Subgroups — C₈₃×#62192 #35290016

Order 21248.

1626 conjugacy classes of subgroups.

The subgroup lattice has 1064 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
2	C₈₃×#3523	C₂	1	1	yes	maximal, characteristic
3	C₈₃×#3387	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₃×#3383	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₃×#3374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₃×#3363	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₃×#3356	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₃×#3352	C₂	1	2	yes	maximal, complemented
9	C₈₃×#3349	C₂	1	2	yes	maximal, complemented
10	C₈₃×#3342	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₃×#3328	C₂	1	2	yes	maximal, complemented
12	C₈₃×#3328	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₃×#3312	C₂	1	2	yes	maximal, complemented
14	C₈₃×#3299	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#3261	C₂	1	2	yes	maximal, complemented
16	C₈₃×#3255	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₃×#3242	C₂	1	2	yes	maximal, complemented
18	C₈₃×#3231	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₃×#3127	C₂	1	2	yes	maximal, complemented
20	C₈₃×#3104	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₃×#3082	C₂	1	2	yes	maximal, complemented
22	C₈₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
23	C₈₃×#2993	C₂	1	1	yes	maximal, characteristic
24	#563×C₈₃	—	2	2	no	—
25	Q₈²×C₈₃	C₂²	1	1	yes	characteristic
26	#557×C₈₃	—	2	1	no	—
27	#557×C₈₃	—	2	1	no	—
28	#557×C₈₃	C₂²	1	1	yes	characteristic
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	—	2	1	no	—
33	#556×C₈₃	C₂²	1	1	yes	characteristic
34	#556×C₈₃	C₂²	1	2	yes	—
35	#556×C₈₃	C₂²	1	1	yes	characteristic
36	#554×C₈₃	C₂²	1	1	yes	characteristic
37	#552×C₈₃	—	2	2	no	—
38	#552×C₈₃	C₂²	1	2	yes	—
39	#552×C₈₃	C₂²	1	2	yes	—
40	D₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
41	D₄×Q₈×C₈₃	C₂²	1	2	yes	—
42	#544×C₈₃	C₂²	1	2	yes	—
43	#542×C₈₃	—	2	1	no	—
44	#541×C₈₃	—	2	2	no	—
45	#541×C₈₃	—	2	2	no	—
46	#541×C₈₃	—	2	1	no	—
47	#541×C₈₃	C₂²	1	2	yes	—
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	C₂×C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
57	#501×C₈₃	C₂²	1	2	yes	—
58	#500×C₈₃	C₂²	1	1	yes	characteristic
59	#499×C₈₃	C₂²	1	2	yes	—
60	#498×C₈₃	C₂²	1	1	yes	characteristic
61	#491×C₈₃	C₂²	1	2	yes	—
62	#487×C₈₃	C₂²	1	1	yes	characteristic
63	#487×C₈₃	C₂²	1	2	yes	—
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	2	yes	—
70	#485×C₈₃	C₂²	1	2	yes	—
71	#484×C₈₃	C₂²	1	2	yes	—
72	#484×C₈₃	C₂²	1	1	yes	characteristic
73	#484×C₈₃	C₂²	1	1	yes	characteristic
74	#483×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	#479×C₈₃	C₂²	1	2	yes	—
81	#479×C₈₃	C₂²	1	2	yes	—
82	#479×C₈₃	C₂²	1	2	yes	—
83	#477×C₈₃	C₂²	1	1	yes	characteristic
84	#477×C₈₃	C₂²	1	1	yes	characteristic
85	#477×C₈₃	C₂²	1	1	yes	characteristic
86	#477×C₈₃	C₂²	1	2	yes	—
87	#477×C₈₃	C₂²	1	1	yes	characteristic
88	#475×C₈₃	C₂²	1	1	yes	characteristic
89	#475×C₈₃	C₂²	1	2	yes	—
90	#475×C₈₃	C₂²	1	1	yes	characteristic
91	#475×C₈₃	C₂²	1	2	yes	—
92	#475×C₈₃	C₂²	1	1	yes	characteristic
93	#475×C₈₃	C₂²	1	1	yes	characteristic
94	#470×C₈₃	C₂²	1	2	yes	—
95	#470×C₈₃	C₂²	1	2	yes	—
96	#470×C₈₃	C₂²	1	2	yes	—
97	#470×C₈₃	C₂²	1	2	yes	—
98	#467×C₈₃	C₂²	1	2	yes	—
99	#467×C₈₃	C₂²	1	2	yes	—
100	#462×C₈₃	C₂²	1	1	yes	characteristic
101	#462×C₈₃	C₂²	1	2	yes	—
102	#462×C₈₃	C₂²	1	1	yes	characteristic
103	#462×C₈₃	C₂²	1	2	yes	—
104	#462×C₈₃	C₂²	1	1	yes	characteristic
105	#462×C₈₃	C₂²	1	1	yes	characteristic
106	#462×C₈₃	C₂²	1	2	yes	—
107	#451×C₈₃	C₂²	1	2	yes	—
108	#451×C₈₃	C₂²	1	1	yes	characteristic
109	#451×C₈₃	C₂²	1	2	yes	—
110	#451×C₈₃	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
117	C₄×Q₁₆×C₈₃	C₂²	1	2	yes	—
118	C₄×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic
119	C₄×Q₁₆×C₈₃	C₂²	1	2	yes	—
120	C₄×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic
121	#436×C₈₃	C₂²	1	2	yes	—
122	#436×C₈₃	C₂²	1	1	yes	characteristic
123	#435×C₈₃	C₂²	1	2	yes	—
124	C₈×D₄×C₈₃	C₂²	1	1	yes	characteristic
125	#433×C₈₃	C₂²	1	2	yes	—
126	#431×C₈₃	C₂²	1	1	yes	characteristic
127	#428×C₈₃	C₂²	1	2	yes	—
128	#428×C₈₃	C₂²	1	2	yes	—
129	#427×C₈₃	C₂²	1	2	yes	—
130	#424×C₈₃	C₂²	1	2	yes	—
131	#423×C₈₃	C₂²	1	1	yes	characteristic
132	#419×C₈₃	C₂²	1	2	yes	—
133	#419×C₈₃	C₂²	1	2	yes	—
134	C₂×#103×C₈₃	C₂²	1	2	yes	—
135	C₂²×Q₈×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	1	yes	characteristic
140	C₂×Q₁₆×C₈₃	C₂³	1	2	yes	—
141	C₂×Q₁₆×C₈₃	C₂³	1	2	yes	—
142	C₂×Q₁₆×C₈₃	C₂³	1	1	yes	characteristic
143	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
144	C₂×M₁₆×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	2	yes	—
155	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
156	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
157	C₄⋊Q₈×C₈₃	C₂³	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	#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	1	no	—
173	#125×C₈₃	—	2	2	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	2	no	—
184	#125×C₈₃	—	2	1	no	—
185	#125×C₈₃	—	2	1	no	—
186	#125×C₈₃	D₄	1	1	yes	characteristic
187	#125×C₈₃	C₂³	1	2	yes	—
188	#125×C₈₃	C₂³	1	2	yes	—
189	#125×C₈₃	C₂³	1	2	yes	—
190	#124×C₈₃	—	2	1	no	—
191	#124×C₈₃	—	2	1	no	—
192	#124×C₈₃	—	2	2	no	—
193	#124×C₈₃	D₄	1	1	yes	characteristic
194	#123×C₈₃	—	2	2	no	—
195	#123×C₈₃	—	2	2	no	—
196	#123×C₈₃	D₄	1	2	yes	—
197	C₂²⋊Q₈×C₈₃	—	2	1	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	D₄	1	1	yes	characteristic
208	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
209	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
210	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
211	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
212	C₂²⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
213	C₂²⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
214	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
215	#121×C₈₃	D₄	1	1	yes	characteristic
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	1	no	—
221	C₄×Q₈×C₈₃	—	2	1	no	—
222	C₄×Q₈×C₈₃	—	2	2	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	—	2	1	no	—
229	C₄×Q₈×C₈₃	—	2	1	no	—
230	C₄×Q₈×C₈₃	—	2	1	no	—
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	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×Q₈×C₈₃	C₂³	1	1	yes	characteristic
239	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
240	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
241	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
242	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₈₃	—	2	2	no	—
244	C₄×D₄×C₈₃	—	2	1	no	—
245	C₄×D₄×C₈₃	—	2	1	no	—
246	C₄×D₄×C₈₃	C₂³	1	2	yes	—
247	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
248	#117×C₈₃	—	2	1	no	—
249	#117×C₈₃	—	2	1	no	—
250	#117×C₈₃	—	2	2	no	—
251	#117×C₈₃	—	2	2	no	—
252	#117×C₈₃	—	2	2	no	—
253	#117×C₈₃	—	2	2	no	—
254	#117×C₈₃	C₂³	1	2	yes	—
255	#117×C₈₃	C₂³	1	2	yes	—
256	#117×C₈₃	C₂³	1	2	yes	—
257	#117×C₈₃	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
259	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
266	#107×C₈₃	C₂³	1	2	yes	—
267	#107×C₈₃	C₂³	1	1	yes	characteristic
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	2	yes	—
274	#106×C₈₃	C₂³	1	2	yes	—
275	#106×C₈₃	C₂³	1	2	yes	—
276	#106×C₈₃	C₂³	1	2	yes	—
277	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
278	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
279	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
280	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
281	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
283	C₄⋊C₈×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	2	yes	—
287	#103×C₈₃	C₂³	1	2	yes	—
288	#103×C₈₃	C₂³	1	2	yes	—
289	#103×C₈₃	C₂³	1	1	yes	characteristic
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	2	yes	—
294	#103×C₈₃	C₂³	1	1	yes	characteristic
295	#103×C₈₃	C₂³	1	2	yes	—
296	#103×C₈₃	C₂³	1	2	yes	—
297	#103×C₈₃	C₂³	1	1	yes	characteristic
298	#103×C₈₃	C₂³	1	1	yes	characteristic
299	#103×C₈₃	C₂³	1	1	yes	characteristic
300	#103×C₈₃	C₂³	1	2	yes	—
301	#103×C₈₃	C₂³	1	2	yes	—
302	#103×C₈₃	C₂³	1	1	yes	characteristic
303	#103×C₈₃	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
306	C₂²⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
307	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
308	#97×C₈₃	C₂³	1	2	yes	—
309	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₈₃	C₂³	1	2	yes	—
311	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
312	C₂×Q₈×C₈₃	—	2	1	no	—
313	C₂×Q₈×C₈₃	—	2	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	2	no	—
319	C₂×Q₈×C₈₃	—	2	2	no	—
320	C₂×Q₈×C₈₃	—	2	4	no	—
321	C₂×Q₈×C₈₃	—	4	2	no	—
322	C₂×Q₈×C₈₃	—	4	1	no	—
323	C₂×Q₈×C₈₃	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
325	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
326	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
328	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
329	C₂×D₄×C₈₃	C₂×D₄	1	1	yes	characteristic
330	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
331	C₂²×C₄×C₈₃	—	2	1	no	—
332	C₂²×C₄×C₈₃	—	2	1	no	—
333	C₂²×C₄×C₈₃	—	2	2	no	—
334	C₂²×C₄×C₈₃	—	2	2	no	—
335	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
336	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
337	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
339	Q₁₆×C₈₃	—	2	2	no	—
340	Q₁₆×C₈₃	—	2	2	no	—
341	Q₁₆×C₈₃	—	4	1	no	—
342	Q₁₆×C₈₃	—	4	2	no	—
343	Q₁₆×C₈₃	—	4	2	no	—
344	Q₁₆×C₈₃	—	4	1	no	—
345	M₁₆×C₈₃	—	4	2	no	—
346	M₁₆×C₈₃	—	4	2	no	—
347	C₂×C₈×C₈₃	—	4	2	no	—
348	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
349	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
350	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
351	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
352	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
353	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
354	C₄⋊C₄×C₈₃	—	2	1	no	—
355	C₄⋊C₄×C₈₃	—	2	1	no	—
356	C₄⋊C₄×C₈₃	—	2	1	no	—
357	C₄⋊C₄×C₈₃	—	2	1	no	—
358	C₄⋊C₄×C₈₃	—	2	1	no	—
359	C₄⋊C₄×C₈₃	—	2	2	no	—
360	C₄⋊C₄×C₈₃	—	2	1	no	—
361	C₄⋊C₄×C₈₃	—	2	2	no	—
362	C₄⋊C₄×C₈₃	—	2	2	no	—
363	C₄⋊C₄×C₈₃	—	2	2	no	—
364	C₄⋊C₄×C₈₃	—	2	1	no	—
365	C₄⋊C₄×C₈₃	—	2	1	no	—
366	C₄⋊C₄×C₈₃	—	2	2	no	—
367	C₄⋊C₄×C₈₃	—	2	2	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	2	no	—
374	C₄⋊C₄×C₈₃	—	2	1	no	—
375	C₄⋊C₄×C₈₃	—	2	2	no	—
376	C₄⋊C₄×C₈₃	—	2	2	no	—
377	C₄⋊C₄×C₈₃	—	2	2	no	—
378	C₄⋊C₄×C₈₃	—	2	2	no	—
379	C₄⋊C₄×C₈₃	—	2	2	no	—
380	C₄⋊C₄×C₈₃	—	2	2	no	—
381	C₄⋊C₄×C₈₃	—	2	2	no	—
382	C₄⋊C₄×C₈₃	—	2	1	no	—
383	C₄⋊C₄×C₈₃	—	2	1	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	—	2	1	no	—
389	C₄⋊C₄×C₈₃	—	2	2	no	—
390	C₄⋊C₄×C₈₃	—	2	2	no	—
391	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
392	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
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	1	yes	characteristic
396	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
398	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
399	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
400	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
402	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
404	C₂²⋊C₄×C₈₃	—	2	2	no	—
405	C₂²⋊C₄×C₈₃	—	2	2	no	—
406	C₂²⋊C₄×C₈₃	—	2	1	no	—
407	C₂²⋊C₄×C₈₃	—	2	1	no	—
408	C₂²⋊C₄×C₈₃	—	2	2	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	2	no	—
413	C₂²⋊C₄×C₈₃	—	2	2	no	—
414	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
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	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	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	C₂²×D₄	1	2	yes	—
439	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
440	Q₈×C₈₃	—	2	2	no	—
441	Q₈×C₈₃	—	2	1	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	1	no	—
449	Q₈×C₈₃	—	2	2	no	—
450	Q₈×C₈₃	—	4	4	no	—
451	Q₈×C₈₃	—	4	2	no	—
452	Q₈×C₈₃	—	4	2	no	—
453	Q₈×C₈₃	—	4	2	no	—
454	Q₈×C₈₃	—	8	1	no	—
455	Q₈×C₈₃	—	8	1	no	—
456	Q₈×C₈₃	—	8	2	no	—
457	Q₈×C₈₃	2₋¹⁺⁴	1	2	yes	—
458	D₄×C₈₃	—	2	2	no	—
459	D₄×C₈₃	—	4	2	no	—
460	C₂×C₄×C₈₃	—	2	1	no	—
461	C₂×C₄×C₈₃	—	2	2	no	—
462	C₂×C₄×C₈₃	—	2	1	no	—
463	C₂×C₄×C₈₃	—	2	2	no	—
464	C₂×C₄×C₈₃	—	2	2	no	—
465	C₂×C₄×C₈₃	—	2	1	no	—
466	C₂×C₄×C₈₃	—	2	1	no	—
467	C₂×C₄×C₈₃	—	2	1	no	—
468	C₂×C₄×C₈₃	—	2	1	no	—
469	C₂×C₄×C₈₃	—	2	2	no	—
470	C₂×C₄×C₈₃	—	2	2	no	—
471	C₂×C₄×C₈₃	—	2	1	no	—
472	C₂×C₄×C₈₃	—	2	1	no	—
473	C₂×C₄×C₈₃	—	2	1	no	—
474	C₂×C₄×C₈₃	—	2	2	no	—
475	C₂×C₄×C₈₃	—	2	2	no	—
476	C₂×C₄×C₈₃	—	2	1	no	—
477	C₂×C₄×C₈₃	—	4	1	no	—
478	C₂×C₄×C₈₃	—	4	2	no	—
479	C₂×C₄×C₈₃	—	4	4	no	—
480	C₂×C₄×C₈₃	—	4	2	no	—
481	C₂×C₄×C₈₃	—	8	2	no	—
482	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
486	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
487	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
488	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
489	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
491	C₈×C₈₃	—	2	1	no	—
492	C₈×C₈₃	—	2	1	no	—
493	C₈×C₈₃	—	2	1	no	—
494	C₈×C₈₃	—	2	2	no	—
495	C₈×C₈₃	—	2	1	no	—
496	C₈×C₈₃	—	2	2	no	—
497	C₂²×C₈₃	—	2	1	no	—
498	C₂²×C₈₃	—	2	2	no	—
499	C₂²×C₈₃	—	2	2	no	—
500	C₂²×C₈₃	—	2	1	no	—
501	C₂²×C₈₃	—	2	1	no	—
502	C₂²×C₈₃	—	2	2	no	—
503	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
504	C₄×C₈₃	—	2	1	no	—
505	C₄×C₈₃	—	2	1	no	—
506	C₄×C₈₃	—	2	2	no	—
507	C₄×C₈₃	—	2	2	no	—
508	C₄×C₈₃	—	2	1	no	—
509	C₄×C₈₃	—	2	2	no	—
510	C₄×C₈₃	—	2	1	no	—
511	C₄×C₈₃	—	2	2	no	—
512	C₄×C₈₃	—	4	1	no	—
513	C₄×C₈₃	—	4	1	no	—
514	C₄×C₈₃	—	4	1	no	—
515	C₄×C₈₃	—	4	2	no	—
516	C₄×C₈₃	—	4	1	no	—
517	C₄×C₈₃	—	4	1	no	—
518	C₄×C₈₃	—	4	2	no	—
519	C₄×C₈₃	—	4	1	no	—
520	C₄×C₈₃	—	4	1	no	—
521	C₄×C₈₃	—	4	2	no	—
522	C₄×C₈₃	—	4	2	no	—
523	C₄×C₈₃	#578	1	2	yes	—
524	C₄×C₈₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
525	C₄×C₈₃	#585	1	1	yes	characteristic
526	#62192	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
527	C₂×C₈₃	—	4	1	no	—
528	C₂×C₈₃	—	4	2	no	—
529	C₂×C₈₃	#3489	1	1	yes	characteristic
530	C₂×C₈₃	C₂×#578	1	1	yes	characteristic
531	C₂×C₈₃	#3586	1	1	yes	characteristic
532	#3555	C₂×C₈₃	1	1	yes	characteristic
533	#3523	C₂×C₈₃	1	1	yes	characteristic
534	#3387	C₂×C₈₃	1	1	yes	characteristic, complemented
535	#3383	C₂×C₈₃	1	1	yes	characteristic, complemented
536	#3374	C₂×C₈₃	1	1	yes	characteristic, complemented
537	#3363	C₂×C₈₃	1	1	yes	characteristic, complemented
538	#3356	C₂×C₈₃	1	1	yes	characteristic, complemented
539	#3352	C₂×C₈₃	1	2	yes	complemented
540	#3349	C₂×C₈₃	1	2	yes	complemented
541	#3342	C₂×C₈₃	1	1	yes	characteristic, complemented
542	#3328	C₂×C₈₃	1	1	yes	characteristic, complemented
543	#3328	C₂×C₈₃	1	2	yes	complemented
544	#3312	C₂×C₈₃	1	2	yes	complemented
545	#3299	C₂×C₈₃	1	1	yes	characteristic, complemented
546	#3261	C₂×C₈₃	1	2	yes	complemented
547	#3255	C₂×C₈₃	1	1	yes	characteristic, complemented
548	#3242	C₂×C₈₃	1	2	yes	complemented
549	#3231	C₂×C₈₃	1	1	yes	characteristic, complemented
550	#3127	C₂×C₈₃	1	2	yes	complemented
551	#3104	C₂×C₈₃	1	1	yes	characteristic, complemented
552	#3082	C₂×C₈₃	1	2	yes	complemented
553	#3078	C₂×C₈₃	1	1	yes	characteristic, complemented
554	#2993	C₂×C₈₃	1	1	yes	characteristic
555	C₈₃	#62192	1	1	yes	characteristic, direct product factor, Sylow
556	#563	—	2	2	no	—
557	Q₈²	C₂²×C₈₃	1	1	yes	characteristic
558	#557	—	2	1	no	—
559	#557	—	2	1	no	—
560	#557	C₂²×C₈₃	1	1	yes	characteristic
561	#557	C₂²×C₈₃	1	1	yes	characteristic
562	#557	C₂²×C₈₃	1	1	yes	characteristic
563	#556	—	2	1	no	—
564	#556	—	2	1	no	—
565	#556	C₂²×C₈₃	1	1	yes	characteristic
566	#556	C₂²×C₈₃	1	2	yes	—
567	#556	C₂²×C₈₃	1	1	yes	characteristic
568	#554	C₂²×C₈₃	1	1	yes	characteristic
569	#552	—	2	2	no	—
570	#552	C₂²×C₈₃	1	2	yes	—
571	#552	C₂²×C₈₃	1	2	yes	—
572	D₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic
573	D₄×Q₈	C₂²×C₈₃	1	2	yes	—
574	#544	C₂²×C₈₃	1	2	yes	—
575	#542	—	2	1	no	—
576	#541	—	2	2	no	—
577	#541	—	2	2	no	—
578	#541	—	2	1	no	—
579	#541	C₂²×C₈₃	1	2	yes	—
580	#541	C₂²×C₈₃	1	2	yes	—
581	#533	—	2	1	no	—
582	#533	C₂²×C₈₃	1	1	yes	characteristic
583	#533	C₂²×C₈₃	1	1	yes	characteristic
584	#533	C₂²×C₈₃	1	1	yes	characteristic
585	#529	—	2	1	no	—
586	#529	C₂²×C₈₃	1	1	yes	characteristic
587	#519	C₂²×C₈₃	1	2	yes	—
588	C₂×C₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic
589	#501	C₂²×C₈₃	1	2	yes	—
590	#500	C₂²×C₈₃	1	1	yes	characteristic
591	#499	C₂²×C₈₃	1	2	yes	—
592	#498	C₂²×C₈₃	1	1	yes	characteristic
593	#491	C₂²×C₈₃	1	2	yes	—
594	#487	C₂²×C₈₃	1	2	yes	—
595	#487	C₂²×C₈₃	1	1	yes	characteristic
596	#487	C₂²×C₈₃	1	1	yes	characteristic
597	#485	C₂²×C₈₃	1	2	yes	—
598	#485	C₂²×C₈₃	1	2	yes	—
599	#485	C₂²×C₈₃	1	2	yes	—
600	#485	C₂²×C₈₃	1	2	yes	—
601	#485	C₂²×C₈₃	1	2	yes	—
602	#485	C₂²×C₈₃	1	2	yes	—
603	#484	C₂²×C₈₃	1	1	yes	characteristic
604	#484	C₂²×C₈₃	1	1	yes	characteristic
605	#484	C₂²×C₈₃	1	2	yes	—
606	#483	C₂²×C₈₃	1	2	yes	—
607	#479	C₂²×C₈₃	1	2	yes	—
608	#479	C₂²×C₈₃	1	2	yes	—
609	#479	C₂²×C₈₃	1	2	yes	—
610	#479	C₂²×C₈₃	1	2	yes	—
611	#479	C₂²×C₈₃	1	2	yes	—
612	#479	C₂²×C₈₃	1	2	yes	—
613	#479	C₂²×C₈₃	1	2	yes	—
614	#479	C₂²×C₈₃	1	2	yes	—
615	#477	C₂²×C₈₃	1	1	yes	characteristic
616	#477	C₂²×C₈₃	1	1	yes	characteristic
617	#477	C₂²×C₈₃	1	1	yes	characteristic
618	#477	C₂²×C₈₃	1	2	yes	—
619	#477	C₂²×C₈₃	1	1	yes	characteristic
620	#475	C₂²×C₈₃	1	1	yes	characteristic
621	#475	C₂²×C₈₃	1	2	yes	—
622	#475	C₂²×C₈₃	1	1	yes	characteristic
623	#475	C₂²×C₈₃	1	2	yes	—
624	#475	C₂²×C₈₃	1	1	yes	characteristic
625	#475	C₂²×C₈₃	1	1	yes	characteristic
626	#470	C₂²×C₈₃	1	2	yes	—
627	#470	C₂²×C₈₃	1	2	yes	—
628	#470	C₂²×C₈₃	1	2	yes	—
629	#470	C₂²×C₈₃	1	2	yes	—
630	#467	C₂²×C₈₃	1	2	yes	—
631	#467	C₂²×C₈₃	1	2	yes	—
632	#462	C₂²×C₈₃	1	1	yes	characteristic
633	#462	C₂²×C₈₃	1	2	yes	—
634	#462	C₂²×C₈₃	1	1	yes	characteristic
635	#462	C₂²×C₈₃	1	1	yes	characteristic
636	#462	C₂²×C₈₃	1	2	yes	—
637	#462	C₂²×C₈₃	1	1	yes	characteristic
638	#462	C₂²×C₈₃	1	2	yes	—
639	#451	C₂²×C₈₃	1	1	yes	characteristic
640	#451	C₂²×C₈₃	1	2	yes	—
641	#451	C₂²×C₈₃	1	2	yes	—
642	#451	C₂²×C₈₃	1	1	yes	characteristic
643	#446	C₂²×C₈₃	1	1	yes	characteristic
644	C₈×Q₈	C₂²×C₈₃	1	1	yes	characteristic
645	#441	C₂²×C₈₃	1	2	yes	—
646	#441	C₂²×C₈₃	1	2	yes	—
647	C₄×Q₁₆	C₂²×C₈₃	1	1	yes	characteristic
648	C₄×Q₁₆	C₂²×C₈₃	1	2	yes	—
649	C₄×Q₁₆	C₂²×C₈₃	1	1	yes	characteristic
650	C₄×Q₁₆	C₂²×C₈₃	1	2	yes	—
651	C₄×Q₁₆	C₂²×C₈₃	1	1	yes	characteristic
652	C₄×Q₁₆	C₂²×C₈₃	1	1	yes	characteristic
653	#436	C₂²×C₈₃	1	2	yes	—
654	#436	C₂²×C₈₃	1	1	yes	characteristic
655	#435	C₂²×C₈₃	1	2	yes	—
656	C₈×D₄	C₂²×C₈₃	1	1	yes	characteristic
657	#433	C₂²×C₈₃	1	2	yes	—
658	#431	C₂²×C₈₃	1	1	yes	characteristic
659	#428	C₂²×C₈₃	1	2	yes	—
660	#428	C₂²×C₈₃	1	2	yes	—
661	#427	C₂²×C₈₃	1	2	yes	—
662	#424	C₂²×C₈₃	1	2	yes	—
663	#423	C₂²×C₈₃	1	1	yes	characteristic
664	#419	C₂²×C₈₃	1	2	yes	—
665	#419	C₂²×C₈₃	1	2	yes	—
666	C₂×#103	C₂²×C₈₃	1	2	yes	—
667	C₂²×Q₈	C₂³×C₈₃	1	1	yes	characteristic
668	C₂²×Q₈	C₂³×C₈₃	1	2	yes	—
669	C₂×Q₁₆	C₂³×C₈₃	1	1	yes	characteristic
670	C₂×Q₁₆	C₂³×C₈₃	1	1	yes	characteristic
671	C₂×Q₁₆	C₂³×C₈₃	1	1	yes	characteristic
672	C₂×Q₁₆	C₂³×C₈₃	1	2	yes	—
673	C₂×Q₁₆	C₂³×C₈₃	1	1	yes	characteristic
674	C₂×Q₁₆	C₂³×C₈₃	1	2	yes	—
675	C₂×M₁₆	C₂³×C₈₃	1	2	yes	—
676	C₂×M₁₆	C₂³×C₈₃	1	2	yes	—
677	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
678	C₄⋊Q₈	—	2	1	no	—
679	C₄⋊Q₈	—	2	1	no	—
680	C₄⋊Q₈	—	2	1	no	—
681	C₄⋊Q₈	—	2	2	no	—
682	C₄⋊Q₈	—	2	2	no	—
683	C₄⋊Q₈	—	2	1	no	—
684	C₄⋊Q₈	—	2	2	no	—
685	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
686	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
687	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
688	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
689	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
690	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
691	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
692	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
693	#126	—	2	2	no	—
694	#126	—	2	2	no	—
695	#126	—	2	2	no	—
696	#126	—	2	2	no	—
697	#126	—	2	2	no	—
698	#126	—	2	2	no	—
699	#126	—	2	2	no	—
700	#126	—	2	2	no	—
701	#126	—	2	2	no	—
702	#126	—	2	2	no	—
703	#126	D₄×C₈₃	1	2	yes	—
704	#125	—	2	1	no	—
705	#125	—	2	2	no	—
706	#125	—	2	2	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	1	no	—
713	#125	—	2	2	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	#125	C₂³×C₈₃	1	2	yes	—
722	#124	—	2	1	no	—
723	#124	—	2	1	no	—
724	#124	—	2	2	no	—
725	#124	D₄×C₈₃	1	1	yes	characteristic
726	#123	—	2	2	no	—
727	#123	—	2	2	no	—
728	#123	D₄×C₈₃	1	2	yes	—
729	C₂²⋊Q₈	—	2	1	no	—
730	C₂²⋊Q₈	—	2	1	no	—
731	C₂²⋊Q₈	—	2	1	no	—
732	C₂²⋊Q₈	—	2	1	no	—
733	C₂²⋊Q₈	—	2	2	no	—
734	C₂²⋊Q₈	—	2	2	no	—
735	C₂²⋊Q₈	—	2	2	no	—
736	C₂²⋊Q₈	—	2	2	no	—
737	C₂²⋊Q₈	—	2	2	no	—
738	C₂²⋊Q₈	—	2	2	no	—
739	C₂²⋊Q₈	D₄×C₈₃	1	1	yes	characteristic
740	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
741	C₂²⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
742	C₂²⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
743	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
744	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
745	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
746	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
747	#121	D₄×C₈₃	1	1	yes	characteristic
748	C₄×Q₈	—	2	1	no	—
749	C₄×Q₈	—	2	1	no	—
750	C₄×Q₈	—	2	2	no	—
751	C₄×Q₈	—	2	2	no	—
752	C₄×Q₈	—	2	1	no	—
753	C₄×Q₈	—	2	1	no	—
754	C₄×Q₈	—	2	2	no	—
755	C₄×Q₈	—	2	1	no	—
756	C₄×Q₈	—	2	1	no	—
757	C₄×Q₈	—	2	1	no	—
758	C₄×Q₈	—	2	1	no	—
759	C₄×Q₈	—	2	1	no	—
760	C₄×Q₈	—	2	1	no	—
761	C₄×Q₈	—	2	1	no	—
762	C₄×Q₈	—	2	1	no	—
763	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
764	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
765	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
766	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
767	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
768	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
769	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
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	1	yes	characteristic
775	C₄×D₄	—	2	2	no	—
776	C₄×D₄	—	2	1	no	—
777	C₄×D₄	—	2	1	no	—
778	C₄×D₄	C₂³×C₈₃	1	2	yes	—
779	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
780	#117	—	2	1	no	—
781	#117	—	2	1	no	—
782	#117	—	2	2	no	—
783	#117	—	2	2	no	—
784	#117	—	2	2	no	—
785	#117	—	2	2	no	—
786	#117	C₂³×C₈₃	1	2	yes	—
787	#117	C₂³×C₈₃	1	2	yes	—
788	#117	C₂³×C₈₃	1	2	yes	—
789	#117	C₂³×C₈₃	1	2	yes	—
790	C₂×C₄⋊C₄	—	2	1	no	—
791	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
792	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
793	C₂×C₄²	—	2	1	no	—
794	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
795	#107	C₂³×C₈₃	1	1	yes	characteristic
796	#107	C₂³×C₈₃	1	2	yes	—
797	#107	C₂³×C₈₃	1	2	yes	—
798	#107	C₂³×C₈₃	1	1	yes	characteristic
799	#107	C₂³×C₈₃	1	2	yes	—
800	#107	C₂³×C₈₃	1	1	yes	characteristic
801	#107	C₂³×C₈₃	1	1	yes	characteristic
802	#107	C₂³×C₈₃	1	2	yes	—
803	#106	C₂³×C₈₃	1	2	yes	—
804	#106	C₂³×C₈₃	1	2	yes	—
805	#106	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	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
810	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
811	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
812	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
813	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
814	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
815	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
816	#103	C₂³×C₈₃	1	1	yes	characteristic
817	#103	C₂³×C₈₃	1	2	yes	—
818	#103	C₂³×C₈₃	1	2	yes	—
819	#103	C₂³×C₈₃	1	2	yes	—
820	#103	C₂³×C₈₃	1	1	yes	characteristic
821	#103	C₂³×C₈₃	1	2	yes	—
822	#103	C₂³×C₈₃	1	2	yes	—
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	1	yes	characteristic
827	#103	C₂³×C₈₃	1	1	yes	characteristic
828	#103	C₂³×C₈₃	1	1	yes	characteristic
829	#103	C₂³×C₈₃	1	1	yes	characteristic
830	#103	C₂³×C₈₃	1	2	yes	—
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	2	yes	—
835	#103	C₂³×C₈₃	1	2	yes	—
836	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
837	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
838	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
839	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
840	#97	C₂³×C₈₃	1	2	yes	—
841	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
842	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
843	C₄×C₈	C₂³×C₈₃	1	2	yes	—
844	C₂×Q₈	—	2	1	no	—
845	C₂×Q₈	—	2	1	no	—
846	C₂×Q₈	—	2	1	no	—
847	C₂×Q₈	—	2	2	no	—
848	C₂×Q₈	—	2	1	no	—
849	C₂×Q₈	—	2	1	no	—
850	C₂×Q₈	—	2	2	no	—
851	C₂×Q₈	—	2	2	no	—
852	C₂×Q₈	—	2	4	no	—
853	C₂×Q₈	—	4	2	no	—
854	C₂×Q₈	—	4	1	no	—
855	C₂×Q₈	C₂×D₄×C₈₃	1	1	yes	characteristic
856	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
857	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
858	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
859	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
860	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
861	C₂×D₄	C₂×D₄×C₈₃	1	1	yes	characteristic
862	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
863	C₂²×C₄	—	2	1	no	—
864	C₂²×C₄	—	2	1	no	—
865	C₂²×C₄	—	2	2	no	—
866	C₂²×C₄	—	2	2	no	—
867	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
868	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
869	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
870	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
871	Q₁₆	—	2	2	no	—
872	Q₁₆	—	2	2	no	—
873	Q₁₆	—	4	1	no	—
874	Q₁₆	—	4	2	no	—
875	Q₁₆	—	4	2	no	—
876	Q₁₆	—	4	1	no	—
877	M₁₆	—	4	2	no	—
878	M₁₆	—	4	2	no	—
879	C₂×C₈	—	4	2	no	—
880	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
881	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
882	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
883	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
884	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
885	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
886	C₄⋊C₄	—	2	1	no	—
887	C₄⋊C₄	—	2	1	no	—
888	C₄⋊C₄	—	2	1	no	—
889	C₄⋊C₄	—	2	1	no	—
890	C₄⋊C₄	—	2	1	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	1	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	1	no	—
897	C₄⋊C₄	—	2	1	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	1	no	—
901	C₄⋊C₄	—	2	1	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	1	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	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	1	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
924	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
925	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
926	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
927	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
928	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
929	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
930	C₄⋊C₄	C₂⁴×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	C₂²⋊C₄	—	2	2	no	—
937	C₂²⋊C₄	—	2	2	no	—
938	C₂²⋊C₄	—	2	1	no	—
939	C₂²⋊C₄	—	2	1	no	—
940	C₂²⋊C₄	—	2	2	no	—
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	2	no	—
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
947	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
948	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
949	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
950	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
951	C₄²	—	2	1	no	—
952	C₄²	—	2	1	no	—
953	C₄²	—	2	1	no	—
954	C₄²	—	2	1	no	—
955	C₄²	—	2	2	no	—
956	C₄²	—	2	2	no	—
957	C₄²	—	2	2	no	—
958	C₄²	—	2	2	no	—
959	C₄²	—	2	2	no	—
960	C₄²	—	2	1	no	—
961	C₄²	—	2	1	no	—
962	C₄²	—	2	2	no	—
963	C₄²	—	2	2	no	—
964	C₄²	—	2	2	no	—
965	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
966	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
967	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
968	C₄²	C₂⁴×C₈₃	1	2	yes	—
969	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
970	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
971	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
972	Q₈	—	2	2	no	—
973	Q₈	—	2	1	no	—
974	Q₈	—	2	1	no	—
975	Q₈	—	2	1	no	—
976	Q₈	—	2	1	no	—
977	Q₈	—	2	2	no	—
978	Q₈	—	2	1	no	—
979	Q₈	—	2	1	no	—
980	Q₈	—	2	1	no	—
981	Q₈	—	2	2	no	—
982	Q₈	—	4	4	no	—
983	Q₈	—	4	2	no	—
984	Q₈	—	4	2	no	—
985	Q₈	—	4	2	no	—
986	Q₈	—	8	1	no	—
987	Q₈	—	8	1	no	—
988	Q₈	—	8	2	no	—
989	Q₈	2₋¹⁺⁴×C₈₃	1	2	yes	—
990	D₄	—	2	2	no	—
991	D₄	—	4	2	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	4	1	no	—
1010	C₂×C₄	—	4	2	no	—
1011	C₂×C₄	—	4	4	no	—
1012	C₂×C₄	—	4	2	no	—
1013	C₂×C₄	—	8	2	no	—
1014	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1015	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1016	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1017	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
1018	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
1019	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
1020	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1021	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1022	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
1023	C₈	—	2	1	no	—
1024	C₈	—	2	1	no	—
1025	C₈	—	2	1	no	—
1026	C₈	—	2	2	no	—
1027	C₈	—	2	1	no	—
1028	C₈	—	2	2	no	—
1029	C₂²	—	2	1	no	—
1030	C₂²	—	2	2	no	—
1031	C₂²	—	2	1	no	—
1032	C₂²	—	2	2	no	—
1033	C₂²	—	2	2	no	—
1034	C₂²	—	2	1	no	—
1035	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
1036	C₄	—	2	1	no	—
1037	C₄	—	2	2	no	—
1038	C₄	—	2	1	no	—
1039	C₄	—	2	1	no	—
1040	C₄	—	2	2	no	—
1041	C₄	—	2	2	no	—
1042	C₄	—	2	1	no	—
1043	C₄	—	2	2	no	—
1044	C₄	—	4	2	no	—
1045	C₄	—	4	2	no	—
1046	C₄	—	4	1	no	—
1047	C₄	—	4	1	no	—
1048	C₄	—	4	1	no	—
1049	C₄	—	4	2	no	—
1050	C₄	—	4	1	no	—
1051	C₄	—	4	1	no	—
1052	C₄	—	4	2	no	—
1053	C₄	—	4	1	no	—
1054	C₄	—	4	1	no	—
1055	C₄	#578×C₈₃	1	2	yes	—
1056	C₄	C₂×2₋¹⁺⁴×C₈₃	1	1	yes	characteristic
1057	C₄	#585×C₈₃	1	1	yes	characteristic
1058	C₂	—	4	1	no	—
1059	C₂	—	4	2	no	—
1060	C₂	C₈₃×#3489	1	1	yes	characteristic
1061	C₂	C₂×#578×C₈₃	1	1	yes	characteristic
1062	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	#121×C₈₃	D₄
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
3. C₈₃×#3387	C₂	semidirect
4. C₈₃×#3383	C₂	semidirect
5. C₈₃×#3374	C₂	semidirect
6. C₈₃×#3363	C₂	semidirect
7. C₈₃×#3356	C₂	semidirect
8. C₈₃×#3352	C₂	semidirect
9. C₈₃×#3349	C₂	semidirect
10. C₈₃×#3342	C₂	semidirect
11. C₈₃×#3328	C₂	semidirect
12. C₈₃×#3328	C₂	semidirect
13. C₈₃×#3312	C₂	semidirect
14. C₈₃×#3299	C₂	semidirect
15. C₈₃×#3261	C₂	semidirect
16. C₈₃×#3255	C₂	semidirect
17. C₈₃×#3242	C₂	semidirect
18. C₈₃×#3231	C₂	semidirect
19. C₈₃×#3127	C₂	semidirect
20. C₈₃×#3104	C₂	semidirect
21. C₈₃×#3082	C₂	semidirect
22. C₈₃×#3078	C₂	semidirect
526. #62192	C₈₃	direct (N × H)
534. #3387	C₂×C₈₃	semidirect
535. #3383	C₂×C₈₃	semidirect
536. #3374	C₂×C₈₃	semidirect
537. #3363	C₂×C₈₃	semidirect
538. #3356	C₂×C₈₃	semidirect
539. #3352	C₂×C₈₃	semidirect
540. #3349	C₂×C₈₃	semidirect
541. #3342	C₂×C₈₃	semidirect
542. #3328	C₂×C₈₃	semidirect
543. #3328	C₂×C₈₃	semidirect
544. #3312	C₂×C₈₃	semidirect
545. #3299	C₂×C₈₃	semidirect
546. #3261	C₂×C₈₃	semidirect
547. #3255	C₂×C₈₃	semidirect
548. #3242	C₂×C₈₃	semidirect
549. #3231	C₂×C₈₃	semidirect
550. #3127	C₂×C₈₃	semidirect
551. #3104	C₂×C₈₃	semidirect
552. #3082	C₂×C₈₃	semidirect
553. #3078	C₂×C₈₃	semidirect
555. C₈₃	#62192	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×#3523	2
C₈₃×#3387	2
C₈₃×#3383	2
C₈₃×#3374	2
C₈₃×#3363	2
C₈₃×#3356	2
C₈₃×#3352	2
C₈₃×#3349	2
C₈₃×#3342	2
C₈₃×#3328	2
C₈₃×#3312	2
C₈₃×#3299	2
C₈₃×#3261	2
C₈₃×#3255	2
C₈₃×#3242	2
C₈₃×#3231	2
C₈₃×#3127	2
C₈₃×#3104	2
C₈₃×#3082	2
C₈₃×#3078	2
C₈₃×#2993	2
#62192	83

Subgroups — C83×#62192 #35290016

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#62192 #35290016