Subgroups — C₈₃×#62236 #35290060

Order 21248.

1698 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3563	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₃×#3514	C₂	1	1	yes	maximal, characteristic
3	C₈₃×#3386	C₂	1	2	yes	maximal, complemented
4	C₈₃×#3371	C₂	1	2	yes	maximal, complemented
5	C₈₃×#3357	C₂	1	2	yes	maximal, complemented
6	C₈₃×#3349	C₂	1	2	yes	maximal, complemented
7	C₈₃×#3348	C₂	1	2	yes	maximal, complemented
8	C₈₃×#3323	C₂	1	2	yes	maximal, complemented
9	C₈₃×#3314	C₂	1	2	yes	maximal, complemented
10	C₈₃×#3310	C₂	1	2	yes	maximal, complemented
11	C₈₃×#3258	C₂	1	2	yes	maximal, complemented
12	C₈₃×#3254	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₃×#3243	C₂	1	2	yes	maximal, complemented
14	C₈₃×#3234	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#3123	C₂	1	2	yes	maximal, complemented
16	C₈₃×#3116	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₃×#3081	C₂	1	2	yes	maximal, complemented
18	C₈₃×#3080	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₃×#2995	C₂	1	1	yes	maximal, characteristic, complemented
20	#564×C₈₃	—	2	1	no	—
21	#563×C₈₃	—	2	1	no	—
22	#559×C₈₃	C₂²	1	1	yes	characteristic
23	#557×C₈₃	C₂²	1	2	yes	complemented
24	#556×C₈₃	C₂²	1	1	yes	characteristic
25	#555×C₈₃	C₂²	1	2	yes	—
26	#554×C₈₃	C₂²	1	2	yes	complemented
27	#552×C₈₃	—	2	2	no	—
28	#552×C₈₃	C₂²	1	2	yes	—
29	#552×C₈₃	C₂²	1	2	yes	complemented
30	#551×C₈₃	—	2	2	no	—
31	D₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
32	#548×C₈₃	—	2	1	no	—
33	#546×C₈₃	—	2	1	no	—
34	#546×C₈₃	C₂²	1	2	yes	—
35	D₄²×C₈₃	C₂²	1	1	yes	characteristic
36	#544×C₈₃	—	2	1	no	—
37	#544×C₈₃	C₂²	1	2	yes	complemented
38	#542×C₈₃	C₂²	1	2	yes	—
39	#541×C₈₃	—	2	2	no	—
40	#541×C₈₃	C₂²	1	2	yes	complemented
41	#539×C₈₃	—	2	1	no	—
42	#538×C₈₃	—	2	2	no	—
43	#533×C₈₃	C₂²	1	1	yes	characteristic, complemented
44	#532×C₈₃	C₂²	1	1	yes	characteristic
45	#529×C₈₃	—	2	1	no	—
46	#529×C₈₃	C₂²	1	1	yes	characteristic
47	C₂×#125×C₈₃	C₂²	1	1	yes	characteristic, complemented
48	C₂×#124×C₈₃	—	2	1	no	—
49	#518×C₈₃	C₂²	1	2	yes	—
50	C₄×#41×C₈₃	C₂²	1	1	yes	characteristic
51	#501×C₈₃	C₂²	1	2	yes	complemented
52	#501×C₈₃	C₂²	1	2	yes	complemented
53	#500×C₈₃	C₂²	1	2	yes	complemented
54	#490×C₈₃	C₂²	1	2	yes	—
55	#489×C₈₃	C₂²	1	2	yes	complemented
56	#488×C₈₃	C₂²	1	2	yes	complemented
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	#482×C₈₃	C₂²	1	2	yes	—
63	#481×C₈₃	C₂²	1	2	yes	complemented
64	#480×C₈₃	C₂²	1	2	yes	—
65	#480×C₈₃	C₂²	1	2	yes	complemented
66	#479×C₈₃	C₂²	1	2	yes	complemented
67	#479×C₈₃	C₂²	1	2	yes	complemented
68	#478×C₈₃	C₂²	1	2	yes	—
69	#478×C₈₃	C₂²	1	2	yes	—
70	#478×C₈₃	C₂²	1	2	yes	—
71	#478×C₈₃	C₂²	1	2	yes	complemented
72	#478×C₈₃	C₂²	1	2	yes	complemented
73	#478×C₈₃	C₂²	1	2	yes	complemented
74	#477×C₈₃	C₂²	1	2	yes	complemented
75	#477×C₈₃	C₂²	1	2	yes	complemented
76	#477×C₈₃	C₂²	1	1	yes	characteristic, complemented
77	#476×C₈₃	C₂²	1	1	yes	characteristic
78	#476×C₈₃	C₂²	1	2	yes	complemented
79	#475×C₈₃	C₂²	1	2	yes	complemented
80	#474×C₈₃	C₂²	1	2	yes	—
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	complemented
85	#468×C₈₃	C₂²	1	2	yes	complemented
86	#467×C₈₃	C₂²	1	2	yes	complemented
87	#465×C₈₃	C₂²	1	2	yes	—
88	#464×C₈₃	C₂²	1	2	yes	complemented
89	#464×C₈₃	C₂²	1	2	yes	complemented
90	#462×C₈₃	C₂²	1	1	yes	characteristic, complemented
91	#461×C₈₃	C₂²	1	1	yes	characteristic
92	#461×C₈₃	C₂²	1	2	yes	complemented
93	#460×C₈₃	C₂²	1	2	yes	—
94	#452×C₈₃	C₂²	1	2	yes	—
95	#450×C₈₃	C₂²	1	2	yes	—
96	#450×C₈₃	C₂²	1	2	yes	—
97	#446×C₈₃	C₂²	1	2	yes	complemented
98	#441×C₈₃	C₂²	1	2	yes	complemented
99	#440×C₈₃	C₂²	1	2	yes	—
100	#440×C₈₃	C₂²	1	2	yes	—
101	#440×C₈₃	C₂²	1	2	yes	complemented
102	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	—
103	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	complemented
104	#436×C₈₃	C₂²	1	2	yes	complemented
105	#435×C₈₃	C₂²	1	2	yes	—
106	#435×C₈₃	C₂²	1	2	yes	complemented
107	#433×C₈₃	C₂²	1	2	yes	complemented
108	#432×C₈₃	C₂²	1	1	yes	characteristic, complemented
109	#428×C₈₃	C₂²	1	1	yes	characteristic, complemented
110	#428×C₈₃	C₂²	1	1	yes	characteristic, complemented
111	#428×C₈₃	C₂²	1	2	yes	complemented
112	#427×C₈₃	C₂²	1	2	yes	complemented
113	#424×C₈₃	C₂²	1	2	yes	complemented
114	#423×C₈₃	C₂²	1	1	yes	characteristic, complemented
115	#418×C₈₃	C₂²	1	2	yes	—
116	#417×C₈₃	C₂²	1	1	yes	characteristic
117	#417×C₈₃	C₂²	1	1	yes	characteristic
118	C₂×#102×C₈₃	C₂²	1	2	yes	—
119	C₂×#41×C₈₃	—	2	1	no	—
120	C₂×#41×C₈₃	C₂³	1	1	yes	characteristic
121	C₂²×Q₈×C₈₃	—	2	1	no	—
122	C₂²×D₄×C₈₃	—	2	1	no	—
123	C₂²×D₄×C₈₃	C₂³	1	2	yes	—
124	C₂×Q₁₆×C₈₃	C₂³	1	2	yes	—
125	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
128	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
129	C₂×M₁₆×C₈₃	C₂³	1	1	yes	characteristic
130	C₂×M₁₆×C₈₃	C₂³	1	1	yes	characteristic
131	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
132	C₄⋊Q₈×C₈₃	—	2	2	no	—
133	C₄⋊Q₈×C₈₃	—	2	2	no	—
134	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
135	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
136	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
137	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
138	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
139	#127×C₈₃	C₂³	1	1	yes	characteristic
140	#126×C₈₃	—	2	2	no	—
141	#126×C₈₃	—	2	2	no	—
142	#126×C₈₃	—	2	2	no	—
143	#126×C₈₃	—	2	2	no	—
144	#126×C₈₃	—	2	2	no	—
145	#126×C₈₃	—	2	2	no	—
146	#126×C₈₃	D₄	1	2	yes	—
147	#125×C₈₃	—	2	2	no	—
148	#125×C₈₃	—	2	2	no	—
149	#125×C₈₃	—	2	2	no	—
150	#125×C₈₃	—	2	2	no	—
151	#125×C₈₃	—	2	2	no	—
152	#125×C₈₃	—	2	2	no	—
153	#125×C₈₃	—	2	2	no	—
154	#125×C₈₃	—	2	2	no	—
155	#125×C₈₃	—	2	1	no	—
156	#125×C₈₃	—	2	1	no	—
157	#125×C₈₃	—	2	1	no	—
158	#125×C₈₃	D₄	1	1	yes	characteristic
159	#125×C₈₃	C₂³	1	2	yes	—
160	#125×C₈₃	C₂³	1	2	yes	—
161	#125×C₈₃	C₂³	1	2	yes	—
162	#124×C₈₃	—	2	1	no	—
163	#124×C₈₃	—	2	1	no	—
164	#124×C₈₃	—	2	2	no	—
165	#124×C₈₃	—	2	2	no	—
166	#124×C₈₃	—	2	2	no	—
167	#124×C₈₃	—	2	1	no	—
168	#124×C₈₃	D₄	1	1	yes	characteristic
169	#124×C₈₃	C₂³	1	2	yes	—
170	#123×C₈₃	—	2	2	no	—
171	#123×C₈₃	—	2	2	no	—
172	#123×C₈₃	—	2	2	no	—
173	#123×C₈₃	—	2	2	no	—
174	#123×C₈₃	—	2	2	no	—
175	#123×C₈₃	D₄	1	2	yes	—
176	C₂²⋊Q₈×C₈₃	—	2	1	no	—
177	C₂²⋊Q₈×C₈₃	—	2	1	no	—
178	C₂²⋊Q₈×C₈₃	—	2	2	no	—
179	C₂²⋊Q₈×C₈₃	—	2	2	no	—
180	C₂²⋊Q₈×C₈₃	—	2	2	no	—
181	C₂²⋊Q₈×C₈₃	—	2	2	no	—
182	C₂²⋊Q₈×C₈₃	—	2	2	no	—
183	C₂²⋊Q₈×C₈₃	—	2	2	no	—
184	C₂²⋊Q₈×C₈₃	D₄	1	1	yes	characteristic
185	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
186	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
187	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
188	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
189	#121×C₈₃	—	2	2	no	—
190	#121×C₈₃	—	2	1	no	—
191	#121×C₈₃	—	2	1	no	—
192	#121×C₈₃	—	2	2	no	—
193	#121×C₈₃	D₄	1	1	yes	characteristic
194	#121×C₈₃	C₂³	1	2	yes	—
195	#121×C₈₃	C₂³	1	2	yes	—
196	#120×C₈₃	—	2	2	no	—
197	#120×C₈₃	—	2	2	no	—
198	C₄×Q₈×C₈₃	—	2	1	no	—
199	C₄×Q₈×C₈₃	—	2	2	no	—
200	C₄×Q₈×C₈₃	—	2	1	no	—
201	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
202	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
203	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
204	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
205	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
206	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
207	C₄×D₄×C₈₃	—	2	2	no	—
208	C₄×D₄×C₈₃	—	2	1	no	—
209	C₄×D₄×C₈₃	—	2	1	no	—
210	C₄×D₄×C₈₃	—	2	2	no	—
211	C₄×D₄×C₈₃	—	2	2	no	—
212	C₄×D₄×C₈₃	—	2	1	no	—
213	C₄×D₄×C₈₃	—	2	1	no	—
214	C₄×D₄×C₈₃	C₂³	1	2	yes	—
215	C₄×D₄×C₈₃	C₂³	1	2	yes	—
216	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
217	C₄×D₄×C₈₃	C₂³	1	2	yes	—
218	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
219	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
220	C₄×D₄×C₈₃	C₂³	1	2	yes	—
221	#117×C₈₃	—	2	1	no	—
222	#117×C₈₃	—	2	2	no	—
223	#117×C₈₃	—	2	2	no	—
224	#117×C₈₃	—	2	2	no	—
225	#117×C₈₃	—	2	1	no	—
226	#117×C₈₃	C₂³	1	2	yes	—
227	#117×C₈₃	C₂³	1	1	yes	characteristic
228	#117×C₈₃	C₂³	1	2	yes	—
229	#117×C₈₃	C₂³	1	2	yes	—
230	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
231	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
232	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
233	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
235	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
236	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
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	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
255	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
256	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
257	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
258	#103×C₈₃	C₂³	1	2	yes	—
259	#103×C₈₃	C₂³	1	2	yes	—
260	#103×C₈₃	C₂³	1	2	yes	—
261	#103×C₈₃	C₂³	1	2	yes	—
262	#103×C₈₃	C₂³	1	2	yes	—
263	#103×C₈₃	C₂³	1	2	yes	—
264	#103×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	#102×C₈₃	C₂³	1	2	yes	—
271	#102×C₈₃	C₂³	1	2	yes	—
272	#102×C₈₃	C₂³	1	2	yes	—
273	#102×C₈₃	C₂³	1	2	yes	—
274	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
275	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
276	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
277	#97×C₈₃	C₂³	1	2	yes	—
278	#97×C₈₃	C₂³	1	2	yes	—
279	C₄×C₈×C₈₃	C₂³	1	2	yes	—
280	C₂⁴×C₈₃	—	2	2	no	—
281	#41×C₈₃	—	2	2	no	—
282	#41×C₈₃	—	4	1	no	—
283	#41×C₈₃	—	8	2	no	—
284	C₂×Q₈×C₈₃	—	2	1	no	—
285	C₂×Q₈×C₈₃	—	2	1	no	—
286	C₂×Q₈×C₈₃	—	2	2	no	—
287	C₂×Q₈×C₈₃	—	2	2	no	—
288	C₂×Q₈×C₈₃	—	8	2	no	—
289	C₂×Q₈×C₈₃	C₂×D₄	1	1	yes	characteristic
290	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
291	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
292	C₂×D₄×C₈₃	—	2	4	no	—
293	C₂×D₄×C₈₃	—	2	1	no	—
294	C₂×D₄×C₈₃	—	2	2	no	—
295	C₂×D₄×C₈₃	—	2	2	no	—
296	C₂×D₄×C₈₃	—	2	2	no	—
297	C₂×D₄×C₈₃	—	2	1	no	—
298	C₂×D₄×C₈₃	—	2	1	no	—
299	C₂×D₄×C₈₃	—	4	2	no	—
300	C₂×D₄×C₈₃	—	8	2	no	—
301	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
302	C₂×D₄×C₈₃	C₂×D₄	1	1	yes	characteristic
303	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
304	C₂×D₄×C₈₃	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₈₃	—	2	1	no	—
306	C₂²×C₄×C₈₃	—	2	1	no	—
307	C₂²×C₄×C₈₃	—	2	2	no	—
308	C₂²×C₄×C₈₃	—	2	1	no	—
309	C₂²×C₄×C₈₃	—	2	1	no	—
310	C₂²×C₄×C₈₃	—	2	1	no	—
311	C₂²×C₄×C₈₃	—	2	2	no	—
312	C₂²×C₄×C₈₃	—	2	2	no	—
313	C₂²×C₄×C₈₃	—	2	2	no	—
314	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
315	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
316	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
318	Q₁₆×C₈₃	—	4	2	no	—
319	SD₁₆×C₈₃	—	2	4	no	—
320	SD₁₆×C₈₃	—	4	2	no	—
321	SD₁₆×C₈₃	—	4	2	no	—
322	M₁₆×C₈₃	—	4	1	no	—
323	M₁₆×C₈₃	—	4	2	no	—
324	M₁₆×C₈₃	—	4	1	no	—
325	C₂×C₈×C₈₃	—	4	2	no	—
326	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
327	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
328	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
329	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
330	C₄⋊C₄×C₈₃	—	2	2	no	—
331	C₄⋊C₄×C₈₃	—	2	2	no	—
332	C₄⋊C₄×C₈₃	—	2	2	no	—
333	C₄⋊C₄×C₈₃	—	2	2	no	—
334	C₄⋊C₄×C₈₃	—	2	1	no	—
335	C₄⋊C₄×C₈₃	—	2	2	no	—
336	C₄⋊C₄×C₈₃	—	2	1	no	—
337	C₄⋊C₄×C₈₃	—	2	1	no	—
338	C₄⋊C₄×C₈₃	—	2	1	no	—
339	C₄⋊C₄×C₈₃	—	2	2	no	—
340	C₄⋊C₄×C₈₃	—	2	1	no	—
341	C₄⋊C₄×C₈₃	—	2	2	no	—
342	C₄⋊C₄×C₈₃	—	2	2	no	—
343	C₄⋊C₄×C₈₃	—	2	2	no	—
344	C₄⋊C₄×C₈₃	—	2	1	no	—
345	C₄⋊C₄×C₈₃	—	2	1	no	—
346	C₄⋊C₄×C₈₃	—	2	2	no	—
347	C₄⋊C₄×C₈₃	—	2	2	no	—
348	C₄⋊C₄×C₈₃	—	2	2	no	—
349	C₄⋊C₄×C₈₃	—	2	2	no	—
350	C₄⋊C₄×C₈₃	—	2	1	no	—
351	C₄⋊C₄×C₈₃	—	2	2	no	—
352	C₄⋊C₄×C₈₃	—	2	2	no	—
353	C₄⋊C₄×C₈₃	—	2	2	no	—
354	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
355	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
356	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
357	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
358	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
359	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
360	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
361	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
362	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
363	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
364	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
365	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
366	C₂²⋊C₄×C₈₃	—	2	2	no	—
367	C₂²⋊C₄×C₈₃	—	2	2	no	—
368	C₂²⋊C₄×C₈₃	—	2	2	no	—
369	C₂²⋊C₄×C₈₃	—	2	2	no	—
370	C₂²⋊C₄×C₈₃	—	2	1	no	—
371	C₂²⋊C₄×C₈₃	—	2	2	no	—
372	C₂²⋊C₄×C₈₃	—	2	2	no	—
373	C₂²⋊C₄×C₈₃	—	2	1	no	—
374	C₂²⋊C₄×C₈₃	—	2	2	no	—
375	C₂²⋊C₄×C₈₃	—	2	2	no	—
376	C₂²⋊C₄×C₈₃	—	2	2	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	2	no	—
382	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
383	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
384	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
385	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
386	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
387	C₄²×C₈₃	—	2	1	no	—
388	C₄²×C₈₃	—	2	1	no	—
389	C₄²×C₈₃	—	2	1	no	—
390	C₄²×C₈₃	—	2	2	no	—
391	C₄²×C₈₃	—	2	2	no	—
392	C₄²×C₈₃	—	2	2	no	—
393	C₄²×C₈₃	—	2	2	no	—
394	C₄²×C₈₃	—	2	2	no	—
395	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
396	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
397	C₄²×C₈₃	C₂⁴	1	2	yes	—
398	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
399	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
400	C₂³×C₈₃	—	2	1	no	—
401	C₂³×C₈₃	—	2	2	no	—
402	C₂³×C₈₃	—	4	4	no	—
403	C₂³×C₈₃	—	8	2	no	—
404	C₂³×C₈₃	—	8	2	no	—
405	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
406	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
407	Q₈×C₈₃	—	2	2	no	—
408	Q₈×C₈₃	—	2	1	no	—
409	Q₈×C₈₃	—	2	2	no	—
410	Q₈×C₈₃	—	2	1	no	—
411	Q₈×C₈₃	—	4	1	no	—
412	Q₈×C₈₃	—	4	2	no	—
413	Q₈×C₈₃	—	8	1	no	—
414	Q₈×C₈₃	—	8	2	no	—
415	Q₈×C₈₃	—	8	2	no	—
416	D₄×C₈₃	—	2	2	no	—
417	D₄×C₈₃	—	2	1	no	—
418	D₄×C₈₃	—	2	2	no	—
419	D₄×C₈₃	—	4	1	no	—
420	D₄×C₈₃	—	4	2	no	—
421	D₄×C₈₃	—	4	4	no	—
422	D₄×C₈₃	—	4	2	no	—
423	D₄×C₈₃	—	4	2	no	—
424	D₄×C₈₃	—	8	1	no	—
425	D₄×C₈₃	—	8	2	no	—
426	D₄×C₈₃	—	8	2	no	—
427	D₄×C₈₃	2₋¹⁺⁴	1	2	yes	—
428	C₂×C₄×C₈₃	—	2	2	no	—
429	C₂×C₄×C₈₃	—	2	1	no	—
430	C₂×C₄×C₈₃	—	2	2	no	—
431	C₂×C₄×C₈₃	—	2	1	no	—
432	C₂×C₄×C₈₃	—	2	1	no	—
433	C₂×C₄×C₈₃	—	2	2	no	—
434	C₂×C₄×C₈₃	—	2	1	no	—
435	C₂×C₄×C₈₃	—	2	1	no	—
436	C₂×C₄×C₈₃	—	2	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	—	4	1	no	—
441	C₂×C₄×C₈₃	—	4	1	no	—
442	C₂×C₄×C₈₃	—	4	2	no	—
443	C₂×C₄×C₈₃	—	4	2	no	—
444	C₂×C₄×C₈₃	—	4	2	no	—
445	C₂×C₄×C₈₃	—	8	1	no	—
446	C₂×C₄×C₈₃	—	8	2	no	—
447	C₂×C₄×C₈₃	—	8	2	no	—
448	C₂×C₄×C₈₃	—	8	2	no	—
449	C₂×C₄×C₈₃	—	8	1	no	—
450	C₂×C₄×C₈₃	—	8	2	no	—
451	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
453	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
457	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
458	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
460	C₈×C₈₃	—	2	2	no	—
461	C₈×C₈₃	—	2	2	no	—
462	C₈×C₈₃	—	2	2	no	—
463	C₈×C₈₃	—	2	2	no	—
464	C₂²×C₈₃	—	2	1	no	—
465	C₂²×C₈₃	—	2	2	no	—
466	C₂²×C₈₃	—	2	1	no	—
467	C₂²×C₈₃	—	2	2	no	—
468	C₂²×C₈₃	—	2	1	no	—
469	C₂²×C₈₃	—	2	2	no	—
470	C₂²×C₈₃	—	2	2	no	—
471	C₂²×C₈₃	—	4	1	no	—
472	C₂²×C₈₃	—	4	1	no	—
473	C₂²×C₈₃	—	4	2	no	—
474	C₂²×C₈₃	—	4	2	no	—
475	C₂²×C₈₃	—	4	2	no	—
476	C₂²×C₈₃	—	16	4	no	—
477	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
478	C₄×C₈₃	—	2	1	no	—
479	C₄×C₈₃	—	2	1	no	—
480	C₄×C₈₃	—	2	2	no	—
481	C₄×C₈₃	—	2	1	no	—
482	C₄×C₈₃	—	2	1	no	—
483	C₄×C₈₃	—	2	2	no	—
484	C₄×C₈₃	—	2	1	no	—
485	C₄×C₈₃	—	2	2	no	—
486	C₄×C₈₃	—	4	1	no	—
487	C₄×C₈₃	—	4	2	no	—
488	C₄×C₈₃	—	4	2	no	—
489	C₄×C₈₃	—	4	2	no	—
490	C₄×C₈₃	—	4	2	no	—
491	C₄×C₈₃	—	4	1	no	—
492	C₄×C₈₃	—	4	1	no	—
493	C₄×C₈₃	—	4	2	no	—
494	C₄×C₈₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
495	C₄×C₈₃	#585	1	1	yes	characteristic
496	#62236	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
497	C₂×C₈₃	—	4	1	no	—
498	C₂×C₈₃	—	4	2	no	—
499	C₂×C₈₃	—	4	2	no	—
500	C₂×C₈₃	—	8	2	no	—
501	C₂×C₈₃	#3489	1	1	yes	characteristic
502	C₂×C₈₃	#3585	1	1	yes	characteristic
503	C₂×C₈₃	#3586	1	1	yes	characteristic
504	#3563	C₂×C₈₃	1	1	yes	characteristic, complemented
505	#3514	C₂×C₈₃	1	1	yes	characteristic
506	#3386	C₂×C₈₃	1	2	yes	complemented
507	#3371	C₂×C₈₃	1	2	yes	complemented
508	#3357	C₂×C₈₃	1	2	yes	complemented
509	#3349	C₂×C₈₃	1	2	yes	complemented
510	#3348	C₂×C₈₃	1	2	yes	complemented
511	#3323	C₂×C₈₃	1	2	yes	complemented
512	#3314	C₂×C₈₃	1	2	yes	complemented
513	#3310	C₂×C₈₃	1	2	yes	complemented
514	#3258	C₂×C₈₃	1	2	yes	complemented
515	#3254	C₂×C₈₃	1	1	yes	characteristic, complemented
516	#3243	C₂×C₈₃	1	2	yes	complemented
517	#3234	C₂×C₈₃	1	1	yes	characteristic, complemented
518	#3123	C₂×C₈₃	1	2	yes	complemented
519	#3116	C₂×C₈₃	1	1	yes	characteristic, complemented
520	#3081	C₂×C₈₃	1	2	yes	complemented
521	#3080	C₂×C₈₃	1	1	yes	characteristic, complemented
522	#2995	C₂×C₈₃	1	1	yes	characteristic, complemented
523	C₈₃	#62236	1	1	yes	characteristic, direct product factor, Sylow
524	#564	—	2	1	no	—
525	#563	—	2	1	no	—
526	#559	C₂²×C₈₃	1	1	yes	characteristic
527	#557	C₂²×C₈₃	1	2	yes	complemented
528	#556	C₂²×C₈₃	1	1	yes	characteristic
529	#555	C₂²×C₈₃	1	2	yes	—
530	#554	C₂²×C₈₃	1	2	yes	complemented
531	#552	—	2	2	no	—
532	#552	C₂²×C₈₃	1	2	yes	—
533	#552	C₂²×C₈₃	1	2	yes	complemented
534	#551	—	2	2	no	—
535	D₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic
536	#548	—	2	1	no	—
537	#546	—	2	1	no	—
538	#546	C₂²×C₈₃	1	2	yes	—
539	D₄²	C₂²×C₈₃	1	1	yes	characteristic
540	#544	—	2	1	no	—
541	#544	C₂²×C₈₃	1	2	yes	complemented
542	#542	C₂²×C₈₃	1	2	yes	—
543	#541	—	2	2	no	—
544	#541	C₂²×C₈₃	1	2	yes	complemented
545	#539	—	2	1	no	—
546	#538	—	2	2	no	—
547	#533	C₂²×C₈₃	1	1	yes	characteristic, complemented
548	#532	C₂²×C₈₃	1	1	yes	characteristic
549	#529	—	2	1	no	—
550	#529	C₂²×C₈₃	1	1	yes	characteristic
551	C₂×#125	C₂²×C₈₃	1	1	yes	characteristic, complemented
552	C₂×#124	—	2	1	no	—
553	#518	C₂²×C₈₃	1	2	yes	—
554	C₄×#41	C₂²×C₈₃	1	1	yes	characteristic
555	#501	C₂²×C₈₃	1	2	yes	complemented
556	#501	C₂²×C₈₃	1	2	yes	complemented
557	#500	C₂²×C₈₃	1	2	yes	complemented
558	#490	C₂²×C₈₃	1	2	yes	—
559	#489	C₂²×C₈₃	1	2	yes	complemented
560	#488	C₂²×C₈₃	1	2	yes	complemented
561	#485	C₂²×C₈₃	1	2	yes	complemented
562	#485	C₂²×C₈₃	1	2	yes	complemented
563	#485	C₂²×C₈₃	1	2	yes	complemented
564	#485	C₂²×C₈₃	1	2	yes	complemented
565	#484	C₂²×C₈₃	1	2	yes	complemented
566	#482	C₂²×C₈₃	1	2	yes	—
567	#481	C₂²×C₈₃	1	2	yes	complemented
568	#480	C₂²×C₈₃	1	2	yes	—
569	#480	C₂²×C₈₃	1	2	yes	complemented
570	#479	C₂²×C₈₃	1	2	yes	complemented
571	#479	C₂²×C₈₃	1	2	yes	complemented
572	#478	C₂²×C₈₃	1	2	yes	—
573	#478	C₂²×C₈₃	1	2	yes	—
574	#478	C₂²×C₈₃	1	2	yes	—
575	#478	C₂²×C₈₃	1	2	yes	complemented
576	#478	C₂²×C₈₃	1	2	yes	complemented
577	#478	C₂²×C₈₃	1	2	yes	complemented
578	#477	C₂²×C₈₃	1	2	yes	complemented
579	#477	C₂²×C₈₃	1	2	yes	complemented
580	#477	C₂²×C₈₃	1	1	yes	characteristic, complemented
581	#476	C₂²×C₈₃	1	1	yes	characteristic
582	#476	C₂²×C₈₃	1	2	yes	complemented
583	#475	C₂²×C₈₃	1	2	yes	complemented
584	#474	C₂²×C₈₃	1	2	yes	—
585	#474	C₂²×C₈₃	1	2	yes	complemented
586	#470	C₂²×C₈₃	1	2	yes	complemented
587	#468	C₂²×C₈₃	1	2	yes	—
588	#468	C₂²×C₈₃	1	2	yes	complemented
589	#468	C₂²×C₈₃	1	2	yes	complemented
590	#467	C₂²×C₈₃	1	2	yes	complemented
591	#465	C₂²×C₈₃	1	2	yes	—
592	#464	C₂²×C₈₃	1	2	yes	complemented
593	#464	C₂²×C₈₃	1	2	yes	complemented
594	#462	C₂²×C₈₃	1	1	yes	characteristic, complemented
595	#461	C₂²×C₈₃	1	1	yes	characteristic
596	#461	C₂²×C₈₃	1	2	yes	complemented
597	#460	C₂²×C₈₃	1	2	yes	—
598	#452	C₂²×C₈₃	1	2	yes	—
599	#450	C₂²×C₈₃	1	2	yes	—
600	#450	C₂²×C₈₃	1	2	yes	—
601	#446	C₂²×C₈₃	1	2	yes	complemented
602	#441	C₂²×C₈₃	1	2	yes	complemented
603	#440	C₂²×C₈₃	1	2	yes	—
604	#440	C₂²×C₈₃	1	2	yes	—
605	#440	C₂²×C₈₃	1	2	yes	complemented
606	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	—
607	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	complemented
608	#436	C₂²×C₈₃	1	2	yes	complemented
609	#435	C₂²×C₈₃	1	2	yes	—
610	#435	C₂²×C₈₃	1	2	yes	complemented
611	#433	C₂²×C₈₃	1	2	yes	complemented
612	#432	C₂²×C₈₃	1	1	yes	characteristic, complemented
613	#428	C₂²×C₈₃	1	1	yes	characteristic, complemented
614	#428	C₂²×C₈₃	1	1	yes	characteristic, complemented
615	#428	C₂²×C₈₃	1	2	yes	complemented
616	#427	C₂²×C₈₃	1	2	yes	complemented
617	#424	C₂²×C₈₃	1	2	yes	complemented
618	#423	C₂²×C₈₃	1	1	yes	characteristic, complemented
619	#418	C₂²×C₈₃	1	2	yes	—
620	#417	C₂²×C₈₃	1	1	yes	characteristic
621	#417	C₂²×C₈₃	1	1	yes	characteristic
622	C₂×#102	C₂²×C₈₃	1	2	yes	—
623	C₂×#41	—	2	1	no	—
624	C₂×#41	C₂³×C₈₃	1	1	yes	characteristic
625	C₂²×Q₈	—	2	1	no	—
626	C₂²×D₄	—	2	1	no	—
627	C₂²×D₄	C₂³×C₈₃	1	2	yes	—
628	C₂×Q₁₆	C₂³×C₈₃	1	2	yes	—
629	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
630	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
631	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
632	C₂×M₁₆	C₂³×C₈₃	1	1	yes	characteristic
633	C₂×M₁₆	C₂³×C₈₃	1	1	yes	characteristic
634	C₂×M₁₆	C₂³×C₈₃	1	2	yes	—
635	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
636	C₄⋊Q₈	—	2	2	no	—
637	C₄⋊Q₈	—	2	2	no	—
638	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
639	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
640	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
641	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
642	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
643	#127	C₂³×C₈₃	1	1	yes	characteristic
644	#126	—	2	2	no	—
645	#126	—	2	2	no	—
646	#126	—	2	2	no	—
647	#126	—	2	2	no	—
648	#126	—	2	2	no	—
649	#126	—	2	2	no	—
650	#126	D₄×C₈₃	1	2	yes	—
651	#125	—	2	2	no	—
652	#125	—	2	2	no	—
653	#125	—	2	2	no	—
654	#125	—	2	2	no	—
655	#125	—	2	2	no	—
656	#125	—	2	2	no	—
657	#125	—	2	2	no	—
658	#125	—	2	2	no	—
659	#125	—	2	1	no	—
660	#125	—	2	1	no	—
661	#125	—	2	1	no	—
662	#125	D₄×C₈₃	1	1	yes	characteristic
663	#125	C₂³×C₈₃	1	2	yes	—
664	#125	C₂³×C₈₃	1	2	yes	—
665	#125	C₂³×C₈₃	1	2	yes	—
666	#124	—	2	1	no	—
667	#124	—	2	1	no	—
668	#124	—	2	2	no	—
669	#124	—	2	2	no	—
670	#124	—	2	2	no	—
671	#124	—	2	1	no	—
672	#124	D₄×C₈₃	1	1	yes	characteristic
673	#124	C₂³×C₈₃	1	2	yes	—
674	#123	—	2	2	no	—
675	#123	—	2	2	no	—
676	#123	—	2	2	no	—
677	#123	—	2	2	no	—
678	#123	—	2	2	no	—
679	#123	D₄×C₈₃	1	2	yes	—
680	C₂²⋊Q₈	—	2	1	no	—
681	C₂²⋊Q₈	—	2	1	no	—
682	C₂²⋊Q₈	—	2	2	no	—
683	C₂²⋊Q₈	—	2	2	no	—
684	C₂²⋊Q₈	—	2	2	no	—
685	C₂²⋊Q₈	—	2	2	no	—
686	C₂²⋊Q₈	—	2	2	no	—
687	C₂²⋊Q₈	—	2	2	no	—
688	C₂²⋊Q₈	D₄×C₈₃	1	1	yes	characteristic
689	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
690	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
691	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
692	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
693	#121	—	2	2	no	—
694	#121	—	2	1	no	—
695	#121	—	2	1	no	—
696	#121	—	2	2	no	—
697	#121	D₄×C₈₃	1	1	yes	characteristic
698	#121	C₂³×C₈₃	1	2	yes	—
699	#121	C₂³×C₈₃	1	2	yes	—
700	#120	—	2	2	no	—
701	#120	—	2	2	no	—
702	C₄×Q₈	—	2	1	no	—
703	C₄×Q₈	—	2	2	no	—
704	C₄×Q₈	—	2	1	no	—
705	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
706	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
707	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
708	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
709	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
710	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
711	C₄×D₄	—	2	2	no	—
712	C₄×D₄	—	2	1	no	—
713	C₄×D₄	—	2	1	no	—
714	C₄×D₄	—	2	2	no	—
715	C₄×D₄	—	2	2	no	—
716	C₄×D₄	—	2	1	no	—
717	C₄×D₄	—	2	1	no	—
718	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
719	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
720	C₄×D₄	C₂³×C₈₃	1	2	yes	—
721	C₄×D₄	C₂³×C₈₃	1	2	yes	—
722	C₄×D₄	C₂³×C₈₃	1	2	yes	—
723	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
724	C₄×D₄	C₂³×C₈₃	1	2	yes	—
725	#117	—	2	1	no	—
726	#117	—	2	2	no	—
727	#117	—	2	2	no	—
728	#117	—	2	2	no	—
729	#117	—	2	1	no	—
730	#117	C₂³×C₈₃	1	1	yes	characteristic
731	#117	C₂³×C₈₃	1	2	yes	—
732	#117	C₂³×C₈₃	1	2	yes	—
733	#117	C₂³×C₈₃	1	2	yes	—
734	C₂×C₄⋊C₄	—	2	1	no	—
735	C₂×C₄⋊C₄	—	2	1	no	—
736	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
737	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
738	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
739	C₂×C₂²⋊C₄	—	2	2	no	—
740	C₂×C₂²⋊C₄	—	2	2	no	—
741	C₂×C₂²⋊C₄	—	2	2	no	—
742	C₂×C₄²	—	2	1	no	—
743	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
744	#107	C₂³×C₈₃	1	2	yes	—
745	#107	C₂³×C₈₃	1	2	yes	—
746	#107	C₂³×C₈₃	1	2	yes	—
747	#107	C₂³×C₈₃	1	2	yes	—
748	#107	C₂³×C₈₃	1	2	yes	—
749	#107	C₂³×C₈₃	1	2	yes	—
750	#107	C₂³×C₈₃	1	2	yes	—
751	#106	C₂³×C₈₃	1	2	yes	—
752	#106	C₂³×C₈₃	1	2	yes	—
753	#106	C₂³×C₈₃	1	2	yes	—
754	#106	C₂³×C₈₃	1	2	yes	—
755	#106	C₂³×C₈₃	1	2	yes	—
756	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
757	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
758	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
759	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
760	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
761	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
762	#103	C₂³×C₈₃	1	2	yes	—
763	#103	C₂³×C₈₃	1	2	yes	—
764	#103	C₂³×C₈₃	1	2	yes	—
765	#103	C₂³×C₈₃	1	2	yes	—
766	#103	C₂³×C₈₃	1	2	yes	—
767	#103	C₂³×C₈₃	1	2	yes	—
768	#103	C₂³×C₈₃	1	2	yes	—
769	#102	C₂³×C₈₃	1	2	yes	—
770	#102	C₂³×C₈₃	1	2	yes	—
771	#102	C₂³×C₈₃	1	2	yes	—
772	#102	C₂³×C₈₃	1	2	yes	—
773	#102	C₂³×C₈₃	1	2	yes	—
774	#102	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	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
779	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
780	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
781	#97	C₂³×C₈₃	1	2	yes	—
782	#97	C₂³×C₈₃	1	2	yes	—
783	C₄×C₈	C₂³×C₈₃	1	2	yes	—
784	C₂⁴	—	2	2	no	—
785	#41	—	2	2	no	—
786	#41	—	4	1	no	—
787	#41	—	8	2	no	—
788	C₂×Q₈	—	2	1	no	—
789	C₂×Q₈	—	2	1	no	—
790	C₂×Q₈	—	2	2	no	—
791	C₂×Q₈	—	2	2	no	—
792	C₂×Q₈	—	8	2	no	—
793	C₂×Q₈	C₂×D₄×C₈₃	1	1	yes	characteristic
794	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
795	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
796	C₂×D₄	—	2	4	no	—
797	C₂×D₄	—	2	1	no	—
798	C₂×D₄	—	2	2	no	—
799	C₂×D₄	—	2	2	no	—
800	C₂×D₄	—	2	2	no	—
801	C₂×D₄	—	2	1	no	—
802	C₂×D₄	—	2	1	no	—
803	C₂×D₄	—	4	2	no	—
804	C₂×D₄	—	8	2	no	—
805	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
806	C₂×D₄	C₂×D₄×C₈₃	1	1	yes	characteristic
807	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
808	C₂×D₄	C₂⁴×C₈₃	1	1	yes	characteristic
809	C₂²×C₄	—	2	1	no	—
810	C₂²×C₄	—	2	1	no	—
811	C₂²×C₄	—	2	2	no	—
812	C₂²×C₄	—	2	1	no	—
813	C₂²×C₄	—	2	1	no	—
814	C₂²×C₄	—	2	1	no	—
815	C₂²×C₄	—	2	2	no	—
816	C₂²×C₄	—	2	2	no	—
817	C₂²×C₄	—	2	2	no	—
818	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
819	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
820	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
821	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
822	Q₁₆	—	4	2	no	—
823	SD₁₆	—	2	4	no	—
824	SD₁₆	—	4	2	no	—
825	SD₁₆	—	4	2	no	—
826	M₁₆	—	4	1	no	—
827	M₁₆	—	4	2	no	—
828	M₁₆	—	4	1	no	—
829	C₂×C₈	—	4	2	no	—
830	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
831	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
832	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
833	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
834	C₄⋊C₄	—	2	2	no	—
835	C₄⋊C₄	—	2	2	no	—
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	2	no	—
838	C₄⋊C₄	—	2	1	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	1	no	—
841	C₄⋊C₄	—	2	1	no	—
842	C₄⋊C₄	—	2	1	no	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	—	2	1	no	—
845	C₄⋊C₄	—	2	2	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	1	no	—
849	C₄⋊C₄	—	2	1	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	2	2	no	—
852	C₄⋊C₄	—	2	2	no	—
853	C₄⋊C₄	—	2	2	no	—
854	C₄⋊C₄	—	2	1	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
859	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
860	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
861	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
862	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
863	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
864	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
865	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
866	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
867	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
868	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
869	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
870	C₂²⋊C₄	—	2	2	no	—
871	C₂²⋊C₄	—	2	2	no	—
872	C₂²⋊C₄	—	2	2	no	—
873	C₂²⋊C₄	—	2	2	no	—
874	C₂²⋊C₄	—	2	1	no	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	2	1	no	—
878	C₂²⋊C₄	—	2	2	no	—
879	C₂²⋊C₄	—	2	2	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	—	2	2	no	—
883	C₂²⋊C₄	—	2	1	no	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
887	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
888	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
889	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
890	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
891	C₄²	—	2	1	no	—
892	C₄²	—	2	1	no	—
893	C₄²	—	2	1	no	—
894	C₄²	—	2	2	no	—
895	C₄²	—	2	2	no	—
896	C₄²	—	2	2	no	—
897	C₄²	—	2	2	no	—
898	C₄²	—	2	2	no	—
899	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
900	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
901	C₄²	C₂⁴×C₈₃	1	2	yes	—
902	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
903	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
904	C₂³	—	2	1	no	—
905	C₂³	—	2	2	no	—
906	C₂³	—	4	4	no	—
907	C₂³	—	8	2	no	—
908	C₂³	—	8	2	no	—
909	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
910	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
911	Q₈	—	2	2	no	—
912	Q₈	—	2	1	no	—
913	Q₈	—	2	2	no	—
914	Q₈	—	2	1	no	—
915	Q₈	—	4	1	no	—
916	Q₈	—	4	2	no	—
917	Q₈	—	8	2	no	—
918	Q₈	—	8	1	no	—
919	Q₈	—	8	2	no	—
920	D₄	—	2	2	no	—
921	D₄	—	2	1	no	—
922	D₄	—	2	2	no	—
923	D₄	—	4	1	no	—
924	D₄	—	4	2	no	—
925	D₄	—	4	4	no	—
926	D₄	—	4	2	no	—
927	D₄	—	4	2	no	—
928	D₄	—	8	1	no	—
929	D₄	—	8	2	no	—
930	D₄	—	8	2	no	—
931	D₄	2₋¹⁺⁴×C₈₃	1	2	yes	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	4	1	no	—
945	C₂×C₄	—	4	1	no	—
946	C₂×C₄	—	4	2	no	—
947	C₂×C₄	—	4	2	no	—
948	C₂×C₄	—	4	2	no	—
949	C₂×C₄	—	8	2	no	—
950	C₂×C₄	—	8	2	no	—
951	C₂×C₄	—	8	1	no	—
952	C₂×C₄	—	8	2	no	—
953	C₂×C₄	—	8	1	no	—
954	C₂×C₄	—	8	2	no	—
955	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
956	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
957	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
958	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
959	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
960	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
961	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
962	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
963	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
964	C₈	—	2	2	no	—
965	C₈	—	2	2	no	—
966	C₈	—	2	2	no	—
967	C₈	—	2	2	no	—
968	C₂²	—	2	1	no	—
969	C₂²	—	2	2	no	—
970	C₂²	—	2	1	no	—
971	C₂²	—	2	2	no	—
972	C₂²	—	2	1	no	—
973	C₂²	—	2	2	no	—
974	C₂²	—	2	2	no	—
975	C₂²	—	4	1	no	—
976	C₂²	—	4	1	no	—
977	C₂²	—	4	2	no	—
978	C₂²	—	4	2	no	—
979	C₂²	—	4	2	no	—
980	C₂²	—	16	4	no	—
981	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
982	C₄	—	2	1	no	—
983	C₄	—	2	1	no	—
984	C₄	—	2	2	no	—
985	C₄	—	2	1	no	—
986	C₄	—	2	1	no	—
987	C₄	—	2	2	no	—
988	C₄	—	2	1	no	—
989	C₄	—	2	2	no	—
990	C₄	—	4	1	no	—
991	C₄	—	4	2	no	—
992	C₄	—	4	2	no	—
993	C₄	—	4	2	no	—
994	C₄	—	4	2	no	—
995	C₄	—	4	1	no	—
996	C₄	—	4	1	no	—
997	C₄	—	4	2	no	—
998	C₄	C₂×2₋¹⁺⁴×C₈₃	1	1	yes	characteristic
999	C₄	#585×C₈₃	1	1	yes	characteristic
1000	C₂	—	4	2	no	—
1001	C₂	—	4	1	no	—
1002	C₂	—	4	2	no	—
1003	C₂	—	8	2	no	—
1004	C₂	C₈₃×#3489	1	1	yes	characteristic
1005	C₂	C₈₃×#3585	1	1	yes	characteristic
1006	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×#3514	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₃ ◁ #529×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₃×#3563	C₂	semidirect
3. C₈₃×#3386	C₂	semidirect
4. C₈₃×#3371	C₂	semidirect
5. C₈₃×#3357	C₂	semidirect
6. C₈₃×#3349	C₂	semidirect
7. C₈₃×#3348	C₂	semidirect
8. C₈₃×#3323	C₂	semidirect
9. C₈₃×#3314	C₂	semidirect
10. C₈₃×#3310	C₂	semidirect
11. C₈₃×#3258	C₂	semidirect
12. C₈₃×#3254	C₂	semidirect
13. C₈₃×#3243	C₂	semidirect
14. C₈₃×#3234	C₂	semidirect
15. C₈₃×#3123	C₂	semidirect
16. C₈₃×#3116	C₂	semidirect
17. C₈₃×#3081	C₂	semidirect
18. C₈₃×#3080	C₂	semidirect
19. C₈₃×#2995	C₂	semidirect
23. #557×C₈₃	C₂²	semidirect
26. #554×C₈₃	C₂²	semidirect
29. #552×C₈₃	C₂²	semidirect
37. #544×C₈₃	C₂²	semidirect
40. #541×C₈₃	C₂²	semidirect
43. #533×C₈₃	C₂²	semidirect
47. C₂×#125×C₈₃	C₂²	semidirect
51. #501×C₈₃	C₂²	semidirect
52. #501×C₈₃	C₂²	semidirect
53. #500×C₈₃	C₂²	semidirect
55. #489×C₈₃	C₂²	semidirect
56. #488×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
63. #481×C₈₃	C₂²	semidirect
65. #480×C₈₃	C₂²	semidirect
66. #479×C₈₃	C₂²	semidirect
67. #479×C₈₃	C₂²	semidirect
71. #478×C₈₃	C₂²	semidirect
72. #478×C₈₃	C₂²	semidirect
73. #478×C₈₃	C₂²	semidirect
74. #477×C₈₃	C₂²	semidirect
75. #477×C₈₃	C₂²	semidirect
76. #477×C₈₃	C₂²	semidirect
78. #476×C₈₃	C₂²	semidirect
79. #475×C₈₃	C₂²	semidirect
81. #474×C₈₃	C₂²	semidirect
82. #470×C₈₃	C₂²	semidirect
84. #468×C₈₃	C₂²	semidirect
85. #468×C₈₃	C₂²	semidirect
86. #467×C₈₃	C₂²	semidirect
88. #464×C₈₃	C₂²	semidirect
89. #464×C₈₃	C₂²	semidirect
90. #462×C₈₃	C₂²	semidirect
92. #461×C₈₃	C₂²	semidirect
97. #446×C₈₃	C₂²	semidirect
98. #441×C₈₃	C₂²	semidirect
101. #440×C₈₃	C₂²	semidirect
103. C₄×SD₁₆×C₈₃	C₂²	semidirect
104. #436×C₈₃	C₂²	semidirect
106. #435×C₈₃	C₂²	semidirect
107. #433×C₈₃	C₂²	semidirect
108. #432×C₈₃	C₂²	semidirect
109. #428×C₈₃	C₂²	semidirect
110. #428×C₈₃	C₂²	semidirect
111. #428×C₈₃	C₂²	semidirect
112. #427×C₈₃	C₂²	semidirect
113. #424×C₈₃	C₂²	semidirect
114. #423×C₈₃	C₂²	semidirect
496. #62236	C₈₃	direct (N × H)
504. #3563	C₂×C₈₃	semidirect
506. #3386	C₂×C₈₃	semidirect
507. #3371	C₂×C₈₃	semidirect
508. #3357	C₂×C₈₃	semidirect
509. #3349	C₂×C₈₃	semidirect
510. #3348	C₂×C₈₃	semidirect
511. #3323	C₂×C₈₃	semidirect
512. #3314	C₂×C₈₃	semidirect
513. #3310	C₂×C₈₃	semidirect
514. #3258	C₂×C₈₃	semidirect
515. #3254	C₂×C₈₃	semidirect
516. #3243	C₂×C₈₃	semidirect
517. #3234	C₂×C₈₃	semidirect
518. #3123	C₂×C₈₃	semidirect
519. #3116	C₂×C₈₃	semidirect
520. #3081	C₂×C₈₃	semidirect
521. #3080	C₂×C₈₃	semidirect
522. #2995	C₂×C₈₃	semidirect
523. C₈₃	#62236	direct (N × H)
527. #557	C₂²×C₈₃	semidirect
530. #554	C₂²×C₈₃	semidirect
533. #552	C₂²×C₈₃	semidirect
541. #544	C₂²×C₈₃	semidirect
544. #541	C₂²×C₈₃	semidirect
547. #533	C₂²×C₈₃	semidirect
551. C₂×#125	C₂²×C₈₃	semidirect
555. #501	C₂²×C₈₃	semidirect
556. #501	C₂²×C₈₃	semidirect
557. #500	C₂²×C₈₃	semidirect
559. #489	C₂²×C₈₃	semidirect
560. #488	C₂²×C₈₃	semidirect
561. #485	C₂²×C₈₃	semidirect
562. #485	C₂²×C₈₃	semidirect
563. #485	C₂²×C₈₃	semidirect
564. #485	C₂²×C₈₃	semidirect
565. #484	C₂²×C₈₃	semidirect
567. #481	C₂²×C₈₃	semidirect
569. #480	C₂²×C₈₃	semidirect
570. #479	C₂²×C₈₃	semidirect
571. #479	C₂²×C₈₃	semidirect
575. #478	C₂²×C₈₃	semidirect
576. #478	C₂²×C₈₃	semidirect
577. #478	C₂²×C₈₃	semidirect
578. #477	C₂²×C₈₃	semidirect
579. #477	C₂²×C₈₃	semidirect
580. #477	C₂²×C₈₃	semidirect
582. #476	C₂²×C₈₃	semidirect
583. #475	C₂²×C₈₃	semidirect
585. #474	C₂²×C₈₃	semidirect
586. #470	C₂²×C₈₃	semidirect
588. #468	C₂²×C₈₃	semidirect
589. #468	C₂²×C₈₃	semidirect
590. #467	C₂²×C₈₃	semidirect
592. #464	C₂²×C₈₃	semidirect
593. #464	C₂²×C₈₃	semidirect
594. #462	C₂²×C₈₃	semidirect
596. #461	C₂²×C₈₃	semidirect
601. #446	C₂²×C₈₃	semidirect
602. #441	C₂²×C₈₃	semidirect
605. #440	C₂²×C₈₃	semidirect
607. C₄×SD₁₆	C₂²×C₈₃	semidirect
608. #436	C₂²×C₈₃	semidirect
610. #435	C₂²×C₈₃	semidirect
611. #433	C₂²×C₈₃	semidirect
612. #432	C₂²×C₈₃	semidirect
613. #428	C₂²×C₈₃	semidirect
614. #428	C₂²×C₈₃	semidirect
615. #428	C₂²×C₈₃	semidirect
616. #427	C₂²×C₈₃	semidirect
617. #424	C₂²×C₈₃	semidirect
618. #423	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×#3563	2
C₈₃×#3514	2
C₈₃×#3386	2
C₈₃×#3371	2
C₈₃×#3357	2
C₈₃×#3349	2
C₈₃×#3348	2
C₈₃×#3323	2
C₈₃×#3314	2
C₈₃×#3310	2
C₈₃×#3258	2
C₈₃×#3254	2
C₈₃×#3243	2
C₈₃×#3234	2
C₈₃×#3123	2
C₈₃×#3116	2
C₈₃×#3081	2
C₈₃×#3080	2
C₈₃×#2995	2
#62236	83

Subgroups — C83×#62236 #35290060

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#62236 #35290060