Subgroups — C₅₃×#3534 #20272471

Order 6784.

1166 conjugacy classes of subgroups.

The subgroup lattice has 640 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×#553	C₂	1	2	yes	maximal, complemented
4	C₅₃×#551	C₂	1	2	yes	maximal, complemented
5	C₅₃×#546	C₂	1	2	yes	maximal, complemented
6	C₅₃×#546	C₂	1	2	yes	maximal, complemented
7	C₅₃×#546	C₂	1	2	yes	maximal, complemented
8	D₄²×C₅₃	C₂	1	2	yes	maximal, complemented
9	C₅₃×#540	C₂	1	2	yes	maximal, complemented
10	C₅₃×#539	C₂	1	2	yes	maximal, complemented
11	C₅₃×#539	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#538	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#538	C₂	1	2	yes	maximal, complemented
14	C₅₃×#537	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#534	C₂	1	2	yes	maximal, complemented
16	C₅₃×#534	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#123×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#121×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
21	C₂×#41×C₅₃	C₂²	1	2	yes	complemented
22	C₂²×D₄×C₅₃	C₂²	1	1	yes	characteristic
23	C₂²×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
24	C₂²×D₄×C₅₃	C₂²	1	2	yes	complemented
25	C₂²×D₄×C₅₃	C₂²	1	2	yes	complemented
26	C₂²×D₄×C₅₃	C₂²	1	2	yes	complemented
27	C₂³×C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
28	#127×C₅₃	C₂²	1	2	yes	complemented
29	#126×C₅₃	C₂²	1	2	yes	complemented
30	#126×C₅₃	C₂²	1	2	yes	complemented
31	#126×C₅₃	C₂²	1	2	yes	complemented
32	#126×C₅₃	C₂²	1	2	yes	complemented
33	#125×C₅₃	C₂²	1	2	yes	complemented
34	#125×C₅₃	C₂²	1	2	yes	complemented
35	#124×C₅₃	C₂²	1	2	yes	complemented
36	#124×C₅₃	C₂²	1	2	yes	complemented
37	#124×C₅₃	C₂²	1	2	yes	complemented
38	#123×C₅₃	C₂²	1	2	yes	complemented
39	#123×C₅₃	C₂²	1	2	yes	complemented
40	#123×C₅₃	C₂²	1	2	yes	complemented
41	#123×C₅₃	C₂²	1	2	yes	complemented
42	#123×C₅₃	C₂²	1	2	yes	complemented
43	#123×C₅₃	C₂²	1	2	yes	complemented
44	#123×C₅₃	C₂²	1	2	yes	complemented
45	#123×C₅₃	C₂²	1	2	yes	complemented
46	#123×C₅₃	C₂²	1	2	yes	complemented
47	#123×C₅₃	C₂²	1	2	yes	complemented
48	#123×C₅₃	C₂²	1	2	yes	complemented
49	#123×C₅₃	C₂²	1	2	yes	complemented
50	#123×C₅₃	C₂²	1	2	yes	complemented
51	#123×C₅₃	C₂²	1	2	yes	complemented
52	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
53	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
54	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
55	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
56	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
57	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
58	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
59	#121×C₅₃	C₂²	1	1	yes	characteristic
60	#121×C₅₃	C₂²	1	2	yes	—
61	#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
62	#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
63	#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
64	#121×C₅₃	C₂²	1	2	yes	complemented
65	#121×C₅₃	C₂²	1	2	yes	complemented
66	#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
67	#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
68	#121×C₅₃	C₂²	1	2	yes	complemented
69	#121×C₅₃	C₂²	1	2	yes	complemented
70	#121×C₅₃	C₂²	1	2	yes	complemented
71	#121×C₅₃	C₂²	1	2	yes	complemented
72	#121×C₅₃	C₂²	1	2	yes	complemented
73	#121×C₅₃	C₂²	1	2	yes	complemented
74	#121×C₅₃	C₂²	1	2	yes	complemented
75	#121×C₅₃	C₂²	1	2	yes	complemented
76	#121×C₅₃	C₂²	1	2	yes	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	#120×C₅₃	C₂²	1	2	yes	—
81	#120×C₅₃	C₂²	1	2	yes	complemented
82	#120×C₅₃	C₂²	1	2	yes	complemented
83	#120×C₅₃	C₂²	1	2	yes	complemented
84	#120×C₅₃	C₂²	1	2	yes	complemented
85	#120×C₅₃	C₂²	1	2	yes	complemented
86	#120×C₅₃	C₂²	1	2	yes	complemented
87	#120×C₅₃	C₂²	1	2	yes	complemented
88	C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
89	C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
90	C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
91	C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
92	C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
93	C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
94	C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
95	C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
96	#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
97	#117×C₅₃	C₂²	1	2	yes	complemented
98	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
99	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
100	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
101	C₂×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
102	C₂×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
103	C₂×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
104	C₂×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
105	C₂×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
106	C₂×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
107	C₂⁴×C₅₃	C₂³	1	1	yes	characteristic
108	C₂⁴×C₅₃	C₂³	1	2	yes	—
109	C₂⁴×C₅₃	C₂³	1	1	yes	characteristic
110	C₂⁴×C₅₃	C₂³	1	2	yes	—
111	#41×C₅₃	—	4	2	no	—
112	#41×C₅₃	—	4	4	no	—
113	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
114	C₂×Q₈×C₅₃	C₂³	1	2	yes	—
115	C₂×D₄×C₅₃	—	4	2	no	—
116	C₂×D₄×C₅₃	—	4	2	no	—
117	C₂×D₄×C₅₃	—	4	4	no	—
118	C₂×D₄×C₅₃	—	4	4	no	—
119	C₂×D₄×C₅₃	—	4	4	no	—
120	C₂×D₄×C₅₃	C₂³	1	2	yes	—
121	C₂×D₄×C₅₃	C₂³	1	2	yes	—
122	C₂×D₄×C₅₃	C₂³	1	2	yes	—
123	C₂×D₄×C₅₃	C₂³	1	2	yes	—
124	C₂×D₄×C₅₃	C₂³	1	2	yes	—
125	C₂×D₄×C₅₃	C₂³	1	2	yes	—
126	C₂×D₄×C₅₃	C₂³	1	2	yes	—
127	C₂×D₄×C₅₃	C₂³	1	2	yes	—
128	C₂×D₄×C₅₃	C₂³	1	2	yes	—
129	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
130	C₂×D₄×C₅₃	C₂³	1	2	yes	—
131	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
132	C₂×D₄×C₅₃	C₂³	1	2	yes	—
133	C₂×D₄×C₅₃	C₂³	1	2	yes	—
134	C₂×D₄×C₅₃	C₂³	1	2	yes	—
135	C₂×D₄×C₅₃	C₂³	1	2	yes	—
136	C₂×D₄×C₅₃	C₂³	1	2	yes	—
137	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
138	C₂×D₄×C₅₃	C₂³	1	2	yes	—
139	C₂×D₄×C₅₃	C₂³	1	2	yes	—
140	C₂²×C₄×C₅₃	—	4	2	no	—
141	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
142	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
143	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
144	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
145	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
146	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
147	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
148	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
149	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
150	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
151	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
152	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
153	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
154	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
155	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
156	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
157	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
158	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
159	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
160	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
161	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
162	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
163	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
164	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
165	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
166	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
167	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
168	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
169	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
170	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
171	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
172	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
173	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
174	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
175	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
176	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
177	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
178	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
179	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
180	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
181	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
182	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
183	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
184	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
185	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
186	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
187	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
188	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
189	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
190	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
191	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
192	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
193	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
194	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
195	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
196	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
197	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
198	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
199	C₄²×C₅₃	C₂³	1	2	yes	—
200	C₄²×C₅₃	C₂³	1	2	yes	—
201	C₄²×C₅₃	C₂³	1	2	yes	—
202	C₂³×C₅₃	—	2	2	no	—
203	C₂³×C₅₃	—	2	2	no	—
204	C₂³×C₅₃	—	2	2	no	—
205	C₂³×C₅₃	—	2	4	no	—
206	C₂³×C₅₃	—	4	1	no	—
207	C₂³×C₅₃	—	4	1	no	—
208	C₂³×C₅₃	—	4	2	no	—
209	C₂³×C₅₃	—	4	2	no	—
210	C₂³×C₅₃	—	4	2	no	—
211	C₂³×C₅₃	—	4	1	no	—
212	C₂³×C₅₃	—	4	2	no	—
213	C₂³×C₅₃	—	4	2	no	—
214	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
215	C₂³×C₅₃	C₂⁴	1	2	yes	—
216	C₂³×C₅₃	C₂⁴	1	2	yes	—
217	C₂³×C₅₃	C₂⁴	1	2	yes	—
218	C₂³×C₅₃	C₂⁴	1	2	yes	—
219	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
220	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
221	Q₈×C₅₃	—	4	1	no	—
222	Q₈×C₅₃	—	4	2	no	—
223	D₄×C₅₃	—	2	4	no	—
224	D₄×C₅₃	—	2	4	no	—
225	D₄×C₅₃	—	2	4	no	—
226	D₄×C₅₃	—	2	4	no	—
227	D₄×C₅₃	—	2	4	no	—
228	D₄×C₅₃	—	4	1	no	—
229	D₄×C₅₃	—	4	2	no	—
230	D₄×C₅₃	—	4	1	no	—
231	D₄×C₅₃	—	4	2	no	—
232	D₄×C₅₃	—	4	2	no	—
233	D₄×C₅₃	—	4	2	no	—
234	D₄×C₅₃	—	4	2	no	—
235	D₄×C₅₃	—	4	2	no	—
236	D₄×C₅₃	—	4	2	no	—
237	D₄×C₅₃	—	4	2	no	—
238	D₄×C₅₃	—	4	2	no	—
239	D₄×C₅₃	—	4	2	no	—
240	D₄×C₅₃	—	4	2	no	—
241	D₄×C₅₃	—	4	1	no	—
242	D₄×C₅₃	—	4	2	no	—
243	C₂×C₄×C₅₃	—	2	2	no	—
244	C₂×C₄×C₅₃	—	2	2	no	—
245	C₂×C₄×C₅₃	—	2	2	no	—
246	C₂×C₄×C₅₃	—	4	1	no	—
247	C₂×C₄×C₅₃	—	4	1	no	—
248	C₂×C₄×C₅₃	—	4	1	no	—
249	C₂×C₄×C₅₃	—	4	1	no	—
250	C₂×C₄×C₅₃	—	4	1	no	—
251	C₂×C₄×C₅₃	—	4	2	no	—
252	C₂×C₄×C₅₃	—	4	1	no	—
253	C₂×C₄×C₅₃	—	4	2	no	—
254	C₂×C₄×C₅₃	—	4	2	no	—
255	C₂×C₄×C₅₃	—	4	2	no	—
256	C₂×C₄×C₅₃	—	4	2	no	—
257	C₂×C₄×C₅₃	—	4	2	no	—
258	C₂×C₄×C₅₃	—	4	2	no	—
259	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
260	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
261	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
262	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
263	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
264	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
265	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
266	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
267	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
268	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
269	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
270	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
271	C₂²×C₅₃	—	2	1	no	—
272	C₂²×C₅₃	—	2	1	no	—
273	C₂²×C₅₃	—	2	1	no	—
274	C₂²×C₅₃	—	2	1	no	—
275	C₂²×C₅₃	—	2	1	no	—
276	C₂²×C₅₃	—	2	2	no	—
277	C₂²×C₅₃	—	2	2	no	—
278	C₂²×C₅₃	—	2	2	no	—
279	C₂²×C₅₃	—	2	2	no	—
280	C₂²×C₅₃	—	2	2	no	—
281	C₂²×C₅₃	—	2	2	no	—
282	C₂²×C₅₃	—	2	2	no	—
283	C₂²×C₅₃	—	2	1	no	—
284	C₂²×C₅₃	—	2	2	no	—
285	C₂²×C₅₃	—	2	2	no	—
286	C₂²×C₅₃	—	2	1	no	—
287	C₂²×C₅₃	—	2	2	no	—
288	C₂²×C₅₃	—	2	2	no	—
289	C₂²×C₅₃	—	2	2	no	—
290	C₂²×C₅₃	—	4	4	no	—
291	C₂²×C₅₃	—	8	4	no	—
292	C₂²×C₅₃	—	8	2	no	—
293	C₂²×C₅₃	—	8	4	no	—
294	C₂²×C₅₃	H(5,𝔽₂)	1	2	yes	—
295	C₂²×C₅₃	H(5,𝔽₂)	1	2	yes	—
296	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
297	C₄×C₅₃	—	2	1	no	—
298	C₄×C₅₃	—	2	1	no	—
299	C₄×C₅₃	—	2	1	no	—
300	C₄×C₅₃	—	2	1	no	—
301	C₄×C₅₃	—	2	2	no	—
302	C₄×C₅₃	—	2	2	no	—
303	C₄×C₅₃	—	2	2	no	—
304	C₄×C₅₃	—	2	2	no	—
305	C₄×C₅₃	—	2	2	no	—
306	C₄×C₅₃	—	2	2	no	—
307	C₄×C₅₃	—	2	2	no	—
308	C₄×C₅₃	—	2	2	no	—
309	#3534	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
310	C₂×C₅₃	—	2	2	no	—
311	C₂×C₅₃	—	2	2	no	—
312	C₂×C₅₃	—	4	1	no	—
313	C₂×C₅₃	—	4	2	no	—
314	C₂×C₅₃	—	4	2	no	—
315	C₂×C₅₃	—	4	2	no	—
316	C₂×C₅₃	—	4	2	no	—
317	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
318	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
319	C₂×C₅₃	#585	1	1	yes	characteristic
320	#562	C₂×C₅₃	1	2	yes	complemented
321	#560	C₂×C₅₃	1	2	yes	complemented
322	#553	C₂×C₅₃	1	2	yes	complemented
323	#551	C₂×C₅₃	1	2	yes	complemented
324	#546	C₂×C₅₃	1	2	yes	complemented
325	#546	C₂×C₅₃	1	2	yes	complemented
326	#546	C₂×C₅₃	1	2	yes	complemented
327	D₄²	C₂×C₅₃	1	2	yes	complemented
328	#540	C₂×C₅₃	1	2	yes	complemented
329	#539	C₂×C₅₃	1	2	yes	complemented
330	#539	C₂×C₅₃	1	1	yes	characteristic, complemented
331	#538	C₂×C₅₃	1	1	yes	characteristic, complemented
332	#538	C₂×C₅₃	1	2	yes	complemented
333	#537	C₂×C₅₃	1	1	yes	characteristic, complemented
334	#534	C₂×C₅₃	1	2	yes	complemented
335	#534	C₂×C₅₃	1	1	yes	characteristic, complemented
336	#525	C₂×C₅₃	1	1	yes	characteristic, complemented
337	C₂×#123	C₂×C₅₃	1	1	yes	characteristic, complemented
338	C₂×#121	C₂×C₅₃	1	1	yes	characteristic, complemented
339	C₅₃	#3534	1	1	yes	characteristic, direct product factor, Sylow
340	C₂×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
341	C₂×#41	C₂²×C₅₃	1	2	yes	complemented
342	C₂²×D₄	C₂²×C₅₃	1	1	yes	characteristic
343	C₂²×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
344	C₂²×D₄	C₂²×C₅₃	1	2	yes	complemented
345	C₂²×D₄	C₂²×C₅₃	1	2	yes	complemented
346	C₂²×D₄	C₂²×C₅₃	1	2	yes	complemented
347	C₂³×C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
348	#127	C₂²×C₅₃	1	2	yes	complemented
349	#126	C₂²×C₅₃	1	2	yes	complemented
350	#126	C₂²×C₅₃	1	2	yes	complemented
351	#126	C₂²×C₅₃	1	2	yes	complemented
352	#126	C₂²×C₅₃	1	2	yes	complemented
353	#125	C₂²×C₅₃	1	2	yes	complemented
354	#125	C₂²×C₅₃	1	2	yes	complemented
355	#124	C₂²×C₅₃	1	2	yes	complemented
356	#124	C₂²×C₅₃	1	2	yes	complemented
357	#124	C₂²×C₅₃	1	2	yes	complemented
358	#123	C₂²×C₅₃	1	2	yes	complemented
359	#123	C₂²×C₅₃	1	2	yes	complemented
360	#123	C₂²×C₅₃	1	2	yes	complemented
361	#123	C₂²×C₅₃	1	2	yes	complemented
362	#123	C₂²×C₅₃	1	2	yes	complemented
363	#123	C₂²×C₅₃	1	2	yes	complemented
364	#123	C₂²×C₅₃	1	2	yes	complemented
365	#123	C₂²×C₅₃	1	2	yes	complemented
366	#123	C₂²×C₅₃	1	2	yes	complemented
367	#123	C₂²×C₅₃	1	2	yes	complemented
368	#123	C₂²×C₅₃	1	2	yes	complemented
369	#123	C₂²×C₅₃	1	2	yes	complemented
370	#123	C₂²×C₅₃	1	2	yes	complemented
371	#123	C₂²×C₅₃	1	2	yes	complemented
372	C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
373	C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
374	C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
375	C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
376	C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
377	C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
378	C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
379	#121	C₂²×C₅₃	1	1	yes	characteristic
380	#121	C₂²×C₅₃	1	2	yes	—
381	#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
382	#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
383	#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
384	#121	C₂²×C₅₃	1	2	yes	complemented
385	#121	C₂²×C₅₃	1	2	yes	complemented
386	#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
387	#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
388	#121	C₂²×C₅₃	1	2	yes	complemented
389	#121	C₂²×C₅₃	1	2	yes	complemented
390	#121	C₂²×C₅₃	1	2	yes	complemented
391	#121	C₂²×C₅₃	1	2	yes	complemented
392	#121	C₂²×C₅₃	1	2	yes	complemented
393	#121	C₂²×C₅₃	1	2	yes	complemented
394	#121	C₂²×C₅₃	1	2	yes	complemented
395	#121	C₂²×C₅₃	1	2	yes	complemented
396	#121	C₂²×C₅₃	1	2	yes	complemented
397	#121	C₂²×C₅₃	1	2	yes	complemented
398	#121	C₂²×C₅₃	1	2	yes	complemented
399	#121	C₂²×C₅₃	1	2	yes	complemented
400	#120	C₂²×C₅₃	1	2	yes	—
401	#120	C₂²×C₅₃	1	2	yes	complemented
402	#120	C₂²×C₅₃	1	2	yes	complemented
403	#120	C₂²×C₅₃	1	2	yes	complemented
404	#120	C₂²×C₅₃	1	2	yes	complemented
405	#120	C₂²×C₅₃	1	2	yes	complemented
406	#120	C₂²×C₅₃	1	2	yes	complemented
407	#120	C₂²×C₅₃	1	2	yes	complemented
408	C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
409	C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
410	C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
411	C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
412	C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
413	C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
414	C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
415	C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
416	#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
417	#117	C₂²×C₅₃	1	2	yes	complemented
418	C₂×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
419	C₂×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
420	C₂×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
421	C₂×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	complemented
422	C₂×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
423	C₂×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
424	C₂×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
425	C₂×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	complemented
426	C₂×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	complemented
427	C₂⁴	C₂³×C₅₃	1	1	yes	characteristic
428	C₂⁴	C₂³×C₅₃	1	2	yes	—
429	C₂⁴	C₂³×C₅₃	1	1	yes	characteristic
430	C₂⁴	C₂³×C₅₃	1	2	yes	—
431	#41	—	4	2	no	—
432	#41	—	4	4	no	—
433	C₂×Q₈	C₂³×C₅₃	1	1	yes	characteristic
434	C₂×Q₈	C₂³×C₅₃	1	2	yes	—
435	C₂×D₄	—	4	2	no	—
436	C₂×D₄	—	4	2	no	—
437	C₂×D₄	—	4	4	no	—
438	C₂×D₄	—	4	4	no	—
439	C₂×D₄	—	4	4	no	—
440	C₂×D₄	C₂³×C₅₃	1	2	yes	—
441	C₂×D₄	C₂³×C₅₃	1	2	yes	—
442	C₂×D₄	C₂³×C₅₃	1	2	yes	—
443	C₂×D₄	C₂³×C₅₃	1	2	yes	—
444	C₂×D₄	C₂³×C₅₃	1	2	yes	—
445	C₂×D₄	C₂³×C₅₃	1	2	yes	—
446	C₂×D₄	C₂³×C₅₃	1	2	yes	—
447	C₂×D₄	C₂³×C₅₃	1	2	yes	—
448	C₂×D₄	C₂³×C₅₃	1	2	yes	—
449	C₂×D₄	C₂³×C₅₃	1	1	yes	characteristic
450	C₂×D₄	C₂³×C₅₃	1	2	yes	—
451	C₂×D₄	C₂³×C₅₃	1	1	yes	characteristic
452	C₂×D₄	C₂³×C₅₃	1	2	yes	—
453	C₂×D₄	C₂³×C₅₃	1	2	yes	—
454	C₂×D₄	C₂³×C₅₃	1	2	yes	—
455	C₂×D₄	C₂³×C₅₃	1	2	yes	—
456	C₂×D₄	C₂³×C₅₃	1	2	yes	—
457	C₂×D₄	C₂³×C₅₃	1	1	yes	characteristic
458	C₂×D₄	C₂³×C₅₃	1	2	yes	—
459	C₂×D₄	C₂³×C₅₃	1	2	yes	—
460	C₂²×C₄	—	4	2	no	—
461	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
462	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
463	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
464	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
465	C₂²×C₄	C₂³×C₅₃	1	2	yes	—
466	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
467	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
468	C₂²×C₄	C₂³×C₅₃	1	2	yes	—
469	C₂²×C₄	C₂³×C₅₃	1	2	yes	—
470	C₂²×C₄	C₂³×C₅₃	1	2	yes	—
471	C₂²×C₄	C₂³×C₅₃	1	2	yes	—
472	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
473	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
474	C₂²×C₄	C₂³×C₅₃	1	2	yes	—
475	C₂²×C₄	C₂³×C₅₃	1	2	yes	—
476	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
477	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
478	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
479	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
480	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
481	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
482	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
483	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
484	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
485	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
486	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
487	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
488	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
489	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
490	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
491	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
492	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
493	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
494	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
495	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
496	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
497	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
498	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
499	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
500	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
501	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
502	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
503	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
504	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
505	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
506	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
507	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
508	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
509	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
510	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
511	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
512	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
513	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
514	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
515	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
516	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
517	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
518	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
519	C₄²	C₂³×C₅₃	1	2	yes	—
520	C₄²	C₂³×C₅₃	1	2	yes	—
521	C₄²	C₂³×C₅₃	1	2	yes	—
522	C₂³	—	2	2	no	—
523	C₂³	—	2	2	no	—
524	C₂³	—	2	2	no	—
525	C₂³	—	2	4	no	—
526	C₂³	—	4	1	no	—
527	C₂³	—	4	1	no	—
528	C₂³	—	4	2	no	—
529	C₂³	—	4	2	no	—
530	C₂³	—	4	2	no	—
531	C₂³	—	4	1	no	—
532	C₂³	—	4	2	no	—
533	C₂³	—	4	2	no	—
534	C₂³	C₂⁴×C₅₃	1	2	yes	—
535	C₂³	C₂⁴×C₅₃	1	2	yes	—
536	C₂³	C₂⁴×C₅₃	1	1	yes	characteristic
537	C₂³	C₂⁴×C₅₃	1	2	yes	—
538	C₂³	C₂⁴×C₅₃	1	2	yes	—
539	C₂³	C₂⁴×C₅₃	1	1	yes	characteristic
540	C₂³	C₂⁴×C₅₃	1	1	yes	characteristic
541	Q₈	—	4	1	no	—
542	Q₈	—	4	2	no	—
543	D₄	—	2	4	no	—
544	D₄	—	2	4	no	—
545	D₄	—	2	4	no	—
546	D₄	—	2	4	no	—
547	D₄	—	2	4	no	—
548	D₄	—	4	1	no	—
549	D₄	—	4	2	no	—
550	D₄	—	4	1	no	—
551	D₄	—	4	2	no	—
552	D₄	—	4	2	no	—
553	D₄	—	4	2	no	—
554	D₄	—	4	2	no	—
555	D₄	—	4	2	no	—
556	D₄	—	4	2	no	—
557	D₄	—	4	2	no	—
558	D₄	—	4	2	no	—
559	D₄	—	4	2	no	—
560	D₄	—	4	2	no	—
561	D₄	—	4	1	no	—
562	D₄	—	4	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	2	no	—
574	C₂×C₄	—	4	2	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	4	2	no	—
577	C₂×C₄	—	4	2	no	—
578	C₂×C₄	—	4	2	no	—
579	C₂×C₄	C₂⁴×C₅₃	1	2	yes	—
580	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
581	C₂×C₄	C₂⁴×C₅₃	1	2	yes	—
582	C₂×C₄	C₂⁴×C₅₃	1	2	yes	—
583	C₂×C₄	C₂⁴×C₅₃	1	2	yes	—
584	C₂×C₄	C₂⁴×C₅₃	1	2	yes	—
585	C₂×C₄	C₂⁴×C₅₃	1	2	yes	—
586	C₂×C₄	C₂⁴×C₅₃	1	2	yes	—
587	C₂×C₄	C₂⁴×C₅₃	1	2	yes	—
588	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
589	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
590	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
591	C₂²	—	2	1	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	2	2	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	2	2	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	2	no	—
605	C₂²	—	2	2	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	4	4	no	—
611	C₂²	—	8	4	no	—
612	C₂²	—	8	2	no	—
613	C₂²	—	8	4	no	—
614	C₂²	H(5,𝔽₂)×C₅₃	1	2	yes	—
615	C₂²	H(5,𝔽₂)×C₅₃	1	2	yes	—
616	C₂²	C₂⁵×C₅₃	1	1	yes	characteristic
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	2	no	—
625	C₄	—	2	2	no	—
626	C₄	—	2	2	no	—
627	C₄	—	2	2	no	—
628	C₄	—	2	2	no	—
629	C₂	—	2	2	no	—
630	C₂	—	2	2	no	—
631	C₂	—	4	1	no	—
632	C₂	—	4	2	no	—
633	C₂	—	4	2	no	—
634	C₂	—	4	2	no	—
635	C₂	—	4	2	no	—
636	C₂	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
637	C₂	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
638	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×#553	C₂	semidirect
4. C₅₃×#551	C₂	semidirect
5. C₅₃×#546	C₂	semidirect
6. C₅₃×#546	C₂	semidirect
7. C₅₃×#546	C₂	semidirect
8. D₄²×C₅₃	C₂	semidirect
9. C₅₃×#540	C₂	semidirect
10. C₅₃×#539	C₂	semidirect
11. C₅₃×#539	C₂	semidirect
12. C₅₃×#538	C₂	semidirect
13. C₅₃×#538	C₂	semidirect
14. C₅₃×#537	C₂	semidirect
15. C₅₃×#534	C₂	semidirect
16. C₅₃×#534	C₂	semidirect
17. C₅₃×#525	C₂	semidirect
18. C₂×#123×C₅₃	C₂	semidirect
19. C₂×#121×C₅₃	C₂	semidirect
20. C₂×#41×C₅₃	C₂²	semidirect
21. C₂×#41×C₅₃	C₂²	semidirect
23. C₂²×D₄×C₅₃	C₂²	semidirect
24. C₂²×D₄×C₅₃	C₂²	semidirect
25. C₂²×D₄×C₅₃	C₂²	semidirect
26. C₂²×D₄×C₅₃	C₂²	semidirect
27. C₂³×C₄×C₅₃	C₂²	semidirect
28. #127×C₅₃	C₂²	semidirect
29. #126×C₅₃	C₂²	semidirect
30. #126×C₅₃	C₂²	semidirect
31. #126×C₅₃	C₂²	semidirect
32. #126×C₅₃	C₂²	semidirect
33. #125×C₅₃	C₂²	semidirect
34. #125×C₅₃	C₂²	semidirect
35. #124×C₅₃	C₂²	semidirect
36. #124×C₅₃	C₂²	semidirect
37. #124×C₅₃	C₂²	semidirect
38. #123×C₅₃	C₂²	semidirect
39. #123×C₅₃	C₂²	semidirect
40. #123×C₅₃	C₂²	semidirect
41. #123×C₅₃	C₂²	semidirect
42. #123×C₅₃	C₂²	semidirect
43. #123×C₅₃	C₂²	semidirect
44. #123×C₅₃	C₂²	semidirect
45. #123×C₅₃	C₂²	semidirect
46. #123×C₅₃	C₂²	semidirect
47. #123×C₅₃	C₂²	semidirect
48. #123×C₅₃	C₂²	semidirect
49. #123×C₅₃	C₂²	semidirect
50. #123×C₅₃	C₂²	semidirect
51. #123×C₅₃	C₂²	semidirect
52. C₂²⋊Q₈×C₅₃	C₂²	semidirect
53. C₂²⋊Q₈×C₅₃	C₂²	semidirect
54. C₂²⋊Q₈×C₅₃	C₂²	semidirect
55. C₂²⋊Q₈×C₅₃	C₂²	semidirect
56. C₂²⋊Q₈×C₅₃	C₂²	semidirect
57. C₂²⋊Q₈×C₅₃	C₂²	semidirect
58. C₂²⋊Q₈×C₅₃	C₂²	semidirect
61. #121×C₅₃	C₂²	semidirect
62. #121×C₅₃	C₂²	semidirect
63. #121×C₅₃	C₂²	semidirect
64. #121×C₅₃	C₂²	semidirect
65. #121×C₅₃	C₂²	semidirect
66. #121×C₅₃	C₂²	semidirect
67. #121×C₅₃	C₂²	semidirect
68. #121×C₅₃	C₂²	semidirect
69. #121×C₅₃	C₂²	semidirect
70. #121×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
81. #120×C₅₃	C₂²	semidirect
82. #120×C₅₃	C₂²	semidirect
83. #120×C₅₃	C₂²	semidirect
84. #120×C₅₃	C₂²	semidirect
85. #120×C₅₃	C₂²	semidirect
86. #120×C₅₃	C₂²	semidirect
87. #120×C₅₃	C₂²	semidirect
88. C₄×D₄×C₅₃	C₂²	semidirect
89. C₄×D₄×C₅₃	C₂²	semidirect
90. C₄×D₄×C₅₃	C₂²	semidirect
91. C₄×D₄×C₅₃	C₂²	semidirect
92. C₄×D₄×C₅₃	C₂²	semidirect
93. C₄×D₄×C₅₃	C₂²	semidirect
94. C₄×D₄×C₅₃	C₂²	semidirect
95. C₄×D₄×C₅₃	C₂²	semidirect
96. #117×C₅₃	C₂²	semidirect
97. #117×C₅₃	C₂²	semidirect
98. C₂×C₄⋊C₄×C₅₃	C₂²	semidirect
99. C₂×C₄⋊C₄×C₅₃	C₂²	semidirect
100. C₂×C₄⋊C₄×C₅₃	C₂²	semidirect
101. C₂×C₂²⋊C₄×C₅₃	C₂²	semidirect
102. C₂×C₂²⋊C₄×C₅₃	C₂²	semidirect
103. C₂×C₂²⋊C₄×C₅₃	C₂²	semidirect
104. C₂×C₂²⋊C₄×C₅₃	C₂²	semidirect
105. C₂×C₂²⋊C₄×C₅₃	C₂²	semidirect
106. C₂×C₂²⋊C₄×C₅₃	C₂²	semidirect
309. #3534	C₅₃	direct (N × H)
320. #562	C₂×C₅₃	semidirect
321. #560	C₂×C₅₃	semidirect
322. #553	C₂×C₅₃	semidirect
323. #551	C₂×C₅₃	semidirect
324. #546	C₂×C₅₃	semidirect
325. #546	C₂×C₅₃	semidirect
326. #546	C₂×C₅₃	semidirect
327. D₄²	C₂×C₅₃	semidirect
328. #540	C₂×C₅₃	semidirect
329. #539	C₂×C₅₃	semidirect
330. #539	C₂×C₅₃	semidirect
331. #538	C₂×C₅₃	semidirect
332. #538	C₂×C₅₃	semidirect
333. #537	C₂×C₅₃	semidirect
334. #534	C₂×C₅₃	semidirect
335. #534	C₂×C₅₃	semidirect
336. #525	C₂×C₅₃	semidirect
337. C₂×#123	C₂×C₅₃	semidirect
338. C₂×#121	C₂×C₅₃	semidirect
339. C₅₃	#3534	direct (N × H)
340. C₂×#41	C₂²×C₅₃	semidirect
341. C₂×#41	C₂²×C₅₃	semidirect
343. C₂²×D₄	C₂²×C₅₃	semidirect
344. C₂²×D₄	C₂²×C₅₃	semidirect
345. C₂²×D₄	C₂²×C₅₃	semidirect
346. C₂²×D₄	C₂²×C₅₃	semidirect
347. C₂³×C₄	C₂²×C₅₃	semidirect
348. #127	C₂²×C₅₃	semidirect
349. #126	C₂²×C₅₃	semidirect
350. #126	C₂²×C₅₃	semidirect
351. #126	C₂²×C₅₃	semidirect
352. #126	C₂²×C₅₃	semidirect
353. #125	C₂²×C₅₃	semidirect
354. #125	C₂²×C₅₃	semidirect
355. #124	C₂²×C₅₃	semidirect
356. #124	C₂²×C₅₃	semidirect
357. #124	C₂²×C₅₃	semidirect
358. #123	C₂²×C₅₃	semidirect
359. #123	C₂²×C₅₃	semidirect
360. #123	C₂²×C₅₃	semidirect
361. #123	C₂²×C₅₃	semidirect
362. #123	C₂²×C₅₃	semidirect
363. #123	C₂²×C₅₃	semidirect
364. #123	C₂²×C₅₃	semidirect
365. #123	C₂²×C₅₃	semidirect
366. #123	C₂²×C₅₃	semidirect
367. #123	C₂²×C₅₃	semidirect
368. #123	C₂²×C₅₃	semidirect
369. #123	C₂²×C₅₃	semidirect
370. #123	C₂²×C₅₃	semidirect
371. #123	C₂²×C₅₃	semidirect
372. C₂²⋊Q₈	C₂²×C₅₃	semidirect
373. C₂²⋊Q₈	C₂²×C₅₃	semidirect
374. C₂²⋊Q₈	C₂²×C₅₃	semidirect
375. C₂²⋊Q₈	C₂²×C₅₃	semidirect
376. C₂²⋊Q₈	C₂²×C₅₃	semidirect
377. C₂²⋊Q₈	C₂²×C₅₃	semidirect
378. C₂²⋊Q₈	C₂²×C₅₃	semidirect
381. #121	C₂²×C₅₃	semidirect
382. #121	C₂²×C₅₃	semidirect
383. #121	C₂²×C₅₃	semidirect
384. #121	C₂²×C₅₃	semidirect
385. #121	C₂²×C₅₃	semidirect
386. #121	C₂²×C₅₃	semidirect
387. #121	C₂²×C₅₃	semidirect
388. #121	C₂²×C₅₃	semidirect
389. #121	C₂²×C₅₃	semidirect
390. #121	C₂²×C₅₃	semidirect
391. #121	C₂²×C₅₃	semidirect
392. #121	C₂²×C₅₃	semidirect
393. #121	C₂²×C₅₃	semidirect
394. #121	C₂²×C₅₃	semidirect
395. #121	C₂²×C₅₃	semidirect
396. #121	C₂²×C₅₃	semidirect
397. #121	C₂²×C₅₃	semidirect
398. #121	C₂²×C₅₃	semidirect
399. #121	C₂²×C₅₃	semidirect
401. #120	C₂²×C₅₃	semidirect
402. #120	C₂²×C₅₃	semidirect
403. #120	C₂²×C₅₃	semidirect
404. #120	C₂²×C₅₃	semidirect
405. #120	C₂²×C₅₃	semidirect
406. #120	C₂²×C₅₃	semidirect
407. #120	C₂²×C₅₃	semidirect
408. C₄×D₄	C₂²×C₅₃	semidirect
409. C₄×D₄	C₂²×C₅₃	semidirect
410. C₄×D₄	C₂²×C₅₃	semidirect
411. C₄×D₄	C₂²×C₅₃	semidirect
412. C₄×D₄	C₂²×C₅₃	semidirect
413. C₄×D₄	C₂²×C₅₃	semidirect
414. C₄×D₄	C₂²×C₅₃	semidirect
415. C₄×D₄	C₂²×C₅₃	semidirect
416. #117	C₂²×C₅₃	semidirect
417. #117	C₂²×C₅₃	semidirect
418. C₂×C₄⋊C₄	C₂²×C₅₃	semidirect
419. C₂×C₄⋊C₄	C₂²×C₅₃	semidirect
420. C₂×C₄⋊C₄	C₂²×C₅₃	semidirect
421. C₂×C₂²⋊C₄	C₂²×C₅₃	semidirect
422. C₂×C₂²⋊C₄	C₂²×C₅₃	semidirect
423. C₂×C₂²⋊C₄	C₂²×C₅₃	semidirect
424. C₂×C₂²⋊C₄	C₂²×C₅₃	semidirect
425. C₂×C₂²⋊C₄	C₂²×C₅₃	semidirect
426. 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×#553	2
C₅₃×#551	2
C₅₃×#546	2
D₄²×C₅₃	2
C₅₃×#540	2
C₅₃×#539	2
C₅₃×#538	2
C₅₃×#537	2
C₅₃×#534	2
C₅₃×#525	2
C₂×#123×C₅₃	2
C₂×#121×C₅₃	2
#3534	53

Subgroups — C53×#3534 #20272471

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#3534 #20272471