Subgroups — C₂×#401×C₁₅₇ #34096758

Order 20096.

516 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#401×C₁₅₇	C₂	1	8	yes	maximal, direct product factor
2	C₂×#95×C₁₅₇	C₂	1	7	yes	maximal
3	C₂³×C₄×C₁₅₇	C₂²	1	7	yes	—
4	#95×C₁₅₇	C₂²	1	28	yes	—
5	C₂⁴×C₁₅₇	C₂³	1	1	yes	characteristic
6	C₂²×C₄×C₁₅₇	—	2	42	no	—
7	C₂²×C₄×C₁₅₇	C₂³	1	14	yes	—
8	C₂³×C₁₅₇	#41	1	14	yes	—
9	C₂³×C₁₅₇	C₂⁴	1	1	yes	characteristic
10	C₂×C₄×C₁₅₇	—	2	42	no	—
11	C₂×C₄×C₁₅₇	—	4	28	no	—
12	C₂²×C₁₅₇	#126	1	28	yes	—
13	C₂²×C₁₅₇	C₂×#41	1	7	yes	—
14	C₄×C₁₅₇	—	4	14	no	—
15	C₂×C₁₅₇	#401	1	8	yes	direct product factor
16	C₂×C₁₅₇	C₂×#126	1	7	yes	—
17	C₁₅₇	C₂×#401	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×#401	C₁₅₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	#401	C₂×C₁₅₇	1	8	yes	direct product factor
20	C₂×#95	C₂×C₁₅₇	1	7	yes	—
21	C₂³×C₄	C₂²×C₁₅₇	1	7	yes	—
22	#95	C₂²×C₁₅₇	1	28	yes	—
23	C₂⁴	C₂³×C₁₅₇	1	1	yes	characteristic
24	C₂²×C₄	—	2	42	no	—
25	C₂²×C₄	C₂³×C₁₅₇	1	14	yes	—
26	C₂³	#41×C₁₅₇	1	14	yes	—
27	C₂³	C₂⁴×C₁₅₇	1	1	yes	characteristic
28	C₂×C₄	—	2	42	no	—
29	C₂×C₄	—	4	28	no	—
30	C₂²	#126×C₁₅₇	1	28	yes	—
31	C₂²	C₂×#41×C₁₅₇	1	7	yes	—
32	C₄	—	4	14	no	—
33	C₂	#401×C₁₅₇	1	8	yes	direct product factor
34	C₂	C₂×#126×C₁₅₇	1	7	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₅₇	C₂³
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₅₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₅₇ ◁ G

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

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