Subgroups — C₈₃×#62215 #35290039

Order 21248.

1762 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₃×#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₃×#3384	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×D₈×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₃×#3373	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₃×#3361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₃×#3353	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₃×#3347	C₂	1	2	yes	maximal, complemented
9	C₈₃×#3341	C₂	1	2	yes	maximal, complemented
10	C₈₃×#3340	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₃×#3325	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₃×#3319	C₂	1	2	yes	maximal, complemented
13	C₈₃×#3297	C₂	1	2	yes	maximal, complemented
14	C₈₃×#3294	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#3257	C₂	1	2	yes	maximal, complemented
16	C₈₃×#3245	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₃×#3243	C₂	1	2	yes	maximal, complemented
18	C₈₃×#3228	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₃×#3122	C₂	1	2	yes	maximal, complemented
20	C₈₃×#3106	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	#562×C₈₃	—	2	2	no	—
25	#559×C₈₃	C₂²	1	1	yes	characteristic
26	#556×C₈₃	C₂²	1	1	yes	characteristic
27	#555×C₈₃	C₂²	1	1	yes	characteristic
28	#555×C₈₃	C₂²	1	2	yes	—
29	#555×C₈₃	C₂²	1	2	yes	complemented
30	#554×C₈₃	C₂²	1	1	yes	characteristic, complemented
31	#553×C₈₃	C₂²	1	2	yes	complemented
32	#552×C₈₃	—	2	1	no	—
33	#551×C₈₃	—	2	2	no	—
34	D₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
35	D₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
36	#548×C₈₃	—	2	1	no	—
37	#548×C₈₃	—	2	1	no	—
38	#547×C₈₃	C₂²	1	1	yes	characteristic
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	2	no	—
44	#542×C₈₃	C₂²	1	2	yes	—
45	#540×C₈₃	C₂²	1	2	yes	complemented
46	#538×C₈₃	—	2	2	no	—
47	#537×C₈₃	—	2	1	no	—
48	#536×C₈₃	—	2	1	no	—
49	#533×C₈₃	C₂²	1	1	yes	characteristic, complemented
50	#532×C₈₃	C₂²	1	1	yes	characteristic
51	#532×C₈₃	C₂²	1	1	yes	characteristic, complemented
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	2	yes	complemented
59	#500×C₈₃	C₂²	1	1	yes	characteristic, 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	#484×C₈₃	C₂²	1	2	yes	complemented
67	#482×C₈₃	C₂²	1	2	yes	—
68	#482×C₈₃	C₂²	1	2	yes	complemented
69	#482×C₈₃	C₂²	1	2	yes	complemented
70	#482×C₈₃	C₂²	1	2	yes	complemented
71	#482×C₈₃	C₂²	1	1	yes	characteristic, complemented
72	#482×C₈₃	C₂²	1	2	yes	complemented
73	#482×C₈₃	C₂²	1	1	yes	characteristic, complemented
74	#480×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	1	yes	characteristic, complemented
83	#476×C₈₃	C₂²	1	1	yes	characteristic
84	#476×C₈₃	C₂²	1	1	yes	characteristic
85	#476×C₈₃	C₂²	1	2	yes	complemented
86	#476×C₈₃	C₂²	1	2	yes	complemented
87	#475×C₈₃	C₂²	1	1	yes	characteristic, complemented
88	#474×C₈₃	C₂²	1	1	yes	characteristic
89	#474×C₈₃	C₂²	1	2	yes	—
90	#474×C₈₃	C₂²	1	2	yes	complemented
91	#474×C₈₃	C₂²	1	1	yes	characteristic, complemented
92	#474×C₈₃	C₂²	1	2	yes	complemented
93	#474×C₈₃	C₂²	1	1	yes	characteristic, complemented
94	#469×C₈₃	C₂²	1	2	yes	—
95	#468×C₈₃	C₂²	1	2	yes	complemented
96	#466×C₈₃	C₂²	1	2	yes	—
97	#466×C₈₃	C₂²	1	2	yes	complemented
98	#466×C₈₃	C₂²	1	2	yes	complemented
99	#465×C₈₃	C₂²	1	2	yes	complemented
100	#463×C₈₃	C₂²	1	2	yes	complemented
101	#463×C₈₃	C₂²	1	2	yes	complemented
102	#460×C₈₃	C₂²	1	1	yes	characteristic, complemented
103	#459×C₈₃	C₂²	1	1	yes	characteristic
104	#459×C₈₃	C₂²	1	1	yes	characteristic
105	#459×C₈₃	C₂²	1	1	yes	characteristic
106	#459×C₈₃	C₂²	1	2	yes	complemented
107	#449×C₈₃	C₂²	1	1	yes	characteristic
108	#449×C₈₃	C₂²	1	1	yes	characteristic
109	#447×C₈₃	C₂²	1	2	yes	—
110	#447×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	#442×C₈₃	C₂²	1	2	yes	—
114	#442×C₈₃	C₂²	1	2	yes	complemented
115	C₄×SD₁₆×C₈₃	C₂²	1	1	yes	characteristic, complemented
116	C₄×SD₁₆×C₈₃	C₂²	1	1	yes	characteristic, complemented
117	C₄×D₈×C₈₃	C₂²	1	1	yes	characteristic
118	C₄×D₈×C₈₃	C₂²	1	2	yes	—
119	C₄×D₈×C₈₃	C₂²	1	1	yes	characteristic
120	C₄×D₈×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	—	2	1	no	—
137	C₂×#41×C₈₃	—	2	1	no	—
138	C₂×#41×C₈₃	C₂³	1	1	yes	characteristic
139	C₂²×Q₈×C₈₃	—	2	1	no	—
140	C₂²×Q₈×C₈₃	—	2	1	no	—
141	C₂²×D₄×C₈₃	—	2	1	no	—
142	C₂²×D₄×C₈₃	C₂³	1	2	yes	—
143	C₂×SD₁₆×C₈₃	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₈₃	C₂³	1	1	yes	characteristic
145	C₂×D₈×C₈₃	C₂³	1	1	yes	characteristic
146	C₂×D₈×C₈₃	C₂³	1	1	yes	characteristic
147	C₂×D₈×C₈₃	C₂³	1	2	yes	—
148	C₂×D₈×C₈₃	C₂³	1	2	yes	—
149	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
150	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
151	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
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	2	yes	—
158	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
159	#127×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	D₄	1	2	yes	—
165	#125×C₈₃	—	2	2	no	—
166	#125×C₈₃	D₄	1	1	yes	characteristic
167	#125×C₈₃	C₂³	1	2	yes	—
168	#125×C₈₃	C₂³	1	2	yes	—
169	#124×C₈₃	—	2	1	no	—
170	#124×C₈₃	—	2	1	no	—
171	#124×C₈₃	—	2	2	no	—
172	#124×C₈₃	—	2	2	no	—
173	#124×C₈₃	—	2	2	no	—
174	#124×C₈₃	—	2	2	no	—
175	#124×C₈₃	—	2	2	no	—
176	#124×C₈₃	—	2	2	no	—
177	#124×C₈₃	—	2	1	no	—
178	#124×C₈₃	—	2	1	no	—
179	#124×C₈₃	D₄	1	1	yes	characteristic
180	#124×C₈₃	C₂³	1	2	yes	—
181	#123×C₈₃	—	2	2	no	—
182	#123×C₈₃	—	2	2	no	—
183	#123×C₈₃	—	2	2	no	—
184	#123×C₈₃	—	2	2	no	—
185	#123×C₈₃	—	2	2	no	—
186	#123×C₈₃	—	2	2	no	—
187	#123×C₈₃	—	2	2	no	—
188	#123×C₈₃	D₄	1	2	yes	—
189	C₂²⋊Q₈×C₈₃	—	2	1	no	—
190	C₂²⋊Q₈×C₈₃	—	2	1	no	—
191	C₂²⋊Q₈×C₈₃	—	2	1	no	—
192	C₂²⋊Q₈×C₈₃	—	2	1	no	—
193	C₂²⋊Q₈×C₈₃	—	2	1	no	—
194	C₂²⋊Q₈×C₈₃	—	2	1	no	—
195	C₂²⋊Q₈×C₈₃	—	2	2	no	—
196	C₂²⋊Q₈×C₈₃	—	2	2	no	—
197	C₂²⋊Q₈×C₈₃	—	2	2	no	—
198	C₂²⋊Q₈×C₈₃	—	2	2	no	—
199	C₂²⋊Q₈×C₈₃	—	2	2	no	—
200	C₂²⋊Q₈×C₈₃	—	2	2	no	—
201	C₂²⋊Q₈×C₈₃	D₄	1	1	yes	characteristic
202	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
203	#121×C₈₃	—	2	1	no	—
204	#121×C₈₃	—	2	2	no	—
205	#121×C₈₃	—	2	2	no	—
206	#121×C₈₃	—	2	2	no	—
207	#121×C₈₃	—	2	1	no	—
208	#121×C₈₃	—	2	1	no	—
209	#121×C₈₃	—	2	1	no	—
210	#121×C₈₃	—	2	2	no	—
211	#121×C₈₃	—	2	2	no	—
212	#121×C₈₃	—	2	2	no	—
213	#121×C₈₃	D₄	1	1	yes	characteristic
214	#121×C₈₃	C₂³	1	2	yes	—
215	#121×C₈₃	C₂³	1	2	yes	—
216	#121×C₈₃	C₂³	1	2	yes	—
217	#121×C₈₃	C₂³	1	2	yes	—
218	#121×C₈₃	C₂³	1	1	yes	characteristic
219	#121×C₈₃	C₂³	1	1	yes	characteristic
220	#120×C₈₃	—	2	2	no	—
221	#120×C₈₃	—	2	2	no	—
222	C₄×Q₈×C₈₃	—	2	1	no	—
223	C₄×Q₈×C₈₃	—	2	1	no	—
224	C₄×Q₈×C₈₃	—	2	1	no	—
225	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
228	C₄×D₄×C₈₃	—	2	1	no	—
229	C₄×D₄×C₈₃	—	2	1	no	—
230	C₄×D₄×C₈₃	—	2	2	no	—
231	C₄×D₄×C₈₃	—	2	2	no	—
232	C₄×D₄×C₈₃	—	2	1	no	—
233	C₄×D₄×C₈₃	—	2	2	no	—
234	C₄×D₄×C₈₃	—	2	1	no	—
235	C₄×D₄×C₈₃	—	2	1	no	—
236	C₄×D₄×C₈₃	C₂³	1	2	yes	—
237	C₄×D₄×C₈₃	C₂³	1	2	yes	—
238	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₈₃	C₂³	1	2	yes	—
240	C₄×D₄×C₈₃	C₂³	1	2	yes	—
241	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₈₃	C₂³	1	2	yes	—
245	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₈₃	C₂³	1	2	yes	—
247	#117×C₈₃	—	2	2	no	—
248	#117×C₈₃	—	2	1	no	—
249	#117×C₈₃	—	2	2	no	—
250	#117×C₈₃	—	2	1	no	—
251	#117×C₈₃	C₂³	1	2	yes	—
252	#117×C₈₃	C₂³	1	1	yes	characteristic
253	#117×C₈₃	C₂³	1	2	yes	—
254	#117×C₈₃	C₂³	1	2	yes	—
255	#117×C₈₃	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
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	2	yes	—
266	#107×C₈₃	C₂³	1	2	yes	—
267	#107×C₈₃	C₂³	1	2	yes	—
268	#107×C₈₃	C₂³	1	1	yes	characteristic
269	#107×C₈₃	C₂³	1	1	yes	characteristic
270	#107×C₈₃	C₂³	1	2	yes	—
271	#106×C₈₃	C₂³	1	2	yes	—
272	#106×C₈₃	C₂³	1	2	yes	—
273	#106×C₈₃	C₂³	1	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	2	yes	—
282	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
288	#102×C₈₃	C₂³	1	2	yes	—
289	#102×C₈₃	C₂³	1	2	yes	—
290	#102×C₈₃	C₂³	1	2	yes	—
291	#102×C₈₃	C₂³	1	1	yes	characteristic
292	#102×C₈₃	C₂³	1	2	yes	—
293	#102×C₈₃	C₂³	1	2	yes	—
294	#102×C₈₃	C₂³	1	2	yes	—
295	#102×C₈₃	C₂³	1	1	yes	characteristic
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	2	yes	—
300	#102×C₈₃	C₂³	1	2	yes	—
301	#102×C₈₃	C₂³	1	2	yes	—
302	#102×C₈₃	C₂³	1	1	yes	characteristic
303	#102×C₈₃	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
307	C₂²⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
308	#97×C₈₃	C₂³	1	2	yes	—
309	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₈₃	C₂³	1	2	yes	—
312	C₂⁴×C₈₃	—	2	2	no	—
313	#41×C₈₃	—	2	2	no	—
314	#41×C₈₃	—	4	1	no	—
315	#41×C₈₃	—	8	2	no	—
316	#41×C₈₃	—	8	2	no	—
317	#41×C₈₃	—	8	2	no	—
318	C₂×Q₈×C₈₃	—	2	1	no	—
319	C₂×Q₈×C₈₃	—	2	1	no	—
320	C₂×Q₈×C₈₃	—	2	1	no	—
321	C₂×Q₈×C₈₃	—	2	2	no	—
322	C₂×Q₈×C₈₃	—	2	2	no	—
323	C₂×Q₈×C₈₃	—	2	1	no	—
324	C₂×Q₈×C₈₃	—	8	2	no	—
325	C₂×Q₈×C₈₃	—	8	2	no	—
326	C₂×Q₈×C₈₃	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₈₃	—	2	4	no	—
329	C₂×D₄×C₈₃	—	2	1	no	—
330	C₂×D₄×C₈₃	—	2	2	no	—
331	C₂×D₄×C₈₃	—	2	2	no	—
332	C₂×D₄×C₈₃	—	2	2	no	—
333	C₂×D₄×C₈₃	—	2	1	no	—
334	C₂×D₄×C₈₃	—	2	2	no	—
335	C₂×D₄×C₈₃	—	2	1	no	—
336	C₂×D₄×C₈₃	—	2	2	no	—
337	C₂×D₄×C₈₃	—	2	1	no	—
338	C₂×D₄×C₈₃	—	2	1	no	—
339	C₂×D₄×C₈₃	—	2	1	no	—
340	C₂×D₄×C₈₃	—	2	1	no	—
341	C₂×D₄×C₈₃	—	4	2	no	—
342	C₂×D₄×C₈₃	—	8	2	no	—
343	C₂×D₄×C₈₃	C₂×D₄	1	1	yes	characteristic
344	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
345	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
346	C₂×D₄×C₈₃	C₂⁴	1	1	yes	characteristic
347	C₂×D₄×C₈₃	C₂⁴	1	1	yes	characteristic
348	C₂×D₄×C₈₃	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₈₃	—	2	2	no	—
350	C₂²×C₄×C₈₃	—	2	1	no	—
351	C₂²×C₄×C₈₃	—	2	1	no	—
352	C₂²×C₄×C₈₃	—	2	1	no	—
353	C₂²×C₄×C₈₃	—	2	1	no	—
354	C₂²×C₄×C₈₃	—	2	1	no	—
355	C₂²×C₄×C₈₃	—	2	2	no	—
356	C₂²×C₄×C₈₃	—	2	2	no	—
357	C₂²×C₄×C₈₃	—	2	2	no	—
358	C₂²×C₄×C₈₃	—	2	2	no	—
359	C₂²×C₄×C₈₃	—	2	2	no	—
360	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
361	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
362	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
363	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
364	SD₁₆×C₈₃	—	4	1	no	—
365	SD₁₆×C₈₃	—	4	1	no	—
366	D₈×C₈₃	—	2	2	no	—
367	D₈×C₈₃	—	2	2	no	—
368	D₈×C₈₃	—	4	2	no	—
369	D₈×C₈₃	—	4	2	no	—
370	M₁₆×C₈₃	—	4	2	no	—
371	C₂×C₈×C₈₃	—	4	2	no	—
372	C₂×C₈×C₈₃	—	4	2	no	—
373	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
378	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
379	C₄⋊C₄×C₈₃	—	2	1	no	—
380	C₄⋊C₄×C₈₃	—	2	2	no	—
381	C₄⋊C₄×C₈₃	—	2	2	no	—
382	C₄⋊C₄×C₈₃	—	2	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	—	2	2	no	—
391	C₄⋊C₄×C₈₃	—	2	2	no	—
392	C₄⋊C₄×C₈₃	—	2	1	no	—
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	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₈₃	C₂×D₄	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	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
406	C₂²⋊C₄×C₈₃	—	2	2	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	1	no	—
412	C₂²⋊C₄×C₈₃	—	2	2	no	—
413	C₂²⋊C₄×C₈₃	—	2	2	no	—
414	C₂²⋊C₄×C₈₃	—	2	2	no	—
415	C₂²⋊C₄×C₈₃	—	2	2	no	—
416	C₂²⋊C₄×C₈₃	—	2	2	no	—
417	C₂²⋊C₄×C₈₃	—	2	1	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	—	2	2	no	—
422	C₂²⋊C₄×C₈₃	—	2	1	no	—
423	C₂²⋊C₄×C₈₃	—	2	2	no	—
424	C₂²⋊C₄×C₈₃	—	2	2	no	—
425	C₂²⋊C₄×C₈₃	—	2	1	no	—
426	C₂²⋊C₄×C₈₃	—	2	2	no	—
427	C₂²⋊C₄×C₈₃	—	2	1	no	—
428	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
429	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
430	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
431	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
433	C₄²×C₈₃	—	2	1	no	—
434	C₄²×C₈₃	—	2	1	no	—
435	C₄²×C₈₃	—	2	1	no	—
436	C₄²×C₈₃	—	2	2	no	—
437	C₄²×C₈₃	—	2	2	no	—
438	C₄²×C₈₃	—	2	2	no	—
439	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
440	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
441	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
442	C₄²×C₈₃	C₂⁴	1	2	yes	—
443	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
444	C₂³×C₈₃	—	2	1	no	—
445	C₂³×C₈₃	—	2	1	no	—
446	C₂³×C₈₃	—	2	1	no	—
447	C₂³×C₈₃	—	2	2	no	—
448	C₂³×C₈₃	—	4	4	no	—
449	C₂³×C₈₃	—	8	2	no	—
450	C₂³×C₈₃	—	8	2	no	—
451	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
452	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
453	Q₈×C₈₃	—	2	2	no	—
454	Q₈×C₈₃	—	2	1	no	—
455	Q₈×C₈₃	—	2	1	no	—
456	Q₈×C₈₃	—	4	2	no	—
457	Q₈×C₈₃	—	4	2	no	—
458	Q₈×C₈₃	—	8	1	no	—
459	Q₈×C₈₃	—	8	2	no	—
460	Q₈×C₈₃	—	8	2	no	—
461	Q₈×C₈₃	—	8	1	no	—
462	D₄×C₈₃	—	2	2	no	—
463	D₄×C₈₃	—	2	1	no	—
464	D₄×C₈₃	—	2	1	no	—
465	D₄×C₈₃	—	2	2	no	—
466	D₄×C₈₃	—	2	1	no	—
467	D₄×C₈₃	—	2	1	no	—
468	D₄×C₈₃	—	2	1	no	—
469	D₄×C₈₃	—	2	2	no	—
470	D₄×C₈₃	—	4	2	no	—
471	D₄×C₈₃	—	4	4	no	—
472	D₄×C₈₃	—	4	2	no	—
473	D₄×C₈₃	—	4	2	no	—
474	D₄×C₈₃	—	8	1	no	—
475	D₄×C₈₃	—	8	1	no	—
476	D₄×C₈₃	—	8	1	no	—
477	D₄×C₈₃	—	8	2	no	—
478	D₄×C₈₃	—	8	2	no	—
479	D₄×C₈₃	—	8	1	no	—
480	D₄×C₈₃	—	8	1	no	—
481	D₄×C₈₃	—	8	2	no	—
482	D₄×C₈₃	—	8	2	no	—
483	D₄×C₈₃	2₋¹⁺⁴	1	2	yes	—
484	C₂×C₄×C₈₃	—	2	2	no	—
485	C₂×C₄×C₈₃	—	2	2	no	—
486	C₂×C₄×C₈₃	—	2	1	no	—
487	C₂×C₄×C₈₃	—	2	1	no	—
488	C₂×C₄×C₈₃	—	2	2	no	—
489	C₂×C₄×C₈₃	—	2	1	no	—
490	C₂×C₄×C₈₃	—	2	1	no	—
491	C₂×C₄×C₈₃	—	2	2	no	—
492	C₂×C₄×C₈₃	—	2	1	no	—
493	C₂×C₄×C₈₃	—	2	1	no	—
494	C₂×C₄×C₈₃	—	2	2	no	—
495	C₂×C₄×C₈₃	—	2	2	no	—
496	C₂×C₄×C₈₃	—	2	1	no	—
497	C₂×C₄×C₈₃	—	4	1	no	—
498	C₂×C₄×C₈₃	—	4	2	no	—
499	C₂×C₄×C₈₃	—	4	2	no	—
500	C₂×C₄×C₈₃	—	4	2	no	—
501	C₂×C₄×C₈₃	—	4	2	no	—
502	C₂×C₄×C₈₃	—	8	1	no	—
503	C₂×C₄×C₈₃	—	8	2	no	—
504	C₂×C₄×C₈₃	—	8	2	no	—
505	C₂×C₄×C₈₃	—	8	2	no	—
506	C₂×C₄×C₈₃	—	8	2	no	—
507	C₂×C₄×C₈₃	—	8	2	no	—
508	C₂×C₄×C₈₃	—	8	2	no	—
509	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
511	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
515	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
516	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
518	C₈×C₈₃	—	2	1	no	—
519	C₈×C₈₃	—	2	1	no	—
520	C₈×C₈₃	—	2	2	no	—
521	C₈×C₈₃	—	2	1	no	—
522	C₈×C₈₃	—	2	2	no	—
523	C₈×C₈₃	—	2	1	no	—
524	C₂²×C₈₃	—	2	1	no	—
525	C₂²×C₈₃	—	2	2	no	—
526	C₂²×C₈₃	—	2	1	no	—
527	C₂²×C₈₃	—	2	2	no	—
528	C₂²×C₈₃	—	2	2	no	—
529	C₂²×C₈₃	—	2	1	no	—
530	C₂²×C₈₃	—	2	2	no	—
531	C₂²×C₈₃	—	4	1	no	—
532	C₂²×C₈₃	—	4	1	no	—
533	C₂²×C₈₃	—	4	1	no	—
534	C₂²×C₈₃	—	4	2	no	—
535	C₂²×C₈₃	—	4	1	no	—
536	C₂²×C₈₃	—	4	2	no	—
537	C₂²×C₈₃	—	4	1	no	—
538	C₂²×C₈₃	—	4	1	no	—
539	C₂²×C₈₃	—	4	1	no	—
540	C₂²×C₈₃	—	4	1	no	—
541	C₂²×C₈₃	—	4	2	no	—
542	C₂²×C₈₃	—	16	4	no	—
543	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
544	C₄×C₈₃	—	2	1	no	—
545	C₄×C₈₃	—	2	1	no	—
546	C₄×C₈₃	—	2	2	no	—
547	C₄×C₈₃	—	2	1	no	—
548	C₄×C₈₃	—	2	2	no	—
549	C₄×C₈₃	—	2	1	no	—
550	C₄×C₈₃	—	2	2	no	—
551	C₄×C₈₃	—	4	1	no	—
552	C₄×C₈₃	—	4	2	no	—
553	C₄×C₈₃	—	4	1	no	—
554	C₄×C₈₃	—	4	1	no	—
555	C₄×C₈₃	—	4	1	no	—
556	C₄×C₈₃	—	4	1	no	—
557	C₄×C₈₃	—	4	2	no	—
558	C₄×C₈₃	—	4	2	no	—
559	C₄×C₈₃	#576	1	2	yes	—
560	C₄×C₈₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
561	C₄×C₈₃	#585	1	1	yes	characteristic
562	#62215	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
563	C₂×C₈₃	—	4	1	no	—
564	C₂×C₈₃	—	4	2	no	—
565	C₂×C₈₃	—	4	2	no	—
566	C₂×C₈₃	—	8	1	no	—
567	C₂×C₈₃	—	8	1	no	—
568	C₂×C₈₃	—	8	2	no	—
569	C₂×C₈₃	#3489	1	1	yes	characteristic
570	C₂×C₈₃	C₂×#576	1	1	yes	characteristic
571	C₂×C₈₃	#3584	1	1	yes	characteristic
572	#3547	C₂×C₈₃	1	1	yes	characteristic, complemented
573	#3514	C₂×C₈₃	1	1	yes	characteristic, complemented
574	#3384	C₂×C₈₃	1	1	yes	characteristic, complemented
575	Q₈×D₈	C₂×C₈₃	1	1	yes	characteristic, complemented
576	#3373	C₂×C₈₃	1	1	yes	characteristic, complemented
577	#3361	C₂×C₈₃	1	1	yes	characteristic, complemented
578	#3353	C₂×C₈₃	1	1	yes	characteristic, complemented
579	#3347	C₂×C₈₃	1	2	yes	complemented
580	#3341	C₂×C₈₃	1	2	yes	complemented
581	#3340	C₂×C₈₃	1	1	yes	characteristic, complemented
582	#3325	C₂×C₈₃	1	1	yes	characteristic, complemented
583	#3319	C₂×C₈₃	1	2	yes	complemented
584	#3297	C₂×C₈₃	1	2	yes	complemented
585	#3294	C₂×C₈₃	1	1	yes	characteristic, complemented
586	#3257	C₂×C₈₃	1	2	yes	complemented
587	#3245	C₂×C₈₃	1	1	yes	characteristic, complemented
588	#3243	C₂×C₈₃	1	2	yes	complemented
589	#3228	C₂×C₈₃	1	1	yes	characteristic, complemented
590	#3122	C₂×C₈₃	1	2	yes	complemented
591	#3106	C₂×C₈₃	1	1	yes	characteristic, complemented
592	#3081	C₂×C₈₃	1	2	yes	complemented
593	#3076	C₂×C₈₃	1	1	yes	characteristic, complemented
594	#2994	C₂×C₈₃	1	1	yes	characteristic, complemented
595	C₈₃	#62215	1	1	yes	characteristic, direct product factor, Sylow
596	#562	—	2	2	no	—
597	#559	C₂²×C₈₃	1	1	yes	characteristic
598	#556	C₂²×C₈₃	1	1	yes	characteristic
599	#555	C₂²×C₈₃	1	1	yes	characteristic
600	#555	C₂²×C₈₃	1	2	yes	—
601	#555	C₂²×C₈₃	1	2	yes	complemented
602	#554	C₂²×C₈₃	1	1	yes	characteristic, complemented
603	#553	C₂²×C₈₃	1	2	yes	complemented
604	#552	—	2	1	no	—
605	#551	—	2	2	no	—
606	D₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic
607	D₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
608	#548	—	2	1	no	—
609	#548	—	2	1	no	—
610	#547	C₂²×C₈₃	1	1	yes	characteristic
611	#546	—	2	1	no	—
612	#546	C₂²×C₈₃	1	2	yes	—
613	D₄²	C₂²×C₈₃	1	1	yes	characteristic
614	#544	C₂²×C₈₃	1	2	yes	complemented
615	#542	—	2	2	no	—
616	#542	C₂²×C₈₃	1	2	yes	—
617	#540	C₂²×C₈₃	1	2	yes	complemented
618	#538	—	2	2	no	—
619	#537	—	2	1	no	—
620	#536	—	2	1	no	—
621	#533	C₂²×C₈₃	1	1	yes	characteristic, complemented
622	#532	C₂²×C₈₃	1	1	yes	characteristic
623	#532	C₂²×C₈₃	1	1	yes	characteristic, complemented
624	#529	—	2	1	no	—
625	#529	C₂²×C₈₃	1	1	yes	characteristic
626	C₂×#124	—	2	1	no	—
627	#518	C₂²×C₈₃	1	2	yes	—
628	C₄×#41	C₂²×C₈₃	1	1	yes	characteristic
629	#501	C₂²×C₈₃	1	2	yes	complemented
630	#500	C₂²×C₈₃	1	2	yes	complemented
631	#500	C₂²×C₈₃	1	1	yes	characteristic, complemented
632	#498	C₂²×C₈₃	1	1	yes	characteristic, complemented
633	#489	C₂²×C₈₃	1	2	yes	complemented
634	#488	C₂²×C₈₃	1	2	yes	complemented
635	#486	C₂²×C₈₃	1	1	yes	characteristic
636	#486	C₂²×C₈₃	1	1	yes	characteristic
637	#485	C₂²×C₈₃	1	2	yes	complemented
638	#484	C₂²×C₈₃	1	2	yes	complemented
639	#482	C₂²×C₈₃	1	2	yes	—
640	#482	C₂²×C₈₃	1	2	yes	complemented
641	#482	C₂²×C₈₃	1	1	yes	characteristic, complemented
642	#482	C₂²×C₈₃	1	2	yes	complemented
643	#482	C₂²×C₈₃	1	2	yes	complemented
644	#482	C₂²×C₈₃	1	1	yes	characteristic, complemented
645	#482	C₂²×C₈₃	1	2	yes	complemented
646	#480	C₂²×C₈₃	1	2	yes	—
647	#479	C₂²×C₈₃	1	2	yes	complemented
648	#478	C₂²×C₈₃	1	2	yes	—
649	#478	C₂²×C₈₃	1	2	yes	—
650	#478	C₂²×C₈₃	1	2	yes	complemented
651	#478	C₂²×C₈₃	1	2	yes	complemented
652	#478	C₂²×C₈₃	1	2	yes	complemented
653	#477	C₂²×C₈₃	1	1	yes	characteristic, complemented
654	#477	C₂²×C₈₃	1	1	yes	characteristic, complemented
655	#476	C₂²×C₈₃	1	1	yes	characteristic
656	#476	C₂²×C₈₃	1	1	yes	characteristic
657	#476	C₂²×C₈₃	1	2	yes	complemented
658	#476	C₂²×C₈₃	1	2	yes	complemented
659	#475	C₂²×C₈₃	1	1	yes	characteristic, complemented
660	#474	C₂²×C₈₃	1	1	yes	characteristic
661	#474	C₂²×C₈₃	1	2	yes	—
662	#474	C₂²×C₈₃	1	2	yes	complemented
663	#474	C₂²×C₈₃	1	1	yes	characteristic, complemented
664	#474	C₂²×C₈₃	1	2	yes	complemented
665	#474	C₂²×C₈₃	1	1	yes	characteristic, complemented
666	#469	C₂²×C₈₃	1	2	yes	—
667	#468	C₂²×C₈₃	1	2	yes	complemented
668	#466	C₂²×C₈₃	1	2	yes	—
669	#466	C₂²×C₈₃	1	2	yes	complemented
670	#466	C₂²×C₈₃	1	2	yes	complemented
671	#465	C₂²×C₈₃	1	2	yes	complemented
672	#463	C₂²×C₈₃	1	2	yes	complemented
673	#463	C₂²×C₈₃	1	2	yes	complemented
674	#460	C₂²×C₈₃	1	1	yes	characteristic, complemented
675	#459	C₂²×C₈₃	1	1	yes	characteristic
676	#459	C₂²×C₈₃	1	1	yes	characteristic
677	#459	C₂²×C₈₃	1	1	yes	characteristic
678	#459	C₂²×C₈₃	1	2	yes	complemented
679	#449	C₂²×C₈₃	1	1	yes	characteristic
680	#449	C₂²×C₈₃	1	1	yes	characteristic
681	#447	C₂²×C₈₃	1	2	yes	—
682	#447	C₂²×C₈₃	1	2	yes	—
683	#446	C₂²×C₈₃	1	1	yes	characteristic, complemented
684	C₈×Q₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
685	#442	C₂²×C₈₃	1	2	yes	—
686	#442	C₂²×C₈₃	1	2	yes	complemented
687	C₄×SD₁₆	C₂²×C₈₃	1	1	yes	characteristic, complemented
688	C₄×SD₁₆	C₂²×C₈₃	1	1	yes	characteristic, complemented
689	C₄×D₈	C₂²×C₈₃	1	1	yes	characteristic
690	C₄×D₈	C₂²×C₈₃	1	1	yes	characteristic
691	C₄×D₈	C₂²×C₈₃	1	2	yes	—
692	C₄×D₈	C₂²×C₈₃	1	2	yes	complemented
693	#436	C₂²×C₈₃	1	1	yes	characteristic
694	#435	C₂²×C₈₃	1	2	yes	complemented
695	C₈×D₄	C₂²×C₈₃	1	1	yes	characteristic
696	C₈×D₄	C₂²×C₈₃	1	2	yes	complemented
697	#433	C₂²×C₈₃	1	2	yes	complemented
698	#431	C₂²×C₈₃	1	1	yes	characteristic, complemented
699	#428	C₂²×C₈₃	1	2	yes	complemented
700	#427	C₂²×C₈₃	1	2	yes	complemented
701	#427	C₂²×C₈₃	1	2	yes	complemented
702	#424	C₂²×C₈₃	1	2	yes	complemented
703	C₂×C₄⋊C₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
704	#418	C₂²×C₈₃	1	2	yes	—
705	#416	C₂²×C₈₃	1	2	yes	—
706	C₂×#102	C₂²×C₈₃	1	2	yes	—
707	C₂×#41	—	2	1	no	—
708	C₂×#41	—	2	1	no	—
709	C₂×#41	—	2	1	no	—
710	C₂×#41	C₂³×C₈₃	1	1	yes	characteristic
711	C₂²×Q₈	—	2	1	no	—
712	C₂²×Q₈	—	2	1	no	—
713	C₂²×D₄	—	2	1	no	—
714	C₂²×D₄	C₂³×C₈₃	1	2	yes	—
715	C₂×SD₁₆	C₂³×C₈₃	1	1	yes	characteristic
716	C₂×SD₁₆	C₂³×C₈₃	1	1	yes	characteristic
717	C₂×D₈	C₂³×C₈₃	1	1	yes	characteristic
718	C₂×D₈	C₂³×C₈₃	1	1	yes	characteristic
719	C₂×D₈	C₂³×C₈₃	1	2	yes	—
720	C₂×D₈	C₂³×C₈₃	1	2	yes	—
721	C₂×M₁₆	C₂³×C₈₃	1	2	yes	—
722	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
723	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
724	C₄⋊Q₈	—	2	2	no	—
725	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
726	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
727	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
728	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
729	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
730	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
731	#127	C₂³×C₈₃	1	1	yes	characteristic
732	#127	C₂³×C₈₃	1	1	yes	characteristic
733	#126	—	2	2	no	—
734	#126	—	2	2	no	—
735	#126	—	2	2	no	—
736	#126	D₄×C₈₃	1	2	yes	—
737	#125	—	2	2	no	—
738	#125	D₄×C₈₃	1	1	yes	characteristic
739	#125	C₂³×C₈₃	1	2	yes	—
740	#125	C₂³×C₈₃	1	2	yes	—
741	#124	—	2	1	no	—
742	#124	—	2	1	no	—
743	#124	—	2	2	no	—
744	#124	—	2	2	no	—
745	#124	—	2	2	no	—
746	#124	—	2	2	no	—
747	#124	—	2	2	no	—
748	#124	—	2	2	no	—
749	#124	—	2	1	no	—
750	#124	—	2	1	no	—
751	#124	D₄×C₈₃	1	1	yes	characteristic
752	#124	C₂³×C₈₃	1	2	yes	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	#123	—	2	2	no	—
757	#123	—	2	2	no	—
758	#123	—	2	2	no	—
759	#123	—	2	2	no	—
760	#123	D₄×C₈₃	1	2	yes	—
761	C₂²⋊Q₈	—	2	1	no	—
762	C₂²⋊Q₈	—	2	1	no	—
763	C₂²⋊Q₈	—	2	1	no	—
764	C₂²⋊Q₈	—	2	1	no	—
765	C₂²⋊Q₈	—	2	1	no	—
766	C₂²⋊Q₈	—	2	1	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	D₄×C₈₃	1	1	yes	characteristic
774	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
775	#121	—	2	1	no	—
776	#121	—	2	2	no	—
777	#121	—	2	2	no	—
778	#121	—	2	2	no	—
779	#121	—	2	1	no	—
780	#121	—	2	1	no	—
781	#121	—	2	1	no	—
782	#121	—	2	2	no	—
783	#121	—	2	2	no	—
784	#121	—	2	2	no	—
785	#121	D₄×C₈₃	1	1	yes	characteristic
786	#121	C₂³×C₈₃	1	2	yes	—
787	#121	C₂³×C₈₃	1	1	yes	characteristic
788	#121	C₂³×C₈₃	1	1	yes	characteristic
789	#121	C₂³×C₈₃	1	2	yes	—
790	#121	C₂³×C₈₃	1	2	yes	—
791	#121	C₂³×C₈₃	1	2	yes	—
792	#120	—	2	2	no	—
793	#120	—	2	2	no	—
794	C₄×Q₈	—	2	1	no	—
795	C₄×Q₈	—	2	1	no	—
796	C₄×Q₈	—	2	1	no	—
797	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
798	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
799	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	—	2	1	no	—
802	C₄×D₄	—	2	2	no	—
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	2	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
809	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
810	C₄×D₄	C₂³×C₈₃	1	2	yes	—
811	C₄×D₄	C₂³×C₈₃	1	2	yes	—
812	C₄×D₄	C₂³×C₈₃	1	2	yes	—
813	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
814	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
815	C₄×D₄	C₂³×C₈₃	1	2	yes	—
816	C₄×D₄	C₂³×C₈₃	1	2	yes	—
817	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
818	C₄×D₄	C₂³×C₈₃	1	2	yes	—
819	#117	—	2	2	no	—
820	#117	—	2	1	no	—
821	#117	—	2	2	no	—
822	#117	—	2	1	no	—
823	#117	C₂³×C₈₃	1	1	yes	characteristic
824	#117	C₂³×C₈₃	1	2	yes	—
825	#117	C₂³×C₈₃	1	2	yes	—
826	#117	C₂³×C₈₃	1	2	yes	—
827	#117	C₂³×C₈₃	1	2	yes	—
828	C₂×C₄⋊C₄	—	2	1	no	—
829	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
830	C₂×C₂²⋊C₄	—	2	2	no	—
831	C₂×C₂²⋊C₄	—	2	2	no	—
832	C₂×C₂²⋊C₄	—	2	2	no	—
833	C₂×C₄²	—	2	1	no	—
834	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
835	#107	C₂³×C₈₃	1	2	yes	—
836	#107	C₂³×C₈₃	1	2	yes	—
837	#107	C₂³×C₈₃	1	2	yes	—
838	#107	C₂³×C₈₃	1	2	yes	—
839	#107	C₂³×C₈₃	1	2	yes	—
840	#107	C₂³×C₈₃	1	1	yes	characteristic
841	#107	C₂³×C₈₃	1	1	yes	characteristic
842	#107	C₂³×C₈₃	1	2	yes	—
843	#106	C₂³×C₈₃	1	1	yes	characteristic
844	#106	C₂³×C₈₃	1	2	yes	—
845	#106	C₂³×C₈₃	1	2	yes	—
846	#106	C₂³×C₈₃	1	2	yes	—
847	#106	C₂³×C₈₃	1	1	yes	characteristic
848	#106	C₂³×C₈₃	1	2	yes	—
849	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
850	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
851	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
852	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
853	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
854	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
855	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
856	#103	C₂³×C₈₃	1	2	yes	—
857	#103	C₂³×C₈₃	1	2	yes	—
858	#103	C₂³×C₈₃	1	1	yes	characteristic
859	#103	C₂³×C₈₃	1	1	yes	characteristic
860	#102	C₂³×C₈₃	1	1	yes	characteristic
861	#102	C₂³×C₈₃	1	2	yes	—
862	#102	C₂³×C₈₃	1	2	yes	—
863	#102	C₂³×C₈₃	1	2	yes	—
864	#102	C₂³×C₈₃	1	2	yes	—
865	#102	C₂³×C₈₃	1	1	yes	characteristic
866	#102	C₂³×C₈₃	1	2	yes	—
867	#102	C₂³×C₈₃	1	2	yes	—
868	#102	C₂³×C₈₃	1	2	yes	—
869	#102	C₂³×C₈₃	1	1	yes	characteristic
870	#102	C₂³×C₈₃	1	1	yes	characteristic
871	#102	C₂³×C₈₃	1	1	yes	characteristic
872	#102	C₂³×C₈₃	1	2	yes	—
873	#102	C₂³×C₈₃	1	1	yes	characteristic
874	#102	C₂³×C₈₃	1	2	yes	—
875	#102	C₂³×C₈₃	1	2	yes	—
876	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
877	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
878	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
879	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
880	#97	C₂³×C₈₃	1	2	yes	—
881	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
882	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
883	C₄×C₈	C₂³×C₈₃	1	2	yes	—
884	C₂⁴	—	2	2	no	—
885	#41	—	2	2	no	—
886	#41	—	4	1	no	—
887	#41	—	8	2	no	—
888	#41	—	8	2	no	—
889	#41	—	8	2	no	—
890	C₂×Q₈	—	2	1	no	—
891	C₂×Q₈	—	2	1	no	—
892	C₂×Q₈	—	2	1	no	—
893	C₂×Q₈	—	2	2	no	—
894	C₂×Q₈	—	2	2	no	—
895	C₂×Q₈	—	2	1	no	—
896	C₂×Q₈	—	8	2	no	—
897	C₂×Q₈	—	8	2	no	—
898	C₂×Q₈	C₂×D₄×C₈₃	1	1	yes	characteristic
899	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
900	C₂×D₄	—	2	4	no	—
901	C₂×D₄	—	2	1	no	—
902	C₂×D₄	—	2	2	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	2	no	—
905	C₂×D₄	—	2	1	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	—	2	1	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	—	2	1	no	—
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	2	1	no	—
913	C₂×D₄	—	4	2	no	—
914	C₂×D₄	—	8	2	no	—
915	C₂×D₄	C₂×D₄×C₈₃	1	1	yes	characteristic
916	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
917	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
918	C₂×D₄	C₂⁴×C₈₃	1	1	yes	characteristic
919	C₂×D₄	C₂⁴×C₈₃	1	1	yes	characteristic
920	C₂×D₄	C₂⁴×C₈₃	1	1	yes	characteristic
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	—	2	2	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
933	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
934	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
935	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
936	SD₁₆	—	4	1	no	—
937	SD₁₆	—	4	1	no	—
938	D₈	—	2	2	no	—
939	D₈	—	2	2	no	—
940	D₈	—	4	2	no	—
941	D₈	—	4	2	no	—
942	M₁₆	—	4	2	no	—
943	C₂×C₈	—	4	2	no	—
944	C₂×C₈	—	4	2	no	—
945	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
946	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
947	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
948	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
949	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
950	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
966	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
967	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
968	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
969	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
970	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
971	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
972	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
973	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
974	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
975	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
976	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
977	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	1	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	1	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	1	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
1001	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
1002	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
1003	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
1004	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
1005	C₄²	—	2	1	no	—
1006	C₄²	—	2	1	no	—
1007	C₄²	—	2	1	no	—
1008	C₄²	—	2	2	no	—
1009	C₄²	—	2	2	no	—
1010	C₄²	—	2	2	no	—
1011	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
1012	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
1013	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
1014	C₄²	C₂⁴×C₈₃	1	2	yes	—
1015	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
1016	C₂³	—	2	1	no	—
1017	C₂³	—	2	1	no	—
1018	C₂³	—	2	1	no	—
1019	C₂³	—	2	2	no	—
1020	C₂³	—	4	4	no	—
1021	C₂³	—	8	2	no	—
1022	C₂³	—	8	2	no	—
1023	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
1024	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
1025	Q₈	—	2	2	no	—
1026	Q₈	—	2	1	no	—
1027	Q₈	—	2	1	no	—
1028	Q₈	—	4	2	no	—
1029	Q₈	—	4	2	no	—
1030	Q₈	—	8	2	no	—
1031	Q₈	—	8	2	no	—
1032	Q₈	—	8	1	no	—
1033	Q₈	—	8	1	no	—
1034	D₄	—	2	2	no	—
1035	D₄	—	2	1	no	—
1036	D₄	—	2	1	no	—
1037	D₄	—	2	2	no	—
1038	D₄	—	2	1	no	—
1039	D₄	—	2	1	no	—
1040	D₄	—	2	1	no	—
1041	D₄	—	2	2	no	—
1042	D₄	—	4	2	no	—
1043	D₄	—	4	4	no	—
1044	D₄	—	4	2	no	—
1045	D₄	—	4	2	no	—
1046	D₄	—	8	1	no	—
1047	D₄	—	8	1	no	—
1048	D₄	—	8	1	no	—
1049	D₄	—	8	2	no	—
1050	D₄	—	8	1	no	—
1051	D₄	—	8	1	no	—
1052	D₄	—	8	2	no	—
1053	D₄	—	8	2	no	—
1054	D₄	—	8	2	no	—
1055	D₄	2₋¹⁺⁴×C₈₃	1	2	yes	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	4	1	no	—
1070	C₂×C₄	—	4	2	no	—
1071	C₂×C₄	—	4	2	no	—
1072	C₂×C₄	—	4	2	no	—
1073	C₂×C₄	—	4	2	no	—
1074	C₂×C₄	—	8	2	no	—
1075	C₂×C₄	—	8	2	no	—
1076	C₂×C₄	—	8	2	no	—
1077	C₂×C₄	—	8	1	no	—
1078	C₂×C₄	—	8	2	no	—
1079	C₂×C₄	—	8	2	no	—
1080	C₂×C₄	—	8	2	no	—
1081	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1082	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
1083	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1084	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1085	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1086	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
1087	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
1088	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1089	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
1090	C₈	—	2	1	no	—
1091	C₈	—	2	1	no	—
1092	C₈	—	2	2	no	—
1093	C₈	—	2	1	no	—
1094	C₈	—	2	2	no	—
1095	C₈	—	2	1	no	—
1096	C₂²	—	2	1	no	—
1097	C₂²	—	2	2	no	—
1098	C₂²	—	2	1	no	—
1099	C₂²	—	2	2	no	—
1100	C₂²	—	2	1	no	—
1101	C₂²	—	2	2	no	—
1102	C₂²	—	2	2	no	—
1103	C₂²	—	4	1	no	—
1104	C₂²	—	4	1	no	—
1105	C₂²	—	4	1	no	—
1106	C₂²	—	4	1	no	—
1107	C₂²	—	4	2	no	—
1108	C₂²	—	4	1	no	—
1109	C₂²	—	4	2	no	—
1110	C₂²	—	4	1	no	—
1111	C₂²	—	4	2	no	—
1112	C₂²	—	4	1	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	—	16	4	no	—
1115	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
1116	C₄	—	2	1	no	—
1117	C₄	—	2	2	no	—
1118	C₄	—	2	1	no	—
1119	C₄	—	2	1	no	—
1120	C₄	—	2	2	no	—
1121	C₄	—	2	1	no	—
1122	C₄	—	2	2	no	—
1123	C₄	—	4	1	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	1	no	—
1126	C₄	—	4	2	no	—
1127	C₄	—	4	2	no	—
1128	C₄	—	4	1	no	—
1129	C₄	—	4	2	no	—
1130	C₄	—	4	1	no	—
1131	C₄	#576×C₈₃	1	2	yes	—
1132	C₄	C₂×2₋¹⁺⁴×C₈₃	1	1	yes	characteristic
1133	C₄	#585×C₈₃	1	1	yes	characteristic
1134	C₂	—	4	2	no	—
1135	C₂	—	4	1	no	—
1136	C₂	—	4	2	no	—
1137	C₂	—	8	2	no	—
1138	C₂	—	8	1	no	—
1139	C₂	—	8	1	no	—
1140	C₂	C₈₃×#3489	1	1	yes	characteristic
1141	C₂	C₂×#576×C₈₃	1	1	yes	characteristic
1142	C₂	C₈₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₃
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×#3547	C₂	semidirect
2. C₈₃×#3514	C₂	semidirect
3. C₈₃×#3384	C₂	semidirect
4. Q₈×D₈×C₈₃	C₂	semidirect
5. C₈₃×#3373	C₂	semidirect
6. C₈₃×#3361	C₂	semidirect
7. C₈₃×#3353	C₂	semidirect
8. C₈₃×#3347	C₂	semidirect
9. C₈₃×#3341	C₂	semidirect
10. C₈₃×#3340	C₂	semidirect
11. C₈₃×#3325	C₂	semidirect
12. C₈₃×#3319	C₂	semidirect
13. C₈₃×#3297	C₂	semidirect
14. C₈₃×#3294	C₂	semidirect
15. C₈₃×#3257	C₂	semidirect
16. C₈₃×#3245	C₂	semidirect
17. C₈₃×#3243	C₂	semidirect
18. C₈₃×#3228	C₂	semidirect
19. C₈₃×#3122	C₂	semidirect
20. C₈₃×#3106	C₂	semidirect
21. C₈₃×#3081	C₂	semidirect
22. C₈₃×#3076	C₂	semidirect
23. C₈₃×#2994	C₂	semidirect
29. #555×C₈₃	C₂²	semidirect
30. #554×C₈₃	C₂²	semidirect
31. #553×C₈₃	C₂²	semidirect
35. D₄×Q₈×C₈₃	C₂²	semidirect
42. #544×C₈₃	C₂²	semidirect
45. #540×C₈₃	C₂²	semidirect
49. #533×C₈₃	C₂²	semidirect
51. #532×C₈₃	C₂²	semidirect
57. #501×C₈₃	C₂²	semidirect
58. #500×C₈₃	C₂²	semidirect
59. #500×C₈₃	C₂²	semidirect
60. #498×C₈₃	C₂²	semidirect
61. #489×C₈₃	C₂²	semidirect
62. #488×C₈₃	C₂²	semidirect
65. #485×C₈₃	C₂²	semidirect
66. #484×C₈₃	C₂²	semidirect
68. #482×C₈₃	C₂²	semidirect
69. #482×C₈₃	C₂²	semidirect
70. #482×C₈₃	C₂²	semidirect
71. #482×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. #476×C₈₃	C₂²	semidirect
87. #475×C₈₃	C₂²	semidirect
90. #474×C₈₃	C₂²	semidirect
91. #474×C₈₃	C₂²	semidirect
92. #474×C₈₃	C₂²	semidirect
93. #474×C₈₃	C₂²	semidirect
95. #468×C₈₃	C₂²	semidirect
97. #466×C₈₃	C₂²	semidirect
98. #466×C₈₃	C₂²	semidirect
99. #465×C₈₃	C₂²	semidirect
100. #463×C₈₃	C₂²	semidirect
101. #463×C₈₃	C₂²	semidirect
102. #460×C₈₃	C₂²	semidirect
106. #459×C₈₃	C₂²	semidirect
111. #446×C₈₃	C₂²	semidirect
112. C₈×Q₈×C₈₃	C₂²	semidirect
114. #442×C₈₃	C₂²	semidirect
115. C₄×SD₁₆×C₈₃	C₂²	semidirect
116. C₄×SD₁₆×C₈₃	C₂²	semidirect
120. C₄×D₈×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
562. #62215	C₈₃	direct (N × H)
572. #3547	C₂×C₈₃	semidirect
573. #3514	C₂×C₈₃	semidirect
574. #3384	C₂×C₈₃	semidirect
575. Q₈×D₈	C₂×C₈₃	semidirect
576. #3373	C₂×C₈₃	semidirect
577. #3361	C₂×C₈₃	semidirect
578. #3353	C₂×C₈₃	semidirect
579. #3347	C₂×C₈₃	semidirect
580. #3341	C₂×C₈₃	semidirect
581. #3340	C₂×C₈₃	semidirect
582. #3325	C₂×C₈₃	semidirect
583. #3319	C₂×C₈₃	semidirect
584. #3297	C₂×C₈₃	semidirect
585. #3294	C₂×C₈₃	semidirect
586. #3257	C₂×C₈₃	semidirect
587. #3245	C₂×C₈₃	semidirect
588. #3243	C₂×C₈₃	semidirect
589. #3228	C₂×C₈₃	semidirect
590. #3122	C₂×C₈₃	semidirect
591. #3106	C₂×C₈₃	semidirect
592. #3081	C₂×C₈₃	semidirect
593. #3076	C₂×C₈₃	semidirect
594. #2994	C₂×C₈₃	semidirect
595. C₈₃	#62215	direct (N × H)
601. #555	C₂²×C₈₃	semidirect
602. #554	C₂²×C₈₃	semidirect
603. #553	C₂²×C₈₃	semidirect
607. D₄×Q₈	C₂²×C₈₃	semidirect
614. #544	C₂²×C₈₃	semidirect
617. #540	C₂²×C₈₃	semidirect
621. #533	C₂²×C₈₃	semidirect
623. #532	C₂²×C₈₃	semidirect
629. #501	C₂²×C₈₃	semidirect
630. #500	C₂²×C₈₃	semidirect
631. #500	C₂²×C₈₃	semidirect
632. #498	C₂²×C₈₃	semidirect
633. #489	C₂²×C₈₃	semidirect
634. #488	C₂²×C₈₃	semidirect
637. #485	C₂²×C₈₃	semidirect
638. #484	C₂²×C₈₃	semidirect
640. #482	C₂²×C₈₃	semidirect
641. #482	C₂²×C₈₃	semidirect
642. #482	C₂²×C₈₃	semidirect
643. #482	C₂²×C₈₃	semidirect
644. #482	C₂²×C₈₃	semidirect
645. #482	C₂²×C₈₃	semidirect
647. #479	C₂²×C₈₃	semidirect
650. #478	C₂²×C₈₃	semidirect
651. #478	C₂²×C₈₃	semidirect
652. #478	C₂²×C₈₃	semidirect
653. #477	C₂²×C₈₃	semidirect
654. #477	C₂²×C₈₃	semidirect
657. #476	C₂²×C₈₃	semidirect
658. #476	C₂²×C₈₃	semidirect
659. #475	C₂²×C₈₃	semidirect
662. #474	C₂²×C₈₃	semidirect
663. #474	C₂²×C₈₃	semidirect
664. #474	C₂²×C₈₃	semidirect
665. #474	C₂²×C₈₃	semidirect
667. #468	C₂²×C₈₃	semidirect
669. #466	C₂²×C₈₃	semidirect
670. #466	C₂²×C₈₃	semidirect
671. #465	C₂²×C₈₃	semidirect
672. #463	C₂²×C₈₃	semidirect
673. #463	C₂²×C₈₃	semidirect
674. #460	C₂²×C₈₃	semidirect
678. #459	C₂²×C₈₃	semidirect
683. #446	C₂²×C₈₃	semidirect
684. C₈×Q₈	C₂²×C₈₃	semidirect
686. #442	C₂²×C₈₃	semidirect
687. C₄×SD₁₆	C₂²×C₈₃	semidirect
688. C₄×SD₁₆	C₂²×C₈₃	semidirect
692. C₄×D₈	C₂²×C₈₃	semidirect
694. #435	C₂²×C₈₃	semidirect
696. C₈×D₄	C₂²×C₈₃	semidirect
697. #433	C₂²×C₈₃	semidirect
698. #431	C₂²×C₈₃	semidirect
699. #428	C₂²×C₈₃	semidirect
700. #427	C₂²×C₈₃	semidirect
701. #427	C₂²×C₈₃	semidirect
702. #424	C₂²×C₈₃	semidirect
703. 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×#3547	2
C₈₃×#3514	2
C₈₃×#3384	2
Q₈×D₈×C₈₃	2
C₈₃×#3373	2
C₈₃×#3361	2
C₈₃×#3353	2
C₈₃×#3347	2
C₈₃×#3341	2
C₈₃×#3340	2
C₈₃×#3325	2
C₈₃×#3319	2
C₈₃×#3297	2
C₈₃×#3294	2
C₈₃×#3257	2
C₈₃×#3245	2
C₈₃×#3243	2
C₈₃×#3228	2
C₈₃×#3122	2
C₈₃×#3106	2
C₈₃×#3081	2
C₈₃×#3076	2
C₈₃×#2994	2
#62215	83

Subgroups — C83×#62215 #35290039

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#62215 #35290039