Subgroups — C₂×C₅₃×#1659 #27226491

Order 13568.

1150 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×H(3,𝔽₄)	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₃×#497	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅₃×#489	C₂	1	2	yes	maximal, complemented
4	C₅₃×#1659	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₅₃×#329	C₂	1	2	yes	maximal, complemented
6	C₂×C₅₃×#329	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×Q₁₆×C₅₃	—	2	1	no	—
8	C₂²×SD₁₆×C₅₃	—	2	1	no	—
9	C₅₃×H(3,𝔽₄)	—	2	4	no	—
10	C₅₃×H(3,𝔽₄)	—	2	2	no	—
11	C₅₃×H(3,𝔽₄)	C₂²	1	4	yes	—
12	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
13	C₂×#124×C₅₃	—	2	1	no	—
14	C₂×#124×C₅₃	—	2	2	no	—
15	C₂×#124×C₅₃	C₂²	1	2	yes	—
16	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
17	C₂×#120×C₅₃	—	2	1	no	—
18	C₂×#120×C₅₃	—	2	2	no	—
19	C₅₃×#497	—	2	2	no	—
20	C₅₃×#497	C₂²	1	4	yes	complemented
21	C₅₃×#489	—	2	4	no	—
22	C₅₃×#489	C₂²	1	8	yes	complemented
23	C₂×#103×C₅₃	—	2	2	no	—
24	C₂×#102×C₅₃	—	2	2	no	—
25	C₂×#97×C₅₃	C₂²	1	2	yes	complemented
26	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic, complemented
27	C₅₃×#329	C₂²	1	4	yes	complemented
28	C₅₃×#329	C₂²	1	8	yes	complemented
29	C₂⁵×C₅₃	—	2	1	no	—
30	C₂²×Q₈×C₅₃	—	2	1	no	—
31	C₂²×Q₈×C₅₃	D₄	1	1	yes	characteristic
32	C₂²×Q₈×C₅₃	D₄	1	2	yes	—
33	C₂²×D₄×C₅₃	—	2	1	no	—
34	C₂²×D₄×C₅₃	—	2	2	no	—
35	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
36	C₂²×D₄×C₅₃	D₄	1	2	yes	—
37	C₂×Q₁₆×C₅₃	—	2	4	no	—
38	C₂×Q₁₆×C₅₃	—	4	4	no	—
39	C₂×SD₁₆×C₅₃	—	2	4	no	—
40	C₂×SD₁₆×C₅₃	—	4	4	no	—
41	C₂²×C₈×C₅₃	—	2	1	no	—
42	C₂²×C₈×C₅₃	—	2	2	no	—
43	C₄⋊Q₈×C₅₃	—	2	1	no	—
44	C₄⋊Q₈×C₅₃	—	2	2	no	—
45	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
46	#124×C₅₃	—	2	4	no	—
47	#124×C₅₃	—	2	8	no	—
48	#124×C₅₃	—	2	2	no	—
49	#124×C₅₃	—	2	2	no	—
50	#124×C₅₃	—	2	2	no	—
51	#124×C₅₃	—	2	8	no	—
52	#124×C₅₃	—	2	4	no	—
53	#124×C₅₃	D₄	1	4	yes	—
54	#124×C₅₃	D₄	1	2	yes	—
55	#124×C₅₃	C₂³	1	4	yes	—
56	#124×C₅₃	C₂³	1	2	yes	—
57	#120×C₅₃	—	2	4	no	—
58	#120×C₅₃	—	2	8	no	—
59	#120×C₅₃	—	2	8	no	—
60	#120×C₅₃	—	2	4	no	—
61	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
64	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
67	C₂×C₄²×C₅₃	—	2	1	no	—
68	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
69	#103×C₅₃	—	2	8	no	—
70	#102×C₅₃	—	2	8	no	—
71	#97×C₅₃	—	2	2	no	—
72	#97×C₅₃	—	2	1	no	—
73	#97×C₅₃	C₂³	1	4	yes	complemented
74	#97×C₅₃	C₂³	1	2	yes	complemented
75	C₂⁴×C₅₃	—	2	4	no	—
76	C₂⁴×C₅₃	—	2	1	no	—
77	C₂⁴×C₅₃	—	2	2	no	—
78	C₂⁴×C₅₃	—	8	2	no	—
79	C₂⁴×C₅₃	—	8	4	no	—
80	C₂×Q₈×C₅₃	—	2	1	no	—
81	C₂×Q₈×C₅₃	—	2	2	no	—
82	C₂×Q₈×C₅₃	—	2	2	no	—
83	C₂×Q₈×C₅₃	—	4	2	no	—
84	C₂×Q₈×C₅₃	—	4	4	no	—
85	C₂×Q₈×C₅₃	—	4	2	no	—
86	C₂×Q₈×C₅₃	—	4	2	no	—
87	C₂×Q₈×C₅₃	—	4	1	no	—
88	C₂×Q₈×C₅₃	C₂×D₄	1	4	yes	—
89	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
90	C₂×D₄×C₅₃	—	2	4	no	—
91	C₂×D₄×C₅₃	—	2	8	no	—
92	C₂×D₄×C₅₃	—	2	1	no	—
93	C₂×D₄×C₅₃	—	2	2	no	—
94	C₂×D₄×C₅₃	—	4	2	no	—
95	C₂×D₄×C₅₃	—	4	4	no	—
96	C₂×D₄×C₅₃	—	8	2	no	—
97	C₂×D₄×C₅₃	—	8	4	no	—
98	C₂×D₄×C₅₃	C₂×D₄	1	4	yes	—
99	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₅₃	—	2	1	no	—
101	C₂²×C₄×C₅₃	—	2	2	no	—
102	C₂²×C₄×C₅₃	—	4	1	no	—
103	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
105	Q₁₆×C₅₃	—	4	8	no	—
106	SD₁₆×C₅₃	—	4	8	no	—
107	C₂×C₈×C₅₃	—	2	4	no	—
108	C₂×C₈×C₅₃	—	2	2	no	—
109	C₂×C₈×C₅₃	—	2	4	no	—
110	C₂×C₈×C₅₃	—	4	4	no	—
111	C₄⋊C₄×C₅₃	—	2	4	no	—
112	C₄⋊C₄×C₅₃	—	4	2	no	—
113	C₂²⋊C₄×C₅₃	—	2	8	no	—
114	C₂²⋊C₄×C₅₃	—	2	4	no	—
115	C₂²⋊C₄×C₅₃	—	2	4	no	—
116	C₂²⋊C₄×C₅₃	—	2	4	no	—
117	C₂²⋊C₄×C₅₃	—	2	4	no	—
118	C₂²⋊C₄×C₅₃	—	2	4	no	—
119	C₂²⋊C₄×C₅₃	—	2	4	no	—
120	C₂²⋊C₄×C₅₃	—	2	4	no	—
121	C₄²×C₅₃	—	2	4	no	—
122	C₄²×C₅₃	C₂×D₄	1	2	yes	—
123	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
125	C₂³×C₅₃	—	2	2	no	—
126	C₂³×C₅₃	—	2	4	no	—
127	C₂³×C₅₃	—	4	2	no	—
128	C₂³×C₅₃	—	4	4	no	—
129	C₂³×C₅₃	—	4	4	no	—
130	C₂³×C₅₃	—	4	4	no	—
131	C₂³×C₅₃	—	4	4	no	—
132	C₂³×C₅₃	—	8	4	no	—
133	C₂³×C₅₃	—	8	8	no	—
134	C₂³×C₅₃	—	8	16	no	—
135	C₂³×C₅₃	#120	1	1	yes	characteristic
136	Q₈×C₅₃	—	4	4	no	—
137	Q₈×C₅₃	—	4	2	no	—
138	Q₈×C₅₃	—	4	2	no	—
139	Q₈×C₅₃	—	4	2	no	—
140	Q₈×C₅₃	—	8	1	no	—
141	Q₈×C₅₃	—	8	2	no	—
142	Q₈×C₅₃	—	8	2	no	—
143	D₄×C₅₃	—	4	4	no	—
144	D₄×C₅₃	—	4	2	no	—
145	D₄×C₅₃	—	8	1	no	—
146	D₄×C₅₃	—	8	2	no	—
147	D₄×C₅₃	—	8	4	no	—
148	D₄×C₅₃	—	8	8	no	—
149	C₂×C₄×C₅₃	—	2	2	no	—
150	C₂×C₄×C₅₃	—	2	4	no	—
151	C₂×C₄×C₅₃	—	2	2	no	—
152	C₂×C₄×C₅₃	—	2	4	no	—
153	C₂×C₄×C₅₃	—	4	2	no	—
154	C₂×C₄×C₅₃	—	4	4	no	—
155	C₂×C₄×C₅₃	—	4	2	no	—
156	C₂×C₄×C₅₃	—	8	2	no	—
157	C₂×C₄×C₅₃	#120	1	1	yes	characteristic
158	C₂×C₄×C₅₃	#120	1	2	yes	—
159	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
161	C₈×C₅₃	—	2	4	no	—
162	C₈×C₅₃	—	4	4	no	—
163	C₂×#1659	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂²×C₅₃	—	4	2	no	—
165	C₂²×C₅₃	—	4	4	no	—
166	C₂²×C₅₃	—	4	4	no	—
167	C₂²×C₅₃	—	4	4	no	—
168	C₂²×C₅₃	—	4	4	no	—
169	C₂²×C₅₃	—	8	16	no	—
170	C₂²×C₅₃	—	8	4	no	—
171	C₂²×C₅₃	—	8	8	no	—
172	C₂²×C₅₃	#453	1	2	yes	—
173	C₂²×C₅₃	#455	1	4	yes	—
174	C₂²×C₅₃	C₂×#120	1	1	yes	characteristic
175	C₄×C₅₃	—	2	1	no	—
176	C₄×C₅₃	—	2	1	no	—
177	C₄×C₅₃	—	2	2	no	—
178	C₄×C₅₃	—	2	2	no	—
179	C₄×C₅₃	—	4	2	no	—
180	C₄×C₅₃	—	4	4	no	—
181	C₄×C₅₃	—	8	2	no	—
182	C₂×H(3,𝔽₄)	C₂×C₅₃	1	1	yes	characteristic
183	C₂×#497	C₂×C₅₃	1	1	yes	characteristic, complemented
184	C₂×#489	C₂×C₅₃	1	2	yes	complemented
185	#1659	C₂×C₅₃	1	8	yes	direct product factor
186	C₂×#329	C₂×C₅₃	1	2	yes	complemented
187	C₂×#329	C₂×C₅₃	1	1	yes	characteristic, complemented
188	C₂×C₅₃	—	8	2	no	—
189	C₂×C₅₃	—	8	4	no	—
190	C₂×C₅₃	#1659	1	4	yes	direct product factor
191	C₂×C₅₃	C₂×#453	1	1	yes	characteristic
192	C₂×C₅₃	C₂×#455	1	2	yes	—
193	C₂²×Q₁₆	—	2	1	no	—
194	C₂²×SD₁₆	—	2	1	no	—
195	H(3,𝔽₄)	—	2	4	no	—
196	H(3,𝔽₄)	—	2	2	no	—
197	H(3,𝔽₄)	C₂²×C₅₃	1	4	yes	—
198	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
199	C₂×#124	—	2	1	no	—
200	C₂×#124	—	2	2	no	—
201	C₂×#124	C₂²×C₅₃	1	2	yes	—
202	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
203	C₂×#120	—	2	1	no	—
204	C₂×#120	—	2	2	no	—
205	#497	—	2	2	no	—
206	#497	C₂²×C₅₃	1	4	yes	complemented
207	#489	—	2	4	no	—
208	#489	C₂²×C₅₃	1	8	yes	complemented
209	C₂×#103	—	2	2	no	—
210	C₂×#102	—	2	2	no	—
211	C₂×#97	C₂²×C₅₃	1	2	yes	complemented
212	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic, complemented
213	#329	C₂²×C₅₃	1	4	yes	complemented
214	#329	C₂²×C₅₃	1	8	yes	complemented
215	C₅₃	C₂×#1659	1	1	yes	characteristic, direct product factor, Sylow
216	C₂⁵	—	2	1	no	—
217	C₂²×Q₈	—	2	1	no	—
218	C₂²×Q₈	D₄×C₅₃	1	1	yes	characteristic
219	C₂²×Q₈	D₄×C₅₃	1	2	yes	—
220	C₂²×D₄	—	2	1	no	—
221	C₂²×D₄	—	2	2	no	—
222	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
223	C₂²×D₄	D₄×C₅₃	1	2	yes	—
224	C₂×Q₁₆	—	2	4	no	—
225	C₂×Q₁₆	—	4	4	no	—
226	C₂×SD₁₆	—	2	4	no	—
227	C₂×SD₁₆	—	4	4	no	—
228	C₂²×C₈	—	2	1	no	—
229	C₂²×C₈	—	2	2	no	—
230	C₄⋊Q₈	—	2	2	no	—
231	C₄⋊Q₈	—	2	1	no	—
232	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	complemented
233	#124	—	2	8	no	—
234	#124	—	2	4	no	—
235	#124	—	2	8	no	—
236	#124	—	2	4	no	—
237	#124	—	2	2	no	—
238	#124	—	2	2	no	—
239	#124	—	2	2	no	—
240	#124	D₄×C₅₃	1	4	yes	—
241	#124	D₄×C₅₃	1	2	yes	—
242	#124	C₂³×C₅₃	1	4	yes	—
243	#124	C₂³×C₅₃	1	2	yes	—
244	#120	—	2	8	no	—
245	#120	—	2	4	no	—
246	#120	—	2	8	no	—
247	#120	—	2	4	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₂²⋊C₄	—	2	2	no	—
250	C₂×C₂²⋊C₄	—	2	1	no	—
251	C₂×C₂²⋊C₄	—	2	2	no	—
252	C₂×C₂²⋊C₄	—	2	2	no	—
253	C₂×C₂²⋊C₄	—	2	2	no	—
254	C₂×C₄²	—	2	1	no	—
255	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
256	#103	—	2	8	no	—
257	#102	—	2	8	no	—
258	#97	—	2	2	no	—
259	#97	—	2	1	no	—
260	#97	C₂³×C₅₃	1	4	yes	complemented
261	#97	C₂³×C₅₃	1	2	yes	complemented
262	C₂⁴	—	2	4	no	—
263	C₂⁴	—	2	1	no	—
264	C₂⁴	—	2	2	no	—
265	C₂⁴	—	8	2	no	—
266	C₂⁴	—	8	4	no	—
267	C₂×Q₈	—	2	2	no	—
268	C₂×Q₈	—	2	1	no	—
269	C₂×Q₈	—	2	2	no	—
270	C₂×Q₈	—	4	2	no	—
271	C₂×Q₈	—	4	4	no	—
272	C₂×Q₈	—	4	2	no	—
273	C₂×Q₈	—	4	2	no	—
274	C₂×Q₈	—	4	1	no	—
275	C₂×Q₈	C₂×D₄×C₅₃	1	4	yes	—
276	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
277	C₂×D₄	—	2	4	no	—
278	C₂×D₄	—	2	8	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	1	no	—
281	C₂×D₄	—	4	2	no	—
282	C₂×D₄	—	4	4	no	—
283	C₂×D₄	—	8	2	no	—
284	C₂×D₄	—	8	4	no	—
285	C₂×D₄	C₂×D₄×C₅₃	1	4	yes	—
286	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
291	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
292	Q₁₆	—	4	8	no	—
293	SD₁₆	—	4	8	no	—
294	C₂×C₈	—	2	4	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	4	no	—
297	C₂×C₈	—	4	4	no	—
298	C₄⋊C₄	—	2	4	no	—
299	C₄⋊C₄	—	4	2	no	—
300	C₂²⋊C₄	—	2	8	no	—
301	C₂²⋊C₄	—	2	4	no	—
302	C₂²⋊C₄	—	2	4	no	—
303	C₂²⋊C₄	—	2	4	no	—
304	C₂²⋊C₄	—	2	4	no	—
305	C₂²⋊C₄	—	2	4	no	—
306	C₂²⋊C₄	—	2	4	no	—
307	C₂²⋊C₄	—	2	4	no	—
308	C₄²	—	2	4	no	—
309	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
310	C₄²	C₂×D₄×C₅₃	1	2	yes	—
311	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
312	C₂³	—	2	2	no	—
313	C₂³	—	2	4	no	—
314	C₂³	—	4	2	no	—
315	C₂³	—	4	4	no	—
316	C₂³	—	4	4	no	—
317	C₂³	—	4	4	no	—
318	C₂³	—	4	4	no	—
319	C₂³	—	8	4	no	—
320	C₂³	—	8	8	no	—
321	C₂³	—	8	16	no	—
322	C₂³	#120×C₅₃	1	1	yes	characteristic
323	Q₈	—	4	2	no	—
324	Q₈	—	4	4	no	—
325	Q₈	—	4	2	no	—
326	Q₈	—	4	2	no	—
327	Q₈	—	8	1	no	—
328	Q₈	—	8	2	no	—
329	Q₈	—	8	2	no	—
330	D₄	—	4	2	no	—
331	D₄	—	4	4	no	—
332	D₄	—	8	1	no	—
333	D₄	—	8	2	no	—
334	D₄	—	8	4	no	—
335	D₄	—	8	8	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	8	2	no	—
344	C₂×C₄	#120×C₅₃	1	2	yes	—
345	C₂×C₄	#120×C₅₃	1	1	yes	characteristic
346	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
347	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
348	C₈	—	2	4	no	—
349	C₈	—	4	4	no	—
350	C₂²	—	4	2	no	—
351	C₂²	—	4	4	no	—
352	C₂²	—	4	4	no	—
353	C₂²	—	4	4	no	—
354	C₂²	—	4	4	no	—
355	C₂²	—	8	16	no	—
356	C₂²	—	8	4	no	—
357	C₂²	—	8	8	no	—
358	C₂²	C₅₃×#453	1	2	yes	—
359	C₂²	C₅₃×#455	1	4	yes	—
360	C₂²	C₂×#120×C₅₃	1	1	yes	characteristic
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	2	no	—
364	C₄	—	2	2	no	—
365	C₄	—	4	2	no	—
366	C₄	—	4	4	no	—
367	C₄	—	8	2	no	—
368	C₂	—	8	2	no	—
369	C₂	—	8	4	no	—
370	C₂	C₅₃×#1659	1	4	yes	direct product factor
371	C₂	C₂×C₅₃×#453	1	1	yes	characteristic
372	C₂	C₂×C₅₃×#455	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₃	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅₃
prime radical	C₂×C₅₃×H(3,𝔽₄)	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ C₂×C₄²×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅₃×#497	C₂	semidirect
3. C₂×C₅₃×#489	C₂	semidirect
4. C₅₃×#1659	C₂	direct (N × H)
5. C₂×C₅₃×#329	C₂	semidirect
6. C₂×C₅₃×#329	C₂	semidirect
12. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
20. C₅₃×#497	C₂²	semidirect
22. C₅₃×#489	C₂²	semidirect
25. C₂×#97×C₅₃	C₂²	semidirect
26. C₂×#97×C₅₃	C₂²	semidirect
27. C₅₃×#329	C₂²	semidirect
28. C₅₃×#329	C₂²	semidirect
45. C₄⋊Q₈×C₅₃	C₂³	semidirect
73. #97×C₅₃	C₂³	semidirect
74. #97×C₅₃	C₂³	semidirect
163. C₂×#1659	C₅₃	direct (N × H)
183. C₂×#497	C₂×C₅₃	semidirect
184. C₂×#489	C₂×C₅₃	semidirect
185. #1659	C₂×C₅₃	direct (N × H)
186. C₂×#329	C₂×C₅₃	semidirect
187. C₂×#329	C₂×C₅₃	semidirect
190. C₂×C₅₃	#1659	direct (N × H)
198. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
206. #497	C₂²×C₅₃	semidirect
208. #489	C₂²×C₅₃	semidirect
211. C₂×#97	C₂²×C₅₃	semidirect
212. C₂×#97	C₂²×C₅₃	semidirect
213. #329	C₂²×C₅₃	semidirect
214. #329	C₂²×C₅₃	semidirect
215. C₅₃	C₂×#1659	direct (N × H)
232. C₄⋊Q₈	C₂³×C₅₃	semidirect
260. #97	C₂³×C₅₃	semidirect
261. #97	C₂³×C₅₃	semidirect
370. C₂	C₅₃×#1659	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×H(3,𝔽₄)	2
C₂×C₅₃×#497	2
C₂×C₅₃×#489	2
C₅₃×#1659	2
C₂×C₅₃×#329	2
C₂×#1659	53

Subgroups — C2×C53×#1659 #27226491

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#1659 #27226491