Subgroups — #379×C₂₅₇ #30656248

Order 16448.

506 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₂₅₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂²⋊C₄×C₂₅₇	C₂	1	6	yes	maximal, complemented
3	C₂⁴×C₂₅₇	—	2	12	no	—
4	C₂⁴×C₂₅₇	C₄	1	4	yes	complemented
5	C₂⁴×C₂₅₇	C₂²	1	3	yes	—
6	C₂²×C₄×C₂₅₇	C₂²	1	4	yes	complemented
7	C₂²⋊C₄×C₂₅₇	—	2	12	no	—
8	C₂³×C₂₅₇	—	2	32	no	—
9	C₂³×C₂₅₇	—	2	24	no	—
10	C₂³×C₂₅₇	—	2	12	no	—
11	C₂³×C₂₅₇	C₂×C₄	1	6	yes	—
12	C₂³×C₂₅₇	D₄	1	12	yes	—
13	C₂³×C₂₅₇	C₂³	1	1	yes	characteristic
14	C₂×C₄×C₂₅₇	—	2	12	no	—
15	C₂²×C₂₅₇	—	2	32	no	—
16	C₂²×C₂₅₇	—	2	12	no	—
17	C₂²×C₂₅₇	—	2	24	no	—
18	C₂²×C₂₅₇	C₂²⋊C₄	1	12	yes	complemented
19	C₂²×C₂₅₇	C₂²×C₄	1	1	yes	characteristic
20	C₂²×C₂₅₇	C₂×D₄	1	6	yes	—
21	C₄×C₂₅₇	—	4	4	no	—
22	C₂×C₂₅₇	—	2	12	no	—
23	C₂×C₂₅₇	C₂×C₂²⋊C₄	1	3	yes	—
24	C₂×C₂₅₇	#120	1	4	yes	—
25	C₂₅₇	#379	1	1	yes	characteristic, direct product factor, Sylow
26	#379	C₂₅₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
27	C₂⁵	C₂×C₂₅₇	1	1	yes	characteristic
28	C₂×C₂²⋊C₄	C₂×C₂₅₇	1	6	yes	complemented
29	C₂⁴	—	2	12	no	—
30	C₂⁴	C₄×C₂₅₇	1	4	yes	complemented
31	C₂⁴	C₂²×C₂₅₇	1	3	yes	—
32	C₂²×C₄	C₂²×C₂₅₇	1	4	yes	complemented
33	C₂²⋊C₄	—	2	12	no	—
34	C₂³	—	2	32	no	—
35	C₂³	—	2	24	no	—
36	C₂³	—	2	12	no	—
37	C₂³	C₂×C₄×C₂₅₇	1	6	yes	—
38	C₂³	D₄×C₂₅₇	1	12	yes	—
39	C₂³	C₂³×C₂₅₇	1	1	yes	characteristic
40	C₂×C₄	—	2	12	no	—
41	C₂²	—	2	32	no	—
42	C₂²	—	2	12	no	—
43	C₂²	—	2	24	no	—
44	C₂²	C₂²⋊C₄×C₂₅₇	1	12	yes	complemented
45	C₂²	C₂²×C₄×C₂₅₇	1	1	yes	characteristic
46	C₂²	C₂×D₄×C₂₅₇	1	6	yes	—
47	C₄	—	4	4	no	—
48	C₂	—	2	12	no	—
49	C₂	C₂×C₂²⋊C₄×C₂₅₇	1	3	yes	—
50	C₂	#120×C₂₅₇	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₅₇	C₂³
commutator	C₂²	C₂²×C₄×C₂₅₇
Frattini, cosocle	C₂³	C₂³×C₂₅₇
prime radical	C₂⁵×C₂₅₇	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₅₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂²⋊C₄×C₂₅₇	C₂	semidirect
4. C₂⁴×C₂₅₇	C₄	semidirect
6. C₂²×C₄×C₂₅₇	C₂²	semidirect
18. C₂²×C₂₅₇	C₂²⋊C₄	semidirect
25. C₂₅₇	#379	direct (N × H)
26. #379	C₂₅₇	direct (N × H)
28. C₂×C₂²⋊C₄	C₂×C₂₅₇	semidirect
30. C₂⁴	C₄×C₂₅₇	semidirect
32. C₂²×C₄	C₂²×C₂₅₇	semidirect
44. C₂²	C₂²⋊C₄×C₂₅₇	semidirect

Maximal subgroups

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

subgroup	index
C₂⁵×C₂₅₇	2
C₂×C₂²⋊C₄×C₂₅₇	2
#379	257

Subgroups — #379×C257 #30656248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #379×C₂₅₇ #30656248