Subgroups — #20289089

Order 6784.

1150 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811363	C₂	1	4	yes	maximal, complemented
2	#16811346	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811326	C₂	1	2	yes	maximal, complemented
4	#16811295	C₂	1	1	yes	maximal, characteristic, complemented
5	#16811294	C₂	1	2	yes	maximal, complemented
6	#16811278	C₂	1	1	yes	maximal, characteristic, complemented
7	#16811269	C₂	1	2	yes	maximal, complemented
8	#16811266	C₂	1	2	yes	maximal, complemented
9	D₄×D₂₁₂	C₂	1	1	yes	maximal, characteristic, complemented
10	#16811244	C₂	1	2	yes	maximal, complemented
11	#16811212	C₂	1	4	yes	maximal, complemented
12	#16811203	C₂	1	2	yes	maximal, complemented
13	#16811192	C₂	1	2	yes	maximal, complemented
14	#16811189	C₂	1	2	yes	maximal, complemented
15	#16811173	C₂	1	1	yes	maximal, characteristic, complemented
16	#16811173	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	C₂×#11719945	C₂²	1	2	yes	complemented
21	C₂×#11719945	C₂²	1	2	yes	complemented
22	C₂²×D₂₁₂	C₂²	1	2	yes	—
23	C₂×D₄×D₅₃	C₂²	1	2	yes	—
24	#13133217	C₂²	1	1	yes	characteristic, complemented
25	#13133217	C₂²	1	1	yes	characteristic, complemented
26	#13133214	C₂²	1	1	yes	characteristic
27	#13133214	C₂²	1	1	yes	characteristic
28	#13133214	C₂²	1	2	yes	complemented
29	#13133213	C₂²	1	4	yes	complemented
30	#13133212	C₂²	1	4	yes	complemented
31	#13133212	C₂²	1	4	yes	complemented
32	#13133205	C₂²	1	2	yes	—
33	#13133205	C₂²	1	2	yes	complemented
34	#13133205	C₂²	1	2	yes	complemented
35	#13133203	C₂²	1	4	yes	complemented
36	#13133202	C₂²	1	4	yes	complemented
37	#13133199	C₂²	1	4	yes	complemented
38	#13133199	C₂²	1	4	yes	complemented
39	#13133196	C₂²	1	2	yes	complemented
40	#13133195	C₂²	1	4	yes	complemented
41	#13133193	C₂²	1	2	yes	complemented
42	#13133192	C₂²	1	2	yes	—
43	#13133192	C₂²	1	2	yes	complemented
44	#13133192	C₂²	1	4	yes	complemented
45	#13133192	C₂²	1	4	yes	complemented
46	#13133192	C₂²	1	4	yes	complemented
47	#13133191	C₂²	1	1	yes	characteristic
48	#13133191	C₂²	1	2	yes	—
49	#13133191	C₂²	1	1	yes	characteristic, complemented
50	#13133191	C₂²	1	2	yes	complemented
51	#13133191	C₂²	1	2	yes	complemented
52	#13133191	C₂²	1	2	yes	complemented
53	#13133190	C₂²	1	4	yes	complemented
54	#13133190	C₂²	1	4	yes	complemented
55	#13133190	C₂²	1	4	yes	complemented
56	#13133188	C₂²	1	2	yes	—
57	#13133187	C₂²	1	4	yes	—
58	#13133187	C₂²	1	4	yes	complemented
59	#13133187	C₂²	1	4	yes	complemented
60	#13133185	C₂²	1	4	yes	complemented
61	C₄×Dic₁₀₆	C₂²	1	2	yes	complemented
62	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
63	C₄×D₂₁₂	C₂²	1	2	yes	complemented
64	C₄×D₂₁₂	C₂²	1	2	yes	complemented
65	C₄×D₂₁₂	C₂²	1	2	yes	complemented
66	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
67	C₄×D₂₁₂	C₂²	1	2	yes	complemented
68	#13133179	C₂²	1	4	yes	complemented
69	#13133175	C₂²	1	2	yes	complemented
70	C₄⋊C₄×D₅₃	C₂²	1	2	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
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	1	yes	characteristic
80	C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
81	#117×C₅₃	C₂²	1	2	yes	complemented
82	C₂×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
83	C₂³×D₅₃	C₂³	1	4	yes	—
84	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
85	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
86	C₂×D₄×C₅₃	C₂³	1	2	yes	—
87	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
90	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
91	C₂×C₂²⋊D₅₃	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	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
96	#11719949	—	4	4	no	—
97	D₄×D₅₃	—	4	4	no	—
98	#11719945	—	4	4	no	—
99	#11719945	—	4	4	no	—
100	#11719945	—	4	4	no	—
101	C₂×D₂₁₂	—	4	4	no	—
102	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
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	4	yes	—
107	C₂×D₂₁₂	C₂³	1	2	yes	—
108	C₂×D₂₁₂	C₂³	1	2	yes	—
109	C₂×D₂₁₂	C₂³	1	4	yes	—
110	C₂×D₂₁₂	C₂³	1	2	yes	—
111	C₂×D₂₁₂	C₂³	1	4	yes	—
112	C₂×C₄×D₅₃	C₂³	1	2	yes	—
113	C₂×C₄×D₅₃	C₂³	1	2	yes	—
114	C₂×C₄×D₅₃	C₂³	1	4	yes	—
115	C₂×C₄×D₅₃	C₂³	1	4	yes	—
116	C₂×C₄×D₅₃	C₂³	1	4	yes	—
117	C₂×Dic₁₀₆	C₂³	1	2	yes	—
118	C₂×Dic₁₀₆	C₂³	1	2	yes	—
119	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
120	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
121	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
122	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
123	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
124	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
125	C₂²⋊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	C₄²×C₅₃	C₂³	1	1	yes	characteristic
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	2	yes	—
135	C₂²⋊Dic₅₃	C₂³	1	4	yes	—
136	#11719921	C₂³	1	2	yes	—
137	#11719921	C₂³	1	4	yes	—
138	#11719921	C₂³	1	4	yes	—
139	#11719921	C₂³	1	2	yes	—
140	#11719921	C₂³	1	4	yes	—
141	#11719921	C₂³	1	2	yes	—
142	#11719921	C₂³	1	4	yes	—
143	#11719921	C₂³	1	4	yes	—
144	#11719921	C₂³	1	4	yes	—
145	#11719921	C₂³	1	2	yes	—
146	C₄⋊Dic₅₃	C₂³	1	2	yes	—
147	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
148	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
149	C₄⋊Dic₅₃	C₂³	1	2	yes	—
150	C₄⋊Dic₅₃	C₂³	1	2	yes	—
151	#11719919	C₂³	1	4	yes	—
152	#11719919	C₂³	1	4	yes	—
153	C₄×Dic₅₃	C₂³	1	4	yes	—
154	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
155	C₂³×C₅₃	C₂⁴	1	2	yes	—
156	C₂²×D₅₃	—	4	4	no	—
157	C₂²×D₅₃	—	4	4	no	—
158	C₂²×D₅₃	—	4	4	no	—
159	C₂²×D₅₃	C₂⁴	1	2	yes	—
160	C₂²×D₅₃	C₂⁴	1	4	yes	—
161	C₂²×D₅₃	C₂⁴	1	2	yes	—
162	Q₈×C₅₃	—	2	2	no	—
163	D₄×C₅₃	—	2	2	no	—
164	D₄×C₅₃	—	4	2	no	—
165	C₂×C₄×C₅₃	—	2	4	no	—
166	C₂×C₄×C₅₃	—	2	2	no	—
167	C₂×C₄×C₅₃	—	2	2	no	—
168	C₂×C₄×C₅₃	—	4	1	no	—
169	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
170	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
172	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
173	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
174	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
175	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
176	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
178	C₂²⋊D₅₃	—	4	4	no	—
179	C₂²⋊D₅₃	—	4	4	no	—
180	C₂²⋊D₅₃	—	4	2	no	—
181	C₂²⋊D₅₃	—	4	2	no	—
182	C₂²⋊D₅₃	—	4	4	no	—
183	C₂×Dic₅₃	C₂⁴	1	2	yes	—
184	C₂×Dic₅₃	C₂⁴	1	4	yes	—
185	C₂×Dic₅₃	C₂⁴	1	2	yes	—
186	D₂₁₂	—	2	2	no	—
187	D₂₁₂	—	2	4	no	—
188	D₂₁₂	—	2	2	no	—
189	D₂₁₂	—	2	4	no	—
190	D₂₁₂	—	4	4	no	—
191	D₂₁₂	—	4	2	no	—
192	D₂₁₂	—	4	2	no	—
193	D₂₁₂	—	4	4	no	—
194	D₂₁₂	—	4	2	no	—
195	D₂₁₂	—	4	4	no	—
196	C₄×D₅₃	—	2	4	no	—
197	C₄×D₅₃	—	2	4	no	—
198	C₄×D₅₃	—	4	4	no	—
199	C₄×D₅₃	—	4	4	no	—
200	C₄×D₅₃	—	4	4	no	—
201	Dic₁₀₆	—	2	4	no	—
202	Dic₁₀₆	—	4	2	no	—
203	C₂²×C₅₃	—	2	1	no	—
204	C₂²×C₅₃	—	2	1	no	—
205	C₂²×C₅₃	—	2	2	no	—
206	C₂²×C₅₃	—	2	2	no	—
207	C₂²×C₅₃	—	2	1	no	—
208	C₂²×C₅₃	—	2	2	no	—
209	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
210	C₂×D₅₃	—	2	2	no	—
211	C₂×D₅₃	—	2	2	no	—
212	C₂×D₅₃	—	2	2	no	—
213	C₂×D₅₃	—	2	4	no	—
214	C₂×D₅₃	—	2	4	no	—
215	C₂×D₅₃	—	2	2	no	—
216	C₂×D₅₃	—	2	2	no	—
217	C₂×D₅₃	—	2	4	no	—
218	C₂×D₅₃	—	2	2	no	—
219	C₂×D₅₃	—	8	8	no	—
220	C₄×C₅₃	—	2	1	no	—
221	C₄×C₅₃	—	2	1	no	—
222	C₄×C₅₃	—	2	2	no	—
223	C₄×C₅₃	—	2	2	no	—
224	C₄×C₅₃	—	2	1	no	—
225	C₄×C₅₃	—	2	1	no	—
226	C₄×C₅₃	—	2	2	no	—
227	C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
228	C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
229	Dic₅₃	—	2	4	no	—
230	Dic₅₃	—	2	2	no	—
231	Dic₅₃	—	2	2	no	—
232	#3546	—	53	1	no	maximal, Sylow
233	C₂×C₅₃	—	4	2	no	—
234	C₂×C₅₃	—	4	1	no	—
235	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
236	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
237	C₂×C₅₃	#585	1	1	yes	characteristic
238	D₅₃	—	4	2	no	—
239	D₅₃	—	4	4	no	—
240	D₅₃	—	4	2	no	—
241	#560	—	53	4	no	—
242	#556	—	53	1	no	—
243	#553	—	53	2	no	—
244	#550	—	53	1	no	—
245	#550	—	53	2	no	—
246	#547	—	53	1	no	—
247	#546	—	53	2	no	—
248	#546	—	53	2	no	—
249	D₄²	—	53	1	no	—
250	#542	—	53	2	no	—
251	#538	—	53	4	no	—
252	#537	—	53	2	no	—
253	#535	—	53	2	no	—
254	#535	—	53	2	no	—
255	#532	—	53	1	no	—
256	#532	—	53	1	no	—
257	#529	D₅₃	1	1	yes	characteristic, complemented
258	C₅₃	#3546	1	1	yes	characteristic, complemented, Sylow
259	C₂×#41	—	53	2	no	—
260	C₂×#41	—	53	2	no	—
261	C₂×#41	—	53	2	no	—
262	C₂×#41	—	53	2	no	—
263	C₂²×D₄	—	53	2	no	—
264	C₂²×D₄	—	53	2	no	—
265	C₄⋊Q₈	—	53	1	no	—
266	C₄⋊Q₈	—	53	1	no	—
267	#127	—	53	4	no	—
268	#127	—	53	1	no	—
269	#127	—	53	1	no	—
270	#127	—	53	2	no	—
271	#126	—	53	4	no	—
272	#126	—	53	4	no	—
273	#126	C₂×D₅₃	1	2	yes	complemented
274	#125	C₂×D₅₃	1	1	yes	characteristic, complemented
275	#124	—	53	4	no	—
276	#124	—	53	2	no	—
277	#124	—	53	2	no	—
278	#124	—	53	2	no	—
279	#124	C₂×D₅₃	1	1	yes	characteristic
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	2	no	—
286	C₂²⋊Q₈	—	53	4	no	—
287	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
288	#121	—	53	2	no	—
289	#121	—	53	2	no	—
290	#121	—	53	1	no	—
291	#121	—	53	1	no	—
292	#121	—	53	2	no	—
293	#121	—	53	2	no	—
294	#121	—	53	2	no	—
295	#121	—	53	4	no	—
296	#121	—	53	2	no	—
297	#121	—	53	4	no	—
298	#121	—	53	2	no	—
299	#121	—	53	4	no	—
300	#121	—	53	4	no	—
301	#121	—	53	4	no	—
302	#121	—	53	4	no	—
303	#121	C₂×D₅₃	1	1	yes	characteristic
304	#120	—	53	4	no	—
305	#120	—	53	4	no	—
306	#120	—	53	4	no	—
307	#120	—	53	4	no	—
308	C₄×Q₈	—	53	2	no	—
309	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
310	C₄×D₄	—	53	4	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	1	no	—
316	C₄×D₄	—	53	2	no	—
317	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
318	C₄×D₄	C₂×D₅₃	1	2	yes	complemented
319	#117	—	53	2	no	—
320	#117	C₂×D₅₃	1	2	yes	complemented
321	C₂×C₄⋊C₄	—	53	2	no	—
322	C₂×C₂²⋊C₄	—	53	4	no	—
323	C₂×C₄²	C₂×D₅₃	1	1	yes	characteristic, complemented
324	C₂⁴	—	53	4	no	—
325	#41	—	212	4	no	—
326	#41	—	212	4	no	—
327	#41	—	212	4	no	—
328	#41	—	212	4	no	—
329	C₂×Q₈	—	53	2	no	—
330	C₂×Q₈	—	53	2	no	—
331	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
332	C₂×D₄	—	53	2	no	—
333	C₂×D₄	—	53	4	no	—
334	C₂×D₄	—	53	4	no	—
335	C₂×D₄	—	53	4	no	—
336	C₂×D₄	—	53	2	no	—
337	C₂×D₄	—	53	2	no	—
338	C₂×D₄	—	53	1	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	—	53	4	no	—
347	C₂×D₄	—	212	4	no	—
348	C₂×D₄	—	212	4	no	—
349	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
350	C₂×D₄	C₂²×D₅₃	1	2	yes	—
351	C₂²×C₄	—	53	2	no	—
352	C₂²×C₄	—	53	2	no	—
353	C₂²×C₄	—	53	4	no	—
354	C₂²×C₄	—	53	4	no	—
355	C₂²×C₄	—	53	4	no	—
356	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
357	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
358	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
359	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
360	C₄⋊C₄	—	53	2	no	—
361	C₄⋊C₄	—	53	4	no	—
362	C₄⋊C₄	—	53	1	no	—
363	C₄⋊C₄	—	53	1	no	—
364	C₄⋊C₄	—	53	2	no	—
365	C₄⋊C₄	—	53	2	no	—
366	C₄⋊C₄	—	53	4	no	—
367	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
368	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
369	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
370	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
371	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
372	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
373	C₂²⋊C₄	—	53	4	no	—
374	C₂²⋊C₄	—	53	2	no	—
375	C₂²⋊C₄	—	53	4	no	—
376	C₂²⋊C₄	—	53	4	no	—
377	C₂²⋊C₄	—	53	2	no	—
378	C₂²⋊C₄	—	53	2	no	—
379	C₂²⋊C₄	—	53	4	no	—
380	C₂²⋊C₄	—	53	4	no	—
381	C₂²⋊C₄	—	53	4	no	—
382	C₂²⋊C₄	—	53	4	no	—
383	C₂²⋊C₄	—	53	2	no	—
384	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
385	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
386	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
387	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
388	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
389	C₄²	—	53	4	no	—
390	C₄²	C₂²×D₅₃	1	1	yes	characteristic
391	C₄²	C₂²×D₅₃	1	1	yes	characteristic
392	C₄²	C₂²×D₅₃	1	1	yes	characteristic
393	C₄²	C₂²×D₅₃	1	1	yes	characteristic
394	C₄²	C₂²×D₅₃	1	2	yes	—
395	C₂³	—	53	2	no	—
396	C₂³	—	53	4	no	—
397	C₂³	—	53	2	no	—
398	C₂³	—	212	4	no	—
399	C₂³	—	212	4	no	—
400	C₂³	—	212	4	no	—
401	C₂³	C₂³×D₅₃	1	2	yes	—
402	C₂³	C₂³×D₅₃	1	1	yes	characteristic
403	Q₈	—	2	2	no	—
404	Q₈	—	106	4	no	—
405	Q₈	—	212	2	no	—
406	D₄	—	2	2	no	—
407	D₄	—	4	2	no	—
408	D₄	—	106	2	no	—
409	D₄	—	106	4	no	—
410	D₄	—	106	4	no	—
411	D₄	—	106	2	no	—
412	D₄	—	212	2	no	—
413	D₄	—	212	2	no	—
414	D₄	—	212	4	no	—
415	D₄	—	212	4	no	—
416	D₄	—	212	2	no	—
417	D₄	—	212	4	no	—
418	D₄	—	212	4	no	—
419	D₄	—	212	2	no	—
420	D₄	—	212	2	no	—
421	D₄	—	212	4	no	—
422	D₄	—	212	4	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	53	2	no	—
428	C₂×C₄	—	53	4	no	—
429	C₂×C₄	—	53	2	no	—
430	C₂×C₄	—	106	4	no	—
431	C₂×C₄	—	106	4	no	—
432	C₂×C₄	—	212	4	no	—
433	C₂×C₄	—	212	4	no	—
434	C₂×C₄	—	212	4	no	—
435	C₂×C₄	C₂³×D₅₃	1	2	yes	—
436	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
437	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
438	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
439	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
440	C₂×C₄	C₂³×D₅₃	1	2	yes	—
441	C₂×C₄	C₂³×D₅₃	1	2	yes	—
442	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
443	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	1	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	106	2	no	—
451	C₂²	—	106	2	no	—
452	C₂²	—	106	2	no	—
453	C₂²	—	106	4	no	—
454	C₂²	—	106	4	no	—
455	C₂²	—	106	2	no	—
456	C₂²	—	106	2	no	—
457	C₂²	—	106	4	no	—
458	C₂²	—	106	2	no	—
459	C₂²	—	424	8	no	—
460	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
461	C₄	—	2	1	no	—
462	C₄	—	2	2	no	—
463	C₄	—	2	1	no	—
464	C₄	—	2	2	no	—
465	C₄	—	2	1	no	—
466	C₄	—	2	1	no	—
467	C₄	—	2	2	no	—
468	C₄	—	106	2	no	—
469	C₄	—	106	2	no	—
470	C₄	—	106	4	no	—
471	C₄	#13133263	1	2	yes	—
472	C₄	#13133263	1	2	yes	—
473	C₂	—	4	2	no	—
474	C₂	—	4	1	no	—
475	C₂	—	212	2	no	—
476	C₂	—	212	4	no	—
477	C₂	—	212	2	no	—
478	C₂	C₂×#13133263	1	1	yes	characteristic
479	C₂	C₂×#13133263	1	1	yes	characteristic
480	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	#3546
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. #16811363	C₂	semidirect
2. #16811346	C₂	semidirect
3. #16811326	C₂	semidirect
4. #16811295	C₂	semidirect
5. #16811294	C₂	semidirect
6. #16811278	C₂	semidirect
7. #16811269	C₂	semidirect
8. #16811266	C₂	semidirect
9. D₄×D₂₁₂	C₂	semidirect
10. #16811244	C₂	semidirect
11. #16811212	C₂	semidirect
12. #16811203	C₂	semidirect
13. #16811192	C₂	semidirect
14. #16811189	C₂	semidirect
15. #16811173	C₂	semidirect
16. #16811173	C₂	semidirect
17. C₅₃×#529	C₂	semidirect
18. C₂×#11719949	C₂²	semidirect
19. C₂×#11719945	C₂²	semidirect
20. C₂×#11719945	C₂²	semidirect
21. C₂×#11719945	C₂²	semidirect
24. #13133217	C₂²	semidirect
25. #13133217	C₂²	semidirect
28. #13133214	C₂²	semidirect
29. #13133213	C₂²	semidirect
30. #13133212	C₂²	semidirect
31. #13133212	C₂²	semidirect
33. #13133205	C₂²	semidirect
34. #13133205	C₂²	semidirect
35. #13133203	C₂²	semidirect
36. #13133202	C₂²	semidirect
37. #13133199	C₂²	semidirect
38. #13133199	C₂²	semidirect
39. #13133196	C₂²	semidirect
40. #13133195	C₂²	semidirect
41. #13133193	C₂²	semidirect
43. #13133192	C₂²	semidirect
44. #13133192	C₂²	semidirect
45. #13133192	C₂²	semidirect
46. #13133192	C₂²	semidirect
49. #13133191	C₂²	semidirect
50. #13133191	C₂²	semidirect
51. #13133191	C₂²	semidirect
52. #13133191	C₂²	semidirect
53. #13133190	C₂²	semidirect
54. #13133190	C₂²	semidirect
55. #13133190	C₂²	semidirect
58. #13133187	C₂²	semidirect
59. #13133187	C₂²	semidirect
60. #13133185	C₂²	semidirect
61. C₄×Dic₁₀₆	C₂²	semidirect
63. C₄×D₂₁₂	C₂²	semidirect
64. C₄×D₂₁₂	C₂²	semidirect
65. C₄×D₂₁₂	C₂²	semidirect
66. C₄×D₂₁₂	C₂²	semidirect
67. C₄×D₂₁₂	C₂²	semidirect
68. #13133179	C₂²	semidirect
69. #13133175	C₂²	semidirect
70. C₄⋊C₄×D₅₃	C₂²	semidirect
71. C₂²⋊C₄×D₅₃	C₂²	semidirect
72. #126×C₅₃	C₂²	semidirect
73. #125×C₅₃	C₂²	semidirect
75. #123×C₅₃	C₂²	semidirect
76. C₂²⋊Q₈×C₅₃	C₂²	semidirect
78. C₄×Q₈×C₅₃	C₂²	semidirect
80. C₄×D₄×C₅₃	C₂²	semidirect
81. #117×C₅₃	C₂²	semidirect
82. C₂×C₄²×C₅₃	C₂²	semidirect
257. #529	D₅₃	semidirect
258. C₅₃	#3546	semidirect
273. #126	C₂×D₅₃	semidirect
274. #125	C₂×D₅₃	semidirect
283. #123	C₂×D₅₃	semidirect
287. C₂²⋊Q₈	C₂×D₅₃	semidirect
309. C₄×Q₈	C₂×D₅₃	semidirect
318. C₄×D₄	C₂×D₅₃	semidirect
320. #117	C₂×D₅₃	semidirect
323. C₂×C₄²	C₂×D₅₃	semidirect