Subgroups — C₂×C₇²×D₁₅₅ #44477201

Order 30380.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×D₁₅₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₇²×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇²×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇²×D₃₁	—	5	1	no	maximal, Hall
5	C₂×C₇×D₁₅₅	C₇	1	8	yes	maximal, direct product factor
6	C₇²×D₃₁	—	5	2	no	—
7	C₂×C₇²×C₃₁	D₅	1	1	yes	characteristic, complemented
8	C₇×D₁₅₅	C₂×C₇	1	16	yes	direct product factor
9	C₂×C₅×C₇×C₃₁	C₂×C₇	1	8	yes	complemented
10	C₇²×C₃₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
11	C₅×C₇×C₃₁	C₂²×C₇	1	8	yes	complemented
12	C₂×C₇²×D₅	—	31	1	no	maximal, Hall
13	C₂×C₇×D₃₁	—	5	8	no	—
14	C₂×D₁₅₅	C₇²	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₅×C₇²	D₃₁	1	1	yes	characteristic, complemented
16	C₇²×D₅	—	31	2	no	—
17	C₂×C₇×C₃₁	C₇×D₅	1	8	yes	complemented
18	C₇×D₃₁	—	5	16	no	—
19	C₂×C₅×C₃₁	C₂×C₇²	1	1	yes	characteristic, complemented
20	D₁₅₅	C₂×C₇²	1	2	yes	direct product factor
21	C₅×C₇²	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
22	C₇×C₃₁	C₂×C₇×D₅	1	8	yes	complemented
23	C₂²×C₇²	—	155	1	no	Hall
24	C₅×C₃₁	C₂²×C₇²	1	1	yes	characteristic, complemented, Hall
25	C₂×C₇×D₅	—	31	8	no	—
26	C₂×D₃₁	—	5	1	no	Hall
27	C₂×C₇²	—	155	2	no	—
28	C₂×C₇²	D₁₅₅	1	1	yes	characteristic, direct product factor
29	C₂×C₅×C₇	C₇×D₃₁	1	8	yes	complemented
30	C₇×D₅	—	31	16	no	—
31	C₂×C₃₁	C₇²×D₅	1	1	yes	characteristic, complemented
32	D₃₁	—	5	2	no	—
33	C₇²	C₂×D₁₅₅	1	1	yes	characteristic, direct product factor, Sylow
34	C₅×C₇	C₂×C₇×D₃₁	1	8	yes	complemented
35	C₃₁	C₂×C₇²×D₅	1	1	yes	characteristic, complemented, Sylow
36	C₂²×C₇	—	155	8	no	—
37	C₂×D₅	—	31	1	no	Hall
38	C₂×C₇	—	155	16	no	—
39	C₂×C₇	C₇×D₁₅₅	1	8	yes	direct product factor
40	C₂×C₅	C₇²×D₃₁	1	1	yes	characteristic, complemented
41	D₅	—	31	2	no	—
42	C₇	C₂×C₇×D₁₅₅	1	8	yes	direct product factor
43	C₅	C₂×C₇²×D₃₁	1	1	yes	characteristic, complemented, Sylow
44	C₂²	—	155	1	no	Sylow
45	C₂	—	155	2	no	—
46	C₂	C₇²×D₁₅₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇²	D₁₅₅
commutator, cosocle, hypocenter	C₅×C₃₁	C₂²×C₇²
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇²×C₃₁	C₂
LCS	G ▷ C₅×C₃₁
UCS	C₁ ◁ C₂×C₇²

Complements

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

N	H ≅ G/N	type
1. C₇²×D₁₅₅	C₂	direct (N × H)
2. C₂×C₅×C₇²×C₃₁	C₂	semidirect
3. C₅×C₇²×C₃₁	C₂²	semidirect
5. C₂×C₇×D₁₅₅	C₇	direct (N × H)
7. C₂×C₇²×C₃₁	D₅	semidirect
8. C₇×D₁₅₅	C₂×C₇	direct (N × H)
9. C₂×C₅×C₇×C₃₁	C₂×C₇	semidirect
10. C₇²×C₃₁	C₂×D₅	semidirect
11. C₅×C₇×C₃₁	C₂²×C₇	semidirect
14. C₂×D₁₅₅	C₇²	direct (N × H)
15. C₂×C₅×C₇²	D₃₁	semidirect
17. C₂×C₇×C₃₁	C₇×D₅	semidirect
19. C₂×C₅×C₃₁	C₂×C₇²	semidirect
20. D₁₅₅	C₂×C₇²	direct (N × H)
21. C₅×C₇²	C₂×D₃₁	semidirect
22. C₇×C₃₁	C₂×C₇×D₅	semidirect
24. C₅×C₃₁	C₂²×C₇²	semidirect
28. C₂×C₇²	D₁₅₅	direct (N × H)
29. C₂×C₅×C₇	C₇×D₃₁	semidirect
31. C₂×C₃₁	C₇²×D₅	semidirect
33. C₇²	C₂×D₁₅₅	direct (N × H)
34. C₅×C₇	C₂×C₇×D₃₁	semidirect
35. C₃₁	C₂×C₇²×D₅	semidirect
39. C₂×C₇	C₇×D₁₅₅	direct (N × H)
40. C₂×C₅	C₇²×D₃₁	semidirect
42. C₇	C₂×C₇×D₁₅₅	direct (N × H)
43. C₅	C₂×C₇²×D₃₁	semidirect
46. C₂	C₇²×D₁₅₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇²×D₁₅₅	2
C₂×C₅×C₇²×C₃₁	2
C₂×C₇²×D₃₁	5
C₂×C₇×D₁₅₅	7
C₂×C₇²×D₅	31

Subgroups — C2×C72×D155 #44477201

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇²×D₁₅₅ #44477201