Subgroups — C₈₃×#61631 #35289455

Order 21248.

2222 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3538	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₃×#3484	C₂	1	1	yes	maximal, characteristic
3	C₈₃×#3310	C₂	1	4	yes	maximal, complemented
4	C₈₃×#3296	C₂	1	4	yes	maximal, complemented
5	D₄×SD₁₆×C₈₃	C₂	1	4	yes	maximal, complemented
6	C₈₃×#3266	C₂	1	4	yes	maximal, complemented
7	C₈₃×#3222	C₂	1	2	yes	maximal, complemented
8	C₈₃×#3200	C₂	1	2	yes	maximal, complemented
9	C₈₃×#3190	C₂	1	2	yes	maximal, complemented
10	C₈₃×#3123	C₂	1	2	yes	maximal, complemented
11	C₈₃×#3009	C₂	1	2	yes	maximal, complemented
12	C₂×#450×C₈₃	C₂	1	2	yes	maximal, complemented
13	C₈₃×#2977	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×H(5,𝔽₂)×C₈₃	C₂²	1	1	yes	characteristic
15	C₂³×D₄×C₈₃	C₂²	1	1	yes	characteristic
16	C₂×#137×C₈₃	C₂²	1	2	yes	complemented
17	C₂²×SD₁₆×C₈₃	C₂²	1	4	yes	complemented
18	C₂²×SD₁₆×C₈₃	C₂²	1	2	yes	complemented
19	#563×C₈₃	—	2	2	no	—
20	#552×C₈₃	C₂²	1	4	yes	complemented
21	#551×C₈₃	—	2	2	no	—
22	D₄×Q₈×C₈₃	C₂²	1	4	yes	complemented
23	#546×C₈₃	—	2	2	no	—
24	#546×C₈₃	C₂²	1	4	yes	—
25	D₄²×C₈₃	—	2	2	no	—
26	D₄²×C₈₃	C₂²	1	4	yes	—
27	#544×C₈₃	—	2	2	no	—
28	#541×C₈₃	C₂²	1	2	yes	complemented
29	#539×C₈₃	—	2	2	no	—
30	#536×C₈₃	C₂²	1	2	yes	complemented
31	#535×C₈₃	C₂²	1	1	yes	characteristic
32	#535×C₈₃	C₂²	1	1	yes	characteristic
33	#534×C₈₃	—	2	2	no	—
34	#525×C₈₃	C₂²	1	1	yes	characteristic
35	#525×C₈₃	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊Q₈×C₈₃	C₂²	1	2	yes	complemented
37	C₂×#120×C₈₃	—	2	2	no	—
38	#518×C₈₃	C₂²	1	1	yes	characteristic
39	#497×C₈₃	C₂²	1	2	yes	complemented
40	#492×C₈₃	C₂²	1	2	yes	complemented
41	#490×C₈₃	C₂²	1	2	yes	complemented
42	#488×C₈₃	C₂²	1	2	yes	complemented
43	#485×C₈₃	C₂²	1	4	yes	complemented
44	#483×C₈₃	C₂²	1	2	yes	complemented
45	#482×C₈₃	C₂²	1	4	yes	complemented
46	#480×C₈₃	C₂²	1	2	yes	complemented
47	#478×C₈₃	C₂²	1	4	yes	complemented
48	#468×C₈₃	C₂²	1	4	yes	complemented
49	#467×C₈₃	C₂²	1	4	yes	complemented
50	#465×C₈₃	C₂²	1	4	yes	complemented
51	#465×C₈₃	C₂²	1	4	yes	complemented
52	#464×C₈₃	C₂²	1	4	yes	complemented
53	#461×C₈₃	C₂²	1	4	yes	complemented
54	#460×C₈₃	C₂²	1	4	yes	complemented
55	#452×C₈₃	C₂²	1	4	yes	complemented
56	#452×C₈₃	C₂²	1	4	yes	complemented
57	#451×C₈₃	C₂²	1	2	yes	complemented
58	#450×C₈₃	C₂²	1	4	yes	—
59	#450×C₈₃	C₂²	1	4	yes	complemented
60	#450×C₈₃	C₂²	1	4	yes	complemented
61	#450×C₈₃	C₂²	1	4	yes	complemented
62	#450×C₈₃	C₂²	1	4	yes	complemented
63	#448×C₈₃	C₂²	1	2	yes	complemented
64	#448×C₈₃	C₂²	1	4	yes	complemented
65	#440×C₈₃	C₂²	1	4	yes	complemented
66	C₄×SD₁₆×C₈₃	C₂²	1	4	yes	complemented
67	#435×C₈₃	C₂²	1	4	yes	complemented
68	C₈×D₄×C₈₃	C₂²	1	4	yes	complemented
69	#433×C₈₃	C₂²	1	2	yes	complemented
70	#418×C₈₃	C₂²	1	2	yes	complemented
71	#416×C₈₃	C₂²	1	2	yes	complemented
72	C₂×#102×C₈₃	C₂²	1	4	yes	complemented
73	#408×C₈₃	C₂²	1	2	yes	complemented
74	C₂×C₂²⋊C₈×C₈₃	C₂²	1	2	yes	complemented
75	C₂⁵×C₈₃	—	2	1	no	—
76	H(5,𝔽₂)×C₈₃	—	4	4	no	—
77	C₂×#41×C₈₃	—	2	1	no	—
78	C₂×#41×C₈₃	C₂³	1	2	yes	—
79	C₂×#41×C₈₃	C₂³	1	1	yes	characteristic
80	C₂×#41×C₈₃	C₂³	1	1	yes	characteristic
81	C₂²×Q₈×C₈₃	C₂³	1	2	yes	—
82	C₂²×Q₈×C₈₃	C₂³	1	2	yes	complemented
83	C₂²×D₄×C₈₃	—	2	2	no	—
84	C₂²×D₄×C₈₃	—	2	1	no	—
85	C₂²×D₄×C₈₃	—	2	4	no	—
86	C₂²×D₄×C₈₃	—	2	1	no	—
87	C₂²×D₄×C₈₃	—	2	2	no	—
88	C₂²×D₄×C₈₃	—	4	4	no	—
89	C₂²×D₄×C₈₃	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₈₃	C₂³	1	2	yes	—
91	C₂²×D₄×C₈₃	C₂³	1	4	yes	—
92	C₂²×D₄×C₈₃	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₈₃	C₂³	1	1	yes	characteristic
94	#137×C₈₃	—	4	4	no	—
95	C₂×Q₁₆×C₈₃	C₂³	1	4	yes	complemented
96	C₂×SD₁₆×C₈₃	—	4	8	no	—
97	C₂×SD₁₆×C₈₃	—	4	4	no	—
98	C₂×SD₁₆×C₈₃	C₂³	1	4	yes	—
99	C₂×SD₁₆×C₈₃	C₂³	1	4	yes	—
100	C₂×SD₁₆×C₈₃	C₂³	1	4	yes	—
101	C₂×SD₁₆×C₈₃	C₂³	1	4	yes	—
102	C₂×SD₁₆×C₈₃	C₂³	1	4	yes	complemented
103	C₂×M₁₆×C₈₃	C₂³	1	2	yes	complemented
104	C₂²×C₈×C₈₃	C₂³	1	4	yes	—
105	C₂²×C₈×C₈₃	C₂³	1	2	yes	complemented
106	C₄⋊Q₈×C₈₃	—	2	2	no	—
107	C₄⋊Q₈×C₈₃	—	2	4	no	—
108	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	complemented
109	#127×C₈₃	—	2	1	no	—
110	#127×C₈₃	C₂³	1	2	yes	—
111	#126×C₈₃	—	2	4	no	—
112	#126×C₈₃	—	2	4	no	—
113	#125×C₈₃	—	2	4	no	—
114	#125×C₈₃	—	2	4	no	—
115	#125×C₈₃	C₂³	1	2	yes	complemented
116	#124×C₈₃	—	2	1	no	—
117	#124×C₈₃	—	2	2	no	—
118	#124×C₈₃	C₂³	1	2	yes	—
119	#123×C₈₃	—	2	2	no	—
120	#123×C₈₃	—	2	2	no	—
121	#123×C₈₃	—	2	4	no	—
122	#123×C₈₃	—	2	1	no	—
123	#123×C₈₃	—	2	4	no	—
124	#123×C₈₃	D₄	1	2	yes	—
125	C₂²⋊Q₈×C₈₃	—	2	2	no	—
126	C₂²⋊Q₈×C₈₃	—	2	2	no	—
127	C₂²⋊Q₈×C₈₃	—	2	4	no	—
128	C₂²⋊Q₈×C₈₃	—	2	4	no	—
129	C₂²⋊Q₈×C₈₃	D₄	1	2	yes	—
130	C₂²⋊Q₈×C₈₃	C₂³	1	4	yes	—
131	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
132	C₂²⋊Q₈×C₈₃	C₂³	1	4	yes	—
133	C₂²⋊Q₈×C₈₃	C₂³	1	4	yes	complemented
134	#121×C₈₃	—	2	4	no	—
135	#121×C₈₃	—	2	2	no	—
136	#121×C₈₃	—	2	4	no	—
137	#121×C₈₃	D₄	1	2	yes	—
138	#121×C₈₃	C₂³	1	2	yes	—
139	#121×C₈₃	C₂³	1	4	yes	—
140	#120×C₈₃	—	2	1	no	—
141	#120×C₈₃	—	2	2	no	—
142	#120×C₈₃	—	2	4	no	—
143	#120×C₈₃	—	2	2	no	—
144	#120×C₈₃	—	2	4	no	—
145	#120×C₈₃	—	2	4	no	—
146	#120×C₈₃	D₄	1	2	yes	—
147	C₄×Q₈×C₈₃	C₂³	1	4	yes	complemented
148	C₄×D₄×C₈₃	—	2	4	no	—
149	C₄×D₄×C₈₃	—	2	2	no	—
150	C₄×D₄×C₈₃	—	2	2	no	—
151	C₄×D₄×C₈₃	C₂³	1	4	yes	—
152	C₄×D₄×C₈₃	C₂³	1	4	yes	—
153	#117×C₈₃	—	2	4	no	—
154	#117×C₈₃	C₂³	1	1	yes	characteristic
155	#117×C₈₃	C₂³	1	1	yes	characteristic
156	#117×C₈₃	C₂³	1	2	yes	complemented
157	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
158	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
160	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
161	C₂×C₂²⋊C₄×C₈₃	—	2	4	no	—
162	#107×C₈₃	C₂³	1	4	yes	complemented
163	#106×C₈₃	C₂³	1	4	yes	complemented
164	C₄⋊C₈×C₈₃	C₂³	1	4	yes	complemented
165	#103×C₈₃	C₂³	1	4	yes	complemented
166	#103×C₈₃	C₂³	1	4	yes	complemented
167	#103×C₈₃	C₂³	1	4	yes	complemented
168	#102×C₈₃	C₂³	1	4	yes	—
169	#102×C₈₃	C₂³	1	4	yes	—
170	#102×C₈₃	C₂³	1	4	yes	—
171	#102×C₈₃	C₂³	1	4	yes	—
172	#102×C₈₃	C₂³	1	4	yes	complemented
173	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
174	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
175	C₂²⋊C₈×C₈₃	C₂³	1	4	yes	—
176	C₂²⋊C₈×C₈₃	C₂³	1	4	yes	complemented
177	#97×C₈₃	C₂³	1	2	yes	complemented
178	C₄×C₈×C₈₃	C₂³	1	2	yes	complemented
179	C₂⁴×C₈₃	—	2	1	no	—
180	C₂⁴×C₈₃	—	2	4	no	—
181	C₂⁴×C₈₃	—	2	1	no	—
182	C₂⁴×C₈₃	—	2	2	no	—
183	C₂⁴×C₈₃	—	4	4	no	—
184	C₂⁴×C₈₃	—	8	4	no	—
185	C₂⁴×C₈₃	C₂×D₄	1	1	yes	characteristic
186	#41×C₈₃	—	2	4	no	—
187	#41×C₈₃	—	4	2	no	—
188	#41×C₈₃	—	4	2	no	—
189	#41×C₈₃	—	4	2	no	—
190	#41×C₈₃	—	4	4	no	—
191	C₂×Q₈×C₈₃	—	2	2	no	—
192	C₂×Q₈×C₈₃	—	2	2	no	—
193	C₂×Q₈×C₈₃	—	4	4	no	—
194	C₂×Q₈×C₈₃	—	4	2	no	—
195	C₂×Q₈×C₈₃	—	4	2	no	—
196	C₂×Q₈×C₈₃	C₂×D₄	1	1	yes	characteristic
197	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
198	C₂×Q₈×C₈₃	C₂⁴	1	4	yes	—
199	C₂×D₄×C₈₃	—	2	4	no	—
200	C₂×D₄×C₈₃	—	2	8	no	—
201	C₂×D₄×C₈₃	—	2	4	no	—
202	C₂×D₄×C₈₃	—	2	2	no	—
203	C₂×D₄×C₈₃	—	2	1	no	—
204	C₂×D₄×C₈₃	—	2	2	no	—
205	C₂×D₄×C₈₃	—	2	4	no	—
206	C₂×D₄×C₈₃	—	2	1	no	—
207	C₂×D₄×C₈₃	—	2	2	no	—
208	C₂×D₄×C₈₃	—	2	4	no	—
209	C₂×D₄×C₈₃	—	2	1	no	—
210	C₂×D₄×C₈₃	—	2	4	no	—
211	C₂×D₄×C₈₃	—	4	4	no	—
212	C₂×D₄×C₈₃	—	4	2	no	—
213	C₂×D₄×C₈₃	—	4	2	no	—
214	C₂×D₄×C₈₃	—	4	8	no	—
215	C₂×D₄×C₈₃	—	4	4	no	—
216	C₂×D₄×C₈₃	—	4	4	no	—
217	C₂×D₄×C₈₃	—	4	8	no	—
218	C₂×D₄×C₈₃	—	8	8	no	—
219	C₂×D₄×C₈₃	C₂×D₄	1	4	yes	—
220	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
221	C₂×D₄×C₈₃	C₂×D₄	1	1	yes	characteristic
222	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
223	C₂×D₄×C₈₃	C₂⁴	1	1	yes	characteristic
224	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₈₃	—	2	2	no	—
226	C₂²×C₄×C₈₃	—	2	2	no	—
227	C₂²×C₄×C₈₃	—	2	2	no	—
228	C₂²×C₄×C₈₃	—	2	2	no	—
229	C₂²×C₄×C₈₃	—	2	1	no	—
230	C₂²×C₄×C₈₃	—	2	4	no	—
231	C₂²×C₄×C₈₃	—	4	2	no	—
232	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
233	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
237	Q₁₆×C₈₃	—	4	4	no	—
238	SD₁₆×C₈₃	—	2	8	no	—
239	SD₁₆×C₈₃	—	2	8	no	—
240	SD₁₆×C₈₃	—	4	4	no	—
241	SD₁₆×C₈₃	—	4	4	no	—
242	SD₁₆×C₈₃	—	4	4	no	—
243	M₁₆×C₈₃	—	4	2	no	—
244	C₂×C₈×C₈₃	—	4	4	no	—
245	C₂×C₈×C₈₃	—	4	2	no	—
246	C₂×C₈×C₈₃	C₂⁴	1	4	yes	—
247	C₂×C₈×C₈₃	C₂⁴	1	4	yes	—
248	C₄⋊C₄×C₈₃	—	2	4	no	—
249	C₄⋊C₄×C₈₃	—	2	4	no	—
250	C₄⋊C₄×C₈₃	—	2	2	no	—
251	C₄⋊C₄×C₈₃	—	2	4	no	—
252	C₄⋊C₄×C₈₃	—	2	4	no	—
253	C₄⋊C₄×C₈₃	—	2	2	no	—
254	C₄⋊C₄×C₈₃	—	2	4	no	—
255	C₄⋊C₄×C₈₃	—	2	4	no	—
256	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
257	C₄⋊C₄×C₈₃	C₂×D₄	1	4	yes	—
258	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
259	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
260	C₂²⋊C₄×C₈₃	—	2	1	no	—
261	C₂²⋊C₄×C₈₃	—	2	2	no	—
262	C₂²⋊C₄×C₈₃	—	2	4	no	—
263	C₂²⋊C₄×C₈₃	—	2	4	no	—
264	C₂²⋊C₄×C₈₃	—	2	2	no	—
265	C₂²⋊C₄×C₈₃	—	2	4	no	—
266	C₂²⋊C₄×C₈₃	—	2	4	no	—
267	C₂²⋊C₄×C₈₃	—	2	4	no	—
268	C₂²⋊C₄×C₈₃	—	2	4	no	—
269	C₂²⋊C₄×C₈₃	—	2	2	no	—
270	C₂²⋊C₄×C₈₃	C₂×D₄	1	4	yes	—
271	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
272	C₂²⋊C₄×C₈₃	C₂×D₄	1	4	yes	—
273	C₄²×C₈₃	—	2	2	no	—
274	C₄²×C₈₃	—	2	4	no	—
275	C₄²×C₈₃	—	2	1	no	—
276	C₄²×C₈₃	C₂⁴	1	2	yes	—
277	C₂³×C₈₃	—	2	4	no	—
278	C₂³×C₈₃	—	2	4	no	—
279	C₂³×C₈₃	—	2	2	no	—
280	C₂³×C₈₃	—	2	2	no	—
281	C₂³×C₈₃	—	2	1	no	—
282	C₂³×C₈₃	—	4	1	no	—
283	C₂³×C₈₃	—	4	8	no	—
284	C₂³×C₈₃	—	4	4	no	—
285	C₂³×C₈₃	—	4	2	no	—
286	C₂³×C₈₃	—	4	8	no	—
287	C₂³×C₈₃	—	8	4	no	—
288	C₂³×C₈₃	—	8	2	no	—
289	C₂³×C₈₃	—	8	2	no	—
290	C₂³×C₈₃	—	8	4	no	—
291	C₂³×C₈₃	—	8	16	no	—
292	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
293	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
294	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
295	Q₈×C₈₃	—	2	4	no	—
296	Q₈×C₈₃	—	2	4	no	—
297	Q₈×C₈₃	—	2	2	no	—
298	Q₈×C₈₃	—	4	1	no	—
299	Q₈×C₈₃	—	8	2	no	—
300	Q₈×C₈₃	—	8	2	no	—
301	D₄×C₈₃	—	2	4	no	—
302	D₄×C₈₃	—	2	8	no	—
303	D₄×C₈₃	—	2	2	no	—
304	D₄×C₈₃	—	2	4	no	—
305	D₄×C₈₃	—	2	2	no	—
306	D₄×C₈₃	—	4	1	no	—
307	D₄×C₈₃	—	4	2	no	—
308	D₄×C₈₃	—	4	8	no	—
309	D₄×C₈₃	—	4	4	no	—
310	D₄×C₈₃	—	4	2	no	—
311	D₄×C₈₃	—	4	4	no	—
312	D₄×C₈₃	—	4	2	no	—
313	D₄×C₈₃	—	4	4	no	—
314	D₄×C₈₃	—	8	4	no	—
315	D₄×C₈₃	—	8	4	no	—
316	D₄×C₈₃	H(5,𝔽₂)	1	4	yes	—
317	C₂×C₄×C₈₃	—	2	4	no	—
318	C₂×C₄×C₈₃	—	2	2	no	—
319	C₂×C₄×C₈₃	—	2	2	no	—
320	C₂×C₄×C₈₃	—	2	2	no	—
321	C₂×C₄×C₈₃	—	2	4	no	—
322	C₂×C₄×C₈₃	—	2	2	no	—
323	C₂×C₄×C₈₃	—	2	4	no	—
324	C₂×C₄×C₈₃	—	2	1	no	—
325	C₂×C₄×C₈₃	—	4	2	no	—
326	C₂×C₄×C₈₃	—	4	1	no	—
327	C₂×C₄×C₈₃	—	4	4	no	—
328	C₂×C₄×C₈₃	—	4	2	no	—
329	C₂×C₄×C₈₃	—	4	4	no	—
330	C₂×C₄×C₈₃	—	8	4	no	—
331	C₂×C₄×C₈₃	—	8	2	no	—
332	C₂×C₄×C₈₃	—	8	2	no	—
333	C₂×C₄×C₈₃	C₂²×D₄	1	4	yes	—
334	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
338	C₈×C₈₃	—	2	4	no	—
339	C₈×C₈₃	—	2	4	no	—
340	C₂²×C₈₃	—	2	2	no	—
341	C₂²×C₈₃	—	2	2	no	—
342	C₂²×C₈₃	—	2	1	no	—
343	C₂²×C₈₃	—	2	2	no	—
344	C₂²×C₈₃	—	2	4	no	—
345	C₂²×C₈₃	—	2	4	no	—
346	C₂²×C₈₃	—	2	2	no	—
347	C₂²×C₈₃	—	4	4	no	—
348	C₂²×C₈₃	—	4	4	no	—
349	C₂²×C₈₃	—	4	1	no	—
350	C₂²×C₈₃	—	4	2	no	—
351	C₂²×C₈₃	—	4	2	no	—
352	C₂²×C₈₃	—	4	4	no	—
353	C₂²×C₈₃	—	8	16	no	—
354	C₂²×C₈₃	—	8	4	no	—
355	C₂²×C₈₃	—	8	4	no	—
356	C₂²×C₈₃	—	16	4	no	—
357	C₂²×C₈₃	#577	1	4	yes	—
358	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
359	C₄×C₈₃	—	2	1	no	—
360	C₄×C₈₃	—	2	2	no	—
361	C₄×C₈₃	—	2	2	no	—
362	C₄×C₈₃	—	2	4	no	—
363	C₄×C₈₃	—	4	1	no	—
364	C₄×C₈₃	—	4	4	no	—
365	C₄×C₈₃	—	4	4	no	—
366	C₄×C₈₃	—	4	2	no	—
367	C₄×C₈₃	C₂×H(5,𝔽₂)	1	2	yes	—
368	#61631	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
369	C₂×C₈₃	—	2	4	no	—
370	C₂×C₈₃	—	4	1	no	—
371	C₂×C₈₃	—	4	2	no	—
372	C₂×C₈₃	—	4	4	no	—
373	C₂×C₈₃	—	8	2	no	—
374	C₂×C₈₃	—	8	1	no	—
375	C₂×C₈₃	#3484	1	1	yes	characteristic
376	C₂×C₈₃	C₂×#577	1	2	yes	—
377	#3538	C₂×C₈₃	1	1	yes	characteristic, complemented
378	#3484	C₂×C₈₃	1	1	yes	characteristic
379	#3310	C₂×C₈₃	1	4	yes	complemented
380	#3296	C₂×C₈₃	1	4	yes	complemented
381	D₄×SD₁₆	C₂×C₈₃	1	4	yes	complemented
382	#3266	C₂×C₈₃	1	4	yes	complemented
383	#3222	C₂×C₈₃	1	2	yes	complemented
384	#3200	C₂×C₈₃	1	2	yes	complemented
385	#3190	C₂×C₈₃	1	2	yes	complemented
386	#3123	C₂×C₈₃	1	2	yes	complemented
387	#3009	C₂×C₈₃	1	2	yes	complemented
388	C₂×#450	C₂×C₈₃	1	2	yes	complemented
389	#2977	C₂×C₈₃	1	1	yes	characteristic, complemented
390	C₈₃	#61631	1	1	yes	characteristic, direct product factor, Sylow
391	C₂×H(5,𝔽₂)	C₂²×C₈₃	1	1	yes	characteristic
392	C₂³×D₄	C₂²×C₈₃	1	1	yes	characteristic
393	C₂×#137	C₂²×C₈₃	1	2	yes	complemented
394	C₂²×SD₁₆	C₂²×C₈₃	1	4	yes	complemented
395	C₂²×SD₁₆	C₂²×C₈₃	1	2	yes	complemented
396	#563	—	2	2	no	—
397	#552	C₂²×C₈₃	1	4	yes	complemented
398	#551	—	2	2	no	—
399	D₄×Q₈	C₂²×C₈₃	1	4	yes	complemented
400	#546	—	2	2	no	—
401	#546	C₂²×C₈₃	1	4	yes	—
402	D₄²	—	2	2	no	—
403	D₄²	C₂²×C₈₃	1	4	yes	—
404	#544	—	2	2	no	—
405	#541	C₂²×C₈₃	1	2	yes	complemented
406	#539	—	2	2	no	—
407	#536	C₂²×C₈₃	1	2	yes	complemented
408	#535	C₂²×C₈₃	1	1	yes	characteristic
409	#535	C₂²×C₈₃	1	1	yes	characteristic
410	#534	—	2	2	no	—
411	#525	C₂²×C₈₃	1	1	yes	characteristic
412	#525	C₂²×C₈₃	1	1	yes	characteristic
413	C₂×C₂²⋊Q₈	C₂²×C₈₃	1	2	yes	complemented
414	C₂×#120	—	2	2	no	—
415	#518	C₂²×C₈₃	1	1	yes	characteristic
416	#497	C₂²×C₈₃	1	2	yes	complemented
417	#492	C₂²×C₈₃	1	2	yes	complemented
418	#490	C₂²×C₈₃	1	2	yes	complemented
419	#488	C₂²×C₈₃	1	2	yes	complemented
420	#485	C₂²×C₈₃	1	4	yes	complemented
421	#483	C₂²×C₈₃	1	2	yes	complemented
422	#482	C₂²×C₈₃	1	4	yes	complemented
423	#480	C₂²×C₈₃	1	2	yes	complemented
424	#478	C₂²×C₈₃	1	4	yes	complemented
425	#468	C₂²×C₈₃	1	4	yes	complemented
426	#467	C₂²×C₈₃	1	4	yes	complemented
427	#465	C₂²×C₈₃	1	4	yes	complemented
428	#465	C₂²×C₈₃	1	4	yes	complemented
429	#464	C₂²×C₈₃	1	4	yes	complemented
430	#461	C₂²×C₈₃	1	4	yes	complemented
431	#460	C₂²×C₈₃	1	4	yes	complemented
432	#452	C₂²×C₈₃	1	4	yes	complemented
433	#452	C₂²×C₈₃	1	4	yes	complemented
434	#451	C₂²×C₈₃	1	2	yes	complemented
435	#450	C₂²×C₈₃	1	4	yes	—
436	#450	C₂²×C₈₃	1	4	yes	complemented
437	#450	C₂²×C₈₃	1	4	yes	complemented
438	#450	C₂²×C₈₃	1	4	yes	complemented
439	#450	C₂²×C₈₃	1	4	yes	complemented
440	#448	C₂²×C₈₃	1	2	yes	complemented
441	#448	C₂²×C₈₃	1	4	yes	complemented
442	#440	C₂²×C₈₃	1	4	yes	complemented
443	C₄×SD₁₆	C₂²×C₈₃	1	4	yes	complemented
444	#435	C₂²×C₈₃	1	4	yes	complemented
445	C₈×D₄	C₂²×C₈₃	1	4	yes	complemented
446	#433	C₂²×C₈₃	1	2	yes	complemented
447	#418	C₂²×C₈₃	1	2	yes	complemented
448	#416	C₂²×C₈₃	1	2	yes	complemented
449	C₂×#102	C₂²×C₈₃	1	4	yes	complemented
450	#408	C₂²×C₈₃	1	2	yes	complemented
451	C₂×C₂²⋊C₈	C₂²×C₈₃	1	2	yes	complemented
452	C₂⁵	—	2	1	no	—
453	H(5,𝔽₂)	—	4	4	no	—
454	C₂×#41	—	2	1	no	—
455	C₂×#41	C₂³×C₈₃	1	2	yes	—
456	C₂×#41	C₂³×C₈₃	1	1	yes	characteristic
457	C₂×#41	C₂³×C₈₃	1	1	yes	characteristic
458	C₂²×Q₈	C₂³×C₈₃	1	2	yes	—
459	C₂²×Q₈	C₂³×C₈₃	1	2	yes	complemented
460	C₂²×D₄	—	2	2	no	—
461	C₂²×D₄	—	2	1	no	—
462	C₂²×D₄	—	2	4	no	—
463	C₂²×D₄	—	2	1	no	—
464	C₂²×D₄	—	2	2	no	—
465	C₂²×D₄	—	4	4	no	—
466	C₂²×D₄	C₂³×C₈₃	1	1	yes	characteristic
467	C₂²×D₄	C₂³×C₈₃	1	2	yes	—
468	C₂²×D₄	C₂³×C₈₃	1	4	yes	—
469	C₂²×D₄	C₂³×C₈₃	1	1	yes	characteristic
470	C₂³×C₄	C₂³×C₈₃	1	1	yes	characteristic
471	#137	—	4	4	no	—
472	C₂×Q₁₆	C₂³×C₈₃	1	4	yes	complemented
473	C₂×SD₁₆	—	4	8	no	—
474	C₂×SD₁₆	—	4	4	no	—
475	C₂×SD₁₆	C₂³×C₈₃	1	4	yes	—
476	C₂×SD₁₆	C₂³×C₈₃	1	4	yes	—
477	C₂×SD₁₆	C₂³×C₈₃	1	4	yes	—
478	C₂×SD₁₆	C₂³×C₈₃	1	4	yes	—
479	C₂×SD₁₆	C₂³×C₈₃	1	4	yes	complemented
480	C₂×M₁₆	C₂³×C₈₃	1	2	yes	complemented
481	C₂²×C₈	C₂³×C₈₃	1	4	yes	—
482	C₂²×C₈	C₂³×C₈₃	1	2	yes	complemented
483	C₄⋊Q₈	—	2	2	no	—
484	C₄⋊Q₈	—	2	4	no	—
485	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	complemented
486	#127	—	2	1	no	—
487	#127	C₂³×C₈₃	1	2	yes	—
488	#126	—	2	4	no	—
489	#126	—	2	4	no	—
490	#125	—	2	4	no	—
491	#125	—	2	4	no	—
492	#125	C₂³×C₈₃	1	2	yes	complemented
493	#124	—	2	1	no	—
494	#124	—	2	2	no	—
495	#124	C₂³×C₈₃	1	2	yes	—
496	#123	—	2	2	no	—
497	#123	—	2	2	no	—
498	#123	—	2	4	no	—
499	#123	—	2	1	no	—
500	#123	—	2	4	no	—
501	#123	D₄×C₈₃	1	2	yes	—
502	C₂²⋊Q₈	—	2	2	no	—
503	C₂²⋊Q₈	—	2	2	no	—
504	C₂²⋊Q₈	—	2	4	no	—
505	C₂²⋊Q₈	—	2	4	no	—
506	C₂²⋊Q₈	D₄×C₈₃	1	2	yes	—
507	C₂²⋊Q₈	C₂³×C₈₃	1	4	yes	—
508	C₂²⋊Q₈	C₂³×C₈₃	1	4	yes	—
509	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
510	C₂²⋊Q₈	C₂³×C₈₃	1	4	yes	complemented
511	#121	—	2	4	no	—
512	#121	—	2	2	no	—
513	#121	—	2	4	no	—
514	#121	D₄×C₈₃	1	2	yes	—
515	#121	C₂³×C₈₃	1	2	yes	—
516	#121	C₂³×C₈₃	1	4	yes	—
517	#120	—	2	1	no	—
518	#120	—	2	2	no	—
519	#120	—	2	4	no	—
520	#120	—	2	2	no	—
521	#120	—	2	4	no	—
522	#120	—	2	4	no	—
523	#120	D₄×C₈₃	1	2	yes	—
524	C₄×Q₈	C₂³×C₈₃	1	4	yes	complemented
525	C₄×D₄	—	2	4	no	—
526	C₄×D₄	—	2	2	no	—
527	C₄×D₄	—	2	2	no	—
528	C₄×D₄	C₂³×C₈₃	1	4	yes	—
529	C₄×D₄	C₂³×C₈₃	1	4	yes	—
530	#117	—	2	4	no	—
531	#117	C₂³×C₈₃	1	1	yes	characteristic
532	#117	C₂³×C₈₃	1	1	yes	characteristic
533	#117	C₂³×C₈₃	1	2	yes	complemented
534	C₂×C₄⋊C₄	—	2	2	no	—
535	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
536	C₂×C₂²⋊C₄	—	2	2	no	—
537	C₂×C₂²⋊C₄	—	2	2	no	—
538	C₂×C₂²⋊C₄	—	2	4	no	—
539	#107	C₂³×C₈₃	1	4	yes	complemented
540	#106	C₂³×C₈₃	1	4	yes	complemented
541	C₄⋊C₈	C₂³×C₈₃	1	4	yes	complemented
542	#103	C₂³×C₈₃	1	4	yes	complemented
543	#103	C₂³×C₈₃	1	4	yes	complemented
544	#103	C₂³×C₈₃	1	4	yes	complemented
545	#102	C₂³×C₈₃	1	4	yes	—
546	#102	C₂³×C₈₃	1	4	yes	—
547	#102	C₂³×C₈₃	1	4	yes	—
548	#102	C₂³×C₈₃	1	4	yes	—
549	#102	C₂³×C₈₃	1	4	yes	complemented
550	C₂²⋊C₈	C₂³×C₈₃	1	4	yes	—
551	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
552	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
553	C₂²⋊C₈	C₂³×C₈₃	1	4	yes	complemented
554	#97	C₂³×C₈₃	1	2	yes	complemented
555	C₄×C₈	C₂³×C₈₃	1	2	yes	complemented
556	C₂⁴	—	2	1	no	—
557	C₂⁴	—	2	4	no	—
558	C₂⁴	—	2	1	no	—
559	C₂⁴	—	2	2	no	—
560	C₂⁴	—	4	4	no	—
561	C₂⁴	—	8	4	no	—
562	C₂⁴	C₂×D₄×C₈₃	1	1	yes	characteristic
563	#41	—	2	4	no	—
564	#41	—	4	2	no	—
565	#41	—	4	2	no	—
566	#41	—	4	2	no	—
567	#41	—	4	4	no	—
568	C₂×Q₈	—	2	2	no	—
569	C₂×Q₈	—	2	2	no	—
570	C₂×Q₈	—	4	4	no	—
571	C₂×Q₈	—	4	2	no	—
572	C₂×Q₈	—	4	2	no	—
573	C₂×Q₈	C₂×D₄×C₈₃	1	1	yes	characteristic
574	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
575	C₂×Q₈	C₂⁴×C₈₃	1	4	yes	—
576	C₂×D₄	—	2	4	no	—
577	C₂×D₄	—	2	8	no	—
578	C₂×D₄	—	2	4	no	—
579	C₂×D₄	—	2	2	no	—
580	C₂×D₄	—	2	1	no	—
581	C₂×D₄	—	2	2	no	—
582	C₂×D₄	—	2	4	no	—
583	C₂×D₄	—	2	1	no	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	—	2	1	no	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	4	4	no	—
589	C₂×D₄	—	4	2	no	—
590	C₂×D₄	—	4	2	no	—
591	C₂×D₄	—	4	8	no	—
592	C₂×D₄	—	4	4	no	—
593	C₂×D₄	—	4	4	no	—
594	C₂×D₄	—	4	8	no	—
595	C₂×D₄	—	8	8	no	—
596	C₂×D₄	C₂×D₄×C₈₃	1	4	yes	—
597	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
598	C₂×D₄	C₂×D₄×C₈₃	1	1	yes	characteristic
599	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
600	C₂×D₄	C₂⁴×C₈₃	1	1	yes	characteristic
601	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	4	no	—
608	C₂²×C₄	—	4	2	no	—
609	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
610	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
611	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
612	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
613	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
614	Q₁₆	—	4	4	no	—
615	SD₁₆	—	2	8	no	—
616	SD₁₆	—	2	8	no	—
617	SD₁₆	—	4	4	no	—
618	SD₁₆	—	4	4	no	—
619	SD₁₆	—	4	4	no	—
620	M₁₆	—	4	2	no	—
621	C₂×C₈	—	4	4	no	—
622	C₂×C₈	—	4	2	no	—
623	C₂×C₈	C₂⁴×C₈₃	1	4	yes	—
624	C₂×C₈	C₂⁴×C₈₃	1	4	yes	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	2	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	2	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
634	C₄⋊C₄	C₂×D₄×C₈₃	1	4	yes	—
635	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
636	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
637	C₂²⋊C₄	—	2	1	no	—
638	C₂²⋊C₄	—	2	2	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	—	2	2	no	—
647	C₂²⋊C₄	C₂×D₄×C₈₃	1	4	yes	—
648	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
649	C₂²⋊C₄	C₂×D₄×C₈₃	1	4	yes	—
650	C₄²	—	2	2	no	—
651	C₄²	—	2	4	no	—
652	C₄²	—	2	1	no	—
653	C₄²	C₂⁴×C₈₃	1	2	yes	—
654	C₂³	—	2	4	no	—
655	C₂³	—	2	4	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	1	no	—
659	C₂³	—	4	1	no	—
660	C₂³	—	4	8	no	—
661	C₂³	—	4	4	no	—
662	C₂³	—	4	2	no	—
663	C₂³	—	4	8	no	—
664	C₂³	—	8	4	no	—
665	C₂³	—	8	2	no	—
666	C₂³	—	8	2	no	—
667	C₂³	—	8	4	no	—
668	C₂³	—	8	16	no	—
669	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
670	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
671	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
672	Q₈	—	2	4	no	—
673	Q₈	—	2	4	no	—
674	Q₈	—	2	2	no	—
675	Q₈	—	4	1	no	—
676	Q₈	—	8	2	no	—
677	Q₈	—	8	2	no	—
678	D₄	—	2	4	no	—
679	D₄	—	2	8	no	—
680	D₄	—	2	2	no	—
681	D₄	—	2	4	no	—
682	D₄	—	2	2	no	—
683	D₄	—	4	1	no	—
684	D₄	—	4	2	no	—
685	D₄	—	4	8	no	—
686	D₄	—	4	4	no	—
687	D₄	—	4	2	no	—
688	D₄	—	4	4	no	—
689	D₄	—	4	2	no	—
690	D₄	—	4	4	no	—
691	D₄	—	8	4	no	—
692	D₄	—	8	4	no	—
693	D₄	H(5,𝔽₂)×C₈₃	1	4	yes	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	4	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	4	2	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	4	4	no	—
705	C₂×C₄	—	4	2	no	—
706	C₂×C₄	—	4	4	no	—
707	C₂×C₄	—	8	4	no	—
708	C₂×C₄	—	8	2	no	—
709	C₂×C₄	—	8	2	no	—
710	C₂×C₄	C₂²×D₄×C₈₃	1	4	yes	—
711	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
712	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
713	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
714	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
715	C₈	—	2	4	no	—
716	C₈	—	2	4	no	—
717	C₂²	—	2	2	no	—
718	C₂²	—	2	2	no	—
719	C₂²	—	2	4	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	1	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	4	no	—
724	C₂²	—	4	4	no	—
725	C₂²	—	4	4	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	4	4	no	—
728	C₂²	—	4	1	no	—
729	C₂²	—	4	2	no	—
730	C₂²	—	8	16	no	—
731	C₂²	—	8	4	no	—
732	C₂²	—	8	4	no	—
733	C₂²	—	16	4	no	—
734	C₂²	#577×C₈₃	1	4	yes	—
735	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
736	C₄	—	2	4	no	—
737	C₄	—	2	1	no	—
738	C₄	—	2	2	no	—
739	C₄	—	2	2	no	—
740	C₄	—	4	4	no	—
741	C₄	—	4	2	no	—
742	C₄	—	4	1	no	—
743	C₄	—	4	4	no	—
744	C₄	C₂×H(5,𝔽₂)×C₈₃	1	2	yes	—
745	C₂	—	2	4	no	—
746	C₂	—	4	1	no	—
747	C₂	—	4	2	no	—
748	C₂	—	4	4	no	—
749	C₂	—	8	2	no	—
750	C₂	—	8	1	no	—
751	C₂	C₈₃×#3484	1	1	yes	characteristic
752	C₂	C₂×#577×C₈₃	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₈₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₃
prime radical	C₈₃×#3484	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₃ ◁ #525×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₃×#3538	C₂	semidirect
3. C₈₃×#3310	C₂	semidirect
4. C₈₃×#3296	C₂	semidirect
5. D₄×SD₁₆×C₈₃	C₂	semidirect
6. C₈₃×#3266	C₂	semidirect
7. C₈₃×#3222	C₂	semidirect
8. C₈₃×#3200	C₂	semidirect
9. C₈₃×#3190	C₂	semidirect
10. C₈₃×#3123	C₂	semidirect
11. C₈₃×#3009	C₂	semidirect
12. C₂×#450×C₈₃	C₂	semidirect
13. C₈₃×#2977	C₂	semidirect
16. C₂×#137×C₈₃	C₂²	semidirect
17. C₂²×SD₁₆×C₈₃	C₂²	semidirect
18. C₂²×SD₁₆×C₈₃	C₂²	semidirect
20. #552×C₈₃	C₂²	semidirect
22. D₄×Q₈×C₈₃	C₂²	semidirect
28. #541×C₈₃	C₂²	semidirect
30. #536×C₈₃	C₂²	semidirect
36. C₂×C₂²⋊Q₈×C₈₃	C₂²	semidirect
39. #497×C₈₃	C₂²	semidirect
40. #492×C₈₃	C₂²	semidirect
41. #490×C₈₃	C₂²	semidirect
42. #488×C₈₃	C₂²	semidirect
43. #485×C₈₃	C₂²	semidirect
44. #483×C₈₃	C₂²	semidirect
45. #482×C₈₃	C₂²	semidirect
46. #480×C₈₃	C₂²	semidirect
47. #478×C₈₃	C₂²	semidirect
48. #468×C₈₃	C₂²	semidirect
49. #467×C₈₃	C₂²	semidirect
50. #465×C₈₃	C₂²	semidirect
51. #465×C₈₃	C₂²	semidirect
52. #464×C₈₃	C₂²	semidirect
53. #461×C₈₃	C₂²	semidirect
54. #460×C₈₃	C₂²	semidirect
55. #452×C₈₃	C₂²	semidirect
56. #452×C₈₃	C₂²	semidirect
57. #451×C₈₃	C₂²	semidirect
59. #450×C₈₃	C₂²	semidirect
60. #450×C₈₃	C₂²	semidirect
61. #450×C₈₃	C₂²	semidirect
62. #450×C₈₃	C₂²	semidirect
63. #448×C₈₃	C₂²	semidirect
64. #448×C₈₃	C₂²	semidirect
65. #440×C₈₃	C₂²	semidirect
66. C₄×SD₁₆×C₈₃	C₂²	semidirect
67. #435×C₈₃	C₂²	semidirect
68. C₈×D₄×C₈₃	C₂²	semidirect
69. #433×C₈₃	C₂²	semidirect
70. #418×C₈₃	C₂²	semidirect
71. #416×C₈₃	C₂²	semidirect
72. C₂×#102×C₈₃	C₂²	semidirect
73. #408×C₈₃	C₂²	semidirect
74. C₂×C₂²⋊C₈×C₈₃	C₂²	semidirect
82. C₂²×Q₈×C₈₃	C₂³	semidirect
95. C₂×Q₁₆×C₈₃	C₂³	semidirect
102. C₂×SD₁₆×C₈₃	C₂³	semidirect
103. C₂×M₁₆×C₈₃	C₂³	semidirect
105. C₂²×C₈×C₈₃	C₂³	semidirect
108. C₄⋊Q₈×C₈₃	C₂³	semidirect
115. #125×C₈₃	C₂³	semidirect
133. C₂²⋊Q₈×C₈₃	C₂³	semidirect
147. C₄×Q₈×C₈₃	C₂³	semidirect
156. #117×C₈₃	C₂³	semidirect
162. #107×C₈₃	C₂³	semidirect
163. #106×C₈₃	C₂³	semidirect
164. C₄⋊C₈×C₈₃	C₂³	semidirect
165. #103×C₈₃	C₂³	semidirect
166. #103×C₈₃	C₂³	semidirect
167. #103×C₈₃	C₂³	semidirect
172. #102×C₈₃	C₂³	semidirect
176. C₂²⋊C₈×C₈₃	C₂³	semidirect
177. #97×C₈₃	C₂³	semidirect
178. C₄×C₈×C₈₃	C₂³	semidirect
368. #61631	C₈₃	direct (N × H)
377. #3538	C₂×C₈₃	semidirect
379. #3310	C₂×C₈₃	semidirect
380. #3296	C₂×C₈₃	semidirect
381. D₄×SD₁₆	C₂×C₈₃	semidirect
382. #3266	C₂×C₈₃	semidirect
383. #3222	C₂×C₈₃	semidirect
384. #3200	C₂×C₈₃	semidirect
385. #3190	C₂×C₈₃	semidirect
386. #3123	C₂×C₈₃	semidirect
387. #3009	C₂×C₈₃	semidirect
388. C₂×#450	C₂×C₈₃	semidirect
389. #2977	C₂×C₈₃	semidirect
390. C₈₃	#61631	direct (N × H)
393. C₂×#137	C₂²×C₈₃	semidirect
394. C₂²×SD₁₆	C₂²×C₈₃	semidirect
395. C₂²×SD₁₆	C₂²×C₈₃	semidirect
397. #552	C₂²×C₈₃	semidirect
399. D₄×Q₈	C₂²×C₈₃	semidirect
405. #541	C₂²×C₈₃	semidirect
407. #536	C₂²×C₈₃	semidirect
413. C₂×C₂²⋊Q₈	C₂²×C₈₃	semidirect
416. #497	C₂²×C₈₃	semidirect
417. #492	C₂²×C₈₃	semidirect
418. #490	C₂²×C₈₃	semidirect
419. #488	C₂²×C₈₃	semidirect
420. #485	C₂²×C₈₃	semidirect
421. #483	C₂²×C₈₃	semidirect
422. #482	C₂²×C₈₃	semidirect
423. #480	C₂²×C₈₃	semidirect
424. #478	C₂²×C₈₃	semidirect
425. #468	C₂²×C₈₃	semidirect
426. #467	C₂²×C₈₃	semidirect
427. #465	C₂²×C₈₃	semidirect
428. #465	C₂²×C₈₃	semidirect
429. #464	C₂²×C₈₃	semidirect
430. #461	C₂²×C₈₃	semidirect
431. #460	C₂²×C₈₃	semidirect
432. #452	C₂²×C₈₃	semidirect
433. #452	C₂²×C₈₃	semidirect
434. #451	C₂²×C₈₃	semidirect
436. #450	C₂²×C₈₃	semidirect
437. #450	C₂²×C₈₃	semidirect
438. #450	C₂²×C₈₃	semidirect
439. #450	C₂²×C₈₃	semidirect
440. #448	C₂²×C₈₃	semidirect
441. #448	C₂²×C₈₃	semidirect
442. #440	C₂²×C₈₃	semidirect
443. C₄×SD₁₆	C₂²×C₈₃	semidirect
444. #435	C₂²×C₈₃	semidirect
445. C₈×D₄	C₂²×C₈₃	semidirect
446. #433	C₂²×C₈₃	semidirect
447. #418	C₂²×C₈₃	semidirect
448. #416	C₂²×C₈₃	semidirect
449. C₂×#102	C₂²×C₈₃	semidirect
450. #408	C₂²×C₈₃	semidirect
451. C₂×C₂²⋊C₈	C₂²×C₈₃	semidirect
459. C₂²×Q₈	C₂³×C₈₃	semidirect
472. C₂×Q₁₆	C₂³×C₈₃	semidirect
479. C₂×SD₁₆	C₂³×C₈₃	semidirect
480. C₂×M₁₆	C₂³×C₈₃	semidirect
482. C₂²×C₈	C₂³×C₈₃	semidirect
485. C₄⋊Q₈	C₂³×C₈₃	semidirect
492. #125	C₂³×C₈₃	semidirect
510. C₂²⋊Q₈	C₂³×C₈₃	semidirect
524. C₄×Q₈	C₂³×C₈₃	semidirect
533. #117	C₂³×C₈₃	semidirect
539. #107	C₂³×C₈₃	semidirect
540. #106	C₂³×C₈₃	semidirect
541. C₄⋊C₈	C₂³×C₈₃	semidirect
542. #103	C₂³×C₈₃	semidirect
543. #103	C₂³×C₈₃	semidirect
544. #103	C₂³×C₈₃	semidirect
549. #102	C₂³×C₈₃	semidirect
553. C₂²⋊C₈	C₂³×C₈₃	semidirect
554. #97	C₂³×C₈₃	semidirect
555. C₄×C₈	C₂³×C₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₈₃×#3538	2
C₈₃×#3484	2
C₈₃×#3310	2
C₈₃×#3296	2
D₄×SD₁₆×C₈₃	2
C₈₃×#3266	2
C₈₃×#3222	2
C₈₃×#3200	2
C₈₃×#3190	2
C₈₃×#3123	2
C₈₃×#3009	2
C₂×#450×C₈₃	2
C₈₃×#2977	2
#61631	83

Subgroups — C83×#61631 #35289455

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#61631 #35289455