Subgroups — #28571446

Order 15104.

598 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21434682	C₂	1	1	yes	maximal, characteristic, complemented
2	#21434167	C₂	1	2	yes	maximal
3	#21423650	C₂	1	2	yes	maximal, complemented
4	#21423643	C₂	1	2	yes	maximal, complemented
5	#21423614	C₂	1	1	yes	maximal, characteristic, complemented
6	#21423609	C₂	1	1	yes	maximal, characteristic, complemented
7	#21423590	C₂	1	1	yes	maximal, characteristic, complemented
8	#21423585	C₂	1	1	yes	maximal, characteristic, complemented
9	#21422844	C₂	1	1	yes	maximal, characteristic, complemented
10	#21422760	C₂	1	2	yes	maximal, complemented
11	C₅₉×#2965	C₂	1	1	yes	maximal, characteristic
12	#16837959	C₂²	1	2	yes	—
13	#16837807	C₂²	1	1	yes	characteristic
14	#16837782	C₂²	1	1	yes	characteristic
15	#16837753	C₂²	1	2	yes	—
16	#16837743	—	2	2	no	—
17	#16837687	C₂²	1	2	yes	—
18	#16837682	C₂²	1	2	yes	—
19	#16837643	—	2	1	no	—
20	#16837643	—	2	1	no	—
21	#16837612	C₂²	1	2	yes	—
22	#16837607	C₂²	1	2	yes	—
23	#16837564	—	2	2	no	—
24	C₄×Dic₂₃₆	—	2	1	no	—
25	C₄×Dic₂₃₆	—	2	1	no	—
26	C₄×#11745672	—	2	2	no	—
27	C₄×#11745670	—	2	2	no	—
28	#16837455	C₂²	1	2	yes	—
29	#16837155	C₂²	1	2	yes	—
30	#16837153	C₂²	1	1	yes	characteristic
31	#16837153	C₂²	1	1	yes	characteristic
32	#16837149	C₂²	1	2	yes	—
33	#16837149	C₂²	1	2	yes	—
34	#16837147	C₂²	1	2	yes	—
35	#16837147	C₂²	1	2	yes	—
36	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
37	C₅₉×#446	C₂²	1	1	yes	characteristic
38	C₅₉×#446	C₂²	1	1	yes	characteristic
39	C₅₉×#436	C₂²	1	1	yes	characteristic
40	C₅₉×#436	C₂²	1	1	yes	characteristic
41	C₅₉×#435	—	2	1	no	—
42	C₅₉×#435	—	2	1	no	—
43	C₅₉×#431	—	2	1	no	—
44	C₅₉×#431	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×C₅₉	—	2	1	no	—
46	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
47	C₂×Dic₂₃₆	—	2	1	no	—
48	C₂×Dic₂₃₆	—	2	1	no	—
49	C₂×#11745672	—	2	2	no	—
50	C₂×#11745670	—	2	2	no	—
51	#14273727	C₂³	1	2	yes	—
52	#14273727	C₂³	1	2	yes	—
53	#14273719	—	2	2	no	—
54	#14273706	—	2	2	no	—
55	#14273706	—	2	2	no	—
56	C₄×Dic₁₁₈	—	2	2	no	—
57	C₄×Dic₁₁₈	—	2	2	no	—
58	#14273686	—	2	2	no	—
59	#14273661	—	2	1	no	—
60	#14273661	—	2	1	no	—
61	#14273660	—	2	2	no	—
62	#14273658	—	2	2	no	—
63	C₄⋊(C₅₉⋊C₈)	C₂³	1	2	yes	—
64	C₄⋊(C₅₉⋊C₈)	C₂³	1	2	yes	—
65	#14273652	—	2	2	no	—
66	#14273652	—	2	2	no	—
67	#14273651	—	2	2	no	—
68	#14273650	—	2	2	no	—
69	#14273650	—	2	2	no	—
70	#14273648	—	2	2	no	—
71	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
72	C₄×C₅₉⋊C₈	—	2	2	no	—
73	C₂×#41×C₅₉	D₄	1	1	yes	characteristic
74	C₂×M₁₆×C₅₉	—	2	1	no	—
75	C₂×M₁₆×C₅₉	—	2	1	no	—
76	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
77	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
78	C₄×Q₈×C₅₉	D₄	1	1	yes	characteristic
79	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
80	C₄×D₄×C₅₉	—	2	1	no	—
81	C₄×D₄×C₅₉	—	2	1	no	—
82	C₄×D₄×C₅₉	D₄	1	1	yes	characteristic
83	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
84	#117×C₅₉	—	2	1	no	—
85	#117×C₅₉	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₅₉	—	2	1	no	—
87	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₅₉	—	2	1	no	—
89	C₄⋊C₈×C₅₉	—	2	1	no	—
90	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
92	C₂²⋊C₈×C₅₉	—	2	1	no	—
93	C₂²⋊C₈×C₅₉	—	2	1	no	—
94	C₂²⋊C₈×C₅₉	—	2	1	no	—
95	#97×C₅₉	—	2	1	no	—
96	#97×C₅₉	—	2	1	no	—
97	C₄×C₈×C₅₉	—	2	1	no	—
98	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
99	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
100	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
102	#41×C₅₉	—	4	2	no	—
103	C₂×Q₈×C₅₉	C₂×D₄	1	1	yes	characteristic
104	C₂×D₄×C₅₉	—	2	1	no	—
105	C₂×D₄×C₅₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₅₉	—	2	1	no	—
107	C₂²×C₄×C₅₉	—	2	1	no	—
108	C₂²×C₄×C₅₉	—	2	1	no	—
109	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
112	C₂×Dic₁₁₈	—	2	2	no	—
113	C₂×Dic₁₁₈	—	2	2	no	—
114	M₁₆×C₅₉	—	4	2	no	—
115	M₁₆×C₅₉	—	4	2	no	—
116	C₂×C₈×C₅₉	—	2	2	no	—
117	C₂×C₈×C₅₉	—	2	1	no	—
118	C₂×C₈×C₅₉	—	2	1	no	—
119	C₂×C₈×C₅₉	—	4	1	no	—
120	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
124	C₄⋊C₄×C₅₉	—	2	1	no	—
125	C₄⋊C₄×C₅₉	—	2	1	no	—
126	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
127	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
128	C₂²⋊C₄×C₅₉	—	2	1	no	—
129	C₂²⋊C₄×C₅₉	—	2	1	no	—
130	C₂²⋊C₄×C₅₉	—	2	1	no	—
131	C₄²×C₅₉	—	2	1	no	—
132	C₄²×C₅₉	—	2	1	no	—
133	C₄²×C₅₉	—	2	1	no	—
134	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₅₉	#41	1	1	yes	characteristic
137	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
138	C₂²⋊Dic₅₉	—	4	2	no	—
139	#11745672	—	4	4	no	—
140	#11745670	—	4	4	no	—
141	C₄⋊Dic₅₉	—	2	2	no	—
142	C₄⋊Dic₅₉	—	2	2	no	—
143	C₄⋊Dic₅₉	—	2	2	no	—
144	C₄⋊Dic₅₉	—	2	2	no	—
145	Dic₅₉⋊C₄	—	4	2	no	—
146	Dic₅₉⋊C₄	—	4	2	no	—
147	C₄×Dic₅₉	—	4	2	no	—
148	C₂×C₅₉⋊C₈	—	2	2	no	—
149	C₂×C₅₉⋊C₈	—	2	2	no	—
150	Dic₂₃₆	—	4	2	no	—
151	Dic₂₃₆	—	4	2	no	—
152	C₂³×C₅₉	—	2	1	no	—
153	C₂³×C₅₉	#121	1	1	yes	characteristic
154	Q₈×C₅₉	—	2	2	no	—
155	D₄×C₅₉	—	2	2	no	—
156	D₄×C₅₉	—	4	2	no	—
157	C₂×C₄×C₅₉	—	2	1	no	—
158	C₂×C₄×C₅₉	—	2	1	no	—
159	C₂×C₄×C₅₉	—	2	2	no	—
160	C₂×C₄×C₅₉	—	2	2	no	—
161	C₂×C₄×C₅₉	—	2	1	no	—
162	C₂×C₄×C₅₉	—	2	1	no	—
163	C₂×C₄×C₅₉	—	2	1	no	—
164	C₂×C₄×C₅₉	—	4	2	no	—
165	C₂×C₄×C₅₉	—	4	1	no	—
166	C₂×C₄×C₅₉	—	4	1	no	—
167	C₂×C₄×C₅₉	—	4	2	no	—
168	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
169	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
170	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
171	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
174	C₂×Dic₅₉	—	4	2	no	—
175	C₂×Dic₅₉	—	4	2	no	—
176	Dic₁₁₈	—	4	2	no	—
177	Dic₁₁₈	—	4	2	no	—
178	Dic₁₁₈	—	4	2	no	—
179	Dic₁₁₈	—	4	2	no	—
180	C₈×C₅₉	—	2	1	no	—
181	C₈×C₅₉	—	2	1	no	—
182	C₈×C₅₉	—	2	1	no	—
183	C₈×C₅₉	—	4	1	no	—
184	C₈×C₅₉	—	4	1	no	—
185	C₈×C₅₉	#135	1	2	yes	—
186	C₅₉⋊C₈	—	4	2	no	—
187	C₅₉⋊C₈	—	4	2	no	—
188	#19161	—	59	1	no	maximal, Sylow
189	C₂²×C₅₉	—	2	1	no	—
190	C₂²×C₅₉	—	2	1	no	—
191	C₂²×C₅₉	—	2	1	no	—
192	C₂²×C₅₉	—	4	1	no	—
193	C₂²×C₅₉	—	4	1	no	—
194	C₂²×C₅₉	—	4	1	no	—
195	C₂²×C₅₉	C₂×#121	1	1	yes	characteristic
196	C₄×C₅₉	—	2	1	no	—
197	C₄×C₅₉	—	2	1	no	—
198	C₄×C₅₉	—	2	1	no	—
199	C₄×C₅₉	—	4	1	no	—
200	C₄×C₅₉	—	4	1	no	—
201	C₄×C₅₉	—	4	1	no	—
202	C₄×C₅₉	#473	1	2	yes	—
203	C₄×C₅₉	C₂×#135	1	1	yes	characteristic
204	C₄×C₅₉	#575	1	1	yes	characteristic
205	C₄×C₅₉	#575	1	2	yes	—
206	Dic₅₉	—	8	2	no	—
207	Dic₅₉	—	8	2	no	—
208	#3170	—	59	1	no	—
209	#3107	—	59	2	no	—
210	#2965	D₅₉	1	1	yes	characteristic
211	#1700	—	59	2	no	—
212	#1699	—	59	2	no	—
213	#1694	—	59	1	no	—
214	#1693	—	59	1	no	—
215	#1690	—	59	1	no	—
216	#1689	—	59	1	no	—
217	#1564	—	59	1	no	—
218	#1544	—	59	2	no	—
219	C₂×C₅₉	—	4	1	no	—
220	C₂×C₅₉	—	8	1	no	—
221	C₂×C₅₉	#3035	1	1	yes	characteristic
222	C₂×C₅₉	#3054	1	1	yes	characteristic
223	C₂×C₅₉	C₂×#473	1	1	yes	characteristic
224	#533	—	59	2	no	—
225	C₄×#41	C₂×D₅₉	1	1	yes	characteristic
226	#500	—	59	1	no	—
227	#494	—	59	1	no	—
228	#487	—	59	2	no	—
229	#485	—	118	2	no	—
230	#475	—	59	2	no	—
231	#474	—	59	2	no	—
232	#467	—	118	1	no	—
233	#467	—	118	1	no	—
234	#462	—	59	2	no	—
235	#461	—	59	2	no	—
236	#452	—	118	2	no	—
237	#446	C₂×D₅₉	1	1	yes	characteristic
238	#446	C₂×D₅₉	1	1	yes	characteristic
239	C₄×Q₁₆	—	118	2	no	—
240	C₄×Q₁₆	—	118	1	no	—
241	C₄×Q₁₆	—	118	1	no	—
242	C₄×SD₁₆	—	118	2	no	—
243	#436	C₂×D₅₉	1	1	yes	characteristic
244	#436	C₂×D₅₉	1	1	yes	characteristic
245	#435	—	2	1	no	—
246	#435	—	2	1	no	—
247	#431	—	2	1	no	—
248	#431	—	59	2	no	—
249	#431	C₂×D₅₉	1	1	yes	characteristic
250	C₄×M₁₆	—	2	1	no	—
251	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
252	#335	—	59	2	no	—
253	#334	—	59	1	no	—
254	#334	—	59	1	no	—
255	#332	—	59	2	no	—
256	#332	—	59	2	no	—
257	#332	—	59	2	no	—
258	#332	—	59	2	no	—
259	C₅₉	#19161	1	1	yes	characteristic, complemented, Sylow
260	C₂×#41	D₂₃₆	1	1	yes	characteristic
261	C₂×Q₁₆	—	118	2	no	—
262	C₂×Q₁₆	—	118	1	no	—
263	C₂×Q₁₆	—	118	1	no	—
264	C₂×SD₁₆	—	118	2	no	—
265	C₂×M₁₆	—	2	1	no	—
266	C₂×M₁₆	—	2	1	no	—
267	C₂²×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
268	C₂²×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
269	C₄⋊Q₈	—	59	2	no	—
270	C₄⋊Q₈	—	59	2	no	—
271	#125	—	118	2	no	—
272	C₂²⋊Q₈	—	118	2	no	—
273	C₂²⋊Q₈	—	118	2	no	—
274	C₄×Q₈	—	118	2	no	—
275	C₄×Q₈	—	118	2	no	—
276	C₄×Q₈	D₂₃₆	1	1	yes	characteristic
277	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
278	C₄×D₄	—	2	1	no	—
279	C₄×D₄	—	2	1	no	—
280	C₄×D₄	D₂₃₆	1	1	yes	characteristic
281	C₄×D₄	C₂²×D₅₉	1	1	yes	characteristic
282	#117	—	2	1	no	—
283	#117	—	118	2	no	—
284	#117	D₂₃₆	1	1	yes	characteristic
285	C₂×C₄²	—	2	1	no	—
286	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
287	#107	—	118	1	no	—
288	#107	—	118	1	no	—
289	#107	—	118	2	no	—
290	#106	—	118	2	no	—
291	C₄⋊C₈	—	2	1	no	—
292	C₄⋊C₈	—	2	1	no	—
293	C₄⋊C₈	—	59	2	no	—
294	C₄⋊C₈	—	59	2	no	—
295	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
296	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
297	#103	—	118	2	no	—
298	#103	—	118	2	no	—
299	#103	—	118	2	no	—
300	#103	—	118	2	no	—
301	#103	—	118	2	no	—
302	#102	—	118	2	no	—
303	C₂²⋊C₈	—	2	1	no	—
304	C₂²⋊C₈	—	2	1	no	—
305	C₂²⋊C₈	—	2	1	no	—
306	C₂²⋊C₈	—	118	2	no	—
307	#97	—	2	1	no	—
308	#97	—	2	1	no	—
309	C₄×C₈	—	2	1	no	—
310	C₄×C₈	—	118	2	no	—
311	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
312	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
313	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
314	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
315	#41	—	4	2	no	—
316	C₂×Q₈	—	118	2	no	—
317	C₂×Q₈	—	118	2	no	—
318	C₂×Q₈	C₂×D₂₃₆	1	1	yes	characteristic
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	C₂×D₂₃₆	1	1	yes	characteristic
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	C₂×D₂₃₆	1	1	yes	characteristic
325	C₂²×C₄	#11745685	1	1	yes	characteristic
326	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
327	Q₁₆	—	236	2	no	—
328	Q₁₆	—	236	4	no	—
329	Q₁₆	—	236	2	no	—
330	SD₁₆	—	236	4	no	—
331	M₁₆	—	4	2	no	—
332	M₁₆	—	4	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	4	1	no	—
337	C₂×C₈	—	118	2	no	—
338	C₂×C₈	—	118	2	no	—
339	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
340	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
341	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
342	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	118	2	no	—
346	C₄⋊C₄	—	118	2	no	—
347	C₄⋊C₄	—	118	2	no	—
348	C₄⋊C₄	—	118	2	no	—
349	C₄⋊C₄	—	236	2	no	—
350	C₄⋊C₄	—	236	2	no	—
351	C₄⋊C₄	C₂×D₂₃₆	1	1	yes	characteristic
352	C₄⋊C₄	C₂×D₂₃₆	1	1	yes	characteristic
353	C₂²⋊C₄	—	2	1	no	—
354	C₂²⋊C₄	—	2	1	no	—
355	C₂²⋊C₄	—	2	1	no	—
356	C₂²⋊C₄	—	236	2	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	236	2	no	—
361	C₄²	C₂×D₂₃₆	1	1	yes	characteristic
362	C₄²	#11745685	1	1	yes	characteristic
363	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
364	C₄²	C₂³×D₅₉	1	1	yes	characteristic
365	C₂³	—	2	1	no	—
366	C₂³	#14273701	1	1	yes	characteristic
367	Q₈	—	2	2	no	—
368	Q₈	—	236	2	no	—
369	Q₈	—	236	2	no	—
370	Q₈	—	236	2	no	—
371	Q₈	—	236	2	no	—
372	D₄	—	2	2	no	—
373	D₄	—	4	2	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	236	2	no	—
386	C₂×C₄	—	236	2	no	—
387	C₂×C₄	#14273701	1	1	yes	characteristic
388	C₂×C₄	#14273701	1	1	yes	characteristic
389	C₂×C₄	#14273701	1	1	yes	characteristic
390	C₂×C₄	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
391	C₂×C₄	C₂²×D₂₃₆	1	1	yes	characteristic
392	C₂×C₄	C₂×#11745685	1	1	yes	characteristic
393	C₈	—	2	1	no	—
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	—	4	1	no	—
397	C₈	—	4	1	no	—
398	C₈	—	236	2	no	—
399	C₈	—	236	2	no	—
400	C₈	#14273747	1	2	yes	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	—	4	1	no	—
407	C₂²	C₂×#14273701	1	1	yes	characteristic
408	C₄	—	2	1	no	—
409	C₄	—	2	1	no	—
410	C₄	—	2	1	no	—
411	C₄	—	4	1	no	—
412	C₄	—	4	1	no	—
413	C₄	—	4	1	no	—
414	C₄	—	472	2	no	—
415	C₄	—	472	2	no	—
416	C₄	#16837677	1	2	yes	—
417	C₄	C₂×#14273747	1	1	yes	characteristic
418	C₄	#16838200	1	1	yes	characteristic
419	C₄	#16838202	1	2	yes	—
420	C₂	—	4	1	no	—
421	C₂	—	8	1	no	—
422	C₂	#21433551	1	1	yes	characteristic
423	C₂	#21433705	1	1	yes	characteristic
424	C₂	C₂×#16837677	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14273701
commutator, cosocle	C₄²×C₅₉	C₂⁴
Frattini	C₄²	C₂³×D₅₉
Fitting	C₅₉×#2965	C₂
socle	C₂²×C₅₉	C₂×#121
prime radical	C₂×#41×C₅₉	D₄
hypercenter	#2965	D₅₉
hypocenter	C₅₉	#19161
LCS	G ▷ C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2965

Complements

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

N	H ≅ G/N	type
1. #21434682	C₂	semidirect
3. #21423650	C₂	semidirect
4. #21423643	C₂	semidirect
5. #21423614	C₂	semidirect
6. #21423609	C₂	semidirect
7. #21423590	C₂	semidirect
8. #21423585	C₂	semidirect
9. #21422844	C₂	semidirect
10. #21422760	C₂	semidirect
259. C₅₉	#19161	semidirect

Maximal subgroups

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

subgroup	index
#21434682	2
#21434167	2
#21423650	2
#21423643	2
#21423614	2
#21423609	2
#21423590	2
#21423585	2
#21422844	2
#21422760	2
C₅₉×#2965	2
#19161	59