Subgroups — #20288271

Order 6784.

1132 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	#16811342	C₂	1	1	yes	maximal, characteristic, complemented
2	#16811337	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811329	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811318	C₂	1	2	yes	maximal, complemented
5	#16811311	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811309	C₂	1	2	yes	maximal, complemented
7	#16811307	C₂	1	1	yes	maximal, characteristic, complemented
8	#16811301	C₂	1	2	yes	maximal, complemented
9	#16811298	C₂	1	2	yes	maximal, complemented
10	#16811275	C₂	1	1	yes	maximal, characteristic, complemented
11	#16811270	C₂	1	1	yes	maximal, characteristic, complemented
12	#16811266	C₂	1	1	yes	maximal, characteristic, complemented
13	#16811177	C₂	1	1	yes	maximal, characteristic, complemented
14	#16811155	C₂	1	1	yes	maximal, characteristic, complemented
15	#16811155	C₂	1	2	yes	maximal, complemented
16	#16811151	C₂	1	2	yes	maximal, complemented
17	#16811132	C₂	1	2	yes	maximal, complemented
18	C₄×#11719949	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#11719945	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#11719945	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
22	#117×D₅₃	C₂	1	2	yes	maximal, complemented
23	C₅₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11719949	C₂²	1	1	yes	characteristic
25	C₂×#11719945	C₂²	1	1	yes	characteristic
26	C₂×#11719945	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₅₃	C₂²	1	2	yes	—
29	#13133216	C₂²	1	1	yes	characteristic, complemented
30	#13133215	C₂²	1	1	yes	characteristic, complemented
31	#13133212	C₂²	1	2	yes	complemented
32	#13133210	C₂²	1	2	yes	complemented
33	#13133210	C₂²	1	2	yes	complemented
34	#13133210	C₂²	1	2	yes	complemented
35	#13133210	C₂²	1	2	yes	complemented
36	#13133208	C₂²	1	1	yes	characteristic, complemented
37	#13133208	C₂²	1	2	yes	complemented
38	#13133207	C₂²	1	2	yes	complemented
39	#13133207	C₂²	1	2	yes	complemented
40	#13133204	C₂²	1	1	yes	characteristic
41	#13133204	C₂²	1	2	yes	complemented
42	#13133203	C₂²	1	2	yes	complemented
43	#13133202	C₂²	1	2	yes	—
44	#13133202	C₂²	1	2	yes	complemented
45	#13133199	C₂²	1	2	yes	—
46	#13133199	C₂²	1	2	yes	—
47	#13133199	C₂²	1	2	yes	—
48	#13133199	C₂²	1	2	yes	complemented
49	#13133199	C₂²	1	2	yes	complemented
50	#13133197	C₂²	1	1	yes	characteristic
51	#13133197	C₂²	1	1	yes	characteristic, complemented
52	#13133197	C₂²	1	2	yes	complemented
53	#13133195	C₂²	1	2	yes	—
54	#13133195	C₂²	1	2	yes	complemented
55	#13133195	C₂²	1	2	yes	complemented
56	#13133194	C₂²	1	2	yes	complemented
57	#13133193	C₂²	1	1	yes	characteristic
58	#13133190	C₂²	1	2	yes	—
59	#13133190	C₂²	1	2	yes	complemented
60	#13133189	C₂²	1	2	yes	complemented
61	#13133188	C₂²	1	1	yes	characteristic
62	#13133188	C₂²	1	2	yes	—
63	#13133187	C₂²	1	2	yes	—
64	#13133185	C₂²	1	2	yes	—
65	Q₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
66	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
67	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
68	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
69	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
70	C₄×Dic₁₀₆	C₂²	1	2	yes	complemented
71	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
72	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
73	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
74	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
75	C₄×D₂₁₂	C₂²	1	2	yes	complemented
76	D₄×Dic₅₃	C₂²	1	1	yes	characteristic
77	#13133179	C₂²	1	1	yes	characteristic
78	#13133179	C₂²	1	1	yes	characteristic
79	#13133179	C₂²	1	2	yes	complemented
80	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
81	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
82	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	—
83	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
84	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
85	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
86	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
87	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
88	#13133177	C₂²	1	2	yes	—
89	#13133176	C₂²	1	1	yes	characteristic, complemented
90	#13133176	C₂²	1	2	yes	complemented
91	#13133176	C₂²	1	1	yes	characteristic, complemented
92	#13133175	C₂²	1	2	yes	—
93	#13133175	C₂²	1	2	yes	—
94	#13133175	C₂²	1	2	yes	complemented
95	#13133175	C₂²	1	1	yes	characteristic, complemented
96	#13133174	C₂²	1	1	yes	characteristic
97	#13133174	C₂²	1	2	yes	—
98	#13133174	C₂²	1	2	yes	complemented
99	#13133174	C₂²	1	1	yes	characteristic, complemented
100	#13133173	C₂²	1	2	yes	complemented
101	#13133173	C₂²	1	2	yes	complemented
102	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
103	C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
104	C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
105	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
106	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
107	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
108	C₄²×D₅₃	C₂²	1	1	yes	characteristic
109	C₄²×D₅₃	C₂²	1	2	yes	complemented
110	C₄²×D₅₃	C₂²	1	2	yes	complemented
111	C₄²×D₅₃	C₂²	1	1	yes	characteristic, complemented
112	#126×C₅₃	C₂²	1	2	yes	complemented
113	#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
114	#124×C₅₃	C₂²	1	1	yes	characteristic
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
118	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
120	C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
121	#117×C₅₃	C₂²	1	2	yes	complemented
122	C₂×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₅₃	C₂³	1	2	yes	—
124	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₅₃	C₂³	1	2	yes	—
127	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
130	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
136	C₂²×Dic₅₃	C₂³	1	2	yes	—
137	#11719949	—	2	4	no	—
138	D₄×D₅₃	—	2	4	no	—
139	#11719945	—	2	4	no	—
140	#11719945	—	2	4	no	—
141	C₂×D₂₁₂	C₂³	1	2	yes	—
142	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
143	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₅₃	—	2	8	no	—
145	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
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×C₄×D₅₃	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₅₃	C₂³	1	2	yes	—
152	C₂×C₄×D₅₃	C₂³	1	2	yes	—
153	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₅₃	C₂³	1	2	yes	—
155	C₂×C₄×D₅₃	C₂³	1	2	yes	—
156	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
158	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
159	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
160	C₂×Dic₁₀₆	C₂³	1	2	yes	—
161	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
162	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
163	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
164	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
165	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
166	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
167	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
168	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
169	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
170	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
171	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
172	C₄²×C₅₃	C₂³	1	1	yes	characteristic
173	C₄²×C₅₃	C₂³	1	1	yes	characteristic
174	C₄²×C₅₃	C₂³	1	1	yes	characteristic
175	C₄²×C₅₃	C₂³	1	1	yes	characteristic
176	C₄²×C₅₃	C₂³	1	2	yes	—
177	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
178	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
179	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
180	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
183	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
184	#11719921	C₂³	1	1	yes	characteristic
185	#11719921	C₂³	1	1	yes	characteristic
186	#11719921	C₂³	1	2	yes	—
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	1	yes	characteristic
192	#11719921	C₂³	1	1	yes	characteristic
193	#11719921	C₂³	1	2	yes	—
194	#11719921	C₂³	1	2	yes	—
195	#11719921	C₂³	1	2	yes	—
196	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
197	C₄⋊Dic₅₃	C₂³	1	2	yes	—
198	C₄⋊Dic₅₃	C₂³	1	2	yes	—
199	C₄⋊Dic₅₃	C₂³	1	2	yes	—
200	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
202	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
203	C₄⋊Dic₅₃	C₂³	1	2	yes	—
204	#11719919	C₂³	1	2	yes	—
205	#11719919	C₂³	1	1	yes	characteristic
206	#11719919	C₂³	1	1	yes	characteristic
207	#11719919	C₂³	1	2	yes	—
208	#11719919	C₂³	1	2	yes	—
209	#11719919	C₂³	1	1	yes	characteristic
210	#11719919	C₂³	1	1	yes	characteristic
211	#11719919	C₂³	1	2	yes	—
212	#11719919	C₂³	1	2	yes	—
213	#11719919	C₂³	1	2	yes	—
214	#11719919	C₂³	1	2	yes	—
215	#11719919	C₂³	1	2	yes	—
216	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
217	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
218	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
219	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
220	C₄×Dic₅₃	C₂³	1	2	yes	—
221	C₄×Dic₅₃	C₂³	1	2	yes	—
222	C₄×Dic₅₃	C₂³	1	2	yes	—
223	C₄×Dic₅₃	C₂³	1	2	yes	—
224	C₄×Dic₅₃	C₂³	1	2	yes	—
225	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
226	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
227	C₂³×C₅₃	C₂⁴	1	2	yes	—
228	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
229	C₂²×D₅₃	—	2	4	no	—
230	C₂²×D₅₃	—	2	4	no	—
231	C₂²×D₅₃	—	4	2	no	—
232	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
233	C₂²×D₅₃	C₂⁴	1	2	yes	—
234	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
235	Q₈×C₅₃	—	2	2	no	—
236	D₄×C₅₃	—	2	2	no	—
237	D₄×C₅₃	—	4	2	no	—
238	C₂×C₄×C₅₃	—	2	4	no	—
239	C₂×C₄×C₅₃	—	2	2	no	—
240	C₂×C₄×C₅₃	—	2	2	no	—
241	C₂×C₄×C₅₃	—	4	1	no	—
242	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
243	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
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	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
248	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
249	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
251	C₂²⋊D₅₃	—	2	2	no	—
252	C₂²⋊D₅₃	—	2	4	no	—
253	C₂²⋊D₅₃	—	2	4	no	—
254	C₂²⋊D₅₃	—	2	2	no	—
255	C₂²⋊D₅₃	—	4	2	no	—
256	C₂×Dic₅₃	—	2	4	no	—
257	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₅₃	C₂⁴	1	2	yes	—
260	C₂×Dic₅₃	C₂⁴	1	2	yes	—
261	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₅₃	C₂⁴	1	2	yes	—
264	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
266	D₂₁₂	—	2	2	no	—
267	D₂₁₂	—	2	4	no	—
268	D₂₁₂	#41	1	4	yes	complemented
269	C₄×D₅₃	—	2	4	no	—
270	C₄×D₅₃	—	2	4	no	—
271	C₄×D₅₃	—	2	4	no	—
272	C₄×D₅₃	—	2	4	no	—
273	C₄×D₅₃	—	2	2	no	—
274	C₄×D₅₃	—	2	2	no	—
275	C₄×D₅₃	—	2	2	no	—
276	C₄×D₅₃	—	2	4	no	—
277	C₄×D₅₃	—	4	1	no	—
278	C₄×D₅₃	—	4	2	no	—
279	C₄×D₅₃	—	4	2	no	—
280	C₄×D₅₃	—	4	1	no	—
281	C₄×D₅₃	#41	1	4	yes	complemented
282	Dic₁₀₆	—	2	2	no	—
283	Dic₁₀₆	—	2	2	no	—
284	Dic₁₀₆	—	4	2	no	—
285	C₂²×C₅₃	—	2	2	no	—
286	C₂²×C₅₃	—	2	1	no	—
287	C₂²×C₅₃	—	2	1	no	—
288	C₂²×C₅₃	—	2	2	no	—
289	C₂²×C₅₃	—	2	2	no	—
290	C₂²×C₅₃	—	2	1	no	—
291	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
292	C₂×D₅₃	—	2	2	no	—
293	C₂×D₅₃	—	2	1	no	—
294	C₂×D₅₃	—	2	2	no	—
295	C₂×D₅₃	—	2	1	no	—
296	C₂×D₅₃	—	2	1	no	—
297	C₂×D₅₃	—	2	1	no	—
298	C₂×D₅₃	—	2	1	no	—
299	C₂×D₅₃	—	4	8	no	—
300	C₂×D₅₃	C₂×#41	1	2	yes	—
301	C₂×D₅₃	C₂×#41	1	4	yes	—
302	C₄×C₅₃	—	2	1	no	—
303	C₄×C₅₃	—	2	1	no	—
304	C₄×C₅₃	—	2	2	no	—
305	C₄×C₅₃	—	2	2	no	—
306	C₄×C₅₃	—	2	2	no	—
307	C₄×C₅₃	—	2	1	no	—
308	C₄×C₅₃	—	2	1	no	—
309	C₄×C₅₃	C₂×#41	1	2	yes	—
310	C₄×C₅₃	C₂×#41	1	2	yes	—
311	Dic₅₃	—	2	2	no	—
312	Dic₅₃	—	2	1	no	—
313	Dic₅₃	—	2	1	no	—
314	Dic₅₃	—	2	2	no	—
315	Dic₅₃	—	2	1	no	—
316	Dic₅₃	—	2	1	no	—
317	Dic₅₃	—	2	2	no	—
318	Dic₅₃	—	2	1	no	—
319	Dic₅₃	C₂×#41	1	2	yes	—
320	#3475	—	53	1	no	maximal, Sylow
321	C₂×C₅₃	—	4	2	no	—
322	C₂×C₅₃	—	4	1	no	—
323	C₂×C₅₃	C₂²×#41	1	1	yes	characteristic
324	C₂×C₅₃	C₂²×#41	1	1	yes	characteristic
325	C₂×C₅₃	#585	1	1	yes	characteristic
326	D₅₃	—	2	2	no	—
327	D₅₃	—	2	4	no	—
328	D₅₃	—	4	1	no	—
329	#556	—	53	1	no	—
330	#555	—	53	1	no	—
331	#554	—	53	1	no	—
332	#553	—	53	2	no	—
333	#552	—	53	2	no	—
334	#552	—	53	1	no	—
335	#552	—	53	1	no	—
336	#551	—	53	2	no	—
337	#551	—	53	2	no	—
338	#547	—	53	1	no	—
339	#546	—	53	1	no	—
340	#546	—	53	1	no	—
341	#533	—	53	1	no	—
342	#529	—	53	1	no	—
343	#529	—	53	2	no	—
344	#529	—	53	2	no	—
345	#529	D₅₃	1	1	yes	characteristic, complemented
346	#525	—	53	2	no	—
347	C₄×#41	—	53	1	no	—
348	C₄×#41	—	53	1	no	—
349	C₄×#41	—	53	1	no	—
350	C₂×C₄×D₄	—	53	1	no	—
351	C₂×#117	—	53	2	no	—
352	C₅₃	#3475	1	1	yes	characteristic, complemented, Sylow
353	C₂×#41	—	53	1	no	—
354	C₂×#41	—	53	1	no	—
355	C₂×#41	—	53	1	no	—
356	C₂²×D₄	—	53	1	no	—
357	C₂³×C₄	—	53	2	no	—
358	C₄⋊Q₈	—	53	1	no	—
359	C₄⋊Q₈	—	53	1	no	—
360	#126	—	53	2	no	—
361	#126	—	53	2	no	—
362	#126	—	53	2	no	—
363	#126	—	53	2	no	—
364	#126	—	53	2	no	—
365	#126	C₂×D₅₃	1	2	yes	complemented
366	#125	—	53	2	no	—
367	#125	—	53	2	no	—
368	#125	—	53	1	no	—
369	#125	—	53	2	no	—
370	#125	C₂×D₅₃	1	1	yes	characteristic, complemented
371	#124	—	53	1	no	—
372	#124	—	53	2	no	—
373	#124	—	53	2	no	—
374	#124	C₂×D₅₃	1	1	yes	characteristic
375	#123	—	53	2	no	—
376	#123	—	53	2	no	—
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	C₂×D₅₃	1	2	yes	complemented
383	C₂²⋊Q₈	—	53	1	no	—
384	C₂²⋊Q₈	—	53	2	no	—
385	C₂²⋊Q₈	—	53	1	no	—
386	C₂²⋊Q₈	—	53	2	no	—
387	C₂²⋊Q₈	—	53	2	no	—
388	C₂²⋊Q₈	—	53	1	no	—
389	C₂²⋊Q₈	—	53	2	no	—
390	C₂²⋊Q₈	—	53	2	no	—
391	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
392	#121	—	53	2	no	—
393	#121	—	53	2	no	—
394	#121	—	53	1	no	—
395	#121	—	53	2	no	—
396	#121	—	53	2	no	—
397	#121	C₂×D₅₃	1	1	yes	characteristic
398	#120	—	53	2	no	—
399	#120	—	53	2	no	—
400	C₄×Q₈	—	53	1	no	—
401	C₄×Q₈	—	53	1	no	—
402	C₄×Q₈	—	53	1	no	—
403	C₄×Q₈	—	53	1	no	—
404	C₄×Q₈	—	53	1	no	—
405	C₄×Q₈	—	53	2	no	—
406	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
407	C₄×D₄	—	53	1	no	—
408	C₄×D₄	—	53	2	no	—
409	C₄×D₄	—	53	2	no	—
410	C₄×D₄	—	53	1	no	—
411	C₄×D₄	—	53	1	no	—
412	C₄×D₄	—	53	1	no	—
413	C₄×D₄	—	53	2	no	—
414	C₄×D₄	—	53	1	no	—
415	C₄×D₄	—	53	2	no	—
416	C₄×D₄	—	53	1	no	—
417	C₄×D₄	—	53	1	no	—
418	C₄×D₄	—	53	2	no	—
419	C₄×D₄	—	53	2	no	—
420	C₄×D₄	—	53	1	no	—
421	C₄×D₄	—	53	2	no	—
422	C₄×D₄	—	53	1	no	—
423	C₄×D₄	—	53	1	no	—
424	C₄×D₄	—	53	1	no	—
425	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
426	C₄×D₄	C₂×D₅₃	1	2	yes	complemented
427	#117	—	53	2	no	—
428	#117	—	53	1	no	—
429	#117	—	53	1	no	—
430	#117	—	53	2	no	—
431	#117	—	53	2	no	—
432	#117	—	53	2	no	—
433	#117	—	53	1	no	—
434	#117	—	53	2	no	—
435	#117	—	53	2	no	—
436	#117	—	53	1	no	—
437	#117	—	53	2	no	—
438	#117	—	53	1	no	—
439	#117	—	53	2	no	—
440	#117	C₂×D₅₃	1	2	yes	complemented
441	C₂×C₄⋊C₄	—	53	2	no	—
442	C₂×C₄⋊C₄	—	53	2	no	—
443	C₂×C₄⋊C₄	—	53	1	no	—
444	C₂×C₂²⋊C₄	—	53	2	no	—
445	C₂×C₂²⋊C₄	—	53	2	no	—
446	C₂×C₂²⋊C₄	—	53	2	no	—
447	C₂×C₄²	—	53	2	no	—
448	C₂×C₄²	—	53	2	no	—
449	C₂×C₄²	—	53	1	no	—
450	C₂×C₄²	—	53	1	no	—
451	C₂×C₄²	C₂×D₅₃	1	1	yes	characteristic, complemented
452	C₂⁴	—	53	2	no	—
453	#41	—	106	4	no	—
454	#41	—	106	4	no	—
455	#41	—	106	4	no	—
456	C₂×Q₈	—	53	1	no	—
457	C₂×Q₈	—	53	1	no	—
458	C₂×Q₈	—	53	2	no	—
459	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
460	C₂×D₄	—	53	1	no	—
461	C₂×D₄	—	53	2	no	—
462	C₂×D₄	—	53	1	no	—
463	C₂×D₄	—	53	2	no	—
464	C₂×D₄	—	53	2	no	—
465	C₂×D₄	—	53	1	no	—
466	C₂×D₄	—	53	1	no	—
467	C₂×D₄	—	53	2	no	—
468	C₂×D₄	—	106	4	no	—
469	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
470	C₂×D₄	C₂²×D₅₃	1	2	yes	—
471	C₂²×C₄	—	53	1	no	—
472	C₂²×C₄	—	53	2	no	—
473	C₂²×C₄	—	53	2	no	—
474	C₂²×C₄	—	53	2	no	—
475	C₂²×C₄	—	53	1	no	—
476	C₂²×C₄	—	53	1	no	—
477	C₂²×C₄	—	53	2	no	—
478	C₂²×C₄	—	53	2	no	—
479	C₂²×C₄	—	53	2	no	—
480	C₂²×C₄	—	53	1	no	—
481	C₂²×C₄	—	53	1	no	—
482	C₂²×C₄	—	53	2	no	—
483	C₂²×C₄	—	53	2	no	—
484	C₂²×C₄	—	53	1	no	—
485	C₂²×C₄	—	106	8	no	—
486	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
487	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
488	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
489	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
490	C₄⋊C₄	—	53	1	no	—
491	C₄⋊C₄	—	53	1	no	—
492	C₄⋊C₄	—	53	1	no	—
493	C₄⋊C₄	—	53	2	no	—
494	C₄⋊C₄	—	53	2	no	—
495	C₄⋊C₄	—	53	2	no	—
496	C₄⋊C₄	—	53	2	no	—
497	C₄⋊C₄	—	53	2	no	—
498	C₄⋊C₄	—	53	1	no	—
499	C₄⋊C₄	—	53	1	no	—
500	C₄⋊C₄	—	53	1	no	—
501	C₄⋊C₄	—	53	2	no	—
502	C₄⋊C₄	—	53	2	no	—
503	C₄⋊C₄	—	53	2	no	—
504	C₄⋊C₄	—	53	1	no	—
505	C₄⋊C₄	—	53	1	no	—
506	C₄⋊C₄	—	53	2	no	—
507	C₄⋊C₄	—	53	2	no	—
508	C₄⋊C₄	—	53	2	no	—
509	C₄⋊C₄	—	53	2	no	—
510	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
511	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
512	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
513	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
514	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
515	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
516	C₂²⋊C₄	—	53	2	no	—
517	C₂²⋊C₄	—	53	2	no	—
518	C₂²⋊C₄	—	53	2	no	—
519	C₂²⋊C₄	—	53	1	no	—
520	C₂²⋊C₄	—	53	2	no	—
521	C₂²⋊C₄	—	53	1	no	—
522	C₂²⋊C₄	—	53	2	no	—
523	C₂²⋊C₄	—	53	1	no	—
524	C₂²⋊C₄	—	53	1	no	—
525	C₂²⋊C₄	—	53	2	no	—
526	C₂²⋊C₄	—	53	2	no	—
527	C₂²⋊C₄	—	53	2	no	—
528	C₂²⋊C₄	—	53	2	no	—
529	C₂²⋊C₄	—	53	2	no	—
530	C₂²⋊C₄	—	53	2	no	—
531	C₂²⋊C₄	—	53	1	no	—
532	C₂²⋊C₄	—	53	2	no	—
533	C₂²⋊C₄	—	53	1	no	—
534	C₂²⋊C₄	—	53	2	no	—
535	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
536	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
537	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
538	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
539	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
540	C₄²	—	53	2	no	—
541	C₄²	—	53	2	no	—
542	C₄²	—	53	2	no	—
543	C₄²	—	53	2	no	—
544	C₄²	—	53	1	no	—
545	C₄²	—	53	1	no	—
546	C₄²	—	53	1	no	—
547	C₄²	—	53	1	no	—
548	C₄²	—	53	1	no	—
549	C₄²	—	53	1	no	—
550	C₄²	—	53	2	no	—
551	C₄²	C₂²×D₅₃	1	1	yes	characteristic
552	C₄²	C₂²×D₅₃	1	1	yes	characteristic
553	C₄²	C₂²×D₅₃	1	1	yes	characteristic
554	C₄²	C₂²×D₅₃	1	1	yes	characteristic
555	C₄²	C₂²×D₅₃	1	2	yes	—
556	C₂³	—	53	1	no	—
557	C₂³	—	53	2	no	—
558	C₂³	—	53	1	no	—
559	C₂³	—	106	4	no	—
560	C₂³	—	106	4	no	—
561	C₂³	—	212	2	no	—
562	C₂³	C₂³×D₅₃	1	2	yes	—
563	C₂³	C₂³×D₅₃	1	1	yes	characteristic
564	Q₈	—	2	2	no	—
565	Q₈	—	106	2	no	—
566	Q₈	—	106	2	no	—
567	Q₈	—	212	2	no	—
568	D₄	—	2	2	no	—
569	D₄	—	4	2	no	—
570	D₄	—	53	4	no	—
571	D₄	—	106	2	no	—
572	D₄	—	106	4	no	—
573	D₄	—	106	2	no	—
574	D₄	—	106	4	no	—
575	D₄	—	106	2	no	—
576	D₄	—	106	4	no	—
577	D₄	—	212	2	no	—
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	53	1	no	—
583	C₂×C₄	—	53	4	no	—
584	C₂×C₄	—	53	1	no	—
585	C₂×C₄	—	53	2	no	—
586	C₂×C₄	—	53	1	no	—
587	C₂×C₄	—	53	1	no	—
588	C₂×C₄	—	53	1	no	—
589	C₂×C₄	—	53	2	no	—
590	C₂×C₄	—	53	2	no	—
591	C₂×C₄	—	53	1	no	—
592	C₂×C₄	—	106	4	no	—
593	C₂×C₄	—	106	4	no	—
594	C₂×C₄	—	106	4	no	—
595	C₂×C₄	—	106	4	no	—
596	C₂×C₄	—	106	4	no	—
597	C₂×C₄	—	106	4	no	—
598	C₂×C₄	—	106	2	no	—
599	C₂×C₄	—	106	2	no	—
600	C₂×C₄	—	106	2	no	—
601	C₂×C₄	—	212	1	no	—
602	C₂×C₄	—	212	2	no	—
603	C₂×C₄	—	212	1	no	—
604	C₂×C₄	—	212	2	no	—
605	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
606	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
607	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
608	C₂×C₄	C₂³×D₅₃	1	2	yes	—
609	C₂×C₄	C₂³×D₅₃	1	2	yes	—
610	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₅₃	1	2	yes	—
612	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
613	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
614	C₂²	—	2	2	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	53	2	no	—
621	C₂²	—	53	4	no	—
622	C₂²	—	106	2	no	—
623	C₂²	—	106	1	no	—
624	C₂²	—	106	2	no	—
625	C₂²	—	106	1	no	—
626	C₂²	—	106	1	no	—
627	C₂²	—	106	1	no	—
628	C₂²	—	106	1	no	—
629	C₂²	—	212	8	no	—
630	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
631	C₄	—	2	2	no	—
632	C₄	—	2	1	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	1	no	—
637	C₄	—	2	2	no	—
638	C₄	—	53	2	no	—
639	C₄	—	106	2	no	—
640	C₄	—	106	1	no	—
641	C₄	—	106	1	no	—
642	C₄	—	106	1	no	—
643	C₄	—	106	2	no	—
644	C₄	—	106	1	no	—
645	C₄	—	106	2	no	—
646	C₄	—	106	1	no	—
647	C₄	#41×D₅₃	1	2	yes	—
648	C₄	#41×D₅₃	1	2	yes	—
649	C₂	—	4	2	no	—
650	C₂	—	4	1	no	—
651	C₂	—	106	2	no	—
652	C₂	—	106	4	no	—
653	C₂	—	212	1	no	—
654	C₂	C₂×#41×D₅₃	1	1	yes	characteristic
655	C₂	C₂×#41×D₅₃	1	1	yes	characteristic
656	C₂	#16811459	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Frattini	C₂²	C₂⁴×D₅₃
Fitting	C₅₃×#529	C₂
hypercenter	#529	D₅₃
hypocenter	C₅₃	#3475
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ #529

Complements

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

N	H ≅ G/N	type
1. #16811342	C₂	semidirect
2. #16811337	C₂	semidirect
3. #16811329	C₂	semidirect
4. #16811318	C₂	semidirect
5. #16811311	C₂	semidirect
6. #16811309	C₂	semidirect
7. #16811307	C₂	semidirect
8. #16811301	C₂	semidirect
9. #16811298	C₂	semidirect
10. #16811275	C₂	semidirect
11. #16811270	C₂	semidirect
12. #16811266	C₂	semidirect
13. #16811177	C₂	semidirect
14. #16811155	C₂	semidirect
15. #16811155	C₂	semidirect
16. #16811151	C₂	semidirect
17. #16811132	C₂	semidirect
18. C₄×#11719949	C₂	semidirect
19. C₄×#11719945	C₂	semidirect
20. C₄×#11719945	C₂	semidirect
21. C₄×D₄×D₅₃	C₂	semidirect
22. #117×D₅₃	C₂	semidirect
23. C₅₃×#529	C₂	semidirect
29. #13133216	C₂²	semidirect
30. #13133215	C₂²	semidirect
31. #13133212	C₂²	semidirect
32. #13133210	C₂²	semidirect
33. #13133210	C₂²	semidirect
34. #13133210	C₂²	semidirect
35. #13133210	C₂²	semidirect
36. #13133208	C₂²	semidirect
37. #13133208	C₂²	semidirect
38. #13133207	C₂²	semidirect
39. #13133207	C₂²	semidirect
41. #13133204	C₂²	semidirect
42. #13133203	C₂²	semidirect
44. #13133202	C₂²	semidirect
48. #13133199	C₂²	semidirect
49. #13133199	C₂²	semidirect
51. #13133197	C₂²	semidirect
52. #13133197	C₂²	semidirect
54. #13133195	C₂²	semidirect
55. #13133195	C₂²	semidirect
56. #13133194	C₂²	semidirect
59. #13133190	C₂²	semidirect
60. #13133189	C₂²	semidirect
65. Q₈×Dic₅₃	C₂²	semidirect
66. C₄×Dic₁₀₆	C₂²	semidirect
67. C₄×Dic₁₀₆	C₂²	semidirect
68. C₄×Dic₁₀₆	C₂²	semidirect
69. C₄×Dic₁₀₆	C₂²	semidirect
70. C₄×Dic₁₀₆	C₂²	semidirect
75. C₄×D₂₁₂	C₂²	semidirect
79. #13133179	C₂²	semidirect
83. C₄×C₂²⋊D₅₃	C₂²	semidirect
84. C₄×C₂²⋊D₅₃	C₂²	semidirect
85. C₄×C₂²⋊D₅₃	C₂²	semidirect
86. C₄×C₂²⋊D₅₃	C₂²	semidirect
87. C₄×C₂²⋊D₅₃	C₂²	semidirect
89. #13133176	C₂²	semidirect
90. #13133176	C₂²	semidirect
91. #13133176	C₂²	semidirect
94. #13133175	C₂²	semidirect
95. #13133175	C₂²	semidirect
98. #13133174	C₂²	semidirect
99. #13133174	C₂²	semidirect
100. #13133173	C₂²	semidirect
101. #13133173	C₂²	semidirect
103. C₄⋊C₄×D₅₃	C₂²	semidirect
104. C₄⋊C₄×D₅₃	C₂²	semidirect
109. C₄²×D₅₃	C₂²	semidirect
110. C₄²×D₅₃	C₂²	semidirect
111. C₄²×D₅₃	C₂²	semidirect
112. #126×C₅₃	C₂²	semidirect
113. #125×C₅₃	C₂²	semidirect
115. #123×C₅₃	C₂²	semidirect
116. C₂²⋊Q₈×C₅₃	C₂²	semidirect
118. C₄×Q₈×C₅₃	C₂²	semidirect
120. C₄×D₄×C₅₃	C₂²	semidirect
121. #117×C₅₃	C₂²	semidirect
122. C₂×C₄²×C₅₃	C₂²	semidirect
268. D₂₁₂	#41	semidirect
281. C₄×D₅₃	#41	semidirect
345. #529	D₅₃	semidirect
352. C₅₃	#3475	semidirect
365. #126	C₂×D₅₃	semidirect
370. #125	C₂×D₅₃	semidirect
382. #123	C₂×D₅₃	semidirect
391. C₂²⋊Q₈	C₂×D₅₃	semidirect
406. C₄×Q₈	C₂×D₅₃	semidirect
426. C₄×D₄	C₂×D₅₃	semidirect
440. #117	C₂×D₅₃	semidirect
451. C₂×C₄²	C₂×D₅₃	semidirect