Subgroups — C₅₃×#3554 #20272491

Order 6784.

1022 conjugacy classes of subgroups.

The subgroup lattice has 442 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	4	yes	maximal, complemented
2	C₅₃×#559	C₂	1	2	yes	maximal, complemented
3	C₅₃×#559	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#554	C₂	1	2	yes	maximal, complemented
6	C₅₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
7	D₄×Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#548	C₂	1	2	yes	maximal, complemented
9	C₅₃×#547	C₂	1	2	yes	maximal, complemented
10	C₅₃×#542	C₂	1	2	yes	maximal, complemented
11	C₅₃×#542	C₂	1	2	yes	maximal, complemented
12	C₅₃×#540	C₂	1	2	yes	maximal, complemented
13	C₅₃×#539	C₂	1	4	yes	maximal, complemented
14	C₅₃×#536	C₂	1	2	yes	maximal, complemented
15	C₅₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#41×C₅₃	C₂²	1	2	yes	—
19	C₂×#41×C₅₃	C₂²	1	2	yes	—
20	C₂²×Q₈×C₅₃	C₂²	1	2	yes	—
21	C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
22	C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
23	C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
24	C₄⋊Q₈×C₅₃	C₂²	1	2	yes	—
25	C₄⋊Q₈×C₅₃	C₂²	1	2	yes	—
26	#127×C₅₃	C₂²	1	1	yes	characteristic
27	#127×C₅₃	C₂²	1	2	yes	—
28	#126×C₅₃	C₂²	1	2	yes	—
29	#126×C₅₃	C₂²	1	4	yes	—
30	#125×C₅₃	C₂²	1	1	yes	characteristic
31	#125×C₅₃	C₂²	1	2	yes	—
32	#125×C₅₃	C₂²	1	4	yes	—
33	#125×C₅₃	C₂²	1	2	yes	—
34	#124×C₅₃	C₂²	1	1	yes	characteristic
35	#124×C₅₃	C₂²	1	2	yes	—
36	#124×C₅₃	C₂²	1	2	yes	—
37	#124×C₅₃	C₂²	1	4	yes	—
38	#124×C₅₃	C₂²	1	2	yes	—
39	#124×C₅₃	C₂²	1	4	yes	—
40	#123×C₅₃	C₂²	1	2	yes	—
41	#123×C₅₃	C₂²	1	4	yes	—
42	#123×C₅₃	C₂²	1	4	yes	—
43	#123×C₅₃	C₂²	1	4	yes	—
44	#123×C₅₃	C₂²	1	4	yes	—
45	#123×C₅₃	C₂²	1	4	yes	—
46	#123×C₅₃	C₂²	1	4	yes	—
47	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
48	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
49	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
50	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
51	C₂²⋊Q₈×C₅₃	C₂²	1	4	yes	—
52	C₂²⋊Q₈×C₅₃	C₂²	1	4	yes	—
53	C₂²⋊Q₈×C₅₃	C₂²	1	4	yes	—
54	C₂²⋊Q₈×C₅₃	C₂²	1	4	yes	—
55	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
56	C₂²⋊Q₈×C₅₃	C₂²	1	4	yes	—
57	#121×C₅₃	C₂²	1	1	yes	characteristic
58	#121×C₅₃	C₂²	1	2	yes	—
59	#121×C₅₃	C₂²	1	2	yes	—
60	#121×C₅₃	C₂²	1	4	yes	—
61	#121×C₅₃	C₂²	1	4	yes	—
62	#121×C₅₃	C₂²	1	4	yes	—
63	#121×C₅₃	C₂²	1	2	yes	—
64	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
65	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
66	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
67	C₄×Q₈×C₅₃	C₂²	1	2	yes	—
68	C₄×Q₈×C₅₃	C₂²	1	2	yes	—
69	C₄×Q₈×C₅₃	C₂²	1	2	yes	—
70	C₄×D₄×C₅₃	C₂²	1	2	yes	—
71	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
72	C₄×D₄×C₅₃	C₂²	1	2	yes	—
73	C₄×D₄×C₅₃	C₂²	1	2	yes	—
74	C₄×D₄×C₅₃	C₂²	1	4	yes	—
75	C₄×D₄×C₅₃	C₂²	1	2	yes	—
76	C₄×D₄×C₅₃	C₂²	1	2	yes	—
77	C₄×D₄×C₅₃	C₂²	1	2	yes	—
78	C₄×D₄×C₅₃	C₂²	1	2	yes	—
79	#117×C₅₃	C₂²	1	2	yes	—
80	#117×C₅₃	C₂²	1	2	yes	—
81	C₂×C₄⋊C₄×C₅₃	C₂²	1	4	yes	—
82	C₂×C₄²×C₅₃	C₂²	1	1	yes	characteristic
83	#41×C₅₃	—	4	4	no	—
84	#41×C₅₃	—	4	4	no	—
85	C₂×Q₈×C₅₃	—	4	4	no	—
86	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
87	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
88	C₂×Q₈×C₅₃	C₂³	1	2	yes	—
89	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
90	C₂×Q₈×C₅₃	C₂³	1	2	yes	—
91	C₂×Q₈×C₅₃	C₂³	1	4	yes	—
92	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
93	C₂×D₄×C₅₃	C₂³	1	2	yes	—
94	C₂×D₄×C₅₃	C₂³	1	2	yes	—
95	C₂×D₄×C₅₃	C₂³	1	2	yes	—
96	C₂×D₄×C₅₃	C₂³	1	2	yes	—
97	C₂×D₄×C₅₃	C₂³	1	4	yes	—
98	C₂×D₄×C₅₃	C₂³	1	4	yes	—
99	C₂×D₄×C₅₃	C₂³	1	4	yes	—
100	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
101	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
102	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
103	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
104	C₂²×C₄×C₅₃	C₂³	1	4	yes	—
105	C₂²×C₄×C₅₃	C₂³	1	4	yes	—
106	C₂²×C₄×C₅₃	C₂³	1	4	yes	—
107	C₂²×C₄×C₅₃	C₂³	1	4	yes	—
108	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
109	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
110	C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
111	C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
112	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
113	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
114	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
115	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
116	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
117	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
118	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
119	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
120	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
121	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
122	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
123	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
124	C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
125	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
126	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
127	C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
128	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
129	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
130	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
131	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
132	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
133	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
134	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
135	C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
136	C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
137	C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
138	C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
139	C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
140	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
141	C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
142	C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
143	C₄²×C₅₃	C₂³	1	1	yes	characteristic
144	C₄²×C₅₃	C₂³	1	1	yes	characteristic
145	C₄²×C₅₃	C₂³	1	1	yes	characteristic
146	C₄²×C₅₃	C₂³	1	1	yes	characteristic
147	C₄²×C₅₃	C₂³	1	2	yes	—
148	C₄²×C₅₃	C₂³	1	2	yes	—
149	C₄²×C₅₃	C₂³	1	2	yes	—
150	C₄²×C₅₃	C₂³	1	4	yes	—
151	C₂³×C₅₃	C₂⁴	1	2	yes	—
152	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
153	C₂³×C₅₃	C₂⁴	1	4	yes	—
154	Q₈×C₅₃	—	2	2	no	—
155	Q₈×C₅₃	—	2	4	no	—
156	Q₈×C₅₃	—	2	2	no	—
157	Q₈×C₅₃	—	2	2	no	—
158	Q₈×C₅₃	—	4	4	no	—
159	Q₈×C₅₃	—	4	2	no	—
160	D₄×C₅₃	—	2	4	no	—
161	D₄×C₅₃	—	2	2	no	—
162	D₄×C₅₃	—	2	4	no	—
163	D₄×C₅₃	—	4	2	no	—
164	D₄×C₅₃	—	4	2	no	—
165	D₄×C₅₃	—	4	4	no	—
166	D₄×C₅₃	—	4	4	no	—
167	D₄×C₅₃	—	4	4	no	—
168	C₂×C₄×C₅₃	—	2	4	no	—
169	C₂×C₄×C₅₃	—	2	2	no	—
170	C₂×C₄×C₅₃	—	2	2	no	—
171	C₂×C₄×C₅₃	—	4	4	no	—
172	C₂×C₄×C₅₃	—	4	1	no	—
173	C₂×C₄×C₅₃	—	4	4	no	—
174	C₂×C₄×C₅₃	—	4	4	no	—
175	C₂×C₄×C₅₃	—	4	4	no	—
176	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
178	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
179	C₂×C₄×C₅₃	C₂⁴	1	4	yes	—
180	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
181	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
182	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
183	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
184	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
185	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
186	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
187	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
188	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
189	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
190	C₂²×C₅₃	—	2	2	no	—
191	C₂²×C₅₃	—	2	1	no	—
192	C₂²×C₅₃	—	2	4	no	—
193	C₂²×C₅₃	—	2	1	no	—
194	C₂²×C₅₃	—	2	2	no	—
195	C₂²×C₅₃	—	2	4	no	—
196	C₂²×C₅₃	—	2	1	no	—
197	C₂²×C₅₃	—	2	4	no	—
198	C₂²×C₅₃	—	2	2	no	—
199	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
200	C₄×C₅₃	—	2	1	no	—
201	C₄×C₅₃	—	2	2	no	—
202	C₄×C₅₃	—	2	2	no	—
203	C₄×C₅₃	—	2	4	no	—
204	C₄×C₅₃	—	2	2	no	—
205	C₄×C₅₃	—	2	1	no	—
206	C₄×C₅₃	—	2	2	no	—
207	C₄×C₅₃	—	2	2	no	—
208	C₄×C₅₃	—	2	2	no	—
209	C₄×C₅₃	—	2	1	no	—
210	C₄×C₅₃	—	2	1	no	—
211	C₄×C₅₃	—	2	2	no	—
212	C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
213	C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
214	#3554	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₂×C₅₃	—	4	2	no	—
216	C₂×C₅₃	—	4	1	no	—
217	C₂×C₅₃	—	4	4	no	—
218	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
219	C₂×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
220	C₂×C₅₃	#585	1	1	yes	characteristic
221	#562	C₂×C₅₃	1	4	yes	complemented
222	#559	C₂×C₅₃	1	2	yes	complemented
223	#559	C₂×C₅₃	1	1	yes	characteristic, complemented
224	#557	C₂×C₅₃	1	1	yes	characteristic, complemented
225	#554	C₂×C₅₃	1	2	yes	complemented
226	#550	C₂×C₅₃	1	1	yes	characteristic, complemented
227	D₄×Q₈	C₂×C₅₃	1	1	yes	characteristic, complemented
228	#548	C₂×C₅₃	1	2	yes	complemented
229	#547	C₂×C₅₃	1	2	yes	complemented
230	#542	C₂×C₅₃	1	2	yes	complemented
231	#542	C₂×C₅₃	1	2	yes	complemented
232	#540	C₂×C₅₃	1	2	yes	complemented
233	#539	C₂×C₅₃	1	4	yes	complemented
234	#536	C₂×C₅₃	1	2	yes	complemented
235	#533	C₂×C₅₃	1	1	yes	characteristic, complemented
236	#532	C₂×C₅₃	1	1	yes	characteristic, complemented
237	#529	C₂×C₅₃	1	1	yes	characteristic, complemented
238	C₅₃	#3554	1	1	yes	characteristic, direct product factor, Sylow
239	C₂×#41	C₂²×C₅₃	1	2	yes	—
240	C₂×#41	C₂²×C₅₃	1	2	yes	—
241	C₂²×Q₈	C₂²×C₅₃	1	2	yes	—
242	C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
243	C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
244	C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
245	C₄⋊Q₈	C₂²×C₅₃	1	2	yes	—
246	C₄⋊Q₈	C₂²×C₅₃	1	2	yes	—
247	#127	C₂²×C₅₃	1	1	yes	characteristic
248	#127	C₂²×C₅₃	1	2	yes	—
249	#126	C₂²×C₅₃	1	2	yes	—
250	#126	C₂²×C₅₃	1	4	yes	—
251	#125	C₂²×C₅₃	1	1	yes	characteristic
252	#125	C₂²×C₅₃	1	2	yes	—
253	#125	C₂²×C₅₃	1	4	yes	—
254	#125	C₂²×C₅₃	1	2	yes	—
255	#124	C₂²×C₅₃	1	1	yes	characteristic
256	#124	C₂²×C₅₃	1	2	yes	—
257	#124	C₂²×C₅₃	1	2	yes	—
258	#124	C₂²×C₅₃	1	4	yes	—
259	#124	C₂²×C₅₃	1	2	yes	—
260	#124	C₂²×C₅₃	1	4	yes	—
261	#123	C₂²×C₅₃	1	2	yes	—
262	#123	C₂²×C₅₃	1	4	yes	—
263	#123	C₂²×C₅₃	1	4	yes	—
264	#123	C₂²×C₅₃	1	4	yes	—
265	#123	C₂²×C₅₃	1	4	yes	—
266	#123	C₂²×C₅₃	1	4	yes	—
267	#123	C₂²×C₅₃	1	4	yes	—
268	C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
269	C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
270	C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
271	C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
272	C₂²⋊Q₈	C₂²×C₅₃	1	4	yes	—
273	C₂²⋊Q₈	C₂²×C₅₃	1	4	yes	—
274	C₂²⋊Q₈	C₂²×C₅₃	1	4	yes	—
275	C₂²⋊Q₈	C₂²×C₅₃	1	4	yes	—
276	C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
277	C₂²⋊Q₈	C₂²×C₅₃	1	4	yes	—
278	#121	C₂²×C₅₃	1	1	yes	characteristic
279	#121	C₂²×C₅₃	1	2	yes	—
280	#121	C₂²×C₅₃	1	2	yes	—
281	#121	C₂²×C₅₃	1	4	yes	—
282	#121	C₂²×C₅₃	1	4	yes	—
283	#121	C₂²×C₅₃	1	4	yes	—
284	#121	C₂²×C₅₃	1	2	yes	—
285	C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
286	C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
287	C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
288	C₄×Q₈	C₂²×C₅₃	1	2	yes	—
289	C₄×Q₈	C₂²×C₅₃	1	2	yes	—
290	C₄×Q₈	C₂²×C₅₃	1	2	yes	—
291	C₄×D₄	C₂²×C₅₃	1	2	yes	—
292	C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
293	C₄×D₄	C₂²×C₅₃	1	2	yes	—
294	C₄×D₄	C₂²×C₅₃	1	2	yes	—
295	C₄×D₄	C₂²×C₅₃	1	4	yes	—
296	C₄×D₄	C₂²×C₅₃	1	2	yes	—
297	C₄×D₄	C₂²×C₅₃	1	2	yes	—
298	C₄×D₄	C₂²×C₅₃	1	2	yes	—
299	C₄×D₄	C₂²×C₅₃	1	2	yes	—
300	#117	C₂²×C₅₃	1	2	yes	—
301	#117	C₂²×C₅₃	1	2	yes	—
302	C₂×C₄⋊C₄	C₂²×C₅₃	1	4	yes	—
303	C₂×C₄²	C₂²×C₅₃	1	1	yes	characteristic
304	#41	—	4	4	no	—
305	#41	—	4	4	no	—
306	C₂×Q₈	—	4	4	no	—
307	C₂×Q₈	C₂³×C₅₃	1	1	yes	characteristic
308	C₂×Q₈	C₂³×C₅₃	1	1	yes	characteristic
309	C₂×Q₈	C₂³×C₅₃	1	2	yes	—
310	C₂×Q₈	C₂³×C₅₃	1	1	yes	characteristic
311	C₂×Q₈	C₂³×C₅₃	1	2	yes	—
312	C₂×Q₈	C₂³×C₅₃	1	4	yes	—
313	C₂×D₄	C₂³×C₅₃	1	1	yes	characteristic
314	C₂×D₄	C₂³×C₅₃	1	2	yes	—
315	C₂×D₄	C₂³×C₅₃	1	2	yes	—
316	C₂×D₄	C₂³×C₅₃	1	2	yes	—
317	C₂×D₄	C₂³×C₅₃	1	2	yes	—
318	C₂×D₄	C₂³×C₅₃	1	4	yes	—
319	C₂×D₄	C₂³×C₅₃	1	4	yes	—
320	C₂×D₄	C₂³×C₅₃	1	4	yes	—
321	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
322	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
323	C₂²×C₄	C₂³×C₅₃	1	2	yes	—
324	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
325	C₂²×C₄	C₂³×C₅₃	1	4	yes	—
326	C₂²×C₄	C₂³×C₅₃	1	4	yes	—
327	C₂²×C₄	C₂³×C₅₃	1	4	yes	—
328	C₂²×C₄	C₂³×C₅₃	1	4	yes	—
329	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
330	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
331	C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
332	C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
333	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
334	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
335	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
336	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
337	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
338	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
339	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
340	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
341	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
342	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
343	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
344	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
345	C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
346	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
347	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
348	C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
349	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
350	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
351	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
352	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
353	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
354	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
355	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
356	C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
357	C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
358	C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
359	C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
360	C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
361	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
362	C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
363	C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
364	C₄²	C₂³×C₅₃	1	1	yes	characteristic
365	C₄²	C₂³×C₅₃	1	1	yes	characteristic
366	C₄²	C₂³×C₅₃	1	1	yes	characteristic
367	C₄²	C₂³×C₅₃	1	1	yes	characteristic
368	C₄²	C₂³×C₅₃	1	2	yes	—
369	C₄²	C₂³×C₅₃	1	2	yes	—
370	C₄²	C₂³×C₅₃	1	2	yes	—
371	C₄²	C₂³×C₅₃	1	4	yes	—
372	C₂³	C₂⁴×C₅₃	1	2	yes	—
373	C₂³	C₂⁴×C₅₃	1	1	yes	characteristic
374	C₂³	C₂⁴×C₅₃	1	4	yes	—
375	Q₈	—	2	2	no	—
376	Q₈	—	2	4	no	—
377	Q₈	—	2	2	no	—
378	Q₈	—	2	2	no	—
379	Q₈	—	4	4	no	—
380	Q₈	—	4	2	no	—
381	D₄	—	2	4	no	—
382	D₄	—	2	2	no	—
383	D₄	—	2	4	no	—
384	D₄	—	4	2	no	—
385	D₄	—	4	2	no	—
386	D₄	—	4	4	no	—
387	D₄	—	4	4	no	—
388	D₄	—	4	4	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	4	no	—
395	C₂×C₄	—	4	4	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	C₂⁴×C₅₃	1	2	yes	—
398	C₂×C₄	C₂⁴×C₅₃	1	2	yes	—
399	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
400	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
401	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
402	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
403	C₂×C₄	C₂⁴×C₅₃	1	2	yes	—
404	C₂×C₄	C₂⁴×C₅₃	1	2	yes	—
405	C₂×C₄	C₂⁴×C₅₃	1	2	yes	—
406	C₂×C₄	C₂⁴×C₅₃	1	4	yes	—
407	C₂×C₄	C₂⁴×C₅₃	1	2	yes	—
408	C₂×C₄	C₂⁴×C₅₃	1	2	yes	—
409	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
410	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
411	C₂²	—	2	2	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	2	4	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	4	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	4	no	—
419	C₂²	—	2	2	no	—
420	C₂²	C₂⁵×C₅₃	1	1	yes	characteristic
421	C₄	—	2	1	no	—
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	2	4	no	—
425	C₄	—	2	2	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	2	no	—
428	C₄	—	2	2	no	—
429	C₄	—	2	2	no	—
430	C₄	—	2	1	no	—
431	C₄	—	2	1	no	—
432	C₄	—	2	2	no	—
433	C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
434	C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
435	C₂	—	4	2	no	—
436	C₂	—	4	1	no	—
437	C₂	—	4	4	no	—
438	C₂	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
439	C₂	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
440	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×#559	C₂	semidirect
3. C₅₃×#559	C₂	semidirect
4. C₅₃×#557	C₂	semidirect
5. C₅₃×#554	C₂	semidirect
6. C₅₃×#550	C₂	semidirect
7. D₄×Q₈×C₅₃	C₂	semidirect
8. C₅₃×#548	C₂	semidirect
9. C₅₃×#547	C₂	semidirect
10. C₅₃×#542	C₂	semidirect
11. C₅₃×#542	C₂	semidirect
12. C₅₃×#540	C₂	semidirect
13. C₅₃×#539	C₂	semidirect
14. C₅₃×#536	C₂	semidirect
15. C₅₃×#533	C₂	semidirect
16. C₅₃×#532	C₂	semidirect
17. C₅₃×#529	C₂	semidirect
214. #3554	C₅₃	direct (N × H)
221. #562	C₂×C₅₃	semidirect
222. #559	C₂×C₅₃	semidirect
223. #559	C₂×C₅₃	semidirect
224. #557	C₂×C₅₃	semidirect
225. #554	C₂×C₅₃	semidirect
226. #550	C₂×C₅₃	semidirect
227. D₄×Q₈	C₂×C₅₃	semidirect
228. #548	C₂×C₅₃	semidirect
229. #547	C₂×C₅₃	semidirect
230. #542	C₂×C₅₃	semidirect
231. #542	C₂×C₅₃	semidirect
232. #540	C₂×C₅₃	semidirect
233. #539	C₂×C₅₃	semidirect
234. #536	C₂×C₅₃	semidirect
235. #533	C₂×C₅₃	semidirect
236. #532	C₂×C₅₃	semidirect
237. #529	C₂×C₅₃	semidirect
238. C₅₃	#3554	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×#562	2
C₅₃×#559	2
C₅₃×#557	2
C₅₃×#554	2
C₅₃×#550	2
D₄×Q₈×C₅₃	2
C₅₃×#548	2
C₅₃×#547	2
C₅₃×#542	2
C₅₃×#540	2
C₅₃×#539	2
C₅₃×#536	2
C₅₃×#533	2
C₅₃×#532	2
C₅₃×#529	2
#3554	53

Subgroups — C53×#3554 #20272491

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#3554 #20272491