Subgroups — C₅₃×#63066 #27270578

Order 13568.

7352 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3558	C₂	1	6	yes	maximal, complemented
2	C₅₃×#3551	C₂	1	6	yes	maximal, complemented
3	C₅₃×#3549	C₂	1	3	yes	maximal, complemented
4	C₅₃×#3543	C₂	1	12	yes	maximal, complemented
5	C₅₃×#3542	C₂	1	12	yes	maximal, complemented
6	C₅₃×#3537	C₂	1	6	yes	maximal, complemented
7	C₅₃×#3529	C₂	1	3	yes	maximal, complemented
8	C₅₃×#3524	C₂	1	4	yes	maximal, complemented
9	C₅₃×#3517	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3500	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3498	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3488	C₂	1	4	yes	maximal, complemented
13	C₅₃×#3487	C₂	1	2	yes	maximal, complemented
14	C₂×2₋¹⁺⁴×C₅₃	C₂²	1	1	yes	characteristic, complemented
15	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	2	yes	complemented
16	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic, complemented
17	C₂²×#41×C₅₃	C₂²	1	2	yes	complemented
18	C₅₃×#563	C₂²	1	1	yes	characteristic, complemented
19	C₅₃×#563	C₂²	1	6	yes	complemented
20	C₅₃×#562	C₂²	1	12	yes	complemented
21	C₅₃×#562	C₂²	1	6	yes	complemented
22	C₅₃×H(3,𝔽₄)	C₂²	1	3	yes	complemented
23	C₅₃×H(3,𝔽₄)	C₂²	1	6	yes	complemented
24	C₅₃×#560	C₂²	1	6	yes	complemented
25	C₅₃×#560	C₂²	1	12	yes	complemented
26	C₅₃×#560	C₂²	1	12	yes	complemented
27	C₅₃×#560	C₂²	1	12	yes	complemented
28	C₅₃×#559	C₂²	1	12	yes	complemented
29	C₅₃×#557	C₂²	1	2	yes	complemented
30	C₅₃×#555	C₂²	1	12	yes	complemented
31	C₅₃×#555	C₂²	1	6	yes	complemented
32	C₅₃×#553	C₂²	1	12	yes	complemented
33	C₅₃×#553	C₂²	1	12	yes	complemented
34	C₅₃×#552	C₂²	1	12	yes	complemented
35	C₅₃×#551	C₂²	1	12	yes	complemented
36	C₅₃×#550	C₂²	1	4	yes	complemented
37	C₅₃×#550	C₂²	1	12	yes	complemented
38	C₅₃×#550	C₂²	1	2	yes	complemented
39	C₅₃×#550	C₂²	1	4	yes	complemented
40	C₅₃×#550	C₂²	1	6	yes	complemented
41	C₅₃×#548	C₂²	1	4	yes	complemented
42	C₅₃×#548	C₂²	1	12	yes	complemented
43	C₅₃×#548	C₂²	1	4	yes	complemented
44	C₅₃×#547	C₂²	1	6	yes	complemented
45	C₅₃×#546	C₂²	1	12	yes	complemented
46	C₅₃×#546	C₂²	1	12	yes	complemented
47	C₅₃×#546	C₂²	1	12	yes	complemented
48	C₅₃×#546	C₂²	1	24	yes	complemented
49	D₄²×C₅₃	C₂²	1	12	yes	complemented
50	D₄²×C₅₃	C₂²	1	12	yes	complemented
51	D₄²×C₅₃	C₂²	1	12	yes	complemented
52	D₄²×C₅₃	C₂²	1	12	yes	complemented
53	D₄²×C₅₃	C₂²	1	6	yes	complemented
54	D₄²×C₅₃	C₂²	1	12	yes	complemented
55	C₅₃×#542	C₂²	1	12	yes	complemented
56	C₅₃×#540	C₂²	1	12	yes	complemented
57	C₅₃×#540	C₂²	1	12	yes	complemented
58	C₅₃×#540	C₂²	1	24	yes	complemented
59	C₅₃×#538	C₂²	1	24	yes	complemented
60	C₅₃×#538	C₂²	1	12	yes	complemented
61	C₅₃×#537	C₂²	1	12	yes	complemented
62	C₅₃×#536	C₂²	1	3	yes	complemented
63	C₅₃×#535	C₂²	1	6	yes	complemented
64	C₅₃×#535	C₂²	1	6	yes	complemented
65	C₅₃×#535	C₂²	1	12	yes	complemented
66	C₅₃×#535	C₂²	1	6	yes	complemented
67	C₅₃×#535	C₂²	1	6	yes	complemented
68	C₅₃×#535	C₂²	1	3	yes	complemented
69	C₅₃×#535	C₂²	1	24	yes	complemented
70	C₅₃×#534	C₂²	1	24	yes	complemented
71	C₅₃×#534	C₂²	1	12	yes	complemented
72	C₅₃×#532	C₂²	1	6	yes	complemented
73	C₅₃×#532	C₂²	1	3	yes	complemented
74	C₅₃×#532	C₂²	1	6	yes	complemented
75	C₂×#127×C₅₃	C₂²	1	6	yes	complemented
76	C₅₃×#529	C₂²	1	6	yes	complemented
77	C₅₃×#529	C₂²	1	12	yes	complemented
78	C₅₃×#529	C₂²	1	12	yes	complemented
79	C₂×#124×C₅₃	C₂²	1	3	yes	complemented
80	C₅₃×#525	C₂²	1	6	yes	complemented
81	C₅₃×#525	C₂²	1	6	yes	complemented
82	C₅₃×#525	C₂²	1	12	yes	complemented
83	C₂×#121×C₅₃	C₂²	1	12	yes	complemented
84	C₅₃×#520	C₂²	1	4	yes	complemented
85	C₅₃×#519	C₂²	1	2	yes	complemented
86	C₄×#41×C₅₃	C₂²	1	2	yes	complemented
87	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
88	2₋¹⁺⁴×C₅₃	—	4	4	no	—
89	H(5,𝔽₂)×C₅₃	—	4	8	no	—
90	H(5,𝔽₂)×C₅₃	—	4	4	no	—
91	C₂×#41×C₅₃	—	4	8	no	—
92	C₂×#41×C₅₃	C₂³	1	2	yes	—
93	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
94	C₂×#41×C₅₃	C₂³	1	4	yes	—
95	C₂×#41×C₅₃	C₂³	1	3	yes	—
96	C₂×#41×C₅₃	C₂³	1	6	yes	—
97	C₂×#41×C₅₃	C₂³	1	6	yes	—
98	C₂×#41×C₅₃	C₂³	1	3	yes	—
99	C₂×#41×C₅₃	C₂³	1	12	yes	—
100	C₂×#41×C₅₃	C₂³	1	12	yes	—
101	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
102	C₂²×Q₈×C₅₃	C₂³	1	3	yes	—
103	C₂²×D₄×C₅₃	C₂³	1	12	yes	—
104	C₂²×D₄×C₅₃	C₂³	1	3	yes	—
105	C₂²×D₄×C₅₃	C₂³	1	6	yes	—
106	C₂²×D₄×C₅₃	C₂³	1	6	yes	—
107	C₂²×D₄×C₅₃	C₂³	1	6	yes	—
108	C₂²×D₄×C₅₃	C₂³	1	24	yes	—
109	C₂²×D₄×C₅₃	C₂³	1	24	yes	—
110	C₂³×C₄×C₅₃	C₂³	1	6	yes	—
111	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
112	C₄⋊Q₈×C₅₃	C₂³	1	3	yes	—
113	C₄⋊Q₈×C₅₃	C₂³	1	6	yes	—
114	#127×C₅₃	C₂³	1	6	yes	—
115	#127×C₅₃	C₂³	1	12	yes	—
116	#127×C₅₃	C₂³	1	12	yes	—
117	#127×C₅₃	C₂³	1	12	yes	—
118	#127×C₅₃	C₂³	1	6	yes	—
119	#127×C₅₃	C₂³	1	3	yes	—
120	#127×C₅₃	C₂³	1	12	yes	—
121	#126×C₅₃	C₂³	1	4	yes	—
122	#126×C₅₃	C₂³	1	12	yes	—
123	#126×C₅₃	C₂³	1	12	yes	—
124	#126×C₅₃	C₂³	1	24	yes	—
125	#125×C₅₃	C₂³	1	2	yes	—
126	#125×C₅₃	C₂³	1	12	yes	—
127	#125×C₅₃	C₂³	1	12	yes	—
128	#124×C₅₃	C₂³	1	3	yes	—
129	#124×C₅₃	C₂³	1	6	yes	—
130	#124×C₅₃	C₂³	1	12	yes	—
131	#124×C₅₃	C₂³	1	6	yes	—
132	#124×C₅₃	C₂³	1	12	yes	—
133	#124×C₅₃	C₂³	1	12	yes	—
134	#124×C₅₃	C₂³	1	1	yes	characteristic
135	#124×C₅₃	C₂³	1	6	yes	—
136	#124×C₅₃	C₂³	1	6	yes	—
137	#124×C₅₃	C₂³	1	12	yes	—
138	#124×C₅₃	C₂³	1	24	yes	—
139	#123×C₅₃	C₂³	1	2	yes	—
140	#123×C₅₃	C₂³	1	6	yes	—
141	#123×C₅₃	C₂³	1	12	yes	—
142	#123×C₅₃	C₂³	1	12	yes	—
143	#123×C₅₃	C₂³	1	24	yes	—
144	#123×C₅₃	C₂³	1	12	yes	—
145	#123×C₅₃	C₂³	1	12	yes	—
146	#123×C₅₃	C₂³	1	12	yes	—
147	#123×C₅₃	C₂³	1	24	yes	—
148	#123×C₅₃	C₂³	1	24	yes	—
149	#123×C₅₃	C₂³	1	12	yes	—
150	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
151	C₂²⋊Q₈×C₅₃	C₂³	1	12	yes	—
152	C₂²⋊Q₈×C₅₃	C₂³	1	12	yes	—
153	C₂²⋊Q₈×C₅₃	C₂³	1	12	yes	—
154	C₂²⋊Q₈×C₅₃	C₂³	1	12	yes	—
155	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	—
156	C₂²⋊Q₈×C₅₃	C₂³	1	12	yes	—
157	#121×C₅₃	C₂³	1	12	yes	—
158	#121×C₅₃	C₂³	1	24	yes	—
159	#121×C₅₃	C₂³	1	12	yes	—
160	#121×C₅₃	C₂³	1	12	yes	—
161	#121×C₅₃	C₂³	1	12	yes	—
162	#121×C₅₃	C₂³	1	12	yes	—
163	#121×C₅₃	C₂³	1	12	yes	—
164	#121×C₅₃	C₂³	1	12	yes	—
165	#121×C₅₃	C₂³	1	12	yes	—
166	#121×C₅₃	C₂³	1	6	yes	—
167	#121×C₅₃	C₂³	1	12	yes	—
168	#121×C₅₃	C₂³	1	12	yes	—
169	#121×C₅₃	C₂³	1	12	yes	—
170	#121×C₅₃	C₂³	1	12	yes	—
171	#121×C₅₃	C₂³	1	12	yes	—
172	#121×C₅₃	C₂³	1	12	yes	—
173	#121×C₅₃	C₂³	1	12	yes	—
174	#121×C₅₃	C₂³	1	24	yes	—
175	#121×C₅₃	C₂³	1	24	yes	—
176	#121×C₅₃	C₂³	1	24	yes	—
177	#121×C₅₃	C₂³	1	24	yes	—
178	#121×C₅₃	C₂³	1	24	yes	—
179	#120×C₅₃	C₂³	1	12	yes	—
180	#120×C₅₃	C₂³	1	12	yes	—
181	#120×C₅₃	C₂³	1	6	yes	—
182	#120×C₅₃	C₂³	1	12	yes	—
183	#120×C₅₃	C₂³	1	6	yes	—
184	#120×C₅₃	C₂³	1	12	yes	—
185	#120×C₅₃	C₂³	1	24	yes	—
186	#120×C₅₃	C₂³	1	24	yes	—
187	#120×C₅₃	C₂³	1	24	yes	—
188	#120×C₅₃	C₂³	1	12	yes	—
189	#120×C₅₃	C₂³	1	12	yes	—
190	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
191	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
192	C₄×Q₈×C₅₃	C₂³	1	12	yes	—
193	C₄×Q₈×C₅₃	C₂³	1	6	yes	—
194	C₄×D₄×C₅₃	C₂³	1	6	yes	—
195	C₄×D₄×C₅₃	C₂³	1	12	yes	—
196	C₄×D₄×C₅₃	C₂³	1	12	yes	—
197	C₄×D₄×C₅₃	C₂³	1	12	yes	—
198	C₄×D₄×C₅₃	C₂³	1	12	yes	—
199	C₄×D₄×C₅₃	C₂³	1	6	yes	—
200	C₄×D₄×C₅₃	C₂³	1	12	yes	—
201	C₄×D₄×C₅₃	C₂³	1	12	yes	—
202	C₄×D₄×C₅₃	C₂³	1	12	yes	—
203	C₄×D₄×C₅₃	C₂³	1	24	yes	—
204	C₄×D₄×C₅₃	C₂³	1	24	yes	—
205	C₄×D₄×C₅₃	C₂³	1	12	yes	—
206	#117×C₅₃	C₂³	1	6	yes	—
207	#117×C₅₃	C₂³	1	3	yes	—
208	#117×C₅₃	C₂³	1	6	yes	—
209	#117×C₅₃	C₂³	1	6	yes	—
210	#117×C₅₃	C₂³	1	12	yes	—
211	#117×C₅₃	C₂³	1	24	yes	—
212	C₂×C₄⋊C₄×C₅₃	C₂³	1	12	yes	—
213	C₂×C₂²⋊C₄×C₅₃	C₂³	1	24	yes	—
214	C₂×C₂²⋊C₄×C₅₃	C₂³	1	12	yes	—
215	C₂×C₄²×C₅₃	C₂³	1	3	yes	—
216	C₂×C₄²×C₅₃	C₂³	1	6	yes	—
217	C₂⁴×C₅₃	C₂⁴	1	6	yes	—
218	C₂⁴×C₅₃	C₂⁴	1	12	yes	—
219	C₂⁴×C₅₃	C₂⁴	1	6	yes	—
220	#41×C₅₃	—	2	16	no	—
221	#41×C₅₃	—	2	8	no	—
222	#41×C₅₃	—	2	4	no	—
223	#41×C₅₃	—	4	12	no	—
224	#41×C₅₃	—	4	6	no	—
225	#41×C₅₃	—	4	6	no	—
226	#41×C₅₃	—	4	24	no	—
227	#41×C₅₃	—	4	12	no	—
228	#41×C₅₃	—	8	12	no	—
229	C₂×Q₈×C₅₃	—	2	8	no	—
230	C₂×Q₈×C₅₃	—	4	6	no	—
231	C₂×Q₈×C₅₃	C₂⁴	1	6	yes	—
232	C₂×Q₈×C₅₃	C₂⁴	1	6	yes	—
233	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
234	C₂×Q₈×C₅₃	C₂⁴	1	3	yes	—
235	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
236	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
237	C₂×D₄×C₅₃	—	4	12	no	—
238	C₂×D₄×C₅₃	—	4	24	no	—
239	C₂×D₄×C₅₃	—	4	12	no	—
240	C₂×D₄×C₅₃	—	4	12	no	—
241	C₂×D₄×C₅₃	—	4	6	no	—
242	C₂×D₄×C₅₃	—	8	24	no	—
243	C₂×D₄×C₅₃	—	8	24	no	—
244	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
245	C₂×D₄×C₅₃	C₂⁴	1	12	yes	—
246	C₂×D₄×C₅₃	C₂⁴	1	3	yes	—
247	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
248	C₂×D₄×C₅₃	C₂⁴	1	12	yes	—
249	C₂×D₄×C₅₃	C₂⁴	1	24	yes	—
250	C₂×D₄×C₅₃	C₂⁴	1	24	yes	—
251	C₂×D₄×C₅₃	C₂⁴	1	12	yes	—
252	C₂×D₄×C₅₃	C₂⁴	1	12	yes	—
253	C₂×D₄×C₅₃	C₂⁴	1	12	yes	—
254	C₂×D₄×C₅₃	C₂⁴	1	12	yes	—
255	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
256	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
257	C₂×D₄×C₅₃	C₂⁴	1	12	yes	—
258	C₂×D₄×C₅₃	C₂⁴	1	3	yes	—
259	C₂×D₄×C₅₃	C₂⁴	1	12	yes	—
260	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
261	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
262	C₂²×C₄×C₅₃	—	4	12	no	—
263	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
264	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
265	C₂²×C₄×C₅₃	C₂⁴	1	12	yes	—
266	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
267	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
268	C₂²×C₄×C₅₃	C₂⁴	1	12	yes	—
269	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
270	C₂²×C₄×C₅₃	C₂⁴	1	12	yes	—
271	C₂²×C₄×C₅₃	C₂⁴	1	24	yes	—
272	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
273	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
274	C₄⋊C₄×C₅₃	C₂⁴	1	12	yes	—
275	C₄⋊C₄×C₅₃	C₂⁴	1	12	yes	—
276	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
277	C₄⋊C₄×C₅₃	C₂⁴	1	12	yes	—
278	C₄⋊C₄×C₅₃	C₂⁴	1	12	yes	—
279	C₄⋊C₄×C₅₃	C₂⁴	1	12	yes	—
280	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
281	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
282	C₄⋊C₄×C₅₃	C₂⁴	1	12	yes	—
283	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
284	C₄⋊C₄×C₅₃	C₂⁴	1	12	yes	—
285	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
286	C₂²⋊C₄×C₅₃	C₂⁴	1	12	yes	—
287	C₂²⋊C₄×C₅₃	C₂⁴	1	24	yes	—
288	C₂²⋊C₄×C₅₃	C₂⁴	1	12	yes	—
289	C₂²⋊C₄×C₅₃	C₂⁴	1	12	yes	—
290	C₂²⋊C₄×C₅₃	C₂⁴	1	24	yes	—
291	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
292	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
293	C₂²⋊C₄×C₅₃	C₂⁴	1	12	yes	—
294	C₂²⋊C₄×C₅₃	C₂⁴	1	12	yes	—
295	C₂²⋊C₄×C₅₃	C₂⁴	1	12	yes	—
296	C₂²⋊C₄×C₅₃	C₂⁴	1	12	yes	—
297	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
298	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
299	C₂²⋊C₄×C₅₃	C₂⁴	1	12	yes	—
300	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
301	C₂²⋊C₄×C₅₃	C₂⁴	1	12	yes	—
302	C₂²⋊C₄×C₅₃	C₂⁴	1	12	yes	—
303	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
304	C₄²×C₅₃	C₂⁴	1	2	yes	—
305	C₄²×C₅₃	C₂⁴	1	6	yes	—
306	C₄²×C₅₃	C₂⁴	1	6	yes	—
307	C₄²×C₅₃	C₂⁴	1	12	yes	—
308	C₄²×C₅₃	C₂⁴	1	3	yes	—
309	C₄²×C₅₃	C₂⁴	1	12	yes	—
310	C₂³×C₅₃	—	4	6	no	—
311	C₂³×C₅₃	—	4	12	no	—
312	C₂³×C₅₃	—	4	6	no	—
313	C₂³×C₅₃	—	4	12	no	—
314	C₂³×C₅₃	—	4	24	no	—
315	C₂³×C₅₃	—	4	12	no	—
316	C₂³×C₅₃	C₂⁵	1	3	yes	—
317	C₂³×C₅₃	C₂⁵	1	2	yes	—
318	C₂³×C₅₃	C₂⁵	1	12	yes	—
319	C₂³×C₅₃	C₂⁵	1	6	yes	—
320	Q₈×C₅₃	—	2	12	no	—
321	Q₈×C₅₃	—	4	3	no	—
322	Q₈×C₅₃	—	4	2	no	—
323	Q₈×C₅₃	—	4	1	no	—
324	Q₈×C₅₃	—	4	6	no	—
325	Q₈×C₅₃	H(5,𝔽₂)	1	4	yes	—
326	D₄×C₅₃	—	2	12	no	—
327	D₄×C₅₃	—	2	24	no	—
328	D₄×C₅₃	—	2	6	no	—
329	D₄×C₅₃	—	4	12	no	—
330	D₄×C₅₃	—	4	6	no	—
331	D₄×C₅₃	—	4	6	no	—
332	D₄×C₅₃	—	4	3	no	—
333	D₄×C₅₃	—	4	12	no	—
334	D₄×C₅₃	—	4	12	no	—
335	D₄×C₅₃	—	4	12	no	—
336	D₄×C₅₃	—	4	12	no	—
337	D₄×C₅₃	—	4	12	no	—
338	D₄×C₅₃	—	4	24	no	—
339	D₄×C₅₃	—	4	12	no	—
340	D₄×C₅₃	—	4	24	no	—
341	D₄×C₅₃	—	4	1	no	—
342	D₄×C₅₃	—	4	6	no	—
343	D₄×C₅₃	—	4	6	no	—
344	C₂×C₄×C₅₃	—	2	12	no	—
345	C₂×C₄×C₅₃	—	2	24	no	—
346	C₂×C₄×C₅₃	—	2	12	no	—
347	C₂×C₄×C₅₃	—	2	6	no	—
348	C₂×C₄×C₅₃	—	4	2	no	—
349	C₂×C₄×C₅₃	—	4	12	no	—
350	C₂×C₄×C₅₃	—	4	12	no	—
351	C₂×C₄×C₅₃	—	4	24	no	—
352	C₂×C₄×C₅₃	—	4	6	no	—
353	C₂×C₄×C₅₃	—	4	6	no	—
354	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
355	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
356	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
357	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
358	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
359	C₂×C₄×C₅₃	C₂⁵	1	12	yes	—
360	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
361	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
362	C₂×C₄×C₅₃	C₂⁵	1	3	yes	—
363	#63066	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
364	C₂²×C₅₃	—	2	2	no	—
365	C₂²×C₅₃	—	2	3	no	—
366	C₂²×C₅₃	—	2	12	no	—
367	C₂²×C₅₃	—	2	6	no	—
368	C₂²×C₅₃	—	2	12	no	—
369	C₂²×C₅₃	—	2	6	no	—
370	C₂²×C₅₃	—	2	12	no	—
371	C₂²×C₅₃	—	2	4	no	—
372	C₂²×C₅₃	—	2	12	no	—
373	C₂²×C₅₃	—	8	12	no	—
374	C₂²×C₅₃	—	16	12	no	—
375	C₂²×C₅₃	—	16	6	no	—
376	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
377	C₄×C₅₃	—	2	4	no	—
378	C₄×C₅₃	—	2	2	no	—
379	C₄×C₅₃	—	2	1	no	—
380	C₄×C₅₃	—	2	6	no	—
381	C₄×C₅₃	—	2	6	no	—
382	C₄×C₅₃	—	2	4	no	—
383	C₄×C₅₃	—	2	12	no	—
384	C₄×C₅₃	—	2	2	no	—
385	C₄×C₅₃	C₂×H(5,𝔽₂)	1	6	yes	—
386	#3558	C₂×C₅₃	1	6	yes	complemented
387	#3551	C₂×C₅₃	1	6	yes	complemented
388	#3549	C₂×C₅₃	1	3	yes	complemented
389	#3543	C₂×C₅₃	1	12	yes	complemented
390	#3542	C₂×C₅₃	1	12	yes	complemented
391	#3537	C₂×C₅₃	1	6	yes	complemented
392	#3529	C₂×C₅₃	1	3	yes	complemented
393	#3524	C₂×C₅₃	1	4	yes	complemented
394	#3517	C₂×C₅₃	1	2	yes	complemented
395	#3500	C₂×C₅₃	1	1	yes	characteristic, complemented
396	#3498	C₂×C₅₃	1	2	yes	complemented
397	#3488	C₂×C₅₃	1	4	yes	complemented
398	#3487	C₂×C₅₃	1	2	yes	complemented
399	C₂×C₅₃	—	4	2	no	—
400	C₂×C₅₃	—	4	12	no	—
401	C₂×C₅₃	—	4	3	no	—
402	C₂×C₅₃	—	4	6	no	—
403	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
404	C₂×C₅₃	H(7,𝔽₂)	1	2	yes	—
405	C₂×2₋¹⁺⁴	C₂²×C₅₃	1	1	yes	characteristic, complemented
406	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	2	yes	complemented
407	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	1	yes	characteristic, complemented
408	C₂²×#41	C₂²×C₅₃	1	2	yes	complemented
409	#563	C₂²×C₅₃	1	1	yes	characteristic, complemented
410	#563	C₂²×C₅₃	1	6	yes	complemented
411	#562	C₂²×C₅₃	1	12	yes	complemented
412	#562	C₂²×C₅₃	1	6	yes	complemented
413	H(3,𝔽₄)	C₂²×C₅₃	1	3	yes	complemented
414	H(3,𝔽₄)	C₂²×C₅₃	1	6	yes	complemented
415	#560	C₂²×C₅₃	1	6	yes	complemented
416	#560	C₂²×C₅₃	1	12	yes	complemented
417	#560	C₂²×C₅₃	1	12	yes	complemented
418	#560	C₂²×C₅₃	1	12	yes	complemented
419	#559	C₂²×C₅₃	1	12	yes	complemented
420	#557	C₂²×C₅₃	1	2	yes	complemented
421	#555	C₂²×C₅₃	1	12	yes	complemented
422	#555	C₂²×C₅₃	1	6	yes	complemented
423	#553	C₂²×C₅₃	1	12	yes	complemented
424	#553	C₂²×C₅₃	1	12	yes	complemented
425	#552	C₂²×C₅₃	1	12	yes	complemented
426	#551	C₂²×C₅₃	1	12	yes	complemented
427	#550	C₂²×C₅₃	1	4	yes	complemented
428	#550	C₂²×C₅₃	1	12	yes	complemented
429	#550	C₂²×C₅₃	1	2	yes	complemented
430	#550	C₂²×C₅₃	1	4	yes	complemented
431	#550	C₂²×C₅₃	1	6	yes	complemented
432	#548	C₂²×C₅₃	1	4	yes	complemented
433	#548	C₂²×C₅₃	1	12	yes	complemented
434	#548	C₂²×C₅₃	1	4	yes	complemented
435	#547	C₂²×C₅₃	1	6	yes	complemented
436	#546	C₂²×C₅₃	1	12	yes	complemented
437	#546	C₂²×C₅₃	1	12	yes	complemented
438	#546	C₂²×C₅₃	1	12	yes	complemented
439	#546	C₂²×C₅₃	1	24	yes	complemented
440	D₄²	C₂²×C₅₃	1	12	yes	complemented
441	D₄²	C₂²×C₅₃	1	12	yes	complemented
442	D₄²	C₂²×C₅₃	1	12	yes	complemented
443	D₄²	C₂²×C₅₃	1	12	yes	complemented
444	D₄²	C₂²×C₅₃	1	6	yes	complemented
445	D₄²	C₂²×C₅₃	1	12	yes	complemented
446	#542	C₂²×C₅₃	1	12	yes	complemented
447	#540	C₂²×C₅₃	1	12	yes	complemented
448	#540	C₂²×C₅₃	1	12	yes	complemented
449	#540	C₂²×C₅₃	1	24	yes	complemented
450	#538	C₂²×C₅₃	1	24	yes	complemented
451	#538	C₂²×C₅₃	1	12	yes	complemented
452	#537	C₂²×C₅₃	1	12	yes	complemented
453	#536	C₂²×C₅₃	1	3	yes	complemented
454	#535	C₂²×C₅₃	1	6	yes	complemented
455	#535	C₂²×C₅₃	1	6	yes	complemented
456	#535	C₂²×C₅₃	1	12	yes	complemented
457	#535	C₂²×C₅₃	1	6	yes	complemented
458	#535	C₂²×C₅₃	1	6	yes	complemented
459	#535	C₂²×C₅₃	1	3	yes	complemented
460	#535	C₂²×C₅₃	1	24	yes	complemented
461	#534	C₂²×C₅₃	1	24	yes	complemented
462	#534	C₂²×C₅₃	1	12	yes	complemented
463	#532	C₂²×C₅₃	1	6	yes	complemented
464	#532	C₂²×C₅₃	1	3	yes	complemented
465	#532	C₂²×C₅₃	1	6	yes	complemented
466	C₂×#127	C₂²×C₅₃	1	6	yes	complemented
467	#529	C₂²×C₅₃	1	6	yes	complemented
468	#529	C₂²×C₅₃	1	12	yes	complemented
469	#529	C₂²×C₅₃	1	12	yes	complemented
470	C₂×#124	C₂²×C₅₃	1	3	yes	complemented
471	#525	C₂²×C₅₃	1	6	yes	complemented
472	#525	C₂²×C₅₃	1	6	yes	complemented
473	#525	C₂²×C₅₃	1	12	yes	complemented
474	C₂×#121	C₂²×C₅₃	1	12	yes	complemented
475	#520	C₂²×C₅₃	1	4	yes	complemented
476	#519	C₂²×C₅₃	1	2	yes	complemented
477	C₄×#41	C₂²×C₅₃	1	2	yes	complemented
478	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
479	C₅₃	#63066	1	1	yes	characteristic, direct product factor, Sylow
480	2₋¹⁺⁴	—	4	4	no	—
481	H(5,𝔽₂)	—	4	8	no	—
482	H(5,𝔽₂)	—	4	4	no	—
483	C₂×#41	—	4	8	no	—
484	C₂×#41	C₂³×C₅₃	1	2	yes	—
485	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
486	C₂×#41	C₂³×C₅₃	1	4	yes	—
487	C₂×#41	C₂³×C₅₃	1	3	yes	—
488	C₂×#41	C₂³×C₅₃	1	6	yes	—
489	C₂×#41	C₂³×C₅₃	1	6	yes	—
490	C₂×#41	C₂³×C₅₃	1	3	yes	—
491	C₂×#41	C₂³×C₅₃	1	12	yes	—
492	C₂×#41	C₂³×C₅₃	1	12	yes	—
493	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
494	C₂²×Q₈	C₂³×C₅₃	1	3	yes	—
495	C₂²×D₄	C₂³×C₅₃	1	12	yes	—
496	C₂²×D₄	C₂³×C₅₃	1	3	yes	—
497	C₂²×D₄	C₂³×C₅₃	1	6	yes	—
498	C₂²×D₄	C₂³×C₅₃	1	6	yes	—
499	C₂²×D₄	C₂³×C₅₃	1	6	yes	—
500	C₂²×D₄	C₂³×C₅₃	1	24	yes	—
501	C₂²×D₄	C₂³×C₅₃	1	24	yes	—
502	C₂³×C₄	C₂³×C₅₃	1	6	yes	—
503	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
504	C₄⋊Q₈	C₂³×C₅₃	1	3	yes	—
505	C₄⋊Q₈	C₂³×C₅₃	1	6	yes	—
506	#127	C₂³×C₅₃	1	6	yes	—
507	#127	C₂³×C₅₃	1	12	yes	—
508	#127	C₂³×C₅₃	1	12	yes	—
509	#127	C₂³×C₅₃	1	12	yes	—
510	#127	C₂³×C₅₃	1	6	yes	—
511	#127	C₂³×C₅₃	1	3	yes	—
512	#127	C₂³×C₅₃	1	12	yes	—
513	#126	C₂³×C₅₃	1	4	yes	—
514	#126	C₂³×C₅₃	1	12	yes	—
515	#126	C₂³×C₅₃	1	12	yes	—
516	#126	C₂³×C₅₃	1	24	yes	—
517	#125	C₂³×C₅₃	1	2	yes	—
518	#125	C₂³×C₅₃	1	12	yes	—
519	#125	C₂³×C₅₃	1	12	yes	—
520	#124	C₂³×C₅₃	1	3	yes	—
521	#124	C₂³×C₅₃	1	6	yes	—
522	#124	C₂³×C₅₃	1	12	yes	—
523	#124	C₂³×C₅₃	1	6	yes	—
524	#124	C₂³×C₅₃	1	12	yes	—
525	#124	C₂³×C₅₃	1	12	yes	—
526	#124	C₂³×C₅₃	1	1	yes	characteristic
527	#124	C₂³×C₅₃	1	6	yes	—
528	#124	C₂³×C₅₃	1	6	yes	—
529	#124	C₂³×C₅₃	1	12	yes	—
530	#124	C₂³×C₅₃	1	24	yes	—
531	#123	C₂³×C₅₃	1	2	yes	—
532	#123	C₂³×C₅₃	1	6	yes	—
533	#123	C₂³×C₅₃	1	12	yes	—
534	#123	C₂³×C₅₃	1	12	yes	—
535	#123	C₂³×C₅₃	1	24	yes	—
536	#123	C₂³×C₅₃	1	12	yes	—
537	#123	C₂³×C₅₃	1	12	yes	—
538	#123	C₂³×C₅₃	1	12	yes	—
539	#123	C₂³×C₅₃	1	24	yes	—
540	#123	C₂³×C₅₃	1	24	yes	—
541	#123	C₂³×C₅₃	1	12	yes	—
542	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
543	C₂²⋊Q₈	C₂³×C₅₃	1	12	yes	—
544	C₂²⋊Q₈	C₂³×C₅₃	1	12	yes	—
545	C₂²⋊Q₈	C₂³×C₅₃	1	12	yes	—
546	C₂²⋊Q₈	C₂³×C₅₃	1	12	yes	—
547	C₂²⋊Q₈	C₂³×C₅₃	1	6	yes	—
548	C₂²⋊Q₈	C₂³×C₅₃	1	12	yes	—
549	#121	C₂³×C₅₃	1	12	yes	—
550	#121	C₂³×C₅₃	1	24	yes	—
551	#121	C₂³×C₅₃	1	12	yes	—
552	#121	C₂³×C₅₃	1	12	yes	—
553	#121	C₂³×C₅₃	1	12	yes	—
554	#121	C₂³×C₅₃	1	12	yes	—
555	#121	C₂³×C₅₃	1	12	yes	—
556	#121	C₂³×C₅₃	1	12	yes	—
557	#121	C₂³×C₅₃	1	12	yes	—
558	#121	C₂³×C₅₃	1	6	yes	—
559	#121	C₂³×C₅₃	1	12	yes	—
560	#121	C₂³×C₅₃	1	12	yes	—
561	#121	C₂³×C₅₃	1	12	yes	—
562	#121	C₂³×C₅₃	1	12	yes	—
563	#121	C₂³×C₅₃	1	12	yes	—
564	#121	C₂³×C₅₃	1	12	yes	—
565	#121	C₂³×C₅₃	1	12	yes	—
566	#121	C₂³×C₅₃	1	24	yes	—
567	#121	C₂³×C₅₃	1	24	yes	—
568	#121	C₂³×C₅₃	1	24	yes	—
569	#121	C₂³×C₅₃	1	24	yes	—
570	#121	C₂³×C₅₃	1	24	yes	—
571	#120	C₂³×C₅₃	1	12	yes	—
572	#120	C₂³×C₅₃	1	12	yes	—
573	#120	C₂³×C₅₃	1	6	yes	—
574	#120	C₂³×C₅₃	1	6	yes	—
575	#120	C₂³×C₅₃	1	12	yes	—
576	#120	C₂³×C₅₃	1	12	yes	—
577	#120	C₂³×C₅₃	1	24	yes	—
578	#120	C₂³×C₅₃	1	24	yes	—
579	#120	C₂³×C₅₃	1	24	yes	—
580	#120	C₂³×C₅₃	1	12	yes	—
581	#120	C₂³×C₅₃	1	12	yes	—
582	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
583	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
584	C₄×Q₈	C₂³×C₅₃	1	12	yes	—
585	C₄×Q₈	C₂³×C₅₃	1	6	yes	—
586	C₄×D₄	C₂³×C₅₃	1	6	yes	—
587	C₄×D₄	C₂³×C₅₃	1	12	yes	—
588	C₄×D₄	C₂³×C₅₃	1	12	yes	—
589	C₄×D₄	C₂³×C₅₃	1	12	yes	—
590	C₄×D₄	C₂³×C₅₃	1	12	yes	—
591	C₄×D₄	C₂³×C₅₃	1	6	yes	—
592	C₄×D₄	C₂³×C₅₃	1	12	yes	—
593	C₄×D₄	C₂³×C₅₃	1	12	yes	—
594	C₄×D₄	C₂³×C₅₃	1	12	yes	—
595	C₄×D₄	C₂³×C₅₃	1	24	yes	—
596	C₄×D₄	C₂³×C₅₃	1	24	yes	—
597	C₄×D₄	C₂³×C₅₃	1	12	yes	—
598	#117	C₂³×C₅₃	1	6	yes	—
599	#117	C₂³×C₅₃	1	3	yes	—
600	#117	C₂³×C₅₃	1	6	yes	—
601	#117	C₂³×C₅₃	1	6	yes	—
602	#117	C₂³×C₅₃	1	12	yes	—
603	#117	C₂³×C₅₃	1	24	yes	—
604	C₂×C₄⋊C₄	C₂³×C₅₃	1	12	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₅₃	1	24	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₅₃	1	12	yes	—
607	C₂×C₄²	C₂³×C₅₃	1	3	yes	—
608	C₂×C₄²	C₂³×C₅₃	1	6	yes	—
609	C₂⁴	C₂⁴×C₅₃	1	6	yes	—
610	C₂⁴	C₂⁴×C₅₃	1	12	yes	—
611	C₂⁴	C₂⁴×C₅₃	1	6	yes	—
612	#41	—	2	16	no	—
613	#41	—	2	8	no	—
614	#41	—	2	4	no	—
615	#41	—	4	12	no	—
616	#41	—	4	6	no	—
617	#41	—	4	6	no	—
618	#41	—	4	24	no	—
619	#41	—	4	12	no	—
620	#41	—	8	12	no	—
621	C₂×Q₈	—	2	8	no	—
622	C₂×Q₈	—	4	6	no	—
623	C₂×Q₈	C₂⁴×C₅₃	1	6	yes	—
624	C₂×Q₈	C₂⁴×C₅₃	1	6	yes	—
625	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
626	C₂×Q₈	C₂⁴×C₅₃	1	3	yes	—
627	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
628	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
629	C₂×D₄	—	4	12	no	—
630	C₂×D₄	—	4	24	no	—
631	C₂×D₄	—	4	12	no	—
632	C₂×D₄	—	4	12	no	—
633	C₂×D₄	—	4	6	no	—
634	C₂×D₄	—	8	24	no	—
635	C₂×D₄	—	8	24	no	—
636	C₂×D₄	C₂⁴×C₅₃	1	6	yes	—
637	C₂×D₄	C₂⁴×C₅₃	1	12	yes	—
638	C₂×D₄	C₂⁴×C₅₃	1	3	yes	—
639	C₂×D₄	C₂⁴×C₅₃	1	6	yes	—
640	C₂×D₄	C₂⁴×C₅₃	1	12	yes	—
641	C₂×D₄	C₂⁴×C₅₃	1	24	yes	—
642	C₂×D₄	C₂⁴×C₅₃	1	24	yes	—
643	C₂×D₄	C₂⁴×C₅₃	1	12	yes	—
644	C₂×D₄	C₂⁴×C₅₃	1	12	yes	—
645	C₂×D₄	C₂⁴×C₅₃	1	12	yes	—
646	C₂×D₄	C₂⁴×C₅₃	1	12	yes	—
647	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
648	C₂×D₄	C₂⁴×C₅₃	1	6	yes	—
649	C₂×D₄	C₂⁴×C₅₃	1	12	yes	—
650	C₂×D₄	C₂⁴×C₅₃	1	3	yes	—
651	C₂×D₄	C₂⁴×C₅₃	1	12	yes	—
652	C₂×D₄	C₂⁴×C₅₃	1	6	yes	—
653	C₂×D₄	C₂⁴×C₅₃	1	6	yes	—
654	C₂²×C₄	—	4	12	no	—
655	C₂²×C₄	C₂⁴×C₅₃	1	3	yes	—
656	C₂²×C₄	C₂⁴×C₅₃	1	6	yes	—
657	C₂²×C₄	C₂⁴×C₅₃	1	12	yes	—
658	C₂²×C₄	C₂⁴×C₅₃	1	6	yes	—
659	C₂²×C₄	C₂⁴×C₅₃	1	6	yes	—
660	C₂²×C₄	C₂⁴×C₅₃	1	12	yes	—
661	C₂²×C₄	C₂⁴×C₅₃	1	6	yes	—
662	C₂²×C₄	C₂⁴×C₅₃	1	12	yes	—
663	C₂²×C₄	C₂⁴×C₅₃	1	24	yes	—
664	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
665	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
666	C₄⋊C₄	C₂⁴×C₅₃	1	12	yes	—
667	C₄⋊C₄	C₂⁴×C₅₃	1	12	yes	—
668	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
669	C₄⋊C₄	C₂⁴×C₅₃	1	12	yes	—
670	C₄⋊C₄	C₂⁴×C₅₃	1	12	yes	—
671	C₄⋊C₄	C₂⁴×C₅₃	1	12	yes	—
672	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
673	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
674	C₄⋊C₄	C₂⁴×C₅₃	1	12	yes	—
675	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
676	C₄⋊C₄	C₂⁴×C₅₃	1	12	yes	—
677	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
678	C₂²⋊C₄	C₂⁴×C₅₃	1	12	yes	—
679	C₂²⋊C₄	C₂⁴×C₅₃	1	24	yes	—
680	C₂²⋊C₄	C₂⁴×C₅₃	1	12	yes	—
681	C₂²⋊C₄	C₂⁴×C₅₃	1	12	yes	—
682	C₂²⋊C₄	C₂⁴×C₅₃	1	24	yes	—
683	C₂²⋊C₄	C₂⁴×C₅₃	1	2	yes	—
684	C₂²⋊C₄	C₂⁴×C₅₃	1	6	yes	—
685	C₂²⋊C₄	C₂⁴×C₅₃	1	12	yes	—
686	C₂²⋊C₄	C₂⁴×C₅₃	1	12	yes	—
687	C₂²⋊C₄	C₂⁴×C₅₃	1	12	yes	—
688	C₂²⋊C₄	C₂⁴×C₅₃	1	12	yes	—
689	C₂²⋊C₄	C₂⁴×C₅₃	1	6	yes	—
690	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
691	C₂²⋊C₄	C₂⁴×C₅₃	1	12	yes	—
692	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
693	C₂²⋊C₄	C₂⁴×C₅₃	1	12	yes	—
694	C₂²⋊C₄	C₂⁴×C₅₃	1	12	yes	—
695	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
696	C₄²	C₂⁴×C₅₃	1	2	yes	—
697	C₄²	C₂⁴×C₅₃	1	6	yes	—
698	C₄²	C₂⁴×C₅₃	1	6	yes	—
699	C₄²	C₂⁴×C₅₃	1	12	yes	—
700	C₄²	C₂⁴×C₅₃	1	3	yes	—
701	C₄²	C₂⁴×C₅₃	1	12	yes	—
702	C₂³	—	4	6	no	—
703	C₂³	—	4	12	no	—
704	C₂³	—	4	6	no	—
705	C₂³	—	4	12	no	—
706	C₂³	—	4	24	no	—
707	C₂³	—	4	12	no	—
708	C₂³	C₂⁵×C₅₃	1	6	yes	—
709	C₂³	C₂⁵×C₅₃	1	2	yes	—
710	C₂³	C₂⁵×C₅₃	1	12	yes	—
711	C₂³	C₂⁵×C₅₃	1	3	yes	—
712	Q₈	—	2	12	no	—
713	Q₈	—	4	3	no	—
714	Q₈	—	4	2	no	—
715	Q₈	—	4	1	no	—
716	Q₈	—	4	6	no	—
717	Q₈	H(5,𝔽₂)×C₅₃	1	4	yes	—
718	D₄	—	2	12	no	—
719	D₄	—	2	24	no	—
720	D₄	—	2	6	no	—
721	D₄	—	4	12	no	—
722	D₄	—	4	6	no	—
723	D₄	—	4	6	no	—
724	D₄	—	4	3	no	—
725	D₄	—	4	12	no	—
726	D₄	—	4	12	no	—
727	D₄	—	4	12	no	—
728	D₄	—	4	12	no	—
729	D₄	—	4	12	no	—
730	D₄	—	4	24	no	—
731	D₄	—	4	12	no	—
732	D₄	—	4	24	no	—
733	D₄	—	4	1	no	—
734	D₄	—	4	6	no	—
735	D₄	—	4	6	no	—
736	C₂×C₄	—	2	12	no	—
737	C₂×C₄	—	2	24	no	—
738	C₂×C₄	—	2	12	no	—
739	C₂×C₄	—	2	6	no	—
740	C₂×C₄	—	4	2	no	—
741	C₂×C₄	—	4	12	no	—
742	C₂×C₄	—	4	12	no	—
743	C₂×C₄	—	4	24	no	—
744	C₂×C₄	—	4	6	no	—
745	C₂×C₄	—	4	6	no	—
746	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
747	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
748	C₂×C₄	C₂⁵×C₅₃	1	12	yes	—
749	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
750	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
751	C₂×C₄	C₂⁵×C₅₃	1	6	yes	—
752	C₂×C₄	C₂⁵×C₅₃	1	6	yes	—
753	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
754	C₂×C₄	C₂⁵×C₅₃	1	3	yes	—
755	C₂²	—	2	2	no	—
756	C₂²	—	2	3	no	—
757	C₂²	—	2	12	no	—
758	C₂²	—	2	6	no	—
759	C₂²	—	2	12	no	—
760	C₂²	—	2	6	no	—
761	C₂²	—	2	12	no	—
762	C₂²	—	2	4	no	—
763	C₂²	—	2	12	no	—
764	C₂²	—	8	12	no	—
765	C₂²	—	16	12	no	—
766	C₂²	—	16	6	no	—
767	C₂²	C₂⁶×C₅₃	1	1	yes	characteristic
768	C₄	—	2	4	no	—
769	C₄	—	2	2	no	—
770	C₄	—	2	1	no	—
771	C₄	—	2	6	no	—
772	C₄	—	2	6	no	—
773	C₄	—	2	4	no	—
774	C₄	—	2	12	no	—
775	C₄	—	2	2	no	—
776	C₄	C₂×H(5,𝔽₂)×C₅₃	1	6	yes	—
777	C₂	—	4	2	no	—
778	C₂	—	4	12	no	—
779	C₂	—	4	6	no	—
780	C₂	—	4	3	no	—
781	C₂	C₂²×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
782	C₂	C₅₃×H(7,𝔽₂)	1	2	yes	—

	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×#3558	C₂	semidirect
2. C₅₃×#3551	C₂	semidirect
3. C₅₃×#3549	C₂	semidirect
4. C₅₃×#3543	C₂	semidirect
5. C₅₃×#3542	C₂	semidirect
6. C₅₃×#3537	C₂	semidirect
7. C₅₃×#3529	C₂	semidirect
8. C₅₃×#3524	C₂	semidirect
9. C₅₃×#3517	C₂	semidirect
10. C₅₃×#3500	C₂	semidirect
11. C₅₃×#3498	C₂	semidirect
12. C₅₃×#3488	C₂	semidirect
13. C₅₃×#3487	C₂	semidirect
14. C₂×2₋¹⁺⁴×C₅₃	C₂²	semidirect
15. C₂×H(5,𝔽₂)×C₅₃	C₂²	semidirect
16. C₂×H(5,𝔽₂)×C₅₃	C₂²	semidirect
17. C₂²×#41×C₅₃	C₂²	semidirect
18. C₅₃×#563	C₂²	semidirect
19. C₅₃×#563	C₂²	semidirect
20. C₅₃×#562	C₂²	semidirect
21. C₅₃×#562	C₂²	semidirect
22. C₅₃×H(3,𝔽₄)	C₂²	semidirect
23. C₅₃×H(3,𝔽₄)	C₂²	semidirect
24. C₅₃×#560	C₂²	semidirect
25. C₅₃×#560	C₂²	semidirect
26. C₅₃×#560	C₂²	semidirect
27. C₅₃×#560	C₂²	semidirect
28. C₅₃×#559	C₂²	semidirect
29. C₅₃×#557	C₂²	semidirect
30. C₅₃×#555	C₂²	semidirect
31. C₅₃×#555	C₂²	semidirect
32. C₅₃×#553	C₂²	semidirect
33. C₅₃×#553	C₂²	semidirect
34. C₅₃×#552	C₂²	semidirect
35. C₅₃×#551	C₂²	semidirect
36. C₅₃×#550	C₂²	semidirect
37. C₅₃×#550	C₂²	semidirect
38. C₅₃×#550	C₂²	semidirect
39. C₅₃×#550	C₂²	semidirect
40. C₅₃×#550	C₂²	semidirect
41. C₅₃×#548	C₂²	semidirect
42. C₅₃×#548	C₂²	semidirect
43. C₅₃×#548	C₂²	semidirect
44. C₅₃×#547	C₂²	semidirect
45. C₅₃×#546	C₂²	semidirect
46. C₅₃×#546	C₂²	semidirect
47. C₅₃×#546	C₂²	semidirect
48. C₅₃×#546	C₂²	semidirect
49. D₄²×C₅₃	C₂²	semidirect
50. D₄²×C₅₃	C₂²	semidirect
51. D₄²×C₅₃	C₂²	semidirect
52. D₄²×C₅₃	C₂²	semidirect
53. D₄²×C₅₃	C₂²	semidirect
54. D₄²×C₅₃	C₂²	semidirect
55. C₅₃×#542	C₂²	semidirect
56. C₅₃×#540	C₂²	semidirect
57. C₅₃×#540	C₂²	semidirect
58. C₅₃×#540	C₂²	semidirect
59. C₅₃×#538	C₂²	semidirect
60. C₅₃×#538	C₂²	semidirect
61. C₅₃×#537	C₂²	semidirect
62. C₅₃×#536	C₂²	semidirect
63. C₅₃×#535	C₂²	semidirect
64. C₅₃×#535	C₂²	semidirect
65. C₅₃×#535	C₂²	semidirect
66. C₅₃×#535	C₂²	semidirect
67. C₅₃×#535	C₂²	semidirect
68. C₅₃×#535	C₂²	semidirect
69. C₅₃×#535	C₂²	semidirect
70. C₅₃×#534	C₂²	semidirect
71. C₅₃×#534	C₂²	semidirect
72. C₅₃×#532	C₂²	semidirect
73. C₅₃×#532	C₂²	semidirect
74. C₅₃×#532	C₂²	semidirect
75. C₂×#127×C₅₃	C₂²	semidirect
76. C₅₃×#529	C₂²	semidirect
77. C₅₃×#529	C₂²	semidirect
78. C₅₃×#529	C₂²	semidirect
79. C₂×#124×C₅₃	C₂²	semidirect
80. C₅₃×#525	C₂²	semidirect
81. C₅₃×#525	C₂²	semidirect
82. C₅₃×#525	C₂²	semidirect
83. C₂×#121×C₅₃	C₂²	semidirect
84. C₅₃×#520	C₂²	semidirect
85. C₅₃×#519	C₂²	semidirect
86. C₄×#41×C₅₃	C₂²	semidirect
87. C₄×#41×C₅₃	C₂²	semidirect
363. #63066	C₅₃	direct (N × H)
386. #3558	C₂×C₅₃	semidirect
387. #3551	C₂×C₅₃	semidirect
388. #3549	C₂×C₅₃	semidirect
389. #3543	C₂×C₅₃	semidirect
390. #3542	C₂×C₅₃	semidirect
391. #3537	C₂×C₅₃	semidirect
392. #3529	C₂×C₅₃	semidirect
393. #3524	C₂×C₅₃	semidirect
394. #3517	C₂×C₅₃	semidirect
395. #3500	C₂×C₅₃	semidirect
396. #3498	C₂×C₅₃	semidirect
397. #3488	C₂×C₅₃	semidirect
398. #3487	C₂×C₅₃	semidirect
405. C₂×2₋¹⁺⁴	C₂²×C₅₃	semidirect
406. C₂×H(5,𝔽₂)	C₂²×C₅₃	semidirect
407. C₂×H(5,𝔽₂)	C₂²×C₅₃	semidirect
408. C₂²×#41	C₂²×C₅₃	semidirect
409. #563	C₂²×C₅₃	semidirect
410. #563	C₂²×C₅₃	semidirect
411. #562	C₂²×C₅₃	semidirect
412. #562	C₂²×C₅₃	semidirect
413. H(3,𝔽₄)	C₂²×C₅₃	semidirect
414. H(3,𝔽₄)	C₂²×C₅₃	semidirect
415. #560	C₂²×C₅₃	semidirect
416. #560	C₂²×C₅₃	semidirect
417. #560	C₂²×C₅₃	semidirect
418. #560	C₂²×C₅₃	semidirect
419. #559	C₂²×C₅₃	semidirect
420. #557	C₂²×C₅₃	semidirect
421. #555	C₂²×C₅₃	semidirect
422. #555	C₂²×C₅₃	semidirect
423. #553	C₂²×C₅₃	semidirect
424. #553	C₂²×C₅₃	semidirect
425. #552	C₂²×C₅₃	semidirect
426. #551	C₂²×C₅₃	semidirect
427. #550	C₂²×C₅₃	semidirect
428. #550	C₂²×C₅₃	semidirect
429. #550	C₂²×C₅₃	semidirect
430. #550	C₂²×C₅₃	semidirect
431. #550	C₂²×C₅₃	semidirect
432. #548	C₂²×C₅₃	semidirect
433. #548	C₂²×C₅₃	semidirect
434. #548	C₂²×C₅₃	semidirect
435. #547	C₂²×C₅₃	semidirect
436. #546	C₂²×C₅₃	semidirect
437. #546	C₂²×C₅₃	semidirect
438. #546	C₂²×C₅₃	semidirect
439. #546	C₂²×C₅₃	semidirect
440. D₄²	C₂²×C₅₃	semidirect
441. D₄²	C₂²×C₅₃	semidirect
442. D₄²	C₂²×C₅₃	semidirect
443. D₄²	C₂²×C₅₃	semidirect
444. D₄²	C₂²×C₅₃	semidirect
445. D₄²	C₂²×C₅₃	semidirect
446. #542	C₂²×C₅₃	semidirect
447. #540	C₂²×C₅₃	semidirect
448. #540	C₂²×C₅₃	semidirect
449. #540	C₂²×C₅₃	semidirect
450. #538	C₂²×C₅₃	semidirect
451. #538	C₂²×C₅₃	semidirect
452. #537	C₂²×C₅₃	semidirect
453. #536	C₂²×C₅₃	semidirect
454. #535	C₂²×C₅₃	semidirect
455. #535	C₂²×C₅₃	semidirect
456. #535	C₂²×C₅₃	semidirect
457. #535	C₂²×C₅₃	semidirect
458. #535	C₂²×C₅₃	semidirect
459. #535	C₂²×C₅₃	semidirect
460. #535	C₂²×C₅₃	semidirect
461. #534	C₂²×C₅₃	semidirect
462. #534	C₂²×C₅₃	semidirect
463. #532	C₂²×C₅₃	semidirect
464. #532	C₂²×C₅₃	semidirect
465. #532	C₂²×C₅₃	semidirect
466. C₂×#127	C₂²×C₅₃	semidirect
467. #529	C₂²×C₅₃	semidirect
468. #529	C₂²×C₅₃	semidirect
469. #529	C₂²×C₅₃	semidirect
470. C₂×#124	C₂²×C₅₃	semidirect
471. #525	C₂²×C₅₃	semidirect
472. #525	C₂²×C₅₃	semidirect
473. #525	C₂²×C₅₃	semidirect
474. C₂×#121	C₂²×C₅₃	semidirect
475. #520	C₂²×C₅₃	semidirect
476. #519	C₂²×C₅₃	semidirect
477. C₄×#41	C₂²×C₅₃	semidirect
478. C₄×#41	C₂²×C₅₃	semidirect
479. C₅₃	#63066	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×#3558	2
C₅₃×#3551	2
C₅₃×#3549	2
C₅₃×#3543	2
C₅₃×#3542	2
C₅₃×#3537	2
C₅₃×#3529	2
C₅₃×#3524	2
C₅₃×#3517	2
C₅₃×#3500	2
C₅₃×#3498	2
C₅₃×#3488	2
C₅₃×#3487	2
#63066	53

Subgroups — C53×#63066 #27270578

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#63066 #27270578