Subgroups — C₅×#20791 #11943511

Order 1280.

1350 conjugacy classes of subgroups.

The subgroup lattice has 138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#423	C₂	1	6	yes	maximal
2	C₂×C₄³×C₅	C₂	1	1	yes	maximal, characteristic
3	C₅×#1842	C₂	1	8	yes	maximal, complemented
4	C₂²×C₅×M₁₆	C₂²	1	4	yes	—
5	C₂²×C₄²×C₅	C₄	1	4	yes	—
6	C₂²×C₄²×C₅	C₂²	1	3	yes	—
7	C₅×#423	—	2	24	no	—
8	C₂×C₅×C₄⋊C₈	C₂²	1	24	yes	—
9	C₄³×C₅	C₄	1	3	yes	—
10	C₄³×C₅	C₄	1	1	yes	characteristic
11	C₄³×C₅	C₂²	1	4	yes	—
12	#20791	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂³×C₄×C₅	C₂×C₄	1	6	yes	—
14	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
15	C₂×C₅×M₁₆	—	2	24	no	—
16	C₂²×C₅×C₈	C₂³	1	8	yes	—
17	C₂×C₄²×C₅	—	2	16	no	—
18	C₂×C₄²×C₅	C₂×C₄	1	12	yes	—
19	C₂×C₄²×C₅	C₂×C₄	1	3	yes	—
20	C₂×C₄²×C₅	C₂×C₄	1	3	yes	—
21	C₂×C₄²×C₅	C₂×C₄	1	4	yes	—
22	C₂×C₄²×C₅	D₄	1	12	yes	—
23	C₂×C₄²×C₅	Q₈	1	12	yes	—
24	C₂×C₄²×C₅	C₂³	1	6	yes	—
25	C₅×C₄⋊C₈	—	2	48	no	—
26	C₂×#423	C₂×C₅	1	6	yes	—
27	C₂×C₄³	C₂×C₅	1	1	yes	characteristic
28	#1842	C₂×C₅	1	8	yes	complemented
29	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
30	C₂²×C₄×C₅	—	2	24	no	—
31	C₂²×C₄×C₅	C₄⋊C₄	1	24	yes	—
32	C₂²×C₄×C₅	C₂²×C₄	1	6	yes	—
33	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
34	C₂²×C₄×C₅	C₂²×C₄	1	6	yes	—
35	C₂²×C₄×C₅	C₂×D₄	1	6	yes	—
36	C₂²×C₄×C₅	C₂×Q₈	1	6	yes	—
37	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
38	C₅×M₁₆	—	4	16	no	—
39	C₂×C₅×C₈	—	2	24	no	—
40	C₄²×C₅	—	2	24	no	—
41	C₄²×C₅	C₄⋊C₄	1	12	yes	—
42	C₄²×C₅	C₄⋊C₄	1	12	yes	—
43	C₄²×C₅	M₁₆	1	16	yes	complemented
44	C₄²×C₅	C₂×D₄	1	12	yes	—
45	C₄²×C₅	C₂×Q₈	1	12	yes	—
46	C₂²×M₁₆	C₂²×C₅	1	4	yes	—
47	C₂²×C₄²	C₄×C₅	1	4	yes	—
48	C₂²×C₄²	C₂²×C₅	1	3	yes	—
49	#423	—	2	24	no	—
50	C₂×C₄⋊C₈	C₂²×C₅	1	24	yes	—
51	C₄³	C₄×C₅	1	3	yes	—
52	C₄³	C₄×C₅	1	1	yes	characteristic
53	C₄³	C₂²×C₅	1	4	yes	—
54	C₂³×C₅	—	2	4	no	—
55	C₂³×C₅	C₂×C₄⋊C₄	1	6	yes	—
56	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
57	C₂×C₄×C₅	—	2	12	no	—
58	C₂×C₄×C₅	—	2	48	no	—
59	C₂×C₄×C₅	C₂×C₄⋊C₄	1	12	yes	—
60	C₂×C₄×C₅	C₂×C₄⋊C₄	1	6	yes	—
61	C₂×C₄×C₅	C₂×C₄⋊C₄	1	12	yes	—
62	C₂×C₄×C₅	#127	1	4	yes	—
63	C₂×C₄×C₅	C₄⋊Q₈	1	12	yes	—
64	C₂×C₄×C₅	C₂×M₁₆	1	24	yes	—
65	C₂×C₄×C₅	C₂²×D₄	1	3	yes	—
66	C₂×C₄×C₅	C₂²×Q₈	1	3	yes	—
67	C₅×C₈	—	4	8	no	—
68	C₂³×C₄	C₂×C₄×C₅	1	6	yes	—
69	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
70	C₂×M₁₆	—	2	24	no	—
71	C₂²×C₈	C₂³×C₅	1	8	yes	—
72	C₂×C₄²	—	2	16	no	—
73	C₂×C₄²	C₂×C₄×C₅	1	12	yes	—
74	C₂×C₄²	C₂×C₄×C₅	1	3	yes	—
75	C₂×C₄²	C₂×C₄×C₅	1	3	yes	—
76	C₂×C₄²	C₂×C₄×C₅	1	4	yes	—
77	C₂×C₄²	C₅×D₄	1	12	yes	—
78	C₂×C₄²	C₅×Q₈	1	12	yes	—
79	C₂×C₄²	C₂³×C₅	1	6	yes	—
80	C₄⋊C₈	—	2	48	no	—
81	C₂²×C₅	—	2	12	no	—
82	C₂²×C₅	#384	1	4	yes	—
83	C₂²×C₅	C₂²×C₄⋊C₄	1	3	yes	—
84	C₂²×C₅	C₂²×M₁₆	1	4	yes	—
85	C₄×C₅	—	2	12	no	—
86	C₄×C₅	#384	1	4	yes	—
87	C₄×C₅	#423	1	24	yes	complemented
88	C₄×C₅	C₂×#127	1	1	yes	characteristic
89	C₄×C₅	C₂×C₄⋊Q₈	1	3	yes	—
90	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
91	C₂²×C₄	—	2	24	no	—
92	C₂²×C₄	C₅×C₄⋊C₄	1	24	yes	—
93	C₂²×C₄	C₂²×C₄×C₅	1	6	yes	—
94	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
95	C₂²×C₄	C₂²×C₄×C₅	1	6	yes	—
96	C₂²×C₄	C₂×C₅×D₄	1	6	yes	—
97	C₂²×C₄	C₂×C₅×Q₈	1	6	yes	—
98	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
99	M₁₆	—	4	16	no	—
100	C₂×C₈	—	2	24	no	—
101	C₄²	—	2	24	no	—
102	C₄²	C₅×C₄⋊C₄	1	12	yes	—
103	C₄²	C₅×C₄⋊C₄	1	12	yes	—
104	C₄²	C₅×M₁₆	1	16	yes	complemented
105	C₄²	C₂×C₅×D₄	1	12	yes	—
106	C₄²	C₂×C₅×Q₈	1	12	yes	—
107	C₂×C₅	—	2	4	no	—
108	C₂×C₅	C₂×#384	1	1	yes	characteristic
109	C₂×C₅	C₂×#423	1	6	yes	—
110	C₂³	—	2	4	no	—
111	C₂³	C₂×C₅×C₄⋊C₄	1	6	yes	—
112	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
113	C₂×C₄	—	2	12	no	—
114	C₂×C₄	—	2	48	no	—
115	C₂×C₄	C₂×C₅×C₄⋊C₄	1	12	yes	—
116	C₂×C₄	C₂×C₅×C₄⋊C₄	1	6	yes	—
117	C₂×C₄	C₂×C₅×C₄⋊C₄	1	12	yes	—
118	C₂×C₄	C₅×#127	1	4	yes	—
119	C₂×C₄	C₅×C₄⋊Q₈	1	12	yes	—
120	C₂×C₄	C₂×C₅×M₁₆	1	24	yes	—
121	C₂×C₄	C₂²×C₅×D₄	1	3	yes	—
122	C₂×C₄	C₂²×C₅×Q₈	1	3	yes	—
123	C₈	—	4	8	no	—
124	C₅	#20791	1	1	yes	characteristic, direct product factor, Sylow
125	C₂²	—	2	12	no	—
126	C₂²	C₅×#384	1	4	yes	—
127	C₂²	C₂²×C₅×C₄⋊C₄	1	3	yes	—
128	C₂²	C₂²×C₅×M₁₆	1	4	yes	—
129	C₄	—	2	12	no	—
130	C₄	C₅×#384	1	4	yes	—
131	C₄	C₅×#423	1	24	yes	complemented
132	C₄	C₂×C₅×#127	1	1	yes	characteristic
133	C₄	C₂×C₅×C₄⋊Q₈	1	3	yes	—
134	C₂	—	2	4	no	—
135	C₂	C₂×C₅×#384	1	1	yes	characteristic
136	C₂	C₂×C₅×#423	1	6	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₅×#1842	C₂	semidirect
12. #20791	C₅	direct (N × H)
28. #1842	C₂×C₅	semidirect
43. C₄²×C₅	M₁₆	semidirect
87. C₄×C₅	#423	semidirect
104. C₄²	C₅×M₁₆	semidirect
124. C₅	#20791	direct (N × H)
131. C₄	C₅×#423	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#423	2
C₂×C₄³×C₅	2
C₅×#1842	2
#20791	5

Subgroups — C5×#20791 #11943511

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#20791 #11943511