Subgroups — C₈₃×#61793 #35289617

Order 21248.

1738 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3546	C₂	1	1	yes	maximal, characteristic
2	C₈₃×#3507	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₃×#3350	C₂	1	2	yes	maximal, complemented
4	C₈₃×#3349	C₂	1	2	yes	maximal, complemented
5	C₈₃×#3346	C₂	1	2	yes	maximal, complemented
6	C₈₃×#3343	C₂	1	2	yes	maximal, complemented
7	C₈₃×#3317	C₂	1	2	yes	maximal, complemented
8	C₈₃×#3314	C₂	1	2	yes	maximal, complemented
9	C₈₃×#3311	C₂	1	2	yes	maximal, complemented
10	C₈₃×#3310	C₂	1	2	yes	maximal, complemented
11	C₈₃×#3240	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₃×#3235	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₃×#3201	C₂	1	2	yes	maximal, complemented
14	C₈₃×#3200	C₂	1	2	yes	maximal, complemented
15	C₈₃×#3117	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₃×#3112	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₃×#3098	C₂	1	2	yes	maximal, complemented
18	C₈₃×#3096	C₂	1	2	yes	maximal, complemented
19	C₈₃×#2980	C₂	1	1	yes	maximal, characteristic, complemented
20	#560×C₈₃	—	2	2	no	—
21	#559×C₈₃	—	2	1	no	—
22	#557×C₈₃	—	2	1	no	—
23	#556×C₈₃	—	2	2	no	—
24	#556×C₈₃	C₂²	1	1	yes	characteristic
25	#556×C₈₃	C₂²	1	2	yes	complemented
26	#554×C₈₃	C₂²	1	2	yes	complemented
27	#553×C₈₃	C₂²	1	2	yes	—
28	#552×C₈₃	C₂²	1	2	yes	—
29	#552×C₈₃	C₂²	1	2	yes	complemented
30	#550×C₈₃	—	2	1	no	—
31	#550×C₈₃	C₂²	1	1	yes	characteristic
32	#547×C₈₃	C₂²	1	1	yes	characteristic
33	#546×C₈₃	—	2	1	no	—
34	#546×C₈₃	C₂²	1	2	yes	—
35	D₄²×C₈₃	C₂²	1	1	yes	characteristic
36	#542×C₈₃	—	2	1	no	—
37	#539×C₈₃	—	2	1	no	—
38	#539×C₈₃	—	2	1	no	—
39	#538×C₈₃	—	2	2	no	—
40	#537×C₈₃	C₂²	1	2	yes	—
41	#536×C₈₃	C₂²	1	2	yes	complemented
42	#535×C₈₃	—	2	1	no	—
43	#535×C₈₃	C₂²	1	2	yes	—
44	#533×C₈₃	C₂²	1	1	yes	characteristic, complemented
45	#532×C₈₃	C₂²	1	1	yes	characteristic
46	#532×C₈₃	C₂²	1	1	yes	characteristic
47	#529×C₈₃	—	2	2	no	—
48	#529×C₈₃	C₂²	1	1	yes	characteristic
49	#520×C₈₃	C₂²	1	2	yes	complemented
50	C₂×C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
51	#501×C₈₃	C₂²	1	2	yes	complemented
52	#501×C₈₃	C₂²	1	1	yes	characteristic, complemented
53	#501×C₈₃	C₂²	1	1	yes	characteristic, complemented
54	#490×C₈₃	C₂²	1	2	yes	—
55	#489×C₈₃	C₂²	1	1	yes	characteristic
56	#489×C₈₃	C₂²	1	1	yes	characteristic
57	#485×C₈₃	C₂²	1	2	yes	complemented
58	#485×C₈₃	C₂²	1	2	yes	complemented
59	#485×C₈₃	C₂²	1	2	yes	complemented
60	#485×C₈₃	C₂²	1	2	yes	complemented
61	#484×C₈₃	C₂²	1	2	yes	complemented
62	#484×C₈₃	C₂²	1	2	yes	complemented
63	#484×C₈₃	C₂²	1	1	yes	characteristic, complemented
64	#483×C₈₃	C₂²	1	2	yes	complemented
65	#482×C₈₃	C₂²	1	2	yes	—
66	#482×C₈₃	C₂²	1	2	yes	—
67	#482×C₈₃	C₂²	1	2	yes	—
68	#482×C₈₃	C₂²	1	2	yes	complemented
69	#482×C₈₃	C₂²	1	2	yes	complemented
70	#482×C₈₃	C₂²	1	2	yes	complemented
71	#481×C₈₃	C₂²	1	1	yes	characteristic
72	#481×C₈₃	C₂²	1	2	yes	complemented
73	#480×C₈₃	C₂²	1	2	yes	—
74	#480×C₈₃	C₂²	1	2	yes	—
75	#480×C₈₃	C₂²	1	2	yes	complemented
76	#479×C₈₃	C₂²	1	2	yes	complemented
77	#479×C₈₃	C₂²	1	2	yes	complemented
78	#478×C₈₃	C₂²	1	2	yes	—
79	#477×C₈₃	C₂²	1	2	yes	complemented
80	#476×C₈₃	C₂²	1	2	yes	complemented
81	#474×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	#468×C₈₃	C₂²	1	2	yes	complemented
86	#467×C₈₃	C₂²	1	2	yes	complemented
87	#465×C₈₃	C₂²	1	2	yes	—
88	#465×C₈₃	C₂²	1	2	yes	—
89	#465×C₈₃	C₂²	1	2	yes	complemented
90	#464×C₈₃	C₂²	1	2	yes	—
91	#460×C₈₃	C₂²	1	2	yes	—
92	#452×C₈₃	C₂²	1	2	yes	complemented
93	#452×C₈₃	C₂²	1	2	yes	complemented
94	#451×C₈₃	C₂²	1	1	yes	characteristic, complemented
95	#450×C₈₃	C₂²	1	2	yes	—
96	#450×C₈₃	C₂²	1	2	yes	—
97	#448×C₈₃	C₂²	1	1	yes	characteristic
98	#448×C₈₃	C₂²	1	2	yes	complemented
99	#441×C₈₃	C₂²	1	2	yes	complemented
100	#440×C₈₃	C₂²	1	2	yes	—
101	#440×C₈₃	C₂²	1	2	yes	complemented
102	#440×C₈₃	C₂²	1	2	yes	complemented
103	#435×C₈₃	C₂²	1	2	yes	—
104	#435×C₈₃	C₂²	1	2	yes	complemented
105	#435×C₈₃	C₂²	1	2	yes	complemented
106	#435×C₈₃	C₂²	1	2	yes	complemented
107	#432×C₈₃	C₂²	1	1	yes	characteristic, complemented
108	#432×C₈₃	C₂²	1	1	yes	characteristic, complemented
109	#428×C₈₃	C₂²	1	2	yes	complemented
110	#428×C₈₃	C₂²	1	2	yes	complemented
111	#427×C₈₃	C₂²	1	2	yes	complemented
112	C₂×#107×C₈₃	C₂²	1	2	yes	complemented
113	#418×C₈₃	C₂²	1	2	yes	—
114	#417×C₈₃	C₂²	1	2	yes	complemented
115	#416×C₈₃	C₂²	1	2	yes	complemented
116	C₂×#102×C₈₃	C₂²	1	2	yes	—
117	#408×C₈₃	C₂²	1	2	yes	complemented
118	#408×C₈₃	C₂²	1	2	yes	complemented
119	C₂×#41×C₈₃	—	2	1	no	—
120	C₂×#41×C₈₃	—	2	1	no	—
121	C₂×#41×C₈₃	C₂³	1	2	yes	—
122	C₂×#41×C₈₃	C₂³	1	2	yes	—
123	C₂²×Q₈×C₈₃	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₈₃	—	2	1	no	—
125	C₂²×D₄×C₈₃	C₂³	1	2	yes	—
126	C₂×Q₁₆×C₈₃	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
129	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
130	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
131	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
132	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
133	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
134	C₄⋊Q₈×C₈₃	—	2	2	no	—
135	C₄⋊Q₈×C₈₃	D₄	1	1	yes	characteristic
136	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
137	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
138	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
139	#127×C₈₃	—	2	1	no	—
140	#127×C₈₃	—	2	2	no	—
141	#127×C₈₃	D₄	1	1	yes	characteristic
142	#127×C₈₃	C₂³	1	1	yes	characteristic
143	#126×C₈₃	—	2	2	no	—
144	#126×C₈₃	—	2	2	no	—
145	#126×C₈₃	—	2	2	no	—
146	#126×C₈₃	—	2	2	no	—
147	#126×C₈₃	—	2	2	no	—
148	#126×C₈₃	—	2	2	no	—
149	#126×C₈₃	—	2	1	no	—
150	#125×C₈₃	—	2	2	no	—
151	#125×C₈₃	—	2	2	no	—
152	#125×C₈₃	—	2	2	no	—
153	#125×C₈₃	C₂³	1	2	yes	—
154	#125×C₈₃	C₂³	1	1	yes	characteristic
155	#124×C₈₃	—	2	2	no	—
156	#124×C₈₃	—	2	2	no	—
157	#124×C₈₃	—	2	1	no	—
158	#124×C₈₃	—	2	2	no	—
159	#124×C₈₃	—	2	1	no	—
160	#124×C₈₃	D₄	1	2	yes	—
161	#124×C₈₃	C₂³	1	1	yes	characteristic
162	#123×C₈₃	—	2	2	no	—
163	#123×C₈₃	—	2	2	no	—
164	#123×C₈₃	—	2	2	no	—
165	#123×C₈₃	—	2	2	no	—
166	#123×C₈₃	—	2	1	no	—
167	#123×C₈₃	—	2	2	no	—
168	#123×C₈₃	—	2	2	no	—
169	#123×C₈₃	—	2	2	no	—
170	C₂²⋊Q₈×C₈₃	—	2	2	no	—
171	C₂²⋊Q₈×C₈₃	—	2	1	no	—
172	C₂²⋊Q₈×C₈₃	—	2	1	no	—
173	C₂²⋊Q₈×C₈₃	—	2	1	no	—
174	C₂²⋊Q₈×C₈₃	—	2	2	no	—
175	C₂²⋊Q₈×C₈₃	—	2	2	no	—
176	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
177	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
178	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
179	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
180	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
181	C₂²⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
182	#121×C₈₃	—	2	2	no	—
183	#121×C₈₃	—	2	2	no	—
184	#121×C₈₃	—	2	2	no	—
185	#121×C₈₃	—	2	2	no	—
186	#121×C₈₃	—	2	1	no	—
187	#121×C₈₃	—	2	1	no	—
188	#121×C₈₃	—	2	2	no	—
189	#121×C₈₃	—	2	2	no	—
190	#121×C₈₃	D₄	1	2	yes	—
191	#121×C₈₃	D₄	1	1	yes	characteristic
192	#121×C₈₃	D₄	1	1	yes	characteristic
193	#121×C₈₃	C₂³	1	2	yes	—
194	#121×C₈₃	C₂³	1	2	yes	—
195	#121×C₈₃	C₂³	1	2	yes	—
196	#121×C₈₃	C₂³	1	2	yes	—
197	#121×C₈₃	C₂³	1	1	yes	characteristic
198	#120×C₈₃	—	2	2	no	—
199	#120×C₈₃	—	2	2	no	—
200	#120×C₈₃	—	2	2	no	—
201	#120×C₈₃	—	2	2	no	—
202	C₄×Q₈×C₈₃	—	2	2	no	—
203	C₄×Q₈×C₈₃	—	2	2	no	—
204	C₄×Q₈×C₈₃	—	2	1	no	—
205	C₄×Q₈×C₈₃	—	2	1	no	—
206	C₄×Q₈×C₈₃	—	2	1	no	—
207	C₄×Q₈×C₈₃	—	2	1	no	—
208	C₄×Q₈×C₈₃	—	2	1	no	—
209	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
210	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
211	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
212	C₄×D₄×C₈₃	—	2	2	no	—
213	C₄×D₄×C₈₃	—	2	2	no	—
214	C₄×D₄×C₈₃	—	2	2	no	—
215	C₄×D₄×C₈₃	—	2	2	no	—
216	C₄×D₄×C₈₃	—	2	1	no	—
217	C₄×D₄×C₈₃	—	2	1	no	—
218	C₄×D₄×C₈₃	—	2	2	no	—
219	C₄×D₄×C₈₃	—	2	1	no	—
220	C₄×D₄×C₈₃	C₂³	1	2	yes	—
221	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
222	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
223	C₄×D₄×C₈₃	C₂³	1	2	yes	—
224	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
225	#117×C₈₃	—	2	2	no	—
226	#117×C₈₃	—	2	2	no	—
227	#117×C₈₃	—	2	1	no	—
228	#117×C₈₃	C₂³	1	2	yes	—
229	#117×C₈₃	C₂³	1	2	yes	—
230	#117×C₈₃	C₂³	1	2	yes	—
231	#117×C₈₃	C₂³	1	2	yes	—
232	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
233	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
234	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
235	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
237	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
238	C₂×C₄²×C₈₃	—	2	1	no	—
239	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
240	#107×C₈₃	C₂³	1	2	yes	—
241	#107×C₈₃	C₂³	1	2	yes	—
242	#107×C₈₃	C₂³	1	2	yes	—
243	#107×C₈₃	C₂³	1	2	yes	—
244	#107×C₈₃	C₂³	1	2	yes	—
245	#107×C₈₃	C₂³	1	2	yes	—
246	#107×C₈₃	C₂³	1	2	yes	—
247	#106×C₈₃	C₂³	1	2	yes	—
248	#106×C₈₃	C₂³	1	2	yes	—
249	#106×C₈₃	C₂³	1	2	yes	—
250	#106×C₈₃	C₂³	1	2	yes	—
251	#106×C₈₃	C₂³	1	2	yes	—
252	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
253	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
254	#103×C₈₃	C₂³	1	2	yes	—
255	#103×C₈₃	C₂³	1	2	yes	—
256	#103×C₈₃	C₂³	1	2	yes	—
257	#103×C₈₃	C₂³	1	2	yes	—
258	#103×C₈₃	C₂³	1	2	yes	—
259	#103×C₈₃	C₂³	1	2	yes	—
260	#103×C₈₃	C₂³	1	2	yes	—
261	#102×C₈₃	C₂³	1	2	yes	—
262	#102×C₈₃	C₂³	1	2	yes	—
263	#102×C₈₃	C₂³	1	2	yes	—
264	#102×C₈₃	C₂³	1	2	yes	—
265	#102×C₈₃	C₂³	1	2	yes	—
266	#102×C₈₃	C₂³	1	2	yes	—
267	#102×C₈₃	C₂³	1	2	yes	—
268	#102×C₈₃	C₂³	1	2	yes	—
269	#102×C₈₃	C₂³	1	2	yes	—
270	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
271	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
272	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
273	C₂²⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
274	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
275	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
276	C₂²⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
277	#97×C₈₃	C₂³	1	1	yes	characteristic
278	#97×C₈₃	C₂³	1	1	yes	characteristic
279	#97×C₈₃	C₂³	1	2	yes	—
280	C₂⁴×C₈₃	—	2	2	no	—
281	#41×C₈₃	—	4	2	no	—
282	#41×C₈₃	—	4	2	no	—
283	#41×C₈₃	—	4	2	no	—
284	#41×C₈₃	—	4	2	no	—
285	#41×C₈₃	—	8	2	no	—
286	#41×C₈₃	—	8	2	no	—
287	C₂×Q₈×C₈₃	—	2	1	no	—
288	C₂×Q₈×C₈₃	—	2	1	no	—
289	C₂×Q₈×C₈₃	—	2	1	no	—
290	C₂×Q₈×C₈₃	—	2	1	no	—
291	C₂×Q₈×C₈₃	—	4	2	no	—
292	C₂×Q₈×C₈₃	C₂×D₄	1	2	yes	—
293	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
294	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
295	C₂×D₄×C₈₃	—	2	1	no	—
296	C₂×D₄×C₈₃	—	2	2	no	—
297	C₂×D₄×C₈₃	—	2	2	no	—
298	C₂×D₄×C₈₃	—	2	2	no	—
299	C₂×D₄×C₈₃	—	2	2	no	—
300	C₂×D₄×C₈₃	—	2	2	no	—
301	C₂×D₄×C₈₃	—	2	1	no	—
302	C₂×D₄×C₈₃	—	2	1	no	—
303	C₂×D₄×C₈₃	—	2	2	no	—
304	C₂×D₄×C₈₃	—	4	2	no	—
305	C₂×D₄×C₈₃	—	4	2	no	—
306	C₂×D₄×C₈₃	—	8	2	no	—
307	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
308	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
309	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
310	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
311	C₂×D₄×C₈₃	C₂×D₄	1	1	yes	characteristic
312	C₂×D₄×C₈₃	C₂×D₄	1	1	yes	characteristic
313	C₂×D₄×C₈₃	C₂⁴	1	1	yes	characteristic
314	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₈₃	—	2	1	no	—
316	C₂²×C₄×C₈₃	—	2	1	no	—
317	C₂²×C₄×C₈₃	—	2	2	no	—
318	C₂²×C₄×C₈₃	—	2	2	no	—
319	C₂²×C₄×C₈₃	—	2	2	no	—
320	C₂²×C₄×C₈₃	—	2	1	no	—
321	C₂²×C₄×C₈₃	—	2	2	no	—
322	C₂²×C₄×C₈₃	—	2	2	no	—
323	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
324	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
325	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
327	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
328	Q₁₆×C₈₃	—	4	2	no	—
329	SD₁₆×C₈₃	—	4	2	no	—
330	SD₁₆×C₈₃	—	4	2	no	—
331	SD₁₆×C₈₃	—	4	2	no	—
332	M₁₆×C₈₃	—	4	2	no	—
333	M₁₆×C₈₃	—	4	2	no	—
334	C₂×C₈×C₈₃	—	4	2	no	—
335	C₂×C₈×C₈₃	—	4	2	no	—
336	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
337	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
338	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
339	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
340	C₄⋊C₄×C₈₃	—	2	2	no	—
341	C₄⋊C₄×C₈₃	—	2	2	no	—
342	C₄⋊C₄×C₈₃	—	2	1	no	—
343	C₄⋊C₄×C₈₃	—	2	2	no	—
344	C₄⋊C₄×C₈₃	—	2	2	no	—
345	C₄⋊C₄×C₈₃	—	2	2	no	—
346	C₄⋊C₄×C₈₃	—	2	2	no	—
347	C₄⋊C₄×C₈₃	—	2	1	no	—
348	C₄⋊C₄×C₈₃	—	2	1	no	—
349	C₄⋊C₄×C₈₃	—	2	2	no	—
350	C₄⋊C₄×C₈₃	—	2	2	no	—
351	C₄⋊C₄×C₈₃	—	2	1	no	—
352	C₄⋊C₄×C₈₃	—	2	1	no	—
353	C₄⋊C₄×C₈₃	—	2	1	no	—
354	C₄⋊C₄×C₈₃	—	2	2	no	—
355	C₄⋊C₄×C₈₃	—	2	2	no	—
356	C₄⋊C₄×C₈₃	—	2	1	no	—
357	C₄⋊C₄×C₈₃	—	2	2	no	—
358	C₄⋊C₄×C₈₃	—	2	2	no	—
359	C₄⋊C₄×C₈₃	—	2	1	no	—
360	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
361	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
362	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
363	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
364	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
365	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
366	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
367	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
368	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
369	C₂²⋊C₄×C₈₃	—	2	2	no	—
370	C₂²⋊C₄×C₈₃	—	2	2	no	—
371	C₂²⋊C₄×C₈₃	—	2	2	no	—
372	C₂²⋊C₄×C₈₃	—	2	2	no	—
373	C₂²⋊C₄×C₈₃	—	2	2	no	—
374	C₂²⋊C₄×C₈₃	—	2	2	no	—
375	C₂²⋊C₄×C₈₃	—	2	2	no	—
376	C₂²⋊C₄×C₈₃	—	2	1	no	—
377	C₂²⋊C₄×C₈₃	—	2	2	no	—
378	C₂²⋊C₄×C₈₃	—	2	2	no	—
379	C₂²⋊C₄×C₈₃	—	2	1	no	—
380	C₂²⋊C₄×C₈₃	—	2	2	no	—
381	C₂²⋊C₄×C₈₃	—	2	1	no	—
382	C₂²⋊C₄×C₈₃	—	2	1	no	—
383	C₂²⋊C₄×C₈₃	—	2	2	no	—
384	C₂²⋊C₄×C₈₃	—	2	2	no	—
385	C₂²⋊C₄×C₈₃	—	2	2	no	—
386	C₂²⋊C₄×C₈₃	—	2	1	no	—
387	C₂²⋊C₄×C₈₃	—	2	2	no	—
388	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
389	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
390	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
391	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
392	C₄²×C₈₃	—	2	2	no	—
393	C₄²×C₈₃	—	2	2	no	—
394	C₄²×C₈₃	—	2	2	no	—
395	C₄²×C₈₃	—	2	2	no	—
396	C₄²×C₈₃	—	2	1	no	—
397	C₄²×C₈₃	—	2	2	no	—
398	C₄²×C₈₃	—	2	2	no	—
399	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
400	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
401	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
402	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
403	C₂³×C₈₃	—	2	1	no	—
404	C₂³×C₈₃	—	2	2	no	—
405	C₂³×C₈₃	—	8	2	no	—
406	C₂³×C₈₃	—	8	2	no	—
407	C₂³×C₈₃	—	8	2	no	—
408	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
409	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
410	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
411	Q₈×C₈₃	—	2	2	no	—
412	Q₈×C₈₃	—	2	2	no	—
413	Q₈×C₈₃	—	2	2	no	—
414	Q₈×C₈₃	—	4	2	no	—
415	Q₈×C₈₃	—	4	2	no	—
416	Q₈×C₈₃	—	4	2	no	—
417	Q₈×C₈₃	—	4	2	no	—
418	Q₈×C₈₃	—	8	1	no	—
419	D₄×C₈₃	—	2	2	no	—
420	D₄×C₈₃	—	2	2	no	—
421	D₄×C₈₃	—	2	2	no	—
422	D₄×C₈₃	—	4	1	no	—
423	D₄×C₈₃	—	4	2	no	—
424	D₄×C₈₃	—	4	2	no	—
425	D₄×C₈₃	—	4	2	no	—
426	D₄×C₈₃	—	4	2	no	—
427	D₄×C₈₃	—	4	1	no	—
428	D₄×C₈₃	—	4	2	no	—
429	D₄×C₈₃	—	8	1	no	—
430	D₄×C₈₃	—	8	2	no	—
431	D₄×C₈₃	—	8	1	no	—
432	D₄×C₈₃	—	8	2	no	—
433	D₄×C₈₃	—	8	2	no	—
434	D₄×C₈₃	—	8	2	no	—
435	D₄×C₈₃	—	8	2	no	—
436	D₄×C₈₃	—	8	2	no	—
437	C₂×C₄×C₈₃	—	2	2	no	—
438	C₂×C₄×C₈₃	—	2	2	no	—
439	C₂×C₄×C₈₃	—	2	2	no	—
440	C₂×C₄×C₈₃	—	2	2	no	—
441	C₂×C₄×C₈₃	—	2	2	no	—
442	C₂×C₄×C₈₃	—	2	2	no	—
443	C₂×C₄×C₈₃	—	2	2	no	—
444	C₂×C₄×C₈₃	—	2	1	no	—
445	C₂×C₄×C₈₃	—	2	2	no	—
446	C₂×C₄×C₈₃	—	2	1	no	—
447	C₂×C₄×C₈₃	—	2	2	no	—
448	C₂×C₄×C₈₃	—	2	2	no	—
449	C₂×C₄×C₈₃	—	2	1	no	—
450	C₂×C₄×C₈₃	—	4	1	no	—
451	C₂×C₄×C₈₃	—	4	1	no	—
452	C₂×C₄×C₈₃	—	4	2	no	—
453	C₂×C₄×C₈₃	—	4	2	no	—
454	C₂×C₄×C₈₃	—	8	2	no	—
455	C₂×C₄×C₈₃	—	8	2	no	—
456	C₂×C₄×C₈₃	—	8	1	no	—
457	C₂×C₄×C₈₃	—	8	2	no	—
458	C₂×C₄×C₈₃	—	8	2	no	—
459	C₂×C₄×C₈₃	—	8	2	no	—
460	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
462	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
463	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
464	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
466	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
468	C₈×C₈₃	—	2	2	no	—
469	C₈×C₈₃	—	2	2	no	—
470	C₈×C₈₃	—	2	2	no	—
471	C₈×C₈₃	—	2	2	no	—
472	C₂²×C₈₃	—	2	1	no	—
473	C₂²×C₈₃	—	2	2	no	—
474	C₂²×C₈₃	—	2	2	no	—
475	C₂²×C₈₃	—	2	1	no	—
476	C₂²×C₈₃	—	2	2	no	—
477	C₂²×C₈₃	—	2	2	no	—
478	C₂²×C₈₃	—	2	1	no	—
479	C₂²×C₈₃	—	2	2	no	—
480	C₂²×C₈₃	—	2	2	no	—
481	C₂²×C₈₃	—	4	1	no	—
482	C₂²×C₈₃	—	4	2	no	—
483	C₂²×C₈₃	—	4	2	no	—
484	C₂²×C₈₃	—	4	1	no	—
485	C₂²×C₈₃	—	4	2	no	—
486	C₂²×C₈₃	—	4	1	no	—
487	C₂²×C₈₃	—	16	4	no	—
488	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
489	C₄×C₈₃	—	2	1	no	—
490	C₄×C₈₃	—	2	1	no	—
491	C₄×C₈₃	—	2	1	no	—
492	C₄×C₈₃	—	2	1	no	—
493	C₄×C₈₃	—	2	2	no	—
494	C₄×C₈₃	—	2	1	no	—
495	C₄×C₈₃	—	2	2	no	—
496	C₄×C₈₃	—	4	1	no	—
497	C₄×C₈₃	—	4	2	no	—
498	C₄×C₈₃	—	4	2	no	—
499	C₄×C₈₃	—	4	2	no	—
500	C₄×C₈₃	—	4	1	no	—
501	C₄×C₈₃	—	4	2	no	—
502	C₄×C₈₃	—	4	2	no	—
503	C₄×C₈₃	—	4	1	no	—
504	C₄×C₈₃	#585	1	2	yes	—
505	#61793	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
506	C₂×C₈₃	—	4	1	no	—
507	C₂×C₈₃	—	4	2	no	—
508	C₂×C₈₃	—	4	2	no	—
509	C₂×C₈₃	—	8	2	no	—
510	C₂×C₈₃	—	8	1	no	—
511	C₂×C₈₃	#3485	1	1	yes	characteristic
512	C₂×C₈₃	#3585	1	1	yes	characteristic
513	C₂×C₈₃	#3586	1	1	yes	characteristic
514	#3546	C₂×C₈₃	1	1	yes	characteristic
515	#3507	C₂×C₈₃	1	1	yes	characteristic, complemented
516	#3350	C₂×C₈₃	1	2	yes	complemented
517	#3349	C₂×C₈₃	1	2	yes	complemented
518	#3346	C₂×C₈₃	1	2	yes	complemented
519	#3343	C₂×C₈₃	1	2	yes	complemented
520	#3317	C₂×C₈₃	1	2	yes	complemented
521	#3314	C₂×C₈₃	1	2	yes	complemented
522	#3311	C₂×C₈₃	1	2	yes	complemented
523	#3310	C₂×C₈₃	1	2	yes	complemented
524	#3240	C₂×C₈₃	1	1	yes	characteristic, complemented
525	#3235	C₂×C₈₃	1	1	yes	characteristic, complemented
526	#3201	C₂×C₈₃	1	2	yes	complemented
527	#3200	C₂×C₈₃	1	2	yes	complemented
528	#3117	C₂×C₈₃	1	1	yes	characteristic, complemented
529	#3112	C₂×C₈₃	1	1	yes	characteristic, complemented
530	#3098	C₂×C₈₃	1	2	yes	complemented
531	#3096	C₂×C₈₃	1	2	yes	complemented
532	#2980	C₂×C₈₃	1	1	yes	characteristic, complemented
533	C₈₃	#61793	1	1	yes	characteristic, direct product factor, Sylow
534	#560	—	2	2	no	—
535	#559	—	2	1	no	—
536	#557	—	2	1	no	—
537	#556	—	2	2	no	—
538	#556	C₂²×C₈₃	1	1	yes	characteristic
539	#556	C₂²×C₈₃	1	2	yes	complemented
540	#554	C₂²×C₈₃	1	2	yes	complemented
541	#553	C₂²×C₈₃	1	2	yes	—
542	#552	C₂²×C₈₃	1	2	yes	—
543	#552	C₂²×C₈₃	1	2	yes	complemented
544	#550	—	2	1	no	—
545	#550	C₂²×C₈₃	1	1	yes	characteristic
546	#547	C₂²×C₈₃	1	1	yes	characteristic
547	#546	—	2	1	no	—
548	#546	C₂²×C₈₃	1	2	yes	—
549	D₄²	C₂²×C₈₃	1	1	yes	characteristic
550	#542	—	2	1	no	—
551	#539	—	2	1	no	—
552	#539	—	2	1	no	—
553	#538	—	2	2	no	—
554	#537	C₂²×C₈₃	1	2	yes	—
555	#536	C₂²×C₈₃	1	2	yes	complemented
556	#535	—	2	1	no	—
557	#535	C₂²×C₈₃	1	2	yes	—
558	#533	C₂²×C₈₃	1	1	yes	characteristic, complemented
559	#532	C₂²×C₈₃	1	1	yes	characteristic
560	#532	C₂²×C₈₃	1	1	yes	characteristic
561	#529	—	2	2	no	—
562	#529	C₂²×C₈₃	1	1	yes	characteristic
563	#520	C₂²×C₈₃	1	2	yes	complemented
564	C₂×C₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
565	#501	C₂²×C₈₃	1	2	yes	complemented
566	#501	C₂²×C₈₃	1	1	yes	characteristic, complemented
567	#501	C₂²×C₈₃	1	1	yes	characteristic, complemented
568	#490	C₂²×C₈₃	1	2	yes	—
569	#489	C₂²×C₈₃	1	1	yes	characteristic
570	#489	C₂²×C₈₃	1	1	yes	characteristic
571	#485	C₂²×C₈₃	1	2	yes	complemented
572	#485	C₂²×C₈₃	1	2	yes	complemented
573	#485	C₂²×C₈₃	1	2	yes	complemented
574	#485	C₂²×C₈₃	1	2	yes	complemented
575	#484	C₂²×C₈₃	1	2	yes	complemented
576	#484	C₂²×C₈₃	1	2	yes	complemented
577	#484	C₂²×C₈₃	1	1	yes	characteristic, complemented
578	#483	C₂²×C₈₃	1	2	yes	complemented
579	#482	C₂²×C₈₃	1	2	yes	—
580	#482	C₂²×C₈₃	1	2	yes	—
581	#482	C₂²×C₈₃	1	2	yes	—
582	#482	C₂²×C₈₃	1	2	yes	complemented
583	#482	C₂²×C₈₃	1	2	yes	complemented
584	#482	C₂²×C₈₃	1	2	yes	complemented
585	#481	C₂²×C₈₃	1	1	yes	characteristic
586	#481	C₂²×C₈₃	1	2	yes	complemented
587	#480	C₂²×C₈₃	1	2	yes	—
588	#480	C₂²×C₈₃	1	2	yes	—
589	#480	C₂²×C₈₃	1	2	yes	complemented
590	#479	C₂²×C₈₃	1	2	yes	complemented
591	#479	C₂²×C₈₃	1	2	yes	complemented
592	#478	C₂²×C₈₃	1	2	yes	—
593	#477	C₂²×C₈₃	1	2	yes	complemented
594	#476	C₂²×C₈₃	1	2	yes	complemented
595	#474	C₂²×C₈₃	1	2	yes	complemented
596	#470	C₂²×C₈₃	1	2	yes	complemented
597	#468	C₂²×C₈₃	1	2	yes	—
598	#468	C₂²×C₈₃	1	2	yes	—
599	#468	C₂²×C₈₃	1	2	yes	complemented
600	#467	C₂²×C₈₃	1	2	yes	complemented
601	#465	C₂²×C₈₃	1	2	yes	—
602	#465	C₂²×C₈₃	1	2	yes	—
603	#465	C₂²×C₈₃	1	2	yes	complemented
604	#464	C₂²×C₈₃	1	2	yes	—
605	#460	C₂²×C₈₃	1	2	yes	—
606	#452	C₂²×C₈₃	1	2	yes	complemented
607	#452	C₂²×C₈₃	1	2	yes	complemented
608	#451	C₂²×C₈₃	1	1	yes	characteristic, complemented
609	#450	C₂²×C₈₃	1	2	yes	—
610	#450	C₂²×C₈₃	1	2	yes	—
611	#448	C₂²×C₈₃	1	1	yes	characteristic
612	#448	C₂²×C₈₃	1	2	yes	complemented
613	#441	C₂²×C₈₃	1	2	yes	complemented
614	#440	C₂²×C₈₃	1	2	yes	—
615	#440	C₂²×C₈₃	1	2	yes	complemented
616	#440	C₂²×C₈₃	1	2	yes	complemented
617	#435	C₂²×C₈₃	1	2	yes	—
618	#435	C₂²×C₈₃	1	2	yes	complemented
619	#435	C₂²×C₈₃	1	2	yes	complemented
620	#435	C₂²×C₈₃	1	2	yes	complemented
621	#432	C₂²×C₈₃	1	1	yes	characteristic, complemented
622	#432	C₂²×C₈₃	1	1	yes	characteristic, complemented
623	#428	C₂²×C₈₃	1	2	yes	complemented
624	#428	C₂²×C₈₃	1	2	yes	complemented
625	#427	C₂²×C₈₃	1	2	yes	complemented
626	C₂×#107	C₂²×C₈₃	1	2	yes	complemented
627	#418	C₂²×C₈₃	1	2	yes	—
628	#417	C₂²×C₈₃	1	2	yes	complemented
629	#416	C₂²×C₈₃	1	2	yes	complemented
630	C₂×#102	C₂²×C₈₃	1	2	yes	—
631	#408	C₂²×C₈₃	1	2	yes	complemented
632	#408	C₂²×C₈₃	1	2	yes	complemented
633	C₂×#41	—	2	1	no	—
634	C₂×#41	—	2	1	no	—
635	C₂×#41	C₂³×C₈₃	1	2	yes	—
636	C₂×#41	C₂³×C₈₃	1	2	yes	—
637	C₂²×Q₈	C₂³×C₈₃	1	1	yes	characteristic
638	C₂²×D₄	—	2	1	no	—
639	C₂²×D₄	C₂³×C₈₃	1	2	yes	—
640	C₂×Q₁₆	C₂³×C₈₃	1	2	yes	—
641	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
642	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
643	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
644	C₂×M₁₆	C₂³×C₈₃	1	2	yes	—
645	C₂×M₁₆	C₂³×C₈₃	1	2	yes	—
646	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
647	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
648	C₄⋊Q₈	—	2	2	no	—
649	C₄⋊Q₈	D₄×C₈₃	1	1	yes	characteristic
650	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
651	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
652	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
653	#127	—	2	1	no	—
654	#127	—	2	2	no	—
655	#127	D₄×C₈₃	1	1	yes	characteristic
656	#127	C₂³×C₈₃	1	1	yes	characteristic
657	#126	—	2	2	no	—
658	#126	—	2	2	no	—
659	#126	—	2	2	no	—
660	#126	—	2	2	no	—
661	#126	—	2	2	no	—
662	#126	—	2	2	no	—
663	#126	—	2	1	no	—
664	#125	—	2	2	no	—
665	#125	—	2	2	no	—
666	#125	—	2	2	no	—
667	#125	C₂³×C₈₃	1	1	yes	characteristic
668	#125	C₂³×C₈₃	1	2	yes	—
669	#124	—	2	2	no	—
670	#124	—	2	2	no	—
671	#124	—	2	1	no	—
672	#124	—	2	2	no	—
673	#124	—	2	1	no	—
674	#124	D₄×C₈₃	1	2	yes	—
675	#124	C₂³×C₈₃	1	1	yes	characteristic
676	#123	—	2	2	no	—
677	#123	—	2	2	no	—
678	#123	—	2	2	no	—
679	#123	—	2	2	no	—
680	#123	—	2	1	no	—
681	#123	—	2	2	no	—
682	#123	—	2	2	no	—
683	#123	—	2	2	no	—
684	C₂²⋊Q₈	—	2	2	no	—
685	C₂²⋊Q₈	—	2	1	no	—
686	C₂²⋊Q₈	—	2	1	no	—
687	C₂²⋊Q₈	—	2	1	no	—
688	C₂²⋊Q₈	—	2	2	no	—
689	C₂²⋊Q₈	—	2	2	no	—
690	C₂²⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
691	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
692	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
693	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
694	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
695	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
696	#121	—	2	2	no	—
697	#121	—	2	2	no	—
698	#121	—	2	2	no	—
699	#121	—	2	2	no	—
700	#121	—	2	1	no	—
701	#121	—	2	1	no	—
702	#121	—	2	2	no	—
703	#121	—	2	2	no	—
704	#121	D₄×C₈₃	1	2	yes	—
705	#121	D₄×C₈₃	1	1	yes	characteristic
706	#121	D₄×C₈₃	1	1	yes	characteristic
707	#121	C₂³×C₈₃	1	1	yes	characteristic
708	#121	C₂³×C₈₃	1	2	yes	—
709	#121	C₂³×C₈₃	1	2	yes	—
710	#121	C₂³×C₈₃	1	2	yes	—
711	#121	C₂³×C₈₃	1	2	yes	—
712	#120	—	2	2	no	—
713	#120	—	2	2	no	—
714	#120	—	2	2	no	—
715	#120	—	2	2	no	—
716	C₄×Q₈	—	2	2	no	—
717	C₄×Q₈	—	2	2	no	—
718	C₄×Q₈	—	2	1	no	—
719	C₄×Q₈	—	2	1	no	—
720	C₄×Q₈	—	2	1	no	—
721	C₄×Q₈	—	2	1	no	—
722	C₄×Q₈	—	2	1	no	—
723	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
724	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
725	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
726	C₄×D₄	—	2	2	no	—
727	C₄×D₄	—	2	2	no	—
728	C₄×D₄	—	2	2	no	—
729	C₄×D₄	—	2	2	no	—
730	C₄×D₄	—	2	1	no	—
731	C₄×D₄	—	2	1	no	—
732	C₄×D₄	—	2	2	no	—
733	C₄×D₄	—	2	1	no	—
734	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
735	C₄×D₄	C₂³×C₈₃	1	2	yes	—
736	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
737	C₄×D₄	C₂³×C₈₃	1	2	yes	—
738	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
739	#117	—	2	2	no	—
740	#117	—	2	2	no	—
741	#117	—	2	1	no	—
742	#117	C₂³×C₈₃	1	2	yes	—
743	#117	C₂³×C₈₃	1	2	yes	—
744	#117	C₂³×C₈₃	1	2	yes	—
745	#117	C₂³×C₈₃	1	2	yes	—
746	C₂×C₄⋊C₄	—	2	1	no	—
747	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
748	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
749	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
750	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
751	C₂×C₂²⋊C₄	—	2	2	no	—
752	C₂×C₄²	—	2	1	no	—
753	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
754	#107	C₂³×C₈₃	1	2	yes	—
755	#107	C₂³×C₈₃	1	2	yes	—
756	#107	C₂³×C₈₃	1	2	yes	—
757	#107	C₂³×C₈₃	1	2	yes	—
758	#107	C₂³×C₈₃	1	2	yes	—
759	#107	C₂³×C₈₃	1	2	yes	—
760	#107	C₂³×C₈₃	1	2	yes	—
761	#106	C₂³×C₈₃	1	2	yes	—
762	#106	C₂³×C₈₃	1	2	yes	—
763	#106	C₂³×C₈₃	1	2	yes	—
764	#106	C₂³×C₈₃	1	2	yes	—
765	#106	C₂³×C₈₃	1	2	yes	—
766	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
767	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
768	#103	C₂³×C₈₃	1	2	yes	—
769	#103	C₂³×C₈₃	1	2	yes	—
770	#103	C₂³×C₈₃	1	2	yes	—
771	#103	C₂³×C₈₃	1	2	yes	—
772	#103	C₂³×C₈₃	1	2	yes	—
773	#103	C₂³×C₈₃	1	2	yes	—
774	#103	C₂³×C₈₃	1	2	yes	—
775	#102	C₂³×C₈₃	1	2	yes	—
776	#102	C₂³×C₈₃	1	2	yes	—
777	#102	C₂³×C₈₃	1	2	yes	—
778	#102	C₂³×C₈₃	1	2	yes	—
779	#102	C₂³×C₈₃	1	2	yes	—
780	#102	C₂³×C₈₃	1	2	yes	—
781	#102	C₂³×C₈₃	1	2	yes	—
782	#102	C₂³×C₈₃	1	2	yes	—
783	#102	C₂³×C₈₃	1	2	yes	—
784	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
785	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
786	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
787	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
788	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
789	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
790	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
791	#97	C₂³×C₈₃	1	2	yes	—
792	#97	C₂³×C₈₃	1	1	yes	characteristic
793	#97	C₂³×C₈₃	1	1	yes	characteristic
794	C₂⁴	—	2	2	no	—
795	#41	—	4	2	no	—
796	#41	—	4	2	no	—
797	#41	—	4	2	no	—
798	#41	—	4	2	no	—
799	#41	—	8	2	no	—
800	#41	—	8	2	no	—
801	C₂×Q₈	—	2	1	no	—
802	C₂×Q₈	—	2	1	no	—
803	C₂×Q₈	—	2	1	no	—
804	C₂×Q₈	—	2	1	no	—
805	C₂×Q₈	—	4	2	no	—
806	C₂×Q₈	C₂×D₄×C₈₃	1	2	yes	—
807	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
808	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
809	C₂×D₄	—	2	1	no	—
810	C₂×D₄	—	2	2	no	—
811	C₂×D₄	—	2	2	no	—
812	C₂×D₄	—	2	2	no	—
813	C₂×D₄	—	2	2	no	—
814	C₂×D₄	—	2	2	no	—
815	C₂×D₄	—	2	1	no	—
816	C₂×D₄	—	2	1	no	—
817	C₂×D₄	—	2	2	no	—
818	C₂×D₄	—	4	2	no	—
819	C₂×D₄	—	4	2	no	—
820	C₂×D₄	—	8	2	no	—
821	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
822	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
823	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
824	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
825	C₂×D₄	C₂×D₄×C₈₃	1	1	yes	characteristic
826	C₂×D₄	C₂×D₄×C₈₃	1	1	yes	characteristic
827	C₂×D₄	C₂⁴×C₈₃	1	1	yes	characteristic
828	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
829	C₂²×C₄	—	2	1	no	—
830	C₂²×C₄	—	2	1	no	—
831	C₂²×C₄	—	2	2	no	—
832	C₂²×C₄	—	2	2	no	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	—	2	1	no	—
835	C₂²×C₄	—	2	2	no	—
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
838	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
839	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
840	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
841	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
842	Q₁₆	—	4	2	no	—
843	SD₁₆	—	4	2	no	—
844	SD₁₆	—	4	2	no	—
845	SD₁₆	—	4	2	no	—
846	M₁₆	—	4	2	no	—
847	M₁₆	—	4	2	no	—
848	C₂×C₈	—	4	2	no	—
849	C₂×C₈	—	4	2	no	—
850	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
851	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
852	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
853	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	1	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	—	2	1	no	—
862	C₄⋊C₄	—	2	1	no	—
863	C₄⋊C₄	—	2	2	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	1	no	—
866	C₄⋊C₄	—	2	1	no	—
867	C₄⋊C₄	—	2	1	no	—
868	C₄⋊C₄	—	2	2	no	—
869	C₄⋊C₄	—	2	2	no	—
870	C₄⋊C₄	—	2	1	no	—
871	C₄⋊C₄	—	2	2	no	—
872	C₄⋊C₄	—	2	2	no	—
873	C₄⋊C₄	—	2	1	no	—
874	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
875	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
876	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
877	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
878	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
879	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
880	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
881	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
882	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	2	no	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	1	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	2	1	no	—
894	C₂²⋊C₄	—	2	2	no	—
895	C₂²⋊C₄	—	2	1	no	—
896	C₂²⋊C₄	—	2	1	no	—
897	C₂²⋊C₄	—	2	2	no	—
898	C₂²⋊C₄	—	2	2	no	—
899	C₂²⋊C₄	—	2	2	no	—
900	C₂²⋊C₄	—	2	1	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
903	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
904	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
905	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
906	C₄²	—	2	2	no	—
907	C₄²	—	2	2	no	—
908	C₄²	—	2	2	no	—
909	C₄²	—	2	2	no	—
910	C₄²	—	2	1	no	—
911	C₄²	—	2	2	no	—
912	C₄²	—	2	2	no	—
913	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
914	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
915	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
916	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
917	C₂³	—	2	1	no	—
918	C₂³	—	2	2	no	—
919	C₂³	—	8	2	no	—
920	C₂³	—	8	2	no	—
921	C₂³	—	8	2	no	—
922	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
923	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
924	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
925	Q₈	—	2	2	no	—
926	Q₈	—	2	2	no	—
927	Q₈	—	2	2	no	—
928	Q₈	—	4	2	no	—
929	Q₈	—	4	2	no	—
930	Q₈	—	4	2	no	—
931	Q₈	—	4	2	no	—
932	Q₈	—	8	1	no	—
933	D₄	—	2	2	no	—
934	D₄	—	2	2	no	—
935	D₄	—	2	2	no	—
936	D₄	—	4	1	no	—
937	D₄	—	4	2	no	—
938	D₄	—	4	2	no	—
939	D₄	—	4	2	no	—
940	D₄	—	4	1	no	—
941	D₄	—	4	2	no	—
942	D₄	—	4	2	no	—
943	D₄	—	8	2	no	—
944	D₄	—	8	1	no	—
945	D₄	—	8	2	no	—
946	D₄	—	8	2	no	—
947	D₄	—	8	2	no	—
948	D₄	—	8	2	no	—
949	D₄	—	8	1	no	—
950	D₄	—	8	2	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	4	1	no	—
965	C₂×C₄	—	4	1	no	—
966	C₂×C₄	—	4	2	no	—
967	C₂×C₄	—	4	2	no	—
968	C₂×C₄	—	8	2	no	—
969	C₂×C₄	—	8	2	no	—
970	C₂×C₄	—	8	2	no	—
971	C₂×C₄	—	8	1	no	—
972	C₂×C₄	—	8	2	no	—
973	C₂×C₄	—	8	2	no	—
974	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
975	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
976	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
977	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
978	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
979	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
980	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
981	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
982	C₈	—	2	2	no	—
983	C₈	—	2	2	no	—
984	C₈	—	2	2	no	—
985	C₈	—	2	2	no	—
986	C₂²	—	2	1	no	—
987	C₂²	—	2	2	no	—
988	C₂²	—	2	2	no	—
989	C₂²	—	2	1	no	—
990	C₂²	—	2	2	no	—
991	C₂²	—	2	2	no	—
992	C₂²	—	2	1	no	—
993	C₂²	—	2	2	no	—
994	C₂²	—	2	2	no	—
995	C₂²	—	4	1	no	—
996	C₂²	—	4	2	no	—
997	C₂²	—	4	2	no	—
998	C₂²	—	4	1	no	—
999	C₂²	—	4	2	no	—
1000	C₂²	—	4	1	no	—
1001	C₂²	—	16	4	no	—
1002	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
1003	C₄	—	2	1	no	—
1004	C₄	—	2	1	no	—
1005	C₄	—	2	1	no	—
1006	C₄	—	2	1	no	—
1007	C₄	—	2	2	no	—
1008	C₄	—	2	1	no	—
1009	C₄	—	2	2	no	—
1010	C₄	—	4	1	no	—
1011	C₄	—	4	2	no	—
1012	C₄	—	4	2	no	—
1013	C₄	—	4	2	no	—
1014	C₄	—	4	1	no	—
1015	C₄	—	4	2	no	—
1016	C₄	—	4	2	no	—
1017	C₄	—	4	1	no	—
1018	C₄	#585×C₈₃	1	2	yes	—
1019	C₂	—	4	2	no	—
1020	C₂	—	4	1	no	—
1021	C₂	—	4	2	no	—
1022	C₂	—	8	1	no	—
1023	C₂	—	8	2	no	—
1024	C₂	C₈₃×#3485	1	1	yes	characteristic
1025	C₂	C₈₃×#3585	1	1	yes	characteristic
1026	C₂	C₈₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₃
prime radical	C₈₃×#3546	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₃ ◁ #532×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈₃×#3507	C₂	semidirect
3. C₈₃×#3350	C₂	semidirect
4. C₈₃×#3349	C₂	semidirect
5. C₈₃×#3346	C₂	semidirect
6. C₈₃×#3343	C₂	semidirect
7. C₈₃×#3317	C₂	semidirect
8. C₈₃×#3314	C₂	semidirect
9. C₈₃×#3311	C₂	semidirect
10. C₈₃×#3310	C₂	semidirect
11. C₈₃×#3240	C₂	semidirect
12. C₈₃×#3235	C₂	semidirect
13. C₈₃×#3201	C₂	semidirect
14. C₈₃×#3200	C₂	semidirect
15. C₈₃×#3117	C₂	semidirect
16. C₈₃×#3112	C₂	semidirect
17. C₈₃×#3098	C₂	semidirect
18. C₈₃×#3096	C₂	semidirect
19. C₈₃×#2980	C₂	semidirect
25. #556×C₈₃	C₂²	semidirect
26. #554×C₈₃	C₂²	semidirect
29. #552×C₈₃	C₂²	semidirect
41. #536×C₈₃	C₂²	semidirect
44. #533×C₈₃	C₂²	semidirect
49. #520×C₈₃	C₂²	semidirect
50. C₂×C₄×Q₈×C₈₃	C₂²	semidirect
51. #501×C₈₃	C₂²	semidirect
52. #501×C₈₃	C₂²	semidirect
53. #501×C₈₃	C₂²	semidirect
57. #485×C₈₃	C₂²	semidirect
58. #485×C₈₃	C₂²	semidirect
59. #485×C₈₃	C₂²	semidirect
60. #485×C₈₃	C₂²	semidirect
61. #484×C₈₃	C₂²	semidirect
62. #484×C₈₃	C₂²	semidirect
63. #484×C₈₃	C₂²	semidirect
64. #483×C₈₃	C₂²	semidirect
68. #482×C₈₃	C₂²	semidirect
69. #482×C₈₃	C₂²	semidirect
70. #482×C₈₃	C₂²	semidirect
72. #481×C₈₃	C₂²	semidirect
75. #480×C₈₃	C₂²	semidirect
76. #479×C₈₃	C₂²	semidirect
77. #479×C₈₃	C₂²	semidirect
79. #477×C₈₃	C₂²	semidirect
80. #476×C₈₃	C₂²	semidirect
81. #474×C₈₃	C₂²	semidirect
82. #470×C₈₃	C₂²	semidirect
85. #468×C₈₃	C₂²	semidirect
86. #467×C₈₃	C₂²	semidirect
89. #465×C₈₃	C₂²	semidirect
92. #452×C₈₃	C₂²	semidirect
93. #452×C₈₃	C₂²	semidirect
94. #451×C₈₃	C₂²	semidirect
98. #448×C₈₃	C₂²	semidirect
99. #441×C₈₃	C₂²	semidirect
101. #440×C₈₃	C₂²	semidirect
102. #440×C₈₃	C₂²	semidirect
104. #435×C₈₃	C₂²	semidirect
105. #435×C₈₃	C₂²	semidirect
106. #435×C₈₃	C₂²	semidirect
107. #432×C₈₃	C₂²	semidirect
108. #432×C₈₃	C₂²	semidirect
109. #428×C₈₃	C₂²	semidirect
110. #428×C₈₃	C₂²	semidirect
111. #427×C₈₃	C₂²	semidirect
112. C₂×#107×C₈₃	C₂²	semidirect
114. #417×C₈₃	C₂²	semidirect
115. #416×C₈₃	C₂²	semidirect
117. #408×C₈₃	C₂²	semidirect
118. #408×C₈₃	C₂²	semidirect
505. #61793	C₈₃	direct (N × H)
515. #3507	C₂×C₈₃	semidirect
516. #3350	C₂×C₈₃	semidirect
517. #3349	C₂×C₈₃	semidirect
518. #3346	C₂×C₈₃	semidirect
519. #3343	C₂×C₈₃	semidirect
520. #3317	C₂×C₈₃	semidirect
521. #3314	C₂×C₈₃	semidirect
522. #3311	C₂×C₈₃	semidirect
523. #3310	C₂×C₈₃	semidirect
524. #3240	C₂×C₈₃	semidirect
525. #3235	C₂×C₈₃	semidirect
526. #3201	C₂×C₈₃	semidirect
527. #3200	C₂×C₈₃	semidirect
528. #3117	C₂×C₈₃	semidirect
529. #3112	C₂×C₈₃	semidirect
530. #3098	C₂×C₈₃	semidirect
531. #3096	C₂×C₈₃	semidirect
532. #2980	C₂×C₈₃	semidirect
533. C₈₃	#61793	direct (N × H)
539. #556	C₂²×C₈₃	semidirect
540. #554	C₂²×C₈₃	semidirect
543. #552	C₂²×C₈₃	semidirect
555. #536	C₂²×C₈₃	semidirect
558. #533	C₂²×C₈₃	semidirect
563. #520	C₂²×C₈₃	semidirect
564. C₂×C₄×Q₈	C₂²×C₈₃	semidirect
565. #501	C₂²×C₈₃	semidirect
566. #501	C₂²×C₈₃	semidirect
567. #501	C₂²×C₈₃	semidirect
571. #485	C₂²×C₈₃	semidirect
572. #485	C₂²×C₈₃	semidirect
573. #485	C₂²×C₈₃	semidirect
574. #485	C₂²×C₈₃	semidirect
575. #484	C₂²×C₈₃	semidirect
576. #484	C₂²×C₈₃	semidirect
577. #484	C₂²×C₈₃	semidirect
578. #483	C₂²×C₈₃	semidirect
582. #482	C₂²×C₈₃	semidirect
583. #482	C₂²×C₈₃	semidirect
584. #482	C₂²×C₈₃	semidirect
586. #481	C₂²×C₈₃	semidirect
589. #480	C₂²×C₈₃	semidirect
590. #479	C₂²×C₈₃	semidirect
591. #479	C₂²×C₈₃	semidirect
593. #477	C₂²×C₈₃	semidirect
594. #476	C₂²×C₈₃	semidirect
595. #474	C₂²×C₈₃	semidirect
596. #470	C₂²×C₈₃	semidirect
599. #468	C₂²×C₈₃	semidirect
600. #467	C₂²×C₈₃	semidirect
603. #465	C₂²×C₈₃	semidirect
606. #452	C₂²×C₈₃	semidirect
607. #452	C₂²×C₈₃	semidirect
608. #451	C₂²×C₈₃	semidirect
612. #448	C₂²×C₈₃	semidirect
613. #441	C₂²×C₈₃	semidirect
615. #440	C₂²×C₈₃	semidirect
616. #440	C₂²×C₈₃	semidirect
618. #435	C₂²×C₈₃	semidirect
619. #435	C₂²×C₈₃	semidirect
620. #435	C₂²×C₈₃	semidirect
621. #432	C₂²×C₈₃	semidirect
622. #432	C₂²×C₈₃	semidirect
623. #428	C₂²×C₈₃	semidirect
624. #428	C₂²×C₈₃	semidirect
625. #427	C₂²×C₈₃	semidirect
626. C₂×#107	C₂²×C₈₃	semidirect
628. #417	C₂²×C₈₃	semidirect
629. #416	C₂²×C₈₃	semidirect
631. #408	C₂²×C₈₃	semidirect
632. #408	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×#3546	2
C₈₃×#3507	2
C₈₃×#3350	2
C₈₃×#3349	2
C₈₃×#3346	2
C₈₃×#3343	2
C₈₃×#3317	2
C₈₃×#3314	2
C₈₃×#3311	2
C₈₃×#3310	2
C₈₃×#3240	2
C₈₃×#3235	2
C₈₃×#3201	2
C₈₃×#3200	2
C₈₃×#3117	2
C₈₃×#3112	2
C₈₃×#3098	2
C₈₃×#3096	2
C₈₃×#2980	2
#61793	83

Subgroups — C83×#61793 #35289617

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#61793 #35289617