Subgroups — #12068550

Order 1280.

634 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10611065	C₂	1	1	yes	maximal, characteristic
2	#10611009	C₂	1	1	yes	maximal, characteristic
3	#10610743	C₂	1	1	yes	maximal, characteristic
4	C₅×#1573	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601588	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601546	C₂	1	1	yes	maximal, characteristic, complemented
7	#10601213	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599368	C₂	1	1	yes	maximal, characteristic, complemented
9	#10599365	C₂	1	1	yes	maximal, characteristic, complemented
10	#10599362	C₂	1	1	yes	maximal, characteristic, complemented
11	#10599361	C₂	1	1	yes	maximal, characteristic, complemented
12	#10599327	C₂	1	1	yes	maximal, characteristic, complemented
13	#10599325	C₂	1	1	yes	maximal, characteristic, complemented
14	#10599324	C₂	1	1	yes	maximal, characteristic, complemented
15	D₅×#334	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#4047	—	2	1	no	—
17	C₄×#709	C₂²	1	1	yes	characteristic
18	C₅×#432	C₂²	1	1	yes	characteristic
19	C₅×#431	C₂²	1	1	yes	characteristic
20	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	#65391	—	2	1	no	—
22	#65214	C₂²	1	1	yes	characteristic
23	#65213	C₂²	1	1	yes	characteristic
24	C₄×#681	C₂²	1	1	yes	characteristic
25	#65128	—	2	1	no	—
26	#65128	—	2	1	no	—
27	#65126	C₂²	1	1	yes	characteristic
28	#65126	C₂²	1	1	yes	characteristic
29	#65126	C₂²	1	1	yes	characteristic
30	#65125	C₄	1	1	yes	characteristic
31	#65125	C₄	1	1	yes	characteristic
32	#65124	C₂²	1	1	yes	characteristic
33	#65122	C₂²	1	1	yes	characteristic
34	D₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	D₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
36	D₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	#65117	C₄	1	1	yes	characteristic
38	#65117	C₄	1	1	yes	characteristic
39	#65018	C₄	1	1	yes	characteristic
40	#65018	C₄	1	1	yes	characteristic
41	#65017	C₄	1	1	yes	characteristic
42	#65017	C₄	1	1	yes	characteristic
43	#65016	—	2	1	no	—
44	#65009	—	2	1	no	—
45	#64998	—	2	1	no	—
46	#64997	—	2	1	no	—
47	C₄×#676	C₂²	1	1	yes	characteristic
48	#64974	C₂²	1	1	yes	characteristic
49	#64974	C₂²	1	1	yes	characteristic
50	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
51	C₅×#335	C₂²	1	1	yes	characteristic
52	C₅×#335	C₂²	1	1	yes	characteristic
53	C₅×#334	C₂²	1	1	yes	characteristic
54	C₅×#334	C₂²	1	1	yes	characteristic
55	#64700	C₂²	1	1	yes	characteristic
56	#64700	C₂²	1	1	yes	characteristic
57	#64700	C₂²	1	1	yes	characteristic
58	#64700	C₂²	1	1	yes	characteristic
59	#64699	C₂²	1	1	yes	characteristic
60	#64699	C₂²	1	1	yes	characteristic
61	#64699	C₂²	1	1	yes	characteristic
62	#64699	C₂²	1	1	yes	characteristic
63	#64678	C₂²	1	1	yes	characteristic
64	#64678	C₂²	1	1	yes	characteristic
65	#64677	C₂²	1	1	yes	characteristic
66	#64677	C₂²	1	1	yes	characteristic
67	#17830	—	5	1	no	maximal, Sylow
68	C₂×#709	D₄	1	1	yes	characteristic
69	C₂²×C₅×C₈	—	2	1	no	—
70	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
71	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
72	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
73	C₄×C₂²⋊D₅	Q₈	1	1	yes	characteristic
74	C₄×C₂²⋊D₅	Q₈	1	1	yes	characteristic
75	#4072	D₄	1	1	yes	characteristic
76	C₂×#681	—	2	1	no	—
77	C₂×#681	C₂×C₄	1	1	yes	characteristic
78	C₂×#681	C₂×C₄	1	1	yes	characteristic
79	#4047	—	4	4	no	—
80	C₂×#676	—	2	1	no	—
81	C₂×#676	—	2	1	no	—
82	C₂×#676	—	2	1	no	—
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	C₂×C₄	1	1	yes	characteristic
89	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
90	C₄×D₂₀	C₂×C₄	1	1	yes	characteristic
91	C₄×D₂₀	Q₈	1	1	yes	characteristic
92	#4018	D₄	1	1	yes	characteristic
93	#4018	D₄	1	1	yes	characteristic
94	C₄²×D₅	C₂³	1	1	yes	characteristic
95	C₄²×D₅	C₂³	1	1	yes	characteristic
96	C₄×Dic₁₀	C₂×C₄	1	1	yes	characteristic
97	C₄×Dic₁₀	Q₈	1	1	yes	characteristic
98	C₅×C₄⋊C₈	—	2	1	no	—
99	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
100	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
101	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
102	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
103	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
104	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
105	C₅×C₂²⋊C₈	—	2	1	no	—
106	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
107	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
108	C₅×#97	—	2	1	no	—
109	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
110	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
111	C₂²⋊#168	—	2	1	no	—
112	#3952	—	2	1	no	—
113	#3952	—	2	1	no	—
114	#3952	C₂×C₄	1	1	yes	characteristic
115	#3952	C₂×C₄	1	1	yes	characteristic
116	#3952	C₂×C₄	1	1	yes	characteristic
117	#3952	C₂×C₄	1	1	yes	characteristic
118	#3947	—	2	1	no	—
119	#3947	C₂×C₄	1	1	yes	characteristic
120	#3947	C₂×C₄	1	1	yes	characteristic
121	#3946	—	2	1	no	—
122	#3946	—	2	1	no	—
123	#3946	—	2	1	no	—
124	#3946	—	2	1	no	—
125	#3946	—	2	1	no	—
126	#3946	—	2	1	no	—
127	#3946	C₂×C₄	1	1	yes	characteristic
128	#3946	C₂×C₄	1	1	yes	characteristic
129	#3946	C₂×C₄	1	1	yes	characteristic
130	#3946	C₂×C₄	1	1	yes	characteristic
131	C₈×Dic₅	—	2	1	no	—
132	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
133	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
134	C₄⋊#168	—	2	1	no	—
135	C₄⋊#168	C₂³	1	1	yes	characteristic
136	C₄⋊#168	C₂³	1	1	yes	characteristic
137	C₄⋊#168	C₂³	1	1	yes	characteristic
138	C₄⋊#168	C₂³	1	1	yes	characteristic
139	#3935	C₂×C₄	1	1	yes	characteristic
140	#3935	C₂×C₄	1	1	yes	characteristic
141	C₄×#168	—	2	1	no	—
142	C₄×#168	C₂³	1	1	yes	characteristic
143	C₄×#168	C₂³	1	1	yes	characteristic
144	#2965	—	5	1	no	—
145	#2925	—	5	1	no	—
146	#2906	—	5	1	no	—
147	#1574	—	5	1	no	—
148	#1574	—	5	1	no	—
149	#1573	—	5	1	no	—
150	#1573	D₅	1	1	yes	characteristic, complemented
151	#1571	—	5	1	no	—
152	#1570	—	5	1	no	—
153	#1569	—	5	1	no	—
154	#1569	—	5	1	no	—
155	#1567	—	5	1	no	—
156	#1565	—	5	1	no	—
157	#1565	—	5	1	no	—
158	C₂×#334	—	5	1	no	—
159	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
162	C₂×C₂²⋊D₅	C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₂²⋊D₅	C₄⋊C₄	1	1	yes	characteristic
164	#709	—	2	2	no	—
165	#709	—	2	2	no	—
166	C₂×D₂₀	C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
170	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
171	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
172	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
173	C₂×Dic₁₀	C₄⋊C₄	1	1	yes	characteristic
174	C₂×C₅×C₈	—	2	1	no	—
175	C₂×C₅×C₈	—	2	1	no	—
176	C₂×C₅×C₈	—	2	1	no	—
177	C₂×C₅×C₈	—	2	1	no	—
178	C₂×C₅×C₈	—	4	2	no	—
179	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
181	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
182	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
183	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
184	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
185	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
186	C₄²×C₅	C₂⁴	1	1	yes	characteristic
187	C₂²⋊Dic₅	C₄⋊C₄	1	1	yes	characteristic
188	C₂²⋊Dic₅	C₄⋊C₄	1	1	yes	characteristic
189	#685	C₄⋊C₄	1	1	yes	characteristic
190	#685	C₄⋊C₄	1	1	yes	characteristic
191	#685	C₄⋊C₄	1	1	yes	characteristic
192	#685	C₄⋊C₄	1	1	yes	characteristic
193	C₄⋊Dic₅	C₄⋊C₄	1	1	yes	characteristic
194	C₄⋊Dic₅	C₄⋊C₄	1	1	yes	characteristic
195	#683	C₄⋊C₄	1	1	yes	characteristic
196	#683	C₄⋊C₄	1	1	yes	characteristic
197	#683	C₄⋊C₄	1	1	yes	characteristic
198	#683	C₄⋊C₄	1	1	yes	characteristic
199	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
200	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
201	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
202	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
203	C₄×Dic₅	C₂×Q₈	1	1	yes	characteristic
204	C₄×Dic₅	C₂×Q₈	1	1	yes	characteristic
205	#681	—	2	2	no	—
206	#681	—	4	1	no	—
207	#681	—	4	2	no	—
208	C₂×#168	—	2	1	no	—
209	C₂×#168	—	2	1	no	—
210	C₂×#168	—	2	1	no	—
211	C₂×#168	—	2	1	no	—
212	C₂×#168	C₂²×C₄	1	1	yes	characteristic
213	C₂×#168	C₂²×C₄	1	1	yes	characteristic
214	C₂×#168	C₂²×C₄	1	1	yes	characteristic
215	C₂×#168	C₂²×C₄	1	1	yes	characteristic
216	#676	—	2	2	no	—
217	#676	—	4	1	no	—
218	#676	—	4	2	no	—
219	#676	—	4	2	no	—
220	#676	—	4	2	no	—
221	C₈×D₅	—	2	2	no	—
222	C₈×D₅	—	4	1	no	—
223	C₈×D₅	—	4	2	no	—
224	C₈×D₅	—	4	2	no	—
225	C₈×D₅	—	4	2	no	—
226	C₂×#131	—	10	1	no	—
227	C₄×#41	—	5	1	no	—
228	#446	—	5	1	no	—
229	#446	—	5	1	no	—
230	#436	—	5	1	no	—
231	#436	—	5	1	no	—
232	#435	—	5	1	no	—
233	#435	—	5	1	no	—
234	#435	—	5	1	no	—
235	#435	—	5	1	no	—
236	#433	—	10	1	no	—
237	#433	—	10	1	no	—
238	#432	—	5	1	no	—
239	#432	C₂×D₅	1	1	yes	characteristic
240	#431	—	5	1	no	—
241	#431	—	5	1	no	—
242	#431	—	5	1	no	—
243	#431	—	5	1	no	—
244	#431	C₂×D₅	1	1	yes	characteristic
245	#424	—	10	1	no	—
246	#424	—	10	1	no	—
247	#424	—	10	1	no	—
248	#423	—	5	1	no	—
249	#423	—	5	1	no	—
250	#423	—	5	1	no	—
251	#423	—	5	1	no	—
252	C₂×C₄⋊C₈	—	5	1	no	—
253	C₂×C₄⋊C₈	—	5	1	no	—
254	C₂×C₄⋊C₈	—	5	1	no	—
255	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
256	#408	—	10	1	no	—
257	#405	—	10	1	no	—
258	C₄×M₁₆	—	5	1	no	—
259	C₄×M₁₆	—	5	1	no	—
260	C₂×C₄×C₈	—	5	1	no	—
261	#335	—	5	1	no	—
262	#335	—	5	1	no	—
263	#335	—	5	1	no	—
264	#335	—	5	1	no	—
265	#335	—	5	1	no	—
266	#335	—	5	1	no	—
267	#335	C₂×D₅	1	1	yes	characteristic
268	#335	C₂×D₅	1	1	yes	characteristic
269	#334	—	5	1	no	—
270	#334	—	5	1	no	—
271	#334	—	5	1	no	—
272	#334	—	5	1	no	—
273	#334	—	5	1	no	—
274	#334	—	5	1	no	—
275	#334	C₂×D₅	1	1	yes	characteristic
276	#334	C₂×D₅	1	1	yes	characteristic
277	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
278	C₂²×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
279	C₂²×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
280	C₂×C₄×C₅	—	2	1	no	—
281	C₂×C₄×C₅	—	2	1	no	—
282	C₂×C₄×C₅	—	2	1	no	—
283	C₂×C₄×C₅	—	2	1	no	—
284	C₂×C₄×C₅	—	4	1	no	—
285	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
286	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
287	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
288	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
289	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
290	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
291	C₂²⋊D₅	—	2	2	no	—
292	C₂²⋊D₅	—	2	2	no	—
293	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
294	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
295	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
296	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
297	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
298	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
299	D₂₀	—	2	2	no	—
300	C₄×D₅	—	2	1	no	—
301	C₄×D₅	—	2	1	no	—
302	C₄×D₅	—	2	1	no	—
303	C₄×D₅	—	2	1	no	—
304	C₄×D₅	—	2	1	no	—
305	C₄×D₅	—	2	1	no	—
306	C₄×D₅	—	4	1	no	—
307	C₄×D₅	—	4	1	no	—
308	C₄×D₅	AGL(1,ℤ/8)	1	2	yes	—
309	C₄×D₅	#137	1	2	yes	—
310	Dic₁₀	—	2	2	no	—
311	C₅×C₈	—	2	1	no	—
312	C₅×C₈	—	2	1	no	—
313	C₅×C₈	—	2	1	no	—
314	C₅×C₈	—	2	1	no	—
315	C₅×C₈	—	4	1	no	—
316	C₅×C₈	—	4	1	no	—
317	C₅×C₈	—	4	1	no	—
318	C₅×C₈	—	4	1	no	—
319	#168	—	2	1	no	—
320	#168	—	2	1	no	—
321	#168	—	2	1	no	—
322	#168	—	4	1	no	—
323	#168	—	4	1	no	—
324	#168	—	4	1	no	—
325	#168	—	4	1	no	—
326	#168	#131	1	2	yes	complemented
327	C₂×#41	—	5	1	no	—
328	#131	—	20	4	no	—
329	C₂×M₁₆	—	5	1	no	—
330	C₂×M₁₆	—	5	1	no	—
331	C₂×M₁₆	—	5	1	no	—
332	C₂×M₁₆	—	5	1	no	—
333	C₂×M₁₆	—	10	1	no	—
334	C₂×M₁₆	—	10	1	no	—
335	C₂×M₁₆	—	10	1	no	—
336	C₂×M₁₆	—	10	1	no	—
337	C₂²×C₈	—	2	1	no	—
338	C₂²×C₈	—	5	1	no	—
339	C₂²×C₈	—	5	1	no	—
340	C₂²×C₈	—	10	1	no	—
341	C₂²×C₈	—	10	1	no	—
342	C₂²×C₈	—	10	1	no	—
343	C₄×Q₈	—	5	1	no	—
344	C₄×Q₈	—	5	1	no	—
345	C₄×D₄	—	5	1	no	—
346	C₄×D₄	—	5	1	no	—
347	C₄×D₄	—	5	1	no	—
348	C₄×D₄	—	5	1	no	—
349	C₄×D₄	—	5	1	no	—
350	C₄×D₄	—	5	1	no	—
351	#117	—	5	1	no	—
352	#117	—	5	1	no	—
353	#117	—	5	1	no	—
354	C₂×C₄²	—	5	1	no	—
355	C₂×C₄²	—	5	1	no	—
356	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
357	C₄⋊C₈	—	2	1	no	—
358	C₄⋊C₈	—	5	1	no	—
359	C₄⋊C₈	—	5	1	no	—
360	C₄⋊C₈	—	5	1	no	—
361	C₄⋊C₈	—	5	1	no	—
362	C₄⋊C₈	—	5	1	no	—
363	C₄⋊C₈	—	5	1	no	—
364	C₄⋊C₈	—	5	1	no	—
365	C₄⋊C₈	—	5	1	no	—
366	C₄⋊C₈	—	10	1	no	—
367	C₄⋊C₈	—	10	1	no	—
368	C₄⋊C₈	—	10	1	no	—
369	C₄⋊C₈	—	10	1	no	—
370	C₄⋊C₈	—	10	1	no	—
371	C₄⋊C₈	—	10	1	no	—
372	C₄⋊C₈	—	10	1	no	—
373	C₄⋊C₈	C₄×D₅	1	1	yes	characteristic
374	C₄⋊C₈	C₄×D₅	1	1	yes	characteristic
375	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
376	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
377	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
378	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
379	C₂²⋊C₈	—	2	1	no	—
380	C₂²⋊C₈	—	5	1	no	—
381	C₂²⋊C₈	—	5	1	no	—
382	C₂²⋊C₈	—	5	1	no	—
383	C₂²⋊C₈	—	5	1	no	—
384	C₂²⋊C₈	—	10	1	no	—
385	C₂²⋊C₈	—	10	1	no	—
386	C₂²⋊C₈	—	10	1	no	—
387	C₂²⋊C₈	C₄×D₅	1	1	yes	characteristic
388	C₂²⋊C₈	C₄×D₅	1	1	yes	characteristic
389	#97	—	2	1	no	—
390	#97	—	5	1	no	—
391	#97	—	5	1	no	—
392	#97	—	5	1	no	—
393	#97	—	5	1	no	—
394	#97	—	10	1	no	—
395	C₄×C₈	—	5	1	no	—
396	C₄×C₈	—	5	1	no	—
397	C₄×C₈	—	5	1	no	—
398	C₄×C₈	—	5	1	no	—
399	C₄×C₈	—	10	1	no	—
400	C₄×C₈	—	10	1	no	—
401	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
402	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
403	C₂²×C₅	—	2	1	no	—
404	C₂²×C₅	—	2	1	no	—
405	C₂²×C₅	—	2	1	no	—
406	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
407	C₂×D₅	—	2	1	no	—
408	C₂×D₅	—	2	1	no	—
409	C₂×D₅	—	2	1	no	—
410	C₂×D₅	—	2	1	no	—
411	C₂×D₅	—	2	1	no	—
412	C₂×D₅	#428	1	2	yes	—
413	C₄×C₅	—	2	1	no	—
414	C₄×C₅	—	2	1	no	—
415	C₄×C₅	—	2	1	no	—
416	C₄×C₅	—	2	1	no	—
417	C₄×C₅	C₂×#131	1	1	yes	characteristic
418	C₄×C₅	#568	1	1	yes	characteristic
419	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
420	C₄×C₅	C₂×#137	1	1	yes	characteristic
421	Dic₅	—	2	1	no	—
422	Dic₅	—	2	1	no	—
423	Dic₅	—	2	1	no	—
424	Dic₅	—	2	1	no	—
425	Dic₅	—	2	1	no	—
426	Dic₅	#428	1	2	yes	—
427	#41	—	10	2	no	—
428	#41	—	10	2	no	—
429	C₂×Q₈	—	5	1	no	—
430	C₂×D₄	—	5	1	no	—
431	C₂×D₄	—	5	1	no	—
432	C₂×D₄	—	5	1	no	—
433	C₂²×C₄	—	5	1	no	—
434	C₂²×C₄	—	5	1	no	—
435	C₂²×C₄	—	5	1	no	—
436	C₂²×C₄	—	5	1	no	—
437	C₂²×C₄	—	5	1	no	—
438	C₂²×C₄	—	5	1	no	—
439	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
440	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
441	C₂²×C₄	Q₈×D₅	1	1	yes	characteristic
442	M₁₆	—	10	2	no	—
443	M₁₆	—	10	2	no	—
444	M₁₆	—	20	1	no	—
445	M₁₆	—	20	2	no	—
446	M₁₆	—	20	2	no	—
447	M₁₆	—	20	2	no	—
448	M₁₆	—	20	1	no	—
449	M₁₆	—	20	2	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	4	2	no	—
455	C₂×C₈	—	5	1	no	—
456	C₂×C₈	—	5	1	no	—
457	C₂×C₈	—	5	1	no	—
458	C₂×C₈	—	5	1	no	—
459	C₂×C₈	—	10	2	no	—
460	C₂×C₈	—	10	1	no	—
461	C₂×C₈	—	10	1	no	—
462	C₂×C₈	—	10	1	no	—
463	C₂×C₈	—	10	1	no	—
464	C₂×C₈	—	20	1	no	—
465	C₂×C₈	—	20	2	no	—
466	C₂×C₈	—	20	2	no	—
467	C₂×C₈	—	20	2	no	—
468	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
469	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
470	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
471	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
472	C₄⋊C₄	—	5	1	no	—
473	C₄⋊C₄	—	5	1	no	—
474	C₄⋊C₄	—	5	1	no	—
475	C₄⋊C₄	—	5	1	no	—
476	C₄⋊C₄	—	5	1	no	—
477	C₄⋊C₄	—	5	1	no	—
478	C₂²⋊C₄	—	5	1	no	—
479	C₂²⋊C₄	—	5	1	no	—
480	C₂²⋊C₄	—	5	1	no	—
481	C₂²⋊C₄	—	5	1	no	—
482	C₂²⋊C₄	—	5	1	no	—
483	C₂²⋊C₄	—	5	1	no	—
484	C₄²	—	5	1	no	—
485	C₄²	—	5	1	no	—
486	C₄²	—	5	1	no	—
487	C₄²	—	5	1	no	—
488	C₄²	—	5	1	no	—
489	C₄²	—	5	1	no	—
490	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
491	C₄²	D₄×D₅	1	1	yes	characteristic
492	C₄²	Q₈×D₅	1	1	yes	characteristic
493	C₄²	C₂³×D₅	1	1	yes	characteristic
494	C₂×C₅	—	4	1	no	—
495	C₂×C₅	#2906	1	1	yes	characteristic
496	C₂×C₅	C₂×#428	1	1	yes	characteristic
497	C₂×C₅	#2916	1	1	yes	characteristic
498	D₅	—	2	2	no	—
499	D₅	—	4	1	no	—
500	C₂³	—	5	1	no	—
501	C₂³	—	5	1	no	—
502	C₂³	D₅×C₄⋊C₄	1	1	yes	characteristic
503	Q₈	—	10	2	no	—
504	D₄	—	10	2	no	—
505	D₄	—	10	2	no	—
506	D₄	—	10	2	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	5	1	no	—
513	C₂×C₄	—	5	2	no	—
514	C₂×C₄	—	5	2	no	—
515	C₂×C₄	—	5	1	no	—
516	C₂×C₄	—	5	1	no	—
517	C₂×C₄	—	5	1	no	—
518	C₂×C₄	—	5	1	no	—
519	C₂×C₄	—	5	1	no	—
520	C₂×C₄	—	10	1	no	—
521	C₂×C₄	—	10	1	no	—
522	C₂×C₄	—	10	1	no	—
523	C₂×C₄	—	10	1	no	—
524	C₂×C₄	—	10	1	no	—
525	C₂×C₄	—	10	1	no	—
526	C₂×C₄	—	20	1	no	—
527	C₂×C₄	—	20	1	no	—
528	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
529	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
530	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
531	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
532	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
533	C₂×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
534	C₈	—	2	1	no	—
535	C₈	—	2	1	no	—
536	C₈	—	2	1	no	—
537	C₈	—	2	1	no	—
538	C₈	—	4	1	no	—
539	C₈	—	4	1	no	—
540	C₈	—	4	1	no	—
541	C₈	—	4	1	no	—
542	C₈	—	5	2	no	—
543	C₈	—	10	1	no	—
544	C₈	—	10	1	no	—
545	C₈	—	10	1	no	—
546	C₈	—	20	1	no	—
547	C₈	—	20	1	no	—
548	C₈	—	20	1	no	—
549	C₈	—	20	1	no	—
550	C₅	#17830	1	1	yes	characteristic, complemented, Sylow
551	C₂²	—	2	1	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	2	1	no	—
554	C₂²	—	5	2	no	—
555	C₂²	—	10	1	no	—
556	C₂²	—	10	1	no	—
557	C₂²	—	10	1	no	—
558	C₂²	—	10	1	no	—
559	C₂²	—	10	1	no	—
560	C₂²	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	2	1	no	—
564	C₄	—	2	1	no	—
565	C₄	—	5	2	no	—
566	C₄	—	10	1	no	—
567	C₄	—	10	1	no	—
568	C₄	—	10	1	no	—
569	C₄	—	10	1	no	—
570	C₄	—	10	1	no	—
571	C₄	D₅×#131	1	1	yes	characteristic
572	C₄	#66084	1	1	yes	characteristic
573	C₄	D₅×AGL(1,ℤ/8)	1	1	yes	characteristic
574	C₄	D₅×#137	1	1	yes	characteristic
575	C₂	—	4	1	no	—
576	C₂	—	10	2	no	—
577	C₂	—	20	1	no	—
578	C₂	#10610812	1	1	yes	characteristic
579	C₂	D₅×#428	1	1	yes	characteristic
580	C₂	#10610983	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×#1573	C₂
socle	C₂²×C₅	C₂²×C₄⋊C₄
prime radical	C₂×#709	D₄
cosocle	C₄²×C₅	C₂⁴
hypercenter	#1573	D₅
hypocenter	C₅	#17830
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1573

Complements

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

N	H ≅ G/N	type
4. C₅×#1573	C₂	semidirect
5. #10601588	C₂	semidirect
6. #10601546	C₂	semidirect
7. #10601213	C₂	semidirect
8. #10599368	C₂	semidirect
9. #10599365	C₂	semidirect
10. #10599362	C₂	semidirect
11. #10599361	C₂	semidirect
12. #10599327	C₂	semidirect
13. #10599325	C₂	semidirect
14. #10599324	C₂	semidirect
15. D₅×#334	C₂	semidirect
150. #1573	D₅	semidirect
326. #168	#131	semidirect
550. C₅	#17830	semidirect

Maximal subgroups

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

subgroup	index
#10611065	2
#10611009	2
#10610743	2
C₅×#1573	2
#10601588	2
#10601546	2
#10601213	2
#10599368	2
#10599365	2
#10599362	2
#10599361	2
#10599327	2
#10599325	2
#10599324	2
D₅×#334	2
#17830	5