Subgroups — C₅×#33500 #11956220

Order 1280.

460 conjugacy classes of subgroups.

The subgroup lattice has 168 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	4	yes	maximal, complemented
3	C₅×Q₈×C₁₆	C₂	1	4	yes	maximal, complemented
4	C₅×#2164	C₂	1	4	yes	maximal
5	C₅×#2162	C₂	1	2	yes	maximal
6	C₅×#533	C₄	1	1	yes	characteristic
7	C₅×#446	C₄	1	4	yes	—
8	C₅×C₈×Q₈	C₂²	1	4	yes	—
9	C₅×#424	C₄	1	2	yes	—
10	C₅×#423	C₄	1	1	yes	characteristic
11	C₅×#405	C₂²	1	2	yes	—
12	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₅×C₄⋊C₁₆	C₂²	1	2	yes	—
14	C₅×C₄⋊C₁₆	C₂²	1	2	yes	—
15	C₅×C₄⋊C₁₆	C₂²	1	8	yes	—
16	C₅×C₂²⋊C₁₆	C₂²	1	4	yes	—
17	C₅×#346	C₂²	1	4	yes	—
18	C₄×C₅×C₁₆	C₂²	1	4	yes	—
19	C₄×C₅×C₁₆	C₂²	1	4	yes	—
20	#33500	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
22	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
24	C₅×C₄⋊Q₈	C₈	1	2	yes	—
25	C₅×#125	C₈	1	2	yes	—
26	C₅×C₂²⋊Q₈	C₈	1	4	yes	—
27	C₄×C₅×Q₈	C₂×C₄	1	4	yes	—
28	C₅×#117	C₂×C₄	1	2	yes	—
29	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
30	C₂×C₅×C₁₆	C₂³	1	4	yes	—
31	C₂×C₅×C₁₆	C₂³	1	4	yes	—
32	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
33	C₅×C₄⋊C₈	C₂×C₄	1	8	yes	—
34	C₅×#97	C₂×C₄	1	4	yes	—
35	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
36	C₄×C₅×C₈	C₂³	1	2	yes	—
37	C₄×C₅×C₈	C₂³	1	4	yes	—
38	#2960	C₂×C₅	1	1	yes	characteristic
39	#2183	C₂×C₅	1	4	yes	complemented
40	Q₈×C₁₆	C₂×C₅	1	4	yes	complemented
41	#2164	C₂×C₅	1	4	yes	—
42	#2162	C₂×C₅	1	2	yes	—
43	C₂×C₅×Q₈	C₂×C₈	1	4	yes	—
44	C₂²×C₄×C₅	C₂×C₈	1	2	yes	—
45	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
46	C₅×M₁₆	—	4	2	no	—
47	C₂×C₅×C₈	—	2	2	no	—
48	C₂×C₅×C₈	—	4	1	no	—
49	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
50	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
52	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
53	C₅×C₄⋊C₄	C₂×C₈	1	4	yes	—
54	C₅×C₄⋊C₄	C₂×C₈	1	8	yes	—
55	C₅×C₄⋊C₄	C₂×C₈	1	4	yes	—
56	C₅×C₂²⋊C₄	C₂×C₈	1	4	yes	—
57	C₄²×C₅	C₂×C₈	1	1	yes	characteristic
58	C₄²×C₅	C₂×C₈	1	1	yes	characteristic
59	C₄²×C₅	C₂²×C₄	1	2	yes	—
60	C₄²×C₅	C₂²×C₄	1	4	yes	—
61	C₅×C₁₆	—	2	4	no	—
62	C₅×C₁₆	—	2	4	no	—
63	#533	C₄×C₅	1	1	yes	characteristic
64	#446	C₄×C₅	1	4	yes	—
65	C₈×Q₈	C₂²×C₅	1	4	yes	—
66	#424	C₄×C₅	1	2	yes	—
67	#423	C₄×C₅	1	1	yes	characteristic
68	#405	C₂²×C₅	1	2	yes	—
69	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
70	C₄⋊C₁₆	C₂²×C₅	1	2	yes	—
71	C₄⋊C₁₆	C₂²×C₅	1	2	yes	—
72	C₄⋊C₁₆	C₂²×C₅	1	8	yes	—
73	C₂²⋊C₁₆	C₂²×C₅	1	4	yes	—
74	#346	C₂²×C₅	1	4	yes	—
75	C₄×C₁₆	C₂²×C₅	1	4	yes	—
76	C₄×C₁₆	C₂²×C₅	1	4	yes	—
77	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
78	C₅×Q₈	—	2	8	no	—
79	C₂×C₄×C₅	—	2	1	no	—
80	C₂×C₄×C₅	—	2	1	no	—
81	C₂×C₄×C₅	—	2	4	no	—
82	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
83	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
84	C₂×C₄×C₅	C₂²×C₈	1	8	yes	—
85	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
86	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
87	C₅×C₈	—	2	1	no	—
88	C₅×C₈	—	2	2	no	—
89	C₅×C₈	—	2	4	no	—
90	C₅×C₈	2₋¹⁺⁴	1	2	yes	—
91	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
92	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
93	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
94	C₄⋊Q₈	C₅×C₈	1	2	yes	—
95	#125	C₅×C₈	1	2	yes	—
96	C₂²⋊Q₈	C₅×C₈	1	4	yes	—
97	C₄×Q₈	C₂×C₄×C₅	1	4	yes	—
98	#117	C₂×C₄×C₅	1	2	yes	—
99	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
100	C₂×C₁₆	C₂³×C₅	1	4	yes	—
101	C₂×C₁₆	C₂³×C₅	1	4	yes	—
102	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
103	C₄⋊C₈	C₂×C₄×C₅	1	8	yes	—
104	#97	C₂×C₄×C₅	1	4	yes	—
105	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
106	C₄×C₈	C₂³×C₅	1	2	yes	—
107	C₄×C₈	C₂³×C₅	1	4	yes	—
108	C₂²×C₅	—	2	2	no	—
109	C₂²×C₅	—	2	1	no	—
110	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
111	C₄×C₅	—	2	2	no	—
112	C₄×C₅	—	2	8	no	—
113	C₄×C₅	—	2	1	no	—
114	C₄×C₅	#504	1	4	yes	—
115	C₄×C₅	#519	1	1	yes	characteristic
116	C₄×C₅	#568	1	1	yes	characteristic
117	C₂×Q₈	C₂×C₅×C₈	1	4	yes	—
118	C₂²×C₄	C₂×C₅×C₈	1	2	yes	—
119	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
120	M₁₆	—	4	2	no	—
121	C₂×C₈	—	2	2	no	—
122	C₂×C₈	—	4	1	no	—
123	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
124	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
125	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
126	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
127	C₄⋊C₄	C₂×C₅×C₈	1	4	yes	—
128	C₄⋊C₄	C₂×C₅×C₈	1	8	yes	—
129	C₄⋊C₄	C₂×C₅×C₈	1	4	yes	—
130	C₂²⋊C₄	C₂×C₅×C₈	1	4	yes	—
131	C₄²	C₂×C₅×C₈	1	1	yes	characteristic
132	C₄²	C₂×C₅×C₈	1	1	yes	characteristic
133	C₄²	C₂²×C₄×C₅	1	2	yes	—
134	C₄²	C₂²×C₄×C₅	1	4	yes	—
135	C₁₆	—	2	4	no	—
136	C₁₆	—	2	4	no	—
137	C₂×C₅	—	4	1	no	—
138	C₂×C₅	#2982	1	1	yes	characteristic
139	C₂×C₅	C₂×#504	1	2	yes	—
140	C₂³	C₂²×C₅×C₈	1	1	yes	characteristic
141	Q₈	—	2	8	no	—
142	C₂×C₄	—	2	4	no	—
143	C₂×C₄	—	2	1	no	—
144	C₂×C₄	—	2	1	no	—
145	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
146	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
147	C₂×C₄	C₂²×C₅×C₈	1	8	yes	—
148	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
149	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
150	C₈	—	2	1	no	—
151	C₈	—	2	2	no	—
152	C₈	—	2	4	no	—
153	C₈	C₅×2₋¹⁺⁴	1	2	yes	—
154	C₅	#33500	1	1	yes	characteristic, direct product factor, Sylow
155	C₂²	—	2	1	no	—
156	C₂²	—	2	2	no	—
157	C₂²	C₂³×C₅×C₈	1	1	yes	characteristic
158	C₄	—	2	1	no	—
159	C₄	—	2	2	no	—
160	C₄	—	2	8	no	—
161	C₄	C₅×#504	1	4	yes	—
162	C₄	C₅×#519	1	1	yes	characteristic
163	C₄	C₅×#568	1	1	yes	characteristic
164	C₂	—	4	1	no	—
165	C₂	C₅×#2982	1	1	yes	characteristic
166	C₂	C₂×C₅×#504	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
3. C₅×Q₈×C₁₆	C₂	semidirect
20. #33500	C₅	direct (N × H)
39. #2183	C₂×C₅	semidirect
40. Q₈×C₁₆	C₂×C₅	semidirect
154. C₅	#33500	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×Q₈×C₁₆	2
C₅×#2164	2
C₅×#2162	2
#33500	5

Subgroups — C5×#33500 #11956220

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33500 #11956220