Subgroups — C₈₃×#62254 #35290078

Order 21248.

1862 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3505	C₂	1	1	yes	maximal, characteristic
2	C₈₃×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₃×#3346	C₂	1	2	yes	maximal, complemented
4	C₈₃×#3344	C₂	1	2	yes	maximal, complemented
5	C₈₃×#3320	C₂	1	2	yes	maximal, complemented
6	C₈₃×#3316	C₂	1	2	yes	maximal, complemented
7	C₈₃×#3314	C₂	1	2	yes	maximal, complemented
8	C₈₃×#3312	C₂	1	2	yes	maximal, complemented
9	C₈₃×#3270	C₂	1	2	yes	maximal, complemented
10	C₈₃×#3266	C₂	1	2	yes	maximal, complemented
11	C₈₃×#3248	C₂	1	2	yes	maximal, complemented
12	C₈₃×#3190	C₂	1	2	yes	maximal, complemented
13	C₈₃×#3189	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₃×#3187	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#3181	C₂	1	2	yes	maximal, complemented
16	C₈₃×#3056	C₂	1	2	yes	maximal, complemented
17	C₂×#467×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#465×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#435×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#137×C₈₃	C₂²	1	2	yes	complemented
21	C₂²×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic, complemented
22	C₂²×SD₁₆×C₈₃	C₂²	1	1	yes	characteristic, complemented
23	C₂²×M₁₆×C₈₃	C₂²	1	1	yes	characteristic, complemented
24	C₂³×C₈×C₈₃	C₂²	1	1	yes	characteristic
25	#554×C₈₃	—	2	2	no	—
26	#554×C₈₃	—	2	2	no	—
27	#554×C₈₃	C₂²	1	2	yes	—
28	#554×C₈₃	C₂²	1	2	yes	complemented
29	#553×C₈₃	—	2	2	no	—
30	#553×C₈₃	C₂²	1	2	yes	—
31	#552×C₈₃	C₂²	1	2	yes	—
32	#551×C₈₃	—	2	2	no	—
33	D₄×Q₈×C₈₃	C₂²	1	2	yes	—
34	D₄×Q₈×C₈₃	C₂²	1	2	yes	complemented
35	#548×C₈₃	C₂²	1	2	yes	—
36	#546×C₈₃	C₂²	1	2	yes	—
37	#544×C₈₃	—	2	1	no	—
38	#543×C₈₃	—	2	1	no	—
39	#543×C₈₃	—	2	1	no	—
40	#539×C₈₃	—	2	1	no	—
41	#538×C₈₃	—	2	1	no	—
42	#534×C₈₃	—	2	1	no	—
43	#533×C₈₃	C₂²	1	2	yes	complemented
44	#529×C₈₃	C₂²	1	2	yes	—
45	#525×C₈₃	C₂²	1	2	yes	—
46	C₂×C₂²⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
48	C₂×C₂²⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
49	C₂×C₂²⋊Q₈×C₈₃	C₂²	1	2	yes	complemented
50	C₂×#121×C₈₃	C₂²	1	1	yes	characteristic
51	#518×C₈₃	—	2	1	no	—
52	#518×C₈₃	—	2	1	no	—
53	C₂×C₄×D₄×C₈₃	C₂²	1	1	yes	characteristic
54	#501×C₈₃	C₂²	1	2	yes	complemented
55	#497×C₈₃	C₂²	1	2	yes	complemented
56	#491×C₈₃	C₂²	1	2	yes	complemented
57	#489×C₈₃	C₂²	1	2	yes	complemented
58	#485×C₈₃	C₂²	1	2	yes	complemented
59	#485×C₈₃	C₂²	1	2	yes	complemented
60	#484×C₈₃	C₂²	1	2	yes	complemented
61	#484×C₈₃	C₂²	1	2	yes	complemented
62	#483×C₈₃	C₂²	1	2	yes	complemented
63	#483×C₈₃	C₂²	1	2	yes	complemented
64	#481×C₈₃	C₂²	1	2	yes	complemented
65	#480×C₈₃	C₂²	1	2	yes	complemented
66	#479×C₈₃	C₂²	1	2	yes	complemented
67	#479×C₈₃	C₂²	1	2	yes	complemented
68	#475×C₈₃	C₂²	1	2	yes	complemented
69	#474×C₈₃	C₂²	1	2	yes	complemented
70	#470×C₈₃	C₂²	1	2	yes	complemented
71	#470×C₈₃	C₂²	1	2	yes	complemented
72	#468×C₈₃	C₂²	1	2	yes	complemented
73	#468×C₈₃	C₂²	1	2	yes	complemented
74	#467×C₈₃	C₂²	1	2	yes	complemented
75	#467×C₈₃	C₂²	1	2	yes	complemented
76	#467×C₈₃	C₂²	1	2	yes	complemented
77	#467×C₈₃	C₂²	1	2	yes	complemented
78	#467×C₈₃	C₂²	1	2	yes	complemented
79	#467×C₈₃	C₂²	1	2	yes	complemented
80	#465×C₈₃	C₂²	1	2	yes	—
81	#465×C₈₃	C₂²	1	2	yes	—
82	#465×C₈₃	C₂²	1	2	yes	—
83	#465×C₈₃	C₂²	1	2	yes	—
84	#465×C₈₃	C₂²	1	2	yes	complemented
85	#465×C₈₃	C₂²	1	2	yes	complemented
86	#464×C₈₃	C₂²	1	2	yes	complemented
87	#464×C₈₃	C₂²	1	2	yes	complemented
88	#462×C₈₃	C₂²	1	2	yes	complemented
89	#461×C₈₃	C₂²	1	2	yes	complemented
90	#452×C₈₃	C₂²	1	2	yes	complemented
91	#452×C₈₃	C₂²	1	2	yes	complemented
92	#451×C₈₃	C₂²	1	2	yes	complemented
93	#451×C₈₃	C₂²	1	2	yes	complemented
94	#451×C₈₃	C₂²	1	2	yes	complemented
95	#450×C₈₃	C₂²	1	2	yes	complemented
96	#448×C₈₃	C₂²	1	2	yes	complemented
97	#448×C₈₃	C₂²	1	2	yes	complemented
98	#441×C₈₃	C₂²	1	2	yes	complemented
99	#441×C₈₃	C₂²	1	2	yes	complemented
100	#440×C₈₃	C₂²	1	2	yes	complemented
101	#440×C₈₃	C₂²	1	2	yes	complemented
102	#435×C₈₃	C₂²	1	2	yes	—
103	#435×C₈₃	C₂²	1	2	yes	—
104	#435×C₈₃	C₂²	1	2	yes	complemented
105	#435×C₈₃	C₂²	1	2	yes	complemented
106	#428×C₈₃	C₂²	1	2	yes	complemented
107	C₂×#107×C₈₃	C₂²	1	1	yes	characteristic, complemented
108	C₂×#106×C₈₃	C₂²	1	1	yes	characteristic, complemented
109	C₂×C₄⋊C₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
110	#419×C₈₃	C₂²	1	2	yes	complemented
111	#417×C₈₃	C₂²	1	2	yes	complemented
112	C₂×#103×C₈₃	C₂²	1	1	yes	characteristic, complemented
113	C₂×#103×C₈₃	C₂²	1	1	yes	characteristic, complemented
114	C₂×#103×C₈₃	C₂²	1	1	yes	characteristic, complemented
115	C₂×#102×C₈₃	C₂²	1	1	yes	characteristic, complemented
116	C₂×C₂²⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
117	C₂×C₂²⋊C₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
118	C₂×#97×C₈₃	C₂²	1	1	yes	characteristic, complemented
119	C₂×#41×C₈₃	C₂³	1	2	yes	—
120	C₂²×Q₈×C₈₃	C₂³	1	1	yes	characteristic
121	C₂²×Q₈×C₈₃	C₂³	1	1	yes	characteristic
122	C₂²×Q₈×C₈₃	C₂³	1	1	yes	characteristic
123	C₂²×Q₈×C₈₃	C₂³	1	2	yes	—
124	C₂²×D₄×C₈₃	—	2	1	no	—
125	C₂²×D₄×C₈₃	D₄	1	1	yes	characteristic
126	C₂²×D₄×C₈₃	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₈₃	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₈₃	C₂³	1	1	yes	characteristic
129	#137×C₈₃	—	4	4	no	—
130	C₂×Q₁₆×C₈₃	—	4	2	no	—
131	C₂×Q₁₆×C₈₃	C₂³	1	2	yes	—
132	C₂×Q₁₆×C₈₃	C₂³	1	2	yes	—
133	C₂×Q₁₆×C₈₃	C₂³	1	2	yes	—
134	C₂×Q₁₆×C₈₃	C₂³	1	2	yes	—
135	C₂×SD₁₆×C₈₃	—	4	2	no	—
136	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
137	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
138	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
139	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
140	C₂×M₁₆×C₈₃	—	4	2	no	—
141	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
142	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
143	C₂²×C₈×C₈₃	—	4	2	no	—
144	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
145	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
146	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
147	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
148	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
149	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
151	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
152	C₄⋊Q₈×C₈₃	—	2	2	no	—
153	C₄⋊Q₈×C₈₃	—	2	2	no	—
154	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
155	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
156	#126×C₈₃	—	2	2	no	—
157	#126×C₈₃	—	2	2	no	—
158	#126×C₈₃	—	2	2	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	C₂³	1	2	yes	—
164	#124×C₈₃	—	2	2	no	—
165	#124×C₈₃	C₂³	1	2	yes	—
166	#123×C₈₃	—	2	2	no	—
167	#123×C₈₃	—	2	2	no	—
168	#123×C₈₃	—	2	2	no	—
169	#123×C₈₃	—	2	2	no	—
170	#123×C₈₃	—	2	2	no	—
171	C₂²⋊Q₈×C₈₃	—	2	1	no	—
172	C₂²⋊Q₈×C₈₃	—	2	1	no	—
173	C₂²⋊Q₈×C₈₃	—	2	1	no	—
174	C₂²⋊Q₈×C₈₃	—	2	1	no	—
175	C₂²⋊Q₈×C₈₃	—	2	1	no	—
176	C₂²⋊Q₈×C₈₃	—	2	1	no	—
177	C₂²⋊Q₈×C₈₃	—	2	2	no	—
178	C₂²⋊Q₈×C₈₃	—	2	2	no	—
179	C₂²⋊Q₈×C₈₃	—	2	2	no	—
180	C₂²⋊Q₈×C₈₃	—	2	2	no	—
181	C₂²⋊Q₈×C₈₃	—	2	2	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	—	2	2	no	—
187	C₂²⋊Q₈×C₈₃	—	2	2	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	2	yes	—
194	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
195	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
196	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
197	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
198	#121×C₈₃	—	2	2	no	—
199	#121×C₈₃	—	2	2	no	—
200	#121×C₈₃	—	2	1	no	—
201	#121×C₈₃	—	2	1	no	—
202	#121×C₈₃	—	2	2	no	—
203	#121×C₈₃	C₂³	1	2	yes	—
204	#121×C₈₃	C₂³	1	2	yes	—
205	#121×C₈₃	C₂³	1	2	yes	—
206	#120×C₈₃	—	2	2	no	—
207	#120×C₈₃	—	2	2	no	—
208	C₄×Q₈×C₈₃	—	2	2	no	—
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×D₄×C₈₃	—	2	2	no	—
213	C₄×D₄×C₈₃	—	2	2	no	—
214	C₄×D₄×C₈₃	—	2	2	no	—
215	C₄×D₄×C₈₃	—	2	2	no	—
216	C₄×D₄×C₈₃	—	2	2	no	—
217	C₄×D₄×C₈₃	—	2	2	no	—
218	C₄×D₄×C₈₃	—	2	2	no	—
219	C₄×D₄×C₈₃	—	2	2	no	—
220	C₄×D₄×C₈₃	—	2	2	no	—
221	C₄×D₄×C₈₃	D₄	1	2	yes	—
222	C₄×D₄×C₈₃	D₄	1	2	yes	—
223	C₄×D₄×C₈₃	C₂³	1	2	yes	—
224	C₄×D₄×C₈₃	C₂³	1	2	yes	—
225	C₄×D₄×C₈₃	C₂³	1	2	yes	—
226	#117×C₈₃	—	2	2	no	—
227	#117×C₈₃	—	2	2	no	—
228	#117×C₈₃	—	2	2	no	—
229	#117×C₈₃	C₂³	1	2	yes	—
230	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
231	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
232	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
233	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
234	C₂×C₄⋊C₄×C₈₃	D₄	1	1	yes	characteristic
235	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
236	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
240	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
241	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
242	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
243	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
244	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
245	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
246	C₂×C₂²⋊C₄×C₈₃	D₄	1	1	yes	characteristic
247	C₂×C₂²⋊C₄×C₈₃	D₄	1	1	yes	characteristic
248	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
249	#107×C₈₃	C₂³	1	2	yes	—
250	#107×C₈₃	C₂³	1	2	yes	—
251	#107×C₈₃	C₂³	1	2	yes	—
252	#107×C₈₃	C₂³	1	2	yes	—
253	#106×C₈₃	C₂³	1	2	yes	—
254	#106×C₈₃	C₂³	1	2	yes	—
255	#106×C₈₃	C₂³	1	2	yes	—
256	#106×C₈₃	C₂³	1	2	yes	—
257	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
258	C₄⋊C₈×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	#103×C₈₃	C₂³	1	2	yes	—
268	#103×C₈₃	C₂³	1	2	yes	—
269	#103×C₈₃	C₂³	1	2	yes	—
270	#103×C₈₃	C₂³	1	2	yes	—
271	#102×C₈₃	C₂³	1	2	yes	—
272	#102×C₈₃	C₂³	1	2	yes	—
273	#102×C₈₃	C₂³	1	2	yes	—
274	#102×C₈₃	C₂³	1	2	yes	—
275	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
276	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
277	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
278	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
279	#97×C₈₃	C₂³	1	2	yes	—
280	#97×C₈₃	C₂³	1	2	yes	—
281	C₂⁴×C₈₃	—	2	1	no	—
282	C₂⁴×C₈₃	C₂×D₄	1	1	yes	characteristic
283	C₂⁴×C₈₃	C₂×D₄	1	1	yes	characteristic
284	#41×C₈₃	—	4	2	no	—
285	#41×C₈₃	—	4	2	no	—
286	C₂×Q₈×C₈₃	—	2	2	no	—
287	C₂×Q₈×C₈₃	—	2	1	no	—
288	C₂×Q₈×C₈₃	—	2	2	no	—
289	C₂×Q₈×C₈₃	—	2	1	no	—
290	C₂×Q₈×C₈₃	—	2	1	no	—
291	C₂×Q₈×C₈₃	—	4	1	no	—
292	C₂×Q₈×C₈₃	—	4	1	no	—
293	C₂×Q₈×C₈₃	—	4	1	no	—
294	C₂×Q₈×C₈₃	—	4	2	no	—
295	C₂×Q₈×C₈₃	—	4	1	no	—
296	C₂×Q₈×C₈₃	—	4	1	no	—
297	C₂×Q₈×C₈₃	—	4	1	no	—
298	C₂×Q₈×C₈₃	—	4	2	no	—
299	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
300	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
301	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
302	C₂×D₄×C₈₃	—	2	4	no	—
303	C₂×D₄×C₈₃	—	2	2	no	—
304	C₂×D₄×C₈₃	—	2	2	no	—
305	C₂×D₄×C₈₃	—	2	2	no	—
306	C₂×D₄×C₈₃	—	2	2	no	—
307	C₂×D₄×C₈₃	—	2	1	no	—
308	C₂×D₄×C₈₃	—	4	1	no	—
309	C₂×D₄×C₈₃	—	4	1	no	—
310	C₂×D₄×C₈₃	—	4	4	no	—
311	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
312	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
313	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₈₃	—	2	1	no	—
315	C₂²×C₄×C₈₃	—	2	1	no	—
316	C₂²×C₄×C₈₃	—	2	2	no	—
317	C₂²×C₄×C₈₃	—	2	1	no	—
318	C₂²×C₄×C₈₃	—	2	1	no	—
319	C₂²×C₄×C₈₃	—	2	1	no	—
320	C₂²×C₄×C₈₃	—	2	2	no	—
321	C₂²×C₄×C₈₃	—	2	1	no	—
322	C₂²×C₄×C₈₃	—	2	1	no	—
323	C₂²×C₄×C₈₃	—	2	2	no	—
324	C₂²×C₄×C₈₃	—	2	2	no	—
325	C₂²×C₄×C₈₃	—	4	1	no	—
326	C₂²×C₄×C₈₃	—	4	1	no	—
327	C₂²×C₄×C₈₃	—	4	1	no	—
328	C₂²×C₄×C₈₃	—	4	1	no	—
329	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
330	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
331	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
332	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
333	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
334	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
335	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
336	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
339	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
340	Q₁₆×C₈₃	—	2	4	no	—
341	Q₁₆×C₈₃	—	4	2	no	—
342	Q₁₆×C₈₃	—	4	2	no	—
343	Q₁₆×C₈₃	—	4	2	no	—
344	SD₁₆×C₈₃	—	2	4	no	—
345	SD₁₆×C₈₃	—	4	2	no	—
346	SD₁₆×C₈₃	—	4	2	no	—
347	SD₁₆×C₈₃	—	4	2	no	—
348	M₁₆×C₈₃	—	2	4	no	—
349	M₁₆×C₈₃	—	4	2	no	—
350	C₂×C₈×C₈₃	—	2	2	no	—
351	C₂×C₈×C₈₃	—	2	2	no	—
352	C₂×C₈×C₈₃	—	2	2	no	—
353	C₂×C₈×C₈₃	—	4	1	no	—
354	C₂×C₈×C₈₃	—	4	1	no	—
355	C₂×C₈×C₈₃	—	4	1	no	—
356	C₂×C₈×C₈₃	—	4	1	no	—
357	C₂×C₈×C₈₃	—	4	1	no	—
358	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
359	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
362	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
363	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
364	C₄⋊C₄×C₈₃	—	2	2	no	—
365	C₄⋊C₄×C₈₃	—	2	2	no	—
366	C₄⋊C₄×C₈₃	—	2	2	no	—
367	C₄⋊C₄×C₈₃	—	2	2	no	—
368	C₄⋊C₄×C₈₃	—	2	2	no	—
369	C₄⋊C₄×C₈₃	—	2	2	no	—
370	C₄⋊C₄×C₈₃	—	2	2	no	—
371	C₄⋊C₄×C₈₃	—	2	2	no	—
372	C₄⋊C₄×C₈₃	—	2	1	no	—
373	C₄⋊C₄×C₈₃	—	2	2	no	—
374	C₄⋊C₄×C₈₃	—	2	1	no	—
375	C₄⋊C₄×C₈₃	—	2	1	no	—
376	C₄⋊C₄×C₈₃	—	2	1	no	—
377	C₄⋊C₄×C₈₃	—	2	2	no	—
378	C₄⋊C₄×C₈₃	—	2	2	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	2	no	—
384	C₄⋊C₄×C₈₃	—	2	2	no	—
385	C₄⋊C₄×C₈₃	—	2	2	no	—
386	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
387	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
388	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
389	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
390	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
391	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
392	C₂²⋊C₄×C₈₃	—	2	2	no	—
393	C₂²⋊C₄×C₈₃	—	2	2	no	—
394	C₂²⋊C₄×C₈₃	—	2	2	no	—
395	C₂²⋊C₄×C₈₃	—	2	2	no	—
396	C₂²⋊C₄×C₈₃	—	2	2	no	—
397	C₂²⋊C₄×C₈₃	—	2	2	no	—
398	C₂²⋊C₄×C₈₃	—	2	2	no	—
399	C₂²⋊C₄×C₈₃	—	2	2	no	—
400	C₂²⋊C₄×C₈₃	—	2	2	no	—
401	C₂²⋊C₄×C₈₃	—	2	2	no	—
402	C₂²⋊C₄×C₈₃	—	2	2	no	—
403	C₂²⋊C₄×C₈₃	—	2	2	no	—
404	C₂²⋊C₄×C₈₃	—	2	2	no	—
405	C₂²⋊C₄×C₈₃	—	2	2	no	—
406	C₂²⋊C₄×C₈₃	—	2	2	no	—
407	C₂²⋊C₄×C₈₃	—	2	2	no	—
408	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
409	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
410	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
411	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
412	C₄²×C₈₃	—	2	2	no	—
413	C₄²×C₈₃	—	2	2	no	—
414	C₄²×C₈₃	—	2	2	no	—
415	C₄²×C₈₃	—	2	2	no	—
416	C₄²×C₈₃	C₂×D₄	1	2	yes	—
417	C₄²×C₈₃	C₂⁴	1	2	yes	—
418	C₂³×C₈₃	—	2	2	no	—
419	C₂³×C₈₃	—	2	2	no	—
420	C₂³×C₈₃	—	4	1	no	—
421	C₂³×C₈₃	—	4	1	no	—
422	C₂³×C₈₃	—	4	1	no	—
423	C₂³×C₈₃	—	4	1	no	—
424	C₂³×C₈₃	—	4	2	no	—
425	C₂³×C₈₃	—	8	1	no	—
426	C₂³×C₈₃	—	8	1	no	—
427	C₂³×C₈₃	#137	1	4	yes	complemented
428	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
429	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
430	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
431	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
432	Q₈×C₈₃	—	2	2	no	—
433	Q₈×C₈₃	—	2	2	no	—
434	Q₈×C₈₃	—	2	2	no	—
435	Q₈×C₈₃	—	2	2	no	—
436	Q₈×C₈₃	—	2	2	no	—
437	Q₈×C₈₃	—	2	2	no	—
438	Q₈×C₈₃	—	8	2	no	—
439	Q₈×C₈₃	—	8	2	no	—
440	Q₈×C₈₃	—	8	1	no	—
441	Q₈×C₈₃	—	8	1	no	—
442	Q₈×C₈₃	—	8	1	no	—
443	D₄×C₈₃	—	2	4	no	—
444	D₄×C₈₃	—	2	4	no	—
445	D₄×C₈₃	—	2	2	no	—
446	D₄×C₈₃	—	2	2	no	—
447	D₄×C₈₃	—	4	4	no	—
448	D₄×C₈₃	—	4	4	no	—
449	D₄×C₈₃	—	8	1	no	—
450	D₄×C₈₃	—	8	2	no	—
451	D₄×C₈₃	—	8	2	no	—
452	C₂×C₄×C₈₃	—	2	2	no	—
453	C₂×C₄×C₈₃	—	2	1	no	—
454	C₂×C₄×C₈₃	—	2	1	no	—
455	C₂×C₄×C₈₃	—	2	1	no	—
456	C₂×C₄×C₈₃	—	2	2	no	—
457	C₂×C₄×C₈₃	—	2	1	no	—
458	C₂×C₄×C₈₃	—	2	1	no	—
459	C₂×C₄×C₈₃	—	2	1	no	—
460	C₂×C₄×C₈₃	—	2	2	no	—
461	C₂×C₄×C₈₃	—	2	2	no	—
462	C₂×C₄×C₈₃	—	2	2	no	—
463	C₂×C₄×C₈₃	—	2	2	no	—
464	C₂×C₄×C₈₃	—	2	2	no	—
465	C₂×C₄×C₈₃	—	2	2	no	—
466	C₂×C₄×C₈₃	—	2	2	no	—
467	C₂×C₄×C₈₃	—	2	2	no	—
468	C₂×C₄×C₈₃	—	4	2	no	—
469	C₂×C₄×C₈₃	—	4	1	no	—
470	C₂×C₄×C₈₃	—	4	1	no	—
471	C₂×C₄×C₈₃	—	4	1	no	—
472	C₂×C₄×C₈₃	—	4	1	no	—
473	C₂×C₄×C₈₃	—	4	1	no	—
474	C₂×C₄×C₈₃	—	4	2	no	—
475	C₂×C₄×C₈₃	—	8	2	no	—
476	C₂×C₄×C₈₃	—	8	2	no	—
477	C₂×C₄×C₈₃	—	8	1	no	—
478	C₂×C₄×C₈₃	—	8	1	no	—
479	C₂×C₄×C₈₃	—	8	1	no	—
480	C₂×C₄×C₈₃	—	8	2	no	—
481	C₂×C₄×C₈₃	—	8	1	no	—
482	C₂×C₄×C₈₃	—	8	1	no	—
483	C₂×C₄×C₈₃	—	8	1	no	—
484	C₂×C₄×C₈₃	—	8	2	no	—
485	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
486	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
487	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
488	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
489	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
492	C₈×C₈₃	—	2	1	no	—
493	C₈×C₈₃	—	2	1	no	—
494	C₈×C₈₃	—	2	1	no	—
495	C₈×C₈₃	—	2	2	no	—
496	C₈×C₈₃	—	2	2	no	—
497	C₈×C₈₃	H(5,𝔽₂)	1	2	yes	—
498	C₂²×C₈₃	—	2	1	no	—
499	C₂²×C₈₃	—	2	1	no	—
500	C₂²×C₈₃	—	2	1	no	—
501	C₂²×C₈₃	—	2	1	no	—
502	C₂²×C₈₃	—	2	1	no	—
503	C₂²×C₈₃	—	2	1	no	—
504	C₂²×C₈₃	—	2	2	no	—
505	C₂²×C₈₃	—	2	2	no	—
506	C₂²×C₈₃	—	2	2	no	—
507	C₂²×C₈₃	—	4	4	no	—
508	C₂²×C₈₃	—	4	2	no	—
509	C₂²×C₈₃	—	4	2	no	—
510	C₂²×C₈₃	—	4	2	no	—
511	C₂²×C₈₃	—	8	2	no	—
512	C₂²×C₈₃	—	16	2	no	—
513	C₂²×C₈₃	C₂×#137	1	2	yes	—
514	C₂²×C₈₃	C₂×#137	1	2	yes	—
515	C₂²×C₈₃	C₂×#137	1	2	yes	—
516	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
517	C₄×C₈₃	—	2	2	no	—
518	C₄×C₈₃	—	2	1	no	—
519	C₄×C₈₃	—	2	2	no	—
520	C₄×C₈₃	—	2	1	no	—
521	C₄×C₈₃	—	2	1	no	—
522	C₄×C₈₃	—	2	2	no	—
523	C₄×C₈₃	—	4	2	no	—
524	C₄×C₈₃	—	4	2	no	—
525	C₄×C₈₃	—	4	2	no	—
526	C₄×C₈₃	—	4	2	no	—
527	C₄×C₈₃	—	4	2	no	—
528	C₄×C₈₃	—	4	2	no	—
529	C₄×C₈₃	—	4	2	no	—
530	C₄×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
531	C₄×C₈₃	#585	1	1	yes	characteristic
532	#62254	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
533	C₂×C₈₃	—	2	2	no	—
534	C₂×C₈₃	—	2	2	no	—
535	C₂×C₈₃	—	2	2	no	—
536	C₂×C₈₃	—	4	2	no	—
537	C₂×C₈₃	—	8	2	no	—
538	C₂×C₈₃	#3496	1	1	yes	characteristic
539	C₂×C₈₃	C₂²×#137	1	1	yes	characteristic
540	C₂×C₈₃	#3584	1	1	yes	characteristic
541	#3505	C₂×C₈₃	1	1	yes	characteristic
542	#3501	C₂×C₈₃	1	1	yes	characteristic, complemented
543	#3346	C₂×C₈₃	1	2	yes	complemented
544	#3344	C₂×C₈₃	1	2	yes	complemented
545	#3320	C₂×C₈₃	1	2	yes	complemented
546	#3316	C₂×C₈₃	1	2	yes	complemented
547	#3314	C₂×C₈₃	1	2	yes	complemented
548	#3312	C₂×C₈₃	1	2	yes	complemented
549	#3270	C₂×C₈₃	1	2	yes	complemented
550	#3266	C₂×C₈₃	1	2	yes	complemented
551	#3248	C₂×C₈₃	1	2	yes	complemented
552	#3190	C₂×C₈₃	1	2	yes	complemented
553	#3189	C₂×C₈₃	1	1	yes	characteristic, complemented
554	#3187	C₂×C₈₃	1	1	yes	characteristic, complemented
555	#3181	C₂×C₈₃	1	2	yes	complemented
556	#3056	C₂×C₈₃	1	2	yes	complemented
557	C₂×#467	C₂×C₈₃	1	1	yes	characteristic, complemented
558	C₂×#465	C₂×C₈₃	1	1	yes	characteristic, complemented
559	C₂×#435	C₂×C₈₃	1	1	yes	characteristic, complemented
560	C₈₃	#62254	1	1	yes	characteristic, direct product factor, Sylow
561	C₂×#137	C₂²×C₈₃	1	2	yes	complemented
562	C₂²×Q₁₆	C₂²×C₈₃	1	1	yes	characteristic, complemented
563	C₂²×SD₁₆	C₂²×C₈₃	1	1	yes	characteristic, complemented
564	C₂²×M₁₆	C₂²×C₈₃	1	1	yes	characteristic, complemented
565	C₂³×C₈	C₂²×C₈₃	1	1	yes	characteristic
566	#554	—	2	2	no	—
567	#554	—	2	2	no	—
568	#554	C₂²×C₈₃	1	2	yes	—
569	#554	C₂²×C₈₃	1	2	yes	complemented
570	#553	—	2	2	no	—
571	#553	C₂²×C₈₃	1	2	yes	—
572	#552	C₂²×C₈₃	1	2	yes	—
573	#551	—	2	2	no	—
574	D₄×Q₈	C₂²×C₈₃	1	2	yes	—
575	D₄×Q₈	C₂²×C₈₃	1	2	yes	complemented
576	#548	C₂²×C₈₃	1	2	yes	—
577	#546	C₂²×C₈₃	1	2	yes	—
578	#544	—	2	1	no	—
579	#543	—	2	1	no	—
580	#543	—	2	1	no	—
581	#539	—	2	1	no	—
582	#538	—	2	1	no	—
583	#534	—	2	1	no	—
584	#533	C₂²×C₈₃	1	2	yes	complemented
585	#529	C₂²×C₈₃	1	2	yes	—
586	#525	C₂²×C₈₃	1	2	yes	—
587	C₂×C₂²⋊Q₈	C₂²×C₈₃	1	1	yes	characteristic
588	C₂×C₂²⋊Q₈	C₂²×C₈₃	1	1	yes	characteristic
589	C₂×C₂²⋊Q₈	C₂²×C₈₃	1	1	yes	characteristic
590	C₂×C₂²⋊Q₈	C₂²×C₈₃	1	2	yes	complemented
591	C₂×#121	C₂²×C₈₃	1	1	yes	characteristic
592	#518	—	2	1	no	—
593	#518	—	2	1	no	—
594	C₂×C₄×D₄	C₂²×C₈₃	1	1	yes	characteristic
595	#501	C₂²×C₈₃	1	2	yes	complemented
596	#497	C₂²×C₈₃	1	2	yes	complemented
597	#491	C₂²×C₈₃	1	2	yes	complemented
598	#489	C₂²×C₈₃	1	2	yes	complemented
599	#485	C₂²×C₈₃	1	2	yes	complemented
600	#485	C₂²×C₈₃	1	2	yes	complemented
601	#484	C₂²×C₈₃	1	2	yes	complemented
602	#484	C₂²×C₈₃	1	2	yes	complemented
603	#483	C₂²×C₈₃	1	2	yes	complemented
604	#483	C₂²×C₈₃	1	2	yes	complemented
605	#481	C₂²×C₈₃	1	2	yes	complemented
606	#480	C₂²×C₈₃	1	2	yes	complemented
607	#479	C₂²×C₈₃	1	2	yes	complemented
608	#479	C₂²×C₈₃	1	2	yes	complemented
609	#475	C₂²×C₈₃	1	2	yes	complemented
610	#474	C₂²×C₈₃	1	2	yes	complemented
611	#470	C₂²×C₈₃	1	2	yes	complemented
612	#470	C₂²×C₈₃	1	2	yes	complemented
613	#468	C₂²×C₈₃	1	2	yes	complemented
614	#468	C₂²×C₈₃	1	2	yes	complemented
615	#467	C₂²×C₈₃	1	2	yes	complemented
616	#467	C₂²×C₈₃	1	2	yes	complemented
617	#467	C₂²×C₈₃	1	2	yes	complemented
618	#467	C₂²×C₈₃	1	2	yes	complemented
619	#467	C₂²×C₈₃	1	2	yes	complemented
620	#467	C₂²×C₈₃	1	2	yes	complemented
621	#465	C₂²×C₈₃	1	2	yes	—
622	#465	C₂²×C₈₃	1	2	yes	—
623	#465	C₂²×C₈₃	1	2	yes	—
624	#465	C₂²×C₈₃	1	2	yes	—
625	#465	C₂²×C₈₃	1	2	yes	complemented
626	#465	C₂²×C₈₃	1	2	yes	complemented
627	#464	C₂²×C₈₃	1	2	yes	complemented
628	#464	C₂²×C₈₃	1	2	yes	complemented
629	#462	C₂²×C₈₃	1	2	yes	complemented
630	#461	C₂²×C₈₃	1	2	yes	complemented
631	#452	C₂²×C₈₃	1	2	yes	complemented
632	#452	C₂²×C₈₃	1	2	yes	complemented
633	#451	C₂²×C₈₃	1	2	yes	complemented
634	#451	C₂²×C₈₃	1	2	yes	complemented
635	#451	C₂²×C₈₃	1	2	yes	complemented
636	#450	C₂²×C₈₃	1	2	yes	complemented
637	#448	C₂²×C₈₃	1	2	yes	complemented
638	#448	C₂²×C₈₃	1	2	yes	complemented
639	#441	C₂²×C₈₃	1	2	yes	complemented
640	#441	C₂²×C₈₃	1	2	yes	complemented
641	#440	C₂²×C₈₃	1	2	yes	complemented
642	#440	C₂²×C₈₃	1	2	yes	complemented
643	#435	C₂²×C₈₃	1	2	yes	—
644	#435	C₂²×C₈₃	1	2	yes	—
645	#435	C₂²×C₈₃	1	2	yes	complemented
646	#435	C₂²×C₈₃	1	2	yes	complemented
647	#428	C₂²×C₈₃	1	2	yes	complemented
648	C₂×#107	C₂²×C₈₃	1	1	yes	characteristic, complemented
649	C₂×#106	C₂²×C₈₃	1	1	yes	characteristic, complemented
650	C₂×C₄⋊C₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
651	#419	C₂²×C₈₃	1	2	yes	complemented
652	#417	C₂²×C₈₃	1	2	yes	complemented
653	C₂×#103	C₂²×C₈₃	1	1	yes	characteristic, complemented
654	C₂×#103	C₂²×C₈₃	1	1	yes	characteristic, complemented
655	C₂×#103	C₂²×C₈₃	1	1	yes	characteristic, complemented
656	C₂×#102	C₂²×C₈₃	1	1	yes	characteristic, complemented
657	C₂×C₂²⋊C₈	C₂²×C₈₃	1	1	yes	characteristic
658	C₂×C₂²⋊C₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
659	C₂×#97	C₂²×C₈₃	1	1	yes	characteristic, complemented
660	C₂×#41	C₂³×C₈₃	1	2	yes	—
661	C₂²×Q₈	C₂³×C₈₃	1	1	yes	characteristic
662	C₂²×Q₈	C₂³×C₈₃	1	1	yes	characteristic
663	C₂²×Q₈	C₂³×C₈₃	1	1	yes	characteristic
664	C₂²×Q₈	C₂³×C₈₃	1	2	yes	—
665	C₂²×D₄	—	2	1	no	—
666	C₂²×D₄	D₄×C₈₃	1	1	yes	characteristic
667	C₂²×D₄	C₂³×C₈₃	1	1	yes	characteristic
668	C₂³×C₄	C₂³×C₈₃	1	1	yes	characteristic
669	C₂³×C₄	C₂³×C₈₃	1	1	yes	characteristic
670	#137	—	4	4	no	—
671	C₂×Q₁₆	—	4	2	no	—
672	C₂×Q₁₆	C₂³×C₈₃	1	2	yes	—
673	C₂×Q₁₆	C₂³×C₈₃	1	2	yes	—
674	C₂×Q₁₆	C₂³×C₈₃	1	2	yes	—
675	C₂×Q₁₆	C₂³×C₈₃	1	2	yes	—
676	C₂×SD₁₆	—	4	2	no	—
677	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
678	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
679	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
680	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
681	C₂×M₁₆	—	4	2	no	—
682	C₂×M₁₆	C₂³×C₈₃	1	2	yes	—
683	C₂×M₁₆	C₂³×C₈₃	1	2	yes	—
684	C₂²×C₈	—	4	2	no	—
685	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
686	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
687	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
688	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
689	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
690	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
691	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
692	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
693	C₄⋊Q₈	—	2	2	no	—
694	C₄⋊Q₈	—	2	2	no	—
695	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
696	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
697	#126	—	2	2	no	—
698	#126	—	2	2	no	—
699	#126	—	2	2	no	—
700	#125	—	2	2	no	—
701	#125	—	2	2	no	—
702	#125	—	2	2	no	—
703	#125	—	2	2	no	—
704	#125	C₂³×C₈₃	1	2	yes	—
705	#124	—	2	2	no	—
706	#124	C₂³×C₈₃	1	2	yes	—
707	#123	—	2	2	no	—
708	#123	—	2	2	no	—
709	#123	—	2	2	no	—
710	#123	—	2	2	no	—
711	#123	—	2	2	no	—
712	C₂²⋊Q₈	—	2	1	no	—
713	C₂²⋊Q₈	—	2	1	no	—
714	C₂²⋊Q₈	—	2	1	no	—
715	C₂²⋊Q₈	—	2	1	no	—
716	C₂²⋊Q₈	—	2	1	no	—
717	C₂²⋊Q₈	—	2	1	no	—
718	C₂²⋊Q₈	—	2	2	no	—
719	C₂²⋊Q₈	—	2	2	no	—
720	C₂²⋊Q₈	—	2	2	no	—
721	C₂²⋊Q₈	—	2	2	no	—
722	C₂²⋊Q₈	—	2	2	no	—
723	C₂²⋊Q₈	—	2	2	no	—
724	C₂²⋊Q₈	—	2	2	no	—
725	C₂²⋊Q₈	—	2	2	no	—
726	C₂²⋊Q₈	—	2	2	no	—
727	C₂²⋊Q₈	—	2	2	no	—
728	C₂²⋊Q₈	—	2	2	no	—
729	C₂²⋊Q₈	—	2	2	no	—
730	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
731	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
732	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
733	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
734	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
735	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
736	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
737	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
738	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
739	#121	—	2	2	no	—
740	#121	—	2	2	no	—
741	#121	—	2	1	no	—
742	#121	—	2	1	no	—
743	#121	—	2	2	no	—
744	#121	C₂³×C₈₃	1	2	yes	—
745	#121	C₂³×C₈₃	1	2	yes	—
746	#121	C₂³×C₈₃	1	2	yes	—
747	#120	—	2	2	no	—
748	#120	—	2	2	no	—
749	C₄×Q₈	—	2	2	no	—
750	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
751	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
752	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
753	C₄×D₄	—	2	2	no	—
754	C₄×D₄	—	2	2	no	—
755	C₄×D₄	—	2	2	no	—
756	C₄×D₄	—	2	2	no	—
757	C₄×D₄	—	2	2	no	—
758	C₄×D₄	—	2	2	no	—
759	C₄×D₄	—	2	2	no	—
760	C₄×D₄	—	2	2	no	—
761	C₄×D₄	—	2	2	no	—
762	C₄×D₄	D₄×C₈₃	1	2	yes	—
763	C₄×D₄	D₄×C₈₃	1	2	yes	—
764	C₄×D₄	C₂³×C₈₃	1	2	yes	—
765	C₄×D₄	C₂³×C₈₃	1	2	yes	—
766	C₄×D₄	C₂³×C₈₃	1	2	yes	—
767	#117	—	2	2	no	—
768	#117	—	2	2	no	—
769	#117	—	2	2	no	—
770	#117	C₂³×C₈₃	1	2	yes	—
771	C₂×C₄⋊C₄	—	2	1	no	—
772	C₂×C₄⋊C₄	—	2	1	no	—
773	C₂×C₄⋊C₄	—	2	1	no	—
774	C₂×C₄⋊C₄	—	2	2	no	—
775	C₂×C₄⋊C₄	D₄×C₈₃	1	1	yes	characteristic
776	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
777	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
778	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
779	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
780	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
781	C₂×C₂²⋊C₄	—	2	1	no	—
782	C₂×C₂²⋊C₄	—	2	1	no	—
783	C₂×C₂²⋊C₄	—	2	1	no	—
784	C₂×C₂²⋊C₄	—	2	2	no	—
785	C₂×C₂²⋊C₄	—	2	1	no	—
786	C₂×C₂²⋊C₄	—	2	2	no	—
787	C₂×C₂²⋊C₄	D₄×C₈₃	1	1	yes	characteristic
788	C₂×C₂²⋊C₄	D₄×C₈₃	1	1	yes	characteristic
789	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
790	#107	C₂³×C₈₃	1	2	yes	—
791	#107	C₂³×C₈₃	1	2	yes	—
792	#107	C₂³×C₈₃	1	2	yes	—
793	#107	C₂³×C₈₃	1	2	yes	—
794	#106	C₂³×C₈₃	1	2	yes	—
795	#106	C₂³×C₈₃	1	2	yes	—
796	#106	C₂³×C₈₃	1	2	yes	—
797	#106	C₂³×C₈₃	1	2	yes	—
798	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
799	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
800	#103	C₂³×C₈₃	1	2	yes	—
801	#103	C₂³×C₈₃	1	2	yes	—
802	#103	C₂³×C₈₃	1	2	yes	—
803	#103	C₂³×C₈₃	1	2	yes	—
804	#103	C₂³×C₈₃	1	2	yes	—
805	#103	C₂³×C₈₃	1	2	yes	—
806	#103	C₂³×C₈₃	1	2	yes	—
807	#103	C₂³×C₈₃	1	2	yes	—
808	#103	C₂³×C₈₃	1	2	yes	—
809	#103	C₂³×C₈₃	1	2	yes	—
810	#103	C₂³×C₈₃	1	2	yes	—
811	#103	C₂³×C₈₃	1	2	yes	—
812	#102	C₂³×C₈₃	1	2	yes	—
813	#102	C₂³×C₈₃	1	2	yes	—
814	#102	C₂³×C₈₃	1	2	yes	—
815	#102	C₂³×C₈₃	1	2	yes	—
816	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
817	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
818	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
819	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
820	#97	C₂³×C₈₃	1	2	yes	—
821	#97	C₂³×C₈₃	1	2	yes	—
822	C₂⁴	—	2	1	no	—
823	C₂⁴	C₂×D₄×C₈₃	1	1	yes	characteristic
824	C₂⁴	C₂×D₄×C₈₃	1	1	yes	characteristic
825	#41	—	4	2	no	—
826	#41	—	4	2	no	—
827	C₂×Q₈	—	2	2	no	—
828	C₂×Q₈	—	2	1	no	—
829	C₂×Q₈	—	2	2	no	—
830	C₂×Q₈	—	2	1	no	—
831	C₂×Q₈	—	2	1	no	—
832	C₂×Q₈	—	4	1	no	—
833	C₂×Q₈	—	4	1	no	—
834	C₂×Q₈	—	4	1	no	—
835	C₂×Q₈	—	4	2	no	—
836	C₂×Q₈	—	4	1	no	—
837	C₂×Q₈	—	4	1	no	—
838	C₂×Q₈	—	4	1	no	—
839	C₂×Q₈	—	4	2	no	—
840	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
841	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
842	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
843	C₂×D₄	—	2	4	no	—
844	C₂×D₄	—	2	2	no	—
845	C₂×D₄	—	2	2	no	—
846	C₂×D₄	—	2	2	no	—
847	C₂×D₄	—	2	2	no	—
848	C₂×D₄	—	2	1	no	—
849	C₂×D₄	—	4	1	no	—
850	C₂×D₄	—	4	1	no	—
851	C₂×D₄	—	4	4	no	—
852	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
853	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
854	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
855	C₂²×C₄	—	2	1	no	—
856	C₂²×C₄	—	2	1	no	—
857	C₂²×C₄	—	2	2	no	—
858	C₂²×C₄	—	2	1	no	—
859	C₂²×C₄	—	2	1	no	—
860	C₂²×C₄	—	2	1	no	—
861	C₂²×C₄	—	2	2	no	—
862	C₂²×C₄	—	2	1	no	—
863	C₂²×C₄	—	2	1	no	—
864	C₂²×C₄	—	2	2	no	—
865	C₂²×C₄	—	2	2	no	—
866	C₂²×C₄	—	4	1	no	—
867	C₂²×C₄	—	4	1	no	—
868	C₂²×C₄	—	4	1	no	—
869	C₂²×C₄	—	4	1	no	—
870	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
871	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
872	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
873	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
874	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
875	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
876	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
877	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
878	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
879	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
880	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
881	Q₁₆	—	2	4	no	—
882	Q₁₆	—	4	2	no	—
883	Q₁₆	—	4	2	no	—
884	Q₁₆	—	4	2	no	—
885	SD₁₆	—	2	4	no	—
886	SD₁₆	—	4	2	no	—
887	SD₁₆	—	4	2	no	—
888	SD₁₆	—	4	2	no	—
889	M₁₆	—	2	4	no	—
890	M₁₆	—	4	2	no	—
891	C₂×C₈	—	2	2	no	—
892	C₂×C₈	—	2	2	no	—
893	C₂×C₈	—	2	2	no	—
894	C₂×C₈	—	4	1	no	—
895	C₂×C₈	—	4	1	no	—
896	C₂×C₈	—	4	1	no	—
897	C₂×C₈	—	4	1	no	—
898	C₂×C₈	—	4	1	no	—
899	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
900	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
901	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
902	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
903	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
904	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	1	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
928	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
929	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
930	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
931	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
932	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
933	C₂²⋊C₄	—	2	2	no	—
934	C₂²⋊C₄	—	2	2	no	—
935	C₂²⋊C₄	—	2	2	no	—
936	C₂²⋊C₄	—	2	2	no	—
937	C₂²⋊C₄	—	2	2	no	—
938	C₂²⋊C₄	—	2	2	no	—
939	C₂²⋊C₄	—	2	2	no	—
940	C₂²⋊C₄	—	2	2	no	—
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	2	no	—
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	—	2	2	no	—
947	C₂²⋊C₄	—	2	2	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
950	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
951	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
952	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
953	C₄²	—	2	2	no	—
954	C₄²	—	2	2	no	—
955	C₄²	—	2	2	no	—
956	C₄²	—	2	2	no	—
957	C₄²	C₂×D₄×C₈₃	1	2	yes	—
958	C₄²	C₂⁴×C₈₃	1	2	yes	—
959	C₂³	—	2	2	no	—
960	C₂³	—	2	2	no	—
961	C₂³	—	4	1	no	—
962	C₂³	—	4	1	no	—
963	C₂³	—	4	1	no	—
964	C₂³	—	4	1	no	—
965	C₂³	—	4	2	no	—
966	C₂³	—	8	1	no	—
967	C₂³	—	8	1	no	—
968	C₂³	#137×C₈₃	1	4	yes	complemented
969	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
970	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
971	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
972	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
973	Q₈	—	2	2	no	—
974	Q₈	—	2	2	no	—
975	Q₈	—	2	2	no	—
976	Q₈	—	2	2	no	—
977	Q₈	—	2	2	no	—
978	Q₈	—	2	2	no	—
979	Q₈	—	8	2	no	—
980	Q₈	—	8	1	no	—
981	Q₈	—	8	1	no	—
982	Q₈	—	8	1	no	—
983	Q₈	—	8	2	no	—
984	D₄	—	2	4	no	—
985	D₄	—	2	4	no	—
986	D₄	—	2	2	no	—
987	D₄	—	2	2	no	—
988	D₄	—	4	4	no	—
989	D₄	—	4	4	no	—
990	D₄	—	8	1	no	—
991	D₄	—	8	2	no	—
992	D₄	—	8	2	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	2	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	4	2	no	—
1010	C₂×C₄	—	4	1	no	—
1011	C₂×C₄	—	4	1	no	—
1012	C₂×C₄	—	4	1	no	—
1013	C₂×C₄	—	4	1	no	—
1014	C₂×C₄	—	4	1	no	—
1015	C₂×C₄	—	4	2	no	—
1016	C₂×C₄	—	8	2	no	—
1017	C₂×C₄	—	8	2	no	—
1018	C₂×C₄	—	8	1	no	—
1019	C₂×C₄	—	8	1	no	—
1020	C₂×C₄	—	8	1	no	—
1021	C₂×C₄	—	8	2	no	—
1022	C₂×C₄	—	8	1	no	—
1023	C₂×C₄	—	8	1	no	—
1024	C₂×C₄	—	8	1	no	—
1025	C₂×C₄	—	8	2	no	—
1026	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
1027	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
1028	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
1029	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1030	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1031	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1032	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
1033	C₈	—	2	1	no	—
1034	C₈	—	2	1	no	—
1035	C₈	—	2	1	no	—
1036	C₈	—	2	2	no	—
1037	C₈	—	2	2	no	—
1038	C₈	H(5,𝔽₂)×C₈₃	1	2	yes	—
1039	C₂²	—	2	1	no	—
1040	C₂²	—	2	1	no	—
1041	C₂²	—	2	1	no	—
1042	C₂²	—	2	1	no	—
1043	C₂²	—	2	1	no	—
1044	C₂²	—	2	1	no	—
1045	C₂²	—	2	2	no	—
1046	C₂²	—	2	2	no	—
1047	C₂²	—	2	2	no	—
1048	C₂²	—	4	4	no	—
1049	C₂²	—	4	2	no	—
1050	C₂²	—	4	2	no	—
1051	C₂²	—	4	2	no	—
1052	C₂²	—	8	2	no	—
1053	C₂²	—	16	2	no	—
1054	C₂²	C₂×#137×C₈₃	1	2	yes	—
1055	C₂²	C₂×#137×C₈₃	1	2	yes	—
1056	C₂²	C₂×#137×C₈₃	1	2	yes	—
1057	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
1058	C₄	—	2	2	no	—
1059	C₄	—	2	2	no	—
1060	C₄	—	2	1	no	—
1061	C₄	—	2	2	no	—
1062	C₄	—	2	1	no	—
1063	C₄	—	2	1	no	—
1064	C₄	—	4	2	no	—
1065	C₄	—	4	2	no	—
1066	C₄	—	4	2	no	—
1067	C₄	—	4	2	no	—
1068	C₄	—	4	2	no	—
1069	C₄	—	4	2	no	—
1070	C₄	—	4	2	no	—
1071	C₄	C₂×H(5,𝔽₂)×C₈₃	1	1	yes	characteristic
1072	C₄	#585×C₈₃	1	1	yes	characteristic
1073	C₂	—	2	2	no	—
1074	C₂	—	2	2	no	—
1075	C₂	—	2	2	no	—
1076	C₂	—	4	2	no	—
1077	C₂	—	8	2	no	—
1078	C₂	C₈₃×#3496	1	1	yes	characteristic
1079	C₂	C₂²×#137×C₈₃	1	1	yes	characteristic
1080	C₂	C₈₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₃
prime radical	C₈₃×#3505	C₂
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
2. C₈₃×#3501	C₂	semidirect
3. C₈₃×#3346	C₂	semidirect
4. C₈₃×#3344	C₂	semidirect
5. C₈₃×#3320	C₂	semidirect
6. C₈₃×#3316	C₂	semidirect
7. C₈₃×#3314	C₂	semidirect
8. C₈₃×#3312	C₂	semidirect
9. C₈₃×#3270	C₂	semidirect
10. C₈₃×#3266	C₂	semidirect
11. C₈₃×#3248	C₂	semidirect
12. C₈₃×#3190	C₂	semidirect
13. C₈₃×#3189	C₂	semidirect
14. C₈₃×#3187	C₂	semidirect
15. C₈₃×#3181	C₂	semidirect
16. C₈₃×#3056	C₂	semidirect
17. C₂×#467×C₈₃	C₂	semidirect
18. C₂×#465×C₈₃	C₂	semidirect
19. C₂×#435×C₈₃	C₂	semidirect
20. C₂×#137×C₈₃	C₂²	semidirect
21. C₂²×Q₁₆×C₈₃	C₂²	semidirect
22. C₂²×SD₁₆×C₈₃	C₂²	semidirect
23. C₂²×M₁₆×C₈₃	C₂²	semidirect
28. #554×C₈₃	C₂²	semidirect
34. D₄×Q₈×C₈₃	C₂²	semidirect
43. #533×C₈₃	C₂²	semidirect
49. C₂×C₂²⋊Q₈×C₈₃	C₂²	semidirect
54. #501×C₈₃	C₂²	semidirect
55. #497×C₈₃	C₂²	semidirect
56. #491×C₈₃	C₂²	semidirect
57. #489×C₈₃	C₂²	semidirect
58. #485×C₈₃	C₂²	semidirect
59. #485×C₈₃	C₂²	semidirect
60. #484×C₈₃	C₂²	semidirect
61. #484×C₈₃	C₂²	semidirect
62. #483×C₈₃	C₂²	semidirect
63. #483×C₈₃	C₂²	semidirect
64. #481×C₈₃	C₂²	semidirect
65. #480×C₈₃	C₂²	semidirect
66. #479×C₈₃	C₂²	semidirect
67. #479×C₈₃	C₂²	semidirect
68. #475×C₈₃	C₂²	semidirect
69. #474×C₈₃	C₂²	semidirect
70. #470×C₈₃	C₂²	semidirect
71. #470×C₈₃	C₂²	semidirect
72. #468×C₈₃	C₂²	semidirect
73. #468×C₈₃	C₂²	semidirect
74. #467×C₈₃	C₂²	semidirect
75. #467×C₈₃	C₂²	semidirect
76. #467×C₈₃	C₂²	semidirect
77. #467×C₈₃	C₂²	semidirect
78. #467×C₈₃	C₂²	semidirect
79. #467×C₈₃	C₂²	semidirect
84. #465×C₈₃	C₂²	semidirect
85. #465×C₈₃	C₂²	semidirect
86. #464×C₈₃	C₂²	semidirect
87. #464×C₈₃	C₂²	semidirect
88. #462×C₈₃	C₂²	semidirect
89. #461×C₈₃	C₂²	semidirect
90. #452×C₈₃	C₂²	semidirect
91. #452×C₈₃	C₂²	semidirect
92. #451×C₈₃	C₂²	semidirect
93. #451×C₈₃	C₂²	semidirect
94. #451×C₈₃	C₂²	semidirect
95. #450×C₈₃	C₂²	semidirect
96. #448×C₈₃	C₂²	semidirect
97. #448×C₈₃	C₂²	semidirect
98. #441×C₈₃	C₂²	semidirect
99. #441×C₈₃	C₂²	semidirect
100. #440×C₈₃	C₂²	semidirect
101. #440×C₈₃	C₂²	semidirect
104. #435×C₈₃	C₂²	semidirect
105. #435×C₈₃	C₂²	semidirect
106. #428×C₈₃	C₂²	semidirect
107. C₂×#107×C₈₃	C₂²	semidirect
108. C₂×#106×C₈₃	C₂²	semidirect
109. C₂×C₄⋊C₈×C₈₃	C₂²	semidirect
110. #419×C₈₃	C₂²	semidirect
111. #417×C₈₃	C₂²	semidirect
112. C₂×#103×C₈₃	C₂²	semidirect
113. C₂×#103×C₈₃	C₂²	semidirect
114. C₂×#103×C₈₃	C₂²	semidirect
115. C₂×#102×C₈₃	C₂²	semidirect
117. C₂×C₂²⋊C₈×C₈₃	C₂²	semidirect
118. C₂×#97×C₈₃	C₂²	semidirect
427. C₂³×C₈₃	#137	semidirect
532. #62254	C₈₃	direct (N × H)
542. #3501	C₂×C₈₃	semidirect
543. #3346	C₂×C₈₃	semidirect
544. #3344	C₂×C₈₃	semidirect
545. #3320	C₂×C₈₃	semidirect
546. #3316	C₂×C₈₃	semidirect
547. #3314	C₂×C₈₃	semidirect
548. #3312	C₂×C₈₃	semidirect
549. #3270	C₂×C₈₃	semidirect
550. #3266	C₂×C₈₃	semidirect
551. #3248	C₂×C₈₃	semidirect
552. #3190	C₂×C₈₃	semidirect
553. #3189	C₂×C₈₃	semidirect
554. #3187	C₂×C₈₃	semidirect
555. #3181	C₂×C₈₃	semidirect
556. #3056	C₂×C₈₃	semidirect
557. C₂×#467	C₂×C₈₃	semidirect
558. C₂×#465	C₂×C₈₃	semidirect
559. C₂×#435	C₂×C₈₃	semidirect
560. C₈₃	#62254	direct (N × H)
561. C₂×#137	C₂²×C₈₃	semidirect
562. C₂²×Q₁₆	C₂²×C₈₃	semidirect
563. C₂²×SD₁₆	C₂²×C₈₃	semidirect
564. C₂²×M₁₆	C₂²×C₈₃	semidirect
569. #554	C₂²×C₈₃	semidirect
575. D₄×Q₈	C₂²×C₈₃	semidirect
584. #533	C₂²×C₈₃	semidirect
590. C₂×C₂²⋊Q₈	C₂²×C₈₃	semidirect
595. #501	C₂²×C₈₃	semidirect
596. #497	C₂²×C₈₃	semidirect
597. #491	C₂²×C₈₃	semidirect
598. #489	C₂²×C₈₃	semidirect
599. #485	C₂²×C₈₃	semidirect
600. #485	C₂²×C₈₃	semidirect
601. #484	C₂²×C₈₃	semidirect
602. #484	C₂²×C₈₃	semidirect
603. #483	C₂²×C₈₃	semidirect
604. #483	C₂²×C₈₃	semidirect
605. #481	C₂²×C₈₃	semidirect
606. #480	C₂²×C₈₃	semidirect
607. #479	C₂²×C₈₃	semidirect
608. #479	C₂²×C₈₃	semidirect
609. #475	C₂²×C₈₃	semidirect
610. #474	C₂²×C₈₃	semidirect
611. #470	C₂²×C₈₃	semidirect
612. #470	C₂²×C₈₃	semidirect
613. #468	C₂²×C₈₃	semidirect
614. #468	C₂²×C₈₃	semidirect
615. #467	C₂²×C₈₃	semidirect
616. #467	C₂²×C₈₃	semidirect
617. #467	C₂²×C₈₃	semidirect
618. #467	C₂²×C₈₃	semidirect
619. #467	C₂²×C₈₃	semidirect
620. #467	C₂²×C₈₃	semidirect
625. #465	C₂²×C₈₃	semidirect
626. #465	C₂²×C₈₃	semidirect
627. #464	C₂²×C₈₃	semidirect
628. #464	C₂²×C₈₃	semidirect
629. #462	C₂²×C₈₃	semidirect
630. #461	C₂²×C₈₃	semidirect
631. #452	C₂²×C₈₃	semidirect
632. #452	C₂²×C₈₃	semidirect
633. #451	C₂²×C₈₃	semidirect
634. #451	C₂²×C₈₃	semidirect
635. #451	C₂²×C₈₃	semidirect
636. #450	C₂²×C₈₃	semidirect
637. #448	C₂²×C₈₃	semidirect
638. #448	C₂²×C₈₃	semidirect
639. #441	C₂²×C₈₃	semidirect
640. #441	C₂²×C₈₃	semidirect
641. #440	C₂²×C₈₃	semidirect
642. #440	C₂²×C₈₃	semidirect
645. #435	C₂²×C₈₃	semidirect
646. #435	C₂²×C₈₃	semidirect
647. #428	C₂²×C₈₃	semidirect
648. C₂×#107	C₂²×C₈₃	semidirect
649. C₂×#106	C₂²×C₈₃	semidirect
650. C₂×C₄⋊C₈	C₂²×C₈₃	semidirect
651. #419	C₂²×C₈₃	semidirect
652. #417	C₂²×C₈₃	semidirect
653. C₂×#103	C₂²×C₈₃	semidirect
654. C₂×#103	C₂²×C₈₃	semidirect
655. C₂×#103	C₂²×C₈₃	semidirect
656. C₂×#102	C₂²×C₈₃	semidirect
658. C₂×C₂²⋊C₈	C₂²×C₈₃	semidirect
659. C₂×#97	C₂²×C₈₃	semidirect
968. C₂³	#137×C₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₈₃×#3505	2
C₈₃×#3501	2
C₈₃×#3346	2
C₈₃×#3344	2
C₈₃×#3320	2
C₈₃×#3316	2
C₈₃×#3314	2
C₈₃×#3312	2
C₈₃×#3270	2
C₈₃×#3266	2
C₈₃×#3248	2
C₈₃×#3190	2
C₈₃×#3189	2
C₈₃×#3187	2
C₈₃×#3181	2
C₈₃×#3056	2
C₂×#467×C₈₃	2
C₂×#465×C₈₃	2
C₂×#435×C₈₃	2
#62254	83

Subgroups — C83×#62254 #35290078

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#62254 #35290078