Subgroups — C₂×C₅×#1745 #11943082

Order 1280.

1310 conjugacy classes of subgroups.

The subgroup lattice has 162 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#97	C₂	1	2	yes	maximal
2	C₂×C₄³×C₅	C₂	1	1	yes	maximal, characteristic
3	C₅×#1745	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₅×#336	C₂	1	4	yes	maximal
5	C₂³×C₅×C₈	C₂²	1	4	yes	—
6	C₂²×C₄²×C₅	C₄	1	4	yes	—
7	C₂²×C₄²×C₅	C₂²	1	2	yes	—
8	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
9	C₂×C₅×#97	C₄	1	16	yes	complemented
10	C₂×C₅×#97	C₂²	1	8	yes	—
11	C₄³×C₅	C₄	1	4	yes	—
12	C₄³×C₅	C₂²	1	4	yes	—
13	C₅×#336	C₂²	1	16	yes	—
14	C₂×#1745	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₂³×C₄×C₅	C₂×C₄	1	2	yes	—
16	C₂³×C₄×C₅	C₂×C₄	1	4	yes	—
17	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
18	C₂²×C₅×C₈	—	2	16	no	—
19	C₂²×C₅×C₈	C₂×C₄	1	16	yes	—
20	C₂²×C₅×C₈	C₂³	1	8	yes	—
21	C₂×C₄²×C₅	—	2	16	no	—
22	C₂×C₄²×C₅	—	2	8	no	—
23	C₂×C₄²×C₅	C₂×C₄	1	4	yes	—
24	C₂×C₄²×C₅	C₂×C₄	1	16	yes	—
25	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
26	C₂×C₄²×C₅	C₂×C₄	1	8	yes	—
27	C₂×C₄²×C₅	C₂³	1	4	yes	—
28	C₂×C₄²×C₅	C₂³	1	2	yes	—
29	C₅×#97	C₂×C₄	1	32	yes	complemented
30	C₂²×#97	C₂×C₅	1	2	yes	—
31	C₂×C₄³	C₂×C₅	1	1	yes	characteristic
32	#1745	C₂×C₅	1	8	yes	direct product factor
33	C₂×#336	C₂×C₅	1	4	yes	—
34	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
35	C₂²×C₄×C₅	—	2	8	no	—
36	C₂²×C₄×C₅	—	2	8	no	—
37	C₂²×C₄×C₅	—	2	8	no	—
38	C₂²×C₄×C₅	C₄²	1	8	yes	—
39	C₂²×C₄×C₅	M₁₆	1	16	yes	—
40	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
41	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
42	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
43	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
44	C₂²×C₄×C₅	#41	1	8	yes	—
45	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
46	C₂×C₅×C₈	—	2	32	no	—
47	C₂×C₅×C₈	—	2	16	no	—
48	C₂×C₅×C₈	C₂²×C₄	1	16	yes	—
49	C₄²×C₅	—	2	8	no	—
50	C₄²×C₅	—	2	32	no	—
51	C₄²×C₅	—	2	8	no	—
52	C₄²×C₅	C₄²	1	8	yes	—
53	C₄²×C₅	C₂²×C₄	1	8	yes	—
54	C₂³×C₈	C₂²×C₅	1	4	yes	—
55	C₂²×C₄²	C₄×C₅	1	4	yes	—
56	C₂²×C₄²	C₂²×C₅	1	2	yes	—
57	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
58	C₂×#97	C₄×C₅	1	16	yes	complemented
59	C₂×#97	C₂²×C₅	1	8	yes	—
60	C₄³	C₄×C₅	1	4	yes	—
61	C₄³	C₂²×C₅	1	4	yes	—
62	#336	C₂²×C₅	1	16	yes	—
63	C₂³×C₅	C₂×C₄²	1	2	yes	—
64	C₂³×C₅	#117	1	4	yes	—
65	C₂³×C₅	C₂×M₁₆	1	8	yes	—
66	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
67	C₂×C₄×C₅	—	2	8	no	—
68	C₂×C₄×C₅	—	2	8	no	—
69	C₂×C₄×C₅	—	2	8	no	—
70	C₂×C₄×C₅	—	2	16	no	—
71	C₂×C₄×C₅	—	2	32	no	—
72	C₂×C₄×C₅	C₂×C₄²	1	8	yes	—
73	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
74	C₂×C₄×C₅	#117	1	16	yes	—
75	C₂×C₄×C₅	#117	1	4	yes	—
76	C₂×C₄×C₅	C₂×M₁₆	1	16	yes	—
77	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
78	C₂×C₄×C₅	C₂×#41	1	4	yes	—
79	C₅×C₈	—	2	16	no	—
80	C₂³×C₄	C₂×C₄×C₅	1	2	yes	—
81	C₂³×C₄	C₂×C₄×C₅	1	4	yes	—
82	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
83	C₂²×C₈	—	2	16	no	—
84	C₂²×C₈	C₂×C₄×C₅	1	16	yes	—
85	C₂²×C₈	C₂³×C₅	1	8	yes	—
86	C₂×C₄²	—	2	16	no	—
87	C₂×C₄²	—	2	8	no	—
88	C₂×C₄²	C₂×C₄×C₅	1	4	yes	—
89	C₂×C₄²	C₂×C₄×C₅	1	16	yes	—
90	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
91	C₂×C₄²	C₂×C₄×C₅	1	8	yes	—
92	C₂×C₄²	C₂³×C₅	1	4	yes	—
93	C₂×C₄²	C₂³×C₅	1	2	yes	—
94	#97	C₂×C₄×C₅	1	32	yes	complemented
95	C₂²×C₅	#376	1	4	yes	—
96	C₂²×C₅	C₄×M₁₆	1	8	yes	—
97	C₂²×C₅	#432	1	16	yes	—
98	C₂²×C₅	C₂²×C₄²	1	1	yes	characteristic
99	C₂²×C₅	C₂×#117	1	2	yes	—
100	C₂²×C₅	C₂²×M₁₆	1	4	yes	—
101	C₄×C₅	—	2	8	no	—
102	C₄×C₅	—	2	16	no	—
103	C₄×C₅	#376	1	4	yes	—
104	C₄×C₅	C₂×#117	1	4	yes	—
105	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
106	C₂²×C₄	—	2	8	no	—
107	C₂²×C₄	—	2	8	no	—
108	C₂²×C₄	—	2	8	no	—
109	C₂²×C₄	C₄²×C₅	1	8	yes	—
110	C₂²×C₄	C₅×M₁₆	1	16	yes	—
111	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
112	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
113	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
114	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
115	C₂²×C₄	C₅×#41	1	8	yes	—
116	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
117	C₂×C₈	—	2	32	no	—
118	C₂×C₈	—	2	16	no	—
119	C₂×C₈	C₂²×C₄×C₅	1	16	yes	—
120	C₄²	—	2	8	no	—
121	C₄²	—	2	32	no	—
122	C₄²	—	2	8	no	—
123	C₄²	C₄²×C₅	1	8	yes	—
124	C₄²	C₂²×C₄×C₅	1	8	yes	—
125	C₂×C₅	#1745	1	8	yes	direct product factor
126	C₂×C₅	C₂×#376	1	1	yes	characteristic
127	C₂×C₅	C₂×C₄×M₁₆	1	2	yes	—
128	C₂×C₅	C₂×#432	1	4	yes	—
129	C₂³	C₂×C₄²×C₅	1	2	yes	—
130	C₂³	C₅×#117	1	4	yes	—
131	C₂³	C₂×C₅×M₁₆	1	8	yes	—
132	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
133	C₂×C₄	—	2	16	no	—
134	C₂×C₄	—	2	32	no	—
135	C₂×C₄	—	2	8	no	—
136	C₂×C₄	—	2	8	no	—
137	C₂×C₄	—	2	8	no	—
138	C₂×C₄	C₂×C₄²×C₅	1	8	yes	—
139	C₂×C₄	C₂×C₄²×C₅	1	2	yes	—
140	C₂×C₄	C₅×#117	1	4	yes	—
141	C₂×C₄	C₅×#117	1	16	yes	—
142	C₂×C₄	C₂×C₅×M₁₆	1	16	yes	—
143	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
144	C₂×C₄	C₂×C₅×#41	1	4	yes	—
145	C₈	—	2	16	no	—
146	C₅	C₂×#1745	1	1	yes	characteristic, direct product factor, Sylow
147	C₂²	C₅×#376	1	4	yes	—
148	C₂²	C₄×C₅×M₁₆	1	8	yes	—
149	C₂²	C₅×#432	1	16	yes	—
150	C₂²	C₂²×C₄²×C₅	1	1	yes	characteristic
151	C₂²	C₂×C₅×#117	1	2	yes	—
152	C₂²	C₂²×C₅×M₁₆	1	4	yes	—
153	C₄	—	2	8	no	—
154	C₄	—	2	16	no	—
155	C₄	C₅×#376	1	4	yes	—
156	C₄	C₂×C₅×#117	1	4	yes	—
157	C₂	C₅×#1745	1	8	yes	direct product factor
158	C₂	C₂×C₅×#376	1	1	yes	characteristic
159	C₂	C₂×C₄×C₅×M₁₆	1	2	yes	—
160	C₂	C₂×C₅×#432	1	4	yes	—

	subgroup	G/H
center	C₂³×C₄×C₅	C₂³
commutator	C₂²	C₂²×C₄²×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle, prime radical	C₂⁴×C₅	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅×#1745	C₂	direct (N × H)
9. C₂×C₅×#97	C₄	semidirect
14. C₂×#1745	C₅	direct (N × H)
29. C₅×#97	C₂×C₄	semidirect
32. #1745	C₂×C₅	direct (N × H)
58. C₂×#97	C₄×C₅	semidirect
94. #97	C₂×C₄×C₅	semidirect
125. C₂×C₅	#1745	direct (N × H)
146. C₅	C₂×#1745	direct (N × H)
157. C₂	C₅×#1745	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅×#97	2
C₂×C₄³×C₅	2
C₅×#1745	2
C₂×C₅×#336	2
C₂×#1745	5

Subgroups — C2×C5×#1745 #11943082

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#1745 #11943082