Subgroups — C₈₃×#62218 #35290042

Order 21248.

1698 conjugacy classes of subgroups.

The subgroup lattice has 1114 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₃×#3515	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₃×#3384	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₃×#3380	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₃×#3372	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₃×#3359	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₃×#3357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₃×#3348	C₂	1	2	yes	maximal, complemented
9	C₈₃×#3337	C₂	1	2	yes	maximal, complemented
10	C₈₃×#3335	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₃×#3330	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₃×#3307	C₂	1	2	yes	maximal, complemented
13	C₈₃×#3303	C₂	1	2	yes	maximal, complemented
14	C₈₃×#3303	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#3260	C₂	1	2	yes	maximal, complemented
16	C₈₃×#3246	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₃×#3242	C₂	1	2	yes	maximal, complemented
18	C₈₃×#3231	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₃×#3119	C₂	1	2	yes	maximal, complemented
20	C₈₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₃×#3084	C₂	1	2	yes	maximal, complemented
22	C₈₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
23	C₈₃×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	#562×C₈₃	—	2	2	no	—
25	#557×C₈₃	C₂²	1	1	yes	characteristic
26	#555×C₈₃	C₂²	1	2	yes	—
27	#555×C₈₃	C₂²	1	1	yes	characteristic
28	#554×C₈₃	C₂²	1	1	yes	characteristic
29	#554×C₈₃	C₂²	1	1	yes	characteristic
30	#554×C₈₃	C₂²	1	1	yes	characteristic
31	#553×C₈₃	—	2	1	no	—
32	#553×C₈₃	C₂²	1	2	yes	—
33	#552×C₈₃	—	2	2	no	—
34	#552×C₈₃	—	2	1	no	—
35	#552×C₈₃	—	2	1	no	—
36	#552×C₈₃	C₂²	1	2	yes	—
37	D₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
38	#548×C₈₃	—	2	1	no	—
39	#547×C₈₃	C₂²	1	2	yes	—
40	#547×C₈₃	C₂²	1	1	yes	characteristic
41	#547×C₈₃	C₂²	1	1	yes	characteristic
42	#544×C₈₃	C₂²	1	2	yes	—
43	#542×C₈₃	—	2	2	no	—
44	#541×C₈₃	C₂²	1	2	yes	—
45	#540×C₈₃	C₂²	1	2	yes	—
46	#539×C₈₃	—	2	2	no	—
47	#537×C₈₃	—	2	1	no	—
48	#536×C₈₃	—	2	1	no	—
49	#533×C₈₃	C₂²	1	1	yes	characteristic
50	#533×C₈₃	C₂²	1	1	yes	characteristic
51	#532×C₈₃	C₂²	1	1	yes	characteristic
52	#529×C₈₃	—	2	1	no	—
53	#529×C₈₃	C₂²	1	1	yes	characteristic
54	C₂×#125×C₈₃	—	2	1	no	—
55	#520×C₈₃	C₂²	1	2	yes	—
56	C₄×#41×C₈₃	C₂²	1	1	yes	characteristic
57	#501×C₈₃	C₂²	1	2	yes	—
58	#500×C₈₃	C₂²	1	1	yes	characteristic
59	#499×C₈₃	C₂²	1	2	yes	—
60	#498×C₈₃	C₂²	1	1	yes	characteristic
61	#491×C₈₃	C₂²	1	2	yes	—
62	#487×C₈₃	C₂²	1	2	yes	—
63	#487×C₈₃	C₂²	1	1	yes	characteristic
64	#487×C₈₃	C₂²	1	1	yes	characteristic
65	#485×C₈₃	C₂²	1	2	yes	—
66	#485×C₈₃	C₂²	1	2	yes	—
67	#485×C₈₃	C₂²	1	2	yes	—
68	#485×C₈₃	C₂²	1	2	yes	—
69	#484×C₈₃	C₂²	1	2	yes	—
70	#483×C₈₃	C₂²	1	2	yes	—
71	#482×C₈₃	C₂²	1	1	yes	characteristic
72	#482×C₈₃	C₂²	1	1	yes	characteristic
73	#481×C₈₃	C₂²	1	2	yes	—
74	#480×C₈₃	C₂²	1	2	yes	—
75	#479×C₈₃	C₂²	1	2	yes	—
76	#479×C₈₃	C₂²	1	2	yes	—
77	#479×C₈₃	C₂²	1	2	yes	—
78	#479×C₈₃	C₂²	1	2	yes	—
79	#478×C₈₃	C₂²	1	2	yes	—
80	#478×C₈₃	C₂²	1	2	yes	—
81	#478×C₈₃	C₂²	1	2	yes	—
82	#478×C₈₃	C₂²	1	2	yes	—
83	#477×C₈₃	C₂²	1	1	yes	characteristic
84	#477×C₈₃	C₂²	1	1	yes	characteristic
85	#476×C₈₃	C₂²	1	1	yes	characteristic
86	#476×C₈₃	C₂²	1	2	yes	—
87	#476×C₈₃	C₂²	1	1	yes	characteristic
88	#476×C₈₃	C₂²	1	1	yes	characteristic
89	#476×C₈₃	C₂²	1	1	yes	characteristic
90	#475×C₈₃	C₂²	1	1	yes	characteristic
91	#475×C₈₃	C₂²	1	2	yes	—
92	#475×C₈₃	C₂²	1	2	yes	—
93	#474×C₈₃	C₂²	1	1	yes	characteristic
94	#468×C₈₃	C₂²	1	2	yes	—
95	#468×C₈₃	C₂²	1	2	yes	—
96	#465×C₈₃	C₂²	1	2	yes	—
97	#465×C₈₃	C₂²	1	2	yes	—
98	#465×C₈₃	C₂²	1	2	yes	—
99	#465×C₈₃	C₂²	1	2	yes	—
100	#461×C₈₃	C₂²	1	1	yes	characteristic
101	#461×C₈₃	C₂²	1	2	yes	—
102	#461×C₈₃	C₂²	1	2	yes	—
103	#461×C₈₃	C₂²	1	1	yes	characteristic
104	#460×C₈₃	C₂²	1	1	yes	characteristic
105	#460×C₈₃	C₂²	1	2	yes	—
106	#459×C₈₃	C₂²	1	1	yes	characteristic
107	#449×C₈₃	C₂²	1	1	yes	characteristic
108	#449×C₈₃	C₂²	1	2	yes	—
109	#449×C₈₃	C₂²	1	2	yes	—
110	#449×C₈₃	C₂²	1	1	yes	characteristic
111	#446×C₈₃	C₂²	1	1	yes	characteristic
112	C₈×Q₈×C₈₃	C₂²	1	1	yes	characteristic
113	#442×C₈₃	C₂²	1	2	yes	—
114	#440×C₈₃	C₂²	1	2	yes	—
115	C₄×SD₁₆×C₈₃	C₂²	1	1	yes	characteristic
116	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	—
117	C₄×SD₁₆×C₈₃	C₂²	1	1	yes	characteristic
118	C₄×D₈×C₈₃	C₂²	1	1	yes	characteristic
119	C₄×D₈×C₈₃	C₂²	1	2	yes	—
120	C₄×D₈×C₈₃	C₂²	1	1	yes	characteristic
121	#436×C₈₃	C₂²	1	1	yes	characteristic
122	#435×C₈₃	C₂²	1	2	yes	—
123	C₈×D₄×C₈₃	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₈₃	C₂²	1	2	yes	—
125	#433×C₈₃	C₂²	1	2	yes	—
126	#431×C₈₃	C₂²	1	1	yes	characteristic
127	#428×C₈₃	C₂²	1	2	yes	—
128	#427×C₈₃	C₂²	1	2	yes	—
129	C₂×#106×C₈₃	C₂²	1	2	yes	—
130	#424×C₈₃	C₂²	1	2	yes	—
131	C₂×C₄⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
132	#417×C₈₃	C₂²	1	2	yes	—
133	#416×C₈₃	C₂²	1	2	yes	—
134	#416×C₈₃	C₂²	1	2	yes	—
135	C₂×#41×C₈₃	—	2	1	no	—
136	C₂×#41×C₈₃	—	2	1	no	—
137	C₂×#41×C₈₃	C₂³	1	1	yes	characteristic
138	C₂×#41×C₈₃	C₂³	1	2	yes	—
139	C₂²×Q₈×C₈₃	—	2	1	no	—
140	C₂×SD₁₆×C₈₃	C₂³	1	1	yes	characteristic
141	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
142	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
143	C₂×SD₁₆×C₈₃	C₂³	1	1	yes	characteristic
144	C₂×D₈×C₈₃	C₂³	1	1	yes	characteristic
145	C₂×D₈×C₈₃	C₂³	1	1	yes	characteristic
146	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
147	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
148	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
149	C₄⋊Q₈×C₈₃	—	2	2	no	—
150	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
151	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
152	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
153	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
154	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
155	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
156	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
157	#127×C₈₃	C₂³	1	1	yes	characteristic
158	#126×C₈₃	—	2	2	no	—
159	#126×C₈₃	—	2	2	no	—
160	#126×C₈₃	—	2	2	no	—
161	#126×C₈₃	—	2	2	no	—
162	#126×C₈₃	D₄	1	2	yes	—
163	#125×C₈₃	—	2	2	no	—
164	#125×C₈₃	—	2	2	no	—
165	#125×C₈₃	—	2	1	no	—
166	#125×C₈₃	—	2	1	no	—
167	#125×C₈₃	—	2	2	no	—
168	#125×C₈₃	—	2	2	no	—
169	#125×C₈₃	—	2	2	no	—
170	#125×C₈₃	—	2	1	no	—
171	#125×C₈₃	D₄	1	1	yes	characteristic
172	#125×C₈₃	C₂³	1	2	yes	—
173	#125×C₈₃	C₂³	1	2	yes	—
174	#125×C₈₃	C₂³	1	2	yes	—
175	#124×C₈₃	—	2	2	no	—
176	#124×C₈₃	—	2	2	no	—
177	#124×C₈₃	—	2	2	no	—
178	#124×C₈₃	—	2	1	no	—
179	#124×C₈₃	D₄	1	1	yes	characteristic
180	#123×C₈₃	—	2	2	no	—
181	#123×C₈₃	—	2	2	no	—
182	#123×C₈₃	—	2	2	no	—
183	#123×C₈₃	—	2	2	no	—
184	#123×C₈₃	—	2	2	no	—
185	#123×C₈₃	—	2	2	no	—
186	#123×C₈₃	—	2	2	no	—
187	#123×C₈₃	—	2	2	no	—
188	#123×C₈₃	D₄	1	2	yes	—
189	C₂²⋊Q₈×C₈₃	—	2	1	no	—
190	C₂²⋊Q₈×C₈₃	—	2	1	no	—
191	C₂²⋊Q₈×C₈₃	—	2	1	no	—
192	C₂²⋊Q₈×C₈₃	—	2	1	no	—
193	C₂²⋊Q₈×C₈₃	—	2	1	no	—
194	C₂²⋊Q₈×C₈₃	—	2	1	no	—
195	C₂²⋊Q₈×C₈₃	—	2	1	no	—
196	C₂²⋊Q₈×C₈₃	—	2	2	no	—
197	C₂²⋊Q₈×C₈₃	—	2	2	no	—
198	C₂²⋊Q₈×C₈₃	—	2	2	no	—
199	C₂²⋊Q₈×C₈₃	—	2	2	no	—
200	C₂²⋊Q₈×C₈₃	—	2	2	no	—
201	C₂²⋊Q₈×C₈₃	—	2	2	no	—
202	C₂²⋊Q₈×C₈₃	D₄	1	1	yes	characteristic
203	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
204	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
205	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
206	#121×C₈₃	—	2	1	no	—
207	#121×C₈₃	—	2	1	no	—
208	#121×C₈₃	—	2	2	no	—
209	#121×C₈₃	—	2	2	no	—
210	#121×C₈₃	—	2	2	no	—
211	#121×C₈₃	—	2	1	no	—
212	#121×C₈₃	—	2	2	no	—
213	#121×C₈₃	—	2	2	no	—
214	#121×C₈₃	D₄	1	1	yes	characteristic
215	#121×C₈₃	C₂³	1	1	yes	characteristic
216	#121×C₈₃	C₂³	1	1	yes	characteristic
217	#121×C₈₃	C₂³	1	2	yes	—
218	#121×C₈₃	C₂³	1	2	yes	—
219	C₄×Q₈×C₈₃	—	2	1	no	—
220	C₄×Q₈×C₈₃	—	2	1	no	—
221	C₄×Q₈×C₈₃	—	2	1	no	—
222	C₄×Q₈×C₈₃	—	2	1	no	—
223	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
225	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
226	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
228	C₄×D₄×C₈₃	—	2	1	no	—
229	C₄×D₄×C₈₃	—	2	1	no	—
230	C₄×D₄×C₈₃	—	2	1	no	—
231	C₄×D₄×C₈₃	—	2	2	no	—
232	C₄×D₄×C₈₃	—	2	2	no	—
233	C₄×D₄×C₈₃	—	2	2	no	—
234	C₄×D₄×C₈₃	—	2	1	no	—
235	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₈₃	C₂³	1	2	yes	—
238	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₈₃	C₂³	1	2	yes	—
241	C₄×D₄×C₈₃	C₂³	1	2	yes	—
242	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₈₃	C₂³	1	2	yes	—
244	#117×C₈₃	—	2	1	no	—
245	#117×C₈₃	—	2	2	no	—
246	#117×C₈₃	—	2	1	no	—
247	#117×C₈₃	—	2	2	no	—
248	#117×C₈₃	—	2	2	no	—
249	#117×C₈₃	—	2	1	no	—
250	#117×C₈₃	C₂³	1	1	yes	characteristic
251	#117×C₈₃	C₂³	1	2	yes	—
252	#117×C₈₃	C₂³	1	2	yes	—
253	#117×C₈₃	C₂³	1	2	yes	—
254	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
255	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
256	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
257	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
258	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
259	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
261	C₂×C₄²×C₈₃	—	2	1	no	—
262	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
263	#107×C₈₃	C₂³	1	2	yes	—
264	#107×C₈₃	C₂³	1	2	yes	—
265	#107×C₈₃	C₂³	1	2	yes	—
266	#107×C₈₃	C₂³	1	1	yes	characteristic
267	#107×C₈₃	C₂³	1	1	yes	characteristic
268	#107×C₈₃	C₂³	1	2	yes	—
269	#106×C₈₃	C₂³	1	2	yes	—
270	#106×C₈₃	C₂³	1	2	yes	—
271	#106×C₈₃	C₂³	1	2	yes	—
272	#106×C₈₃	C₂³	1	2	yes	—
273	#106×C₈₃	C₂³	1	1	yes	characteristic
274	#106×C₈₃	C₂³	1	2	yes	—
275	#106×C₈₃	C₂³	1	1	yes	characteristic
276	#106×C₈₃	C₂³	1	2	yes	—
277	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
278	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
279	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
280	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
281	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
282	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
284	#103×C₈₃	C₂³	1	2	yes	—
285	#103×C₈₃	C₂³	1	2	yes	—
286	#103×C₈₃	C₂³	1	2	yes	—
287	#103×C₈₃	C₂³	1	2	yes	—
288	#103×C₈₃	C₂³	1	2	yes	—
289	#103×C₈₃	C₂³	1	2	yes	—
290	#103×C₈₃	C₂³	1	1	yes	characteristic
291	#103×C₈₃	C₂³	1	1	yes	characteristic
292	#103×C₈₃	C₂³	1	2	yes	—
293	#103×C₈₃	C₂³	1	2	yes	—
294	#102×C₈₃	C₂³	1	2	yes	—
295	#102×C₈₃	C₂³	1	1	yes	characteristic
296	#102×C₈₃	C₂³	1	2	yes	—
297	#102×C₈₃	C₂³	1	1	yes	characteristic
298	#102×C₈₃	C₂³	1	2	yes	—
299	#102×C₈₃	C₂³	1	1	yes	characteristic
300	#102×C₈₃	C₂³	1	2	yes	—
301	#102×C₈₃	C₂³	1	1	yes	characteristic
302	#102×C₈₃	C₂³	1	1	yes	characteristic
303	#102×C₈₃	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
307	C₂²⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
308	#97×C₈₃	C₂³	1	2	yes	—
309	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₈₃	C₂³	1	2	yes	—
311	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
312	#41×C₈₃	—	2	2	no	—
313	#41×C₈₃	—	2	4	no	—
314	#41×C₈₃	—	4	1	no	—
315	#41×C₈₃	—	4	2	no	—
316	#41×C₈₃	—	8	2	no	—
317	#41×C₈₃	—	8	2	no	—
318	C₂×Q₈×C₈₃	—	2	1	no	—
319	C₂×Q₈×C₈₃	—	2	1	no	—
320	C₂×Q₈×C₈₃	—	2	1	no	—
321	C₂×Q₈×C₈₃	—	2	2	no	—
322	C₂×Q₈×C₈₃	—	2	1	no	—
323	C₂×Q₈×C₈₃	—	8	2	no	—
324	C₂×Q₈×C₈₃	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
326	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
327	C₂×D₄×C₈₃	—	2	1	no	—
328	C₂×D₄×C₈₃	—	2	2	no	—
329	C₂×D₄×C₈₃	—	2	2	no	—
330	C₂×D₄×C₈₃	—	2	1	no	—
331	C₂×D₄×C₈₃	—	2	2	no	—
332	C₂×D₄×C₈₃	—	2	1	no	—
333	C₂×D₄×C₈₃	—	2	1	no	—
334	C₂×D₄×C₈₃	—	2	1	no	—
335	C₂×D₄×C₈₃	C₂×D₄	1	1	yes	characteristic
336	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
337	C₂×D₄×C₈₃	C₂⁴	1	1	yes	characteristic
338	C₂×D₄×C₈₃	C₂⁴	1	1	yes	characteristic
339	C₂×D₄×C₈₃	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₈₃	—	2	2	no	—
341	C₂²×C₄×C₈₃	—	2	2	no	—
342	C₂²×C₄×C₈₃	—	2	1	no	—
343	C₂²×C₄×C₈₃	—	2	1	no	—
344	C₂²×C₄×C₈₃	—	2	2	no	—
345	C₂²×C₄×C₈₃	—	2	1	no	—
346	C₂²×C₄×C₈₃	—	2	1	no	—
347	C₂²×C₄×C₈₃	—	2	1	no	—
348	C₂²×C₄×C₈₃	—	2	2	no	—
349	C₂²×C₄×C₈₃	—	2	2	no	—
350	C₂²×C₄×C₈₃	—	2	2	no	—
351	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
352	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
353	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
355	SD₁₆×C₈₃	—	4	1	no	—
356	SD₁₆×C₈₃	—	4	2	no	—
357	SD₁₆×C₈₃	—	4	2	no	—
358	SD₁₆×C₈₃	—	4	1	no	—
359	D₈×C₈₃	—	2	2	no	—
360	D₈×C₈₃	—	2	2	no	—
361	M₁₆×C₈₃	—	4	2	no	—
362	C₂×C₈×C₈₃	—	4	2	no	—
363	C₂×C₈×C₈₃	—	4	2	no	—
364	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
365	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
366	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
367	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
368	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
370	C₄⋊C₄×C₈₃	—	2	2	no	—
371	C₄⋊C₄×C₈₃	—	2	1	no	—
372	C₄⋊C₄×C₈₃	—	2	1	no	—
373	C₄⋊C₄×C₈₃	—	2	1	no	—
374	C₄⋊C₄×C₈₃	—	2	2	no	—
375	C₄⋊C₄×C₈₃	—	2	2	no	—
376	C₄⋊C₄×C₈₃	—	2	2	no	—
377	C₄⋊C₄×C₈₃	—	2	2	no	—
378	C₄⋊C₄×C₈₃	—	2	2	no	—
379	C₄⋊C₄×C₈₃	—	2	2	no	—
380	C₄⋊C₄×C₈₃	—	2	2	no	—
381	C₄⋊C₄×C₈₃	—	2	2	no	—
382	C₄⋊C₄×C₈₃	—	2	2	no	—
383	C₄⋊C₄×C₈₃	—	2	1	no	—
384	C₄⋊C₄×C₈₃	—	2	1	no	—
385	C₄⋊C₄×C₈₃	—	2	2	no	—
386	C₄⋊C₄×C₈₃	—	2	2	no	—
387	C₄⋊C₄×C₈₃	—	2	1	no	—
388	C₄⋊C₄×C₈₃	—	2	2	no	—
389	C₄⋊C₄×C₈₃	—	2	2	no	—
390	C₄⋊C₄×C₈₃	—	2	2	no	—
391	C₄⋊C₄×C₈₃	—	2	1	no	—
392	C₄⋊C₄×C₈₃	—	2	1	no	—
393	C₄⋊C₄×C₈₃	—	2	2	no	—
394	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
395	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
396	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
402	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
407	C₂²⋊C₄×C₈₃	—	2	2	no	—
408	C₂²⋊C₄×C₈₃	—	2	2	no	—
409	C₂²⋊C₄×C₈₃	—	2	1	no	—
410	C₂²⋊C₄×C₈₃	—	2	2	no	—
411	C₂²⋊C₄×C₈₃	—	2	2	no	—
412	C₂²⋊C₄×C₈₃	—	2	2	no	—
413	C₂²⋊C₄×C₈₃	—	2	1	no	—
414	C₂²⋊C₄×C₈₃	—	2	1	no	—
415	C₂²⋊C₄×C₈₃	—	2	1	no	—
416	C₂²⋊C₄×C₈₃	—	2	2	no	—
417	C₂²⋊C₄×C₈₃	—	2	2	no	—
418	C₂²⋊C₄×C₈₃	—	2	2	no	—
419	C₂²⋊C₄×C₈₃	—	2	1	no	—
420	C₂²⋊C₄×C₈₃	—	2	2	no	—
421	C₂²⋊C₄×C₈₃	—	2	1	no	—
422	C₂²⋊C₄×C₈₃	—	2	2	no	—
423	C₂²⋊C₄×C₈₃	—	2	1	no	—
424	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
425	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
426	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
427	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
428	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
429	C₄²×C₈₃	—	2	1	no	—
430	C₄²×C₈₃	—	2	1	no	—
431	C₄²×C₈₃	—	2	1	no	—
432	C₄²×C₈₃	—	2	2	no	—
433	C₄²×C₈₃	—	2	2	no	—
434	C₄²×C₈₃	—	2	2	no	—
435	C₄²×C₈₃	—	2	2	no	—
436	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
437	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
438	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
439	C₄²×C₈₃	C₂⁴	1	2	yes	—
440	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
441	C₂³×C₈₃	—	2	1	no	—
442	C₂³×C₈₃	—	2	1	no	—
443	C₂³×C₈₃	—	2	1	no	—
444	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
445	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
446	Q₈×C₈₃	—	2	2	no	—
447	Q₈×C₈₃	—	2	2	no	—
448	Q₈×C₈₃	—	2	1	no	—
449	Q₈×C₈₃	—	2	2	no	—
450	Q₈×C₈₃	—	2	1	no	—
451	Q₈×C₈₃	—	4	2	no	—
452	Q₈×C₈₃	—	8	1	no	—
453	Q₈×C₈₃	—	8	1	no	—
454	Q₈×C₈₃	—	8	2	no	—
455	Q₈×C₈₃	—	8	1	no	—
456	D₄×C₈₃	—	2	2	no	—
457	D₄×C₈₃	—	2	1	no	—
458	D₄×C₈₃	—	2	1	no	—
459	D₄×C₈₃	—	2	1	no	—
460	D₄×C₈₃	—	2	1	no	—
461	D₄×C₈₃	—	2	1	no	—
462	D₄×C₈₃	—	4	2	no	—
463	D₄×C₈₃	—	4	2	no	—
464	D₄×C₈₃	—	4	4	no	—
465	D₄×C₈₃	—	8	1	no	—
466	D₄×C₈₃	—	8	1	no	—
467	D₄×C₈₃	—	8	2	no	—
468	D₄×C₈₃	—	8	1	no	—
469	D₄×C₈₃	—	8	1	no	—
470	D₄×C₈₃	—	8	2	no	—
471	D₄×C₈₃	2₋¹⁺⁴	1	2	yes	—
472	C₂×C₄×C₈₃	—	2	2	no	—
473	C₂×C₄×C₈₃	—	2	1	no	—
474	C₂×C₄×C₈₃	—	2	2	no	—
475	C₂×C₄×C₈₃	—	2	1	no	—
476	C₂×C₄×C₈₃	—	2	2	no	—
477	C₂×C₄×C₈₃	—	2	1	no	—
478	C₂×C₄×C₈₃	—	2	1	no	—
479	C₂×C₄×C₈₃	—	2	2	no	—
480	C₂×C₄×C₈₃	—	2	1	no	—
481	C₂×C₄×C₈₃	—	2	1	no	—
482	C₂×C₄×C₈₃	—	2	2	no	—
483	C₂×C₄×C₈₃	—	2	2	no	—
484	C₂×C₄×C₈₃	—	2	2	no	—
485	C₂×C₄×C₈₃	—	2	1	no	—
486	C₂×C₄×C₈₃	—	4	1	no	—
487	C₂×C₄×C₈₃	—	4	2	no	—
488	C₂×C₄×C₈₃	—	4	4	no	—
489	C₂×C₄×C₈₃	—	4	2	no	—
490	C₂×C₄×C₈₃	—	4	2	no	—
491	C₂×C₄×C₈₃	—	4	2	no	—
492	C₂×C₄×C₈₃	—	8	1	no	—
493	C₂×C₄×C₈₃	—	8	2	no	—
494	C₂×C₄×C₈₃	—	8	2	no	—
495	C₂×C₄×C₈₃	—	8	2	no	—
496	C₂×C₄×C₈₃	—	8	2	no	—
497	C₂×C₄×C₈₃	—	8	2	no	—
498	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
502	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
503	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
505	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
507	C₈×C₈₃	—	2	1	no	—
508	C₈×C₈₃	—	2	1	no	—
509	C₈×C₈₃	—	2	1	no	—
510	C₈×C₈₃	—	2	2	no	—
511	C₈×C₈₃	—	2	2	no	—
512	C₈×C₈₃	—	2	1	no	—
513	C₂²×C₈₃	—	2	1	no	—
514	C₂²×C₈₃	—	2	2	no	—
515	C₂²×C₈₃	—	2	1	no	—
516	C₂²×C₈₃	—	2	2	no	—
517	C₂²×C₈₃	—	2	2	no	—
518	C₂²×C₈₃	—	2	1	no	—
519	C₂²×C₈₃	—	2	2	no	—
520	C₂²×C₈₃	—	4	1	no	—
521	C₂²×C₈₃	—	4	1	no	—
522	C₂²×C₈₃	—	4	1	no	—
523	C₂²×C₈₃	—	4	1	no	—
524	C₂²×C₈₃	—	4	1	no	—
525	C₂²×C₈₃	—	4	1	no	—
526	C₂²×C₈₃	—	4	1	no	—
527	C₂²×C₈₃	—	4	1	no	—
528	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
529	C₄×C₈₃	—	2	1	no	—
530	C₄×C₈₃	—	2	1	no	—
531	C₄×C₈₃	—	2	2	no	—
532	C₄×C₈₃	—	2	1	no	—
533	C₄×C₈₃	—	2	2	no	—
534	C₄×C₈₃	—	2	1	no	—
535	C₄×C₈₃	—	2	2	no	—
536	C₄×C₈₃	—	4	1	no	—
537	C₄×C₈₃	—	4	2	no	—
538	C₄×C₈₃	—	4	2	no	—
539	C₄×C₈₃	—	4	1	no	—
540	C₄×C₈₃	—	4	2	no	—
541	C₄×C₈₃	—	4	1	no	—
542	C₄×C₈₃	—	4	1	no	—
543	C₄×C₈₃	—	4	1	no	—
544	C₄×C₈₃	—	4	2	no	—
545	C₄×C₈₃	#577	1	2	yes	—
546	C₄×C₈₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
547	C₄×C₈₃	#585	1	1	yes	characteristic
548	#62218	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
549	C₂×C₈₃	—	4	1	no	—
550	C₂×C₈₃	—	4	2	no	—
551	C₂×C₈₃	—	4	2	no	—
552	C₂×C₈₃	—	8	1	no	—
553	C₂×C₈₃	—	8	1	no	—
554	C₂×C₈₃	#3489	1	1	yes	characteristic
555	C₂×C₈₃	C₂×#577	1	1	yes	characteristic
556	C₂×C₈₃	#3584	1	1	yes	characteristic
557	#3547	C₂×C₈₃	1	1	yes	characteristic, complemented
558	#3515	C₂×C₈₃	1	1	yes	characteristic, complemented
559	#3384	C₂×C₈₃	1	1	yes	characteristic, complemented
560	#3380	C₂×C₈₃	1	1	yes	characteristic, complemented
561	#3372	C₂×C₈₃	1	1	yes	characteristic, complemented
562	#3359	C₂×C₈₃	1	1	yes	characteristic, complemented
563	#3357	C₂×C₈₃	1	1	yes	characteristic, complemented
564	#3348	C₂×C₈₃	1	2	yes	complemented
565	#3337	C₂×C₈₃	1	2	yes	complemented
566	#3335	C₂×C₈₃	1	1	yes	characteristic, complemented
567	#3330	C₂×C₈₃	1	1	yes	characteristic, complemented
568	#3307	C₂×C₈₃	1	2	yes	complemented
569	#3303	C₂×C₈₃	1	1	yes	characteristic, complemented
570	#3303	C₂×C₈₃	1	2	yes	complemented
571	#3260	C₂×C₈₃	1	2	yes	complemented
572	#3246	C₂×C₈₃	1	1	yes	characteristic, complemented
573	#3242	C₂×C₈₃	1	2	yes	complemented
574	#3231	C₂×C₈₃	1	1	yes	characteristic, complemented
575	#3119	C₂×C₈₃	1	2	yes	complemented
576	#3106	C₂×C₈₃	1	1	yes	characteristic, complemented
577	#3084	C₂×C₈₃	1	2	yes	complemented
578	#3076	C₂×C₈₃	1	1	yes	characteristic, complemented
579	#2994	C₂×C₈₃	1	1	yes	characteristic, complemented
580	C₈₃	#62218	1	1	yes	characteristic, direct product factor, Sylow
581	#562	—	2	2	no	—
582	#557	C₂²×C₈₃	1	1	yes	characteristic
583	#555	C₂²×C₈₃	1	2	yes	—
584	#555	C₂²×C₈₃	1	1	yes	characteristic
585	#554	C₂²×C₈₃	1	1	yes	characteristic
586	#554	C₂²×C₈₃	1	1	yes	characteristic
587	#554	C₂²×C₈₃	1	1	yes	characteristic
588	#553	—	2	1	no	—
589	#553	C₂²×C₈₃	1	2	yes	—
590	#552	—	2	2	no	—
591	#552	—	2	1	no	—
592	#552	—	2	1	no	—
593	#552	C₂²×C₈₃	1	2	yes	—
594	D₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic
595	#548	—	2	1	no	—
596	#547	C₂²×C₈₃	1	1	yes	characteristic
597	#547	C₂²×C₈₃	1	2	yes	—
598	#547	C₂²×C₈₃	1	1	yes	characteristic
599	#544	C₂²×C₈₃	1	2	yes	—
600	#542	—	2	2	no	—
601	#541	C₂²×C₈₃	1	2	yes	—
602	#540	C₂²×C₈₃	1	2	yes	—
603	#539	—	2	2	no	—
604	#537	—	2	1	no	—
605	#536	—	2	1	no	—
606	#533	C₂²×C₈₃	1	1	yes	characteristic
607	#533	C₂²×C₈₃	1	1	yes	characteristic
608	#532	C₂²×C₈₃	1	1	yes	characteristic
609	#529	—	2	1	no	—
610	#529	C₂²×C₈₃	1	1	yes	characteristic
611	C₂×#125	—	2	1	no	—
612	#520	C₂²×C₈₃	1	2	yes	—
613	C₄×#41	C₂²×C₈₃	1	1	yes	characteristic
614	#501	C₂²×C₈₃	1	2	yes	—
615	#500	C₂²×C₈₃	1	1	yes	characteristic
616	#499	C₂²×C₈₃	1	2	yes	—
617	#498	C₂²×C₈₃	1	1	yes	characteristic
618	#491	C₂²×C₈₃	1	2	yes	—
619	#487	C₂²×C₈₃	1	1	yes	characteristic
620	#487	C₂²×C₈₃	1	2	yes	—
621	#487	C₂²×C₈₃	1	1	yes	characteristic
622	#485	C₂²×C₈₃	1	2	yes	—
623	#485	C₂²×C₈₃	1	2	yes	—
624	#485	C₂²×C₈₃	1	2	yes	—
625	#485	C₂²×C₈₃	1	2	yes	—
626	#484	C₂²×C₈₃	1	2	yes	—
627	#483	C₂²×C₈₃	1	2	yes	—
628	#482	C₂²×C₈₃	1	1	yes	characteristic
629	#482	C₂²×C₈₃	1	1	yes	characteristic
630	#481	C₂²×C₈₃	1	2	yes	—
631	#480	C₂²×C₈₃	1	2	yes	—
632	#479	C₂²×C₈₃	1	2	yes	—
633	#479	C₂²×C₈₃	1	2	yes	—
634	#479	C₂²×C₈₃	1	2	yes	—
635	#479	C₂²×C₈₃	1	2	yes	—
636	#478	C₂²×C₈₃	1	2	yes	—
637	#478	C₂²×C₈₃	1	2	yes	—
638	#478	C₂²×C₈₃	1	2	yes	—
639	#478	C₂²×C₈₃	1	2	yes	—
640	#477	C₂²×C₈₃	1	1	yes	characteristic
641	#477	C₂²×C₈₃	1	1	yes	characteristic
642	#476	C₂²×C₈₃	1	1	yes	characteristic
643	#476	C₂²×C₈₃	1	1	yes	characteristic
644	#476	C₂²×C₈₃	1	1	yes	characteristic
645	#476	C₂²×C₈₃	1	2	yes	—
646	#476	C₂²×C₈₃	1	1	yes	characteristic
647	#475	C₂²×C₈₃	1	1	yes	characteristic
648	#475	C₂²×C₈₃	1	2	yes	—
649	#475	C₂²×C₈₃	1	2	yes	—
650	#474	C₂²×C₈₃	1	1	yes	characteristic
651	#468	C₂²×C₈₃	1	2	yes	—
652	#468	C₂²×C₈₃	1	2	yes	—
653	#465	C₂²×C₈₃	1	2	yes	—
654	#465	C₂²×C₈₃	1	2	yes	—
655	#465	C₂²×C₈₃	1	2	yes	—
656	#465	C₂²×C₈₃	1	2	yes	—
657	#461	C₂²×C₈₃	1	1	yes	characteristic
658	#461	C₂²×C₈₃	1	1	yes	characteristic
659	#461	C₂²×C₈₃	1	2	yes	—
660	#461	C₂²×C₈₃	1	2	yes	—
661	#460	C₂²×C₈₃	1	1	yes	characteristic
662	#460	C₂²×C₈₃	1	2	yes	—
663	#459	C₂²×C₈₃	1	1	yes	characteristic
664	#449	C₂²×C₈₃	1	2	yes	—
665	#449	C₂²×C₈₃	1	1	yes	characteristic
666	#449	C₂²×C₈₃	1	1	yes	characteristic
667	#449	C₂²×C₈₃	1	2	yes	—
668	#446	C₂²×C₈₃	1	1	yes	characteristic
669	C₈×Q₈	C₂²×C₈₃	1	1	yes	characteristic
670	#442	C₂²×C₈₃	1	2	yes	—
671	#440	C₂²×C₈₃	1	2	yes	—
672	C₄×SD₁₆	C₂²×C₈₃	1	1	yes	characteristic
673	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	—
674	C₄×SD₁₆	C₂²×C₈₃	1	1	yes	characteristic
675	C₄×D₈	C₂²×C₈₃	1	1	yes	characteristic
676	C₄×D₈	C₂²×C₈₃	1	1	yes	characteristic
677	C₄×D₈	C₂²×C₈₃	1	2	yes	—
678	#436	C₂²×C₈₃	1	1	yes	characteristic
679	#435	C₂²×C₈₃	1	2	yes	—
680	C₈×D₄	C₂²×C₈₃	1	1	yes	characteristic
681	C₈×D₄	C₂²×C₈₃	1	2	yes	—
682	#433	C₂²×C₈₃	1	2	yes	—
683	#431	C₂²×C₈₃	1	1	yes	characteristic
684	#428	C₂²×C₈₃	1	2	yes	—
685	#427	C₂²×C₈₃	1	2	yes	—
686	C₂×#106	C₂²×C₈₃	1	2	yes	—
687	#424	C₂²×C₈₃	1	2	yes	—
688	C₂×C₄⋊C₈	C₂²×C₈₃	1	1	yes	characteristic
689	#417	C₂²×C₈₃	1	2	yes	—
690	#416	C₂²×C₈₃	1	2	yes	—
691	#416	C₂²×C₈₃	1	2	yes	—
692	C₂×#41	—	2	1	no	—
693	C₂×#41	—	2	1	no	—
694	C₂×#41	C₂³×C₈₃	1	1	yes	characteristic
695	C₂×#41	C₂³×C₈₃	1	2	yes	—
696	C₂²×Q₈	—	2	1	no	—
697	C₂×SD₁₆	C₂³×C₈₃	1	1	yes	characteristic
698	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
699	C₂×SD₁₆	C₂³×C₈₃	1	1	yes	characteristic
700	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
701	C₂×D₈	C₂³×C₈₃	1	1	yes	characteristic
702	C₂×D₈	C₂³×C₈₃	1	1	yes	characteristic
703	C₂×M₁₆	C₂³×C₈₃	1	2	yes	—
704	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
705	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
706	C₄⋊Q₈	—	2	2	no	—
707	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
708	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
709	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
710	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
711	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
712	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
713	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
714	#127	C₂³×C₈₃	1	1	yes	characteristic
715	#126	—	2	2	no	—
716	#126	—	2	2	no	—
717	#126	—	2	2	no	—
718	#126	—	2	2	no	—
719	#126	D₄×C₈₃	1	2	yes	—
720	#125	—	2	2	no	—
721	#125	—	2	2	no	—
722	#125	—	2	1	no	—
723	#125	—	2	1	no	—
724	#125	—	2	2	no	—
725	#125	—	2	2	no	—
726	#125	—	2	2	no	—
727	#125	—	2	1	no	—
728	#125	D₄×C₈₃	1	1	yes	characteristic
729	#125	C₂³×C₈₃	1	2	yes	—
730	#125	C₂³×C₈₃	1	2	yes	—
731	#125	C₂³×C₈₃	1	2	yes	—
732	#124	—	2	2	no	—
733	#124	—	2	2	no	—
734	#124	—	2	2	no	—
735	#124	—	2	1	no	—
736	#124	D₄×C₈₃	1	1	yes	characteristic
737	#123	—	2	2	no	—
738	#123	—	2	2	no	—
739	#123	—	2	2	no	—
740	#123	—	2	2	no	—
741	#123	—	2	2	no	—
742	#123	—	2	2	no	—
743	#123	—	2	2	no	—
744	#123	—	2	2	no	—
745	#123	D₄×C₈₃	1	2	yes	—
746	C₂²⋊Q₈	—	2	1	no	—
747	C₂²⋊Q₈	—	2	1	no	—
748	C₂²⋊Q₈	—	2	1	no	—
749	C₂²⋊Q₈	—	2	1	no	—
750	C₂²⋊Q₈	—	2	1	no	—
751	C₂²⋊Q₈	—	2	1	no	—
752	C₂²⋊Q₈	—	2	1	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	D₄×C₈₃	1	1	yes	characteristic
760	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
761	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
762	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
763	#121	—	2	1	no	—
764	#121	—	2	1	no	—
765	#121	—	2	2	no	—
766	#121	—	2	2	no	—
767	#121	—	2	2	no	—
768	#121	—	2	1	no	—
769	#121	—	2	2	no	—
770	#121	—	2	2	no	—
771	#121	D₄×C₈₃	1	1	yes	characteristic
772	#121	C₂³×C₈₃	1	1	yes	characteristic
773	#121	C₂³×C₈₃	1	1	yes	characteristic
774	#121	C₂³×C₈₃	1	2	yes	—
775	#121	C₂³×C₈₃	1	2	yes	—
776	C₄×Q₈	—	2	1	no	—
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	—	2	1	no	—
779	C₄×Q₈	—	2	1	no	—
780	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
781	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
782	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
783	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
784	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
785	C₄×D₄	—	2	1	no	—
786	C₄×D₄	—	2	1	no	—
787	C₄×D₄	—	2	1	no	—
788	C₄×D₄	—	2	2	no	—
789	C₄×D₄	—	2	2	no	—
790	C₄×D₄	—	2	2	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
793	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
794	C₄×D₄	C₂³×C₈₃	1	2	yes	—
795	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
796	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
797	C₄×D₄	C₂³×C₈₃	1	2	yes	—
798	C₄×D₄	C₂³×C₈₃	1	2	yes	—
799	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
800	C₄×D₄	C₂³×C₈₃	1	2	yes	—
801	#117	—	2	1	no	—
802	#117	—	2	2	no	—
803	#117	—	2	1	no	—
804	#117	—	2	2	no	—
805	#117	—	2	2	no	—
806	#117	—	2	1	no	—
807	#117	C₂³×C₈₃	1	1	yes	characteristic
808	#117	C₂³×C₈₃	1	2	yes	—
809	#117	C₂³×C₈₃	1	2	yes	—
810	#117	C₂³×C₈₃	1	2	yes	—
811	C₂×C₄⋊C₄	—	2	2	no	—
812	C₂×C₄⋊C₄	—	2	1	no	—
813	C₂×C₄⋊C₄	—	2	2	no	—
814	C₂×C₄⋊C₄	—	2	1	no	—
815	C₂×C₄⋊C₄	—	2	1	no	—
816	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
817	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
818	C₂×C₄²	—	2	1	no	—
819	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
820	#107	C₂³×C₈₃	1	2	yes	—
821	#107	C₂³×C₈₃	1	2	yes	—
822	#107	C₂³×C₈₃	1	2	yes	—
823	#107	C₂³×C₈₃	1	1	yes	characteristic
824	#107	C₂³×C₈₃	1	1	yes	characteristic
825	#107	C₂³×C₈₃	1	2	yes	—
826	#106	C₂³×C₈₃	1	1	yes	characteristic
827	#106	C₂³×C₈₃	1	2	yes	—
828	#106	C₂³×C₈₃	1	2	yes	—
829	#106	C₂³×C₈₃	1	2	yes	—
830	#106	C₂³×C₈₃	1	2	yes	—
831	#106	C₂³×C₈₃	1	1	yes	characteristic
832	#106	C₂³×C₈₃	1	2	yes	—
833	#106	C₂³×C₈₃	1	2	yes	—
834	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
835	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
836	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
837	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
838	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
839	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
840	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
841	#103	C₂³×C₈₃	1	2	yes	—
842	#103	C₂³×C₈₃	1	2	yes	—
843	#103	C₂³×C₈₃	1	2	yes	—
844	#103	C₂³×C₈₃	1	2	yes	—
845	#103	C₂³×C₈₃	1	2	yes	—
846	#103	C₂³×C₈₃	1	2	yes	—
847	#103	C₂³×C₈₃	1	1	yes	characteristic
848	#103	C₂³×C₈₃	1	1	yes	characteristic
849	#103	C₂³×C₈₃	1	2	yes	—
850	#103	C₂³×C₈₃	1	2	yes	—
851	#102	C₂³×C₈₃	1	1	yes	characteristic
852	#102	C₂³×C₈₃	1	2	yes	—
853	#102	C₂³×C₈₃	1	2	yes	—
854	#102	C₂³×C₈₃	1	1	yes	characteristic
855	#102	C₂³×C₈₃	1	2	yes	—
856	#102	C₂³×C₈₃	1	1	yes	characteristic
857	#102	C₂³×C₈₃	1	1	yes	characteristic
858	#102	C₂³×C₈₃	1	1	yes	characteristic
859	#102	C₂³×C₈₃	1	1	yes	characteristic
860	#102	C₂³×C₈₃	1	2	yes	—
861	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
862	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
863	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
864	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
865	#97	C₂³×C₈₃	1	2	yes	—
866	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
867	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
868	C₄×C₈	C₂³×C₈₃	1	2	yes	—
869	#41	—	2	2	no	—
870	#41	—	2	4	no	—
871	#41	—	4	1	no	—
872	#41	—	4	2	no	—
873	#41	—	8	2	no	—
874	#41	—	8	2	no	—
875	C₂×Q₈	—	2	1	no	—
876	C₂×Q₈	—	2	1	no	—
877	C₂×Q₈	—	2	1	no	—
878	C₂×Q₈	—	2	2	no	—
879	C₂×Q₈	—	2	1	no	—
880	C₂×Q₈	—	8	2	no	—
881	C₂×Q₈	C₂×D₄×C₈₃	1	1	yes	characteristic
882	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
883	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
884	C₂×D₄	—	2	1	no	—
885	C₂×D₄	—	2	2	no	—
886	C₂×D₄	—	2	2	no	—
887	C₂×D₄	—	2	1	no	—
888	C₂×D₄	—	2	2	no	—
889	C₂×D₄	—	2	1	no	—
890	C₂×D₄	—	2	1	no	—
891	C₂×D₄	—	2	1	no	—
892	C₂×D₄	C₂×D₄×C₈₃	1	1	yes	characteristic
893	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
894	C₂×D₄	C₂⁴×C₈₃	1	1	yes	characteristic
895	C₂×D₄	C₂⁴×C₈₃	1	1	yes	characteristic
896	C₂×D₄	C₂⁴×C₈₃	1	1	yes	characteristic
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	—	2	2	no	—
899	C₂²×C₄	—	2	1	no	—
900	C₂²×C₄	—	2	1	no	—
901	C₂²×C₄	—	2	2	no	—
902	C₂²×C₄	—	2	1	no	—
903	C₂²×C₄	—	2	1	no	—
904	C₂²×C₄	—	2	1	no	—
905	C₂²×C₄	—	2	2	no	—
906	C₂²×C₄	—	2	2	no	—
907	C₂²×C₄	—	2	2	no	—
908	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
909	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
910	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
911	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
912	SD₁₆	—	4	1	no	—
913	SD₁₆	—	4	2	no	—
914	SD₁₆	—	4	2	no	—
915	SD₁₆	—	4	1	no	—
916	D₈	—	2	2	no	—
917	D₈	—	2	2	no	—
918	M₁₆	—	4	2	no	—
919	C₂×C₈	—	4	2	no	—
920	C₂×C₈	—	4	2	no	—
921	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
922	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
923	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
924	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
925	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
926	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
952	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
953	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
954	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
955	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
956	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
957	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
958	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
959	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
960	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
961	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
962	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
963	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	1	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	1	no	—
971	C₂²⋊C₄	—	2	1	no	—
972	C₂²⋊C₄	—	2	1	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	1	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	1	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
982	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
983	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
984	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
985	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
986	C₄²	—	2	1	no	—
987	C₄²	—	2	1	no	—
988	C₄²	—	2	1	no	—
989	C₄²	—	2	2	no	—
990	C₄²	—	2	2	no	—
991	C₄²	—	2	2	no	—
992	C₄²	—	2	2	no	—
993	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
994	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
995	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
996	C₄²	C₂⁴×C₈₃	1	2	yes	—
997	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
998	C₂³	—	2	1	no	—
999	C₂³	—	2	1	no	—
1000	C₂³	—	2	1	no	—
1001	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
1002	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
1003	Q₈	—	2	2	no	—
1004	Q₈	—	2	2	no	—
1005	Q₈	—	2	1	no	—
1006	Q₈	—	2	2	no	—
1007	Q₈	—	2	1	no	—
1008	Q₈	—	4	2	no	—
1009	Q₈	—	8	2	no	—
1010	Q₈	—	8	1	no	—
1011	Q₈	—	8	1	no	—
1012	Q₈	—	8	1	no	—
1013	D₄	—	2	2	no	—
1014	D₄	—	2	1	no	—
1015	D₄	—	2	1	no	—
1016	D₄	—	2	1	no	—
1017	D₄	—	2	1	no	—
1018	D₄	—	2	1	no	—
1019	D₄	—	4	2	no	—
1020	D₄	—	4	2	no	—
1021	D₄	—	4	4	no	—
1022	D₄	—	8	1	no	—
1023	D₄	—	8	1	no	—
1024	D₄	—	8	1	no	—
1025	D₄	—	8	1	no	—
1026	D₄	—	8	2	no	—
1027	D₄	—	8	2	no	—
1028	D₄	2₋¹⁺⁴×C₈₃	1	2	yes	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	2	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	4	1	no	—
1044	C₂×C₄	—	4	2	no	—
1045	C₂×C₄	—	4	4	no	—
1046	C₂×C₄	—	4	2	no	—
1047	C₂×C₄	—	4	2	no	—
1048	C₂×C₄	—	4	2	no	—
1049	C₂×C₄	—	8	2	no	—
1050	C₂×C₄	—	8	1	no	—
1051	C₂×C₄	—	8	2	no	—
1052	C₂×C₄	—	8	2	no	—
1053	C₂×C₄	—	8	2	no	—
1054	C₂×C₄	—	8	2	no	—
1055	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1056	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1057	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1058	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
1059	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
1060	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1061	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
1062	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1063	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
1064	C₈	—	2	1	no	—
1065	C₈	—	2	1	no	—
1066	C₈	—	2	1	no	—
1067	C₈	—	2	2	no	—
1068	C₈	—	2	2	no	—
1069	C₈	—	2	1	no	—
1070	C₂²	—	2	1	no	—
1071	C₂²	—	2	2	no	—
1072	C₂²	—	2	1	no	—
1073	C₂²	—	2	2	no	—
1074	C₂²	—	2	1	no	—
1075	C₂²	—	2	2	no	—
1076	C₂²	—	2	2	no	—
1077	C₂²	—	4	1	no	—
1078	C₂²	—	4	1	no	—
1079	C₂²	—	4	1	no	—
1080	C₂²	—	4	1	no	—
1081	C₂²	—	4	1	no	—
1082	C₂²	—	4	1	no	—
1083	C₂²	—	4	1	no	—
1084	C₂²	—	4	1	no	—
1085	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
1086	C₄	—	2	1	no	—
1087	C₄	—	2	2	no	—
1088	C₄	—	2	1	no	—
1089	C₄	—	2	1	no	—
1090	C₄	—	2	2	no	—
1091	C₄	—	2	1	no	—
1092	C₄	—	2	2	no	—
1093	C₄	—	4	1	no	—
1094	C₄	—	4	1	no	—
1095	C₄	—	4	1	no	—
1096	C₄	—	4	2	no	—
1097	C₄	—	4	1	no	—
1098	C₄	—	4	2	no	—
1099	C₄	—	4	2	no	—
1100	C₄	—	4	1	no	—
1101	C₄	—	4	2	no	—
1102	C₄	#577×C₈₃	1	2	yes	—
1103	C₄	C₂×2₋¹⁺⁴×C₈₃	1	1	yes	characteristic
1104	C₄	#585×C₈₃	1	1	yes	characteristic
1105	C₂	—	4	1	no	—
1106	C₂	—	4	2	no	—
1107	C₂	—	4	2	no	—
1108	C₂	—	8	1	no	—
1109	C₂	—	8	1	no	—
1110	C₂	C₈₃×#3489	1	1	yes	characteristic
1111	C₂	C₂×#577×C₈₃	1	1	yes	characteristic
1112	C₂	C₈₃×#3584	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 ◁ #529×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₃×#3547	C₂	semidirect
2. C₈₃×#3515	C₂	semidirect
3. C₈₃×#3384	C₂	semidirect
4. C₈₃×#3380	C₂	semidirect
5. C₈₃×#3372	C₂	semidirect
6. C₈₃×#3359	C₂	semidirect
7. C₈₃×#3357	C₂	semidirect
8. C₈₃×#3348	C₂	semidirect
9. C₈₃×#3337	C₂	semidirect
10. C₈₃×#3335	C₂	semidirect
11. C₈₃×#3330	C₂	semidirect
12. C₈₃×#3307	C₂	semidirect
13. C₈₃×#3303	C₂	semidirect
14. C₈₃×#3303	C₂	semidirect
15. C₈₃×#3260	C₂	semidirect
16. C₈₃×#3246	C₂	semidirect
17. C₈₃×#3242	C₂	semidirect
18. C₈₃×#3231	C₂	semidirect
19. C₈₃×#3119	C₂	semidirect
20. C₈₃×#3106	C₂	semidirect
21. C₈₃×#3084	C₂	semidirect
22. C₈₃×#3076	C₂	semidirect
23. C₈₃×#2994	C₂	semidirect
548. #62218	C₈₃	direct (N × H)
557. #3547	C₂×C₈₃	semidirect
558. #3515	C₂×C₈₃	semidirect
559. #3384	C₂×C₈₃	semidirect
560. #3380	C₂×C₈₃	semidirect
561. #3372	C₂×C₈₃	semidirect
562. #3359	C₂×C₈₃	semidirect
563. #3357	C₂×C₈₃	semidirect
564. #3348	C₂×C₈₃	semidirect
565. #3337	C₂×C₈₃	semidirect
566. #3335	C₂×C₈₃	semidirect
567. #3330	C₂×C₈₃	semidirect
568. #3307	C₂×C₈₃	semidirect
569. #3303	C₂×C₈₃	semidirect
570. #3303	C₂×C₈₃	semidirect
571. #3260	C₂×C₈₃	semidirect
572. #3246	C₂×C₈₃	semidirect
573. #3242	C₂×C₈₃	semidirect
574. #3231	C₂×C₈₃	semidirect
575. #3119	C₂×C₈₃	semidirect
576. #3106	C₂×C₈₃	semidirect
577. #3084	C₂×C₈₃	semidirect
578. #3076	C₂×C₈₃	semidirect
579. #2994	C₂×C₈₃	semidirect
580. C₈₃	#62218	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₃×#3547	2
C₈₃×#3515	2
C₈₃×#3384	2
C₈₃×#3380	2
C₈₃×#3372	2
C₈₃×#3359	2
C₈₃×#3357	2
C₈₃×#3348	2
C₈₃×#3337	2
C₈₃×#3335	2
C₈₃×#3330	2
C₈₃×#3307	2
C₈₃×#3303	2
C₈₃×#3260	2
C₈₃×#3246	2
C₈₃×#3242	2
C₈₃×#3231	2
C₈₃×#3119	2
C₈₃×#3106	2
C₈₃×#3084	2
C₈₃×#3076	2
C₈₃×#2994	2
#62218	83

Subgroups — C83×#62218 #35290042

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#62218 #35290042