Subgroups — C₈₃×#60915 #35288739

Order 21248.

1790 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3455	C₂	1	2	yes	maximal, complemented
2	C₈₃×#3263	C₂	1	2	yes	maximal, complemented
3	C₈₃×#3262	C₂	1	2	yes	maximal, complemented
4	C₈₃×#3261	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₃×#3260	C₂	1	2	yes	maximal, complemented
6	C₈₃×#3259	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₃×#3258	C₂	1	4	yes	maximal, complemented
8	C₈₃×#3257	C₂	1	4	yes	maximal, complemented
9	C₈₃×#3076	C₂	1	4	yes	maximal, complemented
10	C₈₃×#3054	C₂	1	2	yes	maximal, complemented
11	C₈₃×#3050	C₂	1	2	yes	maximal, complemented
12	C₈₃×#3035	C₂	1	4	yes	maximal, complemented
13	C₂×#424×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#135×C₈₃	C₂²	1	2	yes	—
15	C₂×#135×C₈₃	C₂²	1	2	yes	—
16	C₂²×M₁₆×C₈₃	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₈₃	C₂²	1	1	yes	characteristic
18	#542×C₈₃	C₂²	1	4	yes	—
19	#542×C₈₃	C₂²	1	4	yes	—
20	#541×C₈₃	C₂²	1	2	yes	—
21	#541×C₈₃	C₂²	1	2	yes	—
22	#540×C₈₃	C₂²	1	2	yes	—
23	#540×C₈₃	C₂²	1	2	yes	—
24	#539×C₈₃	—	2	4	no	—
25	#538×C₈₃	—	2	4	no	—
26	#533×C₈₃	C₂²	1	2	yes	—
27	#532×C₈₃	C₂²	1	2	yes	—
28	#529×C₈₃	—	2	4	no	—
29	#529×C₈₃	—	2	4	no	—
30	#525×C₈₃	C₂²	1	4	yes	—
31	C₄×#41×C₈₃	C₂²	1	4	yes	—
32	C₂×#117×C₈₃	C₂²	1	1	yes	characteristic
33	#479×C₈₃	C₂²	1	4	yes	complemented
34	#479×C₈₃	C₂²	1	4	yes	complemented
35	#478×C₈₃	C₂²	1	4	yes	complemented
36	#478×C₈₃	C₂²	1	4	yes	complemented
37	#477×C₈₃	C₂²	1	4	yes	complemented
38	#476×C₈₃	C₂²	1	4	yes	complemented
39	#475×C₈₃	C₂²	1	4	yes	complemented
40	#474×C₈₃	C₂²	1	4	yes	complemented
41	#470×C₈₃	C₂²	1	2	yes	—
42	#470×C₈₃	C₂²	1	2	yes	—
43	#469×C₈₃	C₂²	1	2	yes	—
44	#469×C₈₃	C₂²	1	2	yes	—
45	#468×C₈₃	C₂²	1	4	yes	—
46	#468×C₈₃	C₂²	1	4	yes	—
47	#467×C₈₃	C₂²	1	2	yes	—
48	#467×C₈₃	C₂²	1	2	yes	—
49	#466×C₈₃	C₂²	1	2	yes	—
50	#466×C₈₃	C₂²	1	2	yes	—
51	#465×C₈₃	C₂²	1	4	yes	—
52	#465×C₈₃	C₂²	1	4	yes	—
53	#464×C₈₃	C₂²	1	4	yes	complemented
54	#464×C₈₃	C₂²	1	4	yes	complemented
55	#463×C₈₃	C₂²	1	4	yes	complemented
56	#463×C₈₃	C₂²	1	4	yes	complemented
57	#462×C₈₃	C₂²	1	4	yes	complemented
58	#461×C₈₃	C₂²	1	4	yes	complemented
59	#460×C₈₃	C₂²	1	4	yes	complemented
60	#459×C₈₃	C₂²	1	4	yes	complemented
61	#427×C₈₃	C₂²	1	2	yes	—
62	#427×C₈₃	C₂²	1	2	yes	—
63	#424×C₈₃	C₂²	1	4	yes	—
64	#424×C₈₃	C₂²	1	1	yes	characteristic
65	#424×C₈₃	C₂²	1	1	yes	characteristic
66	#424×C₈₃	C₂²	1	1	yes	characteristic
67	#424×C₈₃	C₂²	1	1	yes	characteristic
68	C₂×C₄⋊C₈×C₈₃	C₂²	1	4	yes	—
69	#416×C₈₃	C₂²	1	4	yes	—
70	#416×C₈₃	C₂²	1	4	yes	—
71	C₂×#41×C₈₃	C₂³	1	4	yes	—
72	C₂³×C₄×C₈₃	C₂³	1	1	yes	characteristic
73	#135×C₈₃	—	4	4	no	—
74	#135×C₈₃	—	4	4	no	—
75	C₂×Q₁₆×C₈₃	C₂³	1	2	yes	—
76	C₂×Q₁₆×C₈₃	C₂³	1	2	yes	—
77	C₂×SD₁₆×C₈₃	C₂³	1	4	yes	—
78	C₂×SD₁₆×C₈₃	C₂³	1	4	yes	—
79	C₂×D₈×C₈₃	C₂³	1	2	yes	—
80	C₂×D₈×C₈₃	C₂³	1	2	yes	—
81	C₂×M₁₆×C₈₃	—	4	2	no	—
82	C₂×M₁₆×C₈₃	C₂³	1	1	yes	characteristic
83	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
84	C₂×M₁₆×C₈₃	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₈₃	—	4	2	no	—
86	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
87	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
88	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
90	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
91	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
92	C₄⋊Q₈×C₈₃	C₂³	1	4	yes	—
93	#127×C₈₃	C₂³	1	2	yes	—
94	#126×C₈₃	—	2	4	no	—
95	#126×C₈₃	—	2	4	no	—
96	#126×C₈₃	—	2	4	no	—
97	#126×C₈₃	—	2	4	no	—
98	#125×C₈₃	—	2	4	no	—
99	#125×C₈₃	—	2	4	no	—
100	#125×C₈₃	C₂³	1	2	yes	—
101	#125×C₈₃	C₂³	1	2	yes	—
102	#124×C₈₃	—	2	4	no	—
103	#124×C₈₃	—	2	4	no	—
104	#124×C₈₃	C₂³	1	4	yes	—
105	#123×C₈₃	—	2	4	no	—
106	#123×C₈₃	—	2	4	no	—
107	#123×C₈₃	—	2	4	no	—
108	#123×C₈₃	—	2	4	no	—
109	#123×C₈₃	—	2	4	no	—
110	C₂²⋊Q₈×C₈₃	—	2	4	no	—
111	C₂²⋊Q₈×C₈₃	—	2	4	no	—
112	C₂²⋊Q₈×C₈₃	—	2	4	no	—
113	C₂²⋊Q₈×C₈₃	C₂³	1	4	yes	—
114	C₂²⋊Q₈×C₈₃	C₂³	1	4	yes	—
115	#121×C₈₃	—	2	4	no	—
116	#121×C₈₃	—	2	4	no	—
117	#121×C₈₃	—	2	4	no	—
118	#121×C₈₃	C₂³	1	4	yes	—
119	#121×C₈₃	C₂³	1	4	yes	—
120	#120×C₈₃	—	2	4	no	—
121	C₄×Q₈×C₈₃	—	2	4	no	—
122	C₄×Q₈×C₈₃	C₂³	1	4	yes	—
123	C₄×Q₈×C₈₃	C₂³	1	4	yes	—
124	C₄×D₄×C₈₃	—	2	4	no	—
125	C₄×D₄×C₈₃	—	2	4	no	—
126	C₄×D₄×C₈₃	—	2	4	no	—
127	C₄×D₄×C₈₃	—	2	4	no	—
128	C₄×D₄×C₈₃	—	2	4	no	—
129	C₄×D₄×C₈₃	C₂³	1	4	yes	—
130	C₄×D₄×C₈₃	C₂³	1	4	yes	—
131	#117×C₈₃	—	2	4	no	—
132	#117×C₈₃	D₄	1	2	yes	—
133	#117×C₈₃	D₄	1	2	yes	—
134	#117×C₈₃	C₂³	1	4	yes	—
135	#117×C₈₃	C₂³	1	1	yes	characteristic
136	#117×C₈₃	C₂³	1	2	yes	—
137	#117×C₈₃	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₈₃	D₄	1	2	yes	—
139	C₂×C₂²⋊C₄×C₈₃	D₄	1	2	yes	—
140	C₂×C₄²×C₈₃	—	2	4	no	—
141	C₂×C₄²×C₈₃	C₂³	1	2	yes	—
142	#107×C₈₃	C₂³	1	2	yes	—
143	#107×C₈₃	C₂³	1	2	yes	—
144	#107×C₈₃	C₂³	1	4	yes	—
145	#106×C₈₃	C₂³	1	4	yes	—
146	#106×C₈₃	C₂³	1	2	yes	—
147	#106×C₈₃	C₂³	1	2	yes	—
148	C₄⋊C₈×C₈₃	C₂³	1	4	yes	—
149	C₄⋊C₈×C₈₃	C₂³	1	4	yes	—
150	C₄⋊C₈×C₈₃	C₂³	1	4	yes	—
151	C₄⋊C₈×C₈₃	C₂³	1	4	yes	—
152	#103×C₈₃	C₂³	1	4	yes	—
153	#103×C₈₃	C₂³	1	4	yes	—
154	#103×C₈₃	C₂³	1	4	yes	—
155	#103×C₈₃	C₂³	1	4	yes	—
156	#102×C₈₃	C₂³	1	4	yes	—
157	#102×C₈₃	C₂³	1	4	yes	—
158	#102×C₈₃	C₂³	1	4	yes	—
159	#102×C₈₃	C₂³	1	4	yes	—
160	C₂⁴×C₈₃	C₂×D₄	1	1	yes	characteristic
161	#41×C₈₃	—	2	8	no	—
162	#41×C₈₃	—	2	8	no	—
163	C₂×Q₈×C₈₃	—	2	4	no	—
164	C₂×Q₈×C₈₃	C₂⁴	1	4	yes	—
165	C₂×D₄×C₈₃	—	2	4	no	—
166	C₂×D₄×C₈₃	—	2	4	no	—
167	C₂×D₄×C₈₃	—	2	4	no	—
168	C₂×D₄×C₈₃	—	2	4	no	—
169	C₂×D₄×C₈₃	C₂⁴	1	4	yes	—
170	C₂²×C₄×C₈₃	—	2	2	no	—
171	C₂²×C₄×C₈₃	—	2	2	no	—
172	C₂²×C₄×C₈₃	—	2	4	no	—
173	C₂²×C₄×C₈₃	—	2	4	no	—
174	C₂²×C₄×C₈₃	—	2	4	no	—
175	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₈₃	C₂×D₄	1	4	yes	—
179	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
180	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
181	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
182	Q₁₆×C₈₃	—	4	2	no	—
183	Q₁₆×C₈₃	—	4	2	no	—
184	SD₁₆×C₈₃	—	4	4	no	—
185	SD₁₆×C₈₃	—	4	4	no	—
186	D₈×C₈₃	—	4	2	no	—
187	D₈×C₈₃	—	4	2	no	—
188	M₁₆×C₈₃	—	4	1	no	—
189	M₁₆×C₈₃	—	4	2	no	—
190	M₁₆×C₈₃	—	4	1	no	—
191	C₂×C₈×C₈₃	—	2	4	no	—
192	C₂×C₈×C₈₃	—	2	4	no	—
193	C₂×C₈×C₈₃	—	4	1	no	—
194	C₂×C₈×C₈₃	—	4	2	no	—
195	C₂×C₈×C₈₃	—	4	1	no	—
196	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
197	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
198	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
199	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
200	C₄⋊C₄×C₈₃	—	2	4	no	—
201	C₄⋊C₄×C₈₃	—	2	4	no	—
202	C₄⋊C₄×C₈₃	—	2	4	no	—
203	C₄⋊C₄×C₈₃	—	2	4	no	—
204	C₄⋊C₄×C₈₃	—	2	4	no	—
205	C₄⋊C₄×C₈₃	—	2	4	no	—
206	C₄⋊C₄×C₈₃	—	2	4	no	—
207	C₄⋊C₄×C₈₃	—	2	4	no	—
208	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
209	C₄⋊C₄×C₈₃	C₂×D₄	1	4	yes	—
210	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
211	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
212	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
213	C₂²⋊C₄×C₈₃	—	2	4	no	—
214	C₂²⋊C₄×C₈₃	—	2	4	no	—
215	C₂²⋊C₄×C₈₃	—	2	4	no	—
216	C₂²⋊C₄×C₈₃	—	2	4	no	—
217	C₂²⋊C₄×C₈₃	—	2	4	no	—
218	C₂²⋊C₄×C₈₃	—	2	4	no	—
219	C₂²⋊C₄×C₈₃	—	2	4	no	—
220	C₂²⋊C₄×C₈₃	—	2	4	no	—
221	C₂²⋊C₄×C₈₃	—	2	4	no	—
222	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
223	C₂²⋊C₄×C₈₃	C₂×D₄	1	4	yes	—
224	C₂²⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
225	C₄²×C₈₃	—	2	4	no	—
226	C₄²×C₈₃	—	2	4	no	—
227	C₄²×C₈₃	—	2	4	no	—
228	C₄²×C₈₃	C₂×D₄	1	4	yes	—
229	C₄²×C₈₃	C₂⁴	1	2	yes	—
230	C₄²×C₈₃	C₂⁴	1	2	yes	—
231	C₂³×C₈₃	—	2	2	no	—
232	C₂³×C₈₃	—	2	4	no	—
233	C₂³×C₈₃	—	4	2	no	—
234	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
235	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
236	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
237	Q₈×C₈₃	—	2	4	no	—
238	Q₈×C₈₃	—	2	4	no	—
239	Q₈×C₈₃	—	8	4	no	—
240	D₄×C₈₃	—	2	4	no	—
241	D₄×C₈₃	—	2	4	no	—
242	D₄×C₈₃	—	4	8	no	—
243	D₄×C₈₃	—	8	4	no	—
244	D₄×C₈₃	—	8	4	no	—
245	D₄×C₈₃	—	8	4	no	—
246	C₂×C₄×C₈₃	—	2	2	no	—
247	C₂×C₄×C₈₃	—	2	2	no	—
248	C₂×C₄×C₈₃	—	2	2	no	—
249	C₂×C₄×C₈₃	—	2	1	no	—
250	C₂×C₄×C₈₃	—	2	1	no	—
251	C₂×C₄×C₈₃	—	2	1	no	—
252	C₂×C₄×C₈₃	—	2	1	no	—
253	C₂×C₄×C₈₃	—	2	4	no	—
254	C₂×C₄×C₈₃	—	2	4	no	—
255	C₂×C₄×C₈₃	—	2	4	no	—
256	C₂×C₄×C₈₃	—	4	4	no	—
257	C₂×C₄×C₈₃	—	4	8	no	—
258	C₂×C₄×C₈₃	—	8	4	no	—
259	C₂×C₄×C₈₃	—	8	4	no	—
260	C₂×C₄×C₈₃	C₂²×D₄	1	4	yes	—
261	C₂×C₄×C₈₃	C₂²×D₄	1	4	yes	—
262	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₈₃	H(5,𝔽₂)	1	2	yes	—
266	C₂×C₄×C₈₃	2₋¹⁺⁴	1	2	yes	—
267	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
268	C₈×C₈₃	—	2	2	no	—
269	C₈×C₈₃	—	2	2	no	—
270	C₈×C₈₃	—	2	2	no	—
271	C₈×C₈₃	—	2	2	no	—
272	C₂²×C₈₃	—	2	2	no	—
273	C₂²×C₈₃	—	2	2	no	—
274	C₂²×C₈₃	—	2	2	no	—
275	C₂²×C₈₃	—	2	1	no	—
276	C₂²×C₈₃	—	2	1	no	—
277	C₂²×C₈₃	—	4	4	no	—
278	C₂²×C₈₃	—	4	4	no	—
279	C₂²×C₈₃	—	4	4	no	—
280	C₂²×C₈₃	—	4	4	no	—
281	C₂²×C₈₃	#537	1	2	yes	—
282	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
283	C₄×C₈₃	—	2	4	no	—
284	C₄×C₈₃	—	2	4	no	—
285	C₄×C₈₃	—	2	1	no	—
286	C₄×C₈₃	—	2	1	no	—
287	C₄×C₈₃	—	4	4	no	—
288	C₄×C₈₃	—	4	4	no	—
289	C₄×C₈₃	—	4	4	no	—
290	C₄×C₈₃	#537	1	2	yes	—
291	C₄×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
292	C₄×C₈₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
293	#60915	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
294	C₂×C₈₃	—	2	2	no	—
295	C₂×C₈₃	—	4	1	no	—
296	C₂×C₈₃	—	4	1	no	—
297	C₂×C₈₃	—	8	4	no	—
298	C₂×C₈₃	C₂×#537	1	1	yes	characteristic
299	C₂×C₈₃	#3584	1	2	yes	—
300	#3455	C₂×C₈₃	1	2	yes	complemented
301	#3263	C₂×C₈₃	1	2	yes	complemented
302	#3262	C₂×C₈₃	1	2	yes	complemented
303	#3261	C₂×C₈₃	1	1	yes	characteristic, complemented
304	#3260	C₂×C₈₃	1	2	yes	complemented
305	#3259	C₂×C₈₃	1	1	yes	characteristic, complemented
306	#3258	C₂×C₈₃	1	4	yes	complemented
307	#3257	C₂×C₈₃	1	4	yes	complemented
308	#3076	C₂×C₈₃	1	4	yes	complemented
309	#3054	C₂×C₈₃	1	2	yes	complemented
310	#3050	C₂×C₈₃	1	2	yes	complemented
311	#3035	C₂×C₈₃	1	4	yes	complemented
312	C₂×#424	C₂×C₈₃	1	1	yes	characteristic, complemented
313	C₈₃	#60915	1	1	yes	characteristic, direct product factor, Sylow
314	C₂×#135	C₂²×C₈₃	1	2	yes	—
315	C₂×#135	C₂²×C₈₃	1	2	yes	—
316	C₂²×M₁₆	C₂²×C₈₃	1	1	yes	characteristic
317	C₂³×C₈	C₂²×C₈₃	1	1	yes	characteristic
318	#542	C₂²×C₈₃	1	4	yes	—
319	#542	C₂²×C₈₃	1	4	yes	—
320	#541	C₂²×C₈₃	1	2	yes	—
321	#541	C₂²×C₈₃	1	2	yes	—
322	#540	C₂²×C₈₃	1	2	yes	—
323	#540	C₂²×C₈₃	1	2	yes	—
324	#539	—	2	4	no	—
325	#538	—	2	4	no	—
326	#533	C₂²×C₈₃	1	2	yes	—
327	#532	C₂²×C₈₃	1	2	yes	—
328	#529	—	2	4	no	—
329	#529	—	2	4	no	—
330	#525	C₂²×C₈₃	1	4	yes	—
331	C₄×#41	C₂²×C₈₃	1	4	yes	—
332	C₂×#117	C₂²×C₈₃	1	1	yes	characteristic
333	#479	C₂²×C₈₃	1	4	yes	complemented
334	#479	C₂²×C₈₃	1	4	yes	complemented
335	#478	C₂²×C₈₃	1	4	yes	complemented
336	#478	C₂²×C₈₃	1	4	yes	complemented
337	#477	C₂²×C₈₃	1	4	yes	complemented
338	#476	C₂²×C₈₃	1	4	yes	complemented
339	#475	C₂²×C₈₃	1	4	yes	complemented
340	#474	C₂²×C₈₃	1	4	yes	complemented
341	#470	C₂²×C₈₃	1	2	yes	—
342	#470	C₂²×C₈₃	1	2	yes	—
343	#469	C₂²×C₈₃	1	2	yes	—
344	#469	C₂²×C₈₃	1	2	yes	—
345	#468	C₂²×C₈₃	1	4	yes	—
346	#468	C₂²×C₈₃	1	4	yes	—
347	#467	C₂²×C₈₃	1	2	yes	—
348	#467	C₂²×C₈₃	1	2	yes	—
349	#466	C₂²×C₈₃	1	2	yes	—
350	#466	C₂²×C₈₃	1	2	yes	—
351	#465	C₂²×C₈₃	1	4	yes	—
352	#465	C₂²×C₈₃	1	4	yes	—
353	#464	C₂²×C₈₃	1	4	yes	complemented
354	#464	C₂²×C₈₃	1	4	yes	complemented
355	#463	C₂²×C₈₃	1	4	yes	complemented
356	#463	C₂²×C₈₃	1	4	yes	complemented
357	#462	C₂²×C₈₃	1	4	yes	complemented
358	#461	C₂²×C₈₃	1	4	yes	complemented
359	#460	C₂²×C₈₃	1	4	yes	complemented
360	#459	C₂²×C₈₃	1	4	yes	complemented
361	#427	C₂²×C₈₃	1	2	yes	—
362	#427	C₂²×C₈₃	1	2	yes	—
363	#424	C₂²×C₈₃	1	4	yes	—
364	#424	C₂²×C₈₃	1	1	yes	characteristic
365	#424	C₂²×C₈₃	1	1	yes	characteristic
366	#424	C₂²×C₈₃	1	1	yes	characteristic
367	#424	C₂²×C₈₃	1	1	yes	characteristic
368	C₂×C₄⋊C₈	C₂²×C₈₃	1	4	yes	—
369	#416	C₂²×C₈₃	1	4	yes	—
370	#416	C₂²×C₈₃	1	4	yes	—
371	C₂×#41	C₂³×C₈₃	1	4	yes	—
372	C₂³×C₄	C₂³×C₈₃	1	1	yes	characteristic
373	#135	—	4	4	no	—
374	#135	—	4	4	no	—
375	C₂×Q₁₆	C₂³×C₈₃	1	2	yes	—
376	C₂×Q₁₆	C₂³×C₈₃	1	2	yes	—
377	C₂×SD₁₆	C₂³×C₈₃	1	4	yes	—
378	C₂×SD₁₆	C₂³×C₈₃	1	4	yes	—
379	C₂×D₈	C₂³×C₈₃	1	2	yes	—
380	C₂×D₈	C₂³×C₈₃	1	2	yes	—
381	C₂×M₁₆	—	4	2	no	—
382	C₂×M₁₆	C₂³×C₈₃	1	1	yes	characteristic
383	C₂×M₁₆	C₂³×C₈₃	1	2	yes	—
384	C₂×M₁₆	C₂³×C₈₃	1	1	yes	characteristic
385	C₂²×C₈	—	4	2	no	—
386	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
387	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
388	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
389	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
390	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
391	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
392	C₄⋊Q₈	C₂³×C₈₃	1	4	yes	—
393	#127	C₂³×C₈₃	1	2	yes	—
394	#126	—	2	4	no	—
395	#126	—	2	4	no	—
396	#126	—	2	4	no	—
397	#126	—	2	4	no	—
398	#125	—	2	4	no	—
399	#125	—	2	4	no	—
400	#125	C₂³×C₈₃	1	2	yes	—
401	#125	C₂³×C₈₃	1	2	yes	—
402	#124	—	2	4	no	—
403	#124	—	2	4	no	—
404	#124	C₂³×C₈₃	1	4	yes	—
405	#123	—	2	4	no	—
406	#123	—	2	4	no	—
407	#123	—	2	4	no	—
408	#123	—	2	4	no	—
409	#123	—	2	4	no	—
410	C₂²⋊Q₈	—	2	4	no	—
411	C₂²⋊Q₈	—	2	4	no	—
412	C₂²⋊Q₈	—	2	4	no	—
413	C₂²⋊Q₈	C₂³×C₈₃	1	4	yes	—
414	C₂²⋊Q₈	C₂³×C₈₃	1	4	yes	—
415	#121	—	2	4	no	—
416	#121	—	2	4	no	—
417	#121	—	2	4	no	—
418	#121	C₂³×C₈₃	1	4	yes	—
419	#121	C₂³×C₈₃	1	4	yes	—
420	#120	—	2	4	no	—
421	C₄×Q₈	—	2	4	no	—
422	C₄×Q₈	C₂³×C₈₃	1	4	yes	—
423	C₄×Q₈	C₂³×C₈₃	1	4	yes	—
424	C₄×D₄	—	2	4	no	—
425	C₄×D₄	—	2	4	no	—
426	C₄×D₄	—	2	4	no	—
427	C₄×D₄	—	2	4	no	—
428	C₄×D₄	—	2	4	no	—
429	C₄×D₄	C₂³×C₈₃	1	4	yes	—
430	C₄×D₄	C₂³×C₈₃	1	4	yes	—
431	#117	—	2	4	no	—
432	#117	D₄×C₈₃	1	2	yes	—
433	#117	D₄×C₈₃	1	2	yes	—
434	#117	C₂³×C₈₃	1	4	yes	—
435	#117	C₂³×C₈₃	1	1	yes	characteristic
436	#117	C₂³×C₈₃	1	2	yes	—
437	#117	C₂³×C₈₃	1	1	yes	characteristic
438	C₂×C₄⋊C₄	D₄×C₈₃	1	2	yes	—
439	C₂×C₂²⋊C₄	D₄×C₈₃	1	2	yes	—
440	C₂×C₄²	—	2	4	no	—
441	C₂×C₄²	C₂³×C₈₃	1	2	yes	—
442	#107	C₂³×C₈₃	1	2	yes	—
443	#107	C₂³×C₈₃	1	2	yes	—
444	#107	C₂³×C₈₃	1	4	yes	—
445	#106	C₂³×C₈₃	1	4	yes	—
446	#106	C₂³×C₈₃	1	2	yes	—
447	#106	C₂³×C₈₃	1	2	yes	—
448	C₄⋊C₈	C₂³×C₈₃	1	4	yes	—
449	C₄⋊C₈	C₂³×C₈₃	1	4	yes	—
450	C₄⋊C₈	C₂³×C₈₃	1	4	yes	—
451	C₄⋊C₈	C₂³×C₈₃	1	4	yes	—
452	#103	C₂³×C₈₃	1	4	yes	—
453	#103	C₂³×C₈₃	1	4	yes	—
454	#103	C₂³×C₈₃	1	4	yes	—
455	#103	C₂³×C₈₃	1	4	yes	—
456	#102	C₂³×C₈₃	1	4	yes	—
457	#102	C₂³×C₈₃	1	4	yes	—
458	#102	C₂³×C₈₃	1	4	yes	—
459	#102	C₂³×C₈₃	1	4	yes	—
460	C₂⁴	C₂×D₄×C₈₃	1	1	yes	characteristic
461	#41	—	2	8	no	—
462	#41	—	2	8	no	—
463	C₂×Q₈	—	2	4	no	—
464	C₂×Q₈	C₂⁴×C₈₃	1	4	yes	—
465	C₂×D₄	—	2	4	no	—
466	C₂×D₄	—	2	4	no	—
467	C₂×D₄	—	2	4	no	—
468	C₂×D₄	—	2	4	no	—
469	C₂×D₄	C₂⁴×C₈₃	1	4	yes	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	4	no	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	4	no	—
475	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
476	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₄×C₈₃	1	4	yes	—
479	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
480	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
481	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
482	Q₁₆	—	4	2	no	—
483	Q₁₆	—	4	2	no	—
484	SD₁₆	—	4	4	no	—
485	SD₁₆	—	4	4	no	—
486	D₈	—	4	2	no	—
487	D₈	—	4	2	no	—
488	M₁₆	—	4	1	no	—
489	M₁₆	—	4	2	no	—
490	M₁₆	—	4	1	no	—
491	C₂×C₈	—	2	4	no	—
492	C₂×C₈	—	2	4	no	—
493	C₂×C₈	—	4	1	no	—
494	C₂×C₈	—	4	2	no	—
495	C₂×C₈	—	4	1	no	—
496	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
497	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
498	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
499	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
500	C₄⋊C₄	—	2	4	no	—
501	C₄⋊C₄	—	2	4	no	—
502	C₄⋊C₄	—	2	4	no	—
503	C₄⋊C₄	—	2	4	no	—
504	C₄⋊C₄	—	2	4	no	—
505	C₄⋊C₄	—	2	4	no	—
506	C₄⋊C₄	—	2	4	no	—
507	C₄⋊C₄	—	2	4	no	—
508	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
509	C₄⋊C₄	C₂×D₄×C₈₃	1	4	yes	—
510	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
511	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
512	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
513	C₂²⋊C₄	—	2	4	no	—
514	C₂²⋊C₄	—	2	4	no	—
515	C₂²⋊C₄	—	2	4	no	—
516	C₂²⋊C₄	—	2	4	no	—
517	C₂²⋊C₄	—	2	4	no	—
518	C₂²⋊C₄	—	2	4	no	—
519	C₂²⋊C₄	—	2	4	no	—
520	C₂²⋊C₄	—	2	4	no	—
521	C₂²⋊C₄	—	2	4	no	—
522	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
523	C₂²⋊C₄	C₂×D₄×C₈₃	1	4	yes	—
524	C₂²⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
525	C₄²	—	2	4	no	—
526	C₄²	—	2	4	no	—
527	C₄²	—	2	4	no	—
528	C₄²	C₂×D₄×C₈₃	1	4	yes	—
529	C₄²	C₂⁴×C₈₃	1	2	yes	—
530	C₄²	C₂⁴×C₈₃	1	2	yes	—
531	C₂³	—	2	2	no	—
532	C₂³	—	2	4	no	—
533	C₂³	—	4	2	no	—
534	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
535	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
536	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
537	Q₈	—	2	4	no	—
538	Q₈	—	2	4	no	—
539	Q₈	—	8	4	no	—
540	D₄	—	2	4	no	—
541	D₄	—	2	4	no	—
542	D₄	—	4	8	no	—
543	D₄	—	8	4	no	—
544	D₄	—	8	4	no	—
545	D₄	—	8	4	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	4	4	no	—
557	C₂×C₄	—	4	8	no	—
558	C₂×C₄	—	8	4	no	—
559	C₂×C₄	—	8	4	no	—
560	C₂×C₄	C₂²×D₄×C₈₃	1	4	yes	—
561	C₂×C₄	C₂²×D₄×C₈₃	1	4	yes	—
562	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
563	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
564	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
565	C₂×C₄	H(5,𝔽₂)×C₈₃	1	2	yes	—
566	C₂×C₄	2₋¹⁺⁴×C₈₃	1	2	yes	—
567	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
568	C₈	—	2	2	no	—
569	C₈	—	2	2	no	—
570	C₈	—	2	2	no	—
571	C₈	—	2	2	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	4	4	no	—
578	C₂²	—	4	4	no	—
579	C₂²	—	4	4	no	—
580	C₂²	—	4	4	no	—
581	C₂²	#537×C₈₃	1	2	yes	—
582	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
583	C₄	—	2	4	no	—
584	C₄	—	2	4	no	—
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	4	4	no	—
588	C₄	—	4	4	no	—
589	C₄	—	4	4	no	—
590	C₄	#537×C₈₃	1	2	yes	—
591	C₄	C₂×H(5,𝔽₂)×C₈₃	1	1	yes	characteristic
592	C₄	C₂×2₋¹⁺⁴×C₈₃	1	1	yes	characteristic
593	C₂	—	2	2	no	—
594	C₂	—	4	1	no	—
595	C₂	—	4	1	no	—
596	C₂	—	8	4	no	—
597	C₂	C₂×#537×C₈₃	1	1	yes	characteristic
598	C₂	C₈₃×#3584	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₈₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₃
socle	C₂²×C₈₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₈₃ ◁ C₂×#117×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₃×#3455	C₂	semidirect
2. C₈₃×#3263	C₂	semidirect
3. C₈₃×#3262	C₂	semidirect
4. C₈₃×#3261	C₂	semidirect
5. C₈₃×#3260	C₂	semidirect
6. C₈₃×#3259	C₂	semidirect
7. C₈₃×#3258	C₂	semidirect
8. C₈₃×#3257	C₂	semidirect
9. C₈₃×#3076	C₂	semidirect
10. C₈₃×#3054	C₂	semidirect
11. C₈₃×#3050	C₂	semidirect
12. C₈₃×#3035	C₂	semidirect
13. C₂×#424×C₈₃	C₂	semidirect
33. #479×C₈₃	C₂²	semidirect
34. #479×C₈₃	C₂²	semidirect
35. #478×C₈₃	C₂²	semidirect
36. #478×C₈₃	C₂²	semidirect
37. #477×C₈₃	C₂²	semidirect
38. #476×C₈₃	C₂²	semidirect
39. #475×C₈₃	C₂²	semidirect
40. #474×C₈₃	C₂²	semidirect
53. #464×C₈₃	C₂²	semidirect
54. #464×C₈₃	C₂²	semidirect
55. #463×C₈₃	C₂²	semidirect
56. #463×C₈₃	C₂²	semidirect
57. #462×C₈₃	C₂²	semidirect
58. #461×C₈₃	C₂²	semidirect
59. #460×C₈₃	C₂²	semidirect
60. #459×C₈₃	C₂²	semidirect
293. #60915	C₈₃	direct (N × H)
300. #3455	C₂×C₈₃	semidirect
301. #3263	C₂×C₈₃	semidirect
302. #3262	C₂×C₈₃	semidirect
303. #3261	C₂×C₈₃	semidirect
304. #3260	C₂×C₈₃	semidirect
305. #3259	C₂×C₈₃	semidirect
306. #3258	C₂×C₈₃	semidirect
307. #3257	C₂×C₈₃	semidirect
308. #3076	C₂×C₈₃	semidirect
309. #3054	C₂×C₈₃	semidirect
310. #3050	C₂×C₈₃	semidirect
311. #3035	C₂×C₈₃	semidirect
312. C₂×#424	C₂×C₈₃	semidirect
313. C₈₃	#60915	direct (N × H)
333. #479	C₂²×C₈₃	semidirect
334. #479	C₂²×C₈₃	semidirect
335. #478	C₂²×C₈₃	semidirect
336. #478	C₂²×C₈₃	semidirect
337. #477	C₂²×C₈₃	semidirect
338. #476	C₂²×C₈₃	semidirect
339. #475	C₂²×C₈₃	semidirect
340. #474	C₂²×C₈₃	semidirect
353. #464	C₂²×C₈₃	semidirect
354. #464	C₂²×C₈₃	semidirect
355. #463	C₂²×C₈₃	semidirect
356. #463	C₂²×C₈₃	semidirect
357. #462	C₂²×C₈₃	semidirect
358. #461	C₂²×C₈₃	semidirect
359. #460	C₂²×C₈₃	semidirect
360. #459	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×#3455	2
C₈₃×#3263	2
C₈₃×#3262	2
C₈₃×#3261	2
C₈₃×#3260	2
C₈₃×#3259	2
C₈₃×#3258	2
C₈₃×#3257	2
C₈₃×#3076	2
C₈₃×#3054	2
C₈₃×#3050	2
C₈₃×#3035	2
C₂×#424×C₈₃	2
#60915	83

Subgroups — C83×#60915 #35288739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#60915 #35288739