Subgroups — #28611551

Order 15104.

820 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433812	C₂	1	1	yes	maximal, characteristic
2	#21433003	C₂	1	2	yes	maximal, complemented
3	#21432704	C₂	1	1	yes	maximal, characteristic, complemented
4	#21424990	C₂	1	1	yes	maximal, characteristic, complemented
5	#21424886	C₂	1	1	yes	maximal, characteristic, complemented
6	#21424768	C₂	1	2	yes	maximal, complemented
7	#21424455	C₂	1	2	yes	maximal, complemented
8	#21424316	C₂	1	2	yes	maximal, complemented
9	#21424004	C₂	1	1	yes	maximal, characteristic, complemented
10	#21423942	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2957	C₂	1	1	yes	maximal, characteristic, complemented
12	#16838200	C₂²	1	2	yes	—
13	#16838168	C₂²	1	2	yes	—
14	C₂×#14273733	C₂²	1	1	yes	characteristic
15	#16837674	C₄	1	2	yes	complemented
16	#16837669	C₄	1	2	yes	complemented
17	#16837662	C₄	1	4	yes	complemented
18	#16837522	—	2	4	no	—
19	#16837517	—	2	4	no	—
20	#16837450	C₂²	1	2	yes	—
21	#16837450	C₂²	1	2	yes	—
22	#16837449	—	2	2	no	—
23	C₂×#14273663	C₂²	1	1	yes	characteristic
24	C₂×#14273663	C₂²	1	1	yes	characteristic
25	#108×D₅₉	—	2	2	no	—
26	C₂×#14273654	C₂²	1	2	yes	—
27	C₂×#14273653	C₂²	1	1	yes	characteristic
28	#16837396	C₂²	1	1	yes	characteristic
29	#16837386	C₂²	1	2	yes	—
30	#16837369	C₂²	1	2	yes	—
31	M₁₆×Dic₅₉	C₂²	1	2	yes	—
32	C₂×#14273637	C₂²	1	1	yes	characteristic
33	#16837172	C₂²	1	2	yes	—
34	#16837166	C₂²	1	1	yes	characteristic
35	#16837166	C₂²	1	2	yes	—
36	#16837161	C₂²	1	1	yes	characteristic
37	C₂×#135×C₅₉	C₂²	1	1	yes	characteristic
38	C₅₉×#568	C₂²	1	2	yes	—
39	C₅₉×#444	—	2	2	no	—
40	C₅₉×#443	—	2	2	no	—
41	C₂×#108×C₅₉	C₂²	1	1	yes	characteristic
42	C₅₉×#421	C₂²	1	2	yes	—
43	C₅₉×#405	C₂²	1	1	yes	characteristic
44	C₂×#11745685	C₂³	1	1	yes	characteristic
45	#14273758	C₂×C₄	1	4	yes	—
46	#14273757	—	2	2	no	—
47	#14273753	C₂×C₄	1	4	yes	—
48	#14273752	—	2	2	no	—
49	#14273747	—	2	4	no	—
50	#14273735	—	4	2	no	—
51	#14273733	—	2	1	no	—
52	#14273733	—	2	1	no	—
53	#14273733	—	2	4	no	—
54	#14273733	C₂×C₄	1	2	yes	—
55	#14273733	C₂×C₄	1	2	yes	—
56	C₂×#11745664	C₂³	1	2	yes	—
57	C₂×#11745664	C₂³	1	1	yes	characteristic
58	C₂×#11745664	C₂³	1	2	yes	—
59	C₂×#11745659	—	2	1	no	—
60	M₁₆×D₅₉	—	2	4	no	—
61	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
62	C₂×C₈×D₅₉	—	2	1	no	—
63	C₂×C₄×Dic₅₉	C₂³	1	1	yes	characteristic
64	#14273663	—	2	1	no	—
65	#14273663	—	2	1	no	—
66	#14273663	C₂×C₄	1	2	yes	—
67	#14273663	C₂×C₄	1	2	yes	—
68	#14273662	—	2	4	no	—
69	#14273662	—	2	4	no	—
70	#14273654	—	2	2	no	—
71	#14273654	—	2	2	no	—
72	#14273653	D₄	1	4	yes	—
73	#14273650	—	2	1	no	—
74	#14273647	—	2	1	no	—
75	#14273646	C₂×C₄	1	4	yes	—
76	#14273644	C₂×C₄	1	4	yes	—
77	C₂²⋊(C₅₉⋊C₈)	—	4	2	no	—
78	#14273637	—	2	1	no	—
79	#14273637	—	2	1	no	—
80	#14273637	—	2	2	no	—
81	C₈×Dic₅₉	—	2	2	no	—
82	C₂×#41×C₅₉	C₂³	1	2	yes	—
83	#135×C₅₉	—	2	1	no	—
84	#135×C₅₉	—	2	1	no	—
85	#135×C₅₉	—	2	1	no	—
86	#135×C₅₉	—	2	1	no	—
87	C₂×Q₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
88	C₂×SD₁₆×C₅₉	C₂×C₄	1	2	yes	—
89	C₂×D₈×C₅₉	C₂×C₄	1	1	yes	characteristic
90	#131×C₅₉	—	2	4	no	—
91	#131×C₅₉	—	2	4	no	—
92	C₂×M₁₆×C₅₉	—	4	2	no	—
93	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
94	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
96	#117×C₅₉	C₂³	1	1	yes	characteristic
97	#108×C₅₉	D₄	1	2	yes	—
98	#108×C₅₉	D₄	1	2	yes	—
99	#104×C₅₉	—	2	4	no	—
100	#97×C₅₉	—	2	1	no	—
101	C₄×C₈×C₅₉	—	2	1	no	—
102	#41×C₅₉	—	2	2	no	—
103	#41×C₅₉	—	2	2	no	—
104	#41×C₅₉	—	2	2	no	—
105	#41×C₅₉	—	2	2	no	—
106	C₂×Q₈×C₅₉	C₂²×C₄	1	2	yes	—
107	C₂×D₄×C₅₉	—	2	2	no	—
108	C₂×D₄×C₅₉	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₅₉	—	2	2	no	—
110	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
111	C₂×C₂²⋊D₅₉	—	2	1	no	—
112	C₂²×Dic₅₉	—	2	1	no	—
113	#11745685	—	2	1	no	—
114	#11745685	—	2	1	no	—
115	#11745685	C₂²×C₄	1	2	yes	—
116	#11745685	C₂×D₄	1	2	yes	—
117	C₂×D₂₃₆	#41	1	1	yes	characteristic
118	C₂×C₄×D₅₉	—	2	1	no	—
119	C₂×Dic₁₁₈	#41	1	1	yes	characteristic
120	Q₁₆×C₅₉	—	2	1	no	—
121	Q₁₆×C₅₉	—	2	1	no	—
122	SD₁₆×C₅₉	—	2	2	no	—
123	SD₁₆×C₅₉	—	2	2	no	—
124	D₈×C₅₉	—	2	1	no	—
125	D₈×C₅₉	—	2	1	no	—
126	M₁₆×C₅₉	—	2	1	no	—
127	M₁₆×C₅₉	—	2	2	no	—
128	M₁₆×C₅₉	—	4	4	no	—
129	M₁₆×C₅₉	C₂×D₄	1	2	yes	—
130	M₁₆×C₅₉	C₂×D₄	1	4	yes	—
131	C₂×C₈×C₅₉	—	2	1	no	—
132	C₂×C₈×C₅₉	—	2	2	no	—
133	C₂×C₈×C₅₉	—	4	4	no	—
134	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
139	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
140	C₄⋊C₄×C₅₉	—	2	1	no	—
141	C₂²⋊C₄×C₅₉	—	2	1	no	—
142	C₄²×C₅₉	—	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	C₂×D₄	1	2	yes	—
149	#11745664	—	2	1	no	—
150	#11745664	—	2	2	no	—
151	#11745664	—	2	2	no	—
152	#11745664	—	2	2	no	—
153	#11745664	C₂²×C₄	1	2	yes	—
154	#11745664	C₂²×C₄	1	4	yes	—
155	C₂×C₅₉⋊C₈	—	2	2	no	—
156	C₂×C₅₉⋊C₈	—	2	1	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	2	no	—
161	#11745659	—	2	2	no	—
162	#11745659	—	2	2	no	—
163	#11745659	—	4	4	no	—
164	C₈×D₅₉	—	2	2	no	—
165	C₈×D₅₉	—	2	2	no	—
166	C₈×D₅₉	—	4	4	no	—
167	C₂³×C₅₉	—	2	2	no	—
168	C₂³×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
169	C₂²×D₅₉	—	2	1	no	—
170	Q₈×C₅₉	—	2	2	no	—
171	Q₈×C₅₉	—	2	2	no	—
172	D₄×C₅₉	—	2	2	no	—
173	D₄×C₅₉	—	2	2	no	—
174	D₄×C₅₉	—	4	2	no	—
175	D₄×C₅₉	—	4	2	no	—
176	C₂×C₄×C₅₉	—	2	2	no	—
177	C₂×C₄×C₅₉	—	4	2	no	—
178	C₂×C₄×C₅₉	—	4	2	no	—
179	C₂×C₄×C₅₉	—	4	1	no	—
180	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
181	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
185	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
186	C₂²⋊D₅₉	—	2	2	no	—
187	C₂²⋊D₅₉	—	2	2	no	—
188	C₂×Dic₅₉	—	2	1	no	—
189	C₂×Dic₅₉	—	2	2	no	—
190	C₂×Dic₅₉	—	8	1	no	—
191	D₂₃₆	—	2	1	no	—
192	D₂₃₆	C₄×D₄	1	2	yes	—
193	C₄×D₅₉	—	2	2	no	—
194	C₄×D₅₉	—	2	2	no	—
195	Dic₁₁₈	—	2	1	no	—
196	Dic₁₁₈	C₄×D₄	1	2	yes	—
197	C₈×C₅₉	—	2	4	no	—
198	C₈×C₅₉	—	2	2	no	—
199	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
200	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
201	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
202	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
203	C₅₉⋊C₈	—	2	2	no	—
204	C₅₉⋊C₈	—	2	4	no	—
205	C₅₉⋊C₈	—	4	2	no	—
206	C₅₉⋊C₈	—	4	1	no	—
207	#23043	—	59	1	no	maximal, Sylow
208	C₂²×C₅₉	—	4	1	no	—
209	C₂²×C₅₉	—	4	2	no	—
210	C₂²×C₅₉	—	8	2	no	—
211	C₂²×C₅₉	#520	1	1	yes	characteristic
212	C₂²×C₅₉	#547	1	1	yes	characteristic
213	C₂²×C₅₉	#548	1	1	yes	characteristic
214	C₂×D₅₉	—	2	2	no	—
215	C₂×D₅₉	—	8	1	no	—
216	C₄×C₅₉	—	4	2	no	—
217	C₄×C₅₉	—	8	1	no	—
218	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
219	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
220	C₄×C₅₉	D₄²	1	1	yes	characteristic
221	C₄×C₅₉	#553	1	1	yes	characteristic
222	Dic₅₉	—	2	2	no	—
223	Dic₅₉	—	4	2	no	—
224	#3067	—	59	1	no	—
225	#2957	D₅₉	1	1	yes	characteristic, complemented
226	#2956	—	59	2	no	—
227	#2916	—	59	1	no	—
228	#1975	—	59	1	no	—
229	#1953	—	59	1	no	—
230	#1932	—	59	2	no	—
231	#1881	—	59	2	no	—
232	#1858	—	59	2	no	—
233	#1778	—	59	1	no	—
234	#1765	—	59	1	no	—
235	C₂×C₅₉	—	2	1	no	—
236	C₂×C₅₉	—	2	1	no	—
237	C₂×C₅₉	—	2	1	no	—
238	C₂×C₅₉	—	8	2	no	—
239	C₂×C₅₉	#2361	1	1	yes	characteristic
240	D₅₉	—	4	2	no	—
241	#575	—	59	2	no	—
242	C₂×#135	C₂×D₅₉	1	1	yes	characteristic
243	#568	—	59	2	no	—
244	#568	C₂×D₅₉	1	2	yes	—
245	C₂×#131	—	59	1	no	—
246	#473	—	59	2	no	—
247	#472	—	59	2	no	—
248	#471	—	59	4	no	—
249	#444	—	2	2	no	—
250	#444	—	118	4	no	—
251	#443	—	2	2	no	—
252	#443	—	118	4	no	—
253	#430	—	59	2	no	—
254	#430	—	59	2	no	—
255	#430	—	118	2	no	—
256	C₂×#108	—	59	1	no	—
257	C₂×#108	—	59	1	no	—
258	C₂×#108	—	118	2	no	—
259	C₂×#108	C₂×D₅₉	1	1	yes	characteristic
260	#421	C₂×D₅₉	1	2	yes	—
261	C₂×#104	—	59	1	no	—
262	C₂×#104	—	59	2	no	—
263	#416	—	59	1	no	—
264	#413	—	59	2	no	—
265	#408	—	59	2	no	—
266	#405	C₂×D₅₉	1	1	yes	characteristic
267	C₄×M₁₆	—	59	2	no	—
268	C₂×#97	—	59	1	no	—
269	#344	—	59	2	no	—
270	#341	—	59	1	no	—
271	#341	—	59	2	no	—
272	#339	—	59	1	no	—
273	C₅₉	#23043	1	1	yes	characteristic, complemented, Sylow
274	C₂×#41	—	59	1	no	—
275	C₂×#41	C₂²×D₅₉	1	2	yes	—
276	#137	—	59	4	no	—
277	#137	—	118	2	no	—
278	AGL(1,ℤ/8)	—	59	4	no	—
279	AGL(1,ℤ/8)	—	118	2	no	—
280	#135	—	2	1	no	—
281	#135	—	2	1	no	—
282	#135	—	2	1	no	—
283	#135	—	2	1	no	—
284	#135	—	118	4	no	—
285	C₂×Q₁₆	C₄×D₅₉	1	1	yes	characteristic
286	C₂×SD₁₆	C₄×D₅₉	1	2	yes	—
287	C₂×D₈	C₄×D₅₉	1	1	yes	characteristic
288	#131	—	2	4	no	—
289	#131	—	2	4	no	—
290	#131	—	59	2	no	—
291	#131	—	59	2	no	—
292	#131	—	118	4	no	—
293	#131	—	118	1	no	—
294	#131	—	118	1	no	—
295	#131	—	236	2	no	—
296	C₂×M₁₆	—	4	2	no	—
297	C₂×M₁₆	—	59	1	no	—
298	C₂×M₁₆	—	59	2	no	—
299	C₂×M₁₆	—	59	2	no	—
300	C₂×M₁₆	—	118	1	no	—
301	C₂×M₁₆	—	118	4	no	—
302	C₂×M₁₆	C₂²×D₅₉	1	1	yes	characteristic
303	C₂×M₁₆	C₂²×D₅₉	1	2	yes	—
304	C₂²×C₈	—	59	1	no	—
305	C₂²×C₈	—	118	1	no	—
306	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
307	#117	C₂²×D₅₉	1	1	yes	characteristic
308	C₂×C₄²	—	59	1	no	—
309	#108	—	59	2	no	—
310	#108	—	59	2	no	—
311	#108	—	118	4	no	—
312	#108	—	118	4	no	—
313	#108	—	118	1	no	—
314	#108	—	118	1	no	—
315	#108	C₂²⋊D₅₉	1	2	yes	—
316	#108	C₂²⋊D₅₉	1	2	yes	—
317	#104	—	2	4	no	—
318	#104	—	59	4	no	—
319	#104	—	118	2	no	—
320	#104	—	118	2	no	—
321	#103	—	118	1	no	—
322	#102	—	118	1	no	—
323	#101	—	59	4	no	—
324	#100	—	59	4	no	—
325	C₂²⋊C₈	—	236	2	no	—
326	#97	—	2	1	no	—
327	#97	—	118	2	no	—
328	#97	—	118	1	no	—
329	#97	—	118	1	no	—
330	C₄×C₈	—	2	1	no	—
331	C₄×C₈	—	118	2	no	—
332	#41	—	2	2	no	—
333	#41	—	2	2	no	—
334	#41	—	2	2	no	—
335	#41	—	2	2	no	—
336	#41	—	59	2	no	—
337	#41	—	59	2	no	—
338	#41	—	118	1	no	—
339	#41	—	118	1	no	—
340	C₂×Q₈	—	59	1	no	—
341	C₂×Q₈	C₂×C₄×D₅₉	1	2	yes	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	59	1	no	—
344	C₂×D₄	—	118	1	no	—
345	C₂×D₄	C₂×C₄×D₅₉	1	2	yes	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	118	1	no	—
348	C₂²×C₄	—	118	1	no	—
349	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
350	Q₁₆	—	2	1	no	—
351	Q₁₆	—	2	1	no	—
352	Q₁₆	—	118	4	no	—
353	SD₁₆	—	2	2	no	—
354	SD₁₆	—	2	2	no	—
355	SD₁₆	—	118	4	no	—
356	SD₁₆	—	118	4	no	—
357	D₈	—	2	1	no	—
358	D₈	—	2	1	no	—
359	D₈	—	118	4	no	—
360	M₁₆	—	2	1	no	—
361	M₁₆	—	2	2	no	—
362	M₁₆	—	4	4	no	—
363	M₁₆	—	59	2	no	—
364	M₁₆	—	59	4	no	—
365	M₁₆	—	118	2	no	—
366	M₁₆	—	118	1	no	—
367	M₁₆	—	118	2	no	—
368	M₁₆	—	118	2	no	—
369	M₁₆	—	118	2	no	—
370	M₁₆	—	118	2	no	—
371	M₁₆	—	236	4	no	—
372	M₁₆	D₄×D₅₉	1	2	yes	—
373	M₁₆	C₂×C₂²⋊D₅₉	1	4	yes	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	4	4	no	—
377	C₂×C₈	—	118	2	no	—
378	C₂×C₈	—	118	1	no	—
379	C₂×C₈	—	118	2	no	—
380	C₂×C₈	—	118	2	no	—
381	C₂×C₈	—	118	1	no	—
382	C₂×C₈	—	118	1	no	—
383	C₂×C₈	—	118	1	no	—
384	C₂×C₈	—	118	2	no	—
385	C₂×C₈	—	236	4	no	—
386	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
387	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
388	C₂×C₈	#11745685	1	1	yes	characteristic
389	C₂×C₈	#11745685	1	1	yes	characteristic
390	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
391	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
392	C₄⋊C₄	—	2	1	no	—
393	C₂²⋊C₄	—	2	1	no	—
394	C₄²	—	2	1	no	—
395	C₄²	—	59	2	no	—
396	C₄²	—	118	1	no	—
397	C₂³	—	2	2	no	—
398	C₂³	—	118	1	no	—
399	C₂³	#14273774	1	1	yes	characteristic
400	Q₈	—	2	2	no	—
401	Q₈	—	2	2	no	—
402	Q₈	—	59	2	no	—
403	Q₈	—	118	1	no	—
404	D₄	—	2	2	no	—
405	D₄	—	2	2	no	—
406	D₄	—	4	2	no	—
407	D₄	—	4	2	no	—
408	D₄	—	59	2	no	—
409	D₄	—	118	2	no	—
410	D₄	—	118	2	no	—
411	D₄	—	118	1	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	118	1	no	—
417	C₂×C₄	—	118	2	no	—
418	C₂×C₄	—	118	2	no	—
419	C₂×C₄	—	118	2	no	—
420	C₂×C₄	—	472	1	no	—
421	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
422	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
423	C₂×C₄	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
424	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
425	C₂×C₄	C₂×#11745685	1	1	yes	characteristic
426	C₂×C₄	#14273772	1	1	yes	characteristic
427	C₈	—	2	2	no	—
428	C₈	—	2	4	no	—
429	C₈	—	118	4	no	—
430	C₈	—	118	2	no	—
431	C₈	—	236	2	no	—
432	C₈	—	236	1	no	—
433	C₈	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
434	C₈	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
435	C₈	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
436	C₈	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
437	C₂²	—	4	1	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	8	2	no	—
440	C₂²	—	118	2	no	—
441	C₂²	—	472	1	no	—
442	C₂²	#16837881	1	1	yes	characteristic
443	C₂²	#16838057	1	1	yes	characteristic
444	C₂²	#16838059	1	1	yes	characteristic
445	C₄	—	4	2	no	—
446	C₄	—	8	1	no	—
447	C₄	—	118	2	no	—
448	C₄	—	236	2	no	—
449	C₄	C₄×D₄×D₅₉	1	1	yes	characteristic
450	C₄	C₂×C₄×C₂²⋊D₅₉	1	1	yes	characteristic
451	C₄	D₄×C₂²⋊D₅₉	1	1	yes	characteristic
452	C₄	#16838102	1	1	yes	characteristic
453	C₂	—	2	1	no	—
454	C₂	—	2	1	no	—
455	C₂	—	2	1	no	—
456	C₂	—	8	2	no	—
457	C₂	—	236	2	no	—
458	C₂	#21427108	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×#2957	C₂
socle	C₂×C₅₉	#2361
prime radical	#21433812	C₂
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	#2957	D₅₉
hypocenter	C₅₉	#23043
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #2957

Complements

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

N	H ≅ G/N	type
2. #21433003	C₂	semidirect
3. #21432704	C₂	semidirect
4. #21424990	C₂	semidirect
5. #21424886	C₂	semidirect
6. #21424768	C₂	semidirect
7. #21424455	C₂	semidirect
8. #21424316	C₂	semidirect
9. #21424004	C₂	semidirect
10. #21423942	C₂	semidirect
11. C₅₉×#2957	C₂	semidirect
15. #16837674	C₄	semidirect
16. #16837669	C₄	semidirect
17. #16837662	C₄	semidirect
225. #2957	D₅₉	semidirect
273. C₅₉	#23043	semidirect

Maximal subgroups

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

subgroup	index
#21433812	2
#21433003	2
#21432704	2
#21424990	2
#21424886	2
#21424768	2
#21424455	2
#21424316	2
#21424004	2
#21423942	2
C₅₉×#2957	2
#23043	59