Subgroups — C₃×C₇×C₂₃×A₅ #44394685

Order 28980.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₂₃×A₅	C₃	1	1	yes	maximal, characteristic, direct product factor
2	C₃×C₇×A₄×C₂₃	—	5	1	no	maximal, Hall
3	C₃×C₇×D₅×C₂₃	—	6	1	no	maximal
4	C₃×C₂₃×A₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×D₃×C₇×C₂₃	—	10	1	no	maximal
6	C₃×C₅×C₇×C₂₃	—	6	1	no	—
7	C₂²×C₃×C₇×C₂₃	—	5	1	no	—
8	C₇×A₄×C₂₃	—	5	1	no	—
9	C₇×A₄×C₂₃	—	5	2	no	—
10	C₇×D₅×C₂₃	—	6	1	no	—
11	C₃²×C₇×C₂₃	—	10	1	no	Hall
12	C₂₃×A₅	C₃×C₇	1	1	yes	characteristic, direct product factor
13	C₃×C₇×A₅	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₃×C₇×C₂₃	—	15	1	no	—
15	D₃×C₇×C₂₃	—	10	1	no	—
16	C₃×A₄×C₂₃	—	5	1	no	Hall
17	C₅×C₇×C₂₃	—	6	1	no	Hall
18	C₃×D₅×C₂₃	—	6	1	no	—
19	C₂²×C₇×C₂₃	—	5	1	no	Hall
20	C₃×C₇×C₂₃	—	10	1	no	—
21	C₃×C₇×C₂₃	—	20	1	no	—
22	C₃×C₇×C₂₃	A₅	1	1	yes	maximal normal, characteristic, direct product factor
23	C₇×A₅	C₃×C₂₃	1	1	yes	characteristic, direct product factor
24	C₃×D₃×C₂₃	—	10	1	no	—
25	C₃×C₅×C₂₃	—	6	1	no	—
26	C₂×C₇×C₂₃	—	15	1	no	—
27	C₂²×C₃×C₂₃	—	5	1	no	—
28	A₄×C₂₃	—	5	1	no	—
29	A₄×C₂₃	—	5	2	no	—
30	C₃×C₇×A₄	—	5	1	no	Hall
31	D₅×C₂₃	—	6	1	no	—
32	C₃×C₇×D₅	—	6	1	no	—
33	C₃²×C₂₃	—	10	1	no	Hall
34	C₃×A₅	C₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
35	C₇×C₂₃	C₃×A₅	1	1	yes	characteristic, direct product factor, Hall
36	C₂×C₃×C₂₃	—	15	1	no	—
37	D₃×C₂₃	—	10	1	no	—
38	C₃×D₃×C₇	—	10	1	no	—
39	C₅×C₂₃	—	6	1	no	Hall
40	C₃×C₅×C₇	—	6	1	no	—
41	C₂²×C₂₃	—	5	1	no	Hall
42	C₂²×C₃×C₇	—	5	1	no	—
43	C₇×A₄	—	5	1	no	—
44	C₇×A₄	—	5	2	no	—
45	C₇×D₅	—	6	1	no	—
46	C₃×C₂₃	—	10	1	no	—
47	C₃×C₂₃	—	20	1	no	—
48	C₃×C₂₃	C₇×A₅	1	1	yes	characteristic, direct product factor
49	C₃²×C₇	—	10	1	no	Hall
50	A₅	C₃×C₇×C₂₃	1	1	yes	characteristic, direct product factor
51	C₂×C₂₃	—	15	1	no	—
52	C₂×C₃×C₇	—	15	1	no	—
53	D₃×C₇	—	10	1	no	—
54	C₃×A₄	—	5	1	no	Hall
55	C₅×C₇	—	6	1	no	Hall
56	C₃×D₅	—	6	1	no	—
57	C₂²×C₇	—	5	1	no	Hall
58	C₂₃	C₃×C₇×A₅	1	1	yes	characteristic, direct product factor, Sylow
59	C₃×C₇	—	10	1	no	—
60	C₃×C₇	—	20	1	no	—
61	C₃×C₇	C₂₃×A₅	1	1	yes	characteristic, direct product factor
62	C₃×D₃	—	10	1	no	—
63	C₃×C₅	—	6	1	no	—
64	C₂×C₇	—	15	1	no	—
65	C₂²×C₃	—	5	1	no	—
66	A₄	—	5	1	no	—
67	A₄	—	5	2	no	—
68	D₅	—	6	1	no	—
69	C₃²	—	10	1	no	Sylow
70	C₇	C₃×C₂₃×A₅	1	1	yes	characteristic, direct product factor, Sylow
71	C₂×C₃	—	15	1	no	—
72	D₃	—	10	1	no	—
73	C₅	—	6	1	no	Sylow
74	C₂²	—	5	1	no	Sylow
75	C₃	—	10	1	no	—
76	C₃	—	20	1	no	—
77	C₃	C₇×C₂₃×A₅	1	1	yes	characteristic, direct product factor
78	C₂	—	15	1	no	—

	subgroup	G/H
center, Fitting, hypercenter	C₃×C₇×C₂₃	A₅
commutator, hypocenter	A₅	C₃×C₇×C₂₃
Frattini	C₁	G
LCS	G ▷ A₅
UCS	C₁ ◁ C₃×C₇×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₇×C₂₃×A₅	C₃	direct (N × H)
4. C₃×C₂₃×A₅	C₇	direct (N × H)
12. C₂₃×A₅	C₃×C₇	direct (N × H)
13. C₃×C₇×A₅	C₂₃	direct (N × H)
22. C₃×C₇×C₂₃	A₅	direct (N × H)
23. C₇×A₅	C₃×C₂₃	direct (N × H)
34. C₃×A₅	C₇×C₂₃	direct (N × H)
35. C₇×C₂₃	C₃×A₅	direct (N × H)
48. C₃×C₂₃	C₇×A₅	direct (N × H)
50. A₅	C₃×C₇×C₂₃	direct (N × H)
58. C₂₃	C₃×C₇×A₅	direct (N × H)
61. C₃×C₇	C₂₃×A₅	direct (N × H)
70. C₇	C₃×C₂₃×A₅	direct (N × H)
77. C₃	C₇×C₂₃×A₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₂₃×A₅	3
C₃×C₇×A₄×C₂₃	5
C₃×C₇×D₅×C₂₃	6
C₃×C₂₃×A₅	7
C₃×D₃×C₇×C₂₃	10
C₃×C₇×A₅	23

Subgroups — C3×C7×C23×A5 #44394685

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×C₂₃×A₅ #44394685