Subgroups — #50306254

Order 38336.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#34062707	C₂	1	1	yes	maximal, characteristic, complemented
2	#34062636	C₂	1	4	yes	maximal, complemented
3	#34062626	C₂	1	1	yes	maximal, characteristic, complemented
4	#127×C₅₉₉	C₂	1	1	yes	maximal, characteristic
5	C₂×C₅₉₉⋊C₈	C₂²	1	2	yes	—
6	C₄⋊Dic₅₉₉	C₂²	1	2	yes	—
7	Dic₅₉₉⋊C₄	—	2	2	no	—
8	C₂×D₄×C₅₉₉	—	2	2	no	—
9	C₂×D₄×C₅₉₉	C₂²	1	2	yes	—
10	C₄²×C₅₉₉	C₂²	1	1	yes	characteristic
11	C₂×Dic₅₉₉	—	2	2	no	—
12	C₅₉₉⋊C₈	—	2	2	no	—
13	C₂³×C₅₉₉	—	2	2	no	—
14	D₄×C₅₉₉	—	2	4	no	—
15	D₄×C₅₉₉	—	4	4	no	—
16	C₂×C₄×C₅₉₉	D₄	1	2	yes	—
17	C₂×C₄×C₅₉₉	C₂³	1	1	yes	characteristic
18	C₂²×C₅₉₉	—	4	2	no	—
19	C₂²×C₅₉₉	—	4	4	no	—
20	C₂²×C₅₉₉	C₂×D₄	1	1	yes	characteristic
21	C₄×C₅₉₉	—	2	2	no	—
22	C₄×C₅₉₉	#41	1	2	yes	—
23	Dic₅₉₉	—	4	2	no	—
24	C₂×C₅₉₉	—	8	2	no	—
25	C₂×C₅₉₉	#124	1	1	yes	characteristic
26	C₂×C₅₉₉	AGL(1,ℤ/8)	1	2	yes	—
27	C₅₉₉	#490	1	1	yes	characteristic, complemented, Sylow
28	#490	—	599	1	no	maximal, Sylow
29	#127	D₅₉₉	1	1	yes	characteristic
30	#125	—	599	1	no	—
31	#102	—	599	4	no	—
32	#97	—	599	1	no	—
33	C₂×D₄	—	2	2	no	—
34	C₂×D₄	C₂×D₅₉₉	1	2	yes	—
35	C₂×C₈	—	599	2	no	—
36	C₄⋊C₄	—	599	2	no	—
37	C₄⋊C₄	—	1198	2	no	—
38	C₄²	C₂×D₅₉₉	1	1	yes	characteristic
39	C₂³	—	2	2	no	—
40	D₄	—	2	4	no	—
41	D₄	—	4	4	no	—
42	C₂×C₄	—	1198	2	no	—
43	C₂×C₄	C₂²⋊D₅₉₉	1	2	yes	—
44	C₂×C₄	C₂²×D₅₉₉	1	1	yes	characteristic
45	C₈	—	1198	2	no	—
46	C₂²	—	4	2	no	—
47	C₂²	—	4	4	no	—
48	C₂²	C₂×C₂²⋊D₅₉₉	1	1	yes	characteristic
49	C₄	—	2	2	no	—
50	C₄	—	2396	2	no	—
51	C₄	#23751077	1	2	yes	—
52	C₂	—	8	2	no	—
53	C₂	#34062702	1	1	yes	characteristic
54	C₂	#34062741	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₅₉₉
commutator, cosocle	C₂×C₄×C₅₉₉	C₂³
Frattini	C₂×C₄	C₂²×D₅₉₉
Fitting, prime radical	#127×C₅₉₉	C₂
socle	C₂²×C₅₉₉	C₂×D₄
hypercenter	#127	D₅₉₉
hypocenter	C₅₉₉	#490
LCS	G ▷ C₂×C₄×C₅₉₉ ▷ C₂×C₅₉₉ ▷ C₅₉₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #127

Complements

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

N	H ≅ G/N	type
1. #34062707	C₂	semidirect
2. #34062636	C₂	semidirect
3. #34062626	C₂	semidirect
27. C₅₉₉	#490	semidirect

Maximal subgroups

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

subgroup	index
#34062707	2
#34062636	2
#34062626	2
#127×C₅₉₉	2
#490	599