Subgroups — #20289261

Order 6784.

1056 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811375	C₂	1	2	yes	maximal, complemented
2	#16811364	C₂	1	2	yes	maximal, complemented
3	#16811322	C₂	1	2	yes	maximal, complemented
4	#16811317	C₂	1	2	yes	maximal, complemented
5	#16811297	C₂	1	2	yes	maximal, complemented
6	#16811271	C₂	1	2	yes	maximal, complemented
7	#16811268	C₂	1	2	yes	maximal, complemented
8	#16811265	C₂	1	2	yes	maximal, complemented
9	#16811245	C₂	1	2	yes	maximal, complemented
10	#16811222	C₂	1	1	yes	maximal, characteristic, complemented
11	#16811221	C₂	1	2	yes	maximal, complemented
12	#16811213	C₂	1	1	yes	maximal, characteristic, complemented
13	#16811207	C₂	1	2	yes	maximal, complemented
14	#16811206	C₂	1	2	yes	maximal, complemented
15	#16811200	C₂	1	1	yes	maximal, characteristic, complemented
16	#16811181	C₂	1	1	yes	maximal, characteristic, complemented
17	#16811173	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13133211	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#11719945	C₂²	1	2	yes	complemented
21	C₂×#11719947	C₂²	1	2	yes	complemented
22	C₂×D₄×D₅₃	C₂²	1	2	yes	—
23	#13133217	C₂²	1	1	yes	characteristic, complemented
24	#13133216	C₂²	1	2	yes	complemented
25	#13133214	C₂²	1	1	yes	characteristic, complemented
26	#13133212	C₂²	1	2	yes	complemented
27	#13133212	C₂²	1	2	yes	complemented
28	#13133211	C₂²	1	2	yes	complemented
29	#13133211	C₂²	1	2	yes	complemented
30	#13133211	C₂²	1	2	yes	complemented
31	#13133211	C₂²	1	2	yes	complemented
32	#13133211	C₂²	1	2	yes	complemented
33	#13133210	C₂²	1	2	yes	complemented
34	#13133208	C₂²	1	2	yes	complemented
35	#13133207	C₂²	1	2	yes	complemented
36	#13133206	C₂²	1	2	yes	complemented
37	#13133205	C₂²	1	2	yes	—
38	#13133205	C₂²	1	2	yes	complemented
39	#13133203	C₂²	1	2	yes	—
40	#13133202	C₂²	1	2	yes	—
41	#13133202	C₂²	1	2	yes	—
42	#13133202	C₂²	1	2	yes	complemented
43	#13133202	C₂²	1	2	yes	complemented
44	#13133202	C₂²	1	2	yes	complemented
45	#13133202	C₂²	1	2	yes	complemented
46	#13133201	C₂²	1	2	yes	—
47	#13133201	C₂²	1	2	yes	complemented
48	#13133200	C₂²	1	2	yes	complemented
49	#13133199	C₂²	1	2	yes	—
50	#13133199	C₂²	1	2	yes	complemented
51	#13133197	C₂²	1	2	yes	complemented
52	#13133195	C₂²	1	2	yes	complemented
53	#13133195	C₂²	1	2	yes	complemented
54	#13133195	C₂²	1	2	yes	complemented
55	#13133194	C₂²	1	2	yes	complemented
56	#13133194	C₂²	1	2	yes	complemented
57	#13133193	C₂²	1	2	yes	complemented
58	#13133192	C₂²	1	2	yes	—
59	#13133192	C₂²	1	2	yes	—
60	#13133192	C₂²	1	2	yes	complemented
61	#13133191	C₂²	1	2	yes	—
62	#13133191	C₂²	1	1	yes	characteristic
63	#13133191	C₂²	1	2	yes	complemented
64	#13133191	C₂²	1	1	yes	characteristic, complemented
65	#13133190	C₂²	1	2	yes	—
66	#13133190	C₂²	1	2	yes	complemented
67	#13133190	C₂²	1	2	yes	complemented
68	#13133190	C₂²	1	2	yes	complemented
69	#13133189	C₂²	1	2	yes	—
70	#13133189	C₂²	1	2	yes	complemented
71	#13133189	C₂²	1	2	yes	complemented
72	#13133187	C₂²	1	2	yes	—
73	#13133187	C₂²	1	2	yes	—
74	#13133187	C₂²	1	2	yes	complemented
75	#13133187	C₂²	1	2	yes	complemented
76	#13133185	C₂²	1	2	yes	—
77	C₄×D₂₁₂	C₂²	1	2	yes	complemented
78	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
79	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
80	C₄×D₂₁₂	C₂²	1	2	yes	complemented
81	#13133179	C₂²	1	2	yes	complemented
82	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
83	#13133177	C₂²	1	2	yes	complemented
84	#13133177	C₂²	1	2	yes	complemented
85	#13133177	C₂²	1	2	yes	complemented
86	#13133174	C₂²	1	2	yes	complemented
87	C₂×#11719919	C₂²	1	1	yes	characteristic, complemented
88	C₂×#11719919	C₂²	1	1	yes	characteristic, complemented
89	C₂×#11719919	C₂²	1	1	yes	characteristic, complemented
90	C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
91	C₂×#11719921	C₂²	1	1	yes	characteristic
92	C₂×#11719921	C₂²	1	1	yes	characteristic
93	C₂×#11719921	C₂²	1	1	yes	characteristic
94	C₂×#11719921	C₂²	1	2	yes	complemented
95	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	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	2	yes	complemented
104	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
105	#117×C₅₃	C₂²	1	2	yes	complemented
106	C₂×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₅₃	C₂³	1	1	yes	characteristic
108	C₂³×D₅₃	C₂³	1	2	yes	—
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	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
120	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
121	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
122	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
123	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
124	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
125	C₂²×Dic₅₃	C₂³	1	2	yes	—
126	#11719947	—	4	4	no	—
127	D₄×D₅₃	—	4	4	no	—
128	#11719945	—	4	4	no	—
129	C₂×D₂₁₂	C₂³	1	2	yes	—
130	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
131	C₂×D₂₁₂	C₂³	1	2	yes	—
132	C₂×D₂₁₂	C₂³	1	2	yes	—
133	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
134	C₂×D₂₁₂	C₂³	1	2	yes	—
135	C₂×D₂₁₂	C₂³	1	2	yes	—
136	C₂×C₄×D₅₃	C₂³	1	2	yes	—
137	C₂×C₄×D₅₃	C₂³	1	2	yes	—
138	C₂×C₄×D₅₃	C₂³	1	2	yes	—
139	C₂×C₄×D₅₃	C₂³	1	2	yes	—
140	C₂×C₄×D₅₃	C₂³	1	2	yes	—
141	C₂×C₄×D₅₃	C₂³	1	2	yes	—
142	C₂×Dic₁₀₆	C₂³	1	2	yes	—
143	C₂×Dic₁₀₆	C₂³	1	2	yes	—
144	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
145	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
146	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
147	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
148	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
149	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
150	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
151	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
152	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
153	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
154	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
155	C₄²×C₅₃	C₂³	1	1	yes	characteristic
156	C₄²×C₅₃	C₂³	1	1	yes	characteristic
157	C₄²×C₅₃	C₂³	1	1	yes	characteristic
158	C₄²×C₅₃	C₂³	1	1	yes	characteristic
159	C₄²×C₅₃	C₂³	1	2	yes	—
160	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
161	C₂²⋊Dic₅₃	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	#11719921	C₂³	1	2	yes	—
172	#11719921	C₂³	1	2	yes	—
173	#11719921	C₂³	1	2	yes	—
174	#11719921	C₂³	1	2	yes	—
175	#11719921	C₂³	1	2	yes	—
176	#11719921	C₂³	1	2	yes	—
177	#11719921	C₂³	1	2	yes	—
178	#11719921	C₂³	1	2	yes	—
179	#11719921	C₂³	1	2	yes	—
180	C₄⋊Dic₅₃	C₂³	1	2	yes	—
181	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
182	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
183	C₄⋊Dic₅₃	C₂³	1	2	yes	—
184	C₄⋊Dic₅₃	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	#11719919	C₂³	1	2	yes	—
192	#11719919	C₂³	1	2	yes	—
193	#11719919	C₂³	1	2	yes	—
194	#11719919	C₂³	1	2	yes	—
195	C₄×Dic₅₃	C₂³	1	2	yes	—
196	C₄×Dic₅₃	C₂³	1	2	yes	—
197	C₂³×C₅₃	C₂⁴	1	2	yes	—
198	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
199	C₂²×D₅₃	—	2	2	no	—
200	C₂²×D₅₃	—	4	2	no	—
201	C₂²×D₅₃	—	4	2	no	—
202	C₂²×D₅₃	—	4	2	no	—
203	C₂²×D₅₃	—	4	1	no	—
204	C₂²×D₅₃	—	4	1	no	—
205	C₂²×D₅₃	C₂⁴	1	2	yes	—
206	C₂²×D₅₃	C₂⁴	1	2	yes	—
207	C₂²×D₅₃	C₂⁴	1	2	yes	—
208	Q₈×C₅₃	—	4	1	no	—
209	D₄×C₅₃	—	2	4	no	—
210	D₄×C₅₃	—	4	1	no	—
211	C₂×C₄×C₅₃	—	2	2	no	—
212	C₂×C₄×C₅₃	—	4	2	no	—
213	C₂×C₄×C₅₃	—	4	1	no	—
214	C₂×C₄×C₅₃	—	4	1	no	—
215	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
216	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
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	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
223	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
224	C₂²⋊D₅₃	—	2	4	no	—
225	C₂²⋊D₅₃	—	2	4	no	—
226	C₂²⋊D₅₃	—	4	2	no	—
227	C₂²⋊D₅₃	—	4	2	no	—
228	C₂²⋊D₅₃	—	4	2	no	—
229	C₂²⋊D₅₃	—	4	2	no	—
230	C₂×Dic₅₃	—	2	2	no	—
231	C₂×Dic₅₃	—	4	2	no	—
232	C₂×Dic₅₃	—	4	1	no	—
233	C₂×Dic₅₃	—	4	1	no	—
234	C₂×Dic₅₃	C₂⁴	1	2	yes	—
235	C₂×Dic₅₃	C₂⁴	1	2	yes	—
236	C₂×Dic₅₃	C₂⁴	1	2	yes	—
237	C₂×Dic₅₃	C₂⁴	1	2	yes	—
238	C₂×Dic₅₃	C₂⁴	1	2	yes	—
239	D₂₁₂	—	4	2	no	—
240	D₂₁₂	—	4	2	no	—
241	D₂₁₂	—	4	2	no	—
242	D₂₁₂	—	4	1	no	—
243	D₂₁₂	—	4	1	no	—
244	D₂₁₂	—	4	2	no	—
245	D₂₁₂	—	4	2	no	—
246	C₄×D₅₃	—	4	2	no	—
247	C₄×D₅₃	—	4	2	no	—
248	C₄×D₅₃	—	4	2	no	—
249	C₄×D₅₃	—	4	2	no	—
250	C₄×D₅₃	—	4	2	no	—
251	C₄×D₅₃	—	4	2	no	—
252	Dic₁₀₆	—	4	2	no	—
253	Dic₁₀₆	—	4	2	no	—
254	C₂²×C₅₃	—	2	1	no	—
255	C₂²×C₅₃	—	2	1	no	—
256	C₂²×C₅₃	—	2	2	no	—
257	C₂²×C₅₃	—	2	2	no	—
258	C₂²×C₅₃	—	2	2	no	—
259	C₂²×C₅₃	H(5,𝔽₂)	1	2	yes	—
260	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
261	C₂×D₅₃	—	2	2	no	—
262	C₂×D₅₃	—	2	2	no	—
263	C₂×D₅₃	—	2	2	no	—
264	C₂×D₅₃	—	2	2	no	—
265	C₂×D₅₃	—	2	2	no	—
266	C₂×D₅₃	—	2	2	no	—
267	C₂×D₅₃	—	2	2	no	—
268	C₂×D₅₃	—	2	2	no	—
269	C₂×D₅₃	—	2	2	no	—
270	C₂×D₅₃	—	8	2	no	—
271	C₂×D₅₃	—	8	4	no	—
272	C₄×C₅₃	—	2	1	no	—
273	C₄×C₅₃	—	2	2	no	—
274	C₄×C₅₃	—	2	1	no	—
275	C₄×C₅₃	—	2	2	no	—
276	C₄×C₅₃	—	2	2	no	—
277	C₄×C₅₃	—	2	1	no	—
278	C₄×C₅₃	—	2	1	no	—
279	C₄×C₅₃	—	2	1	no	—
280	C₄×C₅₃	—	2	1	no	—
281	Dic₅₃	—	2	2	no	—
282	Dic₅₃	—	2	2	no	—
283	Dic₅₃	—	2	2	no	—
284	Dic₅₃	—	2	2	no	—
285	Dic₅₃	—	2	2	no	—
286	#3560	—	53	1	no	maximal, Sylow
287	C₂×C₅₃	—	2	2	no	—
288	C₂×C₅₃	—	4	2	no	—
289	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
290	C₂×C₅₃	#585	1	1	yes	characteristic
291	C₂×C₅₃	#585	1	1	yes	characteristic
292	D₅₃	—	4	2	no	—
293	D₅₃	—	4	2	no	—
294	D₅₃	—	4	2	no	—
295	#563	—	53	2	no	—
296	#560	—	53	2	no	—
297	#553	—	53	2	no	—
298	#553	—	53	2	no	—
299	#551	—	53	2	no	—
300	#547	—	53	2	no	—
301	#546	—	53	2	no	—
302	#546	—	53	2	no	—
303	#542	—	53	2	no	—
304	#539	—	53	2	no	—
305	#539	—	53	1	no	—
306	#538	—	53	2	no	—
307	#538	—	53	1	no	—
308	#538	—	53	2	no	—
309	#537	—	53	1	no	—
310	#534	—	53	1	no	—
311	#532	—	53	1	no	—
312	#529	D₅₃	1	1	yes	characteristic, complemented
313	C₂×#126	—	53	1	no	—
314	C₅₃	#3560	1	1	yes	characteristic, complemented, Sylow
315	C₂×#41	—	53	2	no	—
316	C₂×#41	—	53	2	no	—
317	C₂²×D₄	—	53	2	no	—
318	C₄⋊Q₈	—	53	2	no	—
319	C₄⋊Q₈	—	53	1	no	—
320	#127	—	53	1	no	—
321	#126	—	53	2	no	—
322	#126	—	53	2	no	—
323	#126	—	53	2	no	—
324	#126	—	53	2	no	—
325	#126	—	53	2	no	—
326	#126	—	53	2	no	—
327	#126	—	53	2	no	—
328	#126	—	53	2	no	—
329	#126	C₂×D₅₃	1	2	yes	complemented
330	#125	—	53	2	no	—
331	#125	—	53	2	no	—
332	#125	C₂×D₅₃	1	1	yes	characteristic, complemented
333	#124	—	53	2	no	—
334	#124	—	53	2	no	—
335	#124	—	53	2	no	—
336	#124	—	53	2	no	—
337	#124	C₂×D₅₃	1	1	yes	characteristic, complemented
338	#123	—	53	2	no	—
339	#123	—	53	2	no	—
340	#123	—	53	2	no	—
341	#123	—	53	2	no	—
342	#123	—	53	2	no	—
343	#123	—	53	2	no	—
344	#123	—	53	2	no	—
345	#123	—	53	2	no	—
346	#123	—	53	2	no	—
347	#123	—	53	2	no	—
348	#123	—	53	2	no	—
349	#123	C₂×D₅₃	1	2	yes	complemented
350	C₂²⋊Q₈	—	53	2	no	—
351	C₂²⋊Q₈	—	53	2	no	—
352	C₂²⋊Q₈	—	53	2	no	—
353	C₂²⋊Q₈	—	53	2	no	—
354	C₂²⋊Q₈	—	53	2	no	—
355	C₂²⋊Q₈	—	53	2	no	—
356	C₂²⋊Q₈	—	53	2	no	—
357	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
358	#121	—	53	2	no	—
359	#121	—	53	2	no	—
360	#121	—	53	2	no	—
361	#121	—	53	1	no	—
362	#121	—	53	1	no	—
363	#121	—	53	2	no	—
364	#121	—	53	2	no	—
365	#121	—	53	2	no	—
366	#121	—	53	2	no	—
367	#121	—	53	2	no	—
368	#121	—	53	2	no	—
369	#121	—	53	2	no	—
370	#121	—	53	2	no	—
371	#121	—	53	2	no	—
372	#121	C₂×D₅₃	1	1	yes	characteristic
373	#120	—	53	2	no	—
374	#120	—	53	2	no	—
375	#120	—	53	2	no	—
376	#120	—	53	2	no	—
377	#120	—	53	2	no	—
378	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
379	C₄×D₄	—	53	2	no	—
380	C₄×D₄	—	53	2	no	—
381	C₄×D₄	—	53	2	no	—
382	C₄×D₄	—	53	2	no	—
383	C₄×D₄	—	53	2	no	—
384	C₄×D₄	—	53	2	no	—
385	C₄×D₄	—	53	1	no	—
386	C₄×D₄	—	53	1	no	—
387	C₄×D₄	—	53	2	no	—
388	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
389	C₄×D₄	C₂×D₅₃	1	2	yes	complemented
390	#117	—	53	2	no	—
391	#117	C₂×D₅₃	1	2	yes	complemented
392	C₂×C₄⋊C₄	—	53	1	no	—
393	C₂×C₄⋊C₄	—	53	1	no	—
394	C₂×C₄⋊C₄	—	53	1	no	—
395	C₂×C₄⋊C₄	—	53	2	no	—
396	C₂×C₂²⋊C₄	—	53	1	no	—
397	C₂×C₂²⋊C₄	—	53	1	no	—
398	C₂×C₂²⋊C₄	—	53	1	no	—
399	C₂×C₂²⋊C₄	—	53	2	no	—
400	C₂×C₂²⋊C₄	—	53	2	no	—
401	C₂×C₄²	C₂×D₅₃	1	1	yes	characteristic, complemented
402	C₂⁴	—	53	1	no	—
403	C₂⁴	—	53	2	no	—
404	#41	—	212	4	no	—
405	#41	—	212	4	no	—
406	C₂×Q₈	—	53	2	no	—
407	C₂×Q₈	—	53	2	no	—
408	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
409	C₂×D₄	—	53	2	no	—
410	C₂×D₄	—	53	2	no	—
411	C₂×D₄	—	53	2	no	—
412	C₂×D₄	—	53	2	no	—
413	C₂×D₄	—	53	2	no	—
414	C₂×D₄	—	53	2	no	—
415	C₂×D₄	—	53	2	no	—
416	C₂×D₄	—	53	2	no	—
417	C₂×D₄	—	53	1	no	—
418	C₂×D₄	—	53	2	no	—
419	C₂×D₄	—	53	1	no	—
420	C₂×D₄	—	53	2	no	—
421	C₂×D₄	—	53	2	no	—
422	C₂×D₄	—	212	4	no	—
423	C₂×D₄	C₂²×D₅₃	1	2	yes	—
424	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
425	C₂²×C₄	—	53	1	no	—
426	C₂²×C₄	—	53	1	no	—
427	C₂²×C₄	—	53	1	no	—
428	C₂²×C₄	—	53	2	no	—
429	C₂²×C₄	—	53	2	no	—
430	C₂²×C₄	—	53	2	no	—
431	C₂²×C₄	—	53	2	no	—
432	C₂²×C₄	—	53	2	no	—
433	C₂²×C₄	—	53	2	no	—
434	C₂²×C₄	—	53	2	no	—
435	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
436	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
437	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
438	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
439	C₄⋊C₄	—	53	2	no	—
440	C₄⋊C₄	—	53	2	no	—
441	C₄⋊C₄	—	53	2	no	—
442	C₄⋊C₄	—	53	2	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	1	no	—
450	C₄⋊C₄	—	53	2	no	—
451	C₄⋊C₄	—	53	1	no	—
452	C₄⋊C₄	—	53	2	no	—
453	C₄⋊C₄	—	53	2	no	—
454	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
455	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
456	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
457	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
458	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
459	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
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	—	53	2	no	—
466	C₂²⋊C₄	—	53	2	no	—
467	C₂²⋊C₄	—	53	2	no	—
468	C₂²⋊C₄	—	53	2	no	—
469	C₂²⋊C₄	—	53	2	no	—
470	C₂²⋊C₄	—	53	2	no	—
471	C₂²⋊C₄	—	53	2	no	—
472	C₂²⋊C₄	—	53	2	no	—
473	C₂²⋊C₄	—	53	2	no	—
474	C₂²⋊C₄	—	53	2	no	—
475	C₂²⋊C₄	—	53	2	no	—
476	C₂²⋊C₄	—	53	2	no	—
477	C₂²⋊C₄	—	53	2	no	—
478	C₂²⋊C₄	—	53	2	no	—
479	C₂²⋊C₄	—	53	2	no	—
480	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
481	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
482	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
483	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
484	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
485	C₄²	—	53	2	no	—
486	C₄²	—	53	2	no	—
487	C₄²	C₂²×D₅₃	1	1	yes	characteristic
488	C₄²	C₂²×D₅₃	1	1	yes	characteristic
489	C₄²	C₂²×D₅₃	1	1	yes	characteristic
490	C₄²	C₂²×D₅₃	1	1	yes	characteristic
491	C₄²	C₂²×D₅₃	1	2	yes	—
492	C₂³	—	53	2	no	—
493	C₂³	—	53	2	no	—
494	C₂³	—	53	2	no	—
495	C₂³	—	106	2	no	—
496	C₂³	—	212	2	no	—
497	C₂³	—	212	1	no	—
498	C₂³	—	212	1	no	—
499	C₂³	—	212	2	no	—
500	C₂³	—	212	2	no	—
501	C₂³	C₂³×D₅₃	1	2	yes	—
502	C₂³	C₂³×D₅₃	1	1	yes	characteristic
503	Q₈	—	4	1	no	—
504	Q₈	—	212	2	no	—
505	Q₈	—	212	2	no	—
506	D₄	—	2	4	no	—
507	D₄	—	4	1	no	—
508	D₄	—	106	4	no	—
509	D₄	—	106	4	no	—
510	D₄	—	212	2	no	—
511	D₄	—	212	2	no	—
512	D₄	—	212	1	no	—
513	D₄	—	212	1	no	—
514	D₄	—	212	2	no	—
515	D₄	—	212	2	no	—
516	D₄	—	212	2	no	—
517	D₄	—	212	2	no	—
518	D₄	—	212	2	no	—
519	D₄	—	212	2	no	—
520	D₄	—	212	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	53	2	no	—
526	C₂×C₄	—	53	2	no	—
527	C₂×C₄	—	53	2	no	—
528	C₂×C₄	—	53	2	no	—
529	C₂×C₄	—	53	2	no	—
530	C₂×C₄	—	106	2	no	—
531	C₂×C₄	—	212	2	no	—
532	C₂×C₄	—	212	2	no	—
533	C₂×C₄	—	212	2	no	—
534	C₂×C₄	—	212	2	no	—
535	C₂×C₄	—	212	2	no	—
536	C₂×C₄	—	212	2	no	—
537	C₂×C₄	—	212	1	no	—
538	C₂×C₄	—	212	1	no	—
539	C₂×C₄	—	212	2	no	—
540	C₂×C₄	C₂³×D₅₃	1	2	yes	—
541	C₂×C₄	C₂³×D₅₃	1	2	yes	—
542	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
543	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
544	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
545	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
546	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
547	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
548	C₂×C₄	C₂³×D₅₃	1	2	yes	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	106	2	no	—
555	C₂²	—	106	2	no	—
556	C₂²	—	106	2	no	—
557	C₂²	—	106	2	no	—
558	C₂²	—	106	2	no	—
559	C₂²	—	106	2	no	—
560	C₂²	—	106	2	no	—
561	C₂²	—	106	2	no	—
562	C₂²	—	106	2	no	—
563	C₂²	—	424	2	no	—
564	C₂²	—	424	4	no	—
565	C₂²	#13133263	1	2	yes	—
566	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
567	C₄	—	2	1	no	—
568	C₄	—	2	1	no	—
569	C₄	—	2	2	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	1	no	—
574	C₄	—	2	1	no	—
575	C₄	—	2	2	no	—
576	C₄	—	106	2	no	—
577	C₄	—	106	2	no	—
578	C₄	—	106	2	no	—
579	C₄	—	106	2	no	—
580	C₄	—	106	2	no	—
581	C₂	—	2	2	no	—
582	C₂	—	4	2	no	—
583	C₂	—	212	2	no	—
584	C₂	—	212	2	no	—
585	C₂	—	212	2	no	—
586	C₂	C₂×#13133263	1	1	yes	characteristic
587	C₂	#16811459	1	1	yes	characteristic
588	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	#3560
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. #16811375	C₂	semidirect
2. #16811364	C₂	semidirect
3. #16811322	C₂	semidirect
4. #16811317	C₂	semidirect
5. #16811297	C₂	semidirect
6. #16811271	C₂	semidirect
7. #16811268	C₂	semidirect
8. #16811265	C₂	semidirect
9. #16811245	C₂	semidirect
10. #16811222	C₂	semidirect
11. #16811221	C₂	semidirect
12. #16811213	C₂	semidirect
13. #16811207	C₂	semidirect
14. #16811206	C₂	semidirect
15. #16811200	C₂	semidirect
16. #16811181	C₂	semidirect
17. #16811173	C₂	semidirect
18. C₂×#13133211	C₂	semidirect
19. C₅₃×#529	C₂	semidirect
20. C₂×#11719945	C₂²	semidirect
21. C₂×#11719947	C₂²	semidirect
23. #13133217	C₂²	semidirect
24. #13133216	C₂²	semidirect
25. #13133214	C₂²	semidirect
26. #13133212	C₂²	semidirect
27. #13133212	C₂²	semidirect
28. #13133211	C₂²	semidirect
29. #13133211	C₂²	semidirect
30. #13133211	C₂²	semidirect
31. #13133211	C₂²	semidirect
32. #13133211	C₂²	semidirect
33. #13133210	C₂²	semidirect
34. #13133208	C₂²	semidirect
35. #13133207	C₂²	semidirect
36. #13133206	C₂²	semidirect
38. #13133205	C₂²	semidirect
42. #13133202	C₂²	semidirect
43. #13133202	C₂²	semidirect
44. #13133202	C₂²	semidirect
45. #13133202	C₂²	semidirect
47. #13133201	C₂²	semidirect
48. #13133200	C₂²	semidirect
50. #13133199	C₂²	semidirect
51. #13133197	C₂²	semidirect
52. #13133195	C₂²	semidirect
53. #13133195	C₂²	semidirect
54. #13133195	C₂²	semidirect
55. #13133194	C₂²	semidirect
56. #13133194	C₂²	semidirect
57. #13133193	C₂²	semidirect
60. #13133192	C₂²	semidirect
63. #13133191	C₂²	semidirect
64. #13133191	C₂²	semidirect
66. #13133190	C₂²	semidirect
67. #13133190	C₂²	semidirect
68. #13133190	C₂²	semidirect
70. #13133189	C₂²	semidirect
71. #13133189	C₂²	semidirect
74. #13133187	C₂²	semidirect
75. #13133187	C₂²	semidirect
77. C₄×D₂₁₂	C₂²	semidirect
78. C₄×D₂₁₂	C₂²	semidirect
79. C₄×D₂₁₂	C₂²	semidirect
80. C₄×D₂₁₂	C₂²	semidirect
81. #13133179	C₂²	semidirect
82. C₄×C₂²⋊D₅₃	C₂²	semidirect
83. #13133177	C₂²	semidirect
84. #13133177	C₂²	semidirect
85. #13133177	C₂²	semidirect
86. #13133174	C₂²	semidirect
87. C₂×#11719919	C₂²	semidirect
88. C₂×#11719919	C₂²	semidirect
89. C₂×#11719919	C₂²	semidirect
90. C₄⋊C₄×D₅₃	C₂²	semidirect
94. C₂×#11719921	C₂²	semidirect
95. C₂²⋊C₄×D₅₃	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
312. #529	D₅₃	semidirect
314. C₅₃	#3560	semidirect
329. #126	C₂×D₅₃	semidirect
332. #125	C₂×D₅₃	semidirect
337. #124	C₂×D₅₃	semidirect
349. #123	C₂×D₅₃	semidirect
357. C₂²⋊Q₈	C₂×D₅₃	semidirect
378. C₄×Q₈	C₂×D₅₃	semidirect
388. C₄×D₄	C₂×D₅₃	semidirect
389. C₄×D₄	C₂×D₅₃	semidirect
391. #117	C₂×D₅₃	semidirect
401. C₂×C₄²	C₂×D₅₃	semidirect