Subgroups — C₈₃×#61905 #35289729

Order 21248.

1724 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3523	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#556×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₃×#3402	C₂	1	4	yes	maximal, complemented
4	C₈₃×#3398	C₂	1	2	yes	maximal, complemented
5	C₈₃×#3393	C₂	1	2	yes	maximal, complemented
6	C₈₃×#3377	C₂	1	4	yes	maximal, complemented
7	C₈₃×#3367	C₂	1	2	yes	maximal, complemented
8	C₈₃×#3364	C₂	1	2	yes	maximal, complemented
9	C₈₃×#3218	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₃×#3215	C₂	1	2	yes	maximal, complemented
11	C₈₃×#3211	C₂	1	2	yes	maximal
12	C₈₃×#3209	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₃×#3117	C₂	1	2	yes	maximal, complemented
14	C₈₃×#3110	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#3105	C₂	1	1	yes	maximal, characteristic
16	C₈₃×#3104	C₂	1	2	yes	maximal, complemented
17	C₈₃×#2984	C₂	1	1	yes	maximal, characteristic, complemented
18	#557×C₈₃	C₂²	1	1	yes	characteristic, complemented
19	#557×C₈₃	C₂²	1	1	yes	characteristic, complemented
20	#557×C₈₃	C₂²	1	2	yes	complemented
21	#556×C₈₃	—	2	1	no	—
22	#556×C₈₃	—	2	1	no	—
23	#556×C₈₃	—	2	2	no	—
24	#556×C₈₃	C₂²	1	2	yes	—
25	#556×C₈₃	C₂²	1	2	yes	—
26	#556×C₈₃	C₂²	1	4	yes	—
27	#556×C₈₃	C₂²	1	1	yes	characteristic, complemented
28	#556×C₈₃	C₂²	1	2	yes	complemented
29	#552×C₈₃	—	2	1	no	—
30	#552×C₈₃	—	2	2	no	—
31	D₄×Q₈×C₈₃	—	2	1	no	—
32	D₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
33	#541×C₈₃	—	2	1	no	—
34	#541×C₈₃	—	2	2	no	—
35	#533×C₈₃	C₂²	1	2	yes	—
36	#533×C₈₃	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
38	#529×C₈₃	C₂²	1	1	yes	characteristic
39	#529×C₈₃	C₂²	1	2	yes	—
40	C₂×#126×C₈₃	—	2	2	no	—
41	C₂×#124×C₈₃	C₂²	1	2	yes	—
42	C₂×C₂²⋊Q₈×C₈₃	—	2	1	no	—
43	#519×C₈₃	—	2	1	no	—
44	C₂×C₄×Q₈×C₈₃	C₂²	1	2	yes	—
45	C₂×C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₈₃	C₂²	1	1	yes	characteristic
47	C₂×#117×C₈₃	—	2	1	no	—
48	#497×C₈₃	C₂²	1	4	yes	—
49	#497×C₈₃	C₂²	1	2	yes	complemented
50	#495×C₈₃	C₂²	1	4	yes	—
51	#494×C₈₃	C₂²	1	2	yes	complemented
52	#491×C₈₃	C₂²	1	2	yes	complemented
53	#489×C₈₃	C₂²	1	4	yes	—
54	#488×C₈₃	C₂²	1	4	yes	—
55	#487×C₈₃	C₂²	1	2	yes	complemented
56	#484×C₈₃	C₂²	1	1	yes	characteristic
57	#484×C₈₃	C₂²	1	2	yes	—
58	#481×C₈₃	C₂²	1	1	yes	characteristic
59	#479×C₈₃	C₂²	1	4	yes	complemented
60	#478×C₈₃	C₂²	1	2	yes	—
61	#477×C₈₃	C₂²	1	4	yes	complemented
62	#474×C₈₃	C₂²	1	2	yes	—
63	#464×C₈₃	C₂²	1	4	yes	—
64	#464×C₈₃	C₂²	1	4	yes	—
65	#464×C₈₃	C₂²	1	4	yes	—
66	#464×C₈₃	C₂²	1	4	yes	complemented
67	#463×C₈₃	C₂²	1	2	yes	—
68	#463×C₈₃	C₂²	1	4	yes	—
69	#462×C₈₃	C₂²	1	4	yes	complemented
70	#462×C₈₃	C₂²	1	2	yes	complemented
71	#462×C₈₃	C₂²	1	4	yes	complemented
72	#461×C₈₃	C₂²	1	2	yes	—
73	#461×C₈₃	C₂²	1	2	yes	complemented
74	#451×C₈₃	C₂²	1	2	yes	—
75	#451×C₈₃	C₂²	1	2	yes	—
76	#451×C₈₃	C₂²	1	2	yes	—
77	#450×C₈₃	C₂²	1	1	yes	characteristic
78	#450×C₈₃	C₂²	1	2	yes	—
79	#448×C₈₃	C₂²	1	2	yes	—
80	#447×C₈₃	C₂²	1	1	yes	characteristic
81	#446×C₈₃	C₂²	1	2	yes	complemented
82	#446×C₈₃	C₂²	1	4	yes	complemented
83	C₈×Q₈×C₈₃	C₂²	1	2	yes	complemented
84	#441×C₈₃	C₂²	1	4	yes	complemented
85	#440×C₈₃	C₂²	1	4	yes	—
86	#440×C₈₃	C₂²	1	4	yes	complemented
87	C₄×Q₁₆×C₈₃	C₂²	1	4	yes	complemented
88	C₄×Q₁₆×C₈₃	C₂²	1	4	yes	complemented
89	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	—
90	C₄×D₈×C₈₃	C₂²	1	2	yes	—
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	C₂²×Q₈×C₈₃	—	2	1	no	—
96	C₂²×Q₈×C₈₃	D₄	1	1	yes	characteristic
97	C₂²×Q₈×C₈₃	C₂³	1	2	yes	—
98	C₂²×D₄×C₈₃	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₈₃	—	2	1	no	—
100	C₂×Q₁₆×C₈₃	C₂³	1	4	yes	—
101	C₂×Q₁₆×C₈₃	C₂³	1	4	yes	—
102	C₂×Q₁₆×C₈₃	C₂³	1	4	yes	—
103	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₈₃	C₂³	1	4	yes	—
105	C₂×SD₁₆×C₈₃	C₂³	1	4	yes	—
106	C₂×D₈×C₈₃	C₂³	1	2	yes	—
107	C₄⋊Q₈×C₈₃	—	2	1	no	—
108	C₄⋊Q₈×C₈₃	—	2	2	no	—
109	C₄⋊Q₈×C₈₃	—	2	1	no	—
110	C₄⋊Q₈×C₈₃	—	2	1	no	—
111	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
112	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
113	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
114	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
115	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
116	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
117	#126×C₈₃	—	2	4	no	—
118	#126×C₈₃	—	2	4	no	—
119	#126×C₈₃	—	2	4	no	—
120	#126×C₈₃	—	2	4	no	—
121	#126×C₈₃	—	2	2	no	—
122	#126×C₈₃	—	2	2	no	—
123	#126×C₈₃	—	2	2	no	—
124	#126×C₈₃	—	2	1	no	—
125	#126×C₈₃	—	2	2	no	—
126	#125×C₈₃	—	2	2	no	—
127	#125×C₈₃	—	2	2	no	—
128	#125×C₈₃	—	2	2	no	—
129	#125×C₈₃	—	2	1	no	—
130	#125×C₈₃	—	2	2	no	—
131	#125×C₈₃	—	2	1	no	—
132	#125×C₈₃	—	2	2	no	—
133	#125×C₈₃	C₂³	1	1	yes	characteristic
134	#125×C₈₃	C₂³	1	2	yes	—
135	#124×C₈₃	—	2	2	no	—
136	#124×C₈₃	—	2	2	no	—
137	#124×C₈₃	C₂³	1	1	yes	characteristic
138	#124×C₈₃	C₂³	1	4	yes	—
139	#124×C₈₃	C₂³	1	4	yes	—
140	#124×C₈₃	C₂³	1	2	yes	—
141	#123×C₈₃	—	2	2	no	—
142	#123×C₈₃	—	2	1	no	—
143	C₂²⋊Q₈×C₈₃	—	2	2	no	—
144	C₂²⋊Q₈×C₈₃	—	2	2	no	—
145	C₂²⋊Q₈×C₈₃	—	2	4	no	—
146	C₂²⋊Q₈×C₈₃	—	2	1	no	—
147	C₂²⋊Q₈×C₈₃	—	2	2	no	—
148	C₂²⋊Q₈×C₈₃	—	2	1	no	—
149	C₂²⋊Q₈×C₈₃	—	2	2	no	—
150	C₂²⋊Q₈×C₈₃	—	2	1	no	—
151	C₂²⋊Q₈×C₈₃	—	2	2	no	—
152	C₂²⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
153	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
154	#121×C₈₃	C₂³	1	1	yes	characteristic
155	C₄×Q₈×C₈₃	—	2	1	no	—
156	C₄×Q₈×C₈₃	—	2	1	no	—
157	C₄×Q₈×C₈₃	—	2	2	no	—
158	C₄×Q₈×C₈₃	—	2	2	no	—
159	C₄×Q₈×C₈₃	—	2	2	no	—
160	C₄×Q₈×C₈₃	—	2	1	no	—
161	C₄×Q₈×C₈₃	—	2	2	no	—
162	C₄×Q₈×C₈₃	D₄	1	1	yes	characteristic
163	C₄×Q₈×C₈₃	D₄	1	1	yes	characteristic
164	C₄×Q₈×C₈₃	D₄	1	2	yes	—
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	4	yes	—
169	C₄×Q₈×C₈₃	C₂³	1	4	yes	—
170	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
172	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
173	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
174	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
175	C₄×D₄×C₈₃	—	2	1	no	—
176	C₄×D₄×C₈₃	—	2	2	no	—
177	C₄×D₄×C₈₃	—	2	1	no	—
178	C₄×D₄×C₈₃	—	2	1	no	—
179	C₄×D₄×C₈₃	C₂³	1	2	yes	—
180	C₄×D₄×C₈₃	C₂³	1	2	yes	—
181	C₄×D₄×C₈₃	C₂³	1	2	yes	—
182	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
183	#117×C₈₃	—	2	2	no	—
184	#117×C₈₃	—	2	1	no	—
185	#117×C₈₃	—	2	2	no	—
186	#117×C₈₃	—	2	2	no	—
187	#117×C₈₃	—	2	4	no	—
188	#117×C₈₃	—	2	1	no	—
189	#117×C₈₃	—	2	2	no	—
190	#117×C₈₃	—	2	1	no	—
191	#117×C₈₃	—	2	2	no	—
192	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
193	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
194	C₂×C₄⋊C₄×C₈₃	—	2	1	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	1	no	—
200	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
201	C₂×C₄²×C₈₃	—	2	2	no	—
202	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₈₃	C₂³	1	2	yes	—
204	#107×C₈₃	C₂³	1	4	yes	—
205	#107×C₈₃	C₂³	1	2	yes	—
206	#106×C₈₃	C₂³	1	2	yes	—
207	C₄⋊C₈×C₈₃	C₂³	1	4	yes	—
208	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
209	C₄⋊C₈×C₈₃	C₂³	1	4	yes	—
210	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
211	#103×C₈₃	C₂³	1	4	yes	—
212	#103×C₈₃	C₂³	1	2	yes	—
213	#103×C₈₃	C₂³	1	4	yes	—
214	#103×C₈₃	C₂³	1	4	yes	—
215	#103×C₈₃	C₂³	1	4	yes	—
216	#103×C₈₃	C₂³	1	4	yes	—
217	#102×C₈₃	C₂³	1	4	yes	—
218	#102×C₈₃	C₂³	1	2	yes	—
219	#102×C₈₃	C₂³	1	2	yes	—
220	#102×C₈₃	C₂³	1	2	yes	—
221	C₂²⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
222	C₂²⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
223	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
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	1	no	—
229	C₂×Q₈×C₈₃	—	2	2	no	—
230	C₂×Q₈×C₈₃	—	2	1	no	—
231	C₂×Q₈×C₈₃	—	2	2	no	—
232	C₂×Q₈×C₈₃	—	4	2	no	—
233	C₂×Q₈×C₈₃	—	4	4	no	—
234	C₂×Q₈×C₈₃	—	4	4	no	—
235	C₂×Q₈×C₈₃	C₂×D₄	1	1	yes	characteristic
236	C₂×Q₈×C₈₃	C₂×D₄	1	1	yes	characteristic
237	C₂×Q₈×C₈₃	C₂×D₄	1	2	yes	—
238	C₂×Q₈×C₈₃	C₂⁴	1	4	yes	—
239	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
240	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
241	C₂×D₄×C₈₃	—	2	1	no	—
242	C₂×D₄×C₈₃	—	2	1	no	—
243	C₂×D₄×C₈₃	—	4	2	no	—
244	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
245	C₂×D₄×C₈₃	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₈₃	—	2	1	no	—
247	C₂²×C₄×C₈₃	—	2	2	no	—
248	C₂²×C₄×C₈₃	—	2	2	no	—
249	C₂²×C₄×C₈₃	—	2	2	no	—
250	C₂²×C₄×C₈₃	—	2	2	no	—
251	C₂²×C₄×C₈₃	—	2	1	no	—
252	C₂²×C₄×C₈₃	—	4	4	no	—
253	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
254	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
257	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
258	Q₁₆×C₈₃	—	4	4	no	—
259	Q₁₆×C₈₃	—	4	4	no	—
260	Q₁₆×C₈₃	—	4	4	no	—
261	SD₁₆×C₈₃	—	4	4	no	—
262	SD₁₆×C₈₃	—	4	4	no	—
263	SD₁₆×C₈₃	—	4	2	no	—
264	D₈×C₈₃	—	4	2	no	—
265	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
266	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
267	C₂×C₈×C₈₃	C₂⁴	1	4	yes	—
268	C₄⋊C₄×C₈₃	—	2	2	no	—
269	C₄⋊C₄×C₈₃	—	2	2	no	—
270	C₄⋊C₄×C₈₃	—	2	4	no	—
271	C₄⋊C₄×C₈₃	—	2	4	no	—
272	C₄⋊C₄×C₈₃	—	2	2	no	—
273	C₄⋊C₄×C₈₃	—	2	2	no	—
274	C₄⋊C₄×C₈₃	—	2	1	no	—
275	C₄⋊C₄×C₈₃	—	2	2	no	—
276	C₄⋊C₄×C₈₃	—	2	1	no	—
277	C₄⋊C₄×C₈₃	—	2	1	no	—
278	C₄⋊C₄×C₈₃	—	2	2	no	—
279	C₄⋊C₄×C₈₃	—	2	2	no	—
280	C₄⋊C₄×C₈₃	—	2	1	no	—
281	C₄⋊C₄×C₈₃	—	2	2	no	—
282	C₄⋊C₄×C₈₃	—	2	1	no	—
283	C₄⋊C₄×C₈₃	—	2	2	no	—
284	C₄⋊C₄×C₈₃	—	2	1	no	—
285	C₄⋊C₄×C₈₃	—	2	2	no	—
286	C₄⋊C₄×C₈₃	—	2	1	no	—
287	C₄⋊C₄×C₈₃	—	2	2	no	—
288	C₄⋊C₄×C₈₃	—	2	2	no	—
289	C₄⋊C₄×C₈₃	—	2	2	no	—
290	C₄⋊C₄×C₈₃	—	2	2	no	—
291	C₄⋊C₄×C₈₃	—	2	1	no	—
292	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
293	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
294	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
295	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
296	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
297	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
298	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
299	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
300	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
301	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
302	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
303	C₂²⋊C₄×C₈₃	—	2	1	no	—
304	C₂²⋊C₄×C₈₃	—	2	2	no	—
305	C₂²⋊C₄×C₈₃	—	2	4	no	—
306	C₂²⋊C₄×C₈₃	—	2	4	no	—
307	C₂²⋊C₄×C₈₃	—	2	2	no	—
308	C₂²⋊C₄×C₈₃	—	2	2	no	—
309	C₂²⋊C₄×C₈₃	—	2	4	no	—
310	C₂²⋊C₄×C₈₃	—	2	4	no	—
311	C₂²⋊C₄×C₈₃	—	2	1	no	—
312	C₂²⋊C₄×C₈₃	—	2	2	no	—
313	C₂²⋊C₄×C₈₃	—	2	1	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	C₄²×C₈₃	—	2	4	no	—
319	C₄²×C₈₃	—	2	4	no	—
320	C₄²×C₈₃	—	2	2	no	—
321	C₄²×C₈₃	—	2	2	no	—
322	C₄²×C₈₃	—	2	2	no	—
323	C₄²×C₈₃	—	2	2	no	—
324	C₄²×C₈₃	—	2	1	no	—
325	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
326	C₄²×C₈₃	C₂×D₄	1	2	yes	—
327	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
328	C₄²×C₈₃	C₂×D₄	1	2	yes	—
329	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
330	C₄²×C₈₃	C₂⁴	1	2	yes	—
331	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
332	C₄²×C₈₃	C₂⁴	1	2	yes	—
333	C₂³×C₈₃	—	2	1	no	—
334	C₂³×C₈₃	—	2	2	no	—
335	C₂³×C₈₃	—	4	2	no	—
336	C₂³×C₈₃	—	4	2	no	—
337	C₂³×C₈₃	—	4	2	no	—
338	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
339	Q₈×C₈₃	—	2	2	no	—
340	Q₈×C₈₃	—	2	2	no	—
341	Q₈×C₈₃	—	2	4	no	—
342	Q₈×C₈₃	—	2	2	no	—
343	Q₈×C₈₃	—	2	4	no	—
344	Q₈×C₈₃	—	2	4	no	—
345	Q₈×C₈₃	—	4	2	no	—
346	Q₈×C₈₃	—	4	4	no	—
347	Q₈×C₈₃	—	4	4	no	—
348	Q₈×C₈₃	—	4	2	no	—
349	D₄×C₈₃	—	2	2	no	—
350	D₄×C₈₃	—	2	2	no	—
351	D₄×C₈₃	—	2	2	no	—
352	D₄×C₈₃	—	4	2	no	—
353	D₄×C₈₃	—	4	2	no	—
354	C₂×C₄×C₈₃	—	2	4	no	—
355	C₂×C₄×C₈₃	—	2	2	no	—
356	C₂×C₄×C₈₃	—	2	2	no	—
357	C₂×C₄×C₈₃	—	2	2	no	—
358	C₂×C₄×C₈₃	—	2	2	no	—
359	C₂×C₄×C₈₃	—	2	1	no	—
360	C₂×C₄×C₈₃	—	2	2	no	—
361	C₂×C₄×C₈₃	—	2	1	no	—
362	C₂×C₄×C₈₃	—	2	4	no	—
363	C₂×C₄×C₈₃	—	2	2	no	—
364	C₂×C₄×C₈₃	—	2	1	no	—
365	C₂×C₄×C₈₃	—	4	2	no	—
366	C₂×C₄×C₈₃	—	4	4	no	—
367	C₂×C₄×C₈₃	—	4	4	no	—
368	C₂×C₄×C₈₃	—	4	2	no	—
369	C₂×C₄×C₈₃	—	4	4	no	—
370	C₂×C₄×C₈₃	—	4	4	no	—
371	C₂×C₄×C₈₃	—	4	2	no	—
372	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
373	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
374	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
376	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
379	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
382	C₈×C₈₃	—	2	2	no	—
383	C₈×C₈₃	—	2	4	no	—
384	C₈×C₈₃	—	2	2	no	—
385	C₂²×C₈₃	—	2	1	no	—
386	C₂²×C₈₃	—	2	1	no	—
387	C₂²×C₈₃	—	4	2	no	—
388	C₂²×C₈₃	—	4	1	no	—
389	C₂²×C₈₃	—	4	1	no	—
390	C₂²×C₈₃	—	4	2	no	—
391	C₂²×C₈₃	—	4	1	no	—
392	C₂²×C₈₃	—	4	2	no	—
393	C₂²×C₈₃	—	8	4	no	—
394	C₂²×C₈₃	#578	1	2	yes	—
395	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
396	C₄×C₈₃	—	2	1	no	—
397	C₄×C₈₃	—	2	1	no	—
398	C₄×C₈₃	—	2	2	no	—
399	C₄×C₈₃	—	2	2	no	—
400	C₄×C₈₃	—	2	2	no	—
401	C₄×C₈₃	—	2	2	no	—
402	C₄×C₈₃	—	2	1	no	—
403	C₄×C₈₃	—	2	1	no	—
404	C₄×C₈₃	—	4	4	no	—
405	C₄×C₈₃	—	4	1	no	—
406	C₄×C₈₃	—	4	2	no	—
407	C₄×C₈₃	—	4	2	no	—
408	C₄×C₈₃	—	4	2	no	—
409	C₄×C₈₃	—	4	1	no	—
410	C₄×C₈₃	—	4	1	no	—
411	C₄×C₈₃	#575	1	2	yes	—
412	C₄×C₈₃	#585	1	2	yes	—
413	#61905	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
414	C₂×C₈₃	—	2	2	no	—
415	C₂×C₈₃	—	8	1	no	—
416	C₂×C₈₃	—	8	2	no	—
417	C₂×C₈₃	#3487	1	1	yes	characteristic
418	C₂×C₈₃	C₂×#575	1	1	yes	characteristic
419	C₂×C₈₃	C₂×#578	1	1	yes	characteristic
420	#3523	C₂×C₈₃	1	1	yes	characteristic, complemented
421	C₂×#556	C₂×C₈₃	1	1	yes	characteristic, complemented
422	#3402	C₂×C₈₃	1	4	yes	complemented
423	#3398	C₂×C₈₃	1	2	yes	complemented
424	#3393	C₂×C₈₃	1	2	yes	complemented
425	#3377	C₂×C₈₃	1	4	yes	complemented
426	#3367	C₂×C₈₃	1	2	yes	complemented
427	#3364	C₂×C₈₃	1	2	yes	complemented
428	#3218	C₂×C₈₃	1	1	yes	characteristic, complemented
429	#3215	C₂×C₈₃	1	2	yes	complemented
430	#3211	C₂×C₈₃	1	2	yes	—
431	#3209	C₂×C₈₃	1	1	yes	characteristic, complemented
432	#3117	C₂×C₈₃	1	2	yes	complemented
433	#3110	C₂×C₈₃	1	1	yes	characteristic, complemented
434	#3105	C₂×C₈₃	1	1	yes	characteristic
435	#3104	C₂×C₈₃	1	2	yes	complemented
436	#2984	C₂×C₈₃	1	1	yes	characteristic, complemented
437	C₈₃	#61905	1	1	yes	characteristic, direct product factor, Sylow
438	#557	C₂²×C₈₃	1	1	yes	characteristic, complemented
439	#557	C₂²×C₈₃	1	1	yes	characteristic, complemented
440	#557	C₂²×C₈₃	1	2	yes	complemented
441	#556	—	2	1	no	—
442	#556	—	2	1	no	—
443	#556	—	2	2	no	—
444	#556	C₂²×C₈₃	1	2	yes	—
445	#556	C₂²×C₈₃	1	2	yes	—
446	#556	C₂²×C₈₃	1	4	yes	—
447	#556	C₂²×C₈₃	1	1	yes	characteristic, complemented
448	#556	C₂²×C₈₃	1	2	yes	complemented
449	#552	—	2	1	no	—
450	#552	—	2	2	no	—
451	D₄×Q₈	—	2	1	no	—
452	D₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
453	#541	—	2	1	no	—
454	#541	—	2	2	no	—
455	#533	C₂²×C₈₃	1	2	yes	—
456	#533	C₂²×C₈₃	1	1	yes	characteristic
457	C₂×C₄⋊Q₈	C₂²×C₈₃	1	1	yes	characteristic
458	#529	C₂²×C₈₃	1	1	yes	characteristic
459	#529	C₂²×C₈₃	1	2	yes	—
460	C₂×#126	—	2	2	no	—
461	C₂×#124	C₂²×C₈₃	1	2	yes	—
462	C₂×C₂²⋊Q₈	—	2	1	no	—
463	#519	—	2	1	no	—
464	C₂×C₄×Q₈	C₂²×C₈₃	1	2	yes	—
465	C₂×C₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic
466	C₂×C₄×D₄	C₂²×C₈₃	1	1	yes	characteristic
467	C₂×#117	—	2	1	no	—
468	#497	C₂²×C₈₃	1	4	yes	—
469	#497	C₂²×C₈₃	1	2	yes	complemented
470	#495	C₂²×C₈₃	1	4	yes	—
471	#494	C₂²×C₈₃	1	2	yes	complemented
472	#491	C₂²×C₈₃	1	2	yes	complemented
473	#489	C₂²×C₈₃	1	4	yes	—
474	#488	C₂²×C₈₃	1	4	yes	—
475	#487	C₂²×C₈₃	1	2	yes	complemented
476	#484	C₂²×C₈₃	1	1	yes	characteristic
477	#484	C₂²×C₈₃	1	2	yes	—
478	#481	C₂²×C₈₃	1	1	yes	characteristic
479	#479	C₂²×C₈₃	1	4	yes	complemented
480	#478	C₂²×C₈₃	1	2	yes	—
481	#477	C₂²×C₈₃	1	4	yes	complemented
482	#474	C₂²×C₈₃	1	2	yes	—
483	#464	C₂²×C₈₃	1	4	yes	—
484	#464	C₂²×C₈₃	1	4	yes	—
485	#464	C₂²×C₈₃	1	4	yes	—
486	#464	C₂²×C₈₃	1	4	yes	complemented
487	#463	C₂²×C₈₃	1	2	yes	—
488	#463	C₂²×C₈₃	1	4	yes	—
489	#462	C₂²×C₈₃	1	4	yes	complemented
490	#462	C₂²×C₈₃	1	2	yes	complemented
491	#462	C₂²×C₈₃	1	4	yes	complemented
492	#461	C₂²×C₈₃	1	2	yes	—
493	#461	C₂²×C₈₃	1	2	yes	complemented
494	#451	C₂²×C₈₃	1	2	yes	—
495	#451	C₂²×C₈₃	1	2	yes	—
496	#451	C₂²×C₈₃	1	2	yes	—
497	#450	C₂²×C₈₃	1	1	yes	characteristic
498	#450	C₂²×C₈₃	1	2	yes	—
499	#448	C₂²×C₈₃	1	2	yes	—
500	#447	C₂²×C₈₃	1	1	yes	characteristic
501	#446	C₂²×C₈₃	1	2	yes	complemented
502	#446	C₂²×C₈₃	1	4	yes	complemented
503	C₈×Q₈	C₂²×C₈₃	1	2	yes	complemented
504	#441	C₂²×C₈₃	1	4	yes	complemented
505	#440	C₂²×C₈₃	1	4	yes	—
506	#440	C₂²×C₈₃	1	4	yes	complemented
507	C₄×Q₁₆	C₂²×C₈₃	1	4	yes	complemented
508	C₄×Q₁₆	C₂²×C₈₃	1	4	yes	complemented
509	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	—
510	C₄×D₈	C₂²×C₈₃	1	2	yes	—
511	#432	C₂²×C₈₃	1	1	yes	characteristic
512	#432	C₂²×C₈₃	1	2	yes	—
513	#431	C₂²×C₈₃	1	2	yes	—
514	#431	C₂²×C₈₃	1	1	yes	characteristic
515	C₂²×Q₈	—	2	1	no	—
516	C₂²×Q₈	D₄×C₈₃	1	1	yes	characteristic
517	C₂²×Q₈	C₂³×C₈₃	1	2	yes	—
518	C₂²×D₄	C₂³×C₈₃	1	1	yes	characteristic
519	C₂³×C₄	—	2	1	no	—
520	C₂×Q₁₆	C₂³×C₈₃	1	4	yes	—
521	C₂×Q₁₆	C₂³×C₈₃	1	4	yes	—
522	C₂×Q₁₆	C₂³×C₈₃	1	4	yes	—
523	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
524	C₂×SD₁₆	C₂³×C₈₃	1	4	yes	—
525	C₂×SD₁₆	C₂³×C₈₃	1	4	yes	—
526	C₂×D₈	C₂³×C₈₃	1	2	yes	—
527	C₄⋊Q₈	—	2	1	no	—
528	C₄⋊Q₈	—	2	2	no	—
529	C₄⋊Q₈	—	2	1	no	—
530	C₄⋊Q₈	—	2	1	no	—
531	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
532	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
533	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
534	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
535	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
536	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
537	#126	—	2	4	no	—
538	#126	—	2	4	no	—
539	#126	—	2	4	no	—
540	#126	—	2	4	no	—
541	#126	—	2	2	no	—
542	#126	—	2	2	no	—
543	#126	—	2	2	no	—
544	#126	—	2	1	no	—
545	#126	—	2	2	no	—
546	#125	—	2	2	no	—
547	#125	—	2	2	no	—
548	#125	—	2	2	no	—
549	#125	—	2	1	no	—
550	#125	—	2	2	no	—
551	#125	—	2	1	no	—
552	#125	—	2	2	no	—
553	#125	C₂³×C₈₃	1	1	yes	characteristic
554	#125	C₂³×C₈₃	1	2	yes	—
555	#124	—	2	2	no	—
556	#124	—	2	2	no	—
557	#124	C₂³×C₈₃	1	4	yes	—
558	#124	C₂³×C₈₃	1	4	yes	—
559	#124	C₂³×C₈₃	1	1	yes	characteristic
560	#124	C₂³×C₈₃	1	2	yes	—
561	#123	—	2	2	no	—
562	#123	—	2	1	no	—
563	C₂²⋊Q₈	—	2	2	no	—
564	C₂²⋊Q₈	—	2	2	no	—
565	C₂²⋊Q₈	—	2	4	no	—
566	C₂²⋊Q₈	—	2	1	no	—
567	C₂²⋊Q₈	—	2	2	no	—
568	C₂²⋊Q₈	—	2	1	no	—
569	C₂²⋊Q₈	—	2	2	no	—
570	C₂²⋊Q₈	—	2	1	no	—
571	C₂²⋊Q₈	—	2	2	no	—
572	C₂²⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
573	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
574	#121	C₂³×C₈₃	1	1	yes	characteristic
575	C₄×Q₈	—	2	1	no	—
576	C₄×Q₈	—	2	1	no	—
577	C₄×Q₈	—	2	2	no	—
578	C₄×Q₈	—	2	2	no	—
579	C₄×Q₈	—	2	2	no	—
580	C₄×Q₈	—	2	1	no	—
581	C₄×Q₈	—	2	2	no	—
582	C₄×Q₈	D₄×C₈₃	1	1	yes	characteristic
583	C₄×Q₈	D₄×C₈₃	1	1	yes	characteristic
584	C₄×Q₈	D₄×C₈₃	1	2	yes	—
585	C₄×Q₈	C₂³×C₈₃	1	4	yes	—
586	C₄×Q₈	C₂³×C₈₃	1	4	yes	—
587	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
588	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
589	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
590	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
591	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
592	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
593	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
594	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
595	C₄×D₄	—	2	1	no	—
596	C₄×D₄	—	2	2	no	—
597	C₄×D₄	—	2	1	no	—
598	C₄×D₄	—	2	1	no	—
599	C₄×D₄	C₂³×C₈₃	1	2	yes	—
600	C₄×D₄	C₂³×C₈₃	1	2	yes	—
601	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
602	C₄×D₄	C₂³×C₈₃	1	2	yes	—
603	#117	—	2	2	no	—
604	#117	—	2	1	no	—
605	#117	—	2	2	no	—
606	#117	—	2	2	no	—
607	#117	—	2	4	no	—
608	#117	—	2	1	no	—
609	#117	—	2	2	no	—
610	#117	—	2	1	no	—
611	#117	—	2	2	no	—
612	C₂×C₄⋊C₄	—	2	1	no	—
613	C₂×C₄⋊C₄	—	2	2	no	—
614	C₂×C₄⋊C₄	—	2	1	no	—
615	C₂×C₄⋊C₄	D₄×C₈₃	1	1	yes	characteristic
616	C₂×C₄⋊C₄	D₄×C₈₃	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
618	C₂×C₂²⋊C₄	—	2	2	no	—
619	C₂×C₂²⋊C₄	—	2	1	no	—
620	C₂×C₂²⋊C₄	—	2	2	no	—
621	C₂×C₄²	—	2	2	no	—
622	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
623	C₂×C₄²	C₂³×C₈₃	1	2	yes	—
624	#107	C₂³×C₈₃	1	2	yes	—
625	#107	C₂³×C₈₃	1	4	yes	—
626	#106	C₂³×C₈₃	1	2	yes	—
627	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
628	C₄⋊C₈	C₂³×C₈₃	1	4	yes	—
629	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
630	C₄⋊C₈	C₂³×C₈₃	1	4	yes	—
631	#103	C₂³×C₈₃	1	2	yes	—
632	#103	C₂³×C₈₃	1	4	yes	—
633	#103	C₂³×C₈₃	1	4	yes	—
634	#103	C₂³×C₈₃	1	4	yes	—
635	#103	C₂³×C₈₃	1	4	yes	—
636	#103	C₂³×C₈₃	1	4	yes	—
637	#102	C₂³×C₈₃	1	2	yes	—
638	#102	C₂³×C₈₃	1	2	yes	—
639	#102	C₂³×C₈₃	1	2	yes	—
640	#102	C₂³×C₈₃	1	4	yes	—
641	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
642	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
643	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
644	#97	C₂³×C₈₃	1	2	yes	—
645	#97	C₂³×C₈₃	1	4	yes	—
646	C₄×C₈	C₂³×C₈₃	1	2	yes	—
647	C₄×C₈	C₂³×C₈₃	1	4	yes	—
648	C₂⁴	—	2	1	no	—
649	C₂×Q₈	—	2	2	no	—
650	C₂×Q₈	—	2	1	no	—
651	C₂×Q₈	—	2	2	no	—
652	C₂×Q₈	—	4	2	no	—
653	C₂×Q₈	—	4	4	no	—
654	C₂×Q₈	—	4	4	no	—
655	C₂×Q₈	C₂×D₄×C₈₃	1	1	yes	characteristic
656	C₂×Q₈	C₂×D₄×C₈₃	1	1	yes	characteristic
657	C₂×Q₈	C₂×D₄×C₈₃	1	2	yes	—
658	C₂×Q₈	C₂⁴×C₈₃	1	4	yes	—
659	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
660	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
661	C₂×D₄	—	2	1	no	—
662	C₂×D₄	—	2	1	no	—
663	C₂×D₄	—	4	2	no	—
664	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
665	C₂×D₄	C₂⁴×C₈₃	1	1	yes	characteristic
666	C₂²×C₄	—	2	1	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	1	no	—
672	C₂²×C₄	—	4	4	no	—
673	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
674	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
675	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
676	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
678	Q₁₆	—	4	4	no	—
679	Q₁₆	—	4	4	no	—
680	Q₁₆	—	4	4	no	—
681	SD₁₆	—	4	4	no	—
682	SD₁₆	—	4	4	no	—
683	SD₁₆	—	4	2	no	—
684	D₈	—	4	2	no	—
685	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
686	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
687	C₂×C₈	C₂⁴×C₈₃	1	4	yes	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	4	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	1	no	—
697	C₄⋊C₄	—	2	1	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
713	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
714	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
715	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
716	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
717	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
718	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
719	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
720	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
721	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
722	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
723	C₂²⋊C₄	—	2	1	no	—
724	C₂²⋊C₄	—	2	2	no	—
725	C₂²⋊C₄	—	2	4	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	2	no	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	2	1	no	—
732	C₂²⋊C₄	—	2	2	no	—
733	C₂²⋊C₄	—	2	1	no	—
734	C₂²⋊C₄	—	2	2	no	—
735	C₂²⋊C₄	—	2	1	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	—	2	1	no	—
738	C₄²	—	2	4	no	—
739	C₄²	—	2	4	no	—
740	C₄²	—	2	2	no	—
741	C₄²	—	2	2	no	—
742	C₄²	—	2	2	no	—
743	C₄²	—	2	2	no	—
744	C₄²	—	2	1	no	—
745	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
746	C₄²	C₂×D₄×C₈₃	1	2	yes	—
747	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
748	C₄²	C₂×D₄×C₈₃	1	2	yes	—
749	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
750	C₄²	C₂⁴×C₈₃	1	2	yes	—
751	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
752	C₄²	C₂⁴×C₈₃	1	2	yes	—
753	C₂³	—	2	1	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	4	2	no	—
756	C₂³	—	4	2	no	—
757	C₂³	—	4	2	no	—
758	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
759	Q₈	—	2	2	no	—
760	Q₈	—	2	2	no	—
761	Q₈	—	2	4	no	—
762	Q₈	—	2	2	no	—
763	Q₈	—	2	4	no	—
764	Q₈	—	2	4	no	—
765	Q₈	—	4	2	no	—
766	Q₈	—	4	4	no	—
767	Q₈	—	4	4	no	—
768	Q₈	—	4	2	no	—
769	D₄	—	2	2	no	—
770	D₄	—	2	2	no	—
771	D₄	—	2	2	no	—
772	D₄	—	4	2	no	—
773	D₄	—	4	2	no	—
774	C₂×C₄	—	2	4	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	4	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	4	2	no	—
786	C₂×C₄	—	4	4	no	—
787	C₂×C₄	—	4	4	no	—
788	C₂×C₄	—	4	2	no	—
789	C₂×C₄	—	4	4	no	—
790	C₂×C₄	—	4	4	no	—
791	C₂×C₄	—	4	2	no	—
792	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
793	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
794	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
795	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
796	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
797	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
798	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
799	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
800	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
801	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
802	C₈	—	2	2	no	—
803	C₈	—	2	4	no	—
804	C₈	—	2	2	no	—
805	C₂²	—	2	1	no	—
806	C₂²	—	2	1	no	—
807	C₂²	—	4	1	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	1	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	1	no	—
813	C₂²	—	8	4	no	—
814	C₂²	#578×C₈₃	1	2	yes	—
815	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
816	C₄	—	2	1	no	—
817	C₄	—	2	2	no	—
818	C₄	—	2	2	no	—
819	C₄	—	2	2	no	—
820	C₄	—	2	2	no	—
821	C₄	—	2	1	no	—
822	C₄	—	2	1	no	—
823	C₄	—	2	1	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	2	no	—
826	C₄	—	4	1	no	—
827	C₄	—	4	1	no	—
828	C₄	—	4	4	no	—
829	C₄	—	4	1	no	—
830	C₄	—	4	2	no	—
831	C₄	#575×C₈₃	1	2	yes	—
832	C₄	#585×C₈₃	1	2	yes	—
833	C₂	—	2	2	no	—
834	C₂	—	8	2	no	—
835	C₂	—	8	1	no	—
836	C₂	C₈₃×#3487	1	1	yes	characteristic
837	C₂	C₂×#575×C₈₃	1	1	yes	characteristic
838	C₂	C₂×#578×C₈₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₃
prime radical	#447×C₈₃	C₂²
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×#3523	C₂	semidirect
2. C₂×#556×C₈₃	C₂	semidirect
3. C₈₃×#3402	C₂	semidirect
4. C₈₃×#3398	C₂	semidirect
5. C₈₃×#3393	C₂	semidirect
6. C₈₃×#3377	C₂	semidirect
7. C₈₃×#3367	C₂	semidirect
8. C₈₃×#3364	C₂	semidirect
9. C₈₃×#3218	C₂	semidirect
10. C₈₃×#3215	C₂	semidirect
12. C₈₃×#3209	C₂	semidirect
13. C₈₃×#3117	C₂	semidirect
14. C₈₃×#3110	C₂	semidirect
16. C₈₃×#3104	C₂	semidirect
17. C₈₃×#2984	C₂	semidirect
18. #557×C₈₃	C₂²	semidirect
19. #557×C₈₃	C₂²	semidirect
20. #557×C₈₃	C₂²	semidirect
27. #556×C₈₃	C₂²	semidirect
28. #556×C₈₃	C₂²	semidirect
32. D₄×Q₈×C₈₃	C₂²	semidirect
49. #497×C₈₃	C₂²	semidirect
51. #494×C₈₃	C₂²	semidirect
52. #491×C₈₃	C₂²	semidirect
55. #487×C₈₃	C₂²	semidirect
59. #479×C₈₃	C₂²	semidirect
61. #477×C₈₃	C₂²	semidirect
66. #464×C₈₃	C₂²	semidirect
69. #462×C₈₃	C₂²	semidirect
70. #462×C₈₃	C₂²	semidirect
71. #462×C₈₃	C₂²	semidirect
73. #461×C₈₃	C₂²	semidirect
81. #446×C₈₃	C₂²	semidirect
82. #446×C₈₃	C₂²	semidirect
83. C₈×Q₈×C₈₃	C₂²	semidirect
84. #441×C₈₃	C₂²	semidirect
86. #440×C₈₃	C₂²	semidirect
87. C₄×Q₁₆×C₈₃	C₂²	semidirect
88. C₄×Q₁₆×C₈₃	C₂²	semidirect
413. #61905	C₈₃	direct (N × H)
420. #3523	C₂×C₈₃	semidirect
421. C₂×#556	C₂×C₈₃	semidirect
422. #3402	C₂×C₈₃	semidirect
423. #3398	C₂×C₈₃	semidirect
424. #3393	C₂×C₈₃	semidirect
425. #3377	C₂×C₈₃	semidirect
426. #3367	C₂×C₈₃	semidirect
427. #3364	C₂×C₈₃	semidirect
428. #3218	C₂×C₈₃	semidirect
429. #3215	C₂×C₈₃	semidirect
431. #3209	C₂×C₈₃	semidirect
432. #3117	C₂×C₈₃	semidirect
433. #3110	C₂×C₈₃	semidirect
435. #3104	C₂×C₈₃	semidirect
436. #2984	C₂×C₈₃	semidirect
437. C₈₃	#61905	direct (N × H)
438. #557	C₂²×C₈₃	semidirect
439. #557	C₂²×C₈₃	semidirect
440. #557	C₂²×C₈₃	semidirect
447. #556	C₂²×C₈₃	semidirect
448. #556	C₂²×C₈₃	semidirect
452. D₄×Q₈	C₂²×C₈₃	semidirect
469. #497	C₂²×C₈₃	semidirect
471. #494	C₂²×C₈₃	semidirect
472. #491	C₂²×C₈₃	semidirect
475. #487	C₂²×C₈₃	semidirect
479. #479	C₂²×C₈₃	semidirect
481. #477	C₂²×C₈₃	semidirect
486. #464	C₂²×C₈₃	semidirect
489. #462	C₂²×C₈₃	semidirect
490. #462	C₂²×C₈₃	semidirect
491. #462	C₂²×C₈₃	semidirect
493. #461	C₂²×C₈₃	semidirect
501. #446	C₂²×C₈₃	semidirect
502. #446	C₂²×C₈₃	semidirect
503. C₈×Q₈	C₂²×C₈₃	semidirect
504. #441	C₂²×C₈₃	semidirect
506. #440	C₂²×C₈₃	semidirect
507. C₄×Q₁₆	C₂²×C₈₃	semidirect
508. C₄×Q₁₆	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×#3523	2
C₂×#556×C₈₃	2
C₈₃×#3402	2
C₈₃×#3398	2
C₈₃×#3393	2
C₈₃×#3377	2
C₈₃×#3367	2
C₈₃×#3364	2
C₈₃×#3218	2
C₈₃×#3215	2
C₈₃×#3211	2
C₈₃×#3209	2
C₈₃×#3117	2
C₈₃×#3110	2
C₈₃×#3105	2
C₈₃×#3104	2
C₈₃×#2984	2
#61905	83

Subgroups — C83×#61905 #35289729

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#61905 #35289729