Subgroups — #28482873

Order 15104.

546 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21427043	C₂	1	1	yes	maximal, characteristic
2	#21424859	C₂	1	1	yes	maximal, characteristic, complemented
3	#21424256	C₂	1	1	yes	maximal, characteristic, complemented
4	#21424097	C₂	1	1	yes	maximal, characteristic
5	C₂×#16837131	C₂	1	1	yes	maximal, characteristic
6	#21421980	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₂₃₆	C₂²	1	1	yes	characteristic
9	C₂×#14273685	—	2	1	no	—
10	C₂×#14273661	—	2	2	no	—
11	C₂×#14273658	—	2	1	no	—
12	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×#14273649	—	2	1	no	—
14	#16837304	—	2	1	no	—
15	#16837294	—	2	2	no	—
16	#16837272	C₂²	1	1	yes	characteristic
17	#16837272	C₂²	1	1	yes	characteristic
18	#16837259	—	2	1	no	—
19	C₄×C₄⋊Dic₅₉	—	2	1	no	—
20	#16837165	—	2	1	no	—
21	#16837164	—	2	1	no	—
22	#16837131	C₄	1	4	yes	complemented
23	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
25	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
26	C₂²×D₂₃₆	D₄	1	1	yes	characteristic
27	C₂²×C₄×D₅₉	—	2	1	no	—
28	C₂²×C₅₉⋊C₈	—	2	1	no	—
29	C₄×D₂₃₆	—	2	1	no	—
30	C₄×D₂₃₆	—	2	1	no	—
31	C₄×D₂₃₆	C₂×C₄	1	2	yes	—
32	C₄×D₂₃₆	Q₈	1	2	yes	—
33	#14273685	—	4	2	no	—
34	#14273685	—	4	2	no	—
35	C₂×C₄⋊Dic₅₉	—	2	1	no	—
36	C₂×C₄⋊Dic₅₉	—	2	1	no	—
37	C₂×C₄⋊Dic₅₉	—	2	1	no	—
38	C₂×C₄⋊Dic₅₉	—	2	1	no	—
39	C₂×C₄⋊Dic₅₉	—	2	1	no	—
40	C₂×C₄⋊Dic₅₉	D₄	1	1	yes	characteristic
41	C₂×C₄⋊Dic₅₉	D₄	1	2	yes	—
42	C₂×(C₂×D₅₉)⋊C₄	—	2	1	no	—
43	C₂×(C₂×D₅₉)⋊C₄	—	2	2	no	—
44	C₂×(C₂×D₅₉)⋊C₄	—	2	2	no	—
45	C₂×C₄×Dic₅₉	—	2	2	no	—
46	#14273661	—	4	4	no	—
47	#14273658	—	4	2	no	—
48	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
49	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
50	#14273649	—	4	2	no	—
51	C₅₉⋊#95	—	2	2	no	—
52	C₂²×C₈×C₅₉	—	2	1	no	—
53	C₂²×C₈×C₅₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₅₉	—	2	1	no	—
57	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
58	C₄⋊C₈×C₅₉	—	2	1	no	—
59	C₄⋊C₈×C₅₉	—	2	1	no	—
60	C₄×C₈×C₅₉	—	2	1	no	—
61	C₄×C₈×C₅₉	C₂×C₄	1	2	yes	—
62	#95×C₅₉	—	2	1	no	—
63	C₂³×D₅₉	—	2	1	no	—
64	C₂²×C₄×C₅₉	—	2	1	no	—
65	C₂²×C₄×C₅₉	—	2	1	no	—
66	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
69	C₂²×Dic₅₉	—	2	1	no	—
70	C₂²×Dic₅₉	—	2	2	no	—
71	C₂²×Dic₅₉	—	4	1	no	—
72	C₂×D₂₃₆	—	2	1	no	—
73	C₂×D₂₃₆	—	2	1	no	—
74	C₂×D₂₃₆	—	2	1	no	—
75	C₂×D₂₃₆	—	2	1	no	—
76	C₂×D₂₃₆	—	2	1	no	—
77	C₂×D₂₃₆	C₄⋊C₄	1	2	yes	—
78	C₂×C₄×D₅₉	—	2	2	no	—
79	C₂×C₄×D₅₉	—	2	2	no	—
80	C₂×C₄×D₅₉	—	4	1	no	—
81	C₂×C₄×D₅₉	—	4	1	no	—
82	C₂×C₄×D₅₉	—	4	1	no	—
83	C₂×C₄×D₅₉	—	4	1	no	—
84	C₂×C₈×C₅₉	—	2	2	no	—
85	C₂×C₈×C₅₉	—	2	2	no	—
86	C₂×C₈×C₅₉	—	2	2	no	—
87	C₂×C₈×C₅₉	—	4	1	no	—
88	C₂×C₈×C₅₉	—	4	1	no	—
89	C₂×C₈×C₅₉	—	4	1	no	—
90	C₄⋊C₄×C₅₉	—	2	1	no	—
91	C₄⋊C₄×C₅₉	—	2	1	no	—
92	C₄⋊C₄×C₅₉	—	2	1	no	—
93	C₄⋊C₄×C₅₉	D₈	1	2	yes	—
94	C₄²×C₅₉	—	4	1	no	—
95	C₄²×C₅₉	—	4	1	no	—
96	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
97	C₄²×C₅₉	C₂×Q₈	1	1	yes	characteristic
98	C₄²×C₅₉	#41	1	1	yes	characteristic
99	C₄²×C₅₉	#41	1	1	yes	characteristic
100	(C₂×D₅₉)⋊C₄	—	2	2	no	—
101	(C₂×D₅₉)⋊C₄	—	2	2	no	—
102	(C₂×D₅₉)⋊C₄	—	4	4	no	—
103	(C₂×D₅₉)⋊C₄	—	8	2	no	—
104	C₄⋊Dic₅₉	—	2	1	no	—
105	C₄⋊Dic₅₉	—	4	1	no	—
106	C₄⋊Dic₅₉	—	4	1	no	—
107	C₄⋊Dic₅₉	—	4	1	no	—
108	C₄⋊Dic₅₉	—	4	1	no	—
109	C₄⋊Dic₅₉	—	4	2	no	—
110	C₄⋊Dic₅₉	—	4	2	no	—
111	C₄⋊Dic₅₉	—	4	1	no	—
112	C₄⋊Dic₅₉	—	4	1	no	—
113	C₄⋊Dic₅₉	—	4	1	no	—
114	C₄⋊Dic₅₉	—	4	1	no	—
115	C₄⋊Dic₅₉	C₄⋊C₄	1	2	yes	—
116	C₄×Dic₅₉	—	4	4	no	—
117	C₂×C₅₉⋊C₈	—	2	2	no	—
118	C₂×C₅₉⋊C₈	—	4	1	no	—
119	C₂×C₅₉⋊C₈	—	4	1	no	—
120	C₂³×C₅₉	#120	1	1	yes	characteristic
121	C₂²×D₅₉	—	2	2	no	—
122	C₂²×D₅₉	—	4	1	no	—
123	C₂²×D₅₉	—	4	1	no	—
124	C₂²×D₅₉	—	4	1	no	—
125	C₂²×D₅₉	—	4	1	no	—
126	C₂²×D₅₉	—	4	1	no	—
127	C₂²×D₅₉	—	4	1	no	—
128	C₂×C₄×C₅₉	—	2	1	no	—
129	C₂×C₄×C₅₉	—	2	1	no	—
130	C₂×C₄×C₅₉	—	2	2	no	—
131	C₂×C₄×C₅₉	—	4	1	no	—
132	C₂×C₄×C₅₉	—	4	1	no	—
133	C₂×C₄×C₅₉	—	4	1	no	—
134	C₂×C₄×C₅₉	—	4	1	no	—
135	C₂×C₄×C₅₉	—	4	1	no	—
136	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
138	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
139	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
140	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
141	C₂×C₄×C₅₉	#123	1	1	yes	characteristic
142	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
143	C₂×C₄×C₅₉	#135	1	1	yes	characteristic
144	C₂×C₄×C₅₉	#135	1	1	yes	characteristic
145	C₂×C₄×C₅₉	#135	1	1	yes	characteristic
146	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
147	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
148	C₂×C₄×C₅₉	#137	1	1	yes	characteristic
149	C₂×C₄×C₅₉	#137	1	1	yes	characteristic
150	C₂×Dic₅₉	—	2	2	no	—
151	C₂×Dic₅₉	—	4	1	no	—
152	C₂×Dic₅₉	—	4	1	no	—
153	C₂×Dic₅₉	—	4	2	no	—
154	C₂×Dic₅₉	—	4	2	no	—
155	C₂×Dic₅₉	—	4	2	no	—
156	C₂×Dic₅₉	—	8	1	no	—
157	C₂×Dic₅₉	—	8	1	no	—
158	C₂×Dic₅₉	—	8	1	no	—
159	D₂₃₆	—	2	2	no	—
160	D₂₃₆	—	2	2	no	—
161	D₂₃₆	—	4	1	no	—
162	D₂₃₆	—	4	1	no	—
163	C₄×D₅₉	—	4	2	no	—
164	C₄×D₅₉	—	4	2	no	—
165	C₄×D₅₉	—	4	2	no	—
166	C₄×D₅₉	—	4	2	no	—
167	C₈×C₅₉	—	2	4	no	—
168	C₈×C₅₉	—	8	1	no	—
169	C₅₉⋊C₈	—	4	2	no	—
170	#8885	—	59	1	no	maximal, Sylow
171	C₂²×C₅₉	#385	1	1	yes	characteristic
172	C₂²×C₅₉	#447	1	1	yes	characteristic
173	C₂²×C₅₉	#449	1	1	yes	characteristic
174	C₂²×C₅₉	#452	1	1	yes	characteristic
175	C₂²×C₅₉	#452	1	1	yes	characteristic
176	C₂²×C₅₉	#453	1	1	yes	characteristic
177	C₂²×C₅₉	#456	1	1	yes	characteristic
178	C₂×D₅₉	—	4	2	no	—
179	C₂×D₅₉	—	4	2	no	—
180	C₂×D₅₉	—	4	2	no	—
181	C₂×D₅₉	—	8	1	no	—
182	C₂×D₅₉	—	8	1	no	—
183	C₂×D₅₉	—	8	1	no	—
184	C₂×D₅₉	—	8	1	no	—
185	C₄×C₅₉	—	2	1	no	—
186	C₄×C₅₉	—	2	1	no	—
187	C₄×C₅₉	—	4	2	no	—
188	C₄×C₅₉	—	8	1	no	—
189	C₄×C₅₉	#427	1	1	yes	characteristic
190	C₄×C₅₉	#428	1	1	yes	characteristic
191	C₄×C₅₉	C₄×D₈	1	1	yes	characteristic
192	C₄×C₅₉	#440	1	1	yes	characteristic
193	C₄×C₅₉	#474	1	1	yes	characteristic
194	C₄×C₅₉	#478	1	1	yes	characteristic
195	C₄×C₅₉	#482	1	1	yes	characteristic
196	C₄×C₅₉	#485	1	1	yes	characteristic
197	Dic₅₉	—	4	2	no	—
198	Dic₅₉	—	8	2	no	—
199	Dic₅₉	—	16	1	no	—
200	#2354	—	59	1	no	—
201	#1948	—	59	1	no	—
202	#1845	—	59	1	no	—
203	#1802	—	59	1	no	—
204	C₂×D₄⋊C₈	—	59	1	no	—
205	#1296	—	59	1	no	—
206	#1279	D₅₉	1	1	yes	characteristic, complemented
207	C₂×C₅₉	#1621	1	1	yes	characteristic
208	C₂×C₅₉	#1634	1	1	yes	characteristic
209	C₂×C₅₉	#1647	1	1	yes	characteristic
210	C₂×C₅₉	#1650	1	1	yes	characteristic
211	C₂×C₅₉	#1854	1	1	yes	characteristic
212	C₂×C₅₉	#1859	1	1	yes	characteristic
213	C₂×C₅₉	#1862	1	1	yes	characteristic
214	D₅₉	—	8	2	no	—
215	C₂×C₄×D₄	—	59	1	no	—
216	C₂×#117	—	118	1	no	—
217	C₂×#107	—	118	2	no	—
218	C₂×#106	—	118	1	no	—
219	C₂×C₄⋊C₈	—	59	1	no	—
220	C₂×C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
221	C₂×#102	—	118	1	no	—
222	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
223	#390	—	118	1	no	—
224	#388	—	118	2	no	—
225	#384	—	59	1	no	—
226	#384	—	59	1	no	—
227	#380	—	118	1	no	—
228	C₄×C₄⋊C₄	—	118	1	no	—
229	C₄×C₄⋊C₄	C₂×D₅₉	1	1	yes	characteristic
230	#340	—	118	1	no	—
231	#340	—	118	1	no	—
232	D₄⋊C₈	—	59	4	no	—
233	C₅₉	#8885	1	1	yes	characteristic, complemented, Sylow
234	C₂²×D₄	—	59	1	no	—
235	C₂³×C₄	—	118	1	no	—
236	C₂²×C₈	—	2	1	no	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	—	118	1	no	—
239	C₄×D₄	—	59	2	no	—
240	C₄×D₄	—	59	2	no	—
241	C₄×D₄	—	118	1	no	—
242	C₄×D₄	—	118	1	no	—
243	#117	—	236	2	no	—
244	#117	—	236	2	no	—
245	C₂×C₄⋊C₄	—	59	1	no	—
246	C₂×C₄⋊C₄	—	59	2	no	—
247	C₂×C₄⋊C₄	—	118	1	no	—
248	C₂×C₄⋊C₄	—	118	1	no	—
249	C₂×C₄⋊C₄	—	118	1	no	—
250	C₂×C₄⋊C₄	—	118	1	no	—
251	C₂×C₄⋊C₄	—	118	1	no	—
252	C₂×C₄⋊C₄	D₂₃₆	1	1	yes	characteristic
253	C₂×C₄⋊C₄	D₂₃₆	1	1	yes	characteristic
254	C₂×C₂²⋊C₄	—	118	1	no	—
255	C₂×C₂²⋊C₄	—	118	2	no	—
256	C₂×C₂²⋊C₄	—	118	2	no	—
257	C₂×C₄²	—	2	1	no	—
258	C₂×C₄²	—	118	2	no	—
259	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
260	#107	—	236	4	no	—
261	#106	—	236	2	no	—
262	C₄⋊C₈	—	2	1	no	—
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	—	59	2	no	—
265	C₄⋊C₈	—	118	1	no	—
266	#102	—	236	2	no	—
267	C₄×C₈	—	2	1	no	—
268	C₄×C₈	C₄×D₅₉	1	2	yes	—
269	#95	—	2	1	no	—
270	#95	—	118	2	no	—
271	C₂⁴	—	118	1	no	—
272	C₂×D₄	—	59	2	no	—
273	C₂×D₄	—	118	1	no	—
274	C₂×D₄	—	118	1	no	—
275	C₂×D₄	—	118	1	no	—
276	C₂×D₄	—	118	1	no	—
277	C₂×D₄	—	118	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	118	1	no	—
281	C₂²×C₄	—	118	2	no	—
282	C₂²×C₄	—	118	2	no	—
283	C₂²×C₄	—	118	2	no	—
284	C₂²×C₄	—	236	1	no	—
285	C₂²×C₄	—	236	1	no	—
286	C₂²×C₄	—	236	1	no	—
287	C₂²×C₄	—	236	1	no	—
288	C₂²×C₄	—	236	1	no	—
289	C₂²×C₄	C₂×D₂₃₆	1	1	yes	characteristic
290	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
291	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	4	1	no	—
296	C₂×C₈	—	4	1	no	—
297	C₂×C₈	—	4	1	no	—
298	C₂×C₈	—	118	2	no	—
299	C₂×C₈	—	236	1	no	—
300	C₂×C₈	—	236	1	no	—
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	—	2	1	no	—
303	C₄⋊C₄	—	2	1	no	—
304	C₄⋊C₄	—	59	2	no	—
305	C₄⋊C₄	—	118	1	no	—
306	C₄⋊C₄	—	236	2	no	—
307	C₄⋊C₄	—	236	2	no	—
308	C₄⋊C₄	—	236	1	no	—
309	C₄⋊C₄	—	236	1	no	—
310	C₄⋊C₄	—	236	1	no	—
311	C₄⋊C₄	—	236	1	no	—
312	C₄⋊C₄	—	236	1	no	—
313	C₄⋊C₄	—	236	1	no	—
314	C₄⋊C₄	—	236	1	no	—
315	C₄⋊C₄	—	236	1	no	—
316	C₄⋊C₄	D₄₇₂	1	2	yes	—
317	C₂²⋊C₄	—	118	2	no	—
318	C₂²⋊C₄	—	118	2	no	—
319	C₂²⋊C₄	—	472	2	no	—
320	C₂²⋊C₄	—	236	4	no	—
321	C₄²	—	4	1	no	—
322	C₄²	—	4	1	no	—
323	C₄²	—	236	4	no	—
324	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
325	C₄²	#11745685	1	1	yes	characteristic
326	C₄²	#11745687	1	1	yes	characteristic
327	C₄²	Q₈×D₅₉	1	1	yes	characteristic
328	C₂³	—	118	2	no	—
329	C₂³	—	236	1	no	—
330	C₂³	—	236	1	no	—
331	C₂³	—	236	1	no	—
332	C₂³	—	236	1	no	—
333	C₂³	—	236	1	no	—
334	C₂³	—	236	1	no	—
335	C₂³	#14273697	1	1	yes	characteristic
336	D₄	—	118	2	no	—
337	D₄	—	118	2	no	—
338	D₄	—	236	1	no	—
339	D₄	—	236	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	118	2	no	—
349	C₂×C₄	—	472	1	no	—
350	C₂×C₄	—	472	1	no	—
351	C₂×C₄	—	472	1	no	—
352	C₂×C₄	—	236	2	no	—
353	C₂×C₄	—	236	2	no	—
354	C₂×C₄	—	236	2	no	—
355	C₂×C₄	—	236	1	no	—
356	C₂×C₄	—	236	1	no	—
357	C₂×C₄	—	236	2	no	—
358	C₂×C₄	—	236	2	no	—
359	C₂×C₄	—	236	2	no	—
360	C₂×C₄	—	236	2	no	—
361	C₂×C₄	C₄⋊C₄×D₅₉	1	1	yes	characteristic
362	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
363	C₂×C₄	C₄×D₂₃₆	1	1	yes	characteristic
364	C₂×C₄	#14273705	1	1	yes	characteristic
365	C₂×C₄	#14273707	1	1	yes	characteristic
366	C₂×C₄	#14273709	1	1	yes	characteristic
367	C₂×C₄	C₂×D₄₇₂	1	1	yes	characteristic
368	C₂×C₄	#14273746	1	1	yes	characteristic
369	C₂×C₄	#14273749	1	1	yes	characteristic
370	C₂×C₄	#14273750	1	1	yes	characteristic
371	C₂×C₄	#14273754	1	1	yes	characteristic
372	C₂×C₄	#14273755	1	1	yes	characteristic
373	C₂×C₄	#14273756	1	1	yes	characteristic
374	C₂×C₄	#14273760	1	1	yes	characteristic
375	C₈	—	2	4	no	—
376	C₈	—	8	1	no	—
377	C₈	—	236	2	no	—
378	C₂²	—	472	1	no	—
379	C₂²	—	472	1	no	—
380	C₂²	—	472	1	no	—
381	C₂²	—	472	1	no	—
382	C₂²	—	236	2	no	—
383	C₂²	—	236	2	no	—
384	C₂²	—	236	2	no	—
385	C₂²	#16837276	1	1	yes	characteristic
386	C₂²	#16837538	1	1	yes	characteristic
387	C₂²	#16837550	1	1	yes	characteristic
388	C₂²	#16837565	1	1	yes	characteristic
389	C₂²	#16837566	1	1	yes	characteristic
390	C₂²	#16837571	1	1	yes	characteristic
391	C₂²	#16837586	1	1	yes	characteristic
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	4	2	no	—
395	C₄	—	8	1	no	—
396	C₄	—	944	1	no	—
397	C₄	—	472	2	no	—
398	C₄	—	236	2	no	—
399	C₄	#16837439	1	1	yes	characteristic
400	C₄	#16837441	1	1	yes	characteristic
401	C₄	C₄×D₄₇₂	1	1	yes	characteristic
402	C₄	#16837504	1	1	yes	characteristic
403	C₄	#16837683	1	1	yes	characteristic
404	C₄	#16837703	1	1	yes	characteristic
405	C₄	#16837724	1	1	yes	characteristic
406	C₄	#16837742	1	1	yes	characteristic
407	C₂	—	472	2	no	—
408	C₂	#21423163	1	1	yes	characteristic
409	C₂	#21423243	1	1	yes	characteristic
410	C₂	#21423333	1	1	yes	characteristic
411	C₂	#21423355	1	1	yes	characteristic
412	C₂	#21424298	1	1	yes	characteristic
413	C₂	#21424323	1	1	yes	characteristic
414	C₂	#21424346	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#14273697
commutator	C₄²×C₅₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₅₉
Fitting	C₅₉×#1279	C₂
socle	C₂³×C₅₉	#120
prime radical	C₂²×D₂₃₆	D₄
cosocle	C₂×C₄²×C₅₉	C₂³
hypercenter	#1279	D₅₉
hypocenter	C₅₉	#8885
LCS	G ▷ C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
2. #21424859	C₂	semidirect
3. #21424256	C₂	semidirect
6. #21421980	C₂	semidirect
7. C₅₉×#1279	C₂	semidirect
22. #16837131	C₄	semidirect
206. #1279	D₅₉	semidirect
233. C₅₉	#8885	semidirect

Maximal subgroups

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

subgroup	index
#21427043	2
#21424859	2
#21424256	2
#21424097	2
C₂×#16837131	2
#21421980	2
C₅₉×#1279	2
#8885	59