Subgroups — #20288277

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	#16811345	C₂	1	1	yes	maximal, characteristic, complemented
2	#16811336	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811332	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811322	C₂	1	2	yes	maximal, complemented
5	#16811314	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811312	C₂	1	1	yes	maximal, characteristic, complemented
7	#16811306	C₂	1	2	yes	maximal, complemented
8	#16811302	C₂	1	2	yes	maximal, complemented
9	#16811297	C₂	1	2	yes	maximal, complemented
10	#16811272	C₂	1	1	yes	maximal, characteristic, complemented
11	#16811268	C₂	1	1	yes	maximal, characteristic, complemented
12	#16811261	C₂	1	1	yes	maximal, characteristic, complemented
13	#16811177	C₂	1	1	yes	maximal, characteristic, complemented
14	#16811160	C₂	1	1	yes	maximal, characteristic, complemented
15	#16811157	C₂	1	2	yes	maximal, complemented
16	#16811157	C₂	1	1	yes	maximal, characteristic, complemented
17	#16811153	C₂	1	2	yes	maximal, complemented
18	#16811132	C₂	1	2	yes	maximal, complemented
19	C₄×#11719945	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#11719947	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#13133174	C₂	1	2	yes	maximal, complemented
23	C₄×#41×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11719945	C₂²	1	1	yes	characteristic
25	C₂×#11719947	C₂²	1	1	yes	characteristic
26	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₅₃	C₂²	1	2	yes	—
28	#13133216	C₂²	1	1	yes	characteristic, complemented
29	#13133215	C₂²	1	1	yes	characteristic, complemented
30	#13133212	C₂²	1	2	yes	complemented
31	#13133212	C₂²	1	2	yes	complemented
32	#13133211	C₂²	1	2	yes	complemented
33	#13133211	C₂²	1	2	yes	complemented
34	#13133211	C₂²	1	2	yes	complemented
35	#13133210	C₂²	1	2	yes	complemented
36	#13133209	C₂²	1	2	yes	complemented
37	#13133209	C₂²	1	1	yes	characteristic, complemented
38	#13133208	C₂²	1	1	yes	characteristic, complemented
39	#13133207	C₂²	1	2	yes	complemented
40	#13133207	C₂²	1	2	yes	complemented
41	#13133206	C₂²	1	1	yes	characteristic
42	#13133205	C₂²	1	1	yes	characteristic
43	#13133205	C₂²	1	2	yes	complemented
44	#13133203	C₂²	1	2	yes	complemented
45	#13133202	C₂²	1	2	yes	—
46	#13133202	C₂²	1	2	yes	complemented
47	#13133201	C₂²	1	2	yes	—
48	#13133200	C₂²	1	2	yes	—
49	#13133200	C₂²	1	2	yes	complemented
50	#13133200	C₂²	1	2	yes	complemented
51	#13133199	C₂²	1	2	yes	—
52	#13133198	C₂²	1	2	yes	complemented
53	#13133197	C₂²	1	1	yes	characteristic
54	#13133196	C₂²	1	1	yes	characteristic, complemented
55	#13133196	C₂²	1	2	yes	complemented
56	#13133195	C₂²	1	2	yes	—
57	#13133195	C₂²	1	2	yes	complemented
58	#13133194	C₂²	1	2	yes	complemented
59	#13133194	C₂²	1	2	yes	complemented
60	#13133193	C₂²	1	1	yes	characteristic
61	#13133193	C₂²	1	1	yes	characteristic, complemented
62	#13133192	C₂²	1	1	yes	characteristic
63	#13133191	C₂²	1	2	yes	—
64	#13133191	C₂²	1	1	yes	characteristic
65	#13133190	C₂²	1	2	yes	complemented
66	#13133189	C₂²	1	2	yes	—
67	#13133189	C₂²	1	2	yes	complemented
68	#13133187	C₂²	1	2	yes	—
69	#13133185	C₂²	1	2	yes	—
70	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
71	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
72	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
73	C₄×Dic₁₀₆	C₂²	1	2	yes	complemented
74	#13133182	C₂²	1	1	yes	characteristic, complemented
75	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
76	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
77	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
78	C₄×D₂₁₂	C₂²	1	2	yes	complemented
79	D₄×Dic₅₃	C₂²	1	1	yes	characteristic
80	D₄×Dic₅₃	C₂²	1	1	yes	characteristic
81	#13133179	C₂²	1	1	yes	characteristic
82	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
83	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
84	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	—
85	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
86	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
87	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
88	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
89	#13133177	C₂²	1	2	yes	—
90	#13133177	C₂²	1	2	yes	complemented
91	#13133176	C₂²	1	1	yes	characteristic, complemented
92	#13133175	C₂²	1	1	yes	characteristic, complemented
93	#13133174	C₂²	1	2	yes	—
94	#13133174	C₂²	1	2	yes	—
95	#13133174	C₂²	1	1	yes	characteristic
96	#13133174	C₂²	1	2	yes	—
97	#13133174	C₂²	1	2	yes	complemented
98	#13133174	C₂²	1	2	yes	complemented
99	#13133174	C₂²	1	2	yes	complemented
100	#13133174	C₂²	1	2	yes	complemented
101	#13133174	C₂²	1	1	yes	characteristic, complemented
102	#13133173	C₂²	1	2	yes	complemented
103	C₂×#11719919	C₂²	1	2	yes	complemented
104	C₂×#11719919	C₂²	1	2	yes	complemented
105	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
106	C₂×#11719921	C₂²	1	2	yes	—
107	C₂×#11719921	C₂²	1	2	yes	—
108	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
109	C₂×C₄×Dic₅₃	C₂²	1	2	yes	complemented
110	C₄²×D₅₃	C₂²	1	1	yes	characteristic
111	C₄²×D₅₃	C₂²	1	1	yes	characteristic, complemented
112	C₂×#41×C₅₃	C₂²	1	1	yes	characteristic
113	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
114	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
115	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
116	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
117	C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
118	C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
119	#117×C₅₃	C₂²	1	2	yes	complemented
120	#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
121	C₂×C₄²×C₅₃	C₂²	1	2	yes	complemented
122	C₂×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₅₃	C₂³	1	2	yes	—
124	#41×C₅₃	—	2	4	no	—
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	2	yes	—
129	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
131	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
133	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
139	C₂²×Dic₅₃	C₂³	1	2	yes	—
140	C₂²×Dic₅₃	C₂³	1	2	yes	—
141	C₂²×Dic₅₃	C₂³	1	2	yes	—
142	#11719947	—	2	4	no	—
143	D₄×D₅₃	—	2	4	no	—
144	#11719945	—	2	4	no	—
145	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
146	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
147	C₂×D₂₁₂	C₂³	1	2	yes	—
148	C₂×C₄×D₅₃	—	2	8	no	—
149	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₅₃	C₂³	1	2	yes	—
153	C₂×C₄×D₅₃	C₂³	1	2	yes	—
154	C₂×C₄×D₅₃	C₂³	1	2	yes	—
155	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
162	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
163	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
164	C₄⋊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	C₄²×C₅₃	C₂³	1	1	yes	characteristic
169	C₄²×C₅₃	C₂³	1	2	yes	—
170	C₄²×C₅₃	C₂³	1	1	yes	characteristic
171	C₄²×C₅₃	C₂³	1	1	yes	characteristic
172	C₄²×C₅₃	C₂³	1	1	yes	characteristic
173	C₄²×C₅₃	C₂³	1	2	yes	—
174	C₄²×C₅₃	C₂³	1	2	yes	—
175	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
176	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
177	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
180	#11719921	C₂³	1	2	yes	—
181	#11719921	C₂³	1	2	yes	—
182	#11719921	C₂³	1	1	yes	characteristic
183	#11719921	C₂³	1	1	yes	characteristic
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	—
189	#11719921	C₂³	1	2	yes	—
190	#11719921	C₂³	1	1	yes	characteristic
191	#11719921	C₂³	1	1	yes	characteristic
192	#11719921	C₂³	1	2	yes	—
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	1	yes	characteristic
198	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
200	C₄⋊Dic₅₃	C₂³	1	2	yes	—
201	C₄⋊Dic₅₃	C₂³	1	2	yes	—
202	#11719919	C₂³	1	2	yes	—
203	#11719919	C₂³	1	1	yes	characteristic
204	#11719919	C₂³	1	1	yes	characteristic
205	#11719919	C₂³	1	2	yes	—
206	#11719919	C₂³	1	2	yes	—
207	#11719919	C₂³	1	2	yes	—
208	#11719919	C₂³	1	2	yes	—
209	#11719919	C₂³	1	2	yes	—
210	#11719919	C₂³	1	2	yes	—
211	#11719919	C₂³	1	2	yes	—
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	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
219	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
220	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
221	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
222	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
223	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
224	C₄×Dic₅₃	C₂³	1	2	yes	—
225	C₄×Dic₅₃	C₂³	1	2	yes	—
226	C₄×Dic₅₃	C₂³	1	2	yes	—
227	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
228	C₂³×C₅₃	C₂⁴	1	2	yes	—
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	4	no	—
237	D₄×C₅₃	#41	1	4	yes	complemented
238	C₂×C₄×C₅₃	—	2	4	no	—
239	C₂×C₄×C₅₃	—	2	4	no	—
240	C₂×C₄×C₅₃	—	2	2	no	—
241	C₂×C₄×C₅₃	—	2	2	no	—
242	C₂×C₄×C₅₃	—	4	2	no	—
243	C₂×C₄×C₅₃	—	4	1	no	—
244	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
246	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
247	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
251	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
253	C₂²⋊D₅₃	—	2	4	no	—
254	C₂²⋊D₅₃	—	2	4	no	—
255	C₂²⋊D₅₃	—	2	2	no	—
256	C₂²⋊D₅₃	—	2	2	no	—
257	C₂²⋊D₅₃	—	4	2	no	—
258	C₂×Dic₅₃	—	2	4	no	—
259	C₂×Dic₅₃	—	2	4	no	—
260	C₂×Dic₅₃	—	4	2	no	—
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	2	yes	—
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	1	yes	characteristic
269	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
270	D₂₁₂	—	2	2	no	—
271	D₂₁₂	—	2	2	no	—
272	D₂₁₂	—	4	2	no	—
273	C₄×D₅₃	—	2	4	no	—
274	C₄×D₅₃	—	2	4	no	—
275	C₄×D₅₃	—	2	2	no	—
276	C₄×D₅₃	—	2	2	no	—
277	C₄×D₅₃	—	2	2	no	—
278	C₄×D₅₃	—	2	4	no	—
279	C₄×D₅₃	—	4	1	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	2	no	—
287	C₂²×C₅₃	—	2	1	no	—
288	C₂²×C₅₃	—	2	1	no	—
289	C₂²×C₅₃	—	2	1	no	—
290	C₂²×C₅₃	C₂×#41	1	4	yes	—
291	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
292	C₂×D₅₃	—	2	1	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	2	no	—
298	C₂×D₅₃	—	2	1	no	—
299	C₂×D₅₃	—	2	2	no	—
300	C₂×D₅₃	—	4	8	no	—
301	C₂×D₅₃	C₂×#41	1	2	yes	—
302	C₄×C₅₃	—	2	1	no	—
303	C₄×C₅₃	—	2	2	no	—
304	C₄×C₅₃	—	2	1	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	1	no	—
312	Dic₅₃	—	2	2	no	—
313	Dic₅₃	—	2	2	no	—
314	Dic₅₃	—	2	1	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	—	2	4	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	—	4	1	no	—
328	D₅₃	—	4	2	no	—
329	#556	—	53	1	no	—
330	#555	—	53	1	no	—
331	#554	—	53	1	no	—
332	#553	—	53	2	no	—
333	#552	—	53	1	no	—
334	#552	—	53	2	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	—	53	1	no	—
346	#525	—	53	2	no	—
347	C₄×#41	—	53	1	no	—
348	C₄×#41	—	53	1	no	—
349	C₄×#41	D₅₃	1	1	yes	characteristic, complemented
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	C₂×D₅₃	1	1	yes	characteristic
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	—	53	2	no	—
366	#125	—	53	2	no	—
367	#125	—	53	1	no	—
368	#125	—	53	2	no	—
369	#125	—	53	2	no	—
370	#125	—	53	1	no	—
371	#124	—	53	1	no	—
372	#124	—	53	2	no	—
373	#124	—	53	1	no	—
374	#124	—	53	2	no	—
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	—	53	2	no	—
383	C₂²⋊Q₈	—	53	1	no	—
384	C₂²⋊Q₈	—	53	1	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	—	53	2	no	—
392	#121	—	53	2	no	—
393	#121	—	53	2	no	—
394	#121	—	53	2	no	—
395	#121	—	53	1	no	—
396	#121	—	53	1	no	—
397	#121	—	53	2	no	—
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	2	no	—
405	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
406	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
407	C₄×D₄	—	53	1	no	—
408	C₄×D₄	—	53	1	no	—
409	C₄×D₄	—	53	2	no	—
410	C₄×D₄	—	53	2	no	—
411	C₄×D₄	—	53	1	no	—
412	C₄×D₄	—	53	1	no	—
413	C₄×D₄	—	53	1	no	—
414	C₄×D₄	—	53	1	no	—
415	C₄×D₄	—	53	2	no	—
416	C₄×D₄	—	53	1	no	—
417	C₄×D₄	—	53	2	no	—
418	C₄×D₄	—	53	2	no	—
419	C₄×D₄	—	53	1	no	—
420	C₄×D₄	—	53	1	no	—
421	C₄×D₄	—	53	1	no	—
422	C₄×D₄	—	53	2	no	—
423	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
424	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
425	C₄×D₄	C₂×D₅₃	1	2	yes	complemented
426	C₄×D₄	C₂×D₅₃	1	2	yes	complemented
427	#117	—	53	1	no	—
428	#117	—	53	1	no	—
429	#117	—	53	2	no	—
430	#117	—	53	1	no	—
431	#117	—	53	2	no	—
432	#117	—	53	2	no	—
433	#117	—	53	2	no	—
434	#117	—	53	2	no	—
435	#117	—	53	2	no	—
436	#117	—	53	2	no	—
437	#117	—	53	2	no	—
438	#117	—	53	1	no	—
439	#117	C₂×D₅₃	1	2	yes	complemented
440	#117	C₂×D₅₃	1	1	yes	characteristic, 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	1	no	—
449	C₂×C₄²	—	53	1	no	—
450	C₂×C₄²	C₂×D₅₃	1	2	yes	complemented
451	C₂×C₄²	C₂×D₅₃	1	1	yes	characteristic, complemented
452	C₂⁴	—	53	2	no	—
453	#41	—	2	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	2	yes	—
470	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
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	1	no	—
480	C₂²×C₄	—	53	2	no	—
481	C₂²×C₄	—	53	1	no	—
482	C₂²×C₄	—	53	1	no	—
483	C₂²×C₄	—	106	8	no	—
484	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
485	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
486	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
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	2	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	2	no	—
500	C₄⋊C₄	—	53	1	no	—
501	C₄⋊C₄	—	53	1	no	—
502	C₄⋊C₄	—	53	1	no	—
503	C₄⋊C₄	—	53	2	no	—
504	C₄⋊C₄	—	53	2	no	—
505	C₄⋊C₄	—	53	1	no	—
506	C₄⋊C₄	—	53	1	no	—
507	C₄⋊C₄	—	53	2	no	—
508	C₄⋊C₄	—	53	2	no	—
509	C₄⋊C₄	—	53	2	no	—
510	C₄⋊C₄	—	53	2	no	—
511	C₄⋊C₄	—	53	2	no	—
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	1	no	—
519	C₂²⋊C₄	—	53	1	no	—
520	C₂²⋊C₄	—	53	2	no	—
521	C₂²⋊C₄	—	53	1	no	—
522	C₂²⋊C₄	—	53	1	no	—
523	C₂²⋊C₄	—	53	2	no	—
524	C₂²⋊C₄	—	53	2	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	—	53	2	no	—
536	C₂²⋊C₄	—	53	2	no	—
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	1	no	—
543	C₄²	—	53	1	no	—
544	C₄²	—	53	1	no	—
545	C₄²	—	53	1	no	—
546	C₄²	—	53	1	no	—
547	C₄²	—	53	1	no	—
548	C₄²	—	53	2	no	—
549	C₄²	C₂²×D₅₃	1	2	yes	—
550	C₄²	C₂²×D₅₃	1	2	yes	—
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	1	yes	characteristic
563	C₂³	C₂³×D₅₃	1	2	yes	—
564	Q₈	—	2	2	no	—
565	Q₈	—	106	2	no	—
566	Q₈	—	106	2	no	—
567	Q₈	—	212	2	no	—
568	D₄	—	2	4	no	—
569	D₄	—	106	2	no	—
570	D₄	—	106	2	no	—
571	D₄	—	106	2	no	—
572	D₄	—	106	4	no	—
573	D₄	—	106	4	no	—
574	D₄	—	106	2	no	—
575	D₄	—	212	2	no	—
576	D₄	—	212	2	no	—
577	D₄	#11719945	1	4	yes	complemented
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	53	1	no	—
585	C₂×C₄	—	53	4	no	—
586	C₂×C₄	—	53	1	no	—
587	C₂×C₄	—	53	1	no	—
588	C₂×C₄	—	53	1	no	—
589	C₂×C₄	—	53	1	no	—
590	C₂×C₄	—	53	2	no	—
591	C₂×C₄	—	53	2	no	—
592	C₂×C₄	—	53	1	no	—
593	C₂×C₄	—	53	2	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	4	no	—
599	C₂×C₄	—	106	2	no	—
600	C₂×C₄	—	106	2	no	—
601	C₂×C₄	—	106	2	no	—
602	C₂×C₄	—	212	1	no	—
603	C₂×C₄	—	212	1	no	—
604	C₂×C₄	—	212	2	no	—
605	C₂×C₄	C₂³×D₅₃	1	2	yes	—
606	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
607	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
608	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
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	2	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	53	2	no	—
620	C₂²	—	106	1	no	—
621	C₂²	—	106	1	no	—
622	C₂²	—	106	2	no	—
623	C₂²	—	106	1	no	—
624	C₂²	—	106	1	no	—
625	C₂²	—	106	2	no	—
626	C₂²	—	106	1	no	—
627	C₂²	—	106	2	no	—
628	C₂²	—	212	8	no	—
629	C₂²	C₂×#11719945	1	4	yes	—
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	C₂×#11719945	1	2	yes	—
649	C₂	—	2	4	no	—
650	C₂	—	4	1	no	—
651	C₂	—	106	2	no	—
652	C₂	—	212	2	no	—
653	C₂	—	212	1	no	—
654	C₂	C₂×#41×D₅₃	1	1	yes	characteristic
655	C₂	C₂²×#11719945	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	C₄×#41×C₅₃	C₂
hypercenter	C₄×#41	D₅₃
hypocenter	C₅₃	#3475
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41

Complements

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

N	H ≅ G/N	type
1. #16811345	C₂	semidirect
2. #16811336	C₂	semidirect
3. #16811332	C₂	semidirect
4. #16811322	C₂	semidirect
5. #16811314	C₂	semidirect
6. #16811312	C₂	semidirect
7. #16811306	C₂	semidirect
8. #16811302	C₂	semidirect
9. #16811297	C₂	semidirect
10. #16811272	C₂	semidirect
11. #16811268	C₂	semidirect
12. #16811261	C₂	semidirect
13. #16811177	C₂	semidirect
14. #16811160	C₂	semidirect
15. #16811157	C₂	semidirect
16. #16811157	C₂	semidirect
17. #16811153	C₂	semidirect
18. #16811132	C₂	semidirect
19. C₄×#11719945	C₂	semidirect
20. C₄×#11719947	C₂	semidirect
21. C₄×D₄×D₅₃	C₂	semidirect
22. C₂×#13133174	C₂	semidirect
23. C₄×#41×C₅₃	C₂	semidirect
28. #13133216	C₂²	semidirect
29. #13133215	C₂²	semidirect
30. #13133212	C₂²	semidirect
31. #13133212	C₂²	semidirect
32. #13133211	C₂²	semidirect
33. #13133211	C₂²	semidirect
34. #13133211	C₂²	semidirect
35. #13133210	C₂²	semidirect
36. #13133209	C₂²	semidirect
37. #13133209	C₂²	semidirect
38. #13133208	C₂²	semidirect
39. #13133207	C₂²	semidirect
40. #13133207	C₂²	semidirect
43. #13133205	C₂²	semidirect
44. #13133203	C₂²	semidirect
46. #13133202	C₂²	semidirect
49. #13133200	C₂²	semidirect
50. #13133200	C₂²	semidirect
52. #13133198	C₂²	semidirect
54. #13133196	C₂²	semidirect
55. #13133196	C₂²	semidirect
57. #13133195	C₂²	semidirect
58. #13133194	C₂²	semidirect
59. #13133194	C₂²	semidirect
61. #13133193	C₂²	semidirect
65. #13133190	C₂²	semidirect
67. #13133189	C₂²	semidirect
70. C₄×Dic₁₀₆	C₂²	semidirect
71. C₄×Dic₁₀₆	C₂²	semidirect
72. C₄×Dic₁₀₆	C₂²	semidirect
73. C₄×Dic₁₀₆	C₂²	semidirect
74. #13133182	C₂²	semidirect
78. C₄×D₂₁₂	C₂²	semidirect
85. C₄×C₂²⋊D₅₃	C₂²	semidirect
86. C₄×C₂²⋊D₅₃	C₂²	semidirect
87. C₄×C₂²⋊D₅₃	C₂²	semidirect
88. C₄×C₂²⋊D₅₃	C₂²	semidirect
90. #13133177	C₂²	semidirect
91. #13133176	C₂²	semidirect
92. #13133175	C₂²	semidirect
97. #13133174	C₂²	semidirect
98. #13133174	C₂²	semidirect
99. #13133174	C₂²	semidirect
100. #13133174	C₂²	semidirect
101. #13133174	C₂²	semidirect
102. #13133173	C₂²	semidirect
103. C₂×#11719919	C₂²	semidirect
104. C₂×#11719919	C₂²	semidirect
109. C₂×C₄×Dic₅₃	C₂²	semidirect
111. C₄²×D₅₃	C₂²	semidirect
113. C₄×Q₈×C₅₃	C₂²	semidirect
114. C₄×Q₈×C₅₃	C₂²	semidirect
117. C₄×D₄×C₅₃	C₂²	semidirect
118. C₄×D₄×C₅₃	C₂²	semidirect
119. #117×C₅₃	C₂²	semidirect
120. #117×C₅₃	C₂²	semidirect
121. C₂×C₄²×C₅₃	C₂²	semidirect
122. C₂×C₄²×C₅₃	C₂²	semidirect
237. D₄×C₅₃	#41	semidirect
281. C₄×D₅₃	#41	semidirect
349. C₄×#41	D₅₃	semidirect
352. C₅₃	#3475	semidirect
405. C₄×Q₈	C₂×D₅₃	semidirect
406. C₄×Q₈	C₂×D₅₃	semidirect
425. C₄×D₄	C₂×D₅₃	semidirect
426. C₄×D₄	C₂×D₅₃	semidirect
439. #117	C₂×D₅₃	semidirect
440. #117	C₂×D₅₃	semidirect
450. C₂×C₄²	C₂×D₅₃	semidirect
451. C₂×C₄²	C₂×D₅₃	semidirect
577. D₄	#11719945	semidirect