Subgroups — C₅×#22283 #11945003

Order 1280.

826 conjugacy classes of subgroups.

The subgroup lattice has 214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3150	C₂	1	1	yes	maximal, characteristic
2	C₅×#2932	C₂	1	2	yes	maximal, complemented
3	C₅×#1962	C₂	1	2	yes	maximal, complemented
4	C₅×#1876	C₂	1	8	yes	maximal, complemented
5	C₅×#1838	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1745	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#135	C₂²	1	4	yes	—
8	C₂×C₅×#131	C₂²	1	4	yes	—
9	C₅×#532	C₂²	1	2	yes	—
10	C₅×#497	C₄	1	4	yes	complemented
11	C₅×#496	C₄	1	4	yes	complemented
12	C₅×#435	—	2	8	no	—
13	C₅×#423	C₂²	1	2	yes	—
14	C₂×C₅×#104	C₂²	1	8	yes	—
15	C₅×#408	C₂²	1	4	yes	—
16	C₂×C₅×#97	C₂²	1	1	yes	characteristic
17	C₂×C₅×#97	C₂²	1	1	yes	characteristic
18	C₄³×C₅	C₂²	1	1	yes	characteristic
19	C₅×#341	C₂²	1	4	yes	—
20	C₅×#336	C₂²	1	4	yes	—
21	#22283	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₂×C₅×#41	C₂³	1	4	yes	—
23	C₅×#135	—	4	8	no	—
24	C₂×C₅×Q₁₆	C₂×C₄	1	4	yes	—
25	C₂×C₅×SD₁₆	C₂×C₄	1	8	yes	—
26	C₂×C₅×D₈	C₂×C₄	1	4	yes	—
27	C₅×#131	—	4	8	no	—
28	C₂×C₅×M₁₆	—	2	4	no	—
29	C₂×C₅×M₁₆	C₂³	1	4	yes	—
30	C₂²×C₅×C₈	—	2	4	no	—
31	C₂²×C₅×C₈	C₂³	1	2	yes	—
32	C₂²×C₅×C₈	C₂³	1	2	yes	—
33	C₅×C₄⋊Q₈	C₂×C₄	1	2	yes	—
34	C₅×#127	C₂×C₄	1	2	yes	—
35	C₅×#124	C₂×C₄	1	4	yes	—
36	C₅×#121	—	2	4	no	—
37	C₄×C₅×D₄	—	2	4	no	—
38	C₂×C₄²×C₅	—	2	2	no	—
39	C₂×C₄²×C₅	C₂³	1	2	yes	—
40	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
41	C₅×C₄⋊C₈	—	2	4	no	—
42	C₅×#104	—	4	8	no	—
43	C₅×C₂²⋊C₈	—	2	8	no	—
44	C₅×#97	C₂×C₄	1	4	yes	—
45	C₅×#97	D₄	1	4	yes	—
46	#3150	C₂×C₅	1	1	yes	characteristic
47	#2932	C₂×C₅	1	2	yes	complemented
48	#1962	C₂×C₅	1	2	yes	complemented
49	#1876	C₂×C₅	1	8	yes	complemented
50	#1838	C₂×C₅	1	1	yes	characteristic, complemented
51	#1745	C₂×C₅	1	1	yes	characteristic, complemented
52	C₅×#41	—	2	8	no	—
53	C₅×#41	—	2	8	no	—
54	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
55	C₂×C₅×D₄	—	2	4	no	—
56	C₂×C₅×D₄	—	2	4	no	—
57	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
58	C₂²×C₄×C₅	—	2	2	no	—
59	C₂²×C₄×C₅	—	2	4	no	—
60	C₂²×C₄×C₅	#41	1	2	yes	—
61	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
62	C₅×Q₁₆	—	4	4	no	—
63	C₅×SD₁₆	—	4	8	no	—
64	C₅×D₈	—	4	4	no	—
65	C₅×M₁₆	—	2	8	no	—
66	C₅×M₁₆	—	4	8	no	—
67	C₂×C₅×C₈	—	2	4	no	—
68	C₂×C₅×C₈	—	2	4	no	—
69	C₂×C₅×C₈	—	2	4	no	—
70	C₂×C₅×C₈	—	4	8	no	—
71	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
72	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
73	C₅×C₄⋊C₄	—	2	4	no	—
74	C₅×C₂²⋊C₄	—	2	8	no	—
75	C₄²×C₅	—	2	4	no	—
76	C₄²×C₅	—	4	4	no	—
77	C₄²×C₅	C₂²×C₄	1	2	yes	—
78	C₄²×C₅	C₂×D₄	1	2	yes	—
79	C₂×#135	C₂²×C₅	1	4	yes	—
80	C₂×#131	C₂²×C₅	1	4	yes	—
81	#532	C₂²×C₅	1	2	yes	—
82	#497	C₄×C₅	1	4	yes	complemented
83	#496	C₄×C₅	1	4	yes	complemented
84	#435	—	2	8	no	—
85	#423	C₂²×C₅	1	2	yes	—
86	C₂×#104	C₂²×C₅	1	8	yes	—
87	#408	C₂²×C₅	1	4	yes	—
88	C₂×#97	C₂²×C₅	1	1	yes	characteristic
89	C₂×#97	C₂²×C₅	1	1	yes	characteristic
90	C₄³	C₂²×C₅	1	1	yes	characteristic
91	#341	C₂²×C₅	1	4	yes	—
92	#336	C₂²×C₅	1	4	yes	—
93	C₂³×C₅	—	2	4	no	—
94	C₂³×C₅	C₂×#41	1	1	yes	characteristic
95	C₅×Q₈	—	2	8	no	—
96	C₅×D₄	—	2	8	no	—
97	C₅×D₄	—	4	8	no	—
98	C₅×D₄	—	8	4	no	—
99	C₂×C₄×C₅	—	2	4	no	—
100	C₂×C₄×C₅	—	2	4	no	—
101	C₂×C₄×C₅	—	4	2	no	—
102	C₂×C₄×C₅	—	4	2	no	—
103	C₂×C₄×C₅	—	4	2	no	—
104	C₂×C₄×C₅	—	4	4	no	—
105	C₂×C₄×C₅	—	4	4	no	—
106	C₂×C₄×C₅	C₄×D₄	1	4	yes	—
107	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
108	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
109	C₂×C₄×C₅	H(5,𝔽₂)	1	4	yes	—
110	C₅×C₈	—	2	4	no	—
111	C₅×C₈	—	2	4	no	—
112	C₅×C₈	—	4	4	no	—
113	C₂×#41	C₂³×C₅	1	4	yes	—
114	#135	—	4	8	no	—
115	C₂×Q₁₆	C₂×C₄×C₅	1	4	yes	—
116	C₂×SD₁₆	C₂×C₄×C₅	1	8	yes	—
117	C₂×D₈	C₂×C₄×C₅	1	4	yes	—
118	#131	—	4	8	no	—
119	C₂×M₁₆	—	2	4	no	—
120	C₂×M₁₆	C₂³×C₅	1	4	yes	—
121	C₂²×C₈	—	2	4	no	—
122	C₂²×C₈	C₂³×C₅	1	2	yes	—
123	C₂²×C₈	C₂³×C₅	1	2	yes	—
124	C₄⋊Q₈	C₂×C₄×C₅	1	2	yes	—
125	#127	C₂×C₄×C₅	1	2	yes	—
126	#124	C₂×C₄×C₅	1	4	yes	—
127	#121	—	2	4	no	—
128	C₄×D₄	—	2	4	no	—
129	C₂×C₄²	—	2	2	no	—
130	C₂×C₄²	C₂³×C₅	1	2	yes	—
131	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
132	C₄⋊C₈	—	2	4	no	—
133	#104	—	4	8	no	—
134	C₂²⋊C₈	—	2	8	no	—
135	#97	C₂×C₄×C₅	1	4	yes	—
136	#97	C₅×D₄	1	4	yes	—
137	C₂²×C₅	—	2	2	no	—
138	C₂²×C₅	—	4	4	no	—
139	C₂²×C₅	—	4	8	no	—
140	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
141	C₂²×C₅	#540	1	2	yes	—
142	C₄×C₅	—	2	4	no	—
143	C₄×C₅	—	4	4	no	—
144	C₄×C₅	—	4	4	no	—
145	C₄×C₅	#518	1	2	yes	—
146	C₄×C₅	#535	1	2	yes	—
147	#41	—	2	8	no	—
148	#41	—	2	8	no	—
149	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
150	C₂×D₄	—	2	4	no	—
151	C₂×D₄	—	2	4	no	—
152	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
153	C₂²×C₄	—	2	2	no	—
154	C₂²×C₄	—	2	4	no	—
155	C₂²×C₄	C₅×#41	1	2	yes	—
156	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
157	Q₁₆	—	4	4	no	—
158	SD₁₆	—	4	8	no	—
159	D₈	—	4	4	no	—
160	M₁₆	—	2	8	no	—
161	M₁₆	—	4	8	no	—
162	C₂×C₈	—	2	4	no	—
163	C₂×C₈	—	2	4	no	—
164	C₂×C₈	—	2	4	no	—
165	C₂×C₈	—	4	8	no	—
166	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
167	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
168	C₄⋊C₄	—	2	4	no	—
169	C₂²⋊C₄	—	2	8	no	—
170	C₄²	—	2	4	no	—
171	C₄²	—	4	4	no	—
172	C₄²	C₂²×C₄×C₅	1	2	yes	—
173	C₄²	C₂×C₅×D₄	1	2	yes	—
174	C₂×C₅	—	2	2	no	—
175	C₂×C₅	—	8	4	no	—
176	C₂×C₅	#2328	1	1	yes	characteristic
177	C₂×C₅	#2956	1	2	yes	—
178	C₂³	—	2	4	no	—
179	C₂³	C₂×C₅×#41	1	1	yes	characteristic
180	Q₈	—	2	8	no	—
181	D₄	—	2	8	no	—
182	D₄	—	4	8	no	—
183	D₄	—	8	4	no	—
184	C₂×C₄	—	2	4	no	—
185	C₂×C₄	—	2	4	no	—
186	C₂×C₄	—	4	2	no	—
187	C₂×C₄	—	4	2	no	—
188	C₂×C₄	—	4	2	no	—
189	C₂×C₄	—	4	4	no	—
190	C₂×C₄	—	4	4	no	—
191	C₂×C₄	C₄×C₅×D₄	1	4	yes	—
192	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
193	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
194	C₂×C₄	C₅×H(5,𝔽₂)	1	4	yes	—
195	C₈	—	2	4	no	—
196	C₈	—	2	4	no	—
197	C₈	—	4	4	no	—
198	C₅	#22283	1	1	yes	characteristic, direct product factor, Sylow
199	C₂²	—	2	2	no	—
200	C₂²	—	4	4	no	—
201	C₂²	—	4	8	no	—
202	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
203	C₂²	C₅×#540	1	2	yes	—
204	C₄	—	2	4	no	—
205	C₄	—	4	4	no	—
206	C₄	—	4	4	no	—
207	C₄	C₅×#518	1	2	yes	—
208	C₄	C₅×#535	1	2	yes	—
209	C₂	—	2	2	no	—
210	C₂	—	8	4	no	—
211	C₂	C₅×#2328	1	1	yes	characteristic
212	C₂	C₅×#2956	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₅×#3150	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₅×#97 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2932	C₂	semidirect
3. C₅×#1962	C₂	semidirect
4. C₅×#1876	C₂	semidirect
5. C₅×#1838	C₂	semidirect
6. C₅×#1745	C₂	semidirect
10. C₅×#497	C₄	semidirect
11. C₅×#496	C₄	semidirect
21. #22283	C₅	direct (N × H)
47. #2932	C₂×C₅	semidirect
48. #1962	C₂×C₅	semidirect
49. #1876	C₂×C₅	semidirect
50. #1838	C₂×C₅	semidirect
51. #1745	C₂×C₅	semidirect
82. #497	C₄×C₅	semidirect
83. #496	C₄×C₅	semidirect
198. C₅	#22283	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×#3150	2
C₅×#2932	2
C₅×#1962	2
C₅×#1876	2
C₅×#1838	2
C₅×#1745	2
#22283	5

Subgroups — C5×#22283 #11945003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22283 #11945003