Subgroups — #20289317

Order 6784.

912 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃⋊#564	C₂	1	2	yes	maximal, complemented
2	#16811374	C₂	1	2	yes	maximal, complemented
3	#16811350	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811348	C₂	1	1	yes	maximal, characteristic, complemented
5	#16811334	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811328	C₂	1	1	yes	maximal, characteristic, complemented
7	#16811312	C₂	1	1	yes	maximal, characteristic, complemented
8	#16811312	C₂	1	1	yes	maximal, characteristic, complemented
9	#16811311	C₂	1	1	yes	maximal, characteristic, complemented
10	#16811308	C₂	1	1	yes	maximal, characteristic, complemented
11	#16811307	C₂	1	2	yes	maximal, complemented
12	#16811305	C₂	1	2	yes	maximal, complemented
13	#16811250	C₂	1	1	yes	maximal, characteristic, complemented
14	#16811250	C₂	1	2	yes	maximal, complemented
15	#16811236	C₂	1	1	yes	maximal, characteristic, complemented
16	#16811235	C₂	1	1	yes	maximal, characteristic, complemented
17	#16811234	C₂	1	2	yes	maximal, complemented
18	#16811233	C₂	1	2	yes	maximal, complemented
19	#16811219	C₂	1	2	yes	maximal
20	#16811178	C₂	1	1	yes	maximal, characteristic, complemented
21	#16811151	C₂	1	1	yes	maximal, characteristic
22	#125×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
24	#13133217	C₂²	1	1	yes	characteristic
25	#13133216	C₂²	1	1	yes	characteristic
26	#13133216	C₂²	1	2	yes	—
27	#13133215	C₂²	1	2	yes	—
28	#13133215	C₂²	1	2	yes	—
29	#13133212	C₂²	1	2	yes	—
30	#13133212	C₂²	1	2	yes	—
31	#13133212	C₂²	1	2	yes	—
32	#13133212	C₂²	1	1	yes	characteristic
33	#13133212	C₂²	1	2	yes	—
34	#13133210	C₂²	1	2	yes	—
35	#13133210	C₂²	1	2	yes	—
36	#13133210	C₂²	1	2	yes	—
37	#13133210	C₂²	1	1	yes	characteristic
38	#13133210	C₂²	1	2	yes	—
39	#13133209	C₂²	1	2	yes	—
40	#13133209	C₂²	1	2	yes	—
41	#13133209	C₂²	1	1	yes	characteristic
42	#13133208	C₂²	1	2	yes	—
43	#13133208	C₂²	1	1	yes	characteristic
44	#13133208	C₂²	1	2	yes	—
45	#13133208	C₂²	1	1	yes	characteristic
46	#13133208	C₂²	1	1	yes	characteristic
47	#13133208	C₂²	1	2	yes	—
48	#13133208	C₂²	1	2	yes	—
49	#13133208	C₂²	1	2	yes	—
50	#13133207	C₂²	1	2	yes	—
51	#13133207	C₂²	1	2	yes	—
52	#13133207	C₂²	1	2	yes	—
53	#13133207	C₂²	1	2	yes	—
54	#13133207	C₂²	1	2	yes	—
55	#13133207	C₂²	1	2	yes	—
56	#13133207	C₂²	1	2	yes	—
57	#13133207	C₂²	1	2	yes	—
58	#13133207	C₂²	1	2	yes	—
59	#13133207	C₂²	1	1	yes	characteristic
60	#13133207	C₂²	1	2	yes	—
61	#13133207	C₂²	1	2	yes	—
62	#13133203	C₂²	1	1	yes	characteristic
63	#13133202	C₂²	1	1	yes	characteristic
64	#13133202	C₂²	1	2	yes	—
65	#13133200	C₂²	1	2	yes	—
66	#13133199	C₂²	1	1	yes	characteristic
67	#13133199	C₂²	1	2	yes	—
68	#13133199	C₂²	1	2	yes	—
69	#13133197	C₂²	1	1	yes	characteristic
70	#13133197	C₂²	1	1	yes	characteristic
71	#13133197	C₂²	1	1	yes	characteristic
72	#13133197	C₂²	1	1	yes	characteristic
73	#13133196	C₂²	1	1	yes	characteristic
74	#13133196	C₂²	1	1	yes	characteristic
75	#13133196	C₂²	1	2	yes	—
76	#13133195	C₂²	1	2	yes	—
77	#13133195	C₂²	1	2	yes	—
78	#13133195	C₂²	1	1	yes	characteristic
79	#13133193	C₂²	1	2	yes	—
80	#13133193	C₂²	1	2	yes	—
81	#13133193	C₂²	1	2	yes	—
82	#13133193	C₂²	1	2	yes	—
83	#13133190	C₂²	1	1	yes	characteristic
84	Q₈×Dic₅₃	C₂²	1	2	yes	—
85	Q₈×Dic₅₃	C₂²	1	2	yes	—
86	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
87	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
88	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
89	#13133182	C₂²	1	2	yes	—
90	#13133182	C₂²	1	1	yes	characteristic
91	#13133182	C₂²	1	1	yes	characteristic
92	#13133182	C₂²	1	1	yes	characteristic
93	#13133182	C₂²	1	1	yes	characteristic
94	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
95	#13133179	C₂²	1	2	yes	—
96	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	—
97	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
98	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
99	#13133176	C₂²	1	2	yes	—
100	#13133175	C₂²	1	2	yes	—
101	#13133175	C₂²	1	2	yes	—
102	#13133175	C₂²	1	1	yes	characteristic
103	#13133174	C₂²	1	2	yes	—
104	#13133174	C₂²	1	2	yes	—
105	#13133174	C₂²	1	1	yes	characteristic
106	C₄⋊C₄×D₅₃	C₂²	1	2	yes	—
107	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
108	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
109	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
110	C₄⋊C₄×D₅₃	C₂²	1	2	yes	—
111	C₄²×D₅₃	C₂²	1	1	yes	characteristic
112	C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
113	C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
114	C₄⋊Q₈×C₅₃	C₂²	1	2	yes	—
115	#125×C₅₃	C₂²	1	2	yes	—
116	#125×C₅₃	C₂²	1	1	yes	characteristic
117	#125×C₅₃	C₂²	1	1	yes	characteristic
118	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
119	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
120	#117×C₅₃	C₂²	1	1	yes	characteristic
121	#117×C₅₃	C₂²	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
123	C₂×Q₈×C₅₃	C₂³	1	2	yes	—
124	C₂×Q₈×C₅₃	C₂³	1	2	yes	—
125	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
126	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
127	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
128	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
129	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
130	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
131	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
132	C₂×C₄×D₅₃	C₂³	1	2	yes	—
133	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
134	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
135	C₂×C₄×D₅₃	C₂³	1	2	yes	—
136	C₂×C₄×D₅₃	C₂³	1	2	yes	—
137	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
138	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
139	C₂×Dic₁₀₆	C₂³	1	2	yes	—
140	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
141	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
142	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
143	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
144	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
145	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
146	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
147	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
148	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
149	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
150	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
151	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
152	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
153	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
154	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
155	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
156	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
157	C₄²×C₅₃	C₂³	1	1	yes	characteristic
158	C₄²×C₅₃	C₂³	1	2	yes	—
159	C₄²×C₅₃	C₂³	1	1	yes	characteristic
160	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
161	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
162	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
163	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
164	#11719921	C₂³	1	1	yes	characteristic
165	#11719921	C₂³	1	1	yes	characteristic
166	#11719921	C₂³	1	2	yes	—
167	#11719921	C₂³	1	1	yes	characteristic
168	#11719921	C₂³	1	1	yes	characteristic
169	#11719921	C₂³	1	2	yes	—
170	#11719921	C₂³	1	2	yes	—
171	#11719921	C₂³	1	1	yes	characteristic
172	#11719921	C₂³	1	2	yes	—
173	#11719921	C₂³	1	2	yes	—
174	#11719921	C₂³	1	1	yes	characteristic
175	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
176	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
177	C₄⋊Dic₅₃	C₂³	1	2	yes	—
178	C₄⋊Dic₅₃	C₂³	1	2	yes	—
179	C₄⋊Dic₅₃	C₂³	1	2	yes	—
180	C₄⋊Dic₅₃	C₂³	1	2	yes	—
181	C₄⋊Dic₅₃	C₂³	1	2	yes	—
182	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
183	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
184	C₄⋊Dic₅₃	C₂³	1	2	yes	—
185	C₄⋊Dic₅₃	C₂³	1	2	yes	—
186	C₄⋊Dic₅₃	C₂³	1	2	yes	—
187	C₄⋊Dic₅₃	C₂³	1	2	yes	—
188	#11719919	C₂³	1	2	yes	—
189	#11719919	C₂³	1	2	yes	—
190	#11719919	C₂³	1	2	yes	—
191	#11719919	C₂³	1	2	yes	—
192	#11719919	C₂³	1	2	yes	—
193	#11719919	C₂³	1	2	yes	—
194	#11719919	C₂³	1	2	yes	—
195	#11719919	C₂³	1	2	yes	—
196	#11719919	C₂³	1	2	yes	—
197	#11719919	C₂³	1	1	yes	characteristic
198	#11719919	C₂³	1	2	yes	—
199	#11719919	C₂³	1	1	yes	characteristic
200	#11719919	C₂³	1	2	yes	—
201	#11719919	C₂³	1	1	yes	characteristic
202	#11719919	C₂³	1	1	yes	characteristic
203	#11719919	C₂³	1	1	yes	characteristic
204	#11719919	C₂³	1	2	yes	—
205	#11719919	C₂³	1	2	yes	—
206	#11719919	C₂³	1	2	yes	—
207	#11719919	C₂³	1	2	yes	—
208	#11719919	C₂³	1	1	yes	characteristic
209	#11719919	C₂³	1	2	yes	—
210	#11719919	C₂³	1	2	yes	—
211	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
212	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
213	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
214	C₄×Dic₅₃	C₂³	1	2	yes	—
215	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
216	C₄×Dic₅₃	C₂³	1	2	yes	—
217	C₄×Dic₅₃	C₂³	1	2	yes	—
218	C₄×Dic₅₃	C₂³	1	2	yes	—
219	C₄×Dic₅₃	C₂³	1	2	yes	—
220	C₄×Dic₅₃	C₂³	1	2	yes	—
221	C₄×Dic₅₃	C₂³	1	2	yes	—
222	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
223	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
224	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
225	Q₈×C₅₃	—	4	2	no	—
226	Q₈×C₅₃	—	4	2	no	—
227	C₂×C₄×C₅₃	—	2	2	no	—
228	C₂×C₄×C₅₃	—	4	2	no	—
229	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
230	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
231	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
232	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
233	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
234	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
235	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
236	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
238	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
239	C₂²⋊D₅₃	—	2	2	no	—
240	C₂²⋊D₅₃	—	4	1	no	—
241	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
242	C₂×Dic₅₃	C₂⁴	1	2	yes	—
243	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
244	C₂×Dic₅₃	C₂⁴	1	2	yes	—
245	C₂×Dic₅₃	C₂⁴	1	2	yes	—
246	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
247	C₂×Dic₅₃	C₂⁴	1	2	yes	—
248	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
249	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
251	D₂₁₂	—	2	2	no	—
252	C₄×D₅₃	—	2	2	no	—
253	C₄×D₅₃	—	2	4	no	—
254	C₄×D₅₃	—	2	2	no	—
255	C₄×D₅₃	—	2	2	no	—
256	C₄×D₅₃	—	4	2	no	—
257	C₄×D₅₃	—	4	2	no	—
258	C₄×D₅₃	—	4	1	no	—
259	Dic₁₀₆	—	2	2	no	—
260	Dic₁₀₆	—	2	2	no	—
261	Dic₁₀₆	—	4	2	no	—
262	Dic₁₀₆	—	4	1	no	—
263	C₂²×C₅₃	—	2	1	no	—
264	C₂²×C₅₃	—	2	1	no	—
265	C₂²×C₅₃	—	2	1	no	—
266	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
267	C₂×D₅₃	—	2	1	no	—
268	C₂×D₅₃	—	2	1	no	—
269	C₂×D₅₃	—	2	1	no	—
270	C₂×D₅₃	—	2	1	no	—
271	C₂×D₅₃	—	2	1	no	—
272	C₂×D₅₃	2₋¹⁺⁴	1	2	yes	—
273	C₄×C₅₃	—	2	1	no	—
274	C₄×C₅₃	—	2	2	no	—
275	C₄×C₅₃	—	2	1	no	—
276	C₄×C₅₃	—	2	1	no	—
277	C₄×C₅₃	—	2	2	no	—
278	C₄×C₅₃	—	2	1	no	—
279	C₄×C₅₃	—	2	2	no	—
280	C₄×C₅₃	—	2	2	no	—
281	C₄×C₅₃	—	2	1	no	—
282	C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
283	Dic₅₃	—	2	2	no	—
284	Dic₅₃	—	2	2	no	—
285	Dic₅₃	—	2	1	no	—
286	Dic₅₃	—	2	2	no	—
287	Dic₅₃	—	2	1	no	—
288	Dic₅₃	—	2	1	no	—
289	Dic₅₃	—	2	1	no	—
290	Dic₅₃	—	2	1	no	—
291	Dic₅₃	—	2	2	no	—
292	Dic₅₃	—	2	1	no	—
293	#3563	—	53	1	no	maximal, Sylow
294	C₂×C₅₃	—	4	1	no	—
295	C₂×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
296	C₂×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
297	C₂×C₅₃	#585	1	1	yes	characteristic
298	D₅₃	—	2	2	no	—
299	D₅₃	—	4	1	no	—
300	#564	—	53	2	no	—
301	#563	—	53	2	no	—
302	#557	—	53	1	no	—
303	#557	—	53	1	no	—
304	#554	—	53	1	no	—
305	#554	—	53	1	no	—
306	#552	—	53	2	no	—
307	#552	—	53	1	no	—
308	#552	—	53	2	no	—
309	#552	—	53	1	no	—
310	#552	—	53	1	no	—
311	#552	—	53	1	no	—
312	#544	—	53	2	no	—
313	#544	—	53	1	no	—
314	#544	D₅₃	1	1	yes	characteristic, complemented
315	#541	—	53	2	no	—
316	#541	—	53	1	no	—
317	#541	—	53	2	no	—
318	#541	—	53	1	no	—
319	#539	—	53	2	no	—
320	#533	—	53	1	no	—
321	#529	—	53	1	no	—
322	C₂×#125	—	53	1	no	—
323	C₅₃	#3563	1	1	yes	characteristic, complemented, Sylow
324	C₄⋊Q₈	—	53	2	no	—
325	C₄⋊Q₈	—	53	2	no	—
326	C₄⋊Q₈	—	53	1	no	—
327	C₄⋊Q₈	—	53	2	no	—
328	C₄⋊Q₈	—	53	1	no	—
329	C₄⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
330	C₄⋊Q₈	C₂×D₅₃	1	2	yes	—
331	C₄⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
332	#126	—	53	1	no	—
333	#126	—	53	2	no	—
334	#126	—	53	2	no	—
335	#126	—	53	2	no	—
336	#126	—	53	2	no	—
337	#126	—	53	1	no	—
338	#126	—	53	2	no	—
339	#126	—	53	2	no	—
340	#126	—	53	2	no	—
341	#126	—	53	2	no	—
342	#125	—	53	2	no	—
343	#125	—	53	1	no	—
344	#125	—	53	1	no	—
345	#125	—	53	2	no	—
346	#125	—	53	1	no	—
347	#125	—	53	2	no	—
348	#125	—	53	2	no	—
349	#125	—	53	2	no	—
350	#125	—	53	2	no	—
351	#125	—	53	2	no	—
352	#125	—	53	2	no	—
353	#125	—	53	2	no	—
354	#125	—	53	2	no	—
355	#125	—	53	2	no	—
356	#125	—	53	2	no	—
357	#125	—	53	2	no	—
358	#125	—	53	2	no	—
359	#125	—	53	1	no	—
360	#125	—	53	2	no	—
361	#125	—	53	2	no	—
362	#125	—	53	1	no	—
363	#125	—	53	2	no	—
364	#125	—	53	2	no	—
365	#125	C₂×D₅₃	1	1	yes	characteristic
366	#125	C₂×D₅₃	1	1	yes	characteristic
367	#125	C₂×D₅₃	1	2	yes	—
368	#124	—	53	1	no	—
369	#123	—	53	2	no	—
370	#123	—	53	1	no	—
371	#123	—	53	2	no	—
372	#123	—	53	1	no	—
373	#123	—	53	2	no	—
374	#123	—	53	2	no	—
375	C₂²⋊Q₈	—	53	2	no	—
376	C₂²⋊Q₈	—	53	2	no	—
377	C₂²⋊Q₈	—	53	2	no	—
378	C₂²⋊Q₈	—	53	2	no	—
379	C₂²⋊Q₈	—	53	1	no	—
380	C₂²⋊Q₈	—	53	1	no	—
381	C₂²⋊Q₈	—	53	2	no	—
382	C₂²⋊Q₈	—	53	1	no	—
383	C₂²⋊Q₈	—	53	1	no	—
384	C₂²⋊Q₈	—	53	1	no	—
385	C₂²⋊Q₈	—	53	1	no	—
386	C₂²⋊Q₈	—	53	1	no	—
387	C₂²⋊Q₈	—	53	2	no	—
388	C₂²⋊Q₈	—	53	2	no	—
389	C₂²⋊Q₈	C₂×D₅₃	1	2	yes	—
390	C₂²⋊Q₈	C₂×D₅₃	1	2	yes	—
391	#121	—	53	1	no	—
392	C₄×Q₈	—	53	2	no	—
393	C₄×Q₈	—	53	2	no	—
394	C₄×Q₈	—	53	1	no	—
395	C₄×Q₈	—	53	1	no	—
396	C₄×Q₈	—	53	2	no	—
397	C₄×Q₈	—	53	1	no	—
398	C₄×Q₈	—	53	1	no	—
399	C₄×Q₈	—	53	1	no	—
400	C₄×Q₈	—	53	1	no	—
401	C₄×Q₈	—	53	1	no	—
402	C₄×D₄	—	53	1	no	—
403	C₄×D₄	—	53	1	no	—
404	C₄×D₄	—	53	2	no	—
405	C₄×D₄	—	53	2	no	—
406	C₄×D₄	—	53	1	no	—
407	#117	—	53	2	no	—
408	#117	—	53	2	no	—
409	#117	—	53	1	no	—
410	#117	—	53	2	no	—
411	#117	—	53	1	no	—
412	#117	—	53	2	no	—
413	#117	—	53	2	no	—
414	#117	C₂×D₅₃	1	1	yes	characteristic
415	#117	C₂×D₅₃	1	1	yes	characteristic
416	C₂×C₄⋊C₄	—	53	2	no	—
417	C₂×C₄⋊C₄	—	53	1	no	—
418	C₂×C₄⋊C₄	—	53	2	no	—
419	C₂×C₄⋊C₄	—	53	1	no	—
420	C₂×C₄⋊C₄	—	53	1	no	—
421	C₂×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
422	C₂×C₄²	—	53	1	no	—
423	C₂×Q₈	—	53	1	no	—
424	C₂×Q₈	—	53	1	no	—
425	C₂×Q₈	—	53	2	no	—
426	C₂×Q₈	—	53	1	no	—
427	C₂×Q₈	C₂²×D₅₃	1	2	yes	—
428	C₂×Q₈	C₂²×D₅₃	1	2	yes	—
429	C₂×D₄	—	53	1	no	—
430	C₂×D₄	—	53	1	no	—
431	C₂×D₄	—	53	1	no	—
432	C₂²×C₄	—	53	1	no	—
433	C₂²×C₄	—	53	1	no	—
434	C₂²×C₄	—	53	2	no	—
435	C₂²×C₄	—	53	1	no	—
436	C₂²×C₄	—	53	1	no	—
437	C₂²×C₄	—	53	2	no	—
438	C₂²×C₄	—	53	2	no	—
439	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
440	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
441	C₄⋊C₄	—	53	1	no	—
442	C₄⋊C₄	—	53	1	no	—
443	C₄⋊C₄	—	53	2	no	—
444	C₄⋊C₄	—	53	2	no	—
445	C₄⋊C₄	—	53	2	no	—
446	C₄⋊C₄	—	53	2	no	—
447	C₄⋊C₄	—	53	2	no	—
448	C₄⋊C₄	—	53	2	no	—
449	C₄⋊C₄	—	53	2	no	—
450	C₄⋊C₄	—	53	2	no	—
451	C₄⋊C₄	—	53	2	no	—
452	C₄⋊C₄	—	53	2	no	—
453	C₄⋊C₄	—	53	2	no	—
454	C₄⋊C₄	—	53	2	no	—
455	C₄⋊C₄	—	53	2	no	—
456	C₄⋊C₄	—	53	1	no	—
457	C₄⋊C₄	—	53	2	no	—
458	C₄⋊C₄	—	53	1	no	—
459	C₄⋊C₄	—	53	2	no	—
460	C₄⋊C₄	—	53	1	no	—
461	C₄⋊C₄	—	53	2	no	—
462	C₄⋊C₄	—	53	1	no	—
463	C₄⋊C₄	—	53	1	no	—
464	C₄⋊C₄	—	53	1	no	—
465	C₄⋊C₄	—	53	1	no	—
466	C₄⋊C₄	—	53	1	no	—
467	C₄⋊C₄	—	53	2	no	—
468	C₄⋊C₄	—	53	2	no	—
469	C₄⋊C₄	—	53	2	no	—
470	C₄⋊C₄	—	53	2	no	—
471	C₄⋊C₄	—	53	2	no	—
472	C₄⋊C₄	—	53	2	no	—
473	C₄⋊C₄	—	53	2	no	—
474	C₄⋊C₄	—	53	2	no	—
475	C₄⋊C₄	—	53	2	no	—
476	C₄⋊C₄	—	53	2	no	—
477	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
478	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
479	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
480	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
481	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
482	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
483	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
484	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
485	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
486	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
487	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
488	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
489	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
490	C₂²⋊C₄	—	53	1	no	—
491	C₂²⋊C₄	—	53	2	no	—
492	C₂²⋊C₄	—	53	2	no	—
493	C₂²⋊C₄	—	53	1	no	—
494	C₂²⋊C₄	—	53	2	no	—
495	C₂²⋊C₄	—	53	2	no	—
496	C₂²⋊C₄	—	53	1	no	—
497	C₂²⋊C₄	—	53	1	no	—
498	C₂²⋊C₄	—	53	1	no	—
499	C₂²⋊C₄	—	53	1	no	—
500	C₂²⋊C₄	—	53	2	no	—
501	C₂²⋊C₄	—	53	1	no	—
502	C₂²⋊C₄	—	53	2	no	—
503	C₂²⋊C₄	—	53	2	no	—
504	C₂²⋊C₄	—	53	1	no	—
505	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
506	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
507	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
508	C₄²	—	53	1	no	—
509	C₄²	—	53	1	no	—
510	C₄²	—	53	1	no	—
511	C₄²	—	53	2	no	—
512	C₄²	—	53	2	no	—
513	C₄²	—	53	2	no	—
514	C₄²	—	53	1	no	—
515	C₄²	—	53	2	no	—
516	C₄²	—	53	2	no	—
517	C₄²	—	53	2	no	—
518	C₄²	—	53	2	no	—
519	C₄²	C₂²×D₅₃	1	1	yes	characteristic
520	C₄²	C₂²×D₅₃	1	2	yes	—
521	C₄²	C₂²×D₅₃	1	1	yes	characteristic
522	C₂³	—	53	1	no	—
523	C₂³	—	53	1	no	—
524	C₂³	C₂³×D₅₃	1	1	yes	characteristic
525	Q₈	—	4	2	no	—
526	Q₈	—	4	2	no	—
527	Q₈	—	106	2	no	—
528	Q₈	—	106	2	no	—
529	Q₈	—	212	2	no	—
530	Q₈	—	212	1	no	—
531	D₄	—	106	2	no	—
532	D₄	—	106	2	no	—
533	D₄	—	212	1	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	53	1	no	—
537	C₂×C₄	—	53	2	no	—
538	C₂×C₄	—	53	2	no	—
539	C₂×C₄	—	53	1	no	—
540	C₂×C₄	—	53	1	no	—
541	C₂×C₄	—	53	2	no	—
542	C₂×C₄	—	53	1	no	—
543	C₂×C₄	—	53	1	no	—
544	C₂×C₄	—	53	1	no	—
545	C₂×C₄	—	53	2	no	—
546	C₂×C₄	—	106	2	no	—
547	C₂×C₄	—	106	4	no	—
548	C₂×C₄	—	106	2	no	—
549	C₂×C₄	—	106	2	no	—
550	C₂×C₄	—	212	2	no	—
551	C₂×C₄	—	212	2	no	—
552	C₂×C₄	—	212	1	no	—
553	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
554	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
555	C₂×C₄	C₂³×D₅₃	1	2	yes	—
556	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
557	C₂×C₄	C₂³×D₅₃	1	2	yes	—
558	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
559	C₂×C₄	C₂³×D₅₃	1	2	yes	—
560	C₂×C₄	C₂³×D₅₃	1	2	yes	—
561	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
562	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
563	C₂²	—	2	1	no	—
564	C₂²	—	2	1	no	—
565	C₂²	—	2	1	no	—
566	C₂²	—	53	2	no	—
567	C₂²	—	106	1	no	—
568	C₂²	—	106	1	no	—
569	C₂²	—	106	1	no	—
570	C₂²	—	106	1	no	—
571	C₂²	—	106	1	no	—
572	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
573	C₄	—	2	1	no	—
574	C₄	—	2	2	no	—
575	C₄	—	2	1	no	—
576	C₄	—	2	1	no	—
577	C₄	—	2	2	no	—
578	C₄	—	2	2	no	—
579	C₄	—	2	2	no	—
580	C₄	—	2	1	no	—
581	C₄	—	2	1	no	—
582	C₄	—	106	1	no	—
583	C₄	—	106	2	no	—
584	C₄	—	106	1	no	—
585	C₄	—	106	1	no	—
586	C₄	—	106	1	no	—
587	C₄	—	106	2	no	—
588	C₄	—	106	2	no	—
589	C₄	—	106	2	no	—
590	C₄	—	106	1	no	—
591	C₄	—	106	1	no	—
592	C₄	#13133265	1	2	yes	—
593	C₂	—	4	1	no	—
594	C₂	—	106	2	no	—
595	C₂	—	212	1	no	—
596	C₂	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
597	C₂	C₂×#13133265	1	1	yes	characteristic
598	C₂	#16811458	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#544	C₂
hypercenter	#544	D₅₃
hypocenter	C₅₃	#3563
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #544

Complements

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

N	H ≅ G/N	type
1. C₅₃⋊#564	C₂	semidirect
2. #16811374	C₂	semidirect
3. #16811350	C₂	semidirect
4. #16811348	C₂	semidirect
5. #16811334	C₂	semidirect
6. #16811328	C₂	semidirect
7. #16811312	C₂	semidirect
8. #16811312	C₂	semidirect
9. #16811311	C₂	semidirect
10. #16811308	C₂	semidirect
11. #16811307	C₂	semidirect
12. #16811305	C₂	semidirect
13. #16811250	C₂	semidirect
14. #16811250	C₂	semidirect
15. #16811236	C₂	semidirect
16. #16811235	C₂	semidirect
17. #16811234	C₂	semidirect
18. #16811233	C₂	semidirect
20. #16811178	C₂	semidirect
22. #125×D₅₃	C₂	semidirect
23. C₅₃×#544	C₂	semidirect
314. #544	D₅₃	semidirect
323. C₅₃	#3563	semidirect