Subgroups — #20288584

Order 6784.

1232 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811356	C₂	1	2	yes	maximal, complemented
2	#16811355	C₂	1	2	yes	maximal, complemented
3	#16811292	C₂	1	2	yes	maximal, complemented
4	#16811291	C₂	1	2	yes	maximal, complemented
5	#16811270	C₂	1	2	yes	maximal, complemented
6	#16811268	C₂	1	2	yes	maximal, complemented
7	#16811266	C₂	1	2	yes	maximal, complemented
8	#16811261	C₂	1	2	yes	maximal, complemented
9	#16811226	C₂	1	2	yes	maximal, complemented
10	#16811224	C₂	1	2	yes	maximal, complemented
11	#16811189	C₂	1	2	yes	maximal, complemented
12	#16811178	C₂	1	1	yes	maximal, characteristic, complemented
13	#16811174	C₂	1	1	yes	maximal, characteristic, complemented
14	#16811173	C₂	1	1	yes	maximal, characteristic, complemented
15	#16811171	C₂	1	1	yes	maximal, characteristic, complemented
16	#127×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
17	#16811095	C₂	1	2	yes	maximal, complemented
18	C₄×#11719945	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#11719949	C₂²	1	2	yes	complemented
21	C₂×#11719945	C₂²	1	1	yes	characteristic
22	C₂×#11719945	C₂²	1	2	yes	complemented
23	C₂×#11719947	C₂²	1	2	yes	complemented
24	C₂×D₄×D₅₃	C₂²	1	2	yes	—
25	C₂×D₄×D₅₃	C₂²	1	2	yes	—
26	C₂×D₄×D₅₃	C₂²	1	2	yes	—
27	#13133217	C₂²	1	1	yes	characteristic, complemented
28	#13133214	C₂²	1	1	yes	characteristic
29	#13133213	C₂²	1	2	yes	—
30	#13133213	C₂²	1	2	yes	—
31	#13133213	C₂²	1	2	yes	—
32	#13133213	C₂²	1	4	yes	complemented
33	#13133208	C₂²	1	2	yes	complemented
34	#13133206	C₂²	1	2	yes	complemented
35	#13133205	C₂²	1	2	yes	complemented
36	#13133204	C₂²	1	2	yes	complemented
37	#13133203	C₂²	1	4	yes	complemented
38	#13133201	C₂²	1	4	yes	complemented
39	#13133200	C₂²	1	4	yes	complemented
40	#13133199	C₂²	1	4	yes	complemented
41	#13133199	C₂²	1	4	yes	complemented
42	#13133197	C₂²	1	2	yes	—
43	#13133193	C₂²	1	2	yes	—
44	#13133192	C₂²	1	2	yes	complemented
45	#13133192	C₂²	1	2	yes	complemented
46	#13133191	C₂²	1	4	yes	complemented
47	#13133191	C₂²	1	2	yes	complemented
48	#13133191	C₂²	1	2	yes	complemented
49	#13133190	C₂²	1	4	yes	complemented
50	#13133189	C₂²	1	4	yes	complemented
51	#13133188	C₂²	1	2	yes	complemented
52	#13133188	C₂²	1	4	yes	complemented
53	#13133188	C₂²	1	2	yes	complemented
54	#13133187	C₂²	1	4	yes	—
55	#13133185	C₂²	1	4	yes	—
56	Q₈×Dic₅₃	C₂²	1	2	yes	complemented
57	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
58	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
59	#13133182	C₂²	1	2	yes	complemented
60	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
61	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
62	C₄×D₂₁₂	C₂²	1	2	yes	complemented
63	C₄×D₂₁₂	C₂²	1	2	yes	complemented
64	D₄×Dic₅₃	C₂²	1	2	yes	complemented
65	D₄×Dic₅₃	C₂²	1	2	yes	complemented
66	#13133179	C₂²	1	2	yes	complemented
67	#13133179	C₂²	1	2	yes	complemented
68	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
69	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
70	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
71	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
72	C₄×C₂²⋊D₅₃	C₂²	1	4	yes	complemented
73	#13133177	C₂²	1	4	yes	complemented
74	#13133176	C₂²	1	1	yes	characteristic, complemented
75	#13133175	C₂²	1	2	yes	—
76	#13133174	C₂²	1	1	yes	characteristic
77	#13133174	C₂²	1	1	yes	characteristic, complemented
78	C₂×#11719921	C₂²	1	4	yes	—
79	C₂²⋊C₄×D₅₃	C₂²	1	4	yes	—
80	C₄²×D₅₃	C₂²	1	1	yes	characteristic
81	C₄²×D₅₃	C₂²	1	1	yes	characteristic, complemented
82	C₂×#41×C₅₃	C₂²	1	2	yes	complemented
83	C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
84	#127×C₅₃	C₂²	1	1	yes	characteristic
85	#124×C₅₃	C₂²	1	2	yes	complemented
86	#121×C₅₃	C₂²	1	2	yes	complemented
87	#121×C₅₃	C₂²	1	2	yes	complemented
88	C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
89	C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
90	C₂×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
91	C₂³×D₅₃	C₂³	1	4	yes	—
92	#41×C₅₃	—	4	4	no	—
93	C₂×Q₈×C₅₃	C₂³	1	2	yes	—
94	C₂×D₄×C₅₃	C₂³	1	2	yes	—
95	C₂×D₄×C₅₃	C₂³	1	2	yes	—
96	C₂×D₄×C₅₃	C₂³	1	2	yes	—
97	C₂×D₄×C₅₃	C₂³	1	4	yes	—
98	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
99	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
100	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
101	C₂²×C₄×C₅₃	C₂³	1	4	yes	—
102	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
103	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
104	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
105	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
106	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
107	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
108	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
109	C₂²×Dic₅₃	C₂³	1	4	yes	—
110	#11719949	—	4	4	no	—
111	#11719947	—	4	4	no	—
112	D₄×D₅₃	—	2	8	no	—
113	D₄×D₅₃	—	4	4	no	—
114	D₄×D₅₃	—	4	4	no	—
115	#11719945	—	2	4	no	—
116	#11719945	—	4	4	no	—
117	C₂×D₂₁₂	C₂³	1	2	yes	—
118	C₂×D₂₁₂	C₂³	1	2	yes	—
119	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
120	C₂×D₂₁₂	C₂³	1	2	yes	—
121	C₂×D₂₁₂	C₂³	1	4	yes	—
122	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
123	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
124	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
125	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
126	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
127	C₂×C₄×D₅₃	C₂³	1	4	yes	—
128	C₂×C₄×D₅₃	C₂³	1	4	yes	—
129	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
130	C₂×Dic₁₀₆	C₂³	1	2	yes	—
131	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
132	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
133	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
134	C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
135	C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
136	C₄²×C₅₃	C₂³	1	1	yes	characteristic
137	C₄²×C₅₃	C₂³	1	1	yes	characteristic
138	C₄²×C₅₃	C₂³	1	1	yes	characteristic
139	C₄²×C₅₃	C₂³	1	1	yes	characteristic
140	C₂²⋊Dic₅₃	C₂³	1	4	yes	—
141	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
142	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
143	C₂²⋊Dic₅₃	C₂³	1	4	yes	—
144	#11719921	C₂³	1	1	yes	characteristic
145	#11719921	C₂³	1	4	yes	—
146	#11719921	C₂³	1	1	yes	characteristic
147	#11719921	C₂³	1	4	yes	—
148	#11719921	C₂³	1	4	yes	—
149	#11719921	C₂³	1	1	yes	characteristic
150	#11719921	C₂³	1	1	yes	characteristic
151	#11719921	C₂³	1	4	yes	—
152	#11719921	C₂³	1	4	yes	—
153	C₄⋊Dic₅₃	C₂³	1	2	yes	—
154	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
155	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
156	C₄⋊Dic₅₃	C₂³	1	2	yes	—
157	C₄⋊Dic₅₃	C₂³	1	4	yes	—
158	#11719919	C₂³	1	1	yes	characteristic
159	#11719919	C₂³	1	1	yes	characteristic
160	#11719919	C₂³	1	1	yes	characteristic
161	#11719919	C₂³	1	1	yes	characteristic
162	#11719919	C₂³	1	4	yes	—
163	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
164	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
165	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
166	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
167	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
168	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
169	C₄×Dic₅₃	C₂³	1	4	yes	—
170	C₂³×C₅₃	C₂⁴	1	4	yes	—
171	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
172	C₂²×D₅₃	—	2	8	no	—
173	C₂²×D₅₃	—	4	4	no	—
174	C₂²×D₅₃	—	4	4	no	—
175	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
176	C₂²×D₅₃	C₂⁴	1	4	yes	—
177	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
178	Q₈×C₅₃	—	2	4	no	—
179	D₄×C₅₃	—	2	4	no	—
180	D₄×C₅₃	—	2	4	no	—
181	D₄×C₅₃	—	2	4	no	—
182	D₄×C₅₃	—	4	4	no	—
183	C₂×C₄×C₅₃	—	2	2	no	—
184	C₂×C₄×C₅₃	—	2	2	no	—
185	C₂×C₄×C₅₃	—	2	2	no	—
186	C₂×C₄×C₅₃	—	4	4	no	—
187	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
188	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
189	C₂×C₄×C₅₃	C₂⁴	1	4	yes	—
190	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
191	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
192	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
193	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
194	C₂²⋊D₅₃	—	2	2	no	—
195	C₂²⋊D₅₃	—	2	2	no	—
196	C₂²⋊D₅₃	—	2	8	no	—
197	C₂²⋊D₅₃	—	4	4	no	—
198	C₂²⋊D₅₃	—	4	4	no	—
199	C₂²⋊D₅₃	—	4	4	no	—
200	C₂²⋊D₅₃	—	4	4	no	—
201	C₂×Dic₅₃	—	4	4	no	—
202	C₂×Dic₅₃	C₂⁴	1	4	yes	—
203	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
204	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
205	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
206	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
207	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
208	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
209	D₂₁₂	—	2	2	no	—
210	D₂₁₂	—	2	4	no	—
211	D₂₁₂	—	2	4	no	—
212	D₂₁₂	—	2	4	no	—
213	D₂₁₂	—	4	4	no	—
214	C₄×D₅₃	—	2	2	no	—
215	C₄×D₅₃	—	2	2	no	—
216	C₄×D₅₃	—	2	2	no	—
217	C₄×D₅₃	—	2	2	no	—
218	C₄×D₅₃	—	2	2	no	—
219	C₄×D₅₃	—	4	4	no	—
220	C₄×D₅₃	—	4	4	no	—
221	C₄×D₅₃	#41	1	4	yes	complemented
222	Dic₁₀₆	—	2	4	no	—
223	Dic₁₀₆	—	2	2	no	—
224	C₂²×C₅₃	—	2	1	no	—
225	C₂²×C₅₃	—	2	4	no	—
226	C₂²×C₅₃	—	2	4	no	—
227	C₂²×C₅₃	—	2	1	no	—
228	C₂²×C₅₃	—	2	4	no	—
229	C₂²×C₅₃	—	2	1	no	—
230	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
231	C₂×D₅₃	—	2	1	no	—
232	C₂×D₅₃	—	2	1	no	—
233	C₂×D₅₃	—	2	1	no	—
234	C₂×D₅₃	—	2	4	no	—
235	C₂×D₅₃	—	2	1	no	—
236	C₂×D₅₃	—	2	1	no	—
237	C₂×D₅₃	—	2	4	no	—
238	C₂×D₅₃	—	2	4	no	—
239	C₂×D₅₃	—	8	8	no	—
240	C₂×D₅₃	C₂×#41	1	2	yes	—
241	C₄×C₅₃	—	2	1	no	—
242	C₄×C₅₃	—	2	1	no	—
243	C₄×C₅₃	—	2	4	no	—
244	C₄×C₅₃	—	2	1	no	—
245	C₄×C₅₃	C₂×#41	1	2	yes	—
246	C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
247	C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
248	Dic₅₃	—	2	1	no	—
249	Dic₅₃	—	2	4	no	—
250	Dic₅₃	—	2	1	no	—
251	Dic₅₃	—	2	1	no	—
252	Dic₅₃	—	2	1	no	—
253	Dic₅₃	—	2	1	no	—
254	Dic₅₃	C₂×#41	1	2	yes	—
255	#3508	—	53	1	no	maximal, Sylow
256	C₂×C₅₃	—	4	4	no	—
257	C₂×C₅₃	—	4	1	no	—
258	C₂×C₅₃	C₂²×#41	1	1	yes	characteristic
259	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
260	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
261	D₅₃	—	2	2	no	—
262	D₅₃	—	4	1	no	—
263	D₅₃	—	4	4	no	—
264	#559	—	53	2	no	—
265	#559	—	53	2	no	—
266	#550	—	53	2	no	—
267	#550	—	53	2	no	—
268	#546	—	53	2	no	—
269	#546	—	53	2	no	—
270	#546	—	53	2	no	—
271	#546	—	53	2	no	—
272	#540	—	53	2	no	—
273	#540	—	53	2	no	—
274	#535	—	53	2	no	—
275	#533	—	53	1	no	—
276	#532	—	53	1	no	—
277	#532	—	53	1	no	—
278	#532	—	53	1	no	—
279	#532	D₅₃	1	1	yes	characteristic, complemented
280	C₂×#127	—	53	1	no	—
281	#518	—	53	2	no	—
282	C₄×#41	—	53	1	no	—
283	C₅₃	#3508	1	1	yes	characteristic, complemented, Sylow
284	C₂×#41	—	53	2	no	—
285	C₂×#41	—	53	2	no	—
286	C₂×#41	—	53	1	no	—
287	C₂×#41	—	53	2	no	—
288	C₂×#41	C₂×D₅₃	1	2	yes	complemented
289	C₂²×D₄	—	53	2	no	—
290	C₂²×D₄	—	53	2	no	—
291	C₂²×D₄	—	53	2	no	—
292	C₄⋊Q₈	—	53	1	no	—
293	C₄⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
294	#127	—	53	2	no	—
295	#127	—	53	2	no	—
296	#127	—	53	2	no	—
297	#127	—	53	4	no	—
298	#127	—	53	1	no	—
299	#127	C₂×D₅₃	1	1	yes	characteristic
300	#125	—	53	2	no	—
301	#124	—	53	2	no	—
302	#124	—	53	2	no	—
303	#124	—	53	4	no	—
304	#124	—	53	2	no	—
305	#124	C₂×D₅₃	1	2	yes	complemented
306	#123	—	53	4	no	—
307	#123	—	53	4	no	—
308	#123	—	53	4	no	—
309	#123	—	53	4	no	—
310	C₂²⋊Q₈	—	53	2	no	—
311	C₂²⋊Q₈	—	53	2	no	—
312	#121	—	53	2	no	—
313	#121	—	53	2	no	—
314	#121	—	53	4	no	—
315	#121	—	53	4	no	—
316	#121	—	53	2	no	—
317	#121	—	53	2	no	—
318	#121	—	53	4	no	—
319	#121	—	53	2	no	—
320	#121	—	53	2	no	—
321	#121	—	53	4	no	—
322	#121	C₂×D₅₃	1	2	yes	complemented
323	#121	C₂×D₅₃	1	2	yes	complemented
324	#120	—	53	4	no	—
325	#120	—	53	4	no	—
326	C₄×Q₈	—	53	2	no	—
327	C₄×Q₈	—	53	2	no	—
328	C₄×Q₈	—	53	1	no	—
329	C₄×Q₈	—	53	1	no	—
330	C₄×D₄	—	53	2	no	—
331	C₄×D₄	—	53	2	no	—
332	C₄×D₄	—	53	1	no	—
333	C₄×D₄	—	53	1	no	—
334	C₄×D₄	—	53	1	no	—
335	C₄×D₄	—	53	1	no	—
336	C₄×D₄	—	53	4	no	—
337	C₄×D₄	—	53	2	no	—
338	C₄×D₄	—	53	2	no	—
339	C₄×D₄	—	53	4	no	—
340	C₄×D₄	—	53	1	no	—
341	C₄×D₄	—	53	1	no	—
342	C₄×D₄	—	53	2	no	—
343	C₄×D₄	—	53	2	no	—
344	C₄×D₄	C₂×D₅₃	1	2	yes	complemented
345	C₄×D₄	C₂×D₅₃	1	2	yes	complemented
346	#117	—	53	1	no	—
347	#117	—	53	2	no	—
348	#117	—	53	1	no	—
349	#117	—	53	1	no	—
350	C₂×C₂²⋊C₄	—	53	4	no	—
351	C₂×C₂²⋊C₄	—	53	4	no	—
352	C₂×C₄²	—	53	1	no	—
353	C₂×C₄²	—	53	1	no	—
354	C₂×C₄²	C₂×D₅₃	1	1	yes	characteristic, complemented
355	C₂⁴	—	53	4	no	—
356	#41	—	4	4	no	—
357	#41	—	106	4	no	—
358	#41	—	212	4	no	—
359	#41	—	212	4	no	—
360	#41	—	212	4	no	—
361	C₂×Q₈	—	53	1	no	—
362	C₂×Q₈	—	53	2	no	—
363	C₂×Q₈	C₂²×D₅₃	1	2	yes	—
364	C₂×D₄	—	53	1	no	—
365	C₂×D₄	—	53	4	no	—
366	C₂×D₄	—	53	1	no	—
367	C₂×D₄	—	53	4	no	—
368	C₂×D₄	—	53	4	no	—
369	C₂×D₄	—	53	4	no	—
370	C₂×D₄	—	53	4	no	—
371	C₂×D₄	—	53	1	no	—
372	C₂×D₄	—	53	2	no	—
373	C₂×D₄	—	53	2	no	—
374	C₂×D₄	—	53	2	no	—
375	C₂×D₄	—	53	4	no	—
376	C₂×D₄	—	106	8	no	—
377	C₂×D₄	—	212	4	no	—
378	C₂×D₄	—	212	4	no	—
379	C₂×D₄	C₂²×D₅₃	1	2	yes	—
380	C₂×D₄	C₂²×D₅₃	1	2	yes	—
381	C₂×D₄	C₂²×D₅₃	1	2	yes	—
382	C₂×D₄	C₂²×D₅₃	1	4	yes	—
383	C₂²×C₄	—	53	1	no	—
384	C₂²×C₄	—	53	4	no	—
385	C₂²×C₄	—	53	1	no	—
386	C₂²×C₄	—	53	1	no	—
387	C₂²×C₄	—	53	1	no	—
388	C₂²×C₄	—	53	1	no	—
389	C₂²×C₄	—	53	1	no	—
390	C₂²×C₄	—	53	4	no	—
391	C₂²×C₄	—	53	4	no	—
392	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
393	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
394	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
395	C₂²×C₄	C₂²×D₅₃	1	4	yes	—
396	C₄⋊C₄	—	53	1	no	—
397	C₄⋊C₄	—	53	1	no	—
398	C₄⋊C₄	—	53	2	no	—
399	C₄⋊C₄	—	53	1	no	—
400	C₄⋊C₄	—	53	1	no	—
401	C₄⋊C₄	—	53	1	no	—
402	C₄⋊C₄	—	53	1	no	—
403	C₄⋊C₄	—	53	2	no	—
404	C₄⋊C₄	—	53	4	no	—
405	C₄⋊C₄	—	53	4	no	—
406	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
407	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
408	C₂²⋊C₄	—	53	4	no	—
409	C₂²⋊C₄	—	53	1	no	—
410	C₂²⋊C₄	—	53	1	no	—
411	C₂²⋊C₄	—	53	4	no	—
412	C₂²⋊C₄	—	53	1	no	—
413	C₂²⋊C₄	—	53	1	no	—
414	C₂²⋊C₄	—	53	4	no	—
415	C₂²⋊C₄	—	53	4	no	—
416	C₂²⋊C₄	—	53	4	no	—
417	C₂²⋊C₄	—	53	1	no	—
418	C₂²⋊C₄	—	53	1	no	—
419	C₂²⋊C₄	—	53	4	no	—
420	C₂²⋊C₄	—	53	4	no	—
421	C₂²⋊C₄	C₂²×D₅₃	1	4	yes	—
422	C₂²⋊C₄	C₂²×D₅₃	1	4	yes	—
423	C₄²	—	53	1	no	—
424	C₄²	—	53	1	no	—
425	C₄²	—	53	1	no	—
426	C₄²	—	53	1	no	—
427	C₄²	—	53	1	no	—
428	C₄²	—	53	1	no	—
429	C₄²	—	53	4	no	—
430	C₄²	C₂²×D₅₃	1	1	yes	characteristic
431	C₄²	C₂²×D₅₃	1	1	yes	characteristic
432	C₄²	C₂²×D₅₃	1	1	yes	characteristic
433	C₄²	C₂²×D₅₃	1	1	yes	characteristic
434	C₂³	—	53	1	no	—
435	C₂³	—	53	4	no	—
436	C₂³	—	53	1	no	—
437	C₂³	—	106	8	no	—
438	C₂³	—	212	4	no	—
439	C₂³	—	212	4	no	—
440	C₂³	C₂³×D₅₃	1	4	yes	—
441	C₂³	C₂³×D₅₃	1	1	yes	characteristic
442	Q₈	—	2	4	no	—
443	Q₈	—	106	2	no	—
444	Q₈	—	106	4	no	—
445	D₄	—	2	4	no	—
446	D₄	—	2	4	no	—
447	D₄	—	2	4	no	—
448	D₄	—	4	4	no	—
449	D₄	—	106	2	no	—
450	D₄	—	106	8	no	—
451	D₄	—	106	2	no	—
452	D₄	—	106	2	no	—
453	D₄	—	106	4	no	—
454	D₄	—	106	4	no	—
455	D₄	—	106	4	no	—
456	D₄	—	212	4	no	—
457	D₄	—	212	4	no	—
458	D₄	—	212	4	no	—
459	D₄	—	212	4	no	—
460	D₄	—	212	4	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	—	53	1	no	—
466	C₂×C₄	—	53	4	no	—
467	C₂×C₄	—	53	1	no	—
468	C₂×C₄	—	53	1	no	—
469	C₂×C₄	—	53	1	no	—
470	C₂×C₄	—	53	1	no	—
471	C₂×C₄	—	53	1	no	—
472	C₂×C₄	—	53	4	no	—
473	C₂×C₄	—	106	2	no	—
474	C₂×C₄	—	106	2	no	—
475	C₂×C₄	—	106	2	no	—
476	C₂×C₄	—	106	2	no	—
477	C₂×C₄	—	106	2	no	—
478	C₂×C₄	—	212	4	no	—
479	C₂×C₄	—	212	4	no	—
480	C₂×C₄	—	212	4	no	—
481	C₂×C₄	C₂³×D₅₃	1	4	yes	—
482	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
483	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
484	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
485	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
486	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
487	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
488	C₂²	—	2	1	no	—
489	C₂²	—	2	4	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	4	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	2	4	no	—
494	C₂²	—	53	2	no	—
495	C₂²	—	106	1	no	—
496	C₂²	—	106	1	no	—
497	C₂²	—	106	1	no	—
498	C₂²	—	106	4	no	—
499	C₂²	—	106	1	no	—
500	C₂²	—	106	4	no	—
501	C₂²	—	106	1	no	—
502	C₂²	—	106	4	no	—
503	C₂²	—	424	8	no	—
504	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
505	C₄	—	2	1	no	—
506	C₄	—	2	1	no	—
507	C₄	—	2	4	no	—
508	C₄	—	2	1	no	—
509	C₄	—	53	2	no	—
510	C₄	—	106	1	no	—
511	C₄	—	106	1	no	—
512	C₄	—	106	1	no	—
513	C₄	—	106	1	no	—
514	C₄	—	106	1	no	—
515	C₄	—	106	4	no	—
516	C₄	#41×D₅₃	1	2	yes	—
517	C₄	#13133262	1	2	yes	—
518	C₄	#13133263	1	2	yes	—
519	C₂	—	4	4	no	—
520	C₂	—	4	1	no	—
521	C₂	—	106	2	no	—
522	C₂	—	212	4	no	—
523	C₂	—	212	1	no	—
524	C₂	C₂×#41×D₅₃	1	1	yes	characteristic
525	C₂	C₂×#13133262	1	1	yes	characteristic
526	C₂	C₂×#13133263	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#532	C₂
hypercenter	#532	D₅₃
hypocenter	C₅₃	#3508
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #532

Complements

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

N	H ≅ G/N	type
1. #16811356	C₂	semidirect
2. #16811355	C₂	semidirect
3. #16811292	C₂	semidirect
4. #16811291	C₂	semidirect
5. #16811270	C₂	semidirect
6. #16811268	C₂	semidirect
7. #16811266	C₂	semidirect
8. #16811261	C₂	semidirect
9. #16811226	C₂	semidirect
10. #16811224	C₂	semidirect
11. #16811189	C₂	semidirect
12. #16811178	C₂	semidirect
13. #16811174	C₂	semidirect
14. #16811173	C₂	semidirect
15. #16811171	C₂	semidirect
16. #127×D₅₃	C₂	semidirect
17. #16811095	C₂	semidirect
18. C₄×#11719945	C₂	semidirect
19. C₅₃×#532	C₂	semidirect
20. C₂×#11719949	C₂²	semidirect
22. C₂×#11719945	C₂²	semidirect
23. C₂×#11719947	C₂²	semidirect
27. #13133217	C₂²	semidirect
32. #13133213	C₂²	semidirect
33. #13133208	C₂²	semidirect
34. #13133206	C₂²	semidirect
35. #13133205	C₂²	semidirect
36. #13133204	C₂²	semidirect
37. #13133203	C₂²	semidirect
38. #13133201	C₂²	semidirect
39. #13133200	C₂²	semidirect
40. #13133199	C₂²	semidirect
41. #13133199	C₂²	semidirect
44. #13133192	C₂²	semidirect
45. #13133192	C₂²	semidirect
46. #13133191	C₂²	semidirect
47. #13133191	C₂²	semidirect
48. #13133191	C₂²	semidirect
49. #13133190	C₂²	semidirect
50. #13133189	C₂²	semidirect
51. #13133188	C₂²	semidirect
52. #13133188	C₂²	semidirect
53. #13133188	C₂²	semidirect
56. Q₈×Dic₅₃	C₂²	semidirect
57. C₄×Dic₁₀₆	C₂²	semidirect
58. C₄×Dic₁₀₆	C₂²	semidirect
59. #13133182	C₂²	semidirect
62. C₄×D₂₁₂	C₂²	semidirect
63. C₄×D₂₁₂	C₂²	semidirect
64. D₄×Dic₅₃	C₂²	semidirect
65. D₄×Dic₅₃	C₂²	semidirect
66. #13133179	C₂²	semidirect
67. #13133179	C₂²	semidirect
70. C₄×C₂²⋊D₅₃	C₂²	semidirect
71. C₄×C₂²⋊D₅₃	C₂²	semidirect
72. C₄×C₂²⋊D₅₃	C₂²	semidirect
73. #13133177	C₂²	semidirect
74. #13133176	C₂²	semidirect
77. #13133174	C₂²	semidirect
81. C₄²×D₅₃	C₂²	semidirect
82. C₂×#41×C₅₃	C₂²	semidirect
83. C₄⋊Q₈×C₅₃	C₂²	semidirect
85. #124×C₅₃	C₂²	semidirect
86. #121×C₅₃	C₂²	semidirect
87. #121×C₅₃	C₂²	semidirect
88. C₄×D₄×C₅₃	C₂²	semidirect
89. C₄×D₄×C₅₃	C₂²	semidirect
90. C₂×C₄²×C₅₃	C₂²	semidirect
221. C₄×D₅₃	#41	semidirect
279. #532	D₅₃	semidirect
283. C₅₃	#3508	semidirect
288. C₂×#41	C₂×D₅₃	semidirect
293. C₄⋊Q₈	C₂×D₅₃	semidirect
305. #124	C₂×D₅₃	semidirect
322. #121	C₂×D₅₃	semidirect
323. #121	C₂×D₅₃	semidirect
344. C₄×D₄	C₂×D₅₃	semidirect
345. C₄×D₄	C₂×D₅₃	semidirect
354. C₂×C₄²	C₂×D₅₃	semidirect