Subgroups — #20289017

Order 6784.

1160 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811370	C₂	1	2	yes	maximal, complemented
2	#16811361	C₂	1	2	yes	maximal, complemented
3	#16811338	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811325	C₂	1	1	yes	maximal, characteristic, complemented
5	#16811315	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811299	C₂	1	2	yes	maximal, complemented
7	#16811292	C₂	1	1	yes	maximal, characteristic, complemented
8	#16811277	C₂	1	1	yes	maximal, characteristic, complemented
9	#16811266	C₂	1	1	yes	maximal, characteristic, complemented
10	#16811260	C₂	1	2	yes	maximal, complemented
11	D₄×C₂²⋊D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#16811242	C₂	1	1	yes	maximal, characteristic, complemented
13	#16811226	C₂	1	2	yes	maximal, complemented
14	#16811224	C₂	1	1	yes	maximal, characteristic, complemented
15	#16811209	C₂	1	2	yes	maximal, complemented
16	#16811201	C₂	1	1	yes	maximal, characteristic, complemented
17	#16811189	C₂	1	1	yes	maximal, characteristic, complemented
18	#16811188	C₂	1	2	yes	maximal, complemented
19	#16811185	C₂	1	2	yes	maximal, complemented
20	#16811136	C₂	1	1	yes	maximal, characteristic, complemented
21	#16811132	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#13133188	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11719949	C₂²	1	1	yes	characteristic, complemented
25	C₂×#11719945	C₂²	1	1	yes	characteristic, complemented
26	C₂×#11719947	C₂²	1	2	yes	complemented
27	C₂²×C₂²⋊D₅₃	C₂²	1	2	yes	—
28	C₂²×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
29	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
31	#13133217	C₂²	1	1	yes	characteristic, complemented
32	#13133213	C₂²	1	2	yes	complemented
33	#13133213	C₂²	1	1	yes	characteristic, complemented
34	#13133213	C₂²	1	2	yes	complemented
35	#13133212	C₂²	1	2	yes	complemented
36	#13133210	C₂²	1	2	yes	complemented
37	#13133210	C₂²	1	2	yes	complemented
38	#13133208	C₂²	1	1	yes	characteristic, complemented
39	#13133208	C₂²	1	2	yes	complemented
40	#13133203	C₂²	1	2	yes	complemented
41	#13133203	C₂²	1	2	yes	complemented
42	#13133203	C₂²	1	2	yes	complemented
43	#13133203	C₂²	1	2	yes	complemented
44	#13133202	C₂²	1	2	yes	complemented
45	#13133202	C₂²	1	1	yes	characteristic, complemented
46	#13133201	C₂²	1	2	yes	—
47	#13133201	C₂²	1	2	yes	complemented
48	#13133201	C₂²	1	2	yes	complemented
49	#13133201	C₂²	1	2	yes	complemented
50	#13133201	C₂²	1	2	yes	complemented
51	#13133200	C₂²	1	2	yes	complemented
52	#13133199	C₂²	1	2	yes	complemented
53	#13133199	C₂²	1	2	yes	complemented
54	#13133199	C₂²	1	1	yes	characteristic, complemented
55	#13133197	C₂²	1	2	yes	complemented
56	#13133196	C₂²	1	2	yes	complemented
57	#13133195	C₂²	1	1	yes	characteristic, complemented
58	#13133194	C₂²	1	1	yes	characteristic, complemented
59	#13133194	C₂²	1	2	yes	complemented
60	#13133193	C₂²	1	1	yes	characteristic, complemented
61	#13133193	C₂²	1	1	yes	characteristic, complemented
62	#13133192	C₂²	1	1	yes	characteristic, complemented
63	#13133191	C₂²	1	1	yes	characteristic
64	#13133191	C₂²	1	1	yes	characteristic, complemented
65	#13133191	C₂²	1	2	yes	complemented
66	#13133191	C₂²	1	2	yes	complemented
67	#13133191	C₂²	1	2	yes	complemented
68	#13133191	C₂²	1	2	yes	complemented
69	#13133190	C₂²	1	2	yes	complemented
70	#13133190	C₂²	1	1	yes	characteristic, complemented
71	#13133190	C₂²	1	2	yes	complemented
72	#13133189	C₂²	1	1	yes	characteristic
73	#13133189	C₂²	1	2	yes	complemented
74	#13133189	C₂²	1	2	yes	complemented
75	#13133189	C₂²	1	2	yes	complemented
76	#13133189	C₂²	1	2	yes	complemented
77	#13133188	C₂²	1	1	yes	characteristic
78	#13133188	C₂²	1	1	yes	characteristic
79	#13133188	C₂²	1	1	yes	characteristic, complemented
80	#13133188	C₂²	1	2	yes	complemented
81	#13133188	C₂²	1	1	yes	characteristic, complemented
82	#13133188	C₂²	1	2	yes	complemented
83	#13133188	C₂²	1	1	yes	characteristic, complemented
84	#13133188	C₂²	1	2	yes	complemented
85	#13133187	C₂²	1	1	yes	characteristic
86	#13133187	C₂²	1	2	yes	complemented
87	#13133187	C₂²	1	2	yes	complemented
88	#13133187	C₂²	1	2	yes	complemented
89	#13133186	C₂²	1	2	yes	—
90	#13133185	C₂²	1	2	yes	complemented
91	#13133185	C₂²	1	2	yes	complemented
92	#13133185	C₂²	1	1	yes	characteristic, complemented
93	Q₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
94	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
95	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
96	D₄×Dic₅₃	C₂²	1	2	yes	complemented
97	D₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
98	#13133179	C₂²	1	2	yes	complemented
99	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
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	#13133176	C₂²	1	2	yes	complemented
104	#13133175	C₂²	1	1	yes	characteristic, complemented
105	#13133175	C₂²	1	1	yes	characteristic, complemented
106	#13133174	C₂²	1	1	yes	characteristic, complemented
107	#13133173	C₂²	1	2	yes	complemented
108	C₂×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
109	C₂×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
110	C₂×C₂²⋊Dic₅₃	C₂²	1	2	yes	complemented
111	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
112	C₂×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
113	C₂²×D₄×C₅₃	C₂²	1	1	yes	characteristic
114	#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
115	#123×C₅₃	C₂²	1	2	yes	complemented
116	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
117	#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
118	#121×C₅₃	C₂²	1	2	yes	complemented
119	#120×C₅₃	C₂²	1	2	yes	complemented
120	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
123	C₂⁴×C₅₃	C₂³	1	2	yes	—
124	C₂³×D₅₃	C₂³	1	1	yes	characteristic
125	C₂³×D₅₃	C₂³	1	2	yes	—
126	#41×C₅₃	—	4	2	no	—
127	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₅₃	—	4	2	no	—
129	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
130	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
131	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
132	C₂×D₄×C₅₃	C₂³	1	2	yes	—
133	C₂×D₄×C₅₃	C₂³	1	2	yes	—
134	C₂×D₄×C₅₃	C₂³	1	2	yes	—
135	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
138	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₅₃	—	4	4	no	—
140	C₂×C₂²⋊D₅₃	—	4	4	no	—
141	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
146	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
150	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
151	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
152	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
153	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
154	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
155	C₂²×Dic₅₃	C₂³	1	2	yes	—
156	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
157	C₂²×Dic₅₃	C₂³	1	2	yes	—
158	C₂²×Dic₅₃	C₂³	1	2	yes	—
159	#11719949	—	4	2	no	—
160	#11719947	—	4	4	no	—
161	D₄×D₅₃	—	4	2	no	—
162	#11719945	—	4	2	no	—
163	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
164	C₂×D₂₁₂	C₂³	1	2	yes	—
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×C₄×D₅₃	—	4	2	no	—
169	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
170	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
171	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
172	C₂×C₄×D₅₃	C₂³	1	2	yes	—
173	C₂×C₄×D₅₃	C₂³	1	2	yes	—
174	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
175	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
176	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
177	C₂×Dic₁₀₆	C₂³	1	2	yes	—
178	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
179	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
180	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
181	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
182	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
183	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
184	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
185	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
186	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
187	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
188	C₄²×C₅₃	C₂³	1	1	yes	characteristic
189	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
190	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
191	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
192	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
193	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
194	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
195	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
196	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
197	#11719921	C₂³	1	1	yes	characteristic
198	#11719921	C₂³	1	2	yes	—
199	#11719921	C₂³	1	1	yes	characteristic
200	#11719921	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
206	#11719921	C₂³	1	2	yes	—
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	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
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	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
217	C₄⋊Dic₅₃	C₂³	1	2	yes	—
218	C₄⋊Dic₅₃	C₂³	1	2	yes	—
219	C₄⋊Dic₅₃	C₂³	1	2	yes	—
220	#11719919	C₂³	1	2	yes	—
221	#11719919	C₂³	1	2	yes	—
222	#11719919	C₂³	1	1	yes	characteristic
223	#11719919	C₂³	1	1	yes	characteristic
224	#11719919	C₂³	1	2	yes	—
225	#11719919	C₂³	1	1	yes	characteristic
226	#11719919	C₂³	1	1	yes	characteristic
227	C₄×Dic₅₃	C₂³	1	2	yes	—
228	C₄×Dic₅₃	C₂³	1	2	yes	—
229	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
230	C₄×Dic₅₃	C₂³	1	2	yes	—
231	C₂³×C₅₃	—	2	4	no	—
232	C₂³×C₅₃	—	4	2	no	—
233	C₂³×C₅₃	—	4	2	no	—
234	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
235	C₂³×C₅₃	C₂⁴	1	2	yes	—
236	C₂³×C₅₃	C₂⁴	1	2	yes	—
237	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
238	C₂²×D₅₃	—	2	2	no	—
239	C₂²×D₅₃	—	4	1	no	—
240	C₂²×D₅₃	—	4	1	no	—
241	C₂²×D₅₃	—	4	2	no	—
242	C₂²×D₅₃	—	4	2	no	—
243	C₂²×D₅₃	—	4	2	no	—
244	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
245	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
246	C₂²×D₅₃	C₂⁴	1	2	yes	—
247	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
248	Q₈×C₅₃	—	2	2	no	—
249	D₄×C₅₃	—	2	2	no	—
250	D₄×C₅₃	—	2	2	no	—
251	D₄×C₅₃	—	2	2	no	—
252	D₄×C₅₃	—	4	2	no	—
253	D₄×C₅₃	—	4	2	no	—
254	D₄×C₅₃	—	4	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	1	yes	characteristic
260	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
261	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
262	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
263	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
264	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
265	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
266	C₂²⋊D₅₃	—	2	4	no	—
267	C₂²⋊D₅₃	—	2	2	no	—
268	C₂²⋊D₅₃	—	4	1	no	—
269	C₂²⋊D₅₃	—	4	1	no	—
270	C₂²⋊D₅₃	—	4	2	no	—
271	C₂²⋊D₅₃	—	4	2	no	—
272	C₂²⋊D₅₃	—	4	2	no	—
273	C₂²⋊D₅₃	—	4	2	no	—
274	C₂²⋊D₅₃	—	4	2	no	—
275	C₂²⋊D₅₃	—	4	2	no	—
276	C₂²⋊D₅₃	—	4	2	no	—
277	C₂²⋊D₅₃	—	4	2	no	—
278	C₂²⋊D₅₃	—	4	2	no	—
279	C₂²⋊D₅₃	—	4	1	no	—
280	C₂×Dic₅₃	—	2	4	no	—
281	C₂×Dic₅₃	—	4	1	no	—
282	C₂×Dic₅₃	—	4	2	no	—
283	C₂×Dic₅₃	—	4	2	no	—
284	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
285	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
286	C₂×Dic₅₃	C₂⁴	1	2	yes	—
287	C₂×Dic₅₃	C₂⁴	1	2	yes	—
288	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
289	C₂×Dic₅₃	C₂⁴	1	2	yes	—
290	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
291	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
292	D₂₁₂	—	2	2	no	—
293	D₂₁₂	—	4	1	no	—
294	D₂₁₂	—	4	2	no	—
295	D₂₁₂	—	4	1	no	—
296	D₂₁₂	—	4	2	no	—
297	C₄×D₅₃	—	2	2	no	—
298	C₄×D₅₃	—	2	2	no	—
299	C₄×D₅₃	—	2	2	no	—
300	C₄×D₅₃	—	4	1	no	—
301	C₄×D₅₃	—	4	1	no	—
302	C₄×D₅₃	—	4	2	no	—
303	C₄×D₅₃	—	4	2	no	—
304	Dic₁₀₆	—	4	1	no	—
305	Dic₁₀₆	—	4	2	no	—
306	C₂²×C₅₃	—	2	1	no	—
307	C₂²×C₅₃	—	2	1	no	—
308	C₂²×C₅₃	—	2	1	no	—
309	C₂²×C₅₃	—	2	2	no	—
310	C₂²×C₅₃	—	2	2	no	—
311	C₂²×C₅₃	—	2	1	no	—
312	C₂²×C₅₃	—	2	2	no	—
313	C₂²×C₅₃	—	2	2	no	—
314	C₂²×C₅₃	—	2	2	no	—
315	C₂²×C₅₃	—	2	1	no	—
316	C₂²×C₅₃	—	2	2	no	—
317	C₂²×C₅₃	—	8	4	no	—
318	C₂²×C₅₃	H(5,𝔽₂)	1	2	yes	—
319	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
320	C₂×D₅₃	—	2	1	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	1	no	—
326	C₂×D₅₃	—	2	1	no	—
327	C₂×D₅₃	—	2	1	no	—
328	C₂×D₅₃	—	2	1	no	—
329	C₂×D₅₃	—	2	1	no	—
330	C₂×D₅₃	—	2	2	no	—
331	C₂×D₅₃	—	2	1	no	—
332	C₂×D₅₃	—	4	4	no	—
333	C₂×D₅₃	—	8	4	no	—
334	C₄×C₅₃	—	2	1	no	—
335	C₄×C₅₃	—	2	1	no	—
336	C₄×C₅₃	—	2	1	no	—
337	C₄×C₅₃	—	2	2	no	—
338	C₄×C₅₃	—	2	1	no	—
339	C₄×C₅₃	—	2	2	no	—
340	C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
341	Dic₅₃	—	2	1	no	—
342	Dic₅₃	—	2	1	no	—
343	Dic₅₃	—	2	2	no	—
344	Dic₅₃	—	2	2	no	—
345	Dic₅₃	—	2	1	no	—
346	Dic₅₃	—	2	2	no	—
347	Dic₅₃	—	2	1	no	—
348	Dic₅₃	—	2	1	no	—
349	#3542	—	53	1	no	maximal, Sylow
350	C₂×C₅₃	—	2	2	no	—
351	C₂×C₅₃	—	4	2	no	—
352	C₂×C₅₃	—	4	1	no	—
353	C₂×C₅₃	—	4	2	no	—
354	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
355	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
356	C₂×C₅₃	#585	1	1	yes	characteristic
357	D₅₃	—	4	1	no	—
358	D₅₃	—	4	1	no	—
359	D₅₃	—	4	2	no	—
360	D₅₃	—	4	1	no	—
361	#562	—	53	2	no	—
362	#560	—	53	2	no	—
363	#555	—	53	1	no	—
364	#553	—	53	1	no	—
365	#552	—	53	1	no	—
366	#551	—	53	2	no	—
367	#550	—	53	1	no	—
368	#547	—	53	1	no	—
369	#546	—	53	1	no	—
370	#546	—	53	2	no	—
371	#546	D₅₃	1	1	yes	characteristic, complemented
372	D₄²	—	53	1	no	—
373	#542	—	53	1	no	—
374	#540	—	53	2	no	—
375	#540	—	53	1	no	—
376	#538	—	53	2	no	—
377	#537	—	53	1	no	—
378	#535	—	53	1	no	—
379	#535	—	53	2	no	—
380	#534	—	53	2	no	—
381	#525	—	53	1	no	—
382	#525	—	53	1	no	—
383	C₂×#121	—	53	1	no	—
384	C₅₃	#3542	1	1	yes	characteristic, complemented, Sylow
385	C₂×#41	—	53	1	no	—
386	C₂×#41	—	53	2	no	—
387	C₂×#41	—	53	1	no	—
388	C₂×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
389	C₂²×D₄	—	53	2	no	—
390	C₂²×D₄	—	53	2	no	—
391	C₂²×D₄	—	53	1	no	—
392	C₂²×D₄	C₂×D₅₃	1	1	yes	characteristic
393	C₂³×C₄	—	53	1	no	—
394	C₄⋊Q₈	—	53	1	no	—
395	#127	—	53	2	no	—
396	#127	—	53	2	no	—
397	#127	—	53	1	no	—
398	#126	—	53	2	no	—
399	#126	—	53	2	no	—
400	#126	—	53	2	no	—
401	#125	—	53	1	no	—
402	#125	—	53	2	no	—
403	#124	—	53	2	no	—
404	#124	—	53	2	no	—
405	#124	—	53	2	no	—
406	#124	—	53	2	no	—
407	#124	C₂×D₅₃	1	1	yes	characteristic, complemented
408	#123	—	53	2	no	—
409	#123	—	53	1	no	—
410	#123	—	53	2	no	—
411	#123	—	53	1	no	—
412	#123	—	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	C₂×D₅₃	1	2	yes	complemented
420	C₂²⋊Q₈	—	53	1	no	—
421	C₂²⋊Q₈	—	53	1	no	—
422	C₂²⋊Q₈	—	53	2	no	—
423	C₂²⋊Q₈	—	53	1	no	—
424	C₂²⋊Q₈	—	53	2	no	—
425	C₂²⋊Q₈	—	53	1	no	—
426	C₂²⋊Q₈	—	53	2	no	—
427	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
428	#121	—	53	1	no	—
429	#121	—	53	1	no	—
430	#121	—	53	2	no	—
431	#121	—	53	1	no	—
432	#121	—	53	1	no	—
433	#121	—	53	2	no	—
434	#121	—	53	1	no	—
435	#121	—	53	2	no	—
436	#121	—	53	2	no	—
437	#121	—	53	1	no	—
438	#121	—	53	2	no	—
439	#121	—	53	2	no	—
440	#121	—	53	2	no	—
441	#121	—	53	1	no	—
442	#121	—	53	2	no	—
443	#121	—	53	2	no	—
444	#121	—	53	2	no	—
445	#121	—	53	2	no	—
446	#121	—	53	1	no	—
447	#121	—	53	1	no	—
448	#121	—	53	1	no	—
449	#121	—	53	2	no	—
450	#121	—	53	2	no	—
451	#121	C₂×D₅₃	1	1	yes	characteristic, complemented
452	#121	C₂×D₅₃	1	2	yes	complemented
453	#120	—	53	2	no	—
454	#120	—	53	1	no	—
455	#120	—	53	2	no	—
456	#120	—	53	2	no	—
457	#120	—	53	1	no	—
458	#120	—	53	2	no	—
459	#120	—	53	2	no	—
460	#120	—	53	2	no	—
461	#120	C₂×D₅₃	1	2	yes	complemented
462	C₄×Q₈	—	53	1	no	—
463	C₄×D₄	—	53	2	no	—
464	C₄×D₄	—	53	1	no	—
465	C₄×D₄	—	53	1	no	—
466	C₄×D₄	—	53	1	no	—
467	C₄×D₄	—	53	2	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	C₂×D₅₃	1	1	yes	characteristic, complemented
473	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
474	#117	—	53	2	no	—
475	#117	—	53	1	no	—
476	#117	—	53	1	no	—
477	#117	—	53	2	no	—
478	#117	—	53	1	no	—
479	C₂×C₄⋊C₄	—	53	1	no	—
480	C₂×C₄⋊C₄	—	53	1	no	—
481	C₂×C₂²⋊C₄	—	53	2	no	—
482	C₂×C₂²⋊C₄	—	53	2	no	—
483	C₂×C₂²⋊C₄	C₂×D₅₃	1	2	yes	complemented
484	C₂⁴	—	53	1	no	—
485	C₂⁴	—	53	2	no	—
486	C₂⁴	C₂²×D₅₃	1	2	yes	—
487	#41	—	4	2	no	—
488	#41	—	212	2	no	—
489	#41	—	212	4	no	—
490	#41	—	212	2	no	—
491	C₂×Q₈	—	53	1	no	—
492	C₂×Q₈	—	53	2	no	—
493	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
494	C₂×D₄	—	4	2	no	—
495	C₂×D₄	—	53	2	no	—
496	C₂×D₄	—	53	1	no	—
497	C₂×D₄	—	53	2	no	—
498	C₂×D₄	—	53	1	no	—
499	C₂×D₄	—	53	1	no	—
500	C₂×D₄	—	53	2	no	—
501	C₂×D₄	—	53	2	no	—
502	C₂×D₄	—	53	2	no	—
503	C₂×D₄	—	53	2	no	—
504	C₂×D₄	—	53	2	no	—
505	C₂×D₄	—	53	1	no	—
506	C₂×D₄	—	53	2	no	—
507	C₂×D₄	—	53	2	no	—
508	C₂×D₄	—	53	2	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	—	212	2	no	—
515	C₂×D₄	—	212	4	no	—
516	C₂×D₄	—	212	4	no	—
517	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
518	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
519	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
520	C₂×D₄	C₂²×D₅₃	1	2	yes	—
521	C₂×D₄	C₂²×D₅₃	1	2	yes	—
522	C₂×D₄	C₂²×D₅₃	1	2	yes	—
523	C₂²×C₄	—	53	2	no	—
524	C₂²×C₄	—	53	1	no	—
525	C₂²×C₄	—	53	2	no	—
526	C₂²×C₄	—	53	2	no	—
527	C₂²×C₄	—	53	1	no	—
528	C₂²×C₄	—	53	1	no	—
529	C₂²×C₄	—	53	1	no	—
530	C₂²×C₄	—	53	2	no	—
531	C₂²×C₄	—	53	2	no	—
532	C₂²×C₄	—	53	1	no	—
533	C₂²×C₄	—	53	1	no	—
534	C₂²×C₄	—	212	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	2	yes	—
538	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
539	C₄⋊C₄	—	53	1	no	—
540	C₄⋊C₄	—	53	1	no	—
541	C₄⋊C₄	—	53	1	no	—
542	C₄⋊C₄	—	53	2	no	—
543	C₄⋊C₄	—	53	2	no	—
544	C₄⋊C₄	—	53	1	no	—
545	C₄⋊C₄	—	53	2	no	—
546	C₄⋊C₄	—	53	2	no	—
547	C₄⋊C₄	—	53	1	no	—
548	C₄⋊C₄	—	53	1	no	—
549	C₄⋊C₄	—	53	2	no	—
550	C₄⋊C₄	—	53	1	no	—
551	C₄⋊C₄	—	53	1	no	—
552	C₄⋊C₄	—	53	2	no	—
553	C₄⋊C₄	—	53	2	no	—
554	C₄⋊C₄	—	53	2	no	—
555	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
556	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
557	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
558	C₂²⋊C₄	—	53	2	no	—
559	C₂²⋊C₄	—	53	2	no	—
560	C₂²⋊C₄	—	53	2	no	—
561	C₂²⋊C₄	—	53	2	no	—
562	C₂²⋊C₄	—	53	1	no	—
563	C₂²⋊C₄	—	53	2	no	—
564	C₂²⋊C₄	—	53	1	no	—
565	C₂²⋊C₄	—	53	2	no	—
566	C₂²⋊C₄	—	53	1	no	—
567	C₂²⋊C₄	—	53	2	no	—
568	C₂²⋊C₄	—	53	2	no	—
569	C₂²⋊C₄	—	53	1	no	—
570	C₂²⋊C₄	—	53	2	no	—
571	C₂²⋊C₄	—	53	1	no	—
572	C₂²⋊C₄	—	53	1	no	—
573	C₂²⋊C₄	—	53	2	no	—
574	C₂²⋊C₄	—	53	1	no	—
575	C₂²⋊C₄	—	53	2	no	—
576	C₂²⋊C₄	—	53	2	no	—
577	C₂²⋊C₄	—	53	1	no	—
578	C₂²⋊C₄	—	53	2	no	—
579	C₂²⋊C₄	—	53	2	no	—
580	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
581	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
582	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
583	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
584	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
585	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
586	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
587	C₄²	—	53	2	no	—
588	C₄²	—	53	2	no	—
589	C₄²	—	53	1	no	—
590	C₄²	—	53	2	no	—
591	C₄²	C₂²×D₅₃	1	1	yes	characteristic
592	C₂³	—	2	4	no	—
593	C₂³	—	4	2	no	—
594	C₂³	—	4	2	no	—
595	C₂³	—	53	1	no	—
596	C₂³	—	53	1	no	—
597	C₂³	—	53	1	no	—
598	C₂³	—	53	2	no	—
599	C₂³	—	106	2	no	—
600	C₂³	—	212	2	no	—
601	C₂³	—	212	2	no	—
602	C₂³	—	212	2	no	—
603	C₂³	—	212	1	no	—
604	C₂³	—	212	1	no	—
605	C₂³	C₂³×D₅₃	1	2	yes	—
606	C₂³	C₂³×D₅₃	1	2	yes	—
607	C₂³	C₂³×D₅₃	1	1	yes	characteristic
608	C₂³	C₂³×D₅₃	1	1	yes	characteristic
609	Q₈	—	2	2	no	—
610	Q₈	—	212	1	no	—
611	Q₈	—	212	2	no	—
612	D₄	—	2	2	no	—
613	D₄	—	2	2	no	—
614	D₄	—	2	2	no	—
615	D₄	—	4	2	no	—
616	D₄	—	4	2	no	—
617	D₄	—	4	2	no	—
618	D₄	—	106	2	no	—
619	D₄	—	106	4	no	—
620	D₄	—	106	2	no	—
621	D₄	—	212	1	no	—
622	D₄	—	212	2	no	—
623	D₄	—	212	1	no	—
624	D₄	—	212	2	no	—
625	D₄	—	212	2	no	—
626	D₄	—	212	1	no	—
627	D₄	—	212	2	no	—
628	D₄	—	212	2	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	1	no	—
635	D₄	—	212	1	no	—
636	D₄	—	212	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	4	2	no	—
640	C₂×C₄	—	4	2	no	—
641	C₂×C₄	—	53	1	no	—
642	C₂×C₄	—	53	1	no	—
643	C₂×C₄	—	53	1	no	—
644	C₂×C₄	—	53	2	no	—
645	C₂×C₄	—	53	2	no	—
646	C₂×C₄	—	53	1	no	—
647	C₂×C₄	—	53	1	no	—
648	C₂×C₄	—	53	2	no	—
649	C₂×C₄	—	106	4	no	—
650	C₂×C₄	—	106	2	no	—
651	C₂×C₄	—	106	2	no	—
652	C₂×C₄	—	106	2	no	—
653	C₂×C₄	—	212	1	no	—
654	C₂×C₄	—	212	1	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	—	212	2	no	—
660	C₂×C₄	C₂³×D₅₃	1	2	yes	—
661	C₂×C₄	C₂³×D₅₃	1	2	yes	—
662	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
663	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
664	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
665	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
666	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
667	C₂²	—	2	1	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	2	2	no	—
671	C₂²	—	2	2	no	—
672	C₂²	—	2	1	no	—
673	C₂²	—	2	2	no	—
674	C₂²	—	2	2	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	2	1	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	8	4	no	—
679	C₂²	—	106	1	no	—
680	C₂²	—	106	1	no	—
681	C₂²	—	106	1	no	—
682	C₂²	—	106	2	no	—
683	C₂²	—	106	2	no	—
684	C₂²	—	106	1	no	—
685	C₂²	—	106	1	no	—
686	C₂²	—	106	1	no	—
687	C₂²	—	106	2	no	—
688	C₂²	—	106	1	no	—
689	C₂²	—	106	1	no	—
690	C₂²	—	106	1	no	—
691	C₂²	—	424	4	no	—
692	C₂²	—	212	4	no	—
693	C₂²	#13133263	1	2	yes	—
694	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
695	C₄	—	2	1	no	—
696	C₄	—	2	1	no	—
697	C₄	—	2	2	no	—
698	C₄	—	2	1	no	—
699	C₄	—	2	1	no	—
700	C₄	—	2	2	no	—
701	C₄	—	106	1	no	—
702	C₄	—	106	1	no	—
703	C₄	—	106	1	no	—
704	C₄	—	106	2	no	—
705	C₄	—	106	2	no	—
706	C₄	—	106	1	no	—
707	C₄	—	106	2	no	—
708	C₄	—	106	1	no	—
709	C₄	#13133262	1	2	yes	—
710	C₂	—	2	2	no	—
711	C₂	—	4	2	no	—
712	C₂	—	4	2	no	—
713	C₂	—	4	1	no	—
714	C₂	—	212	1	no	—
715	C₂	—	212	2	no	—
716	C₂	—	212	1	no	—
717	C₂	—	212	1	no	—
718	C₂	C₂×#13133262	1	1	yes	characteristic
719	C₂	C₂×#13133263	1	1	yes	characteristic
720	C₂	#16811458	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#546	C₂
hypercenter	#546	D₅₃
hypocenter	C₅₃	#3542
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. #16811370	C₂	semidirect
2. #16811361	C₂	semidirect
3. #16811338	C₂	semidirect
4. #16811325	C₂	semidirect
5. #16811315	C₂	semidirect
6. #16811299	C₂	semidirect
7. #16811292	C₂	semidirect
8. #16811277	C₂	semidirect
9. #16811266	C₂	semidirect
10. #16811260	C₂	semidirect
11. D₄×C₂²⋊D₅₃	C₂	semidirect
12. #16811242	C₂	semidirect
13. #16811226	C₂	semidirect
14. #16811224	C₂	semidirect
15. #16811209	C₂	semidirect
16. #16811201	C₂	semidirect
17. #16811189	C₂	semidirect
18. #16811188	C₂	semidirect
19. #16811185	C₂	semidirect
20. #16811136	C₂	semidirect
21. #16811132	C₂	semidirect
22. C₂×#13133188	C₂	semidirect
23. C₅₃×#546	C₂	semidirect
24. C₂×#11719949	C₂²	semidirect
25. C₂×#11719945	C₂²	semidirect
26. C₂×#11719947	C₂²	semidirect
28. C₂²×C₂²⋊D₅₃	C₂²	semidirect
29. C₂×D₄×D₅₃	C₂²	semidirect
30. C₂²×C₄×D₅₃	C₂²	semidirect
31. #13133217	C₂²	semidirect
32. #13133213	C₂²	semidirect
33. #13133213	C₂²	semidirect
34. #13133213	C₂²	semidirect
35. #13133212	C₂²	semidirect
36. #13133210	C₂²	semidirect
37. #13133210	C₂²	semidirect
38. #13133208	C₂²	semidirect
39. #13133208	C₂²	semidirect
40. #13133203	C₂²	semidirect
41. #13133203	C₂²	semidirect
42. #13133203	C₂²	semidirect
43. #13133203	C₂²	semidirect
44. #13133202	C₂²	semidirect
45. #13133202	C₂²	semidirect
47. #13133201	C₂²	semidirect
48. #13133201	C₂²	semidirect
49. #13133201	C₂²	semidirect
50. #13133201	C₂²	semidirect
51. #13133200	C₂²	semidirect
52. #13133199	C₂²	semidirect
53. #13133199	C₂²	semidirect
54. #13133199	C₂²	semidirect
55. #13133197	C₂²	semidirect
56. #13133196	C₂²	semidirect
57. #13133195	C₂²	semidirect
58. #13133194	C₂²	semidirect
59. #13133194	C₂²	semidirect
60. #13133193	C₂²	semidirect
61. #13133193	C₂²	semidirect
62. #13133192	C₂²	semidirect
64. #13133191	C₂²	semidirect
65. #13133191	C₂²	semidirect
66. #13133191	C₂²	semidirect
67. #13133191	C₂²	semidirect
68. #13133191	C₂²	semidirect
69. #13133190	C₂²	semidirect
70. #13133190	C₂²	semidirect
71. #13133190	C₂²	semidirect
73. #13133189	C₂²	semidirect
74. #13133189	C₂²	semidirect
75. #13133189	C₂²	semidirect
76. #13133189	C₂²	semidirect
79. #13133188	C₂²	semidirect
80. #13133188	C₂²	semidirect
81. #13133188	C₂²	semidirect
82. #13133188	C₂²	semidirect
83. #13133188	C₂²	semidirect
84. #13133188	C₂²	semidirect
86. #13133187	C₂²	semidirect
87. #13133187	C₂²	semidirect
88. #13133187	C₂²	semidirect
90. #13133185	C₂²	semidirect
91. #13133185	C₂²	semidirect
92. #13133185	C₂²	semidirect
93. Q₈×Dic₅₃	C₂²	semidirect
94. C₄×D₂₁₂	C₂²	semidirect
95. C₄×D₂₁₂	C₂²	semidirect
96. D₄×Dic₅₃	C₂²	semidirect
97. D₄×Dic₅₃	C₂²	semidirect
98. #13133179	C₂²	semidirect
100. C₄×C₂²⋊D₅₃	C₂²	semidirect
101. C₄×C₂²⋊D₅₃	C₂²	semidirect
102. #13133177	C₂²	semidirect
103. #13133176	C₂²	semidirect
104. #13133175	C₂²	semidirect
105. #13133175	C₂²	semidirect
106. #13133174	C₂²	semidirect
107. #13133173	C₂²	semidirect
108. C₂×C₄⋊Dic₅₃	C₂²	semidirect
109. C₂×C₄⋊Dic₅₃	C₂²	semidirect
110. C₂×C₂²⋊Dic₅₃	C₂²	semidirect
111. C₂²⋊C₄×D₅₃	C₂²	semidirect
112. C₂×#41×C₅₃	C₂²	semidirect
114. #124×C₅₃	C₂²	semidirect
115. #123×C₅₃	C₂²	semidirect
116. C₂²⋊Q₈×C₅₃	C₂²	semidirect
117. #121×C₅₃	C₂²	semidirect
118. #121×C₅₃	C₂²	semidirect
119. #120×C₅₃	C₂²	semidirect
120. C₄×D₄×C₅₃	C₂²	semidirect
121. C₄×D₄×C₅₃	C₂²	semidirect
122. C₂×C₂²⋊C₄×C₅₃	C₂²	semidirect
371. #546	D₅₃	semidirect
384. C₅₃	#3542	semidirect
388. C₂×#41	C₂×D₅₃	semidirect
407. #124	C₂×D₅₃	semidirect
419. #123	C₂×D₅₃	semidirect
427. C₂²⋊Q₈	C₂×D₅₃	semidirect
451. #121	C₂×D₅₃	semidirect
452. #121	C₂×D₅₃	semidirect
461. #120	C₂×D₅₃	semidirect
472. C₄×D₄	C₂×D₅₃	semidirect
473. C₄×D₄	C₂×D₅₃	semidirect
483. C₂×C₂²⋊C₄	C₂×D₅₃	semidirect