Subgroups — C₈₃×#62220 #35290044

Order 21248.

1640 conjugacy classes of subgroups.

The subgroup lattice has 1076 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₃×#3518	C₂	1	1	yes	maximal, characteristic
3	C₈₃×#3387	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×Q₁₆×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₃×#3369	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₃×#3364	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₃×#3357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₃×#3349	C₂	1	2	yes	maximal, complemented
9	C₈₃×#3342	C₂	1	2	yes	maximal, complemented
10	C₈₃×#3340	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₃×#3328	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₃×#3313	C₂	1	2	yes	maximal, complemented
13	C₈₃×#3300	C₂	1	2	yes	maximal, complemented
14	C₈₃×#3299	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#3258	C₂	1	2	yes	maximal, complemented
16	C₈₃×#3249	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₃×#3243	C₂	1	2	yes	maximal, complemented
18	C₈₃×#3231	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₃×#3127	C₂	1	2	yes	maximal, complemented
20	C₈₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₃×#3082	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	#563×C₈₃	—	2	2	no	—
25	Q₈²×C₈₃	C₂²	1	1	yes	characteristic
26	Q₈²×C₈₃	C₂²	1	1	yes	characteristic
27	#557×C₈₃	—	2	1	no	—
28	#557×C₈₃	C₂²	1	1	yes	characteristic
29	#556×C₈₃	—	2	2	no	—
30	#556×C₈₃	—	2	1	no	—
31	#556×C₈₃	—	2	1	no	—
32	#556×C₈₃	C₂²	1	1	yes	characteristic
33	#556×C₈₃	C₂²	1	2	yes	—
34	#556×C₈₃	C₂²	1	1	yes	characteristic
35	#556×C₈₃	C₂²	1	2	yes	—
36	#555×C₈₃	—	2	1	no	—
37	#555×C₈₃	C₂²	1	1	yes	characteristic
38	#554×C₈₃	C₂²	1	1	yes	characteristic
39	#552×C₈₃	C₂²	1	2	yes	—
40	D₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
41	#548×C₈₃	C₂²	1	2	yes	—
42	#544×C₈₃	C₂²	1	2	yes	—
43	#542×C₈₃	—	2	2	no	—
44	#542×C₈₃	—	2	1	no	—
45	#542×C₈₃	C₂²	1	2	yes	—
46	#541×C₈₃	—	2	2	no	—
47	#541×C₈₃	—	2	1	no	—
48	#541×C₈₃	C₂²	1	2	yes	—
49	#533×C₈₃	—	2	1	no	—
50	#533×C₈₃	C₂²	1	1	yes	characteristic
51	#533×C₈₃	C₂²	1	1	yes	characteristic
52	#533×C₈₃	C₂²	1	1	yes	characteristic
53	#529×C₈₃	—	2	1	no	—
54	#529×C₈₃	C₂²	1	1	yes	characteristic
55	#519×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	2	yes	—
59	#500×C₈₃	C₂²	1	1	yes	characteristic
60	#498×C₈₃	C₂²	1	1	yes	characteristic
61	#489×C₈₃	C₂²	1	2	yes	—
62	#488×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	#485×C₈₃	C₂²	1	1	yes	characteristic
70	#485×C₈₃	C₂²	1	2	yes	—
71	#485×C₈₃	C₂²	1	1	yes	characteristic
72	#484×C₈₃	C₂²	1	2	yes	—
73	#482×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	#479×C₈₃	C₂²	1	2	yes	—
80	#478×C₈₃	C₂²	1	2	yes	—
81	#477×C₈₃	C₂²	1	1	yes	characteristic
82	#477×C₈₃	C₂²	1	2	yes	—
83	#477×C₈₃	C₂²	1	2	yes	—
84	#477×C₈₃	C₂²	1	1	yes	characteristic
85	#477×C₈₃	C₂²	1	2	yes	—
86	#477×C₈₃	C₂²	1	1	yes	characteristic
87	#476×C₈₃	C₂²	1	1	yes	characteristic
88	#475×C₈₃	C₂²	1	1	yes	characteristic
89	#475×C₈₃	C₂²	1	1	yes	characteristic
90	#475×C₈₃	C₂²	1	2	yes	—
91	#475×C₈₃	C₂²	1	2	yes	—
92	#474×C₈₃	C₂²	1	1	yes	characteristic
93	#474×C₈₃	C₂²	1	1	yes	characteristic
94	#470×C₈₃	C₂²	1	2	yes	—
95	#468×C₈₃	C₂²	1	2	yes	—
96	#467×C₈₃	C₂²	1	2	yes	—
97	#467×C₈₃	C₂²	1	2	yes	—
98	#467×C₈₃	C₂²	1	2	yes	—
99	#465×C₈₃	C₂²	1	2	yes	—
100	#464×C₈₃	C₂²	1	2	yes	—
101	#464×C₈₃	C₂²	1	2	yes	—
102	#462×C₈₃	C₂²	1	1	yes	characteristic
103	#462×C₈₃	C₂²	1	1	yes	characteristic
104	#462×C₈₃	C₂²	1	1	yes	characteristic
105	#462×C₈₃	C₂²	1	2	yes	—
106	#461×C₈₃	C₂²	1	1	yes	characteristic
107	#452×C₈₃	C₂²	1	1	yes	characteristic
108	#452×C₈₃	C₂²	1	1	yes	characteristic
109	#451×C₈₃	C₂²	1	2	yes	—
110	#451×C₈₃	C₂²	1	2	yes	—
111	#446×C₈₃	C₂²	1	1	yes	characteristic
112	C₈×Q₈×C₈₃	C₂²	1	1	yes	characteristic
113	#441×C₈₃	C₂²	1	2	yes	—
114	#441×C₈₃	C₂²	1	2	yes	—
115	C₄×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic
116	C₄×Q₁₆×C₈₃	C₂²	1	2	yes	—
117	C₄×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic
118	C₄×Q₁₆×C₈₃	C₂²	1	2	yes	—
119	C₄×SD₁₆×C₈₃	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×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	#427×C₈₃	C₂²	1	2	yes	—
130	#424×C₈₃	C₂²	1	2	yes	—
131	C₂×C₄⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
132	#419×C₈₃	C₂²	1	2	yes	—
133	#416×C₈₃	C₂²	1	2	yes	—
134	C₂×#103×C₈₃	C₂²	1	2	yes	—
135	C₂×#41×C₈₃	C₂³	1	1	yes	characteristic
136	C₂²×Q₈×C₈₃	C₂³	1	2	yes	—
137	C₂×Q₁₆×C₈₃	C₂³	1	1	yes	characteristic
138	C₂×Q₁₆×C₈₃	C₂³	1	1	yes	characteristic
139	C₂×Q₁₆×C₈₃	C₂³	1	2	yes	—
140	C₂×Q₁₆×C₈₃	C₂³	1	2	yes	—
141	C₂×SD₁₆×C₈₃	C₂³	1	1	yes	characteristic
142	C₂×SD₁₆×C₈₃	C₂³	1	1	yes	characteristic
143	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
144	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
145	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
146	C₄⋊Q₈×C₈₃	—	2	1	no	—
147	C₄⋊Q₈×C₈₃	—	2	1	no	—
148	C₄⋊Q₈×C₈₃	—	2	1	no	—
149	C₄⋊Q₈×C₈₃	—	2	2	no	—
150	C₄⋊Q₈×C₈₃	—	2	2	no	—
151	C₄⋊Q₈×C₈₃	—	2	1	no	—
152	C₄⋊Q₈×C₈₃	—	2	2	no	—
153	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
154	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
155	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
156	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
157	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
158	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
159	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
161	#126×C₈₃	—	2	2	no	—
162	#126×C₈₃	—	2	2	no	—
163	#126×C₈₃	—	2	2	no	—
164	#126×C₈₃	—	2	2	no	—
165	#126×C₈₃	—	2	2	no	—
166	#126×C₈₃	—	2	2	no	—
167	#126×C₈₃	—	2	2	no	—
168	#126×C₈₃	—	2	2	no	—
169	#126×C₈₃	—	2	2	no	—
170	#126×C₈₃	—	2	2	no	—
171	#126×C₈₃	D₄	1	2	yes	—
172	#125×C₈₃	—	2	2	no	—
173	#125×C₈₃	—	2	2	no	—
174	#125×C₈₃	—	2	2	no	—
175	#125×C₈₃	—	2	1	no	—
176	#125×C₈₃	—	2	2	no	—
177	#125×C₈₃	—	2	2	no	—
178	#125×C₈₃	—	2	1	no	—
179	#125×C₈₃	—	2	1	no	—
180	#125×C₈₃	D₄	1	1	yes	characteristic
181	#125×C₈₃	C₂³	1	2	yes	—
182	#125×C₈₃	C₂³	1	2	yes	—
183	#124×C₈₃	—	2	2	no	—
184	#124×C₈₃	—	2	1	no	—
185	#124×C₈₃	—	2	2	no	—
186	#124×C₈₃	—	2	2	no	—
187	#124×C₈₃	—	2	2	no	—
188	#124×C₈₃	—	2	2	no	—
189	#124×C₈₃	D₄	1	1	yes	characteristic
190	#124×C₈₃	C₂³	1	2	yes	—
191	#123×C₈₃	—	2	2	no	—
192	#123×C₈₃	—	2	2	no	—
193	#123×C₈₃	D₄	1	2	yes	—
194	C₂²⋊Q₈×C₈₃	—	2	1	no	—
195	C₂²⋊Q₈×C₈₃	—	2	1	no	—
196	C₂²⋊Q₈×C₈₃	—	2	1	no	—
197	C₂²⋊Q₈×C₈₃	—	2	1	no	—
198	C₂²⋊Q₈×C₈₃	—	2	1	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	—	2	2	no	—
203	C₂²⋊Q₈×C₈₃	—	2	2	no	—
204	C₂²⋊Q₈×C₈₃	—	2	2	no	—
205	C₂²⋊Q₈×C₈₃	D₄	1	1	yes	characteristic
206	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
207	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
208	C₂²⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
209	C₂²⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
210	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
211	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
212	#121×C₈₃	—	2	1	no	—
213	#121×C₈₃	—	2	2	no	—
214	#121×C₈₃	D₄	1	1	yes	characteristic
215	#121×C₈₃	C₂³	1	2	yes	—
216	C₄×Q₈×C₈₃	—	2	1	no	—
217	C₄×Q₈×C₈₃	—	2	1	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	2	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	2	yes	—
233	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
234	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
235	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₈₃	—	2	1	no	—
239	C₄×D₄×C₈₃	—	2	1	no	—
240	C₄×D₄×C₈₃	—	2	1	no	—
241	C₄×D₄×C₈₃	—	2	1	no	—
242	C₄×D₄×C₈₃	—	2	2	no	—
243	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₈₃	C₂³	1	2	yes	—
246	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
247	#117×C₈₃	—	2	1	no	—
248	#117×C₈₃	—	2	1	no	—
249	#117×C₈₃	—	2	1	no	—
250	#117×C₈₃	—	2	1	no	—
251	#117×C₈₃	—	2	2	no	—
252	#117×C₈₃	—	2	2	no	—
253	#117×C₈₃	—	2	2	no	—
254	#117×C₈₃	—	2	1	no	—
255	#117×C₈₃	C₂³	1	2	yes	—
256	#117×C₈₃	C₂³	1	1	yes	characteristic
257	#117×C₈₃	C₂³	1	2	yes	—
258	#117×C₈₃	C₂³	1	2	yes	—
259	#117×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	2	yes	—
267	#107×C₈₃	C₂³	1	2	yes	—
268	#107×C₈₃	C₂³	1	1	yes	characteristic
269	#107×C₈₃	C₂³	1	1	yes	characteristic
270	#107×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	2	yes	—
278	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
279	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
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	1	yes	characteristic
288	#103×C₈₃	C₂³	1	2	yes	—
289	#103×C₈₃	C₂³	1	2	yes	—
290	#103×C₈₃	C₂³	1	2	yes	—
291	#103×C₈₃	C₂³	1	1	yes	characteristic
292	#103×C₈₃	C₂³	1	1	yes	characteristic
293	#103×C₈₃	C₂³	1	1	yes	characteristic
294	#103×C₈₃	C₂³	1	2	yes	—
295	#103×C₈₃	C₂³	1	2	yes	—
296	#103×C₈₃	C₂³	1	2	yes	—
297	#103×C₈₃	C₂³	1	2	yes	—
298	#103×C₈₃	C₂³	1	1	yes	characteristic
299	#103×C₈₃	C₂³	1	1	yes	characteristic
300	#102×C₈₃	C₂³	1	2	yes	—
301	#102×C₈₃	C₂³	1	2	yes	—
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	1	yes	characteristic
311	C₄×C₈×C₈₃	C₂³	1	2	yes	—
312	#41×C₈₃	—	2	2	no	—
313	#41×C₈₃	—	4	1	no	—
314	C₂×Q₈×C₈₃	—	2	1	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	2	no	—
320	C₂×Q₈×C₈₃	—	2	2	no	—
321	C₂×Q₈×C₈₃	—	2	4	no	—
322	C₂×Q₈×C₈₃	—	4	2	no	—
323	C₂×Q₈×C₈₃	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
325	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₈₃	—	2	1	no	—
329	C₂×D₄×C₈₃	—	2	2	no	—
330	C₂×D₄×C₈₃	C₂×D₄	1	1	yes	characteristic
331	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
332	C₂×D₄×C₈₃	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₈₃	—	2	2	no	—
334	C₂²×C₄×C₈₃	—	2	2	no	—
335	C₂²×C₄×C₈₃	—	2	1	no	—
336	C₂²×C₄×C₈₃	—	2	1	no	—
337	C₂²×C₄×C₈₃	—	2	1	no	—
338	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
339	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
340	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
342	Q₁₆×C₈₃	—	2	2	no	—
343	Q₁₆×C₈₃	—	2	2	no	—
344	Q₁₆×C₈₃	—	4	2	no	—
345	Q₁₆×C₈₃	—	4	2	no	—
346	SD₁₆×C₈₃	—	4	1	no	—
347	SD₁₆×C₈₃	—	4	1	no	—
348	M₁₆×C₈₃	—	4	2	no	—
349	C₂×C₈×C₈₃	—	4	2	no	—
350	C₂×C₈×C₈₃	—	4	2	no	—
351	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
352	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
353	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
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	C₄⋊C₄×C₈₃	—	2	2	no	—
358	C₄⋊C₄×C₈₃	—	2	1	no	—
359	C₄⋊C₄×C₈₃	—	2	1	no	—
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	2	no	—
364	C₄⋊C₄×C₈₃	—	2	2	no	—
365	C₄⋊C₄×C₈₃	—	2	2	no	—
366	C₄⋊C₄×C₈₃	—	2	1	no	—
367	C₄⋊C₄×C₈₃	—	2	2	no	—
368	C₄⋊C₄×C₈₃	—	2	1	no	—
369	C₄⋊C₄×C₈₃	—	2	2	no	—
370	C₄⋊C₄×C₈₃	—	2	1	no	—
371	C₄⋊C₄×C₈₃	—	2	1	no	—
372	C₄⋊C₄×C₈₃	—	2	1	no	—
373	C₄⋊C₄×C₈₃	—	2	2	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	1	no	—
379	C₄⋊C₄×C₈₃	—	2	1	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	C₂×D₄	1	1	yes	characteristic
388	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
393	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
394	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
395	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
396	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
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	C₂²⋊C₄×C₈₃	—	2	2	no	—
401	C₂²⋊C₄×C₈₃	—	2	2	no	—
402	C₂²⋊C₄×C₈₃	—	2	1	no	—
403	C₂²⋊C₄×C₈₃	—	2	1	no	—
404	C₂²⋊C₄×C₈₃	—	2	2	no	—
405	C₂²⋊C₄×C₈₃	—	2	1	no	—
406	C₂²⋊C₄×C₈₃	—	2	2	no	—
407	C₂²⋊C₄×C₈₃	—	2	2	no	—
408	C₂²⋊C₄×C₈₃	—	2	2	no	—
409	C₂²⋊C₄×C₈₃	—	2	2	no	—
410	C₂²⋊C₄×C₈₃	—	2	1	no	—
411	C₂²⋊C₄×C₈₃	—	2	1	no	—
412	C₂²⋊C₄×C₈₃	—	2	2	no	—
413	C₂²⋊C₄×C₈₃	—	2	2	no	—
414	C₂²⋊C₄×C₈₃	—	2	2	no	—
415	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
416	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
417	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
418	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
419	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
420	C₄²×C₈₃	—	2	1	no	—
421	C₄²×C₈₃	—	2	1	no	—
422	C₄²×C₈₃	—	2	1	no	—
423	C₄²×C₈₃	—	2	2	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	1	no	—
429	C₄²×C₈₃	—	2	1	no	—
430	C₄²×C₈₃	—	2	2	no	—
431	C₄²×C₈₃	—	2	2	no	—
432	C₄²×C₈₃	—	2	2	no	—
433	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
434	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
435	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
436	C₄²×C₈₃	C₂⁴	1	2	yes	—
437	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
438	C₂³×C₈₃	—	2	1	no	—
439	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
440	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
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	2	no	—
446	Q₈×C₈₃	—	2	1	no	—
447	Q₈×C₈₃	—	2	1	no	—
448	Q₈×C₈₃	—	2	2	no	—
449	Q₈×C₈₃	—	4	4	no	—
450	Q₈×C₈₃	—	4	2	no	—
451	Q₈×C₈₃	—	8	1	no	—
452	Q₈×C₈₃	—	8	1	no	—
453	Q₈×C₈₃	—	8	1	no	—
454	Q₈×C₈₃	—	8	2	no	—
455	Q₈×C₈₃	—	8	2	no	—
456	Q₈×C₈₃	2₋¹⁺⁴	1	2	yes	—
457	D₄×C₈₃	—	2	2	no	—
458	D₄×C₈₃	—	2	1	no	—
459	D₄×C₈₃	—	2	1	no	—
460	D₄×C₈₃	—	4	2	no	—
461	D₄×C₈₃	—	4	2	no	—
462	D₄×C₈₃	—	8	2	no	—
463	C₂×C₄×C₈₃	—	2	1	no	—
464	C₂×C₄×C₈₃	—	2	2	no	—
465	C₂×C₄×C₈₃	—	2	2	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	2	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	—	4	4	no	—
482	C₂×C₄×C₈₃	—	4	2	no	—
483	C₂×C₄×C₈₃	—	8	1	no	—
484	C₂×C₄×C₈₃	—	8	2	no	—
485	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
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	1	yes	characteristic
491	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
494	C₈×C₈₃	—	2	1	no	—
495	C₈×C₈₃	—	2	1	no	—
496	C₈×C₈₃	—	2	1	no	—
497	C₈×C₈₃	—	2	2	no	—
498	C₈×C₈₃	—	2	2	no	—
499	C₈×C₈₃	—	2	1	no	—
500	C₂²×C₈₃	—	2	1	no	—
501	C₂²×C₈₃	—	2	2	no	—
502	C₂²×C₈₃	—	2	2	no	—
503	C₂²×C₈₃	—	2	1	no	—
504	C₂²×C₈₃	—	2	1	no	—
505	C₂²×C₈₃	—	2	2	no	—
506	C₂²×C₈₃	—	4	1	no	—
507	C₂²×C₈₃	—	4	1	no	—
508	C₂²×C₈₃	—	4	1	no	—
509	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
510	C₄×C₈₃	—	2	1	no	—
511	C₄×C₈₃	—	2	1	no	—
512	C₄×C₈₃	—	2	2	no	—
513	C₄×C₈₃	—	2	1	no	—
514	C₄×C₈₃	—	2	2	no	—
515	C₄×C₈₃	—	2	2	no	—
516	C₄×C₈₃	—	2	1	no	—
517	C₄×C₈₃	—	2	2	no	—
518	C₄×C₈₃	—	4	1	no	—
519	C₄×C₈₃	—	4	1	no	—
520	C₄×C₈₃	—	4	2	no	—
521	C₄×C₈₃	—	4	2	no	—
522	C₄×C₈₃	—	4	1	no	—
523	C₄×C₈₃	—	4	2	no	—
524	C₄×C₈₃	—	4	1	no	—
525	C₄×C₈₃	—	4	1	no	—
526	C₄×C₈₃	—	4	1	no	—
527	C₄×C₈₃	—	4	2	no	—
528	C₄×C₈₃	#578	1	2	yes	—
529	C₄×C₈₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
530	C₄×C₈₃	#585	1	1	yes	characteristic
531	#62220	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
532	C₂×C₈₃	—	4	1	no	—
533	C₂×C₈₃	—	4	2	no	—
534	C₂×C₈₃	—	8	1	no	—
535	C₂×C₈₃	#3489	1	1	yes	characteristic
536	C₂×C₈₃	C₂×#578	1	1	yes	characteristic
537	C₂×C₈₃	#3584	1	1	yes	characteristic
538	#3555	C₂×C₈₃	1	1	yes	characteristic, complemented
539	#3518	C₂×C₈₃	1	1	yes	characteristic
540	#3387	C₂×C₈₃	1	1	yes	characteristic, complemented
541	Q₈×Q₁₆	C₂×C₈₃	1	1	yes	characteristic, complemented
542	#3369	C₂×C₈₃	1	1	yes	characteristic, complemented
543	#3364	C₂×C₈₃	1	1	yes	characteristic, complemented
544	#3357	C₂×C₈₃	1	1	yes	characteristic, complemented
545	#3349	C₂×C₈₃	1	2	yes	complemented
546	#3342	C₂×C₈₃	1	2	yes	complemented
547	#3340	C₂×C₈₃	1	1	yes	characteristic, complemented
548	#3328	C₂×C₈₃	1	1	yes	characteristic, complemented
549	#3313	C₂×C₈₃	1	2	yes	complemented
550	#3300	C₂×C₈₃	1	2	yes	complemented
551	#3299	C₂×C₈₃	1	1	yes	characteristic, complemented
552	#3258	C₂×C₈₃	1	2	yes	complemented
553	#3249	C₂×C₈₃	1	1	yes	characteristic, complemented
554	#3243	C₂×C₈₃	1	2	yes	complemented
555	#3231	C₂×C₈₃	1	1	yes	characteristic, complemented
556	#3127	C₂×C₈₃	1	2	yes	complemented
557	#3107	C₂×C₈₃	1	1	yes	characteristic, complemented
558	#3082	C₂×C₈₃	1	2	yes	complemented
559	#3076	C₂×C₈₃	1	1	yes	characteristic, complemented
560	#2994	C₂×C₈₃	1	1	yes	characteristic, complemented
561	C₈₃	#62220	1	1	yes	characteristic, direct product factor, Sylow
562	#563	—	2	2	no	—
563	Q₈²	C₂²×C₈₃	1	1	yes	characteristic
564	Q₈²	C₂²×C₈₃	1	1	yes	characteristic
565	#557	—	2	1	no	—
566	#557	C₂²×C₈₃	1	1	yes	characteristic
567	#556	—	2	2	no	—
568	#556	—	2	1	no	—
569	#556	—	2	1	no	—
570	#556	C₂²×C₈₃	1	1	yes	characteristic
571	#556	C₂²×C₈₃	1	1	yes	characteristic
572	#556	C₂²×C₈₃	1	2	yes	—
573	#556	C₂²×C₈₃	1	2	yes	—
574	#555	—	2	1	no	—
575	#555	C₂²×C₈₃	1	1	yes	characteristic
576	#554	C₂²×C₈₃	1	1	yes	characteristic
577	#552	C₂²×C₈₃	1	2	yes	—
578	D₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic
579	#548	C₂²×C₈₃	1	2	yes	—
580	#544	C₂²×C₈₃	1	2	yes	—
581	#542	—	2	2	no	—
582	#542	—	2	1	no	—
583	#542	C₂²×C₈₃	1	2	yes	—
584	#541	—	2	2	no	—
585	#541	—	2	1	no	—
586	#541	C₂²×C₈₃	1	2	yes	—
587	#533	—	2	1	no	—
588	#533	C₂²×C₈₃	1	1	yes	characteristic
589	#533	C₂²×C₈₃	1	1	yes	characteristic
590	#533	C₂²×C₈₃	1	1	yes	characteristic
591	#529	—	2	1	no	—
592	#529	C₂²×C₈₃	1	1	yes	characteristic
593	#519	C₂²×C₈₃	1	2	yes	—
594	C₄×#41	C₂²×C₈₃	1	1	yes	characteristic
595	#501	C₂²×C₈₃	1	2	yes	—
596	#500	C₂²×C₈₃	1	2	yes	—
597	#500	C₂²×C₈₃	1	1	yes	characteristic
598	#498	C₂²×C₈₃	1	1	yes	characteristic
599	#489	C₂²×C₈₃	1	2	yes	—
600	#488	C₂²×C₈₃	1	2	yes	—
601	#487	C₂²×C₈₃	1	1	yes	characteristic
602	#487	C₂²×C₈₃	1	1	yes	characteristic
603	#485	C₂²×C₈₃	1	2	yes	—
604	#485	C₂²×C₈₃	1	2	yes	—
605	#485	C₂²×C₈₃	1	1	yes	characteristic
606	#485	C₂²×C₈₃	1	2	yes	—
607	#485	C₂²×C₈₃	1	2	yes	—
608	#485	C₂²×C₈₃	1	1	yes	characteristic
609	#485	C₂²×C₈₃	1	2	yes	—
610	#484	C₂²×C₈₃	1	2	yes	—
611	#482	C₂²×C₈₃	1	2	yes	—
612	#480	C₂²×C₈₃	1	2	yes	—
613	#479	C₂²×C₈₃	1	2	yes	—
614	#479	C₂²×C₈₃	1	2	yes	—
615	#479	C₂²×C₈₃	1	2	yes	—
616	#479	C₂²×C₈₃	1	2	yes	—
617	#479	C₂²×C₈₃	1	2	yes	—
618	#478	C₂²×C₈₃	1	2	yes	—
619	#477	C₂²×C₈₃	1	1	yes	characteristic
620	#477	C₂²×C₈₃	1	2	yes	—
621	#477	C₂²×C₈₃	1	2	yes	—
622	#477	C₂²×C₈₃	1	1	yes	characteristic
623	#477	C₂²×C₈₃	1	2	yes	—
624	#477	C₂²×C₈₃	1	1	yes	characteristic
625	#476	C₂²×C₈₃	1	1	yes	characteristic
626	#475	C₂²×C₈₃	1	1	yes	characteristic
627	#475	C₂²×C₈₃	1	1	yes	characteristic
628	#475	C₂²×C₈₃	1	2	yes	—
629	#475	C₂²×C₈₃	1	2	yes	—
630	#474	C₂²×C₈₃	1	1	yes	characteristic
631	#474	C₂²×C₈₃	1	1	yes	characteristic
632	#470	C₂²×C₈₃	1	2	yes	—
633	#468	C₂²×C₈₃	1	2	yes	—
634	#467	C₂²×C₈₃	1	2	yes	—
635	#467	C₂²×C₈₃	1	2	yes	—
636	#467	C₂²×C₈₃	1	2	yes	—
637	#465	C₂²×C₈₃	1	2	yes	—
638	#464	C₂²×C₈₃	1	2	yes	—
639	#464	C₂²×C₈₃	1	2	yes	—
640	#462	C₂²×C₈₃	1	1	yes	characteristic
641	#462	C₂²×C₈₃	1	1	yes	characteristic
642	#462	C₂²×C₈₃	1	1	yes	characteristic
643	#462	C₂²×C₈₃	1	2	yes	—
644	#461	C₂²×C₈₃	1	1	yes	characteristic
645	#452	C₂²×C₈₃	1	1	yes	characteristic
646	#452	C₂²×C₈₃	1	1	yes	characteristic
647	#451	C₂²×C₈₃	1	2	yes	—
648	#451	C₂²×C₈₃	1	2	yes	—
649	#446	C₂²×C₈₃	1	1	yes	characteristic
650	C₈×Q₈	C₂²×C₈₃	1	1	yes	characteristic
651	#441	C₂²×C₈₃	1	2	yes	—
652	#441	C₂²×C₈₃	1	2	yes	—
653	C₄×Q₁₆	C₂²×C₈₃	1	1	yes	characteristic
654	C₄×Q₁₆	C₂²×C₈₃	1	2	yes	—
655	C₄×Q₁₆	C₂²×C₈₃	1	1	yes	characteristic
656	C₄×Q₁₆	C₂²×C₈₃	1	2	yes	—
657	C₄×SD₁₆	C₂²×C₈₃	1	1	yes	characteristic
658	C₄×SD₁₆	C₂²×C₈₃	1	1	yes	characteristic
659	#436	C₂²×C₈₃	1	1	yes	characteristic
660	#435	C₂²×C₈₃	1	2	yes	—
661	C₈×D₄	C₂²×C₈₃	1	1	yes	characteristic
662	C₈×D₄	C₂²×C₈₃	1	2	yes	—
663	#433	C₂²×C₈₃	1	2	yes	—
664	#431	C₂²×C₈₃	1	1	yes	characteristic
665	#428	C₂²×C₈₃	1	2	yes	—
666	#427	C₂²×C₈₃	1	2	yes	—
667	#427	C₂²×C₈₃	1	2	yes	—
668	#424	C₂²×C₈₃	1	2	yes	—
669	C₂×C₄⋊C₈	C₂²×C₈₃	1	1	yes	characteristic
670	#419	C₂²×C₈₃	1	2	yes	—
671	#416	C₂²×C₈₃	1	2	yes	—
672	C₂×#103	C₂²×C₈₃	1	2	yes	—
673	C₂×#41	C₂³×C₈₃	1	1	yes	characteristic
674	C₂²×Q₈	C₂³×C₈₃	1	2	yes	—
675	C₂×Q₁₆	C₂³×C₈₃	1	1	yes	characteristic
676	C₂×Q₁₆	C₂³×C₈₃	1	1	yes	characteristic
677	C₂×Q₁₆	C₂³×C₈₃	1	2	yes	—
678	C₂×Q₁₆	C₂³×C₈₃	1	2	yes	—
679	C₂×SD₁₆	C₂³×C₈₃	1	1	yes	characteristic
680	C₂×SD₁₆	C₂³×C₈₃	1	1	yes	characteristic
681	C₂×M₁₆	C₂³×C₈₃	1	2	yes	—
682	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
683	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
684	C₄⋊Q₈	—	2	1	no	—
685	C₄⋊Q₈	—	2	1	no	—
686	C₄⋊Q₈	—	2	1	no	—
687	C₄⋊Q₈	—	2	2	no	—
688	C₄⋊Q₈	—	2	2	no	—
689	C₄⋊Q₈	—	2	1	no	—
690	C₄⋊Q₈	—	2	2	no	—
691	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
692	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
693	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
694	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
695	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
696	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
697	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
698	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
699	#126	—	2	2	no	—
700	#126	—	2	2	no	—
701	#126	—	2	2	no	—
702	#126	—	2	2	no	—
703	#126	—	2	2	no	—
704	#126	—	2	2	no	—
705	#126	—	2	2	no	—
706	#126	—	2	2	no	—
707	#126	—	2	2	no	—
708	#126	—	2	2	no	—
709	#126	D₄×C₈₃	1	2	yes	—
710	#125	—	2	2	no	—
711	#125	—	2	2	no	—
712	#125	—	2	2	no	—
713	#125	—	2	1	no	—
714	#125	—	2	2	no	—
715	#125	—	2	2	no	—
716	#125	—	2	1	no	—
717	#125	—	2	1	no	—
718	#125	D₄×C₈₃	1	1	yes	characteristic
719	#125	C₂³×C₈₃	1	2	yes	—
720	#125	C₂³×C₈₃	1	2	yes	—
721	#124	—	2	2	no	—
722	#124	—	2	1	no	—
723	#124	—	2	2	no	—
724	#124	—	2	2	no	—
725	#124	—	2	2	no	—
726	#124	—	2	2	no	—
727	#124	D₄×C₈₃	1	1	yes	characteristic
728	#124	C₂³×C₈₃	1	2	yes	—
729	#123	—	2	2	no	—
730	#123	—	2	2	no	—
731	#123	D₄×C₈₃	1	2	yes	—
732	C₂²⋊Q₈	—	2	1	no	—
733	C₂²⋊Q₈	—	2	1	no	—
734	C₂²⋊Q₈	—	2	1	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	2	no	—
742	C₂²⋊Q₈	—	2	2	no	—
743	C₂²⋊Q₈	D₄×C₈₃	1	1	yes	characteristic
744	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
745	C₂²⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
746	C₂²⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
747	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
748	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
749	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
750	#121	—	2	1	no	—
751	#121	—	2	2	no	—
752	#121	D₄×C₈₃	1	1	yes	characteristic
753	#121	C₂³×C₈₃	1	2	yes	—
754	C₄×Q₈	—	2	1	no	—
755	C₄×Q₈	—	2	1	no	—
756	C₄×Q₈	—	2	2	no	—
757	C₄×Q₈	—	2	2	no	—
758	C₄×Q₈	—	2	2	no	—
759	C₄×Q₈	—	2	2	no	—
760	C₄×Q₈	—	2	1	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	C₂³×C₈₃	1	1	yes	characteristic
767	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
768	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
769	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
770	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
771	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
772	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
773	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
774	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
775	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
776	C₄×D₄	—	2	1	no	—
777	C₄×D₄	—	2	1	no	—
778	C₄×D₄	—	2	1	no	—
779	C₄×D₄	—	2	1	no	—
780	C₄×D₄	—	2	2	no	—
781	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
782	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
783	C₄×D₄	C₂³×C₈₃	1	2	yes	—
784	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
785	#117	—	2	1	no	—
786	#117	—	2	1	no	—
787	#117	—	2	1	no	—
788	#117	—	2	1	no	—
789	#117	—	2	2	no	—
790	#117	—	2	2	no	—
791	#117	—	2	2	no	—
792	#117	—	2	1	no	—
793	#117	C₂³×C₈₃	1	1	yes	characteristic
794	#117	C₂³×C₈₃	1	2	yes	—
795	#117	C₂³×C₈₃	1	2	yes	—
796	#117	C₂³×C₈₃	1	2	yes	—
797	#117	C₂³×C₈₃	1	2	yes	—
798	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
799	C₂×C₄²	—	2	1	no	—
800	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
801	#107	C₂³×C₈₃	1	2	yes	—
802	#107	C₂³×C₈₃	1	2	yes	—
803	#107	C₂³×C₈₃	1	2	yes	—
804	#107	C₂³×C₈₃	1	2	yes	—
805	#107	C₂³×C₈₃	1	2	yes	—
806	#107	C₂³×C₈₃	1	1	yes	characteristic
807	#107	C₂³×C₈₃	1	1	yes	characteristic
808	#107	C₂³×C₈₃	1	2	yes	—
809	#106	C₂³×C₈₃	1	1	yes	characteristic
810	#106	C₂³×C₈₃	1	2	yes	—
811	#106	C₂³×C₈₃	1	2	yes	—
812	#106	C₂³×C₈₃	1	2	yes	—
813	#106	C₂³×C₈₃	1	1	yes	characteristic
814	#106	C₂³×C₈₃	1	2	yes	—
815	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
816	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
817	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
818	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
819	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
820	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
821	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
822	#103	C₂³×C₈₃	1	1	yes	characteristic
823	#103	C₂³×C₈₃	1	2	yes	—
824	#103	C₂³×C₈₃	1	2	yes	—
825	#103	C₂³×C₈₃	1	2	yes	—
826	#103	C₂³×C₈₃	1	2	yes	—
827	#103	C₂³×C₈₃	1	1	yes	characteristic
828	#103	C₂³×C₈₃	1	2	yes	—
829	#103	C₂³×C₈₃	1	2	yes	—
830	#103	C₂³×C₈₃	1	1	yes	characteristic
831	#103	C₂³×C₈₃	1	1	yes	characteristic
832	#103	C₂³×C₈₃	1	2	yes	—
833	#103	C₂³×C₈₃	1	1	yes	characteristic
834	#103	C₂³×C₈₃	1	1	yes	characteristic
835	#103	C₂³×C₈₃	1	2	yes	—
836	#103	C₂³×C₈₃	1	2	yes	—
837	#103	C₂³×C₈₃	1	2	yes	—
838	#102	C₂³×C₈₃	1	2	yes	—
839	#102	C₂³×C₈₃	1	2	yes	—
840	#102	C₂³×C₈₃	1	1	yes	characteristic
841	#102	C₂³×C₈₃	1	1	yes	characteristic
842	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
843	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
844	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
845	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
846	#97	C₂³×C₈₃	1	2	yes	—
847	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
848	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
849	C₄×C₈	C₂³×C₈₃	1	2	yes	—
850	#41	—	2	2	no	—
851	#41	—	4	1	no	—
852	C₂×Q₈	—	2	1	no	—
853	C₂×Q₈	—	2	2	no	—
854	C₂×Q₈	—	2	1	no	—
855	C₂×Q₈	—	2	1	no	—
856	C₂×Q₈	—	2	1	no	—
857	C₂×Q₈	—	2	2	no	—
858	C₂×Q₈	—	2	2	no	—
859	C₂×Q₈	—	2	4	no	—
860	C₂×Q₈	—	4	2	no	—
861	C₂×Q₈	C₂×D₄×C₈₃	1	1	yes	characteristic
862	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
863	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
864	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
865	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
866	C₂×D₄	—	2	1	no	—
867	C₂×D₄	—	2	2	no	—
868	C₂×D₄	C₂×D₄×C₈₃	1	1	yes	characteristic
869	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
870	C₂×D₄	C₂⁴×C₈₃	1	1	yes	characteristic
871	C₂²×C₄	—	2	2	no	—
872	C₂²×C₄	—	2	2	no	—
873	C₂²×C₄	—	2	1	no	—
874	C₂²×C₄	—	2	1	no	—
875	C₂²×C₄	—	2	1	no	—
876	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
877	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
878	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
879	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
880	Q₁₆	—	2	2	no	—
881	Q₁₆	—	2	2	no	—
882	Q₁₆	—	4	2	no	—
883	Q₁₆	—	4	2	no	—
884	SD₁₆	—	4	1	no	—
885	SD₁₆	—	4	1	no	—
886	M₁₆	—	4	2	no	—
887	C₂×C₈	—	4	2	no	—
888	C₂×C₈	—	4	2	no	—
889	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
890	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
891	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
892	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
893	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
894	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	1	no	—
897	C₄⋊C₄	—	2	1	no	—
898	C₄⋊C₄	—	2	1	no	—
899	C₄⋊C₄	—	2	1	no	—
900	C₄⋊C₄	—	2	1	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
926	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
927	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
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	C₂⁴×C₈₃	1	2	yes	—
932	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
933	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
934	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
935	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
936	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
937	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
938	C₂²⋊C₄	—	2	2	no	—
939	C₂²⋊C₄	—	2	2	no	—
940	C₂²⋊C₄	—	2	1	no	—
941	C₂²⋊C₄	—	2	1	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	1	no	—
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	—	2	2	no	—
947	C₂²⋊C₄	—	2	2	no	—
948	C₂²⋊C₄	—	2	1	no	—
949	C₂²⋊C₄	—	2	1	no	—
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	—	2	2	no	—
952	C₂²⋊C₄	—	2	2	no	—
953	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
954	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
955	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
956	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
957	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
958	C₄²	—	2	1	no	—
959	C₄²	—	2	1	no	—
960	C₄²	—	2	1	no	—
961	C₄²	—	2	2	no	—
962	C₄²	—	2	2	no	—
963	C₄²	—	2	2	no	—
964	C₄²	—	2	2	no	—
965	C₄²	—	2	2	no	—
966	C₄²	—	2	1	no	—
967	C₄²	—	2	1	no	—
968	C₄²	—	2	2	no	—
969	C₄²	—	2	2	no	—
970	C₄²	—	2	2	no	—
971	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
972	C₄²	C₂×D₄×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	1	yes	characteristic
976	C₂³	—	2	1	no	—
977	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
978	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
979	Q₈	—	2	2	no	—
980	Q₈	—	2	1	no	—
981	Q₈	—	2	1	no	—
982	Q₈	—	2	1	no	—
983	Q₈	—	2	2	no	—
984	Q₈	—	2	1	no	—
985	Q₈	—	2	1	no	—
986	Q₈	—	2	2	no	—
987	Q₈	—	4	4	no	—
988	Q₈	—	4	2	no	—
989	Q₈	—	8	1	no	—
990	Q₈	—	8	1	no	—
991	Q₈	—	8	1	no	—
992	Q₈	—	8	2	no	—
993	Q₈	—	8	2	no	—
994	Q₈	2₋¹⁺⁴×C₈₃	1	2	yes	—
995	D₄	—	2	2	no	—
996	D₄	—	2	1	no	—
997	D₄	—	2	1	no	—
998	D₄	—	4	2	no	—
999	D₄	—	4	2	no	—
1000	D₄	—	8	2	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	4	1	no	—
1018	C₂×C₄	—	4	2	no	—
1019	C₂×C₄	—	4	4	no	—
1020	C₂×C₄	—	4	2	no	—
1021	C₂×C₄	—	8	1	no	—
1022	C₂×C₄	—	8	2	no	—
1023	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1024	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1025	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
1026	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
1027	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
1028	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1029	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1030	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1031	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
1032	C₈	—	2	1	no	—
1033	C₈	—	2	1	no	—
1034	C₈	—	2	1	no	—
1035	C₈	—	2	2	no	—
1036	C₈	—	2	2	no	—
1037	C₈	—	2	1	no	—
1038	C₂²	—	2	1	no	—
1039	C₂²	—	2	2	no	—
1040	C₂²	—	2	1	no	—
1041	C₂²	—	2	2	no	—
1042	C₂²	—	2	2	no	—
1043	C₂²	—	2	1	no	—
1044	C₂²	—	4	1	no	—
1045	C₂²	—	4	1	no	—
1046	C₂²	—	4	1	no	—
1047	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
1048	C₄	—	2	1	no	—
1049	C₄	—	2	2	no	—
1050	C₄	—	2	1	no	—
1051	C₄	—	2	1	no	—
1052	C₄	—	2	2	no	—
1053	C₄	—	2	1	no	—
1054	C₄	—	2	2	no	—
1055	C₄	—	2	2	no	—
1056	C₄	—	4	1	no	—
1057	C₄	—	4	2	no	—
1058	C₄	—	4	1	no	—
1059	C₄	—	4	1	no	—
1060	C₄	—	4	2	no	—
1061	C₄	—	4	2	no	—
1062	C₄	—	4	1	no	—
1063	C₄	—	4	2	no	—
1064	C₄	—	4	1	no	—
1065	C₄	—	4	1	no	—
1066	C₄	#578×C₈₃	1	2	yes	—
1067	C₄	C₂×2₋¹⁺⁴×C₈₃	1	1	yes	characteristic
1068	C₄	#585×C₈₃	1	1	yes	characteristic
1069	C₂	—	4	1	no	—
1070	C₂	—	4	2	no	—
1071	C₂	—	8	1	no	—
1072	C₂	C₈₃×#3489	1	1	yes	characteristic
1073	C₂	C₂×#578×C₈₃	1	1	yes	characteristic
1074	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×#3518	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×#3555	C₂	semidirect
3. C₈₃×#3387	C₂	semidirect
4. Q₈×Q₁₆×C₈₃	C₂	semidirect
5. C₈₃×#3369	C₂	semidirect
6. C₈₃×#3364	C₂	semidirect
7. C₈₃×#3357	C₂	semidirect
8. C₈₃×#3349	C₂	semidirect
9. C₈₃×#3342	C₂	semidirect
10. C₈₃×#3340	C₂	semidirect
11. C₈₃×#3328	C₂	semidirect
12. C₈₃×#3313	C₂	semidirect
13. C₈₃×#3300	C₂	semidirect
14. C₈₃×#3299	C₂	semidirect
15. C₈₃×#3258	C₂	semidirect
16. C₈₃×#3249	C₂	semidirect
17. C₈₃×#3243	C₂	semidirect
18. C₈₃×#3231	C₂	semidirect
19. C₈₃×#3127	C₂	semidirect
20. C₈₃×#3107	C₂	semidirect
21. C₈₃×#3082	C₂	semidirect
22. C₈₃×#3076	C₂	semidirect
23. C₈₃×#2994	C₂	semidirect
531. #62220	C₈₃	direct (N × H)
538. #3555	C₂×C₈₃	semidirect
540. #3387	C₂×C₈₃	semidirect
541. Q₈×Q₁₆	C₂×C₈₃	semidirect
542. #3369	C₂×C₈₃	semidirect
543. #3364	C₂×C₈₃	semidirect
544. #3357	C₂×C₈₃	semidirect
545. #3349	C₂×C₈₃	semidirect
546. #3342	C₂×C₈₃	semidirect
547. #3340	C₂×C₈₃	semidirect
548. #3328	C₂×C₈₃	semidirect
549. #3313	C₂×C₈₃	semidirect
550. #3300	C₂×C₈₃	semidirect
551. #3299	C₂×C₈₃	semidirect
552. #3258	C₂×C₈₃	semidirect
553. #3249	C₂×C₈₃	semidirect
554. #3243	C₂×C₈₃	semidirect
555. #3231	C₂×C₈₃	semidirect
556. #3127	C₂×C₈₃	semidirect
557. #3107	C₂×C₈₃	semidirect
558. #3082	C₂×C₈₃	semidirect
559. #3076	C₂×C₈₃	semidirect
560. #2994	C₂×C₈₃	semidirect
561. C₈₃	#62220	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×#3555	2
C₈₃×#3518	2
C₈₃×#3387	2
Q₈×Q₁₆×C₈₃	2
C₈₃×#3369	2
C₈₃×#3364	2
C₈₃×#3357	2
C₈₃×#3349	2
C₈₃×#3342	2
C₈₃×#3340	2
C₈₃×#3328	2
C₈₃×#3313	2
C₈₃×#3300	2
C₈₃×#3299	2
C₈₃×#3258	2
C₈₃×#3249	2
C₈₃×#3243	2
C₈₃×#3231	2
C₈₃×#3127	2
C₈₃×#3107	2
C₈₃×#3082	2
C₈₃×#3076	2
C₈₃×#2994	2
#62220	83

Subgroups — C83×#62220 #35290044

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#62220 #35290044