Subgroups — C₈₃×#62858 #35290682

Order 21248.

7310 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3524	C₂	1	4	yes	maximal, complemented
2	C₈₃×#3519	C₂	1	12	yes	maximal, complemented
3	C₈₃×#3517	C₂	1	4	yes	maximal, complemented
4	C₈₃×#3513	C₂	1	12	yes	maximal, complemented
5	C₈₃×#3512	C₂	1	3	yes	maximal, complemented
6	C₈₃×#3508	C₂	1	3	yes	maximal, complemented
7	C₈₃×#3504	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₃×#3498	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₃×#3494	C₂	1	6	yes	maximal, complemented
10	C₈₃×#3488	C₂	1	2	yes	maximal, complemented
11	C₈₃×#3460	C₂	1	6	yes	maximal, complemented
12	C₈₃×#3455	C₂	1	3	yes	maximal, complemented
13	C₂×#540×C₈₃	C₂	1	3	yes	maximal, complemented
14	C₄×H(5,𝔽₂)×C₈₃	C₂	1	2	yes	maximal, complemented
15	C₈₃×#3428	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×H(5,𝔽₂)×C₈₃	C₂²	1	2	yes	—
17	C₂²×#41×C₈₃	C₂²	1	1	yes	characteristic
18	#559×C₈₃	C₂²	1	12	yes	complemented
19	#557×C₈₃	C₂²	1	4	yes	complemented
20	#555×C₈₃	C₂²	1	12	yes	complemented
21	#554×C₈₃	C₂²	1	12	yes	complemented
22	#553×C₈₃	C₂²	1	12	yes	complemented
23	#553×C₈₃	C₂²	1	12	yes	complemented
24	#553×C₈₃	C₂²	1	24	yes	complemented
25	#553×C₈₃	C₂²	1	12	yes	complemented
26	#552×C₈₃	C₂²	1	12	yes	complemented
27	#551×C₈₃	C₂²	1	24	yes	complemented
28	#550×C₈₃	C₂²	1	4	yes	complemented
29	#550×C₈₃	C₂²	1	4	yes	complemented
30	#550×C₈₃	C₂²	1	12	yes	complemented
31	#548×C₈₃	C₂²	1	4	yes	complemented
32	#547×C₈₃	C₂²	1	12	yes	complemented
33	#546×C₈₃	C₂²	1	12	yes	complemented
34	#546×C₈₃	C₂²	1	24	yes	complemented
35	#546×C₈₃	C₂²	1	24	yes	complemented
36	D₄²×C₈₃	C₂²	1	12	yes	complemented
37	D₄²×C₈₃	C₂²	1	12	yes	complemented
38	#544×C₈₃	C₂²	1	6	yes	complemented
39	#542×C₈₃	C₂²	1	6	yes	complemented
40	#542×C₈₃	C₂²	1	6	yes	complemented
41	#542×C₈₃	C₂²	1	12	yes	complemented
42	#541×C₈₃	C₂²	1	1	yes	characteristic, complemented
43	#541×C₈₃	C₂²	1	3	yes	complemented
44	#540×C₈₃	C₂²	1	3	yes	complemented
45	#540×C₈₃	C₂²	1	6	yes	complemented
46	#540×C₈₃	C₂²	1	6	yes	complemented
47	#540×C₈₃	C₂²	1	6	yes	complemented
48	#540×C₈₃	C₂²	1	12	yes	complemented
49	#540×C₈₃	C₂²	1	12	yes	complemented
50	#540×C₈₃	C₂²	1	3	yes	complemented
51	#540×C₈₃	C₂²	1	12	yes	complemented
52	#539×C₈₃	C₂²	1	12	yes	complemented
53	#538×C₈₃	C₂²	1	12	yes	complemented
54	#538×C₈₃	C₂²	1	24	yes	complemented
55	#537×C₈₃	C₂²	1	6	yes	complemented
56	#535×C₈₃	C₂²	1	6	yes	complemented
57	#535×C₈₃	C₂²	1	6	yes	complemented
58	#533×C₈₃	C₂²	1	3	yes	complemented
59	#532×C₈₃	C₂²	1	3	yes	complemented
60	#532×C₈₃	C₂²	1	12	yes	complemented
61	#532×C₈₃	C₂²	1	12	yes	complemented
62	C₂×#127×C₈₃	C₂²	1	3	yes	complemented
63	#529×C₈₃	C₂²	1	12	yes	complemented
64	#529×C₈₃	C₂²	1	12	yes	complemented
65	#529×C₈₃	C₂²	1	12	yes	complemented
66	#529×C₈₃	C₂²	1	12	yes	complemented
67	C₂×#125×C₈₃	C₂²	1	3	yes	complemented
68	#525×C₈₃	C₂²	1	6	yes	complemented
69	#525×C₈₃	C₂²	1	24	yes	complemented
70	C₂×#123×C₈₃	C₂²	1	12	yes	complemented
71	C₂×#121×C₈₃	C₂²	1	6	yes	complemented
72	C₂×#121×C₈₃	C₂²	1	12	yes	complemented
73	#520×C₈₃	C₂²	1	2	yes	—
74	#520×C₈₃	C₂²	1	6	yes	complemented
75	#520×C₈₃	C₂²	1	2	yes	complemented
76	#520×C₈₃	C₂²	1	6	yes	complemented
77	#520×C₈₃	C₂²	1	4	yes	complemented
78	#519×C₈₃	C₂²	1	2	yes	complemented
79	#518×C₈₃	C₂²	1	6	yes	complemented
80	#518×C₈₃	C₂²	1	6	yes	complemented
81	#518×C₈₃	C₂²	1	12	yes	complemented
82	C₄×#41×C₈₃	C₂²	1	1	yes	characteristic
83	C₄×#41×C₈₃	C₂²	1	1	yes	characteristic
84	C₄×#41×C₈₃	C₂²	1	3	yes	complemented
85	C₄×#41×C₈₃	C₂²	1	3	yes	complemented
86	C₄×#41×C₈₃	C₂²	1	6	yes	complemented
87	C₄×#41×C₈₃	C₂²	1	4	yes	complemented
88	C₂×C₄×D₄×C₈₃	C₂²	1	6	yes	complemented
89	C₂×C₄×D₄×C₈₃	C₂²	1	12	yes	complemented
90	C₂×#117×C₈₃	C₂²	1	3	yes	complemented
91	C₂×#117×C₈₃	C₂²	1	3	yes	complemented
92	H(5,𝔽₂)×C₈₃	—	2	16	no	—
93	C₂×#41×C₈₃	—	2	8	no	—
94	C₂×#41×C₈₃	C₂³	1	3	yes	—
95	C₂×#41×C₈₃	C₂³	1	6	yes	—
96	C₂×#41×C₈₃	C₂³	1	4	yes	—
97	C₂×#41×C₈₃	C₂³	1	3	yes	—
98	C₂×#41×C₈₃	C₂³	1	1	yes	characteristic
99	C₂×#41×C₈₃	C₂³	1	24	yes	—
100	C₂×#41×C₈₃	C₂³	1	1	yes	characteristic
101	C₂²×Q₈×C₈₃	C₂³	1	1	yes	characteristic
102	C₂²×D₄×C₈₃	C₂³	1	6	yes	—
103	C₂²×D₄×C₈₃	C₂³	1	12	yes	—
104	C₂²×D₄×C₈₃	C₂³	1	3	yes	—
105	C₂²×D₄×C₈₃	C₂³	1	12	yes	—
106	C₂²×D₄×C₈₃	C₂³	1	12	yes	—
107	C₂³×C₄×C₈₃	C₂³	1	3	yes	—
108	C₂³×C₄×C₈₃	C₂³	1	12	yes	—
109	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
110	C₄⋊Q₈×C₈₃	C₂³	1	6	yes	—
111	C₄⋊Q₈×C₈₃	C₂³	1	12	yes	—
112	#127×C₈₃	C₂³	1	3	yes	—
113	#127×C₈₃	C₂³	1	6	yes	—
114	#127×C₈₃	C₂³	1	12	yes	—
115	#127×C₈₃	C₂³	1	12	yes	—
116	#126×C₈₃	C₂³	1	4	yes	—
117	#126×C₈₃	C₂³	1	12	yes	—
118	#126×C₈₃	C₂³	1	12	yes	—
119	#126×C₈₃	C₂³	1	24	yes	—
120	#126×C₈₃	C₂³	1	12	yes	—
121	#125×C₈₃	C₂³	1	3	yes	—
122	#125×C₈₃	C₂³	1	6	yes	—
123	#125×C₈₃	C₂³	1	12	yes	—
124	#125×C₈₃	C₂³	1	4	yes	—
125	#125×C₈₃	C₂³	1	12	yes	—
126	#125×C₈₃	C₂³	1	12	yes	—
127	#125×C₈₃	C₂³	1	1	yes	characteristic
128	#124×C₈₃	C₂³	1	6	yes	—
129	#124×C₈₃	C₂³	1	12	yes	—
130	#124×C₈₃	C₂³	1	12	yes	—
131	#124×C₈₃	C₂³	1	12	yes	—
132	#124×C₈₃	C₂³	1	24	yes	—
133	#123×C₈₃	C₂³	1	12	yes	—
134	#123×C₈₃	C₂³	1	24	yes	—
135	#123×C₈₃	C₂³	1	24	yes	—
136	#123×C₈₃	C₂³	1	24	yes	—
137	#123×C₈₃	C₂³	1	12	yes	—
138	#123×C₈₃	C₂³	1	12	yes	—
139	#123×C₈₃	C₂³	1	24	yes	—
140	#123×C₈₃	C₂³	1	12	yes	—
141	#123×C₈₃	C₂³	1	12	yes	—
142	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
143	C₂²⋊Q₈×C₈₃	C₂³	1	12	yes	—
144	C₂²⋊Q₈×C₈₃	C₂³	1	6	yes	—
145	C₂²⋊Q₈×C₈₃	C₂³	1	24	yes	—
146	C₂²⋊Q₈×C₈₃	C₂³	1	12	yes	—
147	C₂²⋊Q₈×C₈₃	C₂³	1	12	yes	—
148	C₂²⋊Q₈×C₈₃	C₂³	1	12	yes	—
149	#121×C₈₃	C₂³	1	6	yes	—
150	#121×C₈₃	C₂³	1	12	yes	—
151	#121×C₈₃	C₂³	1	24	yes	—
152	#121×C₈₃	C₂³	1	12	yes	—
153	#121×C₈₃	C₂³	1	12	yes	—
154	#121×C₈₃	C₂³	1	24	yes	—
155	#121×C₈₃	C₂³	1	12	yes	—
156	#121×C₈₃	C₂³	1	24	yes	—
157	#121×C₈₃	C₂³	1	6	yes	—
158	#121×C₈₃	C₂³	1	24	yes	—
159	#121×C₈₃	C₂³	1	12	yes	—
160	#121×C₈₃	C₂³	1	12	yes	—
161	#121×C₈₃	C₂³	1	12	yes	—
162	#121×C₈₃	C₂³	1	12	yes	—
163	#121×C₈₃	C₂³	1	12	yes	—
164	#121×C₈₃	C₂³	1	24	yes	—
165	#120×C₈₃	C₂³	1	24	yes	—
166	#120×C₈₃	C₂³	1	24	yes	—
167	#120×C₈₃	C₂³	1	12	yes	—
168	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
169	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
170	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
171	C₄×Q₈×C₈₃	C₂³	1	6	yes	—
172	C₄×Q₈×C₈₃	C₂³	1	6	yes	—
173	C₄×Q₈×C₈₃	C₂³	1	4	yes	—
174	C₄×Q₈×C₈₃	C₂³	1	6	yes	—
175	C₄×Q₈×C₈₃	C₂³	1	12	yes	—
176	C₄×D₄×C₈₃	C₂³	1	6	yes	—
177	C₄×D₄×C₈₃	C₂³	1	12	yes	—
178	C₄×D₄×C₈₃	C₂³	1	6	yes	—
179	C₄×D₄×C₈₃	C₂³	1	12	yes	—
180	C₄×D₄×C₈₃	C₂³	1	12	yes	—
181	C₄×D₄×C₈₃	C₂³	1	12	yes	—
182	C₄×D₄×C₈₃	C₂³	1	12	yes	—
183	C₄×D₄×C₈₃	C₂³	1	24	yes	—
184	C₄×D₄×C₈₃	C₂³	1	12	yes	—
185	C₄×D₄×C₈₃	C₂³	1	6	yes	—
186	C₄×D₄×C₈₃	C₂³	1	12	yes	—
187	C₄×D₄×C₈₃	C₂³	1	6	yes	—
188	C₄×D₄×C₈₃	C₂³	1	12	yes	—
189	C₄×D₄×C₈₃	C₂³	1	12	yes	—
190	C₄×D₄×C₈₃	C₂³	1	6	yes	—
191	C₄×D₄×C₈₃	C₂³	1	12	yes	—
192	C₄×D₄×C₈₃	C₂³	1	6	yes	—
193	C₄×D₄×C₈₃	C₂³	1	12	yes	—
194	C₄×D₄×C₈₃	C₂³	1	12	yes	—
195	C₄×D₄×C₈₃	C₂³	1	24	yes	—
196	C₄×D₄×C₈₃	C₂³	1	24	yes	—
197	C₄×D₄×C₈₃	C₂³	1	12	yes	—
198	#117×C₈₃	C₂³	1	1	yes	characteristic
199	#117×C₈₃	C₂³	1	3	yes	—
200	#117×C₈₃	C₂³	1	3	yes	—
201	#117×C₈₃	C₂³	1	3	yes	—
202	#117×C₈₃	C₂³	1	3	yes	—
203	#117×C₈₃	C₂³	1	3	yes	—
204	#117×C₈₃	C₂³	1	6	yes	—
205	#117×C₈₃	C₂³	1	6	yes	—
206	#117×C₈₃	C₂³	1	6	yes	—
207	#117×C₈₃	C₂³	1	6	yes	—
208	#117×C₈₃	C₂³	1	6	yes	—
209	#117×C₈₃	C₂³	1	12	yes	—
210	#117×C₈₃	C₂³	1	12	yes	—
211	#117×C₈₃	C₂³	1	24	yes	—
212	C₂×C₄⋊C₄×C₈₃	C₂³	1	6	yes	—
213	C₂×C₄⋊C₄×C₈₃	C₂³	1	6	yes	—
214	C₂×C₄⋊C₄×C₈₃	C₂³	1	6	yes	—
215	C₂×C₄⋊C₄×C₈₃	C₂³	1	12	yes	—
216	C₂×C₄⋊C₄×C₈₃	C₂³	1	12	yes	—
217	C₂×C₂²⋊C₄×C₈₃	C₂³	1	6	yes	—
218	C₂×C₂²⋊C₄×C₈₃	C₂³	1	6	yes	—
219	C₂×C₂²⋊C₄×C₈₃	C₂³	1	12	yes	—
220	C₂×C₂²⋊C₄×C₈₃	C₂³	1	24	yes	—
221	C₂×C₂²⋊C₄×C₈₃	C₂³	1	12	yes	—
222	C₂×C₄²×C₈₃	C₂³	1	3	yes	—
223	C₂×C₄²×C₈₃	C₂³	1	3	yes	—
224	C₂×C₄²×C₈₃	C₂³	1	6	yes	—
225	C₂×C₄²×C₈₃	C₂³	1	12	yes	—
226	C₂⁴×C₈₃	C₂⁴	1	3	yes	—
227	C₂⁴×C₈₃	C₂⁴	1	12	yes	—
228	#41×C₈₃	—	2	4	no	—
229	#41×C₈₃	—	2	16	no	—
230	#41×C₈₃	—	2	12	no	—
231	#41×C₈₃	—	2	12	no	—
232	#41×C₈₃	—	2	24	no	—
233	#41×C₈₃	—	8	24	no	—
234	#41×C₈₃	#41	1	8	yes	complemented
235	C₂×Q₈×C₈₃	—	2	4	no	—
236	C₂×Q₈×C₈₃	C₂⁴	1	3	yes	—
237	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
238	C₂×Q₈×C₈₃	C₂⁴	1	12	yes	—
239	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
240	C₂×D₄×C₈₃	—	2	12	no	—
241	C₂×D₄×C₈₃	—	2	48	no	—
242	C₂×D₄×C₈₃	—	2	24	no	—
243	C₂×D₄×C₈₃	—	8	12	no	—
244	C₂×D₄×C₈₃	—	8	12	no	—
245	C₂×D₄×C₈₃	C₂⁴	1	6	yes	—
246	C₂×D₄×C₈₃	C₂⁴	1	12	yes	—
247	C₂×D₄×C₈₃	C₂⁴	1	6	yes	—
248	C₂×D₄×C₈₃	C₂⁴	1	12	yes	—
249	C₂×D₄×C₈₃	C₂⁴	1	3	yes	—
250	C₂×D₄×C₈₃	C₂⁴	1	12	yes	—
251	C₂×D₄×C₈₃	C₂⁴	1	24	yes	—
252	C₂×D₄×C₈₃	C₂⁴	1	12	yes	—
253	C₂×D₄×C₈₃	C₂⁴	1	24	yes	—
254	C₂×D₄×C₈₃	C₂⁴	1	12	yes	—
255	C₂×D₄×C₈₃	C₂⁴	1	3	yes	—
256	C₂²×C₄×C₈₃	—	2	12	no	—
257	C₂²×C₄×C₈₃	—	8	12	no	—
258	C₂²×C₄×C₈₃	C₂⁴	1	3	yes	—
259	C₂²×C₄×C₈₃	C₂⁴	1	12	yes	—
260	C₂²×C₄×C₈₃	C₂⁴	1	3	yes	—
261	C₂²×C₄×C₈₃	C₂⁴	1	3	yes	—
262	C₂²×C₄×C₈₃	C₂⁴	1	3	yes	—
263	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₈₃	C₂⁴	1	6	yes	—
265	C₂²×C₄×C₈₃	C₂⁴	1	12	yes	—
266	C₂²×C₄×C₈₃	C₂⁴	1	6	yes	—
267	C₂²×C₄×C₈₃	C₂⁴	1	12	yes	—
268	C₂²×C₄×C₈₃	C₂⁴	1	12	yes	—
269	C₂²×C₄×C₈₃	C₂⁴	1	12	yes	—
270	C₂²×C₄×C₈₃	C₂⁴	1	24	yes	—
271	C₂²×C₄×C₈₃	C₂⁴	1	3	yes	—
272	C₄⋊C₄×C₈₃	C₂⁴	1	6	yes	—
273	C₄⋊C₄×C₈₃	C₂⁴	1	6	yes	—
274	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
275	C₄⋊C₄×C₈₃	C₂⁴	1	6	yes	—
276	C₄⋊C₄×C₈₃	C₂⁴	1	12	yes	—
277	C₄⋊C₄×C₈₃	C₂⁴	1	12	yes	—
278	C₄⋊C₄×C₈₃	C₂⁴	1	12	yes	—
279	C₄⋊C₄×C₈₃	C₂⁴	1	6	yes	—
280	C₄⋊C₄×C₈₃	C₂⁴	1	6	yes	—
281	C₄⋊C₄×C₈₃	C₂⁴	1	6	yes	—
282	C₄⋊C₄×C₈₃	C₂⁴	1	24	yes	—
283	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
284	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
285	C₄⋊C₄×C₈₃	C₂⁴	1	12	yes	—
286	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
287	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
288	C₄⋊C₄×C₈₃	C₂⁴	1	12	yes	—
289	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
290	C₂²⋊C₄×C₈₃	C₂⁴	1	6	yes	—
291	C₂²⋊C₄×C₈₃	C₂⁴	1	2	yes	—
292	C₂²⋊C₄×C₈₃	C₂⁴	1	6	yes	—
293	C₂²⋊C₄×C₈₃	C₂⁴	1	12	yes	—
294	C₂²⋊C₄×C₈₃	C₂⁴	1	12	yes	—
295	C₂²⋊C₄×C₈₃	C₂⁴	1	24	yes	—
296	C₂²⋊C₄×C₈₃	C₂⁴	1	12	yes	—
297	C₂²⋊C₄×C₈₃	C₂⁴	1	12	yes	—
298	C₂²⋊C₄×C₈₃	C₂⁴	1	6	yes	—
299	C₂²⋊C₄×C₈₃	C₂⁴	1	6	yes	—
300	C₂²⋊C₄×C₈₃	C₂⁴	1	6	yes	—
301	C₂²⋊C₄×C₈₃	C₂⁴	1	24	yes	—
302	C₂²⋊C₄×C₈₃	C₂⁴	1	12	yes	—
303	C₂²⋊C₄×C₈₃	C₂⁴	1	4	yes	—
304	C₂²⋊C₄×C₈₃	C₂⁴	1	12	yes	—
305	C₂²⋊C₄×C₈₃	C₂⁴	1	12	yes	—
306	C₂²⋊C₄×C₈₃	C₂⁴	1	12	yes	—
307	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
308	C₄²×C₈₃	C₂⁴	1	3	yes	—
309	C₄²×C₈₃	C₂⁴	1	6	yes	—
310	C₄²×C₈₃	C₂⁴	1	3	yes	—
311	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
312	C₄²×C₈₃	C₂⁴	1	4	yes	—
313	C₄²×C₈₃	C₂⁴	1	12	yes	—
314	C₄²×C₈₃	C₂⁴	1	12	yes	—
315	C₄²×C₈₃	C₂⁴	1	12	yes	—
316	C₄²×C₈₃	C₂⁴	1	6	yes	—
317	C₂³×C₈₃	—	2	6	no	—
318	C₂³×C₈₃	—	2	24	no	—
319	C₂³×C₈₃	—	4	12	no	—
320	C₂³×C₈₃	—	4	6	no	—
321	C₂³×C₈₃	—	4	12	no	—
322	C₂³×C₈₃	C₂⁵	1	1	yes	characteristic
323	C₂³×C₈₃	C₂⁵	1	12	yes	—
324	C₂³×C₈₃	C₂⁵	1	3	yes	—
325	C₂³×C₈₃	C₂⁵	1	3	yes	—
326	Q₈×C₈₃	—	2	6	no	—
327	Q₈×C₈₃	—	2	4	no	—
328	Q₈×C₈₃	—	4	12	no	—
329	Q₈×C₈₃	C₂×#41	1	4	yes	—
330	D₄×C₈₃	—	2	24	no	—
331	D₄×C₈₃	—	2	12	no	—
332	D₄×C₈₃	—	2	24	no	—
333	D₄×C₈₃	—	2	12	no	—
334	D₄×C₈₃	—	2	6	no	—
335	D₄×C₈₃	—	4	12	no	—
336	D₄×C₈₃	—	4	12	no	—
337	D₄×C₈₃	—	4	24	no	—
338	D₄×C₈₃	—	4	24	no	—
339	D₄×C₈₃	—	4	12	no	—
340	D₄×C₈₃	C₂×#41	1	12	yes	—
341	C₂×C₄×C₈₃	—	2	6	no	—
342	C₂×C₄×C₈₃	—	2	2	no	—
343	C₂×C₄×C₈₃	—	2	6	no	—
344	C₂×C₄×C₈₃	—	2	6	no	—
345	C₂×C₄×C₈₃	—	2	6	no	—
346	C₂×C₄×C₈₃	—	2	24	no	—
347	C₂×C₄×C₈₃	—	4	6	no	—
348	C₂×C₄×C₈₃	—	4	12	no	—
349	C₂×C₄×C₈₃	—	4	12	no	—
350	C₂×C₄×C₈₃	—	4	24	no	—
351	C₂×C₄×C₈₃	—	4	6	no	—
352	C₂×C₄×C₈₃	—	4	12	no	—
353	C₂×C₄×C₈₃	—	4	12	no	—
354	C₂×C₄×C₈₃	C₂×#41	1	12	yes	—
355	C₂×C₄×C₈₃	C₂⁵	1	2	yes	—
356	C₂×C₄×C₈₃	C₂⁵	1	6	yes	—
357	C₂×C₄×C₈₃	C₂⁵	1	3	yes	—
358	C₂×C₄×C₈₃	C₂⁵	1	4	yes	—
359	C₂×C₄×C₈₃	C₂⁵	1	4	yes	—
360	C₂×C₄×C₈₃	C₂⁵	1	6	yes	—
361	C₂×C₄×C₈₃	C₂⁵	1	2	yes	—
362	C₂×C₄×C₈₃	C₂⁵	1	12	yes	—
363	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
364	C₂×C₄×C₈₃	C₂⁵	1	3	yes	—
365	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
366	C₂²×C₈₃	—	2	6	no	—
367	C₂²×C₈₃	—	2	1	no	—
368	C₂²×C₈₃	—	2	3	no	—
369	C₂²×C₈₃	—	2	12	no	—
370	C₂²×C₈₃	—	2	12	no	—
371	C₂²×C₈₃	—	2	6	no	—
372	C₂²×C₈₃	—	2	12	no	—
373	C₂²×C₈₃	—	2	2	no	—
374	C₂²×C₈₃	—	8	6	no	—
375	C₂²×C₈₃	—	8	24	no	—
376	C₂²×C₈₃	C₂²×#41	1	6	yes	—
377	C₂²×C₈₃	C₂⁶	1	1	yes	characteristic
378	C₄×C₈₃	—	2	1	no	—
379	C₄×C₈₃	—	2	4	no	—
380	C₄×C₈₃	—	2	3	no	—
381	C₄×C₈₃	—	2	2	no	—
382	C₄×C₈₃	—	2	6	no	—
383	C₄×C₈₃	—	2	12	no	—
384	C₄×C₈₃	—	2	2	no	—
385	C₄×C₈₃	—	2	6	no	—
386	C₄×C₈₃	—	2	4	no	—
387	C₄×C₈₃	C₂²×#41	1	6	yes	—
388	C₄×C₈₃	C₂²×#41	1	2	yes	—
389	#62858	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
390	C₂×C₈₃	—	2	6	no	—
391	C₂×C₈₃	—	4	3	no	—
392	C₂×C₈₃	—	4	12	no	—
393	C₂×C₈₃	—	4	1	no	—
394	C₂×C₈₃	C₂³×#41	1	1	yes	characteristic
395	C₂×C₈₃	H(7,𝔽₂)	1	2	yes	—
396	#3524	C₂×C₈₃	1	4	yes	complemented
397	#3519	C₂×C₈₃	1	12	yes	complemented
398	#3517	C₂×C₈₃	1	4	yes	complemented
399	#3513	C₂×C₈₃	1	12	yes	complemented
400	#3512	C₂×C₈₃	1	3	yes	complemented
401	#3508	C₂×C₈₃	1	3	yes	complemented
402	#3504	C₂×C₈₃	1	1	yes	characteristic, complemented
403	#3498	C₂×C₈₃	1	1	yes	characteristic, complemented
404	#3494	C₂×C₈₃	1	6	yes	complemented
405	#3488	C₂×C₈₃	1	2	yes	complemented
406	#3460	C₂×C₈₃	1	6	yes	complemented
407	#3455	C₂×C₈₃	1	3	yes	complemented
408	C₂×#540	C₂×C₈₃	1	3	yes	complemented
409	C₄×H(5,𝔽₂)	C₂×C₈₃	1	2	yes	complemented
410	#3428	C₂×C₈₃	1	1	yes	characteristic, complemented
411	C₈₃	#62858	1	1	yes	characteristic, direct product factor, Sylow
412	C₂×H(5,𝔽₂)	C₂²×C₈₃	1	2	yes	—
413	C₂²×#41	C₂²×C₈₃	1	1	yes	characteristic
414	#559	C₂²×C₈₃	1	12	yes	complemented
415	#557	C₂²×C₈₃	1	4	yes	complemented
416	#555	C₂²×C₈₃	1	12	yes	complemented
417	#554	C₂²×C₈₃	1	12	yes	complemented
418	#553	C₂²×C₈₃	1	12	yes	complemented
419	#553	C₂²×C₈₃	1	12	yes	complemented
420	#553	C₂²×C₈₃	1	24	yes	complemented
421	#553	C₂²×C₈₃	1	12	yes	complemented
422	#552	C₂²×C₈₃	1	12	yes	complemented
423	#551	C₂²×C₈₃	1	24	yes	complemented
424	#550	C₂²×C₈₃	1	4	yes	complemented
425	#550	C₂²×C₈₃	1	4	yes	complemented
426	#550	C₂²×C₈₃	1	12	yes	complemented
427	#548	C₂²×C₈₃	1	4	yes	complemented
428	#547	C₂²×C₈₃	1	12	yes	complemented
429	#546	C₂²×C₈₃	1	12	yes	complemented
430	#546	C₂²×C₈₃	1	24	yes	complemented
431	#546	C₂²×C₈₃	1	24	yes	complemented
432	D₄²	C₂²×C₈₃	1	12	yes	complemented
433	D₄²	C₂²×C₈₃	1	12	yes	complemented
434	#544	C₂²×C₈₃	1	6	yes	complemented
435	#542	C₂²×C₈₃	1	6	yes	complemented
436	#542	C₂²×C₈₃	1	6	yes	complemented
437	#542	C₂²×C₈₃	1	12	yes	complemented
438	#541	C₂²×C₈₃	1	1	yes	characteristic, complemented
439	#541	C₂²×C₈₃	1	3	yes	complemented
440	#540	C₂²×C₈₃	1	3	yes	complemented
441	#540	C₂²×C₈₃	1	6	yes	complemented
442	#540	C₂²×C₈₃	1	6	yes	complemented
443	#540	C₂²×C₈₃	1	6	yes	complemented
444	#540	C₂²×C₈₃	1	12	yes	complemented
445	#540	C₂²×C₈₃	1	12	yes	complemented
446	#540	C₂²×C₈₃	1	3	yes	complemented
447	#540	C₂²×C₈₃	1	12	yes	complemented
448	#539	C₂²×C₈₃	1	12	yes	complemented
449	#538	C₂²×C₈₃	1	12	yes	complemented
450	#538	C₂²×C₈₃	1	24	yes	complemented
451	#537	C₂²×C₈₃	1	6	yes	complemented
452	#535	C₂²×C₈₃	1	6	yes	complemented
453	#535	C₂²×C₈₃	1	6	yes	complemented
454	#533	C₂²×C₈₃	1	3	yes	complemented
455	#532	C₂²×C₈₃	1	3	yes	complemented
456	#532	C₂²×C₈₃	1	12	yes	complemented
457	#532	C₂²×C₈₃	1	12	yes	complemented
458	C₂×#127	C₂²×C₈₃	1	3	yes	complemented
459	#529	C₂²×C₈₃	1	12	yes	complemented
460	#529	C₂²×C₈₃	1	12	yes	complemented
461	#529	C₂²×C₈₃	1	12	yes	complemented
462	#529	C₂²×C₈₃	1	12	yes	complemented
463	C₂×#125	C₂²×C₈₃	1	3	yes	complemented
464	#525	C₂²×C₈₃	1	6	yes	complemented
465	#525	C₂²×C₈₃	1	24	yes	complemented
466	C₂×#123	C₂²×C₈₃	1	12	yes	complemented
467	C₂×#121	C₂²×C₈₃	1	6	yes	complemented
468	C₂×#121	C₂²×C₈₃	1	12	yes	complemented
469	#520	C₂²×C₈₃	1	2	yes	—
470	#520	C₂²×C₈₃	1	6	yes	complemented
471	#520	C₂²×C₈₃	1	2	yes	complemented
472	#520	C₂²×C₈₃	1	6	yes	complemented
473	#520	C₂²×C₈₃	1	4	yes	complemented
474	#519	C₂²×C₈₃	1	2	yes	complemented
475	#518	C₂²×C₈₃	1	6	yes	complemented
476	#518	C₂²×C₈₃	1	6	yes	complemented
477	#518	C₂²×C₈₃	1	12	yes	complemented
478	C₄×#41	C₂²×C₈₃	1	1	yes	characteristic
479	C₄×#41	C₂²×C₈₃	1	1	yes	characteristic
480	C₄×#41	C₂²×C₈₃	1	3	yes	complemented
481	C₄×#41	C₂²×C₈₃	1	3	yes	complemented
482	C₄×#41	C₂²×C₈₃	1	6	yes	complemented
483	C₄×#41	C₂²×C₈₃	1	4	yes	complemented
484	C₂×C₄×D₄	C₂²×C₈₃	1	6	yes	complemented
485	C₂×C₄×D₄	C₂²×C₈₃	1	12	yes	complemented
486	C₂×#117	C₂²×C₈₃	1	3	yes	complemented
487	C₂×#117	C₂²×C₈₃	1	3	yes	complemented
488	H(5,𝔽₂)	—	2	16	no	—
489	C₂×#41	—	2	8	no	—
490	C₂×#41	C₂³×C₈₃	1	3	yes	—
491	C₂×#41	C₂³×C₈₃	1	6	yes	—
492	C₂×#41	C₂³×C₈₃	1	4	yes	—
493	C₂×#41	C₂³×C₈₃	1	3	yes	—
494	C₂×#41	C₂³×C₈₃	1	1	yes	characteristic
495	C₂×#41	C₂³×C₈₃	1	24	yes	—
496	C₂×#41	C₂³×C₈₃	1	1	yes	characteristic
497	C₂²×Q₈	C₂³×C₈₃	1	1	yes	characteristic
498	C₂²×D₄	C₂³×C₈₃	1	6	yes	—
499	C₂²×D₄	C₂³×C₈₃	1	12	yes	—
500	C₂²×D₄	C₂³×C₈₃	1	3	yes	—
501	C₂²×D₄	C₂³×C₈₃	1	12	yes	—
502	C₂²×D₄	C₂³×C₈₃	1	12	yes	—
503	C₂³×C₄	C₂³×C₈₃	1	3	yes	—
504	C₂³×C₄	C₂³×C₈₃	1	12	yes	—
505	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
506	C₄⋊Q₈	C₂³×C₈₃	1	6	yes	—
507	C₄⋊Q₈	C₂³×C₈₃	1	12	yes	—
508	#127	C₂³×C₈₃	1	3	yes	—
509	#127	C₂³×C₈₃	1	6	yes	—
510	#127	C₂³×C₈₃	1	12	yes	—
511	#127	C₂³×C₈₃	1	12	yes	—
512	#126	C₂³×C₈₃	1	4	yes	—
513	#126	C₂³×C₈₃	1	12	yes	—
514	#126	C₂³×C₈₃	1	12	yes	—
515	#126	C₂³×C₈₃	1	24	yes	—
516	#126	C₂³×C₈₃	1	12	yes	—
517	#125	C₂³×C₈₃	1	3	yes	—
518	#125	C₂³×C₈₃	1	6	yes	—
519	#125	C₂³×C₈₃	1	12	yes	—
520	#125	C₂³×C₈₃	1	4	yes	—
521	#125	C₂³×C₈₃	1	12	yes	—
522	#125	C₂³×C₈₃	1	12	yes	—
523	#125	C₂³×C₈₃	1	1	yes	characteristic
524	#124	C₂³×C₈₃	1	6	yes	—
525	#124	C₂³×C₈₃	1	12	yes	—
526	#124	C₂³×C₈₃	1	12	yes	—
527	#124	C₂³×C₈₃	1	12	yes	—
528	#124	C₂³×C₈₃	1	24	yes	—
529	#123	C₂³×C₈₃	1	12	yes	—
530	#123	C₂³×C₈₃	1	24	yes	—
531	#123	C₂³×C₈₃	1	24	yes	—
532	#123	C₂³×C₈₃	1	24	yes	—
533	#123	C₂³×C₈₃	1	12	yes	—
534	#123	C₂³×C₈₃	1	12	yes	—
535	#123	C₂³×C₈₃	1	24	yes	—
536	#123	C₂³×C₈₃	1	12	yes	—
537	#123	C₂³×C₈₃	1	12	yes	—
538	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
539	C₂²⋊Q₈	C₂³×C₈₃	1	12	yes	—
540	C₂²⋊Q₈	C₂³×C₈₃	1	6	yes	—
541	C₂²⋊Q₈	C₂³×C₈₃	1	24	yes	—
542	C₂²⋊Q₈	C₂³×C₈₃	1	12	yes	—
543	C₂²⋊Q₈	C₂³×C₈₃	1	12	yes	—
544	C₂²⋊Q₈	C₂³×C₈₃	1	12	yes	—
545	#121	C₂³×C₈₃	1	6	yes	—
546	#121	C₂³×C₈₃	1	12	yes	—
547	#121	C₂³×C₈₃	1	24	yes	—
548	#121	C₂³×C₈₃	1	12	yes	—
549	#121	C₂³×C₈₃	1	12	yes	—
550	#121	C₂³×C₈₃	1	24	yes	—
551	#121	C₂³×C₈₃	1	12	yes	—
552	#121	C₂³×C₈₃	1	24	yes	—
553	#121	C₂³×C₈₃	1	6	yes	—
554	#121	C₂³×C₈₃	1	24	yes	—
555	#121	C₂³×C₈₃	1	12	yes	—
556	#121	C₂³×C₈₃	1	12	yes	—
557	#121	C₂³×C₈₃	1	12	yes	—
558	#121	C₂³×C₈₃	1	12	yes	—
559	#121	C₂³×C₈₃	1	12	yes	—
560	#121	C₂³×C₈₃	1	24	yes	—
561	#120	C₂³×C₈₃	1	24	yes	—
562	#120	C₂³×C₈₃	1	24	yes	—
563	#120	C₂³×C₈₃	1	12	yes	—
564	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
565	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
566	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
567	C₄×Q₈	C₂³×C₈₃	1	6	yes	—
568	C₄×Q₈	C₂³×C₈₃	1	6	yes	—
569	C₄×Q₈	C₂³×C₈₃	1	4	yes	—
570	C₄×Q₈	C₂³×C₈₃	1	6	yes	—
571	C₄×Q₈	C₂³×C₈₃	1	12	yes	—
572	C₄×D₄	C₂³×C₈₃	1	6	yes	—
573	C₄×D₄	C₂³×C₈₃	1	12	yes	—
574	C₄×D₄	C₂³×C₈₃	1	6	yes	—
575	C₄×D₄	C₂³×C₈₃	1	12	yes	—
576	C₄×D₄	C₂³×C₈₃	1	12	yes	—
577	C₄×D₄	C₂³×C₈₃	1	12	yes	—
578	C₄×D₄	C₂³×C₈₃	1	12	yes	—
579	C₄×D₄	C₂³×C₈₃	1	24	yes	—
580	C₄×D₄	C₂³×C₈₃	1	12	yes	—
581	C₄×D₄	C₂³×C₈₃	1	6	yes	—
582	C₄×D₄	C₂³×C₈₃	1	12	yes	—
583	C₄×D₄	C₂³×C₈₃	1	6	yes	—
584	C₄×D₄	C₂³×C₈₃	1	12	yes	—
585	C₄×D₄	C₂³×C₈₃	1	12	yes	—
586	C₄×D₄	C₂³×C₈₃	1	6	yes	—
587	C₄×D₄	C₂³×C₈₃	1	12	yes	—
588	C₄×D₄	C₂³×C₈₃	1	6	yes	—
589	C₄×D₄	C₂³×C₈₃	1	12	yes	—
590	C₄×D₄	C₂³×C₈₃	1	12	yes	—
591	C₄×D₄	C₂³×C₈₃	1	24	yes	—
592	C₄×D₄	C₂³×C₈₃	1	24	yes	—
593	C₄×D₄	C₂³×C₈₃	1	12	yes	—
594	#117	C₂³×C₈₃	1	1	yes	characteristic
595	#117	C₂³×C₈₃	1	3	yes	—
596	#117	C₂³×C₈₃	1	3	yes	—
597	#117	C₂³×C₈₃	1	3	yes	—
598	#117	C₂³×C₈₃	1	3	yes	—
599	#117	C₂³×C₈₃	1	3	yes	—
600	#117	C₂³×C₈₃	1	6	yes	—
601	#117	C₂³×C₈₃	1	6	yes	—
602	#117	C₂³×C₈₃	1	6	yes	—
603	#117	C₂³×C₈₃	1	6	yes	—
604	#117	C₂³×C₈₃	1	6	yes	—
605	#117	C₂³×C₈₃	1	12	yes	—
606	#117	C₂³×C₈₃	1	12	yes	—
607	#117	C₂³×C₈₃	1	24	yes	—
608	C₂×C₄⋊C₄	C₂³×C₈₃	1	6	yes	—
609	C₂×C₄⋊C₄	C₂³×C₈₃	1	6	yes	—
610	C₂×C₄⋊C₄	C₂³×C₈₃	1	6	yes	—
611	C₂×C₄⋊C₄	C₂³×C₈₃	1	12	yes	—
612	C₂×C₄⋊C₄	C₂³×C₈₃	1	12	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₈₃	1	6	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₈₃	1	6	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₈₃	1	12	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₈₃	1	24	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₈₃	1	12	yes	—
618	C₂×C₄²	C₂³×C₈₃	1	3	yes	—
619	C₂×C₄²	C₂³×C₈₃	1	3	yes	—
620	C₂×C₄²	C₂³×C₈₃	1	6	yes	—
621	C₂×C₄²	C₂³×C₈₃	1	12	yes	—
622	C₂⁴	C₂⁴×C₈₃	1	3	yes	—
623	C₂⁴	C₂⁴×C₈₃	1	12	yes	—
624	#41	—	2	4	no	—
625	#41	—	2	16	no	—
626	#41	—	2	12	no	—
627	#41	—	2	12	no	—
628	#41	—	2	24	no	—
629	#41	—	8	24	no	—
630	#41	#41×C₈₃	1	8	yes	complemented
631	C₂×Q₈	—	2	4	no	—
632	C₂×Q₈	C₂⁴×C₈₃	1	3	yes	—
633	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
634	C₂×Q₈	C₂⁴×C₈₃	1	12	yes	—
635	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
636	C₂×D₄	—	2	12	no	—
637	C₂×D₄	—	2	48	no	—
638	C₂×D₄	—	2	24	no	—
639	C₂×D₄	—	8	12	no	—
640	C₂×D₄	—	8	12	no	—
641	C₂×D₄	C₂⁴×C₈₃	1	6	yes	—
642	C₂×D₄	C₂⁴×C₈₃	1	12	yes	—
643	C₂×D₄	C₂⁴×C₈₃	1	6	yes	—
644	C₂×D₄	C₂⁴×C₈₃	1	12	yes	—
645	C₂×D₄	C₂⁴×C₈₃	1	3	yes	—
646	C₂×D₄	C₂⁴×C₈₃	1	12	yes	—
647	C₂×D₄	C₂⁴×C₈₃	1	24	yes	—
648	C₂×D₄	C₂⁴×C₈₃	1	12	yes	—
649	C₂×D₄	C₂⁴×C₈₃	1	24	yes	—
650	C₂×D₄	C₂⁴×C₈₃	1	12	yes	—
651	C₂×D₄	C₂⁴×C₈₃	1	3	yes	—
652	C₂²×C₄	—	2	12	no	—
653	C₂²×C₄	—	8	12	no	—
654	C₂²×C₄	C₂⁴×C₈₃	1	3	yes	—
655	C₂²×C₄	C₂⁴×C₈₃	1	12	yes	—
656	C₂²×C₄	C₂⁴×C₈₃	1	3	yes	—
657	C₂²×C₄	C₂⁴×C₈₃	1	3	yes	—
658	C₂²×C₄	C₂⁴×C₈₃	1	3	yes	—
659	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
660	C₂²×C₄	C₂⁴×C₈₃	1	6	yes	—
661	C₂²×C₄	C₂⁴×C₈₃	1	12	yes	—
662	C₂²×C₄	C₂⁴×C₈₃	1	6	yes	—
663	C₂²×C₄	C₂⁴×C₈₃	1	12	yes	—
664	C₂²×C₄	C₂⁴×C₈₃	1	12	yes	—
665	C₂²×C₄	C₂⁴×C₈₃	1	12	yes	—
666	C₂²×C₄	C₂⁴×C₈₃	1	24	yes	—
667	C₂²×C₄	C₂⁴×C₈₃	1	3	yes	—
668	C₄⋊C₄	C₂⁴×C₈₃	1	6	yes	—
669	C₄⋊C₄	C₂⁴×C₈₃	1	6	yes	—
670	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
671	C₄⋊C₄	C₂⁴×C₈₃	1	6	yes	—
672	C₄⋊C₄	C₂⁴×C₈₃	1	12	yes	—
673	C₄⋊C₄	C₂⁴×C₈₃	1	12	yes	—
674	C₄⋊C₄	C₂⁴×C₈₃	1	12	yes	—
675	C₄⋊C₄	C₂⁴×C₈₃	1	6	yes	—
676	C₄⋊C₄	C₂⁴×C₈₃	1	6	yes	—
677	C₄⋊C₄	C₂⁴×C₈₃	1	6	yes	—
678	C₄⋊C₄	C₂⁴×C₈₃	1	24	yes	—
679	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
680	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
681	C₄⋊C₄	C₂⁴×C₈₃	1	12	yes	—
682	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
683	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
684	C₄⋊C₄	C₂⁴×C₈₃	1	12	yes	—
685	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
686	C₂²⋊C₄	C₂⁴×C₈₃	1	6	yes	—
687	C₂²⋊C₄	C₂⁴×C₈₃	1	2	yes	—
688	C₂²⋊C₄	C₂⁴×C₈₃	1	6	yes	—
689	C₂²⋊C₄	C₂⁴×C₈₃	1	12	yes	—
690	C₂²⋊C₄	C₂⁴×C₈₃	1	12	yes	—
691	C₂²⋊C₄	C₂⁴×C₈₃	1	24	yes	—
692	C₂²⋊C₄	C₂⁴×C₈₃	1	12	yes	—
693	C₂²⋊C₄	C₂⁴×C₈₃	1	12	yes	—
694	C₂²⋊C₄	C₂⁴×C₈₃	1	6	yes	—
695	C₂²⋊C₄	C₂⁴×C₈₃	1	6	yes	—
696	C₂²⋊C₄	C₂⁴×C₈₃	1	6	yes	—
697	C₂²⋊C₄	C₂⁴×C₈₃	1	24	yes	—
698	C₂²⋊C₄	C₂⁴×C₈₃	1	12	yes	—
699	C₂²⋊C₄	C₂⁴×C₈₃	1	4	yes	—
700	C₂²⋊C₄	C₂⁴×C₈₃	1	12	yes	—
701	C₂²⋊C₄	C₂⁴×C₈₃	1	12	yes	—
702	C₂²⋊C₄	C₂⁴×C₈₃	1	12	yes	—
703	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
704	C₄²	C₂⁴×C₈₃	1	3	yes	—
705	C₄²	C₂⁴×C₈₃	1	6	yes	—
706	C₄²	C₂⁴×C₈₃	1	3	yes	—
707	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
708	C₄²	C₂⁴×C₈₃	1	4	yes	—
709	C₄²	C₂⁴×C₈₃	1	12	yes	—
710	C₄²	C₂⁴×C₈₃	1	12	yes	—
711	C₄²	C₂⁴×C₈₃	1	12	yes	—
712	C₄²	C₂⁴×C₈₃	1	6	yes	—
713	C₂³	—	2	6	no	—
714	C₂³	—	2	24	no	—
715	C₂³	—	4	12	no	—
716	C₂³	—	4	6	no	—
717	C₂³	—	4	12	no	—
718	C₂³	C₂⁵×C₈₃	1	1	yes	characteristic
719	C₂³	C₂⁵×C₈₃	1	12	yes	—
720	C₂³	C₂⁵×C₈₃	1	3	yes	—
721	C₂³	C₂⁵×C₈₃	1	3	yes	—
722	Q₈	—	2	6	no	—
723	Q₈	—	2	4	no	—
724	Q₈	—	4	12	no	—
725	Q₈	C₂×#41×C₈₃	1	4	yes	—
726	D₄	—	2	24	no	—
727	D₄	—	2	12	no	—
728	D₄	—	2	24	no	—
729	D₄	—	2	12	no	—
730	D₄	—	2	6	no	—
731	D₄	—	4	12	no	—
732	D₄	—	4	12	no	—
733	D₄	—	4	24	no	—
734	D₄	—	4	24	no	—
735	D₄	—	4	12	no	—
736	D₄	C₂×#41×C₈₃	1	12	yes	—
737	C₂×C₄	—	2	6	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	6	no	—
740	C₂×C₄	—	2	6	no	—
741	C₂×C₄	—	2	6	no	—
742	C₂×C₄	—	2	24	no	—
743	C₂×C₄	—	4	6	no	—
744	C₂×C₄	—	4	12	no	—
745	C₂×C₄	—	4	12	no	—
746	C₂×C₄	—	4	24	no	—
747	C₂×C₄	—	4	6	no	—
748	C₂×C₄	—	4	12	no	—
749	C₂×C₄	—	4	12	no	—
750	C₂×C₄	C₂×#41×C₈₃	1	12	yes	—
751	C₂×C₄	C₂⁵×C₈₃	1	2	yes	—
752	C₂×C₄	C₂⁵×C₈₃	1	6	yes	—
753	C₂×C₄	C₂⁵×C₈₃	1	3	yes	—
754	C₂×C₄	C₂⁵×C₈₃	1	4	yes	—
755	C₂×C₄	C₂⁵×C₈₃	1	4	yes	—
756	C₂×C₄	C₂⁵×C₈₃	1	6	yes	—
757	C₂×C₄	C₂⁵×C₈₃	1	2	yes	—
758	C₂×C₄	C₂⁵×C₈₃	1	12	yes	—
759	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
760	C₂×C₄	C₂⁵×C₈₃	1	3	yes	—
761	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
762	C₂²	—	2	6	no	—
763	C₂²	—	2	1	no	—
764	C₂²	—	2	3	no	—
765	C₂²	—	2	12	no	—
766	C₂²	—	2	12	no	—
767	C₂²	—	2	6	no	—
768	C₂²	—	2	12	no	—
769	C₂²	—	2	2	no	—
770	C₂²	—	8	6	no	—
771	C₂²	—	8	24	no	—
772	C₂²	C₂²×#41×C₈₃	1	6	yes	—
773	C₂²	C₂⁶×C₈₃	1	1	yes	characteristic
774	C₄	—	2	1	no	—
775	C₄	—	2	4	no	—
776	C₄	—	2	3	no	—
777	C₄	—	2	2	no	—
778	C₄	—	2	6	no	—
779	C₄	—	2	12	no	—
780	C₄	—	2	2	no	—
781	C₄	—	2	6	no	—
782	C₄	—	2	4	no	—
783	C₄	C₂²×#41×C₈₃	1	6	yes	—
784	C₄	C₂²×#41×C₈₃	1	2	yes	—
785	C₂	—	2	6	no	—
786	C₂	—	4	1	no	—
787	C₂	—	4	12	no	—
788	C₂	—	4	3	no	—
789	C₂	C₂³×#41×C₈₃	1	1	yes	characteristic
790	C₂	C₈₃×H(7,𝔽₂)	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₈₃	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₈₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₃×#3524	C₂	semidirect
2. C₈₃×#3519	C₂	semidirect
3. C₈₃×#3517	C₂	semidirect
4. C₈₃×#3513	C₂	semidirect
5. C₈₃×#3512	C₂	semidirect
6. C₈₃×#3508	C₂	semidirect
7. C₈₃×#3504	C₂	semidirect
8. C₈₃×#3498	C₂	semidirect
9. C₈₃×#3494	C₂	semidirect
10. C₈₃×#3488	C₂	semidirect
11. C₈₃×#3460	C₂	semidirect
12. C₈₃×#3455	C₂	semidirect
13. C₂×#540×C₈₃	C₂	semidirect
14. C₄×H(5,𝔽₂)×C₈₃	C₂	semidirect
15. C₈₃×#3428	C₂	semidirect
18. #559×C₈₃	C₂²	semidirect
19. #557×C₈₃	C₂²	semidirect
20. #555×C₈₃	C₂²	semidirect
21. #554×C₈₃	C₂²	semidirect
22. #553×C₈₃	C₂²	semidirect
23. #553×C₈₃	C₂²	semidirect
24. #553×C₈₃	C₂²	semidirect
25. #553×C₈₃	C₂²	semidirect
26. #552×C₈₃	C₂²	semidirect
27. #551×C₈₃	C₂²	semidirect
28. #550×C₈₃	C₂²	semidirect
29. #550×C₈₃	C₂²	semidirect
30. #550×C₈₃	C₂²	semidirect
31. #548×C₈₃	C₂²	semidirect
32. #547×C₈₃	C₂²	semidirect
33. #546×C₈₃	C₂²	semidirect
34. #546×C₈₃	C₂²	semidirect
35. #546×C₈₃	C₂²	semidirect
36. D₄²×C₈₃	C₂²	semidirect
37. D₄²×C₈₃	C₂²	semidirect
38. #544×C₈₃	C₂²	semidirect
39. #542×C₈₃	C₂²	semidirect
40. #542×C₈₃	C₂²	semidirect
41. #542×C₈₃	C₂²	semidirect
42. #541×C₈₃	C₂²	semidirect
43. #541×C₈₃	C₂²	semidirect
44. #540×C₈₃	C₂²	semidirect
45. #540×C₈₃	C₂²	semidirect
46. #540×C₈₃	C₂²	semidirect
47. #540×C₈₃	C₂²	semidirect
48. #540×C₈₃	C₂²	semidirect
49. #540×C₈₃	C₂²	semidirect
50. #540×C₈₃	C₂²	semidirect
51. #540×C₈₃	C₂²	semidirect
52. #539×C₈₃	C₂²	semidirect
53. #538×C₈₃	C₂²	semidirect
54. #538×C₈₃	C₂²	semidirect
55. #537×C₈₃	C₂²	semidirect
56. #535×C₈₃	C₂²	semidirect
57. #535×C₈₃	C₂²	semidirect
58. #533×C₈₃	C₂²	semidirect
59. #532×C₈₃	C₂²	semidirect
60. #532×C₈₃	C₂²	semidirect
61. #532×C₈₃	C₂²	semidirect
62. C₂×#127×C₈₃	C₂²	semidirect
63. #529×C₈₃	C₂²	semidirect
64. #529×C₈₃	C₂²	semidirect
65. #529×C₈₃	C₂²	semidirect
66. #529×C₈₃	C₂²	semidirect
67. C₂×#125×C₈₃	C₂²	semidirect
68. #525×C₈₃	C₂²	semidirect
69. #525×C₈₃	C₂²	semidirect
70. C₂×#123×C₈₃	C₂²	semidirect
71. C₂×#121×C₈₃	C₂²	semidirect
72. C₂×#121×C₈₃	C₂²	semidirect
74. #520×C₈₃	C₂²	semidirect
75. #520×C₈₃	C₂²	semidirect
76. #520×C₈₃	C₂²	semidirect
77. #520×C₈₃	C₂²	semidirect
78. #519×C₈₃	C₂²	semidirect
79. #518×C₈₃	C₂²	semidirect
80. #518×C₈₃	C₂²	semidirect
81. #518×C₈₃	C₂²	semidirect
84. C₄×#41×C₈₃	C₂²	semidirect
85. C₄×#41×C₈₃	C₂²	semidirect
86. C₄×#41×C₈₃	C₂²	semidirect
87. C₄×#41×C₈₃	C₂²	semidirect
88. C₂×C₄×D₄×C₈₃	C₂²	semidirect
89. C₂×C₄×D₄×C₈₃	C₂²	semidirect
90. C₂×#117×C₈₃	C₂²	semidirect
91. C₂×#117×C₈₃	C₂²	semidirect
234. #41×C₈₃	#41	semidirect
389. #62858	C₈₃	direct (N × H)
396. #3524	C₂×C₈₃	semidirect
397. #3519	C₂×C₈₃	semidirect
398. #3517	C₂×C₈₃	semidirect
399. #3513	C₂×C₈₃	semidirect
400. #3512	C₂×C₈₃	semidirect
401. #3508	C₂×C₈₃	semidirect
402. #3504	C₂×C₈₃	semidirect
403. #3498	C₂×C₈₃	semidirect
404. #3494	C₂×C₈₃	semidirect
405. #3488	C₂×C₈₃	semidirect
406. #3460	C₂×C₈₃	semidirect
407. #3455	C₂×C₈₃	semidirect
408. C₂×#540	C₂×C₈₃	semidirect
409. C₄×H(5,𝔽₂)	C₂×C₈₃	semidirect
410. #3428	C₂×C₈₃	semidirect
411. C₈₃	#62858	direct (N × H)
414. #559	C₂²×C₈₃	semidirect
415. #557	C₂²×C₈₃	semidirect
416. #555	C₂²×C₈₃	semidirect
417. #554	C₂²×C₈₃	semidirect
418. #553	C₂²×C₈₃	semidirect
419. #553	C₂²×C₈₃	semidirect
420. #553	C₂²×C₈₃	semidirect
421. #553	C₂²×C₈₃	semidirect
422. #552	C₂²×C₈₃	semidirect
423. #551	C₂²×C₈₃	semidirect
424. #550	C₂²×C₈₃	semidirect
425. #550	C₂²×C₈₃	semidirect
426. #550	C₂²×C₈₃	semidirect
427. #548	C₂²×C₈₃	semidirect
428. #547	C₂²×C₈₃	semidirect
429. #546	C₂²×C₈₃	semidirect
430. #546	C₂²×C₈₃	semidirect
431. #546	C₂²×C₈₃	semidirect
432. D₄²	C₂²×C₈₃	semidirect
433. D₄²	C₂²×C₈₃	semidirect
434. #544	C₂²×C₈₃	semidirect
435. #542	C₂²×C₈₃	semidirect
436. #542	C₂²×C₈₃	semidirect
437. #542	C₂²×C₈₃	semidirect
438. #541	C₂²×C₈₃	semidirect
439. #541	C₂²×C₈₃	semidirect
440. #540	C₂²×C₈₃	semidirect
441. #540	C₂²×C₈₃	semidirect
442. #540	C₂²×C₈₃	semidirect
443. #540	C₂²×C₈₃	semidirect
444. #540	C₂²×C₈₃	semidirect
445. #540	C₂²×C₈₃	semidirect
446. #540	C₂²×C₈₃	semidirect
447. #540	C₂²×C₈₃	semidirect
448. #539	C₂²×C₈₃	semidirect
449. #538	C₂²×C₈₃	semidirect
450. #538	C₂²×C₈₃	semidirect
451. #537	C₂²×C₈₃	semidirect
452. #535	C₂²×C₈₃	semidirect
453. #535	C₂²×C₈₃	semidirect
454. #533	C₂²×C₈₃	semidirect
455. #532	C₂²×C₈₃	semidirect
456. #532	C₂²×C₈₃	semidirect
457. #532	C₂²×C₈₃	semidirect
458. C₂×#127	C₂²×C₈₃	semidirect
459. #529	C₂²×C₈₃	semidirect
460. #529	C₂²×C₈₃	semidirect
461. #529	C₂²×C₈₃	semidirect
462. #529	C₂²×C₈₃	semidirect
463. C₂×#125	C₂²×C₈₃	semidirect
464. #525	C₂²×C₈₃	semidirect
465. #525	C₂²×C₈₃	semidirect
466. C₂×#123	C₂²×C₈₃	semidirect
467. C₂×#121	C₂²×C₈₃	semidirect
468. C₂×#121	C₂²×C₈₃	semidirect
470. #520	C₂²×C₈₃	semidirect
471. #520	C₂²×C₈₃	semidirect
472. #520	C₂²×C₈₃	semidirect
473. #520	C₂²×C₈₃	semidirect
474. #519	C₂²×C₈₃	semidirect
475. #518	C₂²×C₈₃	semidirect
476. #518	C₂²×C₈₃	semidirect
477. #518	C₂²×C₈₃	semidirect
480. C₄×#41	C₂²×C₈₃	semidirect
481. C₄×#41	C₂²×C₈₃	semidirect
482. C₄×#41	C₂²×C₈₃	semidirect
483. C₄×#41	C₂²×C₈₃	semidirect
484. C₂×C₄×D₄	C₂²×C₈₃	semidirect
485. C₂×C₄×D₄	C₂²×C₈₃	semidirect
486. C₂×#117	C₂²×C₈₃	semidirect
487. C₂×#117	C₂²×C₈₃	semidirect
630. #41	#41×C₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₈₃×#3524	2
C₈₃×#3519	2
C₈₃×#3517	2
C₈₃×#3513	2
C₈₃×#3512	2
C₈₃×#3508	2
C₈₃×#3504	2
C₈₃×#3498	2
C₈₃×#3494	2
C₈₃×#3488	2
C₈₃×#3460	2
C₈₃×#3455	2
C₂×#540×C₈₃	2
C₄×H(5,𝔽₂)×C₈₃	2
C₈₃×#3428	2
#62858	83

Subgroups — C83×#62858 #35290682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#62858 #35290682