Subgroups — C₈₃×#61898 #35289722

Order 21248.

1844 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3522	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#559×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₃×#3403	C₂	1	4	yes	maximal, complemented
4	C₈₃×#3399	C₂	1	2	yes	maximal, complemented
5	C₈₃×#3396	C₂	1	2	yes	maximal, complemented
6	C₈₃×#3375	C₂	1	2	yes	maximal, complemented
7	C₈₃×#3370	C₂	1	4	yes	maximal, complemented
8	C₈₃×#3361	C₂	1	2	yes	maximal, complemented
9	C₈₃×#3217	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₃×#3213	C₂	1	2	yes	maximal, complemented
11	C₈₃×#3211	C₂	1	2	yes	maximal, complemented
12	C₈₃×#3205	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₃×#3114	C₂	1	2	yes	maximal, complemented
14	C₈₃×#3112	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#3108	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₃×#3100	C₂	1	2	yes	maximal, complemented
17	C₈₃×#2984	C₂	1	1	yes	maximal, characteristic, complemented
18	#559×C₈₃	—	2	1	no	—
19	#559×C₈₃	—	2	1	no	—
20	#559×C₈₃	—	2	2	no	—
21	#559×C₈₃	C₂²	1	2	yes	—
22	#559×C₈₃	C₂²	1	4	yes	—
23	#559×C₈₃	C₂²	1	2	yes	—
24	#559×C₈₃	C₂²	1	1	yes	characteristic, complemented
25	#559×C₈₃	C₂²	1	2	yes	complemented
26	Q₈²×C₈₃	C₂²	1	1	yes	characteristic, complemented
27	#554×C₈₃	C₂²	1	1	yes	characteristic, complemented
28	#554×C₈₃	C₂²	1	2	yes	complemented
29	#550×C₈₃	C₂²	1	1	yes	characteristic, complemented
30	#548×C₈₃	—	2	1	no	—
31	#547×C₈₃	—	2	1	no	—
32	#547×C₈₃	—	2	2	no	—
33	#542×C₈₃	—	2	2	no	—
34	#542×C₈₃	—	2	1	no	—
35	#532×C₈₃	C₂²	1	2	yes	—
36	#532×C₈₃	C₂²	1	1	yes	characteristic
37	C₂×#127×C₈₃	C₂²	1	1	yes	characteristic
38	#529×C₈₃	C₂²	1	1	yes	characteristic
39	#529×C₈₃	C₂²	1	2	yes	—
40	C₂×#124×C₈₃	—	2	1	no	—
41	C₂×#124×C₈₃	C₂²	1	2	yes	—
42	C₂×#123×C₈₃	—	2	2	no	—
43	#520×C₈₃	—	2	1	no	—
44	C₂×C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₈₃	—	2	1	no	—
47	C₂×C₄×D₄×C₈₃	C₂²	1	2	yes	—
48	#496×C₈₃	C₂²	1	2	yes	—
49	#496×C₈₃	C₂²	1	4	yes	complemented
50	#495×C₈₃	C₂²	1	4	yes	complemented
51	#493×C₈₃	C₂²	1	2	yes	—
52	#490×C₈₃	C₂²	1	2	yes	—
53	#489×C₈₃	C₂²	1	4	yes	complemented
54	#488×C₈₃	C₂²	1	4	yes	complemented
55	#486×C₈₃	C₂²	1	2	yes	—
56	#483×C₈₃	C₂²	1	1	yes	characteristic
57	#480×C₈₃	C₂²	1	1	yes	characteristic
58	#480×C₈₃	C₂²	1	2	yes	—
59	#479×C₈₃	C₂²	1	2	yes	complemented
60	#478×C₈₃	C₂²	1	4	yes	complemented
61	#477×C₈₃	C₂²	1	2	yes	complemented
62	#474×C₈₃	C₂²	1	4	yes	complemented
63	#464×C₈₃	C₂²	1	2	yes	complemented
64	#464×C₈₃	C₂²	1	4	yes	complemented
65	#463×C₈₃	C₂²	1	4	yes	complemented
66	#463×C₈₃	C₂²	1	4	yes	complemented
67	#463×C₈₃	C₂²	1	4	yes	complemented
68	#463×C₈₃	C₂²	1	4	yes	complemented
69	#460×C₈₃	C₂²	1	2	yes	—
70	#460×C₈₃	C₂²	1	2	yes	complemented
71	#459×C₈₃	C₂²	1	2	yes	—
72	#459×C₈₃	C₂²	1	4	yes	—
73	#459×C₈₃	C₂²	1	4	yes	complemented
74	#451×C₈₃	C₂²	1	1	yes	characteristic
75	#450×C₈₃	C₂²	1	2	yes	—
76	#448×C₈₃	C₂²	1	1	yes	characteristic
77	#448×C₈₃	C₂²	1	2	yes	—
78	#447×C₈₃	C₂²	1	2	yes	—
79	#447×C₈₃	C₂²	1	2	yes	—
80	#447×C₈₃	C₂²	1	2	yes	—
81	#446×C₈₃	C₂²	1	4	yes	complemented
82	#446×C₈₃	C₂²	1	2	yes	complemented
83	C₈×Q₈×C₈₃	C₂²	1	2	yes	complemented
84	#442×C₈₃	C₂²	1	4	yes	complemented
85	#440×C₈₃	C₂²	1	4	yes	complemented
86	#440×C₈₃	C₂²	1	4	yes	complemented
87	C₄×Q₁₆×C₈₃	C₂²	1	2	yes	complemented
88	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	complemented
89	C₄×D₈×C₈₃	C₂²	1	4	yes	complemented
90	C₄×D₈×C₈₃	C₂²	1	4	yes	complemented
91	#432×C₈₃	C₂²	1	1	yes	characteristic
92	#432×C₈₃	C₂²	1	2	yes	—
93	#431×C₈₃	C₂²	1	2	yes	—
94	#431×C₈₃	C₂²	1	1	yes	characteristic
95	C₂×#41×C₈₃	—	2	1	no	—
96	C₂×#41×C₈₃	—	2	2	no	—
97	C₂×#41×C₈₃	—	2	1	no	—
98	C₂²×Q₈×C₈₃	D₄	1	1	yes	characteristic
99	C₂²×Q₈×C₈₃	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₈₃	—	2	1	no	—
101	C₂²×D₄×C₈₃	—	2	1	no	—
102	C₂²×D₄×C₈₃	C₂³	1	2	yes	—
103	C₂³×C₄×C₈₃	—	2	2	no	—
104	C₂×Q₁₆×C₈₃	C₂³	1	2	yes	—
105	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
106	C₂×SD₁₆×C₈₃	C₂³	1	4	yes	—
107	C₂×SD₁₆×C₈₃	C₂³	1	4	yes	—
108	C₂×D₈×C₈₃	C₂³	1	4	yes	—
109	C₂×D₈×C₈₃	C₂³	1	4	yes	—
110	C₂×D₈×C₈₃	C₂³	1	4	yes	—
111	C₄⋊Q₈×C₈₃	—	2	1	no	—
112	C₄⋊Q₈×C₈₃	—	2	2	no	—
113	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
114	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
115	#127×C₈₃	—	2	1	no	—
116	#127×C₈₃	—	2	1	no	—
117	#127×C₈₃	C₂³	1	2	yes	—
118	#127×C₈₃	C₂³	1	2	yes	—
119	#127×C₈₃	C₂³	1	1	yes	characteristic
120	#127×C₈₃	C₂³	1	2	yes	—
121	#126×C₈₃	—	2	2	no	—
122	#126×C₈₃	—	2	1	no	—
123	#125×C₈₃	C₂³	1	2	yes	—
124	#125×C₈₃	C₂³	1	1	yes	characteristic
125	#124×C₈₃	—	2	2	no	—
126	#124×C₈₃	—	2	2	no	—
127	#124×C₈₃	—	2	4	no	—
128	#124×C₈₃	—	2	1	no	—
129	#124×C₈₃	—	2	2	no	—
130	#124×C₈₃	—	2	2	no	—
131	#124×C₈₃	—	2	2	no	—
132	#124×C₈₃	—	2	2	no	—
133	#124×C₈₃	—	2	1	no	—
134	#124×C₈₃	C₂³	1	4	yes	—
135	#124×C₈₃	C₂³	1	2	yes	—
136	#124×C₈₃	C₂³	1	4	yes	—
137	#124×C₈₃	C₂³	1	1	yes	characteristic
138	#123×C₈₃	—	2	2	no	—
139	#123×C₈₃	—	2	1	no	—
140	#123×C₈₃	—	2	4	no	—
141	#123×C₈₃	—	2	4	no	—
142	#123×C₈₃	—	2	4	no	—
143	#123×C₈₃	—	2	4	no	—
144	#123×C₈₃	—	2	2	no	—
145	#123×C₈₃	—	2	2	no	—
146	#123×C₈₃	—	2	2	no	—
147	C₂²⋊Q₈×C₈₃	—	2	1	no	—
148	C₂²⋊Q₈×C₈₃	—	2	2	no	—
149	C₂²⋊Q₈×C₈₃	—	2	2	no	—
150	C₂²⋊Q₈×C₈₃	—	2	2	no	—
151	C₂²⋊Q₈×C₈₃	—	2	2	no	—
152	C₂²⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
153	#121×C₈₃	—	2	1	no	—
154	#121×C₈₃	—	2	2	no	—
155	#121×C₈₃	—	2	1	no	—
156	#121×C₈₃	—	2	2	no	—
157	#121×C₈₃	C₂³	1	1	yes	characteristic
158	#121×C₈₃	C₂³	1	2	yes	—
159	C₄×Q₈×C₈₃	—	2	1	no	—
160	C₄×Q₈×C₈₃	—	2	1	no	—
161	C₄×Q₈×C₈₃	—	2	1	no	—
162	C₄×Q₈×C₈₃	D₄	1	1	yes	characteristic
163	C₄×Q₈×C₈₃	D₄	1	2	yes	—
164	C₄×Q₈×C₈₃	D₄	1	1	yes	characteristic
165	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
166	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
167	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
168	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
169	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
170	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
172	C₄×D₄×C₈₃	—	2	1	no	—
173	C₄×D₄×C₈₃	—	2	2	no	—
174	C₄×D₄×C₈₃	—	2	2	no	—
175	C₄×D₄×C₈₃	—	2	2	no	—
176	C₄×D₄×C₈₃	—	2	4	no	—
177	C₄×D₄×C₈₃	—	2	1	no	—
178	C₄×D₄×C₈₃	—	2	2	no	—
179	C₄×D₄×C₈₃	—	2	2	no	—
180	C₄×D₄×C₈₃	—	2	2	no	—
181	C₄×D₄×C₈₃	—	2	2	no	—
182	C₄×D₄×C₈₃	—	2	1	no	—
183	C₄×D₄×C₈₃	C₂³	1	2	yes	—
184	C₄×D₄×C₈₃	C₂³	1	2	yes	—
185	C₄×D₄×C₈₃	C₂³	1	2	yes	—
186	C₄×D₄×C₈₃	C₂³	1	4	yes	—
187	C₄×D₄×C₈₃	C₂³	1	4	yes	—
188	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
189	C₄×D₄×C₈₃	C₂³	1	2	yes	—
190	#117×C₈₃	—	2	2	no	—
191	#117×C₈₃	—	2	1	no	—
192	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
193	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
194	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
195	C₂×C₄⋊C₄×C₈₃	D₄	1	1	yes	characteristic
196	C₂×C₄⋊C₄×C₈₃	D₄	1	2	yes	—
197	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
199	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
200	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
201	C₂×C₄²×C₈₃	—	2	1	no	—
202	C₂×C₄²×C₈₃	C₂³	1	2	yes	—
203	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
204	#107×C₈₃	C₂³	1	2	yes	—
205	#107×C₈₃	C₂³	1	4	yes	—
206	#106×C₈₃	C₂³	1	2	yes	—
207	C₄⋊C₈×C₈₃	C₂³	1	4	yes	—
208	C₄⋊C₈×C₈₃	C₂³	1	4	yes	—
209	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
210	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
211	#103×C₈₃	C₂³	1	2	yes	—
212	#103×C₈₃	C₂³	1	2	yes	—
213	#103×C₈₃	C₂³	1	2	yes	—
214	#103×C₈₃	C₂³	1	4	yes	—
215	#102×C₈₃	C₂³	1	4	yes	—
216	#102×C₈₃	C₂³	1	4	yes	—
217	#102×C₈₃	C₂³	1	4	yes	—
218	#102×C₈₃	C₂³	1	4	yes	—
219	#102×C₈₃	C₂³	1	4	yes	—
220	#102×C₈₃	C₂³	1	2	yes	—
221	C₂²⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
222	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
223	C₂²⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
224	#97×C₈₃	C₂³	1	4	yes	—
225	#97×C₈₃	C₂³	1	2	yes	—
226	C₄×C₈×C₈₃	C₂³	1	2	yes	—
227	C₄×C₈×C₈₃	C₂³	1	4	yes	—
228	C₂⁴×C₈₃	—	2	2	no	—
229	#41×C₈₃	—	4	4	no	—
230	#41×C₈₃	—	8	4	no	—
231	#41×C₈₃	—	8	2	no	—
232	C₂×Q₈×C₈₃	—	2	1	no	—
233	C₂×Q₈×C₈₃	—	2	2	no	—
234	C₂×Q₈×C₈₃	—	2	1	no	—
235	C₂×Q₈×C₈₃	—	4	2	no	—
236	C₂×Q₈×C₈₃	—	4	2	no	—
237	C₂×Q₈×C₈₃	C₂×D₄	1	1	yes	characteristic
238	C₂×Q₈×C₈₃	C₂×D₄	1	1	yes	characteristic
239	C₂×Q₈×C₈₃	C₂×D₄	1	2	yes	—
240	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
241	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
242	C₂×D₄×C₈₃	—	2	1	no	—
243	C₂×D₄×C₈₃	—	2	2	no	—
244	C₂×D₄×C₈₃	—	2	2	no	—
245	C₂×D₄×C₈₃	—	2	1	no	—
246	C₂×D₄×C₈₃	—	2	2	no	—
247	C₂×D₄×C₈₃	—	2	2	no	—
248	C₂×D₄×C₈₃	—	2	2	no	—
249	C₂×D₄×C₈₃	—	2	2	no	—
250	C₂×D₄×C₈₃	—	2	1	no	—
251	C₂×D₄×C₈₃	—	2	2	no	—
252	C₂×D₄×C₈₃	—	2	2	no	—
253	C₂×D₄×C₈₃	—	4	4	no	—
254	C₂×D₄×C₈₃	—	4	4	no	—
255	C₂×D₄×C₈₃	—	8	2	no	—
256	C₂×D₄×C₈₃	C₂⁴	1	4	yes	—
257	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
258	C₂×D₄×C₈₃	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₈₃	—	2	1	no	—
260	C₂²×C₄×C₈₃	—	2	1	no	—
261	C₂²×C₄×C₈₃	—	2	2	no	—
262	C₂²×C₄×C₈₃	—	2	1	no	—
263	C₂²×C₄×C₈₃	—	2	2	no	—
264	C₂²×C₄×C₈₃	—	2	2	no	—
265	C₂²×C₄×C₈₃	—	2	2	no	—
266	C₂²×C₄×C₈₃	—	2	4	no	—
267	C₂²×C₄×C₈₃	—	2	4	no	—
268	C₂²×C₄×C₈₃	—	8	4	no	—
269	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
271	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
273	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
274	Q₁₆×C₈₃	—	4	2	no	—
275	SD₁₆×C₈₃	—	4	2	no	—
276	SD₁₆×C₈₃	—	4	4	no	—
277	SD₁₆×C₈₃	—	4	4	no	—
278	D₈×C₈₃	—	4	4	no	—
279	D₈×C₈₃	—	4	4	no	—
280	D₈×C₈₃	—	4	4	no	—
281	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
282	C₂×C₈×C₈₃	C₂⁴	1	4	yes	—
283	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
284	C₄⋊C₄×C₈₃	—	2	2	no	—
285	C₄⋊C₄×C₈₃	—	2	1	no	—
286	C₄⋊C₄×C₈₃	—	2	2	no	—
287	C₄⋊C₄×C₈₃	—	2	1	no	—
288	C₄⋊C₄×C₈₃	—	2	2	no	—
289	C₄⋊C₄×C₈₃	—	2	2	no	—
290	C₄⋊C₄×C₈₃	—	2	1	no	—
291	C₄⋊C₄×C₈₃	—	2	1	no	—
292	C₄⋊C₄×C₈₃	—	2	1	no	—
293	C₄⋊C₄×C₈₃	—	2	2	no	—
294	C₄⋊C₄×C₈₃	—	2	2	no	—
295	C₄⋊C₄×C₈₃	—	2	1	no	—
296	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
297	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
298	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
299	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
300	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
301	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
302	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
303	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
304	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
305	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
306	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
307	C₂²⋊C₄×C₈₃	—	2	1	no	—
308	C₂²⋊C₄×C₈₃	—	2	4	no	—
309	C₂²⋊C₄×C₈₃	—	2	4	no	—
310	C₂²⋊C₄×C₈₃	—	2	4	no	—
311	C₂²⋊C₄×C₈₃	—	2	4	no	—
312	C₂²⋊C₄×C₈₃	—	2	4	no	—
313	C₂²⋊C₄×C₈₃	—	2	4	no	—
314	C₂²⋊C₄×C₈₃	—	2	2	no	—
315	C₂²⋊C₄×C₈₃	—	2	1	no	—
316	C₂²⋊C₄×C₈₃	—	2	2	no	—
317	C₂²⋊C₄×C₈₃	—	2	1	no	—
318	C₂²⋊C₄×C₈₃	—	2	1	no	—
319	C₂²⋊C₄×C₈₃	—	2	2	no	—
320	C₂²⋊C₄×C₈₃	—	2	2	no	—
321	C₂²⋊C₄×C₈₃	—	2	1	no	—
322	C₂²⋊C₄×C₈₃	—	2	2	no	—
323	C₂²⋊C₄×C₈₃	—	2	2	no	—
324	C₂²⋊C₄×C₈₃	—	2	2	no	—
325	C₄²×C₈₃	—	2	2	no	—
326	C₄²×C₈₃	—	2	2	no	—
327	C₄²×C₈₃	—	2	2	no	—
328	C₄²×C₈₃	—	2	1	no	—
329	C₄²×C₈₃	C₂×D₄	1	2	yes	—
330	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₈₃	C₂×D₄	1	2	yes	—
332	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
333	C₄²×C₈₃	C₂⁴	1	2	yes	—
334	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
335	C₄²×C₈₃	C₂⁴	1	2	yes	—
336	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
337	C₂³×C₈₃	—	2	2	no	—
338	C₂³×C₈₃	—	2	1	no	—
339	C₂³×C₈₃	—	2	4	no	—
340	C₂³×C₈₃	—	4	4	no	—
341	C₂³×C₈₃	—	4	4	no	—
342	C₂³×C₈₃	—	4	4	no	—
343	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
344	Q₈×C₈₃	—	2	2	no	—
345	Q₈×C₈₃	—	2	2	no	—
346	Q₈×C₈₃	—	2	2	no	—
347	Q₈×C₈₃	—	2	2	no	—
348	Q₈×C₈₃	—	2	2	no	—
349	Q₈×C₈₃	—	4	2	no	—
350	Q₈×C₈₃	—	4	2	no	—
351	Q₈×C₈₃	—	8	2	no	—
352	Q₈×C₈₃	—	8	1	no	—
353	D₄×C₈₃	—	2	4	no	—
354	D₄×C₈₃	—	2	2	no	—
355	D₄×C₈₃	—	2	4	no	—
356	D₄×C₈₃	—	2	4	no	—
357	D₄×C₈₃	—	4	4	no	—
358	D₄×C₈₃	—	4	4	no	—
359	D₄×C₈₃	—	4	4	no	—
360	D₄×C₈₃	—	4	2	no	—
361	D₄×C₈₃	—	4	4	no	—
362	D₄×C₈₃	—	4	4	no	—
363	D₄×C₈₃	—	4	2	no	—
364	D₄×C₈₃	—	8	2	no	—
365	D₄×C₈₃	—	8	2	no	—
366	D₄×C₈₃	—	8	2	no	—
367	D₄×C₈₃	—	8	1	no	—
368	C₂×C₄×C₈₃	—	2	4	no	—
369	C₂×C₄×C₈₃	—	2	2	no	—
370	C₂×C₄×C₈₃	—	2	2	no	—
371	C₂×C₄×C₈₃	—	2	2	no	—
372	C₂×C₄×C₈₃	—	2	1	no	—
373	C₂×C₄×C₈₃	—	2	2	no	—
374	C₂×C₄×C₈₃	—	2	2	no	—
375	C₂×C₄×C₈₃	—	2	2	no	—
376	C₂×C₄×C₈₃	—	2	1	no	—
377	C₂×C₄×C₈₃	—	2	1	no	—
378	C₂×C₄×C₈₃	—	4	2	no	—
379	C₂×C₄×C₈₃	—	4	4	no	—
380	C₂×C₄×C₈₃	—	4	2	no	—
381	C₂×C₄×C₈₃	—	4	2	no	—
382	C₂×C₄×C₈₃	—	4	2	no	—
383	C₂×C₄×C₈₃	—	8	4	no	—
384	C₂×C₄×C₈₃	—	8	4	no	—
385	C₂×C₄×C₈₃	—	8	2	no	—
386	C₂×C₄×C₈₃	—	8	2	no	—
387	C₂×C₄×C₈₃	—	8	2	no	—
388	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
390	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
392	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
393	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
394	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
398	C₈×C₈₃	—	2	2	no	—
399	C₈×C₈₃	—	2	2	no	—
400	C₈×C₈₃	—	2	4	no	—
401	C₂²×C₈₃	—	2	1	no	—
402	C₂²×C₈₃	—	2	1	no	—
403	C₂²×C₈₃	—	4	4	no	—
404	C₂²×C₈₃	—	4	2	no	—
405	C₂²×C₈₃	—	4	1	no	—
406	C₂²×C₈₃	—	4	2	no	—
407	C₂²×C₈₃	—	4	1	no	—
408	C₂²×C₈₃	—	4	4	no	—
409	C₂²×C₈₃	—	4	1	no	—
410	C₂²×C₈₃	—	4	2	no	—
411	C₂²×C₈₃	—	4	4	no	—
412	C₂²×C₈₃	—	8	8	no	—
413	C₂²×C₈₃	#576	1	2	yes	—
414	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
415	C₄×C₈₃	—	2	1	no	—
416	C₄×C₈₃	—	2	1	no	—
417	C₄×C₈₃	—	2	2	no	—
418	C₄×C₈₃	—	2	2	no	—
419	C₄×C₈₃	—	2	2	no	—
420	C₄×C₈₃	—	2	1	no	—
421	C₄×C₈₃	—	2	2	no	—
422	C₄×C₈₃	—	2	1	no	—
423	C₄×C₈₃	—	4	2	no	—
424	C₄×C₈₃	—	4	1	no	—
425	C₄×C₈₃	—	4	1	no	—
426	C₄×C₈₃	—	4	2	no	—
427	C₄×C₈₃	—	4	1	no	—
428	C₄×C₈₃	—	4	2	no	—
429	C₄×C₈₃	#575	1	2	yes	—
430	C₄×C₈₃	#585	1	2	yes	—
431	#61898	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
432	C₂×C₈₃	—	2	2	no	—
433	C₂×C₈₃	—	8	2	no	—
434	C₂×C₈₃	—	8	1	no	—
435	C₂×C₈₃	—	8	4	no	—
436	C₂×C₈₃	#3487	1	1	yes	characteristic
437	C₂×C₈₃	C₂×#575	1	1	yes	characteristic
438	C₂×C₈₃	C₂×#576	1	1	yes	characteristic
439	#3522	C₂×C₈₃	1	1	yes	characteristic, complemented
440	C₂×#559	C₂×C₈₃	1	1	yes	characteristic, complemented
441	#3403	C₂×C₈₃	1	4	yes	complemented
442	#3399	C₂×C₈₃	1	2	yes	complemented
443	#3396	C₂×C₈₃	1	2	yes	complemented
444	#3375	C₂×C₈₃	1	2	yes	complemented
445	#3370	C₂×C₈₃	1	4	yes	complemented
446	#3361	C₂×C₈₃	1	2	yes	complemented
447	#3217	C₂×C₈₃	1	1	yes	characteristic, complemented
448	#3213	C₂×C₈₃	1	2	yes	complemented
449	#3211	C₂×C₈₃	1	2	yes	complemented
450	#3205	C₂×C₈₃	1	1	yes	characteristic, complemented
451	#3114	C₂×C₈₃	1	2	yes	complemented
452	#3112	C₂×C₈₃	1	1	yes	characteristic, complemented
453	#3108	C₂×C₈₃	1	1	yes	characteristic, complemented
454	#3100	C₂×C₈₃	1	2	yes	complemented
455	#2984	C₂×C₈₃	1	1	yes	characteristic, complemented
456	C₈₃	#61898	1	1	yes	characteristic, direct product factor, Sylow
457	#559	—	2	1	no	—
458	#559	—	2	1	no	—
459	#559	—	2	2	no	—
460	#559	C₂²×C₈₃	1	2	yes	—
461	#559	C₂²×C₈₃	1	4	yes	—
462	#559	C₂²×C₈₃	1	2	yes	—
463	#559	C₂²×C₈₃	1	1	yes	characteristic, complemented
464	#559	C₂²×C₈₃	1	2	yes	complemented
465	Q₈²	C₂²×C₈₃	1	1	yes	characteristic, complemented
466	#554	C₂²×C₈₃	1	1	yes	characteristic, complemented
467	#554	C₂²×C₈₃	1	2	yes	complemented
468	#550	C₂²×C₈₃	1	1	yes	characteristic, complemented
469	#548	—	2	1	no	—
470	#547	—	2	1	no	—
471	#547	—	2	2	no	—
472	#542	—	2	2	no	—
473	#542	—	2	1	no	—
474	#532	C₂²×C₈₃	1	2	yes	—
475	#532	C₂²×C₈₃	1	1	yes	characteristic
476	C₂×#127	C₂²×C₈₃	1	1	yes	characteristic
477	#529	C₂²×C₈₃	1	1	yes	characteristic
478	#529	C₂²×C₈₃	1	2	yes	—
479	C₂×#124	—	2	1	no	—
480	C₂×#124	C₂²×C₈₃	1	2	yes	—
481	C₂×#123	—	2	2	no	—
482	#520	—	2	1	no	—
483	C₂×C₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic
484	C₂×C₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic
485	C₂×C₄×D₄	—	2	1	no	—
486	C₂×C₄×D₄	C₂²×C₈₃	1	2	yes	—
487	#496	C₂²×C₈₃	1	2	yes	—
488	#496	C₂²×C₈₃	1	4	yes	complemented
489	#495	C₂²×C₈₃	1	4	yes	complemented
490	#493	C₂²×C₈₃	1	2	yes	—
491	#490	C₂²×C₈₃	1	2	yes	—
492	#489	C₂²×C₈₃	1	4	yes	complemented
493	#488	C₂²×C₈₃	1	4	yes	complemented
494	#486	C₂²×C₈₃	1	2	yes	—
495	#483	C₂²×C₈₃	1	1	yes	characteristic
496	#480	C₂²×C₈₃	1	1	yes	characteristic
497	#480	C₂²×C₈₃	1	2	yes	—
498	#479	C₂²×C₈₃	1	2	yes	complemented
499	#478	C₂²×C₈₃	1	4	yes	complemented
500	#477	C₂²×C₈₃	1	2	yes	complemented
501	#474	C₂²×C₈₃	1	4	yes	complemented
502	#464	C₂²×C₈₃	1	2	yes	complemented
503	#464	C₂²×C₈₃	1	4	yes	complemented
504	#463	C₂²×C₈₃	1	4	yes	complemented
505	#463	C₂²×C₈₃	1	4	yes	complemented
506	#463	C₂²×C₈₃	1	4	yes	complemented
507	#463	C₂²×C₈₃	1	4	yes	complemented
508	#460	C₂²×C₈₃	1	2	yes	—
509	#460	C₂²×C₈₃	1	2	yes	complemented
510	#459	C₂²×C₈₃	1	2	yes	—
511	#459	C₂²×C₈₃	1	4	yes	—
512	#459	C₂²×C₈₃	1	4	yes	complemented
513	#451	C₂²×C₈₃	1	1	yes	characteristic
514	#450	C₂²×C₈₃	1	2	yes	—
515	#448	C₂²×C₈₃	1	1	yes	characteristic
516	#448	C₂²×C₈₃	1	2	yes	—
517	#447	C₂²×C₈₃	1	2	yes	—
518	#447	C₂²×C₈₃	1	2	yes	—
519	#447	C₂²×C₈₃	1	2	yes	—
520	#446	C₂²×C₈₃	1	4	yes	complemented
521	#446	C₂²×C₈₃	1	2	yes	complemented
522	C₈×Q₈	C₂²×C₈₃	1	2	yes	complemented
523	#442	C₂²×C₈₃	1	4	yes	complemented
524	#440	C₂²×C₈₃	1	4	yes	complemented
525	#440	C₂²×C₈₃	1	4	yes	complemented
526	C₄×Q₁₆	C₂²×C₈₃	1	2	yes	complemented
527	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	complemented
528	C₄×D₈	C₂²×C₈₃	1	4	yes	complemented
529	C₄×D₈	C₂²×C₈₃	1	4	yes	complemented
530	#432	C₂²×C₈₃	1	1	yes	characteristic
531	#432	C₂²×C₈₃	1	2	yes	—
532	#431	C₂²×C₈₃	1	2	yes	—
533	#431	C₂²×C₈₃	1	1	yes	characteristic
534	C₂×#41	—	2	1	no	—
535	C₂×#41	—	2	2	no	—
536	C₂×#41	—	2	1	no	—
537	C₂²×Q₈	D₄×C₈₃	1	1	yes	characteristic
538	C₂²×Q₈	C₂³×C₈₃	1	1	yes	characteristic
539	C₂²×D₄	—	2	1	no	—
540	C₂²×D₄	—	2	1	no	—
541	C₂²×D₄	C₂³×C₈₃	1	2	yes	—
542	C₂³×C₄	—	2	2	no	—
543	C₂×Q₁₆	C₂³×C₈₃	1	2	yes	—
544	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
545	C₂×SD₁₆	C₂³×C₈₃	1	4	yes	—
546	C₂×SD₁₆	C₂³×C₈₃	1	4	yes	—
547	C₂×D₈	C₂³×C₈₃	1	4	yes	—
548	C₂×D₈	C₂³×C₈₃	1	4	yes	—
549	C₂×D₈	C₂³×C₈₃	1	4	yes	—
550	C₄⋊Q₈	—	2	1	no	—
551	C₄⋊Q₈	—	2	2	no	—
552	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
553	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
554	#127	—	2	1	no	—
555	#127	—	2	1	no	—
556	#127	C₂³×C₈₃	1	2	yes	—
557	#127	C₂³×C₈₃	1	2	yes	—
558	#127	C₂³×C₈₃	1	2	yes	—
559	#127	C₂³×C₈₃	1	1	yes	characteristic
560	#126	—	2	2	no	—
561	#126	—	2	1	no	—
562	#125	C₂³×C₈₃	1	2	yes	—
563	#125	C₂³×C₈₃	1	1	yes	characteristic
564	#124	—	2	2	no	—
565	#124	—	2	2	no	—
566	#124	—	2	4	no	—
567	#124	—	2	1	no	—
568	#124	—	2	2	no	—
569	#124	—	2	2	no	—
570	#124	—	2	2	no	—
571	#124	—	2	2	no	—
572	#124	—	2	1	no	—
573	#124	C₂³×C₈₃	1	4	yes	—
574	#124	C₂³×C₈₃	1	4	yes	—
575	#124	C₂³×C₈₃	1	2	yes	—
576	#124	C₂³×C₈₃	1	1	yes	characteristic
577	#123	—	2	2	no	—
578	#123	—	2	1	no	—
579	#123	—	2	4	no	—
580	#123	—	2	4	no	—
581	#123	—	2	4	no	—
582	#123	—	2	4	no	—
583	#123	—	2	2	no	—
584	#123	—	2	2	no	—
585	#123	—	2	2	no	—
586	C₂²⋊Q₈	—	2	1	no	—
587	C₂²⋊Q₈	—	2	2	no	—
588	C₂²⋊Q₈	—	2	2	no	—
589	C₂²⋊Q₈	—	2	2	no	—
590	C₂²⋊Q₈	—	2	2	no	—
591	C₂²⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
592	#121	—	2	1	no	—
593	#121	—	2	2	no	—
594	#121	—	2	1	no	—
595	#121	—	2	2	no	—
596	#121	C₂³×C₈₃	1	1	yes	characteristic
597	#121	C₂³×C₈₃	1	2	yes	—
598	C₄×Q₈	—	2	1	no	—
599	C₄×Q₈	—	2	1	no	—
600	C₄×Q₈	—	2	1	no	—
601	C₄×Q₈	D₄×C₈₃	1	1	yes	characteristic
602	C₄×Q₈	D₄×C₈₃	1	2	yes	—
603	C₄×Q₈	D₄×C₈₃	1	1	yes	characteristic
604	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
605	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
606	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
607	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
608	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
609	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
610	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
611	C₄×D₄	—	2	1	no	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	—	2	4	no	—
616	C₄×D₄	—	2	1	no	—
617	C₄×D₄	—	2	2	no	—
618	C₄×D₄	—	2	2	no	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	2	no	—
621	C₄×D₄	—	2	1	no	—
622	C₄×D₄	C₂³×C₈₃	1	4	yes	—
623	C₄×D₄	C₂³×C₈₃	1	4	yes	—
624	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
625	C₄×D₄	C₂³×C₈₃	1	2	yes	—
626	C₄×D₄	C₂³×C₈₃	1	2	yes	—
627	C₄×D₄	C₂³×C₈₃	1	2	yes	—
628	C₄×D₄	C₂³×C₈₃	1	2	yes	—
629	#117	—	2	2	no	—
630	#117	—	2	1	no	—
631	C₂×C₄⋊C₄	—	2	1	no	—
632	C₂×C₄⋊C₄	—	2	1	no	—
633	C₂×C₄⋊C₄	—	2	2	no	—
634	C₂×C₄⋊C₄	D₄×C₈₃	1	1	yes	characteristic
635	C₂×C₄⋊C₄	D₄×C₈₃	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
637	C₂×C₂²⋊C₄	—	2	2	no	—
638	C₂×C₂²⋊C₄	—	2	2	no	—
639	C₂×C₂²⋊C₄	—	2	2	no	—
640	C₂×C₄²	—	2	1	no	—
641	C₂×C₄²	C₂³×C₈₃	1	2	yes	—
642	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
643	#107	C₂³×C₈₃	1	2	yes	—
644	#107	C₂³×C₈₃	1	4	yes	—
645	#106	C₂³×C₈₃	1	2	yes	—
646	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
647	C₄⋊C₈	C₂³×C₈₃	1	4	yes	—
648	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
649	C₄⋊C₈	C₂³×C₈₃	1	4	yes	—
650	#103	C₂³×C₈₃	1	2	yes	—
651	#103	C₂³×C₈₃	1	2	yes	—
652	#103	C₂³×C₈₃	1	2	yes	—
653	#103	C₂³×C₈₃	1	4	yes	—
654	#102	C₂³×C₈₃	1	2	yes	—
655	#102	C₂³×C₈₃	1	4	yes	—
656	#102	C₂³×C₈₃	1	4	yes	—
657	#102	C₂³×C₈₃	1	4	yes	—
658	#102	C₂³×C₈₃	1	4	yes	—
659	#102	C₂³×C₈₃	1	4	yes	—
660	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
661	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
662	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
663	#97	C₂³×C₈₃	1	2	yes	—
664	#97	C₂³×C₈₃	1	4	yes	—
665	C₄×C₈	C₂³×C₈₃	1	4	yes	—
666	C₄×C₈	C₂³×C₈₃	1	2	yes	—
667	C₂⁴	—	2	2	no	—
668	#41	—	4	4	no	—
669	#41	—	8	4	no	—
670	#41	—	8	2	no	—
671	C₂×Q₈	—	2	1	no	—
672	C₂×Q₈	—	2	2	no	—
673	C₂×Q₈	—	2	1	no	—
674	C₂×Q₈	—	4	2	no	—
675	C₂×Q₈	—	4	2	no	—
676	C₂×Q₈	C₂×D₄×C₈₃	1	1	yes	characteristic
677	C₂×Q₈	C₂×D₄×C₈₃	1	1	yes	characteristic
678	C₂×Q₈	C₂×D₄×C₈₃	1	2	yes	—
679	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
680	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	1	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	2	2	no	—
688	C₂×D₄	—	2	2	no	—
689	C₂×D₄	—	2	1	no	—
690	C₂×D₄	—	2	2	no	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	4	4	no	—
693	C₂×D₄	—	4	4	no	—
694	C₂×D₄	—	8	2	no	—
695	C₂×D₄	C₂⁴×C₈₃	1	4	yes	—
696	C₂×D₄	C₂⁴×C₈₃	1	1	yes	characteristic
697	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
698	C₂²×C₄	—	2	1	no	—
699	C₂²×C₄	—	2	1	no	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	2	1	no	—
702	C₂²×C₄	—	2	2	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	2	no	—
705	C₂²×C₄	—	2	4	no	—
706	C₂²×C₄	—	2	4	no	—
707	C₂²×C₄	—	8	4	no	—
708	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
709	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
710	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
711	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
713	Q₁₆	—	4	2	no	—
714	SD₁₆	—	4	2	no	—
715	SD₁₆	—	4	4	no	—
716	SD₁₆	—	4	4	no	—
717	D₈	—	4	4	no	—
718	D₈	—	4	4	no	—
719	D₈	—	4	4	no	—
720	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
721	C₂×C₈	C₂⁴×C₈₃	1	4	yes	—
722	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	1	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
736	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
737	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
738	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
739	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
740	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
741	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
742	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
743	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
744	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
745	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
746	C₂²⋊C₄	—	2	1	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	1	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	1	no	—
757	C₂²⋊C₄	—	2	1	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	—	2	1	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₄²	—	2	2	no	—
765	C₄²	—	2	2	no	—
766	C₄²	—	2	2	no	—
767	C₄²	—	2	1	no	—
768	C₄²	C₂×D₄×C₈₃	1	2	yes	—
769	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
770	C₄²	C₂×D₄×C₈₃	1	2	yes	—
771	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
772	C₄²	C₂⁴×C₈₃	1	2	yes	—
773	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
774	C₄²	C₂⁴×C₈₃	1	2	yes	—
775	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
776	C₂³	—	2	2	no	—
777	C₂³	—	2	1	no	—
778	C₂³	—	2	4	no	—
779	C₂³	—	4	4	no	—
780	C₂³	—	4	4	no	—
781	C₂³	—	4	4	no	—
782	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
783	Q₈	—	2	2	no	—
784	Q₈	—	2	2	no	—
785	Q₈	—	2	2	no	—
786	Q₈	—	2	2	no	—
787	Q₈	—	2	2	no	—
788	Q₈	—	4	2	no	—
789	Q₈	—	4	2	no	—
790	Q₈	—	8	2	no	—
791	Q₈	—	8	1	no	—
792	D₄	—	2	4	no	—
793	D₄	—	2	2	no	—
794	D₄	—	2	4	no	—
795	D₄	—	2	4	no	—
796	D₄	—	4	4	no	—
797	D₄	—	4	4	no	—
798	D₄	—	4	4	no	—
799	D₄	—	4	2	no	—
800	D₄	—	4	4	no	—
801	D₄	—	4	4	no	—
802	D₄	—	4	2	no	—
803	D₄	—	8	2	no	—
804	D₄	—	8	2	no	—
805	D₄	—	8	2	no	—
806	D₄	—	8	1	no	—
807	C₂×C₄	—	2	4	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	4	2	no	—
818	C₂×C₄	—	4	4	no	—
819	C₂×C₄	—	4	2	no	—
820	C₂×C₄	—	4	2	no	—
821	C₂×C₄	—	4	2	no	—
822	C₂×C₄	—	8	4	no	—
823	C₂×C₄	—	8	4	no	—
824	C₂×C₄	—	8	2	no	—
825	C₂×C₄	—	8	2	no	—
826	C₂×C₄	—	8	2	no	—
827	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
828	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
829	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
830	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
831	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
832	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
833	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
834	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
835	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
836	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
837	C₈	—	2	2	no	—
838	C₈	—	2	2	no	—
839	C₈	—	2	4	no	—
840	C₂²	—	2	1	no	—
841	C₂²	—	2	1	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	4	1	no	—
844	C₂²	—	4	4	no	—
845	C₂²	—	4	1	no	—
846	C₂²	—	4	2	no	—
847	C₂²	—	4	4	no	—
848	C₂²	—	4	4	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	4	1	no	—
851	C₂²	—	8	8	no	—
852	C₂²	#576×C₈₃	1	2	yes	—
853	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
854	C₄	—	2	1	no	—
855	C₄	—	2	2	no	—
856	C₄	—	2	2	no	—
857	C₄	—	2	2	no	—
858	C₄	—	2	1	no	—
859	C₄	—	2	2	no	—
860	C₄	—	2	1	no	—
861	C₄	—	2	1	no	—
862	C₄	—	4	1	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	1	no	—
865	C₄	—	4	2	no	—
866	C₄	—	4	2	no	—
867	C₄	—	4	1	no	—
868	C₄	#575×C₈₃	1	2	yes	—
869	C₄	#585×C₈₃	1	2	yes	—
870	C₂	—	2	2	no	—
871	C₂	—	8	4	no	—
872	C₂	—	8	2	no	—
873	C₂	—	8	1	no	—
874	C₂	C₈₃×#3487	1	1	yes	characteristic
875	C₂	C₂×#575×C₈₃	1	1	yes	characteristic
876	C₂	C₂×#576×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 ◁ C₂×C₄×Q₈×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₃×#3522	C₂	semidirect
2. C₂×#559×C₈₃	C₂	semidirect
3. C₈₃×#3403	C₂	semidirect
4. C₈₃×#3399	C₂	semidirect
5. C₈₃×#3396	C₂	semidirect
6. C₈₃×#3375	C₂	semidirect
7. C₈₃×#3370	C₂	semidirect
8. C₈₃×#3361	C₂	semidirect
9. C₈₃×#3217	C₂	semidirect
10. C₈₃×#3213	C₂	semidirect
11. C₈₃×#3211	C₂	semidirect
12. C₈₃×#3205	C₂	semidirect
13. C₈₃×#3114	C₂	semidirect
14. C₈₃×#3112	C₂	semidirect
15. C₈₃×#3108	C₂	semidirect
16. C₈₃×#3100	C₂	semidirect
17. C₈₃×#2984	C₂	semidirect
24. #559×C₈₃	C₂²	semidirect
25. #559×C₈₃	C₂²	semidirect
26. Q₈²×C₈₃	C₂²	semidirect
27. #554×C₈₃	C₂²	semidirect
28. #554×C₈₃	C₂²	semidirect
29. #550×C₈₃	C₂²	semidirect
49. #496×C₈₃	C₂²	semidirect
50. #495×C₈₃	C₂²	semidirect
53. #489×C₈₃	C₂²	semidirect
54. #488×C₈₃	C₂²	semidirect
59. #479×C₈₃	C₂²	semidirect
60. #478×C₈₃	C₂²	semidirect
61. #477×C₈₃	C₂²	semidirect
62. #474×C₈₃	C₂²	semidirect
63. #464×C₈₃	C₂²	semidirect
64. #464×C₈₃	C₂²	semidirect
65. #463×C₈₃	C₂²	semidirect
66. #463×C₈₃	C₂²	semidirect
67. #463×C₈₃	C₂²	semidirect
68. #463×C₈₃	C₂²	semidirect
70. #460×C₈₃	C₂²	semidirect
73. #459×C₈₃	C₂²	semidirect
81. #446×C₈₃	C₂²	semidirect
82. #446×C₈₃	C₂²	semidirect
83. C₈×Q₈×C₈₃	C₂²	semidirect
84. #442×C₈₃	C₂²	semidirect
85. #440×C₈₃	C₂²	semidirect
86. #440×C₈₃	C₂²	semidirect
87. C₄×Q₁₆×C₈₃	C₂²	semidirect
88. C₄×SD₁₆×C₈₃	C₂²	semidirect
89. C₄×D₈×C₈₃	C₂²	semidirect
90. C₄×D₈×C₈₃	C₂²	semidirect
431. #61898	C₈₃	direct (N × H)
439. #3522	C₂×C₈₃	semidirect
440. C₂×#559	C₂×C₈₃	semidirect
441. #3403	C₂×C₈₃	semidirect
442. #3399	C₂×C₈₃	semidirect
443. #3396	C₂×C₈₃	semidirect
444. #3375	C₂×C₈₃	semidirect
445. #3370	C₂×C₈₃	semidirect
446. #3361	C₂×C₈₃	semidirect
447. #3217	C₂×C₈₃	semidirect
448. #3213	C₂×C₈₃	semidirect
449. #3211	C₂×C₈₃	semidirect
450. #3205	C₂×C₈₃	semidirect
451. #3114	C₂×C₈₃	semidirect
452. #3112	C₂×C₈₃	semidirect
453. #3108	C₂×C₈₃	semidirect
454. #3100	C₂×C₈₃	semidirect
455. #2984	C₂×C₈₃	semidirect
456. C₈₃	#61898	direct (N × H)
463. #559	C₂²×C₈₃	semidirect
464. #559	C₂²×C₈₃	semidirect
465. Q₈²	C₂²×C₈₃	semidirect
466. #554	C₂²×C₈₃	semidirect
467. #554	C₂²×C₈₃	semidirect
468. #550	C₂²×C₈₃	semidirect
488. #496	C₂²×C₈₃	semidirect
489. #495	C₂²×C₈₃	semidirect
492. #489	C₂²×C₈₃	semidirect
493. #488	C₂²×C₈₃	semidirect
498. #479	C₂²×C₈₃	semidirect
499. #478	C₂²×C₈₃	semidirect
500. #477	C₂²×C₈₃	semidirect
501. #474	C₂²×C₈₃	semidirect
502. #464	C₂²×C₈₃	semidirect
503. #464	C₂²×C₈₃	semidirect
504. #463	C₂²×C₈₃	semidirect
505. #463	C₂²×C₈₃	semidirect
506. #463	C₂²×C₈₃	semidirect
507. #463	C₂²×C₈₃	semidirect
509. #460	C₂²×C₈₃	semidirect
512. #459	C₂²×C₈₃	semidirect
520. #446	C₂²×C₈₃	semidirect
521. #446	C₂²×C₈₃	semidirect
522. C₈×Q₈	C₂²×C₈₃	semidirect
523. #442	C₂²×C₈₃	semidirect
524. #440	C₂²×C₈₃	semidirect
525. #440	C₂²×C₈₃	semidirect
526. C₄×Q₁₆	C₂²×C₈₃	semidirect
527. C₄×SD₁₆	C₂²×C₈₃	semidirect
528. C₄×D₈	C₂²×C₈₃	semidirect
529. C₄×D₈	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×#3522	2
C₂×#559×C₈₃	2
C₈₃×#3403	2
C₈₃×#3399	2
C₈₃×#3396	2
C₈₃×#3375	2
C₈₃×#3370	2
C₈₃×#3361	2
C₈₃×#3217	2
C₈₃×#3213	2
C₈₃×#3211	2
C₈₃×#3205	2
C₈₃×#3114	2
C₈₃×#3112	2
C₈₃×#3108	2
C₈₃×#3100	2
C₈₃×#2984	2
#61898	83

Subgroups — C83×#61898 #35289722

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#61898 #35289722