Subgroups — #20288383

Order 6784.

1658 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13133263	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#41×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811292	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811285	C₂	1	1	yes	maximal, characteristic, complemented
5	#16811280	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811270	C₂	1	3	yes	maximal, complemented
7	#16811269	C₂	1	3	yes	maximal, complemented
8	#16811258	C₂	1	3	yes	maximal, complemented
9	#16811257	C₂	1	3	yes	maximal, complemented
10	#16811202	C₂	1	3	yes	maximal, complemented
11	#16811186	C₂	1	3	yes	maximal, complemented
12	#16811132	C₂	1	3	yes	maximal, complemented
13	#121×D₅₃	C₂	1	3	yes	maximal, complemented
14	#16811105	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
16	#13133263	—	2	8	no	—
17	C₂×#11719949	C₂²	1	1	yes	characteristic
18	C₂×#11719949	C₂²	1	1	yes	characteristic, complemented
19	C₂×#11719945	C₂²	1	3	yes	complemented
20	C₂×#11719945	C₂²	1	3	yes	complemented
21	C₂×#11719947	C₂²	1	3	yes	complemented
22	#41×D₅₃	—	2	8	no	—
23	C₂×Q₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
24	C₂²×D₂₁₂	C₂²	1	3	yes	complemented
25	C₂×D₄×D₅₃	C₂²	1	3	yes	complemented
26	C₂×D₄×D₅₃	C₂²	1	3	yes	complemented
27	C₂×D₄×D₅₃	C₂²	1	3	yes	complemented
28	C₂×D₄×D₅₃	C₂²	1	6	yes	complemented
29	C₂²×C₄×D₅₃	C₂²	1	3	yes	complemented
30	#13133213	C₂²	1	3	yes	complemented
31	#13133205	C₂²	1	3	yes	complemented
32	#13133204	C₂²	1	3	yes	complemented
33	#13133202	C₂²	1	3	yes	complemented
34	#13133199	C₂²	1	3	yes	complemented
35	#13133197	C₂²	1	3	yes	complemented
36	#13133196	C₂²	1	3	yes	complemented
37	#13133195	C₂²	1	1	yes	characteristic, complemented
38	#13133194	C₂²	1	3	yes	complemented
39	#13133192	C₂²	1	3	yes	complemented
40	#13133191	C₂²	1	3	yes	complemented
41	#13133190	C₂²	1	6	yes	complemented
42	#13133190	C₂²	1	3	yes	complemented
43	#13133189	C₂²	1	6	yes	complemented
44	#13133189	C₂²	1	3	yes	complemented
45	#13133188	C₂²	1	6	yes	complemented
46	#13133188	C₂²	1	3	yes	complemented
47	#13133188	C₂²	1	3	yes	complemented
48	#13133187	C₂²	1	3	yes	complemented
49	#13133185	C₂²	1	6	yes	complemented
50	#13133185	C₂²	1	6	yes	complemented
51	#13133185	C₂²	1	3	yes	complemented
52	Q₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
53	C₄×D₂₁₂	C₂²	1	3	yes	complemented
54	C₄×D₂₁₂	C₂²	1	3	yes	complemented
55	#13133179	C₂²	1	3	yes	complemented
56	C₄×C₂²⋊D₅₃	C₂²	1	3	yes	complemented
57	C₄×C₂²⋊D₅₃	C₂²	1	3	yes	complemented
58	#13133174	C₂²	1	3	yes	complemented
59	C₄⋊C₄×D₅₃	C₂²	1	3	yes	complemented
60	C₂²⋊C₄×D₅₃	C₂²	1	6	yes	complemented
61	C₂×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
62	C₂×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
63	#127×C₅₃	C₂²	1	3	yes	complemented
64	#121×C₅₃	C₂²	1	3	yes	complemented
65	#121×C₅₃	C₂²	1	3	yes	complemented
66	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
67	C₄×D₄×C₅₃	C₂²	1	3	yes	complemented
68	C₂³×D₅₃	C₂³	1	3	yes	—
69	C₂³×D₅₃	C₂³	1	6	yes	—
70	#41×C₅₃	—	2	4	no	—
71	#41×C₅₃	—	2	4	no	—
72	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
73	C₂×D₄×C₅₃	C₂³	1	3	yes	—
74	C₂×D₄×C₅₃	C₂³	1	3	yes	—
75	C₂×D₄×C₅₃	C₂³	1	3	yes	—
76	C₂×D₄×C₅₃	C₂³	1	6	yes	—
77	C₂²×C₄×C₅₃	C₂³	1	3	yes	—
78	C₂²×C₄×C₅₃	C₂³	1	3	yes	—
79	C₂×C₂²⋊D₅₃	C₂³	1	3	yes	—
80	C₂×C₂²⋊D₅₃	C₂³	1	6	yes	—
81	C₂×C₂²⋊D₅₃	C₂³	1	3	yes	—
82	C₂×C₂²⋊D₅₃	C₂³	1	3	yes	—
83	C₂×C₂²⋊D₅₃	C₂³	1	3	yes	—
84	C₂×C₂²⋊D₅₃	C₂³	1	6	yes	—
85	C₂²×Dic₅₃	C₂³	1	3	yes	—
86	#11719949	—	2	4	no	—
87	#11719949	D₄	1	8	yes	complemented
88	Q₈×D₅₃	—	2	4	no	—
89	#11719947	—	2	12	no	—
90	D₄×D₅₃	—	2	12	no	—
91	D₄×D₅₃	—	2	12	no	—
92	D₄×D₅₃	—	2	12	no	—
93	D₄×D₅₃	—	4	12	no	—
94	#11719945	—	2	12	no	—
95	#11719945	—	2	12	no	—
96	C₂×D₂₁₂	—	2	12	no	—
97	C₂×D₂₁₂	C₂³	1	3	yes	—
98	C₂×D₂₁₂	C₂³	1	3	yes	—
99	C₂×D₂₁₂	C₂³	1	3	yes	—
100	C₂×D₂₁₂	C₂³	1	3	yes	—
101	C₂×C₄×D₅₃	—	2	12	no	—
102	C₂×C₄×D₅₃	C₂³	1	3	yes	—
103	C₂×C₄×D₅₃	C₂³	1	3	yes	—
104	C₂×C₄×D₅₃	C₂³	1	3	yes	—
105	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
106	C₂×C₄×D₅₃	C₂³	1	6	yes	—
107	C₂×C₄×D₅₃	C₂³	1	3	yes	—
108	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
109	C₂×Dic₁₀₆	C₂³	1	3	yes	—
110	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
111	C₄⋊C₄×C₅₃	C₂³	1	3	yes	—
112	C₂²⋊C₄×C₅₃	C₂³	1	3	yes	—
113	C₂²⋊C₄×C₅₃	C₂³	1	3	yes	—
114	C₄²×C₅₃	C₂³	1	3	yes	—
115	C₂²⋊Dic₅₃	C₂³	1	6	yes	—
116	C₂²⋊Dic₅₃	C₂³	1	3	yes	—
117	C₂²⋊Dic₅₃	C₂³	1	3	yes	—
118	#11719921	C₂³	1	3	yes	—
119	#11719921	C₂³	1	6	yes	—
120	#11719921	C₂³	1	3	yes	—
121	#11719921	C₂³	1	3	yes	—
122	#11719921	C₂³	1	1	yes	characteristic
123	#11719921	C₂³	1	1	yes	characteristic
124	#11719921	C₂³	1	3	yes	—
125	C₄⋊Dic₅₃	C₂³	1	3	yes	—
126	C₄⋊Dic₅₃	C₂³	1	3	yes	—
127	#11719919	C₂³	1	3	yes	—
128	#11719919	C₂³	1	1	yes	characteristic
129	#11719919	C₂³	1	1	yes	characteristic
130	#11719919	C₂³	1	3	yes	—
131	C₄×Dic₅₃	C₂³	1	3	yes	—
132	C₂³×C₅₃	C₂⁴	1	3	yes	—
133	C₂³×C₅₃	C₂⁴	1	3	yes	—
134	C₂²×D₅₃	—	2	6	no	—
135	C₂²×D₅₃	—	2	6	no	—
136	C₂²×D₅₃	—	2	12	no	—
137	C₂²×D₅₃	—	4	3	no	—
138	C₂²×D₅₃	—	4	6	no	—
139	C₂²×D₅₃	—	4	6	no	—
140	C₂²×D₅₃	C₂⁴	1	3	yes	—
141	C₂²×D₅₃	C₂⁴	1	3	yes	—
142	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
143	Q₈×C₅₃	C₂×D₄	1	4	yes	complemented
144	D₄×C₅₃	—	2	6	no	—
145	D₄×C₅₃	—	2	6	no	—
146	D₄×C₅₃	—	4	6	no	—
147	D₄×C₅₃	—	4	3	no	—
148	C₂×C₄×C₅₃	—	2	6	no	—
149	C₂×C₄×C₅₃	—	2	6	no	—
150	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
151	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
152	C₂×C₄×C₅₃	C₂⁴	1	3	yes	—
153	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
154	C₂×C₄×C₅₃	C₂⁴	1	3	yes	—
155	C₂²⋊D₅₃	—	2	6	no	—
156	C₂²⋊D₅₃	—	2	12	no	—
157	C₂²⋊D₅₃	—	2	6	no	—
158	C₂²⋊D₅₃	—	2	6	no	—
159	C₂²⋊D₅₃	—	4	6	no	—
160	C₂²⋊D₅₃	—	4	3	no	—
161	C₂×Dic₅₃	—	2	6	no	—
162	C₂×Dic₅₃	C₂⁴	1	3	yes	—
163	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
164	C₂×Dic₅₃	C₂⁴	1	3	yes	—
165	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
166	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
167	D₂₁₂	—	2	6	no	—
168	D₂₁₂	—	2	6	no	—
169	D₂₁₂	—	2	6	no	—
170	D₂₁₂	C₂×D₄	1	12	yes	complemented
171	C₄×D₅₃	—	2	6	no	—
172	C₄×D₅₃	—	2	6	no	—
173	C₄×D₅₃	—	2	6	no	—
174	C₄×D₅₃	—	2	2	no	—
175	C₄×D₅₃	—	4	6	no	—
176	C₄×D₅₃	C₂×D₄	1	12	yes	complemented
177	Dic₁₀₆	—	2	6	no	—
178	Dic₁₀₆	—	2	2	no	—
179	C₂²×C₅₃	—	2	3	no	—
180	C₂²×C₅₃	—	2	3	no	—
181	C₂²×C₅₃	—	2	3	no	—
182	C₂²×C₅₃	—	2	3	no	—
183	C₂²×C₅₃	—	2	3	no	—
184	C₂²×C₅₃	—	2	3	no	—
185	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
186	C₂×D₅₃	—	2	1	no	—
187	C₂×D₅₃	—	2	3	no	—
188	C₂×D₅₃	—	2	1	no	—
189	C₂×D₅₃	—	2	3	no	—
190	C₂×D₅₃	—	2	3	no	—
191	C₂×D₅₃	—	2	3	no	—
192	C₂×D₅₃	—	2	3	no	—
193	C₂×D₅₃	—	4	12	no	—
194	C₂×D₅₃	—	8	12	no	—
195	C₂×D₅₃	C₂²×D₄	1	6	yes	—
196	C₂×D₅₃	H(5,𝔽₂)	1	2	yes	complemented
197	C₄×C₅₃	—	2	1	no	—
198	C₄×C₅₃	—	2	1	no	—
199	C₄×C₅₃	—	2	3	no	—
200	C₄×C₅₃	—	2	1	no	—
201	C₄×C₅₃	C₂²×D₄	1	6	yes	—
202	Dic₅₃	—	2	3	no	—
203	Dic₅₃	—	2	1	no	—
204	Dic₅₃	—	2	3	no	—
205	Dic₅₃	—	2	1	no	—
206	Dic₅₃	C₂²×D₄	1	2	yes	—
207	#3488	—	53	1	no	maximal, Sylow
208	C₂×C₅₃	—	4	3	no	—
209	C₂×C₅₃	—	4	3	no	—
210	C₂×C₅₃	C₂³×D₄	1	1	yes	characteristic
211	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
212	C₂×C₅₃	#585	1	1	yes	characteristic
213	D₅₃	—	2	2	no	—
214	D₅₃	—	2	6	no	—
215	D₅₃	—	4	3	no	—
216	C₂×H(5,𝔽₂)	—	53	1	no	—
217	C₂²×#41	—	53	1	no	—
218	#550	—	53	1	no	—
219	#550	D₅₃	1	1	yes	characteristic, complemented
220	#548	—	53	1	no	—
221	#548	—	53	1	no	—
222	#546	—	53	3	no	—
223	#546	—	53	3	no	—
224	D₄²	—	53	3	no	—
225	D₄²	—	53	3	no	—
226	#537	—	53	3	no	—
227	#535	—	53	3	no	—
228	#525	—	53	3	no	—
229	C₂×#121	—	53	3	no	—
230	#520	—	53	1	no	—
231	C₅₃	#3488	1	1	yes	characteristic, complemented, Sylow
232	H(5,𝔽₂)	—	106	8	no	—
233	C₂×#41	—	53	1	no	—
234	C₂×#41	—	53	1	no	—
235	C₂×#41	—	53	3	no	—
236	C₂×#41	—	53	3	no	—
237	C₂×#41	—	53	3	no	—
238	C₂×#41	—	106	8	no	—
239	C₂×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
240	C₂×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
241	C₂²×Q₈	—	53	1	no	—
242	C₂²×D₄	—	53	3	no	—
243	C₂²×D₄	—	53	3	no	—
244	C₂²×D₄	—	53	3	no	—
245	C₂²×D₄	—	53	6	no	—
246	C₂²×D₄	—	53	3	no	—
247	C₂³×C₄	—	53	3	no	—
248	#127	—	53	3	no	—
249	#127	C₂×D₅₃	1	3	yes	complemented
250	#124	—	53	3	no	—
251	#124	—	53	3	no	—
252	#123	—	53	3	no	—
253	#123	—	53	3	no	—
254	C₂²⋊Q₈	—	53	3	no	—
255	C₂²⋊Q₈	—	53	1	no	—
256	C₂²⋊Q₈	—	53	3	no	—
257	C₂²⋊Q₈	—	53	3	no	—
258	#121	—	53	6	no	—
259	#121	—	53	3	no	—
260	#121	—	53	3	no	—
261	#121	—	53	6	no	—
262	#121	—	53	3	no	—
263	#121	—	53	3	no	—
264	#121	—	53	3	no	—
265	#121	—	53	3	no	—
266	#121	—	53	6	no	—
267	#121	C₂×D₅₃	1	3	yes	complemented
268	#121	C₂×D₅₃	1	3	yes	complemented
269	#120	—	53	3	no	—
270	#120	—	53	6	no	—
271	#120	—	53	6	no	—
272	#120	—	53	3	no	—
273	C₄×Q₈	—	53	1	no	—
274	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
275	C₄×D₄	—	53	3	no	—
276	C₄×D₄	—	53	3	no	—
277	C₄×D₄	—	53	3	no	—
278	C₄×D₄	—	53	3	no	—
279	C₄×D₄	—	53	3	no	—
280	C₄×D₄	C₂×D₅₃	1	3	yes	complemented
281	#117	—	53	3	no	—
282	C₂×C₄⋊C₄	—	53	3	no	—
283	C₂×C₂²⋊C₄	—	53	6	no	—
284	C₂⁴	—	53	3	no	—
285	C₂⁴	—	53	6	no	—
286	#41	—	2	4	no	—
287	#41	—	2	4	no	—
288	#41	—	53	8	no	—
289	#41	—	106	12	no	—
290	#41	—	106	12	no	—
291	#41	—	106	12	no	—
292	#41	—	106	4	no	—
293	C₂×Q₈	—	53	1	no	—
294	C₂×Q₈	—	53	3	no	—
295	C₂×Q₈	—	106	4	no	—
296	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
297	C₂×D₄	—	53	3	no	—
298	C₂×D₄	—	53	6	no	—
299	C₂×D₄	—	53	3	no	—
300	C₂×D₄	—	53	3	no	—
301	C₂×D₄	—	53	3	no	—
302	C₂×D₄	—	53	6	no	—
303	C₂×D₄	—	53	3	no	—
304	C₂×D₄	—	53	3	no	—
305	C₂×D₄	—	53	3	no	—
306	C₂×D₄	—	53	3	no	—
307	C₂×D₄	—	106	12	no	—
308	C₂×D₄	—	106	12	no	—
309	C₂×D₄	—	106	12	no	—
310	C₂×D₄	—	106	12	no	—
311	C₂×D₄	—	212	12	no	—
312	C₂×D₄	C₂²×D₅₃	1	3	yes	—
313	C₂×D₄	C₂²×D₅₃	1	3	yes	—
314	C₂×D₄	C₂²×D₅₃	1	3	yes	—
315	C₂×D₄	C₂²×D₅₃	1	6	yes	—
316	C₂²×C₄	—	53	3	no	—
317	C₂²×C₄	—	53	3	no	—
318	C₂²×C₄	—	53	3	no	—
319	C₂²×C₄	—	53	3	no	—
320	C₂²×C₄	—	53	3	no	—
321	C₂²×C₄	—	53	1	no	—
322	C₂²×C₄	—	53	6	no	—
323	C₂²×C₄	—	106	12	no	—
324	C₂²×C₄	C₂²×D₅₃	1	3	yes	—
325	C₂²×C₄	C₂²×D₅₃	1	3	yes	—
326	C₄⋊C₄	—	53	3	no	—
327	C₄⋊C₄	—	53	3	no	—
328	C₄⋊C₄	—	53	1	no	—
329	C₄⋊C₄	—	53	1	no	—
330	C₄⋊C₄	—	53	3	no	—
331	C₄⋊C₄	—	53	3	no	—
332	C₄⋊C₄	C₂²×D₅₃	1	3	yes	—
333	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
334	C₂²⋊C₄	—	53	6	no	—
335	C₂²⋊C₄	—	53	3	no	—
336	C₂²⋊C₄	—	53	3	no	—
337	C₂²⋊C₄	—	53	3	no	—
338	C₂²⋊C₄	—	53	6	no	—
339	C₂²⋊C₄	—	53	3	no	—
340	C₂²⋊C₄	—	53	3	no	—
341	C₂²⋊C₄	—	53	1	no	—
342	C₂²⋊C₄	—	53	1	no	—
343	C₂²⋊C₄	—	53	3	no	—
344	C₂²⋊C₄	C₂²×D₅₃	1	3	yes	—
345	C₂²⋊C₄	C₂²×D₅₃	1	3	yes	—
346	C₄²	—	53	3	no	—
347	C₄²	C₂²×D₅₃	1	3	yes	—
348	C₂³	—	53	3	no	—
349	C₂³	—	53	1	no	—
350	C₂³	—	53	3	no	—
351	C₂³	—	106	12	no	—
352	C₂³	—	106	6	no	—
353	C₂³	—	106	6	no	—
354	C₂³	—	212	6	no	—
355	C₂³	—	212	6	no	—
356	C₂³	—	212	3	no	—
357	C₂³	C₂³×D₅₃	1	3	yes	—
358	C₂³	C₂³×D₅₃	1	3	yes	—
359	Q₈	—	106	2	no	—
360	Q₈	—	106	6	no	—
361	Q₈	D₄×D₅₃	1	4	yes	complemented
362	D₄	—	2	6	no	—
363	D₄	—	2	6	no	—
364	D₄	—	4	6	no	—
365	D₄	—	4	3	no	—
366	D₄	—	53	12	no	—
367	D₄	—	106	6	no	—
368	D₄	—	106	6	no	—
369	D₄	—	106	6	no	—
370	D₄	—	106	6	no	—
371	D₄	—	106	12	no	—
372	D₄	—	106	6	no	—
373	D₄	—	106	6	no	—
374	D₄	—	212	3	no	—
375	D₄	—	212	6	no	—
376	C₂×C₄	—	2	6	no	—
377	C₂×C₄	—	2	6	no	—
378	C₂×C₄	—	53	1	no	—
379	C₂×C₄	—	53	12	no	—
380	C₂×C₄	—	53	1	no	—
381	C₂×C₄	—	53	3	no	—
382	C₂×C₄	—	53	3	no	—
383	C₂×C₄	—	53	1	no	—
384	C₂×C₄	—	106	2	no	—
385	C₂×C₄	—	106	6	no	—
386	C₂×C₄	—	106	6	no	—
387	C₂×C₄	—	106	6	no	—
388	C₂×C₄	—	106	6	no	—
389	C₂×C₄	—	212	6	no	—
390	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
391	C₂×C₄	C₂³×D₅₃	1	3	yes	—
392	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
393	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
394	C₂×C₄	C₂³×D₅₃	1	3	yes	—
395	C₂²	—	2	3	no	—
396	C₂²	—	2	3	no	—
397	C₂²	—	2	3	no	—
398	C₂²	—	2	3	no	—
399	C₂²	—	2	3	no	—
400	C₂²	—	2	3	no	—
401	C₂²	—	53	6	no	—
402	C₂²	—	53	2	no	—
403	C₂²	—	106	1	no	—
404	C₂²	—	106	3	no	—
405	C₂²	—	106	3	no	—
406	C₂²	—	106	1	no	—
407	C₂²	—	106	3	no	—
408	C₂²	—	106	3	no	—
409	C₂²	—	106	3	no	—
410	C₂²	—	424	12	no	—
411	C₂²	—	212	12	no	—
412	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	3	no	—
416	C₄	—	2	1	no	—
417	C₄	—	53	2	no	—
418	C₄	—	106	1	no	—
419	C₄	—	106	3	no	—
420	C₄	—	106	3	no	—
421	C₄	—	106	1	no	—
422	C₄	C₂×D₄×D₅₃	1	6	yes	—
423	C₂	—	4	3	no	—
424	C₂	—	4	3	no	—
425	C₂	—	106	6	no	—
426	C₂	—	106	2	no	—
427	C₂	—	212	3	no	—
428	C₂	C₂²×D₄×D₅₃	1	1	yes	characteristic
429	C₂	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
430	C₂	#16811459	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#550	C₂
hypercenter	#550	D₅₃
hypocenter	C₅₃	#3488
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #550

Complements

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

N	H ≅ G/N	type
1. C₂×#13133263	C₂	semidirect
2. C₂×#41×D₅₃	C₂	semidirect
3. #16811292	C₂	semidirect
4. #16811285	C₂	semidirect
5. #16811280	C₂	semidirect
6. #16811270	C₂	semidirect
7. #16811269	C₂	semidirect
8. #16811258	C₂	semidirect
9. #16811257	C₂	semidirect
10. #16811202	C₂	semidirect
11. #16811186	C₂	semidirect
12. #16811132	C₂	semidirect
13. #121×D₅₃	C₂	semidirect
14. #16811105	C₂	semidirect
15. C₅₃×#550	C₂	semidirect
18. C₂×#11719949	C₂²	semidirect
19. C₂×#11719945	C₂²	semidirect
20. C₂×#11719945	C₂²	semidirect
21. C₂×#11719947	C₂²	semidirect
23. C₂×Q₈×D₅₃	C₂²	semidirect
24. C₂²×D₂₁₂	C₂²	semidirect
25. C₂×D₄×D₅₃	C₂²	semidirect
26. C₂×D₄×D₅₃	C₂²	semidirect
27. C₂×D₄×D₅₃	C₂²	semidirect
28. C₂×D₄×D₅₃	C₂²	semidirect
29. C₂²×C₄×D₅₃	C₂²	semidirect
30. #13133213	C₂²	semidirect
31. #13133205	C₂²	semidirect
32. #13133204	C₂²	semidirect
33. #13133202	C₂²	semidirect
34. #13133199	C₂²	semidirect
35. #13133197	C₂²	semidirect
36. #13133196	C₂²	semidirect
37. #13133195	C₂²	semidirect
38. #13133194	C₂²	semidirect
39. #13133192	C₂²	semidirect
40. #13133191	C₂²	semidirect
41. #13133190	C₂²	semidirect
42. #13133190	C₂²	semidirect
43. #13133189	C₂²	semidirect
44. #13133189	C₂²	semidirect
45. #13133188	C₂²	semidirect
46. #13133188	C₂²	semidirect
47. #13133188	C₂²	semidirect
48. #13133187	C₂²	semidirect
49. #13133185	C₂²	semidirect
50. #13133185	C₂²	semidirect
51. #13133185	C₂²	semidirect
52. Q₈×Dic₅₃	C₂²	semidirect
53. C₄×D₂₁₂	C₂²	semidirect
54. C₄×D₂₁₂	C₂²	semidirect
55. #13133179	C₂²	semidirect
56. C₄×C₂²⋊D₅₃	C₂²	semidirect
57. C₄×C₂²⋊D₅₃	C₂²	semidirect
58. #13133174	C₂²	semidirect
59. C₄⋊C₄×D₅₃	C₂²	semidirect
60. C₂²⋊C₄×D₅₃	C₂²	semidirect
61. C₂×#41×C₅₃	C₂²	semidirect
62. C₂×#41×C₅₃	C₂²	semidirect
63. #127×C₅₃	C₂²	semidirect
64. #121×C₅₃	C₂²	semidirect
65. #121×C₅₃	C₂²	semidirect
66. C₄×Q₈×C₅₃	C₂²	semidirect
67. C₄×D₄×C₅₃	C₂²	semidirect
87. #11719949	D₄	semidirect
143. Q₈×C₅₃	C₂×D₄	semidirect
170. D₂₁₂	C₂×D₄	semidirect
176. C₄×D₅₃	C₂×D₄	semidirect
196. C₂×D₅₃	H(5,𝔽₂)	semidirect
219. #550	D₅₃	semidirect
231. C₅₃	#3488	semidirect
239. C₂×#41	C₂×D₅₃	semidirect
240. C₂×#41	C₂×D₅₃	semidirect
249. #127	C₂×D₅₃	semidirect
267. #121	C₂×D₅₃	semidirect
268. #121	C₂×D₅₃	semidirect
274. C₄×Q₈	C₂×D₅₃	semidirect
280. C₄×D₄	C₂×D₅₃	semidirect
361. Q₈	D₄×D₅₃	semidirect