Subgroups — C₂×C₈₃×#3200 #35288568

Order 21248.

2314 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#536×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#535×C₈₃	C₂	1	1	yes	maximal, characteristic
3	C₈₃×#3200	C₂	1	16	yes	maximal, direct product factor
4	C₂×#485×C₈₃	C₂	1	2	yes	maximal, complemented
5	C₂×#482×C₈₃	C₂	1	2	yes	maximal, complemented
6	C₂×#468×C₈₃	C₂	1	2	yes	maximal, complemented
7	C₂×#465×C₈₃	C₂	1	2	yes	maximal, complemented
8	C₂×#448×C₈₃	C₂	1	2	yes	maximal, complemented
9	C₂×#450×C₈₃	C₂	1	2	yes	maximal, complemented
10	C₂×#408×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#41×C₈₃	C₂²	1	1	yes	characteristic
12	C₂³×Q₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
13	C₂³×D₄×C₈₃	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₈₃	C₂²	1	2	yes	—
15	C₂²×SD₁₆×C₈₃	C₂²	1	2	yes	—
16	C₂²×M₁₆×C₈₃	C₂²	1	1	yes	characteristic, complemented
17	C₂³×C₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
18	#536×C₈₃	—	2	4	no	—
19	#536×C₈₃	C₂²	1	8	yes	complemented
20	#535×C₈₃	—	2	4	no	—
21	#535×C₈₃	C₂²	1	8	yes	—
22	C₂×C₄⋊Q₈×C₈₃	—	2	1	no	—
23	C₂×#127×C₈₃	—	2	1	no	—
24	C₂×#124×C₈₃	—	2	1	no	—
25	C₂×#124×C₈₃	—	2	1	no	—
26	C₂×#123×C₈₃	—	2	1	no	—
27	C₂×#123×C₈₃	—	2	1	no	—
28	C₂×C₂²⋊Q₈×C₈₃	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₈₃	C₂²	1	2	yes	complemented
30	C₂×#121×C₈₃	C₂²	1	2	yes	—
31	C₂×#121×C₈₃	C₂²	1	2	yes	—
32	C₂×#120×C₈₃	—	2	1	no	—
33	C₂×#120×C₈₃	—	2	1	no	—
34	C₂×#117×C₈₃	C₂²	1	1	yes	characteristic
35	C₂×#117×C₈₃	C₂²	1	1	yes	characteristic, complemented
36	#485×C₈₃	C₂²	1	16	yes	complemented
37	#482×C₈₃	C₂²	1	16	yes	complemented
38	#468×C₈₃	C₂²	1	16	yes	complemented
39	#465×C₈₃	C₂²	1	16	yes	complemented
40	#450×C₈₃	C₂²	1	16	yes	complemented
41	#448×C₈₃	C₂²	1	16	yes	complemented
42	C₂×#107×C₈₃	C₂²	1	2	yes	complemented
43	C₂×#106×C₈₃	C₂²	1	2	yes	complemented
44	C₂×#103×C₈₃	C₂²	1	2	yes	complemented
45	C₂×#103×C₈₃	C₂²	1	2	yes	complemented
46	C₂×#102×C₈₃	C₂²	1	2	yes	—
47	C₂×#102×C₈₃	C₂²	1	2	yes	—
48	#408×C₈₃	C₂²	1	8	yes	complemented
49	C₂×C₂²⋊C₈×C₈₃	C₂²	1	2	yes	—
50	C₂×C₂²⋊C₈×C₈₃	C₂²	1	2	yes	complemented
51	C₂⁵×C₈₃	—	2	1	no	—
52	C₂×#41×C₈₃	—	4	2	no	—
53	C₂×#41×C₈₃	—	4	2	no	—
54	C₂×#41×C₈₃	D₄	1	4	yes	—
55	C₂×#41×C₈₃	C₂³	1	4	yes	—
56	C₂²×Q₈×C₈₃	—	2	1	no	—
57	C₂²×Q₈×C₈₃	—	2	2	no	—
58	C₂²×Q₈×C₈₃	—	4	2	no	—
59	C₂²×Q₈×C₈₃	—	4	2	no	—
60	C₂²×Q₈×C₈₃	D₄	1	1	yes	characteristic
61	C₂²×Q₈×C₈₃	C₂³	1	2	yes	—
62	C₂²×Q₈×C₈₃	C₂³	1	4	yes	complemented
63	C₂²×D₄×C₈₃	—	2	2	no	—
64	C₂²×D₄×C₈₃	—	2	2	no	—
65	C₂²×D₄×C₈₃	—	2	1	no	—
66	C₂²×D₄×C₈₃	—	2	2	no	—
67	C₂²×D₄×C₈₃	—	4	2	no	—
68	C₂²×D₄×C₈₃	—	4	2	no	—
69	C₂²×D₄×C₈₃	D₄	1	1	yes	characteristic
70	C₂²×D₄×C₈₃	D₄	1	1	yes	characteristic
71	C₂²×D₄×C₈₃	D₄	1	1	yes	characteristic
72	C₂²×D₄×C₈₃	C₂³	1	2	yes	—
73	C₂²×D₄×C₈₃	C₂³	1	4	yes	—
74	C₂³×C₄×C₈₃	—	2	1	no	—
75	C₂³×C₄×C₈₃	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₈₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₈₃	C₂³	1	1	yes	characteristic
78	C₂×SD₁₆×C₈₃	—	4	4	no	—
79	C₂×SD₁₆×C₈₃	—	4	4	no	—
80	C₂×SD₁₆×C₈₃	C₂³	1	8	yes	—
81	C₂×SD₁₆×C₈₃	C₂³	1	8	yes	—
82	C₂×M₁₆×C₈₃	—	4	2	no	—
83	C₂×M₁₆×C₈₃	C₂³	1	4	yes	complemented
84	C₂²×C₈×C₈₃	—	4	2	no	—
85	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
86	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
87	C₂²×C₈×C₈₃	C₂³	1	4	yes	complemented
88	C₄⋊Q₈×C₈₃	—	2	8	no	—
89	#127×C₈₃	—	2	8	no	—
90	#124×C₈₃	—	2	8	no	—
91	#124×C₈₃	—	2	8	no	—
92	#123×C₈₃	—	2	8	no	—
93	#123×C₈₃	—	2	8	no	—
94	C₂²⋊Q₈×C₈₃	—	2	4	no	—
95	C₂²⋊Q₈×C₈₃	—	2	4	no	—
96	C₂²⋊Q₈×C₈₃	C₂³	1	8	yes	—
97	C₂²⋊Q₈×C₈₃	C₂³	1	8	yes	complemented
98	#121×C₈₃	—	2	4	no	—
99	#121×C₈₃	—	2	4	no	—
100	#121×C₈₃	C₂³	1	8	yes	—
101	#121×C₈₃	C₂³	1	8	yes	—
102	#120×C₈₃	—	2	8	no	—
103	#120×C₈₃	—	2	8	no	—
104	#117×C₈₃	—	2	2	no	—
105	#117×C₈₃	—	2	2	no	—
106	#117×C₈₃	C₂³	1	4	yes	—
107	#117×C₈₃	C₂³	1	4	yes	complemented
108	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
109	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
110	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
112	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
115	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
116	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
117	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
118	C₂×C₄²×C₈₃	—	2	1	no	—
119	C₂×C₄²×C₈₃	—	2	1	no	—
120	#107×C₈₃	C₂³	1	8	yes	complemented
121	#106×C₈₃	C₂³	1	8	yes	complemented
122	#103×C₈₃	C₂³	1	8	yes	complemented
123	#103×C₈₃	C₂³	1	8	yes	complemented
124	#102×C₈₃	C₂³	1	8	yes	—
125	#102×C₈₃	C₂³	1	8	yes	—
126	C₂²⋊C₈×C₈₃	C₂³	1	8	yes	—
127	C₂²⋊C₈×C₈₃	C₂³	1	8	yes	complemented
128	C₂⁴×C₈₃	—	2	2	no	—
129	C₂⁴×C₈₃	—	2	4	no	—
130	C₂⁴×C₈₃	—	4	4	no	—
131	C₂⁴×C₈₃	—	8	4	no	—
132	C₂⁴×C₈₃	C₂×D₄	1	1	yes	characteristic
133	C₂⁴×C₈₃	C₂×D₄	1	1	yes	characteristic
134	C₂⁴×C₈₃	C₂×D₄	1	1	yes	characteristic
135	#41×C₈₃	—	4	8	no	—
136	#41×C₈₃	—	4	4	no	—
137	#41×C₈₃	—	4	4	no	—
138	C₂×Q₈×C₈₃	—	2	2	no	—
139	C₂×Q₈×C₈₃	—	2	4	no	—
140	C₂×Q₈×C₈₃	—	2	4	no	—
141	C₂×Q₈×C₈₃	—	2	4	no	—
142	C₂×Q₈×C₈₃	—	4	2	no	—
143	C₂×Q₈×C₈₃	—	4	4	no	—
144	C₂×Q₈×C₈₃	—	4	4	no	—
145	C₂×Q₈×C₈₃	—	4	4	no	—
146	C₂×Q₈×C₈₃	—	4	8	no	—
147	C₂×Q₈×C₈₃	C₂×D₄	1	4	yes	—
148	C₂×Q₈×C₈₃	C₂⁴	1	4	yes	—
149	C₂×D₄×C₈₃	—	2	8	no	—
150	C₂×D₄×C₈₃	—	2	8	no	—
151	C₂×D₄×C₈₃	—	2	2	no	—
152	C₂×D₄×C₈₃	—	2	4	no	—
153	C₂×D₄×C₈₃	—	2	4	no	—
154	C₂×D₄×C₈₃	—	2	4	no	—
155	C₂×D₄×C₈₃	—	4	4	no	—
156	C₂×D₄×C₈₃	—	4	4	no	—
157	C₂×D₄×C₈₃	—	4	2	no	—
158	C₂×D₄×C₈₃	—	4	2	no	—
159	C₂×D₄×C₈₃	—	4	2	no	—
160	C₂×D₄×C₈₃	—	4	4	no	—
161	C₂×D₄×C₈₃	—	4	8	no	—
162	C₂×D₄×C₈₃	—	8	4	no	—
163	C₂×D₄×C₈₃	—	8	4	no	—
164	C₂×D₄×C₈₃	C₂×D₄	1	4	yes	—
165	C₂×D₄×C₈₃	C₂×D₄	1	4	yes	—
166	C₂×D₄×C₈₃	C₂×D₄	1	4	yes	—
167	C₂×D₄×C₈₃	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₈₃	—	2	2	no	—
169	C₂²×C₄×C₈₃	—	2	2	no	—
170	C₂²×C₄×C₈₃	—	2	2	no	—
171	C₂²×C₄×C₈₃	—	2	2	no	—
172	C₂²×C₄×C₈₃	—	2	2	no	—
173	C₂²×C₄×C₈₃	—	2	2	no	—
174	C₂²×C₄×C₈₃	—	2	4	no	—
175	C₂²×C₄×C₈₃	—	2	2	no	—
176	C₂²×C₄×C₈₃	—	2	2	no	—
177	C₂²×C₄×C₈₃	—	2	2	no	—
178	C₂²×C₄×C₈₃	—	4	4	no	—
179	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
180	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
181	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
182	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
189	SD₁₆×C₈₃	—	4	8	no	—
190	SD₁₆×C₈₃	—	4	8	no	—
191	M₁₆×C₈₃	—	4	4	no	—
192	C₂×C₈×C₈₃	—	2	4	no	—
193	C₂×C₈×C₈₃	—	2	4	no	—
194	C₂×C₈×C₈₃	—	4	4	no	—
195	C₂×C₈×C₈₃	C₂⁴	1	4	yes	—
196	C₂×C₈×C₈₃	C₂⁴	1	4	yes	—
197	C₄⋊C₄×C₈₃	—	2	8	no	—
198	C₄⋊C₄×C₈₃	—	2	8	no	—
199	C₄⋊C₄×C₈₃	—	2	2	no	—
200	C₄⋊C₄×C₈₃	—	2	2	no	—
201	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
202	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
203	C₂²⋊C₄×C₈₃	—	2	4	no	—
204	C₂²⋊C₄×C₈₃	—	2	4	no	—
205	C₂²⋊C₄×C₈₃	—	2	8	no	—
206	C₂²⋊C₄×C₈₃	—	2	8	no	—
207	C₂²⋊C₄×C₈₃	—	2	8	no	—
208	C₂²⋊C₄×C₈₃	—	2	8	no	—
209	C₄²×C₈₃	—	2	4	no	—
210	C₄²×C₈₃	—	2	4	no	—
211	C₂³×C₈₃	—	2	2	no	—
212	C₂³×C₈₃	—	2	2	no	—
213	C₂³×C₈₃	—	2	2	no	—
214	C₂³×C₈₃	—	2	4	no	—
215	C₂³×C₈₃	—	2	4	no	—
216	C₂³×C₈₃	—	2	4	no	—
217	C₂³×C₈₃	—	2	4	no	—
218	C₂³×C₈₃	—	4	8	no	—
219	C₂³×C₈₃	—	4	4	no	—
220	C₂³×C₈₃	—	4	4	no	—
221	C₂³×C₈₃	—	4	4	no	—
222	C₂³×C₈₃	—	8	8	no	—
223	C₂³×C₈₃	—	8	16	no	—
224	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
225	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
226	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
227	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
228	Q₈×C₈₃	—	2	4	no	—
229	Q₈×C₈₃	—	2	4	no	—
230	Q₈×C₈₃	—	4	4	no	—
231	Q₈×C₈₃	—	4	8	no	—
232	Q₈×C₈₃	—	4	4	no	—
233	D₄×C₈₃	—	2	4	no	—
234	D₄×C₈₃	—	2	4	no	—
235	D₄×C₈₃	—	4	4	no	—
236	D₄×C₈₃	—	4	4	no	—
237	D₄×C₈₃	—	4	4	no	—
238	D₄×C₈₃	—	4	8	no	—
239	D₄×C₈₃	—	4	4	no	—
240	D₄×C₈₃	—	8	8	no	—
241	D₄×C₈₃	—	8	8	no	—
242	C₂×C₄×C₈₃	—	2	2	no	—
243	C₂×C₄×C₈₃	—	2	2	no	—
244	C₂×C₄×C₈₃	—	2	2	no	—
245	C₂×C₄×C₈₃	—	2	4	no	—
246	C₂×C₄×C₈₃	—	2	4	no	—
247	C₂×C₄×C₈₃	—	2	4	no	—
248	C₂×C₄×C₈₃	—	2	2	no	—
249	C₂×C₄×C₈₃	—	2	2	no	—
250	C₂×C₄×C₈₃	—	2	2	no	—
251	C₂×C₄×C₈₃	—	2	2	no	—
252	C₂×C₄×C₈₃	—	2	2	no	—
253	C₂×C₄×C₈₃	—	2	2	no	—
254	C₂×C₄×C₈₃	—	2	4	no	—
255	C₂×C₄×C₈₃	—	2	4	no	—
256	C₂×C₄×C₈₃	—	2	4	no	—
257	C₂×C₄×C₈₃	—	4	8	no	—
258	C₂×C₄×C₈₃	—	4	4	no	—
259	C₂×C₄×C₈₃	—	4	4	no	—
260	C₂×C₄×C₈₃	—	4	4	no	—
261	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
262	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
263	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
264	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₈₃	H(5,𝔽₂)	1	2	yes	—
266	C₂×C₄×C₈₃	H(5,𝔽₂)	1	2	yes	—
267	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
268	C₈×C₈₃	—	2	4	no	—
269	C₈×C₈₃	—	2	4	no	—
270	C₂²×C₈₃	—	2	2	no	—
271	C₂²×C₈₃	—	2	2	no	—
272	C₂²×C₈₃	—	2	2	no	—
273	C₂²×C₈₃	—	2	4	no	—
274	C₂²×C₈₃	—	2	4	no	—
275	C₂²×C₈₃	—	2	4	no	—
276	C₂²×C₈₃	—	4	4	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	—	4	4	no	—
282	C₂²×C₈₃	—	8	16	no	—
283	C₂²×C₈₃	—	8	8	no	—
284	C₂²×C₈₃	#534	1	2	yes	—
285	C₂²×C₈₃	#577	1	4	yes	—
286	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
287	C₄×C₈₃	—	2	2	no	—
288	C₄×C₈₃	—	2	2	no	—
289	C₄×C₈₃	—	2	2	no	—
290	C₄×C₈₃	—	4	4	no	—
291	C₄×C₈₃	—	4	4	no	—
292	C₄×C₈₃	—	4	4	no	—
293	C₄×C₈₃	#534	1	2	yes	—
294	C₄×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
295	C₄×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
296	C₂×#3200	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
297	C₂×C₈₃	—	4	2	no	—
298	C₂×C₈₃	—	4	2	no	—
299	C₂×C₈₃	—	4	2	no	—
300	C₂×C₈₃	—	8	4	no	—
301	C₂×C₈₃	#3200	1	4	yes	direct product factor
302	C₂×C₈₃	C₂×#534	1	1	yes	characteristic
303	C₂×C₈₃	C₂×#577	1	2	yes	—
304	C₂×#536	C₂×C₈₃	1	1	yes	characteristic, complemented
305	C₂×#535	C₂×C₈₃	1	1	yes	characteristic
306	#3200	C₂×C₈₃	1	16	yes	direct product factor
307	C₂×#485	C₂×C₈₃	1	2	yes	complemented
308	C₂×#482	C₂×C₈₃	1	2	yes	complemented
309	C₂×#468	C₂×C₈₃	1	2	yes	complemented
310	C₂×#465	C₂×C₈₃	1	2	yes	complemented
311	C₂×#448	C₂×C₈₃	1	2	yes	complemented
312	C₂×#450	C₂×C₈₃	1	2	yes	complemented
313	C₂×#408	C₂×C₈₃	1	1	yes	characteristic, complemented
314	C₈₃	C₂×#3200	1	1	yes	characteristic, direct product factor, Sylow
315	C₂²×#41	C₂²×C₈₃	1	1	yes	characteristic
316	C₂³×Q₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
317	C₂³×D₄	C₂²×C₈₃	1	1	yes	characteristic
318	C₂²×SD₁₆	C₂²×C₈₃	1	2	yes	—
319	C₂²×SD₁₆	C₂²×C₈₃	1	2	yes	—
320	C₂²×M₁₆	C₂²×C₈₃	1	1	yes	characteristic, complemented
321	C₂³×C₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
322	#536	—	2	4	no	—
323	#536	C₂²×C₈₃	1	8	yes	complemented
324	#535	—	2	4	no	—
325	#535	C₂²×C₈₃	1	8	yes	—
326	C₂×C₄⋊Q₈	—	2	1	no	—
327	C₂×#127	—	2	1	no	—
328	C₂×#124	—	2	1	no	—
329	C₂×#124	—	2	1	no	—
330	C₂×#123	—	2	1	no	—
331	C₂×#123	—	2	1	no	—
332	C₂×C₂²⋊Q₈	C₂²×C₈₃	1	2	yes	—
333	C₂×C₂²⋊Q₈	C₂²×C₈₃	1	2	yes	complemented
334	C₂×#121	C₂²×C₈₃	1	2	yes	—
335	C₂×#121	C₂²×C₈₃	1	2	yes	—
336	C₂×#120	—	2	1	no	—
337	C₂×#120	—	2	1	no	—
338	C₂×#117	C₂²×C₈₃	1	1	yes	characteristic
339	C₂×#117	C₂²×C₈₃	1	1	yes	characteristic, complemented
340	#485	C₂²×C₈₃	1	16	yes	complemented
341	#482	C₂²×C₈₃	1	16	yes	complemented
342	#468	C₂²×C₈₃	1	16	yes	complemented
343	#465	C₂²×C₈₃	1	16	yes	complemented
344	#450	C₂²×C₈₃	1	16	yes	complemented
345	#448	C₂²×C₈₃	1	16	yes	complemented
346	C₂×#107	C₂²×C₈₃	1	2	yes	complemented
347	C₂×#106	C₂²×C₈₃	1	2	yes	complemented
348	C₂×#103	C₂²×C₈₃	1	2	yes	complemented
349	C₂×#103	C₂²×C₈₃	1	2	yes	complemented
350	C₂×#102	C₂²×C₈₃	1	2	yes	—
351	C₂×#102	C₂²×C₈₃	1	2	yes	—
352	#408	C₂²×C₈₃	1	8	yes	complemented
353	C₂×C₂²⋊C₈	C₂²×C₈₃	1	2	yes	—
354	C₂×C₂²⋊C₈	C₂²×C₈₃	1	2	yes	complemented
355	C₂⁵	—	2	1	no	—
356	C₂×#41	—	4	2	no	—
357	C₂×#41	—	4	2	no	—
358	C₂×#41	D₄×C₈₃	1	4	yes	—
359	C₂×#41	C₂³×C₈₃	1	4	yes	—
360	C₂²×Q₈	—	2	1	no	—
361	C₂²×Q₈	—	2	2	no	—
362	C₂²×Q₈	—	4	2	no	—
363	C₂²×Q₈	—	4	2	no	—
364	C₂²×Q₈	D₄×C₈₃	1	1	yes	characteristic
365	C₂²×Q₈	C₂³×C₈₃	1	2	yes	—
366	C₂²×Q₈	C₂³×C₈₃	1	4	yes	complemented
367	C₂²×D₄	—	2	2	no	—
368	C₂²×D₄	—	2	2	no	—
369	C₂²×D₄	—	2	1	no	—
370	C₂²×D₄	—	2	2	no	—
371	C₂²×D₄	—	4	2	no	—
372	C₂²×D₄	—	4	2	no	—
373	C₂²×D₄	D₄×C₈₃	1	1	yes	characteristic
374	C₂²×D₄	D₄×C₈₃	1	1	yes	characteristic
375	C₂²×D₄	D₄×C₈₃	1	1	yes	characteristic
376	C₂²×D₄	C₂³×C₈₃	1	2	yes	—
377	C₂²×D₄	C₂³×C₈₃	1	4	yes	—
378	C₂³×C₄	—	2	1	no	—
379	C₂³×C₄	C₂³×C₈₃	1	1	yes	characteristic
380	C₂³×C₄	C₂³×C₈₃	1	1	yes	characteristic
381	C₂³×C₄	C₂³×C₈₃	1	1	yes	characteristic
382	C₂×SD₁₆	—	4	4	no	—
383	C₂×SD₁₆	—	4	4	no	—
384	C₂×SD₁₆	C₂³×C₈₃	1	8	yes	—
385	C₂×SD₁₆	C₂³×C₈₃	1	8	yes	—
386	C₂×M₁₆	—	4	2	no	—
387	C₂×M₁₆	C₂³×C₈₃	1	4	yes	complemented
388	C₂²×C₈	—	4	2	no	—
389	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
390	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
391	C₂²×C₈	C₂³×C₈₃	1	4	yes	complemented
392	C₄⋊Q₈	—	2	8	no	—
393	#127	—	2	8	no	—
394	#124	—	2	8	no	—
395	#124	—	2	8	no	—
396	#123	—	2	8	no	—
397	#123	—	2	8	no	—
398	C₂²⋊Q₈	—	2	4	no	—
399	C₂²⋊Q₈	—	2	4	no	—
400	C₂²⋊Q₈	C₂³×C₈₃	1	8	yes	—
401	C₂²⋊Q₈	C₂³×C₈₃	1	8	yes	complemented
402	#121	—	2	4	no	—
403	#121	—	2	4	no	—
404	#121	C₂³×C₈₃	1	8	yes	—
405	#121	C₂³×C₈₃	1	8	yes	—
406	#120	—	2	8	no	—
407	#120	—	2	8	no	—
408	#117	—	2	2	no	—
409	#117	—	2	2	no	—
410	#117	C₂³×C₈₃	1	4	yes	—
411	#117	C₂³×C₈₃	1	4	yes	complemented
412	C₂×C₄⋊C₄	—	2	2	no	—
413	C₂×C₄⋊C₄	—	2	2	no	—
414	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
415	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
416	C₂×C₂²⋊C₄	—	2	1	no	—
417	C₂×C₂²⋊C₄	—	2	1	no	—
418	C₂×C₂²⋊C₄	—	2	2	no	—
419	C₂×C₂²⋊C₄	—	2	2	no	—
420	C₂×C₂²⋊C₄	—	2	2	no	—
421	C₂×C₂²⋊C₄	—	2	2	no	—
422	C₂×C₄²	—	2	1	no	—
423	C₂×C₄²	—	2	1	no	—
424	#107	C₂³×C₈₃	1	8	yes	complemented
425	#106	C₂³×C₈₃	1	8	yes	complemented
426	#103	C₂³×C₈₃	1	8	yes	complemented
427	#103	C₂³×C₈₃	1	8	yes	complemented
428	#102	C₂³×C₈₃	1	8	yes	—
429	#102	C₂³×C₈₃	1	8	yes	—
430	C₂²⋊C₈	C₂³×C₈₃	1	8	yes	—
431	C₂²⋊C₈	C₂³×C₈₃	1	8	yes	complemented
432	C₂⁴	—	2	2	no	—
433	C₂⁴	—	2	4	no	—
434	C₂⁴	—	4	4	no	—
435	C₂⁴	—	8	4	no	—
436	C₂⁴	C₂×D₄×C₈₃	1	1	yes	characteristic
437	C₂⁴	C₂×D₄×C₈₃	1	1	yes	characteristic
438	C₂⁴	C₂×D₄×C₈₃	1	1	yes	characteristic
439	#41	—	4	8	no	—
440	#41	—	4	4	no	—
441	#41	—	4	4	no	—
442	C₂×Q₈	—	2	2	no	—
443	C₂×Q₈	—	2	4	no	—
444	C₂×Q₈	—	2	4	no	—
445	C₂×Q₈	—	2	4	no	—
446	C₂×Q₈	—	4	2	no	—
447	C₂×Q₈	—	4	4	no	—
448	C₂×Q₈	—	4	4	no	—
449	C₂×Q₈	—	4	4	no	—
450	C₂×Q₈	—	4	8	no	—
451	C₂×Q₈	C₂×D₄×C₈₃	1	4	yes	—
452	C₂×Q₈	C₂⁴×C₈₃	1	4	yes	—
453	C₂×D₄	—	2	8	no	—
454	C₂×D₄	—	2	8	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	—	2	4	no	—
457	C₂×D₄	—	2	4	no	—
458	C₂×D₄	—	2	4	no	—
459	C₂×D₄	—	4	4	no	—
460	C₂×D₄	—	4	4	no	—
461	C₂×D₄	—	4	2	no	—
462	C₂×D₄	—	4	2	no	—
463	C₂×D₄	—	4	2	no	—
464	C₂×D₄	—	4	4	no	—
465	C₂×D₄	—	4	8	no	—
466	C₂×D₄	—	8	4	no	—
467	C₂×D₄	—	8	4	no	—
468	C₂×D₄	C₂×D₄×C₈₃	1	4	yes	—
469	C₂×D₄	C₂×D₄×C₈₃	1	4	yes	—
470	C₂×D₄	C₂×D₄×C₈₃	1	4	yes	—
471	C₂×D₄	C₂⁴×C₈₃	1	4	yes	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	4	no	—
482	C₂²×C₄	—	4	4	no	—
483	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
484	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
485	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
486	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
487	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
488	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
489	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
490	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
491	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
492	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
493	SD₁₆	—	4	8	no	—
494	SD₁₆	—	4	8	no	—
495	M₁₆	—	4	4	no	—
496	C₂×C₈	—	2	4	no	—
497	C₂×C₈	—	2	4	no	—
498	C₂×C₈	—	4	4	no	—
499	C₂×C₈	C₂⁴×C₈₃	1	4	yes	—
500	C₂×C₈	C₂⁴×C₈₃	1	4	yes	—
501	C₄⋊C₄	—	2	8	no	—
502	C₄⋊C₄	—	2	8	no	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	—	2	2	no	—
505	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
506	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
507	C₂²⋊C₄	—	2	4	no	—
508	C₂²⋊C₄	—	2	4	no	—
509	C₂²⋊C₄	—	2	8	no	—
510	C₂²⋊C₄	—	2	8	no	—
511	C₂²⋊C₄	—	2	8	no	—
512	C₂²⋊C₄	—	2	8	no	—
513	C₄²	—	2	4	no	—
514	C₄²	—	2	4	no	—
515	C₂³	—	2	2	no	—
516	C₂³	—	2	2	no	—
517	C₂³	—	2	2	no	—
518	C₂³	—	2	4	no	—
519	C₂³	—	2	4	no	—
520	C₂³	—	2	4	no	—
521	C₂³	—	2	4	no	—
522	C₂³	—	4	8	no	—
523	C₂³	—	4	4	no	—
524	C₂³	—	4	4	no	—
525	C₂³	—	4	4	no	—
526	C₂³	—	8	8	no	—
527	C₂³	—	8	16	no	—
528	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
529	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
530	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
531	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
532	Q₈	—	2	4	no	—
533	Q₈	—	2	4	no	—
534	Q₈	—	4	4	no	—
535	Q₈	—	4	8	no	—
536	Q₈	—	4	4	no	—
537	D₄	—	2	4	no	—
538	D₄	—	2	4	no	—
539	D₄	—	4	4	no	—
540	D₄	—	4	4	no	—
541	D₄	—	4	4	no	—
542	D₄	—	4	8	no	—
543	D₄	—	4	4	no	—
544	D₄	—	8	8	no	—
545	D₄	—	8	8	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	4	no	—
550	C₂×C₄	—	2	4	no	—
551	C₂×C₄	—	2	4	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	4	no	—
560	C₂×C₄	—	2	4	no	—
561	C₂×C₄	—	4	8	no	—
562	C₂×C₄	—	4	4	no	—
563	C₂×C₄	—	4	4	no	—
564	C₂×C₄	—	4	4	no	—
565	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
566	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
567	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
568	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
569	C₂×C₄	H(5,𝔽₂)×C₈₃	1	2	yes	—
570	C₂×C₄	H(5,𝔽₂)×C₈₃	1	2	yes	—
571	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
572	C₈	—	2	4	no	—
573	C₈	—	2	4	no	—
574	C₂²	—	2	4	no	—
575	C₂²	—	2	4	no	—
576	C₂²	—	2	4	no	—
577	C₂²	—	2	2	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	4	4	no	—
581	C₂²	—	4	4	no	—
582	C₂²	—	4	4	no	—
583	C₂²	—	4	4	no	—
584	C₂²	—	4	4	no	—
585	C₂²	—	4	4	no	—
586	C₂²	—	8	16	no	—
587	C₂²	—	8	8	no	—
588	C₂²	#534×C₈₃	1	2	yes	—
589	C₂²	#577×C₈₃	1	4	yes	—
590	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
591	C₄	—	2	2	no	—
592	C₄	—	2	2	no	—
593	C₄	—	2	2	no	—
594	C₄	—	4	4	no	—
595	C₄	—	4	4	no	—
596	C₄	—	4	4	no	—
597	C₄	#534×C₈₃	1	2	yes	—
598	C₄	C₂×H(5,𝔽₂)×C₈₃	1	1	yes	characteristic
599	C₄	C₂×H(5,𝔽₂)×C₈₃	1	1	yes	characteristic
600	C₂	—	4	2	no	—
601	C₂	—	4	2	no	—
602	C₂	—	4	2	no	—
603	C₂	—	8	4	no	—
604	C₂	C₈₃×#3200	1	4	yes	direct product factor
605	C₂	C₂×#534×C₈₃	1	1	yes	characteristic
606	C₂	C₂×#577×C₈₃	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₃
prime radical	C₂×#535×C₈₃	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₃ ◁ C₂²×#41×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#536×C₈₃	C₂	semidirect
3. C₈₃×#3200	C₂	direct (N × H)
4. C₂×#485×C₈₃	C₂	semidirect
5. C₂×#482×C₈₃	C₂	semidirect
6. C₂×#468×C₈₃	C₂	semidirect
7. C₂×#465×C₈₃	C₂	semidirect
8. C₂×#448×C₈₃	C₂	semidirect
9. C₂×#450×C₈₃	C₂	semidirect
10. C₂×#408×C₈₃	C₂	semidirect
12. C₂³×Q₈×C₈₃	C₂²	semidirect
16. C₂²×M₁₆×C₈₃	C₂²	semidirect
17. C₂³×C₈×C₈₃	C₂²	semidirect
19. #536×C₈₃	C₂²	semidirect
29. C₂×C₂²⋊Q₈×C₈₃	C₂²	semidirect
35. C₂×#117×C₈₃	C₂²	semidirect
36. #485×C₈₃	C₂²	semidirect
37. #482×C₈₃	C₂²	semidirect
38. #468×C₈₃	C₂²	semidirect
39. #465×C₈₃	C₂²	semidirect
40. #450×C₈₃	C₂²	semidirect
41. #448×C₈₃	C₂²	semidirect
42. C₂×#107×C₈₃	C₂²	semidirect
43. C₂×#106×C₈₃	C₂²	semidirect
44. C₂×#103×C₈₃	C₂²	semidirect
45. C₂×#103×C₈₃	C₂²	semidirect
48. #408×C₈₃	C₂²	semidirect
50. C₂×C₂²⋊C₈×C₈₃	C₂²	semidirect
62. C₂²×Q₈×C₈₃	C₂³	semidirect
83. C₂×M₁₆×C₈₃	C₂³	semidirect
87. C₂²×C₈×C₈₃	C₂³	semidirect
97. C₂²⋊Q₈×C₈₃	C₂³	semidirect
107. #117×C₈₃	C₂³	semidirect
120. #107×C₈₃	C₂³	semidirect
121. #106×C₈₃	C₂³	semidirect
122. #103×C₈₃	C₂³	semidirect
123. #103×C₈₃	C₂³	semidirect
127. C₂²⋊C₈×C₈₃	C₂³	semidirect
296. C₂×#3200	C₈₃	direct (N × H)
301. C₂×C₈₃	#3200	direct (N × H)
304. C₂×#536	C₂×C₈₃	semidirect
306. #3200	C₂×C₈₃	direct (N × H)
307. C₂×#485	C₂×C₈₃	semidirect
308. C₂×#482	C₂×C₈₃	semidirect
309. C₂×#468	C₂×C₈₃	semidirect
310. C₂×#465	C₂×C₈₃	semidirect
311. C₂×#448	C₂×C₈₃	semidirect
312. C₂×#450	C₂×C₈₃	semidirect
313. C₂×#408	C₂×C₈₃	semidirect
314. C₈₃	C₂×#3200	direct (N × H)
316. C₂³×Q₈	C₂²×C₈₃	semidirect
320. C₂²×M₁₆	C₂²×C₈₃	semidirect
321. C₂³×C₈	C₂²×C₈₃	semidirect
323. #536	C₂²×C₈₃	semidirect
333. C₂×C₂²⋊Q₈	C₂²×C₈₃	semidirect
339. C₂×#117	C₂²×C₈₃	semidirect
340. #485	C₂²×C₈₃	semidirect
341. #482	C₂²×C₈₃	semidirect
342. #468	C₂²×C₈₃	semidirect
343. #465	C₂²×C₈₃	semidirect
344. #450	C₂²×C₈₃	semidirect
345. #448	C₂²×C₈₃	semidirect
346. C₂×#107	C₂²×C₈₃	semidirect
347. C₂×#106	C₂²×C₈₃	semidirect
348. C₂×#103	C₂²×C₈₃	semidirect
349. C₂×#103	C₂²×C₈₃	semidirect
352. #408	C₂²×C₈₃	semidirect
354. C₂×C₂²⋊C₈	C₂²×C₈₃	semidirect
366. C₂²×Q₈	C₂³×C₈₃	semidirect
387. C₂×M₁₆	C₂³×C₈₃	semidirect
391. C₂²×C₈	C₂³×C₈₃	semidirect
401. C₂²⋊Q₈	C₂³×C₈₃	semidirect
411. #117	C₂³×C₈₃	semidirect
424. #107	C₂³×C₈₃	semidirect
425. #106	C₂³×C₈₃	semidirect
426. #103	C₂³×C₈₃	semidirect
427. #103	C₂³×C₈₃	semidirect
431. C₂²⋊C₈	C₂³×C₈₃	semidirect
604. C₂	C₈₃×#3200	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#536×C₈₃	2
C₂×#535×C₈₃	2
C₈₃×#3200	2
C₂×#485×C₈₃	2
C₂×#482×C₈₃	2
C₂×#468×C₈₃	2
C₂×#465×C₈₃	2
C₂×#448×C₈₃	2
C₂×#450×C₈₃	2
C₂×#408×C₈₃	2
C₂×#3200	83

Subgroups — C2×C83×#3200 #35288568

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₃×#3200 #35288568