Subgroups — C₈₃×#62252 #35290076

Order 21248.

1886 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3520	C₂	1	2	yes	maximal, complemented
2	C₈₃×#3342	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₃×#3336	C₂	1	2	yes	maximal, complemented
4	C₈₃×#3334	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₃×#3302	C₂	1	2	yes	maximal, complemented
6	C₈₃×#3300	C₂	1	4	yes	maximal, complemented
7	C₈₃×#3298	C₂	1	2	yes	maximal, complemented
8	D₄×Q₁₆×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₃×#3285	C₂	1	2	yes	maximal, complemented
10	C₈₃×#3283	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₃×#3248	C₂	1	2	yes	maximal, complemented
12	C₈₃×#3190	C₂	1	4	yes	maximal, complemented
13	C₈₃×#3170	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₃×#3168	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#3050	C₂	1	2	yes	maximal, complemented
16	C₂×#467×C₈₃	C₂	1	2	yes	maximal, complemented
17	C₂×C₈×D₄×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#135×C₈₃	C₂²	1	2	yes	complemented
19	C₂²×Q₁₆×C₈₃	C₂²	1	2	yes	complemented
20	C₂³×C₈×C₈₃	C₂²	1	2	yes	—
21	#556×C₈₃	C₂²	1	2	yes	—
22	#554×C₈₃	—	2	2	no	—
23	#552×C₈₃	C₂²	1	4	yes	—
24	#551×C₈₃	—	2	4	no	—
25	D₄×Q₈×C₈₃	C₂²	1	2	yes	—
26	#548×C₈₃	C₂²	1	4	yes	—
27	#547×C₈₃	C₂²	1	2	yes	—
28	#547×C₈₃	C₂²	1	2	yes	—
29	#546×C₈₃	—	2	2	no	—
30	#542×C₈₃	—	2	2	no	—
31	#539×C₈₃	—	2	4	no	—
32	#533×C₈₃	C₂²	1	2	yes	—
33	#529×C₈₃	C₂²	1	2	yes	—
34	#525×C₈₃	C₂²	1	4	yes	—
35	C₂×C₂²⋊Q₈×C₈₃	C₂²	1	4	yes	—
36	#520×C₈₃	—	2	2	no	—
37	C₂×C₄×D₄×C₈₃	C₂²	1	1	yes	characteristic
38	#500×C₈₃	C₂²	1	1	yes	characteristic, complemented
39	#499×C₈₃	C₂²	1	1	yes	characteristic, complemented
40	#495×C₈₃	C₂²	1	1	yes	characteristic, complemented
41	#494×C₈₃	C₂²	1	1	yes	characteristic, complemented
42	#488×C₈₃	C₂²	1	2	yes	complemented
43	#487×C₈₃	C₂²	1	2	yes	complemented
44	#485×C₈₃	C₂²	1	4	yes	complemented
45	#485×C₈₃	C₂²	1	4	yes	complemented
46	#483×C₈₃	C₂²	1	4	yes	complemented
47	#480×C₈₃	C₂²	1	4	yes	complemented
48	#479×C₈₃	C₂²	1	4	yes	complemented
49	#475×C₈₃	C₂²	1	2	yes	complemented
50	#474×C₈₃	C₂²	1	2	yes	complemented
51	#467×C₈₃	C₂²	1	1	yes	characteristic
52	#467×C₈₃	C₂²	1	2	yes	—
53	#467×C₈₃	C₂²	1	4	yes	—
54	#467×C₈₃	C₂²	1	2	yes	—
55	#467×C₈₃	C₂²	1	2	yes	complemented
56	#467×C₈₃	C₂²	1	2	yes	complemented
57	#467×C₈₃	C₂²	1	2	yes	complemented
58	#467×C₈₃	C₂²	1	4	yes	complemented
59	#466×C₈₃	C₂²	1	1	yes	characteristic
60	#466×C₈₃	C₂²	1	2	yes	complemented
61	#465×C₈₃	C₂²	1	4	yes	—
62	#465×C₈₃	C₂²	1	2	yes	—
63	#465×C₈₃	C₂²	1	4	yes	complemented
64	#464×C₈₃	C₂²	1	4	yes	complemented
65	#462×C₈₃	C₂²	1	2	yes	complemented
66	#461×C₈₃	C₂²	1	2	yes	complemented
67	#452×C₈₃	C₂²	1	4	yes	complemented
68	#452×C₈₃	C₂²	1	4	yes	complemented
69	#451×C₈₃	C₂²	1	4	yes	complemented
70	#448×C₈₃	C₂²	1	4	yes	complemented
71	C₄×Q₁₆×C₈₃	C₂²	1	2	yes	complemented
72	C₄×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic, complemented
73	C₄×Q₁₆×C₈₃	C₂²	1	2	yes	complemented
74	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	complemented
75	C₄×D₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
76	C₈×D₄×C₈₃	C₂²	1	1	yes	characteristic
77	C₈×D₄×C₈₃	C₂²	1	2	yes	—
78	C₈×D₄×C₈₃	C₂²	1	1	yes	characteristic
79	C₈×D₄×C₈₃	C₂²	1	1	yes	characteristic
80	C₈×D₄×C₈₃	C₂²	1	2	yes	—
81	C₈×D₄×C₈₃	C₂²	1	1	yes	characteristic
82	#427×C₈₃	C₂²	1	2	yes	complemented
83	C₂×#107×C₈₃	C₂²	1	2	yes	complemented
84	C₂×C₄⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
85	#416×C₈₃	C₂²	1	4	yes	complemented
86	C₂×#103×C₈₃	C₂²	1	4	yes	complemented
87	C₂×C₂²⋊C₈×C₈₃	C₂²	1	2	yes	—
88	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
89	C₂×#41×C₈₃	—	2	2	no	—
90	C₂×#41×C₈₃	C₂³	1	4	yes	—
91	C₂²×Q₈×C₈₃	C₂³	1	4	yes	—
92	C₂²×D₄×C₈₃	D₄	1	1	yes	characteristic
93	C₂³×C₄×C₈₃	C₂³	1	2	yes	—
94	#135×C₈₃	—	4	4	no	—
95	C₂×Q₁₆×C₈₃	—	4	4	no	—
96	C₂×Q₁₆×C₈₃	C₂³	1	2	yes	—
97	C₂×Q₁₆×C₈₃	C₂³	1	1	yes	characteristic
98	C₂×Q₁₆×C₈₃	C₂³	1	4	yes	—
99	C₂×Q₁₆×C₈₃	C₂³	1	2	yes	—
100	C₂×SD₁₆×C₈₃	C₂³	1	4	yes	—
101	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
102	C₂×D₈×C₈₃	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₈₃	—	4	4	no	—
104	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
106	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
107	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
108	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
110	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
111	C₄⋊Q₈×C₈₃	—	2	2	no	—
112	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
113	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
114	#126×C₈₃	—	2	4	no	—
115	#126×C₈₃	—	2	4	no	—
116	#126×C₈₃	—	2	2	no	—
117	#125×C₈₃	—	2	4	no	—
118	#125×C₈₃	—	2	2	no	—
119	#125×C₈₃	C₂³	1	2	yes	—
120	#124×C₈₃	—	2	2	no	—
121	#124×C₈₃	—	2	4	no	—
122	#124×C₈₃	C₂³	1	2	yes	—
123	#123×C₈₃	—	2	4	no	—
124	#123×C₈₃	—	2	4	no	—
125	#123×C₈₃	—	2	2	no	—
126	#123×C₈₃	—	2	4	no	—
127	#123×C₈₃	—	2	4	no	—
128	C₂²⋊Q₈×C₈₃	—	2	4	no	—
129	C₂²⋊Q₈×C₈₃	—	2	4	no	—
130	C₂²⋊Q₈×C₈₃	—	2	2	no	—
131	C₂²⋊Q₈×C₈₃	—	2	4	no	—
132	C₂²⋊Q₈×C₈₃	—	2	2	no	—
133	C₂²⋊Q₈×C₈₃	—	2	4	no	—
134	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
135	C₂²⋊Q₈×C₈₃	C₂³	1	4	yes	—
136	C₂²⋊Q₈×C₈₃	C₂³	1	4	yes	—
137	C₂²⋊Q₈×C₈₃	C₂³	1	4	yes	—
138	C₂²⋊Q₈×C₈₃	C₂³	1	4	yes	—
139	#121×C₈₃	—	2	4	no	—
140	#121×C₈₃	—	2	2	no	—
141	#121×C₈₃	C₂³	1	2	yes	—
142	#121×C₈₃	C₂³	1	4	yes	—
143	#120×C₈₃	—	2	4	no	—
144	C₄×Q₈×C₈₃	—	2	2	no	—
145	C₄×Q₈×C₈₃	—	2	2	no	—
146	C₄×Q₈×C₈₃	C₂³	1	4	yes	—
147	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
148	C₄×D₄×C₈₃	—	2	2	no	—
149	C₄×D₄×C₈₃	—	2	4	no	—
150	C₄×D₄×C₈₃	—	2	4	no	—
151	C₄×D₄×C₈₃	—	2	2	no	—
152	C₄×D₄×C₈₃	—	2	4	no	—
153	C₄×D₄×C₈₃	D₄	1	1	yes	characteristic
154	C₄×D₄×C₈₃	D₄	1	2	yes	—
155	C₄×D₄×C₈₃	D₄	1	1	yes	characteristic
156	C₄×D₄×C₈₃	C₂³	1	2	yes	—
157	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
158	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
159	C₄×D₄×C₈₃	C₂³	1	2	yes	—
160	#117×C₈₃	—	2	2	no	—
161	#117×C₈₃	—	2	4	no	—
162	#117×C₈₃	—	2	2	no	—
163	#117×C₈₃	C₂³	1	4	yes	—
164	C₂×C₄⋊C₄×C₈₃	—	2	4	no	—
165	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
166	C₂×C₄⋊C₄×C₈₃	D₄	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₈₃	C₂³	1	4	yes	—
168	C₂×C₂²⋊C₄×C₈₃	—	2	4	no	—
169	C₂×C₂²⋊C₄×C₈₃	D₄	1	2	yes	—
170	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
171	#107×C₈₃	C₂³	1	1	yes	characteristic
172	#107×C₈₃	C₂³	1	2	yes	—
173	#107×C₈₃	C₂³	1	1	yes	characteristic
174	#107×C₈₃	C₂³	1	4	yes	—
175	#107×C₈₃	C₂³	1	2	yes	—
176	#106×C₈₃	C₂³	1	4	yes	—
177	#106×C₈₃	C₂³	1	2	yes	—
178	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
179	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
180	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
181	#103×C₈₃	C₂³	1	4	yes	—
182	#103×C₈₃	C₂³	1	4	yes	—
183	#103×C₈₃	C₂³	1	2	yes	—
184	#103×C₈₃	C₂³	1	4	yes	—
185	#103×C₈₃	C₂³	1	2	yes	—
186	#103×C₈₃	C₂³	1	4	yes	—
187	#103×C₈₃	C₂³	1	4	yes	—
188	#102×C₈₃	C₂³	1	4	yes	—
189	#102×C₈₃	C₂³	1	2	yes	—
190	#102×C₈₃	C₂³	1	2	yes	—
191	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
192	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
193	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
194	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
195	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
198	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
199	C₂⁴×C₈₃	C₂×D₄	1	2	yes	—
200	#41×C₈₃	—	4	4	no	—
201	#41×C₈₃	—	4	4	no	—
202	#41×C₈₃	—	4	8	no	—
203	C₂×Q₈×C₈₃	—	2	2	no	—
204	C₂×Q₈×C₈₃	—	2	4	no	—
205	C₂×Q₈×C₈₃	—	4	4	no	—
206	C₂×Q₈×C₈₃	—	4	4	no	—
207	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
208	C₂×Q₈×C₈₃	C₂⁴	1	4	yes	—
209	C₂×D₄×C₈₃	—	2	4	no	—
210	C₂×D₄×C₈₃	—	2	2	no	—
211	C₂×D₄×C₈₃	—	2	4	no	—
212	C₂×D₄×C₈₃	—	2	4	no	—
213	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
214	C₂×D₄×C₈₃	C₂×D₄	1	1	yes	characteristic
215	C₂×D₄×C₈₃	C₂×D₄	1	1	yes	characteristic
216	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₈₃	—	2	4	no	—
218	C₂²×C₄×C₈₃	—	2	4	no	—
219	C₂²×C₄×C₈₃	—	2	2	no	—
220	C₂²×C₄×C₈₃	—	2	4	no	—
221	C₂²×C₄×C₈₃	—	4	2	no	—
222	C₂²×C₄×C₈₃	—	4	2	no	—
223	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
226	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
227	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
228	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
231	Q₁₆×C₈₃	—	2	2	no	—
232	Q₁₆×C₈₃	—	2	4	no	—
233	Q₁₆×C₈₃	—	4	4	no	—
234	Q₁₆×C₈₃	—	4	2	no	—
235	SD₁₆×C₈₃	—	4	2	no	—
236	SD₁₆×C₈₃	—	4	4	no	—
237	D₈×C₈₃	—	2	2	no	—
238	C₂×C₈×C₈₃	—	2	2	no	—
239	C₂×C₈×C₈₃	—	2	4	no	—
240	C₂×C₈×C₈₃	—	2	4	no	—
241	C₂×C₈×C₈₃	—	4	2	no	—
242	C₂×C₈×C₈₃	—	4	2	no	—
243	C₂×C₈×C₈₃	—	4	2	no	—
244	C₂×C₈×C₈₃	—	4	1	no	—
245	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
246	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
247	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
248	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
249	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
250	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
251	C₄⋊C₄×C₈₃	—	2	2	no	—
252	C₄⋊C₄×C₈₃	—	2	4	no	—
253	C₄⋊C₄×C₈₃	—	2	2	no	—
254	C₄⋊C₄×C₈₃	—	2	4	no	—
255	C₄⋊C₄×C₈₃	—	2	4	no	—
256	C₄⋊C₄×C₈₃	—	2	4	no	—
257	C₄⋊C₄×C₈₃	—	2	2	no	—
258	C₄⋊C₄×C₈₃	—	2	2	no	—
259	C₄⋊C₄×C₈₃	—	2	2	no	—
260	C₄⋊C₄×C₈₃	—	2	4	no	—
261	C₄⋊C₄×C₈₃	—	2	2	no	—
262	C₄⋊C₄×C₈₃	—	2	4	no	—
263	C₄⋊C₄×C₈₃	—	2	2	no	—
264	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
265	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
266	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
267	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
268	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
269	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
270	C₂²⋊C₄×C₈₃	—	2	2	no	—
271	C₂²⋊C₄×C₈₃	—	2	4	no	—
272	C₂²⋊C₄×C₈₃	—	2	4	no	—
273	C₂²⋊C₄×C₈₃	—	2	4	no	—
274	C₂²⋊C₄×C₈₃	—	2	4	no	—
275	C₂²⋊C₄×C₈₃	—	2	4	no	—
276	C₂²⋊C₄×C₈₃	—	2	2	no	—
277	C₂²⋊C₄×C₈₃	—	2	2	no	—
278	C₂²⋊C₄×C₈₃	—	2	2	no	—
279	C₂²⋊C₄×C₈₃	—	2	4	no	—
280	C₂²⋊C₄×C₈₃	—	2	2	no	—
281	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
282	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
283	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
284	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
285	C₄²×C₈₃	—	2	4	no	—
286	C₄²×C₈₃	—	2	4	no	—
287	C₄²×C₈₃	—	2	2	no	—
288	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
289	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
290	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
291	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
292	C₂³×C₈₃	—	2	4	no	—
293	C₂³×C₈₃	—	2	4	no	—
294	C₂³×C₈₃	—	2	2	no	—
295	C₂³×C₈₃	—	4	2	no	—
296	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
297	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
298	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
299	Q₈×C₈₃	—	2	4	no	—
300	Q₈×C₈₃	—	2	2	no	—
301	Q₈×C₈₃	—	2	2	no	—
302	Q₈×C₈₃	—	2	4	no	—
303	Q₈×C₈₃	—	4	4	no	—
304	Q₈×C₈₃	—	8	4	no	—
305	D₄×C₈₃	—	2	4	no	—
306	D₄×C₈₃	—	2	2	no	—
307	D₄×C₈₃	—	2	2	no	—
308	D₄×C₈₃	—	2	2	no	—
309	D₄×C₈₃	—	4	8	no	—
310	D₄×C₈₃	—	4	4	no	—
311	D₄×C₈₃	—	8	4	no	—
312	D₄×C₈₃	#135	1	4	yes	complemented
313	C₂×C₄×C₈₃	—	2	2	no	—
314	C₂×C₄×C₈₃	—	2	2	no	—
315	C₂×C₄×C₈₃	—	2	1	no	—
316	C₂×C₄×C₈₃	—	2	2	no	—
317	C₂×C₄×C₈₃	—	2	2	no	—
318	C₂×C₄×C₈₃	—	2	1	no	—
319	C₂×C₄×C₈₃	—	2	2	no	—
320	C₂×C₄×C₈₃	—	2	2	no	—
321	C₂×C₄×C₈₃	—	2	2	no	—
322	C₂×C₄×C₈₃	—	2	4	no	—
323	C₂×C₄×C₈₃	—	2	2	no	—
324	C₂×C₄×C₈₃	—	2	4	no	—
325	C₂×C₄×C₈₃	—	2	2	no	—
326	C₂×C₄×C₈₃	—	4	2	no	—
327	C₂×C₄×C₈₃	—	4	2	no	—
328	C₂×C₄×C₈₃	—	4	2	no	—
329	C₂×C₄×C₈₃	—	4	8	no	—
330	C₂×C₄×C₈₃	—	4	4	no	—
331	C₂×C₄×C₈₃	—	8	4	no	—
332	C₂×C₄×C₈₃	—	8	4	no	—
333	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
334	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
339	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
341	C₈×C₈₃	—	2	1	no	—
342	C₈×C₈₃	—	2	2	no	—
343	C₈×C₈₃	—	2	2	no	—
344	C₈×C₈₃	—	2	1	no	—
345	C₈×C₈₃	—	2	1	no	—
346	C₈×C₈₃	H(5,𝔽₂)	1	2	yes	—
347	C₂²×C₈₃	—	2	1	no	—
348	C₂²×C₈₃	—	2	2	no	—
349	C₂²×C₈₃	—	2	1	no	—
350	C₂²×C₈₃	—	2	2	no	—
351	C₂²×C₈₃	—	2	2	no	—
352	C₂²×C₈₃	—	2	2	no	—
353	C₂²×C₈₃	—	2	2	no	—
354	C₂²×C₈₃	—	4	8	no	—
355	C₂²×C₈₃	—	4	2	no	—
356	C₂²×C₈₃	—	4	2	no	—
357	C₂²×C₈₃	—	4	2	no	—
358	C₂²×C₈₃	C₂×#135	1	4	yes	—
359	C₂²×C₈₃	#578	1	2	yes	—
360	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
361	C₄×C₈₃	—	2	1	no	—
362	C₄×C₈₃	—	2	2	no	—
363	C₄×C₈₃	—	2	2	no	—
364	C₄×C₈₃	—	2	1	no	—
365	C₄×C₈₃	—	2	1	no	—
366	C₄×C₈₃	—	2	1	no	—
367	C₄×C₈₃	—	4	4	no	—
368	C₄×C₈₃	—	4	2	no	—
369	C₄×C₈₃	—	4	2	no	—
370	C₄×C₈₃	—	4	4	no	—
371	C₄×C₈₃	—	4	2	no	—
372	C₄×C₈₃	C₂×#135	1	2	yes	—
373	C₄×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
374	C₄×C₈₃	#585	1	1	yes	characteristic
375	#62252	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
376	C₂×C₈₃	—	2	2	no	—
377	C₂×C₈₃	—	2	4	no	—
378	C₂×C₈₃	—	4	2	no	—
379	C₂×C₈₃	—	8	2	no	—
380	C₂×C₈₃	#3496	1	1	yes	characteristic
381	C₂×C₈₃	C₂²×#135	1	1	yes	characteristic
382	C₂×C₈₃	C₂×#578	1	1	yes	characteristic
383	#3520	C₂×C₈₃	1	2	yes	complemented
384	#3342	C₂×C₈₃	1	1	yes	characteristic, complemented
385	#3336	C₂×C₈₃	1	2	yes	complemented
386	#3334	C₂×C₈₃	1	1	yes	characteristic, complemented
387	#3302	C₂×C₈₃	1	2	yes	complemented
388	#3300	C₂×C₈₃	1	4	yes	complemented
389	#3298	C₂×C₈₃	1	2	yes	complemented
390	D₄×Q₁₆	C₂×C₈₃	1	1	yes	characteristic, complemented
391	#3285	C₂×C₈₃	1	2	yes	complemented
392	#3283	C₂×C₈₃	1	1	yes	characteristic, complemented
393	#3248	C₂×C₈₃	1	2	yes	complemented
394	#3190	C₂×C₈₃	1	4	yes	complemented
395	#3170	C₂×C₈₃	1	1	yes	characteristic, complemented
396	#3168	C₂×C₈₃	1	1	yes	characteristic, complemented
397	#3050	C₂×C₈₃	1	2	yes	complemented
398	C₂×#467	C₂×C₈₃	1	2	yes	complemented
399	C₂×C₈×D₄	C₂×C₈₃	1	1	yes	characteristic, complemented
400	C₈₃	#62252	1	1	yes	characteristic, direct product factor, Sylow
401	C₂×#135	C₂²×C₈₃	1	2	yes	complemented
402	C₂²×Q₁₆	C₂²×C₈₃	1	2	yes	complemented
403	C₂³×C₈	C₂²×C₈₃	1	2	yes	—
404	#556	C₂²×C₈₃	1	2	yes	—
405	#554	—	2	2	no	—
406	#552	C₂²×C₈₃	1	4	yes	—
407	#551	—	2	4	no	—
408	D₄×Q₈	C₂²×C₈₃	1	2	yes	—
409	#548	C₂²×C₈₃	1	4	yes	—
410	#547	C₂²×C₈₃	1	2	yes	—
411	#547	C₂²×C₈₃	1	2	yes	—
412	#546	—	2	2	no	—
413	#542	—	2	2	no	—
414	#539	—	2	4	no	—
415	#533	C₂²×C₈₃	1	2	yes	—
416	#529	C₂²×C₈₃	1	2	yes	—
417	#525	C₂²×C₈₃	1	4	yes	—
418	C₂×C₂²⋊Q₈	C₂²×C₈₃	1	4	yes	—
419	#520	—	2	2	no	—
420	C₂×C₄×D₄	C₂²×C₈₃	1	1	yes	characteristic
421	#500	C₂²×C₈₃	1	1	yes	characteristic, complemented
422	#499	C₂²×C₈₃	1	1	yes	characteristic, complemented
423	#495	C₂²×C₈₃	1	1	yes	characteristic, complemented
424	#494	C₂²×C₈₃	1	1	yes	characteristic, complemented
425	#488	C₂²×C₈₃	1	2	yes	complemented
426	#487	C₂²×C₈₃	1	2	yes	complemented
427	#485	C₂²×C₈₃	1	4	yes	complemented
428	#485	C₂²×C₈₃	1	4	yes	complemented
429	#483	C₂²×C₈₃	1	4	yes	complemented
430	#480	C₂²×C₈₃	1	4	yes	complemented
431	#479	C₂²×C₈₃	1	4	yes	complemented
432	#475	C₂²×C₈₃	1	2	yes	complemented
433	#474	C₂²×C₈₃	1	2	yes	complemented
434	#467	C₂²×C₈₃	1	1	yes	characteristic
435	#467	C₂²×C₈₃	1	2	yes	—
436	#467	C₂²×C₈₃	1	2	yes	—
437	#467	C₂²×C₈₃	1	4	yes	—
438	#467	C₂²×C₈₃	1	2	yes	complemented
439	#467	C₂²×C₈₃	1	2	yes	complemented
440	#467	C₂²×C₈₃	1	2	yes	complemented
441	#467	C₂²×C₈₃	1	4	yes	complemented
442	#466	C₂²×C₈₃	1	1	yes	characteristic
443	#466	C₂²×C₈₃	1	2	yes	complemented
444	#465	C₂²×C₈₃	1	2	yes	—
445	#465	C₂²×C₈₃	1	4	yes	—
446	#465	C₂²×C₈₃	1	4	yes	complemented
447	#464	C₂²×C₈₃	1	4	yes	complemented
448	#462	C₂²×C₈₃	1	2	yes	complemented
449	#461	C₂²×C₈₃	1	2	yes	complemented
450	#452	C₂²×C₈₃	1	4	yes	complemented
451	#452	C₂²×C₈₃	1	4	yes	complemented
452	#451	C₂²×C₈₃	1	4	yes	complemented
453	#448	C₂²×C₈₃	1	4	yes	complemented
454	C₄×Q₁₆	C₂²×C₈₃	1	2	yes	complemented
455	C₄×Q₁₆	C₂²×C₈₃	1	1	yes	characteristic, complemented
456	C₄×Q₁₆	C₂²×C₈₃	1	2	yes	complemented
457	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	complemented
458	C₄×D₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
459	C₈×D₄	C₂²×C₈₃	1	1	yes	characteristic
460	C₈×D₄	C₂²×C₈₃	1	2	yes	—
461	C₈×D₄	C₂²×C₈₃	1	1	yes	characteristic
462	C₈×D₄	C₂²×C₈₃	1	1	yes	characteristic
463	C₈×D₄	C₂²×C₈₃	1	2	yes	—
464	C₈×D₄	C₂²×C₈₃	1	1	yes	characteristic
465	#427	C₂²×C₈₃	1	2	yes	complemented
466	C₂×#107	C₂²×C₈₃	1	2	yes	complemented
467	C₂×C₄⋊C₈	C₂²×C₈₃	1	1	yes	characteristic
468	#416	C₂²×C₈₃	1	4	yes	complemented
469	C₂×#103	C₂²×C₈₃	1	4	yes	complemented
470	C₂×C₂²⋊C₈	C₂²×C₈₃	1	2	yes	—
471	C₂×C₄×C₈	C₂²×C₈₃	1	1	yes	characteristic
472	C₂×#41	—	2	2	no	—
473	C₂×#41	C₂³×C₈₃	1	4	yes	—
474	C₂²×Q₈	C₂³×C₈₃	1	4	yes	—
475	C₂²×D₄	D₄×C₈₃	1	1	yes	characteristic
476	C₂³×C₄	C₂³×C₈₃	1	2	yes	—
477	#135	—	4	4	no	—
478	C₂×Q₁₆	—	4	4	no	—
479	C₂×Q₁₆	C₂³×C₈₃	1	1	yes	characteristic
480	C₂×Q₁₆	C₂³×C₈₃	1	2	yes	—
481	C₂×Q₁₆	C₂³×C₈₃	1	4	yes	—
482	C₂×Q₁₆	C₂³×C₈₃	1	2	yes	—
483	C₂×SD₁₆	C₂³×C₈₃	1	4	yes	—
484	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
485	C₂×D₈	C₂³×C₈₃	1	1	yes	characteristic
486	C₂²×C₈	—	4	4	no	—
487	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
488	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
489	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
490	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
491	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
492	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
493	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
494	C₄⋊Q₈	—	2	2	no	—
495	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
496	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
497	#126	—	2	4	no	—
498	#126	—	2	4	no	—
499	#126	—	2	2	no	—
500	#125	—	2	4	no	—
501	#125	—	2	2	no	—
502	#125	C₂³×C₈₃	1	2	yes	—
503	#124	—	2	2	no	—
504	#124	—	2	4	no	—
505	#124	C₂³×C₈₃	1	2	yes	—
506	#123	—	2	4	no	—
507	#123	—	2	4	no	—
508	#123	—	2	2	no	—
509	#123	—	2	4	no	—
510	#123	—	2	4	no	—
511	C₂²⋊Q₈	—	2	4	no	—
512	C₂²⋊Q₈	—	2	4	no	—
513	C₂²⋊Q₈	—	2	2	no	—
514	C₂²⋊Q₈	—	2	4	no	—
515	C₂²⋊Q₈	—	2	2	no	—
516	C₂²⋊Q₈	—	2	4	no	—
517	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
518	C₂²⋊Q₈	C₂³×C₈₃	1	4	yes	—
519	C₂²⋊Q₈	C₂³×C₈₃	1	4	yes	—
520	C₂²⋊Q₈	C₂³×C₈₃	1	4	yes	—
521	C₂²⋊Q₈	C₂³×C₈₃	1	4	yes	—
522	#121	—	2	4	no	—
523	#121	—	2	2	no	—
524	#121	C₂³×C₈₃	1	2	yes	—
525	#121	C₂³×C₈₃	1	4	yes	—
526	#120	—	2	4	no	—
527	C₄×Q₈	—	2	2	no	—
528	C₄×Q₈	—	2	2	no	—
529	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
530	C₄×Q₈	C₂³×C₈₃	1	4	yes	—
531	C₄×D₄	—	2	2	no	—
532	C₄×D₄	—	2	4	no	—
533	C₄×D₄	—	2	4	no	—
534	C₄×D₄	—	2	2	no	—
535	C₄×D₄	—	2	4	no	—
536	C₄×D₄	D₄×C₈₃	1	1	yes	characteristic
537	C₄×D₄	D₄×C₈₃	1	2	yes	—
538	C₄×D₄	D₄×C₈₃	1	1	yes	characteristic
539	C₄×D₄	C₂³×C₈₃	1	2	yes	—
540	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
541	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
542	C₄×D₄	C₂³×C₈₃	1	2	yes	—
543	#117	—	2	2	no	—
544	#117	—	2	4	no	—
545	#117	—	2	2	no	—
546	#117	C₂³×C₈₃	1	4	yes	—
547	C₂×C₄⋊C₄	—	2	4	no	—
548	C₂×C₄⋊C₄	—	2	2	no	—
549	C₂×C₄⋊C₄	D₄×C₈₃	1	1	yes	characteristic
550	C₂×C₄⋊C₄	C₂³×C₈₃	1	4	yes	—
551	C₂×C₂²⋊C₄	—	2	4	no	—
552	C₂×C₂²⋊C₄	D₄×C₈₃	1	2	yes	—
553	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
554	#107	C₂³×C₈₃	1	1	yes	characteristic
555	#107	C₂³×C₈₃	1	2	yes	—
556	#107	C₂³×C₈₃	1	4	yes	—
557	#107	C₂³×C₈₃	1	1	yes	characteristic
558	#107	C₂³×C₈₃	1	2	yes	—
559	#106	C₂³×C₈₃	1	4	yes	—
560	#106	C₂³×C₈₃	1	2	yes	—
561	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
562	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
563	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
564	#103	C₂³×C₈₃	1	2	yes	—
565	#103	C₂³×C₈₃	1	4	yes	—
566	#103	C₂³×C₈₃	1	4	yes	—
567	#103	C₂³×C₈₃	1	4	yes	—
568	#103	C₂³×C₈₃	1	4	yes	—
569	#103	C₂³×C₈₃	1	4	yes	—
570	#103	C₂³×C₈₃	1	2	yes	—
571	#102	C₂³×C₈₃	1	2	yes	—
572	#102	C₂³×C₈₃	1	4	yes	—
573	#102	C₂³×C₈₃	1	2	yes	—
574	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
575	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
576	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
577	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
578	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
579	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
580	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
581	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
582	C₂⁴	C₂×D₄×C₈₃	1	2	yes	—
583	#41	—	4	4	no	—
584	#41	—	4	4	no	—
585	#41	—	4	8	no	—
586	C₂×Q₈	—	2	2	no	—
587	C₂×Q₈	—	2	4	no	—
588	C₂×Q₈	—	4	4	no	—
589	C₂×Q₈	—	4	4	no	—
590	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
591	C₂×Q₈	C₂⁴×C₈₃	1	4	yes	—
592	C₂×D₄	—	2	4	no	—
593	C₂×D₄	—	2	2	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
597	C₂×D₄	C₂×D₄×C₈₃	1	1	yes	characteristic
598	C₂×D₄	C₂×D₄×C₈₃	1	1	yes	characteristic
599	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
600	C₂²×C₄	—	2	4	no	—
601	C₂²×C₄	—	2	4	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	4	no	—
604	C₂²×C₄	—	4	2	no	—
605	C₂²×C₄	—	4	2	no	—
606	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
607	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
608	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
609	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
610	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
613	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
614	Q₁₆	—	2	2	no	—
615	Q₁₆	—	2	4	no	—
616	Q₁₆	—	4	4	no	—
617	Q₁₆	—	4	2	no	—
618	SD₁₆	—	4	4	no	—
619	SD₁₆	—	4	2	no	—
620	D₈	—	2	2	no	—
621	C₂×C₈	—	2	2	no	—
622	C₂×C₈	—	2	4	no	—
623	C₂×C₈	—	2	4	no	—
624	C₂×C₈	—	4	2	no	—
625	C₂×C₈	—	4	2	no	—
626	C₂×C₈	—	4	2	no	—
627	C₂×C₈	—	4	1	no	—
628	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
629	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
630	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
631	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
632	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
633	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	2	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	2	no	—
641	C₄⋊C₄	—	2	2	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	2	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	2	no	—
647	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
648	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
649	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
650	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
651	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
652	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
653	C₂²⋊C₄	—	2	2	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	2	2	no	—
661	C₂²⋊C₄	—	2	2	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	2	no	—
664	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
665	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
666	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
667	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
668	C₄²	—	2	4	no	—
669	C₄²	—	2	4	no	—
670	C₄²	—	2	2	no	—
671	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
672	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
673	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
674	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
675	C₂³	—	2	4	no	—
676	C₂³	—	2	4	no	—
677	C₂³	—	2	2	no	—
678	C₂³	—	4	2	no	—
679	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
680	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
681	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
682	Q₈	—	2	4	no	—
683	Q₈	—	2	2	no	—
684	Q₈	—	2	2	no	—
685	Q₈	—	2	4	no	—
686	Q₈	—	4	4	no	—
687	Q₈	—	8	4	no	—
688	D₄	—	2	4	no	—
689	D₄	—	2	2	no	—
690	D₄	—	2	2	no	—
691	D₄	—	2	2	no	—
692	D₄	—	4	8	no	—
693	D₄	—	4	4	no	—
694	D₄	—	8	4	no	—
695	D₄	#135×C₈₃	1	4	yes	complemented
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	4	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	4	2	no	—
710	C₂×C₄	—	4	2	no	—
711	C₂×C₄	—	4	2	no	—
712	C₂×C₄	—	4	8	no	—
713	C₂×C₄	—	4	4	no	—
714	C₂×C₄	—	8	4	no	—
715	C₂×C₄	—	8	4	no	—
716	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
717	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
718	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
719	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
720	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
721	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
722	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
723	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
724	C₈	—	2	1	no	—
725	C₈	—	2	2	no	—
726	C₈	—	2	2	no	—
727	C₈	—	2	1	no	—
728	C₈	—	2	1	no	—
729	C₈	H(5,𝔽₂)×C₈₃	1	2	yes	—
730	C₂²	—	2	1	no	—
731	C₂²	—	2	2	no	—
732	C₂²	—	2	1	no	—
733	C₂²	—	2	2	no	—
734	C₂²	—	2	2	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	2	2	no	—
737	C₂²	—	4	8	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	C₂×#135×C₈₃	1	4	yes	—
742	C₂²	#578×C₈₃	1	2	yes	—
743	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
744	C₄	—	2	1	no	—
745	C₄	—	2	1	no	—
746	C₄	—	2	1	no	—
747	C₄	—	2	1	no	—
748	C₄	—	2	2	no	—
749	C₄	—	2	2	no	—
750	C₄	—	4	2	no	—
751	C₄	—	4	4	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	4	no	—
754	C₄	—	4	2	no	—
755	C₄	C₂×#135×C₈₃	1	2	yes	—
756	C₄	C₂×H(5,𝔽₂)×C₈₃	1	1	yes	characteristic
757	C₄	#585×C₈₃	1	1	yes	characteristic
758	C₂	—	2	2	no	—
759	C₂	—	2	4	no	—
760	C₂	—	4	2	no	—
761	C₂	—	8	2	no	—
762	C₂	C₈₃×#3496	1	1	yes	characteristic
763	C₂	C₂²×#135×C₈₃	1	1	yes	characteristic
764	C₂	C₂×#578×C₈₃	1	1	yes	characteristic

	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 ◁ C₂×C₄×D₄×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₃×#3520	C₂	semidirect
2. C₈₃×#3342	C₂	semidirect
3. C₈₃×#3336	C₂	semidirect
4. C₈₃×#3334	C₂	semidirect
5. C₈₃×#3302	C₂	semidirect
6. C₈₃×#3300	C₂	semidirect
7. C₈₃×#3298	C₂	semidirect
8. D₄×Q₁₆×C₈₃	C₂	semidirect
9. C₈₃×#3285	C₂	semidirect
10. C₈₃×#3283	C₂	semidirect
11. C₈₃×#3248	C₂	semidirect
12. C₈₃×#3190	C₂	semidirect
13. C₈₃×#3170	C₂	semidirect
14. C₈₃×#3168	C₂	semidirect
15. C₈₃×#3050	C₂	semidirect
16. C₂×#467×C₈₃	C₂	semidirect
17. C₂×C₈×D₄×C₈₃	C₂	semidirect
18. C₂×#135×C₈₃	C₂²	semidirect
19. C₂²×Q₁₆×C₈₃	C₂²	semidirect
38. #500×C₈₃	C₂²	semidirect
39. #499×C₈₃	C₂²	semidirect
40. #495×C₈₃	C₂²	semidirect
41. #494×C₈₃	C₂²	semidirect
42. #488×C₈₃	C₂²	semidirect
43. #487×C₈₃	C₂²	semidirect
44. #485×C₈₃	C₂²	semidirect
45. #485×C₈₃	C₂²	semidirect
46. #483×C₈₃	C₂²	semidirect
47. #480×C₈₃	C₂²	semidirect
48. #479×C₈₃	C₂²	semidirect
49. #475×C₈₃	C₂²	semidirect
50. #474×C₈₃	C₂²	semidirect
55. #467×C₈₃	C₂²	semidirect
56. #467×C₈₃	C₂²	semidirect
57. #467×C₈₃	C₂²	semidirect
58. #467×C₈₃	C₂²	semidirect
60. #466×C₈₃	C₂²	semidirect
63. #465×C₈₃	C₂²	semidirect
64. #464×C₈₃	C₂²	semidirect
65. #462×C₈₃	C₂²	semidirect
66. #461×C₈₃	C₂²	semidirect
67. #452×C₈₃	C₂²	semidirect
68. #452×C₈₃	C₂²	semidirect
69. #451×C₈₃	C₂²	semidirect
70. #448×C₈₃	C₂²	semidirect
71. C₄×Q₁₆×C₈₃	C₂²	semidirect
72. C₄×Q₁₆×C₈₃	C₂²	semidirect
73. C₄×Q₁₆×C₈₃	C₂²	semidirect
74. C₄×SD₁₆×C₈₃	C₂²	semidirect
75. C₄×D₈×C₈₃	C₂²	semidirect
82. #427×C₈₃	C₂²	semidirect
83. C₂×#107×C₈₃	C₂²	semidirect
85. #416×C₈₃	C₂²	semidirect
86. C₂×#103×C₈₃	C₂²	semidirect
312. D₄×C₈₃	#135	semidirect
375. #62252	C₈₃	direct (N × H)
383. #3520	C₂×C₈₃	semidirect
384. #3342	C₂×C₈₃	semidirect
385. #3336	C₂×C₈₃	semidirect
386. #3334	C₂×C₈₃	semidirect
387. #3302	C₂×C₈₃	semidirect
388. #3300	C₂×C₈₃	semidirect
389. #3298	C₂×C₈₃	semidirect
390. D₄×Q₁₆	C₂×C₈₃	semidirect
391. #3285	C₂×C₈₃	semidirect
392. #3283	C₂×C₈₃	semidirect
393. #3248	C₂×C₈₃	semidirect
394. #3190	C₂×C₈₃	semidirect
395. #3170	C₂×C₈₃	semidirect
396. #3168	C₂×C₈₃	semidirect
397. #3050	C₂×C₈₃	semidirect
398. C₂×#467	C₂×C₈₃	semidirect
399. C₂×C₈×D₄	C₂×C₈₃	semidirect
400. C₈₃	#62252	direct (N × H)
401. C₂×#135	C₂²×C₈₃	semidirect
402. C₂²×Q₁₆	C₂²×C₈₃	semidirect
421. #500	C₂²×C₈₃	semidirect
422. #499	C₂²×C₈₃	semidirect
423. #495	C₂²×C₈₃	semidirect
424. #494	C₂²×C₈₃	semidirect
425. #488	C₂²×C₈₃	semidirect
426. #487	C₂²×C₈₃	semidirect
427. #485	C₂²×C₈₃	semidirect
428. #485	C₂²×C₈₃	semidirect
429. #483	C₂²×C₈₃	semidirect
430. #480	C₂²×C₈₃	semidirect
431. #479	C₂²×C₈₃	semidirect
432. #475	C₂²×C₈₃	semidirect
433. #474	C₂²×C₈₃	semidirect
438. #467	C₂²×C₈₃	semidirect
439. #467	C₂²×C₈₃	semidirect
440. #467	C₂²×C₈₃	semidirect
441. #467	C₂²×C₈₃	semidirect
443. #466	C₂²×C₈₃	semidirect
446. #465	C₂²×C₈₃	semidirect
447. #464	C₂²×C₈₃	semidirect
448. #462	C₂²×C₈₃	semidirect
449. #461	C₂²×C₈₃	semidirect
450. #452	C₂²×C₈₃	semidirect
451. #452	C₂²×C₈₃	semidirect
452. #451	C₂²×C₈₃	semidirect
453. #448	C₂²×C₈₃	semidirect
454. C₄×Q₁₆	C₂²×C₈₃	semidirect
455. C₄×Q₁₆	C₂²×C₈₃	semidirect
456. C₄×Q₁₆	C₂²×C₈₃	semidirect
457. C₄×SD₁₆	C₂²×C₈₃	semidirect
458. C₄×D₈	C₂²×C₈₃	semidirect
465. #427	C₂²×C₈₃	semidirect
466. C₂×#107	C₂²×C₈₃	semidirect
468. #416	C₂²×C₈₃	semidirect
469. C₂×#103	C₂²×C₈₃	semidirect
695. D₄	#135×C₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₈₃×#3520	2
C₈₃×#3342	2
C₈₃×#3336	2
C₈₃×#3334	2
C₈₃×#3302	2
C₈₃×#3300	2
C₈₃×#3298	2
D₄×Q₁₆×C₈₃	2
C₈₃×#3285	2
C₈₃×#3283	2
C₈₃×#3248	2
C₈₃×#3190	2
C₈₃×#3170	2
C₈₃×#3168	2
C₈₃×#3050	2
C₂×#467×C₈₃	2
C₂×C₈×D₄×C₈₃	2
#62252	83

Subgroups — C83×#62252 #35290076

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#62252 #35290076