Subgroups — C₄×C₅×#473 #11944274

Order 1280.

882 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	C₂×C₅×#473	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×#137	C₂	1	2	yes	maximal
3	C₂×C₄×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₅×#131	C₂	1	1	yes	maximal, characteristic
5	C₅×#1979	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1952	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1930	C₂	1	2	yes	maximal, complemented
8	C₅×#1908	C₂	1	2	yes	maximal
9	C₅×#1816	C₂	1	1	yes	maximal, characteristic
10	C₄×C₅×#108	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×#101	C₂	1	2	yes	maximal, complemented
12	C₂×C₅×#137	C₂²	1	2	yes	—
13	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₅×#131	C₂²	1	1	yes	characteristic
15	C₂×C₅×#131	C₂²	1	1	yes	characteristic
16	C₄×C₅×#41	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
18	C₅×#473	C₄	1	8	yes	direct product factor
19	C₅×#441	—	2	2	no	—
20	C₅×#440	—	2	2	no	—
21	C₄×C₅×Q₁₆	—	2	1	no	—
22	C₄×C₅×Q₁₆	—	2	1	no	—
23	C₄×C₅×Q₁₆	—	2	1	no	—
24	C₄×C₅×Q₁₆	—	2	1	no	—
25	C₄×C₅×Q₁₆	—	2	2	no	—
26	C₄×C₅×SD₁₆	—	2	2	no	—
27	C₂×C₅×#108	C₂²	1	1	yes	characteristic
28	C₂×C₅×#108	C₂²	1	1	yes	characteristic
29	C₅×#428	C₂²	1	2	yes	—
30	C₂×C₅×#107	C₂²	1	1	yes	characteristic
31	C₅×#419	C₂²	1	2	yes	—
32	C₅×#417	C₂²	1	2	yes	—
33	C₂×C₅×#103	C₂²	1	2	yes	—
34	C₂×C₅×#101	C₂²	1	2	yes	—
35	C₂×C₅×#101	C₂²	1	2	yes	—
36	C₅×#405	—	2	1	no	—
37	C₅×#405	—	2	1	no	—
38	C₅×#405	C₂²	1	1	yes	characteristic
39	C₅×#405	C₂²	1	1	yes	characteristic
40	C₄×C₅×M₁₆	—	2	1	no	—
41	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
42	C₄×C₅×M₁₆	C₂²	1	2	yes	—
43	C₂×C₄×C₅×C₈	—	2	1	no	—
44	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
45	C₅×#343	C₂²	1	2	yes	—
46	C₅×#343	C₂²	1	2	yes	—
47	C₅×#341	C₂²	1	2	yes	—
48	C₄×#473	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
49	C₂×C₅×#41	C₂³	1	1	yes	characteristic
50	C₂²×C₅×Q₈	C₂³	1	2	yes	—
51	C₅×#137	—	2	4	no	—
52	C₅×#137	C₂×C₄	1	8	yes	—
53	C₂×C₅×Q₁₆	—	2	2	no	—
54	C₂×C₅×Q₁₆	—	2	1	no	—
55	C₂×C₅×Q₁₆	—	2	1	no	—
56	C₂×C₅×Q₁₆	—	2	2	no	—
57	C₂×C₅×Q₁₆	C₂×C₄	1	4	yes	complemented
58	C₂×C₅×SD₁₆	—	2	2	no	—
59	C₅×#131	—	2	2	no	—
60	C₅×#131	—	2	2	no	—
61	C₅×#131	—	2	2	no	—
62	C₅×#131	C₂×C₄	1	4	yes	—
63	C₂×C₅×M₁₆	—	2	1	no	—
64	C₂×C₅×M₁₆	—	2	1	no	—
65	C₂×C₅×M₁₆	C₂³	1	2	yes	—
66	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
67	C₂×C₅×M₁₆	C₂³	1	2	yes	—
68	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
69	C₂²×C₅×C₈	—	2	1	no	—
70	C₂²×C₅×C₈	—	2	1	no	—
71	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
72	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
73	C₄×C₅×Q₈	—	2	2	no	—
74	C₄×C₅×Q₈	—	2	2	no	—
75	C₄×C₅×Q₈	—	2	2	no	—
76	C₄×C₅×Q₈	—	2	2	no	—
77	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
78	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
79	C₄×C₅×D₄	—	2	1	no	—
80	C₄×C₅×D₄	—	2	1	no	—
81	C₄×C₅×D₄	D₄	1	1	yes	characteristic
82	C₄×C₅×D₄	D₄	1	1	yes	characteristic
83	C₅×#117	—	2	1	no	—
84	C₅×#117	C₂³	1	1	yes	characteristic
85	C₂×C₅×C₄⋊C₄	—	2	2	no	—
86	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
87	C₂×C₄²×C₅	—	2	1	no	—
88	C₂×C₄²×C₅	—	2	2	no	—
89	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
90	C₅×#108	—	2	2	no	—
91	C₅×#108	C₂×C₄	1	4	yes	complemented
92	C₅×#107	—	2	1	no	—
93	C₅×#107	—	2	1	no	—
94	C₅×#107	—	2	2	no	—
95	C₅×#106	—	2	2	no	—
96	C₅×#103	—	2	2	no	—
97	C₅×#103	—	2	2	no	—
98	C₅×#103	—	2	2	no	—
99	C₅×#103	—	2	2	no	—
100	C₅×#103	—	2	2	no	—
101	C₅×#102	—	2	2	no	—
102	C₅×#101	—	2	4	no	—
103	C₅×#101	C₂×C₄	1	8	yes	complemented
104	C₅×#97	—	2	1	no	—
105	C₅×#97	—	2	1	no	—
106	C₅×#97	—	2	1	no	—
107	C₅×#97	—	2	2	no	—
108	C₄×C₅×C₈	—	2	1	no	—
109	C₄×C₅×C₈	—	2	1	no	—
110	C₄×C₅×C₈	—	2	1	no	—
111	C₄×C₅×C₈	—	2	2	no	—
112	C₄×C₅×C₈	D₄	1	1	yes	characteristic
113	C₄×C₅×C₈	D₄	1	1	yes	characteristic
114	C₄×C₅×C₈	D₄	1	1	yes	characteristic
115	C₄×C₅×C₈	D₄	1	1	yes	characteristic
116	C₂×#473	C₂×C₅	1	1	yes	characteristic
117	C₄×#137	C₂×C₅	1	2	yes	—
118	C₂×C₄×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
119	C₄×#131	C₂×C₅	1	1	yes	characteristic
120	#1979	C₂×C₅	1	1	yes	characteristic, complemented
121	#1952	C₂×C₅	1	1	yes	characteristic, complemented
122	#1930	C₂×C₅	1	2	yes	complemented
123	#1908	C₂×C₅	1	2	yes	—
124	#1816	C₂×C₅	1	1	yes	characteristic
125	C₄×#108	C₂×C₅	1	1	yes	characteristic, complemented
126	C₄×#101	C₂×C₅	1	2	yes	complemented
127	C₅×#41	—	2	1	no	—
128	C₅×#41	—	2	1	no	—
129	C₅×#41	C₂²×C₄	1	2	yes	—
130	C₅×#41	#41	1	2	yes	—
131	C₂×C₅×Q₈	—	2	2	no	—
132	C₂×C₅×Q₈	—	2	2	no	—
133	C₂×C₅×Q₈	—	2	2	no	—
134	C₂×C₅×Q₈	—	2	2	no	—
135	C₂×C₅×Q₈	—	2	2	no	—
136	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
137	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
138	C₂×C₅×D₄	—	2	1	no	—
139	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₅	—	2	1	no	—
141	C₂²×C₄×C₅	—	2	2	no	—
142	C₂²×C₄×C₅	—	2	1	no	—
143	C₂²×C₄×C₅	—	2	1	no	—
144	C₂²×C₄×C₅	—	2	2	no	—
145	C₂²×C₄×C₅	#41	1	1	yes	characteristic
146	C₂²×C₄×C₅	#41	1	1	yes	characteristic
147	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
148	C₅×Q₁₆	—	2	8	no	—
149	C₅×Q₁₆	—	2	4	no	—
150	C₅×Q₁₆	—	2	4	no	—
151	C₅×SD₁₆	—	2	8	no	—
152	C₅×M₁₆	—	2	4	no	—
153	C₅×M₁₆	—	2	1	no	—
154	C₅×M₁₆	—	2	1	no	—
155	C₅×M₁₆	—	2	2	no	—
156	C₅×M₁₆	—	2	4	no	—
157	C₅×M₁₆	—	2	2	no	—
158	C₅×M₁₆	—	2	2	no	—
159	C₅×M₁₆	C₂²×C₄	1	2	yes	—
160	C₅×M₁₆	C₂²×C₄	1	4	yes	—
161	C₅×M₁₆	#41	1	2	yes	—
162	C₂×C₅×C₈	—	2	4	no	—
163	C₂×C₅×C₈	—	2	1	no	—
164	C₂×C₅×C₈	—	2	1	no	—
165	C₂×C₅×C₈	—	2	2	no	—
166	C₂×C₅×C₈	—	2	1	no	—
167	C₂×C₅×C₈	—	2	1	no	—
168	C₂×C₅×C₈	—	2	4	no	—
169	C₂×C₅×C₈	—	2	2	no	—
170	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
171	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
172	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
173	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
174	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
175	C₂×C₅×C₈	#41	1	2	yes	—
176	C₅×C₄⋊C₄	—	2	1	no	—
177	C₅×C₄⋊C₄	—	2	1	no	—
178	C₅×C₄⋊C₄	—	2	2	no	—
179	C₅×C₄⋊C₄	—	2	2	no	—
180	C₅×C₄⋊C₄	—	4	2	no	—
181	C₅×C₄⋊C₄	—	4	2	no	—
182	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
183	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
184	C₅×C₂²⋊C₄	—	2	1	no	—
185	C₅×C₂²⋊C₄	—	2	1	no	—
186	C₅×C₂²⋊C₄	—	2	1	no	—
187	C₄²×C₅	—	2	1	no	—
188	C₄²×C₅	—	2	1	no	—
189	C₄²×C₅	—	2	1	no	—
190	C₄²×C₅	—	4	2	no	—
191	C₄²×C₅	—	4	2	no	—
192	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
193	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
194	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
195	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
196	C₂×#137	C₂²×C₅	1	2	yes	—
197	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
198	C₂×#131	C₂²×C₅	1	1	yes	characteristic
199	C₂×#131	C₂²×C₅	1	1	yes	characteristic
200	C₄×#41	C₂²×C₅	1	1	yes	characteristic
201	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
202	#473	C₄×C₅	1	8	yes	direct product factor
203	#441	—	2	2	no	—
204	#440	—	2	2	no	—
205	C₄×Q₁₆	—	2	2	no	—
206	C₄×Q₁₆	—	2	1	no	—
207	C₄×Q₁₆	—	2	1	no	—
208	C₄×Q₁₆	—	2	1	no	—
209	C₄×Q₁₆	—	2	1	no	—
210	C₄×SD₁₆	—	2	2	no	—
211	C₂×#108	C₂²×C₅	1	1	yes	characteristic
212	C₂×#108	C₂²×C₅	1	1	yes	characteristic
213	#428	C₂²×C₅	1	2	yes	—
214	C₂×#107	C₂²×C₅	1	1	yes	characteristic
215	#419	C₂²×C₅	1	2	yes	—
216	#417	C₂²×C₅	1	2	yes	—
217	C₂×#103	C₂²×C₅	1	2	yes	—
218	C₂×#101	C₂²×C₅	1	2	yes	—
219	C₂×#101	C₂²×C₅	1	2	yes	—
220	#405	—	2	1	no	—
221	#405	—	2	1	no	—
222	#405	C₂²×C₅	1	1	yes	characteristic
223	#405	C₂²×C₅	1	1	yes	characteristic
224	C₄×M₁₆	—	2	1	no	—
225	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
226	C₄×M₁₆	C₂²×C₅	1	2	yes	—
227	C₂×C₄×C₈	—	2	1	no	—
228	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
229	#343	C₂²×C₅	1	2	yes	—
230	#343	C₂²×C₅	1	2	yes	—
231	#341	C₂²×C₅	1	2	yes	—
232	C₂³×C₅	—	2	1	no	—
233	C₂³×C₅	C₂×#41	1	1	yes	characteristic
234	C₅×Q₈	—	2	1	no	—
235	C₅×Q₈	—	2	4	no	—
236	C₅×Q₈	—	2	4	no	—
237	C₅×Q₈	—	4	2	no	—
238	C₅×Q₈	—	4	2	no	—
239	C₅×Q₈	C₄×D₄	1	2	yes	—
240	C₅×D₄	—	2	2	no	—
241	C₅×D₄	—	2	2	no	—
242	C₅×D₄	—	2	1	no	—
243	C₅×D₄	C₄×D₄	1	2	yes	—
244	C₂×C₄×C₅	—	2	1	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	2	2	no	—
248	C₂×C₄×C₅	—	2	4	no	—
249	C₂×C₄×C₅	—	2	1	no	—
250	C₂×C₄×C₅	—	2	1	no	—
251	C₂×C₄×C₅	—	4	1	no	—
252	C₂×C₄×C₅	—	4	2	no	—
253	C₂×C₄×C₅	—	4	2	no	—
254	C₂×C₄×C₅	—	4	2	no	—
255	C₂×C₄×C₅	—	4	2	no	—
256	C₂×C₄×C₅	—	4	2	no	—
257	C₂×C₄×C₅	—	8	2	no	—
258	C₂×C₄×C₅	#121	1	1	yes	characteristic
259	C₂×C₄×C₅	#121	1	1	yes	characteristic
260	C₂×C₄×C₅	#121	1	1	yes	characteristic
261	C₂×C₄×C₅	#121	1	1	yes	characteristic
262	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
263	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
266	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
267	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
268	C₅×C₈	—	2	2	no	—
269	C₅×C₈	—	2	4	no	—
270	C₅×C₈	—	2	1	no	—
271	C₅×C₈	—	2	2	no	—
272	C₅×C₈	—	2	1	no	—
273	C₅×C₈	—	4	2	no	—
274	C₅×C₈	C₄×D₄	1	2	yes	—
275	C₅×C₈	C₄×D₄	1	2	yes	—
276	C₂×#41	C₂³×C₅	1	1	yes	characteristic
277	C₂²×Q₈	C₂³×C₅	1	2	yes	—
278	#137	—	2	4	no	—
279	#137	C₂×C₄×C₅	1	8	yes	—
280	C₂×Q₁₆	—	2	2	no	—
281	C₂×Q₁₆	—	2	1	no	—
282	C₂×Q₁₆	—	2	1	no	—
283	C₂×Q₁₆	—	2	2	no	—
284	C₂×Q₁₆	C₂×C₄×C₅	1	4	yes	complemented
285	C₂×SD₁₆	—	2	2	no	—
286	#131	—	2	2	no	—
287	#131	—	2	2	no	—
288	#131	—	2	2	no	—
289	#131	C₂×C₄×C₅	1	4	yes	—
290	C₂×M₁₆	—	2	1	no	—
291	C₂×M₁₆	—	2	1	no	—
292	C₂×M₁₆	C₂³×C₅	1	2	yes	—
293	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
294	C₂×M₁₆	C₂³×C₅	1	2	yes	—
295	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
296	C₂²×C₈	—	2	1	no	—
297	C₂²×C₈	—	2	1	no	—
298	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
299	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
300	C₄×Q₈	—	2	2	no	—
301	C₄×Q₈	—	2	2	no	—
302	C₄×Q₈	—	2	2	no	—
303	C₄×Q₈	—	2	2	no	—
304	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
305	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
306	C₄×D₄	—	2	1	no	—
307	C₄×D₄	—	2	1	no	—
308	C₄×D₄	C₅×D₄	1	1	yes	characteristic
309	C₄×D₄	C₅×D₄	1	1	yes	characteristic
310	#117	—	2	1	no	—
311	#117	C₂³×C₅	1	1	yes	characteristic
312	C₂×C₄⋊C₄	—	2	2	no	—
313	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
314	C₂×C₄²	—	2	1	no	—
315	C₂×C₄²	—	2	2	no	—
316	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
317	#108	—	2	2	no	—
318	#108	C₂×C₄×C₅	1	4	yes	complemented
319	#107	—	2	1	no	—
320	#107	—	2	1	no	—
321	#107	—	2	2	no	—
322	#106	—	2	2	no	—
323	#103	—	2	2	no	—
324	#103	—	2	2	no	—
325	#103	—	2	2	no	—
326	#103	—	2	2	no	—
327	#103	—	2	2	no	—
328	#102	—	2	2	no	—
329	#101	—	2	4	no	—
330	#101	C₂×C₄×C₅	1	8	yes	complemented
331	#97	—	2	1	no	—
332	#97	—	2	1	no	—
333	#97	—	2	1	no	—
334	#97	—	2	2	no	—
335	C₄×C₈	—	2	1	no	—
336	C₄×C₈	—	2	1	no	—
337	C₄×C₈	—	2	1	no	—
338	C₄×C₈	—	2	2	no	—
339	C₄×C₈	C₅×D₄	1	1	yes	characteristic
340	C₄×C₈	C₅×D₄	1	1	yes	characteristic
341	C₄×C₈	C₅×D₄	1	1	yes	characteristic
342	C₄×C₈	C₅×D₄	1	1	yes	characteristic
343	C₂²×C₅	—	2	1	no	—
344	C₂²×C₅	—	2	1	no	—
345	C₂²×C₅	—	2	2	no	—
346	C₂²×C₅	—	4	1	no	—
347	C₂²×C₅	—	4	1	no	—
348	C₂²×C₅	C₄×#41	1	1	yes	characteristic
349	C₂²×C₅	C₂×#121	1	1	yes	characteristic
350	C₂²×C₅	#529	1	1	yes	characteristic
351	C₄×C₅	—	2	1	no	—
352	C₄×C₅	—	2	1	no	—
353	C₄×C₅	—	2	1	no	—
354	C₄×C₅	—	2	2	no	—
355	C₄×C₅	—	4	1	no	—
356	C₄×C₅	—	4	1	no	—
357	C₄×C₅	—	4	4	no	—
358	C₄×C₅	—	8	2	no	—
359	C₄×C₅	#473	1	2	yes	direct product factor
360	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
361	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
362	C₄×C₅	#525	1	1	yes	characteristic
363	C₄×C₅	#532	1	1	yes	characteristic
364	#41	—	2	1	no	—
365	#41	—	2	1	no	—
366	#41	C₂²×C₄×C₅	1	2	yes	—
367	#41	C₅×#41	1	2	yes	—
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
374	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	C₅×#41	1	1	yes	characteristic
383	C₂²×C₄	C₅×#41	1	1	yes	characteristic
384	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
385	Q₁₆	—	2	8	no	—
386	Q₁₆	—	2	4	no	—
387	Q₁₆	—	2	4	no	—
388	SD₁₆	—	2	8	no	—
389	M₁₆	—	2	4	no	—
390	M₁₆	—	2	1	no	—
391	M₁₆	—	2	1	no	—
392	M₁₆	—	2	2	no	—
393	M₁₆	—	2	4	no	—
394	M₁₆	—	2	2	no	—
395	M₁₆	—	2	2	no	—
396	M₁₆	C₂²×C₄×C₅	1	2	yes	—
397	M₁₆	C₂²×C₄×C₅	1	4	yes	—
398	M₁₆	C₅×#41	1	2	yes	—
399	C₂×C₈	—	2	4	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	1	no	—
405	C₂×C₈	—	2	4	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
408	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
409	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
410	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
411	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
412	C₂×C₈	C₅×#41	1	2	yes	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	4	2	no	—
418	C₄⋊C₄	—	4	2	no	—
419	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
420	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
421	C₂²⋊C₄	—	2	1	no	—
422	C₂²⋊C₄	—	2	1	no	—
423	C₂²⋊C₄	—	2	1	no	—
424	C₄²	—	2	1	no	—
425	C₄²	—	2	1	no	—
426	C₄²	—	2	1	no	—
427	C₄²	—	4	2	no	—
428	C₄²	—	4	2	no	—
429	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
430	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
431	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
432	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
433	C₂×C₅	—	2	1	no	—
434	C₂×C₅	—	2	1	no	—
435	C₂×C₅	—	4	2	no	—
436	C₂×C₅	C₄×#121	1	1	yes	characteristic
437	C₂×C₅	C₂×#473	1	1	yes	characteristic
438	C₂×C₅	#3067	1	1	yes	characteristic
439	C₂³	—	2	1	no	—
440	C₂³	C₂×C₅×#41	1	1	yes	characteristic
441	Q₈	—	2	1	no	—
442	Q₈	—	2	4	no	—
443	Q₈	—	2	4	no	—
444	Q₈	—	4	2	no	—
445	Q₈	—	4	2	no	—
446	Q₈	C₄×C₅×D₄	1	2	yes	—
447	D₄	—	2	2	no	—
448	D₄	—	2	2	no	—
449	D₄	—	2	1	no	—
450	D₄	C₄×C₅×D₄	1	2	yes	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	8	2	no	—
465	C₂×C₄	C₅×#121	1	1	yes	characteristic
466	C₂×C₄	C₅×#121	1	1	yes	characteristic
467	C₂×C₄	C₅×#121	1	1	yes	characteristic
468	C₂×C₄	C₅×#121	1	1	yes	characteristic
469	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
470	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
471	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
472	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
473	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
474	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
475	C₈	—	2	2	no	—
476	C₈	—	2	4	no	—
477	C₈	—	2	1	no	—
478	C₈	—	2	2	no	—
479	C₈	—	2	1	no	—
480	C₈	—	4	2	no	—
481	C₈	C₄×C₅×D₄	1	2	yes	—
482	C₈	C₄×C₅×D₄	1	2	yes	—
483	C₅	C₄×#473	1	1	yes	characteristic, direct product factor, Sylow
484	C₂²	—	2	1	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	2	2	no	—
487	C₂²	—	4	1	no	—
488	C₂²	—	4	1	no	—
489	C₂²	C₄×C₅×#41	1	1	yes	characteristic
490	C₂²	C₂×C₅×#121	1	1	yes	characteristic
491	C₂²	C₅×#529	1	1	yes	characteristic
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	2	2	no	—
496	C₄	—	4	1	no	—
497	C₄	—	4	1	no	—
498	C₄	—	4	4	no	—
499	C₄	—	8	2	no	—
500	C₄	C₅×#473	1	2	yes	direct product factor
501	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
502	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
503	C₄	C₅×#525	1	1	yes	characteristic
504	C₄	C₅×#532	1	1	yes	characteristic
505	C₂	—	2	1	no	—
506	C₂	—	2	1	no	—
507	C₂	—	4	2	no	—
508	C₂	C₄×C₅×#121	1	1	yes	characteristic
509	C₂	C₂×C₅×#473	1	1	yes	characteristic
510	C₂	C₅×#3067	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	#121
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂²×C₅	C₂×#121
prime radical	C₂×C₅×#41	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×C₅×Q₁₆	C₂	semidirect
5. C₅×#1979	C₂	semidirect
6. C₅×#1952	C₂	semidirect
7. C₅×#1930	C₂	semidirect
10. C₄×C₅×#108	C₂	semidirect
11. C₄×C₅×#101	C₂	semidirect
18. C₅×#473	C₄	direct (N × H)
48. C₄×#473	C₅	direct (N × H)
57. C₂×C₅×Q₁₆	C₂×C₄	semidirect
91. C₅×#108	C₂×C₄	semidirect
103. C₅×#101	C₂×C₄	semidirect
118. C₂×C₄×Q₁₆	C₂×C₅	semidirect
120. #1979	C₂×C₅	semidirect
121. #1952	C₂×C₅	semidirect
122. #1930	C₂×C₅	semidirect
125. C₄×#108	C₂×C₅	semidirect
126. C₄×#101	C₂×C₅	semidirect
202. #473	C₄×C₅	direct (N × H)
284. C₂×Q₁₆	C₂×C₄×C₅	semidirect
318. #108	C₂×C₄×C₅	semidirect
330. #101	C₂×C₄×C₅	semidirect
359. C₄×C₅	#473	direct (N × H)
483. C₅	C₄×#473	direct (N × H)
500. C₄	C₅×#473	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#473	2
C₄×C₅×#137	2
C₂×C₄×C₅×Q₁₆	2
C₄×C₅×#131	2
C₅×#1979	2
C₅×#1952	2
C₅×#1930	2
C₅×#1908	2
C₅×#1816	2
C₄×C₅×#108	2
C₄×C₅×#101	2
C₄×#473	5

Subgroups — C4×C5×#473 #11944274

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×#473 #11944274