Subgroups — #21433147

Order 7552.

422 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837911	C₂	1	1	yes	maximal, characteristic
2	#16837475	C₂	1	1	yes	maximal, characteristic, complemented
3	#16837471	C₂	1	1	yes	maximal, characteristic, complemented
4	#16837470	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#16837467	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×C₂²⋊D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
8	(C₂²⋊D₅₉)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	#16837464	C₂	1	1	yes	maximal, characteristic, complemented
10	#16837462	C₂	1	1	yes	maximal, characteristic, complemented
11	#16837370	C₂	1	1	yes	maximal, characteristic, complemented
12	#16837367	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×(C₂×D₅₉)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²⋊C₈×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#435	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#11745685	C₂²	1	1	yes	characteristic
17	C₂²×C₄×D₅₉	C₂²	1	1	yes	characteristic
18	C₂×#11745659	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
20	C₂²×C₅₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₈×D₅₉	C₂²	1	1	yes	characteristic
22	C₂×C₈×D₅₉	C₂²	1	1	yes	characteristic
23	C₂×C₈×D₅₉	C₂²	1	1	yes	characteristic, complemented
24	#14273712	C₄	1	1	yes	characteristic
25	#14273709	C₄	1	1	yes	characteristic
26	#14273705	C₄	1	1	yes	characteristic
27	#14273704	C₄	1	1	yes	characteristic
28	#14273700	C₄	1	1	yes	characteristic
29	#14273699	C₄	1	1	yes	characteristic
30	#14273697	C₄	1	1	yes	characteristic
31	#14273695	C₄	1	1	yes	characteristic
32	C₄×D₂₃₆	C₂²	1	1	yes	characteristic
33	C₄×C₂²⋊D₅₉	C₂²	1	1	yes	characteristic
34	C₄×C₂²⋊D₅₉	C₂²	1	1	yes	characteristic
35	#14273684	C₂²	1	1	yes	characteristic
36	C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic, complemented
37	Dic₅₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
38	Dic₅₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
39	C₂²⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
40	C₂²⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic, complemented
41	(C₂×D₅₉)⋊C₈	C₂²	1	1	yes	characteristic
42	(C₂×D₅₉)⋊C₈	C₂²	1	1	yes	characteristic
43	(C₂×D₅₉)⋊C₈	C₂²	1	1	yes	characteristic
44	(C₂×D₅₉)⋊C₈	C₂²	1	1	yes	characteristic
45	(C₂×D₅₉)⋊C₈	C₂²	1	1	yes	characteristic
46	(C₂×D₅₉)⋊C₈	C₂²	1	1	yes	characteristic
47	(C₂×D₅₉)⋊C₈	C₂²	1	1	yes	characteristic, complemented
48	(C₂×D₅₉)⋊C₈	C₂²	1	1	yes	characteristic, complemented
49	#14273637	C₂²	1	1	yes	characteristic, complemented
50	C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
51	C₈×Dic₅₉	C₂²	1	1	yes	characteristic, complemented
52	C₂×M₁₆×C₅₉	C₂²	1	1	yes	characteristic, complemented
53	C₂²×C₈×C₅₉	C₂²	1	1	yes	characteristic
54	C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
55	C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
56	C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
57	C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
58	#97×C₅₉	C₂²	1	1	yes	characteristic, complemented
59	C₂³×D₅₉	C₂×C₄	1	1	yes	characteristic
60	C₂×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
62	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
63	C₂×C₂²⋊D₅₉	C₂×C₄	1	1	yes	characteristic
64	C₂×C₂²⋊D₅₉	C₂×C₄	1	1	yes	characteristic
65	C₂×C₂²⋊D₅₉	C₂×C₄	1	1	yes	characteristic
66	C₂×C₂²⋊D₅₉	C₂×C₄	1	1	yes	characteristic
67	C₂²×Dic₅₉	C₂×C₄	1	1	yes	characteristic
68	#11745685	—	4	1	no	—
69	#11745685	—	4	1	no	—
70	C₂×D₂₃₆	C₂×C₄	1	1	yes	characteristic
71	C₂×D₂₃₆	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄×D₅₉	—	4	1	no	—
73	C₂×C₄×D₅₉	—	4	1	no	—
74	C₂×C₄×D₅₉	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄×D₅₉	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄×D₅₉	C₂³	1	1	yes	characteristic
77	C₂×C₄×D₅₉	C₂³	1	1	yes	characteristic
78	C₂×C₄×D₅₉	C₂³	1	1	yes	characteristic
79	C₂×Dic₁₁₈	C₂×C₄	1	1	yes	characteristic
80	M₁₆×C₅₉	—	4	1	no	—
81	C₂×C₈×C₅₉	—	4	1	no	—
82	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
83	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
84	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
85	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
86	C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
87	C₂²⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
88	C₂²⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
89	C₄²×C₅₉	C₂³	1	1	yes	characteristic
90	C₂²⋊Dic₅₉	C₂×C₄	1	1	yes	characteristic
91	C₂²⋊Dic₅₉	C₂×C₄	1	1	yes	characteristic
92	(C₂×D₅₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
93	(C₂×D₅₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
94	(C₂×D₅₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
95	(C₂×D₅₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
96	(C₂×D₅₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
97	(C₂×D₅₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
98	C₄⋊Dic₅₉	C₂×C₄	1	1	yes	characteristic
99	Dic₅₉⋊C₄	C₂×C₄	1	1	yes	characteristic
100	Dic₅₉⋊C₄	C₂×C₄	1	1	yes	characteristic
101	Dic₅₉⋊C₄	C₂×C₄	1	1	yes	characteristic
102	Dic₅₉⋊C₄	C₂×C₄	1	1	yes	characteristic
103	C₄×Dic₅₉	C₂³	1	1	yes	characteristic
104	C₂×C₅₉⋊C₈	—	4	1	no	—
105	C₂×C₅₉⋊C₈	—	4	1	no	—
106	C₂×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
107	C₂×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
108	C₂×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
109	C₂×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
110	#11745659	—	4	1	no	—
111	C₈×D₅₉	—	4	1	no	—
112	C₈×D₅₉	—	4	1	no	—
113	C₈×D₅₉	—	4	1	no	—
114	C₂³×C₅₉	C₂²×C₄	1	1	yes	characteristic
115	C₂³×C₅₉	C₂²×C₄	1	1	yes	characteristic
116	C₂²×D₅₉	—	2	2	no	—
117	C₂²×D₅₉	—	2	2	no	—
118	C₂²×D₅₉	—	4	1	no	—
119	C₂²×D₅₉	C₂²×C₄	1	1	yes	characteristic
120	C₂²×D₅₉	C₂²×C₄	1	1	yes	characteristic
121	C₂²×D₅₉	C₂²×C₄	1	1	yes	characteristic
122	D₄×C₅₉	—	2	2	no	—
123	C₂×C₄×C₅₉	—	2	1	no	—
124	C₂×C₄×C₅₉	—	2	1	no	—
125	C₂×C₄×C₅₉	—	2	1	no	—
126	C₂×C₄×C₅₉	—	2	1	no	—
127	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
132	C₂²⋊D₅₉	—	2	2	no	—
133	C₂²⋊D₅₉	—	2	2	no	—
134	C₂²⋊D₅₉	—	4	1	no	—
135	C₂²⋊D₅₉	—	4	1	no	—
136	C₂×Dic₅₉	—	4	1	no	—
137	C₂×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
138	C₂×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
139	C₂×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
140	C₂×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
141	C₂×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
142	D₂₃₆	—	2	2	no	—
143	D₂₃₆	—	4	1	no	—
144	C₄×D₅₉	—	2	1	no	—
145	C₄×D₅₉	—	2	1	no	—
146	C₄×D₅₉	—	2	1	no	—
147	C₄×D₅₉	—	2	1	no	—
148	C₄×D₅₉	—	2	1	no	—
149	C₄×D₅₉	—	2	1	no	—
150	C₄×D₅₉	—	4	1	no	—
151	C₄×D₅₉	—	4	1	no	—
152	Dic₁₁₈	—	4	1	no	—
153	C₈×C₅₉	—	2	1	no	—
154	C₈×C₅₉	—	2	1	no	—
155	C₈×C₅₉	—	2	1	no	—
156	C₈×C₅₉	—	2	1	no	—
157	C₅₉⋊C₈	—	2	1	no	—
158	C₅₉⋊C₈	—	2	1	no	—
159	C₅₉⋊C₈	—	2	1	no	—
160	C₅₉⋊C₈	—	2	1	no	—
161	C₂²×C₅₉	—	2	1	no	—
162	C₂²×C₅₉	—	2	1	no	—
163	C₂²×C₅₉	—	2	1	no	—
164	C₂²×C₅₉	—	2	1	no	—
165	C₂²×C₅₉	—	2	1	no	—
166	C₂²×C₅₉	#131	1	2	yes	—
167	C₂²×C₅₉	C₂³×C₄	1	1	yes	characteristic
168	C₂×D₅₉	—	2	1	no	—
169	C₂×D₅₉	—	2	1	no	—
170	C₂×D₅₉	—	2	1	no	—
171	C₂×D₅₉	—	2	1	no	—
172	C₂×D₅₉	—	2	1	no	—
173	C₂×D₅₉	—	2	1	no	—
174	C₂×D₅₉	—	2	1	no	—
175	C₂×D₅₉	—	2	1	no	—
176	C₂×D₅₉	—	4	4	no	—
177	C₂×D₅₉	#131	1	2	yes	—
178	C₄×C₅₉	—	2	1	no	—
179	C₄×C₅₉	—	2	1	no	—
180	C₄×C₅₉	—	2	1	no	—
181	C₄×C₅₉	—	2	1	no	—
182	C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
183	C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
184	Dic₅₉	—	2	1	no	—
185	Dic₅₉	—	2	1	no	—
186	Dic₅₉	—	2	1	no	—
187	Dic₅₉	—	2	1	no	—
188	Dic₅₉	—	2	1	no	—
189	#2977	—	59	1	no	maximal, Sylow
190	C₂×C₅₉	—	2	2	no	—
191	C₂×C₅₉	—	4	1	no	—
192	C₂×C₅₉	#518	1	1	yes	characteristic
193	C₂×C₅₉	C₂×#131	1	1	yes	characteristic
194	C₂×C₅₉	C₂×#131	1	1	yes	characteristic
195	D₅₉	—	2	2	no	—
196	D₅₉	—	4	1	no	—
197	D₅₉	—	4	1	no	—
198	#525	—	59	1	no	—
199	#435	—	59	1	no	—
200	#435	—	59	1	no	—
201	#435	—	59	1	no	—
202	#435	D₅₉	1	1	yes	characteristic, complemented
203	C₈×D₄	—	59	1	no	—
204	C₈×D₄	—	59	1	no	—
205	C₈×D₄	—	59	1	no	—
206	C₈×D₄	—	59	1	no	—
207	#433	—	59	1	no	—
208	#433	—	59	1	no	—
209	#408	—	59	1	no	—
210	#408	—	59	1	no	—
211	C₂×C₂²⋊C₈	—	59	1	no	—
212	C₂×C₂²⋊C₈	—	59	1	no	—
213	C₅₉	#2977	1	1	yes	characteristic, complemented, Sylow
214	C₂×#41	—	59	1	no	—
215	C₂³×C₄	—	59	1	no	—
216	C₂×M₁₆	—	59	1	no	—
217	C₂×M₁₆	C₂×D₅₉	1	1	yes	characteristic, complemented
218	C₂²×C₈	—	59	1	no	—
219	C₂²×C₈	—	59	1	no	—
220	C₂²×C₈	—	59	1	no	—
221	C₂²×C₈	—	59	1	no	—
222	C₂²×C₈	—	59	1	no	—
223	C₂²×C₈	C₂×D₅₉	1	1	yes	characteristic
224	#123	—	59	1	no	—
225	#123	—	59	1	no	—
226	C₂²⋊Q₈	—	59	1	no	—
227	C₂²⋊Q₈	—	59	1	no	—
228	#121	—	59	1	no	—
229	#121	—	59	1	no	—
230	#120	—	59	1	no	—
231	#120	—	59	1	no	—
232	C₄×D₄	—	59	1	no	—
233	C₄×D₄	—	59	1	no	—
234	C₄×D₄	—	59	1	no	—
235	C₄×D₄	C₂×D₅₉	1	1	yes	characteristic
236	#117	—	59	1	no	—
237	C₄⋊C₈	—	59	1	no	—
238	C₄⋊C₈	—	59	1	no	—
239	C₄⋊C₈	—	59	1	no	—
240	C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic, complemented
241	C₂²⋊C₈	—	59	1	no	—
242	C₂²⋊C₈	—	59	1	no	—
243	C₂²⋊C₈	—	59	1	no	—
244	C₂²⋊C₈	—	59	1	no	—
245	C₂²⋊C₈	—	59	1	no	—
246	C₂²⋊C₈	—	59	1	no	—
247	C₂²⋊C₈	—	59	1	no	—
248	C₂²⋊C₈	—	59	1	no	—
249	C₂²⋊C₈	—	59	1	no	—
250	C₂²⋊C₈	—	59	1	no	—
251	C₂²⋊C₈	C₂×D₅₉	1	1	yes	characteristic
252	C₂²⋊C₈	C₂×D₅₉	1	1	yes	characteristic, complemented
253	#97	—	59	1	no	—
254	#97	C₂×D₅₉	1	1	yes	characteristic, complemented
255	C₄×C₈	—	59	1	no	—
256	C₄×C₈	—	59	1	no	—
257	C₂⁴	—	59	1	no	—
258	#41	—	236	1	no	—
259	#41	—	236	1	no	—
260	C₂×Q₈	—	59	1	no	—
261	C₂×D₄	—	59	1	no	—
262	C₂×D₄	—	59	1	no	—
263	C₂×D₄	—	59	1	no	—
264	C₂×D₄	—	59	1	no	—
265	C₂×D₄	—	59	1	no	—
266	C₂×D₄	—	59	1	no	—
267	C₂×D₄	C₄×D₅₉	1	1	yes	characteristic
268	C₂²×C₄	—	59	1	no	—
269	C₂²×C₄	—	59	1	no	—
270	C₂²×C₄	—	59	1	no	—
271	C₂²×C₄	—	59	1	no	—
272	C₂²×C₄	—	59	1	no	—
273	C₂²×C₄	—	59	1	no	—
274	C₂²×C₄	—	236	1	no	—
275	C₂²×C₄	—	236	1	no	—
276	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
277	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
278	M₁₆	—	4	1	no	—
279	M₁₆	—	236	1	no	—
280	C₂×C₈	—	4	1	no	—
281	C₂×C₈	—	59	1	no	—
282	C₂×C₈	—	59	1	no	—
283	C₂×C₈	—	59	1	no	—
284	C₂×C₈	—	59	1	no	—
285	C₂×C₈	—	236	1	no	—
286	C₂×C₈	—	236	1	no	—
287	C₂×C₈	—	236	1	no	—
288	C₂×C₈	—	236	1	no	—
289	C₂×C₈	—	236	1	no	—
290	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
291	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
292	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
293	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
294	C₄⋊C₄	—	59	1	no	—
295	C₄⋊C₄	—	59	1	no	—
296	C₄⋊C₄	—	59	1	no	—
297	C₄⋊C₄	—	59	1	no	—
298	C₄⋊C₄	—	59	1	no	—
299	C₄⋊C₄	C₄×D₅₉	1	1	yes	characteristic
300	C₂²⋊C₄	—	59	1	no	—
301	C₂²⋊C₄	—	59	1	no	—
302	C₂²⋊C₄	—	59	1	no	—
303	C₂²⋊C₄	—	59	1	no	—
304	C₂²⋊C₄	—	59	1	no	—
305	C₂²⋊C₄	—	59	1	no	—
306	C₂²⋊C₄	—	59	1	no	—
307	C₂²⋊C₄	—	59	1	no	—
308	C₂²⋊C₄	C₄×D₅₉	1	1	yes	characteristic
309	C₂²⋊C₄	C₄×D₅₉	1	1	yes	characteristic
310	C₄²	—	59	1	no	—
311	C₄²	C₂²×D₅₉	1	1	yes	characteristic
312	C₂³	—	59	1	no	—
313	C₂³	—	59	1	no	—
314	C₂³	—	59	1	no	—
315	C₂³	—	118	2	no	—
316	C₂³	—	118	2	no	—
317	C₂³	—	236	1	no	—
318	C₂³	C₂×C₄×D₅₉	1	1	yes	characteristic
319	C₂³	C₂×C₄×D₅₉	1	1	yes	characteristic
320	Q₈	—	236	1	no	—
321	D₄	—	2	2	no	—
322	D₄	—	118	2	no	—
323	D₄	—	118	2	no	—
324	D₄	—	118	2	no	—
325	D₄	—	236	1	no	—
326	D₄	—	236	1	no	—
327	D₄	—	236	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	59	1	no	—
333	C₂×C₄	—	59	1	no	—
334	C₂×C₄	—	59	1	no	—
335	C₂×C₄	—	59	1	no	—
336	C₂×C₄	—	59	1	no	—
337	C₂×C₄	—	118	1	no	—
338	C₂×C₄	—	118	1	no	—
339	C₂×C₄	—	118	1	no	—
340	C₂×C₄	—	118	1	no	—
341	C₂×C₄	—	118	1	no	—
342	C₂×C₄	—	118	1	no	—
343	C₂×C₄	—	236	1	no	—
344	C₂×C₄	—	236	1	no	—
345	C₂×C₄	—	236	1	no	—
346	C₂×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
347	C₂×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
348	C₂×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
349	C₂×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
350	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
351	C₈	—	2	1	no	—
352	C₈	—	2	1	no	—
353	C₈	—	2	1	no	—
354	C₈	—	2	1	no	—
355	C₈	—	118	1	no	—
356	C₈	—	118	1	no	—
357	C₈	—	118	1	no	—
358	C₈	—	118	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	59	2	no	—
365	C₂²	—	118	1	no	—
366	C₂²	—	118	1	no	—
367	C₂²	—	118	1	no	—
368	C₂²	—	118	1	no	—
369	C₂²	—	118	1	no	—
370	C₂²	—	118	1	no	—
371	C₂²	—	118	1	no	—
372	C₂²	—	118	1	no	—
373	C₂²	—	236	4	no	—
374	C₂²	#14273735	1	2	yes	—
375	C₂²	C₂²×C₄×D₅₉	1	1	yes	characteristic
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	118	1	no	—
381	C₄	—	118	1	no	—
382	C₄	—	118	1	no	—
383	C₄	—	118	1	no	—
384	C₄	—	118	1	no	—
385	C₄	#14273772	1	1	yes	characteristic
386	C₄	#14273773	1	1	yes	characteristic
387	C₂	—	2	2	no	—
388	C₂	—	4	1	no	—
389	C₂	—	118	2	no	—
390	C₂	—	236	1	no	—
391	C₂	—	236	1	no	—
392	C₂	#16837874	1	1	yes	characteristic
393	C₂	#131×D₅₉	1	1	yes	characteristic
394	C₂	C₂×#14273735	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₅₉
commutator, socle	C₂²×C₅₉	C₂³×C₄
Fitting	C₅₉×#435	C₂
hypercenter	#435	D₅₉
hypocenter	C₅₉	#2977
LCS	G ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
2. #16837475	C₂	semidirect
3. #16837471	C₂	semidirect
4. #16837470	C₂	semidirect
5. D₄×C₅₉⋊C₈	C₂	semidirect
6. #16837467	C₂	semidirect
7. C₈×C₂²⋊D₅₉	C₂	semidirect
8. (C₂²⋊D₅₉)⋊C₈	C₂	semidirect
9. #16837464	C₂	semidirect
10. #16837462	C₂	semidirect
11. #16837370	C₂	semidirect
12. #16837367	C₂	semidirect
13. C₂×(C₂×D₅₉)⋊C₈	C₂	semidirect
14. C₂²⋊C₈×D₅₉	C₂	semidirect
15. C₅₉×#435	C₂	semidirect
18. C₂×#11745659	C₂²	semidirect
20. C₂²×C₅₉⋊C₈	C₂²	semidirect
23. C₂×C₈×D₅₉	C₂²	semidirect
36. C₄⋊(C₅₉⋊C₈)	C₂²	semidirect
37. Dic₅₉⋊C₈	C₂²	semidirect
38. Dic₅₉⋊C₈	C₂²	semidirect
40. C₂²⋊(C₅₉⋊C₈)	C₂²	semidirect
47. (C₂×D₅₉)⋊C₈	C₂²	semidirect
48. (C₂×D₅₉)⋊C₈	C₂²	semidirect
49. #14273637	C₂²	semidirect
50. C₄×C₅₉⋊C₈	C₂²	semidirect
51. C₈×Dic₅₉	C₂²	semidirect
52. C₂×M₁₆×C₅₉	C₂²	semidirect
55. C₄⋊C₈×C₅₉	C₂²	semidirect
57. C₂²⋊C₈×C₅₉	C₂²	semidirect
58. #97×C₅₉	C₂²	semidirect
202. #435	D₅₉	semidirect
213. C₅₉	#2977	semidirect
217. C₂×M₁₆	C₂×D₅₉	semidirect
240. C₄⋊C₈	C₂×D₅₉	semidirect
252. C₂²⋊C₈	C₂×D₅₉	semidirect
254. #97	C₂×D₅₉	semidirect