Subgroups — C₅×#32872 #11955592

Order 1280.

482 conjugacy classes of subgroups.

The subgroup lattice has 282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2103	C₂	1	2	yes	maximal, complemented
2	C₅×#2098	C₂	1	1	yes	maximal, characteristic
3	C₅×#2082	C₂	1	2	yes	maximal, complemented
4	C₅×#2070	C₂	1	2	yes	maximal, complemented
5	C₅×#2049	C₂	1	2	yes	maximal
6	C₅×#2047	C₂	1	2	yes	maximal, complemented
7	C₅×#2020	C₂	1	1	yes	maximal, characteristic
8	C₅×#1902	C₂	1	2	yes	maximal
9	C₅×#1858	C₂	1	1	yes	maximal, characteristic
10	C₂×C₅×#137	C₂²	1	2	yes	—
11	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
12	C₅×#568	C₂²	1	1	yes	characteristic
13	C₅×#430	C₂²	1	2	yes	—
14	C₅×#430	C₂²	1	1	yes	characteristic
15	C₅×#430	C₂²	1	2	yes	—
16	C₅×#424	C₂²	1	2	yes	—
17	C₅×#421	C₂²	1	2	yes	—
18	C₅×#419	C₂²	1	2	yes	—
19	C₅×#419	C₂²	1	2	yes	—
20	C₅×#413	C₂²	1	1	yes	characteristic
21	C₂×C₅×#101	C₂²	1	2	yes	—
22	C₂×C₅×#101	C₂²	1	2	yes	—
23	C₂×C₅×#101	C₂²	1	2	yes	—
24	C₅×#408	C₂²	1	1	yes	characteristic
25	C₅×#344	C₂²	1	2	yes	—
26	C₅×#344	C₂²	1	2	yes	—
27	C₅×#341	C₂²	1	1	yes	characteristic
28	C₅×#341	C₂²	1	2	yes	—
29	C₅×#338	C₂²	1	2	yes	—
30	C₅×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
31	#32872	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₂×C₅×#41	C₂³	1	1	yes	characteristic
33	C₂²×C₅×Q₈	C₂³	1	2	yes	—
34	C₅×#137	—	4	2	no	—
35	C₅×#137	—	4	2	no	—
36	C₂×C₅×Q₁₆	—	2	2	no	—
37	C₂×C₅×Q₁₆	—	4	1	no	—
38	C₂×C₅×Q₁₆	—	4	2	no	—
39	C₂×C₅×SD₁₆	—	2	2	no	—
40	C₅×#131	—	4	2	no	—
41	C₂×C₅×M₁₆	—	4	1	no	—
42	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
43	C₂×C₅×M₁₆	C₂³	1	2	yes	—
44	C₂×C₅×M₁₆	C₂³	1	2	yes	—
45	C₂×C₅×M₁₆	C₂³	1	2	yes	—
46	C₂×C₅×M₁₆	C₂³	1	2	yes	—
47	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
48	C₅×#117	C₂³	1	2	yes	—
49	C₅×#108	—	4	1	no	—
50	C₅×#108	—	4	2	no	—
51	C₅×#108	—	4	2	no	—
52	C₅×C₄⋊C₈	—	4	2	no	—
53	C₅×#104	—	4	2	no	—
54	C₅×#103	—	4	2	no	—
55	C₅×#103	—	4	2	no	—
56	C₅×#101	—	2	1	no	—
57	C₅×#101	—	4	2	no	—
58	C₅×#101	—	4	2	no	—
59	C₅×#101	—	4	2	no	—
60	C₅×#100	—	2	1	no	—
61	C₅×C₂²⋊C₈	—	4	1	no	—
62	#2103	C₂×C₅	1	2	yes	complemented
63	#2098	C₂×C₅	1	1	yes	characteristic
64	#2082	C₂×C₅	1	2	yes	complemented
65	#2070	C₂×C₅	1	2	yes	complemented
66	#2049	C₂×C₅	1	2	yes	—
67	#2047	C₂×C₅	1	2	yes	complemented
68	#2020	C₂×C₅	1	1	yes	characteristic
69	#1902	C₂×C₅	1	2	yes	—
70	#1858	C₂×C₅	1	1	yes	characteristic
71	C₅×#41	—	2	2	no	—
72	C₅×#41	—	2	2	no	—
73	C₂×C₅×Q₈	—	2	2	no	—
74	C₂×C₅×Q₈	—	2	2	no	—
75	C₂×C₅×Q₈	—	2	2	no	—
76	C₂×C₅×Q₈	—	2	2	no	—
77	C₂×C₅×Q₈	—	2	2	no	—
78	C₂×C₅×Q₈	—	2	2	no	—
79	C₂×C₅×Q₈	#41	1	1	yes	characteristic
80	C₂×C₅×D₄	—	2	1	no	—
81	C₂×C₅×D₄	#41	1	1	yes	characteristic
82	C₂²×C₄×C₅	—	2	1	no	—
83	C₂²×C₄×C₅	—	2	2	no	—
84	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
85	C₅×Q₁₆	—	4	4	no	—
86	C₅×Q₁₆	—	4	4	no	—
87	C₅×SD₁₆	—	4	4	no	—
88	C₅×M₁₆	—	2	2	no	—
89	C₅×M₁₆	—	2	2	no	—
90	C₅×M₁₆	—	2	2	no	—
91	C₅×M₁₆	—	2	2	no	—
92	C₅×M₁₆	—	2	2	no	—
93	C₅×M₁₆	—	2	2	no	—
94	C₅×M₁₆	—	2	2	no	—
95	C₅×M₁₆	—	2	2	no	—
96	C₅×M₁₆	—	2	2	no	—
97	C₅×M₁₆	—	4	2	no	—
98	C₂×C₅×C₈	—	2	2	no	—
99	C₂×C₅×C₈	—	2	1	no	—
100	C₂×C₅×C₈	—	2	2	no	—
101	C₂×C₅×C₈	—	2	2	no	—
102	C₂×C₅×C₈	—	2	1	no	—
103	C₂×C₅×C₈	—	2	2	no	—
104	C₂×C₅×C₈	—	2	2	no	—
105	C₂×C₅×C₈	—	4	2	no	—
106	C₅×C₄⋊C₄	—	2	2	no	—
107	C₅×C₂²⋊C₄	—	2	2	no	—
108	C₄²×C₅	—	2	2	no	—
109	C₂×#137	C₂²×C₅	1	2	yes	—
110	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
111	#568	C₂²×C₅	1	1	yes	characteristic
112	#430	C₂²×C₅	1	2	yes	—
113	#430	C₂²×C₅	1	1	yes	characteristic
114	#430	C₂²×C₅	1	2	yes	—
115	#424	C₂²×C₅	1	2	yes	—
116	#421	C₂²×C₅	1	2	yes	—
117	#419	C₂²×C₅	1	2	yes	—
118	#419	C₂²×C₅	1	2	yes	—
119	#413	C₂²×C₅	1	1	yes	characteristic
120	C₂×#101	C₂²×C₅	1	2	yes	—
121	C₂×#101	C₂²×C₅	1	2	yes	—
122	C₂×#101	C₂²×C₅	1	2	yes	—
123	#408	C₂²×C₅	1	1	yes	characteristic
124	#344	C₂²×C₅	1	2	yes	—
125	#344	C₂²×C₅	1	2	yes	—
126	#341	C₂²×C₅	1	1	yes	characteristic
127	#341	C₂²×C₅	1	2	yes	—
128	#338	C₂²×C₅	1	2	yes	—
129	H(3,ℤ/4)	C₂²×C₅	1	1	yes	characteristic
130	C₂³×C₅	—	2	1	no	—
131	C₂³×C₅	2₋¹⁺⁴	1	1	yes	characteristic
132	C₅×Q₈	—	2	2	no	—
133	C₅×Q₈	—	4	2	no	—
134	C₅×Q₈	—	4	2	no	—
135	C₅×Q₈	—	4	2	no	—
136	C₅×Q₈	—	4	2	no	—
137	C₅×D₄	—	2	2	no	—
138	C₅×D₄	—	4	2	no	—
139	C₂×C₄×C₅	—	2	1	no	—
140	C₂×C₄×C₅	—	4	1	no	—
141	C₂×C₄×C₅	—	4	1	no	—
142	C₂×C₄×C₅	—	4	2	no	—
143	C₂×C₄×C₅	—	4	2	no	—
144	C₂×C₄×C₅	—	4	2	no	—
145	C₂×C₄×C₅	—	4	2	no	—
146	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
147	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
148	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
149	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
150	C₅×C₈	—	4	2	no	—
151	C₅×C₈	—	4	2	no	—
152	C₅×C₈	—	4	1	no	—
153	C₅×C₈	—	4	2	no	—
154	C₅×C₈	—	4	1	no	—
155	C₅×C₈	—	4	2	no	—
156	C₂×#41	C₂³×C₅	1	1	yes	characteristic
157	C₂²×Q₈	C₂³×C₅	1	2	yes	—
158	#137	—	4	2	no	—
159	#137	—	4	2	no	—
160	C₂×Q₁₆	—	2	2	no	—
161	C₂×Q₁₆	—	4	1	no	—
162	C₂×Q₁₆	—	4	2	no	—
163	C₂×SD₁₆	—	2	2	no	—
164	#131	—	4	2	no	—
165	C₂×M₁₆	—	4	1	no	—
166	C₂×M₁₆	C₂³×C₅	1	2	yes	—
167	C₂×M₁₆	C₂³×C₅	1	2	yes	—
168	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
169	C₂×M₁₆	C₂³×C₅	1	2	yes	—
170	C₂×M₁₆	C₂³×C₅	1	2	yes	—
171	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
172	#117	C₂³×C₅	1	2	yes	—
173	#108	—	4	1	no	—
174	#108	—	4	2	no	—
175	#108	—	4	2	no	—
176	C₄⋊C₈	—	4	2	no	—
177	#104	—	4	2	no	—
178	#103	—	4	2	no	—
179	#103	—	4	2	no	—
180	#101	—	2	1	no	—
181	#101	—	4	2	no	—
182	#101	—	4	2	no	—
183	#101	—	4	2	no	—
184	#100	—	2	1	no	—
185	C₂²⋊C₈	—	4	1	no	—
186	C₂²×C₅	—	4	1	no	—
187	C₂²×C₅	—	4	1	no	—
188	C₂²×C₅	—	8	1	no	—
189	C₂²×C₅	#539	1	1	yes	characteristic
190	C₂²×C₅	#562	1	2	yes	—
191	C₄×C₅	—	4	1	no	—
192	C₄×C₅	—	8	2	no	—
193	C₄×C₅	—	8	2	no	—
194	C₄×C₅	#538	1	2	yes	—
195	C₄×C₅	#560	1	1	yes	characteristic
196	C₄×C₅	#560	1	1	yes	characteristic
197	#41	—	2	2	no	—
198	#41	—	2	2	no	—
199	C₂×Q₈	—	2	2	no	—
200	C₂×Q₈	—	2	2	no	—
201	C₂×Q₈	—	2	2	no	—
202	C₂×Q₈	—	2	2	no	—
203	C₂×Q₈	—	2	2	no	—
204	C₂×Q₈	—	2	2	no	—
205	C₂×Q₈	C₅×#41	1	1	yes	characteristic
206	C₂×D₄	—	2	1	no	—
207	C₂×D₄	C₅×#41	1	1	yes	characteristic
208	C₂²×C₄	—	2	1	no	—
209	C₂²×C₄	—	2	2	no	—
210	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
211	Q₁₆	—	4	4	no	—
212	Q₁₆	—	4	4	no	—
213	SD₁₆	—	4	4	no	—
214	M₁₆	—	2	2	no	—
215	M₁₆	—	2	2	no	—
216	M₁₆	—	2	2	no	—
217	M₁₆	—	2	2	no	—
218	M₁₆	—	2	2	no	—
219	M₁₆	—	2	2	no	—
220	M₁₆	—	2	2	no	—
221	M₁₆	—	2	2	no	—
222	M₁₆	—	2	2	no	—
223	M₁₆	—	4	2	no	—
224	C₂×C₈	—	2	2	no	—
225	C₂×C₈	—	2	1	no	—
226	C₂×C₈	—	2	1	no	—
227	C₂×C₈	—	2	2	no	—
228	C₂×C₈	—	2	2	no	—
229	C₂×C₈	—	2	2	no	—
230	C₂×C₈	—	2	2	no	—
231	C₂×C₈	—	4	2	no	—
232	C₄⋊C₄	—	2	2	no	—
233	C₂²⋊C₄	—	2	2	no	—
234	C₄²	—	2	2	no	—
235	C₂×C₅	—	2	2	no	—
236	C₂×C₅	—	2	1	no	—
237	C₂×C₅	—	8	1	no	—
238	C₂×C₅	#2826	1	1	yes	characteristic
239	C₂³	—	2	1	no	—
240	C₂³	C₅×2₋¹⁺⁴	1	1	yes	characteristic
241	Q₈	—	2	2	no	—
242	Q₈	—	4	2	no	—
243	Q₈	—	4	2	no	—
244	Q₈	—	4	2	no	—
245	Q₈	—	4	2	no	—
246	D₄	—	2	2	no	—
247	D₄	—	4	2	no	—
248	C₂×C₄	—	2	1	no	—
249	C₂×C₄	—	4	1	no	—
250	C₂×C₄	—	4	1	no	—
251	C₂×C₄	—	4	2	no	—
252	C₂×C₄	—	4	2	no	—
253	C₂×C₄	—	4	2	no	—
254	C₂×C₄	—	4	2	no	—
255	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
256	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
257	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
258	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
259	C₈	—	4	2	no	—
260	C₈	—	4	2	no	—
261	C₈	—	4	1	no	—
262	C₈	—	4	2	no	—
263	C₈	—	4	1	no	—
264	C₈	—	4	2	no	—
265	C₅	#32872	1	1	yes	characteristic, direct product factor, Sylow
266	C₂²	—	4	1	no	—
267	C₂²	—	4	1	no	—
268	C₂²	—	8	1	no	—
269	C₂²	C₅×#539	1	1	yes	characteristic
270	C₂²	C₅×#562	1	2	yes	—
271	C₄	—	4	1	no	—
272	C₄	—	8	2	no	—
273	C₄	—	8	2	no	—
274	C₄	C₅×#538	1	2	yes	—
275	C₄	C₅×#560	1	1	yes	characteristic
276	C₄	C₅×#560	1	1	yes	characteristic
277	C₂	—	2	2	no	—
278	C₂	—	2	1	no	—
279	C₂	—	8	1	no	—
280	C₂	C₅×#2826	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₅	#2826
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂×C₅×#41	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅ ◁ C₂²×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#2103	C₂	semidirect
3. C₅×#2082	C₂	semidirect
4. C₅×#2070	C₂	semidirect
6. C₅×#2047	C₂	semidirect
31. #32872	C₅	direct (N × H)
62. #2103	C₂×C₅	semidirect
64. #2082	C₂×C₅	semidirect
65. #2070	C₂×C₅	semidirect
67. #2047	C₂×C₅	semidirect
265. C₅	#32872	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#2103	2
C₅×#2098	2
C₅×#2082	2
C₅×#2070	2
C₅×#2049	2
C₅×#2047	2
C₅×#2020	2
C₅×#1902	2
C₅×#1858	2
#32872	5

Subgroups — C5×#32872 #11955592

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#32872 #11955592