Subgroups — C₅₉×#36602 #28448711

Order 15104.

1830 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#2861	C₂	1	2	yes	maximal, complemented
2	C₅₉×#2858	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2597	C₂	1	4	yes	maximal, complemented
4	C₅₉×#2593	C₂	1	4	yes	maximal, complemented
5	C₅₉×#2592	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2458	C₂	1	4	yes	maximal, complemented
7	C₅₉×#2446	C₂	1	2	yes	maximal, complemented
8	C₅₉×#2445	C₂	1	2	yes	maximal
9	C₅₉×#2374	C₂	1	4	yes	maximal, complemented
10	C₅₉×#2367	C₂	1	2	yes	maximal, complemented
11	C₄×#125×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#124×C₅₉	C₂	1	2	yes	maximal, complemented
13	C₄²×Q₈×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
15	C₂×#127×C₅₉	C₂²	1	1	yes	characteristic
16	C₂×#125×C₅₉	C₂²	1	1	yes	characteristic
17	C₂×#124×C₅₉	C₂²	1	2	yes	—
18	C₂×#124×C₅₉	C₂²	1	2	yes	—
19	C₂×#123×C₅₉	C₂²	1	4	yes	—
20	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
24	C₅₉×#400	C₂²	1	4	yes	—
25	C₅₉×#398	C₂²	1	4	yes	—
26	C₅₉×#397	C₂²	1	4	yes	—
27	C₅₉×#394	C₂²	1	4	yes	—
28	C₅₉×#394	C₂²	1	4	yes	—
29	C₅₉×#393	C₂²	1	4	yes	—
30	C₅₉×#391	C₂²	1	2	yes	—
31	C₅₉×#391	C₂²	1	2	yes	—
32	C₅₉×#391	C₂²	1	2	yes	—
33	C₅₉×#390	C₂²	1	2	yes	—
34	C₅₉×#390	C₂²	1	2	yes	—
35	C₅₉×#390	C₂²	1	4	yes	—
36	C₅₉×#390	C₂²	1	4	yes	—
37	C₅₉×#390	C₂²	1	2	yes	—
38	C₅₉×#389	C₂²	1	2	yes	—
39	C₅₉×#388	C₂²	1	4	yes	—
40	C₅₉×#388	C₂²	1	4	yes	—
41	C₅₉×#388	C₂²	1	4	yes	—
42	C₅₉×#388	C₂²	1	4	yes	—
43	C₅₉×#388	C₂²	1	4	yes	—
44	C₅₉×#388	C₂²	1	4	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×#387	C₂²	1	4	yes	—
50	C₅₉×#387	C₂²	1	4	yes	—
51	C₅₉×#387	C₂²	1	4	yes	—
52	C₅₉×#386	C₂²	1	4	yes	—
53	C₅₉×#385	C₂²	1	4	yes	—
54	C₅₉×#382	C₂²	1	1	yes	characteristic
55	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
56	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
57	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
58	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
59	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
60	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
61	C₄×C₄⋊C₄×C₅₉	C₂²	1	4	yes	—
62	C₄×C₂²⋊C₄×C₅₉	C₂²	1	4	yes	—
63	C₄×C₂²⋊C₄×C₅₉	C₂²	1	4	yes	—
64	C₄×C₂²⋊C₄×C₅₉	C₂²	1	4	yes	—
65	C₄³×C₅₉	C₂²	1	2	yes	—
66	C₄³×C₅₉	C₂²	1	1	yes	characteristic
67	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
68	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
70	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
71	C₂³×C₄×C₅₉	C₂³	1	4	yes	—
72	C₄⋊Q₈×C₅₉	—	4	2	no	—
73	#127×C₅₉	—	4	2	no	—
74	#125×C₅₉	—	2	4	no	—
75	#124×C₅₉	—	2	8	no	—
76	#124×C₅₉	—	2	8	no	—
77	#123×C₅₉	—	2	16	no	—
78	C₄×Q₈×C₅₉	—	2	8	no	—
79	C₄×Q₈×C₅₉	—	2	4	no	—
80	C₄×Q₈×C₅₉	—	4	4	no	—
81	C₄×D₄×C₅₉	—	4	4	no	—
82	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
88	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
89	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
90	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
91	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
92	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
93	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
94	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
95	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
96	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
97	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
98	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
99	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
100	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
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×C₄²×C₅₉	C₂³	1	2	yes	—
105	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
107	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
108	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
109	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
110	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
111	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
112	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
113	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
114	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
115	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
117	#95×C₅₉	C₂³	1	1	yes	characteristic
118	#95×C₅₉	C₂³	1	4	yes	—
119	#95×C₅₉	C₂³	1	4	yes	—
120	#95×C₅₉	C₂³	1	4	yes	—
121	#95×C₅₉	C₂³	1	4	yes	—
122	#95×C₅₉	C₂³	1	2	yes	—
123	#95×C₅₉	C₂³	1	1	yes	characteristic
124	#95×C₅₉	C₂³	1	2	yes	—
125	#95×C₅₉	C₂³	1	4	yes	—
126	#95×C₅₉	C₂³	1	4	yes	—
127	#95×C₅₉	C₂³	1	4	yes	—
128	#95×C₅₉	C₂³	1	4	yes	—
129	#95×C₅₉	C₂³	1	4	yes	—
130	C₂⁴×C₅₉	C₂⁴	1	4	yes	—
131	C₂×Q₈×C₅₉	—	2	4	no	—
132	C₂×Q₈×C₅₉	—	2	2	no	—
133	C₂×Q₈×C₅₉	—	2	4	no	—
134	C₂×Q₈×C₅₉	—	2	4	no	—
135	C₂×Q₈×C₅₉	—	2	4	no	—
136	C₂×D₄×C₅₉	—	2	4	no	—
137	C₂×D₄×C₅₉	—	2	4	no	—
138	C₂×D₄×C₅₉	—	2	8	no	—
139	C₂×D₄×C₅₉	—	2	4	no	—
140	C₂×D₄×C₅₉	—	4	4	no	—
141	C₂×D₄×C₅₉	—	4	4	no	—
142	C₂²×C₄×C₅₉	—	2	8	no	—
143	C₂²×C₄×C₅₉	—	4	4	no	—
144	C₂²×C₄×C₅₉	—	4	4	no	—
145	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
146	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
148	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
150	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
151	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
152	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
153	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
154	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
155	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
156	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
157	C₄⋊C₄×C₅₉	—	2	4	no	—
158	C₄⋊C₄×C₅₉	—	2	4	no	—
159	C₄⋊C₄×C₅₉	—	2	4	no	—
160	C₄⋊C₄×C₅₉	—	2	2	no	—
161	C₄⋊C₄×C₅₉	—	2	8	no	—
162	C₄⋊C₄×C₅₉	—	2	8	no	—
163	C₄⋊C₄×C₅₉	—	2	4	no	—
164	C₄⋊C₄×C₅₉	—	2	4	no	—
165	C₄⋊C₄×C₅₉	—	4	4	no	—
166	C₄⋊C₄×C₅₉	—	4	4	no	—
167	C₄⋊C₄×C₅₉	#41	1	8	yes	—
168	C₂²⋊C₄×C₅₉	—	2	8	no	—
169	C₂²⋊C₄×C₅₉	—	2	8	no	—
170	C₂²⋊C₄×C₅₉	—	2	8	no	—
171	C₂²⋊C₄×C₅₉	—	2	8	no	—
172	C₂²⋊C₄×C₅₉	—	2	8	no	—
173	C₂²⋊C₄×C₅₉	—	2	8	no	—
174	C₂²⋊C₄×C₅₉	—	2	8	no	—
175	C₂²⋊C₄×C₅₉	—	4	4	no	—
176	C₂²⋊C₄×C₅₉	—	4	4	no	—
177	C₂²⋊C₄×C₅₉	—	4	4	no	—
178	C₂²⋊C₄×C₅₉	—	4	4	no	—
179	C₄²×C₅₉	—	2	4	no	—
180	C₄²×C₅₉	—	2	4	no	—
181	C₄²×C₅₉	—	2	4	no	—
182	C₄²×C₅₉	—	2	4	no	—
183	C₄²×C₅₉	—	2	4	no	—
184	C₄²×C₅₉	—	2	2	no	—
185	C₄²×C₅₉	—	4	2	no	—
186	C₄²×C₅₉	—	4	2	no	—
187	C₄²×C₅₉	—	4	2	no	—
188	C₄²×C₅₉	—	4	4	no	—
189	C₄²×C₅₉	—	4	4	no	—
190	C₄²×C₅₉	#41	1	4	yes	—
191	C₄²×C₅₉	#41	1	4	yes	—
192	C₂³×C₅₉	—	2	4	no	—
193	C₂³×C₅₉	—	2	4	no	—
194	C₂³×C₅₉	—	2	4	no	—
195	C₂³×C₅₉	—	2	4	no	—
196	C₂³×C₅₉	—	2	4	no	—
197	C₂³×C₅₉	—	2	4	no	—
198	C₂³×C₅₉	—	2	4	no	—
199	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
200	Q₈×C₅₉	—	2	8	no	—
201	Q₈×C₅₉	—	4	8	no	—
202	D₄×C₅₉	—	4	8	no	—
203	D₄×C₅₉	—	8	8	no	—
204	C₂×C₄×C₅₉	—	2	2	no	—
205	C₂×C₄×C₅₉	—	2	2	no	—
206	C₂×C₄×C₅₉	—	2	2	no	—
207	C₂×C₄×C₅₉	—	2	2	no	—
208	C₂×C₄×C₅₉	—	2	2	no	—
209	C₂×C₄×C₅₉	—	2	2	no	—
210	C₂×C₄×C₅₉	—	2	2	no	—
211	C₂×C₄×C₅₉	—	2	2	no	—
212	C₂×C₄×C₅₉	—	2	2	no	—
213	C₂×C₄×C₅₉	—	2	2	no	—
214	C₂×C₄×C₅₉	—	2	2	no	—
215	C₂×C₄×C₅₉	—	2	2	no	—
216	C₂×C₄×C₅₉	—	2	4	no	—
217	C₂×C₄×C₅₉	—	2	4	no	—
218	C₂×C₄×C₅₉	—	2	4	no	—
219	C₂×C₄×C₅₉	—	2	4	no	—
220	C₂×C₄×C₅₉	—	2	4	no	—
221	C₂×C₄×C₅₉	—	2	2	no	—
222	C₂×C₄×C₅₉	—	2	4	no	—
223	C₂×C₄×C₅₉	—	2	4	no	—
224	C₂×C₄×C₅₉	—	2	4	no	—
225	C₂×C₄×C₅₉	—	2	2	no	—
226	C₂×C₄×C₅₉	—	2	2	no	—
227	C₂×C₄×C₅₉	—	2	2	no	—
228	C₂×C₄×C₅₉	—	2	4	no	—
229	C₂×C₄×C₅₉	—	8	8	no	—
230	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
231	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
232	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
233	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
234	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
235	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
236	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
237	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
238	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
239	#36602	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
240	C₂²×C₅₉	—	4	4	no	—
241	C₂²×C₅₉	—	4	4	no	—
242	C₂²×C₅₉	—	4	4	no	—
243	C₂²×C₅₉	—	4	4	no	—
244	C₂²×C₅₉	—	4	4	no	—
245	C₂²×C₅₉	—	4	4	no	—
246	C₂²×C₅₉	—	4	4	no	—
247	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
248	C₂²×C₅₉	C₂²×#41	1	2	yes	—
249	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
250	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
251	C₂²×C₅₉	#585	1	2	yes	—
252	C₄×C₅₉	—	2	4	no	—
253	C₄×C₅₉	—	2	2	no	—
254	C₄×C₅₉	—	2	4	no	—
255	C₄×C₅₉	—	2	2	no	—
256	C₄×C₅₉	—	2	4	no	—
257	C₄×C₅₉	—	2	4	no	—
258	C₄×C₅₉	—	4	4	no	—
259	C₄×C₅₉	—	4	4	no	—
260	C₄×C₅₉	—	4	2	no	—
261	C₄×C₅₉	—	4	2	no	—
262	C₄×C₅₉	—	4	4	no	—
263	C₄×C₅₉	#559	1	4	yes	—
264	#2861	C₂×C₅₉	1	2	yes	complemented
265	#2858	C₂×C₅₉	1	1	yes	characteristic
266	#2597	C₂×C₅₉	1	4	yes	complemented
267	#2593	C₂×C₅₉	1	4	yes	complemented
268	#2592	C₂×C₅₉	1	2	yes	complemented
269	#2458	C₂×C₅₉	1	4	yes	complemented
270	#2446	C₂×C₅₉	1	2	yes	complemented
271	#2445	C₂×C₅₉	1	2	yes	—
272	#2374	C₂×C₅₉	1	4	yes	complemented
273	#2367	C₂×C₅₉	1	2	yes	complemented
274	C₄×#125	C₂×C₅₉	1	1	yes	characteristic, complemented
275	C₄×#124	C₂×C₅₉	1	2	yes	complemented
276	C₄²×Q₈	C₂×C₅₉	1	1	yes	characteristic, complemented
277	C₂×C₅₉	—	8	4	no	—
278	C₂×C₅₉	#3444	1	1	yes	characteristic
279	C₂×C₅₉	C₂×#559	1	1	yes	characteristic
280	C₂×C₅₉	#3480	1	2	yes	—
281	C₂×C₅₉	#3512	1	1	yes	characteristic
282	C₂×C₅₉	#3514	1	2	yes	—
283	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
284	C₂×#127	C₂²×C₅₉	1	1	yes	characteristic
285	C₂×#125	C₂²×C₅₉	1	1	yes	characteristic
286	C₂×#124	C₂²×C₅₉	1	2	yes	—
287	C₂×#124	C₂²×C₅₉	1	2	yes	—
288	C₂×#123	C₂²×C₅₉	1	4	yes	—
289	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
290	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
291	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
292	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
293	#400	C₂²×C₅₉	1	4	yes	—
294	#398	C₂²×C₅₉	1	4	yes	—
295	#397	C₂²×C₅₉	1	4	yes	—
296	#394	C₂²×C₅₉	1	4	yes	—
297	#394	C₂²×C₅₉	1	4	yes	—
298	#393	C₂²×C₅₉	1	4	yes	—
299	#391	C₂²×C₅₉	1	2	yes	—
300	#391	C₂²×C₅₉	1	2	yes	—
301	#391	C₂²×C₅₉	1	2	yes	—
302	#390	C₂²×C₅₉	1	2	yes	—
303	#390	C₂²×C₅₉	1	2	yes	—
304	#390	C₂²×C₅₉	1	4	yes	—
305	#390	C₂²×C₅₉	1	4	yes	—
306	#390	C₂²×C₅₉	1	2	yes	—
307	#389	C₂²×C₅₉	1	2	yes	—
308	#388	C₂²×C₅₉	1	4	yes	—
309	#388	C₂²×C₅₉	1	4	yes	—
310	#388	C₂²×C₅₉	1	4	yes	—
311	#388	C₂²×C₅₉	1	4	yes	—
312	#388	C₂²×C₅₉	1	4	yes	—
313	#388	C₂²×C₅₉	1	4	yes	—
314	#388	C₂²×C₅₉	1	4	yes	—
315	#388	C₂²×C₅₉	1	4	yes	—
316	#388	C₂²×C₅₉	1	4	yes	—
317	#388	C₂²×C₅₉	1	4	yes	—
318	#387	C₂²×C₅₉	1	4	yes	—
319	#387	C₂²×C₅₉	1	4	yes	—
320	#387	C₂²×C₅₉	1	4	yes	—
321	#386	C₂²×C₅₉	1	4	yes	—
322	#385	C₂²×C₅₉	1	4	yes	—
323	#382	C₂²×C₅₉	1	1	yes	characteristic
324	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
325	C₄×C₄⋊C₄	C₂²×C₅₉	1	4	yes	—
326	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
327	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
328	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
329	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
330	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
331	C₄×C₂²⋊C₄	C₂²×C₅₉	1	4	yes	—
332	C₄×C₂²⋊C₄	C₂²×C₅₉	1	4	yes	—
333	C₄×C₂²⋊C₄	C₂²×C₅₉	1	4	yes	—
334	C₄³	C₂²×C₅₉	1	1	yes	characteristic
335	C₄³	C₂²×C₅₉	1	2	yes	—
336	C₅₉	#36602	1	1	yes	characteristic, direct product factor, Sylow
337	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
338	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
339	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
340	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
341	C₂³×C₄	C₂³×C₅₉	1	4	yes	—
342	C₄⋊Q₈	—	4	2	no	—
343	#127	—	4	2	no	—
344	#125	—	2	4	no	—
345	#124	—	2	8	no	—
346	#124	—	2	8	no	—
347	#123	—	2	16	no	—
348	C₄×Q₈	—	2	8	no	—
349	C₄×Q₈	—	2	4	no	—
350	C₄×Q₈	—	4	4	no	—
351	C₄×D₄	—	4	4	no	—
352	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
353	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
354	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
355	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
356	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
358	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
359	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
360	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
361	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
362	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
363	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
364	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
365	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
366	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
367	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
368	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
369	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
370	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
371	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
372	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
373	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
374	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
375	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
376	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
377	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
378	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
379	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
380	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
381	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
382	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
383	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
384	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
385	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
386	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
387	#95	C₂³×C₅₉	1	1	yes	characteristic
388	#95	C₂³×C₅₉	1	4	yes	—
389	#95	C₂³×C₅₉	1	4	yes	—
390	#95	C₂³×C₅₉	1	4	yes	—
391	#95	C₂³×C₅₉	1	4	yes	—
392	#95	C₂³×C₅₉	1	2	yes	—
393	#95	C₂³×C₅₉	1	1	yes	characteristic
394	#95	C₂³×C₅₉	1	2	yes	—
395	#95	C₂³×C₅₉	1	4	yes	—
396	#95	C₂³×C₅₉	1	4	yes	—
397	#95	C₂³×C₅₉	1	4	yes	—
398	#95	C₂³×C₅₉	1	4	yes	—
399	#95	C₂³×C₅₉	1	4	yes	—
400	C₂⁴	C₂⁴×C₅₉	1	4	yes	—
401	C₂×Q₈	—	2	4	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	4	no	—
404	C₂×Q₈	—	2	4	no	—
405	C₂×Q₈	—	2	4	no	—
406	C₂×D₄	—	2	4	no	—
407	C₂×D₄	—	2	4	no	—
408	C₂×D₄	—	2	8	no	—
409	C₂×D₄	—	2	4	no	—
410	C₂×D₄	—	4	4	no	—
411	C₂×D₄	—	4	4	no	—
412	C₂²×C₄	—	2	8	no	—
413	C₂²×C₄	—	4	4	no	—
414	C₂²×C₄	—	4	4	no	—
415	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
416	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
417	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
418	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
419	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
420	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
421	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
422	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
423	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
424	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
425	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
426	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
427	C₄⋊C₄	—	2	4	no	—
428	C₄⋊C₄	—	2	4	no	—
429	C₄⋊C₄	—	2	4	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	8	no	—
432	C₄⋊C₄	—	2	8	no	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	2	4	no	—
435	C₄⋊C₄	—	4	4	no	—
436	C₄⋊C₄	—	4	4	no	—
437	C₄⋊C₄	#41×C₅₉	1	8	yes	—
438	C₂²⋊C₄	—	2	8	no	—
439	C₂²⋊C₄	—	2	8	no	—
440	C₂²⋊C₄	—	2	8	no	—
441	C₂²⋊C₄	—	2	8	no	—
442	C₂²⋊C₄	—	2	8	no	—
443	C₂²⋊C₄	—	2	8	no	—
444	C₂²⋊C₄	—	2	8	no	—
445	C₂²⋊C₄	—	4	4	no	—
446	C₂²⋊C₄	—	4	4	no	—
447	C₂²⋊C₄	—	4	4	no	—
448	C₂²⋊C₄	—	4	4	no	—
449	C₄²	—	2	4	no	—
450	C₄²	—	2	4	no	—
451	C₄²	—	2	4	no	—
452	C₄²	—	2	4	no	—
453	C₄²	—	2	4	no	—
454	C₄²	—	2	2	no	—
455	C₄²	—	4	4	no	—
456	C₄²	—	4	2	no	—
457	C₄²	—	4	2	no	—
458	C₄²	—	4	2	no	—
459	C₄²	—	4	4	no	—
460	C₄²	#41×C₅₉	1	4	yes	—
461	C₄²	#41×C₅₉	1	4	yes	—
462	C₂³	—	2	4	no	—
463	C₂³	—	2	4	no	—
464	C₂³	—	2	4	no	—
465	C₂³	—	2	4	no	—
466	C₂³	—	2	4	no	—
467	C₂³	—	2	4	no	—
468	C₂³	—	2	4	no	—
469	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
470	Q₈	—	2	8	no	—
471	Q₈	—	4	8	no	—
472	D₄	—	4	8	no	—
473	D₄	—	8	8	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	8	8	no	—
500	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
501	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
502	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
503	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
504	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
505	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
506	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
507	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
508	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
509	C₂²	—	4	4	no	—
510	C₂²	—	4	4	no	—
511	C₂²	—	4	4	no	—
512	C₂²	—	4	4	no	—
513	C₂²	—	4	4	no	—
514	C₂²	—	4	4	no	—
515	C₂²	—	4	4	no	—
516	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
517	C₂²	C₂²×#41×C₅₉	1	2	yes	—
518	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
519	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
520	C₂²	C₅₉×#585	1	2	yes	—
521	C₄	—	2	2	no	—
522	C₄	—	2	4	no	—
523	C₄	—	2	4	no	—
524	C₄	—	2	4	no	—
525	C₄	—	2	2	no	—
526	C₄	—	2	4	no	—
527	C₄	—	4	2	no	—
528	C₄	—	4	4	no	—
529	C₄	—	4	2	no	—
530	C₄	—	4	4	no	—
531	C₄	—	4	4	no	—
532	C₄	C₅₉×#559	1	4	yes	—
533	C₂	—	8	4	no	—
534	C₂	C₅₉×#3444	1	1	yes	characteristic
535	C₂	C₂×C₅₉×#559	1	1	yes	characteristic
536	C₂	C₅₉×#3480	1	2	yes	—
537	C₂	C₅₉×#3512	1	1	yes	characteristic
538	C₂	C₅₉×#3514	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₂×#127×C₅₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₉×#2861	C₂	semidirect
3. C₅₉×#2597	C₂	semidirect
4. C₅₉×#2593	C₂	semidirect
5. C₅₉×#2592	C₂	semidirect
6. C₅₉×#2458	C₂	semidirect
7. C₅₉×#2446	C₂	semidirect
9. C₅₉×#2374	C₂	semidirect
10. C₅₉×#2367	C₂	semidirect
11. C₄×#125×C₅₉	C₂	semidirect
12. C₄×#124×C₅₉	C₂	semidirect
13. C₄²×Q₈×C₅₉	C₂	semidirect
239. #36602	C₅₉	direct (N × H)
264. #2861	C₂×C₅₉	semidirect
266. #2597	C₂×C₅₉	semidirect
267. #2593	C₂×C₅₉	semidirect
268. #2592	C₂×C₅₉	semidirect
269. #2458	C₂×C₅₉	semidirect
270. #2446	C₂×C₅₉	semidirect
272. #2374	C₂×C₅₉	semidirect
273. #2367	C₂×C₅₉	semidirect
274. C₄×#125	C₂×C₅₉	semidirect
275. C₄×#124	C₂×C₅₉	semidirect
276. C₄²×Q₈	C₂×C₅₉	semidirect
336. C₅₉	#36602	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×#2861	2
C₅₉×#2858	2
C₅₉×#2597	2
C₅₉×#2593	2
C₅₉×#2592	2
C₅₉×#2458	2
C₅₉×#2446	2
C₅₉×#2445	2
C₅₉×#2374	2
C₅₉×#2367	2
C₄×#125×C₅₉	2
C₄×#124×C₅₉	2
C₄²×Q₈×C₅₉	2
#36602	59

Subgroups — C59×#36602 #28448711

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#36602 #28448711