Subgroups — C₅₉×#23632 #28435741

Order 15104.

1122 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#418	C₂	1	1	yes	maximal, characteristic
2	C₂²×#102×C₅₉	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2317	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2309	C₂	1	1	yes	maximal, characteristic
5	C₅₉×#2073	C₂	1	4	yes	maximal, complemented
6	C₅₉×#2071	C₂	1	4	yes	maximal, complemented
7	C₅₉×#1736	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#1735	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1729	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₅₉	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₅₉	C₂²	1	1	yes	characteristic
13	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
14	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
15	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
17	C₅₉×#418	—	2	4	no	—
18	C₂×#102×C₅₉	—	2	4	no	—
19	C₂×#102×C₅₉	C₂²	1	2	yes	—
20	C₂×#102×C₅₉	C₂²	1	4	yes	—
21	C₂×#102×C₅₉	C₂²	1	2	yes	—
22	C₅₉×#390	—	2	2	no	—
23	C₅₉×#390	C₂²	1	4	yes	—
24	C₅₉×#389	—	2	2	no	—
25	C₅₉×#385	—	2	2	no	—
26	C₅₉×#384	C₂²	1	2	yes	complemented
27	C₅₉×#382	C₂²	1	2	yes	complemented
28	C₅₉×#379	—	2	2	no	—
29	C₅₉×#340	C₂²	1	2	yes	complemented
30	C₅₉×#340	C₂²	1	2	yes	complemented
31	C₅₉×#340	C₂²	1	4	yes	complemented
32	C₅₉×#336	C₂²	1	4	yes	complemented
33	C₂⁵×C₅₉	—	2	1	no	—
34	C₂²×D₄×C₅₉	—	2	1	no	—
35	C₂²×D₄×C₅₉	—	2	2	no	—
36	C₂²×D₄×C₅₉	—	2	2	no	—
37	C₂²×D₄×C₅₉	—	2	2	no	—
38	C₂²×D₄×C₅₉	—	2	2	no	—
39	C₂²×D₄×C₅₉	—	2	2	no	—
40	C₂²×D₄×C₅₉	D₄	1	4	yes	—
41	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
42	C₂³×C₄×C₅₉	—	2	1	no	—
43	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
44	C₂×M₁₆×C₅₉	—	2	2	no	—
45	C₂×M₁₆×C₅₉	—	2	2	no	—
46	C₂×M₁₆×C₅₉	—	2	2	no	—
47	C₂²×C₈×C₅₉	—	2	2	no	—
48	C₂²×C₈×C₅₉	—	2	2	no	—
49	C₂²×C₈×C₅₉	—	2	2	no	—
50	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
51	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
52	#117×C₅₉	—	2	2	no	—
53	#117×C₅₉	—	2	2	no	—
54	#117×C₅₉	—	2	2	no	—
55	#117×C₅₉	—	2	2	no	—
56	#117×C₅₉	—	2	2	no	—
57	#117×C₅₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
62	C₂×C₄⋊C₄×C₅₉	D₄	1	2	yes	—
63	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₅₉	—	2	4	no	—
70	C₂×C₂²⋊C₄×C₅₉	—	2	4	no	—
71	C₂×C₂²⋊C₄×C₅₉	D₄	1	2	yes	—
72	C₂×C₄²×C₅₉	—	2	1	no	—
73	C₂×C₄²×C₅₉	—	2	1	no	—
74	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
75	#102×C₅₉	—	2	8	no	—
76	#102×C₅₉	—	2	4	no	—
77	#102×C₅₉	—	2	4	no	—
78	#95×C₅₉	—	2	4	no	—
79	C₂⁴×C₅₉	—	2	2	no	—
80	C₂⁴×C₅₉	—	2	4	no	—
81	C₂⁴×C₅₉	—	4	2	no	—
82	C₂⁴×C₅₉	—	4	2	no	—
83	C₂⁴×C₅₉	—	8	2	no	—
84	C₂⁴×C₅₉	—	8	2	no	—
85	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
86	C₂×D₄×C₅₉	—	2	4	no	—
87	C₂×D₄×C₅₉	—	2	8	no	—
88	C₂×D₄×C₅₉	—	2	8	no	—
89	C₂×D₄×C₅₉	—	2	2	no	—
90	C₂×D₄×C₅₉	—	2	2	no	—
91	C₂×D₄×C₅₉	—	2	2	no	—
92	C₂×D₄×C₅₉	—	2	2	no	—
93	C₂×D₄×C₅₉	—	2	2	no	—
94	C₂×D₄×C₅₉	—	4	2	no	—
95	C₂×D₄×C₅₉	—	4	2	no	—
96	C₂×D₄×C₅₉	—	4	4	no	—
97	C₂×D₄×C₅₉	—	4	4	no	—
98	C₂×D₄×C₅₉	C₂×D₄	1	4	yes	—
99	C₂²×C₄×C₅₉	—	2	1	no	—
100	C₂²×C₄×C₅₉	—	2	2	no	—
101	C₂²×C₄×C₅₉	—	2	2	no	—
102	C₂²×C₄×C₅₉	—	2	1	no	—
103	C₂²×C₄×C₅₉	—	4	2	no	—
104	C₂²×C₄×C₅₉	—	8	2	no	—
105	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
106	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₅₉	#41	1	2	yes	—
109	C₂²×C₄×C₅₉	#41	1	2	yes	—
110	C₂²×C₄×C₅₉	#41	1	2	yes	—
111	C₂²×C₄×C₅₉	#41	1	2	yes	—
112	C₂²×C₄×C₅₉	#41	1	2	yes	—
113	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
114	M₁₆×C₅₉	—	4	4	no	—
115	C₂×C₈×C₅₉	—	2	2	no	—
116	C₂×C₈×C₅₉	—	2	2	no	—
117	C₂×C₈×C₅₉	—	2	2	no	—
118	C₂×C₈×C₅₉	—	2	2	no	—
119	C₂×C₈×C₅₉	—	2	2	no	—
120	C₂×C₈×C₅₉	—	2	2	no	—
121	C₂×C₈×C₅₉	—	4	4	no	—
122	C₄⋊C₄×C₅₉	—	2	4	no	—
123	C₄⋊C₄×C₅₉	—	2	2	no	—
124	C₄⋊C₄×C₅₉	—	2	1	no	—
125	C₄⋊C₄×C₅₉	—	2	1	no	—
126	C₄⋊C₄×C₅₉	—	2	2	no	—
127	C₄⋊C₄×C₅₉	—	2	1	no	—
128	C₄⋊C₄×C₅₉	—	2	1	no	—
129	C₄⋊C₄×C₅₉	—	2	2	no	—
130	C₄⋊C₄×C₅₉	—	2	2	no	—
131	C₄⋊C₄×C₅₉	—	4	2	no	—
132	C₄⋊C₄×C₅₉	—	8	4	no	—
133	C₂²⋊C₄×C₅₉	—	2	4	no	—
134	C₂²⋊C₄×C₅₉	—	4	2	no	—
135	C₂²⋊C₄×C₅₉	—	4	2	no	—
136	C₂²⋊C₄×C₅₉	—	8	4	no	—
137	C₂²⋊C₄×C₅₉	—	8	4	no	—
138	C₄²×C₅₉	—	2	2	no	—
139	C₄²×C₅₉	—	2	2	no	—
140	C₄²×C₅₉	—	4	2	no	—
141	C₄²×C₅₉	—	4	2	no	—
142	C₂³×C₅₉	—	2	2	no	—
143	C₂³×C₅₉	—	2	2	no	—
144	C₂³×C₅₉	—	2	4	no	—
145	C₂³×C₅₉	—	4	2	no	—
146	C₂³×C₅₉	—	4	2	no	—
147	C₂³×C₅₉	—	4	4	no	—
148	C₂³×C₅₉	—	4	4	no	—
149	C₂³×C₅₉	—	4	8	no	—
150	C₂³×C₅₉	—	8	4	no	—
151	C₂³×C₅₉	—	8	4	no	—
152	C₂³×C₅₉	—	8	8	no	—
153	C₂³×C₅₉	—	8	8	no	—
154	C₂³×C₅₉	#121	1	2	yes	—
155	C₂³×C₅₉	#123	1	2	yes	—
156	C₂³×C₅₉	#124	1	2	yes	—
157	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
158	D₄×C₅₉	—	2	4	no	—
159	D₄×C₅₉	—	2	4	no	—
160	D₄×C₅₉	—	4	2	no	—
161	D₄×C₅₉	—	4	2	no	—
162	D₄×C₅₉	—	4	8	no	—
163	C₂×C₄×C₅₉	—	2	4	no	—
164	C₂×C₄×C₅₉	—	2	4	no	—
165	C₂×C₄×C₅₉	—	2	4	no	—
166	C₂×C₄×C₅₉	—	4	1	no	—
167	C₂×C₄×C₅₉	—	4	1	no	—
168	C₂×C₄×C₅₉	—	4	2	no	—
169	C₂×C₄×C₅₉	—	4	2	no	—
170	C₂×C₄×C₅₉	—	4	2	no	—
171	C₂×C₄×C₅₉	—	4	2	no	—
172	C₂×C₄×C₅₉	—	4	4	no	—
173	C₂×C₄×C₅₉	—	4	2	no	—
174	C₂×C₄×C₅₉	—	4	2	no	—
175	C₂×C₄×C₅₉	—	8	4	no	—
176	C₂×C₄×C₅₉	#121	1	2	yes	—
177	C₂×C₄×C₅₉	#123	1	4	yes	—
178	C₂×C₄×C₅₉	#123	1	4	yes	—
179	C₂×C₄×C₅₉	#123	1	2	yes	—
180	C₂×C₄×C₅₉	#124	1	2	yes	—
181	C₂×C₄×C₅₉	#126	1	4	yes	—
182	C₂×C₄×C₅₉	#126	1	4	yes	—
183	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
185	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
189	C₈×C₅₉	—	4	2	no	—
190	C₈×C₅₉	—	4	2	no	—
191	#23632	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂²×C₅₉	—	2	4	no	—
193	C₂²×C₅₉	—	2	4	no	—
194	C₂²×C₅₉	—	2	2	no	—
195	C₂²×C₅₉	—	2	2	no	—
196	C₂²×C₅₉	—	4	4	no	—
197	C₂²×C₅₉	—	4	4	no	—
198	C₂²×C₅₉	—	4	4	no	—
199	C₂²×C₅₉	—	8	16	no	—
200	C₂²×C₅₉	—	8	4	no	—
201	C₂²×C₅₉	—	8	4	no	—
202	C₂²×C₅₉	#397	1	4	yes	—
203	C₂²×C₅₉	C₂×#121	1	1	yes	characteristic
204	C₂²×C₅₉	C₂×#123	1	1	yes	characteristic
205	C₂²×C₅₉	C₂×#124	1	1	yes	characteristic
206	C₂²×C₅₉	#576	1	2	yes	—
207	C₂²×C₅₉	#577	1	2	yes	—
208	C₄×C₅₉	—	4	4	no	—
209	C₄×C₅₉	—	8	2	no	—
210	C₄×C₅₉	—	8	1	no	—
211	C₄×C₅₉	—	8	2	no	—
212	C₄×C₅₉	—	8	1	no	—
213	C₄×C₅₉	#397	1	4	yes	—
214	C₄×C₅₉	C₂×#123	1	1	yes	characteristic
215	C₄×C₅₉	C₂×#123	1	1	yes	characteristic
216	C₄×C₅₉	C₂×#126	1	1	yes	characteristic
217	C₄×C₅₉	C₂×#126	1	1	yes	characteristic
218	C₂×#418	C₂×C₅₉	1	1	yes	characteristic
219	C₂²×#102	C₂×C₅₉	1	1	yes	characteristic
220	#2317	C₂×C₅₉	1	1	yes	characteristic, complemented
221	#2309	C₂×C₅₉	1	1	yes	characteristic
222	#2073	C₂×C₅₉	1	4	yes	complemented
223	#2071	C₂×C₅₉	1	4	yes	complemented
224	#1736	C₂×C₅₉	1	1	yes	characteristic, complemented
225	#1735	C₂×C₅₉	1	1	yes	characteristic, complemented
226	#1729	C₂×C₅₉	1	1	yes	characteristic, complemented
227	C₂×C₅₉	—	2	4	no	—
228	C₂×C₅₉	—	8	4	no	—
229	C₂×C₅₉	C₂×#397	1	1	yes	characteristic
230	C₂×C₅₉	#3041	1	1	yes	characteristic
231	C₂×C₅₉	#3042	1	1	yes	characteristic
232	C₂×C₅₉	#3096	1	2	yes	—
233	C₂×C₅₉	#3136	1	2	yes	—
234	C₂³×D₄	C₂²×C₅₉	1	1	yes	characteristic
235	C₂²×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
236	C₂³×C₈	C₂²×C₅₉	1	1	yes	characteristic
237	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
238	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
239	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
240	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
241	#418	—	2	4	no	—
242	C₂×#102	—	2	4	no	—
243	C₂×#102	C₂²×C₅₉	1	2	yes	—
244	C₂×#102	C₂²×C₅₉	1	4	yes	—
245	C₂×#102	C₂²×C₅₉	1	2	yes	—
246	#390	—	2	2	no	—
247	#390	C₂²×C₅₉	1	4	yes	—
248	#389	—	2	2	no	—
249	#385	—	2	2	no	—
250	#384	C₂²×C₅₉	1	2	yes	complemented
251	#382	C₂²×C₅₉	1	2	yes	complemented
252	#379	—	2	2	no	—
253	#340	C₂²×C₅₉	1	2	yes	complemented
254	#340	C₂²×C₅₉	1	4	yes	complemented
255	#340	C₂²×C₅₉	1	2	yes	complemented
256	#336	C₂²×C₅₉	1	4	yes	complemented
257	C₅₉	#23632	1	1	yes	characteristic, direct product factor, Sylow
258	C₂⁵	—	2	1	no	—
259	C₂²×D₄	—	2	1	no	—
260	C₂²×D₄	—	2	2	no	—
261	C₂²×D₄	—	2	2	no	—
262	C₂²×D₄	—	2	2	no	—
263	C₂²×D₄	—	2	2	no	—
264	C₂²×D₄	—	2	2	no	—
265	C₂²×D₄	D₄×C₅₉	1	4	yes	—
266	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
267	C₂³×C₄	—	2	1	no	—
268	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
269	C₂×M₁₆	—	2	2	no	—
270	C₂×M₁₆	—	2	2	no	—
271	C₂×M₁₆	—	2	2	no	—
272	C₂²×C₈	—	2	2	no	—
273	C₂²×C₈	—	2	2	no	—
274	C₂²×C₈	—	2	2	no	—
275	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
276	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
277	#117	—	2	2	no	—
278	#117	—	2	2	no	—
279	#117	—	2	2	no	—
280	#117	—	2	2	no	—
281	#117	—	2	2	no	—
282	#117	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	4	no	—
287	C₂×C₄⋊C₄	D₄×C₅₉	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
289	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
290	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
292	C₂×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₂²⋊C₄	—	2	4	no	—
295	C₂×C₂²⋊C₄	—	2	4	no	—
296	C₂×C₂²⋊C₄	D₄×C₅₉	1	2	yes	—
297	C₂×C₄²	—	2	1	no	—
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
300	#102	—	2	8	no	—
301	#102	—	2	4	no	—
302	#102	—	2	4	no	—
303	#95	—	2	4	no	—
304	C₂⁴	—	2	2	no	—
305	C₂⁴	—	2	4	no	—
306	C₂⁴	—	4	2	no	—
307	C₂⁴	—	4	2	no	—
308	C₂⁴	—	8	2	no	—
309	C₂⁴	—	8	2	no	—
310	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
311	C₂×D₄	—	2	4	no	—
312	C₂×D₄	—	2	8	no	—
313	C₂×D₄	—	2	8	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	4	2	no	—
320	C₂×D₄	—	4	2	no	—
321	C₂×D₄	—	4	4	no	—
322	C₂×D₄	—	4	4	no	—
323	C₂×D₄	C₂×D₄×C₅₉	1	4	yes	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	4	2	no	—
329	C₂²×C₄	—	8	2	no	—
330	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
331	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
333	C₂²×C₄	#41×C₅₉	1	2	yes	—
334	C₂²×C₄	#41×C₅₉	1	2	yes	—
335	C₂²×C₄	#41×C₅₉	1	2	yes	—
336	C₂²×C₄	#41×C₅₉	1	2	yes	—
337	C₂²×C₄	#41×C₅₉	1	2	yes	—
338	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
339	M₁₆	—	4	4	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	4	4	no	—
347	C₄⋊C₄	—	2	4	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	4	2	no	—
357	C₄⋊C₄	—	8	4	no	—
358	C₂²⋊C₄	—	2	4	no	—
359	C₂²⋊C₄	—	4	2	no	—
360	C₂²⋊C₄	—	4	2	no	—
361	C₂²⋊C₄	—	8	4	no	—
362	C₂²⋊C₄	—	8	4	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	4	2	no	—
366	C₄²	—	4	2	no	—
367	C₂³	—	2	2	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	2	4	no	—
370	C₂³	—	4	8	no	—
371	C₂³	—	4	2	no	—
372	C₂³	—	4	2	no	—
373	C₂³	—	4	4	no	—
374	C₂³	—	4	4	no	—
375	C₂³	—	8	4	no	—
376	C₂³	—	8	4	no	—
377	C₂³	—	8	8	no	—
378	C₂³	—	8	8	no	—
379	C₂³	#121×C₅₉	1	2	yes	—
380	C₂³	#123×C₅₉	1	2	yes	—
381	C₂³	#124×C₅₉	1	2	yes	—
382	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
383	D₄	—	2	4	no	—
384	D₄	—	2	4	no	—
385	D₄	—	4	8	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	2	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	4	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	8	4	no	—
401	C₂×C₄	#121×C₅₉	1	2	yes	—
402	C₂×C₄	#123×C₅₉	1	2	yes	—
403	C₂×C₄	#123×C₅₉	1	4	yes	—
404	C₂×C₄	#123×C₅₉	1	4	yes	—
405	C₂×C₄	#124×C₅₉	1	2	yes	—
406	C₂×C₄	#126×C₅₉	1	4	yes	—
407	C₂×C₄	#126×C₅₉	1	4	yes	—
408	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
409	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
410	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
411	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
412	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
413	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
414	C₈	—	4	2	no	—
415	C₈	—	4	2	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	4	no	—
419	C₂²	—	2	4	no	—
420	C₂²	—	4	4	no	—
421	C₂²	—	4	4	no	—
422	C₂²	—	4	4	no	—
423	C₂²	—	8	16	no	—
424	C₂²	—	8	4	no	—
425	C₂²	—	8	4	no	—
426	C₂²	C₅₉×#397	1	4	yes	—
427	C₂²	C₂×#121×C₅₉	1	1	yes	characteristic
428	C₂²	C₂×#123×C₅₉	1	1	yes	characteristic
429	C₂²	C₂×#124×C₅₉	1	1	yes	characteristic
430	C₂²	C₅₉×#576	1	2	yes	—
431	C₂²	C₅₉×#577	1	2	yes	—
432	C₄	—	4	4	no	—
433	C₄	—	8	2	no	—
434	C₄	—	8	1	no	—
435	C₄	—	8	1	no	—
436	C₄	—	8	2	no	—
437	C₄	C₅₉×#397	1	4	yes	—
438	C₄	C₂×#123×C₅₉	1	1	yes	characteristic
439	C₄	C₂×#123×C₅₉	1	1	yes	characteristic
440	C₄	C₂×#126×C₅₉	1	1	yes	characteristic
441	C₄	C₂×#126×C₅₉	1	1	yes	characteristic
442	C₂	—	2	4	no	—
443	C₂	—	8	4	no	—
444	C₂	C₂×C₅₉×#397	1	1	yes	characteristic
445	C₂	C₅₉×#3041	1	1	yes	characteristic
446	C₂	C₅₉×#3042	1	1	yes	characteristic
447	C₂	C₅₉×#3096	1	2	yes	—
448	C₂	C₅₉×#3136	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₂³×D₄×C₅₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₂×#117×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅₉×#2317	C₂	semidirect
5. C₅₉×#2073	C₂	semidirect
6. C₅₉×#2071	C₂	semidirect
7. C₅₉×#1736	C₂	semidirect
8. C₅₉×#1735	C₂	semidirect
9. C₅₉×#1729	C₂	semidirect
26. C₅₉×#384	C₂²	semidirect
27. C₅₉×#382	C₂²	semidirect
29. C₅₉×#340	C₂²	semidirect
30. C₅₉×#340	C₂²	semidirect
31. C₅₉×#340	C₂²	semidirect
32. C₅₉×#336	C₂²	semidirect
191. #23632	C₅₉	direct (N × H)
220. #2317	C₂×C₅₉	semidirect
222. #2073	C₂×C₅₉	semidirect
223. #2071	C₂×C₅₉	semidirect
224. #1736	C₂×C₅₉	semidirect
225. #1735	C₂×C₅₉	semidirect
226. #1729	C₂×C₅₉	semidirect
250. #384	C₂²×C₅₉	semidirect
251. #382	C₂²×C₅₉	semidirect
253. #340	C₂²×C₅₉	semidirect
254. #340	C₂²×C₅₉	semidirect
255. #340	C₂²×C₅₉	semidirect
256. #336	C₂²×C₅₉	semidirect
257. C₅₉	#23632	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅₉×#418	2
C₂²×#102×C₅₉	2
C₅₉×#2317	2
C₅₉×#2309	2
C₅₉×#2073	2
C₅₉×#2071	2
C₅₉×#1736	2
C₅₉×#1735	2
C₅₉×#1729	2
#23632	59

Subgroups — C59×#23632 #28435741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#23632 #28435741