Subgroups — C₈₃×#61858 #35289682

Order 21248.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1074 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×#3503	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×#3387	C₂	1	2	yes	maximal, complemented
6	C₈₃×#3384	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₃×#3381	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈×SD₁₆×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₃×#3376	C₂	1	2	yes	maximal, complemented
10	C₈₃×#3374	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₃×#3369	C₂	1	2	yes	maximal, complemented
12	C₈₃×#3367	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₃×#3364	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₃×#3359	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#3244	C₂	1	2	yes	maximal, complemented
16	C₈₃×#3242	C₂	1	2	yes	maximal, complemented
17	C₈₃×#3239	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₃×#3229	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₃×#3125	C₂	1	2	yes	maximal
20	C₈₃×#3120	C₂	1	2	yes	maximal, complemented
21	C₈₃×#3116	C₂	1	1	yes	maximal, characteristic, complemented
22	C₈₃×#3102	C₂	1	1	yes	maximal, characteristic
23	C₈₃×#2985	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	2	yes	—
27	#557×C₈₃	C₂²	1	1	yes	characteristic
28	#557×C₈₃	C₂²	1	2	yes	—
29	#557×C₈₃	C₂²	1	1	yes	characteristic
30	#557×C₈₃	C₂²	1	1	yes	characteristic
31	#556×C₈₃	—	2	1	no	—
32	#556×C₈₃	C₂²	1	1	yes	characteristic
33	#556×C₈₃	C₂²	1	2	yes	—
34	#554×C₈₃	—	2	2	no	—
35	#554×C₈₃	C₂²	1	1	yes	characteristic
36	#554×C₈₃	C₂²	1	2	yes	—
37	#552×C₈₃	—	2	1	no	—
38	D₄×Q₈×C₈₃	—	2	1	no	—
39	D₄×Q₈×C₈₃	—	2	1	no	—
40	D₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
41	D₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
42	#544×C₈₃	—	2	1	no	—
43	#544×C₈₃	—	2	2	no	—
44	#544×C₈₃	C₂²	1	2	yes	—
45	#542×C₈₃	C₂²	1	2	yes	—
46	#541×C₈₃	—	2	1	no	—
47	#541×C₈₃	—	2	2	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	C₂×C₄⋊Q₈×C₈₃	—	2	1	no	—
53	C₂×C₄⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
54	#529×C₈₃	C₂²	1	1	yes	characteristic
55	#520×C₈₃	C₂²	1	2	yes	—
56	C₄×#41×C₈₃	C₂²	1	1	yes	characteristic
57	#501×C₈₃	C₂²	1	2	yes	—
58	#501×C₈₃	C₂²	1	2	yes	—
59	#501×C₈₃	C₂²	1	2	yes	—
60	#499×C₈₃	C₂²	1	2	yes	—
61	#498×C₈₃	C₂²	1	1	yes	characteristic
62	#498×C₈₃	C₂²	1	2	yes	—
63	#498×C₈₃	C₂²	1	1	yes	characteristic
64	#491×C₈₃	C₂²	1	2	yes	—
65	#489×C₈₃	C₂²	1	2	yes	—
66	#489×C₈₃	C₂²	1	2	yes	—
67	#488×C₈₃	C₂²	1	2	yes	—
68	#487×C₈₃	C₂²	1	1	yes	characteristic
69	#487×C₈₃	C₂²	1	2	yes	—
70	#487×C₈₃	C₂²	1	1	yes	characteristic
71	#485×C₈₃	C₂²	1	1	yes	characteristic
72	#485×C₈₃	C₂²	1	2	yes	—
73	#484×C₈₃	C₂²	1	2	yes	—
74	#483×C₈₃	C₂²	1	2	yes	—
75	#483×C₈₃	C₂²	1	2	yes	—
76	#482×C₈₃	C₂²	1	1	yes	characteristic
77	#481×C₈₃	C₂²	1	2	yes	—
78	#479×C₈₃	C₂²	1	1	yes	characteristic
79	#479×C₈₃	C₂²	1	2	yes	—
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	1	yes	characteristic
84	#478×C₈₃	C₂²	1	2	yes	—
85	#478×C₈₃	C₂²	1	2	yes	—
86	#477×C₈₃	C₂²	1	2	yes	—
87	#477×C₈₃	C₂²	1	1	yes	characteristic
88	#476×C₈₃	C₂²	1	2	yes	—
89	#476×C₈₃	C₂²	1	1	yes	characteristic
90	#476×C₈₃	C₂²	1	2	yes	—
91	#475×C₈₃	C₂²	1	1	yes	characteristic
92	#475×C₈₃	C₂²	1	2	yes	—
93	#475×C₈₃	C₂²	1	2	yes	—
94	#475×C₈₃	C₂²	1	2	yes	—
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	1	yes	characteristic
100	#464×C₈₃	C₂²	1	1	yes	characteristic
101	#464×C₈₃	C₂²	1	2	yes	—
102	#463×C₈₃	C₂²	1	1	yes	characteristic
103	#463×C₈₃	C₂²	1	2	yes	—
104	#462×C₈₃	C₂²	1	1	yes	characteristic
105	#462×C₈₃	C₂²	1	2	yes	—
106	#461×C₈₃	C₂²	1	1	yes	characteristic
107	#461×C₈₃	C₂²	1	2	yes	—
108	#452×C₈₃	C₂²	1	1	yes	characteristic
109	#452×C₈₃	C₂²	1	2	yes	—
110	#449×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	#446×C₈₃	C₂²	1	2	yes	—
115	C₈×Q₈×C₈₃	C₂²	1	1	yes	characteristic
116	C₈×Q₈×C₈₃	C₂²	1	1	yes	characteristic
117	#442×C₈₃	C₂²	1	2	yes	—
118	#441×C₈₃	C₂²	1	2	yes	—
119	#441×C₈₃	C₂²	1	2	yes	—
120	#441×C₈₃	C₂²	1	2	yes	—
121	#440×C₈₃	C₂²	1	2	yes	—
122	#440×C₈₃	C₂²	1	2	yes	—
123	C₄×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic
124	C₄×Q₁₆×C₈₃	C₂²	1	2	yes	—
125	C₄×SD₁₆×C₈₃	C₂²	1	1	yes	characteristic
126	C₄×SD₁₆×C₈₃	C₂²	1	1	yes	characteristic
127	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	—
128	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	—
129	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	—
130	C₄×D₈×C₈₃	C₂²	1	1	yes	characteristic
131	#433×C₈₃	C₂²	1	2	yes	—
132	#433×C₈₃	C₂²	1	2	yes	—
133	#432×C₈₃	C₂²	1	1	yes	characteristic
134	#431×C₈₃	C₂²	1	1	yes	characteristic
135	C₂×#41×C₈₃	C₂³	1	1	yes	characteristic
136	C₂²×Q₈×C₈₃	—	2	1	no	—
137	C₂²×Q₈×C₈₃	—	2	1	no	—
138	C₂²×Q₈×C₈₃	—	2	1	no	—
139	C₂×Q₁₆×C₈₃	C₂³	1	1	yes	characteristic
140	C₂×Q₁₆×C₈₃	C₂³	1	2	yes	—
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×D₈×C₈₃	C₂³	1	1	yes	characteristic
145	C₄⋊Q₈×C₈₃	—	2	1	no	—
146	C₄⋊Q₈×C₈₃	—	2	1	no	—
147	C₄⋊Q₈×C₈₃	—	2	2	no	—
148	C₄⋊Q₈×C₈₃	—	2	2	no	—
149	C₄⋊Q₈×C₈₃	—	2	2	no	—
150	C₄⋊Q₈×C₈₃	—	2	2	no	—
151	C₄⋊Q₈×C₈₃	—	2	2	no	—
152	C₄⋊Q₈×C₈₃	—	2	2	no	—
153	C₄⋊Q₈×C₈₃	—	2	1	no	—
154	C₄⋊Q₈×C₈₃	—	2	1	no	—
155	C₄⋊Q₈×C₈₃	—	2	1	no	—
156	C₄⋊Q₈×C₈₃	D₄	1	1	yes	characteristic
157	C₄⋊Q₈×C₈₃	D₄	1	1	yes	characteristic
158	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
160	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
163	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
164	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
165	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
166	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
172	#126×C₈₃	—	2	2	no	—
173	#126×C₈₃	—	2	1	no	—
174	#125×C₈₃	—	2	2	no	—
175	#125×C₈₃	—	2	2	no	—
176	#125×C₈₃	—	2	2	no	—
177	#125×C₈₃	—	2	2	no	—
178	#125×C₈₃	—	2	2	no	—
179	#125×C₈₃	—	2	2	no	—
180	#125×C₈₃	—	2	1	no	—
181	#125×C₈₃	—	2	2	no	—
182	#125×C₈₃	—	2	2	no	—
183	#125×C₈₃	—	2	1	no	—
184	#125×C₈₃	D₄	1	2	yes	—
185	#125×C₈₃	C₂³	1	2	yes	—
186	#125×C₈₃	C₂³	1	2	yes	—
187	#125×C₈₃	C₂³	1	1	yes	characteristic
188	#125×C₈₃	C₂³	1	2	yes	—
189	#124×C₈₃	—	2	2	no	—
190	#124×C₈₃	C₂³	1	2	yes	—
191	#124×C₈₃	C₂³	1	1	yes	characteristic
192	#123×C₈₃	—	2	1	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	1	no	—
199	C₂²⋊Q₈×C₈₃	—	2	1	no	—
200	C₂²⋊Q₈×C₈₃	—	2	1	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	—	2	2	no	—
206	C₂²⋊Q₈×C₈₃	—	2	2	no	—
207	C₂²⋊Q₈×C₈₃	—	2	2	no	—
208	C₂²⋊Q₈×C₈₃	—	2	2	no	—
209	C₂²⋊Q₈×C₈₃	D₄	1	1	yes	characteristic
210	C₂²⋊Q₈×C₈₃	D₄	1	1	yes	characteristic
211	C₂²⋊Q₈×C₈₃	D₄	1	2	yes	—
212	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
213	C₂²⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
214	#121×C₈₃	C₂³	1	1	yes	characteristic
215	C₄×Q₈×C₈₃	—	2	2	no	—
216	C₄×Q₈×C₈₃	—	2	1	no	—
217	C₄×Q₈×C₈₃	—	2	1	no	—
218	C₄×Q₈×C₈₃	—	2	1	no	—
219	C₄×Q₈×C₈₃	—	2	1	no	—
220	C₄×Q₈×C₈₃	—	2	2	no	—
221	C₄×Q₈×C₈₃	—	2	1	no	—
222	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
223	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
226	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
227	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
228	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
229	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
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×D₄×C₈₃	—	2	1	no	—
235	C₄×D₄×C₈₃	—	2	1	no	—
236	C₄×D₄×C₈₃	—	2	1	no	—
237	C₄×D₄×C₈₃	—	2	2	no	—
238	C₄×D₄×C₈₃	—	2	2	no	—
239	C₄×D₄×C₈₃	C₂³	1	2	yes	—
240	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₈₃	C₂³	1	2	yes	—
243	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₈₃	C₂³	1	2	yes	—
245	#117×C₈₃	—	2	1	no	—
246	#117×C₈₃	—	2	2	no	—
247	#117×C₈₃	—	2	2	no	—
248	#117×C₈₃	—	2	1	no	—
249	#117×C₈₃	—	2	1	no	—
250	#117×C₈₃	—	2	1	no	—
251	#117×C₈₃	C₂³	1	1	yes	characteristic
252	#117×C₈₃	C₂³	1	2	yes	—
253	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
254	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
255	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
256	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
257	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
258	C₂×C₄²×C₈₃	—	2	1	no	—
259	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
260	#107×C₈₃	C₂³	1	2	yes	—
261	#107×C₈₃	C₂³	1	2	yes	—
262	#107×C₈₃	C₂³	1	1	yes	characteristic
263	#107×C₈₃	C₂³	1	2	yes	—
264	#107×C₈₃	C₂³	1	1	yes	characteristic
265	#106×C₈₃	C₂³	1	2	yes	—
266	#106×C₈₃	C₂³	1	2	yes	—
267	#106×C₈₃	C₂³	1	1	yes	characteristic
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	2	yes	—
273	#106×C₈₃	C₂³	1	1	yes	characteristic
274	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
275	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
276	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
277	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
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	2	yes	—
283	#103×C₈₃	C₂³	1	1	yes	characteristic
284	#103×C₈₃	C₂³	1	1	yes	characteristic
285	#103×C₈₃	C₂³	1	2	yes	—
286	#103×C₈₃	C₂³	1	1	yes	characteristic
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	2	yes	—
291	#103×C₈₃	C₂³	1	2	yes	—
292	#103×C₈₃	C₂³	1	2	yes	—
293	#103×C₈₃	C₂³	1	1	yes	characteristic
294	#103×C₈₃	C₂³	1	2	yes	—
295	#102×C₈₃	C₂³	1	2	yes	—
296	#102×C₈₃	C₂³	1	1	yes	characteristic
297	#102×C₈₃	C₂³	1	2	yes	—
298	#102×C₈₃	C₂³	1	1	yes	characteristic
299	#102×C₈₃	C₂³	1	1	yes	characteristic
300	#102×C₈₃	C₂³	1	2	yes	—
301	#102×C₈₃	C₂³	1	1	yes	characteristic
302	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
303	C₂²⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
305	#97×C₈₃	C₂³	1	2	yes	—
306	#97×C₈₃	C₂³	1	2	yes	—
307	#97×C₈₃	C₂³	1	2	yes	—
308	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
313	#41×C₈₃	—	2	2	no	—
314	C₂×Q₈×C₈₃	—	2	1	no	—
315	C₂×Q₈×C₈₃	—	2	1	no	—
316	C₂×Q₈×C₈₃	—	2	1	no	—
317	C₂×Q₈×C₈₃	—	2	2	no	—
318	C₂×Q₈×C₈₃	—	2	2	no	—
319	C₂×Q₈×C₈₃	—	2	2	no	—
320	C₂×Q₈×C₈₃	—	2	2	no	—
321	C₂×Q₈×C₈₃	—	8	2	no	—
322	C₂×Q₈×C₈₃	—	8	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	2	yes	—
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	1	no	—
332	C₂×D₄×C₈₃	C₂⁴	1	1	yes	characteristic
333	C₂×D₄×C₈₃	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₈₃	—	2	1	no	—
335	C₂²×C₄×C₈₃	—	2	2	no	—
336	C₂²×C₄×C₈₃	—	2	1	no	—
337	C₂²×C₄×C₈₃	—	2	1	no	—
338	C₂²×C₄×C₈₃	—	2	1	no	—
339	C₂²×C₄×C₈₃	—	2	2	no	—
340	C₂²×C₄×C₈₃	—	2	2	no	—
341	C₂²×C₄×C₈₃	—	2	2	no	—
342	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
343	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
344	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
345	Q₁₆×C₈₃	—	2	2	no	—
346	Q₁₆×C₈₃	—	2	4	no	—
347	SD₁₆×C₈₃	—	2	2	no	—
348	SD₁₆×C₈₃	—	2	2	no	—
349	SD₁₆×C₈₃	—	2	4	no	—
350	D₈×C₈₃	—	2	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	1	yes	characteristic
354	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
355	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
356	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
357	C₄⋊C₄×C₈₃	—	2	2	no	—
358	C₄⋊C₄×C₈₃	—	2	2	no	—
359	C₄⋊C₄×C₈₃	—	2	1	no	—
360	C₄⋊C₄×C₈₃	—	2	2	no	—
361	C₄⋊C₄×C₈₃	—	2	2	no	—
362	C₄⋊C₄×C₈₃	—	2	1	no	—
363	C₄⋊C₄×C₈₃	—	2	1	no	—
364	C₄⋊C₄×C₈₃	—	2	2	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	1	no	—
369	C₄⋊C₄×C₈₃	—	2	1	no	—
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	1	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	1	yes	characteristic
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	2	yes	—
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	2	yes	—
398	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
399	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
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	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	1	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	1	no	—
414	C₂²⋊C₄×C₈₃	—	2	2	no	—
415	C₂²⋊C₄×C₈₃	—	2	2	no	—
416	C₂²⋊C₄×C₈₃	—	2	1	no	—
417	C₂²⋊C₄×C₈₃	—	2	2	no	—
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	1	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	2	yes	—
434	C₄²×C₈₃	C₂⁴	1	2	yes	—
435	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
436	C₂³×C₈₃	—	2	1	no	—
437	C₂³×C₈₃	—	2	1	no	—
438	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
439	Q₈×C₈₃	—	2	2	no	—
440	Q₈×C₈₃	—	2	2	no	—
441	Q₈×C₈₃	—	2	1	no	—
442	Q₈×C₈₃	—	2	1	no	—
443	Q₈×C₈₃	—	2	2	no	—
444	Q₈×C₈₃	—	2	2	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	—	8	2	no	—
454	Q₈×C₈₃	2₋¹⁺⁴	1	2	yes	—
455	D₄×C₈₃	—	2	4	no	—
456	D₄×C₈₃	—	2	1	no	—
457	D₄×C₈₃	—	2	1	no	—
458	D₄×C₈₃	—	2	1	no	—
459	D₄×C₈₃	—	8	1	no	—
460	D₄×C₈₃	2₋¹⁺⁴	1	2	yes	—
461	C₂×C₄×C₈₃	—	2	4	no	—
462	C₂×C₄×C₈₃	—	2	1	no	—
463	C₂×C₄×C₈₃	—	2	2	no	—
464	C₂×C₄×C₈₃	—	2	1	no	—
465	C₂×C₄×C₈₃	—	2	1	no	—
466	C₂×C₄×C₈₃	—	2	2	no	—
467	C₂×C₄×C₈₃	—	2	1	no	—
468	C₂×C₄×C₈₃	—	2	1	no	—
469	C₂×C₄×C₈₃	—	2	1	no	—
470	C₂×C₄×C₈₃	—	2	1	no	—
471	C₂×C₄×C₈₃	—	2	2	no	—
472	C₂×C₄×C₈₃	—	2	1	no	—
473	C₂×C₄×C₈₃	—	2	2	no	—
474	C₂×C₄×C₈₃	—	2	2	no	—
475	C₂×C₄×C₈₃	—	4	1	no	—
476	C₂×C₄×C₈₃	—	4	2	no	—
477	C₂×C₄×C₈₃	—	4	2	no	—
478	C₂×C₄×C₈₃	—	4	2	no	—
479	C₂×C₄×C₈₃	—	8	2	no	—
480	C₂×C₄×C₈₃	—	8	2	no	—
481	C₂×C₄×C₈₃	—	8	2	no	—
482	C₂×C₄×C₈₃	—	8	2	no	—
483	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
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	C₂⁵	1	1	yes	characteristic
493	C₈×C₈₃	—	2	1	no	—
494	C₈×C₈₃	—	2	1	no	—
495	C₈×C₈₃	—	2	1	no	—
496	C₈×C₈₃	—	2	2	no	—
497	C₈×C₈₃	—	2	1	no	—
498	C₈×C₈₃	—	2	2	no	—
499	C₂²×C₈₃	—	2	1	no	—
500	C₂²×C₈₃	—	2	1	no	—
501	C₂²×C₈₃	—	2	2	no	—
502	C₂²×C₈₃	—	2	1	no	—
503	C₂²×C₈₃	—	4	1	no	—
504	C₂²×C₈₃	—	4	1	no	—
505	C₂²×C₈₃	—	4	1	no	—
506	C₂²×C₈₃	—	4	1	no	—
507	C₂²×C₈₃	—	4	1	no	—
508	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
509	C₄×C₈₃	—	2	1	no	—
510	C₄×C₈₃	—	2	1	no	—
511	C₄×C₈₃	—	2	2	no	—
512	C₄×C₈₃	—	2	2	no	—
513	C₄×C₈₃	—	2	1	no	—
514	C₄×C₈₃	—	2	2	no	—
515	C₄×C₈₃	—	2	1	no	—
516	C₄×C₈₃	—	2	2	no	—
517	C₄×C₈₃	—	2	2	no	—
518	C₄×C₈₃	—	4	1	no	—
519	C₄×C₈₃	—	4	2	no	—
520	C₄×C₈₃	—	4	1	no	—
521	C₄×C₈₃	—	4	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	2	no	—
527	C₄×C₈₃	#577	1	2	yes	—
528	C₄×C₈₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
529	C₄×C₈₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
530	#61858	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
531	C₂×C₈₃	—	4	1	no	—
532	C₂×C₈₃	—	4	2	no	—
533	C₂×C₈₃	—	8	1	no	—
534	C₂×C₈₃	#3486	1	1	yes	characteristic
535	C₂×C₈₃	C₂×#577	1	1	yes	characteristic
536	C₂×C₈₃	#3586	1	1	yes	characteristic
537	#3555	C₂×C₈₃	1	1	yes	characteristic, complemented
538	#3503	C₂×C₈₃	1	1	yes	characteristic, complemented
539	#3388	C₂×C₈₃	1	2	yes	complemented
540	#3387	C₂×C₈₃	1	1	yes	characteristic, complemented
541	#3387	C₂×C₈₃	1	2	yes	complemented
542	#3384	C₂×C₈₃	1	1	yes	characteristic, complemented
543	#3381	C₂×C₈₃	1	1	yes	characteristic, complemented
544	Q₈×SD₁₆	C₂×C₈₃	1	1	yes	characteristic, complemented
545	#3376	C₂×C₈₃	1	2	yes	complemented
546	#3374	C₂×C₈₃	1	1	yes	characteristic, complemented
547	#3369	C₂×C₈₃	1	2	yes	complemented
548	#3367	C₂×C₈₃	1	1	yes	characteristic, complemented
549	#3364	C₂×C₈₃	1	1	yes	characteristic, complemented
550	#3359	C₂×C₈₃	1	1	yes	characteristic, complemented
551	#3244	C₂×C₈₃	1	2	yes	complemented
552	#3242	C₂×C₈₃	1	2	yes	complemented
553	#3239	C₂×C₈₃	1	1	yes	characteristic, complemented
554	#3229	C₂×C₈₃	1	1	yes	characteristic, complemented
555	#3125	C₂×C₈₃	1	2	yes	—
556	#3120	C₂×C₈₃	1	2	yes	complemented
557	#3116	C₂×C₈₃	1	1	yes	characteristic, complemented
558	#3102	C₂×C₈₃	1	1	yes	characteristic
559	#2985	C₂×C₈₃	1	1	yes	characteristic, complemented
560	C₈₃	#61858	1	1	yes	characteristic, direct product factor, Sylow
561	#563	—	2	2	no	—
562	Q₈²	C₂²×C₈₃	1	2	yes	—
563	Q₈²	C₂²×C₈₃	1	1	yes	characteristic
564	#557	C₂²×C₈₃	1	1	yes	characteristic
565	#557	C₂²×C₈₃	1	1	yes	characteristic
566	#557	C₂²×C₈₃	1	1	yes	characteristic
567	#557	C₂²×C₈₃	1	2	yes	—
568	#556	—	2	1	no	—
569	#556	C₂²×C₈₃	1	1	yes	characteristic
570	#556	C₂²×C₈₃	1	2	yes	—
571	#554	—	2	2	no	—
572	#554	C₂²×C₈₃	1	2	yes	—
573	#554	C₂²×C₈₃	1	1	yes	characteristic
574	#552	—	2	1	no	—
575	D₄×Q₈	—	2	1	no	—
576	D₄×Q₈	—	2	1	no	—
577	D₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic
578	D₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic
579	#544	—	2	1	no	—
580	#544	—	2	2	no	—
581	#544	C₂²×C₈₃	1	2	yes	—
582	#542	C₂²×C₈₃	1	2	yes	—
583	#541	—	2	1	no	—
584	#541	—	2	2	no	—
585	#541	C₂²×C₈₃	1	2	yes	—
586	#533	—	2	1	no	—
587	#533	C₂²×C₈₃	1	1	yes	characteristic
588	#533	C₂²×C₈₃	1	1	yes	characteristic
589	C₂×C₄⋊Q₈	—	2	1	no	—
590	C₂×C₄⋊Q₈	C₂²×C₈₃	1	1	yes	characteristic
591	#529	C₂²×C₈₃	1	1	yes	characteristic
592	#520	C₂²×C₈₃	1	2	yes	—
593	C₄×#41	C₂²×C₈₃	1	1	yes	characteristic
594	#501	C₂²×C₈₃	1	2	yes	—
595	#501	C₂²×C₈₃	1	2	yes	—
596	#501	C₂²×C₈₃	1	2	yes	—
597	#499	C₂²×C₈₃	1	2	yes	—
598	#498	C₂²×C₈₃	1	1	yes	characteristic
599	#498	C₂²×C₈₃	1	2	yes	—
600	#498	C₂²×C₈₃	1	1	yes	characteristic
601	#491	C₂²×C₈₃	1	2	yes	—
602	#489	C₂²×C₈₃	1	2	yes	—
603	#489	C₂²×C₈₃	1	2	yes	—
604	#488	C₂²×C₈₃	1	2	yes	—
605	#487	C₂²×C₈₃	1	1	yes	characteristic
606	#487	C₂²×C₈₃	1	2	yes	—
607	#487	C₂²×C₈₃	1	1	yes	characteristic
608	#485	C₂²×C₈₃	1	1	yes	characteristic
609	#485	C₂²×C₈₃	1	2	yes	—
610	#484	C₂²×C₈₃	1	2	yes	—
611	#483	C₂²×C₈₃	1	2	yes	—
612	#483	C₂²×C₈₃	1	2	yes	—
613	#482	C₂²×C₈₃	1	1	yes	characteristic
614	#481	C₂²×C₈₃	1	2	yes	—
615	#479	C₂²×C₈₃	1	1	yes	characteristic
616	#479	C₂²×C₈₃	1	2	yes	—
617	#479	C₂²×C₈₃	1	2	yes	—
618	#479	C₂²×C₈₃	1	2	yes	—
619	#479	C₂²×C₈₃	1	2	yes	—
620	#478	C₂²×C₈₃	1	1	yes	characteristic
621	#478	C₂²×C₈₃	1	2	yes	—
622	#478	C₂²×C₈₃	1	2	yes	—
623	#477	C₂²×C₈₃	1	2	yes	—
624	#477	C₂²×C₈₃	1	1	yes	characteristic
625	#476	C₂²×C₈₃	1	2	yes	—
626	#476	C₂²×C₈₃	1	1	yes	characteristic
627	#476	C₂²×C₈₃	1	2	yes	—
628	#475	C₂²×C₈₃	1	1	yes	characteristic
629	#475	C₂²×C₈₃	1	2	yes	—
630	#475	C₂²×C₈₃	1	2	yes	—
631	#475	C₂²×C₈₃	1	2	yes	—
632	#475	C₂²×C₈₃	1	1	yes	characteristic
633	#475	C₂²×C₈₃	1	2	yes	—
634	#475	C₂²×C₈₃	1	2	yes	—
635	#474	C₂²×C₈₃	1	1	yes	characteristic
636	#474	C₂²×C₈₃	1	1	yes	characteristic
637	#464	C₂²×C₈₃	1	1	yes	characteristic
638	#464	C₂²×C₈₃	1	2	yes	—
639	#463	C₂²×C₈₃	1	1	yes	characteristic
640	#463	C₂²×C₈₃	1	2	yes	—
641	#462	C₂²×C₈₃	1	1	yes	characteristic
642	#462	C₂²×C₈₃	1	2	yes	—
643	#461	C₂²×C₈₃	1	1	yes	characteristic
644	#461	C₂²×C₈₃	1	2	yes	—
645	#452	C₂²×C₈₃	1	1	yes	characteristic
646	#452	C₂²×C₈₃	1	2	yes	—
647	#449	C₂²×C₈₃	1	1	yes	characteristic
648	#446	C₂²×C₈₃	1	1	yes	characteristic
649	#446	C₂²×C₈₃	1	2	yes	—
650	#446	C₂²×C₈₃	1	1	yes	characteristic
651	#446	C₂²×C₈₃	1	2	yes	—
652	C₈×Q₈	C₂²×C₈₃	1	1	yes	characteristic
653	C₈×Q₈	C₂²×C₈₃	1	1	yes	characteristic
654	#442	C₂²×C₈₃	1	2	yes	—
655	#441	C₂²×C₈₃	1	2	yes	—
656	#441	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	C₄×Q₁₆	C₂²×C₈₃	1	1	yes	characteristic
661	C₄×Q₁₆	C₂²×C₈₃	1	2	yes	—
662	C₄×SD₁₆	C₂²×C₈₃	1	1	yes	characteristic
663	C₄×SD₁₆	C₂²×C₈₃	1	1	yes	characteristic
664	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	—
665	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	—
666	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	—
667	C₄×D₈	C₂²×C₈₃	1	1	yes	characteristic
668	#433	C₂²×C₈₃	1	2	yes	—
669	#433	C₂²×C₈₃	1	2	yes	—
670	#432	C₂²×C₈₃	1	1	yes	characteristic
671	#431	C₂²×C₈₃	1	1	yes	characteristic
672	C₂×#41	C₂³×C₈₃	1	1	yes	characteristic
673	C₂²×Q₈	—	2	1	no	—
674	C₂²×Q₈	—	2	1	no	—
675	C₂²×Q₈	—	2	1	no	—
676	C₂×Q₁₆	C₂³×C₈₃	1	1	yes	characteristic
677	C₂×Q₁₆	C₂³×C₈₃	1	2	yes	—
678	C₂×SD₁₆	C₂³×C₈₃	1	1	yes	characteristic
679	C₂×SD₁₆	C₂³×C₈₃	1	1	yes	characteristic
680	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
681	C₂×D₈	C₂³×C₈₃	1	1	yes	characteristic
682	C₄⋊Q₈	—	2	1	no	—
683	C₄⋊Q₈	—	2	1	no	—
684	C₄⋊Q₈	—	2	2	no	—
685	C₄⋊Q₈	—	2	2	no	—
686	C₄⋊Q₈	—	2	2	no	—
687	C₄⋊Q₈	—	2	2	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	1	no	—
693	C₄⋊Q₈	D₄×C₈₃	1	1	yes	characteristic
694	C₄⋊Q₈	D₄×C₈₃	1	1	yes	characteristic
695	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
696	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
697	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
698	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
699	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
700	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
701	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
702	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
703	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
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	—	2	2	no	—
710	#126	—	2	1	no	—
711	#125	—	2	2	no	—
712	#125	—	2	2	no	—
713	#125	—	2	2	no	—
714	#125	—	2	2	no	—
715	#125	—	2	2	no	—
716	#125	—	2	2	no	—
717	#125	—	2	1	no	—
718	#125	—	2	2	no	—
719	#125	—	2	2	no	—
720	#125	—	2	1	no	—
721	#125	D₄×C₈₃	1	2	yes	—
722	#125	C₂³×C₈₃	1	1	yes	characteristic
723	#125	C₂³×C₈₃	1	2	yes	—
724	#125	C₂³×C₈₃	1	2	yes	—
725	#125	C₂³×C₈₃	1	2	yes	—
726	#124	—	2	2	no	—
727	#124	C₂³×C₈₃	1	1	yes	characteristic
728	#124	C₂³×C₈₃	1	2	yes	—
729	#123	—	2	1	no	—
730	#123	—	2	2	no	—
731	C₂²⋊Q₈	—	2	2	no	—
732	C₂²⋊Q₈	—	2	1	no	—
733	C₂²⋊Q₈	—	2	1	no	—
734	C₂²⋊Q₈	—	2	2	no	—
735	C₂²⋊Q₈	—	2	1	no	—
736	C₂²⋊Q₈	—	2	1	no	—
737	C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	—	2	2	no	—
746	C₂²⋊Q₈	D₄×C₈₃	1	1	yes	characteristic
747	C₂²⋊Q₈	D₄×C₈₃	1	1	yes	characteristic
748	C₂²⋊Q₈	D₄×C₈₃	1	2	yes	—
749	C₂²⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
750	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
751	#121	C₂³×C₈₃	1	1	yes	characteristic
752	C₄×Q₈	—	2	2	no	—
753	C₄×Q₈	—	2	1	no	—
754	C₄×Q₈	—	2	1	no	—
755	C₄×Q₈	—	2	1	no	—
756	C₄×Q₈	—	2	1	no	—
757	C₄×Q₈	—	2	2	no	—
758	C₄×Q₈	—	2	1	no	—
759	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
760	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
761	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
762	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
763	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
764	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
765	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
766	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
767	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
768	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
769	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
770	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
771	C₄×D₄	—	2	1	no	—
772	C₄×D₄	—	2	1	no	—
773	C₄×D₄	—	2	1	no	—
774	C₄×D₄	—	2	2	no	—
775	C₄×D₄	—	2	2	no	—
776	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
777	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
778	C₄×D₄	C₂³×C₈₃	1	2	yes	—
779	C₄×D₄	C₂³×C₈₃	1	2	yes	—
780	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
781	C₄×D₄	C₂³×C₈₃	1	2	yes	—
782	#117	—	2	1	no	—
783	#117	—	2	2	no	—
784	#117	—	2	2	no	—
785	#117	—	2	1	no	—
786	#117	—	2	1	no	—
787	#117	—	2	1	no	—
788	#117	C₂³×C₈₃	1	1	yes	characteristic
789	#117	C₂³×C₈₃	1	2	yes	—
790	C₂×C₄⋊C₄	—	2	1	no	—
791	C₂×C₄⋊C₄	—	2	2	no	—
792	C₂×C₄⋊C₄	—	2	2	no	—
793	C₂×C₄⋊C₄	—	2	1	no	—
794	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
795	C₂×C₄²	—	2	1	no	—
796	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
797	#107	C₂³×C₈₃	1	1	yes	characteristic
798	#107	C₂³×C₈₃	1	2	yes	—
799	#107	C₂³×C₈₃	1	1	yes	characteristic
800	#107	C₂³×C₈₃	1	2	yes	—
801	#107	C₂³×C₈₃	1	2	yes	—
802	#106	C₂³×C₈₃	1	2	yes	—
803	#106	C₂³×C₈₃	1	2	yes	—
804	#106	C₂³×C₈₃	1	1	yes	characteristic
805	#106	C₂³×C₈₃	1	2	yes	—
806	#106	C₂³×C₈₃	1	1	yes	characteristic
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	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
812	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
813	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
814	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
815	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
816	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
817	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
818	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
819	#103	C₂³×C₈₃	1	1	yes	characteristic
820	#103	C₂³×C₈₃	1	2	yes	—
821	#103	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	2	yes	—
826	#103	C₂³×C₈₃	1	1	yes	characteristic
827	#103	C₂³×C₈₃	1	2	yes	—
828	#103	C₂³×C₈₃	1	2	yes	—
829	#103	C₂³×C₈₃	1	2	yes	—
830	#103	C₂³×C₈₃	1	2	yes	—
831	#103	C₂³×C₈₃	1	2	yes	—
832	#102	C₂³×C₈₃	1	1	yes	characteristic
833	#102	C₂³×C₈₃	1	1	yes	characteristic
834	#102	C₂³×C₈₃	1	1	yes	characteristic
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	2	yes	—
839	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
840	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
841	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
842	#97	C₂³×C₈₃	1	2	yes	—
843	#97	C₂³×C₈₃	1	2	yes	—
844	#97	C₂³×C₈₃	1	2	yes	—
845	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
846	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
847	C₄×C₈	C₂³×C₈₃	1	2	yes	—
848	C₄×C₈	C₂³×C₈₃	1	2	yes	—
849	#41	—	2	2	no	—
850	#41	—	2	2	no	—
851	C₂×Q₈	—	2	1	no	—
852	C₂×Q₈	—	2	1	no	—
853	C₂×Q₈	—	2	1	no	—
854	C₂×Q₈	—	2	2	no	—
855	C₂×Q₈	—	2	2	no	—
856	C₂×Q₈	—	2	2	no	—
857	C₂×Q₈	—	2	2	no	—
858	C₂×Q₈	—	8	2	no	—
859	C₂×Q₈	—	8	2	no	—
860	C₂×Q₈	—	8	2	no	—
861	C₂×Q₈	C₂×D₄×C₈₃	1	1	yes	characteristic
862	C₂×Q₈	C₂×D₄×C₈₃	1	1	yes	characteristic
863	C₂×Q₈	C₂×D₄×C₈₃	1	2	yes	—
864	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
865	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
866	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
867	C₂×D₄	—	2	1	no	—
868	C₂×D₄	—	2	1	no	—
869	C₂×D₄	C₂⁴×C₈₃	1	1	yes	characteristic
870	C₂×D₄	C₂⁴×C₈₃	1	1	yes	characteristic
871	C₂²×C₄	—	2	1	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	—	2	2	no	—
877	C₂²×C₄	—	2	2	no	—
878	C₂²×C₄	—	2	2	no	—
879	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
880	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
881	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
882	Q₁₆	—	2	2	no	—
883	Q₁₆	—	2	4	no	—
884	SD₁₆	—	2	2	no	—
885	SD₁₆	—	2	2	no	—
886	SD₁₆	—	2	4	no	—
887	D₈	—	2	2	no	—
888	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
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	2	yes	—
893	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	1	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	2	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	1	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	2	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	2	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
933	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
934	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
935	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
936	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
937	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
938	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
939	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
940	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	—	2	1	no	—
943	C₂²⋊C₄	—	2	1	no	—
944	C₂²⋊C₄	—	2	1	no	—
945	C₂²⋊C₄	—	2	1	no	—
946	C₂²⋊C₄	—	2	1	no	—
947	C₂²⋊C₄	—	2	2	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	2	1	no	—
950	C₂²⋊C₄	—	2	1	no	—
951	C₂²⋊C₄	—	2	2	no	—
952	C₂²⋊C₄	—	2	2	no	—
953	C₂²⋊C₄	—	2	1	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
956	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
957	C₄²	—	2	1	no	—
958	C₄²	—	2	1	no	—
959	C₄²	—	2	1	no	—
960	C₄²	—	2	2	no	—
961	C₄²	—	2	2	no	—
962	C₄²	—	2	2	no	—
963	C₄²	—	2	1	no	—
964	C₄²	—	2	2	no	—
965	C₄²	—	2	2	no	—
966	C₄²	—	2	2	no	—
967	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
968	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
969	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
970	C₄²	C₂⁴×C₈₃	1	2	yes	—
971	C₄²	C₂⁴×C₈₃	1	2	yes	—
972	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
973	C₂³	—	2	1	no	—
974	C₂³	—	2	1	no	—
975	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
976	Q₈	—	2	2	no	—
977	Q₈	—	2	2	no	—
978	Q₈	—	2	1	no	—
979	Q₈	—	2	1	no	—
980	Q₈	—	2	2	no	—
981	Q₈	—	2	1	no	—
982	Q₈	—	2	2	no	—
983	Q₈	—	4	2	no	—
984	Q₈	—	4	2	no	—
985	Q₈	—	4	2	no	—
986	Q₈	—	8	2	no	—
987	Q₈	—	8	2	no	—
988	Q₈	—	8	2	no	—
989	Q₈	—	8	1	no	—
990	Q₈	—	8	2	no	—
991	Q₈	2₋¹⁺⁴×C₈₃	1	2	yes	—
992	D₄	—	2	4	no	—
993	D₄	—	2	1	no	—
994	D₄	—	2	1	no	—
995	D₄	—	2	1	no	—
996	D₄	—	8	1	no	—
997	D₄	2₋¹⁺⁴×C₈₃	1	2	yes	—
998	C₂×C₄	—	2	4	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	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	2	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	4	1	no	—
1013	C₂×C₄	—	4	2	no	—
1014	C₂×C₄	—	4	2	no	—
1015	C₂×C₄	—	4	2	no	—
1016	C₂×C₄	—	8	2	no	—
1017	C₂×C₄	—	8	2	no	—
1018	C₂×C₄	—	8	2	no	—
1019	C₂×C₄	—	8	2	no	—
1020	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1021	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
1022	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1023	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1024	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
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	1	yes	characteristic
1028	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1029	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
1030	C₈	—	2	1	no	—
1031	C₈	—	2	1	no	—
1032	C₈	—	2	1	no	—
1033	C₈	—	2	2	no	—
1034	C₈	—	2	1	no	—
1035	C₈	—	2	2	no	—
1036	C₂²	—	2	1	no	—
1037	C₂²	—	2	1	no	—
1038	C₂²	—	2	1	no	—
1039	C₂²	—	2	2	no	—
1040	C₂²	—	4	1	no	—
1041	C₂²	—	4	1	no	—
1042	C₂²	—	4	1	no	—
1043	C₂²	—	4	1	no	—
1044	C₂²	—	4	1	no	—
1045	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
1046	C₄	—	2	1	no	—
1047	C₄	—	2	2	no	—
1048	C₄	—	2	2	no	—
1049	C₄	—	2	1	no	—
1050	C₄	—	2	1	no	—
1051	C₄	—	2	2	no	—
1052	C₄	—	2	2	no	—
1053	C₄	—	2	1	no	—
1054	C₄	—	2	2	no	—
1055	C₄	—	4	1	no	—
1056	C₄	—	4	1	no	—
1057	C₄	—	4	2	no	—
1058	C₄	—	4	2	no	—
1059	C₄	—	4	1	no	—
1060	C₄	—	4	2	no	—
1061	C₄	—	4	1	no	—
1062	C₄	—	4	2	no	—
1063	C₄	—	4	1	no	—
1064	C₄	#577×C₈₃	1	2	yes	—
1065	C₄	C₂×2₋¹⁺⁴×C₈₃	1	1	yes	characteristic
1066	C₄	C₂×2₋¹⁺⁴×C₈₃	1	1	yes	characteristic
1067	C₂	—	4	1	no	—
1068	C₂	—	4	2	no	—
1069	C₂	—	8	1	no	—
1070	C₂	C₈₃×#3486	1	1	yes	characteristic
1071	C₂	C₂×#577×C₈₃	1	1	yes	characteristic
1072	C₂	C₈₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₃
prime radical	#449×C₈₃	C₂²
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
1. C₈₃×#3555	C₂	semidirect
2. C₈₃×#3503	C₂	semidirect
3. C₈₃×#3388	C₂	semidirect
4. C₈₃×#3387	C₂	semidirect
5. C₈₃×#3387	C₂	semidirect
6. C₈₃×#3384	C₂	semidirect
7. C₈₃×#3381	C₂	semidirect
8. Q₈×SD₁₆×C₈₃	C₂	semidirect
9. C₈₃×#3376	C₂	semidirect
10. C₈₃×#3374	C₂	semidirect
11. C₈₃×#3369	C₂	semidirect
12. C₈₃×#3367	C₂	semidirect
13. C₈₃×#3364	C₂	semidirect
14. C₈₃×#3359	C₂	semidirect
15. C₈₃×#3244	C₂	semidirect
16. C₈₃×#3242	C₂	semidirect
17. C₈₃×#3239	C₂	semidirect
18. C₈₃×#3229	C₂	semidirect
20. C₈₃×#3120	C₂	semidirect
21. C₈₃×#3116	C₂	semidirect
23. C₈₃×#2985	C₂	semidirect
530. #61858	C₈₃	direct (N × H)
537. #3555	C₂×C₈₃	semidirect
538. #3503	C₂×C₈₃	semidirect
539. #3388	C₂×C₈₃	semidirect
540. #3387	C₂×C₈₃	semidirect
541. #3387	C₂×C₈₃	semidirect
542. #3384	C₂×C₈₃	semidirect
543. #3381	C₂×C₈₃	semidirect
544. Q₈×SD₁₆	C₂×C₈₃	semidirect
545. #3376	C₂×C₈₃	semidirect
546. #3374	C₂×C₈₃	semidirect
547. #3369	C₂×C₈₃	semidirect
548. #3367	C₂×C₈₃	semidirect
549. #3364	C₂×C₈₃	semidirect
550. #3359	C₂×C₈₃	semidirect
551. #3244	C₂×C₈₃	semidirect
552. #3242	C₂×C₈₃	semidirect
553. #3239	C₂×C₈₃	semidirect
554. #3229	C₂×C₈₃	semidirect
556. #3120	C₂×C₈₃	semidirect
557. #3116	C₂×C₈₃	semidirect
559. #2985	C₂×C₈₃	semidirect
560. C₈₃	#61858	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×#3503	2
C₈₃×#3388	2
C₈₃×#3387	2
C₈₃×#3384	2
C₈₃×#3381	2
Q₈×SD₁₆×C₈₃	2
C₈₃×#3376	2
C₈₃×#3374	2
C₈₃×#3369	2
C₈₃×#3367	2
C₈₃×#3364	2
C₈₃×#3359	2
C₈₃×#3244	2
C₈₃×#3242	2
C₈₃×#3239	2
C₈₃×#3229	2
C₈₃×#3125	2
C₈₃×#3120	2
C₈₃×#3116	2
C₈₃×#3102	2
C₈₃×#2985	2
#61858	83

Subgroups — C83×#61858 #35289682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#61858 #35289682