Subgroups — C₈₃×#61448 #35289272

Order 21248.

1904 conjugacy classes of subgroups.

The subgroup lattice has 1154 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3482	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₃×#3481	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₃×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₃×#3384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₃×#3373	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₃×#3372	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₃×#3356	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₃×#3350	C₂	1	2	yes	maximal, complemented
9	C₈₃×#3331	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₃×#3324	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₃×#3311	C₂	1	2	yes	maximal, complemented
12	C₈₃×#3307	C₂	1	2	yes	maximal, complemented
13	C₈₃×#3272	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₃×#3267	C₂	1	2	yes	maximal, complemented
15	C₈₃×#3172	C₂	1	2	yes	maximal, complemented
16	C₈₃×#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₃×#3102	C₂	1	2	yes	maximal, complemented
20	C₈₃×#3101	C₂	1	2	yes	maximal, complemented
21	C₈₃×#2965	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×AGL(1,ℤ/8)×C₈₃	C₂	1	2	yes	maximal, complemented
23	C₄×#135×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)×C₈₃	C₂²	1	2	yes	—
25	C₂×#135×C₈₃	C₂²	1	1	yes	characteristic
26	#559×C₈₃	C₂²	1	1	yes	characteristic
27	#557×C₈₃	C₂²	1	1	yes	characteristic, complemented
28	#556×C₈₃	C₂²	1	1	yes	characteristic
29	#556×C₈₃	C₂²	1	2	yes	complemented
30	#554×C₈₃	C₂²	1	1	yes	characteristic
31	#554×C₈₃	C₂²	1	1	yes	characteristic
32	#553×C₈₃	—	2	1	no	—
33	#553×C₈₃	C₂²	1	2	yes	—
34	#552×C₈₃	—	2	1	no	—
35	#552×C₈₃	—	2	2	no	—
36	#551×C₈₃	—	2	2	no	—
37	D₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
38	#548×C₈₃	—	2	1	no	—
39	#547×C₈₃	C₂²	1	1	yes	characteristic
40	#547×C₈₃	C₂²	1	2	yes	complemented
41	#546×C₈₃	—	2	1	no	—
42	#546×C₈₃	C₂²	1	2	yes	—
43	D₄²×C₈₃	C₂²	1	1	yes	characteristic
44	#533×C₈₃	C₂²	1	2	yes	complemented
45	#533×C₈₃	C₂²	1	1	yes	characteristic, complemented
46	#532×C₈₃	C₂²	1	1	yes	characteristic
47	#529×C₈₃	—	2	1	no	—
48	#529×C₈₃	—	2	1	no	—
49	#529×C₈₃	—	2	2	no	—
50	#529×C₈₃	C₂²	1	2	yes	—
51	#525×C₈₃	—	2	2	no	—
52	C₄×#41×C₈₃	C₂²	1	1	yes	characteristic
53	C₄×#41×C₈₃	C₂²	1	1	yes	characteristic
54	C₄×#41×C₈₃	C₂²	1	2	yes	complemented
55	C₄×#41×C₈₃	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₄×Q₈×C₈₃	—	2	1	no	—
57	C₂×C₄×D₄×C₈₃	—	2	1	no	—
58	C₂×C₄×D₄×C₈₃	C₂²	1	2	yes	—
59	#501×C₈₃	C₂²	1	2	yes	complemented
60	#498×C₈₃	C₂²	1	1	yes	characteristic, complemented
61	#497×C₈₃	C₂²	1	2	yes	complemented
62	#492×C₈₃	C₂²	1	1	yes	characteristic
63	#491×C₈₃	C₂²	1	2	yes	complemented
64	#489×C₈₃	C₂²	1	2	yes	complemented
65	#487×C₈₃	C₂²	1	1	yes	characteristic, complemented
66	#486×C₈₃	C₂²	1	1	yes	characteristic
67	#485×C₈₃	C₂²	1	2	yes	complemented
68	#485×C₈₃	C₂²	1	2	yes	complemented
69	#483×C₈₃	C₂²	1	2	yes	complemented
70	#483×C₈₃	C₂²	1	2	yes	complemented
71	#482×C₈₃	C₂²	1	2	yes	—
72	#482×C₈₃	C₂²	1	2	yes	complemented
73	#479×C₈₃	C₂²	1	2	yes	complemented
74	#478×C₈₃	C₂²	1	2	yes	complemented
75	#477×C₈₃	C₂²	1	1	yes	characteristic, complemented
76	#476×C₈₃	C₂²	1	2	yes	—
77	#476×C₈₃	C₂²	1	1	yes	characteristic, complemented
78	#476×C₈₃	C₂²	1	2	yes	complemented
79	#475×C₈₃	C₂²	1	1	yes	characteristic, complemented
80	#474×C₈₃	C₂²	1	1	yes	characteristic
81	#470×C₈₃	C₂²	1	2	yes	complemented
82	#470×C₈₃	C₂²	1	2	yes	complemented
83	#468×C₈₃	C₂²	1	2	yes	—
84	#468×C₈₃	C₂²	1	2	yes	—
85	#465×C₈₃	C₂²	1	2	yes	complemented
86	#465×C₈₃	C₂²	1	2	yes	complemented
87	#464×C₈₃	C₂²	1	2	yes	complemented
88	#463×C₈₃	C₂²	1	2	yes	complemented
89	#462×C₈₃	C₂²	1	1	yes	characteristic, complemented
90	#461×C₈₃	C₂²	1	2	yes	—
91	#461×C₈₃	C₂²	1	1	yes	characteristic
92	#461×C₈₃	C₂²	1	2	yes	complemented
93	#460×C₈₃	C₂²	1	1	yes	characteristic
94	#459×C₈₃	C₂²	1	1	yes	characteristic
95	#452×C₈₃	C₂²	1	2	yes	—
96	#452×C₈₃	C₂²	1	2	yes	complemented
97	#450×C₈₃	C₂²	1	2	yes	—
98	#450×C₈₃	C₂²	1	2	yes	—
99	#449×C₈₃	C₂²	1	2	yes	—
100	#449×C₈₃	C₂²	1	2	yes	complemented
101	#446×C₈₃	C₂²	1	1	yes	characteristic, complemented
102	#446×C₈₃	C₂²	1	1	yes	characteristic, complemented
103	#442×C₈₃	C₂²	1	2	yes	—
104	#442×C₈₃	C₂²	1	2	yes	complemented
105	#440×C₈₃	C₂²	1	2	yes	—
106	#440×C₈₃	C₂²	1	2	yes	complemented
107	C₄×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic, complemented
108	C₄×Q₁₆×C₈₃	C₂²	1	2	yes	complemented
109	C₄×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic, complemented
110	C₄×SD₁₆×C₈₃	C₂²	1	1	yes	characteristic
111	C₄×SD₁₆×C₈₃	C₂²	1	1	yes	characteristic
112	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	—
113	C₄×SD₁₆×C₈₃	C₂²	1	1	yes	characteristic, complemented
114	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	complemented
115	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	complemented
116	C₄×SD₁₆×C₈₃	C₂²	1	1	yes	characteristic, complemented
117	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	complemented
118	C₄×D₈×C₈₃	C₂²	1	1	yes	characteristic
119	C₄×D₈×C₈₃	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₈₃	C₂²	1	2	yes	complemented
121	#436×C₈₃	C₂²	1	1	yes	characteristic
122	#436×C₈₃	C₂²	1	1	yes	characteristic
123	#435×C₈₃	C₂²	1	2	yes	complemented
124	#435×C₈₃	C₂²	1	2	yes	complemented
125	#431×C₈₃	C₂²	1	2	yes	complemented
126	#431×C₈₃	C₂²	1	1	yes	characteristic, complemented
127	#428×C₈₃	C₂²	1	2	yes	complemented
128	#427×C₈₃	C₂²	1	1	yes	characteristic, complemented
129	#418×C₈₃	C₂²	1	2	yes	—
130	#417×C₈₃	C₂²	1	2	yes	complemented
131	#416×C₈₃	C₂²	1	1	yes	characteristic
132	#416×C₈₃	C₂²	1	1	yes	characteristic, complemented
133	C₄×M₁₆×C₈₃	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₈₃	—	2	1	no	—
136	C₂×#41×C₈₃	D₄	1	1	yes	characteristic
137	C₂×#41×C₈₃	C₂³	1	1	yes	characteristic
138	C₂×#41×C₈₃	C₂³	1	2	yes	—
139	C₂×#41×C₈₃	C₂³	1	1	yes	characteristic
140	C₂²×Q₈×C₈₃	—	2	1	no	—
141	C₂²×D₄×C₈₃	—	2	1	no	—
142	C₂²×D₄×C₈₃	C₂³	1	2	yes	—
143	C₂³×C₄×C₈₃	—	2	2	no	—
144	AGL(1,ℤ/8)×C₈₃	—	2	8	no	—
145	#135×C₈₃	—	2	4	no	—
146	C₂×Q₁₆×C₈₃	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆×C₈₃	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₈₃	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₈₃	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
154	C₂×D₈×C₈₃	C₂³	1	2	yes	—
155	C₂×D₈×C₈₃	C₂³	1	1	yes	characteristic
156	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
157	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
158	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
159	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
162	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
164	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
165	#127×C₈₃	C₂³	1	1	yes	characteristic
166	#126×C₈₃	—	2	2	no	—
167	#126×C₈₃	—	2	2	no	—
168	#126×C₈₃	—	2	2	no	—
169	#126×C₈₃	—	2	2	no	—
170	#126×C₈₃	—	2	2	no	—
171	#125×C₈₃	—	2	1	no	—
172	#125×C₈₃	—	2	2	no	—
173	#125×C₈₃	—	2	1	no	—
174	#125×C₈₃	—	2	1	no	—
175	#125×C₈₃	—	2	2	no	—
176	#125×C₈₃	C₂³	1	2	yes	—
177	#124×C₈₃	—	2	1	no	—
178	#124×C₈₃	—	2	1	no	—
179	#124×C₈₃	—	2	2	no	—
180	#124×C₈₃	—	2	1	no	—
181	#124×C₈₃	C₂³	1	2	yes	—
182	#123×C₈₃	—	2	2	no	—
183	#123×C₈₃	—	2	2	no	—
184	#123×C₈₃	—	2	2	no	—
185	#123×C₈₃	—	2	2	no	—
186	#123×C₈₃	—	2	2	no	—
187	#123×C₈₃	—	2	2	no	—
188	#123×C₈₃	—	2	2	no	—
189	C₂²⋊Q₈×C₈₃	—	2	1	no	—
190	C₂²⋊Q₈×C₈₃	—	2	1	no	—
191	C₂²⋊Q₈×C₈₃	—	2	2	no	—
192	C₂²⋊Q₈×C₈₃	—	2	2	no	—
193	C₂²⋊Q₈×C₈₃	—	2	1	no	—
194	C₂²⋊Q₈×C₈₃	—	2	2	no	—
195	C₂²⋊Q₈×C₈₃	—	2	2	no	—
196	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
197	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
198	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
199	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
200	#121×C₈₃	—	2	2	no	—
201	#121×C₈₃	—	2	1	no	—
202	#121×C₈₃	—	2	2	no	—
203	#121×C₈₃	—	2	1	no	—
204	#121×C₈₃	—	2	1	no	—
205	#121×C₈₃	—	2	2	no	—
206	#121×C₈₃	C₂³	1	2	yes	—
207	#121×C₈₃	C₂³	1	2	yes	—
208	#120×C₈₃	—	2	2	no	—
209	#120×C₈₃	—	2	2	no	—
210	C₄×Q₈×C₈₃	—	2	1	no	—
211	C₄×Q₈×C₈₃	—	2	1	no	—
212	C₄×Q₈×C₈₃	—	2	2	no	—
213	C₄×Q₈×C₈₃	—	2	1	no	—
214	C₄×Q₈×C₈₃	—	2	2	no	—
215	C₄×Q₈×C₈₃	D₄	1	1	yes	characteristic
216	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
217	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
221	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
223	C₄×D₄×C₈₃	—	2	1	no	—
224	C₄×D₄×C₈₃	—	2	2	no	—
225	C₄×D₄×C₈₃	—	2	1	no	—
226	C₄×D₄×C₈₃	—	2	1	no	—
227	C₄×D₄×C₈₃	—	2	2	no	—
228	C₄×D₄×C₈₃	—	2	1	no	—
229	C₄×D₄×C₈₃	—	2	1	no	—
230	C₄×D₄×C₈₃	—	2	2	no	—
231	C₄×D₄×C₈₃	—	2	1	no	—
232	C₄×D₄×C₈₃	—	2	2	no	—
233	C₄×D₄×C₈₃	—	2	1	no	—
234	C₄×D₄×C₈₃	—	2	2	no	—
235	C₄×D₄×C₈₃	—	2	2	no	—
236	C₄×D₄×C₈₃	D₄	1	1	yes	characteristic
237	C₄×D₄×C₈₃	D₄	1	2	yes	—
238	C₄×D₄×C₈₃	C₂³	1	2	yes	—
239	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₈₃	C₂³	1	2	yes	—
241	C₄×D₄×C₈₃	C₂³	1	2	yes	—
242	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₈₃	C₂³	1	2	yes	—
245	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₈₃	C₂³	1	2	yes	—
248	#117×C₈₃	—	2	2	no	—
249	#117×C₈₃	—	2	1	no	—
250	#117×C₈₃	—	2	1	no	—
251	#117×C₈₃	—	2	1	no	—
252	#117×C₈₃	—	2	2	no	—
253	#117×C₈₃	—	2	2	no	—
254	#117×C₈₃	D₄	1	2	yes	—
255	#117×C₈₃	D₄	1	1	yes	characteristic
256	#117×C₈₃	C₂³	1	2	yes	—
257	#117×C₈₃	C₂³	1	1	yes	characteristic
258	#117×C₈₃	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
260	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
261	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
262	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
263	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
264	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
265	C₂×C₄²×C₈₃	—	2	1	no	—
266	C₂×C₄²×C₈₃	—	2	1	no	—
267	C₂×C₄²×C₈₃	—	2	2	no	—
268	C₂×C₄²×C₈₃	C₂³	1	2	yes	—
269	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
270	#107×C₈₃	C₂³	1	1	yes	characteristic
271	#107×C₈₃	C₂³	1	2	yes	—
272	#107×C₈₃	C₂³	1	2	yes	—
273	#107×C₈₃	C₂³	1	1	yes	characteristic
274	#106×C₈₃	C₂³	1	2	yes	—
275	#106×C₈₃	C₂³	1	2	yes	—
276	#106×C₈₃	C₂³	1	2	yes	—
277	#106×C₈₃	C₂³	1	2	yes	—
278	#106×C₈₃	C₂³	1	1	yes	characteristic
279	#106×C₈₃	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
281	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
282	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
284	#103×C₈₃	C₂³	1	2	yes	—
285	#103×C₈₃	C₂³	1	1	yes	characteristic
286	#103×C₈₃	C₂³	1	2	yes	—
287	#103×C₈₃	C₂³	1	2	yes	—
288	#103×C₈₃	C₂³	1	1	yes	characteristic
289	#103×C₈₃	C₂³	1	2	yes	—
290	#103×C₈₃	C₂³	1	1	yes	characteristic
291	#103×C₈₃	C₂³	1	2	yes	—
292	#103×C₈₃	C₂³	1	1	yes	characteristic
293	#103×C₈₃	C₂³	1	2	yes	—
294	#102×C₈₃	C₂³	1	2	yes	—
295	#102×C₈₃	C₂³	1	2	yes	—
296	#102×C₈₃	C₂³	1	2	yes	—
297	#102×C₈₃	C₂³	1	2	yes	—
298	#102×C₈₃	C₂³	1	2	yes	—
299	#102×C₈₃	C₂³	1	1	yes	characteristic
300	#102×C₈₃	C₂³	1	2	yes	—
301	#102×C₈₃	C₂³	1	1	yes	characteristic
302	#102×C₈₃	C₂³	1	1	yes	characteristic
303	#102×C₈₃	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
307	#97×C₈₃	C₂³	1	2	yes	—
308	#97×C₈₃	C₂³	1	2	yes	—
309	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₈₃	C₂³	1	2	yes	—
314	C₂⁴×C₈₃	—	2	2	no	—
315	#41×C₈₃	—	2	2	no	—
316	#41×C₈₃	—	2	2	no	—
317	#41×C₈₃	—	2	4	no	—
318	#41×C₈₃	—	4	2	no	—
319	#41×C₈₃	—	4	1	no	—
320	#41×C₈₃	—	4	1	no	—
321	#41×C₈₃	—	4	2	no	—
322	#41×C₈₃	—	8	2	no	—
323	C₂×Q₈×C₈₃	—	2	2	no	—
324	C₂×Q₈×C₈₃	—	2	1	no	—
325	C₂×Q₈×C₈₃	—	2	1	no	—
326	C₂×Q₈×C₈₃	—	4	4	no	—
327	C₂×Q₈×C₈₃	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
330	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₈₃	—	2	4	no	—
332	C₂×D₄×C₈₃	—	2	1	no	—
333	C₂×D₄×C₈₃	—	2	2	no	—
334	C₂×D₄×C₈₃	—	2	2	no	—
335	C₂×D₄×C₈₃	—	2	1	no	—
336	C₂×D₄×C₈₃	—	2	2	no	—
337	C₂×D₄×C₈₃	—	2	2	no	—
338	C₂×D₄×C₈₃	—	2	1	no	—
339	C₂×D₄×C₈₃	—	2	1	no	—
340	C₂×D₄×C₈₃	—	4	2	no	—
341	C₂×D₄×C₈₃	—	4	4	no	—
342	C₂×D₄×C₈₃	C₂×D₄	1	1	yes	characteristic
343	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
344	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
345	C₂×D₄×C₈₃	C₂⁴	1	1	yes	characteristic
346	C₂×D₄×C₈₃	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₈₃	—	2	2	no	—
348	C₂²×C₄×C₈₃	—	2	1	no	—
349	C₂²×C₄×C₈₃	—	2	1	no	—
350	C₂²×C₄×C₈₃	—	2	2	no	—
351	C₂²×C₄×C₈₃	—	2	1	no	—
352	C₂²×C₄×C₈₃	—	2	2	no	—
353	C₂²×C₄×C₈₃	—	2	1	no	—
354	C₂²×C₄×C₈₃	—	2	1	no	—
355	C₂²×C₄×C₈₃	—	2	1	no	—
356	C₂²×C₄×C₈₃	—	2	2	no	—
357	C₂²×C₄×C₈₃	—	2	2	no	—
358	C₂²×C₄×C₈₃	—	2	2	no	—
359	C₂²×C₄×C₈₃	—	8	4	no	—
360	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
361	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
362	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
364	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
365	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
366	Q₁₆×C₈₃	—	2	2	no	—
367	Q₁₆×C₈₃	—	4	2	no	—
368	SD₁₆×C₈₃	—	2	2	no	—
369	SD₁₆×C₈₃	—	2	2	no	—
370	SD₁₆×C₈₃	—	2	4	no	—
371	SD₁₆×C₈₃	—	2	4	no	—
372	SD₁₆×C₈₃	—	4	2	no	—
373	SD₁₆×C₈₃	—	4	2	no	—
374	D₈×C₈₃	—	2	4	no	—
375	D₈×C₈₃	#41	1	4	yes	complemented
376	M₁₆×C₈₃	—	2	4	no	—
377	M₁₆×C₈₃	—	4	2	no	—
378	C₂×C₈×C₈₃	—	2	2	no	—
379	C₂×C₈×C₈₃	—	4	1	no	—
380	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
381	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
382	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
383	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
384	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
385	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
386	C₄⋊C₄×C₈₃	—	2	1	no	—
387	C₄⋊C₄×C₈₃	—	2	2	no	—
388	C₄⋊C₄×C₈₃	—	2	2	no	—
389	C₄⋊C₄×C₈₃	—	2	1	no	—
390	C₄⋊C₄×C₈₃	—	2	2	no	—
391	C₄⋊C₄×C₈₃	—	2	2	no	—
392	C₄⋊C₄×C₈₃	—	2	2	no	—
393	C₄⋊C₄×C₈₃	—	2	2	no	—
394	C₄⋊C₄×C₈₃	—	2	1	no	—
395	C₄⋊C₄×C₈₃	—	2	1	no	—
396	C₄⋊C₄×C₈₃	—	2	2	no	—
397	C₄⋊C₄×C₈₃	—	2	1	no	—
398	C₄⋊C₄×C₈₃	—	2	2	no	—
399	C₄⋊C₄×C₈₃	—	2	1	no	—
400	C₄⋊C₄×C₈₃	—	2	2	no	—
401	C₄⋊C₄×C₈₃	—	2	2	no	—
402	C₄⋊C₄×C₈₃	—	2	2	no	—
403	C₄⋊C₄×C₈₃	—	2	1	no	—
404	C₄⋊C₄×C₈₃	—	2	2	no	—
405	C₄⋊C₄×C₈₃	—	2	1	no	—
406	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
407	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
408	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
409	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
411	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
415	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
416	C₂²⋊C₄×C₈₃	—	2	2	no	—
417	C₂²⋊C₄×C₈₃	—	2	2	no	—
418	C₂²⋊C₄×C₈₃	—	2	2	no	—
419	C₂²⋊C₄×C₈₃	—	2	2	no	—
420	C₂²⋊C₄×C₈₃	—	2	1	no	—
421	C₂²⋊C₄×C₈₃	—	2	2	no	—
422	C₂²⋊C₄×C₈₃	—	2	1	no	—
423	C₂²⋊C₄×C₈₃	—	2	1	no	—
424	C₂²⋊C₄×C₈₃	—	2	2	no	—
425	C₂²⋊C₄×C₈₃	—	2	2	no	—
426	C₂²⋊C₄×C₈₃	—	2	2	no	—
427	C₂²⋊C₄×C₈₃	—	2	2	no	—
428	C₂²⋊C₄×C₈₃	—	2	2	no	—
429	C₂²⋊C₄×C₈₃	—	2	1	no	—
430	C₂²⋊C₄×C₈₃	—	2	1	no	—
431	C₂²⋊C₄×C₈₃	—	2	2	no	—
432	C₂²⋊C₄×C₈₃	—	2	1	no	—
433	C₂²⋊C₄×C₈₃	—	2	2	no	—
434	C₂²⋊C₄×C₈₃	—	2	2	no	—
435	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
436	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
438	C₄²×C₈₃	—	2	1	no	—
439	C₄²×C₈₃	—	2	1	no	—
440	C₄²×C₈₃	—	2	2	no	—
441	C₄²×C₈₃	—	2	1	no	—
442	C₄²×C₈₃	—	2	2	no	—
443	C₄²×C₈₃	—	2	1	no	—
444	C₄²×C₈₃	—	2	1	no	—
445	C₄²×C₈₃	—	2	1	no	—
446	C₄²×C₈₃	—	2	2	no	—
447	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
448	C₄²×C₈₃	C₂×D₄	1	2	yes	—
449	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
450	C₄²×C₈₃	C₂×D₄	1	2	yes	—
451	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
452	C₄²×C₈₃	C₂⁴	1	2	yes	—
453	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
454	C₂³×C₈₃	—	2	1	no	—
455	C₂³×C₈₃	—	2	1	no	—
456	C₂³×C₈₃	—	2	2	no	—
457	C₂³×C₈₃	—	4	4	no	—
458	C₂³×C₈₃	—	4	4	no	—
459	C₂³×C₈₃	—	8	2	no	—
460	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
461	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
462	Q₈×C₈₃	—	2	2	no	—
463	Q₈×C₈₃	—	2	2	no	—
464	Q₈×C₈₃	—	2	1	no	—
465	Q₈×C₈₃	—	2	1	no	—
466	Q₈×C₈₃	—	2	1	no	—
467	Q₈×C₈₃	—	2	2	no	—
468	Q₈×C₈₃	—	2	1	no	—
469	Q₈×C₈₃	—	4	4	no	—
470	Q₈×C₈₃	—	4	2	no	—
471	Q₈×C₈₃	—	8	1	no	—
472	D₄×C₈₃	—	2	2	no	—
473	D₄×C₈₃	—	2	2	no	—
474	D₄×C₈₃	—	2	1	no	—
475	D₄×C₈₃	—	2	1	no	—
476	D₄×C₈₃	—	2	2	no	—
477	D₄×C₈₃	—	4	2	no	—
478	D₄×C₈₃	—	4	4	no	—
479	D₄×C₈₃	—	4	2	no	—
480	D₄×C₈₃	—	4	2	no	—
481	D₄×C₈₃	—	4	4	no	—
482	D₄×C₈₃	—	4	4	no	—
483	D₄×C₈₃	—	4	2	no	—
484	D₄×C₈₃	—	8	1	no	—
485	D₄×C₈₃	—	8	2	no	—
486	D₄×C₈₃	C₂×#41	1	2	yes	—
487	D₄×C₈₃	C₂×#41	1	2	yes	—
488	C₂×C₄×C₈₃	—	2	2	no	—
489	C₂×C₄×C₈₃	—	2	4	no	—
490	C₂×C₄×C₈₃	—	2	2	no	—
491	C₂×C₄×C₈₃	—	2	1	no	—
492	C₂×C₄×C₈₃	—	2	2	no	—
493	C₂×C₄×C₈₃	—	2	1	no	—
494	C₂×C₄×C₈₃	—	2	2	no	—
495	C₂×C₄×C₈₃	—	2	1	no	—
496	C₂×C₄×C₈₃	—	2	1	no	—
497	C₂×C₄×C₈₃	—	2	1	no	—
498	C₂×C₄×C₈₃	—	2	2	no	—
499	C₂×C₄×C₈₃	—	2	1	no	—
500	C₂×C₄×C₈₃	—	2	1	no	—
501	C₂×C₄×C₈₃	—	2	2	no	—
502	C₂×C₄×C₈₃	—	2	1	no	—
503	C₂×C₄×C₈₃	—	2	2	no	—
504	C₂×C₄×C₈₃	—	4	2	no	—
505	C₂×C₄×C₈₃	—	4	2	no	—
506	C₂×C₄×C₈₃	—	4	2	no	—
507	C₂×C₄×C₈₃	—	4	4	no	—
508	C₂×C₄×C₈₃	—	4	4	no	—
509	C₂×C₄×C₈₃	—	4	2	no	—
510	C₂×C₄×C₈₃	—	4	2	no	—
511	C₂×C₄×C₈₃	—	4	2	no	—
512	C₂×C₄×C₈₃	—	4	2	no	—
513	C₂×C₄×C₈₃	—	4	4	no	—
514	C₂×C₄×C₈₃	—	8	2	no	—
515	C₂×C₄×C₈₃	—	8	2	no	—
516	C₂×C₄×C₈₃	—	8	2	no	—
517	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
519	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
520	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
522	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
526	C₈×C₈₃	—	2	1	no	—
527	C₈×C₈₃	—	2	2	no	—
528	C₈×C₈₃	—	2	1	no	—
529	C₈×C₈₃	—	2	1	no	—
530	C₈×C₈₃	—	2	2	no	—
531	C₈×C₈₃	C₂×#41	1	2	yes	—
532	C₂²×C₈₃	—	2	1	no	—
533	C₂²×C₈₃	—	2	2	no	—
534	C₂²×C₈₃	—	2	2	no	—
535	C₂²×C₈₃	—	2	2	no	—
536	C₂²×C₈₃	—	2	1	no	—
537	C₂²×C₈₃	—	2	2	no	—
538	C₂²×C₈₃	—	2	2	no	—
539	C₂²×C₈₃	—	2	1	no	—
540	C₂²×C₈₃	—	4	1	no	—
541	C₂²×C₈₃	—	4	1	no	—
542	C₂²×C₈₃	—	4	1	no	—
543	C₂²×C₈₃	—	4	1	no	—
544	C₂²×C₈₃	—	4	2	no	—
545	C₂²×C₈₃	—	4	2	no	—
546	C₂²×C₈₃	—	4	2	no	—
547	C₂²×C₈₃	—	8	8	no	—
548	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
549	C₄×C₈₃	—	2	1	no	—
550	C₄×C₈₃	—	2	2	no	—
551	C₄×C₈₃	—	2	1	no	—
552	C₄×C₈₃	—	2	2	no	—
553	C₄×C₈₃	—	2	2	no	—
554	C₄×C₈₃	—	2	1	no	—
555	C₄×C₈₃	—	4	1	no	—
556	C₄×C₈₃	—	4	2	no	—
557	C₄×C₈₃	—	4	1	no	—
558	C₄×C₈₃	—	4	1	no	—
559	C₄×C₈₃	—	4	2	no	—
560	C₄×C₈₃	—	4	1	no	—
561	C₄×C₈₃	—	4	1	no	—
562	C₄×C₈₃	—	4	1	no	—
563	C₄×C₈₃	—	4	2	no	—
564	C₄×C₈₃	#575	1	2	yes	—
565	C₄×C₈₃	#577	1	2	yes	—
566	C₄×C₈₃	C₂²×#41	1	1	yes	characteristic
567	C₄×C₈₃	#585	1	1	yes	characteristic
568	#61448	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
569	C₂×C₈₃	—	4	1	no	—
570	C₂×C₈₃	—	4	2	no	—
571	C₂×C₈₃	—	4	2	no	—
572	C₂×C₈₃	—	4	2	no	—
573	C₂×C₈₃	—	8	2	no	—
574	C₂×C₈₃	D₄×#41	1	1	yes	characteristic
575	C₂×C₈₃	C₂×#575	1	1	yes	characteristic
576	C₂×C₈₃	C₂×#577	1	1	yes	characteristic
577	#3482	C₂×C₈₃	1	1	yes	characteristic, complemented
578	#3481	C₂×C₈₃	1	1	yes	characteristic, complemented
579	#3400	C₂×C₈₃	1	1	yes	characteristic, complemented
580	#3384	C₂×C₈₃	1	1	yes	characteristic, complemented
581	#3373	C₂×C₈₃	1	1	yes	characteristic, complemented
582	#3372	C₂×C₈₃	1	1	yes	characteristic, complemented
583	#3356	C₂×C₈₃	1	1	yes	characteristic, complemented
584	#3350	C₂×C₈₃	1	2	yes	complemented
585	#3331	C₂×C₈₃	1	1	yes	characteristic, complemented
586	#3324	C₂×C₈₃	1	1	yes	characteristic, complemented
587	#3311	C₂×C₈₃	1	2	yes	complemented
588	#3307	C₂×C₈₃	1	2	yes	complemented
589	#3272	C₂×C₈₃	1	1	yes	characteristic, complemented
590	#3267	C₂×C₈₃	1	2	yes	complemented
591	#3172	C₂×C₈₃	1	2	yes	complemented
592	#3167	C₂×C₈₃	1	1	yes	characteristic, complemented
593	#3107	C₂×C₈₃	1	1	yes	characteristic, complemented
594	#3106	C₂×C₈₃	1	1	yes	characteristic, complemented
595	#3102	C₂×C₈₃	1	2	yes	complemented
596	#3101	C₂×C₈₃	1	2	yes	complemented
597	#2965	C₂×C₈₃	1	1	yes	characteristic, complemented
598	C₄×AGL(1,ℤ/8)	C₂×C₈₃	1	2	yes	complemented
599	C₄×#135	C₂×C₈₃	1	1	yes	characteristic, complemented
600	C₈₃	#61448	1	1	yes	characteristic, direct product factor, Sylow
601	C₂×AGL(1,ℤ/8)	C₂²×C₈₃	1	2	yes	—
602	C₂×#135	C₂²×C₈₃	1	1	yes	characteristic
603	#559	C₂²×C₈₃	1	1	yes	characteristic
604	#557	C₂²×C₈₃	1	1	yes	characteristic, complemented
605	#556	C₂²×C₈₃	1	1	yes	characteristic
606	#556	C₂²×C₈₃	1	2	yes	complemented
607	#554	C₂²×C₈₃	1	1	yes	characteristic
608	#554	C₂²×C₈₃	1	1	yes	characteristic
609	#553	—	2	1	no	—
610	#553	C₂²×C₈₃	1	2	yes	—
611	#552	—	2	1	no	—
612	#552	—	2	2	no	—
613	#551	—	2	2	no	—
614	D₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
615	#548	—	2	1	no	—
616	#547	C₂²×C₈₃	1	1	yes	characteristic
617	#547	C₂²×C₈₃	1	2	yes	complemented
618	#546	—	2	1	no	—
619	#546	C₂²×C₈₃	1	2	yes	—
620	D₄²	C₂²×C₈₃	1	1	yes	characteristic
621	#533	C₂²×C₈₃	1	2	yes	complemented
622	#533	C₂²×C₈₃	1	1	yes	characteristic, complemented
623	#532	C₂²×C₈₃	1	1	yes	characteristic
624	#529	—	2	1	no	—
625	#529	—	2	1	no	—
626	#529	—	2	2	no	—
627	#529	C₂²×C₈₃	1	2	yes	—
628	#525	—	2	2	no	—
629	C₄×#41	C₂²×C₈₃	1	1	yes	characteristic
630	C₄×#41	C₂²×C₈₃	1	1	yes	characteristic
631	C₄×#41	C₂²×C₈₃	1	2	yes	complemented
632	C₄×#41	C₂²×C₈₃	1	1	yes	characteristic, complemented
633	C₂×C₄×Q₈	—	2	1	no	—
634	C₂×C₄×D₄	—	2	1	no	—
635	C₂×C₄×D₄	C₂²×C₈₃	1	2	yes	—
636	#501	C₂²×C₈₃	1	2	yes	complemented
637	#498	C₂²×C₈₃	1	1	yes	characteristic, complemented
638	#497	C₂²×C₈₃	1	2	yes	complemented
639	#492	C₂²×C₈₃	1	1	yes	characteristic
640	#491	C₂²×C₈₃	1	2	yes	complemented
641	#489	C₂²×C₈₃	1	2	yes	complemented
642	#487	C₂²×C₈₃	1	1	yes	characteristic, complemented
643	#486	C₂²×C₈₃	1	1	yes	characteristic
644	#485	C₂²×C₈₃	1	2	yes	complemented
645	#485	C₂²×C₈₃	1	2	yes	complemented
646	#483	C₂²×C₈₃	1	2	yes	complemented
647	#483	C₂²×C₈₃	1	2	yes	complemented
648	#482	C₂²×C₈₃	1	2	yes	—
649	#482	C₂²×C₈₃	1	2	yes	complemented
650	#479	C₂²×C₈₃	1	2	yes	complemented
651	#478	C₂²×C₈₃	1	2	yes	complemented
652	#477	C₂²×C₈₃	1	1	yes	characteristic, complemented
653	#476	C₂²×C₈₃	1	2	yes	—
654	#476	C₂²×C₈₃	1	1	yes	characteristic, complemented
655	#476	C₂²×C₈₃	1	2	yes	complemented
656	#475	C₂²×C₈₃	1	1	yes	characteristic, complemented
657	#474	C₂²×C₈₃	1	1	yes	characteristic
658	#470	C₂²×C₈₃	1	2	yes	complemented
659	#470	C₂²×C₈₃	1	2	yes	complemented
660	#468	C₂²×C₈₃	1	2	yes	—
661	#468	C₂²×C₈₃	1	2	yes	—
662	#465	C₂²×C₈₃	1	2	yes	complemented
663	#465	C₂²×C₈₃	1	2	yes	complemented
664	#464	C₂²×C₈₃	1	2	yes	complemented
665	#463	C₂²×C₈₃	1	2	yes	complemented
666	#462	C₂²×C₈₃	1	1	yes	characteristic, complemented
667	#461	C₂²×C₈₃	1	2	yes	—
668	#461	C₂²×C₈₃	1	1	yes	characteristic
669	#461	C₂²×C₈₃	1	2	yes	complemented
670	#460	C₂²×C₈₃	1	1	yes	characteristic
671	#459	C₂²×C₈₃	1	1	yes	characteristic
672	#452	C₂²×C₈₃	1	2	yes	—
673	#452	C₂²×C₈₃	1	2	yes	complemented
674	#450	C₂²×C₈₃	1	2	yes	—
675	#450	C₂²×C₈₃	1	2	yes	—
676	#449	C₂²×C₈₃	1	2	yes	—
677	#449	C₂²×C₈₃	1	2	yes	complemented
678	#446	C₂²×C₈₃	1	1	yes	characteristic, complemented
679	#446	C₂²×C₈₃	1	1	yes	characteristic, complemented
680	#442	C₂²×C₈₃	1	2	yes	—
681	#442	C₂²×C₈₃	1	2	yes	complemented
682	#440	C₂²×C₈₃	1	2	yes	—
683	#440	C₂²×C₈₃	1	2	yes	complemented
684	C₄×Q₁₆	C₂²×C₈₃	1	1	yes	characteristic, complemented
685	C₄×Q₁₆	C₂²×C₈₃	1	2	yes	complemented
686	C₄×Q₁₆	C₂²×C₈₃	1	1	yes	characteristic, complemented
687	C₄×SD₁₆	C₂²×C₈₃	1	1	yes	characteristic
688	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	—
689	C₄×SD₁₆	C₂²×C₈₃	1	1	yes	characteristic
690	C₄×SD₁₆	C₂²×C₈₃	1	1	yes	characteristic, complemented
691	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	complemented
692	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	complemented
693	C₄×SD₁₆	C₂²×C₈₃	1	1	yes	characteristic, complemented
694	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	complemented
695	C₄×D₈	C₂²×C₈₃	1	1	yes	characteristic
696	C₄×D₈	C₂²×C₈₃	1	1	yes	characteristic
697	C₄×D₈	C₂²×C₈₃	1	2	yes	complemented
698	#436	C₂²×C₈₃	1	1	yes	characteristic
699	#436	C₂²×C₈₃	1	1	yes	characteristic
700	#435	C₂²×C₈₃	1	2	yes	complemented
701	#435	C₂²×C₈₃	1	2	yes	complemented
702	#431	C₂²×C₈₃	1	2	yes	complemented
703	#431	C₂²×C₈₃	1	1	yes	characteristic, complemented
704	#428	C₂²×C₈₃	1	2	yes	complemented
705	#427	C₂²×C₈₃	1	1	yes	characteristic, complemented
706	#418	C₂²×C₈₃	1	2	yes	—
707	#417	C₂²×C₈₃	1	2	yes	complemented
708	#416	C₂²×C₈₃	1	1	yes	characteristic
709	#416	C₂²×C₈₃	1	1	yes	characteristic, complemented
710	C₄×M₁₆	C₂²×C₈₃	1	2	yes	complemented
711	C₂×C₄×C₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
712	C₂×#41	—	2	1	no	—
713	C₂×#41	D₄×C₈₃	1	1	yes	characteristic
714	C₂×#41	C₂³×C₈₃	1	1	yes	characteristic
715	C₂×#41	C₂³×C₈₃	1	2	yes	—
716	C₂×#41	C₂³×C₈₃	1	1	yes	characteristic
717	C₂²×Q₈	—	2	1	no	—
718	C₂²×D₄	—	2	1	no	—
719	C₂²×D₄	C₂³×C₈₃	1	2	yes	—
720	C₂³×C₄	—	2	2	no	—
721	AGL(1,ℤ/8)	—	2	8	no	—
722	#135	—	2	4	no	—
723	C₂×Q₁₆	C₂³×C₈₃	1	1	yes	characteristic
724	C₂×Q₁₆	C₂³×C₈₃	1	2	yes	—
725	C₂×SD₁₆	C₂³×C₈₃	1	1	yes	characteristic
726	C₂×SD₁₆	C₂³×C₈₃	1	1	yes	characteristic
727	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
728	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
729	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
730	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
731	C₂×D₈	C₂³×C₈₃	1	2	yes	—
732	C₂×D₈	C₂³×C₈₃	1	1	yes	characteristic
733	C₂×M₁₆	C₂³×C₈₃	1	2	yes	—
734	C₂×M₁₆	C₂³×C₈₃	1	2	yes	—
735	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
736	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
737	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
738	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
739	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
740	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
741	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
742	#127	C₂³×C₈₃	1	1	yes	characteristic
743	#126	—	2	2	no	—
744	#126	—	2	2	no	—
745	#126	—	2	2	no	—
746	#126	—	2	2	no	—
747	#126	—	2	2	no	—
748	#125	—	2	1	no	—
749	#125	—	2	2	no	—
750	#125	—	2	1	no	—
751	#125	—	2	1	no	—
752	#125	—	2	2	no	—
753	#125	C₂³×C₈₃	1	2	yes	—
754	#124	—	2	1	no	—
755	#124	—	2	1	no	—
756	#124	—	2	2	no	—
757	#124	—	2	1	no	—
758	#124	C₂³×C₈₃	1	2	yes	—
759	#123	—	2	2	no	—
760	#123	—	2	2	no	—
761	#123	—	2	2	no	—
762	#123	—	2	2	no	—
763	#123	—	2	2	no	—
764	#123	—	2	2	no	—
765	#123	—	2	2	no	—
766	C₂²⋊Q₈	—	2	1	no	—
767	C₂²⋊Q₈	—	2	1	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	—	2	1	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
774	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
775	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
776	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
777	#121	—	2	2	no	—
778	#121	—	2	1	no	—
779	#121	—	2	2	no	—
780	#121	—	2	1	no	—
781	#121	—	2	1	no	—
782	#121	—	2	2	no	—
783	#121	C₂³×C₈₃	1	2	yes	—
784	#121	C₂³×C₈₃	1	2	yes	—
785	#120	—	2	2	no	—
786	#120	—	2	2	no	—
787	C₄×Q₈	—	2	1	no	—
788	C₄×Q₈	—	2	1	no	—
789	C₄×Q₈	—	2	2	no	—
790	C₄×Q₈	—	2	1	no	—
791	C₄×Q₈	—	2	2	no	—
792	C₄×Q₈	D₄×C₈₃	1	1	yes	characteristic
793	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
794	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
795	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
796	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
797	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
798	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
799	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	—	2	2	no	—
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	—	2	1	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	—	2	2	no	—
812	C₄×D₄	—	2	2	no	—
813	C₄×D₄	D₄×C₈₃	1	1	yes	characteristic
814	C₄×D₄	D₄×C₈₃	1	2	yes	—
815	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
816	C₄×D₄	C₂³×C₈₃	1	2	yes	—
817	C₄×D₄	C₂³×C₈₃	1	2	yes	—
818	C₄×D₄	C₂³×C₈₃	1	2	yes	—
819	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
820	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
821	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
822	C₄×D₄	C₂³×C₈₃	1	2	yes	—
823	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
824	C₄×D₄	C₂³×C₈₃	1	2	yes	—
825	#117	—	2	2	no	—
826	#117	—	2	1	no	—
827	#117	—	2	1	no	—
828	#117	—	2	1	no	—
829	#117	—	2	2	no	—
830	#117	—	2	2	no	—
831	#117	D₄×C₈₃	1	2	yes	—
832	#117	D₄×C₈₃	1	1	yes	characteristic
833	#117	C₂³×C₈₃	1	1	yes	characteristic
834	#117	C₂³×C₈₃	1	2	yes	—
835	#117	C₂³×C₈₃	1	1	yes	characteristic
836	C₂×C₄⋊C₄	—	2	1	no	—
837	C₂×C₄⋊C₄	—	2	1	no	—
838	C₂×C₄⋊C₄	—	2	2	no	—
839	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
840	C₂×C₂²⋊C₄	—	2	2	no	—
841	C₂×C₂²⋊C₄	—	2	2	no	—
842	C₂×C₄²	—	2	1	no	—
843	C₂×C₄²	—	2	1	no	—
844	C₂×C₄²	—	2	2	no	—
845	C₂×C₄²	C₂³×C₈₃	1	2	yes	—
846	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
847	#107	C₂³×C₈₃	1	1	yes	characteristic
848	#107	C₂³×C₈₃	1	1	yes	characteristic
849	#107	C₂³×C₈₃	1	2	yes	—
850	#107	C₂³×C₈₃	1	2	yes	—
851	#106	C₂³×C₈₃	1	1	yes	characteristic
852	#106	C₂³×C₈₃	1	1	yes	characteristic
853	#106	C₂³×C₈₃	1	2	yes	—
854	#106	C₂³×C₈₃	1	2	yes	—
855	#106	C₂³×C₈₃	1	2	yes	—
856	#106	C₂³×C₈₃	1	2	yes	—
857	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
858	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
859	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
860	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
861	#103	C₂³×C₈₃	1	1	yes	characteristic
862	#103	C₂³×C₈₃	1	1	yes	characteristic
863	#103	C₂³×C₈₃	1	1	yes	characteristic
864	#103	C₂³×C₈₃	1	1	yes	characteristic
865	#103	C₂³×C₈₃	1	2	yes	—
866	#103	C₂³×C₈₃	1	2	yes	—
867	#103	C₂³×C₈₃	1	2	yes	—
868	#103	C₂³×C₈₃	1	2	yes	—
869	#103	C₂³×C₈₃	1	2	yes	—
870	#103	C₂³×C₈₃	1	2	yes	—
871	#102	C₂³×C₈₃	1	1	yes	characteristic
872	#102	C₂³×C₈₃	1	1	yes	characteristic
873	#102	C₂³×C₈₃	1	1	yes	characteristic
874	#102	C₂³×C₈₃	1	1	yes	characteristic
875	#102	C₂³×C₈₃	1	2	yes	—
876	#102	C₂³×C₈₃	1	2	yes	—
877	#102	C₂³×C₈₃	1	2	yes	—
878	#102	C₂³×C₈₃	1	2	yes	—
879	#102	C₂³×C₈₃	1	2	yes	—
880	#102	C₂³×C₈₃	1	2	yes	—
881	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
882	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
883	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
884	#97	C₂³×C₈₃	1	2	yes	—
885	#97	C₂³×C₈₃	1	2	yes	—
886	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
887	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
888	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
889	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
890	C₄×C₈	C₂³×C₈₃	1	2	yes	—
891	C₂⁴	—	2	2	no	—
892	#41	—	2	2	no	—
893	#41	—	2	2	no	—
894	#41	—	2	4	no	—
895	#41	—	4	2	no	—
896	#41	—	4	1	no	—
897	#41	—	4	1	no	—
898	#41	—	4	2	no	—
899	#41	—	8	2	no	—
900	C₂×Q₈	—	2	2	no	—
901	C₂×Q₈	—	2	1	no	—
902	C₂×Q₈	—	2	1	no	—
903	C₂×Q₈	—	4	4	no	—
904	C₂×Q₈	C₂×D₄×C₈₃	1	1	yes	characteristic
905	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
906	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
907	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
908	C₂×D₄	—	2	4	no	—
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	—	2	2	no	—
911	C₂×D₄	—	2	2	no	—
912	C₂×D₄	—	2	1	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	1	no	—
917	C₂×D₄	—	4	2	no	—
918	C₂×D₄	—	4	4	no	—
919	C₂×D₄	C₂×D₄×C₈₃	1	1	yes	characteristic
920	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
921	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
922	C₂×D₄	C₂⁴×C₈₃	1	1	yes	characteristic
923	C₂×D₄	C₂⁴×C₈₃	1	1	yes	characteristic
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	2	1	no	—
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	—	2	1	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	2	no	—
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	—	2	2	no	—
936	C₂²×C₄	—	8	4	no	—
937	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
938	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
939	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
940	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
941	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
942	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
943	Q₁₆	—	2	2	no	—
944	Q₁₆	—	4	2	no	—
945	SD₁₆	—	2	2	no	—
946	SD₁₆	—	2	2	no	—
947	SD₁₆	—	2	4	no	—
948	SD₁₆	—	2	4	no	—
949	SD₁₆	—	4	2	no	—
950	SD₁₆	—	4	2	no	—
951	D₈	—	2	4	no	—
952	D₈	#41×C₈₃	1	4	yes	complemented
953	M₁₆	—	2	4	no	—
954	M₁₆	—	4	2	no	—
955	C₂×C₈	—	2	2	no	—
956	C₂×C₈	—	4	1	no	—
957	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
958	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
959	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
960	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
961	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
962	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
984	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
985	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
986	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
987	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
988	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
989	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
990	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
991	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
992	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
1013	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
1014	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
1015	C₄²	—	2	1	no	—
1016	C₄²	—	2	1	no	—
1017	C₄²	—	2	2	no	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	1	no	—
1020	C₄²	—	2	2	no	—
1021	C₄²	—	2	1	no	—
1022	C₄²	—	2	2	no	—
1023	C₄²	—	2	1	no	—
1024	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
1025	C₄²	C₂×D₄×C₈₃	1	2	yes	—
1026	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
1027	C₄²	C₂×D₄×C₈₃	1	2	yes	—
1028	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
1029	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
1030	C₄²	C₂⁴×C₈₃	1	2	yes	—
1031	C₂³	—	2	1	no	—
1032	C₂³	—	2	1	no	—
1033	C₂³	—	2	2	no	—
1034	C₂³	—	4	4	no	—
1035	C₂³	—	4	4	no	—
1036	C₂³	—	8	2	no	—
1037	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
1038	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
1039	Q₈	—	2	2	no	—
1040	Q₈	—	2	2	no	—
1041	Q₈	—	2	1	no	—
1042	Q₈	—	2	1	no	—
1043	Q₈	—	2	1	no	—
1044	Q₈	—	2	2	no	—
1045	Q₈	—	2	1	no	—
1046	Q₈	—	4	4	no	—
1047	Q₈	—	4	2	no	—
1048	Q₈	—	8	1	no	—
1049	D₄	—	2	2	no	—
1050	D₄	—	2	2	no	—
1051	D₄	—	2	1	no	—
1052	D₄	—	2	1	no	—
1053	D₄	—	2	2	no	—
1054	D₄	—	4	2	no	—
1055	D₄	—	4	4	no	—
1056	D₄	—	4	2	no	—
1057	D₄	—	4	2	no	—
1058	D₄	—	4	4	no	—
1059	D₄	—	4	4	no	—
1060	D₄	—	4	2	no	—
1061	D₄	—	8	1	no	—
1062	D₄	—	8	2	no	—
1063	D₄	C₂×#41×C₈₃	1	2	yes	—
1064	D₄	C₂×#41×C₈₃	1	2	yes	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	4	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	4	2	no	—
1082	C₂×C₄	—	4	2	no	—
1083	C₂×C₄	—	4	2	no	—
1084	C₂×C₄	—	4	4	no	—
1085	C₂×C₄	—	4	4	no	—
1086	C₂×C₄	—	4	2	no	—
1087	C₂×C₄	—	4	2	no	—
1088	C₂×C₄	—	4	2	no	—
1089	C₂×C₄	—	4	4	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	8	2	no	—
1092	C₂×C₄	—	8	2	no	—
1093	C₂×C₄	—	8	2	no	—
1094	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1095	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
1096	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
1097	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1098	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
1099	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1100	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1101	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1102	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
1103	C₈	—	2	1	no	—
1104	C₈	—	2	2	no	—
1105	C₈	—	2	1	no	—
1106	C₈	—	2	1	no	—
1107	C₈	—	2	2	no	—
1108	C₈	C₂×#41×C₈₃	1	2	yes	—
1109	C₂²	—	2	1	no	—
1110	C₂²	—	2	2	no	—
1111	C₂²	—	2	2	no	—
1112	C₂²	—	2	1	no	—
1113	C₂²	—	2	1	no	—
1114	C₂²	—	2	2	no	—
1115	C₂²	—	2	2	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	4	1	no	—
1118	C₂²	—	4	1	no	—
1119	C₂²	—	4	1	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	2	no	—
1122	C₂²	—	4	2	no	—
1123	C₂²	—	4	2	no	—
1124	C₂²	—	8	8	no	—
1125	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
1126	C₄	—	2	1	no	—
1127	C₄	—	2	2	no	—
1128	C₄	—	2	2	no	—
1129	C₄	—	2	1	no	—
1130	C₄	—	2	1	no	—
1131	C₄	—	2	2	no	—
1132	C₄	—	4	1	no	—
1133	C₄	—	4	2	no	—
1134	C₄	—	4	1	no	—
1135	C₄	—	4	1	no	—
1136	C₄	—	4	2	no	—
1137	C₄	—	4	1	no	—
1138	C₄	—	4	1	no	—
1139	C₄	—	4	2	no	—
1140	C₄	—	4	1	no	—
1141	C₄	#575×C₈₃	1	2	yes	—
1142	C₄	#577×C₈₃	1	2	yes	—
1143	C₄	C₂²×#41×C₈₃	1	1	yes	characteristic
1144	C₄	#585×C₈₃	1	1	yes	characteristic
1145	C₂	—	4	2	no	—
1146	C₂	—	4	1	no	—
1147	C₂	—	4	2	no	—
1148	C₂	—	4	2	no	—
1149	C₂	—	8	2	no	—
1150	C₂	D₄×#41×C₈₃	1	1	yes	characteristic
1151	C₂	C₂×#575×C₈₃	1	1	yes	characteristic
1152	C₂	C₂×#577×C₈₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₈₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₃
socle	C₂²×C₈₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₈₃ ◁ C₄×#41×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₃×#3482	C₂	semidirect
2. C₈₃×#3481	C₂	semidirect
3. C₈₃×#3400	C₂	semidirect
4. C₈₃×#3384	C₂	semidirect
5. C₈₃×#3373	C₂	semidirect
6. C₈₃×#3372	C₂	semidirect
7. C₈₃×#3356	C₂	semidirect
8. C₈₃×#3350	C₂	semidirect
9. C₈₃×#3331	C₂	semidirect
10. C₈₃×#3324	C₂	semidirect
11. C₈₃×#3311	C₂	semidirect
12. C₈₃×#3307	C₂	semidirect
13. C₈₃×#3272	C₂	semidirect
14. C₈₃×#3267	C₂	semidirect
15. C₈₃×#3172	C₂	semidirect
16. C₈₃×#3167	C₂	semidirect
17. C₈₃×#3107	C₂	semidirect
18. C₈₃×#3106	C₂	semidirect
19. C₈₃×#3102	C₂	semidirect
20. C₈₃×#3101	C₂	semidirect
21. C₈₃×#2965	C₂	semidirect
22. C₄×AGL(1,ℤ/8)×C₈₃	C₂	semidirect
23. C₄×#135×C₈₃	C₂	semidirect
27. #557×C₈₃	C₂²	semidirect
29. #556×C₈₃	C₂²	semidirect
37. D₄×Q₈×C₈₃	C₂²	semidirect
40. #547×C₈₃	C₂²	semidirect
44. #533×C₈₃	C₂²	semidirect
45. #533×C₈₃	C₂²	semidirect
54. C₄×#41×C₈₃	C₂²	semidirect
55. C₄×#41×C₈₃	C₂²	semidirect
59. #501×C₈₃	C₂²	semidirect
60. #498×C₈₃	C₂²	semidirect
61. #497×C₈₃	C₂²	semidirect
63. #491×C₈₃	C₂²	semidirect
64. #489×C₈₃	C₂²	semidirect
65. #487×C₈₃	C₂²	semidirect
67. #485×C₈₃	C₂²	semidirect
68. #485×C₈₃	C₂²	semidirect
69. #483×C₈₃	C₂²	semidirect
70. #483×C₈₃	C₂²	semidirect
72. #482×C₈₃	C₂²	semidirect
73. #479×C₈₃	C₂²	semidirect
74. #478×C₈₃	C₂²	semidirect
75. #477×C₈₃	C₂²	semidirect
77. #476×C₈₃	C₂²	semidirect
78. #476×C₈₃	C₂²	semidirect
79. #475×C₈₃	C₂²	semidirect
81. #470×C₈₃	C₂²	semidirect
82. #470×C₈₃	C₂²	semidirect
85. #465×C₈₃	C₂²	semidirect
86. #465×C₈₃	C₂²	semidirect
87. #464×C₈₃	C₂²	semidirect
88. #463×C₈₃	C₂²	semidirect
89. #462×C₈₃	C₂²	semidirect
92. #461×C₈₃	C₂²	semidirect
96. #452×C₈₃	C₂²	semidirect
100. #449×C₈₃	C₂²	semidirect
101. #446×C₈₃	C₂²	semidirect
102. #446×C₈₃	C₂²	semidirect
104. #442×C₈₃	C₂²	semidirect
106. #440×C₈₃	C₂²	semidirect
107. C₄×Q₁₆×C₈₃	C₂²	semidirect
108. C₄×Q₁₆×C₈₃	C₂²	semidirect
109. C₄×Q₁₆×C₈₃	C₂²	semidirect
113. C₄×SD₁₆×C₈₃	C₂²	semidirect
114. C₄×SD₁₆×C₈₃	C₂²	semidirect
115. C₄×SD₁₆×C₈₃	C₂²	semidirect
116. C₄×SD₁₆×C₈₃	C₂²	semidirect
117. C₄×SD₁₆×C₈₃	C₂²	semidirect
120. C₄×D₈×C₈₃	C₂²	semidirect
123. #435×C₈₃	C₂²	semidirect
124. #435×C₈₃	C₂²	semidirect
125. #431×C₈₃	C₂²	semidirect
126. #431×C₈₃	C₂²	semidirect
127. #428×C₈₃	C₂²	semidirect
128. #427×C₈₃	C₂²	semidirect
130. #417×C₈₃	C₂²	semidirect
132. #416×C₈₃	C₂²	semidirect
133. C₄×M₁₆×C₈₃	C₂²	semidirect
134. C₂×C₄×C₈×C₈₃	C₂²	semidirect
375. D₈×C₈₃	#41	semidirect
568. #61448	C₈₃	direct (N × H)
577. #3482	C₂×C₈₃	semidirect
578. #3481	C₂×C₈₃	semidirect
579. #3400	C₂×C₈₃	semidirect
580. #3384	C₂×C₈₃	semidirect
581. #3373	C₂×C₈₃	semidirect
582. #3372	C₂×C₈₃	semidirect
583. #3356	C₂×C₈₃	semidirect
584. #3350	C₂×C₈₃	semidirect
585. #3331	C₂×C₈₃	semidirect
586. #3324	C₂×C₈₃	semidirect
587. #3311	C₂×C₈₃	semidirect
588. #3307	C₂×C₈₃	semidirect
589. #3272	C₂×C₈₃	semidirect
590. #3267	C₂×C₈₃	semidirect
591. #3172	C₂×C₈₃	semidirect
592. #3167	C₂×C₈₃	semidirect
593. #3107	C₂×C₈₃	semidirect
594. #3106	C₂×C₈₃	semidirect
595. #3102	C₂×C₈₃	semidirect
596. #3101	C₂×C₈₃	semidirect
597. #2965	C₂×C₈₃	semidirect
598. C₄×AGL(1,ℤ/8)	C₂×C₈₃	semidirect
599. C₄×#135	C₂×C₈₃	semidirect
600. C₈₃	#61448	direct (N × H)
604. #557	C₂²×C₈₃	semidirect
606. #556	C₂²×C₈₃	semidirect
614. D₄×Q₈	C₂²×C₈₃	semidirect
617. #547	C₂²×C₈₃	semidirect
621. #533	C₂²×C₈₃	semidirect
622. #533	C₂²×C₈₃	semidirect
631. C₄×#41	C₂²×C₈₃	semidirect
632. C₄×#41	C₂²×C₈₃	semidirect
636. #501	C₂²×C₈₃	semidirect
637. #498	C₂²×C₈₃	semidirect
638. #497	C₂²×C₈₃	semidirect
640. #491	C₂²×C₈₃	semidirect
641. #489	C₂²×C₈₃	semidirect
642. #487	C₂²×C₈₃	semidirect
644. #485	C₂²×C₈₃	semidirect
645. #485	C₂²×C₈₃	semidirect
646. #483	C₂²×C₈₃	semidirect
647. #483	C₂²×C₈₃	semidirect
649. #482	C₂²×C₈₃	semidirect
650. #479	C₂²×C₈₃	semidirect
651. #478	C₂²×C₈₃	semidirect
652. #477	C₂²×C₈₃	semidirect
654. #476	C₂²×C₈₃	semidirect
655. #476	C₂²×C₈₃	semidirect
656. #475	C₂²×C₈₃	semidirect
658. #470	C₂²×C₈₃	semidirect
659. #470	C₂²×C₈₃	semidirect
662. #465	C₂²×C₈₃	semidirect
663. #465	C₂²×C₈₃	semidirect
664. #464	C₂²×C₈₃	semidirect
665. #463	C₂²×C₈₃	semidirect
666. #462	C₂²×C₈₃	semidirect
669. #461	C₂²×C₈₃	semidirect
673. #452	C₂²×C₈₃	semidirect
677. #449	C₂²×C₈₃	semidirect
678. #446	C₂²×C₈₃	semidirect
679. #446	C₂²×C₈₃	semidirect
681. #442	C₂²×C₈₃	semidirect
683. #440	C₂²×C₈₃	semidirect
684. C₄×Q₁₆	C₂²×C₈₃	semidirect
685. C₄×Q₁₆	C₂²×C₈₃	semidirect
686. C₄×Q₁₆	C₂²×C₈₃	semidirect
690. C₄×SD₁₆	C₂²×C₈₃	semidirect
691. C₄×SD₁₆	C₂²×C₈₃	semidirect
692. C₄×SD₁₆	C₂²×C₈₃	semidirect
693. C₄×SD₁₆	C₂²×C₈₃	semidirect
694. C₄×SD₁₆	C₂²×C₈₃	semidirect
697. C₄×D₈	C₂²×C₈₃	semidirect
700. #435	C₂²×C₈₃	semidirect
701. #435	C₂²×C₈₃	semidirect
702. #431	C₂²×C₈₃	semidirect
703. #431	C₂²×C₈₃	semidirect
704. #428	C₂²×C₈₃	semidirect
705. #427	C₂²×C₈₃	semidirect
707. #417	C₂²×C₈₃	semidirect
709. #416	C₂²×C₈₃	semidirect
710. C₄×M₁₆	C₂²×C₈₃	semidirect
711. C₂×C₄×C₈	C₂²×C₈₃	semidirect
952. 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×#3482	2
C₈₃×#3481	2
C₈₃×#3400	2
C₈₃×#3384	2
C₈₃×#3373	2
C₈₃×#3372	2
C₈₃×#3356	2
C₈₃×#3350	2
C₈₃×#3331	2
C₈₃×#3324	2
C₈₃×#3311	2
C₈₃×#3307	2
C₈₃×#3272	2
C₈₃×#3267	2
C₈₃×#3172	2
C₈₃×#3167	2
C₈₃×#3107	2
C₈₃×#3106	2
C₈₃×#3102	2
C₈₃×#3101	2
C₈₃×#2965	2
C₄×AGL(1,ℤ/8)×C₈₃	2
C₄×#135×C₈₃	2
#61448	83

Subgroups — C83×#61448 #35289272

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#61448 #35289272