Subgroups — C₂⁵×C₄×C₁₇₃ #36351372

Order 22144.

10552 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁶×C₁₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×C₄×C₁₇₃	C₂	1	62	yes	maximal, direct product factor
3	C₂⁵×C₁₇₃	C₄	1	32	yes	direct product factor
4	C₂⁵×C₁₇₃	C₂²	1	31	yes	—
5	C₂³×C₄×C₁₇₃	C₂²	1	620	yes	direct product factor
6	C₂⁴×C₁₇₃	C₂×C₄	1	496	yes	direct product factor
7	C₂⁴×C₁₇₃	C₂³	1	155	yes	—
8	C₂²×C₄×C₁₇₃	C₂³	1	1240	yes	direct product factor
9	C₂³×C₁₇₃	C₂²×C₄	1	1240	yes	direct product factor
10	C₂³×C₁₇₃	C₂⁴	1	155	yes	—
11	C₂×C₄×C₁₇₃	C₂⁴	1	496	yes	direct product factor
12	C₂²×C₁₇₃	C₂³×C₄	1	620	yes	direct product factor
13	C₂²×C₁₇₃	C₂⁵	1	31	yes	—
14	C₄×C₁₇₃	C₂⁵	1	32	yes	direct product factor
15	C₂×C₁₇₃	C₂⁴×C₄	1	62	yes	direct product factor
16	C₂×C₁₇₃	C₂⁶	1	1	yes	characteristic
17	C₁₇₃	C₂⁵×C₄	1	1	yes	characteristic, direct product factor, Sylow
18	C₂⁵×C₄	C₁₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂⁶	C₂×C₁₇₃	1	1	yes	characteristic
20	C₂⁴×C₄	C₂×C₁₇₃	1	62	yes	direct product factor
21	C₂⁵	C₄×C₁₇₃	1	32	yes	direct product factor
22	C₂⁵	C₂²×C₁₇₃	1	31	yes	—
23	C₂³×C₄	C₂²×C₁₇₃	1	620	yes	direct product factor
24	C₂⁴	C₂×C₄×C₁₇₃	1	496	yes	direct product factor
25	C₂⁴	C₂³×C₁₇₃	1	155	yes	—
26	C₂²×C₄	C₂³×C₁₇₃	1	1240	yes	direct product factor
27	C₂³	C₂²×C₄×C₁₇₃	1	1240	yes	direct product factor
28	C₂³	C₂⁴×C₁₇₃	1	155	yes	—
29	C₂×C₄	C₂⁴×C₁₇₃	1	496	yes	direct product factor
30	C₂²	C₂³×C₄×C₁₇₃	1	620	yes	direct product factor
31	C₂²	C₂⁵×C₁₇₃	1	31	yes	—
32	C₄	C₂⁵×C₁₇₃	1	32	yes	direct product factor
33	C₂	C₂⁴×C₄×C₁₇₃	1	62	yes	direct product factor
34	C₂	C₂⁶×C₁₇₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂⁶×C₁₇₃
socle, prime radical	C₂⁶×C₁₇₃	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂⁴×C₄×C₁₇₃	C₂	direct (N × H)
3. C₂⁵×C₁₇₃	C₄	direct (N × H)
5. C₂³×C₄×C₁₇₃	C₂²	direct (N × H)
6. C₂⁴×C₁₇₃	C₂×C₄	direct (N × H)
8. C₂²×C₄×C₁₇₃	C₂³	direct (N × H)
9. C₂³×C₁₇₃	C₂²×C₄	direct (N × H)
11. C₂×C₄×C₁₇₃	C₂⁴	direct (N × H)
12. C₂²×C₁₇₃	C₂³×C₄	direct (N × H)
14. C₄×C₁₇₃	C₂⁵	direct (N × H)
15. C₂×C₁₇₃	C₂⁴×C₄	direct (N × H)
17. C₁₇₃	C₂⁵×C₄	direct (N × H)
18. C₂⁵×C₄	C₁₇₃	direct (N × H)
20. C₂⁴×C₄	C₂×C₁₇₃	direct (N × H)
21. C₂⁵	C₄×C₁₇₃	direct (N × H)
23. C₂³×C₄	C₂²×C₁₇₃	direct (N × H)
24. C₂⁴	C₂×C₄×C₁₇₃	direct (N × H)
26. C₂²×C₄	C₂³×C₁₇₃	direct (N × H)
27. C₂³	C₂²×C₄×C₁₇₃	direct (N × H)
29. C₂×C₄	C₂⁴×C₁₇₃	direct (N × H)
30. C₂²	C₂³×C₄×C₁₇₃	direct (N × H)
32. C₄	C₂⁵×C₁₇₃	direct (N × H)
33. C₂	C₂⁴×C₄×C₁₇₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁶×C₁₇₃	2
C₂⁴×C₄×C₁₇₃	2
C₂⁵×C₄	173

Subgroups — C25×C4×C173 #36351372

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×C₄×C₁₇₃ #36351372