Subgroups — C₈₃×#62931 #35290755

Order 21248.

7074 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3562	C₂	1	8	yes	maximal, complemented
2	C₈₃×#3561	C₂	1	8	yes	maximal, complemented
3	C₈₃×#3560	C₂	1	8	yes	maximal, complemented
4	C₈₃×#3552	C₂	1	4	yes	maximal, complemented
5	C₈₃×#3546	C₂	1	4	yes	maximal, complemented
6	C₈₃×#3536	C₂	1	4	yes	maximal, complemented
7	C₈₃×#3514	C₂	1	4	yes	maximal, complemented
8	C₈₃×#3511	C₂	1	4	yes	maximal, complemented
9	C₈₃×#3500	C₂	1	4	yes	maximal, complemented
10	C₈₃×#3499	C₂	1	2	yes	maximal, complemented
11	C₈₃×#3497	C₂	1	2	yes	maximal, complemented
12	C₈₃×#3496	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₃×#3494	C₂	1	4	yes	maximal, complemented
14	C₈₃×#3480	C₂	1	2	yes	maximal, complemented
15	C₂×#556×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₃×#3461	C₂	1	2	yes	maximal, complemented
17	C₈₃×#3460	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×2₋¹⁺⁴×C₈₃	C₂²	1	4	yes	complemented
19	C₂×H(5,𝔽₂)×C₈₃	C₂²	1	2	yes	—
20	#563×C₈₃	C₂²	1	16	yes	complemented
21	#562×C₈₃	C₂²	1	16	yes	complemented
22	#560×C₈₃	C₂²	1	16	yes	complemented
23	#559×C₈₃	C₂²	1	4	yes	complemented
24	#559×C₈₃	C₂²	1	2	yes	complemented
25	#557×C₈₃	C₂²	1	2	yes	complemented
26	#556×C₈₃	C₂²	1	4	yes	complemented
27	#556×C₈₃	C₂²	1	4	yes	complemented
28	#556×C₈₃	C₂²	1	8	yes	complemented
29	#556×C₈₃	C₂²	1	4	yes	complemented
30	#556×C₈₃	C₂²	1	2	yes	complemented
31	#555×C₈₃	C₂²	1	8	yes	complemented
32	#554×C₈₃	C₂²	1	8	yes	complemented
33	#553×C₈₃	C₂²	1	8	yes	complemented
34	#553×C₈₃	C₂²	1	8	yes	complemented
35	#553×C₈₃	C₂²	1	16	yes	complemented
36	#553×C₈₃	C₂²	1	4	yes	complemented
37	#551×C₈₃	C₂²	1	16	yes	complemented
38	#551×C₈₃	C₂²	1	16	yes	complemented
39	#550×C₈₃	C₂²	1	2	yes	complemented
40	#550×C₈₃	C₂²	1	8	yes	complemented
41	D₄×Q₈×C₈₃	C₂²	1	8	yes	complemented
42	D₄×Q₈×C₈₃	C₂²	1	4	yes	complemented
43	D₄×Q₈×C₈₃	C₂²	1	4	yes	complemented
44	#548×C₈₃	C₂²	1	4	yes	complemented
45	#548×C₈₃	C₂²	1	8	yes	complemented
46	#548×C₈₃	C₂²	1	8	yes	complemented
47	#548×C₈₃	C₂²	1	8	yes	complemented
48	#548×C₈₃	C₂²	1	8	yes	complemented
49	#547×C₈₃	C₂²	1	4	yes	—
50	#547×C₈₃	C₂²	1	8	yes	complemented
51	#547×C₈₃	C₂²	1	4	yes	complemented
52	#547×C₈₃	C₂²	1	8	yes	complemented
53	#547×C₈₃	C₂²	1	4	yes	complemented
54	#546×C₈₃	C₂²	1	8	yes	—
55	#546×C₈₃	C₂²	1	8	yes	complemented
56	#546×C₈₃	C₂²	1	16	yes	complemented
57	#546×C₈₃	C₂²	1	8	yes	complemented
58	#546×C₈₃	C₂²	1	16	yes	complemented
59	#546×C₈₃	C₂²	1	8	yes	complemented
60	D₄²×C₈₃	C₂²	1	4	yes	—
61	#544×C₈₃	C₂²	1	4	yes	complemented
62	#544×C₈₃	C₂²	1	1	yes	characteristic, complemented
63	#543×C₈₃	C₂²	1	8	yes	complemented
64	#542×C₈₃	C₂²	1	8	yes	complemented
65	#542×C₈₃	C₂²	1	8	yes	complemented
66	#542×C₈₃	C₂²	1	16	yes	complemented
67	#542×C₈₃	C₂²	1	4	yes	complemented
68	#542×C₈₃	C₂²	1	8	yes	complemented
69	#541×C₈₃	C₂²	1	8	yes	complemented
70	#540×C₈₃	C₂²	1	4	yes	complemented
71	#540×C₈₃	C₂²	1	8	yes	complemented
72	#539×C₈₃	C₂²	1	8	yes	complemented
73	#539×C₈₃	C₂²	1	16	yes	complemented
74	#538×C₈₃	C₂²	1	8	yes	complemented
75	#538×C₈₃	C₂²	1	16	yes	complemented
76	#538×C₈₃	C₂²	1	4	yes	complemented
77	#538×C₈₃	C₂²	1	16	yes	complemented
78	#537×C₈₃	C₂²	1	2	yes	—
79	#537×C₈₃	C₂²	1	8	yes	complemented
80	#537×C₈₃	C₂²	1	8	yes	complemented
81	#537×C₈₃	C₂²	1	1	yes	characteristic, complemented
82	#536×C₈₃	C₂²	1	8	yes	complemented
83	#536×C₈₃	C₂²	1	8	yes	complemented
84	#536×C₈₃	C₂²	1	4	yes	complemented
85	#535×C₈₃	C₂²	1	2	yes	—
86	#535×C₈₃	C₂²	1	4	yes	complemented
87	#535×C₈₃	C₂²	1	8	yes	complemented
88	#534×C₈₃	C₂²	1	4	yes	—
89	#533×C₈₃	C₂²	1	8	yes	complemented
90	#532×C₈₃	C₂²	1	2	yes	—
91	#532×C₈₃	C₂²	1	4	yes	complemented
92	#532×C₈₃	C₂²	1	4	yes	complemented
93	#532×C₈₃	C₂²	1	8	yes	complemented
94	#532×C₈₃	C₂²	1	8	yes	complemented
95	#532×C₈₃	C₂²	1	4	yes	complemented
96	C₂×C₄⋊Q₈×C₈₃	C₂²	1	4	yes	complemented
97	C₂×C₄⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
98	#529×C₈₃	C₂²	1	4	yes	complemented
99	#529×C₈₃	C₂²	1	4	yes	complemented
100	#529×C₈₃	C₂²	1	8	yes	complemented
101	#529×C₈₃	C₂²	1	8	yes	complemented
102	#529×C₈₃	C₂²	1	8	yes	complemented
103	C₂×#126×C₈₃	C₂²	1	4	yes	complemented
104	C₂×#124×C₈₃	C₂²	1	2	yes	—
105	C₂×#124×C₈₃	C₂²	1	8	yes	complemented
106	#525×C₈₃	C₂²	1	4	yes	complemented
107	C₂×C₂²⋊Q₈×C₈₃	C₂²	1	2	yes	complemented
108	C₂×#121×C₈₃	C₂²	1	4	yes	—
109	#520×C₈₃	C₂²	1	4	yes	complemented
110	#518×C₈₃	C₂²	1	4	yes	complemented
111	C₄×#41×C₈₃	C₂²	1	2	yes	complemented
112	C₄×#41×C₈₃	C₂²	1	4	yes	complemented
113	C₄×#41×C₈₃	C₂²	1	4	yes	complemented
114	C₂×C₄×Q₈×C₈₃	C₂²	1	2	yes	complemented
115	C₂×C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
116	C₂×C₄×D₄×C₈₃	C₂²	1	1	yes	characteristic
117	C₂×#117×C₈₃	C₂²	1	2	yes	complemented
118	2₋¹⁺⁴×C₈₃	—	4	16	no	—
119	H(5,𝔽₂)×C₈₃	—	4	8	no	—
120	C₂×#41×C₈₃	C₂³	1	4	yes	—
121	C₂×#41×C₈₃	C₂³	1	2	yes	—
122	C₂×#41×C₈₃	C₂³	1	4	yes	—
123	C₂×#41×C₈₃	C₂³	1	4	yes	—
124	C₂×#41×C₈₃	C₂³	1	8	yes	—
125	C₂×#41×C₈₃	C₂³	1	8	yes	—
126	C₂×#41×C₈₃	C₂³	1	8	yes	—
127	C₂×#41×C₈₃	C₂³	1	16	yes	—
128	C₂²×Q₈×C₈₃	C₂³	1	2	yes	—
129	C₂²×Q₈×C₈₃	C₂³	1	1	yes	characteristic
130	C₂²×Q₈×C₈₃	C₂³	1	8	yes	—
131	C₂²×Q₈×C₈₃	C₂³	1	8	yes	—
132	C₂²×D₄×C₈₃	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₈₃	C₂³	1	4	yes	—
134	C₂²×D₄×C₈₃	C₂³	1	8	yes	—
135	C₂²×D₄×C₈₃	C₂³	1	8	yes	—
136	C₂³×C₄×C₈₃	C₂³	1	2	yes	—
137	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
138	C₄⋊Q₈×C₈₃	C₂³	1	4	yes	—
139	C₄⋊Q₈×C₈₃	C₂³	1	8	yes	—
140	C₄⋊Q₈×C₈₃	C₂³	1	4	yes	—
141	C₄⋊Q₈×C₈₃	C₂³	1	8	yes	—
142	C₄⋊Q₈×C₈₃	C₂³	1	8	yes	—
143	C₄⋊Q₈×C₈₃	C₂³	1	4	yes	—
144	C₄⋊Q₈×C₈₃	C₂³	1	4	yes	—
145	C₄⋊Q₈×C₈₃	C₂³	1	8	yes	—
146	#127×C₈₃	C₂³	1	2	yes	—
147	#127×C₈₃	C₂³	1	4	yes	—
148	#127×C₈₃	C₂³	1	4	yes	—
149	#127×C₈₃	C₂³	1	8	yes	—
150	#126×C₈₃	C₂³	1	16	yes	—
151	#126×C₈₃	C₂³	1	16	yes	—
152	#126×C₈₃	C₂³	1	16	yes	—
153	#126×C₈₃	C₂³	1	8	yes	—
154	#126×C₈₃	C₂³	1	8	yes	—
155	#126×C₈₃	C₂³	1	16	yes	—
156	#126×C₈₃	C₂³	1	8	yes	—
157	#126×C₈₃	C₂³	1	8	yes	—
158	#125×C₈₃	C₂³	1	4	yes	—
159	#125×C₈₃	C₂³	1	8	yes	—
160	#125×C₈₃	C₂³	1	8	yes	—
161	#125×C₈₃	C₂³	1	4	yes	—
162	#125×C₈₃	C₂³	1	16	yes	—
163	#124×C₈₃	C₂³	1	8	yes	—
164	#124×C₈₃	C₂³	1	8	yes	—
165	#124×C₈₃	C₂³	1	4	yes	—
166	#124×C₈₃	C₂³	1	4	yes	—
167	#124×C₈₃	C₂³	1	8	yes	—
168	#124×C₈₃	C₂³	1	16	yes	—
169	#124×C₈₃	C₂³	1	16	yes	—
170	#124×C₈₃	C₂³	1	8	yes	—
171	#124×C₈₃	C₂³	1	8	yes	—
172	#124×C₈₃	C₂³	1	4	yes	—
173	#124×C₈₃	C₂³	1	4	yes	—
174	#124×C₈₃	C₂³	1	4	yes	—
175	#124×C₈₃	C₂³	1	8	yes	—
176	#124×C₈₃	C₂³	1	16	yes	—
177	#123×C₈₃	C₂³	1	8	yes	—
178	#123×C₈₃	C₂³	1	16	yes	—
179	#123×C₈₃	C₂³	1	8	yes	—
180	#123×C₈₃	C₂³	1	8	yes	—
181	#123×C₈₃	C₂³	1	8	yes	—
182	#123×C₈₃	C₂³	1	16	yes	—
183	#123×C₈₃	C₂³	1	8	yes	—
184	#123×C₈₃	C₂³	1	16	yes	—
185	#123×C₈₃	C₂³	1	16	yes	—
186	#123×C₈₃	C₂³	1	16	yes	—
187	#123×C₈₃	C₂³	1	16	yes	—
188	#123×C₈₃	C₂³	1	16	yes	—
189	C₂²⋊Q₈×C₈₃	C₂³	1	8	yes	—
190	C₂²⋊Q₈×C₈₃	C₂³	1	8	yes	—
191	C₂²⋊Q₈×C₈₃	C₂³	1	4	yes	—
192	C₂²⋊Q₈×C₈₃	C₂³	1	4	yes	—
193	C₂²⋊Q₈×C₈₃	C₂³	1	8	yes	—
194	C₂²⋊Q₈×C₈₃	C₂³	1	4	yes	—
195	C₂²⋊Q₈×C₈₃	C₂³	1	4	yes	—
196	C₂²⋊Q₈×C₈₃	C₂³	1	8	yes	—
197	C₂²⋊Q₈×C₈₃	C₂³	1	8	yes	—
198	C₂²⋊Q₈×C₈₃	C₂³	1	8	yes	—
199	C₂²⋊Q₈×C₈₃	C₂³	1	16	yes	—
200	C₂²⋊Q₈×C₈₃	C₂³	1	16	yes	—
201	C₂²⋊Q₈×C₈₃	C₂³	1	16	yes	—
202	C₂²⋊Q₈×C₈₃	C₂³	1	16	yes	—
203	C₂²⋊Q₈×C₈₃	C₂³	1	16	yes	—
204	C₂²⋊Q₈×C₈₃	C₂³	1	16	yes	—
205	C₂²⋊Q₈×C₈₃	C₂³	1	16	yes	—
206	#121×C₈₃	C₂³	1	4	yes	—
207	#121×C₈₃	C₂³	1	8	yes	—
208	#121×C₈₃	C₂³	1	8	yes	—
209	#121×C₈₃	C₂³	1	8	yes	—
210	#121×C₈₃	C₂³	1	4	yes	—
211	#121×C₈₃	C₂³	1	4	yes	—
212	#121×C₈₃	C₂³	1	4	yes	—
213	#121×C₈₃	C₂³	1	4	yes	—
214	#121×C₈₃	C₂³	1	8	yes	—
215	#121×C₈₃	C₂³	1	8	yes	—
216	#121×C₈₃	C₂³	1	4	yes	—
217	#121×C₈₃	C₂³	1	8	yes	—
218	#121×C₈₃	C₂³	1	4	yes	—
219	#121×C₈₃	C₂³	1	8	yes	—
220	#121×C₈₃	C₂³	1	8	yes	—
221	#121×C₈₃	C₂³	1	4	yes	—
222	#121×C₈₃	C₂³	1	16	yes	—
223	#121×C₈₃	C₂³	1	8	yes	—
224	#121×C₈₃	C₂³	1	16	yes	—
225	#121×C₈₃	C₂³	1	8	yes	—
226	#121×C₈₃	C₂³	1	16	yes	—
227	#121×C₈₃	C₂³	1	16	yes	—
228	#121×C₈₃	C₂³	1	16	yes	—
229	#121×C₈₃	C₂³	1	16	yes	—
230	#120×C₈₃	C₂³	1	8	yes	—
231	#120×C₈₃	C₂³	1	16	yes	—
232	#120×C₈₃	C₂³	1	16	yes	—
233	#120×C₈₃	C₂³	1	16	yes	—
234	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
235	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
236	C₄×Q₈×C₈₃	C₂³	1	4	yes	—
237	C₄×Q₈×C₈₃	C₂³	1	8	yes	—
238	C₄×Q₈×C₈₃	C₂³	1	8	yes	—
239	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
240	C₄×Q₈×C₈₃	C₂³	1	4	yes	—
241	C₄×Q₈×C₈₃	C₂³	1	4	yes	—
242	C₄×Q₈×C₈₃	C₂³	1	4	yes	—
243	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
244	C₄×Q₈×C₈₃	C₂³	1	8	yes	—
245	C₄×D₄×C₈₃	C₂³	1	4	yes	—
246	C₄×D₄×C₈₃	C₂³	1	4	yes	—
247	C₄×D₄×C₈₃	C₂³	1	4	yes	—
248	C₄×D₄×C₈₃	C₂³	1	4	yes	—
249	C₄×D₄×C₈₃	C₂³	1	8	yes	—
250	C₄×D₄×C₈₃	C₂³	1	4	yes	—
251	C₄×D₄×C₈₃	C₂³	1	4	yes	—
252	C₄×D₄×C₈₃	C₂³	1	8	yes	—
253	C₄×D₄×C₈₃	C₂³	1	2	yes	—
254	C₄×D₄×C₈₃	C₂³	1	4	yes	—
255	C₄×D₄×C₈₃	C₂³	1	8	yes	—
256	C₄×D₄×C₈₃	C₂³	1	8	yes	—
257	C₄×D₄×C₈₃	C₂³	1	2	yes	—
258	C₄×D₄×C₈₃	C₂³	1	4	yes	—
259	C₄×D₄×C₈₃	C₂³	1	8	yes	—
260	C₄×D₄×C₈₃	C₂³	1	8	yes	—
261	C₄×D₄×C₈₃	C₂³	1	8	yes	—
262	C₄×D₄×C₈₃	C₂³	1	8	yes	—
263	C₄×D₄×C₈₃	C₂³	1	16	yes	—
264	C₄×D₄×C₈₃	C₂³	1	8	yes	—
265	C₄×D₄×C₈₃	C₂³	1	4	yes	—
266	C₄×D₄×C₈₃	C₂³	1	8	yes	—
267	C₄×D₄×C₈₃	C₂³	1	8	yes	—
268	C₄×D₄×C₈₃	C₂³	1	16	yes	—
269	C₄×D₄×C₈₃	C₂³	1	16	yes	—
270	#117×C₈₃	C₂³	1	4	yes	—
271	#117×C₈₃	C₂³	1	4	yes	—
272	#117×C₈₃	C₂³	1	8	yes	—
273	#117×C₈₃	C₂³	1	2	yes	—
274	#117×C₈₃	C₂³	1	4	yes	—
275	#117×C₈₃	C₂³	1	8	yes	—
276	#117×C₈₃	C₂³	1	4	yes	—
277	#117×C₈₃	C₂³	1	8	yes	—
278	#117×C₈₃	C₂³	1	4	yes	—
279	#117×C₈₃	C₂³	1	16	yes	—
280	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
281	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
282	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
283	C₂×C₄⋊C₄×C₈₃	C₂³	1	4	yes	—
284	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
285	C₂×C₄⋊C₄×C₈₃	C₂³	1	4	yes	—
286	C₂×C₄⋊C₄×C₈₃	C₂³	1	8	yes	—
287	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
288	C₂×C₄⋊C₄×C₈₃	C₂³	1	8	yes	—
289	C₂×C₂²⋊C₄×C₈₃	C₂³	1	4	yes	—
290	C₂×C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
291	C₂×C₂²⋊C₄×C₈₃	C₂³	1	16	yes	—
292	C₂×C₂²⋊C₄×C₈₃	C₂³	1	8	yes	—
293	C₂×C₂²⋊C₄×C₈₃	C₂³	1	4	yes	—
294	C₂×C₂²⋊C₄×C₈₃	C₂³	1	16	yes	—
295	C₂×C₄²×C₈₃	C₂³	1	4	yes	—
296	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
297	C₂×C₄²×C₈₃	C₂³	1	2	yes	—
298	C₂×C₄²×C₈₃	C₂³	1	8	yes	—
299	C₂×C₄²×C₈₃	C₂³	1	4	yes	—
300	C₂⁴×C₈₃	C₂⁴	1	2	yes	—
301	C₂⁴×C₈₃	C₂⁴	1	8	yes	—
302	#41×C₈₃	—	2	16	no	—
303	#41×C₈₃	—	2	8	no	—
304	#41×C₈₃	—	4	8	no	—
305	#41×C₈₃	—	4	32	no	—
306	#41×C₈₃	—	4	8	no	—
307	#41×C₈₃	—	4	16	no	—
308	#41×C₈₃	—	4	16	no	—
309	#41×C₈₃	—	4	16	no	—
310	C₂×Q₈×C₈₃	—	2	8	no	—
311	C₂×Q₈×C₈₃	—	4	2	no	—
312	C₂×Q₈×C₈₃	—	4	16	no	—
313	C₂×Q₈×C₈₃	—	4	16	no	—
314	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
315	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
316	C₂×Q₈×C₈₃	C₂⁴	1	8	yes	—
317	C₂×Q₈×C₈₃	C₂⁴	1	4	yes	—
318	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
319	C₂×Q₈×C₈₃	C₂⁴	1	4	yes	—
320	C₂×Q₈×C₈₃	C₂⁴	1	16	yes	—
321	C₂×D₄×C₈₃	—	2	4	no	—
322	C₂×D₄×C₈₃	—	4	8	no	—
323	C₂×D₄×C₈₃	—	4	16	no	—
324	C₂×D₄×C₈₃	—	4	16	no	—
325	C₂×D₄×C₈₃	C₂⁴	1	4	yes	—
326	C₂×D₄×C₈₃	C₂⁴	1	4	yes	—
327	C₂×D₄×C₈₃	C₂⁴	1	8	yes	—
328	C₂×D₄×C₈₃	C₂⁴	1	4	yes	—
329	C₂×D₄×C₈₃	C₂⁴	1	4	yes	—
330	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
331	C₂×D₄×C₈₃	C₂⁴	1	4	yes	—
332	C₂×D₄×C₈₃	C₂⁴	1	8	yes	—
333	C₂×D₄×C₈₃	C₂⁴	1	8	yes	—
334	C₂×D₄×C₈₃	C₂⁴	1	8	yes	—
335	C₂×D₄×C₈₃	C₂⁴	1	8	yes	—
336	C₂×D₄×C₈₃	C₂⁴	1	8	yes	—
337	C₂×D₄×C₈₃	C₂⁴	1	4	yes	—
338	C₂×D₄×C₈₃	C₂⁴	1	16	yes	—
339	C₂×D₄×C₈₃	C₂⁴	1	16	yes	—
340	C₂²×C₄×C₈₃	—	4	4	no	—
341	C₂²×C₄×C₈₃	C₂⁴	1	4	yes	—
342	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₈₃	C₂⁴	1	4	yes	—
344	C₂²×C₄×C₈₃	C₂⁴	1	4	yes	—
345	C₂²×C₄×C₈₃	C₂⁴	1	8	yes	—
346	C₂²×C₄×C₈₃	C₂⁴	1	4	yes	—
347	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
348	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
349	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
351	C₂²×C₄×C₈₃	C₂⁴	1	8	yes	—
352	C₂²×C₄×C₈₃	C₂⁴	1	8	yes	—
353	C₂²×C₄×C₈₃	C₂⁴	1	4	yes	—
354	C₂²×C₄×C₈₃	C₂⁴	1	4	yes	—
355	C₂²×C₄×C₈₃	C₂⁴	1	16	yes	—
356	C₂²×C₄×C₈₃	C₂⁴	1	8	yes	—
357	C₂²×C₄×C₈₃	C₂⁴	1	16	yes	—
358	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
359	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
360	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
361	C₄⋊C₄×C₈₃	C₂⁴	1	8	yes	—
362	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
363	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
364	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
365	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
366	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
367	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
368	C₄⋊C₄×C₈₃	C₂⁴	1	16	yes	—
369	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
370	C₄⋊C₄×C₈₃	C₂⁴	1	8	yes	—
371	C₄⋊C₄×C₈₃	C₂⁴	1	16	yes	—
372	C₄⋊C₄×C₈₃	C₂⁴	1	16	yes	—
373	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
374	C₄⋊C₄×C₈₃	C₂⁴	1	8	yes	—
375	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
376	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
377	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
378	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
379	C₄⋊C₄×C₈₃	C₂⁴	1	8	yes	—
380	C₄⋊C₄×C₈₃	C₂⁴	1	8	yes	—
381	C₄⋊C₄×C₈₃	C₂⁴	1	8	yes	—
382	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
383	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
384	C₄⋊C₄×C₈₃	C₂⁴	1	8	yes	—
385	C₂²⋊C₄×C₈₃	C₂⁴	1	8	yes	—
386	C₂²⋊C₄×C₈₃	C₂⁴	1	8	yes	—
387	C₂²⋊C₄×C₈₃	C₂⁴	1	8	yes	—
388	C₂²⋊C₄×C₈₃	C₂⁴	1	16	yes	—
389	C₂²⋊C₄×C₈₃	C₂⁴	1	8	yes	—
390	C₂²⋊C₄×C₈₃	C₂⁴	1	8	yes	—
391	C₂²⋊C₄×C₈₃	C₂⁴	1	8	yes	—
392	C₂²⋊C₄×C₈₃	C₂⁴	1	8	yes	—
393	C₂²⋊C₄×C₈₃	C₂⁴	1	16	yes	—
394	C₂²⋊C₄×C₈₃	C₂⁴	1	16	yes	—
395	C₂²⋊C₄×C₈₃	C₂⁴	1	8	yes	—
396	C₂²⋊C₄×C₈₃	C₂⁴	1	16	yes	—
397	C₂²⋊C₄×C₈₃	C₂⁴	1	4	yes	—
398	C₂²⋊C₄×C₈₃	C₂⁴	1	8	yes	—
399	C₂²⋊C₄×C₈₃	C₂⁴	1	8	yes	—
400	C₂²⋊C₄×C₈₃	C₂⁴	1	8	yes	—
401	C₂²⋊C₄×C₈₃	C₂⁴	1	8	yes	—
402	C₂²⋊C₄×C₈₃	C₂⁴	1	4	yes	—
403	C₂²⋊C₄×C₈₃	C₂⁴	1	4	yes	—
404	C₂²⋊C₄×C₈₃	C₂⁴	1	8	yes	—
405	C₂²⋊C₄×C₈₃	C₂⁴	1	8	yes	—
406	C₄²×C₈₃	C₂⁴	1	4	yes	—
407	C₄²×C₈₃	C₂⁴	1	2	yes	—
408	C₄²×C₈₃	C₂⁴	1	4	yes	—
409	C₄²×C₈₃	C₂⁴	1	8	yes	—
410	C₄²×C₈₃	C₂⁴	1	8	yes	—
411	C₄²×C₈₃	C₂⁴	1	4	yes	—
412	C₄²×C₈₃	C₂⁴	1	2	yes	—
413	C₄²×C₈₃	C₂⁴	1	4	yes	—
414	C₄²×C₈₃	C₂⁴	1	4	yes	—
415	C₄²×C₈₃	C₂⁴	1	8	yes	—
416	C₄²×C₈₃	C₂⁴	1	8	yes	—
417	C₂³×C₈₃	—	2	4	no	—
418	C₂³×C₈₃	—	4	2	no	—
419	C₂³×C₈₃	—	4	2	no	—
420	C₂³×C₈₃	—	4	8	no	—
421	C₂³×C₈₃	—	4	8	no	—
422	C₂³×C₈₃	—	4	8	no	—
423	C₂³×C₈₃	C₂⁵	1	4	yes	—
424	C₂³×C₈₃	C₂⁵	1	8	yes	—
425	C₂³×C₈₃	C₂⁵	1	4	yes	—
426	C₂³×C₈₃	C₂⁵	1	1	yes	characteristic
427	Q₈×C₈₃	—	2	16	no	—
428	Q₈×C₈₃	—	2	4	no	—
429	Q₈×C₈₃	—	2	8	no	—
430	Q₈×C₈₃	—	2	4	no	—
431	Q₈×C₈₃	—	4	16	no	—
432	Q₈×C₈₃	—	4	2	no	—
433	Q₈×C₈₃	—	4	4	no	—
434	D₄×C₈₃	—	2	16	no	—
435	D₄×C₈₃	—	2	8	no	—
436	D₄×C₈₃	—	2	8	no	—
437	D₄×C₈₃	—	2	8	no	—
438	D₄×C₈₃	—	2	4	no	—
439	D₄×C₈₃	—	2	8	no	—
440	D₄×C₈₃	—	4	16	no	—
441	D₄×C₈₃	—	4	8	no	—
442	D₄×C₈₃	—	4	8	no	—
443	D₄×C₈₃	—	4	4	no	—
444	D₄×C₈₃	—	4	8	no	—
445	D₄×C₈₃	—	4	4	no	—
446	D₄×C₈₃	—	4	8	no	—
447	D₄×C₈₃	—	4	8	no	—
448	D₄×C₈₃	—	4	16	no	—
449	C₂×C₄×C₈₃	—	2	8	no	—
450	C₂×C₄×C₈₃	—	2	16	no	—
451	C₂×C₄×C₈₃	—	2	8	no	—
452	C₂×C₄×C₈₃	—	2	2	no	—
453	C₂×C₄×C₈₃	—	2	8	no	—
454	C₂×C₄×C₈₃	—	2	8	no	—
455	C₂×C₄×C₈₃	—	4	4	no	—
456	C₂×C₄×C₈₃	—	4	2	no	—
457	C₂×C₄×C₈₃	—	4	8	no	—
458	C₂×C₄×C₈₃	—	4	2	no	—
459	C₂×C₄×C₈₃	—	4	1	no	—
460	C₂×C₄×C₈₃	—	4	4	no	—
461	C₂×C₄×C₈₃	—	4	8	no	—
462	C₂×C₄×C₈₃	—	4	2	no	—
463	C₂×C₄×C₈₃	—	4	16	no	—
464	C₂×C₄×C₈₃	—	4	16	no	—
465	C₂×C₄×C₈₃	—	4	8	no	—
466	C₂×C₄×C₈₃	H(5,𝔽₂)	1	4	yes	—
467	C₂×C₄×C₈₃	C₂⁵	1	2	yes	—
468	C₂×C₄×C₈₃	C₂⁵	1	2	yes	—
469	C₂×C₄×C₈₃	C₂⁵	1	4	yes	—
470	C₂×C₄×C₈₃	C₂⁵	1	2	yes	—
471	C₂×C₄×C₈₃	C₂⁵	1	4	yes	—
472	C₂×C₄×C₈₃	C₂⁵	1	4	yes	—
473	C₂×C₄×C₈₃	C₂⁵	1	4	yes	—
474	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
475	C₂×C₄×C₈₃	C₂⁵	1	4	yes	—
476	C₂×C₄×C₈₃	C₂⁵	1	8	yes	—
477	C₂×C₄×C₈₃	C₂⁵	1	8	yes	—
478	C₂×C₄×C₈₃	C₂⁵	1	2	yes	—
479	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
480	C₂²×C₈₃	—	2	1	no	—
481	C₂²×C₈₃	—	2	1	no	—
482	C₂²×C₈₃	—	2	4	no	—
483	C₂²×C₈₃	—	2	8	no	—
484	C₂²×C₈₃	—	2	4	no	—
485	C₂²×C₈₃	—	2	4	no	—
486	C₂²×C₈₃	—	2	4	no	—
487	C₂²×C₈₃	—	2	8	no	—
488	C₂²×C₈₃	—	2	4	no	—
489	C₂²×C₈₃	—	2	8	no	—
490	C₂²×C₈₃	—	2	4	no	—
491	C₂²×C₈₃	—	8	4	no	—
492	C₂²×C₈₃	—	16	8	no	—
493	C₂²×C₈₃	C₂×H(5,𝔽₂)	1	2	yes	—
494	C₂²×C₈₃	C₂⁶	1	1	yes	characteristic
495	C₄×C₈₃	—	2	8	no	—
496	C₄×C₈₃	—	2	4	no	—
497	C₄×C₈₃	—	2	8	no	—
498	C₄×C₈₃	—	2	1	no	—
499	C₄×C₈₃	—	2	4	no	—
500	C₄×C₈₃	—	2	4	no	—
501	C₄×C₈₃	—	2	4	no	—
502	C₄×C₈₃	—	2	2	no	—
503	C₄×C₈₃	—	2	4	no	—
504	C₄×C₈₃	—	2	2	no	—
505	C₄×C₈₃	—	2	2	no	—
506	C₄×C₈₃	C₂×H(5,𝔽₂)	1	4	yes	—
507	C₄×C₈₃	#585	1	2	yes	—
508	#62931	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
509	C₂×C₈₃	—	2	2	no	—
510	C₂×C₈₃	—	4	4	no	—
511	C₂×C₈₃	—	4	4	no	—
512	C₂×C₈₃	—	4	8	no	—
513	C₂×C₈₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
514	C₂×C₈₃	C₂×#585	1	1	yes	characteristic
515	C₂×C₈₃	2₋¹⁺⁶	1	1	yes	characteristic
516	#3562	C₂×C₈₃	1	8	yes	complemented
517	#3561	C₂×C₈₃	1	8	yes	complemented
518	#3560	C₂×C₈₃	1	8	yes	complemented
519	#3552	C₂×C₈₃	1	4	yes	complemented
520	#3546	C₂×C₈₃	1	4	yes	complemented
521	#3536	C₂×C₈₃	1	4	yes	complemented
522	#3514	C₂×C₈₃	1	4	yes	complemented
523	#3511	C₂×C₈₃	1	4	yes	complemented
524	#3500	C₂×C₈₃	1	4	yes	complemented
525	#3499	C₂×C₈₃	1	2	yes	complemented
526	#3497	C₂×C₈₃	1	2	yes	complemented
527	#3496	C₂×C₈₃	1	1	yes	characteristic, complemented
528	#3494	C₂×C₈₃	1	4	yes	complemented
529	#3480	C₂×C₈₃	1	2	yes	complemented
530	C₂×#556	C₂×C₈₃	1	1	yes	characteristic, complemented
531	#3461	C₂×C₈₃	1	2	yes	complemented
532	#3460	C₂×C₈₃	1	1	yes	characteristic, complemented
533	C₈₃	#62931	1	1	yes	characteristic, direct product factor, Sylow
534	C₂×2₋¹⁺⁴	C₂²×C₈₃	1	4	yes	complemented
535	C₂×H(5,𝔽₂)	C₂²×C₈₃	1	2	yes	—
536	#563	C₂²×C₈₃	1	16	yes	complemented
537	#562	C₂²×C₈₃	1	16	yes	complemented
538	#560	C₂²×C₈₃	1	16	yes	complemented
539	#559	C₂²×C₈₃	1	2	yes	complemented
540	#559	C₂²×C₈₃	1	4	yes	complemented
541	#557	C₂²×C₈₃	1	2	yes	complemented
542	#556	C₂²×C₈₃	1	4	yes	complemented
543	#556	C₂²×C₈₃	1	4	yes	complemented
544	#556	C₂²×C₈₃	1	8	yes	complemented
545	#556	C₂²×C₈₃	1	2	yes	complemented
546	#556	C₂²×C₈₃	1	4	yes	complemented
547	#555	C₂²×C₈₃	1	8	yes	complemented
548	#554	C₂²×C₈₃	1	8	yes	complemented
549	#553	C₂²×C₈₃	1	4	yes	complemented
550	#553	C₂²×C₈₃	1	8	yes	complemented
551	#553	C₂²×C₈₃	1	8	yes	complemented
552	#553	C₂²×C₈₃	1	16	yes	complemented
553	#551	C₂²×C₈₃	1	16	yes	complemented
554	#551	C₂²×C₈₃	1	16	yes	complemented
555	#550	C₂²×C₈₃	1	2	yes	complemented
556	#550	C₂²×C₈₃	1	8	yes	complemented
557	D₄×Q₈	C₂²×C₈₃	1	8	yes	complemented
558	D₄×Q₈	C₂²×C₈₃	1	4	yes	complemented
559	D₄×Q₈	C₂²×C₈₃	1	4	yes	complemented
560	#548	C₂²×C₈₃	1	4	yes	complemented
561	#548	C₂²×C₈₃	1	8	yes	complemented
562	#548	C₂²×C₈₃	1	8	yes	complemented
563	#548	C₂²×C₈₃	1	8	yes	complemented
564	#548	C₂²×C₈₃	1	8	yes	complemented
565	#547	C₂²×C₈₃	1	4	yes	—
566	#547	C₂²×C₈₃	1	8	yes	complemented
567	#547	C₂²×C₈₃	1	4	yes	complemented
568	#547	C₂²×C₈₃	1	8	yes	complemented
569	#547	C₂²×C₈₃	1	4	yes	complemented
570	#546	C₂²×C₈₃	1	8	yes	—
571	#546	C₂²×C₈₃	1	16	yes	complemented
572	#546	C₂²×C₈₃	1	8	yes	complemented
573	#546	C₂²×C₈₃	1	16	yes	complemented
574	#546	C₂²×C₈₃	1	8	yes	complemented
575	#546	C₂²×C₈₃	1	8	yes	complemented
576	D₄²	C₂²×C₈₃	1	4	yes	—
577	#544	C₂²×C₈₃	1	1	yes	characteristic, complemented
578	#544	C₂²×C₈₃	1	4	yes	complemented
579	#543	C₂²×C₈₃	1	8	yes	complemented
580	#542	C₂²×C₈₃	1	4	yes	complemented
581	#542	C₂²×C₈₃	1	8	yes	complemented
582	#542	C₂²×C₈₃	1	8	yes	complemented
583	#542	C₂²×C₈₃	1	16	yes	complemented
584	#542	C₂²×C₈₃	1	8	yes	complemented
585	#541	C₂²×C₈₃	1	8	yes	complemented
586	#540	C₂²×C₈₃	1	4	yes	complemented
587	#540	C₂²×C₈₃	1	8	yes	complemented
588	#539	C₂²×C₈₃	1	8	yes	complemented
589	#539	C₂²×C₈₃	1	16	yes	complemented
590	#538	C₂²×C₈₃	1	4	yes	complemented
591	#538	C₂²×C₈₃	1	16	yes	complemented
592	#538	C₂²×C₈₃	1	8	yes	complemented
593	#538	C₂²×C₈₃	1	16	yes	complemented
594	#537	C₂²×C₈₃	1	2	yes	—
595	#537	C₂²×C₈₃	1	1	yes	characteristic, complemented
596	#537	C₂²×C₈₃	1	8	yes	complemented
597	#537	C₂²×C₈₃	1	8	yes	complemented
598	#536	C₂²×C₈₃	1	4	yes	complemented
599	#536	C₂²×C₈₃	1	8	yes	complemented
600	#536	C₂²×C₈₃	1	8	yes	complemented
601	#535	C₂²×C₈₃	1	2	yes	—
602	#535	C₂²×C₈₃	1	4	yes	complemented
603	#535	C₂²×C₈₃	1	8	yes	complemented
604	#534	C₂²×C₈₃	1	4	yes	—
605	#533	C₂²×C₈₃	1	8	yes	complemented
606	#532	C₂²×C₈₃	1	2	yes	—
607	#532	C₂²×C₈₃	1	4	yes	complemented
608	#532	C₂²×C₈₃	1	4	yes	complemented
609	#532	C₂²×C₈₃	1	8	yes	complemented
610	#532	C₂²×C₈₃	1	4	yes	complemented
611	#532	C₂²×C₈₃	1	8	yes	complemented
612	C₂×C₄⋊Q₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
613	C₂×C₄⋊Q₈	C₂²×C₈₃	1	4	yes	complemented
614	#529	C₂²×C₈₃	1	4	yes	complemented
615	#529	C₂²×C₈₃	1	8	yes	complemented
616	#529	C₂²×C₈₃	1	8	yes	complemented
617	#529	C₂²×C₈₃	1	4	yes	complemented
618	#529	C₂²×C₈₃	1	8	yes	complemented
619	C₂×#126	C₂²×C₈₃	1	4	yes	complemented
620	C₂×#124	C₂²×C₈₃	1	2	yes	—
621	C₂×#124	C₂²×C₈₃	1	8	yes	complemented
622	#525	C₂²×C₈₃	1	4	yes	complemented
623	C₂×C₂²⋊Q₈	C₂²×C₈₃	1	2	yes	complemented
624	C₂×#121	C₂²×C₈₃	1	4	yes	—
625	#520	C₂²×C₈₃	1	4	yes	complemented
626	#518	C₂²×C₈₃	1	4	yes	complemented
627	C₄×#41	C₂²×C₈₃	1	2	yes	complemented
628	C₄×#41	C₂²×C₈₃	1	4	yes	complemented
629	C₄×#41	C₂²×C₈₃	1	4	yes	complemented
630	C₂×C₄×Q₈	C₂²×C₈₃	1	2	yes	complemented
631	C₂×C₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
632	C₂×C₄×D₄	C₂²×C₈₃	1	1	yes	characteristic
633	C₂×#117	C₂²×C₈₃	1	2	yes	complemented
634	2₋¹⁺⁴	—	4	16	no	—
635	H(5,𝔽₂)	—	4	8	no	—
636	C₂×#41	C₂³×C₈₃	1	4	yes	—
637	C₂×#41	C₂³×C₈₃	1	2	yes	—
638	C₂×#41	C₂³×C₈₃	1	4	yes	—
639	C₂×#41	C₂³×C₈₃	1	4	yes	—
640	C₂×#41	C₂³×C₈₃	1	8	yes	—
641	C₂×#41	C₂³×C₈₃	1	8	yes	—
642	C₂×#41	C₂³×C₈₃	1	8	yes	—
643	C₂×#41	C₂³×C₈₃	1	16	yes	—
644	C₂²×Q₈	C₂³×C₈₃	1	2	yes	—
645	C₂²×Q₈	C₂³×C₈₃	1	1	yes	characteristic
646	C₂²×Q₈	C₂³×C₈₃	1	8	yes	—
647	C₂²×Q₈	C₂³×C₈₃	1	8	yes	—
648	C₂²×D₄	C₂³×C₈₃	1	1	yes	characteristic
649	C₂²×D₄	C₂³×C₈₃	1	4	yes	—
650	C₂²×D₄	C₂³×C₈₃	1	8	yes	—
651	C₂²×D₄	C₂³×C₈₃	1	8	yes	—
652	C₂³×C₄	C₂³×C₈₃	1	2	yes	—
653	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
654	C₄⋊Q₈	C₂³×C₈₃	1	4	yes	—
655	C₄⋊Q₈	C₂³×C₈₃	1	8	yes	—
656	C₄⋊Q₈	C₂³×C₈₃	1	4	yes	—
657	C₄⋊Q₈	C₂³×C₈₃	1	8	yes	—
658	C₄⋊Q₈	C₂³×C₈₃	1	8	yes	—
659	C₄⋊Q₈	C₂³×C₈₃	1	4	yes	—
660	C₄⋊Q₈	C₂³×C₈₃	1	4	yes	—
661	C₄⋊Q₈	C₂³×C₈₃	1	8	yes	—
662	#127	C₂³×C₈₃	1	2	yes	—
663	#127	C₂³×C₈₃	1	4	yes	—
664	#127	C₂³×C₈₃	1	4	yes	—
665	#127	C₂³×C₈₃	1	8	yes	—
666	#126	C₂³×C₈₃	1	16	yes	—
667	#126	C₂³×C₈₃	1	16	yes	—
668	#126	C₂³×C₈₃	1	16	yes	—
669	#126	C₂³×C₈₃	1	8	yes	—
670	#126	C₂³×C₈₃	1	8	yes	—
671	#126	C₂³×C₈₃	1	16	yes	—
672	#126	C₂³×C₈₃	1	8	yes	—
673	#126	C₂³×C₈₃	1	8	yes	—
674	#125	C₂³×C₈₃	1	4	yes	—
675	#125	C₂³×C₈₃	1	8	yes	—
676	#125	C₂³×C₈₃	1	8	yes	—
677	#125	C₂³×C₈₃	1	4	yes	—
678	#125	C₂³×C₈₃	1	16	yes	—
679	#124	C₂³×C₈₃	1	8	yes	—
680	#124	C₂³×C₈₃	1	8	yes	—
681	#124	C₂³×C₈₃	1	4	yes	—
682	#124	C₂³×C₈₃	1	4	yes	—
683	#124	C₂³×C₈₃	1	8	yes	—
684	#124	C₂³×C₈₃	1	16	yes	—
685	#124	C₂³×C₈₃	1	16	yes	—
686	#124	C₂³×C₈₃	1	8	yes	—
687	#124	C₂³×C₈₃	1	8	yes	—
688	#124	C₂³×C₈₃	1	4	yes	—
689	#124	C₂³×C₈₃	1	4	yes	—
690	#124	C₂³×C₈₃	1	4	yes	—
691	#124	C₂³×C₈₃	1	8	yes	—
692	#124	C₂³×C₈₃	1	16	yes	—
693	#123	C₂³×C₈₃	1	8	yes	—
694	#123	C₂³×C₈₃	1	16	yes	—
695	#123	C₂³×C₈₃	1	8	yes	—
696	#123	C₂³×C₈₃	1	8	yes	—
697	#123	C₂³×C₈₃	1	8	yes	—
698	#123	C₂³×C₈₃	1	16	yes	—
699	#123	C₂³×C₈₃	1	8	yes	—
700	#123	C₂³×C₈₃	1	16	yes	—
701	#123	C₂³×C₈₃	1	16	yes	—
702	#123	C₂³×C₈₃	1	16	yes	—
703	#123	C₂³×C₈₃	1	16	yes	—
704	#123	C₂³×C₈₃	1	16	yes	—
705	C₂²⋊Q₈	C₂³×C₈₃	1	8	yes	—
706	C₂²⋊Q₈	C₂³×C₈₃	1	8	yes	—
707	C₂²⋊Q₈	C₂³×C₈₃	1	4	yes	—
708	C₂²⋊Q₈	C₂³×C₈₃	1	4	yes	—
709	C₂²⋊Q₈	C₂³×C₈₃	1	8	yes	—
710	C₂²⋊Q₈	C₂³×C₈₃	1	4	yes	—
711	C₂²⋊Q₈	C₂³×C₈₃	1	4	yes	—
712	C₂²⋊Q₈	C₂³×C₈₃	1	8	yes	—
713	C₂²⋊Q₈	C₂³×C₈₃	1	8	yes	—
714	C₂²⋊Q₈	C₂³×C₈₃	1	8	yes	—
715	C₂²⋊Q₈	C₂³×C₈₃	1	16	yes	—
716	C₂²⋊Q₈	C₂³×C₈₃	1	16	yes	—
717	C₂²⋊Q₈	C₂³×C₈₃	1	16	yes	—
718	C₂²⋊Q₈	C₂³×C₈₃	1	16	yes	—
719	C₂²⋊Q₈	C₂³×C₈₃	1	16	yes	—
720	C₂²⋊Q₈	C₂³×C₈₃	1	16	yes	—
721	C₂²⋊Q₈	C₂³×C₈₃	1	16	yes	—
722	#121	C₂³×C₈₃	1	4	yes	—
723	#121	C₂³×C₈₃	1	8	yes	—
724	#121	C₂³×C₈₃	1	8	yes	—
725	#121	C₂³×C₈₃	1	8	yes	—
726	#121	C₂³×C₈₃	1	4	yes	—
727	#121	C₂³×C₈₃	1	4	yes	—
728	#121	C₂³×C₈₃	1	4	yes	—
729	#121	C₂³×C₈₃	1	4	yes	—
730	#121	C₂³×C₈₃	1	8	yes	—
731	#121	C₂³×C₈₃	1	8	yes	—
732	#121	C₂³×C₈₃	1	4	yes	—
733	#121	C₂³×C₈₃	1	8	yes	—
734	#121	C₂³×C₈₃	1	4	yes	—
735	#121	C₂³×C₈₃	1	8	yes	—
736	#121	C₂³×C₈₃	1	8	yes	—
737	#121	C₂³×C₈₃	1	4	yes	—
738	#121	C₂³×C₈₃	1	16	yes	—
739	#121	C₂³×C₈₃	1	8	yes	—
740	#121	C₂³×C₈₃	1	16	yes	—
741	#121	C₂³×C₈₃	1	8	yes	—
742	#121	C₂³×C₈₃	1	16	yes	—
743	#121	C₂³×C₈₃	1	16	yes	—
744	#121	C₂³×C₈₃	1	16	yes	—
745	#121	C₂³×C₈₃	1	16	yes	—
746	#120	C₂³×C₈₃	1	8	yes	—
747	#120	C₂³×C₈₃	1	16	yes	—
748	#120	C₂³×C₈₃	1	16	yes	—
749	#120	C₂³×C₈₃	1	16	yes	—
750	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
751	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
752	C₄×Q₈	C₂³×C₈₃	1	4	yes	—
753	C₄×Q₈	C₂³×C₈₃	1	8	yes	—
754	C₄×Q₈	C₂³×C₈₃	1	8	yes	—
755	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
756	C₄×Q₈	C₂³×C₈₃	1	4	yes	—
757	C₄×Q₈	C₂³×C₈₃	1	4	yes	—
758	C₄×Q₈	C₂³×C₈₃	1	4	yes	—
759	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
760	C₄×Q₈	C₂³×C₈₃	1	8	yes	—
761	C₄×D₄	C₂³×C₈₃	1	4	yes	—
762	C₄×D₄	C₂³×C₈₃	1	4	yes	—
763	C₄×D₄	C₂³×C₈₃	1	4	yes	—
764	C₄×D₄	C₂³×C₈₃	1	4	yes	—
765	C₄×D₄	C₂³×C₈₃	1	8	yes	—
766	C₄×D₄	C₂³×C₈₃	1	4	yes	—
767	C₄×D₄	C₂³×C₈₃	1	4	yes	—
768	C₄×D₄	C₂³×C₈₃	1	8	yes	—
769	C₄×D₄	C₂³×C₈₃	1	2	yes	—
770	C₄×D₄	C₂³×C₈₃	1	4	yes	—
771	C₄×D₄	C₂³×C₈₃	1	8	yes	—
772	C₄×D₄	C₂³×C₈₃	1	8	yes	—
773	C₄×D₄	C₂³×C₈₃	1	2	yes	—
774	C₄×D₄	C₂³×C₈₃	1	4	yes	—
775	C₄×D₄	C₂³×C₈₃	1	8	yes	—
776	C₄×D₄	C₂³×C₈₃	1	8	yes	—
777	C₄×D₄	C₂³×C₈₃	1	8	yes	—
778	C₄×D₄	C₂³×C₈₃	1	8	yes	—
779	C₄×D₄	C₂³×C₈₃	1	16	yes	—
780	C₄×D₄	C₂³×C₈₃	1	8	yes	—
781	C₄×D₄	C₂³×C₈₃	1	4	yes	—
782	C₄×D₄	C₂³×C₈₃	1	8	yes	—
783	C₄×D₄	C₂³×C₈₃	1	8	yes	—
784	C₄×D₄	C₂³×C₈₃	1	16	yes	—
785	C₄×D₄	C₂³×C₈₃	1	16	yes	—
786	#117	C₂³×C₈₃	1	4	yes	—
787	#117	C₂³×C₈₃	1	4	yes	—
788	#117	C₂³×C₈₃	1	8	yes	—
789	#117	C₂³×C₈₃	1	2	yes	—
790	#117	C₂³×C₈₃	1	4	yes	—
791	#117	C₂³×C₈₃	1	8	yes	—
792	#117	C₂³×C₈₃	1	4	yes	—
793	#117	C₂³×C₈₃	1	8	yes	—
794	#117	C₂³×C₈₃	1	4	yes	—
795	#117	C₂³×C₈₃	1	16	yes	—
796	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
797	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
798	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
799	C₂×C₄⋊C₄	C₂³×C₈₃	1	4	yes	—
800	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
801	C₂×C₄⋊C₄	C₂³×C₈₃	1	4	yes	—
802	C₂×C₄⋊C₄	C₂³×C₈₃	1	8	yes	—
803	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
804	C₂×C₄⋊C₄	C₂³×C₈₃	1	8	yes	—
805	C₂×C₂²⋊C₄	C₂³×C₈₃	1	4	yes	—
806	C₂×C₂²⋊C₄	C₂³×C₈₃	1	2	yes	—
807	C₂×C₂²⋊C₄	C₂³×C₈₃	1	16	yes	—
808	C₂×C₂²⋊C₄	C₂³×C₈₃	1	8	yes	—
809	C₂×C₂²⋊C₄	C₂³×C₈₃	1	4	yes	—
810	C₂×C₂²⋊C₄	C₂³×C₈₃	1	16	yes	—
811	C₂×C₄²	C₂³×C₈₃	1	4	yes	—
812	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
813	C₂×C₄²	C₂³×C₈₃	1	2	yes	—
814	C₂×C₄²	C₂³×C₈₃	1	8	yes	—
815	C₂×C₄²	C₂³×C₈₃	1	4	yes	—
816	C₂⁴	C₂⁴×C₈₃	1	2	yes	—
817	C₂⁴	C₂⁴×C₈₃	1	8	yes	—
818	#41	—	2	16	no	—
819	#41	—	2	8	no	—
820	#41	—	4	8	no	—
821	#41	—	4	32	no	—
822	#41	—	4	16	no	—
823	#41	—	4	16	no	—
824	#41	—	4	16	no	—
825	#41	—	4	8	no	—
826	C₂×Q₈	—	2	8	no	—
827	C₂×Q₈	—	4	16	no	—
828	C₂×Q₈	—	4	16	no	—
829	C₂×Q₈	—	4	2	no	—
830	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
831	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
832	C₂×Q₈	C₂⁴×C₈₃	1	8	yes	—
833	C₂×Q₈	C₂⁴×C₈₃	1	4	yes	—
834	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
835	C₂×Q₈	C₂⁴×C₈₃	1	4	yes	—
836	C₂×Q₈	C₂⁴×C₈₃	1	16	yes	—
837	C₂×D₄	—	2	4	no	—
838	C₂×D₄	—	4	16	no	—
839	C₂×D₄	—	4	8	no	—
840	C₂×D₄	—	4	16	no	—
841	C₂×D₄	C₂⁴×C₈₃	1	4	yes	—
842	C₂×D₄	C₂⁴×C₈₃	1	4	yes	—
843	C₂×D₄	C₂⁴×C₈₃	1	8	yes	—
844	C₂×D₄	C₂⁴×C₈₃	1	4	yes	—
845	C₂×D₄	C₂⁴×C₈₃	1	4	yes	—
846	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
847	C₂×D₄	C₂⁴×C₈₃	1	4	yes	—
848	C₂×D₄	C₂⁴×C₈₃	1	8	yes	—
849	C₂×D₄	C₂⁴×C₈₃	1	8	yes	—
850	C₂×D₄	C₂⁴×C₈₃	1	8	yes	—
851	C₂×D₄	C₂⁴×C₈₃	1	8	yes	—
852	C₂×D₄	C₂⁴×C₈₃	1	8	yes	—
853	C₂×D₄	C₂⁴×C₈₃	1	4	yes	—
854	C₂×D₄	C₂⁴×C₈₃	1	16	yes	—
855	C₂×D₄	C₂⁴×C₈₃	1	16	yes	—
856	C₂²×C₄	—	4	4	no	—
857	C₂²×C₄	C₂⁴×C₈₃	1	4	yes	—
858	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
859	C₂²×C₄	C₂⁴×C₈₃	1	4	yes	—
860	C₂²×C₄	C₂⁴×C₈₃	1	4	yes	—
861	C₂²×C₄	C₂⁴×C₈₃	1	8	yes	—
862	C₂²×C₄	C₂⁴×C₈₃	1	4	yes	—
863	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
864	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
865	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
866	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
867	C₂²×C₄	C₂⁴×C₈₃	1	8	yes	—
868	C₂²×C₄	C₂⁴×C₈₃	1	8	yes	—
869	C₂²×C₄	C₂⁴×C₈₃	1	4	yes	—
870	C₂²×C₄	C₂⁴×C₈₃	1	4	yes	—
871	C₂²×C₄	C₂⁴×C₈₃	1	16	yes	—
872	C₂²×C₄	C₂⁴×C₈₃	1	8	yes	—
873	C₂²×C₄	C₂⁴×C₈₃	1	16	yes	—
874	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
875	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
876	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
877	C₄⋊C₄	C₂⁴×C₈₃	1	8	yes	—
878	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
879	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
880	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
881	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
882	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
883	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
884	C₄⋊C₄	C₂⁴×C₈₃	1	16	yes	—
885	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
886	C₄⋊C₄	C₂⁴×C₈₃	1	8	yes	—
887	C₄⋊C₄	C₂⁴×C₈₃	1	16	yes	—
888	C₄⋊C₄	C₂⁴×C₈₃	1	16	yes	—
889	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
890	C₄⋊C₄	C₂⁴×C₈₃	1	8	yes	—
891	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
892	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
893	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
894	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
895	C₄⋊C₄	C₂⁴×C₈₃	1	8	yes	—
896	C₄⋊C₄	C₂⁴×C₈₃	1	8	yes	—
897	C₄⋊C₄	C₂⁴×C₈₃	1	8	yes	—
898	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
899	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
900	C₄⋊C₄	C₂⁴×C₈₃	1	8	yes	—
901	C₂²⋊C₄	C₂⁴×C₈₃	1	8	yes	—
902	C₂²⋊C₄	C₂⁴×C₈₃	1	8	yes	—
903	C₂²⋊C₄	C₂⁴×C₈₃	1	8	yes	—
904	C₂²⋊C₄	C₂⁴×C₈₃	1	16	yes	—
905	C₂²⋊C₄	C₂⁴×C₈₃	1	8	yes	—
906	C₂²⋊C₄	C₂⁴×C₈₃	1	8	yes	—
907	C₂²⋊C₄	C₂⁴×C₈₃	1	8	yes	—
908	C₂²⋊C₄	C₂⁴×C₈₃	1	8	yes	—
909	C₂²⋊C₄	C₂⁴×C₈₃	1	16	yes	—
910	C₂²⋊C₄	C₂⁴×C₈₃	1	16	yes	—
911	C₂²⋊C₄	C₂⁴×C₈₃	1	8	yes	—
912	C₂²⋊C₄	C₂⁴×C₈₃	1	16	yes	—
913	C₂²⋊C₄	C₂⁴×C₈₃	1	4	yes	—
914	C₂²⋊C₄	C₂⁴×C₈₃	1	8	yes	—
915	C₂²⋊C₄	C₂⁴×C₈₃	1	8	yes	—
916	C₂²⋊C₄	C₂⁴×C₈₃	1	8	yes	—
917	C₂²⋊C₄	C₂⁴×C₈₃	1	8	yes	—
918	C₂²⋊C₄	C₂⁴×C₈₃	1	4	yes	—
919	C₂²⋊C₄	C₂⁴×C₈₃	1	4	yes	—
920	C₂²⋊C₄	C₂⁴×C₈₃	1	8	yes	—
921	C₂²⋊C₄	C₂⁴×C₈₃	1	8	yes	—
922	C₄²	C₂⁴×C₈₃	1	4	yes	—
923	C₄²	C₂⁴×C₈₃	1	2	yes	—
924	C₄²	C₂⁴×C₈₃	1	4	yes	—
925	C₄²	C₂⁴×C₈₃	1	8	yes	—
926	C₄²	C₂⁴×C₈₃	1	8	yes	—
927	C₄²	C₂⁴×C₈₃	1	4	yes	—
928	C₄²	C₂⁴×C₈₃	1	2	yes	—
929	C₄²	C₂⁴×C₈₃	1	4	yes	—
930	C₄²	C₂⁴×C₈₃	1	4	yes	—
931	C₄²	C₂⁴×C₈₃	1	8	yes	—
932	C₄²	C₂⁴×C₈₃	1	8	yes	—
933	C₂³	—	2	4	no	—
934	C₂³	—	4	2	no	—
935	C₂³	—	4	2	no	—
936	C₂³	—	4	8	no	—
937	C₂³	—	4	8	no	—
938	C₂³	—	4	8	no	—
939	C₂³	C₂⁵×C₈₃	1	4	yes	—
940	C₂³	C₂⁵×C₈₃	1	8	yes	—
941	C₂³	C₂⁵×C₈₃	1	4	yes	—
942	C₂³	C₂⁵×C₈₃	1	1	yes	characteristic
943	Q₈	—	2	16	no	—
944	Q₈	—	2	4	no	—
945	Q₈	—	2	8	no	—
946	Q₈	—	2	4	no	—
947	Q₈	—	4	16	no	—
948	Q₈	—	4	2	no	—
949	Q₈	—	4	4	no	—
950	D₄	—	2	16	no	—
951	D₄	—	2	8	no	—
952	D₄	—	2	8	no	—
953	D₄	—	2	8	no	—
954	D₄	—	2	4	no	—
955	D₄	—	2	8	no	—
956	D₄	—	4	16	no	—
957	D₄	—	4	8	no	—
958	D₄	—	4	16	no	—
959	D₄	—	4	4	no	—
960	D₄	—	4	8	no	—
961	D₄	—	4	8	no	—
962	D₄	—	4	8	no	—
963	D₄	—	4	4	no	—
964	D₄	—	4	8	no	—
965	C₂×C₄	—	2	8	no	—
966	C₂×C₄	—	2	16	no	—
967	C₂×C₄	—	2	8	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	8	no	—
970	C₂×C₄	—	2	8	no	—
971	C₂×C₄	—	4	4	no	—
972	C₂×C₄	—	4	2	no	—
973	C₂×C₄	—	4	8	no	—
974	C₂×C₄	—	4	16	no	—
975	C₂×C₄	—	4	16	no	—
976	C₂×C₄	—	4	2	no	—
977	C₂×C₄	—	4	8	no	—
978	C₂×C₄	—	4	8	no	—
979	C₂×C₄	—	4	2	no	—
980	C₂×C₄	—	4	1	no	—
981	C₂×C₄	—	4	4	no	—
982	C₂×C₄	H(5,𝔽₂)×C₈₃	1	4	yes	—
983	C₂×C₄	C₂⁵×C₈₃	1	2	yes	—
984	C₂×C₄	C₂⁵×C₈₃	1	2	yes	—
985	C₂×C₄	C₂⁵×C₈₃	1	4	yes	—
986	C₂×C₄	C₂⁵×C₈₃	1	2	yes	—
987	C₂×C₄	C₂⁵×C₈₃	1	4	yes	—
988	C₂×C₄	C₂⁵×C₈₃	1	4	yes	—
989	C₂×C₄	C₂⁵×C₈₃	1	4	yes	—
990	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
991	C₂×C₄	C₂⁵×C₈₃	1	4	yes	—
992	C₂×C₄	C₂⁵×C₈₃	1	8	yes	—
993	C₂×C₄	C₂⁵×C₈₃	1	8	yes	—
994	C₂×C₄	C₂⁵×C₈₃	1	2	yes	—
995	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
996	C₂²	—	2	1	no	—
997	C₂²	—	2	1	no	—
998	C₂²	—	2	4	no	—
999	C₂²	—	2	8	no	—
1000	C₂²	—	2	4	no	—
1001	C₂²	—	2	4	no	—
1002	C₂²	—	2	4	no	—
1003	C₂²	—	2	8	no	—
1004	C₂²	—	2	4	no	—
1005	C₂²	—	2	8	no	—
1006	C₂²	—	2	4	no	—
1007	C₂²	—	8	4	no	—
1008	C₂²	—	16	8	no	—
1009	C₂²	C₂×H(5,𝔽₂)×C₈₃	1	2	yes	—
1010	C₂²	C₂⁶×C₈₃	1	1	yes	characteristic
1011	C₄	—	2	8	no	—
1012	C₄	—	2	4	no	—
1013	C₄	—	2	8	no	—
1014	C₄	—	2	1	no	—
1015	C₄	—	2	4	no	—
1016	C₄	—	2	4	no	—
1017	C₄	—	2	4	no	—
1018	C₄	—	2	2	no	—
1019	C₄	—	2	4	no	—
1020	C₄	—	2	2	no	—
1021	C₄	—	2	2	no	—
1022	C₄	C₂×H(5,𝔽₂)×C₈₃	1	4	yes	—
1023	C₄	#585×C₈₃	1	2	yes	—
1024	C₂	—	2	2	no	—
1025	C₂	—	4	4	no	—
1026	C₂	—	4	8	no	—
1027	C₂	—	4	4	no	—
1028	C₂	C₂²×H(5,𝔽₂)×C₈₃	1	1	yes	characteristic
1029	C₂	C₂×#585×C₈₃	1	1	yes	characteristic
1030	C₂	C₈₃×2₋¹⁺⁶	1	1	yes	characteristic

	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×#3562	C₂	semidirect
2. C₈₃×#3561	C₂	semidirect
3. C₈₃×#3560	C₂	semidirect
4. C₈₃×#3552	C₂	semidirect
5. C₈₃×#3546	C₂	semidirect
6. C₈₃×#3536	C₂	semidirect
7. C₈₃×#3514	C₂	semidirect
8. C₈₃×#3511	C₂	semidirect
9. C₈₃×#3500	C₂	semidirect
10. C₈₃×#3499	C₂	semidirect
11. C₈₃×#3497	C₂	semidirect
12. C₈₃×#3496	C₂	semidirect
13. C₈₃×#3494	C₂	semidirect
14. C₈₃×#3480	C₂	semidirect
15. C₂×#556×C₈₃	C₂	semidirect
16. C₈₃×#3461	C₂	semidirect
17. C₈₃×#3460	C₂	semidirect
18. C₂×2₋¹⁺⁴×C₈₃	C₂²	semidirect
20. #563×C₈₃	C₂²	semidirect
21. #562×C₈₃	C₂²	semidirect
22. #560×C₈₃	C₂²	semidirect
23. #559×C₈₃	C₂²	semidirect
24. #559×C₈₃	C₂²	semidirect
25. #557×C₈₃	C₂²	semidirect
26. #556×C₈₃	C₂²	semidirect
27. #556×C₈₃	C₂²	semidirect
28. #556×C₈₃	C₂²	semidirect
29. #556×C₈₃	C₂²	semidirect
30. #556×C₈₃	C₂²	semidirect
31. #555×C₈₃	C₂²	semidirect
32. #554×C₈₃	C₂²	semidirect
33. #553×C₈₃	C₂²	semidirect
34. #553×C₈₃	C₂²	semidirect
35. #553×C₈₃	C₂²	semidirect
36. #553×C₈₃	C₂²	semidirect
37. #551×C₈₃	C₂²	semidirect
38. #551×C₈₃	C₂²	semidirect
39. #550×C₈₃	C₂²	semidirect
40. #550×C₈₃	C₂²	semidirect
41. D₄×Q₈×C₈₃	C₂²	semidirect
42. D₄×Q₈×C₈₃	C₂²	semidirect
43. D₄×Q₈×C₈₃	C₂²	semidirect
44. #548×C₈₃	C₂²	semidirect
45. #548×C₈₃	C₂²	semidirect
46. #548×C₈₃	C₂²	semidirect
47. #548×C₈₃	C₂²	semidirect
48. #548×C₈₃	C₂²	semidirect
50. #547×C₈₃	C₂²	semidirect
51. #547×C₈₃	C₂²	semidirect
52. #547×C₈₃	C₂²	semidirect
53. #547×C₈₃	C₂²	semidirect
55. #546×C₈₃	C₂²	semidirect
56. #546×C₈₃	C₂²	semidirect
57. #546×C₈₃	C₂²	semidirect
58. #546×C₈₃	C₂²	semidirect
59. #546×C₈₃	C₂²	semidirect
61. #544×C₈₃	C₂²	semidirect
62. #544×C₈₃	C₂²	semidirect
63. #543×C₈₃	C₂²	semidirect
64. #542×C₈₃	C₂²	semidirect
65. #542×C₈₃	C₂²	semidirect
66. #542×C₈₃	C₂²	semidirect
67. #542×C₈₃	C₂²	semidirect
68. #542×C₈₃	C₂²	semidirect
69. #541×C₈₃	C₂²	semidirect
70. #540×C₈₃	C₂²	semidirect
71. #540×C₈₃	C₂²	semidirect
72. #539×C₈₃	C₂²	semidirect
73. #539×C₈₃	C₂²	semidirect
74. #538×C₈₃	C₂²	semidirect
75. #538×C₈₃	C₂²	semidirect
76. #538×C₈₃	C₂²	semidirect
77. #538×C₈₃	C₂²	semidirect
79. #537×C₈₃	C₂²	semidirect
80. #537×C₈₃	C₂²	semidirect
81. #537×C₈₃	C₂²	semidirect
82. #536×C₈₃	C₂²	semidirect
83. #536×C₈₃	C₂²	semidirect
84. #536×C₈₃	C₂²	semidirect
86. #535×C₈₃	C₂²	semidirect
87. #535×C₈₃	C₂²	semidirect
89. #533×C₈₃	C₂²	semidirect
91. #532×C₈₃	C₂²	semidirect
92. #532×C₈₃	C₂²	semidirect
93. #532×C₈₃	C₂²	semidirect
94. #532×C₈₃	C₂²	semidirect
95. #532×C₈₃	C₂²	semidirect
96. C₂×C₄⋊Q₈×C₈₃	C₂²	semidirect
97. C₂×C₄⋊Q₈×C₈₃	C₂²	semidirect
98. #529×C₈₃	C₂²	semidirect
99. #529×C₈₃	C₂²	semidirect
100. #529×C₈₃	C₂²	semidirect
101. #529×C₈₃	C₂²	semidirect
102. #529×C₈₃	C₂²	semidirect
103. C₂×#126×C₈₃	C₂²	semidirect
105. C₂×#124×C₈₃	C₂²	semidirect
106. #525×C₈₃	C₂²	semidirect
107. C₂×C₂²⋊Q₈×C₈₃	C₂²	semidirect
109. #520×C₈₃	C₂²	semidirect
110. #518×C₈₃	C₂²	semidirect
111. C₄×#41×C₈₃	C₂²	semidirect
112. C₄×#41×C₈₃	C₂²	semidirect
113. C₄×#41×C₈₃	C₂²	semidirect
114. C₂×C₄×Q₈×C₈₃	C₂²	semidirect
115. C₂×C₄×Q₈×C₈₃	C₂²	semidirect
117. C₂×#117×C₈₃	C₂²	semidirect
508. #62931	C₈₃	direct (N × H)
516. #3562	C₂×C₈₃	semidirect
517. #3561	C₂×C₈₃	semidirect
518. #3560	C₂×C₈₃	semidirect
519. #3552	C₂×C₈₃	semidirect
520. #3546	C₂×C₈₃	semidirect
521. #3536	C₂×C₈₃	semidirect
522. #3514	C₂×C₈₃	semidirect
523. #3511	C₂×C₈₃	semidirect
524. #3500	C₂×C₈₃	semidirect
525. #3499	C₂×C₈₃	semidirect
526. #3497	C₂×C₈₃	semidirect
527. #3496	C₂×C₈₃	semidirect
528. #3494	C₂×C₈₃	semidirect
529. #3480	C₂×C₈₃	semidirect
530. C₂×#556	C₂×C₈₃	semidirect
531. #3461	C₂×C₈₃	semidirect
532. #3460	C₂×C₈₃	semidirect
533. C₈₃	#62931	direct (N × H)
534. C₂×2₋¹⁺⁴	C₂²×C₈₃	semidirect
536. #563	C₂²×C₈₃	semidirect
537. #562	C₂²×C₈₃	semidirect
538. #560	C₂²×C₈₃	semidirect
539. #559	C₂²×C₈₃	semidirect
540. #559	C₂²×C₈₃	semidirect
541. #557	C₂²×C₈₃	semidirect
542. #556	C₂²×C₈₃	semidirect
543. #556	C₂²×C₈₃	semidirect
544. #556	C₂²×C₈₃	semidirect
545. #556	C₂²×C₈₃	semidirect
546. #556	C₂²×C₈₃	semidirect
547. #555	C₂²×C₈₃	semidirect
548. #554	C₂²×C₈₃	semidirect
549. #553	C₂²×C₈₃	semidirect
550. #553	C₂²×C₈₃	semidirect
551. #553	C₂²×C₈₃	semidirect
552. #553	C₂²×C₈₃	semidirect
553. #551	C₂²×C₈₃	semidirect
554. #551	C₂²×C₈₃	semidirect
555. #550	C₂²×C₈₃	semidirect
556. #550	C₂²×C₈₃	semidirect
557. D₄×Q₈	C₂²×C₈₃	semidirect
558. D₄×Q₈	C₂²×C₈₃	semidirect
559. D₄×Q₈	C₂²×C₈₃	semidirect
560. #548	C₂²×C₈₃	semidirect
561. #548	C₂²×C₈₃	semidirect
562. #548	C₂²×C₈₃	semidirect
563. #548	C₂²×C₈₃	semidirect
564. #548	C₂²×C₈₃	semidirect
566. #547	C₂²×C₈₃	semidirect
567. #547	C₂²×C₈₃	semidirect
568. #547	C₂²×C₈₃	semidirect
569. #547	C₂²×C₈₃	semidirect
571. #546	C₂²×C₈₃	semidirect
572. #546	C₂²×C₈₃	semidirect
573. #546	C₂²×C₈₃	semidirect
574. #546	C₂²×C₈₃	semidirect
575. #546	C₂²×C₈₃	semidirect
577. #544	C₂²×C₈₃	semidirect
578. #544	C₂²×C₈₃	semidirect
579. #543	C₂²×C₈₃	semidirect
580. #542	C₂²×C₈₃	semidirect
581. #542	C₂²×C₈₃	semidirect
582. #542	C₂²×C₈₃	semidirect
583. #542	C₂²×C₈₃	semidirect
584. #542	C₂²×C₈₃	semidirect
585. #541	C₂²×C₈₃	semidirect
586. #540	C₂²×C₈₃	semidirect
587. #540	C₂²×C₈₃	semidirect
588. #539	C₂²×C₈₃	semidirect
589. #539	C₂²×C₈₃	semidirect
590. #538	C₂²×C₈₃	semidirect
591. #538	C₂²×C₈₃	semidirect
592. #538	C₂²×C₈₃	semidirect
593. #538	C₂²×C₈₃	semidirect
595. #537	C₂²×C₈₃	semidirect
596. #537	C₂²×C₈₃	semidirect
597. #537	C₂²×C₈₃	semidirect
598. #536	C₂²×C₈₃	semidirect
599. #536	C₂²×C₈₃	semidirect
600. #536	C₂²×C₈₃	semidirect
602. #535	C₂²×C₈₃	semidirect
603. #535	C₂²×C₈₃	semidirect
605. #533	C₂²×C₈₃	semidirect
607. #532	C₂²×C₈₃	semidirect
608. #532	C₂²×C₈₃	semidirect
609. #532	C₂²×C₈₃	semidirect
610. #532	C₂²×C₈₃	semidirect
611. #532	C₂²×C₈₃	semidirect
612. C₂×C₄⋊Q₈	C₂²×C₈₃	semidirect
613. C₂×C₄⋊Q₈	C₂²×C₈₃	semidirect
614. #529	C₂²×C₈₃	semidirect
615. #529	C₂²×C₈₃	semidirect
616. #529	C₂²×C₈₃	semidirect
617. #529	C₂²×C₈₃	semidirect
618. #529	C₂²×C₈₃	semidirect
619. C₂×#126	C₂²×C₈₃	semidirect
621. C₂×#124	C₂²×C₈₃	semidirect
622. #525	C₂²×C₈₃	semidirect
623. C₂×C₂²⋊Q₈	C₂²×C₈₃	semidirect
625. #520	C₂²×C₈₃	semidirect
626. #518	C₂²×C₈₃	semidirect
627. C₄×#41	C₂²×C₈₃	semidirect
628. C₄×#41	C₂²×C₈₃	semidirect
629. C₄×#41	C₂²×C₈₃	semidirect
630. C₂×C₄×Q₈	C₂²×C₈₃	semidirect
631. C₂×C₄×Q₈	C₂²×C₈₃	semidirect
633. C₂×#117	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×#3562	2
C₈₃×#3561	2
C₈₃×#3560	2
C₈₃×#3552	2
C₈₃×#3546	2
C₈₃×#3536	2
C₈₃×#3514	2
C₈₃×#3511	2
C₈₃×#3500	2
C₈₃×#3499	2
C₈₃×#3497	2
C₈₃×#3496	2
C₈₃×#3494	2
C₈₃×#3480	2
C₂×#556×C₈₃	2
C₈₃×#3461	2
C₈₃×#3460	2
#62931	83

Subgroups — C83×#62931 #35290755

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#62931 #35290755