Subgroups — C₅×#12901 #11935621

Order 1280.

342 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×#364	C₂	1	4	yes	maximal
2	C₅×#2150	C₂	1	2	yes	maximal
3	C₅×#1726	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×M₃₂	C₂²	1	4	yes	—
5	C₂×C₅×#97	C₄	1	2	yes	—
6	C₂×C₅×#97	C₄	1	1	yes	characteristic
7	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
8	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
9	C₅×#376	C₄	1	1	yes	characteristic
10	C₅×#364	—	2	8	no	—
11	C₅×C₄⋊C₁₆	—	2	4	no	—
12	#12901	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
15	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
16	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
17	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
18	C₅×M₃₂	—	2	8	no	—
19	C₂×C₅×C₁₆	—	2	4	no	—
20	C₅×#97	—	2	4	no	—
21	C₅×#97	C₈	1	4	yes	—
22	C₄×C₅×C₈	D₄	1	4	yes	—
23	C₄×C₅×C₈	D₄	1	2	yes	—
24	C₄×C₅×C₈	Q₈	1	4	yes	—
25	C₄×C₅×C₈	Q₈	1	2	yes	—
26	C₅×#95	—	2	2	no	—
27	C₂×#364	C₂×C₅	1	4	yes	—
28	#2150	C₂×C₅	1	2	yes	—
29	#1726	C₂×C₅	1	1	yes	characteristic
30	C₂²×C₄×C₅	—	2	2	no	—
31	C₂²×C₄×C₅	M₁₆	1	2	yes	—
32	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₅×C₈	—	2	2	no	—
34	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
35	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	—
36	C₂×C₅×C₈	C₂×C₈	1	4	yes	—
37	C₂×C₅×C₈	M₁₆	1	4	yes	—
38	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
39	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
40	C₂×C₅×C₈	C₂×Q₈	1	1	yes	characteristic
41	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
42	C₄²×C₅	—	2	2	no	—
43	C₄²×C₅	C₄⋊C₄	1	4	yes	—
44	C₄²×C₅	C₄⋊C₄	1	2	yes	—
45	C₄²×C₅	C₂×C₈	1	2	yes	—
46	C₅×C₁₆	—	4	4	no	—
47	C₂×M₃₂	C₂²×C₅	1	4	yes	—
48	C₂×#97	C₄×C₅	1	2	yes	—
49	C₂×#97	C₄×C₅	1	1	yes	characteristic
50	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
51	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
52	#376	C₄×C₅	1	1	yes	characteristic
53	#364	—	2	8	no	—
54	C₄⋊C₁₆	—	2	4	no	—
55	C₂³×C₅	C₂×M₁₆	1	1	yes	characteristic
56	C₂×C₄×C₅	—	2	4	no	—
57	C₂×C₄×C₅	—	4	2	no	—
58	C₂×C₄×C₅	—	4	4	no	—
59	C₂×C₄×C₅	C₄⋊C₈	1	4	yes	—
60	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
61	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
62	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
63	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
64	C₅×C₈	—	2	2	no	—
65	C₅×C₈	C₄⋊C₈	1	8	yes	—
66	C₅×C₈	#127	1	1	yes	characteristic
67	C₅×C₈	C₄⋊Q₈	1	2	yes	—
68	C₅×C₈	C₄⋊Q₈	1	1	yes	characteristic
69	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
70	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
71	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
72	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
73	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
74	M₃₂	—	2	8	no	—
75	C₂×C₁₆	—	2	4	no	—
76	#97	—	2	4	no	—
77	#97	C₅×C₈	1	4	yes	—
78	C₄×C₈	C₅×D₄	1	2	yes	—
79	C₄×C₈	C₅×D₄	1	4	yes	—
80	C₄×C₈	C₅×Q₈	1	4	yes	—
81	C₄×C₈	C₅×Q₈	1	2	yes	—
82	#95	—	2	2	no	—
83	C₂²×C₅	—	2	2	no	—
84	C₂²×C₅	C₂×C₄⋊C₈	1	1	yes	characteristic
85	C₂²×C₅	#423	1	2	yes	—
86	C₄×C₅	—	2	4	no	—
87	C₄×C₅	—	4	4	no	—
88	C₄×C₅	#384	1	1	yes	characteristic
89	C₄×C₅	C₂×C₄⋊C₈	1	2	yes	—
90	C₄×C₅	#423	1	1	yes	characteristic
91	C₂²×C₄	—	2	2	no	—
92	C₂²×C₄	C₅×M₁₆	1	2	yes	—
93	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
94	C₂×C₈	—	2	2	no	—
95	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
96	C₂×C₈	C₅×C₄⋊C₄	1	4	yes	—
97	C₂×C₈	C₂×C₅×C₈	1	4	yes	—
98	C₂×C₈	C₅×M₁₆	1	4	yes	—
99	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
100	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
101	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
102	C₂×C₈	C₂×C₅×Q₈	1	1	yes	characteristic
103	C₄²	—	2	2	no	—
104	C₄²	C₅×C₄⋊C₄	1	4	yes	—
105	C₄²	C₅×C₄⋊C₄	1	2	yes	—
106	C₄²	C₂×C₅×C₈	1	2	yes	—
107	C₁₆	—	4	4	no	—
108	C₂×C₅	—	2	2	no	—
109	C₂×C₅	#1842	1	1	yes	characteristic
110	C₂×C₅	#2153	1	2	yes	—
111	C₂³	C₂×C₅×M₁₆	1	1	yes	characteristic
112	C₂×C₄	—	2	4	no	—
113	C₂×C₄	—	4	2	no	—
114	C₂×C₄	—	4	4	no	—
115	C₂×C₄	C₅×C₄⋊C₈	1	4	yes	—
116	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
117	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
118	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
119	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
120	C₈	—	2	2	no	—
121	C₈	C₅×C₄⋊C₈	1	8	yes	—
122	C₈	C₅×#127	1	1	yes	characteristic
123	C₈	C₅×C₄⋊Q₈	1	1	yes	characteristic
124	C₈	C₅×C₄⋊Q₈	1	2	yes	—
125	C₅	#12901	1	1	yes	characteristic, direct product factor, Sylow
126	C₂²	—	2	2	no	—
127	C₂²	C₂×C₅×C₄⋊C₈	1	1	yes	characteristic
128	C₂²	C₅×#423	1	2	yes	—
129	C₄	—	2	4	no	—
130	C₄	—	4	4	no	—
131	C₄	C₅×#384	1	1	yes	characteristic
132	C₄	C₂×C₅×C₄⋊C₈	1	2	yes	—
133	C₄	C₅×#423	1	1	yes	characteristic
134	C₂	—	2	2	no	—
135	C₂	C₅×#1842	1	1	yes	characteristic
136	C₂	C₅×#2153	1	2	yes	—

	subgroup	G/H
center	C₂×C₅×C₈	C₂×D₄
commutator	C₂×C₄	C₂²×C₅×C₈
Frattini, cosocle	C₂²×C₈	C₂³×C₅
socle	C₂²×C₅	C₂×C₄⋊C₈
prime radical	C₂³×C₅	C₂×M₁₆
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅×C₈ ◁ C₂×C₄×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
12. #12901	C₅	direct (N × H)
125. C₅	#12901	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×#364	2
C₅×#2150	2
C₅×#1726	2
#12901	5

Subgroups — C5×#12901 #11935621

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#12901 #11935621