Subgroups — C₈₃×#61865 #35289689

Order 21248.

1662 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3554	C₂	1	1	yes	maximal, characteristic
2	C₈₃×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₃×#3388	C₂	1	2	yes	maximal, complemented
4	C₈₃×#3387	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₃×#3386	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₃×#3383	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₃×#3381	C₂	1	2	yes	maximal, complemented
8	Q₈×SD₁₆×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₃×#3375	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₃×#3371	C₂	1	2	yes	maximal, complemented
11	C₈₃×#3368	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₃×#3365	C₂	1	2	yes	maximal, complemented
13	C₈₃×#3365	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₃×#3362	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#3244	C₂	1	2	yes	maximal, complemented
16	C₈₃×#3241	C₂	1	2	yes	maximal, complemented
17	C₈₃×#3233	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₃×#3228	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₃×#3126	C₂	1	2	yes	maximal, complemented
20	C₈₃×#3121	C₂	1	2	yes	maximal, complemented
21	C₈₃×#3108	C₂	1	1	yes	maximal, characteristic, complemented
22	C₈₃×#3103	C₂	1	1	yes	maximal, characteristic, complemented
23	C₈₃×#2986	C₂	1	1	yes	maximal, characteristic, complemented
24	#562×C₈₃	—	2	2	no	—
25	#559×C₈₃	C₂²	1	2	yes	—
26	#559×C₈₃	C₂²	1	1	yes	characteristic
27	Q₈²×C₈₃	—	2	1	no	—
28	Q₈²×C₈₃	C₂²	1	1	yes	characteristic
29	Q₈²×C₈₃	C₂²	1	1	yes	characteristic
30	#557×C₈₃	—	2	1	no	—
31	#557×C₈₃	—	2	2	no	—
32	#557×C₈₃	C₂²	1	1	yes	characteristic
33	#557×C₈₃	C₂²	1	1	yes	characteristic
34	#557×C₈₃	C₂²	1	2	yes	—
35	#557×C₈₃	C₂²	1	1	yes	characteristic
36	#557×C₈₃	C₂²	1	2	yes	—
37	#554×C₈₃	C₂²	1	2	yes	—
38	#550×C₈₃	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
40	#548×C₈₃	—	2	1	no	—
41	#547×C₈₃	—	2	1	no	—
42	#544×C₈₃	—	2	2	no	—
43	#544×C₈₃	C₂²	1	2	yes	—
44	#542×C₈₃	—	2	1	no	—
45	#542×C₈₃	C₂²	1	2	yes	—
46	#540×C₈₃	C₂²	1	2	yes	—
47	#539×C₈₃	—	2	2	no	—
48	#536×C₈₃	—	2	1	no	—
49	#533×C₈₃	—	2	1	no	—
50	#533×C₈₃	—	2	1	no	—
51	#533×C₈₃	C₂²	1	1	yes	characteristic
52	#533×C₈₃	C₂²	1	1	yes	characteristic
53	#532×C₈₃	C₂²	1	1	yes	characteristic
54	#529×C₈₃	C₂²	1	1	yes	characteristic
55	#519×C₈₃	C₂²	1	2	yes	—
56	C₂×C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
57	#501×C₈₃	C₂²	1	2	yes	—
58	#501×C₈₃	C₂²	1	2	yes	—
59	#500×C₈₃	C₂²	1	1	yes	characteristic
60	#499×C₈₃	C₂²	1	2	yes	—
61	#499×C₈₃	C₂²	1	2	yes	—
62	#498×C₈₃	C₂²	1	2	yes	—
63	#498×C₈₃	C₂²	1	1	yes	characteristic
64	#490×C₈₃	C₂²	1	2	yes	—
65	#489×C₈₃	C₂²	1	2	yes	—
66	#488×C₈₃	C₂²	1	2	yes	—
67	#488×C₈₃	C₂²	1	2	yes	—
68	#486×C₈₃	C₂²	1	2	yes	—
69	#486×C₈₃	C₂²	1	1	yes	characteristic
70	#486×C₈₃	C₂²	1	1	yes	characteristic
71	#485×C₈₃	C₂²	1	2	yes	—
72	#483×C₈₃	C₂²	1	1	yes	characteristic
73	#482×C₈₃	C₂²	1	2	yes	—
74	#482×C₈₃	C₂²	1	2	yes	—
75	#482×C₈₃	C₂²	1	2	yes	—
76	#481×C₈₃	C₂²	1	2	yes	—
77	#480×C₈₃	C₂²	1	1	yes	characteristic
78	#479×C₈₃	C₂²	1	1	yes	characteristic
79	#479×C₈₃	C₂²	1	1	yes	characteristic
80	#479×C₈₃	C₂²	1	2	yes	—
81	#479×C₈₃	C₂²	1	2	yes	—
82	#479×C₈₃	C₂²	1	2	yes	—
83	#478×C₈₃	C₂²	1	2	yes	—
84	#478×C₈₃	C₂²	1	2	yes	—
85	#478×C₈₃	C₂²	1	2	yes	—
86	#478×C₈₃	C₂²	1	2	yes	—
87	#478×C₈₃	C₂²	1	2	yes	—
88	#477×C₈₃	C₂²	1	1	yes	characteristic
89	#477×C₈₃	C₂²	1	2	yes	—
90	#476×C₈₃	C₂²	1	1	yes	characteristic
91	#476×C₈₃	C₂²	1	2	yes	—
92	#476×C₈₃	C₂²	1	2	yes	—
93	#475×C₈₃	C₂²	1	1	yes	characteristic
94	#475×C₈₃	C₂²	1	1	yes	characteristic
95	#475×C₈₃	C₂²	1	1	yes	characteristic
96	#475×C₈₃	C₂²	1	2	yes	—
97	#475×C₈₃	C₂²	1	2	yes	—
98	#474×C₈₃	C₂²	1	1	yes	characteristic
99	#474×C₈₃	C₂²	1	2	yes	—
100	#464×C₈₃	C₂²	1	1	yes	characteristic
101	#464×C₈₃	C₂²	1	1	yes	characteristic
102	#464×C₈₃	C₂²	1	2	yes	—
103	#464×C₈₃	C₂²	1	2	yes	—
104	#460×C₈₃	C₂²	1	1	yes	characteristic
105	#460×C₈₃	C₂²	1	1	yes	characteristic
106	#460×C₈₃	C₂²	1	2	yes	—
107	#460×C₈₃	C₂²	1	2	yes	—
108	#451×C₈₃	C₂²	1	1	yes	characteristic
109	#448×C₈₃	C₂²	1	2	yes	—
110	#448×C₈₃	C₂²	1	1	yes	characteristic
111	#446×C₈₃	C₂²	1	1	yes	characteristic
112	#446×C₈₃	C₂²	1	2	yes	—
113	#446×C₈₃	C₂²	1	1	yes	characteristic
114	C₈×Q₈×C₈₃	C₂²	1	1	yes	characteristic
115	C₈×Q₈×C₈₃	C₂²	1	1	yes	characteristic
116	C₈×Q₈×C₈₃	C₂²	1	2	yes	—
117	#441×C₈₃	C₂²	1	2	yes	—
118	#440×C₈₃	C₂²	1	2	yes	—
119	#440×C₈₃	C₂²	1	2	yes	—
120	#440×C₈₃	C₂²	1	2	yes	—
121	C₄×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic
122	C₄×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic
123	C₄×Q₁₆×C₈₃	C₂²	1	2	yes	—
124	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	—
125	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	—
126	C₄×SD₁₆×C₈₃	C₂²	1	1	yes	characteristic
127	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	—
128	C₄×SD₁₆×C₈₃	C₂²	1	1	yes	characteristic
129	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	—
130	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	—
131	#433×C₈₃	C₂²	1	2	yes	—
132	#433×C₈₃	C₂²	1	2	yes	—
133	#431×C₈₃	C₂²	1	1	yes	characteristic
134	#431×C₈₃	C₂²	1	1	yes	characteristic
135	C₂×#41×C₈₃	—	2	1	no	—
136	C₂×#41×C₈₃	—	2	1	no	—
137	C₂²×Q₈×C₈₃	—	2	1	no	—
138	C₂²×Q₈×C₈₃	C₂³	1	1	yes	characteristic
139	C₂×Q₁₆×C₈₃	C₂³	1	1	yes	characteristic
140	C₂×Q₁₆×C₈₃	C₂³	1	1	yes	characteristic
141	C₂×SD₁₆×C₈₃	C₂³	1	1	yes	characteristic
142	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
143	C₂×SD₁₆×C₈₃	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
145	C₄⋊Q₈×C₈₃	—	2	1	no	—
146	C₄⋊Q₈×C₈₃	—	2	1	no	—
147	C₄⋊Q₈×C₈₃	—	2	1	no	—
148	C₄⋊Q₈×C₈₃	—	2	2	no	—
149	C₄⋊Q₈×C₈₃	—	2	2	no	—
150	C₄⋊Q₈×C₈₃	—	2	1	no	—
151	C₄⋊Q₈×C₈₃	—	2	1	no	—
152	C₄⋊Q₈×C₈₃	—	2	2	no	—
153	C₄⋊Q₈×C₈₃	—	2	2	no	—
154	C₄⋊Q₈×C₈₃	—	2	2	no	—
155	C₄⋊Q₈×C₈₃	D₄	1	1	yes	characteristic
156	C₄⋊Q₈×C₈₃	D₄	1	1	yes	characteristic
157	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
158	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
159	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
161	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
162	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
163	#127×C₈₃	C₂³	1	1	yes	characteristic
164	#127×C₈₃	C₂³	1	2	yes	—
165	#126×C₈₃	—	2	2	no	—
166	#126×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	2	no	—
171	#125×C₈₃	—	2	2	no	—
172	#125×C₈₃	—	2	2	no	—
173	#125×C₈₃	—	2	2	no	—
174	#125×C₈₃	—	2	2	no	—
175	#125×C₈₃	D₄	1	2	yes	—
176	#125×C₈₃	C₂³	1	2	yes	—
177	#125×C₈₃	C₂³	1	2	yes	—
178	#125×C₈₃	C₂³	1	2	yes	—
179	#125×C₈₃	C₂³	1	1	yes	characteristic
180	#125×C₈₃	C₂³	1	2	yes	—
181	#124×C₈₃	—	2	1	no	—
182	#124×C₈₃	—	2	2	no	—
183	#124×C₈₃	—	2	2	no	—
184	#124×C₈₃	—	2	1	no	—
185	#124×C₈₃	C₂³	1	1	yes	characteristic
186	#124×C₈₃	C₂³	1	2	yes	—
187	#123×C₈₃	—	2	1	no	—
188	#123×C₈₃	—	2	2	no	—
189	#123×C₈₃	—	2	2	no	—
190	#123×C₈₃	—	2	2	no	—
191	#123×C₈₃	—	2	2	no	—
192	#123×C₈₃	—	2	2	no	—
193	#123×C₈₃	—	2	2	no	—
194	C₂²⋊Q₈×C₈₃	—	2	2	no	—
195	C₂²⋊Q₈×C₈₃	—	2	1	no	—
196	C₂²⋊Q₈×C₈₃	—	2	1	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	1	no	—
202	C₂²⋊Q₈×C₈₃	—	2	2	no	—
203	C₂²⋊Q₈×C₈₃	—	2	2	no	—
204	C₂²⋊Q₈×C₈₃	D₄	1	1	yes	characteristic
205	C₂²⋊Q₈×C₈₃	D₄	1	1	yes	characteristic
206	C₂²⋊Q₈×C₈₃	D₄	1	2	yes	—
207	C₂²⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
208	#121×C₈₃	—	2	1	no	—
209	#121×C₈₃	—	2	2	no	—
210	#121×C₈₃	—	2	1	no	—
211	#121×C₈₃	—	2	2	no	—
212	#121×C₈₃	—	2	2	no	—
213	#121×C₈₃	C₂³	1	1	yes	characteristic
214	#121×C₈₃	C₂³	1	2	yes	—
215	C₄×Q₈×C₈₃	—	2	1	no	—
216	C₄×Q₈×C₈₃	—	2	1	no	—
217	C₄×Q₈×C₈₃	—	2	2	no	—
218	C₄×Q₈×C₈₃	—	2	2	no	—
219	C₄×Q₈×C₈₃	—	2	2	no	—
220	C₄×Q₈×C₈₃	—	2	2	no	—
221	C₄×Q₈×C₈₃	—	2	1	no	—
222	C₄×Q₈×C₈₃	—	2	1	no	—
223	C₄×Q₈×C₈₃	—	2	1	no	—
224	C₄×Q₈×C₈₃	—	2	1	no	—
225	C₄×Q₈×C₈₃	—	2	1	no	—
226	C₄×Q₈×C₈₃	—	2	1	no	—
227	C₄×Q₈×C₈₃	—	2	1	no	—
228	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
229	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
230	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
234	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
235	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
237	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
238	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
239	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
240	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
241	C₄×D₄×C₈₃	—	2	1	no	—
242	C₄×D₄×C₈₃	—	2	2	no	—
243	C₄×D₄×C₈₃	—	2	1	no	—
244	C₄×D₄×C₈₃	—	2	1	no	—
245	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₈₃	C₂³	1	2	yes	—
247	C₄×D₄×C₈₃	C₂³	1	2	yes	—
248	C₄×D₄×C₈₃	C₂³	1	2	yes	—
249	C₄×D₄×C₈₃	C₂³	1	2	yes	—
250	#117×C₈₃	—	2	2	no	—
251	#117×C₈₃	—	2	2	no	—
252	#117×C₈₃	—	2	1	no	—
253	#117×C₈₃	C₂³	1	2	yes	—
254	#117×C₈₃	C₂³	1	2	yes	—
255	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
256	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
257	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
258	C₂×C₄²×C₈₃	—	2	1	no	—
259	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
260	#107×C₈₃	C₂³	1	1	yes	characteristic
261	#107×C₈₃	C₂³	1	2	yes	—
262	#107×C₈₃	C₂³	1	2	yes	—
263	#107×C₈₃	C₂³	1	2	yes	—
264	#107×C₈₃	C₂³	1	1	yes	characteristic
265	#107×C₈₃	C₂³	1	2	yes	—
266	#106×C₈₃	C₂³	1	2	yes	—
267	#106×C₈₃	C₂³	1	2	yes	—
268	#106×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	1	yes	characteristic
273	#106×C₈₃	C₂³	1	1	yes	characteristic
274	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
275	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
276	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
277	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
278	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
279	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
281	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
282	#103×C₈₃	C₂³	1	1	yes	characteristic
283	#103×C₈₃	C₂³	1	2	yes	—
284	#103×C₈₃	C₂³	1	2	yes	—
285	#103×C₈₃	C₂³	1	1	yes	characteristic
286	#103×C₈₃	C₂³	1	2	yes	—
287	#103×C₈₃	C₂³	1	1	yes	characteristic
288	#103×C₈₃	C₂³	1	2	yes	—
289	#103×C₈₃	C₂³	1	1	yes	characteristic
290	#103×C₈₃	C₂³	1	1	yes	characteristic
291	#103×C₈₃	C₂³	1	1	yes	characteristic
292	#102×C₈₃	C₂³	1	2	yes	—
293	#102×C₈₃	C₂³	1	1	yes	characteristic
294	#102×C₈₃	C₂³	1	1	yes	characteristic
295	#102×C₈₃	C₂³	1	2	yes	—
296	#102×C₈₃	C₂³	1	2	yes	—
297	#102×C₈₃	C₂³	1	2	yes	—
298	#102×C₈₃	C₂³	1	2	yes	—
299	#102×C₈₃	C₂³	1	2	yes	—
300	#102×C₈₃	C₂³	1	2	yes	—
301	#102×C₈₃	C₂³	1	2	yes	—
302	C₂²⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
303	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
305	#97×C₈₃	C₂³	1	2	yes	—
306	#97×C₈₃	C₂³	1	2	yes	—
307	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
308	C₄×C₈×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	2	yes	—
312	#41×C₈₃	—	8	2	no	—
313	#41×C₈₃	—	8	2	no	—
314	C₂×Q₈×C₈₃	—	2	2	no	—
315	C₂×Q₈×C₈₃	—	2	2	no	—
316	C₂×Q₈×C₈₃	—	2	1	no	—
317	C₂×Q₈×C₈₃	—	2	1	no	—
318	C₂×Q₈×C₈₃	—	2	1	no	—
319	C₂×Q₈×C₈₃	—	2	1	no	—
320	C₂×Q₈×C₈₃	—	2	2	no	—
321	C₂×Q₈×C₈₃	—	2	2	no	—
322	C₂×Q₈×C₈₃	—	2	2	no	—
323	C₂×Q₈×C₈₃	—	8	2	no	—
324	C₂×Q₈×C₈₃	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₈₃	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈×C₈₃	C₂×D₄	1	2	yes	—
327	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
328	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
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	2	no	—
335	C₂×D₄×C₈₃	—	2	2	no	—
336	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
337	C₂×D₄×C₈₃	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₈₃	—	2	1	no	—
339	C₂²×C₄×C₈₃	—	2	1	no	—
340	C₂²×C₄×C₈₃	—	2	1	no	—
341	C₂²×C₄×C₈₃	—	2	2	no	—
342	C₂²×C₄×C₈₃	—	2	2	no	—
343	C₂²×C₄×C₈₃	—	2	2	no	—
344	C₂²×C₄×C₈₃	—	2	2	no	—
345	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
346	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
347	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
348	Q₁₆×C₈₃	—	2	2	no	—
349	Q₁₆×C₈₃	—	2	2	no	—
350	SD₁₆×C₈₃	—	2	2	no	—
351	SD₁₆×C₈₃	—	2	4	no	—
352	SD₁₆×C₈₃	—	2	2	no	—
353	SD₁₆×C₈₃	—	2	4	no	—
354	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
355	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
356	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
357	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
358	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
359	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
360	C₄⋊C₄×C₈₃	—	2	1	no	—
361	C₄⋊C₄×C₈₃	—	2	1	no	—
362	C₄⋊C₄×C₈₃	—	2	1	no	—
363	C₄⋊C₄×C₈₃	—	2	1	no	—
364	C₄⋊C₄×C₈₃	—	2	1	no	—
365	C₄⋊C₄×C₈₃	—	2	2	no	—
366	C₄⋊C₄×C₈₃	—	2	2	no	—
367	C₄⋊C₄×C₈₃	—	2	1	no	—
368	C₄⋊C₄×C₈₃	—	2	2	no	—
369	C₄⋊C₄×C₈₃	—	2	2	no	—
370	C₄⋊C₄×C₈₃	—	2	2	no	—
371	C₄⋊C₄×C₈₃	—	2	2	no	—
372	C₄⋊C₄×C₈₃	—	2	1	no	—
373	C₄⋊C₄×C₈₃	—	2	1	no	—
374	C₄⋊C₄×C₈₃	—	2	1	no	—
375	C₄⋊C₄×C₈₃	—	2	2	no	—
376	C₄⋊C₄×C₈₃	—	2	1	no	—
377	C₄⋊C₄×C₈₃	—	2	2	no	—
378	C₄⋊C₄×C₈₃	—	2	1	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	2	no	—
384	C₄⋊C₄×C₈₃	—	2	2	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	C₂×D₄	1	2	yes	—
389	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
390	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
391	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
392	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
393	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
394	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
395	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
396	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
398	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
399	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
400	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
401	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
403	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
404	C₂²⋊C₄×C₈₃	—	2	2	no	—
405	C₂²⋊C₄×C₈₃	—	2	1	no	—
406	C₂²⋊C₄×C₈₃	—	2	1	no	—
407	C₂²⋊C₄×C₈₃	—	2	1	no	—
408	C₂²⋊C₄×C₈₃	—	2	1	no	—
409	C₂²⋊C₄×C₈₃	—	2	2	no	—
410	C₂²⋊C₄×C₈₃	—	2	2	no	—
411	C₂²⋊C₄×C₈₃	—	2	2	no	—
412	C₂²⋊C₄×C₈₃	—	2	1	no	—
413	C₂²⋊C₄×C₈₃	—	2	2	no	—
414	C₂²⋊C₄×C₈₃	—	2	2	no	—
415	C₂²⋊C₄×C₈₃	—	2	2	no	—
416	C₂²⋊C₄×C₈₃	—	2	2	no	—
417	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
418	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
419	C₄²×C₈₃	—	2	1	no	—
420	C₄²×C₈₃	—	2	1	no	—
421	C₄²×C₈₃	—	2	1	no	—
422	C₄²×C₈₃	—	2	1	no	—
423	C₄²×C₈₃	—	2	1	no	—
424	C₄²×C₈₃	—	2	2	no	—
425	C₄²×C₈₃	—	2	2	no	—
426	C₄²×C₈₃	—	2	2	no	—
427	C₄²×C₈₃	—	2	2	no	—
428	C₄²×C₈₃	—	2	2	no	—
429	C₄²×C₈₃	—	2	2	no	—
430	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
431	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
432	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
433	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
434	C₄²×C₈₃	C₂⁴	1	2	yes	—
435	C₄²×C₈₃	C₂⁴	1	2	yes	—
436	C₂³×C₈₃	—	2	2	no	—
437	C₂³×C₈₃	—	2	1	no	—
438	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
439	Q₈×C₈₃	—	2	4	no	—
440	Q₈×C₈₃	—	2	2	no	—
441	Q₈×C₈₃	—	2	2	no	—
442	Q₈×C₈₃	—	2	1	no	—
443	Q₈×C₈₃	—	2	1	no	—
444	Q₈×C₈₃	—	2	1	no	—
445	Q₈×C₈₃	—	2	1	no	—
446	Q₈×C₈₃	—	4	2	no	—
447	Q₈×C₈₃	—	4	2	no	—
448	Q₈×C₈₃	—	4	2	no	—
449	Q₈×C₈₃	—	8	1	no	—
450	Q₈×C₈₃	—	8	2	no	—
451	Q₈×C₈₃	—	8	2	no	—
452	Q₈×C₈₃	—	8	2	no	—
453	Q₈×C₈₃	2₋¹⁺⁴	1	2	yes	—
454	Q₈×C₈₃	2₋¹⁺⁴	1	2	yes	—
455	D₄×C₈₃	—	2	2	no	—
456	D₄×C₈₃	—	2	1	no	—
457	D₄×C₈₃	—	2	2	no	—
458	D₄×C₈₃	—	2	1	no	—
459	D₄×C₈₃	—	4	2	no	—
460	D₄×C₈₃	—	8	1	no	—
461	D₄×C₈₃	—	8	2	no	—
462	D₄×C₈₃	—	8	2	no	—
463	D₄×C₈₃	—	8	1	no	—
464	D₄×C₈₃	—	8	2	no	—
465	C₂×C₄×C₈₃	—	2	4	no	—
466	C₂×C₄×C₈₃	—	2	1	no	—
467	C₂×C₄×C₈₃	—	2	1	no	—
468	C₂×C₄×C₈₃	—	2	2	no	—
469	C₂×C₄×C₈₃	—	2	1	no	—
470	C₂×C₄×C₈₃	—	2	1	no	—
471	C₂×C₄×C₈₃	—	2	1	no	—
472	C₂×C₄×C₈₃	—	2	2	no	—
473	C₂×C₄×C₈₃	—	2	2	no	—
474	C₂×C₄×C₈₃	—	2	1	no	—
475	C₂×C₄×C₈₃	—	2	1	no	—
476	C₂×C₄×C₈₃	—	2	1	no	—
477	C₂×C₄×C₈₃	—	2	2	no	—
478	C₂×C₄×C₈₃	—	2	1	no	—
479	C₂×C₄×C₈₃	—	4	1	no	—
480	C₂×C₄×C₈₃	—	4	2	no	—
481	C₂×C₄×C₈₃	—	8	2	no	—
482	C₂×C₄×C₈₃	—	8	2	no	—
483	C₂×C₄×C₈₃	—	8	2	no	—
484	C₂×C₄×C₈₃	—	8	2	no	—
485	C₂×C₄×C₈₃	—	8	1	no	—
486	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
488	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
489	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
490	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
491	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
492	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
496	C₈×C₈₃	—	2	1	no	—
497	C₈×C₈₃	—	2	2	no	—
498	C₈×C₈₃	—	2	1	no	—
499	C₈×C₈₃	—	2	2	no	—
500	C₈×C₈₃	—	2	1	no	—
501	C₈×C₈₃	—	2	1	no	—
502	C₂²×C₈₃	—	2	1	no	—
503	C₂²×C₈₃	—	2	1	no	—
504	C₂²×C₈₃	—	2	1	no	—
505	C₂²×C₈₃	—	4	2	no	—
506	C₂²×C₈₃	—	4	1	no	—
507	C₂²×C₈₃	—	4	2	no	—
508	C₂²×C₈₃	—	4	1	no	—
509	C₂²×C₈₃	—	4	1	no	—
510	C₂²×C₈₃	—	4	2	no	—
511	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
512	C₄×C₈₃	—	2	1	no	—
513	C₄×C₈₃	—	2	1	no	—
514	C₄×C₈₃	—	2	2	no	—
515	C₄×C₈₃	—	2	2	no	—
516	C₄×C₈₃	—	2	2	no	—
517	C₄×C₈₃	—	2	2	no	—
518	C₄×C₈₃	—	2	1	no	—
519	C₄×C₈₃	—	2	1	no	—
520	C₄×C₈₃	—	2	2	no	—
521	C₄×C₈₃	—	2	2	no	—
522	C₄×C₈₃	—	4	1	no	—
523	C₄×C₈₃	—	4	1	no	—
524	C₄×C₈₃	—	4	1	no	—
525	C₄×C₈₃	—	4	2	no	—
526	C₄×C₈₃	—	4	1	no	—
527	C₄×C₈₃	—	4	1	no	—
528	C₄×C₈₃	—	4	2	no	—
529	C₄×C₈₃	—	4	2	no	—
530	C₄×C₈₃	#577	1	2	yes	—
531	C₄×C₈₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
532	C₄×C₈₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
533	#61865	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
534	C₂×C₈₃	—	4	1	no	—
535	C₂×C₈₃	—	8	2	no	—
536	C₂×C₈₃	—	8	1	no	—
537	C₂×C₈₃	#3486	1	1	yes	characteristic
538	C₂×C₈₃	C₂×#577	1	1	yes	characteristic
539	C₂×C₈₃	#3584	1	1	yes	characteristic
540	#3554	C₂×C₈₃	1	1	yes	characteristic
541	#3502	C₂×C₈₃	1	1	yes	characteristic, complemented
542	#3388	C₂×C₈₃	1	2	yes	complemented
543	#3387	C₂×C₈₃	1	1	yes	characteristic, complemented
544	#3386	C₂×C₈₃	1	1	yes	characteristic, complemented
545	#3383	C₂×C₈₃	1	1	yes	characteristic, complemented
546	#3381	C₂×C₈₃	1	2	yes	complemented
547	Q₈×SD₁₆	C₂×C₈₃	1	1	yes	characteristic, complemented
548	#3375	C₂×C₈₃	1	1	yes	characteristic, complemented
549	#3371	C₂×C₈₃	1	2	yes	complemented
550	#3368	C₂×C₈₃	1	1	yes	characteristic, complemented
551	#3365	C₂×C₈₃	1	1	yes	characteristic, complemented
552	#3365	C₂×C₈₃	1	2	yes	complemented
553	#3362	C₂×C₈₃	1	1	yes	characteristic, complemented
554	#3244	C₂×C₈₃	1	2	yes	complemented
555	#3241	C₂×C₈₃	1	2	yes	complemented
556	#3233	C₂×C₈₃	1	1	yes	characteristic, complemented
557	#3228	C₂×C₈₃	1	1	yes	characteristic, complemented
558	#3126	C₂×C₈₃	1	2	yes	complemented
559	#3121	C₂×C₈₃	1	2	yes	complemented
560	#3108	C₂×C₈₃	1	1	yes	characteristic, complemented
561	#3103	C₂×C₈₃	1	1	yes	characteristic, complemented
562	#2986	C₂×C₈₃	1	1	yes	characteristic, complemented
563	C₈₃	#61865	1	1	yes	characteristic, direct product factor, Sylow
564	#562	—	2	2	no	—
565	#559	C₂²×C₈₃	1	2	yes	—
566	#559	C₂²×C₈₃	1	1	yes	characteristic
567	Q₈²	—	2	1	no	—
568	Q₈²	C₂²×C₈₃	1	1	yes	characteristic
569	Q₈²	C₂²×C₈₃	1	1	yes	characteristic
570	#557	—	2	1	no	—
571	#557	—	2	2	no	—
572	#557	C₂²×C₈₃	1	1	yes	characteristic
573	#557	C₂²×C₈₃	1	2	yes	—
574	#557	C₂²×C₈₃	1	1	yes	characteristic
575	#557	C₂²×C₈₃	1	2	yes	—
576	#557	C₂²×C₈₃	1	1	yes	characteristic
577	#554	C₂²×C₈₃	1	2	yes	—
578	#550	C₂²×C₈₃	1	1	yes	characteristic
579	D₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic
580	#548	—	2	1	no	—
581	#547	—	2	1	no	—
582	#544	—	2	2	no	—
583	#544	C₂²×C₈₃	1	2	yes	—
584	#542	—	2	1	no	—
585	#542	C₂²×C₈₃	1	2	yes	—
586	#540	C₂²×C₈₃	1	2	yes	—
587	#539	—	2	2	no	—
588	#536	—	2	1	no	—
589	#533	—	2	1	no	—
590	#533	—	2	1	no	—
591	#533	C₂²×C₈₃	1	1	yes	characteristic
592	#533	C₂²×C₈₃	1	1	yes	characteristic
593	#532	C₂²×C₈₃	1	1	yes	characteristic
594	#529	C₂²×C₈₃	1	1	yes	characteristic
595	#519	C₂²×C₈₃	1	2	yes	—
596	C₂×C₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic
597	#501	C₂²×C₈₃	1	2	yes	—
598	#501	C₂²×C₈₃	1	2	yes	—
599	#500	C₂²×C₈₃	1	1	yes	characteristic
600	#499	C₂²×C₈₃	1	2	yes	—
601	#499	C₂²×C₈₃	1	2	yes	—
602	#498	C₂²×C₈₃	1	2	yes	—
603	#498	C₂²×C₈₃	1	1	yes	characteristic
604	#490	C₂²×C₈₃	1	2	yes	—
605	#489	C₂²×C₈₃	1	2	yes	—
606	#488	C₂²×C₈₃	1	2	yes	—
607	#488	C₂²×C₈₃	1	2	yes	—
608	#486	C₂²×C₈₃	1	2	yes	—
609	#486	C₂²×C₈₃	1	1	yes	characteristic
610	#486	C₂²×C₈₃	1	1	yes	characteristic
611	#485	C₂²×C₈₃	1	2	yes	—
612	#483	C₂²×C₈₃	1	1	yes	characteristic
613	#482	C₂²×C₈₃	1	2	yes	—
614	#482	C₂²×C₈₃	1	2	yes	—
615	#482	C₂²×C₈₃	1	2	yes	—
616	#481	C₂²×C₈₃	1	2	yes	—
617	#480	C₂²×C₈₃	1	1	yes	characteristic
618	#479	C₂²×C₈₃	1	1	yes	characteristic
619	#479	C₂²×C₈₃	1	1	yes	characteristic
620	#479	C₂²×C₈₃	1	2	yes	—
621	#479	C₂²×C₈₃	1	2	yes	—
622	#479	C₂²×C₈₃	1	2	yes	—
623	#478	C₂²×C₈₃	1	2	yes	—
624	#478	C₂²×C₈₃	1	2	yes	—
625	#478	C₂²×C₈₃	1	2	yes	—
626	#478	C₂²×C₈₃	1	2	yes	—
627	#478	C₂²×C₈₃	1	2	yes	—
628	#477	C₂²×C₈₃	1	1	yes	characteristic
629	#477	C₂²×C₈₃	1	2	yes	—
630	#476	C₂²×C₈₃	1	1	yes	characteristic
631	#476	C₂²×C₈₃	1	2	yes	—
632	#476	C₂²×C₈₃	1	2	yes	—
633	#475	C₂²×C₈₃	1	1	yes	characteristic
634	#475	C₂²×C₈₃	1	1	yes	characteristic
635	#475	C₂²×C₈₃	1	1	yes	characteristic
636	#475	C₂²×C₈₃	1	2	yes	—
637	#475	C₂²×C₈₃	1	2	yes	—
638	#474	C₂²×C₈₃	1	1	yes	characteristic
639	#474	C₂²×C₈₃	1	2	yes	—
640	#464	C₂²×C₈₃	1	1	yes	characteristic
641	#464	C₂²×C₈₃	1	1	yes	characteristic
642	#464	C₂²×C₈₃	1	2	yes	—
643	#464	C₂²×C₈₃	1	2	yes	—
644	#460	C₂²×C₈₃	1	1	yes	characteristic
645	#460	C₂²×C₈₃	1	1	yes	characteristic
646	#460	C₂²×C₈₃	1	2	yes	—
647	#460	C₂²×C₈₃	1	2	yes	—
648	#451	C₂²×C₈₃	1	1	yes	characteristic
649	#448	C₂²×C₈₃	1	2	yes	—
650	#448	C₂²×C₈₃	1	1	yes	characteristic
651	#446	C₂²×C₈₃	1	1	yes	characteristic
652	#446	C₂²×C₈₃	1	2	yes	—
653	#446	C₂²×C₈₃	1	1	yes	characteristic
654	C₈×Q₈	C₂²×C₈₃	1	1	yes	characteristic
655	C₈×Q₈	C₂²×C₈₃	1	1	yes	characteristic
656	C₈×Q₈	C₂²×C₈₃	1	2	yes	—
657	#441	C₂²×C₈₃	1	2	yes	—
658	#440	C₂²×C₈₃	1	2	yes	—
659	#440	C₂²×C₈₃	1	2	yes	—
660	#440	C₂²×C₈₃	1	2	yes	—
661	C₄×Q₁₆	C₂²×C₈₃	1	1	yes	characteristic
662	C₄×Q₁₆	C₂²×C₈₃	1	1	yes	characteristic
663	C₄×Q₁₆	C₂²×C₈₃	1	2	yes	—
664	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	—
665	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	—
666	C₄×SD₁₆	C₂²×C₈₃	1	1	yes	characteristic
667	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	—
668	C₄×SD₁₆	C₂²×C₈₃	1	1	yes	characteristic
669	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	—
670	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	—
671	#433	C₂²×C₈₃	1	2	yes	—
672	#433	C₂²×C₈₃	1	2	yes	—
673	#431	C₂²×C₈₃	1	1	yes	characteristic
674	#431	C₂²×C₈₃	1	1	yes	characteristic
675	C₂×#41	—	2	1	no	—
676	C₂×#41	—	2	1	no	—
677	C₂²×Q₈	—	2	1	no	—
678	C₂²×Q₈	C₂³×C₈₃	1	1	yes	characteristic
679	C₂×Q₁₆	C₂³×C₈₃	1	1	yes	characteristic
680	C₂×Q₁₆	C₂³×C₈₃	1	1	yes	characteristic
681	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
682	C₂×SD₁₆	C₂³×C₈₃	1	1	yes	characteristic
683	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
684	C₂×SD₁₆	C₂³×C₈₃	1	1	yes	characteristic
685	C₄⋊Q₈	—	2	1	no	—
686	C₄⋊Q₈	—	2	1	no	—
687	C₄⋊Q₈	—	2	1	no	—
688	C₄⋊Q₈	—	2	2	no	—
689	C₄⋊Q₈	—	2	2	no	—
690	C₄⋊Q₈	—	2	1	no	—
691	C₄⋊Q₈	—	2	1	no	—
692	C₄⋊Q₈	—	2	2	no	—
693	C₄⋊Q₈	—	2	2	no	—
694	C₄⋊Q₈	—	2	2	no	—
695	C₄⋊Q₈	D₄×C₈₃	1	1	yes	characteristic
696	C₄⋊Q₈	D₄×C₈₃	1	1	yes	characteristic
697	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
698	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
699	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
700	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
701	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
702	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
703	#127	C₂³×C₈₃	1	1	yes	characteristic
704	#127	C₂³×C₈₃	1	2	yes	—
705	#126	—	2	2	no	—
706	#126	—	2	1	no	—
707	#125	—	2	2	no	—
708	#125	—	2	2	no	—
709	#125	—	2	2	no	—
710	#125	—	2	2	no	—
711	#125	—	2	2	no	—
712	#125	—	2	2	no	—
713	#125	—	2	2	no	—
714	#125	—	2	2	no	—
715	#125	D₄×C₈₃	1	2	yes	—
716	#125	C₂³×C₈₃	1	1	yes	characteristic
717	#125	C₂³×C₈₃	1	2	yes	—
718	#125	C₂³×C₈₃	1	2	yes	—
719	#125	C₂³×C₈₃	1	2	yes	—
720	#125	C₂³×C₈₃	1	2	yes	—
721	#124	—	2	1	no	—
722	#124	—	2	2	no	—
723	#124	—	2	2	no	—
724	#124	—	2	1	no	—
725	#124	C₂³×C₈₃	1	1	yes	characteristic
726	#124	C₂³×C₈₃	1	2	yes	—
727	#123	—	2	1	no	—
728	#123	—	2	2	no	—
729	#123	—	2	2	no	—
730	#123	—	2	2	no	—
731	#123	—	2	2	no	—
732	#123	—	2	2	no	—
733	#123	—	2	2	no	—
734	C₂²⋊Q₈	—	2	2	no	—
735	C₂²⋊Q₈	—	2	1	no	—
736	C₂²⋊Q₈	—	2	1	no	—
737	C₂²⋊Q₈	—	2	2	no	—
738	C₂²⋊Q₈	—	2	2	no	—
739	C₂²⋊Q₈	—	2	2	no	—
740	C₂²⋊Q₈	—	2	2	no	—
741	C₂²⋊Q₈	—	2	1	no	—
742	C₂²⋊Q₈	—	2	2	no	—
743	C₂²⋊Q₈	—	2	2	no	—
744	C₂²⋊Q₈	D₄×C₈₃	1	1	yes	characteristic
745	C₂²⋊Q₈	D₄×C₈₃	1	1	yes	characteristic
746	C₂²⋊Q₈	D₄×C₈₃	1	2	yes	—
747	C₂²⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
748	#121	—	2	1	no	—
749	#121	—	2	2	no	—
750	#121	—	2	1	no	—
751	#121	—	2	2	no	—
752	#121	—	2	2	no	—
753	#121	C₂³×C₈₃	1	1	yes	characteristic
754	#121	C₂³×C₈₃	1	2	yes	—
755	C₄×Q₈	—	2	1	no	—
756	C₄×Q₈	—	2	1	no	—
757	C₄×Q₈	—	2	2	no	—
758	C₄×Q₈	—	2	2	no	—
759	C₄×Q₈	—	2	2	no	—
760	C₄×Q₈	—	2	2	no	—
761	C₄×Q₈	—	2	1	no	—
762	C₄×Q₈	—	2	1	no	—
763	C₄×Q₈	—	2	1	no	—
764	C₄×Q₈	—	2	1	no	—
765	C₄×Q₈	—	2	1	no	—
766	C₄×Q₈	—	2	1	no	—
767	C₄×Q₈	—	2	1	no	—
768	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
769	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
770	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
771	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
772	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
773	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
774	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
775	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
776	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
777	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
778	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
779	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
780	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
781	C₄×D₄	—	2	1	no	—
782	C₄×D₄	—	2	2	no	—
783	C₄×D₄	—	2	1	no	—
784	C₄×D₄	—	2	1	no	—
785	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
786	C₄×D₄	C₂³×C₈₃	1	2	yes	—
787	C₄×D₄	C₂³×C₈₃	1	2	yes	—
788	C₄×D₄	C₂³×C₈₃	1	2	yes	—
789	C₄×D₄	C₂³×C₈₃	1	2	yes	—
790	#117	—	2	2	no	—
791	#117	—	2	2	no	—
792	#117	—	2	1	no	—
793	#117	C₂³×C₈₃	1	2	yes	—
794	#117	C₂³×C₈₃	1	2	yes	—
795	C₂×C₄⋊C₄	—	2	1	no	—
796	C₂×C₄⋊C₄	—	2	2	no	—
797	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
798	C₂×C₄²	—	2	1	no	—
799	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
800	#107	C₂³×C₈₃	1	1	yes	characteristic
801	#107	C₂³×C₈₃	1	2	yes	—
802	#107	C₂³×C₈₃	1	1	yes	characteristic
803	#107	C₂³×C₈₃	1	2	yes	—
804	#107	C₂³×C₈₃	1	2	yes	—
805	#107	C₂³×C₈₃	1	2	yes	—
806	#106	C₂³×C₈₃	1	2	yes	—
807	#106	C₂³×C₈₃	1	2	yes	—
808	#106	C₂³×C₈₃	1	2	yes	—
809	#106	C₂³×C₈₃	1	2	yes	—
810	#106	C₂³×C₈₃	1	2	yes	—
811	#106	C₂³×C₈₃	1	1	yes	characteristic
812	#106	C₂³×C₈₃	1	1	yes	characteristic
813	#106	C₂³×C₈₃	1	2	yes	—
814	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
815	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
816	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
817	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
818	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
819	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
820	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
821	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
822	#103	C₂³×C₈₃	1	1	yes	characteristic
823	#103	C₂³×C₈₃	1	2	yes	—
824	#103	C₂³×C₈₃	1	1	yes	characteristic
825	#103	C₂³×C₈₃	1	1	yes	characteristic
826	#103	C₂³×C₈₃	1	2	yes	—
827	#103	C₂³×C₈₃	1	1	yes	characteristic
828	#103	C₂³×C₈₃	1	1	yes	characteristic
829	#103	C₂³×C₈₃	1	2	yes	—
830	#103	C₂³×C₈₃	1	1	yes	characteristic
831	#103	C₂³×C₈₃	1	2	yes	—
832	#102	C₂³×C₈₃	1	2	yes	—
833	#102	C₂³×C₈₃	1	2	yes	—
834	#102	C₂³×C₈₃	1	2	yes	—
835	#102	C₂³×C₈₃	1	2	yes	—
836	#102	C₂³×C₈₃	1	2	yes	—
837	#102	C₂³×C₈₃	1	1	yes	characteristic
838	#102	C₂³×C₈₃	1	1	yes	characteristic
839	#102	C₂³×C₈₃	1	2	yes	—
840	#102	C₂³×C₈₃	1	2	yes	—
841	#102	C₂³×C₈₃	1	2	yes	—
842	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
843	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
844	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
845	#97	C₂³×C₈₃	1	2	yes	—
846	#97	C₂³×C₈₃	1	2	yes	—
847	C₄×C₈	C₂³×C₈₃	1	2	yes	—
848	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
849	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
850	C₄×C₈	C₂³×C₈₃	1	2	yes	—
851	C₄×C₈	C₂³×C₈₃	1	2	yes	—
852	#41	—	8	2	no	—
853	#41	—	8	2	no	—
854	C₂×Q₈	—	2	2	no	—
855	C₂×Q₈	—	2	2	no	—
856	C₂×Q₈	—	2	1	no	—
857	C₂×Q₈	—	2	1	no	—
858	C₂×Q₈	—	2	1	no	—
859	C₂×Q₈	—	2	1	no	—
860	C₂×Q₈	—	2	2	no	—
861	C₂×Q₈	—	2	2	no	—
862	C₂×Q₈	—	2	2	no	—
863	C₂×Q₈	—	8	2	no	—
864	C₂×Q₈	C₂×D₄×C₈₃	1	1	yes	characteristic
865	C₂×Q₈	C₂×D₄×C₈₃	1	1	yes	characteristic
866	C₂×Q₈	C₂×D₄×C₈₃	1	2	yes	—
867	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
868	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
869	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
870	C₂×D₄	—	2	1	no	—
871	C₂×D₄	—	2	2	no	—
872	C₂×D₄	—	2	1	no	—
873	C₂×D₄	—	2	1	no	—
874	C₂×D₄	—	2	2	no	—
875	C₂×D₄	—	2	2	no	—
876	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
877	C₂×D₄	C₂⁴×C₈₃	1	1	yes	characteristic
878	C₂²×C₄	—	2	1	no	—
879	C₂²×C₄	—	2	1	no	—
880	C₂²×C₄	—	2	1	no	—
881	C₂²×C₄	—	2	2	no	—
882	C₂²×C₄	—	2	2	no	—
883	C₂²×C₄	—	2	2	no	—
884	C₂²×C₄	—	2	2	no	—
885	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
886	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
887	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
888	Q₁₆	—	2	2	no	—
889	Q₁₆	—	2	2	no	—
890	SD₁₆	—	2	4	no	—
891	SD₁₆	—	2	2	no	—
892	SD₁₆	—	2	4	no	—
893	SD₁₆	—	2	2	no	—
894	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
895	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
896	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
897	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
898	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
899	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
900	C₄⋊C₄	—	2	1	no	—
901	C₄⋊C₄	—	2	1	no	—
902	C₄⋊C₄	—	2	1	no	—
903	C₄⋊C₄	—	2	1	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	1	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	1	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	1	no	—
928	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
929	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
930	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
931	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
932	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
933	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
934	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
935	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
936	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
937	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
938	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
939	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
940	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
941	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
942	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
943	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	—	2	1	no	—
946	C₂²⋊C₄	—	2	1	no	—
947	C₂²⋊C₄	—	2	1	no	—
948	C₂²⋊C₄	—	2	1	no	—
949	C₂²⋊C₄	—	2	2	no	—
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	—	2	2	no	—
952	C₂²⋊C₄	—	2	1	no	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
958	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
959	C₄²	—	2	1	no	—
960	C₄²	—	2	1	no	—
961	C₄²	—	2	1	no	—
962	C₄²	—	2	1	no	—
963	C₄²	—	2	1	no	—
964	C₄²	—	2	2	no	—
965	C₄²	—	2	2	no	—
966	C₄²	—	2	2	no	—
967	C₄²	—	2	2	no	—
968	C₄²	—	2	2	no	—
969	C₄²	—	2	2	no	—
970	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
971	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
972	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
973	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
974	C₄²	C₂⁴×C₈₃	1	2	yes	—
975	C₄²	C₂⁴×C₈₃	1	2	yes	—
976	C₂³	—	2	1	no	—
977	C₂³	—	2	2	no	—
978	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
979	Q₈	—	2	4	no	—
980	Q₈	—	2	2	no	—
981	Q₈	—	2	2	no	—
982	Q₈	—	2	1	no	—
983	Q₈	—	2	1	no	—
984	Q₈	—	2	1	no	—
985	Q₈	—	2	1	no	—
986	Q₈	—	4	2	no	—
987	Q₈	—	4	2	no	—
988	Q₈	—	4	2	no	—
989	Q₈	—	8	2	no	—
990	Q₈	—	8	1	no	—
991	Q₈	—	8	2	no	—
992	Q₈	—	8	2	no	—
993	Q₈	2₋¹⁺⁴×C₈₃	1	2	yes	—
994	Q₈	2₋¹⁺⁴×C₈₃	1	2	yes	—
995	D₄	—	2	2	no	—
996	D₄	—	2	1	no	—
997	D₄	—	2	2	no	—
998	D₄	—	2	1	no	—
999	D₄	—	4	2	no	—
1000	D₄	—	8	2	no	—
1001	D₄	—	8	1	no	—
1002	D₄	—	8	2	no	—
1003	D₄	—	8	2	no	—
1004	D₄	—	8	1	no	—
1005	C₂×C₄	—	2	4	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	4	1	no	—
1020	C₂×C₄	—	4	2	no	—
1021	C₂×C₄	—	8	2	no	—
1022	C₂×C₄	—	8	2	no	—
1023	C₂×C₄	—	8	2	no	—
1024	C₂×C₄	—	8	2	no	—
1025	C₂×C₄	—	8	1	no	—
1026	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1027	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1028	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
1029	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
1030	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
1031	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
1032	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1033	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1034	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1035	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
1036	C₈	—	2	2	no	—
1037	C₈	—	2	1	no	—
1038	C₈	—	2	2	no	—
1039	C₈	—	2	1	no	—
1040	C₈	—	2	1	no	—
1041	C₈	—	2	1	no	—
1042	C₂²	—	2	1	no	—
1043	C₂²	—	2	1	no	—
1044	C₂²	—	2	1	no	—
1045	C₂²	—	4	1	no	—
1046	C₂²	—	4	2	no	—
1047	C₂²	—	4	2	no	—
1048	C₂²	—	4	1	no	—
1049	C₂²	—	4	1	no	—
1050	C₂²	—	4	2	no	—
1051	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
1052	C₄	—	2	1	no	—
1053	C₄	—	2	2	no	—
1054	C₄	—	2	2	no	—
1055	C₄	—	2	1	no	—
1056	C₄	—	2	1	no	—
1057	C₄	—	2	2	no	—
1058	C₄	—	2	2	no	—
1059	C₄	—	2	2	no	—
1060	C₄	—	2	2	no	—
1061	C₄	—	2	1	no	—
1062	C₄	—	4	1	no	—
1063	C₄	—	4	2	no	—
1064	C₄	—	4	2	no	—
1065	C₄	—	4	1	no	—
1066	C₄	—	4	1	no	—
1067	C₄	—	4	1	no	—
1068	C₄	—	4	2	no	—
1069	C₄	—	4	1	no	—
1070	C₄	#577×C₈₃	1	2	yes	—
1071	C₄	C₂×2₋¹⁺⁴×C₈₃	1	1	yes	characteristic
1072	C₄	C₂×2₋¹⁺⁴×C₈₃	1	1	yes	characteristic
1073	C₂	—	4	1	no	—
1074	C₂	—	8	1	no	—
1075	C₂	—	8	2	no	—
1076	C₂	C₈₃×#3486	1	1	yes	characteristic
1077	C₂	C₂×#577×C₈₃	1	1	yes	characteristic
1078	C₂	C₈₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₃
prime radical	C₈₃×#3554	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₃ ◁ #533×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈₃×#3502	C₂	semidirect
3. C₈₃×#3388	C₂	semidirect
4. C₈₃×#3387	C₂	semidirect
5. C₈₃×#3386	C₂	semidirect
6. C₈₃×#3383	C₂	semidirect
7. C₈₃×#3381	C₂	semidirect
8. Q₈×SD₁₆×C₈₃	C₂	semidirect
9. C₈₃×#3375	C₂	semidirect
10. C₈₃×#3371	C₂	semidirect
11. C₈₃×#3368	C₂	semidirect
12. C₈₃×#3365	C₂	semidirect
13. C₈₃×#3365	C₂	semidirect
14. C₈₃×#3362	C₂	semidirect
15. C₈₃×#3244	C₂	semidirect
16. C₈₃×#3241	C₂	semidirect
17. C₈₃×#3233	C₂	semidirect
18. C₈₃×#3228	C₂	semidirect
19. C₈₃×#3126	C₂	semidirect
20. C₈₃×#3121	C₂	semidirect
21. C₈₃×#3108	C₂	semidirect
22. C₈₃×#3103	C₂	semidirect
23. C₈₃×#2986	C₂	semidirect
533. #61865	C₈₃	direct (N × H)
541. #3502	C₂×C₈₃	semidirect
542. #3388	C₂×C₈₃	semidirect
543. #3387	C₂×C₈₃	semidirect
544. #3386	C₂×C₈₃	semidirect
545. #3383	C₂×C₈₃	semidirect
546. #3381	C₂×C₈₃	semidirect
547. Q₈×SD₁₆	C₂×C₈₃	semidirect
548. #3375	C₂×C₈₃	semidirect
549. #3371	C₂×C₈₃	semidirect
550. #3368	C₂×C₈₃	semidirect
551. #3365	C₂×C₈₃	semidirect
552. #3365	C₂×C₈₃	semidirect
553. #3362	C₂×C₈₃	semidirect
554. #3244	C₂×C₈₃	semidirect
555. #3241	C₂×C₈₃	semidirect
556. #3233	C₂×C₈₃	semidirect
557. #3228	C₂×C₈₃	semidirect
558. #3126	C₂×C₈₃	semidirect
559. #3121	C₂×C₈₃	semidirect
560. #3108	C₂×C₈₃	semidirect
561. #3103	C₂×C₈₃	semidirect
562. #2986	C₂×C₈₃	semidirect
563. C₈₃	#61865	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×#3554	2
C₈₃×#3502	2
C₈₃×#3388	2
C₈₃×#3387	2
C₈₃×#3386	2
C₈₃×#3383	2
C₈₃×#3381	2
Q₈×SD₁₆×C₈₃	2
C₈₃×#3375	2
C₈₃×#3371	2
C₈₃×#3368	2
C₈₃×#3365	2
C₈₃×#3362	2
C₈₃×#3244	2
C₈₃×#3241	2
C₈₃×#3233	2
C₈₃×#3228	2
C₈₃×#3126	2
C₈₃×#3121	2
C₈₃×#3108	2
C₈₃×#3103	2
C₈₃×#2986	2
#61865	83

Subgroups — C83×#61865 #35289689

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#61865 #35289689