Subgroups — #20288535

Order 6784.

988 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811351	C₂	1	1	yes	maximal, characteristic, complemented
2	#16811350	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811350	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811348	C₂	1	1	yes	maximal, characteristic, complemented
5	#16811332	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811332	C₂	1	1	yes	maximal, characteristic, complemented
7	#16811331	C₂	1	2	yes	maximal, complemented
8	#16811330	C₂	1	1	yes	maximal, characteristic, complemented
9	#16811328	C₂	1	2	yes	maximal, complemented
10	#16811327	C₂	1	2	yes	maximal, complemented
11	#16811327	C₂	1	2	yes	maximal, complemented
12	#16811253	C₂	1	1	yes	maximal, characteristic, complemented
13	#16811252	C₂	1	2	yes	maximal, complemented
14	#16811252	C₂	1	2	yes	maximal, complemented
15	#16811250	C₂	1	1	yes	maximal, characteristic, complemented
16	#16811177	C₂	1	1	yes	maximal, characteristic, complemented
17	#16811175	C₂	1	2	yes	maximal, complemented
18	C₂×#13133207	C₂	1	2	yes	maximal, complemented
19	#125×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
20	#16811102	C₂	1	1	yes	maximal, characteristic
21	#16811102	C₂	1	1	yes	maximal, characteristic
22	C₄×#11719947	C₂	1	1	yes	maximal, characteristic
23	C₅₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11719947	C₂²	1	1	yes	characteristic
25	#13133217	C₂²	1	1	yes	characteristic
26	#13133216	C₂²	1	2	yes	—
27	#13133216	C₂²	1	2	yes	—
28	#13133216	C₂²	1	1	yes	characteristic
29	#13133216	C₂²	1	1	yes	characteristic
30	#13133216	C₂²	1	2	yes	—
31	#13133216	C₂²	1	1	yes	characteristic
32	#13133215	C₂²	1	2	yes	—
33	#13133215	C₂²	1	2	yes	—
34	#13133215	C₂²	1	2	yes	—
35	#13133215	C₂²	1	1	yes	characteristic
36	#13133209	C₂²	1	1	yes	characteristic
37	#13133209	C₂²	1	1	yes	characteristic
38	#13133208	C₂²	1	1	yes	characteristic
39	#13133208	C₂²	1	1	yes	characteristic
40	#13133208	C₂²	1	1	yes	characteristic
41	#13133208	C₂²	1	1	yes	characteristic
42	#13133207	C₂²	1	2	yes	—
43	#13133207	C₂²	1	2	yes	—
44	#13133207	C₂²	1	2	yes	—
45	#13133207	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	#13133207	C₂²	1	2	yes	—
55	#13133207	C₂²	1	1	yes	characteristic
56	#13133197	C₂²	1	2	yes	—
57	#13133197	C₂²	1	1	yes	characteristic
58	#13133196	C₂²	1	2	yes	—
59	#13133196	C₂²	1	2	yes	—
60	#13133196	C₂²	1	2	yes	—
61	#13133195	C₂²	1	1	yes	characteristic
62	#13133195	C₂²	1	2	yes	—
63	#13133195	C₂²	1	2	yes	—
64	#13133195	C₂²	1	1	yes	characteristic
65	#13133194	C₂²	1	2	yes	—
66	#13133194	C₂²	1	2	yes	—
67	#13133194	C₂²	1	2	yes	—
68	#13133194	C₂²	1	2	yes	—
69	#13133194	C₂²	1	2	yes	—
70	#13133194	C₂²	1	2	yes	—
71	#13133193	C₂²	1	1	yes	characteristic
72	#13133193	C₂²	1	2	yes	—
73	Q₈×Dic₅₃	C₂²	1	2	yes	—
74	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
75	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
76	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
77	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
78	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
79	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
80	#13133182	C₂²	1	2	yes	—
81	#13133182	C₂²	1	2	yes	—
82	#13133182	C₂²	1	2	yes	—
83	#13133182	C₂²	1	1	yes	characteristic
84	#13133182	C₂²	1	1	yes	characteristic
85	#13133182	C₂²	1	1	yes	characteristic
86	D₄×Dic₅₃	C₂²	1	1	yes	characteristic
87	D₄×Dic₅₃	C₂²	1	1	yes	characteristic
88	D₄×Dic₅₃	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	—
90	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	—
91	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	—
92	#13133177	C₂²	1	2	yes	—
93	#13133177	C₂²	1	2	yes	—
94	#13133177	C₂²	1	2	yes	—
95	#13133175	C₂²	1	1	yes	characteristic
96	#13133174	C₂²	1	1	yes	characteristic
97	#13133174	C₂²	1	1	yes	characteristic
98	#13133173	C₂²	1	2	yes	—
99	#13133173	C₂²	1	2	yes	—
100	#13133173	C₂²	1	2	yes	—
101	C₂×C₄⋊Dic₅₃	C₂²	1	2	yes	—
102	C₂×#11719919	C₂²	1	2	yes	—
103	C₂×#11719919	C₂²	1	2	yes	—
104	C₂×#11719919	C₂²	1	2	yes	—
105	C₂×#11719919	C₂²	1	2	yes	—
106	C₄⋊C₄×D₅₃	C₂²	1	2	yes	—
107	C₄⋊C₄×D₅₃	C₂²	1	2	yes	—
108	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
109	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
110	C₂×C₄×Dic₅₃	C₂²	1	2	yes	—
111	C₄²×D₅₃	C₂²	1	1	yes	characteristic
112	C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
113	#125×C₅₃	C₂²	1	1	yes	characteristic
114	#125×C₅₃	C₂²	1	1	yes	characteristic
115	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
117	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
118	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
119	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
120	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
121	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
123	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₅₃	C₂³	1	2	yes	—
125	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
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	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
130	C₂²×Dic₅₃	C₂³	1	2	yes	—
131	C₂²×Dic₅₃	C₂³	1	2	yes	—
132	C₂²×Dic₅₃	C₂³	1	2	yes	—
133	C₂²×Dic₅₃	C₂³	1	2	yes	—
134	#11719947	Q₈	1	8	yes	complemented
135	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
136	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
137	C₂×C₄×D₅₃	C₂³	1	2	yes	—
138	C₂×C₄×D₅₃	C₂³	1	2	yes	—
139	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
140	C₂×Dic₁₀₆	C₂³	1	2	yes	—
141	C₂×Dic₁₀₆	C₂³	1	2	yes	—
142	C₂×Dic₁₀₆	C₂³	1	2	yes	—
143	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
144	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
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	2	yes	—
149	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
150	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
151	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
152	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
153	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
154	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
155	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
156	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
157	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
158	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
159	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
160	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
161	C₄²×C₅₃	C₂³	1	1	yes	characteristic
162	C₄²×C₅₃	C₂³	1	1	yes	characteristic
163	C₄²×C₅₃	C₂³	1	1	yes	characteristic
164	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
165	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
166	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
167	#11719921	C₂³	1	1	yes	characteristic
168	#11719921	C₂³	1	1	yes	characteristic
169	#11719921	C₂³	1	1	yes	characteristic
170	#11719921	C₂³	1	1	yes	characteristic
171	#11719921	C₂³	1	2	yes	—
172	C₄⋊Dic₅₃	C₂³	1	2	yes	—
173	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
174	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
175	C₄⋊Dic₅₃	C₂³	1	2	yes	—
176	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
177	C₄⋊Dic₅₃	C₂³	1	2	yes	—
178	C₄⋊Dic₅₃	C₂³	1	2	yes	—
179	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
180	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
181	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
182	C₄⋊Dic₅₃	C₂³	1	2	yes	—
183	#11719919	C₂³	1	2	yes	—
184	#11719919	C₂³	1	2	yes	—
185	#11719919	C₂³	1	2	yes	—
186	#11719919	C₂³	1	2	yes	—
187	#11719919	C₂³	1	2	yes	—
188	#11719919	C₂³	1	2	yes	—
189	#11719919	C₂³	1	1	yes	characteristic
190	#11719919	C₂³	1	1	yes	characteristic
191	#11719919	C₂³	1	1	yes	characteristic
192	#11719919	C₂³	1	1	yes	characteristic
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	2	yes	—
198	#11719919	C₂³	1	2	yes	—
199	#11719919	C₂³	1	2	yes	—
200	#11719919	C₂³	1	2	yes	—
201	#11719919	C₂³	1	1	yes	characteristic
202	#11719919	C₂³	1	1	yes	characteristic
203	#11719919	C₂³	1	2	yes	—
204	#11719919	C₂³	1	2	yes	—
205	#11719919	C₂³	1	1	yes	characteristic
206	#11719919	C₂³	1	1	yes	characteristic
207	#11719919	C₂³	1	2	yes	—
208	#11719919	C₂³	1	2	yes	—
209	#11719919	C₂³	1	1	yes	characteristic
210	#11719919	C₂³	1	1	yes	characteristic
211	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
212	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
213	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
214	C₄×Dic₅₃	C₂³	1	2	yes	—
215	C₄×Dic₅₃	C₂³	1	2	yes	—
216	C₄×Dic₅₃	C₂³	1	2	yes	—
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	1	yes	characteristic
223	C₂³×C₅₃	C₂⁴	1	2	yes	—
224	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
225	Q₈×C₅₃	—	4	1	no	—
226	Q₈×C₅₃	—	4	2	no	—
227	D₄×C₅₃	C₂×Q₈	1	4	yes	—
228	C₂×C₄×C₅₃	—	4	2	no	—
229	C₂×C₄×C₅₃	—	4	2	no	—
230	C₂×C₄×C₅₃	—	4	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	1	yes	characteristic
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	C₂×Q₈	1	8	yes	—
242	C₂×Dic₅₃	—	4	2	no	—
243	C₂×Dic₅₃	—	4	2	no	—
244	C₂×Dic₅₃	—	4	2	no	—
245	C₂×Dic₅₃	C₂×Q₈	1	8	yes	—
246	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
247	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
248	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
249	C₂×Dic₅₃	C₂⁴	1	2	yes	—
250	C₂×Dic₅₃	C₂⁴	1	2	yes	—
251	C₂×Dic₅₃	C₂⁴	1	2	yes	—
252	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₅₃	C₂⁴	1	2	yes	—
256	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
257	C₄×D₅₃	—	4	1	no	—
258	C₄×D₅₃	—	4	2	no	—
259	C₄×D₅₃	—	4	2	no	—
260	C₄×D₅₃	—	4	1	no	—
261	C₄×D₅₃	C₂×Q₈	1	4	yes	—
262	Dic₁₀₆	—	4	1	no	—
263	Dic₁₀₆	—	4	2	no	—
264	Dic₁₀₆	—	4	2	no	—
265	Dic₁₀₆	—	4	1	no	—
266	Dic₁₀₆	—	4	1	no	—
267	Dic₁₀₆	—	4	2	no	—
268	Dic₁₀₆	C₂×Q₈	1	4	yes	—
269	C₂²×C₅₃	—	2	2	no	—
270	C₂²×C₅₃	—	2	2	no	—
271	C₂²×C₅₃	C₂²×Q₈	1	4	yes	—
272	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
273	C₂×D₅₃	—	2	1	no	—
274	C₂×D₅₃	—	2	1	no	—
275	C₂×D₅₃	C₂²×Q₈	1	2	yes	—
276	C₄×C₅₃	—	2	1	no	—
277	C₄×C₅₃	—	2	2	no	—
278	C₄×C₅₃	—	2	1	no	—
279	C₄×C₅₃	—	2	1	no	—
280	C₄×C₅₃	—	2	2	no	—
281	C₄×C₅₃	—	2	1	no	—
282	C₄×C₅₃	—	2	1	no	—
283	C₄×C₅₃	—	2	2	no	—
284	C₄×C₅₃	—	2	1	no	—
285	C₄×C₅₃	C₂²×Q₈	1	2	yes	—
286	Dic₅₃	—	2	1	no	—
287	Dic₅₃	—	2	1	no	—
288	Dic₅₃	—	2	1	no	—
289	Dic₅₃	—	2	2	no	—
290	Dic₅₃	—	2	2	no	—
291	Dic₅₃	—	2	2	no	—
292	Dic₅₃	—	2	1	no	—
293	Dic₅₃	—	2	1	no	—
294	Dic₅₃	—	2	1	no	—
295	Dic₅₃	C₂²×Q₈	1	4	yes	—
296	Dic₅₃	C₂²×Q₈	1	2	yes	—
297	#3504	—	53	1	no	maximal, Sylow
298	C₂×C₅₃	—	2	4	no	—
299	C₂×C₅₃	C₂³×Q₈	1	1	yes	characteristic
300	C₂×C₅₃	#585	1	1	yes	characteristic
301	C₂×C₅₃	#585	1	1	yes	characteristic
302	D₅₃	—	2	2	no	—
303	#557	—	53	1	no	—
304	#557	—	53	1	no	—
305	#557	—	53	1	no	—
306	#557	—	53	1	no	—
307	#554	—	53	2	no	—
308	#554	—	53	2	no	—
309	#554	—	53	2	no	—
310	#554	—	53	1	no	—
311	#554	—	53	1	no	—
312	#554	—	53	1	no	—
313	#554	—	53	2	no	—
314	#554	D₅₃	1	1	yes	characteristic, complemented
315	#544	—	53	1	no	—
316	#544	—	53	1	no	—
317	#544	—	53	2	no	—
318	#544	—	53	2	no	—
319	#533	—	53	2	no	—
320	#533	—	53	1	no	—
321	C₂×#125	—	53	1	no	—
322	C₂×#125	—	53	2	no	—
323	#520	—	53	1	no	—
324	#520	—	53	1	no	—
325	C₄×#41	—	53	1	no	—
326	C₅₃	#3504	1	1	yes	characteristic, complemented, Sylow
327	C₂×#41	—	53	1	no	—
328	C₄⋊Q₈	—	53	2	no	—
329	C₄⋊Q₈	—	53	1	no	—
330	C₄⋊Q₈	—	53	2	no	—
331	C₄⋊Q₈	—	53	2	no	—
332	C₄⋊Q₈	—	53	2	no	—
333	C₄⋊Q₈	—	53	1	no	—
334	C₄⋊Q₈	—	53	2	no	—
335	C₄⋊Q₈	—	53	2	no	—
336	C₄⋊Q₈	—	53	1	no	—
337	C₄⋊Q₈	—	53	1	no	—
338	C₄⋊Q₈	—	53	1	no	—
339	C₄⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
340	#125	—	53	2	no	—
341	#125	—	53	1	no	—
342	#125	—	53	2	no	—
343	#125	—	53	2	no	—
344	#125	—	53	2	no	—
345	#125	—	53	2	no	—
346	#125	—	53	2	no	—
347	#125	—	53	2	no	—
348	#125	—	53	2	no	—
349	#125	—	53	1	no	—
350	#125	—	53	1	no	—
351	#125	—	53	1	no	—
352	#125	—	53	2	no	—
353	#125	—	53	2	no	—
354	#125	—	53	2	no	—
355	#125	—	53	2	no	—
356	#125	—	53	1	no	—
357	#125	—	53	1	no	—
358	#125	—	53	1	no	—
359	#125	—	53	1	no	—
360	#125	C₂×D₅₃	1	1	yes	characteristic
361	#125	C₂×D₅₃	1	1	yes	characteristic
362	C₂²⋊Q₈	—	53	1	no	—
363	C₂²⋊Q₈	—	53	2	no	—
364	C₂²⋊Q₈	—	53	2	no	—
365	C₂²⋊Q₈	—	53	2	no	—
366	C₂²⋊Q₈	—	53	2	no	—
367	C₂²⋊Q₈	—	53	1	no	—
368	C₂²⋊Q₈	—	53	1	no	—
369	C₂²⋊Q₈	—	53	1	no	—
370	C₂²⋊Q₈	—	53	2	no	—
371	C₂²⋊Q₈	—	53	2	no	—
372	C₂²⋊Q₈	—	53	2	no	—
373	C₂²⋊Q₈	—	53	2	no	—
374	C₂²⋊Q₈	—	53	2	no	—
375	C₂²⋊Q₈	—	53	2	no	—
376	C₂²⋊Q₈	—	53	2	no	—
377	C₂²⋊Q₈	—	53	2	no	—
378	C₂²⋊Q₈	—	53	2	no	—
379	C₂²⋊Q₈	C₂×D₅₃	1	2	yes	—
380	C₂²⋊Q₈	C₂×D₅₃	1	2	yes	—
381	C₂²⋊Q₈	C₂×D₅₃	1	2	yes	—
382	C₄×Q₈	—	53	2	no	—
383	C₄×Q₈	—	53	1	no	—
384	C₄×Q₈	—	53	1	no	—
385	C₄×Q₈	—	53	1	no	—
386	C₄×Q₈	—	53	2	no	—
387	C₄×Q₈	—	53	2	no	—
388	C₄×Q₈	—	53	2	no	—
389	C₄×Q₈	—	53	1	no	—
390	C₄×Q₈	—	53	1	no	—
391	C₄×Q₈	—	53	1	no	—
392	C₄×Q₈	—	53	1	no	—
393	C₄×Q₈	—	53	1	no	—
394	C₄×Q₈	—	53	1	no	—
395	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic
396	C₄×D₄	—	53	1	no	—
397	C₄×D₄	—	53	1	no	—
398	C₄×D₄	—	53	1	no	—
399	C₄×D₄	—	53	2	no	—
400	C₄×D₄	—	53	2	no	—
401	C₄×D₄	—	53	2	no	—
402	C₄×D₄	—	53	2	no	—
403	C₄×D₄	—	53	2	no	—
404	C₄×D₄	—	53	2	no	—
405	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
406	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
407	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
408	#117	—	53	1	no	—
409	#117	—	53	2	no	—
410	#117	—	53	2	no	—
411	#117	—	53	2	no	—
412	#117	—	53	1	no	—
413	#117	—	53	1	no	—
414	C₂×C₄⋊C₄	—	53	2	no	—
415	C₂×C₄⋊C₄	—	53	2	no	—
416	C₂×C₄⋊C₄	—	53	2	no	—
417	C₂×C₄⋊C₄	—	53	2	no	—
418	C₂×C₄⋊C₄	—	53	2	no	—
419	C₂×C₄⋊C₄	—	53	1	no	—
420	C₂×C₄⋊C₄	—	53	1	no	—
421	C₂×C₄⋊C₄	—	53	2	no	—
422	C₂×C₄⋊C₄	—	53	2	no	—
423	C₂×C₄⋊C₄	C₂×D₅₃	1	2	yes	—
424	C₂×C₄²	—	53	2	no	—
425	C₂×C₄²	—	53	1	no	—
426	#41	—	53	8	no	—
427	C₂×Q₈	—	53	1	no	—
428	C₂×Q₈	—	53	2	no	—
429	C₂×Q₈	—	53	1	no	—
430	C₂×Q₈	—	53	2	no	—
431	C₂×Q₈	—	53	1	no	—
432	C₂×Q₈	—	53	1	no	—
433	C₂×Q₈	—	53	2	no	—
434	C₂×Q₈	C₂²×D₅₃	1	2	yes	—
435	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
436	C₂×D₄	—	53	2	no	—
437	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
438	C₂²×C₄	—	53	2	no	—
439	C₂²×C₄	—	53	1	no	—
440	C₂²×C₄	—	53	2	no	—
441	C₂²×C₄	—	53	2	no	—
442	C₂²×C₄	—	53	2	no	—
443	C₂²×C₄	—	53	1	no	—
444	C₂²×C₄	—	53	1	no	—
445	C₂²×C₄	—	53	2	no	—
446	C₂²×C₄	—	53	2	no	—
447	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
448	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
449	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
450	C₄⋊C₄	—	53	2	no	—
451	C₄⋊C₄	—	53	2	no	—
452	C₄⋊C₄	—	53	1	no	—
453	C₄⋊C₄	—	53	1	no	—
454	C₄⋊C₄	—	53	2	no	—
455	C₄⋊C₄	—	53	1	no	—
456	C₄⋊C₄	—	53	1	no	—
457	C₄⋊C₄	—	53	2	no	—
458	C₄⋊C₄	—	53	2	no	—
459	C₄⋊C₄	—	53	1	no	—
460	C₄⋊C₄	—	53	2	no	—
461	C₄⋊C₄	—	53	2	no	—
462	C₄⋊C₄	—	53	2	no	—
463	C₄⋊C₄	—	53	2	no	—
464	C₄⋊C₄	—	53	1	no	—
465	C₄⋊C₄	—	53	1	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	2	no	—
471	C₄⋊C₄	—	53	2	no	—
472	C₄⋊C₄	—	53	2	no	—
473	C₄⋊C₄	—	53	2	no	—
474	C₄⋊C₄	—	53	2	no	—
475	C₄⋊C₄	—	53	1	no	—
476	C₄⋊C₄	—	53	1	no	—
477	C₄⋊C₄	—	53	2	no	—
478	C₄⋊C₄	—	53	2	no	—
479	C₄⋊C₄	—	53	1	no	—
480	C₄⋊C₄	—	53	1	no	—
481	C₄⋊C₄	—	53	1	no	—
482	C₄⋊C₄	—	53	1	no	—
483	C₄⋊C₄	—	53	2	no	—
484	C₄⋊C₄	—	53	1	no	—
485	C₄⋊C₄	—	53	2	no	—
486	C₄⋊C₄	—	53	1	no	—
487	C₄⋊C₄	—	53	2	no	—
488	C₄⋊C₄	—	53	1	no	—
489	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
490	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
491	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
492	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
493	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
494	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
495	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
496	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
497	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
498	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
499	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
500	C₂²⋊C₄	—	53	2	no	—
501	C₂²⋊C₄	—	53	2	no	—
502	C₂²⋊C₄	—	53	2	no	—
503	C₂²⋊C₄	—	53	1	no	—
504	C₂²⋊C₄	—	53	1	no	—
505	C₂²⋊C₄	—	53	2	no	—
506	C₂²⋊C₄	—	53	1	no	—
507	C₂²⋊C₄	—	53	1	no	—
508	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
509	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
510	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
511	C₄²	—	53	1	no	—
512	C₄²	—	53	2	no	—
513	C₄²	—	53	1	no	—
514	C₄²	—	53	2	no	—
515	C₄²	—	53	2	no	—
516	C₄²	—	53	1	no	—
517	C₄²	—	53	2	no	—
518	C₄²	—	53	2	no	—
519	C₄²	—	53	2	no	—
520	C₄²	—	53	2	no	—
521	C₄²	—	53	1	no	—
522	C₄²	—	53	1	no	—
523	C₄²	C₂²×D₅₃	1	1	yes	characteristic
524	C₄²	C₂²×D₅₃	1	1	yes	characteristic
525	C₄²	C₂²×D₅₃	1	1	yes	characteristic
526	C₂³	—	53	1	no	—
527	C₂³	C₂³×D₅₃	1	2	yes	—
528	Q₈	—	4	2	no	—
529	Q₈	—	4	1	no	—
530	Q₈	—	53	4	no	—
531	Q₈	—	212	1	no	—
532	Q₈	—	212	2	no	—
533	Q₈	—	212	1	no	—
534	Q₈	—	212	2	no	—
535	Q₈	—	212	1	no	—
536	Q₈	—	212	2	no	—
537	D₄	—	53	8	no	—
538	D₄	Q₈×D₅₃	1	4	yes	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	53	8	no	—
543	C₂×C₄	—	53	2	no	—
544	C₂×C₄	—	53	1	no	—
545	C₂×C₄	—	53	4	no	—
546	C₂×C₄	—	53	1	no	—
547	C₂×C₄	—	53	1	no	—
548	C₂×C₄	—	53	1	no	—
549	C₂×C₄	—	53	1	no	—
550	C₂×C₄	—	53	2	no	—
551	C₂×C₄	—	53	2	no	—
552	C₂×C₄	—	53	1	no	—
553	C₂×C₄	—	53	2	no	—
554	C₂×C₄	—	53	1	no	—
555	C₂×C₄	—	212	1	no	—
556	C₂×C₄	—	212	2	no	—
557	C₂×C₄	—	212	2	no	—
558	C₂×C₄	—	212	1	no	—
559	C₂×C₄	—	212	2	no	—
560	C₂×C₄	—	212	2	no	—
561	C₂×C₄	—	212	2	no	—
562	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
563	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
564	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
565	C₂×C₄	C₂³×D₅₃	1	2	yes	—
566	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
567	C₂×C₄	C₂³×D₅₃	1	2	yes	—
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	1	yes	characteristic
572	C₂²	—	2	2	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	53	2	no	—
575	C₂²	—	106	1	no	—
576	C₂²	—	106	1	no	—
577	C₂²	C₂×Q₈×D₅₃	1	4	yes	—
578	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
579	C₄	—	2	1	no	—
580	C₄	—	2	1	no	—
581	C₄	—	2	2	no	—
582	C₄	—	2	2	no	—
583	C₄	—	2	1	no	—
584	C₄	—	2	1	no	—
585	C₄	—	2	2	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	1	no	—
588	C₄	—	53	2	no	—
589	C₄	—	53	4	no	—
590	C₄	—	106	2	no	—
591	C₄	—	106	1	no	—
592	C₄	—	106	1	no	—
593	C₄	—	106	1	no	—
594	C₄	—	106	1	no	—
595	C₄	—	106	2	no	—
596	C₄	—	106	1	no	—
597	C₄	—	106	2	no	—
598	C₄	—	106	1	no	—
599	C₄	C₂×Q₈×D₅₃	1	2	yes	—
600	C₂	—	2	4	no	—
601	C₂	—	106	2	no	—
602	C₂	C₂²×Q₈×D₅₃	1	1	yes	characteristic
603	C₂	#16811458	1	1	yes	characteristic
604	C₂	#16811459	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#554	C₂
hypercenter	#554	D₅₃
hypocenter	C₅₃	#3504
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. #16811351	C₂	semidirect
2. #16811350	C₂	semidirect
3. #16811350	C₂	semidirect
4. #16811348	C₂	semidirect
5. #16811332	C₂	semidirect
6. #16811332	C₂	semidirect
7. #16811331	C₂	semidirect
8. #16811330	C₂	semidirect
9. #16811328	C₂	semidirect
10. #16811327	C₂	semidirect
11. #16811327	C₂	semidirect
12. #16811253	C₂	semidirect
13. #16811252	C₂	semidirect
14. #16811252	C₂	semidirect
15. #16811250	C₂	semidirect
16. #16811177	C₂	semidirect
17. #16811175	C₂	semidirect
18. C₂×#13133207	C₂	semidirect
19. #125×D₅₃	C₂	semidirect
23. C₅₃×#554	C₂	semidirect
134. #11719947	Q₈	semidirect
314. #554	D₅₃	semidirect
326. C₅₃	#3504	semidirect