Subgroups — C₈₃×#60882 #35288706

Order 21248.

1650 conjugacy classes of subgroups.

The subgroup lattice has 632 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
2	C₈₃×#3504	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₃×#3242	C₂	1	4	yes	maximal, complemented
4	C₈₃×#3241	C₂	1	4	yes	maximal, complemented
5	C₈₃×#3233	C₂	1	4	yes	maximal, complemented
6	C₈₃×#3232	C₂	1	4	yes	maximal, complemented
7	C₈₃×#3166	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#499×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₃×#3142	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₃×#3131	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₃×#3099	C₂	1	2	yes	maximal, complemented
12	C₈₃×#3098	C₂	1	2	yes	maximal, complemented
13	C₈₃×#3084	C₂	1	2	yes	maximal, complemented
14	C₈₃×#3083	C₂	1	2	yes	maximal, complemented
15	C₈₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
16	#557×C₈₃	—	2	2	no	—
17	#554×C₈₃	—	2	4	no	—
18	#554×C₈₃	—	2	2	no	—
19	#553×C₈₃	—	2	4	no	—
20	#553×C₈₃	—	2	2	no	—
21	#552×C₈₃	—	2	2	no	—
22	#544×C₈₃	C₂²	1	2	yes	—
23	#544×C₈₃	C₂²	1	4	yes	—
24	#541×C₈₃	C₂²	1	2	yes	—
25	#540×C₈₃	C₂²	1	2	yes	—
26	#537×C₈₃	C₂²	1	2	yes	—
27	#533×C₈₃	C₂²	1	1	yes	characteristic
28	#533×C₈₃	C₂²	1	2	yes	—
29	#532×C₈₃	C₂²	1	1	yes	characteristic
30	#529×C₈₃	C₂²	1	4	yes	—
31	C₂×#125×C₈₃	C₂²	1	1	yes	characteristic
32	C₂×#125×C₈₃	C₂²	1	1	yes	characteristic
33	C₂×#125×C₈₃	C₂²	1	2	yes	—
34	#520×C₈₃	C₂²	1	2	yes	—
35	#520×C₈₃	C₂²	1	2	yes	—
36	C₄×#41×C₈₃	C₂²	1	1	yes	characteristic
37	#501×C₈₃	C₂²	1	4	yes	—
38	#499×C₈₃	C₂²	1	4	yes	—
39	#499×C₈₃	C₂²	1	4	yes	—
40	#499×C₈₃	C₂²	1	2	yes	—
41	#499×C₈₃	C₂²	1	2	yes	—
42	#491×C₈₃	C₂²	1	2	yes	—
43	#490×C₈₃	C₂²	1	2	yes	—
44	#488×C₈₃	C₂²	1	2	yes	—
45	#488×C₈₃	C₂²	1	2	yes	—
46	#488×C₈₃	C₂²	1	4	yes	—
47	#487×C₈₃	C₂²	1	2	yes	—
48	#486×C₈₃	C₂²	1	2	yes	—
49	#485×C₈₃	C₂²	1	4	yes	—
50	#485×C₈₃	C₂²	1	4	yes	—
51	#484×C₈₃	C₂²	1	4	yes	—
52	#483×C₈₃	C₂²	1	4	yes	—
53	#482×C₈₃	C₂²	1	4	yes	—
54	#482×C₈₃	C₂²	1	4	yes	—
55	#481×C₈₃	C₂²	1	4	yes	—
56	#480×C₈₃	C₂²	1	4	yes	—
57	#479×C₈₃	C₂²	1	4	yes	—
58	#479×C₈₃	C₂²	1	4	yes	—
59	#478×C₈₃	C₂²	1	4	yes	—
60	#478×C₈₃	C₂²	1	4	yes	—
61	#477×C₈₃	C₂²	1	4	yes	—
62	#476×C₈₃	C₂²	1	4	yes	—
63	#475×C₈₃	C₂²	1	4	yes	—
64	#474×C₈₃	C₂²	1	4	yes	—
65	#433×C₈₃	C₂²	1	4	yes	—
66	#431×C₈₃	C₂²	1	4	yes	—
67	#428×C₈₃	C₂²	1	2	yes	—
68	#428×C₈₃	C₂²	1	2	yes	—
69	C₂×#107×C₈₃	C₂²	1	2	yes	—
70	C₂×#106×C₈₃	C₂²	1	2	yes	—
71	#424×C₈₃	C₂²	1	1	yes	characteristic
72	#424×C₈₃	C₂²	1	1	yes	characteristic
73	#417×C₈₃	C₂²	1	2	yes	—
74	#417×C₈₃	C₂²	1	2	yes	—
75	#416×C₈₃	C₂²	1	2	yes	—
76	#416×C₈₃	C₂²	1	2	yes	—
77	#408×C₈₃	C₂²	1	1	yes	characteristic
78	#408×C₈₃	C₂²	1	1	yes	characteristic
79	C₄×M₁₆×C₈₃	C₂²	1	1	yes	characteristic
80	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
81	C₂×#41×C₈₃	C₂³	1	2	yes	—
82	C₂×#41×C₈₃	C₂³	1	1	yes	characteristic
83	C₂×M₁₆×C₈₃	C₂³	1	1	yes	characteristic
84	C₂×M₁₆×C₈₃	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
87	C₄⋊Q₈×C₈₃	—	2	2	no	—
88	C₄⋊Q₈×C₈₃	—	2	4	no	—
89	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
90	C₄⋊Q₈×C₈₃	C₂³	1	4	yes	—
91	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
92	#127×C₈₃	C₂³	1	1	yes	characteristic
93	#126×C₈₃	—	2	4	no	—
94	#126×C₈₃	—	2	4	no	—
95	#125×C₈₃	—	2	4	no	—
96	#125×C₈₃	—	2	2	no	—
97	#125×C₈₃	—	2	4	no	—
98	#125×C₈₃	—	2	2	no	—
99	#125×C₈₃	—	2	4	no	—
100	#125×C₈₃	—	2	2	no	—
101	#125×C₈₃	C₂³	1	4	yes	—
102	#125×C₈₃	C₂³	1	1	yes	characteristic
103	#125×C₈₃	C₂³	1	2	yes	—
104	#125×C₈₃	C₂³	1	1	yes	characteristic
105	#125×C₈₃	C₂³	1	2	yes	—
106	#125×C₈₃	C₂³	1	2	yes	—
107	#125×C₈₃	C₂³	1	2	yes	—
108	#124×C₈₃	C₂³	1	2	yes	—
109	#123×C₈₃	—	2	4	no	—
110	#123×C₈₃	—	2	4	no	—
111	C₂²⋊Q₈×C₈₃	—	2	2	no	—
112	C₂²⋊Q₈×C₈₃	—	2	2	no	—
113	C₂²⋊Q₈×C₈₃	—	2	4	no	—
114	C₂²⋊Q₈×C₈₃	—	2	4	no	—
115	C₂²⋊Q₈×C₈₃	—	2	4	no	—
116	C₂²⋊Q₈×C₈₃	—	2	4	no	—
117	C₂²⋊Q₈×C₈₃	C₂³	1	4	yes	—
118	#121×C₈₃	—	2	2	no	—
119	#121×C₈₃	—	2	4	no	—
120	#121×C₈₃	—	2	2	no	—
121	#121×C₈₃	—	2	4	no	—
122	#121×C₈₃	C₂³	1	4	yes	—
123	C₄×Q₈×C₈₃	—	2	2	no	—
124	C₄×Q₈×C₈₃	—	2	4	no	—
125	C₄×Q₈×C₈₃	—	2	2	no	—
126	C₄×Q₈×C₈₃	D₄	1	2	yes	—
127	C₄×Q₈×C₈₃	C₂³	1	4	yes	—
128	C₄×D₄×C₈₃	—	2	4	no	—
129	C₄×D₄×C₈₃	—	2	2	no	—
130	C₄×D₄×C₈₃	—	2	4	no	—
131	C₄×D₄×C₈₃	—	2	4	no	—
132	C₄×D₄×C₈₃	—	2	2	no	—
133	C₄×D₄×C₈₃	D₄	1	4	yes	—
134	C₄×D₄×C₈₃	D₄	1	2	yes	—
135	C₄×D₄×C₈₃	C₂³	1	4	yes	—
136	#117×C₈₃	—	2	2	no	—
137	#117×C₈₃	—	2	4	no	—
138	#117×C₈₃	C₂³	1	4	yes	—
139	#117×C₈₃	C₂³	1	2	yes	—
140	#117×C₈₃	C₂³	1	1	yes	characteristic
141	#117×C₈₃	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
143	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
144	C₂×C₄⋊C₄×C₈₃	—	2	4	no	—
145	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
146	C₂×C₄⋊C₄×C₈₃	C₂³	1	4	yes	—
147	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
149	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₈₃	C₂³	1	2	yes	—
151	#107×C₈₃	C₂³	1	4	yes	—
152	#107×C₈₃	C₂³	1	4	yes	—
153	#107×C₈₃	C₂³	1	4	yes	—
154	#107×C₈₃	C₂³	1	4	yes	—
155	#106×C₈₃	C₂³	1	4	yes	—
156	#106×C₈₃	C₂³	1	4	yes	—
157	#106×C₈₃	C₂³	1	4	yes	—
158	#106×C₈₃	C₂³	1	4	yes	—
159	C₄⋊C₈×C₈₃	C₂³	1	4	yes	—
160	C₄⋊C₈×C₈₃	C₂³	1	4	yes	—
161	#103×C₈₃	C₂³	1	2	yes	—
162	#103×C₈₃	C₂³	1	4	yes	—
163	#103×C₈₃	C₂³	1	2	yes	—
164	#103×C₈₃	C₂³	1	4	yes	—
165	#103×C₈₃	C₂³	1	2	yes	—
166	#103×C₈₃	C₂³	1	2	yes	—
167	#102×C₈₃	C₂³	1	2	yes	—
168	#102×C₈₃	C₂³	1	4	yes	—
169	#102×C₈₃	C₂³	1	2	yes	—
170	#102×C₈₃	C₂³	1	4	yes	—
171	#102×C₈₃	C₂³	1	2	yes	—
172	#102×C₈₃	C₂³	1	2	yes	—
173	C₂²⋊C₈×C₈₃	C₂³	1	4	yes	—
174	C₂²⋊C₈×C₈₃	C₂³	1	4	yes	—
175	#97×C₈₃	C₂³	1	2	yes	—
176	C₄×C₈×C₈₃	C₂³	1	2	yes	—
177	C₄×C₈×C₈₃	C₂³	1	2	yes	—
178	C₄×C₈×C₈₃	C₂³	1	2	yes	—
179	#41×C₈₃	—	2	2	no	—
180	#41×C₈₃	—	2	2	no	—
181	#41×C₈₃	—	2	4	no	—
182	#41×C₈₃	—	2	4	no	—
183	C₂×Q₈×C₈₃	—	2	4	no	—
184	C₂×Q₈×C₈₃	—	2	2	no	—
185	C₂×Q₈×C₈₃	C₂×D₄	1	1	yes	characteristic
186	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
187	C₂×D₄×C₈₃	—	2	2	no	—
188	C₂×D₄×C₈₃	—	2	4	no	—
189	C₂×D₄×C₈₃	—	2	2	no	—
190	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
191	C₂×D₄×C₈₃	C₂×D₄	1	1	yes	characteristic
192	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₈₃	—	2	2	no	—
194	C₂²×C₄×C₈₃	—	2	4	no	—
195	C₂²×C₄×C₈₃	—	2	2	no	—
196	C₂²×C₄×C₈₃	—	2	2	no	—
197	C₂²×C₄×C₈₃	—	2	4	no	—
198	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
199	C₂²×C₄×C₈₃	C₂×D₄	1	4	yes	—
200	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
202	M₁₆×C₈₃	—	2	2	no	—
203	M₁₆×C₈₃	—	2	2	no	—
204	C₂×C₈×C₈₃	—	2	2	no	—
205	C₂×C₈×C₈₃	—	2	2	no	—
206	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
207	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
208	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
209	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
210	C₄⋊C₄×C₈₃	—	2	4	no	—
211	C₄⋊C₄×C₈₃	—	2	2	no	—
212	C₄⋊C₄×C₈₃	—	2	2	no	—
213	C₄⋊C₄×C₈₃	—	2	4	no	—
214	C₄⋊C₄×C₈₃	—	2	4	no	—
215	C₄⋊C₄×C₈₃	—	2	4	no	—
216	C₄⋊C₄×C₈₃	—	2	4	no	—
217	C₄⋊C₄×C₈₃	—	2	4	no	—
218	C₄⋊C₄×C₈₃	—	2	4	no	—
219	C₄⋊C₄×C₈₃	—	2	4	no	—
220	C₄⋊C₄×C₈₃	—	2	2	no	—
221	C₄⋊C₄×C₈₃	—	2	4	no	—
222	C₄⋊C₄×C₈₃	—	2	2	no	—
223	C₄⋊C₄×C₈₃	—	2	2	no	—
224	C₄⋊C₄×C₈₃	—	2	4	no	—
225	C₄⋊C₄×C₈₃	—	2	2	no	—
226	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
227	C₄⋊C₄×C₈₃	C₂×D₄	1	4	yes	—
228	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
229	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
230	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
231	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
232	C₂²⋊C₄×C₈₃	—	2	4	no	—
233	C₂²⋊C₄×C₈₃	—	2	2	no	—
234	C₂²⋊C₄×C₈₃	—	2	4	no	—
235	C₂²⋊C₄×C₈₃	—	2	2	no	—
236	C₂²⋊C₄×C₈₃	—	2	4	no	—
237	C₂²⋊C₄×C₈₃	—	2	4	no	—
238	C₂²⋊C₄×C₈₃	—	2	2	no	—
239	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
240	C₂²⋊C₄×C₈₃	C₂×D₄	1	4	yes	—
241	C₄²×C₈₃	—	2	4	no	—
242	C₄²×C₈₃	—	2	4	no	—
243	C₄²×C₈₃	—	2	2	no	—
244	C₄²×C₈₃	C₂×D₄	1	4	yes	—
245	C₄²×C₈₃	C₂×D₄	1	2	yes	—
246	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
247	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
248	C₄²×C₈₃	C₂⁴	1	2	yes	—
249	C₂³×C₈₃	—	2	2	no	—
250	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
251	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
252	Q₈×C₈₃	—	2	2	no	—
253	Q₈×C₈₃	—	2	2	no	—
254	Q₈×C₈₃	—	2	2	no	—
255	Q₈×C₈₃	—	8	4	no	—
256	Q₈×C₈₃	—	8	2	no	—
257	D₄×C₈₃	—	2	4	no	—
258	D₄×C₈₃	—	2	2	no	—
259	D₄×C₈₃	—	2	2	no	—
260	D₄×C₈₃	—	2	2	no	—
261	D₄×C₈₃	—	4	4	no	—
262	D₄×C₈₃	—	8	2	no	—
263	D₄×C₈₃	—	8	4	no	—
264	C₂×C₄×C₈₃	—	2	2	no	—
265	C₂×C₄×C₈₃	—	2	2	no	—
266	C₂×C₄×C₈₃	—	2	2	no	—
267	C₂×C₄×C₈₃	—	2	2	no	—
268	C₂×C₄×C₈₃	—	2	4	no	—
269	C₂×C₄×C₈₃	—	2	4	no	—
270	C₂×C₄×C₈₃	—	2	2	no	—
271	C₂×C₄×C₈₃	—	4	4	no	—
272	C₂×C₄×C₈₃	—	4	2	no	—
273	C₂×C₄×C₈₃	—	4	4	no	—
274	C₂×C₄×C₈₃	—	8	4	no	—
275	C₂×C₄×C₈₃	—	8	2	no	—
276	C₂×C₄×C₈₃	—	8	2	no	—
277	C₂×C₄×C₈₃	—	8	4	no	—
278	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
279	C₂×C₄×C₈₃	C₂²×D₄	1	4	yes	—
280	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
281	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
282	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
283	C₂×C₄×C₈₃	2₋¹⁺⁴	1	2	yes	—
284	C₂×C₄×C₈₃	2₋¹⁺⁴	1	2	yes	—
285	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
286	C₈×C₈₃	—	2	2	no	—
287	C₈×C₈₃	—	2	2	no	—
288	C₈×C₈₃	—	2	2	no	—
289	C₈×C₈₃	—	2	2	no	—
290	C₂²×C₈₃	—	2	2	no	—
291	C₂²×C₈₃	—	2	4	no	—
292	C₂²×C₈₃	—	2	2	no	—
293	C₂²×C₈₃	—	4	2	no	—
294	C₂²×C₈₃	—	4	2	no	—
295	C₂²×C₈₃	—	4	2	no	—
296	C₂²×C₈₃	#536	1	2	yes	—
297	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
298	C₄×C₈₃	—	2	2	no	—
299	C₄×C₈₃	—	2	4	no	—
300	C₄×C₈₃	—	2	2	no	—
301	C₄×C₈₃	—	2	2	no	—
302	C₄×C₈₃	—	4	4	no	—
303	C₄×C₈₃	—	4	4	no	—
304	C₄×C₈₃	—	4	2	no	—
305	C₄×C₈₃	—	4	2	no	—
306	C₄×C₈₃	—	4	2	no	—
307	C₄×C₈₃	#536	1	2	yes	—
308	C₄×C₈₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
309	C₄×C₈₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
310	#60882	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
311	C₂×C₈₃	—	2	2	no	—
312	C₂×C₈₃	—	4	2	no	—
313	C₂×C₈₃	—	8	2	no	—
314	C₂×C₈₃	C₂×#536	1	1	yes	characteristic
315	C₂×C₈₃	#3584	1	2	yes	—
316	#3512	C₂×C₈₃	1	1	yes	characteristic
317	#3504	C₂×C₈₃	1	1	yes	characteristic, complemented
318	#3242	C₂×C₈₃	1	4	yes	complemented
319	#3241	C₂×C₈₃	1	4	yes	complemented
320	#3233	C₂×C₈₃	1	4	yes	complemented
321	#3232	C₂×C₈₃	1	4	yes	complemented
322	#3166	C₂×C₈₃	1	1	yes	characteristic, complemented
323	C₂×#499	C₂×C₈₃	1	1	yes	characteristic, complemented
324	#3142	C₂×C₈₃	1	1	yes	characteristic, complemented
325	#3131	C₂×C₈₃	1	1	yes	characteristic, complemented
326	#3099	C₂×C₈₃	1	2	yes	complemented
327	#3098	C₂×C₈₃	1	2	yes	complemented
328	#3084	C₂×C₈₃	1	2	yes	complemented
329	#3083	C₂×C₈₃	1	2	yes	complemented
330	#2922	C₂×C₈₃	1	1	yes	characteristic, complemented
331	C₈₃	#60882	1	1	yes	characteristic, direct product factor, Sylow
332	#557	—	2	2	no	—
333	#554	—	2	4	no	—
334	#554	—	2	2	no	—
335	#553	—	2	4	no	—
336	#553	—	2	2	no	—
337	#552	—	2	2	no	—
338	#544	C₂²×C₈₃	1	2	yes	—
339	#544	C₂²×C₈₃	1	4	yes	—
340	#541	C₂²×C₈₃	1	2	yes	—
341	#540	C₂²×C₈₃	1	2	yes	—
342	#537	C₂²×C₈₃	1	2	yes	—
343	#533	C₂²×C₈₃	1	1	yes	characteristic
344	#533	C₂²×C₈₃	1	2	yes	—
345	#532	C₂²×C₈₃	1	1	yes	characteristic
346	#529	C₂²×C₈₃	1	4	yes	—
347	C₂×#125	C₂²×C₈₃	1	1	yes	characteristic
348	C₂×#125	C₂²×C₈₃	1	1	yes	characteristic
349	C₂×#125	C₂²×C₈₃	1	2	yes	—
350	#520	C₂²×C₈₃	1	2	yes	—
351	#520	C₂²×C₈₃	1	2	yes	—
352	C₄×#41	C₂²×C₈₃	1	1	yes	characteristic
353	#501	C₂²×C₈₃	1	4	yes	—
354	#499	C₂²×C₈₃	1	4	yes	—
355	#499	C₂²×C₈₃	1	4	yes	—
356	#499	C₂²×C₈₃	1	2	yes	—
357	#499	C₂²×C₈₃	1	2	yes	—
358	#491	C₂²×C₈₃	1	2	yes	—
359	#490	C₂²×C₈₃	1	2	yes	—
360	#488	C₂²×C₈₃	1	2	yes	—
361	#488	C₂²×C₈₃	1	2	yes	—
362	#488	C₂²×C₈₃	1	4	yes	—
363	#487	C₂²×C₈₃	1	2	yes	—
364	#486	C₂²×C₈₃	1	2	yes	—
365	#485	C₂²×C₈₃	1	4	yes	—
366	#485	C₂²×C₈₃	1	4	yes	—
367	#484	C₂²×C₈₃	1	4	yes	—
368	#483	C₂²×C₈₃	1	4	yes	—
369	#482	C₂²×C₈₃	1	4	yes	—
370	#482	C₂²×C₈₃	1	4	yes	—
371	#481	C₂²×C₈₃	1	4	yes	—
372	#480	C₂²×C₈₃	1	4	yes	—
373	#479	C₂²×C₈₃	1	4	yes	—
374	#479	C₂²×C₈₃	1	4	yes	—
375	#478	C₂²×C₈₃	1	4	yes	—
376	#478	C₂²×C₈₃	1	4	yes	—
377	#477	C₂²×C₈₃	1	4	yes	—
378	#476	C₂²×C₈₃	1	4	yes	—
379	#475	C₂²×C₈₃	1	4	yes	—
380	#474	C₂²×C₈₃	1	4	yes	—
381	#433	C₂²×C₈₃	1	4	yes	—
382	#431	C₂²×C₈₃	1	4	yes	—
383	#428	C₂²×C₈₃	1	2	yes	—
384	#428	C₂²×C₈₃	1	2	yes	—
385	C₂×#107	C₂²×C₈₃	1	2	yes	—
386	C₂×#106	C₂²×C₈₃	1	2	yes	—
387	#424	C₂²×C₈₃	1	1	yes	characteristic
388	#424	C₂²×C₈₃	1	1	yes	characteristic
389	#417	C₂²×C₈₃	1	2	yes	—
390	#417	C₂²×C₈₃	1	2	yes	—
391	#416	C₂²×C₈₃	1	2	yes	—
392	#416	C₂²×C₈₃	1	2	yes	—
393	#408	C₂²×C₈₃	1	1	yes	characteristic
394	#408	C₂²×C₈₃	1	1	yes	characteristic
395	C₄×M₁₆	C₂²×C₈₃	1	1	yes	characteristic
396	C₂×C₄×C₈	C₂²×C₈₃	1	1	yes	characteristic
397	C₂×#41	C₂³×C₈₃	1	2	yes	—
398	C₂×#41	C₂³×C₈₃	1	1	yes	characteristic
399	C₂×M₁₆	C₂³×C₈₃	1	1	yes	characteristic
400	C₂×M₁₆	C₂³×C₈₃	1	1	yes	characteristic
401	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
402	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
403	C₄⋊Q₈	—	2	2	no	—
404	C₄⋊Q₈	—	2	4	no	—
405	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
406	C₄⋊Q₈	C₂³×C₈₃	1	4	yes	—
407	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
408	#127	C₂³×C₈₃	1	1	yes	characteristic
409	#126	—	2	4	no	—
410	#126	—	2	4	no	—
411	#125	—	2	4	no	—
412	#125	—	2	2	no	—
413	#125	—	2	4	no	—
414	#125	—	2	2	no	—
415	#125	—	2	4	no	—
416	#125	—	2	2	no	—
417	#125	C₂³×C₈₃	1	2	yes	—
418	#125	C₂³×C₈₃	1	1	yes	characteristic
419	#125	C₂³×C₈₃	1	2	yes	—
420	#125	C₂³×C₈₃	1	2	yes	—
421	#125	C₂³×C₈₃	1	4	yes	—
422	#125	C₂³×C₈₃	1	2	yes	—
423	#125	C₂³×C₈₃	1	1	yes	characteristic
424	#124	C₂³×C₈₃	1	2	yes	—
425	#123	—	2	4	no	—
426	#123	—	2	4	no	—
427	C₂²⋊Q₈	—	2	2	no	—
428	C₂²⋊Q₈	—	2	2	no	—
429	C₂²⋊Q₈	—	2	4	no	—
430	C₂²⋊Q₈	—	2	4	no	—
431	C₂²⋊Q₈	—	2	4	no	—
432	C₂²⋊Q₈	—	2	4	no	—
433	C₂²⋊Q₈	C₂³×C₈₃	1	4	yes	—
434	#121	—	2	2	no	—
435	#121	—	2	4	no	—
436	#121	—	2	2	no	—
437	#121	—	2	4	no	—
438	#121	C₂³×C₈₃	1	4	yes	—
439	C₄×Q₈	—	2	2	no	—
440	C₄×Q₈	—	2	4	no	—
441	C₄×Q₈	—	2	2	no	—
442	C₄×Q₈	D₄×C₈₃	1	2	yes	—
443	C₄×Q₈	C₂³×C₈₃	1	4	yes	—
444	C₄×D₄	—	2	4	no	—
445	C₄×D₄	—	2	2	no	—
446	C₄×D₄	—	2	4	no	—
447	C₄×D₄	—	2	4	no	—
448	C₄×D₄	—	2	2	no	—
449	C₄×D₄	D₄×C₈₃	1	4	yes	—
450	C₄×D₄	D₄×C₈₃	1	2	yes	—
451	C₄×D₄	C₂³×C₈₃	1	4	yes	—
452	#117	—	2	2	no	—
453	#117	—	2	4	no	—
454	#117	C₂³×C₈₃	1	2	yes	—
455	#117	C₂³×C₈₃	1	4	yes	—
456	#117	C₂³×C₈₃	1	1	yes	characteristic
457	#117	C₂³×C₈₃	1	2	yes	—
458	C₂×C₄⋊C₄	—	2	2	no	—
459	C₂×C₄⋊C₄	—	2	2	no	—
460	C₂×C₄⋊C₄	—	2	4	no	—
461	C₂×C₄⋊C₄	—	2	2	no	—
462	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
463	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
464	C₂×C₄⋊C₄	C₂³×C₈₃	1	4	yes	—
465	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
466	C₂×C₄²	C₂³×C₈₃	1	2	yes	—
467	#107	C₂³×C₈₃	1	4	yes	—
468	#107	C₂³×C₈₃	1	4	yes	—
469	#107	C₂³×C₈₃	1	4	yes	—
470	#107	C₂³×C₈₃	1	4	yes	—
471	#106	C₂³×C₈₃	1	4	yes	—
472	#106	C₂³×C₈₃	1	4	yes	—
473	#106	C₂³×C₈₃	1	4	yes	—
474	#106	C₂³×C₈₃	1	4	yes	—
475	C₄⋊C₈	C₂³×C₈₃	1	4	yes	—
476	C₄⋊C₈	C₂³×C₈₃	1	4	yes	—
477	#103	C₂³×C₈₃	1	2	yes	—
478	#103	C₂³×C₈₃	1	2	yes	—
479	#103	C₂³×C₈₃	1	2	yes	—
480	#103	C₂³×C₈₃	1	2	yes	—
481	#103	C₂³×C₈₃	1	4	yes	—
482	#103	C₂³×C₈₃	1	4	yes	—
483	#102	C₂³×C₈₃	1	2	yes	—
484	#102	C₂³×C₈₃	1	2	yes	—
485	#102	C₂³×C₈₃	1	2	yes	—
486	#102	C₂³×C₈₃	1	2	yes	—
487	#102	C₂³×C₈₃	1	4	yes	—
488	#102	C₂³×C₈₃	1	4	yes	—
489	C₂²⋊C₈	C₂³×C₈₃	1	4	yes	—
490	C₂²⋊C₈	C₂³×C₈₃	1	4	yes	—
491	#97	C₂³×C₈₃	1	2	yes	—
492	C₄×C₈	C₂³×C₈₃	1	2	yes	—
493	C₄×C₈	C₂³×C₈₃	1	2	yes	—
494	C₄×C₈	C₂³×C₈₃	1	2	yes	—
495	#41	—	2	2	no	—
496	#41	—	2	2	no	—
497	#41	—	2	4	no	—
498	#41	—	2	4	no	—
499	C₂×Q₈	—	2	4	no	—
500	C₂×Q₈	—	2	2	no	—
501	C₂×Q₈	C₂×D₄×C₈₃	1	1	yes	characteristic
502	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
503	C₂×D₄	—	2	2	no	—
504	C₂×D₄	—	2	4	no	—
505	C₂×D₄	—	2	2	no	—
506	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
507	C₂×D₄	C₂×D₄×C₈₃	1	1	yes	characteristic
508	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
509	C₂²×C₄	—	2	2	no	—
510	C₂²×C₄	—	2	4	no	—
511	C₂²×C₄	—	2	2	no	—
512	C₂²×C₄	—	2	2	no	—
513	C₂²×C₄	—	2	4	no	—
514	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
515	C₂²×C₄	C₂×D₄×C₈₃	1	4	yes	—
516	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
517	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
518	M₁₆	—	2	2	no	—
519	M₁₆	—	2	2	no	—
520	C₂×C₈	—	2	2	no	—
521	C₂×C₈	—	2	2	no	—
522	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
523	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
524	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
525	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
526	C₄⋊C₄	—	2	4	no	—
527	C₄⋊C₄	—	2	2	no	—
528	C₄⋊C₄	—	2	2	no	—
529	C₄⋊C₄	—	2	4	no	—
530	C₄⋊C₄	—	2	4	no	—
531	C₄⋊C₄	—	2	4	no	—
532	C₄⋊C₄	—	2	4	no	—
533	C₄⋊C₄	—	2	4	no	—
534	C₄⋊C₄	—	2	4	no	—
535	C₄⋊C₄	—	2	4	no	—
536	C₄⋊C₄	—	2	2	no	—
537	C₄⋊C₄	—	2	4	no	—
538	C₄⋊C₄	—	2	2	no	—
539	C₄⋊C₄	—	2	2	no	—
540	C₄⋊C₄	—	2	4	no	—
541	C₄⋊C₄	—	2	2	no	—
542	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
543	C₄⋊C₄	C₂×D₄×C₈₃	1	4	yes	—
544	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
545	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
546	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
547	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
548	C₂²⋊C₄	—	2	4	no	—
549	C₂²⋊C₄	—	2	2	no	—
550	C₂²⋊C₄	—	2	4	no	—
551	C₂²⋊C₄	—	2	2	no	—
552	C₂²⋊C₄	—	2	4	no	—
553	C₂²⋊C₄	—	2	4	no	—
554	C₂²⋊C₄	—	2	2	no	—
555	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
556	C₂²⋊C₄	C₂×D₄×C₈₃	1	4	yes	—
557	C₄²	—	2	4	no	—
558	C₄²	—	2	4	no	—
559	C₄²	—	2	2	no	—
560	C₄²	C₂×D₄×C₈₃	1	4	yes	—
561	C₄²	C₂×D₄×C₈₃	1	2	yes	—
562	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
563	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
564	C₄²	C₂⁴×C₈₃	1	2	yes	—
565	C₂³	—	2	2	no	—
566	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
567	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
568	Q₈	—	2	2	no	—
569	Q₈	—	2	2	no	—
570	Q₈	—	2	2	no	—
571	Q₈	—	8	4	no	—
572	Q₈	—	8	2	no	—
573	D₄	—	2	4	no	—
574	D₄	—	2	2	no	—
575	D₄	—	2	2	no	—
576	D₄	—	2	2	no	—
577	D₄	—	4	4	no	—
578	D₄	—	8	2	no	—
579	D₄	—	8	4	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	4	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	4	4	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	4	4	no	—
590	C₂×C₄	—	8	4	no	—
591	C₂×C₄	—	8	2	no	—
592	C₂×C₄	—	8	2	no	—
593	C₂×C₄	—	8	4	no	—
594	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
595	C₂×C₄	C₂²×D₄×C₈₃	1	4	yes	—
596	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
597	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
598	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
599	C₂×C₄	2₋¹⁺⁴×C₈₃	1	2	yes	—
600	C₂×C₄	2₋¹⁺⁴×C₈₃	1	2	yes	—
601	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
602	C₈	—	2	2	no	—
603	C₈	—	2	2	no	—
604	C₈	—	2	2	no	—
605	C₈	—	2	2	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	4	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	2	no	—
611	C₂²	—	4	2	no	—
612	C₂²	#536×C₈₃	1	2	yes	—
613	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
614	C₄	—	2	2	no	—
615	C₄	—	2	4	no	—
616	C₄	—	2	2	no	—
617	C₄	—	2	2	no	—
618	C₄	—	4	4	no	—
619	C₄	—	4	4	no	—
620	C₄	—	4	2	no	—
621	C₄	—	4	2	no	—
622	C₄	—	4	2	no	—
623	C₄	#536×C₈₃	1	2	yes	—
624	C₄	C₂×2₋¹⁺⁴×C₈₃	1	1	yes	characteristic
625	C₄	C₂×2₋¹⁺⁴×C₈₃	1	1	yes	characteristic
626	C₂	—	2	2	no	—
627	C₂	—	4	2	no	—
628	C₂	—	8	2	no	—
629	C₂	C₂×#536×C₈₃	1	1	yes	characteristic
630	C₂	C₈₃×#3584	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₈₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₃
prime radical	C₈₃×#3512	C₂
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
2. C₈₃×#3504	C₂	semidirect
3. C₈₃×#3242	C₂	semidirect
4. C₈₃×#3241	C₂	semidirect
5. C₈₃×#3233	C₂	semidirect
6. C₈₃×#3232	C₂	semidirect
7. C₈₃×#3166	C₂	semidirect
8. C₂×#499×C₈₃	C₂	semidirect
9. C₈₃×#3142	C₂	semidirect
10. C₈₃×#3131	C₂	semidirect
11. C₈₃×#3099	C₂	semidirect
12. C₈₃×#3098	C₂	semidirect
13. C₈₃×#3084	C₂	semidirect
14. C₈₃×#3083	C₂	semidirect
15. C₈₃×#2922	C₂	semidirect
310. #60882	C₈₃	direct (N × H)
317. #3504	C₂×C₈₃	semidirect
318. #3242	C₂×C₈₃	semidirect
319. #3241	C₂×C₈₃	semidirect
320. #3233	C₂×C₈₃	semidirect
321. #3232	C₂×C₈₃	semidirect
322. #3166	C₂×C₈₃	semidirect
323. C₂×#499	C₂×C₈₃	semidirect
324. #3142	C₂×C₈₃	semidirect
325. #3131	C₂×C₈₃	semidirect
326. #3099	C₂×C₈₃	semidirect
327. #3098	C₂×C₈₃	semidirect
328. #3084	C₂×C₈₃	semidirect
329. #3083	C₂×C₈₃	semidirect
330. #2922	C₂×C₈₃	semidirect
331. C₈₃	#60882	direct (N × H)

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×#3504	2
C₈₃×#3242	2
C₈₃×#3241	2
C₈₃×#3233	2
C₈₃×#3232	2
C₈₃×#3166	2
C₂×#499×C₈₃	2
C₈₃×#3142	2
C₈₃×#3131	2
C₈₃×#3099	2
C₈₃×#3098	2
C₈₃×#3084	2
C₈₃×#3083	2
C₈₃×#2922	2
#60882	83

Subgroups — C83×#60882 #35288706

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#60882 #35288706