Subgroups — C₈₃×#62201 #35290025

Order 21248.

1744 conjugacy classes of subgroups.

The subgroup lattice has 1126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₃×#3520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₃×#3386	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×D₈×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₃×#3367	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₃×#3364	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₃×#3353	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₃×#3346	C₂	1	2	yes	maximal, complemented
9	C₈₃×#3338	C₂	1	2	yes	maximal, complemented
10	C₈₃×#3334	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₃×#3330	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₃×#3314	C₂	1	2	yes	maximal, complemented
13	C₈₃×#3302	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₃×#3297	C₂	1	2	yes	maximal, complemented
15	C₈₃×#3262	C₂	1	2	yes	maximal, complemented
16	C₈₃×#3248	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₃×#3243	C₂	1	2	yes	maximal, complemented
18	C₈₃×#3230	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₃×#3124	C₂	1	2	yes	maximal, complemented
20	C₈₃×#3105	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₃×#3083	C₂	1	2	yes	maximal, complemented
22	C₂×#474×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₈₃×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	#563×C₈₃	—	2	2	no	—
25	#557×C₈₃	C₂²	1	1	yes	characteristic, complemented
26	#556×C₈₃	C₂²	1	1	yes	characteristic
27	#556×C₈₃	C₂²	1	1	yes	characteristic, complemented
28	#554×C₈₃	C₂²	1	2	yes	—
29	#554×C₈₃	C₂²	1	2	yes	—
30	#553×C₈₃	C₂²	1	2	yes	—
31	#552×C₈₃	—	2	1	no	—
32	#551×C₈₃	—	2	2	no	—
33	D₄×Q₈×C₈₃	—	2	1	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	#547×C₈₃	C₂²	1	1	yes	characteristic
40	#547×C₈₃	C₂²	1	1	yes	characteristic, complemented
41	#546×C₈₃	C₂²	1	2	yes	—
42	#544×C₈₃	C₂²	1	2	yes	complemented
43	#542×C₈₃	C₂²	1	2	yes	—
44	#542×C₈₃	C₂²	1	2	yes	complemented
45	#541×C₈₃	—	2	1	no	—
46	#539×C₈₃	—	2	2	no	—
47	#539×C₈₃	—	2	2	no	—
48	#536×C₈₃	—	2	1	no	—
49	#533×C₈₃	C₂²	1	1	yes	characteristic
50	C₂×C₄⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
51	#529×C₈₃	C₂²	1	1	yes	characteristic
52	#529×C₈₃	C₂²	1	1	yes	characteristic
53	#525×C₈₃	—	2	1	no	—
54	C₂×C₂²⋊Q₈×C₈₃	—	2	1	no	—
55	#520×C₈₃	C₂²	1	2	yes	—
56	C₂×C₄×D₄×C₈₃	C₂²	1	1	yes	characteristic
57	#501×C₈₃	C₂²	1	2	yes	complemented
58	#500×C₈₃	C₂²	1	1	yes	characteristic, complemented
59	#500×C₈₃	C₂²	1	2	yes	complemented
60	#500×C₈₃	C₂²	1	1	yes	characteristic, complemented
61	#489×C₈₃	C₂²	1	2	yes	—
62	#488×C₈₃	C₂²	1	2	yes	—
63	#487×C₈₃	C₂²	1	1	yes	characteristic, complemented
64	#487×C₈₃	C₂²	1	1	yes	characteristic, complemented
65	#485×C₈₃	C₂²	1	2	yes	complemented
66	#484×C₈₃	C₂²	1	2	yes	—
67	#484×C₈₃	C₂²	1	2	yes	—
68	#484×C₈₃	C₂²	1	1	yes	characteristic
69	#484×C₈₃	C₂²	1	2	yes	complemented
70	#484×C₈₃	C₂²	1	2	yes	complemented
71	#482×C₈₃	C₂²	1	2	yes	—
72	#481×C₈₃	C₂²	1	1	yes	characteristic
73	#480×C₈₃	C₂²	1	2	yes	—
74	#480×C₈₃	C₂²	1	2	yes	complemented
75	#479×C₈₃	C₂²	1	2	yes	complemented
76	#479×C₈₃	C₂²	1	2	yes	complemented
77	#478×C₈₃	C₂²	1	2	yes	—
78	#478×C₈₃	C₂²	1	1	yes	characteristic
79	#478×C₈₃	C₂²	1	1	yes	characteristic
80	#477×C₈₃	C₂²	1	2	yes	complemented
81	#477×C₈₃	C₂²	1	2	yes	complemented
82	#477×C₈₃	C₂²	1	2	yes	complemented
83	#477×C₈₃	C₂²	1	2	yes	complemented
84	#475×C₈₃	C₂²	1	1	yes	characteristic, complemented
85	#474×C₈₃	C₂²	1	1	yes	characteristic
86	#474×C₈₃	C₂²	1	2	yes	—
87	#474×C₈₃	C₂²	1	1	yes	characteristic
88	#474×C₈₃	C₂²	1	1	yes	characteristic
89	#474×C₈₃	C₂²	1	2	yes	—
90	#474×C₈₃	C₂²	1	1	yes	characteristic
91	#474×C₈₃	C₂²	1	2	yes	—
92	#474×C₈₃	C₂²	1	1	yes	characteristic, complemented
93	#474×C₈₃	C₂²	1	2	yes	complemented
94	#468×C₈₃	C₂²	1	2	yes	—
95	#468×C₈₃	C₂²	1	2	yes	complemented
96	#467×C₈₃	C₂²	1	2	yes	—
97	#467×C₈₃	C₂²	1	2	yes	complemented
98	#466×C₈₃	C₂²	1	2	yes	—
99	#465×C₈₃	C₂²	1	2	yes	—
100	#464×C₈₃	C₂²	1	2	yes	—
101	#464×C₈₃	C₂²	1	2	yes	complemented
102	#463×C₈₃	C₂²	1	2	yes	—
103	#463×C₈₃	C₂²	1	1	yes	characteristic
104	#463×C₈₃	C₂²	1	1	yes	characteristic
105	#462×C₈₃	C₂²	1	1	yes	characteristic, complemented
106	#461×C₈₃	C₂²	1	1	yes	characteristic, complemented
107	#452×C₈₃	C₂²	1	2	yes	—
108	#450×C₈₃	C₂²	1	1	yes	characteristic
109	#449×C₈₃	C₂²	1	2	yes	—
110	#447×C₈₃	C₂²	1	1	yes	characteristic
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	2	yes	complemented
116	C₄×SD₁₆×C₈₃	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×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	1	yes	characteristic
121	#436×C₈₃	C₂²	1	1	yes	characteristic, complemented
122	#435×C₈₃	C₂²	1	2	yes	—
123	C₈×D₄×C₈₃	C₂²	1	2	yes	—
124	C₈×D₄×C₈₃	C₂²	1	1	yes	characteristic, complemented
125	#433×C₈₃	C₂²	1	2	yes	complemented
126	#431×C₈₃	C₂²	1	1	yes	characteristic
127	#428×C₈₃	C₂²	1	2	yes	complemented
128	C₂×#107×C₈₃	C₂²	1	2	yes	—
129	C₂×#107×C₈₃	C₂²	1	2	yes	complemented
130	#424×C₈₃	C₂²	1	2	yes	complemented
131	C₂×C₄⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
132	#417×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	C₂³	1	2	yes	—
138	C₂²×Q₈×C₈₃	—	2	1	no	—
139	C₂²×Q₈×C₈₃	—	2	1	no	—
140	C₂²×Q₈×C₈₃	—	2	1	no	—
141	C₂²×D₄×C₈₃	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₈₃	—	2	1	no	—
143	C₂×Q₁₆×C₈₃	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₈₃	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₈₃	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
147	C₂×D₈×C₈₃	C₂³	1	1	yes	characteristic
148	C₂×D₈×C₈₃	C₂³	1	1	yes	characteristic
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	1	no	—
153	C₄⋊Q₈×C₈₃	—	2	2	no	—
154	C₄⋊Q₈×C₈₃	—	2	1	no	—
155	C₄⋊Q₈×C₈₃	—	2	1	no	—
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	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
161	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
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	1	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	2	no	—
174	#125×C₈₃	—	2	1	no	—
175	#125×C₈₃	D₄	1	1	yes	characteristic
176	#125×C₈₃	C₂³	1	1	yes	characteristic
177	#125×C₈₃	C₂³	1	2	yes	—
178	#124×C₈₃	—	2	1	no	—
179	#124×C₈₃	—	2	2	no	—
180	#124×C₈₃	—	2	2	no	—
181	#124×C₈₃	D₄	1	1	yes	characteristic
182	#124×C₈₃	C₂³	1	1	yes	characteristic
183	#124×C₈₃	C₂³	1	2	yes	—
184	#123×C₈₃	—	2	1	no	—
185	#123×C₈₃	—	2	2	no	—
186	#123×C₈₃	—	2	2	no	—
187	#123×C₈₃	—	2	2	no	—
188	#123×C₈₃	—	2	2	no	—
189	#123×C₈₃	—	2	2	no	—
190	#123×C₈₃	—	2	2	no	—
191	#123×C₈₃	—	2	2	no	—
192	#123×C₈₃	D₄	1	2	yes	—
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	1	no	—
197	C₂²⋊Q₈×C₈₃	—	2	1	no	—
198	C₂²⋊Q₈×C₈₃	—	2	2	no	—
199	C₂²⋊Q₈×C₈₃	—	2	2	no	—
200	C₂²⋊Q₈×C₈₃	—	2	1	no	—
201	C₂²⋊Q₈×C₈₃	—	2	1	no	—
202	C₂²⋊Q₈×C₈₃	—	2	2	no	—
203	C₂²⋊Q₈×C₈₃	—	2	2	no	—
204	C₂²⋊Q₈×C₈₃	—	2	2	no	—
205	C₂²⋊Q₈×C₈₃	—	2	2	no	—
206	C₂²⋊Q₈×C₈₃	—	2	2	no	—
207	C₂²⋊Q₈×C₈₃	—	2	2	no	—
208	C₂²⋊Q₈×C₈₃	—	2	2	no	—
209	C₂²⋊Q₈×C₈₃	D₄	1	1	yes	characteristic
210	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
211	C₂²⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
212	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
213	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
214	#121×C₈₃	—	2	1	no	—
215	#121×C₈₃	—	2	2	no	—
216	#121×C₈₃	—	2	2	no	—
217	#121×C₈₃	D₄	1	1	yes	characteristic
218	#121×C₈₃	C₂³	1	1	yes	characteristic
219	#121×C₈₃	C₂³	1	2	yes	—
220	#121×C₈₃	C₂³	1	2	yes	—
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	2	yes	—
226	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
227	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
229	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
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	2	no	—
235	C₄×D₄×C₈₃	—	2	2	no	—
236	C₄×D₄×C₈₃	—	2	1	no	—
237	C₄×D₄×C₈₃	—	2	1	no	—
238	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
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	2	yes	—
244	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₈₃	C₂³	1	2	yes	—
246	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
247	#117×C₈₃	—	2	1	no	—
248	#117×C₈₃	—	2	2	no	—
249	#117×C₈₃	—	2	1	no	—
250	#117×C₈₃	—	2	1	no	—
251	#117×C₈₃	C₂³	1	2	yes	—
252	#117×C₈₃	C₂³	1	2	yes	—
253	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
254	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
255	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
256	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
260	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
261	C₂×C₂²⋊C₄×C₈₃	—	2	2	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	2	yes	—
269	#107×C₈₃	C₂³	1	2	yes	—
270	#107×C₈₃	C₂³	1	1	yes	characteristic
271	#107×C₈₃	C₂³	1	2	yes	—
272	#107×C₈₃	C₂³	1	2	yes	—
273	#107×C₈₃	C₂³	1	1	yes	characteristic
274	#106×C₈₃	C₂³	1	2	yes	—
275	#106×C₈₃	C₂³	1	1	yes	characteristic
276	#106×C₈₃	C₂³	1	1	yes	characteristic
277	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
278	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
279	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
281	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
282	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
287	#103×C₈₃	C₂³	1	2	yes	—
288	#103×C₈₃	C₂³	1	2	yes	—
289	#103×C₈₃	C₂³	1	2	yes	—
290	#103×C₈₃	C₂³	1	2	yes	—
291	#103×C₈₃	C₂³	1	2	yes	—
292	#103×C₈₃	C₂³	1	2	yes	—
293	#102×C₈₃	C₂³	1	2	yes	—
294	#102×C₈₃	C₂³	1	1	yes	characteristic
295	#102×C₈₃	C₂³	1	1	yes	characteristic
296	#102×C₈₃	C₂³	1	2	yes	—
297	#102×C₈₃	C₂³	1	2	yes	—
298	#102×C₈₃	C₂³	1	2	yes	—
299	#102×C₈₃	C₂³	1	2	yes	—
300	#102×C₈₃	C₂³	1	1	yes	characteristic
301	#102×C₈₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
306	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
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	1	no	—
313	#41×C₈₃	—	2	4	no	—
314	#41×C₈₃	—	4	2	no	—
315	#41×C₈₃	—	8	2	no	—
316	#41×C₈₃	—	8	2	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	—	2	2	no	—
323	C₂×Q₈×C₈₃	—	8	2	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	2	yes	—
328	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
329	C₂×D₄×C₈₃	—	2	2	no	—
330	C₂×D₄×C₈₃	—	2	1	no	—
331	C₂×D₄×C₈₃	—	2	2	no	—
332	C₂×D₄×C₈₃	—	2	2	no	—
333	C₂×D₄×C₈₃	—	2	2	no	—
334	C₂×D₄×C₈₃	—	2	1	no	—
335	C₂×D₄×C₈₃	—	4	1	no	—
336	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
337	C₂×D₄×C₈₃	C₂×D₄	1	1	yes	characteristic
338	C₂×D₄×C₈₃	C₂⁴	1	1	yes	characteristic
339	C₂×D₄×C₈₃	C₂⁴	1	1	yes	characteristic
340	C₂×D₄×C₈₃	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₈₃	—	2	1	no	—
342	C₂²×C₄×C₈₃	—	2	2	no	—
343	C₂²×C₄×C₈₃	—	2	2	no	—
344	C₂²×C₄×C₈₃	—	2	2	no	—
345	C₂²×C₄×C₈₃	—	2	2	no	—
346	C₂²×C₄×C₈₃	—	2	1	no	—
347	C₂²×C₄×C₈₃	—	2	1	no	—
348	C₂²×C₄×C₈₃	—	2	1	no	—
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	2	no	—
353	C₂²×C₄×C₈₃	—	8	2	no	—
354	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
358	Q₁₆×C₈₃	—	4	2	no	—
359	SD₁₆×C₈₃	—	2	2	no	—
360	SD₁₆×C₈₃	—	4	2	no	—
361	SD₁₆×C₈₃	—	4	1	no	—
362	D₈×C₈₃	—	2	2	no	—
363	D₈×C₈₃	—	4	1	no	—
364	M₁₆×C₈₃	—	4	2	no	—
365	C₂×C₈×C₈₃	—	4	2	no	—
366	C₂×C₈×C₈₃	—	4	2	no	—
367	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
368	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
370	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
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	1	no	—
379	C₄⋊C₄×C₈₃	—	2	2	no	—
380	C₄⋊C₄×C₈₃	—	2	1	no	—
381	C₄⋊C₄×C₈₃	—	2	1	no	—
382	C₄⋊C₄×C₈₃	—	2	2	no	—
383	C₄⋊C₄×C₈₃	—	2	2	no	—
384	C₄⋊C₄×C₈₃	—	2	1	no	—
385	C₄⋊C₄×C₈₃	—	2	1	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	1	no	—
391	C₄⋊C₄×C₈₃	—	2	2	no	—
392	C₄⋊C₄×C₈₃	—	2	2	no	—
393	C₄⋊C₄×C₈₃	—	2	2	no	—
394	C₄⋊C₄×C₈₃	—	2	2	no	—
395	C₄⋊C₄×C₈₃	—	2	2	no	—
396	C₄⋊C₄×C₈₃	—	2	1	no	—
397	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
406	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
407	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
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	1	no	—
416	C₂²⋊C₄×C₈₃	—	2	1	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	2	no	—
423	C₂²⋊C₄×C₈₃	—	2	1	no	—
424	C₂²⋊C₄×C₈₃	—	2	1	no	—
425	C₂²⋊C₄×C₈₃	—	2	2	no	—
426	C₂²⋊C₄×C₈₃	—	2	1	no	—
427	C₂²⋊C₄×C₈₃	—	2	2	no	—
428	C₂²⋊C₄×C₈₃	—	2	1	no	—
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	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
434	C₄²×C₈₃	—	2	2	no	—
435	C₄²×C₈₃	—	2	2	no	—
436	C₄²×C₈₃	—	2	1	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	—	4	2	no	—
448	C₂³×C₈₃	—	4	2	no	—
449	C₂³×C₈₃	—	8	1	no	—
450	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
451	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
452	Q₈×C₈₃	—	2	2	no	—
453	Q₈×C₈₃	—	2	1	no	—
454	Q₈×C₈₃	—	2	2	no	—
455	Q₈×C₈₃	—	2	1	no	—
456	Q₈×C₈₃	—	2	2	no	—
457	Q₈×C₈₃	—	4	2	no	—
458	Q₈×C₈₃	—	4	2	no	—
459	Q₈×C₈₃	—	4	2	no	—
460	Q₈×C₈₃	—	8	2	no	—
461	Q₈×C₈₃	—	8	2	no	—
462	Q₈×C₈₃	—	8	2	no	—
463	D₄×C₈₃	—	2	4	no	—
464	D₄×C₈₃	—	2	2	no	—
465	D₄×C₈₃	—	2	1	no	—
466	D₄×C₈₃	—	2	1	no	—
467	D₄×C₈₃	—	2	1	no	—
468	D₄×C₈₃	—	2	1	no	—
469	D₄×C₈₃	—	2	1	no	—
470	D₄×C₈₃	—	4	2	no	—
471	D₄×C₈₃	—	4	4	no	—
472	D₄×C₈₃	—	4	2	no	—
473	D₄×C₈₃	—	8	2	no	—
474	D₄×C₈₃	—	8	2	no	—
475	D₄×C₈₃	2₋¹⁺⁴	1	2	yes	—
476	C₂×C₄×C₈₃	—	2	2	no	—
477	C₂×C₄×C₈₃	—	2	2	no	—
478	C₂×C₄×C₈₃	—	2	1	no	—
479	C₂×C₄×C₈₃	—	2	2	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	2	no	—
485	C₂×C₄×C₈₃	—	2	1	no	—
486	C₂×C₄×C₈₃	—	2	2	no	—
487	C₂×C₄×C₈₃	—	2	2	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	—	4	4	no	—
492	C₂×C₄×C₈₃	—	4	2	no	—
493	C₂×C₄×C₈₃	—	4	2	no	—
494	C₂×C₄×C₈₃	—	4	2	no	—
495	C₂×C₄×C₈₃	—	8	1	no	—
496	C₂×C₄×C₈₃	—	8	1	no	—
497	C₂×C₄×C₈₃	—	8	2	no	—
498	C₂×C₄×C₈₃	—	8	2	no	—
499	C₂×C₄×C₈₃	—	8	1	no	—
500	C₂×C₄×C₈₃	—	8	2	no	—
501	C₂×C₄×C₈₃	—	8	2	no	—
502	C₂×C₄×C₈₃	—	8	2	no	—
503	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
505	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
506	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
510	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
512	C₈×C₈₃	—	2	1	no	—
513	C₈×C₈₃	—	2	1	no	—
514	C₈×C₈₃	—	2	1	no	—
515	C₈×C₈₃	—	2	2	no	—
516	C₈×C₈₃	—	2	2	no	—
517	C₈×C₈₃	—	2	1	no	—
518	C₂²×C₈₃	—	2	1	no	—
519	C₂²×C₈₃	—	2	1	no	—
520	C₂²×C₈₃	—	2	2	no	—
521	C₂²×C₈₃	—	2	2	no	—
522	C₂²×C₈₃	—	2	2	no	—
523	C₂²×C₈₃	—	2	2	no	—
524	C₂²×C₈₃	—	4	1	no	—
525	C₂²×C₈₃	—	4	1	no	—
526	C₂²×C₈₃	—	4	1	no	—
527	C₂²×C₈₃	—	4	1	no	—
528	C₂²×C₈₃	—	4	1	no	—
529	C₂²×C₈₃	—	4	1	no	—
530	C₂²×C₈₃	—	4	1	no	—
531	C₂²×C₈₃	—	4	1	no	—
532	C₂²×C₈₃	—	8	4	no	—
533	C₂²×C₈₃	#578	1	2	yes	—
534	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
535	C₄×C₈₃	—	2	2	no	—
536	C₄×C₈₃	—	2	1	no	—
537	C₄×C₈₃	—	2	1	no	—
538	C₄×C₈₃	—	2	2	no	—
539	C₄×C₈₃	—	2	1	no	—
540	C₄×C₈₃	—	2	1	no	—
541	C₄×C₈₃	—	2	2	no	—
542	C₄×C₈₃	—	4	2	no	—
543	C₄×C₈₃	—	4	1	no	—
544	C₄×C₈₃	—	4	1	no	—
545	C₄×C₈₃	—	4	1	no	—
546	C₄×C₈₃	—	4	1	no	—
547	C₄×C₈₃	—	4	2	no	—
548	C₄×C₈₃	—	4	2	no	—
549	C₄×C₈₃	—	4	2	no	—
550	C₄×C₈₃	—	4	1	no	—
551	C₄×C₈₃	#576	1	2	yes	—
552	C₄×C₈₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
553	C₄×C₈₃	#585	1	1	yes	characteristic
554	#62201	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
555	C₂×C₈₃	—	2	2	no	—
556	C₂×C₈₃	—	4	2	no	—
557	C₂×C₈₃	—	4	2	no	—
558	C₂×C₈₃	—	8	1	no	—
559	C₂×C₈₃	—	8	1	no	—
560	C₂×C₈₃	#3489	1	1	yes	characteristic
561	C₂×C₈₃	C₂×#576	1	1	yes	characteristic
562	C₂×C₈₃	C₂×#578	1	1	yes	characteristic
563	#3552	C₂×C₈₃	1	1	yes	characteristic, complemented
564	#3520	C₂×C₈₃	1	1	yes	characteristic, complemented
565	#3386	C₂×C₈₃	1	1	yes	characteristic, complemented
566	Q₈×D₈	C₂×C₈₃	1	1	yes	characteristic, complemented
567	#3367	C₂×C₈₃	1	1	yes	characteristic, complemented
568	#3364	C₂×C₈₃	1	1	yes	characteristic, complemented
569	#3353	C₂×C₈₃	1	1	yes	characteristic, complemented
570	#3346	C₂×C₈₃	1	2	yes	complemented
571	#3338	C₂×C₈₃	1	2	yes	complemented
572	#3334	C₂×C₈₃	1	1	yes	characteristic, complemented
573	#3330	C₂×C₈₃	1	1	yes	characteristic, complemented
574	#3314	C₂×C₈₃	1	2	yes	complemented
575	#3302	C₂×C₈₃	1	1	yes	characteristic, complemented
576	#3297	C₂×C₈₃	1	2	yes	complemented
577	#3262	C₂×C₈₃	1	2	yes	complemented
578	#3248	C₂×C₈₃	1	1	yes	characteristic, complemented
579	#3243	C₂×C₈₃	1	2	yes	complemented
580	#3230	C₂×C₈₃	1	1	yes	characteristic, complemented
581	#3124	C₂×C₈₃	1	2	yes	complemented
582	#3105	C₂×C₈₃	1	1	yes	characteristic, complemented
583	#3083	C₂×C₈₃	1	2	yes	complemented
584	C₂×#474	C₂×C₈₃	1	1	yes	characteristic, complemented
585	#2994	C₂×C₈₃	1	1	yes	characteristic, complemented
586	C₈₃	#62201	1	1	yes	characteristic, direct product factor, Sylow
587	#563	—	2	2	no	—
588	#557	C₂²×C₈₃	1	1	yes	characteristic, complemented
589	#556	C₂²×C₈₃	1	1	yes	characteristic
590	#556	C₂²×C₈₃	1	1	yes	characteristic, complemented
591	#554	C₂²×C₈₃	1	2	yes	—
592	#554	C₂²×C₈₃	1	2	yes	—
593	#553	C₂²×C₈₃	1	2	yes	—
594	#552	—	2	1	no	—
595	#551	—	2	2	no	—
596	D₄×Q₈	—	2	1	no	—
597	D₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic
598	D₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
599	#548	—	2	1	no	—
600	#548	—	2	1	no	—
601	#547	C₂²×C₈₃	1	1	yes	characteristic
602	#547	C₂²×C₈₃	1	1	yes	characteristic
603	#547	C₂²×C₈₃	1	1	yes	characteristic, complemented
604	#546	C₂²×C₈₃	1	2	yes	—
605	#544	C₂²×C₈₃	1	2	yes	complemented
606	#542	C₂²×C₈₃	1	2	yes	—
607	#542	C₂²×C₈₃	1	2	yes	complemented
608	#541	—	2	1	no	—
609	#539	—	2	2	no	—
610	#539	—	2	2	no	—
611	#536	—	2	1	no	—
612	#533	C₂²×C₈₃	1	1	yes	characteristic
613	C₂×C₄⋊Q₈	C₂²×C₈₃	1	1	yes	characteristic
614	#529	C₂²×C₈₃	1	1	yes	characteristic
615	#529	C₂²×C₈₃	1	1	yes	characteristic
616	#525	—	2	1	no	—
617	C₂×C₂²⋊Q₈	—	2	1	no	—
618	#520	C₂²×C₈₃	1	2	yes	—
619	C₂×C₄×D₄	C₂²×C₈₃	1	1	yes	characteristic
620	#501	C₂²×C₈₃	1	2	yes	complemented
621	#500	C₂²×C₈₃	1	1	yes	characteristic, complemented
622	#500	C₂²×C₈₃	1	2	yes	complemented
623	#500	C₂²×C₈₃	1	1	yes	characteristic, complemented
624	#489	C₂²×C₈₃	1	2	yes	—
625	#488	C₂²×C₈₃	1	2	yes	—
626	#487	C₂²×C₈₃	1	1	yes	characteristic, complemented
627	#487	C₂²×C₈₃	1	1	yes	characteristic, complemented
628	#485	C₂²×C₈₃	1	2	yes	complemented
629	#484	C₂²×C₈₃	1	1	yes	characteristic
630	#484	C₂²×C₈₃	1	2	yes	—
631	#484	C₂²×C₈₃	1	2	yes	—
632	#484	C₂²×C₈₃	1	2	yes	complemented
633	#484	C₂²×C₈₃	1	2	yes	complemented
634	#482	C₂²×C₈₃	1	2	yes	—
635	#481	C₂²×C₈₃	1	1	yes	characteristic
636	#480	C₂²×C₈₃	1	2	yes	—
637	#480	C₂²×C₈₃	1	2	yes	complemented
638	#479	C₂²×C₈₃	1	2	yes	complemented
639	#479	C₂²×C₈₃	1	2	yes	complemented
640	#478	C₂²×C₈₃	1	1	yes	characteristic
641	#478	C₂²×C₈₃	1	2	yes	—
642	#478	C₂²×C₈₃	1	1	yes	characteristic
643	#477	C₂²×C₈₃	1	2	yes	complemented
644	#477	C₂²×C₈₃	1	2	yes	complemented
645	#477	C₂²×C₈₃	1	2	yes	complemented
646	#477	C₂²×C₈₃	1	2	yes	complemented
647	#475	C₂²×C₈₃	1	1	yes	characteristic, complemented
648	#474	C₂²×C₈₃	1	1	yes	characteristic
649	#474	C₂²×C₈₃	1	1	yes	characteristic
650	#474	C₂²×C₈₃	1	2	yes	—
651	#474	C₂²×C₈₃	1	2	yes	—
652	#474	C₂²×C₈₃	1	1	yes	characteristic
653	#474	C₂²×C₈₃	1	1	yes	characteristic
654	#474	C₂²×C₈₃	1	2	yes	—
655	#474	C₂²×C₈₃	1	1	yes	characteristic, complemented
656	#474	C₂²×C₈₃	1	2	yes	complemented
657	#468	C₂²×C₈₃	1	2	yes	—
658	#468	C₂²×C₈₃	1	2	yes	complemented
659	#467	C₂²×C₈₃	1	2	yes	—
660	#467	C₂²×C₈₃	1	2	yes	complemented
661	#466	C₂²×C₈₃	1	2	yes	—
662	#465	C₂²×C₈₃	1	2	yes	—
663	#464	C₂²×C₈₃	1	2	yes	—
664	#464	C₂²×C₈₃	1	2	yes	complemented
665	#463	C₂²×C₈₃	1	1	yes	characteristic
666	#463	C₂²×C₈₃	1	1	yes	characteristic
667	#463	C₂²×C₈₃	1	2	yes	—
668	#462	C₂²×C₈₃	1	1	yes	characteristic, complemented
669	#461	C₂²×C₈₃	1	1	yes	characteristic, complemented
670	#452	C₂²×C₈₃	1	2	yes	—
671	#450	C₂²×C₈₃	1	1	yes	characteristic
672	#449	C₂²×C₈₃	1	2	yes	—
673	#447	C₂²×C₈₃	1	1	yes	characteristic
674	#446	C₂²×C₈₃	1	1	yes	characteristic, complemented
675	C₈×Q₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
676	#440	C₂²×C₈₃	1	2	yes	—
677	#440	C₂²×C₈₃	1	2	yes	complemented
678	C₄×Q₁₆	C₂²×C₈₃	1	2	yes	complemented
679	C₄×SD₁₆	C₂²×C₈₃	1	1	yes	characteristic
680	C₄×SD₁₆	C₂²×C₈₃	1	1	yes	characteristic
681	C₄×D₈	C₂²×C₈₃	1	1	yes	characteristic
682	C₄×D₈	C₂²×C₈₃	1	1	yes	characteristic
683	C₄×D₈	C₂²×C₈₃	1	2	yes	—
684	#436	C₂²×C₈₃	1	1	yes	characteristic, complemented
685	#435	C₂²×C₈₃	1	2	yes	—
686	C₈×D₄	C₂²×C₈₃	1	2	yes	—
687	C₈×D₄	C₂²×C₈₃	1	1	yes	characteristic, complemented
688	#433	C₂²×C₈₃	1	2	yes	complemented
689	#431	C₂²×C₈₃	1	1	yes	characteristic
690	#428	C₂²×C₈₃	1	2	yes	complemented
691	C₂×#107	C₂²×C₈₃	1	2	yes	—
692	C₂×#107	C₂²×C₈₃	1	2	yes	complemented
693	#424	C₂²×C₈₃	1	2	yes	complemented
694	C₂×C₄⋊C₈	C₂²×C₈₃	1	1	yes	characteristic
695	#417	C₂²×C₈₃	1	2	yes	—
696	#416	C₂²×C₈₃	1	2	yes	—
697	C₂×#102	C₂²×C₈₃	1	2	yes	—
698	C₂×#41	—	2	1	no	—
699	C₂×#41	—	2	1	no	—
700	C₂×#41	C₂³×C₈₃	1	2	yes	—
701	C₂²×Q₈	—	2	1	no	—
702	C₂²×Q₈	—	2	1	no	—
703	C₂²×Q₈	—	2	1	no	—
704	C₂²×D₄	C₂³×C₈₃	1	1	yes	characteristic
705	C₂³×C₄	—	2	1	no	—
706	C₂×Q₁₆	C₂³×C₈₃	1	2	yes	—
707	C₂×SD₁₆	C₂³×C₈₃	1	1	yes	characteristic
708	C₂×SD₁₆	C₂³×C₈₃	1	1	yes	characteristic
709	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
710	C₂×D₈	C₂³×C₈₃	1	1	yes	characteristic
711	C₂×D₈	C₂³×C₈₃	1	1	yes	characteristic
712	C₂×M₁₆	C₂³×C₈₃	1	2	yes	—
713	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
714	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
715	C₄⋊Q₈	—	2	1	no	—
716	C₄⋊Q₈	—	2	2	no	—
717	C₄⋊Q₈	—	2	1	no	—
718	C₄⋊Q₈	—	2	1	no	—
719	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
720	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
721	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
722	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
723	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
724	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
725	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
726	#126	—	2	2	no	—
727	#126	—	2	2	no	—
728	#126	—	2	2	no	—
729	#126	—	2	2	no	—
730	#126	—	2	2	no	—
731	#126	—	2	1	no	—
732	#126	D₄×C₈₃	1	2	yes	—
733	#125	—	2	2	no	—
734	#125	—	2	2	no	—
735	#125	—	2	2	no	—
736	#125	—	2	2	no	—
737	#125	—	2	1	no	—
738	#125	D₄×C₈₃	1	1	yes	characteristic
739	#125	C₂³×C₈₃	1	1	yes	characteristic
740	#125	C₂³×C₈₃	1	2	yes	—
741	#124	—	2	1	no	—
742	#124	—	2	2	no	—
743	#124	—	2	2	no	—
744	#124	D₄×C₈₃	1	1	yes	characteristic
745	#124	C₂³×C₈₃	1	1	yes	characteristic
746	#124	C₂³×C₈₃	1	2	yes	—
747	#123	—	2	1	no	—
748	#123	—	2	2	no	—
749	#123	—	2	2	no	—
750	#123	—	2	2	no	—
751	#123	—	2	2	no	—
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	D₄×C₈₃	1	2	yes	—
756	C₂²⋊Q₈	—	2	1	no	—
757	C₂²⋊Q₈	—	2	1	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	—	2	1	no	—
760	C₂²⋊Q₈	—	2	1	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	—	2	1	no	—
764	C₂²⋊Q₈	—	2	1	no	—
765	C₂²⋊Q₈	—	2	2	no	—
766	C₂²⋊Q₈	—	2	2	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	D₄×C₈₃	1	1	yes	characteristic
773	C₂²⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
774	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
775	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
776	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
777	#121	—	2	1	no	—
778	#121	—	2	2	no	—
779	#121	—	2	2	no	—
780	#121	D₄×C₈₃	1	1	yes	characteristic
781	#121	C₂³×C₈₃	1	1	yes	characteristic
782	#121	C₂³×C₈₃	1	2	yes	—
783	#121	C₂³×C₈₃	1	2	yes	—
784	#120	—	2	2	no	—
785	C₄×Q₈	—	2	1	no	—
786	C₄×Q₈	—	2	1	no	—
787	C₄×Q₈	—	2	1	no	—
788	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
789	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
790	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
791	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
792	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
793	C₄×D₄	—	2	2	no	—
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	2	2	no	—
797	C₄×D₄	—	2	2	no	—
798	C₄×D₄	—	2	2	no	—
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
802	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
803	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
804	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
805	C₄×D₄	C₂³×C₈₃	1	2	yes	—
806	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
807	C₄×D₄	C₂³×C₈₃	1	2	yes	—
808	C₄×D₄	C₂³×C₈₃	1	2	yes	—
809	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
810	#117	—	2	1	no	—
811	#117	—	2	2	no	—
812	#117	—	2	1	no	—
813	#117	—	2	1	no	—
814	#117	C₂³×C₈₃	1	2	yes	—
815	#117	C₂³×C₈₃	1	2	yes	—
816	C₂×C₄⋊C₄	—	2	1	no	—
817	C₂×C₄⋊C₄	—	2	2	no	—
818	C₂×C₄⋊C₄	—	2	1	no	—
819	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
820	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
821	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
822	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
823	C₂×C₂²⋊C₄	—	2	1	no	—
824	C₂×C₂²⋊C₄	—	2	2	no	—
825	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
826	#107	C₂³×C₈₃	1	2	yes	—
827	#107	C₂³×C₈₃	1	2	yes	—
828	#107	C₂³×C₈₃	1	2	yes	—
829	#107	C₂³×C₈₃	1	2	yes	—
830	#107	C₂³×C₈₃	1	1	yes	characteristic
831	#107	C₂³×C₈₃	1	2	yes	—
832	#107	C₂³×C₈₃	1	2	yes	—
833	#107	C₂³×C₈₃	1	2	yes	—
834	#107	C₂³×C₈₃	1	2	yes	—
835	#107	C₂³×C₈₃	1	1	yes	characteristic
836	#107	C₂³×C₈₃	1	2	yes	—
837	#106	C₂³×C₈₃	1	1	yes	characteristic
838	#106	C₂³×C₈₃	1	2	yes	—
839	#106	C₂³×C₈₃	1	1	yes	characteristic
840	C₄⋊C₈	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	1	yes	characteristic
844	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
845	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
846	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
847	#103	C₂³×C₈₃	1	2	yes	—
848	#103	C₂³×C₈₃	1	2	yes	—
849	#103	C₂³×C₈₃	1	2	yes	—
850	#103	C₂³×C₈₃	1	2	yes	—
851	#103	C₂³×C₈₃	1	1	yes	characteristic
852	#103	C₂³×C₈₃	1	1	yes	characteristic
853	#103	C₂³×C₈₃	1	2	yes	—
854	#103	C₂³×C₈₃	1	2	yes	—
855	#103	C₂³×C₈₃	1	2	yes	—
856	#102	C₂³×C₈₃	1	2	yes	—
857	#102	C₂³×C₈₃	1	2	yes	—
858	#102	C₂³×C₈₃	1	2	yes	—
859	#102	C₂³×C₈₃	1	2	yes	—
860	#102	C₂³×C₈₃	1	1	yes	characteristic
861	#102	C₂³×C₈₃	1	1	yes	characteristic
862	#102	C₂³×C₈₃	1	1	yes	characteristic
863	#102	C₂³×C₈₃	1	1	yes	characteristic
864	#102	C₂³×C₈₃	1	1	yes	characteristic
865	#102	C₂³×C₈₃	1	2	yes	—
866	#102	C₂³×C₈₃	1	1	yes	characteristic
867	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
868	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
869	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
870	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
871	#97	C₂³×C₈₃	1	2	yes	—
872	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
873	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
874	C₄×C₈	C₂³×C₈₃	1	2	yes	—
875	C₂⁴	—	2	1	no	—
876	#41	—	2	4	no	—
877	#41	—	4	2	no	—
878	#41	—	8	2	no	—
879	#41	—	8	2	no	—
880	C₂×Q₈	—	2	1	no	—
881	C₂×Q₈	—	2	1	no	—
882	C₂×Q₈	—	2	1	no	—
883	C₂×Q₈	—	2	2	no	—
884	C₂×Q₈	—	2	2	no	—
885	C₂×Q₈	—	2	2	no	—
886	C₂×Q₈	—	8	2	no	—
887	C₂×Q₈	—	8	2	no	—
888	C₂×Q₈	—	8	2	no	—
889	C₂×Q₈	C₂×D₄×C₈₃	1	1	yes	characteristic
890	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
891	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
892	C₂×D₄	—	2	2	no	—
893	C₂×D₄	—	2	1	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	—	2	1	no	—
898	C₂×D₄	—	4	1	no	—
899	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
900	C₂×D₄	C₂×D₄×C₈₃	1	1	yes	characteristic
901	C₂×D₄	C₂⁴×C₈₃	1	1	yes	characteristic
902	C₂×D₄	C₂⁴×C₈₃	1	1	yes	characteristic
903	C₂×D₄	C₂⁴×C₈₃	1	1	yes	characteristic
904	C₂²×C₄	—	2	1	no	—
905	C₂²×C₄	—	2	2	no	—
906	C₂²×C₄	—	2	2	no	—
907	C₂²×C₄	—	2	2	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	1	no	—
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	2	2	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	—	2	2	no	—
916	C₂²×C₄	—	8	2	no	—
917	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
918	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
919	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
920	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
921	Q₁₆	—	4	2	no	—
922	SD₁₆	—	2	2	no	—
923	SD₁₆	—	4	2	no	—
924	SD₁₆	—	4	1	no	—
925	D₈	—	2	2	no	—
926	D₈	—	4	1	no	—
927	M₁₆	—	4	2	no	—
928	C₂×C₈	—	4	2	no	—
929	C₂×C₈	—	4	2	no	—
930	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
931	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
932	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
933	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
934	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
935	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
961	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
962	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
963	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
964	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
965	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
966	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
967	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
968	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
969	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
970	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
971	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
972	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	1	no	—
979	C₂²⋊C₄	—	2	1	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	1	no	—
992	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
993	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
994	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
995	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
996	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
997	C₄²	—	2	2	no	—
998	C₄²	—	2	2	no	—
999	C₄²	—	2	1	no	—
1000	C₄²	—	2	2	no	—
1001	C₄²	—	2	2	no	—
1002	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
1003	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
1004	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
1005	C₄²	C₂⁴×C₈₃	1	2	yes	—
1006	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
1007	C₂³	—	2	1	no	—
1008	C₂³	—	2	1	no	—
1009	C₂³	—	2	1	no	—
1010	C₂³	—	4	2	no	—
1011	C₂³	—	4	2	no	—
1012	C₂³	—	8	1	no	—
1013	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
1014	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
1015	Q₈	—	2	2	no	—
1016	Q₈	—	2	1	no	—
1017	Q₈	—	2	2	no	—
1018	Q₈	—	2	1	no	—
1019	Q₈	—	2	2	no	—
1020	Q₈	—	4	2	no	—
1021	Q₈	—	4	2	no	—
1022	Q₈	—	4	2	no	—
1023	Q₈	—	8	2	no	—
1024	Q₈	—	8	2	no	—
1025	Q₈	—	8	2	no	—
1026	D₄	—	2	4	no	—
1027	D₄	—	2	2	no	—
1028	D₄	—	2	1	no	—
1029	D₄	—	2	1	no	—
1030	D₄	—	2	1	no	—
1031	D₄	—	2	1	no	—
1032	D₄	—	2	1	no	—
1033	D₄	—	4	2	no	—
1034	D₄	—	4	4	no	—
1035	D₄	—	4	2	no	—
1036	D₄	—	8	2	no	—
1037	D₄	—	8	2	no	—
1038	D₄	2₋¹⁺⁴×C₈₃	1	2	yes	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	2	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	4	4	no	—
1055	C₂×C₄	—	4	2	no	—
1056	C₂×C₄	—	4	2	no	—
1057	C₂×C₄	—	4	2	no	—
1058	C₂×C₄	—	8	1	no	—
1059	C₂×C₄	—	8	1	no	—
1060	C₂×C₄	—	8	2	no	—
1061	C₂×C₄	—	8	2	no	—
1062	C₂×C₄	—	8	1	no	—
1063	C₂×C₄	—	8	2	no	—
1064	C₂×C₄	—	8	2	no	—
1065	C₂×C₄	—	8	2	no	—
1066	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1067	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
1068	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
1069	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1070	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1071	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1072	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
1073	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
1074	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
1075	C₈	—	2	1	no	—
1076	C₈	—	2	1	no	—
1077	C₈	—	2	1	no	—
1078	C₈	—	2	2	no	—
1079	C₈	—	2	2	no	—
1080	C₈	—	2	1	no	—
1081	C₂²	—	2	1	no	—
1082	C₂²	—	2	1	no	—
1083	C₂²	—	2	2	no	—
1084	C₂²	—	2	2	no	—
1085	C₂²	—	2	2	no	—
1086	C₂²	—	2	2	no	—
1087	C₂²	—	4	1	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	4	1	no	—
1091	C₂²	—	4	1	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	4	1	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	8	4	no	—
1096	C₂²	#578×C₈₃	1	2	yes	—
1097	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
1098	C₄	—	2	1	no	—
1099	C₄	—	2	2	no	—
1100	C₄	—	2	1	no	—
1101	C₄	—	2	1	no	—
1102	C₄	—	2	2	no	—
1103	C₄	—	2	2	no	—
1104	C₄	—	2	1	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	1	no	—
1108	C₄	—	4	2	no	—
1109	C₄	—	4	2	no	—
1110	C₄	—	4	2	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	4	2	no	—
1113	C₄	—	4	1	no	—
1114	C₄	#576×C₈₃	1	2	yes	—
1115	C₄	C₂×2₋¹⁺⁴×C₈₃	1	1	yes	characteristic
1116	C₄	#585×C₈₃	1	1	yes	characteristic
1117	C₂	—	2	2	no	—
1118	C₂	—	4	2	no	—
1119	C₂	—	4	2	no	—
1120	C₂	—	8	1	no	—
1121	C₂	—	8	1	no	—
1122	C₂	C₈₃×#3489	1	1	yes	characteristic
1123	C₂	C₂×#576×C₈₃	1	1	yes	characteristic
1124	C₂	C₂×#578×C₈₃	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×#3552	C₂	semidirect
2. C₈₃×#3520	C₂	semidirect
3. C₈₃×#3386	C₂	semidirect
4. Q₈×D₈×C₈₃	C₂	semidirect
5. C₈₃×#3367	C₂	semidirect
6. C₈₃×#3364	C₂	semidirect
7. C₈₃×#3353	C₂	semidirect
8. C₈₃×#3346	C₂	semidirect
9. C₈₃×#3338	C₂	semidirect
10. C₈₃×#3334	C₂	semidirect
11. C₈₃×#3330	C₂	semidirect
12. C₈₃×#3314	C₂	semidirect
13. C₈₃×#3302	C₂	semidirect
14. C₈₃×#3297	C₂	semidirect
15. C₈₃×#3262	C₂	semidirect
16. C₈₃×#3248	C₂	semidirect
17. C₈₃×#3243	C₂	semidirect
18. C₈₃×#3230	C₂	semidirect
19. C₈₃×#3124	C₂	semidirect
20. C₈₃×#3105	C₂	semidirect
21. C₈₃×#3083	C₂	semidirect
22. C₂×#474×C₈₃	C₂	semidirect
23. C₈₃×#2994	C₂	semidirect
25. #557×C₈₃	C₂²	semidirect
27. #556×C₈₃	C₂²	semidirect
35. D₄×Q₈×C₈₃	C₂²	semidirect
40. #547×C₈₃	C₂²	semidirect
42. #544×C₈₃	C₂²	semidirect
44. #542×C₈₃	C₂²	semidirect
57. #501×C₈₃	C₂²	semidirect
58. #500×C₈₃	C₂²	semidirect
59. #500×C₈₃	C₂²	semidirect
60. #500×C₈₃	C₂²	semidirect
63. #487×C₈₃	C₂²	semidirect
64. #487×C₈₃	C₂²	semidirect
65. #485×C₈₃	C₂²	semidirect
69. #484×C₈₃	C₂²	semidirect
70. #484×C₈₃	C₂²	semidirect
74. #480×C₈₃	C₂²	semidirect
75. #479×C₈₃	C₂²	semidirect
76. #479×C₈₃	C₂²	semidirect
80. #477×C₈₃	C₂²	semidirect
81. #477×C₈₃	C₂²	semidirect
82. #477×C₈₃	C₂²	semidirect
83. #477×C₈₃	C₂²	semidirect
84. #475×C₈₃	C₂²	semidirect
92. #474×C₈₃	C₂²	semidirect
93. #474×C₈₃	C₂²	semidirect
95. #468×C₈₃	C₂²	semidirect
97. #467×C₈₃	C₂²	semidirect
101. #464×C₈₃	C₂²	semidirect
105. #462×C₈₃	C₂²	semidirect
106. #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
121. #436×C₈₃	C₂²	semidirect
124. C₈×D₄×C₈₃	C₂²	semidirect
125. #433×C₈₃	C₂²	semidirect
127. #428×C₈₃	C₂²	semidirect
129. C₂×#107×C₈₃	C₂²	semidirect
130. #424×C₈₃	C₂²	semidirect
554. #62201	C₈₃	direct (N × H)
563. #3552	C₂×C₈₃	semidirect
564. #3520	C₂×C₈₃	semidirect
565. #3386	C₂×C₈₃	semidirect
566. Q₈×D₈	C₂×C₈₃	semidirect
567. #3367	C₂×C₈₃	semidirect
568. #3364	C₂×C₈₃	semidirect
569. #3353	C₂×C₈₃	semidirect
570. #3346	C₂×C₈₃	semidirect
571. #3338	C₂×C₈₃	semidirect
572. #3334	C₂×C₈₃	semidirect
573. #3330	C₂×C₈₃	semidirect
574. #3314	C₂×C₈₃	semidirect
575. #3302	C₂×C₈₃	semidirect
576. #3297	C₂×C₈₃	semidirect
577. #3262	C₂×C₈₃	semidirect
578. #3248	C₂×C₈₃	semidirect
579. #3243	C₂×C₈₃	semidirect
580. #3230	C₂×C₈₃	semidirect
581. #3124	C₂×C₈₃	semidirect
582. #3105	C₂×C₈₃	semidirect
583. #3083	C₂×C₈₃	semidirect
584. C₂×#474	C₂×C₈₃	semidirect
585. #2994	C₂×C₈₃	semidirect
586. C₈₃	#62201	direct (N × H)
588. #557	C₂²×C₈₃	semidirect
590. #556	C₂²×C₈₃	semidirect
598. D₄×Q₈	C₂²×C₈₃	semidirect
603. #547	C₂²×C₈₃	semidirect
605. #544	C₂²×C₈₃	semidirect
607. #542	C₂²×C₈₃	semidirect
620. #501	C₂²×C₈₃	semidirect
621. #500	C₂²×C₈₃	semidirect
622. #500	C₂²×C₈₃	semidirect
623. #500	C₂²×C₈₃	semidirect
626. #487	C₂²×C₈₃	semidirect
627. #487	C₂²×C₈₃	semidirect
628. #485	C₂²×C₈₃	semidirect
632. #484	C₂²×C₈₃	semidirect
633. #484	C₂²×C₈₃	semidirect
637. #480	C₂²×C₈₃	semidirect
638. #479	C₂²×C₈₃	semidirect
639. #479	C₂²×C₈₃	semidirect
643. #477	C₂²×C₈₃	semidirect
644. #477	C₂²×C₈₃	semidirect
645. #477	C₂²×C₈₃	semidirect
646. #477	C₂²×C₈₃	semidirect
647. #475	C₂²×C₈₃	semidirect
655. #474	C₂²×C₈₃	semidirect
656. #474	C₂²×C₈₃	semidirect
658. #468	C₂²×C₈₃	semidirect
660. #467	C₂²×C₈₃	semidirect
664. #464	C₂²×C₈₃	semidirect
668. #462	C₂²×C₈₃	semidirect
669. #461	C₂²×C₈₃	semidirect
674. #446	C₂²×C₈₃	semidirect
675. C₈×Q₈	C₂²×C₈₃	semidirect
677. #440	C₂²×C₈₃	semidirect
678. C₄×Q₁₆	C₂²×C₈₃	semidirect
684. #436	C₂²×C₈₃	semidirect
687. C₈×D₄	C₂²×C₈₃	semidirect
688. #433	C₂²×C₈₃	semidirect
690. #428	C₂²×C₈₃	semidirect
692. C₂×#107	C₂²×C₈₃	semidirect
693. #424	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×#3552	2
C₈₃×#3520	2
C₈₃×#3386	2
Q₈×D₈×C₈₃	2
C₈₃×#3367	2
C₈₃×#3364	2
C₈₃×#3353	2
C₈₃×#3346	2
C₈₃×#3338	2
C₈₃×#3334	2
C₈₃×#3330	2
C₈₃×#3314	2
C₈₃×#3302	2
C₈₃×#3297	2
C₈₃×#3262	2
C₈₃×#3248	2
C₈₃×#3243	2
C₈₃×#3230	2
C₈₃×#3124	2
C₈₃×#3105	2
C₈₃×#3083	2
C₂×#474×C₈₃	2
C₈₃×#2994	2
#62201	83

Subgroups — C83×#62201 #35290025

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#62201 #35290025