Subgroups — C₈₃×#60725 #35288549

Order 21248.

1962 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	C₈₃×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₃×#3180	C₂	1	4	yes	maximal, complemented
4	C₈₃×#3176	C₂	1	4	yes	maximal, complemented
5	C₈₃×#3174	C₂	1	4	yes	maximal, complemented
6	C₈₃×#3171	C₂	1	4	yes	maximal, complemented
7	C₈₃×#3166	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₃×#3151	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₃×#3135	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#490×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₃×#3062	C₂	1	4	yes	maximal, complemented
12	C₈₃×#2946	C₂	1	4	yes	maximal, complemented
13	C₈₃×#2875	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×AGL(1,ℤ/8)×C₈₃	C₂²	1	4	yes	—
15	C₂×#131×C₈₃	C₂²	1	2	yes	—
16	#559×C₈₃	—	2	2	no	—
17	#553×C₈₃	—	2	4	no	—
18	#553×C₈₃	—	2	2	no	—
19	#552×C₈₃	—	2	2	no	—
20	#550×C₈₃	—	2	2	no	—
21	#546×C₈₃	—	2	4	no	—
22	#541×C₈₃	C₂²	1	2	yes	complemented
23	#540×C₈₃	C₂²	1	4	yes	—
24	#540×C₈₃	C₂²	1	2	yes	complemented
25	#537×C₈₃	C₂²	1	2	yes	—
26	#535×C₈₃	C₂²	1	2	yes	—
27	#533×C₈₃	C₂²	1	1	yes	characteristic
28	#532×C₈₃	C₂²	1	1	yes	characteristic
29	#532×C₈₃	C₂²	1	4	yes	—
30	C₂×#127×C₈₃	C₂²	1	1	yes	characteristic
31	#529×C₈₃	C₂²	1	4	yes	complemented
32	C₂×#125×C₈₃	C₂²	1	1	yes	characteristic
33	#520×C₈₃	C₂²	1	2	yes	—
34	#518×C₈₃	C₂²	1	2	yes	—
35	C₄×#41×C₈₃	C₂²	1	1	yes	characteristic
36	#501×C₈₃	C₂²	1	4	yes	complemented
37	#499×C₈₃	C₂²	1	4	yes	complemented
38	#496×C₈₃	C₂²	1	4	yes	—
39	#493×C₈₃	C₂²	1	2	yes	—
40	#492×C₈₃	C₂²	1	2	yes	—
41	#491×C₈₃	C₂²	1	2	yes	complemented
42	#490×C₈₃	C₂²	1	2	yes	—
43	#490×C₈₃	C₂²	1	4	yes	—
44	#490×C₈₃	C₂²	1	2	yes	—
45	#490×C₈₃	C₂²	1	2	yes	complemented
46	#489×C₈₃	C₂²	1	2	yes	complemented
47	#489×C₈₃	C₂²	1	2	yes	complemented
48	#469×C₈₃	C₂²	1	8	yes	complemented
49	#468×C₈₃	C₂²	1	8	yes	complemented
50	#466×C₈₃	C₂²	1	8	yes	complemented
51	#465×C₈₃	C₂²	1	8	yes	complemented
52	#442×C₈₃	C₂²	1	8	yes	complemented
53	#440×C₈₃	C₂²	1	8	yes	complemented
54	C₄×SD₁₆×C₈₃	C₂²	1	8	yes	complemented
55	C₄×D₈×C₈₃	C₂²	1	8	yes	complemented
56	#428×C₈₃	C₂²	1	4	yes	—
57	#416×C₈₃	C₂²	1	4	yes	—
58	C₂×#102×C₈₃	C₂²	1	4	yes	—
59	#405×C₈₃	C₂²	1	2	yes	—
60	#405×C₈₃	C₂²	1	4	yes	complemented
61	C₄×M₁₆×C₈₃	C₂²	1	1	yes	characteristic
62	C₄×M₁₆×C₈₃	C₂²	1	2	yes	complemented
63	C₂×#97×C₈₃	C₂²	1	1	yes	characteristic
64	C₂×#97×C₈₃	C₂²	1	2	yes	complemented
65	C₂×#41×C₈₃	—	2	4	no	—
66	C₂×#41×C₈₃	C₂³	1	2	yes	—
67	C₂×#41×C₈₃	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₈₃	—	2	2	no	—
69	C₂²×D₄×C₈₃	C₂³	1	2	yes	—
70	AGL(1,ℤ/8)×C₈₃	—	2	16	no	—
71	C₂×SD₁₆×C₈₃	C₂³	1	8	yes	—
72	C₂×D₈×C₈₃	C₂³	1	8	yes	—
73	#131×C₈₃	—	2	8	no	—
74	C₂×M₁₆×C₈₃	C₂³	1	4	yes	—
75	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
76	C₂²×C₈×C₈₃	C₂³	1	4	yes	—
77	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
78	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
79	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
80	#127×C₈₃	—	2	2	no	—
81	#127×C₈₃	—	2	2	no	—
82	#127×C₈₃	C₂³	1	2	yes	—
83	#127×C₈₃	C₂³	1	2	yes	—
84	#127×C₈₃	C₂³	1	1	yes	characteristic
85	#126×C₈₃	—	2	4	no	—
86	#126×C₈₃	—	2	4	no	—
87	#125×C₈₃	—	2	4	no	—
88	#125×C₈₃	—	2	2	no	—
89	#125×C₈₃	C₂³	1	2	yes	—
90	#125×C₈₃	C₂³	1	2	yes	—
91	#125×C₈₃	C₂³	1	2	yes	—
92	#124×C₈₃	—	2	2	no	—
93	#124×C₈₃	—	2	4	no	—
94	#124×C₈₃	C₂³	1	2	yes	—
95	#123×C₈₃	—	2	4	no	—
96	#123×C₈₃	—	2	8	no	—
97	#123×C₈₃	—	2	4	no	—
98	C₂²⋊Q₈×C₈₃	—	2	2	no	—
99	C₂²⋊Q₈×C₈₃	—	2	2	no	—
100	C₂²⋊Q₈×C₈₃	C₂³	1	4	yes	—
101	#121×C₈₃	—	2	2	no	—
102	#121×C₈₃	—	2	4	no	—
103	#121×C₈₃	—	2	4	no	—
104	#121×C₈₃	—	2	2	no	—
105	#121×C₈₃	—	2	8	no	—
106	#121×C₈₃	—	2	4	no	—
107	#121×C₈₃	C₂³	1	8	yes	—
108	#121×C₈₃	C₂³	1	4	yes	—
109	#120×C₈₃	—	2	4	no	—
110	C₄×Q₈×C₈₃	—	2	2	no	—
111	C₄×Q₈×C₈₃	D₄	1	2	yes	—
112	C₄×Q₈×C₈₃	C₂³	1	4	yes	—
113	C₄×D₄×C₈₃	—	2	4	no	—
114	C₄×D₄×C₈₃	—	2	4	no	—
115	C₄×D₄×C₈₃	—	2	4	no	—
116	C₄×D₄×C₈₃	—	2	4	no	—
117	C₄×D₄×C₈₃	—	2	2	no	—
118	C₄×D₄×C₈₃	D₄	1	4	yes	—
119	C₄×D₄×C₈₃	D₄	1	2	yes	—
120	C₄×D₄×C₈₃	C₂³	1	8	yes	—
121	C₄×D₄×C₈₃	C₂³	1	4	yes	—
122	#117×C₈₃	—	2	2	no	—
123	#117×C₈₃	—	2	4	no	—
124	#117×C₈₃	C₂³	1	2	yes	—
125	#117×C₈₃	C₂³	1	1	yes	characteristic
126	#117×C₈₃	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
128	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
129	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₈₃	—	2	4	no	—
131	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₈₃	C₂³	1	2	yes	—
133	#107×C₈₃	C₂³	1	8	yes	—
134	#106×C₈₃	C₂³	1	8	yes	—
135	#103×C₈₃	C₂³	1	4	yes	—
136	#103×C₈₃	C₂³	1	4	yes	—
137	#102×C₈₃	C₂³	1	8	yes	—
138	#102×C₈₃	C₂³	1	4	yes	—
139	#102×C₈₃	C₂³	1	8	yes	—
140	#102×C₈₃	C₂³	1	4	yes	—
141	#97×C₈₃	C₂³	1	1	yes	characteristic
142	#97×C₈₃	C₂³	1	1	yes	characteristic
143	#97×C₈₃	C₂³	1	2	yes	—
144	#97×C₈₃	C₂³	1	2	yes	—
145	#97×C₈₃	C₂³	1	4	yes	—
146	C₄×C₈×C₈₃	C₂³	1	2	yes	—
147	C₄×C₈×C₈₃	C₂³	1	4	yes	—
148	C₂⁴×C₈₃	—	2	2	no	—
149	#41×C₈₃	—	2	4	no	—
150	#41×C₈₃	—	2	8	no	—
151	#41×C₈₃	—	8	8	no	—
152	C₂×Q₈×C₈₃	—	2	2	no	—
153	C₂×Q₈×C₈₃	C₂×D₄	1	1	yes	characteristic
154	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
155	C₂×D₄×C₈₃	—	2	2	no	—
156	C₂×D₄×C₈₃	—	2	4	no	—
157	C₂×D₄×C₈₃	—	2	8	no	—
158	C₂×D₄×C₈₃	—	2	2	no	—
159	C₂×D₄×C₈₃	—	2	4	no	—
160	C₂×D₄×C₈₃	—	2	2	no	—
161	C₂×D₄×C₈₃	—	2	4	no	—
162	C₂×D₄×C₈₃	—	2	8	no	—
163	C₂×D₄×C₈₃	—	8	4	no	—
164	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
165	C₂×D₄×C₈₃	C₂×D₄	1	1	yes	characteristic
166	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
167	C₂×D₄×C₈₃	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₈₃	—	2	2	no	—
169	C₂²×C₄×C₈₃	—	2	2	no	—
170	C₂²×C₄×C₈₃	—	2	8	no	—
171	C₂²×C₄×C₈₃	—	2	4	no	—
172	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
173	C₂²×C₄×C₈₃	C₂×D₄	1	4	yes	—
174	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
175	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
176	SD₁₆×C₈₃	—	2	16	no	—
177	D₈×C₈₃	—	2	16	no	—
178	M₁₆×C₈₃	—	2	8	no	—
179	M₁₆×C₈₃	#41	1	8	yes	complemented
180	C₂×C₈×C₈₃	—	2	4	no	—
181	C₂×C₈×C₈₃	—	2	8	no	—
182	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
183	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
184	C₂×C₈×C₈₃	C₂⁴	1	4	yes	—
185	C₄⋊C₄×C₈₃	—	2	2	no	—
186	C₄⋊C₄×C₈₃	—	2	4	no	—
187	C₄⋊C₄×C₈₃	—	2	4	no	—
188	C₄⋊C₄×C₈₃	—	2	4	no	—
189	C₄⋊C₄×C₈₃	—	2	4	no	—
190	C₄⋊C₄×C₈₃	—	2	2	no	—
191	C₄⋊C₄×C₈₃	—	2	2	no	—
192	C₄⋊C₄×C₈₃	—	2	4	no	—
193	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
194	C₄⋊C₄×C₈₃	C₂×D₄	1	4	yes	—
195	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
196	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
197	C₂²⋊C₄×C₈₃	—	2	2	no	—
198	C₂²⋊C₄×C₈₃	—	2	4	no	—
199	C₂²⋊C₄×C₈₃	—	2	8	no	—
200	C₂²⋊C₄×C₈₃	—	2	2	no	—
201	C₂²⋊C₄×C₈₃	—	2	4	no	—
202	C₂²⋊C₄×C₈₃	—	2	4	no	—
203	C₂²⋊C₄×C₈₃	—	2	2	no	—
204	C₂²⋊C₄×C₈₃	—	2	8	no	—
205	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
206	C₂²⋊C₄×C₈₃	C₂×D₄	1	4	yes	—
207	C₄²×C₈₃	—	2	4	no	—
208	C₄²×C₈₃	—	2	2	no	—
209	C₄²×C₈₃	C₂×D₄	1	4	yes	—
210	C₄²×C₈₃	C₂×D₄	1	2	yes	—
211	C₄²×C₈₃	C₂⁴	1	2	yes	—
212	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
213	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
214	C₂³×C₈₃	—	2	2	no	—
215	C₂³×C₈₃	—	2	4	no	—
216	C₂³×C₈₃	—	4	4	no	—
217	C₂³×C₈₃	—	8	4	no	—
218	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
219	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
220	Q₈×C₈₃	—	2	2	no	—
221	Q₈×C₈₃	—	2	4	no	—
222	Q₈×C₈₃	—	4	4	no	—
223	D₄×C₈₃	—	2	4	no	—
224	D₄×C₈₃	—	2	2	no	—
225	D₄×C₈₃	—	2	4	no	—
226	D₄×C₈₃	—	2	8	no	—
227	D₄×C₈₃	—	4	8	no	—
228	D₄×C₈₃	—	4	4	no	—
229	D₄×C₈₃	—	4	4	no	—
230	D₄×C₈₃	—	8	2	no	—
231	D₄×C₈₃	—	8	4	no	—
232	D₄×C₈₃	—	8	4	no	—
233	D₄×C₈₃	—	8	8	no	—
234	C₂×C₄×C₈₃	—	2	4	no	—
235	C₂×C₄×C₈₃	—	2	2	no	—
236	C₂×C₄×C₈₃	—	2	4	no	—
237	C₂×C₄×C₈₃	—	2	4	no	—
238	C₂×C₄×C₈₃	—	4	2	no	—
239	C₂×C₄×C₈₃	—	4	4	no	—
240	C₂×C₄×C₈₃	—	4	4	no	—
241	C₂×C₄×C₈₃	—	8	4	no	—
242	C₂×C₄×C₈₃	—	8	8	no	—
243	C₂×C₄×C₈₃	—	8	2	no	—
244	C₂×C₄×C₈₃	C₂²×D₄	1	4	yes	—
245	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
246	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
247	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
248	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₈₃	C₂×#41	1	4	yes	—
250	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
251	C₈×C₈₃	—	2	2	no	—
252	C₈×C₈₃	—	2	2	no	—
253	C₈×C₈₃	C₂×#41	1	8	yes	—
254	C₂²×C₈₃	—	2	2	no	—
255	C₂²×C₈₃	—	2	4	no	—
256	C₂²×C₈₃	—	2	2	no	—
257	C₂²×C₈₃	—	4	2	no	—
258	C₂²×C₈₃	—	4	8	no	—
259	C₂²×C₈₃	—	4	2	no	—
260	C₂²×C₈₃	—	4	2	no	—
261	C₂²×C₈₃	—	4	4	no	—
262	C₂²×C₈₃	—	16	4	no	—
263	C₂²×C₈₃	#532	1	2	yes	—
264	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
265	C₄×C₈₃	—	2	2	no	—
266	C₄×C₈₃	—	2	4	no	—
267	C₄×C₈₃	—	2	2	no	—
268	C₄×C₈₃	—	2	2	no	—
269	C₄×C₈₃	—	4	4	no	—
270	C₄×C₈₃	—	4	4	no	—
271	C₄×C₈₃	—	4	2	no	—
272	C₄×C₈₃	#532	1	2	yes	—
273	C₄×C₈₃	C₂²×#41	1	2	yes	—
274	#60725	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
275	C₂×C₈₃	—	2	2	no	—
276	C₂×C₈₃	—	4	2	no	—
277	C₂×C₈₃	—	8	2	no	—
278	C₂×C₈₃	—	8	4	no	—
279	C₂×C₈₃	C₂×#532	1	1	yes	characteristic
280	C₂×C₈₃	#3585	1	2	yes	—
281	#3512	C₂×C₈₃	1	1	yes	characteristic, complemented
282	#3508	C₂×C₈₃	1	1	yes	characteristic, complemented
283	#3180	C₂×C₈₃	1	4	yes	complemented
284	#3176	C₂×C₈₃	1	4	yes	complemented
285	#3174	C₂×C₈₃	1	4	yes	complemented
286	#3171	C₂×C₈₃	1	4	yes	complemented
287	#3166	C₂×C₈₃	1	1	yes	characteristic, complemented
288	#3151	C₂×C₈₃	1	1	yes	characteristic, complemented
289	#3135	C₂×C₈₃	1	1	yes	characteristic, complemented
290	C₂×#490	C₂×C₈₃	1	1	yes	characteristic, complemented
291	#3062	C₂×C₈₃	1	4	yes	complemented
292	#2946	C₂×C₈₃	1	4	yes	complemented
293	#2875	C₂×C₈₃	1	1	yes	characteristic, complemented
294	C₈₃	#60725	1	1	yes	characteristic, direct product factor, Sylow
295	C₂×AGL(1,ℤ/8)	C₂²×C₈₃	1	4	yes	—
296	C₂×#131	C₂²×C₈₃	1	2	yes	—
297	#559	—	2	2	no	—
298	#553	—	2	4	no	—
299	#553	—	2	2	no	—
300	#552	—	2	2	no	—
301	#550	—	2	2	no	—
302	#546	—	2	4	no	—
303	#541	C₂²×C₈₃	1	2	yes	complemented
304	#540	C₂²×C₈₃	1	4	yes	—
305	#540	C₂²×C₈₃	1	2	yes	complemented
306	#537	C₂²×C₈₃	1	2	yes	—
307	#535	C₂²×C₈₃	1	2	yes	—
308	#533	C₂²×C₈₃	1	1	yes	characteristic
309	#532	C₂²×C₈₃	1	1	yes	characteristic
310	#532	C₂²×C₈₃	1	4	yes	—
311	C₂×#127	C₂²×C₈₃	1	1	yes	characteristic
312	#529	C₂²×C₈₃	1	4	yes	complemented
313	C₂×#125	C₂²×C₈₃	1	1	yes	characteristic
314	#520	C₂²×C₈₃	1	2	yes	—
315	#518	C₂²×C₈₃	1	2	yes	—
316	C₄×#41	C₂²×C₈₃	1	1	yes	characteristic
317	#501	C₂²×C₈₃	1	4	yes	complemented
318	#499	C₂²×C₈₃	1	4	yes	complemented
319	#496	C₂²×C₈₃	1	4	yes	—
320	#493	C₂²×C₈₃	1	2	yes	—
321	#492	C₂²×C₈₃	1	2	yes	—
322	#491	C₂²×C₈₃	1	2	yes	complemented
323	#490	C₂²×C₈₃	1	2	yes	—
324	#490	C₂²×C₈₃	1	4	yes	—
325	#490	C₂²×C₈₃	1	2	yes	—
326	#490	C₂²×C₈₃	1	2	yes	complemented
327	#489	C₂²×C₈₃	1	2	yes	complemented
328	#489	C₂²×C₈₃	1	2	yes	complemented
329	#469	C₂²×C₈₃	1	8	yes	complemented
330	#468	C₂²×C₈₃	1	8	yes	complemented
331	#466	C₂²×C₈₃	1	8	yes	complemented
332	#465	C₂²×C₈₃	1	8	yes	complemented
333	#442	C₂²×C₈₃	1	8	yes	complemented
334	#440	C₂²×C₈₃	1	8	yes	complemented
335	C₄×SD₁₆	C₂²×C₈₃	1	8	yes	complemented
336	C₄×D₈	C₂²×C₈₃	1	8	yes	complemented
337	#428	C₂²×C₈₃	1	4	yes	—
338	#416	C₂²×C₈₃	1	4	yes	—
339	C₂×#102	C₂²×C₈₃	1	4	yes	—
340	#405	C₂²×C₈₃	1	2	yes	—
341	#405	C₂²×C₈₃	1	4	yes	complemented
342	C₄×M₁₆	C₂²×C₈₃	1	1	yes	characteristic
343	C₄×M₁₆	C₂²×C₈₃	1	2	yes	complemented
344	C₂×#97	C₂²×C₈₃	1	1	yes	characteristic
345	C₂×#97	C₂²×C₈₃	1	2	yes	complemented
346	C₂×#41	—	2	4	no	—
347	C₂×#41	C₂³×C₈₃	1	2	yes	—
348	C₂×#41	C₂³×C₈₃	1	1	yes	characteristic
349	C₂²×D₄	—	2	2	no	—
350	C₂²×D₄	C₂³×C₈₃	1	2	yes	—
351	AGL(1,ℤ/8)	—	2	16	no	—
352	C₂×SD₁₆	C₂³×C₈₃	1	8	yes	—
353	C₂×D₈	C₂³×C₈₃	1	8	yes	—
354	#131	—	2	8	no	—
355	C₂×M₁₆	C₂³×C₈₃	1	4	yes	—
356	C₂×M₁₆	C₂³×C₈₃	1	2	yes	—
357	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
358	C₂²×C₈	C₂³×C₈₃	1	4	yes	—
359	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
360	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
361	#127	—	2	2	no	—
362	#127	—	2	2	no	—
363	#127	C₂³×C₈₃	1	2	yes	—
364	#127	C₂³×C₈₃	1	2	yes	—
365	#127	C₂³×C₈₃	1	1	yes	characteristic
366	#126	—	2	4	no	—
367	#126	—	2	4	no	—
368	#125	—	2	4	no	—
369	#125	—	2	2	no	—
370	#125	C₂³×C₈₃	1	2	yes	—
371	#125	C₂³×C₈₃	1	2	yes	—
372	#125	C₂³×C₈₃	1	2	yes	—
373	#124	—	2	2	no	—
374	#124	—	2	4	no	—
375	#124	C₂³×C₈₃	1	2	yes	—
376	#123	—	2	4	no	—
377	#123	—	2	8	no	—
378	#123	—	2	4	no	—
379	C₂²⋊Q₈	—	2	2	no	—
380	C₂²⋊Q₈	—	2	2	no	—
381	C₂²⋊Q₈	C₂³×C₈₃	1	4	yes	—
382	#121	—	2	2	no	—
383	#121	—	2	4	no	—
384	#121	—	2	4	no	—
385	#121	—	2	2	no	—
386	#121	—	2	8	no	—
387	#121	—	2	4	no	—
388	#121	C₂³×C₈₃	1	4	yes	—
389	#121	C₂³×C₈₃	1	8	yes	—
390	#120	—	2	4	no	—
391	C₄×Q₈	—	2	2	no	—
392	C₄×Q₈	D₄×C₈₃	1	2	yes	—
393	C₄×Q₈	C₂³×C₈₃	1	4	yes	—
394	C₄×D₄	—	2	4	no	—
395	C₄×D₄	—	2	4	no	—
396	C₄×D₄	—	2	4	no	—
397	C₄×D₄	—	2	4	no	—
398	C₄×D₄	—	2	2	no	—
399	C₄×D₄	D₄×C₈₃	1	4	yes	—
400	C₄×D₄	D₄×C₈₃	1	2	yes	—
401	C₄×D₄	C₂³×C₈₃	1	8	yes	—
402	C₄×D₄	C₂³×C₈₃	1	4	yes	—
403	#117	—	2	2	no	—
404	#117	—	2	4	no	—
405	#117	C₂³×C₈₃	1	2	yes	—
406	#117	C₂³×C₈₃	1	1	yes	characteristic
407	#117	C₂³×C₈₃	1	2	yes	—
408	C₂×C₄⋊C₄	—	2	2	no	—
409	C₂×C₄⋊C₄	—	2	2	no	—
410	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
411	C₂×C₂²⋊C₄	—	2	4	no	—
412	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
413	C₂×C₄²	C₂³×C₈₃	1	2	yes	—
414	#107	C₂³×C₈₃	1	8	yes	—
415	#106	C₂³×C₈₃	1	8	yes	—
416	#103	C₂³×C₈₃	1	4	yes	—
417	#103	C₂³×C₈₃	1	4	yes	—
418	#102	C₂³×C₈₃	1	8	yes	—
419	#102	C₂³×C₈₃	1	8	yes	—
420	#102	C₂³×C₈₃	1	4	yes	—
421	#102	C₂³×C₈₃	1	4	yes	—
422	#97	C₂³×C₈₃	1	1	yes	characteristic
423	#97	C₂³×C₈₃	1	1	yes	characteristic
424	#97	C₂³×C₈₃	1	2	yes	—
425	#97	C₂³×C₈₃	1	2	yes	—
426	#97	C₂³×C₈₃	1	4	yes	—
427	C₄×C₈	C₂³×C₈₃	1	2	yes	—
428	C₄×C₈	C₂³×C₈₃	1	4	yes	—
429	C₂⁴	—	2	2	no	—
430	#41	—	2	4	no	—
431	#41	—	2	8	no	—
432	#41	—	8	8	no	—
433	C₂×Q₈	—	2	2	no	—
434	C₂×Q₈	C₂×D₄×C₈₃	1	1	yes	characteristic
435	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	—	2	4	no	—
438	C₂×D₄	—	2	8	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	4	no	—
441	C₂×D₄	—	2	2	no	—
442	C₂×D₄	—	2	4	no	—
443	C₂×D₄	—	2	8	no	—
444	C₂×D₄	—	8	4	no	—
445	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
446	C₂×D₄	C₂×D₄×C₈₃	1	1	yes	characteristic
447	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
448	C₂×D₄	C₂⁴×C₈₃	1	4	yes	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	8	no	—
452	C₂²×C₄	—	2	4	no	—
453	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
454	C₂²×C₄	C₂×D₄×C₈₃	1	4	yes	—
455	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
456	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
457	SD₁₆	—	2	16	no	—
458	D₈	—	2	16	no	—
459	M₁₆	—	2	8	no	—
460	M₁₆	#41×C₈₃	1	8	yes	complemented
461	C₂×C₈	—	2	4	no	—
462	C₂×C₈	—	2	8	no	—
463	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
464	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
465	C₂×C₈	C₂⁴×C₈₃	1	4	yes	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	4	no	—
468	C₄⋊C₄	—	2	4	no	—
469	C₄⋊C₄	—	2	4	no	—
470	C₄⋊C₄	—	2	4	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	4	no	—
474	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
475	C₄⋊C₄	C₂×D₄×C₈₃	1	4	yes	—
476	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
477	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
478	C₂²⋊C₄	—	2	2	no	—
479	C₂²⋊C₄	—	2	4	no	—
480	C₂²⋊C₄	—	2	8	no	—
481	C₂²⋊C₄	—	2	2	no	—
482	C₂²⋊C₄	—	2	4	no	—
483	C₂²⋊C₄	—	2	4	no	—
484	C₂²⋊C₄	—	2	2	no	—
485	C₂²⋊C₄	—	2	8	no	—
486	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
487	C₂²⋊C₄	C₂×D₄×C₈₃	1	4	yes	—
488	C₄²	—	2	4	no	—
489	C₄²	—	2	2	no	—
490	C₄²	C₂×D₄×C₈₃	1	4	yes	—
491	C₄²	C₂×D₄×C₈₃	1	2	yes	—
492	C₄²	C₂⁴×C₈₃	1	2	yes	—
493	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
494	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
495	C₂³	—	2	2	no	—
496	C₂³	—	2	4	no	—
497	C₂³	—	4	4	no	—
498	C₂³	—	8	4	no	—
499	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
500	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
501	Q₈	—	2	2	no	—
502	Q₈	—	2	4	no	—
503	Q₈	—	4	4	no	—
504	D₄	—	2	4	no	—
505	D₄	—	2	2	no	—
506	D₄	—	2	4	no	—
507	D₄	—	2	8	no	—
508	D₄	—	4	8	no	—
509	D₄	—	4	4	no	—
510	D₄	—	4	4	no	—
511	D₄	—	8	4	no	—
512	D₄	—	8	2	no	—
513	D₄	—	8	8	no	—
514	D₄	—	8	4	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	4	no	—
521	C₂×C₄	—	4	4	no	—
522	C₂×C₄	—	8	8	no	—
523	C₂×C₄	—	8	4	no	—
524	C₂×C₄	—	8	2	no	—
525	C₂×C₄	C₂²×D₄×C₈₃	1	4	yes	—
526	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
527	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
528	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
529	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
530	C₂×C₄	C₂×#41×C₈₃	1	4	yes	—
531	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
532	C₈	—	2	2	no	—
533	C₈	—	2	2	no	—
534	C₈	C₂×#41×C₈₃	1	8	yes	—
535	C₂²	—	2	2	no	—
536	C₂²	—	2	4	no	—
537	C₂²	—	2	2	no	—
538	C₂²	—	4	2	no	—
539	C₂²	—	4	8	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	4	2	no	—
542	C₂²	—	4	4	no	—
543	C₂²	—	16	4	no	—
544	C₂²	#532×C₈₃	1	2	yes	—
545	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
546	C₄	—	2	2	no	—
547	C₄	—	2	4	no	—
548	C₄	—	2	2	no	—
549	C₄	—	2	2	no	—
550	C₄	—	4	4	no	—
551	C₄	—	4	4	no	—
552	C₄	—	4	2	no	—
553	C₄	#532×C₈₃	1	2	yes	—
554	C₄	C₂²×#41×C₈₃	1	2	yes	—
555	C₂	—	2	2	no	—
556	C₂	—	4	2	no	—
557	C₂	—	8	4	no	—
558	C₂	—	8	2	no	—
559	C₂	C₂×#532×C₈₃	1	1	yes	characteristic
560	C₂	C₈₃×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₈₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₃ ◁ C₄×#41×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₃×#3512	C₂	semidirect
2. C₈₃×#3508	C₂	semidirect
3. C₈₃×#3180	C₂	semidirect
4. C₈₃×#3176	C₂	semidirect
5. C₈₃×#3174	C₂	semidirect
6. C₈₃×#3171	C₂	semidirect
7. C₈₃×#3166	C₂	semidirect
8. C₈₃×#3151	C₂	semidirect
9. C₈₃×#3135	C₂	semidirect
10. C₂×#490×C₈₃	C₂	semidirect
11. C₈₃×#3062	C₂	semidirect
12. C₈₃×#2946	C₂	semidirect
13. C₈₃×#2875	C₂	semidirect
22. #541×C₈₃	C₂²	semidirect
24. #540×C₈₃	C₂²	semidirect
31. #529×C₈₃	C₂²	semidirect
36. #501×C₈₃	C₂²	semidirect
37. #499×C₈₃	C₂²	semidirect
41. #491×C₈₃	C₂²	semidirect
45. #490×C₈₃	C₂²	semidirect
46. #489×C₈₃	C₂²	semidirect
47. #489×C₈₃	C₂²	semidirect
48. #469×C₈₃	C₂²	semidirect
49. #468×C₈₃	C₂²	semidirect
50. #466×C₈₃	C₂²	semidirect
51. #465×C₈₃	C₂²	semidirect
52. #442×C₈₃	C₂²	semidirect
53. #440×C₈₃	C₂²	semidirect
54. C₄×SD₁₆×C₈₃	C₂²	semidirect
55. C₄×D₈×C₈₃	C₂²	semidirect
60. #405×C₈₃	C₂²	semidirect
62. C₄×M₁₆×C₈₃	C₂²	semidirect
64. C₂×#97×C₈₃	C₂²	semidirect
179. M₁₆×C₈₃	#41	semidirect
274. #60725	C₈₃	direct (N × H)
281. #3512	C₂×C₈₃	semidirect
282. #3508	C₂×C₈₃	semidirect
283. #3180	C₂×C₈₃	semidirect
284. #3176	C₂×C₈₃	semidirect
285. #3174	C₂×C₈₃	semidirect
286. #3171	C₂×C₈₃	semidirect
287. #3166	C₂×C₈₃	semidirect
288. #3151	C₂×C₈₃	semidirect
289. #3135	C₂×C₈₃	semidirect
290. C₂×#490	C₂×C₈₃	semidirect
291. #3062	C₂×C₈₃	semidirect
292. #2946	C₂×C₈₃	semidirect
293. #2875	C₂×C₈₃	semidirect
294. C₈₃	#60725	direct (N × H)
303. #541	C₂²×C₈₃	semidirect
305. #540	C₂²×C₈₃	semidirect
312. #529	C₂²×C₈₃	semidirect
317. #501	C₂²×C₈₃	semidirect
318. #499	C₂²×C₈₃	semidirect
322. #491	C₂²×C₈₃	semidirect
326. #490	C₂²×C₈₃	semidirect
327. #489	C₂²×C₈₃	semidirect
328. #489	C₂²×C₈₃	semidirect
329. #469	C₂²×C₈₃	semidirect
330. #468	C₂²×C₈₃	semidirect
331. #466	C₂²×C₈₃	semidirect
332. #465	C₂²×C₈₃	semidirect
333. #442	C₂²×C₈₃	semidirect
334. #440	C₂²×C₈₃	semidirect
335. C₄×SD₁₆	C₂²×C₈₃	semidirect
336. C₄×D₈	C₂²×C₈₃	semidirect
341. #405	C₂²×C₈₃	semidirect
343. C₄×M₁₆	C₂²×C₈₃	semidirect
345. C₂×#97	C₂²×C₈₃	semidirect
460. M₁₆	#41×C₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₈₃×#3512	2
C₈₃×#3508	2
C₈₃×#3180	2
C₈₃×#3176	2
C₈₃×#3174	2
C₈₃×#3171	2
C₈₃×#3166	2
C₈₃×#3151	2
C₈₃×#3135	2
C₂×#490×C₈₃	2
C₈₃×#3062	2
C₈₃×#2946	2
C₈₃×#2875	2
#60725	83

Subgroups — C83×#60725 #35288549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#60725 #35288549