Subgroups — C₂×#30659275 #45686185

Order 33300.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²⋊#66526	C₂	1	1	yes	maximal, characteristic, complemented
2	#30659275	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅²×D₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic
4	C₅²⋊#66526	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅²×C₃₇⋊C₃	C₂×C₃	1	1	yes	characteristic
6	C₅²×D₃₇⋊C₃	C₂×C₃	1	2	yes	—
7	C₂×C₅²×D₃₇	C₉	1	1	yes	characteristic, complemented, Hall
8	C₅²×C₃₇⋊C₃	C₂²×C₃	1	1	yes	characteristic
9	C₂×C₅×D₃₇⋊C₃	—	3	2	no	—
10	C₂×C₅²×C₃₇	C₂×C₉	1	1	yes	characteristic, complemented
11	C₅²×D₃₇	C₂×C₉	1	2	yes	complemented
12	C₂×#66526⋊C₂	—	25	1	no	maximal, Hall
13	C₂×C₅×C₃₇⋊C₃	—	3	2	no	—
14	C₅×D₃₇⋊C₃	—	3	4	no	—
15	C₅²×C₃₇	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
16	C₂²×C₅²⋊C₉	—	37	1	no	maximal, Hall
17	C₂×C₅×D₃₇	—	3	2	no	—
18	C₂×#66526	—	25	1	no	—
19	#66526⋊C₂	—	25	2	no	—
20	C₅×C₃₇⋊C₃	—	3	2	no	—
21	C₂×C₅²⋊C₉	—	37	2	no	—
22	C₂×C₅²⋊C₉	—	37	1	no	—
23	C₂×D₃₇⋊C₃	C₅²⋊C₃	1	1	yes	characteristic
24	C₂×C₅×C₃₇	—	3	2	no	—
25	C₅×D₃₇	—	3	4	no	—
26	#66526	—	25	1	no	Hall
27	C₂²×C₃×C₅²	—	37	1	no	—
28	C₅²⋊C₉	—	37	1	no	Hall
29	C₂×C₃₇⋊C₃	C₂×C₅²⋊C₃	1	1	yes	characteristic
30	D₃₇⋊C₃	C₂×C₅²⋊C₃	1	2	yes	—
31	C₅×C₃₇	—	3	2	no	—
32	C₂×C₃×C₅²	—	37	2	no	—
33	C₂×C₃×C₅²	—	37	1	no	—
34	C₂×D₃₇	C₅²⋊C₉	1	1	yes	characteristic, complemented, Hall
35	C₃₇⋊C₃	C₂²×C₅²⋊C₃	1	1	yes	characteristic
36	C₂²×C₅²	—	37	1	no	Hall
37	C₃×C₅²	—	37	1	no	—
38	C₂×C₃₇	C₂×C₅²⋊C₉	1	1	yes	characteristic, complemented
39	D₃₇	C₂×C₅²⋊C₉	1	2	yes	complemented
40	C₂²×C₃×C₅	—	111	2	no	—
41	C₂×C₅²	—	37	2	no	—
42	C₂×C₅²	#66526⋊C₂	1	1	yes	characteristic, complemented
43	C₃₇	C₂²×C₅²⋊C₉	1	1	yes	characteristic, complemented, Sylow
44	C₂²×C₉	—	925	1	no	Hall
45	C₂×C₃×C₅	—	111	2	no	—
46	C₂×C₃×C₅	—	111	4	no	—
47	C₅²	C₂×#66526⋊C₂	1	1	yes	characteristic, complemented, Sylow
48	C₂²×C₅	—	111	2	no	—
49	C₂×C₉	—	925	2	no	—
50	C₂×C₉	—	925	1	no	—
51	C₃×C₅	—	111	2	no	—
52	C₂²×C₃	—	37	1	no	—
53	C₂×C₅	—	3	2	no	—
54	C₂×C₅	—	111	4	no	—
55	C₉	—	925	1	no	Sylow
56	C₂×C₃	—	37	2	no	—
57	C₂×C₃	—	37	1	no	—
58	C₅	—	3	2	no	—
59	C₂²	—	37	1	no	Sylow
60	C₃	—	37	1	no	—
61	C₂	—	37	2	no	—
62	C₂	#30659275	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#30659275
commutator, hypocenter	C₅²×C₃₇	C₂²×C₉
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₃₇	C₂×C₉
prime radical	C₂×C₅²×D₃₇⋊C₃	C₃
cosocle	C₅²×C₃₇⋊C₃	C₂²×C₃
LCS	G ▷ C₅²×C₃₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₅²⋊#66526	C₂	semidirect
2. #30659275	C₂	direct (N × H)
4. C₅²⋊#66526	C₂²	semidirect
7. C₂×C₅²×D₃₇	C₉	semidirect
10. C₂×C₅²×C₃₇	C₂×C₉	semidirect
11. C₅²×D₃₇	C₂×C₉	semidirect
15. C₅²×C₃₇	C₂²×C₉	semidirect
34. C₂×D₃₇	C₅²⋊C₉	semidirect
38. C₂×C₃₇	C₂×C₅²⋊C₉	semidirect
39. D₃₇	C₂×C₅²⋊C₉	semidirect
42. C₂×C₅²	#66526⋊C₂	semidirect
43. C₃₇	C₂²×C₅²⋊C₉	semidirect
47. C₅²	C₂×#66526⋊C₂	semidirect
62. C₂	#30659275	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⋊#66526	2
#30659275	2
C₂×C₅²×D₃₇⋊C₃	3
C₂×#66526⋊C₂	25
C₂²×C₅²⋊C₉	37

Subgroups — C2×#30659275 #45686185

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#30659275 #45686185