Subgroups — C₂×C₅₃×C₂²⋊#95 #27221263

Order 13568.

7630 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₄×C₅₃	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₂²⋊C₄×C₅₃	C₂	1	2	yes	maximal
3	C₂²×#95×C₅₃	C₂	1	4	yes	maximal, complemented
4	C₅₃×C₂²⋊#95	C₂	1	8	yes	maximal, direct product factor
5	C₂⁶×C₅₃	C₂²	1	1	yes	characteristic
6	C₂⁴×C₄×C₅₃	—	2	8	no	—
7	C₂⁴×C₄×C₅₃	—	2	16	no	—
8	C₂⁴×C₄×C₅₃	C₄	1	8	yes	complemented
9	C₂⁴×C₄×C₅₃	C₂²	1	4	yes	—
10	C₂⁴×C₄×C₅₃	C₂²	1	4	yes	—
11	C₂⁴×C₄×C₅₃	C₂²	1	2	yes	—
12	C₂²×C₂²⋊C₄×C₅₃	—	2	8	no	—
13	C₂²×C₂²⋊C₄×C₅₃	—	2	8	no	—
14	C₂²×C₂²⋊C₄×C₅₃	C₄	1	16	yes	complemented
15	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	8	yes	—
16	C₂×#95×C₅₃	—	2	16	no	—
17	C₂×#95×C₅₃	C₂²	1	16	yes	complemented
18	C₂⁵×C₅₃	—	2	8	no	—
19	C₂⁵×C₅₃	—	2	8	no	—
20	C₂⁵×C₅₃	C₂×C₄	1	8	yes	—
21	C₂⁵×C₅₃	C₂×C₄	1	4	yes	—
22	C₂⁵×C₅₃	D₄	1	4	yes	—
23	C₂⁵×C₅₃	D₄	1	8	yes	—
24	C₂⁵×C₅₃	Q₈	1	4	yes	—
25	C₂⁵×C₅₃	C₂³	1	2	yes	—
26	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
27	C₂³×C₄×C₅₃	—	2	128	no	—
28	C₂³×C₄×C₅₃	—	2	32	no	—
29	C₂³×C₄×C₅₃	—	2	16	no	—
30	C₂³×C₄×C₅₃	—	2	8	no	—
31	C₂³×C₄×C₅₃	—	2	8	no	—
32	C₂³×C₄×C₅₃	—	2	64	no	—
33	C₂³×C₄×C₅₃	—	2	32	no	—
34	C₂³×C₄×C₅₃	—	2	8	no	—
35	C₂³×C₄×C₅₃	—	2	8	no	—
36	C₂³×C₄×C₅₃	—	2	16	no	—
37	C₂³×C₄×C₅₃	—	2	16	no	—
38	C₂³×C₄×C₅₃	C₂×C₄	1	8	yes	—
39	C₂³×C₄×C₅₃	C₂×C₄	1	16	yes	complemented
40	C₂³×C₄×C₅₃	C₂×C₄	1	16	yes	complemented
41	C₂³×C₄×C₅₃	D₄	1	16	yes	—
42	C₂³×C₄×C₅₃	C₂³	1	8	yes	—
43	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
44	C₂×C₂²⋊C₄×C₅₃	—	2	64	no	—
45	C₂×C₂²⋊C₄×C₅₃	—	2	16	no	—
46	C₂×C₂²⋊C₄×C₅₃	—	2	16	no	—
47	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	32	yes	complemented
48	#95×C₅₃	—	2	32	no	—
49	C₂⁴×C₅₃	—	2	16	no	—
50	C₂⁴×C₅₃	—	2	16	no	—
51	C₂⁴×C₅₃	—	2	64	no	—
52	C₂⁴×C₅₃	—	2	32	no	—
53	C₂⁴×C₅₃	—	2	32	no	—
54	C₂⁴×C₅₃	—	2	32	no	—
55	C₂⁴×C₅₃	—	2	32	no	—
56	C₂⁴×C₅₃	—	2	8	no	—
57	C₂⁴×C₅₃	—	2	8	no	—
58	C₂⁴×C₅₃	C₄²	1	16	yes	—
59	C₂⁴×C₅₃	C₂²⋊C₄	1	32	yes	—
60	C₂⁴×C₅₃	C₂²⋊C₄	1	16	yes	—
61	C₂⁴×C₅₃	C₄⋊C₄	1	16	yes	—
62	C₂⁴×C₅₃	C₄⋊C₄	1	32	yes	—
63	C₂⁴×C₅₃	C₂²×C₄	1	8	yes	—
64	C₂⁴×C₅₃	C₂²×C₄	1	4	yes	—
65	C₂⁴×C₅₃	C₂²×C₄	1	2	yes	—
66	C₂⁴×C₅₃	C₂²×C₄	1	4	yes	—
67	C₂⁴×C₅₃	C₂×D₄	1	4	yes	—
68	C₂⁴×C₅₃	C₂×D₄	1	8	yes	—
69	C₂⁴×C₅₃	C₂×D₄	1	4	yes	—
70	C₂⁴×C₅₃	C₂×D₄	1	2	yes	—
71	C₂⁴×C₅₃	C₂×D₄	1	8	yes	—
72	C₂⁴×C₅₃	C₂×Q₈	1	4	yes	—
73	C₂⁴×C₅₃	C₂×Q₈	1	2	yes	—
74	C₂⁴×C₅₃	#41	1	8	yes	—
75	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
76	C₂²×C₄×C₅₃	—	2	128	no	—
77	C₂²×C₄×C₅₃	—	2	256	no	—
78	C₂²×C₄×C₅₃	—	2	16	no	—
79	C₂²×C₄×C₅₃	—	2	16	no	—
80	C₂²×C₄×C₅₃	—	2	32	no	—
81	C₂²×C₄×C₅₃	—	2	64	no	—
82	C₂²×C₄×C₅₃	—	2	8	no	—
83	C₂²×C₄×C₅₃	—	2	8	no	—
84	C₂²×C₄×C₅₃	—	2	64	no	—
85	C₂²×C₄×C₅₃	—	2	32	no	—
86	C₂²×C₄×C₅₃	—	2	64	no	—
87	C₂²×C₄×C₅₃	—	2	16	no	—
88	C₂²×C₄×C₅₃	—	2	8	no	—
89	C₂²×C₄×C₅₃	—	2	8	no	—
90	C₂²×C₄×C₅₃	—	2	16	no	—
91	C₂²×C₄×C₅₃	—	4	16	no	—
92	C₂²×C₄×C₅₃	—	4	32	no	—
93	C₂²×C₄×C₅₃	—	4	16	no	—
94	C₂²×C₄×C₅₃	C₂²⋊C₄	1	32	yes	complemented
95	C₂²×C₄×C₅₃	C₂²×C₄	1	8	yes	—
96	C₂²×C₄×C₅₃	C₂²×C₄	1	16	yes	complemented
97	C₂²×C₄×C₅₃	C₂×D₄	1	16	yes	—
98	C₂²⋊C₄×C₅₃	—	2	64	no	—
99	C₂³×C₅₃	—	2	8	no	—
100	C₂³×C₅₃	—	2	8	no	—
101	C₂³×C₅₃	—	2	32	no	—
102	C₂³×C₅₃	—	2	16	no	—
103	C₂³×C₅₃	—	2	16	no	—
104	C₂³×C₅₃	—	2	16	no	—
105	C₂³×C₅₃	—	2	16	no	—
106	C₂³×C₅₃	—	2	64	no	—
107	C₂³×C₅₃	—	2	32	no	—
108	C₂³×C₅₃	—	2	64	no	—
109	C₂³×C₅₃	—	2	32	no	—
110	C₂³×C₅₃	—	2	128	no	—
111	C₂³×C₅₃	—	2	128	no	—
112	C₂³×C₅₃	#95	1	64	yes	complemented
113	C₂³×C₅₃	C₂×C₄²	1	8	yes	—
114	C₂³×C₅₃	C₂×C₄²	1	4	yes	—
115	C₂³×C₅₃	C₂×C₂²⋊C₄	1	8	yes	—
116	C₂³×C₅₃	C₂×C₂²⋊C₄	1	16	yes	—
117	C₂³×C₅₃	C₂×C₂²⋊C₄	1	4	yes	—
118	C₂³×C₅₃	C₂×C₂²⋊C₄	1	8	yes	—
119	C₂³×C₅₃	C₂×C₂²⋊C₄	1	8	yes	—
120	C₂³×C₅₃	C₂×C₄⋊C₄	1	8	yes	—
121	C₂³×C₅₃	C₂×C₄⋊C₄	1	16	yes	—
122	C₂³×C₅₃	C₂×C₄⋊C₄	1	4	yes	—
123	C₂³×C₅₃	C₂×C₄⋊C₄	1	8	yes	—
124	C₂³×C₅₃	#117	1	8	yes	—
125	C₂³×C₅₃	C₄×D₄	1	32	yes	—
126	C₂³×C₅₃	#120	1	16	yes	—
127	C₂³×C₅₃	#121	1	16	yes	—
128	C₂³×C₅₃	C₂²⋊Q₈	1	16	yes	—
129	C₂³×C₅₃	#123	1	16	yes	—
130	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
131	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
132	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
133	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
134	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
135	C₂³×C₅₃	C₂²×Q₈	1	1	yes	characteristic
136	C₂³×C₅₃	C₂×#41	1	4	yes	—
137	C₂×C₄×C₅₃	—	2	128	no	—
138	C₂×C₄×C₅₃	—	2	8	no	—
139	C₂×C₄×C₅₃	—	2	8	no	—
140	C₂×C₄×C₅₃	—	2	32	no	—
141	C₂×C₄×C₅₃	—	2	64	no	—
142	C₂×C₄×C₅₃	—	2	16	no	—
143	C₂×C₄×C₅₃	—	2	32	no	—
144	C₂×C₄×C₅₃	—	4	8	no	—
145	C₂×C₄×C₅₃	—	4	16	no	—
146	C₂×C₄×C₅₃	—	4	8	no	—
147	C₂×C₄×C₅₃	—	4	64	no	—
148	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	16	yes	complemented
149	C₂×C₂²⋊#95	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₂²×C₅₃	—	2	128	no	—
151	C₂²×C₅₃	—	2	16	no	—
152	C₂²×C₅₃	—	2	8	no	—
153	C₂²×C₅₃	—	2	16	no	—
154	C₂²×C₅₃	—	2	8	no	—
155	C₂²×C₅₃	—	2	32	no	—
156	C₂²×C₅₃	—	2	32	no	—
157	C₂²×C₅₃	C₂×#95	1	8	yes	—
158	C₂²×C₅₃	C₂×#95	1	16	yes	complemented
159	C₂²×C₅₃	C₄×C₂²⋊C₄	1	16	yes	—
160	C₂²×C₅₃	#379	1	8	yes	—
161	C₂²×C₅₃	#380	1	16	yes	—
162	C₂²×C₅₃	#381	1	8	yes	—
163	C₂²×C₅₃	#385	1	32	yes	—
164	C₂²×C₅₃	#386	1	32	yes	—
165	C₂²×C₅₃	C₂²×C₄²	1	1	yes	characteristic
166	C₂²×C₅₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
167	C₂²×C₅₃	C₂²×C₂²⋊C₄	1	2	yes	—
168	C₂²×C₅₃	C₂²×C₂²⋊C₄	1	2	yes	—
169	C₂²×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
170	C₂²×C₅₃	C₂²×C₄⋊C₄	1	2	yes	—
171	C₂²×C₅₃	C₂×#117	1	2	yes	—
172	C₂²×C₅₃	C₂×C₄×D₄	1	8	yes	—
173	C₂²×C₅₃	C₂×#120	1	4	yes	—
174	C₂²×C₅₃	C₂×#121	1	4	yes	—
175	C₂²×C₅₃	C₂×C₂²⋊Q₈	1	4	yes	—
176	C₂²×C₅₃	C₂×#123	1	4	yes	—
177	C₄×C₅₃	—	2	16	no	—
178	C₄×C₅₃	—	4	16	no	—
179	C₂⁵×C₄	C₂×C₅₃	1	1	yes	characteristic
180	C₂³×C₂²⋊C₄	C₂×C₅₃	1	2	yes	—
181	C₂²×#95	C₂×C₅₃	1	4	yes	complemented
182	C₂²⋊#95	C₂×C₅₃	1	8	yes	direct product factor
183	C₂×C₅₃	—	2	16	no	—
184	C₂×C₅₃	C₂²⋊#95	1	16	yes	direct product factor
185	C₂×C₅₃	C₂²×#95	1	1	yes	characteristic
186	C₂×C₅₃	C₂×C₄×C₂²⋊C₄	1	2	yes	—
187	C₂×C₅₃	C₂×#379	1	1	yes	characteristic
188	C₂×C₅₃	C₂×#380	1	2	yes	—
189	C₂×C₅₃	C₂×#381	1	1	yes	characteristic
190	C₂×C₅₃	C₂×#385	1	4	yes	—
191	C₂×C₅₃	C₂×#386	1	4	yes	—
192	C₂⁶	C₂²×C₅₃	1	1	yes	characteristic
193	C₂⁴×C₄	—	2	8	no	—
194	C₂⁴×C₄	—	2	16	no	—
195	C₂⁴×C₄	C₄×C₅₃	1	8	yes	complemented
196	C₂⁴×C₄	C₂²×C₅₃	1	4	yes	—
197	C₂⁴×C₄	C₂²×C₅₃	1	4	yes	—
198	C₂⁴×C₄	C₂²×C₅₃	1	2	yes	—
199	C₂²×C₂²⋊C₄	—	2	8	no	—
200	C₂²×C₂²⋊C₄	—	2	8	no	—
201	C₂²×C₂²⋊C₄	C₄×C₅₃	1	16	yes	complemented
202	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	8	yes	—
203	C₂×#95	—	2	16	no	—
204	C₂×#95	C₂²×C₅₃	1	16	yes	complemented
205	C₅₃	C₂×C₂²⋊#95	1	1	yes	characteristic, direct product factor, Sylow
206	C₂⁵	—	2	8	no	—
207	C₂⁵	—	2	8	no	—
208	C₂⁵	C₂×C₄×C₅₃	1	8	yes	—
209	C₂⁵	C₂×C₄×C₅₃	1	4	yes	—
210	C₂⁵	D₄×C₅₃	1	4	yes	—
211	C₂⁵	D₄×C₅₃	1	8	yes	—
212	C₂⁵	Q₈×C₅₃	1	4	yes	—
213	C₂⁵	C₂³×C₅₃	1	2	yes	—
214	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
215	C₂³×C₄	—	2	128	no	—
216	C₂³×C₄	—	2	16	no	—
217	C₂³×C₄	—	2	8	no	—
218	C₂³×C₄	—	2	8	no	—
219	C₂³×C₄	—	2	32	no	—
220	C₂³×C₄	—	2	32	no	—
221	C₂³×C₄	—	2	64	no	—
222	C₂³×C₄	—	2	8	no	—
223	C₂³×C₄	—	2	8	no	—
224	C₂³×C₄	—	2	16	no	—
225	C₂³×C₄	—	2	16	no	—
226	C₂³×C₄	C₂×C₄×C₅₃	1	8	yes	—
227	C₂³×C₄	C₂×C₄×C₅₃	1	16	yes	complemented
228	C₂³×C₄	C₂×C₄×C₅₃	1	16	yes	complemented
229	C₂³×C₄	D₄×C₅₃	1	16	yes	—
230	C₂³×C₄	C₂³×C₅₃	1	8	yes	—
231	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
232	C₂×C₂²⋊C₄	—	2	16	no	—
233	C₂×C₂²⋊C₄	—	2	16	no	—
234	C₂×C₂²⋊C₄	—	2	64	no	—
235	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	32	yes	complemented
236	#95	—	2	32	no	—
237	C₂⁴	—	2	16	no	—
238	C₂⁴	—	2	16	no	—
239	C₂⁴	—	2	64	no	—
240	C₂⁴	—	2	32	no	—
241	C₂⁴	—	2	32	no	—
242	C₂⁴	—	2	32	no	—
243	C₂⁴	—	2	32	no	—
244	C₂⁴	—	2	8	no	—
245	C₂⁴	—	2	8	no	—
246	C₂⁴	C₄²×C₅₃	1	16	yes	—
247	C₂⁴	C₂²⋊C₄×C₅₃	1	32	yes	—
248	C₂⁴	C₂²⋊C₄×C₅₃	1	16	yes	—
249	C₂⁴	C₄⋊C₄×C₅₃	1	16	yes	—
250	C₂⁴	C₄⋊C₄×C₅₃	1	32	yes	—
251	C₂⁴	C₂²×C₄×C₅₃	1	8	yes	—
252	C₂⁴	C₂²×C₄×C₅₃	1	4	yes	—
253	C₂⁴	C₂²×C₄×C₅₃	1	2	yes	—
254	C₂⁴	C₂²×C₄×C₅₃	1	4	yes	—
255	C₂⁴	C₂×D₄×C₅₃	1	4	yes	—
256	C₂⁴	C₂×D₄×C₅₃	1	8	yes	—
257	C₂⁴	C₂×D₄×C₅₃	1	4	yes	—
258	C₂⁴	C₂×D₄×C₅₃	1	2	yes	—
259	C₂⁴	C₂×D₄×C₅₃	1	8	yes	—
260	C₂⁴	C₂×Q₈×C₅₃	1	4	yes	—
261	C₂⁴	C₂×Q₈×C₅₃	1	2	yes	—
262	C₂⁴	#41×C₅₃	1	8	yes	—
263	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
264	C₂²×C₄	—	2	128	no	—
265	C₂²×C₄	—	2	256	no	—
266	C₂²×C₄	—	2	16	no	—
267	C₂²×C₄	—	2	16	no	—
268	C₂²×C₄	—	2	32	no	—
269	C₂²×C₄	—	2	64	no	—
270	C₂²×C₄	—	2	8	no	—
271	C₂²×C₄	—	2	8	no	—
272	C₂²×C₄	—	2	64	no	—
273	C₂²×C₄	—	2	32	no	—
274	C₂²×C₄	—	2	64	no	—
275	C₂²×C₄	—	2	16	no	—
276	C₂²×C₄	—	2	8	no	—
277	C₂²×C₄	—	2	8	no	—
278	C₂²×C₄	—	2	16	no	—
279	C₂²×C₄	—	4	16	no	—
280	C₂²×C₄	—	4	32	no	—
281	C₂²×C₄	—	4	16	no	—
282	C₂²×C₄	C₂²⋊C₄×C₅₃	1	32	yes	complemented
283	C₂²×C₄	C₂²×C₄×C₅₃	1	8	yes	—
284	C₂²×C₄	C₂²×C₄×C₅₃	1	16	yes	complemented
285	C₂²×C₄	C₂×D₄×C₅₃	1	16	yes	—
286	C₂²⋊C₄	—	2	64	no	—
287	C₂³	—	2	8	no	—
288	C₂³	—	2	8	no	—
289	C₂³	—	2	32	no	—
290	C₂³	—	2	16	no	—
291	C₂³	—	2	16	no	—
292	C₂³	—	2	16	no	—
293	C₂³	—	2	16	no	—
294	C₂³	—	2	64	no	—
295	C₂³	—	2	32	no	—
296	C₂³	—	2	64	no	—
297	C₂³	—	2	32	no	—
298	C₂³	—	2	128	no	—
299	C₂³	—	2	128	no	—
300	C₂³	#95×C₅₃	1	64	yes	complemented
301	C₂³	C₂×C₄²×C₅₃	1	8	yes	—
302	C₂³	C₂×C₄²×C₅₃	1	4	yes	—
303	C₂³	C₂×C₂²⋊C₄×C₅₃	1	16	yes	—
304	C₂³	C₂×C₂²⋊C₄×C₅₃	1	8	yes	—
305	C₂³	C₂×C₂²⋊C₄×C₅₃	1	4	yes	—
306	C₂³	C₂×C₂²⋊C₄×C₅₃	1	8	yes	—
307	C₂³	C₂×C₂²⋊C₄×C₅₃	1	8	yes	—
308	C₂³	C₂×C₄⋊C₄×C₅₃	1	8	yes	—
309	C₂³	C₂×C₄⋊C₄×C₅₃	1	16	yes	—
310	C₂³	C₂×C₄⋊C₄×C₅₃	1	4	yes	—
311	C₂³	C₂×C₄⋊C₄×C₅₃	1	8	yes	—
312	C₂³	#117×C₅₃	1	8	yes	—
313	C₂³	C₄×D₄×C₅₃	1	32	yes	—
314	C₂³	#120×C₅₃	1	16	yes	—
315	C₂³	#121×C₅₃	1	16	yes	—
316	C₂³	C₂²⋊Q₈×C₅₃	1	16	yes	—
317	C₂³	#123×C₅₃	1	16	yes	—
318	C₂³	C₂³×C₄×C₅₃	1	1	yes	characteristic
319	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
320	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
321	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
322	C₂³	C₂²×D₄×C₅₃	1	4	yes	—
323	C₂³	C₂²×Q₈×C₅₃	1	1	yes	characteristic
324	C₂³	C₂×#41×C₅₃	1	4	yes	—
325	C₂×C₄	—	2	128	no	—
326	C₂×C₄	—	2	8	no	—
327	C₂×C₄	—	2	8	no	—
328	C₂×C₄	—	2	32	no	—
329	C₂×C₄	—	2	64	no	—
330	C₂×C₄	—	2	16	no	—
331	C₂×C₄	—	2	32	no	—
332	C₂×C₄	—	4	8	no	—
333	C₂×C₄	—	4	16	no	—
334	C₂×C₄	—	4	8	no	—
335	C₂×C₄	—	4	64	no	—
336	C₂×C₄	C₂×C₂²⋊C₄×C₅₃	1	16	yes	complemented
337	C₂²	—	2	128	no	—
338	C₂²	—	2	16	no	—
339	C₂²	—	2	8	no	—
340	C₂²	—	2	16	no	—
341	C₂²	—	2	8	no	—
342	C₂²	—	2	32	no	—
343	C₂²	—	2	32	no	—
344	C₂²	C₂×#95×C₅₃	1	8	yes	—
345	C₂²	C₂×#95×C₅₃	1	16	yes	complemented
346	C₂²	C₄×C₂²⋊C₄×C₅₃	1	16	yes	—
347	C₂²	C₅₃×#379	1	8	yes	—
348	C₂²	C₅₃×#380	1	16	yes	—
349	C₂²	C₅₃×#381	1	8	yes	—
350	C₂²	C₅₃×#385	1	32	yes	—
351	C₂²	C₅₃×#386	1	32	yes	—
352	C₂²	C₂²×C₄²×C₅₃	1	1	yes	characteristic
353	C₂²	C₂²×C₂²⋊C₄×C₅₃	1	1	yes	characteristic
354	C₂²	C₂²×C₂²⋊C₄×C₅₃	1	2	yes	—
355	C₂²	C₂²×C₂²⋊C₄×C₅₃	1	2	yes	—
356	C₂²	C₂²×C₄⋊C₄×C₅₃	1	1	yes	characteristic
357	C₂²	C₂²×C₄⋊C₄×C₅₃	1	2	yes	—
358	C₂²	C₂×#117×C₅₃	1	2	yes	—
359	C₂²	C₂×C₄×D₄×C₅₃	1	8	yes	—
360	C₂²	C₂×#120×C₅₃	1	4	yes	—
361	C₂²	C₂×#121×C₅₃	1	4	yes	—
362	C₂²	C₂×C₂²⋊Q₈×C₅₃	1	4	yes	—
363	C₂²	C₂×#123×C₅₃	1	4	yes	—
364	C₄	—	2	16	no	—
365	C₄	—	4	16	no	—
366	C₂	—	2	16	no	—
367	C₂	C₅₃×C₂²⋊#95	1	16	yes	direct product factor
368	C₂	C₂²×#95×C₅₃	1	1	yes	characteristic
369	C₂	C₂×C₄×C₂²⋊C₄×C₅₃	1	2	yes	—
370	C₂	C₂×C₅₃×#379	1	1	yes	characteristic
371	C₂	C₂×C₅₃×#380	1	2	yes	—
372	C₂	C₂×C₅₃×#381	1	1	yes	characteristic
373	C₂	C₂×C₅₃×#385	1	4	yes	—
374	C₂	C₂×C₅₃×#386	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁵×C₅₃	C₂³
commutator	C₂²	C₂²×C₄²×C₅₃
Frattini, cosocle	C₂⁴	C₂⁴×C₅₃
prime radical	C₂⁶×C₅₃	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁵×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂²×#95×C₅₃	C₂	semidirect
4. C₅₃×C₂²⋊#95	C₂	direct (N × H)
8. C₂⁴×C₄×C₅₃	C₄	semidirect
14. C₂²×C₂²⋊C₄×C₅₃	C₄	semidirect
17. C₂×#95×C₅₃	C₂²	semidirect
39. C₂³×C₄×C₅₃	C₂×C₄	semidirect
40. C₂³×C₄×C₅₃	C₂×C₄	semidirect
47. C₂×C₂²⋊C₄×C₅₃	C₂×C₄	semidirect
94. C₂²×C₄×C₅₃	C₂²⋊C₄	semidirect
96. C₂²×C₄×C₅₃	C₂²×C₄	semidirect
112. C₂³×C₅₃	#95	semidirect
148. C₂×C₄×C₅₃	C₂×C₂²⋊C₄	semidirect
149. C₂×C₂²⋊#95	C₅₃	direct (N × H)
158. C₂²×C₅₃	C₂×#95	semidirect
181. C₂²×#95	C₂×C₅₃	semidirect
182. C₂²⋊#95	C₂×C₅₃	direct (N × H)
184. C₂×C₅₃	C₂²⋊#95	direct (N × H)
195. C₂⁴×C₄	C₄×C₅₃	semidirect
201. C₂²×C₂²⋊C₄	C₄×C₅₃	semidirect
204. C₂×#95	C₂²×C₅₃	semidirect
205. C₅₃	C₂×C₂²⋊#95	direct (N × H)
227. C₂³×C₄	C₂×C₄×C₅₃	semidirect
228. C₂³×C₄	C₂×C₄×C₅₃	semidirect
235. C₂×C₂²⋊C₄	C₂×C₄×C₅₃	semidirect
282. C₂²×C₄	C₂²⋊C₄×C₅₃	semidirect
284. C₂²×C₄	C₂²×C₄×C₅₃	semidirect
300. C₂³	#95×C₅₃	semidirect
336. C₂×C₄	C₂×C₂²⋊C₄×C₅₃	semidirect
345. C₂²	C₂×#95×C₅₃	semidirect
367. C₂	C₅₃×C₂²⋊#95	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×C₄×C₅₃	2
C₂³×C₂²⋊C₄×C₅₃	2
C₂²×#95×C₅₃	2
C₅₃×C₂²⋊#95	2
C₂×C₂²⋊#95	53

Subgroups — C2×C53×C22⋊#95 #27221263

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×C₂²⋊#95 #27221263