Subgroups — C₈₃×#60753 #35288577

Order 21248.

2322 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3449	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#535×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₃×#3200	C₂	1	4	yes	maximal, complemented
4	C₈₃×#3199	C₂	1	4	yes	maximal, complemented
5	C₈₃×#3198	C₂	1	8	yes	maximal, complemented
6	C₈₃×#3094	C₂	1	2	yes	maximal, complemented
7	C₈₃×#3093	C₂	1	2	yes	maximal, complemented
8	C₈₃×#3055	C₂	1	4	yes	maximal, complemented
9	C₈₃×#3006	C₂	1	2	yes	maximal, complemented
10	C₈₃×#3003	C₂	1	2	yes	maximal, complemented
11	C₈₃×#2879	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₈₃	C₂²	1	1	yes	characteristic
13	C₂²×#41×C₈₃	C₂²	1	1	yes	characteristic, complemented
14	C₂³×D₄×C₈₃	C₂²	1	1	yes	characteristic, complemented
15	C₂×AGL(1,ℤ/8)×C₈₃	C₂²	1	4	yes	—
16	C₂²×M₁₆×C₈₃	C₂²	1	2	yes	complemented
17	#537×C₈₃	C₂²	1	4	yes	complemented
18	#536×C₈₃	—	2	1	no	—
19	#536×C₈₃	C₂²	1	2	yes	complemented
20	#535×C₈₃	—	2	2	no	—
21	#535×C₈₃	—	2	2	no	—
22	#535×C₈₃	—	2	1	no	—
23	#535×C₈₃	C₂²	1	4	yes	—
24	#535×C₈₃	C₂²	1	4	yes	complemented
25	#535×C₈₃	C₂²	1	2	yes	complemented
26	#534×C₈₃	—	2	1	no	—
27	#534×C₈₃	—	2	1	no	—
28	#532×C₈₃	—	2	2	no	—
29	C₂×#127×C₈₃	—	2	1	no	—
30	C₂×#124×C₈₃	—	2	1	no	—
31	#525×C₈₃	—	2	2	no	—
32	#525×C₈₃	C₂²	1	2	yes	—
33	#525×C₈₃	C₂²	1	2	yes	complemented
34	C₂×#121×C₈₃	C₂²	1	2	yes	—
35	C₂×#121×C₈₃	C₂²	1	2	yes	complemented
36	C₂×#120×C₈₃	—	2	1	no	—
37	C₂×#120×C₈₃	—	2	1	no	—
38	C₂×#117×C₈₃	C₂²	1	1	yes	characteristic, complemented
39	C₂×#117×C₈₃	C₂²	1	1	yes	characteristic, complemented
40	#485×C₈₃	C₂²	1	8	yes	complemented
41	#482×C₈₃	C₂²	1	8	yes	complemented
42	#482×C₈₃	C₂²	1	8	yes	complemented
43	#481×C₈₃	C₂²	1	4	yes	complemented
44	#480×C₈₃	C₂²	1	4	yes	complemented
45	#469×C₈₃	C₂²	1	8	yes	complemented
46	#468×C₈₃	C₂²	1	8	yes	complemented
47	#466×C₈₃	C₂²	1	8	yes	complemented
48	#465×C₈₃	C₂²	1	8	yes	complemented
49	#450×C₈₃	C₂²	1	8	yes	complemented
50	#449×C₈₃	C₂²	1	8	yes	complemented
51	#448×C₈₃	C₂²	1	4	yes	complemented
52	#447×C₈₃	C₂²	1	8	yes	complemented
53	#447×C₈₃	C₂²	1	4	yes	complemented
54	#428×C₈₃	C₂²	1	4	yes	complemented
55	#418×C₈₃	C₂²	1	4	yes	complemented
56	#417×C₈₃	C₂²	1	4	yes	complemented
57	#408×C₈₃	C₂²	1	4	yes	complemented
58	#408×C₈₃	C₂²	1	4	yes	complemented
59	#407×C₈₃	C₂²	1	2	yes	complemented
60	#407×C₈₃	C₂²	1	2	yes	complemented
61	C₂⁵×C₈₃	—	2	1	no	—
62	C₂×#41×C₈₃	—	2	1	no	—
63	C₂×#41×C₈₃	—	2	1	no	—
64	C₂×#41×C₈₃	—	4	4	no	—
65	C₂×#41×C₈₃	—	4	4	no	—
66	C₂×#41×C₈₃	D₄	1	2	yes	—
67	C₂×#41×C₈₃	D₄	1	2	yes	—
68	C₂×#41×C₈₃	C₂³	1	2	yes	—
69	C₂×#41×C₈₃	C₂³	1	2	yes	—
70	C₂×#41×C₈₃	C₂³	1	2	yes	—
71	C₂×#41×C₈₃	C₂³	1	2	yes	complemented
72	C₂²×Q₈×C₈₃	D₄	1	1	yes	characteristic
73	C₂²×Q₈×C₈₃	C₂³	1	1	yes	characteristic, complemented
74	C₂²×D₄×C₈₃	—	2	1	no	—
75	C₂²×D₄×C₈₃	—	2	2	no	—
76	C₂²×D₄×C₈₃	—	2	2	no	—
77	C₂²×D₄×C₈₃	—	2	1	no	—
78	C₂²×D₄×C₈₃	—	2	2	no	—
79	C₂²×D₄×C₈₃	—	4	4	no	—
80	C₂²×D₄×C₈₃	D₄	1	1	yes	characteristic
81	C₂²×D₄×C₈₃	D₄	1	1	yes	characteristic
82	C₂²×D₄×C₈₃	D₄	1	1	yes	characteristic
83	C₂²×D₄×C₈₃	C₂³	1	2	yes	—
84	C₂²×D₄×C₈₃	C₂³	1	4	yes	—
85	C₂²×D₄×C₈₃	C₂³	1	1	yes	characteristic, complemented
86	C₂³×C₄×C₈₃	—	2	1	no	—
87	C₂³×C₄×C₈₃	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₈₃	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₈₃	C₂³	1	1	yes	characteristic
90	AGL(1,ℤ/8)×C₈₃	—	4	8	no	—
91	C₂×SD₁₆×C₈₃	C₂³	1	8	yes	—
92	C₂×D₈×C₈₃	C₂³	1	8	yes	—
93	C₂×M₁₆×C₈₃	—	4	4	no	—
94	C₂×M₁₆×C₈₃	C₂³	1	4	yes	—
95	C₂×M₁₆×C₈₃	C₂³	1	4	yes	complemented
96	C₂²×C₈×C₈₃	C₂³	1	4	yes	complemented
97	C₄⋊Q₈×C₈₃	—	2	2	no	—
98	#127×C₈₃	—	2	4	no	—
99	#127×C₈₃	—	2	4	no	—
100	#127×C₈₃	—	2	2	no	—
101	#124×C₈₃	—	2	4	no	—
102	#124×C₈₃	—	2	4	no	—
103	#124×C₈₃	—	2	2	no	—
104	#124×C₈₃	—	2	2	no	—
105	#123×C₈₃	—	2	2	no	—
106	#123×C₈₃	—	2	2	no	—
107	#123×C₈₃	—	2	2	no	—
108	#123×C₈₃	—	2	2	no	—
109	C₂²⋊Q₈×C₈₃	—	2	4	no	—
110	C₂²⋊Q₈×C₈₃	C₂³	1	4	yes	—
111	C₂²⋊Q₈×C₈₃	C₂³	1	4	yes	complemented
112	#121×C₈₃	—	2	4	no	—
113	#121×C₈₃	—	2	4	no	—
114	#121×C₈₃	—	2	4	no	—
115	#121×C₈₃	—	2	2	no	—
116	#121×C₈₃	—	2	2	no	—
117	#121×C₈₃	—	2	4	no	—
118	#121×C₈₃	C₂³	1	8	yes	—
119	#121×C₈₃	C₂³	1	4	yes	—
120	#121×C₈₃	C₂³	1	4	yes	—
121	#121×C₈₃	C₂³	1	4	yes	—
122	#121×C₈₃	C₂³	1	4	yes	complemented
123	#120×C₈₃	—	2	2	no	—
124	#120×C₈₃	—	2	2	no	—
125	#120×C₈₃	—	2	4	no	—
126	#120×C₈₃	—	2	4	no	—
127	#120×C₈₃	—	2	4	no	—
128	#120×C₈₃	—	2	4	no	—
129	#120×C₈₃	—	2	2	no	—
130	#120×C₈₃	—	2	2	no	—
131	C₄×D₄×C₈₃	—	2	4	no	—
132	C₄×D₄×C₈₃	—	2	4	no	—
133	#117×C₈₃	—	2	1	no	—
134	#117×C₈₃	—	2	2	no	—
135	#117×C₈₃	—	2	1	no	—
136	#117×C₈₃	C₂³	1	4	yes	—
137	#117×C₈₃	C₂³	1	2	yes	—
138	#117×C₈₃	C₂³	1	2	yes	complemented
139	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	complemented
141	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
142	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
143	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
144	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
145	C₂×C₄²×C₈₃	—	2	1	no	—
146	C₂×C₄²×C₈₃	—	2	1	no	—
147	#107×C₈₃	C₂³	1	8	yes	complemented
148	#106×C₈₃	C₂³	1	8	yes	complemented
149	#103×C₈₃	C₂³	1	8	yes	complemented
150	#102×C₈₃	C₂³	1	8	yes	—
151	#102×C₈₃	C₂³	1	8	yes	—
152	#102×C₈₃	C₂³	1	8	yes	complemented
153	C₂²⋊C₈×C₈₃	C₂³	1	8	yes	—
154	C₂²⋊C₈×C₈₃	C₂³	1	4	yes	complemented
155	C₂²⋊C₈×C₈₃	C₂³	1	4	yes	complemented
156	C₂⁴×C₈₃	—	2	2	no	—
157	C₂⁴×C₈₃	—	2	1	no	—
158	C₂⁴×C₈₃	—	2	4	no	—
159	C₂⁴×C₈₃	—	4	4	no	—
160	C₂⁴×C₈₃	—	8	4	no	—
161	C₂⁴×C₈₃	C₂×D₄	1	1	yes	characteristic
162	C₂⁴×C₈₃	C₂×D₄	1	1	yes	characteristic
163	C₂⁴×C₈₃	C₂×D₄	1	1	yes	characteristic
164	#41×C₈₃	—	2	8	no	—
165	#41×C₈₃	—	4	4	no	—
166	#41×C₈₃	—	4	4	no	—
167	#41×C₈₃	—	4	2	no	—
168	#41×C₈₃	—	4	2	no	—
169	#41×C₈₃	—	4	2	no	—
170	#41×C₈₃	—	4	2	no	—
171	#41×C₈₃	—	4	4	no	—
172	#41×C₈₃	—	4	4	no	—
173	#41×C₈₃	—	4	4	no	—
174	C₂×Q₈×C₈₃	—	2	1	no	—
175	C₂×Q₈×C₈₃	—	4	2	no	—
176	C₂×Q₈×C₈₃	—	4	2	no	—
177	C₂×Q₈×C₈₃	C₂×D₄	1	2	yes	—
178	C₂×Q₈×C₈₃	C₂×D₄	1	2	yes	—
179	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
180	C₂×D₄×C₈₃	—	2	2	no	—
181	C₂×D₄×C₈₃	—	2	2	no	—
182	C₂×D₄×C₈₃	—	2	4	no	—
183	C₂×D₄×C₈₃	—	2	4	no	—
184	C₂×D₄×C₈₃	—	2	4	no	—
185	C₂×D₄×C₈₃	—	2	8	no	—
186	C₂×D₄×C₈₃	—	2	4	no	—
187	C₂×D₄×C₈₃	—	2	2	no	—
188	C₂×D₄×C₈₃	—	2	4	no	—
189	C₂×D₄×C₈₃	—	2	1	no	—
190	C₂×D₄×C₈₃	—	2	8	no	—
191	C₂×D₄×C₈₃	—	4	4	no	—
192	C₂×D₄×C₈₃	—	4	4	no	—
193	C₂×D₄×C₈₃	—	4	2	no	—
194	C₂×D₄×C₈₃	—	4	2	no	—
195	C₂×D₄×C₈₃	—	4	2	no	—
196	C₂×D₄×C₈₃	—	4	2	no	—
197	C₂×D₄×C₈₃	—	4	4	no	—
198	C₂×D₄×C₈₃	—	4	8	no	—
199	C₂×D₄×C₈₃	—	4	4	no	—
200	C₂×D₄×C₈₃	—	8	4	no	—
201	C₂×D₄×C₈₃	—	8	4	no	—
202	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
203	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
204	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
205	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
206	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
207	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
208	C₂×D₄×C₈₃	C₂⁴	1	4	yes	—
209	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₈₃	—	2	4	no	—
211	C₂²×C₄×C₈₃	—	2	4	no	—
212	C₂²×C₄×C₈₃	—	2	4	no	—
213	C₂²×C₄×C₈₃	—	2	2	no	—
214	C₂²×C₄×C₈₃	—	2	1	no	—
215	C₂²×C₄×C₈₃	—	2	2	no	—
216	C₂²×C₄×C₈₃	—	2	2	no	—
217	C₂²×C₄×C₈₃	—	2	2	no	—
218	C₂²×C₄×C₈₃	—	4	4	no	—
219	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
224	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
226	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
231	SD₁₆×C₈₃	—	4	8	no	—
232	D₈×C₈₃	—	4	8	no	—
233	M₁₆×C₈₃	—	2	8	no	—
234	M₁₆×C₈₃	—	4	4	no	—
235	C₂×C₈×C₈₃	—	4	4	no	—
236	C₂×C₈×C₈₃	C₂⁴	1	8	yes	—
237	C₄⋊C₄×C₈₃	—	2	2	no	—
238	C₄⋊C₄×C₈₃	—	2	2	no	—
239	C₄⋊C₄×C₈₃	—	2	4	no	—
240	C₄⋊C₄×C₈₃	—	2	4	no	—
241	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
242	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
243	C₂²⋊C₄×C₈₃	—	2	4	no	—
244	C₂²⋊C₄×C₈₃	—	2	2	no	—
245	C₂²⋊C₄×C₈₃	—	2	2	no	—
246	C₂²⋊C₄×C₈₃	—	2	4	no	—
247	C₂²⋊C₄×C₈₃	—	2	4	no	—
248	C₂²⋊C₄×C₈₃	—	2	4	no	—
249	C₂²⋊C₄×C₈₃	—	2	8	no	—
250	C₂²⋊C₄×C₈₃	—	2	4	no	—
251	C₂²⋊C₄×C₈₃	—	2	4	no	—
252	C₂²⋊C₄×C₈₃	—	2	4	no	—
253	C₄²×C₈₃	—	2	2	no	—
254	C₄²×C₈₃	—	2	4	no	—
255	C₄²×C₈₃	—	2	2	no	—
256	C₂³×C₈₃	—	2	2	no	—
257	C₂³×C₈₃	—	2	2	no	—
258	C₂³×C₈₃	—	2	2	no	—
259	C₂³×C₈₃	—	2	2	no	—
260	C₂³×C₈₃	—	2	4	no	—
261	C₂³×C₈₃	—	4	2	no	—
262	C₂³×C₈₃	—	4	2	no	—
263	C₂³×C₈₃	—	4	2	no	—
264	C₂³×C₈₃	—	4	2	no	—
265	C₂³×C₈₃	—	4	8	no	—
266	C₂³×C₈₃	—	4	4	no	—
267	C₂³×C₈₃	—	4	4	no	—
268	C₂³×C₈₃	—	4	4	no	—
269	C₂³×C₈₃	—	8	2	no	—
270	C₂³×C₈₃	—	8	8	no	—
271	C₂³×C₈₃	—	8	16	no	—
272	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
273	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
274	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
275	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
276	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
277	Q₈×C₈₃	—	2	4	no	—
278	Q₈×C₈₃	—	4	2	no	—
279	Q₈×C₈₃	—	4	2	no	—
280	Q₈×C₈₃	—	4	2	no	—
281	D₄×C₈₃	—	2	4	no	—
282	D₄×C₈₃	—	2	8	no	—
283	D₄×C₈₃	—	4	2	no	—
284	D₄×C₈₃	—	4	2	no	—
285	D₄×C₈₃	—	4	2	no	—
286	D₄×C₈₃	—	4	2	no	—
287	D₄×C₈₃	—	4	2	no	—
288	D₄×C₈₃	—	4	2	no	—
289	D₄×C₈₃	—	4	8	no	—
290	D₄×C₈₃	—	4	2	no	—
291	D₄×C₈₃	—	4	4	no	—
292	D₄×C₈₃	—	4	4	no	—
293	D₄×C₈₃	—	4	4	no	—
294	D₄×C₈₃	—	8	4	no	—
295	D₄×C₈₃	—	8	4	no	—
296	D₄×C₈₃	—	8	4	no	—
297	D₄×C₈₃	—	8	8	no	—
298	D₄×C₈₃	—	8	4	no	—
299	C₂×C₄×C₈₃	—	2	2	no	—
300	C₂×C₄×C₈₃	—	2	2	no	—
301	C₂×C₄×C₈₃	—	2	2	no	—
302	C₂×C₄×C₈₃	—	2	2	no	—
303	C₂×C₄×C₈₃	—	2	4	no	—
304	C₂×C₄×C₈₃	—	2	4	no	—
305	C₂×C₄×C₈₃	—	2	2	no	—
306	C₂×C₄×C₈₃	—	2	2	no	—
307	C₂×C₄×C₈₃	—	2	2	no	—
308	C₂×C₄×C₈₃	—	2	2	no	—
309	C₂×C₄×C₈₃	—	2	2	no	—
310	C₂×C₄×C₈₃	—	2	2	no	—
311	C₂×C₄×C₈₃	—	2	2	no	—
312	C₂×C₄×C₈₃	—	2	4	no	—
313	C₂×C₄×C₈₃	—	2	4	no	—
314	C₂×C₄×C₈₃	—	2	2	no	—
315	C₂×C₄×C₈₃	—	4	4	no	—
316	C₂×C₄×C₈₃	—	4	2	no	—
317	C₂×C₄×C₈₃	—	4	4	no	—
318	C₂×C₄×C₈₃	—	4	4	no	—
319	C₂×C₄×C₈₃	—	8	2	no	—
320	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
322	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
323	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
324	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₈₃	H(5,𝔽₂)	1	4	yes	—
326	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
327	C₈×C₈₃	—	2	8	no	—
328	C₂²×C₈₃	—	2	2	no	—
329	C₂²×C₈₃	—	2	2	no	—
330	C₂²×C₈₃	—	2	4	no	—
331	C₂²×C₈₃	—	2	2	no	—
332	C₂²×C₈₃	—	2	4	no	—
333	C₂²×C₈₃	—	2	1	no	—
334	C₂²×C₈₃	—	2	1	no	—
335	C₂²×C₈₃	—	2	2	no	—
336	C₂²×C₈₃	—	2	2	no	—
337	C₂²×C₈₃	—	4	4	no	—
338	C₂²×C₈₃	—	4	4	no	—
339	C₂²×C₈₃	—	4	4	no	—
340	C₂²×C₈₃	—	4	4	no	—
341	C₂²×C₈₃	—	4	2	no	—
342	C₂²×C₈₃	—	4	4	no	—
343	C₂²×C₈₃	—	8	2	no	—
344	C₂²×C₈₃	—	8	2	no	—
345	C₂²×C₈₃	—	8	8	no	—
346	C₂²×C₈₃	—	8	4	no	—
347	C₂²×C₈₃	—	8	16	no	—
348	C₂²×C₈₃	#534	1	2	yes	—
349	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
350	C₄×C₈₃	—	2	1	no	—
351	C₄×C₈₃	—	2	2	no	—
352	C₄×C₈₃	—	2	1	no	—
353	C₄×C₈₃	—	2	2	no	—
354	C₄×C₈₃	—	4	4	no	—
355	C₄×C₈₃	—	4	4	no	—
356	C₄×C₈₃	—	4	2	no	—
357	C₄×C₈₃	#534	1	2	yes	—
358	C₄×C₈₃	C₂×H(5,𝔽₂)	1	2	yes	—
359	#60753	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
360	C₂×C₈₃	—	2	2	no	—
361	C₂×C₈₃	—	4	2	no	—
362	C₂×C₈₃	—	4	1	no	—
363	C₂×C₈₃	—	4	2	no	—
364	C₂×C₈₃	—	4	1	no	—
365	C₂×C₈₃	—	8	2	no	—
366	C₂×C₈₃	—	8	4	no	—
367	C₂×C₈₃	C₂×#534	1	1	yes	characteristic
368	C₂×C₈₃	#3585	1	2	yes	—
369	#3449	C₂×C₈₃	1	1	yes	characteristic, complemented
370	C₂×#535	C₂×C₈₃	1	1	yes	characteristic, complemented
371	#3200	C₂×C₈₃	1	4	yes	complemented
372	#3199	C₂×C₈₃	1	4	yes	complemented
373	#3198	C₂×C₈₃	1	8	yes	complemented
374	#3094	C₂×C₈₃	1	2	yes	complemented
375	#3093	C₂×C₈₃	1	2	yes	complemented
376	#3055	C₂×C₈₃	1	4	yes	complemented
377	#3006	C₂×C₈₃	1	2	yes	complemented
378	#3003	C₂×C₈₃	1	2	yes	complemented
379	#2879	C₂×C₈₃	1	1	yes	characteristic, complemented
380	C₈₃	#60753	1	1	yes	characteristic, direct product factor, Sylow
381	C₂²×#41	C₂²×C₈₃	1	1	yes	characteristic
382	C₂²×#41	C₂²×C₈₃	1	1	yes	characteristic, complemented
383	C₂³×D₄	C₂²×C₈₃	1	1	yes	characteristic, complemented
384	C₂×AGL(1,ℤ/8)	C₂²×C₈₃	1	4	yes	—
385	C₂²×M₁₆	C₂²×C₈₃	1	2	yes	complemented
386	#537	C₂²×C₈₃	1	4	yes	complemented
387	#536	—	2	1	no	—
388	#536	C₂²×C₈₃	1	2	yes	complemented
389	#535	—	2	2	no	—
390	#535	—	2	2	no	—
391	#535	—	2	1	no	—
392	#535	C₂²×C₈₃	1	4	yes	—
393	#535	C₂²×C₈₃	1	4	yes	complemented
394	#535	C₂²×C₈₃	1	2	yes	complemented
395	#534	—	2	1	no	—
396	#534	—	2	1	no	—
397	#532	—	2	2	no	—
398	C₂×#127	—	2	1	no	—
399	C₂×#124	—	2	1	no	—
400	#525	—	2	2	no	—
401	#525	C₂²×C₈₃	1	2	yes	—
402	#525	C₂²×C₈₃	1	2	yes	complemented
403	C₂×#121	C₂²×C₈₃	1	2	yes	—
404	C₂×#121	C₂²×C₈₃	1	2	yes	complemented
405	C₂×#120	—	2	1	no	—
406	C₂×#120	—	2	1	no	—
407	C₂×#117	C₂²×C₈₃	1	1	yes	characteristic, complemented
408	C₂×#117	C₂²×C₈₃	1	1	yes	characteristic, complemented
409	#485	C₂²×C₈₃	1	8	yes	complemented
410	#482	C₂²×C₈₃	1	8	yes	complemented
411	#482	C₂²×C₈₃	1	8	yes	complemented
412	#481	C₂²×C₈₃	1	4	yes	complemented
413	#480	C₂²×C₈₃	1	4	yes	complemented
414	#469	C₂²×C₈₃	1	8	yes	complemented
415	#468	C₂²×C₈₃	1	8	yes	complemented
416	#466	C₂²×C₈₃	1	8	yes	complemented
417	#465	C₂²×C₈₃	1	8	yes	complemented
418	#450	C₂²×C₈₃	1	8	yes	complemented
419	#449	C₂²×C₈₃	1	8	yes	complemented
420	#448	C₂²×C₈₃	1	4	yes	complemented
421	#447	C₂²×C₈₃	1	8	yes	complemented
422	#447	C₂²×C₈₃	1	4	yes	complemented
423	#428	C₂²×C₈₃	1	4	yes	complemented
424	#418	C₂²×C₈₃	1	4	yes	complemented
425	#417	C₂²×C₈₃	1	4	yes	complemented
426	#408	C₂²×C₈₃	1	4	yes	complemented
427	#408	C₂²×C₈₃	1	4	yes	complemented
428	#407	C₂²×C₈₃	1	2	yes	complemented
429	#407	C₂²×C₈₃	1	2	yes	complemented
430	C₂⁵	—	2	1	no	—
431	C₂×#41	—	2	1	no	—
432	C₂×#41	—	2	1	no	—
433	C₂×#41	—	4	4	no	—
434	C₂×#41	—	4	4	no	—
435	C₂×#41	D₄×C₈₃	1	2	yes	—
436	C₂×#41	D₄×C₈₃	1	2	yes	—
437	C₂×#41	C₂³×C₈₃	1	2	yes	—
438	C₂×#41	C₂³×C₈₃	1	2	yes	—
439	C₂×#41	C₂³×C₈₃	1	2	yes	—
440	C₂×#41	C₂³×C₈₃	1	2	yes	complemented
441	C₂²×Q₈	D₄×C₈₃	1	1	yes	characteristic
442	C₂²×Q₈	C₂³×C₈₃	1	1	yes	characteristic, complemented
443	C₂²×D₄	—	2	1	no	—
444	C₂²×D₄	—	2	2	no	—
445	C₂²×D₄	—	2	2	no	—
446	C₂²×D₄	—	2	1	no	—
447	C₂²×D₄	—	2	2	no	—
448	C₂²×D₄	—	4	4	no	—
449	C₂²×D₄	D₄×C₈₃	1	1	yes	characteristic
450	C₂²×D₄	D₄×C₈₃	1	1	yes	characteristic
451	C₂²×D₄	D₄×C₈₃	1	1	yes	characteristic
452	C₂²×D₄	C₂³×C₈₃	1	2	yes	—
453	C₂²×D₄	C₂³×C₈₃	1	4	yes	—
454	C₂²×D₄	C₂³×C₈₃	1	1	yes	characteristic, complemented
455	C₂³×C₄	—	2	1	no	—
456	C₂³×C₄	C₂³×C₈₃	1	1	yes	characteristic
457	C₂³×C₄	C₂³×C₈₃	1	1	yes	characteristic
458	C₂³×C₄	C₂³×C₈₃	1	1	yes	characteristic
459	AGL(1,ℤ/8)	—	4	8	no	—
460	C₂×SD₁₆	C₂³×C₈₃	1	8	yes	—
461	C₂×D₈	C₂³×C₈₃	1	8	yes	—
462	C₂×M₁₆	—	4	4	no	—
463	C₂×M₁₆	C₂³×C₈₃	1	4	yes	—
464	C₂×M₁₆	C₂³×C₈₃	1	4	yes	complemented
465	C₂²×C₈	C₂³×C₈₃	1	4	yes	complemented
466	C₄⋊Q₈	—	2	2	no	—
467	#127	—	2	4	no	—
468	#127	—	2	4	no	—
469	#127	—	2	2	no	—
470	#124	—	2	4	no	—
471	#124	—	2	4	no	—
472	#124	—	2	2	no	—
473	#124	—	2	2	no	—
474	#123	—	2	2	no	—
475	#123	—	2	2	no	—
476	#123	—	2	2	no	—
477	#123	—	2	2	no	—
478	C₂²⋊Q₈	—	2	4	no	—
479	C₂²⋊Q₈	C₂³×C₈₃	1	4	yes	—
480	C₂²⋊Q₈	C₂³×C₈₃	1	4	yes	complemented
481	#121	—	2	4	no	—
482	#121	—	2	4	no	—
483	#121	—	2	4	no	—
484	#121	—	2	2	no	—
485	#121	—	2	2	no	—
486	#121	—	2	4	no	—
487	#121	C₂³×C₈₃	1	4	yes	—
488	#121	C₂³×C₈₃	1	4	yes	—
489	#121	C₂³×C₈₃	1	8	yes	—
490	#121	C₂³×C₈₃	1	4	yes	—
491	#121	C₂³×C₈₃	1	4	yes	complemented
492	#120	—	2	2	no	—
493	#120	—	2	2	no	—
494	#120	—	2	4	no	—
495	#120	—	2	4	no	—
496	#120	—	2	4	no	—
497	#120	—	2	4	no	—
498	#120	—	2	2	no	—
499	#120	—	2	2	no	—
500	C₄×D₄	—	2	4	no	—
501	C₄×D₄	—	2	4	no	—
502	#117	—	2	1	no	—
503	#117	—	2	2	no	—
504	#117	—	2	1	no	—
505	#117	C₂³×C₈₃	1	2	yes	—
506	#117	C₂³×C₈₃	1	4	yes	—
507	#117	C₂³×C₈₃	1	2	yes	complemented
508	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	complemented
510	C₂×C₂²⋊C₄	—	2	1	no	—
511	C₂×C₂²⋊C₄	—	2	1	no	—
512	C₂×C₂²⋊C₄	—	2	2	no	—
513	C₂×C₂²⋊C₄	—	2	2	no	—
514	C₂×C₄²	—	2	1	no	—
515	C₂×C₄²	—	2	1	no	—
516	#107	C₂³×C₈₃	1	8	yes	complemented
517	#106	C₂³×C₈₃	1	8	yes	complemented
518	#103	C₂³×C₈₃	1	8	yes	complemented
519	#102	C₂³×C₈₃	1	8	yes	—
520	#102	C₂³×C₈₃	1	8	yes	—
521	#102	C₂³×C₈₃	1	8	yes	complemented
522	C₂²⋊C₈	C₂³×C₈₃	1	8	yes	—
523	C₂²⋊C₈	C₂³×C₈₃	1	4	yes	complemented
524	C₂²⋊C₈	C₂³×C₈₃	1	4	yes	complemented
525	C₂⁴	—	2	2	no	—
526	C₂⁴	—	2	1	no	—
527	C₂⁴	—	2	4	no	—
528	C₂⁴	—	4	4	no	—
529	C₂⁴	—	8	4	no	—
530	C₂⁴	C₂×D₄×C₈₃	1	1	yes	characteristic
531	C₂⁴	C₂×D₄×C₈₃	1	1	yes	characteristic
532	C₂⁴	C₂×D₄×C₈₃	1	1	yes	characteristic
533	#41	—	2	8	no	—
534	#41	—	4	4	no	—
535	#41	—	4	4	no	—
536	#41	—	4	2	no	—
537	#41	—	4	2	no	—
538	#41	—	4	2	no	—
539	#41	—	4	2	no	—
540	#41	—	4	4	no	—
541	#41	—	4	4	no	—
542	#41	—	4	4	no	—
543	C₂×Q₈	—	2	1	no	—
544	C₂×Q₈	—	4	2	no	—
545	C₂×Q₈	—	4	2	no	—
546	C₂×Q₈	C₂×D₄×C₈₃	1	2	yes	—
547	C₂×Q₈	C₂×D₄×C₈₃	1	2	yes	—
548	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
549	C₂×D₄	—	2	2	no	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	4	no	—
552	C₂×D₄	—	2	4	no	—
553	C₂×D₄	—	2	4	no	—
554	C₂×D₄	—	2	8	no	—
555	C₂×D₄	—	2	4	no	—
556	C₂×D₄	—	2	2	no	—
557	C₂×D₄	—	2	4	no	—
558	C₂×D₄	—	2	1	no	—
559	C₂×D₄	—	2	8	no	—
560	C₂×D₄	—	4	4	no	—
561	C₂×D₄	—	4	4	no	—
562	C₂×D₄	—	4	2	no	—
563	C₂×D₄	—	4	2	no	—
564	C₂×D₄	—	4	2	no	—
565	C₂×D₄	—	4	2	no	—
566	C₂×D₄	—	4	4	no	—
567	C₂×D₄	—	4	8	no	—
568	C₂×D₄	—	4	4	no	—
569	C₂×D₄	—	8	4	no	—
570	C₂×D₄	—	8	4	no	—
571	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
572	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
573	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
574	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
575	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
576	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
577	C₂×D₄	C₂⁴×C₈₃	1	4	yes	—
578	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
579	C₂²×C₄	—	2	4	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	4	4	no	—
588	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
589	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
590	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
591	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
592	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
593	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
594	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
598	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
600	SD₁₆	—	4	8	no	—
601	D₈	—	4	8	no	—
602	M₁₆	—	2	8	no	—
603	M₁₆	—	4	4	no	—
604	C₂×C₈	—	4	4	no	—
605	C₂×C₈	C₂⁴×C₈₃	1	8	yes	—
606	C₄⋊C₄	—	2	2	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
611	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
612	C₂²⋊C₄	—	2	4	no	—
613	C₂²⋊C₄	—	2	2	no	—
614	C₂²⋊C₄	—	2	2	no	—
615	C₂²⋊C₄	—	2	4	no	—
616	C₂²⋊C₄	—	2	4	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	2	8	no	—
619	C₂²⋊C₄	—	2	4	no	—
620	C₂²⋊C₄	—	2	4	no	—
621	C₂²⋊C₄	—	2	4	no	—
622	C₄²	—	2	2	no	—
623	C₄²	—	2	4	no	—
624	C₄²	—	2	2	no	—
625	C₂³	—	2	2	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	2	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	4	no	—
630	C₂³	—	4	2	no	—
631	C₂³	—	4	2	no	—
632	C₂³	—	4	2	no	—
633	C₂³	—	4	2	no	—
634	C₂³	—	4	8	no	—
635	C₂³	—	4	4	no	—
636	C₂³	—	4	4	no	—
637	C₂³	—	4	4	no	—
638	C₂³	—	8	8	no	—
639	C₂³	—	8	2	no	—
640	C₂³	—	8	16	no	—
641	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
642	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
643	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
644	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
645	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
646	Q₈	—	2	4	no	—
647	Q₈	—	4	2	no	—
648	Q₈	—	4	2	no	—
649	Q₈	—	4	2	no	—
650	D₄	—	2	4	no	—
651	D₄	—	2	8	no	—
652	D₄	—	4	2	no	—
653	D₄	—	4	2	no	—
654	D₄	—	4	2	no	—
655	D₄	—	4	2	no	—
656	D₄	—	4	2	no	—
657	D₄	—	4	2	no	—
658	D₄	—	4	8	no	—
659	D₄	—	4	2	no	—
660	D₄	—	4	4	no	—
661	D₄	—	4	4	no	—
662	D₄	—	4	4	no	—
663	D₄	—	8	4	no	—
664	D₄	—	8	8	no	—
665	D₄	—	8	4	no	—
666	D₄	—	8	4	no	—
667	D₄	—	8	4	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	4	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	4	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	4	no	—
682	C₂×C₄	—	2	4	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	4	4	no	—
685	C₂×C₄	—	4	2	no	—
686	C₂×C₄	—	4	4	no	—
687	C₂×C₄	—	4	4	no	—
688	C₂×C₄	—	8	2	no	—
689	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
690	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
691	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
692	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
693	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
694	C₂×C₄	H(5,𝔽₂)×C₈₃	1	4	yes	—
695	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
696	C₈	—	2	8	no	—
697	C₂²	—	2	2	no	—
698	C₂²	—	2	2	no	—
699	C₂²	—	2	4	no	—
700	C₂²	—	2	2	no	—
701	C₂²	—	2	4	no	—
702	C₂²	—	2	1	no	—
703	C₂²	—	2	1	no	—
704	C₂²	—	2	2	no	—
705	C₂²	—	2	2	no	—
706	C₂²	—	4	4	no	—
707	C₂²	—	4	4	no	—
708	C₂²	—	4	4	no	—
709	C₂²	—	4	4	no	—
710	C₂²	—	4	2	no	—
711	C₂²	—	4	4	no	—
712	C₂²	—	8	2	no	—
713	C₂²	—	8	2	no	—
714	C₂²	—	8	8	no	—
715	C₂²	—	8	16	no	—
716	C₂²	—	8	4	no	—
717	C₂²	#534×C₈₃	1	2	yes	—
718	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
719	C₄	—	2	1	no	—
720	C₄	—	2	2	no	—
721	C₄	—	2	1	no	—
722	C₄	—	2	2	no	—
723	C₄	—	4	4	no	—
724	C₄	—	4	4	no	—
725	C₄	—	4	2	no	—
726	C₄	#534×C₈₃	1	2	yes	—
727	C₄	C₂×H(5,𝔽₂)×C₈₃	1	2	yes	—
728	C₂	—	2	2	no	—
729	C₂	—	4	2	no	—
730	C₂	—	4	1	no	—
731	C₂	—	4	1	no	—
732	C₂	—	4	2	no	—
733	C₂	—	8	4	no	—
734	C₂	—	8	2	no	—
735	C₂	C₂×#534×C₈₃	1	1	yes	characteristic
736	C₂	C₈₃×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₈₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₃ ◁ C₂²×#41×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₃×#3449	C₂	semidirect
2. C₂×#535×C₈₃	C₂	semidirect
3. C₈₃×#3200	C₂	semidirect
4. C₈₃×#3199	C₂	semidirect
5. C₈₃×#3198	C₂	semidirect
6. C₈₃×#3094	C₂	semidirect
7. C₈₃×#3093	C₂	semidirect
8. C₈₃×#3055	C₂	semidirect
9. C₈₃×#3006	C₂	semidirect
10. C₈₃×#3003	C₂	semidirect
11. C₈₃×#2879	C₂	semidirect
13. C₂²×#41×C₈₃	C₂²	semidirect
14. C₂³×D₄×C₈₃	C₂²	semidirect
16. C₂²×M₁₆×C₈₃	C₂²	semidirect
17. #537×C₈₃	C₂²	semidirect
19. #536×C₈₃	C₂²	semidirect
24. #535×C₈₃	C₂²	semidirect
25. #535×C₈₃	C₂²	semidirect
33. #525×C₈₃	C₂²	semidirect
35. C₂×#121×C₈₃	C₂²	semidirect
38. C₂×#117×C₈₃	C₂²	semidirect
39. C₂×#117×C₈₃	C₂²	semidirect
40. #485×C₈₃	C₂²	semidirect
41. #482×C₈₃	C₂²	semidirect
42. #482×C₈₃	C₂²	semidirect
43. #481×C₈₃	C₂²	semidirect
44. #480×C₈₃	C₂²	semidirect
45. #469×C₈₃	C₂²	semidirect
46. #468×C₈₃	C₂²	semidirect
47. #466×C₈₃	C₂²	semidirect
48. #465×C₈₃	C₂²	semidirect
49. #450×C₈₃	C₂²	semidirect
50. #449×C₈₃	C₂²	semidirect
51. #448×C₈₃	C₂²	semidirect
52. #447×C₈₃	C₂²	semidirect
53. #447×C₈₃	C₂²	semidirect
54. #428×C₈₃	C₂²	semidirect
55. #418×C₈₃	C₂²	semidirect
56. #417×C₈₃	C₂²	semidirect
57. #408×C₈₃	C₂²	semidirect
58. #408×C₈₃	C₂²	semidirect
59. #407×C₈₃	C₂²	semidirect
60. #407×C₈₃	C₂²	semidirect
71. C₂×#41×C₈₃	C₂³	semidirect
73. C₂²×Q₈×C₈₃	C₂³	semidirect
85. C₂²×D₄×C₈₃	C₂³	semidirect
95. C₂×M₁₆×C₈₃	C₂³	semidirect
96. C₂²×C₈×C₈₃	C₂³	semidirect
111. C₂²⋊Q₈×C₈₃	C₂³	semidirect
122. #121×C₈₃	C₂³	semidirect
138. #117×C₈₃	C₂³	semidirect
140. C₂×C₄⋊C₄×C₈₃	C₂³	semidirect
147. #107×C₈₃	C₂³	semidirect
148. #106×C₈₃	C₂³	semidirect
149. #103×C₈₃	C₂³	semidirect
152. #102×C₈₃	C₂³	semidirect
154. C₂²⋊C₈×C₈₃	C₂³	semidirect
155. C₂²⋊C₈×C₈₃	C₂³	semidirect
359. #60753	C₈₃	direct (N × H)
369. #3449	C₂×C₈₃	semidirect
370. C₂×#535	C₂×C₈₃	semidirect
371. #3200	C₂×C₈₃	semidirect
372. #3199	C₂×C₈₃	semidirect
373. #3198	C₂×C₈₃	semidirect
374. #3094	C₂×C₈₃	semidirect
375. #3093	C₂×C₈₃	semidirect
376. #3055	C₂×C₈₃	semidirect
377. #3006	C₂×C₈₃	semidirect
378. #3003	C₂×C₈₃	semidirect
379. #2879	C₂×C₈₃	semidirect
380. C₈₃	#60753	direct (N × H)
382. C₂²×#41	C₂²×C₈₃	semidirect
383. C₂³×D₄	C₂²×C₈₃	semidirect
385. C₂²×M₁₆	C₂²×C₈₃	semidirect
386. #537	C₂²×C₈₃	semidirect
388. #536	C₂²×C₈₃	semidirect
393. #535	C₂²×C₈₃	semidirect
394. #535	C₂²×C₈₃	semidirect
402. #525	C₂²×C₈₃	semidirect
404. C₂×#121	C₂²×C₈₃	semidirect
407. C₂×#117	C₂²×C₈₃	semidirect
408. C₂×#117	C₂²×C₈₃	semidirect
409. #485	C₂²×C₈₃	semidirect
410. #482	C₂²×C₈₃	semidirect
411. #482	C₂²×C₈₃	semidirect
412. #481	C₂²×C₈₃	semidirect
413. #480	C₂²×C₈₃	semidirect
414. #469	C₂²×C₈₃	semidirect
415. #468	C₂²×C₈₃	semidirect
416. #466	C₂²×C₈₃	semidirect
417. #465	C₂²×C₈₃	semidirect
418. #450	C₂²×C₈₃	semidirect
419. #449	C₂²×C₈₃	semidirect
420. #448	C₂²×C₈₃	semidirect
421. #447	C₂²×C₈₃	semidirect
422. #447	C₂²×C₈₃	semidirect
423. #428	C₂²×C₈₃	semidirect
424. #418	C₂²×C₈₃	semidirect
425. #417	C₂²×C₈₃	semidirect
426. #408	C₂²×C₈₃	semidirect
427. #408	C₂²×C₈₃	semidirect
428. #407	C₂²×C₈₃	semidirect
429. #407	C₂²×C₈₃	semidirect
440. C₂×#41	C₂³×C₈₃	semidirect
442. C₂²×Q₈	C₂³×C₈₃	semidirect
454. C₂²×D₄	C₂³×C₈₃	semidirect
464. C₂×M₁₆	C₂³×C₈₃	semidirect
465. C₂²×C₈	C₂³×C₈₃	semidirect
480. C₂²⋊Q₈	C₂³×C₈₃	semidirect
491. #121	C₂³×C₈₃	semidirect
507. #117	C₂³×C₈₃	semidirect
509. C₂×C₄⋊C₄	C₂³×C₈₃	semidirect
516. #107	C₂³×C₈₃	semidirect
517. #106	C₂³×C₈₃	semidirect
518. #103	C₂³×C₈₃	semidirect
521. #102	C₂³×C₈₃	semidirect
523. C₂²⋊C₈	C₂³×C₈₃	semidirect
524. C₂²⋊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×#3449	2
C₂×#535×C₈₃	2
C₈₃×#3200	2
C₈₃×#3199	2
C₈₃×#3198	2
C₈₃×#3094	2
C₈₃×#3093	2
C₈₃×#3055	2
C₈₃×#3006	2
C₈₃×#3003	2
C₈₃×#2879	2
#60753	83

Subgroups — C83×#60753 #35288577

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#60753 #35288577