Subgroups — C₈₃×#62251 #35290075

Order 21248.

2014 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3519	C₂	1	2	yes	maximal, complemented
2	C₈₃×#3341	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₃×#3339	C₂	1	2	yes	maximal, complemented
4	C₈₃×#3338	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₃×#3305	C₂	1	2	yes	maximal, complemented
6	C₈₃×#3297	C₂	1	4	yes	maximal, complemented
7	C₈₃×#3295	C₂	1	2	yes	maximal, complemented
8	C₈₃×#3287	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₃×#3280	C₂	1	2	yes	maximal, complemented
10	D₄×D₈×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₃×#3247	C₂	1	2	yes	maximal, complemented
12	C₈₃×#3188	C₂	1	4	yes	maximal, complemented
13	C₈₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₃×#3168	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#3050	C₂	1	2	yes	maximal, complemented
16	C₂×#466×C₈₃	C₂	1	2	yes	maximal, complemented
17	C₂×C₈×D₄×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#135×C₈₃	C₂²	1	2	yes	complemented
19	C₂²×D₈×C₈₃	C₂²	1	2	yes	complemented
20	C₂³×C₈×C₈₃	C₂²	1	2	yes	complemented
21	#555×C₈₃	C₂²	1	2	yes	complemented
22	#554×C₈₃	C₂²	1	2	yes	—
23	#553×C₈₃	—	2	2	no	—
24	#553×C₈₃	C₂²	1	4	yes	complemented
25	#550×C₈₃	C₂²	1	2	yes	complemented
26	#546×C₈₃	—	2	4	no	—
27	#546×C₈₃	C₂²	1	4	yes	complemented
28	D₄²×C₈₃	—	2	2	no	—
29	D₄²×C₈₃	C₂²	1	2	yes	—
30	#540×C₈₃	—	2	2	no	—
31	#538×C₈₃	—	2	4	no	—
32	#532×C₈₃	C₂²	1	2	yes	complemented
33	#529×C₈₃	C₂²	1	2	yes	complemented
34	#525×C₈₃	C₂²	1	4	yes	complemented
35	C₂×#121×C₈₃	C₂²	1	4	yes	complemented
36	#518×C₈₃	—	2	2	no	—
37	C₂×C₄×D₄×C₈₃	C₂²	1	1	yes	characteristic
38	#500×C₈₃	C₂²	1	1	yes	characteristic, complemented
39	#499×C₈₃	C₂²	1	1	yes	characteristic, complemented
40	#495×C₈₃	C₂²	1	1	yes	characteristic, complemented
41	#493×C₈₃	C₂²	1	1	yes	characteristic, complemented
42	#488×C₈₃	C₂²	1	2	yes	complemented
43	#486×C₈₃	C₂²	1	2	yes	complemented
44	#484×C₈₃	C₂²	1	4	yes	complemented
45	#482×C₈₃	C₂²	1	4	yes	complemented
46	#482×C₈₃	C₂²	1	4	yes	complemented
47	#481×C₈₃	C₂²	1	4	yes	complemented
48	#478×C₈₃	C₂²	1	4	yes	complemented
49	#477×C₈₃	C₂²	1	2	yes	complemented
50	#476×C₈₃	C₂²	1	2	yes	complemented
51	#467×C₈₃	C₂²	1	2	yes	complemented
52	#467×C₈₃	C₂²	1	1	yes	characteristic, complemented
53	#466×C₈₃	C₂²	1	1	yes	characteristic
54	#466×C₈₃	C₂²	1	2	yes	complemented
55	#466×C₈₃	C₂²	1	2	yes	complemented
56	#466×C₈₃	C₂²	1	2	yes	complemented
57	#466×C₈₃	C₂²	1	4	yes	complemented
58	#466×C₈₃	C₂²	1	2	yes	complemented
59	#466×C₈₃	C₂²	1	4	yes	complemented
60	#466×C₈₃	C₂²	1	2	yes	complemented
61	#465×C₈₃	C₂²	1	4	yes	complemented
62	#465×C₈₃	C₂²	1	4	yes	complemented
63	#465×C₈₃	C₂²	1	2	yes	complemented
64	#463×C₈₃	C₂²	1	4	yes	complemented
65	#460×C₈₃	C₂²	1	2	yes	complemented
66	#459×C₈₃	C₂²	1	2	yes	complemented
67	#450×C₈₃	C₂²	1	4	yes	complemented
68	#449×C₈₃	C₂²	1	4	yes	complemented
69	#449×C₈₃	C₂²	1	4	yes	complemented
70	#447×C₈₃	C₂²	1	4	yes	complemented
71	C₄×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic, complemented
72	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	complemented
73	C₄×D₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
74	C₄×D₈×C₈₃	C₂²	1	2	yes	complemented
75	C₄×D₈×C₈₃	C₂²	1	2	yes	complemented
76	C₈×D₄×C₈₃	C₂²	1	1	yes	characteristic
77	C₈×D₄×C₈₃	C₂²	1	1	yes	characteristic
78	C₈×D₄×C₈₃	C₂²	1	2	yes	complemented
79	C₈×D₄×C₈₃	C₂²	1	1	yes	characteristic, complemented
80	C₈×D₄×C₈₃	C₂²	1	2	yes	complemented
81	C₈×D₄×C₈₃	C₂²	1	1	yes	characteristic, complemented
82	#427×C₈₃	C₂²	1	2	yes	complemented
83	C₂×#107×C₈₃	C₂²	1	2	yes	complemented
84	C₂×C₄⋊C₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
85	#416×C₈₃	C₂²	1	4	yes	complemented
86	C₂×#102×C₈₃	C₂²	1	4	yes	complemented
87	C₂×C₂²⋊C₈×C₈₃	C₂²	1	2	yes	complemented
88	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
89	C₂×#41×C₈₃	—	2	2	no	—
90	C₂×#41×C₈₃	C₂³	1	4	yes	—
91	C₂²×D₄×C₈₃	—	2	4	no	—
92	C₂²×D₄×C₈₃	—	2	2	no	—
93	C₂²×D₄×C₈₃	D₄	1	1	yes	characteristic
94	C₂²×D₄×C₈₃	C₂³	1	4	yes	—
95	C₂³×C₄×C₈₃	C₂³	1	2	yes	—
96	#135×C₈₃	—	4	4	no	—
97	C₂×Q₁₆×C₈₃	C₂³	1	1	yes	characteristic
98	C₂×SD₁₆×C₈₃	C₂³	1	4	yes	—
99	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
100	C₂×D₈×C₈₃	—	4	4	no	—
101	C₂×D₈×C₈₃	C₂³	1	1	yes	characteristic
102	C₂×D₈×C₈₃	C₂³	1	2	yes	—
103	C₂×D₈×C₈₃	C₂³	1	4	yes	—
104	C₂×D₈×C₈₃	C₂³	1	2	yes	—
105	C₂²×C₈×C₈₃	—	4	4	no	—
106	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
108	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
109	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
110	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
112	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
113	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
114	#127×C₈₃	—	2	2	no	—
115	#127×C₈₃	C₂³	1	2	yes	—
116	#126×C₈₃	—	2	4	no	—
117	#126×C₈₃	—	2	2	no	—
118	#125×C₈₃	—	2	2	no	—
119	#125×C₈₃	C₂³	1	2	yes	—
120	#124×C₈₃	—	2	4	no	—
121	#124×C₈₃	—	2	2	no	—
122	#124×C₈₃	C₂³	1	2	yes	—
123	#123×C₈₃	—	2	4	no	—
124	#123×C₈₃	—	2	2	no	—
125	#123×C₈₃	—	2	4	no	—
126	#123×C₈₃	—	2	4	no	—
127	C₂²⋊Q₈×C₈₃	—	2	4	no	—
128	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
129	C₂²⋊Q₈×C₈₃	C₂³	1	4	yes	—
130	#121×C₈₃	—	2	4	no	—
131	#121×C₈₃	—	2	2	no	—
132	#121×C₈₃	—	2	4	no	—
133	#121×C₈₃	—	2	4	no	—
134	#121×C₈₃	—	2	2	no	—
135	#121×C₈₃	—	2	2	no	—
136	#121×C₈₃	—	2	4	no	—
137	#121×C₈₃	—	2	4	no	—
138	#121×C₈₃	C₂³	1	2	yes	—
139	#121×C₈₃	C₂³	1	4	yes	—
140	#121×C₈₃	C₂³	1	4	yes	—
141	#121×C₈₃	C₂³	1	4	yes	—
142	#121×C₈₃	C₂³	1	4	yes	—
143	#120×C₈₃	—	2	4	no	—
144	#120×C₈₃	—	2	4	no	—
145	#120×C₈₃	—	2	4	no	—
146	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
147	C₄×D₄×C₈₃	—	2	2	no	—
148	C₄×D₄×C₈₃	—	2	4	no	—
149	C₄×D₄×C₈₃	—	2	4	no	—
150	C₄×D₄×C₈₃	—	2	2	no	—
151	C₄×D₄×C₈₃	—	2	2	no	—
152	C₄×D₄×C₈₃	—	2	4	no	—
153	C₄×D₄×C₈₃	—	2	2	no	—
154	C₄×D₄×C₈₃	D₄	1	1	yes	characteristic
155	C₄×D₄×C₈₃	D₄	1	2	yes	—
156	C₄×D₄×C₈₃	D₄	1	1	yes	characteristic
157	C₄×D₄×C₈₃	C₂³	1	4	yes	—
158	C₄×D₄×C₈₃	C₂³	1	2	yes	—
159	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
160	C₄×D₄×C₈₃	C₂³	1	2	yes	—
161	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
162	#117×C₈₃	—	2	2	no	—
163	#117×C₈₃	—	2	2	no	—
164	#117×C₈₃	C₂³	1	4	yes	—
165	C₂×C₄⋊C₄×C₈₃	D₄	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₈₃	C₂³	1	4	yes	—
167	C₂×C₂²⋊C₄×C₈₃	—	2	4	no	—
168	C₂×C₂²⋊C₄×C₈₃	—	2	4	no	—
169	C₂×C₂²⋊C₄×C₈₃	D₄	1	2	yes	—
170	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
171	#107×C₈₃	C₂³	1	1	yes	characteristic
172	#107×C₈₃	C₂³	1	1	yes	characteristic
173	#107×C₈₃	C₂³	1	2	yes	—
174	#107×C₈₃	C₂³	1	4	yes	—
175	#107×C₈₃	C₂³	1	2	yes	—
176	#106×C₈₃	C₂³	1	4	yes	—
177	#106×C₈₃	C₂³	1	2	yes	—
178	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
179	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
180	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
181	#103×C₈₃	C₂³	1	4	yes	—
182	#103×C₈₃	C₂³	1	2	yes	—
183	#103×C₈₃	C₂³	1	2	yes	—
184	#102×C₈₃	C₂³	1	4	yes	—
185	#102×C₈₃	C₂³	1	4	yes	—
186	#102×C₈₃	C₂³	1	4	yes	—
187	#102×C₈₃	C₂³	1	2	yes	—
188	#102×C₈₃	C₂³	1	2	yes	—
189	#102×C₈₃	C₂³	1	4	yes	—
190	#102×C₈₃	C₂³	1	4	yes	—
191	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
192	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
193	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
194	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
195	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
198	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
199	C₂⁴×C₈₃	—	2	4	no	—
200	C₂⁴×C₈₃	C₂×D₄	1	2	yes	—
201	#41×C₈₃	—	4	4	no	—
202	#41×C₈₃	—	4	4	no	—
203	#41×C₈₃	—	8	4	no	—
204	C₂×Q₈×C₈₃	—	2	2	no	—
205	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
206	C₂×D₄×C₈₃	—	2	4	no	—
207	C₂×D₄×C₈₃	—	2	4	no	—
208	C₂×D₄×C₈₃	—	2	4	no	—
209	C₂×D₄×C₈₃	—	2	2	no	—
210	C₂×D₄×C₈₃	—	2	4	no	—
211	C₂×D₄×C₈₃	—	2	4	no	—
212	C₂×D₄×C₈₃	—	2	4	no	—
213	C₂×D₄×C₈₃	—	2	2	no	—
214	C₂×D₄×C₈₃	—	2	2	no	—
215	C₂×D₄×C₈₃	—	2	4	no	—
216	C₂×D₄×C₈₃	—	4	4	no	—
217	C₂×D₄×C₈₃	—	4	4	no	—
218	C₂×D₄×C₈₃	—	4	8	no	—
219	C₂×D₄×C₈₃	—	8	8	no	—
220	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
221	C₂×D₄×C₈₃	C₂×D₄	1	1	yes	characteristic
222	C₂×D₄×C₈₃	C₂×D₄	1	1	yes	characteristic
223	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
224	C₂×D₄×C₈₃	C₂⁴	1	4	yes	—
225	C₂²×C₄×C₈₃	—	2	4	no	—
226	C₂²×C₄×C₈₃	—	2	2	no	—
227	C₂²×C₄×C₈₃	—	2	4	no	—
228	C₂²×C₄×C₈₃	—	2	4	no	—
229	C₂²×C₄×C₈₃	—	4	2	no	—
230	C₂²×C₄×C₈₃	—	4	2	no	—
231	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
234	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
235	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
236	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
239	Q₁₆×C₈₃	—	2	2	no	—
240	SD₁₆×C₈₃	—	4	2	no	—
241	SD₁₆×C₈₃	—	4	4	no	—
242	D₈×C₈₃	—	2	2	no	—
243	D₈×C₈₃	—	2	4	no	—
244	D₈×C₈₃	—	4	4	no	—
245	D₈×C₈₃	—	4	2	no	—
246	C₂×C₈×C₈₃	—	2	2	no	—
247	C₂×C₈×C₈₃	—	2	4	no	—
248	C₂×C₈×C₈₃	—	2	4	no	—
249	C₂×C₈×C₈₃	—	4	2	no	—
250	C₂×C₈×C₈₃	—	4	2	no	—
251	C₂×C₈×C₈₃	—	4	2	no	—
252	C₂×C₈×C₈₃	—	4	1	no	—
253	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
254	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
255	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
256	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
257	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
258	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
259	C₄⋊C₄×C₈₃	—	2	4	no	—
260	C₄⋊C₄×C₈₃	—	2	2	no	—
261	C₄⋊C₄×C₈₃	—	2	2	no	—
262	C₄⋊C₄×C₈₃	—	2	2	no	—
263	C₄⋊C₄×C₈₃	—	2	2	no	—
264	C₄⋊C₄×C₈₃	—	2	4	no	—
265	C₄⋊C₄×C₈₃	—	2	2	no	—
266	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
267	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
268	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
269	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
270	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
271	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
272	C₂²⋊C₄×C₈₃	—	2	4	no	—
273	C₂²⋊C₄×C₈₃	—	2	4	no	—
274	C₂²⋊C₄×C₈₃	—	2	2	no	—
275	C₂²⋊C₄×C₈₃	—	2	2	no	—
276	C₂²⋊C₄×C₈₃	—	2	2	no	—
277	C₂²⋊C₄×C₈₃	—	2	4	no	—
278	C₂²⋊C₄×C₈₃	—	2	4	no	—
279	C₂²⋊C₄×C₈₃	—	2	4	no	—
280	C₂²⋊C₄×C₈₃	—	2	2	no	—
281	C₂²⋊C₄×C₈₃	—	2	4	no	—
282	C₂²⋊C₄×C₈₃	—	2	2	no	—
283	C₂²⋊C₄×C₈₃	—	2	4	no	—
284	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
285	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
286	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
287	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
288	C₄²×C₈₃	—	2	4	no	—
289	C₄²×C₈₃	—	2	2	no	—
290	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
291	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
292	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
293	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
294	C₂³×C₈₃	—	2	4	no	—
295	C₂³×C₈₃	—	2	4	no	—
296	C₂³×C₈₃	—	2	2	no	—
297	C₂³×C₈₃	—	2	4	no	—
298	C₂³×C₈₃	—	4	2	no	—
299	C₂³×C₈₃	—	4	8	no	—
300	C₂³×C₈₃	—	8	4	no	—
301	C₂³×C₈₃	—	8	4	no	—
302	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
303	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
304	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
305	Q₈×C₈₃	—	2	2	no	—
306	Q₈×C₈₃	—	2	2	no	—
307	Q₈×C₈₃	—	8	2	no	—
308	D₄×C₈₃	—	2	4	no	—
309	D₄×C₈₃	—	2	2	no	—
310	D₄×C₈₃	—	2	2	no	—
311	D₄×C₈₃	—	2	4	no	—
312	D₄×C₈₃	—	2	4	no	—
313	D₄×C₈₃	—	2	2	no	—
314	D₄×C₈₃	—	4	8	no	—
315	D₄×C₈₃	—	4	4	no	—
316	D₄×C₈₃	—	4	8	no	—
317	D₄×C₈₃	—	4	4	no	—
318	D₄×C₈₃	—	8	4	no	—
319	D₄×C₈₃	—	8	2	no	—
320	D₄×C₈₃	—	8	4	no	—
321	D₄×C₈₃	—	8	4	no	—
322	D₄×C₈₃	—	8	4	no	—
323	D₄×C₈₃	#135	1	4	yes	complemented
324	C₂×C₄×C₈₃	—	2	2	no	—
325	C₂×C₄×C₈₃	—	2	2	no	—
326	C₂×C₄×C₈₃	—	2	1	no	—
327	C₂×C₄×C₈₃	—	2	2	no	—
328	C₂×C₄×C₈₃	—	2	2	no	—
329	C₂×C₄×C₈₃	—	2	1	no	—
330	C₂×C₄×C₈₃	—	2	2	no	—
331	C₂×C₄×C₈₃	—	2	2	no	—
332	C₂×C₄×C₈₃	—	2	2	no	—
333	C₂×C₄×C₈₃	—	2	2	no	—
334	C₂×C₄×C₈₃	—	2	4	no	—
335	C₂×C₄×C₈₃	—	2	2	no	—
336	C₂×C₄×C₈₃	—	4	2	no	—
337	C₂×C₄×C₈₃	—	4	2	no	—
338	C₂×C₄×C₈₃	—	4	2	no	—
339	C₂×C₄×C₈₃	—	4	4	no	—
340	C₂×C₄×C₈₃	—	8	4	no	—
341	C₂×C₄×C₈₃	—	8	4	no	—
342	C₂×C₄×C₈₃	—	8	4	no	—
343	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
344	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
346	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
349	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
350	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
351	C₈×C₈₃	—	2	1	no	—
352	C₈×C₈₃	—	2	2	no	—
353	C₈×C₈₃	—	2	2	no	—
354	C₈×C₈₃	—	2	1	no	—
355	C₈×C₈₃	—	2	1	no	—
356	C₈×C₈₃	H(5,𝔽₂)	1	2	yes	—
357	C₂²×C₈₃	—	2	1	no	—
358	C₂²×C₈₃	—	2	2	no	—
359	C₂²×C₈₃	—	2	1	no	—
360	C₂²×C₈₃	—	2	2	no	—
361	C₂²×C₈₃	—	2	2	no	—
362	C₂²×C₈₃	—	2	2	no	—
363	C₂²×C₈₃	—	2	2	no	—
364	C₂²×C₈₃	—	4	8	no	—
365	C₂²×C₈₃	—	4	4	no	—
366	C₂²×C₈₃	—	4	2	no	—
367	C₂²×C₈₃	—	4	2	no	—
368	C₂²×C₈₃	—	4	4	no	—
369	C₂²×C₈₃	—	4	4	no	—
370	C₂²×C₈₃	—	4	2	no	—
371	C₂²×C₈₃	—	16	8	no	—
372	C₂²×C₈₃	C₂×#135	1	4	yes	—
373	C₂²×C₈₃	#576	1	2	yes	—
374	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
375	C₄×C₈₃	—	2	1	no	—
376	C₄×C₈₃	—	2	2	no	—
377	C₄×C₈₃	—	2	2	no	—
378	C₄×C₈₃	—	2	1	no	—
379	C₄×C₈₃	—	2	1	no	—
380	C₄×C₈₃	—	2	1	no	—
381	C₄×C₈₃	—	4	2	no	—
382	C₄×C₈₃	—	4	2	no	—
383	C₄×C₈₃	—	4	2	no	—
384	C₄×C₈₃	—	4	4	no	—
385	C₄×C₈₃	C₂×#135	1	2	yes	—
386	C₄×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
387	C₄×C₈₃	#585	1	1	yes	characteristic
388	#62251	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
389	C₂×C₈₃	—	2	2	no	—
390	C₂×C₈₃	—	2	4	no	—
391	C₂×C₈₃	—	4	2	no	—
392	C₂×C₈₃	—	8	4	no	—
393	C₂×C₈₃	—	8	2	no	—
394	C₂×C₈₃	#3496	1	1	yes	characteristic
395	C₂×C₈₃	C₂²×#135	1	1	yes	characteristic
396	C₂×C₈₃	C₂×#576	1	1	yes	characteristic
397	#3519	C₂×C₈₃	1	2	yes	complemented
398	#3341	C₂×C₈₃	1	1	yes	characteristic, complemented
399	#3339	C₂×C₈₃	1	2	yes	complemented
400	#3338	C₂×C₈₃	1	1	yes	characteristic, complemented
401	#3305	C₂×C₈₃	1	2	yes	complemented
402	#3297	C₂×C₈₃	1	4	yes	complemented
403	#3295	C₂×C₈₃	1	2	yes	complemented
404	#3287	C₂×C₈₃	1	1	yes	characteristic, complemented
405	#3280	C₂×C₈₃	1	2	yes	complemented
406	D₄×D₈	C₂×C₈₃	1	1	yes	characteristic, complemented
407	#3247	C₂×C₈₃	1	2	yes	complemented
408	#3188	C₂×C₈₃	1	4	yes	complemented
409	#3169	C₂×C₈₃	1	1	yes	characteristic, complemented
410	#3168	C₂×C₈₃	1	1	yes	characteristic, complemented
411	#3050	C₂×C₈₃	1	2	yes	complemented
412	C₂×#466	C₂×C₈₃	1	2	yes	complemented
413	C₂×C₈×D₄	C₂×C₈₃	1	1	yes	characteristic, complemented
414	C₈₃	#62251	1	1	yes	characteristic, direct product factor, Sylow
415	C₂×#135	C₂²×C₈₃	1	2	yes	complemented
416	C₂²×D₈	C₂²×C₈₃	1	2	yes	complemented
417	C₂³×C₈	C₂²×C₈₃	1	2	yes	complemented
418	#555	C₂²×C₈₃	1	2	yes	complemented
419	#554	C₂²×C₈₃	1	2	yes	—
420	#553	—	2	2	no	—
421	#553	C₂²×C₈₃	1	4	yes	complemented
422	#550	C₂²×C₈₃	1	2	yes	complemented
423	#546	—	2	4	no	—
424	#546	C₂²×C₈₃	1	4	yes	complemented
425	D₄²	—	2	2	no	—
426	D₄²	C₂²×C₈₃	1	2	yes	—
427	#540	—	2	2	no	—
428	#538	—	2	4	no	—
429	#532	C₂²×C₈₃	1	2	yes	complemented
430	#529	C₂²×C₈₃	1	2	yes	complemented
431	#525	C₂²×C₈₃	1	4	yes	complemented
432	C₂×#121	C₂²×C₈₃	1	4	yes	complemented
433	#518	—	2	2	no	—
434	C₂×C₄×D₄	C₂²×C₈₃	1	1	yes	characteristic
435	#500	C₂²×C₈₃	1	1	yes	characteristic, complemented
436	#499	C₂²×C₈₃	1	1	yes	characteristic, complemented
437	#495	C₂²×C₈₃	1	1	yes	characteristic, complemented
438	#493	C₂²×C₈₃	1	1	yes	characteristic, complemented
439	#488	C₂²×C₈₃	1	2	yes	complemented
440	#486	C₂²×C₈₃	1	2	yes	complemented
441	#484	C₂²×C₈₃	1	4	yes	complemented
442	#482	C₂²×C₈₃	1	4	yes	complemented
443	#482	C₂²×C₈₃	1	4	yes	complemented
444	#481	C₂²×C₈₃	1	4	yes	complemented
445	#478	C₂²×C₈₃	1	4	yes	complemented
446	#477	C₂²×C₈₃	1	2	yes	complemented
447	#476	C₂²×C₈₃	1	2	yes	complemented
448	#467	C₂²×C₈₃	1	2	yes	complemented
449	#467	C₂²×C₈₃	1	1	yes	characteristic, complemented
450	#466	C₂²×C₈₃	1	1	yes	characteristic
451	#466	C₂²×C₈₃	1	2	yes	complemented
452	#466	C₂²×C₈₃	1	2	yes	complemented
453	#466	C₂²×C₈₃	1	2	yes	complemented
454	#466	C₂²×C₈₃	1	2	yes	complemented
455	#466	C₂²×C₈₃	1	2	yes	complemented
456	#466	C₂²×C₈₃	1	4	yes	complemented
457	#466	C₂²×C₈₃	1	4	yes	complemented
458	#465	C₂²×C₈₃	1	2	yes	complemented
459	#465	C₂²×C₈₃	1	4	yes	complemented
460	#465	C₂²×C₈₃	1	4	yes	complemented
461	#463	C₂²×C₈₃	1	4	yes	complemented
462	#460	C₂²×C₈₃	1	2	yes	complemented
463	#459	C₂²×C₈₃	1	2	yes	complemented
464	#450	C₂²×C₈₃	1	4	yes	complemented
465	#449	C₂²×C₈₃	1	4	yes	complemented
466	#449	C₂²×C₈₃	1	4	yes	complemented
467	#447	C₂²×C₈₃	1	4	yes	complemented
468	C₄×Q₁₆	C₂²×C₈₃	1	1	yes	characteristic, complemented
469	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	complemented
470	C₄×D₈	C₂²×C₈₃	1	2	yes	complemented
471	C₄×D₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
472	C₄×D₈	C₂²×C₈₃	1	2	yes	complemented
473	C₈×D₄	C₂²×C₈₃	1	1	yes	characteristic
474	C₈×D₄	C₂²×C₈₃	1	1	yes	characteristic
475	C₈×D₄	C₂²×C₈₃	1	2	yes	complemented
476	C₈×D₄	C₂²×C₈₃	1	1	yes	characteristic, complemented
477	C₈×D₄	C₂²×C₈₃	1	2	yes	complemented
478	C₈×D₄	C₂²×C₈₃	1	1	yes	characteristic, complemented
479	#427	C₂²×C₈₃	1	2	yes	complemented
480	C₂×#107	C₂²×C₈₃	1	2	yes	complemented
481	C₂×C₄⋊C₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
482	#416	C₂²×C₈₃	1	4	yes	complemented
483	C₂×#102	C₂²×C₈₃	1	4	yes	complemented
484	C₂×C₂²⋊C₈	C₂²×C₈₃	1	2	yes	complemented
485	C₂×C₄×C₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
486	C₂×#41	—	2	2	no	—
487	C₂×#41	C₂³×C₈₃	1	4	yes	—
488	C₂²×D₄	—	2	4	no	—
489	C₂²×D₄	—	2	2	no	—
490	C₂²×D₄	D₄×C₈₃	1	1	yes	characteristic
491	C₂²×D₄	C₂³×C₈₃	1	4	yes	—
492	C₂³×C₄	C₂³×C₈₃	1	2	yes	—
493	#135	—	4	4	no	—
494	C₂×Q₁₆	C₂³×C₈₃	1	1	yes	characteristic
495	C₂×SD₁₆	C₂³×C₈₃	1	4	yes	—
496	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
497	C₂×D₈	—	4	4	no	—
498	C₂×D₈	C₂³×C₈₃	1	1	yes	characteristic
499	C₂×D₈	C₂³×C₈₃	1	2	yes	—
500	C₂×D₈	C₂³×C₈₃	1	4	yes	—
501	C₂×D₈	C₂³×C₈₃	1	2	yes	—
502	C₂²×C₈	—	4	4	no	—
503	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
504	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
505	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
506	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
507	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
508	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
509	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
510	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
511	#127	—	2	2	no	—
512	#127	C₂³×C₈₃	1	2	yes	—
513	#126	—	2	4	no	—
514	#126	—	2	2	no	—
515	#125	—	2	2	no	—
516	#125	C₂³×C₈₃	1	2	yes	—
517	#124	—	2	4	no	—
518	#124	—	2	2	no	—
519	#124	C₂³×C₈₃	1	2	yes	—
520	#123	—	2	4	no	—
521	#123	—	2	2	no	—
522	#123	—	2	4	no	—
523	#123	—	2	4	no	—
524	C₂²⋊Q₈	—	2	4	no	—
525	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
526	C₂²⋊Q₈	C₂³×C₈₃	1	4	yes	—
527	#121	—	2	4	no	—
528	#121	—	2	2	no	—
529	#121	—	2	4	no	—
530	#121	—	2	4	no	—
531	#121	—	2	2	no	—
532	#121	—	2	2	no	—
533	#121	—	2	4	no	—
534	#121	—	2	4	no	—
535	#121	C₂³×C₈₃	1	2	yes	—
536	#121	C₂³×C₈₃	1	4	yes	—
537	#121	C₂³×C₈₃	1	4	yes	—
538	#121	C₂³×C₈₃	1	4	yes	—
539	#121	C₂³×C₈₃	1	4	yes	—
540	#120	—	2	4	no	—
541	#120	—	2	4	no	—
542	#120	—	2	4	no	—
543	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
544	C₄×D₄	—	2	2	no	—
545	C₄×D₄	—	2	4	no	—
546	C₄×D₄	—	2	4	no	—
547	C₄×D₄	—	2	2	no	—
548	C₄×D₄	—	2	2	no	—
549	C₄×D₄	—	2	4	no	—
550	C₄×D₄	—	2	2	no	—
551	C₄×D₄	D₄×C₈₃	1	1	yes	characteristic
552	C₄×D₄	D₄×C₈₃	1	2	yes	—
553	C₄×D₄	D₄×C₈₃	1	1	yes	characteristic
554	C₄×D₄	C₂³×C₈₃	1	2	yes	—
555	C₄×D₄	C₂³×C₈₃	1	4	yes	—
556	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
557	C₄×D₄	C₂³×C₈₃	1	2	yes	—
558	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
559	#117	—	2	2	no	—
560	#117	—	2	2	no	—
561	#117	C₂³×C₈₃	1	4	yes	—
562	C₂×C₄⋊C₄	D₄×C₈₃	1	1	yes	characteristic
563	C₂×C₄⋊C₄	C₂³×C₈₃	1	4	yes	—
564	C₂×C₂²⋊C₄	—	2	4	no	—
565	C₂×C₂²⋊C₄	—	2	4	no	—
566	C₂×C₂²⋊C₄	D₄×C₈₃	1	2	yes	—
567	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
568	#107	C₂³×C₈₃	1	1	yes	characteristic
569	#107	C₂³×C₈₃	1	2	yes	—
570	#107	C₂³×C₈₃	1	4	yes	—
571	#107	C₂³×C₈₃	1	1	yes	characteristic
572	#107	C₂³×C₈₃	1	2	yes	—
573	#106	C₂³×C₈₃	1	4	yes	—
574	#106	C₂³×C₈₃	1	2	yes	—
575	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
576	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
577	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
578	#103	C₂³×C₈₃	1	2	yes	—
579	#103	C₂³×C₈₃	1	4	yes	—
580	#103	C₂³×C₈₃	1	2	yes	—
581	#102	C₂³×C₈₃	1	2	yes	—
582	#102	C₂³×C₈₃	1	4	yes	—
583	#102	C₂³×C₈₃	1	4	yes	—
584	#102	C₂³×C₈₃	1	4	yes	—
585	#102	C₂³×C₈₃	1	4	yes	—
586	#102	C₂³×C₈₃	1	2	yes	—
587	#102	C₂³×C₈₃	1	4	yes	—
588	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
589	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
590	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
591	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
592	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
593	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
594	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
595	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
596	C₂⁴	—	2	4	no	—
597	C₂⁴	C₂×D₄×C₈₃	1	2	yes	—
598	#41	—	4	4	no	—
599	#41	—	4	4	no	—
600	#41	—	8	4	no	—
601	C₂×Q₈	—	2	2	no	—
602	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	4	no	—
605	C₂×D₄	—	2	4	no	—
606	C₂×D₄	—	2	2	no	—
607	C₂×D₄	—	2	4	no	—
608	C₂×D₄	—	2	4	no	—
609	C₂×D₄	—	2	4	no	—
610	C₂×D₄	—	2	2	no	—
611	C₂×D₄	—	2	2	no	—
612	C₂×D₄	—	2	4	no	—
613	C₂×D₄	—	4	4	no	—
614	C₂×D₄	—	4	4	no	—
615	C₂×D₄	—	4	8	no	—
616	C₂×D₄	—	8	8	no	—
617	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
618	C₂×D₄	C₂×D₄×C₈₃	1	1	yes	characteristic
619	C₂×D₄	C₂×D₄×C₈₃	1	1	yes	characteristic
620	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
621	C₂×D₄	C₂⁴×C₈₃	1	4	yes	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	2	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	—	2	4	no	—
626	C₂²×C₄	—	4	2	no	—
627	C₂²×C₄	—	4	2	no	—
628	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
629	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
630	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
631	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
632	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
636	Q₁₆	—	2	2	no	—
637	SD₁₆	—	4	4	no	—
638	SD₁₆	—	4	2	no	—
639	D₈	—	2	2	no	—
640	D₈	—	2	4	no	—
641	D₈	—	4	4	no	—
642	D₈	—	4	2	no	—
643	C₂×C₈	—	2	2	no	—
644	C₂×C₈	—	2	4	no	—
645	C₂×C₈	—	2	4	no	—
646	C₂×C₈	—	4	2	no	—
647	C₂×C₈	—	4	2	no	—
648	C₂×C₈	—	4	2	no	—
649	C₂×C₈	—	4	1	no	—
650	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
651	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
652	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
653	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
654	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
655	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	2	no	—
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	2	no	—
663	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
664	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
665	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
666	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
667	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
668	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	2	no	—
672	C₂²⋊C₄	—	2	2	no	—
673	C₂²⋊C₄	—	2	2	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	2	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	2	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
682	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
683	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
684	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
685	C₄²	—	2	4	no	—
686	C₄²	—	2	2	no	—
687	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
688	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
689	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
690	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
691	C₂³	—	2	4	no	—
692	C₂³	—	2	4	no	—
693	C₂³	—	2	2	no	—
694	C₂³	—	2	4	no	—
695	C₂³	—	4	2	no	—
696	C₂³	—	4	8	no	—
697	C₂³	—	8	4	no	—
698	C₂³	—	8	4	no	—
699	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
700	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
701	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
702	Q₈	—	2	2	no	—
703	Q₈	—	2	2	no	—
704	Q₈	—	8	2	no	—
705	D₄	—	2	4	no	—
706	D₄	—	2	2	no	—
707	D₄	—	2	2	no	—
708	D₄	—	2	4	no	—
709	D₄	—	2	4	no	—
710	D₄	—	2	2	no	—
711	D₄	—	4	8	no	—
712	D₄	—	4	4	no	—
713	D₄	—	4	8	no	—
714	D₄	—	4	4	no	—
715	D₄	—	8	4	no	—
716	D₄	—	8	2	no	—
717	D₄	—	8	4	no	—
718	D₄	—	8	4	no	—
719	D₄	—	8	4	no	—
720	D₄	#135×C₈₃	1	4	yes	complemented
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	4	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	4	2	no	—
734	C₂×C₄	—	4	2	no	—
735	C₂×C₄	—	4	2	no	—
736	C₂×C₄	—	4	4	no	—
737	C₂×C₄	—	8	4	no	—
738	C₂×C₄	—	8	4	no	—
739	C₂×C₄	—	8	4	no	—
740	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
741	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
742	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
743	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
744	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
745	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
746	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
747	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
748	C₈	—	2	1	no	—
749	C₈	—	2	2	no	—
750	C₈	—	2	2	no	—
751	C₈	—	2	1	no	—
752	C₈	—	2	1	no	—
753	C₈	H(5,𝔽₂)×C₈₃	1	2	yes	—
754	C₂²	—	2	1	no	—
755	C₂²	—	2	2	no	—
756	C₂²	—	2	1	no	—
757	C₂²	—	2	2	no	—
758	C₂²	—	2	2	no	—
759	C₂²	—	2	2	no	—
760	C₂²	—	2	2	no	—
761	C₂²	—	4	8	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	4	no	—
764	C₂²	—	4	4	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	4	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	16	8	no	—
769	C₂²	C₂×#135×C₈₃	1	4	yes	—
770	C₂²	#576×C₈₃	1	2	yes	—
771	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
772	C₄	—	2	1	no	—
773	C₄	—	2	1	no	—
774	C₄	—	2	1	no	—
775	C₄	—	2	1	no	—
776	C₄	—	2	2	no	—
777	C₄	—	2	2	no	—
778	C₄	—	4	2	no	—
779	C₄	—	4	2	no	—
780	C₄	—	4	4	no	—
781	C₄	—	4	2	no	—
782	C₄	C₂×#135×C₈₃	1	2	yes	—
783	C₄	C₂×H(5,𝔽₂)×C₈₃	1	1	yes	characteristic
784	C₄	#585×C₈₃	1	1	yes	characteristic
785	C₂	—	2	2	no	—
786	C₂	—	2	4	no	—
787	C₂	—	4	2	no	—
788	C₂	—	8	2	no	—
789	C₂	—	8	4	no	—
790	C₂	C₈₃×#3496	1	1	yes	characteristic
791	C₂	C₂²×#135×C₈₃	1	1	yes	characteristic
792	C₂	C₂×#576×C₈₃	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×D₄×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₃×#3519	C₂	semidirect
2. C₈₃×#3341	C₂	semidirect
3. C₈₃×#3339	C₂	semidirect
4. C₈₃×#3338	C₂	semidirect
5. C₈₃×#3305	C₂	semidirect
6. C₈₃×#3297	C₂	semidirect
7. C₈₃×#3295	C₂	semidirect
8. C₈₃×#3287	C₂	semidirect
9. C₈₃×#3280	C₂	semidirect
10. D₄×D₈×C₈₃	C₂	semidirect
11. C₈₃×#3247	C₂	semidirect
12. C₈₃×#3188	C₂	semidirect
13. C₈₃×#3169	C₂	semidirect
14. C₈₃×#3168	C₂	semidirect
15. C₈₃×#3050	C₂	semidirect
16. C₂×#466×C₈₃	C₂	semidirect
17. C₂×C₈×D₄×C₈₃	C₂	semidirect
18. C₂×#135×C₈₃	C₂²	semidirect
19. C₂²×D₈×C₈₃	C₂²	semidirect
20. C₂³×C₈×C₈₃	C₂²	semidirect
21. #555×C₈₃	C₂²	semidirect
24. #553×C₈₃	C₂²	semidirect
25. #550×C₈₃	C₂²	semidirect
27. #546×C₈₃	C₂²	semidirect
32. #532×C₈₃	C₂²	semidirect
33. #529×C₈₃	C₂²	semidirect
34. #525×C₈₃	C₂²	semidirect
35. C₂×#121×C₈₃	C₂²	semidirect
38. #500×C₈₃	C₂²	semidirect
39. #499×C₈₃	C₂²	semidirect
40. #495×C₈₃	C₂²	semidirect
41. #493×C₈₃	C₂²	semidirect
42. #488×C₈₃	C₂²	semidirect
43. #486×C₈₃	C₂²	semidirect
44. #484×C₈₃	C₂²	semidirect
45. #482×C₈₃	C₂²	semidirect
46. #482×C₈₃	C₂²	semidirect
47. #481×C₈₃	C₂²	semidirect
48. #478×C₈₃	C₂²	semidirect
49. #477×C₈₃	C₂²	semidirect
50. #476×C₈₃	C₂²	semidirect
51. #467×C₈₃	C₂²	semidirect
52. #467×C₈₃	C₂²	semidirect
54. #466×C₈₃	C₂²	semidirect
55. #466×C₈₃	C₂²	semidirect
56. #466×C₈₃	C₂²	semidirect
57. #466×C₈₃	C₂²	semidirect
58. #466×C₈₃	C₂²	semidirect
59. #466×C₈₃	C₂²	semidirect
60. #466×C₈₃	C₂²	semidirect
61. #465×C₈₃	C₂²	semidirect
62. #465×C₈₃	C₂²	semidirect
63. #465×C₈₃	C₂²	semidirect
64. #463×C₈₃	C₂²	semidirect
65. #460×C₈₃	C₂²	semidirect
66. #459×C₈₃	C₂²	semidirect
67. #450×C₈₃	C₂²	semidirect
68. #449×C₈₃	C₂²	semidirect
69. #449×C₈₃	C₂²	semidirect
70. #447×C₈₃	C₂²	semidirect
71. C₄×Q₁₆×C₈₃	C₂²	semidirect
72. C₄×SD₁₆×C₈₃	C₂²	semidirect
73. C₄×D₈×C₈₃	C₂²	semidirect
74. C₄×D₈×C₈₃	C₂²	semidirect
75. C₄×D₈×C₈₃	C₂²	semidirect
78. C₈×D₄×C₈₃	C₂²	semidirect
79. C₈×D₄×C₈₃	C₂²	semidirect
80. C₈×D₄×C₈₃	C₂²	semidirect
81. C₈×D₄×C₈₃	C₂²	semidirect
82. #427×C₈₃	C₂²	semidirect
83. C₂×#107×C₈₃	C₂²	semidirect
84. C₂×C₄⋊C₈×C₈₃	C₂²	semidirect
85. #416×C₈₃	C₂²	semidirect
86. C₂×#102×C₈₃	C₂²	semidirect
87. C₂×C₂²⋊C₈×C₈₃	C₂²	semidirect
88. C₂×C₄×C₈×C₈₃	C₂²	semidirect
323. D₄×C₈₃	#135	semidirect
388. #62251	C₈₃	direct (N × H)
397. #3519	C₂×C₈₃	semidirect
398. #3341	C₂×C₈₃	semidirect
399. #3339	C₂×C₈₃	semidirect
400. #3338	C₂×C₈₃	semidirect
401. #3305	C₂×C₈₃	semidirect
402. #3297	C₂×C₈₃	semidirect
403. #3295	C₂×C₈₃	semidirect
404. #3287	C₂×C₈₃	semidirect
405. #3280	C₂×C₈₃	semidirect
406. D₄×D₈	C₂×C₈₃	semidirect
407. #3247	C₂×C₈₃	semidirect
408. #3188	C₂×C₈₃	semidirect
409. #3169	C₂×C₈₃	semidirect
410. #3168	C₂×C₈₃	semidirect
411. #3050	C₂×C₈₃	semidirect
412. C₂×#466	C₂×C₈₃	semidirect
413. C₂×C₈×D₄	C₂×C₈₃	semidirect
414. C₈₃	#62251	direct (N × H)
415. C₂×#135	C₂²×C₈₃	semidirect
416. C₂²×D₈	C₂²×C₈₃	semidirect
417. C₂³×C₈	C₂²×C₈₃	semidirect
418. #555	C₂²×C₈₃	semidirect
421. #553	C₂²×C₈₃	semidirect
422. #550	C₂²×C₈₃	semidirect
424. #546	C₂²×C₈₃	semidirect
429. #532	C₂²×C₈₃	semidirect
430. #529	C₂²×C₈₃	semidirect
431. #525	C₂²×C₈₃	semidirect
432. C₂×#121	C₂²×C₈₃	semidirect
435. #500	C₂²×C₈₃	semidirect
436. #499	C₂²×C₈₃	semidirect
437. #495	C₂²×C₈₃	semidirect
438. #493	C₂²×C₈₃	semidirect
439. #488	C₂²×C₈₃	semidirect
440. #486	C₂²×C₈₃	semidirect
441. #484	C₂²×C₈₃	semidirect
442. #482	C₂²×C₈₃	semidirect
443. #482	C₂²×C₈₃	semidirect
444. #481	C₂²×C₈₃	semidirect
445. #478	C₂²×C₈₃	semidirect
446. #477	C₂²×C₈₃	semidirect
447. #476	C₂²×C₈₃	semidirect
448. #467	C₂²×C₈₃	semidirect
449. #467	C₂²×C₈₃	semidirect
451. #466	C₂²×C₈₃	semidirect
452. #466	C₂²×C₈₃	semidirect
453. #466	C₂²×C₈₃	semidirect
454. #466	C₂²×C₈₃	semidirect
455. #466	C₂²×C₈₃	semidirect
456. #466	C₂²×C₈₃	semidirect
457. #466	C₂²×C₈₃	semidirect
458. #465	C₂²×C₈₃	semidirect
459. #465	C₂²×C₈₃	semidirect
460. #465	C₂²×C₈₃	semidirect
461. #463	C₂²×C₈₃	semidirect
462. #460	C₂²×C₈₃	semidirect
463. #459	C₂²×C₈₃	semidirect
464. #450	C₂²×C₈₃	semidirect
465. #449	C₂²×C₈₃	semidirect
466. #449	C₂²×C₈₃	semidirect
467. #447	C₂²×C₈₃	semidirect
468. C₄×Q₁₆	C₂²×C₈₃	semidirect
469. C₄×SD₁₆	C₂²×C₈₃	semidirect
470. C₄×D₈	C₂²×C₈₃	semidirect
471. C₄×D₈	C₂²×C₈₃	semidirect
472. C₄×D₈	C₂²×C₈₃	semidirect
475. C₈×D₄	C₂²×C₈₃	semidirect
476. C₈×D₄	C₂²×C₈₃	semidirect
477. C₈×D₄	C₂²×C₈₃	semidirect
478. C₈×D₄	C₂²×C₈₃	semidirect
479. #427	C₂²×C₈₃	semidirect
480. C₂×#107	C₂²×C₈₃	semidirect
481. C₂×C₄⋊C₈	C₂²×C₈₃	semidirect
482. #416	C₂²×C₈₃	semidirect
483. C₂×#102	C₂²×C₈₃	semidirect
484. C₂×C₂²⋊C₈	C₂²×C₈₃	semidirect
485. C₂×C₄×C₈	C₂²×C₈₃	semidirect
720. D₄	#135×C₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₈₃×#3519	2
C₈₃×#3341	2
C₈₃×#3339	2
C₈₃×#3338	2
C₈₃×#3305	2
C₈₃×#3297	2
C₈₃×#3295	2
C₈₃×#3287	2
C₈₃×#3280	2
D₄×D₈×C₈₃	2
C₈₃×#3247	2
C₈₃×#3188	2
C₈₃×#3169	2
C₈₃×#3168	2
C₈₃×#3050	2
C₂×#466×C₈₃	2
C₂×C₈×D₄×C₈₃	2
#62251	83

Subgroups — C83×#62251 #35290075

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#62251 #35290075