Subgroups — D₇×C₂₃⋊(D₁₃⋊C₃) #38737372

Order 25116.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃⋊((C₁₃⋊C₃)⋊D₇)	C₂	1	1	yes	maximal, characteristic, complemented
2	D₇×C₂₃×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₂₃⋊(D₁₃⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×D₂₉₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₇×C₂₃×C₁₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₀₉₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₃×D₇×C₂₃	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇×D₂₉₉	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂×C₂₃⋊(D₁₃⋊C₃)	—	7	1	no	maximal, Hall
10	C₇×C₁₃×C₂₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₃×D₇×D₂₃	—	13	1	no	maximal, Hall
12	C₂×C₂₃×C₁₃⋊C₃	—	7	1	no	—
13	C₂₃⋊(D₁₃⋊C₃)	—	7	1	no	—
14	C₂₃⋊(D₁₃⋊C₃)	D₇	1	1	yes	characteristic, direct product factor
15	C₂×D₂₉₉	—	7	1	no	Hall
16	D₇×D₁₃⋊C₃	—	23	1	no	maximal, Hall
17	C₃×D₁₆₁	—	13	1	no	—
18	C₃×D₇×C₂₃	—	26	1	no	—
19	C₃×C₇×D₂₃	—	13	1	no	—
20	C₂₃×C₁₃⋊C₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
21	D₇×D₂₃	—	13	1	no	Hall
22	C₂×C₁₃×C₂₃	—	7	1	no	—
23	D₂₉₉	—	7	1	no	—
24	D₂₉₉	C₃×D₇	1	1	yes	characteristic, complemented
25	(C₁₃⋊C₃)⋊D₇	—	23	1	no	—
26	D₇×C₁₃⋊C₃	D₂₃	1	1	yes	characteristic, complemented
27	C₇×D₁₃⋊C₃	—	23	1	no	—
28	C₃×C₇×C₂₃	—	26	1	no	Hall
29	D₇×D₁₃	—	23	1	no	Hall
30	D₁₆₁	—	13	1	no	—
31	C₇×D₂₃	—	13	1	no	—
32	D₇×C₂₃	D₁₃⋊C₃	1	1	yes	characteristic, complemented
33	C₁₃×C₂₃	C₂×C₃×D₇	1	1	yes	characteristic, complemented, Hall
34	C₂×C₃×D₂₃	—	91	1	no	Hall
35	C₇×C₁₃⋊C₃	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
36	D₉₁	—	23	1	no	—
37	C₇×D₁₃	—	23	1	no	—
38	C₁₃×D₇	C₃×D₂₃	1	1	yes	characteristic, complemented
39	C₇×C₂₃	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
40	C₂×D₁₃⋊C₃	—	161	1	no	Hall
41	C₂×C₃×C₂₃	—	182	1	no	—
42	C₃×D₂₃	—	13	1	no	—
43	C₃×D₂₃	—	91	1	no	—
44	C₂×D₂₃	—	91	1	no	Hall
45	C₇×C₁₃	C₂×C₃×D₂₃	1	1	yes	characteristic, complemented, Hall
46	C₂×C₃×D₇	—	299	1	no	Hall
47	C₂×C₁₃⋊C₃	—	7	1	no	—
48	D₁₃⋊C₃	—	23	1	no	—
49	D₁₃⋊C₃	—	161	1	no	—
50	C₃×C₂₃	—	26	1	no	Hall
51	C₂×D₁₃	—	161	1	no	Hall
52	C₂×C₂₃	—	7	1	no	—
53	D₂₃	—	13	1	no	—
54	D₂₃	—	91	1	no	—
55	C₂×C₃×C₇	—	299	1	no	—
56	C₃×D₇	—	26	1	no	—
57	C₃×D₇	—	299	1	no	—
58	C₁₃⋊C₃	D₇×D₂₃	1	1	yes	characteristic, complemented, Hall
59	C₂×D₇	—	299	1	no	Hall
60	C₂×C₁₃	—	7	1	no	—
61	D₁₃	—	23	1	no	—
62	D₁₃	—	161	1	no	—
63	C₂₃	D₇×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
64	C₃×C₇	—	26	1	no	Hall
65	C₂×C₇	—	299	1	no	—
66	D₇	—	299	1	no	—
67	D₇	C₂₃⋊(D₁₃⋊C₃)	1	1	yes	characteristic, direct product factor
68	C₁₃	C₃×D₇×D₂₃	1	1	yes	characteristic, complemented, Sylow
69	C₂²×C₃	—	2093	1	no	Hall
70	C₇	C₂×C₂₃⋊(D₁₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₃	—	299	1	no	—
72	C₂×C₃	—	2093	1	no	—
73	C₂×C₃	—	182	1	no	—
74	C₂²	—	2093	1	no	Sylow
75	C₃	—	26	1	no	Sylow
76	C₂	—	7	1	no	—
77	C₂	—	299	1	no	—
78	C₂	—	2093	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₃×C₂₃	C₂²×C₃
LCS	G ▷ C₇×C₁₃×C₂₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₂₃⋊((C₁₃⋊C₃)⋊D₇)	C₂	semidirect
2. D₇×C₂₃×C₁₃⋊C₃	C₂	semidirect
3. C₇×C₂₃⋊(D₁₃⋊C₃)	C₂	semidirect
4. D₇×D₂₉₉	C₃	semidirect
5. C₇×C₂₃×C₁₃⋊C₃	C₂²	semidirect
6. D₂₀₉₃	C₂×C₃	semidirect
7. C₁₃×D₇×C₂₃	C₂×C₃	semidirect
8. C₇×D₂₉₉	C₂×C₃	semidirect
10. C₇×C₁₃×C₂₃	C₂²×C₃	semidirect
14. C₂₃⋊(D₁₃⋊C₃)	D₇	direct (N × H)
20. C₂₃×C₁₃⋊C₃	C₂×D₇	semidirect
24. D₂₉₉	C₃×D₇	semidirect
26. D₇×C₁₃⋊C₃	D₂₃	semidirect
32. D₇×C₂₃	D₁₃⋊C₃	semidirect
33. C₁₃×C₂₃	C₂×C₃×D₇	semidirect
35. C₇×C₁₃⋊C₃	C₂×D₂₃	semidirect
38. C₁₃×D₇	C₃×D₂₃	semidirect
39. C₇×C₂₃	C₂×D₁₃⋊C₃	semidirect
45. C₇×C₁₃	C₂×C₃×D₂₃	semidirect
58. C₁₃⋊C₃	D₇×D₂₃	semidirect
63. C₂₃	D₇×D₁₃⋊C₃	semidirect
67. D₇	C₂₃⋊(D₁₃⋊C₃)	direct (N × H)
68. C₁₃	C₃×D₇×D₂₃	semidirect
70. C₇	C₂×C₂₃⋊(D₁₃⋊C₃)	semidirect

Maximal subgroups

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

subgroup	index
C₂₃⋊((C₁₃⋊C₃)⋊D₇)	2
D₇×C₂₃×C₁₃⋊C₃	2
C₇×C₂₃⋊(D₁₃⋊C₃)	2
D₇×D₂₉₉	3
C₂×C₂₃⋊(D₁₃⋊C₃)	7
C₃×D₇×D₂₃	13
D₇×D₁₃⋊C₃	23

Subgroups — D7×C23⋊(D13⋊C3) #38737372

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×C₂₃⋊(D₁₃⋊C₃) #38737372