Subgroups — #12068711

Order 1280.

802 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#713	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#4060	C₂	1	1	yes	maximal, characteristic
3	C₈×D₄×D₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601730	C₂	1	1	yes	maximal, characteristic, complemented
6	SD₁₆×#168	C₂	1	1	yes	maximal, characteristic, complemented
7	#10601633	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599361	C₂	1	1	yes	maximal, characteristic, complemented
9	#10599349	C₂	1	1	yes	maximal, characteristic, complemented
10	#10599023	C₂	1	1	yes	maximal, characteristic, complemented
11	#10599005	C₂	1	1	yes	maximal, characteristic, complemented
12	#10598960	C₂	1	1	yes	maximal, characteristic, complemented
13	#10598941	C₂	1	1	yes	maximal, characteristic, complemented
14	#10598870	C₂	1	1	yes	maximal, characteristic, complemented
15	#10598860	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#4060	C₄	1	1	yes	characteristic
17	C₂²×C₈×D₅	—	2	1	no	—
18	C₄×#713	C₂²	1	1	yes	characteristic
19	C₄×D₄×D₅	C₂²	1	1	yes	characteristic
20	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
22	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
23	#65453	C₄	1	1	yes	characteristic
24	C₈×C₂²⋊D₅	—	2	1	no	—
25	C₄×#688	C₂²	1	1	yes	characteristic
26	Q₈×#168	C₂²	1	1	yes	characteristic, complemented
27	C₄×#686	C₂²	1	1	yes	characteristic
28	D₄×#168	C₂²	1	1	yes	characteristic
29	#65158	C₄	1	1	yes	characteristic
30	#65150	C₄	1	1	yes	characteristic
31	#65123	—	2	1	no	—
32	#65123	C₂²	1	1	yes	characteristic
33	#65123	C₂²	1	1	yes	characteristic, complemented
34	#65122	—	2	1	no	—
35	#65122	C₂²	1	1	yes	characteristic
36	D₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	#65106	C₄	1	1	yes	characteristic
38	#65092	C₄	1	1	yes	characteristic
39	#65074	C₄	1	1	yes	characteristic
40	#65059	C₄	1	1	yes	characteristic
41	#65014	—	2	1	no	—
42	D₅×C₂²⋊C₈	—	2	1	no	—
43	C₄×D₄₀	C₂²	1	1	yes	characteristic
44	C₄×#676	C₂²	1	1	yes	characteristic
45	C₈×D₂₀	—	2	1	no	—
46	C₈×D₂₀	C₂²	1	1	yes	characteristic
47	C₈×D₂₀	C₂²	1	1	yes	characteristic, complemented
48	#64974	C₂²	1	1	yes	characteristic
49	C₄×C₈×D₅	—	2	1	no	—
50	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
51	C₅×#335	C₂²	1	1	yes	characteristic, complemented
52	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
54	C₅×#322	C₂²	1	1	yes	characteristic, complemented
55	Q₈⋊#168	C₂²	1	1	yes	characteristic, complemented
56	D₄⋊#168	C₂²	1	1	yes	characteristic
57	#64703	C₂²	1	1	yes	characteristic
58	#64703	C₂²	1	1	yes	characteristic, complemented
59	#64700	C₂²	1	1	yes	characteristic, complemented
60	#64699	C₂²	1	1	yes	characteristic, complemented
61	#64679	C₂²	1	1	yes	characteristic
62	#64679	C₂²	1	1	yes	characteristic, complemented
63	#64677	C₂²	1	1	yes	characteristic, complemented
64	#64674	C₂²	1	1	yes	characteristic, complemented
65	C₈×#168	C₂²	1	1	yes	characteristic, complemented
66	C₈×#168	C₂²	1	1	yes	characteristic, complemented
67	C₈×AGL(1,ℤ/8)	—	5	1	no	maximal, Sylow
68	C₂×#713	C₂×C₄	1	1	yes	characteristic
69	C₂×D₄×D₅	C₂×C₄	1	1	yes	characteristic
70	C₂²×C₄×D₅	—	2	1	no	—
71	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
72	C₂²×C₅×C₈	—	2	1	no	—
73	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
74	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
75	Q₈×Dic₅	C₂×C₄	1	1	yes	characteristic
76	C₂×#688	C₂×C₄	1	1	yes	characteristic
77	D₄×Dic₅	C₂×C₄	1	1	yes	characteristic
78	C₂×#686	C₂×C₄	1	1	yes	characteristic
79	C₄×C₂²⋊D₅	—	2	1	no	—
80	C₂²×#168	—	2	1	no	—
81	#4060	C₈	1	8	yes	complemented
82	C₂×D₄₀	C₂×C₄	1	1	yes	characteristic
83	C₂×#676	C₂×C₄	1	1	yes	characteristic
84	C₂×#676	C₂×C₄	1	1	yes	characteristic
85	C₂×C₈×D₅	—	2	1	no	—
86	C₂×C₈×D₅	—	2	1	no	—
87	C₂×C₈×D₅	—	2	1	no	—
88	C₂×C₈×D₅	—	2	1	no	—
89	C₂×C₈×D₅	—	2	1	no	—
90	C₂×C₈×D₅	—	4	4	no	—
91	C₂×C₈×D₅	D₄	1	1	yes	characteristic
92	C₂×C₈×D₅	D₄	1	1	yes	characteristic
93	#4039	—	2	1	no	—
94	#4039	C₂×C₄	1	1	yes	characteristic
95	#4039	C₂×C₄	1	1	yes	characteristic
96	#4038	—	2	1	no	—
97	#4038	C₂×C₄	1	1	yes	characteristic
98	D₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
99	#4027	—	2	1	no	—
100	D₅×C₂²⋊C₄	—	2	1	no	—
101	C₄×D₂₀	—	2	1	no	—
102	C₄×D₂₀	C₂³	1	1	yes	characteristic
103	C₄×D₂₀	C₂³	1	1	yes	characteristic
104	C₄²×D₅	—	2	1	no	—
105	C₄²×D₅	C₂³	1	1	yes	characteristic
106	C₅×#106	C₂×C₄	1	1	yes	characteristic
107	C₅×C₄⋊C₈	—	2	1	no	—
108	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
109	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
110	C₅×#103	C₂×C₄	1	1	yes	characteristic
111	C₅×#102	C₂×C₄	1	1	yes	characteristic
112	C₅×C₂²⋊C₈	—	2	1	no	—
113	C₄×C₅×C₈	—	2	1	no	—
114	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
115	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
116	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
117	#3967	C₂×C₄	1	1	yes	characteristic
118	#3964	C₂×C₄	1	1	yes	characteristic
119	C₂²⋊#168	—	2	1	no	—
120	#3953	C₂×C₄	1	1	yes	characteristic
121	#3953	C₂×C₄	1	1	yes	characteristic
122	#3952	—	2	1	no	—
123	#3952	—	2	1	no	—
124	#3952	—	2	1	no	—
125	#3952	—	2	1	no	—
126	#3952	—	2	1	no	—
127	#3952	—	2	1	no	—
128	#3950	C₂×C₄	1	1	yes	characteristic
129	#3947	C₂×C₄	1	1	yes	characteristic
130	#3947	C₂×C₄	1	1	yes	characteristic
131	#3946	—	2	1	no	—
132	#3946	—	2	1	no	—
133	C₈×Dic₅	—	2	1	no	—
134	C₈×Dic₅	D₄	1	1	yes	characteristic
135	C₈×Dic₅	D₄	1	1	yes	characteristic
136	#3941	C₂×C₄	1	1	yes	characteristic
137	#3941	C₂×C₄	1	1	yes	characteristic
138	#3940	C₂×C₄	1	1	yes	characteristic
139	#3939	C₂×C₄	1	1	yes	characteristic
140	C₄⋊#168	—	2	1	no	—
141	C₄⋊#168	C₂³	1	1	yes	characteristic
142	C₄⋊#168	C₂³	1	1	yes	characteristic
143	C₄×#168	—	2	1	no	—
144	C₄×#168	C₂³	1	1	yes	characteristic
145	C₄×#168	C₂³	1	1	yes	characteristic
146	C₄×#168	C₂³	1	1	yes	characteristic
147	C₈×#41	—	5	1	no	—
148	C₄×AGL(1,ℤ/8)	—	5	1	no	—
149	C₂×C₈×D₄	—	5	1	no	—
150	#1580	—	5	1	no	—
151	#1580	—	5	1	no	—
152	SD₁₆⋊C₈	—	5	1	no	—
153	SD₁₆⋊C₈	D₅	1	1	yes	characteristic, complemented
154	C₈×SD₁₆	—	5	1	no	—
155	C₈×SD₁₆	—	5	1	no	—
156	C₈×D₈	—	5	1	no	—
157	C₈×D₈	—	5	1	no	—
158	#1565	—	5	1	no	—
159	#1478	—	5	1	no	—
160	#1477	—	5	1	no	—
161	C₈×M₁₆	—	5	1	no	—
162	C₂³×D₅	—	2	1	no	—
163	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₅	—	2	1	no	—
166	C₂×C₂²⋊D₅	—	2	1	no	—
167	C₂²×Dic₅	—	2	1	no	—
168	#713	—	2	2	no	—
169	#713	C₂×C₈	1	4	yes	complemented
170	D₄×D₅	—	2	2	no	—
171	D₄×D₅	C₂×C₈	1	4	yes	complemented
172	C₂×D₂₀	—	2	1	no	—
173	C₂×D₂₀	C₂²×C₄	1	1	yes	characteristic
174	C₂×D₂₀	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₄×D₅	—	2	1	no	—
176	C₂×C₄×D₅	—	2	1	no	—
177	C₂×C₄×D₅	—	2	1	no	—
178	C₂×C₄×D₅	—	2	1	no	—
179	C₂×C₄×D₅	—	2	1	no	—
180	C₂×C₄×D₅	—	2	1	no	—
181	C₂×C₄×D₅	—	4	2	no	—
182	C₂×C₄×D₅	—	4	2	no	—
183	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
185	C₂×C₄×D₅	#41	1	1	yes	characteristic
186	C₅×SD₁₆	C₂×C₈	1	4	yes	complemented
187	C₂×C₅×C₈	—	2	1	no	—
188	C₂×C₅×C₈	—	2	1	no	—
189	C₂×C₅×C₈	—	2	1	no	—
190	C₂×C₅×C₈	—	4	2	no	—
191	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
192	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
193	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
194	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
195	C₅×C₄⋊C₄	—	2	1	no	—
196	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
197	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
198	C₅×C₂²⋊C₄	—	2	1	no	—
199	C₄²×C₅	—	2	1	no	—
200	C₄²×C₅	C₂⁴	1	1	yes	characteristic
201	C₂²⋊Dic₅	—	2	1	no	—
202	#688	C₂×C₈	1	4	yes	complemented
203	#686	C₂×C₈	1	4	yes	complemented
204	#685	—	2	1	no	—
205	#685	—	2	1	no	—
206	#685	—	2	1	no	—
207	#685	—	2	1	no	—
208	#685	—	2	1	no	—
209	C₄⋊Dic₅	—	2	1	no	—
210	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
211	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
212	#683	—	2	1	no	—
213	C₄×Dic₅	—	2	1	no	—
214	C₄×Dic₅	—	2	1	no	—
215	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
216	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
217	C₄×Dic₅	#41	1	1	yes	characteristic
218	C₂×#168	—	2	1	no	—
219	C₂×#168	—	2	1	no	—
220	C₂×#168	—	2	1	no	—
221	C₂×#168	—	4	2	no	—
222	C₂×#168	C₂²×C₄	1	1	yes	characteristic
223	C₂×#168	C₂²×C₄	1	1	yes	characteristic
224	C₂×#168	C₂×D₄	1	1	yes	characteristic
225	C₂×#168	C₂×D₄	1	1	yes	characteristic
226	D₄₀	C₂×C₈	1	4	yes	complemented
227	#676	—	2	2	no	—
228	#676	C₂×C₈	1	4	yes	complemented
229	C₈×D₅	—	2	2	no	—
230	C₈×D₅	—	4	1	no	—
231	C₈×D₅	—	4	2	no	—
232	C₈×D₅	—	4	2	no	—
233	C₈×D₅	—	4	2	no	—
234	C₈×D₅	—	4	2	no	—
235	C₈×D₅	—	4	2	no	—
236	C₂×AGL(1,ℤ/8)	—	5	1	no	—
237	C₂³×C₈	—	10	1	no	—
238	C₄×#41	—	5	1	no	—
239	C₂×C₄×D₄	—	5	1	no	—
240	C₈×Q₈	—	5	1	no	—
241	C₈×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
242	#442	—	5	1	no	—
243	#442	—	5	1	no	—
244	#440	—	5	1	no	—
245	#440	—	5	1	no	—
246	C₄×SD₁₆	—	5	1	no	—
247	C₄×SD₁₆	C₂×D₅	1	1	yes	characteristic
248	C₄×D₈	—	5	1	no	—
249	C₄×D₈	—	5	1	no	—
250	C₈×D₄	—	5	1	no	—
251	C₈×D₄	—	5	1	no	—
252	C₈×D₄	—	5	1	no	—
253	C₈×D₄	—	5	1	no	—
254	C₈×D₄	—	5	1	no	—
255	C₈×D₄	—	10	1	no	—
256	C₈×D₄	—	10	1	no	—
257	C₈×D₄	—	10	1	no	—
258	C₈×D₄	—	10	1	no	—
259	C₈×D₄	C₂×D₅	1	1	yes	characteristic
260	#431	—	5	1	no	—
261	#431	—	5	1	no	—
262	#431	—	10	1	no	—
263	#428	—	5	1	no	—
264	C₂×C₄⋊C₈	—	5	1	no	—
265	#418	—	5	1	no	—
266	#417	—	5	1	no	—
267	C₂×C₂²⋊C₈	—	10	1	no	—
268	C₄×M₁₆	—	5	1	no	—
269	C₂×C₄×C₈	—	5	1	no	—
270	C₂×C₄×C₈	—	10	1	no	—
271	#335	—	5	1	no	—
272	#335	C₂×D₅	1	1	yes	characteristic, complemented
273	#334	—	5	1	no	—
274	#334	—	5	1	no	—
275	Q₈⋊C₈	—	5	1	no	—
276	Q₈⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
277	D₄⋊C₈	—	5	1	no	—
278	D₄⋊C₈	—	5	1	no	—
279	D₄⋊C₈	—	5	1	no	—
280	D₄⋊C₈	—	5	1	no	—
281	D₄⋊C₈	—	5	1	no	—
282	D₄⋊C₈	C₂×D₅	1	1	yes	characteristic
283	#322	—	5	1	no	—
284	#322	C₂×D₅	1	1	yes	characteristic, complemented
285	C₈²	—	5	1	no	—
286	C₈²	—	5	1	no	—
287	C₂³×C₅	—	2	1	no	—
288	C₂²×D₅	—	2	1	no	—
289	C₂²×D₅	—	2	1	no	—
290	C₂²×D₅	—	2	4	no	—
291	C₂²×D₅	—	4	2	no	—
292	C₂²×D₅	—	4	2	no	—
293	C₂²×D₅	C₄×D₄	1	1	yes	characteristic
294	C₅×Q₈	—	2	1	no	—
295	C₅×Q₈	C₂²×C₈	1	2	yes	complemented
296	C₅×D₄	—	2	1	no	—
297	C₅×D₄	C₂²×C₈	1	2	yes	—
298	C₂×C₄×C₅	—	2	1	no	—
299	C₂×C₄×C₅	—	2	1	no	—
300	C₂×C₄×C₅	—	2	1	no	—
301	C₂×C₄×C₅	—	4	1	no	—
302	C₂×C₄×C₅	—	4	1	no	—
303	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
304	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
305	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
306	C₂²⋊D₅	—	2	4	no	—
307	C₂×Dic₅	—	2	1	no	—
308	C₂×Dic₅	—	2	1	no	—
309	C₂×Dic₅	—	4	2	no	—
310	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
311	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
312	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
313	D₂₀	—	2	4	no	—
314	D₂₀	—	2	1	no	—
315	D₂₀	—	2	1	no	—
316	D₂₀	C₂²×C₈	1	2	yes	—
317	D₂₀	C₂²×C₈	1	2	yes	complemented
318	C₄×D₅	—	2	1	no	—
319	C₄×D₅	—	2	1	no	—
320	C₄×D₅	—	2	4	no	—
321	C₄×D₅	—	4	1	no	—
322	C₄×D₅	—	4	2	no	—
323	C₄×D₅	—	4	2	no	—
324	C₄×D₅	—	4	2	no	—
325	C₄×D₅	—	4	1	no	—
326	C₄×D₅	—	4	1	no	—
327	C₄×D₅	—	4	1	no	—
328	C₄×D₅	—	4	1	no	—
329	C₄×D₅	C₂²×C₈	1	2	yes	—
330	C₄×D₅	#131	1	2	yes	—
331	C₅×C₈	—	2	1	no	—
332	C₅×C₈	—	2	1	no	—
333	C₅×C₈	—	2	1	no	—
334	C₅×C₈	—	4	1	no	—
335	C₅×C₈	—	4	1	no	—
336	C₅×C₈	—	4	1	no	—
337	C₅×C₈	C₂²×C₈	1	2	yes	complemented
338	#168	—	2	1	no	—
339	#168	—	2	1	no	—
340	#168	—	4	1	no	—
341	#168	—	4	1	no	—
342	#168	—	4	1	no	—
343	#168	C₂²×C₈	1	2	yes	complemented
344	#168	AGL(1,ℤ/8)	1	2	yes	complemented
345	C₂×#41	—	5	1	no	—
346	C₂²×D₄	—	5	1	no	—
347	C₂³×C₄	—	10	1	no	—
348	AGL(1,ℤ/8)	—	5	8	no	—
349	C₂×SD₁₆	—	5	1	no	—
350	C₂×SD₁₆	C₄×D₅	1	1	yes	characteristic
351	C₂×D₈	—	5	1	no	—
352	C₂×D₈	—	5	1	no	—
353	C₂×M₁₆	—	5	1	no	—
354	C₂×M₁₆	—	5	1	no	—
355	C₂²×C₈	—	2	1	no	—
356	C₂²×C₈	—	5	1	no	—
357	C₂²×C₈	—	5	1	no	—
358	C₂²×C₈	—	10	1	no	—
359	C₂²×C₈	—	10	1	no	—
360	C₂²×C₈	—	10	1	no	—
361	C₂²×C₈	—	10	1	no	—
362	C₂²×C₈	—	10	1	no	—
363	C₂²×C₈	—	10	1	no	—
364	C₂²×C₈	—	20	4	no	—
365	C₄×Q₈	—	5	1	no	—
366	C₄×Q₈	C₂²×D₅	1	1	yes	characteristic
367	C₄×D₄	—	5	1	no	—
368	C₄×D₄	—	5	1	no	—
369	C₄×D₄	—	5	1	no	—
370	C₄×D₄	—	5	1	no	—
371	C₄×D₄	—	5	1	no	—
372	C₄×D₄	—	10	1	no	—
373	C₄×D₄	—	10	1	no	—
374	C₄×D₄	—	10	1	no	—
375	C₄×D₄	—	10	1	no	—
376	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
377	#117	—	5	1	no	—
378	#117	—	10	1	no	—
379	C₂×C₄⋊C₄	—	5	1	no	—
380	C₂×C₂²⋊C₄	—	10	1	no	—
381	C₂×C₄²	—	5	1	no	—
382	C₂×C₄²	—	10	1	no	—
383	#107	—	5	1	no	—
384	#107	—	5	1	no	—
385	#106	—	5	1	no	—
386	#106	C₄×D₅	1	1	yes	characteristic
387	C₄⋊C₈	—	2	1	no	—
388	C₄⋊C₈	—	5	1	no	—
389	C₄⋊C₈	—	5	1	no	—
390	C₄⋊C₈	—	10	1	no	—
391	C₄⋊C₈	—	10	1	no	—
392	C₄⋊C₈	—	10	1	no	—
393	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
394	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
395	#103	—	5	1	no	—
396	#103	C₄×D₅	1	1	yes	characteristic
397	#102	—	5	1	no	—
398	#102	—	5	1	no	—
399	#102	—	5	1	no	—
400	#102	—	5	1	no	—
401	#102	—	5	1	no	—
402	#102	C₄×D₅	1	1	yes	characteristic
403	C₂²⋊C₈	—	2	1	no	—
404	C₂²⋊C₈	—	10	1	no	—
405	C₂²⋊C₈	—	10	1	no	—
406	C₂²⋊C₈	—	10	1	no	—
407	C₂²⋊C₈	—	10	1	no	—
408	C₂²⋊C₈	—	10	1	no	—
409	C₂²⋊C₈	—	10	1	no	—
410	C₂²⋊C₈	—	10	1	no	—
411	#97	—	5	1	no	—
412	#97	—	5	1	no	—
413	C₄×C₈	—	2	1	no	—
414	C₄×C₈	—	5	1	no	—
415	C₄×C₈	—	5	1	no	—
416	C₄×C₈	—	5	1	no	—
417	C₄×C₈	—	5	1	no	—
418	C₄×C₈	—	5	1	no	—
419	C₄×C₈	—	10	1	no	—
420	C₄×C₈	—	10	1	no	—
421	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
422	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
423	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
424	C₂²×C₅	—	2	2	no	—
425	C₂²×C₅	—	4	1	no	—
426	C₂²×C₅	—	4	1	no	—
427	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
428	C₂×D₅	—	2	1	no	—
429	C₂×D₅	—	2	1	no	—
430	C₂×D₅	—	2	2	no	—
431	C₂×D₅	—	2	2	no	—
432	C₂×D₅	—	4	8	no	—
433	C₂×D₅	—	4	1	no	—
434	C₂×D₅	—	4	1	no	—
435	C₂×D₅	—	4	1	no	—
436	C₂×D₅	—	4	1	no	—
437	C₂×D₅	C₈×D₄	1	2	yes	—
438	C₄×C₅	—	2	2	no	—
439	C₄×C₅	—	2	1	no	—
440	C₄×C₅	—	4	1	no	—
441	C₄×C₅	—	4	1	no	—
442	C₄×C₅	C₂³×C₈	1	1	yes	characteristic
443	C₄×C₅	C₂×#131	1	1	yes	characteristic
444	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
445	C₄×C₅	#575	1	1	yes	characteristic
446	Dic₅	—	2	1	no	—
447	Dic₅	—	2	1	no	—
448	Dic₅	—	4	1	no	—
449	Dic₅	—	4	1	no	—
450	Dic₅	C₈×D₄	1	2	yes	—
451	C₂⁴	—	10	1	no	—
452	#41	—	5	4	no	—
453	#41	—	10	2	no	—
454	C₂×Q₈	C₂×C₄×D₅	1	1	yes	characteristic
455	C₂×D₄	—	5	4	no	—
456	C₂×D₄	—	5	1	no	—
457	C₂×D₄	—	5	1	no	—
458	C₂×D₄	—	10	1	no	—
459	C₂×D₄	—	10	2	no	—
460	C₂×D₄	—	10	1	no	—
461	C₂×D₄	C₂×C₄×D₅	1	1	yes	characteristic
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	5	1	no	—
464	C₂²×C₄	—	5	1	no	—
465	C₂²×C₄	—	5	1	no	—
466	C₂²×C₄	—	10	1	no	—
467	C₂²×C₄	—	10	1	no	—
468	C₂²×C₄	—	10	1	no	—
469	C₂²×C₄	—	10	1	no	—
470	C₂²×C₄	—	10	1	no	—
471	C₂²×C₄	—	10	1	no	—
472	C₂²×C₄	—	10	1	no	—
473	C₂²×C₄	—	20	2	no	—
474	C₂²×C₄	—	20	2	no	—
475	SD₁₆	—	5	4	no	—
476	SD₁₆	C₈×D₅	1	4	yes	complemented
477	D₈	—	5	4	no	—
478	D₈	—	5	4	no	—
479	M₁₆	—	5	4	no	—
480	M₁₆	—	10	2	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	4	2	no	—
485	C₂×C₈	—	5	1	no	—
486	C₂×C₈	—	5	1	no	—
487	C₂×C₈	—	5	1	no	—
488	C₂×C₈	—	5	1	no	—
489	C₂×C₈	—	10	2	no	—
490	C₂×C₈	—	10	1	no	—
491	C₂×C₈	—	10	1	no	—
492	C₂×C₈	—	10	1	no	—
493	C₂×C₈	—	20	1	no	—
494	C₂×C₈	—	20	2	no	—
495	C₂×C₈	—	20	2	no	—
496	C₂×C₈	—	20	2	no	—
497	C₂×C₈	—	20	2	no	—
498	C₂×C₈	—	20	2	no	—
499	C₂×C₈	—	20	2	no	—
500	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
501	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
502	C₂×C₈	D₄×D₅	1	1	yes	characteristic
503	C₂×C₈	D₄×D₅	1	1	yes	characteristic
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	5	1	no	—
506	C₄⋊C₄	—	5	1	no	—
507	C₄⋊C₄	—	10	1	no	—
508	C₄⋊C₄	—	10	1	no	—
509	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
510	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
511	C₂²⋊C₄	—	2	1	no	—
512	C₂²⋊C₄	—	10	1	no	—
513	C₂²⋊C₄	—	10	1	no	—
514	C₂²⋊C₄	—	10	1	no	—
515	C₂²⋊C₄	—	10	1	no	—
516	C₂²⋊C₄	—	10	1	no	—
517	C₂²⋊C₄	—	10	1	no	—
518	C₄²	—	2	1	no	—
519	C₄²	—	5	1	no	—
520	C₄²	—	5	1	no	—
521	C₄²	—	5	1	no	—
522	C₄²	—	10	1	no	—
523	C₄²	—	10	1	no	—
524	C₄²	C₂³×D₅	1	1	yes	characteristic
525	C₂×C₅	—	4	2	no	—
526	C₂×C₅	C₂×C₈×D₄	1	1	yes	characteristic
527	C₂×C₅	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
528	C₂×C₅	#2955	1	1	yes	characteristic
529	D₅	—	2	2	no	—
530	D₅	—	4	2	no	—
531	D₅	—	4	2	no	—
532	C₂³	—	2	1	no	—
533	C₂³	—	5	1	no	—
534	C₂³	—	10	4	no	—
535	C₂³	—	10	1	no	—
536	C₂³	—	10	1	no	—
537	C₂³	—	20	2	no	—
538	C₂³	—	20	2	no	—
539	Q₈	—	2	1	no	—
540	Q₈	C₂×C₈×D₅	1	2	yes	complemented
541	D₄	—	2	1	no	—
542	D₄	—	5	2	no	—
543	D₄	—	5	2	no	—
544	D₄	—	10	4	no	—
545	D₄	—	10	4	no	—
546	D₄	—	10	1	no	—
547	D₄	—	10	1	no	—
548	D₄	C₂×C₈×D₅	1	2	yes	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	5	1	no	—
555	C₂×C₄	—	5	2	no	—
556	C₂×C₄	—	5	2	no	—
557	C₂×C₄	—	5	1	no	—
558	C₂×C₄	—	5	1	no	—
559	C₂×C₄	—	10	4	no	—
560	C₂×C₄	—	10	1	no	—
561	C₂×C₄	—	10	1	no	—
562	C₂×C₄	—	10	1	no	—
563	C₂×C₄	—	10	1	no	—
564	C₂×C₄	—	20	1	no	—
565	C₂×C₄	—	20	2	no	—
566	C₂×C₄	—	20	2	no	—
567	C₂×C₄	—	20	2	no	—
568	C₂×C₄	—	20	2	no	—
569	C₂×C₄	—	20	1	no	—
570	C₂×C₄	—	20	1	no	—
571	C₂×C₄	—	20	1	no	—
572	C₂×C₄	—	20	1	no	—
573	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
574	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
575	C₂×C₄	D₅×#41	1	1	yes	characteristic
576	C₈	—	2	1	no	—
577	C₈	—	2	1	no	—
578	C₈	—	2	1	no	—
579	C₈	—	4	1	no	—
580	C₈	—	4	1	no	—
581	C₈	—	4	1	no	—
582	C₈	—	5	2	no	—
583	C₈	—	5	2	no	—
584	C₈	—	10	1	no	—
585	C₈	—	10	1	no	—
586	C₈	—	20	1	no	—
587	C₈	—	20	1	no	—
588	C₈	—	20	1	no	—
589	C₈	C₂×C₈×D₅	1	2	yes	complemented
590	C₅	C₈×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
591	C₂²	—	2	2	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	5	2	no	—
595	C₂²	—	10	1	no	—
596	C₂²	—	10	1	no	—
597	C₂²	—	10	2	no	—
598	C₂²	—	10	2	no	—
599	C₂²	—	20	8	no	—
600	C₂²	—	20	1	no	—
601	C₂²	—	20	1	no	—
602	C₂²	—	20	1	no	—
603	C₂²	—	20	1	no	—
604	C₂²	C₄×D₄×D₅	1	1	yes	characteristic
605	C₄	—	2	1	no	—
606	C₄	—	2	2	no	—
607	C₄	—	4	1	no	—
608	C₄	—	4	1	no	—
609	C₄	—	5	2	no	—
610	C₄	—	10	1	no	—
611	C₄	—	10	1	no	—
612	C₄	—	20	1	no	—
613	C₄	—	20	1	no	—
614	C₄	C₂²×C₈×D₅	1	1	yes	characteristic
615	C₄	D₅×#131	1	1	yes	characteristic
616	C₄	D₅×AGL(1,ℤ/8)	1	1	yes	characteristic
617	C₄	#66111	1	1	yes	characteristic
618	C₂	—	4	2	no	—
619	C₂	—	10	2	no	—
620	C₂	—	20	2	no	—
621	C₂	—	20	2	no	—
622	C₂	C₈×D₄×D₅	1	1	yes	characteristic
623	C₂	#10611504	1	1	yes	characteristic
624	C₂	#10611628	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅
commutator	C₄×C₅	C₂³×C₈
Frattini	C₄²	C₂³×D₅
Fitting	C₅×SD₁₆⋊C₈	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂×#4060	C₄
cosocle	C₄²×C₅	C₂⁴
hypercenter	SD₁₆⋊C₈	D₅
hypocenter	C₅	C₈×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ SD₁₆⋊C₈

Complements

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

N	H ≅ G/N	type
1. C₈×#713	C₂	semidirect
3. C₈×D₄×D₅	C₂	semidirect
4. C₅×SD₁₆⋊C₈	C₂	semidirect
5. #10601730	C₂	semidirect
6. SD₁₆×#168	C₂	semidirect
7. #10601633	C₂	semidirect
8. #10599361	C₂	semidirect
9. #10599349	C₂	semidirect
10. #10599023	C₂	semidirect
11. #10599005	C₂	semidirect
12. #10598960	C₂	semidirect
13. #10598941	C₂	semidirect
14. #10598870	C₂	semidirect
15. #10598860	C₂	semidirect
20. C₅×C₈×Q₈	C₂²	semidirect
26. Q₈×#168	C₂²	semidirect
33. #65123	C₂²	semidirect
47. C₈×D₂₀	C₂²	semidirect
51. C₅×#335	C₂²	semidirect
52. C₅×Q₈⋊C₈	C₂²	semidirect
54. C₅×#322	C₂²	semidirect
55. Q₈⋊#168	C₂²	semidirect
58. #64703	C₂²	semidirect
59. #64700	C₂²	semidirect
60. #64699	C₂²	semidirect
62. #64679	C₂²	semidirect
63. #64677	C₂²	semidirect
64. #64674	C₂²	semidirect
65. C₈×#168	C₂²	semidirect
66. C₈×#168	C₂²	semidirect
81. #4060	C₈	semidirect
153. SD₁₆⋊C₈	D₅	semidirect
169. #713	C₂×C₈	semidirect
171. D₄×D₅	C₂×C₈	semidirect
186. C₅×SD₁₆	C₂×C₈	semidirect
202. #688	C₂×C₈	semidirect
203. #686	C₂×C₈	semidirect
226. D₄₀	C₂×C₈	semidirect
228. #676	C₂×C₈	semidirect
241. C₈×Q₈	C₂×D₅	semidirect
272. #335	C₂×D₅	semidirect
276. Q₈⋊C₈	C₂×D₅	semidirect
284. #322	C₂×D₅	semidirect
295. C₅×Q₈	C₂²×C₈	semidirect
317. D₂₀	C₂²×C₈	semidirect
337. C₅×C₈	C₂²×C₈	semidirect
343. #168	C₂²×C₈	semidirect
344. #168	AGL(1,ℤ/8)	semidirect
476. SD₁₆	C₈×D₅	semidirect
540. Q₈	C₂×C₈×D₅	semidirect
589. C₈	C₂×C₈×D₅	semidirect
590. C₅	C₈×AGL(1,ℤ/8)	semidirect

Maximal subgroups

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

subgroup	index
C₈×#713	2
C₄×#4060	2
C₈×D₄×D₅	2
C₅×SD₁₆⋊C₈	2
#10601730	2
SD₁₆×#168	2
#10601633	2
#10599361	2
#10599349	2
#10599023	2
#10599005	2
#10598960	2
#10598941	2
#10598870	2
#10598860	2
C₈×AGL(1,ℤ/8)	5