Subgroups — C₈₃×#61743 #35289567

Order 21248.

1770 conjugacy classes of subgroups.

The subgroup lattice has 1138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₃×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₃×#3356	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₃×#3353	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₃×#3348	C₂	1	2	yes	maximal, complemented
6	C₈₃×#3347	C₂	1	2	yes	maximal, complemented
7	C₈₃×#3342	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₃×#3340	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₃×#3333	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₃×#3332	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₃×#3315	C₂	1	2	yes	maximal, complemented
12	C₈₃×#3307	C₂	1	2	yes	maximal, complemented
13	C₈₃×#3305	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₃×#3304	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#3237	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₃×#3228	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₃×#3197	C₂	1	2	yes	maximal, complemented
18	C₈₃×#3191	C₂	1	2	yes	maximal, complemented
19	C₈₃×#3115	C₂	1	1	yes	maximal, characteristic, complemented
20	C₈₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₃×#3093	C₂	1	2	yes	maximal, complemented
22	C₈₃×#3091	C₂	1	2	yes	maximal, complemented
23	C₈₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
24	#559×C₈₃	—	2	1	no	—
25	#559×C₈₃	—	2	1	no	—
26	#556×C₈₃	C₂²	1	1	yes	characteristic
27	#556×C₈₃	C₂²	1	1	yes	characteristic
28	#556×C₈₃	C₂²	1	1	yes	characteristic
29	#555×C₈₃	C₂²	1	1	yes	characteristic
30	#555×C₈₃	C₂²	1	2	yes	—
31	#554×C₈₃	C₂²	1	1	yes	characteristic
32	#553×C₈₃	—	2	2	no	—
33	#553×C₈₃	C₂²	1	2	yes	—
34	#552×C₈₃	—	2	1	no	—
35	#552×C₈₃	C₂²	1	2	yes	—
36	#551×C₈₃	—	2	2	no	—
37	#550×C₈₃	C₂²	1	1	yes	characteristic
38	#550×C₈₃	C₂²	1	1	yes	characteristic
39	#547×C₈₃	C₂²	1	2	yes	—
40	#547×C₈₃	C₂²	1	1	yes	characteristic
41	#546×C₈₃	—	2	1	no	—
42	#538×C₈₃	—	2	2	no	—
43	#535×C₈₃	—	2	1	no	—
44	#533×C₈₃	C₂²	1	1	yes	characteristic
45	#533×C₈₃	C₂²	1	1	yes	characteristic
46	#532×C₈₃	C₂²	1	1	yes	characteristic
47	#529×C₈₃	—	2	2	no	—
48	#529×C₈₃	—	2	1	no	—
49	#525×C₈₃	C₂²	1	2	yes	—
50	#525×C₈₃	C₂²	1	2	yes	—
51	#525×C₈₃	C₂²	1	2	yes	—
52	#520×C₈₃	—	2	1	no	—
53	C₄×#41×C₈₃	—	2	1	no	—
54	C₄×#41×C₈₃	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄×C₈₃	C₂²	1	1	yes	characteristic
56	C₂×#117×C₈₃	C₂²	1	2	yes	—
57	#501×C₈₃	C₂²	1	2	yes	complemented
58	#500×C₈₃	C₂²	1	1	yes	characteristic, complemented
59	#498×C₈₃	C₂²	1	1	yes	characteristic, complemented
60	#491×C₈₃	C₂²	1	2	yes	complemented
61	#486×C₈₃	C₂²	1	1	yes	characteristic, complemented
62	#486×C₈₃	C₂²	1	1	yes	characteristic, complemented
63	#485×C₈₃	C₂²	1	1	yes	characteristic
64	#485×C₈₃	C₂²	1	2	yes	—
65	#485×C₈₃	C₂²	1	1	yes	characteristic
66	#485×C₈₃	C₂²	1	2	yes	—
67	#485×C₈₃	C₂²	1	2	yes	complemented
68	#485×C₈₃	C₂²	1	2	yes	complemented
69	#485×C₈₃	C₂²	1	2	yes	complemented
70	#485×C₈₃	C₂²	1	2	yes	complemented
71	#484×C₈₃	C₂²	1	2	yes	complemented
72	#483×C₈₃	C₂²	1	2	yes	complemented
73	#482×C₈₃	C₂²	1	2	yes	—
74	#482×C₈₃	C₂²	1	2	yes	—
75	#482×C₈₃	C₂²	1	2	yes	—
76	#482×C₈₃	C₂²	1	2	yes	complemented
77	#482×C₈₃	C₂²	1	2	yes	complemented
78	#482×C₈₃	C₂²	1	2	yes	complemented
79	#482×C₈₃	C₂²	1	2	yes	complemented
80	#481×C₈₃	C₂²	1	2	yes	complemented
81	#480×C₈₃	C₂²	1	2	yes	complemented
82	#478×C₈₃	C₂²	1	2	yes	complemented
83	#478×C₈₃	C₂²	1	2	yes	complemented
84	#477×C₈₃	C₂²	1	1	yes	characteristic, complemented
85	#477×C₈₃	C₂²	1	1	yes	characteristic, complemented
86	#475×C₈₃	C₂²	1	1	yes	characteristic, complemented
87	#475×C₈₃	C₂²	1	1	yes	characteristic, complemented
88	#475×C₈₃	C₂²	1	1	yes	characteristic, complemented
89	#475×C₈₃	C₂²	1	1	yes	characteristic, complemented
90	#474×C₈₃	C₂²	1	1	yes	characteristic, complemented
91	#474×C₈₃	C₂²	1	1	yes	characteristic, complemented
92	#470×C₈₃	C₂²	1	2	yes	complemented
93	#469×C₈₃	C₂²	1	2	yes	complemented
94	#468×C₈₃	C₂²	1	2	yes	complemented
95	#468×C₈₃	C₂²	1	2	yes	complemented
96	#467×C₈₃	C₂²	1	2	yes	complemented
97	#466×C₈₃	C₂²	1	2	yes	complemented
98	#465×C₈₃	C₂²	1	2	yes	complemented
99	#465×C₈₃	C₂²	1	2	yes	complemented
100	#462×C₈₃	C₂²	1	1	yes	characteristic, complemented
101	#461×C₈₃	C₂²	1	1	yes	characteristic, complemented
102	#460×C₈₃	C₂²	1	1	yes	characteristic, complemented
103	#459×C₈₃	C₂²	1	1	yes	characteristic, complemented
104	#452×C₈₃	C₂²	1	1	yes	characteristic
105	#452×C₈₃	C₂²	1	1	yes	characteristic
106	#452×C₈₃	C₂²	1	2	yes	complemented
107	#452×C₈₃	C₂²	1	2	yes	complemented
108	#449×C₈₃	C₂²	1	2	yes	—
109	#449×C₈₃	C₂²	1	2	yes	complemented
110	#449×C₈₃	C₂²	1	2	yes	complemented
111	#442×C₈₃	C₂²	1	2	yes	complemented
112	#440×C₈₃	C₂²	1	2	yes	complemented
113	C₄×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic, complemented
114	C₄×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic, complemented
115	C₄×SD₁₆×C₈₃	C₂²	1	1	yes	characteristic, complemented
116	C₄×SD₁₆×C₈₃	C₂²	1	1	yes	characteristic, complemented
117	#436×C₈₃	C₂²	1	1	yes	characteristic
118	#436×C₈₃	C₂²	1	1	yes	characteristic
119	#435×C₈₃	C₂²	1	2	yes	—
120	#435×C₈₃	C₂²	1	2	yes	—
121	C₈×D₄×C₈₃	C₂²	1	1	yes	characteristic
122	C₈×D₄×C₈₃	C₂²	1	1	yes	characteristic
123	#432×C₈₃	C₂²	1	1	yes	characteristic
124	#431×C₈₃	C₂²	1	1	yes	characteristic
125	#428×C₈₃	C₂²	1	2	yes	complemented
126	#428×C₈₃	C₂²	1	2	yes	complemented
127	#427×C₈₃	C₂²	1	2	yes	complemented
128	#427×C₈₃	C₂²	1	2	yes	complemented
129	#417×C₈₃	C₂²	1	2	yes	complemented
130	#417×C₈₃	C₂²	1	2	yes	complemented
131	#416×C₈₃	C₂²	1	2	yes	complemented
132	#416×C₈₃	C₂²	1	2	yes	complemented
133	#407×C₈₃	C₂²	1	2	yes	—
134	C₂×C₂²⋊C₈×C₈₃	C₂²	1	2	yes	—
135	C₂×#41×C₈₃	—	2	1	no	—
136	C₂×#41×C₈₃	—	2	1	no	—
137	C₂×#41×C₈₃	C₂³	1	1	yes	characteristic
138	C₂×#41×C₈₃	C₂³	1	2	yes	—
139	C₂×#41×C₈₃	C₂³	1	2	yes	—
140	C₂²×D₄×C₈₃	D₄	1	1	yes	characteristic
141	C₂³×C₄×C₈₃	C₂³	1	2	yes	—
142	C₂×Q₁₆×C₈₃	C₂³	1	1	yes	characteristic
143	C₂×Q₁₆×C₈₃	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₈₃	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₈₃	C₂³	1	1	yes	characteristic
147	C₂×D₈×C₈₃	C₂³	1	2	yes	—
148	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
149	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
150	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
151	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
152	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
153	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
154	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
155	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
156	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
157	#127×C₈₃	—	2	1	no	—
158	#127×C₈₃	—	2	1	no	—
159	#127×C₈₃	C₂³	1	1	yes	characteristic
160	#126×C₈₃	—	2	2	no	—
161	#126×C₈₃	—	2	2	no	—
162	#126×C₈₃	—	2	2	no	—
163	#126×C₈₃	—	2	2	no	—
164	#126×C₈₃	—	2	2	no	—
165	#125×C₈₃	—	2	2	no	—
166	#125×C₈₃	—	2	1	no	—
167	#125×C₈₃	—	2	1	no	—
168	#125×C₈₃	C₂³	1	2	yes	—
169	#124×C₈₃	—	2	1	no	—
170	#124×C₈₃	—	2	1	no	—
171	#124×C₈₃	—	2	1	no	—
172	#124×C₈₃	—	2	2	no	—
173	#124×C₈₃	—	2	2	no	—
174	#124×C₈₃	—	2	2	no	—
175	#124×C₈₃	—	2	1	no	—
176	#123×C₈₃	—	2	2	no	—
177	#123×C₈₃	—	2	2	no	—
178	#123×C₈₃	—	2	2	no	—
179	#123×C₈₃	—	2	2	no	—
180	#123×C₈₃	—	2	2	no	—
181	#123×C₈₃	—	2	2	no	—
182	#123×C₈₃	—	2	2	no	—
183	#123×C₈₃	—	2	2	no	—
184	C₂²⋊Q₈×C₈₃	—	2	1	no	—
185	C₂²⋊Q₈×C₈₃	—	2	1	no	—
186	C₂²⋊Q₈×C₈₃	—	2	1	no	—
187	C₂²⋊Q₈×C₈₃	—	2	1	no	—
188	C₂²⋊Q₈×C₈₃	—	2	2	no	—
189	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
190	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
191	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
192	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
193	C₂²⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
194	C₂²⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
195	#121×C₈₃	—	2	2	no	—
196	#121×C₈₃	—	2	1	no	—
197	#121×C₈₃	—	2	2	no	—
198	#121×C₈₃	—	2	2	no	—
199	#121×C₈₃	—	2	1	no	—
200	#121×C₈₃	—	2	2	no	—
201	#121×C₈₃	—	2	2	no	—
202	#121×C₈₃	C₂³	1	2	yes	—
203	#121×C₈₃	C₂³	1	2	yes	—
204	#121×C₈₃	C₂³	1	2	yes	—
205	#121×C₈₃	C₂³	1	2	yes	—
206	#121×C₈₃	C₂³	1	2	yes	—
207	#120×C₈₃	—	2	2	no	—
208	#120×C₈₃	—	2	2	no	—
209	#120×C₈₃	—	2	2	no	—
210	C₄×Q₈×C₈₃	—	2	1	no	—
211	C₄×Q₈×C₈₃	—	2	1	no	—
212	C₄×Q₈×C₈₃	—	2	1	no	—
213	C₄×Q₈×C₈₃	—	2	1	no	—
214	C₄×Q₈×C₈₃	—	2	1	no	—
215	C₄×Q₈×C₈₃	—	2	1	no	—
216	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
217	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
220	C₄×D₄×C₈₃	—	2	1	no	—
221	C₄×D₄×C₈₃	—	2	2	no	—
222	C₄×D₄×C₈₃	—	2	1	no	—
223	C₄×D₄×C₈₃	—	2	1	no	—
224	C₄×D₄×C₈₃	—	2	2	no	—
225	C₄×D₄×C₈₃	—	2	2	no	—
226	C₄×D₄×C₈₃	—	2	2	no	—
227	C₄×D₄×C₈₃	—	2	2	no	—
228	C₄×D₄×C₈₃	—	2	2	no	—
229	C₄×D₄×C₈₃	—	2	1	no	—
230	C₄×D₄×C₈₃	—	2	1	no	—
231	C₄×D₄×C₈₃	—	2	2	no	—
232	C₄×D₄×C₈₃	—	2	1	no	—
233	C₄×D₄×C₈₃	D₄	1	1	yes	characteristic
234	C₄×D₄×C₈₃	D₄	1	2	yes	—
235	C₄×D₄×C₈₃	D₄	1	1	yes	characteristic
236	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₈₃	C₂³	1	2	yes	—
239	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₈₃	C₂³	1	2	yes	—
241	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
242	#117×C₈₃	—	2	2	no	—
243	#117×C₈₃	—	2	2	no	—
244	#117×C₈₃	—	2	1	no	—
245	#117×C₈₃	—	2	1	no	—
246	#117×C₈₃	—	2	2	no	—
247	#117×C₈₃	—	2	2	no	—
248	#117×C₈₃	—	2	1	no	—
249	#117×C₈₃	C₂³	1	1	yes	characteristic
250	#117×C₈₃	C₂³	1	2	yes	—
251	#117×C₈₃	C₂³	1	2	yes	—
252	#117×C₈₃	C₂³	1	2	yes	—
253	#117×C₈₃	C₂³	1	2	yes	—
254	#117×C₈₃	C₂³	1	2	yes	—
255	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
256	C₂×C₄⋊C₄×C₈₃	D₄	1	1	yes	characteristic
257	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
259	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
260	C₂×C₂²⋊C₄×C₈₃	D₄	1	2	yes	—
261	C₂×C₄²×C₈₃	—	2	2	no	—
262	C₂×C₄²×C₈₃	—	2	1	no	—
263	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
264	#107×C₈₃	C₂³	1	2	yes	—
265	#107×C₈₃	C₂³	1	2	yes	—
266	#107×C₈₃	C₂³	1	2	yes	—
267	#107×C₈₃	C₂³	1	2	yes	—
268	#107×C₈₃	C₂³	1	1	yes	characteristic
269	#107×C₈₃	C₂³	1	2	yes	—
270	#107×C₈₃	C₂³	1	1	yes	characteristic
271	#106×C₈₃	C₂³	1	2	yes	—
272	#106×C₈₃	C₂³	1	2	yes	—
273	#106×C₈₃	C₂³	1	2	yes	—
274	#106×C₈₃	C₂³	1	2	yes	—
275	#106×C₈₃	C₂³	1	1	yes	characteristic
276	#106×C₈₃	C₂³	1	2	yes	—
277	#106×C₈₃	C₂³	1	1	yes	characteristic
278	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
279	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
282	#103×C₈₃	C₂³	1	1	yes	characteristic
283	#103×C₈₃	C₂³	1	2	yes	—
284	#103×C₈₃	C₂³	1	2	yes	—
285	#103×C₈₃	C₂³	1	2	yes	—
286	#103×C₈₃	C₂³	1	1	yes	characteristic
287	#103×C₈₃	C₂³	1	2	yes	—
288	#103×C₈₃	C₂³	1	2	yes	—
289	#103×C₈₃	C₂³	1	1	yes	characteristic
290	#103×C₈₃	C₂³	1	1	yes	characteristic
291	#103×C₈₃	C₂³	1	1	yes	characteristic
292	#103×C₈₃	C₂³	1	1	yes	characteristic
293	#102×C₈₃	C₂³	1	2	yes	—
294	#102×C₈₃	C₂³	1	2	yes	—
295	#102×C₈₃	C₂³	1	1	yes	characteristic
296	#102×C₈₃	C₂³	1	2	yes	—
297	#102×C₈₃	C₂³	1	2	yes	—
298	#102×C₈₃	C₂³	1	1	yes	characteristic
299	#102×C₈₃	C₂³	1	2	yes	—
300	#102×C₈₃	C₂³	1	2	yes	—
301	#102×C₈₃	C₂³	1	2	yes	—
302	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
303	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
305	C₂²⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
306	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
308	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
309	#97×C₈₃	C₂³	1	2	yes	—
310	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
312	C₂⁴×C₈₃	C₂×D₄	1	2	yes	—
313	#41×C₈₃	—	4	1	no	—
314	#41×C₈₃	—	4	1	no	—
315	#41×C₈₃	—	4	4	no	—
316	#41×C₈₃	—	4	2	no	—
317	#41×C₈₃	—	4	2	no	—
318	#41×C₈₃	—	4	2	no	—
319	#41×C₈₃	—	4	2	no	—
320	#41×C₈₃	—	4	4	no	—
321	C₂×Q₈×C₈₃	—	2	1	no	—
322	C₂×Q₈×C₈₃	—	2	1	no	—
323	C₂×Q₈×C₈₃	—	2	1	no	—
324	C₂×Q₈×C₈₃	—	2	1	no	—
325	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₈₃	—	2	2	no	—
329	C₂×D₄×C₈₃	—	2	1	no	—
330	C₂×D₄×C₈₃	—	2	2	no	—
331	C₂×D₄×C₈₃	—	2	2	no	—
332	C₂×D₄×C₈₃	—	2	2	no	—
333	C₂×D₄×C₈₃	—	2	2	no	—
334	C₂×D₄×C₈₃	—	2	2	no	—
335	C₂×D₄×C₈₃	—	2	2	no	—
336	C₂×D₄×C₈₃	—	2	1	no	—
337	C₂×D₄×C₈₃	—	2	1	no	—
338	C₂×D₄×C₈₃	—	4	2	no	—
339	C₂×D₄×C₈₃	C₂×D₄	1	1	yes	characteristic
340	C₂×D₄×C₈₃	C₂×D₄	1	1	yes	characteristic
341	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
342	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
343	C₂×D₄×C₈₃	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₈₃	—	2	2	no	—
345	C₂²×C₄×C₈₃	—	2	2	no	—
346	C₂²×C₄×C₈₃	—	2	1	no	—
347	C₂²×C₄×C₈₃	—	2	1	no	—
348	C₂²×C₄×C₈₃	—	2	2	no	—
349	C₂²×C₄×C₈₃	—	2	1	no	—
350	C₂²×C₄×C₈₃	—	2	2	no	—
351	C₂²×C₄×C₈₃	—	2	2	no	—
352	C₂²×C₄×C₈₃	—	4	2	no	—
353	C₂²×C₄×C₈₃	—	4	2	no	—
354	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
356	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
357	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
358	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
359	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
361	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
362	Q₁₆×C₈₃	—	4	1	no	—
363	Q₁₆×C₈₃	—	4	1	no	—
364	SD₁₆×C₈₃	—	4	1	no	—
365	SD₁₆×C₈₃	—	4	2	no	—
366	SD₁₆×C₈₃	—	4	1	no	—
367	D₈×C₈₃	—	4	2	no	—
368	M₁₆×C₈₃	—	4	2	no	—
369	M₁₆×C₈₃	—	4	2	no	—
370	C₂×C₈×C₈₃	—	4	2	no	—
371	C₂×C₈×C₈₃	—	4	2	no	—
372	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
377	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
378	C₄⋊C₄×C₈₃	—	2	1	no	—
379	C₄⋊C₄×C₈₃	—	2	2	no	—
380	C₄⋊C₄×C₈₃	—	2	2	no	—
381	C₄⋊C₄×C₈₃	—	2	2	no	—
382	C₄⋊C₄×C₈₃	—	2	2	no	—
383	C₄⋊C₄×C₈₃	—	2	1	no	—
384	C₄⋊C₄×C₈₃	—	2	1	no	—
385	C₄⋊C₄×C₈₃	—	2	2	no	—
386	C₄⋊C₄×C₈₃	—	2	2	no	—
387	C₄⋊C₄×C₈₃	—	2	1	no	—
388	C₄⋊C₄×C₈₃	—	2	1	no	—
389	C₄⋊C₄×C₈₃	—	2	1	no	—
390	C₄⋊C₄×C₈₃	—	2	1	no	—
391	C₄⋊C₄×C₈₃	—	2	1	no	—
392	C₄⋊C₄×C₈₃	—	2	2	no	—
393	C₄⋊C₄×C₈₃	—	2	2	no	—
394	C₄⋊C₄×C₈₃	—	2	1	no	—
395	C₄⋊C₄×C₈₃	—	2	1	no	—
396	C₄⋊C₄×C₈₃	—	2	1	no	—
397	C₄⋊C₄×C₈₃	—	2	1	no	—
398	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
406	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
408	C₂²⋊C₄×C₈₃	—	2	1	no	—
409	C₂²⋊C₄×C₈₃	—	2	2	no	—
410	C₂²⋊C₄×C₈₃	—	2	2	no	—
411	C₂²⋊C₄×C₈₃	—	2	2	no	—
412	C₂²⋊C₄×C₈₃	—	2	1	no	—
413	C₂²⋊C₄×C₈₃	—	2	1	no	—
414	C₂²⋊C₄×C₈₃	—	2	2	no	—
415	C₂²⋊C₄×C₈₃	—	2	2	no	—
416	C₂²⋊C₄×C₈₃	—	2	2	no	—
417	C₂²⋊C₄×C₈₃	—	2	2	no	—
418	C₂²⋊C₄×C₈₃	—	2	2	no	—
419	C₂²⋊C₄×C₈₃	—	2	2	no	—
420	C₂²⋊C₄×C₈₃	—	2	2	no	—
421	C₂²⋊C₄×C₈₃	—	2	2	no	—
422	C₂²⋊C₄×C₈₃	—	2	2	no	—
423	C₂²⋊C₄×C₈₃	—	2	1	no	—
424	C₂²⋊C₄×C₈₃	—	2	1	no	—
425	C₂²⋊C₄×C₈₃	—	2	2	no	—
426	C₂²⋊C₄×C₈₃	—	2	2	no	—
427	C₂²⋊C₄×C₈₃	—	2	2	no	—
428	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
429	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
430	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
431	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
432	C₄²×C₈₃	—	2	1	no	—
433	C₄²×C₈₃	—	2	2	no	—
434	C₄²×C₈₃	—	2	1	no	—
435	C₄²×C₈₃	—	2	2	no	—
436	C₄²×C₈₃	—	2	2	no	—
437	C₄²×C₈₃	—	2	1	no	—
438	C₄²×C₈₃	—	2	2	no	—
439	C₄²×C₈₃	—	2	2	no	—
440	C₄²×C₈₃	—	2	1	no	—
441	C₄²×C₈₃	—	2	1	no	—
442	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
443	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
444	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
445	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
446	C₂³×C₈₃	—	2	1	no	—
447	C₂³×C₈₃	—	2	2	no	—
448	C₂³×C₈₃	—	4	2	no	—
449	C₂³×C₈₃	—	4	2	no	—
450	C₂³×C₈₃	—	4	2	no	—
451	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
452	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
453	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
454	Q₈×C₈₃	—	2	1	no	—
455	Q₈×C₈₃	—	2	1	no	—
456	Q₈×C₈₃	—	2	1	no	—
457	Q₈×C₈₃	—	2	1	no	—
458	Q₈×C₈₃	—	2	1	no	—
459	Q₈×C₈₃	—	2	1	no	—
460	Q₈×C₈₃	—	4	2	no	—
461	Q₈×C₈₃	—	4	2	no	—
462	Q₈×C₈₃	—	8	1	no	—
463	Q₈×C₈₃	—	8	1	no	—
464	D₄×C₈₃	—	2	2	no	—
465	D₄×C₈₃	—	2	2	no	—
466	D₄×C₈₃	—	2	1	no	—
467	D₄×C₈₃	—	2	2	no	—
468	D₄×C₈₃	—	2	1	no	—
469	D₄×C₈₃	—	2	2	no	—
470	D₄×C₈₃	—	4	2	no	—
471	D₄×C₈₃	—	4	2	no	—
472	D₄×C₈₃	—	4	4	no	—
473	D₄×C₈₃	—	4	4	no	—
474	D₄×C₈₃	—	4	2	no	—
475	D₄×C₈₃	—	8	1	no	—
476	D₄×C₈₃	—	8	2	no	—
477	D₄×C₈₃	—	8	2	no	—
478	D₄×C₈₃	—	8	2	no	—
479	D₄×C₈₃	—	8	2	no	—
480	D₄×C₈₃	—	8	2	no	—
481	C₂×C₄×C₈₃	—	2	2	no	—
482	C₂×C₄×C₈₃	—	2	2	no	—
483	C₂×C₄×C₈₃	—	2	2	no	—
484	C₂×C₄×C₈₃	—	2	2	no	—
485	C₂×C₄×C₈₃	—	2	2	no	—
486	C₂×C₄×C₈₃	—	2	1	no	—
487	C₂×C₄×C₈₃	—	2	1	no	—
488	C₂×C₄×C₈₃	—	2	1	no	—
489	C₂×C₄×C₈₃	—	2	1	no	—
490	C₂×C₄×C₈₃	—	2	1	no	—
491	C₂×C₄×C₈₃	—	2	1	no	—
492	C₂×C₄×C₈₃	—	2	2	no	—
493	C₂×C₄×C₈₃	—	2	1	no	—
494	C₂×C₄×C₈₃	—	2	2	no	—
495	C₂×C₄×C₈₃	—	2	2	no	—
496	C₂×C₄×C₈₃	—	2	1	no	—
497	C₂×C₄×C₈₃	—	2	1	no	—
498	C₂×C₄×C₈₃	—	4	2	no	—
499	C₂×C₄×C₈₃	—	4	2	no	—
500	C₂×C₄×C₈₃	—	4	2	no	—
501	C₂×C₄×C₈₃	—	4	1	no	—
502	C₂×C₄×C₈₃	—	4	2	no	—
503	C₂×C₄×C₈₃	—	4	4	no	—
504	C₂×C₄×C₈₃	—	4	4	no	—
505	C₂×C₄×C₈₃	—	4	2	no	—
506	C₂×C₄×C₈₃	—	8	1	no	—
507	C₂×C₄×C₈₃	—	8	2	no	—
508	C₂×C₄×C₈₃	—	8	2	no	—
509	C₂×C₄×C₈₃	—	8	2	no	—
510	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
512	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
514	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
518	C₈×C₈₃	—	2	1	no	—
519	C₈×C₈₃	—	2	1	no	—
520	C₈×C₈₃	—	2	2	no	—
521	C₈×C₈₃	—	2	2	no	—
522	C₈×C₈₃	—	2	1	no	—
523	C₈×C₈₃	—	2	1	no	—
524	C₂²×C₈₃	—	2	1	no	—
525	C₂²×C₈₃	—	2	2	no	—
526	C₂²×C₈₃	—	2	2	no	—
527	C₂²×C₈₃	—	2	1	no	—
528	C₂²×C₈₃	—	2	2	no	—
529	C₂²×C₈₃	—	2	2	no	—
530	C₂²×C₈₃	—	2	1	no	—
531	C₂²×C₈₃	—	2	2	no	—
532	C₂²×C₈₃	—	2	2	no	—
533	C₂²×C₈₃	—	4	1	no	—
534	C₂²×C₈₃	—	4	2	no	—
535	C₂²×C₈₃	—	4	1	no	—
536	C₂²×C₈₃	—	4	2	no	—
537	C₂²×C₈₃	—	4	2	no	—
538	C₂²×C₈₃	—	4	1	no	—
539	C₂²×C₈₃	—	8	4	no	—
540	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
541	C₄×C₈₃	—	2	1	no	—
542	C₄×C₈₃	—	2	1	no	—
543	C₄×C₈₃	—	2	1	no	—
544	C₄×C₈₃	—	2	2	no	—
545	C₄×C₈₃	—	2	2	no	—
546	C₄×C₈₃	—	2	1	no	—
547	C₄×C₈₃	—	4	1	no	—
548	C₄×C₈₃	—	4	2	no	—
549	C₄×C₈₃	—	4	1	no	—
550	C₄×C₈₃	—	4	1	no	—
551	C₄×C₈₃	—	4	1	no	—
552	C₄×C₈₃	—	4	1	no	—
553	C₄×C₈₃	—	4	1	no	—
554	C₄×C₈₃	—	4	1	no	—
555	C₄×C₈₃	—	4	2	no	—
556	C₄×C₈₃	—	4	2	no	—
557	C₄×C₈₃	#575	1	2	yes	—
558	C₄×C₈₃	#585	1	1	yes	characteristic
559	C₄×C₈₃	#585	1	1	yes	characteristic
560	#61743	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
561	C₂×C₈₃	—	4	2	no	—
562	C₂×C₈₃	—	4	2	no	—
563	C₂×C₈₃	—	4	1	no	—
564	C₂×C₈₃	—	8	1	no	—
565	C₂×C₈₃	—	8	2	no	—
566	C₂×C₈₃	#3485	1	1	yes	characteristic
567	C₂×C₈₃	C₂×#575	1	1	yes	characteristic
568	C₂×C₈₃	#3584	1	1	yes	characteristic
569	#3506	C₂×C₈₃	1	1	yes	characteristic, complemented
570	#3475	C₂×C₈₃	1	1	yes	characteristic, complemented
571	#3356	C₂×C₈₃	1	1	yes	characteristic, complemented
572	#3353	C₂×C₈₃	1	1	yes	characteristic, complemented
573	#3348	C₂×C₈₃	1	2	yes	complemented
574	#3347	C₂×C₈₃	1	2	yes	complemented
575	#3342	C₂×C₈₃	1	1	yes	characteristic, complemented
576	#3340	C₂×C₈₃	1	1	yes	characteristic, complemented
577	#3333	C₂×C₈₃	1	1	yes	characteristic, complemented
578	#3332	C₂×C₈₃	1	1	yes	characteristic, complemented
579	#3315	C₂×C₈₃	1	2	yes	complemented
580	#3307	C₂×C₈₃	1	2	yes	complemented
581	#3305	C₂×C₈₃	1	1	yes	characteristic, complemented
582	#3304	C₂×C₈₃	1	1	yes	characteristic, complemented
583	#3237	C₂×C₈₃	1	1	yes	characteristic, complemented
584	#3228	C₂×C₈₃	1	1	yes	characteristic, complemented
585	#3197	C₂×C₈₃	1	2	yes	complemented
586	#3191	C₂×C₈₃	1	2	yes	complemented
587	#3115	C₂×C₈₃	1	1	yes	characteristic, complemented
588	#3107	C₂×C₈₃	1	1	yes	characteristic, complemented
589	#3093	C₂×C₈₃	1	2	yes	complemented
590	#3091	C₂×C₈₃	1	2	yes	complemented
591	#2974	C₂×C₈₃	1	1	yes	characteristic, complemented
592	C₈₃	#61743	1	1	yes	characteristic, direct product factor, Sylow
593	#559	—	2	1	no	—
594	#559	—	2	1	no	—
595	#556	C₂²×C₈₃	1	1	yes	characteristic
596	#556	C₂²×C₈₃	1	1	yes	characteristic
597	#556	C₂²×C₈₃	1	1	yes	characteristic
598	#555	C₂²×C₈₃	1	1	yes	characteristic
599	#555	C₂²×C₈₃	1	2	yes	—
600	#554	C₂²×C₈₃	1	1	yes	characteristic
601	#553	—	2	2	no	—
602	#553	C₂²×C₈₃	1	2	yes	—
603	#552	—	2	1	no	—
604	#552	C₂²×C₈₃	1	2	yes	—
605	#551	—	2	2	no	—
606	#550	C₂²×C₈₃	1	1	yes	characteristic
607	#550	C₂²×C₈₃	1	1	yes	characteristic
608	#547	C₂²×C₈₃	1	2	yes	—
609	#547	C₂²×C₈₃	1	1	yes	characteristic
610	#546	—	2	1	no	—
611	#538	—	2	2	no	—
612	#535	—	2	1	no	—
613	#533	C₂²×C₈₃	1	1	yes	characteristic
614	#533	C₂²×C₈₃	1	1	yes	characteristic
615	#532	C₂²×C₈₃	1	1	yes	characteristic
616	#529	—	2	2	no	—
617	#529	—	2	1	no	—
618	#525	C₂²×C₈₃	1	2	yes	—
619	#525	C₂²×C₈₃	1	2	yes	—
620	#525	C₂²×C₈₃	1	2	yes	—
621	#520	—	2	1	no	—
622	C₄×#41	—	2	1	no	—
623	C₄×#41	C₂²×C₈₃	1	1	yes	characteristic
624	C₂×C₄×D₄	C₂²×C₈₃	1	1	yes	characteristic
625	C₂×#117	C₂²×C₈₃	1	2	yes	—
626	#501	C₂²×C₈₃	1	2	yes	complemented
627	#500	C₂²×C₈₃	1	1	yes	characteristic, complemented
628	#498	C₂²×C₈₃	1	1	yes	characteristic, complemented
629	#491	C₂²×C₈₃	1	2	yes	complemented
630	#486	C₂²×C₈₃	1	1	yes	characteristic, complemented
631	#486	C₂²×C₈₃	1	1	yes	characteristic, complemented
632	#485	C₂²×C₈₃	1	1	yes	characteristic
633	#485	C₂²×C₈₃	1	2	yes	—
634	#485	C₂²×C₈₃	1	1	yes	characteristic
635	#485	C₂²×C₈₃	1	2	yes	—
636	#485	C₂²×C₈₃	1	2	yes	complemented
637	#485	C₂²×C₈₃	1	2	yes	complemented
638	#485	C₂²×C₈₃	1	2	yes	complemented
639	#485	C₂²×C₈₃	1	2	yes	complemented
640	#484	C₂²×C₈₃	1	2	yes	complemented
641	#483	C₂²×C₈₃	1	2	yes	complemented
642	#482	C₂²×C₈₃	1	2	yes	—
643	#482	C₂²×C₈₃	1	2	yes	—
644	#482	C₂²×C₈₃	1	2	yes	—
645	#482	C₂²×C₈₃	1	2	yes	complemented
646	#482	C₂²×C₈₃	1	2	yes	complemented
647	#482	C₂²×C₈₃	1	2	yes	complemented
648	#482	C₂²×C₈₃	1	2	yes	complemented
649	#481	C₂²×C₈₃	1	2	yes	complemented
650	#480	C₂²×C₈₃	1	2	yes	complemented
651	#478	C₂²×C₈₃	1	2	yes	complemented
652	#478	C₂²×C₈₃	1	2	yes	complemented
653	#477	C₂²×C₈₃	1	1	yes	characteristic, complemented
654	#477	C₂²×C₈₃	1	1	yes	characteristic, complemented
655	#475	C₂²×C₈₃	1	1	yes	characteristic, complemented
656	#475	C₂²×C₈₃	1	1	yes	characteristic, complemented
657	#475	C₂²×C₈₃	1	1	yes	characteristic, complemented
658	#475	C₂²×C₈₃	1	1	yes	characteristic, complemented
659	#474	C₂²×C₈₃	1	1	yes	characteristic, complemented
660	#474	C₂²×C₈₃	1	1	yes	characteristic, complemented
661	#470	C₂²×C₈₃	1	2	yes	complemented
662	#469	C₂²×C₈₃	1	2	yes	complemented
663	#468	C₂²×C₈₃	1	2	yes	complemented
664	#468	C₂²×C₈₃	1	2	yes	complemented
665	#467	C₂²×C₈₃	1	2	yes	complemented
666	#466	C₂²×C₈₃	1	2	yes	complemented
667	#465	C₂²×C₈₃	1	2	yes	complemented
668	#465	C₂²×C₈₃	1	2	yes	complemented
669	#462	C₂²×C₈₃	1	1	yes	characteristic, complemented
670	#461	C₂²×C₈₃	1	1	yes	characteristic, complemented
671	#460	C₂²×C₈₃	1	1	yes	characteristic, complemented
672	#459	C₂²×C₈₃	1	1	yes	characteristic, complemented
673	#452	C₂²×C₈₃	1	1	yes	characteristic
674	#452	C₂²×C₈₃	1	1	yes	characteristic
675	#452	C₂²×C₈₃	1	2	yes	complemented
676	#452	C₂²×C₈₃	1	2	yes	complemented
677	#449	C₂²×C₈₃	1	2	yes	—
678	#449	C₂²×C₈₃	1	2	yes	complemented
679	#449	C₂²×C₈₃	1	2	yes	complemented
680	#442	C₂²×C₈₃	1	2	yes	complemented
681	#440	C₂²×C₈₃	1	2	yes	complemented
682	C₄×Q₁₆	C₂²×C₈₃	1	1	yes	characteristic, complemented
683	C₄×Q₁₆	C₂²×C₈₃	1	1	yes	characteristic, complemented
684	C₄×SD₁₆	C₂²×C₈₃	1	1	yes	characteristic, complemented
685	C₄×SD₁₆	C₂²×C₈₃	1	1	yes	characteristic, complemented
686	#436	C₂²×C₈₃	1	1	yes	characteristic
687	#436	C₂²×C₈₃	1	1	yes	characteristic
688	#435	C₂²×C₈₃	1	2	yes	—
689	#435	C₂²×C₈₃	1	2	yes	—
690	C₈×D₄	C₂²×C₈₃	1	1	yes	characteristic
691	C₈×D₄	C₂²×C₈₃	1	1	yes	characteristic
692	#432	C₂²×C₈₃	1	1	yes	characteristic
693	#431	C₂²×C₈₃	1	1	yes	characteristic
694	#428	C₂²×C₈₃	1	2	yes	complemented
695	#428	C₂²×C₈₃	1	2	yes	complemented
696	#427	C₂²×C₈₃	1	2	yes	complemented
697	#427	C₂²×C₈₃	1	2	yes	complemented
698	#417	C₂²×C₈₃	1	2	yes	complemented
699	#417	C₂²×C₈₃	1	2	yes	complemented
700	#416	C₂²×C₈₃	1	2	yes	complemented
701	#416	C₂²×C₈₃	1	2	yes	complemented
702	#407	C₂²×C₈₃	1	2	yes	—
703	C₂×C₂²⋊C₈	C₂²×C₈₃	1	2	yes	—
704	C₂×#41	—	2	1	no	—
705	C₂×#41	—	2	1	no	—
706	C₂×#41	C₂³×C₈₃	1	1	yes	characteristic
707	C₂×#41	C₂³×C₈₃	1	2	yes	—
708	C₂×#41	C₂³×C₈₃	1	2	yes	—
709	C₂²×D₄	D₄×C₈₃	1	1	yes	characteristic
710	C₂³×C₄	C₂³×C₈₃	1	2	yes	—
711	C₂×Q₁₆	C₂³×C₈₃	1	1	yes	characteristic
712	C₂×Q₁₆	C₂³×C₈₃	1	1	yes	characteristic
713	C₂×SD₁₆	C₂³×C₈₃	1	1	yes	characteristic
714	C₂×SD₁₆	C₂³×C₈₃	1	1	yes	characteristic
715	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
716	C₂×D₈	C₂³×C₈₃	1	2	yes	—
717	C₂×M₁₆	C₂³×C₈₃	1	2	yes	—
718	C₂×M₁₆	C₂³×C₈₃	1	2	yes	—
719	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
720	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
721	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
722	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
723	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
724	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
725	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
726	#127	—	2	1	no	—
727	#127	—	2	1	no	—
728	#127	C₂³×C₈₃	1	1	yes	characteristic
729	#126	—	2	2	no	—
730	#126	—	2	2	no	—
731	#126	—	2	2	no	—
732	#126	—	2	2	no	—
733	#126	—	2	2	no	—
734	#125	—	2	2	no	—
735	#125	—	2	1	no	—
736	#125	—	2	1	no	—
737	#125	C₂³×C₈₃	1	2	yes	—
738	#124	—	2	1	no	—
739	#124	—	2	1	no	—
740	#124	—	2	1	no	—
741	#124	—	2	2	no	—
742	#124	—	2	2	no	—
743	#124	—	2	2	no	—
744	#124	—	2	1	no	—
745	#123	—	2	2	no	—
746	#123	—	2	2	no	—
747	#123	—	2	2	no	—
748	#123	—	2	2	no	—
749	#123	—	2	2	no	—
750	#123	—	2	2	no	—
751	#123	—	2	2	no	—
752	#123	—	2	2	no	—
753	C₂²⋊Q₈	—	2	1	no	—
754	C₂²⋊Q₈	—	2	1	no	—
755	C₂²⋊Q₈	—	2	1	no	—
756	C₂²⋊Q₈	—	2	1	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
759	C₂²⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
760	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
761	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
762	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
763	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
764	#121	—	2	2	no	—
765	#121	—	2	1	no	—
766	#121	—	2	2	no	—
767	#121	—	2	2	no	—
768	#121	—	2	1	no	—
769	#121	—	2	2	no	—
770	#121	—	2	2	no	—
771	#121	C₂³×C₈₃	1	2	yes	—
772	#121	C₂³×C₈₃	1	2	yes	—
773	#121	C₂³×C₈₃	1	2	yes	—
774	#121	C₂³×C₈₃	1	2	yes	—
775	#121	C₂³×C₈₃	1	2	yes	—
776	#120	—	2	2	no	—
777	#120	—	2	2	no	—
778	#120	—	2	2	no	—
779	C₄×Q₈	—	2	1	no	—
780	C₄×Q₈	—	2	1	no	—
781	C₄×Q₈	—	2	1	no	—
782	C₄×Q₈	—	2	1	no	—
783	C₄×Q₈	—	2	1	no	—
784	C₄×Q₈	—	2	1	no	—
785	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
786	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
787	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
788	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	2	2	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	2	no	—
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	—	2	2	no	—
797	C₄×D₄	—	2	2	no	—
798	C₄×D₄	—	2	1	no	—
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	—	2	2	no	—
801	C₄×D₄	—	2	1	no	—
802	C₄×D₄	D₄×C₈₃	1	1	yes	characteristic
803	C₄×D₄	D₄×C₈₃	1	2	yes	—
804	C₄×D₄	D₄×C₈₃	1	1	yes	characteristic
805	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
806	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
807	C₄×D₄	C₂³×C₈₃	1	2	yes	—
808	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
809	C₄×D₄	C₂³×C₈₃	1	2	yes	—
810	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
811	#117	—	2	2	no	—
812	#117	—	2	2	no	—
813	#117	—	2	1	no	—
814	#117	—	2	1	no	—
815	#117	—	2	2	no	—
816	#117	—	2	2	no	—
817	#117	—	2	1	no	—
818	#117	C₂³×C₈₃	1	1	yes	characteristic
819	#117	C₂³×C₈₃	1	2	yes	—
820	#117	C₂³×C₈₃	1	2	yes	—
821	#117	C₂³×C₈₃	1	2	yes	—
822	#117	C₂³×C₈₃	1	2	yes	—
823	#117	C₂³×C₈₃	1	2	yes	—
824	C₂×C₄⋊C₄	—	2	2	no	—
825	C₂×C₄⋊C₄	D₄×C₈₃	1	1	yes	characteristic
826	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
827	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
828	C₂×C₂²⋊C₄	—	2	2	no	—
829	C₂×C₂²⋊C₄	D₄×C₈₃	1	2	yes	—
830	C₂×C₄²	—	2	2	no	—
831	C₂×C₄²	—	2	1	no	—
832	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
833	#107	C₂³×C₈₃	1	1	yes	characteristic
834	#107	C₂³×C₈₃	1	2	yes	—
835	#107	C₂³×C₈₃	1	2	yes	—
836	#107	C₂³×C₈₃	1	2	yes	—
837	#107	C₂³×C₈₃	1	1	yes	characteristic
838	#107	C₂³×C₈₃	1	2	yes	—
839	#107	C₂³×C₈₃	1	2	yes	—
840	#106	C₂³×C₈₃	1	1	yes	characteristic
841	#106	C₂³×C₈₃	1	2	yes	—
842	#106	C₂³×C₈₃	1	2	yes	—
843	#106	C₂³×C₈₃	1	2	yes	—
844	#106	C₂³×C₈₃	1	1	yes	characteristic
845	#106	C₂³×C₈₃	1	2	yes	—
846	#106	C₂³×C₈₃	1	2	yes	—
847	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
848	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
849	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
850	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
851	#103	C₂³×C₈₃	1	1	yes	characteristic
852	#103	C₂³×C₈₃	1	1	yes	characteristic
853	#103	C₂³×C₈₃	1	2	yes	—
854	#103	C₂³×C₈₃	1	2	yes	—
855	#103	C₂³×C₈₃	1	1	yes	characteristic
856	#103	C₂³×C₈₃	1	1	yes	characteristic
857	#103	C₂³×C₈₃	1	2	yes	—
858	#103	C₂³×C₈₃	1	2	yes	—
859	#103	C₂³×C₈₃	1	1	yes	characteristic
860	#103	C₂³×C₈₃	1	1	yes	characteristic
861	#103	C₂³×C₈₃	1	2	yes	—
862	#102	C₂³×C₈₃	1	2	yes	—
863	#102	C₂³×C₈₃	1	2	yes	—
864	#102	C₂³×C₈₃	1	2	yes	—
865	#102	C₂³×C₈₃	1	2	yes	—
866	#102	C₂³×C₈₃	1	2	yes	—
867	#102	C₂³×C₈₃	1	2	yes	—
868	#102	C₂³×C₈₃	1	1	yes	characteristic
869	#102	C₂³×C₈₃	1	1	yes	characteristic
870	#102	C₂³×C₈₃	1	2	yes	—
871	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
872	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
873	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
874	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
875	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
876	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
877	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
878	#97	C₂³×C₈₃	1	2	yes	—
879	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
880	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
881	C₂⁴	C₂×D₄×C₈₃	1	2	yes	—
882	#41	—	4	1	no	—
883	#41	—	4	1	no	—
884	#41	—	4	4	no	—
885	#41	—	4	2	no	—
886	#41	—	4	2	no	—
887	#41	—	4	2	no	—
888	#41	—	4	2	no	—
889	#41	—	4	4	no	—
890	C₂×Q₈	—	2	1	no	—
891	C₂×Q₈	—	2	1	no	—
892	C₂×Q₈	—	2	1	no	—
893	C₂×Q₈	—	2	1	no	—
894	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
895	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
896	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	—	2	1	no	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	—	2	2	no	—
902	C₂×D₄	—	2	2	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	2	no	—
905	C₂×D₄	—	2	1	no	—
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	4	2	no	—
908	C₂×D₄	C₂×D₄×C₈₃	1	1	yes	characteristic
909	C₂×D₄	C₂×D₄×C₈₃	1	1	yes	characteristic
910	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
911	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
912	C₂×D₄	C₂⁴×C₈₃	1	1	yes	characteristic
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	—	2	2	no	—
915	C₂²×C₄	—	2	1	no	—
916	C₂²×C₄	—	2	1	no	—
917	C₂²×C₄	—	2	2	no	—
918	C₂²×C₄	—	2	1	no	—
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	—	4	2	no	—
922	C₂²×C₄	—	4	2	no	—
923	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
924	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
925	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
926	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
927	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
928	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
929	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
930	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
931	Q₁₆	—	4	1	no	—
932	Q₁₆	—	4	1	no	—
933	SD₁₆	—	4	1	no	—
934	SD₁₆	—	4	2	no	—
935	SD₁₆	—	4	1	no	—
936	D₈	—	4	2	no	—
937	M₁₆	—	4	2	no	—
938	M₁₆	—	4	2	no	—
939	C₂×C₈	—	4	2	no	—
940	C₂×C₈	—	4	2	no	—
941	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
942	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
943	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
944	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
945	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
946	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
968	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
969	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
970	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
971	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
972	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
973	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
974	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
975	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
976	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
998	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
999	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
1000	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
1001	C₄²	—	2	1	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	—	2	1	no	—
1004	C₄²	—	2	2	no	—
1005	C₄²	—	2	2	no	—
1006	C₄²	—	2	1	no	—
1007	C₄²	—	2	2	no	—
1008	C₄²	—	2	2	no	—
1009	C₄²	—	2	1	no	—
1010	C₄²	—	2	1	no	—
1011	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
1012	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
1013	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
1014	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
1015	C₂³	—	2	1	no	—
1016	C₂³	—	2	2	no	—
1017	C₂³	—	4	2	no	—
1018	C₂³	—	4	2	no	—
1019	C₂³	—	4	2	no	—
1020	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
1021	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
1022	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
1023	Q₈	—	2	1	no	—
1024	Q₈	—	2	1	no	—
1025	Q₈	—	2	1	no	—
1026	Q₈	—	2	1	no	—
1027	Q₈	—	2	1	no	—
1028	Q₈	—	2	1	no	—
1029	Q₈	—	4	2	no	—
1030	Q₈	—	4	2	no	—
1031	Q₈	—	8	1	no	—
1032	Q₈	—	8	1	no	—
1033	D₄	—	2	2	no	—
1034	D₄	—	2	2	no	—
1035	D₄	—	2	1	no	—
1036	D₄	—	2	2	no	—
1037	D₄	—	2	1	no	—
1038	D₄	—	2	2	no	—
1039	D₄	—	4	2	no	—
1040	D₄	—	4	4	no	—
1041	D₄	—	4	4	no	—
1042	D₄	—	4	2	no	—
1043	D₄	—	4	2	no	—
1044	D₄	—	8	1	no	—
1045	D₄	—	8	2	no	—
1046	D₄	—	8	2	no	—
1047	D₄	—	8	2	no	—
1048	D₄	—	8	2	no	—
1049	D₄	—	8	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	4	2	no	—
1068	C₂×C₄	—	4	2	no	—
1069	C₂×C₄	—	4	2	no	—
1070	C₂×C₄	—	4	1	no	—
1071	C₂×C₄	—	4	4	no	—
1072	C₂×C₄	—	4	2	no	—
1073	C₂×C₄	—	4	4	no	—
1074	C₂×C₄	—	4	2	no	—
1075	C₂×C₄	—	8	2	no	—
1076	C₂×C₄	—	8	2	no	—
1077	C₂×C₄	—	8	1	no	—
1078	C₂×C₄	—	8	2	no	—
1079	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1080	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
1081	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1082	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
1083	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1084	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1085	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1086	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
1087	C₈	—	2	1	no	—
1088	C₈	—	2	1	no	—
1089	C₈	—	2	2	no	—
1090	C₈	—	2	2	no	—
1091	C₈	—	2	1	no	—
1092	C₈	—	2	1	no	—
1093	C₂²	—	2	1	no	—
1094	C₂²	—	2	2	no	—
1095	C₂²	—	2	2	no	—
1096	C₂²	—	2	1	no	—
1097	C₂²	—	2	2	no	—
1098	C₂²	—	2	2	no	—
1099	C₂²	—	2	1	no	—
1100	C₂²	—	2	2	no	—
1101	C₂²	—	2	2	no	—
1102	C₂²	—	4	2	no	—
1103	C₂²	—	4	1	no	—
1104	C₂²	—	4	1	no	—
1105	C₂²	—	4	2	no	—
1106	C₂²	—	4	1	no	—
1107	C₂²	—	4	2	no	—
1108	C₂²	—	8	4	no	—
1109	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
1110	C₄	—	2	1	no	—
1111	C₄	—	2	1	no	—
1112	C₄	—	2	1	no	—
1113	C₄	—	2	1	no	—
1114	C₄	—	2	2	no	—
1115	C₄	—	2	2	no	—
1116	C₄	—	4	1	no	—
1117	C₄	—	4	2	no	—
1118	C₄	—	4	2	no	—
1119	C₄	—	4	1	no	—
1120	C₄	—	4	2	no	—
1121	C₄	—	4	1	no	—
1122	C₄	—	4	1	no	—
1123	C₄	—	4	1	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	1	no	—
1126	C₄	#575×C₈₃	1	2	yes	—
1127	C₄	#585×C₈₃	1	1	yes	characteristic
1128	C₄	#585×C₈₃	1	1	yes	characteristic
1129	C₂	—	4	1	no	—
1130	C₂	—	4	2	no	—
1131	C₂	—	4	2	no	—
1132	C₂	—	8	1	no	—
1133	C₂	—	8	2	no	—
1134	C₂	C₈₃×#3485	1	1	yes	characteristic
1135	C₂	C₂×#575×C₈₃	1	1	yes	characteristic
1136	C₂	C₈₃×#3584	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×#3506	C₂	semidirect
2. C₈₃×#3475	C₂	semidirect
3. C₈₃×#3356	C₂	semidirect
4. C₈₃×#3353	C₂	semidirect
5. C₈₃×#3348	C₂	semidirect
6. C₈₃×#3347	C₂	semidirect
7. C₈₃×#3342	C₂	semidirect
8. C₈₃×#3340	C₂	semidirect
9. C₈₃×#3333	C₂	semidirect
10. C₈₃×#3332	C₂	semidirect
11. C₈₃×#3315	C₂	semidirect
12. C₈₃×#3307	C₂	semidirect
13. C₈₃×#3305	C₂	semidirect
14. C₈₃×#3304	C₂	semidirect
15. C₈₃×#3237	C₂	semidirect
16. C₈₃×#3228	C₂	semidirect
17. C₈₃×#3197	C₂	semidirect
18. C₈₃×#3191	C₂	semidirect
19. C₈₃×#3115	C₂	semidirect
20. C₈₃×#3107	C₂	semidirect
21. C₈₃×#3093	C₂	semidirect
22. C₈₃×#3091	C₂	semidirect
23. C₈₃×#2974	C₂	semidirect
57. #501×C₈₃	C₂²	semidirect
58. #500×C₈₃	C₂²	semidirect
59. #498×C₈₃	C₂²	semidirect
60. #491×C₈₃	C₂²	semidirect
61. #486×C₈₃	C₂²	semidirect
62. #486×C₈₃	C₂²	semidirect
67. #485×C₈₃	C₂²	semidirect
68. #485×C₈₃	C₂²	semidirect
69. #485×C₈₃	C₂²	semidirect
70. #485×C₈₃	C₂²	semidirect
71. #484×C₈₃	C₂²	semidirect
72. #483×C₈₃	C₂²	semidirect
76. #482×C₈₃	C₂²	semidirect
77. #482×C₈₃	C₂²	semidirect
78. #482×C₈₃	C₂²	semidirect
79. #482×C₈₃	C₂²	semidirect
80. #481×C₈₃	C₂²	semidirect
81. #480×C₈₃	C₂²	semidirect
82. #478×C₈₃	C₂²	semidirect
83. #478×C₈₃	C₂²	semidirect
84. #477×C₈₃	C₂²	semidirect
85. #477×C₈₃	C₂²	semidirect
86. #475×C₈₃	C₂²	semidirect
87. #475×C₈₃	C₂²	semidirect
88. #475×C₈₃	C₂²	semidirect
89. #475×C₈₃	C₂²	semidirect
90. #474×C₈₃	C₂²	semidirect
91. #474×C₈₃	C₂²	semidirect
92. #470×C₈₃	C₂²	semidirect
93. #469×C₈₃	C₂²	semidirect
94. #468×C₈₃	C₂²	semidirect
95. #468×C₈₃	C₂²	semidirect
96. #467×C₈₃	C₂²	semidirect
97. #466×C₈₃	C₂²	semidirect
98. #465×C₈₃	C₂²	semidirect
99. #465×C₈₃	C₂²	semidirect
100. #462×C₈₃	C₂²	semidirect
101. #461×C₈₃	C₂²	semidirect
102. #460×C₈₃	C₂²	semidirect
103. #459×C₈₃	C₂²	semidirect
106. #452×C₈₃	C₂²	semidirect
107. #452×C₈₃	C₂²	semidirect
109. #449×C₈₃	C₂²	semidirect
110. #449×C₈₃	C₂²	semidirect
111. #442×C₈₃	C₂²	semidirect
112. #440×C₈₃	C₂²	semidirect
113. C₄×Q₁₆×C₈₃	C₂²	semidirect
114. C₄×Q₁₆×C₈₃	C₂²	semidirect
115. C₄×SD₁₆×C₈₃	C₂²	semidirect
116. C₄×SD₁₆×C₈₃	C₂²	semidirect
125. #428×C₈₃	C₂²	semidirect
126. #428×C₈₃	C₂²	semidirect
127. #427×C₈₃	C₂²	semidirect
128. #427×C₈₃	C₂²	semidirect
129. #417×C₈₃	C₂²	semidirect
130. #417×C₈₃	C₂²	semidirect
131. #416×C₈₃	C₂²	semidirect
132. #416×C₈₃	C₂²	semidirect
560. #61743	C₈₃	direct (N × H)
569. #3506	C₂×C₈₃	semidirect
570. #3475	C₂×C₈₃	semidirect
571. #3356	C₂×C₈₃	semidirect
572. #3353	C₂×C₈₃	semidirect
573. #3348	C₂×C₈₃	semidirect
574. #3347	C₂×C₈₃	semidirect
575. #3342	C₂×C₈₃	semidirect
576. #3340	C₂×C₈₃	semidirect
577. #3333	C₂×C₈₃	semidirect
578. #3332	C₂×C₈₃	semidirect
579. #3315	C₂×C₈₃	semidirect
580. #3307	C₂×C₈₃	semidirect
581. #3305	C₂×C₈₃	semidirect
582. #3304	C₂×C₈₃	semidirect
583. #3237	C₂×C₈₃	semidirect
584. #3228	C₂×C₈₃	semidirect
585. #3197	C₂×C₈₃	semidirect
586. #3191	C₂×C₈₃	semidirect
587. #3115	C₂×C₈₃	semidirect
588. #3107	C₂×C₈₃	semidirect
589. #3093	C₂×C₈₃	semidirect
590. #3091	C₂×C₈₃	semidirect
591. #2974	C₂×C₈₃	semidirect
592. C₈₃	#61743	direct (N × H)
626. #501	C₂²×C₈₃	semidirect
627. #500	C₂²×C₈₃	semidirect
628. #498	C₂²×C₈₃	semidirect
629. #491	C₂²×C₈₃	semidirect
630. #486	C₂²×C₈₃	semidirect
631. #486	C₂²×C₈₃	semidirect
636. #485	C₂²×C₈₃	semidirect
637. #485	C₂²×C₈₃	semidirect
638. #485	C₂²×C₈₃	semidirect
639. #485	C₂²×C₈₃	semidirect
640. #484	C₂²×C₈₃	semidirect
641. #483	C₂²×C₈₃	semidirect
645. #482	C₂²×C₈₃	semidirect
646. #482	C₂²×C₈₃	semidirect
647. #482	C₂²×C₈₃	semidirect
648. #482	C₂²×C₈₃	semidirect
649. #481	C₂²×C₈₃	semidirect
650. #480	C₂²×C₈₃	semidirect
651. #478	C₂²×C₈₃	semidirect
652. #478	C₂²×C₈₃	semidirect
653. #477	C₂²×C₈₃	semidirect
654. #477	C₂²×C₈₃	semidirect
655. #475	C₂²×C₈₃	semidirect
656. #475	C₂²×C₈₃	semidirect
657. #475	C₂²×C₈₃	semidirect
658. #475	C₂²×C₈₃	semidirect
659. #474	C₂²×C₈₃	semidirect
660. #474	C₂²×C₈₃	semidirect
661. #470	C₂²×C₈₃	semidirect
662. #469	C₂²×C₈₃	semidirect
663. #468	C₂²×C₈₃	semidirect
664. #468	C₂²×C₈₃	semidirect
665. #467	C₂²×C₈₃	semidirect
666. #466	C₂²×C₈₃	semidirect
667. #465	C₂²×C₈₃	semidirect
668. #465	C₂²×C₈₃	semidirect
669. #462	C₂²×C₈₃	semidirect
670. #461	C₂²×C₈₃	semidirect
671. #460	C₂²×C₈₃	semidirect
672. #459	C₂²×C₈₃	semidirect
675. #452	C₂²×C₈₃	semidirect
676. #452	C₂²×C₈₃	semidirect
678. #449	C₂²×C₈₃	semidirect
679. #449	C₂²×C₈₃	semidirect
680. #442	C₂²×C₈₃	semidirect
681. #440	C₂²×C₈₃	semidirect
682. C₄×Q₁₆	C₂²×C₈₃	semidirect
683. C₄×Q₁₆	C₂²×C₈₃	semidirect
684. C₄×SD₁₆	C₂²×C₈₃	semidirect
685. C₄×SD₁₆	C₂²×C₈₃	semidirect
694. #428	C₂²×C₈₃	semidirect
695. #428	C₂²×C₈₃	semidirect
696. #427	C₂²×C₈₃	semidirect
697. #427	C₂²×C₈₃	semidirect
698. #417	C₂²×C₈₃	semidirect
699. #417	C₂²×C₈₃	semidirect
700. #416	C₂²×C₈₃	semidirect
701. #416	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×#3506	2
C₈₃×#3475	2
C₈₃×#3356	2
C₈₃×#3353	2
C₈₃×#3348	2
C₈₃×#3347	2
C₈₃×#3342	2
C₈₃×#3340	2
C₈₃×#3333	2
C₈₃×#3332	2
C₈₃×#3315	2
C₈₃×#3307	2
C₈₃×#3305	2
C₈₃×#3304	2
C₈₃×#3237	2
C₈₃×#3228	2
C₈₃×#3197	2
C₈₃×#3191	2
C₈₃×#3115	2
C₈₃×#3107	2
C₈₃×#3093	2
C₈₃×#3091	2
C₈₃×#2974	2
#61743	83

Subgroups — C83×#61743 #35289567

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#61743 #35289567