Subgroups — C₈₃×#61794 #35289618

Order 21248.

1674 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3547	C₂	1	1	yes	maximal, characteristic
2	C₈₃×#3507	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₃×#3349	C₂	1	2	yes	maximal, complemented
4	C₈₃×#3348	C₂	1	2	yes	maximal, complemented
5	C₈₃×#3344	C₂	1	2	yes	maximal, complemented
6	C₈₃×#3344	C₂	1	2	yes	maximal, complemented
7	C₈₃×#3316	C₂	1	2	yes	maximal, complemented
8	C₈₃×#3315	C₂	1	2	yes	maximal, complemented
9	C₈₃×#3313	C₂	1	2	yes	maximal, complemented
10	C₈₃×#3312	C₂	1	2	yes	maximal, complemented
11	C₈₃×#3240	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₃×#3237	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₃×#3202	C₂	1	2	yes	maximal, complemented
14	C₈₃×#3201	C₂	1	2	yes	maximal, complemented
15	C₈₃×#3117	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₃×#3113	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₃×#3099	C₂	1	2	yes	maximal, complemented
18	C₈₃×#3097	C₂	1	2	yes	maximal, complemented
19	C₈₃×#2980	C₂	1	1	yes	maximal, characteristic, complemented
20	#562×C₈₃	—	2	2	no	—
21	#559×C₈₃	—	2	1	no	—
22	#557×C₈₃	—	2	1	no	—
23	#556×C₈₃	—	2	2	no	—
24	#556×C₈₃	C₂²	1	2	yes	—
25	#555×C₈₃	—	2	1	no	—
26	#555×C₈₃	C₂²	1	1	yes	characteristic
27	#554×C₈₃	C₂²	1	1	yes	characteristic
28	#554×C₈₃	C₂²	1	2	yes	—
29	#553×C₈₃	—	2	1	no	—
30	#552×C₈₃	C₂²	1	2	yes	—
31	#552×C₈₃	C₂²	1	2	yes	—
32	#552×C₈₃	C₂²	1	2	yes	—
33	D₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
34	#548×C₈₃	C₂²	1	2	yes	—
35	#547×C₈₃	C₂²	1	1	yes	characteristic
36	#544×C₈₃	—	2	1	no	—
37	#542×C₈₃	—	2	2	no	—
38	#540×C₈₃	—	2	1	no	—
39	#539×C₈₃	—	2	1	no	—
40	#539×C₈₃	—	2	1	no	—
41	#537×C₈₃	C₂²	1	2	yes	—
42	#536×C₈₃	C₂²	1	2	yes	—
43	#536×C₈₃	C₂²	1	2	yes	—
44	#533×C₈₃	C₂²	1	1	yes	characteristic
45	#533×C₈₃	C₂²	1	1	yes	characteristic
46	#532×C₈₃	C₂²	1	1	yes	characteristic
47	#529×C₈₃	—	2	2	no	—
48	#529×C₈₃	C₂²	1	1	yes	characteristic
49	#520×C₈₃	C₂²	1	2	yes	—
50	C₂×C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
51	#501×C₈₃	C₂²	1	1	yes	characteristic
52	#501×C₈₃	C₂²	1	2	yes	—
53	#501×C₈₃	C₂²	1	1	yes	characteristic
54	#491×C₈₃	C₂²	1	2	yes	—
55	#489×C₈₃	C₂²	1	1	yes	characteristic
56	#489×C₈₃	C₂²	1	1	yes	characteristic
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	—
62	#485×C₈₃	C₂²	1	2	yes	—
63	#485×C₈₃	C₂²	1	2	yes	—
64	#485×C₈₃	C₂²	1	2	yes	—
65	#484×C₈₃	C₂²	1	2	yes	—
66	#484×C₈₃	C₂²	1	2	yes	—
67	#484×C₈₃	C₂²	1	1	yes	characteristic
68	#483×C₈₃	C₂²	1	2	yes	—
69	#483×C₈₃	C₂²	1	2	yes	—
70	#483×C₈₃	C₂²	1	2	yes	—
71	#483×C₈₃	C₂²	1	2	yes	—
72	#482×C₈₃	C₂²	1	2	yes	—
73	#482×C₈₃	C₂²	1	2	yes	—
74	#481×C₈₃	C₂²	1	2	yes	—
75	#481×C₈₃	C₂²	1	1	yes	characteristic
76	#479×C₈₃	C₂²	1	2	yes	—
77	#479×C₈₃	C₂²	1	2	yes	—
78	#478×C₈₃	C₂²	1	2	yes	—
79	#477×C₈₃	C₂²	1	2	yes	—
80	#475×C₈₃	C₂²	1	2	yes	—
81	#475×C₈₃	C₂²	1	2	yes	—
82	#470×C₈₃	C₂²	1	2	yes	—
83	#470×C₈₃	C₂²	1	2	yes	—
84	#470×C₈₃	C₂²	1	2	yes	—
85	#468×C₈₃	C₂²	1	2	yes	—
86	#467×C₈₃	C₂²	1	2	yes	—
87	#467×C₈₃	C₂²	1	2	yes	—
88	#467×C₈₃	C₂²	1	2	yes	—
89	#465×C₈₃	C₂²	1	2	yes	—
90	#464×C₈₃	C₂²	1	2	yes	—
91	#462×C₈₃	C₂²	1	2	yes	—
92	#452×C₈₃	C₂²	1	2	yes	—
93	#452×C₈₃	C₂²	1	2	yes	—
94	#451×C₈₃	C₂²	1	2	yes	—
95	#451×C₈₃	C₂²	1	2	yes	—
96	#451×C₈₃	C₂²	1	2	yes	—
97	#451×C₈₃	C₂²	1	1	yes	characteristic
98	#448×C₈₃	C₂²	1	1	yes	characteristic
99	#441×C₈₃	C₂²	1	2	yes	—
100	#441×C₈₃	C₂²	1	2	yes	—
101	#441×C₈₃	C₂²	1	2	yes	—
102	#440×C₈₃	C₂²	1	2	yes	—
103	#435×C₈₃	C₂²	1	2	yes	—
104	#435×C₈₃	C₂²	1	2	yes	—
105	#435×C₈₃	C₂²	1	2	yes	—
106	#435×C₈₃	C₂²	1	2	yes	—
107	#432×C₈₃	C₂²	1	1	yes	characteristic
108	#432×C₈₃	C₂²	1	1	yes	characteristic
109	#428×C₈₃	C₂²	1	2	yes	—
110	#428×C₈₃	C₂²	1	2	yes	—
111	#427×C₈₃	C₂²	1	2	yes	—
112	C₂×#106×C₈₃	C₂²	1	2	yes	—
113	#419×C₈₃	C₂²	1	2	yes	—
114	#417×C₈₃	C₂²	1	2	yes	—
115	#416×C₈₃	C₂²	1	2	yes	—
116	C₂×#103×C₈₃	C₂²	1	2	yes	—
117	#408×C₈₃	C₂²	1	2	yes	—
118	#408×C₈₃	C₂²	1	2	yes	—
119	C₂×#41×C₈₃	C₂³	1	2	yes	—
120	C₂×#41×C₈₃	C₂³	1	2	yes	—
121	C₂²×Q₈×C₈₃	C₂³	1	1	yes	characteristic
122	C₂²×Q₈×C₈₃	C₂³	1	2	yes	—
123	C₂×Q₁₆×C₈₃	C₂³	1	2	yes	—
124	C₂×Q₁₆×C₈₃	C₂³	1	2	yes	—
125	C₂×Q₁₆×C₈₃	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
127	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
128	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
129	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
130	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
131	C₄⋊Q₈×C₈₃	—	2	2	no	—
132	C₄⋊Q₈×C₈₃	—	2	2	no	—
133	C₄⋊Q₈×C₈₃	—	2	1	no	—
134	C₄⋊Q₈×C₈₃	D₄	1	1	yes	characteristic
135	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
136	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
137	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
138	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
139	#127×C₈₃	D₄	1	1	yes	characteristic
140	#126×C₈₃	—	2	2	no	—
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	—	2	1	no	—
146	#125×C₈₃	—	2	2	no	—
147	#125×C₈₃	—	2	2	no	—
148	#125×C₈₃	—	2	2	no	—
149	#125×C₈₃	—	2	2	no	—
150	#125×C₈₃	—	2	1	no	—
151	#125×C₈₃	—	2	1	no	—
152	#125×C₈₃	C₂³	1	2	yes	—
153	#125×C₈₃	C₂³	1	1	yes	characteristic
154	#124×C₈₃	—	2	2	no	—
155	#124×C₈₃	—	2	2	no	—
156	#124×C₈₃	—	2	2	no	—
157	#124×C₈₃	—	2	2	no	—
158	#124×C₈₃	—	2	2	no	—
159	#124×C₈₃	D₄	1	2	yes	—
160	#124×C₈₃	C₂³	1	1	yes	characteristic
161	#123×C₈₃	—	2	2	no	—
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	1	no	—
169	#123×C₈₃	—	2	2	no	—
170	C₂²⋊Q₈×C₈₃	—	2	2	no	—
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	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	C₂³	1	2	yes	—
180	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
181	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
182	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
183	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
184	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
185	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
186	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
187	C₂²⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
188	#121×C₈₃	—	2	2	no	—
189	#121×C₈₃	—	2	2	no	—
190	#121×C₈₃	—	2	2	no	—
191	#121×C₈₃	—	2	1	no	—
192	#121×C₈₃	—	2	2	no	—
193	#121×C₈₃	—	2	1	no	—
194	#121×C₈₃	D₄	1	2	yes	—
195	#121×C₈₃	D₄	1	1	yes	characteristic
196	#121×C₈₃	D₄	1	1	yes	characteristic
197	#121×C₈₃	C₂³	1	2	yes	—
198	#121×C₈₃	C₂³	1	1	yes	characteristic
199	C₄×Q₈×C₈₃	—	2	2	no	—
200	C₄×Q₈×C₈₃	—	2	2	no	—
201	C₄×Q₈×C₈₃	—	2	1	no	—
202	C₄×Q₈×C₈₃	—	2	1	no	—
203	C₄×Q₈×C₈₃	—	2	1	no	—
204	C₄×Q₈×C₈₃	—	2	1	no	—
205	C₄×Q₈×C₈₃	—	2	1	no	—
206	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
207	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
208	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
209	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
210	C₄×D₄×C₈₃	—	2	2	no	—
211	C₄×D₄×C₈₃	—	2	2	no	—
212	C₄×D₄×C₈₃	—	2	2	no	—
213	C₄×D₄×C₈₃	—	2	2	no	—
214	C₄×D₄×C₈₃	—	2	1	no	—
215	C₄×D₄×C₈₃	—	2	1	no	—
216	C₄×D₄×C₈₃	—	2	1	no	—
217	C₄×D₄×C₈₃	—	2	2	no	—
218	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
219	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
220	C₄×D₄×C₈₃	C₂³	1	2	yes	—
221	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
222	#117×C₈₃	—	2	1	no	—
223	#117×C₈₃	—	2	1	no	—
224	#117×C₈₃	—	2	2	no	—
225	#117×C₈₃	—	2	2	no	—
226	#117×C₈₃	—	2	2	no	—
227	#117×C₈₃	—	2	1	no	—
228	#117×C₈₃	C₂³	1	2	yes	—
229	#117×C₈₃	C₂³	1	2	yes	—
230	#117×C₈₃	C₂³	1	2	yes	—
231	#117×C₈₃	C₂³	1	2	yes	—
232	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
233	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
234	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
236	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
237	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
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	#103×C₈₃	C₂³	1	2	yes	—
255	#103×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	#102×C₈₃	C₂³	1	2	yes	—
268	#102×C₈₃	C₂³	1	2	yes	—
269	#102×C₈₃	C₂³	1	2	yes	—
270	C₂²⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
271	C₂²⋊C₈×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	1	yes	characteristic
277	#97×C₈₃	C₂³	1	1	yes	characteristic
278	#97×C₈₃	C₂³	1	1	yes	characteristic
279	#97×C₈₃	C₂³	1	2	yes	—
280	#41×C₈₃	—	4	2	no	—
281	#41×C₈₃	—	4	2	no	—
282	#41×C₈₃	—	4	2	no	—
283	#41×C₈₃	—	4	2	no	—
284	C₂×Q₈×C₈₃	—	2	1	no	—
285	C₂×Q₈×C₈₃	—	2	1	no	—
286	C₂×Q₈×C₈₃	—	2	1	no	—
287	C₂×Q₈×C₈₃	—	2	1	no	—
288	C₂×Q₈×C₈₃	—	2	2	no	—
289	C₂×Q₈×C₈₃	—	4	2	no	—
290	C₂×Q₈×C₈₃	—	4	2	no	—
291	C₂×Q₈×C₈₃	—	4	2	no	—
292	C₂×Q₈×C₈₃	C₂×D₄	1	2	yes	—
293	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
294	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
295	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
296	C₂×D₄×C₈₃	—	2	1	no	—
297	C₂×D₄×C₈₃	—	2	2	no	—
298	C₂×D₄×C₈₃	—	2	2	no	—
299	C₂×D₄×C₈₃	C₂×D₄	1	1	yes	characteristic
300	C₂×D₄×C₈₃	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
304	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
305	C₂×D₄×C₈₃	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₈₃	—	2	1	no	—
307	C₂²×C₄×C₈₃	—	2	1	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	2	no	—
312	C₂²×C₄×C₈₃	—	2	1	no	—
313	C₂²×C₄×C₈₃	—	2	2	no	—
314	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
315	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
316	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
319	Q₁₆×C₈₃	—	4	2	no	—
320	Q₁₆×C₈₃	—	4	2	no	—
321	Q₁₆×C₈₃	—	4	2	no	—
322	SD₁₆×C₈₃	—	4	2	no	—
323	M₁₆×C₈₃	—	4	2	no	—
324	M₁₆×C₈₃	—	4	2	no	—
325	C₂×C₈×C₈₃	—	4	2	no	—
326	C₂×C₈×C₈₃	—	4	2	no	—
327	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
328	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
329	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
330	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
331	C₄⋊C₄×C₈₃	—	2	1	no	—
332	C₄⋊C₄×C₈₃	—	2	2	no	—
333	C₄⋊C₄×C₈₃	—	2	2	no	—
334	C₄⋊C₄×C₈₃	—	2	2	no	—
335	C₄⋊C₄×C₈₃	—	2	1	no	—
336	C₄⋊C₄×C₈₃	—	2	2	no	—
337	C₄⋊C₄×C₈₃	—	2	2	no	—
338	C₄⋊C₄×C₈₃	—	2	2	no	—
339	C₄⋊C₄×C₈₃	—	2	1	no	—
340	C₄⋊C₄×C₈₃	—	2	1	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	1	no	—
346	C₄⋊C₄×C₈₃	—	2	1	no	—
347	C₄⋊C₄×C₈₃	—	2	1	no	—
348	C₄⋊C₄×C₈₃	—	2	2	no	—
349	C₄⋊C₄×C₈₃	—	2	2	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	2	no	—
354	C₄⋊C₄×C₈₃	—	2	2	no	—
355	C₄⋊C₄×C₈₃	—	2	2	no	—
356	C₄⋊C₄×C₈₃	—	2	1	no	—
357	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
358	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
359	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
360	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
361	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
362	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
363	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
364	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
365	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
366	C₂²⋊C₄×C₈₃	—	2	2	no	—
367	C₂²⋊C₄×C₈₃	—	2	2	no	—
368	C₂²⋊C₄×C₈₃	—	2	2	no	—
369	C₂²⋊C₄×C₈₃	—	2	2	no	—
370	C₂²⋊C₄×C₈₃	—	2	2	no	—
371	C₂²⋊C₄×C₈₃	—	2	2	no	—
372	C₂²⋊C₄×C₈₃	—	2	2	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	1	no	—
380	C₂²⋊C₄×C₈₃	—	2	1	no	—
381	C₂²⋊C₄×C₈₃	—	2	2	no	—
382	C₂²⋊C₄×C₈₃	—	2	1	no	—
383	C₂²⋊C₄×C₈₃	—	2	1	no	—
384	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
385	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
386	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
387	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
388	C₄²×C₈₃	—	2	2	no	—
389	C₄²×C₈₃	—	2	2	no	—
390	C₄²×C₈₃	—	2	2	no	—
391	C₄²×C₈₃	—	2	2	no	—
392	C₄²×C₈₃	—	2	2	no	—
393	C₄²×C₈₃	—	2	2	no	—
394	C₄²×C₈₃	—	2	1	no	—
395	C₄²×C₈₃	—	2	2	no	—
396	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
397	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
398	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
399	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
400	C₂³×C₈₃	—	2	1	no	—
401	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
402	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
403	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
404	Q₈×C₈₃	—	2	2	no	—
405	Q₈×C₈₃	—	2	2	no	—
406	Q₈×C₈₃	—	2	2	no	—
407	Q₈×C₈₃	—	2	2	no	—
408	Q₈×C₈₃	—	2	2	no	—
409	Q₈×C₈₃	—	4	2	no	—
410	Q₈×C₈₃	—	4	2	no	—
411	Q₈×C₈₃	—	4	2	no	—
412	Q₈×C₈₃	—	8	1	no	—
413	Q₈×C₈₃	—	8	1	no	—
414	Q₈×C₈₃	—	8	2	no	—
415	D₄×C₈₃	—	2	2	no	—
416	D₄×C₈₃	—	4	1	no	—
417	D₄×C₈₃	—	4	1	no	—
418	D₄×C₈₃	—	4	2	no	—
419	D₄×C₈₃	—	4	2	no	—
420	D₄×C₈₃	—	4	2	no	—
421	D₄×C₈₃	—	4	2	no	—
422	D₄×C₈₃	—	8	1	no	—
423	D₄×C₈₃	—	8	2	no	—
424	D₄×C₈₃	—	8	2	no	—
425	C₂×C₄×C₈₃	—	2	2	no	—
426	C₂×C₄×C₈₃	—	2	2	no	—
427	C₂×C₄×C₈₃	—	2	2	no	—
428	C₂×C₄×C₈₃	—	2	2	no	—
429	C₂×C₄×C₈₃	—	2	2	no	—
430	C₂×C₄×C₈₃	—	2	2	no	—
431	C₂×C₄×C₈₃	—	2	2	no	—
432	C₂×C₄×C₈₃	—	2	1	no	—
433	C₂×C₄×C₈₃	—	2	2	no	—
434	C₂×C₄×C₈₃	—	2	2	no	—
435	C₂×C₄×C₈₃	—	2	1	no	—
436	C₂×C₄×C₈₃	—	2	1	no	—
437	C₂×C₄×C₈₃	—	2	2	no	—
438	C₂×C₄×C₈₃	—	2	2	no	—
439	C₂×C₄×C₈₃	—	4	1	no	—
440	C₂×C₄×C₈₃	—	4	1	no	—
441	C₂×C₄×C₈₃	—	4	2	no	—
442	C₂×C₄×C₈₃	—	4	2	no	—
443	C₂×C₄×C₈₃	—	8	2	no	—
444	C₂×C₄×C₈₃	—	8	1	no	—
445	C₂×C₄×C₈₃	—	8	2	no	—
446	C₂×C₄×C₈₃	—	8	2	no	—
447	C₂×C₄×C₈₃	—	8	2	no	—
448	C₂×C₄×C₈₃	—	8	2	no	—
449	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
454	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
456	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
457	C₈×C₈₃	—	2	2	no	—
458	C₈×C₈₃	—	2	2	no	—
459	C₈×C₈₃	—	2	2	no	—
460	C₈×C₈₃	—	2	2	no	—
461	C₂²×C₈₃	—	2	1	no	—
462	C₂²×C₈₃	—	2	1	no	—
463	C₂²×C₈₃	—	2	2	no	—
464	C₂²×C₈₃	—	2	2	no	—
465	C₂²×C₈₃	—	2	2	no	—
466	C₂²×C₈₃	—	2	2	no	—
467	C₂²×C₈₃	—	2	1	no	—
468	C₂²×C₈₃	—	2	2	no	—
469	C₂²×C₈₃	—	2	2	no	—
470	C₂²×C₈₃	—	4	1	no	—
471	C₂²×C₈₃	—	4	1	no	—
472	C₂²×C₈₃	—	4	1	no	—
473	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
474	C₄×C₈₃	—	2	1	no	—
475	C₄×C₈₃	—	2	1	no	—
476	C₄×C₈₃	—	2	1	no	—
477	C₄×C₈₃	—	2	1	no	—
478	C₄×C₈₃	—	2	2	no	—
479	C₄×C₈₃	—	2	1	no	—
480	C₄×C₈₃	—	2	2	no	—
481	C₄×C₈₃	—	4	1	no	—
482	C₄×C₈₃	—	4	2	no	—
483	C₄×C₈₃	—	4	1	no	—
484	C₄×C₈₃	—	4	2	no	—
485	C₄×C₈₃	—	4	2	no	—
486	C₄×C₈₃	—	4	2	no	—
487	C₄×C₈₃	—	4	2	no	—
488	C₄×C₈₃	—	4	2	no	—
489	C₄×C₈₃	—	4	1	no	—
490	C₄×C₈₃	#585	1	2	yes	—
491	#61794	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
492	C₂×C₈₃	—	4	1	no	—
493	C₂×C₈₃	—	4	2	no	—
494	C₂×C₈₃	—	4	2	no	—
495	C₂×C₈₃	—	8	1	no	—
496	C₂×C₈₃	#3485	1	1	yes	characteristic
497	C₂×C₈₃	#3586	1	1	yes	characteristic
498	C₂×C₈₃	#3586	1	1	yes	characteristic
499	#3547	C₂×C₈₃	1	1	yes	characteristic
500	#3507	C₂×C₈₃	1	1	yes	characteristic, complemented
501	#3349	C₂×C₈₃	1	2	yes	complemented
502	#3348	C₂×C₈₃	1	2	yes	complemented
503	#3344	C₂×C₈₃	1	2	yes	complemented
504	#3344	C₂×C₈₃	1	2	yes	complemented
505	#3316	C₂×C₈₃	1	2	yes	complemented
506	#3315	C₂×C₈₃	1	2	yes	complemented
507	#3313	C₂×C₈₃	1	2	yes	complemented
508	#3312	C₂×C₈₃	1	2	yes	complemented
509	#3240	C₂×C₈₃	1	1	yes	characteristic, complemented
510	#3237	C₂×C₈₃	1	1	yes	characteristic, complemented
511	#3202	C₂×C₈₃	1	2	yes	complemented
512	#3201	C₂×C₈₃	1	2	yes	complemented
513	#3117	C₂×C₈₃	1	1	yes	characteristic, complemented
514	#3113	C₂×C₈₃	1	1	yes	characteristic, complemented
515	#3099	C₂×C₈₃	1	2	yes	complemented
516	#3097	C₂×C₈₃	1	2	yes	complemented
517	#2980	C₂×C₈₃	1	1	yes	characteristic, complemented
518	C₈₃	#61794	1	1	yes	characteristic, direct product factor, Sylow
519	#562	—	2	2	no	—
520	#559	—	2	1	no	—
521	#557	—	2	1	no	—
522	#556	—	2	2	no	—
523	#556	C₂²×C₈₃	1	2	yes	—
524	#555	—	2	1	no	—
525	#555	C₂²×C₈₃	1	1	yes	characteristic
526	#554	C₂²×C₈₃	1	1	yes	characteristic
527	#554	C₂²×C₈₃	1	2	yes	—
528	#553	—	2	1	no	—
529	#552	C₂²×C₈₃	1	2	yes	—
530	#552	C₂²×C₈₃	1	2	yes	—
531	#552	C₂²×C₈₃	1	2	yes	—
532	D₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic
533	#548	C₂²×C₈₃	1	2	yes	—
534	#547	C₂²×C₈₃	1	1	yes	characteristic
535	#544	—	2	1	no	—
536	#542	—	2	2	no	—
537	#540	—	2	1	no	—
538	#539	—	2	1	no	—
539	#539	—	2	1	no	—
540	#537	C₂²×C₈₃	1	2	yes	—
541	#536	C₂²×C₈₃	1	2	yes	—
542	#536	C₂²×C₈₃	1	2	yes	—
543	#533	C₂²×C₈₃	1	1	yes	characteristic
544	#533	C₂²×C₈₃	1	1	yes	characteristic
545	#532	C₂²×C₈₃	1	1	yes	characteristic
546	#529	—	2	2	no	—
547	#529	C₂²×C₈₃	1	1	yes	characteristic
548	#520	C₂²×C₈₃	1	2	yes	—
549	C₂×C₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic
550	#501	C₂²×C₈₃	1	1	yes	characteristic
551	#501	C₂²×C₈₃	1	2	yes	—
552	#501	C₂²×C₈₃	1	1	yes	characteristic
553	#491	C₂²×C₈₃	1	2	yes	—
554	#489	C₂²×C₈₃	1	1	yes	characteristic
555	#489	C₂²×C₈₃	1	1	yes	characteristic
556	#485	C₂²×C₈₃	1	2	yes	—
557	#485	C₂²×C₈₃	1	2	yes	—
558	#485	C₂²×C₈₃	1	2	yes	—
559	#485	C₂²×C₈₃	1	2	yes	—
560	#485	C₂²×C₈₃	1	2	yes	—
561	#485	C₂²×C₈₃	1	2	yes	—
562	#485	C₂²×C₈₃	1	2	yes	—
563	#485	C₂²×C₈₃	1	2	yes	—
564	#484	C₂²×C₈₃	1	2	yes	—
565	#484	C₂²×C₈₃	1	2	yes	—
566	#484	C₂²×C₈₃	1	1	yes	characteristic
567	#483	C₂²×C₈₃	1	2	yes	—
568	#483	C₂²×C₈₃	1	2	yes	—
569	#483	C₂²×C₈₃	1	2	yes	—
570	#483	C₂²×C₈₃	1	2	yes	—
571	#482	C₂²×C₈₃	1	2	yes	—
572	#482	C₂²×C₈₃	1	2	yes	—
573	#481	C₂²×C₈₃	1	2	yes	—
574	#481	C₂²×C₈₃	1	1	yes	characteristic
575	#479	C₂²×C₈₃	1	2	yes	—
576	#479	C₂²×C₈₃	1	2	yes	—
577	#478	C₂²×C₈₃	1	2	yes	—
578	#477	C₂²×C₈₃	1	2	yes	—
579	#475	C₂²×C₈₃	1	2	yes	—
580	#475	C₂²×C₈₃	1	2	yes	—
581	#470	C₂²×C₈₃	1	2	yes	—
582	#470	C₂²×C₈₃	1	2	yes	—
583	#470	C₂²×C₈₃	1	2	yes	—
584	#468	C₂²×C₈₃	1	2	yes	—
585	#467	C₂²×C₈₃	1	2	yes	—
586	#467	C₂²×C₈₃	1	2	yes	—
587	#467	C₂²×C₈₃	1	2	yes	—
588	#465	C₂²×C₈₃	1	2	yes	—
589	#464	C₂²×C₈₃	1	2	yes	—
590	#462	C₂²×C₈₃	1	2	yes	—
591	#452	C₂²×C₈₃	1	2	yes	—
592	#452	C₂²×C₈₃	1	2	yes	—
593	#451	C₂²×C₈₃	1	2	yes	—
594	#451	C₂²×C₈₃	1	1	yes	characteristic
595	#451	C₂²×C₈₃	1	2	yes	—
596	#451	C₂²×C₈₃	1	2	yes	—
597	#448	C₂²×C₈₃	1	1	yes	characteristic
598	#441	C₂²×C₈₃	1	2	yes	—
599	#441	C₂²×C₈₃	1	2	yes	—
600	#441	C₂²×C₈₃	1	2	yes	—
601	#440	C₂²×C₈₃	1	2	yes	—
602	#435	C₂²×C₈₃	1	2	yes	—
603	#435	C₂²×C₈₃	1	2	yes	—
604	#435	C₂²×C₈₃	1	2	yes	—
605	#435	C₂²×C₈₃	1	2	yes	—
606	#432	C₂²×C₈₃	1	1	yes	characteristic
607	#432	C₂²×C₈₃	1	1	yes	characteristic
608	#428	C₂²×C₈₃	1	2	yes	—
609	#428	C₂²×C₈₃	1	2	yes	—
610	#427	C₂²×C₈₃	1	2	yes	—
611	C₂×#106	C₂²×C₈₃	1	2	yes	—
612	#419	C₂²×C₈₃	1	2	yes	—
613	#417	C₂²×C₈₃	1	2	yes	—
614	#416	C₂²×C₈₃	1	2	yes	—
615	C₂×#103	C₂²×C₈₃	1	2	yes	—
616	#408	C₂²×C₈₃	1	2	yes	—
617	#408	C₂²×C₈₃	1	2	yes	—
618	C₂×#41	C₂³×C₈₃	1	2	yes	—
619	C₂×#41	C₂³×C₈₃	1	2	yes	—
620	C₂²×Q₈	C₂³×C₈₃	1	1	yes	characteristic
621	C₂²×Q₈	C₂³×C₈₃	1	2	yes	—
622	C₂×Q₁₆	C₂³×C₈₃	1	2	yes	—
623	C₂×Q₁₆	C₂³×C₈₃	1	2	yes	—
624	C₂×Q₁₆	C₂³×C₈₃	1	2	yes	—
625	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
626	C₂×M₁₆	C₂³×C₈₃	1	2	yes	—
627	C₂×M₁₆	C₂³×C₈₃	1	2	yes	—
628	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
629	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
630	C₄⋊Q₈	—	2	2	no	—
631	C₄⋊Q₈	—	2	2	no	—
632	C₄⋊Q₈	—	2	1	no	—
633	C₄⋊Q₈	D₄×C₈₃	1	1	yes	characteristic
634	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
635	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
636	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
637	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
638	#127	D₄×C₈₃	1	1	yes	characteristic
639	#126	—	2	2	no	—
640	#126	—	2	2	no	—
641	#126	—	2	2	no	—
642	#126	—	2	2	no	—
643	#126	—	2	2	no	—
644	#126	—	2	1	no	—
645	#125	—	2	2	no	—
646	#125	—	2	2	no	—
647	#125	—	2	2	no	—
648	#125	—	2	2	no	—
649	#125	—	2	1	no	—
650	#125	—	2	1	no	—
651	#125	C₂³×C₈₃	1	1	yes	characteristic
652	#125	C₂³×C₈₃	1	2	yes	—
653	#124	—	2	2	no	—
654	#124	—	2	2	no	—
655	#124	—	2	2	no	—
656	#124	—	2	2	no	—
657	#124	—	2	2	no	—
658	#124	D₄×C₈₃	1	2	yes	—
659	#124	C₂³×C₈₃	1	1	yes	characteristic
660	#123	—	2	2	no	—
661	#123	—	2	2	no	—
662	#123	—	2	2	no	—
663	#123	—	2	2	no	—
664	#123	—	2	2	no	—
665	#123	—	2	2	no	—
666	#123	—	2	2	no	—
667	#123	—	2	1	no	—
668	#123	—	2	2	no	—
669	C₂²⋊Q₈	—	2	2	no	—
670	C₂²⋊Q₈	—	2	1	no	—
671	C₂²⋊Q₈	—	2	1	no	—
672	C₂²⋊Q₈	—	2	1	no	—
673	C₂²⋊Q₈	—	2	2	no	—
674	C₂²⋊Q₈	—	2	2	no	—
675	C₂²⋊Q₈	—	2	2	no	—
676	C₂²⋊Q₈	—	2	2	no	—
677	C₂²⋊Q₈	—	2	2	no	—
678	C₂²⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
679	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
680	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
681	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
682	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
683	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
684	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
685	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
686	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
687	#121	—	2	2	no	—
688	#121	—	2	2	no	—
689	#121	—	2	2	no	—
690	#121	—	2	1	no	—
691	#121	—	2	2	no	—
692	#121	—	2	1	no	—
693	#121	D₄×C₈₃	1	2	yes	—
694	#121	D₄×C₈₃	1	1	yes	characteristic
695	#121	D₄×C₈₃	1	1	yes	characteristic
696	#121	C₂³×C₈₃	1	1	yes	characteristic
697	#121	C₂³×C₈₃	1	2	yes	—
698	C₄×Q₈	—	2	2	no	—
699	C₄×Q₈	—	2	2	no	—
700	C₄×Q₈	—	2	1	no	—
701	C₄×Q₈	—	2	1	no	—
702	C₄×Q₈	—	2	1	no	—
703	C₄×Q₈	—	2	1	no	—
704	C₄×Q₈	—	2	1	no	—
705	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
706	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
707	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
708	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
709	C₄×D₄	—	2	2	no	—
710	C₄×D₄	—	2	2	no	—
711	C₄×D₄	—	2	2	no	—
712	C₄×D₄	—	2	2	no	—
713	C₄×D₄	—	2	1	no	—
714	C₄×D₄	—	2	1	no	—
715	C₄×D₄	—	2	1	no	—
716	C₄×D₄	—	2	2	no	—
717	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
718	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
719	C₄×D₄	C₂³×C₈₃	1	2	yes	—
720	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
721	#117	—	2	1	no	—
722	#117	—	2	1	no	—
723	#117	—	2	2	no	—
724	#117	—	2	2	no	—
725	#117	—	2	2	no	—
726	#117	—	2	1	no	—
727	#117	C₂³×C₈₃	1	2	yes	—
728	#117	C₂³×C₈₃	1	2	yes	—
729	#117	C₂³×C₈₃	1	2	yes	—
730	#117	C₂³×C₈₃	1	2	yes	—
731	C₂×C₄⋊C₄	—	2	1	no	—
732	C₂×C₄⋊C₄	—	2	1	no	—
733	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
734	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
735	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
736	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
737	C₂×C₄²	—	2	1	no	—
738	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
739	#107	C₂³×C₈₃	1	2	yes	—
740	#107	C₂³×C₈₃	1	2	yes	—
741	#107	C₂³×C₈₃	1	2	yes	—
742	#107	C₂³×C₈₃	1	2	yes	—
743	#107	C₂³×C₈₃	1	2	yes	—
744	#106	C₂³×C₈₃	1	2	yes	—
745	#106	C₂³×C₈₃	1	2	yes	—
746	#106	C₂³×C₈₃	1	2	yes	—
747	#106	C₂³×C₈₃	1	2	yes	—
748	#106	C₂³×C₈₃	1	2	yes	—
749	#106	C₂³×C₈₃	1	2	yes	—
750	#106	C₂³×C₈₃	1	2	yes	—
751	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
752	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
753	#103	C₂³×C₈₃	1	2	yes	—
754	#103	C₂³×C₈₃	1	2	yes	—
755	#103	C₂³×C₈₃	1	2	yes	—
756	#103	C₂³×C₈₃	1	2	yes	—
757	#103	C₂³×C₈₃	1	2	yes	—
758	#103	C₂³×C₈₃	1	2	yes	—
759	#103	C₂³×C₈₃	1	2	yes	—
760	#103	C₂³×C₈₃	1	2	yes	—
761	#103	C₂³×C₈₃	1	2	yes	—
762	#103	C₂³×C₈₃	1	2	yes	—
763	#103	C₂³×C₈₃	1	2	yes	—
764	#103	C₂³×C₈₃	1	2	yes	—
765	#103	C₂³×C₈₃	1	2	yes	—
766	#102	C₂³×C₈₃	1	2	yes	—
767	#102	C₂³×C₈₃	1	2	yes	—
768	#102	C₂³×C₈₃	1	2	yes	—
769	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
770	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
771	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
772	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
773	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
774	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
775	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
776	#97	C₂³×C₈₃	1	2	yes	—
777	#97	C₂³×C₈₃	1	1	yes	characteristic
778	#97	C₂³×C₈₃	1	1	yes	characteristic
779	#41	—	4	2	no	—
780	#41	—	4	2	no	—
781	#41	—	4	2	no	—
782	#41	—	4	2	no	—
783	C₂×Q₈	—	2	1	no	—
784	C₂×Q₈	—	2	1	no	—
785	C₂×Q₈	—	2	1	no	—
786	C₂×Q₈	—	2	1	no	—
787	C₂×Q₈	—	2	2	no	—
788	C₂×Q₈	—	4	2	no	—
789	C₂×Q₈	—	4	2	no	—
790	C₂×Q₈	—	4	2	no	—
791	C₂×Q₈	C₂×D₄×C₈₃	1	2	yes	—
792	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
793	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
794	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
795	C₂×D₄	—	2	1	no	—
796	C₂×D₄	—	2	2	no	—
797	C₂×D₄	—	2	2	no	—
798	C₂×D₄	C₂×D₄×C₈₃	1	1	yes	characteristic
799	C₂×D₄	C₂×D₄×C₈₃	1	1	yes	characteristic
800	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
801	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
802	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
803	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
804	C₂×D₄	C₂⁴×C₈₃	1	1	yes	characteristic
805	C₂²×C₄	—	2	1	no	—
806	C₂²×C₄	—	2	1	no	—
807	C₂²×C₄	—	2	2	no	—
808	C₂²×C₄	—	2	2	no	—
809	C₂²×C₄	—	2	2	no	—
810	C₂²×C₄	—	2	2	no	—
811	C₂²×C₄	—	2	1	no	—
812	C₂²×C₄	—	2	2	no	—
813	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
814	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
815	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
816	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
817	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
818	Q₁₆	—	4	2	no	—
819	Q₁₆	—	4	2	no	—
820	Q₁₆	—	4	2	no	—
821	SD₁₆	—	4	2	no	—
822	M₁₆	—	4	2	no	—
823	M₁₆	—	4	2	no	—
824	C₂×C₈	—	4	2	no	—
825	C₂×C₈	—	4	2	no	—
826	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
827	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
828	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
829	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
830	C₄⋊C₄	—	2	1	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	1	no	—
835	C₄⋊C₄	—	2	2	no	—
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	2	no	—
838	C₄⋊C₄	—	2	1	no	—
839	C₄⋊C₄	—	2	1	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	—	2	1	no	—
845	C₄⋊C₄	—	2	1	no	—
846	C₄⋊C₄	—	2	1	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	1	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	2	1	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	C₂×D₄×C₈₃	1	1	yes	characteristic
857	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
858	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
859	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
860	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
861	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
862	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
863	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
864	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
865	C₂²⋊C₄	—	2	2	no	—
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	—	2	2	no	—
868	C₂²⋊C₄	—	2	2	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	2	no	—
871	C₂²⋊C₄	—	2	2	no	—
872	C₂²⋊C₄	—	2	2	no	—
873	C₂²⋊C₄	—	2	2	no	—
874	C₂²⋊C₄	—	2	2	no	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	2	1	no	—
878	C₂²⋊C₄	—	2	1	no	—
879	C₂²⋊C₄	—	2	1	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	1	no	—
882	C₂²⋊C₄	—	2	1	no	—
883	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
884	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
885	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
886	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
887	C₄²	—	2	2	no	—
888	C₄²	—	2	2	no	—
889	C₄²	—	2	2	no	—
890	C₄²	—	2	2	no	—
891	C₄²	—	2	2	no	—
892	C₄²	—	2	2	no	—
893	C₄²	—	2	1	no	—
894	C₄²	—	2	2	no	—
895	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
896	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
897	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
898	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
899	C₂³	—	2	1	no	—
900	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
901	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
902	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
903	Q₈	—	2	2	no	—
904	Q₈	—	2	2	no	—
905	Q₈	—	2	2	no	—
906	Q₈	—	2	2	no	—
907	Q₈	—	2	2	no	—
908	Q₈	—	4	2	no	—
909	Q₈	—	4	2	no	—
910	Q₈	—	4	2	no	—
911	Q₈	—	8	2	no	—
912	Q₈	—	8	1	no	—
913	Q₈	—	8	1	no	—
914	D₄	—	2	2	no	—
915	D₄	—	4	2	no	—
916	D₄	—	4	2	no	—
917	D₄	—	4	2	no	—
918	D₄	—	4	1	no	—
919	D₄	—	4	1	no	—
920	D₄	—	4	2	no	—
921	D₄	—	8	2	no	—
922	D₄	—	8	1	no	—
923	D₄	—	8	2	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	4	1	no	—
939	C₂×C₄	—	4	1	no	—
940	C₂×C₄	—	4	2	no	—
941	C₂×C₄	—	4	2	no	—
942	C₂×C₄	—	8	2	no	—
943	C₂×C₄	—	8	2	no	—
944	C₂×C₄	—	8	1	no	—
945	C₂×C₄	—	8	2	no	—
946	C₂×C₄	—	8	2	no	—
947	C₂×C₄	—	8	2	no	—
948	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
949	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
950	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
951	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
952	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
953	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
954	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
955	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
956	C₈	—	2	2	no	—
957	C₈	—	2	2	no	—
958	C₈	—	2	2	no	—
959	C₈	—	2	2	no	—
960	C₂²	—	2	1	no	—
961	C₂²	—	2	1	no	—
962	C₂²	—	2	2	no	—
963	C₂²	—	2	2	no	—
964	C₂²	—	2	2	no	—
965	C₂²	—	2	2	no	—
966	C₂²	—	2	1	no	—
967	C₂²	—	2	2	no	—
968	C₂²	—	2	2	no	—
969	C₂²	—	4	1	no	—
970	C₂²	—	4	1	no	—
971	C₂²	—	4	1	no	—
972	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
973	C₄	—	2	1	no	—
974	C₄	—	2	1	no	—
975	C₄	—	2	1	no	—
976	C₄	—	2	1	no	—
977	C₄	—	2	2	no	—
978	C₄	—	2	1	no	—
979	C₄	—	2	2	no	—
980	C₄	—	4	1	no	—
981	C₄	—	4	2	no	—
982	C₄	—	4	1	no	—
983	C₄	—	4	2	no	—
984	C₄	—	4	2	no	—
985	C₄	—	4	2	no	—
986	C₄	—	4	2	no	—
987	C₄	—	4	2	no	—
988	C₄	—	4	1	no	—
989	C₄	#585×C₈₃	1	2	yes	—
990	C₂	—	4	1	no	—
991	C₂	—	4	2	no	—
992	C₂	—	4	2	no	—
993	C₂	—	8	1	no	—
994	C₂	C₈₃×#3485	1	1	yes	characteristic
995	C₂	C₈₃×#3586	1	1	yes	characteristic
996	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	C₈₃×#3547	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₃ ◁ #532×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈₃×#3507	C₂	semidirect
3. C₈₃×#3349	C₂	semidirect
4. C₈₃×#3348	C₂	semidirect
5. C₈₃×#3344	C₂	semidirect
6. C₈₃×#3344	C₂	semidirect
7. C₈₃×#3316	C₂	semidirect
8. C₈₃×#3315	C₂	semidirect
9. C₈₃×#3313	C₂	semidirect
10. C₈₃×#3312	C₂	semidirect
11. C₈₃×#3240	C₂	semidirect
12. C₈₃×#3237	C₂	semidirect
13. C₈₃×#3202	C₂	semidirect
14. C₈₃×#3201	C₂	semidirect
15. C₈₃×#3117	C₂	semidirect
16. C₈₃×#3113	C₂	semidirect
17. C₈₃×#3099	C₂	semidirect
18. C₈₃×#3097	C₂	semidirect
19. C₈₃×#2980	C₂	semidirect
491. #61794	C₈₃	direct (N × H)
500. #3507	C₂×C₈₃	semidirect
501. #3349	C₂×C₈₃	semidirect
502. #3348	C₂×C₈₃	semidirect
503. #3344	C₂×C₈₃	semidirect
504. #3344	C₂×C₈₃	semidirect
505. #3316	C₂×C₈₃	semidirect
506. #3315	C₂×C₈₃	semidirect
507. #3313	C₂×C₈₃	semidirect
508. #3312	C₂×C₈₃	semidirect
509. #3240	C₂×C₈₃	semidirect
510. #3237	C₂×C₈₃	semidirect
511. #3202	C₂×C₈₃	semidirect
512. #3201	C₂×C₈₃	semidirect
513. #3117	C₂×C₈₃	semidirect
514. #3113	C₂×C₈₃	semidirect
515. #3099	C₂×C₈₃	semidirect
516. #3097	C₂×C₈₃	semidirect
517. #2980	C₂×C₈₃	semidirect
518. C₈₃	#61794	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₈₃×#3547	2
C₈₃×#3507	2
C₈₃×#3349	2
C₈₃×#3348	2
C₈₃×#3344	2
C₈₃×#3316	2
C₈₃×#3315	2
C₈₃×#3313	2
C₈₃×#3312	2
C₈₃×#3240	2
C₈₃×#3237	2
C₈₃×#3202	2
C₈₃×#3201	2
C₈₃×#3117	2
C₈₃×#3113	2
C₈₃×#3099	2
C₈₃×#3097	2
C₈₃×#2980	2
#61794	83

Subgroups — C83×#61794 #35289618

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#61794 #35289618