Subgroups — #35410859

Order 21248.

910 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24916918	C₂	1	1	yes	maximal, characteristic
2	C₂×#19127821	C₂	1	2	yes	maximal, complemented
3	#24916176	C₂	1	1	yes	maximal, characteristic, complemented
4	#24908382	C₂	1	1	yes	maximal, characteristic, complemented
5	#24908238	C₂	1	1	yes	maximal, characteristic, complemented
6	#24908111	C₂	1	2	yes	maximal, complemented
7	#24907790	C₂	1	2	yes	maximal, complemented
8	#24907483	C₂	1	1	yes	maximal, characteristic, complemented
9	#24907330	C₂	1	1	yes	maximal, characteristic, complemented
10	#24907309	C₂	1	2	yes	maximal, complemented
11	C₄×#131×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14581812	C₂²	1	2	yes	—
13	C₂×#14581798	C₂²	1	2	yes	—
14	#19128251	C₂²	1	1	yes	characteristic
15	#19127923	C₄	1	2	yes	complemented
16	#19127916	C₄	1	2	yes	complemented
17	#19127911	C₄	1	1	yes	characteristic, complemented
18	#19127906	C₄	1	1	yes	characteristic, complemented
19	#19127901	C₄	1	1	yes	characteristic, complemented
20	#19127896	C₄	1	1	yes	characteristic, complemented
21	#19127821	—	2	8	no	—
22	#19127780	—	2	1	no	—
23	#19127780	—	2	1	no	—
24	C₈×D₃₃₂	—	2	1	no	—
25	C₈×D₃₃₂	—	2	1	no	—
26	C₂×#14581727	C₂²	1	2	yes	—
27	#19127725	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
29	C₂×#14581719	C₂²	1	2	yes	—
30	C₂×#14581718	C₂²	1	2	yes	—
31	C₂×#14581718	C₂²	1	2	yes	—
32	#19127695	C₂²	1	2	yes	—
33	#19127667	C₂²	1	2	yes	—
34	C₂×#14581702	C₂²	1	2	yes	—
35	C₄×C₄⋊Dic₈₃	C₂²	1	1	yes	characteristic
36	#19127465	C₂²	1	2	yes	—
37	#19127460	C₂²	1	2	yes	—
38	#19127455	C₂²	1	2	yes	—
39	C₂×#131×C₈₃	C₂²	1	1	yes	characteristic
40	C₂×#131×C₈₃	C₂²	1	1	yes	characteristic
41	C₄×#41×C₈₃	C₂²	1	1	yes	characteristic
42	#405×C₈₃	—	2	1	no	—
43	#405×C₈₃	—	2	1	no	—
44	#405×C₈₃	C₂²	1	1	yes	characteristic
45	#405×C₈₃	C₂²	1	1	yes	characteristic
46	C₄×M₁₆×C₈₃	—	2	1	no	—
47	C₄×M₁₆×C₈₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₈×C₈₃	—	2	1	no	—
49	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
50	C₂×#13050590	C₂³	1	2	yes	—
51	#14581812	—	2	4	no	—
52	#14581812	—	2	4	no	—
53	C₂×#13050580	C₂×C₄	1	2	yes	—
54	C₂×#13050578	C₂×C₄	1	2	yes	—
55	C₂×#13050577	C₂×C₄	1	2	yes	—
56	C₂×#13050575	C₂×C₄	1	2	yes	—
57	#14581798	—	2	4	no	—
58	#14581798	—	2	4	no	—
59	C₂×#13050574	C₂³	1	2	yes	—
60	C₂×#13050573	—	2	2	no	—
61	C₂²×C₈₃⋊C₈	C₂³	1	2	yes	—
62	C₂×C₈×D₈₃	—	2	2	no	—
63	#14581792	C₂×C₄	1	1	yes	characteristic
64	#14581789	C₂×C₄	1	1	yes	characteristic
65	#14581780	C₂×C₄	1	2	yes	—
66	#14581766	—	2	1	no	—
67	#14581766	—	2	1	no	—
68	C₄×D₃₃₂	—	2	1	no	—
69	C₄×D₃₃₂	—	2	1	no	—
70	C₂×C₄⋊Dic₈₃	—	2	1	no	—
71	C₂×C₄×Dic₈₃	C₂³	1	2	yes	—
72	#14581727	—	2	4	no	—
73	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
74	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
75	C₄⋊(C₈₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
76	C₄⋊(C₈₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
77	C₄⋊(C₈₃⋊C₈)	C₂×C₄	1	2	yes	—
78	#14581719	—	2	4	no	—
79	#14581718	—	2	4	no	—
80	#14581718	—	2	4	no	—
81	#14581715	C₂×C₄	1	2	yes	—
82	#14581715	C₂×C₄	1	2	yes	—
83	#14581712	C₂×C₄	1	2	yes	—
84	#14581712	C₂×C₄	1	2	yes	—
85	(C₂×D₈₃)⋊C₈	—	2	2	no	—
86	(C₂×D₈₃)⋊C₈	—	2	2	no	—
87	#14581702	—	2	4	no	—
88	C₈₃⋊#95	—	2	1	no	—
89	C₂×#41×C₈₃	C₂³	1	1	yes	characteristic
90	#131×C₈₃	—	2	2	no	—
91	#131×C₈₃	—	2	2	no	—
92	#131×C₈₃	—	2	2	no	—
93	#131×C₈₃	D₄	1	4	yes	complemented
94	C₂×M₁₆×C₈₃	—	2	1	no	—
95	C₂×M₁₆×C₈₃	—	2	1	no	—
96	C₂×M₁₆×C₈₃	C₂³	1	1	yes	characteristic
97	C₂×M₁₆×C₈₃	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₈₃	—	2	1	no	—
99	C₂²×C₈×C₈₃	—	2	1	no	—
100	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
102	C₄×Q₈×C₈₃	C₂×C₄	1	1	yes	characteristic
103	C₄×Q₈×C₈₃	C₂×C₄	1	1	yes	characteristic
104	C₄×D₄×C₈₃	—	2	1	no	—
105	C₄×D₄×C₈₃	—	2	1	no	—
106	C₄×D₄×C₈₃	C₂×C₄	1	1	yes	characteristic
107	C₄×D₄×C₈₃	C₂×C₄	1	1	yes	characteristic
108	#117×C₈₃	—	2	1	no	—
109	#117×C₈₃	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₈₃	—	2	1	no	—
111	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
112	#97×C₈₃	—	2	1	no	—
113	#97×C₈₃	—	2	1	no	—
114	#97×C₈₃	—	2	1	no	—
115	C₄×C₈×C₈₃	—	2	1	no	—
116	C₄×C₈×C₈₃	—	2	1	no	—
117	C₄×C₈×C₈₃	—	2	1	no	—
118	C₄×C₈×C₈₃	D₄	1	1	yes	characteristic
119	C₄×C₈×C₈₃	D₄	1	1	yes	characteristic
120	C₄×C₈×C₈₃	D₄	1	1	yes	characteristic
121	C₄×C₈×C₈₃	D₄	1	1	yes	characteristic
122	#13050590	—	2	2	no	—
123	#13050590	—	2	2	no	—
124	#13050590	—	2	2	no	—
125	#13050590	—	2	2	no	—
126	C₂×Dic₁₆₆	C₂²×C₄	1	2	yes	—
127	C₂×D₃₃₂	—	2	1	no	—
128	C₂×D₃₃₂	—	2	1	no	—
129	C₂×D₃₃₂	C₂²×C₄	1	2	yes	—
130	C₂×C₂²⋊D₈₃	—	2	2	no	—
131	C₂²×Dic₈₃	—	2	2	no	—
132	C₂×C₄×D₈₃	—	2	2	no	—
133	#13050580	—	2	4	no	—
134	#13050578	—	2	4	no	—
135	#13050577	—	2	4	no	—
136	#13050575	—	2	4	no	—
137	#13050574	—	2	2	no	—
138	#13050574	—	2	2	no	—
139	#13050573	—	4	4	no	—
140	C₂×C₈₃⋊C₈	—	2	2	no	—
141	C₂×C₈₃⋊C₈	—	2	2	no	—
142	C₂×C₈₃⋊C₈	—	2	2	no	—
143	C₂×C₈₃⋊C₈	C₂²×C₄	1	2	yes	—
144	C₂×C₈₃⋊C₈	C₂²×C₄	1	2	yes	—
145	C₈×D₈₃	—	4	4	no	—
146	C₄⋊Dic₈₃	—	2	1	no	—
147	C₄⋊Dic₈₃	—	2	1	no	—
148	C₄⋊Dic₈₃	—	4	2	no	—
149	(C₂×D₈₃)⋊C₄	—	2	2	no	—
150	(C₂×D₈₃)⋊C₄	—	2	2	no	—
151	C₄×Dic₈₃	—	2	2	no	—
152	C₄×Dic₈₃	—	2	2	no	—
153	#41×C₈₃	—	2	1	no	—
154	#41×C₈₃	—	2	1	no	—
155	#41×C₈₃	C₂×D₄	1	2	yes	—
156	#41×C₈₃	#41	1	2	yes	—
157	C₂×Q₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
158	C₂×D₄×C₈₃	—	2	1	no	—
159	C₂×D₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₈₃	—	2	1	no	—
161	C₂²×C₄×C₈₃	—	2	1	no	—
162	C₂²×C₄×C₈₃	—	2	1	no	—
163	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
164	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
165	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
166	M₁₆×C₈₃	—	2	4	no	—
167	M₁₆×C₈₃	—	2	1	no	—
168	M₁₆×C₈₃	—	2	1	no	—
169	M₁₆×C₈₃	—	2	4	no	—
170	M₁₆×C₈₃	C₂×D₄	1	2	yes	—
171	M₁₆×C₈₃	#41	1	2	yes	—
172	C₂×C₈×C₈₃	—	2	4	no	—
173	C₂×C₈×C₈₃	—	2	1	no	—
174	C₂×C₈×C₈₃	—	2	1	no	—
175	C₂×C₈×C₈₃	—	2	1	no	—
176	C₂×C₈×C₈₃	—	2	1	no	—
177	C₂×C₈×C₈₃	—	2	4	no	—
178	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
179	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
180	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
181	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
182	C₂×C₈×C₈₃	C₂×D₄	1	2	yes	—
183	C₂×C₈×C₈₃	#41	1	2	yes	—
184	C₄⋊C₄×C₈₃	—	2	1	no	—
185	C₄⋊C₄×C₈₃	—	2	1	no	—
186	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
187	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
188	C₂²⋊C₄×C₈₃	—	2	1	no	—
189	C₂²⋊C₄×C₈₃	—	2	1	no	—
190	C₂²⋊C₄×C₈₃	—	2	1	no	—
191	C₄²×C₈₃	—	2	1	no	—
192	C₄²×C₈₃	—	2	1	no	—
193	C₄²×C₈₃	—	2	1	no	—
194	C₄²×C₈₃	C₂²×C₄	1	1	yes	characteristic
195	C₄²×C₈₃	C₂²×C₄	1	1	yes	characteristic
196	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
197	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
198	C₂³×C₈₃	—	2	1	no	—
199	C₂³×C₈₃	C₂×#41	1	1	yes	characteristic
200	C₂²×D₈₃	—	2	2	no	—
201	Q₈×C₈₃	—	2	1	no	—
202	Q₈×C₈₃	C₄×D₄	1	2	yes	—
203	D₄×C₈₃	—	2	2	no	—
204	D₄×C₈₃	—	2	2	no	—
205	D₄×C₈₃	—	2	1	no	—
206	D₄×C₈₃	C₄×D₄	1	2	yes	—
207	C₂×C₄×C₈₃	—	2	1	no	—
208	C₂×C₄×C₈₃	—	2	2	no	—
209	C₂×C₄×C₈₃	—	2	2	no	—
210	C₂×C₄×C₈₃	—	2	2	no	—
211	C₂×C₄×C₈₃	—	2	1	no	—
212	C₂×C₄×C₈₃	—	2	1	no	—
213	C₂×C₄×C₈₃	—	4	1	no	—
214	C₂×C₄×C₈₃	—	4	2	no	—
215	C₂×C₄×C₈₃	—	4	2	no	—
216	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
217	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
218	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
219	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
220	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
221	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
226	C₂²⋊D₈₃	—	4	2	no	—
227	C₂²⋊D₈₃	—	4	2	no	—
228	C₂×Dic₈₃	—	2	2	no	—
229	C₂×Dic₈₃	—	4	2	no	—
230	C₂×Dic₈₃	—	4	2	no	—
231	C₂×Dic₈₃	—	4	2	no	—
232	D₃₃₂	—	2	2	no	—
233	D₃₃₂	—	2	2	no	—
234	D₃₃₂	—	4	2	no	—
235	D₃₃₂	—	4	2	no	—
236	C₄×D₈₃	—	4	2	no	—
237	C₄×D₈₃	—	4	2	no	—
238	Dic₁₆₆	—	2	2	no	—
239	Dic₁₆₆	—	2	2	no	—
240	C₈×C₈₃	—	2	2	no	—
241	C₈×C₈₃	—	2	1	no	—
242	C₈×C₈₃	—	2	2	no	—
243	C₈×C₈₃	—	2	1	no	—
244	C₈×C₈₃	#121	1	2	yes	—
245	C₈×C₈₃	#121	1	2	yes	—
246	C₈₃⋊C₈	—	2	2	no	—
247	C₈₃⋊C₈	—	2	2	no	—
248	C₈₃⋊C₈	—	4	2	no	—
249	C₂²×C₈₃	—	2	1	no	—
250	C₂²×C₈₃	—	2	1	no	—
251	C₂²×C₈₃	—	2	2	no	—
252	C₂²×C₈₃	—	4	1	no	—
253	C₂²×C₈₃	—	4	1	no	—
254	C₂²×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
255	C₂²×C₈₃	#529	1	1	yes	characteristic
256	C₂²×C₈₃	#532	1	1	yes	characteristic
257	C₂×D₈₃	—	4	2	no	—
258	C₂×D₈₃	—	4	2	no	—
259	C₂×D₈₃	—	4	2	no	—
260	C₄×C₈₃	—	2	1	no	—
261	C₄×C₈₃	—	2	1	no	—
262	C₄×C₈₃	—	2	1	no	—
263	C₄×C₈₃	—	2	2	no	—
264	C₄×C₈₃	—	4	1	no	—
265	C₄×C₈₃	—	4	1	no	—
266	C₄×C₈₃	#444	1	2	yes	complemented
267	C₄×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
268	C₄×C₈₃	C₄×#41	1	1	yes	characteristic
269	C₄×C₈₃	C₂×#121	1	1	yes	characteristic
270	C₄×C₈₃	#525	1	1	yes	characteristic
271	Dic₈₃	—	4	2	no	—
272	Dic₈₃	—	8	2	no	—
273	#21518	—	83	1	no	maximal, Sylow
274	C₂×C₈₃	—	2	1	no	—
275	C₂×C₈₃	—	2	1	no	—
276	C₂×C₈₃	—	4	2	no	—
277	C₂×C₈₃	C₄×#121	1	1	yes	characteristic
278	C₂×C₈₃	C₂×#444	1	1	yes	characteristic
279	C₂×C₈₃	#2955	1	1	yes	characteristic
280	D₈₃	—	8	2	no	—
281	#3035	—	83	1	no	—
282	C₂×#444	—	83	2	no	—
283	#2931	—	83	1	no	—
284	C₄×#131	D₈₃	1	1	yes	characteristic, complemented
285	#1980	—	83	1	no	—
286	#1950	—	83	1	no	—
287	#1929	—	83	2	no	—
288	#1876	—	83	2	no	—
289	#1806	—	83	1	no	—
290	#1770	—	83	1	no	—
291	#1765	—	83	2	no	—
292	C₈₃	#21518	1	1	yes	characteristic, complemented, Sylow
293	C₂×#135	—	83	2	no	—
294	C₂×#131	—	83	2	no	—
295	C₂×#131	C₂×D₈₃	1	1	yes	characteristic
296	C₂×#131	C₂×D₈₃	1	1	yes	characteristic
297	#532	—	83	1	no	—
298	C₄×#41	C₂×D₈₃	1	1	yes	characteristic
299	#464	—	83	2	no	—
300	#463	—	83	2	no	—
301	#462	—	83	1	no	—
302	#461	—	83	1	no	—
303	#460	—	83	1	no	—
304	#459	—	83	1	no	—
305	#444	—	166	8	no	—
306	#436	—	166	1	no	—
307	#436	—	166	1	no	—
308	C₈×D₄	—	166	1	no	—
309	C₈×D₄	—	166	1	no	—
310	C₂×#108	—	83	2	no	—
311	#423	—	83	1	no	—
312	C₂×C₄⋊C₈	—	83	1	no	—
313	C₂×#104	—	83	2	no	—
314	C₂×#104	—	83	2	no	—
315	C₂×#104	—	83	2	no	—
316	#416	—	83	2	no	—
317	#408	—	83	2	no	—
318	#405	—	2	1	no	—
319	#405	—	2	1	no	—
320	#405	C₂×D₈₃	1	1	yes	characteristic
321	#405	C₂×D₈₃	1	1	yes	characteristic
322	C₄×M₁₆	—	2	1	no	—
323	C₄×M₁₆	C₂×D₈₃	1	1	yes	characteristic
324	C₂×#97	—	83	2	no	—
325	C₂×C₄×C₈	—	2	1	no	—
326	C₂×C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
327	C₄×C₄⋊C₄	—	83	1	no	—
328	#341	—	83	2	no	—
329	#339	—	83	2	no	—
330	#336	—	83	2	no	—
331	C₂×#41	—	83	2	no	—
332	C₂×#41	C₂²×D₈₃	1	1	yes	characteristic
333	#135	—	166	4	no	—
334	#135	—	166	4	no	—
335	C₂×Q₁₆	—	83	2	no	—
336	C₂×SD₁₆	—	83	2	no	—
337	C₂×SD₁₆	—	83	2	no	—
338	C₂×D₈	—	83	2	no	—
339	#131	—	2	2	no	—
340	#131	—	2	2	no	—
341	#131	—	2	2	no	—
342	#131	—	166	4	no	—
343	#131	—	166	4	no	—
344	#131	D₃₃₂	1	4	yes	complemented
345	C₂×M₁₆	—	2	1	no	—
346	C₂×M₁₆	—	2	1	no	—
347	C₂×M₁₆	—	83	2	no	—
348	C₂×M₁₆	—	166	2	no	—
349	C₂×M₁₆	C₂²×D₈₃	1	1	yes	characteristic
350	C₂×M₁₆	C₂²×D₈₃	1	1	yes	characteristic
351	C₂²×C₈	—	2	1	no	—
352	C₂²×C₈	—	2	1	no	—
353	C₂²×C₈	—	83	2	no	—
354	C₂²×C₈	—	166	2	no	—
355	C₂²×C₈	C₂²×D₈₃	1	1	yes	characteristic
356	C₂²×C₈	C₂²×D₈₃	1	1	yes	characteristic
357	C₄⋊Q₈	—	83	1	no	—
358	#127	—	83	1	no	—
359	#124	—	83	2	no	—
360	#121	—	166	1	no	—
361	#121	—	166	1	no	—
362	C₄×Q₈	C₄×D₈₃	1	1	yes	characteristic
363	C₄×Q₈	C₄×D₈₃	1	1	yes	characteristic
364	C₄×D₄	—	2	1	no	—
365	C₄×D₄	—	2	1	no	—
366	C₄×D₄	—	166	1	no	—
367	C₄×D₄	—	166	1	no	—
368	C₄×D₄	C₄×D₈₃	1	1	yes	characteristic
369	C₄×D₄	C₄×D₈₃	1	1	yes	characteristic
370	#117	—	2	1	no	—
371	#117	C₂²×D₈₃	1	1	yes	characteristic
372	C₂×C₄⋊C₄	—	166	1	no	—
373	C₂×C₄²	—	2	1	no	—
374	C₂×C₄²	—	83	2	no	—
375	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
376	#108	—	166	4	no	—
377	C₄⋊C₈	—	83	1	no	—
378	C₄⋊C₈	—	83	1	no	—
379	C₄⋊C₈	—	83	2	no	—
380	C₄⋊C₈	—	166	1	no	—
381	C₄⋊C₈	—	166	1	no	—
382	#104	—	166	4	no	—
383	#104	—	166	4	no	—
384	#104	—	166	4	no	—
385	#103	—	83	2	no	—
386	#103	—	83	2	no	—
387	#102	—	83	2	no	—
388	#102	—	83	2	no	—
389	C₂²⋊C₈	—	166	2	no	—
390	C₂²⋊C₈	—	166	2	no	—
391	#97	—	2	1	no	—
392	#97	—	2	1	no	—
393	#97	—	2	1	no	—
394	#97	—	166	4	no	—
395	C₄×C₈	—	2	1	no	—
396	C₄×C₈	—	2	1	no	—
397	C₄×C₈	—	2	1	no	—
398	C₄×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
399	C₄×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
400	C₄×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
401	C₄×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
402	#95	—	166	1	no	—
403	#41	—	2	1	no	—
404	#41	—	2	1	no	—
405	#41	—	166	2	no	—
406	#41	—	166	2	no	—
407	#41	—	166	2	no	—
408	#41	—	166	2	no	—
409	#41	C₂×D₃₃₂	1	2	yes	—
410	#41	#13050590	1	2	yes	—
411	C₂×Q₈	—	83	2	no	—
412	C₂×Q₈	C₂×C₄×D₈₃	1	1	yes	characteristic
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	83	2	no	—
415	C₂×D₄	—	166	2	no	—
416	C₂×D₄	—	166	1	no	—
417	C₂×D₄	—	166	1	no	—
418	C₂×D₄	C₂×C₄×D₈₃	1	1	yes	characteristic
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	166	2	no	—
423	C₂²×C₄	—	166	2	no	—
424	C₂²×C₄	#13050590	1	1	yes	characteristic
425	C₂²×C₄	#13050590	1	1	yes	characteristic
426	C₂²×C₄	C₂³×D₈₃	1	1	yes	characteristic
427	Q₁₆	—	166	4	no	—
428	SD₁₆	—	166	4	no	—
429	SD₁₆	—	166	4	no	—
430	D₈	—	166	4	no	—
431	M₁₆	—	2	4	no	—
432	M₁₆	—	2	1	no	—
433	M₁₆	—	2	1	no	—
434	M₁₆	—	2	4	no	—
435	M₁₆	—	332	4	no	—
436	M₁₆	—	166	2	no	—
437	M₁₆	—	166	2	no	—
438	M₁₆	C₂×D₃₃₂	1	2	yes	—
439	M₁₆	#13050590	1	2	yes	—
440	C₂×C₈	—	2	4	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	4	no	—
446	C₂×C₈	—	332	4	no	—
447	C₂×C₈	—	83	2	no	—
448	C₂×C₈	—	83	2	no	—
449	C₂×C₈	—	166	2	no	—
450	C₂×C₈	—	166	2	no	—
451	C₂×C₈	—	166	2	no	—
452	C₂×C₈	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
453	C₂×C₈	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
454	C₂×C₈	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
455	C₂×C₈	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
456	C₂×C₈	C₂×D₃₃₂	1	2	yes	—
457	C₂×C₈	#13050590	1	2	yes	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	332	2	no	—
461	C₄⋊C₄	—	166	1	no	—
462	C₄⋊C₄	—	166	1	no	—
463	C₄⋊C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
464	C₄⋊C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
465	C₂²⋊C₄	—	2	1	no	—
466	C₂²⋊C₄	—	2	1	no	—
467	C₂²⋊C₄	—	2	1	no	—
468	C₂²⋊C₄	—	166	2	no	—
469	C₂²⋊C₄	—	166	2	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	2	1	no	—
473	C₄²	—	166	2	no	—
474	C₄²	—	166	2	no	—
475	C₄²	C₂×C₄×D₈₃	1	1	yes	characteristic
476	C₄²	C₂×C₄×D₈₃	1	1	yes	characteristic
477	C₄²	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
478	C₄²	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
479	C₂³	—	2	1	no	—
480	C₂³	—	166	2	no	—
481	C₂³	C₂×#13050590	1	1	yes	characteristic
482	Q₈	—	2	1	no	—
483	Q₈	—	166	2	no	—
484	Q₈	—	166	2	no	—
485	Q₈	C₄×D₃₃₂	1	2	yes	—
486	D₄	—	2	2	no	—
487	D₄	—	2	2	no	—
488	D₄	—	2	1	no	—
489	D₄	—	332	2	no	—
490	D₄	—	332	2	no	—
491	D₄	—	332	2	no	—
492	D₄	—	332	2	no	—
493	D₄	—	166	2	no	—
494	D₄	—	166	2	no	—
495	D₄	C₄×D₃₃₂	1	2	yes	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	332	2	no	—
506	C₂×C₄	—	332	2	no	—
507	C₂×C₄	—	332	2	no	—
508	C₂×C₄	—	332	2	no	—
509	C₂×C₄	—	332	2	no	—
510	C₂×C₄	—	166	2	no	—
511	C₂×C₄	C₄×C₂²⋊D₈₃	1	1	yes	characteristic
512	C₂×C₄	C₄×C₂²⋊D₈₃	1	1	yes	characteristic
513	C₂×C₄	C₄×C₂²⋊D₈₃	1	1	yes	characteristic
514	C₂×C₄	C₄×C₂²⋊D₈₃	1	1	yes	characteristic
515	C₂×C₄	C₂²×C₄×D₈₃	1	1	yes	characteristic
516	C₂×C₄	C₂²×C₂²⋊D₈₃	1	1	yes	characteristic
517	C₂×C₄	C₂²×D₃₃₂	1	1	yes	characteristic
518	C₂×C₄	C₂×#13050590	1	1	yes	characteristic
519	C₂×C₄	C₂×#13050590	1	1	yes	characteristic
520	C₂×C₄	C₂×#13050590	1	1	yes	characteristic
521	C₈	—	2	2	no	—
522	C₈	—	2	1	no	—
523	C₈	—	2	2	no	—
524	C₈	—	2	1	no	—
525	C₈	—	332	2	no	—
526	C₈	—	166	2	no	—
527	C₈	—	166	2	no	—
528	C₈	#14581766	1	2	yes	—
529	C₈	#14581766	1	2	yes	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	4	1	no	—
535	C₂²	—	332	2	no	—
536	C₂²	—	332	2	no	—
537	C₂²	—	332	2	no	—
538	C₂²	C₂×C₄×C₂²⋊D₈₃	1	1	yes	characteristic
539	C₂²	#19128235	1	1	yes	characteristic
540	C₂²	#19128251	1	1	yes	characteristic
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	1	no	—
544	C₄	—	2	2	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	332	2	no	—
548	C₄	—	664	2	no	—
549	C₄	#19127821	1	2	yes	complemented
550	C₄	C₂×C₄×D₃₃₂	1	1	yes	characteristic
551	C₄	C₄×#13050590	1	1	yes	characteristic
552	C₄	C₂×#14581766	1	1	yes	characteristic
553	C₄	#19128212	1	1	yes	characteristic
554	C₂	—	2	1	no	—
555	C₂	—	2	1	no	—
556	C₂	—	4	2	no	—
557	C₂	—	664	2	no	—
558	C₂	C₄×#14581766	1	1	yes	characteristic
559	C₂	C₂×#19127821	1	1	yes	characteristic
560	C₂	#24916364	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₈₃
commutator	C₂×C₄×C₈₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₃
Fitting	C₄×#131×C₈₃	C₂
socle	C₂²×C₈₃	C₂×C₄×D₄
prime radical	#24916918	C₂
cosocle	C₂²×C₄×C₈₃	C₂⁴
hypercenter	C₄×#131	D₈₃
hypocenter	C₈₃	#21518
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ C₄×#131

Complements

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

N	H ≅ G/N	type
2. C₂×#19127821	C₂	semidirect
3. #24916176	C₂	semidirect
4. #24908382	C₂	semidirect
5. #24908238	C₂	semidirect
6. #24908111	C₂	semidirect
7. #24907790	C₂	semidirect
8. #24907483	C₂	semidirect
9. #24907330	C₂	semidirect
10. #24907309	C₂	semidirect
11. C₄×#131×C₈₃	C₂	semidirect
15. #19127923	C₄	semidirect
16. #19127916	C₄	semidirect
17. #19127911	C₄	semidirect
18. #19127906	C₄	semidirect
19. #19127901	C₄	semidirect
20. #19127896	C₄	semidirect
93. #131×C₈₃	D₄	semidirect
266. C₄×C₈₃	#444	semidirect
284. C₄×#131	D₈₃	semidirect
292. C₈₃	#21518	semidirect
344. #131	D₃₃₂	semidirect
549. C₄	#19127821	semidirect

Maximal subgroups

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

subgroup	index
#24916918	2
C₂×#19127821	2
#24916176	2
#24908382	2
#24908238	2
#24908111	2
#24907790	2
#24907483	2
#24907330	2
#24907309	2
C₄×#131×C₈₃	2
#21518	83