Subgroups — C₈₃×#2444 #24904129

Order 10624.

610 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#121×C₈₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₄×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#400×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#397×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#397×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#394×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
7	#388×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#387×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#386×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#386×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
11	#386×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#386×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
13	#385×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
14	#381×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#95×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	C₂³×C₄×C₈₃	C₂²	1	1	yes	characteristic
21	C₂³×C₄×C₈₃	C₂²	1	1	yes	characteristic
22	C₂³×C₄×C₈₃	C₂²	1	1	yes	characteristic
23	#121×C₈₃	—	2	4	no	—
24	C₄×D₄×C₈₃	—	2	4	no	—
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×C₄²×C₈₃	C₂²	1	1	yes	characteristic
41	#95×C₈₃	C₂²	1	1	yes	characteristic
42	#95×C₈₃	C₂²	1	1	yes	characteristic
43	#95×C₈₃	C₂²	1	1	yes	characteristic
44	#95×C₈₃	C₂²	1	1	yes	characteristic
45	#95×C₈₃	C₂²	1	1	yes	characteristic
46	#95×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	—	2	2	no	—
62	C₂×D₄×C₈₃	—	2	2	no	—
63	C₂×D₄×C₈₃	—	4	1	no	—
64	C₂×D₄×C₈₃	D₄	1	4	yes	—
65	C₂²×C₄×C₈₃	—	2	2	no	—
66	C₂²×C₄×C₈₃	—	2	2	no	—
67	C₂²×C₄×C₈₃	—	2	2	no	—
68	C₂²×C₄×C₈₃	—	2	2	no	—
69	C₂²×C₄×C₈₃	—	2	2	no	—
70	C₂²×C₄×C₈₃	—	2	2	no	—
71	C₂²×C₄×C₈₃	—	2	2	no	—
72	C₂²×C₄×C₈₃	—	4	1	no	—
73	C₂²×C₄×C₈₃	—	4	1	no	—
74	C₂²×C₄×C₈₃	—	4	1	no	—
75	C₂²×C₄×C₈₃	—	4	1	no	—
76	C₂²×C₄×C₈₃	—	4	1	no	—
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	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
81	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
82	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
83	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
84	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
85	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
86	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
89	C₄⋊C₄×C₈₃	—	2	2	no	—
90	C₄⋊C₄×C₈₃	—	2	2	no	—
91	C₄⋊C₄×C₈₃	—	2	2	no	—
92	C₄⋊C₄×C₈₃	—	4	1	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	—	2	2	no	—
99	C₂²⋊C₄×C₈₃	—	4	1	no	—
100	C₂²⋊C₄×C₈₃	—	4	1	no	—
101	C₂²⋊C₄×C₈₃	—	4	1	no	—
102	C₂²⋊C₄×C₈₃	—	4	1	no	—
103	C₂²⋊C₄×C₈₃	—	4	1	no	—
104	C₄²×C₈₃	—	2	2	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	C₂×D₄	1	2	yes	—
123	C₂³×C₈₃	C₂×D₄	1	2	yes	—
124	C₂³×C₈₃	#41	1	2	yes	—
125	C₂³×C₈₃	#41	1	2	yes	—
126	C₂³×C₈₃	C₂⁴	1	1	yes	characteristic
127	D₄×C₈₃	—	2	8	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	—	2	1	no	—
161	C₂×C₄×C₈₃	—	2	1	no	—
162	C₂×C₄×C₈₃	—	2	1	no	—
163	C₂×C₄×C₈₃	—	4	4	no	—
164	C₂×C₄×C₈₃	—	4	4	no	—
165	C₂×C₄×C₈₃	—	4	4	no	—
166	C₂×C₄×C₈₃	—	4	4	no	—
167	C₂×C₄×C₈₃	C₂×D₄	1	2	yes	—
168	C₂×C₄×C₈₃	#41	1	2	yes	—
169	C₂×C₄×C₈₃	#41	1	2	yes	—
170	C₂²×C₈₃	—	2	2	no	—
171	C₂²×C₈₃	—	2	2	no	—
172	C₂²×C₈₃	—	2	2	no	—
173	C₂²×C₈₃	—	2	2	no	—
174	C₂²×C₈₃	—	2	2	no	—
175	C₂²×C₈₃	—	2	2	no	—
176	C₂²×C₈₃	—	2	2	no	—
177	C₂²×C₈₃	—	2	2	no	—
178	C₂²×C₈₃	—	2	2	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	—	4	1	no	—
189	C₂²×C₈₃	—	4	1	no	—
190	C₂²×C₈₃	#123	1	4	yes	—
191	C₂²×C₈₃	C₂²×D₄	1	1	yes	characteristic
192	C₂²×C₈₃	C₂×#41	1	1	yes	characteristic
193	C₂²×C₈₃	C₂×#41	1	1	yes	characteristic
194	C₂²×C₈₃	C₂×#41	1	1	yes	characteristic
195	C₂²×C₈₃	C₂×#41	1	1	yes	characteristic
196	C₂²×C₈₃	H(5,𝔽₂)	1	1	yes	characteristic
197	C₂²×C₈₃	H(5,𝔽₂)	1	1	yes	characteristic
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	C₄×C₈₃	—	4	1	no	—
208	C₄×C₈₃	—	4	1	no	—
209	C₄×C₈₃	—	4	1	no	—
210	C₂×C₈₃	—	2	4	no	—
211	C₂×C₈₃	—	4	2	no	—
212	C₂×C₈₃	—	8	1	no	—
213	C₂×C₈₃	C₂×#123	1	1	yes	characteristic
214	C₂×C₈₃	#529	1	1	yes	characteristic
215	C₂×C₈₃	#538	1	1	yes	characteristic
216	C₂×C₈₃	#546	1	1	yes	characteristic
217	C₂×C₈₃	#546	1	1	yes	characteristic
218	C₂×C₈₃	#553	1	1	yes	characteristic
219	C₂×C₈₃	#553	1	1	yes	characteristic
220	#2444	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
221	C₈₃	#2444	1	1	yes	characteristic, direct product factor, Sylow
222	C₂×#121	C₂×C₈₃	1	1	yes	characteristic
223	C₂×C₄×D₄	C₂×C₈₃	1	1	yes	characteristic, complemented
224	#400	C₂×C₈₃	1	1	yes	characteristic, complemented
225	#397	C₂×C₈₃	1	1	yes	characteristic, complemented
226	#397	C₂×C₈₃	1	1	yes	characteristic, complemented
227	#394	C₂×C₈₃	1	1	yes	characteristic, complemented
228	#388	C₂×C₈₃	1	1	yes	characteristic, complemented
229	#387	C₂×C₈₃	1	1	yes	characteristic, complemented
230	#386	C₂×C₈₃	1	1	yes	characteristic, complemented
231	#386	C₂×C₈₃	1	1	yes	characteristic, complemented
232	#386	C₂×C₈₃	1	1	yes	characteristic, complemented
233	#386	C₂×C₈₃	1	1	yes	characteristic, complemented
234	#385	C₂×C₈₃	1	1	yes	characteristic, complemented
235	#381	C₂×C₈₃	1	1	yes	characteristic, complemented
236	C₂×#95	C₂×C₈₃	1	1	yes	characteristic, complemented
237	C₂²×D₄	C₂²×C₈₃	1	1	yes	characteristic
238	C₂²×D₄	C₂²×C₈₃	1	1	yes	characteristic
239	C₂²×D₄	C₂²×C₈₃	1	1	yes	characteristic
240	C₂³×C₄	C₂²×C₈₃	1	1	yes	characteristic
241	C₂³×C₄	C₂²×C₈₃	1	1	yes	characteristic
242	C₂³×C₄	C₂²×C₈₃	1	1	yes	characteristic
243	C₂³×C₄	C₂²×C₈₃	1	1	yes	characteristic
244	#121	—	2	4	no	—
245	C₄×D₄	—	2	4	no	—
246	C₂×C₄⋊C₄	C₂²×C₈₃	1	1	yes	characteristic
247	C₂×C₄⋊C₄	C₂²×C₈₃	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₂²×C₈₃	1	1	yes	characteristic
249	C₂×C₄⋊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	#95	C₂²×C₈₃	1	1	yes	characteristic
263	#95	C₂²×C₈₃	1	1	yes	characteristic
264	#95	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	#95	C₂²×C₈₃	1	1	yes	characteristic
272	#95	C₂²×C₈₃	1	1	yes	characteristic
273	#95	C₂²×C₈₃	1	1	yes	characteristic
274	C₂⁴	C₂³×C₈₃	1	1	yes	characteristic
275	C₂⁴	C₂³×C₈₃	1	1	yes	characteristic
276	C₂⁴	C₂³×C₈₃	1	1	yes	characteristic
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	4	1	no	—
285	C₂×D₄	D₄×C₈₃	1	4	yes	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	4	1	no	—
294	C₂²×C₄	—	4	1	no	—
295	C₂²×C₄	—	4	1	no	—
296	C₂²×C₄	—	4	1	no	—
297	C₂²×C₄	—	4	1	no	—
298	C₂²×C₄	C₂³×C₈₃	1	1	yes	characteristic
299	C₂²×C₄	C₂³×C₈₃	1	1	yes	characteristic
300	C₂²×C₄	C₂³×C₈₃	1	1	yes	characteristic
301	C₂²×C₄	C₂³×C₈₃	1	1	yes	characteristic
302	C₂²×C₄	C₂³×C₈₃	1	1	yes	characteristic
303	C₂²×C₄	C₂³×C₈₃	1	1	yes	characteristic
304	C₂²×C₄	C₂³×C₈₃	1	1	yes	characteristic
305	C₂²×C₄	C₂³×C₈₃	1	1	yes	characteristic
306	C₂²×C₄	C₂³×C₈₃	1	1	yes	characteristic
307	C₂²×C₄	C₂³×C₈₃	1	1	yes	characteristic
308	C₂²×C₄	C₂³×C₈₃	1	1	yes	characteristic
309	C₂²×C₄	C₂³×C₈₃	1	1	yes	characteristic
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	4	1	no	—
314	C₂²⋊C₄	—	2	2	no	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₂²⋊C₄	—	2	2	no	—
317	C₂²⋊C₄	—	2	2	no	—
318	C₂²⋊C₄	—	2	2	no	—
319	C₂²⋊C₄	—	2	2	no	—
320	C₂²⋊C₄	—	4	1	no	—
321	C₂²⋊C₄	—	4	1	no	—
322	C₂²⋊C₄	—	4	1	no	—
323	C₂²⋊C₄	—	4	1	no	—
324	C₂²⋊C₄	—	4	1	no	—
325	C₄²	—	2	2	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	C₂×D₄×C₈₃	1	2	yes	—
344	C₂³	C₂×D₄×C₈₃	1	2	yes	—
345	C₂³	#41×C₈₃	1	2	yes	—
346	C₂³	#41×C₈₃	1	2	yes	—
347	C₂³	C₂⁴×C₈₃	1	1	yes	characteristic
348	D₄	—	2	8	no	—
349	D₄	—	4	4	no	—
350	D₄	—	4	4	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	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	4	4	no	—
385	C₂×C₄	—	4	4	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	C₂×D₄×C₈₃	1	2	yes	—
389	C₂×C₄	#41×C₈₃	1	2	yes	—
390	C₂×C₄	#41×C₈₃	1	2	yes	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	2	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	—	4	1	no	—
407	C₂²	—	4	1	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	1	no	—
410	C₂²	—	4	1	no	—
411	C₂²	#123×C₈₃	1	4	yes	—
412	C₂²	C₂²×D₄×C₈₃	1	1	yes	characteristic
413	C₂²	C₂×#41×C₈₃	1	1	yes	characteristic
414	C₂²	C₂×#41×C₈₃	1	1	yes	characteristic
415	C₂²	C₂×#41×C₈₃	1	1	yes	characteristic
416	C₂²	C₂×#41×C₈₃	1	1	yes	characteristic
417	C₂²	H(5,𝔽₂)×C₈₃	1	1	yes	characteristic
418	C₂²	H(5,𝔽₂)×C₈₃	1	1	yes	characteristic
419	C₄	—	2	2	no	—
420	C₄	—	2	2	no	—
421	C₄	—	2	2	no	—
422	C₄	—	4	1	no	—
423	C₄	—	4	1	no	—
424	C₄	—	4	1	no	—
425	C₄	—	4	1	no	—
426	C₄	—	4	1	no	—
427	C₄	—	4	1	no	—
428	C₄	—	4	1	no	—
429	C₄	—	4	1	no	—
430	C₄	—	4	1	no	—
431	C₂	—	2	4	no	—
432	C₂	—	4	2	no	—
433	C₂	—	8	1	no	—
434	C₂	C₂×#123×C₈₃	1	1	yes	characteristic
435	C₂	#529×C₈₃	1	1	yes	characteristic
436	C₂	#538×C₈₃	1	1	yes	characteristic
437	C₂	#546×C₈₃	1	1	yes	characteristic
438	C₂	#546×C₈₃	1	1	yes	characteristic
439	C₂	#553×C₈₃	1	1	yes	characteristic
440	C₂	#553×C₈₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₈₃
prime radical	C₂×#121×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
2. C₂×C₄×D₄×C₈₃	C₂	semidirect
3. #400×C₈₃	C₂	semidirect
4. #397×C₈₃	C₂	semidirect
5. #397×C₈₃	C₂	semidirect
6. #394×C₈₃	C₂	semidirect
7. #388×C₈₃	C₂	semidirect
8. #387×C₈₃	C₂	semidirect
9. #386×C₈₃	C₂	semidirect
10. #386×C₈₃	C₂	semidirect
11. #386×C₈₃	C₂	semidirect
12. #386×C₈₃	C₂	semidirect
13. #385×C₈₃	C₂	semidirect
14. #381×C₈₃	C₂	semidirect
15. C₂×#95×C₈₃	C₂	semidirect
220. #2444	C₈₃	direct (N × H)
221. C₈₃	#2444	direct (N × H)
223. C₂×C₄×D₄	C₂×C₈₃	semidirect
224. #400	C₂×C₈₃	semidirect
225. #397	C₂×C₈₃	semidirect
226. #397	C₂×C₈₃	semidirect
227. #394	C₂×C₈₃	semidirect
228. #388	C₂×C₈₃	semidirect
229. #387	C₂×C₈₃	semidirect
230. #386	C₂×C₈₃	semidirect
231. #386	C₂×C₈₃	semidirect
232. #386	C₂×C₈₃	semidirect
233. #386	C₂×C₈₃	semidirect
234. #385	C₂×C₈₃	semidirect
235. #381	C₂×C₈₃	semidirect
236. C₂×#95	C₂×C₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#121×C₈₃	2
C₂×C₄×D₄×C₈₃	2
#400×C₈₃	2
#397×C₈₃	2
#394×C₈₃	2
#388×C₈₃	2
#387×C₈₃	2
#386×C₈₃	2
#385×C₈₃	2
#381×C₈₃	2
C₂×#95×C₈₃	2
#2444	83

Subgroups — C83×#2444 #24904129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#2444 #24904129