Subgroups — C₂×#26045007 #37557217

Order 23700.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²⋊(C₇₉⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	#26045007	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅⋊D₃₉₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅²⋊(C₇₉⋊C₃)	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₅⋊D₃₉₅	C₂×C₃	1	2	yes	complemented
6	C₂×C₅²×C₇₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅²×C₇₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₃₉₅	—	15	2	no	—
9	C₂×D₇₉⋊C₃	—	25	1	no	maximal, Hall
10	C₂×C₅×C₇₉	—	3	2	no	—
11	D₃₉₅	—	15	4	no	—
12	C₂×C₇₉⋊C₃	—	50	1	no	—
13	D₇₉⋊C₃	—	25	2	no	—
14	C₅×C₇₉	—	3	2	no	—
15	C₂×D₇₉	—	25	1	no	Hall
16	C₂×(C₅⋊D₅)⋊C₃	—	79	1	no	maximal, Hall
17	C₇₉⋊C₃	—	50	1	no	Hall
18	C₂×C₇₉	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented
19	D₇₉	—	25	2	no	—
20	C₂×C₅²⋊C₃	—	158	1	no	—
21	(C₅⋊D₅)⋊C₃	—	79	2	no	—
22	C₂×C₅⋊D₅	—	79	1	no	Hall
23	C₇₉	C₂×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₅²⋊C₃	—	158	1	no	Hall
25	C₂×C₅²	D₇₉⋊C₃	1	1	yes	characteristic, complemented
26	C₅⋊D₅	—	79	2	no	—
27	C₅²	C₂×D₇₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×D₅	—	1185	2	no	—
29	C₂²×C₃	—	1975	1	no	Hall
30	C₂×C₅	—	3	2	no	—
31	D₅	—	1185	4	no	—
32	C₂×C₃	—	3950	1	no	—
33	C₂×C₃	—	1975	2	no	—
34	C₅	—	3	2	no	—
35	C₂²	—	1975	1	no	Sylow
36	C₃	—	3950	1	no	Sylow
37	C₂	—	1975	2	no	—
38	C₂	#26045007	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#26045007
commutator, cosocle, hypocenter	C₅²×C₇₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₇₉	C₂×C₃
LCS	G ▷ C₅²×C₇₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₅²⋊(C₇₉⋊C₃)	C₂	semidirect
2. #26045007	C₂	direct (N × H)
3. C₂×C₅⋊D₃₉₅	C₃	semidirect
4. C₅²⋊(C₇₉⋊C₃)	C₂²	semidirect
5. C₅⋊D₃₉₅	C₂×C₃	semidirect
6. C₂×C₅²×C₇₉	C₂×C₃	semidirect
7. C₅²×C₇₉	C₂²×C₃	semidirect
18. C₂×C₇₉	(C₅⋊D₅)⋊C₃	semidirect
23. C₇₉	C₂×(C₅⋊D₅)⋊C₃	semidirect
25. C₂×C₅²	D₇₉⋊C₃	semidirect
27. C₅²	C₂×D₇₉⋊C₃	semidirect
38. C₂	#26045007	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅²⋊(C₇₉⋊C₃)	2
#26045007	2
C₂×C₅⋊D₃₉₅	3
C₂×D₇₉⋊C₃	25
C₂×(C₅⋊D₅)⋊C₃	79

Subgroups — C2×#26045007 #37557217

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#26045007 #37557217