes	—
814	C₂³	H(5,𝔽₂)×C₅₉	1	4	yes	—
815	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
816	D₄	—	2	8	no	—
817	D₄	—	2	16	no	—
818	D₄	—	2	16	no	—
819	D₄	—	2	8	no	—
820	D₄	—	4	16	no	—
821	D₄	—	4	16	no	—
822	D₄	—	4	8	no	—
823	D₄	—	4	16	no	—
824	D₄	—	4	16	no	—
825	D₄	—	4	16	no	—
826	D₄	—	4	8	no	—
827	D₄	—	8	4	no	—
828	D₄	—	8	8	no	—
829	D₄	#121×C₅₉	1	16	yes	complemented
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	4	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	8	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	4	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	4	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	4	no	—
852	C₂×C₄	—	2	4	no	—
853	C₂×C₄	—	4	8	no	—
854	C₂×C₄	—	4	16	no	—
855	C₂×C₄	—	4	8	no	—
856	C₂×C₄	—	8	4	no	—
857	C₂×C₄	—	8	4	no	—
858	C₂×C₄	—	8	4	no	—
859	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
860	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
861	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
862	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
863	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
864	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
865	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
866	C₂×C₄	H(5,𝔽₂)×C₅₉	1	4	yes	—
867	C₂²	—	2	8	no	—
868	C₂²	—	2	4	no	—
869	C₂²	—	2	8	no	—
870	C₂²	—	2	4	no	—
871	C₂²	—	2	4	no	—
872	C₂²	—	2	2	no	—
873	C₂²	—	2	4	no	—
874	C₂²	—	2	4	no	—
875	C₂²	—	2	4	no	—
876	C₂²	—	2	4	no	—
877	C₂²	—	2	8	no	—
878	C₂²	—	4	2	no	—
879	C₂²	—	4	2	no	—
880	C₂²	—	4	4	no	—
881	C₂²	—	4	2	no	—
882	C₂²	—	4	2	no	—
883	C₂²	—	4	1	no	—
884	C₂²	—	4	2	no	—
885	C₂²	—	4	2	no	—
886	C₂²	—	4	1	no	—
887	C₂²	—	4	2	no	—
888	C₂²	—	4	4	no	—
889	C₂²	—	4	4	no	—
890	C₂²	—	4	4	no	—
891	C₂²	—	4	4	no	—
892	C₂²	—	4	4	no	—
893	C₂²	—	4	4	no	—
894	C₂²	—	4	4	no	—
895	C₂²	—	8	16	no	—
896	C₂²	—	8	32	no	—
897	C₂²	C₂×#121×C₅₉	1	8	yes	—
898	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
899	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
900	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
901	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	2	yes	—
902	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	2	yes	—
903	C₄	—	2	2	no	—
904	C₄	—	2	2	no	—
905	C₄	—	2	4	no	—
906	C₄	—	2	4	no	—
907	C₄	—	2	2	no	—
908	C₄	—	4	2	no	—
909	C₄	—	4	4	no	—
910	C₄	—	4	1	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	2	no	—
913	C₄	—	4	1	no	—
914	C₄	C₂×#121×C₅₉	1	4	yes	—
915	C₂	—	2	8	no	—
916	C₂	—	4	4	no	—
917	C₂	—	4	2	no	—
918	C₂	—	4	4	no	—
919	C₂	—	8	4	no	—
920	C₂	C₂²×#121×C₅₉	1	1	yes	characteristic
921	C₂	C₅₉×#3484	1	1	yes	characteristic
922	C₂	C₅₉×#3484	1	2	yes	—
923	C₂	C₅₉×#3498	1	1	yes	characteristic
924	C₂	C₅₉×#3519	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×D₄²×C₅₉	C₂	semidirect
2. C₂×D₄²×C₅₉	C₂	semidirect
3. C₂×C₅₉×#518	C₂	semidirect
4. C₅₉×#2619	C₂	semidirect
5. C₅₉×#2617	C₂	semidirect
6. C₅₉×#2543	C₂	semidirect
7. C₅₉×#2541	C₂	semidirect
8. C₅₉×#2535	C₂	semidirect
9. C₅₉×#2428	C₂	semidirect
10. C₅₉×#2424	C₂	semidirect
11. C₅₉×#2414	C₂	semidirect
12. C₅₉×#2410	C₂	semidirect
13. C₅₉×#2408	C₂	semidirect
14. C₅₉×#2392	C₂	semidirect
15. C₂×C₅₉×#392	C₂	semidirect
16. C₅₉×#2349	C₂	semidirect
17. D₄×C₂²⋊C₄×C₅₉	C₂	semidirect
20. C₂³×D₄×C₅₉	C₂²	semidirect
21. C₂³×D₄×C₅₉	C₂²	semidirect
24. C₂×#127×C₅₉	C₂²	semidirect
25. C₂×#127×C₅₉	C₂²	semidirect
26. C₂×#121×C₅₉	C₂²	semidirect
27. C₂×#121×C₅₉	C₂²	semidirect
28. C₂×#121×C₅₉	C₂²	semidirect
29. C₂×#121×C₅₉	C₂²	semidirect
30. C₂×#121×C₅₉	C₂²	semidirect
31. C₂×#121×C₅₉	C₂²	semidirect
32. C₂×#121×C₅₉	C₂²	semidirect
33. C₂×#120×C₅₉	C₂²	semidirect
34. C₂×#120×C₅₉	C₂²	semidirect
35. C₂×#120×C₅₉	C₂²	semidirect
40. C₂×C₄×D₄×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×C₄×D₄×C₅₉	C₂²	semidirect
45. C₂×C₄×D₄×C₅₉	C₂²	semidirect
46. C₂×#117×C₅₉	C₂²	semidirect
47. C₂×#117×C₅₉	C₂²	semidirect
48. C₂²×C₂²⋊C₄×C₅₉	C₂²	semidirect
49. C₂²×C₂²⋊C₄×C₅₉	C₂²	semidirect
50. C₂²×C₂²⋊C₄×C₅₉	C₂²	semidirect
51. C₅₉×#398	C₂²	semidirect
52. C₅₉×#397	C₂²	semidirect
53. C₅₉×#397	C₂²	semidirect
54. C₅₉×#396	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
62. C₅₉×#392	C₂²	semidirect
63. C₅₉×#392	C₂²	semidirect
64. C₅₉×#392	C₂²	semidirect
65. C₅₉×#392	C₂²	semidirect
66. C₅₉×#392	C₂²	semidirect
67. C₅₉×#392	C₂²	semidirect
68. C₅₉×#392	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×#386	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
98. C₂²×D₄×C₅₉	D₄	semidirect
140. C₄×D₄×C₅₉	D₄	semidirect
199. C₂⁴×C₅₉	C₂×D₄	semidirect
245. C₂×D₄×C₅₉	C₂×D₄	semidirect
246. C₂×D₄×C₅₉	C₂×D₄	semidirect
263. C₂²×C₄×C₅₉	C₂×D₄	semidirect
264. C₂²×C₄×C₅₉	C₂×D₄	semidirect
285. C₄⋊C₄×C₅₉	C₂×D₄	semidirect
306. C₂²⋊C₄×C₅₉	C₂×D₄	semidirect
310. C₄²×C₅₉	C₂×D₄	semidirect
366. D₄×C₅₉	#121	semidirect
404. #35691	C₅₉	direct (N × H)
453. C₂×D₄²	C₂×C₅₉	semidirect
454. C₂×D₄²	C₂×C₅₉	semidirect
455. C₂×#518	C₂×C₅₉	semidirect
456. #2619	C₂×C₅₉	semidirect
457. #2617	C₂×C₅₉	semidirect
458. #2543	C₂×C₅₉	semidirect
459. #2541	C₂×C₅₉	semidirect
460. #2535	C₂×C₅₉	semidirect
461. #2428	C₂×C₅₉	semidirect
462. #2424	C₂×C₅₉	semidirect
463. #2414	C₂×C₅₉	semidirect
464. #2410	C₂×C₅₉	semidirect
465. #2408	C₂×C₅₉	semidirect
466. #2392	C₂×C₅₉	semidirect
467. C₂×#392	C₂×C₅₉	semidirect
468. #2349	C₂×C₅₉	semidirect
469. D₄×C₂²⋊C₄	C₂×C₅₉	semidirect
482. C₂³×D₄	C₂²×C₅₉	semidirect
483. C₂³×D₄	C₂²×C₅₉	semidirect
486. C₂×#127	C₂²×C₅₉	semidirect
487. C₂×#127	C₂²×C₅₉	semidirect
488. C₂×#121	C₂²×C₅₉	semidirect
489. C₂×#121	C₂²×C₅₉	semidirect
490. C₂×#121	C₂²×C₅₉	semidirect
491. C₂×#121	C₂²×C₅₉	semidirect
492. C₂×#121	C₂²×C₅₉	semidirect
493. C₂×#121	C₂²×C₅₉	semidirect
494. C₂×#121	C₂²×C₅₉	semidirect
495. C₂×#120	C₂²×C₅₉	semidirect
496. C₂×#120	C₂²×C₅₉	semidirect
497. C₂×#120	C₂²×C₅₉	semidirect
502. C₂×C₄×D₄	C₂²×C₅₉	semidirect
503. C₂×C₄×D₄	C₂²×C₅₉	semidirect
504. C₂×C₄×D₄	C₂²×C₅₉	semidirect
505. C₂×C₄×D₄	C₂²×C₅₉	semidirect
506. C₂×C₄×D₄	C₂²×C₅₉	semidirect
507. C₂×C₄×D₄	C₂²×C₅₉	semidirect
508. C₂×#117	C₂²×C₅₉	semidirect
509. C₂×#117	C₂²×C₅₉	semidirect
510. C₂²×C₂²⋊C₄	C₂²×C₅₉	semidirect
511. C₂²×C₂²⋊C₄	C₂²×C₅₉	semidirect
512. C₂²×C₂²⋊C₄	C₂²×C₅₉	semidirect
513. #398	C₂²×C₅₉	semidirect
514. #397	C₂²×C₅₉	semidirect
515. #397	C₂²×C₅₉	semidirect
516. #396	C₂²×C₅₉	semidirect
517. #394	C₂²×C₅₉	semidirect
518. #394	C₂²×C₅₉	semidirect
519. #394	C₂²×C₅₉	semidirect
520. #394	C₂²×C₅₉	semidirect
521. #394	C₂²×C₅₉	semidirect
522. #394	C₂²×C₅₉	semidirect
524. #392	C₂²×C₅₉	semidirect
525. #392	C₂²×C₅₉	semidirect
526. #392	C₂²×C₅₉	semidirect
527. #392	C₂²×C₅₉	semidirect
528. #392	C₂²×C₅₉	semidirect
529. #392	C₂²×C₅₉	semidirect
530. #392	C₂²×C₅₉	semidirect
531. #390	C₂²×C₅₉	semidirect
532. #390	C₂²×C₅₉	semidirect
533. #390	C₂²×C₅₉	semidirect
534. #389	C₂²×C₅₉	semidirect
535. #388	C₂²×C₅₉	semidirect
536. #386	C₂²×C₅₉	semidirect
537. #386	C₂²×C₅₉	semidirect
538. #386	C₂²×C₅₉	semidirect
539. #386	C₂²×C₅₉	semidirect
540. #385	C₂²×C₅₉	semidirect
541. #382	C₂²×C₅₉	semidirect
542. #380	C₂²×C₅₉	semidirect
543. #380	C₂²×C₅₉	semidirect
544. #379	C₂²×C₅₉	semidirect
545. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
546. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
547. C₂×#95	C₂²×C₅₉	semidirect
548. C₅₉	#35691	direct (N × H)
561. C₂²×D₄	D₄×C₅₉	semidirect
603. C₄×D₄	D₄×C₅₉	semidirect
662. C₂⁴	C₂×D₄×C₅₉	semidirect
708. C₂×D₄	C₂×D₄×C₅₉	semidirect
709. C₂×D₄	C₂×D₄×C₅₉	semidirect
726. C₂²×C₄	C₂×D₄×C₅₉	semidirect
727. C₂²×C₄	C₂×D₄×C₅₉	semidirect
748. C₄⋊C₄	C₂×D₄×C₅₉	semidirect
769. C₂²⋊C₄	C₂×D₄×C₅₉	semidirect
773. C₄²	C₂×D₄×C₅₉	semidirect
829. 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×D₄²×C₅₉	2
C₂×C₅₉×#518	2
C₅₉×#2619	2
C₅₉×#2617	2
C₅₉×#2543	2
C₅₉×#2541	2
C₅₉×#2535	2
C₅₉×#2428	2
C₅₉×#2424	2
C₅₉×#2414	2
C₅₉×#2410	2
C₅₉×#2408	2
C₅₉×#2392	2
C₂×C₅₉×#392	2
C₅₉×#2349	2
D₄×C₂²⋊C₄×C₅₉	2
#35691	59

Subgroups — C59×#35691 #28447800

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35691 #28447800