Subgroups — C₅×#73290 #14511014

Order 1920.

214 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2811	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₂²⋊SL(2,𝔽₃)	—	4	2	no	maximal
3	C₂×C₅×C₄²⋊C₃	—	4	3	no	maximal
4	#73290	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×#395	—	3	2	no	—
6	C₅×#391	—	3	3	no	—
7	C₅×C₄²⋊C₃	—	4	3	no	—
8	C₂²×C₅×Q₈	—	3	1	no	—
9	C₂²×C₅×Q₈	A₄	1	2	yes	—
10	C₂×C₅×C₄⋊C₄	—	3	3	no	—
11	C₂×C₄²×C₅	A₄	1	3	yes	—
12	C₅×#95	—	3	6	no	—
13	#2811	C₃×C₅	1	1	yes	characteristic, complemented, Sylow
14	C₂×C₅×A₄	—	16	1	no	—
15	C₅×SL(2,𝔽₃)	—	16	8	no	—
16	C₂²⋊SL(2,𝔽₃)	—	4	2	no	—
17	C₂×C₄²⋊C₃	—	4	3	no	—
18	C₂×C₅×Q₈	—	3	4	no	—
19	C₂×C₅×Q₈	—	12	2	no	—
20	C₂×C₅×Q₈	—	12	1	no	—
21	C₂×C₅×Q₈	—	12	1	no	—
22	C₂²×C₄×C₅	—	3	3	no	—
23	C₂²×C₄×C₅	—	3	2	no	—
24	C₅×C₄⋊C₄	—	12	3	no	—
25	C₄²×C₅	—	4	3	no	—
26	#395	—	3	2	no	—
27	#391	—	3	3	no	—
28	C₅×A₄	—	16	1	no	—
29	C₄²⋊C₃	—	4	3	no	—
30	C₂³×C₅	C₂²⋊A₄	1	1	yes	characteristic
31	C₅×Q₈	—	4	8	no	—
32	C₅×Q₈	—	12	4	no	—
33	C₂×C₄×C₅	—	3	6	no	—
34	C₂×C₄×C₅	—	6	3	no	—
35	C₂×C₄×C₅	—	6	3	no	—
36	C₂×C₄×C₅	—	6	6	no	—
37	C₂²×Q₈	—	3	1	no	—
38	C₂²×Q₈	C₅×A₄	1	2	yes	—
39	C₂×C₄⋊C₄	—	3	3	no	—
40	C₂×C₄²	C₅×A₄	1	3	yes	—
41	#95	—	3	6	no	—
42	C₂×C₃×C₅	—	64	1	no	—
43	C₂×A₄	—	16	1	no	—
44	SL(2,𝔽₃)	—	16	8	no	—
45	C₂²×C₅	—	3	1	no	—
46	C₂²×C₅	—	3	1	no	—
47	C₂²×C₅	#997	1	1	yes	characteristic
48	C₄×C₅	—	6	6	no	—
49	C₄×C₅	—	12	2	no	—
50	C₂×Q₈	—	3	4	no	—
51	C₂×Q₈	—	12	2	no	—
52	C₂×Q₈	—	12	1	no	—
53	C₂×Q₈	—	12	1	no	—
54	C₂²×C₄	—	3	3	no	—
55	C₂²×C₄	—	3	2	no	—
56	C₄⋊C₄	—	12	3	no	—
57	C₄²	—	4	3	no	—
58	C₃×C₅	—	64	1	no	Hall
59	A₄	—	16	1	no	—
60	C₂×C₅	—	3	1	no	—
61	C₂×C₅	—	3	1	no	—
62	C₂×C₅	#5464	1	1	yes	characteristic
63	C₂³	C₅×C₂²⋊A₄	1	1	yes	characteristic
64	Q₈	—	4	8	no	—
65	Q₈	—	12	4	no	—
66	C₂×C₄	—	3	6	no	—
67	C₂×C₄	—	6	3	no	—
68	C₂×C₄	—	6	3	no	—
69	C₂×C₄	—	6	6	no	—
70	C₂×C₃	—	64	1	no	—
71	C₅	#73290	1	1	yes	characteristic, direct product factor, Sylow
72	C₂²	—	3	1	no	—
73	C₂²	—	3	1	no	—
74	C₂²	C₅×#997	1	1	yes	characteristic
75	C₄	—	6	6	no	—
76	C₄	—	12	2	no	—
77	C₃	—	64	1	no	Sylow
78	C₂	—	3	1	no	—
79	C₂	—	3	1	no	—
80	C₂	C₅×#5464	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅	#5464
commutator, cosocle, hypocenter	#2811	C₃×C₅
Frattini	C₂³	C₅×C₂²⋊A₄
Fitting	C₅×#2811	C₃
socle	C₂³×C₅	C₂²⋊A₄
LCS	G ▷ #2811
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×#2811	C₃	semidirect
4. #73290	C₅	direct (N × H)
13. #2811	C₃×C₅	semidirect
71. C₅	#73290	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#2811	3
C₅×C₂²⋊SL(2,𝔽₃)	4
C₂×C₅×C₄²⋊C₃	4
#73290	5

Subgroups — C5×#73290 #14511014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#73290 #14511014