Subgroups — C₈₃×#61405 #35289229

Order 21248.

1996 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3480	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#559×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₃×#3403	C₂	1	4	yes	maximal, complemented
4	C₈₃×#3401	C₂	1	4	yes	maximal, complemented
5	C₈₃×#3400	C₂	1	2	yes	maximal, complemented
6	C₈₃×#3399	C₂	1	2	yes	maximal, complemented
7	C₈₃×#3396	C₂	1	2	yes	maximal, complemented
8	C₈₃×#3394	C₂	1	2	yes	maximal, complemented
9	C₈₃×#3153	C₂	1	2	yes	maximal, complemented
10	C₈₃×#3151	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₃×#3040	C₂	1	2	yes	maximal, complemented
12	C₈₃×#3038	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₃×#3037	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₃×#3036	C₂	1	2	yes	maximal, complemented
15	Q₈×M₁₆×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#137×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×AGL(1,ℤ/8)×C₈₃	C₂	1	2	yes	maximal, complemented
18	C₂×#137×C₈₃	C₂²	1	1	yes	characteristic
19	C₂×#137×C₈₃	C₂²	1	2	yes	—
20	C₂×AGL(1,ℤ/8)×C₈₃	C₂²	1	2	yes	—
21	C₂×AGL(1,ℤ/8)×C₈₃	C₂²	1	2	yes	—
22	C₂×AGL(1,ℤ/8)×C₈₃	C₂²	1	2	yes	—
23	#559×C₈₃	—	2	1	no	—
24	#559×C₈₃	—	2	1	no	—
25	#559×C₈₃	—	2	2	no	—
26	#559×C₈₃	C₂²	1	2	yes	—
27	#559×C₈₃	C₂²	1	2	yes	—
28	#559×C₈₃	C₂²	1	4	yes	—
29	#559×C₈₃	C₂²	1	1	yes	characteristic, complemented
30	#559×C₈₃	C₂²	1	2	yes	complemented
31	#557×C₈₃	C₂²	1	1	yes	characteristic, complemented
32	#556×C₈₃	C₂²	1	1	yes	characteristic, complemented
33	#556×C₈₃	C₂²	1	2	yes	complemented
34	#553×C₈₃	—	2	1	no	—
35	#553×C₈₃	—	2	2	no	—
36	#550×C₈₃	C₂²	1	1	yes	characteristic, complemented
37	#548×C₈₃	—	2	1	no	—
38	#532×C₈₃	C₂²	1	2	yes	—
39	#532×C₈₃	C₂²	1	1	yes	characteristic
40	C₂×#127×C₈₃	C₂²	1	1	yes	characteristic
41	#529×C₈₃	—	2	2	no	—
42	#529×C₈₃	—	2	1	no	—
43	C₂×#124×C₈₃	—	2	1	no	—
44	C₂×#124×C₈₃	C₂²	1	2	yes	—
45	C₂×#123×C₈₃	—	2	2	no	—
46	C₄×#41×C₈₃	—	2	1	no	—
47	C₄×#41×C₈₃	C₂²	1	1	yes	characteristic
48	C₄×#41×C₈₃	C₂²	1	2	yes	—
49	C₂×C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
50	C₂×C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄×C₈₃	—	2	1	no	—
52	C₂×C₄×D₄×C₈₃	C₂²	1	2	yes	—
53	#497×C₈₃	C₂²	1	4	yes	complemented
54	#496×C₈₃	C₂²	1	4	yes	—
55	#496×C₈₃	C₂²	1	4	yes	complemented
56	#495×C₈₃	C₂²	1	4	yes	complemented
57	#495×C₈₃	C₂²	1	4	yes	complemented
58	#493×C₈₃	C₂²	1	2	yes	—
59	#492×C₈₃	C₂²	1	2	yes	—
60	#464×C₈₃	C₂²	1	4	yes	complemented
61	#464×C₈₃	C₂²	1	4	yes	complemented
62	#464×C₈₃	C₂²	1	4	yes	complemented
63	#463×C₈₃	C₂²	1	4	yes	complemented
64	#463×C₈₃	C₂²	1	4	yes	complemented
65	#463×C₈₃	C₂²	1	4	yes	complemented
66	#463×C₈₃	C₂²	1	4	yes	complemented
67	#462×C₈₃	C₂²	1	2	yes	complemented
68	#461×C₈₃	C₂²	1	4	yes	complemented
69	#460×C₈₃	C₂²	1	2	yes	—
70	#460×C₈₃	C₂²	1	2	yes	—
71	#460×C₈₃	C₂²	1	2	yes	complemented
72	#459×C₈₃	C₂²	1	2	yes	—
73	#459×C₈₃	C₂²	1	2	yes	—
74	#459×C₈₃	C₂²	1	4	yes	complemented
75	#446×C₈₃	C₂²	1	2	yes	complemented
76	#446×C₈₃	C₂²	1	4	yes	complemented
77	C₈×Q₈×C₈₃	C₂²	1	2	yes	complemented
78	#442×C₈₃	C₂²	1	4	yes	complemented
79	#441×C₈₃	C₂²	1	2	yes	complemented
80	#440×C₈₃	C₂²	1	4	yes	complemented
81	#440×C₈₃	C₂²	1	2	yes	complemented
82	C₄×Q₁₆×C₈₃	C₂²	1	2	yes	complemented
83	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	complemented
84	C₄×SD₁₆×C₈₃	C₂²	1	4	yes	complemented
85	C₄×D₈×C₈₃	C₂²	1	4	yes	complemented
86	#428×C₈₃	C₂²	1	1	yes	characteristic
87	#423×C₈₃	C₂²	1	2	yes	—
88	#423×C₈₃	C₂²	1	1	yes	characteristic
89	#419×C₈₃	C₂²	1	1	yes	characteristic
90	#418×C₈₃	C₂²	1	2	yes	—
91	#417×C₈₃	C₂²	1	1	yes	characteristic
92	#417×C₈₃	C₂²	1	2	yes	—
93	C₄×M₁₆×C₈₃	C₂²	1	1	yes	characteristic
94	C₄×M₁₆×C₈₃	C₂²	1	2	yes	—
95	C₂×#41×C₈₃	—	2	1	no	—
96	C₂×#41×C₈₃	C₂³	1	2	yes	—
97	C₂×#41×C₈₃	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₈₃	D₄	1	1	yes	characteristic
99	C₂²×Q₈×C₈₃	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₈₃	—	2	1	no	—
101	C₂²×D₄×C₈₃	—	2	1	no	—
102	C₂²×D₄×C₈₃	C₂³	1	2	yes	—
103	C₂³×C₄×C₈₃	—	2	2	no	—
104	#137×C₈₃	—	2	4	no	—
105	#137×C₈₃	—	4	4	no	—
106	AGL(1,ℤ/8)×C₈₃	—	2	8	no	—
107	AGL(1,ℤ/8)×C₈₃	—	4	4	no	—
108	AGL(1,ℤ/8)×C₈₃	—	4	4	no	—
109	C₂×Q₁₆×C₈₃	C₂³	1	2	yes	—
110	C₂×Q₁₆×C₈₃	C₂³	1	4	yes	—
111	C₂×SD₁₆×C₈₃	C₂³	1	4	yes	—
112	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
113	C₂×SD₁₆×C₈₃	C₂³	1	4	yes	—
114	C₂×SD₁₆×C₈₃	C₂³	1	4	yes	—
115	C₂×SD₁₆×C₈₃	C₂³	1	4	yes	—
116	C₂×D₈×C₈₃	C₂³	1	4	yes	—
117	C₂×D₈×C₈₃	C₂³	1	4	yes	—
118	C₂×D₈×C₈₃	C₂³	1	4	yes	—
119	C₂×M₁₆×C₈₃	C₂³	1	1	yes	characteristic
120	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
121	C₂×M₁₆×C₈₃	C₂³	1	1	yes	characteristic
122	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
123	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
124	#127×C₈₃	—	2	1	no	—
125	#127×C₈₃	—	2	1	no	—
126	#127×C₈₃	C₂³	1	2	yes	—
127	#127×C₈₃	C₂³	1	1	yes	characteristic
128	#127×C₈₃	C₂³	1	2	yes	—
129	#127×C₈₃	C₂³	1	2	yes	—
130	#126×C₈₃	—	2	2	no	—
131	#126×C₈₃	—	2	2	no	—
132	#126×C₈₃	—	2	2	no	—
133	#125×C₈₃	—	2	1	no	—
134	#125×C₈₃	—	2	2	no	—
135	#124×C₈₃	—	2	2	no	—
136	#124×C₈₃	—	2	2	no	—
137	#124×C₈₃	—	2	4	no	—
138	#124×C₈₃	—	2	1	no	—
139	#124×C₈₃	—	2	2	no	—
140	#124×C₈₃	—	2	2	no	—
141	#124×C₈₃	—	2	2	no	—
142	#124×C₈₃	C₂³	1	2	yes	—
143	#124×C₈₃	C₂³	1	2	yes	—
144	#124×C₈₃	C₂³	1	4	yes	—
145	#124×C₈₃	C₂³	1	4	yes	—
146	#124×C₈₃	C₂³	1	2	yes	—
147	#123×C₈₃	—	2	4	no	—
148	#123×C₈₃	—	2	4	no	—
149	#123×C₈₃	—	2	4	no	—
150	#123×C₈₃	—	2	4	no	—
151	#123×C₈₃	—	2	2	no	—
152	#123×C₈₃	—	2	2	no	—
153	#123×C₈₃	—	2	2	no	—
154	C₂²⋊Q₈×C₈₃	—	2	1	no	—
155	C₂²⋊Q₈×C₈₃	—	2	2	no	—
156	#121×C₈₃	—	2	1	no	—
157	#121×C₈₃	—	2	2	no	—
158	#121×C₈₃	—	2	2	no	—
159	#121×C₈₃	—	2	1	no	—
160	#121×C₈₃	—	2	1	no	—
161	#121×C₈₃	—	2	2	no	—
162	C₄×Q₈×C₈₃	—	2	1	no	—
163	C₄×Q₈×C₈₃	—	2	1	no	—
164	C₄×Q₈×C₈₃	—	2	1	no	—
165	C₄×Q₈×C₈₃	D₄	1	1	yes	characteristic
166	C₄×Q₈×C₈₃	D₄	1	2	yes	—
167	C₄×Q₈×C₈₃	D₄	1	1	yes	characteristic
168	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
169	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
170	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
171	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
172	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
173	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
174	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
175	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
176	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
177	C₄×D₄×C₈₃	—	2	1	no	—
178	C₄×D₄×C₈₃	—	2	2	no	—
179	C₄×D₄×C₈₃	—	2	2	no	—
180	C₄×D₄×C₈₃	—	2	1	no	—
181	C₄×D₄×C₈₃	—	2	2	no	—
182	C₄×D₄×C₈₃	—	2	2	no	—
183	C₄×D₄×C₈₃	—	2	4	no	—
184	C₄×D₄×C₈₃	—	2	1	no	—
185	C₄×D₄×C₈₃	—	2	2	no	—
186	C₄×D₄×C₈₃	—	2	2	no	—
187	C₄×D₄×C₈₃	—	2	2	no	—
188	C₄×D₄×C₈₃	—	2	2	no	—
189	C₄×D₄×C₈₃	—	2	1	no	—
190	C₄×D₄×C₈₃	—	2	2	no	—
191	C₄×D₄×C₈₃	—	2	1	no	—
192	C₄×D₄×C₈₃	C₂³	1	4	yes	—
193	C₄×D₄×C₈₃	C₂³	1	2	yes	—
194	C₄×D₄×C₈₃	C₂³	1	2	yes	—
195	C₄×D₄×C₈₃	C₂³	1	4	yes	—
196	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
197	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
198	#117×C₈₃	—	2	1	no	—
199	#117×C₈₃	—	2	2	no	—
200	#117×C₈₃	—	2	2	no	—
201	#117×C₈₃	—	2	1	no	—
202	#117×C₈₃	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
204	C₂×C₄⋊C₄×C₈₃	D₄	1	1	yes	characteristic
205	C₂×C₄⋊C₄×C₈₃	D₄	1	2	yes	—
206	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
208	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
209	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
210	C₂×C₄²×C₈₃	—	2	1	no	—
211	C₂×C₄²×C₈₃	—	2	2	no	—
212	C₂×C₄²×C₈₃	—	2	1	no	—
213	C₂×C₄²×C₈₃	C₂³	1	2	yes	—
214	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
215	#107×C₈₃	C₂³	1	2	yes	—
216	#106×C₈₃	C₂³	1	2	yes	—
217	C₄⋊C₈×C₈₃	C₂³	1	4	yes	—
218	C₄⋊C₈×C₈₃	C₂³	1	4	yes	—
219	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
220	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
221	#103×C₈₃	C₂³	1	2	yes	—
222	#103×C₈₃	C₂³	1	2	yes	—
223	#103×C₈₃	C₂³	1	2	yes	—
224	#103×C₈₃	C₂³	1	4	yes	—
225	#102×C₈₃	C₂³	1	2	yes	—
226	#102×C₈₃	C₂³	1	4	yes	—
227	#102×C₈₃	C₂³	1	4	yes	—
228	#102×C₈₃	C₂³	1	4	yes	—
229	#97×C₈₃	C₂³	1	2	yes	—
230	#97×C₈₃	C₂³	1	4	yes	—
231	C₄×C₈×C₈₃	C₂³	1	2	yes	—
232	C₄×C₈×C₈₃	C₂³	1	4	yes	—
233	C₂⁴×C₈₃	—	2	2	no	—
234	#41×C₈₃	—	2	4	no	—
235	#41×C₈₃	—	2	2	no	—
236	#41×C₈₃	—	2	2	no	—
237	#41×C₈₃	—	2	4	no	—
238	#41×C₈₃	—	4	4	no	—
239	C₂×Q₈×C₈₃	—	2	1	no	—
240	C₂×Q₈×C₈₃	—	2	2	no	—
241	C₂×Q₈×C₈₃	—	2	2	no	—
242	C₂×Q₈×C₈₃	—	4	2	no	—
243	C₂×Q₈×C₈₃	C₂×D₄	1	1	yes	characteristic
244	C₂×Q₈×C₈₃	C₂×D₄	1	1	yes	characteristic
245	C₂×Q₈×C₈₃	C₂×D₄	1	2	yes	—
246	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
247	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
248	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
249	C₂×D₄×C₈₃	—	2	2	no	—
250	C₂×D₄×C₈₃	—	2	1	no	—
251	C₂×D₄×C₈₃	—	2	2	no	—
252	C₂×D₄×C₈₃	—	2	1	no	—
253	C₂×D₄×C₈₃	—	2	2	no	—
254	C₂×D₄×C₈₃	—	2	2	no	—
255	C₂×D₄×C₈₃	—	2	2	no	—
256	C₂×D₄×C₈₃	—	2	2	no	—
257	C₂×D₄×C₈₃	—	2	1	no	—
258	C₂×D₄×C₈₃	—	2	2	no	—
259	C₂×D₄×C₈₃	—	2	2	no	—
260	C₂×D₄×C₈₃	—	2	4	no	—
261	C₂×D₄×C₈₃	—	2	4	no	—
262	C₂×D₄×C₈₃	—	4	4	no	—
263	C₂×D₄×C₈₃	—	8	2	no	—
264	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
265	C₂×D₄×C₈₃	C₂⁴	1	1	yes	characteristic
266	C₂×D₄×C₈₃	C₂⁴	1	4	yes	—
267	C₂²×C₄×C₈₃	—	2	1	no	—
268	C₂²×C₄×C₈₃	—	2	1	no	—
269	C₂²×C₄×C₈₃	—	2	2	no	—
270	C₂²×C₄×C₈₃	—	2	1	no	—
271	C₂²×C₄×C₈₃	—	2	2	no	—
272	C₂²×C₄×C₈₃	—	2	1	no	—
273	C₂²×C₄×C₈₃	—	2	2	no	—
274	C₂²×C₄×C₈₃	—	2	1	no	—
275	C₂²×C₄×C₈₃	—	2	4	no	—
276	C₂²×C₄×C₈₃	—	2	4	no	—
277	C₂²×C₄×C₈₃	—	8	4	no	—
278	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
279	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
280	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
281	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
283	Q₁₆×C₈₃	—	2	4	no	—
284	Q₁₆×C₈₃	—	4	4	no	—
285	SD₁₆×C₈₃	—	2	8	no	—
286	SD₁₆×C₈₃	—	2	4	no	—
287	SD₁₆×C₈₃	—	4	4	no	—
288	SD₁₆×C₈₃	—	4	4	no	—
289	SD₁₆×C₈₃	—	4	4	no	—
290	D₈×C₈₃	—	2	8	no	—
291	D₈×C₈₃	—	4	4	no	—
292	D₈×C₈₃	—	4	4	no	—
293	M₁₆×C₈₃	—	2	2	no	—
294	M₁₆×C₈₃	—	2	4	no	—
295	M₁₆×C₈₃	#41	1	4	yes	complemented
296	C₂×C₈×C₈₃	C₂⁴	1	4	yes	—
297	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
298	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
299	C₄⋊C₄×C₈₃	—	2	2	no	—
300	C₄⋊C₄×C₈₃	—	2	2	no	—
301	C₄⋊C₄×C₈₃	—	2	1	no	—
302	C₄⋊C₄×C₈₃	—	2	2	no	—
303	C₄⋊C₄×C₈₃	—	2	1	no	—
304	C₄⋊C₄×C₈₃	—	2	1	no	—
305	C₄⋊C₄×C₈₃	—	2	2	no	—
306	C₄⋊C₄×C₈₃	—	2	2	no	—
307	C₄⋊C₄×C₈₃	—	2	1	no	—
308	C₄⋊C₄×C₈₃	—	2	2	no	—
309	C₄⋊C₄×C₈₃	—	2	1	no	—
310	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
311	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
312	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
313	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
314	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
315	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
316	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
317	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
318	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
319	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
320	C₂²⋊C₄×C₈₃	—	2	1	no	—
321	C₂²⋊C₄×C₈₃	—	2	4	no	—
322	C₂²⋊C₄×C₈₃	—	2	4	no	—
323	C₂²⋊C₄×C₈₃	—	2	4	no	—
324	C₂²⋊C₄×C₈₃	—	2	4	no	—
325	C₂²⋊C₄×C₈₃	—	2	4	no	—
326	C₂²⋊C₄×C₈₃	—	2	4	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	1	no	—
332	C₂²⋊C₄×C₈₃	—	2	1	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	—	2	2	no	—
337	C₄²×C₈₃	—	2	1	no	—
338	C₄²×C₈₃	—	2	2	no	—
339	C₄²×C₈₃	—	2	1	no	—
340	C₄²×C₈₃	—	2	2	no	—
341	C₄²×C₈₃	—	2	2	no	—
342	C₄²×C₈₃	—	2	2	no	—
343	C₄²×C₈₃	—	2	1	no	—
344	C₄²×C₈₃	C₂×D₄	1	2	yes	—
345	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
346	C₄²×C₈₃	C₂×D₄	1	2	yes	—
347	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
348	C₄²×C₈₃	C₂⁴	1	2	yes	—
349	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
350	C₄²×C₈₃	C₂⁴	1	2	yes	—
351	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
352	C₂³×C₈₃	—	2	2	no	—
353	C₂³×C₈₃	—	2	1	no	—
354	C₂³×C₈₃	—	2	4	no	—
355	C₂³×C₈₃	—	4	4	no	—
356	C₂³×C₈₃	—	4	4	no	—
357	C₂³×C₈₃	—	4	4	no	—
358	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
359	Q₈×C₈₃	—	2	2	no	—
360	Q₈×C₈₃	—	2	2	no	—
361	Q₈×C₈₃	—	2	2	no	—
362	Q₈×C₈₃	—	2	2	no	—
363	Q₈×C₈₃	—	2	1	no	—
364	Q₈×C₈₃	—	2	1	no	—
365	Q₈×C₈₃	—	2	2	no	—
366	Q₈×C₈₃	—	2	2	no	—
367	Q₈×C₈₃	—	4	2	no	—
368	Q₈×C₈₃	—	4	2	no	—
369	D₄×C₈₃	—	2	2	no	—
370	D₄×C₈₃	—	2	4	no	—
371	D₄×C₈₃	—	2	1	no	—
372	D₄×C₈₃	—	2	1	no	—
373	D₄×C₈₃	—	2	4	no	—
374	D₄×C₈₃	—	2	2	no	—
375	D₄×C₈₃	—	4	4	no	—
376	D₄×C₈₃	—	4	4	no	—
377	D₄×C₈₃	—	4	4	no	—
378	D₄×C₈₃	—	4	2	no	—
379	D₄×C₈₃	—	4	4	no	—
380	D₄×C₈₃	—	4	4	no	—
381	D₄×C₈₃	—	4	2	no	—
382	D₄×C₈₃	—	8	2	no	—
383	D₄×C₈₃	—	8	1	no	—
384	D₄×C₈₃	—	8	2	no	—
385	D₄×C₈₃	—	8	2	no	—
386	C₂×C₄×C₈₃	—	2	2	no	—
387	C₂×C₄×C₈₃	—	2	1	no	—
388	C₂×C₄×C₈₃	—	2	1	no	—
389	C₂×C₄×C₈₃	—	2	2	no	—
390	C₂×C₄×C₈₃	—	2	2	no	—
391	C₂×C₄×C₈₃	—	2	1	no	—
392	C₂×C₄×C₈₃	—	2	2	no	—
393	C₂×C₄×C₈₃	—	4	2	no	—
394	C₂×C₄×C₈₃	—	4	1	no	—
395	C₂×C₄×C₈₃	—	4	2	no	—
396	C₂×C₄×C₈₃	—	4	4	no	—
397	C₂×C₄×C₈₃	—	4	2	no	—
398	C₂×C₄×C₈₃	—	4	2	no	—
399	C₂×C₄×C₈₃	—	4	4	no	—
400	C₂×C₄×C₈₃	—	4	2	no	—
401	C₂×C₄×C₈₃	—	4	2	no	—
402	C₂×C₄×C₈₃	—	8	2	no	—
403	C₂×C₄×C₈₃	—	8	1	no	—
404	C₂×C₄×C₈₃	—	8	4	no	—
405	C₂×C₄×C₈₃	—	8	4	no	—
406	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
408	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
409	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
411	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
412	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₈₃	C₂×#41	1	2	yes	—
416	C₂×C₄×C₈₃	H(5,𝔽₂)	1	2	yes	—
417	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
418	C₈×C₈₃	—	2	2	no	—
419	C₈×C₈₃	—	2	4	no	—
420	C₈×C₈₃	C₂×#41	1	4	yes	—
421	C₂²×C₈₃	—	2	1	no	—
422	C₂²×C₈₃	—	2	1	no	—
423	C₂²×C₈₃	—	4	4	no	—
424	C₂²×C₈₃	—	4	2	no	—
425	C₂²×C₈₃	—	4	1	no	—
426	C₂²×C₈₃	—	4	2	no	—
427	C₂²×C₈₃	—	4	1	no	—
428	C₂²×C₈₃	—	4	4	no	—
429	C₂²×C₈₃	—	4	2	no	—
430	C₂²×C₈₃	—	4	1	no	—
431	C₂²×C₈₃	—	4	4	no	—
432	C₂²×C₈₃	—	8	8	no	—
433	C₂²×C₈₃	#550	1	2	yes	—
434	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
435	C₄×C₈₃	—	2	2	no	—
436	C₄×C₈₃	—	2	2	no	—
437	C₄×C₈₃	—	2	1	no	—
438	C₄×C₈₃	—	2	1	no	—
439	C₄×C₈₃	—	2	1	no	—
440	C₄×C₈₃	—	2	2	no	—
441	C₄×C₈₃	—	2	2	no	—
442	C₄×C₈₃	—	4	2	no	—
443	C₄×C₈₃	—	4	1	no	—
444	C₄×C₈₃	—	4	2	no	—
445	C₄×C₈₃	—	4	1	no	—
446	C₄×C₈₃	—	4	2	no	—
447	C₄×C₈₃	—	4	1	no	—
448	C₄×C₈₃	#550	1	2	yes	—
449	C₄×C₈₃	#575	1	2	yes	—
450	C₄×C₈₃	C₂²×#41	1	1	yes	characteristic
451	C₄×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
452	#61405	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
453	C₂×C₈₃	—	2	2	no	—
454	C₂×C₈₃	—	8	2	no	—
455	C₂×C₈₃	—	8	1	no	—
456	C₂×C₈₃	—	8	4	no	—
457	C₂×C₈₃	C₂×#550	1	1	yes	characteristic
458	C₂×C₈₃	C₂×#575	1	1	yes	characteristic
459	C₂×C₈₃	#3585	1	1	yes	characteristic
460	#3480	C₂×C₈₃	1	1	yes	characteristic, complemented
461	C₂×#559	C₂×C₈₃	1	1	yes	characteristic, complemented
462	#3403	C₂×C₈₃	1	4	yes	complemented
463	#3401	C₂×C₈₃	1	4	yes	complemented
464	#3400	C₂×C₈₃	1	2	yes	complemented
465	#3399	C₂×C₈₃	1	2	yes	complemented
466	#3396	C₂×C₈₃	1	2	yes	complemented
467	#3394	C₂×C₈₃	1	2	yes	complemented
468	#3153	C₂×C₈₃	1	2	yes	complemented
469	#3151	C₂×C₈₃	1	1	yes	characteristic, complemented
470	#3040	C₂×C₈₃	1	2	yes	complemented
471	#3038	C₂×C₈₃	1	1	yes	characteristic, complemented
472	#3037	C₂×C₈₃	1	1	yes	characteristic, complemented
473	#3036	C₂×C₈₃	1	2	yes	complemented
474	Q₈×M₁₆	C₂×C₈₃	1	1	yes	characteristic, complemented
475	C₄×#137	C₂×C₈₃	1	1	yes	characteristic, complemented
476	C₄×AGL(1,ℤ/8)	C₂×C₈₃	1	2	yes	complemented
477	C₈₃	#61405	1	1	yes	characteristic, direct product factor, Sylow
478	C₂×#137	C₂²×C₈₃	1	1	yes	characteristic
479	C₂×#137	C₂²×C₈₃	1	2	yes	—
480	C₂×AGL(1,ℤ/8)	C₂²×C₈₃	1	2	yes	—
481	C₂×AGL(1,ℤ/8)	C₂²×C₈₃	1	2	yes	—
482	C₂×AGL(1,ℤ/8)	C₂²×C₈₃	1	2	yes	—
483	#559	—	2	1	no	—
484	#559	—	2	1	no	—
485	#559	—	2	2	no	—
486	#559	C₂²×C₈₃	1	2	yes	—
487	#559	C₂²×C₈₃	1	2	yes	—
488	#559	C₂²×C₈₃	1	4	yes	—
489	#559	C₂²×C₈₃	1	1	yes	characteristic, complemented
490	#559	C₂²×C₈₃	1	2	yes	complemented
491	#557	C₂²×C₈₃	1	1	yes	characteristic, complemented
492	#556	C₂²×C₈₃	1	1	yes	characteristic, complemented
493	#556	C₂²×C₈₃	1	2	yes	complemented
494	#553	—	2	1	no	—
495	#553	—	2	2	no	—
496	#550	C₂²×C₈₃	1	1	yes	characteristic, complemented
497	#548	—	2	1	no	—
498	#532	C₂²×C₈₃	1	1	yes	characteristic
499	#532	C₂²×C₈₃	1	2	yes	—
500	C₂×#127	C₂²×C₈₃	1	1	yes	characteristic
501	#529	—	2	2	no	—
502	#529	—	2	1	no	—
503	C₂×#124	—	2	1	no	—
504	C₂×#124	C₂²×C₈₃	1	2	yes	—
505	C₂×#123	—	2	2	no	—
506	C₄×#41	—	2	1	no	—
507	C₄×#41	C₂²×C₈₃	1	2	yes	—
508	C₄×#41	C₂²×C₈₃	1	1	yes	characteristic
509	C₂×C₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic
510	C₂×C₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic
511	C₂×C₄×D₄	—	2	1	no	—
512	C₂×C₄×D₄	C₂²×C₈₃	1	2	yes	—
513	#497	C₂²×C₈₃	1	4	yes	complemented
514	#496	C₂²×C₈₃	1	4	yes	—
515	#496	C₂²×C₈₃	1	4	yes	complemented
516	#495	C₂²×C₈₃	1	4	yes	complemented
517	#495	C₂²×C₈₃	1	4	yes	complemented
518	#493	C₂²×C₈₃	1	2	yes	—
519	#492	C₂²×C₈₃	1	2	yes	—
520	#464	C₂²×C₈₃	1	4	yes	complemented
521	#464	C₂²×C₈₃	1	4	yes	complemented
522	#464	C₂²×C₈₃	1	4	yes	complemented
523	#463	C₂²×C₈₃	1	4	yes	complemented
524	#463	C₂²×C₈₃	1	4	yes	complemented
525	#463	C₂²×C₈₃	1	4	yes	complemented
526	#463	C₂²×C₈₃	1	4	yes	complemented
527	#462	C₂²×C₈₃	1	2	yes	complemented
528	#461	C₂²×C₈₃	1	4	yes	complemented
529	#460	C₂²×C₈₃	1	2	yes	—
530	#460	C₂²×C₈₃	1	2	yes	—
531	#460	C₂²×C₈₃	1	2	yes	complemented
532	#459	C₂²×C₈₃	1	2	yes	—
533	#459	C₂²×C₈₃	1	2	yes	—
534	#459	C₂²×C₈₃	1	4	yes	complemented
535	#446	C₂²×C₈₃	1	2	yes	complemented
536	#446	C₂²×C₈₃	1	4	yes	complemented
537	C₈×Q₈	C₂²×C₈₃	1	2	yes	complemented
538	#442	C₂²×C₈₃	1	4	yes	complemented
539	#441	C₂²×C₈₃	1	2	yes	complemented
540	#440	C₂²×C₈₃	1	4	yes	complemented
541	#440	C₂²×C₈₃	1	2	yes	complemented
542	C₄×Q₁₆	C₂²×C₈₃	1	2	yes	complemented
543	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	complemented
544	C₄×SD₁₆	C₂²×C₈₃	1	4	yes	complemented
545	C₄×D₈	C₂²×C₈₃	1	4	yes	complemented
546	#428	C₂²×C₈₃	1	1	yes	characteristic
547	#423	C₂²×C₈₃	1	2	yes	—
548	#423	C₂²×C₈₃	1	1	yes	characteristic
549	#419	C₂²×C₈₃	1	1	yes	characteristic
550	#418	C₂²×C₈₃	1	2	yes	—
551	#417	C₂²×C₈₃	1	2	yes	—
552	#417	C₂²×C₈₃	1	1	yes	characteristic
553	C₄×M₁₆	C₂²×C₈₃	1	1	yes	characteristic
554	C₄×M₁₆	C₂²×C₈₃	1	2	yes	—
555	C₂×#41	—	2	1	no	—
556	C₂×#41	C₂³×C₈₃	1	2	yes	—
557	C₂×#41	C₂³×C₈₃	1	1	yes	characteristic
558	C₂²×Q₈	D₄×C₈₃	1	1	yes	characteristic
559	C₂²×Q₈	C₂³×C₈₃	1	1	yes	characteristic
560	C₂²×D₄	—	2	1	no	—
561	C₂²×D₄	—	2	1	no	—
562	C₂²×D₄	C₂³×C₈₃	1	2	yes	—
563	C₂³×C₄	—	2	2	no	—
564	#137	—	2	4	no	—
565	#137	—	4	4	no	—
566	AGL(1,ℤ/8)	—	2	8	no	—
567	AGL(1,ℤ/8)	—	4	4	no	—
568	AGL(1,ℤ/8)	—	4	4	no	—
569	C₂×Q₁₆	C₂³×C₈₃	1	2	yes	—
570	C₂×Q₁₆	C₂³×C₈₃	1	4	yes	—
571	C₂×SD₁₆	C₂³×C₈₃	1	4	yes	—
572	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
573	C₂×SD₁₆	C₂³×C₈₃	1	4	yes	—
574	C₂×SD₁₆	C₂³×C₈₃	1	4	yes	—
575	C₂×SD₁₆	C₂³×C₈₃	1	4	yes	—
576	C₂×D₈	C₂³×C₈₃	1	4	yes	—
577	C₂×D₈	C₂³×C₈₃	1	4	yes	—
578	C₂×D₈	C₂³×C₈₃	1	4	yes	—
579	C₂×M₁₆	C₂³×C₈₃	1	1	yes	characteristic
580	C₂×M₁₆	C₂³×C₈₃	1	2	yes	—
581	C₂×M₁₆	C₂³×C₈₃	1	1	yes	characteristic
582	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
583	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
584	#127	—	2	1	no	—
585	#127	—	2	1	no	—
586	#127	C₂³×C₈₃	1	2	yes	—
587	#127	C₂³×C₈₃	1	2	yes	—
588	#127	C₂³×C₈₃	1	2	yes	—
589	#127	C₂³×C₈₃	1	1	yes	characteristic
590	#126	—	2	2	no	—
591	#126	—	2	2	no	—
592	#126	—	2	2	no	—
593	#125	—	2	1	no	—
594	#125	—	2	2	no	—
595	#124	—	2	2	no	—
596	#124	—	2	2	no	—
597	#124	—	2	4	no	—
598	#124	—	2	1	no	—
599	#124	—	2	2	no	—
600	#124	—	2	2	no	—
601	#124	—	2	2	no	—
602	#124	C₂³×C₈₃	1	4	yes	—
603	#124	C₂³×C₈₃	1	4	yes	—
604	#124	C₂³×C₈₃	1	2	yes	—
605	#124	C₂³×C₈₃	1	2	yes	—
606	#124	C₂³×C₈₃	1	2	yes	—
607	#123	—	2	4	no	—
608	#123	—	2	4	no	—
609	#123	—	2	4	no	—
610	#123	—	2	4	no	—
611	#123	—	2	2	no	—
612	#123	—	2	2	no	—
613	#123	—	2	2	no	—
614	C₂²⋊Q₈	—	2	1	no	—
615	C₂²⋊Q₈	—	2	2	no	—
616	#121	—	2	1	no	—
617	#121	—	2	2	no	—
618	#121	—	2	2	no	—
619	#121	—	2	1	no	—
620	#121	—	2	1	no	—
621	#121	—	2	2	no	—
622	C₄×Q₈	—	2	1	no	—
623	C₄×Q₈	—	2	1	no	—
624	C₄×Q₈	—	2	1	no	—
625	C₄×Q₈	D₄×C₈₃	1	1	yes	characteristic
626	C₄×Q₈	D₄×C₈₃	1	2	yes	—
627	C₄×Q₈	D₄×C₈₃	1	1	yes	characteristic
628	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
629	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
630	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
631	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
632	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
633	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
634	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
635	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
636	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
637	C₄×D₄	—	2	1	no	—
638	C₄×D₄	—	2	2	no	—
639	C₄×D₄	—	2	2	no	—
640	C₄×D₄	—	2	1	no	—
641	C₄×D₄	—	2	2	no	—
642	C₄×D₄	—	2	2	no	—
643	C₄×D₄	—	2	4	no	—
644	C₄×D₄	—	2	1	no	—
645	C₄×D₄	—	2	2	no	—
646	C₄×D₄	—	2	2	no	—
647	C₄×D₄	—	2	2	no	—
648	C₄×D₄	—	2	2	no	—
649	C₄×D₄	—	2	1	no	—
650	C₄×D₄	—	2	2	no	—
651	C₄×D₄	—	2	1	no	—
652	C₄×D₄	C₂³×C₈₃	1	4	yes	—
653	C₄×D₄	C₂³×C₈₃	1	4	yes	—
654	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
655	C₄×D₄	C₂³×C₈₃	1	2	yes	—
656	C₄×D₄	C₂³×C₈₃	1	2	yes	—
657	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
658	#117	—	2	1	no	—
659	#117	—	2	2	no	—
660	#117	—	2	2	no	—
661	#117	—	2	1	no	—
662	#117	C₂³×C₈₃	1	1	yes	characteristic
663	C₂×C₄⋊C₄	—	2	1	no	—
664	C₂×C₄⋊C₄	D₄×C₈₃	1	1	yes	characteristic
665	C₂×C₄⋊C₄	D₄×C₈₃	1	2	yes	—
666	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
667	C₂×C₂²⋊C₄	—	2	2	no	—
668	C₂×C₂²⋊C₄	—	2	2	no	—
669	C₂×C₂²⋊C₄	—	2	2	no	—
670	C₂×C₄²	—	2	1	no	—
671	C₂×C₄²	—	2	2	no	—
672	C₂×C₄²	—	2	1	no	—
673	C₂×C₄²	C₂³×C₈₃	1	2	yes	—
674	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
675	#107	C₂³×C₈₃	1	2	yes	—
676	#106	C₂³×C₈₃	1	2	yes	—
677	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
678	C₄⋊C₈	C₂³×C₈₃	1	4	yes	—
679	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
680	C₄⋊C₈	C₂³×C₈₃	1	4	yes	—
681	#103	C₂³×C₈₃	1	4	yes	—
682	#103	C₂³×C₈₃	1	2	yes	—
683	#103	C₂³×C₈₃	1	2	yes	—
684	#103	C₂³×C₈₃	1	2	yes	—
685	#102	C₂³×C₈₃	1	4	yes	—
686	#102	C₂³×C₈₃	1	2	yes	—
687	#102	C₂³×C₈₃	1	4	yes	—
688	#102	C₂³×C₈₃	1	4	yes	—
689	#97	C₂³×C₈₃	1	2	yes	—
690	#97	C₂³×C₈₃	1	4	yes	—
691	C₄×C₈	C₂³×C₈₃	1	4	yes	—
692	C₄×C₈	C₂³×C₈₃	1	2	yes	—
693	C₂⁴	—	2	2	no	—
694	#41	—	2	4	no	—
695	#41	—	2	2	no	—
696	#41	—	2	2	no	—
697	#41	—	2	4	no	—
698	#41	—	4	4	no	—
699	C₂×Q₈	—	2	1	no	—
700	C₂×Q₈	—	2	2	no	—
701	C₂×Q₈	—	2	2	no	—
702	C₂×Q₈	—	4	2	no	—
703	C₂×Q₈	C₂×D₄×C₈₃	1	1	yes	characteristic
704	C₂×Q₈	C₂×D₄×C₈₃	1	1	yes	characteristic
705	C₂×Q₈	C₂×D₄×C₈₃	1	2	yes	—
706	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
707	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
708	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
709	C₂×D₄	—	2	2	no	—
710	C₂×D₄	—	2	1	no	—
711	C₂×D₄	—	2	2	no	—
712	C₂×D₄	—	2	1	no	—
713	C₂×D₄	—	2	2	no	—
714	C₂×D₄	—	2	2	no	—
715	C₂×D₄	—	2	2	no	—
716	C₂×D₄	—	2	2	no	—
717	C₂×D₄	—	2	1	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	4	no	—
721	C₂×D₄	—	2	4	no	—
722	C₂×D₄	—	4	4	no	—
723	C₂×D₄	—	8	2	no	—
724	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
725	C₂×D₄	C₂⁴×C₈₃	1	1	yes	characteristic
726	C₂×D₄	C₂⁴×C₈₃	1	4	yes	—
727	C₂²×C₄	—	2	1	no	—
728	C₂²×C₄	—	2	1	no	—
729	C₂²×C₄	—	2	2	no	—
730	C₂²×C₄	—	2	1	no	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	2	1	no	—
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	2	1	no	—
735	C₂²×C₄	—	2	4	no	—
736	C₂²×C₄	—	2	4	no	—
737	C₂²×C₄	—	8	4	no	—
738	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
739	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
740	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
741	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
742	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
743	Q₁₆	—	2	4	no	—
744	Q₁₆	—	4	4	no	—
745	SD₁₆	—	2	8	no	—
746	SD₁₆	—	2	4	no	—
747	SD₁₆	—	4	4	no	—
748	SD₁₆	—	4	4	no	—
749	SD₁₆	—	4	4	no	—
750	D₈	—	2	8	no	—
751	D₈	—	4	4	no	—
752	D₈	—	4	4	no	—
753	M₁₆	—	2	2	no	—
754	M₁₆	—	2	4	no	—
755	M₁₆	#41×C₈₃	1	4	yes	complemented
756	C₂×C₈	C₂⁴×C₈₃	1	4	yes	—
757	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
758	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	1	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	1	no	—
764	C₄⋊C₄	—	2	1	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	2	no	—
767	C₄⋊C₄	—	2	1	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	1	no	—
770	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
771	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
772	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
773	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
774	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
775	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
776	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
777	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
778	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
779	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
780	C₂²⋊C₄	—	2	1	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	2	4	no	—
783	C₂²⋊C₄	—	2	4	no	—
784	C₂²⋊C₄	—	2	4	no	—
785	C₂²⋊C₄	—	2	4	no	—
786	C₂²⋊C₄	—	2	4	no	—
787	C₂²⋊C₄	—	2	2	no	—
788	C₂²⋊C₄	—	2	2	no	—
789	C₂²⋊C₄	—	2	2	no	—
790	C₂²⋊C₄	—	2	2	no	—
791	C₂²⋊C₄	—	2	1	no	—
792	C₂²⋊C₄	—	2	1	no	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	2	no	—
795	C₂²⋊C₄	—	2	2	no	—
796	C₂²⋊C₄	—	2	2	no	—
797	C₄²	—	2	1	no	—
798	C₄²	—	2	2	no	—
799	C₄²	—	2	1	no	—
800	C₄²	—	2	2	no	—
801	C₄²	—	2	2	no	—
802	C₄²	—	2	2	no	—
803	C₄²	—	2	1	no	—
804	C₄²	C₂×D₄×C₈₃	1	2	yes	—
805	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
806	C₄²	C₂×D₄×C₈₃	1	2	yes	—
807	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
808	C₄²	C₂⁴×C₈₃	1	2	yes	—
809	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
810	C₄²	C₂⁴×C₈₃	1	2	yes	—
811	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
812	C₂³	—	2	2	no	—
813	C₂³	—	2	1	no	—
814	C₂³	—	2	4	no	—
815	C₂³	—	4	4	no	—
816	C₂³	—	4	4	no	—
817	C₂³	—	4	4	no	—
818	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
819	Q₈	—	2	2	no	—
820	Q₈	—	2	2	no	—
821	Q₈	—	2	2	no	—
822	Q₈	—	2	2	no	—
823	Q₈	—	2	1	no	—
824	Q₈	—	2	1	no	—
825	Q₈	—	2	2	no	—
826	Q₈	—	2	2	no	—
827	Q₈	—	4	2	no	—
828	Q₈	—	4	2	no	—
829	D₄	—	2	2	no	—
830	D₄	—	2	4	no	—
831	D₄	—	2	1	no	—
832	D₄	—	2	1	no	—
833	D₄	—	2	4	no	—
834	D₄	—	2	2	no	—
835	D₄	—	4	4	no	—
836	D₄	—	4	4	no	—
837	D₄	—	4	4	no	—
838	D₄	—	4	2	no	—
839	D₄	—	4	4	no	—
840	D₄	—	4	4	no	—
841	D₄	—	4	2	no	—
842	D₄	—	8	2	no	—
843	D₄	—	8	2	no	—
844	D₄	—	8	2	no	—
845	D₄	—	8	1	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	4	2	no	—
854	C₂×C₄	—	4	1	no	—
855	C₂×C₄	—	4	2	no	—
856	C₂×C₄	—	4	4	no	—
857	C₂×C₄	—	4	2	no	—
858	C₂×C₄	—	4	2	no	—
859	C₂×C₄	—	4	4	no	—
860	C₂×C₄	—	4	2	no	—
861	C₂×C₄	—	4	2	no	—
862	C₂×C₄	—	8	4	no	—
863	C₂×C₄	—	8	4	no	—
864	C₂×C₄	—	8	2	no	—
865	C₂×C₄	—	8	1	no	—
866	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
867	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
868	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
869	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
870	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
871	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
872	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
873	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
874	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
875	C₂×C₄	C₂×#41×C₈₃	1	2	yes	—
876	C₂×C₄	H(5,𝔽₂)×C₈₃	1	2	yes	—
877	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
878	C₈	—	2	2	no	—
879	C₈	—	2	4	no	—
880	C₈	C₂×#41×C₈₃	1	4	yes	—
881	C₂²	—	2	1	no	—
882	C₂²	—	2	1	no	—
883	C₂²	—	4	2	no	—
884	C₂²	—	4	1	no	—
885	C₂²	—	4	4	no	—
886	C₂²	—	4	4	no	—
887	C₂²	—	4	2	no	—
888	C₂²	—	4	1	no	—
889	C₂²	—	4	2	no	—
890	C₂²	—	4	1	no	—
891	C₂²	—	4	4	no	—
892	C₂²	—	8	8	no	—
893	C₂²	#550×C₈₃	1	2	yes	—
894	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
895	C₄	—	2	1	no	—
896	C₄	—	2	2	no	—
897	C₄	—	2	2	no	—
898	C₄	—	2	2	no	—
899	C₄	—	2	2	no	—
900	C₄	—	2	1	no	—
901	C₄	—	2	1	no	—
902	C₄	—	4	1	no	—
903	C₄	—	4	2	no	—
904	C₄	—	4	1	no	—
905	C₄	—	4	2	no	—
906	C₄	—	4	1	no	—
907	C₄	—	4	2	no	—
908	C₄	#550×C₈₃	1	2	yes	—
909	C₄	#575×C₈₃	1	2	yes	—
910	C₄	C₂²×#41×C₈₃	1	1	yes	characteristic
911	C₄	C₂×H(5,𝔽₂)×C₈₃	1	1	yes	characteristic
912	C₂	—	2	2	no	—
913	C₂	—	8	4	no	—
914	C₂	—	8	2	no	—
915	C₂	—	8	1	no	—
916	C₂	C₂×#550×C₈₃	1	1	yes	characteristic
917	C₂	C₂×#575×C₈₃	1	1	yes	characteristic
918	C₂	C₈₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₃ ◁ C₂×C₄×Q₈×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₃×#3480	C₂	semidirect
2. C₂×#559×C₈₃	C₂	semidirect
3. C₈₃×#3403	C₂	semidirect
4. C₈₃×#3401	C₂	semidirect
5. C₈₃×#3400	C₂	semidirect
6. C₈₃×#3399	C₂	semidirect
7. C₈₃×#3396	C₂	semidirect
8. C₈₃×#3394	C₂	semidirect
9. C₈₃×#3153	C₂	semidirect
10. C₈₃×#3151	C₂	semidirect
11. C₈₃×#3040	C₂	semidirect
12. C₈₃×#3038	C₂	semidirect
13. C₈₃×#3037	C₂	semidirect
14. C₈₃×#3036	C₂	semidirect
15. Q₈×M₁₆×C₈₃	C₂	semidirect
16. C₄×#137×C₈₃	C₂	semidirect
17. C₄×AGL(1,ℤ/8)×C₈₃	C₂	semidirect
29. #559×C₈₃	C₂²	semidirect
30. #559×C₈₃	C₂²	semidirect
31. #557×C₈₃	C₂²	semidirect
32. #556×C₈₃	C₂²	semidirect
33. #556×C₈₃	C₂²	semidirect
36. #550×C₈₃	C₂²	semidirect
53. #497×C₈₃	C₂²	semidirect
55. #496×C₈₃	C₂²	semidirect
56. #495×C₈₃	C₂²	semidirect
57. #495×C₈₃	C₂²	semidirect
60. #464×C₈₃	C₂²	semidirect
61. #464×C₈₃	C₂²	semidirect
62. #464×C₈₃	C₂²	semidirect
63. #463×C₈₃	C₂²	semidirect
64. #463×C₈₃	C₂²	semidirect
65. #463×C₈₃	C₂²	semidirect
66. #463×C₈₃	C₂²	semidirect
67. #462×C₈₃	C₂²	semidirect
68. #461×C₈₃	C₂²	semidirect
71. #460×C₈₃	C₂²	semidirect
74. #459×C₈₃	C₂²	semidirect
75. #446×C₈₃	C₂²	semidirect
76. #446×C₈₃	C₂²	semidirect
77. C₈×Q₈×C₈₃	C₂²	semidirect
78. #442×C₈₃	C₂²	semidirect
79. #441×C₈₃	C₂²	semidirect
80. #440×C₈₃	C₂²	semidirect
81. #440×C₈₃	C₂²	semidirect
82. C₄×Q₁₆×C₈₃	C₂²	semidirect
83. C₄×SD₁₆×C₈₃	C₂²	semidirect
84. C₄×SD₁₆×C₈₃	C₂²	semidirect
85. C₄×D₈×C₈₃	C₂²	semidirect
295. M₁₆×C₈₃	#41	semidirect
452. #61405	C₈₃	direct (N × H)
460. #3480	C₂×C₈₃	semidirect
461. C₂×#559	C₂×C₈₃	semidirect
462. #3403	C₂×C₈₃	semidirect
463. #3401	C₂×C₈₃	semidirect
464. #3400	C₂×C₈₃	semidirect
465. #3399	C₂×C₈₃	semidirect
466. #3396	C₂×C₈₃	semidirect
467. #3394	C₂×C₈₃	semidirect
468. #3153	C₂×C₈₃	semidirect
469. #3151	C₂×C₈₃	semidirect
470. #3040	C₂×C₈₃	semidirect
471. #3038	C₂×C₈₃	semidirect
472. #3037	C₂×C₈₃	semidirect
473. #3036	C₂×C₈₃	semidirect
474. Q₈×M₁₆	C₂×C₈₃	semidirect
475. C₄×#137	C₂×C₈₃	semidirect
476. C₄×AGL(1,ℤ/8)	C₂×C₈₃	semidirect
477. C₈₃	#61405	direct (N × H)
489. #559	C₂²×C₈₃	semidirect
490. #559	C₂²×C₈₃	semidirect
491. #557	C₂²×C₈₃	semidirect
492. #556	C₂²×C₈₃	semidirect
493. #556	C₂²×C₈₃	semidirect
496. #550	C₂²×C₈₃	semidirect
513. #497	C₂²×C₈₃	semidirect
515. #496	C₂²×C₈₃	semidirect
516. #495	C₂²×C₈₃	semidirect
517. #495	C₂²×C₈₃	semidirect
520. #464	C₂²×C₈₃	semidirect
521. #464	C₂²×C₈₃	semidirect
522. #464	C₂²×C₈₃	semidirect
523. #463	C₂²×C₈₃	semidirect
524. #463	C₂²×C₈₃	semidirect
525. #463	C₂²×C₈₃	semidirect
526. #463	C₂²×C₈₃	semidirect
527. #462	C₂²×C₈₃	semidirect
528. #461	C₂²×C₈₃	semidirect
531. #460	C₂²×C₈₃	semidirect
534. #459	C₂²×C₈₃	semidirect
535. #446	C₂²×C₈₃	semidirect
536. #446	C₂²×C₈₃	semidirect
537. C₈×Q₈	C₂²×C₈₃	semidirect
538. #442	C₂²×C₈₃	semidirect
539. #441	C₂²×C₈₃	semidirect
540. #440	C₂²×C₈₃	semidirect
541. #440	C₂²×C₈₃	semidirect
542. C₄×Q₁₆	C₂²×C₈₃	semidirect
543. C₄×SD₁₆	C₂²×C₈₃	semidirect
544. C₄×SD₁₆	C₂²×C₈₃	semidirect
545. C₄×D₈	C₂²×C₈₃	semidirect
755. M₁₆	#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×#3480	2
C₂×#559×C₈₃	2
C₈₃×#3403	2
C₈₃×#3401	2
C₈₃×#3400	2
C₈₃×#3399	2
C₈₃×#3396	2
C₈₃×#3394	2
C₈₃×#3153	2
C₈₃×#3151	2
C₈₃×#3040	2
C₈₃×#3038	2
C₈₃×#3037	2
C₈₃×#3036	2
Q₈×M₁₆×C₈₃	2
C₄×#137×C₈₃	2
C₄×AGL(1,ℤ/8)×C₈₃	2
#61405	83

Subgroups — C83×#61405 #35289229

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#61405 #35289229