Subgroups — C₂×C₈₃×#3201 #35288569

Order 21248.

2186 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#537×C₈₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#536×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₃×#3201	C₂	1	16	yes	maximal, direct product factor
4	C₂×#484×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#485×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#482×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#483×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#470×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#468×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#467×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#465×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#452×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#452×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#451×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#448×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#408×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₈₃	C₂²	1	1	yes	characteristic
18	C₂²×#41×C₈₃	C₂²	1	1	yes	characteristic
19	C₂³×Q₈×C₈₃	C₂²	1	1	yes	characteristic
20	C₂²×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic
21	C₂²×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic
22	C₂²×SD₁₆×C₈₃	C₂²	1	1	yes	characteristic
23	C₂²×SD₁₆×C₈₃	C₂²	1	1	yes	characteristic
24	C₂²×M₁₆×C₈₃	C₂²	1	1	yes	characteristic
25	C₂³×C₈×C₈₃	C₂²	1	1	yes	characteristic
26	#537×C₈₃	—	2	4	no	—
27	#537×C₈₃	C₂²	1	8	yes	—
28	#536×C₈₃	—	2	4	no	—
29	#536×C₈₃	C₂²	1	8	yes	complemented
30	C₂×C₄⋊Q₈×C₈₃	—	2	1	no	—
31	C₂×#124×C₈₃	—	2	1	no	—
32	C₂×#123×C₈₃	—	2	1	no	—
33	C₂×#123×C₈₃	—	2	1	no	—
34	C₂×C₂²⋊Q₈×C₈₃	—	2	1	no	—
35	C₂×C₂²⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
41	C₂×#121×C₈₃	—	2	1	no	—
42	C₂×#121×C₈₃	—	2	1	no	—
43	C₂×#121×C₈₃	—	2	1	no	—
44	C₂×#121×C₈₃	C₂²	1	1	yes	characteristic
45	C₂×#121×C₈₃	C₂²	1	1	yes	characteristic
46	C₂×#117×C₈₃	C₂²	1	1	yes	characteristic
47	C₂²×C₄⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
48	#485×C₈₃	C₂²	1	8	yes	complemented
49	#484×C₈₃	C₂²	1	8	yes	complemented
50	#483×C₈₃	C₂²	1	8	yes	complemented
51	#482×C₈₃	C₂²	1	8	yes	complemented
52	#470×C₈₃	C₂²	1	8	yes	complemented
53	#468×C₈₃	C₂²	1	8	yes	complemented
54	#467×C₈₃	C₂²	1	8	yes	complemented
55	#465×C₈₃	C₂²	1	8	yes	complemented
56	#452×C₈₃	C₂²	1	8	yes	complemented
57	#452×C₈₃	C₂²	1	8	yes	complemented
58	#451×C₈₃	C₂²	1	8	yes	complemented
59	#448×C₈₃	C₂²	1	8	yes	complemented
60	C₂×#107×C₈₃	C₂²	1	1	yes	characteristic
61	C₂×#107×C₈₃	C₂²	1	1	yes	characteristic
62	C₂×#106×C₈₃	C₂²	1	1	yes	characteristic
63	C₂×#106×C₈₃	C₂²	1	1	yes	characteristic
64	C₂×#103×C₈₃	C₂²	1	1	yes	characteristic
65	C₂×#103×C₈₃	C₂²	1	1	yes	characteristic
66	C₂×#103×C₈₃	C₂²	1	1	yes	characteristic
67	C₂×#103×C₈₃	C₂²	1	1	yes	characteristic
68	C₂×#103×C₈₃	C₂²	1	1	yes	characteristic
69	C₂×#103×C₈₃	C₂²	1	1	yes	characteristic
70	C₂×#102×C₈₃	C₂²	1	1	yes	characteristic
71	C₂×#102×C₈₃	C₂²	1	1	yes	characteristic
72	#408×C₈₃	C₂²	1	8	yes	complemented
73	C₂×C₂²⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
74	C₂×C₂²⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
75	C₂×C₂²⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
76	C₂×C₂²⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
77	C₂×#41×C₈₃	—	2	2	no	—
78	C₂×#41×C₈₃	—	4	2	no	—
79	C₂×#41×C₈₃	—	4	2	no	—
80	C₂×#41×C₈₃	—	4	2	no	—
81	C₂×#41×C₈₃	—	4	2	no	—
82	C₂×#41×C₈₃	D₄	1	4	yes	—
83	C₂×#41×C₈₃	C₂³	1	4	yes	—
84	C₂×#41×C₈₃	C₂³	1	4	yes	—
85	C₂²×Q₈×C₈₃	—	2	1	no	—
86	C₂²×Q₈×C₈₃	—	2	2	no	—
87	C₂²×Q₈×C₈₃	—	4	2	no	—
88	C₂²×Q₈×C₈₃	—	4	2	no	—
89	C₂²×Q₈×C₈₃	D₄	1	1	yes	characteristic
90	C₂²×Q₈×C₈₃	C₂³	1	1	yes	characteristic
91	C₂²×Q₈×C₈₃	C₂³	1	1	yes	characteristic
92	C₂²×Q₈×C₈₃	C₂³	1	1	yes	characteristic
93	C₂²×Q₈×C₈₃	C₂³	1	4	yes	—
94	C₂²×D₄×C₈₃	—	2	1	no	—
95	C₂²×D₄×C₈₃	—	2	1	no	—
96	C₂²×D₄×C₈₃	—	2	1	no	—
97	C₂²×D₄×C₈₃	D₄	1	1	yes	characteristic
98	C₂²×D₄×C₈₃	D₄	1	1	yes	characteristic
99	C₂²×D₄×C₈₃	D₄	1	1	yes	characteristic
100	C₂²×D₄×C₈₃	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₈₃	—	2	1	no	—
102	C₂³×C₄×C₈₃	—	2	1	no	—
103	C₂³×C₄×C₈₃	—	2	1	no	—
104	C₂³×C₄×C₈₃	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₈₃	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₈₃	C₂³	1	1	yes	characteristic
107	C₂×Q₁₆×C₈₃	—	4	2	no	—
108	C₂×Q₁₆×C₈₃	—	4	2	no	—
109	C₂×Q₁₆×C₈₃	C₂³	1	4	yes	—
110	C₂×Q₁₆×C₈₃	C₂³	1	4	yes	—
111	C₂×SD₁₆×C₈₃	—	4	2	no	—
112	C₂×SD₁₆×C₈₃	—	4	2	no	—
113	C₂×SD₁₆×C₈₃	C₂³	1	4	yes	—
114	C₂×SD₁₆×C₈₃	C₂³	1	4	yes	—
115	C₂×M₁₆×C₈₃	—	4	2	no	—
116	C₂×M₁₆×C₈₃	C₂³	1	4	yes	—
117	C₂²×C₈×C₈₃	—	4	2	no	—
118	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
119	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
121	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
122	C₂²×C₈×C₈₃	C₂³	1	4	yes	—
123	C₄⋊Q₈×C₈₃	—	2	8	no	—
124	#124×C₈₃	—	2	8	no	—
125	#123×C₈₃	—	2	8	no	—
126	#123×C₈₃	—	2	8	no	—
127	C₂²⋊Q₈×C₈₃	—	2	8	no	—
128	C₂²⋊Q₈×C₈₃	—	2	2	no	—
129	C₂²⋊Q₈×C₈₃	—	2	2	no	—
130	C₂²⋊Q₈×C₈₃	—	2	2	no	—
131	C₂²⋊Q₈×C₈₃	—	2	2	no	—
132	C₂²⋊Q₈×C₈₃	—	2	2	no	—
133	C₂²⋊Q₈×C₈₃	—	2	2	no	—
134	C₂²⋊Q₈×C₈₃	C₂³	1	4	yes	—
135	C₂²⋊Q₈×C₈₃	C₂³	1	4	yes	—
136	C₂²⋊Q₈×C₈₃	C₂³	1	4	yes	—
137	C₂²⋊Q₈×C₈₃	C₂³	1	4	yes	—
138	C₂²⋊Q₈×C₈₃	C₂³	1	4	yes	—
139	C₂²⋊Q₈×C₈₃	C₂³	1	4	yes	—
140	#121×C₈₃	—	2	8	no	—
141	#121×C₈₃	—	2	8	no	—
142	#121×C₈₃	—	2	8	no	—
143	#121×C₈₃	—	2	2	no	—
144	#121×C₈₃	—	2	2	no	—
145	#121×C₈₃	C₂³	1	4	yes	—
146	#121×C₈₃	C₂³	1	4	yes	—
147	#117×C₈₃	—	2	2	no	—
148	#117×C₈₃	C₂³	1	4	yes	—
149	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
150	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
151	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
152	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
153	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
154	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
155	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
156	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
157	C₂×C₄⋊C₄×C₈₃	C₂³	1	4	yes	—
158	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
162	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
163	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
164	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
165	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
166	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
167	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
168	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
169	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
170	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
171	C₂×C₄²×C₈₃	—	2	1	no	—
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	#103×C₈₃	C₂³	1	4	yes	—
177	#103×C₈₃	C₂³	1	4	yes	—
178	#103×C₈₃	C₂³	1	4	yes	—
179	#103×C₈₃	C₂³	1	4	yes	—
180	#103×C₈₃	C₂³	1	4	yes	—
181	#103×C₈₃	C₂³	1	4	yes	—
182	#102×C₈₃	C₂³	1	4	yes	—
183	#102×C₈₃	C₂³	1	4	yes	—
184	C₂²⋊C₈×C₈₃	C₂³	1	4	yes	—
185	C₂²⋊C₈×C₈₃	C₂³	1	4	yes	—
186	C₂²⋊C₈×C₈₃	C₂³	1	4	yes	—
187	C₂²⋊C₈×C₈₃	C₂³	1	4	yes	—
188	C₂⁴×C₈₃	—	2	1	no	—
189	C₂⁴×C₈₃	C₂×D₄	1	1	yes	characteristic
190	C₂⁴×C₈₃	C₂×D₄	1	1	yes	characteristic
191	C₂⁴×C₈₃	C₂×D₄	1	1	yes	characteristic
192	#41×C₈₃	—	4	8	no	—
193	#41×C₈₃	—	4	4	no	—
194	#41×C₈₃	—	4	4	no	—
195	#41×C₈₃	—	4	4	no	—
196	#41×C₈₃	—	4	4	no	—
197	#41×C₈₃	—	4	8	no	—
198	C₂×Q₈×C₈₃	—	2	1	no	—
199	C₂×Q₈×C₈₃	—	2	1	no	—
200	C₂×Q₈×C₈₃	—	2	1	no	—
201	C₂×Q₈×C₈₃	—	2	4	no	—
202	C₂×Q₈×C₈₃	—	2	2	no	—
203	C₂×Q₈×C₈₃	—	2	2	no	—
204	C₂×Q₈×C₈₃	—	2	2	no	—
205	C₂×Q₈×C₈₃	—	2	2	no	—
206	C₂×Q₈×C₈₃	—	2	2	no	—
207	C₂×Q₈×C₈₃	—	2	2	no	—
208	C₂×Q₈×C₈₃	—	4	2	no	—
209	C₂×Q₈×C₈₃	—	4	4	no	—
210	C₂×Q₈×C₈₃	—	4	4	no	—
211	C₂×Q₈×C₈₃	—	4	4	no	—
212	C₂×Q₈×C₈₃	—	4	8	no	—
213	C₂×Q₈×C₈₃	C₂×D₄	1	4	yes	—
214	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
215	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
216	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
217	C₂×D₄×C₈₃	—	2	4	no	—
218	C₂×D₄×C₈₃	—	2	4	no	—
219	C₂×D₄×C₈₃	—	2	4	no	—
220	C₂×D₄×C₈₃	—	2	1	no	—
221	C₂×D₄×C₈₃	—	2	2	no	—
222	C₂×D₄×C₈₃	—	2	2	no	—
223	C₂×D₄×C₈₃	—	4	2	no	—
224	C₂×D₄×C₈₃	—	4	2	no	—
225	C₂×D₄×C₈₃	—	4	2	no	—
226	C₂×D₄×C₈₃	—	4	4	no	—
227	C₂×D₄×C₈₃	—	8	2	no	—
228	C₂×D₄×C₈₃	—	8	2	no	—
229	C₂×D₄×C₈₃	C₂×D₄	1	4	yes	—
230	C₂×D₄×C₈₃	C₂×D₄	1	4	yes	—
231	C₂×D₄×C₈₃	C₂×D₄	1	4	yes	—
232	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₈₃	—	2	2	no	—
234	C₂²×C₄×C₈₃	—	2	2	no	—
235	C₂²×C₄×C₈₃	—	2	2	no	—
236	C₂²×C₄×C₈₃	—	2	2	no	—
237	C₂²×C₄×C₈₃	—	2	2	no	—
238	C₂²×C₄×C₈₃	—	2	2	no	—
239	C₂²×C₄×C₈₃	—	2	4	no	—
240	C₂²×C₄×C₈₃	—	2	1	no	—
241	C₂²×C₄×C₈₃	—	2	1	no	—
242	C₂²×C₄×C₈₃	—	2	1	no	—
243	C₂²×C₄×C₈₃	—	2	1	no	—
244	C₂²×C₄×C₈₃	—	2	1	no	—
245	C₂²×C₄×C₈₃	—	2	1	no	—
246	C₂²×C₄×C₈₃	—	2	1	no	—
247	C₂²×C₄×C₈₃	—	2	4	no	—
248	C₂²×C₄×C₈₃	—	2	4	no	—
249	C₂²×C₄×C₈₃	—	4	4	no	—
250	C₂²×C₄×C₈₃	—	4	4	no	—
251	C₂²×C₄×C₈₃	—	8	2	no	—
252	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
253	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
254	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
255	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
262	Q₁₆×C₈₃	—	4	4	no	—
263	Q₁₆×C₈₃	—	4	4	no	—
264	SD₁₆×C₈₃	—	4	4	no	—
265	SD₁₆×C₈₃	—	4	4	no	—
266	M₁₆×C₈₃	—	4	4	no	—
267	C₂×C₈×C₈₃	—	2	2	no	—
268	C₂×C₈×C₈₃	—	2	2	no	—
269	C₂×C₈×C₈₃	—	2	2	no	—
270	C₂×C₈×C₈₃	—	2	2	no	—
271	C₂×C₈×C₈₃	—	4	4	no	—
272	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
273	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
274	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
275	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
276	C₄⋊C₄×C₈₃	—	2	4	no	—
277	C₄⋊C₄×C₈₃	—	2	1	no	—
278	C₄⋊C₄×C₈₃	—	2	1	no	—
279	C₄⋊C₄×C₈₃	—	2	4	no	—
280	C₄⋊C₄×C₈₃	—	2	4	no	—
281	C₄⋊C₄×C₈₃	—	2	4	no	—
282	C₄⋊C₄×C₈₃	—	2	4	no	—
283	C₄⋊C₄×C₈₃	—	2	4	no	—
284	C₄⋊C₄×C₈₃	—	2	4	no	—
285	C₄⋊C₄×C₈₃	—	2	1	no	—
286	C₄⋊C₄×C₈₃	—	2	1	no	—
287	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
288	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
289	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
290	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
291	C₂²⋊C₄×C₈₃	—	2	4	no	—
292	C₂²⋊C₄×C₈₃	—	2	4	no	—
293	C₂²⋊C₄×C₈₃	—	2	4	no	—
294	C₂²⋊C₄×C₈₃	—	2	4	no	—
295	C₂²⋊C₄×C₈₃	—	2	4	no	—
296	C₂²⋊C₄×C₈₃	—	2	4	no	—
297	C₂²⋊C₄×C₈₃	—	2	4	no	—
298	C₂²⋊C₄×C₈₃	—	2	4	no	—
299	C₂²⋊C₄×C₈₃	—	2	4	no	—
300	C₄²×C₈₃	—	2	4	no	—
301	C₂³×C₈₃	—	2	2	no	—
302	C₂³×C₈₃	—	2	2	no	—
303	C₂³×C₈₃	—	2	2	no	—
304	C₂³×C₈₃	—	2	2	no	—
305	C₂³×C₈₃	—	2	2	no	—
306	C₂³×C₈₃	—	2	2	no	—
307	C₂³×C₈₃	—	2	2	no	—
308	C₂³×C₈₃	—	2	2	no	—
309	C₂³×C₈₃	—	2	2	no	—
310	C₂³×C₈₃	—	2	2	no	—
311	C₂³×C₈₃	—	4	2	no	—
312	C₂³×C₈₃	—	4	2	no	—
313	C₂³×C₈₃	—	4	2	no	—
314	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
315	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
316	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
317	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
318	Q₈×C₈₃	—	2	2	no	—
319	Q₈×C₈₃	—	2	2	no	—
320	Q₈×C₈₃	—	2	2	no	—
321	Q₈×C₈₃	—	2	2	no	—
322	Q₈×C₈₃	—	2	2	no	—
323	Q₈×C₈₃	—	2	2	no	—
324	Q₈×C₈₃	—	4	4	no	—
325	Q₈×C₈₃	—	4	8	no	—
326	Q₈×C₈₃	—	4	2	no	—
327	Q₈×C₈₃	—	4	2	no	—
328	Q₈×C₈₃	—	4	2	no	—
329	D₄×C₈₃	—	2	2	no	—
330	D₄×C₈₃	—	2	2	no	—
331	D₄×C₈₃	—	4	4	no	—
332	D₄×C₈₃	—	4	4	no	—
333	D₄×C₈₃	—	4	4	no	—
334	D₄×C₈₃	—	4	8	no	—
335	D₄×C₈₃	—	4	2	no	—
336	D₄×C₈₃	—	8	4	no	—
337	D₄×C₈₃	—	8	4	no	—
338	C₂×C₄×C₈₃	—	2	2	no	—
339	C₂×C₄×C₈₃	—	2	2	no	—
340	C₂×C₄×C₈₃	—	2	2	no	—
341	C₂×C₄×C₈₃	—	2	4	no	—
342	C₂×C₄×C₈₃	—	2	4	no	—
343	C₂×C₄×C₈₃	—	2	4	no	—
344	C₂×C₄×C₈₃	—	2	2	no	—
345	C₂×C₄×C₈₃	—	2	2	no	—
346	C₂×C₄×C₈₃	—	2	2	no	—
347	C₂×C₄×C₈₃	—	2	2	no	—
348	C₂×C₄×C₈₃	—	2	2	no	—
349	C₂×C₄×C₈₃	—	2	2	no	—
350	C₂×C₄×C₈₃	—	2	2	no	—
351	C₂×C₄×C₈₃	—	2	2	no	—
352	C₂×C₄×C₈₃	—	2	2	no	—
353	C₂×C₄×C₈₃	—	2	2	no	—
354	C₂×C₄×C₈₃	—	2	2	no	—
355	C₂×C₄×C₈₃	—	2	2	no	—
356	C₂×C₄×C₈₃	—	2	2	no	—
357	C₂×C₄×C₈₃	—	4	8	no	—
358	C₂×C₄×C₈₃	—	4	8	no	—
359	C₂×C₄×C₈₃	—	4	2	no	—
360	C₂×C₄×C₈₃	—	4	2	no	—
361	C₂×C₄×C₈₃	—	4	2	no	—
362	C₂×C₄×C₈₃	—	4	2	no	—
363	C₂×C₄×C₈₃	—	4	2	no	—
364	C₂×C₄×C₈₃	—	4	2	no	—
365	C₂×C₄×C₈₃	—	4	2	no	—
366	C₂×C₄×C₈₃	—	8	4	no	—
367	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
368	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
369	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
370	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
371	C₂×C₄×C₈₃	H(5,𝔽₂)	1	2	yes	—
372	C₂×C₄×C₈₃	H(5,𝔽₂)	1	2	yes	—
373	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
374	C₈×C₈₃	—	2	2	no	—
375	C₈×C₈₃	—	2	2	no	—
376	C₈×C₈₃	—	2	2	no	—
377	C₈×C₈₃	—	2	2	no	—
378	C₂²×C₈₃	—	2	2	no	—
379	C₂²×C₈₃	—	2	2	no	—
380	C₂²×C₈₃	—	2	2	no	—
381	C₂²×C₈₃	—	2	2	no	—
382	C₂²×C₈₃	—	2	2	no	—
383	C₂²×C₈₃	—	2	2	no	—
384	C₂²×C₈₃	—	2	2	no	—
385	C₂²×C₈₃	—	2	2	no	—
386	C₂²×C₈₃	—	2	2	no	—
387	C₂²×C₈₃	—	4	4	no	—
388	C₂²×C₈₃	—	4	4	no	—
389	C₂²×C₈₃	—	4	4	no	—
390	C₂²×C₈₃	—	4	2	no	—
391	C₂²×C₈₃	—	4	2	no	—
392	C₂²×C₈₃	—	4	2	no	—
393	C₂²×C₈₃	—	8	4	no	—
394	C₂²×C₈₃	#534	1	2	yes	—
395	C₂²×C₈₃	#577	1	2	yes	—
396	C₂²×C₈₃	#578	1	2	yes	—
397	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
398	C₄×C₈₃	—	2	2	no	—
399	C₄×C₈₃	—	2	2	no	—
400	C₄×C₈₃	—	2	2	no	—
401	C₄×C₈₃	—	4	2	no	—
402	C₄×C₈₃	—	4	2	no	—
403	C₄×C₈₃	—	4	2	no	—
404	C₄×C₈₃	—	4	2	no	—
405	C₄×C₈₃	—	4	2	no	—
406	C₄×C₈₃	—	4	2	no	—
407	C₄×C₈₃	—	4	2	no	—
408	C₄×C₈₃	#534	1	2	yes	—
409	C₄×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
410	C₄×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
411	C₂×#3201	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
412	C₂×C₈₃	—	4	2	no	—
413	C₂×C₈₃	—	4	2	no	—
414	C₂×C₈₃	—	4	2	no	—
415	C₂×C₈₃	—	8	2	no	—
416	C₂×C₈₃	#3201	1	4	yes	direct product factor
417	C₂×C₈₃	C₂×#534	1	1	yes	characteristic
418	C₂×C₈₃	C₂×#577	1	1	yes	characteristic
419	C₂×C₈₃	C₂×#578	1	1	yes	characteristic
420	C₂×#537	C₂×C₈₃	1	1	yes	characteristic
421	C₂×#536	C₂×C₈₃	1	1	yes	characteristic, complemented
422	#3201	C₂×C₈₃	1	16	yes	direct product factor
423	C₂×#484	C₂×C₈₃	1	1	yes	characteristic, complemented
424	C₂×#485	C₂×C₈₃	1	1	yes	characteristic, complemented
425	C₂×#482	C₂×C₈₃	1	1	yes	characteristic, complemented
426	C₂×#483	C₂×C₈₃	1	1	yes	characteristic, complemented
427	C₂×#470	C₂×C₈₃	1	1	yes	characteristic, complemented
428	C₂×#468	C₂×C₈₃	1	1	yes	characteristic, complemented
429	C₂×#467	C₂×C₈₃	1	1	yes	characteristic, complemented
430	C₂×#465	C₂×C₈₃	1	1	yes	characteristic, complemented
431	C₂×#452	C₂×C₈₃	1	1	yes	characteristic, complemented
432	C₂×#452	C₂×C₈₃	1	1	yes	characteristic, complemented
433	C₂×#451	C₂×C₈₃	1	1	yes	characteristic, complemented
434	C₂×#448	C₂×C₈₃	1	1	yes	characteristic, complemented
435	C₂×#408	C₂×C₈₃	1	1	yes	characteristic, complemented
436	C₈₃	C₂×#3201	1	1	yes	characteristic, direct product factor, Sylow
437	C₂²×#41	C₂²×C₈₃	1	1	yes	characteristic
438	C₂²×#41	C₂²×C₈₃	1	1	yes	characteristic
439	C₂³×Q₈	C₂²×C₈₃	1	1	yes	characteristic
440	C₂²×Q₁₆	C₂²×C₈₃	1	1	yes	characteristic
441	C₂²×Q₁₆	C₂²×C₈₃	1	1	yes	characteristic
442	C₂²×SD₁₆	C₂²×C₈₃	1	1	yes	characteristic
443	C₂²×SD₁₆	C₂²×C₈₃	1	1	yes	characteristic
444	C₂²×M₁₆	C₂²×C₈₃	1	1	yes	characteristic
445	C₂³×C₈	C₂²×C₈₃	1	1	yes	characteristic
446	#537	—	2	4	no	—
447	#537	C₂²×C₈₃	1	8	yes	—
448	#536	—	2	4	no	—
449	#536	C₂²×C₈₃	1	8	yes	complemented
450	C₂×C₄⋊Q₈	—	2	1	no	—
451	C₂×#124	—	2	1	no	—
452	C₂×#123	—	2	1	no	—
453	C₂×#123	—	2	1	no	—
454	C₂×C₂²⋊Q₈	—	2	1	no	—
455	C₂×C₂²⋊Q₈	C₂²×C₈₃	1	1	yes	characteristic
456	C₂×C₂²⋊Q₈	C₂²×C₈₃	1	1	yes	characteristic
457	C₂×C₂²⋊Q₈	C₂²×C₈₃	1	1	yes	characteristic
458	C₂×C₂²⋊Q₈	C₂²×C₈₃	1	1	yes	characteristic
459	C₂×C₂²⋊Q₈	C₂²×C₈₃	1	1	yes	characteristic
460	C₂×C₂²⋊Q₈	C₂²×C₈₃	1	1	yes	characteristic
461	C₂×#121	—	2	1	no	—
462	C₂×#121	—	2	1	no	—
463	C₂×#121	—	2	1	no	—
464	C₂×#121	C₂²×C₈₃	1	1	yes	characteristic
465	C₂×#121	C₂²×C₈₃	1	1	yes	characteristic
466	C₂×#117	C₂²×C₈₃	1	1	yes	characteristic
467	C₂²×C₄⋊C₄	C₂²×C₈₃	1	1	yes	characteristic
468	#485	C₂²×C₈₃	1	8	yes	complemented
469	#484	C₂²×C₈₃	1	8	yes	complemented
470	#483	C₂²×C₈₃	1	8	yes	complemented
471	#482	C₂²×C₈₃	1	8	yes	complemented
472	#470	C₂²×C₈₃	1	8	yes	complemented
473	#468	C₂²×C₈₃	1	8	yes	complemented
474	#467	C₂²×C₈₃	1	8	yes	complemented
475	#465	C₂²×C₈₃	1	8	yes	complemented
476	#452	C₂²×C₈₃	1	8	yes	complemented
477	#452	C₂²×C₈₃	1	8	yes	complemented
478	#451	C₂²×C₈₃	1	8	yes	complemented
479	#448	C₂²×C₈₃	1	8	yes	complemented
480	C₂×#107	C₂²×C₈₃	1	1	yes	characteristic
481	C₂×#107	C₂²×C₈₃	1	1	yes	characteristic
482	C₂×#106	C₂²×C₈₃	1	1	yes	characteristic
483	C₂×#106	C₂²×C₈₃	1	1	yes	characteristic
484	C₂×#103	C₂²×C₈₃	1	1	yes	characteristic
485	C₂×#103	C₂²×C₈₃	1	1	yes	characteristic
486	C₂×#103	C₂²×C₈₃	1	1	yes	characteristic
487	C₂×#103	C₂²×C₈₃	1	1	yes	characteristic
488	C₂×#103	C₂²×C₈₃	1	1	yes	characteristic
489	C₂×#103	C₂²×C₈₃	1	1	yes	characteristic
490	C₂×#102	C₂²×C₈₃	1	1	yes	characteristic
491	C₂×#102	C₂²×C₈₃	1	1	yes	characteristic
492	#408	C₂²×C₈₃	1	8	yes	complemented
493	C₂×C₂²⋊C₈	C₂²×C₈₃	1	1	yes	characteristic
494	C₂×C₂²⋊C₈	C₂²×C₈₃	1	1	yes	characteristic
495	C₂×C₂²⋊C₈	C₂²×C₈₃	1	1	yes	characteristic
496	C₂×C₂²⋊C₈	C₂²×C₈₃	1	1	yes	characteristic
497	C₂×#41	—	2	2	no	—
498	C₂×#41	—	4	2	no	—
499	C₂×#41	—	4	2	no	—
500	C₂×#41	—	4	2	no	—
501	C₂×#41	—	4	2	no	—
502	C₂×#41	D₄×C₈₃	1	4	yes	—
503	C₂×#41	C₂³×C₈₃	1	4	yes	—
504	C₂×#41	C₂³×C₈₃	1	4	yes	—
505	C₂²×Q₈	—	2	1	no	—
506	C₂²×Q₈	—	2	2	no	—
507	C₂²×Q₈	—	4	2	no	—
508	C₂²×Q₈	—	4	2	no	—
509	C₂²×Q₈	D₄×C₈₃	1	1	yes	characteristic
510	C₂²×Q₈	C₂³×C₈₃	1	1	yes	characteristic
511	C₂²×Q₈	C₂³×C₈₃	1	1	yes	characteristic
512	C₂²×Q₈	C₂³×C₈₃	1	1	yes	characteristic
513	C₂²×Q₈	C₂³×C₈₃	1	4	yes	—
514	C₂²×D₄	—	2	1	no	—
515	C₂²×D₄	—	2	1	no	—
516	C₂²×D₄	—	2	1	no	—
517	C₂²×D₄	D₄×C₈₃	1	1	yes	characteristic
518	C₂²×D₄	D₄×C₈₃	1	1	yes	characteristic
519	C₂²×D₄	D₄×C₈₃	1	1	yes	characteristic
520	C₂²×D₄	C₂³×C₈₃	1	1	yes	characteristic
521	C₂³×C₄	—	2	1	no	—
522	C₂³×C₄	—	2	1	no	—
523	C₂³×C₄	—	2	1	no	—
524	C₂³×C₄	C₂³×C₈₃	1	1	yes	characteristic
525	C₂³×C₄	C₂³×C₈₃	1	1	yes	characteristic
526	C₂³×C₄	C₂³×C₈₃	1	1	yes	characteristic
527	C₂×Q₁₆	—	4	2	no	—
528	C₂×Q₁₆	—	4	2	no	—
529	C₂×Q₁₆	C₂³×C₈₃	1	4	yes	—
530	C₂×Q₁₆	C₂³×C₈₃	1	4	yes	—
531	C₂×SD₁₆	—	4	2	no	—
532	C₂×SD₁₆	—	4	2	no	—
533	C₂×SD₁₆	C₂³×C₈₃	1	4	yes	—
534	C₂×SD₁₆	C₂³×C₈₃	1	4	yes	—
535	C₂×M₁₆	—	4	2	no	—
536	C₂×M₁₆	C₂³×C₈₃	1	4	yes	—
537	C₂²×C₈	—	4	2	no	—
538	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
539	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
540	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
541	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
542	C₂²×C₈	C₂³×C₈₃	1	4	yes	—
543	C₄⋊Q₈	—	2	8	no	—
544	#124	—	2	8	no	—
545	#123	—	2	8	no	—
546	#123	—	2	8	no	—
547	C₂²⋊Q₈	—	2	8	no	—
548	C₂²⋊Q₈	—	2	2	no	—
549	C₂²⋊Q₈	—	2	2	no	—
550	C₂²⋊Q₈	—	2	2	no	—
551	C₂²⋊Q₈	—	2	2	no	—
552	C₂²⋊Q₈	—	2	2	no	—
553	C₂²⋊Q₈	—	2	2	no	—
554	C₂²⋊Q₈	C₂³×C₈₃	1	4	yes	—
555	C₂²⋊Q₈	C₂³×C₈₃	1	4	yes	—
556	C₂²⋊Q₈	C₂³×C₈₃	1	4	yes	—
557	C₂²⋊Q₈	C₂³×C₈₃	1	4	yes	—
558	C₂²⋊Q₈	C₂³×C₈₃	1	4	yes	—
559	C₂²⋊Q₈	C₂³×C₈₃	1	4	yes	—
560	#121	—	2	8	no	—
561	#121	—	2	8	no	—
562	#121	—	2	8	no	—
563	#121	—	2	2	no	—
564	#121	—	2	2	no	—
565	#121	C₂³×C₈₃	1	4	yes	—
566	#121	C₂³×C₈₃	1	4	yes	—
567	#117	—	2	2	no	—
568	#117	C₂³×C₈₃	1	4	yes	—
569	C₂×C₄⋊C₄	—	2	1	no	—
570	C₂×C₄⋊C₄	—	2	2	no	—
571	C₂×C₄⋊C₄	—	2	1	no	—
572	C₂×C₄⋊C₄	—	2	1	no	—
573	C₂×C₄⋊C₄	—	2	1	no	—
574	C₂×C₄⋊C₄	—	2	1	no	—
575	C₂×C₄⋊C₄	—	2	1	no	—
576	C₂×C₄⋊C₄	—	2	1	no	—
577	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
578	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
579	C₂×C₄⋊C₄	C₂³×C₈₃	1	4	yes	—
580	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
582	C₂×C₂²⋊C₄	—	2	1	no	—
583	C₂×C₂²⋊C₄	—	2	1	no	—
584	C₂×C₂²⋊C₄	—	2	1	no	—
585	C₂×C₂²⋊C₄	—	2	1	no	—
586	C₂×C₂²⋊C₄	—	2	1	no	—
587	C₂×C₂²⋊C₄	—	2	1	no	—
588	C₂×C₂²⋊C₄	—	2	1	no	—
589	C₂×C₂²⋊C₄	—	2	1	no	—
590	C₂×C₂²⋊C₄	—	2	1	no	—
591	C₂×C₄²	—	2	1	no	—
592	#107	C₂³×C₈₃	1	4	yes	—
593	#107	C₂³×C₈₃	1	4	yes	—
594	#106	C₂³×C₈₃	1	4	yes	—
595	#106	C₂³×C₈₃	1	4	yes	—
596	#103	C₂³×C₈₃	1	4	yes	—
597	#103	C₂³×C₈₃	1	4	yes	—
598	#103	C₂³×C₈₃	1	4	yes	—
599	#103	C₂³×C₈₃	1	4	yes	—
600	#103	C₂³×C₈₃	1	4	yes	—
601	#103	C₂³×C₈₃	1	4	yes	—
602	#102	C₂³×C₈₃	1	4	yes	—
603	#102	C₂³×C₈₃	1	4	yes	—
604	C₂²⋊C₈	C₂³×C₈₃	1	4	yes	—
605	C₂²⋊C₈	C₂³×C₈₃	1	4	yes	—
606	C₂²⋊C₈	C₂³×C₈₃	1	4	yes	—
607	C₂²⋊C₈	C₂³×C₈₃	1	4	yes	—
608	C₂⁴	—	2	1	no	—
609	C₂⁴	C₂×D₄×C₈₃	1	1	yes	characteristic
610	C₂⁴	C₂×D₄×C₈₃	1	1	yes	characteristic
611	C₂⁴	C₂×D₄×C₈₃	1	1	yes	characteristic
612	#41	—	4	8	no	—
613	#41	—	4	4	no	—
614	#41	—	4	4	no	—
615	#41	—	4	4	no	—
616	#41	—	4	4	no	—
617	#41	—	4	8	no	—
618	C₂×Q₈	—	2	1	no	—
619	C₂×Q₈	—	2	1	no	—
620	C₂×Q₈	—	2	1	no	—
621	C₂×Q₈	—	2	4	no	—
622	C₂×Q₈	—	2	2	no	—
623	C₂×Q₈	—	2	2	no	—
624	C₂×Q₈	—	2	2	no	—
625	C₂×Q₈	—	2	2	no	—
626	C₂×Q₈	—	2	2	no	—
627	C₂×Q₈	—	2	2	no	—
628	C₂×Q₈	—	4	2	no	—
629	C₂×Q₈	—	4	4	no	—
630	C₂×Q₈	—	4	4	no	—
631	C₂×Q₈	—	4	4	no	—
632	C₂×Q₈	—	4	8	no	—
633	C₂×Q₈	C₂×D₄×C₈₃	1	4	yes	—
634	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
635	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
636	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
637	C₂×D₄	—	2	4	no	—
638	C₂×D₄	—	2	4	no	—
639	C₂×D₄	—	2	4	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	2	2	no	—
642	C₂×D₄	—	2	2	no	—
643	C₂×D₄	—	4	2	no	—
644	C₂×D₄	—	4	2	no	—
645	C₂×D₄	—	4	2	no	—
646	C₂×D₄	—	4	4	no	—
647	C₂×D₄	—	8	2	no	—
648	C₂×D₄	—	8	2	no	—
649	C₂×D₄	C₂×D₄×C₈₃	1	4	yes	—
650	C₂×D₄	C₂×D₄×C₈₃	1	4	yes	—
651	C₂×D₄	C₂×D₄×C₈₃	1	4	yes	—
652	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
653	C₂²×C₄	—	2	2	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	2	2	no	—
656	C₂²×C₄	—	2	2	no	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	2	1	no	—
660	C₂²×C₄	—	2	1	no	—
661	C₂²×C₄	—	2	1	no	—
662	C₂²×C₄	—	2	1	no	—
663	C₂²×C₄	—	2	1	no	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	4	no	—
667	C₂²×C₄	—	2	4	no	—
668	C₂²×C₄	—	2	4	no	—
669	C₂²×C₄	—	4	4	no	—
670	C₂²×C₄	—	4	4	no	—
671	C₂²×C₄	—	8	2	no	—
672	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
673	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
674	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
675	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
676	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
677	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
678	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
681	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
682	Q₁₆	—	4	4	no	—
683	Q₁₆	—	4	4	no	—
684	SD₁₆	—	4	4	no	—
685	SD₁₆	—	4	4	no	—
686	M₁₆	—	4	4	no	—
687	C₂×C₈	—	2	2	no	—
688	C₂×C₈	—	2	2	no	—
689	C₂×C₈	—	2	2	no	—
690	C₂×C₈	—	2	2	no	—
691	C₂×C₈	—	4	4	no	—
692	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
693	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
694	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
695	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	2	1	no	—
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	—	2	4	no	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	4	no	—
704	C₄⋊C₄	—	2	4	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
708	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
709	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
710	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	2	4	no	—
716	C₂²⋊C₄	—	2	4	no	—
717	C₂²⋊C₄	—	2	4	no	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	2	4	no	—
720	C₄²	—	2	4	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	2	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	2	no	—
729	C₂³	—	2	2	no	—
730	C₂³	—	2	2	no	—
731	C₂³	—	4	2	no	—
732	C₂³	—	4	2	no	—
733	C₂³	—	4	2	no	—
734	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
735	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
736	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
737	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
738	Q₈	—	2	2	no	—
739	Q₈	—	2	2	no	—
740	Q₈	—	2	2	no	—
741	Q₈	—	2	2	no	—
742	Q₈	—	2	2	no	—
743	Q₈	—	2	2	no	—
744	Q₈	—	4	4	no	—
745	Q₈	—	4	8	no	—
746	Q₈	—	4	2	no	—
747	Q₈	—	4	2	no	—
748	Q₈	—	4	2	no	—
749	D₄	—	2	2	no	—
750	D₄	—	2	2	no	—
751	D₄	—	4	4	no	—
752	D₄	—	4	4	no	—
753	D₄	—	4	4	no	—
754	D₄	—	4	8	no	—
755	D₄	—	4	2	no	—
756	D₄	—	8	4	no	—
757	D₄	—	8	4	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	4	no	—
762	C₂×C₄	—	2	4	no	—
763	C₂×C₄	—	2	4	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	4	8	no	—
778	C₂×C₄	—	4	8	no	—
779	C₂×C₄	—	4	2	no	—
780	C₂×C₄	—	4	2	no	—
781	C₂×C₄	—	4	2	no	—
782	C₂×C₄	—	4	2	no	—
783	C₂×C₄	—	4	2	no	—
784	C₂×C₄	—	4	2	no	—
785	C₂×C₄	—	4	2	no	—
786	C₂×C₄	—	8	4	no	—
787	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
788	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
789	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
790	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
791	C₂×C₄	H(5,𝔽₂)×C₈₃	1	2	yes	—
792	C₂×C₄	H(5,𝔽₂)×C₈₃	1	2	yes	—
793	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
794	C₈	—	2	2	no	—
795	C₈	—	2	2	no	—
796	C₈	—	2	2	no	—
797	C₈	—	2	2	no	—
798	C₂²	—	2	2	no	—
799	C₂²	—	2	2	no	—
800	C₂²	—	2	2	no	—
801	C₂²	—	2	2	no	—
802	C₂²	—	2	2	no	—
803	C₂²	—	2	2	no	—
804	C₂²	—	2	2	no	—
805	C₂²	—	2	2	no	—
806	C₂²	—	2	2	no	—
807	C₂²	—	4	4	no	—
808	C₂²	—	4	4	no	—
809	C₂²	—	4	4	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	2	no	—
813	C₂²	—	8	4	no	—
814	C₂²	#534×C₈₃	1	2	yes	—
815	C₂²	#577×C₈₃	1	2	yes	—
816	C₂²	#578×C₈₃	1	2	yes	—
817	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
818	C₄	—	2	2	no	—
819	C₄	—	2	2	no	—
820	C₄	—	2	2	no	—
821	C₄	—	4	2	no	—
822	C₄	—	4	2	no	—
823	C₄	—	4	2	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	2	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	2	no	—
828	C₄	#534×C₈₃	1	2	yes	—
829	C₄	C₂×H(5,𝔽₂)×C₈₃	1	1	yes	characteristic
830	C₄	C₂×H(5,𝔽₂)×C₈₃	1	1	yes	characteristic
831	C₂	—	4	2	no	—
832	C₂	—	4	2	no	—
833	C₂	—	4	2	no	—
834	C₂	—	8	2	no	—
835	C₂	C₈₃×#3201	1	4	yes	direct product factor
836	C₂	C₂×#534×C₈₃	1	1	yes	characteristic
837	C₂	C₂×#577×C₈₃	1	1	yes	characteristic
838	C₂	C₂×#578×C₈₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₃
prime radical	C₂×#537×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
2. C₂×#536×C₈₃	C₂	semidirect
3. C₈₃×#3201	C₂	direct (N × H)
4. C₂×#484×C₈₃	C₂	semidirect
5. C₂×#485×C₈₃	C₂	semidirect
6. C₂×#482×C₈₃	C₂	semidirect
7. C₂×#483×C₈₃	C₂	semidirect
8. C₂×#470×C₈₃	C₂	semidirect
9. C₂×#468×C₈₃	C₂	semidirect
10. C₂×#467×C₈₃	C₂	semidirect
11. C₂×#465×C₈₃	C₂	semidirect
12. C₂×#452×C₈₃	C₂	semidirect
13. C₂×#452×C₈₃	C₂	semidirect
14. C₂×#451×C₈₃	C₂	semidirect
15. C₂×#448×C₈₃	C₂	semidirect
16. C₂×#408×C₈₃	C₂	semidirect
29. #536×C₈₃	C₂²	semidirect
48. #485×C₈₃	C₂²	semidirect
49. #484×C₈₃	C₂²	semidirect
50. #483×C₈₃	C₂²	semidirect
51. #482×C₈₃	C₂²	semidirect
52. #470×C₈₃	C₂²	semidirect
53. #468×C₈₃	C₂²	semidirect
54. #467×C₈₃	C₂²	semidirect
55. #465×C₈₃	C₂²	semidirect
56. #452×C₈₃	C₂²	semidirect
57. #452×C₈₃	C₂²	semidirect
58. #451×C₈₃	C₂²	semidirect
59. #448×C₈₃	C₂²	semidirect
72. #408×C₈₃	C₂²	semidirect
411. C₂×#3201	C₈₃	direct (N × H)
416. C₂×C₈₃	#3201	direct (N × H)
421. C₂×#536	C₂×C₈₃	semidirect
422. #3201	C₂×C₈₃	direct (N × H)
423. C₂×#484	C₂×C₈₃	semidirect
424. C₂×#485	C₂×C₈₃	semidirect
425. C₂×#482	C₂×C₈₃	semidirect
426. C₂×#483	C₂×C₈₃	semidirect
427. C₂×#470	C₂×C₈₃	semidirect
428. C₂×#468	C₂×C₈₃	semidirect
429. C₂×#467	C₂×C₈₃	semidirect
430. C₂×#465	C₂×C₈₃	semidirect
431. C₂×#452	C₂×C₈₃	semidirect
432. C₂×#452	C₂×C₈₃	semidirect
433. C₂×#451	C₂×C₈₃	semidirect
434. C₂×#448	C₂×C₈₃	semidirect
435. C₂×#408	C₂×C₈₃	semidirect
436. C₈₃	C₂×#3201	direct (N × H)
449. #536	C₂²×C₈₃	semidirect
468. #485	C₂²×C₈₃	semidirect
469. #484	C₂²×C₈₃	semidirect
470. #483	C₂²×C₈₃	semidirect
471. #482	C₂²×C₈₃	semidirect
472. #470	C₂²×C₈₃	semidirect
473. #468	C₂²×C₈₃	semidirect
474. #467	C₂²×C₈₃	semidirect
475. #465	C₂²×C₈₃	semidirect
476. #452	C₂²×C₈₃	semidirect
477. #452	C₂²×C₈₃	semidirect
478. #451	C₂²×C₈₃	semidirect
479. #448	C₂²×C₈₃	semidirect
492. #408	C₂²×C₈₃	semidirect
835. C₂	C₈₃×#3201	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×#537×C₈₃	2
C₂×#536×C₈₃	2
C₈₃×#3201	2
C₂×#484×C₈₃	2
C₂×#485×C₈₃	2
C₂×#482×C₈₃	2
C₂×#483×C₈₃	2
C₂×#470×C₈₃	2
C₂×#468×C₈₃	2
C₂×#467×C₈₃	2
C₂×#465×C₈₃	2
C₂×#452×C₈₃	2
C₂×#451×C₈₃	2
C₂×#448×C₈₃	2
C₂×#408×C₈₃	2
C₂×#3201	83

Subgroups — C2×C83×#3201 #35288569

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₃×#3201 #35288569