Subgroups — C₂²×C₅×Dic₁₄ #11765421

Order 1120.

312 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₅×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×Dic₇	C₂	1	2	yes	maximal
3	C₂×C₅×Dic₁₄	C₂	1	12	yes	maximal, direct product factor
4	C₂³×C₅×C₇	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₅×C₇	C₂²	1	6	yes	—
6	C₂×C₅×Dic₇	C₂²	1	12	yes	—
7	C₅×Dic₁₄	C₂²	1	16	yes	direct product factor
8	C₂²×Dic₁₄	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₅×Q₈	—	7	1	no	maximal, Hall
10	C₂²×C₅×C₇	Q₈	1	4	yes	complemented
11	C₂²×C₅×C₇	C₂³	1	3	yes	—
12	C₄×C₅×C₇	C₂³	1	4	yes	—
13	C₅×Dic₇	C₂³	1	8	yes	—
14	C₂²×C₄×C₇	C₂×C₅	1	1	yes	characteristic
15	C₂²×Dic₇	C₂×C₅	1	2	yes	—
16	C₂×Dic₁₄	C₂×C₅	1	12	yes	direct product factor
17	C₂×C₅×Q₈	—	7	12	no	—
18	C₂²×C₄×C₅	—	7	2	no	—
19	C₂²×C₄×C₅	D₇	1	1	yes	characteristic
20	C₂×C₅×C₇	C₂×Q₈	1	6	yes	complemented
21	C₂×C₅×C₇	C₂⁴	1	1	yes	characteristic
22	C₂³×C₇	C₂²×C₅	1	1	yes	characteristic
23	C₂×C₄×C₇	C₂²×C₅	1	6	yes	—
24	C₂×Dic₇	C₂²×C₅	1	12	yes	—
25	Dic₁₄	C₂²×C₅	1	16	yes	direct product factor
26	C₂³×C₅	C₂×D₇	1	1	yes	characteristic
27	C₅×Q₈	—	7	16	no	—
28	C₂×C₄×C₅	—	7	12	no	—
29	C₂×C₄×C₅	C₂×D₇	1	6	yes	—
30	C₅×C₇	C₂²×Q₈	1	1	yes	characteristic, complemented, Hall
31	C₂²×Q₈	—	7	1	no	Sylow
32	C₂²×C₇	C₅×Q₈	1	4	yes	complemented
33	C₂²×C₇	C₂³×C₅	1	3	yes	—
34	C₄×C₇	C₂³×C₅	1	4	yes	—
35	Dic₇	C₂³×C₅	1	8	yes	—
36	C₂²×C₅	Dic₁₄	1	4	yes	direct product factor
37	C₂²×C₅	C₂²×D₇	1	3	yes	—
38	C₄×C₅	—	7	8	no	—
39	C₄×C₅	C₂²×D₇	1	4	yes	—
40	C₂×Q₈	—	7	12	no	—
41	C₂²×C₄	—	7	2	no	—
42	C₂²×C₄	C₅×D₇	1	1	yes	characteristic
43	C₂×C₇	C₂×C₅×Q₈	1	6	yes	complemented
44	C₂×C₇	C₂⁴×C₅	1	1	yes	characteristic
45	C₂×C₅	C₂×Dic₁₄	1	6	yes	direct product factor
46	C₂×C₅	C₂³×D₇	1	1	yes	characteristic
47	C₂³	C₂×C₅×D₇	1	1	yes	characteristic
48	Q₈	—	7	16	no	—
49	C₂×C₄	—	7	12	no	—
50	C₂×C₄	C₂×C₅×D₇	1	6	yes	—
51	C₇	C₂²×C₅×Q₈	1	1	yes	characteristic, complemented, Sylow
52	C₅	C₂²×Dic₁₄	1	1	yes	characteristic, direct product factor, Sylow
53	C₂²	C₅×Dic₁₄	1	4	yes	direct product factor
54	C₂²	C₂²×C₅×D₇	1	3	yes	—
55	C₄	—	7	8	no	—
56	C₄	C₂²×C₅×D₇	1	4	yes	—
57	C₂	C₂×C₅×Dic₁₄	1	6	yes	direct product factor
58	C₂	C₂³×C₅×D₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂×D₇
commutator, cosocle	C₂×C₇	C₂⁴×C₅
Frattini	C₂	C₂³×C₅×D₇
Fitting	C₂²×C₄×C₅×C₇	C₂
socle, prime radical	C₂³×C₅×C₇	C₂²
hypercenter	C₂²×C₄×C₅	D₇
hypocenter	C₇	C₂²×C₅×Q₈
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄×C₅

Complements

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

N	H ≅ G/N	type
3. C₂×C₅×Dic₁₄	C₂	direct (N × H)
7. C₅×Dic₁₄	C₂²	direct (N × H)
8. C₂²×Dic₁₄	C₅	direct (N × H)
10. C₂²×C₅×C₇	Q₈	semidirect
16. C₂×Dic₁₄	C₂×C₅	direct (N × H)
20. C₂×C₅×C₇	C₂×Q₈	semidirect
25. Dic₁₄	C₂²×C₅	direct (N × H)
30. C₅×C₇	C₂²×Q₈	semidirect
32. C₂²×C₇	C₅×Q₈	semidirect
36. C₂²×C₅	Dic₁₄	direct (N × H)
43. C₂×C₇	C₂×C₅×Q₈	semidirect
45. C₂×C₅	C₂×Dic₁₄	direct (N × H)
51. C₇	C₂²×C₅×Q₈	semidirect
52. C₅	C₂²×Dic₁₄	direct (N × H)
53. C₂²	C₅×Dic₁₄	direct (N × H)
57. C₂	C₂×C₅×Dic₁₄	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×C₄×C₅×C₇	2
C₂²×C₅×Dic₇	2
C₂×C₅×Dic₁₄	2
C₂²×Dic₁₄	5
C₂²×C₅×Q₈	7

Subgroups — C22×C5×Dic14 #11765421

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅×Dic₁₄ #11765421