Subgroups — #28293201

Order 13568.

11618 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811460	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#13133263	C₂	1	1	yes	maximal, characteristic, complemented
3	#20288506	C₂	1	8	yes	maximal, complemented
4	#20288492	C₂	1	8	yes	maximal, complemented
5	#20288383	C₂	1	8	yes	maximal, complemented
6	#20288381	C₂	1	8	yes	maximal, complemented
7	#20288374	C₂	1	1	yes	maximal, characteristic, complemented
8	#20288373	C₂	1	1	yes	maximal, characteristic, complemented
9	#20288370	C₂	1	1	yes	maximal, characteristic, complemented
10	#20288349	C₂	1	6	yes	maximal, complemented
11	#20288348	C₂	1	6	yes	maximal, complemented
12	#20288045	C₂	1	6	yes	maximal, complemented
13	#535×D₅₃	C₂	1	6	yes	maximal, complemented
14	#20287917	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3487	C₂	1	1	yes	maximal, characteristic, complemented
16	#16811460	—	2	16	no	—
17	C₂×#13133265	C₂²	1	1	yes	characteristic, complemented
18	C₂×#13133265	C₂²	1	4	yes	complemented
19	C₂×#13133263	—	2	16	no	—
20	C₂×#13133263	C₂²	1	8	yes	complemented
21	C₂×#13133263	C₂²	1	8	yes	complemented
22	C₂×#13133263	C₂²	1	6	yes	complemented
23	C₂×#13133263	C₂²	1	4	yes	complemented
24	C₂²×#11719949	C₂²	1	1	yes	characteristic
25	C₂²×#11719949	C₂²	1	1	yes	characteristic, complemented
26	C₂²×#11719949	C₂²	1	4	yes	complemented
27	C₂²×#11719945	C₂²	1	3	yes	complemented
28	C₂×#41×D₅₃	C₂²	1	6	yes	complemented
29	C₂×#41×D₅₃	C₂²	1	4	yes	complemented
30	C₂³×D₂₁₂	C₂²	1	3	yes	complemented
31	C₂²×D₄×D₅₃	C₂²	1	3	yes	complemented
32	C₂²×D₄×D₅₃	C₂²	1	3	yes	complemented
33	#16811295	C₂²	1	8	yes	complemented
34	#16811292	C₂²	1	8	yes	complemented
35	#16811292	C₂²	1	8	yes	complemented
36	#16811285	C₂²	1	8	yes	complemented
37	#16811284	C₂²	1	8	yes	complemented
38	#16811280	C₂²	1	8	yes	complemented
39	#16811270	C₂²	1	24	yes	complemented
40	#16811269	C₂²	1	24	yes	complemented
41	#16811266	C₂²	1	24	yes	complemented
42	#16811264	C₂²	1	24	yes	complemented
43	D₄×D₂₁₂	C₂²	1	24	yes	complemented
44	#16811258	C₂²	1	24	yes	complemented
45	#16811257	C₂²	1	24	yes	complemented
46	#16811257	C₂²	1	24	yes	complemented
47	#16811203	C₂²	1	12	yes	complemented
48	#16811202	C₂²	1	12	yes	complemented
49	#16811196	C₂²	1	12	yes	complemented
50	#16811195	C₂²	1	4	yes	complemented
51	#16811192	C₂²	1	6	yes	complemented
52	#16811191	C₂²	1	12	yes	complemented
53	#16811190	C₂²	1	6	yes	complemented
54	#16811189	C₂²	1	24	yes	complemented
55	#16811189	C₂²	1	12	yes	complemented
56	#16811188	C₂²	1	12	yes	complemented
57	#16811187	C₂²	1	6	yes	complemented
58	#16811186	C₂²	1	12	yes	complemented
59	#16811184	C₂²	1	12	yes	complemented
60	#16811183	C₂²	1	12	yes	complemented
61	#16811170	C₂²	1	24	yes	complemented
62	#127×D₅₃	C₂²	1	12	yes	complemented
63	#124×D₅₃	C₂²	1	12	yes	complemented
64	#16811135	C₂²	1	6	yes	complemented
65	#16811134	C₂²	1	6	yes	complemented
66	#16811132	C₂²	1	24	yes	complemented
67	#16811130	C₂²	1	6	yes	complemented
68	#121×D₅₃	C₂²	1	24	yes	complemented
69	#120×D₅₃	C₂²	1	24	yes	complemented
70	#16811105	C₂²	1	8	yes	complemented
71	#16811101	C₂²	1	1	yes	characteristic, complemented
72	#16811097	C₂²	1	6	yes	complemented
73	C₄×#11719949	C₂²	1	8	yes	complemented
74	#117×D₅₃	C₂²	1	6	yes	complemented
75	C₂×2₋¹⁺⁴×C₅₃	C₂²	1	1	yes	characteristic, complemented
76	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#550	C₂²	1	8	yes	complemented
78	C₅₃×#548	C₂²	1	8	yes	complemented
79	C₅₃×#535	C₂²	1	6	yes	complemented
80	C₅₃×#525	C₂²	1	6	yes	complemented
81	C₅₃×#519	C₂²	1	1	yes	characteristic, complemented
82	C₂⁴×D₅₃	C₂³	1	6	yes	—
83	#13133265	—	2	8	no	—
84	#13133265	—	2	32	no	—
85	#13133263	—	2	64	no	—
86	#13133263	—	2	64	no	—
87	#13133263	—	2	32	no	—
88	#13133263	—	2	48	no	—
89	C₂×#11719949	—	2	8	no	—
90	C₂×#11719949	—	2	32	no	—
91	C₂×#11719949	D₄	1	16	yes	complemented
92	C₂×#11719949	C₂³	1	8	yes	—
93	C₂×#11719949	C₂³	1	4	yes	—
94	C₂×#11719949	C₂³	1	4	yes	—
95	C₂×#11719949	C₂³	1	12	yes	complemented
96	C₂×#11719949	C₂³	1	4	yes	complemented
97	C₂×#11719949	C₂³	1	6	yes	complemented
98	C₂×#11719945	—	2	24	no	—
99	C₂×#11719945	C₂³	1	12	yes	—
100	C₂×#11719945	C₂³	1	6	yes	—
101	C₂×#11719945	C₂³	1	12	yes	—
102	C₂×#11719945	C₂³	1	12	yes	complemented
103	C₂×#11719945	C₂³	1	12	yes	complemented
104	C₂×#11719947	C₂³	1	4	yes	—
105	C₂×#11719947	C₂³	1	6	yes	complemented
106	#41×D₅₃	—	2	32	no	—
107	#41×D₅₃	—	2	48	no	—
108	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
109	C₂×Q₈×D₅₃	C₂³	1	4	yes	complemented
110	C₂×Q₈×D₅₃	C₂³	1	6	yes	complemented
111	C₂²×D₂₁₂	—	2	24	no	—
112	C₂²×D₂₁₂	C₂³	1	24	yes	—
113	C₂²×D₂₁₂	C₂³	1	3	yes	—
114	C₂²×D₂₁₂	C₂³	1	3	yes	—
115	C₂²×D₂₁₂	C₂³	1	3	yes	—
116	C₂²×D₂₁₂	C₂³	1	12	yes	complemented
117	C₂²×C₂²⋊D₅₃	C₂³	1	3	yes	—
118	C₂²×C₂²⋊D₅₃	C₂³	1	3	yes	—
119	C₂×D₄×D₅₃	—	2	24	no	—
120	C₂×D₄×D₅₃	—	2	24	no	—
121	C₂×D₄×D₅₃	C₂³	1	24	yes	—
122	C₂×D₄×D₅₃	C₂³	1	12	yes	—
123	C₂×D₄×D₅₃	C₂³	1	12	yes	—
124	C₂×D₄×D₅₃	C₂³	1	12	yes	—
125	C₂×D₄×D₅₃	C₂³	1	6	yes	complemented
126	C₂×D₄×D₅₃	C₂³	1	12	yes	complemented
127	C₂×D₄×D₅₃	C₂³	1	48	yes	complemented
128	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
129	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
130	C₂²×C₄×D₅₃	C₂³	1	12	yes	complemented
131	#13133216	C₂³	1	8	yes	complemented
132	#13133214	C₂³	1	12	yes	complemented
133	#13133213	C₂³	1	12	yes	complemented
134	#13133213	C₂³	1	12	yes	complemented
135	#13133213	C₂³	1	24	yes	complemented
136	#13133206	C₂³	1	12	yes	complemented
137	#13133205	C₂³	1	12	yes	complemented
138	#13133204	C₂³	1	12	yes	complemented
139	#13133203	C₂³	1	24	yes	complemented
140	#13133203	C₂³	1	8	yes	complemented
141	#13133202	C₂³	1	24	yes	complemented
142	#13133201	C₂³	1	4	yes	—
143	#13133200	C₂³	1	4	yes	—
144	#13133199	C₂³	1	24	yes	complemented
145	#13133198	C₂³	1	4	yes	—
146	#13133197	C₂³	1	12	yes	complemented
147	#13133196	C₂³	1	12	yes	complemented
148	#13133195	C₂³	1	8	yes	complemented
149	#13133194	C₂³	1	8	yes	complemented
150	#13133193	C₂³	1	12	yes	complemented
151	#13133192	C₂³	1	24	yes	complemented
152	#13133192	C₂³	1	24	yes	complemented
153	#13133192	C₂³	1	12	yes	complemented
154	#13133191	C₂³	1	24	yes	complemented
155	#13133191	C₂³	1	12	yes	complemented
156	#13133190	C₂³	1	24	yes	complemented
157	#13133190	C₂³	1	24	yes	complemented
158	#13133190	C₂³	1	24	yes	complemented
159	#13133189	C₂³	1	24	yes	complemented
160	#13133188	C₂³	1	24	yes	complemented
161	#13133188	C₂³	1	24	yes	complemented
162	#13133188	C₂³	1	12	yes	complemented
163	#13133187	C₂³	1	12	yes	—
164	#13133187	C₂³	1	48	yes	complemented
165	#13133187	C₂³	1	24	yes	complemented
166	#13133186	C₂³	1	12	yes	—
167	#13133185	C₂³	1	12	yes	—
168	#13133185	C₂³	1	48	yes	complemented
169	#13133185	C₂³	1	24	yes	complemented
170	Q₈×Dic₅₃	C₂³	1	8	yes	complemented
171	C₄×D₂₁₂	C₂³	1	24	yes	complemented
172	C₄×D₂₁₂	C₂³	1	24	yes	complemented
173	#13133179	C₂³	1	24	yes	complemented
174	C₄×C₂²⋊D₅₃	C₂³	1	24	yes	complemented
175	C₄×C₂²⋊D₅₃	C₂³	1	24	yes	complemented
176	#13133176	C₂³	1	6	yes	—
177	#13133175	C₂³	1	12	yes	complemented
178	#13133174	C₂³	1	12	yes	complemented
179	#13133173	C₂³	1	4	yes	—
180	C₄⋊C₄×D₅₃	C₂³	1	12	yes	complemented
181	C₂²⋊C₄×D₅₃	C₂³	1	12	yes	—
182	C₂²⋊C₄×D₅₃	C₂³	1	48	yes	complemented
183	C₄²×D₅₃	C₂³	1	12	yes	complemented
184	2₋¹⁺⁴×C₅₃	—	2	8	no	—
185	C₂×#41×C₅₃	—	2	8	no	—
186	C₂×#41×C₅₃	C₂³	1	8	yes	—
187	C₂×#41×C₅₃	C₂³	1	6	yes	—
188	C₂×#41×C₅₃	C₂³	1	4	yes	complemented
189	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
190	C₂²×Q₈×C₅₃	C₂³	1	4	yes	complemented
191	C₂²×D₄×C₅₃	C₂³	1	3	yes	—
192	C₂³×C₄×C₅₃	C₂³	1	3	yes	—
193	#127×C₅₃	C₂³	1	12	yes	complemented
194	#124×C₅₃	C₂³	1	12	yes	complemented
195	#123×C₅₃	C₂³	1	4	yes	—
196	C₂²⋊Q₈×C₅₃	C₂³	1	12	yes	complemented
197	#121×C₅₃	C₂³	1	24	yes	complemented
198	#121×C₅₃	C₂³	1	12	yes	complemented
199	#120×C₅₃	C₂³	1	12	yes	—
200	C₄×Q₈×C₅₃	C₂³	1	8	yes	complemented
201	C₄×D₄×C₅₃	C₂³	1	24	yes	complemented
202	#117×C₅₃	C₂³	1	6	yes	—
203	C₂⁴×C₅₃	C₂⁴	1	3	yes	—
204	C₂³×D₅₃	—	2	24	no	—
205	C₂³×D₅₃	—	8	12	no	—
206	C₂³×D₅₃	C₂⁴	1	24	yes	—
207	C₂³×D₅₃	C₂⁴	1	3	yes	—
208	C₂³×D₅₃	C₂⁴	1	12	yes	—
209	C₂³×D₅₃	C₂⁴	1	3	yes	—
210	#41×C₅₃	—	2	32	no	—
211	#41×C₅₃	—	2	16	no	—
212	#41×C₅₃	—	2	24	no	—
213	C₂×Q₈×C₅₃	—	2	16	no	—
214	C₂×Q₈×C₅₃	C₂×D₄	1	8	yes	complemented
215	C₂×Q₈×C₅₃	C₂⁴	1	6	yes	—
216	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
217	C₂×D₄×C₅₃	—	2	12	no	—
218	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
219	C₂×D₄×C₅₃	C₂⁴	1	12	yes	—
220	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
221	C₂×D₄×C₅₃	C₂⁴	1	24	yes	—
222	C₂²×C₄×C₅₃	—	2	12	no	—
223	C₂²×C₄×C₅₃	C₂⁴	1	12	yes	—
224	C₂²×C₄×C₅₃	C₂⁴	1	12	yes	—
225	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
227	C₂×C₂²⋊D₅₃	—	2	12	no	—
228	C₂×C₂²⋊D₅₃	—	2	12	no	—
229	C₂×C₂²⋊D₅₃	C₂⁴	1	12	yes	—
230	C₂×C₂²⋊D₅₃	C₂⁴	1	12	yes	—
231	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
232	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
233	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
234	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
235	C₂×C₂²⋊D₅₃	C₂⁴	1	24	yes	—
236	C₂×C₂²⋊D₅₃	C₂⁴	1	24	yes	—
237	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
238	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
239	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
240	#11719949	—	2	32	no	—
241	#11719949	—	2	16	no	—
242	#11719949	—	2	48	no	—
243	#11719949	—	2	24	no	—
244	#11719949	C₂×D₄	1	32	yes	complemented
245	#11719949	C₂×D₄	1	32	yes	complemented
246	Q₈×D₅₃	—	2	16	no	—
247	Q₈×D₅₃	—	2	24	no	—
248	#11719947	—	2	16	no	—
249	#11719947	—	2	24	no	—
250	D₄×D₅₃	—	2	48	no	—
251	D₄×D₅₃	—	2	96	no	—
252	D₄×D₅₃	—	2	48	no	—
253	D₄×D₅₃	—	2	48	no	—
254	D₄×D₅₃	—	2	48	no	—
255	D₄×D₅₃	—	2	24	no	—
256	D₄×D₅₃	—	8	48	no	—
257	#11719945	—	2	24	no	—
258	#11719945	—	2	48	no	—
259	#11719945	—	2	48	no	—
260	#11719945	—	2	48	no	—
261	#11719945	—	2	48	no	—
262	C₂×D₂₁₂	—	2	12	no	—
263	C₂×D₂₁₂	—	2	12	no	—
264	C₂×D₂₁₂	—	2	96	no	—
265	C₂×D₂₁₂	—	2	48	no	—
266	C₂×D₂₁₂	C₂×D₄	1	24	yes	complemented
267	C₂×D₂₁₂	C₂⁴	1	12	yes	—
268	C₂×D₂₁₂	C₂⁴	1	12	yes	—
269	C₂×D₂₁₂	C₂⁴	1	12	yes	—
270	C₂×D₂₁₂	C₂⁴	1	6	yes	—
271	C₂×D₂₁₂	C₂⁴	1	24	yes	—
272	C₂×D₂₁₂	C₂⁴	1	12	yes	—
273	C₂×C₄×D₅₃	—	2	12	no	—
274	C₂×C₄×D₅₃	—	2	48	no	—
275	C₂×C₄×D₅₃	C₂×D₄	1	24	yes	complemented
276	C₂×C₄×D₅₃	C₂⁴	1	12	yes	—
277	C₂×C₄×D₅₃	C₂⁴	1	12	yes	—
278	C₂×C₄×D₅₃	C₂⁴	1	12	yes	—
279	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
280	C₂×C₄×D₅₃	C₂⁴	1	24	yes	—
281	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
282	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
283	C₂×Dic₁₀₆	—	2	4	no	—
284	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
285	C₂×Dic₁₀₆	C₂⁴	1	6	yes	—
286	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
287	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
288	C₄⋊C₄×C₅₃	C₂⁴	1	12	yes	—
289	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
290	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
291	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
292	C₂²⋊C₄×C₅₃	C₂⁴	1	24	yes	—
293	C₄²×C₅₃	C₂⁴	1	12	yes	—
294	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
295	C₂²⋊Dic₅₃	C₂⁴	1	24	yes	—
296	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
297	#11719921	C₂⁴	1	24	yes	—
298	#11719921	C₂⁴	1	24	yes	—
299	#11719921	C₂⁴	1	24	yes	—
300	#11719921	C₂⁴	1	8	yes	—
301	#11719921	C₂⁴	1	8	yes	—
302	C₄⋊Dic₅₃	C₂⁴	1	12	yes	—
303	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
304	#11719919	C₂⁴	1	8	yes	—
305	#11719919	C₂⁴	1	8	yes	—
306	#11719919	C₂⁴	1	8	yes	—
307	C₄×Dic₅₃	C₂⁴	1	8	yes	—
308	C₄×Dic₅₃	C₂⁴	1	12	yes	—
309	C₂³×C₅₃	—	2	6	no	—
310	C₂³×C₅₃	—	4	6	no	—
311	C₂³×C₅₃	C₂⁵	1	4	yes	—
312	C₂³×C₅₃	C₂⁵	1	6	yes	—
313	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
314	C₂²×D₅₃	—	2	6	no	—
315	C₂²×D₅₃	—	2	24	no	—
316	C₂²×D₅₃	—	2	48	no	—
317	C₂²×D₅₃	—	4	6	no	—
318	C₂²×D₅₃	—	4	6	no	—
319	C₂²×D₅₃	—	4	24	no	—
320	C₂²×D₅₃	—	4	48	no	—
321	C₂²×D₅₃	—	8	48	no	—
322	C₂²×D₅₃	C₂²×D₄	1	12	yes	—
323	C₂²×D₅₃	C₂⁵	1	4	yes	—
324	C₂²×D₅₃	C₂⁵	1	6	yes	—
325	C₂²×D₅₃	C₂⁵	1	6	yes	—
326	Q₈×C₅₃	—	2	12	no	—
327	Q₈×C₅₃	C₂²×D₄	1	16	yes	—
328	D₄×C₅₃	—	2	8	no	—
329	D₄×C₅₃	—	2	24	no	—
330	D₄×C₅₃	—	2	12	no	—
331	D₄×C₅₃	—	4	24	no	—
332	C₂×C₄×C₅₃	—	2	2	no	—
333	C₂×C₄×C₅₃	—	2	24	no	—
334	C₂×C₄×C₅₃	—	2	24	no	—
335	C₂×C₄×C₅₃	C₂²×D₄	1	12	yes	—
336	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
337	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
338	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
339	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
340	C₂²⋊D₅₃	—	2	8	no	—
341	C₂²⋊D₅₃	—	2	24	no	—
342	C₂²⋊D₅₃	—	2	24	no	—
343	C₂²⋊D₅₃	—	2	8	no	—
344	C₂²⋊D₅₃	—	2	12	no	—
345	C₂²⋊D₅₃	—	2	12	no	—
346	C₂²⋊D₅₃	—	4	24	no	—
347	C₂²⋊D₅₃	—	4	24	no	—
348	C₂×Dic₅₃	—	2	2	no	—
349	C₂×Dic₅₃	—	2	8	no	—
350	C₂×Dic₅₃	C₂²×D₄	1	4	yes	—
351	C₂×Dic₅₃	C₂⁵	1	4	yes	—
352	C₂×Dic₅₃	C₂⁵	1	2	yes	—
353	C₂×Dic₅₃	C₂⁵	1	8	yes	—
354	C₂×Dic₅₃	C₂⁵	1	1	yes	characteristic
355	C₂×Dic₅₃	C₂⁵	1	1	yes	characteristic
356	D₂₁₂	—	2	24	no	—
357	D₂₁₂	—	2	24	no	—
358	D₂₁₂	—	2	24	no	—
359	D₂₁₂	—	2	12	no	—
360	D₂₁₂	—	4	24	no	—
361	D₂₁₂	C₂²×D₄	1	48	yes	—
362	C₄×D₅₃	—	2	24	no	—
363	C₄×D₅₃	—	2	24	no	—
364	C₄×D₅₃	—	2	24	no	—
365	C₄×D₅₃	—	2	8	no	—
366	C₄×D₅₃	—	4	24	no	—
367	C₄×D₅₃	C₂²×D₄	1	24	yes	—
368	C₄×D₅₃	C₂²×D₄	1	24	yes	—
369	Dic₁₀₆	—	2	12	no	—
370	Dic₁₀₆	—	2	4	no	—
371	Dic₁₀₆	—	2	4	no	—
372	Dic₁₀₆	—	2	8	no	—
373	#62852	—	53	1	no	maximal, Sylow
374	C₂²×C₅₃	—	2	2	no	—
375	C₂²×C₅₃	—	2	4	no	—
376	C₂²×C₅₃	—	2	6	no	—
377	C₂²×C₅₃	—	2	8	no	—
378	C₂²×C₅₃	—	2	12	no	—
379	C₂²×C₅₃	—	4	12	no	—
380	C₂²×C₅₃	C₂³×D₄	1	2	yes	—
381	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
382	C₂×D₅₃	—	2	12	no	—
383	C₂×D₅₃	—	2	4	no	—
384	C₂×D₅₃	—	2	6	no	—
385	C₂×D₅₃	—	2	8	no	—
386	C₂×D₅₃	—	2	12	no	—
387	C₂×D₅₃	—	4	12	no	—
388	C₂×D₅₃	—	4	12	no	—
389	C₂×D₅₃	—	8	24	no	—
390	C₂×D₅₃	—	8	48	no	—
391	C₂×D₅₃	C₂³×D₄	1	12	yes	—
392	C₄×C₅₃	—	2	2	no	—
393	C₄×C₅₃	—	2	4	no	—
394	C₄×C₅₃	—	2	8	no	—
395	C₄×C₅₃	C₂³×D₄	1	12	yes	—
396	Dic₅₃	—	2	4	no	—
397	Dic₅₃	—	2	2	no	—
398	Dic₅₃	—	2	8	no	—
399	Dic₅₃	C₂³×D₄	1	2	yes	—
400	Dic₅₃	C₂³×D₄	1	2	yes	—
401	C₂×#585	—	53	1	no	—
402	C₂²×H(5,𝔽₂)	—	53	1	no	—
403	#3500	—	53	8	no	—
404	#3498	—	53	8	no	—
405	#3488	—	53	8	no	—
406	#3488	—	53	8	no	—
407	#3487	—	53	1	no	—
408	#3487	—	53	1	no	—
409	#3487	—	53	1	no	—
410	#3487	D₅₃	1	1	yes	characteristic, complemented
411	#3484	—	53	6	no	—
412	#3484	—	53	6	no	—
413	#3449	—	53	6	no	—
414	C₂×#535	—	53	6	no	—
415	#3428	—	53	1	no	—
416	C₂×C₅₃	—	2	2	no	—
417	C₂×C₅₃	—	4	6	no	—
418	C₂×C₅₃	—	4	4	no	—
419	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
420	C₂×C₅₃	H(7,𝔽₂)	1	2	yes	—
421	D₅₃	—	2	12	no	—
422	D₅₃	—	4	6	no	—
423	D₅₃	—	4	4	no	—
424	#585	—	106	16	no	—
425	C₂×2₋¹⁺⁴	—	53	1	no	—
426	C₂×2₋¹⁺⁴	—	53	4	no	—
427	C₂×2₋¹⁺⁴	C₂×D₅₃	1	1	yes	characteristic, complemented
428	C₂×H(5,𝔽₂)	—	53	8	no	—
429	C₂×H(5,𝔽₂)	—	53	8	no	—
430	C₂×H(5,𝔽₂)	—	53	6	no	—
431	C₂×H(5,𝔽₂)	—	53	4	no	—
432	C₂×H(5,𝔽₂)	—	106	16	no	—
433	C₂²×#41	—	53	6	no	—
434	C₂²×#41	—	53	4	no	—
435	C₂²×#41	—	53	1	no	—
436	C₂²×#41	—	53	1	no	—
437	C₂²×#41	—	53	4	no	—
438	C₂²×#41	—	53	3	no	—
439	C₂²×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
440	C₂³×D₄	—	53	3	no	—
441	C₂³×D₄	—	53	3	no	—
442	C₂³×D₄	—	53	3	no	—
443	#550	—	53	8	no	—
444	#550	—	53	8	no	—
445	#550	—	53	8	no	—
446	#550	C₂×D₅₃	1	8	yes	complemented
447	#548	—	53	8	no	—
448	#548	—	53	8	no	—
449	#548	—	53	8	no	—
450	#548	C₂×D₅₃	1	8	yes	complemented
451	#546	—	53	24	no	—
452	#546	—	53	24	no	—
453	#546	—	53	24	no	—
454	#546	—	53	24	no	—
455	D₄²	—	53	24	no	—
456	D₄²	—	53	24	no	—
457	D₄²	—	53	24	no	—
458	D₄²	—	53	24	no	—
459	#537	—	53	12	no	—
460	#537	—	53	12	no	—
461	#536	—	53	4	no	—
462	#536	—	53	12	no	—
463	#535	—	53	6	no	—
464	#535	—	53	6	no	—
465	#535	—	53	12	no	—
466	#535	—	53	12	no	—
467	#535	—	53	24	no	—
468	#535	—	53	12	no	—
469	#535	—	53	12	no	—
470	#535	—	53	6	no	—
471	#535	C₂×D₅₃	1	6	yes	complemented
472	#534	—	53	12	no	—
473	#534	—	53	12	no	—
474	#532	—	53	24	no	—
475	C₂×#127	—	53	12	no	—
476	C₂×#124	—	53	12	no	—
477	#525	—	53	6	no	—
478	#525	—	53	6	no	—
479	#525	—	53	24	no	—
480	#525	—	53	6	no	—
481	#525	C₂×D₅₃	1	6	yes	complemented
482	C₂×#121	—	53	24	no	—
483	C₂×#120	—	53	24	no	—
484	#520	—	53	8	no	—
485	#519	—	53	1	no	—
486	#519	C₂×D₅₃	1	1	yes	characteristic, complemented
487	#518	—	53	6	no	—
488	C₄×#41	—	53	8	no	—
489	C₂×#117	—	53	6	no	—
490	C₅₃	#62852	1	1	yes	characteristic, complemented, Sylow
491	C₂⁵	—	53	6	no	—
492	2₋¹⁺⁴	—	2	8	no	—
493	2₋¹⁺⁴	—	106	32	no	—
494	2₋¹⁺⁴	—	106	8	no	—
495	H(5,𝔽₂)	—	106	48	no	—
496	H(5,𝔽₂)	—	106	64	no	—
497	H(5,𝔽₂)	—	106	64	no	—
498	H(5,𝔽₂)	—	106	32	no	—
499	C₂×#41	—	2	8	no	—
500	C₂×#41	—	53	16	no	—
501	C₂×#41	—	53	4	no	—
502	C₂×#41	—	53	4	no	—
503	C₂×#41	—	53	6	no	—
504	C₂×#41	—	53	12	no	—
505	C₂×#41	—	53	8	no	—
506	C₂×#41	—	53	4	no	—
507	C₂×#41	—	53	4	no	—
508	C₂×#41	—	53	6	no	—
509	C₂×#41	—	53	6	no	—
510	C₂×#41	—	53	12	no	—
511	C₂×#41	—	53	12	no	—
512	C₂×#41	—	53	12	no	—
513	C₂×#41	—	53	12	no	—
514	C₂×#41	—	106	24	no	—
515	C₂×#41	—	106	48	no	—
516	C₂×#41	—	106	32	no	—
517	C₂×#41	—	106	32	no	—
518	C₂×#41	—	106	8	no	—
519	C₂×#41	C₂²×D₅₃	1	6	yes	—
520	C₂×#41	C₂²×D₅₃	1	8	yes	—
521	C₂×#41	C₂²×D₅₃	1	4	yes	complemented
522	C₂²×Q₈	—	53	6	no	—
523	C₂²×Q₈	—	53	4	no	—
524	C₂²×Q₈	—	53	1	no	—
525	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
526	C₂²×Q₈	C₂²×D₅₃	1	4	yes	complemented
527	C₂²×D₄	—	53	3	no	—
528	C₂²×D₄	—	53	3	no	—
529	C₂²×D₄	—	53	12	no	—
530	C₂²×D₄	—	53	12	no	—
531	C₂²×D₄	—	53	12	no	—
532	C₂²×D₄	—	53	6	no	—
533	C₂²×D₄	—	53	12	no	—
534	C₂²×D₄	—	53	24	no	—
535	C₂²×D₄	—	53	48	no	—
536	C₂²×D₄	—	53	3	no	—
537	C₂²×D₄	—	53	3	no	—
538	C₂²×D₄	—	53	3	no	—
539	C₂²×D₄	—	53	12	no	—
540	C₂²×D₄	—	53	24	no	—
541	C₂²×D₄	—	106	24	no	—
542	C₂²×D₄	—	106	24	no	—
543	C₂²×D₄	—	106	24	no	—
544	C₂²×D₄	C₂²×D₅₃	1	3	yes	—
545	C₂³×C₄	—	53	3	no	—
546	C₂³×C₄	—	53	12	no	—
547	C₂³×C₄	—	53	3	no	—
548	C₂³×C₄	C₂²×D₅₃	1	3	yes	—
549	C₄⋊Q₈	—	53	8	no	—
550	#127	—	53	24	no	—
551	#127	—	53	12	no	—
552	#127	—	53	12	no	—
553	#127	—	53	12	no	—
554	#127	C₂²×D₅₃	1	12	yes	complemented
555	#124	—	53	12	no	—
556	#124	—	53	12	no	—
557	#124	—	53	24	no	—
558	#124	—	53	8	no	—
559	#124	—	53	12	no	—
560	#124	C₂²×D₅₃	1	12	yes	complemented
561	#123	—	53	4	no	—
562	#123	—	53	4	no	—
563	#123	—	53	24	no	—
564	#123	—	53	4	no	—
565	#123	—	53	24	no	—
566	#123	C₂²×D₅₃	1	4	yes	—
567	C₂²⋊Q₈	—	53	12	no	—
568	C₂²⋊Q₈	—	53	12	no	—
569	C₂²⋊Q₈	—	53	8	no	—
570	C₂²⋊Q₈	—	53	12	no	—
571	C₂²⋊Q₈	—	53	8	no	—
572	C₂²⋊Q₈	C₂²×D₅₃	1	12	yes	complemented
573	#121	—	53	24	no	—
574	#121	—	53	24	no	—
575	#121	—	53	12	no	—
576	#121	—	53	24	no	—
577	#121	—	53	24	no	—
578	#121	—	53	12	no	—
579	#121	—	53	24	no	—
580	#121	—	53	12	no	—
581	#121	—	53	24	no	—
582	#121	—	53	24	no	—
583	#121	—	53	24	no	—
584	#121	—	53	24	no	—
585	#121	C₂²×D₅₃	1	24	yes	complemented
586	#121	C₂²×D₅₃	1	12	yes	complemented
587	#120	—	53	12	no	—
588	#120	—	53	12	no	—
589	#120	—	53	48	no	—
590	#120	—	53	24	no	—
591	#120	—	53	12	no	—
592	#120	—	53	48	no	—
593	#120	—	53	24	no	—
594	#120	C₂²×D₅₃	1	12	yes	—
595	C₄×Q₈	—	53	8	no	—
596	C₄×Q₈	C₂²×D₅₃	1	8	yes	complemented
597	C₄×D₄	—	53	24	no	—
598	C₄×D₄	—	53	24	no	—
599	C₄×D₄	—	53	24	no	—
600	C₄×D₄	—	53	24	no	—
601	C₄×D₄	—	53	24	no	—
602	C₄×D₄	C₂²×D₅₃	1	24	yes	complemented
603	#117	—	53	6	no	—
604	#117	—	53	12	no	—
605	#117	—	53	4	no	—
606	#117	—	53	12	no	—
607	#117	C₂²×D₅₃	1	6	yes	—
608	C₂×C₄⋊C₄	—	53	12	no	—
609	C₂×C₂²⋊C₄	—	53	12	no	—
610	C₂×C₂²⋊C₄	—	53	48	no	—
611	C₂×C₄²	—	53	12	no	—
612	C₂⁴	—	53	3	no	—
613	C₂⁴	—	53	24	no	—
614	C₂⁴	—	53	3	no	—
615	C₂⁴	—	53	12	no	—
616	C₂⁴	—	106	24	no	—
617	C₂⁴	—	424	12	no	—
618	C₂⁴	C₂³×D₅₃	1	3	yes	—
619	#41	—	2	32	no	—
620	#41	—	2	16	no	—
621	#41	—	2	24	no	—
622	#41	—	53	32	no	—
623	#41	—	53	32	no	—
624	#41	—	106	48	no	—
625	#41	—	106	48	no	—
626	#41	—	106	48	no	—
627	#41	—	106	48	no	—
628	#41	—	106	16	no	—
629	#41	—	106	24	no	—
630	#41	—	106	24	no	—
631	#41	—	106	48	no	—
632	#41	—	106	32	no	—
633	#41	—	106	16	no	—
634	#41	—	106	24	no	—
635	C₂×Q₈	—	2	16	no	—
636	C₂×Q₈	—	53	2	no	—
637	C₂×Q₈	—	53	6	no	—
638	C₂×Q₈	—	53	4	no	—
639	C₂×Q₈	—	53	2	no	—
640	C₂×Q₈	—	106	4	no	—
641	C₂×Q₈	—	106	24	no	—
642	C₂×Q₈	—	106	16	no	—
643	C₂×Q₈	D₄×D₅₃	1	8	yes	complemented
644	C₂×Q₈	C₂³×D₅₃	1	6	yes	—
645	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
646	C₂×D₄	—	2	12	no	—
647	C₂×D₄	—	53	4	no	—
648	C₂×D₄	—	53	12	no	—
649	C₂×D₄	—	53	12	no	—
650	C₂×D₄	—	53	6	no	—
651	C₂×D₄	—	53	6	no	—
652	C₂×D₄	—	53	4	no	—
653	C₂×D₄	—	53	24	no	—
654	C₂×D₄	—	53	24	no	—
655	C₂×D₄	—	53	24	no	—
656	C₂×D₄	—	53	12	no	—
657	C₂×D₄	—	53	12	no	—
658	C₂×D₄	—	53	12	no	—
659	C₂×D₄	—	53	12	no	—
660	C₂×D₄	—	53	6	no	—
661	C₂×D₄	—	53	24	no	—
662	C₂×D₄	—	106	96	no	—
663	C₂×D₄	—	106	48	no	—
664	C₂×D₄	—	106	12	no	—
665	C₂×D₄	—	106	48	no	—
666	C₂×D₄	—	106	48	no	—
667	C₂×D₄	—	106	24	no	—
668	C₂×D₄	—	106	12	no	—
669	C₂×D₄	—	106	96	no	—
670	C₂×D₄	—	106	48	no	—
671	C₂×D₄	—	106	48	no	—
672	C₂×D₄	—	106	12	no	—
673	C₂×D₄	—	106	12	no	—
674	C₂×D₄	—	424	48	no	—
675	C₂×D₄	C₂³×D₅₃	1	4	yes	—
676	C₂×D₄	C₂³×D₅₃	1	12	yes	—
677	C₂×D₄	C₂³×D₅₃	1	6	yes	—
678	C₂×D₄	C₂³×D₅₃	1	24	yes	—
679	C₂²×C₄	—	2	12	no	—
680	C₂²×C₄	—	53	1	no	—
681	C₂²×C₄	—	53	24	no	—
682	C₂²×C₄	—	53	6	no	—
683	C₂²×C₄	—	53	6	no	—
684	C₂²×C₄	—	53	4	no	—
685	C₂²×C₄	—	53	1	no	—
686	C₂²×C₄	—	53	12	no	—
687	C₂²×C₄	—	53	12	no	—
688	C₂²×C₄	—	53	12	no	—
689	C₂²×C₄	—	53	4	no	—
690	C₂²×C₄	—	53	24	no	—
691	C₂²×C₄	—	106	48	no	—
692	C₂²×C₄	—	106	12	no	—
693	C₂²×C₄	C₂³×D₅₃	1	12	yes	—
694	C₂²×C₄	C₂³×D₅₃	1	12	yes	—
695	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
696	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
697	C₄⋊C₄	—	53	8	no	—
698	C₄⋊C₄	—	53	12	no	—
699	C₄⋊C₄	—	53	8	no	—
700	C₄⋊C₄	—	53	8	no	—
701	C₄⋊C₄	—	53	8	no	—
702	C₄⋊C₄	C₂³×D₅₃	1	12	yes	—
703	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
704	C₂²⋊C₄	—	53	4	no	—
705	C₂²⋊C₄	—	53	24	no	—
706	C₂²⋊C₄	—	53	8	no	—
707	C₂²⋊C₄	—	53	24	no	—
708	C₂²⋊C₄	—	53	24	no	—
709	C₂²⋊C₄	—	53	24	no	—
710	C₂²⋊C₄	—	53	8	no	—
711	C₂²⋊C₄	—	53	8	no	—
712	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
713	C₂²⋊C₄	C₂³×D₅₃	1	24	yes	—
714	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
715	C₄²	—	53	8	no	—
716	C₄²	—	53	12	no	—
717	C₄²	C₂³×D₅₃	1	12	yes	—
718	C₂³	—	2	6	no	—
719	C₂³	—	4	6	no	—
720	C₂³	—	53	6	no	—
721	C₂³	—	53	12	no	—
722	C₂³	—	53	6	no	—
723	C₂³	—	53	4	no	—
724	C₂³	—	106	24	no	—
725	C₂³	—	106	48	no	—
726	C₂³	—	106	6	no	—
727	C₂³	—	424	48	no	—
728	C₂³	—	212	24	no	—
729	C₂³	—	212	48	no	—
730	C₂³	—	212	6	no	—
731	C₂³	—	212	6	no	—
732	C₂³	C₂⁴×D₅₃	1	6	yes	—
733	C₂³	C₂⁴×D₅₃	1	4	yes	—
734	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
735	Q₈	—	2	12	no	—
736	Q₈	—	106	8	no	—
737	Q₈	—	106	4	no	—
738	Q₈	—	106	4	no	—
739	Q₈	—	106	12	no	—
740	Q₈	C₂×D₄×D₅₃	1	16	yes	—
741	D₄	—	2	8	no	—
742	D₄	—	2	24	no	—
743	D₄	—	2	12	no	—
744	D₄	—	4	24	no	—
745	D₄	—	53	48	no	—
746	D₄	—	106	24	no	—
747	D₄	—	106	24	no	—
748	D₄	—	106	12	no	—
749	D₄	—	106	12	no	—
750	D₄	—	106	8	no	—
751	D₄	—	106	24	no	—
752	D₄	—	106	24	no	—
753	D₄	—	106	8	no	—
754	D₄	—	106	24	no	—
755	D₄	—	106	12	no	—
756	D₄	—	212	24	no	—
757	D₄	—	212	24	no	—
758	D₄	—	212	24	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	24	no	—
761	C₂×C₄	—	2	24	no	—
762	C₂×C₄	—	53	4	no	—
763	C₂×C₄	—	53	1	no	—
764	C₂×C₄	—	53	1	no	—
765	C₂×C₄	—	53	24	no	—
766	C₂×C₄	—	53	24	no	—
767	C₂×C₄	—	53	8	no	—
768	C₂×C₄	—	53	4	no	—
769	C₂×C₄	—	53	2	no	—
770	C₂×C₄	—	106	8	no	—
771	C₂×C₄	—	106	24	no	—
772	C₂×C₄	—	106	8	no	—
773	C₂×C₄	—	106	2	no	—
774	C₂×C₄	—	106	24	no	—
775	C₂×C₄	—	106	24	no	—
776	C₂×C₄	—	212	24	no	—
777	C₂×C₄	C₂×D₄×D₅₃	1	12	yes	—
778	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
779	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
780	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
781	C₂×C₄	C₂⁴×D₅₃	1	6	yes	—
782	C₂²	—	2	2	no	—
783	C₂²	—	2	4	no	—
784	C₂²	—	2	6	no	—
785	C₂²	—	2	8	no	—
786	C₂²	—	2	12	no	—
787	C₂²	—	4	12	no	—
788	C₂²	—	53	12	no	—
789	C₂²	—	106	12	no	—
790	C₂²	—	106	4	no	—
791	C₂²	—	106	6	no	—
792	C₂²	—	106	8	no	—
793	C₂²	—	106	12	no	—
794	C₂²	—	424	48	no	—
795	C₂²	—	424	24	no	—
796	C₂²	—	212	12	no	—
797	C₂²	—	212	12	no	—
798	C₂²	C₂²×D₄×D₅₃	1	2	yes	—
799	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
800	C₄	—	2	2	no	—
801	C₄	—	2	4	no	—
802	C₄	—	2	8	no	—
803	C₄	—	53	2	no	—
804	C₄	—	53	2	no	—
805	C₄	—	106	2	no	—
806	C₄	—	106	4	no	—
807	C₄	—	106	8	no	—
808	C₄	C₂²×D₄×D₅₃	1	12	yes	—
809	C₂	—	2	2	no	—
810	C₂	—	4	6	no	—
811	C₂	—	4	4	no	—
812	C₂	—	106	12	no	—
813	C₂	—	212	6	no	—
814	C₂	—	212	4	no	—
815	C₂	C₂³×D₄×D₅₃	1	1	yes	characteristic
816	C₂	#20289526	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₅₃×#3487	C₂
hypercenter	#3487	D₅₃
hypocenter	C₅₃	#62852
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #3487

Complements

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

N	H ≅ G/N	type
1. C₂×#16811460	C₂	semidirect
2. C₂²×#13133263	C₂	semidirect
3. #20288506	C₂	semidirect
4. #20288492	C₂	semidirect
5. #20288383	C₂	semidirect
6. #20288381	C₂	semidirect
7. #20288374	C₂	semidirect
8. #20288373	C₂	semidirect
9. #20288370	C₂	semidirect
10. #20288349	C₂	semidirect
11. #20288348	C₂	semidirect
12. #20288045	C₂	semidirect
13. #535×D₅₃	C₂	semidirect
14. #20287917	C₂	semidirect
15. C₅₃×#3487	C₂	semidirect
17. C₂×#13133265	C₂²	semidirect
18. C₂×#13133265	C₂²	semidirect
20. C₂×#13133263	C₂²	semidirect
21. C₂×#13133263	C₂²	semidirect
22. C₂×#13133263	C₂²	semidirect
23. C₂×#13133263	C₂²	semidirect
25. C₂²×#11719949	C₂²	semidirect
26. C₂²×#11719949	C₂²	semidirect
27. C₂²×#11719945	C₂²	semidirect
28. C₂×#41×D₅₃	C₂²	semidirect
29. C₂×#41×D₅₃	C₂²	semidirect
30. C₂³×D₂₁₂	C₂²	semidirect
31. C₂²×D₄×D₅₃	C₂²	semidirect
32. C₂²×D₄×D₅₃	C₂²	semidirect
33. #16811295	C₂²	semidirect
34. #16811292	C₂²	semidirect
35. #16811292	C₂²	semidirect
36. #16811285	C₂²	semidirect
37. #16811284	C₂²	semidirect
38. #16811280	C₂²	semidirect
39. #16811270	C₂²	semidirect
40. #16811269	C₂²	semidirect
41. #16811266	C₂²	semidirect
42. #16811264	C₂²	semidirect
43. D₄×D₂₁₂	C₂²	semidirect
44. #16811258	C₂²	semidirect
45. #16811257	C₂²	semidirect
46. #16811257	C₂²	semidirect
47. #16811203	C₂²	semidirect
48. #16811202	C₂²	semidirect
49. #16811196	C₂²	semidirect
50. #16811195	C₂²	semidirect
51. #16811192	C₂²	semidirect
52. #16811191	C₂²	semidirect
53. #16811190	C₂²	semidirect
54. #16811189	C₂²	semidirect
55. #16811189	C₂²	semidirect
56. #16811188	C₂²	semidirect
57. #16811187	C₂²	semidirect
58. #16811186	C₂²	semidirect
59. #16811184	C₂²	semidirect
60. #16811183	C₂²	semidirect
61. #16811170	C₂²	semidirect
62. #127×D₅₃	C₂²	semidirect
63. #124×D₅₃	C₂²	semidirect
64. #16811135	C₂²	semidirect
65. #16811134	C₂²	semidirect
66. #16811132	C₂²	semidirect
67. #16811130	C₂²	semidirect
68. #121×D₅₃	C₂²	semidirect
69. #120×D₅₃	C₂²	semidirect
70. #16811105	C₂²	semidirect
71. #16811101	C₂²	semidirect
72. #16811097	C₂²	semidirect
73. C₄×#11719949	C₂²	semidirect
74. #117×D₅₃	C₂²	semidirect
75. C₂×2₋¹⁺⁴×C₅₃	C₂²	semidirect
76. C₂²×#41×C₅₃	C₂²	semidirect
77. C₅₃×#550	C₂²	semidirect
78. C₅₃×#548	C₂²	semidirect
79. C₅₃×#535	C₂²	semidirect
80. C₅₃×#525	C₂²	semidirect
81. C₅₃×#519	C₂²	semidirect
91. C₂×#11719949	D₄	semidirect
95. C₂×#11719949	C₂³	semidirect
96. C₂×#11719949	C₂³	semidirect
97. C₂×#11719949	C₂³	semidirect
102. C₂×#11719945	C₂³	semidirect
103. C₂×#11719945	C₂³	semidirect
105. C₂×#11719947	C₂³	semidirect
109. C₂×Q₈×D₅₃	C₂³	semidirect
110. C₂×Q₈×D₅₃	C₂³	semidirect
116. C₂²×D₂₁₂	C₂³	semidirect
125. C₂×D₄×D₅₃	C₂³	semidirect
126. C₂×D₄×D₅₃	C₂³	semidirect
127. C₂×D₄×D₅₃	C₂³	semidirect
130. C₂²×C₄×D₅₃	C₂³	semidirect
131. #13133216	C₂³	semidirect
132. #13133214	C₂³	semidirect
133. #13133213	C₂³	semidirect
134. #13133213	C₂³	semidirect
135. #13133213	C₂³	semidirect
136. #13133206	C₂³	semidirect
137. #13133205	C₂³	semidirect
138. #13133204	C₂³	semidirect
139. #13133203	C₂³	semidirect
140. #13133203	C₂³	semidirect
141. #13133202	C₂³	semidirect
144. #13133199	C₂³	semidirect
146. #13133197	C₂³	semidirect
147. #13133196	C₂³	semidirect
148. #13133195	C₂³	semidirect
149. #13133194	C₂³	semidirect
150. #13133193	C₂³	semidirect
151. #13133192	C₂³	semidirect
152. #13133192	C₂³	semidirect
153. #13133192	C₂³	semidirect
154. #13133191	C₂³	semidirect
155. #13133191	C₂³	semidirect
156. #13133190	C₂³	semidirect
157. #13133190	C₂³	semidirect
158. #13133190	C₂³	semidirect
159. #13133189	C₂³	semidirect
160. #13133188	C₂³	semidirect
161. #13133188	C₂³	semidirect
162. #13133188	C₂³	semidirect
164. #13133187	C₂³	semidirect
165. #13133187	C₂³	semidirect
168. #13133185	C₂³	semidirect
169. #13133185	C₂³	semidirect
170. Q₈×Dic₅₃	C₂³	semidirect
171. C₄×D₂₁₂	C₂³	semidirect
172. C₄×D₂₁₂	C₂³	semidirect
173. #13133179	C₂³	semidirect
174. C₄×C₂²⋊D₅₃	C₂³	semidirect
175. C₄×C₂²⋊D₅₃	C₂³	semidirect
177. #13133175	C₂³	semidirect
178. #13133174	C₂³	semidirect
180. C₄⋊C₄×D₅₃	C₂³	semidirect
182. C₂²⋊C₄×D₅₃	C₂³	semidirect
183. C₄²×D₅₃	C₂³	semidirect
188. C₂×#41×C₅₃	C₂³	semidirect
190. C₂²×Q₈×C₅₃	C₂³	semidirect
193. #127×C₅₃	C₂³	semidirect
194. #124×C₅₃	C₂³	semidirect
196. C₂²⋊Q₈×C₅₃	C₂³	semidirect
197. #121×C₅₃	C₂³	semidirect
198. #121×C₅₃	C₂³	semidirect
200. C₄×Q₈×C₅₃	C₂³	semidirect
201. C₄×D₄×C₅₃	C₂³	semidirect
214. C₂×Q₈×C₅₃	C₂×D₄	semidirect
244. #11719949	C₂×D₄	semidirect
245. #11719949	C₂×D₄	semidirect
266. C₂×D₂₁₂	C₂×D₄	semidirect
275. C₂×C₄×D₅₃	C₂×D₄	semidirect
410. #3487	D₅₃	semidirect
427. C₂×2₋¹⁺⁴	C₂×D₅₃	semidirect
439. C₂²×#41	C₂×D₅₃	semidirect
446. #550	C₂×D₅₃	semidirect
450. #548	C₂×D₅₃	semidirect
471. #535	C₂×D₅₃	semidirect
481. #525	C₂×D₅₃	semidirect
486. #519	C₂×D₅₃	semidirect
490. C₅₃	#62852	semidirect
521. C₂×#41	C₂²×D₅₃	semidirect
526. C₂²×Q₈	C₂²×D₅₃	semidirect
554. #127	C₂²×D₅₃	semidirect
560. #124	C₂²×D₅₃	semidirect
572. C₂²⋊Q₈	C₂²×D₅₃	semidirect
585. #121	C₂²×D₅₃	semidirect
586. #121	C₂²×D₅₃	semidirect
596. C₄×Q₈	C₂²×D₅₃	semidirect
602. C₄×D₄	C₂²×D₅₃	semidirect
643. C₂×Q₈	D₄×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16811460	2
C₂²×#13133263	2
#20288506	2
#20288492	2
#20288383	2
#20288381	2
#20288374	2
#20288373	2
#20288370	2
#20288349	2
#20288348	2
#20288045	2
#535×D₅₃	2
#20287917	2
C₅₃×#3487	2
#62852	53