Subgroups — C₈₃×#60892 #35288716

Order 21248.

1736 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₃×#3460	C₂	1	1	yes	maximal, characteristic
3	C₈₃×#3244	C₂	1	4	yes	maximal, complemented
4	C₈₃×#3241	C₂	1	4	yes	maximal, complemented
5	C₈₃×#3238	C₂	1	2	yes	maximal, complemented
6	C₈₃×#3235	C₂	1	2	yes	maximal, complemented
7	C₈₃×#3233	C₂	1	2	yes	maximal, complemented
8	C₈₃×#3227	C₂	1	2	yes	maximal, complemented
9	C₈₃×#3163	C₂	1	2	yes	maximal, complemented
10	C₈₃×#3136	C₂	1	2	yes	maximal, complemented
11	C₈₃×#3099	C₂	1	2	yes	maximal, complemented
12	C₈₃×#3096	C₂	1	2	yes	maximal, complemented
13	C₈₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#476×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
18	Q₈²×C₈₃	—	2	1	no	—
19	#557×C₈₃	—	2	1	no	—
20	#554×C₈₃	—	2	2	no	—
21	#554×C₈₃	—	2	1	no	—
22	D₄×Q₈×C₈₃	—	2	2	no	—
23	D₄×Q₈×C₈₃	—	2	1	no	—
24	#544×C₈₃	C₂²	1	2	yes	—
25	#544×C₈₃	C₂²	1	1	yes	characteristic
26	#544×C₈₃	C₂²	1	4	yes	complemented
27	#542×C₈₃	—	2	1	no	—
28	#542×C₈₃	C₂²	1	2	yes	—
29	#540×C₈₃	—	2	1	no	—
30	#540×C₈₃	C₂²	1	2	yes	—
31	#538×C₈₃	—	2	2	no	—
32	#537×C₈₃	C₂²	1	1	yes	characteristic
33	#535×C₈₃	C₂²	1	1	yes	characteristic
34	#535×C₈₃	C₂²	1	1	yes	characteristic
35	#533×C₈₃	C₂²	1	1	yes	characteristic
36	#533×C₈₃	C₂²	1	2	yes	complemented
37	#532×C₈₃	—	2	1	no	—
38	#532×C₈₃	C₂²	1	2	yes	—
39	C₂×C₄⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊Q₈×C₈₃	C₂²	1	2	yes	complemented
41	#529×C₈₃	—	2	1	no	—
42	#529×C₈₃	C₂²	1	2	yes	—
43	#525×C₈₃	—	2	2	no	—
44	#520×C₈₃	C₂²	1	2	yes	—
45	C₄×#41×C₈₃	C₂²	1	1	yes	characteristic
46	C₄×#41×C₈₃	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₈₃	C₂²	1	1	yes	characteristic
48	#501×C₈₃	C₂²	1	4	yes	complemented
49	#501×C₈₃	C₂²	1	4	yes	complemented
50	#499×C₈₃	C₂²	1	4	yes	complemented
51	#498×C₈₃	C₂²	1	4	yes	complemented
52	#490×C₈₃	C₂²	1	4	yes	—
53	#489×C₈₃	C₂²	1	4	yes	—
54	#488×C₈₃	C₂²	1	4	yes	—
55	#486×C₈₃	C₂²	1	4	yes	—
56	#485×C₈₃	C₂²	1	4	yes	complemented
57	#483×C₈₃	C₂²	1	4	yes	complemented
58	#482×C₈₃	C₂²	1	4	yes	—
59	#482×C₈₃	C₂²	1	4	yes	—
60	#482×C₈₃	C₂²	1	4	yes	complemented
61	#481×C₈₃	C₂²	1	4	yes	—
62	#481×C₈₃	C₂²	1	4	yes	complemented
63	#480×C₈₃	C₂²	1	4	yes	—
64	#479×C₈₃	C₂²	1	2	yes	complemented
65	#478×C₈₃	C₂²	1	4	yes	—
66	#478×C₈₃	C₂²	1	2	yes	complemented
67	#477×C₈₃	C₂²	1	1	yes	characteristic, complemented
68	#477×C₈₃	C₂²	1	2	yes	complemented
69	#476×C₈₃	C₂²	1	2	yes	—
70	#476×C₈₃	C₂²	1	2	yes	—
71	#476×C₈₃	C₂²	1	4	yes	—
72	#476×C₈₃	C₂²	1	2	yes	—
73	#476×C₈₃	C₂²	1	1	yes	characteristic, complemented
74	#476×C₈₃	C₂²	1	2	yes	complemented
75	#475×C₈₃	C₂²	1	1	yes	characteristic, complemented
76	#475×C₈₃	C₂²	1	2	yes	complemented
77	#474×C₈₃	C₂²	1	2	yes	—
78	#474×C₈₃	C₂²	1	1	yes	characteristic, complemented
79	#474×C₈₃	C₂²	1	2	yes	complemented
80	#433×C₈₃	C₂²	1	4	yes	complemented
81	#432×C₈₃	C₂²	1	2	yes	complemented
82	#431×C₈₃	C₂²	1	2	yes	complemented
83	#428×C₈₃	C₂²	1	2	yes	—
84	#428×C₈₃	C₂²	1	2	yes	—
85	#427×C₈₃	C₂²	1	2	yes	—
86	C₂×#106×C₈₃	C₂²	1	2	yes	—
87	#423×C₈₃	C₂²	1	1	yes	characteristic
88	C₂×C₄⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
89	#418×C₈₃	C₂²	1	2	yes	—
90	#417×C₈₃	C₂²	1	2	yes	—
91	#416×C₈₃	C₂²	1	2	yes	—
92	C₂×#102×C₈₃	C₂²	1	2	yes	—
93	#408×C₈₃	C₂²	1	2	yes	—
94	#405×C₈₃	C₂²	1	2	yes	—
95	C₂×#41×C₈₃	—	2	2	no	—
96	C₂×#41×C₈₃	C₂³	1	1	yes	characteristic
97	C₂×#41×C₈₃	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₈₃	—	2	1	no	—
99	C₂²×Q₈×C₈₃	—	2	2	no	—
100	C₂²×D₄×C₈₃	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₈₃	—	2	1	no	—
102	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
103	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
104	C₄⋊Q₈×C₈₃	—	2	1	no	—
105	C₄⋊Q₈×C₈₃	—	2	2	no	—
106	C₄⋊Q₈×C₈₃	—	2	4	no	—
107	C₄⋊Q₈×C₈₃	—	2	1	no	—
108	C₄⋊Q₈×C₈₃	—	2	1	no	—
109	C₄⋊Q₈×C₈₃	—	2	2	no	—
110	C₄⋊Q₈×C₈₃	—	2	2	no	—
111	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
112	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
113	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
114	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
115	C₄⋊Q₈×C₈₃	C₂³	1	4	yes	—
116	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
117	#127×C₈₃	—	2	1	no	—
118	#127×C₈₃	C₂³	1	2	yes	—
119	#126×C₈₃	—	2	2	no	—
120	#126×C₈₃	—	2	2	no	—
121	#125×C₈₃	—	2	1	no	—
122	#125×C₈₃	—	2	2	no	—
123	#125×C₈₃	—	2	4	no	—
124	#125×C₈₃	C₂³	1	2	yes	—
125	#125×C₈₃	C₂³	1	4	yes	—
126	#125×C₈₃	C₂³	1	2	yes	—
127	#124×C₈₃	—	2	1	no	—
128	#124×C₈₃	—	2	2	no	—
129	#124×C₈₃	—	2	2	no	—
130	#124×C₈₃	C₂³	1	2	yes	—
131	#123×C₈₃	—	2	2	no	—
132	#123×C₈₃	—	2	2	no	—
133	#123×C₈₃	—	2	2	no	—
134	#123×C₈₃	—	2	2	no	—
135	C₂²⋊Q₈×C₈₃	—	2	1	no	—
136	C₂²⋊Q₈×C₈₃	—	2	1	no	—
137	C₂²⋊Q₈×C₈₃	—	2	1	no	—
138	C₂²⋊Q₈×C₈₃	—	2	2	no	—
139	C₂²⋊Q₈×C₈₃	—	2	2	no	—
140	C₂²⋊Q₈×C₈₃	—	2	2	no	—
141	C₂²⋊Q₈×C₈₃	—	2	2	no	—
142	C₂²⋊Q₈×C₈₃	—	2	4	no	—
143	C₂²⋊Q₈×C₈₃	—	2	4	no	—
144	C₂²⋊Q₈×C₈₃	—	2	4	no	—
145	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
146	#121×C₈₃	—	2	2	no	—
147	#121×C₈₃	—	2	1	no	—
148	#121×C₈₃	—	2	2	no	—
149	#121×C₈₃	—	2	1	no	—
150	#121×C₈₃	—	2	1	no	—
151	#121×C₈₃	—	2	2	no	—
152	#121×C₈₃	—	2	2	no	—
153	#121×C₈₃	C₂³	1	2	yes	—
154	#121×C₈₃	C₂³	1	2	yes	—
155	#121×C₈₃	C₂³	1	2	yes	—
156	#120×C₈₃	—	2	2	no	—
157	#120×C₈₃	—	2	2	no	—
158	C₄×Q₈×C₈₃	—	2	2	no	—
159	C₄×Q₈×C₈₃	—	2	1	no	—
160	C₄×Q₈×C₈₃	—	2	1	no	—
161	C₄×Q₈×C₈₃	—	2	2	no	—
162	C₄×Q₈×C₈₃	—	2	2	no	—
163	C₄×Q₈×C₈₃	D₄	1	1	yes	characteristic
164	C₄×Q₈×C₈₃	D₄	1	1	yes	characteristic
165	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
167	C₄×D₄×C₈₃	—	2	4	no	—
168	C₄×D₄×C₈₃	—	2	2	no	—
169	C₄×D₄×C₈₃	—	2	1	no	—
170	C₄×D₄×C₈₃	—	2	1	no	—
171	C₄×D₄×C₈₃	—	2	2	no	—
172	C₄×D₄×C₈₃	—	2	1	no	—
173	C₄×D₄×C₈₃	—	2	1	no	—
174	C₄×D₄×C₈₃	—	2	2	no	—
175	C₄×D₄×C₈₃	D₄	1	2	yes	—
176	C₄×D₄×C₈₃	D₄	1	1	yes	characteristic
177	C₄×D₄×C₈₃	D₄	1	2	yes	—
178	C₄×D₄×C₈₃	D₄	1	1	yes	characteristic
179	C₄×D₄×C₈₃	C₂³	1	2	yes	—
180	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
181	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
182	C₄×D₄×C₈₃	C₂³	1	2	yes	—
183	#117×C₈₃	—	2	1	no	—
184	#117×C₈₃	—	2	2	no	—
185	#117×C₈₃	C₂³	1	4	yes	—
186	#117×C₈₃	C₂³	1	1	yes	characteristic
187	#117×C₈₃	C₂³	1	2	yes	—
188	#117×C₈₃	C₂³	1	1	yes	characteristic
189	#117×C₈₃	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
191	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
192	C₂×C₄⋊C₄×C₈₃	C₂³	1	4	yes	—
193	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
194	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
196	C₂×C₄²×C₈₃	—	2	1	no	—
197	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₈₃	C₂³	1	2	yes	—
199	#107×C₈₃	C₂³	1	4	yes	—
200	#107×C₈₃	C₂³	1	4	yes	—
201	#107×C₈₃	C₂³	1	2	yes	—
202	#107×C₈₃	C₂³	1	2	yes	—
203	#106×C₈₃	C₂³	1	4	yes	—
204	#106×C₈₃	C₂³	1	2	yes	—
205	#106×C₈₃	C₂³	1	4	yes	—
206	#106×C₈₃	C₂³	1	4	yes	—
207	#106×C₈₃	C₂³	1	4	yes	—
208	#106×C₈₃	C₂³	1	2	yes	—
209	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
210	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
211	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
212	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
213	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
214	#103×C₈₃	C₂³	1	4	yes	—
215	#103×C₈₃	C₂³	1	2	yes	—
216	#103×C₈₃	C₂³	1	2	yes	—
217	#102×C₈₃	C₂³	1	4	yes	—
218	#102×C₈₃	C₂³	1	4	yes	—
219	#102×C₈₃	C₂³	1	2	yes	—
220	#102×C₈₃	C₂³	1	4	yes	—
221	#102×C₈₃	C₂³	1	4	yes	—
222	#102×C₈₃	C₂³	1	4	yes	—
223	#102×C₈₃	C₂³	1	2	yes	—
224	C₂²⋊C₈×C₈₃	C₂³	1	4	yes	—
225	C₂²⋊C₈×C₈₃	C₂³	1	4	yes	—
226	#97×C₈₃	C₂³	1	4	yes	—
227	C₄×C₈×C₈₃	C₂³	1	4	yes	—
228	C₂⁴×C₈₃	—	2	1	no	—
229	#41×C₈₃	—	2	2	no	—
230	#41×C₈₃	—	2	2	no	—
231	#41×C₈₃	—	2	2	no	—
232	#41×C₈₃	—	2	2	no	—
233	#41×C₈₃	—	8	4	no	—
234	C₂×Q₈×C₈₃	—	2	1	no	—
235	C₂×Q₈×C₈₃	—	2	1	no	—
236	C₂×Q₈×C₈₃	—	2	2	no	—
237	C₂×Q₈×C₈₃	—	2	2	no	—
238	C₂×Q₈×C₈₃	—	2	2	no	—
239	C₂×Q₈×C₈₃	—	2	4	no	—
240	C₂×Q₈×C₈₃	—	8	2	no	—
241	C₂×Q₈×C₈₃	—	8	4	no	—
242	C₂×Q₈×C₈₃	C₂×D₄	1	1	yes	characteristic
243	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
244	C₂×D₄×C₈₃	—	2	1	no	—
245	C₂×D₄×C₈₃	—	2	2	no	—
246	C₂×D₄×C₈₃	—	2	2	no	—
247	C₂×D₄×C₈₃	—	2	2	no	—
248	C₂×D₄×C₈₃	—	2	1	no	—
249	C₂×D₄×C₈₃	—	2	2	no	—
250	C₂×D₄×C₈₃	—	2	2	no	—
251	C₂×D₄×C₈₃	—	2	2	no	—
252	C₂×D₄×C₈₃	—	2	2	no	—
253	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
254	C₂×D₄×C₈₃	C₂×D₄	1	1	yes	characteristic
255	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
256	C₂×D₄×C₈₃	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₈₃	—	2	1	no	—
258	C₂²×C₄×C₈₃	—	2	4	no	—
259	C₂²×C₄×C₈₃	—	2	2	no	—
260	C₂²×C₄×C₈₃	—	2	1	no	—
261	C₂²×C₄×C₈₃	—	2	1	no	—
262	C₂²×C₄×C₈₃	—	2	2	no	—
263	C₂²×C₄×C₈₃	—	2	1	no	—
264	C₂²×C₄×C₈₃	—	2	2	no	—
265	C₂²×C₄×C₈₃	—	8	2	no	—
266	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
268	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
270	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
272	M₁₆×C₈₃	—	2	4	no	—
273	C₂×C₈×C₈₃	—	2	4	no	—
274	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
275	C₂×C₈×C₈₃	C₂⁴	1	4	yes	—
276	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
277	C₄⋊C₄×C₈₃	—	2	2	no	—
278	C₄⋊C₄×C₈₃	—	2	1	no	—
279	C₄⋊C₄×C₈₃	—	2	2	no	—
280	C₄⋊C₄×C₈₃	—	2	4	no	—
281	C₄⋊C₄×C₈₃	—	2	1	no	—
282	C₄⋊C₄×C₈₃	—	2	4	no	—
283	C₄⋊C₄×C₈₃	—	2	2	no	—
284	C₄⋊C₄×C₈₃	—	2	1	no	—
285	C₄⋊C₄×C₈₃	—	2	1	no	—
286	C₄⋊C₄×C₈₃	—	2	2	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	1	no	—
291	C₄⋊C₄×C₈₃	—	2	2	no	—
292	C₄⋊C₄×C₈₃	—	2	4	no	—
293	C₄⋊C₄×C₈₃	—	2	2	no	—
294	C₄⋊C₄×C₈₃	—	2	4	no	—
295	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
299	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
300	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
301	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
302	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
303	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
304	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
305	C₂²⋊C₄×C₈₃	—	2	1	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	2	no	—
310	C₂²⋊C₄×C₈₃	—	2	2	no	—
311	C₂²⋊C₄×C₈₃	—	2	1	no	—
312	C₂²⋊C₄×C₈₃	—	2	1	no	—
313	C₂²⋊C₄×C₈₃	—	2	2	no	—
314	C₂²⋊C₄×C₈₃	—	2	2	no	—
315	C₂²⋊C₄×C₈₃	—	2	2	no	—
316	C₂²⋊C₄×C₈₃	—	2	2	no	—
317	C₂²⋊C₄×C₈₃	—	2	2	no	—
318	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
319	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
320	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
321	C₄²×C₈₃	—	2	1	no	—
322	C₄²×C₈₃	—	2	1	no	—
323	C₄²×C₈₃	—	2	1	no	—
324	C₄²×C₈₃	—	2	4	no	—
325	C₄²×C₈₃	—	2	2	no	—
326	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
327	C₄²×C₈₃	C₂×D₄	1	2	yes	—
328	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₈₃	C₂×D₄	1	2	yes	—
330	C₄²×C₈₃	C₂⁴	1	2	yes	—
331	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
332	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
333	C₂³×C₈₃	—	2	2	no	—
334	C₂³×C₈₃	—	2	1	no	—
335	C₂³×C₈₃	—	4	2	no	—
336	C₂³×C₈₃	—	8	1	no	—
337	C₂³×C₈₃	—	8	1	no	—
338	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
339	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
340	Q₈×C₈₃	—	2	2	no	—
341	Q₈×C₈₃	—	2	1	no	—
342	Q₈×C₈₃	—	2	1	no	—
343	Q₈×C₈₃	—	4	2	no	—
344	Q₈×C₈₃	—	4	4	no	—
345	Q₈×C₈₃	—	4	2	no	—
346	Q₈×C₈₃	—	8	2	no	—
347	Q₈×C₈₃	—	8	4	no	—
348	Q₈×C₈₃	—	8	2	no	—
349	D₄×C₈₃	—	2	4	no	—
350	D₄×C₈₃	—	2	2	no	—
351	D₄×C₈₃	—	2	2	no	—
352	D₄×C₈₃	—	2	2	no	—
353	D₄×C₈₃	—	2	1	no	—
354	D₄×C₈₃	—	2	1	no	—
355	D₄×C₈₃	—	4	2	no	—
356	D₄×C₈₃	—	4	2	no	—
357	D₄×C₈₃	—	8	2	no	—
358	D₄×C₈₃	—	8	2	no	—
359	D₄×C₈₃	—	8	2	no	—
360	D₄×C₈₃	—	8	2	no	—
361	D₄×C₈₃	—	8	2	no	—
362	C₂×C₄×C₈₃	—	2	2	no	—
363	C₂×C₄×C₈₃	—	2	4	no	—
364	C₂×C₄×C₈₃	—	2	2	no	—
365	C₂×C₄×C₈₃	—	2	2	no	—
366	C₂×C₄×C₈₃	—	2	2	no	—
367	C₂×C₄×C₈₃	—	2	1	no	—
368	C₂×C₄×C₈₃	—	2	1	no	—
369	C₂×C₄×C₈₃	—	2	1	no	—
370	C₂×C₄×C₈₃	—	2	4	no	—
371	C₂×C₄×C₈₃	—	2	2	no	—
372	C₂×C₄×C₈₃	—	2	2	no	—
373	C₂×C₄×C₈₃	—	4	1	no	—
374	C₂×C₄×C₈₃	—	4	2	no	—
375	C₂×C₄×C₈₃	—	4	2	no	—
376	C₂×C₄×C₈₃	—	4	4	no	—
377	C₂×C₄×C₈₃	—	4	2	no	—
378	C₂×C₄×C₈₃	—	8	1	no	—
379	C₂×C₄×C₈₃	—	8	2	no	—
380	C₂×C₄×C₈₃	—	8	1	no	—
381	C₂×C₄×C₈₃	—	8	2	no	—
382	C₂×C₄×C₈₃	—	8	4	no	—
383	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
384	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
388	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
389	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₈₃	2₋¹⁺⁴	1	2	yes	—
392	C₂×C₄×C₈₃	2₋¹⁺⁴	1	2	yes	—
393	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
394	C₈×C₈₃	—	2	2	no	—
395	C₈×C₈₃	—	2	2	no	—
396	C₈×C₈₃	—	2	4	no	—
397	C₂²×C₈₃	—	2	1	no	—
398	C₂²×C₈₃	—	2	1	no	—
399	C₂²×C₈₃	—	2	2	no	—
400	C₂²×C₈₃	—	2	2	no	—
401	C₂²×C₈₃	—	2	2	no	—
402	C₂²×C₈₃	—	4	1	no	—
403	C₂²×C₈₃	—	4	2	no	—
404	C₂²×C₈₃	—	4	1	no	—
405	C₂²×C₈₃	—	4	2	no	—
406	C₂²×C₈₃	—	4	2	no	—
407	C₂²×C₈₃	—	4	1	no	—
408	C₂²×C₈₃	—	8	4	no	—
409	C₂²×C₈₃	#536	1	2	yes	—
410	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
411	C₄×C₈₃	—	2	1	no	—
412	C₄×C₈₃	—	2	1	no	—
413	C₄×C₈₃	—	2	2	no	—
414	C₄×C₈₃	—	2	2	no	—
415	C₄×C₈₃	—	2	1	no	—
416	C₄×C₈₃	—	2	2	no	—
417	C₄×C₈₃	—	4	4	no	—
418	C₄×C₈₃	—	4	2	no	—
419	C₄×C₈₃	—	4	1	no	—
420	C₄×C₈₃	—	4	1	no	—
421	C₄×C₈₃	—	4	2	no	—
422	C₄×C₈₃	—	4	1	no	—
423	C₄×C₈₃	—	4	2	no	—
424	C₄×C₈₃	#536	1	2	yes	—
425	C₄×C₈₃	#577	1	2	yes	—
426	C₄×C₈₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
427	C₄×C₈₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
428	#60892	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
429	C₂×C₈₃	—	2	2	no	—
430	C₂×C₈₃	—	4	2	no	—
431	C₂×C₈₃	—	8	1	no	—
432	C₂×C₈₃	—	8	2	no	—
433	C₂×C₈₃	C₂×#536	1	1	yes	characteristic
434	C₂×C₈₃	C₂×#577	1	1	yes	characteristic
435	C₂×C₈₃	#3585	1	1	yes	characteristic
436	#3503	C₂×C₈₃	1	1	yes	characteristic, complemented
437	#3460	C₂×C₈₃	1	1	yes	characteristic
438	#3244	C₂×C₈₃	1	4	yes	complemented
439	#3241	C₂×C₈₃	1	4	yes	complemented
440	#3238	C₂×C₈₃	1	2	yes	complemented
441	#3235	C₂×C₈₃	1	2	yes	complemented
442	#3233	C₂×C₈₃	1	2	yes	complemented
443	#3227	C₂×C₈₃	1	2	yes	complemented
444	#3163	C₂×C₈₃	1	2	yes	complemented
445	#3136	C₂×C₈₃	1	2	yes	complemented
446	#3099	C₂×C₈₃	1	2	yes	complemented
447	#3096	C₂×C₈₃	1	2	yes	complemented
448	#3079	C₂×C₈₃	1	1	yes	characteristic, complemented
449	#3077	C₂×C₈₃	1	1	yes	characteristic, complemented
450	#3076	C₂×C₈₃	1	1	yes	characteristic, complemented
451	C₂×#476	C₂×C₈₃	1	1	yes	characteristic, complemented
452	#2925	C₂×C₈₃	1	1	yes	characteristic, complemented
453	C₈₃	#60892	1	1	yes	characteristic, direct product factor, Sylow
454	Q₈²	—	2	1	no	—
455	#557	—	2	1	no	—
456	#554	—	2	2	no	—
457	#554	—	2	1	no	—
458	D₄×Q₈	—	2	2	no	—
459	D₄×Q₈	—	2	1	no	—
460	#544	C₂²×C₈₃	1	2	yes	—
461	#544	C₂²×C₈₃	1	1	yes	characteristic
462	#544	C₂²×C₈₃	1	4	yes	complemented
463	#542	—	2	1	no	—
464	#542	C₂²×C₈₃	1	2	yes	—
465	#540	—	2	1	no	—
466	#540	C₂²×C₈₃	1	2	yes	—
467	#538	—	2	2	no	—
468	#537	C₂²×C₈₃	1	1	yes	characteristic
469	#535	C₂²×C₈₃	1	1	yes	characteristic
470	#535	C₂²×C₈₃	1	1	yes	characteristic
471	#533	C₂²×C₈₃	1	1	yes	characteristic
472	#533	C₂²×C₈₃	1	2	yes	complemented
473	#532	—	2	1	no	—
474	#532	C₂²×C₈₃	1	2	yes	—
475	C₂×C₄⋊Q₈	C₂²×C₈₃	1	1	yes	characteristic
476	C₂×C₄⋊Q₈	C₂²×C₈₃	1	2	yes	complemented
477	#529	—	2	1	no	—
478	#529	C₂²×C₈₃	1	2	yes	—
479	#525	—	2	2	no	—
480	#520	C₂²×C₈₃	1	2	yes	—
481	C₄×#41	C₂²×C₈₃	1	1	yes	characteristic
482	C₄×#41	C₂²×C₈₃	1	1	yes	characteristic
483	C₂×C₄×D₄	C₂²×C₈₃	1	1	yes	characteristic
484	#501	C₂²×C₈₃	1	4	yes	complemented
485	#501	C₂²×C₈₃	1	4	yes	complemented
486	#499	C₂²×C₈₃	1	4	yes	complemented
487	#498	C₂²×C₈₃	1	4	yes	complemented
488	#490	C₂²×C₈₃	1	4	yes	—
489	#489	C₂²×C₈₃	1	4	yes	—
490	#488	C₂²×C₈₃	1	4	yes	—
491	#486	C₂²×C₈₃	1	4	yes	—
492	#485	C₂²×C₈₃	1	4	yes	complemented
493	#483	C₂²×C₈₃	1	4	yes	complemented
494	#482	C₂²×C₈₃	1	4	yes	—
495	#482	C₂²×C₈₃	1	4	yes	—
496	#482	C₂²×C₈₃	1	4	yes	complemented
497	#481	C₂²×C₈₃	1	4	yes	—
498	#481	C₂²×C₈₃	1	4	yes	complemented
499	#480	C₂²×C₈₃	1	4	yes	—
500	#479	C₂²×C₈₃	1	2	yes	complemented
501	#478	C₂²×C₈₃	1	4	yes	—
502	#478	C₂²×C₈₃	1	2	yes	complemented
503	#477	C₂²×C₈₃	1	1	yes	characteristic, complemented
504	#477	C₂²×C₈₃	1	2	yes	complemented
505	#476	C₂²×C₈₃	1	2	yes	—
506	#476	C₂²×C₈₃	1	2	yes	—
507	#476	C₂²×C₈₃	1	2	yes	—
508	#476	C₂²×C₈₃	1	4	yes	—
509	#476	C₂²×C₈₃	1	1	yes	characteristic, complemented
510	#476	C₂²×C₈₃	1	2	yes	complemented
511	#475	C₂²×C₈₃	1	1	yes	characteristic, complemented
512	#475	C₂²×C₈₃	1	2	yes	complemented
513	#474	C₂²×C₈₃	1	2	yes	—
514	#474	C₂²×C₈₃	1	1	yes	characteristic, complemented
515	#474	C₂²×C₈₃	1	2	yes	complemented
516	#433	C₂²×C₈₃	1	4	yes	complemented
517	#432	C₂²×C₈₃	1	2	yes	complemented
518	#431	C₂²×C₈₃	1	2	yes	complemented
519	#428	C₂²×C₈₃	1	2	yes	—
520	#428	C₂²×C₈₃	1	2	yes	—
521	#427	C₂²×C₈₃	1	2	yes	—
522	C₂×#106	C₂²×C₈₃	1	2	yes	—
523	#423	C₂²×C₈₃	1	1	yes	characteristic
524	C₂×C₄⋊C₈	C₂²×C₈₃	1	1	yes	characteristic
525	#418	C₂²×C₈₃	1	2	yes	—
526	#417	C₂²×C₈₃	1	2	yes	—
527	#416	C₂²×C₈₃	1	2	yes	—
528	C₂×#102	C₂²×C₈₃	1	2	yes	—
529	#408	C₂²×C₈₃	1	2	yes	—
530	#405	C₂²×C₈₃	1	2	yes	—
531	C₂×#41	—	2	2	no	—
532	C₂×#41	C₂³×C₈₃	1	1	yes	characteristic
533	C₂×#41	C₂³×C₈₃	1	1	yes	characteristic
534	C₂²×Q₈	—	2	1	no	—
535	C₂²×Q₈	—	2	2	no	—
536	C₂²×D₄	C₂³×C₈₃	1	1	yes	characteristic
537	C₂³×C₄	—	2	1	no	—
538	C₂×M₁₆	C₂³×C₈₃	1	2	yes	—
539	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
540	C₄⋊Q₈	—	2	1	no	—
541	C₄⋊Q₈	—	2	2	no	—
542	C₄⋊Q₈	—	2	4	no	—
543	C₄⋊Q₈	—	2	1	no	—
544	C₄⋊Q₈	—	2	1	no	—
545	C₄⋊Q₈	—	2	2	no	—
546	C₄⋊Q₈	—	2	2	no	—
547	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
548	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
549	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
550	C₄⋊Q₈	C₂³×C₈₃	1	4	yes	—
551	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
552	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
553	#127	—	2	1	no	—
554	#127	C₂³×C₈₃	1	2	yes	—
555	#126	—	2	2	no	—
556	#126	—	2	2	no	—
557	#125	—	2	1	no	—
558	#125	—	2	2	no	—
559	#125	—	2	4	no	—
560	#125	C₂³×C₈₃	1	2	yes	—
561	#125	C₂³×C₈₃	1	2	yes	—
562	#125	C₂³×C₈₃	1	4	yes	—
563	#124	—	2	1	no	—
564	#124	—	2	2	no	—
565	#124	—	2	2	no	—
566	#124	C₂³×C₈₃	1	2	yes	—
567	#123	—	2	2	no	—
568	#123	—	2	2	no	—
569	#123	—	2	2	no	—
570	#123	—	2	2	no	—
571	C₂²⋊Q₈	—	2	1	no	—
572	C₂²⋊Q₈	—	2	1	no	—
573	C₂²⋊Q₈	—	2	1	no	—
574	C₂²⋊Q₈	—	2	2	no	—
575	C₂²⋊Q₈	—	2	2	no	—
576	C₂²⋊Q₈	—	2	2	no	—
577	C₂²⋊Q₈	—	2	2	no	—
578	C₂²⋊Q₈	—	2	4	no	—
579	C₂²⋊Q₈	—	2	4	no	—
580	C₂²⋊Q₈	—	2	4	no	—
581	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
582	#121	—	2	2	no	—
583	#121	—	2	1	no	—
584	#121	—	2	2	no	—
585	#121	—	2	1	no	—
586	#121	—	2	1	no	—
587	#121	—	2	2	no	—
588	#121	—	2	2	no	—
589	#121	C₂³×C₈₃	1	2	yes	—
590	#121	C₂³×C₈₃	1	2	yes	—
591	#121	C₂³×C₈₃	1	2	yes	—
592	#120	—	2	2	no	—
593	#120	—	2	2	no	—
594	C₄×Q₈	—	2	2	no	—
595	C₄×Q₈	—	2	1	no	—
596	C₄×Q₈	—	2	1	no	—
597	C₄×Q₈	—	2	2	no	—
598	C₄×Q₈	—	2	2	no	—
599	C₄×Q₈	D₄×C₈₃	1	1	yes	characteristic
600	C₄×Q₈	D₄×C₈₃	1	1	yes	characteristic
601	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
602	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
603	C₄×D₄	—	2	4	no	—
604	C₄×D₄	—	2	2	no	—
605	C₄×D₄	—	2	1	no	—
606	C₄×D₄	—	2	1	no	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	D₄×C₈₃	1	2	yes	—
612	C₄×D₄	D₄×C₈₃	1	1	yes	characteristic
613	C₄×D₄	D₄×C₈₃	1	2	yes	—
614	C₄×D₄	D₄×C₈₃	1	1	yes	characteristic
615	C₄×D₄	C₂³×C₈₃	1	2	yes	—
616	C₄×D₄	C₂³×C₈₃	1	2	yes	—
617	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
618	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
619	#117	—	2	1	no	—
620	#117	—	2	2	no	—
621	#117	C₂³×C₈₃	1	1	yes	characteristic
622	#117	C₂³×C₈₃	1	2	yes	—
623	#117	C₂³×C₈₃	1	4	yes	—
624	#117	C₂³×C₈₃	1	1	yes	characteristic
625	#117	C₂³×C₈₃	1	2	yes	—
626	C₂×C₄⋊C₄	—	2	1	no	—
627	C₂×C₄⋊C₄	—	2	2	no	—
628	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
629	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₈₃	1	4	yes	—
631	C₂×C₂²⋊C₄	—	2	1	no	—
632	C₂×C₄²	—	2	1	no	—
633	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
634	C₂×C₄²	C₂³×C₈₃	1	2	yes	—
635	#107	C₂³×C₈₃	1	2	yes	—
636	#107	C₂³×C₈₃	1	2	yes	—
637	#107	C₂³×C₈₃	1	4	yes	—
638	#107	C₂³×C₈₃	1	4	yes	—
639	#106	C₂³×C₈₃	1	4	yes	—
640	#106	C₂³×C₈₃	1	4	yes	—
641	#106	C₂³×C₈₃	1	2	yes	—
642	#106	C₂³×C₈₃	1	2	yes	—
643	#106	C₂³×C₈₃	1	4	yes	—
644	#106	C₂³×C₈₃	1	4	yes	—
645	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
646	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
647	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
648	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
649	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
650	#103	C₂³×C₈₃	1	2	yes	—
651	#103	C₂³×C₈₃	1	2	yes	—
652	#103	C₂³×C₈₃	1	4	yes	—
653	#102	C₂³×C₈₃	1	4	yes	—
654	#102	C₂³×C₈₃	1	4	yes	—
655	#102	C₂³×C₈₃	1	2	yes	—
656	#102	C₂³×C₈₃	1	2	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	4	yes	—
661	C₂²⋊C₈	C₂³×C₈₃	1	4	yes	—
662	#97	C₂³×C₈₃	1	4	yes	—
663	C₄×C₈	C₂³×C₈₃	1	4	yes	—
664	C₂⁴	—	2	1	no	—
665	#41	—	2	2	no	—
666	#41	—	2	2	no	—
667	#41	—	2	2	no	—
668	#41	—	2	2	no	—
669	#41	—	8	4	no	—
670	C₂×Q₈	—	2	1	no	—
671	C₂×Q₈	—	2	1	no	—
672	C₂×Q₈	—	2	2	no	—
673	C₂×Q₈	—	2	2	no	—
674	C₂×Q₈	—	2	2	no	—
675	C₂×Q₈	—	2	4	no	—
676	C₂×Q₈	—	8	2	no	—
677	C₂×Q₈	—	8	4	no	—
678	C₂×Q₈	C₂×D₄×C₈₃	1	1	yes	characteristic
679	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	2	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	C₂×D₄×C₈₃	1	2	yes	—
690	C₂×D₄	C₂×D₄×C₈₃	1	1	yes	characteristic
691	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
692	C₂×D₄	C₂⁴×C₈₃	1	1	yes	characteristic
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	4	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	1	no	—
697	C₂²×C₄	—	2	1	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	1	no	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	8	2	no	—
702	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
703	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
704	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
705	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
706	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
707	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
708	M₁₆	—	2	4	no	—
709	C₂×C₈	—	2	4	no	—
710	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
711	C₂×C₈	C₂⁴×C₈₃	1	4	yes	—
712	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	1	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	4	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	4	no	—
731	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
732	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
733	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
734	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
735	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
736	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
737	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
738	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
739	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
740	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
741	C₂²⋊C₄	—	2	1	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	2	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	1	no	—
748	C₂²⋊C₄	—	2	1	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
755	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
756	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
757	C₄²	—	2	1	no	—
758	C₄²	—	2	1	no	—
759	C₄²	—	2	1	no	—
760	C₄²	—	2	4	no	—
761	C₄²	—	2	2	no	—
762	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
763	C₄²	C₂×D₄×C₈₃	1	2	yes	—
764	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
765	C₄²	C₂×D₄×C₈₃	1	2	yes	—
766	C₄²	C₂⁴×C₈₃	1	2	yes	—
767	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
768	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
769	C₂³	—	2	2	no	—
770	C₂³	—	2	1	no	—
771	C₂³	—	4	2	no	—
772	C₂³	—	8	1	no	—
773	C₂³	—	8	1	no	—
774	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
775	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
776	Q₈	—	2	2	no	—
777	Q₈	—	2	1	no	—
778	Q₈	—	2	1	no	—
779	Q₈	—	4	2	no	—
780	Q₈	—	4	4	no	—
781	Q₈	—	4	2	no	—
782	Q₈	—	8	2	no	—
783	Q₈	—	8	4	no	—
784	Q₈	—	8	2	no	—
785	D₄	—	2	4	no	—
786	D₄	—	2	2	no	—
787	D₄	—	2	2	no	—
788	D₄	—	2	2	no	—
789	D₄	—	2	1	no	—
790	D₄	—	2	1	no	—
791	D₄	—	4	2	no	—
792	D₄	—	4	2	no	—
793	D₄	—	8	2	no	—
794	D₄	—	8	2	no	—
795	D₄	—	8	2	no	—
796	D₄	—	8	2	no	—
797	D₄	—	8	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	4	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	4	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	4	1	no	—
810	C₂×C₄	—	4	2	no	—
811	C₂×C₄	—	4	2	no	—
812	C₂×C₄	—	4	4	no	—
813	C₂×C₄	—	4	2	no	—
814	C₂×C₄	—	8	2	no	—
815	C₂×C₄	—	8	1	no	—
816	C₂×C₄	—	8	1	no	—
817	C₂×C₄	—	8	2	no	—
818	C₂×C₄	—	8	4	no	—
819	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
820	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
821	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
822	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
823	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
824	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
825	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
826	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
827	C₂×C₄	2₋¹⁺⁴×C₈₃	1	2	yes	—
828	C₂×C₄	2₋¹⁺⁴×C₈₃	1	2	yes	—
829	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
830	C₈	—	2	2	no	—
831	C₈	—	2	2	no	—
832	C₈	—	2	4	no	—
833	C₂²	—	2	1	no	—
834	C₂²	—	2	1	no	—
835	C₂²	—	2	2	no	—
836	C₂²	—	2	2	no	—
837	C₂²	—	2	2	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	1	no	—
840	C₂²	—	4	1	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	1	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	8	4	no	—
845	C₂²	#536×C₈₃	1	2	yes	—
846	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
847	C₄	—	2	1	no	—
848	C₄	—	2	2	no	—
849	C₄	—	2	1	no	—
850	C₄	—	2	1	no	—
851	C₄	—	2	2	no	—
852	C₄	—	2	2	no	—
853	C₄	—	4	2	no	—
854	C₄	—	4	1	no	—
855	C₄	—	4	2	no	—
856	C₄	—	4	4	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	1	no	—
859	C₄	—	4	1	no	—
860	C₄	#536×C₈₃	1	2	yes	—
861	C₄	#577×C₈₃	1	2	yes	—
862	C₄	C₂×2₋¹⁺⁴×C₈₃	1	1	yes	characteristic
863	C₄	C₂×2₋¹⁺⁴×C₈₃	1	1	yes	characteristic
864	C₂	—	2	2	no	—
865	C₂	—	4	2	no	—
866	C₂	—	8	2	no	—
867	C₂	—	8	1	no	—
868	C₂	C₂×#536×C₈₃	1	1	yes	characteristic
869	C₂	C₂×#577×C₈₃	1	1	yes	characteristic
870	C₂	C₈₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₃
prime radical	C₈₃×#3460	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₃ ◁ C₄×#41×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₃×#3503	C₂	semidirect
3. C₈₃×#3244	C₂	semidirect
4. C₈₃×#3241	C₂	semidirect
5. C₈₃×#3238	C₂	semidirect
6. C₈₃×#3235	C₂	semidirect
7. C₈₃×#3233	C₂	semidirect
8. C₈₃×#3227	C₂	semidirect
9. C₈₃×#3163	C₂	semidirect
10. C₈₃×#3136	C₂	semidirect
11. C₈₃×#3099	C₂	semidirect
12. C₈₃×#3096	C₂	semidirect
13. C₈₃×#3079	C₂	semidirect
14. C₈₃×#3077	C₂	semidirect
15. C₈₃×#3076	C₂	semidirect
16. C₂×#476×C₈₃	C₂	semidirect
17. C₈₃×#2925	C₂	semidirect
26. #544×C₈₃	C₂²	semidirect
36. #533×C₈₃	C₂²	semidirect
40. C₂×C₄⋊Q₈×C₈₃	C₂²	semidirect
48. #501×C₈₃	C₂²	semidirect
49. #501×C₈₃	C₂²	semidirect
50. #499×C₈₃	C₂²	semidirect
51. #498×C₈₃	C₂²	semidirect
56. #485×C₈₃	C₂²	semidirect
57. #483×C₈₃	C₂²	semidirect
60. #482×C₈₃	C₂²	semidirect
62. #481×C₈₃	C₂²	semidirect
64. #479×C₈₃	C₂²	semidirect
66. #478×C₈₃	C₂²	semidirect
67. #477×C₈₃	C₂²	semidirect
68. #477×C₈₃	C₂²	semidirect
73. #476×C₈₃	C₂²	semidirect
74. #476×C₈₃	C₂²	semidirect
75. #475×C₈₃	C₂²	semidirect
76. #475×C₈₃	C₂²	semidirect
78. #474×C₈₃	C₂²	semidirect
79. #474×C₈₃	C₂²	semidirect
80. #433×C₈₃	C₂²	semidirect
81. #432×C₈₃	C₂²	semidirect
82. #431×C₈₃	C₂²	semidirect
428. #60892	C₈₃	direct (N × H)
436. #3503	C₂×C₈₃	semidirect
438. #3244	C₂×C₈₃	semidirect
439. #3241	C₂×C₈₃	semidirect
440. #3238	C₂×C₈₃	semidirect
441. #3235	C₂×C₈₃	semidirect
442. #3233	C₂×C₈₃	semidirect
443. #3227	C₂×C₈₃	semidirect
444. #3163	C₂×C₈₃	semidirect
445. #3136	C₂×C₈₃	semidirect
446. #3099	C₂×C₈₃	semidirect
447. #3096	C₂×C₈₃	semidirect
448. #3079	C₂×C₈₃	semidirect
449. #3077	C₂×C₈₃	semidirect
450. #3076	C₂×C₈₃	semidirect
451. C₂×#476	C₂×C₈₃	semidirect
452. #2925	C₂×C₈₃	semidirect
453. C₈₃	#60892	direct (N × H)
462. #544	C₂²×C₈₃	semidirect
472. #533	C₂²×C₈₃	semidirect
476. C₂×C₄⋊Q₈	C₂²×C₈₃	semidirect
484. #501	C₂²×C₈₃	semidirect
485. #501	C₂²×C₈₃	semidirect
486. #499	C₂²×C₈₃	semidirect
487. #498	C₂²×C₈₃	semidirect
492. #485	C₂²×C₈₃	semidirect
493. #483	C₂²×C₈₃	semidirect
496. #482	C₂²×C₈₃	semidirect
498. #481	C₂²×C₈₃	semidirect
500. #479	C₂²×C₈₃	semidirect
502. #478	C₂²×C₈₃	semidirect
503. #477	C₂²×C₈₃	semidirect
504. #477	C₂²×C₈₃	semidirect
509. #476	C₂²×C₈₃	semidirect
510. #476	C₂²×C₈₃	semidirect
511. #475	C₂²×C₈₃	semidirect
512. #475	C₂²×C₈₃	semidirect
514. #474	C₂²×C₈₃	semidirect
515. #474	C₂²×C₈₃	semidirect
516. #433	C₂²×C₈₃	semidirect
517. #432	C₂²×C₈₃	semidirect
518. #431	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×#3503	2
C₈₃×#3460	2
C₈₃×#3244	2
C₈₃×#3241	2
C₈₃×#3238	2
C₈₃×#3235	2
C₈₃×#3233	2
C₈₃×#3227	2
C₈₃×#3163	2
C₈₃×#3136	2
C₈₃×#3099	2
C₈₃×#3096	2
C₈₃×#3079	2
C₈₃×#3077	2
C₈₃×#3076	2
C₂×#476×C₈₃	2
C₈₃×#2925	2
#60892	83

Subgroups — C83×#60892 #35288716

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#60892 #35288716