Subgroups — C₈₃×#61674 #35289498

Order 21248.

2032 conjugacy classes of subgroups.

The subgroup lattice has 794 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×#3500	C₂	1	1	yes	maximal, characteristic
3	C₈₃×#3313	C₂	1	4	yes	maximal, complemented
4	C₈₃×#3311	C₂	1	4	yes	maximal, complemented
5	C₈₃×#3270	C₂	1	4	yes	maximal, complemented
6	C₈₃×#3266	C₂	1	4	yes	maximal, complemented
7	C₈₃×#3215	C₂	1	2	yes	maximal, complemented
8	C₈₃×#3202	C₂	1	2	yes	maximal, complemented
9	C₈₃×#3200	C₂	1	2	yes	maximal, complemented
10	C₈₃×#3116	C₂	1	2	yes	maximal, complemented
11	C₈₃×#3011	C₂	1	2	yes	maximal, complemented
12	C₈₃×#3009	C₂	1	2	yes	maximal, complemented
13	C₈₃×#2980	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×2₋¹⁺⁴×C₈₃	C₂²	1	1	yes	characteristic
15	C₂×H(5,𝔽₂)×C₈₃	C₂²	1	1	yes	characteristic
16	C₂×#137×C₈₃	C₂²	1	2	yes	—
17	C₂×#137×C₈₃	C₂²	1	2	yes	complemented
18	C₂²×Q₁₆×C₈₃	C₂²	1	2	yes	complemented
19	C₂²×SD₁₆×C₈₃	C₂²	1	2	yes	—
20	#563×C₈₃	—	2	1	no	—
21	#563×C₈₃	—	2	1	no	—
22	#559×C₈₃	—	2	1	no	—
23	Q₈²×C₈₃	—	2	1	no	—
24	#556×C₈₃	C₂²	1	4	yes	complemented
25	D₄×Q₈×C₈₃	C₂²	1	4	yes	complemented
26	#548×C₈₃	C₂²	1	4	yes	—
27	#546×C₈₃	—	2	4	no	—
28	#546×C₈₃	C₂²	1	4	yes	—
29	#542×C₈₃	—	2	4	no	—
30	#536×C₈₃	—	2	1	no	—
31	#536×C₈₃	C₂²	1	2	yes	—
32	#536×C₈₃	C₂²	1	1	yes	characteristic
33	#536×C₈₃	C₂²	1	2	yes	complemented
34	#535×C₈₃	—	2	1	no	—
35	#535×C₈₃	C₂²	1	1	yes	characteristic
36	#533×C₈₃	C₂²	1	2	yes	complemented
37	#532×C₈₃	—	2	1	no	—
38	#532×C₈₃	C₂²	1	1	yes	characteristic
39	C₂×#124×C₈₃	—	2	1	no	—
40	C₂×#124×C₈₃	C₂²	1	1	yes	characteristic
41	C₄×#41×C₈₃	C₂²	1	1	yes	characteristic
42	#497×C₈₃	C₂²	1	4	yes	complemented
43	#489×C₈₃	C₂²	1	4	yes	complemented
44	#485×C₈₃	C₂²	1	4	yes	complemented
45	#485×C₈₃	C₂²	1	4	yes	complemented
46	#482×C₈₃	C₂²	1	4	yes	complemented
47	#477×C₈₃	C₂²	1	2	yes	complemented
48	#476×C₈₃	C₂²	1	2	yes	complemented
49	#470×C₈₃	C₂²	1	4	yes	complemented
50	#468×C₈₃	C₂²	1	4	yes	complemented
51	#467×C₈₃	C₂²	1	4	yes	complemented
52	#465×C₈₃	C₂²	1	4	yes	complemented
53	#464×C₈₃	C₂²	1	4	yes	complemented
54	#464×C₈₃	C₂²	1	4	yes	complemented
55	#462×C₈₃	C₂²	1	2	yes	complemented
56	#461×C₈₃	C₂²	1	2	yes	complemented
57	#452×C₈₃	C₂²	1	4	yes	—
58	#452×C₈₃	C₂²	1	4	yes	—
59	#452×C₈₃	C₂²	1	4	yes	complemented
60	#451×C₈₃	C₂²	1	4	yes	complemented
61	#451×C₈₃	C₂²	1	4	yes	complemented
62	#451×C₈₃	C₂²	1	4	yes	complemented
63	#450×C₈₃	C₂²	1	4	yes	—
64	#450×C₈₃	C₂²	1	4	yes	—
65	#448×C₈₃	C₂²	1	4	yes	complemented
66	#441×C₈₃	C₂²	1	4	yes	complemented
67	#440×C₈₃	C₂²	1	4	yes	complemented
68	#435×C₈₃	C₂²	1	4	yes	complemented
69	#435×C₈₃	C₂²	1	4	yes	complemented
70	#432×C₈₃	C₂²	1	2	yes	complemented
71	#419×C₈₃	C₂²	1	2	yes	complemented
72	#418×C₈₃	C₂²	1	2	yes	—
73	#416×C₈₃	C₂²	1	2	yes	—
74	#416×C₈₃	C₂²	1	2	yes	complemented
75	#408×C₈₃	C₂²	1	2	yes	—
76	#408×C₈₃	C₂²	1	2	yes	complemented
77	2₋¹⁺⁴×C₈₃	—	4	2	no	—
78	2₋¹⁺⁴×C₈₃	—	4	2	no	—
79	H(5,𝔽₂)×C₈₃	—	4	2	no	—
80	H(5,𝔽₂)×C₈₃	—	4	2	no	—
81	C₂×#41×C₈₃	—	2	1	no	—
82	C₂×#41×C₈₃	—	2	1	no	—
83	C₂×#41×C₈₃	—	2	2	no	—
84	C₂×#41×C₈₃	C₂³	1	1	yes	characteristic
85	C₂×#41×C₈₃	C₂³	1	2	yes	—
86	C₂×#41×C₈₃	C₂³	1	2	yes	—
87	C₂×#41×C₈₃	C₂³	1	1	yes	characteristic
88	C₂×#41×C₈₃	C₂³	1	1	yes	characteristic
89	C₂²×Q₈×C₈₃	—	2	1	no	—
90	C₂²×Q₈×C₈₃	C₂³	1	2	yes	—
91	C₂²×Q₈×C₈₃	C₂³	1	1	yes	characteristic
92	C₂²×Q₈×C₈₃	C₂³	1	2	yes	—
93	C₂²×Q₈×C₈₃	C₂³	1	2	yes	—
94	C₂²×D₄×C₈₃	—	2	1	no	—
95	C₂²×D₄×C₈₃	—	2	2	no	—
96	C₂²×D₄×C₈₃	C₂³	1	2	yes	—
97	C₂²×D₄×C₈₃	C₂³	1	1	yes	characteristic
98	#137×C₈₃	—	4	4	no	—
99	#137×C₈₃	—	4	4	no	—
100	C₂×Q₁₆×C₈₃	—	4	4	no	—
101	C₂×Q₁₆×C₈₃	C₂³	1	4	yes	—
102	C₂×Q₁₆×C₈₃	C₂³	1	4	yes	—
103	C₂×Q₁₆×C₈₃	C₂³	1	4	yes	—
104	C₂×SD₁₆×C₈₃	—	4	4	no	—
105	C₂×SD₁₆×C₈₃	C₂³	1	4	yes	—
106	C₂×SD₁₆×C₈₃	C₂³	1	4	yes	—
107	C₂×SD₁₆×C₈₃	C₂³	1	4	yes	—
108	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
109	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
110	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
111	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
112	C₄⋊Q₈×C₈₃	—	2	1	no	—
113	C₄⋊Q₈×C₈₃	—	2	2	no	—
114	C₄⋊Q₈×C₈₃	—	2	2	no	—
115	C₄⋊Q₈×C₈₃	—	2	4	no	—
116	C₄⋊Q₈×C₈₃	D₄	1	1	yes	characteristic
117	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
118	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
119	#127×C₈₃	—	2	1	no	—
120	#127×C₈₃	D₄	1	1	yes	characteristic
121	#126×C₈₃	—	2	4	no	—
122	#126×C₈₃	—	2	4	no	—
123	#125×C₈₃	—	2	2	no	—
124	#124×C₈₃	—	2	1	no	—
125	#124×C₈₃	—	2	1	no	—
126	#124×C₈₃	—	2	2	no	—
127	#124×C₈₃	—	2	2	no	—
128	#124×C₈₃	—	2	4	no	—
129	#124×C₈₃	—	2	4	no	—
130	#124×C₈₃	—	2	1	no	—
131	#124×C₈₃	—	2	1	no	—
132	#124×C₈₃	D₄	1	1	yes	characteristic
133	#124×C₈₃	D₄	1	1	yes	characteristic
134	#124×C₈₃	C₂³	1	4	yes	—
135	#123×C₈₃	—	2	2	no	—
136	#123×C₈₃	—	2	2	no	—
137	#123×C₈₃	—	2	2	no	—
138	#123×C₈₃	—	2	2	no	—
139	#123×C₈₃	—	2	2	no	—
140	#123×C₈₃	—	2	4	no	—
141	C₂²⋊Q₈×C₈₃	—	2	2	no	—
142	C₂²⋊Q₈×C₈₃	—	2	4	no	—
143	C₂²⋊Q₈×C₈₃	—	2	4	no	—
144	C₂²⋊Q₈×C₈₃	—	2	4	no	—
145	C₂²⋊Q₈×C₈₃	C₂³	1	4	yes	—
146	C₂²⋊Q₈×C₈₃	C₂³	1	4	yes	—
147	C₂²⋊Q₈×C₈₃	C₂³	1	4	yes	—
148	C₂²⋊Q₈×C₈₃	C₂³	1	4	yes	—
149	#121×C₈₃	—	2	4	no	—
150	#121×C₈₃	—	2	4	no	—
151	#121×C₈₃	D₄	1	4	yes	—
152	#121×C₈₃	C₂³	1	4	yes	—
153	#120×C₈₃	—	2	4	no	—
154	#120×C₈₃	—	2	2	no	—
155	C₄×Q₈×C₈₃	—	2	4	no	—
156	C₄×Q₈×C₈₃	—	2	2	no	—
157	C₄×Q₈×C₈₃	C₂³	1	4	yes	—
158	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
159	C₄×D₄×C₈₃	—	2	4	no	—
160	C₄×D₄×C₈₃	—	2	2	no	—
161	C₄×D₄×C₈₃	—	2	4	no	—
162	C₄×D₄×C₈₃	C₂³	1	2	yes	—
163	C₄×D₄×C₈₃	C₂³	1	4	yes	—
164	#117×C₈₃	—	2	2	no	—
165	#117×C₈₃	—	2	1	no	—
166	#117×C₈₃	C₂³	1	2	yes	—
167	#117×C₈₃	C₂³	1	1	yes	characteristic
168	#117×C₈₃	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
170	C₂×C₂²⋊C₄×C₈₃	—	2	4	no	—
171	C₂×C₄²×C₈₃	—	2	1	no	—
172	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
173	#107×C₈₃	C₂³	1	4	yes	—
174	#106×C₈₃	C₂³	1	4	yes	—
175	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
176	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
177	#103×C₈₃	C₂³	1	4	yes	—
178	#103×C₈₃	C₂³	1	4	yes	—
179	#103×C₈₃	C₂³	1	4	yes	—
180	#103×C₈₃	C₂³	1	4	yes	—
181	#103×C₈₃	C₂³	1	4	yes	—
182	#102×C₈₃	C₂³	1	4	yes	—
183	#102×C₈₃	C₂³	1	4	yes	—
184	#102×C₈₃	C₂³	1	4	yes	—
185	C₂²⋊C₈×C₈₃	C₂³	1	4	yes	—
186	C₂²⋊C₈×C₈₃	C₂³	1	4	yes	—
187	C₂²⋊C₈×C₈₃	C₂³	1	4	yes	—
188	#97×C₈₃	C₂³	1	4	yes	—
189	C₂⁴×C₈₃	—	2	2	no	—
190	C₂⁴×C₈₃	—	2	1	no	—
191	#41×C₈₃	—	2	2	no	—
192	#41×C₈₃	—	2	2	no	—
193	#41×C₈₃	—	2	4	no	—
194	#41×C₈₃	—	2	4	no	—
195	#41×C₈₃	—	4	1	no	—
196	#41×C₈₃	—	4	1	no	—
197	#41×C₈₃	—	4	1	no	—
198	#41×C₈₃	—	4	1	no	—
199	#41×C₈₃	—	4	2	no	—
200	#41×C₈₃	—	4	2	no	—
201	#41×C₈₃	—	4	4	no	—
202	#41×C₈₃	—	4	4	no	—
203	#41×C₈₃	—	4	8	no	—
204	C₂×Q₈×C₈₃	—	2	2	no	—
205	C₂×Q₈×C₈₃	—	2	2	no	—
206	C₂×Q₈×C₈₃	—	2	1	no	—
207	C₂×Q₈×C₈₃	—	2	2	no	—
208	C₂×Q₈×C₈₃	—	2	2	no	—
209	C₂×Q₈×C₈₃	—	2	4	no	—
210	C₂×Q₈×C₈₃	—	4	2	no	—
211	C₂×Q₈×C₈₃	—	4	1	no	—
212	C₂×Q₈×C₈₃	—	4	1	no	—
213	C₂×Q₈×C₈₃	—	4	4	no	—
214	C₂×Q₈×C₈₃	—	4	2	no	—
215	C₂×Q₈×C₈₃	—	4	2	no	—
216	C₂×Q₈×C₈₃	—	4	2	no	—
217	C₂×Q₈×C₈₃	—	4	2	no	—
218	C₂×Q₈×C₈₃	C₂×D₄	1	1	yes	characteristic
219	C₂×Q₈×C₈₃	C₂×D₄	1	1	yes	characteristic
220	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
221	C₂×Q₈×C₈₃	C₂⁴	1	4	yes	—
222	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
223	C₂×D₄×C₈₃	—	2	1	no	—
224	C₂×D₄×C₈₃	—	2	4	no	—
225	C₂×D₄×C₈₃	—	2	2	no	—
226	C₂×D₄×C₈₃	—	2	2	no	—
227	C₂×D₄×C₈₃	—	2	4	no	—
228	C₂×D₄×C₈₃	—	2	2	no	—
229	C₂×D₄×C₈₃	—	2	1	no	—
230	C₂×D₄×C₈₃	—	4	2	no	—
231	C₂×D₄×C₈₃	—	4	1	no	—
232	C₂×D₄×C₈₃	—	4	1	no	—
233	C₂×D₄×C₈₃	—	4	4	no	—
234	C₂×D₄×C₈₃	—	4	8	no	—
235	C₂×D₄×C₈₃	C₂×D₄	1	4	yes	—
236	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
237	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
238	C₂×D₄×C₈₃	C₂×D₄	1	1	yes	characteristic
239	C₂×D₄×C₈₃	C₂×D₄	1	1	yes	characteristic
240	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
241	C₂×D₄×C₈₃	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₈₃	—	2	1	no	—
243	C₂²×C₄×C₈₃	—	2	1	no	—
244	C₂²×C₄×C₈₃	—	2	2	no	—
245	C₂²×C₄×C₈₃	—	2	2	no	—
246	C₂²×C₄×C₈₃	—	2	2	no	—
247	C₂²×C₄×C₈₃	—	2	2	no	—
248	C₂²×C₄×C₈₃	—	2	2	no	—
249	C₂²×C₄×C₈₃	—	2	2	no	—
250	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
251	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
254	Q₁₆×C₈₃	—	2	8	no	—
255	Q₁₆×C₈₃	—	4	4	no	—
256	Q₁₆×C₈₃	—	4	4	no	—
257	SD₁₆×C₈₃	—	2	8	no	—
258	SD₁₆×C₈₃	—	4	4	no	—
259	SD₁₆×C₈₃	—	4	4	no	—
260	M₁₆×C₈₃	—	4	2	no	—
261	M₁₆×C₈₃	—	4	2	no	—
262	C₂×C₈×C₈₃	—	4	2	no	—
263	C₂×C₈×C₈₃	—	4	2	no	—
264	C₂×C₈×C₈₃	C₂⁴	1	4	yes	—
265	C₂×C₈×C₈₃	C₂⁴	1	4	yes	—
266	C₄⋊C₄×C₈₃	—	2	2	no	—
267	C₄⋊C₄×C₈₃	—	2	2	no	—
268	C₄⋊C₄×C₈₃	—	2	2	no	—
269	C₄⋊C₄×C₈₃	—	2	2	no	—
270	C₄⋊C₄×C₈₃	—	2	4	no	—
271	C₄⋊C₄×C₈₃	—	2	4	no	—
272	C₄⋊C₄×C₈₃	—	2	4	no	—
273	C₄⋊C₄×C₈₃	—	2	4	no	—
274	C₄⋊C₄×C₈₃	—	2	4	no	—
275	C₄⋊C₄×C₈₃	C₂×D₄	1	4	yes	—
276	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
277	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
278	C₂²⋊C₄×C₈₃	—	2	4	no	—
279	C₂²⋊C₄×C₈₃	—	2	4	no	—
280	C₂²⋊C₄×C₈₃	—	2	1	no	—
281	C₂²⋊C₄×C₈₃	—	2	2	no	—
282	C₂²⋊C₄×C₈₃	—	2	2	no	—
283	C₂²⋊C₄×C₈₃	—	2	4	no	—
284	C₂²⋊C₄×C₈₃	—	2	4	no	—
285	C₂²⋊C₄×C₈₃	—	2	4	no	—
286	C₂²⋊C₄×C₈₃	—	2	4	no	—
287	C₂²⋊C₄×C₈₃	—	2	4	no	—
288	C₂²⋊C₄×C₈₃	—	2	2	no	—
289	C₂²⋊C₄×C₈₃	C₂×D₄	1	4	yes	—
290	C₂²⋊C₄×C₈₃	C₂×D₄	1	4	yes	—
291	C₄²×C₈₃	—	2	1	no	—
292	C₄²×C₈₃	—	2	2	no	—
293	C₄²×C₈₃	—	2	4	no	—
294	C₄²×C₈₃	—	2	2	no	—
295	C₄²×C₈₃	—	2	2	no	—
296	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
297	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
298	C₄²×C₈₃	C₂⁴	1	2	yes	—
299	C₂³×C₈₃	—	2	1	no	—
300	C₂³×C₈₃	—	2	2	no	—
301	C₂³×C₈₃	—	4	4	no	—
302	C₂³×C₈₃	—	4	2	no	—
303	C₂³×C₈₃	—	8	2	no	—
304	C₂³×C₈₃	—	8	4	no	—
305	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
306	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
307	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
308	Q₈×C₈₃	—	2	1	no	—
309	Q₈×C₈₃	—	2	4	no	—
310	Q₈×C₈₃	—	2	4	no	—
311	Q₈×C₈₃	—	2	2	no	—
312	Q₈×C₈₃	—	2	2	no	—
313	Q₈×C₈₃	—	4	1	no	—
314	Q₈×C₈₃	—	4	1	no	—
315	Q₈×C₈₃	—	4	4	no	—
316	Q₈×C₈₃	—	4	4	no	—
317	Q₈×C₈₃	—	4	2	no	—
318	Q₈×C₈₃	—	8	2	no	—
319	Q₈×C₈₃	—	8	2	no	—
320	Q₈×C₈₃	H(5,𝔽₂)	1	2	yes	—
321	D₄×C₈₃	—	2	4	no	—
322	D₄×C₈₃	—	2	1	no	—
323	D₄×C₈₃	—	2	2	no	—
324	D₄×C₈₃	—	2	2	no	—
325	D₄×C₈₃	—	4	1	no	—
326	D₄×C₈₃	—	4	2	no	—
327	D₄×C₈₃	—	4	4	no	—
328	D₄×C₈₃	—	4	1	no	—
329	D₄×C₈₃	—	4	2	no	—
330	D₄×C₈₃	—	4	4	no	—
331	D₄×C₈₃	—	4	4	no	—
332	D₄×C₈₃	—	4	2	no	—
333	D₄×C₈₃	—	4	4	no	—
334	D₄×C₈₃	—	8	4	no	—
335	D₄×C₈₃	H(5,𝔽₂)	1	2	yes	—
336	C₂×C₄×C₈₃	—	2	4	no	—
337	C₂×C₄×C₈₃	—	2	1	no	—
338	C₂×C₄×C₈₃	—	2	2	no	—
339	C₂×C₄×C₈₃	—	2	2	no	—
340	C₂×C₄×C₈₃	—	2	2	no	—
341	C₂×C₄×C₈₃	—	2	2	no	—
342	C₂×C₄×C₈₃	—	2	1	no	—
343	C₂×C₄×C₈₃	—	2	1	no	—
344	C₂×C₄×C₈₃	—	2	4	no	—
345	C₂×C₄×C₈₃	—	2	2	no	—
346	C₂×C₄×C₈₃	—	2	4	no	—
347	C₂×C₄×C₈₃	—	2	2	no	—
348	C₂×C₄×C₈₃	—	4	2	no	—
349	C₂×C₄×C₈₃	—	4	4	no	—
350	C₂×C₄×C₈₃	—	4	4	no	—
351	C₂×C₄×C₈₃	—	4	4	no	—
352	C₂×C₄×C₈₃	—	4	2	no	—
353	C₂×C₄×C₈₃	—	8	2	no	—
354	C₂×C₄×C₈₃	—	8	2	no	—
355	C₂×C₄×C₈₃	—	8	2	no	—
356	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
357	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
359	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
360	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
361	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
362	C₈×C₈₃	—	2	4	no	—
363	C₈×C₈₃	—	2	4	no	—
364	C₂²×C₈₃	—	2	2	no	—
365	C₂²×C₈₃	—	2	4	no	—
366	C₂²×C₈₃	—	2	4	no	—
367	C₂²×C₈₃	—	2	2	no	—
368	C₂²×C₈₃	—	2	1	no	—
369	C₂²×C₈₃	—	2	2	no	—
370	C₂²×C₈₃	—	2	2	no	—
371	C₂²×C₈₃	—	4	2	no	—
372	C₂²×C₈₃	—	4	4	no	—
373	C₂²×C₈₃	—	4	2	no	—
374	C₂²×C₈₃	—	16	4	no	—
375	C₂²×C₈₃	—	16	2	no	—
376	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
377	C₄×C₈₃	—	2	2	no	—
378	C₄×C₈₃	—	2	2	no	—
379	C₄×C₈₃	—	2	1	no	—
380	C₄×C₈₃	—	2	2	no	—
381	C₄×C₈₃	—	2	2	no	—
382	C₄×C₈₃	—	2	2	no	—
383	C₄×C₈₃	—	4	2	no	—
384	C₄×C₈₃	—	4	4	no	—
385	C₄×C₈₃	—	4	2	no	—
386	C₄×C₈₃	—	4	4	no	—
387	C₄×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
388	C₄×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
389	#61674	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
390	C₂×C₈₃	—	4	2	no	—
391	C₂×C₈₃	—	4	1	no	—
392	C₂×C₈₃	—	4	2	no	—
393	C₂×C₈₃	—	4	2	no	—
394	C₂×C₈₃	—	8	2	no	—
395	C₂×C₈₃	#3484	1	1	yes	characteristic
396	C₂×C₈₃	#3586	1	2	yes	—
397	#3550	C₂×C₈₃	1	1	yes	characteristic, complemented
398	#3500	C₂×C₈₃	1	1	yes	characteristic
399	#3313	C₂×C₈₃	1	4	yes	complemented
400	#3311	C₂×C₈₃	1	4	yes	complemented
401	#3270	C₂×C₈₃	1	4	yes	complemented
402	#3266	C₂×C₈₃	1	4	yes	complemented
403	#3215	C₂×C₈₃	1	2	yes	complemented
404	#3202	C₂×C₈₃	1	2	yes	complemented
405	#3200	C₂×C₈₃	1	2	yes	complemented
406	#3116	C₂×C₈₃	1	2	yes	complemented
407	#3011	C₂×C₈₃	1	2	yes	complemented
408	#3009	C₂×C₈₃	1	2	yes	complemented
409	#2980	C₂×C₈₃	1	1	yes	characteristic, complemented
410	C₈₃	#61674	1	1	yes	characteristic, direct product factor, Sylow
411	C₂×2₋¹⁺⁴	C₂²×C₈₃	1	1	yes	characteristic
412	C₂×H(5,𝔽₂)	C₂²×C₈₃	1	1	yes	characteristic
413	C₂×#137	C₂²×C₈₃	1	2	yes	—
414	C₂×#137	C₂²×C₈₃	1	2	yes	complemented
415	C₂²×Q₁₆	C₂²×C₈₃	1	2	yes	complemented
416	C₂²×SD₁₆	C₂²×C₈₃	1	2	yes	—
417	#563	—	2	1	no	—
418	#563	—	2	1	no	—
419	#559	—	2	1	no	—
420	Q₈²	—	2	1	no	—
421	#556	C₂²×C₈₃	1	4	yes	complemented
422	D₄×Q₈	C₂²×C₈₃	1	4	yes	complemented
423	#548	C₂²×C₈₃	1	4	yes	—
424	#546	—	2	4	no	—
425	#546	C₂²×C₈₃	1	4	yes	—
426	#542	—	2	4	no	—
427	#536	—	2	1	no	—
428	#536	C₂²×C₈₃	1	1	yes	characteristic
429	#536	C₂²×C₈₃	1	2	yes	—
430	#536	C₂²×C₈₃	1	2	yes	complemented
431	#535	—	2	1	no	—
432	#535	C₂²×C₈₃	1	1	yes	characteristic
433	#533	C₂²×C₈₃	1	2	yes	complemented
434	#532	—	2	1	no	—
435	#532	C₂²×C₈₃	1	1	yes	characteristic
436	C₂×#124	—	2	1	no	—
437	C₂×#124	C₂²×C₈₃	1	1	yes	characteristic
438	C₄×#41	C₂²×C₈₃	1	1	yes	characteristic
439	#497	C₂²×C₈₃	1	4	yes	complemented
440	#489	C₂²×C₈₃	1	4	yes	complemented
441	#485	C₂²×C₈₃	1	4	yes	complemented
442	#485	C₂²×C₈₃	1	4	yes	complemented
443	#482	C₂²×C₈₃	1	4	yes	complemented
444	#477	C₂²×C₈₃	1	2	yes	complemented
445	#476	C₂²×C₈₃	1	2	yes	complemented
446	#470	C₂²×C₈₃	1	4	yes	complemented
447	#468	C₂²×C₈₃	1	4	yes	complemented
448	#467	C₂²×C₈₃	1	4	yes	complemented
449	#465	C₂²×C₈₃	1	4	yes	complemented
450	#464	C₂²×C₈₃	1	4	yes	complemented
451	#464	C₂²×C₈₃	1	4	yes	complemented
452	#462	C₂²×C₈₃	1	2	yes	complemented
453	#461	C₂²×C₈₃	1	2	yes	complemented
454	#452	C₂²×C₈₃	1	4	yes	—
455	#452	C₂²×C₈₃	1	4	yes	—
456	#452	C₂²×C₈₃	1	4	yes	complemented
457	#451	C₂²×C₈₃	1	4	yes	complemented
458	#451	C₂²×C₈₃	1	4	yes	complemented
459	#451	C₂²×C₈₃	1	4	yes	complemented
460	#450	C₂²×C₈₃	1	4	yes	—
461	#450	C₂²×C₈₃	1	4	yes	—
462	#448	C₂²×C₈₃	1	4	yes	complemented
463	#441	C₂²×C₈₃	1	4	yes	complemented
464	#440	C₂²×C₈₃	1	4	yes	complemented
465	#435	C₂²×C₈₃	1	4	yes	complemented
466	#435	C₂²×C₈₃	1	4	yes	complemented
467	#432	C₂²×C₈₃	1	2	yes	complemented
468	#419	C₂²×C₈₃	1	2	yes	complemented
469	#418	C₂²×C₈₃	1	2	yes	—
470	#416	C₂²×C₈₃	1	2	yes	—
471	#416	C₂²×C₈₃	1	2	yes	complemented
472	#408	C₂²×C₈₃	1	2	yes	—
473	#408	C₂²×C₈₃	1	2	yes	complemented
474	2₋¹⁺⁴	—	4	2	no	—
475	2₋¹⁺⁴	—	4	2	no	—
476	H(5,𝔽₂)	—	4	2	no	—
477	H(5,𝔽₂)	—	4	2	no	—
478	C₂×#41	—	2	1	no	—
479	C₂×#41	—	2	1	no	—
480	C₂×#41	—	2	2	no	—
481	C₂×#41	C₂³×C₈₃	1	1	yes	characteristic
482	C₂×#41	C₂³×C₈₃	1	2	yes	—
483	C₂×#41	C₂³×C₈₃	1	2	yes	—
484	C₂×#41	C₂³×C₈₃	1	1	yes	characteristic
485	C₂×#41	C₂³×C₈₃	1	1	yes	characteristic
486	C₂²×Q₈	—	2	1	no	—
487	C₂²×Q₈	C₂³×C₈₃	1	2	yes	—
488	C₂²×Q₈	C₂³×C₈₃	1	1	yes	characteristic
489	C₂²×Q₈	C₂³×C₈₃	1	2	yes	—
490	C₂²×Q₈	C₂³×C₈₃	1	2	yes	—
491	C₂²×D₄	—	2	1	no	—
492	C₂²×D₄	—	2	2	no	—
493	C₂²×D₄	C₂³×C₈₃	1	2	yes	—
494	C₂²×D₄	C₂³×C₈₃	1	1	yes	characteristic
495	#137	—	4	4	no	—
496	#137	—	4	4	no	—
497	C₂×Q₁₆	—	4	4	no	—
498	C₂×Q₁₆	C₂³×C₈₃	1	4	yes	—
499	C₂×Q₁₆	C₂³×C₈₃	1	4	yes	—
500	C₂×Q₁₆	C₂³×C₈₃	1	4	yes	—
501	C₂×SD₁₆	—	4	4	no	—
502	C₂×SD₁₆	C₂³×C₈₃	1	4	yes	—
503	C₂×SD₁₆	C₂³×C₈₃	1	4	yes	—
504	C₂×SD₁₆	C₂³×C₈₃	1	4	yes	—
505	C₂×M₁₆	C₂³×C₈₃	1	2	yes	—
506	C₂×M₁₆	C₂³×C₈₃	1	2	yes	—
507	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
508	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
509	C₄⋊Q₈	—	2	1	no	—
510	C₄⋊Q₈	—	2	2	no	—
511	C₄⋊Q₈	—	2	2	no	—
512	C₄⋊Q₈	—	2	4	no	—
513	C₄⋊Q₈	D₄×C₈₃	1	1	yes	characteristic
514	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
515	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
516	#127	—	2	1	no	—
517	#127	D₄×C₈₃	1	1	yes	characteristic
518	#126	—	2	4	no	—
519	#126	—	2	4	no	—
520	#125	—	2	2	no	—
521	#124	—	2	1	no	—
522	#124	—	2	1	no	—
523	#124	—	2	2	no	—
524	#124	—	2	2	no	—
525	#124	—	2	4	no	—
526	#124	—	2	4	no	—
527	#124	—	2	1	no	—
528	#124	—	2	1	no	—
529	#124	D₄×C₈₃	1	1	yes	characteristic
530	#124	D₄×C₈₃	1	1	yes	characteristic
531	#124	C₂³×C₈₃	1	4	yes	—
532	#123	—	2	2	no	—
533	#123	—	2	2	no	—
534	#123	—	2	2	no	—
535	#123	—	2	2	no	—
536	#123	—	2	2	no	—
537	#123	—	2	4	no	—
538	C₂²⋊Q₈	—	2	2	no	—
539	C₂²⋊Q₈	—	2	4	no	—
540	C₂²⋊Q₈	—	2	4	no	—
541	C₂²⋊Q₈	—	2	4	no	—
542	C₂²⋊Q₈	C₂³×C₈₃	1	4	yes	—
543	C₂²⋊Q₈	C₂³×C₈₃	1	4	yes	—
544	C₂²⋊Q₈	C₂³×C₈₃	1	4	yes	—
545	C₂²⋊Q₈	C₂³×C₈₃	1	4	yes	—
546	#121	—	2	4	no	—
547	#121	—	2	4	no	—
548	#121	D₄×C₈₃	1	4	yes	—
549	#121	C₂³×C₈₃	1	4	yes	—
550	#120	—	2	4	no	—
551	#120	—	2	2	no	—
552	C₄×Q₈	—	2	4	no	—
553	C₄×Q₈	—	2	2	no	—
554	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
555	C₄×Q₈	C₂³×C₈₃	1	4	yes	—
556	C₄×D₄	—	2	4	no	—
557	C₄×D₄	—	2	2	no	—
558	C₄×D₄	—	2	4	no	—
559	C₄×D₄	C₂³×C₈₃	1	2	yes	—
560	C₄×D₄	C₂³×C₈₃	1	4	yes	—
561	#117	—	2	2	no	—
562	#117	—	2	1	no	—
563	#117	C₂³×C₈₃	1	1	yes	characteristic
564	#117	C₂³×C₈₃	1	2	yes	—
565	#117	C₂³×C₈₃	1	2	yes	—
566	C₂×C₂²⋊C₄	—	2	2	no	—
567	C₂×C₂²⋊C₄	—	2	4	no	—
568	C₂×C₄²	—	2	1	no	—
569	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
570	#107	C₂³×C₈₃	1	4	yes	—
571	#106	C₂³×C₈₃	1	4	yes	—
572	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
573	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
574	#103	C₂³×C₈₃	1	4	yes	—
575	#103	C₂³×C₈₃	1	4	yes	—
576	#103	C₂³×C₈₃	1	4	yes	—
577	#103	C₂³×C₈₃	1	4	yes	—
578	#103	C₂³×C₈₃	1	4	yes	—
579	#102	C₂³×C₈₃	1	4	yes	—
580	#102	C₂³×C₈₃	1	4	yes	—
581	#102	C₂³×C₈₃	1	4	yes	—
582	C₂²⋊C₈	C₂³×C₈₃	1	4	yes	—
583	C₂²⋊C₈	C₂³×C₈₃	1	4	yes	—
584	C₂²⋊C₈	C₂³×C₈₃	1	4	yes	—
585	#97	C₂³×C₈₃	1	4	yes	—
586	C₂⁴	—	2	2	no	—
587	C₂⁴	—	2	1	no	—
588	#41	—	2	2	no	—
589	#41	—	2	2	no	—
590	#41	—	2	4	no	—
591	#41	—	2	4	no	—
592	#41	—	4	1	no	—
593	#41	—	4	1	no	—
594	#41	—	4	1	no	—
595	#41	—	4	1	no	—
596	#41	—	4	2	no	—
597	#41	—	4	2	no	—
598	#41	—	4	4	no	—
599	#41	—	4	4	no	—
600	#41	—	4	8	no	—
601	C₂×Q₈	—	2	2	no	—
602	C₂×Q₈	—	2	2	no	—
603	C₂×Q₈	—	2	1	no	—
604	C₂×Q₈	—	2	2	no	—
605	C₂×Q₈	—	2	2	no	—
606	C₂×Q₈	—	2	4	no	—
607	C₂×Q₈	—	4	2	no	—
608	C₂×Q₈	—	4	1	no	—
609	C₂×Q₈	—	4	1	no	—
610	C₂×Q₈	—	4	4	no	—
611	C₂×Q₈	—	4	2	no	—
612	C₂×Q₈	—	4	2	no	—
613	C₂×Q₈	—	4	2	no	—
614	C₂×Q₈	—	4	2	no	—
615	C₂×Q₈	C₂×D₄×C₈₃	1	1	yes	characteristic
616	C₂×Q₈	C₂×D₄×C₈₃	1	1	yes	characteristic
617	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
618	C₂×Q₈	C₂⁴×C₈₃	1	4	yes	—
619	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	2	no	—
623	C₂×D₄	—	2	2	no	—
624	C₂×D₄	—	2	4	no	—
625	C₂×D₄	—	2	2	no	—
626	C₂×D₄	—	2	1	no	—
627	C₂×D₄	—	4	2	no	—
628	C₂×D₄	—	4	1	no	—
629	C₂×D₄	—	4	1	no	—
630	C₂×D₄	—	4	4	no	—
631	C₂×D₄	—	4	8	no	—
632	C₂×D₄	C₂×D₄×C₈₃	1	4	yes	—
633	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
634	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
635	C₂×D₄	C₂×D₄×C₈₃	1	1	yes	characteristic
636	C₂×D₄	C₂×D₄×C₈₃	1	1	yes	characteristic
637	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
638	C₂×D₄	C₂⁴×C₈₃	1	1	yes	characteristic
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	2	no	—
644	C₂²×C₄	—	2	2	no	—
645	C₂²×C₄	—	2	2	no	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
648	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
649	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
650	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
651	Q₁₆	—	2	8	no	—
652	Q₁₆	—	4	4	no	—
653	Q₁₆	—	4	4	no	—
654	SD₁₆	—	2	8	no	—
655	SD₁₆	—	4	4	no	—
656	SD₁₆	—	4	4	no	—
657	M₁₆	—	4	2	no	—
658	M₁₆	—	4	2	no	—
659	C₂×C₈	—	4	2	no	—
660	C₂×C₈	—	4	2	no	—
661	C₂×C₈	C₂⁴×C₈₃	1	4	yes	—
662	C₂×C₈	C₂⁴×C₈₃	1	4	yes	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	2	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	2	2	no	—
667	C₄⋊C₄	—	2	4	no	—
668	C₄⋊C₄	—	2	4	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	4	no	—
671	C₄⋊C₄	—	2	4	no	—
672	C₄⋊C₄	C₂×D₄×C₈₃	1	4	yes	—
673	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
674	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	1	no	—
678	C₂²⋊C₄	—	2	2	no	—
679	C₂²⋊C₄	—	2	2	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	4	no	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	4	no	—
684	C₂²⋊C₄	—	2	4	no	—
685	C₂²⋊C₄	—	2	2	no	—
686	C₂²⋊C₄	C₂×D₄×C₈₃	1	4	yes	—
687	C₂²⋊C₄	C₂×D₄×C₈₃	1	4	yes	—
688	C₄²	—	2	1	no	—
689	C₄²	—	2	2	no	—
690	C₄²	—	2	4	no	—
691	C₄²	—	2	2	no	—
692	C₄²	—	2	2	no	—
693	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
694	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
695	C₄²	C₂⁴×C₈₃	1	2	yes	—
696	C₂³	—	2	1	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	4	4	no	—
699	C₂³	—	4	2	no	—
700	C₂³	—	8	2	no	—
701	C₂³	—	8	4	no	—
702	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
703	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
704	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
705	Q₈	—	2	1	no	—
706	Q₈	—	2	4	no	—
707	Q₈	—	2	4	no	—
708	Q₈	—	2	2	no	—
709	Q₈	—	2	2	no	—
710	Q₈	—	4	1	no	—
711	Q₈	—	4	1	no	—
712	Q₈	—	4	4	no	—
713	Q₈	—	4	2	no	—
714	Q₈	—	4	4	no	—
715	Q₈	—	8	2	no	—
716	Q₈	—	8	2	no	—
717	Q₈	H(5,𝔽₂)×C₈₃	1	2	yes	—
718	D₄	—	2	4	no	—
719	D₄	—	2	1	no	—
720	D₄	—	2	2	no	—
721	D₄	—	2	2	no	—
722	D₄	—	4	1	no	—
723	D₄	—	4	2	no	—
724	D₄	—	4	1	no	—
725	D₄	—	4	2	no	—
726	D₄	—	4	4	no	—
727	D₄	—	4	4	no	—
728	D₄	—	4	4	no	—
729	D₄	—	4	2	no	—
730	D₄	—	4	4	no	—
731	D₄	—	8	4	no	—
732	D₄	H(5,𝔽₂)×C₈₃	1	2	yes	—
733	C₂×C₄	—	2	4	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	4	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	4	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	4	2	no	—
746	C₂×C₄	—	4	4	no	—
747	C₂×C₄	—	4	4	no	—
748	C₂×C₄	—	4	4	no	—
749	C₂×C₄	—	4	2	no	—
750	C₂×C₄	—	8	2	no	—
751	C₂×C₄	—	8	2	no	—
752	C₂×C₄	—	8	2	no	—
753	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
754	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
755	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
756	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
757	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
758	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
759	C₈	—	2	4	no	—
760	C₈	—	2	4	no	—
761	C₂²	—	2	2	no	—
762	C₂²	—	2	4	no	—
763	C₂²	—	2	4	no	—
764	C₂²	—	2	2	no	—
765	C₂²	—	2	1	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	2	2	no	—
768	C₂²	—	4	2	no	—
769	C₂²	—	4	4	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	16	4	no	—
772	C₂²	—	16	2	no	—
773	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
774	C₄	—	2	2	no	—
775	C₄	—	2	2	no	—
776	C₄	—	2	1	no	—
777	C₄	—	2	2	no	—
778	C₄	—	2	2	no	—
779	C₄	—	2	2	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	4	no	—
782	C₄	—	4	2	no	—
783	C₄	—	4	4	no	—
784	C₄	C₂×H(5,𝔽₂)×C₈₃	1	1	yes	characteristic
785	C₄	C₂×H(5,𝔽₂)×C₈₃	1	1	yes	characteristic
786	C₂	—	4	1	no	—
787	C₂	—	4	2	no	—
788	C₂	—	4	2	no	—
789	C₂	—	4	2	no	—
790	C₂	—	8	2	no	—
791	C₂	C₈₃×#3484	1	1	yes	characteristic
792	C₂	C₈₃×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₈₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₃
prime radical	C₈₃×#3500	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
1. C₈₃×#3550	C₂	semidirect
3. C₈₃×#3313	C₂	semidirect
4. C₈₃×#3311	C₂	semidirect
5. C₈₃×#3270	C₂	semidirect
6. C₈₃×#3266	C₂	semidirect
7. C₈₃×#3215	C₂	semidirect
8. C₈₃×#3202	C₂	semidirect
9. C₈₃×#3200	C₂	semidirect
10. C₈₃×#3116	C₂	semidirect
11. C₈₃×#3011	C₂	semidirect
12. C₈₃×#3009	C₂	semidirect
13. C₈₃×#2980	C₂	semidirect
17. C₂×#137×C₈₃	C₂²	semidirect
18. C₂²×Q₁₆×C₈₃	C₂²	semidirect
24. #556×C₈₃	C₂²	semidirect
25. D₄×Q₈×C₈₃	C₂²	semidirect
33. #536×C₈₃	C₂²	semidirect
36. #533×C₈₃	C₂²	semidirect
42. #497×C₈₃	C₂²	semidirect
43. #489×C₈₃	C₂²	semidirect
44. #485×C₈₃	C₂²	semidirect
45. #485×C₈₃	C₂²	semidirect
46. #482×C₈₃	C₂²	semidirect
47. #477×C₈₃	C₂²	semidirect
48. #476×C₈₃	C₂²	semidirect
49. #470×C₈₃	C₂²	semidirect
50. #468×C₈₃	C₂²	semidirect
51. #467×C₈₃	C₂²	semidirect
52. #465×C₈₃	C₂²	semidirect
53. #464×C₈₃	C₂²	semidirect
54. #464×C₈₃	C₂²	semidirect
55. #462×C₈₃	C₂²	semidirect
56. #461×C₈₃	C₂²	semidirect
59. #452×C₈₃	C₂²	semidirect
60. #451×C₈₃	C₂²	semidirect
61. #451×C₈₃	C₂²	semidirect
62. #451×C₈₃	C₂²	semidirect
65. #448×C₈₃	C₂²	semidirect
66. #441×C₈₃	C₂²	semidirect
67. #440×C₈₃	C₂²	semidirect
68. #435×C₈₃	C₂²	semidirect
69. #435×C₈₃	C₂²	semidirect
70. #432×C₈₃	C₂²	semidirect
71. #419×C₈₃	C₂²	semidirect
74. #416×C₈₃	C₂²	semidirect
76. #408×C₈₃	C₂²	semidirect
389. #61674	C₈₃	direct (N × H)
397. #3550	C₂×C₈₃	semidirect
399. #3313	C₂×C₈₃	semidirect
400. #3311	C₂×C₈₃	semidirect
401. #3270	C₂×C₈₃	semidirect
402. #3266	C₂×C₈₃	semidirect
403. #3215	C₂×C₈₃	semidirect
404. #3202	C₂×C₈₃	semidirect
405. #3200	C₂×C₈₃	semidirect
406. #3116	C₂×C₈₃	semidirect
407. #3011	C₂×C₈₃	semidirect
408. #3009	C₂×C₈₃	semidirect
409. #2980	C₂×C₈₃	semidirect
410. C₈₃	#61674	direct (N × H)
414. C₂×#137	C₂²×C₈₃	semidirect
415. C₂²×Q₁₆	C₂²×C₈₃	semidirect
421. #556	C₂²×C₈₃	semidirect
422. D₄×Q₈	C₂²×C₈₃	semidirect
430. #536	C₂²×C₈₃	semidirect
433. #533	C₂²×C₈₃	semidirect
439. #497	C₂²×C₈₃	semidirect
440. #489	C₂²×C₈₃	semidirect
441. #485	C₂²×C₈₃	semidirect
442. #485	C₂²×C₈₃	semidirect
443. #482	C₂²×C₈₃	semidirect
444. #477	C₂²×C₈₃	semidirect
445. #476	C₂²×C₈₃	semidirect
446. #470	C₂²×C₈₃	semidirect
447. #468	C₂²×C₈₃	semidirect
448. #467	C₂²×C₈₃	semidirect
449. #465	C₂²×C₈₃	semidirect
450. #464	C₂²×C₈₃	semidirect
451. #464	C₂²×C₈₃	semidirect
452. #462	C₂²×C₈₃	semidirect
453. #461	C₂²×C₈₃	semidirect
456. #452	C₂²×C₈₃	semidirect
457. #451	C₂²×C₈₃	semidirect
458. #451	C₂²×C₈₃	semidirect
459. #451	C₂²×C₈₃	semidirect
462. #448	C₂²×C₈₃	semidirect
463. #441	C₂²×C₈₃	semidirect
464. #440	C₂²×C₈₃	semidirect
465. #435	C₂²×C₈₃	semidirect
466. #435	C₂²×C₈₃	semidirect
467. #432	C₂²×C₈₃	semidirect
468. #419	C₂²×C₈₃	semidirect
471. #416	C₂²×C₈₃	semidirect
473. #408	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×#3550	2
C₈₃×#3500	2
C₈₃×#3313	2
C₈₃×#3311	2
C₈₃×#3270	2
C₈₃×#3266	2
C₈₃×#3215	2
C₈₃×#3202	2
C₈₃×#3200	2
C₈₃×#3116	2
C₈₃×#3011	2
C₈₃×#3009	2
C₈₃×#2980	2
#61674	83

Subgroups — C83×#61674 #35289498

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#61674 #35289498