Subgroups — #27396397

Order 13568.

648 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20284505	C₂	1	1	yes	maximal, characteristic
2	#20283645	C₂	1	1	yes	maximal, characteristic, complemented
3	#20283360	C₂	1	1	yes	maximal, characteristic
4	#20275659	C₂	1	1	yes	maximal, characteristic, complemented
5	#20275461	C₂	1	2	yes	maximal, complemented
6	#20275417	C₂	1	2	yes	maximal
7	#20275362	C₂	1	2	yes	maximal
8	#20275313	C₂	1	2	yes	maximal, complemented
9	#20274732	C₂	1	1	yes	maximal, characteristic
10	#20274580	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#1950	C₂	1	1	yes	maximal, characteristic, complemented
12	#16811180	C₂²	1	1	yes	characteristic
13	C₄×#11719945	C₂²	1	1	yes	characteristic
14	#16810931	C₄	1	2	yes	complemented
15	#16810924	C₄	1	2	yes	complemented
16	#16810919	C₄	1	1	yes	characteristic, complemented
17	#16810914	C₄	1	1	yes	characteristic, complemented
18	#16810909	C₄	1	1	yes	characteristic, complemented
19	#16810904	C₄	1	1	yes	characteristic, complemented
20	#16810750	—	2	1	no	—
21	#16810750	—	2	1	no	—
22	#16810747	—	2	1	no	—
23	#16810747	—	2	1	no	—
24	#16810685	—	2	1	no	—
25	#16810685	—	2	1	no	—
26	#16810674	—	2	1	no	—
27	#16810674	—	2	1	no	—
28	#16810661	C₂²	1	2	yes	—
29	#16810651	C₂²	1	1	yes	characteristic
30	#16810651	C₂²	1	2	yes	—
31	#16810651	C₂²	1	1	yes	characteristic
32	C₂×#13133143	C₂²	1	2	yes	—
33	#16810620	C₂²	1	2	yes	—
34	#16810591	C₂²	1	1	yes	characteristic
35	#16810591	C₂²	1	1	yes	characteristic
36	#16810581	C₂²	1	2	yes	—
37	C₂×C₄×#88322	C₂²	1	1	yes	characteristic
38	C₂×C₈×Dic₅₃	C₂²	1	2	yes	—
39	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
40	#16810384	C₂²	1	2	yes	—
41	#16810384	C₂²	1	2	yes	—
42	#16810384	C₂²	1	2	yes	—
43	#16810377	C₂²	1	2	yes	—
44	C₂×#108×C₅₃	C₂²	1	2	yes	—
45	C₅₃×#423	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
47	C₄×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
48	C₅₃×#341	C₂²	1	2	yes	—
49	C₂×#11719945	C₂³	1	1	yes	characteristic
50	C₂²×#88322	C₂³	1	1	yes	characteristic
51	C₂²×#88322	C₂³	1	1	yes	characteristic
52	#13133217	C₂×C₄	1	1	yes	characteristic
53	#13133217	C₂×C₄	1	1	yes	characteristic
54	#13133209	C₂×C₄	1	2	yes	—
55	#13133196	—	2	1	no	—
56	#13133196	—	2	1	no	—
57	C₄×Dic₁₀₆	—	2	1	no	—
58	C₄×Dic₁₀₆	—	2	1	no	—
59	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
60	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
61	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
62	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
63	C₄×C₂²⋊D₅₃	—	2	1	no	—
64	C₄×C₂²⋊D₅₃	—	2	1	no	—
65	#13133176	C₂³	1	1	yes	characteristic
66	#13133176	C₂³	1	2	yes	—
67	#13133174	—	2	1	no	—
68	C₂×C₄⋊Dic₅₃	—	2	1	no	—
69	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
70	C₄²×D₅₃	—	2	1	no	—
71	#13133151	C₂×C₄	1	2	yes	—
72	#13133151	C₂×C₄	1	2	yes	—
73	#13133149	C₂×C₄	1	2	yes	—
74	#13133149	C₂×C₄	1	2	yes	—
75	#13133146	—	2	1	no	—
76	#13133146	—	2	1	no	—
77	#13133146	—	2	1	no	—
78	#13133146	—	2	1	no	—
79	#13133146	—	2	2	no	—
80	#13133146	—	2	2	no	—
81	#13133143	—	4	2	no	—
82	#13133142	C₂×C₄	1	2	yes	—
83	#13133142	C₂×C₄	1	2	yes	—
84	#13133139	C₂×C₄	1	2	yes	—
85	#13133139	C₂×C₄	1	2	yes	—
86	#13133129	—	2	1	no	—
87	#13133129	—	2	1	no	—
88	#13133129	—	2	1	no	—
89	#13133129	—	2	1	no	—
90	#13133127	—	2	2	no	—
91	C₄×#88322	D₄	1	1	yes	characteristic
92	C₄×#88322	D₄	1	1	yes	characteristic
93	C₄×#88322	D₄	1	1	yes	characteristic
94	C₄×#88322	D₄	1	1	yes	characteristic
95	C₈×Dic₅₃	—	2	2	no	—
96	C₈×Dic₅₃	—	4	2	no	—
97	#13133124	—	2	1	no	—
98	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
99	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
100	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
102	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
103	#108×C₅₃	—	4	2	no	—
104	C₄⋊C₈×C₅₃	—	2	1	no	—
105	C₄⋊C₈×C₅₃	—	2	1	no	—
106	C₄⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
107	C₄⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
108	C₄⋊C₈×C₅₃	C₂×C₄	1	2	yes	—
109	#97×C₅₃	—	2	1	no	—
110	C₄×C₈×C₅₃	—	2	1	no	—
111	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
112	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
113	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
114	C₂×C₂²⋊D₅₃	—	2	1	no	—
115	C₂²×Dic₅₃	—	2	2	no	—
116	#11719945	—	2	1	no	—
117	#11719945	—	2	1	no	—
118	#11719945	—	2	1	no	—
119	#11719945	—	2	1	no	—
120	C₂×D₂₁₂	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₄×D₅₃	—	2	1	no	—
122	C₂×C₄×D₅₃	—	2	1	no	—
123	C₂×C₄×D₅₃	—	2	1	no	—
124	C₂×Dic₁₀₆	—	2	1	no	—
125	C₂×Dic₁₀₆	—	2	1	no	—
126	C₂×Dic₁₀₆	C₂²×C₄	1	1	yes	characteristic
127	M₁₆×C₅₃	—	2	1	no	—
128	M₁₆×C₅₃	—	2	2	no	—
129	M₁₆×C₅₃	—	2	1	no	—
130	M₁₆×C₅₃	—	2	1	no	—
131	M₁₆×C₅₃	—	2	2	no	—
132	M₁₆×C₅₃	—	2	1	no	—
133	C₂×C₈×C₅₃	—	2	2	no	—
134	C₂×C₈×C₅₃	—	2	2	no	—
135	C₂×C₈×C₅₃	—	2	1	no	—
136	C₂×C₈×C₅₃	—	2	1	no	—
137	C₂×C₈×C₅₃	—	2	2	no	—
138	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
139	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
140	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
141	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
142	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
144	C₂²⋊Dic₅₃	—	2	1	no	—
145	C₂²⋊Dic₅₃	—	2	2	no	—
146	#11719921	—	2	1	no	—
147	#11719921	—	2	1	no	—
148	C₄⋊Dic₅₃	—	2	4	no	—
149	C₄⋊Dic₅₃	—	2	1	no	—
150	C₄⋊Dic₅₃	—	2	1	no	—
151	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
152	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
153	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
154	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
155	#11719919	—	2	1	no	—
156	#11719919	—	2	1	no	—
157	#11719919	—	2	2	no	—
158	#11719919	—	2	2	no	—
159	C₄×Dic₅₃	—	2	1	no	—
160	C₄×Dic₅₃	—	2	1	no	—
161	C₄×Dic₅₃	—	2	2	no	—
162	C₄×Dic₅₃	—	2	1	no	—
163	C₄×Dic₅₃	—	2	2	no	—
164	C₄×Dic₅₃	—	2	2	no	—
165	C₂×#88322	—	2	1	no	—
166	C₂×#88322	—	2	1	no	—
167	C₂×#88322	—	2	1	no	—
168	C₂×#88322	—	2	1	no	—
169	C₂×#88322	C₂×D₄	1	1	yes	characteristic
170	C₂×#88322	C₂×D₄	1	1	yes	characteristic
171	C₂×#88322	C₂×D₄	1	1	yes	characteristic
172	C₂×#88322	C₂×D₄	1	1	yes	characteristic
173	C₂³×C₅₃	C₂×#41	1	1	yes	characteristic
174	C₂²×D₅₃	—	2	1	no	—
175	C₂×C₄×C₅₃	—	2	2	no	—
176	C₂×C₄×C₅₃	—	4	1	no	—
177	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
178	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
179	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
180	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
181	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
182	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
184	C₂×C₄×C₅₃	2₋¹⁺⁴	1	1	yes	characteristic
185	C₂×C₄×C₅₃	2₋¹⁺⁴	1	1	yes	characteristic
186	C₂×C₄×C₅₃	2₋¹⁺⁴	1	1	yes	characteristic
187	C₂²⋊D₅₃	—	4	1	no	—
188	C₂²⋊D₅₃	—	4	1	no	—
189	C₂×Dic₅₃	—	2	4	no	—
190	C₂×Dic₅₃	—	2	2	no	—
191	C₂×Dic₅₃	—	2	2	no	—
192	C₂×Dic₅₃	—	2	1	no	—
193	C₂×Dic₅₃	—	2	1	no	—
194	C₂×Dic₅₃	—	2	1	no	—
195	C₂×Dic₅₃	—	4	2	no	—
196	C₂×Dic₅₃	—	4	2	no	—
197	D₂₁₂	—	2	1	no	—
198	D₂₁₂	—	2	1	no	—
199	C₄×D₅₃	—	4	2	no	—
200	C₄×D₅₃	—	4	1	no	—
201	C₄×D₅₃	—	4	1	no	—
202	C₄×D₅₃	—	4	2	no	—
203	Dic₁₀₆	—	2	1	no	—
204	Dic₁₀₆	—	2	1	no	—
205	Dic₁₀₆	—	4	2	no	—
206	Dic₁₀₆	—	4	2	no	—
207	C₈×C₅₃	—	2	2	no	—
208	C₈×C₅₃	—	2	2	no	—
209	C₈×C₅₃	—	4	1	no	—
210	C₈×C₅₃	—	4	1	no	—
211	C₈×C₅₃	—	4	2	no	—
212	#88322	—	2	1	no	—
213	#88322	—	2	1	no	—
214	#88322	—	2	1	no	—
215	#88322	—	2	1	no	—
216	#22130	—	53	1	no	maximal, Sylow
217	C₂²×C₅₃	—	2	1	no	—
218	C₂²×C₅₃	—	2	1	no	—
219	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
220	C₂²×C₅₃	#541	1	1	yes	characteristic
221	C₂²×C₅₃	#542	1	1	yes	characteristic
222	C₂×D₅₃	—	4	1	no	—
223	C₂×D₅₃	—	4	1	no	—
224	C₂×D₅₃	—	4	1	no	—
225	C₄×C₅₃	—	2	1	no	—
226	C₄×C₅₃	—	2	1	no	—
227	C₄×C₅₃	—	2	1	no	—
228	C₄×C₅₃	#443	1	2	yes	—
229	C₄×C₅₃	#519	1	1	yes	characteristic
230	C₄×C₅₃	#520	1	1	yes	characteristic
231	C₄×C₅₃	#536	1	1	yes	characteristic
232	C₄×C₅₃	#537	1	1	yes	characteristic
233	Dic₅₃	—	4	4	no	—
234	Dic₅₃	—	4	1	no	—
235	Dic₅₃	—	4	2	no	—
236	Dic₅₃	—	4	1	no	—
237	Dic₅₃	—	4	2	no	—
238	Dic₅₃	—	4	1	no	—
239	#3076	—	53	1	no	—
240	#2960	—	53	1	no	—
241	#2922	—	53	1	no	—
242	#1986	—	53	1	no	—
243	#1950	D₅₃	1	1	yes	characteristic, complemented
244	#1945	—	53	2	no	—
245	#1937	—	53	2	no	—
246	#1929	—	53	2	no	—
247	#1922	—	53	2	no	—
248	#1806	—	53	1	no	—
249	C₈×C₄⋊C₄	—	53	1	no	—
250	C₂×C₅₃	—	2	1	no	—
251	C₂×C₅₃	—	2	1	no	—
252	C₂×C₅₃	#2323	1	1	yes	characteristic
253	C₂×C₅₃	C₂×#443	1	1	yes	characteristic
254	C₂×C₅₃	#2955	1	1	yes	characteristic
255	D₅₃	—	8	1	no	—
256	#533	—	53	1	no	—
257	C₄×#41	—	53	1	no	—
258	#479	—	53	2	no	—
259	#478	—	53	2	no	—
260	#477	—	53	1	no	—
261	#476	—	53	1	no	—
262	#475	—	53	1	no	—
263	#474	—	53	1	no	—
264	#446	—	106	1	no	—
265	#446	—	106	1	no	—
266	C₈×Q₈	—	106	1	no	—
267	C₈×Q₈	—	106	1	no	—
268	#433	—	106	1	no	—
269	#433	—	106	1	no	—
270	#431	—	106	1	no	—
271	#431	—	106	1	no	—
272	C₂×#108	C₂×D₅₃	1	2	yes	—
273	#427	—	53	2	no	—
274	#424	—	53	1	no	—
275	#424	—	53	1	no	—
276	#424	—	53	2	no	—
277	#423	C₂×D₅₃	1	1	yes	characteristic
278	C₂×C₄⋊C₈	C₂×D₅₃	1	1	yes	characteristic
279	C₂×#104	—	53	2	no	—
280	#416	—	53	2	no	—
281	#408	—	53	1	no	—
282	#408	—	53	1	no	—
283	#405	—	53	2	no	—
284	C₄×M₁₆	C₂×D₅₃	1	1	yes	characteristic
285	C₂×C₄×C₈	—	53	1	no	—
286	C₂×C₄×C₈	—	53	2	no	—
287	C₄×C₄⋊C₄	—	53	1	no	—
288	#341	C₂×D₅₃	1	2	yes	—
289	#339	—	53	2	no	—
290	#339	—	53	2	no	—
291	#339	—	53	2	no	—
292	#336	—	53	2	no	—
293	C₅₃	#22130	1	1	yes	characteristic, complemented, Sylow
294	C₂×#41	—	53	1	no	—
295	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
296	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
297	C₂×M₁₆	C₂²×D₅₃	1	2	yes	—
298	C₂²×C₈	—	53	1	no	—
299	C₂²×C₈	—	53	1	no	—
300	C₂²×C₈	C₂²×D₅₃	1	2	yes	—
301	C₄⋊Q₈	—	53	1	no	—
302	C₄⋊Q₈	—	53	1	no	—
303	#125	—	53	2	no	—
304	C₂²⋊Q₈	—	106	1	no	—
305	C₂²⋊Q₈	—	106	1	no	—
306	C₄×Q₈	—	53	1	no	—
307	C₄×Q₈	—	53	1	no	—
308	C₄×Q₈	—	106	1	no	—
309	C₄×Q₈	—	106	1	no	—
310	C₄×D₄	—	53	1	no	—
311	C₄×D₄	—	53	1	no	—
312	C₄×D₄	—	106	1	no	—
313	C₄×D₄	—	106	1	no	—
314	#117	—	53	1	no	—
315	#117	—	53	2	no	—
316	#117	—	106	1	no	—
317	C₂×C₄⋊C₄	—	106	1	no	—
318	C₂×C₄²	—	53	2	no	—
319	C₂×C₄²	—	106	1	no	—
320	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
321	#108	—	4	2	no	—
322	#107	—	53	2	no	—
323	#107	—	53	2	no	—
324	#106	—	53	2	no	—
325	#106	—	53	2	no	—
326	C₄⋊C₈	—	2	1	no	—
327	C₄⋊C₈	—	2	1	no	—
328	C₄⋊C₈	—	106	1	no	—
329	C₄⋊C₈	—	106	1	no	—
330	C₄⋊C₈	—	106	1	no	—
331	C₄⋊C₈	—	106	1	no	—
332	C₄⋊C₈	—	106	2	no	—
333	C₄⋊C₈	—	106	2	no	—
334	C₄⋊C₈	C₄×D₅₃	1	1	yes	characteristic
335	C₄⋊C₈	C₄×D₅₃	1	1	yes	characteristic
336	C₄⋊C₈	C₄×D₅₃	1	2	yes	—
337	#104	—	212	2	no	—
338	#103	—	53	2	no	—
339	#103	—	53	2	no	—
340	#102	—	53	2	no	—
341	#102	—	53	2	no	—
342	C₂²⋊C₈	—	106	1	no	—
343	C₂²⋊C₈	—	106	1	no	—
344	C₂²⋊C₈	—	106	1	no	—
345	C₂²⋊C₈	—	106	1	no	—
346	#97	—	2	1	no	—
347	#97	—	106	2	no	—
348	C₄×C₈	—	2	1	no	—
349	C₄×C₈	—	53	1	no	—
350	C₄×C₈	—	53	1	no	—
351	C₄×C₈	—	53	1	no	—
352	C₄×C₈	—	53	1	no	—
353	C₄×C₈	—	106	2	no	—
354	C₄×C₈	—	212	2	no	—
355	#95	—	106	1	no	—
356	#41	—	106	1	no	—
357	#41	—	106	1	no	—
358	#41	—	106	1	no	—
359	#41	—	106	1	no	—
360	C₂×Q₈	—	53	1	no	—
361	C₂×Q₈	—	106	1	no	—
362	C₂×Q₈	—	106	1	no	—
363	C₂×D₄	—	53	1	no	—
364	C₂×D₄	—	106	1	no	—
365	C₂²×C₄	—	106	2	no	—
366	C₂²×C₄	—	106	1	no	—
367	C₂²×C₄	—	106	1	no	—
368	C₂²×C₄	—	106	1	no	—
369	C₂²×C₄	#11719949	1	1	yes	characteristic
370	C₂²×C₄	#11719949	1	1	yes	characteristic
371	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
372	M₁₆	—	2	2	no	—
373	M₁₆	—	2	1	no	—
374	M₁₆	—	2	1	no	—
375	M₁₆	—	2	1	no	—
376	M₁₆	—	2	2	no	—
377	M₁₆	—	2	1	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	53	1	no	—
384	C₂×C₈	—	53	1	no	—
385	C₂×C₈	—	53	1	no	—
386	C₂×C₈	—	53	1	no	—
387	C₂×C₈	—	106	1	no	—
388	C₂×C₈	—	106	1	no	—
389	C₂×C₈	—	106	1	no	—
390	C₂×C₈	—	106	1	no	—
391	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
392	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
393	C₄⋊C₄	—	53	2	no	—
394	C₄⋊C₄	—	53	2	no	—
395	C₄⋊C₄	—	53	1	no	—
396	C₄⋊C₄	—	53	1	no	—
397	C₄⋊C₄	—	106	4	no	—
398	C₄⋊C₄	—	106	1	no	—
399	C₄⋊C₄	—	106	1	no	—
400	C₄⋊C₄	—	106	2	no	—
401	C₄⋊C₄	—	106	2	no	—
402	C₄⋊C₄	—	106	1	no	—
403	C₄⋊C₄	—	106	1	no	—
404	C₂²⋊C₄	—	106	1	no	—
405	C₂²⋊C₄	—	106	2	no	—
406	C₂²⋊C₄	—	106	1	no	—
407	C₂²⋊C₄	—	106	1	no	—
408	C₄²	—	106	1	no	—
409	C₄²	—	106	1	no	—
410	C₄²	—	106	2	no	—
411	C₄²	—	106	1	no	—
412	C₄²	—	106	2	no	—
413	C₄²	—	106	2	no	—
414	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
415	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
416	C₄²	D₄×D₅₃	1	1	yes	characteristic
417	C₄²	D₄×D₅₃	1	1	yes	characteristic
418	C₂³	—	106	1	no	—
419	C₂³	C₂×#11719949	1	1	yes	characteristic
420	Q₈	—	106	1	no	—
421	Q₈	—	106	1	no	—
422	Q₈	—	212	2	no	—
423	Q₈	—	212	2	no	—
424	D₄	—	106	1	no	—
425	D₄	—	106	1	no	—
426	D₄	—	212	1	no	—
427	D₄	—	212	1	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	106	4	no	—
431	C₂×C₄	—	106	1	no	—
432	C₂×C₄	—	106	1	no	—
433	C₂×C₄	—	106	1	no	—
434	C₂×C₄	—	106	2	no	—
435	C₂×C₄	—	106	2	no	—
436	C₂×C₄	—	212	2	no	—
437	C₂×C₄	—	212	2	no	—
438	C₂×C₄	—	212	2	no	—
439	C₂×C₄	—	212	1	no	—
440	C₂×C₄	—	212	1	no	—
441	C₂×C₄	—	212	2	no	—
442	C₂×C₄	#13133179	1	1	yes	characteristic
443	C₂×C₄	#13133179	1	1	yes	characteristic
444	C₂×C₄	#13133179	1	1	yes	characteristic
445	C₂×C₄	#13133179	1	1	yes	characteristic
446	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
447	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
448	C₂×C₄	#13133262	1	1	yes	characteristic
449	C₂×C₄	#13133264	1	1	yes	characteristic
450	C₂×C₄	#13133264	1	1	yes	characteristic
451	C₂×C₄	#13133265	1	1	yes	characteristic
452	C₈	—	2	2	no	—
453	C₈	—	2	2	no	—
454	C₈	—	4	1	no	—
455	C₈	—	4	1	no	—
456	C₈	—	4	2	no	—
457	C₈	—	106	1	no	—
458	C₈	—	106	1	no	—
459	C₈	—	106	1	no	—
460	C₈	—	106	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	212	1	no	—
464	C₂²	—	212	1	no	—
465	C₂²	—	212	1	no	—
466	C₂²	C₂×#13133179	1	1	yes	characteristic
467	C₂²	#16811236	1	1	yes	characteristic
468	C₂²	#16811247	1	1	yes	characteristic
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	212	4	no	—
473	C₄	—	212	1	no	—
474	C₄	—	212	1	no	—
475	C₄	—	212	2	no	—
476	C₄	—	212	1	no	—
477	C₄	—	212	2	no	—
478	C₄	#16810739	1	2	yes	—
479	C₄	#16811099	1	1	yes	characteristic
480	C₄	#16811102	1	1	yes	characteristic
481	C₄	#16811196	1	1	yes	characteristic
482	C₄	#16811202	1	1	yes	characteristic
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	424	1	no	—
486	C₂	#20277395	1	1	yes	characteristic
487	C₂	C₂×#16810739	1	1	yes	characteristic
488	C₂	#20283617	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₃
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₃
Fitting	C₅₃×#1950	C₂
socle	C₂²×C₅₃	C₂×C₄×D₄
prime radical	C₂×#11719945	C₂³
cosocle	C₂²×C₄×C₅₃	C₂⁴
hypercenter	#1950	D₅₃
hypocenter	C₅₃	#22130
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1950

Complements

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

N	H ≅ G/N	type
2. #20283645	C₂	semidirect
4. #20275659	C₂	semidirect
5. #20275461	C₂	semidirect
8. #20275313	C₂	semidirect
10. #20274580	C₂	semidirect
11. C₅₃×#1950	C₂	semidirect
14. #16810931	C₄	semidirect
15. #16810924	C₄	semidirect
16. #16810919	C₄	semidirect
17. #16810914	C₄	semidirect
18. #16810909	C₄	semidirect
19. #16810904	C₄	semidirect
243. #1950	D₅₃	semidirect
293. C₅₃	#22130	semidirect

Maximal subgroups

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

subgroup	index
#20284505	2
#20283645	2
#20283360	2
#20275659	2
#20275461	2
#20275417	2
#20275362	2
#20275313	2
#20274732	2
#20274580	2
C₅₃×#1950	2
#22130	53