Subgroups — C₈₃×#61730 #35289554

Order 21248.

1752 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3520	C₂	1	1	yes	maximal, characteristic
2	C₂×#556×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₃×#3353	C₂	1	2	yes	maximal, complemented
4	C₈₃×#3349	C₂	1	4	yes	maximal, complemented
5	C₈₃×#3342	C₂	1	2	yes	maximal, complemented
6	C₈₃×#3328	C₂	1	2	yes	maximal, complemented
7	C₈₃×#3313	C₂	1	4	yes	maximal, complemented
8	C₈₃×#3302	C₂	1	2	yes	maximal, complemented
9	C₈₃×#3239	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₃×#3230	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₃×#3196	C₂	1	2	yes	maximal, complemented
12	C₈₃×#3189	C₂	1	2	yes	maximal, complemented
13	C₈₃×#3113	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₃×#3108	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#3095	C₂	1	2	yes	maximal, complemented
16	C₈₃×#3091	C₂	1	2	yes	maximal, complemented
17	C₈₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
18	#556×C₈₃	—	2	1	no	—
19	#556×C₈₃	—	2	2	no	—
20	#556×C₈₃	—	2	1	no	—
21	#556×C₈₃	C₂²	1	2	yes	—
22	#556×C₈₃	C₂²	1	4	yes	—
23	#556×C₈₃	C₂²	1	2	yes	—
24	#556×C₈₃	C₂²	1	1	yes	characteristic
25	#554×C₈₃	—	2	1	no	—
26	#552×C₈₃	C₂²	1	2	yes	—
27	#551×C₈₃	—	2	2	no	—
28	D₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
29	#548×C₈₃	C₂²	1	2	yes	—
30	#547×C₈₃	C₂²	1	1	yes	characteristic
31	#547×C₈₃	C₂²	1	1	yes	characteristic
32	#546×C₈₃	—	2	1	no	—
33	#542×C₈₃	—	2	1	no	—
34	#539×C₈₃	—	2	2	no	—
35	#533×C₈₃	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
37	#529×C₈₃	C₂²	1	1	yes	characteristic
38	C₂×#126×C₈₃	—	2	2	no	—
39	C₂×#124×C₈₃	—	2	1	no	—
40	#525×C₈₃	C₂²	1	2	yes	—
41	C₂×C₂²⋊Q₈×C₈₃	C₂²	1	2	yes	—
42	C₂×C₂²⋊Q₈×C₈₃	C₂²	1	2	yes	—
43	#520×C₈₃	—	2	1	no	—
44	C₂×C₄×Q₈×C₈₃	—	2	1	no	—
45	C₂×C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₈₃	C₂²	1	1	yes	characteristic
47	C₂×#117×C₈₃	C₂²	1	2	yes	—
48	#501×C₈₃	C₂²	1	2	yes	complemented
49	#500×C₈₃	C₂²	1	2	yes	complemented
50	#489×C₈₃	C₂²	1	2	yes	complemented
51	#487×C₈₃	C₂²	1	2	yes	complemented
52	#485×C₈₃	C₂²	1	4	yes	complemented
53	#485×C₈₃	C₂²	1	4	yes	complemented
54	#485×C₈₃	C₂²	1	4	yes	complemented
55	#485×C₈₃	C₂²	1	4	yes	complemented
56	#484×C₈₃	C₂²	1	2	yes	—
57	#484×C₈₃	C₂²	1	2	yes	—
58	#484×C₈₃	C₂²	1	2	yes	—
59	#484×C₈₃	C₂²	1	4	yes	complemented
60	#483×C₈₃	C₂²	1	2	yes	—
61	#483×C₈₃	C₂²	1	1	yes	characteristic
62	#482×C₈₃	C₂²	1	4	yes	complemented
63	#481×C₈₃	C₂²	1	2	yes	—
64	#480×C₈₃	C₂²	1	1	yes	characteristic
65	#479×C₈₃	C₂²	1	2	yes	complemented
66	#477×C₈₃	C₂²	1	4	yes	complemented
67	#475×C₈₃	C₂²	1	2	yes	complemented
68	#475×C₈₃	C₂²	1	2	yes	complemented
69	#474×C₈₃	C₂²	1	2	yes	complemented
70	#470×C₈₃	C₂²	1	4	yes	complemented
71	#468×C₈₃	C₂²	1	4	yes	complemented
72	#467×C₈₃	C₂²	1	4	yes	complemented
73	#467×C₈₃	C₂²	1	4	yes	complemented
74	#464×C₈₃	C₂²	1	2	yes	complemented
75	#462×C₈₃	C₂²	1	2	yes	complemented
76	#452×C₈₃	C₂²	1	4	yes	complemented
77	#451×C₈₃	C₂²	1	1	yes	characteristic
78	#451×C₈₃	C₂²	1	2	yes	—
79	#451×C₈₃	C₂²	1	4	yes	complemented
80	#448×C₈₃	C₂²	1	1	yes	characteristic
81	#441×C₈₃	C₂²	1	4	yes	complemented
82	C₄×Q₁₆×C₈₃	C₂²	1	2	yes	complemented
83	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	complemented
84	#436×C₈₃	C₂²	1	2	yes	—
85	#435×C₈₃	C₂²	1	4	yes	—
86	C₈×D₄×C₈₃	C₂²	1	2	yes	—
87	#432×C₈₃	C₂²	1	1	yes	characteristic
88	#431×C₈₃	C₂²	1	1	yes	characteristic
89	#428×C₈₃	C₂²	1	4	yes	complemented
90	#427×C₈₃	C₂²	1	4	yes	complemented
91	#419×C₈₃	C₂²	1	4	yes	complemented
92	#416×C₈₃	C₂²	1	4	yes	complemented
93	#407×C₈₃	C₂²	1	2	yes	—
94	C₂×C₂²⋊C₈×C₈₃	C₂²	1	2	yes	—
95	C₂×#41×C₈₃	—	2	1	no	—
96	C₂×#41×C₈₃	C₂³	1	2	yes	—
97	C₂²×Q₈×C₈₃	—	2	1	no	—
98	C₂²×Q₈×C₈₃	C₂³	1	1	yes	characteristic
99	C₂²×Q₈×C₈₃	C₂³	1	2	yes	—
100	C₂²×D₄×C₈₃	D₄	1	1	yes	characteristic
101	C₂³×C₄×C₈₃	C₂³	1	2	yes	—
102	C₂×Q₁₆×C₈₃	C₂³	1	2	yes	—
103	C₂×Q₁₆×C₈₃	C₂³	1	4	yes	—
104	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
105	C₂×M₁₆×C₈₃	C₂³	1	4	yes	—
106	C₂²×C₈×C₈₃	C₂³	1	4	yes	—
107	C₄⋊Q₈×C₈₃	—	2	1	no	—
108	C₄⋊Q₈×C₈₃	—	2	1	no	—
109	C₄⋊Q₈×C₈₃	—	2	1	no	—
110	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
111	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
112	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
113	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
114	#126×C₈₃	—	2	4	no	—
115	#126×C₈₃	—	2	4	no	—
116	#126×C₈₃	—	2	4	no	—
117	#126×C₈₃	—	2	4	no	—
118	#126×C₈₃	—	2	2	no	—
119	#126×C₈₃	—	2	2	no	—
120	#126×C₈₃	—	2	1	no	—
121	#125×C₈₃	—	2	2	no	—
122	#125×C₈₃	—	2	1	no	—
123	#125×C₈₃	C₂³	1	1	yes	characteristic
124	#124×C₈₃	—	2	2	no	—
125	#124×C₈₃	—	2	2	no	—
126	#124×C₈₃	—	2	4	no	—
127	#124×C₈₃	—	2	1	no	—
128	#124×C₈₃	—	2	2	no	—
129	#124×C₈₃	C₂³	1	1	yes	characteristic
130	#123×C₈₃	—	2	2	no	—
131	#123×C₈₃	—	2	2	no	—
132	#123×C₈₃	—	2	1	no	—
133	#123×C₈₃	—	2	2	no	—
134	#123×C₈₃	—	2	2	no	—
135	C₂²⋊Q₈×C₈₃	—	2	2	no	—
136	C₂²⋊Q₈×C₈₃	—	2	2	no	—
137	C₂²⋊Q₈×C₈₃	—	2	2	no	—
138	C₂²⋊Q₈×C₈₃	—	2	2	no	—
139	C₂²⋊Q₈×C₈₃	—	2	1	no	—
140	C₂²⋊Q₈×C₈₃	—	2	2	no	—
141	C₂²⋊Q₈×C₈₃	—	2	1	no	—
142	C₂²⋊Q₈×C₈₃	—	2	2	no	—
143	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
144	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
145	C₂²⋊Q₈×C₈₃	C₂³	1	4	yes	—
146	C₂²⋊Q₈×C₈₃	C₂³	1	4	yes	—
147	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
148	C₂²⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
149	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
150	#121×C₈₃	—	2	2	no	—
151	#121×C₈₃	—	2	1	no	—
152	#121×C₈₃	C₂³	1	2	yes	—
153	#121×C₈₃	C₂³	1	1	yes	characteristic
154	#120×C₈₃	—	2	2	no	—
155	C₄×Q₈×C₈₃	—	2	2	no	—
156	C₄×Q₈×C₈₃	—	2	4	no	—
157	C₄×Q₈×C₈₃	—	2	2	no	—
158	C₄×Q₈×C₈₃	—	2	1	no	—
159	C₄×Q₈×C₈₃	—	2	1	no	—
160	C₄×Q₈×C₈₃	—	2	1	no	—
161	C₄×Q₈×C₈₃	—	2	1	no	—
162	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
163	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
164	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
165	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
166	C₄×D₄×C₈₃	—	2	1	no	—
167	C₄×D₄×C₈₃	—	2	2	no	—
168	C₄×D₄×C₈₃	—	2	2	no	—
169	C₄×D₄×C₈₃	—	2	1	no	—
170	C₄×D₄×C₈₃	—	2	2	no	—
171	C₄×D₄×C₈₃	D₄	1	1	yes	characteristic
172	C₄×D₄×C₈₃	D₄	1	2	yes	—
173	C₄×D₄×C₈₃	D₄	1	1	yes	characteristic
174	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
175	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
176	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
177	C₄×D₄×C₈₃	C₂³	1	2	yes	—
178	#117×C₈₃	—	2	2	no	—
179	#117×C₈₃	—	2	2	no	—
180	#117×C₈₃	—	2	1	no	—
181	#117×C₈₃	—	2	2	no	—
182	#117×C₈₃	—	2	1	no	—
183	#117×C₈₃	C₂³	1	4	yes	—
184	#117×C₈₃	C₂³	1	4	yes	—
185	#117×C₈₃	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
187	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
188	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
189	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
190	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
191	C₂×C₄⋊C₄×C₈₃	D₄	1	1	yes	characteristic
192	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
193	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
196	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
197	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
198	C₂×C₂²⋊C₄×C₈₃	D₄	1	2	yes	—
199	C₂×C₄²×C₈₃	—	2	2	no	—
200	C₂×C₄²×C₈₃	—	2	1	no	—
201	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
202	#107×C₈₃	C₂³	1	4	yes	—
203	#107×C₈₃	C₂³	1	4	yes	—
204	#107×C₈₃	C₂³	1	4	yes	—
205	#107×C₈₃	C₂³	1	2	yes	—
206	#106×C₈₃	C₂³	1	4	yes	—
207	#106×C₈₃	C₂³	1	4	yes	—
208	#106×C₈₃	C₂³	1	2	yes	—
209	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
210	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
211	#103×C₈₃	C₂³	1	2	yes	—
212	#103×C₈₃	C₂³	1	2	yes	—
213	#103×C₈₃	C₂³	1	4	yes	—
214	#103×C₈₃	C₂³	1	4	yes	—
215	#103×C₈₃	C₂³	1	4	yes	—
216	#103×C₈₃	C₂³	1	2	yes	—
217	#103×C₈₃	C₂³	1	4	yes	—
218	#103×C₈₃	C₂³	1	4	yes	—
219	#102×C₈₃	C₂³	1	2	yes	—
220	#102×C₈₃	C₂³	1	4	yes	—
221	C₂²⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
222	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
223	C₂²⋊C₈×C₈₃	C₂³	1	4	yes	—
224	C₂²⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
225	C₂²⋊C₈×C₈₃	C₂³	1	4	yes	—
226	#97×C₈₃	C₂³	1	2	yes	—
227	C₄×C₈×C₈₃	C₂³	1	2	yes	—
228	C₂⁴×C₈₃	C₂×D₄	1	2	yes	—
229	#41×C₈₃	—	4	4	no	—
230	#41×C₈₃	—	4	4	no	—
231	C₂×Q₈×C₈₃	—	2	1	no	—
232	C₂×Q₈×C₈₃	—	2	1	no	—
233	C₂×Q₈×C₈₃	—	2	2	no	—
234	C₂×Q₈×C₈₃	—	2	2	no	—
235	C₂×Q₈×C₈₃	—	2	2	no	—
236	C₂×Q₈×C₈₃	—	4	2	no	—
237	C₂×Q₈×C₈₃	—	4	4	no	—
238	C₂×Q₈×C₈₃	—	4	4	no	—
239	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
240	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
241	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
242	C₂×D₄×C₈₃	—	2	1	no	—
243	C₂×D₄×C₈₃	—	2	2	no	—
244	C₂×D₄×C₈₃	—	2	2	no	—
245	C₂×D₄×C₈₃	—	4	2	no	—
246	C₂×D₄×C₈₃	C₂×D₄	1	1	yes	characteristic
247	C₂×D₄×C₈₃	C₂×D₄	1	1	yes	characteristic
248	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
249	C₂×D₄×C₈₃	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₈₃	—	2	1	no	—
251	C₂²×C₄×C₈₃	—	2	1	no	—
252	C₂²×C₄×C₈₃	—	2	2	no	—
253	C₂²×C₄×C₈₃	—	2	2	no	—
254	C₂²×C₄×C₈₃	—	2	2	no	—
255	C₂²×C₄×C₈₃	—	2	1	no	—
256	C₂²×C₄×C₈₃	—	2	2	no	—
257	C₂²×C₄×C₈₃	—	4	4	no	—
258	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
261	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
262	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
263	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
266	Q₁₆×C₈₃	—	4	2	no	—
267	Q₁₆×C₈₃	—	4	4	no	—
268	SD₁₆×C₈₃	—	4	2	no	—
269	M₁₆×C₈₃	—	4	4	no	—
270	C₂×C₈×C₈₃	—	4	4	no	—
271	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
272	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
273	C₂×C₈×C₈₃	C₂⁴	1	4	yes	—
274	C₄⋊C₄×C₈₃	—	2	1	no	—
275	C₄⋊C₄×C₈₃	—	2	2	no	—
276	C₄⋊C₄×C₈₃	—	2	1	no	—
277	C₄⋊C₄×C₈₃	—	2	2	no	—
278	C₄⋊C₄×C₈₃	—	2	2	no	—
279	C₄⋊C₄×C₈₃	—	2	4	no	—
280	C₄⋊C₄×C₈₃	—	2	4	no	—
281	C₄⋊C₄×C₈₃	—	2	2	no	—
282	C₄⋊C₄×C₈₃	—	2	2	no	—
283	C₄⋊C₄×C₈₃	—	2	2	no	—
284	C₄⋊C₄×C₈₃	—	2	2	no	—
285	C₄⋊C₄×C₈₃	—	2	1	no	—
286	C₄⋊C₄×C₈₃	—	2	2	no	—
287	C₄⋊C₄×C₈₃	—	2	2	no	—
288	C₄⋊C₄×C₈₃	—	2	1	no	—
289	C₄⋊C₄×C₈₃	—	2	1	no	—
290	C₄⋊C₄×C₈₃	—	2	1	no	—
291	C₄⋊C₄×C₈₃	—	2	2	no	—
292	C₄⋊C₄×C₈₃	—	2	1	no	—
293	C₄⋊C₄×C₈₃	—	2	2	no	—
294	C₄⋊C₄×C₈₃	—	2	1	no	—
295	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
296	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
297	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
298	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
299	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
300	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
301	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
302	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
303	C₂²⋊C₄×C₈₃	—	2	1	no	—
304	C₂²⋊C₄×C₈₃	—	2	4	no	—
305	C₂²⋊C₄×C₈₃	—	2	4	no	—
306	C₂²⋊C₄×C₈₃	—	2	2	no	—
307	C₂²⋊C₄×C₈₃	—	2	2	no	—
308	C₂²⋊C₄×C₈₃	—	2	2	no	—
309	C₂²⋊C₄×C₈₃	—	2	4	no	—
310	C₂²⋊C₄×C₈₃	—	2	4	no	—
311	C₂²⋊C₄×C₈₃	—	2	2	no	—
312	C₂²⋊C₄×C₈₃	—	2	2	no	—
313	C₂²⋊C₄×C₈₃	—	2	1	no	—
314	C₂²⋊C₄×C₈₃	—	2	1	no	—
315	C₂²⋊C₄×C₈₃	—	2	1	no	—
316	C₂²⋊C₄×C₈₃	—	2	2	no	—
317	C₂²⋊C₄×C₈₃	—	2	1	no	—
318	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
319	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
320	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
321	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
322	C₄²×C₈₃	—	2	4	no	—
323	C₄²×C₈₃	—	2	4	no	—
324	C₄²×C₈₃	—	2	2	no	—
325	C₄²×C₈₃	—	2	2	no	—
326	C₄²×C₈₃	—	2	2	no	—
327	C₄²×C₈₃	—	2	2	no	—
328	C₄²×C₈₃	—	2	1	no	—
329	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
332	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
333	C₂³×C₈₃	—	2	4	no	—
334	C₂³×C₈₃	—	2	1	no	—
335	C₂³×C₈₃	—	4	2	no	—
336	C₂³×C₈₃	—	4	2	no	—
337	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
338	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
339	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
340	Q₈×C₈₃	—	2	2	no	—
341	Q₈×C₈₃	—	2	2	no	—
342	Q₈×C₈₃	—	2	2	no	—
343	Q₈×C₈₃	—	2	4	no	—
344	Q₈×C₈₃	—	4	2	no	—
345	Q₈×C₈₃	—	4	4	no	—
346	Q₈×C₈₃	—	4	4	no	—
347	Q₈×C₈₃	—	4	2	no	—
348	Q₈×C₈₃	—	8	2	no	—
349	D₄×C₈₃	—	2	2	no	—
350	D₄×C₈₃	—	2	2	no	—
351	D₄×C₈₃	—	2	2	no	—
352	D₄×C₈₃	—	4	2	no	—
353	D₄×C₈₃	—	4	4	no	—
354	D₄×C₈₃	—	4	2	no	—
355	D₄×C₈₃	—	8	2	no	—
356	C₂×C₄×C₈₃	—	2	2	no	—
357	C₂×C₄×C₈₃	—	2	2	no	—
358	C₂×C₄×C₈₃	—	2	4	no	—
359	C₂×C₄×C₈₃	—	2	4	no	—
360	C₂×C₄×C₈₃	—	2	2	no	—
361	C₂×C₄×C₈₃	—	2	2	no	—
362	C₂×C₄×C₈₃	—	2	1	no	—
363	C₂×C₄×C₈₃	—	2	2	no	—
364	C₂×C₄×C₈₃	—	2	2	no	—
365	C₂×C₄×C₈₃	—	2	4	no	—
366	C₂×C₄×C₈₃	—	2	1	no	—
367	C₂×C₄×C₈₃	—	2	2	no	—
368	C₂×C₄×C₈₃	—	2	1	no	—
369	C₂×C₄×C₈₃	—	4	2	no	—
370	C₂×C₄×C₈₃	—	4	2	no	—
371	C₂×C₄×C₈₃	—	4	2	no	—
372	C₂×C₄×C₈₃	—	4	2	no	—
373	C₂×C₄×C₈₃	—	4	4	no	—
374	C₂×C₄×C₈₃	—	4	4	no	—
375	C₂×C₄×C₈₃	—	4	2	no	—
376	C₂×C₄×C₈₃	—	4	2	no	—
377	C₂×C₄×C₈₃	—	8	2	no	—
378	C₂×C₄×C₈₃	—	8	2	no	—
379	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
380	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
383	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
387	C₈×C₈₃	—	2	2	no	—
388	C₈×C₈₃	—	2	4	no	—
389	C₈×C₈₃	—	2	2	no	—
390	C₂²×C₈₃	—	2	1	no	—
391	C₂²×C₈₃	—	2	1	no	—
392	C₂²×C₈₃	—	2	2	no	—
393	C₂²×C₈₃	—	2	2	no	—
394	C₂²×C₈₃	—	2	2	no	—
395	C₂²×C₈₃	—	2	2	no	—
396	C₂²×C₈₃	—	2	2	no	—
397	C₂²×C₈₃	—	2	2	no	—
398	C₂²×C₈₃	—	4	1	no	—
399	C₂²×C₈₃	—	4	1	no	—
400	C₂²×C₈₃	—	4	1	no	—
401	C₂²×C₈₃	—	8	4	no	—
402	C₂²×C₈₃	#578	1	2	yes	—
403	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
404	C₄×C₈₃	—	2	1	no	—
405	C₄×C₈₃	—	2	2	no	—
406	C₄×C₈₃	—	2	2	no	—
407	C₄×C₈₃	—	2	1	no	—
408	C₄×C₈₃	—	2	1	no	—
409	C₄×C₈₃	—	2	1	no	—
410	C₄×C₈₃	—	4	2	no	—
411	C₄×C₈₃	—	4	2	no	—
412	C₄×C₈₃	—	4	1	no	—
413	C₄×C₈₃	—	4	1	no	—
414	C₄×C₈₃	—	4	2	no	—
415	C₄×C₈₃	—	4	4	no	—
416	C₄×C₈₃	—	4	2	no	—
417	C₄×C₈₃	—	4	1	no	—
418	C₄×C₈₃	#575	1	2	yes	—
419	C₄×C₈₃	#585	1	2	yes	—
420	#61730	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
421	C₂×C₈₃	—	2	2	no	—
422	C₂×C₈₃	—	4	2	no	—
423	C₂×C₈₃	—	4	2	no	—
424	C₂×C₈₃	—	8	1	no	—
425	C₂×C₈₃	#3485	1	1	yes	characteristic
426	C₂×C₈₃	C₂×#575	1	1	yes	characteristic
427	C₂×C₈₃	C₂×#578	1	1	yes	characteristic
428	#3520	C₂×C₈₃	1	1	yes	characteristic
429	C₂×#556	C₂×C₈₃	1	1	yes	characteristic, complemented
430	#3353	C₂×C₈₃	1	2	yes	complemented
431	#3349	C₂×C₈₃	1	4	yes	complemented
432	#3342	C₂×C₈₃	1	2	yes	complemented
433	#3328	C₂×C₈₃	1	2	yes	complemented
434	#3313	C₂×C₈₃	1	4	yes	complemented
435	#3302	C₂×C₈₃	1	2	yes	complemented
436	#3239	C₂×C₈₃	1	1	yes	characteristic, complemented
437	#3230	C₂×C₈₃	1	1	yes	characteristic, complemented
438	#3196	C₂×C₈₃	1	2	yes	complemented
439	#3189	C₂×C₈₃	1	2	yes	complemented
440	#3113	C₂×C₈₃	1	1	yes	characteristic, complemented
441	#3108	C₂×C₈₃	1	1	yes	characteristic, complemented
442	#3095	C₂×C₈₃	1	2	yes	complemented
443	#3091	C₂×C₈₃	1	2	yes	complemented
444	#2974	C₂×C₈₃	1	1	yes	characteristic, complemented
445	C₈₃	#61730	1	1	yes	characteristic, direct product factor, Sylow
446	#556	—	2	1	no	—
447	#556	—	2	2	no	—
448	#556	—	2	1	no	—
449	#556	C₂²×C₈₃	1	2	yes	—
450	#556	C₂²×C₈₃	1	1	yes	characteristic
451	#556	C₂²×C₈₃	1	2	yes	—
452	#556	C₂²×C₈₃	1	4	yes	—
453	#554	—	2	1	no	—
454	#552	C₂²×C₈₃	1	2	yes	—
455	#551	—	2	2	no	—
456	D₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic
457	#548	C₂²×C₈₃	1	2	yes	—
458	#547	C₂²×C₈₃	1	1	yes	characteristic
459	#547	C₂²×C₈₃	1	1	yes	characteristic
460	#546	—	2	1	no	—
461	#542	—	2	1	no	—
462	#539	—	2	2	no	—
463	#533	C₂²×C₈₃	1	1	yes	characteristic
464	C₂×C₄⋊Q₈	C₂²×C₈₃	1	1	yes	characteristic
465	#529	C₂²×C₈₃	1	1	yes	characteristic
466	C₂×#126	—	2	2	no	—
467	C₂×#124	—	2	1	no	—
468	#525	C₂²×C₈₃	1	2	yes	—
469	C₂×C₂²⋊Q₈	C₂²×C₈₃	1	2	yes	—
470	C₂×C₂²⋊Q₈	C₂²×C₈₃	1	2	yes	—
471	#520	—	2	1	no	—
472	C₂×C₄×Q₈	—	2	1	no	—
473	C₂×C₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic
474	C₂×C₄×D₄	C₂²×C₈₃	1	1	yes	characteristic
475	C₂×#117	C₂²×C₈₃	1	2	yes	—
476	#501	C₂²×C₈₃	1	2	yes	complemented
477	#500	C₂²×C₈₃	1	2	yes	complemented
478	#489	C₂²×C₈₃	1	2	yes	complemented
479	#487	C₂²×C₈₃	1	2	yes	complemented
480	#485	C₂²×C₈₃	1	4	yes	complemented
481	#485	C₂²×C₈₃	1	4	yes	complemented
482	#485	C₂²×C₈₃	1	4	yes	complemented
483	#485	C₂²×C₈₃	1	4	yes	complemented
484	#484	C₂²×C₈₃	1	2	yes	—
485	#484	C₂²×C₈₃	1	2	yes	—
486	#484	C₂²×C₈₃	1	2	yes	—
487	#484	C₂²×C₈₃	1	4	yes	complemented
488	#483	C₂²×C₈₃	1	2	yes	—
489	#483	C₂²×C₈₃	1	1	yes	characteristic
490	#482	C₂²×C₈₃	1	4	yes	complemented
491	#481	C₂²×C₈₃	1	2	yes	—
492	#480	C₂²×C₈₃	1	1	yes	characteristic
493	#479	C₂²×C₈₃	1	2	yes	complemented
494	#477	C₂²×C₈₃	1	4	yes	complemented
495	#475	C₂²×C₈₃	1	2	yes	complemented
496	#475	C₂²×C₈₃	1	2	yes	complemented
497	#474	C₂²×C₈₃	1	2	yes	complemented
498	#470	C₂²×C₈₃	1	4	yes	complemented
499	#468	C₂²×C₈₃	1	4	yes	complemented
500	#467	C₂²×C₈₃	1	4	yes	complemented
501	#467	C₂²×C₈₃	1	4	yes	complemented
502	#464	C₂²×C₈₃	1	2	yes	complemented
503	#462	C₂²×C₈₃	1	2	yes	complemented
504	#452	C₂²×C₈₃	1	4	yes	complemented
505	#451	C₂²×C₈₃	1	1	yes	characteristic
506	#451	C₂²×C₈₃	1	2	yes	—
507	#451	C₂²×C₈₃	1	4	yes	complemented
508	#448	C₂²×C₈₃	1	1	yes	characteristic
509	#441	C₂²×C₈₃	1	4	yes	complemented
510	C₄×Q₁₆	C₂²×C₈₃	1	2	yes	complemented
511	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	complemented
512	#436	C₂²×C₈₃	1	2	yes	—
513	#435	C₂²×C₈₃	1	4	yes	—
514	C₈×D₄	C₂²×C₈₃	1	2	yes	—
515	#432	C₂²×C₈₃	1	1	yes	characteristic
516	#431	C₂²×C₈₃	1	1	yes	characteristic
517	#428	C₂²×C₈₃	1	4	yes	complemented
518	#427	C₂²×C₈₃	1	4	yes	complemented
519	#419	C₂²×C₈₃	1	4	yes	complemented
520	#416	C₂²×C₈₃	1	4	yes	complemented
521	#407	C₂²×C₈₃	1	2	yes	—
522	C₂×C₂²⋊C₈	C₂²×C₈₃	1	2	yes	—
523	C₂×#41	—	2	1	no	—
524	C₂×#41	C₂³×C₈₃	1	2	yes	—
525	C₂²×Q₈	—	2	1	no	—
526	C₂²×Q₈	C₂³×C₈₃	1	1	yes	characteristic
527	C₂²×Q₈	C₂³×C₈₃	1	2	yes	—
528	C₂²×D₄	D₄×C₈₃	1	1	yes	characteristic
529	C₂³×C₄	C₂³×C₈₃	1	2	yes	—
530	C₂×Q₁₆	C₂³×C₈₃	1	2	yes	—
531	C₂×Q₁₆	C₂³×C₈₃	1	4	yes	—
532	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
533	C₂×M₁₆	C₂³×C₈₃	1	4	yes	—
534	C₂²×C₈	C₂³×C₈₃	1	4	yes	—
535	C₄⋊Q₈	—	2	1	no	—
536	C₄⋊Q₈	—	2	1	no	—
537	C₄⋊Q₈	—	2	1	no	—
538	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
539	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
540	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
541	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
542	#126	—	2	4	no	—
543	#126	—	2	4	no	—
544	#126	—	2	4	no	—
545	#126	—	2	4	no	—
546	#126	—	2	2	no	—
547	#126	—	2	2	no	—
548	#126	—	2	1	no	—
549	#125	—	2	2	no	—
550	#125	—	2	1	no	—
551	#125	C₂³×C₈₃	1	1	yes	characteristic
552	#124	—	2	2	no	—
553	#124	—	2	2	no	—
554	#124	—	2	4	no	—
555	#124	—	2	1	no	—
556	#124	—	2	2	no	—
557	#124	C₂³×C₈₃	1	1	yes	characteristic
558	#123	—	2	2	no	—
559	#123	—	2	2	no	—
560	#123	—	2	1	no	—
561	#123	—	2	2	no	—
562	#123	—	2	2	no	—
563	C₂²⋊Q₈	—	2	2	no	—
564	C₂²⋊Q₈	—	2	2	no	—
565	C₂²⋊Q₈	—	2	2	no	—
566	C₂²⋊Q₈	—	2	2	no	—
567	C₂²⋊Q₈	—	2	1	no	—
568	C₂²⋊Q₈	—	2	2	no	—
569	C₂²⋊Q₈	—	2	1	no	—
570	C₂²⋊Q₈	—	2	2	no	—
571	C₂²⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
572	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
573	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
574	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
575	C₂²⋊Q₈	C₂³×C₈₃	1	4	yes	—
576	C₂²⋊Q₈	C₂³×C₈₃	1	4	yes	—
577	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
578	#121	—	2	2	no	—
579	#121	—	2	1	no	—
580	#121	C₂³×C₈₃	1	1	yes	characteristic
581	#121	C₂³×C₈₃	1	2	yes	—
582	#120	—	2	2	no	—
583	C₄×Q₈	—	2	2	no	—
584	C₄×Q₈	—	2	4	no	—
585	C₄×Q₈	—	2	2	no	—
586	C₄×Q₈	—	2	1	no	—
587	C₄×Q₈	—	2	1	no	—
588	C₄×Q₈	—	2	1	no	—
589	C₄×Q₈	—	2	1	no	—
590	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
591	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
592	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
593	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
594	C₄×D₄	—	2	1	no	—
595	C₄×D₄	—	2	2	no	—
596	C₄×D₄	—	2	2	no	—
597	C₄×D₄	—	2	1	no	—
598	C₄×D₄	—	2	2	no	—
599	C₄×D₄	D₄×C₈₃	1	1	yes	characteristic
600	C₄×D₄	D₄×C₈₃	1	2	yes	—
601	C₄×D₄	D₄×C₈₃	1	1	yes	characteristic
602	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
603	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
604	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
605	C₄×D₄	C₂³×C₈₃	1	2	yes	—
606	#117	—	2	2	no	—
607	#117	—	2	2	no	—
608	#117	—	2	1	no	—
609	#117	—	2	2	no	—
610	#117	—	2	1	no	—
611	#117	C₂³×C₈₃	1	4	yes	—
612	#117	C₂³×C₈₃	1	4	yes	—
613	#117	C₂³×C₈₃	1	2	yes	—
614	C₂×C₄⋊C₄	—	2	2	no	—
615	C₂×C₄⋊C₄	—	2	1	no	—
616	C₂×C₄⋊C₄	—	2	2	no	—
617	C₂×C₄⋊C₄	—	2	1	no	—
618	C₂×C₄⋊C₄	—	2	1	no	—
619	C₂×C₄⋊C₄	D₄×C₈₃	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
623	C₂×C₂²⋊C₄	—	2	2	no	—
624	C₂×C₂²⋊C₄	—	2	2	no	—
625	C₂×C₂²⋊C₄	—	2	2	no	—
626	C₂×C₂²⋊C₄	D₄×C₈₃	1	2	yes	—
627	C₂×C₄²	—	2	2	no	—
628	C₂×C₄²	—	2	1	no	—
629	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
630	#107	C₂³×C₈₃	1	2	yes	—
631	#107	C₂³×C₈₃	1	4	yes	—
632	#107	C₂³×C₈₃	1	4	yes	—
633	#107	C₂³×C₈₃	1	4	yes	—
634	#106	C₂³×C₈₃	1	4	yes	—
635	#106	C₂³×C₈₃	1	4	yes	—
636	#106	C₂³×C₈₃	1	2	yes	—
637	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
638	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
639	#103	C₂³×C₈₃	1	4	yes	—
640	#103	C₂³×C₈₃	1	4	yes	—
641	#103	C₂³×C₈₃	1	2	yes	—
642	#103	C₂³×C₈₃	1	4	yes	—
643	#103	C₂³×C₈₃	1	4	yes	—
644	#103	C₂³×C₈₃	1	2	yes	—
645	#103	C₂³×C₈₃	1	2	yes	—
646	#103	C₂³×C₈₃	1	4	yes	—
647	#102	C₂³×C₈₃	1	2	yes	—
648	#102	C₂³×C₈₃	1	4	yes	—
649	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
650	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
651	C₂²⋊C₈	C₂³×C₈₃	1	4	yes	—
652	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
653	C₂²⋊C₈	C₂³×C₈₃	1	4	yes	—
654	#97	C₂³×C₈₃	1	2	yes	—
655	C₄×C₈	C₂³×C₈₃	1	2	yes	—
656	C₂⁴	C₂×D₄×C₈₃	1	2	yes	—
657	#41	—	4	4	no	—
658	#41	—	4	4	no	—
659	C₂×Q₈	—	2	1	no	—
660	C₂×Q₈	—	2	1	no	—
661	C₂×Q₈	—	2	2	no	—
662	C₂×Q₈	—	2	2	no	—
663	C₂×Q₈	—	2	2	no	—
664	C₂×Q₈	—	4	2	no	—
665	C₂×Q₈	—	4	4	no	—
666	C₂×Q₈	—	4	4	no	—
667	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
668	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
669	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
670	C₂×D₄	—	2	1	no	—
671	C₂×D₄	—	2	2	no	—
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	—	4	2	no	—
674	C₂×D₄	C₂×D₄×C₈₃	1	1	yes	characteristic
675	C₂×D₄	C₂×D₄×C₈₃	1	1	yes	characteristic
676	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
677	C₂×D₄	C₂⁴×C₈₃	1	1	yes	characteristic
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	2	1	no	—
680	C₂²×C₄	—	2	2	no	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	1	no	—
684	C₂²×C₄	—	2	2	no	—
685	C₂²×C₄	—	4	4	no	—
686	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
687	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
688	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
689	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
690	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
692	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
693	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
694	Q₁₆	—	4	2	no	—
695	Q₁₆	—	4	4	no	—
696	SD₁₆	—	4	2	no	—
697	M₁₆	—	4	4	no	—
698	C₂×C₈	—	4	4	no	—
699	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
700	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
701	C₂×C₈	C₂⁴×C₈₃	1	4	yes	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	4	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
724	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
725	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
726	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
727	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
728	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
729	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
730	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
731	C₂²⋊C₄	—	2	1	no	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	2	no	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	—	2	4	no	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	1	no	—
742	C₂²⋊C₄	—	2	1	no	—
743	C₂²⋊C₄	—	2	1	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
747	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
748	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
749	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
750	C₄²	—	2	4	no	—
751	C₄²	—	2	4	no	—
752	C₄²	—	2	2	no	—
753	C₄²	—	2	2	no	—
754	C₄²	—	2	2	no	—
755	C₄²	—	2	2	no	—
756	C₄²	—	2	1	no	—
757	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
758	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
759	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
760	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
761	C₂³	—	2	4	no	—
762	C₂³	—	2	1	no	—
763	C₂³	—	4	2	no	—
764	C₂³	—	4	2	no	—
765	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
766	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
767	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
768	Q₈	—	2	2	no	—
769	Q₈	—	2	2	no	—
770	Q₈	—	2	2	no	—
771	Q₈	—	2	4	no	—
772	Q₈	—	4	4	no	—
773	Q₈	—	4	2	no	—
774	Q₈	—	4	4	no	—
775	Q₈	—	4	2	no	—
776	Q₈	—	8	2	no	—
777	D₄	—	2	2	no	—
778	D₄	—	2	2	no	—
779	D₄	—	2	2	no	—
780	D₄	—	4	2	no	—
781	D₄	—	4	4	no	—
782	D₄	—	4	2	no	—
783	D₄	—	8	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	4	no	—
787	C₂×C₄	—	2	4	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	4	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	4	2	no	—
798	C₂×C₄	—	4	2	no	—
799	C₂×C₄	—	4	2	no	—
800	C₂×C₄	—	4	4	no	—
801	C₂×C₄	—	4	2	no	—
802	C₂×C₄	—	4	4	no	—
803	C₂×C₄	—	4	2	no	—
804	C₂×C₄	—	4	2	no	—
805	C₂×C₄	—	8	2	no	—
806	C₂×C₄	—	8	2	no	—
807	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
808	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
809	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
810	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
811	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
812	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
813	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
814	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
815	C₈	—	2	2	no	—
816	C₈	—	2	4	no	—
817	C₈	—	2	2	no	—
818	C₂²	—	2	1	no	—
819	C₂²	—	2	1	no	—
820	C₂²	—	2	2	no	—
821	C₂²	—	2	2	no	—
822	C₂²	—	2	2	no	—
823	C₂²	—	2	2	no	—
824	C₂²	—	2	2	no	—
825	C₂²	—	2	2	no	—
826	C₂²	—	4	1	no	—
827	C₂²	—	4	1	no	—
828	C₂²	—	4	1	no	—
829	C₂²	—	8	4	no	—
830	C₂²	#578×C₈₃	1	2	yes	—
831	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
832	C₄	—	2	1	no	—
833	C₄	—	2	1	no	—
834	C₄	—	2	1	no	—
835	C₄	—	2	1	no	—
836	C₄	—	2	2	no	—
837	C₄	—	2	2	no	—
838	C₄	—	4	1	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	4	no	—
841	C₄	—	4	2	no	—
842	C₄	—	4	1	no	—
843	C₄	—	4	2	no	—
844	C₄	—	4	2	no	—
845	C₄	—	4	1	no	—
846	C₄	#575×C₈₃	1	2	yes	—
847	C₄	#585×C₈₃	1	2	yes	—
848	C₂	—	2	2	no	—
849	C₂	—	4	2	no	—
850	C₂	—	4	2	no	—
851	C₂	—	8	1	no	—
852	C₂	C₈₃×#3485	1	1	yes	characteristic
853	C₂	C₂×#575×C₈₃	1	1	yes	characteristic
854	C₂	C₂×#578×C₈₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₃
prime radical	C₈₃×#3520	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₃ ◁ C₂×C₄×D₄×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#556×C₈₃	C₂	semidirect
3. C₈₃×#3353	C₂	semidirect
4. C₈₃×#3349	C₂	semidirect
5. C₈₃×#3342	C₂	semidirect
6. C₈₃×#3328	C₂	semidirect
7. C₈₃×#3313	C₂	semidirect
8. C₈₃×#3302	C₂	semidirect
9. C₈₃×#3239	C₂	semidirect
10. C₈₃×#3230	C₂	semidirect
11. C₈₃×#3196	C₂	semidirect
12. C₈₃×#3189	C₂	semidirect
13. C₈₃×#3113	C₂	semidirect
14. C₈₃×#3108	C₂	semidirect
15. C₈₃×#3095	C₂	semidirect
16. C₈₃×#3091	C₂	semidirect
17. C₈₃×#2974	C₂	semidirect
48. #501×C₈₃	C₂²	semidirect
49. #500×C₈₃	C₂²	semidirect
50. #489×C₈₃	C₂²	semidirect
51. #487×C₈₃	C₂²	semidirect
52. #485×C₈₃	C₂²	semidirect
53. #485×C₈₃	C₂²	semidirect
54. #485×C₈₃	C₂²	semidirect
55. #485×C₈₃	C₂²	semidirect
59. #484×C₈₃	C₂²	semidirect
62. #482×C₈₃	C₂²	semidirect
65. #479×C₈₃	C₂²	semidirect
66. #477×C₈₃	C₂²	semidirect
67. #475×C₈₃	C₂²	semidirect
68. #475×C₈₃	C₂²	semidirect
69. #474×C₈₃	C₂²	semidirect
70. #470×C₈₃	C₂²	semidirect
71. #468×C₈₃	C₂²	semidirect
72. #467×C₈₃	C₂²	semidirect
73. #467×C₈₃	C₂²	semidirect
74. #464×C₈₃	C₂²	semidirect
75. #462×C₈₃	C₂²	semidirect
76. #452×C₈₃	C₂²	semidirect
79. #451×C₈₃	C₂²	semidirect
81. #441×C₈₃	C₂²	semidirect
82. C₄×Q₁₆×C₈₃	C₂²	semidirect
83. C₄×SD₁₆×C₈₃	C₂²	semidirect
89. #428×C₈₃	C₂²	semidirect
90. #427×C₈₃	C₂²	semidirect
91. #419×C₈₃	C₂²	semidirect
92. #416×C₈₃	C₂²	semidirect
420. #61730	C₈₃	direct (N × H)
429. C₂×#556	C₂×C₈₃	semidirect
430. #3353	C₂×C₈₃	semidirect
431. #3349	C₂×C₈₃	semidirect
432. #3342	C₂×C₈₃	semidirect
433. #3328	C₂×C₈₃	semidirect
434. #3313	C₂×C₈₃	semidirect
435. #3302	C₂×C₈₃	semidirect
436. #3239	C₂×C₈₃	semidirect
437. #3230	C₂×C₈₃	semidirect
438. #3196	C₂×C₈₃	semidirect
439. #3189	C₂×C₈₃	semidirect
440. #3113	C₂×C₈₃	semidirect
441. #3108	C₂×C₈₃	semidirect
442. #3095	C₂×C₈₃	semidirect
443. #3091	C₂×C₈₃	semidirect
444. #2974	C₂×C₈₃	semidirect
445. C₈₃	#61730	direct (N × H)
476. #501	C₂²×C₈₃	semidirect
477. #500	C₂²×C₈₃	semidirect
478. #489	C₂²×C₈₃	semidirect
479. #487	C₂²×C₈₃	semidirect
480. #485	C₂²×C₈₃	semidirect
481. #485	C₂²×C₈₃	semidirect
482. #485	C₂²×C₈₃	semidirect
483. #485	C₂²×C₈₃	semidirect
487. #484	C₂²×C₈₃	semidirect
490. #482	C₂²×C₈₃	semidirect
493. #479	C₂²×C₈₃	semidirect
494. #477	C₂²×C₈₃	semidirect
495. #475	C₂²×C₈₃	semidirect
496. #475	C₂²×C₈₃	semidirect
497. #474	C₂²×C₈₃	semidirect
498. #470	C₂²×C₈₃	semidirect
499. #468	C₂²×C₈₃	semidirect
500. #467	C₂²×C₈₃	semidirect
501. #467	C₂²×C₈₃	semidirect
502. #464	C₂²×C₈₃	semidirect
503. #462	C₂²×C₈₃	semidirect
504. #452	C₂²×C₈₃	semidirect
507. #451	C₂²×C₈₃	semidirect
509. #441	C₂²×C₈₃	semidirect
510. C₄×Q₁₆	C₂²×C₈₃	semidirect
511. C₄×SD₁₆	C₂²×C₈₃	semidirect
517. #428	C₂²×C₈₃	semidirect
518. #427	C₂²×C₈₃	semidirect
519. #419	C₂²×C₈₃	semidirect
520. #416	C₂²×C₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₈₃×#3520	2
C₂×#556×C₈₃	2
C₈₃×#3353	2
C₈₃×#3349	2
C₈₃×#3342	2
C₈₃×#3328	2
C₈₃×#3313	2
C₈₃×#3302	2
C₈₃×#3239	2
C₈₃×#3230	2
C₈₃×#3196	2
C₈₃×#3189	2
C₈₃×#3113	2
C₈₃×#3108	2
C₈₃×#3095	2
C₈₃×#3091	2
C₈₃×#2974	2
#61730	83

Subgroups — C83×#61730 #35289554

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#61730 #35289554