Subgroups — #20288678

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	#16811343	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811338	C₂	1	2	yes	maximal, complemented
4	#16811298	C₂	1	4	yes	maximal, complemented
5	Q₈×D₂₁₂	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811283	C₂	1	2	yes	maximal, complemented
7	#16811270	C₂	1	2	yes	maximal, complemented
8	#16811269	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	#16811209	C₂	1	4	yes	maximal, complemented
12	#16811173	C₂	1	1	yes	maximal, characteristic, complemented
13	#16811158	C₂	1	2	yes	maximal, complemented
14	#124×D₅₃	C₂	1	2	yes	maximal, complemented
15	#16811097	C₂	1	2	yes	maximal, complemented
16	C₄×#11719945	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#11719945	C₂²	1	1	yes	characteristic
19	C₂×#11719945	C₂²	1	2	yes	complemented
20	C₂×Q₈×D₅₃	C₂²	1	2	yes	complemented
21	C₂²×D₂₁₂	C₂²	1	2	yes	—
22	C₂×D₄×D₅₃	C₂²	1	2	yes	—
23	#13133217	C₂²	1	2	yes	complemented
24	#13133217	C₂²	1	1	yes	characteristic, complemented
25	#13133214	C₂²	1	1	yes	characteristic
26	#13133212	C₂²	1	4	yes	complemented
27	#13133210	C₂²	1	4	yes	complemented
28	#13133206	C₂²	1	2	yes	complemented
29	#13133205	C₂²	1	2	yes	complemented
30	#13133205	C₂²	1	2	yes	complemented
31	#13133204	C₂²	1	2	yes	—
32	#13133203	C₂²	1	4	yes	complemented
33	#13133203	C₂²	1	4	yes	complemented
34	#13133203	C₂²	1	4	yes	complemented
35	#13133202	C₂²	1	4	yes	complemented
36	#13133202	C₂²	1	4	yes	complemented
37	#13133199	C₂²	1	4	yes	complemented
38	#13133197	C₂²	1	2	yes	complemented
39	#13133197	C₂²	1	4	yes	complemented
40	#13133196	C₂²	1	2	yes	complemented
41	#13133195	C₂²	1	4	yes	complemented
42	#13133192	C₂²	1	2	yes	—
43	#13133191	C₂²	1	2	yes	—
44	#13133191	C₂²	1	2	yes	complemented
45	#13133191	C₂²	1	2	yes	complemented
46	#13133190	C₂²	1	4	yes	complemented
47	#13133188	C₂²	1	4	yes	complemented
48	#13133187	C₂²	1	4	yes	—
49	#13133185	C₂²	1	4	yes	complemented
50	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
51	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
52	#13133182	C₂²	1	2	yes	complemented
53	C₄×D₂₁₂	C₂²	1	2	yes	—
54	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
55	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
56	C₄×D₂₁₂	C₂²	1	2	yes	complemented
57	C₄×D₂₁₂	C₂²	1	2	yes	complemented
58	C₄×D₂₁₂	C₂²	1	2	yes	complemented
59	#13133179	C₂²	1	2	yes	complemented
60	#13133179	C₂²	1	4	yes	complemented
61	#13133179	C₂²	1	4	yes	complemented
62	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
63	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
64	#13133176	C₂²	1	1	yes	characteristic, complemented
65	#13133176	C₂²	1	2	yes	complemented
66	#13133175	C₂²	1	4	yes	complemented
67	#13133174	C₂²	1	2	yes	complemented
68	C₂²⋊C₄×D₅₃	C₂²	1	4	yes	complemented
69	C₂²⋊C₄×D₅₃	C₂²	1	4	yes	complemented
70	C₂²⋊C₄×D₅₃	C₂²	1	4	yes	complemented
71	C₄²×D₅₃	C₂²	1	2	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	Q₈×D₅₃	—	4	4	no	—
95	D₄×D₅₃	—	4	4	no	—
96	#11719945	—	2	4	no	—
97	#11719945	—	4	4	no	—
98	C₂×D₂₁₂	—	2	8	no	—
99	C₂×D₂₁₂	C₂³	1	4	yes	—
100	C₂×D₂₁₂	C₂³	1	2	yes	—
101	C₂×D₂₁₂	C₂³	1	2	yes	—
102	C₂×D₂₁₂	C₂³	1	2	yes	—
103	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
104	C₂×C₄×D₅₃	C₂³	1	2	yes	—
105	C₂×C₄×D₅₃	C₂³	1	2	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×C₄×D₅₃	C₂³	1	4	yes	—
110	C₂×Dic₁₀₆	C₂³	1	2	yes	—
111	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
112	C₂×Dic₁₀₆	C₂³	1	4	yes	—
113	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
114	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
115	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
116	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
117	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
118	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
119	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
120	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
121	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
122	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
123	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
124	C₄²×C₅₃	C₂³	1	1	yes	characteristic
125	C₄²×C₅₃	C₂³	1	1	yes	characteristic
126	C₄²×C₅₃	C₂³	1	1	yes	characteristic
127	C₄²×C₅₃	C₂³	1	1	yes	characteristic
128	C₄²×C₅₃	C₂³	1	2	yes	—
129	C₂²⋊Dic₅₃	C₂³	1	4	yes	—
130	C₂²⋊Dic₅₃	C₂³	1	4	yes	—
131	C₂²⋊Dic₅₃	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	2	yes	—
139	#11719921	C₂³	1	4	yes	—
140	#11719921	C₂³	1	4	yes	—
141	C₄⋊Dic₅₃	C₂³	1	4	yes	—
142	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
143	C₄⋊Dic₅₃	C₂³	1	2	yes	—
144	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
145	C₄⋊Dic₅₃	C₂³	1	2	yes	—
146	#11719919	C₂³	1	2	yes	—
147	#11719919	C₂³	1	2	yes	—
148	#11719919	C₂³	1	4	yes	—
149	C₄×Dic₅₃	C₂³	1	2	yes	—
150	C₄×Dic₅₃	C₂³	1	2	yes	—
151	C₄×Dic₅₃	C₂³	1	2	yes	—
152	C₄×Dic₅₃	C₂³	1	4	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	2	no	—
162	D₄×C₅₃	—	4	2	no	—
163	C₂×C₄×C₅₃	—	2	4	no	—
164	C₂×C₄×C₅₃	—	2	2	no	—
165	C₂×C₄×C₅₃	—	2	2	no	—
166	C₂×C₄×C₅₃	—	4	1	no	—
167	C₂×C₄×C₅₃	C₂⁴	1	2	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	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	1	yes	characteristic
176	C₂²⋊D₅₃	—	2	4	no	—
177	C₂²⋊D₅₃	—	4	4	no	—
178	C₂²⋊D₅₃	—	4	4	no	—
179	C₂×Dic₅₃	C₂⁴	1	4	yes	—
180	C₂×Dic₅₃	C₂⁴	1	2	yes	—
181	C₂×Dic₅₃	C₂⁴	1	2	yes	—
182	C₂×Dic₅₃	C₂⁴	1	2	yes	—
183	D₂₁₂	—	2	8	no	—
184	D₂₁₂	—	2	4	no	—
185	D₂₁₂	—	2	4	no	—
186	D₂₁₂	—	4	2	no	—
187	D₂₁₂	#41	1	4	yes	complemented
188	C₄×D₅₃	—	2	4	no	—
189	C₄×D₅₃	—	2	4	no	—
190	C₄×D₅₃	—	4	2	no	—
191	C₄×D₅₃	—	4	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	1	no	—
198	C₂²×C₅₃	—	2	2	no	—
199	C₂²×C₅₃	—	2	1	no	—
200	C₂²×C₅₃	—	2	2	no	—
201	C₂²×C₅₃	—	2	1	no	—
202	C₂²×C₅₃	—	2	2	no	—
203	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
204	C₂×D₅₃	—	2	2	no	—
205	C₂×D₅₃	—	2	2	no	—
206	C₂×D₅₃	—	2	4	no	—
207	C₂×D₅₃	—	2	4	no	—
208	C₂×D₅₃	—	2	4	no	—
209	C₂×D₅₃	—	8	8	no	—
210	C₂×D₅₃	C₂×#41	1	4	yes	—
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	1	no	—
216	C₄×C₅₃	—	2	2	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	4	no	—
222	Dic₅₃	—	2	2	no	—
223	Dic₅₃	—	2	2	no	—
224	#3514	—	53	1	no	maximal, Sylow
225	C₂×C₅₃	—	4	2	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	—	2	4	no	—
231	D₅₃	—	4	4	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	D₅₃	1	1	yes	characteristic, complemented
246	C₂×#124	—	53	2	no	—
247	#518	—	53	2	no	—
248	C₄×#41	—	53	1	no	—
249	C₅₃	#3514	1	1	yes	characteristic, complemented, Sylow
250	C₂×#41	—	53	1	no	—
251	C₂×#41	—	53	2	no	—
252	C₂²×Q₈	—	53	2	no	—
253	C₂²×D₄	—	53	2	no	—
254	C₂²×D₄	—	53	2	no	—
255	C₄⋊Q₈	—	53	1	no	—
256	C₄⋊Q₈	—	53	2	no	—
257	#127	—	53	1	no	—
258	#126	—	53	4	no	—
259	#126	—	53	4	no	—
260	#126	C₂×D₅₃	1	2	yes	complemented
261	#125	C₂×D₅₃	1	1	yes	characteristic, complemented
262	#124	—	53	2	no	—
263	#124	—	53	2	no	—
264	#124	—	53	4	no	—
265	#124	—	53	4	no	—
266	#124	—	53	4	no	—
267	#124	—	53	2	no	—
268	#124	—	53	2	no	—
269	#124	C₂×D₅₃	1	1	yes	characteristic
270	#123	—	53	4	no	—
271	#123	—	53	4	no	—
272	#123	—	53	4	no	—
273	#123	C₂×D₅₃	1	2	yes	complemented
274	C₂²⋊Q₈	—	53	2	no	—
275	C₂²⋊Q₈	—	53	2	no	—
276	C₂²⋊Q₈	—	53	4	no	—
277	C₂²⋊Q₈	—	53	4	no	—
278	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
279	#121	—	53	4	no	—
280	#121	—	53	2	no	—
281	#121	—	53	2	no	—
282	#121	—	53	2	no	—
283	#121	—	53	2	no	—
284	#121	—	53	4	no	—
285	#121	C₂×D₅₃	1	1	yes	characteristic
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	—	53	1	no	—
291	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
292	C₄×D₄	—	53	2	no	—
293	C₄×D₄	—	53	2	no	—
294	C₄×D₄	—	53	4	no	—
295	C₄×D₄	—	53	4	no	—
296	C₄×D₄	—	53	2	no	—
297	C₄×D₄	—	53	1	no	—
298	C₄×D₄	—	53	1	no	—
299	C₄×D₄	—	53	2	no	—
300	C₄×D₄	—	53	2	no	—
301	C₄×D₄	—	53	2	no	—
302	C₄×D₄	—	53	2	no	—
303	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
304	C₄×D₄	C₂×D₅₃	1	2	yes	complemented
305	#117	—	53	1	no	—
306	#117	—	53	2	no	—
307	#117	—	53	4	no	—
308	#117	—	53	2	no	—
309	#117	C₂×D₅₃	1	2	yes	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	—	53	2	no	—
314	C₂×C₄²	C₂×D₅₃	1	1	yes	characteristic, complemented
315	C₂⁴	—	53	4	no	—
316	#41	—	106	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	2	no	—
324	C₂×D₄	—	53	4	no	—
325	C₂×D₄	—	53	4	no	—
326	C₂×D₄	—	53	1	no	—
327	C₂×D₄	—	53	4	no	—
328	C₂×D₄	—	53	2	no	—
329	C₂×D₄	—	53	2	no	—
330	C₂×D₄	—	53	2	no	—
331	C₂×D₄	—	106	8	no	—
332	C₂×D₄	—	212	4	no	—
333	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
334	C₂×D₄	C₂²×D₅₃	1	2	yes	—
335	C₂²×C₄	—	53	2	no	—
336	C₂²×C₄	—	53	2	no	—
337	C₂²×C₄	—	53	2	no	—
338	C₂²×C₄	—	53	4	no	—
339	C₂²×C₄	—	53	4	no	—
340	C₂²×C₄	—	53	4	no	—
341	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
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	1	no	—
346	C₄⋊C₄	—	53	2	no	—
347	C₄⋊C₄	—	53	1	no	—
348	C₄⋊C₄	—	53	2	no	—
349	C₄⋊C₄	—	53	2	no	—
350	C₄⋊C₄	—	53	4	no	—
351	C₄⋊C₄	—	53	2	no	—
352	C₄⋊C₄	—	53	4	no	—
353	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
354	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
355	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
356	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
357	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
358	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
359	C₂²⋊C₄	—	53	4	no	—
360	C₂²⋊C₄	—	53	4	no	—
361	C₂²⋊C₄	—	53	2	no	—
362	C₂²⋊C₄	—	53	2	no	—
363	C₂²⋊C₄	—	53	4	no	—
364	C₂²⋊C₄	—	53	4	no	—
365	C₂²⋊C₄	—	53	4	no	—
366	C₂²⋊C₄	—	53	4	no	—
367	C₂²⋊C₄	—	53	4	no	—
368	C₂²⋊C₄	—	53	2	no	—
369	C₂²⋊C₄	—	53	4	no	—
370	C₂²⋊C₄	—	53	4	no	—
371	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
372	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
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	2	no	—
377	C₄²	—	53	2	no	—
378	C₄²	—	53	2	no	—
379	C₄²	—	53	4	no	—
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	1	yes	characteristic
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	2	yes	—
391	C₂³	C₂³×D₅₃	1	1	yes	characteristic
392	Q₈	—	2	2	no	—
393	Q₈	—	106	2	no	—
394	Q₈	—	106	4	no	—
395	Q₈	—	212	4	no	—
396	D₄	—	2	2	no	—
397	D₄	—	4	2	no	—
398	D₄	—	53	4	no	—
399	D₄	—	106	8	no	—
400	D₄	—	106	4	no	—
401	D₄	—	106	4	no	—
402	D₄	—	106	4	no	—
403	D₄	—	212	2	no	—
404	D₄	—	212	4	no	—
405	D₄	—	212	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	53	2	no	—
411	C₂×C₄	—	53	2	no	—
412	C₂×C₄	—	53	2	no	—
413	C₂×C₄	—	53	4	no	—
414	C₂×C₄	—	106	4	no	—
415	C₂×C₄	—	106	4	no	—
416	C₂×C₄	—	212	2	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	1	yes	characteristic
421	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
422	C₂×C₄	C₂³×D₅₃	1	2	yes	—
423	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
424	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
425	C₂×C₄	C₂³×D₅₃	1	2	yes	—
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	1	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	53	4	no	—
436	C₂²	—	106	2	no	—
437	C₂²	—	106	2	no	—
438	C₂²	—	106	4	no	—
439	C₂²	—	106	4	no	—
440	C₂²	—	106	4	no	—
441	C₂²	—	424	8	no	—
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	1	no	—
449	C₄	—	2	2	no	—
450	C₄	—	106	2	no	—
451	C₄	—	106	2	no	—
452	C₄	—	106	4	no	—
453	C₄	—	106	2	no	—
454	C₄	#41×D₅₃	1	2	yes	—
455	C₄	#13133263	1	2	yes	—
456	C₂	—	4	2	no	—
457	C₂	—	4	1	no	—
458	C₂	—	106	4	no	—
459	C₂	—	212	4	no	—
460	C₂	C₂×#41×D₅₃	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	C₅₃×#529	C₂
hypercenter	#529	D₅₃
hypocenter	C₅₃	#3514
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. #16811358	C₂	semidirect
2. #16811343	C₂	semidirect
3. #16811338	C₂	semidirect
4. #16811298	C₂	semidirect
5. Q₈×D₂₁₂	C₂	semidirect
6. #16811283	C₂	semidirect
7. #16811270	C₂	semidirect
8. #16811269	C₂	semidirect
9. D₄×D₂₁₂	C₂	semidirect
10. #16811244	C₂	semidirect
11. #16811209	C₂	semidirect
12. #16811173	C₂	semidirect
13. #16811158	C₂	semidirect
14. #124×D₅₃	C₂	semidirect
15. #16811097	C₂	semidirect
16. C₄×#11719945	C₂	semidirect
17. C₅₃×#529	C₂	semidirect
19. C₂×#11719945	C₂²	semidirect
20. C₂×Q₈×D₅₃	C₂²	semidirect
23. #13133217	C₂²	semidirect
24. #13133217	C₂²	semidirect
26. #13133212	C₂²	semidirect
27. #13133210	C₂²	semidirect
28. #13133206	C₂²	semidirect
29. #13133205	C₂²	semidirect
30. #13133205	C₂²	semidirect
32. #13133203	C₂²	semidirect
33. #13133203	C₂²	semidirect
34. #13133203	C₂²	semidirect
35. #13133202	C₂²	semidirect
36. #13133202	C₂²	semidirect
37. #13133199	C₂²	semidirect
38. #13133197	C₂²	semidirect
39. #13133197	C₂²	semidirect
40. #13133196	C₂²	semidirect
41. #13133195	C₂²	semidirect
44. #13133191	C₂²	semidirect
45. #13133191	C₂²	semidirect
46. #13133190	C₂²	semidirect
47. #13133188	C₂²	semidirect
49. #13133185	C₂²	semidirect
50. C₄×Dic₁₀₆	C₂²	semidirect
51. C₄×Dic₁₀₆	C₂²	semidirect
52. #13133182	C₂²	semidirect
56. C₄×D₂₁₂	C₂²	semidirect
57. C₄×D₂₁₂	C₂²	semidirect
58. C₄×D₂₁₂	C₂²	semidirect
59. #13133179	C₂²	semidirect
60. #13133179	C₂²	semidirect
61. #13133179	C₂²	semidirect
62. C₄×C₂²⋊D₅₃	C₂²	semidirect
63. C₄×C₂²⋊D₅₃	C₂²	semidirect
64. #13133176	C₂²	semidirect
65. #13133176	C₂²	semidirect
66. #13133175	C₂²	semidirect
67. #13133174	C₂²	semidirect
68. C₂²⋊C₄×D₅₃	C₂²	semidirect
69. C₂²⋊C₄×D₅₃	C₂²	semidirect
70. C₂²⋊C₄×D₅₃	C₂²	semidirect
71. C₄²×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
187. D₂₁₂	#41	semidirect
245. #529	D₅₃	semidirect
249. C₅₃	#3514	semidirect
260. #126	C₂×D₅₃	semidirect
261. #125	C₂×D₅₃	semidirect
273. #123	C₂×D₅₃	semidirect
278. C₂²⋊Q₈	C₂×D₅₃	semidirect
291. C₄×Q₈	C₂×D₅₃	semidirect
304. C₄×D₄	C₂×D₅₃	semidirect
309. #117	C₂×D₅₃	semidirect
314. C₂×C₄²	C₂×D₅₃	semidirect