Subgroups — C₈₃×#61875 #35289699

Order 21248.

1598 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3555	C₂	1	1	yes	maximal, characteristic
2	C₈₃×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₃×#3390	C₂	1	2	yes	maximal, complemented
4	C₈₃×#3388	C₂	1	2	yes	maximal, complemented
5	C₈₃×#3387	C₂	1	2	yes	maximal, complemented
6	C₈₃×#3387	C₂	1	2	yes	maximal, complemented
7	C₈₃×#3377	C₂	1	2	yes	maximal, complemented
8	C₈₃×#3377	C₂	1	2	yes	maximal, complemented
9	C₈₃×#3374	C₂	1	2	yes	maximal, complemented
10	C₈₃×#3369	C₂	1	2	yes	maximal, complemented
11	C₈₃×#3244	C₂	1	2	yes	maximal
12	C₈₃×#3242	C₂	1	2	yes	maximal, complemented
13	C₈₃×#3240	C₂	1	1	yes	maximal, characteristic
14	C₈₃×#3237	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#3127	C₂	1	2	yes	maximal, complemented
16	C₈₃×#3121	C₂	1	2	yes	maximal
17	C₈₃×#3117	C₂	1	1	yes	maximal, characteristic
18	C₈₃×#3113	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₃×#2987	C₂	1	1	yes	maximal, characteristic, complemented
20	#563×C₈₃	—	2	2	no	—
21	Q₈²×C₈₃	—	2	1	no	—
22	Q₈²×C₈₃	C₂²	1	1	yes	characteristic
23	Q₈²×C₈₃	C₂²	1	2	yes	—
24	#557×C₈₃	—	2	1	no	—
25	#557×C₈₃	—	2	2	no	—
26	#557×C₈₃	C₂²	1	1	yes	characteristic
27	#557×C₈₃	C₂²	1	2	yes	—
28	#557×C₈₃	C₂²	1	2	yes	—
29	#557×C₈₃	C₂²	1	2	yes	—
30	#557×C₈₃	C₂²	1	2	yes	—
31	#556×C₈₃	—	2	1	no	—
32	#556×C₈₃	C₂²	1	2	yes	—
33	#556×C₈₃	C₂²	1	1	yes	characteristic
34	#554×C₈₃	C₂²	1	1	yes	characteristic
35	#552×C₈₃	—	2	1	no	—
36	#544×C₈₃	—	2	1	no	—
37	#544×C₈₃	—	2	1	no	—
38	#544×C₈₃	—	2	1	no	—
39	#544×C₈₃	C₂²	1	2	yes	—
40	#542×C₈₃	C₂²	1	2	yes	—
41	#541×C₈₃	—	2	1	no	—
42	#541×C₈₃	—	2	2	no	—
43	#541×C₈₃	C₂²	1	2	yes	—
44	#533×C₈₃	—	2	2	no	—
45	#533×C₈₃	C₂²	1	1	yes	characteristic
46	#533×C₈₃	C₂²	1	1	yes	characteristic
47	#533×C₈₃	C₂²	1	1	yes	characteristic
48	#529×C₈₃	C₂²	1	1	yes	characteristic
49	#519×C₈₃	C₂²	1	2	yes	—
50	C₂×C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
51	#501×C₈₃	C₂²	1	1	yes	characteristic
52	#501×C₈₃	C₂²	1	2	yes	—
53	#501×C₈₃	C₂²	1	2	yes	—
54	#501×C₈₃	C₂²	1	2	yes	—
55	#501×C₈₃	C₂²	1	1	yes	characteristic
56	#499×C₈₃	C₂²	1	2	yes	—
57	#498×C₈₃	C₂²	1	2	yes	—
58	#491×C₈₃	C₂²	1	2	yes	—
59	#491×C₈₃	C₂²	1	2	yes	—
60	#489×C₈₃	C₂²	1	1	yes	characteristic
61	#489×C₈₃	C₂²	1	2	yes	—
62	#489×C₈₃	C₂²	1	1	yes	characteristic
63	#488×C₈₃	C₂²	1	2	yes	—
64	#487×C₈₃	C₂²	1	2	yes	—
65	#485×C₈₃	C₂²	1	2	yes	—
66	#485×C₈₃	C₂²	1	2	yes	—
67	#485×C₈₃	C₂²	1	2	yes	—
68	#484×C₈₃	C₂²	1	1	yes	characteristic
69	#483×C₈₃	C₂²	1	2	yes	—
70	#482×C₈₃	C₂²	1	2	yes	—
71	#481×C₈₃	C₂²	1	1	yes	characteristic
72	#479×C₈₃	C₂²	1	2	yes	—
73	#479×C₈₃	C₂²	1	2	yes	—
74	#479×C₈₃	C₂²	1	2	yes	—
75	#479×C₈₃	C₂²	1	2	yes	—
76	#479×C₈₃	C₂²	1	2	yes	—
77	#479×C₈₃	C₂²	1	2	yes	—
78	#479×C₈₃	C₂²	1	2	yes	—
79	#478×C₈₃	C₂²	1	2	yes	—
80	#478×C₈₃	C₂²	1	2	yes	—
81	#477×C₈₃	C₂²	1	2	yes	—
82	#477×C₈₃	C₂²	1	2	yes	—
83	#477×C₈₃	C₂²	1	2	yes	—
84	#476×C₈₃	C₂²	1	2	yes	—
85	#475×C₈₃	C₂²	1	2	yes	—
86	#475×C₈₃	C₂²	1	2	yes	—
87	#475×C₈₃	C₂²	1	2	yes	—
88	#475×C₈₃	C₂²	1	2	yes	—
89	#475×C₈₃	C₂²	1	2	yes	—
90	#464×C₈₃	C₂²	1	2	yes	—
91	#464×C₈₃	C₂²	1	2	yes	—
92	#464×C₈₃	C₂²	1	2	yes	—
93	#462×C₈₃	C₂²	1	2	yes	—
94	#462×C₈₃	C₂²	1	2	yes	—
95	#462×C₈₃	C₂²	1	2	yes	—
96	#451×C₈₃	C₂²	1	2	yes	—
97	#451×C₈₃	C₂²	1	1	yes	characteristic
98	#448×C₈₃	C₂²	1	1	yes	characteristic
99	#446×C₈₃	C₂²	1	2	yes	—
100	#446×C₈₃	C₂²	1	2	yes	—
101	#446×C₈₃	C₂²	1	2	yes	—
102	#446×C₈₃	C₂²	1	2	yes	—
103	#441×C₈₃	C₂²	1	2	yes	—
104	#441×C₈₃	C₂²	1	2	yes	—
105	#441×C₈₃	C₂²	1	2	yes	—
106	#441×C₈₃	C₂²	1	2	yes	—
107	#441×C₈₃	C₂²	1	2	yes	—
108	#441×C₈₃	C₂²	1	2	yes	—
109	#440×C₈₃	C₂²	1	2	yes	—
110	#440×C₈₃	C₂²	1	2	yes	—
111	C₄×Q₁₆×C₈₃	C₂²	1	2	yes	—
112	C₄×Q₁₆×C₈₃	C₂²	1	2	yes	—
113	C₄×Q₁₆×C₈₃	C₂²	1	2	yes	—
114	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	—
115	#433×C₈₃	C₂²	1	2	yes	—
116	#433×C₈₃	C₂²	1	2	yes	—
117	#432×C₈₃	C₂²	1	1	yes	characteristic
118	#432×C₈₃	C₂²	1	1	yes	characteristic
119	C₂²×Q₈×C₈₃	C₂³	1	1	yes	characteristic
120	C₂×Q₁₆×C₈₃	C₂³	1	2	yes	—
121	C₂×Q₁₆×C₈₃	C₂³	1	2	yes	—
122	C₂×Q₁₆×C₈₃	C₂³	1	2	yes	—
123	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
124	C₄⋊Q₈×C₈₃	—	2	2	no	—
125	C₄⋊Q₈×C₈₃	—	2	2	no	—
126	C₄⋊Q₈×C₈₃	—	2	2	no	—
127	C₄⋊Q₈×C₈₃	—	2	2	no	—
128	C₄⋊Q₈×C₈₃	—	2	2	no	—
129	C₄⋊Q₈×C₈₃	—	2	2	no	—
130	C₄⋊Q₈×C₈₃	—	2	1	no	—
131	C₄⋊Q₈×C₈₃	—	2	2	no	—
132	C₄⋊Q₈×C₈₃	—	2	2	no	—
133	C₄⋊Q₈×C₈₃	—	2	2	no	—
134	C₄⋊Q₈×C₈₃	D₄	1	1	yes	characteristic
135	C₄⋊Q₈×C₈₃	D₄	1	1	yes	characteristic
136	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
137	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
138	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
139	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
140	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
141	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
142	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
143	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
144	#126×C₈₃	—	2	2	no	—
145	#126×C₈₃	—	2	2	no	—
146	#126×C₈₃	—	2	2	no	—
147	#126×C₈₃	—	2	2	no	—
148	#126×C₈₃	—	2	2	no	—
149	#126×C₈₃	—	2	2	no	—
150	#126×C₈₃	—	2	1	no	—
151	#125×C₈₃	—	2	2	no	—
152	#125×C₈₃	—	2	2	no	—
153	#125×C₈₃	—	2	2	no	—
154	#125×C₈₃	—	2	2	no	—
155	#125×C₈₃	—	2	2	no	—
156	#125×C₈₃	—	2	2	no	—
157	#125×C₈₃	—	2	2	no	—
158	#125×C₈₃	—	2	1	no	—
159	#125×C₈₃	—	2	2	no	—
160	#125×C₈₃	—	2	2	no	—
161	#125×C₈₃	—	2	2	no	—
162	#125×C₈₃	—	2	2	no	—
163	#125×C₈₃	—	2	2	no	—
164	#125×C₈₃	—	2	1	no	—
165	#125×C₈₃	D₄	1	2	yes	—
166	#125×C₈₃	C₂³	1	2	yes	—
167	#125×C₈₃	C₂³	1	2	yes	—
168	#125×C₈₃	C₂³	1	2	yes	—
169	#125×C₈₃	C₂³	1	2	yes	—
170	#125×C₈₃	C₂³	1	1	yes	characteristic
171	#124×C₈₃	—	2	2	no	—
172	#124×C₈₃	C₂³	1	2	yes	—
173	#124×C₈₃	C₂³	1	1	yes	characteristic
174	#123×C₈₃	—	2	1	no	—
175	#123×C₈₃	—	2	2	no	—
176	C₂²⋊Q₈×C₈₃	—	2	1	no	—
177	C₂²⋊Q₈×C₈₃	—	2	1	no	—
178	C₂²⋊Q₈×C₈₃	—	2	2	no	—
179	C₂²⋊Q₈×C₈₃	—	2	1	no	—
180	C₂²⋊Q₈×C₈₃	—	2	1	no	—
181	C₂²⋊Q₈×C₈₃	—	2	1	no	—
182	C₂²⋊Q₈×C₈₃	—	2	2	no	—
183	C₂²⋊Q₈×C₈₃	—	2	2	no	—
184	C₂²⋊Q₈×C₈₃	—	2	2	no	—
185	C₂²⋊Q₈×C₈₃	—	2	2	no	—
186	C₂²⋊Q₈×C₈₃	D₄	1	2	yes	—
187	C₂²⋊Q₈×C₈₃	D₄	1	1	yes	characteristic
188	C₂²⋊Q₈×C₈₃	D₄	1	1	yes	characteristic
189	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
190	C₂²⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
191	#121×C₈₃	C₂³	1	1	yes	characteristic
192	C₄×Q₈×C₈₃	—	2	2	no	—
193	C₄×Q₈×C₈₃	—	2	1	no	—
194	C₄×Q₈×C₈₃	—	2	1	no	—
195	C₄×Q₈×C₈₃	—	2	2	no	—
196	C₄×Q₈×C₈₃	—	2	2	no	—
197	C₄×Q₈×C₈₃	—	2	2	no	—
198	C₄×Q₈×C₈₃	—	2	2	no	—
199	C₄×Q₈×C₈₃	—	2	2	no	—
200	C₄×Q₈×C₈₃	—	2	2	no	—
201	C₄×Q₈×C₈₃	—	2	1	no	—
202	C₄×Q₈×C₈₃	—	2	1	no	—
203	C₄×Q₈×C₈₃	—	2	1	no	—
204	C₄×Q₈×C₈₃	—	2	1	no	—
205	C₄×Q₈×C₈₃	—	2	1	no	—
206	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
207	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
208	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
209	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
210	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
211	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
212	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
213	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
214	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
215	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
216	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
217	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
219	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
220	C₄×D₄×C₈₃	—	2	1	no	—
221	C₄×D₄×C₈₃	C₂³	1	2	yes	—
222	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
223	#117×C₈₃	—	2	1	no	—
224	#117×C₈₃	—	2	2	no	—
225	#117×C₈₃	—	2	1	no	—
226	#117×C₈₃	—	2	2	no	—
227	#117×C₈₃	—	2	2	no	—
228	#117×C₈₃	—	2	1	no	—
229	#117×C₈₃	C₂³	1	2	yes	—
230	#117×C₈₃	C₂³	1	2	yes	—
231	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
232	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
233	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₈₃	—	2	1	no	—
235	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
236	#107×C₈₃	C₂³	1	2	yes	—
237	#107×C₈₃	C₂³	1	2	yes	—
238	#107×C₈₃	C₂³	1	2	yes	—
239	#107×C₈₃	C₂³	1	2	yes	—
240	#107×C₈₃	C₂³	1	2	yes	—
241	#106×C₈₃	C₂³	1	2	yes	—
242	#106×C₈₃	C₂³	1	2	yes	—
243	#106×C₈₃	C₂³	1	2	yes	—
244	#106×C₈₃	C₂³	1	2	yes	—
245	#106×C₈₃	C₂³	1	2	yes	—
246	#106×C₈₃	C₂³	1	2	yes	—
247	#106×C₈₃	C₂³	1	2	yes	—
248	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
249	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
250	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
251	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
252	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
253	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
254	#103×C₈₃	C₂³	1	2	yes	—
255	#103×C₈₃	C₂³	1	2	yes	—
256	#103×C₈₃	C₂³	1	2	yes	—
257	#103×C₈₃	C₂³	1	2	yes	—
258	#103×C₈₃	C₂³	1	2	yes	—
259	#103×C₈₃	C₂³	1	2	yes	—
260	#103×C₈₃	C₂³	1	2	yes	—
261	#103×C₈₃	C₂³	1	2	yes	—
262	#103×C₈₃	C₂³	1	2	yes	—
263	#103×C₈₃	C₂³	1	2	yes	—
264	#103×C₈₃	C₂³	1	2	yes	—
265	#103×C₈₃	C₂³	1	2	yes	—
266	#103×C₈₃	C₂³	1	2	yes	—
267	#102×C₈₃	C₂³	1	2	yes	—
268	#102×C₈₃	C₂³	1	2	yes	—
269	#102×C₈₃	C₂³	1	2	yes	—
270	C₂²⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
271	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
272	C₂²⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
273	#97×C₈₃	C₂³	1	1	yes	characteristic
274	#97×C₈₃	C₂³	1	1	yes	characteristic
275	#97×C₈₃	C₂³	1	2	yes	—
276	#97×C₈₃	C₂³	1	2	yes	—
277	#97×C₈₃	C₂³	1	2	yes	—
278	C₄×C₈×C₈₃	C₂³	1	2	yes	—
279	C₄×C₈×C₈₃	C₂³	1	2	yes	—
280	C₂×Q₈×C₈₃	—	2	4	no	—
281	C₂×Q₈×C₈₃	—	2	1	no	—
282	C₂×Q₈×C₈₃	—	2	1	no	—
283	C₂×Q₈×C₈₃	—	2	1	no	—
284	C₂×Q₈×C₈₃	—	2	2	no	—
285	C₂×Q₈×C₈₃	—	2	1	no	—
286	C₂×Q₈×C₈₃	—	2	2	no	—
287	C₂×Q₈×C₈₃	—	2	2	no	—
288	C₂×Q₈×C₈₃	C₂×D₄	1	2	yes	—
289	C₂×Q₈×C₈₃	C₂×D₄	1	1	yes	characteristic
290	C₂×Q₈×C₈₃	C₂×D₄	1	1	yes	characteristic
291	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
292	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
293	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
294	C₂×D₄×C₈₃	—	2	1	no	—
295	C₂×D₄×C₈₃	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₈₃	—	2	1	no	—
297	C₂²×C₄×C₈₃	—	2	1	no	—
298	C₂²×C₄×C₈₃	—	2	1	no	—
299	C₂²×C₄×C₈₃	—	2	2	no	—
300	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
302	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
303	Q₁₆×C₈₃	—	2	4	no	—
304	Q₁₆×C₈₃	—	2	4	no	—
305	Q₁₆×C₈₃	—	2	4	no	—
306	SD₁₆×C₈₃	—	2	4	no	—
307	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
308	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
309	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
310	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
311	C₄⋊C₄×C₈₃	—	2	1	no	—
312	C₄⋊C₄×C₈₃	—	2	2	no	—
313	C₄⋊C₄×C₈₃	—	2	2	no	—
314	C₄⋊C₄×C₈₃	—	2	2	no	—
315	C₄⋊C₄×C₈₃	—	2	1	no	—
316	C₄⋊C₄×C₈₃	—	2	1	no	—
317	C₄⋊C₄×C₈₃	—	2	2	no	—
318	C₄⋊C₄×C₈₃	—	2	2	no	—
319	C₄⋊C₄×C₈₃	—	2	2	no	—
320	C₄⋊C₄×C₈₃	—	2	2	no	—
321	C₄⋊C₄×C₈₃	—	2	2	no	—
322	C₄⋊C₄×C₈₃	—	2	1	no	—
323	C₄⋊C₄×C₈₃	—	2	1	no	—
324	C₄⋊C₄×C₈₃	—	2	1	no	—
325	C₄⋊C₄×C₈₃	—	2	2	no	—
326	C₄⋊C₄×C₈₃	—	2	1	no	—
327	C₄⋊C₄×C₈₃	—	2	2	no	—
328	C₄⋊C₄×C₈₃	—	2	2	no	—
329	C₄⋊C₄×C₈₃	—	2	1	no	—
330	C₄⋊C₄×C₈₃	—	2	2	no	—
331	C₄⋊C₄×C₈₃	—	2	2	no	—
332	C₄⋊C₄×C₈₃	—	2	2	no	—
333	C₄⋊C₄×C₈₃	—	2	2	no	—
334	C₄⋊C₄×C₈₃	—	2	2	no	—
335	C₄⋊C₄×C₈₃	—	2	2	no	—
336	C₄⋊C₄×C₈₃	—	2	2	no	—
337	C₄⋊C₄×C₈₃	—	2	1	no	—
338	C₄⋊C₄×C₈₃	—	2	2	no	—
339	C₄⋊C₄×C₈₃	—	2	2	no	—
340	C₄⋊C₄×C₈₃	—	2	2	no	—
341	C₄⋊C₄×C₈₃	—	2	2	no	—
342	C₄⋊C₄×C₈₃	—	2	2	no	—
343	C₄⋊C₄×C₈₃	—	2	2	no	—
344	C₄⋊C₄×C₈₃	—	2	1	no	—
345	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
346	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
347	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
348	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
349	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
350	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
351	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
352	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
353	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
354	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
355	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
356	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
357	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
358	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
359	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
360	C₂²⋊C₄×C₈₃	—	2	2	no	—
361	C₂²⋊C₄×C₈₃	—	2	2	no	—
362	C₂²⋊C₄×C₈₃	—	2	1	no	—
363	C₂²⋊C₄×C₈₃	—	2	1	no	—
364	C₂²⋊C₄×C₈₃	—	2	1	no	—
365	C₂²⋊C₄×C₈₃	—	2	1	no	—
366	C₂²⋊C₄×C₈₃	—	2	2	no	—
367	C₂²⋊C₄×C₈₃	—	2	2	no	—
368	C₂²⋊C₄×C₈₃	—	2	1	no	—
369	C₂²⋊C₄×C₈₃	—	2	2	no	—
370	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
371	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
372	C₄²×C₈₃	—	2	2	no	—
373	C₄²×C₈₃	—	2	2	no	—
374	C₄²×C₈₃	—	2	2	no	—
375	C₄²×C₈₃	—	2	1	no	—
376	C₄²×C₈₃	—	2	2	no	—
377	C₄²×C₈₃	—	2	2	no	—
378	C₄²×C₈₃	—	2	2	no	—
379	C₄²×C₈₃	—	2	2	no	—
380	C₄²×C₈₃	—	2	2	no	—
381	C₄²×C₈₃	—	2	2	no	—
382	C₄²×C₈₃	—	2	2	no	—
383	C₄²×C₈₃	—	2	2	no	—
384	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
385	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
386	C₄²×C₈₃	C₂⁴	1	2	yes	—
387	C₄²×C₈₃	C₂⁴	1	2	yes	—
388	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
389	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
390	C₂³×C₈₃	—	2	1	no	—
391	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
392	Q₈×C₈₃	—	2	4	no	—
393	Q₈×C₈₃	—	2	2	no	—
394	Q₈×C₈₃	—	2	2	no	—
395	Q₈×C₈₃	—	2	2	no	—
396	Q₈×C₈₃	—	2	2	no	—
397	Q₈×C₈₃	—	4	1	no	—
398	Q₈×C₈₃	—	4	1	no	—
399	Q₈×C₈₃	—	4	2	no	—
400	Q₈×C₈₃	—	4	2	no	—
401	Q₈×C₈₃	—	8	1	no	—
402	Q₈×C₈₃	—	8	1	no	—
403	Q₈×C₈₃	—	8	2	no	—
404	Q₈×C₈₃	—	8	2	no	—
405	Q₈×C₈₃	—	8	2	no	—
406	Q₈×C₈₃	2₋¹⁺⁴	1	4	yes	—
407	D₄×C₈₃	—	2	2	no	—
408	D₄×C₈₃	—	8	1	no	—
409	C₂×C₄×C₈₃	—	2	4	no	—
410	C₂×C₄×C₈₃	—	2	2	no	—
411	C₂×C₄×C₈₃	—	2	2	no	—
412	C₂×C₄×C₈₃	—	2	2	no	—
413	C₂×C₄×C₈₃	—	2	1	no	—
414	C₂×C₄×C₈₃	—	2	2	no	—
415	C₂×C₄×C₈₃	—	2	1	no	—
416	C₂×C₄×C₈₃	—	2	2	no	—
417	C₂×C₄×C₈₃	—	2	1	no	—
418	C₂×C₄×C₈₃	—	2	2	no	—
419	C₂×C₄×C₈₃	—	2	2	no	—
420	C₂×C₄×C₈₃	—	4	1	no	—
421	C₂×C₄×C₈₃	—	4	1	no	—
422	C₂×C₄×C₈₃	—	4	2	no	—
423	C₂×C₄×C₈₃	—	8	2	no	—
424	C₂×C₄×C₈₃	—	8	1	no	—
425	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
427	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
430	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
431	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
432	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
433	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
434	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
435	C₈×C₈₃	—	2	2	no	—
436	C₈×C₈₃	—	2	2	no	—
437	C₈×C₈₃	—	2	2	no	—
438	C₈×C₈₃	—	2	2	no	—
439	C₂²×C₈₃	—	2	1	no	—
440	C₂²×C₈₃	—	2	1	no	—
441	C₂²×C₈₃	—	2	1	no	—
442	C₂²×C₈₃	—	4	1	no	—
443	C₂²×C₈₃	—	4	1	no	—
444	C₂²×C₈₃	—	4	1	no	—
445	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
446	C₄×C₈₃	—	2	1	no	—
447	C₄×C₈₃	—	2	1	no	—
448	C₄×C₈₃	—	2	1	no	—
449	C₄×C₈₃	—	2	1	no	—
450	C₄×C₈₃	—	2	2	no	—
451	C₄×C₈₃	—	2	2	no	—
452	C₄×C₈₃	—	2	2	no	—
453	C₄×C₈₃	—	2	2	no	—
454	C₄×C₈₃	—	2	4	no	—
455	C₄×C₈₃	—	2	1	no	—
456	C₄×C₈₃	—	4	1	no	—
457	C₄×C₈₃	—	4	2	no	—
458	C₄×C₈₃	—	4	2	no	—
459	C₄×C₈₃	—	4	1	no	—
460	C₄×C₈₃	—	4	2	no	—
461	C₄×C₈₃	—	4	2	no	—
462	C₄×C₈₃	—	4	2	no	—
463	C₄×C₈₃	—	4	1	no	—
464	C₄×C₈₃	C₂×2₋¹⁺⁴	1	2	yes	—
465	#61875	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
466	C₂×C₈₃	—	4	1	no	—
467	C₂×C₈₃	—	8	1	no	—
468	C₂×C₈₃	#3486	1	1	yes	characteristic
469	C₂×C₈₃	#3586	1	1	yes	characteristic
470	C₂×C₈₃	#3586	1	1	yes	characteristic
471	#3555	C₂×C₈₃	1	1	yes	characteristic
472	#3502	C₂×C₈₃	1	1	yes	characteristic, complemented
473	#3390	C₂×C₈₃	1	2	yes	complemented
474	#3388	C₂×C₈₃	1	2	yes	complemented
475	#3387	C₂×C₈₃	1	2	yes	complemented
476	#3387	C₂×C₈₃	1	2	yes	complemented
477	#3377	C₂×C₈₃	1	2	yes	complemented
478	#3377	C₂×C₈₃	1	2	yes	complemented
479	#3374	C₂×C₈₃	1	2	yes	complemented
480	#3369	C₂×C₈₃	1	2	yes	complemented
481	#3244	C₂×C₈₃	1	2	yes	—
482	#3242	C₂×C₈₃	1	2	yes	complemented
483	#3240	C₂×C₈₃	1	1	yes	characteristic
484	#3237	C₂×C₈₃	1	1	yes	characteristic, complemented
485	#3127	C₂×C₈₃	1	2	yes	complemented
486	#3121	C₂×C₈₃	1	2	yes	—
487	#3117	C₂×C₈₃	1	1	yes	characteristic
488	#3113	C₂×C₈₃	1	1	yes	characteristic, complemented
489	#2987	C₂×C₈₃	1	1	yes	characteristic, complemented
490	C₈₃	#61875	1	1	yes	characteristic, direct product factor, Sylow
491	#563	—	2	2	no	—
492	Q₈²	—	2	1	no	—
493	Q₈²	C₂²×C₈₃	1	2	yes	—
494	Q₈²	C₂²×C₈₃	1	1	yes	characteristic
495	#557	—	2	1	no	—
496	#557	—	2	2	no	—
497	#557	C₂²×C₈₃	1	1	yes	characteristic
498	#557	C₂²×C₈₃	1	2	yes	—
499	#557	C₂²×C₈₃	1	2	yes	—
500	#557	C₂²×C₈₃	1	2	yes	—
501	#557	C₂²×C₈₃	1	2	yes	—
502	#556	—	2	1	no	—
503	#556	C₂²×C₈₃	1	2	yes	—
504	#556	C₂²×C₈₃	1	1	yes	characteristic
505	#554	C₂²×C₈₃	1	1	yes	characteristic
506	#552	—	2	1	no	—
507	#544	—	2	1	no	—
508	#544	—	2	1	no	—
509	#544	—	2	1	no	—
510	#544	C₂²×C₈₃	1	2	yes	—
511	#542	C₂²×C₈₃	1	2	yes	—
512	#541	—	2	1	no	—
513	#541	—	2	2	no	—
514	#541	C₂²×C₈₃	1	2	yes	—
515	#533	—	2	2	no	—
516	#533	C₂²×C₈₃	1	1	yes	characteristic
517	#533	C₂²×C₈₃	1	1	yes	characteristic
518	#533	C₂²×C₈₃	1	1	yes	characteristic
519	#529	C₂²×C₈₃	1	1	yes	characteristic
520	#519	C₂²×C₈₃	1	2	yes	—
521	C₂×C₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic
522	#501	C₂²×C₈₃	1	1	yes	characteristic
523	#501	C₂²×C₈₃	1	2	yes	—
524	#501	C₂²×C₈₃	1	2	yes	—
525	#501	C₂²×C₈₃	1	2	yes	—
526	#501	C₂²×C₈₃	1	1	yes	characteristic
527	#499	C₂²×C₈₃	1	2	yes	—
528	#498	C₂²×C₈₃	1	2	yes	—
529	#491	C₂²×C₈₃	1	2	yes	—
530	#491	C₂²×C₈₃	1	2	yes	—
531	#489	C₂²×C₈₃	1	1	yes	characteristic
532	#489	C₂²×C₈₃	1	2	yes	—
533	#489	C₂²×C₈₃	1	1	yes	characteristic
534	#488	C₂²×C₈₃	1	2	yes	—
535	#487	C₂²×C₈₃	1	2	yes	—
536	#485	C₂²×C₈₃	1	2	yes	—
537	#485	C₂²×C₈₃	1	2	yes	—
538	#485	C₂²×C₈₃	1	2	yes	—
539	#484	C₂²×C₈₃	1	1	yes	characteristic
540	#483	C₂²×C₈₃	1	2	yes	—
541	#482	C₂²×C₈₃	1	2	yes	—
542	#481	C₂²×C₈₃	1	1	yes	characteristic
543	#479	C₂²×C₈₃	1	2	yes	—
544	#479	C₂²×C₈₃	1	2	yes	—
545	#479	C₂²×C₈₃	1	2	yes	—
546	#479	C₂²×C₈₃	1	2	yes	—
547	#479	C₂²×C₈₃	1	2	yes	—
548	#479	C₂²×C₈₃	1	2	yes	—
549	#479	C₂²×C₈₃	1	2	yes	—
550	#478	C₂²×C₈₃	1	2	yes	—
551	#478	C₂²×C₈₃	1	2	yes	—
552	#477	C₂²×C₈₃	1	2	yes	—
553	#477	C₂²×C₈₃	1	2	yes	—
554	#477	C₂²×C₈₃	1	2	yes	—
555	#476	C₂²×C₈₃	1	2	yes	—
556	#475	C₂²×C₈₃	1	2	yes	—
557	#475	C₂²×C₈₃	1	2	yes	—
558	#475	C₂²×C₈₃	1	2	yes	—
559	#475	C₂²×C₈₃	1	2	yes	—
560	#475	C₂²×C₈₃	1	2	yes	—
561	#464	C₂²×C₈₃	1	2	yes	—
562	#464	C₂²×C₈₃	1	2	yes	—
563	#464	C₂²×C₈₃	1	2	yes	—
564	#462	C₂²×C₈₃	1	2	yes	—
565	#462	C₂²×C₈₃	1	2	yes	—
566	#462	C₂²×C₈₃	1	2	yes	—
567	#451	C₂²×C₈₃	1	2	yes	—
568	#451	C₂²×C₈₃	1	1	yes	characteristic
569	#448	C₂²×C₈₃	1	1	yes	characteristic
570	#446	C₂²×C₈₃	1	2	yes	—
571	#446	C₂²×C₈₃	1	2	yes	—
572	#446	C₂²×C₈₃	1	2	yes	—
573	#446	C₂²×C₈₃	1	2	yes	—
574	#441	C₂²×C₈₃	1	2	yes	—
575	#441	C₂²×C₈₃	1	2	yes	—
576	#441	C₂²×C₈₃	1	2	yes	—
577	#441	C₂²×C₈₃	1	2	yes	—
578	#441	C₂²×C₈₃	1	2	yes	—
579	#441	C₂²×C₈₃	1	2	yes	—
580	#440	C₂²×C₈₃	1	2	yes	—
581	#440	C₂²×C₈₃	1	2	yes	—
582	C₄×Q₁₆	C₂²×C₈₃	1	2	yes	—
583	C₄×Q₁₆	C₂²×C₈₃	1	2	yes	—
584	C₄×Q₁₆	C₂²×C₈₃	1	2	yes	—
585	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	—
586	#433	C₂²×C₈₃	1	2	yes	—
587	#433	C₂²×C₈₃	1	2	yes	—
588	#432	C₂²×C₈₃	1	1	yes	characteristic
589	#432	C₂²×C₈₃	1	1	yes	characteristic
590	C₂²×Q₈	C₂³×C₈₃	1	1	yes	characteristic
591	C₂×Q₁₆	C₂³×C₈₃	1	2	yes	—
592	C₂×Q₁₆	C₂³×C₈₃	1	2	yes	—
593	C₂×Q₁₆	C₂³×C₈₃	1	2	yes	—
594	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
595	C₄⋊Q₈	—	2	2	no	—
596	C₄⋊Q₈	—	2	2	no	—
597	C₄⋊Q₈	—	2	2	no	—
598	C₄⋊Q₈	—	2	2	no	—
599	C₄⋊Q₈	—	2	2	no	—
600	C₄⋊Q₈	—	2	2	no	—
601	C₄⋊Q₈	—	2	1	no	—
602	C₄⋊Q₈	—	2	2	no	—
603	C₄⋊Q₈	—	2	2	no	—
604	C₄⋊Q₈	—	2	2	no	—
605	C₄⋊Q₈	D₄×C₈₃	1	1	yes	characteristic
606	C₄⋊Q₈	D₄×C₈₃	1	1	yes	characteristic
607	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
608	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
609	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
610	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
611	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
612	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
613	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
614	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
615	#126	—	2	2	no	—
616	#126	—	2	2	no	—
617	#126	—	2	2	no	—
618	#126	—	2	2	no	—
619	#126	—	2	2	no	—
620	#126	—	2	2	no	—
621	#126	—	2	1	no	—
622	#125	—	2	2	no	—
623	#125	—	2	2	no	—
624	#125	—	2	2	no	—
625	#125	—	2	2	no	—
626	#125	—	2	2	no	—
627	#125	—	2	2	no	—
628	#125	—	2	2	no	—
629	#125	—	2	1	no	—
630	#125	—	2	2	no	—
631	#125	—	2	2	no	—
632	#125	—	2	2	no	—
633	#125	—	2	2	no	—
634	#125	—	2	2	no	—
635	#125	—	2	1	no	—
636	#125	D₄×C₈₃	1	2	yes	—
637	#125	C₂³×C₈₃	1	1	yes	characteristic
638	#125	C₂³×C₈₃	1	2	yes	—
639	#125	C₂³×C₈₃	1	2	yes	—
640	#125	C₂³×C₈₃	1	2	yes	—
641	#125	C₂³×C₈₃	1	2	yes	—
642	#124	—	2	2	no	—
643	#124	C₂³×C₈₃	1	1	yes	characteristic
644	#124	C₂³×C₈₃	1	2	yes	—
645	#123	—	2	1	no	—
646	#123	—	2	2	no	—
647	C₂²⋊Q₈	—	2	1	no	—
648	C₂²⋊Q₈	—	2	1	no	—
649	C₂²⋊Q₈	—	2	2	no	—
650	C₂²⋊Q₈	—	2	1	no	—
651	C₂²⋊Q₈	—	2	1	no	—
652	C₂²⋊Q₈	—	2	1	no	—
653	C₂²⋊Q₈	—	2	2	no	—
654	C₂²⋊Q₈	—	2	2	no	—
655	C₂²⋊Q₈	—	2	2	no	—
656	C₂²⋊Q₈	—	2	2	no	—
657	C₂²⋊Q₈	D₄×C₈₃	1	2	yes	—
658	C₂²⋊Q₈	D₄×C₈₃	1	1	yes	characteristic
659	C₂²⋊Q₈	D₄×C₈₃	1	1	yes	characteristic
660	C₂²⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
661	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
662	#121	C₂³×C₈₃	1	1	yes	characteristic
663	C₄×Q₈	—	2	2	no	—
664	C₄×Q₈	—	2	1	no	—
665	C₄×Q₈	—	2	1	no	—
666	C₄×Q₈	—	2	2	no	—
667	C₄×Q₈	—	2	2	no	—
668	C₄×Q₈	—	2	2	no	—
669	C₄×Q₈	—	2	2	no	—
670	C₄×Q₈	—	2	2	no	—
671	C₄×Q₈	—	2	2	no	—
672	C₄×Q₈	—	2	1	no	—
673	C₄×Q₈	—	2	1	no	—
674	C₄×Q₈	—	2	1	no	—
675	C₄×Q₈	—	2	1	no	—
676	C₄×Q₈	—	2	1	no	—
677	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
678	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
679	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
680	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
681	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
682	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
683	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
684	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
685	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
686	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
687	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
688	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
689	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
690	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
691	C₄×D₄	—	2	1	no	—
692	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
693	C₄×D₄	C₂³×C₈₃	1	2	yes	—
694	#117	—	2	1	no	—
695	#117	—	2	2	no	—
696	#117	—	2	1	no	—
697	#117	—	2	2	no	—
698	#117	—	2	2	no	—
699	#117	—	2	1	no	—
700	#117	C₂³×C₈₃	1	2	yes	—
701	#117	C₂³×C₈₃	1	2	yes	—
702	C₂×C₄⋊C₄	—	2	1	no	—
703	C₂×C₄⋊C₄	—	2	1	no	—
704	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
705	C₂×C₄²	—	2	1	no	—
706	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
707	#107	C₂³×C₈₃	1	2	yes	—
708	#107	C₂³×C₈₃	1	2	yes	—
709	#107	C₂³×C₈₃	1	2	yes	—
710	#107	C₂³×C₈₃	1	2	yes	—
711	#107	C₂³×C₈₃	1	2	yes	—
712	#106	C₂³×C₈₃	1	2	yes	—
713	#106	C₂³×C₈₃	1	2	yes	—
714	#106	C₂³×C₈₃	1	2	yes	—
715	#106	C₂³×C₈₃	1	2	yes	—
716	#106	C₂³×C₈₃	1	2	yes	—
717	#106	C₂³×C₈₃	1	2	yes	—
718	#106	C₂³×C₈₃	1	2	yes	—
719	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
720	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
721	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
722	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
723	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
724	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
725	#103	C₂³×C₈₃	1	2	yes	—
726	#103	C₂³×C₈₃	1	2	yes	—
727	#103	C₂³×C₈₃	1	2	yes	—
728	#103	C₂³×C₈₃	1	2	yes	—
729	#103	C₂³×C₈₃	1	2	yes	—
730	#103	C₂³×C₈₃	1	2	yes	—
731	#103	C₂³×C₈₃	1	2	yes	—
732	#103	C₂³×C₈₃	1	2	yes	—
733	#103	C₂³×C₈₃	1	2	yes	—
734	#103	C₂³×C₈₃	1	2	yes	—
735	#103	C₂³×C₈₃	1	2	yes	—
736	#103	C₂³×C₈₃	1	2	yes	—
737	#103	C₂³×C₈₃	1	2	yes	—
738	#102	C₂³×C₈₃	1	2	yes	—
739	#102	C₂³×C₈₃	1	2	yes	—
740	#102	C₂³×C₈₃	1	2	yes	—
741	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
742	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
743	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
744	#97	C₂³×C₈₃	1	2	yes	—
745	#97	C₂³×C₈₃	1	1	yes	characteristic
746	#97	C₂³×C₈₃	1	1	yes	characteristic
747	#97	C₂³×C₈₃	1	2	yes	—
748	#97	C₂³×C₈₃	1	2	yes	—
749	C₄×C₈	C₂³×C₈₃	1	2	yes	—
750	C₄×C₈	C₂³×C₈₃	1	2	yes	—
751	C₂×Q₈	—	2	4	no	—
752	C₂×Q₈	—	2	1	no	—
753	C₂×Q₈	—	2	1	no	—
754	C₂×Q₈	—	2	1	no	—
755	C₂×Q₈	—	2	2	no	—
756	C₂×Q₈	—	2	1	no	—
757	C₂×Q₈	—	2	2	no	—
758	C₂×Q₈	—	2	2	no	—
759	C₂×Q₈	C₂×D₄×C₈₃	1	2	yes	—
760	C₂×Q₈	C₂×D₄×C₈₃	1	1	yes	characteristic
761	C₂×Q₈	C₂×D₄×C₈₃	1	1	yes	characteristic
762	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
763	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
764	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
765	C₂×D₄	—	2	1	no	—
766	C₂×D₄	C₂⁴×C₈₃	1	1	yes	characteristic
767	C₂²×C₄	—	2	1	no	—
768	C₂²×C₄	—	2	1	no	—
769	C₂²×C₄	—	2	1	no	—
770	C₂²×C₄	—	2	2	no	—
771	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
772	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
773	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
774	Q₁₆	—	2	4	no	—
775	Q₁₆	—	2	4	no	—
776	Q₁₆	—	2	4	no	—
777	SD₁₆	—	2	4	no	—
778	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
779	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
780	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
781	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
782	C₄⋊C₄	—	2	1	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	1	no	—
787	C₄⋊C₄	—	2	1	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	1	no	—
794	C₄⋊C₄	—	2	1	no	—
795	C₄⋊C₄	—	2	1	no	—
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	2	1	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	1	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	1	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	1	no	—
816	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
817	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
818	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
819	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
820	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
821	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
822	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
823	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
824	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
825	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
826	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
827	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
828	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
829	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
830	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	1	no	—
834	C₂²⋊C₄	—	2	1	no	—
835	C₂²⋊C₄	—	2	1	no	—
836	C₂²⋊C₄	—	2	1	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	1	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
842	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
843	C₄²	—	2	2	no	—
844	C₄²	—	2	2	no	—
845	C₄²	—	2	2	no	—
846	C₄²	—	2	1	no	—
847	C₄²	—	2	2	no	—
848	C₄²	—	2	2	no	—
849	C₄²	—	2	2	no	—
850	C₄²	—	2	2	no	—
851	C₄²	—	2	2	no	—
852	C₄²	—	2	2	no	—
853	C₄²	—	2	2	no	—
854	C₄²	—	2	2	no	—
855	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
856	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
857	C₄²	C₂⁴×C₈₃	1	2	yes	—
858	C₄²	C₂⁴×C₈₃	1	2	yes	—
859	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
860	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
861	C₂³	—	2	1	no	—
862	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
863	Q₈	—	2	4	no	—
864	Q₈	—	2	2	no	—
865	Q₈	—	2	2	no	—
866	Q₈	—	2	2	no	—
867	Q₈	—	2	2	no	—
868	Q₈	—	4	1	no	—
869	Q₈	—	4	1	no	—
870	Q₈	—	4	2	no	—
871	Q₈	—	4	2	no	—
872	Q₈	—	8	1	no	—
873	Q₈	—	8	1	no	—
874	Q₈	—	8	2	no	—
875	Q₈	—	8	2	no	—
876	Q₈	—	8	2	no	—
877	Q₈	2₋¹⁺⁴×C₈₃	1	4	yes	—
878	D₄	—	2	2	no	—
879	D₄	—	8	1	no	—
880	C₂×C₄	—	2	4	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	4	1	no	—
892	C₂×C₄	—	4	1	no	—
893	C₂×C₄	—	4	2	no	—
894	C₂×C₄	—	8	2	no	—
895	C₂×C₄	—	8	1	no	—
896	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
897	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
898	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
899	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
900	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
901	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
902	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
903	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
904	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
905	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
906	C₈	—	2	2	no	—
907	C₈	—	2	2	no	—
908	C₈	—	2	2	no	—
909	C₈	—	2	2	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	1	no	—
913	C₂²	—	4	1	no	—
914	C₂²	—	4	1	no	—
915	C₂²	—	4	1	no	—
916	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
917	C₄	—	2	1	no	—
918	C₄	—	2	1	no	—
919	C₄	—	2	1	no	—
920	C₄	—	2	1	no	—
921	C₄	—	2	2	no	—
922	C₄	—	2	2	no	—
923	C₄	—	2	2	no	—
924	C₄	—	2	2	no	—
925	C₄	—	2	4	no	—
926	C₄	—	2	1	no	—
927	C₄	—	4	1	no	—
928	C₄	—	4	2	no	—
929	C₄	—	4	2	no	—
930	C₄	—	4	1	no	—
931	C₄	—	4	2	no	—
932	C₄	—	4	2	no	—
933	C₄	—	4	2	no	—
934	C₄	—	4	1	no	—
935	C₄	C₂×2₋¹⁺⁴×C₈₃	1	2	yes	—
936	C₂	—	4	1	no	—
937	C₂	—	8	1	no	—
938	C₂	C₈₃×#3486	1	1	yes	characteristic
939	C₂	C₈₃×#3586	1	1	yes	characteristic
940	C₂	C₈₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₃
prime radical	#121×C₈₃	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₃ ◁ #533×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈₃×#3502	C₂	semidirect
3. C₈₃×#3390	C₂	semidirect
4. C₈₃×#3388	C₂	semidirect
5. C₈₃×#3387	C₂	semidirect
6. C₈₃×#3387	C₂	semidirect
7. C₈₃×#3377	C₂	semidirect
8. C₈₃×#3377	C₂	semidirect
9. C₈₃×#3374	C₂	semidirect
10. C₈₃×#3369	C₂	semidirect
12. C₈₃×#3242	C₂	semidirect
14. C₈₃×#3237	C₂	semidirect
15. C₈₃×#3127	C₂	semidirect
18. C₈₃×#3113	C₂	semidirect
19. C₈₃×#2987	C₂	semidirect
465. #61875	C₈₃	direct (N × H)
472. #3502	C₂×C₈₃	semidirect
473. #3390	C₂×C₈₃	semidirect
474. #3388	C₂×C₈₃	semidirect
475. #3387	C₂×C₈₃	semidirect
476. #3387	C₂×C₈₃	semidirect
477. #3377	C₂×C₈₃	semidirect
478. #3377	C₂×C₈₃	semidirect
479. #3374	C₂×C₈₃	semidirect
480. #3369	C₂×C₈₃	semidirect
482. #3242	C₂×C₈₃	semidirect
484. #3237	C₂×C₈₃	semidirect
485. #3127	C₂×C₈₃	semidirect
488. #3113	C₂×C₈₃	semidirect
489. #2987	C₂×C₈₃	semidirect
490. C₈₃	#61875	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×#3555	2
C₈₃×#3502	2
C₈₃×#3390	2
C₈₃×#3388	2
C₈₃×#3387	2
C₈₃×#3377	2
C₈₃×#3374	2
C₈₃×#3369	2
C₈₃×#3244	2
C₈₃×#3242	2
C₈₃×#3240	2
C₈₃×#3237	2
C₈₃×#3127	2
C₈₃×#3121	2
C₈₃×#3117	2
C₈₃×#3113	2
C₈₃×#2987	2
#61875	83

Subgroups — C83×#61875 #35289699

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#61875 #35289699