Subgroups — #20289077

Order 6784.

1150 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811361	C₂	1	2	yes	maximal, complemented
2	#16811361	C₂	1	2	yes	maximal, complemented
3	#16811344	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811321	C₂	1	1	yes	maximal, characteristic, complemented
5	#16811320	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811292	C₂	1	1	yes	maximal, characteristic, complemented
7	#16811291	C₂	1	2	yes	maximal, complemented
8	#16811274	C₂	1	1	yes	maximal, characteristic, complemented
9	#16811264	C₂	1	1	yes	maximal, characteristic, complemented
10	#16811262	C₂	1	2	yes	maximal, complemented
11	#16811261	C₂	1	1	yes	maximal, characteristic, complemented
12	#16811257	C₂	1	1	yes	maximal, characteristic, complemented
13	#16811243	C₂	1	2	yes	maximal, complemented
14	#16811213	C₂	1	2	yes	maximal, complemented
15	#16811205	C₂	1	2	yes	maximal, complemented
16	#16811203	C₂	1	1	yes	maximal, characteristic, complemented
17	#16811189	C₂	1	1	yes	maximal, characteristic, complemented
18	#16811189	C₂	1	2	yes	maximal, complemented
19	#16811187	C₂	1	1	yes	maximal, characteristic, complemented
20	#16811169	C₂	1	1	yes	maximal, characteristic, complemented
21	#16811168	C₂	1	1	yes	maximal, characteristic, complemented
22	#16811159	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#537	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11719949	C₂²	1	1	yes	characteristic, complemented
25	C₂×#11719945	C₂²	1	2	yes	complemented
26	C₂×#11719945	C₂²	1	1	yes	characteristic, complemented
27	C₂×#11719947	C₂²	1	2	yes	complemented
28	C₂²×D₂₁₂	C₂²	1	1	yes	characteristic
29	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic
30	C₂×D₄×D₅₃	C₂²	1	2	yes	—
31	#13133216	C₂²	1	1	yes	characteristic, complemented
32	#13133215	C₂²	1	1	yes	characteristic, complemented
33	#13133213	C₂²	1	1	yes	characteristic
34	#13133213	C₂²	1	1	yes	characteristic
35	#13133213	C₂²	1	2	yes	complemented
36	#13133213	C₂²	1	2	yes	complemented
37	#13133213	C₂²	1	2	yes	complemented
38	#13133212	C₂²	1	2	yes	complemented
39	#13133212	C₂²	1	2	yes	complemented
40	#13133212	C₂²	1	2	yes	complemented
41	#13133210	C₂²	1	2	yes	complemented
42	#13133210	C₂²	1	2	yes	complemented
43	#13133208	C₂²	1	1	yes	characteristic, complemented
44	#13133206	C₂²	1	1	yes	characteristic
45	#13133206	C₂²	1	1	yes	characteristic, complemented
46	#13133206	C₂²	1	2	yes	complemented
47	#13133204	C₂²	1	1	yes	characteristic, complemented
48	#13133203	C₂²	1	2	yes	—
49	#13133203	C₂²	1	2	yes	complemented
50	#13133203	C₂²	1	2	yes	complemented
51	#13133202	C₂²	1	2	yes	complemented
52	#13133202	C₂²	1	2	yes	complemented
53	#13133202	C₂²	1	2	yes	complemented
54	#13133201	C₂²	1	2	yes	complemented
55	#13133200	C₂²	1	2	yes	complemented
56	#13133200	C₂²	1	2	yes	complemented
57	#13133198	C₂²	1	2	yes	complemented
58	#13133195	C₂²	1	2	yes	complemented
59	#13133195	C₂²	1	2	yes	complemented
60	#13133193	C₂²	1	1	yes	characteristic, complemented
61	#13133192	C₂²	1	1	yes	characteristic
62	#13133192	C₂²	1	1	yes	characteristic
63	#13133192	C₂²	1	2	yes	complemented
64	#13133192	C₂²	1	2	yes	complemented
65	#13133191	C₂²	1	1	yes	characteristic
66	#13133191	C₂²	1	1	yes	characteristic
67	#13133191	C₂²	1	1	yes	characteristic, complemented
68	#13133191	C₂²	1	2	yes	complemented
69	#13133191	C₂²	1	2	yes	complemented
70	#13133191	C₂²	1	1	yes	characteristic, complemented
71	#13133190	C₂²	1	2	yes	—
72	#13133190	C₂²	1	2	yes	complemented
73	#13133190	C₂²	1	2	yes	complemented
74	#13133189	C₂²	1	1	yes	characteristic
75	#13133189	C₂²	1	1	yes	characteristic, complemented
76	#13133189	C₂²	1	2	yes	complemented
77	#13133189	C₂²	1	2	yes	complemented
78	#13133189	C₂²	1	1	yes	characteristic, complemented
79	#13133189	C₂²	1	1	yes	characteristic, complemented
80	#13133188	C₂²	1	1	yes	characteristic, complemented
81	#13133188	C₂²	1	2	yes	complemented
82	#13133188	C₂²	1	2	yes	complemented
83	#13133187	C₂²	1	2	yes	—
84	#13133187	C₂²	1	2	yes	complemented
85	#13133187	C₂²	1	2	yes	complemented
86	#13133185	C₂²	1	2	yes	—
87	#13133185	C₂²	1	2	yes	complemented
88	#13133185	C₂²	1	2	yes	complemented
89	#13133185	C₂²	1	2	yes	complemented
90	#13133185	C₂²	1	2	yes	complemented
91	Q₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
92	#13133182	C₂²	1	2	yes	complemented
93	D₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
94	#13133179	C₂²	1	1	yes	characteristic
95	#13133179	C₂²	1	1	yes	characteristic, complemented
96	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
97	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
98	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
99	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
100	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
101	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
102	#13133177	C₂²	1	2	yes	complemented
103	#13133177	C₂²	1	2	yes	complemented
104	#13133177	C₂²	1	2	yes	complemented
105	#13133176	C₂²	1	1	yes	characteristic, complemented
106	#13133175	C₂²	1	1	yes	characteristic, complemented
107	#13133175	C₂²	1	2	yes	complemented
108	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
109	C₂×#11719921	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
111	C₂×C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
112	C₂×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
113	C₂×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
114	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
115	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
116	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
117	#121×C₅₃	C₂²	1	1	yes	characteristic
118	#121×C₅₃	C₂²	1	2	yes	complemented
119	#121×C₅₃	C₂²	1	2	yes	complemented
120	#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
121	#121×C₅₃	C₂²	1	2	yes	complemented
122	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₅₃	C₂³	1	2	yes	—
124	C₂³×D₅₃	C₂³	1	2	yes	—
125	#41×C₅₃	—	4	2	no	—
126	#41×C₅₃	—	4	2	no	—
127	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
128	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
129	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
130	C₂×D₄×C₅₃	C₂³	1	2	yes	—
131	C₂×D₄×C₅₃	C₂³	1	2	yes	—
132	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
133	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
134	C₂×D₄×C₅₃	C₂³	1	2	yes	—
135	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
140	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
149	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
150	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
151	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
153	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
154	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
155	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
156	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
157	C₂²×Dic₅₃	C₂³	1	2	yes	—
158	#11719949	—	4	2	no	—
159	#11719947	—	4	4	no	—
160	D₄×D₅₃	—	4	2	no	—
161	D₄×D₅₃	—	4	4	no	—
162	#11719945	—	4	4	no	—
163	#11719945	—	4	2	no	—
164	C₂×D₂₁₂	—	4	2	no	—
165	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
166	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
167	C₂×D₂₁₂	C₂³	1	2	yes	—
168	C₂×D₂₁₂	C₂³	1	2	yes	—
169	C₂×D₂₁₂	C₂³	1	2	yes	—
170	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
171	C₂×D₂₁₂	C₂³	1	2	yes	—
172	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
173	C₂×C₄×D₅₃	C₂³	1	2	yes	—
174	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
175	C₂×C₄×D₅₃	C₂³	1	2	yes	—
176	C₂×C₄×D₅₃	C₂³	1	2	yes	—
177	C₂×C₄×D₅₃	C₂³	1	2	yes	—
178	C₂×Dic₁₀₆	C₂³	1	2	yes	—
179	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
180	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
181	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
182	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
183	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
184	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
185	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
186	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
187	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
188	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
189	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
190	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
191	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
192	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
193	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
194	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
195	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
196	#11719921	C₂³	1	2	yes	—
197	#11719921	C₂³	1	2	yes	—
198	#11719921	C₂³	1	1	yes	characteristic
199	#11719921	C₂³	1	2	yes	—
200	#11719921	C₂³	1	2	yes	—
201	#11719921	C₂³	1	2	yes	—
202	#11719921	C₂³	1	2	yes	—
203	#11719921	C₂³	1	2	yes	—
204	#11719921	C₂³	1	1	yes	characteristic
205	#11719921	C₂³	1	2	yes	—
206	#11719921	C₂³	1	1	yes	characteristic
207	#11719921	C₂³	1	2	yes	—
208	#11719921	C₂³	1	2	yes	—
209	#11719921	C₂³	1	1	yes	characteristic
210	#11719921	C₂³	1	2	yes	—
211	#11719921	C₂³	1	2	yes	—
212	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
213	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
214	C₄⋊Dic₅₃	C₂³	1	2	yes	—
215	C₄⋊Dic₅₃	C₂³	1	2	yes	—
216	#11719919	C₂³	1	2	yes	—
217	#11719919	C₂³	1	2	yes	—
218	#11719919	C₂³	1	2	yes	—
219	#11719919	C₂³	1	1	yes	characteristic
220	#11719919	C₂³	1	1	yes	characteristic
221	#11719919	C₂³	1	1	yes	characteristic
222	#11719919	C₂³	1	1	yes	characteristic
223	#11719919	C₂³	1	2	yes	—
224	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
225	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
226	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
227	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
228	C₄×Dic₅₃	C₂³	1	2	yes	—
229	C₄×Dic₅₃	C₂³	1	2	yes	—
230	C₄×Dic₅₃	C₂³	1	2	yes	—
231	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
232	C₂³×C₅₃	C₂⁴	1	2	yes	—
233	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
234	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
235	C₂²×D₅₃	—	4	2	no	—
236	C₂²×D₅₃	—	4	2	no	—
237	C₂²×D₅₃	—	4	2	no	—
238	C₂²×D₅₃	—	4	2	no	—
239	C₂²×D₅₃	—	4	2	no	—
240	C₂²×D₅₃	—	4	2	no	—
241	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
242	C₂²×D₅₃	C₂⁴	1	2	yes	—
243	C₂²×D₅₃	C₂⁴	1	2	yes	—
244	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
245	Q₈×C₅₃	—	2	2	no	—
246	Q₈×C₅₃	—	4	1	no	—
247	D₄×C₅₃	—	2	2	no	—
248	D₄×C₅₃	—	4	2	no	—
249	D₄×C₅₃	—	4	2	no	—
250	D₄×C₅₃	—	4	1	no	—
251	D₄×C₅₃	—	4	2	no	—
252	D₄×C₅₃	—	4	1	no	—
253	D₄×C₅₃	—	4	1	no	—
254	C₂×C₄×C₅₃	—	2	2	no	—
255	C₂×C₄×C₅₃	—	2	2	no	—
256	C₂×C₄×C₅₃	—	2	2	no	—
257	C₂×C₄×C₅₃	—	4	2	no	—
258	C₂×C₄×C₅₃	—	4	2	no	—
259	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
260	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
261	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
262	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
263	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
264	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
265	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
266	C₂²⋊D₅₃	—	2	2	no	—
267	C₂²⋊D₅₃	—	2	2	no	—
268	C₂²⋊D₅₃	—	2	4	no	—
269	C₂²⋊D₅₃	—	4	2	no	—
270	C₂²⋊D₅₃	—	4	1	no	—
271	C₂²⋊D₅₃	—	4	1	no	—
272	C₂²⋊D₅₃	—	4	2	no	—
273	C₂²⋊D₅₃	—	4	2	no	—
274	C₂²⋊D₅₃	—	4	1	no	—
275	C₂²⋊D₅₃	—	4	2	no	—
276	C₂²⋊D₅₃	—	4	1	no	—
277	C₂²⋊D₅₃	—	4	2	no	—
278	C₂²⋊D₅₃	—	4	2	no	—
279	C₂²⋊D₅₃	—	4	2	no	—
280	C₂×Dic₅₃	—	2	2	no	—
281	C₂×Dic₅₃	—	4	2	no	—
282	C₂×Dic₅₃	—	4	1	no	—
283	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
284	C₂×Dic₅₃	C₂⁴	1	2	yes	—
285	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
286	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
287	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
288	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
289	C₂×Dic₅₃	C₂⁴	1	2	yes	—
290	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
291	D₂₁₂	—	2	2	no	—
292	D₂₁₂	—	2	2	no	—
293	D₂₁₂	—	4	2	no	—
294	D₂₁₂	—	4	2	no	—
295	D₂₁₂	—	4	1	no	—
296	D₂₁₂	—	4	2	no	—
297	D₂₁₂	—	4	2	no	—
298	C₄×D₅₃	—	2	2	no	—
299	C₄×D₅₃	—	2	2	no	—
300	C₄×D₅₃	—	2	4	no	—
301	C₄×D₅₃	—	4	2	no	—
302	C₄×D₅₃	—	4	2	no	—
303	C₄×D₅₃	—	4	2	no	—
304	Dic₁₀₆	—	2	4	no	—
305	Dic₁₀₆	—	4	1	no	—
306	C₂²×C₅₃	—	2	1	no	—
307	C₂²×C₅₃	—	2	2	no	—
308	C₂²×C₅₃	—	2	1	no	—
309	C₂²×C₅₃	—	2	1	no	—
310	C₂²×C₅₃	—	2	1	no	—
311	C₂²×C₅₃	—	2	2	no	—
312	C₂²×C₅₃	—	2	1	no	—
313	C₂²×C₅₃	—	2	1	no	—
314	C₂²×C₅₃	—	2	1	no	—
315	C₂²×C₅₃	—	2	1	no	—
316	C₂²×C₅₃	—	2	2	no	—
317	C₂²×C₅₃	—	2	1	no	—
318	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
319	C₂×D₅₃	—	2	1	no	—
320	C₂×D₅₃	—	2	2	no	—
321	C₂×D₅₃	—	2	1	no	—
322	C₂×D₅₃	—	2	1	no	—
323	C₂×D₅₃	—	2	2	no	—
324	C₂×D₅₃	—	2	2	no	—
325	C₂×D₅₃	—	2	2	no	—
326	C₂×D₅₃	—	2	1	no	—
327	C₂×D₅₃	—	2	1	no	—
328	C₂×D₅₃	—	2	2	no	—
329	C₂×D₅₃	—	2	2	no	—
330	C₂×D₅₃	—	2	1	no	—
331	C₂×D₅₃	—	8	4	no	—
332	C₂×D₅₃	—	8	4	no	—
333	C₄×C₅₃	—	2	2	no	—
334	C₄×C₅₃	—	2	1	no	—
335	C₄×C₅₃	—	2	2	no	—
336	C₄×C₅₃	—	2	2	no	—
337	C₄×C₅₃	—	2	1	no	—
338	C₄×C₅₃	—	2	1	no	—
339	C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
340	Dic₅₃	—	2	2	no	—
341	Dic₅₃	—	2	1	no	—
342	Dic₅₃	—	2	1	no	—
343	Dic₅₃	—	2	1	no	—
344	Dic₅₃	—	2	1	no	—
345	Dic₅₃	—	2	1	no	—
346	Dic₅₃	—	2	2	no	—
347	Dic₅₃	H(5,𝔽₂)	1	2	yes	—
348	#3546	—	53	1	no	maximal, Sylow
349	C₂×C₅₃	—	4	1	no	—
350	C₂×C₅₃	—	4	2	no	—
351	C₂×C₅₃	—	4	1	no	—
352	C₂×C₅₃	—	4	1	no	—
353	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
354	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
355	C₂×C₅₃	#585	1	1	yes	characteristic
356	D₅₃	—	4	1	no	—
357	D₅₃	—	4	2	no	—
358	D₅₃	—	4	2	no	—
359	D₅₃	—	4	1	no	—
360	#560	—	53	2	no	—
361	#560	—	53	2	no	—
362	#556	—	53	1	no	—
363	#553	—	53	1	no	—
364	#553	—	53	1	no	—
365	#550	—	53	1	no	—
366	#550	—	53	2	no	—
367	#547	—	53	1	no	—
368	#546	—	53	1	no	—
369	#546	—	53	1	no	—
370	#546	—	53	2	no	—
371	D₄²	—	53	1	no	—
372	#542	—	53	2	no	—
373	#538	—	53	2	no	—
374	#538	—	53	2	no	—
375	#537	—	53	1	no	—
376	#537	D₅₃	1	1	yes	characteristic, complemented
377	#535	—	53	1	no	—
378	#535	—	53	2	no	—
379	#535	—	53	1	no	—
380	#532	—	53	1	no	—
381	#532	—	53	1	no	—
382	#529	—	53	1	no	—
383	C₅₃	#3546	1	1	yes	characteristic, complemented, Sylow
384	C₂×#41	—	53	1	no	—
385	C₂×#41	—	53	2	no	—
386	C₂×#41	—	53	1	no	—
387	C₂×#41	—	53	2	no	—
388	C₂×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
389	C₂×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
390	C₂²×D₄	—	53	2	no	—
391	C₂²×D₄	—	53	1	no	—
392	C₂²×D₄	—	53	1	no	—
393	C₄⋊Q₈	—	53	1	no	—
394	C₄⋊Q₈	—	53	1	no	—
395	#127	—	53	1	no	—
396	#127	—	53	1	no	—
397	#127	—	53	2	no	—
398	#127	—	53	2	no	—
399	#127	—	53	2	no	—
400	#126	—	53	2	no	—
401	#126	—	53	2	no	—
402	#126	—	53	2	no	—
403	#126	—	53	2	no	—
404	#126	—	53	2	no	—
405	#125	—	53	1	no	—
406	#124	—	53	1	no	—
407	#124	—	53	1	no	—
408	#124	—	53	2	no	—
409	#124	—	53	1	no	—
410	#124	—	53	2	no	—
411	#124	—	53	2	no	—
412	#124	—	53	2	no	—
413	#123	—	53	2	no	—
414	#123	—	53	2	no	—
415	#123	—	53	2	no	—
416	#123	—	53	2	no	—
417	#123	—	53	2	no	—
418	#123	—	53	2	no	—
419	#123	—	53	2	no	—
420	C₂²⋊Q₈	—	53	1	no	—
421	C₂²⋊Q₈	—	53	2	no	—
422	C₂²⋊Q₈	—	53	2	no	—
423	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
424	C₂²⋊Q₈	C₂×D₅₃	1	2	yes	complemented
425	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
426	#121	—	53	1	no	—
427	#121	—	53	1	no	—
428	#121	—	53	1	no	—
429	#121	—	53	2	no	—
430	#121	—	53	1	no	—
431	#121	—	53	1	no	—
432	#121	—	53	2	no	—
433	#121	—	53	2	no	—
434	#121	—	53	2	no	—
435	#121	—	53	1	no	—
436	#121	—	53	1	no	—
437	#121	—	53	1	no	—
438	#121	—	53	1	no	—
439	#121	—	53	2	no	—
440	#121	—	53	2	no	—
441	#121	—	53	2	no	—
442	#121	—	53	1	no	—
443	#121	—	53	1	no	—
444	#121	—	53	2	no	—
445	#121	—	53	2	no	—
446	#121	—	53	2	no	—
447	#121	—	53	2	no	—
448	#121	C₂×D₅₃	1	1	yes	characteristic
449	#121	C₂×D₅₃	1	1	yes	characteristic, complemented
450	#121	C₂×D₅₃	1	2	yes	complemented
451	#121	C₂×D₅₃	1	2	yes	complemented
452	#121	C₂×D₅₃	1	2	yes	complemented
453	#120	—	53	2	no	—
454	#120	—	53	2	no	—
455	#120	—	53	2	no	—
456	#120	—	53	2	no	—
457	#120	—	53	2	no	—
458	#120	—	53	2	no	—
459	#120	—	53	2	no	—
460	#120	—	53	2	no	—
461	C₄×Q₈	—	53	1	no	—
462	C₄×Q₈	—	53	2	no	—
463	C₄×D₄	—	53	1	no	—
464	C₄×D₄	—	53	1	no	—
465	C₄×D₄	—	53	1	no	—
466	C₄×D₄	—	53	1	no	—
467	C₄×D₄	—	53	1	no	—
468	C₄×D₄	—	53	2	no	—
469	C₄×D₄	—	53	2	no	—
470	C₄×D₄	—	53	1	no	—
471	C₄×D₄	—	53	1	no	—
472	C₄×D₄	—	53	2	no	—
473	C₄×D₄	—	53	2	no	—
474	C₄×D₄	—	53	2	no	—
475	#117	—	53	1	no	—
476	#117	—	53	2	no	—
477	#117	—	53	1	no	—
478	C₂×C₄⋊C₄	—	53	1	no	—
479	C₂×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
480	C₂×C₂²⋊C₄	—	53	2	no	—
481	C₂×C₂²⋊C₄	—	53	2	no	—
482	C₂×C₄²	—	53	1	no	—
483	C₂⁴	—	53	2	no	—
484	C₂⁴	—	53	2	no	—
485	#41	—	4	2	no	—
486	#41	—	4	2	no	—
487	#41	—	212	2	no	—
488	#41	—	212	4	no	—
489	#41	—	212	4	no	—
490	#41	—	212	2	no	—
491	C₂×Q₈	—	53	2	no	—
492	C₂×Q₈	—	53	1	no	—
493	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
494	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
495	C₂×D₄	—	53	1	no	—
496	C₂×D₄	—	53	2	no	—
497	C₂×D₄	—	53	1	no	—
498	C₂×D₄	—	53	1	no	—
499	C₂×D₄	—	53	2	no	—
500	C₂×D₄	—	53	1	no	—
501	C₂×D₄	—	53	2	no	—
502	C₂×D₄	—	53	2	no	—
503	C₂×D₄	—	53	2	no	—
504	C₂×D₄	—	53	1	no	—
505	C₂×D₄	—	53	2	no	—
506	C₂×D₄	—	53	2	no	—
507	C₂×D₄	—	53	2	no	—
508	C₂×D₄	—	53	1	no	—
509	C₂×D₄	—	53	1	no	—
510	C₂×D₄	—	53	1	no	—
511	C₂×D₄	—	53	2	no	—
512	C₂×D₄	—	53	1	no	—
513	C₂×D₄	—	53	2	no	—
514	C₂×D₄	—	53	2	no	—
515	C₂×D₄	—	53	2	no	—
516	C₂×D₄	—	212	2	no	—
517	C₂×D₄	—	212	2	no	—
518	C₂×D₄	—	212	4	no	—
519	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
520	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
521	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
522	C₂×D₄	C₂²×D₅₃	1	2	yes	—
523	C₂×D₄	C₂²×D₅₃	1	2	yes	—
524	C₂×D₄	C₂²×D₅₃	1	2	yes	—
525	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
526	C₂²×C₄	—	53	1	no	—
527	C₂²×C₄	—	53	1	no	—
528	C₂²×C₄	—	53	2	no	—
529	C₂²×C₄	—	53	1	no	—
530	C₂²×C₄	—	53	2	no	—
531	C₂²×C₄	—	53	1	no	—
532	C₂²×C₄	—	53	2	no	—
533	C₂²×C₄	—	53	2	no	—
534	C₂²×C₄	—	53	2	no	—
535	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
536	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
537	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
538	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
539	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
540	C₄⋊C₄	—	53	1	no	—
541	C₄⋊C₄	—	53	2	no	—
542	C₄⋊C₄	—	53	1	no	—
543	C₄⋊C₄	—	53	2	no	—
544	C₄⋊C₄	—	53	1	no	—
545	C₄⋊C₄	—	53	2	no	—
546	C₄⋊C₄	—	53	1	no	—
547	C₄⋊C₄	—	53	1	no	—
548	C₄⋊C₄	—	53	2	no	—
549	C₄⋊C₄	—	53	1	no	—
550	C₄⋊C₄	—	53	2	no	—
551	C₄⋊C₄	—	53	2	no	—
552	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
553	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
554	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
555	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
556	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
557	C₂²⋊C₄	—	53	1	no	—
558	C₂²⋊C₄	—	53	2	no	—
559	C₂²⋊C₄	—	53	1	no	—
560	C₂²⋊C₄	—	53	1	no	—
561	C₂²⋊C₄	—	53	2	no	—
562	C₂²⋊C₄	—	53	2	no	—
563	C₂²⋊C₄	—	53	1	no	—
564	C₂²⋊C₄	—	53	2	no	—
565	C₂²⋊C₄	—	53	1	no	—
566	C₂²⋊C₄	—	53	2	no	—
567	C₂²⋊C₄	—	53	2	no	—
568	C₂²⋊C₄	—	53	2	no	—
569	C₂²⋊C₄	—	53	2	no	—
570	C₂²⋊C₄	—	53	2	no	—
571	C₂²⋊C₄	—	53	2	no	—
572	C₂²⋊C₄	—	53	1	no	—
573	C₂²⋊C₄	—	53	1	no	—
574	C₂²⋊C₄	—	53	2	no	—
575	C₂²⋊C₄	—	53	2	no	—
576	C₂²⋊C₄	—	53	2	no	—
577	C₂²⋊C₄	—	53	2	no	—
578	C₂²⋊C₄	—	53	2	no	—
579	C₂²⋊C₄	—	53	1	no	—
580	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
581	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
582	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
583	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
584	C₄²	—	53	1	no	—
585	C₄²	—	53	1	no	—
586	C₄²	—	53	1	no	—
587	C₄²	—	53	1	no	—
588	C₄²	—	53	2	no	—
589	C₄²	—	53	2	no	—
590	C₄²	—	53	2	no	—
591	C₂³	—	53	2	no	—
592	C₂³	—	53	1	no	—
593	C₂³	—	53	2	no	—
594	C₂³	—	53	1	no	—
595	C₂³	—	212	2	no	—
596	C₂³	—	212	2	no	—
597	C₂³	—	212	2	no	—
598	C₂³	—	212	2	no	—
599	C₂³	—	212	2	no	—
600	C₂³	—	212	2	no	—
601	C₂³	C₂³×D₅₃	1	1	yes	characteristic
602	C₂³	C₂³×D₅₃	1	2	yes	—
603	C₂³	C₂³×D₅₃	1	1	yes	characteristic
604	C₂³	C₂³×D₅₃	1	1	yes	characteristic
605	Q₈	—	2	2	no	—
606	Q₈	—	4	1	no	—
607	Q₈	—	106	4	no	—
608	Q₈	—	212	1	no	—
609	D₄	—	2	2	no	—
610	D₄	—	4	2	no	—
611	D₄	—	4	1	no	—
612	D₄	—	4	1	no	—
613	D₄	—	4	1	no	—
614	D₄	—	4	2	no	—
615	D₄	—	4	2	no	—
616	D₄	—	106	2	no	—
617	D₄	—	106	4	no	—
618	D₄	—	106	2	no	—
619	D₄	—	106	2	no	—
620	D₄	—	106	2	no	—
621	D₄	—	212	2	no	—
622	D₄	—	212	2	no	—
623	D₄	—	212	2	no	—
624	D₄	—	212	1	no	—
625	D₄	—	212	2	no	—
626	D₄	—	212	1	no	—
627	D₄	—	212	2	no	—
628	D₄	—	212	1	no	—
629	D₄	—	212	2	no	—
630	D₄	—	212	2	no	—
631	D₄	—	212	2	no	—
632	D₄	—	212	2	no	—
633	D₄	—	212	2	no	—
634	D₄	—	212	2	no	—
635	D₄	—	212	1	no	—
636	D₄	—	212	1	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	4	2	no	—
641	C₂×C₄	—	4	2	no	—
642	C₂×C₄	—	53	1	no	—
643	C₂×C₄	—	53	2	no	—
644	C₂×C₄	—	53	1	no	—
645	C₂×C₄	—	53	1	no	—
646	C₂×C₄	—	53	1	no	—
647	C₂×C₄	—	53	1	no	—
648	C₂×C₄	—	53	2	no	—
649	C₂×C₄	—	53	1	no	—
650	C₂×C₄	—	106	4	no	—
651	C₂×C₄	—	106	2	no	—
652	C₂×C₄	—	106	2	no	—
653	C₂×C₄	—	106	2	no	—
654	C₂×C₄	—	212	2	no	—
655	C₂×C₄	—	212	2	no	—
656	C₂×C₄	—	212	2	no	—
657	C₂×C₄	—	212	1	no	—
658	C₂×C₄	—	212	2	no	—
659	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
660	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
661	C₂×C₄	C₂³×D₅₃	1	2	yes	—
662	C₂×C₄	C₂³×D₅₃	1	2	yes	—
663	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
664	C₂×C₄	C₂³×D₅₃	1	2	yes	—
665	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
666	C₂²	—	2	1	no	—
667	C₂²	—	2	1	no	—
668	C₂²	—	2	2	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	2	1	no	—
671	C₂²	—	2	1	no	—
672	C₂²	—	2	1	no	—
673	C₂²	—	2	2	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	1	no	—
678	C₂²	—	106	2	no	—
679	C₂²	—	106	1	no	—
680	C₂²	—	106	2	no	—
681	C₂²	—	106	1	no	—
682	C₂²	—	106	1	no	—
683	C₂²	—	106	1	no	—
684	C₂²	—	106	2	no	—
685	C₂²	—	106	2	no	—
686	C₂²	—	106	1	no	—
687	C₂²	—	106	2	no	—
688	C₂²	—	106	2	no	—
689	C₂²	—	106	1	no	—
690	C₂²	—	424	4	no	—
691	C₂²	—	424	4	no	—
692	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
693	C₄	—	2	2	no	—
694	C₄	—	2	2	no	—
695	C₄	—	2	1	no	—
696	C₄	—	2	1	no	—
697	C₄	—	2	1	no	—
698	C₄	—	2	2	no	—
699	C₄	—	53	2	no	—
700	C₄	—	106	1	no	—
701	C₄	—	106	2	no	—
702	C₄	—	106	1	no	—
703	C₄	—	106	1	no	—
704	C₄	—	106	1	no	—
705	C₄	—	106	1	no	—
706	C₄	—	106	2	no	—
707	C₄	#13133262	1	2	yes	—
708	C₂	—	4	1	no	—
709	C₂	—	4	2	no	—
710	C₂	—	4	1	no	—
711	C₂	—	4	1	no	—
712	C₂	—	212	2	no	—
713	C₂	—	212	1	no	—
714	C₂	—	212	2	no	—
715	C₂	—	212	1	no	—
716	C₂	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
717	C₂	C₂×#13133262	1	1	yes	characteristic
718	C₂	#16811460	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#537	C₂
hypercenter	#537	D₅₃
hypocenter	C₅₃	#3546
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #537

Complements

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

N	H ≅ G/N	type
1. #16811361	C₂	semidirect
2. #16811361	C₂	semidirect
3. #16811344	C₂	semidirect
4. #16811321	C₂	semidirect
5. #16811320	C₂	semidirect
6. #16811292	C₂	semidirect
7. #16811291	C₂	semidirect
8. #16811274	C₂	semidirect
9. #16811264	C₂	semidirect
10. #16811262	C₂	semidirect
11. #16811261	C₂	semidirect
12. #16811257	C₂	semidirect
13. #16811243	C₂	semidirect
14. #16811213	C₂	semidirect
15. #16811205	C₂	semidirect
16. #16811203	C₂	semidirect
17. #16811189	C₂	semidirect
18. #16811189	C₂	semidirect
19. #16811187	C₂	semidirect
20. #16811169	C₂	semidirect
21. #16811168	C₂	semidirect
22. #16811159	C₂	semidirect
23. C₅₃×#537	C₂	semidirect
24. C₂×#11719949	C₂²	semidirect
25. C₂×#11719945	C₂²	semidirect
26. C₂×#11719945	C₂²	semidirect
27. C₂×#11719947	C₂²	semidirect
31. #13133216	C₂²	semidirect
32. #13133215	C₂²	semidirect
35. #13133213	C₂²	semidirect
36. #13133213	C₂²	semidirect
37. #13133213	C₂²	semidirect
38. #13133212	C₂²	semidirect
39. #13133212	C₂²	semidirect
40. #13133212	C₂²	semidirect
41. #13133210	C₂²	semidirect
42. #13133210	C₂²	semidirect
43. #13133208	C₂²	semidirect
45. #13133206	C₂²	semidirect
46. #13133206	C₂²	semidirect
47. #13133204	C₂²	semidirect
49. #13133203	C₂²	semidirect
50. #13133203	C₂²	semidirect
51. #13133202	C₂²	semidirect
52. #13133202	C₂²	semidirect
53. #13133202	C₂²	semidirect
54. #13133201	C₂²	semidirect
55. #13133200	C₂²	semidirect
56. #13133200	C₂²	semidirect
57. #13133198	C₂²	semidirect
58. #13133195	C₂²	semidirect
59. #13133195	C₂²	semidirect
60. #13133193	C₂²	semidirect
63. #13133192	C₂²	semidirect
64. #13133192	C₂²	semidirect
67. #13133191	C₂²	semidirect
68. #13133191	C₂²	semidirect
69. #13133191	C₂²	semidirect
70. #13133191	C₂²	semidirect
72. #13133190	C₂²	semidirect
73. #13133190	C₂²	semidirect
75. #13133189	C₂²	semidirect
76. #13133189	C₂²	semidirect
77. #13133189	C₂²	semidirect
78. #13133189	C₂²	semidirect
79. #13133189	C₂²	semidirect
80. #13133188	C₂²	semidirect
81. #13133188	C₂²	semidirect
82. #13133188	C₂²	semidirect
84. #13133187	C₂²	semidirect
85. #13133187	C₂²	semidirect
87. #13133185	C₂²	semidirect
88. #13133185	C₂²	semidirect
89. #13133185	C₂²	semidirect
90. #13133185	C₂²	semidirect
91. Q₈×Dic₅₃	C₂²	semidirect
92. #13133182	C₂²	semidirect
93. D₄×Dic₅₃	C₂²	semidirect
95. #13133179	C₂²	semidirect
97. C₄×C₂²⋊D₅₃	C₂²	semidirect
98. C₄×C₂²⋊D₅₃	C₂²	semidirect
99. C₄×C₂²⋊D₅₃	C₂²	semidirect
100. C₄×C₂²⋊D₅₃	C₂²	semidirect
101. C₄×C₂²⋊D₅₃	C₂²	semidirect
102. #13133177	C₂²	semidirect
103. #13133177	C₂²	semidirect
104. #13133177	C₂²	semidirect
105. #13133176	C₂²	semidirect
106. #13133175	C₂²	semidirect
107. #13133175	C₂²	semidirect
108. C₄⋊C₄×D₅₃	C₂²	semidirect
109. C₂×#11719921	C₂²	semidirect
110. C₂²⋊C₄×D₅₃	C₂²	semidirect
111. C₂×C₄×Dic₅₃	C₂²	semidirect
112. C₂×#41×C₅₃	C₂²	semidirect
113. C₂×#41×C₅₃	C₂²	semidirect
114. C₂²⋊Q₈×C₅₃	C₂²	semidirect
115. C₂²⋊Q₈×C₅₃	C₂²	semidirect
116. C₂²⋊Q₈×C₅₃	C₂²	semidirect
118. #121×C₅₃	C₂²	semidirect
119. #121×C₅₃	C₂²	semidirect
120. #121×C₅₃	C₂²	semidirect
121. #121×C₅₃	C₂²	semidirect
122. C₂×C₄⋊C₄×C₅₃	C₂²	semidirect
376. #537	D₅₃	semidirect
383. C₅₃	#3546	semidirect
388. C₂×#41	C₂×D₅₃	semidirect
389. C₂×#41	C₂×D₅₃	semidirect
423. C₂²⋊Q₈	C₂×D₅₃	semidirect
424. C₂²⋊Q₈	C₂×D₅₃	semidirect
425. C₂²⋊Q₈	C₂×D₅₃	semidirect
449. #121	C₂×D₅₃	semidirect
450. #121	C₂×D₅₃	semidirect
451. #121	C₂×D₅₃	semidirect
452. #121	C₂×D₅₃	semidirect
479. C₂×C₄⋊C₄	C₂×D₅₃	semidirect