Subgroups — C₈₃×#62216 #35290040

Order 21248.

1706 conjugacy classes of subgroups.

The subgroup lattice has 1106 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×#3514	C₂	1	1	yes	maximal, characteristic
3	C₈₃×#3386	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×SD₁₆×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₃×#3375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₃×#3365	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₃×#3356	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₃×#3348	C₂	1	2	yes	maximal, complemented
9	C₈₃×#3342	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₃×#3340	C₂	1	2	yes	maximal, complemented
11	C₈₃×#3324	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₃×#3311	C₂	1	2	yes	maximal, complemented
13	C₈₃×#3296	C₂	1	2	yes	maximal, complemented
14	C₈₃×#3295	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#3258	C₂	1	2	yes	maximal, complemented
16	C₈₃×#3246	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₃×#3244	C₂	1	2	yes	maximal, complemented
18	C₈₃×#3228	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₃×#3123	C₂	1	2	yes	maximal, complemented
20	C₈₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₃×#3081	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	#559×C₈₃	C₂²	1	1	yes	characteristic
26	Q₈²×C₈₃	C₂²	1	1	yes	characteristic, complemented
27	#557×C₈₃	—	2	1	no	—
28	#557×C₈₃	C₂²	1	1	yes	characteristic, complemented
29	#556×C₈₃	—	2	1	no	—
30	#556×C₈₃	C₂²	1	1	yes	characteristic
31	#556×C₈₃	C₂²	1	1	yes	characteristic
32	#556×C₈₃	C₂²	1	2	yes	complemented
33	#555×C₈₃	C₂²	1	2	yes	—
34	#554×C₈₃	C₂²	1	1	yes	characteristic
35	#552×C₈₃	C₂²	1	2	yes	complemented
36	#551×C₈₃	—	2	2	no	—
37	D₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
38	#548×C₈₃	—	2	1	no	—
39	#546×C₈₃	—	2	1	no	—
40	#546×C₈₃	C₂²	1	2	yes	—
41	D₄²×C₈₃	C₂²	1	1	yes	characteristic
42	#544×C₈₃	C₂²	1	2	yes	complemented
43	#542×C₈₃	—	2	1	no	—
44	#542×C₈₃	C₂²	1	2	yes	—
45	#541×C₈₃	—	2	2	no	—
46	#541×C₈₃	—	2	1	no	—
47	#541×C₈₃	C₂²	1	2	yes	complemented
48	#538×C₈₃	—	2	2	no	—
49	#533×C₈₃	C₂²	1	1	yes	characteristic, complemented
50	#533×C₈₃	C₂²	1	1	yes	characteristic, complemented
51	#532×C₈₃	C₂²	1	1	yes	characteristic
52	#529×C₈₃	—	2	1	no	—
53	#529×C₈₃	C₂²	1	1	yes	characteristic
54	C₂×#124×C₈₃	—	2	1	no	—
55	#518×C₈₃	C₂²	1	2	yes	—
56	C₄×#41×C₈₃	C₂²	1	1	yes	characteristic
57	#501×C₈₃	C₂²	1	2	yes	complemented
58	#500×C₈₃	C₂²	1	1	yes	characteristic, complemented
59	#498×C₈₃	C₂²	1	2	yes	complemented
60	#498×C₈₃	C₂²	1	1	yes	characteristic, complemented
61	#489×C₈₃	C₂²	1	2	yes	complemented
62	#488×C₈₃	C₂²	1	2	yes	complemented
63	#486×C₈₃	C₂²	1	1	yes	characteristic
64	#486×C₈₃	C₂²	1	1	yes	characteristic
65	#485×C₈₃	C₂²	1	2	yes	complemented
66	#485×C₈₃	C₂²	1	1	yes	characteristic, complemented
67	#485×C₈₃	C₂²	1	2	yes	complemented
68	#485×C₈₃	C₂²	1	2	yes	complemented
69	#485×C₈₃	C₂²	1	1	yes	characteristic, complemented
70	#483×C₈₃	C₂²	1	2	yes	complemented
71	#482×C₈₃	C₂²	1	2	yes	—
72	#482×C₈₃	C₂²	1	2	yes	complemented
73	#482×C₈₃	C₂²	1	2	yes	complemented
74	#481×C₈₃	C₂²	1	2	yes	—
75	#479×C₈₃	C₂²	1	2	yes	complemented
76	#478×C₈₃	C₂²	1	2	yes	—
77	#478×C₈₃	C₂²	1	2	yes	—
78	#478×C₈₃	C₂²	1	2	yes	complemented
79	#478×C₈₃	C₂²	1	2	yes	complemented
80	#478×C₈₃	C₂²	1	2	yes	complemented
81	#477×C₈₃	C₂²	1	1	yes	characteristic, complemented
82	#477×C₈₃	C₂²	1	2	yes	complemented
83	#476×C₈₃	C₂²	1	1	yes	characteristic
84	#476×C₈₃	C₂²	1	2	yes	—
85	#476×C₈₃	C₂²	1	2	yes	complemented
86	#475×C₈₃	C₂²	1	1	yes	characteristic, complemented
87	#475×C₈₃	C₂²	1	1	yes	characteristic, complemented
88	#475×C₈₃	C₂²	1	2	yes	complemented
89	#475×C₈₃	C₂²	1	1	yes	characteristic, complemented
90	#475×C₈₃	C₂²	1	1	yes	characteristic, complemented
91	#474×C₈₃	C₂²	1	1	yes	characteristic
92	#474×C₈₃	C₂²	1	1	yes	characteristic
93	#474×C₈₃	C₂²	1	2	yes	complemented
94	#470×C₈₃	C₂²	1	2	yes	complemented
95	#468×C₈₃	C₂²	1	2	yes	—
96	#467×C₈₃	C₂²	1	2	yes	complemented
97	#465×C₈₃	C₂²	1	2	yes	—
98	#465×C₈₃	C₂²	1	2	yes	complemented
99	#465×C₈₃	C₂²	1	2	yes	complemented
100	#464×C₈₃	C₂²	1	2	yes	complemented
101	#464×C₈₃	C₂²	1	2	yes	complemented
102	#462×C₈₃	C₂²	1	1	yes	characteristic, complemented
103	#461×C₈₃	C₂²	1	1	yes	characteristic
104	#461×C₈₃	C₂²	1	2	yes	complemented
105	#460×C₈₃	C₂²	1	1	yes	characteristic
106	#460×C₈₃	C₂²	1	1	yes	characteristic
107	#452×C₈₃	C₂²	1	1	yes	characteristic
108	#452×C₈₃	C₂²	1	1	yes	characteristic
109	#450×C₈₃	C₂²	1	2	yes	—
110	#450×C₈₃	C₂²	1	2	yes	—
111	#446×C₈₃	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
113	#440×C₈₃	C₂²	1	2	yes	—
114	#440×C₈₃	C₂²	1	2	yes	complemented
115	C₄×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic, complemented
116	C₄×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic, complemented
117	C₄×SD₁₆×C₈₃	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	—
119	C₄×SD₁₆×C₈₃	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	complemented
121	#436×C₈₃	C₂²	1	1	yes	characteristic
122	#435×C₈₃	C₂²	1	2	yes	complemented
123	C₈×D₄×C₈₃	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₈₃	C₂²	1	2	yes	complemented
125	#433×C₈₃	C₂²	1	2	yes	complemented
126	#431×C₈₃	C₂²	1	1	yes	characteristic, complemented
127	#428×C₈₃	C₂²	1	2	yes	complemented
128	#427×C₈₃	C₂²	1	2	yes	complemented
129	#427×C₈₃	C₂²	1	2	yes	complemented
130	#424×C₈₃	C₂²	1	2	yes	complemented
131	C₂×C₄⋊C₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
132	#418×C₈₃	C₂²	1	2	yes	—
133	#416×C₈₃	C₂²	1	2	yes	—
134	C₂×#102×C₈₃	C₂²	1	2	yes	—
135	C₂×#41×C₈₃	—	2	1	no	—
136	C₂×#41×C₈₃	C₂³	1	1	yes	characteristic
137	C₂²×Q₈×C₈₃	—	2	1	no	—
138	C₂²×D₄×C₈₃	—	2	1	no	—
139	C₂²×D₄×C₈₃	C₂³	1	2	yes	—
140	C₂×Q₁₆×C₈₃	C₂³	1	1	yes	characteristic
141	C₂×Q₁₆×C₈₃	C₂³	1	1	yes	characteristic
142	C₂×SD₁₆×C₈₃	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₈₃	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
146	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
147	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
148	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
149	C₄⋊Q₈×C₈₃	—	2	1	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	2	yes	—
157	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
158	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
159	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
160	#127×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	D₄	1	2	yes	—
170	#125×C₈₃	—	2	2	no	—
171	#125×C₈₃	—	2	2	no	—
172	#125×C₈₃	—	2	2	no	—
173	#125×C₈₃	—	2	1	no	—
174	#125×C₈₃	—	2	2	no	—
175	#125×C₈₃	—	2	2	no	—
176	#125×C₈₃	—	2	1	no	—
177	#125×C₈₃	D₄	1	1	yes	characteristic
178	#125×C₈₃	C₂³	1	2	yes	—
179	#125×C₈₃	C₂³	1	2	yes	—
180	#124×C₈₃	—	2	1	no	—
181	#124×C₈₃	—	2	1	no	—
182	#124×C₈₃	—	2	1	no	—
183	#124×C₈₃	—	2	2	no	—
184	#124×C₈₃	—	2	2	no	—
185	#124×C₈₃	—	2	2	no	—
186	#124×C₈₃	—	2	2	no	—
187	#124×C₈₃	—	2	1	no	—
188	#124×C₈₃	D₄	1	1	yes	characteristic
189	#124×C₈₃	C₂³	1	2	yes	—
190	#123×C₈₃	—	2	2	no	—
191	#123×C₈₃	—	2	2	no	—
192	#123×C₈₃	—	2	2	no	—
193	#123×C₈₃	—	2	2	no	—
194	#123×C₈₃	D₄	1	2	yes	—
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	D₄	1	1	yes	characteristic
205	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
206	C₂²⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
207	C₂²⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
208	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
209	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
210	#121×C₈₃	—	2	2	no	—
211	#121×C₈₃	—	2	1	no	—
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	#121×C₈₃	C₂³	1	2	yes	—
217	#120×C₈₃	—	2	2	no	—
218	#120×C₈₃	—	2	2	no	—
219	C₄×Q₈×C₈₃	—	2	1	no	—
220	C₄×Q₈×C₈₃	—	2	1	no	—
221	C₄×Q₈×C₈₃	—	2	1	no	—
222	C₄×Q₈×C₈₃	—	2	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	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	1	yes	characteristic
231	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
240	C₄×D₄×C₈₃	—	2	1	no	—
241	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₈₃	C₂³	1	2	yes	—
244	C₄×D₄×C₈₃	C₂³	1	2	yes	—
245	C₄×D₄×C₈₃	C₂³	1	2	yes	—
246	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₈₃	C₂³	1	2	yes	—
248	#117×C₈₃	—	2	1	no	—
249	#117×C₈₃	—	2	2	no	—
250	#117×C₈₃	—	2	2	no	—
251	#117×C₈₃	—	2	1	no	—
252	#117×C₈₃	C₂³	1	2	yes	—
253	#117×C₈₃	C₂³	1	2	yes	—
254	#117×C₈₃	C₂³	1	1	yes	characteristic
255	#117×C₈₃	C₂³	1	2	yes	—
256	#117×C₈₃	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
258	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
259	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
260	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
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	1	yes	characteristic
267	#107×C₈₃	C₂³	1	2	yes	—
268	#107×C₈₃	C₂³	1	2	yes	—
269	#106×C₈₃	C₂³	1	2	yes	—
270	#106×C₈₃	C₂³	1	2	yes	—
271	#106×C₈₃	C₂³	1	2	yes	—
272	#106×C₈₃	C₂³	1	2	yes	—
273	#106×C₈₃	C₂³	1	2	yes	—
274	#106×C₈₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
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	#102×C₈₃	C₂³	1	2	yes	—
295	#102×C₈₃	C₂³	1	2	yes	—
296	#102×C₈₃	C₂³	1	2	yes	—
297	#102×C₈₃	C₂³	1	2	yes	—
298	#102×C₈₃	C₂³	1	1	yes	characteristic
299	#102×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	2	yes	—
303	#102×C₈₃	C₂³	1	2	yes	—
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	C₂⁴×C₈₃	—	2	2	no	—
313	#41×C₈₃	—	2	2	no	—
314	#41×C₈₃	—	4	1	no	—
315	#41×C₈₃	—	8	2	no	—
316	C₂×Q₈×C₈₃	—	2	1	no	—
317	C₂×Q₈×C₈₃	—	2	1	no	—
318	C₂×Q₈×C₈₃	—	2	1	no	—
319	C₂×Q₈×C₈₃	—	2	1	no	—
320	C₂×Q₈×C₈₃	—	2	2	no	—
321	C₂×Q₈×C₈₃	—	2	2	no	—
322	C₂×Q₈×C₈₃	—	8	2	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	1	yes	characteristic
326	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
327	C₂×D₄×C₈₃	—	2	4	no	—
328	C₂×D₄×C₈₃	—	2	1	no	—
329	C₂×D₄×C₈₃	—	2	2	no	—
330	C₂×D₄×C₈₃	—	2	2	no	—
331	C₂×D₄×C₈₃	—	2	2	no	—
332	C₂×D₄×C₈₃	—	2	1	no	—
333	C₂×D₄×C₈₃	—	2	1	no	—
334	C₂×D₄×C₈₃	—	4	2	no	—
335	C₂×D₄×C₈₃	—	8	2	no	—
336	C₂×D₄×C₈₃	C₂×D₄	1	1	yes	characteristic
337	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
338	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
339	C₂×D₄×C₈₃	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₈₃	—	2	2	no	—
341	C₂²×C₄×C₈₃	—	2	1	no	—
342	C₂²×C₄×C₈₃	—	2	1	no	—
343	C₂²×C₄×C₈₃	—	2	1	no	—
344	C₂²×C₄×C₈₃	—	2	2	no	—
345	C₂²×C₄×C₈₃	—	2	2	no	—
346	C₂²×C₄×C₈₃	—	2	2	no	—
347	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
349	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
351	Q₁₆×C₈₃	—	4	1	no	—
352	Q₁₆×C₈₃	—	4	1	no	—
353	SD₁₆×C₈₃	—	2	2	no	—
354	SD₁₆×C₈₃	—	2	2	no	—
355	SD₁₆×C₈₃	—	4	2	no	—
356	SD₁₆×C₈₃	—	4	2	no	—
357	M₁₆×C₈₃	—	4	2	no	—
358	C₂×C₈×C₈₃	—	4	2	no	—
359	C₂×C₈×C₈₃	—	4	2	no	—
360	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
362	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
363	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
365	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
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	2	no	—
373	C₄⋊C₄×C₈₃	—	2	1	no	—
374	C₄⋊C₄×C₈₃	—	2	1	no	—
375	C₄⋊C₄×C₈₃	—	2	1	no	—
376	C₄⋊C₄×C₈₃	—	2	1	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	1	no	—
387	C₄⋊C₄×C₈₃	—	2	1	no	—
388	C₄⋊C₄×C₈₃	—	2	2	no	—
389	C₄⋊C₄×C₈₃	—	2	2	no	—
390	C₄⋊C₄×C₈₃	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	C₂×D₄	1	1	yes	characteristic
394	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
395	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
396	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
397	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
398	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
399	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
400	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
401	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
403	C₂²⋊C₄×C₈₃	—	2	2	no	—
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	2	no	—
408	C₂²⋊C₄×C₈₃	—	2	1	no	—
409	C₂²⋊C₄×C₈₃	—	2	2	no	—
410	C₂²⋊C₄×C₈₃	—	2	2	no	—
411	C₂²⋊C₄×C₈₃	—	2	2	no	—
412	C₂²⋊C₄×C₈₃	—	2	1	no	—
413	C₂²⋊C₄×C₈₃	—	2	2	no	—
414	C₂²⋊C₄×C₈₃	—	2	2	no	—
415	C₂²⋊C₄×C₈₃	—	2	2	no	—
416	C₂²⋊C₄×C₈₃	—	2	2	no	—
417	C₂²⋊C₄×C₈₃	—	2	2	no	—
418	C₂²⋊C₄×C₈₃	—	2	1	no	—
419	C₂²⋊C₄×C₈₃	—	2	2	no	—
420	C₂²⋊C₄×C₈₃	—	2	2	no	—
421	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
422	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
423	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
424	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
425	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
426	C₄²×C₈₃	—	2	1	no	—
427	C₄²×C₈₃	—	2	1	no	—
428	C₄²×C₈₃	—	2	1	no	—
429	C₄²×C₈₃	—	2	2	no	—
430	C₄²×C₈₃	—	2	2	no	—
431	C₄²×C₈₃	—	2	1	no	—
432	C₄²×C₈₃	—	2	1	no	—
433	C₄²×C₈₃	—	2	2	no	—
434	C₄²×C₈₃	—	2	2	no	—
435	C₄²×C₈₃	—	2	2	no	—
436	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
437	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
438	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
439	C₄²×C₈₃	C₂⁴	1	2	yes	—
440	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
441	C₂³×C₈₃	—	2	1	no	—
442	C₂³×C₈₃	—	2	2	no	—
443	C₂³×C₈₃	—	4	4	no	—
444	C₂³×C₈₃	—	8	2	no	—
445	C₂³×C₈₃	—	8	2	no	—
446	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
447	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
448	Q₈×C₈₃	—	2	2	no	—
449	Q₈×C₈₃	—	2	1	no	—
450	Q₈×C₈₃	—	2	1	no	—
451	Q₈×C₈₃	—	2	1	no	—
452	Q₈×C₈₃	—	2	1	no	—
453	Q₈×C₈₃	—	2	1	no	—
454	Q₈×C₈₃	—	2	1	no	—
455	Q₈×C₈₃	—	4	2	no	—
456	Q₈×C₈₃	—	4	2	no	—
457	Q₈×C₈₃	—	8	1	no	—
458	Q₈×C₈₃	—	8	1	no	—
459	Q₈×C₈₃	—	8	2	no	—
460	Q₈×C₈₃	—	8	2	no	—
461	D₄×C₈₃	—	2	2	no	—
462	D₄×C₈₃	—	2	2	no	—
463	D₄×C₈₃	—	2	1	no	—
464	D₄×C₈₃	—	2	2	no	—
465	D₄×C₈₃	—	4	2	no	—
466	D₄×C₈₃	—	4	4	no	—
467	D₄×C₈₃	—	4	2	no	—
468	D₄×C₈₃	—	4	2	no	—
469	D₄×C₈₃	—	8	1	no	—
470	D₄×C₈₃	—	8	2	no	—
471	D₄×C₈₃	—	8	2	no	—
472	D₄×C₈₃	2₋¹⁺⁴	1	2	yes	—
473	C₂×C₄×C₈₃	—	2	2	no	—
474	C₂×C₄×C₈₃	—	2	2	no	—
475	C₂×C₄×C₈₃	—	2	1	no	—
476	C₂×C₄×C₈₃	—	2	1	no	—
477	C₂×C₄×C₈₃	—	2	2	no	—
478	C₂×C₄×C₈₃	—	2	1	no	—
479	C₂×C₄×C₈₃	—	2	1	no	—
480	C₂×C₄×C₈₃	—	2	1	no	—
481	C₂×C₄×C₈₃	—	2	2	no	—
482	C₂×C₄×C₈₃	—	2	1	no	—
483	C₂×C₄×C₈₃	—	2	1	no	—
484	C₂×C₄×C₈₃	—	2	1	no	—
485	C₂×C₄×C₈₃	—	2	2	no	—
486	C₂×C₄×C₈₃	—	2	2	no	—
487	C₂×C₄×C₈₃	—	2	1	no	—
488	C₂×C₄×C₈₃	—	4	1	no	—
489	C₂×C₄×C₈₃	—	4	2	no	—
490	C₂×C₄×C₈₃	—	4	2	no	—
491	C₂×C₄×C₈₃	—	8	1	no	—
492	C₂×C₄×C₈₃	—	8	2	no	—
493	C₂×C₄×C₈₃	—	8	2	no	—
494	C₂×C₄×C₈₃	—	8	2	no	—
495	C₂×C₄×C₈₃	—	8	2	no	—
496	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
498	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
500	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
501	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
505	C₈×C₈₃	—	2	1	no	—
506	C₈×C₈₃	—	2	1	no	—
507	C₈×C₈₃	—	2	2	no	—
508	C₈×C₈₃	—	2	1	no	—
509	C₈×C₈₃	—	2	2	no	—
510	C₈×C₈₃	—	2	1	no	—
511	C₂²×C₈₃	—	2	1	no	—
512	C₂²×C₈₃	—	2	2	no	—
513	C₂²×C₈₃	—	2	1	no	—
514	C₂²×C₈₃	—	2	2	no	—
515	C₂²×C₈₃	—	2	2	no	—
516	C₂²×C₈₃	—	2	1	no	—
517	C₂²×C₈₃	—	2	2	no	—
518	C₂²×C₈₃	—	4	1	no	—
519	C₂²×C₈₃	—	4	1	no	—
520	C₂²×C₈₃	—	4	2	no	—
521	C₂²×C₈₃	—	4	2	no	—
522	C₂²×C₈₃	—	4	2	no	—
523	C₂²×C₈₃	—	16	4	no	—
524	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
525	C₄×C₈₃	—	2	1	no	—
526	C₄×C₈₃	—	2	1	no	—
527	C₄×C₈₃	—	2	2	no	—
528	C₄×C₈₃	—	2	1	no	—
529	C₄×C₈₃	—	2	2	no	—
530	C₄×C₈₃	—	2	1	no	—
531	C₄×C₈₃	—	2	2	no	—
532	C₄×C₈₃	—	4	1	no	—
533	C₄×C₈₃	—	4	1	no	—
534	C₄×C₈₃	—	4	2	no	—
535	C₄×C₈₃	—	4	1	no	—
536	C₄×C₈₃	—	4	1	no	—
537	C₄×C₈₃	—	4	1	no	—
538	C₄×C₈₃	—	4	1	no	—
539	C₄×C₈₃	—	4	1	no	—
540	C₄×C₈₃	—	4	2	no	—
541	C₄×C₈₃	—	4	2	no	—
542	C₄×C₈₃	#577	1	2	yes	—
543	C₄×C₈₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
544	C₄×C₈₃	#585	1	1	yes	characteristic
545	#62216	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
546	C₂×C₈₃	—	4	1	no	—
547	C₂×C₈₃	—	4	2	no	—
548	C₂×C₈₃	—	4	2	no	—
549	C₂×C₈₃	—	8	2	no	—
550	C₂×C₈₃	#3489	1	1	yes	characteristic
551	C₂×C₈₃	C₂×#577	1	1	yes	characteristic
552	C₂×C₈₃	#3584	1	1	yes	characteristic
553	#3555	C₂×C₈₃	1	1	yes	characteristic, complemented
554	#3514	C₂×C₈₃	1	1	yes	characteristic
555	#3386	C₂×C₈₃	1	1	yes	characteristic, complemented
556	Q₈×SD₁₆	C₂×C₈₃	1	1	yes	characteristic, complemented
557	#3375	C₂×C₈₃	1	1	yes	characteristic, complemented
558	#3365	C₂×C₈₃	1	1	yes	characteristic, complemented
559	#3356	C₂×C₈₃	1	1	yes	characteristic, complemented
560	#3348	C₂×C₈₃	1	2	yes	complemented
561	#3342	C₂×C₈₃	1	1	yes	characteristic, complemented
562	#3340	C₂×C₈₃	1	2	yes	complemented
563	#3324	C₂×C₈₃	1	1	yes	characteristic, complemented
564	#3311	C₂×C₈₃	1	2	yes	complemented
565	#3296	C₂×C₈₃	1	2	yes	complemented
566	#3295	C₂×C₈₃	1	1	yes	characteristic, complemented
567	#3258	C₂×C₈₃	1	2	yes	complemented
568	#3246	C₂×C₈₃	1	1	yes	characteristic, complemented
569	#3244	C₂×C₈₃	1	2	yes	complemented
570	#3228	C₂×C₈₃	1	1	yes	characteristic, complemented
571	#3123	C₂×C₈₃	1	2	yes	complemented
572	#3107	C₂×C₈₃	1	1	yes	characteristic, complemented
573	#3081	C₂×C₈₃	1	2	yes	complemented
574	#3076	C₂×C₈₃	1	1	yes	characteristic, complemented
575	#2994	C₂×C₈₃	1	1	yes	characteristic, complemented
576	C₈₃	#62216	1	1	yes	characteristic, direct product factor, Sylow
577	#563	—	2	2	no	—
578	#559	C₂²×C₈₃	1	1	yes	characteristic
579	Q₈²	C₂²×C₈₃	1	1	yes	characteristic, complemented
580	#557	—	2	1	no	—
581	#557	C₂²×C₈₃	1	1	yes	characteristic, complemented
582	#556	—	2	1	no	—
583	#556	C₂²×C₈₃	1	1	yes	characteristic
584	#556	C₂²×C₈₃	1	1	yes	characteristic
585	#556	C₂²×C₈₃	1	2	yes	complemented
586	#555	C₂²×C₈₃	1	2	yes	—
587	#554	C₂²×C₈₃	1	1	yes	characteristic
588	#552	C₂²×C₈₃	1	2	yes	complemented
589	#551	—	2	2	no	—
590	D₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic
591	#548	—	2	1	no	—
592	#546	—	2	1	no	—
593	#546	C₂²×C₈₃	1	2	yes	—
594	D₄²	C₂²×C₈₃	1	1	yes	characteristic
595	#544	C₂²×C₈₃	1	2	yes	complemented
596	#542	—	2	1	no	—
597	#542	C₂²×C₈₃	1	2	yes	—
598	#541	—	2	2	no	—
599	#541	—	2	1	no	—
600	#541	C₂²×C₈₃	1	2	yes	complemented
601	#538	—	2	2	no	—
602	#533	C₂²×C₈₃	1	1	yes	characteristic, complemented
603	#533	C₂²×C₈₃	1	1	yes	characteristic, complemented
604	#532	C₂²×C₈₃	1	1	yes	characteristic
605	#529	—	2	1	no	—
606	#529	C₂²×C₈₃	1	1	yes	characteristic
607	C₂×#124	—	2	1	no	—
608	#518	C₂²×C₈₃	1	2	yes	—
609	C₄×#41	C₂²×C₈₃	1	1	yes	characteristic
610	#501	C₂²×C₈₃	1	2	yes	complemented
611	#500	C₂²×C₈₃	1	1	yes	characteristic, complemented
612	#498	C₂²×C₈₃	1	2	yes	complemented
613	#498	C₂²×C₈₃	1	1	yes	characteristic, complemented
614	#489	C₂²×C₈₃	1	2	yes	complemented
615	#488	C₂²×C₈₃	1	2	yes	complemented
616	#486	C₂²×C₈₃	1	1	yes	characteristic
617	#486	C₂²×C₈₃	1	1	yes	characteristic
618	#485	C₂²×C₈₃	1	1	yes	characteristic, complemented
619	#485	C₂²×C₈₃	1	2	yes	complemented
620	#485	C₂²×C₈₃	1	2	yes	complemented
621	#485	C₂²×C₈₃	1	2	yes	complemented
622	#485	C₂²×C₈₃	1	1	yes	characteristic, complemented
623	#483	C₂²×C₈₃	1	2	yes	complemented
624	#482	C₂²×C₈₃	1	2	yes	—
625	#482	C₂²×C₈₃	1	2	yes	complemented
626	#482	C₂²×C₈₃	1	2	yes	complemented
627	#481	C₂²×C₈₃	1	2	yes	—
628	#479	C₂²×C₈₃	1	2	yes	complemented
629	#478	C₂²×C₈₃	1	2	yes	—
630	#478	C₂²×C₈₃	1	2	yes	—
631	#478	C₂²×C₈₃	1	2	yes	complemented
632	#478	C₂²×C₈₃	1	2	yes	complemented
633	#478	C₂²×C₈₃	1	2	yes	complemented
634	#477	C₂²×C₈₃	1	1	yes	characteristic, complemented
635	#477	C₂²×C₈₃	1	2	yes	complemented
636	#476	C₂²×C₈₃	1	1	yes	characteristic
637	#476	C₂²×C₈₃	1	2	yes	—
638	#476	C₂²×C₈₃	1	2	yes	complemented
639	#475	C₂²×C₈₃	1	1	yes	characteristic, complemented
640	#475	C₂²×C₈₃	1	1	yes	characteristic, complemented
641	#475	C₂²×C₈₃	1	2	yes	complemented
642	#475	C₂²×C₈₃	1	1	yes	characteristic, complemented
643	#475	C₂²×C₈₃	1	1	yes	characteristic, complemented
644	#474	C₂²×C₈₃	1	1	yes	characteristic
645	#474	C₂²×C₈₃	1	1	yes	characteristic
646	#474	C₂²×C₈₃	1	2	yes	complemented
647	#470	C₂²×C₈₃	1	2	yes	complemented
648	#468	C₂²×C₈₃	1	2	yes	—
649	#467	C₂²×C₈₃	1	2	yes	complemented
650	#465	C₂²×C₈₃	1	2	yes	—
651	#465	C₂²×C₈₃	1	2	yes	complemented
652	#465	C₂²×C₈₃	1	2	yes	complemented
653	#464	C₂²×C₈₃	1	2	yes	complemented
654	#464	C₂²×C₈₃	1	2	yes	complemented
655	#462	C₂²×C₈₃	1	1	yes	characteristic, complemented
656	#461	C₂²×C₈₃	1	1	yes	characteristic
657	#461	C₂²×C₈₃	1	2	yes	complemented
658	#460	C₂²×C₈₃	1	1	yes	characteristic
659	#460	C₂²×C₈₃	1	1	yes	characteristic
660	#452	C₂²×C₈₃	1	1	yes	characteristic
661	#452	C₂²×C₈₃	1	1	yes	characteristic
662	#450	C₂²×C₈₃	1	2	yes	—
663	#450	C₂²×C₈₃	1	2	yes	—
664	#446	C₂²×C₈₃	1	1	yes	characteristic, complemented
665	C₈×Q₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
666	#440	C₂²×C₈₃	1	2	yes	—
667	#440	C₂²×C₈₃	1	2	yes	complemented
668	C₄×Q₁₆	C₂²×C₈₃	1	1	yes	characteristic, complemented
669	C₄×Q₁₆	C₂²×C₈₃	1	1	yes	characteristic, complemented
670	C₄×SD₁₆	C₂²×C₈₃	1	1	yes	characteristic
671	C₄×SD₁₆	C₂²×C₈₃	1	1	yes	characteristic
672	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	—
673	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	complemented
674	#436	C₂²×C₈₃	1	1	yes	characteristic
675	#435	C₂²×C₈₃	1	2	yes	complemented
676	C₈×D₄	C₂²×C₈₃	1	1	yes	characteristic
677	C₈×D₄	C₂²×C₈₃	1	2	yes	complemented
678	#433	C₂²×C₈₃	1	2	yes	complemented
679	#431	C₂²×C₈₃	1	1	yes	characteristic, complemented
680	#428	C₂²×C₈₃	1	2	yes	complemented
681	#427	C₂²×C₈₃	1	2	yes	complemented
682	#427	C₂²×C₈₃	1	2	yes	complemented
683	#424	C₂²×C₈₃	1	2	yes	complemented
684	C₂×C₄⋊C₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
685	#418	C₂²×C₈₃	1	2	yes	—
686	#416	C₂²×C₈₃	1	2	yes	—
687	C₂×#102	C₂²×C₈₃	1	2	yes	—
688	C₂×#41	—	2	1	no	—
689	C₂×#41	C₂³×C₈₃	1	1	yes	characteristic
690	C₂²×Q₈	—	2	1	no	—
691	C₂²×D₄	—	2	1	no	—
692	C₂²×D₄	C₂³×C₈₃	1	2	yes	—
693	C₂×Q₁₆	C₂³×C₈₃	1	1	yes	characteristic
694	C₂×Q₁₆	C₂³×C₈₃	1	1	yes	characteristic
695	C₂×SD₁₆	C₂³×C₈₃	1	1	yes	characteristic
696	C₂×SD₁₆	C₂³×C₈₃	1	1	yes	characteristic
697	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
698	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
699	C₂×M₁₆	C₂³×C₈₃	1	2	yes	—
700	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
701	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
702	C₄⋊Q₈	—	2	1	no	—
703	C₄⋊Q₈	—	2	2	no	—
704	C₄⋊Q₈	—	2	1	no	—
705	C₄⋊Q₈	—	2	2	no	—
706	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
707	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
708	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
709	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
710	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
711	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
712	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
713	#127	C₂³×C₈₃	1	1	yes	characteristic
714	#126	—	2	2	no	—
715	#126	—	2	2	no	—
716	#126	—	2	2	no	—
717	#126	—	2	2	no	—
718	#126	—	2	2	no	—
719	#126	—	2	2	no	—
720	#126	—	2	2	no	—
721	#126	—	2	2	no	—
722	#126	D₄×C₈₃	1	2	yes	—
723	#125	—	2	2	no	—
724	#125	—	2	2	no	—
725	#125	—	2	2	no	—
726	#125	—	2	1	no	—
727	#125	—	2	2	no	—
728	#125	—	2	2	no	—
729	#125	—	2	1	no	—
730	#125	D₄×C₈₃	1	1	yes	characteristic
731	#125	C₂³×C₈₃	1	2	yes	—
732	#125	C₂³×C₈₃	1	2	yes	—
733	#124	—	2	1	no	—
734	#124	—	2	1	no	—
735	#124	—	2	1	no	—
736	#124	—	2	2	no	—
737	#124	—	2	2	no	—
738	#124	—	2	2	no	—
739	#124	—	2	2	no	—
740	#124	—	2	1	no	—
741	#124	D₄×C₈₃	1	1	yes	characteristic
742	#124	C₂³×C₈₃	1	2	yes	—
743	#123	—	2	2	no	—
744	#123	—	2	2	no	—
745	#123	—	2	2	no	—
746	#123	—	2	2	no	—
747	#123	D₄×C₈₃	1	2	yes	—
748	C₂²⋊Q₈	—	2	1	no	—
749	C₂²⋊Q₈	—	2	1	no	—
750	C₂²⋊Q₈	—	2	1	no	—
751	C₂²⋊Q₈	—	2	1	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	D₄×C₈₃	1	1	yes	characteristic
758	C₂²⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
759	C₂²⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
760	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
761	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
762	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
763	#121	—	2	2	no	—
764	#121	—	2	1	no	—
765	#121	—	2	1	no	—
766	#121	—	2	2	no	—
767	#121	D₄×C₈₃	1	1	yes	characteristic
768	#121	C₂³×C₈₃	1	2	yes	—
769	#121	C₂³×C₈₃	1	2	yes	—
770	#120	—	2	2	no	—
771	#120	—	2	2	no	—
772	C₄×Q₈	—	2	1	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	2	2	no	—
776	C₄×Q₈	—	2	1	no	—
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	—	2	1	no	—
779	C₄×Q₈	—	2	1	no	—
780	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
781	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
782	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
783	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
784	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
785	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
786	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
787	C₄×D₄	—	2	1	no	—
788	C₄×D₄	—	2	1	no	—
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	2	2	no	—
791	C₄×D₄	—	2	2	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
795	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
796	C₄×D₄	C₂³×C₈₃	1	2	yes	—
797	C₄×D₄	C₂³×C₈₃	1	2	yes	—
798	C₄×D₄	C₂³×C₈₃	1	2	yes	—
799	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
800	C₄×D₄	C₂³×C₈₃	1	2	yes	—
801	#117	—	2	1	no	—
802	#117	—	2	2	no	—
803	#117	—	2	2	no	—
804	#117	—	2	1	no	—
805	#117	C₂³×C₈₃	1	1	yes	characteristic
806	#117	C₂³×C₈₃	1	2	yes	—
807	#117	C₂³×C₈₃	1	2	yes	—
808	#117	C₂³×C₈₃	1	2	yes	—
809	#117	C₂³×C₈₃	1	2	yes	—
810	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
811	C₂×C₂²⋊C₄	—	2	2	no	—
812	C₂×C₂²⋊C₄	—	2	2	no	—
813	C₂×C₂²⋊C₄	—	2	2	no	—
814	C₂×C₄²	—	2	1	no	—
815	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
816	#107	C₂³×C₈₃	1	1	yes	characteristic
817	#107	C₂³×C₈₃	1	2	yes	—
818	#107	C₂³×C₈₃	1	2	yes	—
819	#107	C₂³×C₈₃	1	2	yes	—
820	#107	C₂³×C₈₃	1	1	yes	characteristic
821	#107	C₂³×C₈₃	1	2	yes	—
822	#106	C₂³×C₈₃	1	2	yes	—
823	#106	C₂³×C₈₃	1	2	yes	—
824	#106	C₂³×C₈₃	1	2	yes	—
825	#106	C₂³×C₈₃	1	2	yes	—
826	#106	C₂³×C₈₃	1	2	yes	—
827	#106	C₂³×C₈₃	1	1	yes	characteristic
828	#106	C₂³×C₈₃	1	1	yes	characteristic
829	#106	C₂³×C₈₃	1	2	yes	—
830	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
831	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
832	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
833	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
834	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
835	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
836	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
837	#103	C₂³×C₈₃	1	2	yes	—
838	#103	C₂³×C₈₃	1	2	yes	—
839	#103	C₂³×C₈₃	1	2	yes	—
840	#103	C₂³×C₈₃	1	1	yes	characteristic
841	#103	C₂³×C₈₃	1	1	yes	characteristic
842	#103	C₂³×C₈₃	1	1	yes	characteristic
843	#103	C₂³×C₈₃	1	1	yes	characteristic
844	#103	C₂³×C₈₃	1	1	yes	characteristic
845	#103	C₂³×C₈₃	1	1	yes	characteristic
846	#103	C₂³×C₈₃	1	2	yes	—
847	#102	C₂³×C₈₃	1	1	yes	characteristic
848	#102	C₂³×C₈₃	1	2	yes	—
849	#102	C₂³×C₈₃	1	2	yes	—
850	#102	C₂³×C₈₃	1	2	yes	—
851	#102	C₂³×C₈₃	1	2	yes	—
852	#102	C₂³×C₈₃	1	1	yes	characteristic
853	#102	C₂³×C₈₃	1	2	yes	—
854	#102	C₂³×C₈₃	1	2	yes	—
855	#102	C₂³×C₈₃	1	2	yes	—
856	#102	C₂³×C₈₃	1	2	yes	—
857	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
858	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
859	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
860	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
861	#97	C₂³×C₈₃	1	2	yes	—
862	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
863	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
864	C₄×C₈	C₂³×C₈₃	1	2	yes	—
865	C₂⁴	—	2	2	no	—
866	#41	—	2	2	no	—
867	#41	—	4	1	no	—
868	#41	—	8	2	no	—
869	C₂×Q₈	—	2	1	no	—
870	C₂×Q₈	—	2	1	no	—
871	C₂×Q₈	—	2	1	no	—
872	C₂×Q₈	—	2	1	no	—
873	C₂×Q₈	—	2	2	no	—
874	C₂×Q₈	—	2	2	no	—
875	C₂×Q₈	—	8	2	no	—
876	C₂×Q₈	C₂×D₄×C₈₃	1	1	yes	characteristic
877	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
878	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
879	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
880	C₂×D₄	—	2	4	no	—
881	C₂×D₄	—	2	1	no	—
882	C₂×D₄	—	2	2	no	—
883	C₂×D₄	—	2	2	no	—
884	C₂×D₄	—	2	2	no	—
885	C₂×D₄	—	2	1	no	—
886	C₂×D₄	—	2	1	no	—
887	C₂×D₄	—	4	2	no	—
888	C₂×D₄	—	8	2	no	—
889	C₂×D₄	C₂×D₄×C₈₃	1	1	yes	characteristic
890	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
891	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
892	C₂×D₄	C₂⁴×C₈₃	1	1	yes	characteristic
893	C₂²×C₄	—	2	2	no	—
894	C₂²×C₄	—	2	1	no	—
895	C₂²×C₄	—	2	1	no	—
896	C₂²×C₄	—	2	1	no	—
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	—	2	2	no	—
899	C₂²×C₄	—	2	2	no	—
900	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
901	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
902	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
903	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
904	Q₁₆	—	4	1	no	—
905	Q₁₆	—	4	1	no	—
906	SD₁₆	—	2	2	no	—
907	SD₁₆	—	2	2	no	—
908	SD₁₆	—	4	2	no	—
909	SD₁₆	—	4	2	no	—
910	M₁₆	—	4	2	no	—
911	C₂×C₈	—	4	2	no	—
912	C₂×C₈	—	4	2	no	—
913	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
914	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
915	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
916	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
917	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
918	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	1	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
944	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
945	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
946	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
947	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
948	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
949	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
950	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
951	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
952	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
953	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
954	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
955	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₂²⋊C₄	—	2	1	no	—
959	C₂²⋊C₄	—	2	1	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	1	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	1	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	1	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
975	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
976	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
977	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
978	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
979	C₄²	—	2	1	no	—
980	C₄²	—	2	1	no	—
981	C₄²	—	2	1	no	—
982	C₄²	—	2	2	no	—
983	C₄²	—	2	2	no	—
984	C₄²	—	2	1	no	—
985	C₄²	—	2	1	no	—
986	C₄²	—	2	2	no	—
987	C₄²	—	2	2	no	—
988	C₄²	—	2	2	no	—
989	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
990	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
991	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
992	C₄²	C₂⁴×C₈₃	1	2	yes	—
993	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
994	C₂³	—	2	1	no	—
995	C₂³	—	2	2	no	—
996	C₂³	—	4	4	no	—
997	C₂³	—	8	2	no	—
998	C₂³	—	8	2	no	—
999	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
1000	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
1001	Q₈	—	2	2	no	—
1002	Q₈	—	2	1	no	—
1003	Q₈	—	2	1	no	—
1004	Q₈	—	2	1	no	—
1005	Q₈	—	2	1	no	—
1006	Q₈	—	2	1	no	—
1007	Q₈	—	2	1	no	—
1008	Q₈	—	4	2	no	—
1009	Q₈	—	4	2	no	—
1010	Q₈	—	8	2	no	—
1011	Q₈	—	8	1	no	—
1012	Q₈	—	8	1	no	—
1013	Q₈	—	8	2	no	—
1014	D₄	—	2	2	no	—
1015	D₄	—	2	2	no	—
1016	D₄	—	2	1	no	—
1017	D₄	—	2	2	no	—
1018	D₄	—	4	2	no	—
1019	D₄	—	4	4	no	—
1020	D₄	—	4	2	no	—
1021	D₄	—	4	2	no	—
1022	D₄	—	8	1	no	—
1023	D₄	—	8	2	no	—
1024	D₄	—	8	2	no	—
1025	D₄	2₋¹⁺⁴×C₈₃	1	2	yes	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	4	1	no	—
1042	C₂×C₄	—	4	2	no	—
1043	C₂×C₄	—	4	2	no	—
1044	C₂×C₄	—	8	2	no	—
1045	C₂×C₄	—	8	2	no	—
1046	C₂×C₄	—	8	1	no	—
1047	C₂×C₄	—	8	2	no	—
1048	C₂×C₄	—	8	2	no	—
1049	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1050	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
1051	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1052	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
1053	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
1054	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1055	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1056	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1057	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
1058	C₈	—	2	1	no	—
1059	C₈	—	2	1	no	—
1060	C₈	—	2	2	no	—
1061	C₈	—	2	1	no	—
1062	C₈	—	2	2	no	—
1063	C₈	—	2	1	no	—
1064	C₂²	—	2	1	no	—
1065	C₂²	—	2	2	no	—
1066	C₂²	—	2	1	no	—
1067	C₂²	—	2	2	no	—
1068	C₂²	—	2	1	no	—
1069	C₂²	—	2	2	no	—
1070	C₂²	—	2	2	no	—
1071	C₂²	—	4	1	no	—
1072	C₂²	—	4	1	no	—
1073	C₂²	—	4	2	no	—
1074	C₂²	—	4	2	no	—
1075	C₂²	—	4	2	no	—
1076	C₂²	—	16	4	no	—
1077	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
1078	C₄	—	2	1	no	—
1079	C₄	—	2	2	no	—
1080	C₄	—	2	1	no	—
1081	C₄	—	2	1	no	—
1082	C₄	—	2	2	no	—
1083	C₄	—	2	1	no	—
1084	C₄	—	2	2	no	—
1085	C₄	—	4	1	no	—
1086	C₄	—	4	2	no	—
1087	C₄	—	4	2	no	—
1088	C₄	—	4	1	no	—
1089	C₄	—	4	1	no	—
1090	C₄	—	4	2	no	—
1091	C₄	—	4	1	no	—
1092	C₄	—	4	1	no	—
1093	C₄	—	4	1	no	—
1094	C₄	—	4	1	no	—
1095	C₄	#577×C₈₃	1	2	yes	—
1096	C₄	C₂×2₋¹⁺⁴×C₈₃	1	1	yes	characteristic
1097	C₄	#585×C₈₃	1	1	yes	characteristic
1098	C₂	—	4	2	no	—
1099	C₂	—	4	1	no	—
1100	C₂	—	4	2	no	—
1101	C₂	—	8	2	no	—
1102	C₂	C₈₃×#3489	1	1	yes	characteristic
1103	C₂	C₂×#577×C₈₃	1	1	yes	characteristic
1104	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×#3514	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×#3386	C₂	semidirect
4. Q₈×SD₁₆×C₈₃	C₂	semidirect
5. C₈₃×#3375	C₂	semidirect
6. C₈₃×#3365	C₂	semidirect
7. C₈₃×#3356	C₂	semidirect
8. C₈₃×#3348	C₂	semidirect
9. C₈₃×#3342	C₂	semidirect
10. C₈₃×#3340	C₂	semidirect
11. C₈₃×#3324	C₂	semidirect
12. C₈₃×#3311	C₂	semidirect
13. C₈₃×#3296	C₂	semidirect
14. C₈₃×#3295	C₂	semidirect
15. C₈₃×#3258	C₂	semidirect
16. C₈₃×#3246	C₂	semidirect
17. C₈₃×#3244	C₂	semidirect
18. C₈₃×#3228	C₂	semidirect
19. C₈₃×#3123	C₂	semidirect
20. C₈₃×#3107	C₂	semidirect
21. C₈₃×#3081	C₂	semidirect
22. C₈₃×#3076	C₂	semidirect
23. C₈₃×#2994	C₂	semidirect
26. Q₈²×C₈₃	C₂²	semidirect
28. #557×C₈₃	C₂²	semidirect
32. #556×C₈₃	C₂²	semidirect
35. #552×C₈₃	C₂²	semidirect
42. #544×C₈₃	C₂²	semidirect
47. #541×C₈₃	C₂²	semidirect
49. #533×C₈₃	C₂²	semidirect
50. #533×C₈₃	C₂²	semidirect
57. #501×C₈₃	C₂²	semidirect
58. #500×C₈₃	C₂²	semidirect
59. #498×C₈₃	C₂²	semidirect
60. #498×C₈₃	C₂²	semidirect
61. #489×C₈₃	C₂²	semidirect
62. #488×C₈₃	C₂²	semidirect
65. #485×C₈₃	C₂²	semidirect
66. #485×C₈₃	C₂²	semidirect
67. #485×C₈₃	C₂²	semidirect
68. #485×C₈₃	C₂²	semidirect
69. #485×C₈₃	C₂²	semidirect
70. #483×C₈₃	C₂²	semidirect
72. #482×C₈₃	C₂²	semidirect
73. #482×C₈₃	C₂²	semidirect
75. #479×C₈₃	C₂²	semidirect
78. #478×C₈₃	C₂²	semidirect
79. #478×C₈₃	C₂²	semidirect
80. #478×C₈₃	C₂²	semidirect
81. #477×C₈₃	C₂²	semidirect
82. #477×C₈₃	C₂²	semidirect
85. #476×C₈₃	C₂²	semidirect
86. #475×C₈₃	C₂²	semidirect
87. #475×C₈₃	C₂²	semidirect
88. #475×C₈₃	C₂²	semidirect
89. #475×C₈₃	C₂²	semidirect
90. #475×C₈₃	C₂²	semidirect
93. #474×C₈₃	C₂²	semidirect
94. #470×C₈₃	C₂²	semidirect
96. #467×C₈₃	C₂²	semidirect
98. #465×C₈₃	C₂²	semidirect
99. #465×C₈₃	C₂²	semidirect
100. #464×C₈₃	C₂²	semidirect
101. #464×C₈₃	C₂²	semidirect
102. #462×C₈₃	C₂²	semidirect
104. #461×C₈₃	C₂²	semidirect
111. #446×C₈₃	C₂²	semidirect
112. C₈×Q₈×C₈₃	C₂²	semidirect
114. #440×C₈₃	C₂²	semidirect
115. C₄×Q₁₆×C₈₃	C₂²	semidirect
116. C₄×Q₁₆×C₈₃	C₂²	semidirect
120. C₄×SD₁₆×C₈₃	C₂²	semidirect
122. #435×C₈₃	C₂²	semidirect
124. C₈×D₄×C₈₃	C₂²	semidirect
125. #433×C₈₃	C₂²	semidirect
126. #431×C₈₃	C₂²	semidirect
127. #428×C₈₃	C₂²	semidirect
128. #427×C₈₃	C₂²	semidirect
129. #427×C₈₃	C₂²	semidirect
130. #424×C₈₃	C₂²	semidirect
131. C₂×C₄⋊C₈×C₈₃	C₂²	semidirect
545. #62216	C₈₃	direct (N × H)
553. #3555	C₂×C₈₃	semidirect
555. #3386	C₂×C₈₃	semidirect
556. Q₈×SD₁₆	C₂×C₈₃	semidirect
557. #3375	C₂×C₈₃	semidirect
558. #3365	C₂×C₈₃	semidirect
559. #3356	C₂×C₈₃	semidirect
560. #3348	C₂×C₈₃	semidirect
561. #3342	C₂×C₈₃	semidirect
562. #3340	C₂×C₈₃	semidirect
563. #3324	C₂×C₈₃	semidirect
564. #3311	C₂×C₈₃	semidirect
565. #3296	C₂×C₈₃	semidirect
566. #3295	C₂×C₈₃	semidirect
567. #3258	C₂×C₈₃	semidirect
568. #3246	C₂×C₈₃	semidirect
569. #3244	C₂×C₈₃	semidirect
570. #3228	C₂×C₈₃	semidirect
571. #3123	C₂×C₈₃	semidirect
572. #3107	C₂×C₈₃	semidirect
573. #3081	C₂×C₈₃	semidirect
574. #3076	C₂×C₈₃	semidirect
575. #2994	C₂×C₈₃	semidirect
576. C₈₃	#62216	direct (N × H)
579. Q₈²	C₂²×C₈₃	semidirect
581. #557	C₂²×C₈₃	semidirect
585. #556	C₂²×C₈₃	semidirect
588. #552	C₂²×C₈₃	semidirect
595. #544	C₂²×C₈₃	semidirect
600. #541	C₂²×C₈₃	semidirect
602. #533	C₂²×C₈₃	semidirect
603. #533	C₂²×C₈₃	semidirect
610. #501	C₂²×C₈₃	semidirect
611. #500	C₂²×C₈₃	semidirect
612. #498	C₂²×C₈₃	semidirect
613. #498	C₂²×C₈₃	semidirect
614. #489	C₂²×C₈₃	semidirect
615. #488	C₂²×C₈₃	semidirect
618. #485	C₂²×C₈₃	semidirect
619. #485	C₂²×C₈₃	semidirect
620. #485	C₂²×C₈₃	semidirect
621. #485	C₂²×C₈₃	semidirect
622. #485	C₂²×C₈₃	semidirect
623. #483	C₂²×C₈₃	semidirect
625. #482	C₂²×C₈₃	semidirect
626. #482	C₂²×C₈₃	semidirect
628. #479	C₂²×C₈₃	semidirect
631. #478	C₂²×C₈₃	semidirect
632. #478	C₂²×C₈₃	semidirect
633. #478	C₂²×C₈₃	semidirect
634. #477	C₂²×C₈₃	semidirect
635. #477	C₂²×C₈₃	semidirect
638. #476	C₂²×C₈₃	semidirect
639. #475	C₂²×C₈₃	semidirect
640. #475	C₂²×C₈₃	semidirect
641. #475	C₂²×C₈₃	semidirect
642. #475	C₂²×C₈₃	semidirect
643. #475	C₂²×C₈₃	semidirect
646. #474	C₂²×C₈₃	semidirect
647. #470	C₂²×C₈₃	semidirect
649. #467	C₂²×C₈₃	semidirect
651. #465	C₂²×C₈₃	semidirect
652. #465	C₂²×C₈₃	semidirect
653. #464	C₂²×C₈₃	semidirect
654. #464	C₂²×C₈₃	semidirect
655. #462	C₂²×C₈₃	semidirect
657. #461	C₂²×C₈₃	semidirect
664. #446	C₂²×C₈₃	semidirect
665. C₈×Q₈	C₂²×C₈₃	semidirect
667. #440	C₂²×C₈₃	semidirect
668. C₄×Q₁₆	C₂²×C₈₃	semidirect
669. C₄×Q₁₆	C₂²×C₈₃	semidirect
673. C₄×SD₁₆	C₂²×C₈₃	semidirect
675. #435	C₂²×C₈₃	semidirect
677. C₈×D₄	C₂²×C₈₃	semidirect
678. #433	C₂²×C₈₃	semidirect
679. #431	C₂²×C₈₃	semidirect
680. #428	C₂²×C₈₃	semidirect
681. #427	C₂²×C₈₃	semidirect
682. #427	C₂²×C₈₃	semidirect
683. #424	C₂²×C₈₃	semidirect
684. C₂×C₄⋊C₈	C₂²×C₈₃	semidirect

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×#3514	2
C₈₃×#3386	2
Q₈×SD₁₆×C₈₃	2
C₈₃×#3375	2
C₈₃×#3365	2
C₈₃×#3356	2
C₈₃×#3348	2
C₈₃×#3342	2
C₈₃×#3340	2
C₈₃×#3324	2
C₈₃×#3311	2
C₈₃×#3296	2
C₈₃×#3295	2
C₈₃×#3258	2
C₈₃×#3246	2
C₈₃×#3244	2
C₈₃×#3228	2
C₈₃×#3123	2
C₈₃×#3107	2
C₈₃×#3081	2
C₈₃×#3076	2
C₈₃×#2994	2
#62216	83

Subgroups — C83×#62216 #35290040

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#62216 #35290040