Subgroups — #12069820

Order 1280.

682 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10611689	C₂	1	1	yes	maximal, characteristic, complemented
2	#10611393	C₂	1	1	yes	maximal, characteristic
3	#10611269	C₂	1	1	yes	maximal, characteristic
4	C₅×#1590	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601743	C₂	1	1	yes	maximal, characteristic, complemented
6	SD₁₆×#168	C₂	1	1	yes	maximal, characteristic, complemented
7	#10601659	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599322	C₂	1	1	yes	maximal, characteristic, complemented
9	#10599309	C₂	1	1	yes	maximal, characteristic, complemented
10	#10599033	C₂	1	1	yes	maximal, characteristic, complemented
11	#10599005	C₂	1	1	yes	maximal, characteristic, complemented
12	#10598969	C₂	1	1	yes	maximal, characteristic
13	#10598942	C₂	1	1	yes	maximal, characteristic, complemented
14	#10598848	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈²×D₅	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#4053	—	2	1	no	—
17	#65912	C₂²	1	1	yes	characteristic
18	#65882	C₂²	1	1	yes	characteristic
19	C₅×#446	C₂²	1	1	yes	characteristic
20	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
21	C₅×#436	C₂²	1	1	yes	characteristic
22	#65464	C₄	1	1	yes	characteristic
23	#65460	C₄	1	1	yes	characteristic
24	#65417	—	2	1	no	—
25	C₄×#688	C₂²	1	1	yes	characteristic
26	Q₈×#168	C₂²	1	1	yes	characteristic
27	C₄×#687	C₂²	1	1	yes	characteristic
28	D₄×#168	C₂²	1	1	yes	characteristic
29	#65153	C₄	1	1	yes	characteristic
30	#65144	C₄	1	1	yes	characteristic
31	#65128	—	2	1	no	—
32	#65126	C₂²	1	1	yes	characteristic
33	#65126	C₂²	1	1	yes	characteristic
34	#65123	C₂²	1	1	yes	characteristic
35	#65119	—	2	1	no	—
36	#65119	C₂²	1	1	yes	characteristic
37	#65096	C₄	1	1	yes	characteristic
38	#65081	C₄	1	1	yes	characteristic
39	#65067	C₄	1	1	yes	characteristic
40	#65049	C₄	1	1	yes	characteristic
41	#65016	—	2	1	no	—
42	#65014	—	2	1	no	—
43	#64997	—	2	1	no	—
44	#64990	—	2	1	no	—
45	C₄×#677	C₂²	1	1	yes	characteristic
46	#64977	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
48	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
49	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
50	#64968	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	C₈×#168	C₂²	1	1	yes	characteristic
65	C₈×#168	C₂²	1	1	yes	characteristic
66	C₈×#168	C₂²	1	1	yes	characteristic
67	#17957	—	5	1	no	maximal, Sylow
68	C₂×#709	—	2	1	no	—
69	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
70	C₂×C₅×M₁₆	—	2	1	no	—
71	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
72	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
73	#4092	C₂×C₄	1	1	yes	characteristic
74	#4090	C₂×C₄	1	1	yes	characteristic
75	C₂×#688	C₂×C₄	1	1	yes	characteristic
76	#4086	C₂×C₄	1	1	yes	characteristic
77	#4084	C₂×C₄	1	1	yes	characteristic
78	C₂×#687	C₂×C₄	1	1	yes	characteristic
79	C₄×C₂²⋊D₅	—	2	1	no	—
80	C₂²×#168	—	2	1	no	—
81	#4053	—	4	4	no	—
82	C₂×#677	C₂×C₄	1	1	yes	characteristic
83	C₂×#676	—	2	1	no	—
84	C₂×#676	—	2	1	no	—
85	C₂×#676	—	2	1	no	—
86	C₂×C₈×D₅	—	2	1	no	—
87	C₂×C₈×D₅	—	2	1	no	—
88	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
89	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
90	C₂×C₈×D₅	D₄	1	1	yes	characteristic
91	C₂×C₈×D₅	D₄	1	1	yes	characteristic
92	#4043	C₂×C₄	1	1	yes	characteristic
93	#4042	—	2	1	no	—
94	#4041	C₂×C₄	1	1	yes	characteristic
95	#4035	—	2	1	no	—
96	#4034	C₂×C₄	1	1	yes	characteristic
97	#4034	C₂×C₄	1	1	yes	characteristic
98	#4031	—	2	1	no	—
99	#4030	—	2	1	no	—
100	C₄×D₂₀	C₂³	1	1	yes	characteristic
101	#4018	—	2	1	no	—
102	C₄²×D₅	C₂³	1	1	yes	characteristic
103	C₄×Dic₁₀	—	2	1	no	—
104	C₄×Dic₁₀	C₂³	1	1	yes	characteristic
105	C₅×#106	C₂×C₄	1	1	yes	characteristic
106	C₅×C₄⋊C₈	—	2	1	no	—
107	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
108	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
109	C₅×#103	C₂×C₄	1	1	yes	characteristic
110	C₅×#102	C₂×C₄	1	1	yes	characteristic
111	C₅×C₂²⋊C₈	—	2	1	no	—
112	C₅×#97	—	2	1	no	—
113	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
114	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
115	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
116	#3967	C₂×C₄	1	1	yes	characteristic
117	#3964	C₂×C₄	1	1	yes	characteristic
118	C₂²⋊#168	—	2	1	no	—
119	#3953	C₂×C₄	1	1	yes	characteristic
120	#3952	—	2	1	no	—
121	#3952	—	2	1	no	—
122	#3949	C₂×C₄	1	1	yes	characteristic
123	#3948	C₂×C₄	1	1	yes	characteristic
124	#3947	—	2	1	no	—
125	#3946	—	2	1	no	—
126	#3946	—	2	1	no	—
127	#3946	—	2	1	no	—
128	#3946	—	2	1	no	—
129	C₈×Dic₅	—	2	1	no	—
130	C₈×Dic₅	—	2	1	no	—
131	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
132	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
133	C₈×Dic₅	D₄	1	1	yes	characteristic
134	C₈×Dic₅	D₄	1	1	yes	characteristic
135	#3942	C₂×C₄	1	1	yes	characteristic
136	#3941	C₂×C₄	1	1	yes	characteristic
137	#3940	C₂×C₄	1	1	yes	characteristic
138	#3940	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	#3167	—	5	1	no	—
147	#2960	—	5	1	no	—
148	#2931	—	5	1	no	—
149	#1590	—	5	1	no	—
150	#1590	—	5	1	no	—
151	#1590	—	5	1	no	—
152	#1590	D₅	1	1	yes	characteristic, complemented
153	C₈×SD₁₆	—	5	1	no	—
154	C₈×SD₁₆	—	5	1	no	—
155	C₈×SD₁₆	—	5	1	no	—
156	C₈×SD₁₆	—	5	1	no	—
157	#1566	—	5	1	no	—
158	#1493	—	5	1	no	—
159	#1492	—	5	1	no	—
160	C₂×C₈²	—	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	C₂×C₂²⋊D₅	—	2	1	no	—
166	C₂×C₂²⋊D₅	—	2	1	no	—
167	#709	—	4	2	no	—
168	#709	—	4	2	no	—
169	C₂×D₂₀	—	2	1	no	—
170	C₂×D₂₀	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₄×D₅	—	2	1	no	—
172	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
174	C₂×C₄×D₅	#41	1	1	yes	characteristic
175	C₂×Dic₁₀	—	2	1	no	—
176	C₂×Dic₁₀	—	2	1	no	—
177	C₂×Dic₁₀	C₂²×C₄	1	1	yes	characteristic
178	C₅×SD₁₆	—	2	2	no	—
179	C₅×M₁₆	—	4	2	no	—
180	C₂×C₅×C₈	—	2	1	no	—
181	C₂×C₅×C₈	—	2	1	no	—
182	C₂×C₅×C₈	—	2	1	no	—
183	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
186	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
187	C₅×C₄⋊C₄	—	2	1	no	—
188	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
189	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
190	C₅×C₂²⋊C₄	—	2	1	no	—
191	C₄²×C₅	—	2	1	no	—
192	C₄²×C₅	C₂⁴	1	1	yes	characteristic
193	C₂²⋊Dic₅	—	2	1	no	—
194	#688	—	2	2	no	—
195	#687	—	2	2	no	—
196	#685	—	2	1	no	—
197	#685	—	2	1	no	—
198	#685	—	2	1	no	—
199	#685	—	2	1	no	—
200	C₄⋊Dic₅	—	2	1	no	—
201	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
202	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
203	#683	—	2	1	no	—
204	#683	—	2	1	no	—
205	#683	—	2	1	no	—
206	#683	—	2	1	no	—
207	#683	—	2	1	no	—
208	#683	—	2	1	no	—
209	C₄×Dic₅	—	2	1	no	—
210	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
211	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
212	C₄×Dic₅	#41	1	1	yes	characteristic
213	C₂×#168	—	2	1	no	—
214	C₂×#168	—	2	1	no	—
215	C₂×#168	—	2	1	no	—
216	C₂×#168	—	4	2	no	—
217	C₂×#168	C₂²×C₄	1	1	yes	characteristic
218	C₂×#168	C₂²×C₄	1	1	yes	characteristic
219	C₂×#168	C₂×D₄	1	1	yes	characteristic
220	C₂×#168	C₂×D₄	1	1	yes	characteristic
221	#677	—	2	2	no	—
222	#676	—	4	2	no	—
223	#676	—	4	2	no	—
224	#676	—	4	2	no	—
225	C₈×D₅	—	2	4	no	—
226	C₈×D₅	—	2	2	no	—
227	C₈×D₅	—	2	2	no	—
228	C₈×D₅	—	2	2	no	—
229	C₈×D₅	—	4	2	no	—
230	C₈×D₅	SD₁₆	1	4	yes	complemented
231	C₂×#131	—	10	1	no	—
232	#533	—	5	1	no	—
233	#532	—	5	1	no	—
234	#498	—	5	1	no	—
235	#492	—	5	1	no	—
236	#487	—	5	1	no	—
237	#486	—	5	1	no	—
238	#465	—	5	1	no	—
239	#465	—	5	1	no	—
240	#465	—	5	1	no	—
241	#465	—	5	1	no	—
242	#446	—	5	1	no	—
243	#446	—	10	1	no	—
244	#446	C₂×D₅	1	1	yes	characteristic
245	C₈×Q₈	—	5	1	no	—
246	C₈×Q₈	—	5	1	no	—
247	C₈×Q₈	—	10	1	no	—
248	C₄×SD₁₆	—	5	1	no	—
249	C₄×SD₁₆	—	5	1	no	—
250	C₄×SD₁₆	—	5	1	no	—
251	C₄×SD₁₆	C₂×D₅	1	1	yes	characteristic
252	#436	—	5	1	no	—
253	#436	—	10	1	no	—
254	#436	C₂×D₅	1	1	yes	characteristic
255	C₈×D₄	—	5	1	no	—
256	C₈×D₄	—	5	1	no	—
257	C₈×D₄	—	10	1	no	—
258	#424	—	10	1	no	—
259	#423	—	5	1	no	—
260	#423	—	5	1	no	—
261	#408	—	10	1	no	—
262	#405	—	10	1	no	—
263	C₂×C₄×C₈	—	5	1	no	—
264	C₂×C₄×C₈	—	5	1	no	—
265	C₂×C₄×C₈	—	5	1	no	—
266	#334	—	5	1	no	—
267	#334	—	5	1	no	—
268	#334	—	5	1	no	—
269	#334	C₂×D₅	1	1	yes	characteristic
270	Q₈⋊C₈	—	5	1	no	—
271	Q₈⋊C₈	—	5	1	no	—
272	Q₈⋊C₈	—	5	1	no	—
273	Q₈⋊C₈	C₂×D₅	1	1	yes	characteristic
274	D₄⋊C₈	—	5	1	no	—
275	D₄⋊C₈	—	5	1	no	—
276	D₄⋊C₈	—	5	1	no	—
277	D₄⋊C₈	C₂×D₅	1	1	yes	characteristic
278	C₈²	—	5	1	no	—
279	C₈²	—	5	1	no	—
280	C₈²	—	5	1	no	—
281	C₈²	C₂×D₅	1	1	yes	characteristic
282	C₂³×C₅	—	2	1	no	—
283	C₂²×D₅	—	2	1	no	—
284	C₂²×D₅	C₄×D₄	1	1	yes	characteristic
285	C₅×Q₈	—	2	1	no	—
286	C₅×Q₈	—	2	1	no	—
287	C₅×D₄	—	2	1	no	—
288	C₅×D₄	—	2	1	no	—
289	C₂×C₄×C₅	—	2	1	no	—
290	C₂×C₄×C₅	—	2	1	no	—
291	C₂×C₄×C₅	—	2	1	no	—
292	C₂×C₄×C₅	—	4	1	no	—
293	C₂×C₄×C₅	—	4	1	no	—
294	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
295	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
296	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
297	C₂²⋊D₅	—	4	2	no	—
298	C₂²⋊D₅	—	4	2	no	—
299	C₂²⋊D₅	—	4	2	no	—
300	C₂×Dic₅	—	2	1	no	—
301	C₂×Dic₅	—	2	1	no	—
302	C₂×Dic₅	—	2	1	no	—
303	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
304	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
305	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
306	D₂₀	—	2	1	no	—
307	D₂₀	—	2	1	no	—
308	D₂₀	—	4	2	no	—
309	C₄×D₅	—	2	1	no	—
310	C₄×D₅	—	2	1	no	—
311	C₄×D₅	—	2	2	no	—
312	C₄×D₅	—	4	1	no	—
313	C₄×D₅	—	4	1	no	—
314	C₄×D₅	C₂×SD₁₆	1	2	yes	—
315	C₄×D₅	#135	1	2	yes	—
316	Dic₁₀	—	2	1	no	—
317	Dic₁₀	—	2	1	no	—
318	Dic₁₀	—	4	2	no	—
319	Dic₁₀	—	4	2	no	—
320	C₅×C₈	—	2	2	no	—
321	C₅×C₈	—	2	1	no	—
322	C₅×C₈	—	2	1	no	—
323	C₅×C₈	—	4	1	no	—
324	C₅×C₈	—	4	1	no	—
325	C₅×C₈	#131	1	2	yes	complemented
326	C₅×C₈	C₂×SD₁₆	1	2	yes	—
327	#168	—	2	2	no	—
328	#168	—	2	1	no	—
329	#168	—	2	1	no	—
330	#168	—	4	1	no	—
331	#168	—	4	1	no	—
332	#168	#131	1	2	yes	complemented
333	#168	C₂×SD₁₆	1	2	yes	—
334	C₂×#41	—	10	1	no	—
335	C₂×SD₁₆	—	5	1	no	—
336	C₂×SD₁₆	—	5	1	no	—
337	C₂×SD₁₆	—	5	1	no	—
338	C₂×SD₁₆	C₄×D₅	1	1	yes	characteristic
339	#131	—	20	4	no	—
340	C₂×M₁₆	—	2	1	no	—
341	C₂×M₁₆	—	10	1	no	—
342	C₂×M₁₆	—	10	1	no	—
343	C₂×M₁₆	—	10	1	no	—
344	C₂²×C₈	—	5	1	no	—
345	C₂²×C₈	—	5	1	no	—
346	C₂²×C₈	—	5	1	no	—
347	C₂²×C₈	—	5	1	no	—
348	C₂²×C₈	—	10	1	no	—
349	C₂²×C₈	—	10	1	no	—
350	C₂²×C₈	—	10	1	no	—
351	C₄⋊Q₈	—	5	1	no	—
352	C₄⋊Q₈	—	5	1	no	—
353	C₄⋊Q₈	—	5	1	no	—
354	#127	—	5	1	no	—
355	#125	—	10	1	no	—
356	#124	—	10	1	no	—
357	C₂²⋊Q₈	—	5	1	no	—
358	C₂²⋊Q₈	—	5	1	no	—
359	C₂²⋊Q₈	—	10	1	no	—
360	#121	—	5	1	no	—
361	#121	—	5	1	no	—
362	#121	—	10	1	no	—
363	C₄×Q₈	—	5	1	no	—
364	C₄×Q₈	—	10	1	no	—
365	C₄×Q₈	C₂²×D₅	1	1	yes	characteristic
366	C₄×D₄	—	5	1	no	—
367	C₄×D₄	—	10	1	no	—
368	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
369	#117	—	10	1	no	—
370	C₂×C₄²	—	5	1	no	—
371	#106	—	5	1	no	—
372	#106	—	5	1	no	—
373	#106	—	5	1	no	—
374	#106	C₄×D₅	1	1	yes	characteristic
375	C₄⋊C₈	—	2	1	no	—
376	C₄⋊C₈	—	5	1	no	—
377	C₄⋊C₈	—	5	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	—	10	1	no	—
383	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
384	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
385	#103	—	5	1	no	—
386	#103	—	5	1	no	—
387	#103	—	5	1	no	—
388	#103	C₄×D₅	1	1	yes	characteristic
389	#102	—	5	1	no	—
390	#102	—	5	1	no	—
391	#102	—	5	1	no	—
392	#102	C₄×D₅	1	1	yes	characteristic
393	C₂²⋊C₈	—	2	1	no	—
394	C₂²⋊C₈	—	10	1	no	—
395	C₂²⋊C₈	—	10	1	no	—
396	C₂²⋊C₈	—	10	1	no	—
397	#97	—	2	1	no	—
398	#97	—	10	1	no	—
399	C₄×C₈	—	5	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	—	5	1	no	—
406	C₄×C₈	—	10	1	no	—
407	C₄×C₈	—	10	1	no	—
408	C₄×C₈	—	10	1	no	—
409	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
410	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
411	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
412	C₂²×C₅	—	4	1	no	—
413	C₂²×C₅	—	4	1	no	—
414	C₂²×C₅	—	4	1	no	—
415	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
416	C₂×D₅	—	2	1	no	—
417	C₂×D₅	—	2	1	no	—
418	C₂×D₅	—	4	1	no	—
419	C₂×D₅	—	4	1	no	—
420	C₂×D₅	—	4	1	no	—
421	C₂×D₅	C₄×SD₁₆	1	2	yes	—
422	C₄×C₅	—	2	1	no	—
423	C₄×C₅	—	4	1	no	—
424	C₄×C₅	—	4	1	no	—
425	C₄×C₅	—	4	1	no	—
426	C₄×C₅	C₂×#131	1	1	yes	characteristic
427	C₄×C₅	C₂×#131	1	1	yes	characteristic
428	C₄×C₅	C₂²×SD₁₆	1	1	yes	characteristic
429	C₄×C₅	C₂×#135	1	1	yes	characteristic
430	Dic₅	—	2	1	no	—
431	Dic₅	—	4	1	no	—
432	Dic₅	—	4	1	no	—
433	Dic₅	—	4	1	no	—
434	Dic₅	C₄×SD₁₆	1	2	yes	—
435	Dic₅	#443	1	2	yes	—
436	#41	—	20	2	no	—
437	#41	—	20	2	no	—
438	C₂×Q₈	—	5	1	no	—
439	C₂×Q₈	—	10	1	no	—
440	C₂×Q₈	—	10	1	no	—
441	C₂×Q₈	C₂×C₄×D₅	1	1	yes	characteristic
442	C₂×D₄	—	5	1	no	—
443	C₂×D₄	—	10	1	no	—
444	C₂×D₄	—	10	1	no	—
445	C₂×D₄	—	10	1	no	—
446	C₂×D₄	—	10	1	no	—
447	C₂×D₄	C₂×C₄×D₅	1	1	yes	characteristic
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	5	1	no	—
450	C₂²×C₄	—	5	1	no	—
451	C₂²×C₄	—	5	1	no	—
452	C₂²×C₄	—	10	1	no	—
453	SD₁₆	—	2	2	no	—
454	SD₁₆	—	10	2	no	—
455	SD₁₆	—	10	2	no	—
456	SD₁₆	—	10	2	no	—
457	M₁₆	—	4	2	no	—
458	M₁₆	—	20	2	no	—
459	M₁₆	—	20	2	no	—
460	M₁₆	—	20	2	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	5	1	no	—
465	C₂×C₈	—	5	1	no	—
466	C₂×C₈	—	5	4	no	—
467	C₂×C₈	—	5	1	no	—
468	C₂×C₈	—	5	1	no	—
469	C₂×C₈	—	10	2	no	—
470	C₂×C₈	—	10	2	no	—
471	C₂×C₈	—	10	4	no	—
472	C₂×C₈	—	10	1	no	—
473	C₂×C₈	—	10	2	no	—
474	C₂×C₈	—	10	1	no	—
475	C₂×C₈	—	10	1	no	—
476	C₂×C₈	—	20	2	no	—
477	C₂×C₈	—	20	2	no	—
478	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
479	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
480	C₂×C₈	D₄×D₅	1	1	yes	characteristic
481	C₂×C₈	D₄×D₅	1	1	yes	characteristic
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	5	1	no	—
484	C₄⋊C₄	—	5	1	no	—
485	C₄⋊C₄	—	10	1	no	—
486	C₄⋊C₄	—	10	1	no	—
487	C₄⋊C₄	—	10	1	no	—
488	C₄⋊C₄	—	10	1	no	—
489	C₄⋊C₄	—	10	1	no	—
490	C₄⋊C₄	—	10	1	no	—
491	C₄⋊C₄	—	10	1	no	—
492	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
493	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
494	C₂²⋊C₄	—	2	1	no	—
495	C₂²⋊C₄	—	10	1	no	—
496	C₂²⋊C₄	—	10	1	no	—
497	C₂²⋊C₄	—	10	1	no	—
498	C₂²⋊C₄	—	10	1	no	—
499	C₂²⋊C₄	—	10	1	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	5	1	no	—
502	C₄²	—	5	1	no	—
503	C₄²	—	5	1	no	—
504	C₄²	—	10	1	no	—
505	C₄²	C₂³×D₅	1	1	yes	characteristic
506	C₂×C₅	—	8	1	no	—
507	C₂×C₅	#2931	1	1	yes	characteristic
508	C₂×C₅	C₂×C₄×SD₁₆	1	1	yes	characteristic
509	C₂×C₅	C₂×#443	1	1	yes	characteristic
510	D₅	—	2	2	no	—
511	D₅	—	8	1	no	—
512	C₂³	—	2	1	no	—
513	C₂³	—	5	1	no	—
514	C₂³	—	10	1	no	—
515	Q₈	—	2	1	no	—
516	Q₈	—	2	1	no	—
517	Q₈	—	10	1	no	—
518	Q₈	—	10	1	no	—
519	Q₈	—	20	2	no	—
520	Q₈	—	20	2	no	—
521	D₄	—	2	1	no	—
522	D₄	—	2	1	no	—
523	D₄	—	10	1	no	—
524	D₄	—	10	1	no	—
525	D₄	—	20	2	no	—
526	D₄	—	20	2	no	—
527	D₄	—	20	2	no	—
528	D₄	—	20	2	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	5	1	no	—
535	C₂×C₄	—	5	1	no	—
536	C₂×C₄	—	5	2	no	—
537	C₂×C₄	—	5	2	no	—
538	C₂×C₄	—	5	1	no	—
539	C₂×C₄	—	10	2	no	—
540	C₂×C₄	—	10	1	no	—
541	C₂×C₄	—	10	1	no	—
542	C₂×C₄	—	10	1	no	—
543	C₂×C₄	—	10	1	no	—
544	C₂×C₄	—	10	1	no	—
545	C₂×C₄	—	20	1	no	—
546	C₂×C₄	—	20	1	no	—
547	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
548	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
549	C₂×C₄	D₅×#41	1	1	yes	characteristic
550	C₈	—	2	2	no	—
551	C₈	—	2	1	no	—
552	C₈	—	2	1	no	—
553	C₈	—	4	1	no	—
554	C₈	—	4	1	no	—
555	C₈	—	5	2	no	—
556	C₈	—	5	2	no	—
557	C₈	—	10	2	no	—
558	C₈	—	10	1	no	—
559	C₈	—	10	1	no	—
560	C₈	—	20	1	no	—
561	C₈	—	20	1	no	—
562	C₈	#4053	1	2	yes	complemented
563	C₈	D₅×SD₁₆	1	2	yes	—
564	C₅	#17957	1	1	yes	characteristic, complemented, Sylow
565	C₂²	—	4	1	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	5	2	no	—
569	C₂²	—	10	1	no	—
570	C₂²	—	10	1	no	—
571	C₂²	—	20	1	no	—
572	C₂²	—	20	1	no	—
573	C₂²	—	20	1	no	—
574	C₂²	C₄×D₄×D₅	1	1	yes	characteristic
575	C₄	—	2	1	no	—
576	C₄	—	4	1	no	—
577	C₄	—	4	1	no	—
578	C₄	—	4	1	no	—
579	C₄	—	5	2	no	—
580	C₄	—	5	2	no	—
581	C₄	—	10	1	no	—
582	C₄	—	20	1	no	—
583	C₄	—	20	1	no	—
584	C₄	—	20	1	no	—
585	C₄	C₂×#4053	1	1	yes	characteristic
586	C₄	D₅×#131	1	1	yes	characteristic
587	C₄	C₂×D₅×SD₁₆	1	1	yes	characteristic
588	C₄	D₅×#135	1	1	yes	characteristic
589	C₂	—	8	1	no	—
590	C₂	—	10	2	no	—
591	C₂	—	40	1	no	—
592	C₂	#10611269	1	1	yes	characteristic
593	C₂	C₄×D₅×SD₁₆	1	1	yes	characteristic
594	C₂	D₅×#443	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₄²	C₂³×D₅
Fitting	C₅×#1590	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	#65882	C₂²
cosocle	C₄²×C₅	C₂⁴
hypercenter	#1590	D₅
hypocenter	C₅	#17957
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1590

Complements

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

N	H ≅ G/N	type
1. #10611689	C₂	semidirect
4. C₅×#1590	C₂	semidirect
5. #10601743	C₂	semidirect
6. SD₁₆×#168	C₂	semidirect
7. #10601659	C₂	semidirect
8. #10599322	C₂	semidirect
9. #10599309	C₂	semidirect
10. #10599033	C₂	semidirect
11. #10599005	C₂	semidirect
13. #10598942	C₂	semidirect
14. #10598848	C₂	semidirect
15. C₈²×D₅	C₂	semidirect
152. #1590	D₅	semidirect
230. C₈×D₅	SD₁₆	semidirect
325. C₅×C₈	#131	semidirect
332. #168	#131	semidirect
562. C₈	#4053	semidirect
564. C₅	#17957	semidirect

Maximal subgroups

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

subgroup	index
#10611689	2
#10611393	2
#10611269	2
C₅×#1590	2
#10601743	2
SD₁₆×#168	2
#10601659	2
#10599322	2
#10599309	2
#10599033	2
#10599005	2
#10598969	2
#10598942	2
#10598848	2
C₈²×D₅	2
#17957	5