Subgroups — D₅₃⋊#2957 #28329565

Order 13568.

2642 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₃⋊#568	C₂	1	2	yes	maximal, complemented
2	#20291495	C₂	1	2	yes	maximal, complemented
3	#20291494	C₂	1	4	yes	maximal, complemented
4	#20291493	C₂	1	4	yes	maximal, complemented
5	#20291492	C₂	1	4	yes	maximal, complemented
6	#20291491	C₂	1	2	yes	maximal, complemented
7	D₅₃⋊#444	C₂	1	4	yes	maximal, complemented
8	D₅₃⋊#443	C₂	1	4	yes	maximal, complemented
9	C₂×D₅₃⋊#108	C₂	1	1	yes	maximal, characteristic, complemented
10	D₅₃⋊#421	C₂	1	2	yes	maximal, complemented
11	C₂×#16811586	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×D₅₃	C₂	1	1	yes	maximal, characteristic
13	#16811703	C₂²	1	4	yes	complemented
14	#16811702	—	2	4	no	—
15	#16811702	C₂²	1	8	yes	complemented
16	#16811701	—	2	4	no	—
17	#16811701	C₂²	1	4	yes	complemented
18	D₅₃⋊#131	—	2	4	no	—
19	D₅₃⋊#131	C₂²	1	8	yes	complemented
20	C₂×D₅₃⋊M₁₆	—	2	4	no	—
21	C₂×D₅₃⋊M₁₆	C₂²	1	2	yes	—
22	C₂×D₅₃⋊M₁₆	C₂²	1	1	yes	characteristic
23	C₂×#13133296	C₂²	1	1	yes	characteristic
24	#16811670	C₂²	1	8	yes	complemented
25	#16811669	C₂²	1	8	yes	complemented
26	#16811668	C₂²	1	16	yes	complemented
27	#16811667	C₂²	1	8	yes	complemented
28	#16811666	C₂²	1	16	yes	complemented
29	#16811665	C₂²	1	8	yes	complemented
30	C₂×#13133288	C₂²	1	2	yes	complemented
31	D₅₃⋊#108	C₂²	1	2	yes	complemented
32	D₅₃⋊#108	C₂²	1	2	yes	complemented
33	D₅₃⋊#108	C₂²	1	2	yes	complemented
34	D₅₃⋊#108	C₂²	1	2	yes	complemented
35	C₂×#13133287	C₂²	1	2	yes	complemented
36	#16811622	C₂²	1	4	yes	complemented
37	#16811621	C₂²	1	4	yes	complemented
38	#16811620	C₂²	1	8	yes	complemented
39	D₅₃⋊#104	C₂²	1	8	yes	complemented
40	#16811586	C₂²	1	2	yes	complemented
41	#16811586	C₂²	1	2	yes	complemented
42	#16811586	C₂²	1	2	yes	complemented
43	#16811586	C₂²	1	2	yes	complemented
44	C₂×#13133271	C₂²	1	2	yes	complemented
45	C₂×C₈×#6157	C₂²	1	2	yes	complemented
46	C₂×#41×D₅₃	C₂²	1	2	yes	—
47	C₂×#13133240	C₂²	1	1	yes	characteristic
48	C₂×#13133239	C₄	1	1	yes	characteristic, complemented
49	C₂×#13133238	C₂²	1	2	yes	—
50	C₂×#13133237	C₄	1	2	yes	complemented
51	C₂×#13133236	C₂²	1	1	yes	characteristic
52	#135×D₅₃	C₄	1	2	yes	complemented
53	#135×D₅₃	C₄	1	2	yes	complemented
54	#135×D₅₃	C₄	1	2	yes	complemented
55	#135×D₅₃	C₄	1	2	yes	complemented
56	#135×D₅₃	C₂²	1	2	yes	—
57	#135×D₅₃	C₂²	1	2	yes	—
58	#135×D₅₃	C₂²	1	2	yes	—
59	#135×D₅₃	C₂²	1	2	yes	—
60	C₂×Q₁₆×D₅₃	C₄	1	1	yes	characteristic, complemented
61	C₂×SD₁₆×D₅₃	C₄	1	2	yes	complemented
62	C₂×D₈×D₅₃	C₄	1	1	yes	characteristic, complemented
63	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
64	C₂×#135×C₅₃	C₄	1	1	yes	characteristic, complemented
65	#13133305	—	2	8	no	—
66	#13133305	C₂³	1	16	yes	complemented
67	#13133304	—	2	16	no	—
68	#13133304	—	2	16	no	—
69	#13133304	—	2	8	no	—
70	#13133304	C₂³	1	16	yes	complemented
71	C₂×#11719936	—	2	8	no	—
72	C₂×#11719936	D₄	1	2	yes	—
73	C₂×#11719936	C₂³	1	4	yes	—
74	D₅₃⋊M₁₆	—	2	8	no	—
75	D₅₃⋊M₁₆	—	2	2	no	—
76	D₅₃⋊M₁₆	—	2	2	no	—
77	D₅₃⋊M₁₆	—	2	8	no	—
78	D₅₃⋊M₁₆	—	2	8	no	—
79	D₅₃⋊M₁₆	D₄	1	2	yes	—
80	D₅₃⋊M₁₆	D₄	1	2	yes	—
81	D₅₃⋊M₁₆	C₂³	1	2	yes	—
82	D₅₃⋊M₁₆	C₂³	1	2	yes	—
83	D₅₃⋊M₁₆	C₂³	1	4	yes	—
84	D₅₃⋊M₁₆	C₂³	1	4	yes	—
85	C₂×#11719940	—	2	2	no	—
86	C₂×#11719940	—	2	8	no	—
87	C₂×#11719940	D₄	1	2	yes	—
88	C₂×D₅₃⋊C₈	—	2	8	no	—
89	C₂×D₅₃⋊C₈	—	2	2	no	—
90	C₂×D₅₃⋊C₈	C₂³	1	2	yes	—
91	#13133296	—	2	1	no	—
92	#13133296	—	2	1	no	—
93	#13133296	C₂³	1	2	yes	—
94	#13133296	C₂³	1	2	yes	—
95	C₂×C₄⋊#6157	—	2	1	no	—
96	C₂×C₂²⋊#6157	—	2	1	no	—
97	C₂×C₄×#6157	C₂³	1	2	yes	—
98	#13133288	C₂³	1	4	yes	complemented
99	#13133288	C₂³	1	4	yes	complemented
100	#13133287	C₂³	1	4	yes	complemented
101	#13133287	C₂³	1	4	yes	complemented
102	#13133282	C₂³	1	16	yes	complemented
103	#13133281	C₂³	1	16	yes	complemented
104	#13133271	C₂³	1	4	yes	complemented
105	#13133271	C₂³	1	4	yes	complemented
106	C₈×#6157	C₂³	1	4	yes	complemented
107	C₈×#6157	C₂³	1	4	yes	complemented
108	C₂×#11719949	C₂³	1	2	yes	—
109	C₂×#11719945	—	2	2	no	—
110	C₂×#11719945	C₂×C₄	1	2	yes	—
111	C₂×#11719947	—	2	2	no	—
112	C₂×#11719947	C₂³	1	2	yes	—
113	#41×D₅₃	—	2	2	no	—
114	#41×D₅₃	—	2	2	no	—
115	#41×D₅₃	—	2	2	no	—
116	#41×D₅₃	—	2	2	no	—
117	#41×D₅₃	C₂×C₄	1	4	yes	—
118	#41×D₅₃	C₂×C₄	1	4	yes	—
119	#41×D₅₃	C₂³	1	4	yes	—
120	#41×D₅₃	C₂³	1	4	yes	—
121	C₂×Q₈×D₅₃	C₂×C₄	1	2	yes	—
122	C₂×D₄×D₅₃	—	2	2	no	—
123	C₂×D₄×D₅₃	C₂×C₄	1	2	yes	—
124	C₂²×C₄×D₅₃	—	2	2	no	—
125	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
126	#13133240	C₂×C₄	1	2	yes	complemented
127	#13133240	C₂×C₄	1	2	yes	complemented
128	#13133240	C₂³	1	2	yes	—
129	#13133240	C₂³	1	2	yes	—
130	#13133239	C₂×C₄	1	2	yes	—
131	#13133239	C₂×C₄	1	2	yes	—
132	#13133239	C₂×C₄	1	2	yes	complemented
133	#13133239	C₂×C₄	1	2	yes	complemented
134	#13133238	C₂×C₄	1	4	yes	complemented
135	#13133238	C₂×C₄	1	4	yes	complemented
136	#13133238	C₂³	1	4	yes	—
137	#13133238	C₂³	1	4	yes	—
138	#13133237	C₂×C₄	1	4	yes	—
139	#13133237	C₂×C₄	1	4	yes	—
140	#13133237	C₂×C₄	1	4	yes	complemented
141	#13133237	C₂×C₄	1	4	yes	complemented
142	#13133236	C₂×C₄	1	2	yes	complemented
143	#13133236	C₂×C₄	1	2	yes	complemented
144	#13133236	C₂³	1	2	yes	—
145	#13133236	C₂³	1	2	yes	—
146	C₂×Dic₂₁₂	C₂×C₄	1	1	yes	characteristic, complemented
147	C₂×#11719925	C₂×C₄	1	2	yes	complemented
148	Q₁₆×D₅₃	C₂×C₄	1	2	yes	—
149	Q₁₆×D₅₃	C₂×C₄	1	2	yes	—
150	Q₁₆×D₅₃	C₂×C₄	1	2	yes	complemented
151	Q₁₆×D₅₃	C₂×C₄	1	2	yes	complemented
152	C₂×#11719913	C₂×C₄	1	2	yes	complemented
153	C₂×#11719923	C₂×C₄	1	2	yes	complemented
154	C₂×#11719924	C₂×C₄	1	2	yes	complemented
155	SD₁₆×D₅₃	C₂×C₄	1	4	yes	—
156	SD₁₆×D₅₃	C₂×C₄	1	4	yes	—
157	SD₁₆×D₅₃	C₂×C₄	1	4	yes	complemented
158	SD₁₆×D₅₃	C₂×C₄	1	4	yes	complemented
159	C₂×D₄₂₄	C₂×C₄	1	1	yes	characteristic, complemented
160	C₂×#11719922	C₂×C₄	1	2	yes	complemented
161	D₈×D₅₃	C₂×C₄	1	2	yes	—
162	D₈×D₅₃	C₂×C₄	1	2	yes	—
163	D₈×D₅₃	C₂×C₄	1	2	yes	complemented
164	D₈×D₅₃	C₂×C₄	1	2	yes	complemented
165	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
166	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
167	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
168	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
169	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
170	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
171	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
172	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
173	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
174	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
175	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
176	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
177	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
178	C₂×#41×C₅₃	C₂×C₄	1	2	yes	—
179	#135×C₅₃	C₂×C₄	1	2	yes	—
180	#135×C₅₃	C₂×C₄	1	2	yes	—
181	#135×C₅₃	C₂×C₄	1	2	yes	complemented
182	#135×C₅₃	C₂×C₄	1	2	yes	complemented
183	C₂×Q₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic, complemented
184	C₂×SD₁₆×C₅₃	C₂×C₄	1	2	yes	complemented
185	C₂×D₈×C₅₃	C₂×C₄	1	1	yes	characteristic, complemented
186	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
187	C₂³×D₅₃	—	2	2	no	—
188	C₂³×D₅₃	#41	1	1	yes	characteristic
189	C₂²×#6157	—	2	2	no	—
190	#41×C₅₃	—	2	2	no	—
191	#41×C₅₃	—	2	2	no	—
192	#41×C₅₃	C₂²×C₄	1	4	yes	—
193	#41×C₅₃	C₂²×C₄	1	4	yes	—
194	C₂×Q₈×C₅₃	C₂²×C₄	1	2	yes	—
195	C₂×D₄×C₅₃	—	2	2	no	—
196	C₂×D₄×C₅₃	C₂²×C₄	1	2	yes	—
197	C₂²×C₄×C₅₃	—	2	2	no	—
198	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₂²⋊D₅₃	—	2	2	no	—
200	C₂×C₂²⋊D₅₃	—	2	2	no	—
201	C₂×C₂²⋊D₅₃	—	2	2	no	—
202	C₂²×Dic₅₃	—	2	2	no	—
203	C₂²×Dic₅₃	C₂×D₄	1	1	yes	characteristic
204	#11719949	—	2	2	no	—
205	#11719949	—	2	2	no	—
206	#11719949	C₂²×C₄	1	4	yes	—
207	#11719949	C₂⁴	1	4	yes	—
208	Q₈×D₅₃	—	2	2	no	—
209	Q₈×D₅₃	—	2	2	no	—
210	Q₈×D₅₃	C₂²×C₄	1	4	yes	—
211	Q₈×D₅₃	C₂²×C₄	1	4	yes	—
212	#11719947	—	2	4	no	—
213	#11719947	—	2	4	no	—
214	#11719947	—	2	4	no	—
215	#11719947	—	2	4	no	—
216	#11719947	—	2	2	no	—
217	#11719947	—	2	2	no	—
218	#11719947	C₂²×C₄	1	4	yes	—
219	#11719947	C₂⁴	1	4	yes	—
220	D₄×D₅₃	—	2	4	no	—
221	D₄×D₅₃	—	2	4	no	—
222	D₄×D₅₃	—	2	4	no	—
223	D₄×D₅₃	—	2	4	no	—
224	D₄×D₅₃	—	2	2	no	—
225	D₄×D₅₃	—	2	2	no	—
226	D₄×D₅₃	C₂²×C₄	1	4	yes	—
227	D₄×D₅₃	C₂²×C₄	1	4	yes	—
228	#11719945	—	2	2	no	—
229	#11719945	—	2	2	no	—
230	#11719945	—	2	4	no	—
231	#11719945	—	2	4	no	—
232	#11719945	—	2	4	no	—
233	#11719945	—	2	4	no	—
234	#11719945	C₂²×C₄	1	4	yes	—
235	#11719945	C₂²×C₄	1	4	yes	—
236	C₂×D₂₁₂	—	2	2	no	—
237	C₂×D₂₁₂	C₂²×C₄	1	2	yes	—
238	C₂×C₄×D₅₃	—	2	2	no	—
239	C₂×C₄×D₅₃	—	2	2	no	—
240	C₂×C₄×D₅₃	—	2	2	no	—
241	C₂×C₄×D₅₃	—	2	4	no	—
242	C₂×C₄×D₅₃	—	2	4	no	—
243	C₂×C₄×D₅₃	—	2	4	no	—
244	C₂×C₄×D₅₃	—	2	4	no	—
245	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
246	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
247	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
248	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
249	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
250	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
251	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
252	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
253	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
254	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₁₀₆	—	2	2	no	—
258	C₂×Dic₁₀₆	C₂²×C₄	1	2	yes	—
259	C₂²⋊#6157	—	2	2	no	—
260	C₂²⋊#6157	—	2	2	no	—
261	#11719940	—	2	4	no	—
262	#11719940	—	2	4	no	—
263	#11719940	—	2	16	no	—
264	#11719940	C₂×D₄	1	4	yes	—
265	#11719940	C₂×D₄	1	4	yes	—
266	C₂×#88324	—	2	4	no	—
267	C₂×#88324	—	2	16	no	—
268	C₂×#88324	C₂×D₄	1	4	yes	—
269	C₄⋊#6157	—	2	2	no	—
270	C₄⋊#6157	—	2	2	no	—
271	C₄×#6157	—	2	2	no	—
272	C₄×#6157	C₂⁴	1	4	yes	—
273	#11719936	—	2	4	no	—
274	#11719936	—	2	16	no	—
275	#11719936	C₂×D₄	1	4	yes	—
276	#11719936	C₂×D₄	1	4	yes	—
277	#11719936	C₂⁴	1	8	yes	—
278	D₅₃⋊C₈	—	2	4	no	—
279	D₅₃⋊C₈	—	2	4	no	—
280	D₅₃⋊C₈	—	2	16	no	—
281	D₅₃⋊C₈	C₂×D₄	1	4	yes	—
282	D₅₃⋊C₈	C₂⁴	1	4	yes	—
283	Q₁₆×C₅₃	C₂²×C₄	1	2	yes	—
284	Q₁₆×C₅₃	C₂²×C₄	1	2	yes	—
285	SD₁₆×C₅₃	C₂²×C₄	1	4	yes	—
286	SD₁₆×C₅₃	C₂²×C₄	1	4	yes	—
287	D₈×C₅₃	C₂²×C₄	1	2	yes	—
288	D₈×C₅₃	C₂²×C₄	1	2	yes	—
289	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
290	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
291	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
292	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
293	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
294	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
295	#11719925	C₂²×C₄	1	4	yes	—
296	#11719925	C₂²×C₄	1	4	yes	—
297	#11719924	C₂²×C₄	1	4	yes	—
298	#11719924	C₂²×C₄	1	4	yes	—
299	#11719923	C₂²×C₄	1	4	yes	—
300	#11719923	C₂²×C₄	1	4	yes	—
301	#11719922	C₂²×C₄	1	4	yes	—
302	#11719922	C₂²×C₄	1	4	yes	—
303	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
304	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
305	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
306	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
307	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
308	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
309	Dic₂₁₂	C₂²×C₄	1	2	yes	—
310	Dic₂₁₂	C₂²×C₄	1	2	yes	—
311	D₄₂₄	C₂²×C₄	1	2	yes	—
312	D₄₂₄	C₂²×C₄	1	2	yes	—
313	#11719913	C₂²×C₄	1	4	yes	—
314	#11719913	C₂²×C₄	1	4	yes	—
315	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
316	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
317	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
318	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
319	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
320	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
321	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
322	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
323	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
324	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
325	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
326	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
327	C₈×D₅₃	C₂⁴	1	1	yes	characteristic
328	C₈×D₅₃	C₂⁴	1	1	yes	characteristic
329	C₈×D₅₃	C₂⁴	1	1	yes	characteristic
330	C₈×D₅₃	C₂⁴	1	1	yes	characteristic
331	C₂³×C₅₃	—	2	2	no	—
332	C₂³×C₅₃	C₄×D₄	1	1	yes	characteristic
333	C₂²×D₅₃	—	2	2	no	—
334	C₂²×D₅₃	—	2	4	no	—
335	C₂²×D₅₃	—	2	4	no	—
336	C₂²×D₅₃	—	4	2	no	—
337	C₂²×D₅₃	—	8	4	no	—
338	C₂²×D₅₃	C₄×D₄	1	1	yes	characteristic
339	C₂²×D₅₃	C₄×D₄	1	1	yes	characteristic
340	C₂²×D₅₃	C₄×D₄	1	1	yes	characteristic
341	C₂²×D₅₃	C₂×#41	1	1	yes	characteristic
342	C₂²×D₅₃	C₂×#41	1	1	yes	characteristic
343	C₂²×D₅₃	C₂×#41	1	1	yes	characteristic
344	C₂×#6157	—	2	4	no	—
345	C₂×#6157	—	4	4	no	—
346	Q₈×C₅₃	—	2	2	no	—
347	Q₈×C₅₃	C₂³×C₄	1	4	yes	—
348	D₄×C₅₃	—	2	4	no	—
349	D₄×C₅₃	—	2	4	no	—
350	D₄×C₅₃	—	2	2	no	—
351	D₄×C₅₃	C₂³×C₄	1	4	yes	—
352	C₂×C₄×C₅₃	—	2	2	no	—
353	C₂×C₄×C₅₃	—	2	4	no	—
354	C₂×C₄×C₅₃	—	2	4	no	—
355	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
356	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
357	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
358	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
359	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
360	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
361	C₂²⋊D₅₃	—	2	4	no	—
362	C₂²⋊D₅₃	—	2	4	no	—
363	C₂²⋊D₅₃	—	2	4	no	—
364	C₂²⋊D₅₃	—	2	4	no	—
365	C₂²⋊D₅₃	—	2	4	no	—
366	C₂²⋊D₅₃	—	2	4	no	—
367	C₂×Dic₅₃	—	2	2	no	—
368	C₂×Dic₅₃	—	2	4	no	—
369	C₂×Dic₅₃	—	2	4	no	—
370	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
371	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
372	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
373	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
374	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
375	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
376	D₂₁₂	—	2	4	no	—
377	D₂₁₂	—	2	4	no	—
378	D₂₁₂	—	2	2	no	—
379	D₂₁₂	C₂³×C₄	1	4	yes	—
380	C₄×D₅₃	—	2	4	no	—
381	C₄×D₅₃	—	2	4	no	—
382	C₄×D₅₃	—	2	4	no	—
383	C₄×D₅₃	—	2	4	no	—
384	C₄×D₅₃	—	2	4	no	—
385	C₄×D₅₃	—	2	4	no	—
386	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
387	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
388	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
389	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
390	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
391	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
392	C₄×D₅₃	C₂³×C₄	1	1	yes	characteristic
393	C₄×D₅₃	C₂³×C₄	1	1	yes	characteristic
394	C₄×D₅₃	C₂³×C₄	1	1	yes	characteristic
395	C₄×D₅₃	C₂²×D₄	1	1	yes	characteristic
396	C₄×D₅₃	C₂²×D₄	1	1	yes	characteristic
397	C₄×D₅₃	C₂²×D₄	1	1	yes	characteristic
398	C₄×D₅₃	C₂×#41	1	1	yes	characteristic
399	C₄×D₅₃	C₂×#41	1	1	yes	characteristic
400	C₄×D₅₃	C₂×#41	1	1	yes	characteristic
401	C₄×D₅₃	C₂⁵	1	1	yes	characteristic
402	Dic₁₀₆	—	2	2	no	—
403	Dic₁₀₆	—	2	4	no	—
404	Dic₁₀₆	—	2	4	no	—
405	Dic₁₀₆	C₂³×C₄	1	4	yes	—
406	#88324	—	2	8	no	—
407	#88324	C₂²×D₄	1	8	yes	—
408	C₈×C₅₃	C₂³×C₄	1	1	yes	characteristic
409	C₈×C₅₃	C₂³×C₄	1	1	yes	characteristic
410	C₈×C₅₃	C₂³×C₄	1	1	yes	characteristic
411	C₈×C₅₃	C₂³×C₄	1	1	yes	characteristic
412	#88322	C₂³×C₄	1	1	yes	characteristic
413	#88322	C₂³×C₄	1	1	yes	characteristic
414	#88322	C₂³×C₄	1	1	yes	characteristic
415	#88322	C₂³×C₄	1	1	yes	characteristic
416	C₂×#2957	—	53	1	no	maximal, Sylow
417	C₂²×C₅₃	—	2	4	no	—
418	C₂²×C₅₃	—	4	1	no	—
419	C₂²×C₅₃	—	8	2	no	—
420	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
421	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
422	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
423	C₂×D₅₃	—	2	2	no	—
424	C₂×D₅₃	—	2	2	no	—
425	C₂×D₅₃	—	2	2	no	—
426	C₂×D₅₃	—	2	4	no	—
427	C₂×D₅₃	—	4	1	no	—
428	C₂×D₅₃	—	4	1	no	—
429	C₂×D₅₃	—	4	1	no	—
430	C₂×D₅₃	—	4	8	no	—
431	C₂×D₅₃	—	8	4	no	—
432	C₂×D₅₃	—	8	2	no	—
433	C₂×D₅₃	C₂×C₄×D₄	1	1	yes	characteristic
434	C₂×D₅₃	C₂×C₄×D₄	1	1	yes	characteristic
435	C₂×D₅₃	C₂×C₄×D₄	1	1	yes	characteristic
436	C₂×D₅₃	C₂²×#41	1	1	yes	characteristic
437	#6157	—	4	4	no	—
438	C₄×C₅₃	—	2	4	no	—
439	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
440	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
441	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
442	C₄×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
443	Dic₅₃	—	2	4	no	—
444	Dic₅₃	C₂×C₄×D₄	1	1	yes	characteristic
445	Dic₅₃	C₂×C₄×D₄	1	1	yes	characteristic
446	Dic₅₃	C₂×C₄×D₄	1	1	yes	characteristic
447	Dic₅₃	C₂³×D₄	1	1	yes	characteristic
448	C₂²×#135	—	53	1	no	—
449	C₂×#568	—	53	2	no	—
450	#2957	—	53	2	no	—
451	#2957	—	53	4	no	—
452	#2957	—	53	4	no	—
453	#2957	—	53	4	no	—
454	#2957	—	53	2	no	—
455	C₂×#444	—	53	4	no	—
456	C₂×#443	—	53	4	no	—
457	C₂²×#108	—	53	1	no	—
458	C₂×#421	—	53	2	no	—
459	C₂×#405	—	53	1	no	—
460	C₂×C₅₃	—	2	1	no	—
461	C₂×C₅₃	—	2	1	no	—
462	C₂×C₅₃	—	2	1	no	—
463	C₂×C₅₃	—	4	4	no	—
464	C₂×C₅₃	C₂²×C₄×D₄	1	1	yes	characteristic
465	D₅₃	—	2	1	no	—
466	D₅₃	—	2	1	no	—
467	D₅₃	—	2	1	no	—
468	D₅₃	—	4	4	no	—
469	D₅₃	#2957	1	2	yes	complemented
470	C₂²×#41	—	53	2	no	—
471	C₂×#135	—	53	2	no	—
472	C₂×#135	—	53	2	no	—
473	C₂×#135	—	53	2	no	—
474	C₂×#135	—	53	2	no	—
475	C₂×#135	—	53	2	no	—
476	C₂×#135	—	53	2	no	—
477	C₂×#135	—	53	2	no	—
478	C₂×#135	—	53	2	no	—
479	C₂×#135	—	53	2	no	—
480	C₂×#135	—	53	1	no	—
481	C₂×#135	—	53	2	no	—
482	C₂×#135	—	53	1	no	—
483	C₂×#135	—	53	1	no	—
484	C₂×#135	#6157	1	1	yes	characteristic, complemented
485	C₂²×Q₁₆	—	53	1	no	—
486	C₂²×SD₁₆	—	53	2	no	—
487	C₂²×D₈	—	53	1	no	—
488	#568	—	53	4	no	—
489	#568	—	53	8	no	—
490	#568	—	53	4	no	—
491	#568	—	106	4	no	—
492	#568	—	106	4	no	—
493	C₂×#131	—	53	8	no	—
494	C₂×#131	—	106	4	no	—
495	C₂²×M₁₆	—	53	1	no	—
496	C₂²×M₁₆	—	53	2	no	—
497	C₂²×M₁₆	—	106	4	no	—
498	C₂³×C₈	—	53	1	no	—
499	C₂×#117	—	53	1	no	—
500	#444	—	53	16	no	—
501	#444	—	53	8	no	—
502	#444	—	53	8	no	—
503	#443	—	53	8	no	—
504	#443	—	53	16	no	—
505	#443	—	53	8	no	—
506	C₂×#108	—	53	2	no	—
507	C₂×#108	—	53	2	no	—
508	C₂×#108	—	53	2	no	—
509	C₂×#108	—	53	2	no	—
510	C₂×#108	—	53	2	no	—
511	C₂×#108	—	53	2	no	—
512	#421	—	53	8	no	—
513	#421	—	53	4	no	—
514	#421	—	53	4	no	—
515	C₂×#104	—	53	8	no	—
516	#405	—	53	2	no	—
517	#405	—	53	2	no	—
518	#405	—	53	2	no	—
519	#405	—	53	2	no	—
520	C₂×#97	—	53	2	no	—
521	C₂×C₄×C₈	—	53	2	no	—
522	C₅₃	C₂×#2957	1	1	yes	characteristic, complemented, Sylow
523	C₂×#41	—	53	4	no	—
524	C₂×#41	—	53	4	no	—
525	C₂×#41	—	53	4	no	—
526	C₂×#41	—	53	4	no	—
527	C₂×#41	—	53	2	no	—
528	C₂×#41	—	53	2	no	—
529	C₂×#41	—	53	2	no	—
530	C₂×#41	—	106	2	no	—
531	C₂×#41	—	106	2	no	—
532	C₂×#41	—	106	2	no	—
533	C₂×#41	—	106	2	no	—
534	C₂×#41	—	106	2	no	—
535	C₂×#41	—	106	2	no	—
536	C₂×#41	C₂×#6157	1	2	yes	—
537	C₂²×Q₈	—	53	2	no	—
538	C₂²×D₄	—	53	2	no	—
539	C₂²×D₄	—	106	2	no	—
540	C₂³×C₄	—	53	1	no	—
541	C₂³×C₄	—	106	2	no	—
542	#135	—	53	4	no	—
543	#135	—	53	4	no	—
544	#135	—	53	4	no	—
545	#135	—	53	4	no	—
546	#135	—	53	2	no	—
547	#135	—	53	2	no	—
548	#135	—	53	2	no	—
549	#135	—	53	2	no	—
550	#135	—	53	4	no	—
551	#135	—	53	4	no	—
552	#135	—	53	4	no	—
553	#135	—	53	4	no	—
554	#135	—	53	2	no	—
555	#135	—	53	2	no	—
556	#135	—	53	2	no	—
557	#135	—	53	2	no	—
558	#135	—	53	2	no	—
559	#135	—	53	2	no	—
560	#135	—	53	2	no	—
561	#135	—	53	2	no	—
562	#135	C₂×#6157	1	2	yes	—
563	#135	C₂×#6157	1	2	yes	—
564	#135	C₂×#6157	1	2	yes	complemented
565	#135	C₂×#6157	1	2	yes	complemented
566	C₂×Q₁₆	—	53	2	no	—
567	C₂×Q₁₆	—	53	2	no	—
568	C₂×Q₁₆	—	53	2	no	—
569	C₂×Q₁₆	—	53	2	no	—
570	C₂×Q₁₆	—	53	2	no	—
571	C₂×Q₁₆	—	53	1	no	—
572	C₂×Q₁₆	C₂×#6157	1	1	yes	characteristic, complemented
573	C₂×SD₁₆	—	53	2	no	—
574	C₂×SD₁₆	—	53	2	no	—
575	C₂×SD₁₆	—	53	4	no	—
576	C₂×SD₁₆	—	53	4	no	—
577	C₂×SD₁₆	—	53	4	no	—
578	C₂×SD₁₆	—	53	4	no	—
579	C₂×SD₁₆	—	53	2	no	—
580	C₂×SD₁₆	C₂×#6157	1	2	yes	complemented
581	C₂×D₈	—	53	2	no	—
582	C₂×D₈	—	53	2	no	—
583	C₂×D₈	—	53	2	no	—
584	C₂×D₈	—	53	2	no	—
585	C₂×D₈	—	53	2	no	—
586	C₂×D₈	—	53	1	no	—
587	C₂×D₈	C₂×#6157	1	1	yes	characteristic, complemented
588	#131	—	53	16	no	—
589	#131	—	53	16	no	—
590	#131	—	106	16	no	—
591	#131	—	106	8	no	—
592	#131	—	106	16	no	—
593	#131	—	106	8	no	—
594	C₂×M₁₆	—	53	2	no	—
595	C₂×M₁₆	—	53	2	no	—
596	C₂×M₁₆	—	53	2	no	—
597	C₂×M₁₆	—	53	2	no	—
598	C₂×M₁₆	—	53	2	no	—
599	C₂×M₁₆	—	53	2	no	—
600	C₂×M₁₆	—	53	4	no	—
601	C₂×M₁₆	—	53	4	no	—
602	C₂×M₁₆	—	53	4	no	—
603	C₂×M₁₆	—	106	8	no	—
604	C₂×M₁₆	—	106	8	no	—
605	C₂×M₁₆	—	106	8	no	—
606	C₂×M₁₆	—	106	8	no	—
607	C₂×M₁₆	—	106	8	no	—
608	C₂×M₁₆	—	106	2	no	—
609	C₂×M₁₆	—	106	2	no	—
610	C₂×M₁₆	—	106	2	no	—
611	C₂²×C₈	—	53	2	no	—
612	C₂²×C₈	—	53	1	no	—
613	C₂²×C₈	—	53	1	no	—
614	C₂²×C₈	—	53	1	no	—
615	C₂²×C₈	—	53	1	no	—
616	C₂²×C₈	—	53	1	no	—
617	C₂²×C₈	—	53	1	no	—
618	C₂²×C₈	—	53	1	no	—
619	C₂²×C₈	—	53	1	no	—
620	C₂²×C₈	—	53	1	no	—
621	C₂²×C₈	—	53	1	no	—
622	C₂²×C₈	—	53	1	no	—
623	C₂²×C₈	—	53	1	no	—
624	C₂²×C₈	—	53	1	no	—
625	C₂²×C₈	—	106	8	no	—
626	C₂²×C₈	—	106	2	no	—
627	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
628	#117	—	53	2	no	—
629	#117	—	53	2	no	—
630	#117	—	106	1	no	—
631	#117	—	106	1	no	—
632	C₂×C₄⋊C₄	—	106	1	no	—
633	C₂×C₂²⋊C₄	—	106	1	no	—
634	C₂×C₄²	—	53	2	no	—
635	#108	—	53	4	no	—
636	#108	—	53	4	no	—
637	#108	—	53	4	no	—
638	#108	—	53	4	no	—
639	#104	—	53	16	no	—
640	#104	—	53	16	no	—
641	#97	—	53	4	no	—
642	#97	—	53	4	no	—
643	C₄×C₈	—	53	4	no	—
644	C₄×C₈	—	53	4	no	—
645	C₂⁴	—	53	1	no	—
646	C₂⁴	—	106	2	no	—
647	#41	—	2	2	no	—
648	#41	—	2	2	no	—
649	#41	—	53	4	no	—
650	#41	—	53	4	no	—
651	#41	—	53	4	no	—
652	#41	—	53	4	no	—
653	#41	—	53	4	no	—
654	#41	—	53	4	no	—
655	#41	—	106	4	no	—
656	#41	—	106	4	no	—
657	#41	—	106	4	no	—
658	#41	—	106	4	no	—
659	#41	—	106	4	no	—
660	#41	—	106	4	no	—
661	#41	—	106	2	no	—
662	#41	—	106	4	no	—
663	#41	—	106	4	no	—
664	#41	—	106	2	no	—
665	#41	—	106	2	no	—
666	#41	—	106	2	no	—
667	#41	—	106	2	no	—
668	#41	—	106	2	no	—
669	#41	C₂²×#6157	1	4	yes	—
670	#41	C₂²×#6157	1	4	yes	—
671	C₂×Q₈	—	53	4	no	—
672	C₂×Q₈	—	53	4	no	—
673	C₂×Q₈	—	53	2	no	—
674	C₂×Q₈	—	106	2	no	—
675	C₂×Q₈	—	106	2	no	—
676	C₂×Q₈	—	106	2	no	—
677	C₂×Q₈	C₂²×#6157	1	2	yes	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	53	4	no	—
680	C₂×D₄	—	53	4	no	—
681	C₂×D₄	—	53	2	no	—
682	C₂×D₄	—	106	2	no	—
683	C₂×D₄	—	106	2	no	—
684	C₂×D₄	—	106	2	no	—
685	C₂×D₄	—	106	2	no	—
686	C₂×D₄	—	106	4	no	—
687	C₂×D₄	—	106	4	no	—
688	C₂×D₄	—	106	4	no	—
689	C₂×D₄	—	106	4	no	—
690	C₂×D₄	—	106	2	no	—
691	C₂×D₄	—	106	2	no	—
692	C₂×D₄	C₂²×#6157	1	2	yes	—
693	C₂²×C₄	—	2	2	no	—
694	C₂²×C₄	—	53	1	no	—
695	C₂²×C₄	—	53	1	no	—
696	C₂²×C₄	—	53	1	no	—
697	C₂²×C₄	—	53	1	no	—
698	C₂²×C₄	—	53	1	no	—
699	C₂²×C₄	—	53	1	no	—
700	C₂²×C₄	—	53	1	no	—
701	C₂²×C₄	—	53	1	no	—
702	C₂²×C₄	—	53	1	no	—
703	C₂²×C₄	—	53	1	no	—
704	C₂²×C₄	—	53	1	no	—
705	C₂²×C₄	—	53	1	no	—
706	C₂²×C₄	—	53	1	no	—
707	C₂²×C₄	—	106	4	no	—
708	C₂²×C₄	—	106	2	no	—
709	C₂²×C₄	—	106	4	no	—
710	C₂²×C₄	—	106	4	no	—
711	C₂²×C₄	—	106	4	no	—
712	C₂²×C₄	—	106	2	no	—
713	C₂²×C₄	—	106	2	no	—
714	C₂²×C₄	—	106	2	no	—
715	C₂²×C₄	—	106	2	no	—
716	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
717	Q₁₆	—	53	4	no	—
718	Q₁₆	—	53	4	no	—
719	Q₁₆	—	53	2	no	—
720	Q₁₆	—	53	2	no	—
721	Q₁₆	C₂²×#6157	1	2	yes	—
722	Q₁₆	C₂²×#6157	1	2	yes	—
723	SD₁₆	—	53	4	no	—
724	SD₁₆	—	53	4	no	—
725	SD₁₆	—	53	4	no	—
726	SD₁₆	—	53	4	no	—
727	SD₁₆	—	53	4	no	—
728	SD₁₆	—	53	4	no	—
729	SD₁₆	C₂²×#6157	1	4	yes	—
730	SD₁₆	C₂²×#6157	1	4	yes	—
731	D₈	—	53	4	no	—
732	D₈	—	53	4	no	—
733	D₈	—	53	2	no	—
734	D₈	—	53	2	no	—
735	D₈	C₂²×#6157	1	2	yes	—
736	D₈	C₂²×#6157	1	2	yes	—
737	M₁₆	—	53	4	no	—
738	M₁₆	—	53	4	no	—
739	M₁₆	—	53	4	no	—
740	M₁₆	—	53	4	no	—
741	M₁₆	—	53	8	no	—
742	M₁₆	—	106	16	no	—
743	M₁₆	—	106	16	no	—
744	M₁₆	—	106	4	no	—
745	M₁₆	—	106	4	no	—
746	M₁₆	—	106	4	no	—
747	C₂×C₈	—	53	4	no	—
748	C₂×C₈	—	53	4	no	—
749	C₂×C₈	—	53	4	no	—
750	C₂×C₈	—	53	1	no	—
751	C₂×C₈	—	53	1	no	—
752	C₂×C₈	—	53	1	no	—
753	C₂×C₈	—	53	1	no	—
754	C₂×C₈	—	53	1	no	—
755	C₂×C₈	—	53	1	no	—
756	C₂×C₈	—	53	1	no	—
757	C₂×C₈	—	53	1	no	—
758	C₂×C₈	—	53	1	no	—
759	C₂×C₈	—	53	1	no	—
760	C₂×C₈	—	53	1	no	—
761	C₂×C₈	—	53	1	no	—
762	C₂×C₈	—	53	1	no	—
763	C₂×C₈	—	53	1	no	—
764	C₂×C₈	—	53	1	no	—
765	C₂×C₈	—	53	1	no	—
766	C₂×C₈	—	53	1	no	—
767	C₂×C₈	—	53	1	no	—
768	C₂×C₈	—	53	1	no	—
769	C₂×C₈	—	53	1	no	—
770	C₂×C₈	—	53	1	no	—
771	C₂×C₈	—	53	1	no	—
772	C₂×C₈	—	106	16	no	—
773	C₂×C₈	—	106	16	no	—
774	C₂×C₈	—	106	4	no	—
775	C₂×C₈	—	106	4	no	—
776	C₂×C₈	—	106	4	no	—
777	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
778	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
779	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
780	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
781	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
782	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
783	C₄⋊C₄	—	106	2	no	—
784	C₄⋊C₄	—	106	2	no	—
785	C₂²⋊C₄	—	106	2	no	—
786	C₂²⋊C₄	—	106	2	no	—
787	C₄²	—	53	4	no	—
788	C₄²	—	106	2	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	53	1	no	—
791	C₂³	—	53	1	no	—
792	C₂³	—	53	1	no	—
793	C₂³	—	53	1	no	—
794	C₂³	—	53	1	no	—
795	C₂³	—	53	1	no	—
796	C₂³	—	106	4	no	—
797	C₂³	—	106	4	no	—
798	C₂³	—	106	2	no	—
799	C₂³	—	424	4	no	—
800	C₂³	—	212	2	no	—
801	C₂³	D₄×#6157	1	1	yes	characteristic
802	Q₈	—	2	2	no	—
803	Q₈	—	53	4	no	—
804	Q₈	—	106	4	no	—
805	Q₈	—	106	4	no	—
806	Q₈	—	106	2	no	—
807	Q₈	C₂³×#6157	1	4	yes	—
808	D₄	—	2	4	no	—
809	D₄	—	2	4	no	—
810	D₄	—	2	2	no	—
811	D₄	—	53	4	no	—
812	D₄	—	106	4	no	—
813	D₄	—	106	4	no	—
814	D₄	—	106	4	no	—
815	D₄	—	106	4	no	—
816	D₄	—	106	4	no	—
817	D₄	—	106	4	no	—
818	D₄	—	106	4	no	—
819	D₄	—	106	4	no	—
820	D₄	—	106	2	no	—
821	D₄	C₂³×#6157	1	4	yes	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	4	no	—
824	C₂×C₄	—	2	4	no	—
825	C₂×C₄	—	53	1	no	—
826	C₂×C₄	—	53	1	no	—
827	C₂×C₄	—	53	1	no	—
828	C₂×C₄	—	53	1	no	—
829	C₂×C₄	—	53	1	no	—
830	C₂×C₄	—	53	1	no	—
831	C₂×C₄	—	53	1	no	—
832	C₂×C₄	—	53	1	no	—
833	C₂×C₄	—	53	1	no	—
834	C₂×C₄	—	53	1	no	—
835	C₂×C₄	—	53	1	no	—
836	C₂×C₄	—	53	1	no	—
837	C₂×C₄	—	53	1	no	—
838	C₂×C₄	—	53	1	no	—
839	C₂×C₄	—	53	1	no	—
840	C₂×C₄	—	53	1	no	—
841	C₂×C₄	—	53	1	no	—
842	C₂×C₄	—	53	1	no	—
843	C₂×C₄	—	53	1	no	—
844	C₂×C₄	—	53	1	no	—
845	C₂×C₄	—	53	1	no	—
846	C₂×C₄	—	53	1	no	—
847	C₂×C₄	—	106	4	no	—
848	C₂×C₄	—	106	4	no	—
849	C₂×C₄	—	106	4	no	—
850	C₂×C₄	—	106	4	no	—
851	C₂×C₄	—	106	4	no	—
852	C₂×C₄	—	106	4	no	—
853	C₂×C₄	—	106	2	no	—
854	C₂×C₄	—	106	4	no	—
855	C₂×C₄	—	106	4	no	—
856	C₂×C₄	—	106	4	no	—
857	C₂×C₄	—	212	4	no	—
858	C₂×C₄	D₄×#6157	1	1	yes	characteristic
859	C₂×C₄	D₄×#6157	1	1	yes	characteristic
860	C₂×C₄	D₄×#6157	1	1	yes	characteristic
861	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
862	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
863	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
864	C₈	—	53	8	no	—
865	C₈	—	53	1	no	—
866	C₈	—	53	1	no	—
867	C₈	—	53	1	no	—
868	C₈	—	53	1	no	—
869	C₈	—	106	8	no	—
870	C₈	C₂³×#6157	1	1	yes	characteristic
871	C₈	C₂³×#6157	1	1	yes	characteristic
872	C₈	C₂³×#6157	1	1	yes	characteristic
873	C₈	C₂³×#6157	1	1	yes	characteristic
874	C₂²	—	2	4	no	—
875	C₂²	—	4	1	no	—
876	C₂²	—	8	2	no	—
877	C₂²	—	53	1	no	—
878	C₂²	—	53	1	no	—
879	C₂²	—	53	1	no	—
880	C₂²	—	53	1	no	—
881	C₂²	—	106	2	no	—
882	C₂²	—	106	2	no	—
883	C₂²	—	106	2	no	—
884	C₂²	—	106	4	no	—
885	C₂²	—	424	2	no	—
886	C₂²	—	424	4	no	—
887	C₂²	—	212	1	no	—
888	C₂²	—	212	1	no	—
889	C₂²	—	212	1	no	—
890	C₂²	—	212	8	no	—
891	C₂²	C₂×D₄×#6157	1	1	yes	characteristic
892	C₂²	C₂×D₄×#6157	1	1	yes	characteristic
893	C₂²	C₂×D₄×#6157	1	1	yes	characteristic
894	C₄	—	2	4	no	—
895	C₄	—	53	1	no	—
896	C₄	—	53	1	no	—
897	C₄	—	53	1	no	—
898	C₄	—	53	1	no	—
899	C₄	—	106	4	no	—
900	C₄	—	212	4	no	—
901	C₄	C₂×D₄×#6157	1	1	yes	characteristic
902	C₄	C₂×D₄×#6157	1	1	yes	characteristic
903	C₄	C₂×D₄×#6157	1	1	yes	characteristic
904	C₄	C₂⁴×#6157	1	1	yes	characteristic
905	C₂	—	2	1	no	—
906	C₂	—	2	1	no	—
907	C₂	—	2	1	no	—
908	C₂	—	4	4	no	—
909	C₂	—	53	2	no	—
910	C₂	—	106	1	no	—
911	C₂	—	106	1	no	—
912	C₂	—	106	1	no	—
913	C₂	—	212	4	no	—
914	C₂	C₂²×D₄×#6157	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₄×#6157
commutator	C₄×C₅₃	C₂⁴×C₄
Frattini	C₄	C₂⁴×#6157
Fitting	C₂×#135×C₅₃	C₄
socle	C₂×C₅₃	C₂²×C₄×D₄
prime radical	C₂×#135×D₅₃	C₂
cosocle	C₄×D₅₃	C₂⁵
hypercenter	C₂×#135	#6157
hypocenter	C₅₃	C₂×#2957
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#135

Complements

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

N	H ≅ G/N	type
1. D₅₃⋊#568	C₂	semidirect
2. #20291495	C₂	semidirect
3. #20291494	C₂	semidirect
4. #20291493	C₂	semidirect
5. #20291492	C₂	semidirect
6. #20291491	C₂	semidirect
7. D₅₃⋊#444	C₂	semidirect
8. D₅₃⋊#443	C₂	semidirect
9. C₂×D₅₃⋊#108	C₂	semidirect
10. D₅₃⋊#421	C₂	semidirect
11. C₂×#16811586	C₂	semidirect
13. #16811703	C₂²	semidirect
15. #16811702	C₂²	semidirect
17. #16811701	C₂²	semidirect
19. D₅₃⋊#131	C₂²	semidirect
24. #16811670	C₂²	semidirect
25. #16811669	C₂²	semidirect
26. #16811668	C₂²	semidirect
27. #16811667	C₂²	semidirect
28. #16811666	C₂²	semidirect
29. #16811665	C₂²	semidirect
30. C₂×#13133288	C₂²	semidirect
31. D₅₃⋊#108	C₂²	semidirect
32. D₅₃⋊#108	C₂²	semidirect
33. D₅₃⋊#108	C₂²	semidirect
34. D₅₃⋊#108	C₂²	semidirect
35. C₂×#13133287	C₂²	semidirect
36. #16811622	C₂²	semidirect
37. #16811621	C₂²	semidirect
38. #16811620	C₂²	semidirect
39. D₅₃⋊#104	C₂²	semidirect
40. #16811586	C₂²	semidirect
41. #16811586	C₂²	semidirect
42. #16811586	C₂²	semidirect
43. #16811586	C₂²	semidirect
44. C₂×#13133271	C₂²	semidirect
45. C₂×C₈×#6157	C₂²	semidirect
48. C₂×#13133239	C₄	semidirect
50. C₂×#13133237	C₄	semidirect
52. #135×D₅₃	C₄	semidirect
53. #135×D₅₃	C₄	semidirect
54. #135×D₅₃	C₄	semidirect
55. #135×D₅₃	C₄	semidirect
60. C₂×Q₁₆×D₅₃	C₄	semidirect
61. C₂×SD₁₆×D₅₃	C₄	semidirect
62. C₂×D₈×D₅₃	C₄	semidirect
64. C₂×#135×C₅₃	C₄	semidirect
66. #13133305	C₂³	semidirect
70. #13133304	C₂³	semidirect
98. #13133288	C₂³	semidirect
99. #13133288	C₂³	semidirect
100. #13133287	C₂³	semidirect
101. #13133287	C₂³	semidirect
102. #13133282	C₂³	semidirect
103. #13133281	C₂³	semidirect
104. #13133271	C₂³	semidirect
105. #13133271	C₂³	semidirect
106. C₈×#6157	C₂³	semidirect
107. C₈×#6157	C₂³	semidirect
126. #13133240	C₂×C₄	semidirect
127. #13133240	C₂×C₄	semidirect
132. #13133239	C₂×C₄	semidirect
133. #13133239	C₂×C₄	semidirect
134. #13133238	C₂×C₄	semidirect
135. #13133238	C₂×C₄	semidirect
140. #13133237	C₂×C₄	semidirect
141. #13133237	C₂×C₄	semidirect
142. #13133236	C₂×C₄	semidirect
143. #13133236	C₂×C₄	semidirect
146. C₂×Dic₂₁₂	C₂×C₄	semidirect
147. C₂×#11719925	C₂×C₄	semidirect
150. Q₁₆×D₅₃	C₂×C₄	semidirect
151. Q₁₆×D₅₃	C₂×C₄	semidirect
152. C₂×#11719913	C₂×C₄	semidirect
153. C₂×#11719923	C₂×C₄	semidirect
154. C₂×#11719924	C₂×C₄	semidirect
157. SD₁₆×D₅₃	C₂×C₄	semidirect
158. SD₁₆×D₅₃	C₂×C₄	semidirect
159. C₂×D₄₂₄	C₂×C₄	semidirect
160. C₂×#11719922	C₂×C₄	semidirect
163. D₈×D₅₃	C₂×C₄	semidirect
164. D₈×D₅₃	C₂×C₄	semidirect
181. #135×C₅₃	C₂×C₄	semidirect
182. #135×C₅₃	C₂×C₄	semidirect
183. C₂×Q₁₆×C₅₃	C₂×C₄	semidirect
184. C₂×SD₁₆×C₅₃	C₂×C₄	semidirect
185. C₂×D₈×C₅₃	C₂×C₄	semidirect
469. D₅₃	#2957	semidirect
484. C₂×#135	#6157	semidirect
522. C₅₃	C₂×#2957	semidirect
564. #135	C₂×#6157	semidirect
565. #135	C₂×#6157	semidirect
572. C₂×Q₁₆	C₂×#6157	semidirect
580. C₂×SD₁₆	C₂×#6157	semidirect
587. C₂×D₈	C₂×#6157	semidirect

Maximal subgroups

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

subgroup	index
D₅₃⋊#568	2
#20291495	2
#20291494	2
#20291493	2
#20291492	2
#20291491	2
D₅₃⋊#444	2
D₅₃⋊#443	2
C₂×D₅₃⋊#108	2
D₅₃⋊#421	2
C₂×#16811586	2
C₂×#135×D₅₃	2
C₂×#2957	53

Subgroups — D53⋊#2957 #28329565

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃⋊#2957 #28329565