Subgroups — #20288401

Order 6784.

1328 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811303	C₂	1	2	yes	maximal, complemented
2	#16811301	C₂	1	2	yes	maximal, complemented
3	#16811298	C₂	1	2	yes	maximal, complemented
4	#16811298	C₂	1	2	yes	maximal, complemented
5	#16811270	C₂	1	2	yes	maximal, complemented
6	#16811266	C₂	1	2	yes	maximal, complemented
7	#16811265	C₂	1	2	yes	maximal, complemented
8	#16811262	C₂	1	2	yes	maximal, complemented
9	#16811248	C₂	1	1	yes	maximal, characteristic, complemented
10	#16811211	C₂	1	1	yes	maximal, characteristic, complemented
11	#16811208	C₂	1	2	yes	maximal, complemented
12	#16811181	C₂	1	1	yes	maximal, characteristic, complemented
13	#16811136	C₂	1	1	yes	maximal, characteristic, complemented
14	#16811133	C₂	1	1	yes	maximal, characteristic, complemented
15	#16811132	C₂	1	2	yes	maximal, complemented
16	#120×D₅₃	C₂	1	2	yes	maximal, complemented
17	#16811095	C₂	1	2	yes	maximal, complemented
18	C₂×C₂²⋊C₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#538	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×D₅₃	C₂²	1	1	yes	characteristic
21	C₂×#11719949	C₂²	1	1	yes	characteristic, complemented
22	C₂×#11719945	C₂²	1	2	yes	complemented
23	C₂×#11719947	C₂²	1	1	yes	characteristic, complemented
24	C₂×D₄×D₅₃	C₂²	1	2	yes	—
25	C₂×D₄×D₅₃	C₂²	1	2	yes	complemented
26	C₂×D₄×D₅₃	C₂²	1	2	yes	complemented
27	C₂²×C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
29	#13133210	C₂²	1	2	yes	complemented
30	#13133210	C₂²	1	2	yes	complemented
31	#13133210	C₂²	1	2	yes	complemented
32	#13133204	C₂²	1	2	yes	complemented
33	#13133203	C₂²	1	2	yes	complemented
34	#13133203	C₂²	1	2	yes	complemented
35	#13133202	C₂²	1	2	yes	complemented
36	#13133202	C₂²	1	2	yes	complemented
37	#13133202	C₂²	1	2	yes	complemented
38	#13133199	C₂²	1	2	yes	complemented
39	#13133199	C₂²	1	2	yes	complemented
40	#13133199	C₂²	1	2	yes	complemented
41	#13133199	C₂²	1	2	yes	complemented
42	#13133199	C₂²	1	2	yes	complemented
43	#13133198	C₂²	1	2	yes	complemented
44	#13133197	C₂²	1	2	yes	complemented
45	#13133197	C₂²	1	1	yes	characteristic, complemented
46	#13133196	C₂²	1	1	yes	characteristic, complemented
47	#13133195	C₂²	1	2	yes	complemented
48	#13133195	C₂²	1	2	yes	complemented
49	#13133195	C₂²	1	2	yes	complemented
50	#13133194	C₂²	1	2	yes	complemented
51	#13133193	C₂²	1	2	yes	complemented
52	#13133193	C₂²	1	1	yes	characteristic, complemented
53	#13133192	C₂²	1	1	yes	characteristic, complemented
54	#13133191	C₂²	1	1	yes	characteristic, complemented
55	#13133190	C₂²	1	2	yes	complemented
56	#13133190	C₂²	1	2	yes	complemented
57	#13133189	C₂²	1	2	yes	complemented
58	#13133189	C₂²	1	2	yes	complemented
59	#13133188	C₂²	1	1	yes	characteristic, complemented
60	#13133188	C₂²	1	2	yes	complemented
61	#13133187	C₂²	1	2	yes	—
62	#13133187	C₂²	1	2	yes	—
63	#13133187	C₂²	1	2	yes	complemented
64	#13133187	C₂²	1	2	yes	complemented
65	#13133186	C₂²	1	2	yes	complemented
66	#13133185	C₂²	1	2	yes	—
67	#13133185	C₂²	1	2	yes	—
68	#13133185	C₂²	1	2	yes	complemented
69	#13133185	C₂²	1	2	yes	complemented
70	C₄×D₂₁₂	C₂²	1	2	yes	complemented
71	C₄×D₂₁₂	C₂²	1	2	yes	complemented
72	D₄×Dic₅₃	C₂²	1	2	yes	complemented
73	#13133179	C₂²	1	2	yes	complemented
74	#13133179	C₂²	1	2	yes	complemented
75	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
76	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
77	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
78	#13133177	C₂²	1	2	yes	complemented
79	#13133177	C₂²	1	2	yes	complemented
80	#13133177	C₂²	1	2	yes	complemented
81	#13133175	C₂²	1	1	yes	characteristic, complemented
82	#13133175	C₂²	1	2	yes	complemented
83	#13133175	C₂²	1	1	yes	characteristic, complemented
84	#13133174	C₂²	1	2	yes	complemented
85	#13133174	C₂²	1	2	yes	complemented
86	C₂×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
87	C₂×#11719921	C₂²	1	1	yes	characteristic
88	C₂×#11719921	C₂²	1	1	yes	characteristic
89	C₂×#11719921	C₂²	1	2	yes	complemented
90	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
91	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
92	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
93	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
94	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
95	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
96	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
97	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
98	#126×C₅₃	C₂²	1	2	yes	complemented
99	#124×C₅₃	C₂²	1	2	yes	complemented
100	#123×C₅₃	C₂²	1	2	yes	complemented
101	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
102	#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
103	#121×C₅₃	C₂²	1	2	yes	complemented
104	#120×C₅₃	C₂²	1	2	yes	complemented
105	C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
106	C₂×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
107	C₂⁴×C₅₃	C₂³	1	1	yes	characteristic
108	C₂³×D₅₃	—	2	4	no	—
109	C₂³×D₅₃	—	4	2	no	—
110	C₂³×D₅₃	—	4	2	no	—
111	C₂³×D₅₃	C₂³	1	1	yes	characteristic
112	C₂³×D₅₃	C₂³	1	2	yes	—
113	C₂³×D₅₃	C₂³	1	2	yes	—
114	C₂³×D₅₃	C₂³	1	2	yes	—
115	C₂³×D₅₃	C₂³	1	1	yes	characteristic
116	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
117	C₂×D₄×C₅₃	C₂³	1	2	yes	—
118	C₂×D₄×C₅₃	C₂³	1	2	yes	—
119	C₂×D₄×C₅₃	C₂³	1	2	yes	—
120	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
121	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
122	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
123	C₂²×C₄×C₅₃	C₂³	1	2	yes	complemented
124	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
125	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
126	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
127	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
128	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	complemented
131	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
132	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
133	C₂²×Dic₅₃	C₂³	1	2	yes	complemented
134	#11719949	—	4	2	no	—
135	#11719947	—	4	2	no	—
136	D₄×D₅₃	—	2	8	no	—
137	D₄×D₅₃	—	4	4	no	—
138	D₄×D₅₃	—	4	4	no	—
139	#11719945	—	4	4	no	—
140	C₂×D₂₁₂	C₂³	1	2	yes	—
141	C₂×D₂₁₂	C₂³	1	2	yes	—
142	C₂×D₂₁₂	C₂³	1	2	yes	—
143	C₂×D₂₁₂	C₂³	1	1	yes	characteristic, complemented
144	C₂×C₄×D₅₃	—	4	2	no	—
145	C₂×C₄×D₅₃	—	4	2	no	—
146	C₂×C₄×D₅₃	C₂³	1	2	yes	—
147	C₂×C₄×D₅₃	C₂³	1	2	yes	—
148	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₅₃	C₂³	1	2	yes	—
151	C₂×C₄×D₅₃	C₂³	1	2	yes	—
152	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₅₃	C₂³	1	2	yes	—
154	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₅₃	C₂³	1	2	yes	complemented
156	C₂×C₄×D₅₃	C₂³	1	2	yes	complemented
157	C₂×Dic₁₀₆	C₂³	1	2	yes	complemented
158	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic, complemented
159	C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
160	C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
161	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
162	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
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	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	complemented
169	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	complemented
170	C₄²×C₅₃	C₂³	1	2	yes	complemented
171	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
172	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
173	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
174	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
175	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
176	C₂²⋊Dic₅₃	C₂³	1	2	yes	complemented
177	C₂²⋊Dic₅₃	C₂³	1	2	yes	complemented
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	#11719921	C₂³	1	2	yes	complemented
189	#11719921	C₂³	1	2	yes	complemented
190	#11719921	C₂³	1	2	yes	complemented
191	#11719921	C₂³	1	2	yes	complemented
192	C₄⋊Dic₅₃	C₂³	1	2	yes	complemented
193	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic, complemented
194	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic, complemented
195	C₄⋊Dic₅₃	C₂³	1	2	yes	complemented
196	#11719919	C₂³	1	2	yes	complemented
197	#11719919	C₂³	1	2	yes	complemented
198	#11719919	C₂³	1	2	yes	complemented
199	#11719919	C₂³	1	2	yes	complemented
200	#11719919	C₂³	1	2	yes	complemented
201	#11719919	C₂³	1	2	yes	complemented
202	C₄×Dic₅₃	C₂³	1	2	yes	complemented
203	C₄×Dic₅₃	C₂³	1	2	yes	complemented
204	C₄×Dic₅₃	C₂³	1	2	yes	complemented
205	C₂³×C₅₃	—	2	2	no	—
206	C₂³×C₅₃	—	4	1	no	—
207	C₂³×C₅₃	—	4	1	no	—
208	C₂³×C₅₃	C₂⁴	1	2	yes	—
209	C₂³×C₅₃	C₂⁴	1	2	yes	—
210	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
211	C₂²×D₅₃	—	2	2	no	—
212	C₂²×D₅₃	—	2	2	no	—
213	C₂²×D₅₃	—	2	2	no	—
214	C₂²×D₅₃	—	2	4	no	—
215	C₂²×D₅₃	—	2	4	no	—
216	C₂²×D₅₃	—	2	4	no	—
217	C₂²×D₅₃	—	2	4	no	—
218	C₂²×D₅₃	—	2	4	no	—
219	C₂²×D₅₃	—	4	2	no	—
220	C₂²×D₅₃	—	4	2	no	—
221	C₂²×D₅₃	—	4	1	no	—
222	C₂²×D₅₃	—	4	1	no	—
223	C₂²×D₅₃	—	4	2	no	—
224	C₂²×D₅₃	—	4	2	no	—
225	C₂²×D₅₃	—	4	16	no	—
226	C₂²×D₅₃	#41	1	4	yes	complemented
227	C₂²×D₅₃	C₂⁴	1	2	yes	—
228	C₂²×D₅₃	C₂⁴	1	2	yes	—
229	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
230	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
231	Q₈×C₅₃	—	4	1	no	—
232	D₄×C₅₃	—	2	4	no	—
233	D₄×C₅₃	—	4	2	no	—
234	D₄×C₅₃	—	4	2	no	—
235	D₄×C₅₃	—	4	1	no	—
236	C₂×C₄×C₅₃	—	4	1	no	—
237	C₂×C₄×C₅₃	—	4	1	no	—
238	C₂×C₄×C₅₃	—	4	2	no	—
239	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
241	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
242	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
244	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
245	C₂²⋊D₅₃	—	2	4	no	—
246	C₂²⋊D₅₃	—	2	4	no	—
247	C₂²⋊D₅₃	—	2	4	no	—
248	C₂²⋊D₅₃	—	2	4	no	—
249	C₂²⋊D₅₃	—	4	2	no	—
250	C₂²⋊D₅₃	—	4	2	no	—
251	C₂²⋊D₅₃	—	4	2	no	—
252	C₂×Dic₅₃	—	4	1	no	—
253	C₂×Dic₅₃	—	4	1	no	—
254	C₂×Dic₅₃	—	4	2	no	—
255	C₂×Dic₅₃	C₂⁴	1	2	yes	—
256	C₂×Dic₅₃	C₂⁴	1	2	yes	—
257	C₂×Dic₅₃	C₂⁴	1	2	yes	—
258	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₅₃	C₂⁴	1	2	yes	—
261	D₂₁₂	—	2	4	no	—
262	D₂₁₂	—	2	4	no	—
263	D₂₁₂	—	2	4	no	—
264	D₂₁₂	—	4	1	no	—
265	C₄×D₅₃	—	2	4	no	—
266	C₄×D₅₃	—	2	4	no	—
267	C₄×D₅₃	—	2	2	no	—
268	C₄×D₅₃	—	2	2	no	—
269	C₄×D₅₃	—	4	2	no	—
270	C₄×D₅₃	—	4	1	no	—
271	C₄×D₅₃	—	4	1	no	—
272	C₄×D₅₃	—	4	2	no	—
273	C₄×D₅₃	—	4	2	no	—
274	C₄×D₅₃	—	4	2	no	—
275	C₄×D₅₃	—	4	2	no	—
276	Dic₁₀₆	—	4	2	no	—
277	Dic₁₀₆	—	4	1	no	—
278	C₂²×C₅₃	—	2	1	no	—
279	C₂²×C₅₃	—	2	1	no	—
280	C₂²×C₅₃	—	2	2	no	—
281	C₂²×C₅₃	—	2	2	no	—
282	C₂²×C₅₃	—	2	2	no	—
283	C₂²×C₅₃	—	2	2	no	—
284	C₂²×C₅₃	—	2	2	no	—
285	C₂²×C₅₃	—	2	2	no	—
286	C₂²×C₅₃	—	4	4	no	—
287	C₂²×C₅₃	C₂×#41	1	2	yes	—
288	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
289	C₂×D₅₃	—	2	8	no	—
290	C₂×D₅₃	—	2	1	no	—
291	C₂×D₅₃	—	2	1	no	—
292	C₂×D₅₃	—	2	1	no	—
293	C₂×D₅₃	—	2	1	no	—
294	C₂×D₅₃	—	2	2	no	—
295	C₂×D₅₃	—	2	2	no	—
296	C₂×D₅₃	—	2	2	no	—
297	C₂×D₅₃	—	2	2	no	—
298	C₂×D₅₃	—	2	2	no	—
299	C₂×D₅₃	—	4	4	no	—
300	C₂×D₅₃	—	4	8	no	—
301	C₂×D₅₃	—	4	8	no	—
302	C₂×D₅₃	—	8	4	no	—
303	C₂×D₅₃	C₂×#41	1	4	yes	—
304	C₂×D₅₃	H(5,𝔽₂)	1	2	yes	—
305	C₂×D₅₃	H(5,𝔽₂)	1	2	yes	—
306	C₄×C₅₃	—	2	2	no	—
307	C₄×C₅₃	—	2	1	no	—
308	C₄×C₅₃	—	2	2	no	—
309	C₄×C₅₃	—	2	2	no	—
310	C₄×C₅₃	—	2	1	no	—
311	C₄×C₅₃	—	2	2	no	—
312	Dic₅₃	—	2	2	no	—
313	Dic₅₃	—	2	2	no	—
314	Dic₅₃	—	2	2	no	—
315	Dic₅₃	—	2	2	no	—
316	Dic₅₃	—	2	1	no	—
317	Dic₅₃	—	2	1	no	—
318	#3490	—	53	1	no	maximal, Sylow
319	C₂×C₅₃	—	2	2	no	—
320	C₂×C₅₃	—	4	2	no	—
321	C₂×C₅₃	—	4	2	no	—
322	C₂×C₅₃	C₂²×#41	1	1	yes	characteristic
323	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
324	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
325	D₅₃	—	2	2	no	—
326	D₅₃	—	2	2	no	—
327	D₅₃	—	2	4	no	—
328	D₅₃	—	4	2	no	—
329	#551	—	53	2	no	—
330	#551	—	53	2	no	—
331	#551	—	53	2	no	—
332	#551	—	53	2	no	—
333	#546	—	53	2	no	—
334	#546	—	53	2	no	—
335	#546	—	53	2	no	—
336	#546	—	53	2	no	—
337	#543	—	53	1	no	—
338	#538	—	53	2	no	—
339	#538	—	53	1	no	—
340	#538	D₅₃	1	1	yes	characteristic, complemented
341	#534	—	53	1	no	—
342	#525	—	53	1	no	—
343	#525	—	53	1	no	—
344	#525	—	53	2	no	—
345	C₂×#120	—	53	2	no	—
346	#518	—	53	2	no	—
347	C₂²×C₂²⋊C₄	—	53	1	no	—
348	C₅₃	#3490	1	1	yes	characteristic, complemented, Sylow
349	C₂⁵	—	53	1	no	—
350	C₂×#41	—	53	1	no	—
351	C₂×#41	—	53	1	no	—
352	C₂×#41	—	53	2	no	—
353	C₂²×D₄	—	53	2	no	—
354	C₂²×D₄	—	53	2	no	—
355	C₂²×D₄	—	53	2	no	—
356	C₂³×C₄	—	53	1	no	—
357	C₂³×C₄	—	53	1	no	—
358	#126	—	53	2	no	—
359	#126	—	53	2	no	—
360	#126	—	53	2	no	—
361	#126	C₂×D₅₃	1	2	yes	complemented
362	#124	—	53	2	no	—
363	#124	—	53	2	no	—
364	#124	—	53	2	no	—
365	#124	C₂×D₅₃	1	2	yes	complemented
366	#123	—	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	C₂×D₅₃	1	2	yes	complemented
376	C₂²⋊Q₈	—	53	1	no	—
377	C₂²⋊Q₈	—	53	2	no	—
378	C₂²⋊Q₈	—	53	1	no	—
379	C₂²⋊Q₈	—	53	2	no	—
380	C₂²⋊Q₈	—	53	1	no	—
381	C₂²⋊Q₈	—	53	2	no	—
382	C₂²⋊Q₈	—	53	2	no	—
383	C₂²⋊Q₈	—	53	2	no	—
384	C₂²⋊Q₈	—	53	2	no	—
385	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
386	#121	—	53	2	no	—
387	#121	—	53	2	no	—
388	#121	—	53	2	no	—
389	#121	—	53	1	no	—
390	#121	—	53	1	no	—
391	#121	—	53	1	no	—
392	#121	—	53	2	no	—
393	#121	—	53	2	no	—
394	#121	C₂×D₅₃	1	2	yes	complemented
395	#121	C₂×D₅₃	1	1	yes	characteristic, complemented
396	#120	—	53	2	no	—
397	#120	—	53	2	no	—
398	#120	—	53	2	no	—
399	#120	—	53	2	no	—
400	#120	—	53	2	no	—
401	#120	—	53	2	no	—
402	#120	—	53	2	no	—
403	#120	—	53	2	no	—
404	#120	—	53	2	no	—
405	#120	C₂×D₅₃	1	2	yes	complemented
406	C₄×D₄	—	53	2	no	—
407	C₄×D₄	—	53	2	no	—
408	C₄×D₄	—	53	2	no	—
409	C₄×D₄	—	53	2	no	—
410	C₄×D₄	—	53	2	no	—
411	C₄×D₄	—	53	2	no	—
412	C₄×D₄	—	53	2	no	—
413	C₄×D₄	—	53	2	no	—
414	C₄×D₄	—	53	2	no	—
415	C₄×D₄	—	53	2	no	—
416	C₄×D₄	—	53	2	no	—
417	C₄×D₄	C₂×D₅₃	1	2	yes	complemented
418	#117	—	53	2	no	—
419	#117	—	53	1	no	—
420	#117	—	53	1	no	—
421	#117	—	53	2	no	—
422	#117	—	53	2	no	—
423	C₂×C₂²⋊C₄	—	53	1	no	—
424	C₂×C₂²⋊C₄	—	53	1	no	—
425	C₂×C₂²⋊C₄	—	53	1	no	—
426	C₂×C₂²⋊C₄	—	53	2	no	—
427	C₂×C₂²⋊C₄	—	53	2	no	—
428	C₂×C₂²⋊C₄	—	53	2	no	—
429	C₂×C₂²⋊C₄	—	53	2	no	—
430	C₂×C₂²⋊C₄	—	53	2	no	—
431	C₂×C₂²⋊C₄	—	53	2	no	—
432	C₂×C₂²⋊C₄	—	53	2	no	—
433	C₂×C₂²⋊C₄	—	53	2	no	—
434	C₂×C₂²⋊C₄	—	53	2	no	—
435	C₂×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
436	C₂⁴	—	53	1	no	—
437	C₂⁴	—	53	1	no	—
438	C₂⁴	—	53	2	no	—
439	C₂⁴	—	53	2	no	—
440	C₂⁴	—	53	2	no	—
441	C₂⁴	—	106	4	no	—
442	C₂⁴	—	212	2	no	—
443	C₂⁴	—	212	2	no	—
444	C₂⁴	C₂²×D₅₃	1	1	yes	characteristic
445	#41	—	212	4	no	—
446	#41	—	212	2	no	—
447	#41	—	212	2	no	—
448	C₂×Q₈	—	53	1	no	—
449	C₂×Q₈	—	53	2	no	—
450	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
451	C₂×D₄	—	53	2	no	—
452	C₂×D₄	—	53	2	no	—
453	C₂×D₄	—	53	2	no	—
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	2	no	—
459	C₂×D₄	—	53	2	no	—
460	C₂×D₄	—	53	2	no	—
461	C₂×D₄	—	53	1	no	—
462	C₂×D₄	—	106	8	no	—
463	C₂×D₄	—	212	4	no	—
464	C₂×D₄	—	212	4	no	—
465	C₂×D₄	C₂²×D₅₃	1	2	yes	—
466	C₂×D₄	C₂²×D₅₃	1	2	yes	—
467	C₂×D₄	C₂²×D₅₃	1	2	yes	—
468	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
469	C₂²×C₄	—	53	1	no	—
470	C₂²×C₄	—	53	1	no	—
471	C₂²×C₄	—	53	2	no	—
472	C₂²×C₄	—	53	2	no	—
473	C₂²×C₄	—	53	1	no	—
474	C₂²×C₄	—	53	1	no	—
475	C₂²×C₄	—	53	2	no	—
476	C₂²×C₄	—	53	1	no	—
477	C₂²×C₄	—	53	1	no	—
478	C₂²×C₄	—	53	2	no	—
479	C₂²×C₄	—	53	2	no	—
480	C₂²×C₄	—	53	2	no	—
481	C₂²×C₄	—	53	2	no	—
482	C₂²×C₄	—	53	2	no	—
483	C₂²×C₄	—	212	2	no	—
484	C₂²×C₄	—	212	2	no	—
485	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
486	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
487	C₂²×C₄	C₂²×D₅₃	1	2	yes	complemented
488	C₄⋊C₄	—	53	2	no	—
489	C₄⋊C₄	—	53	2	no	—
490	C₄⋊C₄	—	53	2	no	—
491	C₄⋊C₄	—	53	2	no	—
492	C₄⋊C₄	—	53	1	no	—
493	C₄⋊C₄	—	53	2	no	—
494	C₄⋊C₄	—	53	1	no	—
495	C₄⋊C₄	—	53	2	no	—
496	C₄⋊C₄	—	53	2	no	—
497	C₄⋊C₄	—	53	2	no	—
498	C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
499	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
500	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
501	C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
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	C₂²⋊C₄	—	53	2	no	—
514	C₂²⋊C₄	—	53	2	no	—
515	C₂²⋊C₄	—	53	2	no	—
516	C₂²⋊C₄	—	53	2	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	C₂²×D₅₃	1	2	yes	—
524	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
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	complemented
529	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	complemented
530	C₄²	—	53	2	no	—
531	C₄²	—	53	2	no	—
532	C₄²	—	53	2	no	—
533	C₄²	C₂²×D₅₃	1	2	yes	complemented
534	C₂³	—	2	2	no	—
535	C₂³	—	4	1	no	—
536	C₂³	—	4	1	no	—
537	C₂³	—	53	2	no	—
538	C₂³	—	53	1	no	—
539	C₂³	—	53	1	no	—
540	C₂³	—	53	4	no	—
541	C₂³	—	53	2	no	—
542	C₂³	—	106	2	no	—
543	C₂³	—	106	2	no	—
544	C₂³	—	106	4	no	—
545	C₂³	—	106	4	no	—
546	C₂³	—	106	4	no	—
547	C₂³	—	106	4	no	—
548	C₂³	—	106	4	no	—
549	C₂³	—	106	2	no	—
550	C₂³	—	212	2	no	—
551	C₂³	—	212	2	no	—
552	C₂³	—	212	1	no	—
553	C₂³	—	212	1	no	—
554	C₂³	—	212	2	no	—
555	C₂³	—	212	2	no	—
556	C₂³	—	212	16	no	—
557	C₂³	C₂³×D₅₃	1	2	yes	—
558	C₂³	C₂³×D₅₃	1	2	yes	—
559	C₂³	C₂³×D₅₃	1	1	yes	characteristic
560	Q₈	—	4	1	no	—
561	Q₈	—	212	1	no	—
562	Q₈	—	212	2	no	—
563	D₄	—	2	4	no	—
564	D₄	—	4	2	no	—
565	D₄	—	4	2	no	—
566	D₄	—	4	1	no	—
567	D₄	—	106	4	no	—
568	D₄	—	106	4	no	—
569	D₄	—	106	4	no	—
570	D₄	—	106	4	no	—
571	D₄	—	106	4	no	—
572	D₄	—	106	4	no	—
573	D₄	—	106	4	no	—
574	D₄	—	212	1	no	—
575	D₄	—	212	2	no	—
576	D₄	—	212	2	no	—
577	D₄	—	212	2	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	53	2	no	—
582	C₂×C₄	—	53	1	no	—
583	C₂×C₄	—	53	1	no	—
584	C₂×C₄	—	53	2	no	—
585	C₂×C₄	—	53	2	no	—
586	C₂×C₄	—	53	2	no	—
587	C₂×C₄	—	106	4	no	—
588	C₂×C₄	—	106	2	no	—
589	C₂×C₄	—	106	2	no	—
590	C₂×C₄	—	106	4	no	—
591	C₂×C₄	—	212	2	no	—
592	C₂×C₄	—	212	1	no	—
593	C₂×C₄	—	212	1	no	—
594	C₂×C₄	—	212	2	no	—
595	C₂×C₄	—	212	2	no	—
596	C₂×C₄	—	212	2	no	—
597	C₂×C₄	—	212	2	no	—
598	C₂×C₄	—	212	1	no	—
599	C₂×C₄	—	212	1	no	—
600	C₂×C₄	—	212	2	no	—
601	C₂×C₄	C₂³×D₅₃	1	2	yes	—
602	C₂×C₄	C₂³×D₅₃	1	2	yes	—
603	C₂×C₄	C₂³×D₅₃	1	2	yes	—
604	C₂×C₄	C₂³×D₅₃	1	2	yes	—
605	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
606	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
607	C₂²	—	2	1	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	2	2	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	4	4	no	—
616	C₂²	—	53	4	no	—
617	C₂²	—	53	2	no	—
618	C₂²	—	53	2	no	—
619	C₂²	—	106	8	no	—
620	C₂²	—	106	1	no	—
621	C₂²	—	106	1	no	—
622	C₂²	—	106	1	no	—
623	C₂²	—	106	1	no	—
624	C₂²	—	106	2	no	—
625	C₂²	—	106	2	no	—
626	C₂²	—	106	2	no	—
627	C₂²	—	106	2	no	—
628	C₂²	—	106	2	no	—
629	C₂²	—	424	4	no	—
630	C₂²	—	212	4	no	—
631	C₂²	—	212	8	no	—
632	C₂²	—	212	8	no	—
633	C₂²	#41×D₅₃	1	2	yes	—
634	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
635	C₄	—	2	2	no	—
636	C₄	—	2	2	no	—
637	C₄	—	2	1	no	—
638	C₄	—	2	1	no	—
639	C₄	—	2	2	no	—
640	C₄	—	2	2	no	—
641	C₄	—	106	2	no	—
642	C₄	—	106	1	no	—
643	C₄	—	106	1	no	—
644	C₄	—	106	2	no	—
645	C₄	—	106	2	no	—
646	C₄	—	106	2	no	—
647	C₂	—	2	2	no	—
648	C₂	—	4	2	no	—
649	C₂	—	4	2	no	—
650	C₂	—	106	2	no	—
651	C₂	—	106	2	no	—
652	C₂	—	106	4	no	—
653	C₂	—	212	2	no	—
654	C₂	C₂×#41×D₅₃	1	1	yes	characteristic
655	C₂	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
656	C₂	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#538	C₂
hypercenter	#538	D₅₃
hypocenter	C₅₃	#3490
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #538

Complements

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

N	H ≅ G/N	type
1. #16811303	C₂	semidirect
2. #16811301	C₂	semidirect
3. #16811298	C₂	semidirect
4. #16811298	C₂	semidirect
5. #16811270	C₂	semidirect
6. #16811266	C₂	semidirect
7. #16811265	C₂	semidirect
8. #16811262	C₂	semidirect
9. #16811248	C₂	semidirect
10. #16811211	C₂	semidirect
11. #16811208	C₂	semidirect
12. #16811181	C₂	semidirect
13. #16811136	C₂	semidirect
14. #16811133	C₂	semidirect
15. #16811132	C₂	semidirect
16. #120×D₅₃	C₂	semidirect
17. #16811095	C₂	semidirect
18. C₂×C₂²⋊C₄×D₅₃	C₂	semidirect
19. C₅₃×#538	C₂	semidirect
21. C₂×#11719949	C₂²	semidirect
22. C₂×#11719945	C₂²	semidirect
23. C₂×#11719947	C₂²	semidirect
25. C₂×D₄×D₅₃	C₂²	semidirect
26. C₂×D₄×D₅₃	C₂²	semidirect
27. C₂²×C₄×D₅₃	C₂²	semidirect
28. C₂²×C₄×D₅₃	C₂²	semidirect
29. #13133210	C₂²	semidirect
30. #13133210	C₂²	semidirect
31. #13133210	C₂²	semidirect
32. #13133204	C₂²	semidirect
33. #13133203	C₂²	semidirect
34. #13133203	C₂²	semidirect
35. #13133202	C₂²	semidirect
36. #13133202	C₂²	semidirect
37. #13133202	C₂²	semidirect
38. #13133199	C₂²	semidirect
39. #13133199	C₂²	semidirect
40. #13133199	C₂²	semidirect
41. #13133199	C₂²	semidirect
42. #13133199	C₂²	semidirect
43. #13133198	C₂²	semidirect
44. #13133197	C₂²	semidirect
45. #13133197	C₂²	semidirect
46. #13133196	C₂²	semidirect
47. #13133195	C₂²	semidirect
48. #13133195	C₂²	semidirect
49. #13133195	C₂²	semidirect
50. #13133194	C₂²	semidirect
51. #13133193	C₂²	semidirect
52. #13133193	C₂²	semidirect
53. #13133192	C₂²	semidirect
54. #13133191	C₂²	semidirect
55. #13133190	C₂²	semidirect
56. #13133190	C₂²	semidirect
57. #13133189	C₂²	semidirect
58. #13133189	C₂²	semidirect
59. #13133188	C₂²	semidirect
60. #13133188	C₂²	semidirect
63. #13133187	C₂²	semidirect
64. #13133187	C₂²	semidirect
65. #13133186	C₂²	semidirect
68. #13133185	C₂²	semidirect
69. #13133185	C₂²	semidirect
70. C₄×D₂₁₂	C₂²	semidirect
71. C₄×D₂₁₂	C₂²	semidirect
72. D₄×Dic₅₃	C₂²	semidirect
73. #13133179	C₂²	semidirect
74. #13133179	C₂²	semidirect
75. C₄×C₂²⋊D₅₃	C₂²	semidirect
76. C₄×C₂²⋊D₅₃	C₂²	semidirect
77. C₄×C₂²⋊D₅₃	C₂²	semidirect
78. #13133177	C₂²	semidirect
79. #13133177	C₂²	semidirect
80. #13133177	C₂²	semidirect
81. #13133175	C₂²	semidirect
82. #13133175	C₂²	semidirect
83. #13133175	C₂²	semidirect
84. #13133174	C₂²	semidirect
85. #13133174	C₂²	semidirect
86. C₂×C₂²⋊Dic₅₃	C₂²	semidirect
89. C₂×#11719921	C₂²	semidirect
91. C₂²⋊C₄×D₅₃	C₂²	semidirect
92. C₂²⋊C₄×D₅₃	C₂²	semidirect
93. C₂²⋊C₄×D₅₃	C₂²	semidirect
94. C₂²⋊C₄×D₅₃	C₂²	semidirect
95. C₂²⋊C₄×D₅₃	C₂²	semidirect
96. C₂²⋊C₄×D₅₃	C₂²	semidirect
97. C₂²⋊C₄×D₅₃	C₂²	semidirect
98. #126×C₅₃	C₂²	semidirect
99. #124×C₅₃	C₂²	semidirect
100. #123×C₅₃	C₂²	semidirect
101. C₂²⋊Q₈×C₅₃	C₂²	semidirect
102. #121×C₅₃	C₂²	semidirect
103. #121×C₅₃	C₂²	semidirect
104. #120×C₅₃	C₂²	semidirect
105. C₄×D₄×C₅₃	C₂²	semidirect
106. C₂×C₂²⋊C₄×C₅₃	C₂²	semidirect
116. C₂×Q₈×C₅₃	C₂³	semidirect
120. C₂×D₄×C₅₃	C₂³	semidirect
123. C₂²×C₄×C₅₃	C₂³	semidirect
130. C₂×C₂²⋊D₅₃	C₂³	semidirect
133. C₂²×Dic₅₃	C₂³	semidirect
143. C₂×D₂₁₂	C₂³	semidirect
155. C₂×C₄×D₅₃	C₂³	semidirect
156. C₂×C₄×D₅₃	C₂³	semidirect
157. C₂×Dic₁₀₆	C₂³	semidirect
158. C₂×Dic₁₀₆	C₂³	semidirect
159. C₄⋊C₄×C₅₃	C₂³	semidirect
160. C₄⋊C₄×C₅₃	C₂³	semidirect
161. C₄⋊C₄×C₅₃	C₂³	semidirect
162. C₄⋊C₄×C₅₃	C₂³	semidirect
168. C₂²⋊C₄×C₅₃	C₂³	semidirect
169. C₂²⋊C₄×C₅₃	C₂³	semidirect
170. C₄²×C₅₃	C₂³	semidirect
176. C₂²⋊Dic₅₃	C₂³	semidirect
177. C₂²⋊Dic₅₃	C₂³	semidirect
188. #11719921	C₂³	semidirect
189. #11719921	C₂³	semidirect
190. #11719921	C₂³	semidirect
191. #11719921	C₂³	semidirect
192. C₄⋊Dic₅₃	C₂³	semidirect
193. C₄⋊Dic₅₃	C₂³	semidirect
194. C₄⋊Dic₅₃	C₂³	semidirect
195. C₄⋊Dic₅₃	C₂³	semidirect
196. #11719919	C₂³	semidirect
197. #11719919	C₂³	semidirect
198. #11719919	C₂³	semidirect
199. #11719919	C₂³	semidirect
200. #11719919	C₂³	semidirect
201. #11719919	C₂³	semidirect
202. C₄×Dic₅₃	C₂³	semidirect
203. C₄×Dic₅₃	C₂³	semidirect
204. C₄×Dic₅₃	C₂³	semidirect
226. C₂²×D₅₃	#41	semidirect
340. #538	D₅₃	semidirect
348. C₅₃	#3490	semidirect
361. #126	C₂×D₅₃	semidirect
365. #124	C₂×D₅₃	semidirect
375. #123	C₂×D₅₃	semidirect
385. C₂²⋊Q₈	C₂×D₅₃	semidirect
394. #121	C₂×D₅₃	semidirect
395. #121	C₂×D₅₃	semidirect
405. #120	C₂×D₅₃	semidirect
417. C₄×D₄	C₂×D₅₃	semidirect
435. C₂×C₂²⋊C₄	C₂×D₅₃	semidirect
450. C₂×Q₈	C₂²×D₅₃	semidirect
468. C₂×D₄	C₂²×D₅₃	semidirect
487. C₂²×C₄	C₂²×D₅₃	semidirect
498. C₄⋊C₄	C₂²×D₅₃	semidirect
499. C₄⋊C₄	C₂²×D₅₃	semidirect
500. C₄⋊C₄	C₂²×D₅₃	semidirect
501. C₄⋊C₄	C₂²×D₅₃	semidirect
528. C₂²⋊C₄	C₂²×D₅₃	semidirect
529. C₂²⋊C₄	C₂²×D₅₃	semidirect
533. C₄²	C₂²×D₅₃	semidirect