Subgroups — #20288747

Order 6784.

1252 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811338	C₂	1	1	yes	maximal, characteristic, complemented
2	#16811330	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811321	C₂	1	2	yes	maximal, complemented
4	#16811319	C₂	1	2	yes	maximal, complemented
5	#16811294	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811269	C₂	1	2	yes	maximal, complemented
7	#16811263	C₂	1	4	yes	maximal, complemented
8	D₄×D₂₁₂	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×C₂²⋊D₅₃	C₂	1	2	yes	maximal, complemented
10	#16811224	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	#16811134	C₂	1	2	yes	maximal, complemented
15	C₂×#13133191	C₂	1	2	yes	maximal, complemented
16	#16811095	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#11719945	C₂²	1	2	yes	complemented
19	C₂×#11719945	C₂²	1	2	yes	complemented
20	C₂²×D₂₁₂	C₂²	1	2	yes	complemented
21	C₂²×C₂²⋊D₅₃	C₂²	1	4	yes	complemented
22	C₂×D₄×D₅₃	C₂²	1	2	yes	—
23	#13133217	C₂²	1	1	yes	characteristic, complemented
24	#13133214	C₂²	1	1	yes	characteristic, complemented
25	#13133213	C₂²	1	2	yes	complemented
26	#13133212	C₂²	1	4	yes	complemented
27	#13133211	C₂²	1	2	yes	complemented
28	#13133209	C₂²	1	1	yes	characteristic, complemented
29	#13133208	C₂²	1	2	yes	complemented
30	#13133205	C₂²	1	1	yes	characteristic, complemented
31	#13133205	C₂²	1	2	yes	complemented
32	#13133203	C₂²	1	4	yes	complemented
33	#13133202	C₂²	1	4	yes	complemented
34	#13133200	C₂²	1	4	yes	complemented
35	#13133200	C₂²	1	2	yes	complemented
36	#13133199	C₂²	1	4	yes	complemented
37	#13133196	C₂²	1	2	yes	complemented
38	#13133196	C₂²	1	1	yes	characteristic, complemented
39	#13133194	C₂²	1	4	yes	complemented
40	#13133192	C₂²	1	2	yes	complemented
41	#13133191	C₂²	1	1	yes	characteristic
42	#13133191	C₂²	1	2	yes	complemented
43	#13133191	C₂²	1	2	yes	complemented
44	#13133191	C₂²	1	2	yes	complemented
45	#13133191	C₂²	1	4	yes	complemented
46	#13133191	C₂²	1	2	yes	complemented
47	#13133191	C₂²	1	2	yes	complemented
48	#13133191	C₂²	1	4	yes	complemented
49	#13133190	C₂²	1	4	yes	complemented
50	#13133190	C₂²	1	4	yes	complemented
51	#13133189	C₂²	1	4	yes	complemented
52	#13133188	C₂²	1	2	yes	complemented
53	#13133187	C₂²	1	4	yes	complemented
54	#13133186	C₂²	1	4	yes	complemented
55	#13133185	C₂²	1	4	yes	complemented
56	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
57	C₄×D₂₁₂	C₂²	1	2	yes	complemented
58	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
59	C₄×D₂₁₂	C₂²	1	2	yes	complemented
60	D₄×Dic₅₃	C₂²	1	2	yes	—
61	#13133179	C₂²	1	2	yes	complemented
62	C₄×C₂²⋊D₅₃	C₂²	1	4	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	#13133176	C₂²	1	2	yes	complemented
67	#13133175	C₂²	1	2	yes	complemented
68	#13133174	C₂²	1	2	yes	complemented
69	C₂×C₄⋊Dic₅₃	C₂²	1	2	yes	complemented
70	C₂×#11719921	C₂²	1	4	yes	complemented
71	C₂²⋊C₄×D₅₃	C₂²	1	4	yes	complemented
72	C₂²×D₄×C₅₃	C₂²	1	1	yes	characteristic
73	C₂³×C₄×C₅₃	C₂²	1	2	yes	complemented
74	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
75	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
76	C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
77	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
78	C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
79	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
80	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
82	C₂×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
83	C₂⁴×C₅₃	C₂³	1	2	yes	—
84	C₂³×D₅₃	C₂³	1	4	yes	—
85	C₂×D₄×C₅₃	—	2	4	no	—
86	C₂×D₄×C₅₃	C₂³	1	2	yes	—
87	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
88	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₅₃	—	4	4	no	—
90	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
91	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
93	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
94	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
95	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
96	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
97	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
98	C₂×C₂²⋊D₅₃	—	4	8	no	—
99	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
100	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
101	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
102	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
103	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
104	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
105	C₂²×Dic₅₃	C₂³	1	4	yes	—
106	D₄×D₅₃	—	2	8	no	—
107	#11719945	—	4	4	no	—
108	#11719945	—	4	4	no	—
109	C₂×D₂₁₂	—	4	4	no	—
110	C₂×D₂₁₂	C₂³	1	2	yes	—
111	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
112	C₂×D₂₁₂	C₂³	1	2	yes	—
113	C₂×D₂₁₂	C₂³	1	2	yes	—
114	C₂×D₂₁₂	C₂³	1	4	yes	—
115	C₂×C₄×D₅₃	C₂³	1	2	yes	—
116	C₂×C₄×D₅₃	C₂³	1	4	yes	—
117	C₂×C₄×D₅₃	C₂³	1	4	yes	—
118	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
119	C₂×Dic₁₀₆	C₂³	1	2	yes	—
120	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
121	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
122	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
123	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
124	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
125	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
126	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
127	C₄²×C₅₃	C₂³	1	1	yes	characteristic
128	C₄²×C₅₃	C₂³	1	1	yes	characteristic
129	C₄²×C₅₃	C₂³	1	1	yes	characteristic
130	C₄²×C₅₃	C₂³	1	1	yes	characteristic
131	C₂²⋊Dic₅₃	C₂³	1	4	yes	—
132	C₂²⋊Dic₅₃	C₂³	1	4	yes	—
133	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
134	#11719921	C₂³	1	2	yes	—
135	#11719921	C₂³	1	4	yes	—
136	#11719921	C₂³	1	2	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	#11719921	C₂³	1	4	yes	—
142	#11719921	C₂³	1	2	yes	—
143	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
144	C₄⋊Dic₅₃	C₂³	1	2	yes	—
145	C₄⋊Dic₅₃	C₂³	1	4	yes	—
146	C₄⋊Dic₅₃	C₂³	1	2	yes	—
147	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
148	#11719919	C₂³	1	2	yes	—
149	#11719919	C₂³	1	2	yes	—
150	#11719919	C₂³	1	2	yes	—
151	#11719919	C₂³	1	4	yes	—
152	#11719919	C₂³	1	2	yes	—
153	C₄×Dic₅₃	C₂³	1	2	yes	—
154	C₄×Dic₅₃	C₂³	1	4	yes	—
155	C₂³×C₅₃	—	2	4	no	—
156	C₂³×C₅₃	—	2	4	no	—
157	C₂³×C₅₃	—	4	2	no	—
158	C₂³×C₅₃	C₂⁴	1	2	yes	—
159	C₂³×C₅₃	C₂⁴	1	2	yes	—
160	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
161	C₂²×D₅₃	—	2	8	no	—
162	C₂²×D₅₃	—	4	4	no	—
163	C₂²×D₅₃	—	4	4	no	—
164	C₂²×D₅₃	C₂⁴	1	4	yes	—
165	C₂²×D₅₃	C₂⁴	1	2	yes	—
166	D₄×C₅₃	—	2	4	no	—
167	D₄×C₅₃	—	2	2	no	—
168	D₄×C₅₃	#41	1	4	yes	complemented
169	C₂×C₄×C₅₃	—	2	2	no	—
170	C₂×C₄×C₅₃	—	2	2	no	—
171	C₂×C₄×C₅₃	—	2	4	no	—
172	C₂×C₄×C₅₃	—	2	4	no	—
173	C₂×C₄×C₅₃	—	2	2	no	—
174	C₂×C₄×C₅₃	—	4	2	no	—
175	C₂×C₄×C₅₃	—	4	2	no	—
176	C₂×C₄×C₅₃	—	4	2	no	—
177	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
178	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
179	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
180	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
181	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
182	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
183	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
184	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
185	C₂²⋊D₅₃	—	2	8	no	—
186	C₂²⋊D₅₃	—	2	8	no	—
187	C₂²⋊D₅₃	—	2	4	no	—
188	C₂²⋊D₅₃	—	4	4	no	—
189	C₂²⋊D₅₃	—	4	4	no	—
190	C₂²⋊D₅₃	—	4	4	no	—
191	C₂×Dic₅₃	—	4	4	no	—
192	C₂×Dic₅₃	C₂⁴	1	2	yes	—
193	C₂×Dic₅₃	C₂⁴	1	4	yes	—
194	C₂×Dic₅₃	C₂⁴	1	2	yes	—
195	C₂×Dic₅₃	C₂⁴	1	2	yes	—
196	D₂₁₂	—	2	4	no	—
197	D₂₁₂	—	2	2	no	—
198	D₂₁₂	—	2	4	no	—
199	D₂₁₂	—	4	4	no	—
200	D₂₁₂	—	4	2	no	—
201	C₄×D₅₃	—	2	4	no	—
202	C₄×D₅₃	—	4	4	no	—
203	C₄×D₅₃	—	4	4	no	—
204	Dic₁₀₆	—	2	2	no	—
205	Dic₁₀₆	—	4	2	no	—
206	C₂²×C₅₃	—	2	1	no	—
207	C₂²×C₅₃	—	2	2	no	—
208	C₂²×C₅₃	—	2	1	no	—
209	C₂²×C₅₃	—	2	2	no	—
210	C₂²×C₅₃	—	2	2	no	—
211	C₂²×C₅₃	—	2	2	no	—
212	C₂²×C₅₃	—	2	2	no	—
213	C₂²×C₅₃	—	4	8	no	—
214	C₂²×C₅₃	C₂×#41	1	4	yes	—
215	C₂²×C₅₃	H(5,𝔽₂)	1	2	yes	—
216	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
217	C₂×D₅₃	—	2	2	no	—
218	C₂×D₅₃	—	2	4	no	—
219	C₂×D₅₃	—	2	4	no	—
220	C₂×D₅₃	—	2	4	no	—
221	C₂×D₅₃	—	2	2	no	—
222	C₂×D₅₃	—	2	2	no	—
223	C₂×D₅₃	—	8	8	no	—
224	C₄×C₅₃	—	2	1	no	—
225	C₄×C₅₃	—	2	1	no	—
226	C₄×C₅₃	—	2	1	no	—
227	C₄×C₅₃	—	2	2	no	—
228	C₄×C₅₃	—	2	2	no	—
229	C₄×C₅₃	—	2	1	no	—
230	C₄×C₅₃	C₂×#41	1	2	yes	—
231	C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
232	Dic₅₃	—	2	2	no	—
233	Dic₅₃	—	2	2	no	—
234	Dic₅₃	—	2	4	no	—
235	Dic₅₃	—	2	2	no	—
236	#3519	—	53	1	no	maximal, Sylow
237	C₂×C₅₃	—	2	4	no	—
238	C₂×C₅₃	—	2	2	no	—
239	C₂×C₅₃	—	4	2	no	—
240	C₂×C₅₃	C₂²×#41	1	1	yes	characteristic
241	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
242	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
243	D₅₃	—	4	4	no	—
244	D₅₃	—	4	2	no	—
245	#555	—	53	1	no	—
246	#554	—	53	1	no	—
247	#553	—	53	2	no	—
248	#553	—	53	2	no	—
249	#550	—	53	1	no	—
250	#546	—	53	2	no	—
251	#546	—	53	4	no	—
252	D₄²	—	53	2	no	—
253	D₄²	—	53	1	no	—
254	#540	—	53	2	no	—
255	#538	—	53	4	no	—
256	#532	—	53	1	no	—
257	#529	—	53	1	no	—
258	#525	—	53	2	no	—
259	C₂×#121	—	53	2	no	—
260	#518	—	53	2	no	—
261	C₂×C₄×D₄	D₅₃	1	1	yes	characteristic, complemented
262	C₅₃	#3519	1	1	yes	characteristic, complemented, Sylow
263	C₂×#41	—	53	2	no	—
264	C₂×#41	—	53	2	no	—
265	C₂²×D₄	—	53	4	no	—
266	C₂²×D₄	—	53	2	no	—
267	C₂²×D₄	—	53	2	no	—
268	C₂²×D₄	C₂×D₅₃	1	1	yes	characteristic
269	C₂³×C₄	C₂×D₅₃	1	2	yes	complemented
270	C₄⋊Q₈	—	53	1	no	—
271	#127	—	53	2	no	—
272	#127	—	53	1	no	—
273	#126	—	53	4	no	—
274	#126	—	53	2	no	—
275	#125	—	53	2	no	—
276	#125	—	53	1	no	—
277	#124	—	53	4	no	—
278	#124	—	53	1	no	—
279	#124	—	53	2	no	—
280	#123	—	53	4	no	—
281	#123	—	53	2	no	—
282	#123	—	53	4	no	—
283	#123	—	53	4	no	—
284	C₂²⋊Q₈	—	53	1	no	—
285	C₂²⋊Q₈	—	53	2	no	—
286	C₂²⋊Q₈	—	53	4	no	—
287	#121	—	53	4	no	—
288	#121	—	53	2	no	—
289	#121	—	53	1	no	—
290	#121	—	53	2	no	—
291	#121	—	53	4	no	—
292	#121	—	53	4	no	—
293	#121	—	53	2	no	—
294	#121	—	53	2	no	—
295	#121	—	53	2	no	—
296	#121	—	53	2	no	—
297	#121	—	53	2	no	—
298	#121	—	53	4	no	—
299	#121	—	53	4	no	—
300	#120	—	53	4	no	—
301	#120	—	53	4	no	—
302	#120	—	53	4	no	—
303	C₄×Q₈	—	53	1	no	—
304	C₄×D₄	—	53	2	no	—
305	C₄×D₄	—	53	4	no	—
306	C₄×D₄	—	53	4	no	—
307	C₄×D₄	—	53	2	no	—
308	C₄×D₄	—	53	2	no	—
309	C₄×D₄	—	53	4	no	—
310	C₄×D₄	—	53	2	no	—
311	C₄×D₄	—	53	1	no	—
312	C₄×D₄	—	53	2	no	—
313	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
314	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
315	C₄×D₄	C₂×D₅₃	1	2	yes	complemented
316	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
317	C₄×D₄	C₂×D₅₃	1	2	yes	complemented
318	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
319	#117	—	53	2	no	—
320	#117	—	53	2	no	—
321	#117	—	53	2	no	—
322	C₂×C₄⋊C₄	—	53	2	no	—
323	C₂×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
324	C₂×C₂²⋊C₄	—	53	4	no	—
325	C₂×C₂²⋊C₄	—	53	4	no	—
326	C₂×C₂²⋊C₄	C₂×D₅₃	1	2	yes	complemented
327	C₂×C₄²	C₂×D₅₃	1	1	yes	characteristic, complemented
328	C₂⁴	—	53	4	no	—
329	C₂⁴	C₂²×D₅₃	1	2	yes	—
330	#41	—	212	4	no	—
331	#41	—	212	4	no	—
332	C₂×Q₈	—	53	1	no	—
333	C₂×Q₈	—	53	2	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	53	4	no	—
336	C₂×D₄	—	53	4	no	—
337	C₂×D₄	—	53	2	no	—
338	C₂×D₄	—	53	4	no	—
339	C₂×D₄	—	53	4	no	—
340	C₂×D₄	—	53	4	no	—
341	C₂×D₄	—	53	2	no	—
342	C₂×D₄	—	53	1	no	—
343	C₂×D₄	—	53	2	no	—
344	C₂×D₄	—	53	2	no	—
345	C₂×D₄	—	53	4	no	—
346	C₂×D₄	—	106	8	no	—
347	C₂×D₄	—	212	4	no	—
348	C₂×D₄	—	212	8	no	—
349	C₂×D₄	C₂²×D₅₃	1	2	yes	—
350	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
351	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
352	C₂²×C₄	—	4	4	no	—
353	C₂²×C₄	—	53	4	no	—
354	C₂²×C₄	—	53	2	no	—
355	C₂²×C₄	—	53	4	no	—
356	C₂²×C₄	—	53	4	no	—
357	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
358	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
359	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
360	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
361	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
362	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
363	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
364	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
365	C₄⋊C₄	—	53	1	no	—
366	C₄⋊C₄	—	53	2	no	—
367	C₄⋊C₄	—	53	4	no	—
368	C₄⋊C₄	—	53	1	no	—
369	C₄⋊C₄	—	53	2	no	—
370	C₄⋊C₄	—	53	2	no	—
371	C₄⋊C₄	—	53	2	no	—
372	C₄⋊C₄	—	53	2	no	—
373	C₄⋊C₄	—	53	4	no	—
374	C₄⋊C₄	—	53	2	no	—
375	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
376	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
377	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
378	C₂²⋊C₄	—	53	4	no	—
379	C₂²⋊C₄	—	53	4	no	—
380	C₂²⋊C₄	—	53	2	no	—
381	C₂²⋊C₄	—	53	2	no	—
382	C₂²⋊C₄	—	53	4	no	—
383	C₂²⋊C₄	—	53	2	no	—
384	C₂²⋊C₄	—	53	4	no	—
385	C₂²⋊C₄	—	53	4	no	—
386	C₂²⋊C₄	—	53	2	no	—
387	C₂²⋊C₄	—	53	2	no	—
388	C₂²⋊C₄	—	53	4	no	—
389	C₂²⋊C₄	—	53	4	no	—
390	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
391	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
392	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
393	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
394	C₄²	—	53	4	no	—
395	C₄²	—	53	2	no	—
396	C₄²	C₂²×D₅₃	1	1	yes	characteristic
397	C₄²	C₂²×D₅₃	1	1	yes	characteristic
398	C₄²	C₂²×D₅₃	1	1	yes	characteristic
399	C₄²	C₂²×D₅₃	1	1	yes	characteristic
400	C₂³	—	2	4	no	—
401	C₂³	—	2	4	no	—
402	C₂³	—	4	2	no	—
403	C₂³	—	53	2	no	—
404	C₂³	—	53	4	no	—
405	C₂³	—	106	8	no	—
406	C₂³	—	212	4	no	—
407	C₂³	—	212	4	no	—
408	C₂³	C₂³×D₅₃	1	2	yes	—
409	C₂³	C₂³×D₅₃	1	2	yes	—
410	C₂³	C₂³×D₅₃	1	1	yes	characteristic
411	Q₈	—	106	2	no	—
412	Q₈	—	212	2	no	—
413	D₄	—	2	4	no	—
414	D₄	—	2	2	no	—
415	D₄	—	106	8	no	—
416	D₄	—	106	4	no	—
417	D₄	—	106	8	no	—
418	D₄	—	106	4	no	—
419	D₄	—	106	2	no	—
420	D₄	—	106	4	no	—
421	D₄	—	212	4	no	—
422	D₄	—	212	2	no	—
423	D₄	—	212	4	no	—
424	D₄	—	212	4	no	—
425	D₄	—	212	4	no	—
426	D₄	#11719945	1	4	yes	complemented
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	53	2	no	—
436	C₂×C₄	—	53	2	no	—
437	C₂×C₄	—	53	4	no	—
438	C₂×C₄	—	53	2	no	—
439	C₂×C₄	—	106	4	no	—
440	C₂×C₄	—	212	4	no	—
441	C₂×C₄	—	212	4	no	—
442	C₂×C₄	—	212	4	no	—
443	C₂×C₄	C₂³×D₅₃	1	2	yes	—
444	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
445	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
446	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
447	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
448	C₂×C₄	C₂³×D₅₃	1	2	yes	—
449	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
450	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
451	C₂²	—	2	1	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	2	2	no	—
458	C₂²	—	4	8	no	—
459	C₂²	—	106	2	no	—
460	C₂²	—	106	4	no	—
461	C₂²	—	106	4	no	—
462	C₂²	—	106	2	no	—
463	C₂²	—	106	4	no	—
464	C₂²	—	106	2	no	—
465	C₂²	—	424	8	no	—
466	C₂²	C₂×#11719945	1	4	yes	—
467	C₂²	#13133263	1	2	yes	—
468	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	2	no	—
472	C₄	—	2	2	no	—
473	C₄	—	2	1	no	—
474	C₄	—	2	1	no	—
475	C₄	—	106	2	no	—
476	C₄	—	106	2	no	—
477	C₄	—	106	2	no	—
478	C₄	—	106	4	no	—
479	C₄	C₂×#11719945	1	2	yes	—
480	C₄	#13133262	1	2	yes	—
481	C₂	—	2	2	no	—
482	C₂	—	2	4	no	—
483	C₂	—	4	2	no	—
484	C₂	—	212	2	no	—
485	C₂	—	212	4	no	—
486	C₂	C₂²×#11719945	1	1	yes	characteristic
487	C₂	C₂×#13133262	1	1	yes	characteristic
488	C₂	C₂×#13133263	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₂×C₄×D₄×C₅₃	C₂
hypercenter	C₂×C₄×D₄	D₅₃
hypocenter	C₅₃	#3519
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #16811338	C₂	semidirect
2. #16811330	C₂	semidirect
3. #16811321	C₂	semidirect
4. #16811319	C₂	semidirect
5. #16811294	C₂	semidirect
6. #16811269	C₂	semidirect
7. #16811263	C₂	semidirect
8. D₄×D₂₁₂	C₂	semidirect
9. D₄×C₂²⋊D₅₃	C₂	semidirect
10. #16811224	C₂	semidirect
11. #16811206	C₂	semidirect
12. #16811173	C₂	semidirect
13. #16811157	C₂	semidirect
14. #16811134	C₂	semidirect
15. C₂×#13133191	C₂	semidirect
16. #16811095	C₂	semidirect
17. C₂×C₄×D₄×C₅₃	C₂	semidirect
18. C₂×#11719945	C₂²	semidirect
19. C₂×#11719945	C₂²	semidirect
20. C₂²×D₂₁₂	C₂²	semidirect
21. C₂²×C₂²⋊D₅₃	C₂²	semidirect
23. #13133217	C₂²	semidirect
24. #13133214	C₂²	semidirect
25. #13133213	C₂²	semidirect
26. #13133212	C₂²	semidirect
27. #13133211	C₂²	semidirect
28. #13133209	C₂²	semidirect
29. #13133208	C₂²	semidirect
30. #13133205	C₂²	semidirect
31. #13133205	C₂²	semidirect
32. #13133203	C₂²	semidirect
33. #13133202	C₂²	semidirect
34. #13133200	C₂²	semidirect
35. #13133200	C₂²	semidirect
36. #13133199	C₂²	semidirect
37. #13133196	C₂²	semidirect
38. #13133196	C₂²	semidirect
39. #13133194	C₂²	semidirect
40. #13133192	C₂²	semidirect
42. #13133191	C₂²	semidirect
43. #13133191	C₂²	semidirect
44. #13133191	C₂²	semidirect
45. #13133191	C₂²	semidirect
46. #13133191	C₂²	semidirect
47. #13133191	C₂²	semidirect
48. #13133191	C₂²	semidirect
49. #13133190	C₂²	semidirect
50. #13133190	C₂²	semidirect
51. #13133189	C₂²	semidirect
52. #13133188	C₂²	semidirect
53. #13133187	C₂²	semidirect
54. #13133186	C₂²	semidirect
55. #13133185	C₂²	semidirect
56. C₄×Dic₁₀₆	C₂²	semidirect
57. C₄×D₂₁₂	C₂²	semidirect
58. C₄×D₂₁₂	C₂²	semidirect
59. C₄×D₂₁₂	C₂²	semidirect
61. #13133179	C₂²	semidirect
62. C₄×C₂²⋊D₅₃	C₂²	semidirect
63. C₄×C₂²⋊D₅₃	C₂²	semidirect
64. C₄×C₂²⋊D₅₃	C₂²	semidirect
65. #13133177	C₂²	semidirect
66. #13133176	C₂²	semidirect
67. #13133175	C₂²	semidirect
68. #13133174	C₂²	semidirect
69. C₂×C₄⋊Dic₅₃	C₂²	semidirect
70. C₂×#11719921	C₂²	semidirect
71. C₂²⋊C₄×D₅₃	C₂²	semidirect
73. C₂³×C₄×C₅₃	C₂²	semidirect
76. C₄×D₄×C₅₃	C₂²	semidirect
77. C₄×D₄×C₅₃	C₂²	semidirect
78. C₄×D₄×C₅₃	C₂²	semidirect
79. C₄×D₄×C₅₃	C₂²	semidirect
80. C₂×C₄⋊C₄×C₅₃	C₂²	semidirect
81. C₂×C₂²⋊C₄×C₅₃	C₂²	semidirect
82. C₂×C₄²×C₅₃	C₂²	semidirect
168. D₄×C₅₃	#41	semidirect
261. C₂×C₄×D₄	D₅₃	semidirect
262. C₅₃	#3519	semidirect
269. C₂³×C₄	C₂×D₅₃	semidirect
315. C₄×D₄	C₂×D₅₃	semidirect
316. C₄×D₄	C₂×D₅₃	semidirect
317. C₄×D₄	C₂×D₅₃	semidirect
318. C₄×D₄	C₂×D₅₃	semidirect
323. C₂×C₄⋊C₄	C₂×D₅₃	semidirect
326. C₂×C₂²⋊C₄	C₂×D₅₃	semidirect
327. C₂×C₄²	C₂×D₅₃	semidirect
426. D₄	#11719945	semidirect