Subgroups — C₅₉×#35295 #28447404

Order 15104.

1886 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#2860	C₂	1	2	yes	maximal, complemented
2	C₅₉×#2856	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2851	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2647	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2641	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#2624	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2597	C₂	1	4	yes	maximal, complemented
8	C₅₉×#2559	C₂	1	4	yes	maximal, complemented
9	C₅₉×#2479	C₂	1	4	yes	maximal, complemented
10	C₅₉×#2476	C₂	1	4	yes	maximal, complemented
11	C₅₉×#2330	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#2328	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₉×#2324	C₂	1	2	yes	maximal, complemented
14	C₅₉×#2293	C₂	1	2	yes	maximal, complemented
15	C₄×#117×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#127×C₅₉	C₂²	1	1	yes	characteristic
17	C₂×#126×C₅₉	C₂²	1	4	yes	—
18	C₂×#125×C₅₉	C₂²	1	1	yes	characteristic
19	C₂×#121×C₅₉	C₂²	1	2	yes	—
20	C₂×#121×C₅₉	C₂²	1	4	yes	—
21	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
22	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
23	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
24	C₂×#117×C₅₉	C₂²	1	4	yes	—
25	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
26	C₅₉×#400	C₂²	1	4	yes	—
27	C₅₉×#399	C₂²	1	4	yes	—
28	C₅₉×#398	C₂²	1	4	yes	—
29	C₅₉×#397	C₂²	1	4	yes	—
30	C₅₉×#394	C₂²	1	4	yes	—
31	C₅₉×#394	C₂²	1	4	yes	—
32	C₅₉×#394	C₂²	1	4	yes	—
33	C₅₉×#394	C₂²	1	4	yes	—
34	C₅₉×#390	C₂²	1	2	yes	—
35	C₅₉×#390	C₂²	1	2	yes	—
36	C₅₉×#390	C₂²	1	4	yes	—
37	C₅₉×#390	C₂²	1	2	yes	—
38	C₅₉×#390	C₂²	1	2	yes	—
39	C₅₉×#390	C₂²	1	4	yes	—
40	C₅₉×#389	C₂²	1	2	yes	—
41	C₅₉×#389	C₂²	1	2	yes	—
42	C₅₉×#389	C₂²	1	4	yes	—
43	C₅₉×#389	C₂²	1	2	yes	—
44	C₅₉×#389	C₂²	1	2	yes	—
45	C₅₉×#388	C₂²	1	4	yes	—
46	C₅₉×#388	C₂²	1	4	yes	—
47	C₅₉×#388	C₂²	1	4	yes	—
48	C₅₉×#388	C₂²	1	4	yes	—
49	C₅₉×#388	C₂²	1	4	yes	—
50	C₅₉×#388	C₂²	1	4	yes	—
51	C₅₉×#387	C₂²	1	4	yes	—
52	C₅₉×#387	C₂²	1	4	yes	—
53	C₅₉×#386	C₂²	1	4	yes	—
54	C₅₉×#386	C₂²	1	4	yes	—
55	C₅₉×#386	C₂²	1	4	yes	—
56	C₅₉×#385	C₂²	1	4	yes	—
57	C₅₉×#385	C₂²	1	4	yes	—
58	C₅₉×#384	C₂²	1	1	yes	characteristic
59	C₅₉×#382	C₂²	1	1	yes	characteristic
60	C₅₉×#380	C₂²	1	2	yes	—
61	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
62	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
63	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
64	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
65	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
66	C₄×C₂²⋊C₄×C₅₉	C₂²	1	4	yes	—
67	C₅₉×#376	C₂²	1	1	yes	characteristic
68	C₅₉×#376	C₂²	1	1	yes	characteristic
69	C₄³×C₅₉	C₂²	1	1	yes	characteristic
70	C₄³×C₅₉	C₂²	1	1	yes	characteristic
71	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
72	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
73	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
74	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
75	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₅₉	C₂³	1	4	yes	—
77	#127×C₅₉	—	2	4	no	—
78	#126×C₅₉	—	4	8	no	—
79	#125×C₅₉	—	2	4	no	—
80	#121×C₅₉	—	2	8	no	—
81	#121×C₅₉	—	4	8	no	—
82	C₄×D₄×C₅₉	—	2	8	no	—
83	#117×C₅₉	—	2	4	no	—
84	#117×C₅₉	—	2	4	no	—
85	#117×C₅₉	—	4	8	no	—
86	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
90	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
93	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
94	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
95	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
97	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
98	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
99	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
102	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
103	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
104	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
105	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
106	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
107	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
108	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
109	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
110	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
111	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
112	C₂×C₄²×C₅₉	—	2	4	no	—
113	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
118	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
119	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
120	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
121	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
122	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
123	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
124	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
125	#95×C₅₉	C₂³	1	2	yes	—
126	#95×C₅₉	C₂³	1	2	yes	—
127	#95×C₅₉	C₂³	1	2	yes	—
128	#95×C₅₉	C₂³	1	2	yes	—
129	#95×C₅₉	C₂³	1	4	yes	—
130	#95×C₅₉	C₂³	1	4	yes	—
131	#95×C₅₉	C₂³	1	4	yes	—
132	#95×C₅₉	C₂³	1	4	yes	—
133	#95×C₅₉	C₂³	1	4	yes	—
134	#95×C₅₉	C₂³	1	4	yes	—
135	#95×C₅₉	C₂³	1	4	yes	—
136	C₂⁴×C₅₉	C₂⁴	1	4	yes	—
137	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
138	C₂×D₄×C₅₉	—	2	8	no	—
139	C₂×D₄×C₅₉	—	2	4	no	—
140	C₂×D₄×C₅₉	—	2	4	no	—
141	C₂×D₄×C₅₉	—	2	4	no	—
142	C₂×D₄×C₅₉	—	2	8	no	—
143	C₂×D₄×C₅₉	—	4	4	no	—
144	C₂×D₄×C₅₉	—	4	4	no	—
145	C₂×D₄×C₅₉	—	4	4	no	—
146	C₂×D₄×C₅₉	—	4	4	no	—
147	C₂²×C₄×C₅₉	—	2	2	no	—
148	C₂²×C₄×C₅₉	—	2	2	no	—
149	C₂²×C₄×C₅₉	—	2	4	no	—
150	C₂²×C₄×C₅₉	—	2	8	no	—
151	C₂²×C₄×C₅₉	—	2	4	no	—
152	C₂²×C₄×C₅₉	—	4	4	no	—
153	C₂²×C₄×C₅₉	—	4	2	no	—
154	C₂²×C₄×C₅₉	—	4	4	no	—
155	C₂²×C₄×C₅₉	#41	1	4	yes	—
156	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
157	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
158	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
159	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
160	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
161	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
162	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
163	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
164	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
165	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
166	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
167	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
169	C₄⋊C₄×C₅₉	—	2	4	no	—
170	C₄⋊C₄×C₅₉	—	2	2	no	—
171	C₄⋊C₄×C₅₉	—	2	2	no	—
172	C₄⋊C₄×C₅₉	—	2	4	no	—
173	C₄⋊C₄×C₅₉	—	2	4	no	—
174	C₄⋊C₄×C₅₉	—	2	8	no	—
175	C₄⋊C₄×C₅₉	—	2	4	no	—
176	C₄⋊C₄×C₅₉	—	2	8	no	—
177	C₄⋊C₄×C₅₉	—	4	4	no	—
178	C₄⋊C₄×C₅₉	—	4	4	no	—
179	C₄⋊C₄×C₅₉	—	4	4	no	—
180	C₄⋊C₄×C₅₉	—	4	4	no	—
181	C₂²⋊C₄×C₅₉	—	2	2	no	—
182	C₂²⋊C₄×C₅₉	—	2	2	no	—
183	C₂²⋊C₄×C₅₉	—	2	4	no	—
184	C₂²⋊C₄×C₅₉	—	2	8	no	—
185	C₂²⋊C₄×C₅₉	—	2	8	no	—
186	C₂²⋊C₄×C₅₉	—	2	8	no	—
187	C₂²⋊C₄×C₅₉	—	2	8	no	—
188	C₂²⋊C₄×C₅₉	—	4	4	no	—
189	C₂²⋊C₄×C₅₉	—	4	4	no	—
190	C₂²⋊C₄×C₅₉	—	4	4	no	—
191	C₂²⋊C₄×C₅₉	—	4	4	no	—
192	C₂²⋊C₄×C₅₉	—	4	4	no	—
193	C₂²⋊C₄×C₅₉	—	4	4	no	—
194	C₂²⋊C₄×C₅₉	—	4	4	no	—
195	C₄²×C₅₉	—	2	4	no	—
196	C₄²×C₅₉	—	2	2	no	—
197	C₄²×C₅₉	—	2	2	no	—
198	C₄²×C₅₉	—	2	2	no	—
199	C₄²×C₅₉	—	2	2	no	—
200	C₄²×C₅₉	—	2	4	no	—
201	C₄²×C₅₉	—	2	4	no	—
202	C₄²×C₅₉	—	4	2	no	—
203	C₄²×C₅₉	—	4	2	no	—
204	C₄²×C₅₉	—	4	4	no	—
205	C₄²×C₅₉	#41	1	4	yes	—
206	C₄²×C₅₉	#41	1	4	yes	—
207	C₂³×C₅₉	—	2	1	no	—
208	C₂³×C₅₉	—	2	1	no	—
209	C₂³×C₅₉	—	2	2	no	—
210	C₂³×C₅₉	—	2	2	no	—
211	C₂³×C₅₉	—	2	4	no	—
212	C₂³×C₅₉	—	2	4	no	—
213	C₂³×C₅₉	—	2	4	no	—
214	C₂³×C₅₉	—	2	4	no	—
215	C₂³×C₅₉	—	2	4	no	—
216	C₂³×C₅₉	—	2	4	no	—
217	C₂³×C₅₉	—	2	4	no	—
218	C₂³×C₅₉	C₂×#41	1	2	yes	—
219	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
220	D₄×C₅₉	—	4	8	no	—
221	D₄×C₅₉	—	8	8	no	—
222	D₄×C₅₉	—	8	8	no	—
223	C₂×C₄×C₅₉	—	2	1	no	—
224	C₂×C₄×C₅₉	—	2	2	no	—
225	C₂×C₄×C₅₉	—	2	1	no	—
226	C₂×C₄×C₅₉	—	2	2	no	—
227	C₂×C₄×C₅₉	—	2	2	no	—
228	C₂×C₄×C₅₉	—	2	2	no	—
229	C₂×C₄×C₅₉	—	2	2	no	—
230	C₂×C₄×C₅₉	—	2	2	no	—
231	C₂×C₄×C₅₉	—	2	8	no	—
232	C₂×C₄×C₅₉	—	2	2	no	—
233	C₂×C₄×C₅₉	—	2	1	no	—
234	C₂×C₄×C₅₉	—	2	1	no	—
235	C₂×C₄×C₅₉	—	2	1	no	—
236	C₂×C₄×C₅₉	—	2	1	no	—
237	C₂×C₄×C₅₉	—	2	4	no	—
238	C₂×C₄×C₅₉	—	2	4	no	—
239	C₂×C₄×C₅₉	—	2	4	no	—
240	C₂×C₄×C₅₉	—	2	2	no	—
241	C₂×C₄×C₅₉	—	2	2	no	—
242	C₂×C₄×C₅₉	—	2	2	no	—
243	C₂×C₄×C₅₉	—	2	4	no	—
244	C₂×C₄×C₅₉	—	2	4	no	—
245	C₂×C₄×C₅₉	—	2	4	no	—
246	C₂×C₄×C₅₉	—	2	4	no	—
247	C₂×C₄×C₅₉	—	2	2	no	—
248	C₂×C₄×C₅₉	—	2	2	no	—
249	C₂×C₄×C₅₉	—	2	2	no	—
250	C₂×C₄×C₅₉	—	2	4	no	—
251	C₂×C₄×C₅₉	—	2	4	no	—
252	C₂×C₄×C₅₉	—	4	8	no	—
253	C₂×C₄×C₅₉	—	4	16	no	—
254	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
255	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
256	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
257	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
258	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
259	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
260	C₂×C₄×C₅₉	H(5,𝔽₂)	1	4	yes	—
261	#35295	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
262	C₂²×C₅₉	—	2	2	no	—
263	C₂²×C₅₉	—	2	2	no	—
264	C₂²×C₅₉	—	2	2	no	—
265	C₂²×C₅₉	—	4	2	no	—
266	C₂²×C₅₉	—	4	2	no	—
267	C₂²×C₅₉	—	4	4	no	—
268	C₂²×C₅₉	—	4	4	no	—
269	C₂²×C₅₉	—	4	4	no	—
270	C₂²×C₅₉	—	4	4	no	—
271	C₂²×C₅₉	—	4	4	no	—
272	C₂²×C₅₉	—	4	4	no	—
273	C₂²×C₅₉	—	4	4	no	—
274	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
275	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
276	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
277	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	2	yes	—
278	C₂²×C₅₉	#585	1	2	yes	—
279	C₄×C₅₉	—	2	2	no	—
280	C₄×C₅₉	—	2	4	no	—
281	C₄×C₅₉	—	2	4	no	—
282	C₄×C₅₉	—	2	4	no	—
283	C₄×C₅₉	—	4	2	no	—
284	C₄×C₅₉	—	4	4	no	—
285	C₄×C₅₉	—	4	4	no	—
286	C₄×C₅₉	—	4	1	no	—
287	C₄×C₅₉	—	4	1	no	—
288	C₄×C₅₉	—	4	4	no	—
289	C₄×C₅₉	—	4	1	no	—
290	C₄×C₅₉	—	4	1	no	—
291	C₄×C₅₉	#529	1	4	yes	—
292	#2860	C₂×C₅₉	1	2	yes	complemented
293	#2856	C₂×C₅₉	1	1	yes	characteristic
294	#2851	C₂×C₅₉	1	1	yes	characteristic, complemented
295	#2647	C₂×C₅₉	1	1	yes	characteristic, complemented
296	#2641	C₂×C₅₉	1	1	yes	characteristic, complemented
297	#2624	C₂×C₅₉	1	2	yes	complemented
298	#2597	C₂×C₅₉	1	4	yes	complemented
299	#2559	C₂×C₅₉	1	4	yes	complemented
300	#2479	C₂×C₅₉	1	4	yes	complemented
301	#2476	C₂×C₅₉	1	4	yes	complemented
302	#2330	C₂×C₅₉	1	1	yes	characteristic, complemented
303	#2328	C₂×C₅₉	1	1	yes	characteristic, complemented
304	#2324	C₂×C₅₉	1	2	yes	complemented
305	#2293	C₂×C₅₉	1	2	yes	complemented
306	C₄×#117	C₂×C₅₉	1	1	yes	characteristic, complemented
307	C₂×C₅₉	—	4	2	no	—
308	C₂×C₅₉	—	8	4	no	—
309	C₂×C₅₉	C₂×#529	1	1	yes	characteristic
310	C₂×C₅₉	#3460	1	2	yes	—
311	C₂×C₅₉	#3494	1	2	yes	—
312	C₂×C₅₉	#3508	1	1	yes	characteristic
313	C₂×C₅₉	#3512	1	1	yes	characteristic
314	C₂×#127	C₂²×C₅₉	1	1	yes	characteristic
315	C₂×#126	C₂²×C₅₉	1	4	yes	—
316	C₂×#125	C₂²×C₅₉	1	1	yes	characteristic
317	C₂×#121	C₂²×C₅₉	1	2	yes	—
318	C₂×#121	C₂²×C₅₉	1	4	yes	—
319	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
320	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
321	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
322	C₂×#117	C₂²×C₅₉	1	4	yes	—
323	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
324	#400	C₂²×C₅₉	1	4	yes	—
325	#399	C₂²×C₅₉	1	4	yes	—
326	#398	C₂²×C₅₉	1	4	yes	—
327	#397	C₂²×C₅₉	1	4	yes	—
328	#394	C₂²×C₅₉	1	4	yes	—
329	#394	C₂²×C₅₉	1	4	yes	—
330	#394	C₂²×C₅₉	1	4	yes	—
331	#394	C₂²×C₅₉	1	4	yes	—
332	#390	C₂²×C₅₉	1	2	yes	—
333	#390	C₂²×C₅₉	1	4	yes	—
334	#390	C₂²×C₅₉	1	2	yes	—
335	#390	C₂²×C₅₉	1	4	yes	—
336	#390	C₂²×C₅₉	1	2	yes	—
337	#390	C₂²×C₅₉	1	2	yes	—
338	#389	C₂²×C₅₉	1	2	yes	—
339	#389	C₂²×C₅₉	1	2	yes	—
340	#389	C₂²×C₅₉	1	4	yes	—
341	#389	C₂²×C₅₉	1	2	yes	—
342	#389	C₂²×C₅₉	1	2	yes	—
343	#388	C₂²×C₅₉	1	4	yes	—
344	#388	C₂²×C₅₉	1	4	yes	—
345	#388	C₂²×C₅₉	1	4	yes	—
346	#388	C₂²×C₅₉	1	4	yes	—
347	#388	C₂²×C₅₉	1	4	yes	—
348	#388	C₂²×C₅₉	1	4	yes	—
349	#387	C₂²×C₅₉	1	4	yes	—
350	#387	C₂²×C₅₉	1	4	yes	—
351	#386	C₂²×C₅₉	1	4	yes	—
352	#386	C₂²×C₅₉	1	4	yes	—
353	#386	C₂²×C₅₉	1	4	yes	—
354	#385	C₂²×C₅₉	1	4	yes	—
355	#385	C₂²×C₅₉	1	4	yes	—
356	#384	C₂²×C₅₉	1	1	yes	characteristic
357	#382	C₂²×C₅₉	1	1	yes	characteristic
358	#380	C₂²×C₅₉	1	2	yes	—
359	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
360	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
361	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
362	C₄×C₂²⋊C₄	C₂²×C₅₉	1	4	yes	—
363	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
364	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
365	#376	C₂²×C₅₉	1	1	yes	characteristic
366	#376	C₂²×C₅₉	1	1	yes	characteristic
367	C₄³	C₂²×C₅₉	1	1	yes	characteristic
368	C₄³	C₂²×C₅₉	1	1	yes	characteristic
369	C₅₉	#35295	1	1	yes	characteristic, direct product factor, Sylow
370	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
371	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
372	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
373	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
374	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
375	C₂³×C₄	C₂³×C₅₉	1	4	yes	—
376	#127	—	2	4	no	—
377	#126	—	4	8	no	—
378	#125	—	2	4	no	—
379	#121	—	2	8	no	—
380	#121	—	4	8	no	—
381	C₄×D₄	—	2	8	no	—
382	#117	—	2	4	no	—
383	#117	—	2	4	no	—
384	#117	—	4	8	no	—
385	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
386	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
387	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
389	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
390	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
391	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
392	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
393	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
394	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
395	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
396	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
397	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
398	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
399	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
400	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
401	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
402	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
403	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
404	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
405	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
406	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
407	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
408	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
409	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
410	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
411	C₂×C₄²	—	2	4	no	—
412	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
413	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
414	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
415	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
416	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
417	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
418	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
419	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
420	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
421	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
422	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
423	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
424	#95	C₂³×C₅₉	1	2	yes	—
425	#95	C₂³×C₅₉	1	2	yes	—
426	#95	C₂³×C₅₉	1	2	yes	—
427	#95	C₂³×C₅₉	1	2	yes	—
428	#95	C₂³×C₅₉	1	4	yes	—
429	#95	C₂³×C₅₉	1	4	yes	—
430	#95	C₂³×C₅₉	1	4	yes	—
431	#95	C₂³×C₅₉	1	4	yes	—
432	#95	C₂³×C₅₉	1	4	yes	—
433	#95	C₂³×C₅₉	1	4	yes	—
434	#95	C₂³×C₅₉	1	4	yes	—
435	C₂⁴	C₂⁴×C₅₉	1	4	yes	—
436	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
437	C₂×D₄	—	2	8	no	—
438	C₂×D₄	—	2	4	no	—
439	C₂×D₄	—	2	4	no	—
440	C₂×D₄	—	2	4	no	—
441	C₂×D₄	—	2	8	no	—
442	C₂×D₄	—	4	4	no	—
443	C₂×D₄	—	4	4	no	—
444	C₂×D₄	—	4	4	no	—
445	C₂×D₄	—	4	4	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	4	no	—
449	C₂²×C₄	—	2	8	no	—
450	C₂²×C₄	—	2	4	no	—
451	C₂²×C₄	—	4	4	no	—
452	C₂²×C₄	—	4	2	no	—
453	C₂²×C₄	—	4	4	no	—
454	C₂²×C₄	#41×C₅₉	1	4	yes	—
455	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
456	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
457	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
458	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
459	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
460	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
461	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
462	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
463	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
464	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
465	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
466	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
467	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
468	C₄⋊C₄	—	2	4	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	4	no	—
472	C₄⋊C₄	—	2	4	no	—
473	C₄⋊C₄	—	2	8	no	—
474	C₄⋊C₄	—	2	4	no	—
475	C₄⋊C₄	—	2	8	no	—
476	C₄⋊C₄	—	4	4	no	—
477	C₄⋊C₄	—	4	4	no	—
478	C₄⋊C₄	—	4	4	no	—
479	C₄⋊C₄	—	4	4	no	—
480	C₂²⋊C₄	—	2	2	no	—
481	C₂²⋊C₄	—	2	2	no	—
482	C₂²⋊C₄	—	2	4	no	—
483	C₂²⋊C₄	—	2	8	no	—
484	C₂²⋊C₄	—	2	8	no	—
485	C₂²⋊C₄	—	2	8	no	—
486	C₂²⋊C₄	—	2	8	no	—
487	C₂²⋊C₄	—	4	4	no	—
488	C₂²⋊C₄	—	4	4	no	—
489	C₂²⋊C₄	—	4	4	no	—
490	C₂²⋊C₄	—	4	4	no	—
491	C₂²⋊C₄	—	4	4	no	—
492	C₂²⋊C₄	—	4	4	no	—
493	C₂²⋊C₄	—	4	4	no	—
494	C₄²	—	2	4	no	—
495	C₄²	—	2	2	no	—
496	C₄²	—	2	2	no	—
497	C₄²	—	2	2	no	—
498	C₄²	—	2	2	no	—
499	C₄²	—	2	4	no	—
500	C₄²	—	2	4	no	—
501	C₄²	—	4	4	no	—
502	C₄²	—	4	2	no	—
503	C₄²	—	4	2	no	—
504	C₄²	#41×C₅₉	1	4	yes	—
505	C₄²	#41×C₅₉	1	4	yes	—
506	C₂³	—	2	1	no	—
507	C₂³	—	2	1	no	—
508	C₂³	—	2	2	no	—
509	C₂³	—	2	2	no	—
510	C₂³	—	2	4	no	—
511	C₂³	—	2	4	no	—
512	C₂³	—	2	4	no	—
513	C₂³	—	2	4	no	—
514	C₂³	—	2	4	no	—
515	C₂³	—	2	4	no	—
516	C₂³	—	2	4	no	—
517	C₂³	C₂×#41×C₅₉	1	2	yes	—
518	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
519	D₄	—	4	8	no	—
520	D₄	—	8	8	no	—
521	D₄	—	8	8	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	8	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	4	no	—
550	C₂×C₄	—	2	4	no	—
551	C₂×C₄	—	4	8	no	—
552	C₂×C₄	—	4	16	no	—
553	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
554	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
555	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
556	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
557	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
558	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
559	C₂×C₄	H(5,𝔽₂)×C₅₉	1	4	yes	—
560	C₂²	—	2	2	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	4	2	no	—
564	C₂²	—	4	2	no	—
565	C₂²	—	4	4	no	—
566	C₂²	—	4	4	no	—
567	C₂²	—	4	4	no	—
568	C₂²	—	4	4	no	—
569	C₂²	—	4	4	no	—
570	C₂²	—	4	4	no	—
571	C₂²	—	4	4	no	—
572	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
573	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
574	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
575	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	2	yes	—
576	C₂²	C₅₉×#585	1	2	yes	—
577	C₄	—	2	2	no	—
578	C₄	—	2	4	no	—
579	C₄	—	2	4	no	—
580	C₄	—	2	4	no	—
581	C₄	—	4	4	no	—
582	C₄	—	4	1	no	—
583	C₄	—	4	1	no	—
584	C₄	—	4	1	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	4	no	—
587	C₄	—	4	2	no	—
588	C₄	—	4	4	no	—
589	C₄	C₅₉×#529	1	4	yes	—
590	C₂	—	4	2	no	—
591	C₂	—	8	4	no	—
592	C₂	C₂×C₅₉×#529	1	1	yes	characteristic
593	C₂	C₅₉×#3460	1	2	yes	—
594	C₂	C₅₉×#3494	1	2	yes	—
595	C₂	C₅₉×#3508	1	1	yes	characteristic
596	C₂	C₅₉×#3512	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₅₉×#2856	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₉×#2860	C₂	semidirect
3. C₅₉×#2851	C₂	semidirect
4. C₅₉×#2647	C₂	semidirect
5. C₅₉×#2641	C₂	semidirect
6. C₅₉×#2624	C₂	semidirect
7. C₅₉×#2597	C₂	semidirect
8. C₅₉×#2559	C₂	semidirect
9. C₅₉×#2479	C₂	semidirect
10. C₅₉×#2476	C₂	semidirect
11. C₅₉×#2330	C₂	semidirect
12. C₅₉×#2328	C₂	semidirect
13. C₅₉×#2324	C₂	semidirect
14. C₅₉×#2293	C₂	semidirect
15. C₄×#117×C₅₉	C₂	semidirect
261. #35295	C₅₉	direct (N × H)
292. #2860	C₂×C₅₉	semidirect
294. #2851	C₂×C₅₉	semidirect
295. #2647	C₂×C₅₉	semidirect
296. #2641	C₂×C₅₉	semidirect
297. #2624	C₂×C₅₉	semidirect
298. #2597	C₂×C₅₉	semidirect
299. #2559	C₂×C₅₉	semidirect
300. #2479	C₂×C₅₉	semidirect
301. #2476	C₂×C₅₉	semidirect
302. #2330	C₂×C₅₉	semidirect
303. #2328	C₂×C₅₉	semidirect
304. #2324	C₂×C₅₉	semidirect
305. #2293	C₂×C₅₉	semidirect
306. C₄×#117	C₂×C₅₉	semidirect
369. C₅₉	#35295	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₉×#2860	2
C₅₉×#2856	2
C₅₉×#2851	2
C₅₉×#2647	2
C₅₉×#2641	2
C₅₉×#2624	2
C₅₉×#2597	2
C₅₉×#2559	2
C₅₉×#2479	2
C₅₉×#2476	2
C₅₉×#2330	2
C₅₉×#2328	2
C₅₉×#2324	2
C₅₉×#2293	2
C₄×#117×C₅₉	2
#35295	59

Subgroups — C59×#35295 #28447404

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35295 #28447404