Subgroups — #20289222

Order 6784.

930 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811377	C₂	1	2	yes	maximal, complemented
2	#16811372	C₂	1	2	yes	maximal, complemented
3	#16811358	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811358	C₂	1	1	yes	maximal, characteristic, complemented
5	#16811350	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811345	C₂	1	1	yes	maximal, characteristic, complemented
7	#16811345	C₂	1	1	yes	maximal, characteristic, complemented
8	#16811334	C₂	1	1	yes	maximal, characteristic, complemented
9	#16811329	C₂	1	1	yes	maximal, characteristic, complemented
10	#16811314	C₂	1	2	yes	maximal, complemented
11	#16811305	C₂	1	2	yes	maximal, complemented
12	#16811247	C₂	1	1	yes	maximal, characteristic, complemented
13	#16811247	C₂	1	2	yes	maximal, complemented
14	#16811245	C₂	1	2	yes	maximal, complemented
15	#16811245	C₂	1	1	yes	maximal, characteristic, complemented
16	#16811231	C₂	1	1	yes	maximal, characteristic, complemented
17	#16811229	C₂	1	1	yes	maximal, characteristic
18	#16811221	C₂	1	2	yes	maximal, complemented
19	#16811221	C₂	1	2	yes	maximal, complemented
20	#16811177	C₂	1	1	yes	maximal, characteristic, complemented
21	#16811160	C₂	1	1	yes	maximal, characteristic, complemented
22	#16811158	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
24	#13133216	C₂²	1	1	yes	characteristic
25	#13133216	C₂²	1	2	yes	—
26	#13133216	C₂²	1	1	yes	characteristic
27	#13133215	C₂²	1	1	yes	characteristic
28	#13133215	C₂²	1	1	yes	characteristic
29	#13133214	C₂²	1	1	yes	characteristic
30	#13133212	C₂²	1	2	yes	—
31	#13133212	C₂²	1	2	yes	—
32	#13133212	C₂²	1	2	yes	—
33	#13133212	C₂²	1	2	yes	—
34	#13133212	C₂²	1	2	yes	—
35	#13133212	C₂²	1	2	yes	—
36	#13133211	C₂²	1	2	yes	—
37	#13133211	C₂²	1	2	yes	—
38	#13133211	C₂²	1	2	yes	—
39	#13133211	C₂²	1	2	yes	—
40	#13133209	C₂²	1	2	yes	—
41	#13133208	C₂²	1	1	yes	characteristic
42	#13133208	C₂²	1	1	yes	characteristic
43	#13133207	C₂²	1	1	yes	characteristic
44	#13133207	C₂²	1	2	yes	—
45	#13133207	C₂²	1	1	yes	characteristic
46	#13133207	C₂²	1	2	yes	—
47	#13133207	C₂²	1	2	yes	—
48	#13133206	C₂²	1	1	yes	characteristic
49	#13133206	C₂²	1	1	yes	characteristic
50	#13133206	C₂²	1	2	yes	—
51	#13133206	C₂²	1	2	yes	—
52	#13133205	C₂²	1	1	yes	characteristic
53	#13133205	C₂²	1	1	yes	characteristic
54	#13133205	C₂²	1	2	yes	—
55	#13133205	C₂²	1	2	yes	—
56	#13133202	C₂²	1	2	yes	—
57	#13133202	C₂²	1	2	yes	—
58	#13133202	C₂²	1	2	yes	—
59	#13133202	C₂²	1	2	yes	—
60	#13133202	C₂²	1	2	yes	—
61	#13133202	C₂²	1	2	yes	—
62	#13133202	C₂²	1	2	yes	—
63	#13133202	C₂²	1	2	yes	—
64	#13133202	C₂²	1	2	yes	—
65	#13133202	C₂²	1	2	yes	—
66	#13133197	C₂²	1	2	yes	—
67	#13133197	C₂²	1	2	yes	—
68	#13133197	C₂²	1	1	yes	characteristic
69	#13133197	C₂²	1	1	yes	characteristic
70	#13133195	C₂²	1	2	yes	—
71	#13133195	C₂²	1	2	yes	—
72	#13133195	C₂²	1	2	yes	—
73	#13133195	C₂²	1	2	yes	—
74	#13133195	C₂²	1	2	yes	—
75	#13133195	C₂²	1	1	yes	characteristic
76	#13133195	C₂²	1	1	yes	characteristic
77	#13133193	C₂²	1	2	yes	—
78	#13133193	C₂²	1	2	yes	—
79	#13133193	C₂²	1	2	yes	—
80	#13133193	C₂²	1	1	yes	characteristic
81	#13133193	C₂²	1	1	yes	characteristic
82	#13133192	C₂²	1	1	yes	characteristic
83	#13133192	C₂²	1	1	yes	characteristic
84	#13133192	C₂²	1	2	yes	—
85	#13133192	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	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
90	#13133182	C₂²	1	2	yes	—
91	#13133182	C₂²	1	1	yes	characteristic
92	#13133182	C₂²	1	1	yes	characteristic
93	C₄×D₂₁₂	C₂²	1	2	yes	—
94	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
95	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
96	C₄×D₂₁₂	C₂²	1	2	yes	—
97	#13133179	C₂²	1	2	yes	—
98	#13133179	C₂²	1	1	yes	characteristic
99	#13133179	C₂²	1	1	yes	characteristic
100	#13133179	C₂²	1	1	yes	characteristic
101	#13133179	C₂²	1	1	yes	characteristic
102	#13133179	C₂²	1	2	yes	—
103	#13133175	C₂²	1	2	yes	—
104	#13133174	C₂²	1	2	yes	—
105	#13133174	C₂²	1	2	yes	—
106	#13133174	C₂²	1	2	yes	—
107	#13133174	C₂²	1	1	yes	characteristic
108	#13133174	C₂²	1	1	yes	characteristic
109	C₄⋊C₄×D₅₃	C₂²	1	2	yes	—
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	2	yes	—
114	#125×C₅₃	C₂²	1	2	yes	—
115	#125×C₅₃	C₂²	1	1	yes	characteristic
116	#125×C₅₃	C₂²	1	1	yes	characteristic
117	#125×C₅₃	C₂²	1	2	yes	—
118	C₄×Q₈×C₅₃	C₂²	1	2	yes	—
119	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
120	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
121	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
122	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
123	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₅₃	C₂³	1	2	yes	—
125	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
126	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
127	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
128	C₂×D₂₁₂	C₂³	1	2	yes	—
129	C₂×D₂₁₂	C₂³	1	2	yes	—
130	C₂×D₂₁₂	C₂³	1	2	yes	—
131	C₂×D₂₁₂	C₂³	1	2	yes	—
132	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
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×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×Dic₁₀₆	C₂³	1	1	yes	characteristic
142	C₂×Dic₁₀₆	C₂³	1	2	yes	—
143	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
144	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
145	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
150	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
151	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
152	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
153	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
154	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
155	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
156	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
157	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
158	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
159	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
160	C₄²×C₅₃	C₂³	1	1	yes	characteristic
161	C₄²×C₅₃	C₂³	1	2	yes	—
162	C₄²×C₅₃	C₂³	1	1	yes	characteristic
163	C₄²×C₅₃	C₂³	1	2	yes	—
164	C₄²×C₅₃	C₂³	1	1	yes	characteristic
165	C₄²×C₅₃	C₂³	1	2	yes	—
166	#11719921	C₂³	1	2	yes	—
167	#11719921	C₂³	1	2	yes	—
168	#11719921	C₂³	1	1	yes	characteristic
169	#11719921	C₂³	1	1	yes	characteristic
170	#11719921	C₂³	1	2	yes	—
171	#11719921	C₂³	1	1	yes	characteristic
172	#11719921	C₂³	1	2	yes	—
173	#11719921	C₂³	1	1	yes	characteristic
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	#11719921	C₂³	1	2	yes	—
181	#11719921	C₂³	1	2	yes	—
182	#11719921	C₂³	1	2	yes	—
183	#11719921	C₂³	1	2	yes	—
184	#11719921	C₂³	1	2	yes	—
185	#11719921	C₂³	1	2	yes	—
186	#11719921	C₂³	1	2	yes	—
187	#11719921	C₂³	1	2	yes	—
188	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
189	C₄⋊Dic₅₃	C₂³	1	2	yes	—
190	C₄⋊Dic₅₃	C₂³	1	2	yes	—
191	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
192	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
193	C₄⋊Dic₅₃	C₂³	1	2	yes	—
194	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
195	#11719919	C₂³	1	1	yes	characteristic
196	#11719919	C₂³	1	2	yes	—
197	#11719919	C₂³	1	2	yes	—
198	#11719919	C₂³	1	2	yes	—
199	#11719919	C₂³	1	1	yes	characteristic
200	#11719919	C₂³	1	1	yes	characteristic
201	#11719919	C₂³	1	1	yes	characteristic
202	#11719919	C₂³	1	2	yes	—
203	#11719919	C₂³	1	1	yes	characteristic
204	#11719919	C₂³	1	2	yes	—
205	#11719919	C₂³	1	2	yes	—
206	#11719919	C₂³	1	1	yes	characteristic
207	#11719919	C₂³	1	1	yes	characteristic
208	#11719919	C₂³	1	1	yes	characteristic
209	#11719919	C₂³	1	2	yes	—
210	#11719919	C₂³	1	2	yes	—
211	#11719919	C₂³	1	1	yes	characteristic
212	#11719919	C₂³	1	1	yes	characteristic
213	#11719919	C₂³	1	2	yes	—
214	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
215	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
216	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
217	C₄×Dic₅₃	C₂³	1	2	yes	—
218	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
219	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
220	C₄×Dic₅₃	C₂³	1	2	yes	—
221	C₄×Dic₅₃	C₂³	1	2	yes	—
222	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
223	C₂²×D₅₃	C₂⁴	1	2	yes	—
224	C₂²×D₅₃	C₂⁴	1	2	yes	—
225	Q₈×C₅₃	—	2	2	no	—
226	Q₈×C₅₃	—	4	1	no	—
227	Q₈×C₅₃	—	4	2	no	—
228	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
229	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
230	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
231	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
232	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
233	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
234	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
235	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
236	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
238	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
239	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
240	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
241	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
242	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
243	C₂×Dic₅₃	C₂⁴	1	2	yes	—
244	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
245	C₂×Dic₅₃	C₂⁴	1	2	yes	—
246	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
247	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
248	D₂₁₂	—	2	2	no	—
249	D₂₁₂	—	2	2	no	—
250	D₂₁₂	—	4	2	no	—
251	D₂₁₂	—	4	2	no	—
252	D₂₁₂	—	4	2	no	—
253	D₂₁₂	—	4	2	no	—
254	C₄×D₅₃	—	2	2	no	—
255	C₄×D₅₃	—	4	1	no	—
256	C₄×D₅₃	—	4	2	no	—
257	C₄×D₅₃	—	4	2	no	—
258	C₄×D₅₃	—	4	2	no	—
259	C₄×D₅₃	—	4	2	no	—
260	C₄×D₅₃	—	4	2	no	—
261	C₄×D₅₃	—	4	1	no	—
262	C₄×D₅₃	—	4	2	no	—
263	Dic₁₀₆	—	2	2	no	—
264	Dic₁₀₆	—	4	1	no	—
265	Dic₁₀₆	—	4	2	no	—
266	Dic₁₀₆	—	4	1	no	—
267	Dic₁₀₆	—	4	1	no	—
268	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
269	C₂×D₅₃	—	2	1	no	—
270	C₂×D₅₃	—	2	2	no	—
271	C₂×D₅₃	—	2	2	no	—
272	C₂×D₅₃	—	2	2	no	—
273	C₂×D₅₃	—	2	2	no	—
274	C₂×D₅₃	—	2	1	no	—
275	C₂×D₅₃	—	2	2	no	—
276	C₂×D₅₃	—	2	1	no	—
277	C₂×D₅₃	—	2	2	no	—
278	C₄×C₅₃	—	2	2	no	—
279	C₄×C₅₃	—	2	1	no	—
280	C₄×C₅₃	—	2	2	no	—
281	C₄×C₅₃	—	2	1	no	—
282	C₄×C₅₃	—	2	1	no	—
283	C₄×C₅₃	—	2	1	no	—
284	C₄×C₅₃	—	2	2	no	—
285	C₄×C₅₃	—	2	2	no	—
286	C₄×C₅₃	—	2	1	no	—
287	C₄×C₅₃	—	2	1	no	—
288	C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
289	Dic₅₃	—	2	2	no	—
290	Dic₅₃	—	2	1	no	—
291	Dic₅₃	—	2	1	no	—
292	Dic₅₃	—	2	1	no	—
293	Dic₅₃	—	2	1	no	—
294	Dic₅₃	—	2	1	no	—
295	Dic₅₃	—	2	2	no	—
296	Dic₅₃	—	2	1	no	—
297	Dic₅₃	—	2	1	no	—
298	#3557	—	53	1	no	maximal, Sylow
299	C₂×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
300	C₂×C₅₃	#585	1	1	yes	characteristic
301	C₂×C₅₃	#585	1	1	yes	characteristic
302	D₅₃	—	4	1	no	—
303	D₅₃	—	4	2	no	—
304	D₅₃	—	4	2	no	—
305	#563	—	53	2	no	—
306	#563	—	53	2	no	—
307	#559	—	53	1	no	—
308	#559	—	53	1	no	—
309	#557	—	53	1	no	—
310	#557	D₅₃	1	1	yes	characteristic, complemented
311	#556	—	53	1	no	—
312	#556	—	53	1	no	—
313	#554	—	53	1	no	—
314	#554	—	53	1	no	—
315	#552	—	53	2	no	—
316	#552	—	53	2	no	—
317	#542	—	53	1	no	—
318	#542	—	53	2	no	—
319	#542	—	53	1	no	—
320	#542	—	53	2	no	—
321	#541	—	53	1	no	—
322	#540	—	53	1	no	—
323	#539	—	53	2	no	—
324	#539	—	53	2	no	—
325	#533	—	53	1	no	—
326	#529	—	53	1	no	—
327	#529	—	53	1	no	—
328	C₅₃	#3557	1	1	yes	characteristic, complemented, Sylow
329	C₄⋊Q₈	—	53	1	no	—
330	C₄⋊Q₈	—	53	1	no	—
331	C₄⋊Q₈	—	53	1	no	—
332	C₄⋊Q₈	—	53	1	no	—
333	C₄⋊Q₈	—	53	2	no	—
334	C₄⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
335	C₄⋊Q₈	C₂×D₅₃	1	2	yes	—
336	#127	—	53	1	no	—
337	#126	—	53	2	no	—
338	#126	—	53	2	no	—
339	#126	—	53	2	no	—
340	#126	—	53	2	no	—
341	#126	—	53	2	no	—
342	#126	—	53	2	no	—
343	#126	—	53	2	no	—
344	#126	—	53	2	no	—
345	#126	—	53	2	no	—
346	#126	—	53	2	no	—
347	#125	—	53	1	no	—
348	#125	—	53	1	no	—
349	#125	—	53	1	no	—
350	#125	—	53	2	no	—
351	#125	—	53	2	no	—
352	#125	—	53	2	no	—
353	#125	—	53	1	no	—
354	#125	—	53	2	no	—
355	#125	C₂×D₅₃	1	1	yes	characteristic
356	#125	C₂×D₅₃	1	2	yes	—
357	#125	C₂×D₅₃	1	2	yes	—
358	#125	C₂×D₅₃	1	1	yes	characteristic
359	#124	—	53	1	no	—
360	#124	—	53	2	no	—
361	#124	—	53	1	no	—
362	#124	—	53	2	no	—
363	#124	—	53	1	no	—
364	#124	—	53	2	no	—
365	#124	—	53	1	no	—
366	#124	—	53	2	no	—
367	#123	—	53	2	no	—
368	#123	—	53	2	no	—
369	#123	—	53	2	no	—
370	#123	—	53	2	no	—
371	#123	—	53	2	no	—
372	#123	—	53	2	no	—
373	#123	—	53	2	no	—
374	#123	—	53	2	no	—
375	#123	—	53	2	no	—
376	#123	—	53	2	no	—
377	C₂²⋊Q₈	—	53	1	no	—
378	C₂²⋊Q₈	—	53	1	no	—
379	C₂²⋊Q₈	—	53	2	no	—
380	C₂²⋊Q₈	—	53	2	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	2	no	—
387	C₂²⋊Q₈	—	53	2	no	—
388	C₂²⋊Q₈	—	53	2	no	—
389	C₂²⋊Q₈	—	53	2	no	—
390	C₂²⋊Q₈	—	53	2	no	—
391	C₂²⋊Q₈	—	53	2	no	—
392	C₂²⋊Q₈	—	53	2	no	—
393	#121	—	53	1	no	—
394	#121	—	53	1	no	—
395	#121	—	53	2	no	—
396	#121	—	53	2	no	—
397	C₄×Q₈	—	53	1	no	—
398	C₄×Q₈	—	53	2	no	—
399	C₄×Q₈	—	53	1	no	—
400	C₄×Q₈	—	53	1	no	—
401	C₄×Q₈	—	53	1	no	—
402	C₄×Q₈	—	53	1	no	—
403	C₄×Q₈	—	53	1	no	—
404	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic
405	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic
406	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic
407	C₄×Q₈	C₂×D₅₃	1	2	yes	—
408	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic
409	C₄×D₄	—	53	2	no	—
410	C₄×D₄	—	53	1	no	—
411	C₄×D₄	—	53	2	no	—
412	C₄×D₄	—	53	1	no	—
413	C₄×D₄	—	53	1	no	—
414	C₄×D₄	—	53	1	no	—
415	C₄×D₄	—	53	2	no	—
416	C₄×D₄	—	53	1	no	—
417	C₄×D₄	—	53	2	no	—
418	C₄×D₄	—	53	1	no	—
419	#117	—	53	2	no	—
420	#117	—	53	2	no	—
421	#117	—	53	1	no	—
422	#117	—	53	1	no	—
423	#117	—	53	2	no	—
424	#117	—	53	2	no	—
425	C₂×C₄⋊C₄	—	53	2	no	—
426	C₂×C₄⋊C₄	—	53	2	no	—
427	C₂×C₄²	—	53	1	no	—
428	C₂×Q₈	—	53	1	no	—
429	C₂×Q₈	—	53	1	no	—
430	C₂×Q₈	—	53	1	no	—
431	C₂×Q₈	—	53	2	no	—
432	C₂×Q₈	—	53	1	no	—
433	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
434	C₂×Q₈	C₂²×D₅₃	1	2	yes	—
435	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
436	C₂×D₄	—	53	1	no	—
437	C₂×D₄	—	53	1	no	—
438	C₂×D₄	—	53	2	no	—
439	C₂×D₄	—	53	2	no	—
440	C₂×D₄	—	53	2	no	—
441	C₂×D₄	—	53	2	no	—
442	C₂²×C₄	—	53	1	no	—
443	C₂²×C₄	—	53	1	no	—
444	C₂²×C₄	—	53	1	no	—
445	C₂²×C₄	—	53	2	no	—
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	C₄⋊C₄	—	53	1	no	—
452	C₄⋊C₄	—	53	1	no	—
453	C₄⋊C₄	—	53	2	no	—
454	C₄⋊C₄	—	53	2	no	—
455	C₄⋊C₄	—	53	2	no	—
456	C₄⋊C₄	—	53	2	no	—
457	C₄⋊C₄	—	53	1	no	—
458	C₄⋊C₄	—	53	1	no	—
459	C₄⋊C₄	—	53	2	no	—
460	C₄⋊C₄	—	53	2	no	—
461	C₄⋊C₄	—	53	1	no	—
462	C₄⋊C₄	—	53	1	no	—
463	C₄⋊C₄	—	53	2	no	—
464	C₄⋊C₄	—	53	2	no	—
465	C₄⋊C₄	—	53	1	no	—
466	C₄⋊C₄	—	53	1	no	—
467	C₄⋊C₄	—	53	1	no	—
468	C₄⋊C₄	—	53	1	no	—
469	C₄⋊C₄	—	53	2	no	—
470	C₄⋊C₄	—	53	1	no	—
471	C₄⋊C₄	—	53	1	no	—
472	C₄⋊C₄	—	53	1	no	—
473	C₄⋊C₄	—	53	2	no	—
474	C₄⋊C₄	—	53	1	no	—
475	C₄⋊C₄	—	53	2	no	—
476	C₄⋊C₄	—	53	2	no	—
477	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
478	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
479	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
480	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
481	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
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	1	yes	characteristic
486	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
487	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
488	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
489	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
490	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
491	C₂²⋊C₄	—	53	2	no	—
492	C₂²⋊C₄	—	53	2	no	—
493	C₂²⋊C₄	—	53	1	no	—
494	C₂²⋊C₄	—	53	1	no	—
495	C₂²⋊C₄	—	53	2	no	—
496	C₂²⋊C₄	—	53	2	no	—
497	C₂²⋊C₄	—	53	1	no	—
498	C₂²⋊C₄	—	53	1	no	—
499	C₂²⋊C₄	—	53	2	no	—
500	C₂²⋊C₄	—	53	2	no	—
501	C₂²⋊C₄	—	53	2	no	—
502	C₂²⋊C₄	—	53	2	no	—
503	C₂²⋊C₄	—	53	2	no	—
504	C₂²⋊C₄	—	53	2	no	—
505	C₂²⋊C₄	—	53	2	no	—
506	C₂²⋊C₄	—	53	2	no	—
507	C₂²⋊C₄	—	53	2	no	—
508	C₂²⋊C₄	—	53	2	no	—
509	C₂²⋊C₄	—	53	2	no	—
510	C₂²⋊C₄	—	53	2	no	—
511	C₂²⋊C₄	—	53	2	no	—
512	C₂²⋊C₄	—	53	2	no	—
513	C₄²	—	53	1	no	—
514	C₄²	—	53	1	no	—
515	C₄²	—	53	1	no	—
516	C₄²	—	53	2	no	—
517	C₄²	—	53	1	no	—
518	C₄²	—	53	1	no	—
519	C₄²	—	53	2	no	—
520	C₄²	—	53	2	no	—
521	C₄²	C₂²×D₅₃	1	1	yes	characteristic
522	C₄²	C₂²×D₅₃	1	2	yes	—
523	C₄²	C₂²×D₅₃	1	1	yes	characteristic
524	C₄²	C₂²×D₅₃	1	1	yes	characteristic
525	C₄²	C₂²×D₅₃	1	2	yes	—
526	C₄²	C₂²×D₅₃	1	2	yes	—
527	C₂³	—	53	1	no	—
528	C₂³	—	53	2	no	—
529	C₂³	—	53	2	no	—
530	Q₈	—	2	2	no	—
531	Q₈	—	4	2	no	—
532	Q₈	—	4	1	no	—
533	Q₈	—	106	2	no	—
534	Q₈	—	212	1	no	—
535	Q₈	—	212	1	no	—
536	Q₈	—	212	2	no	—
537	Q₈	—	212	1	no	—
538	D₄	—	106	2	no	—
539	D₄	—	106	2	no	—
540	D₄	—	212	2	no	—
541	D₄	—	212	2	no	—
542	D₄	—	212	2	no	—
543	D₄	—	212	2	no	—
544	C₂×C₄	—	53	1	no	—
545	C₂×C₄	—	53	2	no	—
546	C₂×C₄	—	53	1	no	—
547	C₂×C₄	—	53	1	no	—
548	C₂×C₄	—	53	1	no	—
549	C₂×C₄	—	53	1	no	—
550	C₂×C₄	—	53	1	no	—
551	C₂×C₄	—	53	1	no	—
552	C₂×C₄	—	53	2	no	—
553	C₂×C₄	—	106	2	no	—
554	C₂×C₄	—	212	2	no	—
555	C₂×C₄	—	212	2	no	—
556	C₂×C₄	—	212	2	no	—
557	C₂×C₄	—	212	1	no	—
558	C₂×C₄	—	212	2	no	—
559	C₂×C₄	—	212	1	no	—
560	C₂×C₄	—	212	2	no	—
561	C₂×C₄	—	212	2	no	—
562	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
563	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
564	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
565	C₂×C₄	C₂³×D₅₃	1	2	yes	—
566	C₂×C₄	C₂³×D₅₃	1	2	yes	—
567	C₂×C₄	C₂³×D₅₃	1	2	yes	—
568	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
569	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
570	C₂×C₄	C₂³×D₅₃	1	2	yes	—
571	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
572	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
573	C₂²	—	106	1	no	—
574	C₂²	—	106	2	no	—
575	C₂²	—	106	2	no	—
576	C₂²	—	106	2	no	—
577	C₂²	—	106	1	no	—
578	C₂²	—	106	2	no	—
579	C₂²	—	106	2	no	—
580	C₂²	—	106	1	no	—
581	C₂²	—	106	2	no	—
582	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
583	C₄	—	2	2	no	—
584	C₄	—	2	2	no	—
585	C₄	—	2	2	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	2	no	—
592	C₄	—	2	1	no	—
593	C₄	—	106	1	no	—
594	C₄	—	106	2	no	—
595	C₄	—	106	1	no	—
596	C₄	—	106	1	no	—
597	C₄	—	106	1	no	—
598	C₄	—	106	1	no	—
599	C₄	—	106	2	no	—
600	C₄	—	106	1	no	—
601	C₄	—	106	1	no	—
602	C₄	#13133265	1	2	yes	—
603	C₂	—	212	1	no	—
604	C₂	—	212	2	no	—
605	C₂	—	212	2	no	—
606	C₂	C₂×#13133265	1	1	yes	characteristic
607	C₂	#16811459	1	1	yes	characteristic
608	C₂	#16811460	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#557	C₂
hypercenter	#557	D₅₃
hypocenter	C₅₃	#3557
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #557

Complements

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

N	H ≅ G/N	type
1. #16811377	C₂	semidirect
2. #16811372	C₂	semidirect
3. #16811358	C₂	semidirect
4. #16811358	C₂	semidirect
5. #16811350	C₂	semidirect
6. #16811345	C₂	semidirect
7. #16811345	C₂	semidirect
8. #16811334	C₂	semidirect
9. #16811329	C₂	semidirect
10. #16811314	C₂	semidirect
11. #16811305	C₂	semidirect
12. #16811247	C₂	semidirect
13. #16811247	C₂	semidirect
14. #16811245	C₂	semidirect
15. #16811245	C₂	semidirect
16. #16811231	C₂	semidirect
18. #16811221	C₂	semidirect
19. #16811221	C₂	semidirect
20. #16811177	C₂	semidirect
21. #16811160	C₂	semidirect
22. #16811158	C₂	semidirect
23. C₅₃×#557	C₂	semidirect
310. #557	D₅₃	semidirect
328. C₅₃	#3557	semidirect