Subgroups — #20288407

Order 6784.

1052 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811314	C₂	1	2	yes	maximal, complemented
2	#16811312	C₂	1	2	yes	maximal, complemented
3	#16811309	C₂	1	2	yes	maximal, complemented
4	#16811305	C₂	1	2	yes	maximal, complemented
5	#16811303	C₂	1	2	yes	maximal, complemented
6	#16811302	C₂	1	2	yes	maximal, complemented
7	#16811298	C₂	1	2	yes	maximal, complemented
8	#16811297	C₂	1	2	yes	maximal, complemented
9	#16811248	C₂	1	1	yes	maximal, characteristic, complemented
10	#16811222	C₂	1	1	yes	maximal, characteristic, complemented
11	#16811218	C₂	1	1	yes	maximal, characteristic, complemented
12	#16811215	C₂	1	2	yes	maximal, complemented
13	#16811181	C₂	1	1	yes	maximal, characteristic
14	#16811157	C₂	1	1	yes	maximal, characteristic, complemented
15	#16811150	C₂	1	2	yes	maximal, complemented
16	#123×D₅₃	C₂	1	2	yes	maximal, complemented
17	#16811095	C₂	1	2	yes	maximal, complemented
18	C₂×#13133174	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×D₄×D₅₃	C₂²	1	2	yes	—
21	C₂²×C₄×D₅₃	C₂²	1	1	yes	characteristic
22	#13133212	C₂²	1	2	yes	complemented
23	#13133212	C₂²	1	2	yes	complemented
24	#13133211	C₂²	1	2	yes	complemented
25	#13133211	C₂²	1	2	yes	complemented
26	#13133210	C₂²	1	2	yes	complemented
27	#13133210	C₂²	1	2	yes	complemented
28	#13133210	C₂²	1	2	yes	complemented
29	#13133209	C₂²	1	1	yes	characteristic, complemented
30	#13133209	C₂²	1	2	yes	complemented
31	#13133208	C₂²	1	2	yes	complemented
32	#13133207	C₂²	1	2	yes	complemented
33	#13133207	C₂²	1	2	yes	complemented
34	#13133207	C₂²	1	2	yes	complemented
35	#13133205	C₂²	1	1	yes	characteristic, complemented
36	#13133203	C₂²	1	2	yes	complemented
37	#13133202	C₂²	1	2	yes	—
38	#13133202	C₂²	1	2	yes	—
39	#13133202	C₂²	1	2	yes	—
40	#13133202	C₂²	1	2	yes	complemented
41	#13133201	C₂²	1	2	yes	complemented
42	#13133200	C₂²	1	2	yes	complemented
43	#13133200	C₂²	1	2	yes	complemented
44	#13133199	C₂²	1	2	yes	—
45	#13133199	C₂²	1	2	yes	—
46	#13133199	C₂²	1	2	yes	—
47	#13133199	C₂²	1	2	yes	complemented
48	#13133198	C₂²	1	2	yes	complemented
49	#13133198	C₂²	1	2	yes	complemented
50	#13133197	C₂²	1	2	yes	complemented
51	#13133196	C₂²	1	2	yes	complemented
52	#13133196	C₂²	1	1	yes	characteristic, complemented
53	#13133195	C₂²	1	2	yes	complemented
54	#13133195	C₂²	1	2	yes	complemented
55	#13133195	C₂²	1	2	yes	complemented
56	#13133194	C₂²	1	2	yes	complemented
57	#13133194	C₂²	1	2	yes	complemented
58	#13133193	C₂²	1	2	yes	complemented
59	#13133193	C₂²	1	2	yes	complemented
60	#13133191	C₂²	1	1	yes	characteristic
61	#13133189	C₂²	1	2	yes	—
62	#13133187	C₂²	1	2	yes	—
63	#13133185	C₂²	1	2	yes	—
64	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
65	#13133182	C₂²	1	2	yes	complemented
66	C₄×D₂₁₂	C₂²	1	2	yes	—
67	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
68	D₄×Dic₅₃	C₂²	1	2	yes	complemented
69	#13133179	C₂²	1	2	yes	—
70	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	—
71	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
72	#13133177	C₂²	1	2	yes	—
73	#13133177	C₂²	1	2	yes	complemented
74	#13133177	C₂²	1	2	yes	complemented
75	#13133175	C₂²	1	2	yes	complemented
76	#13133175	C₂²	1	2	yes	complemented
77	#13133174	C₂²	1	2	yes	complemented
78	#13133174	C₂²	1	2	yes	complemented
79	#13133174	C₂²	1	2	yes	complemented
80	#13133174	C₂²	1	2	yes	complemented
81	#13133174	C₂²	1	2	yes	complemented
82	#13133174	C₂²	1	2	yes	complemented
83	#13133173	C₂²	1	2	yes	complemented
84	C₂×#11719919	C₂²	1	1	yes	characteristic, complemented
85	C₂×#11719919	C₂²	1	1	yes	characteristic, complemented
86	C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
87	C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
88	C₂×#11719921	C₂²	1	1	yes	characteristic
89	C₂×#11719921	C₂²	1	1	yes	characteristic
90	C₂×#11719921	C₂²	1	2	yes	complemented
91	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
92	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
93	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
94	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
95	C₂×C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
96	#126×C₅₃	C₂²	1	2	yes	complemented
97	#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
98	#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
99	#123×C₅₃	C₂²	1	2	yes	complemented
100	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
101	#121×C₅₃	C₂²	1	1	yes	characteristic
102	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
103	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
104	C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
105	#117×C₅₃	C₂²	1	2	yes	complemented
106	C₂×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₅₃	C₂³	1	2	yes	—
108	C₂³×D₅₃	C₂³	1	1	yes	characteristic
109	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
110	C₂×D₄×C₅₃	C₂³	1	2	yes	—
111	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
112	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
113	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
114	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
115	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
116	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
117	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
118	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
119	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
120	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
121	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
122	C₂²×Dic₅₃	C₂³	1	2	yes	—
123	D₄×D₅₃	—	2	8	no	—
124	C₂×D₂₁₂	C₂³	1	2	yes	—
125	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
126	C₂×C₄×D₅₃	—	2	4	no	—
127	C₂×C₄×D₅₃	C₂³	1	2	yes	—
128	C₂×C₄×D₅₃	C₂³	1	2	yes	—
129	C₂×C₄×D₅₃	C₂³	1	2	yes	—
130	C₂×C₄×D₅₃	C₂³	1	2	yes	—
131	C₂×C₄×D₅₃	C₂³	1	2	yes	—
132	C₂×C₄×D₅₃	C₂³	1	2	yes	—
133	C₂×C₄×D₅₃	C₂³	1	2	yes	—
134	C₂×Dic₁₀₆	C₂³	1	2	yes	—
135	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
136	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
137	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
138	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
139	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
140	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
141	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
142	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
143	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
144	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
145	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
146	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
147	C₄²×C₅₃	C₂³	1	1	yes	characteristic
148	C₄²×C₅₃	C₂³	1	1	yes	characteristic
149	C₄²×C₅₃	C₂³	1	1	yes	characteristic
150	C₄²×C₅₃	C₂³	1	1	yes	characteristic
151	C₄²×C₅₃	C₂³	1	2	yes	—
152	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
153	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
154	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
155	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
156	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
157	#11719921	C₂³	1	2	yes	—
158	#11719921	C₂³	1	2	yes	—
159	#11719921	C₂³	1	2	yes	—
160	#11719921	C₂³	1	2	yes	—
161	#11719921	C₂³	1	2	yes	—
162	#11719921	C₂³	1	2	yes	—
163	#11719921	C₂³	1	2	yes	—
164	#11719921	C₂³	1	2	yes	—
165	#11719921	C₂³	1	2	yes	—
166	#11719921	C₂³	1	2	yes	—
167	#11719921	C₂³	1	2	yes	—
168	#11719921	C₂³	1	2	yes	—
169	#11719921	C₂³	1	2	yes	—
170	#11719921	C₂³	1	2	yes	—
171	C₄⋊Dic₅₃	C₂³	1	2	yes	—
172	C₄⋊Dic₅₃	C₂³	1	2	yes	—
173	C₄⋊Dic₅₃	C₂³	1	2	yes	—
174	C₄⋊Dic₅₃	C₂³	1	2	yes	—
175	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
176	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
177	#11719919	C₂³	1	2	yes	—
178	#11719919	C₂³	1	2	yes	—
179	#11719919	C₂³	1	2	yes	—
180	#11719919	C₂³	1	2	yes	—
181	#11719919	C₂³	1	2	yes	—
182	#11719919	C₂³	1	2	yes	—
183	#11719919	C₂³	1	2	yes	—
184	#11719919	C₂³	1	2	yes	—
185	#11719919	C₂³	1	2	yes	—
186	#11719919	C₂³	1	2	yes	—
187	#11719919	C₂³	1	2	yes	—
188	#11719919	C₂³	1	2	yes	—
189	#11719919	C₂³	1	2	yes	—
190	#11719919	C₂³	1	2	yes	—
191	C₄×Dic₅₃	C₂³	1	2	yes	—
192	C₄×Dic₅₃	C₂³	1	2	yes	—
193	C₄×Dic₅₃	C₂³	1	2	yes	—
194	C₄×Dic₅₃	C₂³	1	2	yes	—
195	C₄×Dic₅₃	C₂³	1	2	yes	—
196	C₂³×C₅₃	C₂⁴	1	2	yes	—
197	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
198	C₂²×D₅₃	—	2	4	no	—
199	C₂²×D₅₃	—	4	1	no	—
200	C₂²×D₅₃	—	4	1	no	—
201	C₂²×D₅₃	—	4	2	no	—
202	C₂²×D₅₃	—	4	2	no	—
203	C₂²×D₅₃	#41	1	4	yes	—
204	C₂²×D₅₃	C₂⁴	1	2	yes	—
205	C₂²×D₅₃	C₂⁴	1	2	yes	—
206	Q₈×C₅₃	—	4	1	no	—
207	D₄×C₅₃	—	2	4	no	—
208	D₄×C₅₃	—	4	1	no	—
209	C₂×C₄×C₅₃	—	2	2	no	—
210	C₂×C₄×C₅₃	—	4	2	no	—
211	C₂×C₄×C₅₃	—	4	1	no	—
212	C₂×C₄×C₅₃	—	4	1	no	—
213	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
214	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
215	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
216	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
217	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
218	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
219	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
220	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
221	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
222	C₂²⋊D₅₃	—	2	4	no	—
223	C₂²⋊D₅₃	—	2	4	no	—
224	C₂²⋊D₅₃	—	4	2	no	—
225	C₂×Dic₅₃	—	2	2	no	—
226	C₂×Dic₅₃	—	4	2	no	—
227	C₂×Dic₅₃	—	4	1	no	—
228	C₂×Dic₅₃	—	4	1	no	—
229	C₂×Dic₅₃	C₂⁴	1	2	yes	—
230	C₂×Dic₅₃	C₂⁴	1	2	yes	—
231	C₂×Dic₅₃	C₂⁴	1	2	yes	—
232	C₂×Dic₅₃	C₂⁴	1	2	yes	—
233	C₂×Dic₅₃	C₂⁴	1	2	yes	—
234	C₂×Dic₅₃	C₂⁴	1	2	yes	—
235	D₂₁₂	—	2	4	no	—
236	D₂₁₂	—	4	1	no	—
237	C₄×D₅₃	—	2	4	no	—
238	C₄×D₅₃	—	2	4	no	—
239	C₄×D₅₃	—	2	4	no	—
240	C₄×D₅₃	—	4	2	no	—
241	C₄×D₅₃	—	4	2	no	—
242	C₄×D₅₃	—	4	2	no	—
243	C₄×D₅₃	—	4	2	no	—
244	Dic₁₀₆	—	4	2	no	—
245	Dic₁₀₆	—	4	1	no	—
246	C₂²×C₅₃	—	2	1	no	—
247	C₂²×C₅₃	—	2	1	no	—
248	C₂²×C₅₃	—	2	2	no	—
249	C₂²×C₅₃	—	2	2	no	—
250	C₂²×C₅₃	—	2	2	no	—
251	C₂²×C₅₃	C₂×#41	1	2	yes	—
252	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
253	C₂×D₅₃	—	2	2	no	—
254	C₂×D₅₃	—	2	2	no	—
255	C₂×D₅₃	—	2	2	no	—
256	C₂×D₅₃	—	2	2	no	—
257	C₂×D₅₃	—	2	2	no	—
258	C₂×D₅₃	—	4	4	no	—
259	C₂×D₅₃	—	8	4	no	—
260	C₂×D₅₃	C₂×#41	1	4	yes	—
261	C₄×C₅₃	—	2	1	no	—
262	C₄×C₅₃	—	2	1	no	—
263	C₄×C₅₃	—	2	2	no	—
264	C₄×C₅₃	—	2	2	no	—
265	C₄×C₅₃	—	2	1	no	—
266	C₄×C₅₃	—	2	1	no	—
267	C₄×C₅₃	—	2	2	no	—
268	C₄×C₅₃	—	2	1	no	—
269	C₄×C₅₃	—	2	1	no	—
270	Dic₅₃	—	2	2	no	—
271	Dic₅₃	—	2	2	no	—
272	Dic₅₃	—	2	2	no	—
273	Dic₅₃	—	2	2	no	—
274	Dic₅₃	—	2	2	no	—
275	Dic₅₃	—	2	2	no	—
276	#3491	—	53	1	no	maximal, Sylow
277	C₂×C₅₃	—	2	2	no	—
278	C₂×C₅₃	—	4	2	no	—
279	C₂×C₅₃	C₂²×#41	1	1	yes	characteristic
280	C₂×C₅₃	#585	1	1	yes	characteristic
281	C₂×C₅₃	#585	1	1	yes	characteristic
282	D₅₃	—	2	4	no	—
283	D₅₃	—	4	2	no	—
284	#552	—	53	2	no	—
285	#552	—	53	2	no	—
286	#552	—	53	2	no	—
287	#552	—	53	2	no	—
288	#551	—	53	2	no	—
289	#551	—	53	2	no	—
290	#551	—	53	2	no	—
291	#551	—	53	2	no	—
292	#543	—	53	1	no	—
293	#539	—	53	1	no	—
294	#539	—	53	1	no	—
295	#539	—	53	2	no	—
296	#534	—	53	1	no	—
297	#529	—	53	2	no	—
298	#529	—	53	1	no	—
299	#529	D₅₃	1	1	yes	characteristic, complemented
300	C₂×#123	—	53	2	no	—
301	#518	—	53	2	no	—
302	C₂×#117	—	53	1	no	—
303	C₅₃	#3491	1	1	yes	characteristic, complemented, Sylow
304	C₂²×D₄	—	53	2	no	—
305	C₂³×C₄	—	53	1	no	—
306	#126	—	53	2	no	—
307	#126	—	53	2	no	—
308	#126	—	53	2	no	—
309	#126	—	53	2	no	—
310	#126	—	53	2	no	—
311	#126	—	53	2	no	—
312	#126	—	53	2	no	—
313	#126	C₂×D₅₃	1	2	yes	complemented
314	#125	—	53	2	no	—
315	#125	—	53	2	no	—
316	#125	—	53	2	no	—
317	#125	—	53	2	no	—
318	#125	—	53	1	no	—
319	#125	—	53	2	no	—
320	#125	C₂×D₅₃	1	1	yes	characteristic, complemented
321	#124	—	53	2	no	—
322	#124	—	53	1	no	—
323	#124	C₂×D₅₃	1	1	yes	characteristic, complemented
324	#123	—	53	2	no	—
325	#123	—	53	2	no	—
326	#123	—	53	2	no	—
327	#123	—	53	2	no	—
328	#123	—	53	2	no	—
329	#123	—	53	2	no	—
330	#123	—	53	2	no	—
331	#123	—	53	2	no	—
332	#123	—	53	2	no	—
333	#123	—	53	2	no	—
334	#123	—	53	2	no	—
335	#123	—	53	2	no	—
336	#123	—	53	2	no	—
337	#123	C₂×D₅₃	1	2	yes	complemented
338	C₂²⋊Q₈	—	53	2	no	—
339	C₂²⋊Q₈	—	53	2	no	—
340	C₂²⋊Q₈	—	53	1	no	—
341	C₂²⋊Q₈	—	53	2	no	—
342	C₂²⋊Q₈	—	53	2	no	—
343	C₂²⋊Q₈	—	53	2	no	—
344	C₂²⋊Q₈	—	53	2	no	—
345	C₂²⋊Q₈	—	53	2	no	—
346	C₂²⋊Q₈	—	53	2	no	—
347	C₂²⋊Q₈	—	53	2	no	—
348	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
349	#121	—	53	2	no	—
350	#121	—	53	1	no	—
351	#121	C₂×D₅₃	1	1	yes	characteristic
352	#120	—	53	2	no	—
353	#120	—	53	2	no	—
354	C₄×Q₈	—	53	2	no	—
355	C₄×Q₈	—	53	1	no	—
356	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
357	C₄×D₄	—	53	2	no	—
358	C₄×D₄	—	53	2	no	—
359	C₄×D₄	—	53	2	no	—
360	C₄×D₄	—	53	2	no	—
361	C₄×D₄	—	53	2	no	—
362	C₄×D₄	—	53	2	no	—
363	C₄×D₄	—	53	2	no	—
364	C₄×D₄	—	53	2	no	—
365	C₄×D₄	—	53	1	no	—
366	C₄×D₄	C₂×D₅₃	1	2	yes	complemented
367	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
368	#117	—	53	2	no	—
369	#117	—	53	2	no	—
370	#117	—	53	2	no	—
371	#117	—	53	2	no	—
372	#117	—	53	2	no	—
373	#117	—	53	2	no	—
374	#117	—	53	2	no	—
375	#117	—	53	2	no	—
376	#117	—	53	2	no	—
377	#117	C₂×D₅₃	1	2	yes	complemented
378	C₂×C₄⋊C₄	—	53	1	no	—
379	C₂×C₄⋊C₄	—	53	1	no	—
380	C₂×C₄⋊C₄	—	53	2	no	—
381	C₂×C₄⋊C₄	—	53	2	no	—
382	C₂×C₂²⋊C₄	—	53	1	no	—
383	C₂×C₂²⋊C₄	—	53	1	no	—
384	C₂×C₂²⋊C₄	—	53	2	no	—
385	C₂×C₂²⋊C₄	—	53	2	no	—
386	C₂×C₂²⋊C₄	—	53	2	no	—
387	C₂×C₂²⋊C₄	—	53	2	no	—
388	C₂×C₂²⋊C₄	—	53	2	no	—
389	C₂×C₄²	—	53	1	no	—
390	C₂×C₄²	C₂×D₅₃	1	1	yes	characteristic, complemented
391	C₂⁴	—	53	1	no	—
392	C₂⁴	—	53	2	no	—
393	C₂×Q₈	—	53	2	no	—
394	C₂×Q₈	—	53	1	no	—
395	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
396	C₂×D₄	—	53	2	no	—
397	C₂×D₄	—	53	2	no	—
398	C₂×D₄	—	53	2	no	—
399	C₂×D₄	—	53	2	no	—
400	C₂×D₄	—	53	1	no	—
401	C₂×D₄	—	106	8	no	—
402	C₂×D₄	C₂²×D₅₃	1	2	yes	—
403	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
404	C₂²×C₄	—	53	1	no	—
405	C₂²×C₄	—	53	1	no	—
406	C₂²×C₄	—	53	1	no	—
407	C₂²×C₄	—	53	2	no	—
408	C₂²×C₄	—	53	2	no	—
409	C₂²×C₄	—	53	2	no	—
410	C₂²×C₄	—	53	2	no	—
411	C₂²×C₄	—	53	2	no	—
412	C₂²×C₄	—	53	2	no	—
413	C₂²×C₄	—	53	2	no	—
414	C₂²×C₄	—	53	2	no	—
415	C₂²×C₄	—	106	4	no	—
416	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
417	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
418	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
419	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
420	C₄⋊C₄	—	53	2	no	—
421	C₄⋊C₄	—	53	2	no	—
422	C₄⋊C₄	—	53	2	no	—
423	C₄⋊C₄	—	53	2	no	—
424	C₄⋊C₄	—	53	2	no	—
425	C₄⋊C₄	—	53	2	no	—
426	C₄⋊C₄	—	53	2	no	—
427	C₄⋊C₄	—	53	2	no	—
428	C₄⋊C₄	—	53	2	no	—
429	C₄⋊C₄	—	53	2	no	—
430	C₄⋊C₄	—	53	2	no	—
431	C₄⋊C₄	—	53	2	no	—
432	C₄⋊C₄	—	53	2	no	—
433	C₄⋊C₄	—	53	2	no	—
434	C₄⋊C₄	—	53	2	no	—
435	C₄⋊C₄	—	53	2	no	—
436	C₄⋊C₄	—	53	2	no	—
437	C₄⋊C₄	—	53	1	no	—
438	C₄⋊C₄	—	53	2	no	—
439	C₄⋊C₄	—	53	1	no	—
440	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
441	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
442	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
443	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
444	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
445	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
446	C₂²⋊C₄	—	53	2	no	—
447	C₂²⋊C₄	—	53	2	no	—
448	C₂²⋊C₄	—	53	2	no	—
449	C₂²⋊C₄	—	53	2	no	—
450	C₂²⋊C₄	—	53	2	no	—
451	C₂²⋊C₄	—	53	2	no	—
452	C₂²⋊C₄	—	53	2	no	—
453	C₂²⋊C₄	—	53	2	no	—
454	C₂²⋊C₄	—	53	2	no	—
455	C₂²⋊C₄	—	53	2	no	—
456	C₂²⋊C₄	—	53	2	no	—
457	C₂²⋊C₄	—	53	2	no	—
458	C₂²⋊C₄	—	53	2	no	—
459	C₂²⋊C₄	—	53	2	no	—
460	C₂²⋊C₄	—	53	2	no	—
461	C₂²⋊C₄	—	53	2	no	—
462	C₂²⋊C₄	—	53	2	no	—
463	C₂²⋊C₄	—	53	2	no	—
464	C₂²⋊C₄	—	53	2	no	—
465	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
466	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
467	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
468	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
469	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
470	C₄²	—	53	2	no	—
471	C₄²	—	53	2	no	—
472	C₄²	—	53	2	no	—
473	C₄²	—	53	2	no	—
474	C₄²	—	53	2	no	—
475	C₄²	C₂²×D₅₃	1	1	yes	characteristic
476	C₄²	C₂²×D₅₃	1	1	yes	characteristic
477	C₄²	C₂²×D₅₃	1	1	yes	characteristic
478	C₄²	C₂²×D₅₃	1	1	yes	characteristic
479	C₄²	C₂²×D₅₃	1	2	yes	—
480	C₂³	—	53	2	no	—
481	C₂³	—	53	4	no	—
482	C₂³	—	53	2	no	—
483	C₂³	—	106	4	no	—
484	C₂³	—	212	2	no	—
485	C₂³	—	212	2	no	—
486	C₂³	—	212	1	no	—
487	C₂³	—	212	1	no	—
488	C₂³	C₂³×D₅₃	1	2	yes	—
489	C₂³	C₂³×D₅₃	1	1	yes	characteristic
490	Q₈	—	4	1	no	—
491	Q₈	—	212	2	no	—
492	Q₈	—	212	1	no	—
493	D₄	—	2	4	no	—
494	D₄	—	4	1	no	—
495	D₄	—	106	4	no	—
496	D₄	—	106	4	no	—
497	D₄	—	106	4	no	—
498	D₄	—	212	1	no	—
499	D₄	—	212	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	53	2	no	—
505	C₂×C₄	—	53	2	no	—
506	C₂×C₄	—	53	2	no	—
507	C₂×C₄	—	53	2	no	—
508	C₂×C₄	—	53	2	no	—
509	C₂×C₄	—	53	2	no	—
510	C₂×C₄	—	106	4	no	—
511	C₂×C₄	—	106	4	no	—
512	C₂×C₄	—	106	4	no	—
513	C₂×C₄	—	106	2	no	—
514	C₂×C₄	—	212	2	no	—
515	C₂×C₄	—	212	2	no	—
516	C₂×C₄	—	212	2	no	—
517	C₂×C₄	—	212	2	no	—
518	C₂×C₄	—	212	1	no	—
519	C₂×C₄	—	212	2	no	—
520	C₂×C₄	—	212	1	no	—
521	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
522	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
523	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
524	C₂×C₄	C₂³×D₅₃	1	2	yes	—
525	C₂×C₄	C₂³×D₅₃	1	2	yes	—
526	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
527	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
528	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
529	C₂×C₄	C₂³×D₅₃	1	2	yes	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	2	2	no	—
535	C₂²	—	53	4	no	—
536	C₂²	—	106	2	no	—
537	C₂²	—	106	2	no	—
538	C₂²	—	106	2	no	—
539	C₂²	—	106	2	no	—
540	C₂²	—	106	2	no	—
541	C₂²	—	424	4	no	—
542	C₂²	—	212	4	no	—
543	C₂²	#41×D₅₃	1	2	yes	—
544	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
545	C₄	—	2	1	no	—
546	C₄	—	2	1	no	—
547	C₄	—	2	2	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	2	2	no	—
551	C₄	—	2	1	no	—
552	C₄	—	2	1	no	—
553	C₄	—	2	2	no	—
554	C₄	—	106	2	no	—
555	C₄	—	106	2	no	—
556	C₄	—	106	2	no	—
557	C₄	—	106	2	no	—
558	C₄	—	106	2	no	—
559	C₄	—	106	2	no	—
560	C₂	—	2	2	no	—
561	C₂	—	4	2	no	—
562	C₂	—	106	4	no	—
563	C₂	—	212	2	no	—
564	C₂	C₂×#41×D₅₃	1	1	yes	characteristic
565	C₂	#16811459	1	1	yes	characteristic
566	C₂	#16811459	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#529	C₂
hypercenter	#529	D₅₃
hypocenter	C₅₃	#3491
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #16811314	C₂	semidirect
2. #16811312	C₂	semidirect
3. #16811309	C₂	semidirect
4. #16811305	C₂	semidirect
5. #16811303	C₂	semidirect
6. #16811302	C₂	semidirect
7. #16811298	C₂	semidirect
8. #16811297	C₂	semidirect
9. #16811248	C₂	semidirect
10. #16811222	C₂	semidirect
11. #16811218	C₂	semidirect
12. #16811215	C₂	semidirect
14. #16811157	C₂	semidirect
15. #16811150	C₂	semidirect
16. #123×D₅₃	C₂	semidirect
17. #16811095	C₂	semidirect
18. C₂×#13133174	C₂	semidirect
19. C₅₃×#529	C₂	semidirect
22. #13133212	C₂²	semidirect
23. #13133212	C₂²	semidirect
24. #13133211	C₂²	semidirect
25. #13133211	C₂²	semidirect
26. #13133210	C₂²	semidirect
27. #13133210	C₂²	semidirect
28. #13133210	C₂²	semidirect
29. #13133209	C₂²	semidirect
30. #13133209	C₂²	semidirect
31. #13133208	C₂²	semidirect
32. #13133207	C₂²	semidirect
33. #13133207	C₂²	semidirect
34. #13133207	C₂²	semidirect
35. #13133205	C₂²	semidirect
36. #13133203	C₂²	semidirect
40. #13133202	C₂²	semidirect
41. #13133201	C₂²	semidirect
42. #13133200	C₂²	semidirect
43. #13133200	C₂²	semidirect
47. #13133199	C₂²	semidirect
48. #13133198	C₂²	semidirect
49. #13133198	C₂²	semidirect
50. #13133197	C₂²	semidirect
51. #13133196	C₂²	semidirect
52. #13133196	C₂²	semidirect
53. #13133195	C₂²	semidirect
54. #13133195	C₂²	semidirect
55. #13133195	C₂²	semidirect
56. #13133194	C₂²	semidirect
57. #13133194	C₂²	semidirect
58. #13133193	C₂²	semidirect
59. #13133193	C₂²	semidirect
64. C₄×Dic₁₀₆	C₂²	semidirect
65. #13133182	C₂²	semidirect
67. C₄×D₂₁₂	C₂²	semidirect
68. D₄×Dic₅₃	C₂²	semidirect
71. C₄×C₂²⋊D₅₃	C₂²	semidirect
73. #13133177	C₂²	semidirect
74. #13133177	C₂²	semidirect
75. #13133175	C₂²	semidirect
76. #13133175	C₂²	semidirect
77. #13133174	C₂²	semidirect
78. #13133174	C₂²	semidirect
79. #13133174	C₂²	semidirect
80. #13133174	C₂²	semidirect
81. #13133174	C₂²	semidirect
82. #13133174	C₂²	semidirect
83. #13133173	C₂²	semidirect
84. C₂×#11719919	C₂²	semidirect
85. C₂×#11719919	C₂²	semidirect
86. C₄⋊C₄×D₅₃	C₂²	semidirect
87. C₄⋊C₄×D₅₃	C₂²	semidirect
90. C₂×#11719921	C₂²	semidirect
92. C₂²⋊C₄×D₅₃	C₂²	semidirect
93. C₂²⋊C₄×D₅₃	C₂²	semidirect
94. C₂²⋊C₄×D₅₃	C₂²	semidirect
95. C₂×C₄×Dic₅₃	C₂²	semidirect
96. #126×C₅₃	C₂²	semidirect
97. #125×C₅₃	C₂²	semidirect
98. #124×C₅₃	C₂²	semidirect
99. #123×C₅₃	C₂²	semidirect
100. C₂²⋊Q₈×C₅₃	C₂²	semidirect
102. C₄×Q₈×C₅₃	C₂²	semidirect
103. C₄×D₄×C₅₃	C₂²	semidirect
104. C₄×D₄×C₅₃	C₂²	semidirect
105. #117×C₅₃	C₂²	semidirect
106. C₂×C₄²×C₅₃	C₂²	semidirect
299. #529	D₅₃	semidirect
303. C₅₃	#3491	semidirect
313. #126	C₂×D₅₃	semidirect
320. #125	C₂×D₅₃	semidirect
323. #124	C₂×D₅₃	semidirect
337. #123	C₂×D₅₃	semidirect
348. C₂²⋊Q₈	C₂×D₅₃	semidirect
356. C₄×Q₈	C₂×D₅₃	semidirect
366. C₄×D₄	C₂×D₅₃	semidirect
367. C₄×D₄	C₂×D₅₃	semidirect
377. #117	C₂×D₅₃	semidirect
390. C₂×C₄²	C₂×D₅₃	semidirect