Subgroups — C₄²×D₃₅ #11765201

Order 1120.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₃₅	C₂	1	3	yes	maximal
2	C₄²×C₅×C₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×Dic₃₅	C₂	1	3	yes	maximal, complemented
4	C₂²×D₃₅	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₅×C₇	C₂²	1	3	yes	—
6	C₂×Dic₃₅	C₂²	1	3	yes	—
7	C₄×D₃₅	C₄	1	12	yes	direct product factor
8	C₄²×D₇	—	5	1	no	maximal, Hall
9	C₄²×D₅	—	7	1	no	maximal, Hall
10	C₂²×C₅×C₇	C₂³	1	1	yes	characteristic
11	C₂×D₃₅	C₂×C₄	1	6	yes	—
12	C₄×C₅×C₇	C₂×C₄	1	6	yes	complemented
13	Dic₃₅	C₂×C₄	1	6	yes	complemented
14	C₂×C₄×D₇	—	5	3	no	—
15	C₄²×C₇	D₅	1	1	yes	characteristic, complemented
16	C₄×Dic₇	—	5	3	no	—
17	C₂×C₄×D₅	—	7	3	no	—
18	C₄²×C₅	D₇	1	1	yes	characteristic, complemented
19	C₄×Dic₅	—	7	3	no	—
20	C₂×C₅×C₇	C₂²×C₄	1	3	yes	—
21	D₃₅	C₄²	1	4	yes	direct product factor
22	C₂²×D₇	—	5	1	no	—
23	C₂×C₄×C₇	C₂×D₅	1	3	yes	—
24	C₂×Dic₇	—	5	3	no	—
25	C₄×D₇	—	5	12	no	—
26	C₂²×D₅	—	7	1	no	—
27	C₂×C₄×C₅	C₂×D₇	1	3	yes	—
28	C₂×Dic₅	—	7	3	no	—
29	C₄×D₅	—	7	12	no	—
30	C₅×C₇	C₂×C₄²	1	1	yes	characteristic, complemented, Hall
31	C₂×C₄²	—	35	1	no	Sylow
32	C₂²×C₇	C₂²×D₅	1	1	yes	characteristic
33	C₂×D₇	—	5	6	no	—
34	C₄×C₇	C₄×D₅	1	6	yes	complemented
35	Dic₇	—	5	6	no	—
36	C₂²×C₅	C₂²×D₇	1	1	yes	characteristic
37	C₂×D₅	—	7	6	no	—
38	C₄×C₅	C₄×D₇	1	6	yes	complemented
39	Dic₅	—	7	6	no	—
40	C₂²×C₄	—	35	3	no	—
41	C₄²	—	35	3	no	—
42	C₄²	D₃₅	1	1	yes	characteristic, direct product factor
43	C₂×C₇	C₂×C₄×D₅	1	3	yes	—
44	D₇	—	5	4	no	—
45	C₂×C₅	C₂×C₄×D₇	1	3	yes	—
46	D₅	—	7	4	no	—
47	C₂³	—	35	1	no	—
48	C₂×C₄	—	35	3	no	—
49	C₂×C₄	—	35	12	no	—
50	C₂×C₄	C₂×D₃₅	1	3	yes	—
51	C₇	C₄²×D₅	1	1	yes	characteristic, complemented, Sylow
52	C₅	C₄²×D₇	1	1	yes	characteristic, complemented, Sylow
53	C₂²	—	35	6	no	—
54	C₂²	C₂²×D₃₅	1	1	yes	characteristic
55	C₄	—	35	6	no	—
56	C₄	C₄×D₃₅	1	6	yes	direct product factor
57	C₂	—	35	4	no	—
58	C₂	C₂×C₄×D₃₅	1	3	yes	—

	subgroup	G/H
center, hypercenter	C₄²	D₃₅
commutator, hypocenter	C₅×C₇	C₂×C₄²
Frattini	C₂²	C₂²×D₃₅
Fitting	C₄²×C₅×C₇	C₂
socle, cosocle	C₂²×C₅×C₇	C₂³
prime radical	C₂²×D₃₅	C₂²
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₄²

Complements

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

N	H ≅ G/N	type
2. C₄²×C₅×C₇	C₂	semidirect
3. C₄×Dic₃₅	C₂	semidirect
7. C₄×D₃₅	C₄	direct (N × H)
12. C₄×C₅×C₇	C₂×C₄	semidirect
13. Dic₃₅	C₂×C₄	semidirect
15. C₄²×C₇	D₅	semidirect
18. C₄²×C₅	D₇	semidirect
21. D₃₅	C₄²	direct (N × H)
30. C₅×C₇	C₂×C₄²	semidirect
34. C₄×C₇	C₄×D₅	semidirect
38. C₄×C₅	C₄×D₇	semidirect
42. C₄²	D₃₅	direct (N × H)
51. C₇	C₄²×D₅	semidirect
52. C₅	C₄²×D₇	semidirect
56. C₄	C₄×D₃₅	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×C₄×D₃₅	2
C₄²×C₅×C₇	2
C₄×Dic₃₅	2
C₄²×D₇	5
C₄²×D₅	7

Subgroups — C42×D35 #11765201

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×D₃₅ #11765201