Subgroups — #20288605

Order 6784.

1040 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811358	C₂	1	1	yes	maximal, characteristic, complemented
2	#16811358	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811356	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811355	C₂	1	1	yes	maximal, characteristic, complemented
5	#16811347	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811345	C₂	1	1	yes	maximal, characteristic, complemented
7	#16811342	C₂	1	1	yes	maximal, characteristic, complemented
8	#16811300	C₂	1	2	yes	maximal, complemented
9	#16811298	C₂	1	2	yes	maximal, complemented
10	#16811298	C₂	1	2	yes	maximal, complemented
11	#16811297	C₂	1	2	yes	maximal, complemented
12	#16811243	C₂	1	2	yes	maximal, complemented
13	#16811239	C₂	1	2	yes	maximal, complemented
14	#16811198	C₂	1	1	yes	maximal, characteristic, complemented
15	#16811191	C₂	1	1	yes	maximal, characteristic
16	#16811177	C₂	1	1	yes	maximal, characteristic, complemented
17	#16811156	C₂	1	2	yes	maximal, complemented
18	#16811151	C₂	1	2	yes	maximal, complemented
19	#124×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
20	#16811099	C₂	1	1	yes	maximal, characteristic, complemented
21	#16811095	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#11719949	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11719949	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₅₃	C₂²	1	1	yes	characteristic
26	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic
27	#13133216	C₂²	1	1	yes	characteristic, complemented
28	#13133215	C₂²	1	1	yes	characteristic, complemented
29	#13133215	C₂²	1	1	yes	characteristic, complemented
30	#13133214	C₂²	1	1	yes	characteristic
31	#13133213	C₂²	1	1	yes	characteristic
32	#13133212	C₂²	1	2	yes	complemented
33	#13133212	C₂²	1	2	yes	complemented
34	#13133212	C₂²	1	2	yes	complemented
35	#13133211	C₂²	1	2	yes	complemented
36	#13133210	C₂²	1	2	yes	complemented
37	#13133210	C₂²	1	2	yes	complemented
38	#13133207	C₂²	1	1	yes	characteristic, complemented
39	#13133207	C₂²	1	1	yes	characteristic, complemented
40	#13133206	C₂²	1	1	yes	characteristic
41	#13133206	C₂²	1	1	yes	characteristic
42	#13133206	C₂²	1	2	yes	complemented
43	#13133206	C₂²	1	1	yes	characteristic, complemented
44	#13133205	C₂²	1	1	yes	characteristic
45	#13133205	C₂²	1	2	yes	complemented
46	#13133205	C₂²	1	1	yes	characteristic, complemented
47	#13133204	C₂²	1	1	yes	characteristic
48	#13133203	C₂²	1	2	yes	—
49	#13133203	C₂²	1	2	yes	—
50	#13133203	C₂²	1	2	yes	complemented
51	#13133203	C₂²	1	2	yes	complemented
52	#13133202	C₂²	1	2	yes	—
53	#13133202	C₂²	1	2	yes	—
54	#13133202	C₂²	1	2	yes	complemented
55	#13133202	C₂²	1	2	yes	complemented
56	#13133202	C₂²	1	2	yes	complemented
57	#13133202	C₂²	1	2	yes	complemented
58	#13133201	C₂²	1	2	yes	complemented
59	#13133200	C₂²	1	2	yes	complemented
60	#13133199	C₂²	1	2	yes	complemented
61	#13133199	C₂²	1	2	yes	complemented
62	#13133197	C₂²	1	1	yes	characteristic
63	#13133197	C₂²	1	2	yes	complemented
64	#13133195	C₂²	1	1	yes	characteristic
65	#13133195	C₂²	1	1	yes	characteristic
66	#13133195	C₂²	1	2	yes	complemented
67	#13133195	C₂²	1	2	yes	complemented
68	#13133195	C₂²	1	2	yes	complemented
69	#13133194	C₂²	1	2	yes	complemented
70	#13133193	C₂²	1	1	yes	characteristic
71	#13133190	C₂²	1	2	yes	—
72	#13133190	C₂²	1	2	yes	—
73	#13133187	C₂²	1	2	yes	—
74	#13133187	C₂²	1	2	yes	—
75	Q₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
76	Q₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
77	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
78	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
79	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
80	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
81	C₄×Dic₁₀₆	C₂²	1	2	yes	complemented
82	#13133182	C₂²	1	1	yes	characteristic, complemented
83	#13133182	C₂²	1	2	yes	complemented
84	C₄×D₂₁₂	C₂²	1	2	yes	—
85	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
86	C₄×D₂₁₂	C₂²	1	2	yes	complemented
87	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
88	D₄×Dic₅₃	C₂²	1	1	yes	characteristic
89	#13133179	C₂²	1	2	yes	—
90	#13133179	C₂²	1	1	yes	characteristic
91	#13133179	C₂²	1	2	yes	complemented
92	#13133179	C₂²	1	1	yes	characteristic, complemented
93	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	—
94	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
95	#13133177	C₂²	1	2	yes	—
96	#13133177	C₂²	1	2	yes	complemented
97	#13133175	C₂²	1	2	yes	—
98	#13133175	C₂²	1	1	yes	characteristic
99	#13133175	C₂²	1	2	yes	complemented
100	#13133175	C₂²	1	2	yes	complemented
101	#13133174	C₂²	1	2	yes	—
102	#13133174	C₂²	1	1	yes	characteristic
103	#13133174	C₂²	1	1	yes	characteristic
104	#13133174	C₂²	1	2	yes	complemented
105	#13133173	C₂²	1	2	yes	complemented
106	C₂×#11719921	C₂²	1	2	yes	—
107	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
108	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
109	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
110	C₄²×D₅₃	C₂²	1	1	yes	characteristic
111	C₄²×D₅₃	C₂²	1	2	yes	complemented
112	C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
113	#126×C₅₃	C₂²	1	2	yes	complemented
114	#126×C₅₃	C₂²	1	2	yes	complemented
115	#124×C₅₃	C₂²	1	1	yes	characteristic
116	#124×C₅₃	C₂²	1	1	yes	characteristic
117	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
118	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
119	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
120	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
122	#117×C₅₃	C₂²	1	2	yes	complemented
123	C₂³×D₅₃	C₂³	1	2	yes	—
124	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
125	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
126	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
132	C₂²×Dic₅₃	C₂³	1	2	yes	—
133	#11719949	—	2	4	no	—
134	Q₈×D₅₃	—	2	4	no	—
135	D₄×D₅₃	—	2	4	no	—
136	C₂×D₂₁₂	C₂³	1	2	yes	—
137	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
138	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
139	C₂×D₂₁₂	C₂³	1	2	yes	—
140	C₂×D₂₁₂	C₂³	1	2	yes	—
141	C₂×C₄×D₅₃	C₂³	1	2	yes	—
142	C₂×C₄×D₅₃	C₂³	1	2	yes	—
143	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₅₃	C₂³	1	2	yes	—
146	C₂×C₄×D₅₃	C₂³	1	2	yes	—
147	C₂×C₄×D₅₃	C₂³	1	2	yes	—
148	C₂×C₄×D₅₃	C₂³	1	2	yes	—
149	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
150	C₂×Dic₁₀₆	C₂³	1	2	yes	—
151	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
152	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
153	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
154	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
155	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
156	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
157	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
158	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
159	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
160	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
161	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
162	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
163	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
164	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
165	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
166	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
167	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
168	C₄²×C₅₃	C₂³	1	2	yes	—
169	C₄²×C₅₃	C₂³	1	2	yes	—
170	C₄²×C₅₃	C₂³	1	1	yes	characteristic
171	C₄²×C₅₃	C₂³	1	1	yes	characteristic
172	C₄²×C₅₃	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
174	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
175	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
176	#11719921	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
183	#11719921	C₂³	1	2	yes	—
184	#11719921	C₂³	1	2	yes	—
185	#11719921	C₂³	1	1	yes	characteristic
186	#11719921	C₂³	1	1	yes	characteristic
187	#11719921	C₂³	1	2	yes	—
188	#11719921	C₂³	1	2	yes	—
189	#11719921	C₂³	1	2	yes	—
190	#11719921	C₂³	1	2	yes	—
191	#11719921	C₂³	1	2	yes	—
192	#11719921	C₂³	1	2	yes	—
193	#11719921	C₂³	1	2	yes	—
194	#11719921	C₂³	1	2	yes	—
195	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
196	C₄⋊Dic₅₃	C₂³	1	2	yes	—
197	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
198	C₄⋊Dic₅₃	C₂³	1	2	yes	—
199	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
200	C₄⋊Dic₅₃	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	1	yes	characteristic
205	#11719919	C₂³	1	1	yes	characteristic
206	#11719919	C₂³	1	2	yes	—
207	#11719919	C₂³	1	1	yes	characteristic
208	#11719919	C₂³	1	2	yes	—
209	#11719919	C₂³	1	1	yes	characteristic
210	#11719919	C₂³	1	2	yes	—
211	#11719919	C₂³	1	1	yes	characteristic
212	#11719919	C₂³	1	1	yes	characteristic
213	#11719919	C₂³	1	1	yes	characteristic
214	#11719919	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	1	yes	characteristic
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	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
223	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
224	C₄×Dic₅₃	C₂³	1	2	yes	—
225	C₂³×C₅₃	C₂⁴	1	2	yes	—
226	C₂²×D₅₃	—	2	4	no	—
227	C₂²×D₅₃	—	4	2	no	—
228	C₂²×D₅₃	—	4	2	no	—
229	C₂²×D₅₃	C₂⁴	1	2	yes	—
230	C₂²×D₅₃	C₂⁴	1	2	yes	—
231	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
232	Q₈×C₅₃	—	2	2	no	—
233	Q₈×C₅₃	—	2	2	no	—
234	Q₈×C₅₃	—	4	1	no	—
235	D₄×C₅₃	—	2	2	no	—
236	C₂×C₄×C₅₃	—	4	2	no	—
237	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
238	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
239	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
243	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
244	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
247	C₂²⋊D₅₃	—	2	4	no	—
248	C₂²⋊D₅₃	—	4	2	no	—
249	C₂²⋊D₅₃	—	4	2	no	—
250	C₂×Dic₅₃	—	4	2	no	—
251	C₂×Dic₅₃	C₂⁴	1	2	yes	—
252	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₅₃	C₂⁴	1	2	yes	—
259	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
260	D₂₁₂	—	2	4	no	—
261	D₂₁₂	—	2	2	no	—
262	D₂₁₂	—	2	2	no	—
263	D₂₁₂	—	4	2	no	—
264	D₂₁₂	—	4	2	no	—
265	C₄×D₅₃	—	2	4	no	—
266	C₄×D₅₃	—	2	4	no	—
267	C₄×D₅₃	—	4	1	no	—
268	C₄×D₅₃	—	4	2	no	—
269	C₄×D₅₃	—	4	1	no	—
270	C₄×D₅₃	—	4	2	no	—
271	C₄×D₅₃	—	4	2	no	—
272	C₄×D₅₃	—	4	2	no	—
273	C₄×D₅₃	#41	1	4	yes	—
274	Dic₁₀₆	—	2	2	no	—
275	Dic₁₀₆	—	2	4	no	—
276	Dic₁₀₆	—	4	1	no	—
277	Dic₁₀₆	—	4	1	no	—
278	Dic₁₀₆	—	4	1	no	—
279	C₂²×C₅₃	—	2	2	no	—
280	C₂²×C₅₃	—	2	2	no	—
281	C₂²×C₅₃	—	2	2	no	—
282	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
283	C₂×D₅₃	—	2	1	no	—
284	C₂×D₅₃	—	2	1	no	—
285	C₂×D₅₃	—	2	2	no	—
286	C₂×D₅₃	—	2	2	no	—
287	C₂×D₅₃	—	2	2	no	—
288	C₂×D₅₃	—	2	2	no	—
289	C₂×D₅₃	—	2	2	no	—
290	C₂×D₅₃	—	2	2	no	—
291	C₂×D₅₃	—	8	4	no	—
292	C₂×D₅₃	C₂×#41	1	2	yes	—
293	C₄×C₅₃	—	2	2	no	—
294	C₄×C₅₃	—	2	2	no	—
295	C₄×C₅₃	—	2	1	no	—
296	C₄×C₅₃	—	2	1	no	—
297	C₄×C₅₃	—	2	1	no	—
298	C₄×C₅₃	—	2	1	no	—
299	C₄×C₅₃	—	2	2	no	—
300	C₄×C₅₃	—	2	1	no	—
301	C₄×C₅₃	—	2	1	no	—
302	C₄×C₅₃	C₂×#41	1	2	yes	—
303	Dic₅₃	—	2	2	no	—
304	Dic₅₃	—	2	1	no	—
305	Dic₅₃	—	2	1	no	—
306	Dic₅₃	—	2	1	no	—
307	Dic₅₃	—	2	1	no	—
308	Dic₅₃	—	2	1	no	—
309	Dic₅₃	—	2	1	no	—
310	Dic₅₃	—	2	2	no	—
311	Dic₅₃	C₂×#41	1	2	yes	—
312	#3510	—	53	1	no	maximal, Sylow
313	C₂×C₅₃	—	4	2	no	—
314	C₂×C₅₃	C₂²×#41	1	1	yes	characteristic
315	C₂×C₅₃	#585	1	1	yes	characteristic
316	C₂×C₅₃	#585	1	1	yes	characteristic
317	D₅₃	—	2	2	no	—
318	D₅₃	—	4	2	no	—
319	D₅₃	—	4	2	no	—
320	#559	—	53	1	no	—
321	#559	—	53	1	no	—
322	#559	—	53	1	no	—
323	#559	—	53	1	no	—
324	#556	—	53	1	no	—
325	#556	—	53	1	no	—
326	#556	—	53	1	no	—
327	#556	D₅₃	1	1	yes	characteristic, complemented
328	#551	—	53	2	no	—
329	#551	—	53	2	no	—
330	#551	—	53	2	no	—
331	#551	—	53	2	no	—
332	#542	—	53	2	no	—
333	#542	—	53	2	no	—
334	#536	—	53	1	no	—
335	#535	—	53	1	no	—
336	#533	—	53	1	no	—
337	#529	—	53	2	no	—
338	#529	—	53	2	no	—
339	C₂×#124	—	53	1	no	—
340	#519	—	53	1	no	—
341	#518	—	53	1	no	—
342	C₄×#41	—	53	1	no	—
343	C₅₃	#3510	1	1	yes	characteristic, complemented, Sylow
344	C₂×#41	—	53	1	no	—
345	C₂²×Q₈	—	53	1	no	—
346	C₂²×D₄	—	53	1	no	—
347	C₄⋊Q₈	—	53	1	no	—
348	C₄⋊Q₈	—	53	1	no	—
349	C₄⋊Q₈	—	53	1	no	—
350	C₄⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
351	#127	—	53	1	no	—
352	#127	—	53	1	no	—
353	#126	—	53	2	no	—
354	#126	—	53	2	no	—
355	#126	—	53	2	no	—
356	#126	—	53	2	no	—
357	#126	—	53	2	no	—
358	#126	—	53	2	no	—
359	#126	C₂×D₅₃	1	2	yes	complemented
360	#126	C₂×D₅₃	1	2	yes	complemented
361	#125	—	53	1	no	—
362	#125	—	53	1	no	—
363	#124	—	53	1	no	—
364	#124	—	53	1	no	—
365	#124	—	53	1	no	—
366	#124	—	53	2	no	—
367	#124	—	53	1	no	—
368	#124	—	53	2	no	—
369	#124	—	53	2	no	—
370	#124	—	53	2	no	—
371	#124	—	53	2	no	—
372	#124	—	53	1	no	—
373	#124	—	53	1	no	—
374	#124	—	53	2	no	—
375	#124	C₂×D₅₃	1	1	yes	characteristic
376	#124	C₂×D₅₃	1	1	yes	characteristic
377	#123	—	53	2	no	—
378	#123	—	53	2	no	—
379	#123	—	53	2	no	—
380	#123	—	53	2	no	—
381	#123	—	53	2	no	—
382	#123	—	53	2	no	—
383	#123	—	53	2	no	—
384	#123	—	53	2	no	—
385	#123	—	53	2	no	—
386	#123	—	53	2	no	—
387	C₂²⋊Q₈	—	53	1	no	—
388	C₂²⋊Q₈	—	53	2	no	—
389	C₂²⋊Q₈	—	53	2	no	—
390	C₂²⋊Q₈	—	53	1	no	—
391	C₂²⋊Q₈	—	53	1	no	—
392	C₂²⋊Q₈	—	53	1	no	—
393	C₂²⋊Q₈	—	53	2	no	—
394	C₂²⋊Q₈	—	53	2	no	—
395	C₂²⋊Q₈	—	53	2	no	—
396	C₂²⋊Q₈	C₂×D₅₃	1	2	yes	complemented
397	#121	—	53	2	no	—
398	#121	—	53	2	no	—
399	#120	—	53	2	no	—
400	#120	—	53	2	no	—
401	C₄×Q₈	—	53	1	no	—
402	C₄×Q₈	—	53	1	no	—
403	C₄×Q₈	—	53	2	no	—
404	C₄×Q₈	—	53	1	no	—
405	C₄×Q₈	—	53	2	no	—
406	C₄×Q₈	—	53	1	no	—
407	C₄×Q₈	—	53	1	no	—
408	C₄×Q₈	—	53	1	no	—
409	C₄×Q₈	—	53	1	no	—
410	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
411	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
412	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
413	C₄×D₄	—	53	1	no	—
414	C₄×D₄	—	53	2	no	—
415	C₄×D₄	—	53	2	no	—
416	C₄×D₄	—	53	2	no	—
417	C₄×D₄	—	53	1	no	—
418	C₄×D₄	—	53	1	no	—
419	C₄×D₄	—	53	2	no	—
420	C₄×D₄	—	53	2	no	—
421	C₄×D₄	—	53	2	no	—
422	C₄×D₄	—	53	2	no	—
423	C₄×D₄	—	53	1	no	—
424	C₄×D₄	—	53	1	no	—
425	C₄×D₄	—	53	2	no	—
426	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
427	#117	—	53	1	no	—
428	#117	—	53	2	no	—
429	#117	—	53	2	no	—
430	#117	—	53	2	no	—
431	#117	—	53	2	no	—
432	#117	—	53	1	no	—
433	#117	—	53	1	no	—
434	#117	—	53	2	no	—
435	#117	—	53	2	no	—
436	#117	C₂×D₅₃	1	2	yes	complemented
437	C₂×C₂²⋊C₄	—	53	2	no	—
438	C₂×C₂²⋊C₄	—	53	2	no	—
439	C₂×C₂²⋊C₄	—	53	2	no	—
440	C₂×C₂²⋊C₄	—	53	2	no	—
441	C₂×C₄²	—	53	1	no	—
442	C₂×C₄²	—	53	2	no	—
443	C₂⁴	—	53	2	no	—
444	#41	—	106	4	no	—
445	C₂×Q₈	—	53	2	no	—
446	C₂×Q₈	—	53	1	no	—
447	C₂×Q₈	—	53	1	no	—
448	C₂×Q₈	—	53	1	no	—
449	C₂×Q₈	—	53	1	no	—
450	C₂×Q₈	—	106	4	no	—
451	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
452	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
453	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
454	C₂×D₄	—	53	2	no	—
455	C₂×D₄	—	53	2	no	—
456	C₂×D₄	—	53	2	no	—
457	C₂×D₄	—	53	2	no	—
458	C₂×D₄	—	53	1	no	—
459	C₂×D₄	—	53	1	no	—
460	C₂×D₄	—	53	2	no	—
461	C₂×D₄	—	53	2	no	—
462	C₂×D₄	—	106	4	no	—
463	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
464	C₂²×C₄	—	53	1	no	—
465	C₂²×C₄	—	53	2	no	—
466	C₂²×C₄	—	53	2	no	—
467	C₂²×C₄	—	53	2	no	—
468	C₂²×C₄	—	53	1	no	—
469	C₂²×C₄	—	53	1	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	C₂²×D₅₃	1	2	yes	—
475	C₄⋊C₄	—	53	1	no	—
476	C₄⋊C₄	—	53	1	no	—
477	C₄⋊C₄	—	53	1	no	—
478	C₄⋊C₄	—	53	1	no	—
479	C₄⋊C₄	—	53	1	no	—
480	C₄⋊C₄	—	53	1	no	—
481	C₄⋊C₄	—	53	2	no	—
482	C₄⋊C₄	—	53	1	no	—
483	C₄⋊C₄	—	53	1	no	—
484	C₄⋊C₄	—	53	2	no	—
485	C₄⋊C₄	—	53	2	no	—
486	C₄⋊C₄	—	53	2	no	—
487	C₄⋊C₄	—	53	2	no	—
488	C₄⋊C₄	—	53	2	no	—
489	C₄⋊C₄	—	53	1	no	—
490	C₄⋊C₄	—	53	1	no	—
491	C₄⋊C₄	—	53	1	no	—
492	C₄⋊C₄	—	53	1	no	—
493	C₄⋊C₄	—	53	1	no	—
494	C₄⋊C₄	—	53	1	no	—
495	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
496	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
497	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
498	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
499	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
500	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
501	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
502	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
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	1	no	—
508	C₂²⋊C₄	—	53	1	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	C₂²⋊C₄	—	53	2	no	—
514	C₂²⋊C₄	—	53	2	no	—
515	C₂²⋊C₄	—	53	1	no	—
516	C₂²⋊C₄	—	53	1	no	—
517	C₂²⋊C₄	—	53	2	no	—
518	C₂²⋊C₄	—	53	2	no	—
519	C₂²⋊C₄	—	53	2	no	—
520	C₂²⋊C₄	—	53	2	no	—
521	C₂²⋊C₄	—	53	2	no	—
522	C₂²⋊C₄	—	53	2	no	—
523	C₂²⋊C₄	—	53	2	no	—
524	C₂²⋊C₄	—	53	2	no	—
525	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
526	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
527	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
528	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
529	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
530	C₄²	—	53	1	no	—
531	C₄²	—	53	2	no	—
532	C₄²	—	53	2	no	—
533	C₄²	—	53	1	no	—
534	C₄²	—	53	1	no	—
535	C₄²	—	53	2	no	—
536	C₄²	—	53	2	no	—
537	C₄²	—	53	2	no	—
538	C₄²	—	53	1	no	—
539	C₄²	—	53	1	no	—
540	C₄²	C₂²×D₅₃	1	2	yes	—
541	C₄²	C₂²×D₅₃	1	1	yes	characteristic
542	C₄²	C₂²×D₅₃	1	2	yes	—
543	C₄²	C₂²×D₅₃	1	1	yes	characteristic
544	C₄²	C₂²×D₅₃	1	1	yes	characteristic
545	C₂³	—	53	1	no	—
546	C₂³	—	53	2	no	—
547	C₂³	—	53	2	no	—
548	C₂³	—	106	4	no	—
549	C₂³	—	212	2	no	—
550	C₂³	—	212	2	no	—
551	C₂³	C₂³×D₅₃	1	2	yes	—
552	Q₈	—	2	2	no	—
553	Q₈	—	2	2	no	—
554	Q₈	—	4	1	no	—
555	Q₈	—	106	4	no	—
556	Q₈	—	106	2	no	—
557	Q₈	—	212	1	no	—
558	Q₈	—	212	1	no	—
559	Q₈	—	212	1	no	—
560	D₄	—	2	2	no	—
561	D₄	—	106	4	no	—
562	D₄	—	106	4	no	—
563	D₄	—	106	2	no	—
564	D₄	—	106	2	no	—
565	D₄	—	212	2	no	—
566	D₄	—	212	2	no	—
567	D₄	—	212	2	no	—
568	D₄	—	212	2	no	—
569	C₂×C₄	—	4	2	no	—
570	C₂×C₄	—	53	1	no	—
571	C₂×C₄	—	53	4	no	—
572	C₂×C₄	—	53	1	no	—
573	C₂×C₄	—	53	2	no	—
574	C₂×C₄	—	53	1	no	—
575	C₂×C₄	—	53	1	no	—
576	C₂×C₄	—	53	2	no	—
577	C₂×C₄	—	53	1	no	—
578	C₂×C₄	—	53	1	no	—
579	C₂×C₄	—	53	1	no	—
580	C₂×C₄	—	106	4	no	—
581	C₂×C₄	—	106	4	no	—
582	C₂×C₄	—	212	2	no	—
583	C₂×C₄	—	212	2	no	—
584	C₂×C₄	—	212	1	no	—
585	C₂×C₄	—	212	2	no	—
586	C₂×C₄	—	212	1	no	—
587	C₂×C₄	—	212	2	no	—
588	C₂×C₄	—	212	2	no	—
589	C₂×C₄	C₂³×D₅₃	1	2	yes	—
590	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
591	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
592	C₂×C₄	C₂³×D₅₃	1	2	yes	—
593	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
594	C₂×C₄	C₂³×D₅₃	1	2	yes	—
595	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
596	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
597	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
598	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
599	C₂²	—	2	2	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	53	2	no	—
603	C₂²	—	106	1	no	—
604	C₂²	—	106	1	no	—
605	C₂²	—	106	2	no	—
606	C₂²	—	106	2	no	—
607	C₂²	—	106	2	no	—
608	C₂²	—	106	2	no	—
609	C₂²	—	106	2	no	—
610	C₂²	—	106	2	no	—
611	C₂²	—	424	4	no	—
612	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
613	C₄	—	2	2	no	—
614	C₄	—	2	2	no	—
615	C₄	—	2	1	no	—
616	C₄	—	2	2	no	—
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	1	no	—
622	C₄	—	53	2	no	—
623	C₄	—	106	2	no	—
624	C₄	—	106	1	no	—
625	C₄	—	106	1	no	—
626	C₄	—	106	1	no	—
627	C₄	—	106	2	no	—
628	C₄	—	106	1	no	—
629	C₄	—	106	1	no	—
630	C₄	—	106	1	no	—
631	C₄	#41×D₅₃	1	2	yes	—
632	C₂	—	4	2	no	—
633	C₂	—	106	2	no	—
634	C₂	—	212	2	no	—
635	C₂	—	212	2	no	—
636	C₂	C₂×#41×D₅₃	1	1	yes	characteristic
637	C₂	#16811459	1	1	yes	characteristic
638	C₂	#16811460	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#556	C₂
hypercenter	#556	D₅₃
hypocenter	C₅₃	#3510
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. #16811358	C₂	semidirect
2. #16811358	C₂	semidirect
3. #16811356	C₂	semidirect
4. #16811355	C₂	semidirect
5. #16811347	C₂	semidirect
6. #16811345	C₂	semidirect
7. #16811342	C₂	semidirect
8. #16811300	C₂	semidirect
9. #16811298	C₂	semidirect
10. #16811298	C₂	semidirect
11. #16811297	C₂	semidirect
12. #16811243	C₂	semidirect
13. #16811239	C₂	semidirect
14. #16811198	C₂	semidirect
16. #16811177	C₂	semidirect
17. #16811156	C₂	semidirect
18. #16811151	C₂	semidirect
19. #124×D₅₃	C₂	semidirect
20. #16811099	C₂	semidirect
21. #16811095	C₂	semidirect
22. C₄×#11719949	C₂	semidirect
23. C₅₃×#556	C₂	semidirect
27. #13133216	C₂²	semidirect
28. #13133215	C₂²	semidirect
29. #13133215	C₂²	semidirect
32. #13133212	C₂²	semidirect
33. #13133212	C₂²	semidirect
34. #13133212	C₂²	semidirect
35. #13133211	C₂²	semidirect
36. #13133210	C₂²	semidirect
37. #13133210	C₂²	semidirect
38. #13133207	C₂²	semidirect
39. #13133207	C₂²	semidirect
42. #13133206	C₂²	semidirect
43. #13133206	C₂²	semidirect
45. #13133205	C₂²	semidirect
46. #13133205	C₂²	semidirect
50. #13133203	C₂²	semidirect
51. #13133203	C₂²	semidirect
54. #13133202	C₂²	semidirect
55. #13133202	C₂²	semidirect
56. #13133202	C₂²	semidirect
57. #13133202	C₂²	semidirect
58. #13133201	C₂²	semidirect
59. #13133200	C₂²	semidirect
60. #13133199	C₂²	semidirect
61. #13133199	C₂²	semidirect
63. #13133197	C₂²	semidirect
66. #13133195	C₂²	semidirect
67. #13133195	C₂²	semidirect
68. #13133195	C₂²	semidirect
69. #13133194	C₂²	semidirect
75. Q₈×Dic₅₃	C₂²	semidirect
76. Q₈×Dic₅₃	C₂²	semidirect
77. C₄×Dic₁₀₆	C₂²	semidirect
78. C₄×Dic₁₀₆	C₂²	semidirect
79. C₄×Dic₁₀₆	C₂²	semidirect
80. C₄×Dic₁₀₆	C₂²	semidirect
81. C₄×Dic₁₀₆	C₂²	semidirect
82. #13133182	C₂²	semidirect
83. #13133182	C₂²	semidirect
86. C₄×D₂₁₂	C₂²	semidirect
87. C₄×D₂₁₂	C₂²	semidirect
91. #13133179	C₂²	semidirect
92. #13133179	C₂²	semidirect
94. C₄×C₂²⋊D₅₃	C₂²	semidirect
96. #13133177	C₂²	semidirect
99. #13133175	C₂²	semidirect
100. #13133175	C₂²	semidirect
104. #13133174	C₂²	semidirect
105. #13133173	C₂²	semidirect
111. C₄²×D₅₃	C₂²	semidirect
112. C₄⋊Q₈×C₅₃	C₂²	semidirect
113. #126×C₅₃	C₂²	semidirect
114. #126×C₅₃	C₂²	semidirect
117. C₂²⋊Q₈×C₅₃	C₂²	semidirect
118. C₄×Q₈×C₅₃	C₂²	semidirect
119. C₄×Q₈×C₅₃	C₂²	semidirect
120. C₄×Q₈×C₅₃	C₂²	semidirect
122. #117×C₅₃	C₂²	semidirect
327. #556	D₅₃	semidirect
343. C₅₃	#3510	semidirect
350. C₄⋊Q₈	C₂×D₅₃	semidirect
359. #126	C₂×D₅₃	semidirect
360. #126	C₂×D₅₃	semidirect
396. C₂²⋊Q₈	C₂×D₅₃	semidirect
410. C₄×Q₈	C₂×D₅₃	semidirect
411. C₄×Q₈	C₂×D₅₃	semidirect
412. C₄×Q₈	C₂×D₅₃	semidirect
436. #117	C₂×D₅₃	semidirect