Subgroups — C₅₉×#8014 #28420123

Order 15104.

850 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#431	C₂	1	1	yes	maximal, characteristic
2	C₅₉×#2285	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊C₄×C₅₉	C₂	1	1	yes	maximal, characteristic
4	C₅₉×#1294	C₂	1	4	yes	maximal
5	C₂×#117×C₅₉	—	2	1	no	—
6	C₂²×C₄⋊C₄×C₅₉	—	2	1	no	—
7	C₂²×C₄²×C₅₉	—	2	1	no	—
8	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
9	C₅₉×#431	—	2	2	no	—
10	C₅₉×#431	C₄	1	4	yes	complemented
11	C₂×C₄⋊C₈×C₅₉	—	2	1	no	—
12	C₂×C₂²⋊C₈×C₅₉	C₂²	1	2	yes	—
13	C₂×C₄×C₈×C₅₉	—	2	1	no	—
14	C₅₉×#384	C₄	1	2	yes	complemented
15	C₅₉×#382	—	2	1	no	—
16	C₅₉×#380	—	2	1	no	—
17	C₅₉×#380	C₂²	1	2	yes	—
18	C₄×C₄⋊C₄×C₅₉	—	2	2	no	—
19	C₄×C₄⋊C₄×C₅₉	—	2	1	no	—
20	C₄×C₄⋊C₄×C₅₉	C₄	1	2	yes	complemented
21	C₄×C₄⋊C₄×C₅₉	C₄	1	4	yes	complemented
22	C₂×#95×C₅₉	C₂²	1	2	yes	—
23	C₂³×C₄×C₅₉	—	2	2	no	—
24	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
25	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
26	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
27	C₂²×C₈×C₅₉	—	2	2	no	—
28	#117×C₅₉	—	4	2	no	—
29	#117×C₅₉	—	4	2	no	—
30	C₂×C₄⋊C₄×C₅₉	—	2	8	no	—
31	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
32	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
33	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
34	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	4	yes	—
35	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
36	C₂×C₄²×C₅₉	—	2	4	no	—
37	C₂×C₄²×C₅₉	—	2	2	no	—
38	C₂×C₄²×C₅₉	—	4	2	no	—
39	C₂×C₄²×C₅₉	—	4	2	no	—
40	C₂×C₄²×C₅₉	C₂×C₄	1	2	yes	—
41	C₂×C₄²×C₅₉	C₂×C₄	1	2	yes	—
42	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₅₉	D₄	1	2	yes	—
45	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₅₉	Q₈	1	2	yes	—
48	C₄⋊C₈×C₅₉	—	2	4	no	—
49	C₂²⋊C₈×C₅₉	—	2	2	no	—
50	C₂²⋊C₈×C₅₉	C₂×C₄	1	4	yes	—
51	C₄×C₈×C₅₉	—	2	4	no	—
52	#95×C₅₉	—	2	2	no	—
53	#95×C₅₉	—	2	2	no	—
54	#95×C₅₉	—	2	2	no	—
55	#95×C₅₉	C₂×C₄	1	4	yes	—
56	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₅₉	—	2	4	no	—
58	C₂²×C₄×C₅₉	—	2	8	no	—
59	C₂²×C₄×C₅₉	—	2	4	no	—
60	C₂²×C₄×C₅₉	—	2	4	no	—
61	C₂²×C₄×C₅₉	—	4	2	no	—
62	C₂²×C₄×C₅₉	—	4	4	no	—
63	C₂²×C₄×C₅₉	—	4	2	no	—
64	C₂²×C₄×C₅₉	—	4	2	no	—
65	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
67	C₂²×C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
68	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₅₉	C₄⋊C₄	1	2	yes	—
72	C₂²×C₄×C₅₉	C₄⋊C₄	1	2	yes	—
73	C₂²×C₄×C₅₉	D₈	1	2	yes	—
74	C₂²×C₄×C₅₉	SD₁₆	1	2	yes	—
75	C₂²×C₄×C₅₉	SD₁₆	1	2	yes	—
76	C₂²×C₄×C₅₉	Q₁₆	1	2	yes	—
77	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
83	C₂×C₈×C₅₉	—	2	4	no	—
84	C₂×C₈×C₅₉	—	4	4	no	—
85	C₄⋊C₄×C₅₉	—	2	16	no	—
86	C₄⋊C₄×C₅₉	—	4	4	no	—
87	C₄⋊C₄×C₅₉	—	4	4	no	—
88	C₄⋊C₄×C₅₉	—	4	4	no	—
89	C₂²⋊C₄×C₅₉	—	4	2	no	—
90	C₂²⋊C₄×C₅₉	—	4	2	no	—
91	C₄²×C₅₉	—	4	8	no	—
92	C₄²×C₅₉	—	4	4	no	—
93	C₄²×C₅₉	C₄²	1	2	yes	—
94	C₄²×C₅₉	C₄²	1	2	yes	—
95	C₄²×C₅₉	C₂²⋊C₄	1	2	yes	—
96	C₄²×C₅₉	C₂²⋊C₄	1	2	yes	—
97	C₄²×C₅₉	C₄⋊C₄	1	2	yes	—
98	C₄²×C₅₉	C₄⋊C₄	1	2	yes	—
99	C₄²×C₅₉	C₄⋊C₄	1	2	yes	—
100	C₄²×C₅₉	C₄⋊C₄	1	2	yes	—
101	C₂³×C₅₉	—	2	2	no	—
102	C₂³×C₅₉	—	2	2	no	—
103	C₂³×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
104	C₂³×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
105	C₂³×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
106	C₂³×C₅₉	C₂×D₈	1	1	yes	characteristic
107	C₂³×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
108	C₂³×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
109	C₂³×C₅₉	C₂×Q₁₆	1	1	yes	characteristic
110	C₂×C₄×C₅₉	—	2	2	no	—
111	C₂×C₄×C₅₉	—	2	2	no	—
112	C₂×C₄×C₅₉	—	2	2	no	—
113	C₂×C₄×C₅₉	—	2	4	no	—
114	C₂×C₄×C₅₉	—	2	4	no	—
115	C₂×C₄×C₅₉	—	2	8	no	—
116	C₂×C₄×C₅₉	—	4	1	no	—
117	C₂×C₄×C₅₉	—	4	1	no	—
118	C₂×C₄×C₅₉	—	4	1	no	—
119	C₂×C₄×C₅₉	—	4	1	no	—
120	C₂×C₄×C₅₉	—	4	4	no	—
121	C₂×C₄×C₅₉	—	4	8	no	—
122	C₂×C₄×C₅₉	—	4	8	no	—
123	C₂×C₄×C₅₉	—	4	4	no	—
124	C₂×C₄×C₅₉	—	4	4	no	—
125	C₂×C₄×C₅₉	—	4	4	no	—
126	C₂×C₄×C₅₉	—	4	4	no	—
127	C₂×C₄×C₅₉	#95	1	2	yes	—
128	C₂×C₄×C₅₉	#95	1	2	yes	—
129	C₂×C₄×C₅₉	#95	1	2	yes	—
130	C₂×C₄×C₅₉	#95	1	2	yes	—
131	C₂×C₄×C₅₉	#102	1	4	yes	—
132	C₂×C₄×C₅₉	#102	1	2	yes	—
133	C₂×C₄×C₅₉	#102	1	2	yes	—
134	C₂×C₄×C₅₉	#103	1	4	yes	—
135	C₂×C₄×C₅₉	#103	1	2	yes	—
136	C₂×C₄×C₅₉	#103	1	2	yes	—
137	C₂×C₄×C₅₉	#104	1	4	yes	—
138	C₂×C₄×C₅₉	#106	1	4	yes	—
139	C₂×C₄×C₅₉	#107	1	4	yes	—
140	C₂×C₄×C₅₉	C₂×C₄²	1	1	yes	characteristic
141	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₈×C₅₉	—	4	4	no	—
145	#8014	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
146	C₂²×C₅₉	—	2	1	no	—
147	C₂²×C₅₉	—	2	1	no	—
148	C₂²×C₅₉	—	2	1	no	—
149	C₂²×C₅₉	—	2	1	no	—
150	C₂²×C₅₉	—	2	2	no	—
151	C₂²×C₅₉	—	2	2	no	—
152	C₂²×C₅₉	—	2	2	no	—
153	C₂²×C₅₉	—	2	2	no	—
154	C₂²×C₅₉	C₂×#95	1	1	yes	characteristic
155	C₂²×C₅₉	#410	1	2	yes	—
156	C₂²×C₅₉	C₂×#102	1	1	yes	characteristic
157	C₂²×C₅₉	C₂×#102	1	1	yes	characteristic
158	C₂²×C₅₉	C₂×#103	1	1	yes	characteristic
159	C₂²×C₅₉	C₂×#103	1	1	yes	characteristic
160	C₂²×C₅₉	C₂×#104	1	2	yes	—
161	C₂²×C₅₉	C₂×#106	1	1	yes	characteristic
162	C₂²×C₅₉	C₂×#107	1	1	yes	characteristic
163	C₄×C₅₉	—	2	2	no	—
164	C₄×C₅₉	—	2	1	no	—
165	C₄×C₅₉	—	2	1	no	—
166	C₄×C₅₉	—	2	1	no	—
167	C₄×C₅₉	—	2	1	no	—
168	C₄×C₅₉	—	4	8	no	—
169	C₄×C₅₉	—	8	4	no	—
170	C₄×C₅₉	#339	1	4	yes	—
171	C₄×C₅₉	#340	1	4	yes	—
172	C₄×C₅₉	#340	1	4	yes	—
173	C₂×#431	C₂×C₅₉	1	1	yes	characteristic
174	#2285	C₂×C₅₉	1	1	yes	characteristic
175	C₂×C₄×C₄⋊C₄	C₂×C₅₉	1	1	yes	characteristic
176	#1294	C₂×C₅₉	1	4	yes	—
177	C₂×C₅₉	—	2	1	no	—
178	C₂×C₅₉	—	2	1	no	—
179	C₂×C₅₉	—	2	1	no	—
180	C₂×C₅₉	—	2	1	no	—
181	C₂×C₅₉	#1502	1	2	yes	—
182	C₂×C₅₉	#1503	1	2	yes	—
183	C₂×C₅₉	C₂×#339	1	1	yes	characteristic
184	C₂×C₅₉	C₂×#340	1	1	yes	characteristic
185	C₂×C₅₉	#1740	1	1	yes	characteristic
186	C₂×#117	—	2	1	no	—
187	C₂²×C₄⋊C₄	—	2	1	no	—
188	C₂²×C₄²	—	2	1	no	—
189	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
190	#431	—	2	2	no	—
191	#431	C₄×C₅₉	1	4	yes	complemented
192	C₂×C₄⋊C₈	—	2	1	no	—
193	C₂×C₂²⋊C₈	C₂²×C₅₉	1	2	yes	—
194	C₂×C₄×C₈	—	2	1	no	—
195	#384	C₄×C₅₉	1	2	yes	complemented
196	#382	—	2	1	no	—
197	#380	—	2	1	no	—
198	#380	C₂²×C₅₉	1	2	yes	—
199	C₄×C₄⋊C₄	—	2	2	no	—
200	C₄×C₄⋊C₄	—	2	1	no	—
201	C₄×C₄⋊C₄	C₄×C₅₉	1	2	yes	complemented
202	C₄×C₄⋊C₄	C₄×C₅₉	1	4	yes	complemented
203	C₂×#95	C₂²×C₅₉	1	2	yes	—
204	C₅₉	#8014	1	1	yes	characteristic, direct product factor, Sylow
205	C₂³×C₄	—	2	2	no	—
206	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
207	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
208	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
209	C₂²×C₈	—	2	2	no	—
210	#117	—	4	2	no	—
211	#117	—	4	2	no	—
212	C₂×C₄⋊C₄	—	2	8	no	—
213	C₂×C₄⋊C₄	—	2	4	no	—
214	C₂×C₄⋊C₄	—	2	2	no	—
215	C₂×C₄⋊C₄	—	2	2	no	—
216	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	4	yes	—
217	C₂×C₂²⋊C₄	—	2	2	no	—
218	C₂×C₄²	—	2	2	no	—
219	C₂×C₄²	—	2	4	no	—
220	C₂×C₄²	—	4	2	no	—
221	C₂×C₄²	—	4	2	no	—
222	C₂×C₄²	C₂×C₄×C₅₉	1	2	yes	—
223	C₂×C₄²	C₂×C₄×C₅₉	1	1	yes	characteristic
224	C₂×C₄²	C₂×C₄×C₅₉	1	2	yes	—
225	C₂×C₄²	C₂×C₄×C₅₉	1	1	yes	characteristic
226	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
227	C₂×C₄²	D₄×C₅₉	1	2	yes	—
228	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
229	C₂×C₄²	Q₈×C₅₉	1	2	yes	—
230	C₄⋊C₈	—	2	4	no	—
231	C₂²⋊C₈	—	2	2	no	—
232	C₂²⋊C₈	C₂×C₄×C₅₉	1	4	yes	—
233	C₄×C₈	—	2	4	no	—
234	#95	—	2	2	no	—
235	#95	—	2	2	no	—
236	#95	—	2	2	no	—
237	#95	C₂×C₄×C₅₉	1	4	yes	—
238	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
239	C₂²×C₄	—	2	4	no	—
240	C₂²×C₄	—	2	8	no	—
241	C₂²×C₄	—	2	4	no	—
242	C₂²×C₄	—	2	4	no	—
243	C₂²×C₄	—	4	2	no	—
244	C₂²×C₄	—	4	4	no	—
245	C₂²×C₄	—	4	2	no	—
246	C₂²×C₄	—	4	2	no	—
247	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
248	C₂²×C₄	C₂²⋊C₄×C₅₉	1	2	yes	—
249	C₂²×C₄	C₂²⋊C₄×C₅₉	1	2	yes	—
250	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
251	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
252	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
253	C₂²×C₄	C₄⋊C₄×C₅₉	1	2	yes	—
254	C₂²×C₄	C₄⋊C₄×C₅₉	1	2	yes	—
255	C₂²×C₄	D₈×C₅₉	1	2	yes	—
256	C₂²×C₄	SD₁₆×C₅₉	1	2	yes	—
257	C₂²×C₄	SD₁₆×C₅₉	1	2	yes	—
258	C₂²×C₄	Q₁₆×C₅₉	1	2	yes	—
259	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
260	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
261	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
262	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
263	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
264	C₂²×C₄	C₂×Q₈×C₅₉	1	1	yes	characteristic
265	C₂×C₈	—	2	4	no	—
266	C₂×C₈	—	4	4	no	—
267	C₄⋊C₄	—	2	16	no	—
268	C₄⋊C₄	—	4	4	no	—
269	C₄⋊C₄	—	4	4	no	—
270	C₄⋊C₄	—	4	4	no	—
271	C₂²⋊C₄	—	4	2	no	—
272	C₂²⋊C₄	—	4	2	no	—
273	C₄²	—	4	8	no	—
274	C₄²	—	4	4	no	—
275	C₄²	C₄²×C₅₉	1	2	yes	—
276	C₄²	C₄²×C₅₉	1	2	yes	—
277	C₄²	C₂²⋊C₄×C₅₉	1	2	yes	—
278	C₄²	C₂²⋊C₄×C₅₉	1	2	yes	—
279	C₄²	C₄⋊C₄×C₅₉	1	2	yes	—
280	C₄²	C₄⋊C₄×C₅₉	1	2	yes	—
281	C₄²	C₄⋊C₄×C₅₉	1	2	yes	—
282	C₄²	C₄⋊C₄×C₅₉	1	2	yes	—
283	C₂³	—	2	2	no	—
284	C₂³	—	2	2	no	—
285	C₂³	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
286	C₂³	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
287	C₂³	C₂×C₄⋊C₄×C₅₉	1	1	yes	characteristic
288	C₂³	C₂×D₈×C₅₉	1	1	yes	characteristic
289	C₂³	C₂×SD₁₆×C₅₉	1	1	yes	characteristic
290	C₂³	C₂×SD₁₆×C₅₉	1	1	yes	characteristic
291	C₂³	C₂×Q₁₆×C₅₉	1	1	yes	characteristic
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	4	no	—
296	C₂×C₄	—	2	4	no	—
297	C₂×C₄	—	2	8	no	—
298	C₂×C₄	—	4	1	no	—
299	C₂×C₄	—	4	1	no	—
300	C₂×C₄	—	4	1	no	—
301	C₂×C₄	—	4	1	no	—
302	C₂×C₄	—	4	4	no	—
303	C₂×C₄	—	4	8	no	—
304	C₂×C₄	—	4	8	no	—
305	C₂×C₄	—	4	4	no	—
306	C₂×C₄	—	4	4	no	—
307	C₂×C₄	—	4	4	no	—
308	C₂×C₄	—	4	4	no	—
309	C₂×C₄	#95×C₅₉	1	2	yes	—
310	C₂×C₄	#95×C₅₉	1	2	yes	—
311	C₂×C₄	#95×C₅₉	1	2	yes	—
312	C₂×C₄	#95×C₅₉	1	2	yes	—
313	C₂×C₄	#102×C₅₉	1	4	yes	—
314	C₂×C₄	#102×C₅₉	1	2	yes	—
315	C₂×C₄	#102×C₅₉	1	2	yes	—
316	C₂×C₄	#103×C₅₉	1	4	yes	—
317	C₂×C₄	#103×C₅₉	1	2	yes	—
318	C₂×C₄	#103×C₅₉	1	2	yes	—
319	C₂×C₄	#104×C₅₉	1	4	yes	—
320	C₂×C₄	#106×C₅₉	1	4	yes	—
321	C₂×C₄	#107×C₅₉	1	4	yes	—
322	C₂×C₄	C₂×C₄²×C₅₉	1	1	yes	characteristic
323	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
324	C₂×C₄	C₂×C₄⋊C₄×C₅₉	1	1	yes	characteristic
325	C₂×C₄	C₂×C₄⋊C₄×C₅₉	1	1	yes	characteristic
326	C₈	—	4	4	no	—
327	C₂²	—	2	1	no	—
328	C₂²	—	2	1	no	—
329	C₂²	—	2	1	no	—
330	C₂²	—	2	1	no	—
331	C₂²	—	2	2	no	—
332	C₂²	—	2	2	no	—
333	C₂²	—	2	2	no	—
334	C₂²	—	2	2	no	—
335	C₂²	C₂×#95×C₅₉	1	1	yes	characteristic
336	C₂²	C₅₉×#410	1	2	yes	—
337	C₂²	C₂×#102×C₅₉	1	1	yes	characteristic
338	C₂²	C₂×#102×C₅₉	1	1	yes	characteristic
339	C₂²	C₂×#103×C₅₉	1	1	yes	characteristic
340	C₂²	C₂×#103×C₅₉	1	1	yes	characteristic
341	C₂²	C₂×#104×C₅₉	1	2	yes	—
342	C₂²	C₂×#106×C₅₉	1	1	yes	characteristic
343	C₂²	C₂×#107×C₅₉	1	1	yes	characteristic
344	C₄	—	2	2	no	—
345	C₄	—	2	1	no	—
346	C₄	—	2	1	no	—
347	C₄	—	2	1	no	—
348	C₄	—	2	1	no	—
349	C₄	—	4	8	no	—
350	C₄	—	8	4	no	—
351	C₄	C₅₉×#339	1	4	yes	—
352	C₄	C₅₉×#340	1	4	yes	—
353	C₄	C₅₉×#340	1	4	yes	—
354	C₂	—	2	1	no	—
355	C₂	—	2	1	no	—
356	C₂	—	2	1	no	—
357	C₂	—	2	1	no	—
358	C₂	C₅₉×#1502	1	2	yes	—
359	C₂	C₅₉×#1503	1	2	yes	—
360	C₂	C₂×C₅₉×#339	1	1	yes	characteristic
361	C₂	C₂×C₅₉×#340	1	1	yes	characteristic
362	C₂	C₅₉×#1740	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅₉	C₂²⋊C₄
commutator	C₂×C₄	C₂×C₄²×C₅₉
Frattini, cosocle	C₂³×C₄	C₂³×C₅₉
socle	C₂³×C₅₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₅₉	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅₉ ◁ C₂²×C₄²×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
10. C₅₉×#431	C₄	semidirect
14. C₅₉×#384	C₄	semidirect
20. C₄×C₄⋊C₄×C₅₉	C₄	semidirect
21. C₄×C₄⋊C₄×C₅₉	C₄	semidirect
145. #8014	C₅₉	direct (N × H)
191. #431	C₄×C₅₉	semidirect
195. #384	C₄×C₅₉	semidirect
201. C₄×C₄⋊C₄	C₄×C₅₉	semidirect
202. C₄×C₄⋊C₄	C₄×C₅₉	semidirect
204. C₅₉	#8014	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×#431	2
C₅₉×#2285	2
C₂×C₄×C₄⋊C₄×C₅₉	2
C₅₉×#1294	2
#8014	59

Subgroups — C59×#8014 #28420123

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#8014 #28420123