Subgroups — C₈₃×#61805 #35289629

Order 21248.

1796 conjugacy classes of subgroups.

The subgroup lattice has 756 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
2	C₈₃×#3507	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₃×#3357	C₂	1	2	yes	maximal, complemented
4	C₈₃×#3348	C₂	1	4	yes	maximal, complemented
5	C₈₃×#3340	C₂	1	2	yes	maximal, complemented
6	C₈₃×#3324	C₂	1	2	yes	maximal, complemented
7	C₈₃×#3310	C₂	1	4	yes	maximal, complemented
8	C₈₃×#3295	C₂	1	2	yes	maximal, complemented
9	C₈₃×#3235	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₃×#3228	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₃×#3200	C₂	1	4	yes	maximal, complemented
12	C₈₃×#3112	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₃×#3103	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₃×#3096	C₂	1	4	yes	maximal, complemented
15	C₈₃×#2981	C₂	1	1	yes	maximal, characteristic, complemented
16	H(3,𝔽₄)×C₈₃	—	2	2	no	—
17	#559×C₈₃	—	2	1	no	—
18	#557×C₈₃	—	2	1	no	—
19	#556×C₈₃	—	2	2	no	—
20	#556×C₈₃	C₂²	1	2	yes	complemented
21	#555×C₈₃	—	2	1	no	—
22	#555×C₈₃	C₂²	1	2	yes	—
23	#555×C₈₃	C₂²	1	2	yes	—
24	#554×C₈₃	C₂²	1	2	yes	complemented
25	#552×C₈₃	C₂²	1	4	yes	complemented
26	D₄²×C₈₃	—	2	1	no	—
27	D₄²×C₈₃	C₂²	1	2	yes	—
28	D₄²×C₈₃	C₂²	1	2	yes	—
29	#539×C₈₃	—	2	2	no	—
30	#536×C₈₃	C₂²	1	2	yes	complemented
31	#535×C₈₃	—	2	2	no	—
32	#535×C₈₃	—	2	2	no	—
33	#535×C₈₃	C₂²	1	4	yes	—
34	#533×C₈₃	C₂²	1	1	yes	characteristic, complemented
35	#532×C₈₃	C₂²	1	1	yes	characteristic
36	#532×C₈₃	C₂²	1	1	yes	characteristic
37	#532×C₈₃	C₂²	1	1	yes	characteristic
38	#529×C₈₃	—	2	2	no	—
39	#520×C₈₃	C₂²	1	2	yes	complemented
40	C₂×C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
41	#501×C₈₃	C₂²	1	2	yes	complemented
42	#500×C₈₃	C₂²	1	1	yes	characteristic, complemented
43	#498×C₈₃	C₂²	1	1	yes	characteristic, complemented
44	#490×C₈₃	C₂²	1	2	yes	—
45	#486×C₈₃	C₂²	1	1	yes	characteristic
46	#486×C₈₃	C₂²	1	1	yes	characteristic
47	#485×C₈₃	C₂²	1	4	yes	complemented
48	#485×C₈₃	C₂²	1	4	yes	complemented
49	#482×C₈₃	C₂²	1	4	yes	complemented
50	#482×C₈₃	C₂²	1	4	yes	complemented
51	#482×C₈₃	C₂²	1	4	yes	complemented
52	#482×C₈₃	C₂²	1	4	yes	complemented
53	#481×C₈₃	C₂²	1	4	yes	complemented
54	#481×C₈₃	C₂²	1	2	yes	complemented
55	#480×C₈₃	C₂²	1	4	yes	complemented
56	#480×C₈₃	C₂²	1	2	yes	complemented
57	#478×C₈₃	C₂²	1	4	yes	complemented
58	#477×C₈₃	C₂²	1	2	yes	complemented
59	#476×C₈₃	C₂²	1	2	yes	complemented
60	#475×C₈₃	C₂²	1	2	yes	complemented
61	#474×C₈₃	C₂²	1	2	yes	complemented
62	#468×C₈₃	C₂²	1	4	yes	complemented
63	#468×C₈₃	C₂²	1	4	yes	complemented
64	#465×C₈₃	C₂²	1	4	yes	complemented
65	#465×C₈₃	C₂²	1	4	yes	complemented
66	#460×C₈₃	C₂²	1	2	yes	—
67	#460×C₈₃	C₂²	1	2	yes	—
68	#450×C₈₃	C₂²	1	4	yes	complemented
69	#450×C₈₃	C₂²	1	4	yes	complemented
70	#448×C₈₃	C₂²	1	2	yes	complemented
71	#448×C₈₃	C₂²	1	2	yes	complemented
72	#440×C₈₃	C₂²	1	4	yes	complemented
73	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	complemented
74	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	complemented
75	#436×C₈₃	C₂²	1	2	yes	complemented
76	#435×C₈₃	C₂²	1	4	yes	complemented
77	C₈×D₄×C₈₃	C₂²	1	2	yes	complemented
78	#432×C₈₃	C₂²	1	1	yes	characteristic, complemented
79	#431×C₈₃	C₂²	1	1	yes	characteristic, complemented
80	#428×C₈₃	C₂²	1	4	yes	complemented
81	#427×C₈₃	C₂²	1	4	yes	complemented
82	#418×C₈₃	C₂²	1	4	yes	complemented
83	C₂×#102×C₈₃	C₂²	1	4	yes	complemented
84	#408×C₈₃	C₂²	1	4	yes	complemented
85	C₂×#41×C₈₃	—	2	1	no	—
86	C₂×#41×C₈₃	—	2	1	no	—
87	C₂×#41×C₈₃	C₂³	1	2	yes	—
88	C₂²×Q₈×C₈₃	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₈₃	—	2	2	no	—
90	C₂²×D₄×C₈₃	—	2	2	no	—
91	C₂²×D₄×C₈₃	C₂³	1	4	yes	—
92	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
93	C₂×SD₁₆×C₈₃	C₂³	1	4	yes	—
94	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
95	C₂×M₁₆×C₈₃	C₂³	1	4	yes	—
96	C₂²×C₈×C₈₃	C₂³	1	4	yes	—
97	C₄⋊Q₈×C₈₃	—	2	2	no	—
98	C₄⋊Q₈×C₈₃	D₄	1	1	yes	characteristic
99	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
100	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
101	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
102	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
103	#127×C₈₃	—	2	4	no	—
104	#127×C₈₃	D₄	1	1	yes	characteristic
105	#127×C₈₃	C₂³	1	1	yes	characteristic
106	#127×C₈₃	C₂³	1	1	yes	characteristic
107	#126×C₈₃	—	2	4	no	—
108	#126×C₈₃	—	2	4	no	—
109	#125×C₈₃	—	2	2	no	—
110	#125×C₈₃	—	2	4	no	—
111	#125×C₈₃	C₂³	1	2	yes	—
112	#124×C₈₃	—	2	4	no	—
113	#124×C₈₃	—	2	2	no	—
114	#124×C₈₃	—	2	2	no	—
115	#124×C₈₃	—	2	4	no	—
116	#124×C₈₃	—	2	4	no	—
117	#124×C₈₃	—	2	1	no	—
118	#124×C₈₃	—	2	1	no	—
119	#124×C₈₃	D₄	1	2	yes	—
120	#123×C₈₃	—	2	4	no	—
121	#123×C₈₃	—	2	4	no	—
122	C₂²⋊Q₈×C₈₃	—	2	1	no	—
123	C₂²⋊Q₈×C₈₃	—	2	1	no	—
124	C₂²⋊Q₈×C₈₃	—	2	4	no	—
125	C₂²⋊Q₈×C₈₃	C₂³	1	4	yes	—
126	C₂²⋊Q₈×C₈₃	C₂³	1	4	yes	—
127	#121×C₈₃	—	2	2	no	—
128	#121×C₈₃	—	2	2	no	—
129	#121×C₈₃	—	2	1	no	—
130	#121×C₈₃	—	2	1	no	—
131	#121×C₈₃	—	2	2	no	—
132	#121×C₈₃	—	2	2	no	—
133	#121×C₈₃	D₄	1	2	yes	—
134	#121×C₈₃	D₄	1	2	yes	—
135	#121×C₈₃	C₂³	1	4	yes	—
136	#121×C₈₃	C₂³	1	4	yes	—
137	#121×C₈₃	C₂³	1	2	yes	—
138	#121×C₈₃	C₂³	1	2	yes	—
139	#120×C₈₃	—	2	4	no	—
140	#120×C₈₃	—	2	4	no	—
141	#120×C₈₃	—	2	4	no	—
142	#120×C₈₃	—	2	4	no	—
143	C₄×Q₈×C₈₃	—	2	2	no	—
144	C₄×Q₈×C₈₃	—	2	2	no	—
145	C₄×Q₈×C₈₃	—	2	1	no	—
146	C₄×Q₈×C₈₃	—	2	1	no	—
147	C₄×Q₈×C₈₃	—	2	1	no	—
148	C₄×Q₈×C₈₃	—	2	1	no	—
149	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
150	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
151	C₄×D₄×C₈₃	—	2	4	no	—
152	C₄×D₄×C₈₃	—	2	2	no	—
153	C₄×D₄×C₈₃	—	2	2	no	—
154	C₄×D₄×C₈₃	—	2	1	no	—
155	C₄×D₄×C₈₃	—	2	1	no	—
156	C₄×D₄×C₈₃	C₂³	1	2	yes	—
157	C₄×D₄×C₈₃	C₂³	1	2	yes	—
158	C₄×D₄×C₈₃	C₂³	1	2	yes	—
159	C₄×D₄×C₈₃	C₂³	1	2	yes	—
160	#117×C₈₃	—	2	2	no	—
161	#117×C₈₃	—	2	2	no	—
162	#117×C₈₃	—	2	4	no	—
163	#117×C₈₃	C₂³	1	2	yes	—
164	#117×C₈₃	C₂³	1	4	yes	—
165	#117×C₈₃	C₂³	1	4	yes	—
166	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
167	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₈₃	C₂³	1	4	yes	—
169	C₂×C₄²×C₈₃	—	2	1	no	—
170	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
171	#107×C₈₃	C₂³	1	4	yes	—
172	#107×C₈₃	C₂³	1	4	yes	—
173	#107×C₈₃	C₂³	1	4	yes	—
174	#106×C₈₃	C₂³	1	4	yes	—
175	#106×C₈₃	C₂³	1	4	yes	—
176	#106×C₈₃	C₂³	1	2	yes	—
177	#106×C₈₃	C₂³	1	2	yes	—
178	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
179	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
180	#103×C₈₃	C₂³	1	2	yes	—
181	#103×C₈₃	C₂³	1	4	yes	—
182	#103×C₈₃	C₂³	1	2	yes	—
183	#102×C₈₃	C₂³	1	4	yes	—
184	#102×C₈₃	C₂³	1	4	yes	—
185	#102×C₈₃	C₂³	1	4	yes	—
186	#102×C₈₃	C₂³	1	4	yes	—
187	#102×C₈₃	C₂³	1	2	yes	—
188	#102×C₈₃	C₂³	1	4	yes	—
189	#102×C₈₃	C₂³	1	2	yes	—
190	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
191	C₂²⋊C₈×C₈₃	C₂³	1	4	yes	—
192	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
193	C₂²⋊C₈×C₈₃	C₂³	1	4	yes	—
194	#97×C₈₃	C₂³	1	2	yes	—
195	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
197	C₂⁴×C₈₃	—	2	4	no	—
198	#41×C₈₃	—	4	4	no	—
199	#41×C₈₃	—	8	2	no	—
200	#41×C₈₃	—	8	2	no	—
201	C₂×Q₈×C₈₃	—	2	1	no	—
202	C₂×Q₈×C₈₃	—	2	1	no	—
203	C₂×Q₈×C₈₃	—	2	1	no	—
204	C₂×Q₈×C₈₃	—	2	1	no	—
205	C₂×Q₈×C₈₃	—	2	1	no	—
206	C₂×Q₈×C₈₃	—	4	2	no	—
207	C₂×Q₈×C₈₃	C₂×D₄	1	2	yes	—
208	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
209	C₂×D₄×C₈₃	—	2	4	no	—
210	C₂×D₄×C₈₃	—	2	4	no	—
211	C₂×D₄×C₈₃	—	2	2	no	—
212	C₂×D₄×C₈₃	—	2	2	no	—
213	C₂×D₄×C₈₃	—	2	1	no	—
214	C₂×D₄×C₈₃	—	2	1	no	—
215	C₂×D₄×C₈₃	—	2	1	no	—
216	C₂×D₄×C₈₃	—	2	1	no	—
217	C₂×D₄×C₈₃	—	2	4	no	—
218	C₂×D₄×C₈₃	—	4	4	no	—
219	C₂×D₄×C₈₃	—	4	4	no	—
220	C₂×D₄×C₈₃	—	8	4	no	—
221	C₂×D₄×C₈₃	—	8	4	no	—
222	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
223	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
224	C₂×D₄×C₈₃	C₂×D₄	1	4	yes	—
225	C₂×D₄×C₈₃	C₂×D₄	1	2	yes	—
226	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
227	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₈₃	—	2	1	no	—
229	C₂²×C₄×C₈₃	—	2	1	no	—
230	C₂²×C₄×C₈₃	—	2	4	no	—
231	C₂²×C₄×C₈₃	—	2	2	no	—
232	C₂²×C₄×C₈₃	—	2	2	no	—
233	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₈₃	C₂⁴	1	4	yes	—
237	SD₁₆×C₈₃	—	4	2	no	—
238	SD₁₆×C₈₃	—	4	4	no	—
239	SD₁₆×C₈₃	—	4	2	no	—
240	M₁₆×C₈₃	—	4	4	no	—
241	C₂×C₈×C₈₃	—	4	4	no	—
242	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
243	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
244	C₂×C₈×C₈₃	C₂⁴	1	4	yes	—
245	C₄⋊C₄×C₈₃	—	2	2	no	—
246	C₄⋊C₄×C₈₃	—	2	2	no	—
247	C₄⋊C₄×C₈₃	—	2	1	no	—
248	C₄⋊C₄×C₈₃	—	2	4	no	—
249	C₄⋊C₄×C₈₃	—	2	1	no	—
250	C₄⋊C₄×C₈₃	—	2	1	no	—
251	C₄⋊C₄×C₈₃	—	2	2	no	—
252	C₄⋊C₄×C₈₃	—	2	4	no	—
253	C₄⋊C₄×C₈₃	—	2	1	no	—
254	C₄⋊C₄×C₈₃	—	2	2	no	—
255	C₄⋊C₄×C₈₃	—	2	1	no	—
256	C₄⋊C₄×C₈₃	—	2	4	no	—
257	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
258	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
259	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
260	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
262	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
263	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
264	C₂²⋊C₄×C₈₃	—	2	4	no	—
265	C₂²⋊C₄×C₈₃	—	2	2	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	4	no	—
270	C₂²⋊C₄×C₈₃	—	2	4	no	—
271	C₂²⋊C₄×C₈₃	—	2	2	no	—
272	C₂²⋊C₄×C₈₃	—	2	2	no	—
273	C₂²⋊C₄×C₈₃	—	2	2	no	—
274	C₂²⋊C₄×C₈₃	—	2	2	no	—
275	C₂²⋊C₄×C₈₃	C₂×D₄	1	4	yes	—
276	C₂²⋊C₄×C₈₃	C₂×D₄	1	4	yes	—
277	C₄²×C₈₃	—	2	2	no	—
278	C₄²×C₈₃	—	2	2	no	—
279	C₄²×C₈₃	—	2	4	no	—
280	C₄²×C₈₃	—	2	4	no	—
281	C₄²×C₈₃	—	2	2	no	—
282	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
283	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
284	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
285	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
286	C₂³×C₈₃	—	2	2	no	—
287	C₂³×C₈₃	—	2	2	no	—
288	C₂³×C₈₃	—	8	4	no	—
289	C₂³×C₈₃	—	8	4	no	—
290	C₂³×C₈₃	—	8	4	no	—
291	C₂³×C₈₃	C₂²×D₄	1	4	yes	—
292	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
293	Q₈×C₈₃	—	2	2	no	—
294	Q₈×C₈₃	—	2	2	no	—
295	Q₈×C₈₃	—	4	2	no	—
296	Q₈×C₈₃	—	4	2	no	—
297	Q₈×C₈₃	—	4	2	no	—
298	Q₈×C₈₃	—	8	1	no	—
299	Q₈×C₈₃	—	8	1	no	—
300	Q₈×C₈₃	—	8	1	no	—
301	D₄×C₈₃	—	2	4	no	—
302	D₄×C₈₃	—	2	2	no	—
303	D₄×C₈₃	—	2	4	no	—
304	D₄×C₈₃	—	2	2	no	—
305	D₄×C₈₃	—	4	2	no	—
306	D₄×C₈₃	—	4	2	no	—
307	D₄×C₈₃	—	4	4	no	—
308	D₄×C₈₃	—	4	2	no	—
309	D₄×C₈₃	—	4	2	no	—
310	D₄×C₈₃	—	8	4	no	—
311	D₄×C₈₃	—	8	1	no	—
312	D₄×C₈₃	—	8	1	no	—
313	D₄×C₈₃	—	8	4	no	—
314	D₄×C₈₃	—	8	4	no	—
315	D₄×C₈₃	—	8	2	no	—
316	D₄×C₈₃	—	8	2	no	—
317	C₂×C₄×C₈₃	—	2	2	no	—
318	C₂×C₄×C₈₃	—	2	4	no	—
319	C₂×C₄×C₈₃	—	2	4	no	—
320	C₂×C₄×C₈₃	—	2	2	no	—
321	C₂×C₄×C₈₃	—	2	2	no	—
322	C₂×C₄×C₈₃	—	2	2	no	—
323	C₂×C₄×C₈₃	—	2	2	no	—
324	C₂×C₄×C₈₃	—	2	2	no	—
325	C₂×C₄×C₈₃	—	2	2	no	—
326	C₂×C₄×C₈₃	—	2	2	no	—
327	C₂×C₄×C₈₃	—	4	1	no	—
328	C₂×C₄×C₈₃	—	4	4	no	—
329	C₂×C₄×C₈₃	—	4	2	no	—
330	C₂×C₄×C₈₃	—	4	4	no	—
331	C₂×C₄×C₈₃	—	8	1	no	—
332	C₂×C₄×C₈₃	—	8	4	no	—
333	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
334	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₈₃	C₂²×D₄	1	4	yes	—
336	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
340	C₈×C₈₃	—	2	2	no	—
341	C₈×C₈₃	—	2	4	no	—
342	C₈×C₈₃	—	2	2	no	—
343	C₂²×C₈₃	—	2	1	no	—
344	C₂²×C₈₃	—	2	4	no	—
345	C₂²×C₈₃	—	2	1	no	—
346	C₂²×C₈₃	—	2	4	no	—
347	C₂²×C₈₃	—	2	1	no	—
348	C₂²×C₈₃	—	2	4	no	—
349	C₂²×C₈₃	—	4	2	no	—
350	C₂²×C₈₃	—	4	2	no	—
351	C₂²×C₈₃	—	4	2	no	—
352	C₂²×C₈₃	—	4	2	no	—
353	C₂²×C₈₃	—	4	2	no	—
354	C₂²×C₈₃	—	4	2	no	—
355	C₂²×C₈₃	—	16	8	no	—
356	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
357	C₄×C₈₃	—	2	1	no	—
358	C₄×C₈₃	—	2	1	no	—
359	C₄×C₈₃	—	2	1	no	—
360	C₄×C₈₃	—	2	4	no	—
361	C₄×C₈₃	—	2	1	no	—
362	C₄×C₈₃	—	4	2	no	—
363	C₄×C₈₃	—	4	2	no	—
364	C₄×C₈₃	—	4	2	no	—
365	C₄×C₈₃	—	4	2	no	—
366	C₄×C₈₃	—	4	2	no	—
367	C₄×C₈₃	—	4	2	no	—
368	C₄×C₈₃	#577	1	2	yes	—
369	C₄×C₈₃	#585	1	2	yes	—
370	#61805	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
371	C₂×C₈₃	—	4	1	no	—
372	C₂×C₈₃	—	4	4	no	—
373	C₂×C₈₃	—	8	2	no	—
374	C₂×C₈₃	—	8	2	no	—
375	C₂×C₈₃	#3485	1	1	yes	characteristic
376	C₂×C₈₃	C₂×#577	1	1	yes	characteristic
377	C₂×C₈₃	#3585	1	1	yes	characteristic
378	#3549	C₂×C₈₃	1	1	yes	characteristic
379	#3507	C₂×C₈₃	1	1	yes	characteristic, complemented
380	#3357	C₂×C₈₃	1	2	yes	complemented
381	#3348	C₂×C₈₃	1	4	yes	complemented
382	#3340	C₂×C₈₃	1	2	yes	complemented
383	#3324	C₂×C₈₃	1	2	yes	complemented
384	#3310	C₂×C₈₃	1	4	yes	complemented
385	#3295	C₂×C₈₃	1	2	yes	complemented
386	#3235	C₂×C₈₃	1	1	yes	characteristic, complemented
387	#3228	C₂×C₈₃	1	1	yes	characteristic, complemented
388	#3200	C₂×C₈₃	1	4	yes	complemented
389	#3112	C₂×C₈₃	1	1	yes	characteristic, complemented
390	#3103	C₂×C₈₃	1	1	yes	characteristic, complemented
391	#3096	C₂×C₈₃	1	4	yes	complemented
392	#2981	C₂×C₈₃	1	1	yes	characteristic, complemented
393	C₈₃	#61805	1	1	yes	characteristic, direct product factor, Sylow
394	H(3,𝔽₄)	—	2	2	no	—
395	#559	—	2	1	no	—
396	#557	—	2	1	no	—
397	#556	—	2	2	no	—
398	#556	C₂²×C₈₃	1	2	yes	complemented
399	#555	—	2	1	no	—
400	#555	C₂²×C₈₃	1	2	yes	—
401	#555	C₂²×C₈₃	1	2	yes	—
402	#554	C₂²×C₈₃	1	2	yes	complemented
403	#552	C₂²×C₈₃	1	4	yes	complemented
404	D₄²	—	2	1	no	—
405	D₄²	C₂²×C₈₃	1	2	yes	—
406	D₄²	C₂²×C₈₃	1	2	yes	—
407	#539	—	2	2	no	—
408	#536	C₂²×C₈₃	1	2	yes	complemented
409	#535	—	2	2	no	—
410	#535	—	2	2	no	—
411	#535	C₂²×C₈₃	1	4	yes	—
412	#533	C₂²×C₈₃	1	1	yes	characteristic, complemented
413	#532	C₂²×C₈₃	1	1	yes	characteristic
414	#532	C₂²×C₈₃	1	1	yes	characteristic
415	#532	C₂²×C₈₃	1	1	yes	characteristic
416	#529	—	2	2	no	—
417	#520	C₂²×C₈₃	1	2	yes	complemented
418	C₂×C₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
419	#501	C₂²×C₈₃	1	2	yes	complemented
420	#500	C₂²×C₈₃	1	1	yes	characteristic, complemented
421	#498	C₂²×C₈₃	1	1	yes	characteristic, complemented
422	#490	C₂²×C₈₃	1	2	yes	—
423	#486	C₂²×C₈₃	1	1	yes	characteristic
424	#486	C₂²×C₈₃	1	1	yes	characteristic
425	#485	C₂²×C₈₃	1	4	yes	complemented
426	#485	C₂²×C₈₃	1	4	yes	complemented
427	#482	C₂²×C₈₃	1	4	yes	complemented
428	#482	C₂²×C₈₃	1	4	yes	complemented
429	#482	C₂²×C₈₃	1	4	yes	complemented
430	#482	C₂²×C₈₃	1	4	yes	complemented
431	#481	C₂²×C₈₃	1	4	yes	complemented
432	#481	C₂²×C₈₃	1	2	yes	complemented
433	#480	C₂²×C₈₃	1	2	yes	complemented
434	#480	C₂²×C₈₃	1	4	yes	complemented
435	#478	C₂²×C₈₃	1	4	yes	complemented
436	#477	C₂²×C₈₃	1	2	yes	complemented
437	#476	C₂²×C₈₃	1	2	yes	complemented
438	#475	C₂²×C₈₃	1	2	yes	complemented
439	#474	C₂²×C₈₃	1	2	yes	complemented
440	#468	C₂²×C₈₃	1	4	yes	complemented
441	#468	C₂²×C₈₃	1	4	yes	complemented
442	#465	C₂²×C₈₃	1	4	yes	complemented
443	#465	C₂²×C₈₃	1	4	yes	complemented
444	#460	C₂²×C₈₃	1	2	yes	—
445	#460	C₂²×C₈₃	1	2	yes	—
446	#450	C₂²×C₈₃	1	4	yes	complemented
447	#450	C₂²×C₈₃	1	4	yes	complemented
448	#448	C₂²×C₈₃	1	2	yes	complemented
449	#448	C₂²×C₈₃	1	2	yes	complemented
450	#440	C₂²×C₈₃	1	4	yes	complemented
451	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	complemented
452	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	complemented
453	#436	C₂²×C₈₃	1	2	yes	complemented
454	#435	C₂²×C₈₃	1	4	yes	complemented
455	C₈×D₄	C₂²×C₈₃	1	2	yes	complemented
456	#432	C₂²×C₈₃	1	1	yes	characteristic, complemented
457	#431	C₂²×C₈₃	1	1	yes	characteristic, complemented
458	#428	C₂²×C₈₃	1	4	yes	complemented
459	#427	C₂²×C₈₃	1	4	yes	complemented
460	#418	C₂²×C₈₃	1	4	yes	complemented
461	C₂×#102	C₂²×C₈₃	1	4	yes	complemented
462	#408	C₂²×C₈₃	1	4	yes	complemented
463	C₂×#41	—	2	1	no	—
464	C₂×#41	—	2	1	no	—
465	C₂×#41	C₂³×C₈₃	1	2	yes	—
466	C₂²×Q₈	C₂³×C₈₃	1	1	yes	characteristic
467	C₂²×D₄	—	2	2	no	—
468	C₂²×D₄	—	2	2	no	—
469	C₂²×D₄	C₂³×C₈₃	1	4	yes	—
470	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
471	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
472	C₂×SD₁₆	C₂³×C₈₃	1	4	yes	—
473	C₂×M₁₆	C₂³×C₈₃	1	4	yes	—
474	C₂²×C₈	C₂³×C₈₃	1	4	yes	—
475	C₄⋊Q₈	—	2	2	no	—
476	C₄⋊Q₈	D₄×C₈₃	1	1	yes	characteristic
477	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
478	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
479	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
480	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
481	#127	—	2	4	no	—
482	#127	D₄×C₈₃	1	1	yes	characteristic
483	#127	C₂³×C₈₃	1	1	yes	characteristic
484	#127	C₂³×C₈₃	1	1	yes	characteristic
485	#126	—	2	4	no	—
486	#126	—	2	4	no	—
487	#125	—	2	2	no	—
488	#125	—	2	4	no	—
489	#125	C₂³×C₈₃	1	2	yes	—
490	#124	—	2	4	no	—
491	#124	—	2	2	no	—
492	#124	—	2	2	no	—
493	#124	—	2	4	no	—
494	#124	—	2	4	no	—
495	#124	—	2	1	no	—
496	#124	—	2	1	no	—
497	#124	D₄×C₈₃	1	2	yes	—
498	#123	—	2	4	no	—
499	#123	—	2	4	no	—
500	C₂²⋊Q₈	—	2	1	no	—
501	C₂²⋊Q₈	—	2	1	no	—
502	C₂²⋊Q₈	—	2	4	no	—
503	C₂²⋊Q₈	C₂³×C₈₃	1	4	yes	—
504	C₂²⋊Q₈	C₂³×C₈₃	1	4	yes	—
505	#121	—	2	2	no	—
506	#121	—	2	2	no	—
507	#121	—	2	1	no	—
508	#121	—	2	1	no	—
509	#121	—	2	2	no	—
510	#121	—	2	2	no	—
511	#121	D₄×C₈₃	1	2	yes	—
512	#121	D₄×C₈₃	1	2	yes	—
513	#121	C₂³×C₈₃	1	2	yes	—
514	#121	C₂³×C₈₃	1	2	yes	—
515	#121	C₂³×C₈₃	1	4	yes	—
516	#121	C₂³×C₈₃	1	4	yes	—
517	#120	—	2	4	no	—
518	#120	—	2	4	no	—
519	#120	—	2	4	no	—
520	#120	—	2	4	no	—
521	C₄×Q₈	—	2	2	no	—
522	C₄×Q₈	—	2	2	no	—
523	C₄×Q₈	—	2	1	no	—
524	C₄×Q₈	—	2	1	no	—
525	C₄×Q₈	—	2	1	no	—
526	C₄×Q₈	—	2	1	no	—
527	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
528	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
529	C₄×D₄	—	2	4	no	—
530	C₄×D₄	—	2	2	no	—
531	C₄×D₄	—	2	2	no	—
532	C₄×D₄	—	2	1	no	—
533	C₄×D₄	—	2	1	no	—
534	C₄×D₄	C₂³×C₈₃	1	2	yes	—
535	C₄×D₄	C₂³×C₈₃	1	2	yes	—
536	C₄×D₄	C₂³×C₈₃	1	2	yes	—
537	C₄×D₄	C₂³×C₈₃	1	2	yes	—
538	#117	—	2	2	no	—
539	#117	—	2	2	no	—
540	#117	—	2	4	no	—
541	#117	C₂³×C₈₃	1	2	yes	—
542	#117	C₂³×C₈₃	1	4	yes	—
543	#117	C₂³×C₈₃	1	4	yes	—
544	C₂×C₄⋊C₄	—	2	1	no	—
545	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
546	C₂×C₄⋊C₄	C₂³×C₈₃	1	4	yes	—
547	C₂×C₄²	—	2	1	no	—
548	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
549	#107	C₂³×C₈₃	1	4	yes	—
550	#107	C₂³×C₈₃	1	4	yes	—
551	#107	C₂³×C₈₃	1	4	yes	—
552	#106	C₂³×C₈₃	1	2	yes	—
553	#106	C₂³×C₈₃	1	4	yes	—
554	#106	C₂³×C₈₃	1	2	yes	—
555	#106	C₂³×C₈₃	1	4	yes	—
556	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
557	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
558	#103	C₂³×C₈₃	1	2	yes	—
559	#103	C₂³×C₈₃	1	2	yes	—
560	#103	C₂³×C₈₃	1	4	yes	—
561	#102	C₂³×C₈₃	1	2	yes	—
562	#102	C₂³×C₈₃	1	4	yes	—
563	#102	C₂³×C₈₃	1	4	yes	—
564	#102	C₂³×C₈₃	1	4	yes	—
565	#102	C₂³×C₈₃	1	2	yes	—
566	#102	C₂³×C₈₃	1	4	yes	—
567	#102	C₂³×C₈₃	1	4	yes	—
568	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
569	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
570	C₂²⋊C₈	C₂³×C₈₃	1	4	yes	—
571	C₂²⋊C₈	C₂³×C₈₃	1	4	yes	—
572	#97	C₂³×C₈₃	1	2	yes	—
573	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
574	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
575	C₂⁴	—	2	4	no	—
576	#41	—	4	4	no	—
577	#41	—	8	2	no	—
578	#41	—	8	2	no	—
579	C₂×Q₈	—	2	1	no	—
580	C₂×Q₈	—	2	1	no	—
581	C₂×Q₈	—	2	1	no	—
582	C₂×Q₈	—	2	1	no	—
583	C₂×Q₈	—	2	1	no	—
584	C₂×Q₈	—	4	2	no	—
585	C₂×Q₈	C₂×D₄×C₈₃	1	2	yes	—
586	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	2	4	no	—
589	C₂×D₄	—	2	2	no	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	2	1	no	—
592	C₂×D₄	—	2	1	no	—
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	—	2	1	no	—
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	—	4	4	no	—
597	C₂×D₄	—	4	4	no	—
598	C₂×D₄	—	8	4	no	—
599	C₂×D₄	—	8	4	no	—
600	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
601	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
602	C₂×D₄	C₂×D₄×C₈₃	1	4	yes	—
603	C₂×D₄	C₂×D₄×C₈₃	1	2	yes	—
604	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
605	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	—	2	2	no	—
610	C₂²×C₄	—	2	2	no	—
611	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
612	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
613	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
614	C₂²×C₄	C₂⁴×C₈₃	1	4	yes	—
615	SD₁₆	—	4	2	no	—
616	SD₁₆	—	4	4	no	—
617	SD₁₆	—	4	2	no	—
618	M₁₆	—	4	4	no	—
619	C₂×C₈	—	4	4	no	—
620	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
621	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
622	C₂×C₈	C₂⁴×C₈₃	1	4	yes	—
623	C₄⋊C₄	—	2	2	no	—
624	C₄⋊C₄	—	2	2	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	2	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
636	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
637	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
638	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
639	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
640	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
641	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	2	no	—
650	C₂²⋊C₄	—	2	2	no	—
651	C₂²⋊C₄	—	2	2	no	—
652	C₂²⋊C₄	—	2	2	no	—
653	C₂²⋊C₄	C₂×D₄×C₈₃	1	4	yes	—
654	C₂²⋊C₄	C₂×D₄×C₈₃	1	4	yes	—
655	C₄²	—	2	2	no	—
656	C₄²	—	2	2	no	—
657	C₄²	—	2	4	no	—
658	C₄²	—	2	4	no	—
659	C₄²	—	2	2	no	—
660	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
661	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
662	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
663	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
664	C₂³	—	2	2	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	8	4	no	—
667	C₂³	—	8	4	no	—
668	C₂³	—	8	4	no	—
669	C₂³	C₂²×D₄×C₈₃	1	4	yes	—
670	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
671	Q₈	—	2	2	no	—
672	Q₈	—	2	2	no	—
673	Q₈	—	4	2	no	—
674	Q₈	—	4	2	no	—
675	Q₈	—	4	2	no	—
676	Q₈	—	8	1	no	—
677	Q₈	—	8	1	no	—
678	Q₈	—	8	1	no	—
679	D₄	—	2	4	no	—
680	D₄	—	2	2	no	—
681	D₄	—	2	4	no	—
682	D₄	—	2	2	no	—
683	D₄	—	4	2	no	—
684	D₄	—	4	2	no	—
685	D₄	—	4	4	no	—
686	D₄	—	4	2	no	—
687	D₄	—	4	2	no	—
688	D₄	—	8	4	no	—
689	D₄	—	8	1	no	—
690	D₄	—	8	1	no	—
691	D₄	—	8	4	no	—
692	D₄	—	8	4	no	—
693	D₄	—	8	2	no	—
694	D₄	—	8	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	4	1	no	—
706	C₂×C₄	—	4	4	no	—
707	C₂×C₄	—	4	2	no	—
708	C₂×C₄	—	4	4	no	—
709	C₂×C₄	—	8	1	no	—
710	C₂×C₄	—	8	4	no	—
711	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
712	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
713	C₂×C₄	C₂²×D₄×C₈₃	1	4	yes	—
714	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
715	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
716	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
717	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
718	C₈	—	2	2	no	—
719	C₈	—	2	4	no	—
720	C₈	—	2	2	no	—
721	C₂²	—	2	1	no	—
722	C₂²	—	2	4	no	—
723	C₂²	—	2	1	no	—
724	C₂²	—	2	4	no	—
725	C₂²	—	2	1	no	—
726	C₂²	—	2	4	no	—
727	C₂²	—	4	2	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	4	2	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	16	8	no	—
734	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
735	C₄	—	2	1	no	—
736	C₄	—	2	1	no	—
737	C₄	—	2	1	no	—
738	C₄	—	2	1	no	—
739	C₄	—	2	4	no	—
740	C₄	—	4	2	no	—
741	C₄	—	4	2	no	—
742	C₄	—	4	2	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	2	no	—
745	C₄	—	4	2	no	—
746	C₄	#577×C₈₃	1	2	yes	—
747	C₄	#585×C₈₃	1	2	yes	—
748	C₂	—	4	4	no	—
749	C₂	—	4	1	no	—
750	C₂	—	8	2	no	—
751	C₂	—	8	2	no	—
752	C₂	C₈₃×#3485	1	1	yes	characteristic
753	C₂	C₂×#577×C₈₃	1	1	yes	characteristic
754	C₂	C₈₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₃
prime radical	C₈₃×#3549	C₂
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
2. C₈₃×#3507	C₂	semidirect
3. C₈₃×#3357	C₂	semidirect
4. C₈₃×#3348	C₂	semidirect
5. C₈₃×#3340	C₂	semidirect
6. C₈₃×#3324	C₂	semidirect
7. C₈₃×#3310	C₂	semidirect
8. C₈₃×#3295	C₂	semidirect
9. C₈₃×#3235	C₂	semidirect
10. C₈₃×#3228	C₂	semidirect
11. C₈₃×#3200	C₂	semidirect
12. C₈₃×#3112	C₂	semidirect
13. C₈₃×#3103	C₂	semidirect
14. C₈₃×#3096	C₂	semidirect
15. C₈₃×#2981	C₂	semidirect
20. #556×C₈₃	C₂²	semidirect
24. #554×C₈₃	C₂²	semidirect
25. #552×C₈₃	C₂²	semidirect
30. #536×C₈₃	C₂²	semidirect
34. #533×C₈₃	C₂²	semidirect
39. #520×C₈₃	C₂²	semidirect
40. C₂×C₄×Q₈×C₈₃	C₂²	semidirect
41. #501×C₈₃	C₂²	semidirect
42. #500×C₈₃	C₂²	semidirect
43. #498×C₈₃	C₂²	semidirect
47. #485×C₈₃	C₂²	semidirect
48. #485×C₈₃	C₂²	semidirect
49. #482×C₈₃	C₂²	semidirect
50. #482×C₈₃	C₂²	semidirect
51. #482×C₈₃	C₂²	semidirect
52. #482×C₈₃	C₂²	semidirect
53. #481×C₈₃	C₂²	semidirect
54. #481×C₈₃	C₂²	semidirect
55. #480×C₈₃	C₂²	semidirect
56. #480×C₈₃	C₂²	semidirect
57. #478×C₈₃	C₂²	semidirect
58. #477×C₈₃	C₂²	semidirect
59. #476×C₈₃	C₂²	semidirect
60. #475×C₈₃	C₂²	semidirect
61. #474×C₈₃	C₂²	semidirect
62. #468×C₈₃	C₂²	semidirect
63. #468×C₈₃	C₂²	semidirect
64. #465×C₈₃	C₂²	semidirect
65. #465×C₈₃	C₂²	semidirect
68. #450×C₈₃	C₂²	semidirect
69. #450×C₈₃	C₂²	semidirect
70. #448×C₈₃	C₂²	semidirect
71. #448×C₈₃	C₂²	semidirect
72. #440×C₈₃	C₂²	semidirect
73. C₄×SD₁₆×C₈₃	C₂²	semidirect
74. C₄×SD₁₆×C₈₃	C₂²	semidirect
75. #436×C₈₃	C₂²	semidirect
76. #435×C₈₃	C₂²	semidirect
77. C₈×D₄×C₈₃	C₂²	semidirect
78. #432×C₈₃	C₂²	semidirect
79. #431×C₈₃	C₂²	semidirect
80. #428×C₈₃	C₂²	semidirect
81. #427×C₈₃	C₂²	semidirect
82. #418×C₈₃	C₂²	semidirect
83. C₂×#102×C₈₃	C₂²	semidirect
84. #408×C₈₃	C₂²	semidirect
370. #61805	C₈₃	direct (N × H)
379. #3507	C₂×C₈₃	semidirect
380. #3357	C₂×C₈₃	semidirect
381. #3348	C₂×C₈₃	semidirect
382. #3340	C₂×C₈₃	semidirect
383. #3324	C₂×C₈₃	semidirect
384. #3310	C₂×C₈₃	semidirect
385. #3295	C₂×C₈₃	semidirect
386. #3235	C₂×C₈₃	semidirect
387. #3228	C₂×C₈₃	semidirect
388. #3200	C₂×C₈₃	semidirect
389. #3112	C₂×C₈₃	semidirect
390. #3103	C₂×C₈₃	semidirect
391. #3096	C₂×C₈₃	semidirect
392. #2981	C₂×C₈₃	semidirect
393. C₈₃	#61805	direct (N × H)
398. #556	C₂²×C₈₃	semidirect
402. #554	C₂²×C₈₃	semidirect
403. #552	C₂²×C₈₃	semidirect
408. #536	C₂²×C₈₃	semidirect
412. #533	C₂²×C₈₃	semidirect
417. #520	C₂²×C₈₃	semidirect
418. C₂×C₄×Q₈	C₂²×C₈₃	semidirect
419. #501	C₂²×C₈₃	semidirect
420. #500	C₂²×C₈₃	semidirect
421. #498	C₂²×C₈₃	semidirect
425. #485	C₂²×C₈₃	semidirect
426. #485	C₂²×C₈₃	semidirect
427. #482	C₂²×C₈₃	semidirect
428. #482	C₂²×C₈₃	semidirect
429. #482	C₂²×C₈₃	semidirect
430. #482	C₂²×C₈₃	semidirect
431. #481	C₂²×C₈₃	semidirect
432. #481	C₂²×C₈₃	semidirect
433. #480	C₂²×C₈₃	semidirect
434. #480	C₂²×C₈₃	semidirect
435. #478	C₂²×C₈₃	semidirect
436. #477	C₂²×C₈₃	semidirect
437. #476	C₂²×C₈₃	semidirect
438. #475	C₂²×C₈₃	semidirect
439. #474	C₂²×C₈₃	semidirect
440. #468	C₂²×C₈₃	semidirect
441. #468	C₂²×C₈₃	semidirect
442. #465	C₂²×C₈₃	semidirect
443. #465	C₂²×C₈₃	semidirect
446. #450	C₂²×C₈₃	semidirect
447. #450	C₂²×C₈₃	semidirect
448. #448	C₂²×C₈₃	semidirect
449. #448	C₂²×C₈₃	semidirect
450. #440	C₂²×C₈₃	semidirect
451. C₄×SD₁₆	C₂²×C₈₃	semidirect
452. C₄×SD₁₆	C₂²×C₈₃	semidirect
453. #436	C₂²×C₈₃	semidirect
454. #435	C₂²×C₈₃	semidirect
455. C₈×D₄	C₂²×C₈₃	semidirect
456. #432	C₂²×C₈₃	semidirect
457. #431	C₂²×C₈₃	semidirect
458. #428	C₂²×C₈₃	semidirect
459. #427	C₂²×C₈₃	semidirect
460. #418	C₂²×C₈₃	semidirect
461. C₂×#102	C₂²×C₈₃	semidirect
462. #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×#3507	2
C₈₃×#3357	2
C₈₃×#3348	2
C₈₃×#3340	2
C₈₃×#3324	2
C₈₃×#3310	2
C₈₃×#3295	2
C₈₃×#3235	2
C₈₃×#3228	2
C₈₃×#3200	2
C₈₃×#3112	2
C₈₃×#3103	2
C₈₃×#3096	2
C₈₃×#2981	2
#61805	83

Subgroups — C83×#61805 #35289629

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#61805 #35289629