Subgroups — C₈₃×#2554 #24904239

Order 10624.

560 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#126×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#123×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#398×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#396×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#394×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#392×C₈₃	C₂	1	1	yes	maximal, characteristic
7	#390×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#390×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#390×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#388×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
11	#388×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#388×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
13	#386×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₄⋊C₄×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₂²⋊C₄×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₄×C₈₃	C₂²	1	1	yes	characteristic
17	C₂²×D₄×C₈₃	C₂²	1	1	yes	characteristic
18	C₂²×D₄×C₈₃	C₂²	1	1	yes	characteristic
19	C₂³×C₄×C₈₃	C₂²	1	1	yes	characteristic
20	#126×C₈₃	—	2	4	no	—
21	#123×C₈₃	—	2	4	no	—
22	C₂×C₄⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
42	C₂×C₂²⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
43	C₂×C₄²×C₈₃	C₂²	1	1	yes	characteristic
44	C₂×C₄²×C₈₃	C₂²	1	1	yes	characteristic
45	C₂×C₄²×C₈₃	C₂²	1	1	yes	characteristic
46	C₂×C₄²×C₈₃	C₂²	1	1	yes	characteristic
47	#95×C₈₃	C₂²	1	1	yes	characteristic
48	#95×C₈₃	C₂²	1	1	yes	characteristic
49	#95×C₈₃	C₂²	1	1	yes	characteristic
50	#95×C₈₃	C₂²	1	1	yes	characteristic
51	#95×C₈₃	C₂²	1	1	yes	characteristic
52	#95×C₈₃	C₂²	1	1	yes	characteristic
53	C₂⁴×C₈₃	C₂³	1	1	yes	characteristic
54	C₂⁴×C₈₃	C₂³	1	1	yes	characteristic
55	C₂⁴×C₈₃	C₂³	1	1	yes	characteristic
56	C₂×D₄×C₈₃	—	2	2	no	—
57	C₂×D₄×C₈₃	—	2	2	no	—
58	C₂×D₄×C₈₃	—	2	2	no	—
59	C₂×D₄×C₈₃	—	2	2	no	—
60	C₂×D₄×C₈₃	—	2	2	no	—
61	C₂×D₄×C₈₃	—	4	1	no	—
62	C₂×D₄×C₈₃	—	4	1	no	—
63	C₂×D₄×C₈₃	—	4	1	no	—
64	C₂×D₄×C₈₃	—	4	1	no	—
65	C₂²×C₄×C₈₃	—	2	2	no	—
66	C₂²×C₄×C₈₃	—	2	2	no	—
67	C₂²×C₄×C₈₃	—	4	1	no	—
68	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
70	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
71	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
72	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
74	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
75	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
76	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
77	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
78	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
79	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
80	C₄⋊C₄×C₈₃	—	2	2	no	—
81	C₄⋊C₄×C₈₃	—	2	2	no	—
82	C₄⋊C₄×C₈₃	—	2	2	no	—
83	C₄⋊C₄×C₈₃	—	2	2	no	—
84	C₄⋊C₄×C₈₃	—	4	1	no	—
85	C₄⋊C₄×C₈₃	—	4	1	no	—
86	C₄⋊C₄×C₈₃	D₄	1	4	yes	complemented
87	C₂²⋊C₄×C₈₃	—	2	2	no	—
88	C₂²⋊C₄×C₈₃	—	2	2	no	—
89	C₂²⋊C₄×C₈₃	—	2	2	no	—
90	C₂²⋊C₄×C₈₃	—	2	2	no	—
91	C₂²⋊C₄×C₈₃	—	2	2	no	—
92	C₂²⋊C₄×C₈₃	—	2	2	no	—
93	C₂²⋊C₄×C₈₃	—	2	2	no	—
94	C₂²⋊C₄×C₈₃	—	2	2	no	—
95	C₂²⋊C₄×C₈₃	—	2	2	no	—
96	C₂²⋊C₄×C₈₃	—	2	2	no	—
97	C₂²⋊C₄×C₈₃	—	2	2	no	—
98	C₂²⋊C₄×C₈₃	—	4	1	no	—
99	C₂²⋊C₄×C₈₃	—	4	1	no	—
100	C₂²⋊C₄×C₈₃	—	4	1	no	—
101	C₄²×C₈₃	—	2	2	no	—
102	C₄²×C₈₃	—	2	2	no	—
103	C₄²×C₈₃	—	4	1	no	—
104	C₄²×C₈₃	—	4	1	no	—
105	C₂³×C₈₃	—	2	1	no	—
106	C₂³×C₈₃	—	2	1	no	—
107	C₂³×C₈₃	—	2	1	no	—
108	C₂³×C₈₃	—	2	1	no	—
109	C₂³×C₈₃	—	2	1	no	—
110	C₂³×C₈₃	—	2	1	no	—
111	C₂³×C₈₃	—	2	1	no	—
112	C₂³×C₈₃	—	2	1	no	—
113	C₂³×C₈₃	—	2	1	no	—
114	C₂³×C₈₃	—	2	1	no	—
115	C₂³×C₈₃	—	2	1	no	—
116	C₂³×C₈₃	—	2	1	no	—
117	C₂³×C₈₃	—	2	1	no	—
118	C₂³×C₈₃	—	2	1	no	—
119	C₂³×C₈₃	—	2	1	no	—
120	C₂³×C₈₃	—	2	1	no	—
121	C₂³×C₈₃	—	2	1	no	—
122	C₂³×C₈₃	—	2	1	no	—
123	C₂³×C₈₃	—	2	1	no	—
124	C₂³×C₈₃	—	2	1	no	—
125	C₂³×C₈₃	#41	1	2	yes	—
126	C₂³×C₈₃	C₂⁴	1	1	yes	characteristic
127	D₄×C₈₃	—	4	4	no	—
128	D₄×C₈₃	—	4	4	no	—
129	D₄×C₈₃	—	4	4	no	—
130	C₂×C₄×C₈₃	—	2	1	no	—
131	C₂×C₄×C₈₃	—	2	1	no	—
132	C₂×C₄×C₈₃	—	2	1	no	—
133	C₂×C₄×C₈₃	—	2	1	no	—
134	C₂×C₄×C₈₃	—	2	1	no	—
135	C₂×C₄×C₈₃	—	2	1	no	—
136	C₂×C₄×C₈₃	—	2	1	no	—
137	C₂×C₄×C₈₃	—	2	1	no	—
138	C₂×C₄×C₈₃	—	2	1	no	—
139	C₂×C₄×C₈₃	—	2	1	no	—
140	C₂×C₄×C₈₃	—	2	1	no	—
141	C₂×C₄×C₈₃	—	2	1	no	—
142	C₂×C₄×C₈₃	—	2	1	no	—
143	C₂×C₄×C₈₃	—	2	1	no	—
144	C₂×C₄×C₈₃	—	2	1	no	—
145	C₂×C₄×C₈₃	—	2	1	no	—
146	C₂×C₄×C₈₃	—	2	1	no	—
147	C₂×C₄×C₈₃	—	2	1	no	—
148	C₂×C₄×C₈₃	—	2	1	no	—
149	C₂×C₄×C₈₃	—	2	1	no	—
150	C₂×C₄×C₈₃	—	2	1	no	—
151	C₂×C₄×C₈₃	—	2	1	no	—
152	C₂×C₄×C₈₃	—	2	1	no	—
153	C₂×C₄×C₈₃	—	2	1	no	—
154	C₂×C₄×C₈₃	—	2	1	no	—
155	C₂×C₄×C₈₃	—	2	1	no	—
156	C₂×C₄×C₈₃	—	2	1	no	—
157	C₂×C₄×C₈₃	—	2	1	no	—
158	C₂×C₄×C₈₃	—	2	1	no	—
159	C₂×C₄×C₈₃	—	2	1	no	—
160	C₂×C₄×C₈₃	—	4	4	no	—
161	C₂×C₄×C₈₃	C₂×D₄	1	2	yes	—
162	C₂×C₄×C₈₃	C₂×D₄	1	2	yes	—
163	C₂×C₄×C₈₃	C₂×D₄	1	2	yes	—
164	C₂×C₄×C₈₃	#41	1	2	yes	—
165	C₂×C₄×C₈₃	#41	1	2	yes	—
166	C₂×C₄×C₈₃	#41	1	2	yes	—
167	C₂²×C₈₃	—	2	2	no	—
168	C₂²×C₈₃	—	2	2	no	—
169	C₂²×C₈₃	—	2	2	no	—
170	C₂²×C₈₃	—	4	1	no	—
171	C₂²×C₈₃	—	4	1	no	—
172	C₂²×C₈₃	—	4	1	no	—
173	C₂²×C₈₃	—	4	1	no	—
174	C₂²×C₈₃	—	4	1	no	—
175	C₂²×C₈₃	—	4	1	no	—
176	C₂²×C₈₃	—	4	1	no	—
177	C₂²×C₈₃	—	4	1	no	—
178	C₂²×C₈₃	—	4	1	no	—
179	C₂²×C₈₃	—	4	1	no	—
180	C₂²×C₈₃	—	4	1	no	—
181	C₂²×C₈₃	—	4	1	no	—
182	C₂²×C₈₃	—	4	1	no	—
183	C₂²×C₈₃	—	4	1	no	—
184	C₂²×C₈₃	—	4	1	no	—
185	C₂²×C₈₃	—	4	1	no	—
186	C₂²×C₈₃	—	4	1	no	—
187	C₂²×C₈₃	—	4	1	no	—
188	C₂²×C₈₃	C₂²×D₄	1	1	yes	characteristic
189	C₂²×C₈₃	C₂×#41	1	1	yes	characteristic
190	C₂²×C₈₃	C₂×#41	1	1	yes	characteristic
191	C₂²×C₈₃	C₂×#41	1	1	yes	characteristic
192	C₂²×C₈₃	C₂×#41	1	1	yes	characteristic
193	C₂²×C₈₃	H(5,𝔽₂)	1	1	yes	characteristic
194	C₂²×C₈₃	H(5,𝔽₂)	1	1	yes	characteristic
195	C₄×C₈₃	—	2	2	no	—
196	C₄×C₈₃	—	2	2	no	—
197	C₄×C₈₃	—	2	2	no	—
198	C₄×C₈₃	—	2	2	no	—
199	C₄×C₈₃	—	2	2	no	—
200	C₄×C₈₃	—	2	2	no	—
201	C₄×C₈₃	—	4	1	no	—
202	C₄×C₈₃	—	4	1	no	—
203	C₄×C₈₃	—	4	1	no	—
204	C₄×C₈₃	—	4	1	no	—
205	C₄×C₈₃	—	4	1	no	—
206	C₄×C₈₃	—	4	1	no	—
207	C₂×C₈₃	—	4	2	no	—
208	C₂×C₈₃	—	8	1	no	—
209	C₂×C₈₃	—	8	1	no	—
210	C₂×C₈₃	#529	1	1	yes	characteristic
211	C₂×C₈₃	#532	1	1	yes	characteristic
212	C₂×C₈₃	#538	1	1	yes	characteristic
213	C₂×C₈₃	#546	1	1	yes	characteristic
214	C₂×C₈₃	#550	1	1	yes	characteristic
215	C₂×C₈₃	#551	1	1	yes	characteristic
216	C₂×C₈₃	#553	1	1	yes	characteristic
217	#2554	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₈₃	#2554	1	1	yes	characteristic, direct product factor, Sylow
219	C₂×#126	C₂×C₈₃	1	1	yes	characteristic, complemented
220	C₂×#123	C₂×C₈₃	1	1	yes	characteristic, complemented
221	#398	C₂×C₈₃	1	1	yes	characteristic, complemented
222	#396	C₂×C₈₃	1	1	yes	characteristic, complemented
223	#394	C₂×C₈₃	1	1	yes	characteristic, complemented
224	#392	C₂×C₈₃	1	1	yes	characteristic
225	#390	C₂×C₈₃	1	1	yes	characteristic, complemented
226	#390	C₂×C₈₃	1	1	yes	characteristic, complemented
227	#390	C₂×C₈₃	1	1	yes	characteristic, complemented
228	#388	C₂×C₈₃	1	1	yes	characteristic, complemented
229	#388	C₂×C₈₃	1	1	yes	characteristic, complemented
230	#388	C₂×C₈₃	1	1	yes	characteristic, complemented
231	#386	C₂×C₈₃	1	1	yes	characteristic, complemented
232	C₄×C₄⋊C₄	C₂×C₈₃	1	1	yes	characteristic, complemented
233	C₄×C₂²⋊C₄	C₂×C₈₃	1	1	yes	characteristic, complemented
234	C₂²×D₄	C₂²×C₈₃	1	1	yes	characteristic
235	C₂²×D₄	C₂²×C₈₃	1	1	yes	characteristic
236	C₂²×D₄	C₂²×C₈₃	1	1	yes	characteristic
237	C₂³×C₄	C₂²×C₈₃	1	1	yes	characteristic
238	#126	—	2	4	no	—
239	#123	—	2	4	no	—
240	C₂×C₄⋊C₄	C₂²×C₈₃	1	1	yes	characteristic
241	C₂×C₄⋊C₄	C₂²×C₈₃	1	1	yes	characteristic
242	C₂×C₄⋊C₄	C₂²×C₈₃	1	1	yes	characteristic
243	C₂×C₄⋊C₄	C₂²×C₈₃	1	1	yes	characteristic
244	C₂×C₄⋊C₄	C₂²×C₈₃	1	1	yes	characteristic
245	C₂×C₄⋊C₄	C₂²×C₈₃	1	1	yes	characteristic
246	C₂×C₄⋊C₄	C₂²×C₈₃	1	1	yes	characteristic
247	C₂×C₂²⋊C₄	C₂²×C₈₃	1	1	yes	characteristic
248	C₂×C₂²⋊C₄	C₂²×C₈₃	1	1	yes	characteristic
249	C₂×C₂²⋊C₄	C₂²×C₈₃	1	1	yes	characteristic
250	C₂×C₂²⋊C₄	C₂²×C₈₃	1	1	yes	characteristic
251	C₂×C₂²⋊C₄	C₂²×C₈₃	1	1	yes	characteristic
252	C₂×C₂²⋊C₄	C₂²×C₈₃	1	1	yes	characteristic
253	C₂×C₂²⋊C₄	C₂²×C₈₃	1	1	yes	characteristic
254	C₂×C₂²⋊C₄	C₂²×C₈₃	1	1	yes	characteristic
255	C₂×C₂²⋊C₄	C₂²×C₈₃	1	1	yes	characteristic
256	C₂×C₂²⋊C₄	C₂²×C₈₃	1	1	yes	characteristic
257	C₂×C₂²⋊C₄	C₂²×C₈₃	1	1	yes	characteristic
258	C₂×C₂²⋊C₄	C₂²×C₈₃	1	1	yes	characteristic
259	C₂×C₂²⋊C₄	C₂²×C₈₃	1	1	yes	characteristic
260	C₂×C₂²⋊C₄	C₂²×C₈₃	1	1	yes	characteristic
261	C₂×C₄²	C₂²×C₈₃	1	1	yes	characteristic
262	C₂×C₄²	C₂²×C₈₃	1	1	yes	characteristic
263	C₂×C₄²	C₂²×C₈₃	1	1	yes	characteristic
264	C₂×C₄²	C₂²×C₈₃	1	1	yes	characteristic
265	#95	C₂²×C₈₃	1	1	yes	characteristic
266	#95	C₂²×C₈₃	1	1	yes	characteristic
267	#95	C₂²×C₈₃	1	1	yes	characteristic
268	#95	C₂²×C₈₃	1	1	yes	characteristic
269	#95	C₂²×C₈₃	1	1	yes	characteristic
270	#95	C₂²×C₈₃	1	1	yes	characteristic
271	C₂⁴	C₂³×C₈₃	1	1	yes	characteristic
272	C₂⁴	C₂³×C₈₃	1	1	yes	characteristic
273	C₂⁴	C₂³×C₈₃	1	1	yes	characteristic
274	C₂×D₄	—	2	2	no	—
275	C₂×D₄	—	2	2	no	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	—	4	1	no	—
280	C₂×D₄	—	4	1	no	—
281	C₂×D₄	—	4	1	no	—
282	C₂×D₄	—	4	1	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	C₂³×C₈₃	1	1	yes	characteristic
287	C₂²×C₄	C₂³×C₈₃	1	1	yes	characteristic
288	C₂²×C₄	C₂³×C₈₃	1	1	yes	characteristic
289	C₂²×C₄	C₂³×C₈₃	1	1	yes	characteristic
290	C₂²×C₄	C₂³×C₈₃	1	1	yes	characteristic
291	C₂²×C₄	C₂³×C₈₃	1	1	yes	characteristic
292	C₂²×C₄	C₂³×C₈₃	1	1	yes	characteristic
293	C₂²×C₄	C₂³×C₈₃	1	1	yes	characteristic
294	C₂²×C₄	C₂³×C₈₃	1	1	yes	characteristic
295	C₂²×C₄	C₂³×C₈₃	1	1	yes	characteristic
296	C₂²×C₄	C₂³×C₈₃	1	1	yes	characteristic
297	C₂²×C₄	C₂³×C₈₃	1	1	yes	characteristic
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	4	1	no	—
303	C₄⋊C₄	—	4	1	no	—
304	C₄⋊C₄	D₄×C₈₃	1	4	yes	complemented
305	C₂²⋊C₄	—	2	2	no	—
306	C₂²⋊C₄	—	2	2	no	—
307	C₂²⋊C₄	—	2	2	no	—
308	C₂²⋊C₄	—	2	2	no	—
309	C₂²⋊C₄	—	2	2	no	—
310	C₂²⋊C₄	—	2	2	no	—
311	C₂²⋊C₄	—	2	2	no	—
312	C₂²⋊C₄	—	2	2	no	—
313	C₂²⋊C₄	—	2	2	no	—
314	C₂²⋊C₄	—	2	2	no	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₂²⋊C₄	—	4	1	no	—
317	C₂²⋊C₄	—	4	1	no	—
318	C₂²⋊C₄	—	4	1	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	4	1	no	—
322	C₄²	—	4	1	no	—
323	C₂³	—	2	1	no	—
324	C₂³	—	2	1	no	—
325	C₂³	—	2	1	no	—
326	C₂³	—	2	1	no	—
327	C₂³	—	2	1	no	—
328	C₂³	—	2	1	no	—
329	C₂³	—	2	1	no	—
330	C₂³	—	2	1	no	—
331	C₂³	—	2	1	no	—
332	C₂³	—	2	1	no	—
333	C₂³	—	2	1	no	—
334	C₂³	—	2	1	no	—
335	C₂³	—	2	1	no	—
336	C₂³	—	2	1	no	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	2	1	no	—
342	C₂³	—	2	1	no	—
343	C₂³	#41×C₈₃	1	2	yes	—
344	C₂³	C₂⁴×C₈₃	1	1	yes	characteristic
345	D₄	—	4	4	no	—
346	D₄	—	4	4	no	—
347	D₄	—	4	4	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	C₂×D₄×C₈₃	1	2	yes	—
380	C₂×C₄	C₂×D₄×C₈₃	1	2	yes	—
381	C₂×C₄	C₂×D₄×C₈₃	1	2	yes	—
382	C₂×C₄	#41×C₈₃	1	2	yes	—
383	C₂×C₄	#41×C₈₃	1	2	yes	—
384	C₂×C₄	#41×C₈₃	1	2	yes	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	2	2	no	—
388	C₂²	—	4	1	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	4	1	no	—
391	C₂²	—	4	1	no	—
392	C₂²	—	4	1	no	—
393	C₂²	—	4	1	no	—
394	C₂²	—	4	1	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	C₂²×D₄×C₈₃	1	1	yes	characteristic
407	C₂²	C₂×#41×C₈₃	1	1	yes	characteristic
408	C₂²	C₂×#41×C₈₃	1	1	yes	characteristic
409	C₂²	C₂×#41×C₈₃	1	1	yes	characteristic
410	C₂²	C₂×#41×C₈₃	1	1	yes	characteristic
411	C₂²	H(5,𝔽₂)×C₈₃	1	1	yes	characteristic
412	C₂²	H(5,𝔽₂)×C₈₃	1	1	yes	characteristic
413	C₄	—	2	2	no	—
414	C₄	—	2	2	no	—
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	2	2	no	—
418	C₄	—	2	2	no	—
419	C₄	—	4	1	no	—
420	C₄	—	4	1	no	—
421	C₄	—	4	1	no	—
422	C₄	—	4	1	no	—
423	C₄	—	4	1	no	—
424	C₄	—	4	1	no	—
425	C₂	—	4	2	no	—
426	C₂	—	8	1	no	—
427	C₂	—	8	1	no	—
428	C₂	#529×C₈₃	1	1	yes	characteristic
429	C₂	#532×C₈₃	1	1	yes	characteristic
430	C₂	#538×C₈₃	1	1	yes	characteristic
431	C₂	#546×C₈₃	1	1	yes	characteristic
432	C₂	#550×C₈₃	1	1	yes	characteristic
433	C₂	#551×C₈₃	1	1	yes	characteristic
434	C₂	#553×C₈₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₈₃
prime radical	#392×C₈₃	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#126×C₈₃	C₂	semidirect
2. C₂×#123×C₈₃	C₂	semidirect
3. #398×C₈₃	C₂	semidirect
4. #396×C₈₃	C₂	semidirect
5. #394×C₈₃	C₂	semidirect
7. #390×C₈₃	C₂	semidirect
8. #390×C₈₃	C₂	semidirect
9. #390×C₈₃	C₂	semidirect
10. #388×C₈₃	C₂	semidirect
11. #388×C₈₃	C₂	semidirect
12. #388×C₈₃	C₂	semidirect
13. #386×C₈₃	C₂	semidirect
14. C₄×C₄⋊C₄×C₈₃	C₂	semidirect
15. C₄×C₂²⋊C₄×C₈₃	C₂	semidirect
86. C₄⋊C₄×C₈₃	D₄	semidirect
217. #2554	C₈₃	direct (N × H)
218. C₈₃	#2554	direct (N × H)
219. C₂×#126	C₂×C₈₃	semidirect
220. C₂×#123	C₂×C₈₃	semidirect
221. #398	C₂×C₈₃	semidirect
222. #396	C₂×C₈₃	semidirect
223. #394	C₂×C₈₃	semidirect
225. #390	C₂×C₈₃	semidirect
226. #390	C₂×C₈₃	semidirect
227. #390	C₂×C₈₃	semidirect
228. #388	C₂×C₈₃	semidirect
229. #388	C₂×C₈₃	semidirect
230. #388	C₂×C₈₃	semidirect
231. #386	C₂×C₈₃	semidirect
232. C₄×C₄⋊C₄	C₂×C₈₃	semidirect
233. C₄×C₂²⋊C₄	C₂×C₈₃	semidirect
304. C₄⋊C₄	D₄×C₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#126×C₈₃	2
C₂×#123×C₈₃	2
#398×C₈₃	2
#396×C₈₃	2
#394×C₈₃	2
#392×C₈₃	2
#390×C₈₃	2
#388×C₈₃	2
#386×C₈₃	2
C₄×C₄⋊C₄×C₈₃	2
C₄×C₂²⋊C₄×C₈₃	2
#2554	83

Subgroups — C83×#2554 #24904239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#2554 #24904239