Subgroups — #95×D₄₃₉ #43243447

Order 28096.

330 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄₃₉	C₂	1	3	yes	maximal
2	C₄₃₉⋊#95	C₂	1	3	yes	maximal, complemented
3	#95×C₄₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×D₄₃₉	C₂²	1	1	yes	characteristic
5	C₂²×Dic₄₃₉	C₂²	1	3	yes	—
6	C₂×C₄×D₄₃₉	—	2	12	no	—
7	C₂×C₄×D₄₃₉	C₄	1	12	yes	complemented
8	C₂²×C₄×C₄₃₉	C₂²	1	3	yes	—
9	C₂²×D₄₃₉	C₂×C₄	1	6	yes	—
10	C₂²×D₄₃₉	D₄	1	6	yes	—
11	C₂²×D₄₃₉	Q₈	1	2	yes	—
12	C₂×Dic₄₃₉	—	2	6	no	—
13	C₂×Dic₄₃₉	C₂×C₄	1	6	yes	complemented
14	C₄×D₄₃₉	—	2	24	no	—
15	C₂³×C₄₃₉	C₂³	1	1	yes	characteristic
16	C₂×C₄×C₄₃₉	—	2	6	no	—
17	C₂×C₄×C₄₃₉	C₂×C₄	1	6	yes	complemented
18	C₂²×C₄₃₉	C₂²×C₄	1	3	yes	—
19	C₂²×C₄₃₉	C₂×D₄	1	3	yes	—
20	C₂²×C₄₃₉	C₂×Q₈	1	1	yes	characteristic
21	C₂×D₄₃₉	C₄²	1	4	yes	—
22	C₂×D₄₃₉	C₂²⋊C₄	1	12	yes	—
23	C₂×D₄₃₉	C₄⋊C₄	1	12	yes	—
24	C₄×C₄₃₉	—	2	6	no	—
25	Dic₄₃₉	—	2	6	no	—
26	C₂×C₄₃₉	C₂×C₄²	1	1	yes	characteristic
27	C₂×C₄₃₉	C₂×C₂²⋊C₄	1	3	yes	—
28	C₂×C₄₃₉	C₂×C₄⋊C₄	1	3	yes	—
29	D₄₃₉	#95	1	8	yes	direct product factor
30	C₄₃₉	C₂×#95	1	1	yes	characteristic, complemented, Sylow
31	C₂×#95	—	439	1	no	maximal, Sylow
32	C₂³×C₄	—	439	3	no	—
33	#95	—	439	3	no	—
34	#95	D₄₃₉	1	1	yes	characteristic, direct product factor
35	C₂⁴	—	439	1	no	—
36	C₂²×C₄	—	878	12	no	—
37	C₂²×C₄	—	439	3	no	—
38	C₂²×C₄	—	439	12	no	—
39	C₂²×C₄	C₂×D₄₃₉	1	3	yes	—
40	C₂³	—	439	6	no	—
41	C₂³	—	439	6	no	—
42	C₂³	—	439	2	no	—
43	C₂³	C₂²×D₄₃₉	1	1	yes	characteristic
44	C₂×C₄	—	2	6	no	—
45	C₂×C₄	—	878	24	no	—
46	C₂×C₄	—	878	6	no	—
47	C₂×C₄	—	439	6	no	—
48	C₂×C₄	C₄×D₄₃₉	1	6	yes	complemented
49	C₂²	—	439	4	no	—
50	C₂²	—	439	12	no	—
51	C₂²	—	439	12	no	—
52	C₂²	C₂×C₄×D₄₃₉	1	3	yes	—
53	C₂²	D₄×D₄₃₉	1	3	yes	—
54	C₂²	Q₈×D₄₃₉	1	1	yes	characteristic
55	C₄	—	2	6	no	—
56	C₄	—	878	6	no	—
57	C₂	—	439	8	no	—
58	C₂	C₄²×D₄₃₉	1	1	yes	characteristic
59	C₂	C₂²⋊C₄×D₄₃₉	1	3	yes	—
60	C₂	C₄⋊C₄×D₄₃₉	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₄₃₉
commutator	C₂×C₄₃₉	C₂×C₄²
Fitting	#95×C₄₃₉	C₂
socle, cosocle	C₂³×C₄₃₉	C₂³
prime radical	C₂³×D₄₃₉	C₂²
hypercenter	#95	D₄₃₉
hypocenter	C₄₃₉	C₂×#95
LCS	G ▷ C₂×C₄₃₉ ▷ C₄₃₉
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
2. C₄₃₉⋊#95	C₂	semidirect
3. #95×C₄₃₉	C₂	semidirect
7. C₂×C₄×D₄₃₉	C₄	semidirect
13. C₂×Dic₄₃₉	C₂×C₄	semidirect
17. C₂×C₄×C₄₃₉	C₂×C₄	semidirect
29. D₄₃₉	#95	direct (N × H)
30. C₄₃₉	C₂×#95	semidirect
34. #95	D₄₃₉	direct (N × H)
48. C₂×C₄	C₄×D₄₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄₃₉	2
C₄₃₉⋊#95	2
#95×C₄₃₉	2
C₂×#95	439

Subgroups — #95×D439 #43243447

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #95×D₄₃₉ #43243447