Subgroups — C₂×D₉₅₁₃ #49184871

Order 38052.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₉₅₁₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₉×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃₁₇₁	—	3	1	no	maximal
4	C₇×C₉×C₁₅₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₃₁₇₁	—	3	2	no	—
6	C₂×C₃×C₇×C₁₅₁	D₃	1	1	yes	characteristic
7	C₂×D₁₃₅₉	—	7	1	no	maximal, Hall
8	C₂×D₁₀₅₇	—	9	1	no	Hall
9	C₃×C₇×C₁₅₁	C₂×D₃	1	1	yes	characteristic
10	D₁₃₅₉	—	7	2	no	—
11	C₂×C₉×C₁₅₁	D₇	1	1	yes	characteristic, complemented
12	C₂×C₇×C₁₅₁	D₉	1	1	yes	characteristic, complemented
13	D₁₀₅₇	—	9	2	no	—
14	C₂×D₄₅₃	—	21	1	no	—
15	C₉×C₁₅₁	C₂×D₇	1	1	yes	characteristic, complemented, Hall
16	C₇×C₁₅₁	C₂×D₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₁₅₁	D₂₁	1	1	yes	characteristic
18	D₄₅₃	—	21	2	no	—
19	C₂×D₁₅₁	—	63	1	no	Hall
20	C₃×C₁₅₁	C₂×D₂₁	1	1	yes	characteristic
21	C₂×C₁₅₁	D₆₃	1	1	yes	characteristic, complemented
22	D₁₅₁	—	63	2	no	—
23	C₂×D₆₃	—	151	1	no	maximal, Hall
24	C₁₅₁	C₂×D₆₃	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₇×C₉	D₁₅₁	1	1	yes	characteristic, complemented
26	D₆₃	—	151	2	no	—
27	C₂×D₂₁	—	453	1	no	—
28	C₇×C₉	C₂×D₁₅₁	1	1	yes	characteristic, complemented, Hall
29	C₂×C₃×C₇	D₄₅₃	1	1	yes	characteristic
30	D₂₁	—	453	2	no	—
31	C₂×D₉	—	1057	1	no	Hall
32	C₂×D₇	—	1359	1	no	Hall
33	C₃×C₇	C₂×D₄₅₃	1	1	yes	characteristic
34	C₂×C₉	D₁₀₅₇	1	1	yes	characteristic, complemented
35	D₉	—	1057	2	no	—
36	C₂×C₇	D₁₃₅₉	1	1	yes	characteristic, complemented
37	D₇	—	1359	2	no	—
38	C₂×D₃	—	3171	1	no	—
39	C₉	C₂×D₁₀₅₇	1	1	yes	characteristic, complemented, Sylow
40	C₇	C₂×D₁₃₅₉	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	D₃₁₇₁	1	1	yes	characteristic
42	D₃	—	3171	2	no	—
43	C₂²	—	9513	1	no	Sylow
44	C₃	C₂×D₃₁₇₁	1	1	yes	characteristic
45	C₂	—	9513	2	no	—
46	C₂	D₉₅₁₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₉₅₁₃
commutator, cosocle, hypocenter	C₇×C₉×C₁₅₁	C₂²
Frattini	C₃	C₂×D₃₁₇₁
Fitting	C₂×C₇×C₉×C₁₅₁	C₂
socle	C₂×C₃×C₇×C₁₅₁	D₃
LCS	G ▷ C₇×C₉×C₁₅₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. D₉₅₁₃	C₂	direct (N × H)
2. C₂×C₇×C₉×C₁₅₁	C₂	semidirect
4. C₇×C₉×C₁₅₁	C₂²	semidirect
11. C₂×C₉×C₁₅₁	D₇	semidirect
12. C₂×C₇×C₁₅₁	D₉	semidirect
15. C₉×C₁₅₁	C₂×D₇	semidirect
16. C₇×C₁₅₁	C₂×D₉	semidirect
21. C₂×C₁₅₁	D₆₃	semidirect
24. C₁₅₁	C₂×D₆₃	semidirect
25. C₂×C₇×C₉	D₁₅₁	semidirect
28. C₇×C₉	C₂×D₁₅₁	semidirect
34. C₂×C₉	D₁₀₅₇	semidirect
36. C₂×C₇	D₁₃₅₉	semidirect
39. C₉	C₂×D₁₀₅₇	semidirect
40. C₇	C₂×D₁₃₅₉	semidirect
46. C₂	D₉₅₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
D₉₅₁₃	2
C₂×C₇×C₉×C₁₅₁	2
C₂×D₃₁₇₁	3
C₂×D₁₃₅₉	7
C₂×D₆₃	151

Subgroups — C2×D9513 #49184871

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₉₅₁₃ #49184871