Subgroups — C₈₃×#61110 #35288934

Order 21248.

2684 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3585	C₂	1	4	yes	maximal, complemented
2	C₈₃×#3292	C₂	1	4	yes	maximal, complemented
3	C₈₃×#3291	C₂	1	4	yes	maximal, complemented
4	C₈₃×#3288	C₂	1	8	yes	maximal, complemented
5	C₈₃×#3151	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₃×#3068	C₂	1	4	yes	maximal, complemented
7	C₈₃×#3018	C₂	1	2	yes	maximal, complemented
8	C₂×#453×C₈₃	C₂	1	2	yes	maximal, complemented
9	C₈₃×#2956	C₂	1	2	yes	maximal, complemented
10	#585×C₈₃	C₂²	1	2	yes	complemented
11	C₂×H(5,𝔽₂)×C₈₃	C₂²	1	2	yes	complemented
12	#577×C₈₃	—	2	8	no	—
13	#577×C₈₃	C₂²	1	16	yes	complemented
14	#576×C₈₃	—	2	8	no	—
15	#576×C₈₃	C₂²	1	16	yes	complemented
16	#575×C₈₃	—	2	8	no	—
17	#575×C₈₃	C₂²	1	2	yes	—
18	#575×C₈₃	C₂²	1	4	yes	complemented
19	C₂×AGL(1,ℤ/8)×C₈₃	—	2	8	no	—
20	C₂×AGL(1,ℤ/8)×C₈₃	C₂²	1	4	yes	complemented
21	C₂×AGL(1,ℤ/8)×C₈₃	C₂²	1	4	yes	complemented
22	#568×C₈₃	C₂²	1	4	yes	complemented
23	#532×C₈₃	C₂²	1	1	yes	characteristic, complemented
24	C₂×#127×C₈₃	C₂²	1	1	yes	characteristic, complemented
25	#496×C₈₃	C₂²	1	4	yes	complemented
26	#493×C₈₃	C₂²	1	2	yes	complemented
27	#492×C₈₃	C₂²	1	2	yes	complemented
28	#472×C₈₃	C₂²	1	16	yes	complemented
29	#471×C₈₃	C₂²	1	16	yes	complemented
30	#456×C₈₃	C₂²	1	4	yes	complemented
31	#455×C₈₃	C₂²	1	4	yes	complemented
32	#454×C₈₃	C₂²	1	4	yes	complemented
33	#453×C₈₃	C₂²	1	8	yes	complemented
34	#453×C₈₃	C₂²	1	8	yes	complemented
35	#453×C₈₃	C₂²	1	4	yes	complemented
36	#444×C₈₃	C₂²	1	8	yes	complemented
37	#443×C₈₃	C₂²	1	8	yes	complemented
38	#430×C₈₃	C₂²	1	2	yes	complemented
39	C₂×#104×C₈₃	C₂²	1	4	yes	complemented
40	#413×C₈₃	C₂²	1	2	yes	complemented
41	C₂×#100×C₈₃	C₂²	1	2	yes	complemented
42	C₄×M₁₆×C₈₃	C₂²	1	1	yes	characteristic, complemented
43	2₋¹⁺⁴×C₈₃	—	2	4	no	—
44	2₋¹⁺⁴×C₈₃	C₂³	1	4	yes	—
45	H(5,𝔽₂)×C₈₃	—	2	8	no	—
46	H(5,𝔽₂)×C₈₃	—	2	4	no	—
47	H(5,𝔽₂)×C₈₃	—	4	2	no	—
48	H(5,𝔽₂)×C₈₃	—	4	2	no	—
49	H(5,𝔽₂)×C₈₃	C₂³	1	4	yes	—
50	H(5,𝔽₂)×C₈₃	C₂³	1	8	yes	complemented
51	C₂×#41×C₈₃	—	2	8	no	—
52	C₂×#41×C₈₃	—	2	4	no	—
53	C₂×#41×C₈₃	—	4	2	no	—
54	C₂×#41×C₈₃	C₂³	1	4	yes	—
55	C₂×#41×C₈₃	C₂³	1	2	yes	—
56	C₂²×D₄×C₈₃	—	2	4	no	—
57	C₂²×D₄×C₈₃	—	4	1	no	—
58	C₂²×D₄×C₈₃	—	4	2	no	—
59	C₂²×D₄×C₈₃	C₂³	1	2	yes	—
60	#137×C₈₃	—	2	4	no	—
61	#137×C₈₃	—	2	16	no	—
62	#137×C₈₃	D₄	1	8	yes	complemented
63	#137×C₈₃	C₂³	1	8	yes	complemented
64	AGL(1,ℤ/8)×C₈₃	—	2	8	no	—
65	AGL(1,ℤ/8)×C₈₃	—	2	4	no	—
66	AGL(1,ℤ/8)×C₈₃	—	2	16	no	—
67	AGL(1,ℤ/8)×C₈₃	—	2	16	no	—
68	AGL(1,ℤ/8)×C₈₃	—	2	16	no	—
69	AGL(1,ℤ/8)×C₈₃	—	2	8	no	—
70	AGL(1,ℤ/8)×C₈₃	—	2	8	no	—
71	AGL(1,ℤ/8)×C₈₃	D₄	1	8	yes	complemented
72	AGL(1,ℤ/8)×C₈₃	C₂³	1	16	yes	—
73	AGL(1,ℤ/8)×C₈₃	C₂³	1	8	yes	complemented
74	#135×C₈₃	—	2	8	no	—
75	#135×C₈₃	—	2	16	no	—
76	#135×C₈₃	—	2	16	no	—
77	#135×C₈₃	C₂³	1	8	yes	—
78	C₂×SD₁₆×C₈₃	—	2	4	no	—
79	C₂×SD₁₆×C₈₃	—	2	16	no	—
80	C₂×SD₁₆×C₈₃	C₂³	1	8	yes	complemented
81	C₂×D₈×C₈₃	—	2	4	no	—
82	C₂×D₈×C₈₃	—	2	16	no	—
83	C₂×D₈×C₈₃	C₂³	1	8	yes	complemented
84	#131×C₈₃	—	2	8	no	—
85	#131×C₈₃	C₂³	1	16	yes	complemented
86	C₂×M₁₆×C₈₃	—	2	8	no	—
87	C₂×M₁₆×C₈₃	C₂³	1	4	yes	—
88	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
89	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic, complemented
90	#127×C₈₃	—	4	1	no	—
91	#127×C₈₃	C₂³	1	2	yes	—
92	#127×C₈₃	C₂³	1	2	yes	—
93	#127×C₈₃	C₂³	1	1	yes	characteristic, complemented
94	#124×C₈₃	C₂³	1	2	yes	complemented
95	#121×C₈₃	—	4	1	no	—
96	C₄×D₄×C₈₃	—	4	1	no	—
97	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
98	#108×C₈₃	C₂³	1	8	yes	complemented
99	#104×C₈₃	C₂³	1	8	yes	complemented
100	#104×C₈₃	C₂³	1	8	yes	complemented
101	#101×C₈₃	C₂³	1	4	yes	complemented
102	#100×C₈₃	C₂³	1	8	yes	complemented
103	#100×C₈₃	C₂³	1	4	yes	complemented
104	#97×C₈₃	C₂³	1	2	yes	complemented
105	C₄×C₈×C₈₃	C₂³	1	2	yes	complemented
106	C₂⁴×C₈₃	—	2	2	no	—
107	C₂⁴×C₈₃	—	4	2	no	—
108	#41×C₈₃	—	2	4	no	—
109	#41×C₈₃	—	2	4	no	—
110	#41×C₈₃	—	2	8	no	—
111	#41×C₈₃	—	2	16	no	—
112	#41×C₈₃	—	2	8	no	—
113	#41×C₈₃	—	2	4	no	—
114	#41×C₈₃	—	2	4	no	—
115	#41×C₈₃	—	4	4	no	—
116	#41×C₈₃	—	4	4	no	—
117	#41×C₈₃	—	4	8	no	—
118	#41×C₈₃	—	4	8	no	—
119	#41×C₈₃	—	4	4	no	—
120	#41×C₈₃	C₂×D₄	1	8	yes	—
121	#41×C₈₃	C₂⁴	1	8	yes	—
122	C₂×Q₈×C₈₃	—	2	8	no	—
123	C₂×Q₈×C₈₃	—	4	2	no	—
124	C₂×Q₈×C₈₃	C₂×D₄	1	4	yes	—
125	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
126	C₂×D₄×C₈₃	—	2	4	no	—
127	C₂×D₄×C₈₃	—	2	8	no	—
128	C₂×D₄×C₈₃	—	2	16	no	—
129	C₂×D₄×C₈₃	—	2	2	no	—
130	C₂×D₄×C₈₃	—	2	4	no	—
131	C₂×D₄×C₈₃	—	2	4	no	—
132	C₂×D₄×C₈₃	—	2	2	no	—
133	C₂×D₄×C₈₃	—	4	8	no	—
134	C₂×D₄×C₈₃	—	4	4	no	—
135	C₂×D₄×C₈₃	—	4	1	no	—
136	C₂×D₄×C₈₃	—	4	2	no	—
137	C₂×D₄×C₈₃	—	4	2	no	—
138	C₂×D₄×C₈₃	—	4	8	no	—
139	C₂×D₄×C₈₃	—	4	4	no	—
140	C₂×D₄×C₈₃	—	4	8	no	—
141	C₂×D₄×C₈₃	—	4	2	no	—
142	C₂×D₄×C₈₃	—	4	8	no	—
143	C₂×D₄×C₈₃	—	8	4	no	—
144	C₂×D₄×C₈₃	C₂×D₄	1	4	yes	—
145	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
146	C₂×D₄×C₈₃	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₈₃	—	2	4	no	—
148	C₂²×C₄×C₈₃	—	2	1	no	—
149	C₂²×C₄×C₈₃	—	2	2	no	—
150	C₂²×C₄×C₈₃	—	4	2	no	—
151	C₂²×C₄×C₈₃	—	4	4	no	—
152	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
153	Q₁₆×C₈₃	—	2	8	no	—
154	Q₁₆×C₈₃	C₂×D₄	1	8	yes	complemented
155	SD₁₆×C₈₃	—	2	16	no	—
156	SD₁₆×C₈₃	—	2	8	no	—
157	SD₁₆×C₈₃	—	2	8	no	—
158	SD₁₆×C₈₃	—	2	16	no	—
159	SD₁₆×C₈₃	C₂×D₄	1	16	yes	complemented
160	D₈×C₈₃	—	2	16	no	—
161	D₈×C₈₃	—	2	8	no	—
162	D₈×C₈₃	—	2	16	no	—
163	D₈×C₈₃	C₂×D₄	1	8	yes	complemented
164	M₁₆×C₈₃	—	2	4	no	—
165	M₁₆×C₈₃	—	2	16	no	—
166	M₁₆×C₈₃	C₂×D₄	1	8	yes	—
167	M₁₆×C₈₃	C₂⁴	1	8	yes	—
168	C₂×C₈×C₈₃	—	2	4	no	—
169	C₂×C₈×C₈₃	—	2	16	no	—
170	C₂×C₈×C₈₃	C₂⁴	1	4	yes	—
171	C₄⋊C₄×C₈₃	—	4	1	no	—
172	C₂²⋊C₄×C₈₃	—	4	2	no	—
173	C₄²×C₈₃	—	2	1	no	—
174	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
175	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
176	C₂³×C₈₃	—	2	4	no	—
177	C₂³×C₈₃	—	2	2	no	—
178	C₂³×C₈₃	—	2	4	no	—
179	C₂³×C₈₃	—	4	4	no	—
180	C₂³×C₈₃	—	4	8	no	—
181	C₂³×C₈₃	—	4	2	no	—
182	C₂³×C₈₃	—	4	2	no	—
183	C₂³×C₈₃	—	8	4	no	—
184	C₂³×C₈₃	—	16	4	no	—
185	C₂³×C₈₃	H(5,𝔽₂)	1	1	yes	characteristic
186	Q₈×C₈₃	—	2	4	no	—
187	Q₈×C₈₃	—	2	4	no	—
188	Q₈×C₈₃	—	4	4	no	—
189	Q₈×C₈₃	C₂²×D₄	1	8	yes	—
190	D₄×C₈₃	—	2	8	no	—
191	D₄×C₈₃	—	2	8	no	—
192	D₄×C₈₃	—	2	4	no	—
193	D₄×C₈₃	—	2	4	no	—
194	D₄×C₈₃	—	2	8	no	—
195	D₄×C₈₃	—	4	16	no	—
196	D₄×C₈₃	—	4	8	no	—
197	D₄×C₈₃	—	4	4	no	—
198	D₄×C₈₃	—	4	4	no	—
199	D₄×C₈₃	—	4	4	no	—
200	D₄×C₈₃	—	8	2	no	—
201	D₄×C₈₃	—	8	4	no	—
202	D₄×C₈₃	—	8	4	no	—
203	D₄×C₈₃	C₂²×D₄	1	8	yes	—
204	C₂×C₄×C₈₃	—	2	4	no	—
205	C₂×C₄×C₈₃	—	2	1	no	—
206	C₂×C₄×C₈₃	—	2	8	no	—
207	C₂×C₄×C₈₃	—	2	8	no	—
208	C₂×C₄×C₈₃	—	2	1	no	—
209	C₂×C₄×C₈₃	—	2	2	no	—
210	C₂×C₄×C₈₃	—	4	8	no	—
211	C₂×C₄×C₈₃	—	4	4	no	—
212	C₂×C₄×C₈₃	—	4	8	no	—
213	C₂×C₄×C₈₃	—	4	2	no	—
214	C₂×C₄×C₈₃	—	4	2	no	—
215	C₂×C₄×C₈₃	—	4	2	no	—
216	C₂×C₄×C₈₃	C₂²×D₄	1	4	yes	—
217	C₂×C₄×C₈₃	H(5,𝔽₂)	1	1	yes	characteristic
218	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
219	C₈×C₈₃	—	2	8	no	—
220	C₈×C₈₃	C₂²×D₄	1	8	yes	—
221	C₂²×C₈₃	—	2	8	no	—
222	C₂²×C₈₃	—	4	1	no	—
223	C₂²×C₈₃	—	4	2	no	—
224	C₂²×C₈₃	—	4	4	no	—
225	C₂²×C₈₃	—	8	4	no	—
226	C₂²×C₈₃	—	8	4	no	—
227	C₂²×C₈₃	—	8	2	no	—
228	C₂²×C₈₃	—	8	4	no	—
229	C₂²×C₈₃	—	16	2	no	—
230	C₂²×C₈₃	—	16	4	no	—
231	C₂²×C₈₃	—	16	8	no	—
232	C₂²×C₈₃	D₄²	1	2	yes	—
233	C₂²×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
234	C₄×C₈₃	—	2	2	no	—
235	C₄×C₈₃	—	2	8	no	—
236	C₄×C₈₃	—	4	1	no	—
237	C₄×C₈₃	—	4	2	no	—
238	C₄×C₈₃	D₄²	1	2	yes	—
239	C₄×C₈₃	C₂³×D₄	1	2	yes	—
240	#61110	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
241	C₂×C₈₃	—	2	1	no	—
242	C₂×C₈₃	—	2	2	no	—
243	C₂×C₈₃	—	4	8	no	—
244	C₂×C₈₃	—	8	4	no	—
245	C₂×C₈₃	—	8	2	no	—
246	C₂×C₈₃	C₂×D₄²	1	1	yes	characteristic
247	#3585	C₂×C₈₃	1	4	yes	complemented
248	#3292	C₂×C₈₃	1	4	yes	complemented
249	#3291	C₂×C₈₃	1	4	yes	complemented
250	#3288	C₂×C₈₃	1	8	yes	complemented
251	#3151	C₂×C₈₃	1	1	yes	characteristic, complemented
252	#3068	C₂×C₈₃	1	4	yes	complemented
253	#3018	C₂×C₈₃	1	2	yes	complemented
254	C₂×#453	C₂×C₈₃	1	2	yes	complemented
255	#2956	C₂×C₈₃	1	2	yes	complemented
256	C₈₃	#61110	1	1	yes	characteristic, direct product factor, Sylow
257	#585	C₂²×C₈₃	1	2	yes	complemented
258	C₂×H(5,𝔽₂)	C₂²×C₈₃	1	2	yes	complemented
259	#577	—	2	8	no	—
260	#577	C₂²×C₈₃	1	16	yes	complemented
261	#576	—	2	8	no	—
262	#576	C₂²×C₈₃	1	16	yes	complemented
263	#575	—	2	8	no	—
264	#575	C₂²×C₈₃	1	2	yes	—
265	#575	C₂²×C₈₃	1	4	yes	complemented
266	C₂×AGL(1,ℤ/8)	—	2	8	no	—
267	C₂×AGL(1,ℤ/8)	C₂²×C₈₃	1	4	yes	complemented
268	C₂×AGL(1,ℤ/8)	C₂²×C₈₃	1	4	yes	complemented
269	#568	C₂²×C₈₃	1	4	yes	complemented
270	#532	C₂²×C₈₃	1	1	yes	characteristic, complemented
271	C₂×#127	C₂²×C₈₃	1	1	yes	characteristic, complemented
272	#496	C₂²×C₈₃	1	4	yes	complemented
273	#493	C₂²×C₈₃	1	2	yes	complemented
274	#492	C₂²×C₈₃	1	2	yes	complemented
275	#472	C₂²×C₈₃	1	16	yes	complemented
276	#471	C₂²×C₈₃	1	16	yes	complemented
277	#456	C₂²×C₈₃	1	4	yes	complemented
278	#455	C₂²×C₈₃	1	4	yes	complemented
279	#454	C₂²×C₈₃	1	4	yes	complemented
280	#453	C₂²×C₈₃	1	8	yes	complemented
281	#453	C₂²×C₈₃	1	8	yes	complemented
282	#453	C₂²×C₈₃	1	4	yes	complemented
283	#444	C₂²×C₈₃	1	8	yes	complemented
284	#443	C₂²×C₈₃	1	8	yes	complemented
285	#430	C₂²×C₈₃	1	2	yes	complemented
286	C₂×#104	C₂²×C₈₃	1	4	yes	complemented
287	#413	C₂²×C₈₃	1	2	yes	complemented
288	C₂×#100	C₂²×C₈₃	1	2	yes	complemented
289	C₄×M₁₆	C₂²×C₈₃	1	1	yes	characteristic, complemented
290	2₋¹⁺⁴	—	2	4	no	—
291	2₋¹⁺⁴	C₂³×C₈₃	1	4	yes	—
292	H(5,𝔽₂)	—	2	8	no	—
293	H(5,𝔽₂)	—	2	4	no	—
294	H(5,𝔽₂)	—	4	2	no	—
295	H(5,𝔽₂)	—	4	2	no	—
296	H(5,𝔽₂)	C₂³×C₈₃	1	4	yes	—
297	H(5,𝔽₂)	C₂³×C₈₃	1	8	yes	complemented
298	C₂×#41	—	2	8	no	—
299	C₂×#41	—	2	4	no	—
300	C₂×#41	—	4	2	no	—
301	C₂×#41	C₂³×C₈₃	1	4	yes	—
302	C₂×#41	C₂³×C₈₃	1	2	yes	—
303	C₂²×D₄	—	2	4	no	—
304	C₂²×D₄	—	4	1	no	—
305	C₂²×D₄	—	4	2	no	—
306	C₂²×D₄	C₂³×C₈₃	1	2	yes	—
307	#137	—	2	4	no	—
308	#137	—	2	16	no	—
309	#137	D₄×C₈₃	1	8	yes	complemented
310	#137	C₂³×C₈₃	1	8	yes	complemented
311	AGL(1,ℤ/8)	—	2	8	no	—
312	AGL(1,ℤ/8)	—	2	4	no	—
313	AGL(1,ℤ/8)	—	2	16	no	—
314	AGL(1,ℤ/8)	—	2	16	no	—
315	AGL(1,ℤ/8)	—	2	16	no	—
316	AGL(1,ℤ/8)	—	2	8	no	—
317	AGL(1,ℤ/8)	—	2	8	no	—
318	AGL(1,ℤ/8)	D₄×C₈₃	1	8	yes	complemented
319	AGL(1,ℤ/8)	C₂³×C₈₃	1	16	yes	—
320	AGL(1,ℤ/8)	C₂³×C₈₃	1	8	yes	complemented
321	#135	—	2	8	no	—
322	#135	—	2	16	no	—
323	#135	—	2	16	no	—
324	#135	C₂³×C₈₃	1	8	yes	—
325	C₂×SD₁₆	—	2	4	no	—
326	C₂×SD₁₆	—	2	16	no	—
327	C₂×SD₁₆	C₂³×C₈₃	1	8	yes	complemented
328	C₂×D₈	—	2	4	no	—
329	C₂×D₈	—	2	16	no	—
330	C₂×D₈	C₂³×C₈₃	1	8	yes	complemented
331	#131	—	2	8	no	—
332	#131	C₂³×C₈₃	1	16	yes	complemented
333	C₂×M₁₆	—	2	8	no	—
334	C₂×M₁₆	C₂³×C₈₃	1	4	yes	—
335	C₂×M₁₆	C₂³×C₈₃	1	2	yes	—
336	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic, complemented
337	#127	—	4	1	no	—
338	#127	C₂³×C₈₃	1	2	yes	—
339	#127	C₂³×C₈₃	1	2	yes	—
340	#127	C₂³×C₈₃	1	1	yes	characteristic, complemented
341	#124	C₂³×C₈₃	1	2	yes	complemented
342	#121	—	4	1	no	—
343	C₄×D₄	—	4	1	no	—
344	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
345	#108	C₂³×C₈₃	1	8	yes	complemented
346	#104	C₂³×C₈₃	1	8	yes	complemented
347	#104	C₂³×C₈₃	1	8	yes	complemented
348	#101	C₂³×C₈₃	1	4	yes	complemented
349	#100	C₂³×C₈₃	1	8	yes	complemented
350	#100	C₂³×C₈₃	1	4	yes	complemented
351	#97	C₂³×C₈₃	1	2	yes	complemented
352	C₄×C₈	C₂³×C₈₃	1	2	yes	complemented
353	C₂⁴	—	2	2	no	—
354	C₂⁴	—	4	2	no	—
355	#41	—	2	4	no	—
356	#41	—	2	4	no	—
357	#41	—	2	8	no	—
358	#41	—	2	16	no	—
359	#41	—	2	8	no	—
360	#41	—	2	4	no	—
361	#41	—	2	4	no	—
362	#41	—	4	4	no	—
363	#41	—	4	4	no	—
364	#41	—	4	8	no	—
365	#41	—	4	8	no	—
366	#41	—	4	4	no	—
367	#41	C₂×D₄×C₈₃	1	8	yes	—
368	#41	C₂⁴×C₈₃	1	8	yes	—
369	C₂×Q₈	—	2	8	no	—
370	C₂×Q₈	—	4	2	no	—
371	C₂×Q₈	C₂×D₄×C₈₃	1	4	yes	—
372	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
373	C₂×D₄	—	2	4	no	—
374	C₂×D₄	—	2	8	no	—
375	C₂×D₄	—	2	16	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	—	2	4	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	4	8	no	—
381	C₂×D₄	—	4	4	no	—
382	C₂×D₄	—	4	1	no	—
383	C₂×D₄	—	4	2	no	—
384	C₂×D₄	—	4	2	no	—
385	C₂×D₄	—	4	8	no	—
386	C₂×D₄	—	4	4	no	—
387	C₂×D₄	—	4	8	no	—
388	C₂×D₄	—	4	2	no	—
389	C₂×D₄	—	4	8	no	—
390	C₂×D₄	—	8	4	no	—
391	C₂×D₄	C₂×D₄×C₈₃	1	4	yes	—
392	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
393	C₂×D₄	C₂⁴×C₈₃	1	4	yes	—
394	C₂²×C₄	—	2	4	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	4	2	no	—
398	C₂²×C₄	—	4	4	no	—
399	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
400	Q₁₆	—	2	8	no	—
401	Q₁₆	C₂×D₄×C₈₃	1	8	yes	complemented
402	SD₁₆	—	2	16	no	—
403	SD₁₆	—	2	8	no	—
404	SD₁₆	—	2	8	no	—
405	SD₁₆	—	2	16	no	—
406	SD₁₆	C₂×D₄×C₈₃	1	16	yes	complemented
407	D₈	—	2	16	no	—
408	D₈	—	2	8	no	—
409	D₈	—	2	16	no	—
410	D₈	C₂×D₄×C₈₃	1	8	yes	complemented
411	M₁₆	—	2	4	no	—
412	M₁₆	—	2	16	no	—
413	M₁₆	C₂×D₄×C₈₃	1	8	yes	—
414	M₁₆	C₂⁴×C₈₃	1	8	yes	—
415	C₂×C₈	—	2	4	no	—
416	C₂×C₈	—	2	16	no	—
417	C₂×C₈	C₂⁴×C₈₃	1	4	yes	—
418	C₄⋊C₄	—	4	1	no	—
419	C₂²⋊C₄	—	4	2	no	—
420	C₄²	—	2	1	no	—
421	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
422	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
423	C₂³	—	2	4	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	2	4	no	—
426	C₂³	—	4	4	no	—
427	C₂³	—	4	8	no	—
428	C₂³	—	4	2	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	8	4	no	—
431	C₂³	—	16	4	no	—
432	C₂³	H(5,𝔽₂)×C₈₃	1	1	yes	characteristic
433	Q₈	—	2	4	no	—
434	Q₈	—	2	4	no	—
435	Q₈	—	4	4	no	—
436	Q₈	C₂²×D₄×C₈₃	1	8	yes	—
437	D₄	—	2	8	no	—
438	D₄	—	2	8	no	—
439	D₄	—	2	4	no	—
440	D₄	—	2	4	no	—
441	D₄	—	2	8	no	—
442	D₄	—	4	16	no	—
443	D₄	—	4	8	no	—
444	D₄	—	4	4	no	—
445	D₄	—	4	4	no	—
446	D₄	—	4	4	no	—
447	D₄	—	8	4	no	—
448	D₄	—	8	2	no	—
449	D₄	—	8	4	no	—
450	D₄	C₂²×D₄×C₈₃	1	8	yes	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	8	no	—
454	C₂×C₄	—	2	8	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	4	8	no	—
458	C₂×C₄	—	4	4	no	—
459	C₂×C₄	—	4	8	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	C₂²×D₄×C₈₃	1	4	yes	—
464	C₂×C₄	H(5,𝔽₂)×C₈₃	1	1	yes	characteristic
465	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
466	C₈	—	2	8	no	—
467	C₈	C₂²×D₄×C₈₃	1	8	yes	—
468	C₂²	—	2	8	no	—
469	C₂²	—	4	1	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	4	no	—
472	C₂²	—	8	4	no	—
473	C₂²	—	8	4	no	—
474	C₂²	—	8	2	no	—
475	C₂²	—	8	4	no	—
476	C₂²	—	16	2	no	—
477	C₂²	—	16	8	no	—
478	C₂²	—	16	4	no	—
479	C₂²	D₄²×C₈₃	1	2	yes	—
480	C₂²	C₂×H(5,𝔽₂)×C₈₃	1	1	yes	characteristic
481	C₄	—	2	2	no	—
482	C₄	—	2	8	no	—
483	C₄	—	4	1	no	—
484	C₄	—	4	2	no	—
485	C₄	D₄²×C₈₃	1	2	yes	—
486	C₄	C₂³×D₄×C₈₃	1	2	yes	—
487	C₂	—	2	1	no	—
488	C₂	—	2	2	no	—
489	C₂	—	4	8	no	—
490	C₂	—	8	4	no	—
491	C₂	—	8	2	no	—
492	C₂	C₂×D₄²×C₈₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₈₃	C₂×D₄²
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈₃ ◁ C₂²×C₄×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₃×#3585	C₂	semidirect
2. C₈₃×#3292	C₂	semidirect
3. C₈₃×#3291	C₂	semidirect
4. C₈₃×#3288	C₂	semidirect
5. C₈₃×#3151	C₂	semidirect
6. C₈₃×#3068	C₂	semidirect
7. C₈₃×#3018	C₂	semidirect
8. C₂×#453×C₈₃	C₂	semidirect
9. C₈₃×#2956	C₂	semidirect
10. #585×C₈₃	C₂²	semidirect
11. C₂×H(5,𝔽₂)×C₈₃	C₂²	semidirect
13. #577×C₈₃	C₂²	semidirect
15. #576×C₈₃	C₂²	semidirect
18. #575×C₈₃	C₂²	semidirect
20. C₂×AGL(1,ℤ/8)×C₈₃	C₂²	semidirect
21. C₂×AGL(1,ℤ/8)×C₈₃	C₂²	semidirect
22. #568×C₈₃	C₂²	semidirect
23. #532×C₈₃	C₂²	semidirect
24. C₂×#127×C₈₃	C₂²	semidirect
25. #496×C₈₃	C₂²	semidirect
26. #493×C₈₃	C₂²	semidirect
27. #492×C₈₃	C₂²	semidirect
28. #472×C₈₃	C₂²	semidirect
29. #471×C₈₃	C₂²	semidirect
30. #456×C₈₃	C₂²	semidirect
31. #455×C₈₃	C₂²	semidirect
32. #454×C₈₃	C₂²	semidirect
33. #453×C₈₃	C₂²	semidirect
34. #453×C₈₃	C₂²	semidirect
35. #453×C₈₃	C₂²	semidirect
36. #444×C₈₃	C₂²	semidirect
37. #443×C₈₃	C₂²	semidirect
38. #430×C₈₃	C₂²	semidirect
39. C₂×#104×C₈₃	C₂²	semidirect
40. #413×C₈₃	C₂²	semidirect
41. C₂×#100×C₈₃	C₂²	semidirect
42. C₄×M₁₆×C₈₃	C₂²	semidirect
50. H(5,𝔽₂)×C₈₃	C₂³	semidirect
62. #137×C₈₃	D₄	semidirect
63. #137×C₈₃	C₂³	semidirect
71. AGL(1,ℤ/8)×C₈₃	D₄	semidirect
73. AGL(1,ℤ/8)×C₈₃	C₂³	semidirect
80. C₂×SD₁₆×C₈₃	C₂³	semidirect
83. C₂×D₈×C₈₃	C₂³	semidirect
85. #131×C₈₃	C₂³	semidirect
89. C₄⋊Q₈×C₈₃	C₂³	semidirect
93. #127×C₈₃	C₂³	semidirect
94. #124×C₈₃	C₂³	semidirect
98. #108×C₈₃	C₂³	semidirect
99. #104×C₈₃	C₂³	semidirect
100. #104×C₈₃	C₂³	semidirect
101. #101×C₈₃	C₂³	semidirect
102. #100×C₈₃	C₂³	semidirect
103. #100×C₈₃	C₂³	semidirect
104. #97×C₈₃	C₂³	semidirect
105. C₄×C₈×C₈₃	C₂³	semidirect
154. Q₁₆×C₈₃	C₂×D₄	semidirect
159. SD₁₆×C₈₃	C₂×D₄	semidirect
163. D₈×C₈₃	C₂×D₄	semidirect
240. #61110	C₈₃	direct (N × H)
247. #3585	C₂×C₈₃	semidirect
248. #3292	C₂×C₈₃	semidirect
249. #3291	C₂×C₈₃	semidirect
250. #3288	C₂×C₈₃	semidirect
251. #3151	C₂×C₈₃	semidirect
252. #3068	C₂×C₈₃	semidirect
253. #3018	C₂×C₈₃	semidirect
254. C₂×#453	C₂×C₈₃	semidirect
255. #2956	C₂×C₈₃	semidirect
256. C₈₃	#61110	direct (N × H)
257. #585	C₂²×C₈₃	semidirect
258. C₂×H(5,𝔽₂)	C₂²×C₈₃	semidirect
260. #577	C₂²×C₈₃	semidirect
262. #576	C₂²×C₈₃	semidirect
265. #575	C₂²×C₈₃	semidirect
267. C₂×AGL(1,ℤ/8)	C₂²×C₈₃	semidirect
268. C₂×AGL(1,ℤ/8)	C₂²×C₈₃	semidirect
269. #568	C₂²×C₈₃	semidirect
270. #532	C₂²×C₈₃	semidirect
271. C₂×#127	C₂²×C₈₃	semidirect
272. #496	C₂²×C₈₃	semidirect
273. #493	C₂²×C₈₃	semidirect
274. #492	C₂²×C₈₃	semidirect
275. #472	C₂²×C₈₃	semidirect
276. #471	C₂²×C₈₃	semidirect
277. #456	C₂²×C₈₃	semidirect
278. #455	C₂²×C₈₃	semidirect
279. #454	C₂²×C₈₃	semidirect
280. #453	C₂²×C₈₃	semidirect
281. #453	C₂²×C₈₃	semidirect
282. #453	C₂²×C₈₃	semidirect
283. #444	C₂²×C₈₃	semidirect
284. #443	C₂²×C₈₃	semidirect
285. #430	C₂²×C₈₃	semidirect
286. C₂×#104	C₂²×C₈₃	semidirect
287. #413	C₂²×C₈₃	semidirect
288. C₂×#100	C₂²×C₈₃	semidirect
289. C₄×M₁₆	C₂²×C₈₃	semidirect
297. H(5,𝔽₂)	C₂³×C₈₃	semidirect
309. #137	D₄×C₈₃	semidirect
310. #137	C₂³×C₈₃	semidirect
318. AGL(1,ℤ/8)	D₄×C₈₃	semidirect
320. AGL(1,ℤ/8)	C₂³×C₈₃	semidirect
327. C₂×SD₁₆	C₂³×C₈₃	semidirect
330. C₂×D₈	C₂³×C₈₃	semidirect
332. #131	C₂³×C₈₃	semidirect
336. C₄⋊Q₈	C₂³×C₈₃	semidirect
340. #127	C₂³×C₈₃	semidirect
341. #124	C₂³×C₈₃	semidirect
345. #108	C₂³×C₈₃	semidirect
346. #104	C₂³×C₈₃	semidirect
347. #104	C₂³×C₈₃	semidirect
348. #101	C₂³×C₈₃	semidirect
349. #100	C₂³×C₈₃	semidirect
350. #100	C₂³×C₈₃	semidirect
351. #97	C₂³×C₈₃	semidirect
352. C₄×C₈	C₂³×C₈₃	semidirect
401. Q₁₆	C₂×D₄×C₈₃	semidirect
406. SD₁₆	C₂×D₄×C₈₃	semidirect
410. D₈	C₂×D₄×C₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₈₃×#3585	2
C₈₃×#3292	2
C₈₃×#3291	2
C₈₃×#3288	2
C₈₃×#3151	2
C₈₃×#3068	2
C₈₃×#3018	2
C₂×#453×C₈₃	2
C₈₃×#2956	2
#61110	83

Subgroups — C83×#61110 #35288934

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#61110 #35288934