Subgroups — #28607210

Order 15104.

812 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433014	C₂	1	1	yes	maximal, characteristic
2	#21433012	C₂	1	1	yes	maximal, characteristic
3	C₂×#16837518	C₂	1	1	yes	maximal, characteristic
4	#21432706	C₂	1	2	yes	maximal, complemented
5	#21424887	C₂	1	1	yes	maximal, characteristic, complemented
6	#21424339	C₂	1	2	yes	maximal, complemented
7	#21424333	C₂	1	2	yes	maximal, complemented
8	#21424266	C₂	1	1	yes	maximal, characteristic, complemented
9	#21424149	C₂	1	2	yes	maximal, complemented
10	#21423976	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#1953	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14273749	C₂²	1	1	yes	characteristic
13	#16838168	C₂²	1	2	yes	—
14	#16838168	C₂²	1	2	yes	—
15	C₂×#14273735	C₂²	1	2	yes	—
16	#16837525	—	2	2	no	—
17	#16837523	—	2	2	no	—
18	#16837520	—	2	2	no	—
19	#16837518	—	2	2	no	—
20	#16837518	C₄	1	2	yes	complemented
21	#16837518	C₄	1	2	yes	complemented
22	#16837518	C₄	1	2	yes	complemented
23	#16837518	C₄	1	2	yes	complemented
24	#16837451	C₂²	1	2	yes	—
25	#16837449	—	2	4	no	—
26	C₂×#14273663	C₂²	1	1	yes	characteristic
27	C₂×#14273662	C₂²	1	2	yes	—
28	C₂×#14273662	C₂²	1	1	yes	characteristic
29	#108×D₅₉	—	2	4	no	—
30	#16837438	C₂²	1	1	yes	characteristic
31	#16837425	C₂²	1	2	yes	—
32	#16837420	C₂²	1	2	yes	—
33	#16837418	C₂²	1	2	yes	—
34	C₂×#14273653	C₂²	1	2	yes	—
35	#16837357	C₂²	1	1	yes	characteristic
36	C₂×C₈×Dic₅₉	C₂²	1	1	yes	characteristic
37	#16837174	C₂²	1	2	yes	—
38	#16837163	C₂²	1	1	yes	characteristic
39	#16837161	C₂²	1	1	yes	characteristic
40	C₅₉×#430	C₂²	1	2	yes	—
41	C₂×#108×C₅₉	C₂²	1	1	yes	characteristic
42	C₂×#108×C₅₉	C₂²	1	1	yes	characteristic
43	C₅₉×#405	C₂²	1	1	yes	characteristic
44	C₅₉×#344	C₂²	1	2	yes	—
45	C₂×#11745685	C₂³	1	2	yes	—
46	#14273749	C₂×C₄	1	2	yes	—
47	#14273749	C₂×C₄	1	2	yes	—
48	#14273749	D₄	1	2	yes	—
49	#14273749	D₄	1	2	yes	—
50	C₂×Dic₂₃₆	Q₈	1	1	yes	characteristic
51	C₂×#11745660	Q₈	1	2	yes	—
52	C₂×D₄₇₂	Q₈	1	1	yes	characteristic
53	#14273735	—	2	2	no	—
54	#14273735	—	2	2	no	—
55	#14273735	—	2	4	no	—
56	#14273735	—	4	2	no	—
57	#14273735	C₂×C₄	1	4	yes	—
58	#14273735	C₂×C₄	1	4	yes	—
59	#14273733	—	2	4	no	—
60	#14273733	—	4	2	no	—
61	C₂×#11745664	C₂³	1	2	yes	—
62	C₂×#11745664	C₂³	1	1	yes	characteristic
63	C₂×#11745659	—	2	2	no	—
64	M₁₆×D₅₉	—	2	4	no	—
65	M₁₆×D₅₉	—	2	4	no	—
66	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
67	C₂×C₈×D₅₉	—	2	2	no	—
68	#14273686	C₂³	1	1	yes	characteristic
69	C₂×C₄×Dic₅₉	C₂³	1	1	yes	characteristic
70	#14273663	—	2	1	no	—
71	#14273663	—	2	1	no	—
72	#14273663	—	2	4	no	—
73	#14273662	—	2	2	no	—
74	#14273662	—	2	2	no	—
75	#14273662	D₄	1	2	yes	—
76	#14273662	D₄	1	2	yes	—
77	#14273660	—	2	1	no	—
78	#14273658	—	2	1	no	—
79	Dic₅₉⋊C₈	—	4	2	no	—
80	#14273655	—	2	4	no	—
81	#14273653	—	2	4	no	—
82	#14273653	C₂×C₄	1	4	yes	—
83	#14273653	C₂×C₄	1	4	yes	—
84	#14273637	—	2	1	no	—
85	C₈×Dic₅₉	—	2	1	no	—
86	C₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
87	C₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
88	C₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
89	C₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
90	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
91	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
92	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
94	#117×C₅₉	C₂³	1	1	yes	characteristic
95	#108×C₅₉	—	2	4	no	—
96	#108×C₅₉	—	2	1	no	—
97	#108×C₅₉	—	2	1	no	—
98	#108×C₅₉	C₂×C₄	1	2	yes	—
99	#108×C₅₉	C₂×C₄	1	2	yes	—
100	#97×C₅₉	—	2	1	no	—
101	C₄×C₈×C₅₉	—	2	1	no	—
102	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
103	C₂×C₂²⋊D₅₉	—	2	2	no	—
104	C₂²×Dic₅₉	—	2	1	no	—
105	#11745685	—	2	2	no	—
106	#11745685	—	2	2	no	—
107	#11745685	C₂²×C₄	1	4	yes	—
108	#11745685	C₂×D₄	1	4	yes	—
109	C₂×D₂₃₆	C₂×Q₈	1	2	yes	—
110	C₂×C₄×D₅₉	—	2	2	no	—
111	C₂×Dic₁₁₈	C₂×Q₈	1	2	yes	—
112	M₁₆×C₅₉	—	2	2	no	—
113	M₁₆×C₅₉	—	2	1	no	—
114	M₁₆×C₅₉	—	2	2	no	—
115	M₁₆×C₅₉	—	2	2	no	—
116	M₁₆×C₅₉	C₂²×C₄	1	4	yes	—
117	M₁₆×C₅₉	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₅₉	—	2	1	no	—
119	C₂×C₈×C₅₉	—	2	2	no	—
120	C₂×C₈×C₅₉	—	2	2	no	—
121	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₅₉	C₂×Q₈	1	1	yes	characteristic
126	C₂×C₈×C₅₉	C₂×Q₈	1	1	yes	characteristic
127	C₄⋊C₄×C₅₉	—	2	1	no	—
128	C₂²⋊C₄×C₅₉	—	2	1	no	—
129	C₄²×C₅₉	—	2	1	no	—
130	C₂²⋊Dic₅₉	—	2	1	no	—
131	C₄⋊Dic₅₉	—	2	1	no	—
132	C₄×Dic₅₉	—	2	1	no	—
133	C₄×Dic₅₉	—	2	1	no	—
134	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
135	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
136	#11745664	—	2	1	no	—
137	#11745664	—	2	2	no	—
138	#11745664	—	2	2	no	—
139	#11745664	C₂×D₄	1	2	yes	—
140	C₂×C₅₉⋊C₈	—	2	1	no	—
141	C₂×C₅₉⋊C₈	—	2	2	no	—
142	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
145	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
146	C₂×C₅₉⋊C₈	#41	1	1	yes	characteristic
147	C₂×C₅₉⋊C₈	#41	1	1	yes	characteristic
148	Dic₂₃₆	C₄⋊C₄	1	2	yes	—
149	Dic₂₃₆	C₄⋊C₄	1	2	yes	—
150	D₄₇₂	C₄⋊C₄	1	2	yes	—
151	D₄₇₂	C₄⋊C₄	1	2	yes	—
152	#11745660	C₄⋊C₄	1	4	yes	—
153	#11745660	C₄⋊C₄	1	4	yes	—
154	#11745659	—	2	4	no	—
155	#11745659	—	2	4	no	—
156	#11745659	—	4	4	no	—
157	#11745659	—	4	4	no	—
158	C₈×D₅₉	—	2	4	no	—
159	C₈×D₅₉	—	2	4	no	—
160	C₈×D₅₉	—	4	4	no	—
161	C₈×D₅₉	—	4	4	no	—
162	C₂³×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
163	C₂²×D₅₉	—	2	2	no	—
164	C₂×C₄×C₅₉	—	4	1	no	—
165	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
169	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
171	C₂²⋊D₅₉	—	2	4	no	—
172	C₂²⋊D₅₉	—	2	4	no	—
173	C₂×Dic₅₉	—	2	1	no	—
174	C₂×Dic₅₉	—	2	2	no	—
175	C₂×Dic₅₉	—	2	1	no	—
176	C₂×Dic₅₉	—	4	2	no	—
177	C₂×Dic₅₉	—	4	1	no	—
178	D₂₃₆	—	2	2	no	—
179	D₂₃₆	C₂×C₄⋊C₄	1	4	yes	—
180	C₄×D₅₉	—	2	4	no	—
181	C₄×D₅₉	—	2	4	no	—
182	Dic₁₁₈	—	2	2	no	—
183	Dic₁₁₈	C₂×C₄⋊C₄	1	4	yes	—
184	C₈×C₅₉	—	2	4	no	—
185	C₈×C₅₉	—	2	2	no	—
186	C₈×C₅₉	—	4	2	no	—
187	C₈×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₈×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₈×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₈×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₅₉⋊C₈	—	2	2	no	—
192	C₅₉⋊C₈	—	4	2	no	—
193	C₅₉⋊C₈	C₄×D₄	1	1	yes	characteristic
194	C₅₉⋊C₈	C₄×D₄	1	1	yes	characteristic
195	C₅₉⋊C₈	C₄×D₄	1	1	yes	characteristic
196	C₅₉⋊C₈	C₄×D₄	1	1	yes	characteristic
197	#22694	—	59	1	no	maximal, Sylow
198	C₂²×C₅₉	—	4	1	no	—
199	C₂²×C₅₉	#520	1	1	yes	characteristic
200	C₂²×C₅₉	#547	1	1	yes	characteristic
201	C₂²×C₅₉	D₄×Q₈	1	1	yes	characteristic
202	C₂×D₅₉	—	2	4	no	—
203	C₂×D₅₉	—	8	2	no	—
204	C₄×C₅₉	—	8	1	no	—
205	C₄×C₅₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
206	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
207	C₄×C₅₉	D₄²	1	1	yes	characteristic
208	C₄×C₅₉	#554	1	1	yes	characteristic
209	Dic₅₉	—	2	2	no	—
210	Dic₅₉	—	2	4	no	—
211	Dic₅₉	—	4	1	no	—
212	Dic₅₉	—	8	1	no	—
213	#2957	—	59	1	no	—
214	#2957	—	59	1	no	—
215	C₂×#443	—	59	1	no	—
216	#2916	—	59	2	no	—
217	#1953	—	59	1	no	—
218	#1953	D₅₉	1	1	yes	characteristic, complemented
219	#1861	—	59	2	no	—
220	#1861	—	59	2	no	—
221	#1848	—	59	1	no	—
222	#1814	—	59	2	no	—
223	#1772	—	59	1	no	—
224	C₂×C₅₉	—	2	1	no	—
225	C₂×C₅₉	—	2	1	no	—
226	C₂×C₅₉	—	2	1	no	—
227	C₂×C₅₉	D₄×C₄⋊C₄	1	1	yes	characteristic
228	D₅₉	—	4	4	no	—
229	C₂×#135	—	59	1	no	—
230	#568	—	59	2	no	—
231	#568	—	59	2	no	—
232	C₂×#131	—	59	2	no	—
233	#444	—	118	2	no	—
234	#444	—	118	2	no	—
235	#443	—	59	2	no	—
236	#443	—	59	2	no	—
237	#443	—	59	2	no	—
238	#443	—	59	2	no	—
239	#443	—	118	2	no	—
240	#443	—	118	2	no	—
241	#430	—	59	2	no	—
242	#430	—	118	4	no	—
243	#430	C₂×D₅₉	1	2	yes	—
244	C₂×#108	—	59	1	no	—
245	C₂×#108	—	59	2	no	—
246	C₂×#108	—	59	1	no	—
247	C₂×#108	—	118	4	no	—
248	C₂×#108	C₂×D₅₉	1	1	yes	characteristic
249	C₂×#108	C₂×D₅₉	1	1	yes	characteristic
250	#427	—	59	1	no	—
251	#423	—	59	2	no	—
252	#421	—	59	2	no	—
253	#421	—	59	2	no	—
254	C₂×#104	—	59	2	no	—
255	#405	—	59	1	no	—
256	#405	C₂×D₅₉	1	1	yes	characteristic
257	C₂×C₄×C₈	—	59	1	no	—
258	#344	—	59	2	no	—
259	#344	C₂×D₅₉	1	2	yes	—
260	#339	—	59	1	no	—
261	#339	—	59	1	no	—
262	C₅₉	#22694	1	1	yes	characteristic, complemented, Sylow
263	C₂×#41	—	59	2	no	—
264	#135	—	59	2	no	—
265	#135	—	59	2	no	—
266	#135	—	59	2	no	—
267	#135	—	59	2	no	—
268	C₂×Q₁₆	—	59	1	no	—
269	C₂×SD₁₆	—	59	2	no	—
270	C₂×D₈	—	59	1	no	—
271	#131	—	59	4	no	—
272	#131	—	59	4	no	—
273	#131	—	118	4	no	—
274	#131	—	118	2	no	—
275	#131	—	118	2	no	—
276	#131	—	118	4	no	—
277	#131	—	236	2	no	—
278	#131	—	236	2	no	—
279	C₂×M₁₆	—	59	1	no	—
280	C₂×M₁₆	—	59	2	no	—
281	C₂×M₁₆	—	118	2	no	—
282	C₂×M₁₆	—	118	4	no	—
283	C₂×M₁₆	—	118	4	no	—
284	C₂×M₁₆	C₂²×D₅₉	1	2	yes	—
285	C₂×M₁₆	C₂²×D₅₉	1	2	yes	—
286	C₂×M₁₆	C₂²×D₅₉	1	1	yes	characteristic
287	C₂²×C₈	—	59	1	no	—
288	C₂²×C₈	—	118	2	no	—
289	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
290	#117	—	59	1	no	—
291	#117	C₂²×D₅₉	1	1	yes	characteristic
292	C₂×C₄²	—	59	1	no	—
293	#108	—	2	4	no	—
294	#108	—	2	1	no	—
295	#108	—	2	1	no	—
296	#108	—	59	2	no	—
297	#108	—	59	2	no	—
298	#108	—	118	4	no	—
299	#108	—	118	2	no	—
300	#108	—	118	2	no	—
301	#108	—	118	1	no	—
302	#108	—	118	1	no	—
303	#108	C₄×D₅₉	1	2	yes	—
304	#108	C₄×D₅₉	1	2	yes	—
305	#107	—	118	1	no	—
306	#106	—	118	1	no	—
307	C₄⋊C₈	—	236	2	no	—
308	#104	—	59	4	no	—
309	#104	—	59	4	no	—
310	#104	—	118	4	no	—
311	#104	—	118	4	no	—
312	#97	—	2	1	no	—
313	#97	—	118	1	no	—
314	C₄×C₈	—	2	1	no	—
315	C₄×C₈	—	59	1	no	—
316	C₄×C₈	—	59	1	no	—
317	C₄×C₈	—	59	1	no	—
318	C₄×C₈	—	59	1	no	—
319	C₄×C₈	—	118	1	no	—
320	#41	—	59	4	no	—
321	#41	—	59	4	no	—
322	#41	—	118	2	no	—
323	#41	—	118	2	no	—
324	C₂×Q₈	—	59	2	no	—
325	C₂×D₄	—	59	2	no	—
326	C₂×D₄	—	118	2	no	—
327	C₂²×C₄	—	118	2	no	—
328	C₂²×C₄	—	118	1	no	—
329	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
330	Q₁₆	—	59	2	no	—
331	Q₁₆	—	59	2	no	—
332	SD₁₆	—	59	4	no	—
333	SD₁₆	—	59	4	no	—
334	D₈	—	59	2	no	—
335	D₈	—	59	2	no	—
336	M₁₆	—	2	2	no	—
337	M₁₆	—	2	1	no	—
338	M₁₆	—	2	2	no	—
339	M₁₆	—	2	2	no	—
340	M₁₆	—	59	2	no	—
341	M₁₆	—	118	4	no	—
342	M₁₆	—	118	4	no	—
343	M₁₆	—	118	1	no	—
344	M₁₆	—	118	2	no	—
345	M₁₆	—	118	2	no	—
346	M₁₆	—	236	4	no	—
347	M₁₆	—	236	4	no	—
348	M₁₆	C₂×C₄×D₅₉	1	4	yes	—
349	M₁₆	D₄×D₅₉	1	2	yes	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	59	1	no	—
354	C₂×C₈	—	59	1	no	—
355	C₂×C₈	—	59	1	no	—
356	C₂×C₈	—	59	1	no	—
357	C₂×C₈	—	59	1	no	—
358	C₂×C₈	—	59	1	no	—
359	C₂×C₈	—	118	4	no	—
360	C₂×C₈	—	118	4	no	—
361	C₂×C₈	—	118	1	no	—
362	C₂×C₈	—	118	2	no	—
363	C₂×C₈	—	236	4	no	—
364	C₂×C₈	—	236	4	no	—
365	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
366	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
367	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
368	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
369	C₂×C₈	Q₈×D₅₉	1	1	yes	characteristic
370	C₂×C₈	Q₈×D₅₉	1	1	yes	characteristic
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	118	1	no	—
373	C₂²⋊C₄	—	2	1	no	—
374	C₂²⋊C₄	—	118	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	59	1	no	—
377	C₄²	—	59	1	no	—
378	C₄²	—	118	1	no	—
379	C₄²	—	118	1	no	—
380	C₂³	—	118	2	no	—
381	C₂³	#14273775	1	1	yes	characteristic
382	Q₈	—	59	4	no	—
383	Q₈	—	118	2	no	—
384	D₄	—	59	4	no	—
385	D₄	—	118	4	no	—
386	D₄	—	118	4	no	—
387	D₄	—	118	2	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	118	2	no	—
390	C₂×C₄	—	118	1	no	—
391	C₂×C₄	—	118	4	no	—
392	C₂×C₄	—	118	4	no	—
393	C₂×C₄	—	118	1	no	—
394	C₂×C₄	—	236	2	no	—
395	C₂×C₄	—	236	1	no	—
396	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
397	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
398	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
399	C₂×C₄	C₂×Q₈×D₅₉	1	1	yes	characteristic
400	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
401	C₂×C₄	#14273773	1	1	yes	characteristic
402	C₈	—	2	2	no	—
403	C₈	—	2	4	no	—
404	C₈	—	4	2	no	—
405	C₈	—	59	1	no	—
406	C₈	—	59	1	no	—
407	C₈	—	59	1	no	—
408	C₈	—	59	1	no	—
409	C₈	—	118	2	no	—
410	C₈	—	236	2	no	—
411	C₈	C₄⋊C₄×D₅₉	1	1	yes	characteristic
412	C₈	C₄⋊C₄×D₅₉	1	1	yes	characteristic
413	C₈	C₄⋊C₄×D₅₉	1	1	yes	characteristic
414	C₈	C₄⋊C₄×D₅₉	1	1	yes	characteristic
415	C₂²	—	4	1	no	—
416	C₂²	—	118	4	no	—
417	C₂²	—	472	2	no	—
418	C₂²	#16837884	1	1	yes	characteristic
419	C₂²	#16838054	1	1	yes	characteristic
420	C₂²	#16838067	1	1	yes	characteristic
421	C₄	—	8	1	no	—
422	C₄	—	118	2	no	—
423	C₄	—	118	4	no	—
424	C₄	—	472	1	no	—
425	C₄	—	236	1	no	—
426	C₄	C₂×C₄⋊C₄×D₅₉	1	1	yes	characteristic
427	C₄	C₄×D₄×D₅₉	1	1	yes	characteristic
428	C₄	#16838036	1	1	yes	characteristic
429	C₄	#16838108	1	1	yes	characteristic
430	C₂	—	2	1	no	—
431	C₂	—	2	1	no	—
432	C₂	—	2	1	no	—
433	C₂	—	236	4	no	—
434	C₂	#21426997	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#16838036
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₉
Fitting	C₅₉×#1953	C₂
socle	C₂×C₅₉	D₄×C₄⋊C₄
prime radical	C₂×#14273749	C₂²
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	#1953	D₅₉
hypocenter	C₅₉	#22694
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #1953

Complements

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

N	H ≅ G/N	type
4. #21432706	C₂	semidirect
5. #21424887	C₂	semidirect
6. #21424339	C₂	semidirect
7. #21424333	C₂	semidirect
8. #21424266	C₂	semidirect
9. #21424149	C₂	semidirect
10. #21423976	C₂	semidirect
11. C₅₉×#1953	C₂	semidirect
20. #16837518	C₄	semidirect
21. #16837518	C₄	semidirect
22. #16837518	C₄	semidirect
23. #16837518	C₄	semidirect
218. #1953	D₅₉	semidirect
262. C₅₉	#22694	semidirect

Maximal subgroups

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

subgroup	index
#21433014	2
#21433012	2
C₂×#16837518	2
#21432706	2
#21424887	2
#21424339	2
#21424333	2
#21424266	2
#21424149	2
#21423976	2
C₅₉×#1953	2
#22694	59