Subgroups — C₅×#33501 #11956221

Order 1280.

444 conjugacy classes of subgroups.

The subgroup lattice has 160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2960	C₂	1	1	yes	maximal, characteristic
2	C₅×#2183	C₂	1	8	yes	maximal, complemented
3	C₅×#2164	C₂	1	4	yes	maximal
4	C₅×#2163	C₂	1	2	yes	maximal
5	C₅×#533	C₄	1	1	yes	characteristic
6	C₅×#446	C₄	1	4	yes	—
7	C₅×C₈×Q₈	C₂²	1	4	yes	—
8	C₅×#424	C₄	1	2	yes	—
9	C₅×#423	C₄	1	1	yes	characteristic
10	C₅×#405	C₂²	1	2	yes	—
11	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₅×C₄⋊C₁₆	C₂²	1	4	yes	—
13	C₅×C₄⋊C₁₆	C₂²	1	8	yes	—
14	C₅×C₂²⋊C₁₆	C₂²	1	4	yes	—
15	C₅×#346	C₂²	1	4	yes	—
16	C₅×#346	C₂²	1	4	yes	—
17	C₄×C₅×C₁₆	C₂²	1	4	yes	—
18	#33501	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
20	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
22	C₅×C₄⋊Q₈	C₈	1	2	yes	—
23	C₅×#125	C₈	1	2	yes	—
24	C₅×C₂²⋊Q₈	C₈	1	4	yes	—
25	C₄×C₅×Q₈	C₂×C₄	1	4	yes	—
26	C₅×#117	C₂×C₄	1	2	yes	—
27	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
28	C₂×C₅×C₁₆	C₂³	1	8	yes	—
29	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
30	C₅×C₄⋊C₈	C₂×C₄	1	8	yes	—
31	C₅×#97	C₂×C₄	1	4	yes	—
32	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
33	C₄×C₅×C₈	C₂³	1	2	yes	—
34	C₄×C₅×C₈	C₂³	1	4	yes	—
35	#2960	C₂×C₅	1	1	yes	characteristic
36	#2183	C₂×C₅	1	8	yes	complemented
37	#2164	C₂×C₅	1	4	yes	—
38	#2163	C₂×C₅	1	2	yes	—
39	C₂×C₅×Q₈	C₂×C₈	1	4	yes	—
40	C₂²×C₄×C₅	C₂×C₈	1	2	yes	—
41	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
42	C₅×M₁₆	—	4	2	no	—
43	C₂×C₅×C₈	—	2	2	no	—
44	C₂×C₅×C₈	—	4	1	no	—
45	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
46	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
47	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
48	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
49	C₅×C₄⋊C₄	C₂×C₈	1	4	yes	—
50	C₅×C₄⋊C₄	C₂×C₈	1	8	yes	—
51	C₅×C₄⋊C₄	C₂×C₈	1	4	yes	—
52	C₅×C₂²⋊C₄	C₂×C₈	1	4	yes	—
53	C₄²×C₅	C₂×C₈	1	1	yes	characteristic
54	C₄²×C₅	C₂×C₈	1	1	yes	characteristic
55	C₄²×C₅	C₂²×C₄	1	2	yes	—
56	C₄²×C₅	C₂²×C₄	1	4	yes	—
57	C₅×C₁₆	—	2	8	no	—
58	#533	C₄×C₅	1	1	yes	characteristic
59	#446	C₄×C₅	1	4	yes	—
60	C₈×Q₈	C₂²×C₅	1	4	yes	—
61	#424	C₄×C₅	1	2	yes	—
62	#423	C₄×C₅	1	1	yes	characteristic
63	#405	C₂²×C₅	1	2	yes	—
64	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
65	C₄⋊C₁₆	C₂²×C₅	1	4	yes	—
66	C₄⋊C₁₆	C₂²×C₅	1	8	yes	—
67	C₂²⋊C₁₆	C₂²×C₅	1	4	yes	—
68	#346	C₂²×C₅	1	4	yes	—
69	#346	C₂²×C₅	1	4	yes	—
70	C₄×C₁₆	C₂²×C₅	1	4	yes	—
71	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
72	C₅×Q₈	—	4	4	no	—
73	C₂×C₄×C₅	—	2	1	no	—
74	C₂×C₄×C₅	—	2	1	no	—
75	C₂×C₄×C₅	—	4	2	no	—
76	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
77	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
78	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
79	C₂×C₄×C₅	C₂²×C₈	1	8	yes	—
80	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
81	C₅×C₈	—	2	1	no	—
82	C₅×C₈	—	2	2	no	—
83	C₅×C₈	—	2	4	no	—
84	C₅×C₈	2₋¹⁺⁴	1	2	yes	—
85	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
86	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
87	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
88	C₄⋊Q₈	C₅×C₈	1	2	yes	—
89	#125	C₅×C₈	1	2	yes	—
90	C₂²⋊Q₈	C₅×C₈	1	4	yes	—
91	C₄×Q₈	C₂×C₄×C₅	1	4	yes	—
92	#117	C₂×C₄×C₅	1	2	yes	—
93	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
94	C₂×C₁₆	C₂³×C₅	1	8	yes	—
95	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
96	C₄⋊C₈	C₂×C₄×C₅	1	8	yes	—
97	#97	C₂×C₄×C₅	1	4	yes	—
98	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
99	C₄×C₈	C₂³×C₅	1	4	yes	—
100	C₄×C₈	C₂³×C₅	1	2	yes	—
101	C₂²×C₅	—	2	2	no	—
102	C₂²×C₅	—	2	1	no	—
103	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
104	C₄×C₅	—	2	2	no	—
105	C₄×C₅	—	2	2	no	—
106	C₄×C₅	—	2	8	no	—
107	C₄×C₅	—	2	1	no	—
108	C₄×C₅	#519	1	1	yes	characteristic
109	C₄×C₅	#568	1	1	yes	characteristic
110	C₂×Q₈	C₂×C₅×C₈	1	4	yes	—
111	C₂²×C₄	C₂×C₅×C₈	1	2	yes	—
112	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
113	M₁₆	—	4	2	no	—
114	C₂×C₈	—	2	2	no	—
115	C₂×C₈	—	4	1	no	—
116	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
117	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
118	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
119	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
120	C₄⋊C₄	C₂×C₅×C₈	1	4	yes	—
121	C₄⋊C₄	C₂×C₅×C₈	1	8	yes	—
122	C₄⋊C₄	C₂×C₅×C₈	1	4	yes	—
123	C₂²⋊C₄	C₂×C₅×C₈	1	4	yes	—
124	C₄²	C₂×C₅×C₈	1	1	yes	characteristic
125	C₄²	C₂×C₅×C₈	1	1	yes	characteristic
126	C₄²	C₂²×C₄×C₅	1	2	yes	—
127	C₄²	C₂²×C₄×C₅	1	4	yes	—
128	C₁₆	—	2	8	no	—
129	C₂×C₅	—	4	1	no	—
130	C₂×C₅	#2982	1	1	yes	characteristic
131	C₂×C₅	#3407	1	2	yes	—
132	C₂³	C₂²×C₅×C₈	1	1	yes	characteristic
133	Q₈	—	4	4	no	—
134	C₂×C₄	—	2	1	no	—
135	C₂×C₄	—	2	1	no	—
136	C₂×C₄	—	4	2	no	—
137	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
138	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
139	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
140	C₂×C₄	C₂²×C₅×C₈	1	8	yes	—
141	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
142	C₈	—	2	1	no	—
143	C₈	—	2	2	no	—
144	C₈	—	2	4	no	—
145	C₈	C₅×2₋¹⁺⁴	1	2	yes	—
146	C₅	#33501	1	1	yes	characteristic, direct product factor, Sylow
147	C₂²	—	2	1	no	—
148	C₂²	—	2	2	no	—
149	C₂²	C₂³×C₅×C₈	1	1	yes	characteristic
150	C₄	—	2	1	no	—
151	C₄	—	2	2	no	—
152	C₄	—	2	2	no	—
153	C₄	—	2	8	no	—
154	C₄	C₅×#519	1	1	yes	characteristic
155	C₄	C₅×#568	1	1	yes	characteristic
156	C₂	—	4	1	no	—
157	C₂	C₅×#2982	1	1	yes	characteristic
158	C₂	C₅×#3407	1	2	yes	—

	subgroup	G/H
center	C₂×C₅×C₈	C₂⁴
commutator	C₂²	C₂³×C₅×C₈
Frattini, cosocle	C₂×C₈	C₂⁴×C₅
socle	C₂²×C₅	C₂³×C₈
prime radical	C₂³×C₅	C₂²×C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2183	C₂	semidirect
18. #33501	C₅	direct (N × H)
36. #2183	C₂×C₅	semidirect
146. C₅	#33501	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×#2960	2
C₅×#2183	2
C₅×#2164	2
C₅×#2163	2
#33501	5

Subgroups — C5×#33501 #11956221

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33501 #11956221