Subgroups — C₅₃×#3535 #20272472

Order 6784.

1038 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#563	C₂	1	2	yes	maximal, complemented
2	C₅₃×#562	C₂	1	2	yes	maximal, complemented
3	C₅₃×#554	C₂	1	2	yes	maximal, complemented
4	C₅₃×#552	C₂	1	2	yes	maximal, complemented
5	C₅₃×#551	C₂	1	2	yes	maximal, complemented
6	C₅₃×#551	C₂	1	2	yes	maximal, complemented
7	C₅₃×#547	C₂	1	2	yes	maximal, complemented
8	C₅₃×#546	C₂	1	2	yes	maximal, complemented
9	C₅₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#543	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#542	C₂	1	2	yes	maximal, complemented
12	C₅₃×#539	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#539	C₂	1	2	yes	maximal, complemented
14	C₅₃×#539	C₂	1	2	yes	maximal, complemented
15	C₅₃×#538	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#536	C₂	1	2	yes	maximal, complemented
17	C₅₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#123×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₂²⋊Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#41×C₅₃	C₂²	1	2	yes	—
21	C₂×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
22	C₂²×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
23	C₂²×D₄×C₅₃	C₂²	1	1	yes	characteristic
24	C₂³×C₄×C₅₃	C₂²	1	1	yes	characteristic
25	C₄⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
26	C₄⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
27	C₄⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
28	#126×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	#126×C₅₃	C₂²	1	2	yes	complemented
34	#125×C₅₃	C₂²	1	2	yes	complemented
35	#125×C₅₃	C₂²	1	2	yes	complemented
36	#125×C₅₃	C₂²	1	2	yes	complemented
37	#125×C₅₃	C₂²	1	2	yes	complemented
38	#125×C₅₃	C₂²	1	2	yes	complemented
39	#124×C₅₃	C₂²	1	2	yes	—
40	#124×C₅₃	C₂²	1	2	yes	complemented
41	#124×C₅₃	C₂²	1	2	yes	complemented
42	#124×C₅₃	C₂²	1	2	yes	complemented
43	#123×C₅₃	C₂²	1	2	yes	—
44	#123×C₅₃	C₂²	1	2	yes	—
45	#123×C₅₃	C₂²	1	2	yes	—
46	#123×C₅₃	C₂²	1	2	yes	—
47	#123×C₅₃	C₂²	1	2	yes	—
48	#123×C₅₃	C₂²	1	2	yes	—
49	#123×C₅₃	C₂²	1	2	yes	—
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	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
58	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
59	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
60	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
61	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
62	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
63	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
64	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
65	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
66	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
67	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
68	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
69	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
70	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
71	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
72	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
73	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
74	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
75	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
76	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
77	#121×C₅₃	C₂²	1	1	yes	characteristic
78	#121×C₅₃	C₂²	1	2	yes	—
79	#121×C₅₃	C₂²	1	2	yes	—
80	#121×C₅₃	C₂²	1	2	yes	—
81	#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
82	#121×C₅₃	C₂²	1	2	yes	complemented
83	#120×C₅₃	C₂²	1	2	yes	—
84	#120×C₅₃	C₂²	1	2	yes	—
85	C₄×Q₈×C₅₃	C₂²	1	2	yes	complemented
86	C₄×D₄×C₅₃	C₂²	1	2	yes	—
87	C₄×D₄×C₅₃	C₂²	1	2	yes	—
88	C₄×D₄×C₅₃	C₂²	1	2	yes	—
89	C₄×D₄×C₅₃	C₂²	1	2	yes	—
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	#117×C₅₃	C₂²	1	2	yes	—
94	#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
95	#117×C₅₃	C₂²	1	2	yes	complemented
96	#117×C₅₃	C₂²	1	2	yes	complemented
97	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
100	C₂×C₄⋊C₄×C₅₃	C₂²	1	2	yes	complemented
101	C₂×C₄⋊C₄×C₅₃	C₂²	1	2	yes	complemented
102	C₂×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
103	C₂×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
106	C₂×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
107	C₂⁴×C₅₃	C₂³	1	1	yes	characteristic
108	C₂⁴×C₅₃	C₂³	1	1	yes	characteristic
109	#41×C₅₃	—	4	4	no	—
110	#41×C₅₃	—	4	2	no	—
111	C₂×Q₈×C₅₃	—	4	2	no	—
112	C₂×Q₈×C₅₃	C₂³	1	2	yes	—
113	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
114	C₂×Q₈×C₅₃	C₂³	1	2	yes	—
115	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
116	C₂×Q₈×C₅₃	C₂³	1	2	yes	—
117	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
118	C₂×D₄×C₅₃	—	4	2	no	—
119	C₂×D₄×C₅₃	C₂³	1	2	yes	—
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	1	yes	characteristic
127	C₂²×C₄×C₅₃	—	4	2	no	—
128	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
130	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
136	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
137	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
138	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
140	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
141	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
142	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
143	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
144	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
145	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
146	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
147	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
148	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
149	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
150	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
151	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
152	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
153	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
154	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
155	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
156	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
157	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
158	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
159	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
160	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
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	2	yes	—
165	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
166	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
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	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	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	C₄²×C₅₃	C₂³	1	2	yes	—
195	C₄²×C₅₃	C₂³	1	2	yes	—
196	C₄²×C₅₃	C₂³	1	2	yes	—
197	C₄²×C₅₃	C₂³	1	2	yes	—
198	C₄²×C₅₃	C₂³	1	2	yes	—
199	C₂³×C₅₃	—	2	2	no	—
200	C₂³×C₅₃	—	2	2	no	—
201	C₂³×C₅₃	—	2	2	no	—
202	C₂³×C₅₃	—	4	1	no	—
203	C₂³×C₅₃	—	4	1	no	—
204	C₂³×C₅₃	—	4	1	no	—
205	C₂³×C₅₃	C₂⁴	1	2	yes	—
206	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
207	C₂³×C₅₃	C₂⁴	1	2	yes	—
208	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
209	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
210	Q₈×C₅₃	—	4	1	no	—
211	Q₈×C₅₃	—	4	2	no	—
212	Q₈×C₅₃	—	4	1	no	—
213	Q₈×C₅₃	—	4	2	no	—
214	Q₈×C₅₃	—	4	1	no	—
215	Q₈×C₅₃	—	4	2	no	—
216	D₄×C₅₃	—	2	4	no	—
217	D₄×C₅₃	—	2	4	no	—
218	D₄×C₅₃	—	2	4	no	—
219	D₄×C₅₃	—	4	2	no	—
220	D₄×C₅₃	—	4	2	no	—
221	D₄×C₅₃	—	4	2	no	—
222	D₄×C₅₃	—	4	1	no	—
223	D₄×C₅₃	—	4	2	no	—
224	C₂×C₄×C₅₃	—	2	2	no	—
225	C₂×C₄×C₅₃	—	2	2	no	—
226	C₂×C₄×C₅₃	—	2	4	no	—
227	C₂×C₄×C₅₃	—	2	2	no	—
228	C₂×C₄×C₅₃	—	4	1	no	—
229	C₂×C₄×C₅₃	—	4	1	no	—
230	C₂×C₄×C₅₃	—	4	1	no	—
231	C₂×C₄×C₅₃	—	4	1	no	—
232	C₂×C₄×C₅₃	—	4	2	no	—
233	C₂×C₄×C₅₃	—	4	2	no	—
234	C₂×C₄×C₅₃	—	4	1	no	—
235	C₂×C₄×C₅₃	—	4	2	no	—
236	C₂×C₄×C₅₃	—	4	1	no	—
237	C₂×C₄×C₅₃	—	4	2	no	—
238	C₂×C₄×C₅₃	—	4	2	no	—
239	C₂×C₄×C₅₃	—	4	2	no	—
240	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
243	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
246	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
247	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
248	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
249	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
250	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
251	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
252	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
253	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
254	C₂²×C₅₃	—	2	1	no	—
255	C₂²×C₅₃	—	2	1	no	—
256	C₂²×C₅₃	—	2	1	no	—
257	C₂²×C₅₃	—	2	1	no	—
258	C₂²×C₅₃	—	2	2	no	—
259	C₂²×C₅₃	—	2	1	no	—
260	C₂²×C₅₃	—	2	2	no	—
261	C₂²×C₅₃	—	2	2	no	—
262	C₂²×C₅₃	—	2	1	no	—
263	C₂²×C₅₃	—	2	2	no	—
264	C₂²×C₅₃	—	2	2	no	—
265	C₂²×C₅₃	—	2	2	no	—
266	C₂²×C₅₃	—	2	1	no	—
267	C₂²×C₅₃	—	4	4	no	—
268	C₂²×C₅₃	—	8	2	no	—
269	C₂²×C₅₃	H(5,𝔽₂)	1	2	yes	—
270	C₂²×C₅₃	2₋¹⁺⁴	1	2	yes	—
271	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
272	C₄×C₅₃	—	2	1	no	—
273	C₄×C₅₃	—	2	1	no	—
274	C₄×C₅₃	—	2	1	no	—
275	C₄×C₅₃	—	2	1	no	—
276	C₄×C₅₃	—	2	2	no	—
277	C₄×C₅₃	—	2	2	no	—
278	C₄×C₅₃	—	2	2	no	—
279	C₄×C₅₃	—	2	2	no	—
280	C₄×C₅₃	—	2	2	no	—
281	C₄×C₅₃	—	2	2	no	—
282	C₄×C₅₃	—	2	2	no	—
283	C₄×C₅₃	—	2	2	no	—
284	C₄×C₅₃	—	2	2	no	—
285	C₄×C₅₃	—	2	2	no	—
286	#3535	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
287	C₂×C₅₃	—	2	2	no	—
288	C₂×C₅₃	—	2	2	no	—
289	C₂×C₅₃	—	4	2	no	—
290	C₂×C₅₃	—	4	1	no	—
291	C₂×C₅₃	—	4	2	no	—
292	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
293	C₂×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
294	C₂×C₅₃	#585	1	1	yes	characteristic
295	#563	C₂×C₅₃	1	2	yes	complemented
296	#562	C₂×C₅₃	1	2	yes	complemented
297	#554	C₂×C₅₃	1	2	yes	complemented
298	#552	C₂×C₅₃	1	2	yes	complemented
299	#551	C₂×C₅₃	1	2	yes	complemented
300	#551	C₂×C₅₃	1	2	yes	complemented
301	#547	C₂×C₅₃	1	2	yes	complemented
302	#546	C₂×C₅₃	1	2	yes	complemented
303	#544	C₂×C₅₃	1	1	yes	characteristic, complemented
304	#543	C₂×C₅₃	1	1	yes	characteristic, complemented
305	#542	C₂×C₅₃	1	2	yes	complemented
306	#539	C₂×C₅₃	1	1	yes	characteristic, complemented
307	#539	C₂×C₅₃	1	2	yes	complemented
308	#539	C₂×C₅₃	1	2	yes	complemented
309	#538	C₂×C₅₃	1	1	yes	characteristic, complemented
310	#536	C₂×C₅₃	1	2	yes	complemented
311	#525	C₂×C₅₃	1	1	yes	characteristic, complemented
312	C₂×#123	C₂×C₅₃	1	1	yes	characteristic, complemented
313	C₂×C₂²⋊Q₈	C₂×C₅₃	1	1	yes	characteristic, complemented
314	C₅₃	#3535	1	1	yes	characteristic, direct product factor, Sylow
315	C₂×#41	C₂²×C₅₃	1	2	yes	—
316	C₂×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
317	C₂²×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
318	C₂²×D₄	C₂²×C₅₃	1	1	yes	characteristic
319	C₂³×C₄	C₂²×C₅₃	1	1	yes	characteristic
320	C₄⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
321	C₄⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
322	C₄⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
323	#126	C₂²×C₅₃	1	2	yes	complemented
324	#126	C₂²×C₅₃	1	2	yes	complemented
325	#126	C₂²×C₅₃	1	2	yes	complemented
326	#126	C₂²×C₅₃	1	2	yes	complemented
327	#126	C₂²×C₅₃	1	2	yes	complemented
328	#126	C₂²×C₅₃	1	2	yes	complemented
329	#125	C₂²×C₅₃	1	2	yes	complemented
330	#125	C₂²×C₅₃	1	2	yes	complemented
331	#125	C₂²×C₅₃	1	2	yes	complemented
332	#125	C₂²×C₅₃	1	2	yes	complemented
333	#125	C₂²×C₅₃	1	2	yes	complemented
334	#124	C₂²×C₅₃	1	2	yes	—
335	#124	C₂²×C₅₃	1	2	yes	complemented
336	#124	C₂²×C₅₃	1	2	yes	complemented
337	#124	C₂²×C₅₃	1	2	yes	complemented
338	#123	C₂²×C₅₃	1	2	yes	—
339	#123	C₂²×C₅₃	1	2	yes	—
340	#123	C₂²×C₅₃	1	2	yes	—
341	#123	C₂²×C₅₃	1	2	yes	—
342	#123	C₂²×C₅₃	1	2	yes	—
343	#123	C₂²×C₅₃	1	2	yes	—
344	#123	C₂²×C₅₃	1	2	yes	—
345	#123	C₂²×C₅₃	1	2	yes	complemented
346	#123	C₂²×C₅₃	1	2	yes	complemented
347	#123	C₂²×C₅₃	1	2	yes	complemented
348	#123	C₂²×C₅₃	1	2	yes	complemented
349	#123	C₂²×C₅₃	1	2	yes	complemented
350	#123	C₂²×C₅₃	1	2	yes	complemented
351	#123	C₂²×C₅₃	1	2	yes	complemented
352	C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
353	C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
354	C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
355	C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
356	C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
357	C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
358	C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
359	C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
360	C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
361	C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
362	C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
363	C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
364	C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
365	C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
366	C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
367	C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
368	C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
369	C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
370	C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
371	C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
372	#121	C₂²×C₅₃	1	1	yes	characteristic
373	#121	C₂²×C₅₃	1	2	yes	—
374	#121	C₂²×C₅₃	1	2	yes	—
375	#121	C₂²×C₅₃	1	2	yes	—
376	#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
377	#121	C₂²×C₅₃	1	2	yes	complemented
378	#120	C₂²×C₅₃	1	2	yes	—
379	#120	C₂²×C₅₃	1	2	yes	—
380	C₄×Q₈	C₂²×C₅₃	1	2	yes	complemented
381	C₄×D₄	C₂²×C₅₃	1	2	yes	—
382	C₄×D₄	C₂²×C₅₃	1	2	yes	—
383	C₄×D₄	C₂²×C₅₃	1	2	yes	—
384	C₄×D₄	C₂²×C₅₃	1	2	yes	—
385	C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
386	C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
387	C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
388	#117	C₂²×C₅₃	1	2	yes	—
389	#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
390	#117	C₂²×C₅₃	1	2	yes	complemented
391	#117	C₂²×C₅₃	1	2	yes	complemented
392	C₂×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
394	C₂×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
395	C₂×C₄⋊C₄	C₂²×C₅₃	1	2	yes	complemented
396	C₂×C₄⋊C₄	C₂²×C₅₃	1	2	yes	complemented
397	C₂×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
398	C₂×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
399	C₂×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
400	C₂×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
401	C₂×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
402	C₂⁴	C₂³×C₅₃	1	1	yes	characteristic
403	C₂⁴	C₂³×C₅₃	1	1	yes	characteristic
404	#41	—	4	4	no	—
405	#41	—	4	2	no	—
406	C₂×Q₈	—	4	2	no	—
407	C₂×Q₈	C₂³×C₅₃	1	2	yes	—
408	C₂×Q₈	C₂³×C₅₃	1	1	yes	characteristic
409	C₂×Q₈	C₂³×C₅₃	1	2	yes	—
410	C₂×Q₈	C₂³×C₅₃	1	1	yes	characteristic
411	C₂×Q₈	C₂³×C₅₃	1	2	yes	—
412	C₂×Q₈	C₂³×C₅₃	1	1	yes	characteristic
413	C₂×D₄	—	4	2	no	—
414	C₂×D₄	C₂³×C₅₃	1	2	yes	—
415	C₂×D₄	C₂³×C₅₃	1	2	yes	—
416	C₂×D₄	C₂³×C₅₃	1	2	yes	—
417	C₂×D₄	C₂³×C₅₃	1	2	yes	—
418	C₂×D₄	C₂³×C₅₃	1	2	yes	—
419	C₂×D₄	C₂³×C₅₃	1	2	yes	—
420	C₂×D₄	C₂³×C₅₃	1	2	yes	—
421	C₂×D₄	C₂³×C₅₃	1	1	yes	characteristic
422	C₂²×C₄	—	4	2	no	—
423	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
424	C₂²×C₄	C₂³×C₅₃	1	2	yes	—
425	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
426	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
427	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
428	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
429	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
430	C₂²×C₄	C₂³×C₅₃	1	2	yes	—
431	C₂²×C₄	C₂³×C₅₃	1	2	yes	—
432	C₂²×C₄	C₂³×C₅₃	1	2	yes	—
433	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
434	C₂²×C₄	C₂³×C₅₃	1	2	yes	—
435	C₂²×C₄	C₂³×C₅₃	1	2	yes	—
436	C₂²×C₄	C₂³×C₅₃	1	2	yes	—
437	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
438	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
439	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
440	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
441	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
442	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
443	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
444	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
445	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
446	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
447	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
448	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
449	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
450	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
451	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
452	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
453	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
454	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
455	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
456	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
457	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
458	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
459	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
460	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
461	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
462	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
463	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
464	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
465	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
466	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
467	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
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	2	yes	—
473	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
474	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
475	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
476	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
477	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
478	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
479	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
480	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
481	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
482	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
483	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
484	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
485	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
486	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
487	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
488	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
489	C₄²	C₂³×C₅₃	1	2	yes	—
490	C₄²	C₂³×C₅₃	1	2	yes	—
491	C₄²	C₂³×C₅₃	1	2	yes	—
492	C₄²	C₂³×C₅₃	1	2	yes	—
493	C₄²	C₂³×C₅₃	1	2	yes	—
494	C₂³	—	2	2	no	—
495	C₂³	—	2	2	no	—
496	C₂³	—	2	2	no	—
497	C₂³	—	4	1	no	—
498	C₂³	—	4	1	no	—
499	C₂³	—	4	1	no	—
500	C₂³	C₂⁴×C₅₃	1	1	yes	characteristic
501	C₂³	C₂⁴×C₅₃	1	2	yes	—
502	C₂³	C₂⁴×C₅₃	1	2	yes	—
503	C₂³	C₂⁴×C₅₃	1	1	yes	characteristic
504	C₂³	C₂⁴×C₅₃	1	1	yes	characteristic
505	Q₈	—	4	1	no	—
506	Q₈	—	4	2	no	—
507	Q₈	—	4	1	no	—
508	Q₈	—	4	2	no	—
509	Q₈	—	4	1	no	—
510	Q₈	—	4	2	no	—
511	D₄	—	2	4	no	—
512	D₄	—	2	4	no	—
513	D₄	—	2	4	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	2	no	—
516	D₄	—	4	2	no	—
517	D₄	—	4	1	no	—
518	D₄	—	4	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	C₂⁴×C₅₃	1	2	yes	—
536	C₂×C₄	C₂⁴×C₅₃	1	2	yes	—
537	C₂×C₄	C₂⁴×C₅₃	1	2	yes	—
538	C₂×C₄	C₂⁴×C₅₃	1	2	yes	—
539	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
540	C₂×C₄	C₂⁴×C₅₃	1	2	yes	—
541	C₂×C₄	C₂⁴×C₅₃	1	2	yes	—
542	C₂×C₄	C₂⁴×C₅₃	1	2	yes	—
543	C₂×C₄	C₂⁴×C₅₃	1	2	yes	—
544	C₂×C₄	C₂⁴×C₅₃	1	2	yes	—
545	C₂×C₄	C₂⁴×C₅₃	1	2	yes	—
546	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
547	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
548	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	2	1	no	—
558	C₂²	—	2	2	no	—
559	C₂²	—	2	2	no	—
560	C₂²	—	2	2	no	—
561	C₂²	—	2	1	no	—
562	C₂²	—	4	4	no	—
563	C₂²	—	8	2	no	—
564	C₂²	H(5,𝔽₂)×C₅₃	1	2	yes	—
565	C₂²	2₋¹⁺⁴×C₅₃	1	2	yes	—
566	C₂²	C₂⁵×C₅₃	1	1	yes	characteristic
567	C₄	—	2	1	no	—
568	C₄	—	2	1	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	2	no	—
573	C₄	—	2	2	no	—
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	2	no	—
577	C₄	—	2	2	no	—
578	C₄	—	2	2	no	—
579	C₄	—	2	2	no	—
580	C₄	—	2	2	no	—
581	C₂	—	2	2	no	—
582	C₂	—	2	2	no	—
583	C₂	—	4	1	no	—
584	C₂	—	4	2	no	—
585	C₂	—	4	2	no	—
586	C₂	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
587	C₂	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
588	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×#563	C₂	semidirect
2. C₅₃×#562	C₂	semidirect
3. C₅₃×#554	C₂	semidirect
4. C₅₃×#552	C₂	semidirect
5. C₅₃×#551	C₂	semidirect
6. C₅₃×#551	C₂	semidirect
7. C₅₃×#547	C₂	semidirect
8. C₅₃×#546	C₂	semidirect
9. C₅₃×#544	C₂	semidirect
10. C₅₃×#543	C₂	semidirect
11. C₅₃×#542	C₂	semidirect
12. C₅₃×#539	C₂	semidirect
13. C₅₃×#539	C₂	semidirect
14. C₅₃×#539	C₂	semidirect
15. C₅₃×#538	C₂	semidirect
16. C₅₃×#536	C₂	semidirect
17. C₅₃×#525	C₂	semidirect
18. C₂×#123×C₅₃	C₂	semidirect
19. C₂×C₂²⋊Q₈×C₅₃	C₂	semidirect
21. C₂×#41×C₅₃	C₂²	semidirect
22. C₂²×Q₈×C₅₃	C₂²	semidirect
25. C₄⋊Q₈×C₅₃	C₂²	semidirect
26. C₄⋊Q₈×C₅₃	C₂²	semidirect
27. C₄⋊Q₈×C₅₃	C₂²	semidirect
28. #126×C₅₃	C₂²	semidirect
29. #126×C₅₃	C₂²	semidirect
30. #126×C₅₃	C₂²	semidirect
31. #126×C₅₃	C₂²	semidirect
32. #126×C₅₃	C₂²	semidirect
33. #126×C₅₃	C₂²	semidirect
34. #125×C₅₃	C₂²	semidirect
35. #125×C₅₃	C₂²	semidirect
36. #125×C₅₃	C₂²	semidirect
37. #125×C₅₃	C₂²	semidirect
38. #125×C₅₃	C₂²	semidirect
40. #124×C₅₃	C₂²	semidirect
41. #124×C₅₃	C₂²	semidirect
42. #124×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
63. C₂²⋊Q₈×C₅₃	C₂²	semidirect
64. C₂²⋊Q₈×C₅₃	C₂²	semidirect
65. C₂²⋊Q₈×C₅₃	C₂²	semidirect
66. C₂²⋊Q₈×C₅₃	C₂²	semidirect
67. C₂²⋊Q₈×C₅₃	C₂²	semidirect
68. C₂²⋊Q₈×C₅₃	C₂²	semidirect
69. C₂²⋊Q₈×C₅₃	C₂²	semidirect
70. C₂²⋊Q₈×C₅₃	C₂²	semidirect
71. C₂²⋊Q₈×C₅₃	C₂²	semidirect
72. C₂²⋊Q₈×C₅₃	C₂²	semidirect
73. C₂²⋊Q₈×C₅₃	C₂²	semidirect
74. C₂²⋊Q₈×C₅₃	C₂²	semidirect
75. C₂²⋊Q₈×C₅₃	C₂²	semidirect
76. C₂²⋊Q₈×C₅₃	C₂²	semidirect
81. #121×C₅₃	C₂²	semidirect
82. #121×C₅₃	C₂²	semidirect
85. C₄×Q₈×C₅₃	C₂²	semidirect
90. C₄×D₄×C₅₃	C₂²	semidirect
91. C₄×D₄×C₅₃	C₂²	semidirect
92. C₄×D₄×C₅₃	C₂²	semidirect
94. #117×C₅₃	C₂²	semidirect
95. #117×C₅₃	C₂²	semidirect
96. #117×C₅₃	C₂²	semidirect
99. C₂×C₄⋊C₄×C₅₃	C₂²	semidirect
100. C₂×C₄⋊C₄×C₅₃	C₂²	semidirect
101. C₂×C₄⋊C₄×C₅₃	C₂²	semidirect
286. #3535	C₅₃	direct (N × H)
295. #563	C₂×C₅₃	semidirect
296. #562	C₂×C₅₃	semidirect
297. #554	C₂×C₅₃	semidirect
298. #552	C₂×C₅₃	semidirect
299. #551	C₂×C₅₃	semidirect
300. #551	C₂×C₅₃	semidirect
301. #547	C₂×C₅₃	semidirect
302. #546	C₂×C₅₃	semidirect
303. #544	C₂×C₅₃	semidirect
304. #543	C₂×C₅₃	semidirect
305. #542	C₂×C₅₃	semidirect
306. #539	C₂×C₅₃	semidirect
307. #539	C₂×C₅₃	semidirect
308. #539	C₂×C₅₃	semidirect
309. #538	C₂×C₅₃	semidirect
310. #536	C₂×C₅₃	semidirect
311. #525	C₂×C₅₃	semidirect
312. C₂×#123	C₂×C₅₃	semidirect
313. C₂×C₂²⋊Q₈	C₂×C₅₃	semidirect
314. C₅₃	#3535	direct (N × H)
316. C₂×#41	C₂²×C₅₃	semidirect
317. C₂²×Q₈	C₂²×C₅₃	semidirect
320. C₄⋊Q₈	C₂²×C₅₃	semidirect
321. C₄⋊Q₈	C₂²×C₅₃	semidirect
322. C₄⋊Q₈	C₂²×C₅₃	semidirect
323. #126	C₂²×C₅₃	semidirect
324. #126	C₂²×C₅₃	semidirect
325. #126	C₂²×C₅₃	semidirect
326. #126	C₂²×C₅₃	semidirect
327. #126	C₂²×C₅₃	semidirect
328. #126	C₂²×C₅₃	semidirect
329. #125	C₂²×C₅₃	semidirect
330. #125	C₂²×C₅₃	semidirect
331. #125	C₂²×C₅₃	semidirect
332. #125	C₂²×C₅₃	semidirect
333. #125	C₂²×C₅₃	semidirect
335. #124	C₂²×C₅₃	semidirect
336. #124	C₂²×C₅₃	semidirect
337. #124	C₂²×C₅₃	semidirect
345. #123	C₂²×C₅₃	semidirect
346. #123	C₂²×C₅₃	semidirect
347. #123	C₂²×C₅₃	semidirect
348. #123	C₂²×C₅₃	semidirect
349. #123	C₂²×C₅₃	semidirect
350. #123	C₂²×C₅₃	semidirect
351. #123	C₂²×C₅₃	semidirect
358. C₂²⋊Q₈	C₂²×C₅₃	semidirect
359. C₂²⋊Q₈	C₂²×C₅₃	semidirect
360. C₂²⋊Q₈	C₂²×C₅₃	semidirect
361. C₂²⋊Q₈	C₂²×C₅₃	semidirect
362. C₂²⋊Q₈	C₂²×C₅₃	semidirect
363. C₂²⋊Q₈	C₂²×C₅₃	semidirect
364. C₂²⋊Q₈	C₂²×C₅₃	semidirect
365. C₂²⋊Q₈	C₂²×C₅₃	semidirect
366. C₂²⋊Q₈	C₂²×C₅₃	semidirect
367. C₂²⋊Q₈	C₂²×C₅₃	semidirect
368. C₂²⋊Q₈	C₂²×C₅₃	semidirect
369. C₂²⋊Q₈	C₂²×C₅₃	semidirect
370. C₂²⋊Q₈	C₂²×C₅₃	semidirect
371. C₂²⋊Q₈	C₂²×C₅₃	semidirect
376. #121	C₂²×C₅₃	semidirect
377. #121	C₂²×C₅₃	semidirect
380. C₄×Q₈	C₂²×C₅₃	semidirect
385. C₄×D₄	C₂²×C₅₃	semidirect
386. C₄×D₄	C₂²×C₅₃	semidirect
387. C₄×D₄	C₂²×C₅₃	semidirect
389. #117	C₂²×C₅₃	semidirect
390. #117	C₂²×C₅₃	semidirect
391. #117	C₂²×C₅₃	semidirect
394. C₂×C₄⋊C₄	C₂²×C₅₃	semidirect
395. C₂×C₄⋊C₄	C₂²×C₅₃	semidirect
396. C₂×C₄⋊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×#563	2
C₅₃×#562	2
C₅₃×#554	2
C₅₃×#552	2
C₅₃×#551	2
C₅₃×#547	2
C₅₃×#546	2
C₅₃×#544	2
C₅₃×#543	2
C₅₃×#542	2
C₅₃×#539	2
C₅₃×#538	2
C₅₃×#536	2
C₅₃×#525	2
C₂×#123×C₅₃	2
C₂×C₂²⋊Q₈×C₅₃	2
#3535	53

Subgroups — C53×#3535 #20272472

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#3535 #20272472