Subgroups — C₈₃×#61757 #35289581

Order 21248.

1674 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3538	C₂	1	1	yes	maximal, characteristic
2	C₈₃×#3495	C₂	1	1	yes	maximal, characteristic
3	C₈₃×#3352	C₂	1	2	yes	maximal, complemented
4	C₈₃×#3349	C₂	1	2	yes	maximal, complemented
5	C₈₃×#3344	C₂	1	2	yes	maximal, complemented
6	C₈₃×#3336	C₂	1	2	yes	maximal, complemented
7	C₈₃×#3328	C₂	1	2	yes	maximal, complemented
8	C₈₃×#3312	C₂	1	2	yes	maximal, complemented
9	C₈₃×#3312	C₂	1	2	yes	maximal, complemented
10	C₈₃×#3299	C₂	1	2	yes	maximal, complemented
11	C₈₃×#3242	C₂	1	2	yes	maximal, complemented
12	C₈₃×#3202	C₂	1	2	yes	maximal, complemented
13	C₈₃×#3195	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₃×#3189	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#3127	C₂	1	2	yes	maximal, complemented
16	C₈₃×#3097	C₂	1	2	yes	maximal, complemented
17	C₈₃×#3095	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#485×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₃×#2976	C₂	1	1	yes	maximal, characteristic
20	#563×C₈₃	—	2	2	no	—
21	#556×C₈₃	C₂²	1	2	yes	—
22	#554×C₈₃	C₂²	1	2	yes	—
23	#552×C₈₃	—	2	2	no	—
24	#552×C₈₃	C₂²	1	2	yes	—
25	#552×C₈₃	C₂²	1	2	yes	—
26	#552×C₈₃	C₂²	1	2	yes	—
27	#552×C₈₃	C₂²	1	2	yes	—
28	#551×C₈₃	—	2	2	no	—
29	#551×C₈₃	—	2	2	no	—
30	D₄×Q₈×C₈₃	C₂²	1	2	yes	—
31	D₄×Q₈×C₈₃	C₂²	1	2	yes	—
32	#544×C₈₃	—	2	1	no	—
33	#544×C₈₃	—	2	1	no	—
34	#544×C₈₃	C₂²	1	1	yes	characteristic
35	#542×C₈₃	—	2	1	no	—
36	#541×C₈₃	—	2	1	no	—
37	#541×C₈₃	C₂²	1	2	yes	—
38	#539×C₈₃	—	2	1	no	—
39	#539×C₈₃	—	2	1	no	—
40	#536×C₈₃	C₂²	1	2	yes	—
41	#536×C₈₃	C₂²	1	1	yes	characteristic
42	#533×C₈₃	—	2	1	no	—
43	#529×C₈₃	—	2	1	no	—
44	#525×C₈₃	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
48	#520×C₈₃	C₂²	1	1	yes	characteristic
49	#519×C₈₃	C₂²	1	1	yes	characteristic
50	C₂×#117×C₈₃	C₂²	1	1	yes	characteristic
51	#501×C₈₃	C₂²	1	2	yes	complemented
52	#499×C₈₃	C₂²	1	2	yes	complemented
53	#491×C₈₃	C₂²	1	2	yes	complemented
54	#487×C₈₃	C₂²	1	2	yes	complemented
55	#485×C₈₃	C₂²	1	2	yes	—
56	#485×C₈₃	C₂²	1	2	yes	—
57	#485×C₈₃	C₂²	1	2	yes	—
58	#485×C₈₃	C₂²	1	2	yes	—
59	#485×C₈₃	C₂²	1	2	yes	—
60	#485×C₈₃	C₂²	1	2	yes	—
61	#485×C₈₃	C₂²	1	2	yes	complemented
62	#485×C₈₃	C₂²	1	2	yes	complemented
63	#485×C₈₃	C₂²	1	2	yes	complemented
64	#485×C₈₃	C₂²	1	2	yes	complemented
65	#484×C₈₃	C₂²	1	2	yes	—
66	#484×C₈₃	C₂²	1	2	yes	—
67	#484×C₈₃	C₂²	1	2	yes	—
68	#484×C₈₃	C₂²	1	2	yes	complemented
69	#483×C₈₃	C₂²	1	2	yes	—
70	#483×C₈₃	C₂²	1	2	yes	—
71	#483×C₈₃	C₂²	1	2	yes	—
72	#483×C₈₃	C₂²	1	2	yes	complemented
73	#479×C₈₃	C₂²	1	2	yes	complemented
74	#479×C₈₃	C₂²	1	2	yes	complemented
75	#479×C₈₃	C₂²	1	2	yes	complemented
76	#479×C₈₃	C₂²	1	2	yes	complemented
77	#477×C₈₃	C₂²	1	2	yes	complemented
78	#475×C₈₃	C₂²	1	2	yes	complemented
79	#470×C₈₃	C₂²	1	2	yes	—
80	#470×C₈₃	C₂²	1	2	yes	—
81	#470×C₈₃	C₂²	1	2	yes	complemented
82	#470×C₈₃	C₂²	1	2	yes	complemented
83	#467×C₈₃	C₂²	1	2	yes	—
84	#467×C₈₃	C₂²	1	2	yes	—
85	#467×C₈₃	C₂²	1	2	yes	complemented
86	#467×C₈₃	C₂²	1	2	yes	complemented
87	#462×C₈₃	C₂²	1	2	yes	complemented
88	#462×C₈₃	C₂²	1	2	yes	complemented
89	#451×C₈₃	C₂²	1	2	yes	—
90	#451×C₈₃	C₂²	1	2	yes	—
91	#451×C₈₃	C₂²	1	2	yes	—
92	#451×C₈₃	C₂²	1	2	yes	—
93	#451×C₈₃	C₂²	1	2	yes	complemented
94	#451×C₈₃	C₂²	1	2	yes	complemented
95	#441×C₈₃	C₂²	1	2	yes	complemented
96	#441×C₈₃	C₂²	1	2	yes	complemented
97	C₄×Q₁₆×C₈₃	C₂²	1	2	yes	complemented
98	C₄×Q₁₆×C₈₃	C₂²	1	2	yes	complemented
99	#436×C₈₃	C₂²	1	2	yes	—
100	#435×C₈₃	C₂²	1	2	yes	—
101	#435×C₈₃	C₂²	1	2	yes	—
102	C₈×D₄×C₈₃	C₂²	1	2	yes	—
103	#433×C₈₃	C₂²	1	2	yes	—
104	#428×C₈₃	C₂²	1	1	yes	characteristic
105	#428×C₈₃	C₂²	1	1	yes	characteristic
106	#428×C₈₃	C₂²	1	2	yes	complemented
107	#427×C₈₃	C₂²	1	2	yes	complemented
108	C₂×#107×C₈₃	C₂²	1	1	yes	characteristic
109	C₂×#106×C₈₃	C₂²	1	1	yes	characteristic
110	#419×C₈₃	C₂²	1	1	yes	characteristic
111	#419×C₈₃	C₂²	1	1	yes	characteristic
112	#419×C₈₃	C₂²	1	2	yes	complemented
113	C₂×#103×C₈₃	C₂²	1	1	yes	characteristic
114	C₂×#103×C₈₃	C₂²	1	1	yes	characteristic
115	C₂×#103×C₈₃	C₂²	1	2	yes	complemented
116	#408×C₈₃	C₂²	1	2	yes	—
117	#407×C₈₃	C₂²	1	1	yes	characteristic
118	C₂×C₂²⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
119	C₂×#41×C₈₃	C₂³	1	1	yes	characteristic
120	C₂²×Q₈×C₈₃	C₂³	1	1	yes	characteristic
121	C₂²×Q₈×C₈₃	C₂³	1	1	yes	characteristic
122	C₂²×Q₈×C₈₃	C₂³	1	1	yes	characteristic
123	C₂²×Q₈×C₈₃	C₂³	1	2	yes	—
124	C₂³×C₄×C₈₃	C₂³	1	1	yes	characteristic
125	C₂×Q₁₆×C₈₃	C₂³	1	2	yes	—
126	C₂×Q₁₆×C₈₃	C₂³	1	2	yes	—
127	C₂×Q₁₆×C₈₃	C₂³	1	2	yes	—
128	C₂×Q₁₆×C₈₃	C₂³	1	2	yes	—
129	C₂×M₁₆×C₈₃	C₂³	1	1	yes	characteristic
130	C₂×M₁₆×C₈₃	C₂³	1	1	yes	characteristic
131	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
132	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
134	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
135	C₄⋊Q₈×C₈₃	—	2	1	no	—
136	C₄⋊Q₈×C₈₃	—	2	2	no	—
137	C₄⋊Q₈×C₈₃	—	2	1	no	—
138	C₄⋊Q₈×C₈₃	—	2	2	no	—
139	C₄⋊Q₈×C₈₃	—	2	2	no	—
140	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
141	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
142	#126×C₈₃	—	2	2	no	—
143	#126×C₈₃	—	2	2	no	—
144	#126×C₈₃	—	2	2	no	—
145	#126×C₈₃	—	2	2	no	—
146	#126×C₈₃	—	2	2	no	—
147	#126×C₈₃	—	2	2	no	—
148	#126×C₈₃	—	2	2	no	—
149	#126×C₈₃	—	2	2	no	—
150	#125×C₈₃	—	2	1	no	—
151	#125×C₈₃	—	2	2	no	—
152	#125×C₈₃	—	2	2	no	—
153	#125×C₈₃	—	2	2	no	—
154	#125×C₈₃	—	2	2	no	—
155	#125×C₈₃	—	2	2	no	—
156	#125×C₈₃	—	2	2	no	—
157	#125×C₈₃	—	2	2	no	—
158	#125×C₈₃	C₂³	1	2	yes	—
159	#125×C₈₃	C₂³	1	2	yes	—
160	#124×C₈₃	—	2	1	no	—
161	#124×C₈₃	—	2	2	no	—
162	#124×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	D₄	1	2	yes	—
171	C₂²⋊Q₈×C₈₃	—	2	1	no	—
172	C₂²⋊Q₈×C₈₃	—	2	1	no	—
173	C₂²⋊Q₈×C₈₃	—	2	1	no	—
174	C₂²⋊Q₈×C₈₃	—	2	1	no	—
175	C₂²⋊Q₈×C₈₃	—	2	1	no	—
176	C₂²⋊Q₈×C₈₃	—	2	1	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	—	2	2	no	—
182	C₂²⋊Q₈×C₈₃	—	2	2	no	—
183	C₂²⋊Q₈×C₈₃	—	2	2	no	—
184	C₂²⋊Q₈×C₈₃	D₄	1	1	yes	characteristic
185	C₂²⋊Q₈×C₈₃	D₄	1	1	yes	characteristic
186	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
187	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
188	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
189	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
190	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
191	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
192	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
193	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
194	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
195	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
196	#121×C₈₃	D₄	1	1	yes	characteristic
197	#121×C₈₃	D₄	1	1	yes	characteristic
198	#120×C₈₃	D₄	1	2	yes	—
199	C₄×Q₈×C₈₃	—	2	1	no	—
200	C₄×Q₈×C₈₃	—	2	1	no	—
201	C₄×Q₈×C₈₃	—	2	1	no	—
202	C₄×Q₈×C₈₃	—	2	2	no	—
203	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
204	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
205	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
206	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
207	C₄×D₄×C₈₃	—	2	1	no	—
208	C₄×D₄×C₈₃	—	2	2	no	—
209	C₄×D₄×C₈₃	—	2	2	no	—
210	C₄×D₄×C₈₃	—	2	2	no	—
211	C₄×D₄×C₈₃	—	2	2	no	—
212	C₄×D₄×C₈₃	C₂³	1	2	yes	—
213	C₄×D₄×C₈₃	C₂³	1	2	yes	—
214	#117×C₈₃	—	2	1	no	—
215	#117×C₈₃	—	2	1	no	—
216	#117×C₈₃	—	2	2	no	—
217	#117×C₈₃	—	2	2	no	—
218	#117×C₈₃	—	2	2	no	—
219	#117×C₈₃	—	2	2	no	—
220	#117×C₈₃	—	2	2	no	—
221	#117×C₈₃	C₂³	1	1	yes	characteristic
222	#117×C₈₃	C₂³	1	1	yes	characteristic
223	#117×C₈₃	C₂³	1	1	yes	characteristic
224	#117×C₈₃	C₂³	1	1	yes	characteristic
225	#117×C₈₃	C₂³	1	2	yes	—
226	#117×C₈₃	C₂³	1	2	yes	—
227	#117×C₈₃	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
229	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
230	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
231	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
235	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
237	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
238	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
239	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
240	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
241	C₂×C₄²×C₈₃	—	2	1	no	—
242	#107×C₈₃	C₂³	1	2	yes	—
243	#107×C₈₃	C₂³	1	2	yes	—
244	#107×C₈₃	C₂³	1	2	yes	—
245	#107×C₈₃	C₂³	1	2	yes	—
246	#107×C₈₃	C₂³	1	2	yes	—
247	#107×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	#106×C₈₃	C₂³	1	2	yes	—
253	#106×C₈₃	C₂³	1	2	yes	—
254	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
255	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
256	#103×C₈₃	C₂³	1	2	yes	—
257	#103×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	#103×C₈₃	C₂³	1	2	yes	—
262	#103×C₈₃	C₂³	1	2	yes	—
263	#103×C₈₃	C₂³	1	2	yes	—
264	#103×C₈₃	C₂³	1	2	yes	—
265	#103×C₈₃	C₂³	1	2	yes	—
266	#103×C₈₃	C₂³	1	2	yes	—
267	#103×C₈₃	C₂³	1	2	yes	—
268	#103×C₈₃	C₂³	1	2	yes	—
269	#103×C₈₃	C₂³	1	2	yes	—
270	#103×C₈₃	C₂³	1	2	yes	—
271	#103×C₈₃	C₂³	1	2	yes	—
272	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
273	C₂²⋊C₈×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	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
278	#97×C₈₃	C₂³	1	2	yes	—
279	C₄×C₈×C₈₃	C₂³	1	2	yes	—
280	C₂⁴×C₈₃	C₂×D₄	1	1	yes	characteristic
281	#41×C₈₃	—	4	1	no	—
282	#41×C₈₃	—	4	1	no	—
283	C₂×Q₈×C₈₃	—	2	1	no	—
284	C₂×Q₈×C₈₃	—	2	2	no	—
285	C₂×Q₈×C₈₃	—	2	1	no	—
286	C₂×Q₈×C₈₃	—	2	1	no	—
287	C₂×Q₈×C₈₃	—	2	2	no	—
288	C₂×Q₈×C₈₃	—	4	1	no	—
289	C₂×Q₈×C₈₃	—	4	1	no	—
290	C₂×Q₈×C₈₃	—	4	1	no	—
291	C₂×Q₈×C₈₃	—	4	1	no	—
292	C₂×Q₈×C₈₃	—	4	2	no	—
293	C₂×Q₈×C₈₃	—	4	1	no	—
294	C₂×Q₈×C₈₃	—	4	1	no	—
295	C₂×Q₈×C₈₃	—	4	2	no	—
296	C₂×Q₈×C₈₃	C₂×D₄	1	1	yes	characteristic
297	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
298	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
299	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
300	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
301	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
302	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
303	C₂×D₄×C₈₃	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₄×C₈₃	—	2	1	no	—
305	C₂²×C₄×C₈₃	—	2	1	no	—
306	C₂²×C₄×C₈₃	—	2	1	no	—
307	C₂²×C₄×C₈₃	—	2	1	no	—
308	C₂²×C₄×C₈₃	—	2	1	no	—
309	C₂²×C₄×C₈₃	—	2	1	no	—
310	C₂²×C₄×C₈₃	—	2	1	no	—
311	C₂²×C₄×C₈₃	—	2	1	no	—
312	C₂²×C₄×C₈₃	—	2	2	no	—
313	C₂²×C₄×C₈₃	—	2	2	no	—
314	C₂²×C₄×C₈₃	—	4	1	no	—
315	C₂²×C₄×C₈₃	—	4	1	no	—
316	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
317	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
318	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
319	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
322	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
323	Q₁₆×C₈₃	—	4	2	no	—
324	Q₁₆×C₈₃	—	4	2	no	—
325	Q₁₆×C₈₃	—	4	2	no	—
326	Q₁₆×C₈₃	—	4	2	no	—
327	M₁₆×C₈₃	—	4	1	no	—
328	M₁₆×C₈₃	—	4	2	no	—
329	M₁₆×C₈₃	—	4	1	no	—
330	C₂×C₈×C₈₃	—	4	1	no	—
331	C₂×C₈×C₈₃	—	4	2	no	—
332	C₂×C₈×C₈₃	—	4	1	no	—
333	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
334	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
335	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
336	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
337	C₄⋊C₄×C₈₃	—	2	2	no	—
338	C₄⋊C₄×C₈₃	—	2	2	no	—
339	C₄⋊C₄×C₈₃	—	2	2	no	—
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	1	no	—
344	C₄⋊C₄×C₈₃	—	2	1	no	—
345	C₄⋊C₄×C₈₃	—	2	1	no	—
346	C₄⋊C₄×C₈₃	—	2	2	no	—
347	C₄⋊C₄×C₈₃	—	2	1	no	—
348	C₄⋊C₄×C₈₃	—	2	1	no	—
349	C₄⋊C₄×C₈₃	—	2	2	no	—
350	C₄⋊C₄×C₈₃	—	2	2	no	—
351	C₄⋊C₄×C₈₃	—	2	2	no	—
352	C₄⋊C₄×C₈₃	—	2	2	no	—
353	C₄⋊C₄×C₈₃	—	2	2	no	—
354	C₄⋊C₄×C₈₃	—	2	2	no	—
355	C₄⋊C₄×C₈₃	—	2	2	no	—
356	C₄⋊C₄×C₈₃	—	2	2	no	—
357	C₄⋊C₄×C₈₃	—	2	2	no	—
358	C₄⋊C₄×C₈₃	—	2	2	no	—
359	C₄⋊C₄×C₈₃	—	2	2	no	—
360	C₄⋊C₄×C₈₃	—	2	2	no	—
361	C₄⋊C₄×C₈₃	—	2	2	no	—
362	C₄⋊C₄×C₈₃	—	2	2	no	—
363	C₄⋊C₄×C₈₃	—	2	2	no	—
364	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
365	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
366	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
367	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
368	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
369	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
370	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
371	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
372	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
373	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
374	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
375	C₂²⋊C₄×C₈₃	—	2	1	no	—
376	C₂²⋊C₄×C₈₃	—	2	1	no	—
377	C₂²⋊C₄×C₈₃	—	2	1	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	—	2	2	no	—
388	C₂²⋊C₄×C₈₃	—	2	2	no	—
389	C₂²⋊C₄×C₈₃	—	2	2	no	—
390	C₂²⋊C₄×C₈₃	—	2	2	no	—
391	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
392	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
393	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
394	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
395	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
396	C₄²×C₈₃	—	2	1	no	—
397	C₄²×C₈₃	—	2	1	no	—
398	C₄²×C₈₃	—	2	1	no	—
399	C₄²×C₈₃	—	2	1	no	—
400	C₄²×C₈₃	—	2	2	no	—
401	C₄²×C₈₃	—	2	2	no	—
402	C₄²×C₈₃	—	2	2	no	—
403	C₄²×C₈₃	—	2	2	no	—
404	C₄²×C₈₃	—	2	2	no	—
405	C₄²×C₈₃	—	2	2	no	—
406	C₄²×C₈₃	C₂⁴	1	2	yes	—
407	C₂³×C₈₃	—	2	2	no	—
408	C₂³×C₈₃	—	4	1	no	—
409	C₂³×C₈₃	—	4	1	no	—
410	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
411	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
412	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
413	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
414	Q₈×C₈₃	—	2	2	no	—
415	Q₈×C₈₃	—	2	2	no	—
416	Q₈×C₈₃	—	2	2	no	—
417	Q₈×C₈₃	—	2	2	no	—
418	Q₈×C₈₃	—	2	2	no	—
419	Q₈×C₈₃	—	2	2	no	—
420	Q₈×C₈₃	—	4	1	no	—
421	Q₈×C₈₃	—	4	2	no	—
422	Q₈×C₈₃	—	8	2	no	—
423	Q₈×C₈₃	—	8	1	no	—
424	Q₈×C₈₃	—	8	1	no	—
425	Q₈×C₈₃	—	8	2	no	—
426	D₄×C₈₃	—	2	4	no	—
427	D₄×C₈₃	—	4	2	no	—
428	D₄×C₈₃	—	4	1	no	—
429	D₄×C₈₃	—	4	2	no	—
430	C₂×C₄×C₈₃	—	2	1	no	—
431	C₂×C₄×C₈₃	—	2	1	no	—
432	C₂×C₄×C₈₃	—	2	2	no	—
433	C₂×C₄×C₈₃	—	2	1	no	—
434	C₂×C₄×C₈₃	—	2	1	no	—
435	C₂×C₄×C₈₃	—	2	2	no	—
436	C₂×C₄×C₈₃	—	2	1	no	—
437	C₂×C₄×C₈₃	—	2	1	no	—
438	C₂×C₄×C₈₃	—	2	1	no	—
439	C₂×C₄×C₈₃	—	2	1	no	—
440	C₂×C₄×C₈₃	—	2	2	no	—
441	C₂×C₄×C₈₃	—	2	1	no	—
442	C₂×C₄×C₈₃	—	2	2	no	—
443	C₂×C₄×C₈₃	—	2	2	no	—
444	C₂×C₄×C₈₃	—	2	1	no	—
445	C₂×C₄×C₈₃	—	2	2	no	—
446	C₂×C₄×C₈₃	—	2	2	no	—
447	C₂×C₄×C₈₃	—	2	2	no	—
448	C₂×C₄×C₈₃	—	4	1	no	—
449	C₂×C₄×C₈₃	—	4	1	no	—
450	C₂×C₄×C₈₃	—	4	1	no	—
451	C₂×C₄×C₈₃	—	4	2	no	—
452	C₂×C₄×C₈₃	—	4	2	no	—
453	C₂×C₄×C₈₃	—	4	2	no	—
454	C₂×C₄×C₈₃	—	4	2	no	—
455	C₂×C₄×C₈₃	—	8	2	no	—
456	C₂×C₄×C₈₃	—	8	1	no	—
457	C₂×C₄×C₈₃	—	8	1	no	—
458	C₂×C₄×C₈₃	—	8	1	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	2	yes	—
463	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
465	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
468	C₈×C₈₃	—	2	2	no	—
469	C₈×C₈₃	—	2	2	no	—
470	C₈×C₈₃	—	2	2	no	—
471	C₈×C₈₃	—	2	2	no	—
472	C₂²×C₈₃	—	2	1	no	—
473	C₂²×C₈₃	—	2	1	no	—
474	C₂²×C₈₃	—	2	1	no	—
475	C₂²×C₈₃	—	2	2	no	—
476	C₂²×C₈₃	—	2	1	no	—
477	C₂²×C₈₃	—	2	1	no	—
478	C₂²×C₈₃	—	2	1	no	—
479	C₂²×C₈₃	—	2	2	no	—
480	C₂²×C₈₃	—	2	2	no	—
481	C₂²×C₈₃	—	2	1	no	—
482	C₂²×C₈₃	—	2	1	no	—
483	C₂²×C₈₃	—	8	2	no	—
484	C₂²×C₈₃	#578	1	2	yes	—
485	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
486	C₄×C₈₃	—	2	2	no	—
487	C₄×C₈₃	—	2	1	no	—
488	C₄×C₈₃	—	2	1	no	—
489	C₄×C₈₃	—	2	1	no	—
490	C₄×C₈₃	—	2	2	no	—
491	C₄×C₈₃	—	2	2	no	—
492	C₄×C₈₃	—	4	2	no	—
493	C₄×C₈₃	—	4	1	no	—
494	C₄×C₈₃	—	4	2	no	—
495	C₄×C₈₃	—	4	1	no	—
496	C₄×C₈₃	—	4	2	no	—
497	C₄×C₈₃	—	4	2	no	—
498	C₄×C₈₃	—	4	2	no	—
499	C₄×C₈₃	—	4	1	no	—
500	C₄×C₈₃	—	4	1	no	—
501	C₄×C₈₃	—	4	2	no	—
502	C₄×C₈₃	#585	1	1	yes	characteristic
503	C₄×C₈₃	#585	1	1	yes	characteristic
504	#61757	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
505	C₂×C₈₃	—	2	2	no	—
506	C₂×C₈₃	—	4	2	no	—
507	C₂×C₈₃	—	4	1	no	—
508	C₂×C₈₃	—	4	1	no	—
509	C₂×C₈₃	#3485	1	1	yes	characteristic
510	C₂×C₈₃	C₂×#578	1	1	yes	characteristic
511	C₂×C₈₃	#3586	1	1	yes	characteristic
512	#3538	C₂×C₈₃	1	1	yes	characteristic
513	#3495	C₂×C₈₃	1	1	yes	characteristic
514	#3352	C₂×C₈₃	1	2	yes	complemented
515	#3349	C₂×C₈₃	1	2	yes	complemented
516	#3344	C₂×C₈₃	1	2	yes	complemented
517	#3336	C₂×C₈₃	1	2	yes	complemented
518	#3328	C₂×C₈₃	1	2	yes	complemented
519	#3312	C₂×C₈₃	1	2	yes	complemented
520	#3312	C₂×C₈₃	1	2	yes	complemented
521	#3299	C₂×C₈₃	1	2	yes	complemented
522	#3242	C₂×C₈₃	1	2	yes	complemented
523	#3202	C₂×C₈₃	1	2	yes	complemented
524	#3195	C₂×C₈₃	1	1	yes	characteristic, complemented
525	#3189	C₂×C₈₃	1	1	yes	characteristic, complemented
526	#3127	C₂×C₈₃	1	2	yes	complemented
527	#3097	C₂×C₈₃	1	2	yes	complemented
528	#3095	C₂×C₈₃	1	1	yes	characteristic, complemented
529	C₂×#485	C₂×C₈₃	1	1	yes	characteristic, complemented
530	#2976	C₂×C₈₃	1	1	yes	characteristic
531	C₈₃	#61757	1	1	yes	characteristic, direct product factor, Sylow
532	#563	—	2	2	no	—
533	#556	C₂²×C₈₃	1	2	yes	—
534	#554	C₂²×C₈₃	1	2	yes	—
535	#552	—	2	2	no	—
536	#552	C₂²×C₈₃	1	2	yes	—
537	#552	C₂²×C₈₃	1	2	yes	—
538	#552	C₂²×C₈₃	1	2	yes	—
539	#552	C₂²×C₈₃	1	2	yes	—
540	#551	—	2	2	no	—
541	#551	—	2	2	no	—
542	D₄×Q₈	C₂²×C₈₃	1	2	yes	—
543	D₄×Q₈	C₂²×C₈₃	1	2	yes	—
544	#544	—	2	1	no	—
545	#544	—	2	1	no	—
546	#544	C₂²×C₈₃	1	1	yes	characteristic
547	#542	—	2	1	no	—
548	#541	—	2	1	no	—
549	#541	C₂²×C₈₃	1	2	yes	—
550	#539	—	2	1	no	—
551	#539	—	2	1	no	—
552	#536	C₂²×C₈₃	1	2	yes	—
553	#536	C₂²×C₈₃	1	1	yes	characteristic
554	#533	—	2	1	no	—
555	#529	—	2	1	no	—
556	#525	C₂²×C₈₃	1	1	yes	characteristic
557	C₂×C₂²⋊Q₈	C₂²×C₈₃	1	1	yes	characteristic
558	C₂×C₂²⋊Q₈	C₂²×C₈₃	1	1	yes	characteristic
559	C₂×C₂²⋊Q₈	C₂²×C₈₃	1	1	yes	characteristic
560	#520	C₂²×C₈₃	1	1	yes	characteristic
561	#519	C₂²×C₈₃	1	1	yes	characteristic
562	C₂×#117	C₂²×C₈₃	1	1	yes	characteristic
563	#501	C₂²×C₈₃	1	2	yes	complemented
564	#499	C₂²×C₈₃	1	2	yes	complemented
565	#491	C₂²×C₈₃	1	2	yes	complemented
566	#487	C₂²×C₈₃	1	2	yes	complemented
567	#485	C₂²×C₈₃	1	2	yes	—
568	#485	C₂²×C₈₃	1	2	yes	—
569	#485	C₂²×C₈₃	1	2	yes	—
570	#485	C₂²×C₈₃	1	2	yes	—
571	#485	C₂²×C₈₃	1	2	yes	—
572	#485	C₂²×C₈₃	1	2	yes	—
573	#485	C₂²×C₈₃	1	2	yes	complemented
574	#485	C₂²×C₈₃	1	2	yes	complemented
575	#485	C₂²×C₈₃	1	2	yes	complemented
576	#485	C₂²×C₈₃	1	2	yes	complemented
577	#484	C₂²×C₈₃	1	2	yes	—
578	#484	C₂²×C₈₃	1	2	yes	—
579	#484	C₂²×C₈₃	1	2	yes	—
580	#484	C₂²×C₈₃	1	2	yes	complemented
581	#483	C₂²×C₈₃	1	2	yes	—
582	#483	C₂²×C₈₃	1	2	yes	—
583	#483	C₂²×C₈₃	1	2	yes	—
584	#483	C₂²×C₈₃	1	2	yes	complemented
585	#479	C₂²×C₈₃	1	2	yes	complemented
586	#479	C₂²×C₈₃	1	2	yes	complemented
587	#479	C₂²×C₈₃	1	2	yes	complemented
588	#479	C₂²×C₈₃	1	2	yes	complemented
589	#477	C₂²×C₈₃	1	2	yes	complemented
590	#475	C₂²×C₈₃	1	2	yes	complemented
591	#470	C₂²×C₈₃	1	2	yes	—
592	#470	C₂²×C₈₃	1	2	yes	—
593	#470	C₂²×C₈₃	1	2	yes	complemented
594	#470	C₂²×C₈₃	1	2	yes	complemented
595	#467	C₂²×C₈₃	1	2	yes	—
596	#467	C₂²×C₈₃	1	2	yes	—
597	#467	C₂²×C₈₃	1	2	yes	complemented
598	#467	C₂²×C₈₃	1	2	yes	complemented
599	#462	C₂²×C₈₃	1	2	yes	complemented
600	#462	C₂²×C₈₃	1	2	yes	complemented
601	#451	C₂²×C₈₃	1	2	yes	—
602	#451	C₂²×C₈₃	1	2	yes	—
603	#451	C₂²×C₈₃	1	2	yes	—
604	#451	C₂²×C₈₃	1	2	yes	—
605	#451	C₂²×C₈₃	1	2	yes	complemented
606	#451	C₂²×C₈₃	1	2	yes	complemented
607	#441	C₂²×C₈₃	1	2	yes	complemented
608	#441	C₂²×C₈₃	1	2	yes	complemented
609	C₄×Q₁₆	C₂²×C₈₃	1	2	yes	complemented
610	C₄×Q₁₆	C₂²×C₈₃	1	2	yes	complemented
611	#436	C₂²×C₈₃	1	2	yes	—
612	#435	C₂²×C₈₃	1	2	yes	—
613	#435	C₂²×C₈₃	1	2	yes	—
614	C₈×D₄	C₂²×C₈₃	1	2	yes	—
615	#433	C₂²×C₈₃	1	2	yes	—
616	#428	C₂²×C₈₃	1	1	yes	characteristic
617	#428	C₂²×C₈₃	1	1	yes	characteristic
618	#428	C₂²×C₈₃	1	2	yes	complemented
619	#427	C₂²×C₈₃	1	2	yes	complemented
620	C₂×#107	C₂²×C₈₃	1	1	yes	characteristic
621	C₂×#106	C₂²×C₈₃	1	1	yes	characteristic
622	#419	C₂²×C₈₃	1	1	yes	characteristic
623	#419	C₂²×C₈₃	1	1	yes	characteristic
624	#419	C₂²×C₈₃	1	2	yes	complemented
625	C₂×#103	C₂²×C₈₃	1	1	yes	characteristic
626	C₂×#103	C₂²×C₈₃	1	1	yes	characteristic
627	C₂×#103	C₂²×C₈₃	1	2	yes	complemented
628	#408	C₂²×C₈₃	1	2	yes	—
629	#407	C₂²×C₈₃	1	1	yes	characteristic
630	C₂×C₂²⋊C₈	C₂²×C₈₃	1	1	yes	characteristic
631	C₂×#41	C₂³×C₈₃	1	1	yes	characteristic
632	C₂²×Q₈	C₂³×C₈₃	1	1	yes	characteristic
633	C₂²×Q₈	C₂³×C₈₃	1	1	yes	characteristic
634	C₂²×Q₈	C₂³×C₈₃	1	1	yes	characteristic
635	C₂²×Q₈	C₂³×C₈₃	1	2	yes	—
636	C₂³×C₄	C₂³×C₈₃	1	1	yes	characteristic
637	C₂×Q₁₆	C₂³×C₈₃	1	2	yes	—
638	C₂×Q₁₆	C₂³×C₈₃	1	2	yes	—
639	C₂×Q₁₆	C₂³×C₈₃	1	2	yes	—
640	C₂×Q₁₆	C₂³×C₈₃	1	2	yes	—
641	C₂×M₁₆	C₂³×C₈₃	1	1	yes	characteristic
642	C₂×M₁₆	C₂³×C₈₃	1	1	yes	characteristic
643	C₂×M₁₆	C₂³×C₈₃	1	2	yes	—
644	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
645	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
646	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
647	C₄⋊Q₈	—	2	1	no	—
648	C₄⋊Q₈	—	2	2	no	—
649	C₄⋊Q₈	—	2	1	no	—
650	C₄⋊Q₈	—	2	2	no	—
651	C₄⋊Q₈	—	2	2	no	—
652	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
653	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
654	#126	—	2	2	no	—
655	#126	—	2	2	no	—
656	#126	—	2	2	no	—
657	#126	—	2	2	no	—
658	#126	—	2	2	no	—
659	#126	—	2	2	no	—
660	#126	—	2	2	no	—
661	#126	—	2	2	no	—
662	#125	—	2	1	no	—
663	#125	—	2	2	no	—
664	#125	—	2	2	no	—
665	#125	—	2	2	no	—
666	#125	—	2	2	no	—
667	#125	—	2	2	no	—
668	#125	—	2	2	no	—
669	#125	—	2	2	no	—
670	#125	C₂³×C₈₃	1	2	yes	—
671	#125	C₂³×C₈₃	1	2	yes	—
672	#124	—	2	1	no	—
673	#124	—	2	2	no	—
674	#124	—	2	2	no	—
675	#123	—	2	2	no	—
676	#123	—	2	2	no	—
677	#123	—	2	2	no	—
678	#123	—	2	2	no	—
679	#123	—	2	2	no	—
680	#123	—	2	2	no	—
681	#123	—	2	2	no	—
682	#123	D₄×C₈₃	1	2	yes	—
683	C₂²⋊Q₈	—	2	1	no	—
684	C₂²⋊Q₈	—	2	1	no	—
685	C₂²⋊Q₈	—	2	1	no	—
686	C₂²⋊Q₈	—	2	1	no	—
687	C₂²⋊Q₈	—	2	1	no	—
688	C₂²⋊Q₈	—	2	1	no	—
689	C₂²⋊Q₈	—	2	2	no	—
690	C₂²⋊Q₈	—	2	2	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	D₄×C₈₃	1	1	yes	characteristic
697	C₂²⋊Q₈	D₄×C₈₃	1	1	yes	characteristic
698	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
699	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
700	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
701	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
702	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
703	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
704	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
705	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
706	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
707	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
708	#121	D₄×C₈₃	1	1	yes	characteristic
709	#121	D₄×C₈₃	1	1	yes	characteristic
710	#120	D₄×C₈₃	1	2	yes	—
711	C₄×Q₈	—	2	1	no	—
712	C₄×Q₈	—	2	1	no	—
713	C₄×Q₈	—	2	1	no	—
714	C₄×Q₈	—	2	2	no	—
715	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
716	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
717	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
718	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
719	C₄×D₄	—	2	1	no	—
720	C₄×D₄	—	2	2	no	—
721	C₄×D₄	—	2	2	no	—
722	C₄×D₄	—	2	2	no	—
723	C₄×D₄	—	2	2	no	—
724	C₄×D₄	C₂³×C₈₃	1	2	yes	—
725	C₄×D₄	C₂³×C₈₃	1	2	yes	—
726	#117	—	2	1	no	—
727	#117	—	2	1	no	—
728	#117	—	2	2	no	—
729	#117	—	2	2	no	—
730	#117	—	2	2	no	—
731	#117	—	2	2	no	—
732	#117	—	2	2	no	—
733	#117	C₂³×C₈₃	1	1	yes	characteristic
734	#117	C₂³×C₈₃	1	1	yes	characteristic
735	#117	C₂³×C₈₃	1	1	yes	characteristic
736	#117	C₂³×C₈₃	1	1	yes	characteristic
737	#117	C₂³×C₈₃	1	2	yes	—
738	#117	C₂³×C₈₃	1	2	yes	—
739	#117	C₂³×C₈₃	1	1	yes	characteristic
740	C₂×C₄⋊C₄	—	2	1	no	—
741	C₂×C₄⋊C₄	—	2	1	no	—
742	C₂×C₄⋊C₄	—	2	1	no	—
743	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
744	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
745	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
746	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
747	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
748	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
749	C₂×C₂²⋊C₄	—	2	1	no	—
750	C₂×C₂²⋊C₄	—	2	1	no	—
751	C₂×C₂²⋊C₄	—	2	1	no	—
752	C₂×C₂²⋊C₄	—	2	1	no	—
753	C₂×C₄²	—	2	1	no	—
754	#107	C₂³×C₈₃	1	2	yes	—
755	#107	C₂³×C₈₃	1	2	yes	—
756	#107	C₂³×C₈₃	1	2	yes	—
757	#107	C₂³×C₈₃	1	2	yes	—
758	#107	C₂³×C₈₃	1	2	yes	—
759	#107	C₂³×C₈₃	1	2	yes	—
760	#106	C₂³×C₈₃	1	2	yes	—
761	#106	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	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
767	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
768	#103	C₂³×C₈₃	1	2	yes	—
769	#103	C₂³×C₈₃	1	2	yes	—
770	#103	C₂³×C₈₃	1	2	yes	—
771	#103	C₂³×C₈₃	1	2	yes	—
772	#103	C₂³×C₈₃	1	2	yes	—
773	#103	C₂³×C₈₃	1	2	yes	—
774	#103	C₂³×C₈₃	1	2	yes	—
775	#103	C₂³×C₈₃	1	2	yes	—
776	#103	C₂³×C₈₃	1	2	yes	—
777	#103	C₂³×C₈₃	1	2	yes	—
778	#103	C₂³×C₈₃	1	2	yes	—
779	#103	C₂³×C₈₃	1	2	yes	—
780	#103	C₂³×C₈₃	1	2	yes	—
781	#103	C₂³×C₈₃	1	2	yes	—
782	#103	C₂³×C₈₃	1	2	yes	—
783	#103	C₂³×C₈₃	1	2	yes	—
784	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
785	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
786	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
787	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
788	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
789	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
790	#97	C₂³×C₈₃	1	2	yes	—
791	C₄×C₈	C₂³×C₈₃	1	2	yes	—
792	C₂⁴	C₂×D₄×C₈₃	1	1	yes	characteristic
793	#41	—	4	1	no	—
794	#41	—	4	1	no	—
795	C₂×Q₈	—	2	1	no	—
796	C₂×Q₈	—	2	2	no	—
797	C₂×Q₈	—	2	1	no	—
798	C₂×Q₈	—	2	1	no	—
799	C₂×Q₈	—	2	2	no	—
800	C₂×Q₈	—	4	1	no	—
801	C₂×Q₈	—	4	1	no	—
802	C₂×Q₈	—	4	1	no	—
803	C₂×Q₈	—	4	1	no	—
804	C₂×Q₈	—	4	2	no	—
805	C₂×Q₈	—	4	1	no	—
806	C₂×Q₈	—	4	1	no	—
807	C₂×Q₈	—	4	2	no	—
808	C₂×Q₈	C₂×D₄×C₈₃	1	1	yes	characteristic
809	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
810	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
811	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
812	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
813	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
814	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
815	C₂×D₄	C₂×D₄×C₈₃	1	1	yes	characteristic
816	C₂²×C₄	—	2	1	no	—
817	C₂²×C₄	—	2	1	no	—
818	C₂²×C₄	—	2	1	no	—
819	C₂²×C₄	—	2	1	no	—
820	C₂²×C₄	—	2	1	no	—
821	C₂²×C₄	—	2	1	no	—
822	C₂²×C₄	—	2	1	no	—
823	C₂²×C₄	—	2	1	no	—
824	C₂²×C₄	—	2	2	no	—
825	C₂²×C₄	—	2	2	no	—
826	C₂²×C₄	—	4	1	no	—
827	C₂²×C₄	—	4	1	no	—
828	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
829	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
830	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
831	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
832	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
833	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
834	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
835	Q₁₆	—	4	2	no	—
836	Q₁₆	—	4	2	no	—
837	Q₁₆	—	4	2	no	—
838	Q₁₆	—	4	2	no	—
839	M₁₆	—	4	1	no	—
840	M₁₆	—	4	2	no	—
841	M₁₆	—	4	1	no	—
842	C₂×C₈	—	4	1	no	—
843	C₂×C₈	—	4	2	no	—
844	C₂×C₈	—	4	1	no	—
845	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
846	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
847	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
848	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	2	2	no	—
852	C₄⋊C₄	—	2	2	no	—
853	C₄⋊C₄	—	2	2	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	1	no	—
856	C₄⋊C₄	—	2	1	no	—
857	C₄⋊C₄	—	2	1	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	1	no	—
860	C₄⋊C₄	—	2	1	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	2	no	—
863	C₄⋊C₄	—	2	2	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	2	no	—
867	C₄⋊C₄	—	2	2	no	—
868	C₄⋊C₄	—	2	2	no	—
869	C₄⋊C₄	—	2	2	no	—
870	C₄⋊C₄	—	2	2	no	—
871	C₄⋊C₄	—	2	2	no	—
872	C₄⋊C₄	—	2	2	no	—
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	—	2	2	no	—
876	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
877	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
878	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
879	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
880	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
881	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
882	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
883	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
884	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
885	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
886	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
887	C₂²⋊C₄	—	2	1	no	—
888	C₂²⋊C₄	—	2	1	no	—
889	C₂²⋊C₄	—	2	1	no	—
890	C₂²⋊C₄	—	2	1	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	2	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	C₂×D₄×C₈₃	1	2	yes	—
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	C₄²	—	2	1	no	—
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	—	2	2	no	—
915	C₄²	—	2	2	no	—
916	C₄²	—	2	2	no	—
917	C₄²	—	2	2	no	—
918	C₄²	C₂⁴×C₈₃	1	2	yes	—
919	C₂³	—	2	2	no	—
920	C₂³	—	4	1	no	—
921	C₂³	—	4	1	no	—
922	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
923	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
924	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
925	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
926	Q₈	—	2	2	no	—
927	Q₈	—	2	2	no	—
928	Q₈	—	2	2	no	—
929	Q₈	—	2	2	no	—
930	Q₈	—	2	2	no	—
931	Q₈	—	2	2	no	—
932	Q₈	—	4	1	no	—
933	Q₈	—	4	2	no	—
934	Q₈	—	8	1	no	—
935	Q₈	—	8	1	no	—
936	Q₈	—	8	2	no	—
937	Q₈	—	8	2	no	—
938	D₄	—	2	4	no	—
939	D₄	—	4	1	no	—
940	D₄	—	4	2	no	—
941	D₄	—	4	2	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	4	1	no	—
961	C₂×C₄	—	4	1	no	—
962	C₂×C₄	—	4	1	no	—
963	C₂×C₄	—	4	2	no	—
964	C₂×C₄	—	4	2	no	—
965	C₂×C₄	—	4	2	no	—
966	C₂×C₄	—	4	2	no	—
967	C₂×C₄	—	8	1	no	—
968	C₂×C₄	—	8	1	no	—
969	C₂×C₄	—	8	2	no	—
970	C₂×C₄	—	8	2	no	—
971	C₂×C₄	—	8	1	no	—
972	C₂×C₄	—	8	1	no	—
973	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
974	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
975	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
976	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
977	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
978	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
979	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
980	C₈	—	2	2	no	—
981	C₈	—	2	2	no	—
982	C₈	—	2	2	no	—
983	C₈	—	2	2	no	—
984	C₂²	—	2	1	no	—
985	C₂²	—	2	1	no	—
986	C₂²	—	2	2	no	—
987	C₂²	—	2	1	no	—
988	C₂²	—	2	1	no	—
989	C₂²	—	2	1	no	—
990	C₂²	—	2	2	no	—
991	C₂²	—	2	1	no	—
992	C₂²	—	2	1	no	—
993	C₂²	—	2	1	no	—
994	C₂²	—	2	2	no	—
995	C₂²	—	8	2	no	—
996	C₂²	#578×C₈₃	1	2	yes	—
997	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
998	C₄	—	2	2	no	—
999	C₄	—	2	2	no	—
1000	C₄	—	2	1	no	—
1001	C₄	—	2	1	no	—
1002	C₄	—	2	1	no	—
1003	C₄	—	2	2	no	—
1004	C₄	—	4	1	no	—
1005	C₄	—	4	1	no	—
1006	C₄	—	4	2	no	—
1007	C₄	—	4	2	no	—
1008	C₄	—	4	1	no	—
1009	C₄	—	4	2	no	—
1010	C₄	—	4	1	no	—
1011	C₄	—	4	2	no	—
1012	C₄	—	4	2	no	—
1013	C₄	—	4	2	no	—
1014	C₄	#585×C₈₃	1	1	yes	characteristic
1015	C₄	#585×C₈₃	1	1	yes	characteristic
1016	C₂	—	2	2	no	—
1017	C₂	—	4	1	no	—
1018	C₂	—	4	1	no	—
1019	C₂	—	4	2	no	—
1020	C₂	C₈₃×#3485	1	1	yes	characteristic
1021	C₂	C₂×#578×C₈₃	1	1	yes	characteristic
1022	C₂	C₈₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₃
prime radical	#525×C₈₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₃ ◁ #525×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₈₃×#3352	C₂	semidirect
4. C₈₃×#3349	C₂	semidirect
5. C₈₃×#3344	C₂	semidirect
6. C₈₃×#3336	C₂	semidirect
7. C₈₃×#3328	C₂	semidirect
8. C₈₃×#3312	C₂	semidirect
9. C₈₃×#3312	C₂	semidirect
10. C₈₃×#3299	C₂	semidirect
11. C₈₃×#3242	C₂	semidirect
12. C₈₃×#3202	C₂	semidirect
13. C₈₃×#3195	C₂	semidirect
14. C₈₃×#3189	C₂	semidirect
15. C₈₃×#3127	C₂	semidirect
16. C₈₃×#3097	C₂	semidirect
17. C₈₃×#3095	C₂	semidirect
18. C₂×#485×C₈₃	C₂	semidirect
51. #501×C₈₃	C₂²	semidirect
52. #499×C₈₃	C₂²	semidirect
53. #491×C₈₃	C₂²	semidirect
54. #487×C₈₃	C₂²	semidirect
61. #485×C₈₃	C₂²	semidirect
62. #485×C₈₃	C₂²	semidirect
63. #485×C₈₃	C₂²	semidirect
64. #485×C₈₃	C₂²	semidirect
68. #484×C₈₃	C₂²	semidirect
72. #483×C₈₃	C₂²	semidirect
73. #479×C₈₃	C₂²	semidirect
74. #479×C₈₃	C₂²	semidirect
75. #479×C₈₃	C₂²	semidirect
76. #479×C₈₃	C₂²	semidirect
77. #477×C₈₃	C₂²	semidirect
78. #475×C₈₃	C₂²	semidirect
81. #470×C₈₃	C₂²	semidirect
82. #470×C₈₃	C₂²	semidirect
85. #467×C₈₃	C₂²	semidirect
86. #467×C₈₃	C₂²	semidirect
87. #462×C₈₃	C₂²	semidirect
88. #462×C₈₃	C₂²	semidirect
93. #451×C₈₃	C₂²	semidirect
94. #451×C₈₃	C₂²	semidirect
95. #441×C₈₃	C₂²	semidirect
96. #441×C₈₃	C₂²	semidirect
97. C₄×Q₁₆×C₈₃	C₂²	semidirect
98. C₄×Q₁₆×C₈₃	C₂²	semidirect
106. #428×C₈₃	C₂²	semidirect
107. #427×C₈₃	C₂²	semidirect
112. #419×C₈₃	C₂²	semidirect
115. C₂×#103×C₈₃	C₂²	semidirect
504. #61757	C₈₃	direct (N × H)
514. #3352	C₂×C₈₃	semidirect
515. #3349	C₂×C₈₃	semidirect
516. #3344	C₂×C₈₃	semidirect
517. #3336	C₂×C₈₃	semidirect
518. #3328	C₂×C₈₃	semidirect
519. #3312	C₂×C₈₃	semidirect
520. #3312	C₂×C₈₃	semidirect
521. #3299	C₂×C₈₃	semidirect
522. #3242	C₂×C₈₃	semidirect
523. #3202	C₂×C₈₃	semidirect
524. #3195	C₂×C₈₃	semidirect
525. #3189	C₂×C₈₃	semidirect
526. #3127	C₂×C₈₃	semidirect
527. #3097	C₂×C₈₃	semidirect
528. #3095	C₂×C₈₃	semidirect
529. C₂×#485	C₂×C₈₃	semidirect
531. C₈₃	#61757	direct (N × H)
563. #501	C₂²×C₈₃	semidirect
564. #499	C₂²×C₈₃	semidirect
565. #491	C₂²×C₈₃	semidirect
566. #487	C₂²×C₈₃	semidirect
573. #485	C₂²×C₈₃	semidirect
574. #485	C₂²×C₈₃	semidirect
575. #485	C₂²×C₈₃	semidirect
576. #485	C₂²×C₈₃	semidirect
580. #484	C₂²×C₈₃	semidirect
584. #483	C₂²×C₈₃	semidirect
585. #479	C₂²×C₈₃	semidirect
586. #479	C₂²×C₈₃	semidirect
587. #479	C₂²×C₈₃	semidirect
588. #479	C₂²×C₈₃	semidirect
589. #477	C₂²×C₈₃	semidirect
590. #475	C₂²×C₈₃	semidirect
593. #470	C₂²×C₈₃	semidirect
594. #470	C₂²×C₈₃	semidirect
597. #467	C₂²×C₈₃	semidirect
598. #467	C₂²×C₈₃	semidirect
599. #462	C₂²×C₈₃	semidirect
600. #462	C₂²×C₈₃	semidirect
605. #451	C₂²×C₈₃	semidirect
606. #451	C₂²×C₈₃	semidirect
607. #441	C₂²×C₈₃	semidirect
608. #441	C₂²×C₈₃	semidirect
609. C₄×Q₁₆	C₂²×C₈₃	semidirect
610. C₄×Q₁₆	C₂²×C₈₃	semidirect
618. #428	C₂²×C₈₃	semidirect
619. #427	C₂²×C₈₃	semidirect
624. #419	C₂²×C₈₃	semidirect
627. C₂×#103	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×#3538	2
C₈₃×#3495	2
C₈₃×#3352	2
C₈₃×#3349	2
C₈₃×#3344	2
C₈₃×#3336	2
C₈₃×#3328	2
C₈₃×#3312	2
C₈₃×#3299	2
C₈₃×#3242	2
C₈₃×#3202	2
C₈₃×#3195	2
C₈₃×#3189	2
C₈₃×#3127	2
C₈₃×#3097	2
C₈₃×#3095	2
C₂×#485×C₈₃	2
C₈₃×#2976	2
#61757	83

Subgroups — C83×#61757 #35289581

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#61757 #35289581