Subgroups — #28318395

Order 13568.

994 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅₃⋊#108	C₂	1	1	yes	maximal, characteristic
2	#20291278	C₂	1	2	yes	maximal
3	C₂×#16811586	C₂	1	1	yes	maximal, characteristic
4	#20290536	C₂	1	4	yes	maximal, complemented
5	#108×#6157	C₂	1	4	yes	maximal, complemented
6	#20290408	C₂	1	2	yes	maximal
7	C₂×#108×D₅₃	C₂	1	1	yes	maximal, characteristic
8	C₂×D₅₃⋊M₁₆	C₂²	1	2	yes	—
9	C₂×D₅₃⋊M₁₆	C₂²	1	1	yes	characteristic
10	C₂×#13133296	C₂²	1	1	yes	characteristic
11	C₂×#13133288	C₄	1	2	yes	complemented
12	D₅₃⋊#108	C₄	1	2	yes	complemented
13	D₅₃⋊#108	C₄	1	2	yes	complemented
14	D₅₃⋊#108	C₂²	1	2	yes	—
15	D₅₃⋊#108	C₂²	1	2	yes	—
16	C₂×#13133287	C₄	1	2	yes	complemented
17	#16811589	—	2	4	no	—
18	#16811586	—	2	4	no	—
19	#16811586	C₄	1	2	yes	—
20	#16811586	C₄	1	2	yes	—
21	#16811586	C₄	1	2	yes	—
22	#16811586	C₄	1	2	yes	—
23	M₁₆×#6157	C₂²	1	8	yes	—
24	C₂×#13133271	C₂²	1	2	yes	—
25	C₂×C₈×#6157	C₂²	1	2	yes	—
26	#16811498	C₂²	1	8	yes	—
27	C₂×M₁₆×D₅₃	C₂²	1	2	yes	—
28	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
29	C₂×#13133153	C₄	1	1	yes	characteristic, complemented
30	C₂×#13133152	C₄	1	2	yes	complemented
31	#108×D₅₃	C₄	1	2	yes	complemented
32	#108×D₅₃	C₄	1	2	yes	complemented
33	#108×D₅₃	C₂²	1	2	yes	—
34	#108×D₅₃	C₂²	1	2	yes	—
35	C₂×#108×C₅₃	C₄	1	1	yes	characteristic, complemented
36	C₂×#11719936	—	2	1	no	—
37	C₂×#11719936	C₂×C₄	1	4	yes	—
38	D₅₃⋊M₁₆	—	2	2	no	—
39	D₅₃⋊M₁₆	—	2	1	no	—
40	D₅₃⋊M₁₆	—	2	1	no	—
41	D₅₃⋊M₁₆	—	2	2	no	—
42	D₅₃⋊M₁₆	C₂×C₄	1	2	yes	—
43	D₅₃⋊M₁₆	C₂×C₄	1	2	yes	—
44	D₅₃⋊M₁₆	C₂×C₄	1	4	yes	—
45	D₅₃⋊M₁₆	C₂³	1	4	yes	—
46	C₂×#11719940	—	2	2	no	—
47	C₂×#11719940	—	2	1	no	—
48	C₂×D₅₃⋊C₈	—	2	2	no	—
49	C₂×D₅₃⋊C₈	C₂³	1	2	yes	—
50	#13133296	C₂×C₄	1	2	yes	—
51	#13133296	C₂×C₄	1	2	yes	—
52	#13133296	D₄	1	2	yes	—
53	#13133296	D₄	1	2	yes	—
54	C₂×C₄⋊#6157	Q₈	1	2	yes	—
55	C₂×C₂²⋊#6157	Q₈	1	2	yes	—
56	C₂×C₄×#6157	C₂³	1	2	yes	—
57	#13133288	C₂×C₄	1	4	yes	—
58	#13133288	C₂×C₄	1	4	yes	—
59	#13133287	C₂×C₄	1	4	yes	—
60	#13133287	C₂×C₄	1	4	yes	—
61	#13133271	—	2	8	no	—
62	#13133271	C₂×C₄	1	4	yes	—
63	#13133271	C₂×C₄	1	4	yes	—
64	C₈×#6157	—	2	8	no	—
65	C₈×#6157	C₂×C₄	1	4	yes	—
66	C₈×#6157	C₂×C₄	1	4	yes	—
67	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
68	C₂×#11719917	C₂×C₄	1	2	yes	—
69	C₂×#11719912	—	2	2	no	—
70	M₁₆×D₅₃	—	2	2	no	—
71	M₁₆×D₅₃	—	2	2	no	—
72	M₁₆×D₅₃	C₂×C₄	1	4	yes	—
73	M₁₆×D₅₃	C₂³	1	4	yes	—
74	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
75	C₂×C₈×D₅₃	—	2	2	no	—
76	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
79	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
80	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
81	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
82	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
83	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
84	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
85	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
86	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
87	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
88	#13133153	C₂×C₄	1	2	yes	—
89	#13133153	C₂×C₄	1	2	yes	—
90	#13133152	C₂×C₄	1	4	yes	—
91	#13133152	C₂×C₄	1	4	yes	—
92	C₂×M₁₆×C₅₃	C₂×C₄	1	2	yes	—
93	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
94	#108×C₅₃	C₂×C₄	1	2	yes	—
95	#108×C₅₃	C₂×C₄	1	2	yes	—
96	C₂³×D₅₃	C₂×Q₈	1	1	yes	characteristic
97	C₂²×#6157	C₂×Q₈	1	4	yes	—
98	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
99	C₂²×Dic₅₃	#41	1	1	yes	characteristic
100	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
106	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
107	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
108	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
109	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
110	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
111	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
112	C₂²⋊#6157	C₄⋊C₄	1	4	yes	—
113	C₂²⋊#6157	C₄⋊C₄	1	4	yes	—
114	#11719940	—	2	2	no	—
115	#11719940	—	2	2	no	—
116	#11719940	—	2	4	no	—
117	#11719940	—	2	4	no	—
118	C₂×#88324	—	2	4	no	—
119	C₂×#88324	—	2	2	no	—
120	C₄⋊#6157	C₄⋊C₄	1	4	yes	—
121	C₄⋊#6157	C₄⋊C₄	1	4	yes	—
122	C₄×#6157	C₂²×C₄	1	4	yes	—
123	C₄×#6157	C₂×D₄	1	4	yes	—
124	#11719936	—	2	2	no	—
125	#11719936	—	2	2	no	—
126	#11719936	—	2	4	no	—
127	#11719936	C₂²×C₄	1	8	yes	—
128	D₅₃⋊C₈	—	2	4	no	—
129	D₅₃⋊C₈	—	2	4	no	—
130	D₅₃⋊C₈	—	2	2	no	—
131	D₅₃⋊C₈	C₂²×C₄	1	4	yes	—
132	M₁₆×C₅₃	—	2	2	no	—
133	M₁₆×C₅₃	C₂²×C₄	1	4	yes	—
134	C₂×C₈×C₅₃	—	2	2	no	—
135	C₂×C₈×C₅₃	C₄²	1	1	yes	characteristic
136	C₂×C₈×C₅₃	C₄²	1	1	yes	characteristic
137	C₂×C₈×C₅₃	C₄²	1	1	yes	characteristic
138	C₂×C₈×C₅₃	C₄²	1	1	yes	characteristic
139	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
141	#11719917	—	2	2	no	—
142	#11719917	C₂²×C₄	1	4	yes	—
143	C₂×#88322	—	2	2	no	—
144	C₂×#88322	C₄²	1	1	yes	characteristic
145	C₂×#88322	C₄²	1	1	yes	characteristic
146	C₂×#88322	C₄²	1	1	yes	characteristic
147	C₂×#88322	C₄²	1	1	yes	characteristic
148	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
149	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
150	#11719912	—	2	4	no	—
151	#11719912	—	2	4	no	—
152	C₈×D₅₃	—	2	4	no	—
153	C₈×D₅₃	—	2	4	no	—
154	C₈×D₅₃	C₄²	1	1	yes	characteristic
155	C₈×D₅₃	C₄²	1	1	yes	characteristic
156	C₈×D₅₃	C₄²	1	1	yes	characteristic
157	C₈×D₅₃	C₄²	1	1	yes	characteristic
158	C₈×D₅₃	C₄²	1	1	yes	characteristic
159	C₈×D₅₃	C₄²	1	1	yes	characteristic
160	C₈×D₅₃	C₄²	1	1	yes	characteristic
161	C₈×D₅₃	C₄²	1	1	yes	characteristic
162	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
163	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
164	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
165	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
166	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
167	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
168	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
169	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
170	C₂³×C₅₃	C₄×Q₈	1	1	yes	characteristic
171	C₂²×D₅₃	—	4	2	no	—
172	C₂²×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂²×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂²×D₅₃	C₄×Q₈	1	1	yes	characteristic
175	C₂²×D₅₃	C₄×Q₈	1	1	yes	characteristic
176	C₂²×D₅₃	C₄×Q₈	1	1	yes	characteristic
177	C₂²×D₅₃	C₂²×Q₈	1	1	yes	characteristic
178	C₂×#6157	—	4	4	no	—
179	C₂×#6157	C₂×C₄⋊C₄	1	8	yes	—
180	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
181	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
182	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₅₃	C₄×Q₈	1	1	yes	characteristic
185	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
186	C₂×Dic₅₃	#117	1	1	yes	characteristic
187	C₂×Dic₅₃	#117	1	1	yes	characteristic
188	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
189	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
190	C₂×Dic₅₃	C₄×Q₈	1	1	yes	characteristic
191	C₂×Dic₅₃	C₂×#41	1	1	yes	characteristic
192	C₄×D₅₃	C₂×C₄²	1	1	yes	characteristic
193	C₄×D₅₃	C₂×C₄²	1	1	yes	characteristic
194	C₄×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
195	C₄×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
196	C₄×D₅₃	#117	1	1	yes	characteristic
197	C₄×D₅₃	#117	1	1	yes	characteristic
198	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
199	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
200	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
201	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
202	C₄×D₅₃	C₄×Q₈	1	1	yes	characteristic
203	C₄×D₅₃	C₄×Q₈	1	1	yes	characteristic
204	C₄×D₅₃	C₂³×C₄	1	1	yes	characteristic
205	C₄×D₅₃	C₂³×C₄	1	1	yes	characteristic
206	C₄×D₅₃	C₂²×D₄	1	1	yes	characteristic
207	C₄×D₅₃	C₂×#41	1	1	yes	characteristic
208	#88324	—	2	4	no	—
209	#88324	—	2	8	no	—
210	C₈×C₅₃	—	2	4	no	—
211	C₈×C₅₃	C₂×C₄²	1	1	yes	characteristic
212	C₈×C₅₃	C₂×C₄²	1	1	yes	characteristic
213	C₈×C₅₃	C₂×C₄²	1	1	yes	characteristic
214	C₈×C₅₃	C₂×C₄²	1	1	yes	characteristic
215	#88322	—	2	4	no	—
216	#88322	C₂×C₄²	1	1	yes	characteristic
217	#88322	C₂×C₄²	1	1	yes	characteristic
218	#88322	C₂×C₄²	1	1	yes	characteristic
219	#88322	C₂×C₄²	1	1	yes	characteristic
220	#20460	—	53	1	no	maximal, Sylow
221	C₂²×C₅₃	—	4	1	no	—
222	C₂²×C₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
223	C₂²×C₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
224	C₂²×C₅₃	C₂×C₄×Q₈	1	1	yes	characteristic
225	C₂×D₅₃	—	2	2	no	—
226	C₂×D₅₃	—	2	2	no	—
227	C₂×D₅₃	—	2	2	no	—
228	C₂×D₅₃	—	4	1	no	—
229	C₂×D₅₃	—	4	1	no	—
230	C₂×D₅₃	—	4	1	no	—
231	C₂×D₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
232	C₂×D₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
233	C₂×D₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
234	C₂×D₅₃	C₂×C₄×Q₈	1	1	yes	characteristic
235	#6157	—	2	8	no	—
236	C₄×C₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
237	C₄×C₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
238	C₄×C₅₃	C₂²×C₄²	1	1	yes	characteristic
239	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
240	Dic₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
241	Dic₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
242	Dic₅₃	C₂×#117	1	1	yes	characteristic
243	Dic₅₃	C₂×C₄×D₄	1	1	yes	characteristic
244	C₂²×#108	—	53	1	no	—
245	C₂²×#108	—	53	1	no	—
246	#2873	—	53	2	no	—
247	C₂×#405	—	53	1	no	—
248	#1778	—	53	4	no	—
249	C₄×#108	—	53	4	no	—
250	#1738	—	53	2	no	—
251	C₂×C₅₃	—	2	1	no	—
252	C₂×C₅₃	—	2	1	no	—
253	C₂×C₅₃	—	2	1	no	—
254	C₂×C₅₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
255	D₅₃	—	2	1	no	—
256	D₅₃	—	2	1	no	—
257	D₅₃	—	2	1	no	—
258	D₅₃	#2916	1	2	yes	—
259	C₂²×M₁₆	—	53	1	no	—
260	C₂²×M₁₆	—	53	2	no	—
261	C₂²×M₁₆	—	53	2	no	—
262	C₂³×C₈	—	53	1	no	—
263	C₂×#117	—	53	1	no	—
264	C₂×#108	—	53	2	no	—
265	C₂×#108	—	53	2	no	—
266	C₂×#108	—	53	2	no	—
267	C₂×#108	—	53	2	no	—
268	C₂×#108	—	53	2	no	—
269	C₂×#108	—	53	2	no	—
270	C₂×#108	—	53	2	no	—
271	C₂×#108	—	53	1	no	—
272	C₂×#108	—	53	2	no	—
273	C₂×#108	—	53	2	no	—
274	C₂×#108	—	53	2	no	—
275	C₂×#108	—	53	2	no	—
276	C₂×#108	#6157	1	1	yes	characteristic, complemented
277	#405	—	53	2	no	—
278	#405	—	53	2	no	—
279	#405	—	53	2	no	—
280	#405	—	53	2	no	—
281	#405	—	106	4	no	—
282	#405	—	106	4	no	—
283	C₄×M₁₆	—	53	8	no	—
284	C₂×#97	—	53	2	no	—
285	C₂×C₄×C₈	—	53	2	no	—
286	#341	—	53	8	no	—
287	C₅₃	#20460	1	1	yes	characteristic, complemented, Sylow
288	C₂³×C₄	—	53	1	no	—
289	C₂×M₁₆	—	53	2	no	—
290	C₂×M₁₆	—	53	2	no	—
291	C₂×M₁₆	—	53	4	no	—
292	C₂×M₁₆	—	53	4	no	—
293	C₂×M₁₆	—	53	4	no	—
294	C₂×M₁₆	—	53	2	no	—
295	C₂×M₁₆	—	53	4	no	—
296	C₂×M₁₆	—	53	4	no	—
297	C₂×M₁₆	—	106	2	no	—
298	C₂×M₁₆	—	106	2	no	—
299	C₂×M₁₆	—	106	2	no	—
300	C₂×M₁₆	—	106	2	no	—
301	C₂×M₁₆	—	106	1	no	—
302	C₂×M₁₆	—	106	2	no	—
303	C₂×M₁₆	—	106	1	no	—
304	C₂×M₁₆	—	106	1	no	—
305	C₂×M₁₆	—	106	2	no	—
306	C₂×M₁₆	—	106	1	no	—
307	C₂×M₁₆	C₂×#6157	1	2	yes	—
308	C₂²×C₈	—	53	1	no	—
309	C₂²×C₈	—	53	1	no	—
310	C₂²×C₈	—	53	1	no	—
311	C₂²×C₈	—	53	1	no	—
312	C₂²×C₈	—	53	1	no	—
313	C₂²×C₈	—	53	1	no	—
314	C₂²×C₈	—	53	1	no	—
315	C₂²×C₈	—	53	1	no	—
316	C₂²×C₈	—	53	1	no	—
317	C₂²×C₈	—	53	1	no	—
318	C₂²×C₈	—	53	1	no	—
319	C₂²×C₈	—	53	1	no	—
320	C₂²×C₈	—	53	1	no	—
321	C₂²×C₈	—	53	2	no	—
322	C₂²×C₈	—	106	2	no	—
323	C₂²×C₈	—	106	2	no	—
324	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
325	#117	—	53	2	no	—
326	#117	—	53	2	no	—
327	#117	—	53	2	no	—
328	#117	—	53	2	no	—
329	C₂×C₄⋊C₄	—	53	2	no	—
330	C₂×C₂²⋊C₄	—	53	2	no	—
331	C₂×C₄²	—	53	2	no	—
332	#108	—	53	4	no	—
333	#108	—	53	4	no	—
334	#108	—	53	4	no	—
335	#108	—	53	4	no	—
336	#108	—	53	4	no	—
337	#108	—	53	4	no	—
338	#108	—	53	2	no	—
339	#108	—	53	2	no	—
340	#108	C₂×#6157	1	2	yes	—
341	#108	C₂×#6157	1	2	yes	—
342	#97	—	53	4	no	—
343	#97	—	53	4	no	—
344	#97	—	106	8	no	—
345	C₄×C₈	—	53	4	no	—
346	C₄×C₈	—	53	4	no	—
347	C₄×C₈	—	106	8	no	—
348	C₂⁴	—	53	1	no	—
349	C₂²×C₄	—	53	1	no	—
350	C₂²×C₄	—	53	1	no	—
351	C₂²×C₄	—	53	1	no	—
352	C₂²×C₄	—	53	1	no	—
353	C₂²×C₄	—	53	1	no	—
354	C₂²×C₄	—	53	1	no	—
355	C₂²×C₄	—	53	1	no	—
356	C₂²×C₄	—	53	1	no	—
357	C₂²×C₄	—	53	1	no	—
358	C₂²×C₄	—	53	1	no	—
359	C₂²×C₄	—	53	1	no	—
360	C₂²×C₄	—	53	1	no	—
361	C₂²×C₄	—	53	1	no	—
362	C₂²×C₄	—	53	4	no	—
363	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
364	M₁₆	—	2	2	no	—
365	M₁₆	—	53	8	no	—
366	M₁₆	—	53	4	no	—
367	M₁₆	—	106	4	no	—
368	M₁₆	—	106	4	no	—
369	M₁₆	—	106	2	no	—
370	M₁₆	—	106	2	no	—
371	M₁₆	—	106	4	no	—
372	M₁₆	—	106	2	no	—
373	M₁₆	—	106	2	no	—
374	M₁₆	—	106	4	no	—
375	M₁₆	—	106	4	no	—
376	M₁₆	—	106	2	no	—
377	M₁₆	C₂²×#6157	1	4	yes	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	53	1	no	—
380	C₂×C₈	—	53	1	no	—
381	C₂×C₈	—	53	1	no	—
382	C₂×C₈	—	53	1	no	—
383	C₂×C₈	—	53	1	no	—
384	C₂×C₈	—	53	1	no	—
385	C₂×C₈	—	53	1	no	—
386	C₂×C₈	—	53	1	no	—
387	C₂×C₈	—	53	1	no	—
388	C₂×C₈	—	53	1	no	—
389	C₂×C₈	—	53	1	no	—
390	C₂×C₈	—	53	1	no	—
391	C₂×C₈	—	53	1	no	—
392	C₂×C₈	—	53	1	no	—
393	C₂×C₈	—	53	1	no	—
394	C₂×C₈	—	53	1	no	—
395	C₂×C₈	—	53	1	no	—
396	C₂×C₈	—	53	1	no	—
397	C₂×C₈	—	53	1	no	—
398	C₂×C₈	—	53	1	no	—
399	C₂×C₈	—	53	1	no	—
400	C₂×C₈	—	53	1	no	—
401	C₂×C₈	—	53	4	no	—
402	C₂×C₈	—	106	4	no	—
403	C₂×C₈	—	106	4	no	—
404	C₂×C₈	—	106	2	no	—
405	C₂×C₈	—	106	4	no	—
406	C₂×C₈	—	106	4	no	—
407	C₂×C₈	—	106	2	no	—
408	C₂×C₈	—	106	4	no	—
409	C₂×C₈	—	106	2	no	—
410	C₂×C₈	C₄×#6157	1	1	yes	characteristic
411	C₂×C₈	C₄×#6157	1	1	yes	characteristic
412	C₂×C₈	C₄×#6157	1	1	yes	characteristic
413	C₂×C₈	C₄×#6157	1	1	yes	characteristic
414	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
415	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
416	C₄⋊C₄	—	53	4	no	—
417	C₄⋊C₄	—	53	4	no	—
418	C₂²⋊C₄	—	53	4	no	—
419	C₂²⋊C₄	—	53	4	no	—
420	C₄²	—	53	4	no	—
421	C₄²	—	53	4	no	—
422	C₂³	—	53	1	no	—
423	C₂³	—	53	1	no	—
424	C₂³	—	53	1	no	—
425	C₂³	—	53	1	no	—
426	C₂³	—	53	1	no	—
427	C₂³	—	53	1	no	—
428	C₂³	—	212	2	no	—
429	C₂³	Q₈×#6157	1	1	yes	characteristic
430	C₂×C₄	—	53	1	no	—
431	C₂×C₄	—	53	1	no	—
432	C₂×C₄	—	53	1	no	—
433	C₂×C₄	—	53	1	no	—
434	C₂×C₄	—	53	1	no	—
435	C₂×C₄	—	53	1	no	—
436	C₂×C₄	—	53	1	no	—
437	C₂×C₄	—	53	1	no	—
438	C₂×C₄	—	53	1	no	—
439	C₂×C₄	—	53	1	no	—
440	C₂×C₄	—	53	1	no	—
441	C₂×C₄	—	53	1	no	—
442	C₂×C₄	—	53	1	no	—
443	C₂×C₄	—	53	1	no	—
444	C₂×C₄	—	53	1	no	—
445	C₂×C₄	—	53	1	no	—
446	C₂×C₄	—	53	1	no	—
447	C₂×C₄	—	53	1	no	—
448	C₂×C₄	—	53	1	no	—
449	C₂×C₄	—	53	1	no	—
450	C₂×C₄	—	53	1	no	—
451	C₂×C₄	—	53	1	no	—
452	C₂×C₄	—	53	8	no	—
453	C₂×C₄	—	212	4	no	—
454	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
455	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
456	C₂×C₄	D₄×#6157	1	1	yes	characteristic
457	C₂×C₄	D₄×#6157	1	1	yes	characteristic
458	C₂×C₄	Q₈×#6157	1	1	yes	characteristic
459	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
460	C₈	—	2	4	no	—
461	C₈	—	53	1	no	—
462	C₈	—	53	1	no	—
463	C₈	—	53	1	no	—
464	C₈	—	53	1	no	—
465	C₈	—	106	4	no	—
466	C₈	—	106	8	no	—
467	C₈	—	106	4	no	—
468	C₈	C₂×C₄×#6157	1	1	yes	characteristic
469	C₈	C₂×C₄×#6157	1	1	yes	characteristic
470	C₈	C₂×C₄×#6157	1	1	yes	characteristic
471	C₈	C₂×C₄×#6157	1	1	yes	characteristic
472	C₂²	—	4	1	no	—
473	C₂²	—	53	1	no	—
474	C₂²	—	53	1	no	—
475	C₂²	—	53	1	no	—
476	C₂²	—	53	1	no	—
477	C₂²	—	106	2	no	—
478	C₂²	—	106	2	no	—
479	C₂²	—	106	2	no	—
480	C₂²	—	212	1	no	—
481	C₂²	—	212	1	no	—
482	C₂²	—	212	1	no	—
483	C₂²	C₄⋊C₄×#6157	1	1	yes	characteristic
484	C₂²	C₄⋊C₄×#6157	1	1	yes	characteristic
485	C₂²	C₂×Q₈×#6157	1	1	yes	characteristic
486	C₄	—	53	1	no	—
487	C₄	—	53	1	no	—
488	C₄	—	53	1	no	—
489	C₄	—	53	1	no	—
490	C₄	—	106	8	no	—
491	C₄	C₄⋊C₄×#6157	1	1	yes	characteristic
492	C₄	C₄⋊C₄×#6157	1	1	yes	characteristic
493	C₄	C₂²×C₄×#6157	1	1	yes	characteristic
494	C₄	C₂×D₄×#6157	1	1	yes	characteristic
495	C₂	—	2	1	no	—
496	C₂	—	2	1	no	—
497	C₂	—	2	1	no	—
498	C₂	—	53	2	no	—
499	C₂	—	106	1	no	—
500	C₂	—	106	1	no	—
501	C₂	—	106	1	no	—
502	C₂	C₂×C₄⋊C₄×#6157	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₄×#6157
commutator	C₄×C₅₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#6157
Fitting	C₂×#108×C₅₃	C₄
socle	C₂×C₅₃	C₂×C₄×C₄⋊C₄
prime radical	C₂³×D₅₃	C₂×Q₈
cosocle	C₂×C₄×D₅₃	C₂⁴
hypercenter	C₂×#108	#6157
hypocenter	C₅₃	#20460
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#108

Complements

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

N	H ≅ G/N	type
4. #20290536	C₂	semidirect
5. #108×#6157	C₂	semidirect
11. C₂×#13133288	C₄	semidirect
12. D₅₃⋊#108	C₄	semidirect
13. D₅₃⋊#108	C₄	semidirect
16. C₂×#13133287	C₄	semidirect
29. C₂×#13133153	C₄	semidirect
30. C₂×#13133152	C₄	semidirect
31. #108×D₅₃	C₄	semidirect
32. #108×D₅₃	C₄	semidirect
35. C₂×#108×C₅₃	C₄	semidirect
276. C₂×#108	#6157	semidirect
287. C₅₃	#20460	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₅₃⋊#108	2
#20291278	2
C₂×#16811586	2
#20290536	2
#108×#6157	2
#20290408	2
C₂×#108×D₅₃	2
#20460	53