Subgroups — #35408825

Order 21248.

730 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24916261	C₂	1	1	yes	maximal, characteristic
2	#24916108	C₂	1	1	yes	maximal, characteristic, complemented
3	#24916107	C₂	1	1	yes	maximal, characteristic, complemented
4	#24908353	C₂	1	1	yes	maximal, characteristic
5	#24908348	C₂	1	1	yes	maximal, characteristic
6	#24908215	C₂	1	1	yes	maximal, characteristic, complemented
7	#24908210	C₂	1	1	yes	maximal, characteristic, complemented
8	#24908175	C₂	1	1	yes	maximal, characteristic, complemented
9	#24908171	C₂	1	1	yes	maximal, characteristic, complemented
10	#24908168	C₂	1	1	yes	maximal, characteristic, complemented
11	#24908164	C₂	1	1	yes	maximal, characteristic, complemented
12	#24907370	C₂	1	1	yes	maximal, characteristic, complemented
13	#24907274	C₂	1	1	yes	maximal, characteristic, complemented
14	#24907150	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#1759	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14581812	C₂²	1	1	yes	characteristic
17	C₄×#13050590	C₂²	1	1	yes	characteristic
18	#19127811	C₄	1	2	yes	complemented
19	#19127806	C₄	1	2	yes	complemented
20	#19127801	C₄	1	2	yes	complemented
21	#19127799	C₄	1	2	yes	complemented
22	#19127763	—	2	2	no	—
23	#19127762	—	2	2	no	—
24	#19127754	—	2	2	no	—
25	#19127752	—	2	2	no	—
26	C₂×#14581727	C₂²	1	1	yes	characteristic
27	C₂×#14581727	C₂²	1	1	yes	characteristic
28	#19127737	C₂²	1	1	yes	characteristic
29	#19127729	C₂²	1	1	yes	characteristic
30	#19127729	C₂²	1	1	yes	characteristic
31	#19127728	C₂²	1	1	yes	characteristic
32	#19127728	C₂²	1	1	yes	characteristic
33	C₂×#14581720	C₂²	1	1	yes	characteristic
34	C₂×#14581720	C₂²	1	1	yes	characteristic
35	#19127697	C₂²	1	1	yes	characteristic
36	#19127695	C₂²	1	1	yes	characteristic
37	#19127669	C₂²	1	1	yes	characteristic
38	#19127669	C₂²	1	1	yes	characteristic
39	#19127668	C₂²	1	1	yes	characteristic
40	#19127668	C₂²	1	1	yes	characteristic
41	C₄×#13050574	C₂²	1	1	yes	characteristic
42	C₂×#14581703	C₂²	1	1	yes	characteristic
43	C₂×#14581703	C₂²	1	1	yes	characteristic
44	C₂×#14581703	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
48	#19127465	C₂²	1	1	yes	characteristic
49	#19127465	C₂²	1	1	yes	characteristic
50	#19127461	C₂²	1	1	yes	characteristic
51	#19127461	C₂²	1	1	yes	characteristic
52	C₄×#41×C₈₃	C₂²	1	1	yes	characteristic
53	C₂×#104×C₈₃	C₂²	1	1	yes	characteristic
54	C₂×#104×C₈₃	C₂²	1	1	yes	characteristic
55	C₄×M₁₆×C₈₃	C₂²	1	1	yes	characteristic
56	#376×C₈₃	C₂²	1	1	yes	characteristic
57	#339×C₈₃	C₂²	1	1	yes	characteristic
58	#339×C₈₃	C₂²	1	1	yes	characteristic
59	C₂×#13050590	C₂³	1	1	yes	characteristic
60	#14581812	—	2	2	no	—
61	#14581812	—	2	2	no	—
62	C₂×#13050580	C₂×C₄	1	1	yes	characteristic
63	C₂×#13050578	C₂×C₄	1	1	yes	characteristic
64	C₂×#13050577	C₂×C₄	1	1	yes	characteristic
65	C₂×#13050575	C₂×C₄	1	1	yes	characteristic
66	C₂×#13050574	C₂³	1	1	yes	characteristic
67	C₂×#13050574	C₂³	1	1	yes	characteristic
68	C₂²×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
72	C₄×Dic₁₆₆	C₂×C₄	1	2	yes	—
73	C₄×D₃₃₂	C₂×C₄	1	2	yes	—
74	C₄×C₂²⋊D₈₃	—	2	2	no	—
75	#14581751	C₂³	1	1	yes	characteristic
76	#14581749	—	2	1	no	—
77	C₄²×D₈₃	—	2	1	no	—
78	#14581727	—	2	2	no	—
79	#14581727	—	2	2	no	—
80	#14581725	C₂×C₄	1	2	yes	—
81	#14581723	C₂×C₄	1	2	yes	—
82	C₄⋊(C₈₃⋊C₈)	—	2	2	no	—
83	C₄⋊(C₈₃⋊C₈)	—	2	2	no	—
84	Dic₈₃⋊C₈	—	2	2	no	—
85	Dic₈₃⋊C₈	—	2	2	no	—
86	#14581720	—	2	2	no	—
87	#14581720	—	2	2	no	—
88	#14581716	C₂×C₄	1	2	yes	—
89	#14581715	C₂×C₄	1	2	yes	—
90	#14581713	C₂×C₄	1	2	yes	—
91	#14581712	C₂×C₄	1	2	yes	—
92	C₂²⋊(C₈₃⋊C₈)	—	2	2	no	—
93	C₂²⋊(C₈₃⋊C₈)	—	2	2	no	—
94	(C₂×D₈₃)⋊C₈	—	2	2	no	—
95	(C₂×D₈₃)⋊C₈	—	2	2	no	—
96	#14581703	—	2	2	no	—
97	#14581703	—	2	1	no	—
98	#14581703	—	2	2	no	—
99	#14581703	C₂×C₄	1	2	yes	—
100	#14581703	C₂×C₄	1	2	yes	—
101	C₄×C₈₃⋊C₈	—	2	2	no	—
102	C₄×C₈₃⋊C₈	—	2	1	no	—
103	C₄×C₈₃⋊C₈	—	2	2	no	—
104	C₄×C₈₃⋊C₈	D₄	1	2	yes	—
105	C₄×C₈₃⋊C₈	D₄	1	2	yes	—
106	C₂×#41×C₈₃	C₂³	1	1	yes	characteristic
107	C₂×M₁₆×C₈₃	C₂³	1	1	yes	characteristic
108	C₂×M₁₆×C₈₃	C₂³	1	1	yes	characteristic
109	C₄×Q₈×C₈₃	C₂×C₄	1	2	yes	—
110	C₄×D₄×C₈₃	—	2	2	no	—
111	C₄×D₄×C₈₃	C₂×C₄	1	2	yes	—
112	#117×C₈₃	—	2	1	no	—
113	#117×C₈₃	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₈₃	—	2	1	no	—
115	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
118	#104×C₈₃	—	2	2	no	—
119	#104×C₈₃	—	2	2	no	—
120	#97×C₈₃	—	2	1	no	—
121	C₄×C₈×C₈₃	—	2	1	no	—
122	#95×C₈₃	—	2	2	no	—
123	#13050590	—	2	1	no	—
124	#13050590	—	2	1	no	—
125	#13050590	—	2	1	no	—
126	#13050590	—	2	1	no	—
127	C₂×Dic₁₆₆	C₂²×C₄	1	1	yes	characteristic
128	C₂×D₃₃₂	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₂²⋊D₈₃	—	2	1	no	—
130	C₂×C₄×D₈₃	—	2	2	no	—
131	C₂×C₄×D₈₃	—	2	1	no	—
132	#13050580	—	2	2	no	—
133	#13050578	—	2	2	no	—
134	#13050577	—	2	2	no	—
135	#13050575	—	2	2	no	—
136	#13050574	—	2	1	no	—
137	#13050574	—	2	1	no	—
138	#13050574	—	2	1	no	—
139	#13050574	—	2	1	no	—
140	C₂×C₈₃⋊C₈	—	2	1	no	—
141	C₂×C₈₃⋊C₈	—	2	1	no	—
142	C₂×C₈₃⋊C₈	—	2	1	no	—
143	C₂×C₈₃⋊C₈	—	2	1	no	—
144	C₂×C₈₃⋊C₈	—	2	1	no	—
145	C₂×C₈₃⋊C₈	—	2	1	no	—
146	C₂×C₈₃⋊C₈	—	2	1	no	—
147	C₂×C₈₃⋊C₈	—	2	1	no	—
148	C₂×C₈₃⋊C₈	C₂²×C₄	1	2	yes	—
149	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₈₃⋊C₈	C₂×D₄	1	2	yes	—
152	C₂×C₈₃⋊C₈	C₂×D₄	1	2	yes	—
153	C₂×C₈₃⋊C₈	#41	1	2	yes	—
154	C₂×C₈₃⋊C₈	#41	1	2	yes	—
155	C₄⋊Dic₈₃	C₂²×C₄	1	2	yes	—
156	Dic₈₃⋊C₄	—	2	2	no	—
157	C₂²⋊Dic₈₃	—	2	1	no	—
158	(C₂×D₈₃)⋊C₄	—	2	2	no	—
159	C₄×Dic₈₃	—	2	2	no	—
160	C₄×Dic₈₃	—	2	1	no	—
161	#41×C₈₃	—	2	1	no	—
162	#41×C₈₃	—	2	1	no	—
163	#41×C₈₃	—	2	1	no	—
164	#41×C₈₃	—	2	1	no	—
165	C₂×Q₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
166	C₂×D₄×C₈₃	—	2	1	no	—
167	C₂×D₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₈₃	—	2	1	no	—
169	C₂²×C₄×C₈₃	—	2	1	no	—
170	C₂²×C₄×C₈₃	—	2	2	no	—
171	C₂²×C₄×C₈₃	—	2	1	no	—
172	C₂²×C₄×C₈₃	#41	1	2	yes	—
173	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
174	M₁₆×C₈₃	—	2	1	no	—
175	M₁₆×C₈₃	—	2	1	no	—
176	M₁₆×C₈₃	—	2	1	no	—
177	M₁₆×C₈₃	—	2	1	no	—
178	C₂×C₈×C₈₃	—	2	1	no	—
179	C₂×C₈×C₈₃	—	2	1	no	—
180	C₄⋊C₄×C₈₃	—	2	2	no	—
181	C₄⋊C₄×C₈₃	C₂²×C₄	1	2	yes	—
182	C₂²⋊C₄×C₈₃	—	2	1	no	—
183	C₂²⋊C₄×C₈₃	—	2	2	no	—
184	C₄²×C₈₃	—	2	2	no	—
185	C₄²×C₈₃	—	2	1	no	—
186	C₄²×C₈₃	—	2	1	no	—
187	C₄²×C₈₃	—	2	1	no	—
188	C₄²×C₈₃	C₂²×C₄	1	2	yes	—
189	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₈₃	#41	1	2	yes	—
192	C₄²×C₈₃	#41	1	2	yes	—
193	C₂³×C₈₃	—	2	1	no	—
194	C₂³×C₈₃	C₂×#41	1	1	yes	characteristic
195	C₂²×D₈₃	—	2	1	no	—
196	Q₈×C₈₃	—	2	1	no	—
197	Q₈×C₈₃	—	2	1	no	—
198	D₄×C₈₃	—	2	1	no	—
199	D₄×C₈₃	—	2	1	no	—
200	D₄×C₈₃	—	4	1	no	—
201	D₄×C₈₃	—	4	1	no	—
202	C₂×C₄×C₈₃	—	2	2	no	—
203	C₂×C₄×C₈₃	—	2	1	no	—
204	C₂×C₄×C₈₃	—	2	2	no	—
205	C₂×C₄×C₈₃	—	2	2	no	—
206	C₂×C₄×C₈₃	—	4	2	no	—
207	C₂×C₄×C₈₃	—	4	4	no	—
208	C₂×C₄×C₈₃	—	4	2	no	—
209	C₂×C₄×C₈₃	—	4	2	no	—
210	C₂×C₄×C₈₃	—	4	1	no	—
211	C₂×C₄×C₈₃	—	4	1	no	—
212	C₂×C₄×C₈₃	C₄×D₄	1	2	yes	—
213	C₂×C₄×C₈₃	C₄×D₄	1	2	yes	—
214	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
215	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
217	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
218	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
220	C₂²⋊D₈₃	—	4	1	no	—
221	C₂²⋊D₈₃	—	4	1	no	—
222	C₂×Dic₈₃	—	2	2	no	—
223	C₂×Dic₈₃	—	2	1	no	—
224	D₃₃₂	—	2	1	no	—
225	D₃₃₂	—	2	1	no	—
226	C₄×D₈₃	—	4	4	no	—
227	C₄×D₈₃	—	4	1	no	—
228	C₄×D₈₃	—	4	1	no	—
229	Dic₁₆₆	—	2	1	no	—
230	Dic₁₆₆	—	2	1	no	—
231	C₈×C₈₃	—	4	1	no	—
232	C₈×C₈₃	—	4	1	no	—
233	C₈₃⋊C₈	—	2	2	no	—
234	C₈₃⋊C₈	—	2	2	no	—
235	C₈₃⋊C₈	—	2	2	no	—
236	C₈₃⋊C₈	—	4	1	no	—
237	C₈₃⋊C₈	—	4	1	no	—
238	C₈₃⋊C₈	#117	1	2	yes	—
239	C₈₃⋊C₈	#117	1	2	yes	—
240	C₂²×C₈₃	—	2	2	no	—
241	C₂²×C₈₃	—	4	2	no	—
242	C₂²×C₈₃	—	4	1	no	—
243	C₂²×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
244	C₂²×C₈₃	#529	1	1	yes	characteristic
245	C₂²×C₈₃	#529	1	1	yes	characteristic
246	C₂×D₈₃	—	4	2	no	—
247	C₂×D₈₃	—	4	1	no	—
248	C₄×C₈₃	—	2	2	no	—
249	C₄×C₈₃	—	2	2	no	—
250	C₄×C₈₃	—	4	2	no	—
251	C₄×C₈₃	—	4	2	no	—
252	C₄×C₈₃	—	4	2	no	—
253	C₄×C₈₃	—	4	1	no	—
254	C₄×C₈₃	C₂×#117	1	1	yes	characteristic
255	C₄×C₈₃	C₄×#41	1	1	yes	characteristic
256	C₄×C₈₃	#532	1	1	yes	characteristic
257	C₄×C₈₃	#532	1	1	yes	characteristic
258	Dic₈₃	—	4	2	no	—
259	Dic₈₃	—	4	1	no	—
260	#21296	—	83	1	no	maximal, Sylow
261	C₂×C₈₃	—	2	1	no	—
262	C₂×C₈₃	—	2	1	no	—
263	C₂×C₈₃	—	8	1	no	—
264	C₂×C₈₃	#2293	1	1	yes	characteristic
265	C₂×C₈₃	#2955	1	2	yes	—
266	D₈₃	—	8	1	no	—
267	#2943	—	83	1	no	—
268	#2922	—	83	1	no	—
269	#2922	—	83	1	no	—
270	#1975	—	83	1	no	—
271	#1974	—	83	1	no	—
272	#1946	—	83	1	no	—
273	#1945	—	83	1	no	—
274	#1938	—	83	1	no	—
275	#1938	—	83	1	no	—
276	#1937	—	83	1	no	—
277	#1937	—	83	1	no	—
278	#1778	—	83	1	no	—
279	#1759	—	83	1	no	—
280	#1759	D₈₃	1	1	yes	characteristic, complemented
281	#1726	—	83	1	no	—
282	C₈₃	#21296	1	1	yes	characteristic, complemented, Sylow
283	C₂×#135	—	83	1	no	—
284	C₄×#41	—	83	1	no	—
285	C₄×#41	C₂×D₈₃	1	1	yes	characteristic
286	#442	—	83	2	no	—
287	#441	—	83	2	no	—
288	#440	—	83	2	no	—
289	#440	—	83	2	no	—
290	#433	—	166	2	no	—
291	#433	—	166	2	no	—
292	#431	—	166	2	no	—
293	#431	—	166	2	no	—
294	C₂×#108	—	83	1	no	—
295	C₂×#108	—	83	1	no	—
296	#427	—	83	1	no	—
297	#424	—	83	1	no	—
298	#424	—	83	1	no	—
299	#424	—	83	1	no	—
300	#424	—	83	1	no	—
301	C₂×#104	—	83	1	no	—
302	C₂×#104	—	83	1	no	—
303	C₂×#104	C₂×D₈₃	1	1	yes	characteristic
304	C₂×#104	C₂×D₈₃	1	1	yes	characteristic
305	#416	—	83	1	no	—
306	#416	—	83	1	no	—
307	#408	—	83	1	no	—
308	#408	—	83	1	no	—
309	#408	—	83	1	no	—
310	#408	—	83	1	no	—
311	C₄×M₁₆	—	83	1	no	—
312	C₄×M₁₆	C₂×D₈₃	1	1	yes	characteristic
313	C₂×#97	—	83	1	no	—
314	C₂×#97	—	83	1	no	—
315	C₂×#97	—	83	1	no	—
316	C₂×C₄×C₈	—	83	1	no	—
317	C₂×C₄×C₈	—	83	1	no	—
318	C₂×C₄×C₈	—	83	1	no	—
319	#376	C₂×D₈₃	1	1	yes	characteristic
320	#341	—	83	1	no	—
321	#341	—	83	1	no	—
322	#339	—	83	1	no	—
323	#339	—	83	1	no	—
324	#339	C₂×D₈₃	1	1	yes	characteristic
325	#339	C₂×D₈₃	1	1	yes	characteristic
326	C₂×#41	—	83	1	no	—
327	C₂×#41	C₂²×D₈₃	1	1	yes	characteristic
328	#135	—	166	2	no	—
329	#135	—	166	2	no	—
330	C₂×Q₁₆	—	83	1	no	—
331	C₂×SD₁₆	—	83	1	no	—
332	C₂×SD₁₆	—	83	1	no	—
333	C₂×D₈	—	83	1	no	—
334	C₂×M₁₆	—	83	1	no	—
335	C₂×M₁₆	—	83	1	no	—
336	C₂×M₁₆	C₂²×D₈₃	1	1	yes	characteristic
337	C₂×M₁₆	C₂²×D₈₃	1	1	yes	characteristic
338	C₂²×C₈	—	83	1	no	—
339	C₂²×C₈	—	83	1	no	—
340	C₂²×C₈	—	83	1	no	—
341	C₂²×C₈	—	83	1	no	—
342	C₄×Q₈	—	83	2	no	—
343	C₄×Q₈	C₄×D₈₃	1	2	yes	—
344	C₄×D₄	—	2	2	no	—
345	C₄×D₄	—	83	2	no	—
346	C₄×D₄	—	166	2	no	—
347	C₄×D₄	C₄×D₈₃	1	2	yes	—
348	#117	—	2	1	no	—
349	#117	—	83	1	no	—
350	#117	—	166	1	no	—
351	#117	C₂²×D₈₃	1	1	yes	characteristic
352	C₂×C₄²	—	2	1	no	—
353	C₂×C₄²	—	166	1	no	—
354	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
355	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
356	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
357	#108	—	166	2	no	—
358	#108	—	166	2	no	—
359	#107	—	83	2	no	—
360	#106	—	83	2	no	—
361	C₄⋊C₈	—	166	2	no	—
362	C₄⋊C₈	—	166	2	no	—
363	C₄⋊C₈	—	166	2	no	—
364	C₄⋊C₈	—	166	2	no	—
365	#104	—	2	2	no	—
366	#104	—	2	2	no	—
367	#104	—	166	2	no	—
368	#104	—	166	2	no	—
369	#103	—	83	2	no	—
370	#103	—	83	2	no	—
371	#102	—	83	2	no	—
372	#102	—	83	2	no	—
373	C₂²⋊C₈	—	166	2	no	—
374	C₂²⋊C₈	—	166	2	no	—
375	C₂²⋊C₈	—	166	2	no	—
376	C₂²⋊C₈	—	166	2	no	—
377	#97	—	2	1	no	—
378	#97	—	83	2	no	—
379	#97	—	83	2	no	—
380	#97	—	166	2	no	—
381	#97	—	166	1	no	—
382	#97	—	166	2	no	—
383	C₄×C₈	—	2	1	no	—
384	C₄×C₈	—	83	2	no	—
385	C₄×C₈	—	83	2	no	—
386	C₄×C₈	—	166	2	no	—
387	C₄×C₈	—	166	1	no	—
388	C₄×C₈	—	166	2	no	—
389	#95	—	2	2	no	—
390	#41	—	2	1	no	—
391	#41	—	2	1	no	—
392	#41	—	2	1	no	—
393	#41	—	2	1	no	—
394	#41	—	166	1	no	—
395	#41	—	166	1	no	—
396	#41	—	166	1	no	—
397	#41	—	166	1	no	—
398	C₂×Q₈	—	83	1	no	—
399	C₂×Q₈	C₂×C₄×D₈₃	1	1	yes	characteristic
400	C₂×D₄	—	2	1	no	—
401	C₂×D₄	—	83	1	no	—
402	C₂×D₄	—	166	1	no	—
403	C₂×D₄	C₂×C₄×D₈₃	1	1	yes	characteristic
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	166	1	no	—
409	C₂²×C₄	—	166	2	no	—
410	C₂²×C₄	#13050589	1	2	yes	—
411	C₂²×C₄	C₂³×D₈₃	1	1	yes	characteristic
412	Q₁₆	—	166	2	no	—
413	SD₁₆	—	166	2	no	—
414	SD₁₆	—	166	2	no	—
415	D₈	—	166	2	no	—
416	M₁₆	—	2	1	no	—
417	M₁₆	—	2	1	no	—
418	M₁₆	—	2	1	no	—
419	M₁₆	—	2	1	no	—
420	M₁₆	—	166	1	no	—
421	M₁₆	—	166	1	no	—
422	M₁₆	—	166	1	no	—
423	M₁₆	—	166	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	83	1	no	—
427	C₂×C₈	—	83	1	no	—
428	C₂×C₈	—	83	2	no	—
429	C₂×C₈	—	83	2	no	—
430	C₂×C₈	—	83	2	no	—
431	C₂×C₈	—	83	2	no	—
432	C₂×C₈	—	83	2	no	—
433	C₂×C₈	—	166	1	no	—
434	C₂×C₈	—	166	1	no	—
435	C₂×C₈	—	166	1	no	—
436	C₂×C₈	—	166	1	no	—
437	C₂×C₈	—	166	1	no	—
438	C₂×C₈	—	166	1	no	—
439	C₂×C₈	—	166	1	no	—
440	C₂×C₈	—	166	1	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	83	2	no	—
443	C₄⋊C₄	—	166	2	no	—
444	C₄⋊C₄	C₂×C₄×D₈₃	1	2	yes	—
445	C₂²⋊C₄	—	2	1	no	—
446	C₂²⋊C₄	—	2	2	no	—
447	C₂²⋊C₄	—	166	1	no	—
448	C₂²⋊C₄	—	166	2	no	—
449	C₄²	—	2	1	no	—
450	C₄²	—	2	1	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	2	2	no	—
453	C₄²	—	166	1	no	—
454	C₄²	—	166	2	no	—
455	C₄²	C₂×C₄×D₈₃	1	2	yes	—
456	C₄²	D₄×D₈₃	1	1	yes	characteristic
457	C₄²	D₄×D₈₃	1	1	yes	characteristic
458	C₄²	#13050590	1	2	yes	—
459	C₄²	#13050590	1	2	yes	—
460	C₂³	—	2	1	no	—
461	C₂³	—	166	1	no	—
462	C₂³	C₂×#13050589	1	1	yes	characteristic
463	Q₈	—	2	1	no	—
464	Q₈	—	2	1	no	—
465	Q₈	—	166	1	no	—
466	Q₈	—	166	1	no	—
467	D₄	—	2	1	no	—
468	D₄	—	2	1	no	—
469	D₄	—	4	1	no	—
470	D₄	—	4	1	no	—
471	D₄	—	332	1	no	—
472	D₄	—	332	1	no	—
473	D₄	—	166	1	no	—
474	D₄	—	166	1	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	4	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	332	4	no	—
486	C₂×C₄	—	332	1	no	—
487	C₂×C₄	—	332	1	no	—
488	C₂×C₄	—	166	2	no	—
489	C₂×C₄	—	166	1	no	—
490	C₂×C₄	(C₂²⋊D₈₃)⋊C₄	1	2	yes	—
491	C₂×C₄	(C₂²⋊D₈₃)⋊C₄	1	2	yes	—
492	C₂×C₄	C₂²×C₄×D₈₃	1	1	yes	characteristic
493	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
494	C₂×C₄	#41×D₈₃	1	1	yes	characteristic
495	C₂×C₄	#41×D₈₃	1	1	yes	characteristic
496	C₂×C₄	C₂×#13050590	1	1	yes	characteristic
497	C₂×C₄	C₂×#13050590	1	1	yes	characteristic
498	C₈	—	4	1	no	—
499	C₈	—	4	1	no	—
500	C₈	—	332	1	no	—
501	C₈	—	332	1	no	—
502	C₈	—	83	2	no	—
503	C₈	—	83	2	no	—
504	C₈	—	166	2	no	—
505	C₈	—	166	2	no	—
506	C₈	—	166	2	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	4	1	no	—
509	C₂²	—	4	2	no	—
510	C₂²	—	332	1	no	—
511	C₂²	—	332	2	no	—
512	C₂²	C₂×(C₂²⋊D₈₃)⋊C₄	1	1	yes	characteristic
513	C₂²	#19128231	1	1	yes	characteristic
514	C₂²	#19128231	1	1	yes	characteristic
515	C₄	—	2	2	no	—
516	C₄	—	2	2	no	—
517	C₄	—	4	2	no	—
518	C₄	—	4	2	no	—
519	C₄	—	4	1	no	—
520	C₄	—	4	2	no	—
521	C₄	—	332	1	no	—
522	C₄	—	332	2	no	—
523	C₄	#117×D₈₃	1	1	yes	characteristic
524	C₄	C₄×#13050590	1	1	yes	characteristic
525	C₄	#19128248	1	1	yes	characteristic
526	C₄	#19128248	1	1	yes	characteristic
527	C₂	—	2	1	no	—
528	C₂	—	2	1	no	—
529	C₂	—	8	1	no	—
530	C₂	—	664	1	no	—
531	C₂	#24909926	1	1	yes	characteristic
532	C₂	#24916362	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₃
commutator	C₂×C₄×C₈₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₃
Fitting	C₈₃×#1759	C₂
socle	C₂²×C₈₃	C₂×C₄×D₄
prime radical	C₂×#14581812	C₂²
cosocle	C₂²×C₄×C₈₃	C₂⁴
hypercenter	#1759	D₈₃
hypocenter	C₈₃	#21296
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1759

Complements

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

N	H ≅ G/N	type
2. #24916108	C₂	semidirect
3. #24916107	C₂	semidirect
6. #24908215	C₂	semidirect
7. #24908210	C₂	semidirect
8. #24908175	C₂	semidirect
9. #24908171	C₂	semidirect
10. #24908168	C₂	semidirect
11. #24908164	C₂	semidirect
12. #24907370	C₂	semidirect
13. #24907274	C₂	semidirect
14. #24907150	C₂	semidirect
15. C₈₃×#1759	C₂	semidirect
18. #19127811	C₄	semidirect
19. #19127806	C₄	semidirect
20. #19127801	C₄	semidirect
21. #19127799	C₄	semidirect
280. #1759	D₈₃	semidirect
282. C₈₃	#21296	semidirect

Maximal subgroups

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

subgroup	index
#24916261	2
#24916108	2
#24916107	2
#24908353	2
#24908348	2
#24908215	2
#24908210	2
#24908175	2
#24908171	2
#24908168	2
#24908164	2
#24907370	2
#24907274	2
#24907150	2
C₈₃×#1759	2
#21296	83