Subgroups — C₂×(C₁₃⋊C₉)⋊D₆₇ #44535608

Order 31356.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₁₃⋊C₉)⋊D₆₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₆₇×C₁₃⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₈₇₁	C₃	1	1	yes	maximal, characteristic
4	C₆₇×C₁₃⋊C₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×D₈₇₁	C₂×C₃	1	2	yes	—
6	C₂×C₃×C₁₃×C₆₇	C₂×C₃	1	1	yes	characteristic
7	C₂×D₈₇₁	C₉	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₃×C₆₇	C₂²×C₃	1	1	yes	characteristic
9	C₂×C₉×D₆₇	—	13	1	no	maximal, Hall
10	C₂×C₁₃×C₆₇	C₂×C₉	1	1	yes	characteristic, complemented
11	D₈₇₁	C₂×C₉	1	2	yes	complemented
12	C₂×C₉×C₆₇	—	13	1	no	—
13	C₉×D₆₇	—	13	2	no	—
14	C₁₃×C₆₇	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×D₆₇	—	13	1	no	—
16	C₉×C₆₇	—	13	1	no	Hall
17	C₂×D₁₃⋊C₉	—	67	1	no	maximal, Hall
18	C₂×C₃×C₆₇	D₁₃⋊C₃	1	1	yes	characteristic
19	C₃×D₆₇	—	13	2	no	—
20	C₂×D₆₇	—	13	1	no	Hall
21	C₂×C₁₃⋊C₉	D₆₇	1	1	yes	characteristic, complemented
22	D₁₃⋊C₉	—	67	2	no	—
23	C₃×C₆₇	C₂×D₁₃⋊C₃	1	1	yes	characteristic
24	C₂×C₃×D₁₃	—	67	1	no	—
25	C₂×C₆₇	D₁₃⋊C₉	1	1	yes	characteristic, complemented
26	D₆₇	—	13	2	no	—
27	C₁₃⋊C₉	C₂×D₆₇	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×C₁₃	C₃×D₆₇	1	1	yes	characteristic
29	C₃×D₁₃	—	67	2	no	—
30	C₆₇	C₂×D₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
31	C₂×D₁₃	—	67	1	no	Hall
32	C₃×C₁₃	C₂×C₃×D₆₇	1	1	yes	characteristic
33	C₂²×C₉	—	871	1	no	Hall
34	C₂×C₁₃	C₉×D₆₇	1	1	yes	characteristic, complemented
35	D₁₃	—	67	2	no	—
36	C₂×C₉	—	13	1	no	—
37	C₂×C₉	—	871	2	no	—
38	C₁₃	C₂×C₉×D₆₇	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₃	—	871	1	no	—
40	C₉	—	13	1	no	Sylow
41	C₂×C₃	—	871	2	no	—
42	C₂×C₃	(C₁₃⋊C₃)⋊D₆₇	1	1	yes	characteristic
43	C₂²	—	871	1	no	Sylow
44	C₃	C₂×(C₁₃⋊C₃)⋊D₆₇	1	1	yes	characteristic
45	C₂	—	871	2	no	—
46	C₂	(C₁₃⋊C₉)⋊D₆₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	(C₁₃⋊C₃)⋊D₆₇
commutator, hypocenter	C₁₃×C₆₇	C₂²×C₉
Frattini	C₃	C₂×(C₁₃⋊C₃)⋊D₆₇
Fitting, socle	C₂×C₃×C₁₃×C₆₇	C₂×C₃
prime radical	C₂×C₃×D₈₇₁	C₃
cosocle	C₃×C₁₃×C₆₇	C₂²×C₃
LCS	G ▷ C₁₃×C₆₇
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. (C₁₃⋊C₉)⋊D₆₇	C₂	direct (N × H)
2. C₂×C₆₇×C₁₃⋊C₉	C₂	semidirect
4. C₆₇×C₁₃⋊C₉	C₂²	semidirect
7. C₂×D₈₇₁	C₉	semidirect
10. C₂×C₁₃×C₆₇	C₂×C₉	semidirect
11. D₈₇₁	C₂×C₉	semidirect
14. C₁₃×C₆₇	C₂²×C₉	semidirect
21. C₂×C₁₃⋊C₉	D₆₇	semidirect
25. C₂×C₆₇	D₁₃⋊C₉	semidirect
27. C₁₃⋊C₉	C₂×D₆₇	semidirect
30. C₆₇	C₂×D₁₃⋊C₉	semidirect
34. C₂×C₁₃	C₉×D₆₇	semidirect
38. C₁₃	C₂×C₉×D₆₇	semidirect
46. C₂	(C₁₃⋊C₉)⋊D₆₇	direct (N × H)

Maximal subgroups

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

subgroup	index
(C₁₃⋊C₉)⋊D₆₇	2
C₂×C₆₇×C₁₃⋊C₉	2
C₂×C₃×D₈₇₁	3
C₂×C₉×D₆₇	13
C₂×D₁₃⋊C₉	67

Subgroups — C2×(C13⋊C9)⋊D67 #44535608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×(C₁₃⋊C₉)⋊D₆₇ #44535608