Subgroups — #28293204

Order 13568.

11618 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811459	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#13133263	C₂	1	1	yes	maximal, characteristic, complemented
3	#20288508	C₂	1	8	yes	maximal, complemented
4	#20288493	C₂	1	8	yes	maximal, complemented
5	#20288385	C₂	1	16	yes	maximal, complemented
6	#20288374	C₂	1	4	yes	maximal, complemented
7	#20288351	C₂	1	12	yes	maximal, complemented
8	#20288048	C₂	1	6	yes	maximal, complemented
9	C₂×#16811192	C₂	1	6	yes	maximal, complemented
10	C₅₃×#3428	C₂	1	1	yes	maximal, characteristic, complemented
11	#16811459	—	2	16	no	—
12	C₂×#13133265	C₂²	1	2	yes	complemented
13	C₂×#13133264	C₂²	1	4	yes	complemented
14	C₂×#13133263	—	2	16	no	—
15	C₂×#13133263	C₂²	1	8	yes	complemented
16	C₂×#13133263	C₂²	1	8	yes	complemented
17	C₂×#13133263	C₂²	1	4	yes	complemented
18	C₂×#13133262	C₂²	1	6	yes	complemented
19	C₂²×#11719949	C₂²	1	2	yes	complemented
20	C₂²×#11719945	C₂²	1	3	yes	complemented
21	C₂²×#11719945	C₂²	1	6	yes	complemented
22	C₂×#41×D₅₃	C₂²	1	8	yes	complemented
23	C₂³×D₂₁₂	C₂²	1	3	yes	complemented
24	C₂²×D₄×D₅₃	C₂²	1	6	yes	complemented
25	#16811295	C₂²	1	32	yes	complemented
26	#16811285	C₂²	1	32	yes	complemented
27	#16811268	C₂²	1	96	yes	complemented
28	D₄×D₂₁₂	C₂²	1	96	yes	complemented
29	#16811204	C₂²	1	24	yes	complemented
30	#16811199	C₂²	1	4	yes	complemented
31	#16811199	C₂²	1	12	yes	complemented
32	#16811192	C₂²	1	12	yes	complemented
33	#16811192	C₂²	1	24	yes	complemented
34	#16811192	C₂²	1	24	yes	complemented
35	#16811192	C₂²	1	24	yes	complemented
36	#16811192	C₂²	1	12	yes	complemented
37	#16811185	C₂²	1	24	yes	complemented
38	#16811173	C₂²	1	24	yes	complemented
39	C₂×#13133214	C₂²	1	12	yes	complemented
40	C₂×#13133205	C₂²	1	12	yes	complemented
41	#16811135	C₂²	1	24	yes	complemented
42	#16811135	C₂²	1	24	yes	complemented
43	C₂×#13133192	C₂²	1	24	yes	complemented
44	C₂×#13133187	C₂²	1	24	yes	complemented
45	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
46	C₅₃×#520	C₂²	1	8	yes	complemented
47	C₅₃×#519	C₂²	1	2	yes	complemented
48	C₅₃×#518	C₂²	1	6	yes	complemented
49	C₄×#41×C₅₃	C₂²	1	8	yes	complemented
50	C₂×#117×C₅₃	C₂²	1	6	yes	complemented
51	C₂⁴×D₅₃	C₂³	1	6	yes	—
52	#13133265	—	2	16	no	—
53	#13133264	—	2	32	no	—
54	#13133263	—	2	64	no	—
55	#13133263	—	2	64	no	—
56	#13133263	—	2	32	no	—
57	#13133262	—	2	48	no	—
58	C₂×#11719949	—	2	16	no	—
59	C₂×#11719949	C₂³	1	16	yes	—
60	C₂×#11719949	C₂³	1	8	yes	complemented
61	C₂×#11719945	—	2	24	no	—
62	C₂×#11719945	—	2	48	no	—
63	C₂×#11719945	C₂³	1	12	yes	—
64	C₂×#11719945	C₂³	1	12	yes	—
65	C₂×#11719945	C₂³	1	12	yes	—
66	C₂×#11719945	C₂³	1	4	yes	—
67	C₂×#11719945	C₂³	1	12	yes	complemented
68	C₂×#11719945	C₂³	1	12	yes	complemented
69	C₂×#11719947	C₂³	1	24	yes	complemented
70	#41×D₅₃	—	2	64	no	—
71	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
72	C₂²×Dic₁₀₆	C₂³	1	6	yes	complemented
73	C₂×Q₈×D₅₃	C₂³	1	8	yes	complemented
74	C₂²×D₂₁₂	—	2	24	no	—
75	C₂²×D₂₁₂	C₂³	1	12	yes	—
76	C₂²×D₂₁₂	C₂³	1	12	yes	—
77	C₂²×D₂₁₂	C₂³	1	6	yes	—
78	C₂²×D₂₁₂	C₂³	1	3	yes	—
79	C₂²×D₂₁₂	C₂³	1	6	yes	complemented
80	C₂²×D₂₁₂	C₂³	1	48	yes	complemented
81	C₂²×C₂²⋊D₅₃	C₂³	1	12	yes	—
82	C₂²×C₂²⋊D₅₃	C₂³	1	6	yes	—
83	C₂×D₄×D₅₃	—	2	48	no	—
84	C₂×D₄×D₅₃	C₂³	1	48	yes	—
85	C₂×D₄×D₅₃	C₂³	1	24	yes	complemented
86	C₂²×C₄×D₅₃	C₂³	1	6	yes	—
87	C₂²×C₄×D₅₃	C₂³	1	12	yes	complemented
88	#13133217	C₂³	1	8	yes	complemented
89	#13133214	C₂³	1	48	yes	complemented
90	#13133214	C₂³	1	24	yes	complemented
91	#13133205	C₂³	1	48	yes	complemented
92	#13133205	C₂³	1	24	yes	complemented
93	#13133205	C₂³	1	8	yes	complemented
94	#13133201	C₂³	1	16	yes	—
95	#13133201	C₂³	1	48	yes	complemented
96	#13133197	C₂³	1	48	yes	complemented
97	#13133197	C₂³	1	16	yes	complemented
98	#13133192	C₂³	1	96	yes	complemented
99	#13133192	C₂³	1	48	yes	complemented
100	#13133192	C₂³	1	48	yes	complemented
101	#13133191	C₂³	1	96	yes	complemented
102	#13133187	C₂³	1	48	yes	—
103	#13133187	C₂³	1	96	yes	complemented
104	#13133187	C₂³	1	48	yes	complemented
105	C₄×D₂₁₂	C₂³	1	96	yes	complemented
106	C₂×#11719921	C₂³	1	48	yes	complemented
107	C₂×#41×C₅₃	D₄	1	16	yes	complemented
108	C₂×#41×C₅₃	C₂³	1	4	yes	—
109	C₂×#41×C₅₃	C₂³	1	4	yes	—
110	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
111	C₂²×D₄×C₅₃	C₂³	1	3	yes	—
112	C₂³×C₄×C₅₃	C₂³	1	3	yes	—
113	C₄×Q₈×C₅₃	C₂³	1	16	yes	complemented
114	C₄×D₄×C₅₃	C₂³	1	48	yes	complemented
115	#117×C₅₃	C₂³	1	4	yes	—
116	#117×C₅₃	C₂³	1	12	yes	—
117	#117×C₅₃	C₂³	1	12	yes	complemented
118	#117×C₅₃	C₂³	1	12	yes	complemented
119	C₂×C₄⋊C₄×C₅₃	C₂³	1	12	yes	complemented
120	C₂×C₂²⋊C₄×C₅₃	C₂³	1	12	yes	—
121	C₂×C₄²×C₅₃	C₂³	1	12	yes	complemented
122	C₂⁴×C₅₃	C₂⁴	1	3	yes	—
123	C₂³×D₅₃	—	2	24	no	—
124	C₂³×D₅₃	—	8	12	no	—
125	C₂³×D₅₃	C₂⁴	1	24	yes	—
126	C₂³×D₅₃	C₂⁴	1	6	yes	—
127	C₂³×D₅₃	C₂⁴	1	12	yes	—
128	#41×C₅₃	C₂×D₄	1	32	yes	complemented
129	#41×C₅₃	C₂×D₄	1	32	yes	complemented
130	C₂×Q₈×C₅₃	C₂×D₄	1	8	yes	complemented
131	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
132	C₂×D₄×C₅₃	C₂×D₄	1	24	yes	complemented
133	C₂×D₄×C₅₃	C₂⁴	1	12	yes	—
134	C₂²×C₄×C₅₃	C₂×D₄	1	24	yes	complemented
135	C₂²×C₄×C₅₃	C₂⁴	1	24	yes	—
136	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
137	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
138	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
139	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
140	C₂×C₂²⋊D₅₃	—	2	24	no	—
141	C₂×C₂²⋊D₅₃	—	2	48	no	—
142	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
143	C₂×C₂²⋊D₅₃	C₂⁴	1	24	yes	—
144	C₂×C₂²⋊D₅₃	C₂⁴	1	24	yes	—
145	C₂²×Dic₅₃	C₂⁴	1	12	yes	—
146	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
147	#11719949	—	2	32	no	—
148	#11719949	—	2	64	no	—
149	Q₈×D₅₃	—	2	32	no	—
150	#11719947	—	2	96	no	—
151	D₄×D₅₃	—	2	192	no	—
152	D₄×D₅₃	—	2	96	no	—
153	#11719945	—	2	48	no	—
154	#11719945	—	2	16	no	—
155	#11719945	—	2	48	no	—
156	#11719945	—	2	48	no	—
157	#11719945	—	2	48	no	—
158	#11719945	—	2	48	no	—
159	C₂×D₂₁₂	—	2	24	no	—
160	C₂×D₂₁₂	—	2	12	no	—
161	C₂×D₂₁₂	—	2	48	no	—
162	C₂×D₂₁₂	—	2	48	no	—
163	C₂×D₂₁₂	—	2	24	no	—
164	C₂×D₂₁₂	—	8	48	no	—
165	C₂×D₂₁₂	C₂⁴	1	6	yes	—
166	C₂×D₂₁₂	C₂⁴	1	24	yes	—
167	C₂×D₂₁₂	C₂⁴	1	12	yes	—
168	C₂×D₂₁₂	C₂⁴	1	6	yes	—
169	C₂×D₂₁₂	C₂⁴	1	4	yes	—
170	C₂×D₂₁₂	C₂⁴	1	96	yes	—
171	C₂×C₄×D₅₃	—	2	24	no	—
172	C₂×C₄×D₅₃	—	2	48	no	—
173	C₂×C₄×D₅₃	C₂⁴	1	24	yes	—
174	C₂×C₄×D₅₃	C₂⁴	1	24	yes	—
175	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
176	C₂×Dic₁₀₆	—	2	4	no	—
177	C₂×Dic₁₀₆	—	2	24	no	—
178	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
179	C₂×Dic₁₀₆	C₂⁴	1	12	yes	—
180	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
181	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
182	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
183	C₄⋊C₄×C₅₃	C₂⁴	1	24	yes	—
184	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
185	C₂²⋊C₄×C₅₃	C₂⁴	1	24	yes	—
186	C₄²×C₅₃	C₂⁴	1	8	yes	—
187	C₄²×C₅₃	C₂⁴	1	24	yes	—
188	#11719921	C₂⁴	1	96	yes	—
189	#11719921	C₂⁴	1	32	yes	—
190	C₄⋊Dic₅₃	C₂⁴	1	32	yes	—
191	C₂³×C₅₃	—	4	6	no	—
192	C₂³×C₅₃	C₂²×D₄	1	12	yes	—
193	C₂³×C₅₃	C₂⁵	1	6	yes	—
194	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
195	C₂²×D₅₃	—	2	12	no	—
196	C₂²×D₅₃	—	2	24	no	—
197	C₂²×D₅₃	—	2	48	no	—
198	C₂²×D₅₃	—	4	12	no	—
199	C₂²×D₅₃	—	4	24	no	—
200	C₂²×D₅₃	—	4	48	no	—
201	C₂²×D₅₃	—	8	48	no	—
202	C₂²×D₅₃	C₂⁵	1	8	yes	—
203	C₂²×D₅₃	C₂⁵	1	12	yes	—
204	Q₈×C₅₃	C₂²×D₄	1	16	yes	—
205	D₄×C₅₃	C₂²×D₄	1	48	yes	—
206	C₂×C₄×C₅₃	—	4	24	no	—
207	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
208	C₂×C₄×C₅₃	C₂²×D₄	1	24	yes	—
209	C₂×C₄×C₅₃	C₂²×D₄	1	12	yes	—
210	C₂×C₄×C₅₃	C₂²×D₄	1	24	yes	—
211	C₂×C₄×C₅₃	C₂⁵	1	16	yes	—
212	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
213	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
214	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
215	C₂²⋊D₅₃	—	2	16	no	—
216	C₂²⋊D₅₃	—	2	48	no	—
217	C₂²⋊D₅₃	—	2	48	no	—
218	C₂×Dic₅₃	—	2	4	no	—
219	C₂×Dic₅₃	—	2	24	no	—
220	C₂×Dic₅₃	C₂⁵	1	8	yes	—
221	C₂×Dic₅₃	C₂⁵	1	4	yes	—
222	D₂₁₂	—	2	12	no	—
223	D₂₁₂	—	2	12	no	—
224	D₂₁₂	—	2	8	no	—
225	D₂₁₂	—	2	48	no	—
226	D₂₁₂	—	2	24	no	—
227	D₂₁₂	—	4	96	no	—
228	C₄×D₅₃	—	2	16	no	—
229	C₄×D₅₃	—	2	48	no	—
230	C₄×D₅₃	—	2	48	no	—
231	Dic₁₀₆	—	2	8	no	—
232	Dic₁₀₆	—	2	4	no	—
233	Dic₁₀₆	—	2	4	no	—
234	Dic₁₀₆	—	2	24	no	—
235	#62852	—	53	1	no	maximal, Sylow
236	C₂²×C₅₃	—	2	12	no	—
237	C₂²×C₅₃	—	2	2	no	—
238	C₂²×C₅₃	—	4	12	no	—
239	C₂²×C₅₃	C₂³×D₄	1	2	yes	—
240	C₂²×C₅₃	C₂³×D₄	1	12	yes	—
241	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
242	C₂×D₅₃	—	2	8	no	—
243	C₂×D₅₃	—	2	12	no	—
244	C₂×D₅₃	—	2	16	no	—
245	C₂×D₅₃	—	2	24	no	—
246	C₂×D₅₃	—	4	24	no	—
247	C₂×D₅₃	—	8	24	no	—
248	C₂×D₅₃	—	8	48	no	—
249	C₄×C₅₃	—	2	16	no	—
250	C₄×C₅₃	C₂³×D₄	1	2	yes	—
251	C₄×C₅₃	C₂³×D₄	1	2	yes	—
252	C₄×C₅₃	C₂³×D₄	1	12	yes	—
253	Dic₅₃	—	2	8	no	—
254	Dic₅₃	—	2	4	no	—
255	C₂×#585	—	53	1	no	—
256	C₂²×H(5,𝔽₂)	—	53	1	no	—
257	#3500	—	53	8	no	—
258	#3498	—	53	8	no	—
259	#3488	—	53	16	no	—
260	#3487	—	53	4	no	—
261	#3484	—	53	12	no	—
262	#3449	—	53	6	no	—
263	C₂×#535	—	53	6	no	—
264	#3428	D₅₃	1	1	yes	characteristic, complemented
265	C₂×C₅₃	—	2	2	no	—
266	C₂×C₅₃	—	2	12	no	—
267	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
268	C₂×C₅₃	H(7,𝔽₂)	1	2	yes	—
269	D₅₃	—	4	12	no	—
270	D₅₃	—	4	8	no	—
271	#585	—	106	16	no	—
272	C₂×2₋¹⁺⁴	—	53	4	no	—
273	C₂×2₋¹⁺⁴	—	53	2	no	—
274	C₂×H(5,𝔽₂)	—	53	8	no	—
275	C₂×H(5,𝔽₂)	—	53	8	no	—
276	C₂×H(5,𝔽₂)	—	53	4	no	—
277	C₂×H(5,𝔽₂)	—	53	6	no	—
278	C₂×H(5,𝔽₂)	—	106	16	no	—
279	C₂²×#41	—	53	8	no	—
280	C₂²×#41	—	53	2	no	—
281	C₂²×#41	—	53	3	no	—
282	C₂²×#41	—	53	6	no	—
283	C₂²×#41	C₂×D₅₃	1	1	yes	characteristic
284	C₂³×D₄	—	53	6	no	—
285	C₂³×D₄	—	53	3	no	—
286	#550	—	53	32	no	—
287	#548	—	53	32	no	—
288	#546	—	53	96	no	—
289	D₄²	—	53	96	no	—
290	#537	—	53	24	no	—
291	#536	—	53	4	no	—
292	#536	—	53	12	no	—
293	#535	—	53	12	no	—
294	#535	—	53	24	no	—
295	#535	—	53	24	no	—
296	#535	—	53	24	no	—
297	#535	—	53	12	no	—
298	#534	—	53	24	no	—
299	#532	—	53	24	no	—
300	C₂×#127	—	53	12	no	—
301	C₂×#124	—	53	12	no	—
302	#525	—	53	24	no	—
303	#525	—	53	24	no	—
304	C₂×#121	—	53	24	no	—
305	C₂×#120	—	53	24	no	—
306	#520	C₂×D₅₃	1	8	yes	complemented
307	#519	C₂×D₅₃	1	2	yes	complemented
308	#518	C₂×D₅₃	1	6	yes	complemented
309	C₄×#41	C₂×D₅₃	1	8	yes	complemented
310	C₂×#117	C₂×D₅₃	1	6	yes	complemented
311	C₅₃	#62852	1	1	yes	characteristic, complemented, Sylow
312	C₂⁵	—	53	6	no	—
313	2₋¹⁺⁴	—	106	32	no	—
314	2₋¹⁺⁴	—	106	16	no	—
315	H(5,𝔽₂)	—	106	64	no	—
316	H(5,𝔽₂)	—	106	64	no	—
317	H(5,𝔽₂)	—	106	32	no	—
318	H(5,𝔽₂)	—	106	48	no	—
319	C₂×#41	—	53	16	no	—
320	C₂×#41	—	53	8	no	—
321	C₂×#41	—	53	24	no	—
322	C₂×#41	—	53	12	no	—
323	C₂×#41	—	53	12	no	—
324	C₂×#41	—	53	12	no	—
325	C₂×#41	—	53	12	no	—
326	C₂×#41	—	53	4	no	—
327	C₂×#41	—	53	12	no	—
328	C₂×#41	—	106	64	no	—
329	C₂×#41	—	106	16	no	—
330	C₂×#41	—	106	24	no	—
331	C₂×#41	—	106	48	no	—
332	C₂×#41	D₂₁₂	1	16	yes	complemented
333	C₂×#41	C₂²×D₅₃	1	4	yes	—
334	C₂×#41	C₂²×D₅₃	1	4	yes	—
335	C₂²×Q₈	—	53	8	no	—
336	C₂²×Q₈	—	53	6	no	—
337	C₂²×Q₈	—	53	1	no	—
338	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
339	C₂²×D₄	—	53	12	no	—
340	C₂²×D₄	—	53	6	no	—
341	C₂²×D₄	—	53	24	no	—
342	C₂²×D₄	—	53	48	no	—
343	C₂²×D₄	—	53	12	no	—
344	C₂²×D₄	—	53	12	no	—
345	C₂²×D₄	—	53	6	no	—
346	C₂²×D₄	—	53	6	no	—
347	C₂²×D₄	—	53	3	no	—
348	C₂²×D₄	—	53	48	no	—
349	C₂²×D₄	—	106	48	no	—
350	C₂²×D₄	—	106	24	no	—
351	C₂²×D₄	C₂²×D₅₃	1	3	yes	—
352	C₂³×C₄	—	53	12	no	—
353	C₂³×C₄	—	53	6	no	—
354	C₂³×C₄	C₂²×D₅₃	1	3	yes	—
355	C₄⋊Q₈	—	53	8	no	—
356	#127	—	53	24	no	—
357	#127	—	53	48	no	—
358	#124	—	53	24	no	—
359	#124	—	53	48	no	—
360	#124	—	53	8	no	—
361	#123	—	53	16	no	—
362	#123	—	53	48	no	—
363	C₂²⋊Q₈	—	53	16	no	—
364	C₂²⋊Q₈	—	53	48	no	—
365	#121	—	53	96	no	—
366	#121	—	53	48	no	—
367	#121	—	53	96	no	—
368	#121	—	53	48	no	—
369	#120	—	53	48	no	—
370	#120	—	53	96	no	—
371	#120	—	53	48	no	—
372	C₄×Q₈	C₂²×D₅₃	1	16	yes	complemented
373	C₄×D₄	—	53	96	no	—
374	C₄×D₄	C₂²×D₅₃	1	48	yes	complemented
375	#117	C₂²×D₅₃	1	4	yes	—
376	#117	C₂²×D₅₃	1	12	yes	—
377	#117	C₂²×D₅₃	1	12	yes	complemented
378	#117	C₂²×D₅₃	1	12	yes	complemented
379	C₂×C₄⋊C₄	C₂²×D₅₃	1	12	yes	complemented
380	C₂×C₂²⋊C₄	—	53	48	no	—
381	C₂×C₂²⋊C₄	C₂²×D₅₃	1	12	yes	—
382	C₂×C₄²	C₂²×D₅₃	1	12	yes	complemented
383	C₂⁴	—	53	24	no	—
384	C₂⁴	—	53	6	no	—
385	C₂⁴	—	53	12	no	—
386	C₂⁴	—	106	24	no	—
387	C₂⁴	—	424	12	no	—
388	C₂⁴	C₂³×D₅₃	1	3	yes	—
389	#41	—	106	64	no	—
390	#41	—	106	32	no	—
391	#41	—	106	96	no	—
392	#41	—	106	48	no	—
393	#41	—	106	16	no	—
394	#41	—	106	48	no	—
395	#41	—	106	48	no	—
396	#41	—	106	48	no	—
397	#41	—	106	48	no	—
398	#41	C₂×D₂₁₂	1	32	yes	complemented
399	#41	C₂×D₂₁₂	1	32	yes	complemented
400	C₂×Q₈	—	53	2	no	—
401	C₂×Q₈	—	53	12	no	—
402	C₂×Q₈	—	53	4	no	—
403	C₂×Q₈	—	53	2	no	—
404	C₂×Q₈	—	106	32	no	—
405	C₂×Q₈	—	106	4	no	—
406	C₂×Q₈	—	106	24	no	—
407	C₂×Q₈	C₂×D₂₁₂	1	8	yes	complemented
408	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
409	C₂×D₄	—	53	8	no	—
410	C₂×D₄	—	53	24	no	—
411	C₂×D₄	—	53	24	no	—
412	C₂×D₄	—	53	6	no	—
413	C₂×D₄	—	53	24	no	—
414	C₂×D₄	—	53	12	no	—
415	C₂×D₄	—	53	6	no	—
416	C₂×D₄	—	53	4	no	—
417	C₂×D₄	—	53	96	no	—
418	C₂×D₄	—	106	24	no	—
419	C₂×D₄	—	106	48	no	—
420	C₂×D₄	—	106	192	no	—
421	C₂×D₄	—	106	96	no	—
422	C₂×D₄	—	106	24	no	—
423	C₂×D₄	—	106	12	no	—
424	C₂×D₄	—	106	48	no	—
425	C₂×D₄	—	106	48	no	—
426	C₂×D₄	—	106	24	no	—
427	C₂×D₄	—	424	48	no	—
428	C₂×D₄	C₂×D₂₁₂	1	24	yes	complemented
429	C₂×D₄	C₂³×D₅₃	1	12	yes	—
430	C₂²×C₄	—	53	12	no	—
431	C₂²×C₄	—	53	2	no	—
432	C₂²×C₄	—	53	24	no	—
433	C₂²×C₄	—	53	24	no	—
434	C₂²×C₄	—	53	8	no	—
435	C₂²×C₄	—	106	24	no	—
436	C₂²×C₄	—	106	48	no	—
437	C₂²×C₄	C₂×D₂₁₂	1	24	yes	complemented
438	C₂²×C₄	C₂³×D₅₃	1	24	yes	—
439	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
440	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
441	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
442	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
443	C₄⋊C₄	—	53	32	no	—
444	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
445	C₄⋊C₄	C₂³×D₅₃	1	24	yes	—
446	C₂²⋊C₄	—	53	96	no	—
447	C₂²⋊C₄	—	53	32	no	—
448	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
449	C₂²⋊C₄	C₂³×D₅₃	1	24	yes	—
450	C₄²	C₂³×D₅₃	1	8	yes	—
451	C₄²	C₂³×D₅₃	1	24	yes	—
452	C₂³	—	4	6	no	—
453	C₂³	—	53	12	no	—
454	C₂³	—	53	8	no	—
455	C₂³	—	106	24	no	—
456	C₂³	—	106	48	no	—
457	C₂³	—	106	12	no	—
458	C₂³	—	424	48	no	—
459	C₂³	—	212	24	no	—
460	C₂³	—	212	48	no	—
461	C₂³	—	212	12	no	—
462	C₂³	C₂²×D₂₁₂	1	12	yes	—
463	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
464	C₂³	C₂⁴×D₅₃	1	6	yes	—
465	Q₈	—	106	24	no	—
466	Q₈	—	106	8	no	—
467	Q₈	—	106	4	no	—
468	Q₈	—	106	4	no	—
469	Q₈	C₂²×D₂₁₂	1	16	yes	—
470	D₄	—	106	48	no	—
471	D₄	—	106	16	no	—
472	D₄	—	106	48	no	—
473	D₄	—	106	12	no	—
474	D₄	—	106	48	no	—
475	D₄	—	106	12	no	—
476	D₄	—	106	24	no	—
477	D₄	—	106	8	no	—
478	D₄	—	212	96	no	—
479	D₄	C₂²×D₂₁₂	1	48	yes	—
480	C₂×C₄	—	4	24	no	—
481	C₂×C₄	—	53	8	no	—
482	C₂×C₄	—	53	4	no	—
483	C₂×C₄	—	106	4	no	—
484	C₂×C₄	—	106	24	no	—
485	C₂×C₄	—	106	16	no	—
486	C₂×C₄	—	106	48	no	—
487	C₂×C₄	—	106	48	no	—
488	C₂×C₄	C₂²×D₂₁₂	1	12	yes	—
489	C₂×C₄	C₂²×D₂₁₂	1	24	yes	—
490	C₂×C₄	C₂²×D₂₁₂	1	4	yes	—
491	C₂×C₄	C₂²×D₂₁₂	1	24	yes	—
492	C₂×C₄	C₂⁴×D₅₃	1	16	yes	—
493	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
494	C₂×C₄	C₂⁴×D₅₃	1	6	yes	—
495	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
496	C₂²	—	2	12	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	4	12	no	—
499	C₂²	—	106	8	no	—
500	C₂²	—	106	12	no	—
501	C₂²	—	106	16	no	—
502	C₂²	—	106	24	no	—
503	C₂²	—	424	48	no	—
504	C₂²	—	424	24	no	—
505	C₂²	—	212	24	no	—
506	C₂²	C₂³×D₂₁₂	1	2	yes	—
507	C₂²	C₂³×D₂₁₂	1	12	yes	—
508	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
509	C₄	—	2	16	no	—
510	C₄	—	106	4	no	—
511	C₄	—	106	8	no	—
512	C₄	C₂³×D₂₁₂	1	2	yes	—
513	C₄	C₂³×D₂₁₂	1	12	yes	—
514	C₄	C₂³×D₂₁₂	1	2	yes	—
515	C₂	—	2	2	no	—
516	C₂	—	2	12	no	—
517	C₂	—	212	12	no	—
518	C₂	—	212	8	no	—
519	C₂	C₂⁴×D₂₁₂	1	1	yes	characteristic
520	C₂	#20289526	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₅₃×#3428	C₂
hypercenter	#3428	D₅₃
hypocenter	C₅₃	#62852
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #3428

Complements

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

N	H ≅ G/N	type
1. C₂×#16811459	C₂	semidirect
2. C₂²×#13133263	C₂	semidirect
3. #20288508	C₂	semidirect
4. #20288493	C₂	semidirect
5. #20288385	C₂	semidirect
6. #20288374	C₂	semidirect
7. #20288351	C₂	semidirect
8. #20288048	C₂	semidirect
9. C₂×#16811192	C₂	semidirect
10. C₅₃×#3428	C₂	semidirect
12. C₂×#13133265	C₂²	semidirect
13. C₂×#13133264	C₂²	semidirect
15. C₂×#13133263	C₂²	semidirect
16. C₂×#13133263	C₂²	semidirect
17. C₂×#13133263	C₂²	semidirect
18. C₂×#13133262	C₂²	semidirect
19. C₂²×#11719949	C₂²	semidirect
20. C₂²×#11719945	C₂²	semidirect
21. C₂²×#11719945	C₂²	semidirect
22. C₂×#41×D₅₃	C₂²	semidirect
23. C₂³×D₂₁₂	C₂²	semidirect
24. C₂²×D₄×D₅₃	C₂²	semidirect
25. #16811295	C₂²	semidirect
26. #16811285	C₂²	semidirect
27. #16811268	C₂²	semidirect
28. D₄×D₂₁₂	C₂²	semidirect
29. #16811204	C₂²	semidirect
30. #16811199	C₂²	semidirect
31. #16811199	C₂²	semidirect
32. #16811192	C₂²	semidirect
33. #16811192	C₂²	semidirect
34. #16811192	C₂²	semidirect
35. #16811192	C₂²	semidirect
36. #16811192	C₂²	semidirect
37. #16811185	C₂²	semidirect
38. #16811173	C₂²	semidirect
39. C₂×#13133214	C₂²	semidirect
40. C₂×#13133205	C₂²	semidirect
41. #16811135	C₂²	semidirect
42. #16811135	C₂²	semidirect
43. C₂×#13133192	C₂²	semidirect
44. C₂×#13133187	C₂²	semidirect
46. C₅₃×#520	C₂²	semidirect
47. C₅₃×#519	C₂²	semidirect
48. C₅₃×#518	C₂²	semidirect
49. C₄×#41×C₅₃	C₂²	semidirect
50. C₂×#117×C₅₃	C₂²	semidirect
60. C₂×#11719949	C₂³	semidirect
67. C₂×#11719945	C₂³	semidirect
68. C₂×#11719945	C₂³	semidirect
69. C₂×#11719947	C₂³	semidirect
72. C₂²×Dic₁₀₆	C₂³	semidirect
73. C₂×Q₈×D₅₃	C₂³	semidirect
79. C₂²×D₂₁₂	C₂³	semidirect
80. C₂²×D₂₁₂	C₂³	semidirect
85. C₂×D₄×D₅₃	C₂³	semidirect
87. C₂²×C₄×D₅₃	C₂³	semidirect
88. #13133217	C₂³	semidirect
89. #13133214	C₂³	semidirect
90. #13133214	C₂³	semidirect
91. #13133205	C₂³	semidirect
92. #13133205	C₂³	semidirect
93. #13133205	C₂³	semidirect
95. #13133201	C₂³	semidirect
96. #13133197	C₂³	semidirect
97. #13133197	C₂³	semidirect
98. #13133192	C₂³	semidirect
99. #13133192	C₂³	semidirect
100. #13133192	C₂³	semidirect
101. #13133191	C₂³	semidirect
103. #13133187	C₂³	semidirect
104. #13133187	C₂³	semidirect
105. C₄×D₂₁₂	C₂³	semidirect
106. C₂×#11719921	C₂³	semidirect
107. C₂×#41×C₅₃	D₄	semidirect
113. C₄×Q₈×C₅₃	C₂³	semidirect
114. C₄×D₄×C₅₃	C₂³	semidirect
117. #117×C₅₃	C₂³	semidirect
118. #117×C₅₃	C₂³	semidirect
119. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
121. C₂×C₄²×C₅₃	C₂³	semidirect
128. #41×C₅₃	C₂×D₄	semidirect
129. #41×C₅₃	C₂×D₄	semidirect
130. C₂×Q₈×C₅₃	C₂×D₄	semidirect
132. C₂×D₄×C₅₃	C₂×D₄	semidirect
134. C₂²×C₄×C₅₃	C₂×D₄	semidirect
264. #3428	D₅₃	semidirect
306. #520	C₂×D₅₃	semidirect
307. #519	C₂×D₅₃	semidirect
308. #518	C₂×D₅₃	semidirect
309. C₄×#41	C₂×D₅₃	semidirect
310. C₂×#117	C₂×D₅₃	semidirect
311. C₅₃	#62852	semidirect
332. C₂×#41	D₂₁₂	semidirect
372. C₄×Q₈	C₂²×D₅₃	semidirect
374. C₄×D₄	C₂²×D₅₃	semidirect
377. #117	C₂²×D₅₃	semidirect
378. #117	C₂²×D₅₃	semidirect
379. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
382. C₂×C₄²	C₂²×D₅₃	semidirect
398. #41	C₂×D₂₁₂	semidirect
399. #41	C₂×D₂₁₂	semidirect
407. C₂×Q₈	C₂×D₂₁₂	semidirect
428. C₂×D₄	C₂×D₂₁₂	semidirect
437. C₂²×C₄	C₂×D₂₁₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16811459	2
C₂²×#13133263	2
#20288508	2
#20288493	2
#20288385	2
#20288374	2
#20288351	2
#20288048	2
C₂×#16811192	2
C₅₃×#3428	2
#62852	53