Subgroups — C₈₃×#61870 #35289694

Order 21248.

1700 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₃×#3386	C₂	1	2	yes	maximal, complemented
4	C₈₃×#3385	C₂	1	2	yes	maximal, complemented
5	Q₈×Q₁₆×C₈₃	C₂	1	2	yes	maximal, complemented
6	Q₈×D₈×C₈₃	C₂	1	2	yes	maximal, complemented
7	C₈₃×#3375	C₂	1	2	yes	maximal, complemented
8	C₈₃×#3367	C₂	1	2	yes	maximal, complemented
9	C₈₃×#3364	C₂	1	2	yes	maximal, complemented
10	C₈₃×#3361	C₂	1	2	yes	maximal, complemented
11	C₈₃×#3243	C₂	1	4	yes	maximal, complemented
12	C₈₃×#3230	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₃×#3226	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₃×#3124	C₂	1	4	yes	maximal, complemented
15	C₈₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₃×#3106	C₂	1	1	yes	maximal, characteristic
17	C₈₃×#2986	C₂	1	1	yes	maximal, characteristic, complemented
18	#563×C₈₃	—	2	2	no	—
19	#559×C₈₃	C₂²	1	2	yes	—
20	Q₈²×C₈₃	C₂²	1	2	yes	—
21	Q₈²×C₈₃	C₂²	1	2	yes	—
22	#557×C₈₃	C₂²	1	2	yes	—
23	#556×C₈₃	—	2	1	no	—
24	#556×C₈₃	C₂²	1	2	yes	—
25	#554×C₈₃	—	2	2	no	—
26	#554×C₈₃	C₂²	1	2	yes	—
27	D₄×Q₈×C₈₃	—	2	1	no	—
28	D₄×Q₈×C₈₃	—	2	2	no	—
29	D₄×Q₈×C₈₃	C₂²	1	2	yes	—
30	D₄×Q₈×C₈₃	C₂²	1	2	yes	—
31	#544×C₈₃	—	2	2	no	—
32	#544×C₈₃	C₂²	1	2	yes	—
33	#542×C₈₃	—	2	2	no	—
34	#542×C₈₃	C₂²	1	4	yes	—
35	#536×C₈₃	—	2	2	no	—
36	#533×C₈₃	—	2	1	no	—
37	#533×C₈₃	C₂²	1	1	yes	characteristic
38	#533×C₈₃	C₂²	1	1	yes	characteristic
39	#532×C₈₃	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊Q₈×C₈₃	—	2	1	no	—
41	C₂×C₄⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
42	#520×C₈₃	C₂²	1	2	yes	—
43	C₄×#41×C₈₃	C₂²	1	1	yes	characteristic
44	#501×C₈₃	C₂²	1	4	yes	—
45	#500×C₈₃	C₂²	1	4	yes	—
46	#500×C₈₃	C₂²	1	2	yes	—
47	#500×C₈₃	C₂²	1	2	yes	—
48	#489×C₈₃	C₂²	1	4	yes	—
49	#488×C₈₃	C₂²	1	4	yes	—
50	#487×C₈₃	C₂²	1	2	yes	—
51	#486×C₈₃	C₂²	1	2	yes	—
52	#485×C₈₃	C₂²	1	2	yes	—
53	#484×C₈₃	C₂²	1	4	yes	—
54	#482×C₈₃	C₂²	1	2	yes	—
55	#480×C₈₃	C₂²	1	4	yes	—
56	#479×C₈₃	C₂²	1	4	yes	—
57	#478×C₈₃	C₂²	1	4	yes	—
58	#477×C₈₃	C₂²	1	2	yes	—
59	#477×C₈₃	C₂²	1	1	yes	characteristic
60	#477×C₈₃	C₂²	1	4	yes	—
61	#477×C₈₃	C₂²	1	2	yes	—
62	#477×C₈₃	C₂²	1	4	yes	—
63	#476×C₈₃	C₂²	1	1	yes	characteristic
64	#475×C₈₃	C₂²	1	1	yes	characteristic
65	#474×C₈₃	C₂²	1	1	yes	characteristic
66	#474×C₈₃	C₂²	1	2	yes	—
67	#474×C₈₃	C₂²	1	2	yes	—
68	#474×C₈₃	C₂²	1	4	yes	—
69	#474×C₈₃	C₂²	1	4	yes	—
70	#464×C₈₃	C₂²	1	4	yes	—
71	#463×C₈₃	C₂²	1	4	yes	—
72	#462×C₈₃	C₂²	1	1	yes	characteristic
73	#461×C₈₃	C₂²	1	1	yes	characteristic
74	#460×C₈₃	C₂²	1	1	yes	characteristic
75	#459×C₈₃	C₂²	1	1	yes	characteristic
76	#452×C₈₃	C₂²	1	2	yes	—
77	#449×C₈₃	C₂²	1	2	yes	—
78	#446×C₈₃	C₂²	1	2	yes	—
79	#446×C₈₃	C₂²	1	2	yes	—
80	C₈×Q₈×C₈₃	C₂²	1	2	yes	—
81	C₈×Q₈×C₈₃	C₂²	1	2	yes	—
82	#440×C₈₃	C₂²	1	4	yes	—
83	#440×C₈₃	C₂²	1	4	yes	—
84	C₄×Q₁₆×C₈₃	C₂²	1	2	yes	—
85	C₄×Q₁₆×C₈₃	C₂²	1	4	yes	—
86	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	—
87	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	—
88	C₄×D₈×C₈₃	C₂²	1	4	yes	—
89	C₄×D₈×C₈₃	C₂²	1	2	yes	—
90	#433×C₈₃	C₂²	1	4	yes	—
91	#431×C₈₃	C₂²	1	1	yes	characteristic
92	#431×C₈₃	C₂²	1	1	yes	characteristic
93	C₂×#41×C₈₃	—	2	1	no	—
94	C₂×#41×C₈₃	C₂³	1	1	yes	characteristic
95	C₂²×Q₈×C₈₃	—	2	2	no	—
96	C₂²×Q₈×C₈₃	—	2	2	no	—
97	C₂²×Q₈×C₈₃	—	2	1	no	—
98	C₂×Q₁₆×C₈₃	C₂³	1	2	yes	—
99	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
100	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
101	C₂×D₈×C₈₃	C₂³	1	2	yes	—
102	C₄⋊Q₈×C₈₃	—	2	2	no	—
103	C₄⋊Q₈×C₈₃	—	2	2	no	—
104	C₄⋊Q₈×C₈₃	—	2	2	no	—
105	C₄⋊Q₈×C₈₃	—	2	4	no	—
106	C₄⋊Q₈×C₈₃	—	2	2	no	—
107	C₄⋊Q₈×C₈₃	—	2	4	no	—
108	C₄⋊Q₈×C₈₃	—	2	1	no	—
109	C₄⋊Q₈×C₈₃	—	2	1	no	—
110	C₄⋊Q₈×C₈₃	D₄	1	1	yes	characteristic
111	C₄⋊Q₈×C₈₃	D₄	1	1	yes	characteristic
112	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
113	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
114	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
115	C₄⋊Q₈×C₈₃	C₂³	1	4	yes	—
116	C₄⋊Q₈×C₈₃	C₂³	1	4	yes	—
117	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
118	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
119	#127×C₈₃	C₂³	1	1	yes	characteristic
120	#126×C₈₃	—	2	4	no	—
121	#126×C₈₃	—	2	4	no	—
122	#125×C₈₃	—	2	2	no	—
123	#125×C₈₃	—	2	4	no	—
124	#125×C₈₃	—	2	1	no	—
125	#125×C₈₃	D₄	1	2	yes	—
126	#125×C₈₃	C₂³	1	4	yes	—
127	#124×C₈₃	—	2	2	no	—
128	#124×C₈₃	—	2	4	no	—
129	#124×C₈₃	—	2	1	no	—
130	#124×C₈₃	C₂³	1	4	yes	—
131	#123×C₈₃	—	2	4	no	—
132	#123×C₈₃	—	2	4	no	—
133	C₂²⋊Q₈×C₈₃	—	2	2	no	—
134	C₂²⋊Q₈×C₈₃	—	2	2	no	—
135	C₂²⋊Q₈×C₈₃	—	2	1	no	—
136	C₂²⋊Q₈×C₈₃	—	2	2	no	—
137	C₂²⋊Q₈×C₈₃	—	2	2	no	—
138	C₂²⋊Q₈×C₈₃	—	2	4	no	—
139	C₂²⋊Q₈×C₈₃	—	2	4	no	—
140	C₂²⋊Q₈×C₈₃	—	2	4	no	—
141	C₂²⋊Q₈×C₈₃	—	2	4	no	—
142	C₂²⋊Q₈×C₈₃	—	2	4	no	—
143	C₂²⋊Q₈×C₈₃	D₄	1	2	yes	—
144	C₂²⋊Q₈×C₈₃	D₄	1	2	yes	—
145	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
146	#121×C₈₃	—	2	1	no	—
147	#121×C₈₃	C₂³	1	2	yes	—
148	C₄×Q₈×C₈₃	—	2	2	no	—
149	C₄×Q₈×C₈₃	—	2	2	no	—
150	C₄×Q₈×C₈₃	—	2	2	no	—
151	C₄×Q₈×C₈₃	—	2	1	no	—
152	C₄×Q₈×C₈₃	C₂³	1	4	yes	—
153	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
154	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
155	C₄×Q₈×C₈₃	C₂³	1	4	yes	—
156	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
157	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
158	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
159	C₄×D₄×C₈₃	—	2	1	no	—
160	C₄×D₄×C₈₃	—	2	1	no	—
161	C₄×D₄×C₈₃	—	2	2	no	—
162	C₄×D₄×C₈₃	—	2	4	no	—
163	C₄×D₄×C₈₃	—	2	1	no	—
164	C₄×D₄×C₈₃	C₂³	1	4	yes	—
165	C₄×D₄×C₈₃	C₂³	1	2	yes	—
166	C₄×D₄×C₈₃	C₂³	1	4	yes	—
167	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
168	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
169	#117×C₈₃	—	2	1	no	—
170	#117×C₈₃	—	2	2	no	—
171	#117×C₈₃	—	2	2	no	—
172	#117×C₈₃	—	2	1	no	—
173	#117×C₈₃	C₂³	1	1	yes	characteristic
174	#117×C₈₃	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
176	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
177	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
178	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
179	C₂×C₄²×C₈₃	—	2	1	no	—
180	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
181	#107×C₈₃	C₂³	1	2	yes	—
182	#107×C₈₃	C₂³	1	4	yes	—
183	#107×C₈₃	C₂³	1	4	yes	—
184	#107×C₈₃	C₂³	1	4	yes	—
185	#107×C₈₃	C₂³	1	2	yes	—
186	#107×C₈₃	C₂³	1	4	yes	—
187	#106×C₈₃	C₂³	1	2	yes	—
188	#106×C₈₃	C₂³	1	2	yes	—
189	C₄⋊C₈×C₈₃	C₂³	1	4	yes	—
190	C₄⋊C₈×C₈₃	C₂³	1	4	yes	—
191	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
192	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
193	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
194	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
195	#103×C₈₃	C₂³	1	4	yes	—
196	#103×C₈₃	C₂³	1	4	yes	—
197	#103×C₈₃	C₂³	1	2	yes	—
198	#103×C₈₃	C₂³	1	2	yes	—
199	#103×C₈₃	C₂³	1	2	yes	—
200	#103×C₈₃	C₂³	1	2	yes	—
201	#102×C₈₃	C₂³	1	4	yes	—
202	#102×C₈₃	C₂³	1	4	yes	—
203	#102×C₈₃	C₂³	1	2	yes	—
204	#102×C₈₃	C₂³	1	2	yes	—
205	#102×C₈₃	C₂³	1	2	yes	—
206	#102×C₈₃	C₂³	1	2	yes	—
207	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
208	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
209	#97×C₈₃	C₂³	1	4	yes	—
210	C₄×C₈×C₈₃	C₂³	1	2	yes	—
211	C₄×C₈×C₈₃	C₂³	1	2	yes	—
212	C₄×C₈×C₈₃	C₂³	1	4	yes	—
213	#41×C₈₃	—	2	2	no	—
214	#41×C₈₃	—	2	2	no	—
215	#41×C₈₃	—	8	2	no	—
216	C₂×Q₈×C₈₃	—	2	1	no	—
217	C₂×Q₈×C₈₃	—	2	2	no	—
218	C₂×Q₈×C₈₃	—	2	4	no	—
219	C₂×Q₈×C₈₃	—	2	4	no	—
220	C₂×Q₈×C₈₃	—	2	2	no	—
221	C₂×Q₈×C₈₃	—	2	1	no	—
222	C₂×Q₈×C₈₃	—	8	2	no	—
223	C₂×Q₈×C₈₃	—	8	4	no	—
224	C₂×Q₈×C₈₃	—	8	4	no	—
225	C₂×Q₈×C₈₃	C₂×D₄	1	2	yes	—
226	C₂×Q₈×C₈₃	C₂×D₄	1	2	yes	—
227	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
228	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
229	C₂×D₄×C₈₃	—	2	1	no	—
230	C₂×D₄×C₈₃	—	2	2	no	—
231	C₂×D₄×C₈₃	—	2	1	no	—
232	C₂×D₄×C₈₃	—	2	1	no	—
233	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
234	C₂×D₄×C₈₃	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₈₃	—	2	1	no	—
236	C₂²×C₄×C₈₃	—	2	2	no	—
237	C₂²×C₄×C₈₃	—	2	1	no	—
238	C₂²×C₄×C₈₃	—	2	1	no	—
239	C₂²×C₄×C₈₃	—	2	2	no	—
240	C₂²×C₄×C₈₃	—	2	4	no	—
241	C₂²×C₄×C₈₃	—	2	4	no	—
242	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
245	Q₁₆×C₈₃	—	2	4	no	—
246	SD₁₆×C₈₃	—	2	4	no	—
247	SD₁₆×C₈₃	—	2	4	no	—
248	D₈×C₈₃	—	2	4	no	—
249	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
250	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
251	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
252	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
253	C₄⋊C₄×C₈₃	—	2	2	no	—
254	C₄⋊C₄×C₈₃	—	2	2	no	—
255	C₄⋊C₄×C₈₃	—	2	4	no	—
256	C₄⋊C₄×C₈₃	—	2	2	no	—
257	C₄⋊C₄×C₈₃	—	2	4	no	—
258	C₄⋊C₄×C₈₃	—	2	1	no	—
259	C₄⋊C₄×C₈₃	—	2	1	no	—
260	C₄⋊C₄×C₈₃	—	2	1	no	—
261	C₄⋊C₄×C₈₃	—	2	1	no	—
262	C₄⋊C₄×C₈₃	—	2	1	no	—
263	C₄⋊C₄×C₈₃	—	2	1	no	—
264	C₄⋊C₄×C₈₃	—	2	4	no	—
265	C₄⋊C₄×C₈₃	—	2	4	no	—
266	C₄⋊C₄×C₈₃	—	2	2	no	—
267	C₄⋊C₄×C₈₃	—	2	4	no	—
268	C₄⋊C₄×C₈₃	—	2	4	no	—
269	C₄⋊C₄×C₈₃	—	2	2	no	—
270	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
271	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
272	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
273	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
274	C₄⋊C₄×C₈₃	C₂×D₄	1	4	yes	—
275	C₄⋊C₄×C₈₃	C₂×D₄	1	4	yes	—
276	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
277	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
278	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
279	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
280	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
281	C₂²⋊C₄×C₈₃	—	2	2	no	—
282	C₂²⋊C₄×C₈₃	—	2	1	no	—
283	C₂²⋊C₄×C₈₃	—	2	1	no	—
284	C₂²⋊C₄×C₈₃	—	2	1	no	—
285	C₂²⋊C₄×C₈₃	—	2	4	no	—
286	C₂²⋊C₄×C₈₃	—	2	4	no	—
287	C₂²⋊C₄×C₈₃	—	2	2	no	—
288	C₂²⋊C₄×C₈₃	—	2	4	no	—
289	C₂²⋊C₄×C₈₃	—	2	2	no	—
290	C₂²⋊C₄×C₈₃	—	2	4	no	—
291	C₂²⋊C₄×C₈₃	C₂×D₄	1	4	yes	—
292	C₄²×C₈₃	—	2	1	no	—
293	C₄²×C₈₃	—	2	1	no	—
294	C₄²×C₈₃	—	2	1	no	—
295	C₄²×C₈₃	—	2	2	no	—
296	C₄²×C₈₃	—	2	4	no	—
297	C₄²×C₈₃	—	2	4	no	—
298	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
299	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
300	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
301	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
302	C₄²×C₈₃	C₂⁴	1	4	yes	—
303	C₂³×C₈₃	—	2	1	no	—
304	C₂³×C₈₃	—	2	2	no	—
305	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
306	Q₈×C₈₃	—	2	4	no	—
307	Q₈×C₈₃	—	2	4	no	—
308	Q₈×C₈₃	—	2	1	no	—
309	Q₈×C₈₃	—	2	2	no	—
310	Q₈×C₈₃	—	2	2	no	—
311	Q₈×C₈₃	—	4	2	no	—
312	Q₈×C₈₃	—	4	4	no	—
313	Q₈×C₈₃	—	8	2	no	—
314	Q₈×C₈₃	—	8	4	no	—
315	Q₈×C₈₃	—	8	4	no	—
316	Q₈×C₈₃	—	8	1	no	—
317	Q₈×C₈₃	2₋¹⁺⁴	1	2	yes	—
318	D₄×C₈₃	—	2	4	no	—
319	D₄×C₈₃	—	2	1	no	—
320	D₄×C₈₃	—	2	2	no	—
321	D₄×C₈₃	—	2	2	no	—
322	D₄×C₈₃	—	4	2	no	—
323	D₄×C₈₃	—	8	1	no	—
324	D₄×C₈₃	—	8	2	no	—
325	D₄×C₈₃	2₋¹⁺⁴	1	2	yes	—
326	C₂×C₄×C₈₃	—	2	4	no	—
327	C₂×C₄×C₈₃	—	2	1	no	—
328	C₂×C₄×C₈₃	—	2	2	no	—
329	C₂×C₄×C₈₃	—	2	2	no	—
330	C₂×C₄×C₈₃	—	2	1	no	—
331	C₂×C₄×C₈₃	—	2	1	no	—
332	C₂×C₄×C₈₃	—	2	2	no	—
333	C₂×C₄×C₈₃	—	2	1	no	—
334	C₂×C₄×C₈₃	—	2	2	no	—
335	C₂×C₄×C₈₃	—	2	1	no	—
336	C₂×C₄×C₈₃	—	2	2	no	—
337	C₂×C₄×C₈₃	—	2	4	no	—
338	C₂×C₄×C₈₃	—	4	2	no	—
339	C₂×C₄×C₈₃	—	4	4	no	—
340	C₂×C₄×C₈₃	—	4	2	no	—
341	C₂×C₄×C₈₃	—	8	4	no	—
342	C₂×C₄×C₈₃	—	8	4	no	—
343	C₂×C₄×C₈₃	—	8	2	no	—
344	C₂×C₄×C₈₃	C₂²×D₄	1	4	yes	—
345	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
346	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₈₃	C₂²×D₄	1	4	yes	—
349	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
350	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
351	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
352	C₈×C₈₃	—	2	2	no	—
353	C₈×C₈₃	—	2	2	no	—
354	C₈×C₈₃	—	2	2	no	—
355	C₈×C₈₃	—	2	2	no	—
356	C₂²×C₈₃	—	2	1	no	—
357	C₂²×C₈₃	—	2	2	no	—
358	C₂²×C₈₃	—	2	1	no	—
359	C₂²×C₈₃	—	2	1	no	—
360	C₂²×C₈₃	—	4	1	no	—
361	C₂²×C₈₃	—	4	1	no	—
362	C₂²×C₈₃	—	4	2	no	—
363	C₂²×C₈₃	—	4	2	no	—
364	C₂²×C₈₃	—	4	2	no	—
365	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
366	C₄×C₈₃	—	2	1	no	—
367	C₄×C₈₃	—	2	2	no	—
368	C₄×C₈₃	—	2	1	no	—
369	C₄×C₈₃	—	2	4	no	—
370	C₄×C₈₃	—	2	1	no	—
371	C₄×C₈₃	—	2	4	no	—
372	C₄×C₈₃	—	4	2	no	—
373	C₄×C₈₃	—	4	2	no	—
374	C₄×C₈₃	—	4	1	no	—
375	C₄×C₈₃	—	4	2	no	—
376	C₄×C₈₃	—	4	4	no	—
377	C₄×C₈₃	—	4	1	no	—
378	C₄×C₈₃	#576	1	2	yes	—
379	C₄×C₈₃	#578	1	2	yes	—
380	C₄×C₈₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
381	C₄×C₈₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
382	#61870	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
383	C₂×C₈₃	—	4	1	no	—
384	C₂×C₈₃	—	4	2	no	—
385	C₂×C₈₃	—	8	2	no	—
386	C₂×C₈₃	#3486	1	1	yes	characteristic
387	C₂×C₈₃	C₂×#576	1	1	yes	characteristic
388	C₂×C₈₃	C₂×#578	1	1	yes	characteristic
389	#3550	C₂×C₈₃	1	1	yes	characteristic, complemented
390	#3503	C₂×C₈₃	1	1	yes	characteristic, complemented
391	#3386	C₂×C₈₃	1	2	yes	complemented
392	#3385	C₂×C₈₃	1	2	yes	complemented
393	Q₈×Q₁₆	C₂×C₈₃	1	2	yes	complemented
394	Q₈×D₈	C₂×C₈₃	1	2	yes	complemented
395	#3375	C₂×C₈₃	1	2	yes	complemented
396	#3367	C₂×C₈₃	1	2	yes	complemented
397	#3364	C₂×C₈₃	1	2	yes	complemented
398	#3361	C₂×C₈₃	1	2	yes	complemented
399	#3243	C₂×C₈₃	1	4	yes	complemented
400	#3230	C₂×C₈₃	1	1	yes	characteristic, complemented
401	#3226	C₂×C₈₃	1	1	yes	characteristic, complemented
402	#3124	C₂×C₈₃	1	4	yes	complemented
403	#3107	C₂×C₈₃	1	1	yes	characteristic, complemented
404	#3106	C₂×C₈₃	1	1	yes	characteristic
405	#2986	C₂×C₈₃	1	1	yes	characteristic, complemented
406	C₈₃	#61870	1	1	yes	characteristic, direct product factor, Sylow
407	#563	—	2	2	no	—
408	#559	C₂²×C₈₃	1	2	yes	—
409	Q₈²	C₂²×C₈₃	1	2	yes	—
410	Q₈²	C₂²×C₈₃	1	2	yes	—
411	#557	C₂²×C₈₃	1	2	yes	—
412	#556	—	2	1	no	—
413	#556	C₂²×C₈₃	1	2	yes	—
414	#554	—	2	2	no	—
415	#554	C₂²×C₈₃	1	2	yes	—
416	D₄×Q₈	—	2	1	no	—
417	D₄×Q₈	—	2	2	no	—
418	D₄×Q₈	C₂²×C₈₃	1	2	yes	—
419	D₄×Q₈	C₂²×C₈₃	1	2	yes	—
420	#544	—	2	2	no	—
421	#544	C₂²×C₈₃	1	2	yes	—
422	#542	—	2	2	no	—
423	#542	C₂²×C₈₃	1	4	yes	—
424	#536	—	2	2	no	—
425	#533	—	2	1	no	—
426	#533	C₂²×C₈₃	1	1	yes	characteristic
427	#533	C₂²×C₈₃	1	1	yes	characteristic
428	#532	C₂²×C₈₃	1	1	yes	characteristic
429	C₂×C₄⋊Q₈	—	2	1	no	—
430	C₂×C₄⋊Q₈	C₂²×C₈₃	1	1	yes	characteristic
431	#520	C₂²×C₈₃	1	2	yes	—
432	C₄×#41	C₂²×C₈₃	1	1	yes	characteristic
433	#501	C₂²×C₈₃	1	4	yes	—
434	#500	C₂²×C₈₃	1	4	yes	—
435	#500	C₂²×C₈₃	1	2	yes	—
436	#500	C₂²×C₈₃	1	2	yes	—
437	#489	C₂²×C₈₃	1	4	yes	—
438	#488	C₂²×C₈₃	1	4	yes	—
439	#487	C₂²×C₈₃	1	2	yes	—
440	#486	C₂²×C₈₃	1	2	yes	—
441	#485	C₂²×C₈₃	1	2	yes	—
442	#484	C₂²×C₈₃	1	4	yes	—
443	#482	C₂²×C₈₃	1	2	yes	—
444	#480	C₂²×C₈₃	1	4	yes	—
445	#479	C₂²×C₈₃	1	4	yes	—
446	#478	C₂²×C₈₃	1	4	yes	—
447	#477	C₂²×C₈₃	1	2	yes	—
448	#477	C₂²×C₈₃	1	1	yes	characteristic
449	#477	C₂²×C₈₃	1	4	yes	—
450	#477	C₂²×C₈₃	1	2	yes	—
451	#477	C₂²×C₈₃	1	4	yes	—
452	#476	C₂²×C₈₃	1	1	yes	characteristic
453	#475	C₂²×C₈₃	1	1	yes	characteristic
454	#474	C₂²×C₈₃	1	1	yes	characteristic
455	#474	C₂²×C₈₃	1	2	yes	—
456	#474	C₂²×C₈₃	1	2	yes	—
457	#474	C₂²×C₈₃	1	4	yes	—
458	#474	C₂²×C₈₃	1	4	yes	—
459	#464	C₂²×C₈₃	1	4	yes	—
460	#463	C₂²×C₈₃	1	4	yes	—
461	#462	C₂²×C₈₃	1	1	yes	characteristic
462	#461	C₂²×C₈₃	1	1	yes	characteristic
463	#460	C₂²×C₈₃	1	1	yes	characteristic
464	#459	C₂²×C₈₃	1	1	yes	characteristic
465	#452	C₂²×C₈₃	1	2	yes	—
466	#449	C₂²×C₈₃	1	2	yes	—
467	#446	C₂²×C₈₃	1	2	yes	—
468	#446	C₂²×C₈₃	1	2	yes	—
469	C₈×Q₈	C₂²×C₈₃	1	2	yes	—
470	C₈×Q₈	C₂²×C₈₃	1	2	yes	—
471	#440	C₂²×C₈₃	1	4	yes	—
472	#440	C₂²×C₈₃	1	4	yes	—
473	C₄×Q₁₆	C₂²×C₈₃	1	2	yes	—
474	C₄×Q₁₆	C₂²×C₈₃	1	4	yes	—
475	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	—
476	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	—
477	C₄×D₈	C₂²×C₈₃	1	4	yes	—
478	C₄×D₈	C₂²×C₈₃	1	2	yes	—
479	#433	C₂²×C₈₃	1	4	yes	—
480	#431	C₂²×C₈₃	1	1	yes	characteristic
481	#431	C₂²×C₈₃	1	1	yes	characteristic
482	C₂×#41	—	2	1	no	—
483	C₂×#41	C₂³×C₈₃	1	1	yes	characteristic
484	C₂²×Q₈	—	2	2	no	—
485	C₂²×Q₈	—	2	2	no	—
486	C₂²×Q₈	—	2	1	no	—
487	C₂×Q₁₆	C₂³×C₈₃	1	2	yes	—
488	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
489	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
490	C₂×D₈	C₂³×C₈₃	1	2	yes	—
491	C₄⋊Q₈	—	2	2	no	—
492	C₄⋊Q₈	—	2	2	no	—
493	C₄⋊Q₈	—	2	2	no	—
494	C₄⋊Q₈	—	2	4	no	—
495	C₄⋊Q₈	—	2	2	no	—
496	C₄⋊Q₈	—	2	4	no	—
497	C₄⋊Q₈	—	2	1	no	—
498	C₄⋊Q₈	—	2	1	no	—
499	C₄⋊Q₈	D₄×C₈₃	1	1	yes	characteristic
500	C₄⋊Q₈	D₄×C₈₃	1	1	yes	characteristic
501	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
502	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
503	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
504	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
505	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
506	C₄⋊Q₈	C₂³×C₈₃	1	4	yes	—
507	C₄⋊Q₈	C₂³×C₈₃	1	4	yes	—
508	#127	C₂³×C₈₃	1	1	yes	characteristic
509	#126	—	2	4	no	—
510	#126	—	2	4	no	—
511	#125	—	2	2	no	—
512	#125	—	2	4	no	—
513	#125	—	2	1	no	—
514	#125	D₄×C₈₃	1	2	yes	—
515	#125	C₂³×C₈₃	1	4	yes	—
516	#124	—	2	2	no	—
517	#124	—	2	4	no	—
518	#124	—	2	1	no	—
519	#124	C₂³×C₈₃	1	4	yes	—
520	#123	—	2	4	no	—
521	#123	—	2	4	no	—
522	C₂²⋊Q₈	—	2	2	no	—
523	C₂²⋊Q₈	—	2	2	no	—
524	C₂²⋊Q₈	—	2	1	no	—
525	C₂²⋊Q₈	—	2	2	no	—
526	C₂²⋊Q₈	—	2	2	no	—
527	C₂²⋊Q₈	—	2	4	no	—
528	C₂²⋊Q₈	—	2	4	no	—
529	C₂²⋊Q₈	—	2	4	no	—
530	C₂²⋊Q₈	—	2	4	no	—
531	C₂²⋊Q₈	—	2	4	no	—
532	C₂²⋊Q₈	D₄×C₈₃	1	2	yes	—
533	C₂²⋊Q₈	D₄×C₈₃	1	2	yes	—
534	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
535	#121	—	2	1	no	—
536	#121	C₂³×C₈₃	1	2	yes	—
537	C₄×Q₈	—	2	2	no	—
538	C₄×Q₈	—	2	2	no	—
539	C₄×Q₈	—	2	2	no	—
540	C₄×Q₈	—	2	1	no	—
541	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
542	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
543	C₄×Q₈	C₂³×C₈₃	1	4	yes	—
544	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
545	C₄×Q₈	C₂³×C₈₃	1	4	yes	—
546	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
547	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
548	C₄×D₄	—	2	1	no	—
549	C₄×D₄	—	2	1	no	—
550	C₄×D₄	—	2	2	no	—
551	C₄×D₄	—	2	4	no	—
552	C₄×D₄	—	2	1	no	—
553	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
554	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
555	C₄×D₄	C₂³×C₈₃	1	4	yes	—
556	C₄×D₄	C₂³×C₈₃	1	2	yes	—
557	C₄×D₄	C₂³×C₈₃	1	4	yes	—
558	#117	—	2	1	no	—
559	#117	—	2	2	no	—
560	#117	—	2	2	no	—
561	#117	—	2	1	no	—
562	#117	C₂³×C₈₃	1	1	yes	characteristic
563	#117	C₂³×C₈₃	1	2	yes	—
564	C₂×C₄⋊C₄	—	2	1	no	—
565	C₂×C₄⋊C₄	—	2	2	no	—
566	C₂×C₄⋊C₄	—	2	2	no	—
567	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
568	C₂×C₄²	—	2	1	no	—
569	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
570	#107	C₂³×C₈₃	1	2	yes	—
571	#107	C₂³×C₈₃	1	4	yes	—
572	#107	C₂³×C₈₃	1	2	yes	—
573	#107	C₂³×C₈₃	1	4	yes	—
574	#107	C₂³×C₈₃	1	4	yes	—
575	#107	C₂³×C₈₃	1	4	yes	—
576	#106	C₂³×C₈₃	1	2	yes	—
577	#106	C₂³×C₈₃	1	2	yes	—
578	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
579	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
580	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
581	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
582	C₄⋊C₈	C₂³×C₈₃	1	4	yes	—
583	C₄⋊C₈	C₂³×C₈₃	1	4	yes	—
584	#103	C₂³×C₈₃	1	2	yes	—
585	#103	C₂³×C₈₃	1	2	yes	—
586	#103	C₂³×C₈₃	1	2	yes	—
587	#103	C₂³×C₈₃	1	2	yes	—
588	#103	C₂³×C₈₃	1	4	yes	—
589	#103	C₂³×C₈₃	1	4	yes	—
590	#102	C₂³×C₈₃	1	2	yes	—
591	#102	C₂³×C₈₃	1	2	yes	—
592	#102	C₂³×C₈₃	1	2	yes	—
593	#102	C₂³×C₈₃	1	4	yes	—
594	#102	C₂³×C₈₃	1	2	yes	—
595	#102	C₂³×C₈₃	1	4	yes	—
596	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
597	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
598	#97	C₂³×C₈₃	1	4	yes	—
599	C₄×C₈	C₂³×C₈₃	1	2	yes	—
600	C₄×C₈	C₂³×C₈₃	1	2	yes	—
601	C₄×C₈	C₂³×C₈₃	1	4	yes	—
602	#41	—	2	2	no	—
603	#41	—	2	2	no	—
604	#41	—	8	2	no	—
605	C₂×Q₈	—	2	1	no	—
606	C₂×Q₈	—	2	2	no	—
607	C₂×Q₈	—	2	4	no	—
608	C₂×Q₈	—	2	4	no	—
609	C₂×Q₈	—	2	2	no	—
610	C₂×Q₈	—	2	1	no	—
611	C₂×Q₈	—	8	2	no	—
612	C₂×Q₈	—	8	4	no	—
613	C₂×Q₈	—	8	4	no	—
614	C₂×Q₈	C₂×D₄×C₈₃	1	2	yes	—
615	C₂×Q₈	C₂×D₄×C₈₃	1	2	yes	—
616	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
617	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	—	2	2	no	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	2	1	no	—
622	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
623	C₂×D₄	C₂⁴×C₈₃	1	1	yes	characteristic
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	—	2	2	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	2	no	—
629	C₂²×C₄	—	2	4	no	—
630	C₂²×C₄	—	2	4	no	—
631	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
632	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
633	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
634	Q₁₆	—	2	4	no	—
635	SD₁₆	—	2	4	no	—
636	SD₁₆	—	2	4	no	—
637	D₈	—	2	4	no	—
638	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
639	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
640	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
641	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	2	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	2	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	—	2	1	no	—
650	C₄⋊C₄	—	2	1	no	—
651	C₄⋊C₄	—	2	1	no	—
652	C₄⋊C₄	—	2	1	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	2	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
660	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
661	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
662	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
663	C₄⋊C₄	C₂×D₄×C₈₃	1	4	yes	—
664	C₄⋊C₄	C₂×D₄×C₈₃	1	4	yes	—
665	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
666	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
667	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
668	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
669	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
670	C₂²⋊C₄	—	2	2	no	—
671	C₂²⋊C₄	—	2	1	no	—
672	C₂²⋊C₄	—	2	1	no	—
673	C₂²⋊C₄	—	2	1	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	2	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	2	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	C₂×D₄×C₈₃	1	4	yes	—
681	C₄²	—	2	1	no	—
682	C₄²	—	2	1	no	—
683	C₄²	—	2	1	no	—
684	C₄²	—	2	2	no	—
685	C₄²	—	2	4	no	—
686	C₄²	—	2	4	no	—
687	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
688	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
689	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
690	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
691	C₄²	C₂⁴×C₈₃	1	4	yes	—
692	C₂³	—	2	1	no	—
693	C₂³	—	2	2	no	—
694	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
695	Q₈	—	2	4	no	—
696	Q₈	—	2	4	no	—
697	Q₈	—	2	1	no	—
698	Q₈	—	2	2	no	—
699	Q₈	—	2	2	no	—
700	Q₈	—	4	2	no	—
701	Q₈	—	4	4	no	—
702	Q₈	—	8	2	no	—
703	Q₈	—	8	4	no	—
704	Q₈	—	8	4	no	—
705	Q₈	—	8	1	no	—
706	Q₈	2₋¹⁺⁴×C₈₃	1	2	yes	—
707	D₄	—	2	4	no	—
708	D₄	—	2	1	no	—
709	D₄	—	2	2	no	—
710	D₄	—	2	2	no	—
711	D₄	—	4	2	no	—
712	D₄	—	8	1	no	—
713	D₄	—	8	2	no	—
714	D₄	2₋¹⁺⁴×C₈₃	1	2	yes	—
715	C₂×C₄	—	2	4	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	4	no	—
727	C₂×C₄	—	4	2	no	—
728	C₂×C₄	—	4	4	no	—
729	C₂×C₄	—	4	2	no	—
730	C₂×C₄	—	8	4	no	—
731	C₂×C₄	—	8	4	no	—
732	C₂×C₄	—	8	2	no	—
733	C₂×C₄	C₂²×D₄×C₈₃	1	4	yes	—
734	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
735	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
736	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
737	C₂×C₄	C₂²×D₄×C₈₃	1	4	yes	—
738	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
739	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
740	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
741	C₈	—	2	2	no	—
742	C₈	—	2	2	no	—
743	C₈	—	2	2	no	—
744	C₈	—	2	2	no	—
745	C₂²	—	2	1	no	—
746	C₂²	—	2	1	no	—
747	C₂²	—	2	1	no	—
748	C₂²	—	2	2	no	—
749	C₂²	—	4	1	no	—
750	C₂²	—	4	1	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	4	2	no	—
754	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
755	C₄	—	2	1	no	—
756	C₄	—	2	4	no	—
757	C₄	—	2	1	no	—
758	C₄	—	2	4	no	—
759	C₄	—	2	1	no	—
760	C₄	—	2	2	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	1	no	—
763	C₄	—	4	2	no	—
764	C₄	—	4	4	no	—
765	C₄	—	4	1	no	—
766	C₄	—	4	2	no	—
767	C₄	#576×C₈₃	1	2	yes	—
768	C₄	#578×C₈₃	1	2	yes	—
769	C₄	C₂×2₋¹⁺⁴×C₈₃	1	1	yes	characteristic
770	C₄	C₂×2₋¹⁺⁴×C₈₃	1	1	yes	characteristic
771	C₂	—	4	1	no	—
772	C₂	—	4	2	no	—
773	C₂	—	8	2	no	—
774	C₂	C₈₃×#3486	1	1	yes	characteristic
775	C₂	C₂×#576×C₈₃	1	1	yes	characteristic
776	C₂	C₂×#578×C₈₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₃
prime radical	C₈₃×#3106	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₃ ◁ #533×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₃×#3550	C₂	semidirect
2. C₈₃×#3503	C₂	semidirect
3. C₈₃×#3386	C₂	semidirect
4. C₈₃×#3385	C₂	semidirect
5. Q₈×Q₁₆×C₈₃	C₂	semidirect
6. Q₈×D₈×C₈₃	C₂	semidirect
7. C₈₃×#3375	C₂	semidirect
8. C₈₃×#3367	C₂	semidirect
9. C₈₃×#3364	C₂	semidirect
10. C₈₃×#3361	C₂	semidirect
11. C₈₃×#3243	C₂	semidirect
12. C₈₃×#3230	C₂	semidirect
13. C₈₃×#3226	C₂	semidirect
14. C₈₃×#3124	C₂	semidirect
15. C₈₃×#3107	C₂	semidirect
17. C₈₃×#2986	C₂	semidirect
382. #61870	C₈₃	direct (N × H)
389. #3550	C₂×C₈₃	semidirect
390. #3503	C₂×C₈₃	semidirect
391. #3386	C₂×C₈₃	semidirect
392. #3385	C₂×C₈₃	semidirect
393. Q₈×Q₁₆	C₂×C₈₃	semidirect
394. Q₈×D₈	C₂×C₈₃	semidirect
395. #3375	C₂×C₈₃	semidirect
396. #3367	C₂×C₈₃	semidirect
397. #3364	C₂×C₈₃	semidirect
398. #3361	C₂×C₈₃	semidirect
399. #3243	C₂×C₈₃	semidirect
400. #3230	C₂×C₈₃	semidirect
401. #3226	C₂×C₈₃	semidirect
402. #3124	C₂×C₈₃	semidirect
403. #3107	C₂×C₈₃	semidirect
405. #2986	C₂×C₈₃	semidirect
406. C₈₃	#61870	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×#3550	2
C₈₃×#3503	2
C₈₃×#3386	2
C₈₃×#3385	2
Q₈×Q₁₆×C₈₃	2
Q₈×D₈×C₈₃	2
C₈₃×#3375	2
C₈₃×#3367	2
C₈₃×#3364	2
C₈₃×#3361	2
C₈₃×#3243	2
C₈₃×#3230	2
C₈₃×#3226	2
C₈₃×#3124	2
C₈₃×#3107	2
C₈₃×#3106	2
C₈₃×#2986	2
#61870	83

Subgroups — C83×#61870 #35289694

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#61870 #35289694