Subgroups — #28292710

Order 13568.

9494 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288870	C₂	1	24	yes	maximal, complemented
2	#20288404	C₂	1	6	yes	maximal, complemented
3	#20288402	C₂	1	12	yes	maximal, complemented
4	#20288350	C₂	1	6	yes	maximal, complemented
5	#20288344	C₂	1	12	yes	maximal, complemented
6	C₂²×#13133186	C₂	1	2	yes	maximal, complemented
7	C₂²×#120×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#13133262	C₂²	1	6	yes	complemented
9	C₂³×C₂²⋊D₅₃	C₂²	1	6	yes	complemented
10	#16811366	C₂²	1	8	yes	complemented
11	#16811362	C₂²	1	24	yes	complemented
12	#16811304	C₂²	1	24	yes	complemented
13	#16811299	C₂²	1	48	yes	complemented
14	#16811267	C₂²	1	48	yes	complemented
15	#16811263	C₂²	1	48	yes	complemented
16	#16811260	C₂²	1	48	yes	complemented
17	D₄×C₂²⋊D₅₃	C₂²	1	48	yes	complemented
18	#16811255	C₂²	1	24	yes	complemented
19	#16811249	C₂²	1	6	yes	complemented
20	#16811211	C₂²	1	24	yes	complemented
21	#16811208	C₂²	1	48	yes	complemented
22	#16811190	C₂²	1	12	yes	complemented
23	#16811188	C₂²	1	24	yes	complemented
24	#16811185	C₂²	1	6	yes	complemented
25	#16811183	C₂²	1	24	yes	complemented
26	#16811182	C₂²	1	12	yes	complemented
27	#16811182	C₂²	1	12	yes	complemented
28	#16811134	C₂²	1	12	yes	complemented
29	#16811129	C₂²	1	24	yes	complemented
30	C₂×#13133186	C₂²	1	12	yes	complemented
31	C₂×#13133186	C₂²	1	12	yes	complemented
32	C₂×#13133186	C₂²	1	24	yes	complemented
33	C₂×#13133186	C₂²	1	4	yes	complemented
34	#120×D₅₃	C₂²	1	8	yes	complemented
35	#16811098	C₂²	1	6	yes	complemented
36	#16811096	C₂²	1	12	yes	complemented
37	C₂²×C₂²⋊Dic₅₃	C₂²	1	6	yes	complemented
38	C₂⁶×C₅₃	C₂²	1	1	yes	characteristic, complemented
39	C₂³×D₄×C₅₃	C₂²	1	3	yes	complemented
40	C₂×#120×C₅₃	C₂²	1	12	yes	complemented
41	C₂×#120×C₅₃	C₂²	1	12	yes	complemented
42	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	3	yes	complemented
43	C₂⁴×D₅₃	C₂³	1	2	yes	complemented
44	#13133262	—	4	24	no	—
45	C₂×#11719945	C₂³	1	12	yes	complemented
46	C₂×#11719947	C₂³	1	24	yes	complemented
47	C₂²×C₂²⋊D₅₃	—	4	24	no	—
48	C₂²×C₂²⋊D₅₃	C₂³	1	12	yes	—
49	C₂²×C₂²⋊D₅₃	C₂³	1	12	yes	complemented
50	C₂²×C₂²⋊D₅₃	C₂³	1	24	yes	complemented
51	C₂²×C₂²⋊D₅₃	C₂³	1	24	yes	complemented
52	C₂²×C₂²⋊D₅₃	C₂³	1	12	yes	complemented
53	C₂×D₄×D₅₃	C₂³	1	24	yes	complemented
54	C₂³×Dic₅₃	C₂³	1	6	yes	complemented
55	#13133213	C₂³	1	24	yes	complemented
56	#13133210	C₂³	1	48	yes	complemented
57	#13133204	C₂³	1	24	yes	complemented
58	#13133203	C₂³	1	48	yes	complemented
59	#13133201	C₂³	1	24	yes	complemented
60	#13133200	C₂³	1	24	yes	complemented
61	#13133199	C₂³	1	48	yes	complemented
62	#13133198	C₂³	1	24	yes	complemented
63	#13133198	C₂³	1	24	yes	complemented
64	#13133196	C₂³	1	24	yes	complemented
65	#13133194	C₂³	1	48	yes	complemented
66	#13133191	C₂³	1	24	yes	complemented
67	#13133190	C₂³	1	48	yes	complemented
68	#13133189	C₂³	1	48	yes	complemented
69	#13133189	C₂³	1	48	yes	complemented
70	#13133188	C₂³	1	48	yes	complemented
71	#13133187	C₂³	1	24	yes	complemented
72	#13133186	C₂³	1	48	yes	—
73	#13133186	C₂³	1	16	yes	complemented
74	#13133186	C₂³	1	8	yes	complemented
75	#13133186	C₂³	1	8	yes	complemented
76	#13133186	C₂³	1	24	yes	complemented
77	#13133186	C₂³	1	24	yes	complemented
78	#13133186	C₂³	1	24	yes	complemented
79	#13133185	C₂³	1	24	yes	complemented
80	#13133185	C₂³	1	24	yes	complemented
81	D₄×Dic₅₃	C₂³	1	48	yes	complemented
82	C₄×C₂²⋊D₅₃	C₂³	1	48	yes	complemented
83	#13133177	C₂³	1	48	yes	complemented
84	#13133176	C₂³	1	12	yes	complemented
85	#13133173	C₂³	1	24	yes	complemented
86	C₂×C₂²⋊Dic₅₃	C₂³	1	12	yes	—
87	C₂×C₂²⋊Dic₅₃	C₂³	1	24	yes	complemented
88	C₂×C₂²⋊Dic₅₃	C₂³	1	24	yes	complemented
89	C₂×C₂²⋊Dic₅₃	C₂³	1	12	yes	complemented
90	C₂×C₂²⋊Dic₅₃	C₂³	1	12	yes	complemented
91	C₂²⋊C₄×D₅₃	C₂³	1	24	yes	complemented
92	C₂⁵×C₅₃	—	4	12	no	—
93	C₂⁵×C₅₃	C₂³	1	3	yes	—
94	C₂⁵×C₅₃	C₂³	1	6	yes	—
95	C₂⁵×C₅₃	C₂³	1	6	yes	—
96	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic, complemented
97	C₂²×D₄×C₅₃	—	4	12	no	—
98	C₂²×D₄×C₅₃	C₂³	1	6	yes	—
99	C₂²×D₄×C₅₃	C₂³	1	24	yes	complemented
100	C₂²×D₄×C₅₃	C₂³	1	6	yes	complemented
101	C₂³×C₄×C₅₃	C₂³	1	3	yes	complemented
102	#120×C₅₃	C₂³	1	24	yes	—
103	#120×C₅₃	C₂³	1	8	yes	complemented
104	#120×C₅₃	C₂³	1	8	yes	complemented
105	#120×C₅₃	C₂³	1	24	yes	complemented
106	C₂×C₂²⋊C₄×C₅₃	C₂³	1	6	yes	—
107	C₂×C₂²⋊C₄×C₅₃	C₂³	1	24	yes	complemented
108	C₂×C₂²⋊C₄×C₅₃	C₂³	1	6	yes	complemented
109	C₂⁴×C₅₃	—	2	12	no	—
110	C₂⁴×C₅₃	—	2	24	no	—
111	C₂⁴×C₅₃	—	4	24	no	—
112	C₂⁴×C₅₃	—	4	12	no	—
113	C₂⁴×C₅₃	—	4	24	no	—
114	C₂⁴×C₅₃	—	4	12	no	—
115	C₂⁴×C₅₃	—	4	6	no	—
116	C₂⁴×C₅₃	—	4	64	no	—
117	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
118	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
119	C₂⁴×C₅₃	C₂⁴	1	12	yes	—
120	C₂⁴×C₅₃	C₂⁴	1	6	yes	—
121	C₂⁴×C₅₃	C₂⁴	1	3	yes	—
122	C₂⁴×C₅₃	C₂⁴	1	6	yes	—
123	C₂⁴×C₅₃	C₂⁴	1	6	yes	—
124	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
125	C₂⁴×C₅₃	C₂⁴	1	3	yes	—
126	C₂³×D₅₃	—	4	12	no	—
127	C₂³×D₅₃	C₂⁴	1	12	yes	—
128	C₂³×D₅₃	C₂⁴	1	4	yes	complemented
129	C₂×D₄×C₅₃	—	2	24	no	—
130	C₂×D₄×C₅₃	—	4	12	no	—
131	C₂×D₄×C₅₃	—	4	48	no	—
132	C₂×D₄×C₅₃	C₂⁴	1	24	yes	—
133	C₂×D₄×C₅₃	C₂⁴	1	24	yes	—
134	C₂²×C₄×C₅₃	—	4	6	no	—
135	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
136	C₂²×C₄×C₅₃	C₂⁴	1	12	yes	—
137	C₂×C₂²⋊D₅₃	—	2	48	no	—
138	C₂×C₂²⋊D₅₃	—	4	24	no	—
139	C₂×C₂²⋊D₅₃	—	4	48	no	—
140	C₂×C₂²⋊D₅₃	—	4	48	no	—
141	C₂×C₂²⋊D₅₃	—	4	24	no	—
142	C₂×C₂²⋊D₅₃	C₂⁴	1	24	yes	—
143	C₂×C₂²⋊D₅₃	C₂⁴	1	24	yes	—
144	C₂×C₂²⋊D₅₃	C₂⁴	1	48	yes	—
145	C₂×C₂²⋊D₅₃	C₂⁴	1	24	yes	complemented
146	C₂²×Dic₅₃	—	4	12	no	—
147	C₂²×Dic₅₃	C₂⁴	1	12	yes	—
148	C₂²×Dic₅₃	C₂⁴	1	24	yes	—
149	C₂²×Dic₅₃	C₂⁴	1	12	yes	complemented
150	#11719947	—	4	48	no	—
151	D₄×D₅₃	—	4	48	no	—
152	#11719945	—	4	24	no	—
153	C₂×D₂₁₂	C₂⁴	1	12	yes	complemented
154	C₂×C₄×D₅₃	C₂⁴	1	24	yes	complemented
155	C₂×Dic₁₀₆	C₂⁴	1	12	yes	complemented
156	C₂²⋊C₄×C₅₃	C₂⁴	1	24	yes	—
157	C₂²⋊C₄×C₅₃	C₂⁴	1	24	yes	—
158	C₂²⋊Dic₅₃	C₂⁴	1	24	yes	—
159	C₂²⋊Dic₅₃	C₂⁴	1	24	yes	—
160	C₂²⋊Dic₅₃	C₂⁴	1	48	yes	—
161	C₂²⋊Dic₅₃	C₂⁴	1	24	yes	complemented
162	#11719921	C₂⁴	1	48	yes	complemented
163	C₄⋊Dic₅₃	C₂⁴	1	24	yes	complemented
164	#11719919	C₂⁴	1	48	yes	complemented
165	C₄×Dic₅₃	C₂⁴	1	24	yes	complemented
166	C₂³×C₅₃	—	2	12	no	—
167	C₂³×C₅₃	—	2	6	no	—
168	C₂³×C₅₃	—	2	24	no	—
169	C₂³×C₅₃	—	2	24	no	—
170	C₂³×C₅₃	—	2	12	no	—
171	C₂³×C₅₃	—	2	24	no	—
172	C₂³×C₅₃	—	2	6	no	—
173	C₂³×C₅₃	—	2	12	no	—
174	C₂³×C₅₃	—	4	6	no	—
175	C₂³×C₅₃	—	4	6	no	—
176	C₂³×C₅₃	—	4	12	no	—
177	C₂³×C₅₃	—	4	12	no	—
178	C₂³×C₅₃	—	4	6	no	—
179	C₂³×C₅₃	—	4	6	no	—
180	C₂³×C₅₃	—	4	12	no	—
181	C₂³×C₅₃	—	4	96	no	—
182	C₂³×C₅₃	—	4	48	no	—
183	C₂³×C₅₃	—	4	96	no	—
184	C₂³×C₅₃	—	8	8	no	—
185	C₂³×C₅₃	H(5,𝔽₂)	1	12	yes	complemented
186	C₂³×C₅₃	C₂⁵	1	4	yes	—
187	C₂³×C₅₃	C₂⁵	1	6	yes	—
188	C₂³×C₅₃	C₂⁵	1	6	yes	—
189	C₂³×C₅₃	C₂⁵	1	3	yes	—
190	C₂²×D₅₃	—	2	24	no	—
191	C₂²×D₅₃	—	4	24	no	—
192	C₂²×D₅₃	—	4	12	no	—
193	C₂²×D₅₃	—	8	16	no	—
194	C₂²×D₅₃	C₂⁵	1	8	yes	—
195	D₄×C₅₃	—	2	48	no	—
196	D₄×C₅₃	—	4	24	no	—
197	C₂×C₄×C₅₃	—	2	12	no	—
198	C₂×C₄×C₅₃	—	4	12	no	—
199	C₂×C₄×C₅₃	C₂⁵	1	12	yes	—
200	C₂²⋊D₅₃	—	2	48	no	—
201	C₂²⋊D₅₃	—	2	48	no	—
202	C₂²⋊D₅₃	—	4	24	no	—
203	C₂²⋊D₅₃	—	4	48	no	—
204	C₂×Dic₅₃	—	2	24	no	—
205	C₂×Dic₅₃	—	4	12	no	—
206	C₂×Dic₅₃	—	4	24	no	—
207	C₂×Dic₅₃	C₂⁵	1	24	yes	—
208	D₂₁₂	—	4	12	no	—
209	C₄×D₅₃	—	4	24	no	—
210	Dic₁₀₆	—	4	12	no	—
211	#62817	—	53	1	no	maximal, Sylow
212	C₂²×C₅₃	—	2	16	no	—
213	C₂²×C₅₃	—	2	8	no	—
214	C₂²×C₅₃	—	2	12	no	—
215	C₂²×C₅₃	—	2	6	no	—
216	C₂²×C₅₃	—	2	12	no	—
217	C₂²×C₅₃	—	2	12	no	—
218	C₂²×C₅₃	—	2	6	no	—
219	C₂²×C₅₃	—	4	12	no	—
220	C₂²×C₅₃	—	4	24	no	—
221	C₂²×C₅₃	—	4	48	no	—
222	C₂²×C₅₃	—	4	24	no	—
223	C₂²×C₅₃	—	4	12	no	—
224	C₂²×C₅₃	—	4	8	no	—
225	C₂²×C₅₃	—	8	12	no	—
226	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	12	yes	—
227	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	6	yes	—
228	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
229	C₂×D₅₃	—	2	24	no	—
230	C₂×D₅₃	—	8	24	no	—
231	C₂×D₅₃	—	16	4	no	—
232	C₄×C₅₃	—	2	12	no	—
233	Dic₅₃	—	2	24	no	—
234	#3532	—	53	24	no	—
235	#3490	—	53	12	no	—
236	#3490	—	53	6	no	—
237	#3484	—	53	6	no	—
238	#3484	—	53	12	no	—
239	C₂²×#120	—	53	2	no	—
240	C₂²×#120	D₅₃	1	1	yes	characteristic, complemented
241	C₂×C₅₃	—	2	12	no	—
242	C₂×C₅₃	—	2	6	no	—
243	C₂×C₅₃	—	4	4	no	—
244	C₂×C₅₃	—	4	6	no	—
245	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	3	yes	—
246	D₅₃	—	4	8	no	—
247	C₂⁶	C₂×D₅₃	1	1	yes	characteristic, complemented
248	C₂×H(5,𝔽₂)	—	53	6	no	—
249	C₂³×D₄	—	53	6	no	—
250	C₂³×D₄	C₂×D₅₃	1	3	yes	complemented
251	H(3,𝔽₄)	—	53	8	no	—
252	#560	—	53	24	no	—
253	#551	—	53	24	no	—
254	#551	—	53	48	no	—
255	#546	—	53	48	no	—
256	#546	—	53	48	no	—
257	#546	—	53	48	no	—
258	D₄²	—	53	48	no	—
259	D₄²	—	53	24	no	—
260	#543	—	53	6	no	—
261	#538	—	53	48	no	—
262	#538	—	53	24	no	—
263	#535	—	53	12	no	—
264	#535	—	53	24	no	—
265	#534	—	53	12	no	—
266	#534	—	53	12	no	—
267	#534	—	53	24	no	—
268	#534	—	53	6	no	—
269	#525	—	53	12	no	—
270	#525	—	53	24	no	—
271	C₂×#120	—	53	12	no	—
272	C₂×#120	—	53	12	no	—
273	C₂×#120	—	53	24	no	—
274	C₂×#120	—	53	4	no	—
275	C₂×#120	—	53	8	no	—
276	C₂×#120	C₂×D₅₃	1	12	yes	complemented
277	C₂×#120	C₂×D₅₃	1	12	yes	complemented
278	#518	—	53	6	no	—
279	#518	—	53	12	no	—
280	C₂²×C₂²⋊C₄	—	53	6	no	—
281	C₂²×C₂²⋊C₄	C₂×D₅₃	1	3	yes	complemented
282	C₅₃	#62817	1	1	yes	characteristic, complemented, Sylow
283	C₂⁵	—	4	12	no	—
284	C₂⁵	—	53	2	no	—
285	C₂⁵	C₂²×D₅₃	1	6	yes	—
286	C₂⁵	C₂²×D₅₃	1	3	yes	—
287	C₂⁵	C₂²×D₅₃	1	6	yes	—
288	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic, complemented
289	H(5,𝔽₂)	—	212	24	no	—
290	C₂×#41	—	53	24	no	—
291	C₂×#41	—	53	12	no	—
292	C₂²×D₄	—	4	12	no	—
293	C₂²×D₄	—	53	12	no	—
294	C₂²×D₄	—	53	12	no	—
295	C₂²×D₄	—	53	24	no	—
296	C₂²×D₄	—	53	24	no	—
297	C₂²×D₄	—	53	12	no	—
298	C₂²×D₄	—	53	24	no	—
299	C₂²×D₄	—	212	24	no	—
300	C₂²×D₄	C₂²×D₅₃	1	6	yes	—
301	C₂²×D₄	C₂²×D₅₃	1	6	yes	complemented
302	C₂²×D₄	C₂²×D₅₃	1	24	yes	complemented
303	C₂³×C₄	—	53	6	no	—
304	C₂³×C₄	C₂²×D₅₃	1	3	yes	complemented
305	#127	—	53	24	no	—
306	#126	—	53	48	no	—
307	#124	—	53	24	no	—
308	#124	—	53	48	no	—
309	#123	—	53	24	no	—
310	#123	—	53	24	no	—
311	#123	—	53	24	no	—
312	#123	—	53	24	no	—
313	#123	—	53	48	no	—
314	C₂²⋊Q₈	—	53	24	no	—
315	C₂²⋊Q₈	—	53	48	no	—
316	#121	—	53	48	no	—
317	#121	—	53	48	no	—
318	#121	—	53	48	no	—
319	#121	—	53	24	no	—
320	#121	—	53	48	no	—
321	#120	—	53	8	no	—
322	#120	—	53	8	no	—
323	#120	—	53	24	no	—
324	#120	—	53	24	no	—
325	#120	—	53	48	no	—
326	#120	—	53	16	no	—
327	#120	—	53	24	no	—
328	#120	—	53	24	no	—
329	#120	—	53	24	no	—
330	#120	—	53	24	no	—
331	#120	C₂²×D₅₃	1	24	yes	—
332	#120	C₂²×D₅₃	1	8	yes	complemented
333	#120	C₂²×D₅₃	1	24	yes	complemented
334	#120	C₂²×D₅₃	1	8	yes	complemented
335	C₄×D₄	—	53	48	no	—
336	C₄×D₄	—	53	48	no	—
337	C₄×D₄	—	53	48	no	—
338	#117	—	53	12	no	—
339	#117	—	53	24	no	—
340	C₂×C₂²⋊C₄	—	53	12	no	—
341	C₂×C₂²⋊C₄	—	53	12	no	—
342	C₂×C₂²⋊C₄	—	53	24	no	—
343	C₂×C₂²⋊C₄	—	53	24	no	—
344	C₂×C₂²⋊C₄	—	53	12	no	—
345	C₂×C₂²⋊C₄	—	53	24	no	—
346	C₂×C₂²⋊C₄	C₂²×D₅₃	1	6	yes	—
347	C₂×C₂²⋊C₄	C₂²×D₅₃	1	6	yes	complemented
348	C₂×C₂²⋊C₄	C₂²×D₅₃	1	24	yes	complemented
349	C₂⁴	—	2	12	no	—
350	C₂⁴	—	2	24	no	—
351	C₂⁴	—	4	12	no	—
352	C₂⁴	—	4	24	no	—
353	C₂⁴	—	4	24	no	—
354	C₂⁴	—	4	12	no	—
355	C₂⁴	—	4	6	no	—
356	C₂⁴	—	4	64	no	—
357	C₂⁴	—	53	12	no	—
358	C₂⁴	—	53	4	no	—
359	C₂⁴	—	212	12	no	—
360	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
361	C₂⁴	C₂³×D₅₃	1	2	yes	—
362	C₂⁴	C₂³×D₅₃	1	6	yes	—
363	C₂⁴	C₂³×D₅₃	1	12	yes	—
364	C₂⁴	C₂³×D₅₃	1	6	yes	—
365	C₂⁴	C₂³×D₅₃	1	6	yes	—
366	C₂⁴	C₂³×D₅₃	1	3	yes	—
367	C₂⁴	C₂³×D₅₃	1	2	yes	—
368	C₂⁴	C₂³×D₅₃	1	3	yes	—
369	#41	—	212	24	no	—
370	#41	—	212	48	no	—
371	C₂×Q₈	—	53	12	no	—
372	C₂×D₄	—	2	24	no	—
373	C₂×D₄	—	4	12	no	—
374	C₂×D₄	—	4	48	no	—
375	C₂×D₄	—	53	24	no	—
376	C₂×D₄	—	53	24	no	—
377	C₂×D₄	—	53	48	no	—
378	C₂×D₄	—	53	24	no	—
379	C₂×D₄	—	53	12	no	—
380	C₂×D₄	—	106	48	no	—
381	C₂×D₄	—	212	24	no	—
382	C₂×D₄	—	212	48	no	—
383	C₂×D₄	—	212	48	no	—
384	C₂×D₄	—	212	48	no	—
385	C₂×D₄	—	212	24	no	—
386	C₂×D₄	C₂³×D₅₃	1	24	yes	—
387	C₂×D₄	C₂³×D₅₃	1	24	yes	—
388	C₂²×C₄	—	4	6	no	—
389	C₂²×C₄	—	53	12	no	—
390	C₂²×C₄	—	53	24	no	—
391	C₂²×C₄	—	53	12	no	—
392	C₂²×C₄	—	53	24	no	—
393	C₂²×C₄	—	212	12	no	—
394	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
395	C₂²×C₄	C₂³×D₅₃	1	12	yes	—
396	C₄⋊C₄	—	53	48	no	—
397	C₄⋊C₄	—	53	24	no	—
398	C₂²⋊C₄	—	53	24	no	—
399	C₂²⋊C₄	—	53	24	no	—
400	C₂²⋊C₄	—	53	48	no	—
401	C₂²⋊C₄	—	53	24	no	—
402	C₂²⋊C₄	—	53	48	no	—
403	C₂²⋊C₄	C₂³×D₅₃	1	24	yes	—
404	C₂²⋊C₄	C₂³×D₅₃	1	24	yes	—
405	C₄²	—	53	24	no	—
406	C₂³	—	2	6	no	—
407	C₂³	—	2	12	no	—
408	C₂³	—	2	24	no	—
409	C₂³	—	2	6	no	—
410	C₂³	—	2	24	no	—
411	C₂³	—	2	24	no	—
412	C₂³	—	2	12	no	—
413	C₂³	—	2	12	no	—
414	C₂³	—	4	6	no	—
415	C₂³	—	4	12	no	—
416	C₂³	—	4	6	no	—
417	C₂³	—	4	6	no	—
418	C₂³	—	4	12	no	—
419	C₂³	—	4	6	no	—
420	C₂³	—	4	12	no	—
421	C₂³	—	4	48	no	—
422	C₂³	—	4	96	no	—
423	C₂³	—	4	96	no	—
424	C₂³	—	8	8	no	—
425	C₂³	—	53	8	no	—
426	C₂³	—	106	24	no	—
427	C₂³	—	424	16	no	—
428	C₂³	—	212	12	no	—
429	C₂³	—	212	24	no	—
430	C₂³	#13133262	1	12	yes	complemented
431	C₂³	C₂⁴×D₅₃	1	6	yes	—
432	C₂³	C₂⁴×D₅₃	1	4	yes	—
433	C₂³	C₂⁴×D₅₃	1	3	yes	—
434	C₂³	C₂⁴×D₅₃	1	6	yes	—
435	Q₈	—	212	12	no	—
436	D₄	—	2	48	no	—
437	D₄	—	4	24	no	—
438	D₄	—	106	48	no	—
439	D₄	—	106	48	no	—
440	D₄	—	212	12	no	—
441	D₄	—	212	48	no	—
442	D₄	—	212	24	no	—
443	C₂×C₄	—	2	12	no	—
444	C₂×C₄	—	4	12	no	—
445	C₂×C₄	—	53	24	no	—
446	C₂×C₄	—	106	24	no	—
447	C₂×C₄	—	212	24	no	—
448	C₂×C₄	—	212	24	no	—
449	C₂×C₄	—	212	12	no	—
450	C₂×C₄	C₂⁴×D₅₃	1	12	yes	—
451	C₂²	—	2	8	no	—
452	C₂²	—	2	16	no	—
453	C₂²	—	2	6	no	—
454	C₂²	—	2	12	no	—
455	C₂²	—	2	12	no	—
456	C₂²	—	2	6	no	—
457	C₂²	—	2	12	no	—
458	C₂²	—	4	12	no	—
459	C₂²	—	4	48	no	—
460	C₂²	—	4	24	no	—
461	C₂²	—	4	12	no	—
462	C₂²	—	4	24	no	—
463	C₂²	—	4	8	no	—
464	C₂²	—	8	12	no	—
465	C₂²	—	848	4	no	—
466	C₂²	—	106	24	no	—
467	C₂²	—	424	24	no	—
468	C₂²	C₂×#13133262	1	6	yes	—
469	C₂²	C₂×#13133262	1	12	yes	—
470	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
471	C₄	—	2	12	no	—
472	C₄	—	106	24	no	—
473	C₂	—	2	6	no	—
474	C₂	—	2	12	no	—
475	C₂	—	4	6	no	—
476	C₂	—	4	4	no	—
477	C₂	—	212	8	no	—
478	C₂	C₂²×#13133262	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₂²×#120×C₅₃	C₂
hypercenter	C₂²×#120	D₅₃
hypocenter	C₅₃	#62817
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂²×#120

Complements

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

N	H ≅ G/N	type
1. #20288870	C₂	semidirect
2. #20288404	C₂	semidirect
3. #20288402	C₂	semidirect
4. #20288350	C₂	semidirect
5. #20288344	C₂	semidirect
6. C₂²×#13133186	C₂	semidirect
7. C₂²×#120×C₅₃	C₂	semidirect
8. C₂×#13133262	C₂²	semidirect
9. C₂³×C₂²⋊D₅₃	C₂²	semidirect
10. #16811366	C₂²	semidirect
11. #16811362	C₂²	semidirect
12. #16811304	C₂²	semidirect
13. #16811299	C₂²	semidirect
14. #16811267	C₂²	semidirect
15. #16811263	C₂²	semidirect
16. #16811260	C₂²	semidirect
17. D₄×C₂²⋊D₅₃	C₂²	semidirect
18. #16811255	C₂²	semidirect
19. #16811249	C₂²	semidirect
20. #16811211	C₂²	semidirect
21. #16811208	C₂²	semidirect
22. #16811190	C₂²	semidirect
23. #16811188	C₂²	semidirect
24. #16811185	C₂²	semidirect
25. #16811183	C₂²	semidirect
26. #16811182	C₂²	semidirect
27. #16811182	C₂²	semidirect
28. #16811134	C₂²	semidirect
29. #16811129	C₂²	semidirect
30. C₂×#13133186	C₂²	semidirect
31. C₂×#13133186	C₂²	semidirect
32. C₂×#13133186	C₂²	semidirect
33. C₂×#13133186	C₂²	semidirect
34. #120×D₅₃	C₂²	semidirect
35. #16811098	C₂²	semidirect
36. #16811096	C₂²	semidirect
37. C₂²×C₂²⋊Dic₅₃	C₂²	semidirect
38. C₂⁶×C₅₃	C₂²	semidirect
39. C₂³×D₄×C₅₃	C₂²	semidirect
40. C₂×#120×C₅₃	C₂²	semidirect
41. C₂×#120×C₅₃	C₂²	semidirect
42. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
43. C₂⁴×D₅₃	C₂³	semidirect
45. C₂×#11719945	C₂³	semidirect
46. C₂×#11719947	C₂³	semidirect
49. C₂²×C₂²⋊D₅₃	C₂³	semidirect
50. C₂²×C₂²⋊D₅₃	C₂³	semidirect
51. C₂²×C₂²⋊D₅₃	C₂³	semidirect
52. C₂²×C₂²⋊D₅₃	C₂³	semidirect
53. C₂×D₄×D₅₃	C₂³	semidirect
54. C₂³×Dic₅₃	C₂³	semidirect
55. #13133213	C₂³	semidirect
56. #13133210	C₂³	semidirect
57. #13133204	C₂³	semidirect
58. #13133203	C₂³	semidirect
59. #13133201	C₂³	semidirect
60. #13133200	C₂³	semidirect
61. #13133199	C₂³	semidirect
62. #13133198	C₂³	semidirect
63. #13133198	C₂³	semidirect
64. #13133196	C₂³	semidirect
65. #13133194	C₂³	semidirect
66. #13133191	C₂³	semidirect
67. #13133190	C₂³	semidirect
68. #13133189	C₂³	semidirect
69. #13133189	C₂³	semidirect
70. #13133188	C₂³	semidirect
71. #13133187	C₂³	semidirect
73. #13133186	C₂³	semidirect
74. #13133186	C₂³	semidirect
75. #13133186	C₂³	semidirect
76. #13133186	C₂³	semidirect
77. #13133186	C₂³	semidirect
78. #13133186	C₂³	semidirect
79. #13133185	C₂³	semidirect
80. #13133185	C₂³	semidirect
81. D₄×Dic₅₃	C₂³	semidirect
82. C₄×C₂²⋊D₅₃	C₂³	semidirect
83. #13133177	C₂³	semidirect
84. #13133176	C₂³	semidirect
85. #13133173	C₂³	semidirect
87. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
88. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
89. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
90. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
91. C₂²⋊C₄×D₅₃	C₂³	semidirect
96. C₂⁵×C₅₃	C₂³	semidirect
99. C₂²×D₄×C₅₃	C₂³	semidirect
100. C₂²×D₄×C₅₃	C₂³	semidirect
101. C₂³×C₄×C₅₃	C₂³	semidirect
103. #120×C₅₃	C₂³	semidirect
104. #120×C₅₃	C₂³	semidirect
105. #120×C₅₃	C₂³	semidirect
107. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
108. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
128. C₂³×D₅₃	C₂⁴	semidirect
145. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
149. C₂²×Dic₅₃	C₂⁴	semidirect
153. C₂×D₂₁₂	C₂⁴	semidirect
154. C₂×C₄×D₅₃	C₂⁴	semidirect
155. C₂×Dic₁₀₆	C₂⁴	semidirect
161. C₂²⋊Dic₅₃	C₂⁴	semidirect
162. #11719921	C₂⁴	semidirect
163. C₄⋊Dic₅₃	C₂⁴	semidirect
164. #11719919	C₂⁴	semidirect
165. C₄×Dic₅₃	C₂⁴	semidirect
185. C₂³×C₅₃	H(5,𝔽₂)	semidirect
240. C₂²×#120	D₅₃	semidirect
247. C₂⁶	C₂×D₅₃	semidirect
250. C₂³×D₄	C₂×D₅₃	semidirect
276. C₂×#120	C₂×D₅₃	semidirect
277. C₂×#120	C₂×D₅₃	semidirect
281. C₂²×C₂²⋊C₄	C₂×D₅₃	semidirect
282. C₅₃	#62817	semidirect
288. C₂⁵	C₂²×D₅₃	semidirect
301. C₂²×D₄	C₂²×D₅₃	semidirect
302. C₂²×D₄	C₂²×D₅₃	semidirect
304. C₂³×C₄	C₂²×D₅₃	semidirect
332. #120	C₂²×D₅₃	semidirect
333. #120	C₂²×D₅₃	semidirect
334. #120	C₂²×D₅₃	semidirect
347. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
348. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
430. C₂³	#13133262	semidirect

Maximal subgroups

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

subgroup	index
#20288870	2
#20288404	2
#20288402	2
#20288350	2
#20288344	2
C₂²×#13133186	2
C₂²×#120×C₅₃	2
#62817	53