Subgroups — #20288759

Order 6784.

1124 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811347	C₂	1	1	yes	maximal, characteristic, complemented
2	#16811331	C₂	1	2	yes	maximal, complemented
3	#16811314	C₂	1	2	yes	maximal, complemented
4	#16811297	C₂	1	4	yes	maximal, complemented
5	#16811288	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811285	C₂	1	2	yes	maximal, complemented
7	#16811276	C₂	1	1	yes	maximal, characteristic, complemented
8	#16811276	C₂	1	1	yes	maximal, characteristic, complemented
9	#16811264	C₂	1	2	yes	maximal, complemented
10	#16811245	C₂	1	2	yes	maximal, complemented
11	#16811221	C₂	1	4	yes	maximal, complemented
12	#16811157	C₂	1	1	yes	maximal, characteristic, complemented
13	#16811136	C₂	1	2	yes	maximal, complemented
14	C₂²⋊Q₈×D₅₃	C₂	1	2	yes	maximal, complemented
15	#16811105	C₂	1	2	yes	maximal, complemented
16	C₂×C₄×D₂₁₂	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#11719949	C₂²	1	2	yes	—
19	C₂×#11719949	C₂²	1	2	yes	complemented
20	C₂×Q₈×D₅₃	C₂²	1	2	yes	complemented
21	C₂²×D₂₁₂	C₂²	1	1	yes	characteristic
22	C₂²×C₄×D₅₃	C₂²	1	2	yes	—
23	#13133216	C₂²	1	2	yes	complemented
24	#13133212	C₂²	1	4	yes	complemented
25	#13133211	C₂²	1	4	yes	complemented
26	#13133211	C₂²	1	2	yes	complemented
27	#13133209	C₂²	1	1	yes	characteristic, complemented
28	#13133207	C₂²	1	4	yes	complemented
29	#13133206	C₂²	1	2	yes	—
30	#13133205	C₂²	1	1	yes	characteristic, complemented
31	#13133205	C₂²	1	4	yes	complemented
32	#13133202	C₂²	1	4	yes	—
33	#13133202	C₂²	1	4	yes	complemented
34	#13133202	C₂²	1	4	yes	complemented
35	#13133202	C₂²	1	4	yes	complemented
36	#13133200	C₂²	1	2	yes	—
37	#13133197	C₂²	1	4	yes	complemented
38	#13133197	C₂²	1	2	yes	complemented
39	#13133196	C₂²	1	1	yes	characteristic
40	#13133195	C₂²	1	4	yes	complemented
41	#13133195	C₂²	1	4	yes	complemented
42	#13133194	C₂²	1	4	yes	—
43	#13133193	C₂²	1	2	yes	complemented
44	#13133193	C₂²	1	2	yes	complemented
45	#13133193	C₂²	1	2	yes	complemented
46	#13133192	C₂²	1	2	yes	—
47	#13133192	C₂²	1	4	yes	—
48	#13133192	C₂²	1	2	yes	complemented
49	#13133191	C₂²	1	1	yes	characteristic
50	#13133187	C₂²	1	4	yes	—
51	Q₈×Dic₅₃	C₂²	1	2	yes	complemented
52	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
53	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
54	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
55	C₄×D₂₁₂	C₂²	1	2	yes	—
56	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
57	C₄×D₂₁₂	C₂²	1	2	yes	—
58	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
59	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
60	C₄×D₂₁₂	C₂²	1	4	yes	complemented
61	#13133179	C₂²	1	2	yes	—
62	#13133179	C₂²	1	4	yes	complemented
63	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	—
64	#13133177	C₂²	1	4	yes	—
65	#13133175	C₂²	1	2	yes	complemented
66	#13133174	C₂²	1	4	yes	complemented
67	#13133174	C₂²	1	2	yes	complemented
68	C₂×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
69	C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
70	C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
71	C₄⋊C₄×D₅₃	C₂²	1	4	yes	complemented
72	C₂×#11719921	C₂²	1	2	yes	—
73	C₂²⋊C₄×D₅₃	C₂²	1	4	yes	—
74	C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
75	C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
76	#125×C₅₃	C₂²	1	2	yes	complemented
77	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
78	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
79	C₄×Q₈×C₅₃	C₂²	1	2	yes	complemented
80	C₄×Q₈×C₅₃	C₂²	1	2	yes	complemented
81	#117×C₅₃	C₂²	1	2	yes	—
82	C₂×C₄²×C₅₃	C₂²	1	1	yes	characteristic
83	C₂³×D₅₃	C₂³	1	2	yes	—
84	C₂×Q₈×C₅₃	C₂³	1	2	yes	—
85	C₂×Q₈×C₅₃	C₂³	1	2	yes	—
86	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
89	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
90	C₂²×Dic₅₃	C₂³	1	2	yes	—
91	#11719949	—	2	8	no	—
92	#11719949	—	4	4	no	—
93	Q₈×D₅₃	—	4	4	no	—
94	C₂×D₂₁₂	—	2	4	no	—
95	C₂×D₂₁₂	C₂³	1	4	yes	—
96	C₂×D₂₁₂	C₂³	1	2	yes	—
97	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
98	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
99	C₂×D₂₁₂	C₂³	1	4	yes	—
100	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
101	C₂×C₄×D₅₃	—	4	4	no	—
102	C₂×C₄×D₅₃	C₂³	1	4	yes	—
103	C₂×C₄×D₅₃	C₂³	1	2	yes	—
104	C₂×C₄×D₅₃	C₂³	1	2	yes	—
105	C₂×C₄×D₅₃	C₂³	1	2	yes	—
106	C₂×C₄×D₅₃	C₂³	1	4	yes	—
107	C₂×C₄×D₅₃	C₂³	1	2	yes	—
108	C₂×C₄×D₅₃	C₂³	1	4	yes	—
109	C₂×C₄×D₅₃	C₂³	1	2	yes	—
110	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
111	C₂×Dic₁₀₆	C₂³	1	4	yes	—
112	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
113	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
114	C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
115	C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
116	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
117	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
118	C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
119	C₄²×C₅₃	C₂³	1	1	yes	characteristic
120	C₄²×C₅₃	C₂³	1	1	yes	characteristic
121	C₄²×C₅₃	C₂³	1	1	yes	characteristic
122	C₄²×C₅₃	C₂³	1	1	yes	characteristic
123	C₄²×C₅₃	C₂³	1	4	yes	—
124	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
125	#11719921	C₂³	1	4	yes	—
126	#11719921	C₂³	1	4	yes	—
127	#11719921	C₂³	1	2	yes	—
128	#11719921	C₂³	1	2	yes	—
129	#11719921	C₂³	1	2	yes	—
130	#11719921	C₂³	1	2	yes	—
131	#11719921	C₂³	1	4	yes	—
132	#11719921	C₂³	1	2	yes	—
133	#11719921	C₂³	1	2	yes	—
134	#11719921	C₂³	1	4	yes	—
135	#11719921	C₂³	1	4	yes	—
136	#11719921	C₂³	1	2	yes	—
137	#11719921	C₂³	1	2	yes	—
138	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
139	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
140	C₄⋊Dic₅₃	C₂³	1	4	yes	—
141	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
142	C₄⋊Dic₅₃	C₂³	1	2	yes	—
143	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
144	#11719919	C₂³	1	4	yes	—
145	#11719919	C₂³	1	2	yes	—
146	#11719919	C₂³	1	4	yes	—
147	#11719919	C₂³	1	2	yes	—
148	#11719919	C₂³	1	4	yes	—
149	#11719919	C₂³	1	2	yes	—
150	#11719919	C₂³	1	2	yes	—
151	C₄×Dic₅₃	C₂³	1	4	yes	—
152	C₄×Dic₅₃	C₂³	1	2	yes	—
153	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
154	C₂²×D₅₃	—	2	4	no	—
155	C₂²×D₅₃	—	2	4	no	—
156	C₂²×D₅₃	—	4	2	no	—
157	C₂²×D₅₃	C₂⁴	1	2	yes	—
158	C₂²×D₅₃	C₂⁴	1	2	yes	—
159	C₂²×D₅₃	C₂⁴	1	2	yes	—
160	Q₈×C₅₃	—	2	4	no	—
161	Q₈×C₅₃	—	2	4	no	—
162	C₂×C₄×C₅₃	—	2	2	no	—
163	C₂×C₄×C₅₃	—	2	2	no	—
164	C₂×C₄×C₅₃	—	2	2	no	—
165	C₂×C₄×C₅₃	C₂⁴	1	4	yes	—
166	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
167	C₂×C₄×C₅₃	C₂⁴	1	4	yes	—
168	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
169	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
170	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
173	C₂²⋊D₅₃	—	2	4	no	—
174	C₂×Dic₅₃	—	4	2	no	—
175	C₂×Dic₅₃	C₂⁴	1	2	yes	—
176	C₂×Dic₅₃	C₂⁴	1	2	yes	—
177	C₂×Dic₅₃	C₂⁴	1	2	yes	—
178	C₂×Dic₅₃	C₂⁴	1	2	yes	—
179	C₂×Dic₅₃	C₂⁴	1	2	yes	—
180	D₂₁₂	—	2	4	no	—
181	D₂₁₂	—	2	8	no	—
182	D₂₁₂	—	2	2	no	—
183	D₂₁₂	—	2	2	no	—
184	D₂₁₂	—	4	4	no	—
185	D₂₁₂	#41	1	4	yes	complemented
186	C₄×D₅₃	—	2	8	no	—
187	C₄×D₅₃	—	2	4	no	—
188	C₄×D₅₃	—	2	4	no	—
189	C₄×D₅₃	—	2	4	no	—
190	C₄×D₅₃	—	4	2	no	—
191	C₄×D₅₃	—	4	2	no	—
192	C₄×D₅₃	—	4	4	no	—
193	C₄×D₅₃	—	4	4	no	—
194	Dic₁₀₆	—	2	2	no	—
195	Dic₁₀₆	—	4	4	no	—
196	C₂²×C₅₃	—	2	1	no	—
197	C₂²×C₅₃	—	2	1	no	—
198	C₂²×C₅₃	2₋¹⁺⁴	1	2	yes	—
199	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
200	C₂×D₅₃	—	2	2	no	—
201	C₂×D₅₃	—	2	2	no	—
202	C₂×D₅₃	—	2	2	no	—
203	C₂×D₅₃	—	2	2	no	—
204	C₂×D₅₃	—	2	2	no	—
205	C₂×D₅₃	—	2	2	no	—
206	C₂×D₅₃	—	2	2	no	—
207	C₂×D₅₃	—	2	2	no	—
208	C₂×D₅₃	—	4	8	no	—
209	C₂×D₅₃	C₂×#41	1	4	yes	—
210	C₄×C₅₃	—	2	4	no	—
211	C₄×C₅₃	—	2	1	no	—
212	C₄×C₅₃	—	2	4	no	—
213	C₄×C₅₃	—	2	1	no	—
214	C₄×C₅₃	—	2	1	no	—
215	C₄×C₅₃	—	2	1	no	—
216	C₄×C₅₃	C₂×#41	1	2	yes	—
217	C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
218	Dic₅₃	—	2	2	no	—
219	Dic₅₃	—	2	2	no	—
220	Dic₅₃	—	2	2	no	—
221	Dic₅₃	—	2	2	no	—
222	Dic₅₃	—	2	2	no	—
223	#3520	—	53	1	no	maximal, Sylow
224	C₂×C₅₃	—	2	2	no	—
225	C₂×C₅₃	C₂²×#41	1	1	yes	characteristic
226	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
227	C₂×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
228	D₅₃	—	2	4	no	—
229	D₅₃	—	4	2	no	—
230	D₅₃	—	4	2	no	—
231	#556	—	53	1	no	—
232	#554	—	53	2	no	—
233	#552	—	53	2	no	—
234	#551	—	53	4	no	—
235	D₄×Q₈	—	53	1	no	—
236	#548	—	53	2	no	—
237	#547	—	53	1	no	—
238	#547	—	53	1	no	—
239	#546	—	53	2	no	—
240	#542	—	53	2	no	—
241	#539	—	53	4	no	—
242	#533	D₅₃	1	1	yes	characteristic, complemented
243	#529	—	53	1	no	—
244	#525	—	53	2	no	—
245	C₂×C₂²⋊Q₈	—	53	2	no	—
246	#520	—	53	2	no	—
247	C₂×C₄×D₄	—	53	1	no	—
248	C₅₃	#3520	1	1	yes	characteristic, complemented, Sylow
249	C₂×#41	—	53	2	no	—
250	C₂×#41	—	53	2	no	—
251	C₂²×Q₈	—	53	2	no	—
252	C₂²×D₄	—	53	1	no	—
253	C₂³×C₄	—	53	2	no	—
254	C₄⋊Q₈	—	53	2	no	—
255	C₄⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
256	C₄⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
257	#126	—	53	4	no	—
258	#126	—	53	2	no	—
259	#126	—	53	4	no	—
260	#125	—	53	4	no	—
261	#125	—	53	1	no	—
262	#125	C₂×D₅₃	1	2	yes	complemented
263	#124	—	53	2	no	—
264	#124	—	53	1	no	—
265	#124	—	53	4	no	—
266	#123	—	53	2	no	—
267	#123	—	53	4	no	—
268	#123	—	53	4	no	—
269	#123	—	53	4	no	—
270	#123	—	53	4	no	—
271	C₂²⋊Q₈	—	53	2	no	—
272	C₂²⋊Q₈	—	53	2	no	—
273	C₂²⋊Q₈	—	53	2	no	—
274	C₂²⋊Q₈	—	53	1	no	—
275	C₂²⋊Q₈	—	53	4	no	—
276	C₂²⋊Q₈	—	53	2	no	—
277	C₂²⋊Q₈	—	53	4	no	—
278	C₂²⋊Q₈	—	53	4	no	—
279	C₂²⋊Q₈	—	53	4	no	—
280	C₂²⋊Q₈	C₂×D₅₃	1	2	yes	—
281	C₂²⋊Q₈	C₂×D₅₃	1	2	yes	—
282	#121	—	53	1	no	—
283	#121	—	53	2	no	—
284	#121	—	53	4	no	—
285	#121	—	53	2	no	—
286	#120	—	53	4	no	—
287	C₄×Q₈	—	53	2	no	—
288	C₄×Q₈	—	53	1	no	—
289	C₄×Q₈	C₂×D₅₃	1	2	yes	complemented
290	C₄×Q₈	C₂×D₅₃	1	2	yes	complemented
291	C₄×D₄	—	53	2	no	—
292	C₄×D₄	—	53	4	no	—
293	C₄×D₄	—	53	2	no	—
294	C₄×D₄	—	53	4	no	—
295	C₄×D₄	—	53	1	no	—
296	C₄×D₄	—	53	2	no	—
297	C₄×D₄	—	53	1	no	—
298	C₄×D₄	—	53	1	no	—
299	C₄×D₄	—	53	1	no	—
300	C₄×D₄	—	53	2	no	—
301	C₄×D₄	—	53	4	no	—
302	C₄×D₄	—	53	1	no	—
303	#117	—	53	2	no	—
304	#117	—	53	2	no	—
305	#117	—	53	4	no	—
306	#117	C₂×D₅₃	1	2	yes	—
307	C₂×C₄⋊C₄	—	53	1	no	—
308	C₂×C₄⋊C₄	—	53	4	no	—
309	C₂×C₄⋊C₄	—	53	2	no	—
310	C₂×C₄⋊C₄	—	53	2	no	—
311	C₂×C₂²⋊C₄	—	53	2	no	—
312	C₂×C₂²⋊C₄	—	53	4	no	—
313	C₂×C₄²	C₂×D₅₃	1	1	yes	characteristic
314	C₂⁴	—	53	2	no	—
315	#41	—	106	8	no	—
316	#41	—	212	4	no	—
317	C₂×Q₈	—	53	1	no	—
318	C₂×Q₈	—	53	4	no	—
319	C₂×Q₈	—	212	4	no	—
320	C₂×Q₈	C₂²×D₅₃	1	2	yes	—
321	C₂×Q₈	C₂²×D₅₃	1	2	yes	—
322	C₂×D₄	—	53	2	no	—
323	C₂×D₄	—	53	1	no	—
324	C₂×D₄	—	53	4	no	—
325	C₂×D₄	—	53	2	no	—
326	C₂×D₄	—	53	1	no	—
327	C₂×D₄	—	53	1	no	—
328	C₂×D₄	—	53	4	no	—
329	C₂×D₄	—	106	4	no	—
330	C₂²×C₄	—	53	2	no	—
331	C₂²×C₄	—	53	4	no	—
332	C₂²×C₄	—	53	2	no	—
333	C₂²×C₄	—	53	2	no	—
334	C₂²×C₄	—	53	2	no	—
335	C₂²×C₄	—	53	4	no	—
336	C₂²×C₄	—	53	2	no	—
337	C₂²×C₄	—	53	4	no	—
338	C₂²×C₄	—	53	2	no	—
339	C₂²×C₄	—	212	4	no	—
340	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
341	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
342	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
343	C₄⋊C₄	—	53	1	no	—
344	C₄⋊C₄	—	53	2	no	—
345	C₄⋊C₄	—	53	4	no	—
346	C₄⋊C₄	—	53	1	no	—
347	C₄⋊C₄	—	53	2	no	—
348	C₄⋊C₄	—	53	1	no	—
349	C₄⋊C₄	—	53	4	no	—
350	C₄⋊C₄	—	53	4	no	—
351	C₄⋊C₄	—	53	2	no	—
352	C₄⋊C₄	—	53	1	no	—
353	C₄⋊C₄	—	53	4	no	—
354	C₄⋊C₄	—	53	2	no	—
355	C₄⋊C₄	—	53	2	no	—
356	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
357	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
358	C₄⋊C₄	C₂²×D₅₃	1	4	yes	—
359	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
360	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
361	C₄⋊C₄	C₂²×D₅₃	1	4	yes	—
362	C₂²⋊C₄	—	53	2	no	—
363	C₂²⋊C₄	—	53	2	no	—
364	C₂²⋊C₄	—	53	2	no	—
365	C₂²⋊C₄	—	53	2	no	—
366	C₂²⋊C₄	—	53	2	no	—
367	C₂²⋊C₄	—	53	4	no	—
368	C₂²⋊C₄	—	53	4	no	—
369	C₂²⋊C₄	—	53	4	no	—
370	C₂²⋊C₄	—	53	2	no	—
371	C₂²⋊C₄	—	53	2	no	—
372	C₂²⋊C₄	—	53	4	no	—
373	C₂²⋊C₄	—	53	2	no	—
374	C₂²⋊C₄	—	53	4	no	—
375	C₂²⋊C₄	—	53	2	no	—
376	C₂²⋊C₄	C₂²×D₅₃	1	4	yes	—
377	C₄²	—	53	4	no	—
378	C₄²	—	53	2	no	—
379	C₄²	C₂²×D₅₃	1	1	yes	characteristic
380	C₄²	C₂²×D₅₃	1	1	yes	characteristic
381	C₄²	C₂²×D₅₃	1	1	yes	characteristic
382	C₄²	C₂²×D₅₃	1	1	yes	characteristic
383	C₄²	C₂²×D₅₃	1	4	yes	—
384	C₂³	—	53	2	no	—
385	C₂³	—	53	2	no	—
386	C₂³	—	53	2	no	—
387	C₂³	—	106	4	no	—
388	C₂³	—	106	4	no	—
389	C₂³	—	212	2	no	—
390	C₂³	C₂³×D₅₃	1	1	yes	characteristic
391	Q₈	—	2	4	no	—
392	Q₈	—	2	4	no	—
393	Q₈	—	106	2	no	—
394	Q₈	—	212	4	no	—
395	D₄	—	53	4	no	—
396	D₄	—	106	4	no	—
397	D₄	—	106	8	no	—
398	D₄	—	106	4	no	—
399	D₄	—	106	2	no	—
400	D₄	—	106	2	no	—
401	D₄	—	212	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	53	2	no	—
406	C₂×C₄	—	53	2	no	—
407	C₂×C₄	—	53	2	no	—
408	C₂×C₄	—	53	2	no	—
409	C₂×C₄	—	53	2	no	—
410	C₂×C₄	—	106	8	no	—
411	C₂×C₄	—	106	4	no	—
412	C₂×C₄	—	106	4	no	—
413	C₂×C₄	—	106	4	no	—
414	C₂×C₄	—	212	2	no	—
415	C₂×C₄	—	212	2	no	—
416	C₂×C₄	—	212	4	no	—
417	C₂×C₄	—	212	4	no	—
418	C₂×C₄	—	212	2	no	—
419	C₂×C₄	C₂³×D₅₃	1	4	yes	—
420	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
421	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
422	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
423	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
424	C₂×C₄	C₂³×D₅₃	1	4	yes	—
425	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
426	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	53	4	no	—
430	C₂²	—	106	2	no	—
431	C₂²	—	106	2	no	—
432	C₂²	—	106	2	no	—
433	C₂²	—	106	2	no	—
434	C₂²	—	106	2	no	—
435	C₂²	—	106	2	no	—
436	C₂²	—	106	2	no	—
437	C₂²	—	106	2	no	—
438	C₂²	—	212	8	no	—
439	C₂²	#13133265	1	2	yes	—
440	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
441	C₄	—	2	1	no	—
442	C₄	—	2	4	no	—
443	C₄	—	2	1	no	—
444	C₄	—	2	4	no	—
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	106	2	no	—
448	C₄	—	106	2	no	—
449	C₄	—	106	2	no	—
450	C₄	—	106	2	no	—
451	C₄	—	106	2	no	—
452	C₄	#41×D₅₃	1	2	yes	—
453	C₄	#13133263	1	2	yes	—
454	C₂	—	2	2	no	—
455	C₂	—	106	4	no	—
456	C₂	—	212	2	no	—
457	C₂	—	212	2	no	—
458	C₂	C₂×#41×D₅₃	1	1	yes	characteristic
459	C₂	C₂×#13133263	1	1	yes	characteristic
460	C₂	C₂×#13133265	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#533	C₂
hypercenter	#533	D₅₃
hypocenter	C₅₃	#3520
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #533

Complements

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

N	H ≅ G/N	type
1. #16811347	C₂	semidirect
2. #16811331	C₂	semidirect
3. #16811314	C₂	semidirect
4. #16811297	C₂	semidirect
5. #16811288	C₂	semidirect
6. #16811285	C₂	semidirect
7. #16811276	C₂	semidirect
8. #16811276	C₂	semidirect
9. #16811264	C₂	semidirect
10. #16811245	C₂	semidirect
11. #16811221	C₂	semidirect
12. #16811157	C₂	semidirect
13. #16811136	C₂	semidirect
14. C₂²⋊Q₈×D₅₃	C₂	semidirect
15. #16811105	C₂	semidirect
16. C₂×C₄×D₂₁₂	C₂	semidirect
17. C₅₃×#533	C₂	semidirect
19. C₂×#11719949	C₂²	semidirect
20. C₂×Q₈×D₅₃	C₂²	semidirect
23. #13133216	C₂²	semidirect
24. #13133212	C₂²	semidirect
25. #13133211	C₂²	semidirect
26. #13133211	C₂²	semidirect
27. #13133209	C₂²	semidirect
28. #13133207	C₂²	semidirect
30. #13133205	C₂²	semidirect
31. #13133205	C₂²	semidirect
33. #13133202	C₂²	semidirect
34. #13133202	C₂²	semidirect
35. #13133202	C₂²	semidirect
37. #13133197	C₂²	semidirect
38. #13133197	C₂²	semidirect
40. #13133195	C₂²	semidirect
41. #13133195	C₂²	semidirect
43. #13133193	C₂²	semidirect
44. #13133193	C₂²	semidirect
45. #13133193	C₂²	semidirect
48. #13133192	C₂²	semidirect
51. Q₈×Dic₅₃	C₂²	semidirect
52. C₄×Dic₁₀₆	C₂²	semidirect
59. C₄×D₂₁₂	C₂²	semidirect
60. C₄×D₂₁₂	C₂²	semidirect
62. #13133179	C₂²	semidirect
65. #13133175	C₂²	semidirect
66. #13133174	C₂²	semidirect
67. #13133174	C₂²	semidirect
69. C₄⋊C₄×D₅₃	C₂²	semidirect
70. C₄⋊C₄×D₅₃	C₂²	semidirect
71. C₄⋊C₄×D₅₃	C₂²	semidirect
74. C₄⋊Q₈×C₅₃	C₂²	semidirect
75. C₄⋊Q₈×C₅₃	C₂²	semidirect
76. #125×C₅₃	C₂²	semidirect
79. C₄×Q₈×C₅₃	C₂²	semidirect
80. C₄×Q₈×C₅₃	C₂²	semidirect
185. D₂₁₂	#41	semidirect
242. #533	D₅₃	semidirect
248. C₅₃	#3520	semidirect
255. C₄⋊Q₈	C₂×D₅₃	semidirect
256. C₄⋊Q₈	C₂×D₅₃	semidirect
262. #125	C₂×D₅₃	semidirect
289. C₄×Q₈	C₂×D₅₃	semidirect
290. C₄×Q₈	C₂×D₅₃	semidirect