Subgroups — C₈₃×#61471 #35289295

Order 21248.

1910 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3513	C₂	1	2	yes	maximal, complemented
2	C₈₃×#3396	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₃×#3380	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₃×#3370	C₂	1	2	yes	maximal, complemented
5	C₈₃×#3339	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₃×#3336	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₃×#3334	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₃×#3322	C₂	1	2	yes	maximal, complemented
9	C₈₃×#3310	C₂	1	2	yes	maximal, complemented
10	C₈₃×#3306	C₂	1	2	yes	maximal, complemented
11	C₈₃×#3280	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₃×#3280	C₂	1	1	yes	maximal, characteristic, complemented
13	D₄×D₈×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₃×#3176	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#3175	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₃×#3168	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₃×#3119	C₂	1	2	yes	maximal, complemented
18	C₈₃×#3118	C₂	1	2	yes	maximal, complemented
19	C₈₃×#3114	C₂	1	2	yes	maximal, complemented
20	C₈₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₃×#2951	C₂	1	1	yes	maximal, characteristic, complemented
22	C₈₃×#2948	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×D₈×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#135×C₈₃	C₂²	1	1	yes	characteristic
25	C₂²×D₈×C₈₃	C₂²	1	1	yes	characteristic
26	C₂²×D₈×C₈₃	C₂²	1	1	yes	characteristic
27	#559×C₈₃	C₂²	1	2	yes	complemented
28	#554×C₈₃	C₂²	1	2	yes	complemented
29	#553×C₈₃	—	2	2	no	—
30	#553×C₈₃	C₂²	1	2	yes	complemented
31	#552×C₈₃	C₂²	1	2	yes	—
32	#551×C₈₃	—	2	2	no	—
33	#551×C₈₃	—	2	2	no	—
34	#547×C₈₃	C₂²	1	2	yes	complemented
35	#546×C₈₃	—	2	2	no	—
36	#546×C₈₃	C₂²	1	2	yes	complemented
37	#546×C₈₃	C₂²	1	2	yes	complemented
38	D₄²×C₈₃	C₂²	1	2	yes	—
39	#542×C₈₃	C₂²	1	2	yes	complemented
40	#540×C₈₃	C₂²	1	2	yes	complemented
41	#539×C₈₃	—	2	2	no	—
42	#538×C₈₃	—	2	2	no	—
43	#529×C₈₃	C₂²	1	1	yes	characteristic
44	#529×C₈₃	C₂²	1	2	yes	complemented
45	#525×C₈₃	—	2	2	no	—
46	C₂×#123×C₈₃	—	2	2	no	—
47	#520×C₈₃	C₂²	1	2	yes	complemented
48	#518×C₈₃	C₂²	1	2	yes	complemented
49	C₂×C₄×D₄×C₈₃	C₂²	1	2	yes	complemented
50	#500×C₈₃	C₂²	1	1	yes	characteristic, complemented
51	#499×C₈₃	C₂²	1	1	yes	characteristic, complemented
52	#499×C₈₃	C₂²	1	1	yes	characteristic, complemented
53	#495×C₈₃	C₂²	1	1	yes	characteristic, complemented
54	#495×C₈₃	C₂²	1	1	yes	characteristic, complemented
55	#493×C₈₃	C₂²	1	1	yes	characteristic
56	#490×C₈₃	C₂²	1	2	yes	complemented
57	#489×C₈₃	C₂²	1	2	yes	complemented
58	#488×C₈₃	C₂²	1	2	yes	complemented
59	#485×C₈₃	C₂²	1	2	yes	complemented
60	#483×C₈₃	C₂²	1	2	yes	complemented
61	#482×C₈₃	C₂²	1	2	yes	complemented
62	#481×C₈₃	C₂²	1	2	yes	complemented
63	#480×C₈₃	C₂²	1	2	yes	complemented
64	#480×C₈₃	C₂²	1	2	yes	complemented
65	#479×C₈₃	C₂²	1	2	yes	complemented
66	#478×C₈₃	C₂²	1	2	yes	complemented
67	#478×C₈₃	C₂²	1	2	yes	complemented
68	#478×C₈₃	C₂²	1	2	yes	complemented
69	#476×C₈₃	C₂²	1	2	yes	complemented
70	#474×C₈₃	C₂²	1	2	yes	complemented
71	#469×C₈₃	C₂²	1	2	yes	complemented
72	#468×C₈₃	C₂²	1	2	yes	complemented
73	#467×C₈₃	C₂²	1	1	yes	characteristic, complemented
74	#467×C₈₃	C₂²	1	1	yes	characteristic, complemented
75	#466×C₈₃	C₂²	1	1	yes	characteristic
76	#466×C₈₃	C₂²	1	1	yes	characteristic
77	#466×C₈₃	C₂²	1	1	yes	characteristic, complemented
78	#466×C₈₃	C₂²	1	1	yes	characteristic, complemented
79	#465×C₈₃	C₂²	1	2	yes	complemented
80	#463×C₈₃	C₂²	1	2	yes	complemented
81	#463×C₈₃	C₂²	1	2	yes	complemented
82	#463×C₈₃	C₂²	1	2	yes	complemented
83	#463×C₈₃	C₂²	1	2	yes	complemented
84	#460×C₈₃	C₂²	1	2	yes	complemented
85	#459×C₈₃	C₂²	1	2	yes	—
86	#450×C₈₃	C₂²	1	2	yes	complemented
87	#450×C₈₃	C₂²	1	2	yes	complemented
88	#449×C₈₃	C₂²	1	2	yes	complemented
89	#449×C₈₃	C₂²	1	2	yes	complemented
90	#447×C₈₃	C₂²	1	2	yes	—
91	#447×C₈₃	C₂²	1	2	yes	—
92	#446×C₈₃	C₂²	1	1	yes	characteristic, complemented
93	C₈×Q₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
94	#442×C₈₃	C₂²	1	2	yes	complemented
95	#442×C₈₃	C₂²	1	2	yes	complemented
96	#442×C₈₃	C₂²	1	2	yes	complemented
97	#440×C₈₃	C₂²	1	2	yes	complemented
98	#440×C₈₃	C₂²	1	2	yes	complemented
99	#440×C₈₃	C₂²	1	2	yes	complemented
100	C₄×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic, complemented
101	C₄×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic, complemented
102	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	complemented
103	C₄×D₈×C₈₃	C₂²	1	1	yes	characteristic
104	C₄×D₈×C₈₃	C₂²	1	1	yes	characteristic
105	C₄×D₈×C₈₃	C₂²	1	1	yes	characteristic
106	C₄×D₈×C₈₃	C₂²	1	1	yes	characteristic
107	C₄×D₈×C₈₃	C₂²	1	2	yes	complemented
108	C₄×D₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
109	C₄×D₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
110	C₄×D₈×C₈₃	C₂²	1	2	yes	complemented
111	C₄×D₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
112	C₄×D₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
113	#436×C₈₃	C₂²	1	1	yes	characteristic, complemented
114	#435×C₈₃	C₂²	1	1	yes	characteristic
115	#435×C₈₃	C₂²	1	1	yes	characteristic, complemented
116	C₈×D₄×C₈₃	C₂²	1	1	yes	characteristic
117	C₈×D₄×C₈₃	C₂²	1	1	yes	characteristic, complemented
118	C₈×D₄×C₈₃	C₂²	1	1	yes	characteristic, complemented
119	#433×C₈₃	C₂²	1	1	yes	characteristic, complemented
120	#433×C₈₃	C₂²	1	1	yes	characteristic, complemented
121	#432×C₈₃	C₂²	1	1	yes	characteristic, complemented
122	#427×C₈₃	C₂²	1	1	yes	characteristic, complemented
123	C₂×#107×C₈₃	C₂²	1	1	yes	characteristic, complemented
124	C₂×#107×C₈₃	C₂²	1	1	yes	characteristic, complemented
125	#418×C₈₃	C₂²	1	2	yes	complemented
126	#417×C₈₃	C₂²	1	2	yes	complemented
127	C₂×#102×C₈₃	C₂²	1	2	yes	complemented
128	#405×C₈₃	C₂²	1	1	yes	characteristic, complemented
129	#405×C₈₃	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
131	C₂×#41×C₈₃	—	2	2	no	—
132	C₂×#41×C₈₃	C₂³	1	2	yes	—
133	C₂²×D₄×C₈₃	—	2	2	no	—
134	C₂²×D₄×C₈₃	C₂³	1	2	yes	—
135	C₂²×D₄×C₈₃	C₂³	1	2	yes	—
136	C₂³×C₄×C₈₃	—	2	2	no	—
137	#135×C₈₃	—	2	4	no	—
138	C₂×Q₁₆×C₈₃	C₂³	1	1	yes	characteristic
139	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
140	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
141	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
142	C₂×D₈×C₈₃	—	2	4	no	—
143	C₂×D₈×C₈₃	—	2	4	no	—
144	C₂×D₈×C₈₃	C₂³	1	2	yes	—
145	C₂×D₈×C₈₃	C₂³	1	2	yes	—
146	C₂×D₈×C₈₃	C₂³	1	1	yes	characteristic
147	C₂×D₈×C₈₃	C₂³	1	1	yes	characteristic
148	C₂×D₈×C₈₃	C₂³	1	2	yes	—
149	C₂×D₈×C₈₃	C₂³	1	1	yes	characteristic
150	C₂×M₁₆×C₈₃	C₂³	1	1	yes	characteristic
151	C₂×M₁₆×C₈₃	C₂³	1	1	yes	characteristic
152	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
153	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
154	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
155	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
156	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
157	#127×C₈₃	C₂³	1	2	yes	—
158	#126×C₈₃	—	2	2	no	—
159	#126×C₈₃	—	2	2	no	—
160	#126×C₈₃	—	2	2	no	—
161	#126×C₈₃	—	2	2	no	—
162	#126×C₈₃	D₄	1	1	yes	characteristic
163	#126×C₈₃	D₄	1	1	yes	characteristic
164	#125×C₈₃	—	2	2	no	—
165	#125×C₈₃	D₄	1	1	yes	characteristic
166	#125×C₈₃	C₂³	1	2	yes	—
167	#125×C₈₃	C₂³	1	2	yes	—
168	#124×C₈₃	—	2	2	no	—
169	#124×C₈₃	—	2	2	no	—
170	#124×C₈₃	D₄	1	1	yes	characteristic
171	#124×C₈₃	C₂³	1	2	yes	—
172	#124×C₈₃	C₂³	1	2	yes	—
173	#123×C₈₃	—	2	2	no	—
174	#123×C₈₃	—	2	2	no	—
175	#123×C₈₃	—	2	2	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	#123×C₈₃	—	2	2	no	—
185	#123×C₈₃	D₄	1	1	yes	characteristic
186	#123×C₈₃	D₄	1	1	yes	characteristic
187	C₂²⋊Q₈×C₈₃	—	2	2	no	—
188	C₂²⋊Q₈×C₈₃	—	2	2	no	—
189	C₂²⋊Q₈×C₈₃	—	2	2	no	—
190	C₂²⋊Q₈×C₈₃	—	2	2	no	—
191	C₂²⋊Q₈×C₈₃	—	2	2	no	—
192	C₂²⋊Q₈×C₈₃	D₄	1	1	yes	characteristic
193	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
194	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
195	#121×C₈₃	—	2	2	no	—
196	#121×C₈₃	—	2	2	no	—
197	#121×C₈₃	—	2	2	no	—
198	#121×C₈₃	—	2	2	no	—
199	#121×C₈₃	—	2	2	no	—
200	#121×C₈₃	—	2	2	no	—
201	#121×C₈₃	D₄	1	1	yes	characteristic
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	#120×C₈₃	—	2	2	no	—
207	#120×C₈₃	—	2	2	no	—
208	#120×C₈₃	—	2	2	no	—
209	#120×C₈₃	—	2	2	no	—
210	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
211	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
212	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
222	C₄×D₄×C₈₃	C₂³	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	C₄×D₄×C₈₃	C₂³	1	2	yes	—
227	C₄×D₄×C₈₃	C₂³	1	2	yes	—
228	C₄×D₄×C₈₃	C₂³	1	2	yes	—
229	C₄×D₄×C₈₃	C₂³	1	2	yes	—
230	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
231	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
232	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
233	#117×C₈₃	—	2	2	no	—
234	#117×C₈₃	—	2	2	no	—
235	#117×C₈₃	—	2	2	no	—
236	#117×C₈₃	C₂³	1	2	yes	—
237	#117×C₈₃	C₂³	1	1	yes	characteristic
238	#117×C₈₃	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
240	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
241	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
242	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
243	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
244	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
245	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
246	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
247	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
248	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
249	#107×C₈₃	C₂³	1	1	yes	characteristic
250	#107×C₈₃	C₂³	1	1	yes	characteristic
251	#107×C₈₃	C₂³	1	1	yes	characteristic
252	#107×C₈₃	C₂³	1	2	yes	—
253	#107×C₈₃	C₂³	1	2	yes	—
254	#107×C₈₃	C₂³	1	2	yes	—
255	#107×C₈₃	C₂³	1	1	yes	characteristic
256	#106×C₈₃	C₂³	1	2	yes	—
257	#106×C₈₃	C₂³	1	2	yes	—
258	#106×C₈₃	C₂³	1	2	yes	—
259	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
260	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
261	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
262	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
263	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
264	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
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	#102×C₈₃	C₂³	1	2	yes	—
270	#102×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	#102×C₈₃	C₂³	1	2	yes	—
276	#102×C₈₃	C₂³	1	2	yes	—
277	#102×C₈₃	C₂³	1	2	yes	—
278	#102×C₈₃	C₂³	1	2	yes	—
279	#102×C₈₃	C₂³	1	2	yes	—
280	#102×C₈₃	C₂³	1	2	yes	—
281	C₂²⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
282	C₂²⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
283	C₂²⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
284	C₂²⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
285	C₂²⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
286	C₂²⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
287	#97×C₈₃	C₂³	1	1	yes	characteristic
288	#97×C₈₃	C₂³	1	1	yes	characteristic
289	#97×C₈₃	C₂³	1	1	yes	characteristic
290	#97×C₈₃	C₂³	1	1	yes	characteristic
291	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
292	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
293	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
294	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
295	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
296	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
297	C₂⁴×C₈₃	—	2	2	no	—
298	C₂⁴×C₈₃	—	2	2	no	—
299	#41×C₈₃	—	2	4	no	—
300	#41×C₈₃	—	4	2	no	—
301	#41×C₈₃	—	8	4	no	—
302	C₂×Q₈×C₈₃	—	2	2	no	—
303	C₂×Q₈×C₈₃	C₂×D₄	1	1	yes	characteristic
304	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
305	C₂×D₄×C₈₃	—	2	4	no	—
306	C₂×D₄×C₈₃	—	2	4	no	—
307	C₂×D₄×C₈₃	—	2	2	no	—
308	C₂×D₄×C₈₃	—	2	2	no	—
309	C₂×D₄×C₈₃	—	2	2	no	—
310	C₂×D₄×C₈₃	—	2	2	no	—
311	C₂×D₄×C₈₃	—	2	2	no	—
312	C₂×D₄×C₈₃	—	2	2	no	—
313	C₂×D₄×C₈₃	—	2	2	no	—
314	C₂×D₄×C₈₃	—	2	2	no	—
315	C₂×D₄×C₈₃	—	2	2	no	—
316	C₂×D₄×C₈₃	—	4	2	no	—
317	C₂×D₄×C₈₃	—	4	2	no	—
318	C₂×D₄×C₈₃	—	8	4	no	—
319	C₂×D₄×C₈₃	C₂×D₄	1	1	yes	characteristic
320	C₂×D₄×C₈₃	C₂×D₄	1	1	yes	characteristic
321	C₂×D₄×C₈₃	C₂×D₄	1	1	yes	characteristic
322	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
323	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
324	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
325	C₂²×C₄×C₈₃	—	2	2	no	—
326	C₂²×C₄×C₈₃	—	2	2	no	—
327	C₂²×C₄×C₈₃	—	2	2	no	—
328	C₂²×C₄×C₈₃	—	2	2	no	—
329	C₂²×C₄×C₈₃	—	2	2	no	—
330	C₂²×C₄×C₈₃	—	2	2	no	—
331	C₂²×C₄×C₈₃	—	2	2	no	—
332	C₂²×C₄×C₈₃	—	2	2	no	—
333	C₂²×C₄×C₈₃	—	2	2	no	—
334	C₂²×C₄×C₈₃	—	2	2	no	—
335	C₂²×C₄×C₈₃	—	2	2	no	—
336	C₂²×C₄×C₈₃	—	8	4	no	—
337	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
338	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
339	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
342	Q₁₆×C₈₃	—	2	2	no	—
343	SD₁₆×C₈₃	—	2	4	no	—
344	SD₁₆×C₈₃	—	4	2	no	—
345	SD₁₆×C₈₃	—	4	2	no	—
346	D₈×C₈₃	—	2	4	no	—
347	D₈×C₈₃	—	2	4	no	—
348	D₈×C₈₃	—	2	2	no	—
349	D₈×C₈₃	—	2	2	no	—
350	D₈×C₈₃	—	4	2	no	—
351	D₈×C₈₃	#41	1	4	yes	complemented
352	M₁₆×C₈₃	—	4	1	no	—
353	M₁₆×C₈₃	—	4	1	no	—
354	C₂×C₈×C₈₃	—	2	2	no	—
355	C₂×C₈×C₈₃	—	2	2	no	—
356	C₂×C₈×C₈₃	—	2	2	no	—
357	C₂×C₈×C₈₃	—	4	1	no	—
358	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
359	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
362	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
363	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
365	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
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	2	no	—
373	C₄⋊C₄×C₈₃	—	2	2	no	—
374	C₄⋊C₄×C₈₃	—	2	2	no	—
375	C₄⋊C₄×C₈₃	—	2	2	no	—
376	C₄⋊C₄×C₈₃	—	2	2	no	—
377	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
378	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
379	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
380	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
381	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
382	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
383	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
384	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
385	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
386	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
387	C₄⋊C₄×C₈₃	C₂⁴	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	C₂²⋊C₄×C₈₃	—	2	2	no	—
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	—	2	2	no	—
409	C₂²⋊C₄×C₈₃	—	2	2	no	—
410	C₂²⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
411	C₂²⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
412	C₂²⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
413	C₂²⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
414	C₂²⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
415	C₂²⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
416	C₂²⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
417	C₂²⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
418	C₂²⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
419	C₂²⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
420	C₄²×C₈₃	—	2	2	no	—
421	C₄²×C₈₃	—	2	2	no	—
422	C₄²×C₈₃	—	2	2	no	—
423	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
424	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
425	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
426	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
427	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
428	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
429	C₂³×C₈₃	—	2	2	no	—
430	C₂³×C₈₃	—	2	2	no	—
431	C₂³×C₈₃	—	2	2	no	—
432	C₂³×C₈₃	—	4	4	no	—
433	C₂³×C₈₃	—	4	4	no	—
434	C₂³×C₈₃	—	4	4	no	—
435	C₂³×C₈₃	—	8	2	no	—
436	C₂³×C₈₃	—	8	2	no	—
437	C₂³×C₈₃	—	8	2	no	—
438	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
439	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
440	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
441	Q₈×C₈₃	—	2	2	no	—
442	Q₈×C₈₃	—	2	2	no	—
443	Q₈×C₈₃	—	4	1	no	—
444	Q₈×C₈₃	—	8	2	no	—
445	D₄×C₈₃	—	2	2	no	—
446	D₄×C₈₃	—	2	2	no	—
447	D₄×C₈₃	—	2	2	no	—
448	D₄×C₈₃	—	2	2	no	—
449	D₄×C₈₃	—	2	2	no	—
450	D₄×C₈₃	—	2	2	no	—
451	D₄×C₈₃	—	2	2	no	—
452	D₄×C₈₃	—	4	1	no	—
453	D₄×C₈₃	—	4	4	no	—
454	D₄×C₈₃	—	4	4	no	—
455	D₄×C₈₃	—	4	4	no	—
456	D₄×C₈₃	—	4	4	no	—
457	D₄×C₈₃	—	8	2	no	—
458	D₄×C₈₃	—	8	2	no	—
459	D₄×C₈₃	—	8	2	no	—
460	D₄×C₈₃	—	8	2	no	—
461	D₄×C₈₃	—	8	2	no	—
462	D₄×C₈₃	C₂×#41	1	4	yes	—
463	C₂×C₄×C₈₃	—	2	2	no	—
464	C₂×C₄×C₈₃	—	2	1	no	—
465	C₂×C₄×C₈₃	—	2	1	no	—
466	C₂×C₄×C₈₃	—	2	1	no	—
467	C₂×C₄×C₈₃	—	2	1	no	—
468	C₂×C₄×C₈₃	—	2	1	no	—
469	C₂×C₄×C₈₃	—	2	1	no	—
470	C₂×C₄×C₈₃	—	2	2	no	—
471	C₂×C₄×C₈₃	—	2	2	no	—
472	C₂×C₄×C₈₃	—	2	2	no	—
473	C₂×C₄×C₈₃	—	2	2	no	—
474	C₂×C₄×C₈₃	—	2	2	no	—
475	C₂×C₄×C₈₃	—	4	1	no	—
476	C₂×C₄×C₈₃	—	4	4	no	—
477	C₂×C₄×C₈₃	—	4	4	no	—
478	C₂×C₄×C₈₃	—	8	2	no	—
479	C₂×C₄×C₈₃	—	8	2	no	—
480	C₂×C₄×C₈₃	—	8	2	no	—
481	C₂×C₄×C₈₃	—	8	2	no	—
482	C₂×C₄×C₈₃	—	8	2	no	—
483	C₂×C₄×C₈₃	—	8	2	no	—
484	C₂×C₄×C₈₃	—	8	2	no	—
485	C₂×C₄×C₈₃	—	8	2	no	—
486	C₂×C₄×C₈₃	—	8	2	no	—
487	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
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	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
499	C₈×C₈₃	—	2	1	no	—
500	C₈×C₈₃	—	2	1	no	—
501	C₈×C₈₃	—	2	1	no	—
502	C₈×C₈₃	—	2	1	no	—
503	C₈×C₈₃	—	2	1	no	—
504	C₈×C₈₃	—	2	1	no	—
505	C₈×C₈₃	—	2	1	no	—
506	C₈×C₈₃	C₂×#41	1	2	yes	—
507	C₂²×C₈₃	—	2	1	no	—
508	C₂²×C₈₃	—	2	1	no	—
509	C₂²×C₈₃	—	2	1	no	—
510	C₂²×C₈₃	—	2	1	no	—
511	C₂²×C₈₃	—	2	1	no	—
512	C₂²×C₈₃	—	2	1	no	—
513	C₂²×C₈₃	—	2	4	no	—
514	C₂²×C₈₃	—	2	1	no	—
515	C₂²×C₈₃	—	2	1	no	—
516	C₂²×C₈₃	—	4	2	no	—
517	C₂²×C₈₃	—	4	2	no	—
518	C₂²×C₈₃	—	4	2	no	—
519	C₂²×C₈₃	—	4	2	no	—
520	C₂²×C₈₃	—	4	2	no	—
521	C₂²×C₈₃	—	4	2	no	—
522	C₂²×C₈₃	—	4	2	no	—
523	C₂²×C₈₃	—	4	2	no	—
524	C₂²×C₈₃	—	8	8	no	—
525	C₂²×C₈₃	—	16	4	no	—
526	C₂²×C₈₃	#576	1	2	yes	—
527	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
528	C₄×C₈₃	—	2	1	no	—
529	C₄×C₈₃	—	2	1	no	—
530	C₄×C₈₃	—	2	1	no	—
531	C₄×C₈₃	—	2	1	no	—
532	C₄×C₈₃	—	2	1	no	—
533	C₄×C₈₃	—	2	1	no	—
534	C₄×C₈₃	—	2	1	no	—
535	C₄×C₈₃	—	2	1	no	—
536	C₄×C₈₃	—	2	1	no	—
537	C₄×C₈₃	—	2	1	no	—
538	C₄×C₈₃	—	2	1	no	—
539	C₄×C₈₃	—	4	2	no	—
540	C₄×C₈₃	—	4	2	no	—
541	C₄×C₈₃	—	4	2	no	—
542	C₄×C₈₃	—	4	2	no	—
543	C₄×C₈₃	—	4	2	no	—
544	C₄×C₈₃	C₂²×#41	1	1	yes	characteristic
545	C₄×C₈₃	#585	1	1	yes	characteristic
546	#61471	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
547	C₂×C₈₃	—	2	2	no	—
548	C₂×C₈₃	—	4	1	no	—
549	C₂×C₈₃	—	4	1	no	—
550	C₂×C₈₃	—	4	4	no	—
551	C₂×C₈₃	—	8	2	no	—
552	C₂×C₈₃	—	8	2	no	—
553	C₂×C₈₃	D₄×#41	1	1	yes	characteristic
554	C₂×C₈₃	C₂×#576	1	1	yes	characteristic
555	C₂×C₈₃	#3584	1	1	yes	characteristic
556	#3513	C₂×C₈₃	1	2	yes	complemented
557	#3396	C₂×C₈₃	1	1	yes	characteristic, complemented
558	#3380	C₂×C₈₃	1	1	yes	characteristic, complemented
559	#3370	C₂×C₈₃	1	2	yes	complemented
560	#3339	C₂×C₈₃	1	1	yes	characteristic, complemented
561	#3336	C₂×C₈₃	1	1	yes	characteristic, complemented
562	#3334	C₂×C₈₃	1	1	yes	characteristic, complemented
563	#3322	C₂×C₈₃	1	2	yes	complemented
564	#3310	C₂×C₈₃	1	2	yes	complemented
565	#3306	C₂×C₈₃	1	2	yes	complemented
566	#3280	C₂×C₈₃	1	1	yes	characteristic, complemented
567	#3280	C₂×C₈₃	1	1	yes	characteristic, complemented
568	D₄×D₈	C₂×C₈₃	1	1	yes	characteristic, complemented
569	#3176	C₂×C₈₃	1	1	yes	characteristic, complemented
570	#3175	C₂×C₈₃	1	1	yes	characteristic, complemented
571	#3168	C₂×C₈₃	1	1	yes	characteristic, complemented
572	#3119	C₂×C₈₃	1	2	yes	complemented
573	#3118	C₂×C₈₃	1	2	yes	complemented
574	#3114	C₂×C₈₃	1	2	yes	complemented
575	#2966	C₂×C₈₃	1	1	yes	characteristic, complemented
576	#2951	C₂×C₈₃	1	1	yes	characteristic, complemented
577	#2948	C₂×C₈₃	1	1	yes	characteristic, complemented
578	C₂×C₄×D₈	C₂×C₈₃	1	1	yes	characteristic, complemented
579	C₈₃	#61471	1	1	yes	characteristic, direct product factor, Sylow
580	C₂×#135	C₂²×C₈₃	1	1	yes	characteristic
581	C₂²×D₈	C₂²×C₈₃	1	1	yes	characteristic
582	C₂²×D₈	C₂²×C₈₃	1	1	yes	characteristic
583	#559	C₂²×C₈₃	1	2	yes	complemented
584	#554	C₂²×C₈₃	1	2	yes	complemented
585	#553	—	2	2	no	—
586	#553	C₂²×C₈₃	1	2	yes	complemented
587	#552	C₂²×C₈₃	1	2	yes	—
588	#551	—	2	2	no	—
589	#551	—	2	2	no	—
590	#547	C₂²×C₈₃	1	2	yes	complemented
591	#546	—	2	2	no	—
592	#546	C₂²×C₈₃	1	2	yes	complemented
593	#546	C₂²×C₈₃	1	2	yes	complemented
594	D₄²	C₂²×C₈₃	1	2	yes	—
595	#542	C₂²×C₈₃	1	2	yes	complemented
596	#540	C₂²×C₈₃	1	2	yes	complemented
597	#539	—	2	2	no	—
598	#538	—	2	2	no	—
599	#529	C₂²×C₈₃	1	1	yes	characteristic
600	#529	C₂²×C₈₃	1	2	yes	complemented
601	#525	—	2	2	no	—
602	C₂×#123	—	2	2	no	—
603	#520	C₂²×C₈₃	1	2	yes	complemented
604	#518	C₂²×C₈₃	1	2	yes	complemented
605	C₂×C₄×D₄	C₂²×C₈₃	1	2	yes	complemented
606	#500	C₂²×C₈₃	1	1	yes	characteristic, complemented
607	#499	C₂²×C₈₃	1	1	yes	characteristic, complemented
608	#499	C₂²×C₈₃	1	1	yes	characteristic, complemented
609	#495	C₂²×C₈₃	1	1	yes	characteristic, complemented
610	#495	C₂²×C₈₃	1	1	yes	characteristic, complemented
611	#493	C₂²×C₈₃	1	1	yes	characteristic
612	#490	C₂²×C₈₃	1	2	yes	complemented
613	#489	C₂²×C₈₃	1	2	yes	complemented
614	#488	C₂²×C₈₃	1	2	yes	complemented
615	#485	C₂²×C₈₃	1	2	yes	complemented
616	#483	C₂²×C₈₃	1	2	yes	complemented
617	#482	C₂²×C₈₃	1	2	yes	complemented
618	#481	C₂²×C₈₃	1	2	yes	complemented
619	#480	C₂²×C₈₃	1	2	yes	complemented
620	#480	C₂²×C₈₃	1	2	yes	complemented
621	#479	C₂²×C₈₃	1	2	yes	complemented
622	#478	C₂²×C₈₃	1	2	yes	complemented
623	#478	C₂²×C₈₃	1	2	yes	complemented
624	#478	C₂²×C₈₃	1	2	yes	complemented
625	#476	C₂²×C₈₃	1	2	yes	complemented
626	#474	C₂²×C₈₃	1	2	yes	complemented
627	#469	C₂²×C₈₃	1	2	yes	complemented
628	#468	C₂²×C₈₃	1	2	yes	complemented
629	#467	C₂²×C₈₃	1	1	yes	characteristic, complemented
630	#467	C₂²×C₈₃	1	1	yes	characteristic, complemented
631	#466	C₂²×C₈₃	1	1	yes	characteristic
632	#466	C₂²×C₈₃	1	1	yes	characteristic
633	#466	C₂²×C₈₃	1	1	yes	characteristic, complemented
634	#466	C₂²×C₈₃	1	1	yes	characteristic, complemented
635	#465	C₂²×C₈₃	1	2	yes	complemented
636	#463	C₂²×C₈₃	1	2	yes	complemented
637	#463	C₂²×C₈₃	1	2	yes	complemented
638	#463	C₂²×C₈₃	1	2	yes	complemented
639	#463	C₂²×C₈₃	1	2	yes	complemented
640	#460	C₂²×C₈₃	1	2	yes	complemented
641	#459	C₂²×C₈₃	1	2	yes	—
642	#450	C₂²×C₈₃	1	2	yes	complemented
643	#450	C₂²×C₈₃	1	2	yes	complemented
644	#449	C₂²×C₈₃	1	2	yes	complemented
645	#449	C₂²×C₈₃	1	2	yes	complemented
646	#447	C₂²×C₈₃	1	2	yes	—
647	#447	C₂²×C₈₃	1	2	yes	—
648	#446	C₂²×C₈₃	1	1	yes	characteristic, complemented
649	C₈×Q₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
650	#442	C₂²×C₈₃	1	2	yes	complemented
651	#442	C₂²×C₈₃	1	2	yes	complemented
652	#442	C₂²×C₈₃	1	2	yes	complemented
653	#440	C₂²×C₈₃	1	2	yes	complemented
654	#440	C₂²×C₈₃	1	2	yes	complemented
655	#440	C₂²×C₈₃	1	2	yes	complemented
656	C₄×Q₁₆	C₂²×C₈₃	1	1	yes	characteristic, complemented
657	C₄×Q₁₆	C₂²×C₈₃	1	1	yes	characteristic, complemented
658	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	complemented
659	C₄×D₈	C₂²×C₈₃	1	1	yes	characteristic
660	C₄×D₈	C₂²×C₈₃	1	1	yes	characteristic
661	C₄×D₈	C₂²×C₈₃	1	1	yes	characteristic
662	C₄×D₈	C₂²×C₈₃	1	1	yes	characteristic
663	C₄×D₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
664	C₄×D₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
665	C₄×D₈	C₂²×C₈₃	1	2	yes	complemented
666	C₄×D₈	C₂²×C₈₃	1	2	yes	complemented
667	C₄×D₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
668	C₄×D₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
669	#436	C₂²×C₈₃	1	1	yes	characteristic, complemented
670	#435	C₂²×C₈₃	1	1	yes	characteristic
671	#435	C₂²×C₈₃	1	1	yes	characteristic, complemented
672	C₈×D₄	C₂²×C₈₃	1	1	yes	characteristic
673	C₈×D₄	C₂²×C₈₃	1	1	yes	characteristic, complemented
674	C₈×D₄	C₂²×C₈₃	1	1	yes	characteristic, complemented
675	#433	C₂²×C₈₃	1	1	yes	characteristic, complemented
676	#433	C₂²×C₈₃	1	1	yes	characteristic, complemented
677	#432	C₂²×C₈₃	1	1	yes	characteristic, complemented
678	#427	C₂²×C₈₃	1	1	yes	characteristic, complemented
679	C₂×#107	C₂²×C₈₃	1	1	yes	characteristic, complemented
680	C₂×#107	C₂²×C₈₃	1	1	yes	characteristic, complemented
681	#418	C₂²×C₈₃	1	2	yes	complemented
682	#417	C₂²×C₈₃	1	2	yes	complemented
683	C₂×#102	C₂²×C₈₃	1	2	yes	complemented
684	#405	C₂²×C₈₃	1	1	yes	characteristic, complemented
685	#405	C₂²×C₈₃	1	1	yes	characteristic, complemented
686	C₂×C₄×C₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
687	C₂×#41	—	2	2	no	—
688	C₂×#41	C₂³×C₈₃	1	2	yes	—
689	C₂²×D₄	—	2	2	no	—
690	C₂²×D₄	C₂³×C₈₃	1	2	yes	—
691	C₂²×D₄	C₂³×C₈₃	1	2	yes	—
692	C₂³×C₄	—	2	2	no	—
693	#135	—	2	4	no	—
694	C₂×Q₁₆	C₂³×C₈₃	1	1	yes	characteristic
695	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
696	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
697	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
698	C₂×D₈	—	2	4	no	—
699	C₂×D₈	—	2	4	no	—
700	C₂×D₈	C₂³×C₈₃	1	2	yes	—
701	C₂×D₈	C₂³×C₈₃	1	1	yes	characteristic
702	C₂×D₈	C₂³×C₈₃	1	1	yes	characteristic
703	C₂×D₈	C₂³×C₈₃	1	2	yes	—
704	C₂×D₈	C₂³×C₈₃	1	2	yes	—
705	C₂×D₈	C₂³×C₈₃	1	1	yes	characteristic
706	C₂×M₁₆	C₂³×C₈₃	1	1	yes	characteristic
707	C₂×M₁₆	C₂³×C₈₃	1	1	yes	characteristic
708	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
709	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
710	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
711	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
712	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
713	#127	C₂³×C₈₃	1	2	yes	—
714	#126	—	2	2	no	—
715	#126	—	2	2	no	—
716	#126	—	2	2	no	—
717	#126	—	2	2	no	—
718	#126	D₄×C₈₃	1	1	yes	characteristic
719	#126	D₄×C₈₃	1	1	yes	characteristic
720	#125	—	2	2	no	—
721	#125	D₄×C₈₃	1	1	yes	characteristic
722	#125	C₂³×C₈₃	1	2	yes	—
723	#125	C₂³×C₈₃	1	2	yes	—
724	#124	—	2	2	no	—
725	#124	—	2	2	no	—
726	#124	D₄×C₈₃	1	1	yes	characteristic
727	#124	C₂³×C₈₃	1	2	yes	—
728	#124	C₂³×C₈₃	1	2	yes	—
729	#123	—	2	2	no	—
730	#123	—	2	2	no	—
731	#123	—	2	2	no	—
732	#123	—	2	2	no	—
733	#123	—	2	2	no	—
734	#123	—	2	2	no	—
735	#123	—	2	2	no	—
736	#123	—	2	2	no	—
737	#123	—	2	2	no	—
738	#123	—	2	2	no	—
739	#123	—	2	2	no	—
740	#123	—	2	2	no	—
741	#123	D₄×C₈₃	1	1	yes	characteristic
742	#123	D₄×C₈₃	1	1	yes	characteristic
743	C₂²⋊Q₈	—	2	2	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	—	2	2	no	—
746	C₂²⋊Q₈	—	2	2	no	—
747	C₂²⋊Q₈	—	2	2	no	—
748	C₂²⋊Q₈	D₄×C₈₃	1	1	yes	characteristic
749	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
750	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
751	#121	—	2	2	no	—
752	#121	—	2	2	no	—
753	#121	—	2	2	no	—
754	#121	—	2	2	no	—
755	#121	—	2	2	no	—
756	#121	—	2	2	no	—
757	#121	D₄×C₈₃	1	1	yes	characteristic
758	#121	C₂³×C₈₃	1	2	yes	—
759	#121	C₂³×C₈₃	1	2	yes	—
760	#121	C₂³×C₈₃	1	2	yes	—
761	#121	C₂³×C₈₃	1	2	yes	—
762	#120	—	2	2	no	—
763	#120	—	2	2	no	—
764	#120	—	2	2	no	—
765	#120	—	2	2	no	—
766	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
767	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
768	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
769	C₄×D₄	—	2	2	no	—
770	C₄×D₄	—	2	2	no	—
771	C₄×D₄	—	2	2	no	—
772	C₄×D₄	—	2	2	no	—
773	C₄×D₄	—	2	2	no	—
774	C₄×D₄	—	2	2	no	—
775	C₄×D₄	—	2	2	no	—
776	C₄×D₄	—	2	2	no	—
777	C₄×D₄	—	2	2	no	—
778	C₄×D₄	C₂³×C₈₃	1	2	yes	—
779	C₄×D₄	C₂³×C₈₃	1	2	yes	—
780	C₄×D₄	C₂³×C₈₃	1	2	yes	—
781	C₄×D₄	C₂³×C₈₃	1	2	yes	—
782	C₄×D₄	C₂³×C₈₃	1	2	yes	—
783	C₄×D₄	C₂³×C₈₃	1	2	yes	—
784	C₄×D₄	C₂³×C₈₃	1	2	yes	—
785	C₄×D₄	C₂³×C₈₃	1	2	yes	—
786	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
787	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
788	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
789	#117	—	2	2	no	—
790	#117	—	2	2	no	—
791	#117	—	2	2	no	—
792	#117	C₂³×C₈₃	1	2	yes	—
793	#117	C₂³×C₈₃	1	1	yes	characteristic
794	#117	C₂³×C₈₃	1	1	yes	characteristic
795	C₂×C₄⋊C₄	—	2	2	no	—
796	C₂×C₄⋊C₄	—	2	2	no	—
797	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
798	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
799	C₂×C₂²⋊C₄	—	2	2	no	—
800	C₂×C₂²⋊C₄	—	2	2	no	—
801	C₂×C₂²⋊C₄	—	2	2	no	—
802	C₂×C₂²⋊C₄	—	2	2	no	—
803	C₂×C₂²⋊C₄	—	2	2	no	—
804	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
805	#107	C₂³×C₈₃	1	1	yes	characteristic
806	#107	C₂³×C₈₃	1	1	yes	characteristic
807	#107	C₂³×C₈₃	1	1	yes	characteristic
808	#107	C₂³×C₈₃	1	2	yes	—
809	#107	C₂³×C₈₃	1	2	yes	—
810	#107	C₂³×C₈₃	1	1	yes	characteristic
811	#107	C₂³×C₈₃	1	2	yes	—
812	#106	C₂³×C₈₃	1	2	yes	—
813	#106	C₂³×C₈₃	1	2	yes	—
814	#106	C₂³×C₈₃	1	2	yes	—
815	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
816	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
817	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
818	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
819	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
820	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
821	#103	C₂³×C₈₃	1	2	yes	—
822	#103	C₂³×C₈₃	1	2	yes	—
823	#103	C₂³×C₈₃	1	2	yes	—
824	#103	C₂³×C₈₃	1	2	yes	—
825	#102	C₂³×C₈₃	1	2	yes	—
826	#102	C₂³×C₈₃	1	2	yes	—
827	#102	C₂³×C₈₃	1	2	yes	—
828	#102	C₂³×C₈₃	1	2	yes	—
829	#102	C₂³×C₈₃	1	2	yes	—
830	#102	C₂³×C₈₃	1	2	yes	—
831	#102	C₂³×C₈₃	1	2	yes	—
832	#102	C₂³×C₈₃	1	2	yes	—
833	#102	C₂³×C₈₃	1	2	yes	—
834	#102	C₂³×C₈₃	1	2	yes	—
835	#102	C₂³×C₈₃	1	2	yes	—
836	#102	C₂³×C₈₃	1	2	yes	—
837	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
838	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
839	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
840	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
841	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
842	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
843	#97	C₂³×C₈₃	1	1	yes	characteristic
844	#97	C₂³×C₈₃	1	1	yes	characteristic
845	#97	C₂³×C₈₃	1	1	yes	characteristic
846	#97	C₂³×C₈₃	1	1	yes	characteristic
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	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
852	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
853	C₂⁴	—	2	2	no	—
854	C₂⁴	—	2	2	no	—
855	#41	—	2	4	no	—
856	#41	—	4	2	no	—
857	#41	—	8	4	no	—
858	C₂×Q₈	—	2	2	no	—
859	C₂×Q₈	C₂×D₄×C₈₃	1	1	yes	characteristic
860	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
861	C₂×D₄	—	2	4	no	—
862	C₂×D₄	—	2	4	no	—
863	C₂×D₄	—	2	2	no	—
864	C₂×D₄	—	2	2	no	—
865	C₂×D₄	—	2	2	no	—
866	C₂×D₄	—	2	2	no	—
867	C₂×D₄	—	2	2	no	—
868	C₂×D₄	—	2	2	no	—
869	C₂×D₄	—	2	2	no	—
870	C₂×D₄	—	2	2	no	—
871	C₂×D₄	—	2	2	no	—
872	C₂×D₄	—	4	2	no	—
873	C₂×D₄	—	4	2	no	—
874	C₂×D₄	—	8	4	no	—
875	C₂×D₄	C₂×D₄×C₈₃	1	1	yes	characteristic
876	C₂×D₄	C₂×D₄×C₈₃	1	1	yes	characteristic
877	C₂×D₄	C₂×D₄×C₈₃	1	1	yes	characteristic
878	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
879	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
880	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
881	C₂²×C₄	—	2	2	no	—
882	C₂²×C₄	—	2	2	no	—
883	C₂²×C₄	—	2	2	no	—
884	C₂²×C₄	—	2	2	no	—
885	C₂²×C₄	—	2	2	no	—
886	C₂²×C₄	—	2	2	no	—
887	C₂²×C₄	—	2	2	no	—
888	C₂²×C₄	—	2	2	no	—
889	C₂²×C₄	—	2	2	no	—
890	C₂²×C₄	—	2	2	no	—
891	C₂²×C₄	—	2	2	no	—
892	C₂²×C₄	—	8	4	no	—
893	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
894	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
895	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
896	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
897	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
898	Q₁₆	—	2	2	no	—
899	SD₁₆	—	2	4	no	—
900	SD₁₆	—	4	2	no	—
901	SD₁₆	—	4	2	no	—
902	D₈	—	2	4	no	—
903	D₈	—	2	4	no	—
904	D₈	—	2	2	no	—
905	D₈	—	2	2	no	—
906	D₈	—	4	2	no	—
907	D₈	#41×C₈₃	1	4	yes	complemented
908	M₁₆	—	4	1	no	—
909	M₁₆	—	4	1	no	—
910	C₂×C₈	—	2	2	no	—
911	C₂×C₈	—	2	2	no	—
912	C₂×C₈	—	2	2	no	—
913	C₂×C₈	—	4	1	no	—
914	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
915	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
916	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
917	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
918	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
919	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
920	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
921	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
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	—	2	2	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
934	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
935	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
936	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
937	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
938	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
939	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
940	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
941	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
942	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
943	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
944	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
945	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
946	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
947	C₂²⋊C₄	—	2	2	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	2	2	no	—
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	—	2	2	no	—
952	C₂²⋊C₄	—	2	2	no	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₂²⋊C₄	—	2	2	no	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
967	C₂²⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
968	C₂²⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
969	C₂²⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
970	C₂²⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
971	C₂²⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
972	C₂²⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
973	C₂²⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
974	C₂²⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
975	C₂²⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
976	C₄²	—	2	2	no	—
977	C₄²	—	2	2	no	—
978	C₄²	—	2	2	no	—
979	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
980	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
981	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
982	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
983	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
984	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
985	C₂³	—	2	2	no	—
986	C₂³	—	2	2	no	—
987	C₂³	—	2	2	no	—
988	C₂³	—	4	4	no	—
989	C₂³	—	4	4	no	—
990	C₂³	—	4	4	no	—
991	C₂³	—	8	2	no	—
992	C₂³	—	8	2	no	—
993	C₂³	—	8	2	no	—
994	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
995	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
996	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
997	Q₈	—	2	2	no	—
998	Q₈	—	2	2	no	—
999	Q₈	—	4	1	no	—
1000	Q₈	—	8	2	no	—
1001	D₄	—	2	2	no	—
1002	D₄	—	2	2	no	—
1003	D₄	—	2	2	no	—
1004	D₄	—	2	2	no	—
1005	D₄	—	2	2	no	—
1006	D₄	—	2	2	no	—
1007	D₄	—	2	2	no	—
1008	D₄	—	4	1	no	—
1009	D₄	—	4	4	no	—
1010	D₄	—	4	4	no	—
1011	D₄	—	4	4	no	—
1012	D₄	—	4	4	no	—
1013	D₄	—	8	2	no	—
1014	D₄	—	8	2	no	—
1015	D₄	—	8	2	no	—
1016	D₄	—	8	2	no	—
1017	D₄	—	8	2	no	—
1018	D₄	C₂×#41×C₈₃	1	4	yes	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	4	1	no	—
1032	C₂×C₄	—	4	4	no	—
1033	C₂×C₄	—	4	4	no	—
1034	C₂×C₄	—	8	2	no	—
1035	C₂×C₄	—	8	2	no	—
1036	C₂×C₄	—	8	2	no	—
1037	C₂×C₄	—	8	2	no	—
1038	C₂×C₄	—	8	2	no	—
1039	C₂×C₄	—	8	2	no	—
1040	C₂×C₄	—	8	2	no	—
1041	C₂×C₄	—	8	2	no	—
1042	C₂×C₄	—	8	2	no	—
1043	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1044	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1045	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1046	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1047	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1048	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1049	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1050	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1051	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1052	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1053	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1054	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
1055	C₈	—	2	1	no	—
1056	C₈	—	2	1	no	—
1057	C₈	—	2	1	no	—
1058	C₈	—	2	1	no	—
1059	C₈	—	2	1	no	—
1060	C₈	—	2	1	no	—
1061	C₈	—	2	1	no	—
1062	C₈	C₂×#41×C₈₃	1	2	yes	—
1063	C₂²	—	2	1	no	—
1064	C₂²	—	2	1	no	—
1065	C₂²	—	2	1	no	—
1066	C₂²	—	2	1	no	—
1067	C₂²	—	2	1	no	—
1068	C₂²	—	2	1	no	—
1069	C₂²	—	2	1	no	—
1070	C₂²	—	2	1	no	—
1071	C₂²	—	2	4	no	—
1072	C₂²	—	4	2	no	—
1073	C₂²	—	4	2	no	—
1074	C₂²	—	4	2	no	—
1075	C₂²	—	4	2	no	—
1076	C₂²	—	4	2	no	—
1077	C₂²	—	4	2	no	—
1078	C₂²	—	4	2	no	—
1079	C₂²	—	4	2	no	—
1080	C₂²	—	8	8	no	—
1081	C₂²	—	16	4	no	—
1082	C₂²	#576×C₈₃	1	2	yes	—
1083	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
1084	C₄	—	2	1	no	—
1085	C₄	—	2	1	no	—
1086	C₄	—	2	1	no	—
1087	C₄	—	2	1	no	—
1088	C₄	—	2	1	no	—
1089	C₄	—	2	1	no	—
1090	C₄	—	2	1	no	—
1091	C₄	—	2	1	no	—
1092	C₄	—	2	1	no	—
1093	C₄	—	2	1	no	—
1094	C₄	—	2	1	no	—
1095	C₄	—	4	2	no	—
1096	C₄	—	4	2	no	—
1097	C₄	—	4	2	no	—
1098	C₄	—	4	2	no	—
1099	C₄	—	4	2	no	—
1100	C₄	C₂²×#41×C₈₃	1	1	yes	characteristic
1101	C₄	#585×C₈₃	1	1	yes	characteristic
1102	C₂	—	2	2	no	—
1103	C₂	—	4	1	no	—
1104	C₂	—	4	1	no	—
1105	C₂	—	4	4	no	—
1106	C₂	—	8	2	no	—
1107	C₂	—	8	2	no	—
1108	C₂	D₄×#41×C₈₃	1	1	yes	characteristic
1109	C₂	C₂×#576×C₈₃	1	1	yes	characteristic
1110	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 ◁ #529×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₃×#3513	C₂	semidirect
2. C₈₃×#3396	C₂	semidirect
3. C₈₃×#3380	C₂	semidirect
4. C₈₃×#3370	C₂	semidirect
5. C₈₃×#3339	C₂	semidirect
6. C₈₃×#3336	C₂	semidirect
7. C₈₃×#3334	C₂	semidirect
8. C₈₃×#3322	C₂	semidirect
9. C₈₃×#3310	C₂	semidirect
10. C₈₃×#3306	C₂	semidirect
11. C₈₃×#3280	C₂	semidirect
12. C₈₃×#3280	C₂	semidirect
13. D₄×D₈×C₈₃	C₂	semidirect
14. C₈₃×#3176	C₂	semidirect
15. C₈₃×#3175	C₂	semidirect
16. C₈₃×#3168	C₂	semidirect
17. C₈₃×#3119	C₂	semidirect
18. C₈₃×#3118	C₂	semidirect
19. C₈₃×#3114	C₂	semidirect
20. C₈₃×#2966	C₂	semidirect
21. C₈₃×#2951	C₂	semidirect
22. C₈₃×#2948	C₂	semidirect
23. C₂×C₄×D₈×C₈₃	C₂	semidirect
27. #559×C₈₃	C₂²	semidirect
28. #554×C₈₃	C₂²	semidirect
30. #553×C₈₃	C₂²	semidirect
34. #547×C₈₃	C₂²	semidirect
36. #546×C₈₃	C₂²	semidirect
37. #546×C₈₃	C₂²	semidirect
39. #542×C₈₃	C₂²	semidirect
40. #540×C₈₃	C₂²	semidirect
44. #529×C₈₃	C₂²	semidirect
47. #520×C₈₃	C₂²	semidirect
48. #518×C₈₃	C₂²	semidirect
49. C₂×C₄×D₄×C₈₃	C₂²	semidirect
50. #500×C₈₃	C₂²	semidirect
51. #499×C₈₃	C₂²	semidirect
52. #499×C₈₃	C₂²	semidirect
53. #495×C₈₃	C₂²	semidirect
54. #495×C₈₃	C₂²	semidirect
56. #490×C₈₃	C₂²	semidirect
57. #489×C₈₃	C₂²	semidirect
58. #488×C₈₃	C₂²	semidirect
59. #485×C₈₃	C₂²	semidirect
60. #483×C₈₃	C₂²	semidirect
61. #482×C₈₃	C₂²	semidirect
62. #481×C₈₃	C₂²	semidirect
63. #480×C₈₃	C₂²	semidirect
64. #480×C₈₃	C₂²	semidirect
65. #479×C₈₃	C₂²	semidirect
66. #478×C₈₃	C₂²	semidirect
67. #478×C₈₃	C₂²	semidirect
68. #478×C₈₃	C₂²	semidirect
69. #476×C₈₃	C₂²	semidirect
70. #474×C₈₃	C₂²	semidirect
71. #469×C₈₃	C₂²	semidirect
72. #468×C₈₃	C₂²	semidirect
73. #467×C₈₃	C₂²	semidirect
74. #467×C₈₃	C₂²	semidirect
77. #466×C₈₃	C₂²	semidirect
78. #466×C₈₃	C₂²	semidirect
79. #465×C₈₃	C₂²	semidirect
80. #463×C₈₃	C₂²	semidirect
81. #463×C₈₃	C₂²	semidirect
82. #463×C₈₃	C₂²	semidirect
83. #463×C₈₃	C₂²	semidirect
84. #460×C₈₃	C₂²	semidirect
86. #450×C₈₃	C₂²	semidirect
87. #450×C₈₃	C₂²	semidirect
88. #449×C₈₃	C₂²	semidirect
89. #449×C₈₃	C₂²	semidirect
92. #446×C₈₃	C₂²	semidirect
93. C₈×Q₈×C₈₃	C₂²	semidirect
94. #442×C₈₃	C₂²	semidirect
95. #442×C₈₃	C₂²	semidirect
96. #442×C₈₃	C₂²	semidirect
97. #440×C₈₃	C₂²	semidirect
98. #440×C₈₃	C₂²	semidirect
99. #440×C₈₃	C₂²	semidirect
100. C₄×Q₁₆×C₈₃	C₂²	semidirect
101. C₄×Q₁₆×C₈₃	C₂²	semidirect
102. C₄×SD₁₆×C₈₃	C₂²	semidirect
107. C₄×D₈×C₈₃	C₂²	semidirect
108. C₄×D₈×C₈₃	C₂²	semidirect
109. C₄×D₈×C₈₃	C₂²	semidirect
110. C₄×D₈×C₈₃	C₂²	semidirect
111. C₄×D₈×C₈₃	C₂²	semidirect
112. C₄×D₈×C₈₃	C₂²	semidirect
113. #436×C₈₃	C₂²	semidirect
115. #435×C₈₃	C₂²	semidirect
117. C₈×D₄×C₈₃	C₂²	semidirect
118. C₈×D₄×C₈₃	C₂²	semidirect
119. #433×C₈₃	C₂²	semidirect
120. #433×C₈₃	C₂²	semidirect
121. #432×C₈₃	C₂²	semidirect
122. #427×C₈₃	C₂²	semidirect
123. C₂×#107×C₈₃	C₂²	semidirect
124. C₂×#107×C₈₃	C₂²	semidirect
125. #418×C₈₃	C₂²	semidirect
126. #417×C₈₃	C₂²	semidirect
127. C₂×#102×C₈₃	C₂²	semidirect
128. #405×C₈₃	C₂²	semidirect
129. #405×C₈₃	C₂²	semidirect
130. C₂×C₄×C₈×C₈₃	C₂²	semidirect
351. D₈×C₈₃	#41	semidirect
546. #61471	C₈₃	direct (N × H)
556. #3513	C₂×C₈₃	semidirect
557. #3396	C₂×C₈₃	semidirect
558. #3380	C₂×C₈₃	semidirect
559. #3370	C₂×C₈₃	semidirect
560. #3339	C₂×C₈₃	semidirect
561. #3336	C₂×C₈₃	semidirect
562. #3334	C₂×C₈₃	semidirect
563. #3322	C₂×C₈₃	semidirect
564. #3310	C₂×C₈₃	semidirect
565. #3306	C₂×C₈₃	semidirect
566. #3280	C₂×C₈₃	semidirect
567. #3280	C₂×C₈₃	semidirect
568. D₄×D₈	C₂×C₈₃	semidirect
569. #3176	C₂×C₈₃	semidirect
570. #3175	C₂×C₈₃	semidirect
571. #3168	C₂×C₈₃	semidirect
572. #3119	C₂×C₈₃	semidirect
573. #3118	C₂×C₈₃	semidirect
574. #3114	C₂×C₈₃	semidirect
575. #2966	C₂×C₈₃	semidirect
576. #2951	C₂×C₈₃	semidirect
577. #2948	C₂×C₈₃	semidirect
578. C₂×C₄×D₈	C₂×C₈₃	semidirect
579. C₈₃	#61471	direct (N × H)
583. #559	C₂²×C₈₃	semidirect
584. #554	C₂²×C₈₃	semidirect
586. #553	C₂²×C₈₃	semidirect
590. #547	C₂²×C₈₃	semidirect
592. #546	C₂²×C₈₃	semidirect
593. #546	C₂²×C₈₃	semidirect
595. #542	C₂²×C₈₃	semidirect
596. #540	C₂²×C₈₃	semidirect
600. #529	C₂²×C₈₃	semidirect
603. #520	C₂²×C₈₃	semidirect
604. #518	C₂²×C₈₃	semidirect
605. C₂×C₄×D₄	C₂²×C₈₃	semidirect
606. #500	C₂²×C₈₃	semidirect
607. #499	C₂²×C₈₃	semidirect
608. #499	C₂²×C₈₃	semidirect
609. #495	C₂²×C₈₃	semidirect
610. #495	C₂²×C₈₃	semidirect
612. #490	C₂²×C₈₃	semidirect
613. #489	C₂²×C₈₃	semidirect
614. #488	C₂²×C₈₃	semidirect
615. #485	C₂²×C₈₃	semidirect
616. #483	C₂²×C₈₃	semidirect
617. #482	C₂²×C₈₃	semidirect
618. #481	C₂²×C₈₃	semidirect
619. #480	C₂²×C₈₃	semidirect
620. #480	C₂²×C₈₃	semidirect
621. #479	C₂²×C₈₃	semidirect
622. #478	C₂²×C₈₃	semidirect
623. #478	C₂²×C₈₃	semidirect
624. #478	C₂²×C₈₃	semidirect
625. #476	C₂²×C₈₃	semidirect
626. #474	C₂²×C₈₃	semidirect
627. #469	C₂²×C₈₃	semidirect
628. #468	C₂²×C₈₃	semidirect
629. #467	C₂²×C₈₃	semidirect
630. #467	C₂²×C₈₃	semidirect
633. #466	C₂²×C₈₃	semidirect
634. #466	C₂²×C₈₃	semidirect
635. #465	C₂²×C₈₃	semidirect
636. #463	C₂²×C₈₃	semidirect
637. #463	C₂²×C₈₃	semidirect
638. #463	C₂²×C₈₃	semidirect
639. #463	C₂²×C₈₃	semidirect
640. #460	C₂²×C₈₃	semidirect
642. #450	C₂²×C₈₃	semidirect
643. #450	C₂²×C₈₃	semidirect
644. #449	C₂²×C₈₃	semidirect
645. #449	C₂²×C₈₃	semidirect
648. #446	C₂²×C₈₃	semidirect
649. C₈×Q₈	C₂²×C₈₃	semidirect
650. #442	C₂²×C₈₃	semidirect
651. #442	C₂²×C₈₃	semidirect
652. #442	C₂²×C₈₃	semidirect
653. #440	C₂²×C₈₃	semidirect
654. #440	C₂²×C₈₃	semidirect
655. #440	C₂²×C₈₃	semidirect
656. C₄×Q₁₆	C₂²×C₈₃	semidirect
657. C₄×Q₁₆	C₂²×C₈₃	semidirect
658. C₄×SD₁₆	C₂²×C₈₃	semidirect
663. C₄×D₈	C₂²×C₈₃	semidirect
664. C₄×D₈	C₂²×C₈₃	semidirect
665. C₄×D₈	C₂²×C₈₃	semidirect
666. C₄×D₈	C₂²×C₈₃	semidirect
667. C₄×D₈	C₂²×C₈₃	semidirect
668. C₄×D₈	C₂²×C₈₃	semidirect
669. #436	C₂²×C₈₃	semidirect
671. #435	C₂²×C₈₃	semidirect
673. C₈×D₄	C₂²×C₈₃	semidirect
674. C₈×D₄	C₂²×C₈₃	semidirect
675. #433	C₂²×C₈₃	semidirect
676. #433	C₂²×C₈₃	semidirect
677. #432	C₂²×C₈₃	semidirect
678. #427	C₂²×C₈₃	semidirect
679. C₂×#107	C₂²×C₈₃	semidirect
680. C₂×#107	C₂²×C₈₃	semidirect
681. #418	C₂²×C₈₃	semidirect
682. #417	C₂²×C₈₃	semidirect
683. C₂×#102	C₂²×C₈₃	semidirect
684. #405	C₂²×C₈₃	semidirect
685. #405	C₂²×C₈₃	semidirect
686. C₂×C₄×C₈	C₂²×C₈₃	semidirect
907. D₈	#41×C₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₈₃×#3513	2
C₈₃×#3396	2
C₈₃×#3380	2
C₈₃×#3370	2
C₈₃×#3339	2
C₈₃×#3336	2
C₈₃×#3334	2
C₈₃×#3322	2
C₈₃×#3310	2
C₈₃×#3306	2
C₈₃×#3280	2
D₄×D₈×C₈₃	2
C₈₃×#3176	2
C₈₃×#3175	2
C₈₃×#3168	2
C₈₃×#3119	2
C₈₃×#3118	2
C₈₃×#3114	2
C₈₃×#2966	2
C₈₃×#2951	2
C₈₃×#2948	2
C₂×C₄×D₈×C₈₃	2
#61471	83

Subgroups — C83×#61471 #35289295

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#61471 #35289295