Subgroups — C₈₃×#61260 #35289084

Order 21248.

1782 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3493	C₂	1	2	yes	maximal, complemented
2	C₈₃×#3349	C₂	1	4	yes	maximal, complemented
3	C₈₃×#3347	C₂	1	4	yes	maximal, complemented
4	C₈₃×#3340	C₂	1	4	yes	maximal, complemented
5	C₈₃×#3337	C₂	1	4	yes	maximal, complemented
6	C₈₃×#3163	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₃×#3098	C₂	1	2	yes	maximal, complemented
8	C₈₃×#3093	C₂	1	2	yes	maximal, complemented
9	C₈₃×#3083	C₂	1	2	yes	maximal, complemented
10	C₈₃×#3060	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₃×#3050	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₃×#2952	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₃×#2929	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₃×#2912	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#427×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#135×C₈₃	C₂²	1	1	yes	characteristic
17	C₂×#131×C₈₃	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₈₃	C₂²	1	1	yes	characteristic
19	#556×C₈₃	—	2	2	no	—
20	#556×C₈₃	C₂²	1	4	yes	—
21	#555×C₈₃	—	2	2	no	—
22	#555×C₈₃	C₂²	1	4	yes	—
23	#553×C₈₃	—	2	2	no	—
24	#553×C₈₃	C₂²	1	4	yes	—
25	#552×C₈₃	—	2	2	no	—
26	#552×C₈₃	C₂²	1	4	yes	—
27	#544×C₈₃	C₂²	1	2	yes	—
28	#538×C₈₃	—	2	4	no	—
29	#537×C₈₃	C₂²	1	2	yes	—
30	#529×C₈₃	—	2	4	no	—
31	#525×C₈₃	C₂²	1	2	yes	—
32	#525×C₈₃	C₂²	1	1	yes	characteristic
33	#520×C₈₃	C₂²	1	2	yes	—
34	#520×C₈₃	C₂²	1	2	yes	—
35	C₂×#117×C₈₃	C₂²	1	2	yes	—
36	#501×C₈₃	C₂²	1	4	yes	complemented
37	#499×C₈₃	C₂²	1	2	yes	complemented
38	#498×C₈₃	C₂²	1	2	yes	complemented
39	#485×C₈₃	C₂²	1	4	yes	—
40	#485×C₈₃	C₂²	1	4	yes	—
41	#485×C₈₃	C₂²	1	4	yes	complemented
42	#484×C₈₃	C₂²	1	4	yes	complemented
43	#482×C₈₃	C₂²	1	4	yes	—
44	#482×C₈₃	C₂²	1	4	yes	—
45	#482×C₈₃	C₂²	1	4	yes	complemented
46	#480×C₈₃	C₂²	1	4	yes	complemented
47	#479×C₈₃	C₂²	1	4	yes	complemented
48	#478×C₈₃	C₂²	1	4	yes	complemented
49	#477×C₈₃	C₂²	1	4	yes	complemented
50	#474×C₈₃	C₂²	1	4	yes	complemented
51	#470×C₈₃	C₂²	1	2	yes	complemented
52	#469×C₈₃	C₂²	1	2	yes	complemented
53	#467×C₈₃	C₂²	1	2	yes	—
54	#466×C₈₃	C₂²	1	2	yes	—
55	#465×C₈₃	C₂²	1	2	yes	—
56	#465×C₈₃	C₂²	1	2	yes	—
57	#465×C₈₃	C₂²	1	4	yes	complemented
58	#442×C₈₃	C₂²	1	2	yes	complemented
59	#441×C₈₃	C₂²	1	2	yes	complemented
60	C₄×SD₁₆×C₈₃	C₂²	1	4	yes	complemented
61	#435×C₈₃	C₂²	1	4	yes	—
62	C₈×D₄×C₈₃	C₂²	1	4	yes	—
63	#428×C₈₃	C₂²	1	2	yes	—
64	#428×C₈₃	C₂²	1	2	yes	—
65	#428×C₈₃	C₂²	1	4	yes	complemented
66	#427×C₈₃	C₂²	1	1	yes	characteristic
67	#427×C₈₃	C₂²	1	4	yes	—
68	#427×C₈₃	C₂²	1	4	yes	—
69	#427×C₈₃	C₂²	1	2	yes	complemented
70	C₂×#107×C₈₃	C₂²	1	2	yes	—
71	C₂×#106×C₈₃	C₂²	1	1	yes	characteristic
72	C₂×#106×C₈₃	C₂²	1	1	yes	characteristic
73	C₂×#106×C₈₃	C₂²	1	2	yes	complemented
74	#424×C₈₃	C₂²	1	1	yes	characteristic
75	#417×C₈₃	C₂²	1	2	yes	—
76	#417×C₈₃	C₂²	1	2	yes	—
77	#416×C₈₃	C₂²	1	2	yes	—
78	#408×C₈₃	C₂²	1	1	yes	characteristic
79	#407×C₈₃	C₂²	1	1	yes	characteristic
80	#405×C₈₃	C₂²	1	1	yes	characteristic
81	C₂×#41×C₈₃	C₂³	1	2	yes	—
82	C₂×#41×C₈₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₈₃	C₂³	1	1	yes	characteristic
84	#135×C₈₃	—	2	4	no	—
85	C₂×Q₁₆×C₈₃	C₂³	1	1	yes	characteristic
86	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
87	C₂×D₈×C₈₃	C₂³	1	1	yes	characteristic
88	#131×C₈₃	—	2	4	no	—
89	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
90	C₂×M₁₆×C₈₃	C₂³	1	1	yes	characteristic
91	C₂×M₁₆×C₈₃	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₈₃	—	2	4	no	—
93	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
94	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
95	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
96	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
98	C₄⋊Q₈×C₈₃	—	2	2	no	—
99	C₄⋊Q₈×C₈₃	C₂³	1	4	yes	—
100	#126×C₈₃	—	2	4	no	—
101	#126×C₈₃	—	2	4	no	—
102	#126×C₈₃	—	2	4	no	—
103	#126×C₈₃	—	2	4	no	—
104	#125×C₈₃	—	2	4	no	—
105	#125×C₈₃	—	2	2	no	—
106	#125×C₈₃	C₂³	1	4	yes	—
107	#124×C₈₃	—	2	4	no	—
108	#124×C₈₃	—	2	4	no	—
109	#124×C₈₃	—	2	4	no	—
110	#123×C₈₃	—	2	4	no	—
111	#123×C₈₃	—	2	2	no	—
112	#123×C₈₃	—	2	4	no	—
113	#123×C₈₃	D₄	1	2	yes	—
114	C₂²⋊Q₈×C₈₃	—	2	2	no	—
115	C₂²⋊Q₈×C₈₃	—	2	4	no	—
116	C₂²⋊Q₈×C₈₃	D₄	1	2	yes	—
117	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
118	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
119	C₂²⋊Q₈×C₈₃	C₂³	1	4	yes	—
120	#121×C₈₃	—	2	4	no	—
121	#121×C₈₃	—	2	2	no	—
122	#121×C₈₃	—	2	4	no	—
123	#121×C₈₃	—	2	4	no	—
124	#121×C₈₃	D₄	1	2	yes	—
125	#121×C₈₃	C₂³	1	2	yes	—
126	#121×C₈₃	C₂³	1	2	yes	—
127	#121×C₈₃	C₂³	1	4	yes	—
128	#120×C₈₃	—	2	2	no	—
129	#120×C₈₃	D₄	1	2	yes	—
130	C₄×Q₈×C₈₃	—	2	2	no	—
131	C₄×Q₈×C₈₃	—	2	4	no	—
132	C₄×Q₈×C₈₃	C₂³	1	4	yes	—
133	C₄×D₄×C₈₃	—	2	4	no	—
134	C₄×D₄×C₈₃	—	2	2	no	—
135	C₄×D₄×C₈₃	—	2	2	no	—
136	C₄×D₄×C₈₃	—	2	2	no	—
137	C₄×D₄×C₈₃	—	2	4	no	—
138	C₄×D₄×C₈₃	—	2	4	no	—
139	C₄×D₄×C₈₃	C₂³	1	4	yes	—
140	C₄×D₄×C₈₃	C₂³	1	4	yes	—
141	#117×C₈₃	—	2	2	no	—
142	#117×C₈₃	—	2	2	no	—
143	#117×C₈₃	—	2	2	no	—
144	#117×C₈₃	—	2	4	no	—
145	#117×C₈₃	—	2	4	no	—
146	#117×C₈₃	C₂³	1	4	yes	—
147	#117×C₈₃	C₂³	1	4	yes	—
148	#117×C₈₃	C₂³	1	4	yes	—
149	#117×C₈₃	C₂³	1	2	yes	—
150	#117×C₈₃	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
152	C₂×C₄⋊C₄×C₈₃	C₂³	1	4	yes	—
153	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
156	C₂×C₄²×C₈₃	—	2	2	no	—
157	#107×C₈₃	C₂³	1	2	yes	—
158	#107×C₈₃	C₂³	1	4	yes	—
159	#107×C₈₃	C₂³	1	4	yes	—
160	#107×C₈₃	C₂³	1	4	yes	—
161	#107×C₈₃	C₂³	1	4	yes	—
162	#106×C₈₃	C₂³	1	1	yes	characteristic
163	#106×C₈₃	C₂³	1	1	yes	characteristic
164	#106×C₈₃	C₂³	1	2	yes	—
165	#106×C₈₃	C₂³	1	2	yes	—
166	#106×C₈₃	C₂³	1	4	yes	—
167	#106×C₈₃	C₂³	1	4	yes	—
168	#106×C₈₃	C₂³	1	2	yes	—
169	#106×C₈₃	C₂³	1	2	yes	—
170	C₄⋊C₈×C₈₃	C₂³	1	4	yes	—
171	#103×C₈₃	C₂³	1	2	yes	—
172	#103×C₈₃	C₂³	1	2	yes	—
173	#103×C₈₃	C₂³	1	4	yes	—
174	#103×C₈₃	C₂³	1	4	yes	—
175	#102×C₈₃	C₂³	1	2	yes	—
176	#102×C₈₃	C₂³	1	2	yes	—
177	#102×C₈₃	C₂³	1	4	yes	—
178	#102×C₈₃	C₂³	1	4	yes	—
179	C₂²⋊C₈×C₈₃	C₂³	1	4	yes	—
180	C₂²⋊C₈×C₈₃	C₂³	1	4	yes	—
181	#97×C₈₃	C₂³	1	2	yes	—
182	C₄×C₈×C₈₃	C₂³	1	2	yes	—
183	C₂⁴×C₈₃	C₂×D₄	1	1	yes	characteristic
184	#41×C₈₃	—	2	2	no	—
185	#41×C₈₃	—	2	2	no	—
186	#41×C₈₃	—	2	4	no	—
187	#41×C₈₃	—	2	4	no	—
188	C₂×Q₈×C₈₃	—	2	4	no	—
189	C₂×Q₈×C₈₃	C₂×D₄	1	1	yes	characteristic
190	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
191	C₂×D₄×C₈₃	—	2	2	no	—
192	C₂×D₄×C₈₃	—	2	2	no	—
193	C₂×D₄×C₈₃	—	2	2	no	—
194	C₂×D₄×C₈₃	—	2	4	no	—
195	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
196	C₂×D₄×C₈₃	C₂×D₄	1	1	yes	characteristic
197	C₂×D₄×C₈₃	C₂×D₄	1	4	yes	—
198	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₈₃	—	2	2	no	—
200	C₂²×C₄×C₈₃	—	2	2	no	—
201	C₂²×C₄×C₈₃	—	2	2	no	—
202	C₂²×C₄×C₈₃	—	2	2	no	—
203	C₂²×C₄×C₈₃	—	2	4	no	—
204	C₂²×C₄×C₈₃	—	2	2	no	—
205	C₂²×C₄×C₈₃	—	2	4	no	—
206	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
208	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
211	Q₁₆×C₈₃	—	2	2	no	—
212	SD₁₆×C₈₃	—	2	4	no	—
213	D₈×C₈₃	—	2	2	no	—
214	M₁₆×C₈₃	—	2	2	no	—
215	M₁₆×C₈₃	—	2	2	no	—
216	M₁₆×C₈₃	—	2	4	no	—
217	C₂×C₈×C₈₃	—	2	2	no	—
218	C₂×C₈×C₈₃	—	2	4	no	—
219	C₂×C₈×C₈₃	—	2	4	no	—
220	C₂×C₈×C₈₃	—	2	4	no	—
221	C₂×C₈×C₈₃	#41	1	4	yes	—
222	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
223	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
224	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
225	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
226	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
227	C₄⋊C₄×C₈₃	—	2	2	no	—
228	C₄⋊C₄×C₈₃	—	2	4	no	—
229	C₄⋊C₄×C₈₃	—	2	2	no	—
230	C₄⋊C₄×C₈₃	—	2	4	no	—
231	C₄⋊C₄×C₈₃	—	2	2	no	—
232	C₄⋊C₄×C₈₃	—	2	4	no	—
233	C₄⋊C₄×C₈₃	—	2	4	no	—
234	C₄⋊C₄×C₈₃	—	2	2	no	—
235	C₄⋊C₄×C₈₃	—	2	4	no	—
236	C₄⋊C₄×C₈₃	—	2	4	no	—
237	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
238	C₄⋊C₄×C₈₃	C₂×D₄	1	4	yes	—
239	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
240	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
241	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
242	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
243	C₂²⋊C₄×C₈₃	—	2	4	no	—
244	C₂²⋊C₄×C₈₃	—	2	4	no	—
245	C₂²⋊C₄×C₈₃	—	2	4	no	—
246	C₂²⋊C₄×C₈₃	—	2	2	no	—
247	C₂²⋊C₄×C₈₃	—	2	4	no	—
248	C₂²⋊C₄×C₈₃	—	2	2	no	—
249	C₂²⋊C₄×C₈₃	—	2	2	no	—
250	C₂²⋊C₄×C₈₃	—	2	2	no	—
251	C₂²⋊C₄×C₈₃	—	2	4	no	—
252	C₂²⋊C₄×C₈₃	—	2	4	no	—
253	C₂²⋊C₄×C₈₃	—	2	2	no	—
254	C₂²⋊C₄×C₈₃	C₂×D₄	1	4	yes	—
255	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
256	C₂²⋊C₄×C₈₃	C₂×D₄	1	4	yes	—
257	C₄²×C₈₃	—	2	4	no	—
258	C₄²×C₈₃	—	2	4	no	—
259	C₄²×C₈₃	—	2	4	no	—
260	C₄²×C₈₃	—	2	4	no	—
261	C₄²×C₈₃	—	2	2	no	—
262	C₄²×C₈₃	C₂⁴	1	2	yes	—
263	C₂³×C₈₃	—	2	2	no	—
264	C₂³×C₈₃	—	2	2	no	—
265	C₂³×C₈₃	—	4	2	no	—
266	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
267	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
268	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
269	Q₈×C₈₃	—	2	2	no	—
270	Q₈×C₈₃	—	2	2	no	—
271	Q₈×C₈₃	—	2	2	no	—
272	Q₈×C₈₃	—	8	4	no	—
273	D₄×C₈₃	—	2	4	no	—
274	D₄×C₈₃	—	2	2	no	—
275	D₄×C₈₃	—	2	2	no	—
276	D₄×C₈₃	—	2	2	no	—
277	D₄×C₈₃	—	4	4	no	—
278	D₄×C₈₃	—	4	4	no	—
279	D₄×C₈₃	—	8	2	no	—
280	D₄×C₈₃	—	8	4	no	—
281	D₄×C₈₃	—	8	2	no	—
282	C₂×C₄×C₈₃	—	2	2	no	—
283	C₂×C₄×C₈₃	—	2	4	no	—
284	C₂×C₄×C₈₃	—	2	2	no	—
285	C₂×C₄×C₈₃	—	2	2	no	—
286	C₂×C₄×C₈₃	—	2	2	no	—
287	C₂×C₄×C₈₃	—	2	2	no	—
288	C₂×C₄×C₈₃	—	2	4	no	—
289	C₂×C₄×C₈₃	—	2	2	no	—
290	C₂×C₄×C₈₃	—	2	2	no	—
291	C₂×C₄×C₈₃	—	2	4	no	—
292	C₂×C₄×C₈₃	—	2	2	no	—
293	C₂×C₄×C₈₃	—	4	4	no	—
294	C₂×C₄×C₈₃	—	8	4	no	—
295	C₂×C₄×C₈₃	—	8	2	no	—
296	C₂×C₄×C₈₃	—	8	4	no	—
297	C₂×C₄×C₈₃	—	8	2	no	—
298	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
299	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
300	C₂×C₄×C₈₃	C₂²×D₄	1	4	yes	—
301	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
302	C₂×C₄×C₈₃	C₂×#41	1	2	yes	—
303	C₂×C₄×C₈₃	2₋¹⁺⁴	1	2	yes	—
304	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
305	C₈×C₈₃	—	2	2	no	—
306	C₈×C₈₃	—	2	2	no	—
307	C₈×C₈₃	—	2	2	no	—
308	C₈×C₈₃	C₂×#41	1	2	yes	—
309	C₈×C₈₃	C₂×#41	1	2	yes	—
310	C₂²×C₈₃	—	2	2	no	—
311	C₂²×C₈₃	—	2	4	no	—
312	C₂²×C₈₃	—	2	2	no	—
313	C₂²×C₈₃	—	2	2	no	—
314	C₂²×C₈₃	—	2	2	no	—
315	C₂²×C₈₃	—	2	2	no	—
316	C₂²×C₈₃	—	4	4	no	—
317	C₂²×C₈₃	—	4	2	no	—
318	C₂²×C₈₃	—	4	2	no	—
319	C₂²×C₈₃	—	4	2	no	—
320	C₂²×C₈₃	#547	1	2	yes	—
321	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
322	C₄×C₈₃	—	2	4	no	—
323	C₄×C₈₃	—	2	2	no	—
324	C₄×C₈₃	—	2	2	no	—
325	C₄×C₈₃	—	4	4	no	—
326	C₄×C₈₃	—	4	2	no	—
327	C₄×C₈₃	—	4	4	no	—
328	C₄×C₈₃	—	4	2	no	—
329	C₄×C₈₃	—	4	2	no	—
330	C₄×C₈₃	#547	1	2	yes	—
331	C₄×C₈₃	C₂²×#41	1	1	yes	characteristic
332	C₄×C₈₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
333	#61260	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
334	C₂×C₈₃	—	2	2	no	—
335	C₂×C₈₃	—	4	2	no	—
336	C₂×C₈₃	—	4	2	no	—
337	C₂×C₈₃	—	8	2	no	—
338	C₂×C₈₃	C₂×#547	1	1	yes	characteristic
339	C₂×C₈₃	#3584	1	2	yes	—
340	#3493	C₂×C₈₃	1	2	yes	complemented
341	#3349	C₂×C₈₃	1	4	yes	complemented
342	#3347	C₂×C₈₃	1	4	yes	complemented
343	#3340	C₂×C₈₃	1	4	yes	complemented
344	#3337	C₂×C₈₃	1	4	yes	complemented
345	#3163	C₂×C₈₃	1	1	yes	characteristic, complemented
346	#3098	C₂×C₈₃	1	2	yes	complemented
347	#3093	C₂×C₈₃	1	2	yes	complemented
348	#3083	C₂×C₈₃	1	2	yes	complemented
349	#3060	C₂×C₈₃	1	1	yes	characteristic, complemented
350	#3050	C₂×C₈₃	1	1	yes	characteristic, complemented
351	#2952	C₂×C₈₃	1	1	yes	characteristic, complemented
352	#2929	C₂×C₈₃	1	1	yes	characteristic, complemented
353	#2912	C₂×C₈₃	1	1	yes	characteristic, complemented
354	C₂×#427	C₂×C₈₃	1	1	yes	characteristic, complemented
355	C₈₃	#61260	1	1	yes	characteristic, direct product factor, Sylow
356	C₂×#135	C₂²×C₈₃	1	1	yes	characteristic
357	C₂×#131	C₂²×C₈₃	1	1	yes	characteristic
358	C₂³×C₈	C₂²×C₈₃	1	1	yes	characteristic
359	#556	—	2	2	no	—
360	#556	C₂²×C₈₃	1	4	yes	—
361	#555	—	2	2	no	—
362	#555	C₂²×C₈₃	1	4	yes	—
363	#553	—	2	2	no	—
364	#553	C₂²×C₈₃	1	4	yes	—
365	#552	—	2	2	no	—
366	#552	C₂²×C₈₃	1	4	yes	—
367	#544	C₂²×C₈₃	1	2	yes	—
368	#538	—	2	4	no	—
369	#537	C₂²×C₈₃	1	2	yes	—
370	#529	—	2	4	no	—
371	#525	C₂²×C₈₃	1	2	yes	—
372	#525	C₂²×C₈₃	1	1	yes	characteristic
373	#520	C₂²×C₈₃	1	2	yes	—
374	#520	C₂²×C₈₃	1	2	yes	—
375	C₂×#117	C₂²×C₈₃	1	2	yes	—
376	#501	C₂²×C₈₃	1	4	yes	complemented
377	#499	C₂²×C₈₃	1	2	yes	complemented
378	#498	C₂²×C₈₃	1	2	yes	complemented
379	#485	C₂²×C₈₃	1	4	yes	—
380	#485	C₂²×C₈₃	1	4	yes	—
381	#485	C₂²×C₈₃	1	4	yes	complemented
382	#484	C₂²×C₈₃	1	4	yes	complemented
383	#482	C₂²×C₈₃	1	4	yes	—
384	#482	C₂²×C₈₃	1	4	yes	—
385	#482	C₂²×C₈₃	1	4	yes	complemented
386	#480	C₂²×C₈₃	1	4	yes	complemented
387	#479	C₂²×C₈₃	1	4	yes	complemented
388	#478	C₂²×C₈₃	1	4	yes	complemented
389	#477	C₂²×C₈₃	1	4	yes	complemented
390	#474	C₂²×C₈₃	1	4	yes	complemented
391	#470	C₂²×C₈₃	1	2	yes	complemented
392	#469	C₂²×C₈₃	1	2	yes	complemented
393	#467	C₂²×C₈₃	1	2	yes	—
394	#466	C₂²×C₈₃	1	2	yes	—
395	#465	C₂²×C₈₃	1	2	yes	—
396	#465	C₂²×C₈₃	1	2	yes	—
397	#465	C₂²×C₈₃	1	4	yes	complemented
398	#442	C₂²×C₈₃	1	2	yes	complemented
399	#441	C₂²×C₈₃	1	2	yes	complemented
400	C₄×SD₁₆	C₂²×C₈₃	1	4	yes	complemented
401	#435	C₂²×C₈₃	1	4	yes	—
402	C₈×D₄	C₂²×C₈₃	1	4	yes	—
403	#428	C₂²×C₈₃	1	2	yes	—
404	#428	C₂²×C₈₃	1	2	yes	—
405	#428	C₂²×C₈₃	1	4	yes	complemented
406	#427	C₂²×C₈₃	1	4	yes	—
407	#427	C₂²×C₈₃	1	4	yes	—
408	#427	C₂²×C₈₃	1	1	yes	characteristic
409	#427	C₂²×C₈₃	1	2	yes	complemented
410	C₂×#107	C₂²×C₈₃	1	2	yes	—
411	C₂×#106	C₂²×C₈₃	1	1	yes	characteristic
412	C₂×#106	C₂²×C₈₃	1	1	yes	characteristic
413	C₂×#106	C₂²×C₈₃	1	2	yes	complemented
414	#424	C₂²×C₈₃	1	1	yes	characteristic
415	#417	C₂²×C₈₃	1	2	yes	—
416	#417	C₂²×C₈₃	1	2	yes	—
417	#416	C₂²×C₈₃	1	2	yes	—
418	#408	C₂²×C₈₃	1	1	yes	characteristic
419	#407	C₂²×C₈₃	1	1	yes	characteristic
420	#405	C₂²×C₈₃	1	1	yes	characteristic
421	C₂×#41	C₂³×C₈₃	1	2	yes	—
422	C₂×#41	C₂³×C₈₃	1	1	yes	characteristic
423	C₂³×C₄	C₂³×C₈₃	1	1	yes	characteristic
424	#135	—	2	4	no	—
425	C₂×Q₁₆	C₂³×C₈₃	1	1	yes	characteristic
426	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
427	C₂×D₈	C₂³×C₈₃	1	1	yes	characteristic
428	#131	—	2	4	no	—
429	C₂×M₁₆	C₂³×C₈₃	1	1	yes	characteristic
430	C₂×M₁₆	C₂³×C₈₃	1	2	yes	—
431	C₂×M₁₆	C₂³×C₈₃	1	1	yes	characteristic
432	C₂²×C₈	—	2	4	no	—
433	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
434	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
435	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
436	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
437	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
438	C₄⋊Q₈	—	2	2	no	—
439	C₄⋊Q₈	C₂³×C₈₃	1	4	yes	—
440	#126	—	2	4	no	—
441	#126	—	2	4	no	—
442	#126	—	2	4	no	—
443	#126	—	2	4	no	—
444	#125	—	2	4	no	—
445	#125	—	2	2	no	—
446	#125	C₂³×C₈₃	1	4	yes	—
447	#124	—	2	4	no	—
448	#124	—	2	4	no	—
449	#124	—	2	4	no	—
450	#123	—	2	4	no	—
451	#123	—	2	2	no	—
452	#123	—	2	4	no	—
453	#123	D₄×C₈₃	1	2	yes	—
454	C₂²⋊Q₈	—	2	2	no	—
455	C₂²⋊Q₈	—	2	4	no	—
456	C₂²⋊Q₈	D₄×C₈₃	1	2	yes	—
457	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
458	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
459	C₂²⋊Q₈	C₂³×C₈₃	1	4	yes	—
460	#121	—	2	4	no	—
461	#121	—	2	2	no	—
462	#121	—	2	4	no	—
463	#121	—	2	4	no	—
464	#121	D₄×C₈₃	1	2	yes	—
465	#121	C₂³×C₈₃	1	2	yes	—
466	#121	C₂³×C₈₃	1	2	yes	—
467	#121	C₂³×C₈₃	1	4	yes	—
468	#120	—	2	2	no	—
469	#120	D₄×C₈₃	1	2	yes	—
470	C₄×Q₈	—	2	2	no	—
471	C₄×Q₈	—	2	4	no	—
472	C₄×Q₈	C₂³×C₈₃	1	4	yes	—
473	C₄×D₄	—	2	4	no	—
474	C₄×D₄	—	2	2	no	—
475	C₄×D₄	—	2	2	no	—
476	C₄×D₄	—	2	2	no	—
477	C₄×D₄	—	2	4	no	—
478	C₄×D₄	—	2	4	no	—
479	C₄×D₄	C₂³×C₈₃	1	4	yes	—
480	C₄×D₄	C₂³×C₈₃	1	4	yes	—
481	#117	—	2	2	no	—
482	#117	—	2	2	no	—
483	#117	—	2	2	no	—
484	#117	—	2	4	no	—
485	#117	—	2	4	no	—
486	#117	C₂³×C₈₃	1	4	yes	—
487	#117	C₂³×C₈₃	1	4	yes	—
488	#117	C₂³×C₈₃	1	2	yes	—
489	#117	C₂³×C₈₃	1	4	yes	—
490	#117	C₂³×C₈₃	1	1	yes	characteristic
491	C₂×C₄⋊C₄	—	2	2	no	—
492	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
493	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₈₃	1	4	yes	—
495	C₂×C₂²⋊C₄	—	2	2	no	—
496	C₂×C₄²	—	2	2	no	—
497	#107	C₂³×C₈₃	1	4	yes	—
498	#107	C₂³×C₈₃	1	4	yes	—
499	#107	C₂³×C₈₃	1	2	yes	—
500	#107	C₂³×C₈₃	1	4	yes	—
501	#107	C₂³×C₈₃	1	4	yes	—
502	#106	C₂³×C₈₃	1	2	yes	—
503	#106	C₂³×C₈₃	1	2	yes	—
504	#106	C₂³×C₈₃	1	2	yes	—
505	#106	C₂³×C₈₃	1	2	yes	—
506	#106	C₂³×C₈₃	1	1	yes	characteristic
507	#106	C₂³×C₈₃	1	4	yes	—
508	#106	C₂³×C₈₃	1	1	yes	characteristic
509	#106	C₂³×C₈₃	1	4	yes	—
510	C₄⋊C₈	C₂³×C₈₃	1	4	yes	—
511	#103	C₂³×C₈₃	1	2	yes	—
512	#103	C₂³×C₈₃	1	2	yes	—
513	#103	C₂³×C₈₃	1	4	yes	—
514	#103	C₂³×C₈₃	1	4	yes	—
515	#102	C₂³×C₈₃	1	2	yes	—
516	#102	C₂³×C₈₃	1	2	yes	—
517	#102	C₂³×C₈₃	1	4	yes	—
518	#102	C₂³×C₈₃	1	4	yes	—
519	C₂²⋊C₈	C₂³×C₈₃	1	4	yes	—
520	C₂²⋊C₈	C₂³×C₈₃	1	4	yes	—
521	#97	C₂³×C₈₃	1	2	yes	—
522	C₄×C₈	C₂³×C₈₃	1	2	yes	—
523	C₂⁴	C₂×D₄×C₈₃	1	1	yes	characteristic
524	#41	—	2	2	no	—
525	#41	—	2	2	no	—
526	#41	—	2	4	no	—
527	#41	—	2	4	no	—
528	C₂×Q₈	—	2	4	no	—
529	C₂×Q₈	C₂×D₄×C₈₃	1	1	yes	characteristic
530	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
531	C₂×D₄	—	2	2	no	—
532	C₂×D₄	—	2	2	no	—
533	C₂×D₄	—	2	2	no	—
534	C₂×D₄	—	2	4	no	—
535	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
536	C₂×D₄	C₂×D₄×C₈₃	1	1	yes	characteristic
537	C₂×D₄	C₂×D₄×C₈₃	1	4	yes	—
538	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
539	C₂²×C₄	—	2	2	no	—
540	C₂²×C₄	—	2	2	no	—
541	C₂²×C₄	—	2	2	no	—
542	C₂²×C₄	—	2	2	no	—
543	C₂²×C₄	—	2	4	no	—
544	C₂²×C₄	—	2	2	no	—
545	C₂²×C₄	—	2	4	no	—
546	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
547	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
548	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
550	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
551	Q₁₆	—	2	2	no	—
552	SD₁₆	—	2	4	no	—
553	D₈	—	2	2	no	—
554	M₁₆	—	2	2	no	—
555	M₁₆	—	2	2	no	—
556	M₁₆	—	2	4	no	—
557	C₂×C₈	—	2	2	no	—
558	C₂×C₈	—	2	4	no	—
559	C₂×C₈	—	2	4	no	—
560	C₂×C₈	—	2	4	no	—
561	C₂×C₈	#41×C₈₃	1	4	yes	—
562	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
563	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
564	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
565	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
566	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
567	C₄⋊C₄	—	2	2	no	—
568	C₄⋊C₄	—	2	4	no	—
569	C₄⋊C₄	—	2	2	no	—
570	C₄⋊C₄	—	2	4	no	—
571	C₄⋊C₄	—	2	2	no	—
572	C₄⋊C₄	—	2	4	no	—
573	C₄⋊C₄	—	2	4	no	—
574	C₄⋊C₄	—	2	2	no	—
575	C₄⋊C₄	—	2	4	no	—
576	C₄⋊C₄	—	2	4	no	—
577	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
578	C₄⋊C₄	C₂×D₄×C₈₃	1	4	yes	—
579	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
580	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
581	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
582	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
583	C₂²⋊C₄	—	2	4	no	—
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	—	2	4	no	—
586	C₂²⋊C₄	—	2	2	no	—
587	C₂²⋊C₄	—	2	4	no	—
588	C₂²⋊C₄	—	2	2	no	—
589	C₂²⋊C₄	—	2	2	no	—
590	C₂²⋊C₄	—	2	2	no	—
591	C₂²⋊C₄	—	2	4	no	—
592	C₂²⋊C₄	—	2	4	no	—
593	C₂²⋊C₄	—	2	2	no	—
594	C₂²⋊C₄	C₂×D₄×C₈₃	1	4	yes	—
595	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
596	C₂²⋊C₄	C₂×D₄×C₈₃	1	4	yes	—
597	C₄²	—	2	4	no	—
598	C₄²	—	2	4	no	—
599	C₄²	—	2	4	no	—
600	C₄²	—	2	4	no	—
601	C₄²	—	2	2	no	—
602	C₄²	C₂⁴×C₈₃	1	2	yes	—
603	C₂³	—	2	2	no	—
604	C₂³	—	2	2	no	—
605	C₂³	—	4	2	no	—
606	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
607	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
608	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
609	Q₈	—	2	2	no	—
610	Q₈	—	2	2	no	—
611	Q₈	—	2	2	no	—
612	Q₈	—	8	4	no	—
613	D₄	—	2	4	no	—
614	D₄	—	2	2	no	—
615	D₄	—	2	2	no	—
616	D₄	—	2	2	no	—
617	D₄	—	4	4	no	—
618	D₄	—	4	4	no	—
619	D₄	—	8	2	no	—
620	D₄	—	8	4	no	—
621	D₄	—	8	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	4	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	4	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	4	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	4	4	no	—
634	C₂×C₄	—	8	4	no	—
635	C₂×C₄	—	8	2	no	—
636	C₂×C₄	—	8	4	no	—
637	C₂×C₄	—	8	2	no	—
638	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
639	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
640	C₂×C₄	C₂²×D₄×C₈₃	1	4	yes	—
641	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
642	C₂×C₄	C₂×#41×C₈₃	1	2	yes	—
643	C₂×C₄	2₋¹⁺⁴×C₈₃	1	2	yes	—
644	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
645	C₈	—	2	2	no	—
646	C₈	—	2	2	no	—
647	C₈	—	2	2	no	—
648	C₈	C₂×#41×C₈₃	1	2	yes	—
649	C₈	C₂×#41×C₈₃	1	2	yes	—
650	C₂²	—	2	2	no	—
651	C₂²	—	2	4	no	—
652	C₂²	—	2	2	no	—
653	C₂²	—	2	2	no	—
654	C₂²	—	2	2	no	—
655	C₂²	—	2	2	no	—
656	C₂²	—	4	4	no	—
657	C₂²	—	4	2	no	—
658	C₂²	—	4	2	no	—
659	C₂²	—	4	2	no	—
660	C₂²	#547×C₈₃	1	2	yes	—
661	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
662	C₄	—	2	4	no	—
663	C₄	—	2	2	no	—
664	C₄	—	2	2	no	—
665	C₄	—	4	4	no	—
666	C₄	—	4	2	no	—
667	C₄	—	4	4	no	—
668	C₄	—	4	2	no	—
669	C₄	—	4	2	no	—
670	C₄	#547×C₈₃	1	2	yes	—
671	C₄	C₂²×#41×C₈₃	1	1	yes	characteristic
672	C₄	C₂×2₋¹⁺⁴×C₈₃	1	1	yes	characteristic
673	C₂	—	2	2	no	—
674	C₂	—	4	2	no	—
675	C₂	—	4	2	no	—
676	C₂	—	8	2	no	—
677	C₂	C₂×#547×C₈₃	1	1	yes	characteristic
678	C₂	C₈₃×#3584	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 ◁ #525×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₃×#3493	C₂	semidirect
2. C₈₃×#3349	C₂	semidirect
3. C₈₃×#3347	C₂	semidirect
4. C₈₃×#3340	C₂	semidirect
5. C₈₃×#3337	C₂	semidirect
6. C₈₃×#3163	C₂	semidirect
7. C₈₃×#3098	C₂	semidirect
8. C₈₃×#3093	C₂	semidirect
9. C₈₃×#3083	C₂	semidirect
10. C₈₃×#3060	C₂	semidirect
11. C₈₃×#3050	C₂	semidirect
12. C₈₃×#2952	C₂	semidirect
13. C₈₃×#2929	C₂	semidirect
14. C₈₃×#2912	C₂	semidirect
15. C₂×#427×C₈₃	C₂	semidirect
36. #501×C₈₃	C₂²	semidirect
37. #499×C₈₃	C₂²	semidirect
38. #498×C₈₃	C₂²	semidirect
41. #485×C₈₃	C₂²	semidirect
42. #484×C₈₃	C₂²	semidirect
45. #482×C₈₃	C₂²	semidirect
46. #480×C₈₃	C₂²	semidirect
47. #479×C₈₃	C₂²	semidirect
48. #478×C₈₃	C₂²	semidirect
49. #477×C₈₃	C₂²	semidirect
50. #474×C₈₃	C₂²	semidirect
51. #470×C₈₃	C₂²	semidirect
52. #469×C₈₃	C₂²	semidirect
57. #465×C₈₃	C₂²	semidirect
58. #442×C₈₃	C₂²	semidirect
59. #441×C₈₃	C₂²	semidirect
60. C₄×SD₁₆×C₈₃	C₂²	semidirect
65. #428×C₈₃	C₂²	semidirect
69. #427×C₈₃	C₂²	semidirect
73. C₂×#106×C₈₃	C₂²	semidirect
333. #61260	C₈₃	direct (N × H)
340. #3493	C₂×C₈₃	semidirect
341. #3349	C₂×C₈₃	semidirect
342. #3347	C₂×C₈₃	semidirect
343. #3340	C₂×C₈₃	semidirect
344. #3337	C₂×C₈₃	semidirect
345. #3163	C₂×C₈₃	semidirect
346. #3098	C₂×C₈₃	semidirect
347. #3093	C₂×C₈₃	semidirect
348. #3083	C₂×C₈₃	semidirect
349. #3060	C₂×C₈₃	semidirect
350. #3050	C₂×C₈₃	semidirect
351. #2952	C₂×C₈₃	semidirect
352. #2929	C₂×C₈₃	semidirect
353. #2912	C₂×C₈₃	semidirect
354. C₂×#427	C₂×C₈₃	semidirect
355. C₈₃	#61260	direct (N × H)
376. #501	C₂²×C₈₃	semidirect
377. #499	C₂²×C₈₃	semidirect
378. #498	C₂²×C₈₃	semidirect
381. #485	C₂²×C₈₃	semidirect
382. #484	C₂²×C₈₃	semidirect
385. #482	C₂²×C₈₃	semidirect
386. #480	C₂²×C₈₃	semidirect
387. #479	C₂²×C₈₃	semidirect
388. #478	C₂²×C₈₃	semidirect
389. #477	C₂²×C₈₃	semidirect
390. #474	C₂²×C₈₃	semidirect
391. #470	C₂²×C₈₃	semidirect
392. #469	C₂²×C₈₃	semidirect
397. #465	C₂²×C₈₃	semidirect
398. #442	C₂²×C₈₃	semidirect
399. #441	C₂²×C₈₃	semidirect
400. C₄×SD₁₆	C₂²×C₈₃	semidirect
405. #428	C₂²×C₈₃	semidirect
409. #427	C₂²×C₈₃	semidirect
413. C₂×#106	C₂²×C₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₈₃×#3493	2
C₈₃×#3349	2
C₈₃×#3347	2
C₈₃×#3340	2
C₈₃×#3337	2
C₈₃×#3163	2
C₈₃×#3098	2
C₈₃×#3093	2
C₈₃×#3083	2
C₈₃×#3060	2
C₈₃×#3050	2
C₈₃×#2952	2
C₈₃×#2929	2
C₈₃×#2912	2
C₂×#427×C₈₃	2
#61260	83

Subgroups — C83×#61260 #35289084

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#61260 #35289084