Subgroups — C₈₃×#61797 #35289621

Order 21248.

1802 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3549	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₃×#3512	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₃×#3348	C₂	1	4	yes	maximal, complemented
4	C₈₃×#3347	C₂	1	4	yes	maximal, complemented
5	C₈₃×#3318	C₂	1	4	yes	maximal, complemented
6	C₈₃×#3310	C₂	1	4	yes	maximal, complemented
7	C₈₃×#3234	C₂	1	2	yes	maximal, complemented
8	C₈₃×#3198	C₂	1	4	yes	maximal, complemented
9	C₈₃×#3115	C₂	1	2	yes	maximal, complemented
10	C₈₃×#3096	C₂	1	4	yes	maximal, complemented
11	C₈₃×#2980	C₂	1	1	yes	maximal, characteristic, complemented
12	H(3,𝔽₄)×C₈₃	—	2	2	no	—
13	#555×C₈₃	—	2	1	no	—
14	#555×C₈₃	C₂²	1	4	yes	—
15	#553×C₈₃	—	2	4	no	—
16	#553×C₈₃	C₂²	1	4	yes	complemented
17	#552×C₈₃	C₂²	1	4	yes	complemented
18	D₄²×C₈₃	—	2	1	no	—
19	D₄²×C₈₃	C₂²	1	4	yes	—
20	#541×C₈₃	—	2	1	no	—
21	#540×C₈₃	—	2	1	no	—
22	#537×C₈₃	C₂²	1	2	yes	complemented
23	#535×C₈₃	—	2	4	no	—
24	#535×C₈₃	C₂²	1	4	yes	—
25	#532×C₈₃	C₂²	1	2	yes	—
26	#532×C₈₃	C₂²	1	1	yes	characteristic
27	#529×C₈₃	—	2	2	no	—
28	C₂×#125×C₈₃	C₂²	1	1	yes	characteristic, complemented
29	#520×C₈₃	C₂²	1	2	yes	complemented
30	C₄×#41×C₈₃	C₂²	1	1	yes	characteristic, complemented
31	#501×C₈₃	C₂²	1	4	yes	complemented
32	#490×C₈₃	C₂²	1	4	yes	—
33	#485×C₈₃	C₂²	1	4	yes	complemented
34	#482×C₈₃	C₂²	1	4	yes	complemented
35	#482×C₈₃	C₂²	1	4	yes	complemented
36	#482×C₈₃	C₂²	1	4	yes	complemented
37	#482×C₈₃	C₂²	1	4	yes	complemented
38	#481×C₈₃	C₂²	1	4	yes	complemented
39	#481×C₈₃	C₂²	1	4	yes	complemented
40	#480×C₈₃	C₂²	1	4	yes	complemented
41	#480×C₈₃	C₂²	1	4	yes	complemented
42	#478×C₈₃	C₂²	1	4	yes	complemented
43	#478×C₈₃	C₂²	1	4	yes	complemented
44	#475×C₈₃	C₂²	1	2	yes	complemented
45	#474×C₈₃	C₂²	1	2	yes	complemented
46	#469×C₈₃	C₂²	1	4	yes	complemented
47	#468×C₈₃	C₂²	1	4	yes	complemented
48	#466×C₈₃	C₂²	1	4	yes	complemented
49	#465×C₈₃	C₂²	1	4	yes	complemented
50	#460×C₈₃	C₂²	1	2	yes	—
51	#459×C₈₃	C₂²	1	2	yes	—
52	#450×C₈₃	C₂²	1	4	yes	complemented
53	#449×C₈₃	C₂²	1	4	yes	complemented
54	#447×C₈₃	C₂²	1	4	yes	complemented
55	#442×C₈₃	C₂²	1	4	yes	complemented
56	#440×C₈₃	C₂²	1	4	yes	complemented
57	#435×C₈₃	C₂²	1	4	yes	complemented
58	#435×C₈₃	C₂²	1	4	yes	complemented
59	#432×C₈₃	C₂²	1	2	yes	complemented
60	#428×C₈₃	C₂²	1	4	yes	complemented
61	#427×C₈₃	C₂²	1	4	yes	complemented
62	#418×C₈₃	C₂²	1	4	yes	complemented
63	C₂×#102×C₈₃	C₂²	1	4	yes	complemented
64	#408×C₈₃	C₂²	1	4	yes	complemented
65	C₂×#41×C₈₃	—	2	2	no	—
66	C₂×#41×C₈₃	C₂³	1	1	yes	characteristic
67	C₂×#41×C₈₃	C₂³	1	2	yes	—
68	C₂²×D₄×C₈₃	—	2	4	no	—
69	C₂²×D₄×C₈₃	C₂³	1	4	yes	—
70	C₂×SD₁₆×C₈₃	C₂³	1	4	yes	—
71	C₂×D₈×C₈₃	C₂³	1	4	yes	—
72	C₂×M₁₆×C₈₃	C₂³	1	4	yes	—
73	C₂²×C₈×C₈₃	C₂³	1	4	yes	—
74	C₄⋊Q₈×C₈₃	D₄	1	1	yes	characteristic
75	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
76	#127×C₈₃	—	2	4	no	—
77	#127×C₈₃	D₄	1	1	yes	characteristic
78	#127×C₈₃	C₂³	1	2	yes	—
79	#126×C₈₃	—	2	4	no	—
80	#126×C₈₃	—	2	4	no	—
81	#125×C₈₃	—	2	4	no	—
82	#125×C₈₃	—	2	1	no	—
83	#125×C₈₃	—	2	1	no	—
84	#125×C₈₃	C₂³	1	4	yes	—
85	#124×C₈₃	—	2	4	no	—
86	#124×C₈₃	—	2	4	no	—
87	#124×C₈₃	—	2	4	no	—
88	#124×C₈₃	—	2	2	no	—
89	#124×C₈₃	D₄	1	2	yes	—
90	#123×C₈₃	—	2	4	no	—
91	#123×C₈₃	—	2	4	no	—
92	C₂²⋊Q₈×C₈₃	—	2	2	no	—
93	C₂²⋊Q₈×C₈₃	C₂³	1	4	yes	—
94	#121×C₈₃	—	2	2	no	—
95	#121×C₈₃	—	2	4	no	—
96	#121×C₈₃	—	2	4	no	—
97	#121×C₈₃	—	2	4	no	—
98	#121×C₈₃	—	2	2	no	—
99	#121×C₈₃	—	2	4	no	—
100	#121×C₈₃	D₄	1	4	yes	—
101	#121×C₈₃	C₂³	1	4	yes	—
102	#121×C₈₃	C₂³	1	4	yes	—
103	#121×C₈₃	C₂³	1	4	yes	—
104	#121×C₈₃	C₂³	1	4	yes	—
105	#120×C₈₃	—	2	4	no	—
106	#120×C₈₃	—	2	4	no	—
107	#120×C₈₃	—	2	4	no	—
108	#120×C₈₃	—	2	4	no	—
109	C₄×Q₈×C₈₃	—	2	2	no	—
110	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
111	C₄×D₄×C₈₃	—	2	2	no	—
112	C₄×D₄×C₈₃	—	2	4	no	—
113	C₄×D₄×C₈₃	—	2	2	no	—
114	C₄×D₄×C₈₃	—	2	4	no	—
115	C₄×D₄×C₈₃	—	2	2	no	—
116	C₄×D₄×C₈₃	C₂³	1	2	yes	—
117	C₄×D₄×C₈₃	C₂³	1	4	yes	—
118	C₄×D₄×C₈₃	C₂³	1	4	yes	—
119	#117×C₈₃	—	2	4	no	—
120	#117×C₈₃	—	2	4	no	—
121	#117×C₈₃	—	2	1	no	—
122	#117×C₈₃	C₂³	1	1	yes	characteristic
123	#117×C₈₃	C₂³	1	4	yes	—
124	#117×C₈₃	C₂³	1	4	yes	—
125	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
126	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₈₃	C₂³	1	4	yes	—
128	C₂×C₄²×C₈₃	—	2	1	no	—
129	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
130	#107×C₈₃	C₂³	1	4	yes	—
131	#107×C₈₃	C₂³	1	4	yes	—
132	#107×C₈₃	C₂³	1	4	yes	—
133	#106×C₈₃	C₂³	1	4	yes	—
134	#106×C₈₃	C₂³	1	4	yes	—
135	#106×C₈₃	C₂³	1	4	yes	—
136	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
137	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
138	#103×C₈₃	C₂³	1	4	yes	—
139	#102×C₈₃	C₂³	1	4	yes	—
140	#102×C₈₃	C₂³	1	4	yes	—
141	#102×C₈₃	C₂³	1	4	yes	—
142	#102×C₈₃	C₂³	1	4	yes	—
143	#102×C₈₃	C₂³	1	4	yes	—
144	#102×C₈₃	C₂³	1	4	yes	—
145	#102×C₈₃	C₂³	1	4	yes	—
146	C₂²⋊C₈×C₈₃	C₂³	1	4	yes	—
147	C₂²⋊C₈×C₈₃	C₂³	1	4	yes	—
148	C₂²⋊C₈×C₈₃	C₂³	1	4	yes	—
149	#97×C₈₃	C₂³	1	4	yes	—
150	C₂⁴×C₈₃	—	2	4	no	—
151	#41×C₈₃	—	4	2	no	—
152	#41×C₈₃	—	4	2	no	—
153	#41×C₈₃	—	4	2	no	—
154	#41×C₈₃	—	8	4	no	—
155	C₂×Q₈×C₈₃	—	2	2	no	—
156	C₂×Q₈×C₈₃	C₂×D₄	1	2	yes	—
157	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
158	C₂×D₄×C₈₃	—	2	1	no	—
159	C₂×D₄×C₈₃	—	2	4	no	—
160	C₂×D₄×C₈₃	—	2	4	no	—
161	C₂×D₄×C₈₃	—	2	4	no	—
162	C₂×D₄×C₈₃	—	2	4	no	—
163	C₂×D₄×C₈₃	—	2	2	no	—
164	C₂×D₄×C₈₃	—	2	2	no	—
165	C₂×D₄×C₈₃	—	2	4	no	—
166	C₂×D₄×C₈₃	—	4	4	no	—
167	C₂×D₄×C₈₃	—	4	4	no	—
168	C₂×D₄×C₈₃	—	8	8	no	—
169	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
170	C₂×D₄×C₈₃	C₂×D₄	1	4	yes	—
171	C₂×D₄×C₈₃	C₂×D₄	1	4	yes	—
172	C₂×D₄×C₈₃	C₂⁴	1	4	yes	—
173	C₂×D₄×C₈₃	C₂⁴	1	1	yes	characteristic
174	C₂²×C₄×C₈₃	—	2	2	no	—
175	C₂²×C₄×C₈₃	—	2	4	no	—
176	C₂²×C₄×C₈₃	—	2	1	no	—
177	C₂²×C₄×C₈₃	—	2	4	no	—
178	C₂²×C₄×C₈₃	—	2	2	no	—
179	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
180	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
181	C₂²×C₄×C₈₃	C₂⁴	1	4	yes	—
182	SD₁₆×C₈₃	—	4	4	no	—
183	D₈×C₈₃	—	4	4	no	—
184	M₁₆×C₈₃	—	4	4	no	—
185	C₂×C₈×C₈₃	—	4	4	no	—
186	C₂×C₈×C₈₃	C₂⁴	1	4	yes	—
187	C₂×C₈×C₈₃	C₂⁴	1	4	yes	—
188	C₄⋊C₄×C₈₃	—	2	4	no	—
189	C₄⋊C₄×C₈₃	—	2	4	no	—
190	C₄⋊C₄×C₈₃	—	2	2	no	—
191	C₄⋊C₄×C₈₃	—	2	4	no	—
192	C₄⋊C₄×C₈₃	—	2	2	no	—
193	C₄⋊C₄×C₈₃	—	2	2	no	—
194	C₄⋊C₄×C₈₃	—	2	4	no	—
195	C₄⋊C₄×C₈₃	C₂×D₄	1	4	yes	—
196	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
197	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
198	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
199	C₂²⋊C₄×C₈₃	—	2	4	no	—
200	C₂²⋊C₄×C₈₃	—	2	1	no	—
201	C₂²⋊C₄×C₈₃	—	2	4	no	—
202	C₂²⋊C₄×C₈₃	—	2	4	no	—
203	C₂²⋊C₄×C₈₃	—	2	2	no	—
204	C₂²⋊C₄×C₈₃	—	2	4	no	—
205	C₂²⋊C₄×C₈₃	—	2	4	no	—
206	C₂²⋊C₄×C₈₃	—	2	4	no	—
207	C₂²⋊C₄×C₈₃	—	2	4	no	—
208	C₂²⋊C₄×C₈₃	—	2	4	no	—
209	C₂²⋊C₄×C₈₃	C₂×D₄	1	4	yes	—
210	C₂²⋊C₄×C₈₃	C₂×D₄	1	4	yes	—
211	C₄²×C₈₃	—	2	2	no	—
212	C₄²×C₈₃	—	2	1	no	—
213	C₄²×C₈₃	—	2	4	no	—
214	C₄²×C₈₃	—	2	4	no	—
215	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
216	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
217	C₄²×C₈₃	C₂⁴	1	2	yes	—
218	C₂³×C₈₃	—	2	1	no	—
219	C₂³×C₈₃	—	2	4	no	—
220	C₂³×C₈₃	—	8	4	no	—
221	C₂³×C₈₃	—	8	4	no	—
222	C₂³×C₈₃	—	8	4	no	—
223	C₂³×C₈₃	C₂²×D₄	1	4	yes	—
224	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
225	Q₈×C₈₃	—	2	2	no	—
226	Q₈×C₈₃	—	4	2	no	—
227	Q₈×C₈₃	—	8	2	no	—
228	D₄×C₈₃	—	2	2	no	—
229	D₄×C₈₃	—	2	4	no	—
230	D₄×C₈₃	—	2	4	no	—
231	D₄×C₈₃	—	4	4	no	—
232	D₄×C₈₃	—	4	2	no	—
233	D₄×C₈₃	—	4	4	no	—
234	D₄×C₈₃	—	4	4	no	—
235	D₄×C₈₃	—	4	2	no	—
236	D₄×C₈₃	—	8	4	no	—
237	D₄×C₈₃	—	8	2	no	—
238	D₄×C₈₃	—	8	4	no	—
239	D₄×C₈₃	—	8	4	no	—
240	D₄×C₈₃	—	8	4	no	—
241	D₄×C₈₃	—	8	4	no	—
242	C₂×C₄×C₈₃	—	2	4	no	—
243	C₂×C₄×C₈₃	—	2	4	no	—
244	C₂×C₄×C₈₃	—	2	2	no	—
245	C₂×C₄×C₈₃	—	2	2	no	—
246	C₂×C₄×C₈₃	—	2	4	no	—
247	C₂×C₄×C₈₃	—	2	1	no	—
248	C₂×C₄×C₈₃	—	2	4	no	—
249	C₂×C₄×C₈₃	—	4	2	no	—
250	C₂×C₄×C₈₃	—	4	8	no	—
251	C₂×C₄×C₈₃	—	4	2	no	—
252	C₂×C₄×C₈₃	—	8	2	no	—
253	C₂×C₄×C₈₃	—	8	4	no	—
254	C₂×C₄×C₈₃	—	8	2	no	—
255	C₂×C₄×C₈₃	C₂²×D₄	1	4	yes	—
256	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
258	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
259	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
260	C₈×C₈₃	—	2	4	no	—
261	C₈×C₈₃	—	2	4	no	—
262	C₂²×C₈₃	—	2	2	no	—
263	C₂²×C₈₃	—	2	4	no	—
264	C₂²×C₈₃	—	2	4	no	—
265	C₂²×C₈₃	—	2	1	no	—
266	C₂²×C₈₃	—	2	4	no	—
267	C₂²×C₈₃	—	4	4	no	—
268	C₂²×C₈₃	—	4	2	no	—
269	C₂²×C₈₃	—	4	4	no	—
270	C₂²×C₈₃	—	4	1	no	—
271	C₂²×C₈₃	—	4	4	no	—
272	C₂²×C₈₃	—	16	8	no	—
273	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
274	C₄×C₈₃	—	2	2	no	—
275	C₄×C₈₃	—	2	2	no	—
276	C₄×C₈₃	—	2	1	no	—
277	C₄×C₈₃	—	2	4	no	—
278	C₄×C₈₃	—	4	4	no	—
279	C₄×C₈₃	—	4	2	no	—
280	C₄×C₈₃	—	4	4	no	—
281	C₄×C₈₃	—	4	1	no	—
282	C₄×C₈₃	#585	1	2	yes	—
283	#61797	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
284	C₂×C₈₃	—	4	1	no	—
285	C₂×C₈₃	—	4	4	no	—
286	C₂×C₈₃	—	8	1	no	—
287	C₂×C₈₃	—	8	4	no	—
288	C₂×C₈₃	#3485	1	1	yes	characteristic
289	C₂×C₈₃	#3585	1	2	yes	—
290	#3549	C₂×C₈₃	1	1	yes	characteristic, complemented
291	#3512	C₂×C₈₃	1	1	yes	characteristic, complemented
292	#3348	C₂×C₈₃	1	4	yes	complemented
293	#3347	C₂×C₈₃	1	4	yes	complemented
294	#3318	C₂×C₈₃	1	4	yes	complemented
295	#3310	C₂×C₈₃	1	4	yes	complemented
296	#3234	C₂×C₈₃	1	2	yes	complemented
297	#3198	C₂×C₈₃	1	4	yes	complemented
298	#3115	C₂×C₈₃	1	2	yes	complemented
299	#3096	C₂×C₈₃	1	4	yes	complemented
300	#2980	C₂×C₈₃	1	1	yes	characteristic, complemented
301	C₈₃	#61797	1	1	yes	characteristic, direct product factor, Sylow
302	H(3,𝔽₄)	—	2	2	no	—
303	#555	—	2	1	no	—
304	#555	C₂²×C₈₃	1	4	yes	—
305	#553	—	2	4	no	—
306	#553	C₂²×C₈₃	1	4	yes	complemented
307	#552	C₂²×C₈₃	1	4	yes	complemented
308	D₄²	—	2	1	no	—
309	D₄²	C₂²×C₈₃	1	4	yes	—
310	#541	—	2	1	no	—
311	#540	—	2	1	no	—
312	#537	C₂²×C₈₃	1	2	yes	complemented
313	#535	—	2	4	no	—
314	#535	C₂²×C₈₃	1	4	yes	—
315	#532	C₂²×C₈₃	1	2	yes	—
316	#532	C₂²×C₈₃	1	1	yes	characteristic
317	#529	—	2	2	no	—
318	C₂×#125	C₂²×C₈₃	1	1	yes	characteristic, complemented
319	#520	C₂²×C₈₃	1	2	yes	complemented
320	C₄×#41	C₂²×C₈₃	1	1	yes	characteristic, complemented
321	#501	C₂²×C₈₃	1	4	yes	complemented
322	#490	C₂²×C₈₃	1	4	yes	—
323	#485	C₂²×C₈₃	1	4	yes	complemented
324	#482	C₂²×C₈₃	1	4	yes	complemented
325	#482	C₂²×C₈₃	1	4	yes	complemented
326	#482	C₂²×C₈₃	1	4	yes	complemented
327	#482	C₂²×C₈₃	1	4	yes	complemented
328	#481	C₂²×C₈₃	1	4	yes	complemented
329	#481	C₂²×C₈₃	1	4	yes	complemented
330	#480	C₂²×C₈₃	1	4	yes	complemented
331	#480	C₂²×C₈₃	1	4	yes	complemented
332	#478	C₂²×C₈₃	1	4	yes	complemented
333	#478	C₂²×C₈₃	1	4	yes	complemented
334	#475	C₂²×C₈₃	1	2	yes	complemented
335	#474	C₂²×C₈₃	1	2	yes	complemented
336	#469	C₂²×C₈₃	1	4	yes	complemented
337	#468	C₂²×C₈₃	1	4	yes	complemented
338	#466	C₂²×C₈₃	1	4	yes	complemented
339	#465	C₂²×C₈₃	1	4	yes	complemented
340	#460	C₂²×C₈₃	1	2	yes	—
341	#459	C₂²×C₈₃	1	2	yes	—
342	#450	C₂²×C₈₃	1	4	yes	complemented
343	#449	C₂²×C₈₃	1	4	yes	complemented
344	#447	C₂²×C₈₃	1	4	yes	complemented
345	#442	C₂²×C₈₃	1	4	yes	complemented
346	#440	C₂²×C₈₃	1	4	yes	complemented
347	#435	C₂²×C₈₃	1	4	yes	complemented
348	#435	C₂²×C₈₃	1	4	yes	complemented
349	#432	C₂²×C₈₃	1	2	yes	complemented
350	#428	C₂²×C₈₃	1	4	yes	complemented
351	#427	C₂²×C₈₃	1	4	yes	complemented
352	#418	C₂²×C₈₃	1	4	yes	complemented
353	C₂×#102	C₂²×C₈₃	1	4	yes	complemented
354	#408	C₂²×C₈₃	1	4	yes	complemented
355	C₂×#41	—	2	2	no	—
356	C₂×#41	C₂³×C₈₃	1	1	yes	characteristic
357	C₂×#41	C₂³×C₈₃	1	2	yes	—
358	C₂²×D₄	—	2	4	no	—
359	C₂²×D₄	C₂³×C₈₃	1	4	yes	—
360	C₂×SD₁₆	C₂³×C₈₃	1	4	yes	—
361	C₂×D₈	C₂³×C₈₃	1	4	yes	—
362	C₂×M₁₆	C₂³×C₈₃	1	4	yes	—
363	C₂²×C₈	C₂³×C₈₃	1	4	yes	—
364	C₄⋊Q₈	D₄×C₈₃	1	1	yes	characteristic
365	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
366	#127	—	2	4	no	—
367	#127	D₄×C₈₃	1	1	yes	characteristic
368	#127	C₂³×C₈₃	1	2	yes	—
369	#126	—	2	4	no	—
370	#126	—	2	4	no	—
371	#125	—	2	4	no	—
372	#125	—	2	1	no	—
373	#125	—	2	1	no	—
374	#125	C₂³×C₈₃	1	4	yes	—
375	#124	—	2	4	no	—
376	#124	—	2	4	no	—
377	#124	—	2	4	no	—
378	#124	—	2	2	no	—
379	#124	D₄×C₈₃	1	2	yes	—
380	#123	—	2	4	no	—
381	#123	—	2	4	no	—
382	C₂²⋊Q₈	—	2	2	no	—
383	C₂²⋊Q₈	C₂³×C₈₃	1	4	yes	—
384	#121	—	2	2	no	—
385	#121	—	2	4	no	—
386	#121	—	2	4	no	—
387	#121	—	2	4	no	—
388	#121	—	2	2	no	—
389	#121	—	2	4	no	—
390	#121	D₄×C₈₃	1	4	yes	—
391	#121	C₂³×C₈₃	1	4	yes	—
392	#121	C₂³×C₈₃	1	4	yes	—
393	#121	C₂³×C₈₃	1	4	yes	—
394	#121	C₂³×C₈₃	1	4	yes	—
395	#120	—	2	4	no	—
396	#120	—	2	4	no	—
397	#120	—	2	4	no	—
398	#120	—	2	4	no	—
399	C₄×Q₈	—	2	2	no	—
400	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
401	C₄×D₄	—	2	2	no	—
402	C₄×D₄	—	2	4	no	—
403	C₄×D₄	—	2	2	no	—
404	C₄×D₄	—	2	4	no	—
405	C₄×D₄	—	2	2	no	—
406	C₄×D₄	C₂³×C₈₃	1	2	yes	—
407	C₄×D₄	C₂³×C₈₃	1	4	yes	—
408	C₄×D₄	C₂³×C₈₃	1	4	yes	—
409	#117	—	2	4	no	—
410	#117	—	2	4	no	—
411	#117	—	2	1	no	—
412	#117	C₂³×C₈₃	1	1	yes	characteristic
413	#117	C₂³×C₈₃	1	4	yes	—
414	#117	C₂³×C₈₃	1	4	yes	—
415	C₂×C₄⋊C₄	—	2	2	no	—
416	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
417	C₂×C₄⋊C₄	C₂³×C₈₃	1	4	yes	—
418	C₂×C₄²	—	2	1	no	—
419	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
420	#107	C₂³×C₈₃	1	4	yes	—
421	#107	C₂³×C₈₃	1	4	yes	—
422	#107	C₂³×C₈₃	1	4	yes	—
423	#106	C₂³×C₈₃	1	4	yes	—
424	#106	C₂³×C₈₃	1	4	yes	—
425	#106	C₂³×C₈₃	1	4	yes	—
426	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
427	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
428	#103	C₂³×C₈₃	1	4	yes	—
429	#102	C₂³×C₈₃	1	4	yes	—
430	#102	C₂³×C₈₃	1	4	yes	—
431	#102	C₂³×C₈₃	1	4	yes	—
432	#102	C₂³×C₈₃	1	4	yes	—
433	#102	C₂³×C₈₃	1	4	yes	—
434	#102	C₂³×C₈₃	1	4	yes	—
435	#102	C₂³×C₈₃	1	4	yes	—
436	C₂²⋊C₈	C₂³×C₈₃	1	4	yes	—
437	C₂²⋊C₈	C₂³×C₈₃	1	4	yes	—
438	C₂²⋊C₈	C₂³×C₈₃	1	4	yes	—
439	#97	C₂³×C₈₃	1	4	yes	—
440	C₂⁴	—	2	4	no	—
441	#41	—	4	2	no	—
442	#41	—	4	2	no	—
443	#41	—	4	2	no	—
444	#41	—	8	4	no	—
445	C₂×Q₈	—	2	2	no	—
446	C₂×Q₈	C₂×D₄×C₈₃	1	2	yes	—
447	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	4	no	—
450	C₂×D₄	—	2	4	no	—
451	C₂×D₄	—	2	4	no	—
452	C₂×D₄	—	2	4	no	—
453	C₂×D₄	—	2	2	no	—
454	C₂×D₄	—	2	2	no	—
455	C₂×D₄	—	2	4	no	—
456	C₂×D₄	—	4	4	no	—
457	C₂×D₄	—	4	4	no	—
458	C₂×D₄	—	8	8	no	—
459	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
460	C₂×D₄	C₂×D₄×C₈₃	1	4	yes	—
461	C₂×D₄	C₂×D₄×C₈₃	1	4	yes	—
462	C₂×D₄	C₂⁴×C₈₃	1	4	yes	—
463	C₂×D₄	C₂⁴×C₈₃	1	1	yes	characteristic
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	4	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	4	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
470	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
471	C₂²×C₄	C₂⁴×C₈₃	1	4	yes	—
472	SD₁₆	—	4	4	no	—
473	D₈	—	4	4	no	—
474	M₁₆	—	4	4	no	—
475	C₂×C₈	—	4	4	no	—
476	C₂×C₈	C₂⁴×C₈₃	1	4	yes	—
477	C₂×C₈	C₂⁴×C₈₃	1	4	yes	—
478	C₄⋊C₄	—	2	4	no	—
479	C₄⋊C₄	—	2	4	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	4	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	4	no	—
485	C₄⋊C₄	C₂×D₄×C₈₃	1	4	yes	—
486	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
487	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
488	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
489	C₂²⋊C₄	—	2	4	no	—
490	C₂²⋊C₄	—	2	1	no	—
491	C₂²⋊C₄	—	2	4	no	—
492	C₂²⋊C₄	—	2	4	no	—
493	C₂²⋊C₄	—	2	2	no	—
494	C₂²⋊C₄	—	2	4	no	—
495	C₂²⋊C₄	—	2	4	no	—
496	C₂²⋊C₄	—	2	4	no	—
497	C₂²⋊C₄	—	2	4	no	—
498	C₂²⋊C₄	—	2	4	no	—
499	C₂²⋊C₄	C₂×D₄×C₈₃	1	4	yes	—
500	C₂²⋊C₄	C₂×D₄×C₈₃	1	4	yes	—
501	C₄²	—	2	2	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	2	4	no	—
504	C₄²	—	2	4	no	—
505	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
506	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
507	C₄²	C₂⁴×C₈₃	1	2	yes	—
508	C₂³	—	2	1	no	—
509	C₂³	—	2	4	no	—
510	C₂³	—	8	4	no	—
511	C₂³	—	8	4	no	—
512	C₂³	—	8	4	no	—
513	C₂³	C₂²×D₄×C₈₃	1	4	yes	—
514	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
515	Q₈	—	2	2	no	—
516	Q₈	—	4	2	no	—
517	Q₈	—	8	2	no	—
518	D₄	—	2	2	no	—
519	D₄	—	2	4	no	—
520	D₄	—	2	4	no	—
521	D₄	—	4	4	no	—
522	D₄	—	4	2	no	—
523	D₄	—	4	4	no	—
524	D₄	—	4	4	no	—
525	D₄	—	4	2	no	—
526	D₄	—	8	4	no	—
527	D₄	—	8	2	no	—
528	D₄	—	8	4	no	—
529	D₄	—	8	4	no	—
530	D₄	—	8	4	no	—
531	D₄	—	8	4	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	8	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	8	2	no	—
543	C₂×C₄	—	8	4	no	—
544	C₂×C₄	—	8	2	no	—
545	C₂×C₄	C₂²×D₄×C₈₃	1	4	yes	—
546	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
547	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
548	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
549	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
550	C₈	—	2	4	no	—
551	C₈	—	2	4	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	4	no	—
554	C₂²	—	2	4	no	—
555	C₂²	—	2	1	no	—
556	C₂²	—	2	4	no	—
557	C₂²	—	4	4	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	4	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	4	no	—
562	C₂²	—	16	8	no	—
563	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
564	C₄	—	2	2	no	—
565	C₄	—	2	2	no	—
566	C₄	—	2	1	no	—
567	C₄	—	2	4	no	—
568	C₄	—	4	4	no	—
569	C₄	—	4	2	no	—
570	C₄	—	4	4	no	—
571	C₄	—	4	1	no	—
572	C₄	#585×C₈₃	1	2	yes	—
573	C₂	—	4	4	no	—
574	C₂	—	4	1	no	—
575	C₂	—	8	4	no	—
576	C₂	—	8	1	no	—
577	C₂	C₈₃×#3485	1	1	yes	characteristic
578	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 ◁ #532×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₃×#3549	C₂	semidirect
2. C₈₃×#3512	C₂	semidirect
3. C₈₃×#3348	C₂	semidirect
4. C₈₃×#3347	C₂	semidirect
5. C₈₃×#3318	C₂	semidirect
6. C₈₃×#3310	C₂	semidirect
7. C₈₃×#3234	C₂	semidirect
8. C₈₃×#3198	C₂	semidirect
9. C₈₃×#3115	C₂	semidirect
10. C₈₃×#3096	C₂	semidirect
11. C₈₃×#2980	C₂	semidirect
16. #553×C₈₃	C₂²	semidirect
17. #552×C₈₃	C₂²	semidirect
22. #537×C₈₃	C₂²	semidirect
28. C₂×#125×C₈₃	C₂²	semidirect
29. #520×C₈₃	C₂²	semidirect
30. C₄×#41×C₈₃	C₂²	semidirect
31. #501×C₈₃	C₂²	semidirect
33. #485×C₈₃	C₂²	semidirect
34. #482×C₈₃	C₂²	semidirect
35. #482×C₈₃	C₂²	semidirect
36. #482×C₈₃	C₂²	semidirect
37. #482×C₈₃	C₂²	semidirect
38. #481×C₈₃	C₂²	semidirect
39. #481×C₈₃	C₂²	semidirect
40. #480×C₈₃	C₂²	semidirect
41. #480×C₈₃	C₂²	semidirect
42. #478×C₈₃	C₂²	semidirect
43. #478×C₈₃	C₂²	semidirect
44. #475×C₈₃	C₂²	semidirect
45. #474×C₈₃	C₂²	semidirect
46. #469×C₈₃	C₂²	semidirect
47. #468×C₈₃	C₂²	semidirect
48. #466×C₈₃	C₂²	semidirect
49. #465×C₈₃	C₂²	semidirect
52. #450×C₈₃	C₂²	semidirect
53. #449×C₈₃	C₂²	semidirect
54. #447×C₈₃	C₂²	semidirect
55. #442×C₈₃	C₂²	semidirect
56. #440×C₈₃	C₂²	semidirect
57. #435×C₈₃	C₂²	semidirect
58. #435×C₈₃	C₂²	semidirect
59. #432×C₈₃	C₂²	semidirect
60. #428×C₈₃	C₂²	semidirect
61. #427×C₈₃	C₂²	semidirect
62. #418×C₈₃	C₂²	semidirect
63. C₂×#102×C₈₃	C₂²	semidirect
64. #408×C₈₃	C₂²	semidirect
283. #61797	C₈₃	direct (N × H)
290. #3549	C₂×C₈₃	semidirect
291. #3512	C₂×C₈₃	semidirect
292. #3348	C₂×C₈₃	semidirect
293. #3347	C₂×C₈₃	semidirect
294. #3318	C₂×C₈₃	semidirect
295. #3310	C₂×C₈₃	semidirect
296. #3234	C₂×C₈₃	semidirect
297. #3198	C₂×C₈₃	semidirect
298. #3115	C₂×C₈₃	semidirect
299. #3096	C₂×C₈₃	semidirect
300. #2980	C₂×C₈₃	semidirect
301. C₈₃	#61797	direct (N × H)
306. #553	C₂²×C₈₃	semidirect
307. #552	C₂²×C₈₃	semidirect
312. #537	C₂²×C₈₃	semidirect
318. C₂×#125	C₂²×C₈₃	semidirect
319. #520	C₂²×C₈₃	semidirect
320. C₄×#41	C₂²×C₈₃	semidirect
321. #501	C₂²×C₈₃	semidirect
323. #485	C₂²×C₈₃	semidirect
324. #482	C₂²×C₈₃	semidirect
325. #482	C₂²×C₈₃	semidirect
326. #482	C₂²×C₈₃	semidirect
327. #482	C₂²×C₈₃	semidirect
328. #481	C₂²×C₈₃	semidirect
329. #481	C₂²×C₈₃	semidirect
330. #480	C₂²×C₈₃	semidirect
331. #480	C₂²×C₈₃	semidirect
332. #478	C₂²×C₈₃	semidirect
333. #478	C₂²×C₈₃	semidirect
334. #475	C₂²×C₈₃	semidirect
335. #474	C₂²×C₈₃	semidirect
336. #469	C₂²×C₈₃	semidirect
337. #468	C₂²×C₈₃	semidirect
338. #466	C₂²×C₈₃	semidirect
339. #465	C₂²×C₈₃	semidirect
342. #450	C₂²×C₈₃	semidirect
343. #449	C₂²×C₈₃	semidirect
344. #447	C₂²×C₈₃	semidirect
345. #442	C₂²×C₈₃	semidirect
346. #440	C₂²×C₈₃	semidirect
347. #435	C₂²×C₈₃	semidirect
348. #435	C₂²×C₈₃	semidirect
349. #432	C₂²×C₈₃	semidirect
350. #428	C₂²×C₈₃	semidirect
351. #427	C₂²×C₈₃	semidirect
352. #418	C₂²×C₈₃	semidirect
353. C₂×#102	C₂²×C₈₃	semidirect
354. #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×#3549	2
C₈₃×#3512	2
C₈₃×#3348	2
C₈₃×#3347	2
C₈₃×#3318	2
C₈₃×#3310	2
C₈₃×#3234	2
C₈₃×#3198	2
C₈₃×#3115	2
C₈₃×#3096	2
C₈₃×#2980	2
#61797	83

Subgroups — C83×#61797 #35289621

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#61797 #35289621