Subgroups — C₂×C₈₃×#3400 #35289221

Order 21248.

1970 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#559×C₈₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#557×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₃×#3400	C₂	1	16	yes	maximal, direct product factor
4	C₂×#497×C₈₃	C₂	1	2	yes	maximal, complemented
5	C₂×#492×C₈₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#464×C₈₃	C₂	1	2	yes	maximal, complemented
7	C₂×#462×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#460×C₈₃	C₂	1	1	yes	maximal, characteristic
9	C₂×#461×C₈₃	C₂	1	2	yes	maximal, complemented
10	C₂×#446×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#440×C₈₃	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×Q₁₆×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic
14	C₂²×Q₁₆×C₈₃	C₂²	1	2	yes	—
15	C₂²×SD₁₆×C₈₃	C₂²	1	2	yes	—
16	C₂²×SD₁₆×C₈₃	C₂²	1	2	yes	—
17	C₂²×SD₁₆×C₈₃	C₂²	1	2	yes	—
18	#559×C₈₃	—	2	4	no	—
19	#559×C₈₃	C₂²	1	8	yes	—
20	#557×C₈₃	—	2	4	no	—
21	#557×C₈₃	C₂²	1	8	yes	complemented
22	C₂×C₄⋊Q₈×C₈₃	C₂²	1	2	yes	—
23	C₂×C₄⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
24	C₂×#127×C₈₃	C₂²	1	1	yes	characteristic
25	C₂×#125×C₈₃	—	2	1	no	—
26	C₂×#125×C₈₃	—	2	2	no	—
27	C₂×#124×C₈₃	—	2	1	no	—
28	C₂×#124×C₈₃	C₂²	1	2	yes	—
29	C₂×#123×C₈₃	—	2	2	no	—
30	C₂×C₄×Q₈×C₈₃	—	2	1	no	—
31	C₂×C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₈₃	C₂²	1	2	yes	—
34	C₂×C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₈₃	—	2	1	no	—
36	C₂×C₄×D₄×C₈₃	C₂²	1	2	yes	—
37	#497×C₈₃	C₂²	1	16	yes	complemented
38	#492×C₈₃	C₂²	1	8	yes	—
39	#464×C₈₃	C₂²	1	16	yes	complemented
40	#462×C₈₃	C₂²	1	8	yes	complemented
41	#461×C₈₃	C₂²	1	16	yes	complemented
42	#460×C₈₃	C₂²	1	8	yes	—
43	#446×C₈₃	C₂²	1	8	yes	complemented
44	#440×C₈₃	C₂²	1	16	yes	complemented
45	C₄×Q₁₆×C₈₃	C₂²	1	8	yes	complemented
46	C₂×#107×C₈₃	C₂²	1	1	yes	characteristic
47	C₂×C₄⋊C₈×C₈₃	C₂²	1	2	yes	—
48	C₂×C₄⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
49	C₂×#103×C₈₃	C₂²	1	1	yes	characteristic
50	C₂×#103×C₈₃	C₂²	1	2	yes	—
51	C₂×#103×C₈₃	C₂²	1	1	yes	characteristic
52	C₂×#102×C₈₃	C₂²	1	2	yes	—
53	C₂×#97×C₈₃	C₂²	1	2	yes	—
54	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
55	C₂²×Q₈×C₈₃	D₄	1	1	yes	characteristic
56	C₂²×Q₈×C₈₃	C₂³	1	1	yes	characteristic
57	C₂²×Q₈×C₈₃	C₂³	1	2	yes	—
58	C₂²×Q₈×C₈₃	C₂³	1	1	yes	characteristic
59	C₂²×D₄×C₈₃	—	2	1	no	—
60	C₂²×D₄×C₈₃	—	2	1	no	—
61	C₂²×D₄×C₈₃	C₂³	1	2	yes	—
62	C₂³×C₄×C₈₃	—	2	2	no	—
63	C₂×Q₁₆×C₈₃	—	2	4	no	—
64	C₂×Q₁₆×C₈₃	—	4	4	no	—
65	C₂×Q₁₆×C₈₃	C₂³	1	4	yes	—
66	C₂×Q₁₆×C₈₃	C₂³	1	8	yes	—
67	C₂×SD₁₆×C₈₃	—	2	8	no	—
68	C₂×SD₁₆×C₈₃	—	4	4	no	—
69	C₂×SD₁₆×C₈₃	—	4	4	no	—
70	C₂×SD₁₆×C₈₃	C₂³	1	8	yes	—
71	C₂×SD₁₆×C₈₃	C₂³	1	8	yes	—
72	C₂×SD₁₆×C₈₃	C₂³	1	8	yes	—
73	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
75	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
76	C₄⋊Q₈×C₈₃	—	2	4	no	—
77	C₄⋊Q₈×C₈₃	—	2	2	no	—
78	C₄⋊Q₈×C₈₃	C₂³	1	4	yes	—
79	C₄⋊Q₈×C₈₃	C₂³	1	8	yes	—
80	#127×C₈₃	—	2	2	no	—
81	#127×C₈₃	C₂³	1	4	yes	—
82	#125×C₈₃	—	2	8	no	—
83	#125×C₈₃	—	2	16	no	—
84	#124×C₈₃	—	2	8	no	—
85	#124×C₈₃	—	2	4	no	—
86	#124×C₈₃	C₂³	1	8	yes	—
87	#123×C₈₃	—	2	16	no	—
88	C₄×Q₈×C₈₃	—	2	8	no	—
89	C₄×Q₈×C₈₃	—	2	4	no	—
90	C₄×Q₈×C₈₃	—	2	2	no	—
91	C₄×Q₈×C₈₃	—	2	2	no	—
92	C₄×Q₈×C₈₃	D₄	1	4	yes	—
93	C₄×Q₈×C₈₃	C₂³	1	8	yes	—
94	C₄×Q₈×C₈₃	C₂³	1	4	yes	—
95	C₄×Q₈×C₈₃	C₂³	1	4	yes	—
96	C₄×Q₈×C₈₃	C₂³	1	4	yes	—
97	C₄×D₄×C₈₃	—	2	8	no	—
98	C₄×D₄×C₈₃	—	2	4	no	—
99	C₄×D₄×C₈₃	C₂³	1	8	yes	—
100	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
101	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
102	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
103	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
104	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
105	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
106	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
107	C₂×C₄⋊C₄×C₈₃	D₄	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₈₃	D₄	1	2	yes	—
109	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
111	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
112	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
113	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
114	C₂×C₄²×C₈₃	—	2	1	no	—
115	C₂×C₄²×C₈₃	—	2	2	no	—
116	C₂×C₄²×C₈₃	—	2	1	no	—
117	C₂×C₄²×C₈₃	C₂³	1	2	yes	—
118	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
119	#107×C₈₃	C₂³	1	4	yes	—
120	C₄⋊C₈×C₈₃	C₂³	1	8	yes	—
121	C₄⋊C₈×C₈₃	C₂³	1	4	yes	—
122	#103×C₈₃	C₂³	1	4	yes	—
123	#103×C₈₃	C₂³	1	4	yes	—
124	#103×C₈₃	C₂³	1	8	yes	—
125	#102×C₈₃	C₂³	1	8	yes	—
126	#97×C₈₃	C₂³	1	8	yes	—
127	C₄×C₈×C₈₃	C₂³	1	4	yes	—
128	C₂⁴×C₈₃	—	2	2	no	—
129	C₂×Q₈×C₈₃	—	2	4	no	—
130	C₂×Q₈×C₈₃	—	2	1	no	—
131	C₂×Q₈×C₈₃	—	2	2	no	—
132	C₂×Q₈×C₈₃	—	2	1	no	—
133	C₂×Q₈×C₈₃	—	2	4	no	—
134	C₂×Q₈×C₈₃	—	2	2	no	—
135	C₂×Q₈×C₈₃	—	2	2	no	—
136	C₂×Q₈×C₈₃	—	2	2	no	—
137	C₂×Q₈×C₈₃	—	2	4	no	—
138	C₂×Q₈×C₈₃	—	2	2	no	—
139	C₂×Q₈×C₈₃	C₂×D₄	1	4	yes	—
140	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
141	C₂×Q₈×C₈₃	C₂⁴	1	4	yes	—
142	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
143	C₂×D₄×C₈₃	—	2	2	no	—
144	C₂×D₄×C₈₃	—	2	4	no	—
145	C₂×D₄×C₈₃	—	2	4	no	—
146	C₂×D₄×C₈₃	—	2	4	no	—
147	C₂×D₄×C₈₃	—	2	4	no	—
148	C₂×D₄×C₈₃	—	4	4	no	—
149	C₂×D₄×C₈₃	—	8	2	no	—
150	C₂×D₄×C₈₃	C₂⁴	1	4	yes	—
151	C₂²×C₄×C₈₃	—	2	1	no	—
152	C₂²×C₄×C₈₃	—	2	1	no	—
153	C₂²×C₄×C₈₃	—	2	1	no	—
154	C₂²×C₄×C₈₃	—	2	2	no	—
155	C₂²×C₄×C₈₃	—	2	1	no	—
156	C₂²×C₄×C₈₃	—	2	8	no	—
157	C₂²×C₄×C₈₃	—	8	4	no	—
158	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
163	Q₁₆×C₈₃	—	2	8	no	—
164	Q₁₆×C₈₃	—	4	8	no	—
165	SD₁₆×C₈₃	—	2	16	no	—
166	SD₁₆×C₈₃	—	4	8	no	—
167	SD₁₆×C₈₃	—	4	8	no	—
168	C₂×C₈×C₈₃	—	2	2	no	—
169	C₂×C₈×C₈₃	—	2	4	no	—
170	C₂×C₈×C₈₃	#41	1	4	yes	—
171	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
172	C₂×C₈×C₈₃	C₂⁴	1	4	yes	—
173	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
174	C₄⋊C₄×C₈₃	—	2	8	no	—
175	C₄⋊C₄×C₈₃	—	2	4	no	—
176	C₄⋊C₄×C₈₃	—	2	4	no	—
177	C₄⋊C₄×C₈₃	—	2	8	no	—
178	C₄⋊C₄×C₈₃	—	2	4	no	—
179	C₄⋊C₄×C₈₃	—	2	8	no	—
180	C₄⋊C₄×C₈₃	—	2	4	no	—
181	C₄⋊C₄×C₈₃	—	2	1	no	—
182	C₄⋊C₄×C₈₃	—	2	1	no	—
183	C₄⋊C₄×C₈₃	C₂×D₄	1	4	yes	—
184	C₄⋊C₄×C₈₃	C₂×D₄	1	8	yes	—
185	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
186	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
187	C₂²⋊C₄×C₈₃	—	2	8	no	—
188	C₂²⋊C₄×C₈₃	—	2	8	no	—
189	C₂²⋊C₄×C₈₃	—	2	8	no	—
190	C₄²×C₈₃	—	2	4	no	—
191	C₄²×C₈₃	—	2	8	no	—
192	C₄²×C₈₃	—	2	4	no	—
193	C₄²×C₈₃	C₂×D₄	1	4	yes	—
194	C₄²×C₈₃	C₂×D₄	1	2	yes	—
195	C₄²×C₈₃	C₂⁴	1	2	yes	—
196	C₄²×C₈₃	C₂⁴	1	4	yes	—
197	C₂³×C₈₃	—	2	4	no	—
198	C₂³×C₈₃	—	4	4	no	—
199	C₂³×C₈₃	—	4	4	no	—
200	C₂³×C₈₃	—	4	4	no	—
201	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
202	Q₈×C₈₃	—	2	8	no	—
203	Q₈×C₈₃	—	2	4	no	—
204	Q₈×C₈₃	—	2	2	no	—
205	Q₈×C₈₃	—	2	2	no	—
206	Q₈×C₈₃	—	2	2	no	—
207	Q₈×C₈₃	—	2	4	no	—
208	Q₈×C₈₃	—	2	2	no	—
209	Q₈×C₈₃	—	4	2	no	—
210	Q₈×C₈₃	—	4	4	no	—
211	Q₈×C₈₃	—	4	2	no	—
212	D₄×C₈₃	—	2	4	no	—
213	D₄×C₈₃	—	2	4	no	—
214	D₄×C₈₃	—	4	4	no	—
215	D₄×C₈₃	—	4	8	no	—
216	D₄×C₈₃	—	8	4	no	—
217	C₂×C₄×C₈₃	—	2	4	no	—
218	C₂×C₄×C₈₃	—	2	4	no	—
219	C₂×C₄×C₈₃	—	2	2	no	—
220	C₂×C₄×C₈₃	—	2	2	no	—
221	C₂×C₄×C₈₃	—	2	2	no	—
222	C₂×C₄×C₈₃	—	2	2	no	—
223	C₂×C₄×C₈₃	—	2	4	no	—
224	C₂×C₄×C₈₃	—	2	2	no	—
225	C₂×C₄×C₈₃	—	4	2	no	—
226	C₂×C₄×C₈₃	—	4	4	no	—
227	C₂×C₄×C₈₃	—	4	2	no	—
228	C₂×C₄×C₈₃	—	4	2	no	—
229	C₂×C₄×C₈₃	—	4	2	no	—
230	C₂×C₄×C₈₃	—	8	8	no	—
231	C₂×C₄×C₈₃	#137	1	4	yes	—
232	C₂×C₄×C₈₃	C₂²×D₄	1	4	yes	—
233	C₂×C₄×C₈₃	C₂²×D₄	1	4	yes	—
234	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
235	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
237	C₂×C₄×C₈₃	C₂×#41	1	2	yes	—
238	C₂×C₄×C₈₃	H(5,𝔽₂)	1	2	yes	—
239	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
240	C₈×C₈₃	—	2	2	no	—
241	C₈×C₈₃	—	2	4	no	—
242	C₈×C₈₃	C₂×#41	1	4	yes	—
243	C₂²×C₈₃	—	4	4	no	—
244	C₂²×C₈₃	—	4	4	no	—
245	C₂²×C₈₃	—	4	4	no	—
246	C₂²×C₈₃	—	8	8	no	—
247	C₂²×C₈₃	#550	1	2	yes	—
248	C₂²×C₈₃	C₂×#137	1	2	yes	—
249	C₂²×C₈₃	#577	1	2	yes	—
250	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
251	C₄×C₈₃	—	2	4	no	—
252	C₄×C₈₃	—	2	4	no	—
253	C₄×C₈₃	—	2	2	no	—
254	C₄×C₈₃	—	4	2	no	—
255	C₄×C₈₃	—	4	4	no	—
256	C₄×C₈₃	—	4	2	no	—
257	C₄×C₈₃	—	4	2	no	—
258	C₄×C₈₃	—	4	2	no	—
259	C₄×C₈₃	#550	1	2	yes	—
260	C₄×C₈₃	C₂×#137	1	4	yes	—
261	C₄×C₈₃	C₂²×#41	1	1	yes	characteristic
262	C₄×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
263	C₂×#3400	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
264	C₂×C₈₃	—	8	4	no	—
265	C₂×C₈₃	#3400	1	4	yes	direct product factor
266	C₂×C₈₃	C₂×#550	1	1	yes	characteristic
267	C₂×C₈₃	C₂²×#137	1	1	yes	characteristic
268	C₂×C₈₃	C₂×#577	1	1	yes	characteristic
269	C₂×#559	C₂×C₈₃	1	1	yes	characteristic
270	C₂×#557	C₂×C₈₃	1	1	yes	characteristic, complemented
271	#3400	C₂×C₈₃	1	16	yes	direct product factor
272	C₂×#497	C₂×C₈₃	1	2	yes	complemented
273	C₂×#492	C₂×C₈₃	1	1	yes	characteristic
274	C₂×#464	C₂×C₈₃	1	2	yes	complemented
275	C₂×#462	C₂×C₈₃	1	1	yes	characteristic, complemented
276	C₂×#460	C₂×C₈₃	1	1	yes	characteristic
277	C₂×#461	C₂×C₈₃	1	2	yes	complemented
278	C₂×#446	C₂×C₈₃	1	1	yes	characteristic, complemented
279	C₂×#440	C₂×C₈₃	1	2	yes	complemented
280	C₂×C₄×Q₁₆	C₂×C₈₃	1	1	yes	characteristic, complemented
281	C₈₃	C₂×#3400	1	1	yes	characteristic, direct product factor, Sylow
282	C₂²×Q₁₆	C₂²×C₈₃	1	1	yes	characteristic
283	C₂²×Q₁₆	C₂²×C₈₃	1	2	yes	—
284	C₂²×SD₁₆	C₂²×C₈₃	1	2	yes	—
285	C₂²×SD₁₆	C₂²×C₈₃	1	2	yes	—
286	C₂²×SD₁₆	C₂²×C₈₃	1	2	yes	—
287	#559	—	2	4	no	—
288	#559	C₂²×C₈₃	1	8	yes	—
289	#557	—	2	4	no	—
290	#557	C₂²×C₈₃	1	8	yes	complemented
291	C₂×C₄⋊Q₈	C₂²×C₈₃	1	1	yes	characteristic
292	C₂×C₄⋊Q₈	C₂²×C₈₃	1	2	yes	—
293	C₂×#127	C₂²×C₈₃	1	1	yes	characteristic
294	C₂×#125	—	2	1	no	—
295	C₂×#125	—	2	2	no	—
296	C₂×#124	—	2	1	no	—
297	C₂×#124	C₂²×C₈₃	1	2	yes	—
298	C₂×#123	—	2	2	no	—
299	C₂×C₄×Q₈	—	2	1	no	—
300	C₂×C₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic
301	C₂×C₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic
302	C₂×C₄×Q₈	C₂²×C₈₃	1	2	yes	—
303	C₂×C₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic
304	C₂×C₄×D₄	—	2	1	no	—
305	C₂×C₄×D₄	C₂²×C₈₃	1	2	yes	—
306	#497	C₂²×C₈₃	1	16	yes	complemented
307	#492	C₂²×C₈₃	1	8	yes	—
308	#464	C₂²×C₈₃	1	16	yes	complemented
309	#462	C₂²×C₈₃	1	8	yes	complemented
310	#461	C₂²×C₈₃	1	16	yes	complemented
311	#460	C₂²×C₈₃	1	8	yes	—
312	#446	C₂²×C₈₃	1	8	yes	complemented
313	#440	C₂²×C₈₃	1	16	yes	complemented
314	C₄×Q₁₆	C₂²×C₈₃	1	8	yes	complemented
315	C₂×#107	C₂²×C₈₃	1	1	yes	characteristic
316	C₂×C₄⋊C₈	C₂²×C₈₃	1	2	yes	—
317	C₂×C₄⋊C₈	C₂²×C₈₃	1	1	yes	characteristic
318	C₂×#103	C₂²×C₈₃	1	1	yes	characteristic
319	C₂×#103	C₂²×C₈₃	1	1	yes	characteristic
320	C₂×#103	C₂²×C₈₃	1	2	yes	—
321	C₂×#102	C₂²×C₈₃	1	2	yes	—
322	C₂×#97	C₂²×C₈₃	1	2	yes	—
323	C₂×C₄×C₈	C₂²×C₈₃	1	1	yes	characteristic
324	C₂²×Q₈	D₄×C₈₃	1	1	yes	characteristic
325	C₂²×Q₈	C₂³×C₈₃	1	1	yes	characteristic
326	C₂²×Q₈	C₂³×C₈₃	1	2	yes	—
327	C₂²×Q₈	C₂³×C₈₃	1	1	yes	characteristic
328	C₂²×D₄	—	2	1	no	—
329	C₂²×D₄	—	2	1	no	—
330	C₂²×D₄	C₂³×C₈₃	1	2	yes	—
331	C₂³×C₄	—	2	2	no	—
332	C₂×Q₁₆	—	2	4	no	—
333	C₂×Q₁₆	—	4	4	no	—
334	C₂×Q₁₆	C₂³×C₈₃	1	4	yes	—
335	C₂×Q₁₆	C₂³×C₈₃	1	8	yes	—
336	C₂×SD₁₆	—	2	8	no	—
337	C₂×SD₁₆	—	4	4	no	—
338	C₂×SD₁₆	—	4	4	no	—
339	C₂×SD₁₆	C₂³×C₈₃	1	8	yes	—
340	C₂×SD₁₆	C₂³×C₈₃	1	8	yes	—
341	C₂×SD₁₆	C₂³×C₈₃	1	8	yes	—
342	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
343	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
344	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
345	C₄⋊Q₈	—	2	4	no	—
346	C₄⋊Q₈	—	2	2	no	—
347	C₄⋊Q₈	C₂³×C₈₃	1	8	yes	—
348	C₄⋊Q₈	C₂³×C₈₃	1	4	yes	—
349	#127	—	2	2	no	—
350	#127	C₂³×C₈₃	1	4	yes	—
351	#125	—	2	8	no	—
352	#125	—	2	16	no	—
353	#124	—	2	8	no	—
354	#124	—	2	4	no	—
355	#124	C₂³×C₈₃	1	8	yes	—
356	#123	—	2	16	no	—
357	C₄×Q₈	—	2	8	no	—
358	C₄×Q₈	—	2	4	no	—
359	C₄×Q₈	—	2	2	no	—
360	C₄×Q₈	—	2	2	no	—
361	C₄×Q₈	D₄×C₈₃	1	4	yes	—
362	C₄×Q₈	C₂³×C₈₃	1	4	yes	—
363	C₄×Q₈	C₂³×C₈₃	1	8	yes	—
364	C₄×Q₈	C₂³×C₈₃	1	4	yes	—
365	C₄×Q₈	C₂³×C₈₃	1	4	yes	—
366	C₄×D₄	—	2	8	no	—
367	C₄×D₄	—	2	4	no	—
368	C₄×D₄	C₂³×C₈₃	1	8	yes	—
369	C₂×C₄⋊C₄	—	2	2	no	—
370	C₂×C₄⋊C₄	—	2	1	no	—
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	—	2	2	no	—
373	C₂×C₄⋊C₄	—	2	1	no	—
374	C₂×C₄⋊C₄	—	2	2	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	D₄×C₈₃	1	1	yes	characteristic
377	C₂×C₄⋊C₄	D₄×C₈₃	1	2	yes	—
378	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
379	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
380	C₂×C₂²⋊C₄	—	2	2	no	—
381	C₂×C₂²⋊C₄	—	2	2	no	—
382	C₂×C₂²⋊C₄	—	2	2	no	—
383	C₂×C₄²	—	2	1	no	—
384	C₂×C₄²	—	2	2	no	—
385	C₂×C₄²	—	2	1	no	—
386	C₂×C₄²	C₂³×C₈₃	1	2	yes	—
387	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
388	#107	C₂³×C₈₃	1	4	yes	—
389	C₄⋊C₈	C₂³×C₈₃	1	4	yes	—
390	C₄⋊C₈	C₂³×C₈₃	1	8	yes	—
391	#103	C₂³×C₈₃	1	4	yes	—
392	#103	C₂³×C₈₃	1	4	yes	—
393	#103	C₂³×C₈₃	1	8	yes	—
394	#102	C₂³×C₈₃	1	8	yes	—
395	#97	C₂³×C₈₃	1	8	yes	—
396	C₄×C₈	C₂³×C₈₃	1	4	yes	—
397	C₂⁴	—	2	2	no	—
398	C₂×Q₈	—	2	4	no	—
399	C₂×Q₈	—	2	1	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	2	1	no	—
402	C₂×Q₈	—	2	4	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	4	no	—
407	C₂×Q₈	—	2	2	no	—
408	C₂×Q₈	C₂×D₄×C₈₃	1	4	yes	—
409	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
410	C₂×Q₈	C₂⁴×C₈₃	1	4	yes	—
411	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	4	no	—
414	C₂×D₄	—	2	4	no	—
415	C₂×D₄	—	2	4	no	—
416	C₂×D₄	—	2	4	no	—
417	C₂×D₄	—	4	4	no	—
418	C₂×D₄	—	8	2	no	—
419	C₂×D₄	C₂⁴×C₈₃	1	4	yes	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	8	no	—
426	C₂²×C₄	—	8	4	no	—
427	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
428	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
429	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
430	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
431	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
432	Q₁₆	—	2	8	no	—
433	Q₁₆	—	4	8	no	—
434	SD₁₆	—	2	16	no	—
435	SD₁₆	—	4	8	no	—
436	SD₁₆	—	4	8	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	2	4	no	—
439	C₂×C₈	#41×C₈₃	1	4	yes	—
440	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
441	C₂×C₈	C₂⁴×C₈₃	1	4	yes	—
442	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
443	C₄⋊C₄	—	2	8	no	—
444	C₄⋊C₄	—	2	4	no	—
445	C₄⋊C₄	—	2	4	no	—
446	C₄⋊C₄	—	2	8	no	—
447	C₄⋊C₄	—	2	4	no	—
448	C₄⋊C₄	—	2	8	no	—
449	C₄⋊C₄	—	2	4	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	C₂×D₄×C₈₃	1	4	yes	—
453	C₄⋊C₄	C₂×D₄×C₈₃	1	8	yes	—
454	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
455	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
456	C₂²⋊C₄	—	2	8	no	—
457	C₂²⋊C₄	—	2	8	no	—
458	C₂²⋊C₄	—	2	8	no	—
459	C₄²	—	2	4	no	—
460	C₄²	—	2	8	no	—
461	C₄²	—	2	4	no	—
462	C₄²	C₂×D₄×C₈₃	1	4	yes	—
463	C₄²	C₂×D₄×C₈₃	1	2	yes	—
464	C₄²	C₂⁴×C₈₃	1	2	yes	—
465	C₄²	C₂⁴×C₈₃	1	4	yes	—
466	C₂³	—	2	4	no	—
467	C₂³	—	4	4	no	—
468	C₂³	—	4	4	no	—
469	C₂³	—	4	4	no	—
470	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
471	Q₈	—	2	8	no	—
472	Q₈	—	2	4	no	—
473	Q₈	—	2	2	no	—
474	Q₈	—	2	2	no	—
475	Q₈	—	2	2	no	—
476	Q₈	—	2	4	no	—
477	Q₈	—	2	2	no	—
478	Q₈	—	4	2	no	—
479	Q₈	—	4	4	no	—
480	Q₈	—	4	2	no	—
481	D₄	—	2	4	no	—
482	D₄	—	2	4	no	—
483	D₄	—	4	4	no	—
484	D₄	—	4	8	no	—
485	D₄	—	8	4	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	4	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	8	8	no	—
500	C₂×C₄	#137×C₈₃	1	4	yes	—
501	C₂×C₄	C₂²×D₄×C₈₃	1	4	yes	—
502	C₂×C₄	C₂²×D₄×C₈₃	1	4	yes	—
503	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
504	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
505	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
506	C₂×C₄	C₂×#41×C₈₃	1	2	yes	—
507	C₂×C₄	H(5,𝔽₂)×C₈₃	1	2	yes	—
508	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
509	C₈	—	2	2	no	—
510	C₈	—	2	4	no	—
511	C₈	C₂×#41×C₈₃	1	4	yes	—
512	C₂²	—	4	4	no	—
513	C₂²	—	4	4	no	—
514	C₂²	—	4	4	no	—
515	C₂²	—	8	8	no	—
516	C₂²	#550×C₈₃	1	2	yes	—
517	C₂²	C₂×#137×C₈₃	1	2	yes	—
518	C₂²	#577×C₈₃	1	2	yes	—
519	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
520	C₄	—	2	4	no	—
521	C₄	—	2	4	no	—
522	C₄	—	2	2	no	—
523	C₄	—	4	2	no	—
524	C₄	—	4	2	no	—
525	C₄	—	4	2	no	—
526	C₄	—	4	4	no	—
527	C₄	—	4	2	no	—
528	C₄	#550×C₈₃	1	2	yes	—
529	C₄	C₂×#137×C₈₃	1	4	yes	—
530	C₄	C₂²×#41×C₈₃	1	1	yes	characteristic
531	C₄	C₂×H(5,𝔽₂)×C₈₃	1	1	yes	characteristic
532	C₂	—	8	4	no	—
533	C₂	C₈₃×#3400	1	4	yes	direct product factor
534	C₂	C₂×#550×C₈₃	1	1	yes	characteristic
535	C₂	C₂²×#137×C₈₃	1	1	yes	characteristic
536	C₂	C₂×#577×C₈₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₃
prime radical	C₂×#127×C₈₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₃ ◁ C₂×C₄×Q₈×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#557×C₈₃	C₂	semidirect
3. C₈₃×#3400	C₂	direct (N × H)
4. C₂×#497×C₈₃	C₂	semidirect
6. C₂×#464×C₈₃	C₂	semidirect
7. C₂×#462×C₈₃	C₂	semidirect
9. C₂×#461×C₈₃	C₂	semidirect
10. C₂×#446×C₈₃	C₂	semidirect
11. C₂×#440×C₈₃	C₂	semidirect
12. C₂×C₄×Q₁₆×C₈₃	C₂	semidirect
21. #557×C₈₃	C₂²	semidirect
37. #497×C₈₃	C₂²	semidirect
39. #464×C₈₃	C₂²	semidirect
40. #462×C₈₃	C₂²	semidirect
41. #461×C₈₃	C₂²	semidirect
43. #446×C₈₃	C₂²	semidirect
44. #440×C₈₃	C₂²	semidirect
45. C₄×Q₁₆×C₈₃	C₂²	semidirect
263. C₂×#3400	C₈₃	direct (N × H)
265. C₂×C₈₃	#3400	direct (N × H)
270. C₂×#557	C₂×C₈₃	semidirect
271. #3400	C₂×C₈₃	direct (N × H)
272. C₂×#497	C₂×C₈₃	semidirect
274. C₂×#464	C₂×C₈₃	semidirect
275. C₂×#462	C₂×C₈₃	semidirect
277. C₂×#461	C₂×C₈₃	semidirect
278. C₂×#446	C₂×C₈₃	semidirect
279. C₂×#440	C₂×C₈₃	semidirect
280. C₂×C₄×Q₁₆	C₂×C₈₃	semidirect
281. C₈₃	C₂×#3400	direct (N × H)
290. #557	C₂²×C₈₃	semidirect
306. #497	C₂²×C₈₃	semidirect
308. #464	C₂²×C₈₃	semidirect
309. #462	C₂²×C₈₃	semidirect
310. #461	C₂²×C₈₃	semidirect
312. #446	C₂²×C₈₃	semidirect
313. #440	C₂²×C₈₃	semidirect
314. C₄×Q₁₆	C₂²×C₈₃	semidirect
533. C₂	C₈₃×#3400	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×#559×C₈₃	2
C₂×#557×C₈₃	2
C₈₃×#3400	2
C₂×#497×C₈₃	2
C₂×#492×C₈₃	2
C₂×#464×C₈₃	2
C₂×#462×C₈₃	2
C₂×#460×C₈₃	2
C₂×#461×C₈₃	2
C₂×#446×C₈₃	2
C₂×#440×C₈₃	2
C₂×C₄×Q₁₆×C₈₃	2
C₂×#3400	83

Subgroups — C2×C83×#3400 #35289221

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₃×#3400 #35289221