Subgroups — #28260398

Order 13568.

2684 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20289491	C₂	1	4	yes	maximal, complemented
2	#20286514	C₂	1	4	yes	maximal, complemented
3	#20286508	C₂	1	4	yes	maximal, complemented
4	#20286481	C₂	1	8	yes	maximal, complemented
5	#20284439	C₂	1	4	yes	maximal, complemented
6	#20284063	C₂	1	2	yes	maximal, complemented
7	C₂×#16810790	C₂	1	2	yes	maximal, complemented
8	#20283626	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3151	C₂	1	1	yes	maximal, characteristic, complemented
10	#16811459	C₂²	1	2	yes	complemented
11	C₂×#13133262	C₂²	1	2	yes	complemented
12	#16811433	—	2	8	no	—
13	#16811429	C₂²	1	16	yes	complemented
14	#16811427	—	2	8	no	—
15	#16811424	C₂²	1	16	yes	complemented
16	#16811423	C₂²	1	2	yes	—
17	#16811421	C₂²	1	4	yes	complemented
18	#16811419	—	2	8	no	—
19	C₂×#13133243	C₂²	1	4	yes	complemented
20	AGL(1,ℤ/8)×D₅₃	—	2	8	no	—
21	#16811389	C₂²	1	4	yes	complemented
22	#16810890	C₂²	1	16	yes	complemented
23	#16810883	C₂²	1	16	yes	complemented
24	#16810805	C₂²	1	4	yes	complemented
25	#16810800	C₂²	1	4	yes	complemented
26	#16810795	C₂²	1	4	yes	complemented
27	#16810790	C₂²	1	8	yes	complemented
28	#16810790	C₂²	1	8	yes	complemented
29	#16810790	C₂²	1	4	yes	complemented
30	#16810746	C₂²	1	8	yes	complemented
31	#16810741	C₂²	1	8	yes	complemented
32	#16810672	C₂²	1	2	yes	complemented
33	C₂×#13133145	C₂²	1	4	yes	complemented
34	#16810607	C₂²	1	2	yes	complemented
35	C₂×#13133134	C₂²	1	2	yes	complemented
36	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	4	yes	complemented
37	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
38	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic, complemented
39	C₅₃×#496	C₂²	1	4	yes	complemented
40	C₅₃×#493	C₂²	1	2	yes	complemented
41	C₅₃×#492	C₂²	1	2	yes	complemented
42	C₄×M₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
43	#13133265	C₂³	1	4	yes	—
44	#13133264	—	2	4	no	—
45	#13133263	—	2	4	no	—
46	#13133262	—	2	8	no	—
47	#13133262	—	4	2	no	—
48	#13133262	—	4	2	no	—
49	#13133262	C₂³	1	4	yes	—
50	#13133262	C₂³	1	8	yes	complemented
51	C₂×#11719945	—	4	2	no	—
52	C₂×#11719945	C₂³	1	4	yes	—
53	C₂×#11719947	—	2	4	no	—
54	#41×D₅₃	—	2	8	no	—
55	C₂²×C₂²⋊D₅₃	—	4	2	no	—
56	C₂×D₄×D₅₃	—	2	4	no	—
57	#13133250	D₄	1	8	yes	complemented
58	#13133248	C₂³	1	8	yes	complemented
59	#13133247	—	2	4	no	—
60	#13133246	—	2	16	no	—
61	#13133245	D₄	1	8	yes	complemented
62	#13133244	—	2	16	no	—
63	#13133243	—	2	8	no	—
64	#13133243	C₂³	1	16	yes	—
65	#13133243	C₂³	1	8	yes	complemented
66	#13133242	—	2	4	no	—
67	#13133241	—	2	16	no	—
68	#13133241	—	2	16	no	—
69	#13133239	C₂³	1	8	yes	—
70	#13133238	—	2	16	no	—
71	#13133237	—	2	8	no	—
72	#13133236	—	2	16	no	—
73	C₂×#11719923	—	2	4	no	—
74	SD₁₆×D₅₃	—	2	16	no	—
75	C₂×#11719922	—	2	4	no	—
76	D₈×D₅₃	—	2	16	no	—
77	#13133225	—	2	8	no	—
78	#13133223	C₂³	1	16	yes	complemented
79	C₂×#11719917	C₂³	1	4	yes	—
80	M₁₆×D₅₃	—	2	8	no	—
81	#13133153	C₂³	1	8	yes	complemented
82	#13133145	C₂³	1	8	yes	complemented
83	#13133145	C₂³	1	8	yes	complemented
84	#13133136	C₂³	1	4	yes	complemented
85	#13133134	C₂³	1	8	yes	complemented
86	#13133134	C₂³	1	4	yes	complemented
87	C₂×#41×C₅₃	C₂³	1	2	yes	—
88	C₂²×D₄×C₅₃	—	4	1	no	—
89	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
90	AGL(1,ℤ/8)×C₅₃	—	2	8	no	—
91	AGL(1,ℤ/8)×C₅₃	—	2	8	no	—
92	C₂×SD₁₆×C₅₃	C₂³	1	8	yes	complemented
93	C₂×D₈×C₅₃	C₂³	1	8	yes	complemented
94	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
95	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
96	#127×C₅₃	—	4	1	no	—
97	#127×C₅₃	C₂³	1	2	yes	—
98	#127×C₅₃	C₂³	1	2	yes	—
99	#127×C₅₃	C₂³	1	1	yes	characteristic, complemented
100	#124×C₅₃	C₂³	1	2	yes	complemented
101	#121×C₅₃	—	4	1	no	—
102	C₄×D₄×C₅₃	—	4	1	no	—
103	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
104	#97×C₅₃	C₂³	1	2	yes	complemented
105	C₄×C₈×C₅₃	C₂³	1	2	yes	complemented
106	C₂⁴×C₅₃	—	2	2	no	—
107	C₂³×D₅₃	—	4	2	no	—
108	#41×C₅₃	—	2	4	no	—
109	#41×C₅₃	—	2	4	no	—
110	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
111	C₂×D₄×C₅₃	—	2	2	no	—
112	C₂×D₄×C₅₃	—	2	4	no	—
113	C₂×D₄×C₅₃	—	2	4	no	—
114	C₂×D₄×C₅₃	—	2	2	no	—
115	C₂×D₄×C₅₃	—	4	1	no	—
116	C₂×D₄×C₅₃	—	4	2	no	—
117	C₂×D₄×C₅₃	—	4	2	no	—
118	C₂×D₄×C₅₃	—	8	4	no	—
119	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
120	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
121	C₂²×C₄×C₅₃	—	2	1	no	—
122	C₂²×C₄×C₅₃	—	2	2	no	—
123	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
124	C₂×C₂²⋊D₅₃	—	2	4	no	—
125	C₂×C₂²⋊D₅₃	—	4	4	no	—
126	C₂×C₂²⋊D₅₃	—	4	8	no	—
127	C₂×C₂²⋊D₅₃	—	4	4	no	—
128	C₂×C₂²⋊D₅₃	—	4	8	no	—
129	C₂²×Dic₅₃	—	4	2	no	—
130	#11719949	—	2	8	no	—
131	Q₈×D₅₃	—	2	8	no	—
132	#11719947	—	2	8	no	—
133	#11719947	—	2	16	no	—
134	#11719947	—	4	8	no	—
135	#11719947	—	4	8	no	—
136	D₄×D₅₃	—	2	8	no	—
137	D₄×D₅₃	—	2	16	no	—
138	D₄×D₅₃	—	4	8	no	—
139	D₄×D₅₃	—	4	8	no	—
140	#11719945	—	2	4	no	—
141	#11719945	—	2	4	no	—
142	#11719945	—	4	4	no	—
143	#11719945	—	4	4	no	—
144	#11719945	—	4	4	no	—
145	#11719945	C₂×D₄	1	8	yes	—
146	#11719945	C₂⁴	1	8	yes	—
147	C₂×D₂₁₂	—	4	2	no	—
148	C₂×D₂₁₂	C₂×D₄	1	4	yes	—
149	C₂×C₄×D₅₃	—	2	4	no	—
150	C₂×C₄×D₅₃	—	4	4	no	—
151	C₂×Dic₁₀₆	—	4	2	no	—
152	C₂×Dic₁₀₆	C₂×D₄	1	4	yes	—
153	SD₁₆×C₅₃	—	2	16	no	—
154	D₈×C₅₃	—	2	16	no	—
155	M₁₆×C₅₃	C₂×D₄	1	8	yes	—
156	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
157	C₄⋊C₄×C₅₃	—	4	1	no	—
158	C₂²⋊C₄×C₅₃	—	4	2	no	—
159	C₄²×C₅₃	—	2	1	no	—
160	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
161	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
162	#11719925	—	2	8	no	—
163	#11719924	—	2	8	no	—
164	#11719923	—	2	16	no	—
165	#11719923	—	2	8	no	—
166	#11719922	—	2	8	no	—
167	#11719922	—	2	16	no	—
168	#11719917	—	2	4	no	—
169	#11719917	C₂⁴	1	8	yes	—
170	C₂×#88322	—	2	4	no	—
171	Dic₂₁₂	C₂×D₄	1	8	yes	complemented
172	D₄₂₄	C₂×D₄	1	8	yes	complemented
173	#11719913	C₂×D₄	1	16	yes	complemented
174	#11719912	—	2	16	no	—
175	C₈×D₅₃	—	2	16	no	—
176	C₂³×C₅₃	—	2	2	no	—
177	C₂³×C₅₃	—	2	4	no	—
178	C₂³×C₅₃	—	4	2	no	—
179	C₂³×C₅₃	—	4	2	no	—
180	C₂³×C₅₃	—	8	4	no	—
181	C₂³×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
182	C₂²×D₅₃	—	2	4	no	—
183	C₂²×D₅₃	—	4	4	no	—
184	C₂²×D₅₃	—	4	8	no	—
185	C₂²×D₅₃	—	16	4	no	—
186	Q₈×C₅₃	—	2	4	no	—
187	D₄×C₅₃	—	2	8	no	—
188	D₄×C₅₃	—	2	4	no	—
189	D₄×C₅₃	—	4	4	no	—
190	D₄×C₅₃	—	4	4	no	—
191	D₄×C₅₃	—	8	2	no	—
192	D₄×C₅₃	—	8	4	no	—
193	D₄×C₅₃	—	8	4	no	—
194	C₂×C₄×C₅₃	—	2	1	no	—
195	C₂×C₄×C₅₃	—	2	2	no	—
196	C₂×C₄×C₅₃	—	2	1	no	—
197	C₂×C₄×C₅₃	—	4	2	no	—
198	C₂×C₄×C₅₃	—	4	2	no	—
199	C₂×C₄×C₅₃	—	4	2	no	—
200	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
201	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
202	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
203	C₂²⋊D₅₃	—	2	8	no	—
204	C₂²⋊D₅₃	—	2	8	no	—
205	C₂²⋊D₅₃	—	4	8	no	—
206	C₂²⋊D₅₃	—	4	16	no	—
207	C₂×Dic₅₃	—	2	4	no	—
208	C₂×Dic₅₃	—	4	4	no	—
209	C₂×Dic₅₃	—	4	8	no	—
210	D₂₁₂	—	2	4	no	—
211	D₂₁₂	—	4	4	no	—
212	D₂₁₂	C₂²×D₄	1	8	yes	—
213	C₄×D₅₃	—	2	8	no	—
214	C₄×D₅₃	—	2	8	no	—
215	C₄×D₅₃	—	4	8	no	—
216	Dic₁₀₆	—	2	4	no	—
217	Dic₁₀₆	—	4	4	no	—
218	Dic₁₀₆	C₂²×D₄	1	8	yes	—
219	C₈×C₅₃	C₂²×D₄	1	8	yes	—
220	#88322	—	2	8	no	—
221	#61110	—	53	1	no	maximal, Sylow
222	C₂²×C₅₃	—	4	1	no	—
223	C₂²×C₅₃	—	4	2	no	—
224	C₂²×C₅₃	—	4	4	no	—
225	C₂²×C₅₃	—	8	4	no	—
226	C₂²×C₅₃	—	8	2	no	—
227	C₂²×C₅₃	—	8	4	no	—
228	C₂²×C₅₃	—	16	2	no	—
229	C₂²×C₅₃	D₄²	1	2	yes	—
230	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
231	C₂×D₅₃	—	2	8	no	—
232	C₂×D₅₃	—	8	4	no	—
233	C₂×D₅₃	—	16	4	no	—
234	C₂×D₅₃	—	16	8	no	—
235	C₄×C₅₃	—	2	2	no	—
236	C₄×C₅₃	—	4	1	no	—
237	C₄×C₅₃	—	4	2	no	—
238	C₄×C₅₃	D₄²	1	2	yes	—
239	C₄×C₅₃	C₂³×D₄	1	2	yes	—
240	Dic₅₃	—	2	8	no	—
241	#3585	—	53	4	no	—
242	#3292	—	53	4	no	—
243	#3291	—	53	4	no	—
244	#3288	—	53	8	no	—
245	#3151	D₅₃	1	1	yes	characteristic, complemented
246	#3068	—	53	4	no	—
247	#3018	—	53	2	no	—
248	C₂×#453	—	53	2	no	—
249	#2956	—	53	2	no	—
250	C₂×C₅₃	—	2	1	no	—
251	C₂×C₅₃	—	2	2	no	—
252	C₂×C₅₃	—	8	2	no	—
253	C₂×C₅₃	—	8	4	no	—
254	C₂×C₅₃	C₂×D₄²	1	1	yes	characteristic
255	D₅₃	—	4	8	no	—
256	#585	—	53	2	no	—
257	C₂×H(5,𝔽₂)	—	53	2	no	—
258	#577	—	53	16	no	—
259	#577	—	106	8	no	—
260	#576	—	53	16	no	—
261	#576	—	106	8	no	—
262	#575	—	53	4	no	—
263	#575	—	53	2	no	—
264	#575	—	106	8	no	—
265	C₂×AGL(1,ℤ/8)	—	53	4	no	—
266	C₂×AGL(1,ℤ/8)	—	106	8	no	—
267	C₂×AGL(1,ℤ/8)	C₂×D₅₃	1	4	yes	complemented
268	#568	—	53	4	no	—
269	#532	C₂×D₅₃	1	1	yes	characteristic, complemented
270	C₂×#127	C₂×D₅₃	1	1	yes	characteristic, complemented
271	#496	C₂×D₅₃	1	4	yes	complemented
272	#493	C₂×D₅₃	1	2	yes	complemented
273	#492	C₂×D₅₃	1	2	yes	complemented
274	#472	—	53	16	no	—
275	#471	—	53	16	no	—
276	#456	—	53	4	no	—
277	#455	—	53	4	no	—
278	#454	—	53	4	no	—
279	#453	—	53	8	no	—
280	#453	—	53	8	no	—
281	#453	—	53	4	no	—
282	#444	—	53	8	no	—
283	#443	—	53	8	no	—
284	#430	—	53	2	no	—
285	C₂×#104	—	53	4	no	—
286	#413	—	53	2	no	—
287	C₂×#100	—	53	2	no	—
288	C₄×M₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
289	C₅₃	#61110	1	1	yes	characteristic, complemented, Sylow
290	2₋¹⁺⁴	—	53	4	no	—
291	2₋¹⁺⁴	—	106	4	no	—
292	H(5,𝔽₂)	—	53	4	no	—
293	H(5,𝔽₂)	—	53	8	no	—
294	H(5,𝔽₂)	—	106	8	no	—
295	H(5,𝔽₂)	—	106	4	no	—
296	H(5,𝔽₂)	—	212	2	no	—
297	H(5,𝔽₂)	—	212	2	no	—
298	C₂×#41	—	53	4	no	—
299	C₂×#41	—	106	4	no	—
300	C₂×#41	—	106	8	no	—
301	C₂×#41	—	212	2	no	—
302	C₂×#41	C₂²×D₅₃	1	2	yes	—
303	C₂²×D₄	—	4	1	no	—
304	C₂²×D₄	—	106	4	no	—
305	C₂²×D₄	—	212	2	no	—
306	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
307	#137	—	53	8	no	—
308	#137	—	53	8	no	—
309	#137	—	106	16	no	—
310	#137	—	106	4	no	—
311	AGL(1,ℤ/8)	—	2	8	no	—
312	AGL(1,ℤ/8)	—	2	8	no	—
313	AGL(1,ℤ/8)	—	53	16	no	—
314	AGL(1,ℤ/8)	—	53	8	no	—
315	AGL(1,ℤ/8)	—	53	8	no	—
316	AGL(1,ℤ/8)	—	106	16	no	—
317	AGL(1,ℤ/8)	—	106	16	no	—
318	AGL(1,ℤ/8)	—	106	16	no	—
319	AGL(1,ℤ/8)	—	106	8	no	—
320	AGL(1,ℤ/8)	—	106	4	no	—
321	#135	—	53	8	no	—
322	#135	—	106	16	no	—
323	#135	—	106	16	no	—
324	#135	—	106	8	no	—
325	C₂×SD₁₆	—	106	16	no	—
326	C₂×SD₁₆	—	106	4	no	—
327	C₂×SD₁₆	C₂²×D₅₃	1	8	yes	complemented
328	C₂×D₈	—	106	16	no	—
329	C₂×D₈	—	106	4	no	—
330	C₂×D₈	C₂²×D₅₃	1	8	yes	complemented
331	#131	—	53	16	no	—
332	#131	—	106	8	no	—
333	C₂×M₁₆	—	53	4	no	—
334	C₂×M₁₆	—	106	8	no	—
335	C₂×M₁₆	C₂²×D₅₃	1	2	yes	—
336	C₄⋊Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
337	#127	—	4	1	no	—
338	#127	C₂²×D₅₃	1	2	yes	—
339	#127	C₂²×D₅₃	1	2	yes	—
340	#127	C₂²×D₅₃	1	1	yes	characteristic, complemented
341	#124	C₂²×D₅₃	1	2	yes	complemented
342	#121	—	4	1	no	—
343	C₄×D₄	—	4	1	no	—
344	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
345	#108	—	53	8	no	—
346	#104	—	53	8	no	—
347	#104	—	53	8	no	—
348	#101	—	53	4	no	—
349	#100	—	53	8	no	—
350	#100	—	53	4	no	—
351	#97	C₂²×D₅₃	1	2	yes	complemented
352	C₄×C₈	C₂²×D₅₃	1	2	yes	complemented
353	C₂⁴	—	2	2	no	—
354	C₂⁴	—	212	2	no	—
355	#41	—	2	4	no	—
356	#41	—	2	4	no	—
357	#41	—	53	8	no	—
358	#41	—	53	8	no	—
359	#41	—	106	4	no	—
360	#41	—	106	4	no	—
361	#41	—	106	8	no	—
362	#41	—	106	16	no	—
363	#41	—	106	8	no	—
364	#41	—	212	4	no	—
365	#41	—	212	4	no	—
366	#41	—	212	4	no	—
367	#41	—	212	8	no	—
368	#41	—	212	8	no	—
369	C₂×Q₈	—	53	4	no	—
370	C₂×Q₈	—	106	8	no	—
371	C₂×Q₈	—	212	2	no	—
372	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	4	no	—
375	C₂×D₄	—	2	4	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	4	1	no	—
378	C₂×D₄	—	4	2	no	—
379	C₂×D₄	—	4	2	no	—
380	C₂×D₄	—	8	4	no	—
381	C₂×D₄	—	53	4	no	—
382	C₂×D₄	—	106	8	no	—
383	C₂×D₄	—	106	16	no	—
384	C₂×D₄	—	106	4	no	—
385	C₂×D₄	—	212	2	no	—
386	C₂×D₄	—	212	8	no	—
387	C₂×D₄	—	212	4	no	—
388	C₂×D₄	—	212	8	no	—
389	C₂×D₄	—	212	8	no	—
390	C₂×D₄	—	212	4	no	—
391	C₂×D₄	—	212	8	no	—
392	C₂×D₄	C₂³×D₅₃	1	2	yes	—
393	C₂×D₄	C₂³×D₅₃	1	4	yes	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	106	4	no	—
397	C₂²×C₄	—	212	4	no	—
398	C₂²×C₄	—	212	2	no	—
399	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
400	Q₁₆	—	53	8	no	—
401	Q₁₆	—	106	8	no	—
402	SD₁₆	—	2	16	no	—
403	SD₁₆	—	53	16	no	—
404	SD₁₆	—	106	16	no	—
405	SD₁₆	—	106	8	no	—
406	SD₁₆	—	106	8	no	—
407	D₈	—	2	16	no	—
408	D₈	—	53	8	no	—
409	D₈	—	106	8	no	—
410	D₈	—	106	16	no	—
411	M₁₆	—	53	8	no	—
412	M₁₆	—	106	4	no	—
413	M₁₆	—	106	16	no	—
414	M₁₆	D₄×D₅₃	1	8	yes	—
415	C₂×C₈	—	106	4	no	—
416	C₂×C₈	—	106	16	no	—
417	C₂×C₈	C₂³×D₅₃	1	4	yes	—
418	C₄⋊C₄	—	4	1	no	—
419	C₂²⋊C₄	—	4	2	no	—
420	C₄²	—	2	1	no	—
421	C₄²	C₂³×D₅₃	1	1	yes	characteristic
422	C₄²	C₂³×D₅₃	1	1	yes	characteristic
423	C₂³	—	2	2	no	—
424	C₂³	—	2	4	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	4	2	no	—
427	C₂³	—	8	4	no	—
428	C₂³	—	848	4	no	—
429	C₂³	—	106	4	no	—
430	C₂³	—	212	4	no	—
431	C₂³	—	212	8	no	—
432	C₂³	#13133262	1	1	yes	characteristic
433	Q₈	—	2	4	no	—
434	Q₈	—	53	8	no	—
435	Q₈	—	106	4	no	—
436	Q₈	—	212	4	no	—
437	D₄	—	2	4	no	—
438	D₄	—	2	8	no	—
439	D₄	—	4	4	no	—
440	D₄	—	4	4	no	—
441	D₄	—	8	2	no	—
442	D₄	—	8	4	no	—
443	D₄	—	8	4	no	—
444	D₄	—	53	8	no	—
445	D₄	—	106	8	no	—
446	D₄	—	106	8	no	—
447	D₄	—	106	4	no	—
448	D₄	—	212	4	no	—
449	D₄	—	212	16	no	—
450	D₄	—	212	8	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	106	4	no	—
458	C₂×C₄	—	106	8	no	—
459	C₂×C₄	—	106	8	no	—
460	C₂×C₄	—	212	8	no	—
461	C₂×C₄	—	212	8	no	—
462	C₂×C₄	—	212	4	no	—
463	C₂×C₄	C₂×D₄×D₅₃	1	4	yes	—
464	C₂×C₄	#13133262	1	1	yes	characteristic
465	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
466	C₈	—	106	8	no	—
467	C₈	C₂×D₄×D₅₃	1	8	yes	—
468	C₂²	—	4	1	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	4	no	—
471	C₂²	—	8	4	no	—
472	C₂²	—	8	2	no	—
473	C₂²	—	8	4	no	—
474	C₂²	—	16	2	no	—
475	C₂²	—	848	8	no	—
476	C₂²	—	848	4	no	—
477	C₂²	—	106	8	no	—
478	C₂²	—	424	4	no	—
479	C₂²	#16811258	1	2	yes	—
480	C₂²	C₂×#13133262	1	1	yes	characteristic
481	C₄	—	2	2	no	—
482	C₄	—	4	1	no	—
483	C₄	—	4	2	no	—
484	C₄	—	106	8	no	—
485	C₄	#16811258	1	2	yes	—
486	C₄	C₂²×D₄×D₅₃	1	2	yes	—
487	C₂	—	2	1	no	—
488	C₂	—	2	2	no	—
489	C₂	—	8	4	no	—
490	C₂	—	8	2	no	—
491	C₂	—	212	8	no	—
492	C₂	C₂×#16811258	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×#16811258
commutator, cosocle	C₂×C₄×C₅₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₅₃
Fitting	C₅₃×#3151	C₂
socle	C₂×C₅₃	C₂×D₄²
hypercenter	#3151	D₅₃
hypocenter	C₅₃	#61110
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #3151

Complements

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

N	H ≅ G/N	type
1. #20289491	C₂	semidirect
2. #20286514	C₂	semidirect
3. #20286508	C₂	semidirect
4. #20286481	C₂	semidirect
5. #20284439	C₂	semidirect
6. #20284063	C₂	semidirect
7. C₂×#16810790	C₂	semidirect
8. #20283626	C₂	semidirect
9. C₅₃×#3151	C₂	semidirect
10. #16811459	C₂²	semidirect
11. C₂×#13133262	C₂²	semidirect
13. #16811429	C₂²	semidirect
15. #16811424	C₂²	semidirect
17. #16811421	C₂²	semidirect
19. C₂×#13133243	C₂²	semidirect
21. #16811389	C₂²	semidirect
22. #16810890	C₂²	semidirect
23. #16810883	C₂²	semidirect
24. #16810805	C₂²	semidirect
25. #16810800	C₂²	semidirect
26. #16810795	C₂²	semidirect
27. #16810790	C₂²	semidirect
28. #16810790	C₂²	semidirect
29. #16810790	C₂²	semidirect
30. #16810746	C₂²	semidirect
31. #16810741	C₂²	semidirect
32. #16810672	C₂²	semidirect
33. C₂×#13133145	C₂²	semidirect
34. #16810607	C₂²	semidirect
35. C₂×#13133134	C₂²	semidirect
36. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
37. C₅₃×#532	C₂²	semidirect
38. C₂×#127×C₅₃	C₂²	semidirect
39. C₅₃×#496	C₂²	semidirect
40. C₅₃×#493	C₂²	semidirect
41. C₅₃×#492	C₂²	semidirect
42. C₄×M₁₆×C₅₃	C₂²	semidirect
50. #13133262	C₂³	semidirect
57. #13133250	D₄	semidirect
58. #13133248	C₂³	semidirect
61. #13133245	D₄	semidirect
65. #13133243	C₂³	semidirect
78. #13133223	C₂³	semidirect
81. #13133153	C₂³	semidirect
82. #13133145	C₂³	semidirect
83. #13133145	C₂³	semidirect
84. #13133136	C₂³	semidirect
85. #13133134	C₂³	semidirect
86. #13133134	C₂³	semidirect
92. C₂×SD₁₆×C₅₃	C₂³	semidirect
93. C₂×D₈×C₅₃	C₂³	semidirect
95. C₄⋊Q₈×C₅₃	C₂³	semidirect
99. #127×C₅₃	C₂³	semidirect
100. #124×C₅₃	C₂³	semidirect
104. #97×C₅₃	C₂³	semidirect
105. C₄×C₈×C₅₃	C₂³	semidirect
171. Dic₂₁₂	C₂×D₄	semidirect
172. D₄₂₄	C₂×D₄	semidirect
173. #11719913	C₂×D₄	semidirect
245. #3151	D₅₃	semidirect
267. C₂×AGL(1,ℤ/8)	C₂×D₅₃	semidirect
269. #532	C₂×D₅₃	semidirect
270. C₂×#127	C₂×D₅₃	semidirect
271. #496	C₂×D₅₃	semidirect
272. #493	C₂×D₅₃	semidirect
273. #492	C₂×D₅₃	semidirect
288. C₄×M₁₆	C₂×D₅₃	semidirect
289. C₅₃	#61110	semidirect
327. C₂×SD₁₆	C₂²×D₅₃	semidirect
330. C₂×D₈	C₂²×D₅₃	semidirect
336. C₄⋊Q₈	C₂²×D₅₃	semidirect
340. #127	C₂²×D₅₃	semidirect
341. #124	C₂²×D₅₃	semidirect
351. #97	C₂²×D₅₃	semidirect
352. C₄×C₈	C₂²×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#20289491	2
#20286514	2
#20286508	2
#20286481	2
#20284439	2
#20284063	2
C₂×#16810790	2
#20283626	2
C₅₃×#3151	2
#61110	53