Subgroups — #20288749

Order 6784.

1252 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811338	C₂	1	1	yes	maximal, characteristic, complemented
2	#16811333	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811326	C₂	1	2	yes	maximal, complemented
4	#16811319	C₂	1	2	yes	maximal, complemented
5	#16811295	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811266	C₂	1	2	yes	maximal, complemented
7	#16811265	C₂	1	4	yes	maximal, complemented
8	D₄×D₂₁₂	C₂	1	2	yes	maximal, complemented
9	D₄×D₂₁₂	C₂	1	1	yes	maximal, characteristic, complemented
10	#16811228	C₂	1	2	yes	maximal, complemented
11	#16811212	C₂	1	4	yes	maximal, complemented
12	#16811173	C₂	1	1	yes	maximal, characteristic, complemented
13	#16811136	C₂	1	2	yes	maximal, complemented
14	#121×D₅₃	C₂	1	2	yes	maximal, complemented
15	#16811097	C₂	1	2	yes	maximal, complemented
16	C₂×C₄×D₂₁₂	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#11719949	C₂²	1	2	yes	complemented
19	C₂×#11719945	C₂²	1	2	yes	complemented
20	C₂²×D₂₁₂	C₂²	1	1	yes	characteristic
21	C₂²×D₂₁₂	C₂²	1	2	yes	—
22	C₂×D₄×D₅₃	C₂²	1	4	yes	complemented
23	C₂×D₄×D₅₃	C₂²	1	2	yes	complemented
24	C₂²×C₄×D₅₃	C₂²	1	2	yes	complemented
25	#13133217	C₂²	1	1	yes	characteristic, complemented
26	#13133214	C₂²	1	1	yes	characteristic, complemented
27	#13133214	C₂²	1	2	yes	complemented
28	#13133212	C₂²	1	4	yes	complemented
29	#13133209	C₂²	1	2	yes	complemented
30	#13133205	C₂²	1	2	yes	complemented
31	#13133203	C₂²	1	4	yes	complemented
32	#13133202	C₂²	1	4	yes	complemented
33	#13133202	C₂²	1	4	yes	complemented
34	#13133199	C₂²	1	4	yes	complemented
35	#13133195	C₂²	1	4	yes	complemented
36	#13133193	C₂²	1	2	yes	complemented
37	#13133192	C₂²	1	4	yes	complemented
38	#13133192	C₂²	1	2	yes	complemented
39	#13133192	C₂²	1	2	yes	complemented
40	#13133192	C₂²	1	4	yes	complemented
41	#13133191	C₂²	1	2	yes	complemented
42	#13133191	C₂²	1	2	yes	complemented
43	#13133191	C₂²	1	2	yes	complemented
44	#13133191	C₂²	1	2	yes	complemented
45	#13133190	C₂²	1	4	yes	complemented
46	#13133190	C₂²	1	4	yes	complemented
47	#13133189	C₂²	1	4	yes	complemented
48	#13133188	C₂²	1	2	yes	complemented
49	#13133187	C₂²	1	4	yes	complemented
50	#13133187	C₂²	1	4	yes	complemented
51	#13133187	C₂²	1	4	yes	complemented
52	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
53	C₄×D₂₁₂	C₂²	1	2	yes	—
54	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
55	C₄×D₂₁₂	C₂²	1	2	yes	complemented
56	C₄×D₂₁₂	C₂²	1	2	yes	complemented
57	C₄×D₂₁₂	C₂²	1	2	yes	complemented
58	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
59	C₄×D₂₁₂	C₂²	1	2	yes	complemented
60	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
61	C₄×D₂₁₂	C₂²	1	2	yes	complemented
62	#13133179	C₂²	1	4	yes	complemented
63	#13133179	C₂²	1	4	yes	complemented
64	#13133177	C₂²	1	4	yes	complemented
65	#13133176	C₂²	1	2	yes	complemented
66	#13133175	C₂²	1	2	yes	complemented
67	C₂×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
68	C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
69	C₂×#11719921	C₂²	1	2	yes	complemented
70	C₂²⋊C₄×D₅₃	C₂²	1	4	yes	complemented
71	C₂²⋊C₄×D₅₃	C₂²	1	4	yes	complemented
72	#126×C₅₃	C₂²	1	2	yes	complemented
73	#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
74	#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
75	#123×C₅₃	C₂²	1	2	yes	complemented
76	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
77	#121×C₅₃	C₂²	1	1	yes	characteristic
78	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
79	C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
80	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
81	#117×C₅₃	C₂²	1	2	yes	complemented
82	C₂×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
83	C₂³×D₅₃	C₂³	1	2	yes	—
84	C₂³×D₅₃	C₂³	1	4	yes	—
85	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
86	C₂×D₄×C₅₃	C₂³	1	2	yes	—
87	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
91	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
92	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
93	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
94	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
95	C₂²×Dic₅₃	C₂³	1	2	yes	—
96	#11719949	—	4	4	no	—
97	D₄×D₅₃	—	4	4	no	—
98	D₄×D₅₃	—	4	8	no	—
99	#11719945	—	4	4	no	—
100	C₂×D₂₁₂	—	2	4	no	—
101	C₂×D₂₁₂	—	2	8	no	—
102	C₂×D₂₁₂	C₂³	1	4	yes	—
103	C₂×D₂₁₂	C₂³	1	2	yes	—
104	C₂×D₂₁₂	C₂³	1	2	yes	—
105	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
106	C₂×D₂₁₂	C₂³	1	2	yes	—
107	C₂×D₂₁₂	C₂³	1	4	yes	—
108	C₂×D₂₁₂	C₂³	1	2	yes	—
109	C₂×D₂₁₂	C₂³	1	4	yes	—
110	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
111	C₂×C₄×D₅₃	—	4	4	no	—
112	C₂×C₄×D₅₃	C₂³	1	2	yes	—
113	C₂×C₄×D₅₃	C₂³	1	2	yes	—
114	C₂×C₄×D₅₃	C₂³	1	2	yes	—
115	C₂×C₄×D₅₃	C₂³	1	4	yes	—
116	C₂×C₄×D₅₃	C₂³	1	4	yes	—
117	C₂×C₄×D₅₃	C₂³	1	4	yes	—
118	C₂×C₄×D₅₃	C₂³	1	2	yes	—
119	C₂×Dic₁₀₆	C₂³	1	2	yes	—
120	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
121	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
122	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
123	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
124	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
125	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
126	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
127	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
128	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
129	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
130	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
131	C₄²×C₅₃	C₂³	1	1	yes	characteristic
132	C₄²×C₅₃	C₂³	1	1	yes	characteristic
133	C₄²×C₅₃	C₂³	1	1	yes	characteristic
134	C₄²×C₅₃	C₂³	1	1	yes	characteristic
135	C₄²×C₅₃	C₂³	1	2	yes	—
136	C₂²⋊Dic₅₃	C₂³	1	4	yes	—
137	#11719921	C₂³	1	2	yes	—
138	#11719921	C₂³	1	4	yes	—
139	#11719921	C₂³	1	4	yes	—
140	#11719921	C₂³	1	4	yes	—
141	#11719921	C₂³	1	2	yes	—
142	#11719921	C₂³	1	2	yes	—
143	#11719921	C₂³	1	2	yes	—
144	#11719921	C₂³	1	4	yes	—
145	#11719921	C₂³	1	4	yes	—
146	#11719921	C₂³	1	4	yes	—
147	C₄⋊Dic₅₃	C₂³	1	2	yes	—
148	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
149	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
150	C₄⋊Dic₅₃	C₂³	1	2	yes	—
151	C₄⋊Dic₅₃	C₂³	1	2	yes	—
152	#11719919	C₂³	1	4	yes	—
153	#11719919	C₂³	1	4	yes	—
154	C₄×Dic₅₃	C₂³	1	4	yes	—
155	C₂³×C₅₃	C₂⁴	1	2	yes	—
156	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
157	C₂²×D₅₃	—	2	4	no	—
158	C₂²×D₅₃	—	2	4	no	—
159	C₂²×D₅₃	—	2	8	no	—
160	C₂²×D₅₃	—	4	2	no	—
161	C₂²×D₅₃	—	4	4	no	—
162	C₂²×D₅₃	—	4	4	no	—
163	C₂²×D₅₃	C₂⁴	1	2	yes	—
164	C₂²×D₅₃	C₂⁴	1	4	yes	—
165	C₂²×D₅₃	C₂⁴	1	2	yes	—
166	Q₈×C₅₃	—	2	2	no	—
167	D₄×C₅₃	—	2	4	no	—
168	D₄×C₅₃	—	2	2	no	—
169	C₂×C₄×C₅₃	—	2	2	no	—
170	C₂×C₄×C₅₃	—	2	2	no	—
171	C₂×C₄×C₅₃	—	2	4	no	—
172	C₂×C₄×C₅₃	—	2	2	no	—
173	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
174	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
175	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
176	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
177	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
178	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
179	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
180	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
181	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
182	C₂²⋊D₅₃	—	2	8	no	—
183	C₂²⋊D₅₃	—	4	4	no	—
184	C₂²⋊D₅₃	—	4	4	no	—
185	C₂×Dic₅₃	—	4	2	no	—
186	C₂×Dic₅₃	C₂⁴	1	4	yes	—
187	C₂×Dic₅₃	C₂⁴	1	2	yes	—
188	C₂×Dic₅₃	C₂⁴	1	2	yes	—
189	D₂₁₂	—	2	8	no	—
190	D₂₁₂	—	2	4	no	—
191	D₂₁₂	—	2	2	no	—
192	D₂₁₂	—	2	4	no	—
193	D₂₁₂	—	2	4	no	—
194	D₂₁₂	—	4	2	no	—
195	D₂₁₂	—	4	4	no	—
196	D₂₁₂	—	4	4	no	—
197	D₂₁₂	#41	1	4	yes	complemented
198	C₄×D₅₃	—	2	4	no	—
199	C₄×D₅₃	—	2	4	no	—
200	C₄×D₅₃	—	4	2	no	—
201	C₄×D₅₃	—	4	2	no	—
202	C₄×D₅₃	—	4	4	no	—
203	C₄×D₅₃	—	4	4	no	—
204	C₄×D₅₃	—	4	4	no	—
205	Dic₁₀₆	—	4	2	no	—
206	C₂²×C₅₃	—	2	1	no	—
207	C₂²×C₅₃	—	2	1	no	—
208	C₂²×C₅₃	—	2	2	no	—
209	C₂²×C₅₃	—	2	2	no	—
210	C₂²×C₅₃	—	2	2	no	—
211	C₂²×C₅₃	H(5,𝔽₂)	1	2	yes	—
212	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
213	C₂×D₅₃	—	2	2	no	—
214	C₂×D₅₃	—	2	2	no	—
215	C₂×D₅₃	—	2	2	no	—
216	C₂×D₅₃	—	2	4	no	—
217	C₂×D₅₃	—	2	2	no	—
218	C₂×D₅₃	—	2	4	no	—
219	C₂×D₅₃	—	2	4	no	—
220	C₂×D₅₃	—	2	2	no	—
221	C₂×D₅₃	—	4	8	no	—
222	C₂×D₅₃	—	8	8	no	—
223	C₂×D₅₃	C₂×#41	1	4	yes	—
224	C₄×C₅₃	—	2	2	no	—
225	C₄×C₅₃	—	2	1	no	—
226	C₄×C₅₃	—	2	1	no	—
227	C₄×C₅₃	—	2	1	no	—
228	C₄×C₅₃	—	2	1	no	—
229	C₄×C₅₃	—	2	2	no	—
230	C₄×C₅₃	—	2	2	no	—
231	C₄×C₅₃	C₂×#41	1	2	yes	—
232	C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
233	Dic₅₃	—	2	4	no	—
234	Dic₅₃	—	2	2	no	—
235	Dic₅₃	—	2	2	no	—
236	#3519	—	53	1	no	maximal, Sylow
237	C₂×C₅₃	—	2	2	no	—
238	C₂×C₅₃	—	4	2	no	—
239	C₂×C₅₃	C₂²×#41	1	1	yes	characteristic
240	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
241	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
242	D₅₃	—	2	4	no	—
243	D₅₃	—	4	2	no	—
244	D₅₃	—	4	4	no	—
245	#555	—	53	1	no	—
246	#554	—	53	1	no	—
247	#553	—	53	2	no	—
248	#553	—	53	2	no	—
249	#550	—	53	1	no	—
250	#546	—	53	2	no	—
251	#546	—	53	4	no	—
252	D₄²	—	53	1	no	—
253	D₄²	—	53	2	no	—
254	#540	—	53	2	no	—
255	#538	—	53	4	no	—
256	#532	—	53	1	no	—
257	#529	D₅₃	1	1	yes	characteristic, complemented
258	#525	—	53	2	no	—
259	C₂×#121	—	53	2	no	—
260	#518	—	53	2	no	—
261	C₂×C₄×D₄	—	53	1	no	—
262	C₅₃	#3519	1	1	yes	characteristic, complemented, Sylow
263	C₂×#41	—	53	2	no	—
264	C₂×#41	—	53	2	no	—
265	C₂²×D₄	—	53	2	no	—
266	C₂²×D₄	—	53	4	no	—
267	C₂²×D₄	—	53	1	no	—
268	C₂²×D₄	—	53	2	no	—
269	C₂³×C₄	—	53	2	no	—
270	C₄⋊Q₈	—	53	1	no	—
271	#127	—	53	1	no	—
272	#127	—	53	2	no	—
273	#126	—	53	4	no	—
274	#126	C₂×D₅₃	1	2	yes	complemented
275	#125	—	53	2	no	—
276	#125	C₂×D₅₃	1	1	yes	characteristic, complemented
277	#124	—	53	4	no	—
278	#124	—	53	2	no	—
279	#124	C₂×D₅₃	1	1	yes	characteristic, complemented
280	#123	—	53	4	no	—
281	#123	—	53	4	no	—
282	#123	—	53	4	no	—
283	#123	C₂×D₅₃	1	2	yes	complemented
284	C₂²⋊Q₈	—	53	2	no	—
285	C₂²⋊Q₈	—	53	4	no	—
286	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
287	#121	—	53	4	no	—
288	#121	—	53	2	no	—
289	#121	—	53	2	no	—
290	#121	—	53	2	no	—
291	#121	—	53	2	no	—
292	#121	—	53	2	no	—
293	#121	—	53	2	no	—
294	#121	—	53	2	no	—
295	#121	—	53	4	no	—
296	#121	—	53	4	no	—
297	#121	—	53	4	no	—
298	#121	—	53	4	no	—
299	#121	C₂×D₅₃	1	1	yes	characteristic
300	#120	—	53	4	no	—
301	#120	—	53	4	no	—
302	#120	—	53	4	no	—
303	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
304	C₄×D₄	—	53	4	no	—
305	C₄×D₄	—	53	4	no	—
306	C₄×D₄	—	53	4	no	—
307	C₄×D₄	—	53	1	no	—
308	C₄×D₄	—	53	2	no	—
309	C₄×D₄	—	53	1	no	—
310	C₄×D₄	—	53	1	no	—
311	C₄×D₄	—	53	2	no	—
312	C₄×D₄	—	53	1	no	—
313	C₄×D₄	—	53	2	no	—
314	C₄×D₄	—	53	2	no	—
315	C₄×D₄	—	53	2	no	—
316	C₄×D₄	—	53	2	no	—
317	C₄×D₄	C₂×D₅₃	1	2	yes	complemented
318	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
319	#117	—	53	2	no	—
320	#117	—	53	2	no	—
321	#117	C₂×D₅₃	1	2	yes	complemented
322	C₂×C₄⋊C₄	—	53	1	no	—
323	C₂×C₄⋊C₄	—	53	2	no	—
324	C₂×C₂²⋊C₄	—	53	2	no	—
325	C₂×C₂²⋊C₄	—	53	4	no	—
326	C₂×C₂²⋊C₄	—	53	4	no	—
327	C₂×C₄²	C₂×D₅₃	1	1	yes	characteristic, complemented
328	C₂⁴	—	53	2	no	—
329	C₂⁴	—	53	4	no	—
330	#41	—	212	4	no	—
331	#41	—	212	4	no	—
332	C₂×Q₈	—	53	2	no	—
333	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
334	C₂×D₄	—	53	4	no	—
335	C₂×D₄	—	53	4	no	—
336	C₂×D₄	—	53	4	no	—
337	C₂×D₄	—	53	1	no	—
338	C₂×D₄	—	53	4	no	—
339	C₂×D₄	—	53	2	no	—
340	C₂×D₄	—	53	1	no	—
341	C₂×D₄	—	53	2	no	—
342	C₂×D₄	—	53	2	no	—
343	C₂×D₄	—	53	4	no	—
344	C₂×D₄	—	53	2	no	—
345	C₂×D₄	—	53	4	no	—
346	C₂×D₄	—	106	8	no	—
347	C₂×D₄	—	106	4	no	—
348	C₂×D₄	—	212	4	no	—
349	C₂×D₄	—	212	8	no	—
350	C₂×D₄	C₂²×D₅₃	1	2	yes	—
351	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
352	C₂²×C₄	—	53	2	no	—
353	C₂²×C₄	—	53	2	no	—
354	C₂²×C₄	—	53	2	no	—
355	C₂²×C₄	—	53	2	no	—
356	C₂²×C₄	—	53	4	no	—
357	C₂²×C₄	—	53	4	no	—
358	C₂²×C₄	—	53	4	no	—
359	C₂²×C₄	—	53	2	no	—
360	C₂²×C₄	—	212	4	no	—
361	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
362	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
363	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
364	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
365	C₄⋊C₄	—	53	1	no	—
366	C₄⋊C₄	—	53	2	no	—
367	C₄⋊C₄	—	53	1	no	—
368	C₄⋊C₄	—	53	2	no	—
369	C₄⋊C₄	—	53	4	no	—
370	C₄⋊C₄	—	53	2	no	—
371	C₄⋊C₄	—	53	4	no	—
372	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
373	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
374	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
375	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
376	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
377	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
378	C₂²⋊C₄	—	53	4	no	—
379	C₂²⋊C₄	—	53	2	no	—
380	C₂²⋊C₄	—	53	4	no	—
381	C₂²⋊C₄	—	53	2	no	—
382	C₂²⋊C₄	—	53	4	no	—
383	C₂²⋊C₄	—	53	2	no	—
384	C₂²⋊C₄	—	53	4	no	—
385	C₂²⋊C₄	—	53	2	no	—
386	C₂²⋊C₄	—	53	4	no	—
387	C₂²⋊C₄	—	53	4	no	—
388	C₂²⋊C₄	—	53	4	no	—
389	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
390	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
391	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
392	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
393	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
394	C₄²	—	53	4	no	—
395	C₄²	C₂²×D₅₃	1	1	yes	characteristic
396	C₄²	C₂²×D₅₃	1	1	yes	characteristic
397	C₄²	C₂²×D₅₃	1	1	yes	characteristic
398	C₄²	C₂²×D₅₃	1	1	yes	characteristic
399	C₄²	C₂²×D₅₃	1	2	yes	—
400	C₂³	—	53	2	no	—
401	C₂³	—	53	2	no	—
402	C₂³	—	53	4	no	—
403	C₂³	—	106	8	no	—
404	C₂³	—	106	4	no	—
405	C₂³	—	106	4	no	—
406	C₂³	—	212	4	no	—
407	C₂³	—	212	4	no	—
408	C₂³	—	212	2	no	—
409	C₂³	C₂³×D₅₃	1	2	yes	—
410	C₂³	C₂³×D₅₃	1	1	yes	characteristic
411	Q₈	—	2	2	no	—
412	Q₈	—	212	2	no	—
413	D₄	—	2	4	no	—
414	D₄	—	2	2	no	—
415	D₄	—	53	4	no	—
416	D₄	—	106	8	no	—
417	D₄	—	106	4	no	—
418	D₄	—	106	8	no	—
419	D₄	—	106	4	no	—
420	D₄	—	106	2	no	—
421	D₄	—	106	4	no	—
422	D₄	—	212	4	no	—
423	D₄	—	212	2	no	—
424	D₄	—	212	4	no	—
425	D₄	—	212	4	no	—
426	D₄	—	212	4	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	53	2	no	—
432	C₂×C₄	—	53	4	no	—
433	C₂×C₄	—	53	2	no	—
434	C₂×C₄	—	106	4	no	—
435	C₂×C₄	—	106	4	no	—
436	C₂×C₄	—	212	2	no	—
437	C₂×C₄	—	212	2	no	—
438	C₂×C₄	—	212	4	no	—
439	C₂×C₄	—	212	4	no	—
440	C₂×C₄	—	212	4	no	—
441	C₂×C₄	—	212	2	no	—
442	C₂×C₄	C₂³×D₅₃	1	2	yes	—
443	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
444	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
445	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
446	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
447	C₂×C₄	C₂³×D₅₃	1	2	yes	—
448	C₂×C₄	C₂³×D₅₃	1	2	yes	—
449	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
450	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
451	C₂²	—	2	1	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	53	4	no	—
457	C₂²	—	106	2	no	—
458	C₂²	—	106	2	no	—
459	C₂²	—	106	4	no	—
460	C₂²	—	106	2	no	—
461	C₂²	—	106	2	no	—
462	C₂²	—	106	4	no	—
463	C₂²	—	106	4	no	—
464	C₂²	—	106	2	no	—
465	C₂²	—	424	8	no	—
466	C₂²	—	212	8	no	—
467	C₂²	#13133263	1	2	yes	—
468	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
469	C₄	—	2	2	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	2	1	no	—
473	C₄	—	2	1	no	—
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	106	2	no	—
477	C₄	—	106	2	no	—
478	C₄	—	106	4	no	—
479	C₄	#41×D₅₃	1	2	yes	—
480	C₄	#13133263	1	2	yes	—
481	C₂	—	2	2	no	—
482	C₂	—	4	2	no	—
483	C₂	—	106	4	no	—
484	C₂	—	212	4	no	—
485	C₂	—	212	2	no	—
486	C₂	C₂×#41×D₅₃	1	1	yes	characteristic
487	C₂	C₂×#13133263	1	1	yes	characteristic
488	C₂	C₂×#13133263	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	#3519
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. #16811338	C₂	semidirect
2. #16811333	C₂	semidirect
3. #16811326	C₂	semidirect
4. #16811319	C₂	semidirect
5. #16811295	C₂	semidirect
6. #16811266	C₂	semidirect
7. #16811265	C₂	semidirect
8. D₄×D₂₁₂	C₂	semidirect
9. D₄×D₂₁₂	C₂	semidirect
10. #16811228	C₂	semidirect
11. #16811212	C₂	semidirect
12. #16811173	C₂	semidirect
13. #16811136	C₂	semidirect
14. #121×D₅₃	C₂	semidirect
15. #16811097	C₂	semidirect
16. C₂×C₄×D₂₁₂	C₂	semidirect
17. C₅₃×#529	C₂	semidirect
18. C₂×#11719949	C₂²	semidirect
19. C₂×#11719945	C₂²	semidirect
22. C₂×D₄×D₅₃	C₂²	semidirect
23. C₂×D₄×D₅₃	C₂²	semidirect
24. C₂²×C₄×D₅₃	C₂²	semidirect
25. #13133217	C₂²	semidirect
26. #13133214	C₂²	semidirect
27. #13133214	C₂²	semidirect
28. #13133212	C₂²	semidirect
29. #13133209	C₂²	semidirect
30. #13133205	C₂²	semidirect
31. #13133203	C₂²	semidirect
32. #13133202	C₂²	semidirect
33. #13133202	C₂²	semidirect
34. #13133199	C₂²	semidirect
35. #13133195	C₂²	semidirect
36. #13133193	C₂²	semidirect
37. #13133192	C₂²	semidirect
38. #13133192	C₂²	semidirect
39. #13133192	C₂²	semidirect
40. #13133192	C₂²	semidirect
41. #13133191	C₂²	semidirect
42. #13133191	C₂²	semidirect
43. #13133191	C₂²	semidirect
44. #13133191	C₂²	semidirect
45. #13133190	C₂²	semidirect
46. #13133190	C₂²	semidirect
47. #13133189	C₂²	semidirect
48. #13133188	C₂²	semidirect
49. #13133187	C₂²	semidirect
50. #13133187	C₂²	semidirect
51. #13133187	C₂²	semidirect
55. C₄×D₂₁₂	C₂²	semidirect
56. C₄×D₂₁₂	C₂²	semidirect
57. C₄×D₂₁₂	C₂²	semidirect
58. C₄×D₂₁₂	C₂²	semidirect
59. C₄×D₂₁₂	C₂²	semidirect
60. C₄×D₂₁₂	C₂²	semidirect
61. C₄×D₂₁₂	C₂²	semidirect
62. #13133179	C₂²	semidirect
63. #13133179	C₂²	semidirect
64. #13133177	C₂²	semidirect
65. #13133176	C₂²	semidirect
66. #13133175	C₂²	semidirect
67. C₂×C₄⋊Dic₅₃	C₂²	semidirect
68. C₄⋊C₄×D₅₃	C₂²	semidirect
69. C₂×#11719921	C₂²	semidirect
70. C₂²⋊C₄×D₅₃	C₂²	semidirect
71. C₂²⋊C₄×D₅₃	C₂²	semidirect
72. #126×C₅₃	C₂²	semidirect
73. #125×C₅₃	C₂²	semidirect
74. #124×C₅₃	C₂²	semidirect
75. #123×C₅₃	C₂²	semidirect
76. C₂²⋊Q₈×C₅₃	C₂²	semidirect
78. C₄×Q₈×C₅₃	C₂²	semidirect
79. C₄×D₄×C₅₃	C₂²	semidirect
80. C₄×D₄×C₅₃	C₂²	semidirect
81. #117×C₅₃	C₂²	semidirect
82. C₂×C₄²×C₅₃	C₂²	semidirect
197. D₂₁₂	#41	semidirect
257. #529	D₅₃	semidirect
262. C₅₃	#3519	semidirect
274. #126	C₂×D₅₃	semidirect
276. #125	C₂×D₅₃	semidirect
279. #124	C₂×D₅₃	semidirect
283. #123	C₂×D₅₃	semidirect
286. C₂²⋊Q₈	C₂×D₅₃	semidirect
303. C₄×Q₈	C₂×D₅₃	semidirect
317. C₄×D₄	C₂×D₅₃	semidirect
318. C₄×D₄	C₂×D₅₃	semidirect
321. #117	C₂×D₅₃	semidirect
327. C₂×C₄²	C₂×D₅₃	semidirect