Subgroups — C₈₃×#61442 #35289266

Order 21248.

1868 conjugacy classes of subgroups.

The subgroup lattice has 962 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3475	C₂	1	2	yes	maximal, complemented
2	C₈₃×#3402	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₃×#3389	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₃×#3376	C₂	1	2	yes	maximal, complemented
5	C₈₃×#3352	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₃×#3348	C₂	1	2	yes	maximal, complemented
7	C₈₃×#3323	C₂	1	2	yes	maximal, complemented
8	C₈₃×#3319	C₂	1	2	yes	maximal, complemented
9	C₈₃×#3315	C₂	1	2	yes	maximal, complemented
10	C₈₃×#3273	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₃×#3267	C₂	1	2	yes	maximal, complemented
12	C₈₃×#3172	C₂	1	2	yes	maximal, complemented
13	C₈₃×#3168	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₃×#3107	C₂	1	2	yes	maximal, complemented
15	C₈₃×#3105	C₂	1	2	yes	maximal, complemented
16	C₈₃×#3102	C₂	1	2	yes	maximal, complemented
17	C₈₃×#2965	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×AGL(1,ℤ/8)×C₈₃	C₂	1	2	yes	maximal, complemented
19	C₄×#135×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×AGL(1,ℤ/8)×C₈₃	C₂²	1	2	yes	—
21	C₂×#135×C₈₃	C₂²	1	1	yes	characteristic
22	#556×C₈₃	C₂²	1	2	yes	complemented
23	#555×C₈₃	C₂²	1	2	yes	—
24	#554×C₈₃	C₂²	1	2	yes	complemented
25	#553×C₈₃	—	2	2	no	—
26	#552×C₈₃	—	2	2	no	—
27	#552×C₈₃	C₂²	1	2	yes	—
28	#552×C₈₃	C₂²	1	2	yes	complemented
29	#551×C₈₃	—	2	2	no	—
30	#551×C₈₃	—	2	2	no	—
31	#547×C₈₃	C₂²	1	2	yes	—
32	#546×C₈₃	C₂²	1	2	yes	—
33	#546×C₈₃	C₂²	1	2	yes	complemented
34	#533×C₈₃	C₂²	1	2	yes	complemented
35	#529×C₈₃	—	2	2	no	—
36	#529×C₈₃	—	2	2	no	—
37	#529×C₈₃	C₂²	1	2	yes	—
38	#529×C₈₃	C₂²	1	2	yes	complemented
39	#525×C₈₃	—	2	2	no	—
40	C₄×#41×C₈₃	C₂²	1	2	yes	—
41	C₄×#41×C₈₃	C₂²	1	1	yes	characteristic
42	C₄×#41×C₈₃	C₂²	1	2	yes	complemented
43	C₂×C₄×D₄×C₈₃	C₂²	1	2	yes	complemented
44	C₂×#117×C₈₃	—	2	2	no	—
45	#501×C₈₃	C₂²	1	2	yes	complemented
46	#499×C₈₃	C₂²	1	1	yes	characteristic, complemented
47	#497×C₈₃	C₂²	1	2	yes	complemented
48	#495×C₈₃	C₂²	1	1	yes	characteristic
49	#491×C₈₃	C₂²	1	2	yes	complemented
50	#489×C₈₃	C₂²	1	2	yes	complemented
51	#488×C₈₃	C₂²	1	2	yes	complemented
52	#485×C₈₃	C₂²	1	2	yes	complemented
53	#485×C₈₃	C₂²	1	2	yes	complemented
54	#485×C₈₃	C₂²	1	2	yes	complemented
55	#484×C₈₃	C₂²	1	2	yes	complemented
56	#482×C₈₃	C₂²	1	2	yes	complemented
57	#481×C₈₃	C₂²	1	2	yes	—
58	#479×C₈₃	C₂²	1	2	yes	complemented
59	#478×C₈₃	C₂²	1	2	yes	complemented
60	#478×C₈₃	C₂²	1	2	yes	complemented
61	#478×C₈₃	C₂²	1	2	yes	complemented
62	#475×C₈₃	C₂²	1	2	yes	complemented
63	#474×C₈₃	C₂²	1	2	yes	complemented
64	#470×C₈₃	C₂²	1	2	yes	complemented
65	#470×C₈₃	C₂²	1	2	yes	complemented
66	#468×C₈₃	C₂²	1	2	yes	—
67	#468×C₈₃	C₂²	1	2	yes	—
68	#467×C₈₃	C₂²	1	1	yes	characteristic, complemented
69	#466×C₈₃	C₂²	1	1	yes	characteristic
70	#465×C₈₃	C₂²	1	2	yes	complemented
71	#464×C₈₃	C₂²	1	2	yes	complemented
72	#463×C₈₃	C₂²	1	2	yes	—
73	#463×C₈₃	C₂²	1	2	yes	—
74	#463×C₈₃	C₂²	1	2	yes	—
75	#462×C₈₃	C₂²	1	2	yes	complemented
76	#461×C₈₃	C₂²	1	2	yes	complemented
77	#452×C₈₃	C₂²	1	2	yes	—
78	#452×C₈₃	C₂²	1	2	yes	—
79	#452×C₈₃	C₂²	1	2	yes	complemented
80	#450×C₈₃	C₂²	1	2	yes	complemented
81	#449×C₈₃	C₂²	1	2	yes	—
82	#447×C₈₃	C₂²	1	2	yes	—
83	#446×C₈₃	C₂²	1	1	yes	characteristic, complemented
84	#446×C₈₃	C₂²	1	1	yes	characteristic, complemented
85	#442×C₈₃	C₂²	1	2	yes	—
86	#442×C₈₃	C₂²	1	2	yes	—
87	#440×C₈₃	C₂²	1	2	yes	complemented
88	#440×C₈₃	C₂²	1	2	yes	complemented
89	C₄×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic, complemented
90	C₄×Q₁₆×C₈₃	C₂²	1	2	yes	complemented
91	C₄×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic, complemented
92	C₄×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic, complemented
93	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	complemented
94	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	complemented
95	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	complemented
96	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	complemented
97	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	complemented
98	C₄×D₈×C₈₃	C₂²	1	2	yes	—
99	C₄×D₈×C₈₃	C₂²	1	1	yes	characteristic
100	C₄×D₈×C₈₃	C₂²	1	1	yes	characteristic
101	C₄×D₈×C₈₃	C₂²	1	1	yes	characteristic
102	#436×C₈₃	C₂²	1	1	yes	characteristic
103	#436×C₈₃	C₂²	1	1	yes	characteristic
104	#435×C₈₃	C₂²	1	2	yes	complemented
105	#435×C₈₃	C₂²	1	2	yes	complemented
106	#431×C₈₃	C₂²	1	1	yes	characteristic, complemented
107	#431×C₈₃	C₂²	1	2	yes	complemented
108	#428×C₈₃	C₂²	1	2	yes	complemented
109	#427×C₈₃	C₂²	1	1	yes	characteristic, complemented
110	#418×C₈₃	C₂²	1	2	yes	complemented
111	#417×C₈₃	C₂²	1	2	yes	—
112	#416×C₈₃	C₂²	1	2	yes	complemented
113	C₄×M₁₆×C₈₃	C₂²	1	2	yes	complemented
114	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
115	C₂×#41×C₈₃	D₄	1	1	yes	characteristic
116	C₂×#41×C₈₃	C₂³	1	2	yes	—
117	C₂×#41×C₈₃	C₂³	1	2	yes	—
118	C₂²×D₄×C₈₃	C₂³	1	2	yes	—
119	C₂³×C₄×C₈₃	—	2	2	no	—
120	AGL(1,ℤ/8)×C₈₃	—	2	8	no	—
121	#135×C₈₃	—	2	4	no	—
122	C₂×Q₁₆×C₈₃	C₂³	1	1	yes	characteristic
123	C₂×Q₁₆×C₈₃	C₂³	1	2	yes	—
124	C₂×Q₁₆×C₈₃	C₂³	1	1	yes	characteristic
125	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
129	C₂×D₈×C₈₃	C₂³	1	2	yes	—
130	C₂×D₈×C₈₃	C₂³	1	1	yes	characteristic
131	C₂×D₈×C₈₃	C₂³	1	1	yes	characteristic
132	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
133	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
134	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
135	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
136	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
137	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
138	#126×C₈₃	—	2	2	no	—
139	#126×C₈₃	—	2	2	no	—
140	#126×C₈₃	—	2	2	no	—
141	#126×C₈₃	—	2	2	no	—
142	#126×C₈₃	—	2	2	no	—
143	#126×C₈₃	—	2	2	no	—
144	#125×C₈₃	—	2	2	no	—
145	#125×C₈₃	—	2	2	no	—
146	#125×C₈₃	—	2	2	no	—
147	#125×C₈₃	C₂³	1	2	yes	—
148	#125×C₈₃	C₂³	1	2	yes	—
149	#124×C₈₃	—	2	2	no	—
150	#124×C₈₃	—	2	2	no	—
151	#124×C₈₃	C₂³	1	2	yes	—
152	#124×C₈₃	C₂³	1	2	yes	—
153	#123×C₈₃	—	2	2	no	—
154	#123×C₈₃	—	2	2	no	—
155	#123×C₈₃	—	2	2	no	—
156	#123×C₈₃	—	2	2	no	—
157	#123×C₈₃	—	2	2	no	—
158	#123×C₈₃	—	2	2	no	—
159	#123×C₈₃	—	2	2	no	—
160	#123×C₈₃	—	2	2	no	—
161	C₂²⋊Q₈×C₈₃	—	2	2	no	—
162	C₂²⋊Q₈×C₈₃	—	2	2	no	—
163	C₂²⋊Q₈×C₈₃	—	2	2	no	—
164	C₂²⋊Q₈×C₈₃	—	2	2	no	—
165	C₂²⋊Q₈×C₈₃	—	2	2	no	—
166	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
167	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
168	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
169	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
170	#121×C₈₃	—	2	2	no	—
171	#121×C₈₃	—	2	2	no	—
172	#121×C₈₃	—	2	2	no	—
173	#121×C₈₃	—	2	2	no	—
174	#121×C₈₃	C₂³	1	2	yes	—
175	#121×C₈₃	C₂³	1	2	yes	—
176	#120×C₈₃	—	2	2	no	—
177	#120×C₈₃	—	2	2	no	—
178	C₄×Q₈×C₈₃	—	2	2	no	—
179	C₄×Q₈×C₈₃	D₄	1	1	yes	characteristic
180	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
181	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
182	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
183	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
184	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
185	C₄×D₄×C₈₃	—	2	2	no	—
186	C₄×D₄×C₈₃	—	2	2	no	—
187	C₄×D₄×C₈₃	—	2	2	no	—
188	C₄×D₄×C₈₃	—	2	2	no	—
189	C₄×D₄×C₈₃	—	2	2	no	—
190	C₄×D₄×C₈₃	—	2	2	no	—
191	C₄×D₄×C₈₃	—	2	2	no	—
192	C₄×D₄×C₈₃	—	2	2	no	—
193	C₄×D₄×C₈₃	D₄	1	1	yes	characteristic
194	C₄×D₄×C₈₃	D₄	1	2	yes	—
195	C₄×D₄×C₈₃	C₂³	1	2	yes	—
196	C₄×D₄×C₈₃	C₂³	1	2	yes	—
197	C₄×D₄×C₈₃	C₂³	1	2	yes	—
198	C₄×D₄×C₈₃	C₂³	1	2	yes	—
199	C₄×D₄×C₈₃	C₂³	1	2	yes	—
200	C₄×D₄×C₈₃	C₂³	1	2	yes	—
201	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
202	C₄×D₄×C₈₃	C₂³	1	2	yes	—
203	#117×C₈₃	—	2	2	no	—
204	#117×C₈₃	—	2	2	no	—
205	#117×C₈₃	—	2	2	no	—
206	#117×C₈₃	—	2	2	no	—
207	#117×C₈₃	—	2	2	no	—
208	#117×C₈₃	—	2	2	no	—
209	#117×C₈₃	—	2	2	no	—
210	#117×C₈₃	—	2	2	no	—
211	#117×C₈₃	—	2	2	no	—
212	#117×C₈₃	D₄	1	2	yes	—
213	#117×C₈₃	D₄	1	1	yes	characteristic
214	#117×C₈₃	C₂³	1	2	yes	—
215	#117×C₈₃	C₂³	1	2	yes	—
216	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
217	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
218	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
219	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
220	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
221	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
222	C₂×C₄²×C₈₃	—	2	2	no	—
223	C₂×C₄²×C₈₃	—	2	2	no	—
224	C₂×C₄²×C₈₃	C₂³	1	2	yes	—
225	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
226	#107×C₈₃	C₂³	1	1	yes	characteristic
227	#107×C₈₃	C₂³	1	1	yes	characteristic
228	#107×C₈₃	C₂³	1	1	yes	characteristic
229	#107×C₈₃	C₂³	1	2	yes	—
230	#107×C₈₃	C₂³	1	2	yes	—
231	#107×C₈₃	C₂³	1	1	yes	characteristic
232	#106×C₈₃	C₂³	1	2	yes	—
233	#106×C₈₃	C₂³	1	2	yes	—
234	#106×C₈₃	C₂³	1	2	yes	—
235	#106×C₈₃	C₂³	1	2	yes	—
236	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
237	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
238	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
239	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
240	#103×C₈₃	C₂³	1	2	yes	—
241	#103×C₈₃	C₂³	1	2	yes	—
242	#103×C₈₃	C₂³	1	2	yes	—
243	#103×C₈₃	C₂³	1	2	yes	—
244	#103×C₈₃	C₂³	1	2	yes	—
245	#103×C₈₃	C₂³	1	2	yes	—
246	#103×C₈₃	C₂³	1	2	yes	—
247	#103×C₈₃	C₂³	1	2	yes	—
248	#102×C₈₃	C₂³	1	2	yes	—
249	#102×C₈₃	C₂³	1	2	yes	—
250	#102×C₈₃	C₂³	1	2	yes	—
251	#102×C₈₃	C₂³	1	2	yes	—
252	#102×C₈₃	C₂³	1	2	yes	—
253	#102×C₈₃	C₂³	1	2	yes	—
254	#102×C₈₃	C₂³	1	2	yes	—
255	#102×C₈₃	C₂³	1	2	yes	—
256	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
257	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
258	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
259	#97×C₈₃	C₂³	1	2	yes	—
260	#97×C₈₃	C₂³	1	2	yes	—
261	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
262	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
263	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
264	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
265	C₄×C₈×C₈₃	C₂³	1	2	yes	—
266	C₂⁴×C₈₃	—	2	2	no	—
267	#41×C₈₃	—	2	4	no	—
268	#41×C₈₃	—	2	4	no	—
269	#41×C₈₃	—	4	2	no	—
270	#41×C₈₃	—	4	2	no	—
271	#41×C₈₃	—	4	2	no	—
272	C₂×Q₈×C₈₃	—	2	2	no	—
273	C₂×Q₈×C₈₃	C₂×D₄	1	1	yes	characteristic
274	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
275	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
276	C₂×D₄×C₈₃	—	2	4	no	—
277	C₂×D₄×C₈₃	—	2	2	no	—
278	C₂×D₄×C₈₃	—	2	2	no	—
279	C₂×D₄×C₈₃	—	2	2	no	—
280	C₂×D₄×C₈₃	—	2	2	no	—
281	C₂×D₄×C₈₃	—	2	2	no	—
282	C₂×D₄×C₈₃	—	4	2	no	—
283	C₂×D₄×C₈₃	C₂×D₄	1	1	yes	characteristic
284	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
285	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
286	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₈₃	—	2	2	no	—
288	C₂²×C₄×C₈₃	—	2	2	no	—
289	C₂²×C₄×C₈₃	—	2	2	no	—
290	C₂²×C₄×C₈₃	—	2	2	no	—
291	C₂²×C₄×C₈₃	—	2	2	no	—
292	C₂²×C₄×C₈₃	—	2	2	no	—
293	C₂²×C₄×C₈₃	—	2	2	no	—
294	C₂²×C₄×C₈₃	—	2	2	no	—
295	C₂²×C₄×C₈₃	—	2	2	no	—
296	C₂²×C₄×C₈₃	—	4	8	no	—
297	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
298	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
299	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
300	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
303	Q₁₆×C₈₃	—	2	2	no	—
304	Q₁₆×C₈₃	—	4	1	no	—
305	Q₁₆×C₈₃	—	4	2	no	—
306	SD₁₆×C₈₃	—	2	4	no	—
307	SD₁₆×C₈₃	—	2	4	no	—
308	SD₁₆×C₈₃	—	2	4	no	—
309	SD₁₆×C₈₃	—	4	2	no	—
310	D₈×C₈₃	—	2	4	no	—
311	D₈×C₈₃	—	4	1	no	—
312	D₈×C₈₃	#41	1	4	yes	complemented
313	M₁₆×C₈₃	—	2	4	no	—
314	M₁₆×C₈₃	—	4	2	no	—
315	C₂×C₈×C₈₃	—	2	2	no	—
316	C₂×C₈×C₈₃	—	4	1	no	—
317	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
318	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
319	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
320	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
321	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
322	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
323	C₄⋊C₄×C₈₃	—	2	2	no	—
324	C₄⋊C₄×C₈₃	—	2	2	no	—
325	C₄⋊C₄×C₈₃	—	2	2	no	—
326	C₄⋊C₄×C₈₃	—	2	2	no	—
327	C₄⋊C₄×C₈₃	—	2	2	no	—
328	C₄⋊C₄×C₈₃	—	2	2	no	—
329	C₄⋊C₄×C₈₃	—	2	2	no	—
330	C₄⋊C₄×C₈₃	—	2	2	no	—
331	C₄⋊C₄×C₈₃	—	2	2	no	—
332	C₄⋊C₄×C₈₃	—	2	2	no	—
333	C₄⋊C₄×C₈₃	—	2	2	no	—
334	C₄⋊C₄×C₈₃	—	2	2	no	—
335	C₄⋊C₄×C₈₃	—	2	2	no	—
336	C₄⋊C₄×C₈₃	—	2	2	no	—
337	C₄⋊C₄×C₈₃	—	2	2	no	—
338	C₄⋊C₄×C₈₃	—	2	2	no	—
339	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
340	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
341	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
342	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
343	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
344	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
345	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
346	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
347	C₂²⋊C₄×C₈₃	—	2	2	no	—
348	C₂²⋊C₄×C₈₃	—	2	2	no	—
349	C₂²⋊C₄×C₈₃	—	2	2	no	—
350	C₂²⋊C₄×C₈₃	—	2	2	no	—
351	C₂²⋊C₄×C₈₃	—	2	2	no	—
352	C₂²⋊C₄×C₈₃	—	2	2	no	—
353	C₂²⋊C₄×C₈₃	—	2	2	no	—
354	C₂²⋊C₄×C₈₃	—	2	2	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	—	2	2	no	—
361	C₂²⋊C₄×C₈₃	—	2	2	no	—
362	C₂²⋊C₄×C₈₃	—	2	2	no	—
363	C₂²⋊C₄×C₈₃	—	2	2	no	—
364	C₂²⋊C₄×C₈₃	—	2	2	no	—
365	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
366	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
367	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
368	C₄²×C₈₃	—	2	2	no	—
369	C₄²×C₈₃	—	2	2	no	—
370	C₄²×C₈₃	—	2	2	no	—
371	C₄²×C₈₃	—	2	2	no	—
372	C₄²×C₈₃	—	2	2	no	—
373	C₄²×C₈₃	—	2	2	no	—
374	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
375	C₄²×C₈₃	C₂×D₄	1	2	yes	—
376	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
377	C₄²×C₈₃	C₂×D₄	1	2	yes	—
378	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
379	C₄²×C₈₃	C₂⁴	1	2	yes	—
380	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
381	C₂³×C₈₃	—	2	2	no	—
382	C₂³×C₈₃	—	2	2	no	—
383	C₂³×C₈₃	—	4	4	no	—
384	C₂³×C₈₃	—	4	4	no	—
385	C₂³×C₈₃	—	8	2	no	—
386	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
387	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
388	Q₈×C₈₃	—	2	2	no	—
389	Q₈×C₈₃	—	2	2	no	—
390	Q₈×C₈₃	—	2	2	no	—
391	Q₈×C₈₃	—	2	2	no	—
392	Q₈×C₈₃	—	4	1	no	—
393	Q₈×C₈₃	—	8	2	no	—
394	D₄×C₈₃	—	2	2	no	—
395	D₄×C₈₃	—	2	2	no	—
396	D₄×C₈₃	—	2	2	no	—
397	D₄×C₈₃	—	4	2	no	—
398	D₄×C₈₃	—	4	1	no	—
399	D₄×C₈₃	—	4	4	no	—
400	D₄×C₈₃	—	4	4	no	—
401	D₄×C₈₃	—	4	4	no	—
402	D₄×C₈₃	—	8	2	no	—
403	D₄×C₈₃	—	8	2	no	—
404	D₄×C₈₃	C₂×#41	1	4	yes	—
405	C₂×C₄×C₈₃	—	2	4	no	—
406	C₂×C₄×C₈₃	—	2	2	no	—
407	C₂×C₄×C₈₃	—	2	1	no	—
408	C₂×C₄×C₈₃	—	2	2	no	—
409	C₂×C₄×C₈₃	—	2	1	no	—
410	C₂×C₄×C₈₃	—	2	2	no	—
411	C₂×C₄×C₈₃	—	2	2	no	—
412	C₂×C₄×C₈₃	—	2	2	no	—
413	C₂×C₄×C₈₃	—	2	2	no	—
414	C₂×C₄×C₈₃	—	2	2	no	—
415	C₂×C₄×C₈₃	—	2	2	no	—
416	C₂×C₄×C₈₃	—	2	2	no	—
417	C₂×C₄×C₈₃	—	4	1	no	—
418	C₂×C₄×C₈₃	—	4	2	no	—
419	C₂×C₄×C₈₃	—	4	4	no	—
420	C₂×C₄×C₈₃	—	4	4	no	—
421	C₂×C₄×C₈₃	—	4	4	no	—
422	C₂×C₄×C₈₃	—	4	4	no	—
423	C₂×C₄×C₈₃	—	4	4	no	—
424	C₂×C₄×C₈₃	—	4	4	no	—
425	C₂×C₄×C₈₃	—	4	4	no	—
426	C₂×C₄×C₈₃	—	8	2	no	—
427	C₂×C₄×C₈₃	—	8	2	no	—
428	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
430	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
431	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
432	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
433	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
434	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
435	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
436	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
437	C₈×C₈₃	—	2	1	no	—
438	C₈×C₈₃	—	2	2	no	—
439	C₈×C₈₃	—	2	1	no	—
440	C₈×C₈₃	—	2	1	no	—
441	C₈×C₈₃	—	2	2	no	—
442	C₈×C₈₃	C₂×#41	1	2	yes	—
443	C₂²×C₈₃	—	2	1	no	—
444	C₂²×C₈₃	—	2	2	no	—
445	C₂²×C₈₃	—	2	1	no	—
446	C₂²×C₈₃	—	2	2	no	—
447	C₂²×C₈₃	—	2	4	no	—
448	C₂²×C₈₃	—	2	2	no	—
449	C₂²×C₈₃	—	2	1	no	—
450	C₂²×C₈₃	—	4	2	no	—
451	C₂²×C₈₃	—	4	2	no	—
452	C₂²×C₈₃	—	4	2	no	—
453	C₂²×C₈₃	—	4	2	no	—
454	C₂²×C₈₃	—	4	2	no	—
455	C₂²×C₈₃	—	8	8	no	—
456	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
457	C₄×C₈₃	—	2	1	no	—
458	C₄×C₈₃	—	2	1	no	—
459	C₄×C₈₃	—	2	2	no	—
460	C₄×C₈₃	—	2	1	no	—
461	C₄×C₈₃	—	2	2	no	—
462	C₄×C₈₃	—	2	2	no	—
463	C₄×C₈₃	—	2	1	no	—
464	C₄×C₈₃	—	4	2	no	—
465	C₄×C₈₃	—	4	2	no	—
466	C₄×C₈₃	—	4	2	no	—
467	C₄×C₈₃	—	4	2	no	—
468	C₄×C₈₃	—	4	2	no	—
469	C₄×C₈₃	—	4	2	no	—
470	C₄×C₈₃	#575	1	2	yes	—
471	C₄×C₈₃	C₂²×#41	1	1	yes	characteristic
472	C₄×C₈₃	#585	1	1	yes	characteristic
473	#61442	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
474	C₂×C₈₃	—	4	1	no	—
475	C₂×C₈₃	—	4	2	no	—
476	C₂×C₈₃	—	4	4	no	—
477	C₂×C₈₃	—	8	2	no	—
478	C₂×C₈₃	D₄×#41	1	1	yes	characteristic
479	C₂×C₈₃	C₂×#575	1	1	yes	characteristic
480	C₂×C₈₃	#3584	1	1	yes	characteristic
481	#3475	C₂×C₈₃	1	2	yes	complemented
482	#3402	C₂×C₈₃	1	1	yes	characteristic, complemented
483	#3389	C₂×C₈₃	1	1	yes	characteristic, complemented
484	#3376	C₂×C₈₃	1	2	yes	complemented
485	#3352	C₂×C₈₃	1	1	yes	characteristic, complemented
486	#3348	C₂×C₈₃	1	2	yes	complemented
487	#3323	C₂×C₈₃	1	2	yes	complemented
488	#3319	C₂×C₈₃	1	2	yes	complemented
489	#3315	C₂×C₈₃	1	2	yes	complemented
490	#3273	C₂×C₈₃	1	1	yes	characteristic, complemented
491	#3267	C₂×C₈₃	1	2	yes	complemented
492	#3172	C₂×C₈₃	1	2	yes	complemented
493	#3168	C₂×C₈₃	1	1	yes	characteristic, complemented
494	#3107	C₂×C₈₃	1	2	yes	complemented
495	#3105	C₂×C₈₃	1	2	yes	complemented
496	#3102	C₂×C₈₃	1	2	yes	complemented
497	#2965	C₂×C₈₃	1	1	yes	characteristic, complemented
498	C₄×AGL(1,ℤ/8)	C₂×C₈₃	1	2	yes	complemented
499	C₄×#135	C₂×C₈₃	1	1	yes	characteristic, complemented
500	C₈₃	#61442	1	1	yes	characteristic, direct product factor, Sylow
501	C₂×AGL(1,ℤ/8)	C₂²×C₈₃	1	2	yes	—
502	C₂×#135	C₂²×C₈₃	1	1	yes	characteristic
503	#556	C₂²×C₈₃	1	2	yes	complemented
504	#555	C₂²×C₈₃	1	2	yes	—
505	#554	C₂²×C₈₃	1	2	yes	complemented
506	#553	—	2	2	no	—
507	#552	—	2	2	no	—
508	#552	C₂²×C₈₃	1	2	yes	—
509	#552	C₂²×C₈₃	1	2	yes	complemented
510	#551	—	2	2	no	—
511	#551	—	2	2	no	—
512	#547	C₂²×C₈₃	1	2	yes	—
513	#546	C₂²×C₈₃	1	2	yes	—
514	#546	C₂²×C₈₃	1	2	yes	complemented
515	#533	C₂²×C₈₃	1	2	yes	complemented
516	#529	—	2	2	no	—
517	#529	—	2	2	no	—
518	#529	C₂²×C₈₃	1	2	yes	—
519	#529	C₂²×C₈₃	1	2	yes	complemented
520	#525	—	2	2	no	—
521	C₄×#41	C₂²×C₈₃	1	2	yes	—
522	C₄×#41	C₂²×C₈₃	1	1	yes	characteristic
523	C₄×#41	C₂²×C₈₃	1	2	yes	complemented
524	C₂×C₄×D₄	C₂²×C₈₃	1	2	yes	complemented
525	C₂×#117	—	2	2	no	—
526	#501	C₂²×C₈₃	1	2	yes	complemented
527	#499	C₂²×C₈₃	1	1	yes	characteristic, complemented
528	#497	C₂²×C₈₃	1	2	yes	complemented
529	#495	C₂²×C₈₃	1	1	yes	characteristic
530	#491	C₂²×C₈₃	1	2	yes	complemented
531	#489	C₂²×C₈₃	1	2	yes	complemented
532	#488	C₂²×C₈₃	1	2	yes	complemented
533	#485	C₂²×C₈₃	1	2	yes	complemented
534	#485	C₂²×C₈₃	1	2	yes	complemented
535	#485	C₂²×C₈₃	1	2	yes	complemented
536	#484	C₂²×C₈₃	1	2	yes	complemented
537	#482	C₂²×C₈₃	1	2	yes	complemented
538	#481	C₂²×C₈₃	1	2	yes	—
539	#479	C₂²×C₈₃	1	2	yes	complemented
540	#478	C₂²×C₈₃	1	2	yes	complemented
541	#478	C₂²×C₈₃	1	2	yes	complemented
542	#478	C₂²×C₈₃	1	2	yes	complemented
543	#475	C₂²×C₈₃	1	2	yes	complemented
544	#474	C₂²×C₈₃	1	2	yes	complemented
545	#470	C₂²×C₈₃	1	2	yes	complemented
546	#470	C₂²×C₈₃	1	2	yes	complemented
547	#468	C₂²×C₈₃	1	2	yes	—
548	#468	C₂²×C₈₃	1	2	yes	—
549	#467	C₂²×C₈₃	1	1	yes	characteristic, complemented
550	#466	C₂²×C₈₃	1	1	yes	characteristic
551	#465	C₂²×C₈₃	1	2	yes	complemented
552	#464	C₂²×C₈₃	1	2	yes	complemented
553	#463	C₂²×C₈₃	1	2	yes	—
554	#463	C₂²×C₈₃	1	2	yes	—
555	#463	C₂²×C₈₃	1	2	yes	—
556	#462	C₂²×C₈₃	1	2	yes	complemented
557	#461	C₂²×C₈₃	1	2	yes	complemented
558	#452	C₂²×C₈₃	1	2	yes	—
559	#452	C₂²×C₈₃	1	2	yes	—
560	#452	C₂²×C₈₃	1	2	yes	complemented
561	#450	C₂²×C₈₃	1	2	yes	complemented
562	#449	C₂²×C₈₃	1	2	yes	—
563	#447	C₂²×C₈₃	1	2	yes	—
564	#446	C₂²×C₈₃	1	1	yes	characteristic, complemented
565	#446	C₂²×C₈₃	1	1	yes	characteristic, complemented
566	#442	C₂²×C₈₃	1	2	yes	—
567	#442	C₂²×C₈₃	1	2	yes	—
568	#440	C₂²×C₈₃	1	2	yes	complemented
569	#440	C₂²×C₈₃	1	2	yes	complemented
570	C₄×Q₁₆	C₂²×C₈₃	1	1	yes	characteristic, complemented
571	C₄×Q₁₆	C₂²×C₈₃	1	2	yes	complemented
572	C₄×Q₁₆	C₂²×C₈₃	1	1	yes	characteristic, complemented
573	C₄×Q₁₆	C₂²×C₈₃	1	1	yes	characteristic, complemented
574	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	complemented
575	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	complemented
576	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	complemented
577	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	complemented
578	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	complemented
579	C₄×D₈	C₂²×C₈₃	1	2	yes	—
580	C₄×D₈	C₂²×C₈₃	1	1	yes	characteristic
581	C₄×D₈	C₂²×C₈₃	1	1	yes	characteristic
582	C₄×D₈	C₂²×C₈₃	1	1	yes	characteristic
583	#436	C₂²×C₈₃	1	1	yes	characteristic
584	#436	C₂²×C₈₃	1	1	yes	characteristic
585	#435	C₂²×C₈₃	1	2	yes	complemented
586	#435	C₂²×C₈₃	1	2	yes	complemented
587	#431	C₂²×C₈₃	1	1	yes	characteristic, complemented
588	#431	C₂²×C₈₃	1	2	yes	complemented
589	#428	C₂²×C₈₃	1	2	yes	complemented
590	#427	C₂²×C₈₃	1	1	yes	characteristic, complemented
591	#418	C₂²×C₈₃	1	2	yes	complemented
592	#417	C₂²×C₈₃	1	2	yes	—
593	#416	C₂²×C₈₃	1	2	yes	complemented
594	C₄×M₁₆	C₂²×C₈₃	1	2	yes	complemented
595	C₂×C₄×C₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
596	C₂×#41	D₄×C₈₃	1	1	yes	characteristic
597	C₂×#41	C₂³×C₈₃	1	2	yes	—
598	C₂×#41	C₂³×C₈₃	1	2	yes	—
599	C₂²×D₄	C₂³×C₈₃	1	2	yes	—
600	C₂³×C₄	—	2	2	no	—
601	AGL(1,ℤ/8)	—	2	8	no	—
602	#135	—	2	4	no	—
603	C₂×Q₁₆	C₂³×C₈₃	1	1	yes	characteristic
604	C₂×Q₁₆	C₂³×C₈₃	1	1	yes	characteristic
605	C₂×Q₁₆	C₂³×C₈₃	1	2	yes	—
606	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
607	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
608	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
609	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
610	C₂×D₈	C₂³×C₈₃	1	2	yes	—
611	C₂×D₈	C₂³×C₈₃	1	1	yes	characteristic
612	C₂×D₈	C₂³×C₈₃	1	1	yes	characteristic
613	C₂×M₁₆	C₂³×C₈₃	1	2	yes	—
614	C₂×M₁₆	C₂³×C₈₃	1	2	yes	—
615	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
616	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
617	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
618	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
619	#126	—	2	2	no	—
620	#126	—	2	2	no	—
621	#126	—	2	2	no	—
622	#126	—	2	2	no	—
623	#126	—	2	2	no	—
624	#126	—	2	2	no	—
625	#125	—	2	2	no	—
626	#125	—	2	2	no	—
627	#125	—	2	2	no	—
628	#125	C₂³×C₈₃	1	2	yes	—
629	#125	C₂³×C₈₃	1	2	yes	—
630	#124	—	2	2	no	—
631	#124	—	2	2	no	—
632	#124	C₂³×C₈₃	1	2	yes	—
633	#124	C₂³×C₈₃	1	2	yes	—
634	#123	—	2	2	no	—
635	#123	—	2	2	no	—
636	#123	—	2	2	no	—
637	#123	—	2	2	no	—
638	#123	—	2	2	no	—
639	#123	—	2	2	no	—
640	#123	—	2	2	no	—
641	#123	—	2	2	no	—
642	C₂²⋊Q₈	—	2	2	no	—
643	C₂²⋊Q₈	—	2	2	no	—
644	C₂²⋊Q₈	—	2	2	no	—
645	C₂²⋊Q₈	—	2	2	no	—
646	C₂²⋊Q₈	—	2	2	no	—
647	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
648	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
649	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
650	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
651	#121	—	2	2	no	—
652	#121	—	2	2	no	—
653	#121	—	2	2	no	—
654	#121	—	2	2	no	—
655	#121	C₂³×C₈₃	1	2	yes	—
656	#121	C₂³×C₈₃	1	2	yes	—
657	#120	—	2	2	no	—
658	#120	—	2	2	no	—
659	C₄×Q₈	—	2	2	no	—
660	C₄×Q₈	D₄×C₈₃	1	1	yes	characteristic
661	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
662	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
663	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
664	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
665	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
666	C₄×D₄	—	2	2	no	—
667	C₄×D₄	—	2	2	no	—
668	C₄×D₄	—	2	2	no	—
669	C₄×D₄	—	2	2	no	—
670	C₄×D₄	—	2	2	no	—
671	C₄×D₄	—	2	2	no	—
672	C₄×D₄	—	2	2	no	—
673	C₄×D₄	—	2	2	no	—
674	C₄×D₄	D₄×C₈₃	1	1	yes	characteristic
675	C₄×D₄	D₄×C₈₃	1	2	yes	—
676	C₄×D₄	C₂³×C₈₃	1	2	yes	—
677	C₄×D₄	C₂³×C₈₃	1	2	yes	—
678	C₄×D₄	C₂³×C₈₃	1	2	yes	—
679	C₄×D₄	C₂³×C₈₃	1	2	yes	—
680	C₄×D₄	C₂³×C₈₃	1	2	yes	—
681	C₄×D₄	C₂³×C₈₃	1	2	yes	—
682	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
683	C₄×D₄	C₂³×C₈₃	1	2	yes	—
684	#117	—	2	2	no	—
685	#117	—	2	2	no	—
686	#117	—	2	2	no	—
687	#117	—	2	2	no	—
688	#117	—	2	2	no	—
689	#117	—	2	2	no	—
690	#117	—	2	2	no	—
691	#117	—	2	2	no	—
692	#117	—	2	2	no	—
693	#117	D₄×C₈₃	1	2	yes	—
694	#117	D₄×C₈₃	1	1	yes	characteristic
695	#117	C₂³×C₈₃	1	2	yes	—
696	#117	C₂³×C₈₃	1	2	yes	—
697	C₂×C₄⋊C₄	—	2	2	no	—
698	C₂×C₄⋊C₄	—	2	2	no	—
699	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
700	C₂×C₂²⋊C₄	—	2	2	no	—
701	C₂×C₂²⋊C₄	—	2	2	no	—
702	C₂×C₂²⋊C₄	—	2	2	no	—
703	C₂×C₄²	—	2	2	no	—
704	C₂×C₄²	—	2	2	no	—
705	C₂×C₄²	C₂³×C₈₃	1	2	yes	—
706	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
707	#107	C₂³×C₈₃	1	1	yes	characteristic
708	#107	C₂³×C₈₃	1	1	yes	characteristic
709	#107	C₂³×C₈₃	1	2	yes	—
710	#107	C₂³×C₈₃	1	1	yes	characteristic
711	#107	C₂³×C₈₃	1	1	yes	characteristic
712	#107	C₂³×C₈₃	1	2	yes	—
713	#106	C₂³×C₈₃	1	2	yes	—
714	#106	C₂³×C₈₃	1	2	yes	—
715	#106	C₂³×C₈₃	1	2	yes	—
716	#106	C₂³×C₈₃	1	2	yes	—
717	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
718	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
719	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
720	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
721	#103	C₂³×C₈₃	1	2	yes	—
722	#103	C₂³×C₈₃	1	2	yes	—
723	#103	C₂³×C₈₃	1	2	yes	—
724	#103	C₂³×C₈₃	1	2	yes	—
725	#103	C₂³×C₈₃	1	2	yes	—
726	#103	C₂³×C₈₃	1	2	yes	—
727	#103	C₂³×C₈₃	1	2	yes	—
728	#103	C₂³×C₈₃	1	2	yes	—
729	#102	C₂³×C₈₃	1	2	yes	—
730	#102	C₂³×C₈₃	1	2	yes	—
731	#102	C₂³×C₈₃	1	2	yes	—
732	#102	C₂³×C₈₃	1	2	yes	—
733	#102	C₂³×C₈₃	1	2	yes	—
734	#102	C₂³×C₈₃	1	2	yes	—
735	#102	C₂³×C₈₃	1	2	yes	—
736	#102	C₂³×C₈₃	1	2	yes	—
737	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
738	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
739	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
740	#97	C₂³×C₈₃	1	2	yes	—
741	#97	C₂³×C₈₃	1	2	yes	—
742	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
743	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
744	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
745	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
746	C₄×C₈	C₂³×C₈₃	1	2	yes	—
747	C₂⁴	—	2	2	no	—
748	#41	—	2	4	no	—
749	#41	—	2	4	no	—
750	#41	—	4	2	no	—
751	#41	—	4	2	no	—
752	#41	—	4	2	no	—
753	C₂×Q₈	—	2	2	no	—
754	C₂×Q₈	C₂×D₄×C₈₃	1	1	yes	characteristic
755	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
756	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
757	C₂×D₄	—	2	4	no	—
758	C₂×D₄	—	2	2	no	—
759	C₂×D₄	—	2	2	no	—
760	C₂×D₄	—	2	2	no	—
761	C₂×D₄	—	2	2	no	—
762	C₂×D₄	—	2	2	no	—
763	C₂×D₄	—	4	2	no	—
764	C₂×D₄	C₂×D₄×C₈₃	1	1	yes	characteristic
765	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
766	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
767	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
768	C₂²×C₄	—	2	2	no	—
769	C₂²×C₄	—	2	2	no	—
770	C₂²×C₄	—	2	2	no	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	2	2	no	—
775	C₂²×C₄	—	2	2	no	—
776	C₂²×C₄	—	2	2	no	—
777	C₂²×C₄	—	4	8	no	—
778	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
779	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
780	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
781	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
782	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
783	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
784	Q₁₆	—	2	2	no	—
785	Q₁₆	—	4	1	no	—
786	Q₁₆	—	4	2	no	—
787	SD₁₆	—	2	4	no	—
788	SD₁₆	—	2	4	no	—
789	SD₁₆	—	2	4	no	—
790	SD₁₆	—	4	2	no	—
791	D₈	—	2	4	no	—
792	D₈	—	4	1	no	—
793	D₈	#41×C₈₃	1	4	yes	complemented
794	M₁₆	—	2	4	no	—
795	M₁₆	—	4	2	no	—
796	C₂×C₈	—	2	2	no	—
797	C₂×C₈	—	4	1	no	—
798	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
799	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
800	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
801	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
802	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
803	C₂×C₈	C₂⁴×C₈₃	1	1	yes	characteristic
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
821	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
822	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
823	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
824	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
825	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
826	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
827	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
828	C₂²⋊C₄	—	2	2	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	2	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	2	no	—
836	C₂²⋊C₄	—	2	2	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	—	2	2	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
847	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
848	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
849	C₄²	—	2	2	no	—
850	C₄²	—	2	2	no	—
851	C₄²	—	2	2	no	—
852	C₄²	—	2	2	no	—
853	C₄²	—	2	2	no	—
854	C₄²	—	2	2	no	—
855	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
856	C₄²	C₂×D₄×C₈₃	1	2	yes	—
857	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
858	C₄²	C₂×D₄×C₈₃	1	2	yes	—
859	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
860	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
861	C₄²	C₂⁴×C₈₃	1	2	yes	—
862	C₂³	—	2	2	no	—
863	C₂³	—	2	2	no	—
864	C₂³	—	4	4	no	—
865	C₂³	—	4	4	no	—
866	C₂³	—	8	2	no	—
867	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
868	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
869	Q₈	—	2	2	no	—
870	Q₈	—	2	2	no	—
871	Q₈	—	2	2	no	—
872	Q₈	—	2	2	no	—
873	Q₈	—	4	1	no	—
874	Q₈	—	8	2	no	—
875	D₄	—	2	2	no	—
876	D₄	—	2	2	no	—
877	D₄	—	2	2	no	—
878	D₄	—	4	2	no	—
879	D₄	—	4	1	no	—
880	D₄	—	4	4	no	—
881	D₄	—	4	4	no	—
882	D₄	—	4	4	no	—
883	D₄	—	8	2	no	—
884	D₄	—	8	2	no	—
885	D₄	C₂×#41×C₈₃	1	4	yes	—
886	C₂×C₄	—	2	4	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	4	1	no	—
899	C₂×C₄	—	4	2	no	—
900	C₂×C₄	—	4	4	no	—
901	C₂×C₄	—	4	4	no	—
902	C₂×C₄	—	4	4	no	—
903	C₂×C₄	—	4	4	no	—
904	C₂×C₄	—	4	4	no	—
905	C₂×C₄	—	4	4	no	—
906	C₂×C₄	—	4	4	no	—
907	C₂×C₄	—	8	2	no	—
908	C₂×C₄	—	8	2	no	—
909	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
910	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
911	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
912	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
913	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
914	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
915	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
916	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
917	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
918	C₈	—	2	1	no	—
919	C₈	—	2	2	no	—
920	C₈	—	2	1	no	—
921	C₈	—	2	1	no	—
922	C₈	—	2	2	no	—
923	C₈	C₂×#41×C₈₃	1	2	yes	—
924	C₂²	—	2	2	no	—
925	C₂²	—	2	1	no	—
926	C₂²	—	2	1	no	—
927	C₂²	—	2	2	no	—
928	C₂²	—	2	1	no	—
929	C₂²	—	2	2	no	—
930	C₂²	—	2	4	no	—
931	C₂²	—	4	2	no	—
932	C₂²	—	4	2	no	—
933	C₂²	—	4	2	no	—
934	C₂²	—	4	2	no	—
935	C₂²	—	4	2	no	—
936	C₂²	—	8	8	no	—
937	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
938	C₄	—	2	2	no	—
939	C₄	—	2	1	no	—
940	C₄	—	2	1	no	—
941	C₄	—	2	1	no	—
942	C₄	—	2	2	no	—
943	C₄	—	2	1	no	—
944	C₄	—	2	2	no	—
945	C₄	—	4	2	no	—
946	C₄	—	4	2	no	—
947	C₄	—	4	2	no	—
948	C₄	—	4	2	no	—
949	C₄	—	4	2	no	—
950	C₄	—	4	2	no	—
951	C₄	#575×C₈₃	1	2	yes	—
952	C₄	C₂²×#41×C₈₃	1	1	yes	characteristic
953	C₄	#585×C₈₃	1	1	yes	characteristic
954	C₂	—	4	2	no	—
955	C₂	—	4	1	no	—
956	C₂	—	4	4	no	—
957	C₂	—	8	2	no	—
958	C₂	D₄×#41×C₈₃	1	1	yes	characteristic
959	C₂	C₂×#575×C₈₃	1	1	yes	characteristic
960	C₂	C₈₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₈₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₃
socle	C₂²×C₈₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₈₃ ◁ C₄×#41×C₈₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₈₃×#3475	C₂	semidirect
2. C₈₃×#3402	C₂	semidirect
3. C₈₃×#3389	C₂	semidirect
4. C₈₃×#3376	C₂	semidirect
5. C₈₃×#3352	C₂	semidirect
6. C₈₃×#3348	C₂	semidirect
7. C₈₃×#3323	C₂	semidirect
8. C₈₃×#3319	C₂	semidirect
9. C₈₃×#3315	C₂	semidirect
10. C₈₃×#3273	C₂	semidirect
11. C₈₃×#3267	C₂	semidirect
12. C₈₃×#3172	C₂	semidirect
13. C₈₃×#3168	C₂	semidirect
14. C₈₃×#3107	C₂	semidirect
15. C₈₃×#3105	C₂	semidirect
16. C₈₃×#3102	C₂	semidirect
17. C₈₃×#2965	C₂	semidirect
18. C₄×AGL(1,ℤ/8)×C₈₃	C₂	semidirect
19. C₄×#135×C₈₃	C₂	semidirect
22. #556×C₈₃	C₂²	semidirect
24. #554×C₈₃	C₂²	semidirect
28. #552×C₈₃	C₂²	semidirect
33. #546×C₈₃	C₂²	semidirect
34. #533×C₈₃	C₂²	semidirect
38. #529×C₈₃	C₂²	semidirect
42. C₄×#41×C₈₃	C₂²	semidirect
43. C₂×C₄×D₄×C₈₃	C₂²	semidirect
45. #501×C₈₃	C₂²	semidirect
46. #499×C₈₃	C₂²	semidirect
47. #497×C₈₃	C₂²	semidirect
49. #491×C₈₃	C₂²	semidirect
50. #489×C₈₃	C₂²	semidirect
51. #488×C₈₃	C₂²	semidirect
52. #485×C₈₃	C₂²	semidirect
53. #485×C₈₃	C₂²	semidirect
54. #485×C₈₃	C₂²	semidirect
55. #484×C₈₃	C₂²	semidirect
56. #482×C₈₃	C₂²	semidirect
58. #479×C₈₃	C₂²	semidirect
59. #478×C₈₃	C₂²	semidirect
60. #478×C₈₃	C₂²	semidirect
61. #478×C₈₃	C₂²	semidirect
62. #475×C₈₃	C₂²	semidirect
63. #474×C₈₃	C₂²	semidirect
64. #470×C₈₃	C₂²	semidirect
65. #470×C₈₃	C₂²	semidirect
68. #467×C₈₃	C₂²	semidirect
70. #465×C₈₃	C₂²	semidirect
71. #464×C₈₃	C₂²	semidirect
75. #462×C₈₃	C₂²	semidirect
76. #461×C₈₃	C₂²	semidirect
79. #452×C₈₃	C₂²	semidirect
80. #450×C₈₃	C₂²	semidirect
83. #446×C₈₃	C₂²	semidirect
84. #446×C₈₃	C₂²	semidirect
87. #440×C₈₃	C₂²	semidirect
88. #440×C₈₃	C₂²	semidirect
89. C₄×Q₁₆×C₈₃	C₂²	semidirect
90. C₄×Q₁₆×C₈₃	C₂²	semidirect
91. C₄×Q₁₆×C₈₃	C₂²	semidirect
92. C₄×Q₁₆×C₈₃	C₂²	semidirect
93. C₄×SD₁₆×C₈₃	C₂²	semidirect
94. C₄×SD₁₆×C₈₃	C₂²	semidirect
95. C₄×SD₁₆×C₈₃	C₂²	semidirect
96. C₄×SD₁₆×C₈₃	C₂²	semidirect
97. C₄×SD₁₆×C₈₃	C₂²	semidirect
104. #435×C₈₃	C₂²	semidirect
105. #435×C₈₃	C₂²	semidirect
106. #431×C₈₃	C₂²	semidirect
107. #431×C₈₃	C₂²	semidirect
108. #428×C₈₃	C₂²	semidirect
109. #427×C₈₃	C₂²	semidirect
110. #418×C₈₃	C₂²	semidirect
112. #416×C₈₃	C₂²	semidirect
113. C₄×M₁₆×C₈₃	C₂²	semidirect
114. C₂×C₄×C₈×C₈₃	C₂²	semidirect
312. D₈×C₈₃	#41	semidirect
473. #61442	C₈₃	direct (N × H)
481. #3475	C₂×C₈₃	semidirect
482. #3402	C₂×C₈₃	semidirect
483. #3389	C₂×C₈₃	semidirect
484. #3376	C₂×C₈₃	semidirect
485. #3352	C₂×C₈₃	semidirect
486. #3348	C₂×C₈₃	semidirect
487. #3323	C₂×C₈₃	semidirect
488. #3319	C₂×C₈₃	semidirect
489. #3315	C₂×C₈₃	semidirect
490. #3273	C₂×C₈₃	semidirect
491. #3267	C₂×C₈₃	semidirect
492. #3172	C₂×C₈₃	semidirect
493. #3168	C₂×C₈₃	semidirect
494. #3107	C₂×C₈₃	semidirect
495. #3105	C₂×C₈₃	semidirect
496. #3102	C₂×C₈₃	semidirect
497. #2965	C₂×C₈₃	semidirect
498. C₄×AGL(1,ℤ/8)	C₂×C₈₃	semidirect
499. C₄×#135	C₂×C₈₃	semidirect
500. C₈₃	#61442	direct (N × H)
503. #556	C₂²×C₈₃	semidirect
505. #554	C₂²×C₈₃	semidirect
509. #552	C₂²×C₈₃	semidirect
514. #546	C₂²×C₈₃	semidirect
515. #533	C₂²×C₈₃	semidirect
519. #529	C₂²×C₈₃	semidirect
523. C₄×#41	C₂²×C₈₃	semidirect
524. C₂×C₄×D₄	C₂²×C₈₃	semidirect
526. #501	C₂²×C₈₃	semidirect
527. #499	C₂²×C₈₃	semidirect
528. #497	C₂²×C₈₃	semidirect
530. #491	C₂²×C₈₃	semidirect
531. #489	C₂²×C₈₃	semidirect
532. #488	C₂²×C₈₃	semidirect
533. #485	C₂²×C₈₃	semidirect
534. #485	C₂²×C₈₃	semidirect
535. #485	C₂²×C₈₃	semidirect
536. #484	C₂²×C₈₃	semidirect
537. #482	C₂²×C₈₃	semidirect
539. #479	C₂²×C₈₃	semidirect
540. #478	C₂²×C₈₃	semidirect
541. #478	C₂²×C₈₃	semidirect
542. #478	C₂²×C₈₃	semidirect
543. #475	C₂²×C₈₃	semidirect
544. #474	C₂²×C₈₃	semidirect
545. #470	C₂²×C₈₃	semidirect
546. #470	C₂²×C₈₃	semidirect
549. #467	C₂²×C₈₃	semidirect
551. #465	C₂²×C₈₃	semidirect
552. #464	C₂²×C₈₃	semidirect
556. #462	C₂²×C₈₃	semidirect
557. #461	C₂²×C₈₃	semidirect
560. #452	C₂²×C₈₃	semidirect
561. #450	C₂²×C₈₃	semidirect
564. #446	C₂²×C₈₃	semidirect
565. #446	C₂²×C₈₃	semidirect
568. #440	C₂²×C₈₃	semidirect
569. #440	C₂²×C₈₃	semidirect
570. C₄×Q₁₆	C₂²×C₈₃	semidirect
571. C₄×Q₁₆	C₂²×C₈₃	semidirect
572. C₄×Q₁₆	C₂²×C₈₃	semidirect
573. C₄×Q₁₆	C₂²×C₈₃	semidirect
574. C₄×SD₁₆	C₂²×C₈₃	semidirect
575. C₄×SD₁₆	C₂²×C₈₃	semidirect
576. C₄×SD₁₆	C₂²×C₈₃	semidirect
577. C₄×SD₁₆	C₂²×C₈₃	semidirect
578. C₄×SD₁₆	C₂²×C₈₃	semidirect
585. #435	C₂²×C₈₃	semidirect
586. #435	C₂²×C₈₃	semidirect
587. #431	C₂²×C₈₃	semidirect
588. #431	C₂²×C₈₃	semidirect
589. #428	C₂²×C₈₃	semidirect
590. #427	C₂²×C₈₃	semidirect
591. #418	C₂²×C₈₃	semidirect
593. #416	C₂²×C₈₃	semidirect
594. C₄×M₁₆	C₂²×C₈₃	semidirect
595. C₂×C₄×C₈	C₂²×C₈₃	semidirect
793. D₈	#41×C₈₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₈₃×#3475	2
C₈₃×#3402	2
C₈₃×#3389	2
C₈₃×#3376	2
C₈₃×#3352	2
C₈₃×#3348	2
C₈₃×#3323	2
C₈₃×#3319	2
C₈₃×#3315	2
C₈₃×#3273	2
C₈₃×#3267	2
C₈₃×#3172	2
C₈₃×#3168	2
C₈₃×#3107	2
C₈₃×#3105	2
C₈₃×#3102	2
C₈₃×#2965	2
C₄×AGL(1,ℤ/8)×C₈₃	2
C₄×#135×C₈₃	2
#61442	83

Subgroups — C83×#61442 #35289266

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#61442 #35289266