Subgroups — #28292973

Order 13568.

8650 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20289045	C₂	1	24	yes	maximal, complemented
2	#20288592	C₂	1	6	yes	maximal, complemented
3	#20288591	C₂	1	6	yes	maximal, complemented
4	#20288493	C₂	1	6	yes	maximal, complemented
5	#20288488	C₂	1	6	yes	maximal, complemented
6	#20288348	C₂	1	12	yes	maximal, complemented
7	#20288011	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#13133214	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3444	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#13133263	C₂²	1	12	yes	complemented
11	C₂³×D₂₁₂	C₂²	1	6	yes	complemented
12	#16811364	C₂²	1	32	yes	complemented
13	#16811358	C₂²	1	24	yes	complemented
14	#16811295	C₂²	1	24	yes	complemented
15	#16811294	C₂²	1	24	yes	complemented
16	#16811269	C₂²	1	48	yes	complemented
17	#16811264	C₂²	1	48	yes	complemented
18	D₄×D₂₁₂	C₂²	1	48	yes	complemented
19	D₄×D₂₁₂	C₂²	1	24	yes	complemented
20	#16811257	C₂²	1	48	yes	complemented
21	#16811229	C₂²	1	24	yes	complemented
22	#16811228	C₂²	1	24	yes	complemented
23	#16811192	C₂²	1	12	yes	complemented
24	#16811192	C₂²	1	24	yes	complemented
25	#16811191	C₂²	1	24	yes	complemented
26	#16811187	C₂²	1	12	yes	complemented
27	#16811184	C₂²	1	48	yes	complemented
28	#16811180	C₂²	1	3	yes	complemented
29	#16811174	C₂²	1	12	yes	complemented
30	#16811173	C₂²	1	3	yes	complemented
31	#16811173	C₂²	1	12	yes	complemented
32	C₂×#13133214	C₂²	1	12	yes	complemented
33	C₂×#13133214	C₂²	1	6	yes	complemented
34	C₂×#13133214	C₂²	1	6	yes	complemented
35	C₂×#13133214	C₂²	1	4	yes	complemented
36	#127×D₅₃	C₂²	1	4	yes	complemented
37	#16811157	C₂²	1	12	yes	complemented
38	#16811134	C₂²	1	6	yes	complemented
39	#120×D₅₃	C₂²	1	16	yes	complemented
40	#16811097	C₂²	1	12	yes	complemented
41	C₄×#11719945	C₂²	1	6	yes	complemented
42	C₅₃×#533	C₂²	1	3	yes	complemented
43	C₅₃×#532	C₂²	1	3	yes	complemented
44	C₅₃×#529	C₂²	1	12	yes	complemented
45	C₅₃×#525	C₂²	1	6	yes	complemented
46	C₄×#41×C₅₃	C₂²	1	6	yes	complemented
47	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
48	C₂⁴×D₅₃	C₂³	1	4	yes	—
49	#13133263	—	4	48	no	—
50	C₂×#11719949	C₂³	1	24	yes	complemented
51	C₂×#11719945	C₂³	1	6	yes	—
52	C₂×#11719945	C₂³	1	24	yes	complemented
53	C₂²×D₂₁₂	—	4	24	no	—
54	C₂²×D₂₁₂	C₂³	1	12	yes	—
55	C₂²×D₂₁₂	C₂³	1	24	yes	—
56	C₂²×D₂₁₂	C₂³	1	24	yes	—
57	C₂²×D₂₁₂	C₂³	1	12	yes	—
58	C₂²×D₂₁₂	C₂³	1	24	yes	complemented
59	C₂×D₄×D₅₃	C₂³	1	48	yes	—
60	C₂×D₄×D₅₃	C₂³	1	24	yes	complemented
61	#13133217	C₂³	1	3	yes	complemented
62	#13133214	C₂³	1	24	yes	—
63	#13133214	C₂³	1	8	yes	—
64	#13133214	C₂³	1	4	yes	—
65	#13133214	C₂³	1	4	yes	—
66	#13133214	C₂³	1	12	yes	—
67	#13133214	C₂³	1	12	yes	—
68	#13133214	C₂³	1	24	yes	complemented
69	#13133214	C₂³	1	1	yes	characteristic, complemented
70	#13133213	C₂³	1	24	yes	complemented
71	#13133211	C₂³	1	8	yes	complemented
72	#13133209	C₂³	1	6	yes	complemented
73	#13133206	C₂³	1	24	yes	complemented
74	#13133205	C₂³	1	24	yes	complemented
75	#13133205	C₂³	1	6	yes	complemented
76	#13133202	C₂³	1	96	yes	complemented
77	#13133200	C₂³	1	12	yes	—
78	#13133196	C₂³	1	12	yes	—
79	#13133192	C₂³	1	96	yes	complemented
80	#13133192	C₂³	1	48	yes	complemented
81	#13133191	C₂³	1	12	yes	—
82	#13133191	C₂³	1	48	yes	complemented
83	#13133190	C₂³	1	96	yes	complemented
84	#13133187	C₂³	1	48	yes	—
85	#13133187	C₂³	1	96	yes	complemented
86	#13133186	C₂³	1	4	yes	—
87	#13133185	C₂³	1	48	yes	—
88	C₄×Dic₁₀₆	C₂³	1	12	yes	complemented
89	C₄×D₂₁₂	C₂³	1	48	yes	complemented
90	C₄×D₂₁₂	C₂³	1	12	yes	complemented
91	#13133179	C₂³	1	48	yes	complemented
92	C₄×C₂²⋊D₅₃	C₂³	1	24	yes	—
93	#13133176	C₂³	1	6	yes	—
94	#13133174	C₂³	1	12	yes	complemented
95	C₂²⋊C₄×D₅₃	C₂³	1	48	yes	—
96	C₄²×D₅₃	C₂³	1	4	yes	complemented
97	C₂×#41×C₅₃	C₂³	1	6	yes	—
98	C₂³×C₄×C₅₃	C₂³	1	3	yes	—
99	C₄⋊Q₈×C₅₃	C₂³	1	3	yes	complemented
100	#127×C₅₃	C₂³	1	1	yes	characteristic, complemented
101	#126×C₅₃	C₂³	1	8	yes	complemented
102	#125×C₅₃	C₂³	1	6	yes	complemented
103	#124×C₅₃	C₂³	1	6	yes	complemented
104	#123×C₅₃	C₂³	1	12	yes	—
105	C₂²⋊Q₈×C₅₃	C₂³	1	12	yes	—
106	#121×C₅₃	C₂³	1	12	yes	—
107	#120×C₅₃	C₂³	1	4	yes	—
108	C₄×Q₈×C₅₃	C₂³	1	12	yes	complemented
109	C₄×D₄×C₅₃	C₂³	1	24	yes	—
110	C₄×D₄×C₅₃	C₂³	1	12	yes	complemented
111	#117×C₅₃	C₂³	1	6	yes	—
112	#117×C₅₃	C₂³	1	12	yes	complemented
113	C₂×C₄²×C₅₃	C₂³	1	3	yes	—
114	C₂×C₄²×C₅₃	C₂³	1	6	yes	—
115	C₂×C₄²×C₅₃	C₂³	1	3	yes	—
116	C₂×C₄²×C₅₃	C₂³	1	4	yes	complemented
117	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
118	C₂³×D₅₃	—	4	24	no	—
119	C₂³×D₅₃	C₂⁴	1	24	yes	—
120	C₂³×D₅₃	C₂⁴	1	16	yes	—
121	#41×C₅₃	—	2	24	no	—
122	C₂×Q₈×C₅₃	C₂⁴	1	6	yes	—
123	C₂×D₄×C₅₃	C₂⁴	1	12	yes	—
124	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
125	C₂²×C₄×C₅₃	—	2	12	no	—
126	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
127	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
128	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
129	C₂²×C₄×C₅₃	C₂⁴	1	12	yes	—
130	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
131	C₂×C₂²⋊D₅₃	C₂⁴	1	12	yes	—
132	C₂×C₂²⋊D₅₃	C₂⁴	1	48	yes	—
133	#11719949	—	4	48	no	—
134	D₄×D₅₃	—	4	48	no	—
135	D₄×D₅₃	—	4	96	no	—
136	#11719945	—	2	24	no	—
137	#11719945	—	4	48	no	—
138	C₂×D₂₁₂	—	2	48	no	—
139	C₂×D₂₁₂	—	4	48	no	—
140	C₂×D₂₁₂	—	4	48	no	—
141	C₂×D₂₁₂	—	4	48	no	—
142	C₂×D₂₁₂	—	4	24	no	—
143	C₂×D₂₁₂	C₂⁴	1	24	yes	—
144	C₂×D₂₁₂	C₂⁴	1	6	yes	—
145	C₂×D₂₁₂	C₂⁴	1	24	yes	—
146	C₂×D₂₁₂	C₂⁴	1	48	yes	—
147	C₂×D₂₁₂	C₂⁴	1	48	yes	—
148	C₂×C₄×D₅₃	C₂⁴	1	12	yes	—
149	C₂×C₄×D₅₃	C₂⁴	1	48	yes	—
150	C₂×Dic₁₀₆	C₂⁴	1	6	yes	—
151	C₄⋊C₄×C₅₃	C₂⁴	1	12	yes	—
152	C₄⋊C₄×C₅₃	C₂⁴	1	24	yes	—
153	C₂²⋊C₄×C₅₃	C₂⁴	1	12	yes	—
154	C₂²⋊C₄×C₅₃	C₂⁴	1	24	yes	—
155	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
156	C₄²×C₅₃	C₂⁴	1	3	yes	—
157	C₄²×C₅₃	C₂⁴	1	6	yes	—
158	C₄²×C₅₃	C₂⁴	1	3	yes	—
159	C₄²×C₅₃	C₂⁴	1	2	yes	—
160	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
161	C₄²×C₅₃	C₂⁴	1	12	yes	—
162	C₂²⋊Dic₅₃	C₂⁴	1	12	yes	—
163	#11719921	C₂⁴	1	96	yes	—
164	#11719921	C₂⁴	1	24	yes	—
165	C₄⋊Dic₅₃	C₂⁴	1	12	yes	—
166	#11719919	C₂⁴	1	24	yes	—
167	C₄×Dic₅₃	C₂⁴	1	12	yes	—
168	C₂³×C₅₃	—	2	6	no	—
169	C₂³×C₅₃	C₂⁵	1	4	yes	—
170	C₂³×C₅₃	C₂⁵	1	3	yes	—
171	C₂²×D₅₃	—	2	48	no	—
172	C₂²×D₅₃	—	4	48	no	—
173	C₂²×D₅₃	—	4	48	no	—
174	C₂²×D₅₃	—	8	32	no	—
175	C₂²×D₅₃	C₂⁵	1	4	yes	—
176	C₂²×D₅₃	C₂⁵	1	16	yes	—
177	Q₈×C₅₃	—	2	12	no	—
178	D₄×C₅₃	—	2	24	no	—
179	D₄×C₅₃	—	2	12	no	—
180	C₂×C₄×C₅₃	—	2	6	no	—
181	C₂×C₄×C₅₃	—	2	12	no	—
182	C₂×C₄×C₅₃	—	2	12	no	—
183	C₂×C₄×C₅₃	—	2	24	no	—
184	C₂×C₄×C₅₃	H(5,𝔽₂)	1	12	yes	complemented
185	C₂×C₄×C₅₃	C₂⁵	1	12	yes	—
186	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
187	C₂×C₄×C₅₃	C₂⁵	1	3	yes	—
188	C₂×C₄×C₅₃	C₂⁵	1	3	yes	—
189	C₂²⋊D₅₃	—	2	24	no	—
190	C₂²⋊D₅₃	—	4	48	no	—
191	C₂×Dic₅₃	C₂⁵	1	12	yes	—
192	D₂₁₂	—	2	48	no	—
193	D₂₁₂	—	2	48	no	—
194	D₂₁₂	—	2	12	no	—
195	D₂₁₂	—	4	48	no	—
196	D₂₁₂	—	4	48	no	—
197	C₄×D₅₃	—	2	24	no	—
198	C₄×D₅₃	—	4	48	no	—
199	Dic₁₀₆	—	2	12	no	—
200	#62832	—	53	1	no	maximal, Sylow
201	C₂²×C₅₃	—	2	8	no	—
202	C₂²×C₅₃	—	2	6	no	—
203	C₂²×C₅₃	—	2	12	no	—
204	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	6	yes	—
205	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
206	C₂×D₅₃	—	2	12	no	—
207	C₂×D₅₃	—	2	48	no	—
208	C₂×D₅₃	—	8	48	no	—
209	C₂×D₅₃	—	16	16	no	—
210	C₄×C₅₃	—	2	12	no	—
211	C₄×C₅₃	—	2	6	no	—
212	C₄×C₅₃	C₂×H(5,𝔽₂)	1	6	yes	—
213	C₄×C₅₃	C₂×H(5,𝔽₂)	1	6	yes	—
214	Dic₅₃	—	2	12	no	—
215	#3543	—	53	24	no	—
216	#3508	—	53	6	no	—
217	#3508	—	53	6	no	—
218	#3498	—	53	6	no	—
219	#3498	—	53	6	no	—
220	#3484	—	53	12	no	—
221	#3444	—	53	1	no	—
222	#3444	D₅₃	1	1	yes	characteristic, complemented
223	C₂²×#127	—	53	1	no	—
224	C₂×C₅₃	—	2	6	no	—
225	C₂×C₅₃	—	4	4	no	—
226	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	3	yes	—
227	D₅₃	—	4	16	no	—
228	D₅₃	—	4	4	no	—
229	C₂×H(5,𝔽₂)	—	53	12	no	—
230	C₂³×D₄	—	53	6	no	—
231	#560	—	53	32	no	—
232	#559	—	53	24	no	—
233	#550	—	53	24	no	—
234	#550	—	53	24	no	—
235	#546	—	53	48	no	—
236	#546	—	53	48	no	—
237	D₄²	—	53	48	no	—
238	D₄²	—	53	48	no	—
239	D₄²	—	53	24	no	—
240	#540	—	53	24	no	—
241	#540	—	53	24	no	—
242	#535	—	53	12	no	—
243	#535	—	53	24	no	—
244	#535	—	53	12	no	—
245	#535	—	53	24	no	—
246	#534	—	53	48	no	—
247	#533	—	53	3	no	—
248	#533	C₂×D₅₃	1	3	yes	complemented
249	#532	—	53	12	no	—
250	#532	—	53	3	no	—
251	#532	—	53	12	no	—
252	#532	C₂×D₅₃	1	3	yes	complemented
253	C₂×#127	—	53	4	no	—
254	C₂×#127	—	53	6	no	—
255	C₂×#127	—	53	6	no	—
256	C₂×#127	—	53	12	no	—
257	C₂×#127	—	53	4	no	—
258	#529	—	53	12	no	—
259	#529	C₂×D₅₃	1	12	yes	complemented
260	#525	—	53	6	no	—
261	#525	C₂×D₅₃	1	6	yes	complemented
262	C₂×#120	—	53	16	no	—
263	#518	—	53	12	no	—
264	C₄×#41	—	53	6	no	—
265	C₄×#41	C₂×D₅₃	1	6	yes	complemented
266	C₂²×C₄²	C₂×D₅₃	1	1	yes	characteristic, complemented
267	C₅₃	#62832	1	1	yes	characteristic, complemented, Sylow
268	C₂⁵	—	53	4	no	—
269	H(5,𝔽₂)	—	212	48	no	—
270	C₂×#41	—	53	24	no	—
271	C₂×#41	—	53	6	no	—
272	C₂×#41	—	53	24	no	—
273	C₂×#41	C₂²×D₅₃	1	6	yes	—
274	C₂²×D₄	—	53	48	no	—
275	C₂²×D₄	—	53	24	no	—
276	C₂²×D₄	—	53	12	no	—
277	C₂²×D₄	—	53	12	no	—
278	C₂²×D₄	—	53	24	no	—
279	C₂²×D₄	—	53	24	no	—
280	C₂²×D₄	—	53	24	no	—
281	C₂²×D₄	—	212	24	no	—
282	C₂³×C₄	C₂²×D₅₃	1	3	yes	—
283	C₄⋊Q₈	—	53	3	no	—
284	C₄⋊Q₈	C₂²×D₅₃	1	3	yes	complemented
285	#127	—	53	24	no	—
286	#127	—	53	4	no	—
287	#127	—	53	4	no	—
288	#127	—	53	1	no	—
289	#127	—	53	12	no	—
290	#127	—	53	12	no	—
291	#127	—	53	24	no	—
292	#127	—	53	8	no	—
293	#127	—	53	24	no	—
294	#127	C₂²×D₅₃	1	1	yes	characteristic, complemented
295	#126	—	53	8	no	—
296	#126	C₂²×D₅₃	1	8	yes	complemented
297	#125	—	53	6	no	—
298	#125	C₂²×D₅₃	1	6	yes	complemented
299	#124	—	53	24	no	—
300	#124	—	53	6	no	—
301	#124	—	53	24	no	—
302	#124	C₂²×D₅₃	1	6	yes	complemented
303	#123	—	53	12	no	—
304	#123	—	53	96	no	—
305	#123	C₂²×D₅₃	1	12	yes	—
306	C₂²⋊Q₈	—	53	12	no	—
307	C₂²⋊Q₈	C₂²×D₅₃	1	12	yes	—
308	#121	—	53	12	no	—
309	#121	—	53	48	no	—
310	#121	—	53	48	no	—
311	#121	—	53	96	no	—
312	#121	—	53	96	no	—
313	#121	C₂²×D₅₃	1	12	yes	—
314	#120	—	53	4	no	—
315	#120	—	53	48	no	—
316	#120	—	53	48	no	—
317	#120	—	53	96	no	—
318	#120	C₂²×D₅₃	1	4	yes	—
319	C₄×Q₈	—	53	12	no	—
320	C₄×Q₈	C₂²×D₅₃	1	12	yes	complemented
321	C₄×D₄	—	53	24	no	—
322	C₄×D₄	—	53	48	no	—
323	C₄×D₄	—	53	12	no	—
324	C₄×D₄	—	53	48	no	—
325	C₄×D₄	C₂²×D₅₃	1	24	yes	—
326	C₄×D₄	C₂²×D₅₃	1	12	yes	complemented
327	#117	—	53	6	no	—
328	#117	—	53	12	no	—
329	#117	C₂²×D₅₃	1	6	yes	—
330	#117	C₂²×D₅₃	1	12	yes	complemented
331	C₂×C₂²⋊C₄	—	53	48	no	—
332	C₂×C₄²	—	53	4	no	—
333	C₂×C₄²	C₂²×D₅₃	1	3	yes	—
334	C₂×C₄²	C₂²×D₅₃	1	3	yes	—
335	C₂×C₄²	C₂²×D₅₃	1	6	yes	—
336	C₂×C₄²	C₂²×D₅₃	1	4	yes	complemented
337	C₂⁴	—	53	24	no	—
338	C₂⁴	—	53	16	no	—
339	C₂⁴	—	212	24	no	—
340	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
341	#41	—	2	24	no	—
342	#41	—	106	24	no	—
343	#41	—	212	48	no	—
344	#41	—	212	48	no	—
345	C₂×Q₈	—	53	6	no	—
346	C₂×Q₈	C₂³×D₅₃	1	6	yes	—
347	C₂×D₄	—	53	12	no	—
348	C₂×D₄	—	53	48	no	—
349	C₂×D₄	—	53	24	no	—
350	C₂×D₄	—	53	24	no	—
351	C₂×D₄	—	53	6	no	—
352	C₂×D₄	—	53	48	no	—
353	C₂×D₄	—	53	48	no	—
354	C₂×D₄	—	106	48	no	—
355	C₂×D₄	—	212	48	no	—
356	C₂×D₄	—	212	48	no	—
357	C₂×D₄	—	212	48	no	—
358	C₂×D₄	—	212	24	no	—
359	C₂×D₄	—	212	48	no	—
360	C₂×D₄	—	212	96	no	—
361	C₂×D₄	C₂³×D₅₃	1	12	yes	—
362	C₂×D₄	C₂³×D₅₃	1	6	yes	—
363	C₂²×C₄	—	2	12	no	—
364	C₂²×C₄	—	53	12	no	—
365	C₂²×C₄	—	53	48	no	—
366	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
367	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
368	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
369	C₂²×C₄	C₂³×D₅₃	1	12	yes	—
370	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
371	C₄⋊C₄	—	53	12	no	—
372	C₄⋊C₄	—	53	24	no	—
373	C₄⋊C₄	C₂³×D₅₃	1	12	yes	—
374	C₄⋊C₄	C₂³×D₅₃	1	24	yes	—
375	C₂²⋊C₄	—	53	12	no	—
376	C₂²⋊C₄	—	53	96	no	—
377	C₂²⋊C₄	—	53	24	no	—
378	C₂²⋊C₄	C₂³×D₅₃	1	12	yes	—
379	C₂²⋊C₄	C₂³×D₅₃	1	24	yes	—
380	C₄²	—	53	12	no	—
381	C₄²	C₂³×D₅₃	1	1	yes	characteristic
382	C₄²	C₂³×D₅₃	1	1	yes	characteristic
383	C₄²	C₂³×D₅₃	1	3	yes	—
384	C₄²	C₂³×D₅₃	1	3	yes	—
385	C₄²	C₂³×D₅₃	1	6	yes	—
386	C₄²	C₂³×D₅₃	1	2	yes	—
387	C₄²	C₂³×D₅₃	1	12	yes	—
388	C₂³	—	2	6	no	—
389	C₂³	—	53	4	no	—
390	C₂³	—	53	16	no	—
391	C₂³	—	106	48	no	—
392	C₂³	—	424	32	no	—
393	C₂³	—	212	48	no	—
394	C₂³	—	212	48	no	—
395	C₂³	C₂⁴×D₅₃	1	4	yes	—
396	C₂³	C₂⁴×D₅₃	1	3	yes	—
397	Q₈	—	2	12	no	—
398	Q₈	—	106	12	no	—
399	D₄	—	2	24	no	—
400	D₄	—	2	12	no	—
401	D₄	—	106	24	no	—
402	D₄	—	106	48	no	—
403	D₄	—	106	48	no	—
404	D₄	—	106	12	no	—
405	D₄	—	212	48	no	—
406	D₄	—	212	48	no	—
407	D₄	—	212	48	no	—
408	C₂×C₄	—	2	6	no	—
409	C₂×C₄	—	2	12	no	—
410	C₂×C₄	—	2	12	no	—
411	C₂×C₄	—	2	24	no	—
412	C₂×C₄	—	53	12	no	—
413	C₂×C₄	—	106	24	no	—
414	C₂×C₄	—	212	48	no	—
415	C₂×C₄	#13133263	1	12	yes	complemented
416	C₂×C₄	C₂⁴×D₅₃	1	6	yes	—
417	C₂×C₄	C₂⁴×D₅₃	1	12	yes	—
418	C₂×C₄	C₂⁴×D₅₃	1	3	yes	—
419	C₂×C₄	C₂⁴×D₅₃	1	3	yes	—
420	C₂²	—	2	8	no	—
421	C₂²	—	2	6	no	—
422	C₂²	—	2	12	no	—
423	C₂²	—	848	16	no	—
424	C₂²	—	106	12	no	—
425	C₂²	—	106	48	no	—
426	C₂²	—	424	48	no	—
427	C₂²	C₂×#13133263	1	6	yes	—
428	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
429	C₄	—	2	6	no	—
430	C₄	—	2	12	no	—
431	C₄	—	106	12	no	—
432	C₄	C₂×#13133263	1	6	yes	—
433	C₄	C₂×#13133263	1	6	yes	—
434	C₂	—	2	6	no	—
435	C₂	—	4	4	no	—
436	C₂	—	212	4	no	—
437	C₂	—	212	16	no	—
438	C₂	C₂²×#13133263	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₅₃×#3444	C₂
hypercenter	#3444	D₅₃
hypocenter	C₅₃	#62832
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #3444

Complements

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

N	H ≅ G/N	type
1. #20289045	C₂	semidirect
2. #20288592	C₂	semidirect
3. #20288591	C₂	semidirect
4. #20288493	C₂	semidirect
5. #20288488	C₂	semidirect
6. #20288348	C₂	semidirect
7. #20288011	C₂	semidirect
8. C₂²×#13133214	C₂	semidirect
9. C₅₃×#3444	C₂	semidirect
10. C₂×#13133263	C₂²	semidirect
11. C₂³×D₂₁₂	C₂²	semidirect
12. #16811364	C₂²	semidirect
13. #16811358	C₂²	semidirect
14. #16811295	C₂²	semidirect
15. #16811294	C₂²	semidirect
16. #16811269	C₂²	semidirect
17. #16811264	C₂²	semidirect
18. D₄×D₂₁₂	C₂²	semidirect
19. D₄×D₂₁₂	C₂²	semidirect
20. #16811257	C₂²	semidirect
21. #16811229	C₂²	semidirect
22. #16811228	C₂²	semidirect
23. #16811192	C₂²	semidirect
24. #16811192	C₂²	semidirect
25. #16811191	C₂²	semidirect
26. #16811187	C₂²	semidirect
27. #16811184	C₂²	semidirect
28. #16811180	C₂²	semidirect
29. #16811174	C₂²	semidirect
30. #16811173	C₂²	semidirect
31. #16811173	C₂²	semidirect
32. C₂×#13133214	C₂²	semidirect
33. C₂×#13133214	C₂²	semidirect
34. C₂×#13133214	C₂²	semidirect
35. C₂×#13133214	C₂²	semidirect
36. #127×D₅₃	C₂²	semidirect
37. #16811157	C₂²	semidirect
38. #16811134	C₂²	semidirect
39. #120×D₅₃	C₂²	semidirect
40. #16811097	C₂²	semidirect
41. C₄×#11719945	C₂²	semidirect
42. C₅₃×#533	C₂²	semidirect
43. C₅₃×#532	C₂²	semidirect
44. C₅₃×#529	C₂²	semidirect
45. C₅₃×#525	C₂²	semidirect
46. C₄×#41×C₅₃	C₂²	semidirect
47. C₂²×C₄²×C₅₃	C₂²	semidirect
50. C₂×#11719949	C₂³	semidirect
52. C₂×#11719945	C₂³	semidirect
58. C₂²×D₂₁₂	C₂³	semidirect
60. C₂×D₄×D₅₃	C₂³	semidirect
61. #13133217	C₂³	semidirect
68. #13133214	C₂³	semidirect
69. #13133214	C₂³	semidirect
70. #13133213	C₂³	semidirect
71. #13133211	C₂³	semidirect
72. #13133209	C₂³	semidirect
73. #13133206	C₂³	semidirect
74. #13133205	C₂³	semidirect
75. #13133205	C₂³	semidirect
76. #13133202	C₂³	semidirect
79. #13133192	C₂³	semidirect
80. #13133192	C₂³	semidirect
82. #13133191	C₂³	semidirect
83. #13133190	C₂³	semidirect
85. #13133187	C₂³	semidirect
88. C₄×Dic₁₀₆	C₂³	semidirect
89. C₄×D₂₁₂	C₂³	semidirect
90. C₄×D₂₁₂	C₂³	semidirect
91. #13133179	C₂³	semidirect
94. #13133174	C₂³	semidirect
96. C₄²×D₅₃	C₂³	semidirect
99. C₄⋊Q₈×C₅₃	C₂³	semidirect
100. #127×C₅₃	C₂³	semidirect
101. #126×C₅₃	C₂³	semidirect
102. #125×C₅₃	C₂³	semidirect
103. #124×C₅₃	C₂³	semidirect
108. C₄×Q₈×C₅₃	C₂³	semidirect
110. C₄×D₄×C₅₃	C₂³	semidirect
112. #117×C₅₃	C₂³	semidirect
116. C₂×C₄²×C₅₃	C₂³	semidirect
184. C₂×C₄×C₅₃	H(5,𝔽₂)	semidirect
222. #3444	D₅₃	semidirect
248. #533	C₂×D₅₃	semidirect
252. #532	C₂×D₅₃	semidirect
259. #529	C₂×D₅₃	semidirect
261. #525	C₂×D₅₃	semidirect
265. C₄×#41	C₂×D₅₃	semidirect
266. C₂²×C₄²	C₂×D₅₃	semidirect
267. C₅₃	#62832	semidirect
284. C₄⋊Q₈	C₂²×D₅₃	semidirect
294. #127	C₂²×D₅₃	semidirect
296. #126	C₂²×D₅₃	semidirect
298. #125	C₂²×D₅₃	semidirect
302. #124	C₂²×D₅₃	semidirect
320. C₄×Q₈	C₂²×D₅₃	semidirect
326. C₄×D₄	C₂²×D₅₃	semidirect
330. #117	C₂²×D₅₃	semidirect
336. C₂×C₄²	C₂²×D₅₃	semidirect
415. C₂×C₄	#13133263	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#20289045	2
#20288592	2
#20288591	2
#20288493	2
#20288488	2
#20288348	2
#20288011	2
C₂²×#13133214	2
C₅₃×#3444	2
#62832	53