Subgroups — C₅₃×#63032 #27270544

Order 13568.

6420 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3563	C₂	1	12	yes	maximal, complemented
2	C₅₃×#3556	C₂	1	3	yes	maximal, complemented
3	C₅₃×#3555	C₂	1	6	yes	maximal, complemented
4	C₅₃×#3552	C₂	1	6	yes	maximal, complemented
5	C₅₃×#3523	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3523	C₂	1	6	yes	maximal, complemented
7	C₅₃×#3516	C₂	1	4	yes	maximal, complemented
8	C₅₃×#3515	C₂	1	6	yes	maximal, complemented
9	C₅₃×#3509	C₂	1	3	yes	maximal, complemented
10	C₅₃×#3503	C₂	1	3	yes	maximal, complemented
11	C₅₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3502	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3482	C₂	1	3	yes	maximal, complemented
14	C₅₃×#3482	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3482	C₂	1	1	yes	maximal, characteristic, complemented
16	Q₈×#41×C₅₃	C₂	1	2	yes	maximal, complemented
17	C₂×C₅₃×#557	C₂	1	2	yes	maximal, complemented
18	C₅₃×#564	C₂²	1	12	yes	—
19	C₅₃×#563	C₂²	1	24	yes	—
20	Q₈²×C₅₃	C₂²	1	2	yes	—
21	Q₈²×C₅₃	C₂²	1	6	yes	—
22	C₅₃×#557	C₂²	1	1	yes	characteristic
23	C₅₃×#557	C₂²	1	4	yes	—
24	C₅₃×#557	C₂²	1	2	yes	—
25	C₅₃×#557	C₂²	1	6	yes	—
26	C₅₃×#557	C₂²	1	6	yes	—
27	C₅₃×#557	C₂²	1	12	yes	—
28	C₅₃×#557	C₂²	1	6	yes	—
29	C₅₃×#557	C₂²	1	1	yes	characteristic
30	C₅₃×#557	C₂²	1	3	yes	—
31	C₅₃×#557	C₂²	1	6	yes	—
32	C₅₃×#557	C₂²	1	12	yes	—
33	C₅₃×#557	C₂²	1	6	yes	—
34	C₅₃×#557	C₂²	1	6	yes	—
35	C₅₃×#556	C₂²	1	3	yes	—
36	C₅₃×#556	C₂²	1	3	yes	—
37	C₅₃×#556	C₂²	1	6	yes	—
38	C₅₃×#556	C₂²	1	3	yes	—
39	C₅₃×#556	C₂²	1	6	yes	—
40	C₅₃×#556	C₂²	1	12	yes	—
41	C₅₃×#554	C₂²	1	6	yes	—
42	C₅₃×#554	C₂²	1	12	yes	—
43	C₅₃×#554	C₂²	1	6	yes	—
44	C₅₃×#554	C₂²	1	12	yes	—
45	C₅₃×#553	C₂²	1	12	yes	—
46	C₅₃×#552	C₂²	1	6	yes	—
47	C₅₃×#552	C₂²	1	12	yes	—
48	C₅₃×#552	C₂²	1	6	yes	—
49	C₅₃×#552	C₂²	1	6	yes	—
50	C₅₃×#552	C₂²	1	12	yes	—
51	C₅₃×#552	C₂²	1	12	yes	—
52	C₅₃×#552	C₂²	1	24	yes	—
53	C₅₃×#552	C₂²	1	12	yes	—
54	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
55	D₄×Q₈×C₅₃	C₂²	1	4	yes	—
56	D₄×Q₈×C₅₃	C₂²	1	3	yes	—
57	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
58	D₄×Q₈×C₅₃	C₂²	1	6	yes	—
59	D₄×Q₈×C₅₃	C₂²	1	12	yes	—
60	C₅₃×#548	C₂²	1	2	yes	—
61	C₅₃×#548	C₂²	1	2	yes	—
62	C₅₃×#548	C₂²	1	6	yes	—
63	C₅₃×#547	C₂²	1	1	yes	characteristic
64	C₅₃×#547	C₂²	1	3	yes	—
65	C₅₃×#547	C₂²	1	6	yes	—
66	C₅₃×#547	C₂²	1	3	yes	—
67	C₅₃×#544	C₂²	1	12	yes	—
68	C₅₃×#544	C₂²	1	6	yes	—
69	C₅₃×#544	C₂²	1	12	yes	—
70	C₅₃×#544	C₂²	1	6	yes	—
71	C₅₃×#542	C₂²	1	12	yes	—
72	C₅₃×#541	C₂²	1	12	yes	—
73	C₅₃×#541	C₂²	1	12	yes	—
74	C₅₃×#541	C₂²	1	12	yes	—
75	C₅₃×#541	C₂²	1	12	yes	—
76	C₅₃×#541	C₂²	1	12	yes	—
77	C₅₃×#541	C₂²	1	24	yes	—
78	C₅₃×#539	C₂²	1	24	yes	—
79	C₅₃×#536	C₂²	1	6	yes	—
80	C₅₃×#533	C₂²	1	6	yes	—
81	C₅₃×#533	C₂²	1	12	yes	—
82	C₅₃×#533	C₂²	1	6	yes	—
83	C₅₃×#533	C₂²	1	3	yes	—
84	C₅₃×#533	C₂²	1	3	yes	—
85	C₅₃×#533	C₂²	1	3	yes	—
86	C₅₃×#533	C₂²	1	6	yes	—
87	C₅₃×#533	C₂²	1	6	yes	—
88	C₂×C₄⋊Q₈×C₅₃	C₂²	1	6	yes	—
89	C₂×C₄⋊Q₈×C₅₃	C₂²	1	3	yes	—
90	C₅₃×#529	C₂²	1	6	yes	—
91	C₅₃×#529	C₂²	1	12	yes	—
92	C₅₃×#529	C₂²	1	6	yes	—
93	C₅₃×#529	C₂²	1	6	yes	—
94	C₅₃×#529	C₂²	1	12	yes	—
95	C₂×#125×C₅₃	C₂²	1	12	yes	—
96	C₅₃×#520	C₂²	1	6	yes	—
97	C₅₃×#520	C₂²	1	2	yes	—
98	C₅₃×#519	C₂²	1	4	yes	—
99	C₅₃×#519	C₂²	1	6	yes	—
100	C₄×#41×C₅₃	C₂²	1	6	yes	—
101	C₄×#41×C₅₃	C₂²	1	3	yes	—
102	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
103	C₄×#41×C₅₃	C₂²	1	3	yes	—
104	C₂×C₄×Q₈×C₅₃	C₂²	1	4	yes	—
105	C₂×C₄×Q₈×C₅₃	C₂²	1	6	yes	—
106	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	—
107	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	—
108	C₂×#41×C₅₃	C₂³	1	2	yes	—
109	C₂×#41×C₅₃	C₂³	1	3	yes	—
110	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
111	C₂×#41×C₅₃	C₂³	1	3	yes	—
112	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
113	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
114	C₂²×Q₈×C₅₃	C₂³	1	6	yes	—
115	C₂²×Q₈×C₅₃	C₂³	1	6	yes	—
116	C₄⋊Q₈×C₅₃	C₂³	1	3	yes	—
117	C₄⋊Q₈×C₅₃	C₂³	1	6	yes	—
118	C₄⋊Q₈×C₅₃	C₂³	1	3	yes	—
119	C₄⋊Q₈×C₅₃	C₂³	1	6	yes	—
120	C₄⋊Q₈×C₅₃	C₂³	1	12	yes	—
121	C₄⋊Q₈×C₅₃	C₂³	1	6	yes	—
122	C₄⋊Q₈×C₅₃	C₂³	1	12	yes	—
123	C₄⋊Q₈×C₅₃	C₂³	1	12	yes	—
124	C₄⋊Q₈×C₅₃	C₂³	1	3	yes	—
125	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
126	C₄⋊Q₈×C₅₃	C₂³	1	3	yes	—
127	C₄⋊Q₈×C₅₃	C₂³	1	3	yes	—
128	C₄⋊Q₈×C₅₃	C₂³	1	6	yes	—
129	C₄⋊Q₈×C₅₃	C₂³	1	12	yes	—
130	C₄⋊Q₈×C₅₃	C₂³	1	12	yes	—
131	C₄⋊Q₈×C₅₃	C₂³	1	6	yes	—
132	C₄⋊Q₈×C₅₃	C₂³	1	24	yes	—
133	#126×C₅₃	C₂³	1	24	yes	—
134	#126×C₅₃	C₂³	1	12	yes	—
135	#126×C₅₃	C₂³	1	12	yes	—
136	#126×C₅₃	C₂³	1	12	yes	—
137	#126×C₅₃	C₂³	1	12	yes	—
138	#126×C₅₃	C₂³	1	12	yes	—
139	#126×C₅₃	C₂³	1	24	yes	—
140	#126×C₅₃	C₂³	1	24	yes	—
141	#125×C₅₃	C₂³	1	6	yes	—
142	#125×C₅₃	C₂³	1	12	yes	—
143	#125×C₅₃	C₂³	1	24	yes	—
144	#125×C₅₃	C₂³	1	24	yes	—
145	#125×C₅₃	C₂³	1	12	yes	—
146	#125×C₅₃	C₂³	1	12	yes	—
147	#125×C₅₃	C₂³	1	6	yes	—
148	#125×C₅₃	C₂³	1	12	yes	—
149	#125×C₅₃	C₂³	1	6	yes	—
150	#125×C₅₃	C₂³	1	12	yes	—
151	#125×C₅₃	C₂³	1	12	yes	—
152	#125×C₅₃	C₂³	1	6	yes	—
153	#125×C₅₃	C₂³	1	24	yes	—
154	#125×C₅₃	C₂³	1	12	yes	—
155	#125×C₅₃	C₂³	1	6	yes	—
156	#125×C₅₃	C₂³	1	6	yes	—
157	#125×C₅₃	C₂³	1	24	yes	—
158	#125×C₅₃	C₂³	1	24	yes	—
159	#125×C₅₃	C₂³	1	24	yes	—
160	#124×C₅₃	C₂³	1	6	yes	—
161	#124×C₅₃	C₂³	1	6	yes	—
162	#124×C₅₃	C₂³	1	6	yes	—
163	#124×C₅₃	C₂³	1	12	yes	—
164	#123×C₅₃	C₂³	1	12	yes	—
165	#123×C₅₃	C₂³	1	4	yes	—
166	#123×C₅₃	C₂³	1	12	yes	—
167	#123×C₅₃	C₂³	1	12	yes	—
168	#123×C₅₃	C₂³	1	12	yes	—
169	#123×C₅₃	C₂³	1	24	yes	—
170	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	—
171	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	—
172	C₂²⋊Q₈×C₅₃	C₂³	1	12	yes	—
173	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	—
174	C₂²⋊Q₈×C₅₃	C₂³	1	12	yes	—
175	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	—
176	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
177	C₂²⋊Q₈×C₅₃	C₂³	1	12	yes	—
178	C₂²⋊Q₈×C₅₃	C₂³	1	12	yes	—
179	C₂²⋊Q₈×C₅₃	C₂³	1	24	yes	—
180	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	—
181	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	—
182	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	—
183	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	—
184	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	—
185	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	—
186	C₂²⋊Q₈×C₅₃	C₂³	1	12	yes	—
187	C₂²⋊Q₈×C₅₃	C₂³	1	12	yes	—
188	C₂²⋊Q₈×C₅₃	C₂³	1	24	yes	—
189	C₂²⋊Q₈×C₅₃	C₂³	1	24	yes	—
190	#121×C₅₃	C₂³	1	2	yes	—
191	#121×C₅₃	C₂³	1	6	yes	—
192	#121×C₅₃	C₂³	1	12	yes	—
193	#121×C₅₃	C₂³	1	6	yes	—
194	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
195	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
196	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
197	C₄×Q₈×C₅₃	C₂³	1	3	yes	—
198	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
199	C₄×Q₈×C₅₃	C₂³	1	6	yes	—
200	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
201	C₄×Q₈×C₅₃	C₂³	1	6	yes	—
202	C₄×Q₈×C₅₃	C₂³	1	6	yes	—
203	C₄×Q₈×C₅₃	C₂³	1	6	yes	—
204	C₄×Q₈×C₅₃	C₂³	1	12	yes	—
205	C₄×Q₈×C₅₃	C₂³	1	12	yes	—
206	C₄×Q₈×C₅₃	C₂³	1	6	yes	—
207	C₄×Q₈×C₅₃	C₂³	1	6	yes	—
208	C₄×Q₈×C₅₃	C₂³	1	6	yes	—
209	C₄×Q₈×C₅₃	C₂³	1	12	yes	—
210	C₄×Q₈×C₅₃	C₂³	1	12	yes	—
211	C₄×Q₈×C₅₃	C₂³	1	3	yes	—
212	C₄×Q₈×C₅₃	C₂³	1	6	yes	—
213	C₄×Q₈×C₅₃	C₂³	1	3	yes	—
214	C₄×Q₈×C₅₃	C₂³	1	3	yes	—
215	C₄×Q₈×C₅₃	C₂³	1	6	yes	—
216	C₄×Q₈×C₅₃	C₂³	1	12	yes	—
217	C₄×Q₈×C₅₃	C₂³	1	12	yes	—
218	C₄×Q₈×C₅₃	C₂³	1	12	yes	—
219	C₄×Q₈×C₅₃	C₂³	1	12	yes	—
220	C₄×Q₈×C₅₃	C₂³	1	12	yes	—
221	C₄×Q₈×C₅₃	C₂³	1	12	yes	—
222	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
223	C₄×D₄×C₅₃	C₂³	1	3	yes	—
224	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
225	C₄×D₄×C₅₃	C₂³	1	6	yes	—
226	C₄×D₄×C₅₃	C₂³	1	3	yes	—
227	C₄×D₄×C₅₃	C₂³	1	3	yes	—
228	C₄×D₄×C₅₃	C₂³	1	6	yes	—
229	C₄×D₄×C₅₃	C₂³	1	3	yes	—
230	C₄×D₄×C₅₃	C₂³	1	6	yes	—
231	C₄×D₄×C₅₃	C₂³	1	6	yes	—
232	C₄×D₄×C₅₃	C₂³	1	6	yes	—
233	C₄×D₄×C₅₃	C₂³	1	12	yes	—
234	C₄×D₄×C₅₃	C₂³	1	12	yes	—
235	C₄×D₄×C₅₃	C₂³	1	24	yes	—
236	C₄×D₄×C₅₃	C₂³	1	12	yes	—
237	#117×C₅₃	C₂³	1	3	yes	—
238	#117×C₅₃	C₂³	1	12	yes	—
239	#117×C₅₃	C₂³	1	6	yes	—
240	#117×C₅₃	C₂³	1	6	yes	—
241	#117×C₅₃	C₂³	1	6	yes	—
242	#117×C₅₃	C₂³	1	3	yes	—
243	#117×C₅₃	C₂³	1	3	yes	—
244	#117×C₅₃	C₂³	1	6	yes	—
245	#117×C₅₃	C₂³	1	12	yes	—
246	#117×C₅₃	C₂³	1	24	yes	—
247	#117×C₅₃	C₂³	1	12	yes	—
248	#117×C₅₃	C₂³	1	6	yes	—
249	#117×C₅₃	C₂³	1	6	yes	—
250	#117×C₅₃	C₂³	1	12	yes	—
251	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
252	C₂×C₄⋊C₄×C₅₃	C₂³	1	12	yes	—
253	C₂×C₄⋊C₄×C₅₃	C₂³	1	6	yes	—
254	C₂×C₄⋊C₄×C₅₃	C₂³	1	12	yes	—
255	C₂×C₄⋊C₄×C₅₃	C₂³	1	6	yes	—
256	C₂×C₄⋊C₄×C₅₃	C₂³	1	12	yes	—
257	C₂×C₄⋊C₄×C₅₃	C₂³	1	6	yes	—
258	C₂×C₄⋊C₄×C₅₃	C₂³	1	6	yes	—
259	C₂×C₄²×C₅₃	C₂³	1	12	yes	—
260	C₂×C₄²×C₅₃	C₂³	1	6	yes	—
261	C₂×C₄²×C₅₃	C₂³	1	6	yes	—
262	C₂×C₄²×C₅₃	C₂³	1	3	yes	—
263	#41×C₅₃	—	2	4	no	—
264	#41×C₅₃	—	2	8	no	—
265	#41×C₅₃	—	2	12	no	—
266	#41×C₅₃	—	4	6	no	—
267	C₂×Q₈×C₅₃	—	2	8	no	—
268	C₂×Q₈×C₅₃	—	2	8	no	—
269	C₂×Q₈×C₅₃	—	4	12	no	—
270	C₂×Q₈×C₅₃	—	4	12	no	—
271	C₂×Q₈×C₅₃	C₂⁴	1	6	yes	—
272	C₂×Q₈×C₅₃	C₂⁴	1	6	yes	—
273	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
274	C₂×Q₈×C₅₃	C₂⁴	1	3	yes	—
275	C₂×Q₈×C₅₃	C₂⁴	1	6	yes	—
276	C₂×Q₈×C₅₃	C₂⁴	1	3	yes	—
277	C₂×Q₈×C₅₃	C₂⁴	1	12	yes	—
278	C₂×Q₈×C₅₃	C₂⁴	1	12	yes	—
279	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
280	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
281	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
282	C₂×D₄×C₅₃	C₂⁴	1	3	yes	—
283	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
284	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
285	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
287	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
288	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
291	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
292	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
293	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
294	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
295	C₂²×C₄×C₅₃	C₂⁴	1	12	yes	—
296	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
297	C₂²×C₄×C₅₃	C₂⁴	1	12	yes	—
298	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
299	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
300	C₄⋊C₄×C₅₃	C₂⁴	1	3	yes	—
301	C₄⋊C₄×C₅₃	C₂⁴	1	12	yes	—
302	C₄⋊C₄×C₅₃	C₂⁴	1	3	yes	—
303	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
304	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
305	C₄⋊C₄×C₅₃	C₂⁴	1	12	yes	—
306	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
307	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
308	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
309	C₄⋊C₄×C₅₃	C₂⁴	1	12	yes	—
310	C₄⋊C₄×C₅₃	C₂⁴	1	24	yes	—
311	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
312	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
313	C₄⋊C₄×C₅₃	C₂⁴	1	12	yes	—
314	C₄⋊C₄×C₅₃	C₂⁴	1	12	yes	—
315	C₄⋊C₄×C₅₃	C₂⁴	1	24	yes	—
316	C₄⋊C₄×C₅₃	C₂⁴	1	12	yes	—
317	C₄⋊C₄×C₅₃	C₂⁴	1	12	yes	—
318	C₄⋊C₄×C₅₃	C₂⁴	1	3	yes	—
319	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
320	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
321	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
322	C₄⋊C₄×C₅₃	C₂⁴	1	3	yes	—
323	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
324	C₄⋊C₄×C₅₃	C₂⁴	1	12	yes	—
325	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
326	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
327	C₄⋊C₄×C₅₃	C₂⁴	1	12	yes	—
328	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
329	C₄⋊C₄×C₅₃	C₂⁴	1	24	yes	—
330	C₄⋊C₄×C₅₃	C₂⁴	1	12	yes	—
331	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
332	C₄⋊C₄×C₅₃	C₂⁴	1	12	yes	—
333	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
334	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
335	C₂²⋊C₄×C₅₃	C₂⁴	1	12	yes	—
336	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
337	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
338	C₂²⋊C₄×C₅₃	C₂⁴	1	12	yes	—
339	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
340	C₂²⋊C₄×C₅₃	C₂⁴	1	12	yes	—
341	C₂²⋊C₄×C₅₃	C₂⁴	1	12	yes	—
342	C₂²⋊C₄×C₅₃	C₂⁴	1	12	yes	—
343	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
344	C₂²⋊C₄×C₅₃	C₂⁴	1	12	yes	—
345	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
346	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
347	C₄²×C₅₃	C₂⁴	1	3	yes	—
348	C₄²×C₅₃	C₂⁴	1	3	yes	—
349	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
350	C₄²×C₅₃	C₂⁴	1	6	yes	—
351	C₄²×C₅₃	C₂⁴	1	3	yes	—
352	C₄²×C₅₃	C₂⁴	1	12	yes	—
353	C₄²×C₅₃	C₂⁴	1	6	yes	—
354	C₄²×C₅₃	C₂⁴	1	6	yes	—
355	C₄²×C₅₃	C₂⁴	1	12	yes	—
356	C₄²×C₅₃	C₂⁴	1	6	yes	—
357	C₄²×C₅₃	C₂⁴	1	6	yes	—
358	C₄²×C₅₃	C₂⁴	1	6	yes	—
359	C₄²×C₅₃	C₂⁴	1	12	yes	—
360	C₄²×C₅₃	C₂⁴	1	24	yes	—
361	C₂³×C₅₃	C₂⁵	1	2	yes	—
362	C₂³×C₅₃	C₂⁵	1	3	yes	—
363	C₂³×C₅₃	C₂⁵	1	2	yes	—
364	Q₈×C₅₃	—	2	12	no	—
365	Q₈×C₅₃	—	2	12	no	—
366	Q₈×C₅₃	—	2	4	no	—
367	Q₈×C₅₃	—	2	6	no	—
368	Q₈×C₅₃	—	2	12	no	—
369	Q₈×C₅₃	—	2	6	no	—
370	Q₈×C₅₃	—	4	12	no	—
371	Q₈×C₅₃	—	4	12	no	—
372	Q₈×C₅₃	2₋¹⁺⁴	1	4	yes	—
373	D₄×C₅₃	—	2	12	no	—
374	D₄×C₅₃	—	2	8	no	—
375	D₄×C₅₃	—	2	6	no	—
376	D₄×C₅₃	—	2	2	no	—
377	D₄×C₅₃	—	4	6	no	—
378	D₄×C₅₃	2₋¹⁺⁴	1	4	yes	—
379	C₂×C₄×C₅₃	—	2	8	no	—
380	C₂×C₄×C₅₃	—	2	12	no	—
381	C₂×C₄×C₅₃	—	2	12	no	—
382	C₂×C₄×C₅₃	—	2	12	no	—
383	C₂×C₄×C₅₃	—	2	6	no	—
384	C₂×C₄×C₅₃	—	2	4	no	—
385	C₂×C₄×C₅₃	—	2	6	no	—
386	C₂×C₄×C₅₃	—	2	4	no	—
387	C₂×C₄×C₅₃	—	2	6	no	—
388	C₂×C₄×C₅₃	—	4	12	no	—
389	C₂×C₄×C₅₃	—	4	12	no	—
390	C₂×C₄×C₅₃	—	4	6	no	—
391	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
392	C₂×C₄×C₅₃	C₂⁵	1	3	yes	—
393	C₂×C₄×C₅₃	C₂⁵	1	12	yes	—
394	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
395	C₂×C₄×C₅₃	C₂⁵	1	3	yes	—
396	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
397	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
398	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
399	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
400	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
401	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
402	C₂×C₄×C₅₃	C₂⁵	1	3	yes	—
403	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
404	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
405	#63032	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
406	C₂²×C₅₃	—	2	2	no	—
407	C₂²×C₅₃	—	2	2	no	—
408	C₂²×C₅₃	—	2	2	no	—
409	C₂²×C₅₃	—	2	2	no	—
410	C₂²×C₅₃	—	2	3	no	—
411	C₂²×C₅₃	—	2	3	no	—
412	C₂²×C₅₃	—	2	3	no	—
413	C₂²×C₅₃	—	2	2	no	—
414	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	4	yes	—
415	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
416	C₄×C₅₃	—	2	2	no	—
417	C₄×C₅₃	—	2	3	no	—
418	C₄×C₅₃	—	2	1	no	—
419	C₄×C₅₃	—	2	4	no	—
420	C₄×C₅₃	—	2	6	no	—
421	C₄×C₅₃	—	2	6	no	—
422	C₄×C₅₃	—	2	6	no	—
423	C₄×C₅₃	—	2	3	no	—
424	C₄×C₅₃	—	2	2	no	—
425	C₄×C₅₃	—	2	6	no	—
426	C₄×C₅₃	—	2	12	no	—
427	C₄×C₅₃	C₂×2₋¹⁺⁴	1	6	yes	—
428	C₄×C₅₃	C₂×2₋¹⁺⁴	1	2	yes	—
429	C₄×C₅₃	#585	1	2	yes	—
430	#3563	C₂×C₅₃	1	12	yes	complemented
431	#3556	C₂×C₅₃	1	3	yes	complemented
432	#3555	C₂×C₅₃	1	6	yes	complemented
433	#3552	C₂×C₅₃	1	6	yes	complemented
434	#3523	C₂×C₅₃	1	2	yes	complemented
435	#3523	C₂×C₅₃	1	6	yes	complemented
436	#3516	C₂×C₅₃	1	4	yes	complemented
437	#3515	C₂×C₅₃	1	6	yes	complemented
438	#3509	C₂×C₅₃	1	3	yes	complemented
439	#3503	C₂×C₅₃	1	3	yes	complemented
440	#3503	C₂×C₅₃	1	1	yes	characteristic, complemented
441	#3502	C₂×C₅₃	1	2	yes	complemented
442	#3482	C₂×C₅₃	1	3	yes	complemented
443	#3482	C₂×C₅₃	1	1	yes	characteristic, complemented
444	#3482	C₂×C₅₃	1	1	yes	characteristic, complemented
445	Q₈×#41	C₂×C₅₃	1	2	yes	complemented
446	C₂×#557	C₂×C₅₃	1	2	yes	complemented
447	C₂×C₅₃	—	2	4	no	—
448	C₂×C₅₃	—	4	2	no	—
449	C₂×C₅₃	—	4	3	no	—
450	C₂×C₅₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
451	C₂×C₅₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
452	C₂×C₅₃	C₂×#585	1	1	yes	characteristic
453	#564	C₂²×C₅₃	1	12	yes	—
454	#563	C₂²×C₅₃	1	24	yes	—
455	Q₈²	C₂²×C₅₃	1	2	yes	—
456	Q₈²	C₂²×C₅₃	1	6	yes	—
457	#557	C₂²×C₅₃	1	1	yes	characteristic
458	#557	C₂²×C₅₃	1	4	yes	—
459	#557	C₂²×C₅₃	1	2	yes	—
460	#557	C₂²×C₅₃	1	6	yes	—
461	#557	C₂²×C₅₃	1	6	yes	—
462	#557	C₂²×C₅₃	1	12	yes	—
463	#557	C₂²×C₅₃	1	6	yes	—
464	#557	C₂²×C₅₃	1	1	yes	characteristic
465	#557	C₂²×C₅₃	1	3	yes	—
466	#557	C₂²×C₅₃	1	6	yes	—
467	#557	C₂²×C₅₃	1	12	yes	—
468	#557	C₂²×C₅₃	1	6	yes	—
469	#557	C₂²×C₅₃	1	6	yes	—
470	#556	C₂²×C₅₃	1	3	yes	—
471	#556	C₂²×C₅₃	1	3	yes	—
472	#556	C₂²×C₅₃	1	6	yes	—
473	#556	C₂²×C₅₃	1	3	yes	—
474	#556	C₂²×C₅₃	1	6	yes	—
475	#556	C₂²×C₅₃	1	12	yes	—
476	#554	C₂²×C₅₃	1	6	yes	—
477	#554	C₂²×C₅₃	1	12	yes	—
478	#554	C₂²×C₅₃	1	6	yes	—
479	#554	C₂²×C₅₃	1	12	yes	—
480	#553	C₂²×C₅₃	1	12	yes	—
481	#552	C₂²×C₅₃	1	6	yes	—
482	#552	C₂²×C₅₃	1	12	yes	—
483	#552	C₂²×C₅₃	1	6	yes	—
484	#552	C₂²×C₅₃	1	6	yes	—
485	#552	C₂²×C₅₃	1	12	yes	—
486	#552	C₂²×C₅₃	1	12	yes	—
487	#552	C₂²×C₅₃	1	24	yes	—
488	#552	C₂²×C₅₃	1	12	yes	—
489	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
490	D₄×Q₈	C₂²×C₅₃	1	4	yes	—
491	D₄×Q₈	C₂²×C₅₃	1	3	yes	—
492	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
493	D₄×Q₈	C₂²×C₅₃	1	6	yes	—
494	D₄×Q₈	C₂²×C₅₃	1	12	yes	—
495	#548	C₂²×C₅₃	1	2	yes	—
496	#548	C₂²×C₅₃	1	2	yes	—
497	#548	C₂²×C₅₃	1	6	yes	—
498	#547	C₂²×C₅₃	1	1	yes	characteristic
499	#547	C₂²×C₅₃	1	3	yes	—
500	#547	C₂²×C₅₃	1	6	yes	—
501	#547	C₂²×C₅₃	1	3	yes	—
502	#544	C₂²×C₅₃	1	12	yes	—
503	#544	C₂²×C₅₃	1	6	yes	—
504	#544	C₂²×C₅₃	1	12	yes	—
505	#544	C₂²×C₅₃	1	6	yes	—
506	#542	C₂²×C₅₃	1	12	yes	—
507	#541	C₂²×C₅₃	1	12	yes	—
508	#541	C₂²×C₅₃	1	12	yes	—
509	#541	C₂²×C₅₃	1	12	yes	—
510	#541	C₂²×C₅₃	1	12	yes	—
511	#541	C₂²×C₅₃	1	12	yes	—
512	#541	C₂²×C₅₃	1	24	yes	—
513	#539	C₂²×C₅₃	1	24	yes	—
514	#536	C₂²×C₅₃	1	6	yes	—
515	#533	C₂²×C₅₃	1	6	yes	—
516	#533	C₂²×C₅₃	1	12	yes	—
517	#533	C₂²×C₅₃	1	6	yes	—
518	#533	C₂²×C₅₃	1	3	yes	—
519	#533	C₂²×C₅₃	1	3	yes	—
520	#533	C₂²×C₅₃	1	3	yes	—
521	#533	C₂²×C₅₃	1	6	yes	—
522	#533	C₂²×C₅₃	1	6	yes	—
523	C₂×C₄⋊Q₈	C₂²×C₅₃	1	6	yes	—
524	C₂×C₄⋊Q₈	C₂²×C₅₃	1	3	yes	—
525	#529	C₂²×C₅₃	1	6	yes	—
526	#529	C₂²×C₅₃	1	12	yes	—
527	#529	C₂²×C₅₃	1	6	yes	—
528	#529	C₂²×C₅₃	1	6	yes	—
529	#529	C₂²×C₅₃	1	12	yes	—
530	C₂×#125	C₂²×C₅₃	1	12	yes	—
531	#520	C₂²×C₅₃	1	6	yes	—
532	#520	C₂²×C₅₃	1	2	yes	—
533	#519	C₂²×C₅₃	1	4	yes	—
534	#519	C₂²×C₅₃	1	6	yes	—
535	C₄×#41	C₂²×C₅₃	1	6	yes	—
536	C₄×#41	C₂²×C₅₃	1	3	yes	—
537	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
538	C₄×#41	C₂²×C₅₃	1	3	yes	—
539	C₂×C₄×Q₈	C₂²×C₅₃	1	4	yes	—
540	C₂×C₄×Q₈	C₂²×C₅₃	1	6	yes	—
541	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	—
542	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	—
543	C₅₃	#63032	1	1	yes	characteristic, direct product factor, Sylow
544	C₂×#41	C₂³×C₅₃	1	2	yes	—
545	C₂×#41	C₂³×C₅₃	1	3	yes	—
546	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
547	C₂×#41	C₂³×C₅₃	1	3	yes	—
548	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
549	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
550	C₂²×Q₈	C₂³×C₅₃	1	6	yes	—
551	C₂²×Q₈	C₂³×C₅₃	1	6	yes	—
552	C₄⋊Q₈	C₂³×C₅₃	1	3	yes	—
553	C₄⋊Q₈	C₂³×C₅₃	1	6	yes	—
554	C₄⋊Q₈	C₂³×C₅₃	1	3	yes	—
555	C₄⋊Q₈	C₂³×C₅₃	1	6	yes	—
556	C₄⋊Q₈	C₂³×C₅₃	1	12	yes	—
557	C₄⋊Q₈	C₂³×C₅₃	1	6	yes	—
558	C₄⋊Q₈	C₂³×C₅₃	1	12	yes	—
559	C₄⋊Q₈	C₂³×C₅₃	1	12	yes	—
560	C₄⋊Q₈	C₂³×C₅₃	1	3	yes	—
561	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
562	C₄⋊Q₈	C₂³×C₅₃	1	3	yes	—
563	C₄⋊Q₈	C₂³×C₅₃	1	3	yes	—
564	C₄⋊Q₈	C₂³×C₅₃	1	6	yes	—
565	C₄⋊Q₈	C₂³×C₅₃	1	12	yes	—
566	C₄⋊Q₈	C₂³×C₅₃	1	12	yes	—
567	C₄⋊Q₈	C₂³×C₅₃	1	6	yes	—
568	C₄⋊Q₈	C₂³×C₅₃	1	24	yes	—
569	#126	C₂³×C₅₃	1	24	yes	—
570	#126	C₂³×C₅₃	1	12	yes	—
571	#126	C₂³×C₅₃	1	12	yes	—
572	#126	C₂³×C₅₃	1	12	yes	—
573	#126	C₂³×C₅₃	1	12	yes	—
574	#126	C₂³×C₅₃	1	12	yes	—
575	#126	C₂³×C₅₃	1	24	yes	—
576	#126	C₂³×C₅₃	1	24	yes	—
577	#125	C₂³×C₅₃	1	6	yes	—
578	#125	C₂³×C₅₃	1	12	yes	—
579	#125	C₂³×C₅₃	1	24	yes	—
580	#125	C₂³×C₅₃	1	24	yes	—
581	#125	C₂³×C₅₃	1	12	yes	—
582	#125	C₂³×C₅₃	1	12	yes	—
583	#125	C₂³×C₅₃	1	6	yes	—
584	#125	C₂³×C₅₃	1	12	yes	—
585	#125	C₂³×C₅₃	1	6	yes	—
586	#125	C₂³×C₅₃	1	12	yes	—
587	#125	C₂³×C₅₃	1	12	yes	—
588	#125	C₂³×C₅₃	1	6	yes	—
589	#125	C₂³×C₅₃	1	24	yes	—
590	#125	C₂³×C₅₃	1	12	yes	—
591	#125	C₂³×C₅₃	1	6	yes	—
592	#125	C₂³×C₅₃	1	6	yes	—
593	#125	C₂³×C₅₃	1	24	yes	—
594	#125	C₂³×C₅₃	1	24	yes	—
595	#125	C₂³×C₅₃	1	24	yes	—
596	#124	C₂³×C₅₃	1	6	yes	—
597	#124	C₂³×C₅₃	1	6	yes	—
598	#124	C₂³×C₅₃	1	6	yes	—
599	#124	C₂³×C₅₃	1	12	yes	—
600	#123	C₂³×C₅₃	1	12	yes	—
601	#123	C₂³×C₅₃	1	4	yes	—
602	#123	C₂³×C₅₃	1	12	yes	—
603	#123	C₂³×C₅₃	1	12	yes	—
604	#123	C₂³×C₅₃	1	12	yes	—
605	#123	C₂³×C₅₃	1	24	yes	—
606	C₂²⋊Q₈	C₂³×C₅₃	1	6	yes	—
607	C₂²⋊Q₈	C₂³×C₅₃	1	6	yes	—
608	C₂²⋊Q₈	C₂³×C₅₃	1	12	yes	—
609	C₂²⋊Q₈	C₂³×C₅₃	1	6	yes	—
610	C₂²⋊Q₈	C₂³×C₅₃	1	12	yes	—
611	C₂²⋊Q₈	C₂³×C₅₃	1	6	yes	—
612	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
613	C₂²⋊Q₈	C₂³×C₅₃	1	12	yes	—
614	C₂²⋊Q₈	C₂³×C₅₃	1	12	yes	—
615	C₂²⋊Q₈	C₂³×C₅₃	1	24	yes	—
616	C₂²⋊Q₈	C₂³×C₅₃	1	6	yes	—
617	C₂²⋊Q₈	C₂³×C₅₃	1	6	yes	—
618	C₂²⋊Q₈	C₂³×C₅₃	1	6	yes	—
619	C₂²⋊Q₈	C₂³×C₅₃	1	6	yes	—
620	C₂²⋊Q₈	C₂³×C₅₃	1	6	yes	—
621	C₂²⋊Q₈	C₂³×C₅₃	1	6	yes	—
622	C₂²⋊Q₈	C₂³×C₅₃	1	12	yes	—
623	C₂²⋊Q₈	C₂³×C₅₃	1	12	yes	—
624	C₂²⋊Q₈	C₂³×C₅₃	1	24	yes	—
625	C₂²⋊Q₈	C₂³×C₅₃	1	24	yes	—
626	#121	C₂³×C₅₃	1	2	yes	—
627	#121	C₂³×C₅₃	1	6	yes	—
628	#121	C₂³×C₅₃	1	12	yes	—
629	#121	C₂³×C₅₃	1	6	yes	—
630	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
631	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
632	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
633	C₄×Q₈	C₂³×C₅₃	1	3	yes	—
634	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
635	C₄×Q₈	C₂³×C₅₃	1	6	yes	—
636	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
637	C₄×Q₈	C₂³×C₅₃	1	6	yes	—
638	C₄×Q₈	C₂³×C₅₃	1	6	yes	—
639	C₄×Q₈	C₂³×C₅₃	1	6	yes	—
640	C₄×Q₈	C₂³×C₅₃	1	12	yes	—
641	C₄×Q₈	C₂³×C₅₃	1	12	yes	—
642	C₄×Q₈	C₂³×C₅₃	1	6	yes	—
643	C₄×Q₈	C₂³×C₅₃	1	6	yes	—
644	C₄×Q₈	C₂³×C₅₃	1	12	yes	—
645	C₄×Q₈	C₂³×C₅₃	1	6	yes	—
646	C₄×Q₈	C₂³×C₅₃	1	12	yes	—
647	C₄×Q₈	C₂³×C₅₃	1	3	yes	—
648	C₄×Q₈	C₂³×C₅₃	1	6	yes	—
649	C₄×Q₈	C₂³×C₅₃	1	3	yes	—
650	C₄×Q₈	C₂³×C₅₃	1	3	yes	—
651	C₄×Q₈	C₂³×C₅₃	1	6	yes	—
652	C₄×Q₈	C₂³×C₅₃	1	12	yes	—
653	C₄×Q₈	C₂³×C₅₃	1	12	yes	—
654	C₄×Q₈	C₂³×C₅₃	1	12	yes	—
655	C₄×Q₈	C₂³×C₅₃	1	12	yes	—
656	C₄×Q₈	C₂³×C₅₃	1	12	yes	—
657	C₄×Q₈	C₂³×C₅₃	1	12	yes	—
658	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
659	C₄×D₄	C₂³×C₅₃	1	3	yes	—
660	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
661	C₄×D₄	C₂³×C₅₃	1	6	yes	—
662	C₄×D₄	C₂³×C₅₃	1	3	yes	—
663	C₄×D₄	C₂³×C₅₃	1	3	yes	—
664	C₄×D₄	C₂³×C₅₃	1	6	yes	—
665	C₄×D₄	C₂³×C₅₃	1	3	yes	—
666	C₄×D₄	C₂³×C₅₃	1	6	yes	—
667	C₄×D₄	C₂³×C₅₃	1	6	yes	—
668	C₄×D₄	C₂³×C₅₃	1	6	yes	—
669	C₄×D₄	C₂³×C₅₃	1	12	yes	—
670	C₄×D₄	C₂³×C₅₃	1	12	yes	—
671	C₄×D₄	C₂³×C₅₃	1	24	yes	—
672	C₄×D₄	C₂³×C₅₃	1	12	yes	—
673	#117	C₂³×C₅₃	1	3	yes	—
674	#117	C₂³×C₅₃	1	12	yes	—
675	#117	C₂³×C₅₃	1	6	yes	—
676	#117	C₂³×C₅₃	1	6	yes	—
677	#117	C₂³×C₅₃	1	3	yes	—
678	#117	C₂³×C₅₃	1	6	yes	—
679	#117	C₂³×C₅₃	1	3	yes	—
680	#117	C₂³×C₅₃	1	6	yes	—
681	#117	C₂³×C₅₃	1	12	yes	—
682	#117	C₂³×C₅₃	1	24	yes	—
683	#117	C₂³×C₅₃	1	12	yes	—
684	#117	C₂³×C₅₃	1	6	yes	—
685	#117	C₂³×C₅₃	1	6	yes	—
686	#117	C₂³×C₅₃	1	12	yes	—
687	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
688	C₂×C₄⋊C₄	C₂³×C₅₃	1	6	yes	—
689	C₂×C₄⋊C₄	C₂³×C₅₃	1	12	yes	—
690	C₂×C₄⋊C₄	C₂³×C₅₃	1	12	yes	—
691	C₂×C₄⋊C₄	C₂³×C₅₃	1	6	yes	—
692	C₂×C₄⋊C₄	C₂³×C₅₃	1	12	yes	—
693	C₂×C₄⋊C₄	C₂³×C₅₃	1	6	yes	—
694	C₂×C₄⋊C₄	C₂³×C₅₃	1	6	yes	—
695	C₂×C₄²	C₂³×C₅₃	1	12	yes	—
696	C₂×C₄²	C₂³×C₅₃	1	6	yes	—
697	C₂×C₄²	C₂³×C₅₃	1	6	yes	—
698	C₂×C₄²	C₂³×C₅₃	1	3	yes	—
699	#41	—	2	4	no	—
700	#41	—	2	8	no	—
701	#41	—	2	12	no	—
702	#41	—	4	6	no	—
703	C₂×Q₈	—	2	8	no	—
704	C₂×Q₈	—	2	8	no	—
705	C₂×Q₈	—	4	12	no	—
706	C₂×Q₈	—	4	12	no	—
707	C₂×Q₈	C₂⁴×C₅₃	1	6	yes	—
708	C₂×Q₈	C₂⁴×C₅₃	1	6	yes	—
709	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
710	C₂×Q₈	C₂⁴×C₅₃	1	3	yes	—
711	C₂×Q₈	C₂⁴×C₅₃	1	6	yes	—
712	C₂×Q₈	C₂⁴×C₅₃	1	3	yes	—
713	C₂×Q₈	C₂⁴×C₅₃	1	12	yes	—
714	C₂×Q₈	C₂⁴×C₅₃	1	12	yes	—
715	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
716	C₂×D₄	C₂⁴×C₅₃	1	6	yes	—
717	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
718	C₂×D₄	C₂⁴×C₅₃	1	3	yes	—
719	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
720	C₂×D₄	C₂⁴×C₅₃	1	6	yes	—
721	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
723	C₂²×C₄	C₂⁴×C₅₃	1	6	yes	—
724	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₅₃	1	6	yes	—
727	C₂²×C₄	C₂⁴×C₅₃	1	3	yes	—
728	C₂²×C₄	C₂⁴×C₅₃	1	3	yes	—
729	C₂²×C₄	C₂⁴×C₅₃	1	6	yes	—
730	C₂²×C₄	C₂⁴×C₅₃	1	3	yes	—
731	C₂²×C₄	C₂⁴×C₅₃	1	12	yes	—
732	C₂²×C₄	C₂⁴×C₅₃	1	6	yes	—
733	C₂²×C₄	C₂⁴×C₅₃	1	12	yes	—
734	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
735	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
736	C₄⋊C₄	C₂⁴×C₅₃	1	3	yes	—
737	C₄⋊C₄	C₂⁴×C₅₃	1	12	yes	—
738	C₄⋊C₄	C₂⁴×C₅₃	1	3	yes	—
739	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
740	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
741	C₄⋊C₄	C₂⁴×C₅₃	1	12	yes	—
742	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
743	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
744	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
745	C₄⋊C₄	C₂⁴×C₅₃	1	12	yes	—
746	C₄⋊C₄	C₂⁴×C₅₃	1	24	yes	—
747	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
748	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
749	C₄⋊C₄	C₂⁴×C₅₃	1	12	yes	—
750	C₄⋊C₄	C₂⁴×C₅₃	1	12	yes	—
751	C₄⋊C₄	C₂⁴×C₅₃	1	24	yes	—
752	C₄⋊C₄	C₂⁴×C₅₃	1	12	yes	—
753	C₄⋊C₄	C₂⁴×C₅₃	1	12	yes	—
754	C₄⋊C₄	C₂⁴×C₅₃	1	3	yes	—
755	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
756	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
757	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
758	C₄⋊C₄	C₂⁴×C₅₃	1	3	yes	—
759	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
760	C₄⋊C₄	C₂⁴×C₅₃	1	12	yes	—
761	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
762	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
763	C₄⋊C₄	C₂⁴×C₅₃	1	12	yes	—
764	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
765	C₄⋊C₄	C₂⁴×C₅₃	1	24	yes	—
766	C₄⋊C₄	C₂⁴×C₅₃	1	12	yes	—
767	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
768	C₄⋊C₄	C₂⁴×C₅₃	1	12	yes	—
769	C₂²⋊C₄	C₂⁴×C₅₃	1	6	yes	—
770	C₂²⋊C₄	C₂⁴×C₅₃	1	6	yes	—
771	C₂²⋊C₄	C₂⁴×C₅₃	1	12	yes	—
772	C₂²⋊C₄	C₂⁴×C₅₃	1	2	yes	—
773	C₂²⋊C₄	C₂⁴×C₅₃	1	2	yes	—
774	C₂²⋊C₄	C₂⁴×C₅₃	1	12	yes	—
775	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
776	C₂²⋊C₄	C₂⁴×C₅₃	1	12	yes	—
777	C₂²⋊C₄	C₂⁴×C₅₃	1	12	yes	—
778	C₂²⋊C₄	C₂⁴×C₅₃	1	12	yes	—
779	C₂²⋊C₄	C₂⁴×C₅₃	1	6	yes	—
780	C₂²⋊C₄	C₂⁴×C₅₃	1	12	yes	—
781	C₂²⋊C₄	C₂⁴×C₅₃	1	6	yes	—
782	C₂²⋊C₄	C₂⁴×C₅₃	1	6	yes	—
783	C₄²	C₂⁴×C₅₃	1	3	yes	—
784	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
785	C₄²	C₂⁴×C₅₃	1	3	yes	—
786	C₄²	C₂⁴×C₅₃	1	6	yes	—
787	C₄²	C₂⁴×C₅₃	1	3	yes	—
788	C₄²	C₂⁴×C₅₃	1	12	yes	—
789	C₄²	C₂⁴×C₅₃	1	6	yes	—
790	C₄²	C₂⁴×C₅₃	1	6	yes	—
791	C₄²	C₂⁴×C₅₃	1	12	yes	—
792	C₄²	C₂⁴×C₅₃	1	6	yes	—
793	C₄²	C₂⁴×C₅₃	1	6	yes	—
794	C₄²	C₂⁴×C₅₃	1	6	yes	—
795	C₄²	C₂⁴×C₅₃	1	12	yes	—
796	C₄²	C₂⁴×C₅₃	1	24	yes	—
797	C₂³	C₂⁵×C₅₃	1	2	yes	—
798	C₂³	C₂⁵×C₅₃	1	3	yes	—
799	C₂³	C₂⁵×C₅₃	1	2	yes	—
800	Q₈	—	2	12	no	—
801	Q₈	—	2	12	no	—
802	Q₈	—	2	4	no	—
803	Q₈	—	2	6	no	—
804	Q₈	—	2	12	no	—
805	Q₈	—	2	6	no	—
806	Q₈	—	4	12	no	—
807	Q₈	—	4	12	no	—
808	Q₈	2₋¹⁺⁴×C₅₃	1	4	yes	—
809	D₄	—	2	12	no	—
810	D₄	—	2	8	no	—
811	D₄	—	2	6	no	—
812	D₄	—	2	2	no	—
813	D₄	—	4	6	no	—
814	D₄	2₋¹⁺⁴×C₅₃	1	4	yes	—
815	C₂×C₄	—	2	8	no	—
816	C₂×C₄	—	2	12	no	—
817	C₂×C₄	—	2	12	no	—
818	C₂×C₄	—	2	12	no	—
819	C₂×C₄	—	2	6	no	—
820	C₂×C₄	—	2	4	no	—
821	C₂×C₄	—	2	6	no	—
822	C₂×C₄	—	2	4	no	—
823	C₂×C₄	—	2	6	no	—
824	C₂×C₄	—	4	12	no	—
825	C₂×C₄	—	4	12	no	—
826	C₂×C₄	—	4	6	no	—
827	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
828	C₂×C₄	C₂⁵×C₅₃	1	6	yes	—
829	C₂×C₄	C₂⁵×C₅₃	1	6	yes	—
830	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
831	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
832	C₂×C₄	C₂⁵×C₅₃	1	6	yes	—
833	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
834	C₂×C₄	C₂⁵×C₅₃	1	3	yes	—
835	C₂×C₄	C₂⁵×C₅₃	1	3	yes	—
836	C₂×C₄	C₂⁵×C₅₃	1	12	yes	—
837	C₂×C₄	C₂⁵×C₅₃	1	6	yes	—
838	C₂×C₄	C₂⁵×C₅₃	1	3	yes	—
839	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
840	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
841	C₂²	—	2	2	no	—
842	C₂²	—	2	2	no	—
843	C₂²	—	2	2	no	—
844	C₂²	—	2	2	no	—
845	C₂²	—	2	3	no	—
846	C₂²	—	2	3	no	—
847	C₂²	—	2	3	no	—
848	C₂²	—	2	2	no	—
849	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	4	yes	—
850	C₂²	C₂⁶×C₅₃	1	1	yes	characteristic
851	C₄	—	2	2	no	—
852	C₄	—	2	3	no	—
853	C₄	—	2	1	no	—
854	C₄	—	2	4	no	—
855	C₄	—	2	6	no	—
856	C₄	—	2	6	no	—
857	C₄	—	2	6	no	—
858	C₄	—	2	3	no	—
859	C₄	—	2	2	no	—
860	C₄	—	2	6	no	—
861	C₄	—	2	12	no	—
862	C₄	C₂×2₋¹⁺⁴×C₅₃	1	6	yes	—
863	C₄	C₂×2₋¹⁺⁴×C₅₃	1	2	yes	—
864	C₄	C₅₃×#585	1	2	yes	—
865	C₂	—	2	4	no	—
866	C₂	—	4	2	no	—
867	C₂	—	4	3	no	—
868	C₂	C₂²×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
869	C₂	C₂²×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
870	C₂	C₂×C₅₃×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₅₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3563	C₂	semidirect
2. C₅₃×#3556	C₂	semidirect
3. C₅₃×#3555	C₂	semidirect
4. C₅₃×#3552	C₂	semidirect
5. C₅₃×#3523	C₂	semidirect
6. C₅₃×#3523	C₂	semidirect
7. C₅₃×#3516	C₂	semidirect
8. C₅₃×#3515	C₂	semidirect
9. C₅₃×#3509	C₂	semidirect
10. C₅₃×#3503	C₂	semidirect
11. C₅₃×#3503	C₂	semidirect
12. C₅₃×#3502	C₂	semidirect
13. C₅₃×#3482	C₂	semidirect
14. C₅₃×#3482	C₂	semidirect
15. C₅₃×#3482	C₂	semidirect
16. Q₈×#41×C₅₃	C₂	semidirect
17. C₂×C₅₃×#557	C₂	semidirect
405. #63032	C₅₃	direct (N × H)
430. #3563	C₂×C₅₃	semidirect
431. #3556	C₂×C₅₃	semidirect
432. #3555	C₂×C₅₃	semidirect
433. #3552	C₂×C₅₃	semidirect
434. #3523	C₂×C₅₃	semidirect
435. #3523	C₂×C₅₃	semidirect
436. #3516	C₂×C₅₃	semidirect
437. #3515	C₂×C₅₃	semidirect
438. #3509	C₂×C₅₃	semidirect
439. #3503	C₂×C₅₃	semidirect
440. #3503	C₂×C₅₃	semidirect
441. #3502	C₂×C₅₃	semidirect
442. #3482	C₂×C₅₃	semidirect
443. #3482	C₂×C₅₃	semidirect
444. #3482	C₂×C₅₃	semidirect
445. Q₈×#41	C₂×C₅₃	semidirect
446. C₂×#557	C₂×C₅₃	semidirect
543. C₅₃	#63032	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₃×#3563	2
C₅₃×#3556	2
C₅₃×#3555	2
C₅₃×#3552	2
C₅₃×#3523	2
C₅₃×#3516	2
C₅₃×#3515	2
C₅₃×#3509	2
C₅₃×#3503	2
C₅₃×#3502	2
C₅₃×#3482	2
Q₈×#41×C₅₃	2
C₂×C₅₃×#557	2
#63032	53

Subgroups — C53×#63032 #27270544

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#63032 #27270544