Subgroups — #20288807

Order 6784.

992 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811350	C₂	1	2	yes	maximal, complemented
2	#16811350	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811348	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811344	C₂	1	1	yes	maximal, characteristic, complemented
5	#16811340	C₂	1	2	yes	maximal, complemented
6	#16811311	C₂	1	1	yes	maximal, characteristic, complemented
7	#16811309	C₂	1	2	yes	maximal, complemented
8	#16811307	C₂	1	1	yes	maximal, characteristic, complemented
9	#16811305	C₂	1	2	yes	maximal, complemented
10	#16811288	C₂	1	1	yes	maximal, characteristic, complemented
11	#16811286	C₂	1	1	yes	maximal, characteristic, complemented
12	#16811286	C₂	1	1	yes	maximal, characteristic, complemented
13	#16811232	C₂	1	2	yes	maximal, complemented
14	#16811231	C₂	1	1	yes	maximal, characteristic, complemented
15	#16811230	C₂	1	2	yes	maximal, complemented
16	#16811179	C₂	1	2	yes	maximal, complemented
17	#16811177	C₂	1	1	yes	maximal, characteristic, complemented
18	#16811156	C₂	1	2	yes	maximal
19	#16811151	C₂	1	1	yes	maximal, characteristic
20	#16811100	C₂	1	1	yes	maximal, characteristic, complemented
21	#16811099	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×Q₈×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#541	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×Dic₁₀₆	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₅₃	C₂²	1	1	yes	characteristic
26	C₂×Q₈×D₅₃	C₂²	1	1	yes	characteristic
27	#13133216	C₂²	1	2	yes	—
28	#13133216	C₂²	1	2	yes	—
29	#13133216	C₂²	1	2	yes	—
30	#13133216	C₂²	1	2	yes	—
31	#13133216	C₂²	1	1	yes	characteristic
32	#13133215	C₂²	1	1	yes	characteristic
33	#13133215	C₂²	1	1	yes	characteristic
34	#13133212	C₂²	1	2	yes	—
35	#13133212	C₂²	1	2	yes	—
36	#13133212	C₂²	1	2	yes	—
37	#13133212	C₂²	1	1	yes	characteristic
38	#13133211	C₂²	1	2	yes	—
39	#13133210	C₂²	1	2	yes	—
40	#13133210	C₂²	1	2	yes	—
41	#13133210	C₂²	1	1	yes	characteristic
42	#13133209	C₂²	1	2	yes	—
43	#13133208	C₂²	1	1	yes	characteristic
44	#13133208	C₂²	1	2	yes	—
45	#13133208	C₂²	1	2	yes	—
46	#13133207	C₂²	1	2	yes	—
47	#13133207	C₂²	1	2	yes	—
48	#13133207	C₂²	1	2	yes	—
49	#13133207	C₂²	1	2	yes	—
50	#13133207	C₂²	1	2	yes	—
51	#13133207	C₂²	1	2	yes	—
52	#13133207	C₂²	1	1	yes	characteristic
53	#13133207	C₂²	1	2	yes	—
54	#13133203	C₂²	1	1	yes	characteristic
55	#13133203	C₂²	1	2	yes	—
56	#13133202	C₂²	1	1	yes	characteristic
57	#13133202	C₂²	1	2	yes	—
58	#13133199	C₂²	1	2	yes	—
59	#13133199	C₂²	1	1	yes	characteristic
60	#13133197	C₂²	1	1	yes	characteristic
61	#13133197	C₂²	1	1	yes	characteristic
62	#13133195	C₂²	1	2	yes	—
63	#13133195	C₂²	1	2	yes	—
64	#13133195	C₂²	1	2	yes	—
65	#13133195	C₂²	1	2	yes	—
66	#13133195	C₂²	1	1	yes	characteristic
67	#13133195	C₂²	1	2	yes	—
68	#13133194	C₂²	1	2	yes	—
69	#13133194	C₂²	1	2	yes	—
70	#13133193	C₂²	1	1	yes	characteristic
71	#13133193	C₂²	1	1	yes	characteristic
72	#13133190	C₂²	1	1	yes	characteristic
73	Q₈×Dic₅₃	C₂²	1	1	yes	characteristic
74	Q₈×Dic₅₃	C₂²	1	1	yes	characteristic
75	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
76	C₄×Dic₁₀₆	C₂²	1	2	yes	—
77	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
78	C₄×Dic₁₀₆	C₂²	1	2	yes	—
79	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
80	C₄×Dic₁₀₆	C₂²	1	2	yes	—
81	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
82	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
83	#13133182	C₂²	1	1	yes	characteristic
84	#13133182	C₂²	1	1	yes	characteristic
85	#13133182	C₂²	1	2	yes	—
86	#13133182	C₂²	1	2	yes	—
87	#13133182	C₂²	1	2	yes	—
88	#13133182	C₂²	1	2	yes	—
89	#13133182	C₂²	1	2	yes	—
90	#13133182	C₂²	1	2	yes	—
91	#13133182	C₂²	1	2	yes	—
92	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
93	#13133179	C₂²	1	2	yes	—
94	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
95	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
96	#13133177	C₂²	1	2	yes	—
97	#13133177	C₂²	1	2	yes	—
98	#13133176	C₂²	1	1	yes	characteristic
99	#13133175	C₂²	1	2	yes	—
100	#13133175	C₂²	1	2	yes	—
101	#13133175	C₂²	1	1	yes	characteristic
102	#13133175	C₂²	1	2	yes	—
103	#13133174	C₂²	1	2	yes	—
104	#13133174	C₂²	1	2	yes	—
105	#13133174	C₂²	1	1	yes	characteristic
106	#13133173	C₂²	1	2	yes	—
107	#13133173	C₂²	1	2	yes	—
108	C₄⋊C₄×D₅₃	C₂²	1	2	yes	—
109	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
110	C₄²×D₅₃	C₂²	1	1	yes	characteristic
111	C₄²×D₅₃	C₂²	1	2	yes	—
112	C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
113	#126×C₅₃	C₂²	1	2	yes	—
114	#126×C₅₃	C₂²	1	2	yes	—
115	#125×C₅₃	C₂²	1	2	yes	—
116	#125×C₅₃	C₂²	1	1	yes	characteristic
117	#125×C₅₃	C₂²	1	2	yes	—
118	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
119	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
120	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
121	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
122	#117×C₅₃	C₂²	1	1	yes	characteristic
123	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
125	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
126	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
127	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
128	C₂²×Dic₅₃	C₂³	1	2	yes	—
129	Q₈×D₅₃	—	2	4	no	—
130	Q₈×D₅₃	—	2	4	no	—
131	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
132	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
133	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
134	C₂×C₄×D₅₃	C₂³	1	2	yes	—
135	C₂×C₄×D₅₃	C₂³	1	2	yes	—
136	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
137	C₂×C₄×D₅₃	C₂³	1	2	yes	—
138	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
139	C₂×Dic₁₀₆	—	2	4	no	—
140	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
141	C₂×Dic₁₀₆	C₂³	1	2	yes	—
142	C₂×Dic₁₀₆	C₂³	1	2	yes	—
143	C₂×Dic₁₀₆	C₂³	1	2	yes	—
144	C₂×Dic₁₀₆	C₂³	1	2	yes	—
145	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
146	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
147	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
148	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
149	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
150	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
151	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
152	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
153	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
154	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
155	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
156	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
157	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
158	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
159	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
160	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
161	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
162	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
163	C₄²×C₅₃	C₂³	1	1	yes	characteristic
164	C₄²×C₅₃	C₂³	1	1	yes	characteristic
165	C₄²×C₅₃	C₂³	1	2	yes	—
166	C₄²×C₅₃	C₂³	1	2	yes	—
167	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
168	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
169	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
170	#11719921	C₂³	1	1	yes	characteristic
171	#11719921	C₂³	1	1	yes	characteristic
172	#11719921	C₂³	1	2	yes	—
173	#11719921	C₂³	1	2	yes	—
174	#11719921	C₂³	1	2	yes	—
175	#11719921	C₂³	1	1	yes	characteristic
176	#11719921	C₂³	1	1	yes	characteristic
177	#11719921	C₂³	1	2	yes	—
178	#11719921	C₂³	1	1	yes	characteristic
179	#11719921	C₂³	1	2	yes	—
180	#11719921	C₂³	1	1	yes	characteristic
181	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
182	C₄⋊Dic₅₃	C₂³	1	2	yes	—
183	C₄⋊Dic₅₃	C₂³	1	2	yes	—
184	C₄⋊Dic₅₃	C₂³	1	2	yes	—
185	C₄⋊Dic₅₃	C₂³	1	2	yes	—
186	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
187	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
188	C₄⋊Dic₅₃	C₂³	1	2	yes	—
189	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
190	#11719919	C₂³	1	2	yes	—
191	#11719919	C₂³	1	2	yes	—
192	#11719919	C₂³	1	2	yes	—
193	#11719919	C₂³	1	2	yes	—
194	#11719919	C₂³	1	2	yes	—
195	#11719919	C₂³	1	2	yes	—
196	#11719919	C₂³	1	2	yes	—
197	#11719919	C₂³	1	1	yes	characteristic
198	#11719919	C₂³	1	1	yes	characteristic
199	#11719919	C₂³	1	2	yes	—
200	#11719919	C₂³	1	2	yes	—
201	#11719919	C₂³	1	2	yes	—
202	#11719919	C₂³	1	2	yes	—
203	#11719919	C₂³	1	1	yes	characteristic
204	#11719919	C₂³	1	1	yes	characteristic
205	#11719919	C₂³	1	1	yes	characteristic
206	#11719919	C₂³	1	2	yes	—
207	#11719919	C₂³	1	2	yes	—
208	#11719919	C₂³	1	2	yes	—
209	#11719919	C₂³	1	2	yes	—
210	#11719919	C₂³	1	1	yes	characteristic
211	C₄×Dic₅₃	C₂³	1	2	yes	—
212	C₄×Dic₅₃	C₂³	1	2	yes	—
213	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
214	C₄×Dic₅₃	C₂³	1	2	yes	—
215	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
216	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
217	C₄×Dic₅₃	C₂³	1	2	yes	—
218	C₄×Dic₅₃	C₂³	1	2	yes	—
219	C₄×Dic₅₃	C₂³	1	2	yes	—
220	C₄×Dic₅₃	C₂³	1	2	yes	—
221	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
222	C₄×Dic₅₃	C₂³	1	2	yes	—
223	C₄×Dic₅₃	C₂³	1	2	yes	—
224	C₄×Dic₅₃	C₂³	1	2	yes	—
225	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
226	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
227	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
228	Q₈×C₅₃	—	2	2	no	—
229	Q₈×C₅₃	—	2	2	no	—
230	C₂×C₄×C₅₃	—	2	2	no	—
231	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
232	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
233	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
234	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
235	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
236	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
238	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
239	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
241	C₂²⋊D₅₃	—	2	2	no	—
242	C₂²⋊D₅₃	—	2	2	no	—
243	C₂×Dic₅₃	—	2	4	no	—
244	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
245	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
246	C₂×Dic₅₃	C₂⁴	1	2	yes	—
247	C₂×Dic₅₃	C₂⁴	1	2	yes	—
248	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
249	C₂×Dic₅₃	C₂⁴	1	2	yes	—
250	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
252	C₂×Dic₅₃	C₂⁴	1	2	yes	—
253	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
254	D₂₁₂	—	2	2	no	—
255	C₄×D₅₃	—	2	2	no	—
256	C₄×D₅₃	—	2	4	no	—
257	C₄×D₅₃	—	2	2	no	—
258	C₄×D₅₃	—	2	2	no	—
259	C₄×D₅₃	—	2	4	no	—
260	C₄×D₅₃	—	2	4	no	—
261	C₄×D₅₃	—	2	2	no	—
262	Dic₁₀₆	—	2	2	no	—
263	Dic₁₀₆	—	2	4	no	—
264	Dic₁₀₆	—	2	4	no	—
265	Dic₁₀₆	—	2	4	no	—
266	Dic₁₀₆	—	2	2	no	—
267	Dic₁₀₆	—	2	4	no	—
268	Dic₁₀₆	#41	1	4	yes	—
269	C₂²×C₅₃	—	2	1	no	—
270	C₂²×C₅₃	—	2	1	no	—
271	C₂²×C₅₃	—	2	1	no	—
272	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
273	C₂×D₅₃	—	2	1	no	—
274	C₂×D₅₃	—	2	1	no	—
275	C₂×D₅₃	—	2	1	no	—
276	C₂×D₅₃	—	2	1	no	—
277	C₂×D₅₃	—	2	1	no	—
278	C₂×D₅₃	2₋¹⁺⁴	1	2	yes	—
279	C₄×C₅₃	—	2	1	no	—
280	C₄×C₅₃	—	2	2	no	—
281	C₄×C₅₃	—	2	2	no	—
282	C₄×C₅₃	—	2	1	no	—
283	C₄×C₅₃	—	2	2	no	—
284	C₄×C₅₃	—	2	1	no	—
285	C₄×C₅₃	—	2	2	no	—
286	C₄×C₅₃	—	2	1	no	—
287	C₄×C₅₃	—	2	1	no	—
288	C₄×C₅₃	C₂×#41	1	2	yes	—
289	Dic₅₃	—	2	1	no	—
290	Dic₅₃	—	2	1	no	—
291	Dic₅₃	—	2	2	no	—
292	Dic₅₃	—	2	2	no	—
293	Dic₅₃	—	2	1	no	—
294	Dic₅₃	—	2	2	no	—
295	Dic₅₃	—	2	1	no	—
296	Dic₅₃	—	2	1	no	—
297	Dic₅₃	C₂×#41	1	4	yes	—
298	Dic₅₃	2₋¹⁺⁴	1	2	yes	—
299	#3523	—	53	1	no	maximal, Sylow
300	C₂×C₅₃	—	4	1	no	—
301	C₂×C₅₃	C₂²×#41	1	1	yes	characteristic
302	C₂×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
303	C₂×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
304	D₅₃	—	2	2	no	—
305	D₅₃	—	4	1	no	—
306	#557	—	53	1	no	—
307	#557	—	53	1	no	—
308	#557	—	53	2	no	—
309	#556	—	53	2	no	—
310	#556	—	53	1	no	—
311	#552	—	53	2	no	—
312	#552	—	53	2	no	—
313	#552	—	53	1	no	—
314	#552	—	53	1	no	—
315	D₄×Q₈	—	53	1	no	—
316	D₄×Q₈	—	53	1	no	—
317	D₄×Q₈	—	53	1	no	—
318	#541	—	53	2	no	—
319	#541	—	53	2	no	—
320	#541	—	53	1	no	—
321	#541	D₅₃	1	1	yes	characteristic, complemented
322	#533	—	53	2	no	—
323	#533	—	53	1	no	—
324	#529	—	53	2	no	—
325	#529	—	53	1	no	—
326	#519	—	53	1	no	—
327	#519	—	53	1	no	—
328	C₂×C₄×Q₈	—	53	1	no	—
329	C₅₃	#3523	1	1	yes	characteristic, complemented, Sylow
330	C₂²×Q₈	—	53	1	no	—
331	C₂²×Q₈	—	53	1	no	—
332	C₂²×Q₈	—	53	1	no	—
333	C₄⋊Q₈	—	53	1	no	—
334	C₄⋊Q₈	—	53	1	no	—
335	C₄⋊Q₈	—	53	2	no	—
336	C₄⋊Q₈	—	53	2	no	—
337	C₄⋊Q₈	—	53	1	no	—
338	C₄⋊Q₈	—	53	2	no	—
339	C₄⋊Q₈	—	53	2	no	—
340	C₄⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
341	#126	—	53	1	no	—
342	#126	—	53	2	no	—
343	#126	—	53	2	no	—
344	#126	—	53	2	no	—
345	#126	—	53	1	no	—
346	#126	—	53	2	no	—
347	#126	—	53	2	no	—
348	#126	—	53	2	no	—
349	#126	C₂×D₅₃	1	2	yes	—
350	#126	C₂×D₅₃	1	2	yes	—
351	#125	—	53	2	no	—
352	#125	—	53	1	no	—
353	#125	—	53	2	no	—
354	#125	—	53	2	no	—
355	#125	—	53	2	no	—
356	#125	—	53	2	no	—
357	#125	—	53	2	no	—
358	#125	—	53	2	no	—
359	#125	—	53	2	no	—
360	#125	—	53	2	no	—
361	#125	—	53	1	no	—
362	#125	—	53	2	no	—
363	#125	C₂×D₅₃	1	2	yes	—
364	#125	C₂×D₅₃	1	2	yes	—
365	#125	C₂×D₅₃	1	1	yes	characteristic
366	#124	—	53	2	no	—
367	#124	—	53	1	no	—
368	#123	—	53	2	no	—
369	#123	—	53	1	no	—
370	#123	—	53	2	no	—
371	#123	—	53	1	no	—
372	C₂²⋊Q₈	—	53	1	no	—
373	C₂²⋊Q₈	—	53	1	no	—
374	C₂²⋊Q₈	—	53	2	no	—
375	C₂²⋊Q₈	—	53	1	no	—
376	C₂²⋊Q₈	—	53	2	no	—
377	C₂²⋊Q₈	—	53	2	no	—
378	C₂²⋊Q₈	—	53	1	no	—
379	C₂²⋊Q₈	—	53	2	no	—
380	C₂²⋊Q₈	—	53	1	no	—
381	C₂²⋊Q₈	—	53	2	no	—
382	C₂²⋊Q₈	—	53	2	no	—
383	C₂²⋊Q₈	—	53	2	no	—
384	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
385	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
386	#121	—	53	1	no	—
387	C₄×Q₈	—	53	1	no	—
388	C₄×Q₈	—	53	1	no	—
389	C₄×Q₈	—	53	1	no	—
390	C₄×Q₈	—	53	2	no	—
391	C₄×Q₈	—	53	2	no	—
392	C₄×Q₈	—	53	2	no	—
393	C₄×Q₈	—	53	1	no	—
394	C₄×Q₈	—	53	2	no	—
395	C₄×Q₈	—	53	2	no	—
396	C₄×Q₈	—	53	2	no	—
397	C₄×Q₈	—	53	2	no	—
398	C₄×Q₈	—	53	1	no	—
399	C₄×Q₈	—	53	2	no	—
400	C₄×Q₈	—	53	1	no	—
401	C₄×Q₈	—	53	1	no	—
402	C₄×Q₈	—	53	1	no	—
403	C₄×Q₈	—	53	2	no	—
404	C₄×Q₈	—	53	1	no	—
405	C₄×Q₈	—	53	2	no	—
406	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic
407	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic
408	C₄×D₄	—	53	1	no	—
409	C₄×D₄	—	53	1	no	—
410	C₄×D₄	—	53	2	no	—
411	C₄×D₄	—	53	2	no	—
412	C₄×D₄	—	53	2	no	—
413	C₄×D₄	—	53	1	no	—
414	#117	—	53	1	no	—
415	#117	—	53	2	no	—
416	#117	—	53	1	no	—
417	#117	—	53	2	no	—
418	#117	—	53	2	no	—
419	#117	—	53	2	no	—
420	#117	—	53	2	no	—
421	#117	—	53	1	no	—
422	#117	—	53	2	no	—
423	#117	—	53	2	no	—
424	#117	C₂×D₅₃	1	1	yes	characteristic
425	C₂×C₄⋊C₄	—	53	2	no	—
426	C₂×C₄⋊C₄	—	53	1	no	—
427	C₂×C₄²	—	53	2	no	—
428	C₂×C₄²	—	53	1	no	—
429	C₂×Q₈	—	53	1	no	—
430	C₂×Q₈	—	53	2	no	—
431	C₂×Q₈	—	53	1	no	—
432	C₂×Q₈	—	53	2	no	—
433	C₂×Q₈	—	53	2	no	—
434	C₂×Q₈	—	53	2	no	—
435	C₂×Q₈	—	53	1	no	—
436	C₂×Q₈	—	106	4	no	—
437	C₂×Q₈	—	106	4	no	—
438	C₂×Q₈	—	106	4	no	—
439	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
440	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
441	C₂×D₄	—	53	1	no	—
442	C₂×D₄	—	53	1	no	—
443	C₂×D₄	—	53	1	no	—
444	C₂²×C₄	—	53	2	no	—
445	C₂²×C₄	—	53	1	no	—
446	C₂²×C₄	—	53	2	no	—
447	C₂²×C₄	—	53	1	no	—
448	C₂²×C₄	—	53	2	no	—
449	C₂²×C₄	—	53	1	no	—
450	C₂²×C₄	—	53	2	no	—
451	C₂²×C₄	—	53	1	no	—
452	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
453	C₄⋊C₄	—	53	2	no	—
454	C₄⋊C₄	—	53	1	no	—
455	C₄⋊C₄	—	53	2	no	—
456	C₄⋊C₄	—	53	2	no	—
457	C₄⋊C₄	—	53	2	no	—
458	C₄⋊C₄	—	53	2	no	—
459	C₄⋊C₄	—	53	2	no	—
460	C₄⋊C₄	—	53	1	no	—
461	C₄⋊C₄	—	53	2	no	—
462	C₄⋊C₄	—	53	1	no	—
463	C₄⋊C₄	—	53	2	no	—
464	C₄⋊C₄	—	53	1	no	—
465	C₄⋊C₄	—	53	2	no	—
466	C₄⋊C₄	—	53	2	no	—
467	C₄⋊C₄	—	53	2	no	—
468	C₄⋊C₄	—	53	2	no	—
469	C₄⋊C₄	—	53	2	no	—
470	C₄⋊C₄	—	53	1	no	—
471	C₄⋊C₄	—	53	2	no	—
472	C₄⋊C₄	—	53	1	no	—
473	C₄⋊C₄	—	53	2	no	—
474	C₄⋊C₄	—	53	1	no	—
475	C₄⋊C₄	—	53	1	no	—
476	C₄⋊C₄	—	53	2	no	—
477	C₄⋊C₄	—	53	2	no	—
478	C₄⋊C₄	—	53	2	no	—
479	C₄⋊C₄	—	53	2	no	—
480	C₄⋊C₄	—	53	2	no	—
481	C₄⋊C₄	—	53	1	no	—
482	C₄⋊C₄	—	53	1	no	—
483	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
484	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
485	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
486	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
487	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
488	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
489	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
490	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
491	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
492	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
493	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
494	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
495	C₂²⋊C₄	—	53	2	no	—
496	C₂²⋊C₄	—	53	1	no	—
497	C₂²⋊C₄	—	53	1	no	—
498	C₂²⋊C₄	—	53	1	no	—
499	C₂²⋊C₄	—	53	2	no	—
500	C₂²⋊C₄	—	53	1	no	—
501	C₂²⋊C₄	—	53	1	no	—
502	C₂²⋊C₄	—	53	2	no	—
503	C₂²⋊C₄	—	53	1	no	—
504	C₂²⋊C₄	—	53	2	no	—
505	C₂²⋊C₄	—	53	1	no	—
506	C₂²⋊C₄	—	53	2	no	—
507	C₂²⋊C₄	—	53	2	no	—
508	C₂²⋊C₄	—	53	1	no	—
509	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
510	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
511	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
512	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
513	C₄²	—	53	2	no	—
514	C₄²	—	53	2	no	—
515	C₄²	—	53	1	no	—
516	C₄²	—	53	2	no	—
517	C₄²	—	53	1	no	—
518	C₄²	—	53	1	no	—
519	C₄²	—	53	2	no	—
520	C₄²	—	53	2	no	—
521	C₄²	—	53	2	no	—
522	C₄²	—	53	2	no	—
523	C₄²	—	53	2	no	—
524	C₄²	—	53	2	no	—
525	C₄²	—	53	2	no	—
526	C₄²	—	53	1	no	—
527	C₄²	C₂²×D₅₃	1	1	yes	characteristic
528	C₄²	C₂²×D₅₃	1	2	yes	—
529	C₄²	C₂²×D₅₃	1	2	yes	—
530	C₄²	C₂²×D₅₃	1	1	yes	characteristic
531	C₂³	—	53	1	no	—
532	C₂³	—	53	1	no	—
533	C₂³	C₂³×D₅₃	1	1	yes	characteristic
534	Q₈	—	2	2	no	—
535	Q₈	—	2	2	no	—
536	Q₈	—	53	4	no	—
537	Q₈	—	106	4	no	—
538	Q₈	—	106	2	no	—
539	Q₈	—	106	4	no	—
540	Q₈	—	106	4	no	—
541	Q₈	—	106	4	no	—
542	Q₈	—	106	2	no	—
543	D₄	—	106	2	no	—
544	D₄	—	106	2	no	—
545	D₄	—	106	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	53	1	no	—
548	C₂×C₄	—	53	2	no	—
549	C₂×C₄	—	53	2	no	—
550	C₂×C₄	—	53	2	no	—
551	C₂×C₄	—	53	1	no	—
552	C₂×C₄	—	53	1	no	—
553	C₂×C₄	—	53	1	no	—
554	C₂×C₄	—	53	1	no	—
555	C₂×C₄	—	53	1	no	—
556	C₂×C₄	—	53	2	no	—
557	C₂×C₄	—	106	2	no	—
558	C₂×C₄	—	106	4	no	—
559	C₂×C₄	—	106	4	no	—
560	C₂×C₄	—	106	2	no	—
561	C₂×C₄	—	106	4	no	—
562	C₂×C₄	—	106	4	no	—
563	C₂×C₄	—	106	2	no	—
564	C₂×C₄	—	106	2	no	—
565	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
566	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
567	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
568	C₂×C₄	C₂³×D₅₃	1	2	yes	—
569	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
570	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
571	C₂×C₄	C₂³×D₅₃	1	2	yes	—
572	C₂×C₄	C₂³×D₅₃	1	2	yes	—
573	C₂×C₄	C₂³×D₅₃	1	2	yes	—
574	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	53	2	no	—
579	C₂²	—	106	1	no	—
580	C₂²	—	106	1	no	—
581	C₂²	—	106	1	no	—
582	C₂²	—	106	1	no	—
583	C₂²	—	106	1	no	—
584	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
585	C₄	—	2	1	no	—
586	C₄	—	2	2	no	—
587	C₄	—	2	2	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	2	no	—
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	2	no	—
594	C₄	—	53	4	no	—
595	C₄	—	53	2	no	—
596	C₄	—	106	2	no	—
597	C₄	—	106	1	no	—
598	C₄	—	106	1	no	—
599	C₄	—	106	2	no	—
600	C₄	—	106	1	no	—
601	C₄	—	106	1	no	—
602	C₄	—	106	2	no	—
603	C₄	—	106	1	no	—
604	C₄	#41×D₅₃	1	2	yes	—
605	C₂	—	4	1	no	—
606	C₂	—	106	2	no	—
607	C₂	—	212	1	no	—
608	C₂	C₂×#41×D₅₃	1	1	yes	characteristic
609	C₂	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
610	C₂	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#541	C₂
hypercenter	#541	D₅₃
hypocenter	C₅₃	#3523
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #541

Complements

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

N	H ≅ G/N	type
1. #16811350	C₂	semidirect
2. #16811350	C₂	semidirect
3. #16811348	C₂	semidirect
4. #16811344	C₂	semidirect
5. #16811340	C₂	semidirect
6. #16811311	C₂	semidirect
7. #16811309	C₂	semidirect
8. #16811307	C₂	semidirect
9. #16811305	C₂	semidirect
10. #16811288	C₂	semidirect
11. #16811286	C₂	semidirect
12. #16811286	C₂	semidirect
13. #16811232	C₂	semidirect
14. #16811231	C₂	semidirect
15. #16811230	C₂	semidirect
16. #16811179	C₂	semidirect
17. #16811177	C₂	semidirect
20. #16811100	C₂	semidirect
21. #16811099	C₂	semidirect
22. C₄×Q₈×D₅₃	C₂	semidirect
23. C₅₃×#541	C₂	semidirect
321. #541	D₅₃	semidirect
329. C₅₃	#3523	semidirect