Subgroups — #20283745

Order 6784.

464 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic
2	#16810699	C₂	1	1	yes	maximal, characteristic, complemented
3	#16810698	C₂	1	1	yes	maximal, characteristic, complemented
4	#16810696	C₂	1	1	yes	maximal, characteristic, complemented
5	#16810695	C₂	1	1	yes	maximal, characteristic, complemented
6	#16810693	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×C₂²⋊D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#16810686	C₂	1	1	yes	maximal, characteristic, complemented
9	#16810678	C₂	1	1	yes	maximal, characteristic, complemented
10	#16810675	C₂	1	1	yes	maximal, characteristic, complemented
11	#16810586	C₂	1	1	yes	maximal, characteristic, complemented
12	#16810585	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#13133129	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²⋊C₈×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₄×D₅₃	C₄	1	1	yes	characteristic
17	C₂²×C₄×D₅₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₅₃	C₂²	1	1	yes	characteristic
19	C₂×#11719917	C₂²	1	1	yes	characteristic, complemented
20	C₂×#11719912	C₂²	1	1	yes	characteristic, complemented
21	C₂×#11719912	C₂²	1	1	yes	characteristic, complemented
22	C₂²×#88322	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
25	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
26	D₄×Dic₅₃	C₄	1	1	yes	characteristic
27	#13133179	C₄	1	1	yes	characteristic
28	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
29	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
30	#13133177	C₄	1	1	yes	characteristic
31	#13133177	C₄	1	1	yes	characteristic
32	C₄⋊C₄×D₅₃	C₄	1	1	yes	characteristic
33	C₂²⋊C₄×D₅₃	C₄	1	1	yes	characteristic
34	C₂²⋊C₄×D₅₃	C₄	1	1	yes	characteristic
35	C₄²×D₅₃	C₂²	1	1	yes	characteristic
36	C₄⋊#88322	C₂²	1	1	yes	characteristic, complemented
37	#13133146	C₂²	1	1	yes	characteristic, complemented
38	#13133146	C₂²	1	1	yes	characteristic, complemented
39	C₂²⋊#88322	C₂²	1	1	yes	characteristic, complemented
40	C₂²⋊#88322	C₂²	1	1	yes	characteristic, complemented
41	#13133129	C₂²	1	1	yes	characteristic
42	#13133129	C₂²	1	1	yes	characteristic
43	#13133129	C₂²	1	1	yes	characteristic
44	#13133129	C₂²	1	1	yes	characteristic
45	#13133129	C₂²	1	1	yes	characteristic, complemented
46	#13133129	C₂²	1	1	yes	characteristic, complemented
47	#13133129	C₂²	1	1	yes	characteristic, complemented
48	#13133129	C₂²	1	1	yes	characteristic, complemented
49	#13133128	C₂²	1	1	yes	characteristic, complemented
50	C₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
51	C₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
52	C₂×M₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
53	C₂²×C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
54	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
55	C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
56	C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
57	C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
58	#97×C₅₃	C₂²	1	1	yes	characteristic, complemented
59	C₂³×D₅₃	C₂×C₄	1	1	yes	characteristic
60	C₂³×D₅₃	C₂×C₄	1	1	yes	characteristic
61	C₂×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
64	C₂×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
66	C₂²×Dic₅₃	C₂×C₄	1	1	yes	characteristic
67	C₂²×Dic₅₃	C₂×C₄	1	1	yes	characteristic
68	D₄×D₅₃	—	2	4	no	—
69	C₂×D₂₁₂	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄×D₅₃	—	4	1	no	—
71	C₂×C₄×D₅₃	—	4	1	no	—
72	C₂×C₄×D₅₃	—	4	1	no	—
73	C₂×C₄×D₅₃	—	4	1	no	—
74	C₂×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
81	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
82	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
83	M₁₆×C₅₃	—	4	1	no	—
84	C₂×C₈×C₅₃	—	4	1	no	—
85	C₂×C₈×C₅₃	C₂³	1	1	yes	characteristic
86	C₂×C₈×C₅₃	C₂³	1	1	yes	characteristic
87	C₂×C₈×C₅₃	C₂³	1	1	yes	characteristic
88	C₂×C₈×C₅₃	C₂³	1	1	yes	characteristic
89	C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
90	C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
91	C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
92	C₄²×C₅₃	C₂³	1	1	yes	characteristic
93	C₂²⋊Dic₅₃	C₂×C₄	1	1	yes	characteristic
94	C₂²⋊Dic₅₃	C₂×C₄	1	1	yes	characteristic
95	#11719921	C₂×C₄	1	1	yes	characteristic
96	#11719921	C₂×C₄	1	1	yes	characteristic
97	#11719921	C₂×C₄	1	1	yes	characteristic
98	#11719921	C₂×C₄	1	1	yes	characteristic
99	C₄⋊Dic₅₃	C₂×C₄	1	1	yes	characteristic
100	#11719919	C₂×C₄	1	1	yes	characteristic
101	#11719919	C₂×C₄	1	1	yes	characteristic
102	C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
103	C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
104	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
105	#11719917	—	4	1	no	—
106	C₂×#88322	—	4	1	no	—
107	C₂×#88322	C₂³	1	1	yes	characteristic
108	C₂×#88322	C₂³	1	1	yes	characteristic
109	C₂×#88322	C₂³	1	1	yes	characteristic
110	C₂×#88322	C₂³	1	1	yes	characteristic
111	#11719912	—	4	1	no	—
112	#11719912	—	4	1	no	—
113	C₈×D₅₃	—	4	1	no	—
114	C₈×D₅₃	—	4	1	no	—
115	C₂³×C₅₃	C₂²×C₄	1	1	yes	characteristic
116	C₂³×C₅₃	C₂²×C₄	1	1	yes	characteristic
117	C₂²×D₅₃	—	2	2	no	—
118	C₂²×D₅₃	—	2	2	no	—
119	C₂²×D₅₃	—	2	2	no	—
120	C₂²×D₅₃	—	2	2	no	—
121	C₂²×D₅₃	—	4	1	no	—
122	C₂²×D₅₃	—	4	1	no	—
123	C₂²×D₅₃	C₂²×C₄	1	1	yes	characteristic
124	C₂²×D₅₃	C₂²×C₄	1	1	yes	characteristic
125	C₂²×D₅₃	C₂²×C₄	1	1	yes	characteristic
126	D₄×C₅₃	—	2	2	no	—
127	C₂×C₄×C₅₃	—	2	1	no	—
128	C₂×C₄×C₅₃	—	2	1	no	—
129	C₂×C₄×C₅₃	—	2	1	no	—
130	C₂×C₄×C₅₃	—	2	1	no	—
131	C₂×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
136	C₂²⋊D₅₃	—	2	2	no	—
137	C₂²⋊D₅₃	M₁₆	1	4	yes	complemented
138	C₂×Dic₅₃	—	4	1	no	—
139	C₂×Dic₅₃	—	4	1	no	—
140	C₂×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
141	C₂×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
142	C₂×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
143	C₂×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
144	C₂×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
145	D₂₁₂	—	2	2	no	—
146	C₄×D₅₃	—	2	2	no	—
147	C₄×D₅₃	—	2	1	no	—
148	C₄×D₅₃	—	2	1	no	—
149	C₄×D₅₃	—	2	1	no	—
150	C₄×D₅₃	—	2	1	no	—
151	C₄×D₅₃	—	2	1	no	—
152	C₄×D₅₃	—	2	1	no	—
153	C₄×D₅₃	—	2	2	no	—
154	C₄×D₅₃	—	4	1	no	—
155	C₄×D₅₃	—	4	1	no	—
156	C₄×D₅₃	—	4	1	no	—
157	C₄×D₅₃	—	4	1	no	—
158	C₈×C₅₃	—	2	1	no	—
159	C₈×C₅₃	—	2	1	no	—
160	C₈×C₅₃	—	2	1	no	—
161	C₈×C₅₃	—	2	1	no	—
162	#88322	—	2	1	no	—
163	#88322	—	2	1	no	—
164	#88322	—	2	1	no	—
165	#88322	—	2	1	no	—
166	C₂²×C₅₃	—	2	1	no	—
167	C₂²×C₅₃	—	2	1	no	—
168	C₂²×C₅₃	—	2	1	no	—
169	C₂²×C₅₃	—	2	1	no	—
170	C₂²×C₅₃	—	2	1	no	—
171	C₂²×C₅₃	C₂×M₁₆	1	2	yes	—
172	C₂²×C₅₃	C₂³×C₄	1	1	yes	characteristic
173	C₂×D₅₃	—	2	1	no	—
174	C₂×D₅₃	—	2	1	no	—
175	C₂×D₅₃	—	2	1	no	—
176	C₂×D₅₃	—	2	1	no	—
177	C₂×D₅₃	—	2	1	no	—
178	C₂×D₅₃	—	2	1	no	—
179	C₂×D₅₃	—	2	1	no	—
180	C₂×D₅₃	—	4	4	no	—
181	C₂×D₅₃	—	4	4	no	—
182	C₂×D₅₃	C₂×M₁₆	1	2	yes	—
183	C₂×D₅₃	#131	1	2	yes	—
184	C₄×C₅₃	—	2	1	no	—
185	C₄×C₅₃	—	2	1	no	—
186	C₄×C₅₃	—	2	1	no	—
187	C₄×C₅₃	—	2	1	no	—
188	C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
189	C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
190	Dic₅₃	—	2	1	no	—
191	Dic₅₃	—	2	1	no	—
192	Dic₅₃	—	2	1	no	—
193	Dic₅₃	—	2	1	no	—
194	Dic₅₃	C₂×M₁₆	1	2	yes	—
195	#2974	—	53	1	no	maximal, Sylow
196	C₂×C₅₃	—	2	2	no	—
197	C₂×C₅₃	—	4	1	no	—
198	C₂×C₅₃	#518	1	1	yes	characteristic
199	C₂×C₅₃	C₂²×M₁₆	1	1	yes	characteristic
200	C₂×C₅₃	C₂×#131	1	1	yes	characteristic
201	D₅₃	—	2	2	no	—
202	D₅₃	—	2	2	no	—
203	D₅₃	—	4	1	no	—
204	C₂×C₄×D₄	—	53	1	no	—
205	#436	—	53	1	no	—
206	#436	—	53	1	no	—
207	#435	—	53	1	no	—
208	#435	—	53	1	no	—
209	#435	—	53	1	no	—
210	#435	D₅₃	1	1	yes	characteristic, complemented
211	C₈×D₄	—	53	1	no	—
212	C₈×D₄	—	53	1	no	—
213	#432	—	53	1	no	—
214	#431	—	53	1	no	—
215	#407	—	53	1	no	—
216	#407	—	53	1	no	—
217	C₂×C₂²⋊C₈	—	53	1	no	—
218	C₂×C₂²⋊C₈	—	53	1	no	—
219	C₅₃	#2974	1	1	yes	characteristic, complemented, Sylow
220	C₂²×D₄	—	53	1	no	—
221	C₂³×C₄	—	53	1	no	—
222	C₂³×C₄	—	53	1	no	—
223	C₂×M₁₆	—	53	1	no	—
224	C₂×M₁₆	—	53	1	no	—
225	C₂×M₁₆	—	53	1	no	—
226	C₂×M₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
227	C₂²×C₈	—	53	1	no	—
228	C₂²×C₈	—	53	1	no	—
229	C₂²×C₈	—	53	1	no	—
230	C₂²×C₈	C₂×D₅₃	1	1	yes	characteristic, complemented
231	C₄×D₄	—	53	1	no	—
232	C₄×D₄	—	53	1	no	—
233	C₄×D₄	—	53	1	no	—
234	C₄×D₄	—	53	1	no	—
235	C₄×D₄	—	53	1	no	—
236	C₄×D₄	—	53	1	no	—
237	C₄×D₄	—	53	1	no	—
238	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
239	C₂×C₄⋊C₄	—	53	1	no	—
240	C₂×C₂²⋊C₄	—	53	1	no	—
241	C₂×C₂²⋊C₄	—	53	1	no	—
242	C₂×C₄²	—	53	1	no	—
243	C₄⋊C₈	—	53	1	no	—
244	C₄⋊C₈	—	53	1	no	—
245	C₄⋊C₈	—	53	1	no	—
246	C₄⋊C₈	C₂×D₅₃	1	1	yes	characteristic, complemented
247	C₂²⋊C₈	—	53	1	no	—
248	C₂²⋊C₈	—	53	1	no	—
249	C₂²⋊C₈	—	53	1	no	—
250	C₂²⋊C₈	—	53	1	no	—
251	C₂²⋊C₈	—	53	1	no	—
252	C₂²⋊C₈	—	53	1	no	—
253	C₂²⋊C₈	—	53	1	no	—
254	C₂²⋊C₈	—	53	1	no	—
255	C₂²⋊C₈	—	53	1	no	—
256	C₂²⋊C₈	—	53	1	no	—
257	C₂²⋊C₈	C₂×D₅₃	1	1	yes	characteristic, complemented
258	C₂²⋊C₈	C₂×D₅₃	1	1	yes	characteristic, complemented
259	#97	—	53	1	no	—
260	#97	C₂×D₅₃	1	1	yes	characteristic, complemented
261	C₄×C₈	—	53	1	no	—
262	C₄×C₈	—	53	1	no	—
263	C₂⁴	—	53	1	no	—
264	C₂⁴	—	53	1	no	—
265	C₂×D₄	—	53	1	no	—
266	C₂×D₄	—	53	1	no	—
267	C₂×D₄	—	53	1	no	—
268	C₂×D₄	—	106	4	no	—
269	C₂×D₄	C₄×D₅₃	1	1	yes	characteristic
270	C₂²×C₄	—	53	1	no	—
271	C₂²×C₄	—	53	1	no	—
272	C₂²×C₄	—	53	1	no	—
273	C₂²×C₄	—	53	1	no	—
274	C₂²×C₄	—	53	1	no	—
275	C₂²×C₄	—	53	1	no	—
276	C₂²×C₄	—	53	1	no	—
277	C₂²×C₄	—	53	1	no	—
278	C₂²×C₄	—	53	1	no	—
279	C₂²×C₄	—	53	1	no	—
280	C₂²×C₄	—	53	1	no	—
281	C₂²×C₄	—	212	1	no	—
282	C₂²×C₄	—	212	1	no	—
283	C₂²×C₄	—	212	1	no	—
284	C₂²×C₄	—	212	1	no	—
285	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
286	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
287	M₁₆	—	4	1	no	—
288	M₁₆	—	212	1	no	—
289	M₁₆	—	212	1	no	—
290	M₁₆	—	212	1	no	—
291	C₂×C₈	—	4	1	no	—
292	C₂×C₈	—	53	1	no	—
293	C₂×C₈	—	53	1	no	—
294	C₂×C₈	—	53	1	no	—
295	C₂×C₈	—	53	1	no	—
296	C₂×C₈	—	212	1	no	—
297	C₂×C₈	—	212	1	no	—
298	C₂×C₈	—	212	1	no	—
299	C₂×C₈	C₂²×D₅₃	1	1	yes	characteristic
300	C₂×C₈	C₂²×D₅₃	1	1	yes	characteristic
301	C₂×C₈	C₂²×D₅₃	1	1	yes	characteristic
302	C₂×C₈	C₂²×D₅₃	1	1	yes	characteristic
303	C₄⋊C₄	—	53	1	no	—
304	C₄⋊C₄	—	53	1	no	—
305	C₄⋊C₄	—	53	1	no	—
306	C₄⋊C₄	C₄×D₅₃	1	1	yes	characteristic
307	C₂²⋊C₄	—	53	1	no	—
308	C₂²⋊C₄	—	53	1	no	—
309	C₂²⋊C₄	—	53	1	no	—
310	C₂²⋊C₄	—	53	1	no	—
311	C₂²⋊C₄	—	53	1	no	—
312	C₂²⋊C₄	—	53	1	no	—
313	C₂²⋊C₄	C₄×D₅₃	1	1	yes	characteristic
314	C₂²⋊C₄	C₄×D₅₃	1	1	yes	characteristic
315	C₄²	—	53	1	no	—
316	C₄²	—	53	1	no	—
317	C₄²	—	53	1	no	—
318	C₄²	C₂²×D₅₃	1	1	yes	characteristic
319	C₂³	—	53	1	no	—
320	C₂³	—	53	1	no	—
321	C₂³	—	53	1	no	—
322	C₂³	—	106	2	no	—
323	C₂³	—	106	2	no	—
324	C₂³	—	106	2	no	—
325	C₂³	—	106	2	no	—
326	C₂³	—	212	1	no	—
327	C₂³	—	212	1	no	—
328	C₂³	C₂×C₄×D₅₃	1	1	yes	characteristic
329	C₂³	C₂×C₄×D₅₃	1	1	yes	characteristic
330	D₄	—	2	2	no	—
331	D₄	—	53	4	no	—
332	D₄	—	106	2	no	—
333	D₄	—	106	2	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	53	1	no	—
339	C₂×C₄	—	53	1	no	—
340	C₂×C₄	—	53	1	no	—
341	C₂×C₄	—	53	1	no	—
342	C₂×C₄	—	53	1	no	—
343	C₂×C₄	—	106	2	no	—
344	C₂×C₄	—	106	2	no	—
345	C₂×C₄	—	106	1	no	—
346	C₂×C₄	—	106	1	no	—
347	C₂×C₄	—	106	1	no	—
348	C₂×C₄	—	106	1	no	—
349	C₂×C₄	—	106	1	no	—
350	C₂×C₄	—	106	1	no	—
351	C₂×C₄	—	212	1	no	—
352	C₂×C₄	—	212	1	no	—
353	C₂×C₄	—	212	1	no	—
354	C₂×C₄	—	212	1	no	—
355	C₂×C₄	—	212	1	no	—
356	C₂×C₄	—	212	1	no	—
357	C₂×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
358	C₂×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
359	C₂×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
360	C₂×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
361	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
362	C₈	—	2	1	no	—
363	C₈	—	2	1	no	—
364	C₈	—	2	1	no	—
365	C₈	—	2	1	no	—
366	C₈	—	106	1	no	—
367	C₈	—	106	1	no	—
368	C₈	—	106	1	no	—
369	C₈	—	106	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	53	2	no	—
376	C₂²	—	53	2	no	—
377	C₂²	—	106	1	no	—
378	C₂²	—	106	1	no	—
379	C₂²	—	106	1	no	—
380	C₂²	—	106	1	no	—
381	C₂²	—	106	1	no	—
382	C₂²	—	106	1	no	—
383	C₂²	—	106	1	no	—
384	C₂²	—	212	4	no	—
385	C₂²	—	212	4	no	—
386	C₂²	M₁₆×D₅₃	1	2	yes	—
387	C₂²	C₂²×C₄×D₅₃	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	53	2	no	—
393	C₄	—	106	1	no	—
394	C₄	—	106	1	no	—
395	C₄	—	106	1	no	—
396	C₄	—	106	1	no	—
397	C₄	#13133262	1	1	yes	characteristic
398	C₄	#13133263	1	1	yes	characteristic
399	C₂	—	2	2	no	—
400	C₂	—	4	1	no	—
401	C₂	—	106	2	no	—
402	C₂	—	106	2	no	—
403	C₂	—	212	1	no	—
404	C₂	#16811095	1	1	yes	characteristic
405	C₂	C₂×M₁₆×D₅₃	1	1	yes	characteristic
406	C₂	#131×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₅₃
commutator, socle	C₂²×C₅₃	C₂³×C₄
Fitting	C₅₃×#435	C₂
hypercenter	#435	D₅₃
hypocenter	C₅₃	#2974
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
2. #16810699	C₂	semidirect
3. #16810698	C₂	semidirect
4. #16810696	C₂	semidirect
5. #16810695	C₂	semidirect
6. #16810693	C₂	semidirect
7. C₈×C₂²⋊D₅₃	C₂	semidirect
8. #16810686	C₂	semidirect
9. #16810678	C₂	semidirect
10. #16810675	C₂	semidirect
11. #16810586	C₂	semidirect
12. #16810585	C₂	semidirect
13. C₂×#13133129	C₂	semidirect
14. C₂²⋊C₈×D₅₃	C₂	semidirect
15. C₅₃×#435	C₂	semidirect
19. C₂×#11719917	C₂²	semidirect
20. C₂×#11719912	C₂²	semidirect
21. C₂×#11719912	C₂²	semidirect
22. C₂²×#88322	C₂²	semidirect
23. C₂×C₈×D₅₃	C₂²	semidirect
24. C₂×C₈×D₅₃	C₂²	semidirect
36. C₄⋊#88322	C₂²	semidirect
37. #13133146	C₂²	semidirect
38. #13133146	C₂²	semidirect
39. C₂²⋊#88322	C₂²	semidirect
40. C₂²⋊#88322	C₂²	semidirect
45. #13133129	C₂²	semidirect
46. #13133129	C₂²	semidirect
47. #13133129	C₂²	semidirect
48. #13133129	C₂²	semidirect
49. #13133128	C₂²	semidirect
50. C₈×Dic₅₃	C₂²	semidirect
51. C₈×Dic₅₃	C₂²	semidirect
52. C₂×M₁₆×C₅₃	C₂²	semidirect
53. C₂²×C₈×C₅₃	C₂²	semidirect
55. C₄⋊C₈×C₅₃	C₂²	semidirect
56. C₂²⋊C₈×C₅₃	C₂²	semidirect
57. C₂²⋊C₈×C₅₃	C₂²	semidirect
58. #97×C₅₃	C₂²	semidirect
137. C₂²⋊D₅₃	M₁₆	semidirect
210. #435	D₅₃	semidirect
219. C₅₃	#2974	semidirect
226. C₂×M₁₆	C₂×D₅₃	semidirect
230. C₂²×C₈	C₂×D₅₃	semidirect
246. C₄⋊C₈	C₂×D₅₃	semidirect
257. C₂²⋊C₈	C₂×D₅₃	semidirect
258. C₂²⋊C₈	C₂×D₅₃	semidirect
260. #97	C₂×D₅₃	semidirect