Subgroups — C₅₃×#3542 #20272479

Order 6784.

1160 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×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×#562	C₂	semidirect
2. C₅₃×#560	C₂	semidirect
3. C₅₃×#555	C₂	semidirect
4. C₅₃×#553	C₂	semidirect
5. C₅₃×#552	C₂	semidirect
6. C₅₃×#551	C₂	semidirect
7. C₅₃×#550	C₂	semidirect
8. C₅₃×#547	C₂	semidirect
9. C₅₃×#546	C₂	semidirect
10. C₅₃×#546	C₂	semidirect
11. C₅₃×#546	C₂	semidirect
12. D₄²×C₅₃	C₂	semidirect
13. C₅₃×#542	C₂	semidirect
14. C₅₃×#540	C₂	semidirect
15. C₅₃×#540	C₂	semidirect
16. C₅₃×#538	C₂	semidirect
17. C₅₃×#537	C₂	semidirect
18. C₅₃×#535	C₂	semidirect
19. C₅₃×#535	C₂	semidirect
20. C₅₃×#534	C₂	semidirect
21. C₅₃×#525	C₂	semidirect
22. C₅₃×#525	C₂	semidirect
23. C₂×#121×C₅₃	C₂	semidirect
24. C₂×#41×C₅₃	C₂²	semidirect
25. C₂×#41×C₅₃	C₂²	semidirect
26. C₂×#41×C₅₃	C₂²	semidirect
27. C₂×#41×C₅₃	C₂²	semidirect
30. C₂²×D₄×C₅₃	C₂²	semidirect
31. C₂²×D₄×C₅₃	C₂²	semidirect
32. C₂³×C₄×C₅₃	C₂²	semidirect
33. C₄⋊Q₈×C₅₃	C₂²	semidirect
34. #127×C₅₃	C₂²	semidirect
35. #127×C₅₃	C₂²	semidirect
36. #127×C₅₃	C₂²	semidirect
37. #126×C₅₃	C₂²	semidirect
38. #126×C₅₃	C₂²	semidirect
39. #126×C₅₃	C₂²	semidirect
40. #125×C₅₃	C₂²	semidirect
41. #125×C₅₃	C₂²	semidirect
42. #124×C₅₃	C₂²	semidirect
43. #124×C₅₃	C₂²	semidirect
44. #124×C₅₃	C₂²	semidirect
45. #124×C₅₃	C₂²	semidirect
46. #124×C₅₃	C₂²	semidirect
48. #123×C₅₃	C₂²	semidirect
49. #123×C₅₃	C₂²	semidirect
50. #123×C₅₃	C₂²	semidirect
51. #123×C₅₃	C₂²	semidirect
52. #123×C₅₃	C₂²	semidirect
53. #123×C₅₃	C₂²	semidirect
54. #123×C₅₃	C₂²	semidirect
55. #123×C₅₃	C₂²	semidirect
56. #123×C₅₃	C₂²	semidirect
57. #123×C₅₃	C₂²	semidirect
58. #123×C₅₃	C₂²	semidirect
59. C₂²⋊Q₈×C₅₃	C₂²	semidirect
60. C₂²⋊Q₈×C₅₃	C₂²	semidirect
61. C₂²⋊Q₈×C₅₃	C₂²	semidirect
62. C₂²⋊Q₈×C₅₃	C₂²	semidirect
63. C₂²⋊Q₈×C₅₃	C₂²	semidirect
64. C₂²⋊Q₈×C₅₃	C₂²	semidirect
65. C₂²⋊Q₈×C₅₃	C₂²	semidirect
66. C₂²⋊Q₈×C₅₃	C₂²	semidirect
71. #121×C₅₃	C₂²	semidirect
72. #121×C₅₃	C₂²	semidirect
73. #121×C₅₃	C₂²	semidirect
74. #121×C₅₃	C₂²	semidirect
75. #121×C₅₃	C₂²	semidirect
76. #121×C₅₃	C₂²	semidirect
77. #121×C₅₃	C₂²	semidirect
78. #121×C₅₃	C₂²	semidirect
79. #121×C₅₃	C₂²	semidirect
80. #121×C₅₃	C₂²	semidirect
81. #121×C₅₃	C₂²	semidirect
82. #121×C₅₃	C₂²	semidirect
83. #121×C₅₃	C₂²	semidirect
84. #121×C₅₃	C₂²	semidirect
85. #121×C₅₃	C₂²	semidirect
86. #121×C₅₃	C₂²	semidirect
87. #121×C₅₃	C₂²	semidirect
88. #121×C₅₃	C₂²	semidirect
89. #121×C₅₃	C₂²	semidirect
90. #121×C₅₃	C₂²	semidirect
91. #121×C₅₃	C₂²	semidirect
94. #120×C₅₃	C₂²	semidirect
95. #120×C₅₃	C₂²	semidirect
96. #120×C₅₃	C₂²	semidirect
97. #120×C₅₃	C₂²	semidirect
98. #120×C₅₃	C₂²	semidirect
99. #120×C₅₃	C₂²	semidirect
100. #120×C₅₃	C₂²	semidirect
101. C₄×Q₈×C₅₃	C₂²	semidirect
103. C₄×D₄×C₅₃	C₂²	semidirect
104. C₄×D₄×C₅₃	C₂²	semidirect
105. C₄×D₄×C₅₃	C₂²	semidirect
106. C₄×D₄×C₅₃	C₂²	semidirect
107. C₄×D₄×C₅₃	C₂²	semidirect
108. C₄×D₄×C₅₃	C₂²	semidirect
109. C₄×D₄×C₅₃	C₂²	semidirect
110. C₄×D₄×C₅₃	C₂²	semidirect
111. C₄×D₄×C₅₃	C₂²	semidirect
112. C₄×D₄×C₅₃	C₂²	semidirect
113. #117×C₅₃	C₂²	semidirect
114. #117×C₅₃	C₂²	semidirect
115. #117×C₅₃	C₂²	semidirect
116. #117×C₅₃	C₂²	semidirect
117. #117×C₅₃	C₂²	semidirect
118. C₂×C₄⋊C₄×C₅₃	C₂²	semidirect
119. C₂×C₄⋊C₄×C₅₃	C₂²	semidirect
120. C₂×C₂²⋊C₄×C₅₃	C₂²	semidirect
121. C₂×C₂²⋊C₄×C₅₃	C₂²	semidirect
122. C₂×C₂²⋊C₄×C₅₃	C₂²	semidirect
349. #3542	C₅₃	direct (N × H)
361. #562	C₂×C₅₃	semidirect
362. #560	C₂×C₅₃	semidirect
363. #555	C₂×C₅₃	semidirect
364. #553	C₂×C₅₃	semidirect
365. #552	C₂×C₅₃	semidirect
366. #551	C₂×C₅₃	semidirect
367. #550	C₂×C₅₃	semidirect
368. #547	C₂×C₅₃	semidirect
369. #546	C₂×C₅₃	semidirect
370. #546	C₂×C₅₃	semidirect
371. #546	C₂×C₅₃	semidirect
372. D₄²	C₂×C₅₃	semidirect
373. #542	C₂×C₅₃	semidirect
374. #540	C₂×C₅₃	semidirect
375. #540	C₂×C₅₃	semidirect
376. #538	C₂×C₅₃	semidirect
377. #537	C₂×C₅₃	semidirect
378. #535	C₂×C₅₃	semidirect
379. #535	C₂×C₅₃	semidirect
380. #534	C₂×C₅₃	semidirect
381. #525	C₂×C₅₃	semidirect
382. #525	C₂×C₅₃	semidirect
383. C₂×#121	C₂×C₅₃	semidirect
384. C₅₃	#3542	direct (N × H)
385. C₂×#41	C₂²×C₅₃	semidirect
386. C₂×#41	C₂²×C₅₃	semidirect
387. C₂×#41	C₂²×C₅₃	semidirect
388. C₂×#41	C₂²×C₅₃	semidirect
391. C₂²×D₄	C₂²×C₅₃	semidirect
392. C₂²×D₄	C₂²×C₅₃	semidirect
393. C₂³×C₄	C₂²×C₅₃	semidirect
394. C₄⋊Q₈	C₂²×C₅₃	semidirect
395. #127	C₂²×C₅₃	semidirect
396. #127	C₂²×C₅₃	semidirect
397. #127	C₂²×C₅₃	semidirect
398. #126	C₂²×C₅₃	semidirect
399. #126	C₂²×C₅₃	semidirect
400. #126	C₂²×C₅₃	semidirect
401. #125	C₂²×C₅₃	semidirect
402. #125	C₂²×C₅₃	semidirect
403. #124	C₂²×C₅₃	semidirect
404. #124	C₂²×C₅₃	semidirect
405. #124	C₂²×C₅₃	semidirect
406. #124	C₂²×C₅₃	semidirect
407. #124	C₂²×C₅₃	semidirect
409. #123	C₂²×C₅₃	semidirect
410. #123	C₂²×C₅₃	semidirect
411. #123	C₂²×C₅₃	semidirect
412. #123	C₂²×C₅₃	semidirect
413. #123	C₂²×C₅₃	semidirect
414. #123	C₂²×C₅₃	semidirect
415. #123	C₂²×C₅₃	semidirect
416. #123	C₂²×C₅₃	semidirect
417. #123	C₂²×C₅₃	semidirect
418. #123	C₂²×C₅₃	semidirect
419. #123	C₂²×C₅₃	semidirect
420. C₂²⋊Q₈	C₂²×C₅₃	semidirect
421. C₂²⋊Q₈	C₂²×C₅₃	semidirect
422. C₂²⋊Q₈	C₂²×C₅₃	semidirect
423. C₂²⋊Q₈	C₂²×C₅₃	semidirect
424. C₂²⋊Q₈	C₂²×C₅₃	semidirect
425. C₂²⋊Q₈	C₂²×C₅₃	semidirect
426. C₂²⋊Q₈	C₂²×C₅₃	semidirect
427. C₂²⋊Q₈	C₂²×C₅₃	semidirect
432. #121	C₂²×C₅₃	semidirect
433. #121	C₂²×C₅₃	semidirect
434. #121	C₂²×C₅₃	semidirect
435. #121	C₂²×C₅₃	semidirect
436. #121	C₂²×C₅₃	semidirect
437. #121	C₂²×C₅₃	semidirect
438. #121	C₂²×C₅₃	semidirect
439. #121	C₂²×C₅₃	semidirect
440. #121	C₂²×C₅₃	semidirect
441. #121	C₂²×C₅₃	semidirect
442. #121	C₂²×C₅₃	semidirect
443. #121	C₂²×C₅₃	semidirect
444. #121	C₂²×C₅₃	semidirect
445. #121	C₂²×C₅₃	semidirect
446. #121	C₂²×C₅₃	semidirect
447. #121	C₂²×C₅₃	semidirect
448. #121	C₂²×C₅₃	semidirect
449. #121	C₂²×C₅₃	semidirect
450. #121	C₂²×C₅₃	semidirect
451. #121	C₂²×C₅₃	semidirect
452. #121	C₂²×C₅₃	semidirect
455. #120	C₂²×C₅₃	semidirect
456. #120	C₂²×C₅₃	semidirect
457. #120	C₂²×C₅₃	semidirect
458. #120	C₂²×C₅₃	semidirect
459. #120	C₂²×C₅₃	semidirect
460. #120	C₂²×C₅₃	semidirect
461. #120	C₂²×C₅₃	semidirect
462. C₄×Q₈	C₂²×C₅₃	semidirect
464. C₄×D₄	C₂²×C₅₃	semidirect
465. C₄×D₄	C₂²×C₅₃	semidirect
466. C₄×D₄	C₂²×C₅₃	semidirect
467. C₄×D₄	C₂²×C₅₃	semidirect
468. C₄×D₄	C₂²×C₅₃	semidirect
469. C₄×D₄	C₂²×C₅₃	semidirect
470. C₄×D₄	C₂²×C₅₃	semidirect
471. C₄×D₄	C₂²×C₅₃	semidirect
472. C₄×D₄	C₂²×C₅₃	semidirect
473. C₄×D₄	C₂²×C₅₃	semidirect
474. #117	C₂²×C₅₃	semidirect
475. #117	C₂²×C₅₃	semidirect
476. #117	C₂²×C₅₃	semidirect
477. #117	C₂²×C₅₃	semidirect
478. #117	C₂²×C₅₃	semidirect
479. C₂×C₄⋊C₄	C₂²×C₅₃	semidirect
480. C₂×C₄⋊C₄	C₂²×C₅₃	semidirect
481. C₂×C₂²⋊C₄	C₂²×C₅₃	semidirect
482. C₂×C₂²⋊C₄	C₂²×C₅₃	semidirect
483. C₂×C₂²⋊C₄	C₂²×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×#562	2
C₅₃×#560	2
C₅₃×#555	2
C₅₃×#553	2
C₅₃×#552	2
C₅₃×#551	2
C₅₃×#550	2
C₅₃×#547	2
C₅₃×#546	2
D₄²×C₅₃	2
C₅₃×#542	2
C₅₃×#540	2
C₅₃×#538	2
C₅₃×#537	2
C₅₃×#535	2
C₅₃×#534	2
C₅₃×#525	2
C₂×#121×C₅₃	2
#3542	53

Subgroups — C53×#3542 #20272479

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#3542 #20272479