Subgroups — C₈₃×#62235 #35290059

Order 21248.

1754 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₃×#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₃×#3384	C₂	1	2	yes	maximal, complemented
4	C₈₃×#3370	C₂	1	2	yes	maximal, complemented
5	C₈₃×#3354	C₂	1	2	yes	maximal, complemented
6	C₈₃×#3350	C₂	1	2	yes	maximal, complemented
7	C₈₃×#3347	C₂	1	2	yes	maximal, complemented
8	C₈₃×#3322	C₂	1	2	yes	maximal, complemented
9	C₈₃×#3318	C₂	1	2	yes	maximal, complemented
10	C₈₃×#3306	C₂	1	2	yes	maximal, complemented
11	C₈₃×#3257	C₂	1	2	yes	maximal, complemented
12	C₈₃×#3253	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₃×#3244	C₂	1	2	yes	maximal, complemented
14	C₈₃×#3234	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#3122	C₂	1	2	yes	maximal, complemented
16	C₈₃×#3115	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₃×#3081	C₂	1	2	yes	maximal, complemented
18	C₈₃×#3080	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₃×#2995	C₂	1	1	yes	maximal, characteristic, complemented
20	#563×C₈₃	—	2	1	no	—
21	#562×C₈₃	—	2	1	no	—
22	#559×C₈₃	C₂²	1	1	yes	characteristic
23	#556×C₈₃	C₂²	1	1	yes	characteristic
24	#555×C₈₃	C₂²	1	2	yes	—
25	#554×C₈₃	C₂²	1	2	yes	complemented
26	#553×C₈₃	C₂²	1	2	yes	—
27	#553×C₈₃	C₂²	1	2	yes	complemented
28	#551×C₈₃	—	2	2	no	—
29	D₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
30	#548×C₈₃	—	2	1	no	—
31	#547×C₈₃	—	2	2	no	—
32	#547×C₈₃	C₂²	1	2	yes	complemented
33	#546×C₈₃	—	2	1	no	—
34	#546×C₈₃	C₂²	1	2	yes	—
35	D₄²×C₈₃	C₂²	1	1	yes	characteristic
36	#544×C₈₃	C₂²	1	2	yes	complemented
37	#542×C₈₃	C₂²	1	2	yes	—
38	#540×C₈₃	C₂²	1	2	yes	complemented
39	#539×C₈₃	—	2	2	no	—
40	#539×C₈₃	—	2	1	no	—
41	#538×C₈₃	—	2	2	no	—
42	#537×C₈₃	—	2	1	no	—
43	#532×C₈₃	C₂²	1	1	yes	characteristic
44	#532×C₈₃	C₂²	1	1	yes	characteristic, complemented
45	#529×C₈₃	—	2	1	no	—
46	#529×C₈₃	C₂²	1	1	yes	characteristic
47	C₂×#125×C₈₃	C₂²	1	1	yes	characteristic, complemented
48	C₂×#124×C₈₃	—	2	1	no	—
49	#518×C₈₃	C₂²	1	2	yes	—
50	C₄×#41×C₈₃	C₂²	1	1	yes	characteristic
51	#501×C₈₃	C₂²	1	2	yes	complemented
52	#501×C₈₃	C₂²	1	2	yes	complemented
53	#498×C₈₃	C₂²	1	2	yes	complemented
54	#490×C₈₃	C₂²	1	2	yes	—
55	#489×C₈₃	C₂²	1	2	yes	complemented
56	#488×C₈₃	C₂²	1	2	yes	complemented
57	#485×C₈₃	C₂²	1	2	yes	complemented
58	#483×C₈₃	C₂²	1	2	yes	complemented
59	#482×C₈₃	C₂²	1	2	yes	—
60	#482×C₈₃	C₂²	1	2	yes	complemented
61	#482×C₈₃	C₂²	1	2	yes	complemented
62	#482×C₈₃	C₂²	1	2	yes	complemented
63	#481×C₈₃	C₂²	1	2	yes	—
64	#481×C₈₃	C₂²	1	2	yes	complemented
65	#480×C₈₃	C₂²	1	2	yes	complemented
66	#479×C₈₃	C₂²	1	2	yes	complemented
67	#479×C₈₃	C₂²	1	2	yes	complemented
68	#478×C₈₃	C₂²	1	2	yes	—
69	#478×C₈₃	C₂²	1	2	yes	—
70	#478×C₈₃	C₂²	1	2	yes	—
71	#478×C₈₃	C₂²	1	2	yes	complemented
72	#478×C₈₃	C₂²	1	2	yes	complemented
73	#478×C₈₃	C₂²	1	2	yes	complemented
74	#476×C₈₃	C₂²	1	2	yes	—
75	#476×C₈₃	C₂²	1	2	yes	complemented
76	#476×C₈₃	C₂²	1	2	yes	complemented
77	#476×C₈₃	C₂²	1	2	yes	complemented
78	#475×C₈₃	C₂²	1	1	yes	characteristic, complemented
79	#474×C₈₃	C₂²	1	1	yes	characteristic
80	#474×C₈₃	C₂²	1	2	yes	complemented
81	#474×C₈₃	C₂²	1	2	yes	complemented
82	#469×C₈₃	C₂²	1	2	yes	—
83	#469×C₈₃	C₂²	1	2	yes	complemented
84	#469×C₈₃	C₂²	1	2	yes	complemented
85	#468×C₈₃	C₂²	1	2	yes	complemented
86	#466×C₈₃	C₂²	1	2	yes	—
87	#465×C₈₃	C₂²	1	2	yes	complemented
88	#463×C₈₃	C₂²	1	2	yes	complemented
89	#463×C₈₃	C₂²	1	2	yes	complemented
90	#460×C₈₃	C₂²	1	1	yes	characteristic, complemented
91	#459×C₈₃	C₂²	1	2	yes	—
92	#459×C₈₃	C₂²	1	1	yes	characteristic
93	#459×C₈₃	C₂²	1	2	yes	complemented
94	#449×C₈₃	C₂²	1	2	yes	—
95	#447×C₈₃	C₂²	1	2	yes	—
96	#447×C₈₃	C₂²	1	2	yes	—
97	#446×C₈₃	C₂²	1	2	yes	complemented
98	#442×C₈₃	C₂²	1	2	yes	—
99	#442×C₈₃	C₂²	1	2	yes	—
100	#442×C₈₃	C₂²	1	2	yes	complemented
101	#440×C₈₃	C₂²	1	2	yes	complemented
102	C₄×D₈×C₈₃	C₂²	1	2	yes	—
103	C₄×D₈×C₈₃	C₂²	1	2	yes	complemented
104	#436×C₈₃	C₂²	1	2	yes	complemented
105	#435×C₈₃	C₂²	1	2	yes	—
106	#435×C₈₃	C₂²	1	2	yes	complemented
107	#433×C₈₃	C₂²	1	2	yes	complemented
108	#432×C₈₃	C₂²	1	1	yes	characteristic, complemented
109	#428×C₈₃	C₂²	1	1	yes	characteristic, complemented
110	#428×C₈₃	C₂²	1	1	yes	characteristic, complemented
111	#428×C₈₃	C₂²	1	2	yes	complemented
112	#427×C₈₃	C₂²	1	2	yes	complemented
113	#424×C₈₃	C₂²	1	2	yes	complemented
114	#423×C₈₃	C₂²	1	1	yes	characteristic, complemented
115	#418×C₈₃	C₂²	1	2	yes	—
116	#417×C₈₃	C₂²	1	1	yes	characteristic
117	#417×C₈₃	C₂²	1	1	yes	characteristic
118	C₂×#102×C₈₃	C₂²	1	2	yes	—
119	C₂×#41×C₈₃	—	2	2	no	—
120	C₂×#41×C₈₃	—	2	1	no	—
121	C₂×#41×C₈₃	—	2	1	no	—
122	C₂×#41×C₈₃	C₂³	1	1	yes	characteristic
123	C₂²×Q₈×C₈₃	—	2	1	no	—
124	C₂²×D₄×C₈₃	—	2	1	no	—
125	C₂²×D₄×C₈₃	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
127	C₂×D₈×C₈₃	C₂³	1	2	yes	—
128	C₂×D₈×C₈₃	C₂³	1	2	yes	—
129	C₂×D₈×C₈₃	C₂³	1	2	yes	—
130	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
131	C₂×M₁₆×C₈₃	C₂³	1	1	yes	characteristic
132	C₂×M₁₆×C₈₃	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
134	C₄⋊Q₈×C₈₃	—	2	2	no	—
135	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
136	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
137	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
138	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
139	#127×C₈₃	C₂³	1	1	yes	characteristic
140	#127×C₈₃	C₂³	1	1	yes	characteristic
141	#126×C₈₃	—	2	2	no	—
142	#126×C₈₃	—	2	2	no	—
143	#126×C₈₃	—	2	2	no	—
144	#126×C₈₃	—	2	2	no	—
145	#126×C₈₃	D₄	1	2	yes	—
146	#125×C₈₃	—	2	2	no	—
147	#125×C₈₃	—	2	1	no	—
148	#125×C₈₃	—	2	1	no	—
149	#125×C₈₃	D₄	1	1	yes	characteristic
150	#125×C₈₃	C₂³	1	2	yes	—
151	#125×C₈₃	C₂³	1	2	yes	—
152	#125×C₈₃	C₂³	1	2	yes	—
153	#124×C₈₃	—	2	1	no	—
154	#124×C₈₃	—	2	1	no	—
155	#124×C₈₃	—	2	2	no	—
156	#124×C₈₃	—	2	2	no	—
157	#124×C₈₃	—	2	2	no	—
158	#124×C₈₃	—	2	1	no	—
159	#124×C₈₃	—	2	1	no	—
160	#124×C₈₃	D₄	1	1	yes	characteristic
161	#124×C₈₃	C₂³	1	2	yes	—
162	#123×C₈₃	—	2	2	no	—
163	#123×C₈₃	—	2	2	no	—
164	#123×C₈₃	—	2	2	no	—
165	#123×C₈₃	—	2	2	no	—
166	#123×C₈₃	—	2	2	no	—
167	#123×C₈₃	—	2	2	no	—
168	#123×C₈₃	—	2	2	no	—
169	#123×C₈₃	—	2	2	no	—
170	#123×C₈₃	—	2	2	no	—
171	#123×C₈₃	D₄	1	2	yes	—
172	C₂²⋊Q₈×C₈₃	—	2	2	no	—
173	C₂²⋊Q₈×C₈₃	—	2	1	no	—
174	C₂²⋊Q₈×C₈₃	—	2	2	no	—
175	C₂²⋊Q₈×C₈₃	—	2	2	no	—
176	C₂²⋊Q₈×C₈₃	—	2	2	no	—
177	C₂²⋊Q₈×C₈₃	—	2	2	no	—
178	C₂²⋊Q₈×C₈₃	—	2	2	no	—
179	C₂²⋊Q₈×C₈₃	—	2	2	no	—
180	C₂²⋊Q₈×C₈₃	—	2	2	no	—
181	C₂²⋊Q₈×C₈₃	D₄	1	1	yes	characteristic
182	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
183	#121×C₈₃	—	2	2	no	—
184	#121×C₈₃	—	2	2	no	—
185	#121×C₈₃	—	2	2	no	—
186	#121×C₈₃	—	2	1	no	—
187	#121×C₈₃	—	2	1	no	—
188	#121×C₈₃	—	2	1	no	—
189	#121×C₈₃	—	2	2	no	—
190	#121×C₈₃	—	2	2	no	—
191	#121×C₈₃	—	2	2	no	—
192	#121×C₈₃	D₄	1	1	yes	characteristic
193	#121×C₈₃	C₂³	1	2	yes	—
194	#121×C₈₃	C₂³	1	2	yes	—
195	#121×C₈₃	C₂³	1	2	yes	—
196	#121×C₈₃	C₂³	1	2	yes	—
197	#121×C₈₃	C₂³	1	2	yes	—
198	#120×C₈₃	—	2	2	no	—
199	#120×C₈₃	—	2	2	no	—
200	C₄×Q₈×C₈₃	—	2	1	no	—
201	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
202	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
203	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
204	C₄×D₄×C₈₃	—	2	1	no	—
205	C₄×D₄×C₈₃	—	2	1	no	—
206	C₄×D₄×C₈₃	—	2	2	no	—
207	C₄×D₄×C₈₃	—	2	2	no	—
208	C₄×D₄×C₈₃	—	2	1	no	—
209	C₄×D₄×C₈₃	—	2	2	no	—
210	C₄×D₄×C₈₃	—	2	2	no	—
211	C₄×D₄×C₈₃	—	2	1	no	—
212	C₄×D₄×C₈₃	—	2	1	no	—
213	C₄×D₄×C₈₃	C₂³	1	2	yes	—
214	C₄×D₄×C₈₃	C₂³	1	2	yes	—
215	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
216	C₄×D₄×C₈₃	C₂³	1	2	yes	—
217	C₄×D₄×C₈₃	C₂³	1	2	yes	—
218	C₄×D₄×C₈₃	C₂³	1	2	yes	—
219	C₄×D₄×C₈₃	C₂³	1	2	yes	—
220	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
221	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
222	C₄×D₄×C₈₃	C₂³	1	2	yes	—
223	#117×C₈₃	—	2	2	no	—
224	#117×C₈₃	—	2	1	no	—
225	#117×C₈₃	C₂³	1	2	yes	—
226	#117×C₈₃	C₂³	1	1	yes	characteristic
227	#117×C₈₃	C₂³	1	2	yes	—
228	#117×C₈₃	C₂³	1	2	yes	—
229	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
230	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
231	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
232	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
234	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
235	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
236	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
237	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
238	C₂×C₄²×C₈₃	—	2	1	no	—
239	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
240	#107×C₈₃	C₂³	1	2	yes	—
241	#107×C₈₃	C₂³	1	2	yes	—
242	#107×C₈₃	C₂³	1	2	yes	—
243	#107×C₈₃	C₂³	1	2	yes	—
244	#107×C₈₃	C₂³	1	2	yes	—
245	#106×C₈₃	C₂³	1	2	yes	—
246	#106×C₈₃	C₂³	1	2	yes	—
247	#106×C₈₃	C₂³	1	2	yes	—
248	#106×C₈₃	C₂³	1	2	yes	—
249	#106×C₈₃	C₂³	1	2	yes	—
250	#106×C₈₃	C₂³	1	2	yes	—
251	#106×C₈₃	C₂³	1	2	yes	—
252	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
253	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
254	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
255	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
256	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
257	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
258	#103×C₈₃	C₂³	1	2	yes	—
259	#103×C₈₃	C₂³	1	2	yes	—
260	#103×C₈₃	C₂³	1	2	yes	—
261	#102×C₈₃	C₂³	1	2	yes	—
262	#102×C₈₃	C₂³	1	2	yes	—
263	#102×C₈₃	C₂³	1	2	yes	—
264	#102×C₈₃	C₂³	1	2	yes	—
265	#102×C₈₃	C₂³	1	2	yes	—
266	#102×C₈₃	C₂³	1	2	yes	—
267	#102×C₈₃	C₂³	1	2	yes	—
268	#102×C₈₃	C₂³	1	2	yes	—
269	#102×C₈₃	C₂³	1	2	yes	—
270	#102×C₈₃	C₂³	1	2	yes	—
271	#102×C₈₃	C₂³	1	2	yes	—
272	#102×C₈₃	C₂³	1	2	yes	—
273	#102×C₈₃	C₂³	1	2	yes	—
274	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
275	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
276	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
277	#97×C₈₃	C₂³	1	2	yes	—
278	#97×C₈₃	C₂³	1	2	yes	—
279	C₄×C₈×C₈₃	C₂³	1	2	yes	—
280	C₂⁴×C₈₃	—	2	2	no	—
281	#41×C₈₃	—	2	2	no	—
282	#41×C₈₃	—	4	1	no	—
283	#41×C₈₃	—	8	2	no	—
284	#41×C₈₃	—	8	4	no	—
285	#41×C₈₃	—	8	2	no	—
286	C₂×Q₈×C₈₃	—	2	1	no	—
287	C₂×Q₈×C₈₃	—	2	2	no	—
288	C₂×Q₈×C₈₃	—	2	2	no	—
289	C₂×Q₈×C₈₃	—	2	1	no	—
290	C₂×Q₈×C₈₃	—	8	2	no	—
291	C₂×Q₈×C₈₃	C₂×D₄	1	1	yes	characteristic
292	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
293	C₂×D₄×C₈₃	—	2	4	no	—
294	C₂×D₄×C₈₃	—	2	1	no	—
295	C₂×D₄×C₈₃	—	2	2	no	—
296	C₂×D₄×C₈₃	—	2	2	no	—
297	C₂×D₄×C₈₃	—	2	2	no	—
298	C₂×D₄×C₈₃	—	2	2	no	—
299	C₂×D₄×C₈₃	—	2	2	no	—
300	C₂×D₄×C₈₃	—	2	2	no	—
301	C₂×D₄×C₈₃	—	2	1	no	—
302	C₂×D₄×C₈₃	—	2	1	no	—
303	C₂×D₄×C₈₃	—	2	1	no	—
304	C₂×D₄×C₈₃	—	2	1	no	—
305	C₂×D₄×C₈₃	—	4	2	no	—
306	C₂×D₄×C₈₃	—	8	2	no	—
307	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
308	C₂×D₄×C₈₃	C₂×D₄	1	1	yes	characteristic
309	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
310	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
311	C₂×D₄×C₈₃	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₈₃	—	2	1	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	1	no	—
317	C₂²×C₄×C₈₃	—	2	1	no	—
318	C₂²×C₄×C₈₃	—	2	2	no	—
319	C₂²×C₄×C₈₃	—	2	2	no	—
320	C₂²×C₄×C₈₃	—	2	2	no	—
321	C₂²×C₄×C₈₃	—	2	2	no	—
322	C₂²×C₄×C₈₃	—	2	2	no	—
323	C₂²×C₄×C₈₃	—	2	2	no	—
324	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
325	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
326	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
328	SD₁₆×C₈₃	—	4	2	no	—
329	D₈×C₈₃	—	2	4	no	—
330	D₈×C₈₃	—	4	2	no	—
331	D₈×C₈₃	—	4	2	no	—
332	M₁₆×C₈₃	—	4	1	no	—
333	M₁₆×C₈₃	—	4	2	no	—
334	M₁₆×C₈₃	—	4	1	no	—
335	C₂×C₈×C₈₃	—	4	2	no	—
336	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
337	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
338	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
339	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
340	C₄⋊C₄×C₈₃	—	2	2	no	—
341	C₄⋊C₄×C₈₃	—	2	2	no	—
342	C₄⋊C₄×C₈₃	—	2	2	no	—
343	C₄⋊C₄×C₈₃	—	2	2	no	—
344	C₄⋊C₄×C₈₃	—	2	2	no	—
345	C₄⋊C₄×C₈₃	—	2	2	no	—
346	C₄⋊C₄×C₈₃	—	2	1	no	—
347	C₄⋊C₄×C₈₃	—	2	2	no	—
348	C₄⋊C₄×C₈₃	—	2	1	no	—
349	C₄⋊C₄×C₈₃	—	2	1	no	—
350	C₄⋊C₄×C₈₃	—	2	1	no	—
351	C₄⋊C₄×C₈₃	—	2	2	no	—
352	C₄⋊C₄×C₈₃	—	2	1	no	—
353	C₄⋊C₄×C₈₃	—	2	1	no	—
354	C₄⋊C₄×C₈₃	—	2	2	no	—
355	C₄⋊C₄×C₈₃	—	2	2	no	—
356	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
357	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
358	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
359	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
360	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
361	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
362	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
363	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
364	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
365	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
366	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
367	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
368	C₂²⋊C₄×C₈₃	—	2	2	no	—
369	C₂²⋊C₄×C₈₃	—	2	2	no	—
370	C₂²⋊C₄×C₈₃	—	2	1	no	—
371	C₂²⋊C₄×C₈₃	—	2	2	no	—
372	C₂²⋊C₄×C₈₃	—	2	1	no	—
373	C₂²⋊C₄×C₈₃	—	2	2	no	—
374	C₂²⋊C₄×C₈₃	—	2	2	no	—
375	C₂²⋊C₄×C₈₃	—	2	2	no	—
376	C₂²⋊C₄×C₈₃	—	2	2	no	—
377	C₂²⋊C₄×C₈₃	—	2	2	no	—
378	C₂²⋊C₄×C₈₃	—	2	1	no	—
379	C₂²⋊C₄×C₈₃	—	2	2	no	—
380	C₂²⋊C₄×C₈₃	—	2	2	no	—
381	C₂²⋊C₄×C₈₃	—	2	2	no	—
382	C₂²⋊C₄×C₈₃	—	2	2	no	—
383	C₂²⋊C₄×C₈₃	—	2	2	no	—
384	C₂²⋊C₄×C₈₃	—	2	2	no	—
385	C₂²⋊C₄×C₈₃	—	2	2	no	—
386	C₂²⋊C₄×C₈₃	—	2	2	no	—
387	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
388	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
389	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
390	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
391	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
392	C₄²×C₈₃	—	2	1	no	—
393	C₄²×C₈₃	—	2	1	no	—
394	C₄²×C₈₃	—	2	1	no	—
395	C₄²×C₈₃	—	2	2	no	—
396	C₄²×C₈₃	—	2	2	no	—
397	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
398	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
399	C₄²×C₈₃	C₂⁴	1	2	yes	—
400	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
401	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
402	C₂³×C₈₃	—	2	1	no	—
403	C₂³×C₈₃	—	2	2	no	—
404	C₂³×C₈₃	—	2	2	no	—
405	C₂³×C₈₃	—	4	4	no	—
406	C₂³×C₈₃	—	8	2	no	—
407	C₂³×C₈₃	—	8	2	no	—
408	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
409	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
410	Q₈×C₈₃	—	2	1	no	—
411	Q₈×C₈₃	—	2	1	no	—
412	Q₈×C₈₃	—	4	1	no	—
413	Q₈×C₈₃	—	4	2	no	—
414	Q₈×C₈₃	—	8	2	no	—
415	Q₈×C₈₃	—	8	1	no	—
416	Q₈×C₈₃	—	8	2	no	—
417	D₄×C₈₃	—	2	2	no	—
418	D₄×C₈₃	—	2	2	no	—
419	D₄×C₈₃	—	2	1	no	—
420	D₄×C₈₃	—	2	2	no	—
421	D₄×C₈₃	—	2	2	no	—
422	D₄×C₈₃	—	4	1	no	—
423	D₄×C₈₃	—	4	2	no	—
424	D₄×C₈₃	—	4	4	no	—
425	D₄×C₈₃	—	4	2	no	—
426	D₄×C₈₃	—	4	2	no	—
427	D₄×C₈₃	—	4	4	no	—
428	D₄×C₈₃	—	8	1	no	—
429	D₄×C₈₃	—	8	1	no	—
430	D₄×C₈₃	—	8	1	no	—
431	D₄×C₈₃	—	8	2	no	—
432	D₄×C₈₃	—	8	2	no	—
433	D₄×C₈₃	—	8	2	no	—
434	D₄×C₈₃	—	8	2	no	—
435	D₄×C₈₃	2₋¹⁺⁴	1	2	yes	—
436	C₂×C₄×C₈₃	—	2	2	no	—
437	C₂×C₄×C₈₃	—	2	1	no	—
438	C₂×C₄×C₈₃	—	2	2	no	—
439	C₂×C₄×C₈₃	—	2	1	no	—
440	C₂×C₄×C₈₃	—	2	1	no	—
441	C₂×C₄×C₈₃	—	2	1	no	—
442	C₂×C₄×C₈₃	—	2	1	no	—
443	C₂×C₄×C₈₃	—	2	2	no	—
444	C₂×C₄×C₈₃	—	2	2	no	—
445	C₂×C₄×C₈₃	—	2	2	no	—
446	C₂×C₄×C₈₃	—	2	2	no	—
447	C₂×C₄×C₈₃	—	4	1	no	—
448	C₂×C₄×C₈₃	—	4	1	no	—
449	C₂×C₄×C₈₃	—	4	2	no	—
450	C₂×C₄×C₈₃	—	4	2	no	—
451	C₂×C₄×C₈₃	—	4	2	no	—
452	C₂×C₄×C₈₃	—	8	1	no	—
453	C₂×C₄×C₈₃	—	8	2	no	—
454	C₂×C₄×C₈₃	—	8	2	no	—
455	C₂×C₄×C₈₃	—	8	2	no	—
456	C₂×C₄×C₈₃	—	8	2	no	—
457	C₂×C₄×C₈₃	—	8	2	no	—
458	C₂×C₄×C₈₃	—	8	2	no	—
459	C₂×C₄×C₈₃	—	8	1	no	—
460	C₂×C₄×C₈₃	—	8	2	no	—
461	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
462	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
463	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
468	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
469	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
470	C₈×C₈₃	—	2	2	no	—
471	C₈×C₈₃	—	2	2	no	—
472	C₈×C₈₃	—	2	2	no	—
473	C₈×C₈₃	—	2	2	no	—
474	C₂²×C₈₃	—	2	1	no	—
475	C₂²×C₈₃	—	2	1	no	—
476	C₂²×C₈₃	—	2	2	no	—
477	C₂²×C₈₃	—	2	2	no	—
478	C₂²×C₈₃	—	2	1	no	—
479	C₂²×C₈₃	—	2	2	no	—
480	C₂²×C₈₃	—	2	2	no	—
481	C₂²×C₈₃	—	4	1	no	—
482	C₂²×C₈₃	—	4	1	no	—
483	C₂²×C₈₃	—	4	2	no	—
484	C₂²×C₈₃	—	4	2	no	—
485	C₂²×C₈₃	—	4	2	no	—
486	C₂²×C₈₃	—	4	2	no	—
487	C₂²×C₈₃	—	4	2	no	—
488	C₂²×C₈₃	—	4	2	no	—
489	C₂²×C₈₃	—	16	4	no	—
490	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
491	C₄×C₈₃	—	2	1	no	—
492	C₄×C₈₃	—	2	1	no	—
493	C₄×C₈₃	—	2	1	no	—
494	C₄×C₈₃	—	2	1	no	—
495	C₄×C₈₃	—	2	2	no	—
496	C₄×C₈₃	—	2	2	no	—
497	C₄×C₈₃	—	2	1	no	—
498	C₄×C₈₃	—	2	2	no	—
499	C₄×C₈₃	—	4	2	no	—
500	C₄×C₈₃	—	4	1	no	—
501	C₄×C₈₃	—	4	1	no	—
502	C₄×C₈₃	—	4	2	no	—
503	C₄×C₈₃	—	4	2	no	—
504	C₄×C₈₃	—	4	2	no	—
505	C₄×C₈₃	—	4	1	no	—
506	C₄×C₈₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
507	C₄×C₈₃	#585	1	1	yes	characteristic
508	#62235	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
509	C₂×C₈₃	—	4	1	no	—
510	C₂×C₈₃	—	4	2	no	—
511	C₂×C₈₃	—	4	2	no	—
512	C₂×C₈₃	—	8	2	no	—
513	C₂×C₈₃	—	8	2	no	—
514	C₂×C₈₃	#3489	1	1	yes	characteristic
515	C₂×C₈₃	#3585	1	1	yes	characteristic
516	C₂×C₈₃	#3585	1	1	yes	characteristic
517	#3559	C₂×C₈₃	1	1	yes	characteristic, complemented
518	#3514	C₂×C₈₃	1	1	yes	characteristic, complemented
519	#3384	C₂×C₈₃	1	2	yes	complemented
520	#3370	C₂×C₈₃	1	2	yes	complemented
521	#3354	C₂×C₈₃	1	2	yes	complemented
522	#3350	C₂×C₈₃	1	2	yes	complemented
523	#3347	C₂×C₈₃	1	2	yes	complemented
524	#3322	C₂×C₈₃	1	2	yes	complemented
525	#3318	C₂×C₈₃	1	2	yes	complemented
526	#3306	C₂×C₈₃	1	2	yes	complemented
527	#3257	C₂×C₈₃	1	2	yes	complemented
528	#3253	C₂×C₈₃	1	1	yes	characteristic, complemented
529	#3244	C₂×C₈₃	1	2	yes	complemented
530	#3234	C₂×C₈₃	1	1	yes	characteristic, complemented
531	#3122	C₂×C₈₃	1	2	yes	complemented
532	#3115	C₂×C₈₃	1	1	yes	characteristic, complemented
533	#3081	C₂×C₈₃	1	2	yes	complemented
534	#3080	C₂×C₈₃	1	1	yes	characteristic, complemented
535	#2995	C₂×C₈₃	1	1	yes	characteristic, complemented
536	C₈₃	#62235	1	1	yes	characteristic, direct product factor, Sylow
537	#563	—	2	1	no	—
538	#562	—	2	1	no	—
539	#559	C₂²×C₈₃	1	1	yes	characteristic
540	#556	C₂²×C₈₃	1	1	yes	characteristic
541	#555	C₂²×C₈₃	1	2	yes	—
542	#554	C₂²×C₈₃	1	2	yes	complemented
543	#553	C₂²×C₈₃	1	2	yes	—
544	#553	C₂²×C₈₃	1	2	yes	complemented
545	#551	—	2	2	no	—
546	D₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic
547	#548	—	2	1	no	—
548	#547	—	2	2	no	—
549	#547	C₂²×C₈₃	1	2	yes	complemented
550	#546	—	2	1	no	—
551	#546	C₂²×C₈₃	1	2	yes	—
552	D₄²	C₂²×C₈₃	1	1	yes	characteristic
553	#544	C₂²×C₈₃	1	2	yes	complemented
554	#542	C₂²×C₈₃	1	2	yes	—
555	#540	C₂²×C₈₃	1	2	yes	complemented
556	#539	—	2	2	no	—
557	#539	—	2	1	no	—
558	#538	—	2	2	no	—
559	#537	—	2	1	no	—
560	#532	C₂²×C₈₃	1	1	yes	characteristic
561	#532	C₂²×C₈₃	1	1	yes	characteristic, complemented
562	#529	—	2	1	no	—
563	#529	C₂²×C₈₃	1	1	yes	characteristic
564	C₂×#125	C₂²×C₈₃	1	1	yes	characteristic, complemented
565	C₂×#124	—	2	1	no	—
566	#518	C₂²×C₈₃	1	2	yes	—
567	C₄×#41	C₂²×C₈₃	1	1	yes	characteristic
568	#501	C₂²×C₈₃	1	2	yes	complemented
569	#501	C₂²×C₈₃	1	2	yes	complemented
570	#498	C₂²×C₈₃	1	2	yes	complemented
571	#490	C₂²×C₈₃	1	2	yes	—
572	#489	C₂²×C₈₃	1	2	yes	complemented
573	#488	C₂²×C₈₃	1	2	yes	complemented
574	#485	C₂²×C₈₃	1	2	yes	complemented
575	#483	C₂²×C₈₃	1	2	yes	complemented
576	#482	C₂²×C₈₃	1	2	yes	—
577	#482	C₂²×C₈₃	1	2	yes	complemented
578	#482	C₂²×C₈₃	1	2	yes	complemented
579	#482	C₂²×C₈₃	1	2	yes	complemented
580	#481	C₂²×C₈₃	1	2	yes	—
581	#481	C₂²×C₈₃	1	2	yes	complemented
582	#480	C₂²×C₈₃	1	2	yes	complemented
583	#479	C₂²×C₈₃	1	2	yes	complemented
584	#479	C₂²×C₈₃	1	2	yes	complemented
585	#478	C₂²×C₈₃	1	2	yes	—
586	#478	C₂²×C₈₃	1	2	yes	—
587	#478	C₂²×C₈₃	1	2	yes	—
588	#478	C₂²×C₈₃	1	2	yes	complemented
589	#478	C₂²×C₈₃	1	2	yes	complemented
590	#478	C₂²×C₈₃	1	2	yes	complemented
591	#476	C₂²×C₈₃	1	2	yes	—
592	#476	C₂²×C₈₃	1	2	yes	complemented
593	#476	C₂²×C₈₃	1	2	yes	complemented
594	#476	C₂²×C₈₃	1	2	yes	complemented
595	#475	C₂²×C₈₃	1	1	yes	characteristic, complemented
596	#474	C₂²×C₈₃	1	1	yes	characteristic
597	#474	C₂²×C₈₃	1	2	yes	complemented
598	#474	C₂²×C₈₃	1	2	yes	complemented
599	#469	C₂²×C₈₃	1	2	yes	—
600	#469	C₂²×C₈₃	1	2	yes	complemented
601	#469	C₂²×C₈₃	1	2	yes	complemented
602	#468	C₂²×C₈₃	1	2	yes	complemented
603	#466	C₂²×C₈₃	1	2	yes	—
604	#465	C₂²×C₈₃	1	2	yes	complemented
605	#463	C₂²×C₈₃	1	2	yes	complemented
606	#463	C₂²×C₈₃	1	2	yes	complemented
607	#460	C₂²×C₈₃	1	1	yes	characteristic, complemented
608	#459	C₂²×C₈₃	1	2	yes	—
609	#459	C₂²×C₈₃	1	1	yes	characteristic
610	#459	C₂²×C₈₃	1	2	yes	complemented
611	#449	C₂²×C₈₃	1	2	yes	—
612	#447	C₂²×C₈₃	1	2	yes	—
613	#447	C₂²×C₈₃	1	2	yes	—
614	#446	C₂²×C₈₃	1	2	yes	complemented
615	#442	C₂²×C₈₃	1	2	yes	—
616	#442	C₂²×C₈₃	1	2	yes	—
617	#442	C₂²×C₈₃	1	2	yes	complemented
618	#440	C₂²×C₈₃	1	2	yes	complemented
619	C₄×D₈	C₂²×C₈₃	1	2	yes	—
620	C₄×D₈	C₂²×C₈₃	1	2	yes	complemented
621	#436	C₂²×C₈₃	1	2	yes	complemented
622	#435	C₂²×C₈₃	1	2	yes	—
623	#435	C₂²×C₈₃	1	2	yes	complemented
624	#433	C₂²×C₈₃	1	2	yes	complemented
625	#432	C₂²×C₈₃	1	1	yes	characteristic, complemented
626	#428	C₂²×C₈₃	1	1	yes	characteristic, complemented
627	#428	C₂²×C₈₃	1	1	yes	characteristic, complemented
628	#428	C₂²×C₈₃	1	2	yes	complemented
629	#427	C₂²×C₈₃	1	2	yes	complemented
630	#424	C₂²×C₈₃	1	2	yes	complemented
631	#423	C₂²×C₈₃	1	1	yes	characteristic, complemented
632	#418	C₂²×C₈₃	1	2	yes	—
633	#417	C₂²×C₈₃	1	1	yes	characteristic
634	#417	C₂²×C₈₃	1	1	yes	characteristic
635	C₂×#102	C₂²×C₈₃	1	2	yes	—
636	C₂×#41	—	2	2	no	—
637	C₂×#41	—	2	1	no	—
638	C₂×#41	—	2	1	no	—
639	C₂×#41	C₂³×C₈₃	1	1	yes	characteristic
640	C₂²×Q₈	—	2	1	no	—
641	C₂²×D₄	—	2	1	no	—
642	C₂²×D₄	C₂³×C₈₃	1	2	yes	—
643	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
644	C₂×D₈	C₂³×C₈₃	1	2	yes	—
645	C₂×D₈	C₂³×C₈₃	1	2	yes	—
646	C₂×D₈	C₂³×C₈₃	1	2	yes	—
647	C₂×M₁₆	C₂³×C₈₃	1	1	yes	characteristic
648	C₂×M₁₆	C₂³×C₈₃	1	1	yes	characteristic
649	C₂×M₁₆	C₂³×C₈₃	1	2	yes	—
650	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
651	C₄⋊Q₈	—	2	2	no	—
652	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
653	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
654	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
655	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
656	#127	C₂³×C₈₃	1	1	yes	characteristic
657	#127	C₂³×C₈₃	1	1	yes	characteristic
658	#126	—	2	2	no	—
659	#126	—	2	2	no	—
660	#126	—	2	2	no	—
661	#126	—	2	2	no	—
662	#126	D₄×C₈₃	1	2	yes	—
663	#125	—	2	2	no	—
664	#125	—	2	1	no	—
665	#125	—	2	1	no	—
666	#125	D₄×C₈₃	1	1	yes	characteristic
667	#125	C₂³×C₈₃	1	2	yes	—
668	#125	C₂³×C₈₃	1	2	yes	—
669	#125	C₂³×C₈₃	1	2	yes	—
670	#124	—	2	1	no	—
671	#124	—	2	1	no	—
672	#124	—	2	2	no	—
673	#124	—	2	2	no	—
674	#124	—	2	2	no	—
675	#124	—	2	1	no	—
676	#124	—	2	1	no	—
677	#124	D₄×C₈₃	1	1	yes	characteristic
678	#124	C₂³×C₈₃	1	2	yes	—
679	#123	—	2	2	no	—
680	#123	—	2	2	no	—
681	#123	—	2	2	no	—
682	#123	—	2	2	no	—
683	#123	—	2	2	no	—
684	#123	—	2	2	no	—
685	#123	—	2	2	no	—
686	#123	—	2	2	no	—
687	#123	—	2	2	no	—
688	#123	D₄×C₈₃	1	2	yes	—
689	C₂²⋊Q₈	—	2	2	no	—
690	C₂²⋊Q₈	—	2	1	no	—
691	C₂²⋊Q₈	—	2	2	no	—
692	C₂²⋊Q₈	—	2	2	no	—
693	C₂²⋊Q₈	—	2	2	no	—
694	C₂²⋊Q₈	—	2	2	no	—
695	C₂²⋊Q₈	—	2	2	no	—
696	C₂²⋊Q₈	—	2	2	no	—
697	C₂²⋊Q₈	—	2	2	no	—
698	C₂²⋊Q₈	D₄×C₈₃	1	1	yes	characteristic
699	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
700	#121	—	2	2	no	—
701	#121	—	2	2	no	—
702	#121	—	2	2	no	—
703	#121	—	2	1	no	—
704	#121	—	2	1	no	—
705	#121	—	2	1	no	—
706	#121	—	2	2	no	—
707	#121	—	2	2	no	—
708	#121	—	2	2	no	—
709	#121	D₄×C₈₃	1	1	yes	characteristic
710	#121	C₂³×C₈₃	1	2	yes	—
711	#121	C₂³×C₈₃	1	2	yes	—
712	#121	C₂³×C₈₃	1	2	yes	—
713	#121	C₂³×C₈₃	1	2	yes	—
714	#121	C₂³×C₈₃	1	2	yes	—
715	#120	—	2	2	no	—
716	#120	—	2	2	no	—
717	C₄×Q₈	—	2	1	no	—
718	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
719	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
720	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
721	C₄×D₄	—	2	1	no	—
722	C₄×D₄	—	2	1	no	—
723	C₄×D₄	—	2	2	no	—
724	C₄×D₄	—	2	2	no	—
725	C₄×D₄	—	2	1	no	—
726	C₄×D₄	—	2	2	no	—
727	C₄×D₄	—	2	2	no	—
728	C₄×D₄	—	2	1	no	—
729	C₄×D₄	—	2	1	no	—
730	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
731	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
732	C₄×D₄	C₂³×C₈₃	1	2	yes	—
733	C₄×D₄	C₂³×C₈₃	1	2	yes	—
734	C₄×D₄	C₂³×C₈₃	1	2	yes	—
735	C₄×D₄	C₂³×C₈₃	1	2	yes	—
736	C₄×D₄	C₂³×C₈₃	1	2	yes	—
737	C₄×D₄	C₂³×C₈₃	1	2	yes	—
738	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
739	C₄×D₄	C₂³×C₈₃	1	2	yes	—
740	#117	—	2	2	no	—
741	#117	—	2	1	no	—
742	#117	C₂³×C₈₃	1	1	yes	characteristic
743	#117	C₂³×C₈₃	1	2	yes	—
744	#117	C₂³×C₈₃	1	2	yes	—
745	#117	C₂³×C₈₃	1	2	yes	—
746	C₂×C₄⋊C₄	—	2	1	no	—
747	C₂×C₄⋊C₄	—	2	1	no	—
748	C₂×C₄⋊C₄	—	2	2	no	—
749	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
750	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
751	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
752	C₂×C₂²⋊C₄	—	2	2	no	—
753	C₂×C₂²⋊C₄	—	2	2	no	—
754	C₂×C₂²⋊C₄	—	2	2	no	—
755	C₂×C₄²	—	2	1	no	—
756	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
757	#107	C₂³×C₈₃	1	2	yes	—
758	#107	C₂³×C₈₃	1	2	yes	—
759	#107	C₂³×C₈₃	1	2	yes	—
760	#107	C₂³×C₈₃	1	2	yes	—
761	#107	C₂³×C₈₃	1	2	yes	—
762	#106	C₂³×C₈₃	1	2	yes	—
763	#106	C₂³×C₈₃	1	2	yes	—
764	#106	C₂³×C₈₃	1	2	yes	—
765	#106	C₂³×C₈₃	1	2	yes	—
766	#106	C₂³×C₈₃	1	2	yes	—
767	#106	C₂³×C₈₃	1	2	yes	—
768	#106	C₂³×C₈₃	1	2	yes	—
769	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
770	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
771	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
772	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
773	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
774	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
775	#103	C₂³×C₈₃	1	2	yes	—
776	#103	C₂³×C₈₃	1	2	yes	—
777	#103	C₂³×C₈₃	1	2	yes	—
778	#102	C₂³×C₈₃	1	2	yes	—
779	#102	C₂³×C₈₃	1	2	yes	—
780	#102	C₂³×C₈₃	1	2	yes	—
781	#102	C₂³×C₈₃	1	2	yes	—
782	#102	C₂³×C₈₃	1	2	yes	—
783	#102	C₂³×C₈₃	1	2	yes	—
784	#102	C₂³×C₈₃	1	2	yes	—
785	#102	C₂³×C₈₃	1	2	yes	—
786	#102	C₂³×C₈₃	1	2	yes	—
787	#102	C₂³×C₈₃	1	2	yes	—
788	#102	C₂³×C₈₃	1	2	yes	—
789	#102	C₂³×C₈₃	1	2	yes	—
790	#102	C₂³×C₈₃	1	2	yes	—
791	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
792	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
793	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
794	#97	C₂³×C₈₃	1	2	yes	—
795	#97	C₂³×C₈₃	1	2	yes	—
796	C₄×C₈	C₂³×C₈₃	1	2	yes	—
797	C₂⁴	—	2	2	no	—
798	#41	—	2	2	no	—
799	#41	—	4	1	no	—
800	#41	—	8	2	no	—
801	#41	—	8	4	no	—
802	#41	—	8	2	no	—
803	C₂×Q₈	—	2	1	no	—
804	C₂×Q₈	—	2	2	no	—
805	C₂×Q₈	—	2	2	no	—
806	C₂×Q₈	—	2	1	no	—
807	C₂×Q₈	—	8	2	no	—
808	C₂×Q₈	C₂×D₄×C₈₃	1	1	yes	characteristic
809	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
810	C₂×D₄	—	2	4	no	—
811	C₂×D₄	—	2	1	no	—
812	C₂×D₄	—	2	2	no	—
813	C₂×D₄	—	2	2	no	—
814	C₂×D₄	—	2	2	no	—
815	C₂×D₄	—	2	2	no	—
816	C₂×D₄	—	2	2	no	—
817	C₂×D₄	—	2	2	no	—
818	C₂×D₄	—	2	1	no	—
819	C₂×D₄	—	2	1	no	—
820	C₂×D₄	—	2	1	no	—
821	C₂×D₄	—	2	1	no	—
822	C₂×D₄	—	4	2	no	—
823	C₂×D₄	—	8	2	no	—
824	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
825	C₂×D₄	C₂×D₄×C₈₃	1	1	yes	characteristic
826	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
827	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
828	C₂×D₄	C₂⁴×C₈₃	1	1	yes	characteristic
829	C₂²×C₄	—	2	1	no	—
830	C₂²×C₄	—	2	1	no	—
831	C₂²×C₄	—	2	2	no	—
832	C₂²×C₄	—	2	1	no	—
833	C₂²×C₄	—	2	1	no	—
834	C₂²×C₄	—	2	1	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	C₂×D₄×C₈₃	1	1	yes	characteristic
842	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
843	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
844	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
845	SD₁₆	—	4	2	no	—
846	D₈	—	2	4	no	—
847	D₈	—	4	2	no	—
848	D₈	—	4	2	no	—
849	M₁₆	—	4	1	no	—
850	M₁₆	—	4	2	no	—
851	M₁₆	—	4	1	no	—
852	C₂×C₈	—	4	2	no	—
853	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
854	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
855	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
856	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	2	no	—
863	C₄⋊C₄	—	2	1	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	1	no	—
866	C₄⋊C₄	—	2	1	no	—
867	C₄⋊C₄	—	2	1	no	—
868	C₄⋊C₄	—	2	2	no	—
869	C₄⋊C₄	—	2	1	no	—
870	C₄⋊C₄	—	2	1	no	—
871	C₄⋊C₄	—	2	2	no	—
872	C₄⋊C₄	—	2	2	no	—
873	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
874	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
875	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
876	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
877	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
878	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
879	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
880	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
881	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
882	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
883	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
884	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	1	no	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	1	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	2	2	no	—
894	C₂²⋊C₄	—	2	2	no	—
895	C₂²⋊C₄	—	2	1	no	—
896	C₂²⋊C₄	—	2	2	no	—
897	C₂²⋊C₄	—	2	2	no	—
898	C₂²⋊C₄	—	2	2	no	—
899	C₂²⋊C₄	—	2	2	no	—
900	C₂²⋊C₄	—	2	2	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	2	2	no	—
903	C₂²⋊C₄	—	2	2	no	—
904	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
905	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
906	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
907	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
908	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
909	C₄²	—	2	1	no	—
910	C₄²	—	2	1	no	—
911	C₄²	—	2	1	no	—
912	C₄²	—	2	2	no	—
913	C₄²	—	2	2	no	—
914	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
915	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
916	C₄²	C₂⁴×C₈₃	1	2	yes	—
917	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
918	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
919	C₂³	—	2	1	no	—
920	C₂³	—	2	2	no	—
921	C₂³	—	2	2	no	—
922	C₂³	—	4	4	no	—
923	C₂³	—	8	2	no	—
924	C₂³	—	8	2	no	—
925	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
926	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
927	Q₈	—	2	1	no	—
928	Q₈	—	2	1	no	—
929	Q₈	—	4	1	no	—
930	Q₈	—	4	2	no	—
931	Q₈	—	8	2	no	—
932	Q₈	—	8	1	no	—
933	Q₈	—	8	2	no	—
934	D₄	—	2	2	no	—
935	D₄	—	2	2	no	—
936	D₄	—	2	1	no	—
937	D₄	—	2	2	no	—
938	D₄	—	2	2	no	—
939	D₄	—	4	1	no	—
940	D₄	—	4	2	no	—
941	D₄	—	4	4	no	—
942	D₄	—	4	2	no	—
943	D₄	—	4	2	no	—
944	D₄	—	4	4	no	—
945	D₄	—	8	1	no	—
946	D₄	—	8	1	no	—
947	D₄	—	8	1	no	—
948	D₄	—	8	2	no	—
949	D₄	—	8	2	no	—
950	D₄	—	8	2	no	—
951	D₄	—	8	2	no	—
952	D₄	2₋¹⁺⁴×C₈₃	1	2	yes	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	4	1	no	—
965	C₂×C₄	—	4	1	no	—
966	C₂×C₄	—	4	2	no	—
967	C₂×C₄	—	4	2	no	—
968	C₂×C₄	—	4	2	no	—
969	C₂×C₄	—	8	2	no	—
970	C₂×C₄	—	8	2	no	—
971	C₂×C₄	—	8	2	no	—
972	C₂×C₄	—	8	2	no	—
973	C₂×C₄	—	8	1	no	—
974	C₂×C₄	—	8	2	no	—
975	C₂×C₄	—	8	2	no	—
976	C₂×C₄	—	8	2	no	—
977	C₂×C₄	—	8	1	no	—
978	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
979	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
980	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
981	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
982	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
983	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
984	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
985	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
986	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
987	C₈	—	2	2	no	—
988	C₈	—	2	2	no	—
989	C₈	—	2	2	no	—
990	C₈	—	2	2	no	—
991	C₂²	—	2	1	no	—
992	C₂²	—	2	1	no	—
993	C₂²	—	2	2	no	—
994	C₂²	—	2	2	no	—
995	C₂²	—	2	1	no	—
996	C₂²	—	2	2	no	—
997	C₂²	—	2	2	no	—
998	C₂²	—	4	1	no	—
999	C₂²	—	4	1	no	—
1000	C₂²	—	4	2	no	—
1001	C₂²	—	4	2	no	—
1002	C₂²	—	4	2	no	—
1003	C₂²	—	4	2	no	—
1004	C₂²	—	4	2	no	—
1005	C₂²	—	4	2	no	—
1006	C₂²	—	16	4	no	—
1007	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
1008	C₄	—	2	1	no	—
1009	C₄	—	2	1	no	—
1010	C₄	—	2	1	no	—
1011	C₄	—	2	1	no	—
1012	C₄	—	2	2	no	—
1013	C₄	—	2	2	no	—
1014	C₄	—	2	1	no	—
1015	C₄	—	2	2	no	—
1016	C₄	—	4	2	no	—
1017	C₄	—	4	1	no	—
1018	C₄	—	4	1	no	—
1019	C₄	—	4	2	no	—
1020	C₄	—	4	2	no	—
1021	C₄	—	4	2	no	—
1022	C₄	—	4	1	no	—
1023	C₄	C₂×2₋¹⁺⁴×C₈₃	1	1	yes	characteristic
1024	C₄	#585×C₈₃	1	1	yes	characteristic
1025	C₂	—	4	2	no	—
1026	C₂	—	4	1	no	—
1027	C₂	—	4	2	no	—
1028	C₂	—	8	2	no	—
1029	C₂	—	8	2	no	—
1030	C₂	C₈₃×#3489	1	1	yes	characteristic
1031	C₂	C₈₃×#3585	1	1	yes	characteristic
1032	C₂	C₈₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₃ ◁ #529×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₃×#3559	C₂	semidirect
2. C₈₃×#3514	C₂	semidirect
3. C₈₃×#3384	C₂	semidirect
4. C₈₃×#3370	C₂	semidirect
5. C₈₃×#3354	C₂	semidirect
6. C₈₃×#3350	C₂	semidirect
7. C₈₃×#3347	C₂	semidirect
8. C₈₃×#3322	C₂	semidirect
9. C₈₃×#3318	C₂	semidirect
10. C₈₃×#3306	C₂	semidirect
11. C₈₃×#3257	C₂	semidirect
12. C₈₃×#3253	C₂	semidirect
13. C₈₃×#3244	C₂	semidirect
14. C₈₃×#3234	C₂	semidirect
15. C₈₃×#3122	C₂	semidirect
16. C₈₃×#3115	C₂	semidirect
17. C₈₃×#3081	C₂	semidirect
18. C₈₃×#3080	C₂	semidirect
19. C₈₃×#2995	C₂	semidirect
25. #554×C₈₃	C₂²	semidirect
27. #553×C₈₃	C₂²	semidirect
32. #547×C₈₃	C₂²	semidirect
36. #544×C₈₃	C₂²	semidirect
38. #540×C₈₃	C₂²	semidirect
44. #532×C₈₃	C₂²	semidirect
47. C₂×#125×C₈₃	C₂²	semidirect
51. #501×C₈₃	C₂²	semidirect
52. #501×C₈₃	C₂²	semidirect
53. #498×C₈₃	C₂²	semidirect
55. #489×C₈₃	C₂²	semidirect
56. #488×C₈₃	C₂²	semidirect
57. #485×C₈₃	C₂²	semidirect
58. #483×C₈₃	C₂²	semidirect
60. #482×C₈₃	C₂²	semidirect
61. #482×C₈₃	C₂²	semidirect
62. #482×C₈₃	C₂²	semidirect
64. #481×C₈₃	C₂²	semidirect
65. #480×C₈₃	C₂²	semidirect
66. #479×C₈₃	C₂²	semidirect
67. #479×C₈₃	C₂²	semidirect
71. #478×C₈₃	C₂²	semidirect
72. #478×C₈₃	C₂²	semidirect
73. #478×C₈₃	C₂²	semidirect
75. #476×C₈₃	C₂²	semidirect
76. #476×C₈₃	C₂²	semidirect
77. #476×C₈₃	C₂²	semidirect
78. #475×C₈₃	C₂²	semidirect
80. #474×C₈₃	C₂²	semidirect
81. #474×C₈₃	C₂²	semidirect
83. #469×C₈₃	C₂²	semidirect
84. #469×C₈₃	C₂²	semidirect
85. #468×C₈₃	C₂²	semidirect
87. #465×C₈₃	C₂²	semidirect
88. #463×C₈₃	C₂²	semidirect
89. #463×C₈₃	C₂²	semidirect
90. #460×C₈₃	C₂²	semidirect
93. #459×C₈₃	C₂²	semidirect
97. #446×C₈₃	C₂²	semidirect
100. #442×C₈₃	C₂²	semidirect
101. #440×C₈₃	C₂²	semidirect
103. C₄×D₈×C₈₃	C₂²	semidirect
104. #436×C₈₃	C₂²	semidirect
106. #435×C₈₃	C₂²	semidirect
107. #433×C₈₃	C₂²	semidirect
108. #432×C₈₃	C₂²	semidirect
109. #428×C₈₃	C₂²	semidirect
110. #428×C₈₃	C₂²	semidirect
111. #428×C₈₃	C₂²	semidirect
112. #427×C₈₃	C₂²	semidirect
113. #424×C₈₃	C₂²	semidirect
114. #423×C₈₃	C₂²	semidirect
508. #62235	C₈₃	direct (N × H)
517. #3559	C₂×C₈₃	semidirect
518. #3514	C₂×C₈₃	semidirect
519. #3384	C₂×C₈₃	semidirect
520. #3370	C₂×C₈₃	semidirect
521. #3354	C₂×C₈₃	semidirect
522. #3350	C₂×C₈₃	semidirect
523. #3347	C₂×C₈₃	semidirect
524. #3322	C₂×C₈₃	semidirect
525. #3318	C₂×C₈₃	semidirect
526. #3306	C₂×C₈₃	semidirect
527. #3257	C₂×C₈₃	semidirect
528. #3253	C₂×C₈₃	semidirect
529. #3244	C₂×C₈₃	semidirect
530. #3234	C₂×C₈₃	semidirect
531. #3122	C₂×C₈₃	semidirect
532. #3115	C₂×C₈₃	semidirect
533. #3081	C₂×C₈₃	semidirect
534. #3080	C₂×C₈₃	semidirect
535. #2995	C₂×C₈₃	semidirect
536. C₈₃	#62235	direct (N × H)
542. #554	C₂²×C₈₃	semidirect
544. #553	C₂²×C₈₃	semidirect
549. #547	C₂²×C₈₃	semidirect
553. #544	C₂²×C₈₃	semidirect
555. #540	C₂²×C₈₃	semidirect
561. #532	C₂²×C₈₃	semidirect
564. C₂×#125	C₂²×C₈₃	semidirect
568. #501	C₂²×C₈₃	semidirect
569. #501	C₂²×C₈₃	semidirect
570. #498	C₂²×C₈₃	semidirect
572. #489	C₂²×C₈₃	semidirect
573. #488	C₂²×C₈₃	semidirect
574. #485	C₂²×C₈₃	semidirect
575. #483	C₂²×C₈₃	semidirect
577. #482	C₂²×C₈₃	semidirect
578. #482	C₂²×C₈₃	semidirect
579. #482	C₂²×C₈₃	semidirect
581. #481	C₂²×C₈₃	semidirect
582. #480	C₂²×C₈₃	semidirect
583. #479	C₂²×C₈₃	semidirect
584. #479	C₂²×C₈₃	semidirect
588. #478	C₂²×C₈₃	semidirect
589. #478	C₂²×C₈₃	semidirect
590. #478	C₂²×C₈₃	semidirect
592. #476	C₂²×C₈₃	semidirect
593. #476	C₂²×C₈₃	semidirect
594. #476	C₂²×C₈₃	semidirect
595. #475	C₂²×C₈₃	semidirect
597. #474	C₂²×C₈₃	semidirect
598. #474	C₂²×C₈₃	semidirect
600. #469	C₂²×C₈₃	semidirect
601. #469	C₂²×C₈₃	semidirect
602. #468	C₂²×C₈₃	semidirect
604. #465	C₂²×C₈₃	semidirect
605. #463	C₂²×C₈₃	semidirect
606. #463	C₂²×C₈₃	semidirect
607. #460	C₂²×C₈₃	semidirect
610. #459	C₂²×C₈₃	semidirect
614. #446	C₂²×C₈₃	semidirect
617. #442	C₂²×C₈₃	semidirect
618. #440	C₂²×C₈₃	semidirect
620. C₄×D₈	C₂²×C₈₃	semidirect
621. #436	C₂²×C₈₃	semidirect
623. #435	C₂²×C₈₃	semidirect
624. #433	C₂²×C₈₃	semidirect
625. #432	C₂²×C₈₃	semidirect
626. #428	C₂²×C₈₃	semidirect
627. #428	C₂²×C₈₃	semidirect
628. #428	C₂²×C₈₃	semidirect
629. #427	C₂²×C₈₃	semidirect
630. #424	C₂²×C₈₃	semidirect
631. #423	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×#3559	2
C₈₃×#3514	2
C₈₃×#3384	2
C₈₃×#3370	2
C₈₃×#3354	2
C₈₃×#3350	2
C₈₃×#3347	2
C₈₃×#3322	2
C₈₃×#3318	2
C₈₃×#3306	2
C₈₃×#3257	2
C₈₃×#3253	2
C₈₃×#3244	2
C₈₃×#3234	2
C₈₃×#3122	2
C₈₃×#3115	2
C₈₃×#3081	2
C₈₃×#3080	2
C₈₃×#2995	2
#62235	83

Subgroups — C83×#62235 #35290059

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#62235 #35290059