Subgroups — C₂×C₅₃×#1300 #27215579

Order 13568.

786 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	C₂×C₅₃×#432	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×M₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅₃×#376	C₂	1	1	yes	maximal, characteristic
4	C₅₃×#1300	C₂	1	4	yes	maximal, direct product factor
5	C₂²×M₁₆×C₅₃	—	2	1	no	—
6	C₂²×C₄²×C₅₃	—	2	1	no	—
7	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
8	C₅₃×#432	—	2	1	no	—
9	C₅₃×#432	—	2	1	no	—
10	C₅₃×#432	C₄	1	2	yes	complemented
11	C₅₃×#432	C₂²	1	2	yes	—
12	C₂×C₄⋊C₈×C₅₃	C₄	1	2	yes	complemented
13	C₂×C₂²⋊C₈×C₅₃	—	2	1	no	—
14	C₄×M₁₆×C₅₃	—	2	1	no	—
15	C₄×M₁₆×C₅₃	—	2	1	no	—
16	C₄×M₁₆×C₅₃	C₄	1	2	yes	complemented
17	C₄×M₁₆×C₅₃	C₂²	1	2	yes	—
18	C₂×#97×C₅₃	—	2	1	no	—
19	C₂×#97×C₅₃	C₄	1	2	yes	complemented
20	C₂×C₄×C₈×C₅₃	—	2	1	no	—
21	C₅₃×#376	—	2	1	no	—
22	C₅₃×#376	—	2	1	no	—
23	C₅₃×#376	C₄	1	2	yes	—
24	C₅₃×#376	C₂²	1	2	yes	—
25	C₂×#95×C₅₃	—	2	1	no	—
26	C₂×#95×C₅₃	C₄	1	2	yes	—
27	C₂³×C₄×C₅₃	—	2	2	no	—
28	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
31	C₂×M₁₆×C₅₃	—	2	8	no	—
32	C₂×M₁₆×C₅₃	—	2	2	no	—
33	C₂×M₁₆×C₅₃	—	2	2	no	—
34	C₂²×C₈×C₅₃	—	2	2	no	—
35	C₂²×C₈×C₅₃	—	2	2	no	—
36	C₂×C₄²×C₅₃	—	2	8	no	—
37	C₂×C₄²×C₅₃	—	2	2	no	—
38	C₂×C₄²×C₅₃	—	2	2	no	—
39	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₅₃	Q₈	1	1	yes	characteristic
49	C₂×C₄²×C₅₃	Q₈	1	1	yes	characteristic
50	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
51	C₄⋊C₈×C₅₃	—	2	2	no	—
52	C₄⋊C₈×C₅₃	C₂×C₄	1	4	yes	complemented
53	C₂²⋊C₈×C₅₃	—	2	2	no	—
54	C₂²⋊C₈×C₅₃	—	2	2	no	—
55	#97×C₅₃	—	2	2	no	—
56	#97×C₅₃	—	2	2	no	—
57	#97×C₅₃	—	2	2	no	—
58	#97×C₅₃	C₂×C₄	1	4	yes	complemented
59	C₄×C₈×C₅₃	—	2	2	no	—
60	C₄×C₈×C₅₃	—	2	2	no	—
61	#95×C₅₃	—	2	2	no	—
62	#95×C₅₃	—	2	2	no	—
63	#95×C₅₃	—	2	2	no	—
64	#95×C₅₃	C₂×C₄	1	4	yes	—
65	C₂⁴×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₅₃	—	2	4	no	—
67	C₂²×C₄×C₅₃	—	2	4	no	—
68	C₂²×C₄×C₅₃	—	2	8	no	—
69	C₂²×C₄×C₅₃	—	2	4	no	—
70	C₂²×C₄×C₅₃	—	4	2	no	—
71	C₂²×C₄×C₅₃	—	4	4	no	—
72	C₂²×C₄×C₅₃	—	4	4	no	—
73	C₂²×C₄×C₅₃	C₄²	1	1	yes	characteristic
74	C₂²×C₄×C₅₃	C₄²	1	1	yes	characteristic
75	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
91	M₁₆×C₅₃	—	2	8	no	—
92	M₁₆×C₅₃	—	2	8	no	—
93	C₂×C₈×C₅₃	—	2	8	no	—
94	C₂×C₈×C₅₃	—	2	4	no	—
95	C₂×C₈×C₅₃	—	2	4	no	—
96	C₂×C₈×C₅₃	—	4	4	no	—
97	C₄²×C₅₃	—	2	8	no	—
98	C₄²×C₅₃	—	2	8	no	—
99	C₄²×C₅₃	C₄²	1	1	yes	characteristic
100	C₄²×C₅₃	C₄²	1	1	yes	characteristic
101	C₄²×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
102	C₄²×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
103	C₄²×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
104	C₄²×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
105	C₄²×C₅₃	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₅₃	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₅₃	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₅₃	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₅₃	C₄⋊C₄	1	1	yes	characteristic
110	C₄²×C₅₃	C₄⋊C₄	1	1	yes	characteristic
111	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₅₃	C₂×Q₈	1	1	yes	characteristic
115	C₂³×C₅₃	—	2	2	no	—
116	C₂³×C₅₃	—	2	2	no	—
117	C₂³×C₅₃	#95	1	1	yes	characteristic
118	C₂³×C₅₃	#95	1	1	yes	characteristic
119	C₂³×C₅₃	#104	1	4	yes	—
120	C₂³×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂×C₄×C₅₃	—	2	2	no	—
122	C₂×C₄×C₅₃	—	2	2	no	—
123	C₂×C₄×C₅₃	—	2	2	no	—
124	C₂×C₄×C₅₃	—	2	2	no	—
125	C₂×C₄×C₅₃	—	2	2	no	—
126	C₂×C₄×C₅₃	—	2	2	no	—
127	C₂×C₄×C₅₃	—	2	2	no	—
128	C₂×C₄×C₅₃	—	2	2	no	—
129	C₂×C₄×C₅₃	—	2	2	no	—
130	C₂×C₄×C₅₃	—	2	2	no	—
131	C₂×C₄×C₅₃	—	2	2	no	—
132	C₂×C₄×C₅₃	—	2	2	no	—
133	C₂×C₄×C₅₃	—	2	2	no	—
134	C₂×C₄×C₅₃	—	2	8	no	—
135	C₂×C₄×C₅₃	—	4	1	no	—
136	C₂×C₄×C₅₃	—	4	1	no	—
137	C₂×C₄×C₅₃	—	4	1	no	—
138	C₂×C₄×C₅₃	—	4	1	no	—
139	C₂×C₄×C₅₃	—	4	16	no	—
140	C₂×C₄×C₅₃	—	4	4	no	—
141	C₂×C₄×C₅₃	—	4	4	no	—
142	C₂×C₄×C₅₃	#95	1	1	yes	characteristic
143	C₂×C₄×C₅₃	#95	1	1	yes	characteristic
144	C₂×C₄×C₅₃	#95	1	1	yes	characteristic
145	C₂×C₄×C₅₃	#95	1	1	yes	characteristic
146	C₂×C₄×C₅₃	#95	1	1	yes	characteristic
147	C₂×C₄×C₅₃	#95	1	1	yes	characteristic
148	C₂×C₄×C₅₃	#104	1	4	yes	—
149	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
150	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₈×C₅₃	—	2	8	no	—
156	C₈×C₅₃	—	4	4	no	—
157	C₂×#1300	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
158	C₂²×C₅₃	—	2	8	no	—
159	C₂²×C₅₃	—	2	1	no	—
160	C₂²×C₅₃	—	2	1	no	—
161	C₂²×C₅₃	—	2	1	no	—
162	C₂²×C₅₃	—	2	1	no	—
163	C₂²×C₅₃	#339	1	2	yes	—
164	C₂²×C₅₃	#339	1	2	yes	—
165	C₂²×C₅₃	#339	1	2	yes	—
166	C₂²×C₅₃	#344	1	2	yes	—
167	C₂²×C₅₃	C₂×#95	1	1	yes	characteristic
168	C₂²×C₅₃	C₂×#104	1	2	yes	—
169	C₄×C₅₃	—	2	1	no	—
170	C₄×C₅₃	—	2	1	no	—
171	C₄×C₅₃	—	2	1	no	—
172	C₄×C₅₃	—	2	1	no	—
173	C₄×C₅₃	—	2	1	no	—
174	C₄×C₅₃	—	2	1	no	—
175	C₄×C₅₃	—	2	1	no	—
176	C₄×C₅₃	—	2	1	no	—
177	C₄×C₅₃	—	2	1	no	—
178	C₄×C₅₃	—	2	1	no	—
179	C₄×C₅₃	—	4	8	no	—
180	C₄×C₅₃	#339	1	2	yes	—
181	C₄×C₅₃	C₂×#104	1	2	yes	—
182	C₂×#432	C₂×C₅₃	1	1	yes	characteristic
183	C₂×C₄×M₁₆	C₂×C₅₃	1	1	yes	characteristic
184	C₂×#376	C₂×C₅₃	1	1	yes	characteristic
185	#1300	C₂×C₅₃	1	4	yes	direct product factor
186	C₂×C₅₃	—	2	2	no	—
187	C₂×C₅₃	—	2	2	no	—
188	C₂×C₅₃	#1300	1	4	yes	direct product factor
189	C₂×C₅₃	C₂×#339	1	1	yes	characteristic
190	C₂×C₅₃	C₂×#339	1	1	yes	characteristic
191	C₂×C₅₃	C₂×#344	1	1	yes	characteristic
192	C₂²×M₁₆	—	2	1	no	—
193	C₂²×C₄²	—	2	1	no	—
194	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
195	#432	—	2	1	no	—
196	#432	—	2	1	no	—
197	#432	C₄×C₅₃	1	2	yes	complemented
198	#432	C₂²×C₅₃	1	2	yes	—
199	C₂×C₄⋊C₈	C₄×C₅₃	1	2	yes	complemented
200	C₂×C₂²⋊C₈	—	2	1	no	—
201	C₄×M₁₆	—	2	1	no	—
202	C₄×M₁₆	—	2	1	no	—
203	C₄×M₁₆	C₄×C₅₃	1	2	yes	complemented
204	C₄×M₁₆	C₂²×C₅₃	1	2	yes	—
205	C₂×#97	—	2	1	no	—
206	C₂×#97	C₄×C₅₃	1	2	yes	complemented
207	C₂×C₄×C₈	—	2	1	no	—
208	#376	—	2	1	no	—
209	#376	—	2	1	no	—
210	#376	C₄×C₅₃	1	2	yes	—
211	#376	C₂²×C₅₃	1	2	yes	—
212	C₂×#95	—	2	1	no	—
213	C₂×#95	C₄×C₅₃	1	2	yes	—
214	C₅₃	C₂×#1300	1	1	yes	characteristic, direct product factor, Sylow
215	C₂³×C₄	—	2	2	no	—
216	C₂³×C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
217	C₂³×C₄	D₄×C₅₃	1	1	yes	characteristic
218	C₂³×C₄	D₄×C₅₃	1	1	yes	characteristic
219	C₂×M₁₆	—	2	8	no	—
220	C₂×M₁₆	—	2	2	no	—
221	C₂×M₁₆	—	2	2	no	—
222	C₂²×C₈	—	2	2	no	—
223	C₂²×C₈	—	2	2	no	—
224	C₂×C₄²	—	2	8	no	—
225	C₂×C₄²	—	2	2	no	—
226	C₂×C₄²	—	2	2	no	—
227	C₂×C₄²	C₂×C₄×C₅₃	1	1	yes	characteristic
228	C₂×C₄²	C₂×C₄×C₅₃	1	1	yes	characteristic
229	C₂×C₄²	C₂×C₄×C₅₃	1	1	yes	characteristic
230	C₂×C₄²	C₂×C₄×C₅₃	1	1	yes	characteristic
231	C₂×C₄²	C₂×C₄×C₅₃	1	1	yes	characteristic
232	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
233	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
234	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
235	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
236	C₂×C₄²	Q₈×C₅₃	1	1	yes	characteristic
237	C₂×C₄²	Q₈×C₅₃	1	1	yes	characteristic
238	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
239	C₄⋊C₈	—	2	2	no	—
240	C₄⋊C₈	C₂×C₄×C₅₃	1	4	yes	complemented
241	C₂²⋊C₈	—	2	2	no	—
242	C₂²⋊C₈	—	2	2	no	—
243	#97	—	2	2	no	—
244	#97	—	2	2	no	—
245	#97	—	2	2	no	—
246	#97	C₂×C₄×C₅₃	1	4	yes	complemented
247	C₄×C₈	—	2	2	no	—
248	C₄×C₈	—	2	2	no	—
249	#95	—	2	2	no	—
250	#95	—	2	2	no	—
251	#95	—	2	2	no	—
252	#95	C₂×C₄×C₅₃	1	4	yes	—
253	C₂⁴	C₂²⋊C₄×C₅₃	1	1	yes	characteristic
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	8	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	4	2	no	—
259	C₂²×C₄	—	4	4	no	—
260	C₂²×C₄	—	4	4	no	—
261	C₂²×C₄	C₄²×C₅₃	1	1	yes	characteristic
262	C₂²×C₄	C₄²×C₅₃	1	1	yes	characteristic
263	C₂²×C₄	C₂²⋊C₄×C₅₃	1	1	yes	characteristic
264	C₂²×C₄	C₂²⋊C₄×C₅₃	1	1	yes	characteristic
265	C₂²×C₄	C₂²⋊C₄×C₅₃	1	1	yes	characteristic
266	C₂²×C₄	C₂²⋊C₄×C₅₃	1	1	yes	characteristic
267	C₂²×C₄	C₂²⋊C₄×C₅₃	1	1	yes	characteristic
268	C₂²×C₄	C₂²⋊C₄×C₅₃	1	1	yes	characteristic
269	C₂²×C₄	C₂²⋊C₄×C₅₃	1	1	yes	characteristic
270	C₂²×C₄	C₄⋊C₄×C₅₃	1	1	yes	characteristic
271	C₂²×C₄	C₄⋊C₄×C₅₃	1	1	yes	characteristic
272	C₂²×C₄	C₄⋊C₄×C₅₃	1	1	yes	characteristic
273	C₂²×C₄	C₄⋊C₄×C₅₃	1	1	yes	characteristic
274	C₂²×C₄	C₄⋊C₄×C₅₃	1	1	yes	characteristic
275	C₂²×C₄	C₄⋊C₄×C₅₃	1	1	yes	characteristic
276	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
277	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
278	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
279	M₁₆	—	2	8	no	—
280	M₁₆	—	2	8	no	—
281	C₂×C₈	—	2	8	no	—
282	C₂×C₈	—	2	4	no	—
283	C₂×C₈	—	2	4	no	—
284	C₂×C₈	—	4	4	no	—
285	C₄²	—	2	8	no	—
286	C₄²	—	2	8	no	—
287	C₄²	C₄²×C₅₃	1	1	yes	characteristic
288	C₄²	C₄²×C₅₃	1	1	yes	characteristic
289	C₄²	C₂²⋊C₄×C₅₃	1	1	yes	characteristic
290	C₄²	C₂²⋊C₄×C₅₃	1	1	yes	characteristic
291	C₄²	C₂²⋊C₄×C₅₃	1	1	yes	characteristic
292	C₄²	C₂²⋊C₄×C₅₃	1	1	yes	characteristic
293	C₄²	C₄⋊C₄×C₅₃	1	1	yes	characteristic
294	C₄²	C₄⋊C₄×C₅₃	1	1	yes	characteristic
295	C₄²	C₄⋊C₄×C₅₃	1	1	yes	characteristic
296	C₄²	C₄⋊C₄×C₅₃	1	1	yes	characteristic
297	C₄²	C₄⋊C₄×C₅₃	1	1	yes	characteristic
298	C₄²	C₄⋊C₄×C₅₃	1	1	yes	characteristic
299	C₄²	C₂²×C₄×C₅₃	1	1	yes	characteristic
300	C₄²	C₂²×C₄×C₅₃	1	1	yes	characteristic
301	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
302	C₄²	C₂×Q₈×C₅₃	1	1	yes	characteristic
303	C₂³	—	2	2	no	—
304	C₂³	—	2	2	no	—
305	C₂³	#95×C₅₃	1	1	yes	characteristic
306	C₂³	#95×C₅₃	1	1	yes	characteristic
307	C₂³	#104×C₅₃	1	4	yes	—
308	C₂³	C₂×C₂²⋊C₄×C₅₃	1	1	yes	characteristic
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	8	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	4	16	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	#95×C₅₃	1	1	yes	characteristic
331	C₂×C₄	#95×C₅₃	1	1	yes	characteristic
332	C₂×C₄	#95×C₅₃	1	1	yes	characteristic
333	C₂×C₄	#95×C₅₃	1	1	yes	characteristic
334	C₂×C₄	#95×C₅₃	1	1	yes	characteristic
335	C₂×C₄	#95×C₅₃	1	1	yes	characteristic
336	C₂×C₄	#104×C₅₃	1	4	yes	—
337	C₂×C₄	C₂×C₄²×C₅₃	1	1	yes	characteristic
338	C₂×C₄	C₂×C₂²⋊C₄×C₅₃	1	1	yes	characteristic
339	C₂×C₄	C₂×C₂²⋊C₄×C₅₃	1	1	yes	characteristic
340	C₂×C₄	C₂×C₄⋊C₄×C₅₃	1	1	yes	characteristic
341	C₂×C₄	C₂×C₄⋊C₄×C₅₃	1	1	yes	characteristic
342	C₂×C₄	C₂×C₄⋊C₄×C₅₃	1	1	yes	characteristic
343	C₈	—	2	8	no	—
344	C₈	—	4	4	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	8	no	—
350	C₂²	C₅₃×#339	1	2	yes	—
351	C₂²	C₅₃×#339	1	2	yes	—
352	C₂²	C₅₃×#339	1	2	yes	—
353	C₂²	C₅₃×#344	1	2	yes	—
354	C₂²	C₂×#95×C₅₃	1	1	yes	characteristic
355	C₂²	C₂×#104×C₅₃	1	2	yes	—
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	4	8	no	—
367	C₄	C₅₃×#339	1	2	yes	—
368	C₄	C₂×#104×C₅₃	1	2	yes	—
369	C₂	—	2	2	no	—
370	C₂	—	2	2	no	—
371	C₂	C₅₃×#1300	1	4	yes	direct product factor
372	C₂	C₂×C₅₃×#339	1	1	yes	characteristic
373	C₂	C₂×C₅₃×#339	1	1	yes	characteristic
374	C₂	C₂×C₅₃×#344	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅₃	C₂²⋊C₄
commutator	C₂×C₄	C₂×C₄²×C₅₃
Frattini, cosocle	C₂×C₄²	C₂³×C₅₃
socle	C₂³×C₅₃	#95
prime radical	C₂⁴×C₅₃	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅₃ ◁ C₂²×C₄²×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅₃×#1300	C₂	direct (N × H)
10. C₅₃×#432	C₄	semidirect
12. C₂×C₄⋊C₈×C₅₃	C₄	semidirect
16. C₄×M₁₆×C₅₃	C₄	semidirect
19. C₂×#97×C₅₃	C₄	semidirect
52. C₄⋊C₈×C₅₃	C₂×C₄	semidirect
58. #97×C₅₃	C₂×C₄	semidirect
157. C₂×#1300	C₅₃	direct (N × H)
185. #1300	C₂×C₅₃	direct (N × H)
188. C₂×C₅₃	#1300	direct (N × H)
197. #432	C₄×C₅₃	semidirect
199. C₂×C₄⋊C₈	C₄×C₅₃	semidirect
203. C₄×M₁₆	C₄×C₅₃	semidirect
206. C₂×#97	C₄×C₅₃	semidirect
214. C₅₃	C₂×#1300	direct (N × H)
240. C₄⋊C₈	C₂×C₄×C₅₃	semidirect
246. #97	C₂×C₄×C₅₃	semidirect
371. C₂	C₅₃×#1300	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅₃×#432	2
C₂×C₄×M₁₆×C₅₃	2
C₂×C₅₃×#376	2
C₅₃×#1300	2
C₂×#1300	53

Subgroups — C2×C53×#1300 #27215579

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#1300 #27215579