Subgroups — #20288450

Order 6784.

1142 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811336	C₂	1	2	yes	maximal, complemented
2	#16811321	C₂	1	2	yes	maximal, complemented
3	#16811317	C₂	1	2	yes	maximal, complemented
4	#16811297	C₂	1	4	yes	maximal, complemented
5	#16811274	C₂	1	2	yes	maximal, complemented
6	#16811263	C₂	1	4	yes	maximal, complemented
7	#16811251	C₂	1	1	yes	maximal, characteristic, complemented
8	#16811244	C₂	1	2	yes	maximal, complemented
9	#16811228	C₂	1	2	yes	maximal, complemented
10	#16811192	C₂	1	1	yes	maximal, characteristic, complemented
11	#16811173	C₂	1	2	yes	maximal, complemented
12	#16811157	C₂	1	2	yes	maximal, complemented
13	#16811134	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#13133191	C₂	1	1	yes	maximal, characteristic, complemented
15	#16811103	C₂	1	1	yes	maximal, characteristic, complemented
16	#16811097	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#117×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#11719945	C₂²	1	1	yes	characteristic
19	C₂×#11719945	C₂²	1	4	yes	complemented
20	C₂²×D₂₁₂	C₂²	1	1	yes	characteristic
21	C₂²×C₂²⋊D₅₃	C₂²	1	2	yes	—
22	#13133217	C₂²	1	2	yes	complemented
23	#13133216	C₂²	1	2	yes	complemented
24	#13133214	C₂²	1	2	yes	complemented
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	#13133205	C₂²	1	4	yes	complemented
30	#13133205	C₂²	1	2	yes	complemented
31	#13133203	C₂²	1	4	yes	complemented
32	#13133202	C₂²	1	4	yes	complemented
33	#13133202	C₂²	1	4	yes	complemented
34	#13133200	C₂²	1	2	yes	—
35	#13133200	C₂²	1	4	yes	complemented
36	#13133199	C₂²	1	4	yes	complemented
37	#13133196	C₂²	1	1	yes	characteristic, complemented
38	#13133196	C₂²	1	1	yes	characteristic, complemented
39	#13133195	C₂²	1	4	yes	complemented
40	#13133194	C₂²	1	4	yes	—
41	#13133192	C₂²	1	2	yes	complemented
42	#13133192	C₂²	1	2	yes	complemented
43	#13133191	C₂²	1	2	yes	—
44	#13133191	C₂²	1	2	yes	—
45	#13133191	C₂²	1	2	yes	—
46	#13133191	C₂²	1	2	yes	—
47	#13133191	C₂²	1	4	yes	complemented
48	#13133191	C₂²	1	1	yes	characteristic, complemented
49	#13133191	C₂²	1	1	yes	characteristic, complemented
50	#13133190	C₂²	1	4	yes	complemented
51	#13133190	C₂²	1	4	yes	complemented
52	#13133187	C₂²	1	4	yes	—
53	#13133186	C₂²	1	2	yes	—
54	C₄×Dic₁₀₆	C₂²	1	2	yes	complemented
55	C₄×D₂₁₂	C₂²	1	4	yes	complemented
56	C₄×D₂₁₂	C₂²	1	2	yes	complemented
57	C₄×D₂₁₂	C₂²	1	2	yes	complemented
58	C₄×D₂₁₂	C₂²	1	2	yes	complemented
59	#13133179	C₂²	1	2	yes	complemented
60	#13133179	C₂²	1	2	yes	complemented
61	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
62	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
63	C₄×C₂²⋊D₅₃	C₂²	1	4	yes	complemented
64	#13133177	C₂²	1	4	yes	—
65	#13133176	C₂²	1	1	yes	characteristic
66	#13133175	C₂²	1	2	yes	complemented
67	#13133174	C₂²	1	4	yes	complemented
68	C₂×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
69	C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
70	C₂×#11719921	C₂²	1	2	yes	—
71	C₂²⋊C₄×D₅₃	C₂²	1	4	yes	—
72	C₂³×C₄×C₅₃	C₂²	1	1	yes	characteristic
73	#117×C₅₃	C₂²	1	2	yes	—
74	#117×C₅₃	C₂²	1	1	yes	characteristic
75	#117×C₅₃	C₂²	1	1	yes	characteristic
76	#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
77	#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
78	#117×C₅₃	C₂²	1	2	yes	complemented
79	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
80	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
82	C₂×C₄²×C₅₃	C₂²	1	2	yes	complemented
83	C₂⁴×C₅₃	C₂³	1	1	yes	characteristic
84	C₂³×D₅₃	C₂³	1	2	yes	—
85	C₂²×C₄×C₅₃	—	2	4	no	—
86	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
88	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
91	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
93	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
94	C₂×C₂²⋊D₅₃	—	4	4	no	—
95	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
96	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
97	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
98	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
99	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
100	C₂²×Dic₅₃	C₂³	1	2	yes	—
101	#11719945	—	2	4	no	—
102	#11719945	—	4	8	no	—
103	C₂×D₂₁₂	—	2	4	no	—
104	C₂×D₂₁₂	C₂³	1	2	yes	—
105	C₂×D₂₁₂	C₂³	1	2	yes	—
106	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
107	C₂×D₂₁₂	C₂³	1	4	yes	—
108	C₂×D₂₁₂	C₂³	1	4	yes	—
109	C₂×C₄×D₅₃	C₂³	1	2	yes	—
110	C₂×C₄×D₅₃	C₂³	1	4	yes	—
111	C₂×C₄×D₅₃	C₂³	1	4	yes	—
112	C₂×C₄×D₅₃	C₂³	1	4	yes	—
113	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
114	C₂×Dic₁₀₆	C₂³	1	4	yes	—
115	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
116	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
117	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
118	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
119	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
120	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
121	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
122	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
123	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
124	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
125	C₄²×C₅₃	C₂³	1	2	yes	—
126	C₄²×C₅₃	C₂³	1	2	yes	—
127	C₄²×C₅₃	C₂³	1	2	yes	—
128	C₄²×C₅₃	C₂³	1	2	yes	—
129	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
130	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
131	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
132	#11719921	C₂³	1	4	yes	—
133	#11719921	C₂³	1	4	yes	—
134	#11719921	C₂³	1	4	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	2	yes	—
141	C₄⋊Dic₅₃	C₂³	1	2	yes	—
142	C₄⋊Dic₅₃	C₂³	1	2	yes	—
143	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
144	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
145	C₄⋊Dic₅₃	C₂³	1	4	yes	—
146	#11719919	C₂³	1	4	yes	—
147	#11719919	C₂³	1	2	yes	—
148	#11719919	C₂³	1	4	yes	—
149	#11719919	C₂³	1	4	yes	—
150	#11719919	C₂³	1	2	yes	—
151	C₄×Dic₅₃	C₂³	1	4	yes	—
152	C₄×Dic₅₃	C₂³	1	2	yes	—
153	C₂³×C₅₃	—	2	2	no	—
154	C₂³×C₅₃	—	2	2	no	—
155	C₂³×C₅₃	—	4	1	no	—
156	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
157	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
158	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
159	C₂²×D₅₃	—	2	4	no	—
160	C₂²×D₅₃	—	4	2	no	—
161	C₂²×D₅₃	—	4	2	no	—
162	C₂²×D₅₃	C₂⁴	1	2	yes	—
163	C₂²×D₅₃	C₂⁴	1	4	yes	—
164	C₂×C₄×C₅₃	—	2	2	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	2	no	—
169	C₂×C₄×C₅₃	—	2	2	no	—
170	C₂×C₄×C₅₃	—	4	2	no	—
171	C₂×C₄×C₅₃	#41	1	4	yes	complemented
172	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
173	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
174	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
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	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
180	C₂²⋊D₅₃	—	2	4	no	—
181	C₂²⋊D₅₃	—	2	4	no	—
182	C₂²⋊D₅₃	—	2	8	no	—
183	C₂²⋊D₅₃	—	4	4	no	—
184	C₂²⋊D₅₃	—	4	2	no	—
185	C₂×Dic₅₃	—	4	2	no	—
186	C₂×Dic₅₃	C₂⁴	1	2	yes	—
187	C₂×Dic₅₃	C₂⁴	1	4	yes	—
188	C₂×Dic₅₃	C₂⁴	1	2	yes	—
189	C₂×Dic₅₃	C₂⁴	1	2	yes	—
190	D₂₁₂	—	2	4	no	—
191	D₂₁₂	—	2	4	no	—
192	D₂₁₂	—	2	2	no	—
193	D₂₁₂	—	4	4	no	—
194	D₂₁₂	—	4	4	no	—
195	C₄×D₅₃	—	2	4	no	—
196	C₄×D₅₃	—	4	4	no	—
197	C₄×D₅₃	—	4	4	no	—
198	C₄×D₅₃	—	4	4	no	—
199	Dic₁₀₆	—	2	2	no	—
200	Dic₁₀₆	—	4	4	no	—
201	C₂²×C₅₃	—	2	1	no	—
202	C₂²×C₅₃	—	2	1	no	—
203	C₂²×C₅₃	—	2	1	no	—
204	C₂²×C₅₃	—	2	1	no	—
205	C₂²×C₅₃	—	2	1	no	—
206	C₂²×C₅₃	—	2	1	no	—
207	C₂²×C₅₃	—	2	1	no	—
208	C₂²×C₅₃	—	4	4	no	—
209	C₂²×C₅₃	C₂×#41	1	2	yes	—
210	C₂²×C₅₃	H(5,𝔽₂)	1	2	yes	—
211	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
212	C₂×D₅₃	—	2	2	no	—
213	C₂×D₅₃	—	2	4	no	—
214	C₂×D₅₃	—	2	2	no	—
215	C₂×D₅₃	—	2	4	no	—
216	C₂×D₅₃	—	2	4	no	—
217	C₂×D₅₃	—	2	2	no	—
218	C₂×D₅₃	—	8	4	no	—
219	C₄×C₅₃	—	2	1	no	—
220	C₄×C₅₃	—	2	1	no	—
221	C₄×C₅₃	—	2	2	no	—
222	C₄×C₅₃	—	2	2	no	—
223	C₄×C₅₃	—	2	2	no	—
224	C₄×C₅₃	—	2	2	no	—
225	C₄×C₅₃	C₂×#41	1	2	yes	—
226	C₄×C₅₃	C₂×#41	1	2	yes	—
227	Dic₅₃	—	2	2	no	—
228	Dic₅₃	—	2	2	no	—
229	Dic₅₃	—	2	4	no	—
230	Dic₅₃	—	2	2	no	—
231	#3494	—	53	1	no	maximal, Sylow
232	C₂×C₅₃	—	2	2	no	—
233	C₂×C₅₃	—	2	2	no	—
234	C₂×C₅₃	—	4	1	no	—
235	C₂×C₅₃	C₂²×#41	1	1	yes	characteristic
236	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
237	C₂×C₅₃	#585	1	1	yes	characteristic
238	D₅₃	—	4	2	no	—
239	D₅₃	—	4	4	no	—
240	#555	—	53	2	no	—
241	#553	—	53	2	no	—
242	#553	—	53	2	no	—
243	#551	—	53	4	no	—
244	#547	—	53	2	no	—
245	#546	—	53	4	no	—
246	#544	—	53	1	no	—
247	#542	—	53	2	no	—
248	#540	—	53	2	no	—
249	#535	—	53	1	no	—
250	#532	—	53	2	no	—
251	#529	—	53	2	no	—
252	#525	—	53	1	no	—
253	C₂×#121	—	53	1	no	—
254	#520	—	53	1	no	—
255	#518	—	53	1	no	—
256	C₂×#117	D₅₃	1	1	yes	characteristic, complemented
257	C₅₃	#3494	1	1	yes	characteristic, complemented, Sylow
258	C₂×#41	—	53	1	no	—
259	C₂×#41	—	53	4	no	—
260	C₂²×D₄	—	53	2	no	—
261	C₂²×D₄	—	53	1	no	—
262	C₂³×C₄	C₂×D₅₃	1	1	yes	characteristic
263	C₄⋊Q₈	—	53	2	no	—
264	C₄⋊Q₈	—	53	2	no	—
265	#127	—	53	2	no	—
266	#126	—	53	4	no	—
267	#126	—	53	4	no	—
268	#125	—	53	2	no	—
269	#125	—	53	2	no	—
270	#124	—	53	4	no	—
271	#124	—	53	2	no	—
272	#124	—	53	4	no	—
273	#123	—	53	2	no	—
274	#123	—	53	4	no	—
275	#123	—	53	4	no	—
276	#123	—	53	4	no	—
277	#123	—	53	4	no	—
278	C₂²⋊Q₈	—	53	1	no	—
279	C₂²⋊Q₈	—	53	1	no	—
280	C₂²⋊Q₈	—	53	4	no	—
281	C₂²⋊Q₈	—	53	4	no	—
282	#121	—	53	2	no	—
283	#121	—	53	2	no	—
284	#121	—	53	2	no	—
285	#121	—	53	2	no	—
286	#121	—	53	1	no	—
287	#121	—	53	1	no	—
288	#121	—	53	4	no	—
289	#121	—	53	2	no	—
290	#121	—	53	2	no	—
291	#121	—	53	4	no	—
292	#121	—	53	4	no	—
293	#120	—	53	2	no	—
294	#120	—	53	4	no	—
295	C₄×Q₈	—	53	2	no	—
296	C₄×D₄	—	53	2	no	—
297	C₄×D₄	—	53	2	no	—
298	C₄×D₄	—	53	4	no	—
299	C₄×D₄	—	53	2	no	—
300	C₄×D₄	—	53	2	no	—
301	C₄×D₄	—	53	4	no	—
302	C₄×D₄	—	53	2	no	—
303	C₄×D₄	—	53	2	no	—
304	C₄×D₄	—	53	2	no	—
305	C₄×D₄	—	53	4	no	—
306	#117	—	53	1	no	—
307	#117	—	53	2	no	—
308	#117	—	53	4	no	—
309	#117	C₂×D₅₃	1	1	yes	characteristic
310	#117	C₂×D₅₃	1	1	yes	characteristic
311	#117	C₂×D₅₃	1	2	yes	—
312	#117	C₂×D₅₃	1	2	yes	complemented
313	#117	C₂×D₅₃	1	1	yes	characteristic, complemented
314	#117	C₂×D₅₃	1	1	yes	characteristic, complemented
315	C₂×C₄⋊C₄	—	53	1	no	—
316	C₂×C₄⋊C₄	—	53	2	no	—
317	C₂×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
318	C₂×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
319	C₂×C₂²⋊C₄	—	53	2	no	—
320	C₂×C₂²⋊C₄	—	53	4	no	—
321	C₂×C₂²⋊C₄	C₂×D₅₃	1	2	yes	—
322	C₂×C₄²	C₂×D₅₃	1	2	yes	complemented
323	C₂⁴	—	53	2	no	—
324	C₂⁴	C₂²×D₅₃	1	1	yes	characteristic
325	#41	—	106	4	no	—
326	#41	—	212	8	no	—
327	C₂×Q₈	—	53	1	no	—
328	C₂×Q₈	—	53	4	no	—
329	C₂×D₄	—	53	2	no	—
330	C₂×D₄	—	53	2	no	—
331	C₂×D₄	—	53	4	no	—
332	C₂×D₄	—	53	2	no	—
333	C₂×D₄	—	53	4	no	—
334	C₂×D₄	—	53	2	no	—
335	C₂×D₄	—	53	2	no	—
336	C₂×D₄	—	53	1	no	—
337	C₂×D₄	—	53	4	no	—
338	C₂×D₄	—	53	4	no	—
339	C₂×D₄	—	106	4	no	—
340	C₂×D₄	—	212	4	no	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	53	2	no	—
343	C₂²×C₄	—	53	2	no	—
344	C₂²×C₄	—	53	4	no	—
345	C₂²×C₄	—	53	4	no	—
346	C₂²×C₄	—	53	4	no	—
347	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
348	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
349	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
350	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
351	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
352	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
353	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
354	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
355	C₄⋊C₄	—	53	2	no	—
356	C₄⋊C₄	—	53	2	no	—
357	C₄⋊C₄	—	53	4	no	—
358	C₄⋊C₄	—	53	2	no	—
359	C₄⋊C₄	—	53	1	no	—
360	C₄⋊C₄	—	53	1	no	—
361	C₄⋊C₄	—	53	4	no	—
362	C₄⋊C₄	—	53	4	no	—
363	C₄⋊C₄	—	53	4	no	—
364	C₄⋊C₄	—	53	2	no	—
365	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
366	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
367	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
368	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
369	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
370	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
371	C₂²⋊C₄	—	53	2	no	—
372	C₂²⋊C₄	—	53	2	no	—
373	C₂²⋊C₄	—	53	2	no	—
374	C₂²⋊C₄	—	53	4	no	—
375	C₂²⋊C₄	—	53	4	no	—
376	C₂²⋊C₄	—	53	4	no	—
377	C₂²⋊C₄	—	53	4	no	—
378	C₂²⋊C₄	—	53	4	no	—
379	C₂²⋊C₄	—	53	4	no	—
380	C₂²⋊C₄	—	53	2	no	—
381	C₂²⋊C₄	—	53	4	no	—
382	C₂²⋊C₄	—	53	2	no	—
383	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
384	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
385	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
386	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
387	C₄²	—	53	4	no	—
388	C₄²	—	53	2	no	—
389	C₄²	C₂²×D₅₃	1	2	yes	—
390	C₄²	C₂²×D₅₃	1	2	yes	—
391	C₄²	C₂²×D₅₃	1	2	yes	—
392	C₄²	C₂²×D₅₃	1	2	yes	—
393	C₂³	—	2	2	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	4	1	no	—
396	C₂³	—	53	4	no	—
397	C₂³	—	53	2	no	—
398	C₂³	—	106	4	no	—
399	C₂³	—	212	2	no	—
400	C₂³	—	212	2	no	—
401	C₂³	C₂³×D₅₃	1	1	yes	characteristic
402	C₂³	C₂³×D₅₃	1	1	yes	characteristic
403	C₂³	C₂³×D₅₃	1	1	yes	characteristic
404	Q₈	—	106	2	no	—
405	Q₈	—	212	4	no	—
406	D₄	—	106	4	no	—
407	D₄	—	106	8	no	—
408	D₄	—	106	4	no	—
409	D₄	—	106	4	no	—
410	D₄	—	106	4	no	—
411	D₄	—	106	2	no	—
412	D₄	—	212	4	no	—
413	D₄	—	212	4	no	—
414	D₄	—	212	2	no	—
415	D₄	—	212	4	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	53	2	no	—
424	C₂×C₄	—	53	2	no	—
425	C₂×C₄	—	53	2	no	—
426	C₂×C₄	—	53	4	no	—
427	C₂×C₄	—	106	4	no	—
428	C₂×C₄	—	212	4	no	—
429	C₂×C₄	—	212	4	no	—
430	C₂×C₄	—	212	4	no	—
431	C₂×C₄	—	212	2	no	—
432	C₂×C₄	#11719945	1	4	yes	complemented
433	C₂×C₄	C₂³×D₅₃	1	2	yes	—
434	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
435	C₂×C₄	C₂³×D₅₃	1	2	yes	—
436	C₂×C₄	C₂³×D₅₃	1	2	yes	—
437	C₂×C₄	C₂³×D₅₃	1	2	yes	—
438	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
439	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
440	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	2	1	no	—
447	C₂²	—	2	1	no	—
448	C₂²	—	4	4	no	—
449	C₂²	—	106	2	no	—
450	C₂²	—	106	4	no	—
451	C₂²	—	106	2	no	—
452	C₂²	—	106	4	no	—
453	C₂²	—	106	4	no	—
454	C₂²	—	106	2	no	—
455	C₂²	—	424	4	no	—
456	C₂²	C₂×#11719945	1	2	yes	—
457	C₂²	#13133263	1	2	yes	—
458	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
459	C₄	—	2	1	no	—
460	C₄	—	2	1	no	—
461	C₄	—	2	2	no	—
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	2	2	no	—
465	C₄	—	106	2	no	—
466	C₄	—	106	4	no	—
467	C₄	—	106	2	no	—
468	C₄	—	106	2	no	—
469	C₄	C₂×#11719945	1	2	yes	—
470	C₄	C₂×#11719945	1	2	yes	—
471	C₂	—	2	2	no	—
472	C₂	—	2	2	no	—
473	C₂	—	4	1	no	—
474	C₂	—	212	4	no	—
475	C₂	—	212	2	no	—
476	C₂	C₂²×#11719945	1	1	yes	characteristic
477	C₂	C₂×#13133263	1	1	yes	characteristic
478	C₂	#16811459	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₂×#117×C₅₃	C₂
hypercenter	C₂×#117	D₅₃
hypocenter	C₅₃	#3494
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂×#117

Complements

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

N	H ≅ G/N	type
1. #16811336	C₂	semidirect
2. #16811321	C₂	semidirect
3. #16811317	C₂	semidirect
4. #16811297	C₂	semidirect
5. #16811274	C₂	semidirect
6. #16811263	C₂	semidirect
7. #16811251	C₂	semidirect
8. #16811244	C₂	semidirect
9. #16811228	C₂	semidirect
10. #16811192	C₂	semidirect
11. #16811173	C₂	semidirect
12. #16811157	C₂	semidirect
13. #16811134	C₂	semidirect
14. C₂×#13133191	C₂	semidirect
15. #16811103	C₂	semidirect
16. #16811097	C₂	semidirect
17. C₂×#117×C₅₃	C₂	semidirect
19. C₂×#11719945	C₂²	semidirect
22. #13133217	C₂²	semidirect
23. #13133216	C₂²	semidirect
24. #13133214	C₂²	semidirect
25. #13133212	C₂²	semidirect
26. #13133211	C₂²	semidirect
27. #13133209	C₂²	semidirect
28. #13133208	C₂²	semidirect
29. #13133205	C₂²	semidirect
30. #13133205	C₂²	semidirect
31. #13133203	C₂²	semidirect
32. #13133202	C₂²	semidirect
33. #13133202	C₂²	semidirect
35. #13133200	C₂²	semidirect
36. #13133199	C₂²	semidirect
37. #13133196	C₂²	semidirect
38. #13133196	C₂²	semidirect
39. #13133195	C₂²	semidirect
41. #13133192	C₂²	semidirect
42. #13133192	C₂²	semidirect
47. #13133191	C₂²	semidirect
48. #13133191	C₂²	semidirect
49. #13133191	C₂²	semidirect
50. #13133190	C₂²	semidirect
51. #13133190	C₂²	semidirect
54. C₄×Dic₁₀₆	C₂²	semidirect
55. C₄×D₂₁₂	C₂²	semidirect
56. C₄×D₂₁₂	C₂²	semidirect
57. C₄×D₂₁₂	C₂²	semidirect
58. C₄×D₂₁₂	C₂²	semidirect
59. #13133179	C₂²	semidirect
60. #13133179	C₂²	semidirect
61. C₄×C₂²⋊D₅₃	C₂²	semidirect
62. C₄×C₂²⋊D₅₃	C₂²	semidirect
63. C₄×C₂²⋊D₅₃	C₂²	semidirect
66. #13133175	C₂²	semidirect
67. #13133174	C₂²	semidirect
69. C₄⋊C₄×D₅₃	C₂²	semidirect
76. #117×C₅₃	C₂²	semidirect
77. #117×C₅₃	C₂²	semidirect
78. #117×C₅₃	C₂²	semidirect
79. C₂×C₄⋊C₄×C₅₃	C₂²	semidirect
80. C₂×C₄⋊C₄×C₅₃	C₂²	semidirect
82. C₂×C₄²×C₅₃	C₂²	semidirect
171. C₂×C₄×C₅₃	#41	semidirect
256. C₂×#117	D₅₃	semidirect
257. C₅₃	#3494	semidirect
312. #117	C₂×D₅₃	semidirect
313. #117	C₂×D₅₃	semidirect
314. #117	C₂×D₅₃	semidirect
317. C₂×C₄⋊C₄	C₂×D₅₃	semidirect
318. C₂×C₄⋊C₄	C₂×D₅₃	semidirect
322. C₂×C₄²	C₂×D₅₃	semidirect
432. C₂×C₄	#11719945	semidirect