Subgroups — #20283964

Order 6784.

806 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13133244	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#13133241	C₂	1	1	yes	maximal, characteristic, complemented
4	#121×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#16810770	C₂	1	1	yes	maximal, characteristic, complemented
6	#16810768	C₂	1	1	yes	maximal, characteristic, complemented
7	#16810766	C₂	1	1	yes	maximal, characteristic, complemented
8	#16810763	C₂	1	1	yes	maximal, characteristic, complemented
9	#16810760	C₂	1	1	yes	maximal, characteristic, complemented
10	#16810758	C₂	1	1	yes	maximal, characteristic, complemented
11	#16810755	C₂	1	1	yes	maximal, characteristic, complemented
12	#16810623	C₂	1	1	yes	maximal, characteristic, complemented
13	#16810621	C₂	1	1	yes	maximal, characteristic, complemented
14	#16810585	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#449	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#11719949	C₂²	1	1	yes	characteristic
17	C₂×#11719945	—	2	1	no	—
18	C₂×#11719945	C₂²	1	1	yes	characteristic, complemented
19	C₂×#11719947	—	2	1	no	—
20	C₂×#11719947	C₂²	1	1	yes	characteristic
21	#41×D₅₃	—	2	4	no	—
22	#41×D₅₃	—	2	4	no	—
23	C₂×Q₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
24	C₂×D₄×D₅₃	—	2	1	no	—
25	C₂×D₄×D₅₃	—	2	1	no	—
26	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
27	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₄×D₅₃	—	2	1	no	—
29	C₂²×C₄×D₅₃	C₂²	1	1	yes	characteristic
30	#13133244	—	2	4	no	—
31	#13133241	—	2	4	no	—
32	C₂×#11719913	C₂²	1	1	yes	characteristic, complemented
33	C₂×#11719923	C₂²	1	1	yes	characteristic, complemented
34	C₂×#11719924	C₂²	1	1	yes	characteristic, complemented
35	C₂×D₄₂₄	C₂²	1	1	yes	characteristic, complemented
36	C₂×#11719922	C₂²	1	1	yes	characteristic, complemented
37	C₂×#11719922	C₂²	1	1	yes	characteristic, complemented
38	C₂×#11719912	C₂²	1	1	yes	characteristic, complemented
39	C₂×#11719912	C₂²	1	1	yes	characteristic, complemented
40	#13133192	C₂²	1	1	yes	characteristic
41	#13133191	C₂²	1	1	yes	characteristic, complemented
42	#13133190	—	2	1	no	—
43	#13133189	—	2	1	no	—
44	#13133188	C₂²	1	1	yes	characteristic
45	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
46	C₂²⋊C₄×D₅₃	—	2	1	no	—
47	#13133142	C₂²	1	1	yes	characteristic, complemented
48	#13133141	C₂²	1	1	yes	characteristic, complemented
49	#13133140	C₂²	1	1	yes	characteristic, complemented
50	#13133139	C₂²	1	1	yes	characteristic, complemented
51	#13133138	C₂²	1	1	yes	characteristic, complemented
52	#13133137	C₂²	1	1	yes	characteristic, complemented
53	C₂²⋊#88322	C₂²	1	1	yes	characteristic, complemented
54	#13133129	C₂²	1	1	yes	characteristic, complemented
55	#13133129	C₂²	1	1	yes	characteristic, complemented
56	C₂×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
57	C₂×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
58	C₂×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
59	#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
60	#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
61	#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
62	C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
63	C₂³×D₅₃	—	2	1	no	—
64	C₂³×D₅₃	—	2	1	no	—
65	C₂³×D₅₃	D₄	1	1	yes	characteristic
66	#41×C₅₃	—	2	2	no	—
67	#41×C₅₃	—	2	2	no	—
68	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
69	C₂×D₄×C₅₃	—	2	1	no	—
70	C₂×D₄×C₅₃	—	2	1	no	—
71	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
72	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₅₃	—	2	1	no	—
74	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊D₅₃	—	2	1	no	—
76	C₂×C₂²⋊D₅₃	—	2	1	no	—
77	C₂×C₂²⋊D₅₃	—	2	1	no	—
78	C₂×C₂²⋊D₅₃	—	2	1	no	—
79	C₂×C₂²⋊D₅₃	—	2	1	no	—
80	C₂×C₂²⋊D₅₃	—	2	1	no	—
81	C₂²×Dic₅₃	—	2	1	no	—
82	C₂²×Dic₅₃	D₄	1	1	yes	characteristic
83	#11719949	—	2	2	no	—
84	#11719949	D₄	1	4	yes	complemented
85	Q₈×D₅₃	—	2	2	no	—
86	Q₈×D₅₃	—	2	2	no	—
87	#11719947	—	2	8	no	—
88	#11719947	—	2	2	no	—
89	#11719947	D₄	1	4	yes	complemented
90	D₄×D₅₃	—	2	8	no	—
91	D₄×D₅₃	—	2	2	no	—
92	D₄×D₅₃	—	2	2	no	—
93	D₄×D₅₃	—	2	2	no	—
94	D₄×D₅₃	—	2	2	no	—
95	D₄×D₅₃	—	4	4	no	—
96	#11719945	—	2	8	no	—
97	#11719945	—	2	2	no	—
98	#11719945	—	2	2	no	—
99	C₂×D₂₁₂	—	2	1	no	—
100	C₂×D₂₁₂	—	2	1	no	—
101	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
102	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
103	C₂×C₄×D₅₃	—	2	8	no	—
104	C₂×C₄×D₅₃	—	2	1	no	—
105	C₂×C₄×D₅₃	—	2	1	no	—
106	C₂×C₄×D₅₃	—	2	1	no	—
107	C₂×C₄×D₅₃	—	2	2	no	—
108	C₂×C₄×D₅₃	—	2	2	no	—
109	C₂×C₄×D₅₃	—	2	1	no	—
110	C₂×C₄×D₅₃	D₄	1	1	yes	characteristic
111	C₂×C₄×D₅₃	D₄	1	1	yes	characteristic
112	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
113	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
114	C₂×Dic₁₀₆	—	2	1	no	—
115	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
116	SD₁₆×C₅₃	—	2	2	no	—
117	D₈×C₅₃	—	2	2	no	—
118	C₂×C₈×C₅₃	C₂³	1	1	yes	characteristic
119	C₂×C₈×C₅₃	C₂³	1	1	yes	characteristic
120	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
121	C₂²⋊C₄×C₅₃	—	2	1	no	—
122	C₂²⋊Dic₅₃	—	2	1	no	—
123	#11719924	—	2	2	no	—
124	#11719923	—	2	2	no	—
125	#11719922	—	2	2	no	—
126	#11719922	—	2	2	no	—
127	#11719921	—	2	1	no	—
128	#11719921	—	2	1	no	—
129	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
130	#11719919	—	2	1	no	—
131	C₂×#88322	C₂³	1	1	yes	characteristic
132	C₂×#88322	C₂³	1	1	yes	characteristic
133	D₄₂₄	—	2	2	no	—
134	#11719913	—	2	2	no	—
135	#11719912	—	2	2	no	—
136	#11719912	—	2	2	no	—
137	C₂³×C₅₃	—	2	1	no	—
138	C₂³×C₅₃	—	2	1	no	—
139	C₂³×C₅₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×D₅₃	—	2	4	no	—
141	C₂²×D₅₃	—	2	1	no	—
142	C₂²×D₅₃	—	2	2	no	—
143	C₂²×D₅₃	—	2	2	no	—
144	C₂²×D₅₃	—	2	1	no	—
145	C₂²×D₅₃	—	4	1	no	—
146	C₂²×D₅₃	—	4	2	no	—
147	C₂²×D₅₃	—	4	2	no	—
148	C₂²×D₅₃	—	4	2	no	—
149	C₂²×D₅₃	—	4	2	no	—
150	C₂²×D₅₃	—	4	2	no	—
151	C₂²×D₅₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×D₅₃	C₂×D₄	1	1	yes	characteristic
153	Q₈×C₅₃	—	2	1	no	—
154	Q₈×C₅₃	C₂×D₄	1	2	yes	complemented
155	D₄×C₅₃	—	2	4	no	—
156	D₄×C₅₃	—	2	1	no	—
157	D₄×C₅₃	—	2	1	no	—
158	D₄×C₅₃	—	2	1	no	—
159	D₄×C₅₃	—	4	2	no	—
160	D₄×C₅₃	C₂×D₄	1	2	yes	complemented
161	C₂×C₄×C₅₃	—	2	4	no	—
162	C₂×C₄×C₅₃	—	2	1	no	—
163	C₂×C₄×C₅₃	—	2	1	no	—
164	C₂×C₄×C₅₃	—	2	1	no	—
165	C₂×C₄×C₅₃	—	2	1	no	—
166	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
167	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
168	C₂²⋊D₅₃	—	2	4	no	—
169	C₂²⋊D₅₃	—	2	4	no	—
170	C₂²⋊D₅₃	—	2	4	no	—
171	C₂²⋊D₅₃	—	4	2	no	—
172	C₂²⋊D₅₃	—	4	2	no	—
173	C₂²⋊D₅₃	—	4	2	no	—
174	C₂×Dic₅₃	—	2	1	no	—
175	C₂×Dic₅₃	—	2	2	no	—
176	C₂×Dic₅₃	—	2	4	no	—
177	C₂×Dic₅₃	—	2	1	no	—
178	C₂×Dic₅₃	C₂×D₄	1	1	yes	characteristic
179	C₂×Dic₅₃	C₂×D₄	1	1	yes	characteristic
180	D₂₁₂	—	2	4	no	—
181	D₂₁₂	—	2	1	no	—
182	D₂₁₂	—	2	1	no	—
183	D₂₁₂	—	2	1	no	—
184	D₂₁₂	—	4	2	no	—
185	D₂₁₂	C₂×D₄	1	2	yes	complemented
186	C₄×D₅₃	—	2	4	no	—
187	C₄×D₅₃	—	2	4	no	—
188	C₄×D₅₃	—	2	2	no	—
189	C₄×D₅₃	—	2	1	no	—
190	C₄×D₅₃	—	2	1	no	—
191	C₄×D₅₃	—	2	2	no	—
192	C₄×D₅₃	—	2	4	no	—
193	C₄×D₅₃	—	4	2	no	—
194	C₄×D₅₃	C₂×D₄	1	2	yes	—
195	C₄×D₅₃	C₂×D₄	1	2	yes	—
196	Dic₁₀₆	—	2	4	no	—
197	Dic₁₀₆	—	2	1	no	—
198	Dic₁₀₆	C₂×D₄	1	2	yes	complemented
199	C₈×C₅₃	—	2	1	no	—
200	C₈×C₅₃	—	2	1	no	—
201	#88322	—	2	1	no	—
202	#88322	—	2	1	no	—
203	C₂²×C₅₃	—	2	1	no	—
204	C₂²×C₅₃	—	2	2	no	—
205	C₂²×C₅₃	—	2	1	no	—
206	C₂²×C₅₃	—	2	1	no	—
207	C₂²×C₅₃	—	4	1	no	—
208	C₂²×C₅₃	—	4	1	no	—
209	C₂²×C₅₃	—	4	1	no	—
210	C₂²×C₅₃	—	4	1	no	—
211	C₂²×C₅₃	—	4	1	no	—
212	C₂²×C₅₃	C₂²×D₄	1	1	yes	characteristic
213	C₂×D₅₃	—	2	1	no	—
214	C₂×D₅₃	—	2	1	no	—
215	C₂×D₅₃	—	2	1	no	—
216	C₂×D₅₃	—	2	1	no	—
217	C₂×D₅₃	—	2	2	no	—
218	C₂×D₅₃	—	4	4	no	—
219	C₂×D₅₃	—	4	8	no	—
220	C₂×D₅₃	—	4	1	no	—
221	C₂×D₅₃	—	4	1	no	—
222	C₂×D₅₃	—	4	1	no	—
223	C₂×D₅₃	—	4	1	no	—
224	C₂×D₅₃	—	4	1	no	—
225	C₂×D₅₃	—	8	4	no	—
226	C₂×D₅₃	#120	1	2	yes	—
227	C₂×D₅₃	AGL(1,ℤ/8)	1	2	yes	complemented
228	C₄×C₅₃	—	2	2	no	—
229	C₄×C₅₃	—	2	1	no	—
230	C₄×C₅₃	—	4	1	no	—
231	C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
232	C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
233	Dic₅₃	—	2	1	no	—
234	Dic₅₃	—	2	2	no	—
235	Dic₅₃	—	4	1	no	—
236	Dic₅₃	#120	1	2	yes	—
237	#3006	—	53	1	no	maximal, Sylow
238	C₂×C₅₃	—	4	1	no	—
239	C₂×C₅₃	—	4	2	no	—
240	C₂×C₅₃	—	8	1	no	—
241	C₂×C₅₃	C₂×#120	1	1	yes	characteristic
242	C₂×C₅₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
243	C₂×C₅₃	#575	1	1	yes	characteristic
244	D₅₃	—	2	2	no	—
245	D₅₃	—	2	2	no	—
246	D₅₃	—	4	2	no	—
247	D₅₃	—	8	1	no	—
248	C₂²×#41	—	53	1	no	—
249	C₂×AGL(1,ℤ/8)	—	53	1	no	—
250	C₂×AGL(1,ℤ/8)	—	53	1	no	—
251	C₂×#121	—	53	1	no	—
252	#449	—	53	1	no	—
253	#449	—	53	1	no	—
254	#449	—	53	1	no	—
255	#449	D₅₃	1	1	yes	characteristic, complemented
256	#448	—	53	1	no	—
257	#448	—	53	1	no	—
258	#447	—	53	1	no	—
259	#447	—	53	1	no	—
260	#417	—	53	1	no	—
261	#417	—	53	1	no	—
262	#407	—	53	1	no	—
263	C₅₃	#3006	1	1	yes	characteristic, complemented, Sylow
264	C₂×#41	—	53	1	no	—
265	C₂×#41	—	53	1	no	—
266	C₂×#41	—	53	1	no	—
267	C₂×#41	—	106	1	no	—
268	C₂×#41	—	106	1	no	—
269	C₂×#41	—	106	4	no	—
270	C₂×#41	—	106	4	no	—
271	C₂×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
272	C₂²×Q₈	—	53	1	no	—
273	C₂²×D₄	—	53	1	no	—
274	C₂²×D₄	—	53	1	no	—
275	C₂²×D₄	—	106	1	no	—
276	C₂²×D₄	—	106	1	no	—
277	C₂³×C₄	—	53	1	no	—
278	C₂³×C₄	—	106	1	no	—
279	AGL(1,ℤ/8)	—	106	4	no	—
280	AGL(1,ℤ/8)	—	106	4	no	—
281	C₂×SD₁₆	—	53	1	no	—
282	C₂×SD₁₆	—	53	1	no	—
283	C₂×SD₁₆	—	53	1	no	—
284	C₂×SD₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
285	C₂×D₈	—	53	1	no	—
286	C₂×D₈	—	53	1	no	—
287	C₂×D₈	—	53	1	no	—
288	C₂×D₈	C₂×D₅₃	1	1	yes	characteristic, complemented
289	C₂×M₁₆	—	53	1	no	—
290	C₂×M₁₆	—	53	1	no	—
291	#121	—	53	1	no	—
292	#121	—	53	1	no	—
293	#121	—	53	1	no	—
294	#121	—	106	1	no	—
295	#121	—	106	1	no	—
296	#121	C₂×D₅₃	1	1	yes	characteristic, complemented
297	C₂×C₄⋊C₄	—	53	1	no	—
298	C₂×C₂²⋊C₄	—	106	1	no	—
299	#103	—	53	1	no	—
300	#103	—	53	1	no	—
301	#103	—	53	1	no	—
302	#103	C₂×D₅₃	1	1	yes	characteristic, complemented
303	#102	—	53	1	no	—
304	#102	—	53	1	no	—
305	#102	—	53	1	no	—
306	#102	C₂×D₅₃	1	1	yes	characteristic, complemented
307	C₂²⋊C₈	—	53	1	no	—
308	C₂²⋊C₈	—	53	1	no	—
309	C₂²⋊C₈	—	53	1	no	—
310	C₂²⋊C₈	C₂×D₅₃	1	1	yes	characteristic, complemented
311	C₂⁴	—	53	1	no	—
312	C₂⁴	—	106	1	no	—
313	C₂⁴	—	106	1	no	—
314	#41	—	2	2	no	—
315	#41	—	2	2	no	—
316	#41	—	53	4	no	—
317	#41	—	53	4	no	—
318	#41	—	106	2	no	—
319	#41	—	106	2	no	—
320	#41	—	106	8	no	—
321	#41	—	106	2	no	—
322	#41	—	106	2	no	—
323	#41	—	106	8	no	—
324	C₂×Q₈	—	53	1	no	—
325	C₂×Q₈	—	106	1	no	—
326	C₂×Q₈	—	106	2	no	—
327	C₂×Q₈	—	106	2	no	—
328	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	53	1	no	—
332	C₂×D₄	—	53	1	no	—
333	C₂×D₄	—	106	1	no	—
334	C₂×D₄	—	106	1	no	—
335	C₂×D₄	—	106	2	no	—
336	C₂×D₄	—	106	2	no	—
337	C₂×D₄	—	106	1	no	—
338	C₂×D₄	—	106	1	no	—
339	C₂×D₄	—	106	2	no	—
340	C₂×D₄	—	106	8	no	—
341	C₂×D₄	—	106	1	no	—
342	C₂×D₄	—	106	1	no	—
343	C₂×D₄	—	106	2	no	—
344	C₂×D₄	—	106	1	no	—
345	C₂×D₄	—	106	1	no	—
346	C₂×D₄	—	212	4	no	—
347	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
348	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	53	1	no	—
351	C₂²×C₄	—	53	1	no	—
352	C₂²×C₄	—	53	1	no	—
353	C₂²×C₄	—	53	1	no	—
354	C₂²×C₄	—	53	1	no	—
355	C₂²×C₄	—	106	2	no	—
356	C₂²×C₄	—	106	2	no	—
357	C₂²×C₄	—	106	1	no	—
358	C₂²×C₄	—	106	1	no	—
359	C₂²×C₄	—	106	8	no	—
360	C₂²×C₄	—	106	1	no	—
361	C₂²×C₄	—	106	1	no	—
362	C₂²×C₄	—	106	1	no	—
363	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
364	SD₁₆	—	2	2	no	—
365	SD₁₆	—	106	2	no	—
366	SD₁₆	—	106	2	no	—
367	SD₁₆	—	106	2	no	—
368	D₈	—	2	2	no	—
369	D₈	—	106	2	no	—
370	D₈	—	106	2	no	—
371	D₈	—	106	2	no	—
372	M₁₆	—	106	2	no	—
373	M₁₆	—	106	2	no	—
374	C₂×C₈	—	53	1	no	—
375	C₂×C₈	—	53	1	no	—
376	C₂×C₈	C₂²×D₅₃	1	1	yes	characteristic
377	C₂×C₈	C₂²×D₅₃	1	1	yes	characteristic
378	C₄⋊C₄	—	53	1	no	—
379	C₄⋊C₄	—	106	1	no	—
380	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
381	C₂²⋊C₄	—	2	1	no	—
382	C₂²⋊C₄	—	106	1	no	—
383	C₂²⋊C₄	—	106	1	no	—
384	C₂²⋊C₄	—	106	1	no	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	1	no	—
387	C₂³	—	53	1	no	—
388	C₂³	—	53	1	no	—
389	C₂³	—	106	2	no	—
390	C₂³	—	106	2	no	—
391	C₂³	—	106	4	no	—
392	C₂³	—	106	1	no	—
393	C₂³	—	106	1	no	—
394	C₂³	—	212	1	no	—
395	C₂³	—	212	2	no	—
396	C₂³	—	212	2	no	—
397	C₂³	—	212	2	no	—
398	C₂³	—	212	2	no	—
399	C₂³	—	212	2	no	—
400	C₂³	D₄×D₅₃	1	1	yes	characteristic
401	Q₈	—	2	1	no	—
402	Q₈	—	53	2	no	—
403	Q₈	—	106	4	no	—
404	Q₈	—	106	1	no	—
405	Q₈	D₄×D₅₃	1	2	yes	complemented
406	D₄	—	2	4	no	—
407	D₄	—	2	1	no	—
408	D₄	—	2	1	no	—
409	D₄	—	2	1	no	—
410	D₄	—	4	2	no	—
411	D₄	—	53	2	no	—
412	D₄	—	106	4	no	—
413	D₄	—	106	4	no	—
414	D₄	—	106	4	no	—
415	D₄	—	106	4	no	—
416	D₄	—	106	1	no	—
417	D₄	—	106	1	no	—
418	D₄	—	106	1	no	—
419	D₄	—	212	2	no	—
420	D₄	—	212	2	no	—
421	D₄	—	212	2	no	—
422	D₄	—	212	2	no	—
423	D₄	D₄×D₅₃	1	2	yes	complemented
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	53	1	no	—
430	C₂×C₄	—	53	2	no	—
431	C₂×C₄	—	53	2	no	—
432	C₂×C₄	—	53	1	no	—
433	C₂×C₄	—	106	2	no	—
434	C₂×C₄	—	106	4	no	—
435	C₂×C₄	—	106	2	no	—
436	C₂×C₄	—	106	4	no	—
437	C₂×C₄	—	106	4	no	—
438	C₂×C₄	—	106	2	no	—
439	C₂×C₄	—	106	4	no	—
440	C₂×C₄	—	106	1	no	—
441	C₂×C₄	—	106	1	no	—
442	C₂×C₄	—	106	1	no	—
443	C₂×C₄	—	106	1	no	—
444	C₂×C₄	—	212	2	no	—
445	C₂×C₄	D₄×D₅₃	1	1	yes	characteristic
446	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
447	C₈	—	2	1	no	—
448	C₈	—	2	1	no	—
449	C₈	—	106	1	no	—
450	C₈	—	106	1	no	—
451	C₂²	—	2	1	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	4	1	no	—
456	C₂²	—	4	1	no	—
457	C₂²	—	4	1	no	—
458	C₂²	—	4	1	no	—
459	C₂²	—	4	1	no	—
460	C₂²	—	53	2	no	—
461	C₂²	—	53	2	no	—
462	C₂²	—	106	1	no	—
463	C₂²	—	106	1	no	—
464	C₂²	—	106	1	no	—
465	C₂²	—	106	1	no	—
466	C₂²	—	106	2	no	—
467	C₂²	—	424	4	no	—
468	C₂²	—	212	4	no	—
469	C₂²	—	212	8	no	—
470	C₂²	—	212	1	no	—
471	C₂²	—	212	1	no	—
472	C₂²	—	212	1	no	—
473	C₂²	—	212	1	no	—
474	C₂²	—	212	1	no	—
475	C₂²	C₂×D₄×D₅₃	1	1	yes	characteristic
476	C₄	—	2	1	no	—
477	C₄	—	2	2	no	—
478	C₄	—	4	1	no	—
479	C₄	—	53	2	no	—
480	C₄	—	106	1	no	—
481	C₄	—	106	2	no	—
482	C₄	—	212	1	no	—
483	C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
484	C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
485	C₂	—	4	1	no	—
486	C₂	—	4	2	no	—
487	C₂	—	8	1	no	—
488	C₂	—	106	2	no	—
489	C₂	—	106	2	no	—
490	C₂	—	424	1	no	—
491	C₂	—	212	2	no	—
492	C₂	#120×D₅₃	1	1	yes	characteristic
493	C₂	AGL(1,ℤ/8)×D₅₃	1	1	yes	characteristic
494	C₂	#16811420	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₅₃
commutator	C₂×C₄×C₅₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₅₃
Fitting	C₅₃×#449	C₂
socle	C₂²×C₅₃	C₂²×D₄
hypercenter	#449	D₅₃
hypocenter	C₅₃	#3006
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #449

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₅₃	C₂	semidirect
2. C₂×#13133244	C₂	semidirect
3. C₂×#13133241	C₂	semidirect
4. #121×D₅₃	C₂	semidirect
5. #16810770	C₂	semidirect
6. #16810768	C₂	semidirect
7. #16810766	C₂	semidirect
8. #16810763	C₂	semidirect
9. #16810760	C₂	semidirect
10. #16810758	C₂	semidirect
11. #16810755	C₂	semidirect
12. #16810623	C₂	semidirect
13. #16810621	C₂	semidirect
14. #16810585	C₂	semidirect
15. C₅₃×#449	C₂	semidirect
18. C₂×#11719945	C₂²	semidirect
23. C₂×Q₈×D₅₃	C₂²	semidirect
26. C₂×D₄×D₅₃	C₂²	semidirect
27. C₂×D₄×D₅₃	C₂²	semidirect
32. C₂×#11719913	C₂²	semidirect
33. C₂×#11719923	C₂²	semidirect
34. C₂×#11719924	C₂²	semidirect
35. C₂×D₄₂₄	C₂²	semidirect
36. C₂×#11719922	C₂²	semidirect
37. C₂×#11719922	C₂²	semidirect
38. C₂×#11719912	C₂²	semidirect
39. C₂×#11719912	C₂²	semidirect
41. #13133191	C₂²	semidirect
45. C₄⋊C₄×D₅₃	C₂²	semidirect
47. #13133142	C₂²	semidirect
48. #13133141	C₂²	semidirect
49. #13133140	C₂²	semidirect
50. #13133139	C₂²	semidirect
51. #13133138	C₂²	semidirect
52. #13133137	C₂²	semidirect
53. C₂²⋊#88322	C₂²	semidirect
54. #13133129	C₂²	semidirect
55. #13133129	C₂²	semidirect
56. C₂×#41×C₅₃	C₂²	semidirect
57. C₂×SD₁₆×C₅₃	C₂²	semidirect
58. C₂×D₈×C₅₃	C₂²	semidirect
59. #121×C₅₃	C₂²	semidirect
60. #103×C₅₃	C₂²	semidirect
61. #102×C₅₃	C₂²	semidirect
62. C₂²⋊C₈×C₅₃	C₂²	semidirect
84. #11719949	D₄	semidirect
89. #11719947	D₄	semidirect
154. Q₈×C₅₃	C₂×D₄	semidirect
160. D₄×C₅₃	C₂×D₄	semidirect
185. D₂₁₂	C₂×D₄	semidirect
198. Dic₁₀₆	C₂×D₄	semidirect
227. C₂×D₅₃	AGL(1,ℤ/8)	semidirect
255. #449	D₅₃	semidirect
263. C₅₃	#3006	semidirect
271. C₂×#41	C₂×D₅₃	semidirect
284. C₂×SD₁₆	C₂×D₅₃	semidirect
288. C₂×D₈	C₂×D₅₃	semidirect
296. #121	C₂×D₅₃	semidirect
302. #103	C₂×D₅₃	semidirect
306. #102	C₂×D₅₃	semidirect
310. C₂²⋊C₈	C₂×D₅₃	semidirect
405. Q₈	D₄×D₅₃	semidirect
423. D₄	D₄×D₅₃	semidirect