Subgroups — #20288990

Order 6784.

1058 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811366	C₂	1	2	yes	maximal, complemented
2	#16811362	C₂	1	2	yes	maximal, complemented
3	#16811357	C₂	1	2	yes	maximal, complemented
4	#16811343	C₂	1	2	yes	maximal, complemented
5	#16811338	C₂	1	2	yes	maximal, complemented
6	#16811301	C₂	1	2	yes	maximal, complemented
7	#16811282	C₂	1	2	yes	maximal, complemented
8	#16811269	C₂	1	2	yes	maximal, complemented
9	#16811244	C₂	1	2	yes	maximal, complemented
10	#16811243	C₂	1	4	yes	maximal, complemented
11	#16811205	C₂	1	4	yes	maximal, complemented
12	#16811194	C₂	1	1	yes	maximal, characteristic, complemented
13	#16811187	C₂	1	1	yes	maximal, characteristic, complemented
14	#16811134	C₂	1	2	yes	maximal, complemented
15	C₅₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#11719945	C₂²	1	2	yes	—
17	C₂²×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
18	C₂²×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
19	#13133217	C₂²	1	2	yes	complemented
20	#13133215	C₂²	1	2	yes	complemented
21	#13133213	C₂²	1	2	yes	—
22	#13133212	C₂²	1	4	yes	complemented
23	#13133210	C₂²	1	4	yes	complemented
24	#13133210	C₂²	1	4	yes	complemented
25	#13133206	C₂²	1	2	yes	complemented
26	#13133205	C₂²	1	2	yes	complemented
27	#13133204	C₂²	1	2	yes	—
28	#13133204	C₂²	1	4	yes	—
29	#13133203	C₂²	1	4	yes	complemented
30	#13133203	C₂²	1	4	yes	complemented
31	#13133203	C₂²	1	4	yes	complemented
32	#13133203	C₂²	1	4	yes	complemented
33	#13133202	C₂²	1	4	yes	complemented
34	#13133200	C₂²	1	4	yes	complemented
35	#13133199	C₂²	1	4	yes	complemented
36	#13133198	C₂²	1	2	yes	complemented
37	#13133198	C₂²	1	2	yes	complemented
38	#13133196	C₂²	1	2	yes	complemented
39	#13133196	C₂²	1	2	yes	complemented
40	#13133196	C₂²	1	2	yes	complemented
41	#13133195	C₂²	1	4	yes	complemented
42	#13133195	C₂²	1	4	yes	complemented
43	#13133191	C₂²	1	2	yes	—
44	#13133191	C₂²	1	2	yes	—
45	#13133191	C₂²	1	2	yes	complemented
46	#13133190	C₂²	1	4	yes	—
47	#13133189	C₂²	1	4	yes	complemented
48	#13133188	C₂²	1	4	yes	complemented
49	#13133186	C₂²	1	4	yes	complemented
50	#13133185	C₂²	1	4	yes	—
51	#13133185	C₂²	1	2	yes	—
52	#13133185	C₂²	1	2	yes	complemented
53	C₄×Dic₁₀₆	C₂²	1	2	yes	complemented
54	#13133182	C₂²	1	4	yes	complemented
55	C₄×D₂₁₂	C₂²	1	2	yes	complemented
56	C₄×C₂²⋊D₅₃	C₂²	1	4	yes	complemented
57	C₄×C₂²⋊D₅₃	C₂²	1	4	yes	complemented
58	#13133177	C₂²	1	4	yes	complemented
59	#13133176	C₂²	1	1	yes	characteristic, complemented
60	#13133176	C₂²	1	2	yes	complemented
61	#13133176	C₂²	1	1	yes	characteristic, complemented
62	#13133175	C₂²	1	4	yes	complemented
63	C₂²⋊C₄×D₅₃	C₂²	1	4	yes	complemented
64	C₂×#41×C₅₃	C₂²	1	1	yes	characteristic
65	C₂³×C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
66	#123×C₅₃	C₂²	1	1	yes	characteristic
67	#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
68	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
69	#121×C₅₃	C₂²	1	2	yes	—
70	#120×C₅₃	C₂²	1	1	yes	characteristic
71	#120×C₅₃	C₂²	1	1	yes	characteristic, complemented
72	C₄×D₄×C₅₃	C₂²	1	2	yes	—
73	C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
74	#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
75	C₂⁴×C₅₃	C₂³	1	1	yes	characteristic
76	C₂³×D₅₃	C₂³	1	2	yes	—
77	#41×C₅₃	—	4	2	no	—
78	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
79	C₂×D₄×C₅₃	C₂³	1	2	yes	—
80	C₂×D₄×C₅₃	C₂³	1	2	yes	—
81	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
82	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
83	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
84	C₂²×C₄×C₅₃	—	4	2	no	—
85	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
86	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
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	4	yes	—
92	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
93	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
94	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
95	C₂²×Dic₅₃	C₂³	1	2	yes	—
96	#11719945	—	4	4	no	—
97	C₂×D₂₁₂	—	4	2	no	—
98	C₂×D₂₁₂	C₂³	1	2	yes	—
99	C₂×D₂₁₂	C₂³	1	2	yes	—
100	C₂×C₄×D₅₃	C₂³	1	4	yes	—
101	C₂×C₄×D₅₃	C₂³	1	4	yes	—
102	C₂×Dic₁₀₆	—	4	2	no	—
103	C₂×Dic₁₀₆	C₂³	1	2	yes	—
104	C₂×Dic₁₀₆	C₂³	1	4	yes	—
105	C₂×Dic₁₀₆	C₂³	1	2	yes	—
106	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
107	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
108	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
109	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
110	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
111	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
112	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
113	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
114	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
115	C₄²×C₅₃	C₂³	1	2	yes	—
116	C₂²⋊Dic₅₃	C₂³	1	4	yes	—
117	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
118	C₂²⋊Dic₅₃	C₂³	1	4	yes	—
119	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
120	C₂²⋊Dic₅₃	C₂³	1	4	yes	—
121	C₂²⋊Dic₅₃	C₂³	1	4	yes	—
122	#11719921	C₂³	1	4	yes	—
123	#11719921	C₂³	1	4	yes	—
124	#11719921	C₂³	1	4	yes	—
125	#11719921	C₂³	1	4	yes	—
126	#11719921	C₂³	1	4	yes	—
127	#11719921	C₂³	1	4	yes	—
128	C₄⋊Dic₅₃	C₂³	1	4	yes	—
129	C₄⋊Dic₅₃	C₂³	1	2	yes	—
130	C₄⋊Dic₅₃	C₂³	1	2	yes	—
131	#11719919	C₂³	1	4	yes	—
132	#11719919	C₂³	1	4	yes	—
133	#11719919	C₂³	1	4	yes	—
134	#11719919	C₂³	1	4	yes	—
135	C₄×Dic₅₃	C₂³	1	2	yes	—
136	C₄×Dic₅₃	C₂³	1	4	yes	—
137	C₄×Dic₅₃	C₂³	1	2	yes	—
138	C₄×Dic₅₃	C₂³	1	4	yes	—
139	C₂³×C₅₃	—	4	1	no	—
140	C₂³×C₅₃	—	4	2	no	—
141	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
142	C₂³×C₅₃	C₂⁴	1	2	yes	—
143	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
144	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
145	C₂²×D₅₃	—	4	2	no	—
146	C₂²×D₅₃	—	4	4	no	—
147	C₂²×D₅₃	C₂⁴	1	4	yes	—
148	Q₈×C₅₃	—	4	1	no	—
149	D₄×C₅₃	—	4	2	no	—
150	D₄×C₅₃	—	4	2	no	—
151	D₄×C₅₃	—	4	1	no	—
152	D₄×C₅₃	—	4	1	no	—
153	D₄×C₅₃	—	4	1	no	—
154	C₂×C₄×C₅₃	—	2	2	no	—
155	C₂×C₄×C₅₃	—	2	2	no	—
156	C₂×C₄×C₅₃	—	2	4	no	—
157	C₂×C₄×C₅₃	—	2	2	no	—
158	C₂×C₄×C₅₃	—	4	1	no	—
159	C₂×C₄×C₅₃	—	4	2	no	—
160	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
161	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
162	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
163	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
164	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
165	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
166	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
167	C₂²⋊D₅₃	—	4	4	no	—
168	C₂²⋊D₅₃	—	4	4	no	—
169	C₂²⋊D₅₃	—	4	4	no	—
170	C₂²⋊D₅₃	—	4	4	no	—
171	C₂×Dic₅₃	—	4	2	no	—
172	C₂×Dic₅₃	C₂⁴	1	4	yes	—
173	C₂×Dic₅₃	C₂⁴	1	4	yes	—
174	C₂×Dic₅₃	C₂⁴	1	4	yes	—
175	D₂₁₂	—	2	4	no	—
176	D₂₁₂	—	4	2	no	—
177	C₄×D₅₃	—	4	4	no	—
178	C₄×D₅₃	—	4	4	no	—
179	Dic₁₀₆	—	2	4	no	—
180	Dic₁₀₆	—	4	2	no	—
181	Dic₁₀₆	—	4	4	no	—
182	C₂²×C₅₃	—	2	1	no	—
183	C₂²×C₅₃	—	2	2	no	—
184	C₂²×C₅₃	—	2	1	no	—
185	C₂²×C₅₃	—	2	1	no	—
186	C₂²×C₅₃	—	2	2	no	—
187	C₂²×C₅₃	—	2	2	no	—
188	C₂²×C₅₃	—	2	2	no	—
189	C₂²×C₅₃	—	2	2	no	—
190	C₂²×C₅₃	—	2	2	no	—
191	C₂²×C₅₃	—	4	4	no	—
192	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
193	C₂×D₅₃	—	2	4	no	—
194	C₂×D₅₃	—	2	4	no	—
195	C₂×D₅₃	—	2	4	no	—
196	C₂×D₅₃	—	8	4	no	—
197	C₄×C₅₃	—	2	1	no	—
198	C₄×C₅₃	—	2	2	no	—
199	C₄×C₅₃	—	2	1	no	—
200	C₄×C₅₃	—	2	1	no	—
201	C₄×C₅₃	—	2	2	no	—
202	C₄×C₅₃	—	2	2	no	—
203	C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
204	Dic₅₃	—	2	4	no	—
205	Dic₅₃	—	2	4	no	—
206	Dic₅₃	—	2	4	no	—
207	#3540	—	53	1	no	maximal, Sylow
208	C₂×C₅₃	—	4	1	no	—
209	C₂×C₅₃	—	4	1	no	—
210	C₂×C₅₃	—	4	2	no	—
211	C₂×C₅₃	—	4	1	no	—
212	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
213	C₂×C₅₃	#585	1	2	yes	—
214	D₅₃	—	4	4	no	—
215	H(3,𝔽₄)	—	53	2	no	—
216	#560	—	53	2	no	—
217	#559	—	53	2	no	—
218	#556	—	53	2	no	—
219	#555	—	53	2	no	—
220	#551	—	53	2	no	—
221	#548	—	53	2	no	—
222	#546	—	53	2	no	—
223	#542	—	53	4	no	—
224	#542	—	53	2	no	—
225	#538	—	53	4	no	—
226	#536	—	53	1	no	—
227	#535	—	53	1	no	—
228	#525	—	53	2	no	—
229	#525	D₅₃	1	1	yes	characteristic, complemented
230	C₅₃	#3540	1	1	yes	characteristic, complemented, Sylow
231	C₂×#41	—	53	2	no	—
232	C₂×#41	C₂×D₅₃	1	1	yes	characteristic
233	C₂²×Q₈	—	53	1	no	—
234	C₂²×D₄	—	53	1	no	—
235	C₂³×C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
236	C₄⋊Q₈	—	53	2	no	—
237	C₄⋊Q₈	—	53	2	no	—
238	#127	—	53	2	no	—
239	#126	—	53	4	no	—
240	#126	—	53	4	no	—
241	#126	—	53	4	no	—
242	#124	—	53	2	no	—
243	#124	—	53	2	no	—
244	#124	—	53	4	no	—
245	#124	—	53	4	no	—
246	#124	—	53	4	no	—
247	#124	—	53	4	no	—
248	#124	—	53	4	no	—
249	#124	—	53	2	no	—
250	#123	—	53	2	no	—
251	#123	—	53	2	no	—
252	#123	—	53	4	no	—
253	#123	—	53	4	no	—
254	#123	—	53	4	no	—
255	#123	C₂×D₅₃	1	1	yes	characteristic
256	#123	C₂×D₅₃	1	1	yes	characteristic, complemented
257	C₂²⋊Q₈	—	53	2	no	—
258	C₂²⋊Q₈	—	53	2	no	—
259	C₂²⋊Q₈	—	53	2	no	—
260	C₂²⋊Q₈	—	53	4	no	—
261	C₂²⋊Q₈	—	53	4	no	—
262	C₂²⋊Q₈	C₂×D₅₃	1	2	yes	complemented
263	#121	—	53	4	no	—
264	#121	—	53	4	no	—
265	#121	—	53	2	no	—
266	#121	—	53	2	no	—
267	#121	—	53	2	no	—
268	#121	—	53	4	no	—
269	#121	C₂×D₅₃	1	2	yes	—
270	#120	—	53	4	no	—
271	#120	—	53	2	no	—
272	#120	—	53	2	no	—
273	#120	—	53	4	no	—
274	#120	C₂×D₅₃	1	1	yes	characteristic
275	#120	C₂×D₅₃	1	1	yes	characteristic, complemented
276	C₄×Q₈	—	53	4	no	—
277	C₄×Q₈	—	53	2	no	—
278	C₄×D₄	—	53	4	no	—
279	C₄×D₄	—	53	4	no	—
280	C₄×D₄	—	53	4	no	—
281	C₄×D₄	—	53	2	no	—
282	C₄×D₄	C₂×D₅₃	1	2	yes	—
283	C₄×D₄	C₂×D₅₃	1	2	yes	complemented
284	#117	—	53	2	no	—
285	#117	—	53	1	no	—
286	#117	—	53	1	no	—
287	#117	—	53	4	no	—
288	#117	C₂×D₅₃	1	1	yes	characteristic, complemented
289	C₂×C₂²⋊C₄	—	53	4	no	—
290	C₂⁴	—	53	2	no	—
291	C₂⁴	C₂²×D₅₃	1	1	yes	characteristic
292	#41	—	4	2	no	—
293	#41	—	212	4	no	—
294	C₂×Q₈	—	53	2	no	—
295	C₂×Q₈	—	53	4	no	—
296	C₂×Q₈	—	53	2	no	—
297	C₂×Q₈	—	212	2	no	—
298	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
299	C₂×D₄	—	53	4	no	—
300	C₂×D₄	—	53	4	no	—
301	C₂×D₄	—	53	4	no	—
302	C₂×D₄	—	53	4	no	—
303	C₂×D₄	—	53	2	no	—
304	C₂×D₄	—	53	2	no	—
305	C₂×D₄	—	212	2	no	—
306	C₂×D₄	C₂²×D₅₃	1	2	yes	—
307	C₂×D₄	C₂²×D₅₃	1	2	yes	—
308	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
309	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
310	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
311	C₂²×C₄	—	4	2	no	—
312	C₂²×C₄	—	53	2	no	—
313	C₂²×C₄	—	53	4	no	—
314	C₂²×C₄	—	53	4	no	—
315	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
316	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
317	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
318	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
319	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
320	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
321	C₄⋊C₄	—	53	2	no	—
322	C₄⋊C₄	—	53	2	no	—
323	C₄⋊C₄	—	53	4	no	—
324	C₄⋊C₄	—	53	4	no	—
325	C₄⋊C₄	—	53	4	no	—
326	C₄⋊C₄	—	53	4	no	—
327	C₄⋊C₄	—	53	4	no	—
328	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
329	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
330	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
331	C₂²⋊C₄	—	53	4	no	—
332	C₂²⋊C₄	—	53	2	no	—
333	C₂²⋊C₄	—	53	4	no	—
334	C₂²⋊C₄	—	53	2	no	—
335	C₂²⋊C₄	—	53	4	no	—
336	C₂²⋊C₄	—	53	4	no	—
337	C₂²⋊C₄	—	53	4	no	—
338	C₂²⋊C₄	—	53	4	no	—
339	C₂²⋊C₄	—	53	4	no	—
340	C₂²⋊C₄	—	53	4	no	—
341	C₂²⋊C₄	—	53	4	no	—
342	C₂²⋊C₄	—	53	4	no	—
343	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
344	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
345	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
346	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
347	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
348	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
349	C₄²	—	53	2	no	—
350	C₄²	—	53	4	no	—
351	C₄²	—	53	2	no	—
352	C₄²	—	53	4	no	—
353	C₄²	C₂²×D₅₃	1	2	yes	—
354	C₂³	—	4	1	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	53	4	no	—
357	C₂³	—	212	2	no	—
358	C₂³	—	212	4	no	—
359	C₂³	C₂³×D₅₃	1	1	yes	characteristic
360	C₂³	C₂³×D₅₃	1	1	yes	characteristic
361	C₂³	C₂³×D₅₃	1	2	yes	—
362	C₂³	C₂³×D₅₃	1	1	yes	characteristic
363	Q₈	—	4	1	no	—
364	Q₈	—	106	4	no	—
365	Q₈	—	212	4	no	—
366	Q₈	—	212	2	no	—
367	D₄	—	4	2	no	—
368	D₄	—	4	2	no	—
369	D₄	—	4	1	no	—
370	D₄	—	4	1	no	—
371	D₄	—	4	1	no	—
372	D₄	—	106	4	no	—
373	D₄	—	212	2	no	—
374	D₄	—	212	4	no	—
375	D₄	—	212	4	no	—
376	D₄	—	212	4	no	—
377	D₄	—	212	4	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	53	4	no	—
385	C₂×C₄	—	53	4	no	—
386	C₂×C₄	—	53	4	no	—
387	C₂×C₄	—	212	4	no	—
388	C₂×C₄	—	212	4	no	—
389	C₂×C₄	—	212	2	no	—
390	C₂×C₄	C₂³×D₅₃	1	2	yes	—
391	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₅₃	1	2	yes	—
393	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
394	C₂×C₄	C₂³×D₅₃	1	2	yes	—
395	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
396	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
397	C₂²	—	2	1	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	4	4	no	—
407	C₂²	—	106	4	no	—
408	C₂²	—	106	4	no	—
409	C₂²	—	106	4	no	—
410	C₂²	—	424	4	no	—
411	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
412	C₄	—	2	2	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	2	no	—
417	C₄	—	2	2	no	—
418	C₄	—	106	4	no	—
419	C₄	—	106	4	no	—
420	C₄	—	106	4	no	—
421	C₄	#13133262	1	2	yes	—
422	C₂	—	4	1	no	—
423	C₂	—	4	2	no	—
424	C₂	—	4	1	no	—
425	C₂	—	4	1	no	—
426	C₂	—	212	4	no	—
427	C₂	C₂×#13133262	1	1	yes	characteristic
428	C₂	#16811459	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#525	C₂
hypercenter	#525	D₅₃
hypocenter	C₅₃	#3540
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #525

Complements

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

N	H ≅ G/N	type
1. #16811366	C₂	semidirect
2. #16811362	C₂	semidirect
3. #16811357	C₂	semidirect
4. #16811343	C₂	semidirect
5. #16811338	C₂	semidirect
6. #16811301	C₂	semidirect
7. #16811282	C₂	semidirect
8. #16811269	C₂	semidirect
9. #16811244	C₂	semidirect
10. #16811243	C₂	semidirect
11. #16811205	C₂	semidirect
12. #16811194	C₂	semidirect
13. #16811187	C₂	semidirect
14. #16811134	C₂	semidirect
15. C₅₃×#525	C₂	semidirect
17. C₂²×Dic₁₀₆	C₂²	semidirect
18. C₂²×D₂₁₂	C₂²	semidirect
19. #13133217	C₂²	semidirect
20. #13133215	C₂²	semidirect
22. #13133212	C₂²	semidirect
23. #13133210	C₂²	semidirect
24. #13133210	C₂²	semidirect
25. #13133206	C₂²	semidirect
26. #13133205	C₂²	semidirect
29. #13133203	C₂²	semidirect
30. #13133203	C₂²	semidirect
31. #13133203	C₂²	semidirect
32. #13133203	C₂²	semidirect
33. #13133202	C₂²	semidirect
34. #13133200	C₂²	semidirect
35. #13133199	C₂²	semidirect
36. #13133198	C₂²	semidirect
37. #13133198	C₂²	semidirect
38. #13133196	C₂²	semidirect
39. #13133196	C₂²	semidirect
40. #13133196	C₂²	semidirect
41. #13133195	C₂²	semidirect
42. #13133195	C₂²	semidirect
45. #13133191	C₂²	semidirect
47. #13133189	C₂²	semidirect
48. #13133188	C₂²	semidirect
49. #13133186	C₂²	semidirect
52. #13133185	C₂²	semidirect
53. C₄×Dic₁₀₆	C₂²	semidirect
54. #13133182	C₂²	semidirect
55. C₄×D₂₁₂	C₂²	semidirect
56. C₄×C₂²⋊D₅₃	C₂²	semidirect
57. C₄×C₂²⋊D₅₃	C₂²	semidirect
58. #13133177	C₂²	semidirect
59. #13133176	C₂²	semidirect
60. #13133176	C₂²	semidirect
61. #13133176	C₂²	semidirect
62. #13133175	C₂²	semidirect
63. C₂²⋊C₄×D₅₃	C₂²	semidirect
65. C₂³×C₄×C₅₃	C₂²	semidirect
67. #123×C₅₃	C₂²	semidirect
68. C₂²⋊Q₈×C₅₃	C₂²	semidirect
71. #120×C₅₃	C₂²	semidirect
73. C₄×D₄×C₅₃	C₂²	semidirect
74. #117×C₅₃	C₂²	semidirect
229. #525	D₅₃	semidirect
230. C₅₃	#3540	semidirect
235. C₂³×C₄	C₂×D₅₃	semidirect
256. #123	C₂×D₅₃	semidirect
262. C₂²⋊Q₈	C₂×D₅₃	semidirect
275. #120	C₂×D₅₃	semidirect
283. C₄×D₄	C₂×D₅₃	semidirect
288. #117	C₂×D₅₃	semidirect