Subgroups — D₃₅×D₂₃₃ #45657111

Order 32620.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₁₅₅	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃₅×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇×D₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₇×C₂₃₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₇×D₂₃₃	—	5	1	no	maximal, Hall
6	D₅×D₂₃₃	—	7	1	no	maximal, Hall
7	D₁₆₃₁	—	5	1	no	—
8	C₇×D₂₃₃	D₅	1	1	yes	characteristic, complemented
9	D₇×C₂₃₃	—	5	1	no	—
10	D₁₁₆₅	—	7	1	no	—
11	C₅×D₂₃₃	D₇	1	1	yes	characteristic, complemented
12	D₅×C₂₃₃	—	7	1	no	—
13	C₇×C₂₃₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
14	C₅×C₂₃₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
15	C₂×D₂₃₃	—	35	1	no	Hall
16	C₂×C₂₃₃	—	35	1	no	—
17	D₂₃₃	—	35	1	no	—
18	D₂₃₃	D₃₅	1	1	yes	characteristic, direct product factor
19	C₂₃₃	C₂×D₃₅	1	1	yes	characteristic, complemented, Sylow
20	C₂×D₃₅	—	233	1	no	maximal, Hall
21	C₂×C₅×C₇	—	233	1	no	—
22	D₃₅	—	233	1	no	—
23	D₃₅	D₂₃₃	1	1	yes	characteristic, direct product factor
24	C₅×C₇	C₂×D₂₃₃	1	1	yes	characteristic, complemented, Hall
25	C₂×D₇	—	1165	1	no	Hall
26	C₂×D₅	—	1631	1	no	Hall
27	C₂×C₇	—	233	1	no	—
28	D₇	—	5	1	no	—
29	D₇	—	1165	1	no	—
30	C₂×C₅	—	233	1	no	—
31	D₅	—	7	1	no	—
32	D₅	—	1631	1	no	—
33	C₇	D₅×D₂₃₃	1	1	yes	characteristic, complemented, Sylow
34	C₅	D₇×D₂₃₃	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	8155	1	no	Sylow
36	C₂	—	35	1	no	—
37	C₂	—	8155	1	no	—
38	C₂	—	233	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₇×C₂₃₃	C₂²
LCS	G ▷ C₅×C₇×C₂₃₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₈₁₅₅	C₂	semidirect
2. D₃₅×C₂₃₃	C₂	semidirect
3. C₅×C₇×D₂₃₃	C₂	semidirect
4. C₅×C₇×C₂₃₃	C₂²	semidirect
8. C₇×D₂₃₃	D₅	semidirect
11. C₅×D₂₃₃	D₇	semidirect
13. C₇×C₂₃₃	C₂×D₅	semidirect
14. C₅×C₂₃₃	C₂×D₇	semidirect
18. D₂₃₃	D₃₅	direct (N × H)
19. C₂₃₃	C₂×D₃₅	semidirect
23. D₃₅	D₂₃₃	direct (N × H)
24. C₅×C₇	C₂×D₂₃₃	semidirect
33. C₇	D₅×D₂₃₃	semidirect
34. C₅	D₇×D₂₃₃	semidirect

Maximal subgroups

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

subgroup	index
D₈₁₅₅	2
D₃₅×C₂₃₃	2
C₅×C₇×D₂₃₃	2
D₇×D₂₃₃	5
D₅×D₂₃₃	7
C₂×D₃₅	233

Subgroups — D35×D233 #45657111

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₅×D₂₃₃ #45657111