Subgroups — C₄×D₄×C₇₃₉ #37556539

Order 23648.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₇₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₇₃₉	C₂	1	2	yes	maximal, complemented
3	C₄⋊C₄×C₇₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²⋊C₄×C₇₃₉	C₂	1	2	yes	maximal, complemented
5	C₄²×C₇₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×C₇₃₉	C₂²	1	2	yes	—
7	D₄×C₇₃₉	C₄	1	4	yes	direct product factor
8	C₂×C₄×C₇₃₉	—	2	4	no	—
9	C₂×C₄×C₇₃₉	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₇₃₉	C₂²	1	2	yes	—
11	C₂×C₄×C₇₃₉	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₇₃₉	C₂²	1	1	yes	characteristic
13	C₂²×C₇₃₉	—	2	2	no	—
14	C₂²×C₇₃₉	—	2	2	no	—
15	C₂²×C₇₃₉	C₂×C₄	1	4	yes	complemented
16	C₂²×C₇₃₉	C₂³	1	1	yes	characteristic
17	C₄×C₇₃₉	—	2	2	no	—
18	C₄×C₇₃₉	—	2	1	no	—
19	C₄×C₇₃₉	C₂×C₄	1	2	yes	complemented
20	C₄×C₇₃₉	D₄	1	2	yes	direct product factor
21	C₂×C₇₃₉	—	2	4	no	—
22	C₂×C₇₃₉	C₂²×C₄	1	1	yes	characteristic
23	C₂×C₇₃₉	C₂×D₄	1	1	yes	characteristic
24	C₂×C₇₃₉	#41	1	1	yes	characteristic
25	C₇₃₉	C₄×D₄	1	1	yes	characteristic, direct product factor, Sylow
26	C₄×D₄	C₇₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
27	C₂×D₄	C₂×C₇₃₉	1	1	yes	characteristic
28	C₂²×C₄	C₂×C₇₃₉	1	2	yes	complemented
29	C₄⋊C₄	C₂×C₇₃₉	1	1	yes	characteristic, complemented
30	C₂²⋊C₄	C₂×C₇₃₉	1	2	yes	complemented
31	C₄²	C₂×C₇₃₉	1	1	yes	characteristic, complemented
32	C₂³	C₂²×C₇₃₉	1	2	yes	—
33	D₄	C₄×C₇₃₉	1	4	yes	direct product factor
34	C₂×C₄	—	2	4	no	—
35	C₂×C₄	C₂²×C₇₃₉	1	1	yes	characteristic
36	C₂×C₄	C₂²×C₇₃₉	1	2	yes	—
37	C₂×C₄	C₂²×C₇₃₉	1	1	yes	characteristic
38	C₂×C₄	C₂²×C₇₃₉	1	1	yes	characteristic
39	C₂²	—	2	2	no	—
40	C₂²	—	2	2	no	—
41	C₂²	C₂×C₄×C₇₃₉	1	4	yes	complemented
42	C₂²	C₂³×C₇₃₉	1	1	yes	characteristic
43	C₄	—	2	2	no	—
44	C₄	—	2	1	no	—
45	C₄	C₂×C₄×C₇₃₉	1	2	yes	complemented
46	C₄	D₄×C₇₃₉	1	2	yes	direct product factor
47	C₂	—	2	4	no	—
48	C₂	C₂²×C₄×C₇₃₉	1	1	yes	characteristic
49	C₂	C₂×D₄×C₇₃₉	1	1	yes	characteristic
50	C₂	#41×C₇₃₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇₃₉	C₂²
commutator	C₂	C₂²×C₄×C₇₃₉
Frattini, cosocle	C₂²	C₂³×C₇₃₉
socle	C₂²×C₇₃₉	C₂³
prime radical	C₂×D₄×C₇₃₉	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×C₇₃₉	C₂	semidirect
3. C₄⋊C₄×C₇₃₉	C₂	semidirect
4. C₂²⋊C₄×C₇₃₉	C₂	semidirect
5. C₄²×C₇₃₉	C₂	semidirect
7. D₄×C₇₃₉	C₄	direct (N × H)
15. C₂²×C₇₃₉	C₂×C₄	semidirect
19. C₄×C₇₃₉	C₂×C₄	semidirect
20. C₄×C₇₃₉	D₄	direct (N × H)
25. C₇₃₉	C₄×D₄	direct (N × H)
26. C₄×D₄	C₇₃₉	direct (N × H)
28. C₂²×C₄	C₂×C₇₃₉	semidirect
29. C₄⋊C₄	C₂×C₇₃₉	semidirect
30. C₂²⋊C₄	C₂×C₇₃₉	semidirect
31. C₄²	C₂×C₇₃₉	semidirect
33. D₄	C₄×C₇₃₉	direct (N × H)
41. C₂²	C₂×C₄×C₇₃₉	semidirect
45. C₄	C₂×C₄×C₇₃₉	semidirect
46. C₄	D₄×C₇₃₉	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×D₄×C₇₃₉	2
C₂²×C₄×C₇₃₉	2
C₄⋊C₄×C₇₃₉	2
C₂²⋊C₄×C₇₃₉	2
C₄²×C₇₃₉	2
C₄×D₄	739

Subgroups — C4×D4×C739 #37556539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₄×C₇₃₉ #37556539