Subgroups — #20288325

Order 6784.

1242 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811358	C₂	1	1	yes	maximal, characteristic, complemented
2	#16811333	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811330	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811319	C₂	1	2	yes	maximal, complemented
5	#16811317	C₂	1	2	yes	maximal, complemented
6	#16811297	C₂	1	4	yes	maximal, complemented
7	#16811269	C₂	1	2	yes	maximal, complemented
8	#16811261	C₂	1	2	yes	maximal, complemented
9	D₄×D₂₁₂	C₂	1	1	yes	maximal, characteristic, complemented
10	#16811173	C₂	1	1	yes	maximal, characteristic, complemented
11	#16811160	C₂	1	2	yes	maximal, complemented
12	#16811157	C₂	1	2	yes	maximal, complemented
13	#16811132	C₂	1	4	yes	maximal, complemented
14	C₄×#11719945	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×D₂₁₂	C₂	1	2	yes	maximal, complemented
16	C₄×D₄×D₅₃	C₂	1	2	yes	maximal, complemented
17	C₄×#41×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#11719945	C₂²	1	1	yes	characteristic
19	C₂×#11719945	C₂²	1	2	yes	complemented
20	C₂²×D₂₁₂	C₂²	1	2	yes	—
21	C₂×D₄×D₅₃	C₂²	1	2	yes	—
22	C₂²×C₄×D₅₃	C₂²	1	4	yes	complemented
23	#13133217	C₂²	1	1	yes	characteristic, complemented
24	#13133214	C₂²	1	1	yes	characteristic
25	#13133212	C₂²	1	4	yes	complemented
26	#13133211	C₂²	1	4	yes	complemented
27	#13133209	C₂²	1	2	yes	complemented
28	#13133208	C₂²	1	2	yes	complemented
29	#13133206	C₂²	1	2	yes	complemented
30	#13133205	C₂²	1	2	yes	complemented
31	#13133205	C₂²	1	2	yes	complemented
32	#13133202	C₂²	1	4	yes	complemented
33	#13133202	C₂²	1	4	yes	complemented
34	#13133200	C₂²	1	4	yes	complemented
35	#13133199	C₂²	1	4	yes	complemented
36	#13133196	C₂²	1	2	yes	complemented
37	#13133195	C₂²	1	4	yes	complemented
38	#13133194	C₂²	1	4	yes	complemented
39	#13133193	C₂²	1	2	yes	complemented
40	#13133192	C₂²	1	2	yes	—
41	#13133191	C₂²	1	2	yes	—
42	#13133191	C₂²	1	2	yes	complemented
43	#13133191	C₂²	1	2	yes	complemented
44	#13133190	C₂²	1	4	yes	complemented
45	#13133189	C₂²	1	4	yes	complemented
46	#13133187	C₂²	1	4	yes	—
47	#13133185	C₂²	1	4	yes	complemented
48	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
49	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
50	C₄×D₂₁₂	C₂²	1	2	yes	—
51	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
52	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
53	C₄×D₂₁₂	C₂²	1	4	yes	complemented
54	C₄×D₂₁₂	C₂²	1	2	yes	complemented
55	C₄×D₂₁₂	C₂²	1	2	yes	complemented
56	C₄×D₂₁₂	C₂²	1	4	yes	complemented
57	C₄×D₂₁₂	C₂²	1	2	yes	complemented
58	D₄×Dic₅₃	C₂²	1	2	yes	—
59	#13133179	C₂²	1	2	yes	complemented
60	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
61	C₄×C₂²⋊D₅₃	C₂²	1	4	yes	complemented
62	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
63	#13133177	C₂²	1	4	yes	complemented
64	#13133176	C₂²	1	1	yes	characteristic, complemented
65	#13133174	C₂²	1	2	yes	complemented
66	#13133174	C₂²	1	4	yes	complemented
67	C₂×C₄⋊Dic₅₃	C₂²	1	2	yes	complemented
68	C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
69	C₂×#11719921	C₂²	1	4	yes	complemented
70	C₂²⋊C₄×D₅₃	C₂²	1	4	yes	complemented
71	C₄²×D₅₃	C₂²	1	2	yes	complemented
72	C₂×#41×C₅₃	C₂²	1	1	yes	characteristic
73	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
74	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
75	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
76	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
77	C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
78	C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
79	#117×C₅₃	C₂²	1	2	yes	complemented
80	#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₄²×C₅₃	C₂²	1	2	yes	complemented
82	C₂×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
83	C₂³×D₅₃	C₂³	1	4	yes	—
84	#41×C₅₃	—	2	4	no	—
85	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
86	C₂×D₄×C₅₃	C₂³	1	2	yes	—
87	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
89	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
91	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
92	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
93	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
94	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
95	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
96	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
97	C₂²×Dic₅₃	C₂³	1	4	yes	—
98	D₄×D₅₃	—	2	8	no	—
99	#11719945	—	2	4	no	—
100	#11719945	—	4	4	no	—
101	C₂×D₂₁₂	—	2	8	no	—
102	C₂×D₂₁₂	C₂³	1	2	yes	—
103	C₂×D₂₁₂	C₂³	1	4	yes	—
104	C₂×D₂₁₂	C₂³	1	2	yes	—
105	C₂×D₂₁₂	C₂³	1	2	yes	—
106	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
107	C₂×C₄×D₅₃	—	4	8	no	—
108	C₂×C₄×D₅₃	C₂³	1	2	yes	—
109	C₂×C₄×D₅₃	C₂³	1	2	yes	—
110	C₂×C₄×D₅₃	C₂³	1	2	yes	—
111	C₂×C₄×D₅₃	C₂³	1	4	yes	—
112	C₂×C₄×D₅₃	C₂³	1	4	yes	—
113	C₂×C₄×D₅₃	C₂³	1	4	yes	—
114	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
115	C₂×Dic₁₀₆	C₂³	1	2	yes	—
116	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
117	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
118	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
119	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
120	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
121	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
122	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
123	C₄²×C₅₃	C₂³	1	1	yes	characteristic
124	C₄²×C₅₃	C₂³	1	1	yes	characteristic
125	C₄²×C₅₃	C₂³	1	2	yes	—
126	C₄²×C₅₃	C₂³	1	1	yes	characteristic
127	C₄²×C₅₃	C₂³	1	1	yes	characteristic
128	C₄²×C₅₃	C₂³	1	2	yes	—
129	C₄²×C₅₃	C₂³	1	2	yes	—
130	C₂²⋊Dic₅₃	C₂³	1	4	yes	—
131	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
132	#11719921	C₂³	1	4	yes	—
133	#11719921	C₂³	1	4	yes	—
134	#11719921	C₂³	1	2	yes	—
135	#11719921	C₂³	1	4	yes	—
136	#11719921	C₂³	1	4	yes	—
137	#11719921	C₂³	1	4	yes	—
138	#11719921	C₂³	1	2	yes	—
139	#11719921	C₂³	1	4	yes	—
140	#11719921	C₂³	1	4	yes	—
141	C₄⋊Dic₅₃	C₂³	1	2	yes	—
142	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
143	C₄⋊Dic₅₃	C₂³	1	2	yes	—
144	C₄⋊Dic₅₃	C₂³	1	4	yes	—
145	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
146	#11719919	C₂³	1	4	yes	—
147	#11719919	C₂³	1	2	yes	—
148	#11719919	C₂³	1	2	yes	—
149	#11719919	C₂³	1	4	yes	—
150	#11719919	C₂³	1	4	yes	—
151	C₄×Dic₅₃	C₂³	1	2	yes	—
152	C₄×Dic₅₃	C₂³	1	2	yes	—
153	C₄×Dic₅₃	C₂³	1	2	yes	—
154	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
155	C₂³×C₅₃	C₂⁴	1	2	yes	—
156	C₂²×D₅₃	—	2	8	no	—
157	C₂²×D₅₃	—	2	8	no	—
158	C₂²×D₅₃	—	4	4	no	—
159	C₂²×D₅₃	C₂⁴	1	4	yes	—
160	C₂²×D₅₃	C₂⁴	1	2	yes	—
161	Q₈×C₅₃	—	2	2	no	—
162	D₄×C₅₃	—	2	4	no	—
163	D₄×C₅₃	#41	1	4	yes	complemented
164	C₂×C₄×C₅₃	—	2	4	no	—
165	C₂×C₄×C₅₃	—	2	4	no	—
166	C₂×C₄×C₅₃	—	2	2	no	—
167	C₂×C₄×C₅₃	—	2	2	no	—
168	C₂×C₄×C₅₃	—	2	4	no	—
169	C₂×C₄×C₅₃	—	2	2	no	—
170	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
172	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
173	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
174	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
175	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
176	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
178	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
179	C₂²⋊D₅₃	—	2	8	no	—
180	C₂²⋊D₅₃	—	2	4	no	—
181	C₂²⋊D₅₃	—	4	4	no	—
182	C₂×Dic₅₃	—	4	4	no	—
183	C₂×Dic₅₃	C₂⁴	1	4	yes	—
184	C₂×Dic₅₃	C₂⁴	1	2	yes	—
185	C₂×Dic₅₃	C₂⁴	1	2	yes	—
186	C₂×Dic₅₃	C₂⁴	1	2	yes	—
187	D₂₁₂	—	2	8	no	—
188	D₂₁₂	—	2	4	no	—
189	D₂₁₂	—	2	4	no	—
190	D₂₁₂	—	4	2	no	—
191	D₂₁₂	#41	1	4	yes	complemented
192	C₄×D₅₃	—	2	4	no	—
193	C₄×D₅₃	—	2	4	no	—
194	C₄×D₅₃	—	2	4	no	—
195	C₄×D₅₃	—	2	8	no	—
196	C₄×D₅₃	—	4	4	no	—
197	C₄×D₅₃	—	4	4	no	—
198	Dic₁₀₆	—	2	2	no	—
199	Dic₁₀₆	—	4	2	no	—
200	C₂²×C₅₃	—	2	2	no	—
201	C₂²×C₅₃	—	2	2	no	—
202	C₂²×C₅₃	—	2	1	no	—
203	C₂²×C₅₃	—	2	1	no	—
204	C₂²×C₅₃	—	2	1	no	—
205	C₂²×C₅₃	C₂×#41	1	4	yes	—
206	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
207	C₂×D₅₃	—	2	2	no	—
208	C₂×D₅₃	—	2	2	no	—
209	C₂×D₅₃	—	2	4	no	—
210	C₂×D₅₃	—	2	4	no	—
211	C₂×D₅₃	—	2	4	no	—
212	C₂×D₅₃	—	4	16	no	—
213	C₂×D₅₃	C₂×#41	1	4	yes	—
214	C₄×C₅₃	—	2	1	no	—
215	C₄×C₅₃	—	2	2	no	—
216	C₄×C₅₃	—	2	1	no	—
217	C₄×C₅₃	—	2	2	no	—
218	C₄×C₅₃	—	2	1	no	—
219	C₄×C₅₃	—	2	2	no	—
220	C₄×C₅₃	C₂×#41	1	2	yes	—
221	C₄×C₅₃	C₂×#41	1	2	yes	—
222	C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
223	Dic₅₃	—	2	2	no	—
224	Dic₅₃	—	2	2	no	—
225	Dic₅₃	—	2	4	no	—
226	Dic₅₃	—	2	2	no	—
227	#3481	—	53	1	no	maximal, Sylow
228	C₂×C₅₃	—	2	4	no	—
229	C₂×C₅₃	—	4	1	no	—
230	C₂×C₅₃	C₂²×#41	1	1	yes	characteristic
231	C₂×C₅₃	C₂²×#41	1	1	yes	characteristic
232	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
233	D₅₃	—	2	4	no	—
234	D₅₃	—	4	4	no	—
235	#559	—	53	1	no	—
236	#554	—	53	1	no	—
237	#554	—	53	1	no	—
238	#553	—	53	2	no	—
239	#553	—	53	2	no	—
240	#551	—	53	4	no	—
241	#546	—	53	2	no	—
242	#546	—	53	2	no	—
243	D₄²	—	53	1	no	—
244	#532	—	53	1	no	—
245	#529	—	53	2	no	—
246	#529	—	53	2	no	—
247	#525	—	53	4	no	—
248	C₄×#41	—	53	1	no	—
249	C₄×#41	D₅₃	1	1	yes	characteristic, complemented
250	C₂×C₄×D₄	—	53	2	no	—
251	C₂×C₄×D₄	—	53	2	no	—
252	C₅₃	#3481	1	1	yes	characteristic, complemented, Sylow
253	C₂×#41	—	53	1	no	—
254	C₂×#41	—	53	2	no	—
255	C₂×#41	C₂×D₅₃	1	1	yes	characteristic
256	C₂²×D₄	—	53	2	no	—
257	C₂²×D₄	—	53	2	no	—
258	C₂³×C₄	—	53	4	no	—
259	C₄⋊Q₈	—	53	1	no	—
260	#127	—	53	1	no	—
261	#126	—	53	4	no	—
262	#126	—	53	4	no	—
263	#125	—	53	2	no	—
264	#125	—	53	2	no	—
265	#124	—	53	2	no	—
266	#124	—	53	2	no	—
267	#124	—	53	2	no	—
268	#123	—	53	4	no	—
269	#123	—	53	4	no	—
270	#123	—	53	4	no	—
271	#123	—	53	4	no	—
272	C₂²⋊Q₈	—	53	2	no	—
273	C₂²⋊Q₈	—	53	2	no	—
274	C₂²⋊Q₈	—	53	4	no	—
275	C₂²⋊Q₈	—	53	4	no	—
276	#121	—	53	4	no	—
277	#121	—	53	2	no	—
278	#121	—	53	2	no	—
279	#121	—	53	2	no	—
280	#121	—	53	2	no	—
281	#121	—	53	4	no	—
282	#120	—	53	4	no	—
283	#120	—	53	4	no	—
284	C₄×Q₈	—	53	1	no	—
285	C₄×Q₈	—	53	1	no	—
286	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
287	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
288	C₄×D₄	—	53	2	no	—
289	C₄×D₄	—	53	4	no	—
290	C₄×D₄	—	53	2	no	—
291	C₄×D₄	—	53	2	no	—
292	C₄×D₄	—	53	2	no	—
293	C₄×D₄	—	53	4	no	—
294	C₄×D₄	—	53	1	no	—
295	C₄×D₄	—	53	4	no	—
296	C₄×D₄	—	53	2	no	—
297	C₄×D₄	—	53	2	no	—
298	C₄×D₄	—	53	2	no	—
299	C₄×D₄	—	53	4	no	—
300	C₄×D₄	—	53	2	no	—
301	C₄×D₄	—	53	1	no	—
302	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
303	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
304	C₄×D₄	C₂×D₅₃	1	2	yes	complemented
305	C₄×D₄	C₂×D₅₃	1	2	yes	complemented
306	#117	—	53	1	no	—
307	#117	—	53	2	no	—
308	#117	—	53	4	no	—
309	#117	C₂×D₅₃	1	2	yes	complemented
310	#117	C₂×D₅₃	1	1	yes	characteristic, complemented
311	C₂×C₄⋊C₄	—	53	2	no	—
312	C₂×C₄⋊C₄	—	53	2	no	—
313	C₂×C₂²⋊C₄	—	53	4	no	—
314	C₂×C₂²⋊C₄	—	53	4	no	—
315	C₂×C₄²	—	53	2	no	—
316	C₂×C₄²	C₂×D₅₃	1	2	yes	complemented
317	C₂×C₄²	C₂×D₅₃	1	1	yes	characteristic, complemented
318	C₂⁴	—	53	4	no	—
319	#41	—	2	4	no	—
320	#41	—	106	4	no	—
321	#41	—	212	4	no	—
322	C₂×Q₈	—	53	1	no	—
323	C₂×Q₈	—	53	2	no	—
324	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
325	C₂×D₄	—	53	2	no	—
326	C₂×D₄	—	53	4	no	—
327	C₂×D₄	—	53	4	no	—
328	C₂×D₄	—	53	1	no	—
329	C₂×D₄	—	53	4	no	—
330	C₂×D₄	—	53	2	no	—
331	C₂×D₄	—	53	2	no	—
332	C₂×D₄	—	53	2	no	—
333	C₂×D₄	—	106	8	no	—
334	C₂×D₄	—	106	8	no	—
335	C₂×D₄	C₂²×D₅₃	1	2	yes	—
336	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
337	C₂²×C₄	—	53	4	no	—
338	C₂²×C₄	—	53	2	no	—
339	C₂²×C₄	—	53	2	no	—
340	C₂²×C₄	—	53	2	no	—
341	C₂²×C₄	—	53	4	no	—
342	C₂²×C₄	—	53	4	no	—
343	C₂²×C₄	—	53	4	no	—
344	C₂²×C₄	—	212	8	no	—
345	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
346	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
347	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
348	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
349	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
350	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
351	C₄⋊C₄	—	53	1	no	—
352	C₄⋊C₄	—	53	2	no	—
353	C₄⋊C₄	—	53	2	no	—
354	C₄⋊C₄	—	53	4	no	—
355	C₄⋊C₄	—	53	4	no	—
356	C₄⋊C₄	—	53	1	no	—
357	C₄⋊C₄	—	53	2	no	—
358	C₄⋊C₄	—	53	2	no	—
359	C₄⋊C₄	—	53	4	no	—
360	C₄⋊C₄	—	53	4	no	—
361	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
362	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
363	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
364	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
365	C₂²⋊C₄	—	53	4	no	—
366	C₂²⋊C₄	—	53	2	no	—
367	C₂²⋊C₄	—	53	2	no	—
368	C₂²⋊C₄	—	53	4	no	—
369	C₂²⋊C₄	—	53	4	no	—
370	C₂²⋊C₄	—	53	4	no	—
371	C₂²⋊C₄	—	53	4	no	—
372	C₂²⋊C₄	—	53	4	no	—
373	C₂²⋊C₄	—	53	2	no	—
374	C₂²⋊C₄	—	53	4	no	—
375	C₂²⋊C₄	—	53	4	no	—
376	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
377	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
378	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
379	C₄²	—	53	2	no	—
380	C₄²	—	53	2	no	—
381	C₄²	—	53	2	no	—
382	C₄²	C₂²×D₅₃	1	1	yes	characteristic
383	C₄²	C₂²×D₅₃	1	2	yes	—
384	C₄²	C₂²×D₅₃	1	2	yes	—
385	C₄²	C₂²×D₅₃	1	1	yes	characteristic
386	C₄²	C₂²×D₅₃	1	1	yes	characteristic
387	C₄²	C₂²×D₅₃	1	1	yes	characteristic
388	C₄²	C₂²×D₅₃	1	2	yes	—
389	C₂³	—	53	2	no	—
390	C₂³	—	53	4	no	—
391	C₂³	—	106	8	no	—
392	C₂³	—	106	8	no	—
393	C₂³	—	212	4	no	—
394	C₂³	C₂³×D₅₃	1	1	yes	characteristic
395	C₂³	C₂³×D₅₃	1	2	yes	—
396	Q₈	—	2	2	no	—
397	Q₈	—	106	2	no	—
398	Q₈	—	212	2	no	—
399	D₄	—	2	4	no	—
400	D₄	—	53	4	no	—
401	D₄	—	106	8	no	—
402	D₄	—	106	4	no	—
403	D₄	—	106	8	no	—
404	D₄	—	106	4	no	—
405	D₄	—	106	4	no	—
406	D₄	—	212	2	no	—
407	D₄	—	212	4	no	—
408	D₄	#11719945	1	4	yes	complemented
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	53	2	no	—
416	C₂×C₄	—	53	2	no	—
417	C₂×C₄	—	53	2	no	—
418	C₂×C₄	—	53	4	no	—
419	C₂×C₄	—	106	4	no	—
420	C₂×C₄	—	106	4	no	—
421	C₂×C₄	—	106	4	no	—
422	C₂×C₄	—	106	8	no	—
423	C₂×C₄	—	212	4	no	—
424	C₂×C₄	—	212	4	no	—
425	C₂×C₄	—	212	4	no	—
426	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
427	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
428	C₂×C₄	C₂³×D₅₃	1	2	yes	—
429	C₂×C₄	C₂³×D₅₃	1	2	yes	—
430	C₂×C₄	C₂³×D₅₃	1	2	yes	—
431	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
432	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
433	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
434	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	2	1	no	—
439	C₂²	—	2	1	no	—
440	C₂²	—	53	4	no	—
441	C₂²	—	106	2	no	—
442	C₂²	—	106	2	no	—
443	C₂²	—	106	4	no	—
444	C₂²	—	106	4	no	—
445	C₂²	—	106	4	no	—
446	C₂²	—	212	16	no	—
447	C₂²	C₂×#11719945	1	4	yes	—
448	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
449	C₄	—	2	1	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	2	no	—
453	C₄	—	2	2	no	—
454	C₄	—	2	1	no	—
455	C₄	—	106	2	no	—
456	C₄	—	106	2	no	—
457	C₄	—	106	2	no	—
458	C₄	—	106	4	no	—
459	C₄	#41×D₅₃	1	2	yes	—
460	C₄	C₂×#11719945	1	2	yes	—
461	C₄	#13133263	1	2	yes	—
462	C₂	—	2	4	no	—
463	C₂	—	4	1	no	—
464	C₂	—	106	4	no	—
465	C₂	—	212	4	no	—
466	C₂	C₂×#41×D₅₃	1	1	yes	characteristic
467	C₂	C₂²×#11719945	1	1	yes	characteristic
468	C₂	C₂×#13133263	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Frattini	C₂²	C₂⁴×D₅₃
Fitting	C₄×#41×C₅₃	C₂
hypercenter	C₄×#41	D₅₃
hypocenter	C₅₃	#3481
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41

Complements

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

N	H ≅ G/N	type
1. #16811358	C₂	semidirect
2. #16811333	C₂	semidirect
3. #16811330	C₂	semidirect
4. #16811319	C₂	semidirect
5. #16811317	C₂	semidirect
6. #16811297	C₂	semidirect
7. #16811269	C₂	semidirect
8. #16811261	C₂	semidirect
9. D₄×D₂₁₂	C₂	semidirect
10. #16811173	C₂	semidirect
11. #16811160	C₂	semidirect
12. #16811157	C₂	semidirect
13. #16811132	C₂	semidirect
14. C₄×#11719945	C₂	semidirect
15. C₂×C₄×D₂₁₂	C₂	semidirect
16. C₄×D₄×D₅₃	C₂	semidirect
17. C₄×#41×C₅₃	C₂	semidirect
19. C₂×#11719945	C₂²	semidirect
22. C₂²×C₄×D₅₃	C₂²	semidirect
23. #13133217	C₂²	semidirect
25. #13133212	C₂²	semidirect
26. #13133211	C₂²	semidirect
27. #13133209	C₂²	semidirect
28. #13133208	C₂²	semidirect
29. #13133206	C₂²	semidirect
30. #13133205	C₂²	semidirect
31. #13133205	C₂²	semidirect
32. #13133202	C₂²	semidirect
33. #13133202	C₂²	semidirect
34. #13133200	C₂²	semidirect
35. #13133199	C₂²	semidirect
36. #13133196	C₂²	semidirect
37. #13133195	C₂²	semidirect
38. #13133194	C₂²	semidirect
39. #13133193	C₂²	semidirect
42. #13133191	C₂²	semidirect
43. #13133191	C₂²	semidirect
44. #13133190	C₂²	semidirect
45. #13133189	C₂²	semidirect
47. #13133185	C₂²	semidirect
48. C₄×Dic₁₀₆	C₂²	semidirect
49. C₄×Dic₁₀₆	C₂²	semidirect
53. C₄×D₂₁₂	C₂²	semidirect
54. C₄×D₂₁₂	C₂²	semidirect
55. C₄×D₂₁₂	C₂²	semidirect
56. C₄×D₂₁₂	C₂²	semidirect
57. C₄×D₂₁₂	C₂²	semidirect
59. #13133179	C₂²	semidirect
60. C₄×C₂²⋊D₅₃	C₂²	semidirect
61. C₄×C₂²⋊D₅₃	C₂²	semidirect
62. C₄×C₂²⋊D₅₃	C₂²	semidirect
63. #13133177	C₂²	semidirect
64. #13133176	C₂²	semidirect
65. #13133174	C₂²	semidirect
66. #13133174	C₂²	semidirect
67. C₂×C₄⋊Dic₅₃	C₂²	semidirect
68. C₄⋊C₄×D₅₃	C₂²	semidirect
69. C₂×#11719921	C₂²	semidirect
70. C₂²⋊C₄×D₅₃	C₂²	semidirect
71. C₄²×D₅₃	C₂²	semidirect
73. C₄×Q₈×C₅₃	C₂²	semidirect
74. C₄×Q₈×C₅₃	C₂²	semidirect
77. C₄×D₄×C₅₃	C₂²	semidirect
78. C₄×D₄×C₅₃	C₂²	semidirect
79. #117×C₅₃	C₂²	semidirect
80. #117×C₅₃	C₂²	semidirect
81. C₂×C₄²×C₅₃	C₂²	semidirect
82. C₂×C₄²×C₅₃	C₂²	semidirect
163. D₄×C₅₃	#41	semidirect
191. D₂₁₂	#41	semidirect
249. C₄×#41	D₅₃	semidirect
252. C₅₃	#3481	semidirect
286. C₄×Q₈	C₂×D₅₃	semidirect
287. C₄×Q₈	C₂×D₅₃	semidirect
304. C₄×D₄	C₂×D₅₃	semidirect
305. C₄×D₄	C₂×D₅₃	semidirect
309. #117	C₂×D₅₃	semidirect
310. #117	C₂×D₅₃	semidirect
316. C₂×C₄²	C₂×D₅₃	semidirect
317. C₂×C₄²	C₂×D₅₃	semidirect
408. D₄	#11719945	semidirect