Subgroups — #3874×D₁₀₇ #44545650

Order 32100.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²⋊C₃×D₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₀₇⋊#3874	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₇×#3874	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₅×D₁₀₇	—	3	1	no	maximal, Hall
5	C₅²⋊C₃×C₁₀₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₅×D₅₃₅	—	3	1	no	—
7	C₅×D₅×C₁₀₇	—	3	1	no	—
8	C₅²×D₁₀₇	D₃	1	1	yes	characteristic, complemented
9	C₅²×C₁₀₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₅×D₁₀₇	—	15	1	no	—
11	D₅×D₁₀₇	—	3	1	no	—
12	D₃×D₁₀₇	—	25	1	no	maximal, Hall
13	C₂×C₅×C₁₀₇	—	15	1	no	—
14	D₅₃₅	—	3	1	no	—
15	C₅×D₁₀₇	—	3	1	no	—
16	C₅×D₁₀₇	—	3	1	no	—
17	C₅×D₁₀₇	—	15	1	no	—
18	D₅×C₁₀₇	—	3	1	no	—
19	D₃₂₁	—	25	1	no	—
20	C₃×D₁₀₇	—	25	1	no	—
21	D₃×C₁₀₇	—	25	1	no	—
22	C₅×C₁₀₇	—	3	1	no	—
23	C₅×C₁₀₇	—	3	1	no	—
24	C₂×D₁₀₇	—	15	1	no	Hall
25	C₃×C₁₀₇	—	25	1	no	Hall
26	C₂×#3874	—	107	1	no	maximal, Hall
27	C₂×C₁₀₇	—	15	1	no	—
28	D₁₀₇	—	15	1	no	—
29	D₁₀₇	#3874	1	1	yes	characteristic, direct product factor
30	C₂×C₅²⋊C₃	—	107	1	no	—
31	#3874	—	107	1	no	—
32	#3874	D₁₀₇	1	1	yes	characteristic, direct product factor
33	C₁₀₇	C₂×#3874	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₅×D₅	—	321	1	no	Hall
35	C₅²⋊C₃	C₂×D₁₀₇	1	1	yes	characteristic, complemented, Hall
36	C₂×C₅²	—	107	1	no	—
37	C₅×D₅	—	3	1	no	—
38	C₅×D₅	—	321	1	no	—
39	C₅²	D₃×D₁₀₇	1	1	yes	characteristic, complemented, Sylow
40	C₂²×C₅	—	1605	1	no	—
41	C₂×D₅	—	321	1	no	—
42	C₂×D₃	—	2675	1	no	Hall
43	C₂×C₅	—	15	1	no	—
44	C₂×C₅	—	321	1	no	—
45	C₂×C₅	—	321	1	no	—
46	C₂×C₅	—	1605	1	no	—
47	D₅	—	3	1	no	—
48	D₅	—	321	1	no	—
49	C₂×C₃	—	2675	1	no	—
50	D₃	—	25	1	no	—
51	D₃	—	2675	1	no	—
52	C₅	—	3	1	no	—
53	C₅	—	3	1	no	—
54	C₂²	—	1605	1	no	Sylow
55	C₃	—	25	1	no	Sylow
56	C₂	—	15	1	no	—
57	C₂	—	1605	1	no	—
58	C₂	—	107	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₅²⋊C₃×C₁₀₇	C₂²
Fitting, socle	C₅²×C₁₀₇	C₂×D₃
LCS	G ▷ C₅²⋊C₃×C₁₀₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅²⋊C₃×D₁₀₇	C₂	semidirect
2. C₁₀₇⋊#3874	C₂	semidirect
3. C₁₀₇×#3874	C₂	semidirect
5. C₅²⋊C₃×C₁₀₇	C₂²	semidirect
8. C₅²×D₁₀₇	D₃	semidirect
9. C₅²×C₁₀₇	C₂×D₃	semidirect
29. D₁₀₇	#3874	direct (N × H)
32. #3874	D₁₀₇	direct (N × H)
33. C₁₀₇	C₂×#3874	semidirect
35. C₅²⋊C₃	C₂×D₁₀₇	semidirect
39. C₅²	D₃×D₁₀₇	semidirect

Maximal subgroups

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

subgroup	index
C₅²⋊C₃×D₁₀₇	2
C₁₀₇⋊#3874	2
C₁₀₇×#3874	2
C₅×D₅×D₁₀₇	3
D₃×D₁₀₇	25
C₂×#3874	107

Subgroups — #3874×D107 #44545650

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3874×D₁₀₇ #44545650