Subgroups — #12068784

Order 1280.

714 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10611637	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#4062	C₂	1	1	yes	maximal, characteristic
3	#10611136	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₈×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601725	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	D₅×#334	C₂	1	1	yes	maximal, characteristic, complemented
9	#10599309	C₂	1	1	yes	maximal, characteristic, complemented
10	#10599023	C₂	1	1	yes	maximal, characteristic, complemented
11	#10599008	C₂	1	1	yes	maximal, characteristic, complemented
12	#10598959	C₂	1	1	yes	maximal, characteristic, complemented
13	#10598944	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×#677	C₂	1	1	yes	maximal, characteristic, complemented
15	#10598840	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#4062	C₄	1	1	yes	characteristic
17	C₄×#713	C₂²	1	1	yes	characteristic
18	C₄×#711	C₂²	1	1	yes	characteristic
19	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
20	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
21	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
22	SD₁₆×Dic₅	C₄	1	1	yes	characteristic
23	C₈×C₂²⋊D₅	—	2	1	no	—
24	C₂×#3946	—	2	1	no	—
25	C₄×#689	C₂²	1	1	yes	characteristic
26	Q₈×#168	C₂²	1	1	yes	characteristic
27	C₄×#686	C₂²	1	1	yes	characteristic
28	D₄×#168	C₂²	1	1	yes	characteristic
29	#65149	C₄	1	1	yes	characteristic
30	#65141	C₄	1	1	yes	characteristic
31	#65123	—	2	1	no	—
32	#65123	C₂²	1	1	yes	characteristic
33	D₅×C₄⋊C₈	—	2	1	no	—
34	D₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	D₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
36	#65119	C₂²	1	1	yes	characteristic
37	#65093	C₄	1	1	yes	characteristic
38	#65079	C₄	1	1	yes	characteristic
39	#65061	C₄	1	1	yes	characteristic
40	#65045	C₄	1	1	yes	characteristic
41	#65014	—	2	1	no	—
42	#65007	—	2	1	no	—
43	C₄×#677	C₂²	1	1	yes	characteristic
44	C₈×D₂₀	—	2	1	no	—
45	C₈×D₂₀	C₂²	1	1	yes	characteristic
46	#64974	—	2	1	no	—
47	#64974	C₂²	1	1	yes	characteristic
48	#64974	C₂²	1	1	yes	characteristic
49	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
50	C₈×Dic₁₀	C₂²	1	1	yes	characteristic
51	C₅×#334	C₂²	1	1	yes	characteristic
52	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
53	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
54	C₅×C₈²	C₂²	1	1	yes	characteristic
55	Q₈⋊#168	C₂²	1	1	yes	characteristic
56	D₄⋊#168	C₂²	1	1	yes	characteristic
57	#64704	C₂²	1	1	yes	characteristic
58	#64703	C₂²	1	1	yes	characteristic
59	#64700	C₂²	1	1	yes	characteristic
60	#64700	C₂²	1	1	yes	characteristic
61	#64679	C₂²	1	1	yes	characteristic
62	#64677	C₂²	1	1	yes	characteristic
63	#64676	C₂²	1	1	yes	characteristic
64	#64674	C₂²	1	1	yes	characteristic
65	#64674	C₂²	1	1	yes	characteristic
66	C₈×#168	C₂²	1	1	yes	characteristic
67	#17858	—	5	1	no	maximal, Sylow
68	C₂×#713	C₂×C₄	1	1	yes	characteristic
69	C₂×#711	C₂×C₄	1	1	yes	characteristic
70	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
71	C₂²×C₅×C₈	—	2	1	no	—
72	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
73	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
74	Q₈×Dic₅	C₂×C₄	1	1	yes	characteristic
75	C₂×#689	C₂×C₄	1	1	yes	characteristic
76	D₄×Dic₅	C₂×C₄	1	1	yes	characteristic
77	C₂×#686	C₂×C₄	1	1	yes	characteristic
78	C₄×C₂²⋊D₅	—	2	1	no	—
79	C₂×C₄×Dic₅	—	2	1	no	—
80	C₂²×#168	—	2	1	no	—
81	#4062	C₈	1	8	yes	complemented
82	C₂×#677	C₂×C₄	1	1	yes	characteristic
83	C₂×C₈×D₅	—	2	1	no	—
84	C₂×C₈×D₅	—	2	1	no	—
85	C₂×C₈×D₅	—	2	1	no	—
86	C₂×C₈×D₅	—	2	1	no	—
87	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
88	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
89	#4039	—	2	1	no	—
90	#4039	C₂×C₄	1	1	yes	characteristic
91	#4038	—	2	1	no	—
92	#4038	C₂×C₄	1	1	yes	characteristic
93	#4038	C₂×C₄	1	1	yes	characteristic
94	#4033	C₂×C₄	1	1	yes	characteristic
95	#4027	—	2	1	no	—
96	#4023	—	2	1	no	—
97	C₄×D₂₀	—	2	1	no	—
98	C₄×D₂₀	C₂³	1	1	yes	characteristic
99	C₄²×D₅	—	2	1	no	—
100	C₄²×D₅	C₂³	1	1	yes	characteristic
101	C₄×Dic₁₀	C₂³	1	1	yes	characteristic
102	C₅×#106	C₂×C₄	1	1	yes	characteristic
103	C₅×C₄⋊C₈	—	2	1	no	—
104	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
105	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
106	C₅×#103	C₂×C₄	1	1	yes	characteristic
107	C₅×#102	C₂×C₄	1	1	yes	characteristic
108	C₅×C₂²⋊C₈	—	2	1	no	—
109	C₄×C₅×C₈	—	2	1	no	—
110	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
111	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
112	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
113	#3967	C₂×C₄	1	1	yes	characteristic
114	#3964	C₂×C₄	1	1	yes	characteristic
115	C₂²⋊#168	—	2	1	no	—
116	#3953	C₂×C₄	1	1	yes	characteristic
117	#3952	—	2	1	no	—
118	#3952	—	2	1	no	—
119	#3952	—	2	1	no	—
120	#3952	D₄	1	1	yes	characteristic
121	#3952	D₄	1	1	yes	characteristic
122	#3949	C₂×C₄	1	1	yes	characteristic
123	#3948	C₂×C₄	1	1	yes	characteristic
124	#3946	—	2	1	no	—
125	#3946	—	2	1	no	—
126	#3946	—	2	1	no	—
127	#3946	—	2	1	no	—
128	#3946	—	2	1	no	—
129	#3946	D₄	1	1	yes	characteristic
130	#3946	D₄	1	1	yes	characteristic
131	C₈×Dic₅	—	2	1	no	—
132	C₈×Dic₅	—	2	1	no	—
133	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
134	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
135	#3942	C₂×C₄	1	1	yes	characteristic
136	#3941	C₂×C₄	1	1	yes	characteristic
137	#3939	C₂×C₄	1	1	yes	characteristic
138	#3939	C₂×C₄	1	1	yes	characteristic
139	C₄⋊#168	—	2	1	no	—
140	C₄⋊#168	C₂³	1	1	yes	characteristic
141	C₄⋊#168	C₂³	1	1	yes	characteristic
142	C₄×#168	—	2	1	no	—
143	C₄×#168	C₂³	1	1	yes	characteristic
144	C₄×#168	C₂³	1	1	yes	characteristic
145	C₄×#168	C₂³	1	1	yes	characteristic
146	#2988	—	5	1	no	—
147	#2988	—	5	1	no	—
148	C₄×#135	—	5	1	no	—
149	#1580	—	5	1	no	—
150	#1580	—	5	1	no	—
151	#1579	—	5	1	no	—
152	#1579	—	5	1	no	—
153	C₈×SD₁₆	—	5	1	no	—
154	C₈×SD₁₆	—	5	1	no	—
155	C₈×SD₁₆	—	5	1	no	—
156	C₈×SD₁₆	D₅	1	1	yes	characteristic, complemented
157	C₂×#334	—	5	1	no	—
158	#1477	—	5	1	no	—
159	#1477	—	5	1	no	—
160	#1450	—	5	1	no	—
161	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₅	—	2	1	no	—
164	C₂×C₂²⋊D₅	—	2	1	no	—
165	C₂²×Dic₅	—	2	1	no	—
166	C₂²×Dic₅	—	2	1	no	—
167	#713	—	2	2	no	—
168	#713	C₂×C₈	1	4	yes	complemented
169	#711	—	2	2	no	—
170	#711	C₂×C₈	1	4	yes	complemented
171	C₂×D₂₀	—	2	1	no	—
172	C₂×D₂₀	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₄×D₅	—	2	1	no	—
174	C₂×C₄×D₅	—	2	1	no	—
175	C₂×C₄×D₅	—	2	1	no	—
176	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
177	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
178	C₂×C₄×D₅	#41	1	1	yes	characteristic
179	C₂×Dic₁₀	C₂²×C₄	1	1	yes	characteristic
180	C₅×SD₁₆	C₂×C₈	1	4	yes	complemented
181	C₂×C₅×C₈	—	2	1	no	—
182	C₂×C₅×C₈	—	2	1	no	—
183	C₂×C₅×C₈	—	2	1	no	—
184	C₂×C₅×C₈	—	8	1	no	—
185	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
188	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
189	C₅×C₄⋊C₄	—	2	1	no	—
190	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
191	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
192	C₅×C₂²⋊C₄	—	2	1	no	—
193	C₄²×C₅	—	2	1	no	—
194	C₄²×C₅	C₂⁴	1	1	yes	characteristic
195	C₂²⋊Dic₅	—	2	1	no	—
196	#689	C₂×C₈	1	4	yes	complemented
197	#686	C₂×C₈	1	4	yes	complemented
198	#685	—	2	1	no	—
199	#685	—	2	1	no	—
200	#685	—	2	1	no	—
201	#685	—	2	1	no	—
202	C₄⋊Dic₅	—	2	1	no	—
203	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
204	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
205	#683	—	2	1	no	—
206	#683	—	2	1	no	—
207	C₄×Dic₅	—	2	1	no	—
208	C₄×Dic₅	—	2	1	no	—
209	C₄×Dic₅	—	2	1	no	—
210	C₄×Dic₅	—	2	1	no	—
211	C₄×Dic₅	—	2	1	no	—
212	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
213	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
214	C₄×Dic₅	#41	1	1	yes	characteristic
215	C₂×#168	—	2	1	no	—
216	C₂×#168	—	2	1	no	—
217	C₂×#168	—	2	1	no	—
218	C₂×#168	—	8	1	no	—
219	C₂×#168	C₂²×C₄	1	1	yes	characteristic
220	C₂×#168	C₂²×C₄	1	1	yes	characteristic
221	C₂×#168	C₂×D₄	1	1	yes	characteristic
222	C₂×#168	C₂×D₄	1	1	yes	characteristic
223	#677	C₂×C₈	1	4	yes	complemented
224	C₈×D₅	—	2	2	no	—
225	C₈×D₅	—	8	1	no	—
226	C₈×D₅	—	8	1	no	—
227	C₈×D₅	—	8	1	no	—
228	C₈×D₅	—	8	1	no	—
229	C₈×D₅	C₂×C₈	1	4	yes	complemented
230	C₂×#135	—	5	1	no	—
231	C₄×#41	—	5	1	no	—
232	C₄×#41	—	5	1	no	—
233	C₈×Q₈	—	5	1	no	—
234	C₈×Q₈	—	5	1	no	—
235	C₈×Q₈	—	5	1	no	—
236	C₈×Q₈	C₂×D₅	1	1	yes	characteristic
237	C₄×Q₁₆	—	5	1	no	—
238	C₄×Q₁₆	—	5	1	no	—
239	C₄×SD₁₆	—	5	1	no	—
240	C₄×SD₁₆	—	5	1	no	—
241	C₄×SD₁₆	—	5	1	no	—
242	C₄×SD₁₆	C₂×D₅	1	1	yes	characteristic
243	C₄×D₈	—	5	1	no	—
244	C₄×D₈	—	5	1	no	—
245	C₈×D₄	—	5	1	no	—
246	C₈×D₄	—	5	1	no	—
247	C₈×D₄	—	5	1	no	—
248	C₈×D₄	—	10	1	no	—
249	C₈×D₄	—	10	1	no	—
250	C₈×D₄	—	10	1	no	—
251	C₈×D₄	—	10	1	no	—
252	C₈×D₄	C₂×D₅	1	1	yes	characteristic
253	#431	—	5	1	no	—
254	#431	—	5	1	no	—
255	#431	—	10	1	no	—
256	#431	—	10	1	no	—
257	#427	—	5	1	no	—
258	C₂×C₄⋊C₈	—	5	1	no	—
259	C₂×C₄⋊C₈	—	5	1	no	—
260	C₂×C₄⋊C₈	—	10	1	no	—
261	C₂×C₄⋊C₈	—	10	1	no	—
262	#416	—	5	1	no	—
263	#416	—	5	1	no	—
264	C₂×C₄×C₈	—	5	1	no	—
265	#334	—	5	1	no	—
266	#334	—	5	1	no	—
267	#334	—	5	1	no	—
268	#334	C₂×D₅	1	1	yes	characteristic
269	Q₈⋊C₈	—	5	1	no	—
270	Q₈⋊C₈	—	5	1	no	—
271	Q₈⋊C₈	—	5	1	no	—
272	Q₈⋊C₈	C₂×D₅	1	1	yes	characteristic
273	D₄⋊C₈	—	5	1	no	—
274	D₄⋊C₈	—	5	1	no	—
275	D₄⋊C₈	—	5	1	no	—
276	D₄⋊C₈	C₂×D₅	1	1	yes	characteristic
277	#322	—	5	1	no	—
278	#322	—	5	1	no	—
279	C₈²	—	5	1	no	—
280	C₈²	C₂×D₅	1	1	yes	characteristic
281	C₂³×C₅	—	2	1	no	—
282	C₂²×D₅	—	2	1	no	—
283	C₂²×D₅	C₄×D₄	1	1	yes	characteristic
284	C₅×Q₈	—	2	1	no	—
285	C₅×Q₈	C₂²×C₈	1	2	yes	—
286	C₅×D₄	—	2	1	no	—
287	C₅×D₄	C₂²×C₈	1	2	yes	—
288	C₂×C₄×C₅	—	2	1	no	—
289	C₂×C₄×C₅	—	2	1	no	—
290	C₂×C₄×C₅	—	2	1	no	—
291	C₂×C₄×C₅	—	4	1	no	—
292	C₂×C₄×C₅	—	4	1	no	—
293	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
294	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
295	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
296	C₂²⋊D₅	—	2	4	no	—
297	C₂×Dic₅	—	2	1	no	—
298	C₂×Dic₅	—	2	4	no	—
299	C₂×Dic₅	—	2	1	no	—
300	C₂×Dic₅	—	2	1	no	—
301	C₂×Dic₅	—	8	1	no	—
302	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
303	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
304	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
305	D₂₀	—	2	4	no	—
306	D₂₀	—	2	1	no	—
307	D₂₀	C₂²×C₈	1	2	yes	—
308	C₄×D₅	—	2	1	no	—
309	C₄×D₅	—	2	1	no	—
310	C₄×D₅	—	2	4	no	—
311	C₄×D₅	—	4	1	no	—
312	C₄×D₅	—	4	1	no	—
313	C₄×D₅	—	4	1	no	—
314	C₄×D₅	—	8	1	no	—
315	C₄×D₅	C₂²×C₈	1	2	yes	—
316	C₄×D₅	#131	1	2	yes	—
317	Dic₁₀	—	2	1	no	—
318	Dic₁₀	C₂²×C₈	1	2	yes	—
319	C₅×C₈	—	2	1	no	—
320	C₅×C₈	—	2	1	no	—
321	C₅×C₈	—	2	1	no	—
322	C₅×C₈	—	4	1	no	—
323	C₅×C₈	—	4	1	no	—
324	C₅×C₈	—	4	1	no	—
325	C₅×C₈	C₂²×C₈	1	2	yes	—
326	#168	—	2	1	no	—
327	#168	—	2	1	no	—
328	#168	—	2	1	no	—
329	#168	—	4	1	no	—
330	#168	—	4	1	no	—
331	#168	—	4	1	no	—
332	#168	C₂²×C₈	1	2	yes	—
333	C₂×#41	—	5	1	no	—
334	C₂×#41	—	5	1	no	—
335	#135	—	5	8	no	—
336	C₂×Q₁₆	—	5	1	no	—
337	C₂×SD₁₆	—	5	1	no	—
338	C₂×SD₁₆	C₄×D₅	1	1	yes	characteristic
339	C₂×D₈	—	5	1	no	—
340	C₂²×C₈	—	2	1	no	—
341	C₂²×C₈	—	5	1	no	—
342	C₂²×C₈	—	5	1	no	—
343	C₂²×C₈	—	10	1	no	—
344	C₂²×C₈	—	10	1	no	—
345	C₂²×C₈	—	10	1	no	—
346	C₂²×C₈	—	10	1	no	—
347	C₂²×C₈	—	10	1	no	—
348	C₄×Q₈	—	5	1	no	—
349	C₄×Q₈	—	5	1	no	—
350	C₄×Q₈	—	5	1	no	—
351	C₄×Q₈	C₂²×D₅	1	1	yes	characteristic
352	C₄×D₄	—	5	1	no	—
353	C₄×D₄	—	5	1	no	—
354	C₄×D₄	—	5	1	no	—
355	C₄×D₄	—	10	1	no	—
356	C₄×D₄	—	10	1	no	—
357	C₄×D₄	—	10	1	no	—
358	C₄×D₄	—	10	1	no	—
359	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
360	#117	—	5	1	no	—
361	#117	—	5	1	no	—
362	#117	—	10	1	no	—
363	#117	—	10	1	no	—
364	C₂×C₄²	—	5	1	no	—
365	C₂×C₄²	—	10	1	no	—
366	C₂×C₄²	—	10	1	no	—
367	#107	—	5	1	no	—
368	#107	—	5	1	no	—
369	#106	—	5	1	no	—
370	#106	C₄×D₅	1	1	yes	characteristic
371	C₄⋊C₈	—	2	1	no	—
372	C₄⋊C₈	—	5	1	no	—
373	C₄⋊C₈	—	5	1	no	—
374	C₄⋊C₈	—	5	1	no	—
375	C₄⋊C₈	—	5	1	no	—
376	C₄⋊C₈	—	10	1	no	—
377	C₄⋊C₈	—	10	1	no	—
378	C₄⋊C₈	—	10	1	no	—
379	C₄⋊C₈	—	10	1	no	—
380	C₄⋊C₈	—	10	1	no	—
381	C₄⋊C₈	—	10	1	no	—
382	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
383	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
384	#103	—	5	1	no	—
385	#103	—	5	1	no	—
386	#103	—	5	1	no	—
387	#103	C₄×D₅	1	1	yes	characteristic
388	#102	—	5	1	no	—
389	#102	—	5	1	no	—
390	#102	—	5	1	no	—
391	#102	C₄×D₅	1	1	yes	characteristic
392	C₂²⋊C₈	—	2	1	no	—
393	C₂²⋊C₈	—	5	1	no	—
394	C₂²⋊C₈	—	5	1	no	—
395	C₂²⋊C₈	—	10	1	no	—
396	C₂²⋊C₈	—	10	1	no	—
397	C₂²⋊C₈	—	10	1	no	—
398	C₂²⋊C₈	—	10	1	no	—
399	C₄×C₈	—	2	1	no	—
400	C₄×C₈	—	5	1	no	—
401	C₄×C₈	—	5	1	no	—
402	C₄×C₈	—	5	1	no	—
403	C₄×C₈	—	5	1	no	—
404	C₄×C₈	—	5	1	no	—
405	C₄×C₈	—	10	1	no	—
406	C₄×C₈	—	10	1	no	—
407	C₄×C₈	—	10	1	no	—
408	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
409	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
410	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
411	C₂²×C₅	—	2	2	no	—
412	C₂²×C₅	—	4	1	no	—
413	C₂²×C₅	—	4	1	no	—
414	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
415	C₂×D₅	—	2	1	no	—
416	C₂×D₅	—	2	1	no	—
417	C₂×D₅	—	2	2	no	—
418	C₂×D₅	—	4	1	no	—
419	C₂×D₅	—	4	1	no	—
420	C₂×D₅	C₈×D₄	1	2	yes	—
421	C₄×C₅	—	2	2	no	—
422	C₄×C₅	—	2	1	no	—
423	C₄×C₅	—	4	1	no	—
424	C₄×C₅	—	4	1	no	—
425	C₄×C₅	C₂³×C₈	1	1	yes	characteristic
426	C₄×C₅	C₂×#131	1	1	yes	characteristic
427	C₄×C₅	#577	1	1	yes	characteristic
428	C₄×C₅	#577	1	1	yes	characteristic
429	Dic₅	—	2	2	no	—
430	Dic₅	—	2	1	no	—
431	Dic₅	—	2	1	no	—
432	Dic₅	—	4	1	no	—
433	Dic₅	—	4	1	no	—
434	Dic₅	C₈×D₄	1	2	yes	—
435	#41	—	5	4	no	—
436	#41	—	5	4	no	—
437	#41	—	10	2	no	—
438	#41	—	10	2	no	—
439	C₂×Q₈	—	5	1	no	—
440	C₂×Q₈	C₂×C₄×D₅	1	1	yes	characteristic
441	C₂×D₄	—	5	1	no	—
442	C₂×D₄	—	10	1	no	—
443	C₂×D₄	—	10	1	no	—
444	C₂×D₄	C₂×C₄×D₅	1	1	yes	characteristic
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	5	1	no	—
447	C₂²×C₄	—	5	1	no	—
448	C₂²×C₄	—	5	1	no	—
449	C₂²×C₄	—	10	1	no	—
450	C₂²×C₄	—	10	1	no	—
451	C₂²×C₄	—	10	1	no	—
452	C₂²×C₄	—	10	1	no	—
453	C₂²×C₄	—	10	1	no	—
454	Q₁₆	—	5	4	no	—
455	SD₁₆	—	5	4	no	—
456	SD₁₆	C₈×D₅	1	4	yes	complemented
457	D₈	—	5	4	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	5	1	no	—
462	C₂×C₈	—	5	4	no	—
463	C₂×C₈	—	5	1	no	—
464	C₂×C₈	—	5	1	no	—
465	C₂×C₈	—	5	1	no	—
466	C₂×C₈	—	8	1	no	—
467	C₂×C₈	—	10	2	no	—
468	C₂×C₈	—	10	1	no	—
469	C₂×C₈	—	10	1	no	—
470	C₂×C₈	—	10	1	no	—
471	C₂×C₈	—	40	1	no	—
472	C₂×C₈	—	40	1	no	—
473	C₂×C₈	—	40	1	no	—
474	C₂×C₈	—	40	1	no	—
475	C₂×C₈	—	40	1	no	—
476	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
477	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
478	C₂×C₈	D₄×D₅	1	1	yes	characteristic
479	C₂×C₈	D₄×D₅	1	1	yes	characteristic
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	5	1	no	—
482	C₄⋊C₄	—	5	1	no	—
483	C₄⋊C₄	—	10	1	no	—
484	C₄⋊C₄	—	10	1	no	—
485	C₄⋊C₄	—	10	1	no	—
486	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
487	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
488	C₂²⋊C₄	—	2	1	no	—
489	C₂²⋊C₄	—	10	1	no	—
490	C₂²⋊C₄	—	10	1	no	—
491	C₂²⋊C₄	—	10	1	no	—
492	C₂²⋊C₄	—	10	1	no	—
493	C₂²⋊C₄	—	10	1	no	—
494	C₄²	—	2	1	no	—
495	C₄²	—	5	1	no	—
496	C₄²	—	5	1	no	—
497	C₄²	—	5	1	no	—
498	C₄²	—	10	1	no	—
499	C₄²	—	10	1	no	—
500	C₄²	—	10	1	no	—
501	C₄²	—	10	1	no	—
502	C₄²	—	10	1	no	—
503	C₄²	C₂³×D₅	1	1	yes	characteristic
504	C₂×C₅	—	4	2	no	—
505	C₂×C₅	C₂×C₈×D₄	1	1	yes	characteristic
506	C₂×C₅	#2952	1	1	yes	characteristic
507	C₂×C₅	#2957	1	1	yes	characteristic
508	D₅	—	2	2	no	—
509	D₅	—	4	2	no	—
510	C₂³	—	2	1	no	—
511	C₂³	—	5	1	no	—
512	C₂³	—	10	1	no	—
513	Q₈	—	2	1	no	—
514	Q₈	—	5	2	no	—
515	Q₈	—	10	1	no	—
516	Q₈	C₂×C₈×D₅	1	2	yes	—
517	D₄	—	2	1	no	—
518	D₄	—	5	2	no	—
519	D₄	—	10	4	no	—
520	D₄	—	10	4	no	—
521	D₄	—	10	1	no	—
522	D₄	C₂×C₈×D₅	1	2	yes	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	5	1	no	—
529	C₂×C₄	—	5	2	no	—
530	C₂×C₄	—	5	2	no	—
531	C₂×C₄	—	5	1	no	—
532	C₂×C₄	—	5	1	no	—
533	C₂×C₄	—	10	4	no	—
534	C₂×C₄	—	10	4	no	—
535	C₂×C₄	—	10	1	no	—
536	C₂×C₄	—	10	1	no	—
537	C₂×C₄	—	10	1	no	—
538	C₂×C₄	—	10	1	no	—
539	C₂×C₄	—	10	1	no	—
540	C₂×C₄	—	20	1	no	—
541	C₂×C₄	—	20	1	no	—
542	C₂×C₄	—	20	1	no	—
543	C₂×C₄	—	40	1	no	—
544	C₂×C₄	—	40	1	no	—
545	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
546	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
547	C₂×C₄	D₅×#41	1	1	yes	characteristic
548	C₈	—	2	1	no	—
549	C₈	—	2	1	no	—
550	C₈	—	2	1	no	—
551	C₈	—	4	1	no	—
552	C₈	—	4	1	no	—
553	C₈	—	4	1	no	—
554	C₈	—	5	2	no	—
555	C₈	—	10	1	no	—
556	C₈	—	10	1	no	—
557	C₈	—	10	1	no	—
558	C₈	—	20	1	no	—
559	C₈	—	20	1	no	—
560	C₈	—	20	1	no	—
561	C₈	C₂×C₈×D₅	1	2	yes	—
562	C₅	#17858	1	1	yes	characteristic, complemented, Sylow
563	C₂²	—	2	2	no	—
564	C₂²	—	4	1	no	—
565	C₂²	—	4	1	no	—
566	C₂²	—	5	2	no	—
567	C₂²	—	10	1	no	—
568	C₂²	—	10	1	no	—
569	C₂²	—	10	2	no	—
570	C₂²	—	20	1	no	—
571	C₂²	—	20	1	no	—
572	C₂²	C₄×D₄×D₅	1	1	yes	characteristic
573	C₄	—	2	1	no	—
574	C₄	—	2	2	no	—
575	C₄	—	4	1	no	—
576	C₄	—	4	1	no	—
577	C₄	—	5	2	no	—
578	C₄	—	10	1	no	—
579	C₄	—	10	1	no	—
580	C₄	—	10	2	no	—
581	C₄	—	20	1	no	—
582	C₄	—	20	1	no	—
583	C₄	C₂²×C₈×D₅	1	1	yes	characteristic
584	C₄	D₅×#131	1	1	yes	characteristic
585	C₄	#66096	1	1	yes	characteristic
586	C₄	#66104	1	1	yes	characteristic
587	C₂	—	4	2	no	—
588	C₂	—	10	2	no	—
589	C₂	—	20	2	no	—
590	C₂	C₈×D₄×D₅	1	1	yes	characteristic
591	C₂	#10611381	1	1	yes	characteristic
592	C₂	#10611621	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅
commutator	C₄×C₅	C₂³×C₈
Frattini	C₄²	C₂³×D₅
Fitting	C₅×C₈×SD₁₆	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂×#4062	C₄
cosocle	C₄²×C₅	C₂⁴
hypercenter	C₈×SD₁₆	D₅
hypocenter	C₅	#17858
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈×SD₁₆

Complements

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

N	H ≅ G/N	type
1. #10611637	C₂	semidirect
3. #10611136	C₂	semidirect
4. C₅×C₈×SD₁₆	C₂	semidirect
5. #10601725	C₂	semidirect
6. SD₁₆×#168	C₂	semidirect
7. #10601633	C₂	semidirect
8. D₅×#334	C₂	semidirect
9. #10599309	C₂	semidirect
10. #10599023	C₂	semidirect
11. #10599008	C₂	semidirect
12. #10598959	C₂	semidirect
13. #10598944	C₂	semidirect
14. C₈×#677	C₂	semidirect
15. #10598840	C₂	semidirect
81. #4062	C₈	semidirect
156. C₈×SD₁₆	D₅	semidirect
168. #713	C₂×C₈	semidirect
170. #711	C₂×C₈	semidirect
180. C₅×SD₁₆	C₂×C₈	semidirect
196. #689	C₂×C₈	semidirect
197. #686	C₂×C₈	semidirect
223. #677	C₂×C₈	semidirect
229. C₈×D₅	C₂×C₈	semidirect
456. SD₁₆	C₈×D₅	semidirect
562. C₅	#17858	semidirect

Maximal subgroups

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

subgroup	index
#10611637	2
C₄×#4062	2
#10611136	2
C₅×C₈×SD₁₆	2
#10601725	2
SD₁₆×#168	2
#10601633	2
D₅×#334	2
#10599309	2
#10599023	2
#10599008	2
#10598959	2
#10598944	2
C₈×#677	2
#10598840	2
#17858	5