Subgroups — C₂²×#120×D₅₃ #28290721

Order 13568.

42862 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁶×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₄×D₅₃	C₂	1	3	yes	maximal, complemented
3	C₂²×#13133187	C₂	1	3	yes	maximal, complemented
4	C₂²×#13133186	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#13133185	C₂	1	3	yes	maximal, complemented
6	C₂×#120×D₅₃	C₂	1	48	yes	maximal, direct product factor
7	C₂²×C₂²⋊C₄×D₅₃	C₂	1	3	yes	maximal, complemented
8	C₂²×#120×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂⁵×D₅₃	—	2	48	no	—
10	C₂⁵×D₅₃	C₂²	1	3	yes	—
11	C₂⁵×D₅₃	C₂²	1	3	yes	complemented
12	C₂⁵×D₅₃	C₂²	1	24	yes	complemented
13	C₂⁵×D₅₃	C₂²	1	1	yes	characteristic, complemented
14	C₂³×D₂₁₂	C₂²	1	3	yes	complemented
15	C₂³×C₂²⋊D₅₃	C₂²	1	3	yes	complemented
16	C₂³×C₂²⋊D₅₃	C₂²	1	3	yes	complemented
17	C₂²×D₄×D₅₃	—	2	48	no	—
18	C₂²×D₄×D₅₃	C₂²	1	72	yes	complemented
19	C₂³×C₄×D₅₃	C₂²	1	3	yes	complemented
20	C₂×#13133187	C₂²	1	72	yes	complemented
21	C₂×#13133186	C₂²	1	24	yes	complemented
22	C₂×#13133185	C₂²	1	72	yes	complemented
23	#120×D₅₃	C₂²	1	256	yes	direct product factor
24	C₂²×C₂²⋊Dic₅₃	C₂²	1	3	yes	complemented
25	C₂²×#11719921	C₂²	1	6	yes	complemented
26	C₂×C₂²⋊C₄×D₅₃	C₂²	1	72	yes	complemented
27	C₂⁶×C₅₃	C₂²	1	1	yes	characteristic, complemented
28	C₂³×D₄×C₅₃	C₂²	1	3	yes	complemented
29	C₂×#120×C₅₃	C₂²	1	24	yes	complemented
30	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	3	yes	complemented
31	C₂⁴×D₅₃	—	2	512	no	—
32	C₂⁴×D₅₃	—	2	24	no	—
33	C₂⁴×D₅₃	—	2	48	no	—
34	C₂⁴×D₅₃	—	2	48	no	—
35	C₂⁴×D₅₃	—	2	576	no	—
36	C₂⁴×D₅₃	—	2	24	no	—
37	C₂⁴×D₅₃	D₄	1	48	yes	complemented
38	C₂⁴×D₅₃	C₂³	1	36	yes	—
39	C₂⁴×D₅₃	C₂³	1	3	yes	—
40	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
41	C₂⁴×D₅₃	C₂³	1	64	yes	complemented
42	C₂⁴×D₅₃	C₂³	1	36	yes	complemented
43	C₂⁴×D₅₃	C₂³	1	12	yes	complemented
44	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic, complemented
45	C₂²×D₂₁₂	—	2	24	no	—
46	C₂²×D₂₁₂	C₂³	1	36	yes	complemented
47	C₂²×C₂²⋊D₅₃	—	2	24	no	—
48	C₂²×C₂²⋊D₅₃	—	2	24	no	—
49	C₂²×C₂²⋊D₅₃	C₂³	1	36	yes	complemented
50	C₂²×C₂²⋊D₅₃	C₂³	1	36	yes	complemented
51	C₂×D₄×D₅₃	—	2	576	no	—
52	C₂×D₄×D₅₃	C₂³	1	192	yes	complemented
53	C₂³×Dic₅₃	C₂³	1	3	yes	complemented
54	C₂²×C₄×D₅₃	—	2	24	no	—
55	C₂²×C₄×D₅₃	C₂³	1	36	yes	complemented
56	#13133187	C₂³	1	192	yes	complemented
57	#13133186	C₂³	1	64	yes	complemented
58	#13133185	C₂³	1	192	yes	complemented
59	C₂×C₂²⋊Dic₅₃	C₂³	1	36	yes	complemented
60	C₂×#11719921	C₂³	1	72	yes	complemented
61	C₂²⋊C₄×D₅₃	C₂³	1	192	yes	complemented
62	C₂⁵×C₅₃	—	2	24	no	—
63	C₂⁵×C₅₃	C₂³	1	3	yes	—
64	C₂⁵×C₅₃	C₂³	1	12	yes	complemented
65	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic, complemented
66	C₂²×D₄×C₅₃	—	2	24	no	—
67	C₂²×D₄×C₅₃	C₂³	1	36	yes	complemented
68	C₂³×C₄×C₅₃	C₂³	1	3	yes	complemented
69	#120×C₅₃	C₂³	1	64	yes	complemented
70	C₂×C₂²⋊C₄×C₅₃	C₂³	1	36	yes	complemented
71	C₂⁴×C₅₃	—	2	128	no	—
72	C₂⁴×C₅₃	—	2	24	no	—
73	C₂⁴×C₅₃	—	2	144	no	—
74	C₂⁴×C₅₃	—	2	12	no	—
75	C₂⁴×C₅₃	C₂×D₄	1	24	yes	complemented
76	C₂⁴×C₅₃	C₂⁴	1	18	yes	—
77	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
78	C₂⁴×C₅₃	C₂⁴	1	16	yes	complemented
79	C₂⁴×C₅₃	C₂⁴	1	6	yes	complemented
80	C₂³×D₅₃	—	2	384	no	—
81	C₂³×D₅₃	—	2	3072	no	—
82	C₂³×D₅₃	—	2	24	no	—
83	C₂³×D₅₃	—	2	144	no	—
84	C₂³×D₅₃	—	2	384	no	—
85	C₂³×D₅₃	—	2	288	no	—
86	C₂³×D₅₃	—	2	288	no	—
87	C₂³×D₅₃	—	2	768	no	—
88	C₂³×D₅₃	—	2	12	no	—
89	C₂³×D₅₃	—	2	144	no	—
90	C₂³×D₅₃	—	4	64	no	—
91	C₂³×D₅₃	C₂×D₄	1	24	yes	—
92	C₂³×D₅₃	C₂×D₄	1	288	yes	complemented
93	C₂³×D₅₃	C₂×D₄	1	24	yes	complemented
94	C₂³×D₅₃	C₂⁴	1	48	yes	—
95	C₂³×D₅₃	C₂⁴	1	18	yes	—
96	C₂³×D₅₃	C₂⁴	1	6	yes	—
97	C₂³×D₅₃	C₂⁴	1	48	yes	complemented
98	C₂³×D₅₃	C₂⁴	1	16	yes	complemented
99	C₂³×D₅₃	C₂⁴	1	6	yes	complemented
100	C₂×D₄×C₅₃	—	2	144	no	—
101	C₂×D₄×C₅₃	C₂⁴	1	48	yes	complemented
102	C₂²×C₄×C₅₃	—	2	12	no	—
103	C₂²×C₄×C₅₃	C₂⁴	1	18	yes	complemented
104	C₂×C₂²⋊D₅₃	—	2	144	no	—
105	C₂×C₂²⋊D₅₃	—	2	144	no	—
106	C₂×C₂²⋊D₅₃	C₂⁴	1	48	yes	complemented
107	C₂×C₂²⋊D₅₃	C₂⁴	1	48	yes	complemented
108	C₂²×Dic₅₃	—	2	12	no	—
109	C₂²×Dic₅₃	C₂⁴	1	18	yes	complemented
110	D₄×D₅₃	—	2	768	no	—
111	C₂×D₂₁₂	—	2	144	no	—
112	C₂×D₂₁₂	C₂⁴	1	48	yes	complemented
113	C₂×C₄×D₅₃	—	2	144	no	—
114	C₂×C₄×D₅₃	C₂⁴	1	48	yes	complemented
115	C₂²⋊C₄×C₅₃	C₂⁴	1	48	yes	complemented
116	C₂²⋊Dic₅₃	C₂⁴	1	48	yes	complemented
117	#11719921	C₂⁴	1	96	yes	complemented
118	C₂³×C₅₃	—	2	384	no	—
119	C₂³×C₅₃	—	2	96	no	—
120	C₂³×C₅₃	—	2	72	no	—
121	C₂³×C₅₃	—	2	96	no	—
122	C₂³×C₅₃	—	2	36	no	—
123	C₂³×C₅₃	—	4	16	no	—
124	C₂³×C₅₃	C₂²×D₄	1	12	yes	—
125	C₂³×C₅₃	C₂²×D₄	1	72	yes	complemented
126	C₂³×C₅₃	C₂⁵	1	12	yes	—
127	C₂³×C₅₃	C₂⁵	1	3	yes	—
128	C₂³×C₅₃	C₂⁵	1	4	yes	complemented
129	C₂²×D₅₃	—	2	1152	no	—
130	C₂²×D₅₃	—	2	2048	no	—
131	C₂²×D₅₃	—	2	96	no	—
132	C₂²×D₅₃	—	2	72	no	—
133	C₂²×D₅₃	—	2	96	no	—
134	C₂²×D₅₃	—	2	1152	no	—
135	C₂²×D₅₃	—	2	192	no	—
136	C₂²×D₅₃	—	2	192	no	—
137	C₂²×D₅₃	—	2	36	no	—
138	C₂²×D₅₃	—	2	96	no	—
139	C₂²×D₅₃	—	4	16	no	—
140	C₂²×D₅₃	—	4	192	no	—
141	C₂²×D₅₃	#120	1	64	yes	direct product factor
142	C₂²×D₅₃	C₂²×D₄	1	72	yes	—
143	C₂²×D₅₃	C₂²×D₄	1	192	yes	complemented
144	C₂²×D₅₃	C₂²×D₄	1	72	yes	complemented
145	C₂²×D₅₃	C₂⁵	1	12	yes	—
146	C₂²×D₅₃	C₂⁵	1	4	yes	—
147	C₂²×D₅₃	C₂⁵	1	4	yes	complemented
148	D₄×C₅₃	—	2	96	no	—
149	C₂×C₄×C₅₃	—	2	36	no	—
150	C₂×C₄×C₅₃	C₂⁵	1	12	yes	complemented
151	C₂²⋊D₅₃	—	2	96	no	—
152	C₂²⋊D₅₃	—	2	96	no	—
153	C₂×Dic₅₃	—	2	36	no	—
154	C₂×Dic₅₃	C₂⁵	1	12	yes	complemented
155	D₂₁₂	—	2	96	no	—
156	C₄×D₅₃	—	2	96	no	—
157	C₂³×#120	—	53	1	no	maximal, Sylow
158	C₂²×C₅₃	—	2	128	no	—
159	C₂²×C₅₃	—	2	24	no	—
160	C₂²×C₅₃	—	2	144	no	—
161	C₂²×C₅₃	—	2	12	no	—
162	C₂²×C₅₃	—	4	24	no	—
163	C₂²×C₅₃	C₂×#120	1	16	yes	complemented
164	C₂²×C₅₃	C₂³×D₄	1	18	yes	—
165	C₂²×C₅₃	C₂³×D₄	1	24	yes	complemented
166	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
167	C₂×D₅₃	—	2	384	no	—
168	C₂×D₅₃	—	2	24	no	—
169	C₂×D₅₃	—	2	144	no	—
170	C₂×D₅₃	—	2	384	no	—
171	C₂×D₅₃	—	2	12	no	—
172	C₂×D₅₃	—	4	24	no	—
173	C₂×D₅₃	—	4	64	no	—
174	C₂×D₅₃	C₂×#120	1	96	yes	direct product factor
175	C₂×D₅₃	C₂³×D₄	1	24	yes	—
176	C₂×D₅₃	C₂³×D₄	1	24	yes	complemented
177	C₄×C₅₃	—	2	12	no	—
178	Dic₅₃	—	2	12	no	—
179	C₂⁷	—	53	1	no	—
180	C₂⁴×D₄	—	53	3	no	—
181	C₂²×#120	—	53	1	no	—
182	C₂²×#120	—	53	3	no	—
183	C₂²×#120	—	53	48	no	—
184	C₂²×#120	—	53	3	no	—
185	C₂²×#120	D₅₃	1	1	yes	characteristic, direct product factor
186	C₂³×C₂²⋊C₄	—	53	3	no	—
187	C₂×C₅₃	—	2	24	no	—
188	C₂×C₅₃	—	4	4	no	—
189	C₂×C₅₃	C₂²×#120	1	12	yes	complemented
190	C₂×C₅₃	C₂⁴×D₄	1	3	yes	—
191	D₅₃	—	2	24	no	—
192	D₅₃	—	4	4	no	—
193	D₅₃	C₂²×#120	1	16	yes	direct product factor
194	C₂⁶	—	53	3	no	—
195	C₂⁶	—	53	3	no	—
196	C₂⁶	—	53	1	no	—
197	C₂⁶	—	53	24	no	—
198	C₂⁶	—	106	48	no	—
199	C₂⁶	C₂×D₅₃	1	1	yes	characteristic, complemented
200	C₂³×D₄	—	53	3	no	—
201	C₂³×D₄	—	53	3	no	—
202	C₂³×D₄	—	53	72	no	—
203	C₂³×D₄	—	53	3	no	—
204	C₂³×D₄	—	106	48	no	—
205	C₂³×D₄	C₂×D₅₃	1	3	yes	complemented
206	C₂⁴×C₄	—	53	3	no	—
207	C₂×#120	—	53	24	no	—
208	C₂×#120	—	53	72	no	—
209	C₂×#120	—	53	256	no	—
210	C₂×#120	—	53	72	no	—
211	C₂×#120	C₂×D₅₃	1	24	yes	direct product factor
212	C₂²×C₂²⋊C₄	—	53	3	no	—
213	C₂²×C₂²⋊C₄	—	53	6	no	—
214	C₂²×C₂²⋊C₄	—	53	72	no	—
215	C₂²×C₂²⋊C₄	C₂×D₅₃	1	3	yes	complemented
216	C₅₃	C₂³×#120	1	1	yes	characteristic, complemented, Sylow
217	C₂⁵	—	2	24	no	—
218	C₂⁵	—	53	1	no	—
219	C₂⁵	—	53	48	no	—
220	C₂⁵	—	53	36	no	—
221	C₂⁵	—	53	3	no	—
222	C₂⁵	—	53	36	no	—
223	C₂⁵	—	53	1	no	—
224	C₂⁵	—	53	64	no	—
225	C₂⁵	—	53	12	no	—
226	C₂⁵	—	106	48	no	—
227	C₂⁵	—	106	48	no	—
228	C₂⁵	—	106	576	no	—
229	C₂⁵	—	106	24	no	—
230	C₂⁵	—	106	512	no	—
231	C₂⁵	—	106	24	no	—
232	C₂⁵	C₂²×D₅₃	1	3	yes	—
233	C₂⁵	C₂²×D₅₃	1	12	yes	complemented
234	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic, complemented
235	C₂²×D₄	—	2	24	no	—
236	C₂²×D₄	—	53	36	no	—
237	C₂²×D₄	—	53	36	no	—
238	C₂²×D₄	—	53	192	no	—
239	C₂²×D₄	—	53	36	no	—
240	C₂²×D₄	—	106	24	no	—
241	C₂²×D₄	—	106	576	no	—
242	C₂²×D₄	—	106	24	no	—
243	C₂²×D₄	—	106	24	no	—
244	C₂²×D₄	C₂²×D₅₃	1	36	yes	complemented
245	C₂³×C₄	—	53	3	no	—
246	C₂³×C₄	—	53	36	no	—
247	C₂³×C₄	—	106	24	no	—
248	C₂³×C₄	C₂²×D₅₃	1	3	yes	complemented
249	#120	—	53	64	no	—
250	#120	—	53	192	no	—
251	#120	—	53	192	no	—
252	#120	C₂²×D₅₃	1	64	yes	direct product factor
253	C₂×C₂²⋊C₄	—	53	36	no	—
254	C₂×C₂²⋊C₄	—	53	72	no	—
255	C₂×C₂²⋊C₄	—	53	192	no	—
256	C₂×C₂²⋊C₄	C₂²×D₅₃	1	36	yes	complemented
257	C₂⁴	—	2	128	no	—
258	C₂⁴	—	2	24	no	—
259	C₂⁴	—	2	144	no	—
260	C₂⁴	—	2	12	no	—
261	C₂⁴	—	53	24	no	—
262	C₂⁴	—	53	6	no	—
263	C₂⁴	—	53	24	no	—
264	C₂⁴	—	53	288	no	—
265	C₂⁴	—	53	48	no	—
266	C₂⁴	—	53	18	no	—
267	C₂⁴	—	53	48	no	—
268	C₂⁴	—	53	6	no	—
269	C₂⁴	—	53	16	no	—
270	C₂⁴	—	106	384	no	—
271	C₂⁴	—	106	288	no	—
272	C₂⁴	—	106	288	no	—
273	C₂⁴	—	106	768	no	—
274	C₂⁴	—	106	144	no	—
275	C₂⁴	—	106	3072	no	—
276	C₂⁴	—	106	384	no	—
277	C₂⁴	—	106	24	no	—
278	C₂⁴	—	106	144	no	—
279	C₂⁴	—	106	12	no	—
280	C₂⁴	—	212	64	no	—
281	C₂⁴	D₄×D₅₃	1	24	yes	complemented
282	C₂⁴	C₂³×D₅₃	1	18	yes	—
283	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
284	C₂⁴	C₂³×D₅₃	1	16	yes	complemented
285	C₂⁴	C₂³×D₅₃	1	6	yes	complemented
286	C₂×D₄	—	2	144	no	—
287	C₂×D₄	—	53	48	no	—
288	C₂×D₄	—	53	48	no	—
289	C₂×D₄	—	53	48	no	—
290	C₂×D₄	—	106	144	no	—
291	C₂×D₄	—	106	768	no	—
292	C₂×D₄	—	106	144	no	—
293	C₂×D₄	—	106	144	no	—
294	C₂×D₄	C₂³×D₅₃	1	48	yes	complemented
295	C₂²×C₄	—	2	12	no	—
296	C₂²×C₄	—	53	18	no	—
297	C₂²×C₄	—	53	48	no	—
298	C₂²×C₄	—	106	144	no	—
299	C₂²×C₄	—	106	12	no	—
300	C₂²×C₄	C₂³×D₅₃	1	18	yes	complemented
301	C₂²⋊C₄	—	53	48	no	—
302	C₂²⋊C₄	—	53	96	no	—
303	C₂²⋊C₄	C₂³×D₅₃	1	48	yes	complemented
304	C₂³	—	2	384	no	—
305	C₂³	—	2	96	no	—
306	C₂³	—	2	72	no	—
307	C₂³	—	2	96	no	—
308	C₂³	—	2	36	no	—
309	C₂³	—	4	16	no	—
310	C₂³	—	53	64	no	—
311	C₂³	—	53	72	no	—
312	C₂³	—	53	4	no	—
313	C₂³	—	53	72	no	—
314	C₂³	—	53	192	no	—
315	C₂³	—	53	12	no	—
316	C₂³	—	53	4	no	—
317	C₂³	—	106	1152	no	—
318	C₂³	—	106	192	no	—
319	C₂³	—	106	192	no	—
320	C₂³	—	106	96	no	—
321	C₂³	—	106	2048	no	—
322	C₂³	—	106	1152	no	—
323	C₂³	—	106	96	no	—
324	C₂³	—	106	72	no	—
325	C₂³	—	106	96	no	—
326	C₂³	—	106	36	no	—
327	C₂³	—	212	192	no	—
328	C₂³	—	212	16	no	—
329	C₂³	C₂×D₄×D₅₃	1	12	yes	—
330	C₂³	C₂×D₄×D₅₃	1	72	yes	complemented
331	C₂³	C₂⁴×D₅₃	1	12	yes	—
332	C₂³	C₂⁴×D₅₃	1	3	yes	—
333	C₂³	C₂⁴×D₅₃	1	4	yes	complemented
334	D₄	—	2	96	no	—
335	D₄	—	106	96	no	—
336	D₄	—	106	96	no	—
337	D₄	—	106	96	no	—
338	C₂×C₄	—	2	36	no	—
339	C₂×C₄	—	53	12	no	—
340	C₂×C₄	—	106	96	no	—
341	C₂×C₄	—	106	36	no	—
342	C₂×C₄	C₂⁴×D₅₃	1	12	yes	complemented
343	C₂²	—	2	128	no	—
344	C₂²	—	2	144	no	—
345	C₂²	—	2	24	no	—
346	C₂²	—	2	12	no	—
347	C₂²	—	4	24	no	—
348	C₂²	—	53	96	no	—
349	C₂²	—	53	24	no	—
350	C₂²	—	53	24	no	—
351	C₂²	—	106	384	no	—
352	C₂²	—	106	384	no	—
353	C₂²	—	106	144	no	—
354	C₂²	—	106	24	no	—
355	C₂²	—	106	12	no	—
356	C₂²	—	212	64	no	—
357	C₂²	—	212	24	no	—
358	C₂²	#120×D₅₃	1	16	yes	direct product factor
359	C₂²	C₂²×D₄×D₅₃	1	18	yes	—
360	C₂²	C₂²×D₄×D₅₃	1	24	yes	complemented
361	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
362	C₄	—	2	12	no	—
363	C₄	—	106	12	no	—
364	C₂	—	2	24	no	—
365	C₂	—	4	4	no	—
366	C₂	—	53	16	no	—
367	C₂	—	106	24	no	—
368	C₂	—	212	4	no	—
369	C₂	C₂×#120×D₅₃	1	12	yes	direct product factor
370	C₂	C₂³×D₄×D₅₃	1	3	yes	—

	subgroup	G/H
center	C₂⁴	C₂³×D₅₃
commutator, cosocle	C₂²×C₅₃	C₂⁶
Frattini	C₂²	C₂⁵×D₅₃
Fitting	C₂²×#120×C₅₃	C₂
socle	C₂⁴×C₅₃	C₂⁴
hypercenter	C₂²×#120	D₅₃
hypocenter	C₅₃	C₂³×#120
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×#120

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂⁶×D₅₃	C₂	semidirect
2. C₂³×D₄×D₅₃	C₂	semidirect
3. C₂²×#13133187	C₂	semidirect
4. C₂²×#13133186	C₂	semidirect
5. C₂²×#13133185	C₂	semidirect
6. C₂×#120×D₅₃	C₂	direct (N × H)
7. C₂²×C₂²⋊C₄×D₅₃	C₂	semidirect
8. C₂²×#120×C₅₃	C₂	semidirect
11. C₂⁵×D₅₃	C₂²	semidirect
12. C₂⁵×D₅₃	C₂²	semidirect
13. C₂⁵×D₅₃	C₂²	semidirect
14. C₂³×D₂₁₂	C₂²	semidirect
15. C₂³×C₂²⋊D₅₃	C₂²	semidirect
16. C₂³×C₂²⋊D₅₃	C₂²	semidirect
18. C₂²×D₄×D₅₃	C₂²	semidirect
19. C₂³×C₄×D₅₃	C₂²	semidirect
20. C₂×#13133187	C₂²	semidirect
21. C₂×#13133186	C₂²	semidirect
22. C₂×#13133185	C₂²	semidirect
23. #120×D₅₃	C₂²	direct (N × H)
24. C₂²×C₂²⋊Dic₅₃	C₂²	semidirect
25. C₂²×#11719921	C₂²	semidirect
26. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
27. C₂⁶×C₅₃	C₂²	semidirect
28. C₂³×D₄×C₅₃	C₂²	semidirect
29. C₂×#120×C₅₃	C₂²	semidirect
30. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
37. C₂⁴×D₅₃	D₄	semidirect
41. C₂⁴×D₅₃	C₂³	semidirect
42. C₂⁴×D₅₃	C₂³	semidirect
43. C₂⁴×D₅₃	C₂³	semidirect
44. C₂⁴×D₅₃	C₂³	semidirect
46. C₂²×D₂₁₂	C₂³	semidirect
49. C₂²×C₂²⋊D₅₃	C₂³	semidirect
50. C₂²×C₂²⋊D₅₃	C₂³	semidirect
52. C₂×D₄×D₅₃	C₂³	semidirect
53. C₂³×Dic₅₃	C₂³	semidirect
55. C₂²×C₄×D₅₃	C₂³	semidirect
56. #13133187	C₂³	semidirect
57. #13133186	C₂³	semidirect
58. #13133185	C₂³	semidirect
59. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
60. C₂×#11719921	C₂³	semidirect
61. C₂²⋊C₄×D₅₃	C₂³	semidirect
64. C₂⁵×C₅₃	C₂³	semidirect
65. C₂⁵×C₅₃	C₂³	semidirect
67. C₂²×D₄×C₅₃	C₂³	semidirect
68. C₂³×C₄×C₅₃	C₂³	semidirect
69. #120×C₅₃	C₂³	semidirect
70. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
75. C₂⁴×C₅₃	C₂×D₄	semidirect
78. C₂⁴×C₅₃	C₂⁴	semidirect
79. C₂⁴×C₅₃	C₂⁴	semidirect
92. C₂³×D₅₃	C₂×D₄	semidirect
93. C₂³×D₅₃	C₂×D₄	semidirect
97. C₂³×D₅₃	C₂⁴	semidirect
98. C₂³×D₅₃	C₂⁴	semidirect
99. C₂³×D₅₃	C₂⁴	semidirect
101. C₂×D₄×C₅₃	C₂⁴	semidirect
103. C₂²×C₄×C₅₃	C₂⁴	semidirect
106. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
107. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
109. C₂²×Dic₅₃	C₂⁴	semidirect
112. C₂×D₂₁₂	C₂⁴	semidirect
114. C₂×C₄×D₅₃	C₂⁴	semidirect
115. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
116. C₂²⋊Dic₅₃	C₂⁴	semidirect
117. #11719921	C₂⁴	semidirect
125. C₂³×C₅₃	C₂²×D₄	semidirect
128. C₂³×C₅₃	C₂⁵	semidirect
141. C₂²×D₅₃	#120	direct (N × H)
143. C₂²×D₅₃	C₂²×D₄	semidirect
144. C₂²×D₅₃	C₂²×D₄	semidirect
147. C₂²×D₅₃	C₂⁵	semidirect
150. C₂×C₄×C₅₃	C₂⁵	semidirect
154. C₂×Dic₅₃	C₂⁵	semidirect
163. C₂²×C₅₃	C₂×#120	semidirect
165. C₂²×C₅₃	C₂³×D₄	semidirect
174. C₂×D₅₃	C₂×#120	direct (N × H)
176. C₂×D₅₃	C₂³×D₄	semidirect
185. C₂²×#120	D₅₃	direct (N × H)
189. C₂×C₅₃	C₂²×#120	semidirect
193. D₅₃	C₂²×#120	direct (N × H)
199. C₂⁶	C₂×D₅₃	semidirect
205. C₂³×D₄	C₂×D₅₃	semidirect
211. C₂×#120	C₂×D₅₃	direct (N × H)
215. C₂²×C₂²⋊C₄	C₂×D₅₃	semidirect
216. C₅₃	C₂³×#120	semidirect
233. C₂⁵	C₂²×D₅₃	semidirect
234. C₂⁵	C₂²×D₅₃	semidirect
244. C₂²×D₄	C₂²×D₅₃	semidirect
248. C₂³×C₄	C₂²×D₅₃	semidirect
252. #120	C₂²×D₅₃	direct (N × H)
256. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
281. C₂⁴	D₄×D₅₃	semidirect
284. C₂⁴	C₂³×D₅₃	semidirect
285. C₂⁴	C₂³×D₅₃	semidirect
294. C₂×D₄	C₂³×D₅₃	semidirect
300. C₂²×C₄	C₂³×D₅₃	semidirect
303. C₂²⋊C₄	C₂³×D₅₃	semidirect
330. C₂³	C₂×D₄×D₅₃	semidirect
333. C₂³	C₂⁴×D₅₃	semidirect
342. C₂×C₄	C₂⁴×D₅₃	semidirect
358. C₂²	#120×D₅₃	direct (N × H)
360. C₂²	C₂²×D₄×D₅₃	semidirect
369. C₂	C₂×#120×D₅₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁶×D₅₃	2
C₂³×D₄×D₅₃	2
C₂²×#13133187	2
C₂²×#13133186	2
C₂²×#13133185	2
C₂×#120×D₅₃	2
C₂²×C₂²⋊C₄×D₅₃	2
C₂²×#120×C₅₃	2
C₂³×#120	53

Subgroups — C22×#120×D53 #28290721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#120×D₅₃ #28290721