Subgroups — #20288465

Order 6784.

1022 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811342	C₂	1	2	yes	maximal, complemented
2	#16811327	C₂	1	2	yes	maximal, complemented
3	#16811310	C₂	1	2	yes	maximal, complemented
4	#16811309	C₂	1	2	yes	maximal, complemented
5	#16811309	C₂	1	2	yes	maximal, complemented
6	#16811307	C₂	1	2	yes	maximal, complemented
7	#16811303	C₂	1	2	yes	maximal, complemented
8	#16811301	C₂	1	2	yes	maximal, complemented
9	#16811250	C₂	1	1	yes	maximal, characteristic, complemented
10	#16811240	C₂	1	1	yes	maximal, characteristic, complemented
11	#16811235	C₂	1	1	yes	maximal, characteristic, complemented
12	#16811233	C₂	1	1	yes	maximal, characteristic, complemented
13	#16811193	C₂	1	1	yes	maximal, characteristic, complemented
14	#16811178	C₂	1	1	yes	maximal, characteristic, complemented
15	#16811177	C₂	1	1	yes	maximal, characteristic, complemented
16	#16811155	C₂	1	1	yes	maximal, characteristic, complemented
17	#16811152	C₂	1	1	yes	maximal, characteristic, complemented
18	#16811133	C₂	1	1	yes	maximal, characteristic
19	C₂²⋊Q₈×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
20	#16811102	C₂	1	1	yes	maximal, characteristic, complemented
21	#16811099	C₂	1	1	yes	maximal, characteristic, complemented
22	#117×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11719947	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₅₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₅₃	C₂²	1	1	yes	characteristic
27	#13133217	C₂²	1	1	yes	characteristic, complemented
28	#13133216	C₂²	1	1	yes	characteristic, complemented
29	#13133215	C₂²	1	2	yes	complemented
30	#13133215	C₂²	1	1	yes	characteristic, complemented
31	#13133210	C₂²	1	2	yes	—
32	#13133210	C₂²	1	2	yes	—
33	#13133210	C₂²	1	2	yes	—
34	#13133210	C₂²	1	2	yes	—
35	#13133210	C₂²	1	2	yes	complemented
36	#13133210	C₂²	1	2	yes	complemented
37	#13133210	C₂²	1	2	yes	complemented
38	#13133209	C₂²	1	1	yes	characteristic, complemented
39	#13133208	C₂²	1	2	yes	complemented
40	#13133208	C₂²	1	2	yes	complemented
41	#13133208	C₂²	1	1	yes	characteristic, complemented
42	#13133207	C₂²	1	2	yes	complemented
43	#13133207	C₂²	1	2	yes	complemented
44	#13133207	C₂²	1	2	yes	complemented
45	#13133207	C₂²	1	2	yes	complemented
46	#13133207	C₂²	1	2	yes	complemented
47	#13133204	C₂²	1	2	yes	—
48	#13133204	C₂²	1	1	yes	characteristic, complemented
49	#13133199	C₂²	1	2	yes	—
50	#13133199	C₂²	1	2	yes	—
51	#13133199	C₂²	1	2	yes	—
52	#13133199	C₂²	1	2	yes	—
53	#13133199	C₂²	1	2	yes	—
54	#13133198	C₂²	1	2	yes	—
55	#13133197	C₂²	1	1	yes	characteristic
56	#13133197	C₂²	1	1	yes	characteristic
57	#13133196	C₂²	1	1	yes	characteristic
58	#13133196	C₂²	1	1	yes	characteristic
59	#13133195	C₂²	1	2	yes	—
60	#13133195	C₂²	1	2	yes	—
61	#13133195	C₂²	1	2	yes	—
62	#13133194	C₂²	1	2	yes	—
63	#13133194	C₂²	1	2	yes	complemented
64	#13133194	C₂²	1	2	yes	complemented
65	#13133194	C₂²	1	2	yes	complemented
66	#13133193	C₂²	1	2	yes	—
67	#13133193	C₂²	1	2	yes	—
68	#13133193	C₂²	1	1	yes	characteristic
69	#13133188	C₂²	1	1	yes	characteristic
70	#13133185	C₂²	1	2	yes	—
71	Q₈×Dic₅₃	C₂²	1	2	yes	complemented
72	Q₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
73	C₄×Dic₁₀₆	C₂²	1	2	yes	complemented
74	C₄×Dic₁₀₆	C₂²	1	2	yes	complemented
75	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
76	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
77	#13133182	C₂²	1	2	yes	complemented
78	#13133182	C₂²	1	1	yes	characteristic, complemented
79	#13133182	C₂²	1	1	yes	characteristic, complemented
80	D₄×Dic₅₃	C₂²	1	2	yes	—
81	D₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
82	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	—
83	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	—
84	#13133177	C₂²	1	2	yes	—
85	#13133177	C₂²	1	2	yes	—
86	#13133177	C₂²	1	2	yes	—
87	#13133176	C₂²	1	1	yes	characteristic
88	#13133176	C₂²	1	2	yes	complemented
89	#13133175	C₂²	1	2	yes	—
90	#13133175	C₂²	1	2	yes	—
91	#13133175	C₂²	1	1	yes	characteristic
92	#13133175	C₂²	1	1	yes	characteristic
93	#13133175	C₂²	1	1	yes	characteristic
94	#13133174	C₂²	1	2	yes	—
95	#13133174	C₂²	1	2	yes	—
96	#13133174	C₂²	1	1	yes	characteristic
97	#13133174	C₂²	1	1	yes	characteristic
98	#13133173	C₂²	1	1	yes	characteristic
99	#13133173	C₂²	1	1	yes	characteristic
100	#13133173	C₂²	1	2	yes	complemented
101	#13133173	C₂²	1	2	yes	complemented
102	C₂×#11719919	C₂²	1	2	yes	complemented
103	C₄⋊C₄×D₅₃	C₂²	1	2	yes	—
104	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
105	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
106	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
107	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
108	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
109	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
110	C₄²×D₅₃	C₂²	1	1	yes	characteristic
111	C₄²×D₅₃	C₂²	1	1	yes	characteristic
112	C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
113	#126×C₅₃	C₂²	1	2	yes	complemented
114	#124×C₅₃	C₂²	1	2	yes	—
115	#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
116	#123×C₅₃	C₂²	1	2	yes	—
117	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
118	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
119	#121×C₅₃	C₂²	1	1	yes	characteristic
120	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
122	#117×C₅₃	C₂²	1	1	yes	characteristic
123	C₂³×D₅₃	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
125	C₂×Q₈×C₅₃	C₂³	1	2	yes	—
126	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₅₃	C₂³	1	2	yes	—
128	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
132	C₂²×Dic₅₃	C₂³	1	2	yes	—
133	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
134	C₂²×Dic₅₃	C₂³	1	2	yes	—
135	Q₈×D₅₃	—	2	4	no	—
136	#11719947	—	2	4	no	—
137	C₂×C₄×D₅₃	—	2	4	no	—
138	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
139	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₅₃	C₂³	1	2	yes	—
142	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₅₃	C₂³	1	2	yes	—
147	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
148	C₂×Dic₁₀₆	C₂³	1	2	yes	—
149	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
150	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
151	C₂×Dic₁₀₆	C₂³	1	2	yes	—
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	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	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
164	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
165	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
166	C₄²×C₅₃	C₂³	1	1	yes	characteristic
167	C₄²×C₅₃	C₂³	1	1	yes	characteristic
168	C₄²×C₅₃	C₂³	1	2	yes	—
169	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
170	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
171	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
172	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
173	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
174	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
175	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
176	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
177	#11719921	C₂³	1	1	yes	characteristic
178	#11719921	C₂³	1	1	yes	characteristic
179	#11719921	C₂³	1	1	yes	characteristic
180	#11719921	C₂³	1	1	yes	characteristic
181	#11719921	C₂³	1	2	yes	—
182	#11719921	C₂³	1	2	yes	—
183	#11719921	C₂³	1	2	yes	—
184	#11719921	C₂³	1	2	yes	—
185	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
186	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
187	C₄⋊Dic₅₃	C₂³	1	2	yes	—
188	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
189	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
190	C₄⋊Dic₅₃	C₂³	1	2	yes	—
191	C₄⋊Dic₅₃	C₂³	1	2	yes	—
192	C₄⋊Dic₅₃	C₂³	1	2	yes	—
193	C₄⋊Dic₅₃	C₂³	1	2	yes	—
194	C₄⋊Dic₅₃	C₂³	1	2	yes	—
195	#11719919	C₂³	1	1	yes	characteristic
196	#11719919	C₂³	1	2	yes	—
197	#11719919	C₂³	1	1	yes	characteristic
198	#11719919	C₂³	1	1	yes	characteristic
199	#11719919	C₂³	1	1	yes	characteristic
200	#11719919	C₂³	1	2	yes	—
201	#11719919	C₂³	1	2	yes	—
202	#11719919	C₂³	1	2	yes	—
203	#11719919	C₂³	1	2	yes	—
204	#11719919	C₂³	1	2	yes	—
205	#11719919	C₂³	1	2	yes	—
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	2	yes	—
211	#11719919	C₂³	1	2	yes	—
212	#11719919	C₂³	1	2	yes	—
213	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
214	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
215	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
216	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
217	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
218	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
219	C₄×Dic₅₃	C₂³	1	2	yes	—
220	C₄×Dic₅₃	C₂³	1	2	yes	—
221	C₄×Dic₅₃	C₂³	1	2	yes	—
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	2	yes	—
226	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
227	C₂²×D₅₃	—	2	2	no	—
228	C₂²×D₅₃	—	2	2	no	—
229	C₂²×D₅₃	—	4	1	no	—
230	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
231	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
232	Q₈×C₅₃	—	2	2	no	—
233	Q₈×C₅₃	—	4	2	no	—
234	D₄×C₅₃	—	2	2	no	—
235	D₄×C₅₃	—	4	2	no	—
236	C₂×C₄×C₅₃	—	2	2	no	—
237	C₂×C₄×C₅₃	—	4	2	no	—
238	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
239	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
240	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
243	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
247	C₂²⋊D₅₃	—	2	4	no	—
248	C₂²⋊D₅₃	—	2	4	no	—
249	C₂×Dic₅₃	—	2	2	no	—
250	C₂×Dic₅₃	—	2	4	no	—
251	C₂×Dic₅₃	—	4	2	no	—
252	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₅₃	C₂⁴	1	2	yes	—
254	C₂×Dic₅₃	C₂⁴	1	2	yes	—
255	C₂×Dic₅₃	C₂⁴	1	2	yes	—
256	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₅₃	C₂⁴	1	2	yes	—
261	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
262	C₄×D₅₃	—	2	2	no	—
263	C₄×D₅₃	—	2	4	no	—
264	C₄×D₅₃	—	2	2	no	—
265	C₄×D₅₃	—	2	2	no	—
266	C₄×D₅₃	—	2	2	no	—
267	C₄×D₅₃	—	2	2	no	—
268	C₄×D₅₃	—	4	1	no	—
269	C₄×D₅₃	—	4	2	no	—
270	C₄×D₅₃	—	4	1	no	—
271	C₄×D₅₃	#41	1	4	yes	—
272	Dic₁₀₆	—	2	2	no	—
273	Dic₁₀₆	—	2	2	no	—
274	Dic₁₀₆	—	2	4	no	—
275	Dic₁₀₆	—	4	2	no	—
276	C₂²×C₅₃	—	2	2	no	—
277	C₂²×C₅₃	—	2	1	no	—
278	C₂²×C₅₃	—	2	2	no	—
279	C₂²×C₅₃	—	2	1	no	—
280	C₂²×C₅₃	—	2	2	no	—
281	C₂²×C₅₃	—	2	1	no	—
282	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
283	C₂×D₅₃	—	2	1	no	—
284	C₂×D₅₃	—	2	1	no	—
285	C₂×D₅₃	—	2	1	no	—
286	C₂×D₅₃	—	2	1	no	—
287	C₂×D₅₃	—	4	4	no	—
288	C₂×D₅₃	C₂×#41	1	2	yes	—
289	C₂×D₅₃	2₋¹⁺⁴	1	2	yes	—
290	C₄×C₅₃	—	2	2	no	—
291	C₄×C₅₃	—	2	1	no	—
292	C₄×C₅₃	—	2	1	no	—
293	C₄×C₅₃	—	2	1	no	—
294	C₄×C₅₃	—	2	2	no	—
295	C₄×C₅₃	—	2	1	no	—
296	C₄×C₅₃	—	2	2	no	—
297	C₄×C₅₃	—	2	1	no	—
298	C₄×C₅₃	C₂×#41	1	2	yes	—
299	Dic₅₃	—	2	2	no	—
300	Dic₅₃	—	2	2	no	—
301	Dic₅₃	—	2	1	no	—
302	Dic₅₃	—	2	1	no	—
303	Dic₅₃	—	2	1	no	—
304	Dic₅₃	—	2	2	no	—
305	Dic₅₃	—	2	1	no	—
306	Dic₅₃	—	2	2	no	—
307	Dic₅₃	—	2	1	no	—
308	Dic₅₃	C₂×#41	1	2	yes	—
309	#3495	—	53	1	no	maximal, Sylow
310	C₂×C₅₃	—	4	1	no	—
311	C₂×C₅₃	—	4	2	no	—
312	C₂×C₅₃	C₂²×#41	1	1	yes	characteristic
313	C₂×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
314	C₂×C₅₃	#585	1	1	yes	characteristic
315	D₅₃	—	2	2	no	—
316	D₅₃	—	2	2	no	—
317	#556	—	53	2	no	—
318	#554	—	53	2	no	—
319	#552	—	53	2	no	—
320	#552	—	53	2	no	—
321	#552	—	53	2	no	—
322	#552	—	53	2	no	—
323	#551	—	53	2	no	—
324	#551	—	53	2	no	—
325	#544	—	53	1	no	—
326	#542	—	53	1	no	—
327	#542	D₅₃	1	1	yes	characteristic, complemented
328	#541	—	53	1	no	—
329	#541	—	53	1	no	—
330	#536	—	53	1	no	—
331	#533	—	53	1	no	—
332	#533	—	53	1	no	—
333	#529	—	53	1	no	—
334	#529	—	53	1	no	—
335	#525	—	53	1	no	—
336	C₂×C₂²⋊Q₈	—	53	1	no	—
337	#520	—	53	1	no	—
338	#519	—	53	1	no	—
339	C₂×#117	—	53	1	no	—
340	C₅₃	#3495	1	1	yes	characteristic, complemented, Sylow
341	C₂×#41	—	53	1	no	—
342	C₂²×Q₈	—	53	1	no	—
343	C₂³×C₄	—	53	1	no	—
344	C₄⋊Q₈	—	53	1	no	—
345	C₄⋊Q₈	—	53	2	no	—
346	C₄⋊Q₈	—	53	1	no	—
347	C₄⋊Q₈	—	53	1	no	—
348	C₄⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
349	#126	—	53	2	no	—
350	#126	—	53	2	no	—
351	#126	—	53	2	no	—
352	#126	—	53	2	no	—
353	#126	—	53	2	no	—
354	#126	—	53	2	no	—
355	#126	—	53	2	no	—
356	#126	C₂×D₅₃	1	2	yes	complemented
357	#125	—	53	1	no	—
358	#125	—	53	2	no	—
359	#125	—	53	2	no	—
360	#125	—	53	2	no	—
361	#125	—	53	2	no	—
362	#125	—	53	2	no	—
363	#125	—	53	2	no	—
364	#125	—	53	2	no	—
365	#125	—	53	1	no	—
366	#124	—	53	1	no	—
367	#124	—	53	2	no	—
368	#124	C₂×D₅₃	1	2	yes	—
369	#124	C₂×D₅₃	1	1	yes	characteristic, complemented
370	#123	—	53	2	no	—
371	#123	—	53	2	no	—
372	#123	—	53	2	no	—
373	#123	—	53	2	no	—
374	#123	—	53	2	no	—
375	#123	—	53	2	no	—
376	#123	C₂×D₅₃	1	2	yes	—
377	C₂²⋊Q₈	—	53	1	no	—
378	C₂²⋊Q₈	—	53	2	no	—
379	C₂²⋊Q₈	—	53	2	no	—
380	C₂²⋊Q₈	—	53	1	no	—
381	C₂²⋊Q₈	—	53	1	no	—
382	C₂²⋊Q₈	—	53	1	no	—
383	C₂²⋊Q₈	—	53	2	no	—
384	C₂²⋊Q₈	—	53	1	no	—
385	C₂²⋊Q₈	—	53	2	no	—
386	C₂²⋊Q₈	—	53	2	no	—
387	C₂²⋊Q₈	—	53	2	no	—
388	C₂²⋊Q₈	—	53	2	no	—
389	C₂²⋊Q₈	—	53	2	no	—
390	C₂²⋊Q₈	—	53	2	no	—
391	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
392	C₂²⋊Q₈	C₂×D₅₃	1	2	yes	complemented
393	#121	—	53	1	no	—
394	#121	C₂×D₅₃	1	1	yes	characteristic
395	#120	—	53	2	no	—
396	C₄×Q₈	—	53	1	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	2	no	—
403	C₄×Q₈	—	53	1	no	—
404	C₄×Q₈	—	53	2	no	—
405	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
406	C₄×D₄	—	53	1	no	—
407	C₄×D₄	—	53	2	no	—
408	C₄×D₄	—	53	2	no	—
409	C₄×D₄	—	53	2	no	—
410	C₄×D₄	—	53	2	no	—
411	C₄×D₄	—	53	2	no	—
412	C₄×D₄	—	53	2	no	—
413	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
414	#117	—	53	1	no	—
415	#117	—	53	2	no	—
416	#117	—	53	1	no	—
417	#117	—	53	1	no	—
418	#117	—	53	1	no	—
419	#117	—	53	2	no	—
420	#117	—	53	2	no	—
421	#117	—	53	1	no	—
422	#117	—	53	1	no	—
423	#117	—	53	2	no	—
424	#117	—	53	2	no	—
425	#117	—	53	1	no	—
426	#117	—	53	1	no	—
427	#117	—	53	2	no	—
428	#117	—	53	2	no	—
429	#117	C₂×D₅₃	1	1	yes	characteristic
430	C₂×C₄⋊C₄	—	53	2	no	—
431	C₂×C₄⋊C₄	—	53	1	no	—
432	C₂×C₄⋊C₄	—	53	1	no	—
433	C₂×C₄⋊C₄	—	53	1	no	—
434	C₂×C₄⋊C₄	—	53	2	no	—
435	C₂×C₂²⋊C₄	—	53	1	no	—
436	C₂×C₂²⋊C₄	—	53	1	no	—
437	C₂×C₂²⋊C₄	—	53	2	no	—
438	C₂×C₄²	—	53	1	no	—
439	C₂×C₄²	—	53	1	no	—
440	C₂⁴	—	53	1	no	—
441	#41	—	106	4	no	—
442	C₂×Q₈	—	53	2	no	—
443	C₂×Q₈	—	53	1	no	—
444	C₂×Q₈	—	53	1	no	—
445	C₂×Q₈	—	53	2	no	—
446	C₂×Q₈	—	106	4	no	—
447	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
448	C₂×Q₈	C₂²×D₅₃	1	2	yes	—
449	C₂×D₄	—	53	2	no	—
450	C₂×D₄	—	53	2	no	—
451	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
452	C₂×D₄	C₂²×D₅₃	1	2	yes	—
453	C₂²×C₄	—	53	1	no	—
454	C₂²×C₄	—	53	2	no	—
455	C₂²×C₄	—	53	1	no	—
456	C₂²×C₄	—	53	2	no	—
457	C₂²×C₄	—	53	1	no	—
458	C₂²×C₄	—	53	1	no	—
459	C₂²×C₄	—	53	1	no	—
460	C₂²×C₄	—	53	2	no	—
461	C₂²×C₄	—	53	1	no	—
462	C₂²×C₄	—	53	1	no	—
463	C₂²×C₄	—	53	1	no	—
464	C₂²×C₄	—	53	1	no	—
465	C₂²×C₄	—	53	2	no	—
466	C₂²×C₄	—	106	4	no	—
467	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
468	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
469	C₄⋊C₄	—	53	1	no	—
470	C₄⋊C₄	—	53	2	no	—
471	C₄⋊C₄	—	53	1	no	—
472	C₄⋊C₄	—	53	1	no	—
473	C₄⋊C₄	—	53	1	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	1	no	—
479	C₄⋊C₄	—	53	2	no	—
480	C₄⋊C₄	—	53	2	no	—
481	C₄⋊C₄	—	53	2	no	—
482	C₄⋊C₄	—	53	1	no	—
483	C₄⋊C₄	—	53	2	no	—
484	C₄⋊C₄	—	53	2	no	—
485	C₄⋊C₄	—	53	2	no	—
486	C₄⋊C₄	—	53	2	no	—
487	C₄⋊C₄	—	53	2	no	—
488	C₄⋊C₄	—	53	2	no	—
489	C₄⋊C₄	—	53	2	no	—
490	C₄⋊C₄	—	53	2	no	—
491	C₄⋊C₄	—	53	2	no	—
492	C₄⋊C₄	—	53	2	no	—
493	C₄⋊C₄	—	53	2	no	—
494	C₄⋊C₄	—	53	2	no	—
495	C₄⋊C₄	—	53	2	no	—
496	C₄⋊C₄	—	53	2	no	—
497	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
498	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
499	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
500	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
501	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
502	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
503	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
504	C₂²⋊C₄	—	53	1	no	—
505	C₂²⋊C₄	—	53	1	no	—
506	C₂²⋊C₄	—	53	2	no	—
507	C₂²⋊C₄	—	53	2	no	—
508	C₂²⋊C₄	—	53	2	no	—
509	C₂²⋊C₄	—	53	2	no	—
510	C₂²⋊C₄	—	53	2	no	—
511	C₂²⋊C₄	—	53	2	no	—
512	C₂²⋊C₄	—	53	1	no	—
513	C₂²⋊C₄	—	53	1	no	—
514	C₂²⋊C₄	—	53	1	no	—
515	C₂²⋊C₄	—	53	1	no	—
516	C₂²⋊C₄	—	53	2	no	—
517	C₂²⋊C₄	—	53	2	no	—
518	C₂²⋊C₄	—	53	2	no	—
519	C₂²⋊C₄	—	53	2	no	—
520	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
521	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
522	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
523	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
524	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
525	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
526	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
527	C₄²	—	53	1	no	—
528	C₄²	—	53	1	no	—
529	C₄²	—	53	1	no	—
530	C₄²	—	53	1	no	—
531	C₄²	—	53	1	no	—
532	C₄²	—	53	1	no	—
533	C₄²	—	53	2	no	—
534	C₄²	—	53	2	no	—
535	C₄²	—	53	2	no	—
536	C₄²	—	53	2	no	—
537	C₄²	—	53	2	no	—
538	C₄²	—	53	2	no	—
539	C₄²	C₂²×D₅₃	1	1	yes	characteristic
540	C₄²	C₂²×D₅₃	1	1	yes	characteristic
541	C₄²	C₂²×D₅₃	1	2	yes	—
542	C₂³	—	53	1	no	—
543	C₂³	—	53	1	no	—
544	C₂³	—	106	2	no	—
545	C₂³	—	106	2	no	—
546	C₂³	—	212	1	no	—
547	C₂³	C₂³×D₅₃	1	1	yes	characteristic
548	C₂³	C₂³×D₅₃	1	2	yes	—
549	Q₈	—	2	2	no	—
550	Q₈	—	4	2	no	—
551	Q₈	—	106	4	no	—
552	Q₈	—	106	2	no	—
553	Q₈	—	106	2	no	—
554	Q₈	—	212	2	no	—
555	D₄	—	2	2	no	—
556	D₄	—	4	2	no	—
557	D₄	—	106	4	no	—
558	D₄	—	106	4	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	53	1	no	—
562	C₂×C₄	—	53	4	no	—
563	C₂×C₄	—	53	1	no	—
564	C₂×C₄	—	53	1	no	—
565	C₂×C₄	—	53	1	no	—
566	C₂×C₄	—	53	2	no	—
567	C₂×C₄	—	53	1	no	—
568	C₂×C₄	—	53	2	no	—
569	C₂×C₄	—	53	1	no	—
570	C₂×C₄	—	53	2	no	—
571	C₂×C₄	—	53	2	no	—
572	C₂×C₄	—	106	2	no	—
573	C₂×C₄	—	106	2	no	—
574	C₂×C₄	—	106	2	no	—
575	C₂×C₄	—	106	2	no	—
576	C₂×C₄	—	106	4	no	—
577	C₂×C₄	—	106	2	no	—
578	C₂×C₄	—	106	4	no	—
579	C₂×C₄	—	106	2	no	—
580	C₂×C₄	—	212	1	no	—
581	C₂×C₄	—	212	2	no	—
582	C₂×C₄	—	212	1	no	—
583	C₂×C₄	—	212	2	no	—
584	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
585	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
586	C₂×C₄	C₂³×D₅₃	1	2	yes	—
587	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
588	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
589	C₂×C₄	C₂³×D₅₃	1	2	yes	—
590	C₂×C₄	C₂³×D₅₃	1	2	yes	—
591	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
592	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
593	C₂²	—	2	1	no	—
594	C₂²	—	2	2	no	—
595	C₂²	—	2	2	no	—
596	C₂²	—	2	1	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	1	no	—
599	C₂²	—	53	2	no	—
600	C₂²	—	53	2	no	—
601	C₂²	—	106	1	no	—
602	C₂²	—	106	1	no	—
603	C₂²	—	106	1	no	—
604	C₂²	—	106	1	no	—
605	C₂²	—	212	4	no	—
606	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
607	C₄	—	2	1	no	—
608	C₄	—	2	2	no	—
609	C₄	—	2	1	no	—
610	C₄	—	2	1	no	—
611	C₄	—	2	1	no	—
612	C₄	—	2	2	no	—
613	C₄	—	2	1	no	—
614	C₄	—	2	2	no	—
615	C₄	—	53	2	no	—
616	C₄	—	106	1	no	—
617	C₄	—	106	2	no	—
618	C₄	—	106	2	no	—
619	C₄	—	106	1	no	—
620	C₄	—	106	1	no	—
621	C₄	—	106	2	no	—
622	C₄	—	106	1	no	—
623	C₄	—	106	2	no	—
624	C₄	—	106	1	no	—
625	C₄	#41×D₅₃	1	2	yes	—
626	C₂	—	4	1	no	—
627	C₂	—	4	2	no	—
628	C₂	—	106	2	no	—
629	C₂	—	106	2	no	—
630	C₂	C₂×#41×D₅₃	1	1	yes	characteristic
631	C₂	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
632	C₂	#16811458	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#542	C₂
hypercenter	#542	D₅₃
hypocenter	C₅₃	#3495
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. #16811342	C₂	semidirect
2. #16811327	C₂	semidirect
3. #16811310	C₂	semidirect
4. #16811309	C₂	semidirect
5. #16811309	C₂	semidirect
6. #16811307	C₂	semidirect
7. #16811303	C₂	semidirect
8. #16811301	C₂	semidirect
9. #16811250	C₂	semidirect
10. #16811240	C₂	semidirect
11. #16811235	C₂	semidirect
12. #16811233	C₂	semidirect
13. #16811193	C₂	semidirect
14. #16811178	C₂	semidirect
15. #16811177	C₂	semidirect
16. #16811155	C₂	semidirect
17. #16811152	C₂	semidirect
19. C₂²⋊Q₈×D₅₃	C₂	semidirect
20. #16811102	C₂	semidirect
21. #16811099	C₂	semidirect
22. #117×D₅₃	C₂	semidirect
23. C₅₃×#542	C₂	semidirect
27. #13133217	C₂²	semidirect
28. #13133216	C₂²	semidirect
29. #13133215	C₂²	semidirect
30. #13133215	C₂²	semidirect
35. #13133210	C₂²	semidirect
36. #13133210	C₂²	semidirect
37. #13133210	C₂²	semidirect
38. #13133209	C₂²	semidirect
39. #13133208	C₂²	semidirect
40. #13133208	C₂²	semidirect
41. #13133208	C₂²	semidirect
42. #13133207	C₂²	semidirect
43. #13133207	C₂²	semidirect
44. #13133207	C₂²	semidirect
45. #13133207	C₂²	semidirect
46. #13133207	C₂²	semidirect
48. #13133204	C₂²	semidirect
63. #13133194	C₂²	semidirect
64. #13133194	C₂²	semidirect
65. #13133194	C₂²	semidirect
71. Q₈×Dic₅₃	C₂²	semidirect
72. Q₈×Dic₅₃	C₂²	semidirect
73. C₄×Dic₁₀₆	C₂²	semidirect
74. C₄×Dic₁₀₆	C₂²	semidirect
75. C₄×Dic₁₀₆	C₂²	semidirect
76. C₄×Dic₁₀₆	C₂²	semidirect
77. #13133182	C₂²	semidirect
78. #13133182	C₂²	semidirect
79. #13133182	C₂²	semidirect
81. D₄×Dic₅₃	C₂²	semidirect
88. #13133176	C₂²	semidirect
100. #13133173	C₂²	semidirect
101. #13133173	C₂²	semidirect
102. C₂×#11719919	C₂²	semidirect
112. C₄⋊Q₈×C₅₃	C₂²	semidirect
113. #126×C₅₃	C₂²	semidirect
115. #124×C₅₃	C₂²	semidirect
118. C₂²⋊Q₈×C₅₃	C₂²	semidirect
120. C₄×Q₈×C₅₃	C₂²	semidirect
121. C₄×D₄×C₅₃	C₂²	semidirect
327. #542	D₅₃	semidirect
340. C₅₃	#3495	semidirect
348. C₄⋊Q₈	C₂×D₅₃	semidirect
356. #126	C₂×D₅₃	semidirect
369. #124	C₂×D₅₃	semidirect
392. C₂²⋊Q₈	C₂×D₅₃	semidirect
405. C₄×Q₈	C₂×D₅₃	semidirect
413. C₄×D₄	C₂×D₅₃	semidirect