Subgroups — C₅×#6728 #11925264

Order 1200.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×SL(2,𝔽₅)	C₂	1	1	yes	maximal, characteristic
2	C₅×#226	—	5	1	no	maximal
3	#6728	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₅×#170	—	6	1	no	maximal
5	C₅×Dic₆	—	10	1	no	maximal
6	C₅×SL(2,𝔽₃)	—	5	1	no	—
7	SL(2,𝔽₅)	C₂×C₅	1	1	yes	characteristic
8	C₅×Dic₅	—	6	1	no	—
9	C₅×Q₁₆	—	15	1	no	—
10	C₃×C₄×C₅	—	10	1	no	—
11	C₅×Dic₃	—	10	1	no	—
12	C₅×Dic₃	—	10	1	no	—
13	C₂×C₅²	—	6	1	no	—
14	#226	—	5	1	no	Hall
15	C₅×Q₈	—	5	1	no	—
16	C₅×Q₈	—	15	1	no	—
17	#170	—	6	1	no	—
18	C₅×C₈	—	15	1	no	—
19	C₂×C₃×C₅	—	10	1	no	—
20	C₅²	—	6	1	no	Sylow
21	Dic₆	—	10	1	no	—
22	SL(2,𝔽₃)	—	5	1	no	—
23	C₄×C₅	—	10	1	no	—
24	C₄×C₅	—	15	1	no	—
25	Dic₅	—	6	1	no	—
26	Q₁₆	—	15	1	no	Sylow
27	C₃×C₅	—	10	1	no	—
28	C₃×C₄	—	10	1	no	—
29	Dic₃	—	10	1	no	—
30	Dic₃	—	10	1	no	—
31	C₂×C₅	—	6	1	no	—
32	C₂×C₅	—	24	1	no	—
33	C₂×C₅	S₅	1	1	yes	characteristic
34	Q₈	—	5	1	no	—
35	Q₈	—	15	1	no	—
36	C₈	—	15	1	no	—
37	C₂×C₃	—	10	1	no	—
38	C₅	—	6	1	no	—
39	C₅	—	24	1	no	—
40	C₅	#6728	1	1	yes	characteristic, direct product factor
41	C₄	—	10	1	no	—
42	C₄	—	15	1	no	—
43	C₃	—	10	1	no	Sylow
44	C₂	C₅×S₅	1	1	yes	characteristic

	subgroup	G/H
center, Fitting, socle, hypercenter	C₂×C₅	S₅
commutator, cosocle, hypocenter	SL(2,𝔽₅)	C₂×C₅
Frattini	C₂	C₅×S₅
prime radical	C₅×SL(2,𝔽₅)	C₂
LCS	G ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂×C₅

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

N	H ≅ G/N	type
3. #6728	C₅	direct (N × H)
40. C₅	#6728	direct (N × H)

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