Subgroups — #28611544

Order 15104.

824 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433816	C₂	1	1	yes	maximal, characteristic
2	#21433012	C₂	1	1	yes	maximal, characteristic, complemented
3	#21433003	C₂	1	2	yes	maximal, complemented
4	#21424982	C₂	1	1	yes	maximal, characteristic, complemented
5	#21424884	C₂	1	1	yes	maximal, characteristic, complemented
6	#21424764	C₂	1	2	yes	maximal, complemented
7	#21424458	C₂	1	2	yes	maximal, complemented
8	#21424314	C₂	1	2	yes	maximal, complemented
9	#108×Dic₅₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#21423931	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2916	C₂	1	1	yes	maximal, characteristic, complemented
12	#16838200	C₂²	1	2	yes	—
13	C₂×#14273749	C₂²	1	1	yes	characteristic
14	#16838168	C₂²	1	2	yes	—
15	#16837677	C₄	1	2	yes	complemented
16	#16837672	C₄	1	2	yes	complemented
17	#16837665	C₄	1	4	yes	complemented
18	#16837523	—	2	2	no	—
19	#16837522	—	2	4	no	—
20	#16837518	—	2	2	no	—
21	#16837517	—	2	4	no	—
22	#16837450	C₂²	1	2	yes	—
23	C₂×#14273663	C₂²	1	1	yes	characteristic
24	#16837418	C₂²	1	2	yes	—
25	C₂×#14273654	C₂²	1	1	yes	characteristic
26	C₂×#14273653	C₂²	1	2	yes	—
27	#16837398	C₂²	1	1	yes	characteristic
28	#16837384	C₂²	1	2	yes	—
29	#16837370	C₂²	1	2	yes	—
30	#16837357	C₂²	1	1	yes	characteristic
31	M₁₆×Dic₅₉	C₂²	1	2	yes	—
32	C₂×C₈×Dic₅₉	C₂²	1	1	yes	characteristic
33	#16837173	C₂²	1	2	yes	—
34	#16837166	C₂²	1	1	yes	characteristic
35	#16837166	C₂²	1	2	yes	—
36	#16837163	C₂²	1	1	yes	characteristic
37	C₅₉×#568	C₂²	1	2	yes	—
38	C₂×#131×C₅₉	C₂²	1	1	yes	characteristic
39	C₅₉×#430	—	2	2	no	—
40	C₅₉×#430	C₂²	1	2	yes	—
41	C₂×#108×C₅₉	—	2	2	no	—
42	C₂×#108×C₅₉	C₂²	1	1	yes	characteristic
43	C₂×#108×C₅₉	C₂²	1	1	yes	characteristic
44	C₂×#11745685	C₂³	1	2	yes	—
45	#14273758	—	2	2	no	—
46	#14273757	C₂×C₄	1	4	yes	—
47	#14273753	—	2	2	no	—
48	#14273752	C₂×C₄	1	4	yes	—
49	#14273749	—	2	1	no	—
50	#14273749	—	2	1	no	—
51	#14273749	—	2	1	no	—
52	#14273749	—	2	1	no	—
53	#14273747	—	2	4	no	—
54	C₂×Dic₂₃₆	C₂×C₄	1	1	yes	characteristic
55	C₂×#11745660	C₂×C₄	1	2	yes	—
56	C₂×D₄₇₂	C₂×C₄	1	1	yes	characteristic
57	#14273735	—	2	4	no	—
58	#14273733	—	2	4	no	—
59	C₂×#11745664	C₂³	1	2	yes	—
60	C₂×#11745664	C₂³	1	1	yes	characteristic
61	M₁₆×D₅₉	—	4	2	no	—
62	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
63	#14273686	C₂³	1	1	yes	characteristic
64	C₂×C₄×Dic₅₉	C₂³	1	1	yes	characteristic
65	#14273663	C₂×C₄	1	2	yes	—
66	#14273663	C₂×C₄	1	2	yes	—
67	#14273662	—	2	4	no	—
68	#14273654	D₄	1	2	yes	—
69	#14273654	D₄	1	2	yes	—
70	#14273653	—	2	4	no	—
71	#14273653	—	2	2	no	—
72	#14273653	—	2	2	no	—
73	#14273651	—	2	1	no	—
74	#14273648	—	2	1	no	—
75	#14273645	C₂×C₄	1	4	yes	—
76	#14273643	C₂×C₄	1	4	yes	—
77	(C₂×D₅₉)⋊C₈	—	4	2	no	—
78	#14273637	—	2	1	no	—
79	#14273637	—	2	2	no	—
80	C₈×Dic₅₉	—	2	1	no	—
81	C₈×Dic₅₉	—	2	1	no	—
82	C₈×Dic₅₉	—	2	1	no	—
83	C₈×Dic₅₉	—	2	2	no	—
84	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
85	#131×C₅₉	—	2	1	no	—
86	#131×C₅₉	—	2	1	no	—
87	#131×C₅₉	—	2	4	no	—
88	#131×C₅₉	—	4	2	no	—
89	#131×C₅₉	C₂×C₄	1	2	yes	—
90	#131×C₅₉	C₂×C₄	1	2	yes	—
91	C₂×M₁₆×C₅₉	—	2	1	no	—
92	C₂×M₁₆×C₅₉	—	2	4	no	—
93	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
94	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
95	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
96	C₂²×C₈×C₅₉	—	2	1	no	—
97	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
98	#108×C₅₉	—	2	4	no	—
99	#108×C₅₉	—	2	1	no	—
100	#108×C₅₉	—	2	1	no	—
101	#108×C₅₉	D₄	1	2	yes	—
102	#108×C₅₉	D₄	1	2	yes	—
103	#41×C₅₉	—	2	1	no	—
104	#41×C₅₉	—	2	1	no	—
105	#41×C₅₉	C₂²×C₄	1	2	yes	—
106	#41×C₅₉	C₂×D₄	1	2	yes	—
107	C₂×Q₈×C₅₉	#41	1	1	yes	characteristic
108	C₂×D₄×C₅₉	—	2	1	no	—
109	C₂×D₄×C₅₉	#41	1	1	yes	characteristic
110	C₂²×C₄×C₅₉	—	2	1	no	—
111	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
112	C₂×C₂²⋊D₅₉	—	2	2	no	—
113	C₂²×Dic₅₉	—	2	1	no	—
114	#11745685	—	2	2	no	—
115	#11745685	—	2	2	no	—
116	#11745685	—	2	2	no	—
117	#11745685	—	2	2	no	—
118	C₂×D₂₃₆	C₂²×C₄	1	2	yes	—
119	C₂×C₄×D₅₉	—	2	2	no	—
120	C₂×Dic₁₁₈	C₂²×C₄	1	2	yes	—
121	M₁₆×C₅₉	—	2	1	no	—
122	M₁₆×C₅₉	—	2	2	no	—
123	M₁₆×C₅₉	—	2	2	no	—
124	M₁₆×C₅₉	—	2	2	no	—
125	M₁₆×C₅₉	—	2	2	no	—
126	M₁₆×C₅₉	—	2	2	no	—
127	M₁₆×C₅₉	—	4	4	no	—
128	M₁₆×C₅₉	C₂²×C₄	1	2	yes	—
129	M₁₆×C₅₉	C₂×D₄	1	4	yes	—
130	C₂×C₈×C₅₉	—	2	1	no	—
131	C₂×C₈×C₅₉	—	2	2	no	—
132	C₂×C₈×C₅₉	—	2	2	no	—
133	C₂×C₈×C₅₉	—	2	2	no	—
134	C₂×C₈×C₅₉	—	2	2	no	—
135	C₂×C₈×C₅₉	—	4	4	no	—
136	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
141	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
142	C₂²⋊Dic₅₉	—	2	1	no	—
143	#11745672	—	2	4	no	—
144	#11745671	—	2	4	no	—
145	#11745670	—	2	4	no	—
146	#11745669	—	2	4	no	—
147	C₄⋊Dic₅₉	—	2	1	no	—
148	C₄×Dic₅₉	—	2	1	no	—
149	C₄×Dic₅₉	—	2	1	no	—
150	C₄×Dic₅₉	C₂×D₄	1	1	yes	characteristic
151	C₄×Dic₅₉	C₂×D₄	1	1	yes	characteristic
152	#11745664	—	2	2	no	—
153	#11745664	—	2	1	no	—
154	#11745664	C₂²×C₄	1	4	yes	—
155	#11745664	C₂×D₄	1	2	yes	—
156	C₂×C₅₉⋊C₈	—	2	2	no	—
157	C₂×C₅₉⋊C₈	—	2	1	no	—
158	C₂×C₅₉⋊C₈	—	2	1	no	—
159	C₂×C₅₉⋊C₈	—	2	1	no	—
160	C₂×C₅₉⋊C₈	—	2	1	no	—
161	Dic₂₃₆	—	2	1	no	—
162	Dic₂₃₆	—	2	1	no	—
163	D₄₇₂	—	2	1	no	—
164	D₄₇₂	—	2	1	no	—
165	#11745660	—	2	2	no	—
166	#11745660	—	2	2	no	—
167	#11745659	—	4	4	no	—
168	C₈×D₅₉	—	4	4	no	—
169	C₂³×C₅₉	—	2	1	no	—
170	C₂³×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
171	C₂²×D₅₉	—	2	2	no	—
172	Q₈×C₅₉	—	2	1	no	—
173	Q₈×C₅₉	C₄×D₄	1	2	yes	—
174	D₄×C₅₉	—	2	2	no	—
175	D₄×C₅₉	—	2	2	no	—
176	D₄×C₅₉	—	2	1	no	—
177	D₄×C₅₉	C₄×D₄	1	2	yes	—
178	C₂×C₄×C₅₉	—	2	1	no	—
179	C₂×C₄×C₅₉	—	2	2	no	—
180	C₂×C₄×C₅₉	—	2	2	no	—
181	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
182	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
185	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
187	C₂²⋊D₅₉	—	4	2	no	—
188	C₂²⋊D₅₉	—	4	2	no	—
189	C₂×Dic₅₉	—	2	1	no	—
190	C₂×Dic₅₉	—	2	2	no	—
191	C₂×Dic₅₉	—	2	1	no	—
192	C₂×Dic₅₉	—	4	2	no	—
193	C₂×Dic₅₉	—	4	1	no	—
194	D₂₃₆	—	2	2	no	—
195	D₂₃₆	—	2	2	no	—
196	C₄×D₅₉	—	4	2	no	—
197	C₄×D₅₉	—	4	2	no	—
198	Dic₁₁₈	—	2	2	no	—
199	Dic₁₁₈	—	2	2	no	—
200	C₈×C₅₉	—	2	2	no	—
201	C₈×C₅₉	—	2	4	no	—
202	C₈×C₅₉	—	4	2	no	—
203	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
204	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
205	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
206	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
207	C₅₉⋊C₈	—	2	4	no	—
208	C₅₉⋊C₈	—	2	2	no	—
209	C₅₉⋊C₈	—	4	1	no	—
210	#23042	—	59	1	no	maximal, Sylow
211	C₂²×C₅₉	—	2	2	no	—
212	C₂²×C₅₉	—	4	1	no	—
213	C₂²×C₅₉	—	8	1	no	—
214	C₂²×C₅₉	#520	1	1	yes	characteristic
215	C₂²×C₅₉	#547	1	1	yes	characteristic
216	C₂²×C₅₉	#548	1	1	yes	characteristic
217	C₂×D₅₉	—	4	2	no	—
218	C₂×D₅₉	—	8	2	no	—
219	C₄×C₅₉	—	2	2	no	—
220	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
221	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
222	C₄×C₅₉	D₄²	1	1	yes	characteristic
223	C₄×C₅₉	#553	1	1	yes	characteristic
224	Dic₅₉	—	2	2	no	—
225	Dic₅₉	—	4	1	no	—
226	Dic₅₉	—	4	2	no	—
227	Dic₅₉	—	8	1	no	—
228	#3067	—	59	1	no	—
229	#2957	—	59	1	no	—
230	#2956	—	59	2	no	—
231	#2916	D₅₉	1	1	yes	characteristic, complemented
232	#1974	—	59	1	no	—
233	#1953	—	59	1	no	—
234	#1932	—	59	2	no	—
235	#1881	—	59	2	no	—
236	#1858	—	59	2	no	—
237	C₄×#108	—	59	1	no	—
238	#1764	—	59	1	no	—
239	C₂×C₅₉	—	2	1	no	—
240	C₂×C₅₉	—	2	1	no	—
241	C₂×C₅₉	—	2	1	no	—
242	C₂×C₅₉	—	4	2	no	—
243	C₂×C₅₉	#2361	1	1	yes	characteristic
244	D₅₉	—	8	2	no	—
245	#575	—	59	2	no	—
246	C₂×#135	—	59	1	no	—
247	#568	—	59	2	no	—
248	#568	C₂×D₅₉	1	2	yes	—
249	C₂×#131	C₂×D₅₉	1	1	yes	characteristic
250	#473	—	59	2	no	—
251	#472	—	59	2	no	—
252	#471	—	59	4	no	—
253	#444	—	118	4	no	—
254	#444	—	118	2	no	—
255	#443	—	118	4	no	—
256	#443	—	118	2	no	—
257	#430	—	2	2	no	—
258	#430	—	59	2	no	—
259	#430	C₂×D₅₉	1	2	yes	—
260	C₂×#108	—	2	2	no	—
261	C₂×#108	—	59	1	no	—
262	C₂×#108	C₂×D₅₉	1	1	yes	characteristic
263	C₂×#108	C₂×D₅₉	1	1	yes	characteristic
264	#421	—	59	2	no	—
265	C₂×#104	—	59	1	no	—
266	C₂×#104	—	59	2	no	—
267	#416	—	59	1	no	—
268	#413	—	59	2	no	—
269	#408	—	59	2	no	—
270	#405	—	59	1	no	—
271	C₄×M₁₆	—	59	2	no	—
272	C₂×C₄×C₈	—	59	1	no	—
273	#344	—	59	2	no	—
274	#341	—	59	1	no	—
275	#341	—	59	2	no	—
276	#339	—	59	1	no	—
277	C₅₉	#23042	1	1	yes	characteristic, complemented, Sylow
278	C₂×#41	—	59	2	no	—
279	C₂×#41	C₂²×D₅₉	1	1	yes	characteristic
280	#137	—	59	4	no	—
281	#137	—	118	2	no	—
282	AGL(1,ℤ/8)	—	59	4	no	—
283	AGL(1,ℤ/8)	—	118	2	no	—
284	#135	—	118	4	no	—
285	#135	—	118	1	no	—
286	#135	—	118	1	no	—
287	#135	—	118	1	no	—
288	#135	—	118	1	no	—
289	C₂×Q₁₆	—	59	1	no	—
290	C₂×SD₁₆	—	59	2	no	—
291	C₂×D₈	—	59	1	no	—
292	#131	—	2	1	no	—
293	#131	—	2	1	no	—
294	#131	—	2	4	no	—
295	#131	—	4	2	no	—
296	#131	—	118	4	no	—
297	#131	—	118	4	no	—
298	#131	C₄×D₅₉	1	2	yes	—
299	#131	C₄×D₅₉	1	2	yes	—
300	C₂×M₁₆	—	2	1	no	—
301	C₂×M₁₆	—	2	4	no	—
302	C₂×M₁₆	—	59	1	no	—
303	C₂×M₁₆	—	59	2	no	—
304	C₂×M₁₆	—	236	2	no	—
305	C₂×M₁₆	C₂²×D₅₉	1	2	yes	—
306	C₂×M₁₆	C₂²×D₅₉	1	1	yes	characteristic
307	C₂×M₁₆	C₂²×D₅₉	1	2	yes	—
308	C₂²×C₈	—	2	1	no	—
309	C₂²×C₈	—	59	1	no	—
310	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
311	#117	—	59	1	no	—
312	C₂×C₄²	—	59	1	no	—
313	#108	—	2	4	no	—
314	#108	—	2	1	no	—
315	#108	—	2	1	no	—
316	#108	—	59	2	no	—
317	#108	—	59	2	no	—
318	#108	—	118	4	no	—
319	#108	C₂²⋊D₅₉	1	2	yes	—
320	#108	C₂²⋊D₅₉	1	2	yes	—
321	#104	—	59	2	no	—
322	#104	—	59	2	no	—
323	#104	—	118	2	no	—
324	#104	—	118	2	no	—
325	#104	—	118	4	no	—
326	#103	—	118	1	no	—
327	#102	—	118	1	no	—
328	#101	—	59	4	no	—
329	#100	—	59	4	no	—
330	C₂²⋊C₈	—	236	2	no	—
331	#97	—	118	2	no	—
332	#97	—	118	1	no	—
333	C₄×C₈	—	118	2	no	—
334	C₄×C₈	—	118	1	no	—
335	C₄×C₈	—	118	1	no	—
336	C₄×C₈	—	118	1	no	—
337	#41	—	2	1	no	—
338	#41	—	2	1	no	—
339	#41	—	118	2	no	—
340	#41	—	118	2	no	—
341	#41	—	118	2	no	—
342	#41	—	118	2	no	—
343	#41	C₂×C₄×D₅₉	1	2	yes	—
344	#41	D₄×D₅₉	1	2	yes	—
345	C₂×Q₈	—	59	2	no	—
346	C₂×Q₈	#11745689	1	1	yes	characteristic
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	59	2	no	—
349	C₂×D₄	—	118	2	no	—
350	C₂×D₄	#11745689	1	1	yes	characteristic
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	118	1	no	—
353	C₂²×C₄	—	118	2	no	—
354	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
355	Q₁₆	—	118	4	no	—
356	Q₁₆	—	118	1	no	—
357	Q₁₆	—	118	1	no	—
358	SD₁₆	—	118	4	no	—
359	SD₁₆	—	118	4	no	—
360	SD₁₆	—	118	2	no	—
361	SD₁₆	—	118	2	no	—
362	D₈	—	118	4	no	—
363	D₈	—	118	1	no	—
364	D₈	—	118	1	no	—
365	M₁₆	—	2	1	no	—
366	M₁₆	—	2	2	no	—
367	M₁₆	—	2	2	no	—
368	M₁₆	—	2	2	no	—
369	M₁₆	—	2	2	no	—
370	M₁₆	—	2	2	no	—
371	M₁₆	—	4	4	no	—
372	M₁₆	—	59	4	no	—
373	M₁₆	—	59	2	no	—
374	M₁₆	—	118	2	no	—
375	M₁₆	—	118	1	no	—
376	M₁₆	—	236	4	no	—
377	M₁₆	C₂×C₄×D₅₉	1	2	yes	—
378	M₁₆	C₂×C₂²⋊D₅₉	1	4	yes	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	4	4	no	—
385	C₂×C₈	—	118	2	no	—
386	C₂×C₈	—	118	1	no	—
387	C₂×C₈	—	118	1	no	—
388	C₂×C₈	—	118	1	no	—
389	C₂×C₈	—	118	1	no	—
390	C₂×C₈	—	236	4	no	—
391	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
392	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
393	C₂×C₈	#11745685	1	1	yes	characteristic
394	C₂×C₈	#11745685	1	1	yes	characteristic
395	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
396	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
397	C₄⋊C₄	—	118	1	no	—
398	C₂²⋊C₄	—	118	1	no	—
399	C₄²	—	59	1	no	—
400	C₄²	—	59	1	no	—
401	C₄²	—	118	1	no	—
402	C₄²	—	118	1	no	—
403	C₂³	—	2	1	no	—
404	C₂³	—	118	2	no	—
405	C₂³	#14273775	1	1	yes	characteristic
406	Q₈	—	2	1	no	—
407	Q₈	—	118	2	no	—
408	Q₈	—	118	2	no	—
409	Q₈	#14273689	1	2	yes	—
410	D₄	—	2	2	no	—
411	D₄	—	2	2	no	—
412	D₄	—	2	1	no	—
413	D₄	—	118	2	no	—
414	D₄	—	118	2	no	—
415	D₄	—	236	2	no	—
416	D₄	—	236	2	no	—
417	D₄	#14273689	1	2	yes	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	118	1	no	—
422	C₂×C₄	—	118	1	no	—
423	C₂×C₄	—	118	2	no	—
424	C₂×C₄	—	236	2	no	—
425	C₂×C₄	—	236	1	no	—
426	C₂×C₄	—	236	2	no	—
427	C₂×C₄	—	236	2	no	—
428	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
429	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
430	C₂×C₄	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
431	C₂×C₄	C₂×#11745685	1	1	yes	characteristic
432	C₂×C₄	C₂×#11745689	1	1	yes	characteristic
433	C₂×C₄	#14273772	1	1	yes	characteristic
434	C₈	—	2	4	no	—
435	C₈	—	2	2	no	—
436	C₈	—	4	2	no	—
437	C₈	—	118	2	no	—
438	C₈	—	118	4	no	—
439	C₈	—	236	1	no	—
440	C₈	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
441	C₈	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
442	C₈	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
443	C₈	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
444	C₂²	—	2	2	no	—
445	C₂²	—	4	1	no	—
446	C₂²	—	8	1	no	—
447	C₂²	—	472	2	no	—
448	C₂²	—	236	2	no	—
449	C₂²	#16837883	1	1	yes	characteristic
450	C₂²	#16838053	1	1	yes	characteristic
451	C₂²	#16838063	1	1	yes	characteristic
452	C₄	—	2	2	no	—
453	C₄	—	118	2	no	—
454	C₄	—	472	1	no	—
455	C₄	—	236	1	no	—
456	C₄	—	236	2	no	—
457	C₄	C₂×C₄×C₂²⋊D₅₉	1	1	yes	characteristic
458	C₄	C₂×#14273689	1	1	yes	characteristic
459	C₄	D₄×C₂²⋊D₅₉	1	1	yes	characteristic
460	C₄	#16838100	1	1	yes	characteristic
461	C₂	—	2	1	no	—
462	C₂	—	2	1	no	—
463	C₂	—	2	1	no	—
464	C₂	—	4	2	no	—
465	C₂	—	472	2	no	—
466	C₂	#21427112	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×C₂²⋊D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₉
Fitting	C₅₉×#2916	C₂
socle	C₂×C₅₉	#2361
prime radical	#21433816	C₂
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	#2916	D₅₉
hypocenter	C₅₉	#23042
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #2916

Complements

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

N	H ≅ G/N	type
2. #21433012	C₂	semidirect
3. #21433003	C₂	semidirect
4. #21424982	C₂	semidirect
5. #21424884	C₂	semidirect
6. #21424764	C₂	semidirect
7. #21424458	C₂	semidirect
8. #21424314	C₂	semidirect
9. #108×Dic₅₉	C₂	semidirect
10. #21423931	C₂	semidirect
11. C₅₉×#2916	C₂	semidirect
15. #16837677	C₄	semidirect
16. #16837672	C₄	semidirect
17. #16837665	C₄	semidirect
231. #2916	D₅₉	semidirect
277. C₅₉	#23042	semidirect

Maximal subgroups

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

subgroup	index
#21433816	2
#21433012	2
#21433003	2
#21424982	2
#21424884	2
#21424764	2
#21424458	2
#21424314	2
#108×Dic₅₉	2
#21423931	2
C₅₉×#2916	2
#23042	59