Subgroups — C₂⁵×#595 #14545781

Order 2176.

10552 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×#595	C₂	1	62	yes	maximal, direct product factor
2	C₂⁵×D₁₇	C₂	1	1	yes	maximal, characteristic
3	C₂⁵×C₁₇	C₄	1	1	yes	characteristic, complemented
4	C₂⁴×D₁₇	C₄	1	31	yes	complemented
5	C₂⁴×D₁₇	C₂²	1	31	yes	—
6	C₂³×#595	C₂²	1	620	yes	direct product factor
7	C₂⁴×C₁₇	C₂×C₄	1	31	yes	complemented
8	C₂³×D₁₇	C₂×C₄	1	465	yes	complemented
9	C₂³×D₁₇	C₂³	1	155	yes	—
10	C₂²×#595	C₂³	1	1240	yes	direct product factor
11	C₂³×C₁₇	C₂²×C₄	1	155	yes	complemented
12	C₂²×D₁₇	C₂²×C₄	1	1085	yes	complemented
13	C₂²×D₁₇	C₂⁴	1	155	yes	—
14	C₂×#595	C₂⁴	1	496	yes	direct product factor
15	C₂⁵×C₄	—	17	1	no	maximal, Sylow
16	C₂²×C₁₇	C₂³×C₄	1	155	yes	complemented
17	C₂×D₁₇	C₂³×C₄	1	465	yes	complemented
18	C₂×D₁₇	C₂⁵	1	31	yes	—
19	#595	C₂⁵	1	32	yes	direct product factor
20	C₂⁶	—	17	1	no	—
21	C₂⁴×C₄	—	17	62	no	—
22	C₂×C₁₇	C₂⁴×C₄	1	31	yes	complemented
23	D₁₇	C₂⁴×C₄	1	31	yes	complemented
24	D₁₇	C₂⁶	1	1	yes	characteristic
25	C₂⁵	—	17	31	no	—
26	C₂⁵	—	17	31	no	—
27	C₂⁵	#595	1	1	yes	characteristic, direct product factor
28	C₂³×C₄	—	17	620	no	—
29	C₁₇	C₂⁵×C₄	1	1	yes	characteristic, complemented, Sylow
30	C₂⁴	—	17	465	no	—
31	C₂⁴	—	17	155	no	—
32	C₂⁴	C₂×#595	1	31	yes	direct product factor
33	C₂²×C₄	—	17	1240	no	—
34	C₂³	—	17	155	no	—
35	C₂³	—	17	1085	no	—
36	C₂³	C₂²×#595	1	155	yes	direct product factor
37	C₂×C₄	—	17	496	no	—
38	C₂²	—	17	31	no	—
39	C₂²	—	17	465	no	—
40	C₂²	C₂³×#595	1	155	yes	direct product factor
41	C₄	—	17	32	no	—
42	C₂	—	17	1	no	—
43	C₂	—	17	31	no	—
44	C₂	C₂⁴×#595	1	31	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁵	#595
commutator, hypocenter	C₁₇	C₂⁵×C₄
Frattini	C₁	G
Fitting, socle	C₂⁵×C₁₇	C₄
prime radical	C₂⁵×D₁₇	C₂
cosocle	D₁₇	C₂⁶
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂⁵

Complements

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

N	H ≅ G/N	type
1. C₂⁴×#595	C₂	direct (N × H)
3. C₂⁵×C₁₇	C₄	semidirect
4. C₂⁴×D₁₇	C₄	semidirect
6. C₂³×#595	C₂²	direct (N × H)
7. C₂⁴×C₁₇	C₂×C₄	semidirect
8. C₂³×D₁₇	C₂×C₄	semidirect
10. C₂²×#595	C₂³	direct (N × H)
11. C₂³×C₁₇	C₂²×C₄	semidirect
12. C₂²×D₁₇	C₂²×C₄	semidirect
14. C₂×#595	C₂⁴	direct (N × H)
16. C₂²×C₁₇	C₂³×C₄	semidirect
17. C₂×D₁₇	C₂³×C₄	semidirect
19. #595	C₂⁵	direct (N × H)
22. C₂×C₁₇	C₂⁴×C₄	semidirect
23. D₁₇	C₂⁴×C₄	semidirect
27. C₂⁵	#595	direct (N × H)
29. C₁₇	C₂⁵×C₄	semidirect
32. C₂⁴	C₂×#595	direct (N × H)
36. C₂³	C₂²×#595	direct (N × H)
40. C₂²	C₂³×#595	direct (N × H)
44. C₂	C₂⁴×#595	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×#595	2
C₂⁵×D₁₇	2
C₂⁵×C₄	17

Subgroups — C25×#595 #14545781

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×#595 #14545781