Subgroups — C₂×#30660576 #45691623

Order 33516.

300 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#89204	C₂	1	1	yes	maximal, characteristic, complemented
2	#30660576	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₇⋊D₁₃₃	C₃	1	1	yes	maximal, characteristic
4	C₁₉×#89204	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₇⋊D₁₃₃	C₂×C₃	1	2	yes	—
6	C₂×C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic
7	C₂×(C₇⋊C₉)⋊D₁₉	—	7	8	no	maximal
8	C₂×C₇⋊D₁₃₃	C₉	1	1	yes	characteristic, complemented, Hall
9	C₃×C₇²×C₁₉	C₂²×C₃	1	1	yes	characteristic
10	C₂×C₁₉×C₇⋊C₉	—	7	8	no	—
11	(C₇⋊C₉)⋊D₁₉	—	7	16	no	—
12	C₂×C₇²×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented
13	C₇⋊D₁₃₃	C₂×C₉	1	2	yes	complemented
14	C₂×#11725077	—	19	1	no	maximal, Hall
15	C₂×C₃×D₁₃₃	—	7	8	no	—
16	C₁₉×C₇⋊C₉	—	7	8	no	—
17	C₇²×C₁₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
18	C₂×#89204	D₁₉	1	1	yes	characteristic, complemented
19	#11725077	—	19	2	no	—
20	C₂×C₃×C₇×C₁₉	AGL(1,𝔽₇)	1	8	yes	—
21	C₃×D₁₃₃	—	7	16	no	—
22	C₂×C₉×D₁₉	—	49	1	no	Hall
23	C₂×C₃×C₇⋊D₇	—	19	1	no	—
24	C₂×D₁₃₃	—	7	8	no	—
25	#89204	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
26	C₃×C₇×C₁₉	C₂×AGL(1,𝔽₇)	1	8	yes	—
27	C₂×C₉×C₁₉	—	49	1	no	—
28	C₉×D₁₉	—	49	2	no	—
29	C₂×C₃×C₇²	C₃×D₁₉	1	1	yes	characteristic
30	C₃×C₇⋊D₇	—	19	2	no	—
31	C₂×C₇×C₁₉	D₇⋊C₉	1	8	yes	complemented
32	D₁₃₃	—	7	16	no	—
33	C₂×D₇⋊C₉	—	133	8	no	—
34	C₂×C₃×D₁₉	—	49	1	no	—
35	C₂×C₇⋊D₇	—	19	1	no	Hall
36	C₉×C₁₉	—	49	1	no	Hall
37	C₃×C₇²	C₂×C₃×D₁₉	1	1	yes	characteristic
38	C₇×C₁₉	C₂×D₇⋊C₉	1	8	yes	complemented
39	C₂×C₇⋊C₉	—	7	8	no	—
40	D₇⋊C₉	—	133	16	no	—
41	C₂×C₃×C₁₉	#64424	1	1	yes	characteristic
42	C₃×D₁₉	—	49	2	no	—
43	C₂×C₇²	C₉×D₁₉	1	1	yes	characteristic, complemented
44	C₇⋊D₇	—	19	2	no	—
45	C₂×C₃×D₇	—	133	8	no	—
46	C₂×D₁₉	—	49	1	no	Hall
47	C₇⋊C₉	—	7	8	no	—
48	C₃×C₁₉	C₂×#64424	1	1	yes	characteristic
49	C₇²	C₂×C₉×D₁₉	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃×C₇	ΓL(1,𝔽₈)⋊D₁₉	1	8	yes	—
51	C₃×D₇	—	133	16	no	—
52	C₂×C₁₉	#11725077	1	1	yes	characteristic, complemented
53	D₁₉	—	49	2	no	—
54	C₂²×C₉	—	931	1	no	Hall
55	C₂×D₇	—	133	8	no	—
56	C₃×C₇	C₂×ΓL(1,𝔽₈)⋊D₁₉	1	8	yes	—
57	C₁₉	C₂×#11725077	1	1	yes	characteristic, complemented, Sylow
58	C₂×C₉	—	49	1	no	—
59	C₂×C₉	—	931	2	no	—
60	C₂×C₇	(C₇⋊C₉)⋊D₁₉	1	8	yes	complemented
61	D₇	—	133	16	no	—
62	C₂²×C₃	—	931	1	no	—
63	C₉	—	49	1	no	Sylow
64	C₇	C₂×(C₇⋊C₉)⋊D₁₉	1	8	yes	complemented
65	C₂×C₃	—	931	2	no	—
66	C₂×C₃	#19150288	1	1	yes	characteristic
67	C₂²	—	931	1	no	Sylow
68	C₃	C₂×#19150288	1	1	yes	characteristic
69	C₂	—	931	2	no	—
70	C₂	#30660576	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	#19150288
commutator, hypocenter	C₇²×C₁₉	C₂²×C₉
Frattini	C₃	C₂×#19150288
Fitting, socle	C₂×C₃×C₇²×C₁₉	C₂×C₃
prime radical	C₂×C₃×C₇⋊D₁₃₃	C₃
cosocle	C₃×C₇²×C₁₉	C₂²×C₃
LCS	G ▷ C₇²×C₁₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#89204	C₂	semidirect
2. #30660576	C₂	direct (N × H)
4. C₁₉×#89204	C₂²	semidirect
8. C₂×C₇⋊D₁₃₃	C₉	semidirect
12. C₂×C₇²×C₁₉	C₂×C₉	semidirect
13. C₇⋊D₁₃₃	C₂×C₉	semidirect
17. C₇²×C₁₉	C₂²×C₉	semidirect
18. C₂×#89204	D₁₉	semidirect
25. #89204	C₂×D₁₉	semidirect
31. C₂×C₇×C₁₉	D₇⋊C₉	semidirect
38. C₇×C₁₉	C₂×D₇⋊C₉	semidirect
43. C₂×C₇²	C₉×D₁₉	semidirect
49. C₇²	C₂×C₉×D₁₉	semidirect
52. C₂×C₁₉	#11725077	semidirect
57. C₁₉	C₂×#11725077	semidirect
60. C₂×C₇	(C₇⋊C₉)⋊D₁₉	semidirect
64. C₇	C₂×(C₇⋊C₉)⋊D₁₉	semidirect
70. C₂	#30660576	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×C₁₉×#89204	2
#30660576	2
C₂×C₃×C₇⋊D₁₃₃	3
C₂×(C₇⋊C₉)⋊D₁₉	7
C₂×#11725077	19

Subgroups — C2×#30660576 #45691623

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#30660576 #45691623