Subgroups — #20288676

Order 6784.

1142 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811358	C₂	1	1	yes	maximal, characteristic, complemented
2	#16811346	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811336	C₂	1	2	yes	maximal, complemented
4	#16811297	C₂	1	4	yes	maximal, complemented
5	D₄×Dic₁₀₆	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811282	C₂	1	2	yes	maximal, complemented
7	#16811269	C₂	1	2	yes	maximal, complemented
8	#16811261	C₂	1	2	yes	maximal, complemented
9	D₄×D₂₁₂	C₂	1	1	yes	maximal, characteristic, complemented
10	#16811245	C₂	1	2	yes	maximal, complemented
11	#16811206	C₂	1	4	yes	maximal, complemented
12	#16811173	C₂	1	1	yes	maximal, characteristic, complemented
13	#16811157	C₂	1	1	yes	maximal, characteristic, complemented
14	#16811157	C₂	1	2	yes	maximal, complemented
15	C₂×#13133205	C₂	1	2	yes	maximal, complemented
16	#16811095	C₂	1	2	yes	maximal, complemented
17	C₄×#41×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#11719945	C₂²	1	2	yes	complemented
19	C₂²×Dic₁₀₆	C₂²	1	2	yes	complemented
20	C₂²×D₂₁₂	C₂²	1	2	yes	—
21	C₂×D₄×D₅₃	C₂²	1	2	yes	—
22	#13133217	C₂²	1	1	yes	characteristic, complemented
23	#13133216	C₂²	1	2	yes	complemented
24	#13133214	C₂²	1	1	yes	characteristic
25	#13133212	C₂²	1	4	yes	complemented
26	#13133211	C₂²	1	2	yes	complemented
27	#13133211	C₂²	1	4	yes	complemented
28	#13133209	C₂²	1	1	yes	characteristic, complemented
29	#13133206	C₂²	1	2	yes	complemented
30	#13133205	C₂²	1	2	yes	—
31	#13133205	C₂²	1	1	yes	characteristic
32	#13133205	C₂²	1	2	yes	complemented
33	#13133205	C₂²	1	4	yes	complemented
34	#13133205	C₂²	1	2	yes	complemented
35	#13133205	C₂²	1	4	yes	complemented
36	#13133203	C₂²	1	4	yes	complemented
37	#13133202	C₂²	1	4	yes	complemented
38	#13133202	C₂²	1	4	yes	complemented
39	#13133200	C₂²	1	4	yes	complemented
40	#13133200	C₂²	1	2	yes	complemented
41	#13133196	C₂²	1	2	yes	complemented
42	#13133196	C₂²	1	1	yes	characteristic, complemented
43	#13133195	C₂²	1	4	yes	complemented
44	#13133194	C₂²	1	4	yes	complemented
45	#13133193	C₂²	1	2	yes	complemented
46	#13133192	C₂²	1	2	yes	—
47	#13133191	C₂²	1	1	yes	characteristic
48	#13133191	C₂²	1	2	yes	—
49	#13133191	C₂²	1	2	yes	complemented
50	#13133191	C₂²	1	2	yes	complemented
51	#13133190	C₂²	1	4	yes	complemented
52	#13133189	C₂²	1	4	yes	complemented
53	#13133187	C₂²	1	4	yes	—
54	#13133185	C₂²	1	4	yes	complemented
55	C₄×Dic₁₀₆	C₂²	1	2	yes	complemented
56	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
57	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
58	C₄×D₂₁₂	C₂²	1	2	yes	complemented
59	C₄×D₂₁₂	C₂²	1	2	yes	complemented
60	C₄×D₂₁₂	C₂²	1	2	yes	complemented
61	D₄×Dic₅₃	C₂²	1	2	yes	—
62	#13133179	C₂²	1	2	yes	complemented
63	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
64	C₄×C₂²⋊D₅₃	C₂²	1	4	yes	complemented
65	#13133177	C₂²	1	4	yes	complemented
66	#13133175	C₂²	1	2	yes	complemented
67	#13133174	C₂²	1	4	yes	complemented
68	#13133174	C₂²	1	2	yes	complemented
69	C₂×#11719921	C₂²	1	4	yes	complemented
70	C₂×#11719921	C₂²	1	4	yes	complemented
71	C₂²⋊C₄×D₅₃	C₂²	1	4	yes	complemented
72	C₂×#41×C₅₃	C₂²	1	1	yes	characteristic
73	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
74	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
75	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
76	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
77	C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
78	C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
79	#117×C₅₃	C₂²	1	2	yes	complemented
80	#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₄²×C₅₃	C₂²	1	2	yes	complemented
82	C₂×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
83	C₂³×D₅₃	C₂³	1	4	yes	—
84	#41×C₅₃	—	2	4	no	—
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	2	yes	—
89	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
91	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
93	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
94	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
95	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
96	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
97	C₂²×Dic₅₃	C₂³	1	4	yes	—
98	D₄×D₅₃	—	2	8	no	—
99	#11719945	—	4	4	no	—
100	C₂×D₂₁₂	—	4	4	no	—
101	C₂×D₂₁₂	C₂³	1	2	yes	—
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	4	yes	—
106	C₂×C₄×D₅₃	C₂³	1	2	yes	—
107	C₂×C₄×D₅₃	C₂³	1	4	yes	—
108	C₂×C₄×D₅₃	C₂³	1	4	yes	—
109	C₂×Dic₁₀₆	—	4	4	no	—
110	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
111	C₂×Dic₁₀₆	C₂³	1	2	yes	—
112	C₂×Dic₁₀₆	C₂³	1	4	yes	—
113	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
114	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
115	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
116	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
117	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
118	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
119	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
120	C₄²×C₅₃	C₂³	1	1	yes	characteristic
121	C₄²×C₅₃	C₂³	1	2	yes	—
122	C₄²×C₅₃	C₂³	1	1	yes	characteristic
123	C₄²×C₅₃	C₂³	1	1	yes	characteristic
124	C₄²×C₅₃	C₂³	1	1	yes	characteristic
125	C₄²×C₅₃	C₂³	1	2	yes	—
126	C₄²×C₅₃	C₂³	1	2	yes	—
127	C₂²⋊Dic₅₃	C₂³	1	4	yes	—
128	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
129	#11719921	C₂³	1	2	yes	—
130	#11719921	C₂³	1	4	yes	—
131	#11719921	C₂³	1	2	yes	—
132	#11719921	C₂³	1	2	yes	—
133	#11719921	C₂³	1	4	yes	—
134	#11719921	C₂³	1	4	yes	—
135	#11719921	C₂³	1	4	yes	—
136	#11719921	C₂³	1	4	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	C₄⋊Dic₅₃	C₂³	1	2	yes	—
142	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
143	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
144	C₄⋊Dic₅₃	C₂³	1	2	yes	—
145	#11719919	C₂³	1	2	yes	—
146	#11719919	C₂³	1	2	yes	—
147	#11719919	C₂³	1	2	yes	—
148	#11719919	C₂³	1	4	yes	—
149	#11719919	C₂³	1	4	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	C₂³×C₅₃	C₂⁴	1	2	yes	—
155	C₂²×D₅₃	—	2	8	no	—
156	C₂²×D₅₃	—	4	4	no	—
157	C₂²×D₅₃	—	4	4	no	—
158	C₂²×D₅₃	C₂⁴	1	4	yes	—
159	C₂²×D₅₃	C₂⁴	1	2	yes	—
160	Q₈×C₅₃	—	2	2	no	—
161	D₄×C₅₃	—	2	4	no	—
162	D₄×C₅₃	#41	1	4	yes	complemented
163	C₂×C₄×C₅₃	—	2	4	no	—
164	C₂×C₄×C₅₃	—	2	2	no	—
165	C₂×C₄×C₅₃	—	2	4	no	—
166	C₂×C₄×C₅₃	—	2	2	no	—
167	C₂×C₄×C₅₃	—	4	2	no	—
168	C₂×C₄×C₅₃	—	4	1	no	—
169	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
170	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
172	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
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	—	2	8	no	—
179	C₂²⋊D₅₃	—	4	4	no	—
180	C₂²⋊D₅₃	—	4	2	no	—
181	C₂×Dic₅₃	—	4	4	no	—
182	C₂×Dic₅₃	C₂⁴	1	2	yes	—
183	C₂×Dic₅₃	C₂⁴	1	4	yes	—
184	C₂×Dic₅₃	C₂⁴	1	2	yes	—
185	C₂×Dic₅₃	C₂⁴	1	2	yes	—
186	D₂₁₂	—	2	4	no	—
187	D₂₁₂	—	2	2	no	—
188	D₂₁₂	—	2	4	no	—
189	D₂₁₂	—	4	4	no	—
190	D₂₁₂	—	4	2	no	—
191	C₄×D₅₃	—	2	4	no	—
192	C₄×D₅₃	—	4	4	no	—
193	C₄×D₅₃	—	4	4	no	—
194	Dic₁₀₆	—	2	2	no	—
195	Dic₁₀₆	—	2	4	no	—
196	Dic₁₀₆	—	4	4	no	—
197	C₂²×C₅₃	—	2	2	no	—
198	C₂²×C₅₃	—	2	2	no	—
199	C₂²×C₅₃	—	2	1	no	—
200	C₂²×C₅₃	—	2	1	no	—
201	C₂²×C₅₃	—	2	1	no	—
202	C₂²×C₅₃	C₂×#41	1	4	yes	—
203	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
204	C₂×D₅₃	—	2	2	no	—
205	C₂×D₅₃	—	2	4	no	—
206	C₂×D₅₃	—	2	4	no	—
207	C₂×D₅₃	—	2	2	no	—
208	C₂×D₅₃	—	2	4	no	—
209	C₂×D₅₃	—	2	2	no	—
210	C₂×D₅₃	—	8	8	no	—
211	C₄×C₅₃	—	2	1	no	—
212	C₄×C₅₃	—	2	2	no	—
213	C₄×C₅₃	—	2	2	no	—
214	C₄×C₅₃	—	2	1	no	—
215	C₄×C₅₃	—	2	2	no	—
216	C₄×C₅₃	—	2	1	no	—
217	C₄×C₅₃	—	2	1	no	—
218	C₄×C₅₃	C₂×#41	1	2	yes	—
219	C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
220	Dic₅₃	—	2	2	no	—
221	Dic₅₃	—	2	2	no	—
222	Dic₅₃	—	2	4	no	—
223	Dic₅₃	—	2	2	no	—
224	#3514	—	53	1	no	maximal, Sylow
225	C₂×C₅₃	—	2	4	no	—
226	C₂×C₅₃	—	4	1	no	—
227	C₂×C₅₃	C₂²×#41	1	1	yes	characteristic
228	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
229	C₂×C₅₃	#585	1	1	yes	characteristic
230	D₅₃	—	4	4	no	—
231	D₅₃	—	4	2	no	—
232	#559	—	53	1	no	—
233	#556	—	53	1	no	—
234	#555	—	53	2	no	—
235	#551	—	53	4	no	—
236	D₄×Q₈	—	53	1	no	—
237	#548	—	53	2	no	—
238	#546	—	53	2	no	—
239	#546	—	53	2	no	—
240	D₄²	—	53	1	no	—
241	#542	—	53	2	no	—
242	#538	—	53	4	no	—
243	#532	—	53	1	no	—
244	#529	—	53	2	no	—
245	#529	—	53	1	no	—
246	C₂×#124	—	53	2	no	—
247	#518	—	53	2	no	—
248	C₄×#41	D₅₃	1	1	yes	characteristic, complemented
249	C₅₃	#3514	1	1	yes	characteristic, complemented, Sylow
250	C₂×#41	—	53	2	no	—
251	C₂×#41	C₂×D₅₃	1	1	yes	characteristic
252	C₂²×Q₈	—	53	2	no	—
253	C₂²×D₄	—	53	2	no	—
254	C₂²×D₄	—	53	2	no	—
255	C₄⋊Q₈	—	53	2	no	—
256	C₄⋊Q₈	—	53	1	no	—
257	#127	—	53	1	no	—
258	#126	—	53	4	no	—
259	#126	—	53	4	no	—
260	#126	—	53	2	no	—
261	#125	—	53	1	no	—
262	#124	—	53	2	no	—
263	#124	—	53	4	no	—
264	#124	—	53	1	no	—
265	#124	—	53	2	no	—
266	#124	—	53	4	no	—
267	#124	—	53	2	no	—
268	#124	—	53	2	no	—
269	#124	—	53	4	no	—
270	#123	—	53	2	no	—
271	#123	—	53	4	no	—
272	#123	—	53	4	no	—
273	#123	—	53	4	no	—
274	C₂²⋊Q₈	—	53	2	no	—
275	C₂²⋊Q₈	—	53	2	no	—
276	C₂²⋊Q₈	—	53	1	no	—
277	C₂²⋊Q₈	—	53	4	no	—
278	C₂²⋊Q₈	—	53	4	no	—
279	#121	—	53	4	no	—
280	#121	—	53	2	no	—
281	#121	—	53	1	no	—
282	#121	—	53	2	no	—
283	#121	—	53	2	no	—
284	#121	—	53	2	no	—
285	#121	—	53	4	no	—
286	#120	—	53	4	no	—
287	#120	—	53	4	no	—
288	C₄×Q₈	—	53	2	no	—
289	C₄×Q₈	—	53	1	no	—
290	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
291	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
292	C₄×D₄	—	53	2	no	—
293	C₄×D₄	—	53	4	no	—
294	C₄×D₄	—	53	2	no	—
295	C₄×D₄	—	53	2	no	—
296	C₄×D₄	—	53	4	no	—
297	C₄×D₄	—	53	2	no	—
298	C₄×D₄	—	53	1	no	—
299	C₄×D₄	—	53	2	no	—
300	C₄×D₄	—	53	2	no	—
301	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
302	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
303	C₄×D₄	C₂×D₅₃	1	2	yes	complemented
304	C₄×D₄	C₂×D₅₃	1	2	yes	complemented
305	#117	—	53	2	no	—
306	#117	—	53	2	no	—
307	#117	—	53	4	no	—
308	#117	C₂×D₅₃	1	2	yes	complemented
309	#117	C₂×D₅₃	1	1	yes	characteristic, complemented
310	C₂×C₂²⋊C₄	—	53	4	no	—
311	C₂×C₂²⋊C₄	—	53	4	no	—
312	C₂×C₂²⋊C₄	—	53	4	no	—
313	C₂×C₄²	C₂×D₅₃	1	2	yes	complemented
314	C₂×C₄²	C₂×D₅₃	1	1	yes	characteristic, complemented
315	C₂⁴	—	53	4	no	—
316	#41	—	2	4	no	—
317	#41	—	212	4	no	—
318	C₂×Q₈	—	53	1	no	—
319	C₂×Q₈	—	53	2	no	—
320	C₂×Q₈	—	53	4	no	—
321	C₂×Q₈	—	212	4	no	—
322	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
323	C₂×D₄	—	53	4	no	—
324	C₂×D₄	—	53	2	no	—
325	C₂×D₄	—	53	4	no	—
326	C₂×D₄	—	53	2	no	—
327	C₂×D₄	—	53	1	no	—
328	C₂×D₄	—	53	2	no	—
329	C₂×D₄	—	53	2	no	—
330	C₂×D₄	—	53	4	no	—
331	C₂×D₄	—	106	8	no	—
332	C₂×D₄	—	212	4	no	—
333	C₂×D₄	C₂²×D₅₃	1	2	yes	—
334	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
335	C₂²×C₄	—	53	4	no	—
336	C₂²×C₄	—	53	2	no	—
337	C₂²×C₄	—	53	4	no	—
338	C₂²×C₄	—	53	4	no	—
339	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
340	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
341	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
342	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
343	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
344	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
345	C₄⋊C₄	—	53	2	no	—
346	C₄⋊C₄	—	53	2	no	—
347	C₄⋊C₄	—	53	2	no	—
348	C₄⋊C₄	—	53	2	no	—
349	C₄⋊C₄	—	53	4	no	—
350	C₄⋊C₄	—	53	1	no	—
351	C₄⋊C₄	—	53	1	no	—
352	C₄⋊C₄	—	53	2	no	—
353	C₄⋊C₄	—	53	4	no	—
354	C₄⋊C₄	—	53	2	no	—
355	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
356	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
357	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
358	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
359	C₂²⋊C₄	—	53	4	no	—
360	C₂²⋊C₄	—	53	2	no	—
361	C₂²⋊C₄	—	53	2	no	—
362	C₂²⋊C₄	—	53	4	no	—
363	C₂²⋊C₄	—	53	2	no	—
364	C₂²⋊C₄	—	53	2	no	—
365	C₂²⋊C₄	—	53	4	no	—
366	C₂²⋊C₄	—	53	4	no	—
367	C₂²⋊C₄	—	53	4	no	—
368	C₂²⋊C₄	—	53	4	no	—
369	C₂²⋊C₄	—	53	4	no	—
370	C₂²⋊C₄	—	53	4	no	—
371	C₂²⋊C₄	—	53	2	no	—
372	C₂²⋊C₄	—	53	4	no	—
373	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
374	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
375	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
376	C₄²	—	53	4	no	—
377	C₄²	—	53	2	no	—
378	C₄²	C₂²×D₅₃	1	1	yes	characteristic
379	C₄²	C₂²×D₅₃	1	2	yes	—
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	2	yes	—
384	C₄²	C₂²×D₅₃	1	2	yes	—
385	C₂³	—	53	2	no	—
386	C₂³	—	53	4	no	—
387	C₂³	—	106	8	no	—
388	C₂³	—	212	4	no	—
389	C₂³	—	212	4	no	—
390	C₂³	C₂³×D₅₃	1	1	yes	characteristic
391	C₂³	C₂³×D₅₃	1	2	yes	—
392	Q₈	—	2	2	no	—
393	Q₈	—	106	2	no	—
394	Q₈	—	106	4	no	—
395	Q₈	—	212	4	no	—
396	D₄	—	2	4	no	—
397	D₄	—	106	8	no	—
398	D₄	—	106	4	no	—
399	D₄	—	106	2	no	—
400	D₄	—	106	4	no	—
401	D₄	—	212	2	no	—
402	D₄	—	212	4	no	—
403	D₄	—	212	2	no	—
404	D₄	—	212	4	no	—
405	D₄	#11719945	1	4	yes	complemented
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	53	2	no	—
413	C₂×C₄	—	53	2	no	—
414	C₂×C₄	—	53	2	no	—
415	C₂×C₄	—	53	4	no	—
416	C₂×C₄	—	106	4	no	—
417	C₂×C₄	—	212	4	no	—
418	C₂×C₄	—	212	4	no	—
419	C₂×C₄	—	212	4	no	—
420	C₂×C₄	C₂³×D₅₃	1	2	yes	—
421	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
422	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
423	C₂×C₄	C₂³×D₅₃	1	2	yes	—
424	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
425	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
426	C₂×C₄	C₂³×D₅₃	1	2	yes	—
427	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
428	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	106	2	no	—
435	C₂²	—	106	4	no	—
436	C₂²	—	106	4	no	—
437	C₂²	—	106	2	no	—
438	C₂²	—	106	4	no	—
439	C₂²	—	106	2	no	—
440	C₂²	—	424	8	no	—
441	C₂²	C₂×#11719945	1	4	yes	—
442	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
443	C₄	—	2	1	no	—
444	C₄	—	2	2	no	—
445	C₄	—	2	1	no	—
446	C₄	—	2	2	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	1	no	—
450	C₄	—	106	2	no	—
451	C₄	—	106	4	no	—
452	C₄	—	106	2	no	—
453	C₄	—	106	2	no	—
454	C₄	C₂×#11719945	1	2	yes	—
455	C₄	#13133263	1	2	yes	—
456	C₂	—	2	4	no	—
457	C₂	—	4	1	no	—
458	C₂	—	212	2	no	—
459	C₂	—	212	4	no	—
460	C₂	C₂²×#11719945	1	1	yes	characteristic
461	C₂	C₂×#13133263	1	1	yes	characteristic
462	C₂	#16811459	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₄×#41×C₅₃	C₂
hypercenter	C₄×#41	D₅₃
hypocenter	C₅₃	#3514
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₄×#41

Complements

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

N	H ≅ G/N	type
1. #16811358	C₂	semidirect
2. #16811346	C₂	semidirect
3. #16811336	C₂	semidirect
4. #16811297	C₂	semidirect
5. D₄×Dic₁₀₆	C₂	semidirect
6. #16811282	C₂	semidirect
7. #16811269	C₂	semidirect
8. #16811261	C₂	semidirect
9. D₄×D₂₁₂	C₂	semidirect
10. #16811245	C₂	semidirect
11. #16811206	C₂	semidirect
12. #16811173	C₂	semidirect
13. #16811157	C₂	semidirect
14. #16811157	C₂	semidirect
15. C₂×#13133205	C₂	semidirect
16. #16811095	C₂	semidirect
17. C₄×#41×C₅₃	C₂	semidirect
18. C₂×#11719945	C₂²	semidirect
19. C₂²×Dic₁₀₆	C₂²	semidirect
22. #13133217	C₂²	semidirect
23. #13133216	C₂²	semidirect
25. #13133212	C₂²	semidirect
26. #13133211	C₂²	semidirect
27. #13133211	C₂²	semidirect
28. #13133209	C₂²	semidirect
29. #13133206	C₂²	semidirect
32. #13133205	C₂²	semidirect
33. #13133205	C₂²	semidirect
34. #13133205	C₂²	semidirect
35. #13133205	C₂²	semidirect
36. #13133203	C₂²	semidirect
37. #13133202	C₂²	semidirect
38. #13133202	C₂²	semidirect
39. #13133200	C₂²	semidirect
40. #13133200	C₂²	semidirect
41. #13133196	C₂²	semidirect
42. #13133196	C₂²	semidirect
43. #13133195	C₂²	semidirect
44. #13133194	C₂²	semidirect
45. #13133193	C₂²	semidirect
49. #13133191	C₂²	semidirect
50. #13133191	C₂²	semidirect
51. #13133190	C₂²	semidirect
52. #13133189	C₂²	semidirect
54. #13133185	C₂²	semidirect
55. C₄×Dic₁₀₆	C₂²	semidirect
56. C₄×Dic₁₀₆	C₂²	semidirect
58. C₄×D₂₁₂	C₂²	semidirect
59. C₄×D₂₁₂	C₂²	semidirect
60. C₄×D₂₁₂	C₂²	semidirect
62. #13133179	C₂²	semidirect
63. C₄×C₂²⋊D₅₃	C₂²	semidirect
64. C₄×C₂²⋊D₅₃	C₂²	semidirect
65. #13133177	C₂²	semidirect
66. #13133175	C₂²	semidirect
67. #13133174	C₂²	semidirect
68. #13133174	C₂²	semidirect
69. C₂×#11719921	C₂²	semidirect
70. C₂×#11719921	C₂²	semidirect
71. C₂²⋊C₄×D₅₃	C₂²	semidirect
73. C₄×Q₈×C₅₃	C₂²	semidirect
74. C₄×Q₈×C₅₃	C₂²	semidirect
77. C₄×D₄×C₅₃	C₂²	semidirect
78. C₄×D₄×C₅₃	C₂²	semidirect
79. #117×C₅₃	C₂²	semidirect
80. #117×C₅₃	C₂²	semidirect
81. C₂×C₄²×C₅₃	C₂²	semidirect
82. C₂×C₄²×C₅₃	C₂²	semidirect
162. D₄×C₅₃	#41	semidirect
248. C₄×#41	D₅₃	semidirect
249. C₅₃	#3514	semidirect
290. C₄×Q₈	C₂×D₅₃	semidirect
291. C₄×Q₈	C₂×D₅₃	semidirect
303. C₄×D₄	C₂×D₅₃	semidirect
304. C₄×D₄	C₂×D₅₃	semidirect
308. #117	C₂×D₅₃	semidirect
309. #117	C₂×D₅₃	semidirect
313. C₂×C₄²	C₂×D₅₃	semidirect
314. C₂×C₄²	C₂×D₅₃	semidirect
405. D₄	#11719945	semidirect