Subgroups — C₂×D₁₃₂₃ #72210550

Order 5292.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃₂₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₂₇×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄₄₁	—	3	1	no	maximal
4	C₂₇×C₄₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₉×C₄₉	D₃	1	1	yes	characteristic
6	D₄₄₁	—	3	2	no	—
7	C₂×D₁₈₉	—	7	1	no	maximal
8	C₂×D₁₄₇	—	9	1	no	—
9	C₉×C₄₉	C₂×D₃	1	1	yes	characteristic
10	C₂×C₇×C₂₇	D₇	1	1	yes	characteristic
11	D₁₈₉	—	7	2	no	—
12	C₂×C₃×C₄₉	D₉	1	1	yes	characteristic
13	D₁₄₇	—	9	2	no	—
14	C₂×D₆₃	—	21	1	no	—
15	C₂×D₄₉	—	27	1	no	Hall
16	C₇×C₂₇	C₂×D₇	1	1	yes	characteristic
17	C₃×C₄₉	C₂×D₉	1	1	yes	characteristic
18	C₂×C₇×C₉	D₂₁	1	1	yes	characteristic
19	D₆₃	—	21	2	no	—
20	C₂×D₂₇	—	49	1	no	Hall
21	C₂×C₄₉	D₂₇	1	1	yes	characteristic, complemented
22	D₄₉	—	27	2	no	—
23	C₂×D₂₁	—	63	1	no	—
24	C₇×C₉	C₂×D₂₁	1	1	yes	characteristic
25	C₂×C₂₇	D₄₉	1	1	yes	characteristic, complemented
26	D₂₇	—	49	2	no	—
27	C₄₉	C₂×D₂₇	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃×C₇	D₆₃	1	1	yes	characteristic
29	D₂₁	—	63	2	no	—
30	C₂×D₉	—	147	1	no	—
31	C₂×D₇	—	189	1	no	—
32	C₂₇	C₂×D₄₉	1	1	yes	characteristic, complemented, Sylow
33	C₃×C₇	C₂×D₆₃	1	1	yes	characteristic
34	C₂×C₉	D₁₄₇	1	1	yes	characteristic
35	D₉	—	147	2	no	—
36	C₂×C₇	D₁₈₉	1	1	yes	characteristic
37	D₇	—	189	2	no	—
38	C₂×D₃	—	441	1	no	—
39	C₉	C₂×D₁₄₇	1	1	yes	characteristic
40	C₇	C₂×D₁₈₉	1	1	yes	characteristic
41	C₂×C₃	D₄₄₁	1	1	yes	characteristic
42	D₃	—	441	2	no	—
43	C₂²	—	1323	1	no	Sylow
44	C₃	C₂×D₄₄₁	1	1	yes	characteristic
45	C₂	—	1323	2	no	—
46	C₂	D₁₃₂₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₁₃₂₃
commutator, cosocle, hypocenter	C₂₇×C₄₉	C₂²
Frattini	C₇×C₉	C₂×D₂₁
Fitting	C₂×C₂₇×C₄₉	C₂
socle	C₂×C₃×C₇	D₆₃
LCS	G ▷ C₂₇×C₄₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. D₁₃₂₃	C₂	direct (N × H)
2. C₂×C₂₇×C₄₉	C₂	semidirect
4. C₂₇×C₄₉	C₂²	semidirect
21. C₂×C₄₉	D₂₇	semidirect
25. C₂×C₂₇	D₄₉	semidirect
27. C₄₉	C₂×D₂₇	semidirect
32. C₂₇	C₂×D₄₉	semidirect
46. C₂	D₁₃₂₃	direct (N × H)

Maximal subgroups

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

subgroup	index
D₁₃₂₃	2
C₂×C₂₇×C₄₉	2
C₂×D₄₄₁	3
C₂×D₁₈₉	7

Subgroups — C2×D1323 #72210550

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₃₂₃ #72210550