Subgroups — #24922241

Order 10624.

1464 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19128538	C₂	1	1	yes	maximal, characteristic, complemented
2	H(5,𝔽₂)×D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#19128510	C₂	1	3	yes	maximal, complemented
4	#19128509	C₂	1	1	yes	maximal, characteristic, complemented
5	#19128507	C₂	1	3	yes	maximal, complemented
6	#19128506	C₂	1	1	yes	maximal, characteristic, complemented
7	#19128505	C₂	1	3	yes	maximal, complemented
8	#19128504	C₂	1	1	yes	maximal, characteristic, complemented
9	#19128503	C₂	1	3	yes	maximal, complemented
10	#19128500	C₂	1	3	yes	maximal, complemented
11	#19128498	C₂	1	3	yes	maximal, complemented
12	C₂×#14581819	C₂	1	3	yes	maximal, complemented
13	AGL(1,ℤ/8)×D₈₃	C₂	1	3	yes	maximal, complemented
14	#19128466	C₂	1	1	yes	maximal, characteristic, complemented
15	#577×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
16	#14581840	—	2	1	no	—
17	#14581840	C₂²	1	3	yes	complemented
18	#14581838	—	2	1	no	—
19	#14581838	—	2	3	no	—
20	#14581838	C₂²	1	1	yes	characteristic, complemented
21	#14581838	C₂²	1	1	yes	characteristic, complemented
22	#14581838	C₂²	1	3	yes	complemented
23	#14581838	C₂²	1	3	yes	complemented
24	#14581837	—	2	3	no	—
25	#14581837	C₂²	1	3	yes	complemented
26	C₂×#13050591	—	2	1	no	—
27	C₂×#13050591	C₂²	1	3	yes	complemented
28	#41×D₈₃	—	2	3	no	—
29	#41×D₈₃	—	2	1	no	—
30	#41×D₈₃	C₂²	1	1	yes	characteristic
31	#41×D₈₃	C₂²	1	3	yes	complemented
32	#41×D₈₃	C₂²	1	3	yes	complemented
33	C₂×D₄×D₈₃	—	2	3	no	—
34	C₂×D₄×D₈₃	C₂²	1	3	yes	complemented
35	#14581824	C₂²	1	3	yes	complemented
36	#14581824	C₂²	1	3	yes	complemented
37	#14581823	C₂²	1	3	yes	complemented
38	#14581821	C₂²	1	1	yes	characteristic, complemented
39	#14581821	C₂²	1	3	yes	complemented
40	#14581820	C₂²	1	3	yes	complemented
41	#14581820	C₂²	1	3	yes	complemented
42	#14581819	C₂²	1	6	yes	complemented
43	#14581819	C₂²	1	3	yes	complemented
44	#14581819	C₂²	1	6	yes	complemented
45	#14581819	C₂²	1	6	yes	complemented
46	#14581819	C₂²	1	3	yes	complemented
47	#14581818	C₂²	1	3	yes	complemented
48	#14581817	C₂²	1	3	yes	complemented
49	#14581817	C₂²	1	3	yes	complemented
50	#14581816	C₂²	1	3	yes	complemented
51	#14581816	C₂²	1	3	yes	complemented
52	#14581815	C₂²	1	6	yes	complemented
53	#14581814	C₂²	1	3	yes	complemented
54	#14581813	C₂²	1	6	yes	complemented
55	#14581812	C₂²	1	3	yes	complemented
56	#14581812	C₂²	1	3	yes	complemented
57	C₂×#13050577	C₂²	1	3	yes	complemented
58	SD₁₆×D₈₃	C₂²	1	6	yes	complemented
59	C₂×D₆₆₄	C₂²	1	3	yes	complemented
60	C₂×#13050575	C₂²	1	3	yes	complemented
61	D₈×D₈₃	C₂²	1	6	yes	complemented
62	#14581800	C₂²	1	3	yes	complemented
63	#14581799	C₂²	1	1	yes	characteristic, complemented
64	#14581798	C₂²	1	3	yes	complemented
65	C₂×#13050573	C₂²	1	3	yes	complemented
66	M₁₆×D₈₃	C₂²	1	3	yes	complemented
67	2₋¹⁺⁴×C₈₃	C₂²	1	1	yes	characteristic, complemented
68	H(5,𝔽₂)×C₈₃	C₂²	1	1	yes	characteristic, complemented
69	#137×C₈₃	C₂²	1	3	yes	complemented
70	AGL(1,ℤ/8)×C₈₃	C₂²	1	3	yes	complemented
71	#135×C₈₃	C₂²	1	3	yes	complemented
72	C₂×SD₁₆×C₈₃	C₂²	1	3	yes	complemented
73	#131×C₈₃	C₂²	1	1	yes	characteristic, complemented
74	C₂³×D₈₃	—	2	3	no	—
75	#13050591	—	2	1	no	—
76	#13050591	—	2	1	no	—
77	#13050591	—	2	3	no	—
78	#13050591	—	2	3	no	—
79	#13050591	—	2	3	no	—
80	#13050591	D₄	1	1	yes	characteristic
81	#13050591	C₂³	1	3	yes	—
82	#13050591	C₂³	1	3	yes	—
83	#13050591	C₂³	1	6	yes	complemented
84	#13050590	—	2	6	no	—
85	#13050590	—	2	3	no	—
86	#13050590	—	2	3	no	—
87	#13050590	—	2	3	no	—
88	#13050590	—	2	3	no	—
89	#13050590	C₂³	1	3	yes	—
90	#13050590	C₂³	1	3	yes	—
91	#13050590	C₂³	1	3	yes	complemented
92	#13050589	—	2	3	no	—
93	#13050589	—	2	3	no	—
94	#13050589	—	2	3	no	—
95	#13050589	D₄	1	3	yes	—
96	#13050589	C₂³	1	3	yes	—
97	#13050589	C₂³	1	1	yes	characteristic
98	Q₈×D₈₃	—	2	3	no	—
99	Q₈×D₈₃	D₄	1	1	yes	characteristic
100	Q₈×D₈₃	C₂³	1	1	yes	characteristic
101	Q₈×D₈₃	C₂³	1	3	yes	complemented
102	C₂×D₃₃₂	—	2	3	no	—
103	C₂×D₃₃₂	—	2	3	no	—
104	C₂×D₃₃₂	—	2	3	no	—
105	C₂×D₃₃₂	C₂³	1	3	yes	—
106	C₂×D₃₃₂	C₂³	1	3	yes	complemented
107	C₂×C₂²⋊D₈₃	—	2	6	no	—
108	C₂×C₂²⋊D₈₃	—	2	3	no	—
109	D₄×D₈₃	—	2	3	no	—
110	D₄×D₈₃	—	2	3	no	—
111	D₄×D₈₃	—	2	3	no	—
112	D₄×D₈₃	—	2	3	no	—
113	D₄×D₈₃	—	2	6	no	—
114	D₄×D₈₃	—	2	6	no	—
115	D₄×D₈₃	—	2	3	no	—
116	D₄×D₈₃	—	2	3	no	—
117	D₄×D₈₃	—	2	3	no	—
118	D₄×D₈₃	D₄	1	3	yes	—
119	D₄×D₈₃	C₂³	1	6	yes	—
120	D₄×D₈₃	C₂³	1	3	yes	—
121	D₄×D₈₃	C₂³	1	3	yes	complemented
122	C₂×C₄×D₈₃	—	2	3	no	—
123	C₂×C₄×D₈₃	—	2	3	no	—
124	C₂×C₄×D₈₃	—	2	3	no	—
125	C₂×C₄×D₈₃	C₂³	1	3	yes	—
126	Dic₃₃₂	C₂³	1	1	yes	characteristic, complemented
127	#13050580	C₂³	1	1	yes	characteristic, complemented
128	#13050580	C₂³	1	3	yes	complemented
129	#13050579	C₂³	1	3	yes	complemented
130	#13050579	C₂³	1	3	yes	complemented
131	#13050578	C₂³	1	3	yes	complemented
132	#13050578	C₂³	1	1	yes	characteristic, complemented
133	#13050577	C₂³	1	6	yes	complemented
134	#13050577	C₂³	1	3	yes	complemented
135	#13050577	C₂³	1	3	yes	complemented
136	D₆₆₄	C₂³	1	6	yes	complemented
137	D₆₆₄	C₂³	1	3	yes	complemented
138	#13050575	C₂³	1	3	yes	complemented
139	#13050575	C₂³	1	6	yes	complemented
140	#13050575	C₂³	1	3	yes	complemented
141	#13050574	C₂³	1	3	yes	complemented
142	#13050573	C₂³	1	3	yes	—
143	#13050573	C₂³	1	1	yes	characteristic
144	#13050573	C₂³	1	3	yes	complemented
145	#13050573	C₂³	1	3	yes	complemented
146	C₂×C₈₃⋊C₈	C₂³	1	3	yes	complemented
147	C₈×D₈₃	C₂³	1	6	yes	complemented
148	#41×C₈₃	—	2	1	no	—
149	#41×C₈₃	—	2	3	no	—
150	#41×C₈₃	C₂³	1	3	yes	—
151	#41×C₈₃	C₂³	1	1	yes	characteristic
152	#41×C₈₃	C₂³	1	3	yes	complemented
153	C₂×Q₈×C₈₃	—	2	1	no	—
154	C₂×Q₈×C₈₃	C₂³	1	3	yes	complemented
155	C₂×D₄×C₈₃	—	2	3	no	—
156	C₂×D₄×C₈₃	C₂³	1	3	yes	—
157	Q₁₆×C₈₃	C₂³	1	3	yes	complemented
158	SD₁₆×C₈₃	C₂³	1	6	yes	complemented
159	SD₁₆×C₈₃	C₂³	1	3	yes	complemented
160	SD₁₆×C₈₃	C₂³	1	1	yes	characteristic, complemented
161	D₈×C₈₃	C₂³	1	3	yes	complemented
162	M₁₆×C₈₃	C₂³	1	3	yes	complemented
163	C₂×C₈×C₈₃	C₂³	1	3	yes	complemented
164	C₂³×C₈₃	—	2	3	no	—
165	C₂²×D₈₃	—	2	3	no	—
166	C₂²×D₈₃	—	2	3	no	—
167	C₂²×D₈₃	—	2	3	no	—
168	C₂²×D₈₃	—	2	3	no	—
169	C₂²×D₈₃	—	2	6	no	—
170	C₂²×D₈₃	—	8	6	no	—
171	C₂²×D₈₃	C₂×D₄	1	3	yes	—
172	Q₈×C₈₃	—	2	3	no	—
173	Q₈×C₈₃	C₂×D₄	1	1	yes	characteristic
174	Q₈×C₈₃	C₂⁴	1	3	yes	—
175	Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
176	D₄×C₈₃	—	2	3	no	—
177	D₄×C₈₃	—	2	3	no	—
178	D₄×C₈₃	—	2	3	no	—
179	D₄×C₈₃	C₂×D₄	1	3	yes	—
180	D₄×C₈₃	C₂⁴	1	1	yes	characteristic
181	D₄×C₈₃	C₂⁴	1	3	yes	—
182	C₂×C₄×C₈₃	—	2	3	no	—
183	C₂×C₄×C₈₃	—	2	3	no	—
184	C₂×C₄×C₈₃	—	2	3	no	—
185	C₂×C₄×C₈₃	C₂⁴	1	3	yes	—
186	C₂²⋊D₈₃	—	2	3	no	—
187	C₂²⋊D₈₃	—	2	3	no	—
188	C₂²⋊D₈₃	—	2	3	no	—
189	C₂²⋊D₈₃	—	2	1	no	—
190	C₂²⋊D₈₃	—	2	6	no	—
191	C₂²⋊D₈₃	—	2	3	no	—
192	C₂²⋊D₈₃	—	2	3	no	—
193	C₂²⋊D₈₃	C₂×D₄	1	6	yes	—
194	C₂×Dic₈₃	—	2	1	no	—
195	C₂×Dic₈₃	—	2	3	no	—
196	C₂×Dic₈₃	C₂×D₄	1	3	yes	—
197	D₃₃₂	—	2	3	no	—
198	D₃₃₂	—	2	3	no	—
199	D₃₃₂	—	2	6	no	—
200	D₃₃₂	—	2	3	no	—
201	D₃₃₂	—	2	3	no	—
202	D₃₃₂	C₂×D₄	1	3	yes	—
203	D₃₃₂	C₂⁴	1	3	yes	—
204	D₃₃₂	C₂⁴	1	3	yes	—
205	C₄×D₈₃	—	2	1	no	—
206	C₄×D₈₃	—	2	3	no	—
207	C₄×D₈₃	—	2	3	no	—
208	C₄×D₈₃	—	2	3	no	—
209	C₄×D₈₃	—	2	3	no	—
210	C₄×D₈₃	—	2	3	no	—
211	C₄×D₈₃	—	2	6	no	—
212	C₄×D₈₃	C₂×D₄	1	3	yes	—
213	C₄×D₈₃	C₂×D₄	1	3	yes	—
214	C₄×D₈₃	C₂⁴	1	3	yes	—
215	C₄×D₈₃	C₂⁴	1	1	yes	characteristic
216	Dic₁₆₆	—	2	3	no	—
217	Dic₁₆₆	—	2	1	no	—
218	Dic₁₆₆	C₂×D₄	1	3	yes	—
219	Dic₁₆₆	C₂⁴	1	1	yes	characteristic
220	Dic₁₆₆	C₂⁴	1	1	yes	characteristic
221	C₈×C₈₃	C₂⁴	1	1	yes	characteristic
222	C₈×C₈₃	C₂⁴	1	3	yes	—
223	C₈₃⋊C₈	C₂⁴	1	3	yes	—
224	C₈₃⋊C₈	C₂⁴	1	1	yes	characteristic
225	C₂²×C₈₃	—	2	1	no	—
226	C₂²×C₈₃	—	2	3	no	—
227	C₂²×C₈₃	—	8	3	no	—
228	C₂²×C₈₃	C₂²×D₄	1	3	yes	—
229	C₂×D₈₃	—	2	3	no	—
230	C₂×D₈₃	—	2	3	no	—
231	C₂×D₈₃	—	4	3	no	—
232	C₂×D₈₃	—	4	6	no	—
233	C₂×D₈₃	—	8	3	no	—
234	C₂×D₈₃	—	8	6	no	—
235	C₂×D₈₃	—	8	3	no	—
236	C₂×D₈₃	—	8	3	no	—
237	C₂×D₈₃	C₂²×D₄	1	1	yes	characteristic
238	C₂×D₈₃	C₂²×D₄	1	3	yes	—
239	C₄×C₈₃	—	2	1	no	—
240	C₄×C₈₃	—	2	3	no	—
241	C₄×C₈₃	C₂²×D₄	1	3	yes	—
242	C₄×C₈₃	C₂⁵	1	1	yes	characteristic
243	Dic₈₃	—	2	1	no	—
244	Dic₈₃	—	2	1	no	—
245	Dic₈₃	C₂²×D₄	1	3	yes	—
246	Dic₈₃	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₈₃	—	2	3	no	—
248	C₂×C₈₃	—	4	3	no	—
249	C₂×C₈₃	—	4	1	no	—
250	C₂×C₈₃	C₂³×D₄	1	1	yes	characteristic
251	D₈₃	—	2	1	no	—
252	D₈₃	—	2	3	no	—
253	D₈₃	—	4	3	no	—
254	D₈₃	—	4	3	no	—
255	#3585	—	83	1	no	maximal, Sylow
256	C₈₃	#3585	1	1	yes	characteristic, complemented, Sylow
257	#585	—	83	1	no	—
258	C₂×H(5,𝔽₂)	—	83	1	no	—
259	#577	—	83	1	no	—
260	#577	—	83	3	no	—
261	#577	—	83	3	no	—
262	#577	D₈₃	1	1	yes	characteristic, complemented
263	#576	—	83	1	no	—
264	#576	—	83	3	no	—
265	#576	—	83	3	no	—
266	#576	—	83	1	no	—
267	#575	—	83	3	no	—
268	#575	—	83	3	no	—
269	C₂×AGL(1,ℤ/8)	—	83	3	no	—
270	C₂×AGL(1,ℤ/8)	—	83	3	no	—
271	#568	—	83	1	no	—
272	2₋¹⁺⁴	—	83	3	no	—
273	2₋¹⁺⁴	—	166	1	no	—
274	2₋¹⁺⁴	C₂×D₈₃	1	1	yes	characteristic, complemented
275	H(5,𝔽₂)	—	83	3	no	—
276	H(5,𝔽₂)	—	83	1	no	—
277	H(5,𝔽₂)	—	83	1	no	—
278	H(5,𝔽₂)	—	83	3	no	—
279	H(5,𝔽₂)	—	83	3	no	—
280	H(5,𝔽₂)	—	166	3	no	—
281	H(5,𝔽₂)	—	166	3	no	—
282	H(5,𝔽₂)	—	166	1	no	—
283	H(5,𝔽₂)	C₂×D₈₃	1	1	yes	characteristic, complemented
284	C₂×#41	—	83	1	no	—
285	C₂×#41	—	83	3	no	—
286	C₂×#41	—	83	3	no	—
287	C₂×#41	—	83	3	no	—
288	C₂×#41	—	166	1	no	—
289	C₂×#41	—	166	1	no	—
290	C₂×#41	—	166	3	no	—
291	C₂²×D₄	—	83	3	no	—
292	C₂²×D₄	—	166	3	no	—
293	#137	—	83	3	no	—
294	#137	—	83	3	no	—
295	#137	—	83	3	no	—
296	#137	—	83	1	no	—
297	#137	—	83	3	no	—
298	#137	C₂×D₈₃	1	3	yes	complemented
299	AGL(1,ℤ/8)	—	83	3	no	—
300	AGL(1,ℤ/8)	—	83	3	no	—
301	AGL(1,ℤ/8)	—	83	3	no	—
302	AGL(1,ℤ/8)	—	83	6	no	—
303	AGL(1,ℤ/8)	—	83	3	no	—
304	AGL(1,ℤ/8)	—	83	6	no	—
305	AGL(1,ℤ/8)	—	83	6	no	—
306	AGL(1,ℤ/8)	—	83	3	no	—
307	AGL(1,ℤ/8)	—	83	3	no	—
308	AGL(1,ℤ/8)	—	83	3	no	—
309	AGL(1,ℤ/8)	—	83	3	no	—
310	AGL(1,ℤ/8)	—	83	3	no	—
311	AGL(1,ℤ/8)	C₂×D₈₃	1	3	yes	complemented
312	#135	—	83	3	no	—
313	#135	—	83	3	no	—
314	#135	—	83	6	no	—
315	#135	—	83	6	no	—
316	#135	—	83	3	no	—
317	#135	C₂×D₈₃	1	3	yes	complemented
318	C₂×SD₁₆	—	83	3	no	—
319	C₂×SD₁₆	—	83	6	no	—
320	C₂×SD₁₆	C₂×D₈₃	1	3	yes	complemented
321	C₂×D₈	—	83	3	no	—
322	C₂×D₈	—	83	6	no	—
323	C₂×D₈	—	83	3	no	—
324	#131	—	83	1	no	—
325	#131	—	83	3	no	—
326	#131	—	83	3	no	—
327	#131	C₂×D₈₃	1	1	yes	characteristic, complemented
328	C₂×M₁₆	—	83	3	no	—
329	C₂×M₁₆	—	83	3	no	—
330	C₂⁴	—	166	3	no	—
331	#41	—	2	1	no	—
332	#41	—	2	3	no	—
333	#41	—	83	1	no	—
334	#41	—	83	3	no	—
335	#41	—	83	3	no	—
336	#41	—	83	6	no	—
337	#41	—	83	3	no	—
338	#41	—	83	3	no	—
339	#41	—	83	3	no	—
340	#41	—	83	1	no	—
341	#41	—	83	3	no	—
342	#41	—	83	3	no	—
343	#41	—	166	3	no	—
344	#41	—	166	3	no	—
345	#41	—	166	6	no	—
346	#41	—	166	3	no	—
347	#41	—	166	3	no	—
348	#41	—	166	3	no	—
349	#41	—	166	3	no	—
350	#41	—	166	3	no	—
351	#41	—	166	3	no	—
352	#41	—	166	3	no	—
353	#41	—	166	3	no	—
354	#41	—	166	1	no	—
355	#41	—	166	1	no	—
356	#41	C₂²×D₈₃	1	3	yes	—
357	#41	C₂²×D₈₃	1	1	yes	characteristic
358	#41	C₂²×D₈₃	1	3	yes	complemented
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	—	83	1	no	—
361	C₂×Q₈	—	83	3	no	—
362	C₂×Q₈	—	83	1	no	—
363	C₂×Q₈	—	166	3	no	—
364	C₂×Q₈	C₂²×D₈₃	1	3	yes	complemented
365	C₂×D₄	—	2	3	no	—
366	C₂×D₄	—	83	3	no	—
367	C₂×D₄	—	83	3	no	—
368	C₂×D₄	—	83	6	no	—
369	C₂×D₄	—	83	3	no	—
370	C₂×D₄	—	83	3	no	—
371	C₂×D₄	—	83	3	no	—
372	C₂×D₄	—	166	3	no	—
373	C₂×D₄	—	166	3	no	—
374	C₂×D₄	—	166	3	no	—
375	C₂×D₄	—	166	3	no	—
376	C₂×D₄	—	166	3	no	—
377	C₂×D₄	—	166	3	no	—
378	C₂×D₄	—	166	6	no	—
379	C₂×D₄	—	166	3	no	—
380	C₂×D₄	—	166	6	no	—
381	C₂×D₄	—	166	3	no	—
382	C₂×D₄	—	166	3	no	—
383	C₂×D₄	—	166	6	no	—
384	C₂×D₄	—	166	3	no	—
385	C₂×D₄	—	166	3	no	—
386	C₂×D₄	C₂²×D₈₃	1	3	yes	—
387	C₂²×C₄	—	83	3	no	—
388	C₂²×C₄	—	166	3	no	—
389	C₂²×C₄	—	166	3	no	—
390	C₂²×C₄	—	166	3	no	—
391	Q₁₆	—	83	1	no	—
392	Q₁₆	—	83	3	no	—
393	Q₁₆	—	83	1	no	—
394	Q₁₆	C₂²×D₈₃	1	3	yes	complemented
395	SD₁₆	—	83	3	no	—
396	SD₁₆	—	83	6	no	—
397	SD₁₆	—	83	3	no	—
398	SD₁₆	—	83	3	no	—
399	SD₁₆	—	83	1	no	—
400	SD₁₆	—	83	3	no	—
401	SD₁₆	—	83	3	no	—
402	SD₁₆	C₂²×D₈₃	1	6	yes	complemented
403	SD₁₆	C₂²×D₈₃	1	3	yes	complemented
404	SD₁₆	C₂²×D₈₃	1	1	yes	characteristic, complemented
405	D₈	—	83	3	no	—
406	D₈	—	83	6	no	—
407	D₈	—	83	3	no	—
408	D₈	—	83	6	no	—
409	D₈	—	83	3	no	—
410	D₈	C₂²×D₈₃	1	3	yes	complemented
411	M₁₆	—	83	3	no	—
412	M₁₆	—	83	3	no	—
413	M₁₆	—	83	1	no	—
414	M₁₆	—	83	3	no	—
415	M₁₆	—	83	3	no	—
416	M₁₆	C₂²×D₈₃	1	3	yes	complemented
417	C₂×C₈	—	83	3	no	—
418	C₂×C₈	—	83	6	no	—
419	C₂×C₈	C₂²×D₈₃	1	3	yes	complemented
420	C₂³	—	2	3	no	—
421	C₂³	—	83	3	no	—
422	C₂³	—	664	6	no	—
423	C₂³	—	166	3	no	—
424	C₂³	—	166	3	no	—
425	C₂³	—	166	6	no	—
426	C₂³	—	166	3	no	—
427	C₂³	—	166	3	no	—
428	Q₈	—	2	3	no	—
429	Q₈	—	83	3	no	—
430	Q₈	—	83	1	no	—
431	Q₈	—	83	1	no	—
432	Q₈	—	166	3	no	—
433	Q₈	—	166	1	no	—
434	Q₈	D₄×D₈₃	1	1	yes	characteristic
435	Q₈	C₂³×D₈₃	1	3	yes	—
436	Q₈	C₂³×D₈₃	1	1	yes	characteristic
437	D₄	—	2	3	no	—
438	D₄	—	2	3	no	—
439	D₄	—	2	3	no	—
440	D₄	—	83	6	no	—
441	D₄	—	83	3	no	—
442	D₄	—	83	3	no	—
443	D₄	—	83	3	no	—
444	D₄	—	166	3	no	—
445	D₄	—	166	3	no	—
446	D₄	—	166	6	no	—
447	D₄	—	166	3	no	—
448	D₄	—	166	6	no	—
449	D₄	—	166	3	no	—
450	D₄	—	166	3	no	—
451	D₄	—	166	1	no	—
452	D₄	—	166	3	no	—
453	D₄	—	166	3	no	—
454	D₄	—	166	3	no	—
455	D₄	—	166	3	no	—
456	D₄	D₄×D₈₃	1	3	yes	—
457	D₄	C₂³×D₈₃	1	1	yes	characteristic
458	D₄	C₂³×D₈₃	1	3	yes	—
459	C₂×C₄	—	2	3	no	—
460	C₂×C₄	—	2	3	no	—
461	C₂×C₄	—	2	3	no	—
462	C₂×C₄	—	83	3	no	—
463	C₂×C₄	—	83	3	no	—
464	C₂×C₄	—	83	3	no	—
465	C₂×C₄	—	83	3	no	—
466	C₂×C₄	—	83	1	no	—
467	C₂×C₄	—	166	3	no	—
468	C₂×C₄	—	166	3	no	—
469	C₂×C₄	—	166	6	no	—
470	C₂×C₄	—	166	1	no	—
471	C₂×C₄	—	166	3	no	—
472	C₂×C₄	—	166	1	no	—
473	C₂×C₄	—	166	3	no	—
474	C₂×C₄	—	166	3	no	—
475	C₂×C₄	—	166	3	no	—
476	C₂×C₄	C₂³×D₈₃	1	3	yes	—
477	C₈	—	83	1	no	—
478	C₈	—	83	3	no	—
479	C₈	C₂³×D₈₃	1	3	yes	—
480	C₈	C₂³×D₈₃	1	1	yes	characteristic
481	C₂²	—	2	1	no	—
482	C₂²	—	2	3	no	—
483	C₂²	—	8	3	no	—
484	C₂²	—	332	3	no	—
485	C₂²	—	332	6	no	—
486	C₂²	—	83	1	no	—
487	C₂²	—	83	3	no	—
488	C₂²	—	664	3	no	—
489	C₂²	—	664	3	no	—
490	C₂²	—	664	6	no	—
491	C₂²	—	664	3	no	—
492	C₂²	—	166	3	no	—
493	C₂²	—	166	3	no	—
494	C₂²	C₂×D₄×D₈₃	1	3	yes	—
495	C₄	—	2	1	no	—
496	C₄	—	2	3	no	—
497	C₄	—	83	1	no	—
498	C₄	—	83	3	no	—
499	C₄	—	166	1	no	—
500	C₄	—	166	1	no	—
501	C₄	C₂×D₄×D₈₃	1	3	yes	—
502	C₄	C₂⁴×D₈₃	1	1	yes	characteristic
503	C₂	—	2	3	no	—
504	C₂	—	4	3	no	—
505	C₂	—	4	1	no	—
506	C₂	—	332	3	no	—
507	C₂	—	332	3	no	—
508	C₂	—	166	1	no	—
509	C₂	—	166	3	no	—
510	C₂	C₂²×D₄×D₈₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₄×D₈₃
commutator, cosocle	C₄×C₈₃	C₂⁵
Frattini	C₄	C₂⁴×D₈₃
Fitting	#577×C₈₃	C₂
socle	C₂×C₈₃	C₂³×D₄
hypercenter	#577	D₈₃
hypocenter	C₈₃	#3585
LCS	G ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂ ◁ #41 ◁ #577

Complements

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

N	H ≅ G/N	type
1. #19128538	C₂	semidirect
2. H(5,𝔽₂)×D₈₃	C₂	semidirect
3. #19128510	C₂	semidirect
4. #19128509	C₂	semidirect
5. #19128507	C₂	semidirect
6. #19128506	C₂	semidirect
7. #19128505	C₂	semidirect
8. #19128504	C₂	semidirect
9. #19128503	C₂	semidirect
10. #19128500	C₂	semidirect
11. #19128498	C₂	semidirect
12. C₂×#14581819	C₂	semidirect
13. AGL(1,ℤ/8)×D₈₃	C₂	semidirect
14. #19128466	C₂	semidirect
15. #577×C₈₃	C₂	semidirect
17. #14581840	C₂²	semidirect
20. #14581838	C₂²	semidirect
21. #14581838	C₂²	semidirect
22. #14581838	C₂²	semidirect
23. #14581838	C₂²	semidirect
25. #14581837	C₂²	semidirect
27. C₂×#13050591	C₂²	semidirect
31. #41×D₈₃	C₂²	semidirect
32. #41×D₈₃	C₂²	semidirect
34. C₂×D₄×D₈₃	C₂²	semidirect
35. #14581824	C₂²	semidirect
36. #14581824	C₂²	semidirect
37. #14581823	C₂²	semidirect
38. #14581821	C₂²	semidirect
39. #14581821	C₂²	semidirect
40. #14581820	C₂²	semidirect
41. #14581820	C₂²	semidirect
42. #14581819	C₂²	semidirect
43. #14581819	C₂²	semidirect
44. #14581819	C₂²	semidirect
45. #14581819	C₂²	semidirect
46. #14581819	C₂²	semidirect
47. #14581818	C₂²	semidirect
48. #14581817	C₂²	semidirect
49. #14581817	C₂²	semidirect
50. #14581816	C₂²	semidirect
51. #14581816	C₂²	semidirect
52. #14581815	C₂²	semidirect
53. #14581814	C₂²	semidirect
54. #14581813	C₂²	semidirect
55. #14581812	C₂²	semidirect
56. #14581812	C₂²	semidirect
57. C₂×#13050577	C₂²	semidirect
58. SD₁₆×D₈₃	C₂²	semidirect
59. C₂×D₆₆₄	C₂²	semidirect
60. C₂×#13050575	C₂²	semidirect
61. D₈×D₈₃	C₂²	semidirect
62. #14581800	C₂²	semidirect
63. #14581799	C₂²	semidirect
64. #14581798	C₂²	semidirect
65. C₂×#13050573	C₂²	semidirect
66. M₁₆×D₈₃	C₂²	semidirect
67. 2₋¹⁺⁴×C₈₃	C₂²	semidirect
68. H(5,𝔽₂)×C₈₃	C₂²	semidirect
69. #137×C₈₃	C₂²	semidirect
70. AGL(1,ℤ/8)×C₈₃	C₂²	semidirect
71. #135×C₈₃	C₂²	semidirect
72. C₂×SD₁₆×C₈₃	C₂²	semidirect
73. #131×C₈₃	C₂²	semidirect
83. #13050591	C₂³	semidirect
91. #13050590	C₂³	semidirect
101. Q₈×D₈₃	C₂³	semidirect
106. C₂×D₃₃₂	C₂³	semidirect
121. D₄×D₈₃	C₂³	semidirect
126. Dic₃₃₂	C₂³	semidirect
127. #13050580	C₂³	semidirect
128. #13050580	C₂³	semidirect
129. #13050579	C₂³	semidirect
130. #13050579	C₂³	semidirect
131. #13050578	C₂³	semidirect
132. #13050578	C₂³	semidirect
133. #13050577	C₂³	semidirect
134. #13050577	C₂³	semidirect
135. #13050577	C₂³	semidirect
136. D₆₆₄	C₂³	semidirect
137. D₆₆₄	C₂³	semidirect
138. #13050575	C₂³	semidirect
139. #13050575	C₂³	semidirect
140. #13050575	C₂³	semidirect
141. #13050574	C₂³	semidirect
144. #13050573	C₂³	semidirect
145. #13050573	C₂³	semidirect
146. C₂×C₈₃⋊C₈	C₂³	semidirect
147. C₈×D₈₃	C₂³	semidirect
152. #41×C₈₃	C₂³	semidirect
154. C₂×Q₈×C₈₃	C₂³	semidirect
157. Q₁₆×C₈₃	C₂³	semidirect
158. SD₁₆×C₈₃	C₂³	semidirect
159. SD₁₆×C₈₃	C₂³	semidirect
160. SD₁₆×C₈₃	C₂³	semidirect
161. D₈×C₈₃	C₂³	semidirect
162. M₁₆×C₈₃	C₂³	semidirect
163. C₂×C₈×C₈₃	C₂³	semidirect
256. C₈₃	#3585	semidirect
262. #577	D₈₃	semidirect
274. 2₋¹⁺⁴	C₂×D₈₃	semidirect
283. H(5,𝔽₂)	C₂×D₈₃	semidirect
298. #137	C₂×D₈₃	semidirect
311. AGL(1,ℤ/8)	C₂×D₈₃	semidirect
317. #135	C₂×D₈₃	semidirect
320. C₂×SD₁₆	C₂×D₈₃	semidirect
327. #131	C₂×D₈₃	semidirect
358. #41	C₂²×D₈₃	semidirect
364. C₂×Q₈	C₂²×D₈₃	semidirect
394. Q₁₆	C₂²×D₈₃	semidirect
402. SD₁₆	C₂²×D₈₃	semidirect
403. SD₁₆	C₂²×D₈₃	semidirect
404. SD₁₆	C₂²×D₈₃	semidirect
410. D₈	C₂²×D₈₃	semidirect
416. M₁₆	C₂²×D₈₃	semidirect
419. C₂×C₈	C₂²×D₈₃	semidirect

Maximal subgroups

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

subgroup	index
#19128538	2
H(5,𝔽₂)×D₈₃	2
#19128510	2
#19128509	2
#19128507	2
#19128506	2
#19128505	2
#19128504	2
#19128503	2
#19128500	2
#19128498	2
C₂×#14581819	2
AGL(1,ℤ/8)×D₈₃	2
#19128466	2
#577×C₈₃	2
#3585	83