Subgroups — #20288649

Order 6784.

1152 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811355	C₂	1	1	yes	maximal, characteristic, complemented
2	#16811329	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811326	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811317	C₂	1	2	yes	maximal, complemented
5	#16811315	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811302	C₂	1	2	yes	maximal, complemented
7	#16811297	C₂	1	2	yes	maximal, complemented
8	#16811273	C₂	1	1	yes	maximal, characteristic, complemented
9	#16811268	C₂	1	2	yes	maximal, complemented
10	#16811266	C₂	1	1	yes	maximal, characteristic, complemented
11	#16811264	C₂	1	1	yes	maximal, characteristic, complemented
12	#16811257	C₂	1	1	yes	maximal, characteristic, complemented
13	#16811245	C₂	1	1	yes	maximal, characteristic, complemented
14	#16811224	C₂	1	1	yes	maximal, characteristic, complemented
15	#16811214	C₂	1	2	yes	maximal, complemented
16	#16811212	C₂	1	2	yes	maximal, complemented
17	#16811157	C₂	1	1	yes	maximal, characteristic, complemented
18	#16811131	C₂	1	2	yes	maximal, complemented
19	#123×D₅₃	C₂	1	2	yes	maximal, complemented
20	#16811105	C₂	1	1	yes	maximal, characteristic, complemented
21	#16811095	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₄×D₂₁₂	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11719949	C₂²	1	1	yes	characteristic
25	C₂×#11719947	C₂²	1	2	yes	complemented
26	C₂²×D₂₁₂	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic
28	C₂×D₄×D₅₃	C₂²	1	2	yes	—
29	C₂²×C₄×D₅₃	C₂²	1	2	yes	complemented
30	#13133216	C₂²	1	1	yes	characteristic, complemented
31	#13133213	C₂²	1	1	yes	characteristic
32	#13133212	C₂²	1	2	yes	complemented
33	#13133212	C₂²	1	2	yes	complemented
34	#13133211	C₂²	1	1	yes	characteristic, complemented
35	#13133211	C₂²	1	2	yes	complemented
36	#13133211	C₂²	1	1	yes	characteristic, complemented
37	#13133209	C₂²	1	1	yes	characteristic, complemented
38	#13133208	C₂²	1	2	yes	complemented
39	#13133208	C₂²	1	1	yes	characteristic, complemented
40	#13133206	C₂²	1	1	yes	characteristic, complemented
41	#13133205	C₂²	1	2	yes	complemented
42	#13133205	C₂²	1	1	yes	characteristic, complemented
43	#13133203	C₂²	1	2	yes	complemented
44	#13133202	C₂²	1	2	yes	complemented
45	#13133202	C₂²	1	2	yes	complemented
46	#13133202	C₂²	1	2	yes	complemented
47	#13133201	C₂²	1	2	yes	—
48	#13133201	C₂²	1	2	yes	complemented
49	#13133200	C₂²	1	1	yes	characteristic
50	#13133200	C₂²	1	2	yes	complemented
51	#13133200	C₂²	1	1	yes	characteristic, complemented
52	#13133199	C₂²	1	2	yes	complemented
53	#13133199	C₂²	1	2	yes	complemented
54	#13133199	C₂²	1	2	yes	complemented
55	#13133199	C₂²	1	2	yes	complemented
56	#13133198	C₂²	1	2	yes	complemented
57	#13133197	C₂²	1	2	yes	complemented
58	#13133196	C₂²	1	1	yes	characteristic, complemented
59	#13133195	C₂²	1	2	yes	complemented
60	#13133195	C₂²	1	2	yes	complemented
61	#13133195	C₂²	1	2	yes	complemented
62	#13133194	C₂²	1	2	yes	complemented
63	#13133193	C₂²	1	1	yes	characteristic, complemented
64	#13133192	C₂²	1	1	yes	characteristic
65	#13133192	C₂²	1	2	yes	complemented
66	#13133192	C₂²	1	1	yes	characteristic, complemented
67	#13133192	C₂²	1	2	yes	complemented
68	#13133191	C₂²	1	1	yes	characteristic
69	#13133191	C₂²	1	2	yes	complemented
70	#13133190	C₂²	1	2	yes	—
71	#13133190	C₂²	1	2	yes	complemented
72	#13133190	C₂²	1	2	yes	complemented
73	#13133188	C₂²	1	1	yes	characteristic, complemented
74	#13133187	C₂²	1	2	yes	—
75	#13133187	C₂²	1	2	yes	complemented
76	#13133187	C₂²	1	2	yes	complemented
77	#13133185	C₂²	1	2	yes	—
78	Q₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
79	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
80	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
81	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
82	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
83	C₄×D₂₁₂	C₂²	1	2	yes	complemented
84	C₄×D₂₁₂	C₂²	1	2	yes	complemented
85	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
86	C₄×D₂₁₂	C₂²	1	2	yes	complemented
87	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
88	D₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
89	#13133179	C₂²	1	1	yes	characteristic
90	#13133179	C₂²	1	1	yes	characteristic
91	#13133179	C₂²	1	2	yes	complemented
92	#13133179	C₂²	1	2	yes	complemented
93	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
94	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
95	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
96	#13133177	C₂²	1	2	yes	complemented
97	#13133177	C₂²	1	2	yes	complemented
98	#13133175	C₂²	1	1	yes	characteristic, complemented
99	#13133174	C₂²	1	2	yes	complemented
100	#13133174	C₂²	1	1	yes	characteristic, complemented
101	#13133174	C₂²	1	1	yes	characteristic, complemented
102	#13133173	C₂²	1	2	yes	complemented
103	C₂×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
104	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
105	C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
106	C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
107	C₂×#11719921	C₂²	1	2	yes	complemented
108	C₂×#11719921	C₂²	1	2	yes	complemented
109	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
111	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	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, 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
118	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
120	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, 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	C₂³×D₅₃	C₂³	1	2	yes	—
125	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₅₃	C₂³	1	2	yes	—
127	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
138	C₂²×Dic₅₃	C₂³	1	2	yes	—
139	C₂²×Dic₅₃	C₂³	1	2	yes	—
140	#11719949	—	2	4	no	—
141	#11719947	—	4	4	no	—
142	D₄×D₅₃	—	2	4	no	—
143	D₄×D₅₃	—	4	4	no	—
144	C₂×D₂₁₂	—	2	4	no	—
145	C₂×D₂₁₂	C₂³	1	2	yes	—
146	C₂×D₂₁₂	C₂³	1	2	yes	—
147	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
148	C₂×D₂₁₂	C₂³	1	2	yes	—
149	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
150	C₂×D₂₁₂	C₂³	1	2	yes	—
151	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₅₃	—	4	4	no	—
153	C₂×C₄×D₅₃	C₂³	1	2	yes	—
154	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₅₃	C₂³	1	2	yes	—
157	C₂×C₄×D₅₃	C₂³	1	2	yes	—
158	C₂×C₄×D₅₃	C₂³	1	2	yes	—
159	C₂×C₄×D₅₃	C₂³	1	2	yes	—
160	C₂×C₄×D₅₃	C₂³	1	2	yes	—
161	C₂×C₄×D₅₃	C₂³	1	2	yes	—
162	C₂×C₄×D₅₃	C₂³	1	2	yes	—
163	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
164	C₂×Dic₁₀₆	C₂³	1	2	yes	—
165	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
166	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
167	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
168	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
169	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
170	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
171	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
172	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
173	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
174	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
175	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
176	C₄²×C₅₃	C₂³	1	1	yes	characteristic
177	C₄²×C₅₃	C₂³	1	1	yes	characteristic
178	C₄²×C₅₃	C₂³	1	1	yes	characteristic
179	C₄²×C₅₃	C₂³	1	1	yes	characteristic
180	C₄²×C₅₃	C₂³	1	2	yes	—
181	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
183	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
184	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
185	#11719921	C₂³	1	1	yes	characteristic
186	#11719921	C₂³	1	1	yes	characteristic
187	#11719921	C₂³	1	2	yes	—
188	#11719921	C₂³	1	2	yes	—
189	#11719921	C₂³	1	2	yes	—
190	#11719921	C₂³	1	2	yes	—
191	#11719921	C₂³	1	2	yes	—
192	#11719921	C₂³	1	1	yes	characteristic
193	#11719921	C₂³	1	2	yes	—
194	#11719921	C₂³	1	2	yes	—
195	#11719921	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	1	yes	characteristic
200	#11719921	C₂³	1	2	yes	—
201	#11719921	C₂³	1	1	yes	characteristic
202	#11719921	C₂³	1	1	yes	characteristic
203	#11719921	C₂³	1	1	yes	characteristic
204	#11719921	C₂³	1	2	yes	—
205	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
206	C₄⋊Dic₅₃	C₂³	1	2	yes	—
207	C₄⋊Dic₅₃	C₂³	1	2	yes	—
208	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
209	C₄⋊Dic₅₃	C₂³	1	2	yes	—
210	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
211	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
212	#11719919	C₂³	1	2	yes	—
213	#11719919	C₂³	1	1	yes	characteristic
214	#11719919	C₂³	1	1	yes	characteristic
215	#11719919	C₂³	1	2	yes	—
216	#11719919	C₂³	1	2	yes	—
217	#11719919	C₂³	1	2	yes	—
218	#11719919	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
224	C₄×Dic₅₃	C₂³	1	2	yes	—
225	C₄×Dic₅₃	C₂³	1	2	yes	—
226	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
227	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
228	C₂³×C₅₃	C₂⁴	1	2	yes	—
229	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
230	C₂²×D₅₃	—	2	4	no	—
231	C₂²×D₅₃	—	2	4	no	—
232	C₂²×D₅₃	—	2	4	no	—
233	C₂²×D₅₃	—	4	2	no	—
234	C₂²×D₅₃	—	4	2	no	—
235	C₂²×D₅₃	—	4	2	no	—
236	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
237	C₂²×D₅₃	C₂⁴	1	2	yes	—
238	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
239	C₂²×D₅₃	C₂⁴	1	2	yes	—
240	Q₈×C₅₃	—	2	2	no	—
241	D₄×C₅₃	—	2	4	no	—
242	D₄×C₅₃	—	2	2	no	—
243	C₂×C₄×C₅₃	—	2	2	no	—
244	C₂×C₄×C₅₃	—	2	2	no	—
245	C₂×C₄×C₅₃	—	4	1	no	—
246	C₂×C₄×C₅₃	—	4	2	no	—
247	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
248	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
252	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
253	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
256	C₂²⋊D₅₃	—	2	2	no	—
257	C₂²⋊D₅₃	—	2	2	no	—
258	C₂²⋊D₅₃	—	2	4	no	—
259	C₂²⋊D₅₃	—	4	2	no	—
260	C₂²⋊D₅₃	—	4	2	no	—
261	C₂²⋊D₅₃	—	4	2	no	—
262	C₂×Dic₅₃	—	2	4	no	—
263	C₂×Dic₅₃	—	4	2	no	—
264	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₅₃	C₂⁴	1	2	yes	—
266	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₅₃	C₂⁴	1	2	yes	—
269	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
272	D₂₁₂	—	2	4	no	—
273	D₂₁₂	—	2	4	no	—
274	D₂₁₂	—	2	2	no	—
275	D₂₁₂	—	4	1	no	—
276	D₂₁₂	—	4	2	no	—
277	D₂₁₂	—	4	2	no	—
278	D₂₁₂	#41	1	4	yes	complemented
279	C₄×D₅₃	—	2	4	no	—
280	C₄×D₅₃	—	2	2	no	—
281	C₄×D₅₃	—	2	2	no	—
282	C₄×D₅₃	—	4	2	no	—
283	C₄×D₅₃	—	4	2	no	—
284	C₄×D₅₃	—	4	2	no	—
285	C₄×D₅₃	—	4	2	no	—
286	C₄×D₅₃	—	4	2	no	—
287	C₄×D₅₃	—	4	2	no	—
288	C₄×D₅₃	—	4	2	no	—
289	Dic₁₀₆	—	4	1	no	—
290	Dic₁₀₆	—	4	2	no	—
291	C₂²×C₅₃	—	2	1	no	—
292	C₂²×C₅₃	—	2	1	no	—
293	C₂²×C₅₃	—	2	2	no	—
294	C₂²×C₅₃	—	2	2	no	—
295	C₂²×C₅₃	—	2	2	no	—
296	C₂²×C₅₃	H(5,𝔽₂)	1	2	yes	—
297	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
298	C₂×D₅₃	—	2	2	no	—
299	C₂×D₅₃	—	2	2	no	—
300	C₂×D₅₃	—	2	1	no	—
301	C₂×D₅₃	—	2	1	no	—
302	C₂×D₅₃	—	2	2	no	—
303	C₂×D₅₃	—	2	2	no	—
304	C₂×D₅₃	—	2	1	no	—
305	C₂×D₅₃	—	2	1	no	—
306	C₂×D₅₃	—	2	1	no	—
307	C₂×D₅₃	—	2	2	no	—
308	C₂×D₅₃	—	2	1	no	—
309	C₂×D₅₃	—	4	8	no	—
310	C₂×D₅₃	—	8	4	no	—
311	C₂×D₅₃	C₂×#41	1	4	yes	—
312	C₄×C₅₃	—	2	2	no	—
313	C₄×C₅₃	—	2	1	no	—
314	C₄×C₅₃	—	2	2	no	—
315	C₄×C₅₃	—	2	1	no	—
316	C₄×C₅₃	—	2	1	no	—
317	C₄×C₅₃	—	2	1	no	—
318	C₄×C₅₃	—	2	2	no	—
319	C₄×C₅₃	—	2	1	no	—
320	C₄×C₅₃	C₂×#41	1	2	yes	—
321	Dic₅₃	—	2	1	no	—
322	Dic₅₃	—	2	1	no	—
323	Dic₅₃	—	2	1	no	—
324	Dic₅₃	—	2	2	no	—
325	Dic₅₃	—	2	2	no	—
326	Dic₅₃	—	2	1	no	—
327	Dic₅₃	—	2	1	no	—
328	Dic₅₃	—	2	1	no	—
329	#3513	—	53	1	no	maximal, Sylow
330	C₂×C₅₃	—	2	2	no	—
331	C₂×C₅₃	—	4	2	no	—
332	C₂×C₅₃	C₂²×#41	1	1	yes	characteristic
333	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
334	C₂×C₅₃	#585	1	1	yes	characteristic
335	D₅₃	—	2	4	no	—
336	D₅₃	—	4	1	no	—
337	D₅₃	—	4	2	no	—
338	D₅₃	—	4	1	no	—
339	#559	—	53	1	no	—
340	#554	—	53	1	no	—
341	#553	—	53	1	no	—
342	#553	—	53	2	no	—
343	#552	—	53	1	no	—
344	#551	—	53	2	no	—
345	#551	—	53	2	no	—
346	#547	—	53	1	no	—
347	#546	—	53	1	no	—
348	#546	—	53	1	no	—
349	#546	—	53	2	no	—
350	D₄²	—	53	1	no	—
351	#542	—	53	1	no	—
352	#540	—	53	1	no	—
353	#539	—	53	2	no	—
354	#538	—	53	2	no	—
355	#529	—	53	1	no	—
356	#529	D₅₃	1	1	yes	characteristic, complemented
357	#525	—	53	2	no	—
358	C₂×#123	—	53	2	no	—
359	#520	—	53	1	no	—
360	#518	—	53	1	no	—
361	C₂×C₄×D₄	—	53	1	no	—
362	C₅₃	#3513	1	1	yes	characteristic, complemented, Sylow
363	C₂×#41	—	53	1	no	—
364	C₂×#41	—	53	2	no	—
365	C₂²×D₄	—	53	1	no	—
366	C₂²×D₄	—	53	2	no	—
367	C₂²×D₄	—	53	1	no	—
368	C₂³×C₄	—	53	2	no	—
369	C₄⋊Q₈	—	53	1	no	—
370	#127	—	53	1	no	—
371	#126	—	53	2	no	—
372	#126	—	53	2	no	—
373	#126	—	53	1	no	—
374	#126	—	53	1	no	—
375	#126	—	53	2	no	—
376	#126	C₂×D₅₃	1	2	yes	complemented
377	#125	—	53	2	no	—
378	#125	—	53	1	no	—
379	#125	—	53	1	no	—
380	#125	C₂×D₅₃	1	1	yes	characteristic, complemented
381	#124	—	53	1	no	—
382	#124	—	53	2	no	—
383	#124	—	53	1	no	—
384	#124	—	53	2	no	—
385	#124	C₂×D₅₃	1	1	yes	characteristic, complemented
386	#123	—	53	2	no	—
387	#123	—	53	1	no	—
388	#123	—	53	1	no	—
389	#123	—	53	2	no	—
390	#123	—	53	2	no	—
391	#123	—	53	2	no	—
392	#123	—	53	2	no	—
393	#123	—	53	2	no	—
394	#123	—	53	2	no	—
395	#123	—	53	2	no	—
396	#123	—	53	2	no	—
397	#123	—	53	2	no	—
398	#123	—	53	2	no	—
399	#123	C₂×D₅₃	1	2	yes	complemented
400	C₂²⋊Q₈	—	53	1	no	—
401	C₂²⋊Q₈	—	53	1	no	—
402	C₂²⋊Q₈	—	53	2	no	—
403	C₂²⋊Q₈	—	53	2	no	—
404	C₂²⋊Q₈	—	53	2	no	—
405	C₂²⋊Q₈	—	53	2	no	—
406	C₂²⋊Q₈	—	53	2	no	—
407	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
408	#121	—	53	1	no	—
409	#121	—	53	1	no	—
410	#121	—	53	2	no	—
411	#121	—	53	2	no	—
412	#121	—	53	2	no	—
413	#121	—	53	1	no	—
414	#121	—	53	1	no	—
415	#121	—	53	2	no	—
416	#121	—	53	2	no	—
417	#121	—	53	2	no	—
418	#121	C₂×D₅₃	1	1	yes	characteristic
419	#120	—	53	2	no	—
420	#120	—	53	2	no	—
421	#120	—	53	2	no	—
422	#120	—	53	2	no	—
423	C₄×Q₈	—	53	1	no	—
424	C₄×Q₈	—	53	1	no	—
425	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
426	C₄×D₄	—	53	1	no	—
427	C₄×D₄	—	53	2	no	—
428	C₄×D₄	—	53	1	no	—
429	C₄×D₄	—	53	1	no	—
430	C₄×D₄	—	53	1	no	—
431	C₄×D₄	—	53	2	no	—
432	C₄×D₄	—	53	1	no	—
433	C₄×D₄	—	53	2	no	—
434	C₄×D₄	—	53	2	no	—
435	C₄×D₄	—	53	2	no	—
436	C₄×D₄	—	53	1	no	—
437	C₄×D₄	—	53	2	no	—
438	C₄×D₄	—	53	1	no	—
439	C₄×D₄	—	53	1	no	—
440	C₄×D₄	—	53	2	no	—
441	C₄×D₄	—	53	1	no	—
442	C₄×D₄	—	53	2	no	—
443	C₄×D₄	—	53	1	no	—
444	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
445	C₄×D₄	C₂×D₅₃	1	2	yes	complemented
446	#117	—	53	1	no	—
447	#117	—	53	2	no	—
448	#117	—	53	1	no	—
449	#117	—	53	1	no	—
450	#117	—	53	2	no	—
451	#117	C₂×D₅₃	1	2	yes	complemented
452	C₂×C₄⋊C₄	—	53	1	no	—
453	C₂×C₄⋊C₄	—	53	2	no	—
454	C₂×C₄⋊C₄	—	53	1	no	—
455	C₂×C₄⋊C₄	—	53	2	no	—
456	C₂×C₂²⋊C₄	—	53	2	no	—
457	C₂×C₂²⋊C₄	—	53	2	no	—
458	C₂×C₂²⋊C₄	—	53	2	no	—
459	C₂×C₂²⋊C₄	—	53	2	no	—
460	C₂×C₂²⋊C₄	—	53	2	no	—
461	C₂×C₄²	C₂×D₅₃	1	1	yes	characteristic, complemented
462	C₂⁴	—	53	2	no	—
463	C₂⁴	—	53	2	no	—
464	#41	—	106	4	no	—
465	#41	—	212	4	no	—
466	C₂×Q₈	—	53	1	no	—
467	C₂×Q₈	—	53	2	no	—
468	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
469	C₂×D₄	—	53	2	no	—
470	C₂×D₄	—	53	1	no	—
471	C₂×D₄	—	53	1	no	—
472	C₂×D₄	—	53	2	no	—
473	C₂×D₄	—	53	2	no	—
474	C₂×D₄	—	53	2	no	—
475	C₂×D₄	—	53	1	no	—
476	C₂×D₄	—	53	2	no	—
477	C₂×D₄	—	53	2	no	—
478	C₂×D₄	—	53	1	no	—
479	C₂×D₄	—	53	1	no	—
480	C₂×D₄	—	53	2	no	—
481	C₂×D₄	—	53	2	no	—
482	C₂×D₄	—	106	4	no	—
483	C₂×D₄	—	106	4	no	—
484	C₂×D₄	—	212	4	no	—
485	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
486	C₂×D₄	C₂²×D₅₃	1	2	yes	—
487	C₂²×C₄	—	53	2	no	—
488	C₂²×C₄	—	53	2	no	—
489	C₂²×C₄	—	53	2	no	—
490	C₂²×C₄	—	53	1	no	—
491	C₂²×C₄	—	53	1	no	—
492	C₂²×C₄	—	53	2	no	—
493	C₂²×C₄	—	53	2	no	—
494	C₂²×C₄	—	53	2	no	—
495	C₂²×C₄	—	53	2	no	—
496	C₂²×C₄	—	53	2	no	—
497	C₂²×C₄	—	53	2	no	—
498	C₂²×C₄	—	53	2	no	—
499	C₂²×C₄	—	212	4	no	—
500	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
501	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
502	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
503	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
504	C₄⋊C₄	—	53	1	no	—
505	C₄⋊C₄	—	53	2	no	—
506	C₄⋊C₄	—	53	1	no	—
507	C₄⋊C₄	—	53	1	no	—
508	C₄⋊C₄	—	53	1	no	—
509	C₄⋊C₄	—	53	2	no	—
510	C₄⋊C₄	—	53	2	no	—
511	C₄⋊C₄	—	53	2	no	—
512	C₄⋊C₄	—	53	2	no	—
513	C₄⋊C₄	—	53	1	no	—
514	C₄⋊C₄	—	53	1	no	—
515	C₄⋊C₄	—	53	1	no	—
516	C₄⋊C₄	—	53	2	no	—
517	C₄⋊C₄	—	53	2	no	—
518	C₄⋊C₄	—	53	1	no	—
519	C₄⋊C₄	—	53	1	no	—
520	C₄⋊C₄	—	53	1	no	—
521	C₄⋊C₄	—	53	1	no	—
522	C₄⋊C₄	—	53	1	no	—
523	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
524	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
525	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
526	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
527	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
528	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
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	2	no	—
534	C₂²⋊C₄	—	53	2	no	—
535	C₂²⋊C₄	—	53	1	no	—
536	C₂²⋊C₄	—	53	1	no	—
537	C₂²⋊C₄	—	53	1	no	—
538	C₂²⋊C₄	—	53	2	no	—
539	C₂²⋊C₄	—	53	2	no	—
540	C₂²⋊C₄	—	53	2	no	—
541	C₂²⋊C₄	—	53	2	no	—
542	C₂²⋊C₄	—	53	2	no	—
543	C₂²⋊C₄	—	53	2	no	—
544	C₂²⋊C₄	—	53	2	no	—
545	C₂²⋊C₄	—	53	2	no	—
546	C₂²⋊C₄	—	53	1	no	—
547	C₂²⋊C₄	—	53	1	no	—
548	C₂²⋊C₄	—	53	1	no	—
549	C₂²⋊C₄	—	53	1	no	—
550	C₂²⋊C₄	—	53	2	no	—
551	C₂²⋊C₄	—	53	2	no	—
552	C₂²⋊C₄	—	53	1	no	—
553	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
555	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
556	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
557	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
558	C₄²	—	53	2	no	—
559	C₄²	—	53	2	no	—
560	C₄²	—	53	1	no	—
561	C₄²	—	53	1	no	—
562	C₄²	C₂²×D₅₃	1	1	yes	characteristic
563	C₄²	C₂²×D₅₃	1	1	yes	characteristic
564	C₄²	C₂²×D₅₃	1	1	yes	characteristic
565	C₄²	C₂²×D₅₃	1	1	yes	characteristic
566	C₄²	C₂²×D₅₃	1	2	yes	—
567	C₂³	—	53	2	no	—
568	C₂³	—	53	1	no	—
569	C₂³	—	53	2	no	—
570	C₂³	—	53	1	no	—
571	C₂³	—	106	4	no	—
572	C₂³	—	106	4	no	—
573	C₂³	—	106	4	no	—
574	C₂³	—	212	2	no	—
575	C₂³	—	212	2	no	—
576	C₂³	—	212	2	no	—
577	C₂³	C₂³×D₅₃	1	2	yes	—
578	C₂³	C₂³×D₅₃	1	1	yes	characteristic
579	Q₈	—	2	2	no	—
580	Q₈	—	212	1	no	—
581	Q₈	—	212	2	no	—
582	D₄	—	2	4	no	—
583	D₄	—	2	2	no	—
584	D₄	—	53	4	no	—
585	D₄	—	106	4	no	—
586	D₄	—	106	4	no	—
587	D₄	—	106	4	no	—
588	D₄	—	106	2	no	—
589	D₄	—	106	2	no	—
590	D₄	—	106	2	no	—
591	D₄	—	212	2	no	—
592	D₄	—	212	1	no	—
593	D₄	—	212	2	no	—
594	D₄	—	212	2	no	—
595	D₄	—	212	2	no	—
596	D₄	—	212	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	53	1	no	—
602	C₂×C₄	—	53	1	no	—
603	C₂×C₄	—	53	2	no	—
604	C₂×C₄	—	53	1	no	—
605	C₂×C₄	—	53	1	no	—
606	C₂×C₄	—	53	1	no	—
607	C₂×C₄	—	53	1	no	—
608	C₂×C₄	—	53	2	no	—
609	C₂×C₄	—	106	4	no	—
610	C₂×C₄	—	106	4	no	—
611	C₂×C₄	—	106	2	no	—
612	C₂×C₄	—	106	2	no	—
613	C₂×C₄	—	212	2	no	—
614	C₂×C₄	—	212	2	no	—
615	C₂×C₄	—	212	2	no	—
616	C₂×C₄	—	212	2	no	—
617	C₂×C₄	—	212	2	no	—
618	C₂×C₄	—	212	2	no	—
619	C₂×C₄	—	212	2	no	—
620	C₂×C₄	—	212	2	no	—
621	C₂×C₄	C₂³×D₅₃	1	2	yes	—
622	C₂×C₄	C₂³×D₅₃	1	2	yes	—
623	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
626	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
627	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
628	C₂×C₄	C₂³×D₅₃	1	2	yes	—
629	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
630	C₂²	—	2	1	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	53	4	no	—
636	C₂²	—	106	2	no	—
637	C₂²	—	106	2	no	—
638	C₂²	—	106	1	no	—
639	C₂²	—	106	1	no	—
640	C₂²	—	106	2	no	—
641	C₂²	—	106	1	no	—
642	C₂²	—	106	2	no	—
643	C₂²	—	106	1	no	—
644	C₂²	—	106	1	no	—
645	C₂²	—	106	2	no	—
646	C₂²	—	106	1	no	—
647	C₂²	—	424	4	no	—
648	C₂²	—	212	8	no	—
649	C₂²	#13133263	1	2	yes	—
650	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
651	C₄	—	2	1	no	—
652	C₄	—	2	2	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	1	no	—
655	C₄	—	2	2	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	1	no	—
659	C₄	—	106	1	no	—
660	C₄	—	106	1	no	—
661	C₄	—	106	2	no	—
662	C₄	—	106	2	no	—
663	C₄	—	106	1	no	—
664	C₄	—	106	1	no	—
665	C₄	—	106	1	no	—
666	C₄	—	106	1	no	—
667	C₄	#41×D₅₃	1	2	yes	—
668	C₂	—	2	2	no	—
669	C₂	—	4	2	no	—
670	C₂	—	106	4	no	—
671	C₂	—	212	1	no	—
672	C₂	—	212	2	no	—
673	C₂	—	212	1	no	—
674	C₂	C₂×#41×D₅₃	1	1	yes	characteristic
675	C₂	C₂×#13133263	1	1	yes	characteristic
676	C₂	#16811459	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#529	C₂
hypercenter	#529	D₅₃
hypocenter	C₅₃	#3513
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #16811355	C₂	semidirect
2. #16811329	C₂	semidirect
3. #16811326	C₂	semidirect
4. #16811317	C₂	semidirect
5. #16811315	C₂	semidirect
6. #16811302	C₂	semidirect
7. #16811297	C₂	semidirect
8. #16811273	C₂	semidirect
9. #16811268	C₂	semidirect
10. #16811266	C₂	semidirect
11. #16811264	C₂	semidirect
12. #16811257	C₂	semidirect
13. #16811245	C₂	semidirect
14. #16811224	C₂	semidirect
15. #16811214	C₂	semidirect
16. #16811212	C₂	semidirect
17. #16811157	C₂	semidirect
18. #16811131	C₂	semidirect
19. #123×D₅₃	C₂	semidirect
20. #16811105	C₂	semidirect
21. #16811095	C₂	semidirect
22. C₂×C₄×D₂₁₂	C₂	semidirect
23. C₅₃×#529	C₂	semidirect
25. C₂×#11719947	C₂²	semidirect
29. C₂²×C₄×D₅₃	C₂²	semidirect
30. #13133216	C₂²	semidirect
32. #13133212	C₂²	semidirect
33. #13133212	C₂²	semidirect
34. #13133211	C₂²	semidirect
35. #13133211	C₂²	semidirect
36. #13133211	C₂²	semidirect
37. #13133209	C₂²	semidirect
38. #13133208	C₂²	semidirect
39. #13133208	C₂²	semidirect
40. #13133206	C₂²	semidirect
41. #13133205	C₂²	semidirect
42. #13133205	C₂²	semidirect
43. #13133203	C₂²	semidirect
44. #13133202	C₂²	semidirect
45. #13133202	C₂²	semidirect
46. #13133202	C₂²	semidirect
48. #13133201	C₂²	semidirect
50. #13133200	C₂²	semidirect
51. #13133200	C₂²	semidirect
52. #13133199	C₂²	semidirect
53. #13133199	C₂²	semidirect
54. #13133199	C₂²	semidirect
55. #13133199	C₂²	semidirect
56. #13133198	C₂²	semidirect
57. #13133197	C₂²	semidirect
58. #13133196	C₂²	semidirect
59. #13133195	C₂²	semidirect
60. #13133195	C₂²	semidirect
61. #13133195	C₂²	semidirect
62. #13133194	C₂²	semidirect
63. #13133193	C₂²	semidirect
65. #13133192	C₂²	semidirect
66. #13133192	C₂²	semidirect
67. #13133192	C₂²	semidirect
69. #13133191	C₂²	semidirect
71. #13133190	C₂²	semidirect
72. #13133190	C₂²	semidirect
73. #13133188	C₂²	semidirect
75. #13133187	C₂²	semidirect
76. #13133187	C₂²	semidirect
78. Q₈×Dic₅₃	C₂²	semidirect
79. C₄×Dic₁₀₆	C₂²	semidirect
82. C₄×D₂₁₂	C₂²	semidirect
83. C₄×D₂₁₂	C₂²	semidirect
84. C₄×D₂₁₂	C₂²	semidirect
85. C₄×D₂₁₂	C₂²	semidirect
86. C₄×D₂₁₂	C₂²	semidirect
87. C₄×D₂₁₂	C₂²	semidirect
88. D₄×Dic₅₃	C₂²	semidirect
91. #13133179	C₂²	semidirect
92. #13133179	C₂²	semidirect
94. C₄×C₂²⋊D₅₃	C₂²	semidirect
95. C₄×C₂²⋊D₅₃	C₂²	semidirect
96. #13133177	C₂²	semidirect
97. #13133177	C₂²	semidirect
98. #13133175	C₂²	semidirect
99. #13133174	C₂²	semidirect
100. #13133174	C₂²	semidirect
101. #13133174	C₂²	semidirect
102. #13133173	C₂²	semidirect
103. C₂×C₄⋊Dic₅₃	C₂²	semidirect
104. C₄⋊C₄×D₅₃	C₂²	semidirect
105. C₄⋊C₄×D₅₃	C₂²	semidirect
106. C₄⋊C₄×D₅₃	C₂²	semidirect
107. C₂×#11719921	C₂²	semidirect
108. C₂×#11719921	C₂²	semidirect
109. C₂²⋊C₄×D₅₃	C₂²	semidirect
110. C₂²⋊C₄×D₅₃	C₂²	semidirect
111. C₂²⋊C₄×D₅₃	C₂²	semidirect
112. #126×C₅₃	C₂²	semidirect
113. #125×C₅₃	C₂²	semidirect
114. #124×C₅₃	C₂²	semidirect
115. #123×C₅₃	C₂²	semidirect
116. C₂²⋊Q₈×C₅₃	C₂²	semidirect
118. C₄×Q₈×C₅₃	C₂²	semidirect
119. C₄×D₄×C₅₃	C₂²	semidirect
120. C₄×D₄×C₅₃	C₂²	semidirect
121. #117×C₅₃	C₂²	semidirect
122. C₂×C₄²×C₅₃	C₂²	semidirect
278. D₂₁₂	#41	semidirect
356. #529	D₅₃	semidirect
362. C₅₃	#3513	semidirect
376. #126	C₂×D₅₃	semidirect
380. #125	C₂×D₅₃	semidirect
385. #124	C₂×D₅₃	semidirect
399. #123	C₂×D₅₃	semidirect
407. C₂²⋊Q₈	C₂×D₅₃	semidirect
425. C₄×Q₈	C₂×D₅₃	semidirect
444. C₄×D₄	C₂×D₅₃	semidirect
445. C₄×D₄	C₂×D₅₃	semidirect
451. #117	C₂×D₅₃	semidirect
461. C₂×C₄²	C₂×D₅₃	semidirect